Properties

Label 624.2.bv.e.49.2
Level $624$
Weight $2$
Character 624.49
Analytic conductor $4.983$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.bv (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.98266508613\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 624.49
Dual form 624.2.bv.e.433.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +0.267949i q^{5} +(-0.633975 - 0.366025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +0.267949i q^{5} +(-0.633975 - 0.366025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(4.09808 - 2.36603i) q^{11} +(2.59808 + 2.50000i) q^{13} +(-0.232051 + 0.133975i) q^{15} +(-1.13397 + 1.96410i) q^{17} +(1.09808 + 0.633975i) q^{19} -0.732051i q^{21} +(3.09808 + 5.36603i) q^{23} +4.92820 q^{25} -1.00000 q^{27} +(-1.23205 - 2.13397i) q^{29} +5.46410i q^{31} +(4.09808 + 2.36603i) q^{33} +(0.0980762 - 0.169873i) q^{35} +(-9.06218 + 5.23205i) q^{37} +(-0.866025 + 3.50000i) q^{39} +(9.86603 - 5.69615i) q^{41} +(-3.83013 + 6.63397i) q^{43} +(-0.232051 - 0.133975i) q^{45} -8.19615i q^{47} +(-3.23205 - 5.59808i) q^{49} -2.26795 q^{51} +0.464102 q^{53} +(0.633975 + 1.09808i) q^{55} +1.26795i q^{57} +(-6.92820 - 4.00000i) q^{59} +(-0.598076 + 1.03590i) q^{61} +(0.633975 - 0.366025i) q^{63} +(-0.669873 + 0.696152i) q^{65} +(9.63397 - 5.56218i) q^{67} +(-3.09808 + 5.36603i) q^{69} +(1.09808 + 0.633975i) q^{71} +9.73205i q^{73} +(2.46410 + 4.26795i) q^{75} -3.46410 q^{77} +9.46410 q^{79} +(-0.500000 - 0.866025i) q^{81} -10.1962i q^{83} +(-0.526279 - 0.303848i) q^{85} +(1.23205 - 2.13397i) q^{87} +(2.19615 - 1.26795i) q^{89} +(-0.732051 - 2.53590i) q^{91} +(-4.73205 + 2.73205i) q^{93} +(-0.169873 + 0.294229i) q^{95} +(5.19615 + 3.00000i) q^{97} +4.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} - 6 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{3} - 6 q^{7} - 2 q^{9} + 6 q^{11} + 6 q^{15} - 8 q^{17} - 6 q^{19} + 2 q^{23} - 8 q^{25} - 4 q^{27} + 2 q^{29} + 6 q^{33} - 10 q^{35} - 12 q^{37} + 36 q^{41} + 2 q^{43} + 6 q^{45} - 6 q^{49} - 16 q^{51} - 12 q^{53} + 6 q^{55} + 8 q^{61} + 6 q^{63} - 20 q^{65} + 42 q^{67} - 2 q^{69} - 6 q^{71} - 4 q^{75} + 24 q^{79} - 2 q^{81} + 36 q^{85} - 2 q^{87} - 12 q^{89} + 4 q^{91} - 12 q^{93} - 18 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0 0
\(5\) 0.267949i 0.119831i 0.998203 + 0.0599153i \(0.0190830\pi\)
−0.998203 + 0.0599153i \(0.980917\pi\)
\(6\) 0 0
\(7\) −0.633975 0.366025i −0.239620 0.138345i 0.375382 0.926870i \(-0.377511\pi\)
−0.615002 + 0.788526i \(0.710845\pi\)
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 4.09808 2.36603i 1.23562 0.713384i 0.267421 0.963580i \(-0.413828\pi\)
0.968195 + 0.250196i \(0.0804951\pi\)
\(12\) 0 0
\(13\) 2.59808 + 2.50000i 0.720577 + 0.693375i
\(14\) 0 0
\(15\) −0.232051 + 0.133975i −0.0599153 + 0.0345921i
\(16\) 0 0
\(17\) −1.13397 + 1.96410i −0.275029 + 0.476365i −0.970143 0.242536i \(-0.922021\pi\)
0.695113 + 0.718900i \(0.255354\pi\)
\(18\) 0 0
\(19\) 1.09808 + 0.633975i 0.251916 + 0.145444i 0.620641 0.784095i \(-0.286872\pi\)
−0.368725 + 0.929538i \(0.620206\pi\)
\(20\) 0 0
\(21\) 0.732051i 0.159747i
\(22\) 0 0
\(23\) 3.09808 + 5.36603i 0.645994 + 1.11889i 0.984071 + 0.177775i \(0.0568901\pi\)
−0.338078 + 0.941118i \(0.609777\pi\)
\(24\) 0 0
\(25\) 4.92820 0.985641
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −1.23205 2.13397i −0.228786 0.396269i 0.728663 0.684873i \(-0.240142\pi\)
−0.957449 + 0.288604i \(0.906809\pi\)
\(30\) 0 0
\(31\) 5.46410i 0.981382i 0.871334 + 0.490691i \(0.163256\pi\)
−0.871334 + 0.490691i \(0.836744\pi\)
\(32\) 0 0
\(33\) 4.09808 + 2.36603i 0.713384 + 0.411872i
\(34\) 0 0
\(35\) 0.0980762 0.169873i 0.0165779 0.0287138i
\(36\) 0 0
\(37\) −9.06218 + 5.23205i −1.48981 + 0.860144i −0.999932 0.0116456i \(-0.996293\pi\)
−0.489881 + 0.871789i \(0.662960\pi\)
\(38\) 0 0
\(39\) −0.866025 + 3.50000i −0.138675 + 0.560449i
\(40\) 0 0
\(41\) 9.86603 5.69615i 1.54081 0.889590i 0.542027 0.840361i \(-0.317657\pi\)
0.998788 0.0492283i \(-0.0156762\pi\)
\(42\) 0 0
\(43\) −3.83013 + 6.63397i −0.584089 + 1.01167i 0.410899 + 0.911681i \(0.365215\pi\)
−0.994988 + 0.0999910i \(0.968119\pi\)
\(44\) 0 0
\(45\) −0.232051 0.133975i −0.0345921 0.0199718i
\(46\) 0 0
\(47\) 8.19615i 1.19553i −0.801671 0.597766i \(-0.796055\pi\)
0.801671 0.597766i \(-0.203945\pi\)
\(48\) 0 0
\(49\) −3.23205 5.59808i −0.461722 0.799725i
\(50\) 0 0
\(51\) −2.26795 −0.317576
\(52\) 0 0
\(53\) 0.464102 0.0637493 0.0318746 0.999492i \(-0.489852\pi\)
0.0318746 + 0.999492i \(0.489852\pi\)
\(54\) 0 0
\(55\) 0.633975 + 1.09808i 0.0854851 + 0.148065i
\(56\) 0 0
\(57\) 1.26795i 0.167944i
\(58\) 0 0
\(59\) −6.92820 4.00000i −0.901975 0.520756i −0.0241347 0.999709i \(-0.507683\pi\)
−0.877841 + 0.478953i \(0.841016\pi\)
\(60\) 0 0
\(61\) −0.598076 + 1.03590i −0.0765758 + 0.132633i −0.901770 0.432215i \(-0.857732\pi\)
0.825195 + 0.564848i \(0.191065\pi\)
\(62\) 0 0
\(63\) 0.633975 0.366025i 0.0798733 0.0461149i
\(64\) 0 0
\(65\) −0.669873 + 0.696152i −0.0830875 + 0.0863471i
\(66\) 0 0
\(67\) 9.63397 5.56218i 1.17698 0.679528i 0.221664 0.975123i \(-0.428851\pi\)
0.955313 + 0.295595i \(0.0955179\pi\)
\(68\) 0 0
\(69\) −3.09808 + 5.36603i −0.372965 + 0.645994i
\(70\) 0 0
\(71\) 1.09808 + 0.633975i 0.130318 + 0.0752389i 0.563742 0.825951i \(-0.309361\pi\)
−0.433424 + 0.901190i \(0.642695\pi\)
\(72\) 0 0
\(73\) 9.73205i 1.13905i 0.821974 + 0.569525i \(0.192873\pi\)
−0.821974 + 0.569525i \(0.807127\pi\)
\(74\) 0 0
\(75\) 2.46410 + 4.26795i 0.284530 + 0.492820i
\(76\) 0 0
\(77\) −3.46410 −0.394771
\(78\) 0 0
\(79\) 9.46410 1.06479 0.532397 0.846495i \(-0.321291\pi\)
0.532397 + 0.846495i \(0.321291\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 10.1962i 1.11917i −0.828772 0.559587i \(-0.810960\pi\)
0.828772 0.559587i \(-0.189040\pi\)
\(84\) 0 0
\(85\) −0.526279 0.303848i −0.0570830 0.0329569i
\(86\) 0 0
\(87\) 1.23205 2.13397i 0.132090 0.228786i
\(88\) 0 0
\(89\) 2.19615 1.26795i 0.232792 0.134402i −0.379068 0.925369i \(-0.623755\pi\)
0.611859 + 0.790967i \(0.290422\pi\)
\(90\) 0 0
\(91\) −0.732051 2.53590i −0.0767398 0.265834i
\(92\) 0 0
\(93\) −4.73205 + 2.73205i −0.490691 + 0.283300i
\(94\) 0 0
\(95\) −0.169873 + 0.294229i −0.0174286 + 0.0301872i
\(96\) 0 0
\(97\) 5.19615 + 3.00000i 0.527589 + 0.304604i 0.740034 0.672569i \(-0.234809\pi\)
−0.212445 + 0.977173i \(0.568143\pi\)
\(98\) 0 0
\(99\) 4.73205i 0.475589i
\(100\) 0 0
\(101\) −5.96410 10.3301i −0.593450 1.02789i −0.993764 0.111508i \(-0.964432\pi\)
0.400313 0.916378i \(-0.368901\pi\)
\(102\) 0 0
\(103\) −18.7321 −1.84572 −0.922862 0.385131i \(-0.874156\pi\)
−0.922862 + 0.385131i \(0.874156\pi\)
\(104\) 0 0
\(105\) 0.196152 0.0191425
\(106\) 0 0
\(107\) −0.0980762 0.169873i −0.00948139 0.0164222i 0.861246 0.508189i \(-0.169685\pi\)
−0.870727 + 0.491766i \(0.836351\pi\)
\(108\) 0 0
\(109\) 5.46410i 0.523366i −0.965154 0.261683i \(-0.915723\pi\)
0.965154 0.261683i \(-0.0842775\pi\)
\(110\) 0 0
\(111\) −9.06218 5.23205i −0.860144 0.496604i
\(112\) 0 0
\(113\) 9.33013 16.1603i 0.877705 1.52023i 0.0238510 0.999716i \(-0.492407\pi\)
0.853854 0.520513i \(-0.174259\pi\)
\(114\) 0 0
\(115\) −1.43782 + 0.830127i −0.134078 + 0.0774097i
\(116\) 0 0
\(117\) −3.46410 + 1.00000i −0.320256 + 0.0924500i
\(118\) 0 0
\(119\) 1.43782 0.830127i 0.131805 0.0760976i
\(120\) 0 0
\(121\) 5.69615 9.86603i 0.517832 0.896911i
\(122\) 0 0
\(123\) 9.86603 + 5.69615i 0.889590 + 0.513605i
\(124\) 0 0
\(125\) 2.66025i 0.237940i
\(126\) 0 0
\(127\) −8.92820 15.4641i −0.792250 1.37222i −0.924571 0.381010i \(-0.875576\pi\)
0.132321 0.991207i \(-0.457757\pi\)
\(128\) 0 0
\(129\) −7.66025 −0.674448
\(130\) 0 0
\(131\) −13.4641 −1.17636 −0.588182 0.808729i \(-0.700156\pi\)
−0.588182 + 0.808729i \(0.700156\pi\)
\(132\) 0 0
\(133\) −0.464102 0.803848i −0.0402427 0.0697024i
\(134\) 0 0
\(135\) 0.267949i 0.0230614i
\(136\) 0 0
\(137\) −1.66987 0.964102i −0.142667 0.0823688i 0.426968 0.904267i \(-0.359582\pi\)
−0.569634 + 0.821898i \(0.692915\pi\)
\(138\) 0 0
\(139\) −4.92820 + 8.53590i −0.418005 + 0.724005i −0.995739 0.0922197i \(-0.970604\pi\)
0.577734 + 0.816225i \(0.303937\pi\)
\(140\) 0 0
\(141\) 7.09808 4.09808i 0.597766 0.345120i
\(142\) 0 0
\(143\) 16.5622 + 4.09808i 1.38500 + 0.342698i
\(144\) 0 0
\(145\) 0.571797 0.330127i 0.0474851 0.0274156i
\(146\) 0 0
\(147\) 3.23205 5.59808i 0.266575 0.461722i
\(148\) 0 0
\(149\) −2.42820 1.40192i −0.198926 0.114850i 0.397228 0.917720i \(-0.369972\pi\)
−0.596154 + 0.802870i \(0.703305\pi\)
\(150\) 0 0
\(151\) 3.26795i 0.265942i 0.991120 + 0.132971i \(0.0424517\pi\)
−0.991120 + 0.132971i \(0.957548\pi\)
\(152\) 0 0
\(153\) −1.13397 1.96410i −0.0916764 0.158788i
\(154\) 0 0
\(155\) −1.46410 −0.117599
\(156\) 0 0
\(157\) −23.5885 −1.88256 −0.941282 0.337622i \(-0.890378\pi\)
−0.941282 + 0.337622i \(0.890378\pi\)
\(158\) 0 0
\(159\) 0.232051 + 0.401924i 0.0184028 + 0.0318746i
\(160\) 0 0
\(161\) 4.53590i 0.357479i
\(162\) 0 0
\(163\) 5.66025 + 3.26795i 0.443345 + 0.255966i 0.705016 0.709192i \(-0.250940\pi\)
−0.261670 + 0.965157i \(0.584273\pi\)
\(164\) 0 0
\(165\) −0.633975 + 1.09808i −0.0493549 + 0.0854851i
\(166\) 0 0
\(167\) −2.19615 + 1.26795i −0.169943 + 0.0981169i −0.582559 0.812788i \(-0.697949\pi\)
0.412616 + 0.910905i \(0.364615\pi\)
\(168\) 0 0
\(169\) 0.500000 + 12.9904i 0.0384615 + 0.999260i
\(170\) 0 0
\(171\) −1.09808 + 0.633975i −0.0839720 + 0.0484812i
\(172\) 0 0
\(173\) −8.19615 + 14.1962i −0.623142 + 1.07931i 0.365755 + 0.930711i \(0.380811\pi\)
−0.988897 + 0.148602i \(0.952523\pi\)
\(174\) 0 0
\(175\) −3.12436 1.80385i −0.236179 0.136358i
\(176\) 0 0
\(177\) 8.00000i 0.601317i
\(178\) 0 0
\(179\) −11.0263 19.0981i −0.824143 1.42746i −0.902573 0.430538i \(-0.858324\pi\)
0.0784298 0.996920i \(-0.475009\pi\)
\(180\) 0 0
\(181\) −8.80385 −0.654385 −0.327192 0.944958i \(-0.606103\pi\)
−0.327192 + 0.944958i \(0.606103\pi\)
\(182\) 0 0
\(183\) −1.19615 −0.0884221
\(184\) 0 0
\(185\) −1.40192 2.42820i −0.103071 0.178525i
\(186\) 0 0
\(187\) 10.7321i 0.784805i
\(188\) 0 0
\(189\) 0.633975 + 0.366025i 0.0461149 + 0.0266244i
\(190\) 0 0
\(191\) 3.46410 6.00000i 0.250654 0.434145i −0.713052 0.701111i \(-0.752688\pi\)
0.963706 + 0.266966i \(0.0860212\pi\)
\(192\) 0 0
\(193\) 7.16025 4.13397i 0.515406 0.297570i −0.219647 0.975579i \(-0.570490\pi\)
0.735053 + 0.678009i \(0.237157\pi\)
\(194\) 0 0
\(195\) −0.937822 0.232051i −0.0671588 0.0166175i
\(196\) 0 0
\(197\) 8.53590 4.92820i 0.608158 0.351120i −0.164086 0.986446i \(-0.552468\pi\)
0.772244 + 0.635326i \(0.219134\pi\)
\(198\) 0 0
\(199\) 1.90192 3.29423i 0.134824 0.233522i −0.790706 0.612196i \(-0.790286\pi\)
0.925530 + 0.378674i \(0.123620\pi\)
\(200\) 0 0
\(201\) 9.63397 + 5.56218i 0.679528 + 0.392326i
\(202\) 0 0
\(203\) 1.80385i 0.126605i
\(204\) 0 0
\(205\) 1.52628 + 2.64359i 0.106600 + 0.184637i
\(206\) 0 0
\(207\) −6.19615 −0.430662
\(208\) 0 0
\(209\) 6.00000 0.415029
\(210\) 0 0
\(211\) −2.19615 3.80385i −0.151189 0.261868i 0.780476 0.625186i \(-0.214977\pi\)
−0.931665 + 0.363319i \(0.881644\pi\)
\(212\) 0 0
\(213\) 1.26795i 0.0868784i
\(214\) 0 0
\(215\) −1.77757 1.02628i −0.121229 0.0699917i
\(216\) 0 0
\(217\) 2.00000 3.46410i 0.135769 0.235159i
\(218\) 0 0
\(219\) −8.42820 + 4.86603i −0.569525 + 0.328816i
\(220\) 0 0
\(221\) −7.85641 + 2.26795i −0.528479 + 0.152559i
\(222\) 0 0
\(223\) 11.3205 6.53590i 0.758077 0.437676i −0.0705277 0.997510i \(-0.522468\pi\)
0.828605 + 0.559834i \(0.189135\pi\)
\(224\) 0 0
\(225\) −2.46410 + 4.26795i −0.164273 + 0.284530i
\(226\) 0 0
\(227\) −1.56218 0.901924i −0.103685 0.0598628i 0.447261 0.894404i \(-0.352400\pi\)
−0.550946 + 0.834541i \(0.685733\pi\)
\(228\) 0 0
\(229\) 15.8564i 1.04782i −0.851773 0.523910i \(-0.824473\pi\)
0.851773 0.523910i \(-0.175527\pi\)
\(230\) 0 0
\(231\) −1.73205 3.00000i −0.113961 0.197386i
\(232\) 0 0
\(233\) −19.8564 −1.30084 −0.650418 0.759576i \(-0.725406\pi\)
−0.650418 + 0.759576i \(0.725406\pi\)
\(234\) 0 0
\(235\) 2.19615 0.143261
\(236\) 0 0
\(237\) 4.73205 + 8.19615i 0.307380 + 0.532397i
\(238\) 0 0
\(239\) 9.66025i 0.624870i 0.949939 + 0.312435i \(0.101145\pi\)
−0.949939 + 0.312435i \(0.898855\pi\)
\(240\) 0 0
\(241\) −15.2321 8.79423i −0.981183 0.566486i −0.0785557 0.996910i \(-0.525031\pi\)
−0.902627 + 0.430424i \(0.858364\pi\)
\(242\) 0 0
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) 1.50000 0.866025i 0.0958315 0.0553283i
\(246\) 0 0
\(247\) 1.26795 + 4.39230i 0.0806777 + 0.279476i
\(248\) 0 0
\(249\) 8.83013 5.09808i 0.559587 0.323077i
\(250\) 0 0
\(251\) −3.26795 + 5.66025i −0.206271 + 0.357272i −0.950537 0.310611i \(-0.899466\pi\)
0.744266 + 0.667883i \(0.232800\pi\)
\(252\) 0 0
\(253\) 25.3923 + 14.6603i 1.59640 + 0.921682i
\(254\) 0 0
\(255\) 0.607695i 0.0380553i
\(256\) 0 0
\(257\) 13.3301 + 23.0885i 0.831510 + 1.44022i 0.896840 + 0.442355i \(0.145857\pi\)
−0.0653297 + 0.997864i \(0.520810\pi\)
\(258\) 0 0
\(259\) 7.66025 0.475985
\(260\) 0 0
\(261\) 2.46410 0.152524
\(262\) 0 0
\(263\) 14.0263 + 24.2942i 0.864897 + 1.49805i 0.867149 + 0.498049i \(0.165950\pi\)
−0.00225153 + 0.999997i \(0.500717\pi\)
\(264\) 0 0
\(265\) 0.124356i 0.00763911i
\(266\) 0 0
\(267\) 2.19615 + 1.26795i 0.134402 + 0.0775972i
\(268\) 0 0
\(269\) 0.732051 1.26795i 0.0446339 0.0773082i −0.842845 0.538156i \(-0.819121\pi\)
0.887479 + 0.460848i \(0.152455\pi\)
\(270\) 0 0
\(271\) 5.07180 2.92820i 0.308090 0.177876i −0.337982 0.941153i \(-0.609744\pi\)
0.646071 + 0.763277i \(0.276411\pi\)
\(272\) 0 0
\(273\) 1.83013 1.90192i 0.110764 0.115110i
\(274\) 0 0
\(275\) 20.1962 11.6603i 1.21787 0.703140i
\(276\) 0 0
\(277\) −1.13397 + 1.96410i −0.0681339 + 0.118011i −0.898080 0.439832i \(-0.855038\pi\)
0.829946 + 0.557844i \(0.188371\pi\)
\(278\) 0 0
\(279\) −4.73205 2.73205i −0.283300 0.163564i
\(280\) 0 0
\(281\) 22.3205i 1.33153i 0.746162 + 0.665765i \(0.231895\pi\)
−0.746162 + 0.665765i \(0.768105\pi\)
\(282\) 0 0
\(283\) −4.16987 7.22243i −0.247873 0.429329i 0.715062 0.699061i \(-0.246398\pi\)
−0.962936 + 0.269732i \(0.913065\pi\)
\(284\) 0 0
\(285\) −0.339746 −0.0201248
\(286\) 0 0
\(287\) −8.33975 −0.492280
\(288\) 0 0
\(289\) 5.92820 + 10.2679i 0.348718 + 0.603997i
\(290\) 0 0
\(291\) 6.00000i 0.351726i
\(292\) 0 0
\(293\) −12.5718 7.25833i −0.734452 0.424036i 0.0855965 0.996330i \(-0.472720\pi\)
−0.820049 + 0.572294i \(0.806054\pi\)
\(294\) 0 0
\(295\) 1.07180 1.85641i 0.0624024 0.108084i
\(296\) 0 0
\(297\) −4.09808 + 2.36603i −0.237795 + 0.137291i
\(298\) 0 0
\(299\) −5.36603 + 21.6865i −0.310325 + 1.25416i
\(300\) 0 0
\(301\) 4.85641 2.80385i 0.279919 0.161611i
\(302\) 0 0
\(303\) 5.96410 10.3301i 0.342629 0.593450i
\(304\) 0 0
\(305\) −0.277568 0.160254i −0.0158935 0.00917612i
\(306\) 0 0
\(307\) 8.58846i 0.490169i 0.969502 + 0.245085i \(0.0788157\pi\)
−0.969502 + 0.245085i \(0.921184\pi\)
\(308\) 0 0
\(309\) −9.36603 16.2224i −0.532815 0.922862i
\(310\) 0 0
\(311\) 15.6603 0.888012 0.444006 0.896024i \(-0.353557\pi\)
0.444006 + 0.896024i \(0.353557\pi\)
\(312\) 0 0
\(313\) 13.4641 0.761036 0.380518 0.924774i \(-0.375746\pi\)
0.380518 + 0.924774i \(0.375746\pi\)
\(314\) 0 0
\(315\) 0.0980762 + 0.169873i 0.00552597 + 0.00957126i
\(316\) 0 0
\(317\) 3.33975i 0.187579i 0.995592 + 0.0937894i \(0.0298980\pi\)
−0.995592 + 0.0937894i \(0.970102\pi\)
\(318\) 0 0
\(319\) −10.0981 5.83013i −0.565384 0.326424i
\(320\) 0 0
\(321\) 0.0980762 0.169873i 0.00547408 0.00948139i
\(322\) 0 0
\(323\) −2.49038 + 1.43782i −0.138569 + 0.0800026i
\(324\) 0 0
\(325\) 12.8038 + 12.3205i 0.710230 + 0.683419i
\(326\) 0 0
\(327\) 4.73205 2.73205i 0.261683 0.151083i
\(328\) 0 0
\(329\) −3.00000 + 5.19615i −0.165395 + 0.286473i
\(330\) 0 0
\(331\) 17.3205 + 10.0000i 0.952021 + 0.549650i 0.893708 0.448649i \(-0.148095\pi\)
0.0583130 + 0.998298i \(0.481428\pi\)
\(332\) 0 0
\(333\) 10.4641i 0.573429i
\(334\) 0 0
\(335\) 1.49038 + 2.58142i 0.0814282 + 0.141038i
\(336\) 0 0
\(337\) −6.85641 −0.373492 −0.186746 0.982408i \(-0.559794\pi\)
−0.186746 + 0.982408i \(0.559794\pi\)
\(338\) 0 0
\(339\) 18.6603 1.01349
\(340\) 0 0
\(341\) 12.9282 + 22.3923i 0.700101 + 1.21261i
\(342\) 0 0
\(343\) 9.85641i 0.532196i
\(344\) 0 0
\(345\) −1.43782 0.830127i −0.0774097 0.0446925i
\(346\) 0 0
\(347\) 4.43782 7.68653i 0.238235 0.412635i −0.721973 0.691921i \(-0.756765\pi\)
0.960208 + 0.279286i \(0.0900979\pi\)
\(348\) 0 0
\(349\) 16.7321 9.66025i 0.895646 0.517102i 0.0198610 0.999803i \(-0.493678\pi\)
0.875785 + 0.482701i \(0.160344\pi\)
\(350\) 0 0
\(351\) −2.59808 2.50000i −0.138675 0.133440i
\(352\) 0 0
\(353\) 17.1340 9.89230i 0.911949 0.526514i 0.0308916 0.999523i \(-0.490165\pi\)
0.881058 + 0.473008i \(0.156832\pi\)
\(354\) 0 0
\(355\) −0.169873 + 0.294229i −0.00901592 + 0.0156160i
\(356\) 0 0
\(357\) 1.43782 + 0.830127i 0.0760976 + 0.0439350i
\(358\) 0 0
\(359\) 23.1244i 1.22046i 0.792226 + 0.610228i \(0.208922\pi\)
−0.792226 + 0.610228i \(0.791078\pi\)
\(360\) 0 0
\(361\) −8.69615 15.0622i −0.457692 0.792746i
\(362\) 0 0
\(363\) 11.3923 0.597941
\(364\) 0 0
\(365\) −2.60770 −0.136493
\(366\) 0 0
\(367\) −7.36603 12.7583i −0.384503 0.665979i 0.607197 0.794551i \(-0.292294\pi\)
−0.991700 + 0.128572i \(0.958961\pi\)
\(368\) 0 0
\(369\) 11.3923i 0.593060i
\(370\) 0 0
\(371\) −0.294229 0.169873i −0.0152756 0.00881937i
\(372\) 0 0
\(373\) 5.13397 8.89230i 0.265827 0.460426i −0.701953 0.712223i \(-0.747688\pi\)
0.967780 + 0.251797i \(0.0810216\pi\)
\(374\) 0 0
\(375\) −2.30385 + 1.33013i −0.118970 + 0.0686875i
\(376\) 0 0
\(377\) 2.13397 8.62436i 0.109905 0.444177i
\(378\) 0 0
\(379\) −1.26795 + 0.732051i −0.0651302 + 0.0376029i −0.532211 0.846611i \(-0.678639\pi\)
0.467081 + 0.884214i \(0.345306\pi\)
\(380\) 0 0
\(381\) 8.92820 15.4641i 0.457406 0.792250i
\(382\) 0 0
\(383\) 4.73205 + 2.73205i 0.241797 + 0.139601i 0.616002 0.787744i \(-0.288751\pi\)
−0.374206 + 0.927346i \(0.622085\pi\)
\(384\) 0 0
\(385\) 0.928203i 0.0473056i
\(386\) 0 0
\(387\) −3.83013 6.63397i −0.194696 0.337224i
\(388\) 0 0
\(389\) 29.7846 1.51014 0.755070 0.655644i \(-0.227603\pi\)
0.755070 + 0.655644i \(0.227603\pi\)
\(390\) 0 0
\(391\) −14.0526 −0.710668
\(392\) 0 0
\(393\) −6.73205 11.6603i −0.339587 0.588182i
\(394\) 0 0
\(395\) 2.53590i 0.127595i
\(396\) 0 0
\(397\) −0.339746 0.196152i −0.0170514 0.00984461i 0.491450 0.870906i \(-0.336467\pi\)
−0.508501 + 0.861061i \(0.669800\pi\)
\(398\) 0 0
\(399\) 0.464102 0.803848i 0.0232341 0.0402427i
\(400\) 0 0
\(401\) −18.9904 + 10.9641i −0.948334 + 0.547521i −0.892563 0.450922i \(-0.851095\pi\)
−0.0557713 + 0.998444i \(0.517762\pi\)
\(402\) 0 0
\(403\) −13.6603 + 14.1962i −0.680466 + 0.707161i
\(404\) 0 0
\(405\) 0.232051 0.133975i 0.0115307 0.00665725i
\(406\) 0 0
\(407\) −24.7583 + 42.8827i −1.22722 + 2.12562i
\(408\) 0 0
\(409\) −12.3564 7.13397i −0.610985 0.352752i 0.162366 0.986731i \(-0.448088\pi\)
−0.773351 + 0.633978i \(0.781421\pi\)
\(410\) 0 0
\(411\) 1.92820i 0.0951113i
\(412\) 0 0
\(413\) 2.92820 + 5.07180i 0.144087 + 0.249567i
\(414\) 0 0
\(415\) 2.73205 0.134111
\(416\) 0 0
\(417\) −9.85641 −0.482670
\(418\) 0 0
\(419\) −5.26795 9.12436i −0.257356 0.445754i 0.708177 0.706035i \(-0.249518\pi\)
−0.965533 + 0.260281i \(0.916185\pi\)
\(420\) 0 0
\(421\) 32.7128i 1.59432i 0.603765 + 0.797162i \(0.293667\pi\)
−0.603765 + 0.797162i \(0.706333\pi\)
\(422\) 0 0
\(423\) 7.09808 + 4.09808i 0.345120 + 0.199255i
\(424\) 0 0
\(425\) −5.58846 + 9.67949i −0.271080 + 0.469524i
\(426\) 0 0
\(427\) 0.758330 0.437822i 0.0366982 0.0211877i
\(428\) 0 0
\(429\) 4.73205 + 16.3923i 0.228466 + 0.791428i
\(430\) 0 0
\(431\) 9.63397 5.56218i 0.464052 0.267921i −0.249694 0.968325i \(-0.580330\pi\)
0.713747 + 0.700404i \(0.246997\pi\)
\(432\) 0 0
\(433\) −7.42820 + 12.8660i −0.356977 + 0.618302i −0.987454 0.157906i \(-0.949526\pi\)
0.630478 + 0.776208i \(0.282859\pi\)
\(434\) 0 0
\(435\) 0.571797 + 0.330127i 0.0274156 + 0.0158284i
\(436\) 0 0
\(437\) 7.85641i 0.375823i
\(438\) 0 0
\(439\) 8.83013 + 15.2942i 0.421439 + 0.729954i 0.996080 0.0884515i \(-0.0281918\pi\)
−0.574642 + 0.818405i \(0.694859\pi\)
\(440\) 0 0
\(441\) 6.46410 0.307814
\(442\) 0 0
\(443\) −36.3923 −1.72905 −0.864525 0.502589i \(-0.832381\pi\)
−0.864525 + 0.502589i \(0.832381\pi\)
\(444\) 0 0
\(445\) 0.339746 + 0.588457i 0.0161055 + 0.0278955i
\(446\) 0 0
\(447\) 2.80385i 0.132617i
\(448\) 0 0
\(449\) −20.1962 11.6603i −0.953115 0.550281i −0.0590680 0.998254i \(-0.518813\pi\)
−0.894047 + 0.447973i \(0.852146\pi\)
\(450\) 0 0
\(451\) 26.9545 46.6865i 1.26924 2.19838i
\(452\) 0 0
\(453\) −2.83013 + 1.63397i −0.132971 + 0.0767708i
\(454\) 0 0
\(455\) 0.679492 0.196152i 0.0318551 0.00919577i
\(456\) 0 0
\(457\) 16.1603 9.33013i 0.755945 0.436445i −0.0718931 0.997412i \(-0.522904\pi\)
0.827838 + 0.560967i \(0.189571\pi\)
\(458\) 0 0
\(459\) 1.13397 1.96410i 0.0529294 0.0916764i
\(460\) 0 0
\(461\) −22.2846 12.8660i −1.03790 0.599231i −0.118661 0.992935i \(-0.537860\pi\)
−0.919237 + 0.393704i \(0.871193\pi\)
\(462\) 0 0
\(463\) 28.0526i 1.30371i −0.758342 0.651856i \(-0.773990\pi\)
0.758342 0.651856i \(-0.226010\pi\)
\(464\) 0 0
\(465\) −0.732051 1.26795i −0.0339480 0.0587997i
\(466\) 0 0
\(467\) −12.5885 −0.582524 −0.291262 0.956643i \(-0.594075\pi\)
−0.291262 + 0.956643i \(0.594075\pi\)
\(468\) 0 0
\(469\) −8.14359 −0.376036
\(470\) 0 0
\(471\) −11.7942 20.4282i −0.543449 0.941282i
\(472\) 0 0
\(473\) 36.2487i 1.66672i
\(474\) 0 0
\(475\) 5.41154 + 3.12436i 0.248299 + 0.143355i
\(476\) 0 0
\(477\) −0.232051 + 0.401924i −0.0106249 + 0.0184028i
\(478\) 0 0
\(479\) 22.9808 13.2679i 1.05002 0.606228i 0.127363 0.991856i \(-0.459349\pi\)
0.922654 + 0.385628i \(0.126015\pi\)
\(480\) 0 0
\(481\) −36.6244 9.06218i −1.66993 0.413200i
\(482\) 0 0
\(483\) 3.92820 2.26795i 0.178739 0.103195i
\(484\) 0 0
\(485\) −0.803848 + 1.39230i −0.0365008 + 0.0632213i
\(486\) 0 0
\(487\) 18.2942 + 10.5622i 0.828991 + 0.478618i 0.853507 0.521081i \(-0.174471\pi\)
−0.0245163 + 0.999699i \(0.507805\pi\)
\(488\) 0 0
\(489\) 6.53590i 0.295564i
\(490\) 0 0
\(491\) −2.63397 4.56218i −0.118870 0.205888i 0.800450 0.599399i \(-0.204594\pi\)
−0.919320 + 0.393511i \(0.871260\pi\)
\(492\) 0 0
\(493\) 5.58846 0.251691
\(494\) 0 0
\(495\) −1.26795 −0.0569901
\(496\) 0 0
\(497\) −0.464102 0.803848i −0.0208178 0.0360575i
\(498\) 0 0
\(499\) 32.0000i 1.43252i −0.697835 0.716258i \(-0.745853\pi\)
0.697835 0.716258i \(-0.254147\pi\)
\(500\) 0 0
\(501\) −2.19615 1.26795i −0.0981169 0.0566478i
\(502\) 0 0
\(503\) −5.49038 + 9.50962i −0.244804 + 0.424013i −0.962076 0.272780i \(-0.912057\pi\)
0.717272 + 0.696793i \(0.245390\pi\)
\(504\) 0 0
\(505\) 2.76795 1.59808i 0.123172 0.0711135i
\(506\) 0 0
\(507\) −11.0000 + 6.92820i −0.488527 + 0.307692i
\(508\) 0 0
\(509\) 8.89230 5.13397i 0.394144 0.227559i −0.289810 0.957084i \(-0.593592\pi\)
0.683954 + 0.729525i \(0.260259\pi\)
\(510\) 0 0
\(511\) 3.56218 6.16987i 0.157581 0.272939i
\(512\) 0 0
\(513\) −1.09808 0.633975i −0.0484812 0.0279907i
\(514\) 0 0
\(515\) 5.01924i 0.221174i
\(516\) 0 0
\(517\) −19.3923 33.5885i −0.852873 1.47722i
\(518\) 0 0
\(519\) −16.3923 −0.719542
\(520\) 0 0
\(521\) −17.4449 −0.764273 −0.382137 0.924106i \(-0.624812\pi\)
−0.382137 + 0.924106i \(0.624812\pi\)
\(522\) 0 0
\(523\) 18.2224 + 31.5622i 0.796811 + 1.38012i 0.921683 + 0.387945i \(0.126815\pi\)
−0.124871 + 0.992173i \(0.539852\pi\)
\(524\) 0 0
\(525\) 3.60770i 0.157453i
\(526\) 0 0
\(527\) −10.7321 6.19615i −0.467495 0.269909i
\(528\) 0 0
\(529\) −7.69615 + 13.3301i −0.334615 + 0.579571i
\(530\) 0 0
\(531\) 6.92820 4.00000i 0.300658 0.173585i
\(532\) 0 0
\(533\) 39.8731 + 9.86603i 1.72709 + 0.427345i
\(534\) 0 0
\(535\) 0.0455173 0.0262794i 0.00196789 0.00113616i
\(536\) 0 0
\(537\) 11.0263 19.0981i 0.475819 0.824143i
\(538\) 0 0
\(539\) −26.4904 15.2942i −1.14102 0.658769i
\(540\) 0 0
\(541\) 40.3205i 1.73351i −0.498731 0.866757i \(-0.666200\pi\)
0.498731 0.866757i \(-0.333800\pi\)
\(542\) 0 0
\(543\) −4.40192 7.62436i −0.188905 0.327192i
\(544\) 0 0
\(545\) 1.46410 0.0627152
\(546\) 0 0
\(547\) −6.19615 −0.264928 −0.132464 0.991188i \(-0.542289\pi\)
−0.132464 + 0.991188i \(0.542289\pi\)
\(548\) 0 0
\(549\) −0.598076 1.03590i −0.0255253 0.0442111i
\(550\) 0 0
\(551\) 3.12436i 0.133102i
\(552\) 0 0
\(553\) −6.00000 3.46410i −0.255146 0.147309i
\(554\) 0 0
\(555\) 1.40192 2.42820i 0.0595084 0.103071i
\(556\) 0 0
\(557\) 26.3038 15.1865i 1.11453 0.643474i 0.174531 0.984652i \(-0.444159\pi\)
0.939999 + 0.341178i \(0.110826\pi\)
\(558\) 0 0
\(559\) −26.5359 + 7.66025i −1.12235 + 0.323994i
\(560\) 0 0
\(561\) −9.29423 + 5.36603i −0.392403 + 0.226554i
\(562\) 0 0
\(563\) −10.5359 + 18.2487i −0.444035 + 0.769091i −0.997984 0.0634589i \(-0.979787\pi\)
0.553949 + 0.832550i \(0.313120\pi\)
\(564\) 0 0
\(565\) 4.33013 + 2.50000i 0.182170 + 0.105176i
\(566\) 0 0
\(567\) 0.732051i 0.0307432i
\(568\) 0 0
\(569\) −19.3205 33.4641i −0.809958 1.40289i −0.912893 0.408200i \(-0.866157\pi\)
0.102935 0.994688i \(-0.467177\pi\)
\(570\) 0 0
\(571\) −24.0526 −1.00657 −0.503284 0.864121i \(-0.667875\pi\)
−0.503284 + 0.864121i \(0.667875\pi\)
\(572\) 0 0
\(573\) 6.92820 0.289430
\(574\) 0 0
\(575\) 15.2679 + 26.4449i 0.636717 + 1.10283i
\(576\) 0 0
\(577\) 0.267949i 0.0111549i 0.999984 + 0.00557744i \(0.00177536\pi\)
−0.999984 + 0.00557744i \(0.998225\pi\)
\(578\) 0 0
\(579\) 7.16025 + 4.13397i 0.297570 + 0.171802i
\(580\) 0 0
\(581\) −3.73205 + 6.46410i −0.154832 + 0.268176i
\(582\) 0 0
\(583\) 1.90192 1.09808i 0.0787696 0.0454777i
\(584\) 0 0
\(585\) −0.267949 0.928203i −0.0110783 0.0383765i
\(586\) 0 0
\(587\) −13.8564 + 8.00000i −0.571915 + 0.330195i −0.757914 0.652355i \(-0.773781\pi\)
0.185999 + 0.982550i \(0.440448\pi\)
\(588\) 0 0
\(589\) −3.46410 + 6.00000i −0.142736 + 0.247226i
\(590\) 0 0
\(591\) 8.53590 + 4.92820i 0.351120 + 0.202719i
\(592\) 0 0
\(593\) 36.8564i 1.51351i 0.653698 + 0.756756i \(0.273217\pi\)
−0.653698 + 0.756756i \(0.726783\pi\)
\(594\) 0 0
\(595\) 0.222432 + 0.385263i 0.00911882 + 0.0157943i
\(596\) 0 0
\(597\) 3.80385 0.155681
\(598\) 0 0
\(599\) 9.46410 0.386693 0.193346 0.981131i \(-0.438066\pi\)
0.193346 + 0.981131i \(0.438066\pi\)
\(600\) 0 0
\(601\) 2.96410 + 5.13397i 0.120908 + 0.209419i 0.920126 0.391622i \(-0.128086\pi\)
−0.799218 + 0.601041i \(0.794753\pi\)
\(602\) 0 0
\(603\) 11.1244i 0.453019i
\(604\) 0 0
\(605\) 2.64359 + 1.52628i 0.107477 + 0.0620521i
\(606\) 0 0
\(607\) 0.392305 0.679492i 0.0159232 0.0275797i −0.857954 0.513726i \(-0.828265\pi\)
0.873877 + 0.486147i \(0.161598\pi\)
\(608\) 0 0
\(609\) −1.56218 + 0.901924i −0.0633026 + 0.0365478i
\(610\) 0 0
\(611\) 20.4904 21.2942i 0.828952 0.861472i
\(612\) 0 0
\(613\) 9.86603 5.69615i 0.398485 0.230065i −0.287345 0.957827i \(-0.592773\pi\)
0.685830 + 0.727762i \(0.259439\pi\)
\(614\) 0 0
\(615\) −1.52628 + 2.64359i −0.0615455 + 0.106600i
\(616\) 0 0
\(617\) −30.5263 17.6244i −1.22894 0.709530i −0.262133 0.965032i \(-0.584426\pi\)
−0.966809 + 0.255502i \(0.917759\pi\)
\(618\) 0 0
\(619\) 10.5359i 0.423474i 0.977327 + 0.211737i \(0.0679119\pi\)
−0.977327 + 0.211737i \(0.932088\pi\)
\(620\) 0 0
\(621\) −3.09808 5.36603i −0.124322 0.215331i
\(622\) 0 0
\(623\) −1.85641 −0.0743754
\(624\) 0 0
\(625\) 23.9282 0.957128
\(626\) 0 0
\(627\) 3.00000 + 5.19615i 0.119808 + 0.207514i
\(628\) 0 0
\(629\) 23.7321i 0.946259i
\(630\) 0 0
\(631\) −41.3205 23.8564i −1.64494 0.949709i −0.979039 0.203671i \(-0.934713\pi\)
−0.665904 0.746037i \(-0.731954\pi\)
\(632\) 0 0
\(633\) 2.19615 3.80385i 0.0872892 0.151189i
\(634\) 0 0
\(635\) 4.14359 2.39230i 0.164433 0.0949357i
\(636\) 0 0
\(637\) 5.59808 22.6244i 0.221804 0.896410i
\(638\) 0 0
\(639\) −1.09808 + 0.633975i −0.0434392 + 0.0250796i
\(640\) 0 0
\(641\) 12.9904 22.5000i 0.513089 0.888697i −0.486796 0.873516i \(-0.661834\pi\)
0.999885 0.0151806i \(-0.00483233\pi\)
\(642\) 0 0
\(643\) 12.0000 + 6.92820i 0.473234 + 0.273222i 0.717592 0.696463i \(-0.245244\pi\)
−0.244359 + 0.969685i \(0.578577\pi\)
\(644\) 0 0
\(645\) 2.05256i 0.0808194i
\(646\) 0 0
\(647\) −13.1244 22.7321i −0.515972 0.893689i −0.999828 0.0185417i \(-0.994098\pi\)
0.483856 0.875147i \(-0.339236\pi\)
\(648\) 0 0
\(649\) −37.8564 −1.48599
\(650\) 0 0
\(651\) 4.00000 0.156772
\(652\) 0 0
\(653\) 5.26795 + 9.12436i 0.206151 + 0.357064i 0.950499 0.310728i \(-0.100573\pi\)
−0.744348 + 0.667792i \(0.767240\pi\)
\(654\) 0 0
\(655\) 3.60770i 0.140964i
\(656\) 0 0
\(657\) −8.42820 4.86603i −0.328816 0.189842i
\(658\) 0 0
\(659\) 19.1244 33.1244i 0.744979 1.29034i −0.205225 0.978715i \(-0.565793\pi\)
0.950205 0.311627i \(-0.100874\pi\)
\(660\) 0 0
\(661\) 8.13397 4.69615i 0.316375 0.182659i −0.333401 0.942785i \(-0.608196\pi\)
0.649776 + 0.760126i \(0.274863\pi\)
\(662\) 0 0
\(663\) −5.89230 5.66987i −0.228838 0.220200i
\(664\) 0 0
\(665\) 0.215390 0.124356i 0.00835248 0.00482231i
\(666\) 0 0
\(667\) 7.63397 13.2224i 0.295589 0.511975i
\(668\) 0 0
\(669\) 11.3205 + 6.53590i 0.437676 + 0.252692i
\(670\) 0 0
\(671\) 5.66025i 0.218512i
\(672\) 0 0
\(673\) 7.03590 + 12.1865i 0.271214 + 0.469756i 0.969173 0.246381i \(-0.0792416\pi\)
−0.697959 + 0.716138i \(0.745908\pi\)
\(674\) 0 0
\(675\) −4.92820 −0.189687
\(676\) 0 0
\(677\) −38.5359 −1.48105 −0.740527 0.672026i \(-0.765424\pi\)
−0.740527 + 0.672026i \(0.765424\pi\)
\(678\) 0 0
\(679\) −2.19615 3.80385i −0.0842806 0.145978i
\(680\) 0 0
\(681\) 1.80385i 0.0691236i
\(682\) 0 0
\(683\) 32.7846 + 18.9282i 1.25447 + 0.724268i 0.971994 0.235007i \(-0.0755114\pi\)
0.282475 + 0.959275i \(0.408845\pi\)
\(684\) 0 0
\(685\) 0.258330 0.447441i 0.00987029 0.0170958i
\(686\) 0 0
\(687\) 13.7321 7.92820i 0.523910 0.302480i
\(688\) 0 0
\(689\) 1.20577 + 1.16025i 0.0459362 + 0.0442022i
\(690\) 0 0
\(691\) −22.8109 + 13.1699i −0.867767 + 0.501006i −0.866606 0.498994i \(-0.833703\pi\)
−0.00116153 + 0.999999i \(0.500370\pi\)
\(692\) 0 0
\(693\) 1.73205 3.00000i 0.0657952 0.113961i
\(694\) 0 0
\(695\) −2.28719 1.32051i −0.0867580 0.0500897i
\(696\) 0 0
\(697\) 25.8372i 0.978653i
\(698\) 0 0
\(699\) −9.92820 17.1962i −0.375519 0.650418i
\(700\) 0 0
\(701\) −31.3205 −1.18296 −0.591480 0.806320i \(-0.701456\pi\)
−0.591480 + 0.806320i \(0.701456\pi\)
\(702\) 0 0
\(703\) −13.2679 −0.500410
\(704\) 0 0
\(705\) 1.09808 + 1.90192i 0.0413559 + 0.0716306i
\(706\) 0 0
\(707\) 8.73205i 0.328403i
\(708\) 0 0
\(709\) 35.3827 + 20.4282i 1.32882 + 0.767197i 0.985118 0.171880i \(-0.0549841\pi\)
0.343707 + 0.939077i \(0.388317\pi\)
\(710\) 0 0
\(711\) −4.73205 + 8.19615i −0.177466 + 0.307380i
\(712\) 0 0
\(713\) −29.3205 + 16.9282i −1.09806 + 0.633966i
\(714\) 0 0
\(715\) −1.09808 + 4.43782i −0.0410657 + 0.165965i
\(716\) 0 0
\(717\) −8.36603 + 4.83013i −0.312435 + 0.180384i
\(718\) 0 0
\(719\) 11.2679 19.5167i 0.420224 0.727849i −0.575737 0.817635i \(-0.695285\pi\)
0.995961 + 0.0897860i \(0.0286183\pi\)
\(720\) 0 0
\(721\) 11.8756 + 6.85641i 0.442272 + 0.255346i
\(722\) 0 0
\(723\) 17.5885i 0.654122i
\(724\) 0 0
\(725\) −6.07180 10.5167i −0.225501 0.390579i
\(726\) 0 0
\(727\) 20.9808 0.778133 0.389067 0.921210i \(-0.372798\pi\)
0.389067 + 0.921210i \(0.372798\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −8.68653 15.0455i −0.321283 0.556479i
\(732\) 0 0
\(733\) 19.0000i 0.701781i 0.936416 + 0.350891i \(0.114121\pi\)
−0.936416 + 0.350891i \(0.885879\pi\)
\(734\) 0 0
\(735\) 1.50000 + 0.866025i 0.0553283 + 0.0319438i
\(736\) 0 0
\(737\) 26.3205 45.5885i 0.969528 1.67927i
\(738\) 0 0
\(739\) −9.46410 + 5.46410i −0.348143 + 0.201000i −0.663867 0.747851i \(-0.731086\pi\)
0.315724 + 0.948851i \(0.397753\pi\)
\(740\) 0 0
\(741\) −3.16987 + 3.29423i −0.116448 + 0.121017i
\(742\) 0 0
\(743\) 23.9090 13.8038i 0.877135 0.506414i 0.00742221 0.999972i \(-0.497637\pi\)
0.869713 + 0.493558i \(0.164304\pi\)
\(744\) 0 0
\(745\) 0.375644 0.650635i 0.0137625 0.0238374i
\(746\) 0 0
\(747\) 8.83013 + 5.09808i 0.323077 + 0.186529i
\(748\) 0 0
\(749\) 0.143594i 0.00524679i
\(750\) 0 0
\(751\) −7.95448 13.7776i −0.290263 0.502751i 0.683609 0.729849i \(-0.260410\pi\)
−0.973872 + 0.227098i \(0.927076\pi\)
\(752\) 0 0
\(753\) −6.53590 −0.238181
\(754\) 0 0
\(755\) −0.875644 −0.0318680
\(756\) 0 0
\(757\) −3.53590 6.12436i −0.128514 0.222593i 0.794587 0.607151i \(-0.207688\pi\)
−0.923101 + 0.384557i \(0.874354\pi\)
\(758\) 0 0
\(759\) 29.3205i 1.06427i
\(760\) 0 0
\(761\) −20.1962 11.6603i −0.732110 0.422684i 0.0870836 0.996201i \(-0.472245\pi\)
−0.819194 + 0.573517i \(0.805579\pi\)
\(762\) 0 0
\(763\) −2.00000 + 3.46410i −0.0724049 + 0.125409i
\(764\) 0 0
\(765\) 0.526279 0.303848i 0.0190277 0.0109856i
\(766\) 0 0
\(767\) −8.00000 27.7128i −0.288863 1.00065i
\(768\) 0 0
\(769\) −13.9808 + 8.07180i −0.504159 + 0.291076i −0.730429 0.682988i \(-0.760680\pi\)
0.226270 + 0.974065i \(0.427347\pi\)
\(770\) 0 0
\(771\) −13.3301 + 23.0885i −0.480073 + 0.831510i
\(772\) 0 0
\(773\) 30.3731 + 17.5359i 1.09244 + 0.630722i 0.934226 0.356682i \(-0.116092\pi\)
0.158217 + 0.987404i \(0.449425\pi\)
\(774\) 0 0
\(775\) 26.9282i 0.967290i
\(776\) 0 0
\(777\) 3.83013 + 6.63397i 0.137405 + 0.237993i
\(778\) 0 0
\(779\) 14.4449 0.517541
\(780\) 0 0
\(781\) 6.00000 0.214697
\(782\) 0 0
\(783\) 1.23205 + 2.13397i 0.0440299 + 0.0762620i
\(784\) 0 0
\(785\) 6.32051i 0.225589i
\(786\) 0 0
\(787\) −34.0526 19.6603i −1.21384 0.700812i −0.250248 0.968182i \(-0.580512\pi\)
−0.963594 + 0.267369i \(0.913846\pi\)
\(788\) 0 0
\(789\) −14.0263 + 24.2942i −0.499349 + 0.864897i
\(790\) 0 0
\(791\) −11.8301 + 6.83013i −0.420631 + 0.242851i
\(792\) 0 0
\(793\) −4.14359 + 1.19615i −0.147143 + 0.0424766i
\(794\)