Properties

Label 245.2.e.g.116.2
Level $245$
Weight $2$
Character 245.116
Analytic conductor $1.956$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 245.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.95633484952\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 116.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 245.116
Dual form 245.2.e.g.226.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 1.22474i) q^{2} +(-0.207107 + 0.358719i) q^{3} +(0.500000 + 0.866025i) q^{5} -0.585786 q^{6} +2.82843 q^{8} +(1.41421 + 2.44949i) q^{9} +O(q^{10})\) \(q+(0.707107 + 1.22474i) q^{2} +(-0.207107 + 0.358719i) q^{3} +(0.500000 + 0.866025i) q^{5} -0.585786 q^{6} +2.82843 q^{8} +(1.41421 + 2.44949i) q^{9} +(-0.707107 + 1.22474i) q^{10} +(0.0857864 - 0.148586i) q^{11} -4.41421 q^{13} -0.414214 q^{15} +(2.00000 + 3.46410i) q^{16} +(1.62132 - 2.80821i) q^{17} +(-2.00000 + 3.46410i) q^{18} +(3.00000 + 5.19615i) q^{19} +0.242641 q^{22} +(-3.70711 - 6.42090i) q^{23} +(-0.585786 + 1.01461i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-3.12132 - 5.40629i) q^{26} -2.41421 q^{27} -8.65685 q^{29} +(-0.292893 - 0.507306i) q^{30} +(5.12132 - 8.87039i) q^{31} +(0.0355339 + 0.0615465i) q^{33} +4.58579 q^{34} +(-1.12132 - 1.94218i) q^{37} +(-4.24264 + 7.34847i) q^{38} +(0.914214 - 1.58346i) q^{39} +(1.41421 + 2.44949i) q^{40} +6.24264 q^{41} +2.00000 q^{43} +(-1.41421 + 2.44949i) q^{45} +(5.24264 - 9.08052i) q^{46} +(-3.62132 - 6.27231i) q^{47} -1.65685 q^{48} -1.41421 q^{50} +(0.671573 + 1.16320i) q^{51} +(-2.12132 + 3.67423i) q^{53} +(-1.70711 - 2.95680i) q^{54} +0.171573 q^{55} -2.48528 q^{57} +(-6.12132 - 10.6024i) q^{58} +(-1.12132 + 1.94218i) q^{59} +(-1.41421 - 2.44949i) q^{61} +14.4853 q^{62} +8.00000 q^{64} +(-2.20711 - 3.82282i) q^{65} +(-0.0502525 + 0.0870399i) q^{66} +(4.12132 - 7.13834i) q^{67} +3.07107 q^{69} -3.17157 q^{71} +(4.00000 + 6.92820i) q^{72} +(-4.24264 + 7.34847i) q^{73} +(1.58579 - 2.74666i) q^{74} +(-0.207107 - 0.358719i) q^{75} +2.58579 q^{78} +(-0.742641 - 1.28629i) q^{79} +(-2.00000 + 3.46410i) q^{80} +(-3.74264 + 6.48244i) q^{81} +(4.41421 + 7.64564i) q^{82} +3.24264 q^{85} +(1.41421 + 2.44949i) q^{86} +(1.79289 - 3.10538i) q^{87} +(0.242641 - 0.420266i) q^{88} +(-4.00000 - 6.92820i) q^{89} -4.00000 q^{90} +(2.12132 + 3.67423i) q^{93} +(5.12132 - 8.87039i) q^{94} +(-3.00000 + 5.19615i) q^{95} -13.2426 q^{97} +0.485281 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{3} + 2q^{5} - 8q^{6} + O(q^{10}) \) \( 4q + 2q^{3} + 2q^{5} - 8q^{6} + 6q^{11} - 12q^{13} + 4q^{15} + 8q^{16} - 2q^{17} - 8q^{18} + 12q^{19} - 16q^{22} - 12q^{23} - 8q^{24} - 2q^{25} - 4q^{26} - 4q^{27} - 12q^{29} - 4q^{30} + 12q^{31} - 14q^{33} + 24q^{34} + 4q^{37} - 2q^{39} + 8q^{41} + 8q^{43} + 4q^{46} - 6q^{47} + 16q^{48} + 14q^{51} - 4q^{54} + 12q^{55} + 24q^{57} - 16q^{58} + 4q^{59} + 24q^{62} + 32q^{64} - 6q^{65} - 20q^{66} + 8q^{67} - 16q^{69} - 24q^{71} + 16q^{72} + 12q^{74} + 2q^{75} + 16q^{78} + 14q^{79} - 8q^{80} + 2q^{81} + 12q^{82} - 4q^{85} + 10q^{87} - 16q^{88} - 16q^{89} - 16q^{90} + 12q^{94} - 12q^{95} - 36q^{97} - 32q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 1.22474i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(3\) −0.207107 + 0.358719i −0.119573 + 0.207107i −0.919599 0.392859i \(-0.871486\pi\)
0.800025 + 0.599966i \(0.204819\pi\)
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) −0.585786 −0.239146
\(7\) 0 0
\(8\) 2.82843 1.00000
\(9\) 1.41421 + 2.44949i 0.471405 + 0.816497i
\(10\) −0.707107 + 1.22474i −0.223607 + 0.387298i
\(11\) 0.0857864 0.148586i 0.0258656 0.0448005i −0.852803 0.522233i \(-0.825099\pi\)
0.878668 + 0.477432i \(0.158432\pi\)
\(12\) 0 0
\(13\) −4.41421 −1.22428 −0.612141 0.790748i \(-0.709692\pi\)
−0.612141 + 0.790748i \(0.709692\pi\)
\(14\) 0 0
\(15\) −0.414214 −0.106949
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 1.62132 2.80821i 0.393228 0.681091i −0.599645 0.800266i \(-0.704692\pi\)
0.992873 + 0.119175i \(0.0380250\pi\)
\(18\) −2.00000 + 3.46410i −0.471405 + 0.816497i
\(19\) 3.00000 + 5.19615i 0.688247 + 1.19208i 0.972404 + 0.233301i \(0.0749529\pi\)
−0.284157 + 0.958778i \(0.591714\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.242641 0.0517312
\(23\) −3.70711 6.42090i −0.772985 1.33885i −0.935920 0.352213i \(-0.885429\pi\)
0.162935 0.986637i \(-0.447904\pi\)
\(24\) −0.585786 + 1.01461i −0.119573 + 0.207107i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −3.12132 5.40629i −0.612141 1.06026i
\(27\) −2.41421 −0.464616
\(28\) 0 0
\(29\) −8.65685 −1.60754 −0.803769 0.594942i \(-0.797175\pi\)
−0.803769 + 0.594942i \(0.797175\pi\)
\(30\) −0.292893 0.507306i −0.0534747 0.0926210i
\(31\) 5.12132 8.87039i 0.919816 1.59317i 0.120124 0.992759i \(-0.461671\pi\)
0.799693 0.600410i \(-0.204996\pi\)
\(32\) 0 0
\(33\) 0.0355339 + 0.0615465i 0.00618566 + 0.0107139i
\(34\) 4.58579 0.786456
\(35\) 0 0
\(36\) 0 0
\(37\) −1.12132 1.94218i −0.184344 0.319293i 0.759011 0.651077i \(-0.225683\pi\)
−0.943355 + 0.331784i \(0.892349\pi\)
\(38\) −4.24264 + 7.34847i −0.688247 + 1.19208i
\(39\) 0.914214 1.58346i 0.146391 0.253557i
\(40\) 1.41421 + 2.44949i 0.223607 + 0.387298i
\(41\) 6.24264 0.974937 0.487468 0.873141i \(-0.337920\pi\)
0.487468 + 0.873141i \(0.337920\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 0 0
\(45\) −1.41421 + 2.44949i −0.210819 + 0.365148i
\(46\) 5.24264 9.08052i 0.772985 1.33885i
\(47\) −3.62132 6.27231i −0.528224 0.914911i −0.999459 0.0329027i \(-0.989525\pi\)
0.471235 0.882008i \(-0.343808\pi\)
\(48\) −1.65685 −0.239146
\(49\) 0 0
\(50\) −1.41421 −0.200000
\(51\) 0.671573 + 1.16320i 0.0940390 + 0.162880i
\(52\) 0 0
\(53\) −2.12132 + 3.67423i −0.291386 + 0.504695i −0.974138 0.225955i \(-0.927450\pi\)
0.682752 + 0.730650i \(0.260783\pi\)
\(54\) −1.70711 2.95680i −0.232308 0.402369i
\(55\) 0.171573 0.0231349
\(56\) 0 0
\(57\) −2.48528 −0.329184
\(58\) −6.12132 10.6024i −0.803769 1.39217i
\(59\) −1.12132 + 1.94218i −0.145983 + 0.252851i −0.929739 0.368218i \(-0.879968\pi\)
0.783756 + 0.621069i \(0.213301\pi\)
\(60\) 0 0
\(61\) −1.41421 2.44949i −0.181071 0.313625i 0.761174 0.648547i \(-0.224623\pi\)
−0.942246 + 0.334922i \(0.891290\pi\)
\(62\) 14.4853 1.83963
\(63\) 0 0
\(64\) 8.00000 1.00000
\(65\) −2.20711 3.82282i −0.273758 0.474163i
\(66\) −0.0502525 + 0.0870399i −0.00618566 + 0.0107139i
\(67\) 4.12132 7.13834i 0.503499 0.872087i −0.496492 0.868041i \(-0.665379\pi\)
0.999992 0.00404550i \(-0.00128773\pi\)
\(68\) 0 0
\(69\) 3.07107 0.369713
\(70\) 0 0
\(71\) −3.17157 −0.376396 −0.188198 0.982131i \(-0.560265\pi\)
−0.188198 + 0.982131i \(0.560265\pi\)
\(72\) 4.00000 + 6.92820i 0.471405 + 0.816497i
\(73\) −4.24264 + 7.34847i −0.496564 + 0.860073i −0.999992 0.00396356i \(-0.998738\pi\)
0.503429 + 0.864037i \(0.332072\pi\)
\(74\) 1.58579 2.74666i 0.184344 0.319293i
\(75\) −0.207107 0.358719i −0.0239146 0.0414214i
\(76\) 0 0
\(77\) 0 0
\(78\) 2.58579 0.292783
\(79\) −0.742641 1.28629i −0.0835536 0.144719i 0.821220 0.570611i \(-0.193294\pi\)
−0.904774 + 0.425892i \(0.859960\pi\)
\(80\) −2.00000 + 3.46410i −0.223607 + 0.387298i
\(81\) −3.74264 + 6.48244i −0.415849 + 0.720272i
\(82\) 4.41421 + 7.64564i 0.487468 + 0.844320i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 3.24264 0.351714
\(86\) 1.41421 + 2.44949i 0.152499 + 0.264135i
\(87\) 1.79289 3.10538i 0.192218 0.332932i
\(88\) 0.242641 0.420266i 0.0258656 0.0448005i
\(89\) −4.00000 6.92820i −0.423999 0.734388i 0.572327 0.820025i \(-0.306041\pi\)
−0.996326 + 0.0856373i \(0.972707\pi\)
\(90\) −4.00000 −0.421637
\(91\) 0 0
\(92\) 0 0
\(93\) 2.12132 + 3.67423i 0.219971 + 0.381000i
\(94\) 5.12132 8.87039i 0.528224 0.914911i
\(95\) −3.00000 + 5.19615i −0.307794 + 0.533114i
\(96\) 0 0
\(97\) −13.2426 −1.34459 −0.672293 0.740285i \(-0.734691\pi\)
−0.672293 + 0.740285i \(0.734691\pi\)
\(98\) 0 0
\(99\) 0.485281 0.0487726
\(100\) 0 0
\(101\) 1.24264 2.15232i 0.123647 0.214164i −0.797556 0.603245i \(-0.793874\pi\)
0.921203 + 0.389081i \(0.127208\pi\)
\(102\) −0.949747 + 1.64501i −0.0940390 + 0.162880i
\(103\) 9.62132 + 16.6646i 0.948017 + 1.64201i 0.749595 + 0.661897i \(0.230248\pi\)
0.198422 + 0.980117i \(0.436418\pi\)
\(104\) −12.4853 −1.22428
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 1.24264 + 2.15232i 0.120131 + 0.208072i 0.919819 0.392343i \(-0.128335\pi\)
−0.799688 + 0.600415i \(0.795002\pi\)
\(108\) 0 0
\(109\) −2.50000 + 4.33013i −0.239457 + 0.414751i −0.960558 0.278078i \(-0.910303\pi\)
0.721102 + 0.692829i \(0.243636\pi\)
\(110\) 0.121320 + 0.210133i 0.0115674 + 0.0200354i
\(111\) 0.928932 0.0881703
\(112\) 0 0
\(113\) −13.0711 −1.22962 −0.614811 0.788674i \(-0.710768\pi\)
−0.614811 + 0.788674i \(0.710768\pi\)
\(114\) −1.75736 3.04384i −0.164592 0.285081i
\(115\) 3.70711 6.42090i 0.345689 0.598752i
\(116\) 0 0
\(117\) −6.24264 10.8126i −0.577132 0.999623i
\(118\) −3.17157 −0.291967
\(119\) 0 0
\(120\) −1.17157 −0.106949
\(121\) 5.48528 + 9.50079i 0.498662 + 0.863708i
\(122\) 2.00000 3.46410i 0.181071 0.313625i
\(123\) −1.29289 + 2.23936i −0.116576 + 0.201916i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 8.24264 0.731416 0.365708 0.930730i \(-0.380827\pi\)
0.365708 + 0.930730i \(0.380827\pi\)
\(128\) 5.65685 + 9.79796i 0.500000 + 0.866025i
\(129\) −0.414214 + 0.717439i −0.0364695 + 0.0631670i
\(130\) 3.12132 5.40629i 0.273758 0.474163i
\(131\) 6.12132 + 10.6024i 0.534822 + 0.926339i 0.999172 + 0.0406873i \(0.0129548\pi\)
−0.464350 + 0.885652i \(0.653712\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 11.6569 1.00700
\(135\) −1.20711 2.09077i −0.103891 0.179945i
\(136\) 4.58579 7.94282i 0.393228 0.681091i
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) 2.17157 + 3.76127i 0.184857 + 0.320181i
\(139\) −7.75736 −0.657971 −0.328985 0.944335i \(-0.606707\pi\)
−0.328985 + 0.944335i \(0.606707\pi\)
\(140\) 0 0
\(141\) 3.00000 0.252646
\(142\) −2.24264 3.88437i −0.188198 0.325969i
\(143\) −0.378680 + 0.655892i −0.0316668 + 0.0548485i
\(144\) −5.65685 + 9.79796i −0.471405 + 0.816497i
\(145\) −4.32843 7.49706i −0.359456 0.622597i
\(146\) −12.0000 −0.993127
\(147\) 0 0
\(148\) 0 0
\(149\) 4.58579 + 7.94282i 0.375682 + 0.650701i 0.990429 0.138024i \(-0.0440751\pi\)
−0.614747 + 0.788725i \(0.710742\pi\)
\(150\) 0.292893 0.507306i 0.0239146 0.0414214i
\(151\) 3.74264 6.48244i 0.304572 0.527534i −0.672594 0.740012i \(-0.734820\pi\)
0.977166 + 0.212478i \(0.0681533\pi\)
\(152\) 8.48528 + 14.6969i 0.688247 + 1.19208i
\(153\) 9.17157 0.741478
\(154\) 0 0
\(155\) 10.2426 0.822709
\(156\) 0 0
\(157\) −7.58579 + 13.1390i −0.605412 + 1.04860i 0.386575 + 0.922258i \(0.373658\pi\)
−0.991986 + 0.126346i \(0.959675\pi\)
\(158\) 1.05025 1.81909i 0.0835536 0.144719i
\(159\) −0.878680 1.52192i −0.0696838 0.120696i
\(160\) 0 0
\(161\) 0 0
\(162\) −10.5858 −0.831698
\(163\) 5.12132 + 8.87039i 0.401133 + 0.694782i 0.993863 0.110619i \(-0.0352833\pi\)
−0.592730 + 0.805401i \(0.701950\pi\)
\(164\) 0 0
\(165\) −0.0355339 + 0.0615465i −0.00276631 + 0.00479139i
\(166\) 0 0
\(167\) −0.757359 −0.0586062 −0.0293031 0.999571i \(-0.509329\pi\)
−0.0293031 + 0.999571i \(0.509329\pi\)
\(168\) 0 0
\(169\) 6.48528 0.498868
\(170\) 2.29289 + 3.97141i 0.175857 + 0.304593i
\(171\) −8.48528 + 14.6969i −0.648886 + 1.12390i
\(172\) 0 0
\(173\) −3.62132 6.27231i −0.275324 0.476875i 0.694893 0.719113i \(-0.255452\pi\)
−0.970217 + 0.242238i \(0.922118\pi\)
\(174\) 5.07107 0.384437
\(175\) 0 0
\(176\) 0.686292 0.0517312
\(177\) −0.464466 0.804479i −0.0349114 0.0604683i
\(178\) 5.65685 9.79796i 0.423999 0.734388i
\(179\) 7.24264 12.5446i 0.541340 0.937629i −0.457487 0.889216i \(-0.651250\pi\)
0.998827 0.0484128i \(-0.0154163\pi\)
\(180\) 0 0
\(181\) 18.7279 1.39204 0.696018 0.718025i \(-0.254953\pi\)
0.696018 + 0.718025i \(0.254953\pi\)
\(182\) 0 0
\(183\) 1.17157 0.0866052
\(184\) −10.4853 18.1610i −0.772985 1.33885i
\(185\) 1.12132 1.94218i 0.0824411 0.142792i
\(186\) −3.00000 + 5.19615i −0.219971 + 0.381000i
\(187\) −0.278175 0.481813i −0.0203421 0.0352336i
\(188\) 0 0
\(189\) 0 0
\(190\) −8.48528 −0.615587
\(191\) −6.98528 12.0989i −0.505437 0.875443i −0.999980 0.00628978i \(-0.997998\pi\)
0.494543 0.869153i \(-0.335335\pi\)
\(192\) −1.65685 + 2.86976i −0.119573 + 0.207107i
\(193\) 8.00000 13.8564i 0.575853 0.997406i −0.420096 0.907480i \(-0.638004\pi\)
0.995948 0.0899262i \(-0.0286631\pi\)
\(194\) −9.36396 16.2189i −0.672293 1.16445i
\(195\) 1.82843 0.130936
\(196\) 0 0
\(197\) 13.4142 0.955723 0.477862 0.878435i \(-0.341412\pi\)
0.477862 + 0.878435i \(0.341412\pi\)
\(198\) 0.343146 + 0.594346i 0.0243863 + 0.0422383i
\(199\) −3.70711 + 6.42090i −0.262790 + 0.455165i −0.966982 0.254844i \(-0.917976\pi\)
0.704192 + 0.710009i \(0.251309\pi\)
\(200\) −1.41421 + 2.44949i −0.100000 + 0.173205i
\(201\) 1.70711 + 2.95680i 0.120410 + 0.208556i
\(202\) 3.51472 0.247295
\(203\) 0 0
\(204\) 0 0
\(205\) 3.12132 + 5.40629i 0.218002 + 0.377591i
\(206\) −13.6066 + 23.5673i −0.948017 + 1.64201i
\(207\) 10.4853 18.1610i 0.728777 1.26228i
\(208\) −8.82843 15.2913i −0.612141 1.06026i
\(209\) 1.02944 0.0712077
\(210\) 0 0
\(211\) 9.00000 0.619586 0.309793 0.950804i \(-0.399740\pi\)
0.309793 + 0.950804i \(0.399740\pi\)
\(212\) 0 0
\(213\) 0.656854 1.13770i 0.0450069 0.0779543i
\(214\) −1.75736 + 3.04384i −0.120131 + 0.208072i
\(215\) 1.00000 + 1.73205i 0.0681994 + 0.118125i
\(216\) −6.82843 −0.464616
\(217\) 0 0
\(218\) −7.07107 −0.478913
\(219\) −1.75736 3.04384i −0.118751 0.205683i
\(220\) 0 0
\(221\) −7.15685 + 12.3960i −0.481422 + 0.833848i
\(222\) 0.656854 + 1.13770i 0.0440852 + 0.0763578i
\(223\) 24.2132 1.62144 0.810718 0.585437i \(-0.199077\pi\)
0.810718 + 0.585437i \(0.199077\pi\)
\(224\) 0 0
\(225\) −2.82843 −0.188562
\(226\) −9.24264 16.0087i −0.614811 1.06488i
\(227\) 7.86396 13.6208i 0.521949 0.904043i −0.477725 0.878510i \(-0.658538\pi\)
0.999674 0.0255332i \(-0.00812837\pi\)
\(228\) 0 0
\(229\) 9.02082 + 15.6245i 0.596112 + 1.03250i 0.993389 + 0.114798i \(0.0366220\pi\)
−0.397277 + 0.917699i \(0.630045\pi\)
\(230\) 10.4853 0.691379
\(231\) 0 0
\(232\) −24.4853 −1.60754
\(233\) 4.58579 + 7.94282i 0.300425 + 0.520351i 0.976232 0.216727i \(-0.0695382\pi\)
−0.675807 + 0.737078i \(0.736205\pi\)
\(234\) 8.82843 15.2913i 0.577132 0.999623i
\(235\) 3.62132 6.27231i 0.236229 0.409160i
\(236\) 0 0
\(237\) 0.615224 0.0399631
\(238\) 0 0
\(239\) −17.4853 −1.13103 −0.565514 0.824738i \(-0.691322\pi\)
−0.565514 + 0.824738i \(0.691322\pi\)
\(240\) −0.828427 1.43488i −0.0534747 0.0926210i
\(241\) −0.363961 + 0.630399i −0.0234448 + 0.0406076i −0.877510 0.479559i \(-0.840797\pi\)
0.854065 + 0.520166i \(0.174130\pi\)
\(242\) −7.75736 + 13.4361i −0.498662 + 0.863708i
\(243\) −5.17157 8.95743i −0.331757 0.574619i
\(244\) 0 0
\(245\) 0 0
\(246\) −3.65685 −0.233153
\(247\) −13.2426 22.9369i −0.842609 1.45944i
\(248\) 14.4853 25.0892i 0.919816 1.59317i
\(249\) 0 0
\(250\) −0.707107 1.22474i −0.0447214 0.0774597i
\(251\) −17.2132 −1.08649 −0.543244 0.839575i \(-0.682804\pi\)
−0.543244 + 0.839575i \(0.682804\pi\)
\(252\) 0 0
\(253\) −1.27208 −0.0799749
\(254\) 5.82843 + 10.0951i 0.365708 + 0.633425i
\(255\) −0.671573 + 1.16320i −0.0420555 + 0.0728423i
\(256\) 0 0
\(257\) −4.75736 8.23999i −0.296756 0.513996i 0.678636 0.734475i \(-0.262571\pi\)
−0.975392 + 0.220479i \(0.929238\pi\)
\(258\) −1.17157 −0.0729389
\(259\) 0 0
\(260\) 0 0
\(261\) −12.2426 21.2049i −0.757800 1.31255i
\(262\) −8.65685 + 14.9941i −0.534822 + 0.926339i
\(263\) 8.31371 14.3998i 0.512645 0.887928i −0.487247 0.873264i \(-0.661999\pi\)
0.999892 0.0146635i \(-0.00466771\pi\)
\(264\) 0.100505 + 0.174080i 0.00618566 + 0.0107139i
\(265\) −4.24264 −0.260623
\(266\) 0 0
\(267\) 3.31371 0.202796
\(268\) 0 0
\(269\) −8.12132 + 14.0665i −0.495166 + 0.857652i −0.999984 0.00557327i \(-0.998226\pi\)
0.504819 + 0.863225i \(0.331559\pi\)
\(270\) 1.70711 2.95680i 0.103891 0.179945i
\(271\) −0.343146 0.594346i −0.0208446 0.0361039i 0.855415 0.517943i \(-0.173302\pi\)
−0.876260 + 0.481839i \(0.839969\pi\)
\(272\) 12.9706 0.786456
\(273\) 0 0
\(274\) −16.9706 −1.02523
\(275\) 0.0857864 + 0.148586i 0.00517312 + 0.00896010i
\(276\) 0 0
\(277\) −7.60660 + 13.1750i −0.457036 + 0.791610i −0.998803 0.0489189i \(-0.984422\pi\)
0.541766 + 0.840529i \(0.317756\pi\)
\(278\) −5.48528 9.50079i −0.328985 0.569819i
\(279\) 28.9706 1.73442
\(280\) 0 0
\(281\) 2.31371 0.138024 0.0690121 0.997616i \(-0.478015\pi\)
0.0690121 + 0.997616i \(0.478015\pi\)
\(282\) 2.12132 + 3.67423i 0.126323 + 0.218797i
\(283\) 12.2782 21.2664i 0.729862 1.26416i −0.227080 0.973876i \(-0.572918\pi\)
0.956941 0.290281i \(-0.0937489\pi\)
\(284\) 0 0
\(285\) −1.24264 2.15232i −0.0736077 0.127492i
\(286\) −1.07107 −0.0633336
\(287\) 0 0
\(288\) 0 0
\(289\) 3.24264 + 5.61642i 0.190744 + 0.330378i
\(290\) 6.12132 10.6024i 0.359456 0.622597i
\(291\) 2.74264 4.75039i 0.160776 0.278473i
\(292\) 0 0
\(293\) −25.7279 −1.50304 −0.751521 0.659710i \(-0.770679\pi\)
−0.751521 + 0.659710i \(0.770679\pi\)
\(294\) 0 0
\(295\) −2.24264 −0.130572
\(296\) −3.17157 5.49333i −0.184344 0.319293i
\(297\) −0.207107 + 0.358719i −0.0120176 + 0.0208150i
\(298\) −6.48528 + 11.2328i −0.375682 + 0.650701i
\(299\) 16.3640 + 28.3432i 0.946352 + 1.63913i
\(300\) 0 0
\(301\) 0 0
\(302\) 10.5858 0.609144
\(303\) 0.514719 + 0.891519i 0.0295698 + 0.0512164i
\(304\) −12.0000 + 20.7846i −0.688247 + 1.19208i
\(305\) 1.41421 2.44949i 0.0809776 0.140257i
\(306\) 6.48528 + 11.2328i 0.370739 + 0.642139i
\(307\) −30.8995 −1.76353 −0.881764 0.471691i \(-0.843644\pi\)
−0.881764 + 0.471691i \(0.843644\pi\)
\(308\) 0 0
\(309\) −7.97056 −0.453429
\(310\) 7.24264 + 12.5446i 0.411354 + 0.712487i
\(311\) −5.00000 + 8.66025i −0.283524 + 0.491078i −0.972250 0.233944i \(-0.924837\pi\)
0.688726 + 0.725022i \(0.258170\pi\)
\(312\) 2.58579 4.47871i 0.146391 0.253557i
\(313\) −9.10660 15.7731i −0.514736 0.891548i −0.999854 0.0170996i \(-0.994557\pi\)
0.485118 0.874449i \(-0.338777\pi\)
\(314\) −21.4558 −1.21082
\(315\) 0 0
\(316\) 0 0
\(317\) 0.171573 + 0.297173i 0.00963649 + 0.0166909i 0.870803 0.491631i \(-0.163599\pi\)
−0.861167 + 0.508322i \(0.830266\pi\)
\(318\) 1.24264 2.15232i 0.0696838 0.120696i
\(319\) −0.742641 + 1.28629i −0.0415799 + 0.0720185i
\(320\) 4.00000 + 6.92820i 0.223607 + 0.387298i
\(321\) −1.02944 −0.0574576
\(322\) 0 0
\(323\) 19.4558 1.08255
\(324\) 0 0
\(325\) 2.20711 3.82282i 0.122428 0.212052i
\(326\) −7.24264 + 12.5446i −0.401133 + 0.694782i
\(327\) −1.03553 1.79360i −0.0572652 0.0991862i
\(328\) 17.6569 0.974937
\(329\) 0 0
\(330\) −0.100505 −0.00553262
\(331\) 13.7279 + 23.7775i 0.754555 + 1.30693i 0.945595 + 0.325345i \(0.105480\pi\)
−0.191040 + 0.981582i \(0.561186\pi\)
\(332\) 0 0
\(333\) 3.17157 5.49333i 0.173801 0.301032i
\(334\) −0.535534 0.927572i −0.0293031 0.0507545i
\(335\) 8.24264 0.450344
\(336\) 0 0
\(337\) 22.2426 1.21163 0.605817 0.795604i \(-0.292846\pi\)
0.605817 + 0.795604i \(0.292846\pi\)
\(338\) 4.58579 + 7.94282i 0.249434 + 0.432032i
\(339\) 2.70711 4.68885i 0.147030 0.254663i
\(340\) 0 0
\(341\) −0.878680 1.52192i −0.0475832 0.0824165i
\(342\) −24.0000 −1.29777
\(343\) 0 0
\(344\) 5.65685 0.304997
\(345\) 1.53553 + 2.65962i 0.0826704 + 0.143189i
\(346\) 5.12132 8.87039i 0.275324 0.476875i
\(347\) −6.53553 + 11.3199i −0.350846 + 0.607683i −0.986398 0.164375i \(-0.947439\pi\)
0.635552 + 0.772058i \(0.280773\pi\)
\(348\) 0 0
\(349\) 10.9706 0.587241 0.293620 0.955922i \(-0.405140\pi\)
0.293620 + 0.955922i \(0.405140\pi\)
\(350\) 0 0
\(351\) 10.6569 0.568821
\(352\) 0 0
\(353\) −3.10660 + 5.38079i −0.165348 + 0.286391i −0.936779 0.349922i \(-0.886208\pi\)
0.771431 + 0.636313i \(0.219541\pi\)
\(354\) 0.656854 1.13770i 0.0349114 0.0604683i
\(355\) −1.58579 2.74666i −0.0841648 0.145778i
\(356\) 0 0
\(357\) 0 0
\(358\) 20.4853 1.08268
\(359\) 5.65685 + 9.79796i 0.298557 + 0.517116i 0.975806 0.218638i \(-0.0701613\pi\)
−0.677249 + 0.735754i \(0.736828\pi\)
\(360\) −4.00000 + 6.92820i −0.210819 + 0.365148i
\(361\) −8.50000 + 14.7224i −0.447368 + 0.774865i
\(362\) 13.2426 + 22.9369i 0.696018 + 1.20554i
\(363\) −4.54416 −0.238506
\(364\) 0 0
\(365\) −8.48528 −0.444140
\(366\) 0.828427 + 1.43488i 0.0433026 + 0.0750023i
\(367\) −11.9350 + 20.6721i −0.623003 + 1.07907i 0.365920 + 0.930646i \(0.380754\pi\)
−0.988923 + 0.148427i \(0.952579\pi\)
\(368\) 14.8284 25.6836i 0.772985 1.33885i
\(369\) 8.82843 + 15.2913i 0.459590 + 0.796032i
\(370\) 3.17157 0.164882
\(371\) 0 0
\(372\) 0 0
\(373\) 8.24264 + 14.2767i 0.426788 + 0.739218i 0.996586 0.0825669i \(-0.0263118\pi\)
−0.569798 + 0.821785i \(0.692978\pi\)
\(374\) 0.393398 0.681386i 0.0203421 0.0352336i
\(375\) 0.207107 0.358719i 0.0106949 0.0185242i
\(376\) −10.2426 17.7408i −0.528224 0.914911i
\(377\) 38.2132 1.96808
\(378\) 0 0
\(379\) 2.00000 0.102733 0.0513665 0.998680i \(-0.483642\pi\)
0.0513665 + 0.998680i \(0.483642\pi\)
\(380\) 0 0
\(381\) −1.70711 + 2.95680i −0.0874577 + 0.151481i
\(382\) 9.87868 17.1104i 0.505437 0.875443i
\(383\) 2.24264 + 3.88437i 0.114594 + 0.198482i 0.917617 0.397465i \(-0.130110\pi\)
−0.803024 + 0.595947i \(0.796777\pi\)
\(384\) −4.68629 −0.239146
\(385\) 0 0
\(386\) 22.6274 1.15171
\(387\) 2.82843 + 4.89898i 0.143777 + 0.249029i
\(388\) 0 0
\(389\) 3.42893 5.93908i 0.173854 0.301124i −0.765910 0.642948i \(-0.777711\pi\)
0.939764 + 0.341824i \(0.111045\pi\)
\(390\) 1.29289 + 2.23936i 0.0654682 + 0.113394i
\(391\) −24.0416 −1.21584
\(392\) 0 0
\(393\) −5.07107 −0.255802
\(394\) 9.48528 + 16.4290i 0.477862 + 0.827681i
\(395\) 0.742641 1.28629i 0.0373663 0.0647203i
\(396\) 0 0
\(397\) 0.792893 + 1.37333i 0.0397942 + 0.0689255i 0.885237 0.465141i \(-0.153996\pi\)
−0.845442 + 0.534067i \(0.820663\pi\)
\(398\) −10.4853 −0.525580
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) −5.91421 10.2437i −0.295342 0.511547i 0.679723 0.733469i \(-0.262100\pi\)
−0.975064 + 0.221922i \(0.928767\pi\)
\(402\) −2.41421 + 4.18154i −0.120410 + 0.208556i
\(403\) −22.6066 + 39.1558i −1.12612 + 1.95049i
\(404\) 0 0
\(405\) −7.48528 −0.371947
\(406\) 0 0
\(407\) −0.384776 −0.0190727
\(408\) 1.89949 + 3.29002i 0.0940390 + 0.162880i
\(409\) 1.24264 2.15232i 0.0614446 0.106425i −0.833667 0.552268i \(-0.813763\pi\)
0.895111 + 0.445843i \(0.147096\pi\)
\(410\) −4.41421 + 7.64564i −0.218002 + 0.377591i
\(411\) −2.48528 4.30463i −0.122590 0.212332i
\(412\) 0 0
\(413\) 0 0
\(414\) 29.6569 1.45755
\(415\) 0 0
\(416\) 0 0
\(417\) 1.60660 2.78272i 0.0786756 0.136270i
\(418\) 0.727922 + 1.26080i 0.0356038 + 0.0616676i
\(419\) −18.7279 −0.914919 −0.457459 0.889230i \(-0.651241\pi\)
−0.457459 + 0.889230i \(0.651241\pi\)
\(420\) 0 0
\(421\) −19.0000 −0.926003 −0.463002 0.886357i \(-0.653228\pi\)
−0.463002 + 0.886357i \(0.653228\pi\)
\(422\) 6.36396 + 11.0227i 0.309793 + 0.536577i
\(423\) 10.2426 17.7408i 0.498014 0.862586i
\(424\) −6.00000 + 10.3923i −0.291386 + 0.504695i
\(425\) 1.62132 + 2.80821i 0.0786456 + 0.136218i
\(426\) 1.85786 0.0900138
\(427\) 0 0
\(428\) 0 0
\(429\) −0.156854 0.271680i −0.00757299 0.0131168i
\(430\) −1.41421 + 2.44949i −0.0681994 + 0.118125i
\(431\) 14.3995 24.9407i 0.693599 1.20135i −0.277051 0.960855i \(-0.589357\pi\)
0.970651 0.240494i \(-0.0773095\pi\)
\(432\) −4.82843 8.36308i −0.232308 0.402369i
\(433\) −10.9706 −0.527212 −0.263606 0.964630i \(-0.584912\pi\)
−0.263606 + 0.964630i \(0.584912\pi\)
\(434\) 0 0
\(435\) 3.58579 0.171925
\(436\) 0 0
\(437\) 22.2426 38.5254i 1.06401 1.84292i
\(438\) 2.48528 4.30463i 0.118751 0.205683i
\(439\) −15.1924 26.3140i −0.725093 1.25590i −0.958936 0.283624i \(-0.908463\pi\)
0.233843 0.972274i \(-0.424870\pi\)
\(440\) 0.485281 0.0231349
\(441\) 0 0
\(442\) −20.2426 −0.962844
\(443\) −7.58579 13.1390i −0.360412 0.624251i 0.627617 0.778522i \(-0.284030\pi\)
−0.988029 + 0.154271i \(0.950697\pi\)
\(444\) 0 0
\(445\) 4.00000 6.92820i 0.189618 0.328428i
\(446\) 17.1213 + 29.6550i 0.810718 + 1.40420i
\(447\) −3.79899 −0.179686
\(448\) 0 0
\(449\) −24.1716 −1.14073 −0.570364 0.821392i \(-0.693198\pi\)
−0.570364 + 0.821392i \(0.693198\pi\)
\(450\) −2.00000 3.46410i −0.0942809 0.163299i
\(451\) 0.535534 0.927572i 0.0252173 0.0436777i
\(452\) 0 0
\(453\) 1.55025 + 2.68512i 0.0728372 + 0.126158i
\(454\) 22.2426 1.04390
\(455\) 0 0
\(456\) −7.02944 −0.329184
\(457\) 5.87868 + 10.1822i 0.274993 + 0.476302i 0.970133 0.242572i \(-0.0779911\pi\)
−0.695140 + 0.718874i \(0.744658\pi\)
\(458\) −12.7574 + 22.0964i −0.596112 + 1.03250i
\(459\) −3.91421 + 6.77962i −0.182700 + 0.316445i
\(460\) 0 0
\(461\) −3.02944 −0.141095 −0.0705475 0.997508i \(-0.522475\pi\)
−0.0705475 + 0.997508i \(0.522475\pi\)
\(462\) 0 0
\(463\) −21.4558 −0.997138 −0.498569 0.866850i \(-0.666141\pi\)
−0.498569 + 0.866850i \(0.666141\pi\)
\(464\) −17.3137 29.9882i −0.803769 1.39217i
\(465\) −2.12132 + 3.67423i −0.0983739 + 0.170389i
\(466\) −6.48528 + 11.2328i −0.300425 + 0.520351i
\(467\) −2.86396 4.96053i −0.132528 0.229546i 0.792122 0.610362i \(-0.208976\pi\)
−0.924651 + 0.380817i \(0.875643\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 10.2426 0.472458
\(471\) −3.14214 5.44234i −0.144782 0.250770i
\(472\) −3.17157 + 5.49333i −0.145983 + 0.252851i
\(473\) 0.171573 0.297173i 0.00788893 0.0136640i
\(474\) 0.435029 + 0.753492i 0.0199815 + 0.0346090i
\(475\) −6.00000 −0.275299
\(476\) 0 0
\(477\) −12.0000 −0.549442
\(478\) −12.3640 21.4150i −0.565514 0.979500i
\(479\) 5.87868 10.1822i 0.268604 0.465235i −0.699898 0.714243i \(-0.746771\pi\)
0.968501 + 0.249008i \(0.0801045\pi\)
\(480\) 0 0
\(481\) 4.94975 + 8.57321i 0.225689 + 0.390905i
\(482\) −1.02944 −0.0468896
\(483\) 0 0
\(484\) 0 0
\(485\) −6.62132 11.4685i −0.300659 0.520756i
\(486\) 7.31371 12.6677i 0.331757 0.574619i
\(487\) −13.8492 + 23.9876i −0.627569 + 1.08698i 0.360469 + 0.932771i \(0.382617\pi\)
−0.988038 + 0.154210i \(0.950717\pi\)
\(488\) −4.00000 6.92820i −0.181071 0.313625i
\(489\) −4.24264 −0.191859
\(490\) 0 0
\(491\) −37.2843 −1.68262 −0.841308 0.540556i \(-0.818214\pi\)
−0.841308 + 0.540556i \(0.818214\pi\)
\(492\) 0 0
\(493\) −14.0355 + 24.3103i −0.632129 + 1.09488i
\(494\) 18.7279 32.4377i 0.842609 1.45944i
\(495\) 0.242641 + 0.420266i 0.0109059 + 0.0188896i
\(496\) 40.9706 1.83963
\(497\) 0 0
\(498\) 0 0
\(499\) −1.50000 2.59808i −0.0671492 0.116306i 0.830496 0.557024i \(-0.188057\pi\)
−0.897645 + 0.440719i \(0.854724\pi\)
\(500\) 0 0
\(501\) 0.156854 0.271680i 0.00700773 0.0121377i
\(502\) −12.1716 21.0818i −0.543244 0.940926i
\(503\) 41.2426 1.83892 0.919459 0.393185i \(-0.128627\pi\)
0.919459 + 0.393185i \(0.128627\pi\)
\(504\) 0 0
\(505\) 2.48528 0.110594
\(506\) −0.899495 1.55797i −0.0399874 0.0692603i
\(507\) −1.34315 + 2.32640i −0.0596512 + 0.103319i
\(508\) 0 0
\(509\) −12.6066 21.8353i −0.558778 0.967832i −0.997599 0.0692571i \(-0.977937\pi\)
0.438821 0.898574i \(-0.355396\pi\)
\(510\) −1.89949 −0.0841110
\(511\) 0 0
\(512\) 22.6274 1.00000
\(513\) −7.24264 12.5446i −0.319770 0.553859i
\(514\) 6.72792 11.6531i 0.296756 0.513996i
\(515\) −9.62132 + 16.6646i −0.423966 + 0.734331i
\(516\) 0 0
\(517\) −1.24264 −0.0546513
\(518\) 0 0
\(519\) 3.00000 0.131685
\(520\) −6.24264 10.8126i −0.273758 0.474163i
\(521\) 7.48528 12.9649i 0.327936 0.568002i −0.654166 0.756351i \(-0.726980\pi\)
0.982102 + 0.188349i \(0.0603136\pi\)
\(522\) 17.3137 29.9882i 0.757800 1.31255i
\(523\) 16.2426 + 28.1331i 0.710241 + 1.23017i 0.964767 + 0.263108i \(0.0847474\pi\)
−0.254525 + 0.967066i \(0.581919\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 23.5147 1.02529
\(527\) −16.6066 28.7635i −0.723395 1.25296i
\(528\) −0.142136 + 0.246186i −0.00618566 + 0.0107139i
\(529\) −15.9853 + 27.6873i −0.695012 + 1.20380i
\(530\) −3.00000 5.19615i −0.130312 0.225706i
\(531\) −6.34315 −0.275269
\(532\) 0 0
\(533\) −27.5563 −1.19360
\(534\) 2.34315 + 4.05845i 0.101398 + 0.175626i
\(535\) −1.24264 + 2.15232i −0.0537240 + 0.0930528i
\(536\) 11.6569 20.1903i 0.503499 0.872087i
\(537\) 3.00000 + 5.19615i 0.129460 + 0.224231i
\(538\) −22.9706 −0.990331
\(539\) 0 0
\(540\) 0 0
\(541\) 10.9853 + 19.0271i 0.472294 + 0.818037i 0.999497 0.0317018i \(-0.0100927\pi\)
−0.527203 + 0.849739i \(0.676759\pi\)
\(542\) 0.485281 0.840532i 0.0208446 0.0361039i
\(543\) −3.87868 + 6.71807i −0.166450 + 0.288300i
\(544\) 0 0
\(545\) −5.00000 −0.214176
\(546\) 0 0
\(547\) −24.4853 −1.04692 −0.523458 0.852052i \(-0.675358\pi\)
−0.523458 + 0.852052i \(0.675358\pi\)
\(548\) 0 0
\(549\) 4.00000 6.92820i 0.170716 0.295689i
\(550\) −0.121320 + 0.210133i −0.00517312 + 0.00896010i
\(551\) −25.9706 44.9823i −1.10638 1.91631i
\(552\) 8.68629 0.369713
\(553\) 0 0
\(554\) −21.5147 −0.914073
\(555\) 0.464466 + 0.804479i 0.0197155 + 0.0341482i
\(556\) 0 0
\(557\) 3.89949 6.75412i 0.165227 0.286181i −0.771509 0.636218i \(-0.780498\pi\)
0.936736 + 0.350037i \(0.113831\pi\)
\(558\) 20.4853 + 35.4815i 0.867211 + 1.50205i
\(559\) −8.82843 −0.373403
\(560\) 0 0
\(561\) 0.230447 0.00972950
\(562\) 1.63604 + 2.83370i 0.0690121 + 0.119533i
\(563\) −15.9706 + 27.6618i −0.673079 + 1.16581i 0.303947 + 0.952689i \(0.401695\pi\)
−0.977026 + 0.213118i \(0.931638\pi\)
\(564\) 0 0
\(565\) −6.53553 11.3199i −0.274952 0.476231i
\(566\) 34.7279 1.45972
\(567\) 0 0
\(568\) −8.97056 −0.376396
\(569\) −13.0711 22.6398i −0.547968 0.949108i −0.998414 0.0563042i \(-0.982068\pi\)
0.450446 0.892804i \(-0.351265\pi\)
\(570\) 1.75736 3.04384i 0.0736077 0.127492i
\(571\) 8.75736 15.1682i 0.366484 0.634769i −0.622529 0.782597i \(-0.713895\pi\)
0.989013 + 0.147828i \(0.0472281\pi\)
\(572\) 0 0
\(573\) 5.78680 0.241747
\(574\) 0 0
\(575\) 7.41421 0.309194
\(576\) 11.3137 + 19.5959i 0.471405 + 0.816497i
\(577\) 7.86396 13.6208i 0.327381 0.567040i −0.654610 0.755966i \(-0.727167\pi\)
0.981991 + 0.188926i \(0.0605006\pi\)
\(578\) −4.58579 + 7.94282i −0.190744 + 0.330378i
\(579\) 3.31371 + 5.73951i 0.137713 + 0.238526i
\(580\) 0 0
\(581\) 0 0
\(582\) 7.75736 0.321553
\(583\) 0.363961 + 0.630399i 0.0150737 + 0.0261085i
\(584\) −12.0000 + 20.7846i −0.496564 + 0.860073i
\(585\) 6.24264 10.8126i 0.258101 0.447045i
\(586\) −18.1924 31.5101i −0.751521 1.30167i
\(587\) 37.4558 1.54597 0.772984 0.634425i \(-0.218763\pi\)
0.772984 + 0.634425i \(0.218763\pi\)
\(588\) 0 0
\(589\) 61.4558 2.53224
\(590\) −1.58579 2.74666i −0.0652858 0.113078i
\(591\) −2.77817 + 4.81194i −0.114279 + 0.197937i
\(592\) 4.48528 7.76874i 0.184344 0.319293i
\(593\) 9.62132 + 16.6646i 0.395100 + 0.684334i 0.993114 0.117152i \(-0.0373765\pi\)
−0.598014 + 0.801486i \(0.704043\pi\)
\(594\) −0.585786 −0.0240351
\(595\) 0 0
\(596\) 0 0
\(597\) −1.53553 2.65962i −0.0628452 0.108851i
\(598\) −23.1421 + 40.0834i −0.946352 + 1.63913i
\(599\) 8.91421 15.4399i 0.364225 0.630856i −0.624427 0.781084i \(-0.714667\pi\)
0.988651 + 0.150228i \(0.0480006\pi\)
\(600\) −0.585786 1.01461i −0.0239146 0.0414214i
\(601\) 10.9706 0.447499 0.223749 0.974647i \(-0.428170\pi\)
0.223749 + 0.974647i \(0.428170\pi\)
\(602\) 0 0
\(603\) 23.3137 0.949408
\(604\) 0 0
\(605\) −5.48528 + 9.50079i −0.223008 + 0.386262i
\(606\) −0.727922 + 1.26080i −0.0295698 + 0.0512164i
\(607\) −2.55025 4.41717i −0.103512 0.179287i 0.809618 0.586958i \(-0.199675\pi\)
−0.913129 + 0.407670i \(0.866341\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 4.00000 0.161955
\(611\) 15.9853 + 27.6873i 0.646695 + 1.12011i
\(612\) 0 0
\(613\) 11.9706 20.7336i 0.483486 0.837423i −0.516334 0.856387i \(-0.672704\pi\)
0.999820 + 0.0189643i \(0.00603690\pi\)
\(614\) −21.8492 37.8440i −0.881764 1.52726i
\(615\) −2.58579 −0.104269
\(616\) 0 0
\(617\) 4.58579 0.184617 0.0923084 0.995730i \(-0.470575\pi\)
0.0923084 + 0.995730i \(0.470575\pi\)
\(618\) −5.63604 9.76191i −0.226715 0.392681i
\(619\) 8.46447 14.6609i 0.340216 0.589271i −0.644257 0.764809i \(-0.722833\pi\)
0.984473 + 0.175538i \(0.0561666\pi\)
\(620\) 0 0
\(621\) 8.94975 + 15.5014i 0.359141 + 0.622050i
\(622\) −14.1421 −0.567048
\(623\) 0 0
\(624\) 7.31371 0.292783
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 12.8787 22.3065i 0.514736 0.891548i
\(627\) −0.213203 + 0.369279i −0.00851453 + 0.0147476i
\(628\) 0 0
\(629\) −7.27208 −0.289957
\(630\) 0 0
\(631\) −42.4558 −1.69014 −0.845070 0.534655i \(-0.820441\pi\)
−0.845070 + 0.534655i \(0.820441\pi\)
\(632\) −2.10051 3.63818i −0.0835536 0.144719i
\(633\) −1.86396 + 3.22848i −0.0740858 + 0.128320i
\(634\) −0.242641 + 0.420266i −0.00963649 + 0.0166909i
\(635\) 4.12132 + 7.13834i 0.163550 + 0.283276i
\(636\) 0 0
\(637\) 0 0
\(638\) −2.10051 −0.0831598
\(639\) −4.48528 7.76874i −0.177435 0.307326i
\(640\) −5.65685 + 9.79796i −0.223607 + 0.387298i
\(641\) 11.6569 20.1903i 0.460418 0.797467i −0.538564 0.842585i \(-0.681033\pi\)
0.998982 + 0.0451174i \(0.0143662\pi\)
\(642\) −0.727922 1.26080i −0.0287288 0.0497597i
\(643\) −2.27208 −0.0896020 −0.0448010 0.998996i \(-0.514265\pi\)
−0.0448010 + 0.998996i \(0.514265\pi\)
\(644\) 0 0
\(645\) −0.828427 −0.0326193
\(646\) 13.7574 + 23.8284i 0.541276 + 0.937518i
\(647\) −5.75736 + 9.97204i −0.226345 + 0.392041i −0.956722 0.291003i \(-0.906011\pi\)
0.730377 + 0.683044i \(0.239344\pi\)
\(648\) −10.5858 + 18.3351i −0.415849 + 0.720272i
\(649\) 0.192388 + 0.333226i 0.00755190 + 0.0130803i
\(650\) 6.24264 0.244857
\(651\) 0 0
\(652\) 0 0
\(653\) −17.4853 30.2854i −0.684252 1.18516i −0.973671 0.227957i \(-0.926796\pi\)
0.289419 0.957202i \(-0.406538\pi\)
\(654\) 1.46447 2.53653i 0.0572652 0.0991862i
\(655\) −6.12132 + 10.6024i −0.239180 + 0.414272i
\(656\) 12.4853 + 21.6251i 0.487468 + 0.844320i
\(657\) −24.0000 −0.936329
\(658\) 0 0
\(659\) 19.9706 0.777943 0.388971 0.921250i \(-0.372831\pi\)
0.388971 + 0.921250i \(0.372831\pi\)
\(660\) 0 0
\(661\) 6.72792 11.6531i 0.261686 0.453253i −0.705004 0.709203i \(-0.749055\pi\)
0.966690 + 0.255950i \(0.0823882\pi\)
\(662\) −19.4142 + 33.6264i −0.754555 + 1.30693i
\(663\) −2.96447 5.13461i −0.115130 0.199412i
\(664\) 0 0
\(665\) 0 0
\(666\) 8.97056 0.347602
\(667\) 32.0919 + 55.5848i 1.24260 + 2.15225i
\(668\) 0 0
\(669\) −5.01472 + 8.68575i −0.193880 + 0.335810i
\(670\) 5.82843 + 10.0951i 0.225172 + 0.390009i
\(671\) −0.485281 −0.0187341
\(672\) 0 0
\(673\) 3.51472 0.135482 0.0677412 0.997703i \(-0.478421\pi\)
0.0677412 + 0.997703i \(0.478421\pi\)
\(674\) 15.7279 + 27.2416i 0.605817 + 1.04931i
\(675\) 1.20711 2.09077i 0.0464616 0.0804738i
\(676\) 0 0
\(677\) 22.1066 + 38.2898i 0.849626 + 1.47159i 0.881543 + 0.472104i \(0.156505\pi\)
−0.0319169 + 0.999491i \(0.510161\pi\)
\(678\) 7.65685 0.294060
\(679\) 0 0
\(680\) 9.17157 0.351714
\(681\) 3.25736 + 5.64191i 0.124822 + 0.216199i
\(682\) 1.24264 2.15232i 0.0475832 0.0824165i
\(683\) −15.8995 + 27.5387i −0.608377 + 1.05374i 0.383131 + 0.923694i \(0.374846\pi\)
−0.991508 + 0.130046i \(0.958487\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 0 0
\(687\) −7.47309 −0.285116
\(688\) 4.00000 + 6.92820i 0.152499 + 0.264135i
\(689\) 9.36396 16.2189i 0.356739 0.617889i
\(690\) −2.17157 + 3.76127i −0.0826704 + 0.143189i
\(691\) 7.41421 + 12.8418i 0.282050 + 0.488525i 0.971890 0.235437i \(-0.0756523\pi\)
−0.689840 + 0.723962i \(0.742319\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −18.4853 −0.701692
\(695\) −3.87868 6.71807i −0.147127 0.254831i
\(696\) 5.07107 8.78335i 0.192218 0.332932i
\(697\) 10.1213 17.5306i 0.383372 0.664020i
\(698\) 7.75736 + 13.4361i 0.293620 + 0.508565i
\(699\) −3.79899 −0.143691
\(700\) 0 0
\(701\) 46.4558 1.75461 0.877307 0.479931i \(-0.159338\pi\)
0.877307 + 0.479931i \(0.159338\pi\)
\(702\) 7.53553 + 13.0519i 0.284410 + 0.492613i
\(703\) 6.72792 11.6531i 0.253748 0.439505i
\(704\) 0.686292 1.18869i 0.0258656 0.0448005i
\(705\) 1.50000 + 2.59808i 0.0564933 + 0.0978492i
\(706\) −8.78680 −0.330695
\(707\) 0 0
\(708\) 0 0
\(709\) −8.50000 14.7224i −0.319224 0.552913i 0.661102 0.750296i \(-0.270089\pi\)
−0.980326 + 0.197383i \(0.936756\pi\)
\(710\) 2.24264 3.88437i 0.0841648 0.145778i
\(711\) 2.10051 3.63818i 0.0787751 0.136442i
\(712\) −11.3137 19.5959i −0.423999 0.734388i
\(713\) −75.9411 −2.84402
\(714\) 0 0
\(715\) −0.757359 −0.0283236
\(716\) 0 0
\(717\) 3.62132 6.27231i 0.135241 0.234244i
\(718\) −8.00000 + 13.8564i −0.298557 + 0.517116i
\(719\) −12.6066 21.8353i −0.470147 0.814318i 0.529270 0.848453i \(-0.322466\pi\)
−0.999417 + 0.0341349i \(0.989132\pi\)
\(720\) −11.3137 −0.421637
\(721\) 0 0
\(722\) −24.0416 −0.894737
\(723\) −0.150758 0.261120i −0.00560674 0.00971115i
\(724\) 0 0
\(725\) 4.32843 7.49706i 0.160754 0.278434i
\(726\) −3.21320 5.56543i −0.119253 0.206553i
\(727\) 6.68629 0.247981 0.123990 0.992283i \(-0.460431\pi\)
0.123990 + 0.992283i \(0.460431\pi\)
\(728\) 0 0
\(729\) −18.1716 −0.673021
\(730\) −6.00000 10.3923i −0.222070 0.384636i
\(731\) 3.24264 5.61642i 0.119933 0.207731i
\(732\) 0 0
\(733\) 7.34924 + 12.7293i 0.271450 + 0.470166i 0.969233 0.246143i \(-0.0791634\pi\)
−0.697783 + 0.716309i \(0.745830\pi\)
\(734\) −33.7574 −1.24601
\(735\) 0 0
\(736\) 0 0
\(737\) −0.707107 1.22474i −0.0260466 0.0451141i
\(738\) −12.4853 + 21.6251i −0.459590 + 0.796032i
\(739\) −14.9853 + 25.9553i −0.551242 + 0.954780i 0.446943 + 0.894563i \(0.352513\pi\)
−0.998185 + 0.0602175i \(0.980821\pi\)
\(740\) 0 0
\(741\) 10.9706 0.403014
\(742\) 0 0
\(743\) 11.2721 0.413532 0.206766 0.978390i \(-0.433706\pi\)
0.206766 + 0.978390i \(0.433706\pi\)
\(744\) 6.00000 + 10.3923i 0.219971 + 0.381000i
\(745\) −4.58579 + 7.94282i −0.168010 + 0.291002i
\(746\) −11.6569 + 20.1903i −0.426788 + 0.739218i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0.585786 0.0213899
\(751\) −14.7426 25.5350i −0.537967 0.931785i −0.999013 0.0444097i \(-0.985859\pi\)
0.461047 0.887376i \(-0.347474\pi\)
\(752\) 14.4853 25.0892i 0.528224 0.914911i
\(753\) 3.56497 6.17471i 0.129915 0.225019i
\(754\) 27.0208 + 46.8014i 0.984040 + 1.70441i
\(755\) 7.48528 0.272417
\(756\) 0 0
\(757\) 0.485281 0.0176379 0.00881893 0.999961i \(-0.497193\pi\)
0.00881893 + 0.999961i \(0.497193\pi\)
\(758\) 1.41421 + 2.44949i 0.0513665 + 0.0889695i
\(759\) 0.263456 0.456319i 0.00956285 0.0165633i
\(760\) −8.48528 + 14.6969i −0.307794 + 0.533114i
\(761\) −6.36396 11.0227i −0.230693 0.399573i 0.727319 0.686300i \(-0.240766\pi\)
−0.958012 + 0.286727i \(0.907433\pi\)
\(762\) −4.82843 −0.174915
\(763\) 0 0
\(764\) 0 0
\(765\) 4.58579 + 7.94282i 0.165799 + 0.287173i
\(766\) −3.17157 + 5.49333i −0.114594 + 0.198482i
\(767\) 4.94975 8.57321i 0.178725 0.309561i
\(768\) 0 0
\(769\) 8.82843 0.318361 0.159181 0.987249i \(-0.449115\pi\)
0.159181 + 0.987249i \(0.449115\pi\)
\(770\) 0 0
\(771\) 3.94113 0.141936
\(772\) 0 0
\(773\) −3.10660 + 5.38079i −0.111737 + 0.193534i −0.916471 0.400102i \(-0.868975\pi\)
0.804734 + 0.593636i \(0.202308\pi\)
\(774\) −4.00000 + 6.92820i −0.143777 + 0.249029i
\(775\) 5.12132 + 8.87039i 0.183963 + 0.318634i
\(776\) −37.4558 −1.34459
\(777\) 0 0
\(778\) 9.69848 0.347708
\(779\) 18.7279 + 32.4377i 0.670997 + 1.16220i
\(780\) 0 0
\(781\) −0.272078 + 0.471253i −0.00973571 + 0.0168628i
\(782\) −17.0000 29.4449i −0.607919 1.05295i
\(783\) 20.8995 0.746887
\(784\) 0 0
\(785\) −15.1716 −0.541497
\(786\) −3.58579 6.21076i −0.127901 0.221531i
\(787\) 10.1360 17.5561i 0.361311 0.625809i −0.626866 0.779127i \(-0.715663\pi\)
0.988177 + 0.153318i \(0.0489960\pi\)
\(788\) 0