Properties

Label 1040.2.da.b.881.4
Level $1040$
Weight $2$
Character 1040.881
Analytic conductor $8.304$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1040.da (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.30444181021\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.22581504.2
Defining polynomial: \(x^{8} - 4 x^{7} + 5 x^{6} + 2 x^{5} - 11 x^{4} + 4 x^{3} + 20 x^{2} - 32 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 881.4
Root \(1.40994 - 0.109843i\) of defining polynomial
Character \(\chi\) \(=\) 1040.881
Dual form 1040.2.da.b.641.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.16612 + 2.01978i) q^{3} -1.00000i q^{5} +(-3.11786 - 1.80010i) q^{7} +(-1.21969 + 2.11256i) q^{9} +O(q^{10})\) \(q+(1.16612 + 2.01978i) q^{3} -1.00000i q^{5} +(-3.11786 - 1.80010i) q^{7} +(-1.21969 + 2.11256i) q^{9} +(4.65213 - 2.68591i) q^{11} +(1.81988 - 3.11256i) q^{13} +(2.01978 - 1.16612i) q^{15} +(-0.565928 + 0.980215i) q^{17} +(1.96410 + 1.13397i) q^{19} -8.39654i q^{21} +(1.94644 + 3.37133i) q^{23} -1.00000 q^{25} +1.30752 q^{27} +(0.0123639 + 0.0214150i) q^{29} -5.46410i q^{31} +(10.8499 + 6.26420i) q^{33} +(-1.80010 + 3.11786i) q^{35} +(7.53794 - 4.35203i) q^{37} +(8.40891 + 0.0461428i) q^{39} +(3.23205 - 1.86603i) q^{41} +(0.565928 - 0.980215i) q^{43} +(2.11256 + 1.21969i) q^{45} +2.58535i q^{47} +(2.98070 + 5.16273i) q^{49} -2.63977 q^{51} -4.43937 q^{53} +(-2.68591 - 4.65213i) q^{55} +5.28942i q^{57} +(0.148458 + 0.0857123i) q^{59} +(-1.68012 + 2.91005i) q^{61} +(7.60563 - 4.39111i) q^{63} +(-3.11256 - 1.81988i) q^{65} +(-5.54239 + 3.19990i) q^{67} +(-4.53957 + 7.86276i) q^{69} +(-9.35076 - 5.39866i) q^{71} +4.70308i q^{73} +(-1.16612 - 2.01978i) q^{75} -19.3396 q^{77} +11.9826 q^{79} +(5.18379 + 8.97859i) q^{81} +12.1286i q^{83} +(0.980215 + 0.565928i) q^{85} +(-0.0288357 + 0.0499450i) q^{87} +(13.9898 - 8.07702i) q^{89} +(-11.2771 + 6.42856i) q^{91} +(11.0363 - 6.37182i) q^{93} +(1.13397 - 1.96410i) q^{95} +(-10.5379 - 6.08408i) q^{97} +13.1039i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9} + O(q^{10}) \) \( 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9} + 6 q^{15} - 2 q^{17} - 12 q^{19} + 10 q^{23} - 8 q^{25} + 4 q^{27} - 8 q^{29} + 42 q^{33} - 10 q^{35} + 6 q^{37} + 12 q^{41} + 2 q^{43} + 12 q^{49} + 8 q^{51} - 24 q^{53} + 12 q^{59} - 28 q^{61} + 24 q^{63} - 8 q^{65} - 6 q^{67} - 16 q^{69} + 2 q^{75} - 36 q^{77} + 16 q^{79} + 8 q^{81} + 18 q^{85} - 22 q^{87} + 24 q^{89} - 28 q^{91} + 16 q^{95} - 30 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(417\) \(561\) \(911\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(3\) 1.16612 + 2.01978i 0.673262 + 1.16612i 0.976974 + 0.213359i \(0.0684405\pi\)
−0.303712 + 0.952764i \(0.598226\pi\)
\(4\) 0 0
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) −3.11786 1.80010i −1.17844 0.680373i −0.222787 0.974867i \(-0.571516\pi\)
−0.955653 + 0.294494i \(0.904849\pi\)
\(8\) 0 0
\(9\) −1.21969 + 2.11256i −0.406562 + 0.704187i
\(10\) 0 0
\(11\) 4.65213 2.68591i 1.40267 0.809832i 0.408004 0.912980i \(-0.366225\pi\)
0.994666 + 0.103149i \(0.0328917\pi\)
\(12\) 0 0
\(13\) 1.81988 3.11256i 0.504745 0.863269i
\(14\) 0 0
\(15\) 2.01978 1.16612i 0.521506 0.301092i
\(16\) 0 0
\(17\) −0.565928 + 0.980215i −0.137258 + 0.237737i −0.926458 0.376399i \(-0.877162\pi\)
0.789200 + 0.614136i \(0.210495\pi\)
\(18\) 0 0
\(19\) 1.96410 + 1.13397i 0.450596 + 0.260152i 0.708082 0.706130i \(-0.249561\pi\)
−0.257486 + 0.966282i \(0.582894\pi\)
\(20\) 0 0
\(21\) 8.39654i 1.83228i
\(22\) 0 0
\(23\) 1.94644 + 3.37133i 0.405860 + 0.702970i 0.994421 0.105483i \(-0.0336387\pi\)
−0.588561 + 0.808453i \(0.700305\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) 1.30752 0.251632
\(28\) 0 0
\(29\) 0.0123639 + 0.0214150i 0.00229593 + 0.00397666i 0.867171 0.498010i \(-0.165936\pi\)
−0.864875 + 0.501987i \(0.832603\pi\)
\(30\) 0 0
\(31\) 5.46410i 0.981382i −0.871334 0.490691i \(-0.836744\pi\)
0.871334 0.490691i \(-0.163256\pi\)
\(32\) 0 0
\(33\) 10.8499 + 6.26420i 1.88873 + 1.09046i
\(34\) 0 0
\(35\) −1.80010 + 3.11786i −0.304272 + 0.527015i
\(36\) 0 0
\(37\) 7.53794 4.35203i 1.23923 0.715470i 0.270293 0.962778i \(-0.412879\pi\)
0.968937 + 0.247309i \(0.0795462\pi\)
\(38\) 0 0
\(39\) 8.40891 + 0.0461428i 1.34650 + 0.00738877i
\(40\) 0 0
\(41\) 3.23205 1.86603i 0.504762 0.291424i −0.225916 0.974147i \(-0.572538\pi\)
0.730678 + 0.682723i \(0.239204\pi\)
\(42\) 0 0
\(43\) 0.565928 0.980215i 0.0863031 0.149481i −0.819643 0.572875i \(-0.805828\pi\)
0.905946 + 0.423394i \(0.139161\pi\)
\(44\) 0 0
\(45\) 2.11256 + 1.21969i 0.314922 + 0.181820i
\(46\) 0 0
\(47\) 2.58535i 0.377113i 0.982062 + 0.188556i \(0.0603808\pi\)
−0.982062 + 0.188556i \(0.939619\pi\)
\(48\) 0 0
\(49\) 2.98070 + 5.16273i 0.425815 + 0.737533i
\(50\) 0 0
\(51\) −2.63977 −0.369641
\(52\) 0 0
\(53\) −4.43937 −0.609795 −0.304897 0.952385i \(-0.598622\pi\)
−0.304897 + 0.952385i \(0.598622\pi\)
\(54\) 0 0
\(55\) −2.68591 4.65213i −0.362168 0.627293i
\(56\) 0 0
\(57\) 5.28942i 0.700600i
\(58\) 0 0
\(59\) 0.148458 + 0.0857123i 0.0193276 + 0.0111588i 0.509633 0.860392i \(-0.329781\pi\)
−0.490305 + 0.871551i \(0.663115\pi\)
\(60\) 0 0
\(61\) −1.68012 + 2.91005i −0.215117 + 0.372594i −0.953309 0.301997i \(-0.902347\pi\)
0.738192 + 0.674591i \(0.235680\pi\)
\(62\) 0 0
\(63\) 7.60563 4.39111i 0.958219 0.553228i
\(64\) 0 0
\(65\) −3.11256 1.81988i −0.386066 0.225729i
\(66\) 0 0
\(67\) −5.54239 + 3.19990i −0.677111 + 0.390930i −0.798766 0.601642i \(-0.794513\pi\)
0.121655 + 0.992572i \(0.461180\pi\)
\(68\) 0 0
\(69\) −4.53957 + 7.86276i −0.546500 + 0.946566i
\(70\) 0 0
\(71\) −9.35076 5.39866i −1.10973 0.640703i −0.170971 0.985276i \(-0.554691\pi\)
−0.938760 + 0.344573i \(0.888024\pi\)
\(72\) 0 0
\(73\) 4.70308i 0.550454i 0.961379 + 0.275227i \(0.0887531\pi\)
−0.961379 + 0.275227i \(0.911247\pi\)
\(74\) 0 0
\(75\) −1.16612 2.01978i −0.134652 0.233225i
\(76\) 0 0
\(77\) −19.3396 −2.20395
\(78\) 0 0
\(79\) 11.9826 1.34815 0.674075 0.738663i \(-0.264543\pi\)
0.674075 + 0.738663i \(0.264543\pi\)
\(80\) 0 0
\(81\) 5.18379 + 8.97859i 0.575976 + 0.997621i
\(82\) 0 0
\(83\) 12.1286i 1.33129i 0.746270 + 0.665643i \(0.231843\pi\)
−0.746270 + 0.665643i \(0.768157\pi\)
\(84\) 0 0
\(85\) 0.980215 + 0.565928i 0.106319 + 0.0613835i
\(86\) 0 0
\(87\) −0.0288357 + 0.0499450i −0.00309152 + 0.00535466i
\(88\) 0 0
\(89\) 13.9898 8.07702i 1.48292 0.856162i 0.483105 0.875562i \(-0.339509\pi\)
0.999812 + 0.0194001i \(0.00617565\pi\)
\(90\) 0 0
\(91\) −11.2771 + 6.42856i −1.18216 + 0.673896i
\(92\) 0 0
\(93\) 11.0363 6.37182i 1.14441 0.660727i
\(94\) 0 0
\(95\) 1.13397 1.96410i 0.116343 0.201513i
\(96\) 0 0
\(97\) −10.5379 6.08408i −1.06997 0.617745i −0.141794 0.989896i \(-0.545287\pi\)
−0.928172 + 0.372151i \(0.878620\pi\)
\(98\) 0 0
\(99\) 13.1039i 1.31699i
\(100\) 0 0
\(101\) −2.02721 3.51122i −0.201714 0.349380i 0.747366 0.664412i \(-0.231318\pi\)
−0.949081 + 0.315032i \(0.897985\pi\)
\(102\) 0 0
\(103\) −17.9035 −1.76408 −0.882041 0.471173i \(-0.843831\pi\)
−0.882041 + 0.471173i \(0.843831\pi\)
\(104\) 0 0
\(105\) −8.39654 −0.819419
\(106\) 0 0
\(107\) −4.56593 7.90842i −0.441405 0.764536i 0.556389 0.830922i \(-0.312186\pi\)
−0.997794 + 0.0663862i \(0.978853\pi\)
\(108\) 0 0
\(109\) 7.37605i 0.706498i 0.935529 + 0.353249i \(0.114923\pi\)
−0.935529 + 0.353249i \(0.885077\pi\)
\(110\) 0 0
\(111\) 17.5803 + 10.1500i 1.66865 + 0.963396i
\(112\) 0 0
\(113\) −3.53794 + 6.12789i −0.332821 + 0.576463i −0.983064 0.183263i \(-0.941334\pi\)
0.650243 + 0.759727i \(0.274667\pi\)
\(114\) 0 0
\(115\) 3.37133 1.94644i 0.314378 0.181506i
\(116\) 0 0
\(117\) 4.35578 + 7.64096i 0.402692 + 0.706407i
\(118\) 0 0
\(119\) 3.52897 2.03745i 0.323500 0.186773i
\(120\) 0 0
\(121\) 8.92820 15.4641i 0.811655 1.40583i
\(122\) 0 0
\(123\) 7.53794 + 4.35203i 0.679673 + 0.392409i
\(124\) 0 0
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 5.71806 + 9.90396i 0.507395 + 0.878835i 0.999963 + 0.00856072i \(0.00272499\pi\)
−0.492568 + 0.870274i \(0.663942\pi\)
\(128\) 0 0
\(129\) 2.63977 0.232418
\(130\) 0 0
\(131\) 10.5680 0.923328 0.461664 0.887055i \(-0.347253\pi\)
0.461664 + 0.887055i \(0.347253\pi\)
\(132\) 0 0
\(133\) −4.08253 7.07115i −0.354000 0.613146i
\(134\) 0 0
\(135\) 1.30752i 0.112533i
\(136\) 0 0
\(137\) 3.27940 + 1.89336i 0.280178 + 0.161761i 0.633504 0.773739i \(-0.281616\pi\)
−0.353326 + 0.935500i \(0.614949\pi\)
\(138\) 0 0
\(139\) 1.00693 1.74406i 0.0854068 0.147929i −0.820158 0.572138i \(-0.806114\pi\)
0.905564 + 0.424209i \(0.139448\pi\)
\(140\) 0 0
\(141\) −5.22186 + 3.01484i −0.439760 + 0.253895i
\(142\) 0 0
\(143\) 0.106280 19.3681i 0.00888757 1.61964i
\(144\) 0 0
\(145\) 0.0214150 0.0123639i 0.00177842 0.00102677i
\(146\) 0 0
\(147\) −6.95174 + 12.0408i −0.573370 + 0.993105i
\(148\) 0 0
\(149\) 4.77855 + 2.75890i 0.391474 + 0.226018i 0.682799 0.730607i \(-0.260763\pi\)
−0.291324 + 0.956624i \(0.594096\pi\)
\(150\) 0 0
\(151\) 4.88961i 0.397911i −0.980009 0.198956i \(-0.936245\pi\)
0.980009 0.198956i \(-0.0637549\pi\)
\(152\) 0 0
\(153\) −1.38051 2.39111i −0.111608 0.193310i
\(154\) 0 0
\(155\) −5.46410 −0.438887
\(156\) 0 0
\(157\) 10.0405 0.801323 0.400661 0.916226i \(-0.368780\pi\)
0.400661 + 0.916226i \(0.368780\pi\)
\(158\) 0 0
\(159\) −5.17686 8.96658i −0.410551 0.711096i
\(160\) 0 0
\(161\) 14.0151i 1.10454i
\(162\) 0 0
\(163\) −5.87273 3.39062i −0.459988 0.265574i 0.252051 0.967714i \(-0.418895\pi\)
−0.712039 + 0.702140i \(0.752228\pi\)
\(164\) 0 0
\(165\) 6.26420 10.8499i 0.487667 0.844664i
\(166\) 0 0
\(167\) 9.08444 5.24490i 0.702975 0.405863i −0.105479 0.994421i \(-0.533638\pi\)
0.808455 + 0.588559i \(0.200304\pi\)
\(168\) 0 0
\(169\) −6.37605 11.3290i −0.490466 0.871460i
\(170\) 0 0
\(171\) −4.79118 + 2.76619i −0.366391 + 0.211536i
\(172\) 0 0
\(173\) −2.22923 + 3.86113i −0.169485 + 0.293557i −0.938239 0.345988i \(-0.887544\pi\)
0.768754 + 0.639545i \(0.220877\pi\)
\(174\) 0 0
\(175\) 3.11786 + 1.80010i 0.235688 + 0.136075i
\(176\) 0 0
\(177\) 0.399804i 0.0300511i
\(178\) 0 0
\(179\) −9.31564 16.1352i −0.696284 1.20600i −0.969746 0.244116i \(-0.921502\pi\)
0.273462 0.961883i \(-0.411831\pi\)
\(180\) 0 0
\(181\) −18.0900 −1.34462 −0.672310 0.740270i \(-0.734698\pi\)
−0.672310 + 0.740270i \(0.734698\pi\)
\(182\) 0 0
\(183\) −7.83690 −0.579320
\(184\) 0 0
\(185\) −4.35203 7.53794i −0.319968 0.554200i
\(186\) 0 0
\(187\) 6.08012i 0.444622i
\(188\) 0 0
\(189\) −4.07666 2.35366i −0.296533 0.171204i
\(190\) 0 0
\(191\) 13.6682 23.6740i 0.988994 1.71299i 0.366361 0.930473i \(-0.380603\pi\)
0.622632 0.782515i \(-0.286063\pi\)
\(192\) 0 0
\(193\) −18.8511 + 10.8837i −1.35693 + 0.783425i −0.989209 0.146510i \(-0.953196\pi\)
−0.367723 + 0.929935i \(0.619863\pi\)
\(194\) 0 0
\(195\) 0.0461428 8.40891i 0.00330436 0.602174i
\(196\) 0 0
\(197\) −1.46940 + 0.848360i −0.104691 + 0.0604432i −0.551431 0.834220i \(-0.685918\pi\)
0.446741 + 0.894664i \(0.352585\pi\)
\(198\) 0 0
\(199\) −12.6627 + 21.9325i −0.897637 + 1.55475i −0.0671309 + 0.997744i \(0.521385\pi\)
−0.830506 + 0.557009i \(0.811949\pi\)
\(200\) 0 0
\(201\) −12.9262 7.46296i −0.911746 0.526397i
\(202\) 0 0
\(203\) 0.0890252i 0.00624834i
\(204\) 0 0
\(205\) −1.86603 3.23205i −0.130329 0.225736i
\(206\) 0 0
\(207\) −9.49617 −0.660030
\(208\) 0 0
\(209\) 12.1830 0.842716
\(210\) 0 0
\(211\) −0.167753 0.290558i −0.0115486 0.0200028i 0.860193 0.509968i \(-0.170343\pi\)
−0.871742 + 0.489965i \(0.837009\pi\)
\(212\) 0 0
\(213\) 25.1820i 1.72544i
\(214\) 0 0
\(215\) −0.980215 0.565928i −0.0668501 0.0385959i
\(216\) 0 0
\(217\) −9.83592 + 17.0363i −0.667706 + 1.15650i
\(218\) 0 0
\(219\) −9.49922 + 5.48438i −0.641898 + 0.370600i
\(220\) 0 0
\(221\) 2.02106 + 3.54536i 0.135951 + 0.238487i
\(222\) 0 0
\(223\) 10.6493 6.14838i 0.713130 0.411726i −0.0990887 0.995079i \(-0.531593\pi\)
0.812219 + 0.583353i \(0.198259\pi\)
\(224\) 0 0
\(225\) 1.21969 2.11256i 0.0813125 0.140837i
\(226\) 0 0
\(227\) −6.60974 3.81613i −0.438704 0.253286i 0.264344 0.964428i \(-0.414845\pi\)
−0.703048 + 0.711143i \(0.748178\pi\)
\(228\) 0 0
\(229\) 14.4008i 0.951631i 0.879545 + 0.475815i \(0.157847\pi\)
−0.879545 + 0.475815i \(0.842153\pi\)
\(230\) 0 0
\(231\) −22.5523 39.0618i −1.48384 2.57008i
\(232\) 0 0
\(233\) −9.49617 −0.622115 −0.311057 0.950391i \(-0.600683\pi\)
−0.311057 + 0.950391i \(0.600683\pi\)
\(234\) 0 0
\(235\) 2.58535 0.168650
\(236\) 0 0
\(237\) 13.9732 + 24.2023i 0.907657 + 1.57211i
\(238\) 0 0
\(239\) 19.9143i 1.28815i 0.764962 + 0.644076i \(0.222758\pi\)
−0.764962 + 0.644076i \(0.777242\pi\)
\(240\) 0 0
\(241\) 20.1493 + 11.6332i 1.29793 + 0.749360i 0.980046 0.198770i \(-0.0636947\pi\)
0.317883 + 0.948130i \(0.397028\pi\)
\(242\) 0 0
\(243\) −10.1286 + 17.5432i −0.649750 + 1.12540i
\(244\) 0 0
\(245\) 5.16273 2.98070i 0.329835 0.190430i
\(246\) 0 0
\(247\) 7.10400 4.04968i 0.452017 0.257675i
\(248\) 0 0
\(249\) −24.4972 + 14.1434i −1.55244 + 0.896304i
\(250\) 0 0
\(251\) −5.92008 + 10.2539i −0.373672 + 0.647219i −0.990127 0.140171i \(-0.955235\pi\)
0.616455 + 0.787390i \(0.288568\pi\)
\(252\) 0 0
\(253\) 18.1101 + 10.4559i 1.13858 + 0.657357i
\(254\) 0 0
\(255\) 2.63977i 0.165309i
\(256\) 0 0
\(257\) −2.77501 4.80646i −0.173100 0.299819i 0.766402 0.642361i \(-0.222045\pi\)
−0.939502 + 0.342543i \(0.888712\pi\)
\(258\) 0 0
\(259\) −31.3363 −1.94714
\(260\) 0 0
\(261\) −0.0603205 −0.00373375
\(262\) 0 0
\(263\) 3.42983 + 5.94065i 0.211493 + 0.366316i 0.952182 0.305532i \(-0.0988342\pi\)
−0.740689 + 0.671848i \(0.765501\pi\)
\(264\) 0 0
\(265\) 4.43937i 0.272709i
\(266\) 0 0
\(267\) 32.6277 + 18.8376i 1.99678 + 1.15284i
\(268\) 0 0
\(269\) 0.710994 1.23148i 0.0433501 0.0750845i −0.843536 0.537072i \(-0.819530\pi\)
0.886886 + 0.461988i \(0.152864\pi\)
\(270\) 0 0
\(271\) −8.63381 + 4.98473i −0.524467 + 0.302801i −0.738760 0.673968i \(-0.764588\pi\)
0.214294 + 0.976769i \(0.431255\pi\)
\(272\) 0 0
\(273\) −26.1347 15.2807i −1.58175 0.924831i
\(274\) 0 0
\(275\) −4.65213 + 2.68591i −0.280534 + 0.161966i
\(276\) 0 0
\(277\) −8.76187 + 15.1760i −0.526449 + 0.911837i 0.473076 + 0.881022i \(0.343144\pi\)
−0.999525 + 0.0308154i \(0.990190\pi\)
\(278\) 0 0
\(279\) 11.5432 + 6.66449i 0.691076 + 0.398993i
\(280\) 0 0
\(281\) 10.7352i 0.640406i −0.947349 0.320203i \(-0.896249\pi\)
0.947349 0.320203i \(-0.103751\pi\)
\(282\) 0 0
\(283\) −0.659192 1.14175i −0.0391849 0.0678702i 0.845768 0.533551i \(-0.179143\pi\)
−0.884953 + 0.465681i \(0.845809\pi\)
\(284\) 0 0
\(285\) 5.28942 0.313318
\(286\) 0 0
\(287\) −13.4361 −0.793109
\(288\) 0 0
\(289\) 7.85945 + 13.6130i 0.462321 + 0.800763i
\(290\) 0 0
\(291\) 28.3792i 1.66362i
\(292\) 0 0
\(293\) 16.2316 + 9.37133i 0.948261 + 0.547479i 0.892540 0.450968i \(-0.148921\pi\)
0.0557207 + 0.998446i \(0.482254\pi\)
\(294\) 0 0
\(295\) 0.0857123 0.148458i 0.00499036 0.00864356i
\(296\) 0 0
\(297\) 6.08275 3.51187i 0.352957 0.203780i
\(298\) 0 0
\(299\) 14.0357 + 0.0770194i 0.811708 + 0.00445415i
\(300\) 0 0
\(301\) −3.52897 + 2.03745i −0.203406 + 0.117437i
\(302\) 0 0
\(303\) 4.72794 8.18904i 0.271613 0.470448i
\(304\) 0 0
\(305\) 2.91005 + 1.68012i 0.166629 + 0.0962032i
\(306\) 0 0
\(307\) 14.3043i 0.816387i 0.912895 + 0.408194i \(0.133841\pi\)
−0.912895 + 0.408194i \(0.866159\pi\)
\(308\) 0 0
\(309\) −20.8777 36.1612i −1.18769 2.05714i
\(310\) 0 0
\(311\) 2.76102 0.156563 0.0782815 0.996931i \(-0.475057\pi\)
0.0782815 + 0.996931i \(0.475057\pi\)
\(312\) 0 0
\(313\) −16.3858 −0.926179 −0.463090 0.886311i \(-0.653259\pi\)
−0.463090 + 0.886311i \(0.653259\pi\)
\(314\) 0 0
\(315\) −4.39111 7.60563i −0.247411 0.428529i
\(316\) 0 0
\(317\) 1.78575i 0.100297i 0.998742 + 0.0501487i \(0.0159695\pi\)
−0.998742 + 0.0501487i \(0.984030\pi\)
\(318\) 0 0
\(319\) 0.115037 + 0.0664168i 0.00644085 + 0.00371863i
\(320\) 0 0
\(321\) 10.6489 18.4444i 0.594362 1.02946i
\(322\) 0 0
\(323\) −2.22308 + 1.28349i −0.123695 + 0.0714156i
\(324\) 0 0
\(325\) −1.81988 + 3.11256i −0.100949 + 0.172654i
\(326\) 0 0
\(327\) −14.8980 + 8.60139i −0.823864 + 0.475658i
\(328\) 0 0
\(329\) 4.65389 8.06077i 0.256577 0.444405i
\(330\) 0 0
\(331\) 6.25652 + 3.61220i 0.343889 + 0.198545i 0.661991 0.749512i \(-0.269712\pi\)
−0.318101 + 0.948057i \(0.603045\pi\)
\(332\) 0 0
\(333\) 21.2325i 1.16353i
\(334\) 0 0
\(335\) 3.19990 + 5.54239i 0.174829 + 0.302813i
\(336\) 0 0
\(337\) 4.36219 0.237624 0.118812 0.992917i \(-0.462091\pi\)
0.118812 + 0.992917i \(0.462091\pi\)
\(338\) 0 0
\(339\) −16.5027 −0.896303
\(340\) 0 0
\(341\) −14.6761 25.4197i −0.794754 1.37655i
\(342\) 0 0
\(343\) 3.73913i 0.201894i
\(344\) 0 0
\(345\) 7.86276 + 4.53957i 0.423317 + 0.244402i
\(346\) 0 0
\(347\) −13.3536 + 23.1291i −0.716858 + 1.24163i 0.245381 + 0.969427i \(0.421087\pi\)
−0.962239 + 0.272207i \(0.912246\pi\)
\(348\) 0 0
\(349\) −20.4131 + 11.7855i −1.09269 + 0.630865i −0.934292 0.356510i \(-0.883967\pi\)
−0.158399 + 0.987375i \(0.550633\pi\)
\(350\) 0 0
\(351\) 2.37953 4.06973i 0.127010 0.217226i
\(352\) 0 0
\(353\) 4.96862 2.86863i 0.264453 0.152682i −0.361911 0.932213i \(-0.617876\pi\)
0.626364 + 0.779531i \(0.284542\pi\)
\(354\) 0 0
\(355\) −5.39866 + 9.35076i −0.286531 + 0.496287i
\(356\) 0 0
\(357\) 8.23042 + 4.75184i 0.435600 + 0.251494i
\(358\) 0 0
\(359\) 24.7583i 1.30669i −0.757059 0.653347i \(-0.773364\pi\)
0.757059 0.653347i \(-0.226636\pi\)
\(360\) 0 0
\(361\) −6.92820 12.0000i −0.364642 0.631579i
\(362\) 0 0
\(363\) 41.6455 2.18582
\(364\) 0 0
\(365\) 4.70308 0.246171
\(366\) 0 0
\(367\) 13.0268 + 22.5630i 0.679992 + 1.17778i 0.974983 + 0.222280i \(0.0713500\pi\)
−0.294991 + 0.955500i \(0.595317\pi\)
\(368\) 0 0
\(369\) 9.10387i 0.473928i
\(370\) 0 0
\(371\) 13.8413 + 7.99131i 0.718607 + 0.414888i
\(372\) 0 0
\(373\) −6.60224 + 11.4354i −0.341851 + 0.592103i −0.984776 0.173826i \(-0.944387\pi\)
0.642926 + 0.765929i \(0.277720\pi\)
\(374\) 0 0
\(375\) −2.01978 + 1.16612i −0.104301 + 0.0602183i
\(376\) 0 0
\(377\) 0.0891563 0.000489234i 0.00459178 2.51968e-5i
\(378\) 0 0
\(379\) −22.5147 + 12.9989i −1.15650 + 0.667707i −0.950463 0.310837i \(-0.899391\pi\)
−0.206039 + 0.978544i \(0.566057\pi\)
\(380\) 0 0
\(381\) −13.3359 + 23.0985i −0.683220 + 1.18337i
\(382\) 0 0
\(383\) −8.31401 4.80010i −0.424826 0.245274i 0.272314 0.962208i \(-0.412211\pi\)
−0.697140 + 0.716935i \(0.745544\pi\)
\(384\) 0 0
\(385\) 19.3396i 0.985637i
\(386\) 0 0
\(387\) 1.38051 + 2.39111i 0.0701752 + 0.121547i
\(388\) 0 0
\(389\) −5.63129 −0.285518 −0.142759 0.989758i \(-0.545597\pi\)
−0.142759 + 0.989758i \(0.545597\pi\)
\(390\) 0 0
\(391\) −4.40617 −0.222829
\(392\) 0 0
\(393\) 12.3236 + 21.3450i 0.621641 + 1.07671i
\(394\) 0 0
\(395\) 11.9826i 0.602911i
\(396\) 0 0
\(397\) −14.5196 8.38291i −0.728719 0.420726i 0.0892344 0.996011i \(-0.471558\pi\)
−0.817953 + 0.575285i \(0.804891\pi\)
\(398\) 0 0
\(399\) 9.52147 16.4917i 0.476670 0.825616i
\(400\) 0 0
\(401\) 12.0187 6.93902i 0.600187 0.346518i −0.168928 0.985628i \(-0.554031\pi\)
0.769115 + 0.639110i \(0.220697\pi\)
\(402\) 0 0
\(403\) −17.0073 9.94402i −0.847196 0.495347i
\(404\) 0 0
\(405\) 8.97859 5.18379i 0.446149 0.257585i
\(406\) 0 0
\(407\) 23.3783 40.4924i 1.15882 2.00713i
\(408\) 0 0
\(409\) −25.4829 14.7125i −1.26005 0.727489i −0.286964 0.957941i \(-0.592646\pi\)
−0.973083 + 0.230453i \(0.925979\pi\)
\(410\) 0 0
\(411\) 8.83157i 0.435629i
\(412\) 0 0
\(413\) −0.308581 0.534478i −0.0151843 0.0262999i
\(414\) 0 0
\(415\) 12.1286 0.595369
\(416\) 0 0
\(417\) 4.69683 0.230005
\(418\) 0 0
\(419\) 3.48397 + 6.03440i 0.170203 + 0.294800i 0.938491 0.345305i \(-0.112224\pi\)
−0.768288 + 0.640104i \(0.778891\pi\)
\(420\) 0 0
\(421\) 7.12125i 0.347069i 0.984828 + 0.173534i \(0.0555188\pi\)
−0.984828 + 0.173534i \(0.944481\pi\)
\(422\) 0 0
\(423\) −5.46171 3.15332i −0.265558 0.153320i
\(424\) 0 0
\(425\) 0.565928 0.980215i 0.0274515 0.0475474i
\(426\) 0 0
\(427\) 10.4767 6.04875i 0.507005 0.292720i
\(428\) 0 0
\(429\) 39.2433 22.3709i 1.89468 1.08008i
\(430\) 0 0
\(431\) −26.1664 + 15.1072i −1.26039 + 0.727687i −0.973150 0.230171i \(-0.926071\pi\)
−0.287241 + 0.957858i \(0.592738\pi\)
\(432\) 0 0
\(433\) 0.600065 1.03934i 0.0288373 0.0499476i −0.851247 0.524766i \(-0.824153\pi\)
0.880084 + 0.474818i \(0.157486\pi\)
\(434\) 0 0
\(435\) 0.0499450 + 0.0288357i 0.00239468 + 0.00138257i
\(436\) 0 0
\(437\) 8.82884i 0.422341i
\(438\) 0 0
\(439\) 8.27705 + 14.3363i 0.395042 + 0.684233i 0.993107 0.117215i \(-0.0373966\pi\)
−0.598064 + 0.801448i \(0.704063\pi\)
\(440\) 0 0
\(441\) −14.5421 −0.692481
\(442\) 0 0
\(443\) −4.55949 −0.216628 −0.108314 0.994117i \(-0.534545\pi\)
−0.108314 + 0.994117i \(0.534545\pi\)
\(444\) 0 0
\(445\) −8.07702 13.9898i −0.382887 0.663180i
\(446\) 0 0
\(447\) 12.8689i 0.608676i
\(448\) 0 0
\(449\) 11.9963 + 6.92608i 0.566142 + 0.326862i 0.755607 0.655025i \(-0.227342\pi\)
−0.189465 + 0.981887i \(0.560675\pi\)
\(450\) 0 0
\(451\) 10.0239 17.3620i 0.472009 0.817544i
\(452\) 0 0
\(453\) 9.87596 5.70189i 0.464013 0.267898i
\(454\) 0 0
\(455\) 6.42856 + 11.2771i 0.301376 + 0.528676i
\(456\) 0 0
\(457\) 34.7402 20.0573i 1.62508 0.938240i 0.639548 0.768751i \(-0.279122\pi\)
0.985532 0.169489i \(-0.0542117\pi\)
\(458\) 0 0
\(459\) −0.739961 + 1.28165i −0.0345384 + 0.0598223i
\(460\) 0 0
\(461\) 6.52897 + 3.76950i 0.304084 + 0.175563i 0.644276 0.764793i \(-0.277159\pi\)
−0.340192 + 0.940356i \(0.610492\pi\)
\(462\) 0 0
\(463\) 23.3031i 1.08299i 0.840705 + 0.541494i \(0.182141\pi\)
−0.840705 + 0.541494i \(0.817859\pi\)
\(464\) 0 0
\(465\) −6.37182 11.0363i −0.295486 0.511797i
\(466\) 0 0
\(467\) −22.6297 −1.04718 −0.523589 0.851971i \(-0.675407\pi\)
−0.523589 + 0.851971i \(0.675407\pi\)
\(468\) 0 0
\(469\) 23.0405 1.06391
\(470\) 0 0
\(471\) 11.7085 + 20.2797i 0.539500 + 0.934441i
\(472\) 0 0
\(473\) 6.08012i 0.279564i
\(474\) 0 0
\(475\) −1.96410 1.13397i −0.0901192 0.0520303i
\(476\) 0 0
\(477\) 5.41465 9.37844i 0.247920 0.429409i
\(478\) 0 0
\(479\) 17.8789 10.3224i 0.816910 0.471643i −0.0324399 0.999474i \(-0.510328\pi\)
0.849350 + 0.527831i \(0.176994\pi\)
\(480\) 0 0
\(481\) 0.172207 31.3825i 0.00785198 1.43092i
\(482\) 0 0
\(483\) 28.3075 16.3433i 1.28804 0.743648i
\(484\) 0 0
\(485\) −6.08408 + 10.5379i −0.276264 + 0.478503i
\(486\) 0 0
\(487\) 2.62929 + 1.51802i 0.119145 + 0.0687882i 0.558388 0.829580i \(-0.311420\pi\)
−0.439243 + 0.898368i \(0.644753\pi\)
\(488\) 0 0
\(489\) 15.8155i 0.715203i
\(490\) 0 0
\(491\) −5.33401 9.23877i −0.240720 0.416940i 0.720199 0.693767i \(-0.244050\pi\)
−0.960920 + 0.276827i \(0.910717\pi\)
\(492\) 0 0
\(493\) −0.0279884 −0.00126053
\(494\) 0 0
\(495\) 13.1039 0.588975
\(496\) 0 0
\(497\) 19.4362 + 33.6646i 0.871835 + 1.51006i
\(498\) 0 0
\(499\) 33.9143i 1.51821i −0.650966 0.759107i \(-0.725636\pi\)
0.650966 0.759107i \(-0.274364\pi\)
\(500\) 0 0
\(501\) 21.1872 + 12.2324i 0.946572 + 0.546504i
\(502\) 0 0
\(503\) −6.31380 + 10.9358i −0.281518 + 0.487604i −0.971759 0.235976i \(-0.924171\pi\)
0.690241 + 0.723580i \(0.257505\pi\)
\(504\) 0 0
\(505\) −3.51122 + 2.02721i −0.156247 + 0.0902095i
\(506\) 0 0
\(507\) 15.4468 26.0893i 0.686019 1.15866i
\(508\) 0 0
\(509\) −20.9168 + 12.0763i −0.927120 + 0.535273i −0.885899 0.463877i \(-0.846458\pi\)
−0.0412201 + 0.999150i \(0.513124\pi\)
\(510\) 0 0
\(511\) 8.46601 14.6636i 0.374514 0.648678i
\(512\) 0 0
\(513\) 2.56810 + 1.48269i 0.113384 + 0.0654625i
\(514\) 0 0
\(515\) 17.9035i 0.788921i
\(516\) 0 0
\(517\) 6.94402 + 12.0274i 0.305398 + 0.528964i
\(518\) 0 0
\(519\) −10.3982 −0.456431
\(520\) 0 0
\(521\) −24.7521 −1.08441 −0.542205 0.840246i \(-0.682410\pi\)
−0.542205 + 0.840246i \(0.682410\pi\)
\(522\) 0 0
\(523\) 18.5163 + 32.0712i 0.809662 + 1.40238i 0.913098 + 0.407739i \(0.133683\pi\)
−0.103436 + 0.994636i \(0.532984\pi\)
\(524\) 0 0
\(525\) 8.39654i 0.366455i
\(526\) 0 0
\(527\) 5.35600 + 3.09229i 0.233311 + 0.134702i
\(528\) 0 0
\(529\) 3.92277 6.79444i 0.170555 0.295410i
\(530\) 0 0
\(531\) −0.362145 + 0.209084i −0.0157157 + 0.00907348i
\(532\) 0 0
\(533\) 0.0738376 13.4559i 0.00319826 0.582840i
\(534\) 0 0
\(535\) −7.90842 + 4.56593i −0.341911 + 0.197402i
\(536\) 0 0
\(537\) 21.7264 37.6312i 0.937562 1.62391i
\(538\) 0 0
\(539\) 27.7332 + 16.0118i 1.19456 + 0.689677i
\(540\) 0 0
\(541\) 8.38144i 0.360346i 0.983635 + 0.180173i \(0.0576658\pi\)
−0.983635 + 0.180173i \(0.942334\pi\)
\(542\) 0 0
\(543\) −21.0952 36.5379i −0.905281 1.56799i
\(544\) 0 0
\(545\) 7.37605 0.315955
\(546\) 0 0
\(547\) 22.7842 0.974181 0.487091 0.873351i \(-0.338058\pi\)
0.487091 + 0.873351i \(0.338058\pi\)
\(548\) 0 0
\(549\) −4.09843 7.09870i −0.174917 0.302965i
\(550\) 0 0
\(551\) 0.0560816i 0.00238915i
\(552\) 0 0
\(553\) −37.3601 21.5699i −1.58871 0.917245i
\(554\) 0 0
\(555\) 10.1500 17.5803i 0.430844 0.746244i
\(556\) 0 0
\(557\) 24.3810 14.0764i 1.03306 0.596435i 0.115197 0.993343i \(-0.463250\pi\)
0.917858 + 0.396908i \(0.129917\pi\)
\(558\) 0 0
\(559\) −2.02106 3.54536i −0.0854816 0.149953i
\(560\) 0 0
\(561\) −12.2805 + 7.09017i −0.518484 + 0.299347i
\(562\) 0 0
\(563\) 9.06514 15.7013i 0.382050 0.661731i −0.609305 0.792936i \(-0.708551\pi\)
0.991355 + 0.131206i \(0.0418848\pi\)
\(564\) 0 0
\(565\) 6.12789 + 3.53794i 0.257802 + 0.148842i
\(566\) 0 0
\(567\) 37.3253i 1.56752i
\(568\) 0 0
\(569\) 20.2992 + 35.1593i 0.850988 + 1.47395i 0.880317 + 0.474385i \(0.157330\pi\)
−0.0293292 + 0.999570i \(0.509337\pi\)
\(570\) 0 0
\(571\) 24.7159 1.03433 0.517164 0.855886i \(-0.326988\pi\)
0.517164 + 0.855886i \(0.326988\pi\)
\(572\) 0 0
\(573\) 63.7551 2.66341
\(574\) 0 0
\(575\) −1.94644 3.37133i −0.0811720 0.140594i
\(576\) 0 0
\(577\) 23.0691i 0.960379i 0.877165 + 0.480189i \(0.159432\pi\)
−0.877165 + 0.480189i \(0.840568\pi\)
\(578\) 0 0
\(579\) −43.9654 25.3834i −1.82714 1.05490i
\(580\) 0 0
\(581\) 21.8327 37.8153i 0.905771 1.56884i
\(582\) 0 0
\(583\) −20.6525 + 11.9237i −0.855341 + 0.493831i
\(584\) 0 0
\(585\) 7.64096 4.35578i 0.315915 0.180089i
\(586\) 0 0
\(587\) 17.6256 10.1762i 0.727487 0.420015i −0.0900152 0.995940i \(-0.528692\pi\)
0.817502 + 0.575926i \(0.195358\pi\)
\(588\) 0 0
\(589\) 6.19615 10.7321i 0.255308 0.442206i
\(590\) 0 0
\(591\) −3.42701 1.97859i −0.140968 0.0813881i
\(592\) 0 0
\(593\) 10.3834i 0.426395i −0.977009 0.213198i \(-0.931612\pi\)
0.977009 0.213198i \(-0.0683878\pi\)
\(594\) 0 0
\(595\) −2.03745 3.52897i −0.0835273 0.144674i
\(596\) 0 0
\(597\) −59.0652 −2.41738
\(598\) 0 0
\(599\) 31.5965 1.29100 0.645499 0.763761i \(-0.276649\pi\)
0.645499 + 0.763761i \(0.276649\pi\)
\(600\) 0 0
\(601\) 21.9423 + 38.0051i 0.895044 + 1.55026i 0.833751 + 0.552141i \(0.186189\pi\)
0.0612928 + 0.998120i \(0.480478\pi\)
\(602\) 0 0
\(603\) 15.6115i 0.635750i
\(604\) 0 0
\(605\) −15.4641 8.92820i −0.628705 0.362983i
\(606\) 0 0
\(607\) 1.08770 1.88395i 0.0441484 0.0764673i −0.843107 0.537746i \(-0.819276\pi\)
0.887255 + 0.461279i \(0.152609\pi\)
\(608\) 0 0
\(609\) 0.179812 0.103814i 0.00728634 0.00420677i
\(610\) 0 0
\(611\) 8.04707 + 4.70504i 0.325550 + 0.190346i
\(612\) 0 0
\(613\) −12.7843 + 7.38100i −0.516352 + 0.298116i −0.735441 0.677589i \(-0.763025\pi\)
0.219089 + 0.975705i \(0.429691\pi\)
\(614\) 0 0
\(615\) 4.35203 7.53794i 0.175491 0.303959i
\(616\) 0 0
\(617\) 17.5779 + 10.1486i 0.707659 + 0.408567i 0.810194 0.586162i \(-0.199362\pi\)
−0.102535 + 0.994729i \(0.532695\pi\)
\(618\) 0 0
\(619\) 9.94207i 0.399605i 0.979836 + 0.199803i \(0.0640301\pi\)
−0.979836 + 0.199803i \(0.935970\pi\)
\(620\) 0 0
\(621\) 2.54500 + 4.40807i 0.102127 + 0.176890i
\(622\) 0 0
\(623\) −58.1577 −2.33004
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 14.2069 + 24.6070i 0.567368 + 0.982711i
\(628\) 0 0
\(629\) 9.85174i 0.392815i
\(630\) 0 0
\(631\) −0.843006 0.486710i −0.0335596 0.0193756i 0.483126 0.875551i \(-0.339501\pi\)
−0.516686 + 0.856175i \(0.672835\pi\)
\(632\) 0 0
\(633\) 0.391243 0.677652i 0.0155505 0.0269342i
\(634\) 0 0
\(635\) 9.90396 5.71806i 0.393027 0.226914i
\(636\) 0 0
\(637\) 21.4938 + 0.117945i 0.851617 + 0.00467314i
\(638\) 0 0
\(639\) 22.8100 13.1694i 0.902350 0.520972i
\(640\) 0 0
\(641\) −6.31047 + 10.9301i −0.249249 + 0.431711i −0.963318 0.268364i \(-0.913517\pi\)
0.714069 + 0.700075i \(0.246850\pi\)
\(642\) 0 0
\(643\) 8.62599 + 4.98022i 0.340176 + 0.196401i 0.660350 0.750958i \(-0.270408\pi\)
−0.320174 + 0.947359i \(0.603741\pi\)
\(644\) 0 0
\(645\) 2.63977i 0.103941i
\(646\) 0 0
\(647\) 18.1381 + 31.4162i 0.713084 + 1.23510i 0.963694 + 0.267009i \(0.0860354\pi\)
−0.250610 + 0.968088i \(0.580631\pi\)
\(648\) 0 0
\(649\) 0.920861 0.0361470
\(650\) 0 0
\(651\) −45.8796 −1.79816
\(652\) 0 0
\(653\) −6.87769 11.9125i −0.269145 0.466172i 0.699497 0.714636i \(-0.253408\pi\)
−0.968641 + 0.248464i \(0.920074\pi\)
\(654\) 0 0
\(655\) 10.5680i 0.412925i
\(656\) 0 0
\(657\) −9.93555 5.73629i −0.387623 0.223794i
\(658\) 0 0
\(659\) −1.29092 + 2.23593i −0.0502869 + 0.0870995i −0.890073 0.455818i \(-0.849347\pi\)
0.839786 + 0.542917i \(0.182680\pi\)
\(660\) 0 0
\(661\) −21.5437 + 12.4382i −0.837951 + 0.483791i −0.856567 0.516036i \(-0.827407\pi\)
0.0186163 + 0.999827i \(0.494074\pi\)
\(662\) 0 0
\(663\) −4.80406 + 8.21643i −0.186574 + 0.319100i
\(664\) 0 0
\(665\) −7.07115 + 4.08253i −0.274207 + 0.158314i
\(666\) 0 0
\(667\) −0.0481312 + 0.0833657i −0.00186365 + 0.00322793i
\(668\) 0 0
\(669\) 24.8368 + 14.3395i 0.960246 + 0.554398i
\(670\) 0 0
\(671\) 18.0506i 0.696834i
\(672\) 0 0
\(673\) 21.6611 + 37.5181i 0.834974 + 1.44622i 0.894052 + 0.447964i \(0.147851\pi\)
−0.0590774 + 0.998253i \(0.518816\pi\)
\(674\) 0 0
\(675\) −1.30752 −0.0503264
\(676\) 0 0
\(677\) −41.3625 −1.58969 −0.794845 0.606813i \(-0.792448\pi\)
−0.794845 + 0.606813i \(0.792448\pi\)
\(678\) 0 0
\(679\) 21.9039 + 37.9386i 0.840594 + 1.45595i
\(680\) 0 0
\(681\) 17.8003i 0.682110i
\(682\) 0 0
\(683\) −2.27495 1.31344i −0.0870484 0.0502574i 0.455844 0.890060i \(-0.349338\pi\)
−0.542892 + 0.839802i \(0.682671\pi\)
\(684\) 0 0
\(685\) 1.89336 3.27940i 0.0723416 0.125299i
\(686\) 0 0
\(687\) −29.0865 + 16.7931i −1.10972 + 0.640696i
\(688\) 0 0
\(689\) −8.07914 + 13.8178i −0.307791 + 0.526417i
\(690\) 0 0
\(691\) 13.2288 7.63765i 0.503247 0.290550i −0.226806 0.973940i \(-0.572828\pi\)
0.730053 + 0.683390i \(0.239495\pi\)
\(692\) 0 0
\(693\) 23.5882 40.8560i 0.896043 1.55199i
\(694\) 0 0
\(695\) −1.74406 1.00693i −0.0661558 0.0381951i
\(696\) 0 0
\(697\) 4.22414i 0.160001i
\(698\) 0 0
\(699\) −11.0737 19.1802i −0.418846 0.725463i
\(700\) 0 0
\(701\) 48.1947 1.82029 0.910144 0.414292i \(-0.135971\pi\)
0.910144 + 0.414292i \(0.135971\pi\)
\(702\) 0 0
\(703\) 19.7404 0.744522
\(704\) 0 0
\(705\) 3.01484 + 5.22186i 0.113546 + 0.196667i
\(706\) 0 0
\(707\) 14.5967i 0.548964i
\(708\) 0 0
\(709\) −33.6624 19.4350i −1.26422 0.729896i −0.290329 0.956927i \(-0.593765\pi\)
−0.973887 + 0.227031i \(0.927098\pi\)
\(710\) 0 0
\(711\) −14.6150 + 25.3140i −0.548107 + 0.949349i
\(712\) 0 0
\(713\) 18.4213 10.6355i 0.689882 0.398304i
\(714\) 0 0
\(715\) −19.3681 0.106280i −0.724325 0.00397464i
\(716\) 0 0
\(717\) −40.2227 + 23.2226i −1.50214 + 0.867263i
\(718\) 0 0
\(719\) −3.30830 + 5.73015i −0.123379 + 0.213698i −0.921098 0.389331i \(-0.872706\pi\)
0.797719 + 0.603029i \(0.206040\pi\)
\(720\) 0 0
\(721\) 55.8205 + 32.2280i 2.07887 + 1.20023i
\(722\) 0 0
\(723\) 54.2629i 2.01806i
\(724\) 0 0
\(725\) −0.0123639 0.0214150i −0.000459185 0.000795332i
\(726\) 0 0
\(727\) −18.3735 −0.681435 −0.340717 0.940166i \(-0.610670\pi\)
−0.340717 + 0.940166i \(0.610670\pi\)
\(728\) 0 0
\(729\) −16.1420 −0.597853
\(730\) 0 0
\(731\) 0.640548 + 1.10946i 0.0236915 + 0.0410349i
\(732\) 0 0
\(733\) 0.791131i 0.0292211i 0.999893 + 0.0146105i \(0.00465084\pi\)
−0.999893 + 0.0146105i \(0.995349\pi\)
\(734\) 0 0
\(735\) 12.0408 + 6.95174i 0.444130 + 0.256419i
\(736\) 0 0
\(737\) −17.1893 + 29.7727i −0.633175 + 1.09669i
\(738\) 0 0
\(739\) 27.0073 15.5926i 0.993478 0.573585i 0.0871658 0.996194i \(-0.472219\pi\)
0.906312 + 0.422609i \(0.138886\pi\)
\(740\) 0 0
\(741\) 16.4636 + 9.62612i 0.604806 + 0.353624i
\(742\) 0 0
\(743\) −4.81773 + 2.78152i −0.176745 + 0.102044i −0.585763 0.810483i \(-0.699205\pi\)
0.409017 + 0.912527i \(0.365872\pi\)
\(744\) 0 0
\(745\) 2.75890 4.77855i 0.101078 0.175073i
\(746\) 0 0
\(747\) −25.6224 14.7931i −0.937474 0.541251i
\(748\) 0 0
\(749\) 32.8765i 1.20128i
\(750\) 0 0
\(751\) 17.6048 + 30.4925i 0.642410 + 1.11269i 0.984893 + 0.173163i \(0.0553987\pi\)
−0.342483 + 0.939524i \(0.611268\pi\)
\(752\) 0 0
\(753\) −27.6142 −1.00632
\(754\) 0 0
\(755\) −4.88961 −0.177951
\(756\) 0 0
\(757\) −25.0223 43.3399i −0.909451 1.57522i −0.814828 0.579703i \(-0.803169\pi\)
−0.0946237 0.995513i \(-0.530165\pi\)
\(758\) 0 0
\(759\) 48.7715i 1.77029i
\(760\) 0 0
\(761\) 38.8161 + 22.4105i 1.40708 + 0.812379i 0.995106 0.0988165i \(-0.0315057\pi\)
0.411975 + 0.911195i \(0.364839\pi\)
\(762\) 0 0
\(763\) 13.2776 22.9975i 0.480682 0.832566i
\(764\) 0 0
\(765\) −2.39111 + 1.38051i −0.0864508 + 0.0499124i
\(766\) 0 0
\(767\) 0.536961 0.306098i 0.0193885 0.0110526i
\(768\) 0 0
\(769\) −34.0897 + 19.6817i −1.22930 + 0.709739i −0.966884 0.255215i \(-0.917854\pi\)
−0.262420 + 0.964954i \(0.584521\pi\)
\(770\) 0 0
\(771\) 6.47201 11.2099i 0.233084 0.403713i
\(772\) 0 0
\(773\) −42.2452 24.3902i −1.51945 0.877256i −0.999737 0.0229167i \(-0.992705\pi\)
−0.519715 0.854340i \(-0.673962\pi\)
\(774\) 0 0
\(775\) 5.46410i 0.196276i
\(776\) 0 0
\(777\) −36.5420 63.2926i −1.31094 2.27061i
\(778\) 0 0
\(779\) 8.46410 0.303258
\(780\) 0 0
\(781\) −58.0013 −2.07545
\(782\) 0 0
\(783\) 0.0161661 + 0.0280005i 0.000577728 + 0.00100066i
\(784\) 0 0
\(785\) 10.0405i 0.358363i
\(786\) 0 0
\(787\) −34.5204 19.9304i −1.23052 0.710442i −0.263382 0.964692i \(-0.584838\pi\)
−0.967139 + 0.254250i \(0.918171\pi\)
\(788\) 0 0
\(789\) −7.99922 + 13.8551i −0.284780 + 0.493253i
\(790\) 0 0
\(791\) 22.0616 12.7373i 0.784420 0.452885i
\(792\) 0 0
\(793\) 6.00008 + 10.5254i 0.213069 + 0.373768i
\(794\) 0 0
\(795\) −8.96658 + 5.17686i −0.318012 + 0.183604i
\(796\) 0 0
\(797\)