Properties

Label 912.2.bn.m.449.2
Level $912$
Weight $2$
Character 912.449
Analytic conductor $7.282$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.bn (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 57)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 449.2
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 912.449
Dual form 912.2.bn.m.65.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.158919 + 1.72474i) q^{3} +(-1.22474 + 0.707107i) q^{5} +3.73205 q^{7} +(-2.94949 - 0.548188i) q^{9} +O(q^{10})\) \(q+(-0.158919 + 1.72474i) q^{3} +(-1.22474 + 0.707107i) q^{5} +3.73205 q^{7} +(-2.94949 - 0.548188i) q^{9} +0.378937i q^{11} +(3.23205 + 1.86603i) q^{13} +(-1.02494 - 2.22474i) q^{15} +(4.24264 - 2.44949i) q^{17} +(1.73205 + 4.00000i) q^{19} +(-0.593092 + 6.43684i) q^{21} +(-0.328169 - 0.189469i) q^{23} +(-1.50000 + 2.59808i) q^{25} +(1.41421 - 5.00000i) q^{27} +(-3.86370 + 6.69213i) q^{29} +4.46410i q^{31} +(-0.653570 - 0.0602202i) q^{33} +(-4.57081 + 2.63896i) q^{35} -4.26795i q^{37} +(-3.73205 + 5.27792i) q^{39} +(-2.82843 - 4.89898i) q^{41} +(1.13397 + 1.96410i) q^{43} +(4.00000 - 1.41421i) q^{45} +(-9.14162 - 5.27792i) q^{47} +6.92820 q^{49} +(3.55051 + 7.70674i) q^{51} +(-3.01790 + 5.22715i) q^{53} +(-0.267949 - 0.464102i) q^{55} +(-7.17423 + 2.35167i) q^{57} +(4.19187 + 7.26054i) q^{59} +(1.76795 - 3.06218i) q^{61} +(-11.0076 - 2.04587i) q^{63} -5.27792 q^{65} +(-0.866025 - 0.500000i) q^{67} +(0.378937 - 0.535898i) q^{69} +(1.79315 + 3.10583i) q^{71} +(1.50000 + 2.59808i) q^{73} +(-4.24264 - 3.00000i) q^{75} +1.41421i q^{77} +(3.06218 - 1.76795i) q^{79} +(8.39898 + 3.23375i) q^{81} +7.72741i q^{83} +(-3.46410 + 6.00000i) q^{85} +(-10.9282 - 7.72741i) q^{87} +(-3.67423 + 6.36396i) q^{89} +(12.0622 + 6.96410i) q^{91} +(-7.69944 - 0.709429i) q^{93} +(-4.94975 - 3.67423i) q^{95} +(6.46410 - 3.73205i) q^{97} +(0.207729 - 1.11767i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 16 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 16 q^{7} - 4 q^{9} + 12 q^{13} - 12 q^{21} - 12 q^{25} + 24 q^{33} - 16 q^{39} + 16 q^{43} + 32 q^{45} + 48 q^{51} - 16 q^{55} - 28 q^{57} + 28 q^{61} - 8 q^{63} + 12 q^{73} - 24 q^{79} + 28 q^{81} - 32 q^{87} + 48 q^{91} - 4 q^{93} + 24 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.158919 + 1.72474i −0.0917517 + 0.995782i
\(4\) 0 0
\(5\) −1.22474 + 0.707107i −0.547723 + 0.316228i −0.748203 0.663470i \(-0.769083\pi\)
0.200480 + 0.979698i \(0.435750\pi\)
\(6\) 0 0
\(7\) 3.73205 1.41058 0.705291 0.708918i \(-0.250816\pi\)
0.705291 + 0.708918i \(0.250816\pi\)
\(8\) 0 0
\(9\) −2.94949 0.548188i −0.983163 0.182729i
\(10\) 0 0
\(11\) 0.378937i 0.114254i 0.998367 + 0.0571270i \(0.0181940\pi\)
−0.998367 + 0.0571270i \(0.981806\pi\)
\(12\) 0 0
\(13\) 3.23205 + 1.86603i 0.896410 + 0.517542i 0.876034 0.482250i \(-0.160180\pi\)
0.0203760 + 0.999792i \(0.493514\pi\)
\(14\) 0 0
\(15\) −1.02494 2.22474i −0.264639 0.574427i
\(16\) 0 0
\(17\) 4.24264 2.44949i 1.02899 0.594089i 0.112296 0.993675i \(-0.464180\pi\)
0.916696 + 0.399586i \(0.130846\pi\)
\(18\) 0 0
\(19\) 1.73205 + 4.00000i 0.397360 + 0.917663i
\(20\) 0 0
\(21\) −0.593092 + 6.43684i −0.129423 + 1.40463i
\(22\) 0 0
\(23\) −0.328169 0.189469i −0.0684280 0.0395070i 0.465396 0.885103i \(-0.345912\pi\)
−0.533824 + 0.845596i \(0.679245\pi\)
\(24\) 0 0
\(25\) −1.50000 + 2.59808i −0.300000 + 0.519615i
\(26\) 0 0
\(27\) 1.41421 5.00000i 0.272166 0.962250i
\(28\) 0 0
\(29\) −3.86370 + 6.69213i −0.717472 + 1.24270i 0.244527 + 0.969643i \(0.421367\pi\)
−0.961998 + 0.273055i \(0.911966\pi\)
\(30\) 0 0
\(31\) 4.46410i 0.801776i 0.916127 + 0.400888i \(0.131298\pi\)
−0.916127 + 0.400888i \(0.868702\pi\)
\(32\) 0 0
\(33\) −0.653570 0.0602202i −0.113772 0.0104830i
\(34\) 0 0
\(35\) −4.57081 + 2.63896i −0.772608 + 0.446065i
\(36\) 0 0
\(37\) 4.26795i 0.701647i −0.936442 0.350823i \(-0.885902\pi\)
0.936442 0.350823i \(-0.114098\pi\)
\(38\) 0 0
\(39\) −3.73205 + 5.27792i −0.597606 + 0.845143i
\(40\) 0 0
\(41\) −2.82843 4.89898i −0.441726 0.765092i 0.556092 0.831121i \(-0.312300\pi\)
−0.997818 + 0.0660290i \(0.978967\pi\)
\(42\) 0 0
\(43\) 1.13397 + 1.96410i 0.172930 + 0.299523i 0.939443 0.342706i \(-0.111343\pi\)
−0.766513 + 0.642228i \(0.778010\pi\)
\(44\) 0 0
\(45\) 4.00000 1.41421i 0.596285 0.210819i
\(46\) 0 0
\(47\) −9.14162 5.27792i −1.33344 0.769863i −0.347617 0.937637i \(-0.613009\pi\)
−0.985826 + 0.167773i \(0.946342\pi\)
\(48\) 0 0
\(49\) 6.92820 0.989743
\(50\) 0 0
\(51\) 3.55051 + 7.70674i 0.497171 + 1.07916i
\(52\) 0 0
\(53\) −3.01790 + 5.22715i −0.414540 + 0.718004i −0.995380 0.0960135i \(-0.969391\pi\)
0.580840 + 0.814018i \(0.302724\pi\)
\(54\) 0 0
\(55\) −0.267949 0.464102i −0.0361303 0.0625794i
\(56\) 0 0
\(57\) −7.17423 + 2.35167i −0.950251 + 0.311486i
\(58\) 0 0
\(59\) 4.19187 + 7.26054i 0.545735 + 0.945241i 0.998560 + 0.0536419i \(0.0170829\pi\)
−0.452825 + 0.891599i \(0.649584\pi\)
\(60\) 0 0
\(61\) 1.76795 3.06218i 0.226363 0.392072i −0.730365 0.683057i \(-0.760650\pi\)
0.956727 + 0.290986i \(0.0939832\pi\)
\(62\) 0 0
\(63\) −11.0076 2.04587i −1.38683 0.257755i
\(64\) 0 0
\(65\) −5.27792 −0.654645
\(66\) 0 0
\(67\) −0.866025 0.500000i −0.105802 0.0610847i 0.446165 0.894951i \(-0.352789\pi\)
−0.551967 + 0.833866i \(0.686123\pi\)
\(68\) 0 0
\(69\) 0.378937 0.535898i 0.0456187 0.0645146i
\(70\) 0 0
\(71\) 1.79315 + 3.10583i 0.212808 + 0.368594i 0.952592 0.304250i \(-0.0984058\pi\)
−0.739784 + 0.672844i \(0.765072\pi\)
\(72\) 0 0
\(73\) 1.50000 + 2.59808i 0.175562 + 0.304082i 0.940356 0.340193i \(-0.110493\pi\)
−0.764794 + 0.644275i \(0.777159\pi\)
\(74\) 0 0
\(75\) −4.24264 3.00000i −0.489898 0.346410i
\(76\) 0 0
\(77\) 1.41421i 0.161165i
\(78\) 0 0
\(79\) 3.06218 1.76795i 0.344522 0.198910i −0.317748 0.948175i \(-0.602927\pi\)
0.662270 + 0.749265i \(0.269593\pi\)
\(80\) 0 0
\(81\) 8.39898 + 3.23375i 0.933220 + 0.359306i
\(82\) 0 0
\(83\) 7.72741i 0.848193i 0.905617 + 0.424097i \(0.139408\pi\)
−0.905617 + 0.424097i \(0.860592\pi\)
\(84\) 0 0
\(85\) −3.46410 + 6.00000i −0.375735 + 0.650791i
\(86\) 0 0
\(87\) −10.9282 7.72741i −1.17163 0.828465i
\(88\) 0 0
\(89\) −3.67423 + 6.36396i −0.389468 + 0.674579i −0.992378 0.123231i \(-0.960674\pi\)
0.602910 + 0.797809i \(0.294008\pi\)
\(90\) 0 0
\(91\) 12.0622 + 6.96410i 1.26446 + 0.730036i
\(92\) 0 0
\(93\) −7.69944 0.709429i −0.798394 0.0735643i
\(94\) 0 0
\(95\) −4.94975 3.67423i −0.507833 0.376969i
\(96\) 0 0
\(97\) 6.46410 3.73205i 0.656330 0.378932i −0.134547 0.990907i \(-0.542958\pi\)
0.790877 + 0.611975i \(0.209625\pi\)
\(98\) 0 0
\(99\) 0.207729 1.11767i 0.0208775 0.112330i
\(100\) 0 0
\(101\) −6.69213 3.86370i −0.665892 0.384453i 0.128626 0.991693i \(-0.458943\pi\)
−0.794518 + 0.607240i \(0.792277\pi\)
\(102\) 0 0
\(103\) 10.4641i 1.03106i −0.856872 0.515529i \(-0.827595\pi\)
0.856872 0.515529i \(-0.172405\pi\)
\(104\) 0 0
\(105\) −3.82514 8.30286i −0.373296 0.810276i
\(106\) 0 0
\(107\) 4.89898 0.473602 0.236801 0.971558i \(-0.423901\pi\)
0.236801 + 0.971558i \(0.423901\pi\)
\(108\) 0 0
\(109\) −12.4641 + 7.19615i −1.19384 + 0.689266i −0.959176 0.282809i \(-0.908734\pi\)
−0.234668 + 0.972076i \(0.575400\pi\)
\(110\) 0 0
\(111\) 7.36112 + 0.678257i 0.698687 + 0.0643773i
\(112\) 0 0
\(113\) 18.6622 1.75559 0.877795 0.479036i \(-0.159014\pi\)
0.877795 + 0.479036i \(0.159014\pi\)
\(114\) 0 0
\(115\) 0.535898 0.0499728
\(116\) 0 0
\(117\) −8.50997 7.27559i −0.786747 0.672629i
\(118\) 0 0
\(119\) 15.8338 9.14162i 1.45148 0.838011i
\(120\) 0 0
\(121\) 10.8564 0.986946
\(122\) 0 0
\(123\) 8.89898 4.09978i 0.802394 0.369664i
\(124\) 0 0
\(125\) 11.3137i 1.01193i
\(126\) 0 0
\(127\) −6.80385 3.92820i −0.603744 0.348572i 0.166769 0.985996i \(-0.446667\pi\)
−0.770513 + 0.637424i \(0.780000\pi\)
\(128\) 0 0
\(129\) −3.56778 + 1.64368i −0.314126 + 0.144718i
\(130\) 0 0
\(131\) 6.03579 3.48477i 0.527350 0.304465i −0.212587 0.977142i \(-0.568189\pi\)
0.739936 + 0.672677i \(0.234856\pi\)
\(132\) 0 0
\(133\) 6.46410 + 14.9282i 0.560509 + 1.29444i
\(134\) 0 0
\(135\) 1.80348 + 7.12372i 0.155219 + 0.613113i
\(136\) 0 0
\(137\) −0.656339 0.378937i −0.0560748 0.0323748i 0.471700 0.881759i \(-0.343640\pi\)
−0.527775 + 0.849384i \(0.676974\pi\)
\(138\) 0 0
\(139\) 6.59808 11.4282i 0.559642 0.969328i −0.437885 0.899031i \(-0.644272\pi\)
0.997526 0.0702964i \(-0.0223945\pi\)
\(140\) 0 0
\(141\) 10.5558 14.9282i 0.888962 1.25718i
\(142\) 0 0
\(143\) −0.707107 + 1.22474i −0.0591312 + 0.102418i
\(144\) 0 0
\(145\) 10.9282i 0.907538i
\(146\) 0 0
\(147\) −1.10102 + 11.9494i −0.0908106 + 0.985568i
\(148\) 0 0
\(149\) 14.6090 8.43451i 1.19682 0.690982i 0.236972 0.971516i \(-0.423845\pi\)
0.959844 + 0.280534i \(0.0905116\pi\)
\(150\) 0 0
\(151\) 2.00000i 0.162758i 0.996683 + 0.0813788i \(0.0259324\pi\)
−0.996683 + 0.0813788i \(0.974068\pi\)
\(152\) 0 0
\(153\) −13.8564 + 4.89898i −1.12022 + 0.396059i
\(154\) 0 0
\(155\) −3.15660 5.46739i −0.253544 0.439151i
\(156\) 0 0
\(157\) −1.76795 3.06218i −0.141098 0.244388i 0.786813 0.617192i \(-0.211730\pi\)
−0.927910 + 0.372804i \(0.878397\pi\)
\(158\) 0 0
\(159\) −8.53590 6.03579i −0.676941 0.478669i
\(160\) 0 0
\(161\) −1.22474 0.707107i −0.0965234 0.0557278i
\(162\) 0 0
\(163\) −5.19615 −0.406994 −0.203497 0.979076i \(-0.565231\pi\)
−0.203497 + 0.979076i \(0.565231\pi\)
\(164\) 0 0
\(165\) 0.843039 0.388390i 0.0656305 0.0302361i
\(166\) 0 0
\(167\) 3.81294 6.60420i 0.295054 0.511048i −0.679944 0.733264i \(-0.737996\pi\)
0.974997 + 0.222216i \(0.0713291\pi\)
\(168\) 0 0
\(169\) 0.464102 + 0.803848i 0.0357001 + 0.0618344i
\(170\) 0 0
\(171\) −2.91591 12.7474i −0.222985 0.974822i
\(172\) 0 0
\(173\) 5.93426 + 10.2784i 0.451173 + 0.781455i 0.998459 0.0554909i \(-0.0176724\pi\)
−0.547286 + 0.836946i \(0.684339\pi\)
\(174\) 0 0
\(175\) −5.59808 + 9.69615i −0.423175 + 0.732960i
\(176\) 0 0
\(177\) −13.1887 + 6.07608i −0.991326 + 0.456706i
\(178\) 0 0
\(179\) −1.41421 −0.105703 −0.0528516 0.998602i \(-0.516831\pi\)
−0.0528516 + 0.998602i \(0.516831\pi\)
\(180\) 0 0
\(181\) −3.00000 1.73205i −0.222988 0.128742i 0.384345 0.923190i \(-0.374427\pi\)
−0.607333 + 0.794447i \(0.707761\pi\)
\(182\) 0 0
\(183\) 5.00052 + 3.53590i 0.369649 + 0.261381i
\(184\) 0 0
\(185\) 3.01790 + 5.22715i 0.221880 + 0.384308i
\(186\) 0 0
\(187\) 0.928203 + 1.60770i 0.0678769 + 0.117566i
\(188\) 0 0
\(189\) 5.27792 18.6603i 0.383912 1.35733i
\(190\) 0 0
\(191\) 1.69161i 0.122401i −0.998125 0.0612005i \(-0.980507\pi\)
0.998125 0.0612005i \(-0.0194929\pi\)
\(192\) 0 0
\(193\) 11.4282 6.59808i 0.822620 0.474940i −0.0286991 0.999588i \(-0.509136\pi\)
0.851319 + 0.524648i \(0.175803\pi\)
\(194\) 0 0
\(195\) 0.838759 9.10306i 0.0600648 0.651884i
\(196\) 0 0
\(197\) 9.14162i 0.651313i −0.945488 0.325657i \(-0.894415\pi\)
0.945488 0.325657i \(-0.105585\pi\)
\(198\) 0 0
\(199\) −6.40192 + 11.0885i −0.453820 + 0.786040i −0.998620 0.0525267i \(-0.983273\pi\)
0.544799 + 0.838567i \(0.316606\pi\)
\(200\) 0 0
\(201\) 1.00000 1.41421i 0.0705346 0.0997509i
\(202\) 0 0
\(203\) −14.4195 + 24.9754i −1.01205 + 1.75293i
\(204\) 0 0
\(205\) 6.92820 + 4.00000i 0.483887 + 0.279372i
\(206\) 0 0
\(207\) 0.864068 + 0.738735i 0.0600569 + 0.0513456i
\(208\) 0 0
\(209\) −1.51575 + 0.656339i −0.104847 + 0.0453999i
\(210\) 0 0
\(211\) 9.52628 5.50000i 0.655816 0.378636i −0.134865 0.990864i \(-0.543060\pi\)
0.790681 + 0.612228i \(0.209727\pi\)
\(212\) 0 0
\(213\) −5.64173 + 2.59915i −0.386565 + 0.178091i
\(214\) 0 0
\(215\) −2.77766 1.60368i −0.189435 0.109370i
\(216\) 0 0
\(217\) 16.6603i 1.13097i
\(218\) 0 0
\(219\) −4.71940 + 2.17423i −0.318907 + 0.146921i
\(220\) 0 0
\(221\) 18.2832 1.22986
\(222\) 0 0
\(223\) 8.13397 4.69615i 0.544691 0.314478i −0.202287 0.979326i \(-0.564837\pi\)
0.746978 + 0.664849i \(0.231504\pi\)
\(224\) 0 0
\(225\) 5.84847 6.84072i 0.389898 0.456048i
\(226\) 0 0
\(227\) 24.5964 1.63252 0.816261 0.577683i \(-0.196043\pi\)
0.816261 + 0.577683i \(0.196043\pi\)
\(228\) 0 0
\(229\) 9.39230 0.620661 0.310330 0.950629i \(-0.399560\pi\)
0.310330 + 0.950629i \(0.399560\pi\)
\(230\) 0 0
\(231\) −2.43916 0.224745i −0.160485 0.0147871i
\(232\) 0 0
\(233\) 3.10583 1.79315i 0.203470 0.117473i −0.394803 0.918766i \(-0.629187\pi\)
0.598273 + 0.801292i \(0.295854\pi\)
\(234\) 0 0
\(235\) 14.9282 0.973809
\(236\) 0 0
\(237\) 2.56262 + 5.56244i 0.166460 + 0.361319i
\(238\) 0 0
\(239\) 29.9759i 1.93898i −0.245133 0.969489i \(-0.578832\pi\)
0.245133 0.969489i \(-0.421168\pi\)
\(240\) 0 0
\(241\) −24.8205 14.3301i −1.59883 0.923085i −0.991713 0.128472i \(-0.958993\pi\)
−0.607116 0.794613i \(-0.707674\pi\)
\(242\) 0 0
\(243\) −6.91215 + 13.9722i −0.443415 + 0.896317i
\(244\) 0 0
\(245\) −8.48528 + 4.89898i −0.542105 + 0.312984i
\(246\) 0 0
\(247\) −1.86603 + 16.1603i −0.118732 + 1.02825i
\(248\) 0 0
\(249\) −13.3278 1.22803i −0.844615 0.0778232i
\(250\) 0 0
\(251\) −12.7279 7.34847i −0.803379 0.463831i 0.0412721 0.999148i \(-0.486859\pi\)
−0.844651 + 0.535317i \(0.820192\pi\)
\(252\) 0 0
\(253\) 0.0717968 0.124356i 0.00451382 0.00781817i
\(254\) 0 0
\(255\) −9.79796 6.92820i −0.613572 0.433861i
\(256\) 0 0
\(257\) −1.60368 + 2.77766i −0.100035 + 0.173266i −0.911699 0.410859i \(-0.865229\pi\)
0.811664 + 0.584125i \(0.198562\pi\)
\(258\) 0 0
\(259\) 15.9282i 0.989730i
\(260\) 0 0
\(261\) 15.0645 17.6203i 0.932469 1.09067i
\(262\) 0 0
\(263\) −0.480473 + 0.277401i −0.0296273 + 0.0171053i −0.514740 0.857346i \(-0.672112\pi\)
0.485113 + 0.874451i \(0.338778\pi\)
\(264\) 0 0
\(265\) 8.53590i 0.524356i
\(266\) 0 0
\(267\) −10.3923 7.34847i −0.635999 0.449719i
\(268\) 0 0
\(269\) −3.01790 5.22715i −0.184004 0.318705i 0.759236 0.650815i \(-0.225573\pi\)
−0.943241 + 0.332110i \(0.892239\pi\)
\(270\) 0 0
\(271\) −3.46410 6.00000i −0.210429 0.364474i 0.741420 0.671042i \(-0.234153\pi\)
−0.951849 + 0.306568i \(0.900819\pi\)
\(272\) 0 0
\(273\) −13.9282 + 19.6975i −0.842973 + 1.19214i
\(274\) 0 0
\(275\) −0.984508 0.568406i −0.0593681 0.0342762i
\(276\) 0 0
\(277\) −9.85641 −0.592214 −0.296107 0.955155i \(-0.595689\pi\)
−0.296107 + 0.955155i \(0.595689\pi\)
\(278\) 0 0
\(279\) 2.44717 13.1668i 0.146508 0.788277i
\(280\) 0 0
\(281\) 7.53794 13.0561i 0.449676 0.778861i −0.548689 0.836027i \(-0.684873\pi\)
0.998365 + 0.0571654i \(0.0182062\pi\)
\(282\) 0 0
\(283\) −10.9282 18.9282i −0.649614 1.12516i −0.983215 0.182450i \(-0.941597\pi\)
0.333601 0.942714i \(-0.391736\pi\)
\(284\) 0 0
\(285\) 7.12372 7.95315i 0.421973 0.471104i
\(286\) 0 0
\(287\) −10.5558 18.2832i −0.623091 1.07923i
\(288\) 0 0
\(289\) 3.50000 6.06218i 0.205882 0.356599i
\(290\) 0 0
\(291\) 5.40957 + 11.7420i 0.317115 + 0.688329i
\(292\) 0 0
\(293\) −25.2528 −1.47528 −0.737641 0.675193i \(-0.764060\pi\)
−0.737641 + 0.675193i \(0.764060\pi\)
\(294\) 0 0
\(295\) −10.2679 5.92820i −0.597823 0.345153i
\(296\) 0 0
\(297\) 1.89469 + 0.535898i 0.109941 + 0.0310960i
\(298\) 0 0
\(299\) −0.707107 1.22474i −0.0408930 0.0708288i
\(300\) 0 0
\(301\) 4.23205 + 7.33013i 0.243931 + 0.422501i
\(302\) 0 0
\(303\) 7.72741 10.9282i 0.443928 0.627809i
\(304\) 0 0
\(305\) 5.00052i 0.286329i
\(306\) 0 0
\(307\) 12.0000 6.92820i 0.684876 0.395413i −0.116814 0.993154i \(-0.537268\pi\)
0.801690 + 0.597740i \(0.203935\pi\)
\(308\) 0 0
\(309\) 18.0479 + 1.66294i 1.02671 + 0.0946014i
\(310\) 0 0
\(311\) 27.1475i 1.53939i 0.638411 + 0.769696i \(0.279592\pi\)
−0.638411 + 0.769696i \(0.720408\pi\)
\(312\) 0 0
\(313\) 12.3923 21.4641i 0.700454 1.21322i −0.267853 0.963460i \(-0.586314\pi\)
0.968307 0.249763i \(-0.0803527\pi\)
\(314\) 0 0
\(315\) 14.9282 5.27792i 0.841109 0.297377i
\(316\) 0 0
\(317\) 6.88160 11.9193i 0.386509 0.669453i −0.605468 0.795870i \(-0.707014\pi\)
0.991977 + 0.126416i \(0.0403474\pi\)
\(318\) 0 0
\(319\) −2.53590 1.46410i −0.141983 0.0819740i
\(320\) 0 0
\(321\) −0.778539 + 8.44949i −0.0434538 + 0.471605i
\(322\) 0 0
\(323\) 17.1464 + 12.7279i 0.954053 + 0.708201i
\(324\) 0 0
\(325\) −9.69615 + 5.59808i −0.537846 + 0.310525i
\(326\) 0 0
\(327\) −10.4307 22.6410i −0.576822 1.25205i
\(328\) 0 0
\(329\) −34.1170 19.6975i −1.88093 1.08596i
\(330\) 0 0
\(331\) 31.9282i 1.75493i 0.479638 + 0.877466i \(0.340768\pi\)
−0.479638 + 0.877466i \(0.659232\pi\)
\(332\) 0 0
\(333\) −2.33964 + 12.5883i −0.128211 + 0.689833i
\(334\) 0 0
\(335\) 1.41421 0.0772667
\(336\) 0 0
\(337\) 6.35641 3.66987i 0.346256 0.199911i −0.316779 0.948499i \(-0.602601\pi\)
0.663035 + 0.748589i \(0.269268\pi\)
\(338\) 0 0
\(339\) −2.96577 + 32.1875i −0.161078 + 1.74818i
\(340\) 0 0
\(341\) −1.69161 −0.0916061
\(342\) 0 0
\(343\) −0.267949 −0.0144679
\(344\) 0 0
\(345\) −0.0851642 + 0.924288i −0.00458509 + 0.0497620i
\(346\) 0 0
\(347\) 21.5414 12.4369i 1.15640 0.667649i 0.205963 0.978560i \(-0.433968\pi\)
0.950439 + 0.310911i \(0.100634\pi\)
\(348\) 0 0
\(349\) −11.3923 −0.609816 −0.304908 0.952382i \(-0.598626\pi\)
−0.304908 + 0.952382i \(0.598626\pi\)
\(350\) 0 0
\(351\) 13.9009 13.5213i 0.741977 0.721713i
\(352\) 0 0
\(353\) 11.9700i 0.637101i 0.947906 + 0.318551i \(0.103196\pi\)
−0.947906 + 0.318551i \(0.896804\pi\)
\(354\) 0 0
\(355\) −4.39230 2.53590i −0.233119 0.134592i
\(356\) 0 0
\(357\) 13.2507 + 28.7620i 0.701301 + 1.52224i
\(358\) 0 0
\(359\) −23.1822 + 13.3843i −1.22351 + 0.706394i −0.965665 0.259792i \(-0.916346\pi\)
−0.257846 + 0.966186i \(0.583013\pi\)
\(360\) 0 0
\(361\) −13.0000 + 13.8564i −0.684211 + 0.729285i
\(362\) 0 0
\(363\) −1.72529 + 18.7245i −0.0905540 + 0.982783i
\(364\) 0 0
\(365\) −3.67423 2.12132i −0.192318 0.111035i
\(366\) 0 0
\(367\) −8.52628 + 14.7679i −0.445068 + 0.770881i −0.998057 0.0623080i \(-0.980154\pi\)
0.552989 + 0.833189i \(0.313487\pi\)
\(368\) 0 0
\(369\) 5.65685 + 16.0000i 0.294484 + 0.832927i
\(370\) 0 0
\(371\) −11.2629 + 19.5080i −0.584743 + 1.01280i
\(372\) 0 0
\(373\) 12.5359i 0.649084i −0.945871 0.324542i \(-0.894790\pi\)
0.945871 0.324542i \(-0.105210\pi\)
\(374\) 0 0
\(375\) 19.5133 + 1.79796i 1.00766 + 0.0928462i
\(376\) 0 0
\(377\) −24.9754 + 14.4195i −1.28630 + 0.742644i
\(378\) 0 0
\(379\) 17.7846i 0.913534i 0.889586 + 0.456767i \(0.150993\pi\)
−0.889586 + 0.456767i \(0.849007\pi\)
\(380\) 0 0
\(381\) 7.85641 11.1106i 0.402496 0.569215i
\(382\) 0 0
\(383\) 13.3335 + 23.0943i 0.681310 + 1.18006i 0.974581 + 0.224034i \(0.0719226\pi\)
−0.293272 + 0.956029i \(0.594744\pi\)
\(384\) 0 0
\(385\) −1.00000 1.73205i −0.0509647 0.0882735i
\(386\) 0 0
\(387\) −2.26795 6.41473i −0.115286 0.326079i
\(388\) 0 0
\(389\) −4.33057 2.50026i −0.219569 0.126768i 0.386182 0.922423i \(-0.373794\pi\)
−0.605751 + 0.795655i \(0.707127\pi\)
\(390\) 0 0
\(391\) −1.85641 −0.0938825
\(392\) 0 0
\(393\) 5.05113 + 10.9640i 0.254796 + 0.553060i
\(394\) 0 0
\(395\) −2.50026 + 4.33057i −0.125802 + 0.217895i
\(396\) 0 0
\(397\) −4.16025 7.20577i −0.208797 0.361647i 0.742539 0.669803i \(-0.233622\pi\)
−0.951336 + 0.308156i \(0.900288\pi\)
\(398\) 0 0
\(399\) −26.7746 + 8.77656i −1.34041 + 0.439377i
\(400\) 0 0
\(401\) 5.74479 + 9.95026i 0.286881 + 0.496892i 0.973064 0.230537i \(-0.0740482\pi\)
−0.686183 + 0.727429i \(0.740715\pi\)
\(402\) 0 0
\(403\) −8.33013 + 14.4282i −0.414953 + 0.718720i
\(404\) 0 0
\(405\) −12.5732 + 1.97846i −0.624768 + 0.0983103i
\(406\) 0 0
\(407\) 1.61729 0.0801659
\(408\) 0 0
\(409\) 24.4641 + 14.1244i 1.20967 + 0.698404i 0.962688 0.270615i \(-0.0872270\pi\)
0.246984 + 0.969019i \(0.420560\pi\)
\(410\) 0 0
\(411\) 0.757875 1.07180i 0.0373832 0.0528678i
\(412\) 0 0
\(413\) 15.6443 + 27.0967i 0.769805 + 1.33334i
\(414\) 0 0
\(415\) −5.46410 9.46410i −0.268222 0.464574i
\(416\) 0 0
\(417\) 18.6622 + 13.1962i 0.913891 + 0.646218i
\(418\) 0 0
\(419\) 32.0464i 1.56557i −0.622292 0.782785i \(-0.713798\pi\)
0.622292 0.782785i \(-0.286202\pi\)
\(420\) 0 0
\(421\) −30.7128 + 17.7321i −1.49685 + 0.864207i −0.999993 0.00362487i \(-0.998846\pi\)
−0.496857 + 0.867832i \(0.665513\pi\)
\(422\) 0 0
\(423\) 24.0698 + 20.5785i 1.17031 + 1.00056i
\(424\) 0 0
\(425\) 14.6969i 0.712906i
\(426\) 0 0
\(427\) 6.59808 11.4282i 0.319303 0.553050i
\(428\) 0 0
\(429\) −2.00000 1.41421i −0.0965609 0.0682789i
\(430\) 0 0
\(431\) 12.7279 22.0454i 0.613082 1.06189i −0.377635 0.925954i \(-0.623263\pi\)
0.990718 0.135935i \(-0.0434040\pi\)
\(432\) 0 0
\(433\) 2.89230 + 1.66987i 0.138995 + 0.0802490i 0.567885 0.823108i \(-0.307762\pi\)
−0.428890 + 0.903357i \(0.641095\pi\)
\(434\) 0 0
\(435\) 18.8484 + 1.73670i 0.903710 + 0.0832682i
\(436\) 0 0
\(437\) 0.189469 1.64085i 0.00906352 0.0784924i
\(438\) 0 0
\(439\) −19.4545 + 11.2321i −0.928512 + 0.536077i −0.886341 0.463034i \(-0.846761\pi\)
−0.0421712 + 0.999110i \(0.513427\pi\)
\(440\) 0 0
\(441\) −20.4347 3.79796i −0.973079 0.180855i
\(442\) 0 0
\(443\) −33.4607 19.3185i −1.58976 0.917850i −0.993345 0.115177i \(-0.963257\pi\)
−0.596419 0.802674i \(-0.703410\pi\)
\(444\) 0 0
\(445\) 10.3923i 0.492642i
\(446\) 0 0
\(447\) 12.2257 + 26.5372i 0.578258 + 1.25517i
\(448\) 0 0
\(449\) 34.4959 1.62796 0.813982 0.580890i \(-0.197296\pi\)
0.813982 + 0.580890i \(0.197296\pi\)
\(450\) 0 0
\(451\) 1.85641 1.07180i 0.0874148 0.0504689i
\(452\) 0 0
\(453\) −3.44949 0.317837i −0.162071 0.0149333i
\(454\) 0 0
\(455\) −19.6975 −0.923431
\(456\) 0 0
\(457\) −20.7128 −0.968905 −0.484452 0.874818i \(-0.660981\pi\)
−0.484452 + 0.874818i \(0.660981\pi\)
\(458\) 0 0
\(459\) −6.24745 24.6773i −0.291606 1.15184i
\(460\) 0 0
\(461\) 28.4737 16.4393i 1.32615 0.765656i 0.341452 0.939899i \(-0.389081\pi\)
0.984703 + 0.174244i \(0.0557481\pi\)
\(462\) 0 0
\(463\) 29.5885 1.37509 0.687546 0.726141i \(-0.258688\pi\)
0.687546 + 0.726141i \(0.258688\pi\)
\(464\) 0 0
\(465\) 9.93149 4.57545i 0.460562 0.212182i
\(466\) 0 0
\(467\) 22.6274i 1.04707i 0.852004 + 0.523536i \(0.175387\pi\)
−0.852004 + 0.523536i \(0.824613\pi\)
\(468\) 0 0
\(469\) −3.23205 1.86603i −0.149242 0.0861650i
\(470\) 0 0
\(471\) 5.56244 2.56262i 0.256304 0.118079i
\(472\) 0 0
\(473\) −0.744272 + 0.429705i −0.0342216 + 0.0197579i
\(474\) 0 0
\(475\) −12.9904 1.50000i −0.596040 0.0688247i
\(476\) 0 0
\(477\) 11.7667 13.7630i 0.538761 0.630167i
\(478\) 0 0
\(479\) 10.2784 + 5.93426i 0.469634 + 0.271143i 0.716086 0.698012i \(-0.245932\pi\)
−0.246453 + 0.969155i \(0.579265\pi\)
\(480\) 0 0
\(481\) 7.96410 13.7942i 0.363132 0.628963i
\(482\) 0 0
\(483\) 1.41421 2.00000i 0.0643489 0.0910032i
\(484\) 0 0
\(485\) −5.27792 + 9.14162i −0.239658 + 0.415100i
\(486\) 0 0
\(487\) 24.9282i 1.12960i −0.825226 0.564802i \(-0.808952\pi\)
0.825226 0.564802i \(-0.191048\pi\)
\(488\) 0 0
\(489\) 0.825765 8.96204i 0.0373424 0.405277i
\(490\) 0 0
\(491\) −8.66115 + 5.00052i −0.390872 + 0.225670i −0.682538 0.730850i \(-0.739124\pi\)
0.291666 + 0.956520i \(0.405790\pi\)
\(492\) 0 0
\(493\) 37.8564i 1.70497i
\(494\) 0 0
\(495\) 0.535898 + 1.51575i 0.0240868 + 0.0681279i
\(496\) 0 0
\(497\) 6.69213 + 11.5911i 0.300183 + 0.519932i
\(498\) 0 0
\(499\) −8.06218 13.9641i −0.360913 0.625119i 0.627199 0.778859i \(-0.284201\pi\)
−0.988111 + 0.153740i \(0.950868\pi\)
\(500\) 0 0
\(501\) 10.7846 + 7.62587i 0.481821 + 0.340699i
\(502\) 0 0
\(503\) 15.8338 + 9.14162i 0.705992 + 0.407605i 0.809575 0.587016i \(-0.199697\pi\)
−0.103583 + 0.994621i \(0.533031\pi\)
\(504\) 0 0
\(505\) 10.9282 0.486299
\(506\) 0 0
\(507\) −1.46019 + 0.672711i −0.0648492 + 0.0298761i
\(508\) 0 0
\(509\) −6.79367 + 11.7670i −0.301124 + 0.521562i −0.976391 0.216011i \(-0.930695\pi\)
0.675267 + 0.737574i \(0.264028\pi\)
\(510\) 0 0
\(511\) 5.59808 + 9.69615i 0.247644 + 0.428933i
\(512\) 0 0
\(513\) 22.4495 3.00340i 0.991169 0.132603i
\(514\) 0 0
\(515\) 7.39924 + 12.8159i 0.326049 + 0.564734i
\(516\) 0 0
\(517\) 2.00000 3.46410i 0.0879599 0.152351i
\(518\) 0 0
\(519\) −18.6707 + 8.60164i −0.819554 + 0.377570i
\(520\) 0 0
\(521\) −4.52004 −0.198027 −0.0990133 0.995086i \(-0.531569\pi\)
−0.0990133 + 0.995086i \(0.531569\pi\)
\(522\) 0 0
\(523\) 14.5981 + 8.42820i 0.638329 + 0.368540i 0.783971 0.620798i \(-0.213191\pi\)
−0.145641 + 0.989337i \(0.546525\pi\)
\(524\) 0 0
\(525\) −15.8338 11.1962i −0.691042 0.488640i
\(526\) 0 0
\(527\) 10.9348 + 18.9396i 0.476326 + 0.825021i
\(528\) 0 0
\(529\) −11.4282 19.7942i −0.496878 0.860619i
\(530\) 0 0
\(531\) −8.38375 23.7128i −0.363824 1.02905i
\(532\) 0 0
\(533\) 21.1117i 0.914448i
\(534\) 0 0
\(535\) −6.00000 + 3.46410i −0.259403 + 0.149766i
\(536\) 0 0
\(537\) 0.224745 2.43916i 0.00969846 0.105257i
\(538\) 0 0
\(539\) 2.62536i 0.113082i
\(540\) 0 0
\(541\) 8.76795 15.1865i 0.376964 0.652920i −0.613655 0.789574i \(-0.710302\pi\)
0.990619 + 0.136654i \(0.0436349\pi\)
\(542\) 0 0
\(543\) 3.46410 4.89898i 0.148659 0.210235i
\(544\) 0 0
\(545\) 10.1769 17.6269i 0.435930 0.755054i
\(546\) 0 0
\(547\) 11.1340 + 6.42820i 0.476054 + 0.274850i 0.718771 0.695247i \(-0.244705\pi\)
−0.242716 + 0.970097i \(0.578038\pi\)
\(548\) 0 0
\(549\) −6.89320 + 8.06269i −0.294195 + 0.344107i
\(550\) 0 0
\(551\) −33.4607 3.86370i −1.42547 0.164599i
\(552\) 0 0
\(553\) 11.4282 6.59808i 0.485977 0.280579i
\(554\) 0 0
\(555\) −9.49510 + 4.37441i −0.403044 + 0.185683i
\(556\) 0 0
\(557\) −2.92996 1.69161i −0.124147 0.0716760i 0.436641 0.899636i \(-0.356168\pi\)
−0.560787 + 0.827960i \(0.689501\pi\)
\(558\) 0 0
\(559\) 8.46410i 0.357993i
\(560\) 0 0
\(561\) −2.92037 + 1.34542i −0.123298 + 0.0568037i
\(562\) 0 0
\(563\) −3.38323 −0.142586 −0.0712931 0.997455i \(-0.522713\pi\)
−0.0712931 + 0.997455i \(0.522713\pi\)
\(564\) 0 0
\(565\) −22.8564 + 13.1962i −0.961576 + 0.555166i
\(566\) 0 0
\(567\) 31.3454 + 12.0685i 1.31638 + 0.506830i
\(568\) 0 0
\(569\) −13.9391 −0.584356 −0.292178 0.956364i \(-0.594380\pi\)
−0.292178 + 0.956364i \(0.594380\pi\)
\(570\) 0 0
\(571\) −25.1962 −1.05443 −0.527213 0.849733i \(-0.676763\pi\)
−0.527213 + 0.849733i \(0.676763\pi\)
\(572\) 0 0
\(573\) 2.91760 + 0.268829i 0.121885 + 0.0112305i
\(574\) 0 0
\(575\) 0.984508 0.568406i 0.0410568 0.0237042i
\(576\) 0 0
\(577\) 42.9282 1.78712 0.893562 0.448939i \(-0.148198\pi\)
0.893562 + 0.448939i \(0.148198\pi\)
\(578\) 0 0
\(579\) 9.56384 + 20.7593i 0.397460 + 0.862727i
\(580\) 0 0
\(581\) 28.8391i 1.19645i
\(582\) 0 0
\(583\) −1.98076 1.14359i −0.0820348 0.0473628i
\(584\) 0 0
\(585\) 15.5672 + 2.89329i 0.643623 + 0.119623i
\(586\) 0 0
\(587\) −9.29392 + 5.36585i −0.383601 + 0.221472i −0.679384 0.733783i \(-0.737753\pi\)
0.295783 + 0.955255i \(0.404420\pi\)
\(588\) 0 0
\(589\) −17.8564 + 7.73205i −0.735760 + 0.318594i
\(590\) 0 0
\(591\) 15.7670 + 1.45277i 0.648566 + 0.0597591i
\(592\) 0 0
\(593\) −21.7816 12.5756i −0.894463 0.516419i −0.0190636 0.999818i \(-0.506069\pi\)
−0.875400 + 0.483400i \(0.839402\pi\)
\(594\) 0 0
\(595\) −12.9282 + 22.3923i −0.530005 + 0.917995i
\(596\) 0 0
\(597\) −18.1074 12.8038i −0.741086 0.524027i
\(598\) 0 0
\(599\) 8.43451 14.6090i 0.344625 0.596908i −0.640661 0.767824i \(-0.721339\pi\)
0.985286 + 0.170916i \(0.0546728\pi\)
\(600\) 0 0
\(601\) 44.3731i 1.81002i 0.425395 + 0.905008i \(0.360135\pi\)
−0.425395 + 0.905008i \(0.639865\pi\)
\(602\) 0 0
\(603\) 2.28024 + 1.94949i 0.0928585 + 0.0793894i
\(604\) 0 0
\(605\) −13.2963 + 7.67664i −0.540573 + 0.312100i
\(606\) 0 0
\(607\) 13.2487i 0.537749i 0.963175 + 0.268874i \(0.0866516\pi\)
−0.963175 + 0.268874i \(0.913348\pi\)
\(608\) 0 0
\(609\) −40.7846 28.8391i −1.65268 1.16862i
\(610\) 0 0
\(611\) −19.6975 34.1170i −0.796874 1.38023i
\(612\) 0 0
\(613\) −11.3205 19.6077i −0.457231 0.791947i 0.541582 0.840648i \(-0.317825\pi\)
−0.998813 + 0.0487003i \(0.984492\pi\)
\(614\) 0 0
\(615\) −8.00000 + 11.3137i −0.322591 + 0.456213i
\(616\) 0 0
\(617\) 22.4379 + 12.9546i 0.903318 + 0.521531i 0.878275 0.478156i \(-0.158695\pi\)
0.0250427 + 0.999686i \(0.492028\pi\)
\(618\) 0 0
\(619\) −2.80385 −0.112696 −0.0563481 0.998411i \(-0.517946\pi\)
−0.0563481 + 0.998411i \(0.517946\pi\)
\(620\) 0 0
\(621\) −1.41145 + 1.37290i −0.0566393 + 0.0550925i
\(622\) 0 0
\(623\) −13.7124 + 23.7506i −0.549377 + 0.951549i
\(624\) 0 0
\(625\) 0.500000 + 0.866025i 0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) −0.891136 2.71859i −0.0355885 0.108570i
\(628\) 0 0
\(629\) −10.4543 18.1074i −0.416840 0.721988i
\(630\) 0 0
\(631\) 24.5263 42.4808i 0.976376 1.69113i 0.301058 0.953606i \(-0.402660\pi\)
0.675318 0.737526i \(-0.264006\pi\)
\(632\) 0 0
\(633\) 7.97219 + 17.3045i 0.316866 + 0.687790i
\(634\) 0 0
\(635\) 11.1106 0.440912
\(636\) 0 0
\(637\) 22.3923 + 12.9282i 0.887215 + 0.512234i
\(638\) 0 0
\(639\) −3.58630 10.1436i −0.141872 0.401274i
\(640\) 0 0
\(641\) −6.41473 11.1106i −0.253367 0.438844i 0.711084 0.703107i \(-0.248205\pi\)
−0.964451 + 0.264263i \(0.914871\pi\)
\(642\) 0 0
\(643\) −21.7942 37.7487i −0.859480 1.48866i −0.872425 0.488748i \(-0.837454\pi\)
0.0129447 0.999916i \(-0.495879\pi\)
\(644\) 0 0
\(645\) 3.20736 4.53590i 0.126290 0.178601i
\(646\) 0 0
\(647\) 20.5569i 0.808174i 0.914721 + 0.404087i \(0.132411\pi\)
−0.914721 + 0.404087i \(0.867589\pi\)
\(648\) 0 0
\(649\) −2.75129 + 1.58846i −0.107998 + 0.0623524i
\(650\) 0 0
\(651\) −28.7347 2.64762i −1.12620 0.103769i
\(652\) 0 0
\(653\) 47.1223i 1.84404i 0.387144 + 0.922019i \(0.373462\pi\)
−0.387144 + 0.922019i \(0.626538\pi\)
\(654\) 0 0
\(655\) −4.92820 + 8.53590i −0.192561 + 0.333525i
\(656\) 0 0
\(657\) −3.00000 8.48528i −0.117041 0.331042i
\(658\) 0 0
\(659\) 16.5409 28.6496i 0.644340 1.11603i −0.340113 0.940385i \(-0.610465\pi\)
0.984453 0.175646i \(-0.0562013\pi\)
\(660\) 0 0
\(661\) 5.32051 + 3.07180i 0.206944 + 0.119479i 0.599890 0.800082i \(-0.295211\pi\)
−0.392946 + 0.919561i \(0.628544\pi\)
\(662\) 0 0
\(663\) −2.90555 + 31.5339i −0.112842 + 1.22468i
\(664\) 0 0
\(665\) −18.4727 13.7124i −0.716341 0.531745i
\(666\) 0 0
\(667\) 2.53590 1.46410i 0.0981904 0.0566902i
\(668\) 0 0
\(669\) 6.80702 + 14.7753i 0.263175 + 0.571248i
\(670\) 0 0
\(671\) 1.16037 + 0.669942i 0.0447957 + 0.0258628i
\(672\) 0 0
\(673\) 21.9808i 0.847296i −0.905827 0.423648i \(-0.860749\pi\)
0.905827 0.423648i \(-0.139251\pi\)
\(674\) 0 0
\(675\) 10.8691 + 11.1742i 0.418350 + 0.430096i
\(676\) 0 0
\(677\) −18.8380 −0.724005 −0.362002 0.932177i \(-0.617907\pi\)
−0.362002 + 0.932177i \(0.617907\pi\)
\(678\) 0 0
\(679\) 24.1244 13.9282i 0.925808 0.534515i
\(680\) 0 0
\(681\) −3.90883 + 42.4226i −0.149787 + 1.62564i
\(682\) 0 0
\(683\) 16.3142 0.624246 0.312123 0.950042i \(-0.398960\pi\)
0.312123 + 0.950042i \(0.398960\pi\)
\(684\) 0 0
\(685\) 1.07180 0.0409512
\(686\) 0 0
\(687\) −1.49261 + 16.1993i −0.0569467 + 0.618043i
\(688\) 0 0
\(689\) −19.5080 + 11.2629i −0.743195 + 0.429084i
\(690\) 0 0
\(691\) −9.85641 −0.374955 −0.187478 0.982269i \(-0.560031\pi\)
−0.187478 + 0.982269i \(0.560031\pi\)
\(692\) 0 0
\(693\) 0.775255 4.17121i 0.0294495 0.158451i
\(694\) 0 0
\(695\) 18.6622i 0.707897i
\(696\) 0 0
\(697\) −24.0000 13.8564i −0.909065 0.524849i
\(698\) 0 0
\(699\) 2.59915 + 5.64173i 0.0983090 + 0.213390i
\(700\) 0 0
\(701\) 17.2344 9.95026i 0.650933 0.375816i −0.137881 0.990449i \(-0.544029\pi\)
0.788814 + 0.614633i \(0.210696\pi\)
\(702\) 0 0
\(703\) 17.0718 7.39230i 0.643875 0.278806i
\(704\) 0 0
\(705\) −2.37237 + 25.7473i −0.0893486 + 0.969701i
\(706\) 0 0
\(707\) −24.9754 14.4195i −0.939295 0.542303i
\(708\) 0 0
\(709\) −21.1603 + 36.6506i −0.794690 + 1.37644i 0.128346 + 0.991729i \(0.459033\pi\)
−0.923036 + 0.384714i \(0.874300\pi\)
\(710\) 0 0
\(711\) −10.0010 + 3.53590i −0.375068 + 0.132607i
\(712\) 0 0
\(713\) 0.845807 1.46498i 0.0316757 0.0548640i
\(714\) 0 0
\(715\) 2.00000i 0.0747958i
\(716\) 0 0
\(717\) 51.7008 + 4.76373i 1.93080 + 0.177905i
\(718\) 0 0
\(719\) 5.22715 3.01790i 0.194940 0.112549i −0.399353 0.916797i \(-0.630765\pi\)
0.594293 + 0.804249i \(0.297432\pi\)
\(720\) 0 0
\(721\) 39.0526i 1.45439i
\(722\) 0 0
\(723\) 28.6603 40.5317i 1.06589 1.50739i
\(724\) 0 0
\(725\) −11.5911 20.0764i −0.430483 0.745618i
\(726\) 0 0
\(727\) −6.79423 11.7679i −0.251984 0.436449i 0.712088 0.702090i \(-0.247750\pi\)
−0.964072 + 0.265641i \(0.914416\pi\)
\(728\) 0 0
\(729\) −23.0000 14.1421i −0.851852 0.523783i
\(730\) 0 0
\(731\) 9.62209 + 5.55532i 0.355886 + 0.205471i
\(732\) 0 0
\(733\) −35.7128 −1.31908 −0.659541 0.751668i \(-0.729249\pi\)
−0.659541 + 0.751668i \(0.729249\pi\)
\(734\) 0 0
\(735\) −7.10102 15.4135i −0.261925 0.568535i
\(736\) 0 0
\(737\) 0.189469 0.328169i 0.00697917 0.0120883i
\(738\) 0 0
\(739\) −17.4019 30.1410i −0.640140 1.10876i −0.985401 0.170249i \(-0.945543\pi\)
0.345261 0.938507i \(-0.387790\pi\)
\(740\) 0 0
\(741\) −27.5758 5.78658i −1.01302 0.212575i
\(742\) 0 0
\(743\) −3.53553 6.12372i −0.129706 0.224658i 0.793857 0.608105i \(-0.208070\pi\)
−0.923563 + 0.383447i \(0.874737\pi\)
\(744\) 0 0
\(745\) −11.9282 + 20.6603i −0.437016 + 0.756933i
\(746\) 0 0
\(747\) 4.23607 22.7919i 0.154990 0.833912i
\(748\) 0 0
\(749\) 18.2832 0.668055
\(750\) 0 0
\(751\) 7.45448 + 4.30385i 0.272018 + 0.157050i 0.629804 0.776754i \(-0.283135\pi\)
−0.357786 + 0.933803i \(0.616468\pi\)
\(752\) 0 0
\(753\) 14.6969 20.7846i 0.535586 0.757433i
\(754\) 0 0
\(755\) −1.41421 2.44949i −0.0514685 0.0891461i
\(756\) 0 0
\(757\) −2.30385 3.99038i −0.0837348 0.145033i 0.821117 0.570760i \(-0.193352\pi\)
−0.904851 + 0.425728i \(0.860018\pi\)
\(758\) 0 0
\(759\) 0.203072 + 0.143594i 0.00737104 + 0.00521212i
\(760\) 0 0
\(761\) 46.2629i 1.67703i −0.544879 0.838514i \(-0.683425\pi\)
0.544879 0.838514i \(-0.316575\pi\)
\(762\) 0 0
\(763\) −46.5167 + 26.8564i −1.68402 + 0.972267i
\(764\) 0 0
\(765\) 13.5065 15.7980i 0.488327 0.571176i
\(766\) 0 0
\(767\) 31.2886i 1.12976i
\(768\) 0 0
\(769\) 0.428203 0.741670i 0.0154414 0.0267453i −0.858201 0.513313i \(-0.828418\pi\)
0.873643 + 0.486568i \(0.161751\pi\)
\(770\) 0 0
\(771\) −4.53590 3.20736i −0.163356 0.115510i
\(772\) 0 0
\(773\) −9.04008 + 15.6579i −0.325149 + 0.563175i −0.981543 0.191244i \(-0.938748\pi\)
0.656393 + 0.754419i \(0.272081\pi\)
\(774\) 0 0
\(775\) −11.5981 6.69615i −0.416615 0.240533i
\(776\) 0 0
\(777\) 27.4721 + 2.53129i 0.985556 + 0.0908095i
\(778\) 0 0
\(779\) 14.6969 19.7990i 0.526572 0.709372i
\(780\) 0 0
\(781\) −1.17691 + 0.679492i −0.0421133 + 0.0243141i
\(782\) 0 0
\(783\) 27.9966 + 28.7826i 1.00052 + 1.02861i
\(784\) 0 0
\(785\) 4.33057 + 2.50026i 0.154565 + 0.0892380i
\(786\) 0 0
\(787\) 24.0718i 0.858067i −0.903289 0.429033i \(-0.858854\pi\)
0.903289 0.429033i \(-0.141146\pi\)
\(788\) 0 0
\(789\) −0.402091 0.872778i −0.0143148 0.0310717i
\(790\) 0 0
\(791\) 69.6482 2.47640
\(792\) 0 0
\(793\) 11.4282