Properties

Label 700.2.c.a.699.1
Level $700$
Weight $2$
Character 700.699
Analytic conductor $5.590$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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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: \(\Q(i, \sqrt{6})\)
Defining polynomial: \(x^{4} + 9\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 699.1
Root \(1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 700.699
Dual form 700.2.c.a.699.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} -2.44949i q^{3} +2.00000i q^{4} +(-2.44949 + 2.44949i) q^{6} +(-1.00000 + 2.44949i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} -2.44949i q^{3} +2.00000i q^{4} +(-2.44949 + 2.44949i) q^{6} +(-1.00000 + 2.44949i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000 q^{9} +5.00000i q^{11} +4.89898 q^{12} +2.44949 q^{13} +(3.44949 - 1.44949i) q^{14} -4.00000 q^{16} +4.89898 q^{17} +(3.00000 + 3.00000i) q^{18} +(6.00000 + 2.44949i) q^{21} +(5.00000 - 5.00000i) q^{22} -1.00000 q^{23} +(-4.89898 - 4.89898i) q^{24} +(-2.44949 - 2.44949i) q^{26} +(-4.89898 - 2.00000i) q^{28} +5.00000 q^{29} +7.34847 q^{31} +(4.00000 + 4.00000i) q^{32} +12.2474 q^{33} +(-4.89898 - 4.89898i) q^{34} -6.00000i q^{36} +3.00000i q^{37} -6.00000i q^{39} +12.2474i q^{41} +(-3.55051 - 8.44949i) q^{42} -11.0000 q^{43} -10.0000 q^{44} +(1.00000 + 1.00000i) q^{46} +4.89898i q^{47} +9.79796i q^{48} +(-5.00000 - 4.89898i) q^{49} -12.0000i q^{51} +4.89898i q^{52} -4.00000i q^{53} +(2.89898 + 6.89898i) q^{56} +(-5.00000 - 5.00000i) q^{58} +12.2474 q^{59} -12.2474i q^{61} +(-7.34847 - 7.34847i) q^{62} +(3.00000 - 7.34847i) q^{63} -8.00000i q^{64} +(-12.2474 - 12.2474i) q^{66} +3.00000 q^{67} +9.79796i q^{68} +2.44949i q^{69} -5.00000i q^{71} +(-6.00000 + 6.00000i) q^{72} +2.44949 q^{73} +(3.00000 - 3.00000i) q^{74} +(-12.2474 - 5.00000i) q^{77} +(-6.00000 + 6.00000i) q^{78} +9.00000i q^{79} -9.00000 q^{81} +(12.2474 - 12.2474i) q^{82} -2.44949i q^{83} +(-4.89898 + 12.0000i) q^{84} +(11.0000 + 11.0000i) q^{86} -12.2474i q^{87} +(10.0000 + 10.0000i) q^{88} +2.44949i q^{89} +(-2.44949 + 6.00000i) q^{91} -2.00000i q^{92} -18.0000i q^{93} +(4.89898 - 4.89898i) q^{94} +(9.79796 - 9.79796i) q^{96} -7.34847 q^{97} +(0.101021 + 9.89898i) q^{98} -15.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} - 4q^{7} + 8q^{8} - 12q^{9} + O(q^{10}) \) \( 4q - 4q^{2} - 4q^{7} + 8q^{8} - 12q^{9} + 4q^{14} - 16q^{16} + 12q^{18} + 24q^{21} + 20q^{22} - 4q^{23} + 20q^{29} + 16q^{32} - 24q^{42} - 44q^{43} - 40q^{44} + 4q^{46} - 20q^{49} - 8q^{56} - 20q^{58} + 12q^{63} + 12q^{67} - 24q^{72} + 12q^{74} - 24q^{78} - 36q^{81} + 44q^{86} + 40q^{88} + 20q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.707107 0.707107i
\(3\) 2.44949i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(4\) 2.00000i 1.00000i
\(5\) 0 0
\(6\) −2.44949 + 2.44949i −1.00000 + 1.00000i
\(7\) −1.00000 + 2.44949i −0.377964 + 0.925820i
\(8\) 2.00000 2.00000i 0.707107 0.707107i
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) 5.00000i 1.50756i 0.657129 + 0.753778i \(0.271771\pi\)
−0.657129 + 0.753778i \(0.728229\pi\)
\(12\) 4.89898 1.41421
\(13\) 2.44949 0.679366 0.339683 0.940540i \(-0.389680\pi\)
0.339683 + 0.940540i \(0.389680\pi\)
\(14\) 3.44949 1.44949i 0.921915 0.387392i
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) 4.89898 1.18818 0.594089 0.804400i \(-0.297513\pi\)
0.594089 + 0.804400i \(0.297513\pi\)
\(18\) 3.00000 + 3.00000i 0.707107 + 0.707107i
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) 6.00000 + 2.44949i 1.30931 + 0.534522i
\(22\) 5.00000 5.00000i 1.06600 1.06600i
\(23\) −1.00000 −0.208514 −0.104257 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) −4.89898 4.89898i −1.00000 1.00000i
\(25\) 0 0
\(26\) −2.44949 2.44949i −0.480384 0.480384i
\(27\) 0 0
\(28\) −4.89898 2.00000i −0.925820 0.377964i
\(29\) 5.00000 0.928477 0.464238 0.885710i \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(30\) 0 0
\(31\) 7.34847 1.31982 0.659912 0.751343i \(-0.270594\pi\)
0.659912 + 0.751343i \(0.270594\pi\)
\(32\) 4.00000 + 4.00000i 0.707107 + 0.707107i
\(33\) 12.2474 2.13201
\(34\) −4.89898 4.89898i −0.840168 0.840168i
\(35\) 0 0
\(36\) 6.00000i 1.00000i
\(37\) 3.00000i 0.493197i 0.969118 + 0.246598i \(0.0793129\pi\)
−0.969118 + 0.246598i \(0.920687\pi\)
\(38\) 0 0
\(39\) 6.00000i 0.960769i
\(40\) 0 0
\(41\) 12.2474i 1.91273i 0.292174 + 0.956365i \(0.405621\pi\)
−0.292174 + 0.956365i \(0.594379\pi\)
\(42\) −3.55051 8.44949i −0.547856 1.30378i
\(43\) −11.0000 −1.67748 −0.838742 0.544529i \(-0.816708\pi\)
−0.838742 + 0.544529i \(0.816708\pi\)
\(44\) −10.0000 −1.50756
\(45\) 0 0
\(46\) 1.00000 + 1.00000i 0.147442 + 0.147442i
\(47\) 4.89898i 0.714590i 0.933992 + 0.357295i \(0.116301\pi\)
−0.933992 + 0.357295i \(0.883699\pi\)
\(48\) 9.79796i 1.41421i
\(49\) −5.00000 4.89898i −0.714286 0.699854i
\(50\) 0 0
\(51\) 12.0000i 1.68034i
\(52\) 4.89898i 0.679366i
\(53\) 4.00000i 0.549442i −0.961524 0.274721i \(-0.911414\pi\)
0.961524 0.274721i \(-0.0885855\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 2.89898 + 6.89898i 0.387392 + 0.921915i
\(57\) 0 0
\(58\) −5.00000 5.00000i −0.656532 0.656532i
\(59\) 12.2474 1.59448 0.797241 0.603661i \(-0.206292\pi\)
0.797241 + 0.603661i \(0.206292\pi\)
\(60\) 0 0
\(61\) 12.2474i 1.56813i −0.620682 0.784063i \(-0.713144\pi\)
0.620682 0.784063i \(-0.286856\pi\)
\(62\) −7.34847 7.34847i −0.933257 0.933257i
\(63\) 3.00000 7.34847i 0.377964 0.925820i
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) −12.2474 12.2474i −1.50756 1.50756i
\(67\) 3.00000 0.366508 0.183254 0.983066i \(-0.441337\pi\)
0.183254 + 0.983066i \(0.441337\pi\)
\(68\) 9.79796i 1.18818i
\(69\) 2.44949i 0.294884i
\(70\) 0 0
\(71\) 5.00000i 0.593391i −0.954972 0.296695i \(-0.904115\pi\)
0.954972 0.296695i \(-0.0958846\pi\)
\(72\) −6.00000 + 6.00000i −0.707107 + 0.707107i
\(73\) 2.44949 0.286691 0.143346 0.989673i \(-0.454214\pi\)
0.143346 + 0.989673i \(0.454214\pi\)
\(74\) 3.00000 3.00000i 0.348743 0.348743i
\(75\) 0 0
\(76\) 0 0
\(77\) −12.2474 5.00000i −1.39573 0.569803i
\(78\) −6.00000 + 6.00000i −0.679366 + 0.679366i
\(79\) 9.00000i 1.01258i 0.862364 + 0.506290i \(0.168983\pi\)
−0.862364 + 0.506290i \(0.831017\pi\)
\(80\) 0 0
\(81\) −9.00000 −1.00000
\(82\) 12.2474 12.2474i 1.35250 1.35250i
\(83\) 2.44949i 0.268866i −0.990923 0.134433i \(-0.957079\pi\)
0.990923 0.134433i \(-0.0429214\pi\)
\(84\) −4.89898 + 12.0000i −0.534522 + 1.30931i
\(85\) 0 0
\(86\) 11.0000 + 11.0000i 1.18616 + 1.18616i
\(87\) 12.2474i 1.31306i
\(88\) 10.0000 + 10.0000i 1.06600 + 1.06600i
\(89\) 2.44949i 0.259645i 0.991537 + 0.129823i \(0.0414408\pi\)
−0.991537 + 0.129823i \(0.958559\pi\)
\(90\) 0 0
\(91\) −2.44949 + 6.00000i −0.256776 + 0.628971i
\(92\) 2.00000i 0.208514i
\(93\) 18.0000i 1.86651i
\(94\) 4.89898 4.89898i 0.505291 0.505291i
\(95\) 0 0
\(96\) 9.79796 9.79796i 1.00000 1.00000i
\(97\) −7.34847 −0.746124 −0.373062 0.927806i \(-0.621692\pi\)
−0.373062 + 0.927806i \(0.621692\pi\)
\(98\) 0.101021 + 9.89898i 0.0102046 + 0.999948i
\(99\) 15.0000i 1.50756i
\(100\) 0 0
\(101\) 12.2474i 1.21867i 0.792914 + 0.609333i \(0.208563\pi\)
−0.792914 + 0.609333i \(0.791437\pi\)
\(102\) −12.0000 + 12.0000i −1.18818 + 1.18818i
\(103\) 14.6969i 1.44813i −0.689730 0.724066i \(-0.742271\pi\)
0.689730 0.724066i \(-0.257729\pi\)
\(104\) 4.89898 4.89898i 0.480384 0.480384i
\(105\) 0 0
\(106\) −4.00000 + 4.00000i −0.388514 + 0.388514i
\(107\) 8.00000 0.773389 0.386695 0.922208i \(-0.373617\pi\)
0.386695 + 0.922208i \(0.373617\pi\)
\(108\) 0 0
\(109\) 15.0000 1.43674 0.718370 0.695662i \(-0.244889\pi\)
0.718370 + 0.695662i \(0.244889\pi\)
\(110\) 0 0
\(111\) 7.34847 0.697486
\(112\) 4.00000 9.79796i 0.377964 0.925820i
\(113\) 11.0000i 1.03479i 0.855746 + 0.517396i \(0.173099\pi\)
−0.855746 + 0.517396i \(0.826901\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 10.0000i 0.928477i
\(117\) −7.34847 −0.679366
\(118\) −12.2474 12.2474i −1.12747 1.12747i
\(119\) −4.89898 + 12.0000i −0.449089 + 1.10004i
\(120\) 0 0
\(121\) −14.0000 −1.27273
\(122\) −12.2474 + 12.2474i −1.10883 + 1.10883i
\(123\) 30.0000 2.70501
\(124\) 14.6969i 1.31982i
\(125\) 0 0
\(126\) −10.3485 + 4.34847i −0.921915 + 0.387392i
\(127\) 3.00000 0.266207 0.133103 0.991102i \(-0.457506\pi\)
0.133103 + 0.991102i \(0.457506\pi\)
\(128\) −8.00000 + 8.00000i −0.707107 + 0.707107i
\(129\) 26.9444i 2.37232i
\(130\) 0 0
\(131\) −4.89898 −0.428026 −0.214013 0.976831i \(-0.568653\pi\)
−0.214013 + 0.976831i \(0.568653\pi\)
\(132\) 24.4949i 2.13201i
\(133\) 0 0
\(134\) −3.00000 3.00000i −0.259161 0.259161i
\(135\) 0 0
\(136\) 9.79796 9.79796i 0.840168 0.840168i
\(137\) 8.00000i 0.683486i 0.939793 + 0.341743i \(0.111017\pi\)
−0.939793 + 0.341743i \(0.888983\pi\)
\(138\) 2.44949 2.44949i 0.208514 0.208514i
\(139\) 12.2474 1.03882 0.519408 0.854527i \(-0.326153\pi\)
0.519408 + 0.854527i \(0.326153\pi\)
\(140\) 0 0
\(141\) 12.0000 1.01058
\(142\) −5.00000 + 5.00000i −0.419591 + 0.419591i
\(143\) 12.2474i 1.02418i
\(144\) 12.0000 1.00000
\(145\) 0 0
\(146\) −2.44949 2.44949i −0.202721 0.202721i
\(147\) −12.0000 + 12.2474i −0.989743 + 1.01015i
\(148\) −6.00000 −0.493197
\(149\) 5.00000 0.409616 0.204808 0.978802i \(-0.434343\pi\)
0.204808 + 0.978802i \(0.434343\pi\)
\(150\) 0 0
\(151\) 5.00000i 0.406894i −0.979086 0.203447i \(-0.934786\pi\)
0.979086 0.203447i \(-0.0652145\pi\)
\(152\) 0 0
\(153\) −14.6969 −1.18818
\(154\) 7.24745 + 17.2474i 0.584016 + 1.38984i
\(155\) 0 0
\(156\) 12.0000 0.960769
\(157\) 17.1464 1.36843 0.684217 0.729279i \(-0.260144\pi\)
0.684217 + 0.729279i \(0.260144\pi\)
\(158\) 9.00000 9.00000i 0.716002 0.716002i
\(159\) −9.79796 −0.777029
\(160\) 0 0
\(161\) 1.00000 2.44949i 0.0788110 0.193047i
\(162\) 9.00000 + 9.00000i 0.707107 + 0.707107i
\(163\) −6.00000 −0.469956 −0.234978 0.972001i \(-0.575502\pi\)
−0.234978 + 0.972001i \(0.575502\pi\)
\(164\) −24.4949 −1.91273
\(165\) 0 0
\(166\) −2.44949 + 2.44949i −0.190117 + 0.190117i
\(167\) 7.34847i 0.568642i −0.958729 0.284321i \(-0.908232\pi\)
0.958729 0.284321i \(-0.0917681\pi\)
\(168\) 16.8990 7.10102i 1.30378 0.547856i
\(169\) −7.00000 −0.538462
\(170\) 0 0
\(171\) 0 0
\(172\) 22.0000i 1.67748i
\(173\) −9.79796 −0.744925 −0.372463 0.928047i \(-0.621486\pi\)
−0.372463 + 0.928047i \(0.621486\pi\)
\(174\) −12.2474 + 12.2474i −0.928477 + 0.928477i
\(175\) 0 0
\(176\) 20.0000i 1.50756i
\(177\) 30.0000i 2.25494i
\(178\) 2.44949 2.44949i 0.183597 0.183597i
\(179\) 14.0000i 1.04641i 0.852207 + 0.523205i \(0.175264\pi\)
−0.852207 + 0.523205i \(0.824736\pi\)
\(180\) 0 0
\(181\) 12.2474i 0.910346i −0.890403 0.455173i \(-0.849577\pi\)
0.890403 0.455173i \(-0.150423\pi\)
\(182\) 8.44949 3.55051i 0.626318 0.263181i
\(183\) −30.0000 −2.21766
\(184\) −2.00000 + 2.00000i −0.147442 + 0.147442i
\(185\) 0 0
\(186\) −18.0000 + 18.0000i −1.31982 + 1.31982i
\(187\) 24.4949i 1.79124i
\(188\) −9.79796 −0.714590
\(189\) 0 0
\(190\) 0 0
\(191\) 10.0000i 0.723575i −0.932261 0.361787i \(-0.882167\pi\)
0.932261 0.361787i \(-0.117833\pi\)
\(192\) −19.5959 −1.41421
\(193\) 21.0000i 1.51161i 0.654795 + 0.755807i \(0.272755\pi\)
−0.654795 + 0.755807i \(0.727245\pi\)
\(194\) 7.34847 + 7.34847i 0.527589 + 0.527589i
\(195\) 0 0
\(196\) 9.79796 10.0000i 0.699854 0.714286i
\(197\) 23.0000i 1.63868i 0.573306 + 0.819341i \(0.305660\pi\)
−0.573306 + 0.819341i \(0.694340\pi\)
\(198\) −15.0000 + 15.0000i −1.06600 + 1.06600i
\(199\) −12.2474 −0.868199 −0.434099 0.900865i \(-0.642933\pi\)
−0.434099 + 0.900865i \(0.642933\pi\)
\(200\) 0 0
\(201\) 7.34847i 0.518321i
\(202\) 12.2474 12.2474i 0.861727 0.861727i
\(203\) −5.00000 + 12.2474i −0.350931 + 0.859602i
\(204\) 24.0000 1.68034
\(205\) 0 0
\(206\) −14.6969 + 14.6969i −1.02398 + 1.02398i
\(207\) 3.00000 0.208514
\(208\) −9.79796 −0.679366
\(209\) 0 0
\(210\) 0 0
\(211\) 10.0000i 0.688428i 0.938891 + 0.344214i \(0.111855\pi\)
−0.938891 + 0.344214i \(0.888145\pi\)
\(212\) 8.00000 0.549442
\(213\) −12.2474 −0.839181
\(214\) −8.00000 8.00000i −0.546869 0.546869i
\(215\) 0 0
\(216\) 0 0
\(217\) −7.34847 + 18.0000i −0.498847 + 1.22192i
\(218\) −15.0000 15.0000i −1.01593 1.01593i
\(219\) 6.00000i 0.405442i
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) −7.34847 7.34847i −0.493197 0.493197i
\(223\) 2.44949i 0.164030i −0.996631 0.0820150i \(-0.973864\pi\)
0.996631 0.0820150i \(-0.0261355\pi\)
\(224\) −13.7980 + 5.79796i −0.921915 + 0.387392i
\(225\) 0 0
\(226\) 11.0000 11.0000i 0.731709 0.731709i
\(227\) 19.5959i 1.30063i −0.759666 0.650313i \(-0.774638\pi\)
0.759666 0.650313i \(-0.225362\pi\)
\(228\) 0 0
\(229\) 9.79796i 0.647467i −0.946148 0.323734i \(-0.895062\pi\)
0.946148 0.323734i \(-0.104938\pi\)
\(230\) 0 0
\(231\) −12.2474 + 30.0000i −0.805823 + 1.97386i
\(232\) 10.0000 10.0000i 0.656532 0.656532i
\(233\) 11.0000i 0.720634i 0.932830 + 0.360317i \(0.117331\pi\)
−0.932830 + 0.360317i \(0.882669\pi\)
\(234\) 7.34847 + 7.34847i 0.480384 + 0.480384i
\(235\) 0 0
\(236\) 24.4949i 1.59448i
\(237\) 22.0454 1.43200
\(238\) 16.8990 7.10102i 1.09540 0.460291i
\(239\) 26.0000i 1.68180i −0.541190 0.840900i \(-0.682026\pi\)
0.541190 0.840900i \(-0.317974\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 14.0000 + 14.0000i 0.899954 + 0.899954i
\(243\) 22.0454i 1.41421i
\(244\) 24.4949 1.56813
\(245\) 0 0
\(246\) −30.0000 30.0000i −1.91273 1.91273i
\(247\) 0 0
\(248\) 14.6969 14.6969i 0.933257 0.933257i
\(249\) −6.00000 −0.380235
\(250\) 0 0
\(251\) −4.89898 −0.309221 −0.154610 0.987976i \(-0.549412\pi\)
−0.154610 + 0.987976i \(0.549412\pi\)
\(252\) 14.6969 + 6.00000i 0.925820 + 0.377964i
\(253\) 5.00000i 0.314347i
\(254\) −3.00000 3.00000i −0.188237 0.188237i
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) −7.34847 −0.458385 −0.229192 0.973381i \(-0.573609\pi\)
−0.229192 + 0.973381i \(0.573609\pi\)
\(258\) 26.9444 26.9444i 1.67748 1.67748i
\(259\) −7.34847 3.00000i −0.456612 0.186411i
\(260\) 0 0
\(261\) −15.0000 −0.928477
\(262\) 4.89898 + 4.89898i 0.302660 + 0.302660i
\(263\) −1.00000 −0.0616626 −0.0308313 0.999525i \(-0.509815\pi\)
−0.0308313 + 0.999525i \(0.509815\pi\)
\(264\) 24.4949 24.4949i 1.50756 1.50756i
\(265\) 0 0
\(266\) 0 0
\(267\) 6.00000 0.367194
\(268\) 6.00000i 0.366508i
\(269\) 22.0454i 1.34413i −0.740491 0.672066i \(-0.765407\pi\)
0.740491 0.672066i \(-0.234593\pi\)
\(270\) 0 0
\(271\) −17.1464 −1.04157 −0.520786 0.853687i \(-0.674361\pi\)
−0.520786 + 0.853687i \(0.674361\pi\)
\(272\) −19.5959 −1.18818
\(273\) 14.6969 + 6.00000i 0.889499 + 0.363137i
\(274\) 8.00000 8.00000i 0.483298 0.483298i
\(275\) 0 0
\(276\) −4.89898 −0.294884
\(277\) 2.00000i 0.120168i −0.998193 0.0600842i \(-0.980863\pi\)
0.998193 0.0600842i \(-0.0191369\pi\)
\(278\) −12.2474 12.2474i −0.734553 0.734553i
\(279\) −22.0454 −1.31982
\(280\) 0 0
\(281\) 17.0000 1.01413 0.507067 0.861906i \(-0.330729\pi\)
0.507067 + 0.861906i \(0.330729\pi\)
\(282\) −12.0000 12.0000i −0.714590 0.714590i
\(283\) 9.79796i 0.582428i 0.956658 + 0.291214i \(0.0940592\pi\)
−0.956658 + 0.291214i \(0.905941\pi\)
\(284\) 10.0000 0.593391
\(285\) 0 0
\(286\) 12.2474 12.2474i 0.724207 0.724207i
\(287\) −30.0000 12.2474i −1.77084 0.722944i
\(288\) −12.0000 12.0000i −0.707107 0.707107i
\(289\) 7.00000 0.411765
\(290\) 0 0
\(291\) 18.0000i 1.05518i
\(292\) 4.89898i 0.286691i
\(293\) 2.44949 0.143101 0.0715504 0.997437i \(-0.477205\pi\)
0.0715504 + 0.997437i \(0.477205\pi\)
\(294\) 24.2474 0.247449i 1.41414 0.0144315i
\(295\) 0 0
\(296\) 6.00000 + 6.00000i 0.348743 + 0.348743i
\(297\) 0 0
\(298\) −5.00000 5.00000i −0.289642 0.289642i
\(299\) −2.44949 −0.141658
\(300\) 0 0
\(301\) 11.0000 26.9444i 0.634029 1.55305i
\(302\) −5.00000 + 5.00000i −0.287718 + 0.287718i
\(303\) 30.0000 1.72345
\(304\) 0 0
\(305\) 0 0
\(306\) 14.6969 + 14.6969i 0.840168 + 0.840168i
\(307\) 4.89898i 0.279600i 0.990180 + 0.139800i \(0.0446459\pi\)
−0.990180 + 0.139800i \(0.955354\pi\)
\(308\) 10.0000 24.4949i 0.569803 1.39573i
\(309\) −36.0000 −2.04797
\(310\) 0 0
\(311\) 19.5959 1.11118 0.555591 0.831456i \(-0.312492\pi\)
0.555591 + 0.831456i \(0.312492\pi\)
\(312\) −12.0000 12.0000i −0.679366 0.679366i
\(313\) −9.79796 −0.553813 −0.276907 0.960897i \(-0.589309\pi\)
−0.276907 + 0.960897i \(0.589309\pi\)
\(314\) −17.1464 17.1464i −0.967629 0.967629i
\(315\) 0 0
\(316\) −18.0000 −1.01258
\(317\) 17.0000i 0.954815i −0.878682 0.477408i \(-0.841577\pi\)
0.878682 0.477408i \(-0.158423\pi\)
\(318\) 9.79796 + 9.79796i 0.549442 + 0.549442i
\(319\) 25.0000i 1.39973i
\(320\) 0 0
\(321\) 19.5959i 1.09374i
\(322\) −3.44949 + 1.44949i −0.192233 + 0.0807769i
\(323\) 0 0
\(324\) 18.0000i 1.00000i
\(325\) 0 0
\(326\) 6.00000 + 6.00000i 0.332309 + 0.332309i
\(327\) 36.7423i 2.03186i
\(328\) 24.4949 + 24.4949i 1.35250 + 1.35250i
\(329\) −12.0000 4.89898i −0.661581 0.270089i
\(330\) 0 0
\(331\) 25.0000i 1.37412i −0.726599 0.687062i \(-0.758900\pi\)
0.726599 0.687062i \(-0.241100\pi\)
\(332\) 4.89898 0.268866
\(333\) 9.00000i 0.493197i
\(334\) −7.34847 + 7.34847i −0.402090 + 0.402090i
\(335\) 0 0
\(336\) −24.0000 9.79796i −1.30931 0.534522i
\(337\) 12.0000i 0.653682i −0.945079 0.326841i \(-0.894016\pi\)
0.945079 0.326841i \(-0.105984\pi\)
\(338\) 7.00000 + 7.00000i 0.380750 + 0.380750i
\(339\) 26.9444 1.46342
\(340\) 0 0
\(341\) 36.7423i 1.98971i
\(342\) 0 0
\(343\) 17.0000 7.34847i 0.917914 0.396780i
\(344\) −22.0000 + 22.0000i −1.18616 + 1.18616i
\(345\) 0 0
\(346\) 9.79796 + 9.79796i 0.526742 + 0.526742i
\(347\) −17.0000 −0.912608 −0.456304 0.889824i \(-0.650827\pi\)
−0.456304 + 0.889824i \(0.650827\pi\)
\(348\) 24.4949 1.31306
\(349\) 9.79796i 0.524473i −0.965004 0.262236i \(-0.915540\pi\)
0.965004 0.262236i \(-0.0844600\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −20.0000 + 20.0000i −1.06600 + 1.06600i
\(353\) −22.0454 −1.17336 −0.586679 0.809819i \(-0.699565\pi\)
−0.586679 + 0.809819i \(0.699565\pi\)
\(354\) −30.0000 + 30.0000i −1.59448 + 1.59448i
\(355\) 0 0
\(356\) −4.89898 −0.259645
\(357\) 29.3939 + 12.0000i 1.55569 + 0.635107i
\(358\) 14.0000 14.0000i 0.739923 0.739923i
\(359\) 19.0000i 1.00278i 0.865221 + 0.501391i \(0.167178\pi\)
−0.865221 + 0.501391i \(0.832822\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) −12.2474 + 12.2474i −0.643712 + 0.643712i
\(363\) 34.2929i 1.79991i
\(364\) −12.0000 4.89898i −0.628971 0.256776i
\(365\) 0 0
\(366\) 30.0000 + 30.0000i 1.56813 + 1.56813i
\(367\) 17.1464i 0.895036i 0.894275 + 0.447518i \(0.147692\pi\)
−0.894275 + 0.447518i \(0.852308\pi\)
\(368\) 4.00000 0.208514
\(369\) 36.7423i 1.91273i
\(370\) 0 0
\(371\) 9.79796 + 4.00000i 0.508685 + 0.207670i
\(372\) 36.0000 1.86651
\(373\) 29.0000i 1.50156i −0.660551 0.750782i \(-0.729677\pi\)
0.660551 0.750782i \(-0.270323\pi\)
\(374\) 24.4949 24.4949i 1.26660 1.26660i
\(375\) 0 0
\(376\) 9.79796 + 9.79796i 0.505291 + 0.505291i
\(377\) 12.2474 0.630776
\(378\) 0 0
\(379\) 1.00000i 0.0513665i −0.999670 0.0256833i \(-0.991824\pi\)
0.999670 0.0256833i \(-0.00817614\pi\)
\(380\) 0 0
\(381\) 7.34847i 0.376473i
\(382\) −10.0000 + 10.0000i −0.511645 + 0.511645i
\(383\) 2.44949i 0.125163i −0.998040 0.0625815i \(-0.980067\pi\)
0.998040 0.0625815i \(-0.0199333\pi\)
\(384\) 19.5959 + 19.5959i 1.00000 + 1.00000i
\(385\) 0 0
\(386\) 21.0000 21.0000i 1.06887 1.06887i
\(387\) 33.0000 1.67748
\(388\) 14.6969i 0.746124i
\(389\) −5.00000 −0.253510 −0.126755 0.991934i \(-0.540456\pi\)
−0.126755 + 0.991934i \(0.540456\pi\)
\(390\) 0 0
\(391\) −4.89898 −0.247752
\(392\) −19.7980 + 0.202041i −0.999948 + 0.0102046i
\(393\) 12.0000i 0.605320i
\(394\) 23.0000 23.0000i 1.15872 1.15872i
\(395\) 0 0
\(396\) 30.0000 1.50756
\(397\) −19.5959 −0.983491 −0.491745 0.870739i \(-0.663641\pi\)
−0.491745 + 0.870739i \(0.663641\pi\)
\(398\) 12.2474 + 12.2474i 0.613909 + 0.613909i
\(399\) 0 0
\(400\) 0 0
\(401\) −23.0000 −1.14857 −0.574283 0.818657i \(-0.694719\pi\)
−0.574283 + 0.818657i \(0.694719\pi\)
\(402\) −7.34847 + 7.34847i −0.366508 + 0.366508i
\(403\) 18.0000 0.896644
\(404\) −24.4949 −1.21867
\(405\) 0 0
\(406\) 17.2474 7.24745i 0.855977 0.359685i
\(407\) −15.0000 −0.743522
\(408\) −24.0000 24.0000i −1.18818 1.18818i
\(409\) 34.2929i 1.69567i −0.530258 0.847836i \(-0.677905\pi\)
0.530258 0.847836i \(-0.322095\pi\)
\(410\) 0 0
\(411\) 19.5959 0.966595
\(412\) 29.3939 1.44813
\(413\) −12.2474 + 30.0000i −0.602658 + 1.47620i
\(414\) −3.00000 3.00000i −0.147442 0.147442i
\(415\) 0 0
\(416\) 9.79796 + 9.79796i 0.480384 + 0.480384i
\(417\) 30.0000i 1.46911i
\(418\) 0 0
\(419\) 12.2474 0.598327 0.299164 0.954202i \(-0.403292\pi\)
0.299164 + 0.954202i \(0.403292\pi\)
\(420\) 0 0
\(421\) −23.0000 −1.12095 −0.560476 0.828171i \(-0.689382\pi\)
−0.560476 + 0.828171i \(0.689382\pi\)
\(422\) 10.0000 10.0000i 0.486792 0.486792i
\(423\) 14.6969i 0.714590i
\(424\) −8.00000 8.00000i −0.388514 0.388514i
\(425\) 0 0
\(426\) 12.2474 + 12.2474i 0.593391 + 0.593391i
\(427\) 30.0000 + 12.2474i 1.45180 + 0.592696i
\(428\) 16.0000i 0.773389i
\(429\) 30.0000 1.44841
\(430\) 0 0
\(431\) 10.0000i 0.481683i −0.970564 0.240842i \(-0.922577\pi\)
0.970564 0.240842i \(-0.0774234\pi\)
\(432\) 0 0
\(433\) 39.1918 1.88344 0.941720 0.336399i \(-0.109209\pi\)
0.941720 + 0.336399i \(0.109209\pi\)
\(434\) 25.3485 10.6515i 1.21677 0.511290i
\(435\) 0 0
\(436\) 30.0000i 1.43674i
\(437\) 0 0
\(438\) −6.00000 + 6.00000i −0.286691 + 0.286691i
\(439\) −12.2474 −0.584539 −0.292269 0.956336i \(-0.594410\pi\)
−0.292269 + 0.956336i \(0.594410\pi\)
\(440\) 0 0
\(441\) 15.0000 + 14.6969i 0.714286 + 0.699854i
\(442\) −12.0000 12.0000i −0.570782 0.570782i
\(443\) 14.0000 0.665160 0.332580 0.943075i \(-0.392081\pi\)
0.332580 + 0.943075i \(0.392081\pi\)
\(444\) 14.6969i 0.697486i
\(445\) 0 0
\(446\) −2.44949 + 2.44949i −0.115987 + 0.115987i
\(447\) 12.2474i 0.579284i
\(448\) 19.5959 + 8.00000i 0.925820 + 0.377964i
\(449\) 25.0000 1.17982 0.589911 0.807468i \(-0.299163\pi\)
0.589911 + 0.807468i \(0.299163\pi\)
\(450\) 0 0
\(451\) −61.2372 −2.88355
\(452\) −22.0000 −1.03479
\(453\) −12.2474 −0.575435
\(454\) −19.5959 + 19.5959i −0.919682 + 0.919682i
\(455\) 0 0
\(456\) 0 0
\(457\) 3.00000i 0.140334i 0.997535 + 0.0701670i \(0.0223532\pi\)
−0.997535 + 0.0701670i \(0.977647\pi\)
\(458\) −9.79796 + 9.79796i −0.457829 + 0.457829i
\(459\) 0 0
\(460\) 0 0
\(461\) 12.2474i 0.570421i 0.958465 + 0.285210i \(0.0920634\pi\)
−0.958465 + 0.285210i \(0.907937\pi\)
\(462\) 42.2474 17.7526i 1.96553 0.825923i
\(463\) −36.0000 −1.67306 −0.836531 0.547920i \(-0.815420\pi\)
−0.836531 + 0.547920i \(0.815420\pi\)
\(464\) −20.0000 −0.928477
\(465\) 0 0
\(466\) 11.0000 11.0000i 0.509565 0.509565i
\(467\) 4.89898i 0.226698i 0.993555 + 0.113349i \(0.0361578\pi\)
−0.993555 + 0.113349i \(0.963842\pi\)
\(468\) 14.6969i 0.679366i
\(469\) −3.00000 + 7.34847i −0.138527 + 0.339321i
\(470\) 0 0
\(471\) 42.0000i 1.93526i
\(472\) 24.4949 24.4949i 1.12747 1.12747i
\(473\) 55.0000i 2.52890i
\(474\) −22.0454 22.0454i −1.01258 1.01258i
\(475\) 0 0
\(476\) −24.0000 9.79796i −1.10004 0.449089i
\(477\) 12.0000i 0.549442i
\(478\) −26.0000 + 26.0000i −1.18921 + 1.18921i
\(479\) −36.7423 −1.67880 −0.839400 0.543514i \(-0.817094\pi\)
−0.839400 + 0.543514i \(0.817094\pi\)
\(480\) 0 0
\(481\) 7.34847i 0.335061i
\(482\) 0 0
\(483\) −6.00000 2.44949i −0.273009 0.111456i
\(484\) 28.0000i 1.27273i
\(485\) 0 0
\(486\) 22.0454 22.0454i 1.00000 1.00000i
\(487\) −7.00000 −0.317200 −0.158600 0.987343i \(-0.550698\pi\)
−0.158600 + 0.987343i \(0.550698\pi\)
\(488\) −24.4949 24.4949i −1.10883 1.10883i
\(489\) 14.6969i 0.664619i
\(490\) 0 0
\(491\) 5.00000i 0.225647i 0.993615 + 0.112823i \(0.0359894\pi\)
−0.993615 + 0.112823i \(0.964011\pi\)
\(492\) 60.0000i 2.70501i
\(493\) 24.4949 1.10319
\(494\) 0 0
\(495\) 0 0
\(496\) −29.3939 −1.31982
\(497\) 12.2474 + 5.00000i 0.549373 + 0.224281i
\(498\) 6.00000 + 6.00000i 0.268866 + 0.268866i
\(499\) 16.0000i 0.716258i −0.933672 0.358129i \(-0.883415\pi\)
0.933672 0.358129i \(-0.116585\pi\)
\(500\) 0 0
\(501\) −18.0000 −0.804181
\(502\) 4.89898 + 4.89898i 0.218652 + 0.218652i
\(503\) 14.6969i 0.655304i −0.944798 0.327652i \(-0.893743\pi\)
0.944798 0.327652i \(-0.106257\pi\)
\(504\) −8.69694 20.6969i −0.387392 0.921915i
\(505\) 0 0
\(506\) −5.00000 + 5.00000i −0.222277 + 0.222277i
\(507\) 17.1464i 0.761500i
\(508\) 6.00000i 0.266207i
\(509\) 26.9444i 1.19429i 0.802134 + 0.597144i \(0.203698\pi\)
−0.802134 + 0.597144i \(0.796302\pi\)
\(510\) 0 0
\(511\) −2.44949 + 6.00000i −0.108359 + 0.265424i
\(512\) −16.0000 16.0000i −0.707107 0.707107i
\(513\) 0 0
\(514\) 7.34847 + 7.34847i 0.324127 + 0.324127i
\(515\) 0 0
\(516\) −53.8888 −2.37232
\(517\) −24.4949 −1.07728
\(518\) 4.34847 + 10.3485i 0.191061 + 0.454686i
\(519\) 24.0000i 1.05348i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 15.0000 + 15.0000i 0.656532 + 0.656532i
\(523\) 9.79796i 0.428435i 0.976786 + 0.214217i \(0.0687201\pi\)
−0.976786 + 0.214217i \(0.931280\pi\)
\(524\) 9.79796i 0.428026i
\(525\) 0 0
\(526\) 1.00000 + 1.00000i 0.0436021 + 0.0436021i
\(527\) 36.0000 1.56818
\(528\) −48.9898 −2.13201
\(529\) −22.0000 −0.956522
\(530\) 0 0
\(531\) −36.7423 −1.59448
\(532\) 0 0
\(533\) 30.0000i 1.29944i
\(534\) −6.00000 6.00000i −0.259645 0.259645i
\(535\) 0 0
\(536\) 6.00000 6.00000i 0.259161 0.259161i
\(537\) 34.2929 1.47985
\(538\) −22.0454 + 22.0454i −0.950445 + 0.950445i
\(539\) 24.4949 25.0000i 1.05507 1.07683i
\(540\) 0 0
\(541\) −13.0000 −0.558914 −0.279457 0.960158i \(-0.590154\pi\)
−0.279457 + 0.960158i \(0.590154\pi\)
\(542\) 17.1464 + 17.1464i 0.736502 + 0.736502i
\(543\) −30.0000 −1.28742
\(544\) 19.5959 + 19.5959i 0.840168 + 0.840168i
\(545\) 0 0
\(546\) −8.69694 20.6969i −0.372195 0.885747i
\(547\) −27.0000 −1.15444 −0.577218 0.816590i \(-0.695862\pi\)
−0.577218 + 0.816590i \(0.695862\pi\)
\(548\) −16.0000 −0.683486
\(549\) 36.7423i 1.56813i
\(550\) 0 0
\(551\) 0 0
\(552\) 4.89898 + 4.89898i 0.208514 + 0.208514i
\(553\) −22.0454 9.00000i −0.937466 0.382719i
\(554\) −2.00000 + 2.00000i −0.0849719 + 0.0849719i
\(555\) 0 0
\(556\) 24.4949i 1.03882i
\(557\) 37.0000i 1.56774i −0.620925 0.783870i \(-0.713243\pi\)
0.620925 0.783870i \(-0.286757\pi\)
\(558\) 22.0454 + 22.0454i 0.933257 + 0.933257i
\(559\) −26.9444 −1.13963
\(560\) 0 0
\(561\) 60.0000 2.53320
\(562\) −17.0000 17.0000i −0.717102 0.717102i
\(563\) 14.6969i 0.619402i −0.950834 0.309701i \(-0.899771\pi\)
0.950834 0.309701i \(-0.100229\pi\)
\(564\) 24.0000i 1.01058i
\(565\) 0 0
\(566\) 9.79796 9.79796i 0.411839 0.411839i
\(567\) 9.00000 22.0454i 0.377964 0.925820i
\(568\) −10.0000 10.0000i −0.419591 0.419591i
\(569\) −5.00000 −0.209611 −0.104805 0.994493i \(-0.533422\pi\)
−0.104805 + 0.994493i \(0.533422\pi\)
\(570\) 0 0
\(571\) 15.0000i 0.627730i −0.949468 0.313865i \(-0.898376\pi\)
0.949468 0.313865i \(-0.101624\pi\)
\(572\) −24.4949 −1.02418
\(573\) −24.4949 −1.02329
\(574\) 17.7526 + 42.2474i 0.740977 + 1.76337i
\(575\) 0 0
\(576\) 24.0000i 1.00000i
\(577\) −44.0908 −1.83552 −0.917762 0.397130i \(-0.870006\pi\)
−0.917762 + 0.397130i \(0.870006\pi\)
\(578\) −7.00000 7.00000i −0.291162 0.291162i
\(579\) 51.4393 2.13774
\(580\) 0 0
\(581\) 6.00000 + 2.44949i 0.248922 + 0.101622i
\(582\) 18.0000 18.0000i 0.746124 0.746124i
\(583\) 20.0000 0.828315
\(584\) 4.89898 4.89898i 0.202721 0.202721i
\(585\) 0 0
\(586\) −2.44949 2.44949i −0.101187 0.101187i
\(587\) 17.1464i 0.707709i 0.935301 + 0.353854i \(0.115129\pi\)
−0.935301 + 0.353854i \(0.884871\pi\)
\(588\) −24.4949 24.0000i −1.01015 0.989743i
\(589\) 0 0
\(590\) 0 0
\(591\) 56.3383 2.31745
\(592\) 12.0000i 0.493197i
\(593\) −9.79796 −0.402354 −0.201177 0.979555i \(-0.564477\pi\)
−0.201177 + 0.979555i \(0.564477\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 10.0000i 0.409616i
\(597\) 30.0000i 1.22782i
\(598\) 2.44949 + 2.44949i 0.100167 + 0.100167i
\(599\) 11.0000i 0.449448i −0.974422 0.224724i \(-0.927852\pi\)
0.974422 0.224724i \(-0.0721480\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) −37.9444 + 15.9444i −1.54650 + 0.649845i
\(603\) −9.00000 −0.366508
\(604\) 10.0000 0.406894
\(605\) 0 0
\(606\) −30.0000 30.0000i −1.21867 1.21867i
\(607\) 7.34847i 0.298265i −0.988817 0.149133i \(-0.952352\pi\)
0.988817 0.149133i \(-0.0476481\pi\)
\(608\) 0 0
\(609\) 30.0000 + 12.2474i 1.21566 + 0.496292i
\(610\) 0 0
\(611\) 12.0000i 0.485468i
\(612\) 29.3939i 1.18818i
\(613\) 11.0000i 0.444286i 0.975014 + 0.222143i \(0.0713052\pi\)
−0.975014 + 0.222143i \(0.928695\pi\)
\(614\) 4.89898 4.89898i 0.197707 0.197707i
\(615\) 0 0
\(616\) −34.4949 + 14.4949i −1.38984 + 0.584016i
\(617\) 13.0000i 0.523360i 0.965155 + 0.261680i \(0.0842766\pi\)
−0.965155 + 0.261680i \(0.915723\pi\)
\(618\) 36.0000 + 36.0000i 1.44813 + 1.44813i
\(619\) −12.2474 −0.492267 −0.246133 0.969236i \(-0.579160\pi\)
−0.246133 + 0.969236i \(0.579160\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −19.5959 19.5959i −0.785725 0.785725i
\(623\) −6.00000 2.44949i −0.240385 0.0981367i
\(624\) 24.0000i 0.960769i
\(625\) 0 0
\(626\) 9.79796 + 9.79796i 0.391605 + 0.391605i
\(627\) 0 0
\(628\) 34.2929i 1.36843i
\(629\) 14.6969i 0.586005i
\(630\) 0 0
\(631\) 45.0000i 1.79142i 0.444637 + 0.895711i \(0.353333\pi\)
−0.444637 + 0.895711i \(0.646667\pi\)
\(632\) 18.0000 + 18.0000i 0.716002 + 0.716002i
\(633\) 24.4949 0.973585
\(634\) −17.0000 + 17.0000i −0.675156 + 0.675156i
\(635\) 0 0
\(636\) 19.5959i 0.777029i
\(637\) −12.2474 12.0000i −0.485262 0.475457i
\(638\) 25.0000 25.0000i 0.989759 0.989759i
\(639\) 15.0000i 0.593391i
\(640\) 0 0
\(641\) 17.0000 0.671460 0.335730 0.941958i \(-0.391017\pi\)
0.335730 + 0.941958i \(0.391017\pi\)
\(642\) −19.5959 + 19.5959i −0.773389 + 0.773389i
\(643\) 39.1918i 1.54558i −0.634665 0.772788i \(-0.718862\pi\)
0.634665 0.772788i \(-0.281138\pi\)
\(644\) 4.89898 + 2.00000i 0.193047 + 0.0788110i
\(645\) 0 0
\(646\) 0 0
\(647\) 29.3939i 1.15559i 0.816181 + 0.577796i \(0.196087\pi\)
−0.816181 + 0.577796i \(0.803913\pi\)
\(648\) −18.0000 + 18.0000i −0.707107 + 0.707107i
\(649\) 61.2372i 2.40377i
\(650\) 0 0
\(651\) 44.0908 + 18.0000i 1.72806 + 0.705476i
\(652\) 12.0000i 0.469956i
\(653\) 16.0000i 0.626128i 0.949732 + 0.313064i \(0.101356\pi\)
−0.949732 + 0.313064i \(0.898644\pi\)
\(654\) −36.7423 + 36.7423i −1.43674 + 1.43674i
\(655\) 0 0
\(656\) 48.9898i 1.91273i
\(657\) −7.34847 −0.286691
\(658\) 7.10102 + 16.8990i 0.276827 + 0.658791i
\(659\) 16.0000i 0.623272i −0.950202 0.311636i \(-0.899123\pi\)
0.950202 0.311636i \(-0.100877\pi\)
\(660\) 0 0
\(661\) 24.4949i 0.952741i −0.879245 0.476371i \(-0.841952\pi\)
0.879245 0.476371i \(-0.158048\pi\)
\(662\) −25.0000 + 25.0000i −0.971653 + 0.971653i
\(663\) 29.3939i 1.14156i
\(664\) −4.89898 4.89898i −0.190117 0.190117i
\(665\) 0 0
\(666\) −9.00000 + 9.00000i −0.348743 + 0.348743i
\(667\) −5.00000 −0.193601
\(668\) 14.6969 0.568642
\(669\) −6.00000 −0.231973
\(670\) 0 0
\(671\) 61.2372 2.36404
\(672\) 14.2020 + 33.7980i 0.547856 + 1.30378i
\(673\) 24.0000i 0.925132i −0.886585 0.462566i \(-0.846929\pi\)
0.886585 0.462566i \(-0.153071\pi\)
\(674\) −12.0000 + 12.0000i −0.462223 + 0.462223i
\(675\) 0 0
\(676\) 14.0000i 0.538462i
\(677\) 29.3939 1.12970 0.564849 0.825194i \(-0.308934\pi\)
0.564849 + 0.825194i \(0.308934\pi\)
\(678\) −26.9444 26.9444i −1.03479 1.03479i
\(679\) 7.34847 18.0000i 0.282008 0.690777i
\(680\) 0 0
\(681\) −48.0000 −1.83936
\(682\) 36.7423 36.7423i 1.40694 1.40694i
\(683\) −11.0000 −0.420903 −0.210452 0.977604i \(-0.567493\pi\)
−0.210452 + 0.977604i \(0.567493\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −24.3485 9.65153i −0.929629 0.368497i
\(687\) −24.0000 −0.915657
\(688\) 44.0000 1.67748
\(689\) 9.79796i 0.373273i
\(690\) 0 0
\(691\) 31.8434 1.21138 0.605689 0.795701i \(-0.292897\pi\)
0.605689 + 0.795701i \(0.292897\pi\)
\(692\) 19.5959i 0.744925i
\(693\) 36.7423 + 15.0000i 1.39573 + 0.569803i
\(694\) 17.0000 + 17.0000i 0.645311 + 0.645311i
\(695\) 0 0
\(696\) −24.4949 24.4949i −0.928477 0.928477i
\(697\) 60.0000i 2.27266i
\(698\) −9.79796 + 9.79796i −0.370858 + 0.370858i
\(699\) 26.9444 1.01913
\(700\) 0 0
\(701\) 22.0000 0.830929 0.415464 0.909610i \(-0.363619\pi\)
0.415464 + 0.909610i \(0.363619\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 40.0000 1.50756
\(705\) 0 0
\(706\) 22.0454 + 22.0454i 0.829690 + 0.829690i
\(707\) −30.0000 12.2474i −1.12827 0.460613i
\(708\) 60.0000 2.25494
\(709\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) 0 0
\(711\) 27.0000i 1.01258i
\(712\) 4.89898 + 4.89898i 0.183597 + 0.183597i
\(713\) −7.34847 −0.275202
\(714\) −17.3939 41.3939i −0.650949 1.54913i
\(715\) 0 0
\(716\) −28.0000 −1.04641
\(717\) −63.6867 −2.37842
\(718\) 19.0000 19.0000i 0.709074 0.709074i
\(719\) 12.2474 0.456753 0.228376 0.973573i \(-0.426658\pi\)
0.228376 + 0.973573i \(0.426658\pi\)
\(720\) 0 0
\(721\) 36.0000 + 14.6969i 1.34071 + 0.547343i
\(722\) 19.0000 + 19.0000i 0.707107 + 0.707107i
\(723\) 0 0
\(724\) 24.4949 0.910346
\(725\) 0 0
\(726\) 34.2929 34.2929i 1.27273 1.27273i
\(727\) 29.3939i 1.09016i 0.838385 + 0.545079i \(0.183500\pi\)
−0.838385 + 0.545079i \(0.816500\pi\)
\(728\) 7.10102 + 16.8990i 0.263181 + 0.626318i
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) −53.8888 −1.99315
\(732\) 60.0000i 2.21766i
\(733\) 39.1918 1.44758 0.723792 0.690018i \(-0.242398\pi\)
0.723792 + 0.690018i \(0.242398\pi\)
\(734\) 17.1464 17.1464i 0.632886 0.632886i
\(735\) 0 0
\(736\) −4.00000 4.00000i −0.147442 0.147442i
\(737\) 15.0000i 0.552532i
\(738\) −36.7423 + 36.7423i −1.35250 + 1.35250i
\(739\) 9.00000i 0.331070i 0.986204 + 0.165535i \(0.0529351\pi\)
−0.986204 + 0.165535i \(0.947065\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −5.79796 13.7980i −0.212850 0.506539i
\(743\) 34.0000 1.24734 0.623670 0.781688i \(-0.285641\pi\)
0.623670 + 0.781688i \(0.285641\pi\)
\(744\) −36.0000 36.0000i −1.31982 1.31982i
\(745\) 0 0
\(746\) −29.0000 + 29.0000i −1.06177 + 1.06177i
\(747\) 7.34847i 0.268866i
\(748\) −48.9898 −1.79124
\(749\) −8.00000 + 19.5959i −0.292314 + 0.716019i
\(750\) 0 0
\(751\) 20.0000i 0.729810i 0.931045 + 0.364905i \(0.118899\pi\)
−0.931045 + 0.364905i \(0.881101\pi\)
\(752\) 19.5959i 0.714590i
\(753\) 12.0000i 0.437304i
\(754\) −12.2474 12.2474i −0.446026 0.446026i
\(755\) 0 0
\(756\) 0 0
\(757\) 3.00000i 0.109037i 0.998513 + 0.0545184i \(0.0173624\pi\)
−0.998513 + 0.0545184i \(0.982638\pi\)
\(758\) −1.00000 + 1.00000i −0.0363216 + 0.0363216i
\(759\) −12.2474 −0.444554
\(760\) 0 0
\(761\) 24.4949i 0.887939i −0.896042 0.443970i \(-0.853570\pi\)
0.896042 0.443970i \(-0.146430\pi\)
\(762\) −7.34847 + 7.34847i −0.266207 + 0.266207i
\(763\) −15.0000 + 36.7423i −0.543036 + 1.33016i
\(764\) 20.0000 0.723575
\(765\) 0 0
\(766\) −2.44949 + 2.44949i −0.0885037 + 0.0885037i
\(767\) 30.0000 1.08324
\(768\) 39.1918i 1.41421i
\(769\) 22.0454i 0.794978i −0.917607 0.397489i \(-0.869882\pi\)
0.917607 0.397489i \(-0.130118\pi\)
\(770\) 0 0
\(771\) 18.0000i 0.648254i
\(772\) −42.0000 −1.51161
\(773\) 26.9444 0.969122 0.484561 0.874757i \(-0.338979\pi\)
0.484561 + 0.874757i \(0.338979\pi\)
\(774\) −33.0000 33.0000i −1.18616 1.18616i
\(775\) 0 0
\(776\) −14.6969 + 14.6969i −0.527589 + 0.527589i
\(777\) −7.34847 + 18.0000i −0.263625 + 0.645746i
\(778\) 5.00000 + 5.00000i 0.179259 + 0.179259i
\(779\) 0 0
\(780\) 0 0
\(781\) 25.0000 0.894570
\(782\) 4.89898 + 4.89898i 0.175187 + 0.175187i
\(783\) 0 0
\(784\) 20.0000 + 19.5959i 0.714286 + 0.699854i
\(785\) 0 0
\(786\) 12.0000 12.0000i 0.428026 0.428026i
\(787\) 17.1464i 0.611204i 0.952159 + 0.305602i \(0.0988577\pi\)
−0.952159 + 0.305602i \(0.901142\pi\)
\(788\) −46.0000 −1.63868
\(789\) 2.44949i 0.0872041i
\(790\) 0 0
\(791\) −26.9444 11.0000i