Properties

Label 1470.2.g.k.589.5
Level $1470$
Weight $2$
Character 1470.589
Analytic conductor $11.738$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.1698758656.6
Defining polynomial: \(x^{8} + 18 x^{6} + 97 x^{4} + 176 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 589.5
Root \(-0.692297i\) of defining polynomial
Character \(\chi\) \(=\) 1470.589
Dual form 1470.2.g.k.589.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.88893 - 1.19663i) q^{5} +1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.88893 - 1.19663i) q^{5} +1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +(1.19663 - 1.88893i) q^{10} +0.979056 q^{11} +1.00000i q^{12} -0.435157i q^{13} +(-1.19663 + 1.88893i) q^{15} +1.00000 q^{16} -2.79881i q^{17} -1.00000i q^{18} -7.34271 q^{19} +(1.88893 + 1.19663i) q^{20} +0.979056i q^{22} +3.34271i q^{23} -1.00000 q^{24} +(2.13613 + 4.52072i) q^{25} +0.435157 q^{26} +1.00000i q^{27} -3.74825 q^{29} +(-1.88893 - 1.19663i) q^{30} +4.97906 q^{31} +1.00000i q^{32} -0.979056i q^{33} +2.79881 q^{34} +1.00000 q^{36} +4.63591i q^{37} -7.34271i q^{38} -0.435157 q^{39} +(-1.19663 + 1.88893i) q^{40} +4.94944 q^{41} +9.97862i q^{43} -0.979056 q^{44} +(1.88893 + 1.19663i) q^{45} -3.34271 q^{46} +4.40554i q^{47} -1.00000i q^{48} +(-4.52072 + 2.13613i) q^{50} -2.79881 q^{51} +0.435157i q^{52} -0.657293i q^{53} -1.00000 q^{54} +(-1.84937 - 1.17157i) q^{55} +7.34271i q^{57} -3.74825i q^{58} -8.27226 q^{59} +(1.19663 - 1.88893i) q^{60} -11.3336 q^{61} +4.97906i q^{62} -1.00000 q^{64} +(-0.520724 + 0.821983i) q^{65} +0.979056 q^{66} +2.36365i q^{67} +2.79881i q^{68} +3.34271 q^{69} -14.1119 q^{71} +1.00000i q^{72} +15.3928i q^{73} -4.63591 q^{74} +(4.52072 - 2.13613i) q^{75} +7.34271 q^{76} -0.435157i q^{78} +2.88767 q^{79} +(-1.88893 - 1.19663i) q^{80} +1.00000 q^{81} +4.94944i q^{82} -14.3842i q^{83} +(-3.34915 + 5.28676i) q^{85} -9.97862 q^{86} +3.74825i q^{87} -0.979056i q^{88} -10.1210 q^{89} +(-1.19663 + 1.88893i) q^{90} -3.34271i q^{92} -4.97906i q^{93} -4.40554 q^{94} +(13.8699 + 8.78654i) q^{95} +1.00000 q^{96} +10.6655i q^{97} -0.979056 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 8q^{4} + 4q^{5} + 8q^{6} - 8q^{9} + O(q^{10}) \) \( 8q - 8q^{4} + 4q^{5} + 8q^{6} - 8q^{9} + 8q^{16} - 24q^{19} - 4q^{20} - 8q^{24} + 4q^{25} + 16q^{29} + 4q^{30} + 32q^{31} - 8q^{34} + 8q^{36} + 24q^{41} - 4q^{45} + 8q^{46} - 4q^{50} + 8q^{51} - 8q^{54} - 40q^{59} + 24q^{61} - 8q^{64} + 28q^{65} - 8q^{69} - 40q^{71} + 16q^{74} + 4q^{75} + 24q^{76} + 16q^{79} + 4q^{80} + 8q^{81} + 28q^{85} + 8q^{86} - 88q^{89} - 24q^{94} + 24q^{95} + 8q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) −1.88893 1.19663i −0.844756 0.535151i
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) 1.19663 1.88893i 0.378409 0.597333i
\(11\) 0.979056 0.295197 0.147598 0.989047i \(-0.452846\pi\)
0.147598 + 0.989047i \(0.452846\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 0.435157i 0.120691i −0.998178 0.0603455i \(-0.980780\pi\)
0.998178 0.0603455i \(-0.0192202\pi\)
\(14\) 0 0
\(15\) −1.19663 + 1.88893i −0.308970 + 0.487720i
\(16\) 1.00000 0.250000
\(17\) 2.79881i 0.678811i −0.940640 0.339405i \(-0.889774\pi\)
0.940640 0.339405i \(-0.110226\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −7.34271 −1.68453 −0.842266 0.539062i \(-0.818779\pi\)
−0.842266 + 0.539062i \(0.818779\pi\)
\(20\) 1.88893 + 1.19663i 0.422378 + 0.267576i
\(21\) 0 0
\(22\) 0.979056i 0.208735i
\(23\) 3.34271i 0.697003i 0.937308 + 0.348501i \(0.113309\pi\)
−0.937308 + 0.348501i \(0.886691\pi\)
\(24\) −1.00000 −0.204124
\(25\) 2.13613 + 4.52072i 0.427226 + 0.904145i
\(26\) 0.435157 0.0853414
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −3.74825 −0.696032 −0.348016 0.937489i \(-0.613144\pi\)
−0.348016 + 0.937489i \(0.613144\pi\)
\(30\) −1.88893 1.19663i −0.344870 0.218475i
\(31\) 4.97906 0.894265 0.447132 0.894468i \(-0.352445\pi\)
0.447132 + 0.894468i \(0.352445\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0.979056i 0.170432i
\(34\) 2.79881 0.479992
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 4.63591i 0.762139i 0.924546 + 0.381069i \(0.124444\pi\)
−0.924546 + 0.381069i \(0.875556\pi\)
\(38\) 7.34271i 1.19114i
\(39\) −0.435157 −0.0696809
\(40\) −1.19663 + 1.88893i −0.189205 + 0.298666i
\(41\) 4.94944 0.772972 0.386486 0.922295i \(-0.373689\pi\)
0.386486 + 0.922295i \(0.373689\pi\)
\(42\) 0 0
\(43\) 9.97862i 1.52172i 0.648913 + 0.760862i \(0.275224\pi\)
−0.648913 + 0.760862i \(0.724776\pi\)
\(44\) −0.979056 −0.147598
\(45\) 1.88893 + 1.19663i 0.281585 + 0.178384i
\(46\) −3.34271 −0.492855
\(47\) 4.40554i 0.642614i 0.946975 + 0.321307i \(0.104122\pi\)
−0.946975 + 0.321307i \(0.895878\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 0 0
\(50\) −4.52072 + 2.13613i −0.639327 + 0.302094i
\(51\) −2.79881 −0.391912
\(52\) 0.435157i 0.0603455i
\(53\) 0.657293i 0.0902861i −0.998981 0.0451431i \(-0.985626\pi\)
0.998981 0.0451431i \(-0.0143744\pi\)
\(54\) −1.00000 −0.136083
\(55\) −1.84937 1.17157i −0.249369 0.157975i
\(56\) 0 0
\(57\) 7.34271i 0.972565i
\(58\) 3.74825i 0.492169i
\(59\) −8.27226 −1.07696 −0.538478 0.842639i \(-0.681001\pi\)
−0.538478 + 0.842639i \(0.681001\pi\)
\(60\) 1.19663 1.88893i 0.154485 0.243860i
\(61\) −11.3336 −1.45112 −0.725559 0.688160i \(-0.758419\pi\)
−0.725559 + 0.688160i \(0.758419\pi\)
\(62\) 4.97906i 0.632341i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −0.520724 + 0.821983i −0.0645879 + 0.101954i
\(66\) 0.979056 0.120513
\(67\) 2.36365i 0.288766i 0.989522 + 0.144383i \(0.0461197\pi\)
−0.989522 + 0.144383i \(0.953880\pi\)
\(68\) 2.79881i 0.339405i
\(69\) 3.34271 0.402415
\(70\) 0 0
\(71\) −14.1119 −1.67477 −0.837387 0.546610i \(-0.815918\pi\)
−0.837387 + 0.546610i \(0.815918\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 15.3928i 1.80159i 0.434240 + 0.900797i \(0.357017\pi\)
−0.434240 + 0.900797i \(0.642983\pi\)
\(74\) −4.63591 −0.538914
\(75\) 4.52072 2.13613i 0.522008 0.246659i
\(76\) 7.34271 0.842266
\(77\) 0 0
\(78\) 0.435157i 0.0492719i
\(79\) 2.88767 0.324888 0.162444 0.986718i \(-0.448062\pi\)
0.162444 + 0.986718i \(0.448062\pi\)
\(80\) −1.88893 1.19663i −0.211189 0.133788i
\(81\) 1.00000 0.111111
\(82\) 4.94944i 0.546574i
\(83\) 14.3842i 1.57887i −0.613837 0.789433i \(-0.710375\pi\)
0.613837 0.789433i \(-0.289625\pi\)
\(84\) 0 0
\(85\) −3.34915 + 5.28676i −0.363266 + 0.573430i
\(86\) −9.97862 −1.07602
\(87\) 3.74825i 0.401854i
\(88\) 0.979056i 0.104368i
\(89\) −10.1210 −1.07282 −0.536412 0.843956i \(-0.680221\pi\)
−0.536412 + 0.843956i \(0.680221\pi\)
\(90\) −1.19663 + 1.88893i −0.126136 + 0.199111i
\(91\) 0 0
\(92\) 3.34271i 0.348501i
\(93\) 4.97906i 0.516304i
\(94\) −4.40554 −0.454397
\(95\) 13.8699 + 8.78654i 1.42302 + 0.901480i
\(96\) 1.00000 0.102062
\(97\) 10.6655i 1.08292i 0.840726 + 0.541460i \(0.182128\pi\)
−0.840726 + 0.541460i \(0.817872\pi\)
\(98\) 0 0
\(99\) −0.979056 −0.0983989
\(100\) −2.13613 4.52072i −0.213613 0.452072i
\(101\) 14.0328 1.39631 0.698157 0.715945i \(-0.254004\pi\)
0.698157 + 0.715945i \(0.254004\pi\)
\(102\) 2.79881i 0.277123i
\(103\) 10.3842i 1.02318i 0.859229 + 0.511591i \(0.170944\pi\)
−0.859229 + 0.511591i \(0.829056\pi\)
\(104\) −0.435157 −0.0426707
\(105\) 0 0
\(106\) 0.657293 0.0638419
\(107\) 20.0410i 1.93744i 0.248161 + 0.968719i \(0.420174\pi\)
−0.248161 + 0.968719i \(0.579826\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −18.6564 −1.78696 −0.893480 0.449102i \(-0.851744\pi\)
−0.893480 + 0.449102i \(0.851744\pi\)
\(110\) 1.17157 1.84937i 0.111705 0.176331i
\(111\) 4.63591 0.440021
\(112\) 0 0
\(113\) 10.4132i 0.979587i −0.871838 0.489794i \(-0.837072\pi\)
0.871838 0.489794i \(-0.162928\pi\)
\(114\) −7.34271 −0.687708
\(115\) 4.00000 6.31415i 0.373002 0.588797i
\(116\) 3.74825 0.348016
\(117\) 0.435157i 0.0402303i
\(118\) 8.27226i 0.761523i
\(119\) 0 0
\(120\) 1.88893 + 1.19663i 0.172435 + 0.109237i
\(121\) −10.0414 −0.912859
\(122\) 11.3336i 1.02610i
\(123\) 4.94944i 0.446276i
\(124\) −4.97906 −0.447132
\(125\) 1.37465 11.0955i 0.122953 0.992413i
\(126\) 0 0
\(127\) 11.6987i 1.03810i −0.854745 0.519048i \(-0.826287\pi\)
0.854745 0.519048i \(-0.173713\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 9.97862 0.878568
\(130\) −0.821983 0.520724i −0.0720926 0.0456706i
\(131\) 5.38459 0.470454 0.235227 0.971940i \(-0.424417\pi\)
0.235227 + 0.971940i \(0.424417\pi\)
\(132\) 0.979056i 0.0852159i
\(133\) 0 0
\(134\) −2.36365 −0.204188
\(135\) 1.19663 1.88893i 0.102990 0.162573i
\(136\) −2.79881 −0.239996
\(137\) 3.68585i 0.314904i 0.987527 + 0.157452i \(0.0503279\pi\)
−0.987527 + 0.157452i \(0.949672\pi\)
\(138\) 3.34271i 0.284550i
\(139\) −8.15378 −0.691595 −0.345797 0.938309i \(-0.612392\pi\)
−0.345797 + 0.938309i \(0.612392\pi\)
\(140\) 0 0
\(141\) 4.40554 0.371013
\(142\) 14.1119i 1.18424i
\(143\) 0.426043i 0.0356275i
\(144\) −1.00000 −0.0833333
\(145\) 7.08018 + 4.48528i 0.587977 + 0.372482i
\(146\) −15.3928 −1.27392
\(147\) 0 0
\(148\) 4.63591i 0.381069i
\(149\) 15.6774 1.28434 0.642170 0.766563i \(-0.278034\pi\)
0.642170 + 0.766563i \(0.278034\pi\)
\(150\) 2.13613 + 4.52072i 0.174414 + 0.369116i
\(151\) 4.27226 0.347672 0.173836 0.984775i \(-0.444384\pi\)
0.173836 + 0.984775i \(0.444384\pi\)
\(152\) 7.34271i 0.595572i
\(153\) 2.79881i 0.226270i
\(154\) 0 0
\(155\) −9.40510 5.95811i −0.755436 0.478567i
\(156\) 0.435157 0.0348405
\(157\) 15.2498i 1.21707i 0.793528 + 0.608534i \(0.208242\pi\)
−0.793528 + 0.608534i \(0.791758\pi\)
\(158\) 2.88767i 0.229730i
\(159\) −0.657293 −0.0521267
\(160\) 1.19663 1.88893i 0.0946023 0.149333i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 7.47599i 0.585564i 0.956179 + 0.292782i \(0.0945811\pi\)
−0.956179 + 0.292782i \(0.905419\pi\)
\(164\) −4.94944 −0.386486
\(165\) −1.17157 + 1.84937i −0.0912068 + 0.143973i
\(166\) 14.3842 1.11643
\(167\) 12.6640i 0.979972i −0.871730 0.489986i \(-0.837002\pi\)
0.871730 0.489986i \(-0.162998\pi\)
\(168\) 0 0
\(169\) 12.8106 0.985434
\(170\) −5.28676 3.34915i −0.405476 0.256868i
\(171\) 7.34271 0.561511
\(172\) 9.97862i 0.760862i
\(173\) 7.12057i 0.541367i −0.962668 0.270684i \(-0.912750\pi\)
0.962668 0.270684i \(-0.0872497\pi\)
\(174\) −3.74825 −0.284154
\(175\) 0 0
\(176\) 0.979056 0.0737991
\(177\) 8.27226i 0.621781i
\(178\) 10.1210i 0.758602i
\(179\) −3.26420 −0.243978 −0.121989 0.992531i \(-0.538927\pi\)
−0.121989 + 0.992531i \(0.538927\pi\)
\(180\) −1.88893 1.19663i −0.140793 0.0891919i
\(181\) 1.93823 0.144067 0.0720337 0.997402i \(-0.477051\pi\)
0.0720337 + 0.997402i \(0.477051\pi\)
\(182\) 0 0
\(183\) 11.3336i 0.837803i
\(184\) 3.34271 0.246428
\(185\) 5.54749 8.75692i 0.407860 0.643822i
\(186\) 4.97906 0.365082
\(187\) 2.74019i 0.200383i
\(188\) 4.40554i 0.321307i
\(189\) 0 0
\(190\) −8.78654 + 13.8699i −0.637443 + 1.00623i
\(191\) 8.07001 0.583925 0.291963 0.956430i \(-0.405692\pi\)
0.291963 + 0.956430i \(0.405692\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 1.95811i 0.140948i −0.997514 0.0704740i \(-0.977549\pi\)
0.997514 0.0704740i \(-0.0224512\pi\)
\(194\) −10.6655 −0.765740
\(195\) 0.821983 + 0.520724i 0.0588634 + 0.0372899i
\(196\) 0 0
\(197\) 17.3418i 1.23555i −0.786353 0.617777i \(-0.788033\pi\)
0.786353 0.617777i \(-0.211967\pi\)
\(198\) 0.979056i 0.0695785i
\(199\) −2.59490 −0.183948 −0.0919738 0.995761i \(-0.529318\pi\)
−0.0919738 + 0.995761i \(0.529318\pi\)
\(200\) 4.52072 2.13613i 0.319663 0.151047i
\(201\) 2.36365 0.166719
\(202\) 14.0328i 0.987343i
\(203\) 0 0
\(204\) 2.79881 0.195956
\(205\) −9.34915 5.92267i −0.652973 0.413657i
\(206\) −10.3842 −0.723498
\(207\) 3.34271i 0.232334i
\(208\) 0.435157i 0.0301727i
\(209\) −7.18892 −0.497268
\(210\) 0 0
\(211\) 15.4127 1.06106 0.530528 0.847668i \(-0.321994\pi\)
0.530528 + 0.847668i \(0.321994\pi\)
\(212\) 0.657293i 0.0451431i
\(213\) 14.1119i 0.966931i
\(214\) −20.0410 −1.36998
\(215\) 11.9408 18.8489i 0.814353 1.28549i
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 18.6564i 1.26357i
\(219\) 15.3928 1.04015
\(220\) 1.84937 + 1.17157i 0.124685 + 0.0789874i
\(221\) −1.21792 −0.0819263
\(222\) 4.63591i 0.311142i
\(223\) 7.61497i 0.509936i −0.966950 0.254968i \(-0.917935\pi\)
0.966950 0.254968i \(-0.0820649\pi\)
\(224\) 0 0
\(225\) −2.13613 4.52072i −0.142409 0.301382i
\(226\) 10.4132 0.692673
\(227\) 8.34227i 0.553696i −0.960914 0.276848i \(-0.910710\pi\)
0.960914 0.276848i \(-0.0892898\pi\)
\(228\) 7.34271i 0.486283i
\(229\) −18.6901 −1.23507 −0.617537 0.786542i \(-0.711869\pi\)
−0.617537 + 0.786542i \(0.711869\pi\)
\(230\) 6.31415 + 4.00000i 0.416343 + 0.263752i
\(231\) 0 0
\(232\) 3.74825i 0.246084i
\(233\) 20.0829i 1.31567i −0.753160 0.657837i \(-0.771471\pi\)
0.753160 0.657837i \(-0.228529\pi\)
\(234\) −0.435157 −0.0284471
\(235\) 5.27182 8.32176i 0.343896 0.542852i
\(236\) 8.27226 0.538478
\(237\) 2.88767i 0.187574i
\(238\) 0 0
\(239\) 22.2714 1.44062 0.720308 0.693654i \(-0.244000\pi\)
0.720308 + 0.693654i \(0.244000\pi\)
\(240\) −1.19663 + 1.88893i −0.0772425 + 0.121930i
\(241\) −6.20075 −0.399426 −0.199713 0.979854i \(-0.564001\pi\)
−0.199713 + 0.979854i \(0.564001\pi\)
\(242\) 10.0414i 0.645489i
\(243\) 1.00000i 0.0641500i
\(244\) 11.3336 0.725559
\(245\) 0 0
\(246\) 4.94944 0.315565
\(247\) 3.19523i 0.203308i
\(248\) 4.97906i 0.316170i
\(249\) −14.3842 −0.911559
\(250\) 11.0955 + 1.37465i 0.701742 + 0.0869406i
\(251\) −27.6560 −1.74563 −0.872815 0.488051i \(-0.837708\pi\)
−0.872815 + 0.488051i \(0.837708\pi\)
\(252\) 0 0
\(253\) 3.27270i 0.205753i
\(254\) 11.6987 0.734044
\(255\) 5.28676 + 3.34915i 0.331070 + 0.209732i
\(256\) 1.00000 0.0625000
\(257\) 11.7681i 0.734076i −0.930206 0.367038i \(-0.880372\pi\)
0.930206 0.367038i \(-0.119628\pi\)
\(258\) 9.97862i 0.621242i
\(259\) 0 0
\(260\) 0.520724 0.821983i 0.0322940 0.0509772i
\(261\) 3.74825 0.232011
\(262\) 5.38459i 0.332661i
\(263\) 0.455042i 0.0280591i 0.999902 + 0.0140295i \(0.00446589\pi\)
−0.999902 + 0.0140295i \(0.995534\pi\)
\(264\) −0.979056 −0.0602567
\(265\) −0.786540 + 1.24158i −0.0483167 + 0.0762698i
\(266\) 0 0
\(267\) 10.1210i 0.619396i
\(268\) 2.36365i 0.144383i
\(269\) −26.1375 −1.59363 −0.796815 0.604223i \(-0.793484\pi\)
−0.796815 + 0.604223i \(0.793484\pi\)
\(270\) 1.88893 + 1.19663i 0.114957 + 0.0728249i
\(271\) 16.7768 1.01912 0.509559 0.860436i \(-0.329808\pi\)
0.509559 + 0.860436i \(0.329808\pi\)
\(272\) 2.79881i 0.169703i
\(273\) 0 0
\(274\) −3.68585 −0.222671
\(275\) 2.09139 + 4.42604i 0.126116 + 0.266900i
\(276\) −3.34271 −0.201207
\(277\) 20.7478i 1.24661i −0.781977 0.623307i \(-0.785789\pi\)
0.781977 0.623307i \(-0.214211\pi\)
\(278\) 8.15378i 0.489031i
\(279\) −4.97906 −0.298088
\(280\) 0 0
\(281\) −18.3141 −1.09253 −0.546265 0.837612i \(-0.683951\pi\)
−0.546265 + 0.837612i \(0.683951\pi\)
\(282\) 4.40554i 0.262346i
\(283\) 11.8525i 0.704560i 0.935895 + 0.352280i \(0.114593\pi\)
−0.935895 + 0.352280i \(0.885407\pi\)
\(284\) 14.1119 0.837387
\(285\) 8.78654 13.8699i 0.520470 0.821581i
\(286\) 0.426043 0.0251925
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) 9.16667 0.539216
\(290\) −4.48528 + 7.08018i −0.263385 + 0.415763i
\(291\) 10.6655 0.625224
\(292\) 15.3928i 0.900797i
\(293\) 14.4770i 0.845758i 0.906186 + 0.422879i \(0.138980\pi\)
−0.906186 + 0.422879i \(0.861020\pi\)
\(294\) 0 0
\(295\) 15.6257 + 9.89887i 0.909766 + 0.576335i
\(296\) 4.63591 0.269457
\(297\) 0.979056i 0.0568106i
\(298\) 15.6774i 0.908165i
\(299\) 1.45460 0.0841219
\(300\) −4.52072 + 2.13613i −0.261004 + 0.123330i
\(301\) 0 0
\(302\) 4.27226i 0.245841i
\(303\) 14.0328i 0.806162i
\(304\) −7.34271 −0.421133
\(305\) 21.4084 + 13.5622i 1.22584 + 0.776568i
\(306\) −2.79881 −0.159997
\(307\) 30.4252i 1.73646i 0.496165 + 0.868228i \(0.334741\pi\)
−0.496165 + 0.868228i \(0.665259\pi\)
\(308\) 0 0
\(309\) 10.3842 0.590734
\(310\) 5.95811 9.40510i 0.338398 0.534174i
\(311\) −9.02856 −0.511963 −0.255981 0.966682i \(-0.582399\pi\)
−0.255981 + 0.966682i \(0.582399\pi\)
\(312\) 0.435157i 0.0246359i
\(313\) 17.1732i 0.970688i −0.874323 0.485344i \(-0.838694\pi\)
0.874323 0.485344i \(-0.161306\pi\)
\(314\) −15.2498 −0.860597
\(315\) 0 0
\(316\) −2.88767 −0.162444
\(317\) 2.61541i 0.146896i 0.997299 + 0.0734479i \(0.0234003\pi\)
−0.997299 + 0.0734479i \(0.976600\pi\)
\(318\) 0.657293i 0.0368592i
\(319\) −3.66974 −0.205466
\(320\) 1.88893 + 1.19663i 0.105595 + 0.0668939i
\(321\) 20.0410 1.11858
\(322\) 0 0
\(323\) 20.5508i 1.14348i
\(324\) −1.00000 −0.0555556
\(325\) 1.96723 0.929553i 0.109122 0.0515623i
\(326\) −7.47599 −0.414057
\(327\) 18.6564i 1.03170i
\(328\) 4.94944i 0.273287i
\(329\) 0 0
\(330\) −1.84937 1.17157i −0.101805 0.0644930i
\(331\) −17.7559 −0.975950 −0.487975 0.872857i \(-0.662264\pi\)
−0.487975 + 0.872857i \(0.662264\pi\)
\(332\) 14.3842i 0.789433i
\(333\) 4.63591i 0.254046i
\(334\) 12.6640 0.692945
\(335\) 2.82843 4.46478i 0.154533 0.243937i
\(336\) 0 0
\(337\) 24.2304i 1.31991i −0.751304 0.659956i \(-0.770575\pi\)
0.751304 0.659956i \(-0.229425\pi\)
\(338\) 12.8106i 0.696807i
\(339\) −10.4132 −0.565565
\(340\) 3.34915 5.28676i 0.181633 0.286715i
\(341\) 4.87478 0.263984
\(342\) 7.34271i 0.397048i
\(343\) 0 0
\(344\) 9.97862 0.538011
\(345\) −6.31415 4.00000i −0.339942 0.215353i
\(346\) 7.12057 0.382804
\(347\) 30.4252i 1.63331i 0.577127 + 0.816654i \(0.304174\pi\)
−0.577127 + 0.816654i \(0.695826\pi\)
\(348\) 3.74825i 0.200927i
\(349\) −30.2623 −1.61990 −0.809951 0.586497i \(-0.800506\pi\)
−0.809951 + 0.586497i \(0.800506\pi\)
\(350\) 0 0
\(351\) 0.435157 0.0232270
\(352\) 0.979056i 0.0521839i
\(353\) 4.37189i 0.232692i −0.993209 0.116346i \(-0.962882\pi\)
0.993209 0.116346i \(-0.0371182\pi\)
\(354\) −8.27226 −0.439666
\(355\) 26.6564 + 16.8868i 1.41478 + 0.896258i
\(356\) 10.1210 0.536412
\(357\) 0 0
\(358\) 3.26420i 0.172519i
\(359\) 15.6850 0.827821 0.413911 0.910318i \(-0.364163\pi\)
0.413911 + 0.910318i \(0.364163\pi\)
\(360\) 1.19663 1.88893i 0.0630682 0.0995555i
\(361\) 34.9153 1.83765
\(362\) 1.93823i 0.101871i
\(363\) 10.0414i 0.527039i
\(364\) 0 0
\(365\) 18.4196 29.0760i 0.964126 1.52191i
\(366\) −11.3336 −0.592416
\(367\) 4.94478i 0.258116i −0.991637 0.129058i \(-0.958805\pi\)
0.991637 0.129058i \(-0.0411953\pi\)
\(368\) 3.34271i 0.174251i
\(369\) −4.94944 −0.257657
\(370\) 8.75692 + 5.54749i 0.455251 + 0.288400i
\(371\) 0 0
\(372\) 4.97906i 0.258152i
\(373\) 6.02138i 0.311775i 0.987775 + 0.155888i \(0.0498238\pi\)
−0.987775 + 0.155888i \(0.950176\pi\)
\(374\) 2.74019 0.141692
\(375\) −11.0955 1.37465i −0.572970 0.0709867i
\(376\) 4.40554 0.227198
\(377\) 1.63108i 0.0840047i
\(378\) 0 0
\(379\) 36.8030 1.89044 0.945222 0.326429i \(-0.105845\pi\)
0.945222 + 0.326429i \(0.105845\pi\)
\(380\) −13.8699 8.78654i −0.711510 0.450740i
\(381\) −11.6987 −0.599345
\(382\) 8.07001i 0.412898i
\(383\) 9.03383i 0.461607i −0.973000 0.230804i \(-0.925864\pi\)
0.973000 0.230804i \(-0.0741355\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 1.95811 0.0996653
\(387\) 9.97862i 0.507242i
\(388\) 10.6655i 0.541460i
\(389\) −33.5646 −1.70179 −0.850896 0.525334i \(-0.823940\pi\)
−0.850896 + 0.525334i \(0.823940\pi\)
\(390\) −0.520724 + 0.821983i −0.0263679 + 0.0416227i
\(391\) 9.35560 0.473133
\(392\) 0 0
\(393\) 5.38459i 0.271617i
\(394\) 17.3418 0.873669
\(395\) −5.45460 3.45548i −0.274451 0.173864i
\(396\) 0.979056 0.0491994
\(397\) 33.9792i 1.70537i −0.522426 0.852685i \(-0.674973\pi\)
0.522426 0.852685i \(-0.325027\pi\)
\(398\) 2.59490i 0.130071i
\(399\) 0 0
\(400\) 2.13613 + 4.52072i 0.106806 + 0.226036i
\(401\) −4.27226 −0.213346 −0.106673 0.994294i \(-0.534020\pi\)
−0.106673 + 0.994294i \(0.534020\pi\)
\(402\) 2.36365i 0.117888i
\(403\) 2.16667i 0.107930i
\(404\) −14.0328 −0.698157
\(405\) −1.88893 1.19663i −0.0938618 0.0594613i
\(406\) 0 0
\(407\) 4.53882i 0.224981i
\(408\) 2.79881i 0.138562i
\(409\) −3.63888 −0.179931 −0.0899656 0.995945i \(-0.528676\pi\)
−0.0899656 + 0.995945i \(0.528676\pi\)
\(410\) 5.92267 9.34915i 0.292500 0.461722i
\(411\) 3.68585 0.181810
\(412\) 10.3842i 0.511591i
\(413\) 0 0
\(414\) 3.34271 0.164285
\(415\) −17.2126 + 27.1707i −0.844932 + 1.33376i
\(416\) 0.435157 0.0213353
\(417\) 8.15378i 0.399293i
\(418\) 7.18892i 0.351622i
\(419\) 26.6274 1.30083 0.650417 0.759577i \(-0.274594\pi\)
0.650417 + 0.759577i \(0.274594\pi\)
\(420\) 0 0
\(421\) −15.1880 −0.740220 −0.370110 0.928988i \(-0.620680\pi\)
−0.370110 + 0.928988i \(0.620680\pi\)
\(422\) 15.4127i 0.750279i
\(423\) 4.40554i 0.214205i
\(424\) −0.657293 −0.0319210
\(425\) 12.6526 5.97862i 0.613743 0.290006i
\(426\) −14.1119 −0.683724
\(427\) 0 0
\(428\) 20.0410i 0.968719i
\(429\) −0.426043 −0.0205696
\(430\) 18.8489 + 11.9408i 0.908976 + 0.575835i
\(431\) −4.23125 −0.203812 −0.101906 0.994794i \(-0.532494\pi\)
−0.101906 + 0.994794i \(0.532494\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 33.9352i 1.63082i 0.578882 + 0.815412i \(0.303489\pi\)
−0.578882 + 0.815412i \(0.696511\pi\)
\(434\) 0 0
\(435\) 4.48528 7.08018i 0.215053 0.339469i
\(436\) 18.6564 0.893480
\(437\) 24.5445i 1.17412i
\(438\) 15.3928i 0.735498i
\(439\) −5.48257 −0.261669 −0.130834 0.991404i \(-0.541766\pi\)
−0.130834 + 0.991404i \(0.541766\pi\)
\(440\) −1.17157 + 1.84937i −0.0558525 + 0.0881653i
\(441\) 0 0
\(442\) 1.21792i 0.0579306i
\(443\) 1.23081i 0.0584776i −0.999572 0.0292388i \(-0.990692\pi\)
0.999572 0.0292388i \(-0.00930832\pi\)
\(444\) −4.63591 −0.220011
\(445\) 19.1179 + 12.1112i 0.906275 + 0.574124i
\(446\) 7.61497 0.360579
\(447\) 15.6774i 0.741514i
\(448\) 0 0
\(449\) −14.6435 −0.691071 −0.345535 0.938406i \(-0.612303\pi\)
−0.345535 + 0.938406i \(0.612303\pi\)
\(450\) 4.52072 2.13613i 0.213109 0.100698i
\(451\) 4.84578 0.228179
\(452\) 10.4132i 0.489794i
\(453\) 4.27226i 0.200728i
\(454\) 8.34227 0.391522
\(455\) 0 0
\(456\) 7.34271 0.343854
\(457\) 31.3289i 1.46551i −0.680495 0.732753i \(-0.738235\pi\)
0.680495 0.732753i \(-0.261765\pi\)
\(458\) 18.6901i 0.873329i
\(459\) 2.79881 0.130637
\(460\) −4.00000 + 6.31415i −0.186501 + 0.294399i
\(461\) −12.7667 −0.594602 −0.297301 0.954784i \(-0.596087\pi\)
−0.297301 + 0.954784i \(0.596087\pi\)
\(462\) 0 0
\(463\) 26.7112i 1.24137i 0.784058 + 0.620687i \(0.213146\pi\)
−0.784058 + 0.620687i \(0.786854\pi\)
\(464\) −3.74825 −0.174008
\(465\) −5.95811 + 9.40510i −0.276301 + 0.436151i
\(466\) 20.0829 0.930322
\(467\) 37.6141i 1.74057i 0.492546 + 0.870286i \(0.336066\pi\)
−0.492546 + 0.870286i \(0.663934\pi\)
\(468\) 0.435157i 0.0201152i
\(469\) 0 0
\(470\) 8.32176 + 5.27182i 0.383854 + 0.243171i
\(471\) 15.2498 0.702675
\(472\) 8.27226i 0.380762i
\(473\) 9.76963i 0.449208i
\(474\) 2.88767 0.132635
\(475\) −15.6850 33.1944i −0.719676 1.52306i
\(476\) 0 0
\(477\) 0.657293i 0.0300954i
\(478\) 22.2714i 1.01867i
\(479\) −23.8235 −1.08852 −0.544262 0.838915i \(-0.683190\pi\)
−0.544262 + 0.838915i \(0.683190\pi\)
\(480\) −1.88893 1.19663i −0.0862176 0.0546187i
\(481\) 2.01735 0.0919833
\(482\) 6.20075i 0.282437i
\(483\) 0 0
\(484\) 10.0414 0.456429
\(485\) 12.7627 20.1465i 0.579526 0.914804i
\(486\) 1.00000 0.0453609
\(487\) 3.75674i 0.170234i −0.996371 0.0851170i \(-0.972874\pi\)
0.996371 0.0851170i \(-0.0271264\pi\)
\(488\) 11.3336i 0.513048i
\(489\) 7.47599 0.338076
\(490\) 0 0
\(491\) 2.00762 0.0906025 0.0453012 0.998973i \(-0.485575\pi\)
0.0453012 + 0.998973i \(0.485575\pi\)
\(492\) 4.94944i 0.223138i
\(493\) 10.4906i 0.472474i
\(494\) −3.19523 −0.143760
\(495\) 1.84937 + 1.17157i 0.0831230 + 0.0526583i
\(496\) 4.97906 0.223566
\(497\) 0 0
\(498\) 14.3842i 0.644569i
\(499\) 0.628294 0.0281263 0.0140632 0.999901i \(-0.495523\pi\)
0.0140632 + 0.999901i \(0.495523\pi\)
\(500\) −1.37465 + 11.0955i −0.0614763 + 0.496206i
\(501\) −12.6640 −0.565787
\(502\) 27.6560i 1.23435i
\(503\) 28.9911i 1.29265i 0.763063 + 0.646324i \(0.223695\pi\)
−0.763063 + 0.646324i \(0.776305\pi\)
\(504\) 0 0
\(505\) −26.5070 16.7921i −1.17954 0.747239i
\(506\) −3.27270 −0.145489
\(507\) 12.8106i 0.568940i
\(508\) 11.6987i 0.519048i
\(509\) −15.5056 −0.687274 −0.343637 0.939103i \(-0.611659\pi\)
−0.343637 + 0.939103i \(0.611659\pi\)
\(510\) −3.34915 + 5.28676i −0.148303 + 0.234102i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 7.34271i 0.324188i
\(514\) 11.7681 0.519070
\(515\) 12.4260 19.6150i 0.547557 0.864339i
\(516\) −9.97862 −0.439284
\(517\) 4.31327i 0.189697i
\(518\) 0 0
\(519\) −7.12057 −0.312558
\(520\) 0.821983 + 0.520724i 0.0360463 + 0.0228353i
\(521\) 13.5532 0.593776 0.296888 0.954912i \(-0.404051\pi\)
0.296888 + 0.954912i \(0.404051\pi\)
\(522\) 3.74825i 0.164056i
\(523\) 22.4542i 0.981852i 0.871201 + 0.490926i \(0.163341\pi\)
−0.871201 + 0.490926i \(0.836659\pi\)
\(524\) −5.38459 −0.235227
\(525\) 0 0
\(526\) −0.455042 −0.0198408
\(527\) 13.9354i 0.607037i
\(528\) 0.979056i 0.0426080i
\(529\) 11.8263 0.514187
\(530\) −1.24158 0.786540i −0.0539309 0.0341651i
\(531\) 8.27226 0.358985
\(532\) 0 0
\(533\) 2.15378i 0.0932907i
\(534\) −10.1210 −0.437979
\(535\) 23.9818 37.8561i 1.03682 1.63666i
\(536\) 2.36365 0.102094
\(537\) 3.26420i 0.140861i
\(538\) 26.1375i 1.12687i
\(539\) 0 0
\(540\) −1.19663 + 1.88893i −0.0514950 + 0.0812867i
\(541\) 10.8111 0.464804 0.232402 0.972620i \(-0.425341\pi\)
0.232402 + 0.972620i \(0.425341\pi\)
\(542\) 16.7768i 0.720625i
\(543\) 1.93823i 0.0831773i
\(544\) 2.79881 0.119998
\(545\) 35.2407 + 22.3249i 1.50955 + 0.956294i
\(546\) 0 0
\(547\) 24.1881i 1.03421i −0.855923 0.517103i \(-0.827010\pi\)
0.855923 0.517103i \(-0.172990\pi\)
\(548\) 3.68585i 0.157452i
\(549\) 11.3336 0.483706
\(550\) −4.42604 + 2.09139i −0.188727 + 0.0891772i
\(551\) 27.5223 1.17249
\(552\) 3.34271i 0.142275i
\(553\) 0 0
\(554\) 20.7478 0.881490
\(555\) −8.75692 5.54749i −0.371711 0.235478i
\(556\) 8.15378 0.345797
\(557\) 26.1529i 1.10813i −0.832472 0.554067i \(-0.813075\pi\)
0.832472 0.554067i \(-0.186925\pi\)
\(558\) 4.97906i 0.210780i
\(559\) 4.34227 0.183658
\(560\) 0 0
\(561\) −2.74019 −0.115691
\(562\) 18.3141i 0.772536i
\(563\) 10.5864i 0.446164i 0.974800 + 0.223082i \(0.0716117\pi\)
−0.974800 + 0.223082i \(0.928388\pi\)
\(564\) −4.40554 −0.185507
\(565\) −12.4607 + 19.6697i −0.524227 + 0.827512i
\(566\) −11.8525 −0.498199
\(567\) 0 0
\(568\) 14.1119i 0.592122i
\(569\) −15.6440 −0.655829 −0.327915 0.944707i \(-0.606346\pi\)
−0.327915 + 0.944707i \(0.606346\pi\)
\(570\) 13.8699 + 8.78654i 0.580945 + 0.368028i
\(571\) 8.50982 0.356125 0.178062 0.984019i \(-0.443017\pi\)
0.178062 + 0.984019i \(0.443017\pi\)
\(572\) 0.426043i 0.0178138i
\(573\) 8.07001i 0.337129i
\(574\) 0 0
\(575\) −15.1115 + 7.14046i −0.630191 + 0.297778i
\(576\) 1.00000 0.0416667
\(577\) 9.67798i 0.402900i 0.979499 + 0.201450i \(0.0645653\pi\)
−0.979499 + 0.201450i \(0.935435\pi\)
\(578\) 9.16667i 0.381283i
\(579\) −1.95811 −0.0813764
\(580\) −7.08018 4.48528i −0.293989 0.186241i
\(581\) 0 0
\(582\) 10.6655i 0.442100i
\(583\) 0.643527i 0.0266522i
\(584\) 15.3928 0.636960
\(585\) 0.520724 0.821983i 0.0215293 0.0339848i
\(586\) −14.4770 −0.598041
\(587\) 16.3013i 0.672825i −0.941715 0.336412i \(-0.890786\pi\)
0.941715 0.336412i \(-0.109214\pi\)
\(588\) 0 0
\(589\) −36.5598 −1.50642
\(590\) −9.89887 + 15.6257i −0.407530 + 0.643301i
\(591\) −17.3418 −0.713348
\(592\) 4.63591i 0.190535i
\(593\) 12.4802i 0.512500i 0.966610 + 0.256250i \(0.0824871\pi\)
−0.966610 + 0.256250i \(0.917513\pi\)
\(594\) −0.979056 −0.0401712
\(595\) 0 0
\(596\) −15.6774 −0.642170
\(597\) 2.59490i 0.106202i
\(598\) 1.45460i 0.0594832i
\(599\) −40.7545 −1.66519 −0.832593 0.553886i \(-0.813144\pi\)
−0.832593 + 0.553886i \(0.813144\pi\)
\(600\) −2.13613 4.52072i −0.0872071 0.184558i
\(601\) −4.94541 −0.201727 −0.100864 0.994900i \(-0.532161\pi\)
−0.100864 + 0.994900i \(0.532161\pi\)
\(602\) 0 0
\(603\) 2.36365i 0.0962553i
\(604\) −4.27226 −0.173836
\(605\) 18.9676 + 12.0159i 0.771143 + 0.488518i
\(606\) 14.0328 0.570042
\(607\) 0.871555i 0.0353753i −0.999844 0.0176877i \(-0.994370\pi\)
0.999844 0.0176877i \(-0.00563045\pi\)
\(608\) 7.34271i 0.297786i
\(609\) 0 0
\(610\) −13.5622 + 21.4084i −0.549116 + 0.866800i
\(611\) 1.91710 0.0775577
\(612\) 2.79881i 0.113135i
\(613\) 36.9007i 1.49041i −0.666838 0.745203i \(-0.732353\pi\)
0.666838 0.745203i \(-0.267647\pi\)
\(614\) −30.4252 −1.22786
\(615\) −5.92267 + 9.34915i −0.238825 + 0.376994i
\(616\) 0 0
\(617\) 28.6911i 1.15506i 0.816369 + 0.577530i \(0.195984\pi\)
−0.816369 + 0.577530i \(0.804016\pi\)
\(618\) 10.3842i 0.417712i
\(619\) −6.31415 −0.253787 −0.126894 0.991916i \(-0.540501\pi\)
−0.126894 + 0.991916i \(0.540501\pi\)
\(620\) 9.40510 + 5.95811i 0.377718 + 0.239284i
\(621\) −3.34271 −0.134138
\(622\) 9.02856i 0.362012i
\(623\) 0 0
\(624\) −0.435157 −0.0174202
\(625\) −15.8739 + 19.3137i −0.634956 + 0.772548i
\(626\) 17.1732 0.686380
\(627\) 7.18892i 0.287098i
\(628\) 15.2498i 0.608534i
\(629\) 12.9750 0.517348
\(630\) 0 0
\(631\) −0.237559 −0.00945707 −0.00472853 0.999989i \(-0.501505\pi\)
−0.00472853 + 0.999989i \(0.501505\pi\)
\(632\) 2.88767i 0.114865i
\(633\) 15.4127i 0.612600i
\(634\) −2.61541 −0.103871
\(635\) −13.9991 + 22.0981i −0.555538 + 0.876938i
\(636\) 0.657293 0.0260634
\(637\) 0 0
\(638\) 3.66974i 0.145287i
\(639\) 14.1119 0.558258
\(640\) −1.19663 + 1.88893i −0.0473011 + 0.0746666i
\(641\) −15.3490 −0.606250 −0.303125 0.952951i \(-0.598030\pi\)
−0.303125 + 0.952951i \(0.598030\pi\)
\(642\) 20.0410i 0.790956i
\(643\) 8.77577i 0.346083i 0.984915 + 0.173041i \(0.0553594\pi\)
−0.984915 + 0.173041i \(0.944641\pi\)
\(644\) 0 0
\(645\) −18.8489 11.9408i −0.742176 0.470167i
\(646\) −20.5508 −0.808562
\(647\) 19.2504i 0.756813i 0.925640 + 0.378406i \(0.123528\pi\)
−0.925640 + 0.378406i \(0.876472\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −8.09901 −0.317914
\(650\) 0.929553 + 1.96723i 0.0364600 + 0.0771610i
\(651\) 0 0
\(652\) 7.47599i 0.292782i
\(653\) 7.45460i 0.291721i −0.989305 0.145861i \(-0.953405\pi\)
0.989305 0.145861i \(-0.0465951\pi\)
\(654\) −18.6564 −0.729524
\(655\) −10.1711 6.44339i −0.397419 0.251764i
\(656\) 4.94944 0.193243
\(657\) 15.3928i 0.600532i
\(658\) 0 0
\(659\) −2.93717 −0.114416 −0.0572079 0.998362i \(-0.518220\pi\)
−0.0572079 + 0.998362i \(0.518220\pi\)
\(660\) 1.17157 1.84937i 0.0456034 0.0719867i
\(661\) −23.6361 −0.919337 −0.459669 0.888090i \(-0.652032\pi\)
−0.459669 + 0.888090i \(0.652032\pi\)
\(662\) 17.7559i 0.690101i
\(663\) 1.21792i 0.0473002i
\(664\) −14.3842 −0.558214
\(665\) 0 0
\(666\) 4.63591 0.179638
\(667\) 12.5293i 0.485136i
\(668\) 12.6640i 0.489986i
\(669\) −7.61497 −0.294412
\(670\) 4.46478 + 2.82843i 0.172489 + 0.109272i
\(671\) −11.0962 −0.428365
\(672\) 0 0
\(673\) 50.9568i 1.96424i 0.188256 + 0.982120i \(0.439717\pi\)
−0.188256 + 0.982120i \(0.560283\pi\)
\(674\) 24.2304 0.933319
\(675\) −4.52072 + 2.13613i −0.174003 + 0.0822197i
\(676\) −12.8106 −0.492717
\(677\) 5.23992i 0.201387i −0.994918 0.100693i \(-0.967894\pi\)
0.994918 0.100693i \(-0.0321061\pi\)
\(678\) 10.4132i 0.399915i
\(679\) 0 0
\(680\) 5.28676 + 3.34915i 0.202738 + 0.128434i
\(681\) −8.34227 −0.319676
\(682\) 4.87478i 0.186665i
\(683\) 32.2648i 1.23458i −0.786736 0.617289i \(-0.788231\pi\)
0.786736 0.617289i \(-0.211769\pi\)
\(684\) −7.34271 −0.280755
\(685\) 4.41062 6.96233i 0.168521 0.266017i
\(686\) 0 0
\(687\) 18.6901i 0.713071i
\(688\) 9.97862i 0.380431i
\(689\) −0.286026 −0.0108967
\(690\) 4.00000 6.31415i 0.152277 0.240375i
\(691\) −20.4470 −0.777840 −0.388920 0.921272i \(-0.627152\pi\)
−0.388920 + 0.921272i \(0.627152\pi\)
\(692\) 7.12057i 0.270684i
\(693\) 0 0
\(694\) −30.4252 −1.15492
\(695\) 15.4019 + 9.75710i 0.584229 + 0.370108i
\(696\) 3.74825 0.142077
\(697\) 13.8525i 0.524702i
\(698\) 30.2623i 1.14544i
\(699\) −20.0829 −0.759605
\(700\) 0 0
\(701\) −15.4969 −0.585311 −0.292655 0.956218i \(-0.594539\pi\)
−0.292655 + 0.956218i \(0.594539\pi\)
\(702\) 0.435157i 0.0164240i
\(703\) 34.0401i 1.28385i
\(704\) −0.979056 −0.0368996
\(705\) −8.32176 5.27182i −0.313416 0.198548i
\(706\) 4.37189 0.164538
\(707\) 0 0
\(708\) 8.27226i 0.310891i
\(709\) −38.9212 −1.46172 −0.730859 0.682529i \(-0.760880\pi\)
−0.730859 + 0.682529i \(0.760880\pi\)
\(710\) −16.8868 + 26.6564i −0.633750 + 1.00040i
\(711\) −2.88767 −0.108296
\(712\) 10.1210i 0.379301i
\(713\) 16.6435i 0.623305i
\(714\) 0 0
\(715\) −0.509819 + 0.804767i −0.0190661 + 0.0300966i
\(716\) 3.26420 0.121989
\(717\) 22.2714i 0.831740i
\(718\) 15.6850i 0.585358i
\(719\) −3.53119 −0.131691 −0.0658456 0.997830i \(-0.520974\pi\)
−0.0658456 + 0.997830i \(0.520974\pi\)
\(720\) 1.88893 + 1.19663i 0.0703963 + 0.0445959i
\(721\) 0 0
\(722\) 34.9153i 1.29941i
\(723\) 6.20075i 0.230608i
\(724\) −1.93823 −0.0720337
\(725\) −8.00674 16.9448i −0.297363 0.629314i
\(726\) −10.0414 −0.372673
\(727\) 45.2934i 1.67984i −0.542712 0.839919i \(-0.682602\pi\)
0.542712 0.839919i \(-0.317398\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 29.0760 + 18.4196i 1.07615 + 0.681740i
\(731\) 27.9282 1.03296
\(732\) 11.3336i 0.418902i
\(733\) 48.5462i 1.79309i 0.442949 + 0.896547i \(0.353932\pi\)
−0.442949 + 0.896547i \(0.646068\pi\)
\(734\) 4.94478 0.182515
\(735\) 0 0
\(736\) −3.34271 −0.123214
\(737\) 2.31415i 0.0852427i
\(738\) 4.94944i 0.182191i
\(739\) −25.7969 −0.948953 −0.474477 0.880268i \(-0.657363\pi\)
−0.474477 + 0.880268i \(0.657363\pi\)
\(740\) −5.54749 + 8.75692i −0.203930 + 0.321911i
\(741\) 3.19523 0.117380
\(742\) 0 0
\(743\) 28.7192i 1.05361i 0.849987 + 0.526803i \(0.176610\pi\)
−0.849987 + 0.526803i \(0.823390\pi\)
\(744\) −4.97906 −0.182541
\(745\) −29.6135 18.7601i −1.08495 0.687316i
\(746\) −6.02138 −0.220458
\(747\) 14.3842i 0.526289i
\(748\) 2.74019i 0.100191i
\(749\) 0 0
\(750\) 1.37465 11.0955i 0.0501952 0.405151i
\(751\) −34.1876 −1.24752 −0.623762 0.781615i \(-0.714396\pi\)
−0.623762 + 0.781615i \(0.714396\pi\)
\(752\) 4.40554i 0.160653i
\(753\) 27.6560i 1.00784i
\(754\) −1.63108 −0.0594003
\(755\) −8.07001 5.11233i −0.293698 0.186057i
\(756\) 0 0
\(757\) 41.4622i 1.50697i −0.657465 0.753485i \(-0.728371\pi\)
0.657465 0.753485i \(-0.271629\pi\)
\(758\) 36.8030i 1.33675i
\(759\) 3.27270 0.118791
\(760\) 8.78654 13.8699i 0.318721 0.503113i
\(761\) −27.6941 −1.00391 −0.501955 0.864894i \(-0.667386\pi\)
−0.501955 + 0.864894i \(0.667386\pi\)
\(762\) 11.6987i 0.423801i
\(763\) 0 0
\(764\) −8.07001 −0.291963
\(765\) 3.34915 5.28676i 0.121089 0.191143i
\(766\) 9.03383 0.326406
\(767\) 3.59973i 0.129979i
\(768\) 1.00000i 0.0360844i
\(769\) 9.74001 0.351234 0.175617 0.984459i \(-0.443808\pi\)
0.175617 + 0.984459i \(0.443808\pi\)
\(770\) 0 0
\(771\) −11.7681 −0.423819
\(772\) 1.95811i 0.0704740i
\(773\) 30.6171i 1.10122i 0.834763 + 0.550610i \(0.185605\pi\)
−0.834763 + 0.550610i \(0.814395\pi\)
\(774\) 9.97862 0.358674
\(775\) 10.6359 + 22.5089i 0.382053 + 0.808545i
\(776\) 10.6655 0.382870
\(777\) 0 0
\(778\) 33.5646i 1.20335i
\(779\) −36.3423 −1.30210
\(780\) −0.821983 0.520724i −0.0294317 0.0186449i
\(781\) −13.8163 −0.494388
\(782\) 9.35560i 0.334555i
\(783\) 3.74825i 0.133951i
\(784\) 0 0
\(785\) 18.2485 28.8059i 0.651316 1.02813i
\(786\) 5.38459 0.192062
\(787\) 15.7977i 0.563129i −0.959542 0.281564i \(-0.909147\pi\)
0.959542 0.281564i \(-0.0908533\pi\)
\(788\) 17.3418i 0.617777i
\(789\) 0.455042 0.0161999
\(790\) 3.45548 5.45460i 0.122940 0.194066i
\(791\) 0 0
\(792\) 0.979056i 0.0347892i