Properties

Label 731.2.m.c.87.1
Level 731
Weight 2
Character 731.87
Analytic conductor 5.837
Analytic rank 0
Dimension 128
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.m (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 87.1
Character \(\chi\) = 731.87
Dual form 731.2.m.c.689.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.95137 - 1.95137i) q^{2} +(1.54767 - 0.641064i) q^{3} +5.61567i q^{4} +(0.779040 + 1.88077i) q^{5} +(-4.27102 - 1.76911i) q^{6} +(-0.326309 + 0.787780i) q^{7} +(7.05550 - 7.05550i) q^{8} +(-0.137012 + 0.137012i) q^{9} +O(q^{10})\) \(q+(-1.95137 - 1.95137i) q^{2} +(1.54767 - 0.641064i) q^{3} +5.61567i q^{4} +(0.779040 + 1.88077i) q^{5} +(-4.27102 - 1.76911i) q^{6} +(-0.326309 + 0.787780i) q^{7} +(7.05550 - 7.05550i) q^{8} +(-0.137012 + 0.137012i) q^{9} +(2.14988 - 5.19027i) q^{10} +(1.25834 + 0.521220i) q^{11} +(3.60001 + 8.69118i) q^{12} +3.25478i q^{13} +(2.17400 - 0.900499i) q^{14} +(2.41139 + 2.41139i) q^{15} -16.3044 q^{16} +(-3.79776 + 1.60530i) q^{17} +0.534723 q^{18} +(-4.59097 - 4.59097i) q^{19} +(-10.5618 + 4.37483i) q^{20} +1.42841i q^{21} +(-1.43838 - 3.47257i) q^{22} +(1.16789 + 0.483757i) q^{23} +(6.39653 - 15.4426i) q^{24} +(0.605144 - 0.605144i) q^{25} +(6.35127 - 6.35127i) q^{26} +(-2.04741 + 4.94288i) q^{27} +(-4.42391 - 1.83244i) q^{28} +(3.67818 + 8.87991i) q^{29} -9.41101i q^{30} +(0.941198 - 0.389857i) q^{31} +(17.7049 + 17.7049i) q^{32} +2.28162 q^{33} +(10.5434 + 4.27829i) q^{34} -1.73584 q^{35} +(-0.769416 - 0.769416i) q^{36} +(-9.31588 + 3.85876i) q^{37} +17.9173i q^{38} +(2.08652 + 5.03731i) q^{39} +(18.7663 + 7.77325i) q^{40} +(-0.940103 + 2.26961i) q^{41} +(2.78734 - 2.78734i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(-2.92700 + 7.06640i) q^{44} +(-0.364427 - 0.150950i) q^{45} +(-1.33500 - 3.22297i) q^{46} +1.19572i q^{47} +(-25.2338 + 10.4522i) q^{48} +(4.43563 + 4.43563i) q^{49} -2.36172 q^{50} +(-4.84857 + 4.91908i) q^{51} -18.2778 q^{52} +(8.68181 + 8.68181i) q^{53} +(13.6406 - 5.65013i) q^{54} +2.77269i q^{55} +(3.25591 + 7.86045i) q^{56} +(-10.0484 - 4.16218i) q^{57} +(10.1505 - 24.5054i) q^{58} +(7.34629 - 7.34629i) q^{59} +(-13.5416 + 13.5416i) q^{60} +(1.30664 - 3.15452i) q^{61} +(-2.59738 - 1.07587i) q^{62} +(-0.0632272 - 0.152644i) q^{63} -36.4886i q^{64} +(-6.12149 + 2.53560i) q^{65} +(-4.45228 - 4.45228i) q^{66} +0.247976 q^{67} +(-9.01485 - 21.3270i) q^{68} +2.11763 q^{69} +(3.38726 + 3.38726i) q^{70} +(-8.72130 + 3.61248i) q^{71} +1.93338i q^{72} +(-0.570430 - 1.37714i) q^{73} +(25.7086 + 10.6488i) q^{74} +(0.548625 - 1.32450i) q^{75} +(25.7814 - 25.7814i) q^{76} +(-0.821212 + 0.821212i) q^{77} +(5.75807 - 13.9012i) q^{78} +(1.72313 + 0.713744i) q^{79} +(-12.7018 - 30.6648i) q^{80} +8.38116i q^{81} +(6.26333 - 2.59435i) q^{82} +(-2.76434 - 2.76434i) q^{83} -8.02145 q^{84} +(-5.97782 - 5.89212i) q^{85} +2.75965 q^{86} +(11.3852 + 11.3852i) q^{87} +(12.5556 - 5.20072i) q^{88} +4.73203i q^{89} +(0.416571 + 1.00569i) q^{90} +(-2.56405 - 1.06206i) q^{91} +(-2.71662 + 6.55849i) q^{92} +(1.20674 - 1.20674i) q^{93} +(2.33329 - 2.33329i) q^{94} +(5.05800 - 12.2111i) q^{95} +(38.7512 + 16.0513i) q^{96} +(-1.15465 - 2.78758i) q^{97} -17.3111i q^{98} +(-0.243821 + 0.100994i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q + 4q^{2} + 4q^{3} + 8q^{5} - 12q^{6} + 4q^{7} - 4q^{8} + 8q^{9} + O(q^{10}) \) \( 128q + 4q^{2} + 4q^{3} + 8q^{5} - 12q^{6} + 4q^{7} - 4q^{8} + 8q^{9} - 8q^{10} - 4q^{11} + 12q^{12} + 12q^{14} - 12q^{15} - 144q^{16} - 12q^{17} + 64q^{18} - 28q^{19} - 8q^{20} - 12q^{22} + 16q^{23} - 16q^{24} - 20q^{25} + 16q^{26} - 8q^{27} + 20q^{28} + 12q^{31} - 4q^{32} - 104q^{33} + 20q^{34} + 32q^{35} - 96q^{36} - 12q^{37} + 8q^{39} + 216q^{40} + 24q^{41} - 4q^{42} + 24q^{44} - 28q^{45} - 48q^{46} + 28q^{48} - 80q^{50} - 20q^{51} + 56q^{52} - 36q^{53} - 12q^{54} - 8q^{56} + 72q^{57} - 32q^{58} + 48q^{59} - 40q^{60} - 76q^{61} - 44q^{62} + 36q^{65} - 68q^{66} - 48q^{67} + 32q^{68} + 216q^{69} - 196q^{70} + 4q^{71} + 20q^{73} + 88q^{74} + 80q^{75} + 72q^{76} + 28q^{77} - 120q^{78} + 68q^{79} - 68q^{80} + 28q^{82} - 36q^{83} - 152q^{84} + 28q^{85} - 24q^{86} - 56q^{87} + 20q^{88} - 112q^{90} + 96q^{91} - 28q^{92} + 24q^{93} - 36q^{94} - 108q^{95} + 272q^{96} + 8q^{97} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.95137 1.95137i −1.37983 1.37983i −0.844899 0.534926i \(-0.820339\pi\)
−0.534926 0.844899i \(-0.679661\pi\)
\(3\) 1.54767 0.641064i 0.893546 0.370119i 0.111811 0.993730i \(-0.464335\pi\)
0.781735 + 0.623611i \(0.214335\pi\)
\(4\) 5.61567i 2.80783i
\(5\) 0.779040 + 1.88077i 0.348397 + 0.841106i 0.996810 + 0.0798162i \(0.0254334\pi\)
−0.648412 + 0.761289i \(0.724567\pi\)
\(6\) −4.27102 1.76911i −1.74364 0.722238i
\(7\) −0.326309 + 0.787780i −0.123333 + 0.297753i −0.973472 0.228806i \(-0.926518\pi\)
0.850139 + 0.526559i \(0.176518\pi\)
\(8\) 7.05550 7.05550i 2.49450 2.49450i
\(9\) −0.137012 + 0.137012i −0.0456708 + 0.0456708i
\(10\) 2.14988 5.19027i 0.679851 1.64131i
\(11\) 1.25834 + 0.521220i 0.379402 + 0.157154i 0.564231 0.825617i \(-0.309173\pi\)
−0.184828 + 0.982771i \(0.559173\pi\)
\(12\) 3.60001 + 8.69118i 1.03923 + 2.50893i
\(13\) 3.25478i 0.902713i 0.892344 + 0.451356i \(0.149060\pi\)
−0.892344 + 0.451356i \(0.850940\pi\)
\(14\) 2.17400 0.900499i 0.581025 0.240668i
\(15\) 2.41139 + 2.41139i 0.622618 + 0.622618i
\(16\) −16.3044 −4.07610
\(17\) −3.79776 + 1.60530i −0.921093 + 0.389343i
\(18\) 0.534723 0.126035
\(19\) −4.59097 4.59097i −1.05324 1.05324i −0.998501 0.0547393i \(-0.982567\pi\)
−0.0547393 0.998501i \(-0.517433\pi\)
\(20\) −10.5618 + 4.37483i −2.36169 + 0.978242i
\(21\) 1.42841i 0.311704i
\(22\) −1.43838 3.47257i −0.306664 0.740354i
\(23\) 1.16789 + 0.483757i 0.243522 + 0.100870i 0.501106 0.865386i \(-0.332926\pi\)
−0.257584 + 0.966256i \(0.582926\pi\)
\(24\) 6.39653 15.4426i 1.30569 3.15221i
\(25\) 0.605144 0.605144i 0.121029 0.121029i
\(26\) 6.35127 6.35127i 1.24559 1.24559i
\(27\) −2.04741 + 4.94288i −0.394024 + 0.951258i
\(28\) −4.42391 1.83244i −0.836040 0.346299i
\(29\) 3.67818 + 8.87991i 0.683021 + 1.64896i 0.758389 + 0.651802i \(0.225987\pi\)
−0.0753686 + 0.997156i \(0.524013\pi\)
\(30\) 9.41101i 1.71821i
\(31\) 0.941198 0.389857i 0.169044 0.0700204i −0.296556 0.955015i \(-0.595838\pi\)
0.465601 + 0.884995i \(0.345838\pi\)
\(32\) 17.7049 + 17.7049i 3.12981 + 3.12981i
\(33\) 2.28162 0.397179
\(34\) 10.5434 + 4.27829i 1.80817 + 0.733721i
\(35\) −1.73584 −0.293410
\(36\) −0.769416 0.769416i −0.128236 0.128236i
\(37\) −9.31588 + 3.85876i −1.53152 + 0.634377i −0.979859 0.199691i \(-0.936006\pi\)
−0.551662 + 0.834068i \(0.686006\pi\)
\(38\) 17.9173i 2.90657i
\(39\) 2.08652 + 5.03731i 0.334111 + 0.806615i
\(40\) 18.7663 + 7.77325i 2.96721 + 1.22906i
\(41\) −0.940103 + 2.26961i −0.146819 + 0.354453i −0.980131 0.198350i \(-0.936442\pi\)
0.833312 + 0.552803i \(0.186442\pi\)
\(42\) 2.78734 2.78734i 0.430096 0.430096i
\(43\) −0.707107 + 0.707107i −0.107833 + 0.107833i
\(44\) −2.92700 + 7.06640i −0.441261 + 1.06530i
\(45\) −0.364427 0.150950i −0.0543255 0.0225024i
\(46\) −1.33500 3.22297i −0.196835 0.475201i
\(47\) 1.19572i 0.174414i 0.996190 + 0.0872068i \(0.0277941\pi\)
−0.996190 + 0.0872068i \(0.972206\pi\)
\(48\) −25.2338 + 10.4522i −3.64218 + 1.50864i
\(49\) 4.43563 + 4.43563i 0.633661 + 0.633661i
\(50\) −2.36172 −0.333997
\(51\) −4.84857 + 4.91908i −0.678935 + 0.688810i
\(52\) −18.2778 −2.53467
\(53\) 8.68181 + 8.68181i 1.19254 + 1.19254i 0.976352 + 0.216187i \(0.0693620\pi\)
0.216187 + 0.976352i \(0.430638\pi\)
\(54\) 13.6406 5.65013i 1.85625 0.768886i
\(55\) 2.77269i 0.373869i
\(56\) 3.25591 + 7.86045i 0.435089 + 1.05040i
\(57\) −10.0484 4.16218i −1.33094 0.551294i
\(58\) 10.1505 24.5054i 1.33282 3.21772i
\(59\) 7.34629 7.34629i 0.956405 0.956405i −0.0426833 0.999089i \(-0.513591\pi\)
0.999089 + 0.0426833i \(0.0135906\pi\)
\(60\) −13.5416 + 13.5416i −1.74821 + 1.74821i
\(61\) 1.30664 3.15452i 0.167299 0.403894i −0.817889 0.575376i \(-0.804856\pi\)
0.985187 + 0.171482i \(0.0548556\pi\)
\(62\) −2.59738 1.07587i −0.329867 0.136636i
\(63\) −0.0632272 0.152644i −0.00796587 0.0192313i
\(64\) 36.4886i 4.56108i
\(65\) −6.12149 + 2.53560i −0.759277 + 0.314503i
\(66\) −4.45228 4.45228i −0.548037 0.548037i
\(67\) 0.247976 0.0302951 0.0151476 0.999885i \(-0.495178\pi\)
0.0151476 + 0.999885i \(0.495178\pi\)
\(68\) −9.01485 21.3270i −1.09321 2.58628i
\(69\) 2.11763 0.254932
\(70\) 3.38726 + 3.38726i 0.404855 + 0.404855i
\(71\) −8.72130 + 3.61248i −1.03503 + 0.428723i −0.834525 0.550970i \(-0.814258\pi\)
−0.200503 + 0.979693i \(0.564258\pi\)
\(72\) 1.93338i 0.227851i
\(73\) −0.570430 1.37714i −0.0667638 0.161182i 0.886976 0.461816i \(-0.152802\pi\)
−0.953740 + 0.300634i \(0.902802\pi\)
\(74\) 25.7086 + 10.6488i 2.98856 + 1.23790i
\(75\) 0.548625 1.32450i 0.0633497 0.152940i
\(76\) 25.7814 25.7814i 2.95732 2.95732i
\(77\) −0.821212 + 0.821212i −0.0935858 + 0.0935858i
\(78\) 5.75807 13.9012i 0.651973 1.57400i
\(79\) 1.72313 + 0.713744i 0.193867 + 0.0803024i 0.477505 0.878629i \(-0.341541\pi\)
−0.283638 + 0.958932i \(0.591541\pi\)
\(80\) −12.7018 30.6648i −1.42010 3.42843i
\(81\) 8.38116i 0.931240i
\(82\) 6.26333 2.59435i 0.691669 0.286499i
\(83\) −2.76434 2.76434i −0.303426 0.303426i 0.538927 0.842353i \(-0.318830\pi\)
−0.842353 + 0.538927i \(0.818830\pi\)
\(84\) −8.02145 −0.875212
\(85\) −5.97782 5.89212i −0.648385 0.639090i
\(86\) 2.75965 0.297581
\(87\) 11.3852 + 11.3852i 1.22062 + 1.22062i
\(88\) 12.5556 5.20072i 1.33844 0.554399i
\(89\) 4.73203i 0.501595i 0.968040 + 0.250797i \(0.0806928\pi\)
−0.968040 + 0.250797i \(0.919307\pi\)
\(90\) 0.416571 + 1.00569i 0.0439104 + 0.106009i
\(91\) −2.56405 1.06206i −0.268785 0.111334i
\(92\) −2.71662 + 6.55849i −0.283227 + 0.683770i
\(93\) 1.20674 1.20674i 0.125133 0.125133i
\(94\) 2.33329 2.33329i 0.240660 0.240660i
\(95\) 5.05800 12.2111i 0.518940 1.25283i
\(96\) 38.7512 + 16.0513i 3.95503 + 1.63823i
\(97\) −1.15465 2.78758i −0.117237 0.283036i 0.854358 0.519685i \(-0.173951\pi\)
−0.971595 + 0.236649i \(0.923951\pi\)
\(98\) 17.3111i 1.74868i
\(99\) −0.243821 + 0.100994i −0.0245049 + 0.0101503i
\(100\) 3.39829 + 3.39829i 0.339829 + 0.339829i
\(101\) 17.5883 1.75010 0.875052 0.484030i \(-0.160827\pi\)
0.875052 + 0.484030i \(0.160827\pi\)
\(102\) 19.0603 0.137606i 1.88725 0.0136251i
\(103\) −8.13309 −0.801377 −0.400689 0.916214i \(-0.631229\pi\)
−0.400689 + 0.916214i \(0.631229\pi\)
\(104\) 22.9641 + 22.9641i 2.25181 + 2.25181i
\(105\) −2.68650 + 1.11279i −0.262176 + 0.108597i
\(106\) 33.8828i 3.29099i
\(107\) −5.94708 14.3575i −0.574926 1.38799i −0.897316 0.441388i \(-0.854486\pi\)
0.322390 0.946607i \(-0.395514\pi\)
\(108\) −27.7576 11.4976i −2.67098 1.10635i
\(109\) 2.72814 6.58631i 0.261308 0.630854i −0.737712 0.675116i \(-0.764094\pi\)
0.999020 + 0.0442620i \(0.0140936\pi\)
\(110\) 5.41054 5.41054i 0.515874 0.515874i
\(111\) −11.9442 + 11.9442i −1.13369 + 1.13369i
\(112\) 5.32027 12.8443i 0.502719 1.21367i
\(113\) −6.10745 2.52979i −0.574540 0.237982i 0.0764436 0.997074i \(-0.475643\pi\)
−0.650984 + 0.759092i \(0.725643\pi\)
\(114\) 11.4862 + 27.7300i 1.07578 + 2.59716i
\(115\) 2.57340i 0.239971i
\(116\) −49.8666 + 20.6554i −4.63000 + 1.91781i
\(117\) −0.445945 0.445945i −0.0412276 0.0412276i
\(118\) −28.6706 −2.63934
\(119\) −0.0253812 3.51562i −0.00232669 0.322277i
\(120\) 34.0271 3.10624
\(121\) −6.46644 6.46644i −0.587858 0.587858i
\(122\) −8.70536 + 3.60588i −0.788146 + 0.326461i
\(123\) 4.11526i 0.371061i
\(124\) 2.18931 + 5.28546i 0.196606 + 0.474648i
\(125\) 11.0134 + 4.56191i 0.985070 + 0.408029i
\(126\) −0.174485 + 0.421244i −0.0155443 + 0.0375274i
\(127\) 10.7753 10.7753i 0.956152 0.956152i −0.0429260 0.999078i \(-0.513668\pi\)
0.999078 + 0.0429260i \(0.0136680\pi\)
\(128\) −35.7930 + 35.7930i −3.16368 + 3.16368i
\(129\) −0.641064 + 1.54767i −0.0564426 + 0.136264i
\(130\) 16.8932 + 6.99738i 1.48163 + 0.613711i
\(131\) 3.98964 + 9.63185i 0.348577 + 0.841539i 0.996789 + 0.0800786i \(0.0255171\pi\)
−0.648212 + 0.761460i \(0.724483\pi\)
\(132\) 12.8128i 1.11521i
\(133\) 5.11474 2.11860i 0.443505 0.183706i
\(134\) −0.483893 0.483893i −0.0418020 0.0418020i
\(135\) −10.8914 −0.937386
\(136\) −15.4689 + 38.1213i −1.32645 + 3.26888i
\(137\) −2.16211 −0.184722 −0.0923608 0.995726i \(-0.529441\pi\)
−0.0923608 + 0.995726i \(0.529441\pi\)
\(138\) −4.13227 4.13227i −0.351762 0.351762i
\(139\) 16.1123 6.67394i 1.36663 0.566076i 0.425757 0.904838i \(-0.360008\pi\)
0.940872 + 0.338761i \(0.110008\pi\)
\(140\) 9.74790i 0.823848i
\(141\) 0.766533 + 1.85057i 0.0645537 + 0.155846i
\(142\) 24.0677 + 9.96919i 2.01972 + 0.836595i
\(143\) −1.69645 + 4.09560i −0.141865 + 0.342492i
\(144\) 2.23390 2.23390i 0.186159 0.186159i
\(145\) −13.8356 + 13.8356i −1.14899 + 1.14899i
\(146\) −1.57419 + 3.80043i −0.130281 + 0.314526i
\(147\) 9.70840 + 4.02135i 0.800735 + 0.331675i
\(148\) −21.6695 52.3149i −1.78122 4.30026i
\(149\) 1.65045i 0.135210i 0.997712 + 0.0676051i \(0.0215358\pi\)
−0.997712 + 0.0676051i \(0.978464\pi\)
\(150\) −3.65515 + 1.51401i −0.298442 + 0.123619i
\(151\) 2.24294 + 2.24294i 0.182528 + 0.182528i 0.792456 0.609929i \(-0.208802\pi\)
−0.609929 + 0.792456i \(0.708802\pi\)
\(152\) −64.7831 −5.25460
\(153\) 0.300394 0.740287i 0.0242854 0.0598486i
\(154\) 3.20497 0.258264
\(155\) 1.46646 + 1.46646i 0.117789 + 0.117789i
\(156\) −28.2879 + 11.7172i −2.26484 + 0.938128i
\(157\) 12.3729i 0.987466i 0.869614 + 0.493733i \(0.164368\pi\)
−0.869614 + 0.493733i \(0.835632\pi\)
\(158\) −1.96968 4.75524i −0.156700 0.378306i
\(159\) 19.0022 + 7.87095i 1.50697 + 0.624207i
\(160\) −19.5060 + 47.0916i −1.54208 + 3.72292i
\(161\) −0.762187 + 0.762187i −0.0600688 + 0.0600688i
\(162\) 16.3547 16.3547i 1.28495 1.28495i
\(163\) −4.73955 + 11.4423i −0.371230 + 0.896228i 0.622313 + 0.782769i \(0.286193\pi\)
−0.993543 + 0.113459i \(0.963807\pi\)
\(164\) −12.7454 5.27931i −0.995246 0.412245i
\(165\) 1.77747 + 4.29120i 0.138376 + 0.334069i
\(166\) 10.7885i 0.837349i
\(167\) 17.4430 7.22514i 1.34978 0.559098i 0.413550 0.910481i \(-0.364289\pi\)
0.936232 + 0.351383i \(0.114289\pi\)
\(168\) 10.0781 + 10.0781i 0.777543 + 0.777543i
\(169\) 2.40642 0.185109
\(170\) 0.167223 + 23.1626i 0.0128254 + 1.77649i
\(171\) 1.25804 0.0962046
\(172\) −3.97088 3.97088i −0.302777 0.302777i
\(173\) −1.21903 + 0.504937i −0.0926808 + 0.0383896i −0.428542 0.903522i \(-0.640973\pi\)
0.335861 + 0.941911i \(0.390973\pi\)
\(174\) 44.4334i 3.36849i
\(175\) 0.279256 + 0.674184i 0.0211098 + 0.0509635i
\(176\) −20.5164 8.49817i −1.54648 0.640574i
\(177\) 6.66016 16.0791i 0.500608 1.20858i
\(178\) 9.23394 9.23394i 0.692113 0.692113i
\(179\) −0.982287 + 0.982287i −0.0734196 + 0.0734196i −0.742863 0.669443i \(-0.766533\pi\)
0.669443 + 0.742863i \(0.266533\pi\)
\(180\) 0.847688 2.04650i 0.0631829 0.152537i
\(181\) −8.00682 3.31653i −0.595142 0.246516i 0.0647190 0.997904i \(-0.479385\pi\)
−0.659861 + 0.751388i \(0.729385\pi\)
\(182\) 2.93092 + 7.07587i 0.217254 + 0.524499i
\(183\) 5.71978i 0.422818i
\(184\) 11.6532 4.82691i 0.859085 0.355845i
\(185\) −14.5149 14.5149i −1.06716 1.06716i
\(186\) −4.70958 −0.345323
\(187\) −5.61558 + 0.0405418i −0.410652 + 0.00296471i
\(188\) −6.71476 −0.489724
\(189\) −3.22581 3.22581i −0.234643 0.234643i
\(190\) −33.6984 + 13.9583i −2.44474 + 1.01264i
\(191\) 12.4129i 0.898164i 0.893490 + 0.449082i \(0.148249\pi\)
−0.893490 + 0.449082i \(0.851751\pi\)
\(192\) −23.3916 56.4722i −1.68814 4.07553i
\(193\) 22.3594 + 9.26157i 1.60947 + 0.666663i 0.992714 0.120495i \(-0.0384481\pi\)
0.616752 + 0.787157i \(0.288448\pi\)
\(194\) −3.18644 + 7.69275i −0.228773 + 0.552307i
\(195\) −7.84854 + 7.84854i −0.562045 + 0.562045i
\(196\) −24.9090 + 24.9090i −1.77922 + 1.77922i
\(197\) −2.06791 + 4.99239i −0.147333 + 0.355693i −0.980267 0.197680i \(-0.936659\pi\)
0.832934 + 0.553373i \(0.186659\pi\)
\(198\) 0.672861 + 0.278708i 0.0478181 + 0.0198069i
\(199\) −0.0293660 0.0708958i −0.00208170 0.00502567i 0.922835 0.385195i \(-0.125866\pi\)
−0.924917 + 0.380169i \(0.875866\pi\)
\(200\) 8.53918i 0.603811i
\(201\) 0.383785 0.158969i 0.0270701 0.0112128i
\(202\) −34.3213 34.3213i −2.41484 2.41484i
\(203\) −8.19563 −0.575221
\(204\) −27.6240 27.2279i −1.93406 1.90634i
\(205\) −5.00099 −0.349284
\(206\) 15.8706 + 15.8706i 1.10576 + 1.10576i
\(207\) −0.226296 + 0.0937349i −0.0157287 + 0.00651503i
\(208\) 53.0672i 3.67955i
\(209\) −3.38407 8.16988i −0.234081 0.565122i
\(210\) 7.41380 + 3.07090i 0.511601 + 0.211912i
\(211\) 8.87785 21.4330i 0.611176 1.47551i −0.250533 0.968108i \(-0.580606\pi\)
0.861710 0.507402i \(-0.169394\pi\)
\(212\) −48.7542 + 48.7542i −3.34845 + 3.34845i
\(213\) −11.1818 + 11.1818i −0.766167 + 0.766167i
\(214\) −16.4119 + 39.6218i −1.12189 + 2.70849i
\(215\) −1.88077 0.779040i −0.128267 0.0531301i
\(216\) 20.4290 + 49.3200i 1.39002 + 3.35580i
\(217\) 0.868671i 0.0589692i
\(218\) −18.1759 + 7.52871i −1.23103 + 0.509908i
\(219\) −1.76567 1.76567i −0.119313 0.119313i
\(220\) −15.5705 −1.04976
\(221\) −5.22491 12.3609i −0.351465 0.831482i
\(222\) 46.6149 3.12859
\(223\) −13.0424 13.0424i −0.873381 0.873381i 0.119458 0.992839i \(-0.461884\pi\)
−0.992839 + 0.119458i \(0.961884\pi\)
\(224\) −19.7248 + 8.17028i −1.31792 + 0.545900i
\(225\) 0.165824i 0.0110550i
\(226\) 6.98133 + 16.8544i 0.464391 + 1.12114i
\(227\) −10.7335 4.44595i −0.712406 0.295088i −0.00310592 0.999995i \(-0.500989\pi\)
−0.709300 + 0.704907i \(0.750989\pi\)
\(228\) 23.3734 56.4284i 1.54794 3.73706i
\(229\) −11.6060 + 11.6060i −0.766943 + 0.766943i −0.977567 0.210624i \(-0.932450\pi\)
0.210624 + 0.977567i \(0.432450\pi\)
\(230\) 5.02165 5.02165i 0.331118 0.331118i
\(231\) −0.744513 + 1.79741i −0.0489854 + 0.118261i
\(232\) 88.6036 + 36.7008i 5.81711 + 2.40953i
\(233\) −5.52181 13.3308i −0.361746 0.873332i −0.995045 0.0994249i \(-0.968300\pi\)
0.633299 0.773907i \(-0.281700\pi\)
\(234\) 1.74040i 0.113774i
\(235\) −2.24887 + 0.931513i −0.146700 + 0.0607652i
\(236\) 41.2543 + 41.2543i 2.68543 + 2.68543i
\(237\) 3.12439 0.202951
\(238\) −6.81075 + 6.90980i −0.441475 + 0.447896i
\(239\) 1.82310 0.117926 0.0589632 0.998260i \(-0.481221\pi\)
0.0589632 + 0.998260i \(0.481221\pi\)
\(240\) −39.3163 39.3163i −2.53785 2.53785i
\(241\) −3.04039 + 1.25937i −0.195849 + 0.0811232i −0.478452 0.878114i \(-0.658802\pi\)
0.282603 + 0.959237i \(0.408802\pi\)
\(242\) 25.2368i 1.62228i
\(243\) −0.769363 1.85741i −0.0493546 0.119153i
\(244\) 17.7147 + 7.33768i 1.13407 + 0.469747i
\(245\) −4.88686 + 11.7979i −0.312210 + 0.753742i
\(246\) 8.03039 8.03039i 0.511999 0.511999i
\(247\) 14.9426 14.9426i 0.950773 0.950773i
\(248\) 3.88999 9.39126i 0.247014 0.596346i
\(249\) −6.05040 2.50616i −0.383429 0.158821i
\(250\) −12.5893 30.3932i −0.796215 1.92223i
\(251\) 25.6059i 1.61623i 0.589025 + 0.808115i \(0.299512\pi\)
−0.589025 + 0.808115i \(0.700488\pi\)
\(252\) 0.857197 0.355063i 0.0539984 0.0223669i
\(253\) 1.21746 + 1.21746i 0.0765408 + 0.0765408i
\(254\) −42.0531 −2.63865
\(255\) −13.0289 5.28687i −0.815901 0.331077i
\(256\) 66.7132 4.16958
\(257\) 15.0470 + 15.0470i 0.938603 + 0.938603i 0.998221 0.0596182i \(-0.0189883\pi\)
−0.0596182 + 0.998221i \(0.518988\pi\)
\(258\) 4.27102 1.76911i 0.265902 0.110140i
\(259\) 8.59801i 0.534254i
\(260\) −14.2391 34.3762i −0.883072 2.13192i
\(261\) −1.72061 0.712701i −0.106503 0.0441151i
\(262\) 11.0100 26.5805i 0.680201 1.64215i
\(263\) 14.2682 14.2682i 0.879818 0.879818i −0.113698 0.993515i \(-0.536270\pi\)
0.993515 + 0.113698i \(0.0362695\pi\)
\(264\) 16.0980 16.0980i 0.990761 0.990761i
\(265\) −9.56501 + 23.0920i −0.587574 + 1.41853i
\(266\) −14.1149 5.84658i −0.865440 0.358477i
\(267\) 3.03354 + 7.32361i 0.185650 + 0.448198i
\(268\) 1.39255i 0.0850637i
\(269\) 11.9062 4.93172i 0.725936 0.300692i 0.0110549 0.999939i \(-0.496481\pi\)
0.714881 + 0.699247i \(0.246481\pi\)
\(270\) 21.2532 + 21.2532i 1.29343 + 1.29343i
\(271\) 3.90023 0.236922 0.118461 0.992959i \(-0.462204\pi\)
0.118461 + 0.992959i \(0.462204\pi\)
\(272\) 61.9202 26.1735i 3.75447 1.58700i
\(273\) −4.64914 −0.281379
\(274\) 4.21907 + 4.21907i 0.254883 + 0.254883i
\(275\) 1.07689 0.446061i 0.0649387 0.0268985i
\(276\) 11.8919i 0.715808i
\(277\) −10.7766 26.0169i −0.647501 1.56321i −0.816345 0.577564i \(-0.804003\pi\)
0.168844 0.985643i \(-0.445997\pi\)
\(278\) −44.4644 18.4177i −2.66680 1.10462i
\(279\) −0.0755405 + 0.182371i −0.00452249 + 0.0109183i
\(280\) −12.2472 + 12.2472i −0.731911 + 0.731911i
\(281\) 22.0570 22.0570i 1.31581 1.31581i 0.398753 0.917058i \(-0.369443\pi\)
0.917058 0.398753i \(-0.130557\pi\)
\(282\) 2.11536 5.10694i 0.125968 0.304114i
\(283\) 9.50148 + 3.93564i 0.564804 + 0.233950i 0.646769 0.762686i \(-0.276120\pi\)
−0.0819652 + 0.996635i \(0.526120\pi\)
\(284\) −20.2865 48.9759i −1.20378 2.90619i
\(285\) 22.1412i 1.31153i
\(286\) 11.3024 4.68162i 0.668327 0.276830i
\(287\) −1.48119 1.48119i −0.0874317 0.0874317i
\(288\) −4.85157 −0.285882
\(289\) 11.8460 12.1931i 0.696824 0.717243i
\(290\) 53.9967 3.17080
\(291\) −3.57404 3.57404i −0.209514 0.209514i
\(292\) 7.73357 3.20335i 0.452573 0.187462i
\(293\) 20.0323i 1.17030i 0.810926 + 0.585149i \(0.198964\pi\)
−0.810926 + 0.585149i \(0.801036\pi\)
\(294\) −11.0975 26.7918i −0.647220 1.56253i
\(295\) 19.5397 + 8.09362i 1.13765 + 0.471229i
\(296\) −38.5027 + 92.9537i −2.23792 + 5.40282i
\(297\) −5.15266 + 5.15266i −0.298987 + 0.298987i
\(298\) 3.22063 3.22063i 0.186566 0.186566i
\(299\) −1.57452 + 3.80123i −0.0910569 + 0.219831i
\(300\) 7.43794 + 3.08089i 0.429429 + 0.177876i
\(301\) −0.326309 0.787780i −0.0188081 0.0454069i
\(302\) 8.75358i 0.503712i
\(303\) 27.2209 11.2752i 1.56380 0.647746i
\(304\) 74.8530 + 74.8530i 4.29311 + 4.29311i
\(305\) 6.95084 0.398004
\(306\) −2.03075 + 0.858392i −0.116090 + 0.0490710i
\(307\) −12.2411 −0.698634 −0.349317 0.937005i \(-0.613586\pi\)
−0.349317 + 0.937005i \(0.613586\pi\)
\(308\) −4.61166 4.61166i −0.262774 0.262774i
\(309\) −12.5873 + 5.21383i −0.716067 + 0.296605i
\(310\) 5.72322i 0.325057i
\(311\) 7.45681 + 18.0023i 0.422837 + 1.02082i 0.981507 + 0.191428i \(0.0613119\pi\)
−0.558670 + 0.829390i \(0.688688\pi\)
\(312\) 50.2622 + 20.8193i 2.84554 + 1.17866i
\(313\) −7.22100 + 17.4330i −0.408155 + 0.985374i 0.577468 + 0.816414i \(0.304041\pi\)
−0.985623 + 0.168960i \(0.945959\pi\)
\(314\) 24.1441 24.1441i 1.36253 1.36253i
\(315\) 0.237831 0.237831i 0.0134003 0.0134003i
\(316\) −4.00815 + 9.67653i −0.225476 + 0.544347i
\(317\) −6.57904 2.72513i −0.369516 0.153058i 0.190195 0.981746i \(-0.439088\pi\)
−0.559711 + 0.828688i \(0.689088\pi\)
\(318\) −21.7211 52.4393i −1.21806 2.94065i
\(319\) 13.0910i 0.732958i
\(320\) 68.6267 28.4261i 3.83635 1.58907i
\(321\) −18.4082 18.4082i −1.02745 1.02745i
\(322\) 2.97461 0.165769
\(323\) 24.8053 + 10.0655i 1.38020 + 0.560060i
\(324\) −47.0658 −2.61477
\(325\) 1.96961 + 1.96961i 0.109254 + 0.109254i
\(326\) 31.5767 13.0795i 1.74887 0.724406i
\(327\) 11.9423i 0.660412i
\(328\) 9.38033 + 22.6461i 0.517942 + 1.25042i
\(329\) −0.941963 0.390174i −0.0519321 0.0215110i
\(330\) 4.90520 11.8422i 0.270023 0.651892i
\(331\) −5.18062 + 5.18062i −0.284752 + 0.284752i −0.835001 0.550249i \(-0.814533\pi\)
0.550249 + 0.835001i \(0.314533\pi\)
\(332\) 15.5236 15.5236i 0.851970 0.851970i
\(333\) 0.747692 1.80509i 0.0409733 0.0989182i
\(334\) −48.1367 19.9389i −2.63392 1.09101i
\(335\) 0.193184 + 0.466386i 0.0105547 + 0.0254814i
\(336\) 23.2893i 1.27053i
\(337\) −26.7596 + 11.0842i −1.45769 + 0.603795i −0.964014 0.265851i \(-0.914347\pi\)
−0.493675 + 0.869646i \(0.664347\pi\)
\(338\) −4.69581 4.69581i −0.255418 0.255418i
\(339\) −11.0740 −0.601460
\(340\) 33.0882 33.5694i 1.79446 1.82056i
\(341\) 1.38754 0.0751398
\(342\) −2.45489 2.45489i −0.132745 0.132745i
\(343\) −10.4561 + 4.33108i −0.564578 + 0.233856i
\(344\) 9.97798i 0.537977i
\(345\) 1.64972 + 3.98277i 0.0888177 + 0.214425i
\(346\) 3.36408 + 1.39345i 0.180854 + 0.0749123i
\(347\) −0.434423 + 1.04879i −0.0233210 + 0.0563020i −0.935111 0.354355i \(-0.884701\pi\)
0.911790 + 0.410657i \(0.134701\pi\)
\(348\) −63.9354 + 63.9354i −3.42730 + 3.42730i
\(349\) 10.9036 10.9036i 0.583658 0.583658i −0.352249 0.935906i \(-0.614583\pi\)
0.935906 + 0.352249i \(0.114583\pi\)
\(350\) 0.770649 1.86051i 0.0411929 0.0994485i
\(351\) −16.0880 6.66386i −0.858713 0.355691i
\(352\) 13.0505 + 31.5068i 0.695597 + 1.67932i
\(353\) 23.2851i 1.23934i −0.784863 0.619670i \(-0.787267\pi\)
0.784863 0.619670i \(-0.212733\pi\)
\(354\) −44.3726 + 18.3797i −2.35837 + 0.976871i
\(355\) −13.5885 13.5885i −0.721202 0.721202i
\(356\) −26.5735 −1.40839
\(357\) −2.29302 5.42474i −0.121360 0.287108i
\(358\) 3.83361 0.202612
\(359\) −9.49136 9.49136i −0.500935 0.500935i 0.410794 0.911728i \(-0.365252\pi\)
−0.911728 + 0.410794i \(0.865252\pi\)
\(360\) −3.63624 + 1.50618i −0.191647 + 0.0793827i
\(361\) 23.1540i 1.21863i
\(362\) 9.15247 + 22.0960i 0.481043 + 1.16134i
\(363\) −14.1533 5.86248i −0.742855 0.307701i
\(364\) 5.96420 14.3988i 0.312609 0.754704i
\(365\) 2.14570 2.14570i 0.112311 0.112311i
\(366\) −11.1614 + 11.1614i −0.583415 + 0.583415i
\(367\) 6.54457 15.8000i 0.341624 0.824753i −0.655928 0.754824i \(-0.727722\pi\)
0.997552 0.0699298i \(-0.0222775\pi\)
\(368\) −19.0418 7.88736i −0.992621 0.411157i
\(369\) −0.182159 0.439770i −0.00948280 0.0228935i
\(370\) 56.6478i 2.94498i
\(371\) −9.67231 + 4.00640i −0.502161 + 0.208002i
\(372\) 6.77664 + 6.77664i 0.351352 + 0.351352i
\(373\) 2.00560 0.103846 0.0519230 0.998651i \(-0.483465\pi\)
0.0519230 + 0.998651i \(0.483465\pi\)
\(374\) 11.0372 + 10.8789i 0.570718 + 0.562537i
\(375\) 19.9696 1.03122
\(376\) 8.43639 + 8.43639i 0.435074 + 0.435074i
\(377\) −28.9021 + 11.9717i −1.48854 + 0.616572i
\(378\) 12.5895i 0.647534i
\(379\) −6.01110 14.5121i −0.308769 0.745435i −0.999746 0.0225576i \(-0.992819\pi\)
0.690976 0.722877i \(-0.257181\pi\)
\(380\) 68.5735 + 28.4041i 3.51775 + 1.45710i
\(381\) 9.76890 23.5842i 0.500476 1.20826i
\(382\) 24.2221 24.2221i 1.23931 1.23931i
\(383\) 20.0752 20.0752i 1.02579 1.02579i 0.0261359 0.999658i \(-0.491680\pi\)
0.999658 0.0261359i \(-0.00832027\pi\)
\(384\) −32.4500 + 78.3412i −1.65596 + 3.99783i
\(385\) −2.18427 0.904754i −0.111321 0.0461105i
\(386\) −25.5587 61.7042i −1.30090 3.14066i
\(387\) 0.193765i 0.00984961i
\(388\) 15.6541 6.48416i 0.794718 0.329183i
\(389\) 9.30279 + 9.30279i 0.471670 + 0.471670i 0.902455 0.430784i \(-0.141763\pi\)
−0.430784 + 0.902455i \(0.641763\pi\)
\(390\) 30.6308 1.55105
\(391\) −5.21195 + 0.0376278i −0.263580 + 0.00190292i
\(392\) 62.5911 3.16133
\(393\) 12.3493 + 12.3493i 0.622938 + 0.622938i
\(394\) 13.7772 5.70672i 0.694087 0.287500i
\(395\) 3.79684i 0.191040i
\(396\) −0.567149 1.36922i −0.0285003 0.0688058i
\(397\) −9.74100 4.03485i −0.488887 0.202503i 0.124602 0.992207i \(-0.460234\pi\)
−0.613489 + 0.789703i \(0.710234\pi\)
\(398\) −0.0810399 + 0.195648i −0.00406216 + 0.00980692i
\(399\) 6.55776 6.55776i 0.328299 0.328299i
\(400\) −9.86651 + 9.86651i −0.493325 + 0.493325i
\(401\) 13.6813 33.0297i 0.683214 1.64942i −0.0748109 0.997198i \(-0.523835\pi\)
0.758025 0.652226i \(-0.226165\pi\)
\(402\) −1.05911 0.438698i −0.0528237 0.0218803i
\(403\) 1.26890 + 3.06339i 0.0632083 + 0.152598i
\(404\) 98.7702i 4.91400i
\(405\) −15.7630 + 6.52926i −0.783271 + 0.324442i
\(406\) 15.9927 + 15.9927i 0.793704 + 0.793704i
\(407\) −13.7338 −0.680757
\(408\) 0.497539 + 68.9157i 0.0246318 + 3.41183i
\(409\) 13.6173 0.673332 0.336666 0.941624i \(-0.390701\pi\)
0.336666 + 0.941624i \(0.390701\pi\)
\(410\) 9.75877 + 9.75877i 0.481951 + 0.481951i
\(411\) −3.34623 + 1.38605i −0.165057 + 0.0683689i
\(412\) 45.6727i 2.25013i
\(413\) 3.39010 + 8.18442i 0.166816 + 0.402729i
\(414\) 0.624498 + 0.258676i 0.0306924 + 0.0127132i
\(415\) 3.04556 7.35262i 0.149500 0.360926i
\(416\) −57.6254 + 57.6254i −2.82532 + 2.82532i
\(417\) 20.6581 20.6581i 1.01163 1.01163i
\(418\) −9.33886 + 22.5460i −0.456779 + 1.10276i
\(419\) −15.5120 6.42529i −0.757812 0.313896i −0.0298873 0.999553i \(-0.509515\pi\)
−0.727924 + 0.685657i \(0.759515\pi\)
\(420\) −6.24903 15.0865i −0.304922 0.736146i
\(421\) 15.1135i 0.736586i −0.929710 0.368293i \(-0.879942\pi\)
0.929710 0.368293i \(-0.120058\pi\)
\(422\) −59.1476 + 24.4998i −2.87926 + 1.19263i
\(423\) −0.163828 0.163828i −0.00796560 0.00796560i
\(424\) 122.509 5.94957
\(425\) −1.32675 + 3.26963i −0.0643570 + 0.158600i
\(426\) 43.6397 2.11435
\(427\) 2.05869 + 2.05869i 0.0996272 + 0.0996272i
\(428\) 80.6271 33.3968i 3.89726 1.61430i
\(429\) 7.42616i 0.358539i
\(430\) 2.14988 + 5.19027i 0.103676 + 0.250297i
\(431\) −24.6128 10.1950i −1.18556 0.491074i −0.299252 0.954174i \(-0.596737\pi\)
−0.886306 + 0.463100i \(0.846737\pi\)
\(432\) 33.3818 80.5907i 1.60608 3.87742i
\(433\) −22.2348 + 22.2348i −1.06854 + 1.06854i −0.0710636 + 0.997472i \(0.522639\pi\)
−0.997472 + 0.0710636i \(0.977361\pi\)
\(434\) 1.69510 1.69510i 0.0813672 0.0813672i
\(435\) −12.5434 + 30.2824i −0.601410 + 1.45193i
\(436\) 36.9865 + 15.3203i 1.77133 + 0.733710i
\(437\) −3.14084 7.58266i −0.150247 0.362728i
\(438\) 6.89095i 0.329262i
\(439\) −17.2583 + 7.14864i −0.823696 + 0.341186i −0.754404 0.656410i \(-0.772074\pi\)
−0.0692920 + 0.997596i \(0.522074\pi\)
\(440\) 19.5627 + 19.5627i 0.932616 + 0.932616i
\(441\) −1.21547 −0.0578796
\(442\) −13.9249 + 34.3163i −0.662340 + 1.63226i
\(443\) 31.5518 1.49907 0.749535 0.661965i \(-0.230277\pi\)
0.749535 + 0.661965i \(0.230277\pi\)
\(444\) −67.0744 67.0744i −3.18321 3.18321i
\(445\) −8.89987 + 3.68645i −0.421894 + 0.174754i
\(446\) 50.9009i 2.41023i
\(447\) 1.05804 + 2.55435i 0.0500438 + 0.120816i
\(448\) 28.7450 + 11.9066i 1.35807 + 0.562533i
\(449\) 2.99236 7.22419i 0.141218 0.340931i −0.837408 0.546578i \(-0.815930\pi\)
0.978626 + 0.205648i \(0.0659301\pi\)
\(450\) 0.323584 0.323584i 0.0152539 0.0152539i
\(451\) −2.36593 + 2.36593i −0.111407 + 0.111407i
\(452\) 14.2064 34.2974i 0.668215 1.61321i
\(453\) 4.90918 + 2.03345i 0.230654 + 0.0955398i
\(454\) 12.2693 + 29.6206i 0.575825 + 1.39016i
\(455\) 5.64977i 0.264865i
\(456\) −100.263 + 41.5302i −4.69523 + 1.94483i
\(457\) −20.1678 20.1678i −0.943408 0.943408i 0.0550746 0.998482i \(-0.482460\pi\)
−0.998482 + 0.0550746i \(0.982460\pi\)
\(458\) 45.2950 2.11650
\(459\) −0.159253 22.0586i −0.00743328 1.02961i
\(460\) −14.4514 −0.673799
\(461\) 8.54921 + 8.54921i 0.398176 + 0.398176i 0.877589 0.479413i \(-0.159150\pi\)
−0.479413 + 0.877589i \(0.659150\pi\)
\(462\) 4.96023 2.05460i 0.230771 0.0955884i
\(463\) 11.9973i 0.557562i −0.960355 0.278781i \(-0.910070\pi\)
0.960355 0.278781i \(-0.0899303\pi\)
\(464\) −59.9705 144.782i −2.78406 6.72132i
\(465\) 3.20969 + 1.32950i 0.148846 + 0.0616540i
\(466\) −15.2383 + 36.7884i −0.705899 + 1.70419i
\(467\) −17.3237 + 17.3237i −0.801644 + 0.801644i −0.983352 0.181709i \(-0.941837\pi\)
0.181709 + 0.983352i \(0.441837\pi\)
\(468\) 2.50428 2.50428i 0.115760 0.115760i
\(469\) −0.0809169 + 0.195351i −0.00373640 + 0.00902046i
\(470\) 6.20610 + 2.57065i 0.286266 + 0.118575i
\(471\) 7.93183 + 19.1491i 0.365480 + 0.882346i
\(472\) 103.663i 4.77150i
\(473\) −1.25834 + 0.521220i −0.0578583 + 0.0239657i
\(474\) −6.09682 6.09682i −0.280036 0.280036i
\(475\) −5.55639 −0.254945
\(476\) 19.7426 0.142532i 0.904900 0.00653295i
\(477\) −2.37903 −0.108928
\(478\) −3.55754 3.55754i −0.162718 0.162718i
\(479\) 8.07082 3.34304i 0.368765 0.152748i −0.190602 0.981667i \(-0.561044\pi\)
0.559367 + 0.828920i \(0.311044\pi\)
\(480\) 85.3867i 3.89735i
\(481\) −12.5594 30.3211i −0.572660 1.38252i
\(482\) 8.39041 + 3.47542i 0.382173 + 0.158301i
\(483\) −0.691000 + 1.66822i −0.0314416 + 0.0759068i
\(484\) 36.3134 36.3134i 1.65061 1.65061i
\(485\) 4.34328 4.34328i 0.197218 0.197218i
\(486\) −2.12317 + 5.12579i −0.0963090 + 0.232511i
\(487\) −6.91374 2.86376i −0.313291 0.129770i 0.220497 0.975388i \(-0.429232\pi\)
−0.533788 + 0.845618i \(0.679232\pi\)
\(488\) −13.0377 31.4757i −0.590187 1.42484i
\(489\) 20.7472i 0.938220i
\(490\) 32.5582 13.4860i 1.47083 0.609237i
\(491\) 16.4576 + 16.4576i 0.742719 + 0.742719i 0.973100 0.230381i \(-0.0739974\pi\)
−0.230381 + 0.973100i \(0.573997\pi\)
\(492\) −23.1100 −1.04188
\(493\) −28.2238 27.8192i −1.27114 1.25291i
\(494\) −58.3169 −2.62380
\(495\) −0.379893 0.379893i −0.0170749 0.0170749i
\(496\) −15.3457 + 6.35639i −0.689041 + 0.285410i
\(497\) 8.04925i 0.361058i
\(498\) 6.91612 + 16.6970i 0.309919 + 0.748210i
\(499\) 22.4507 + 9.29937i 1.00503 + 0.416297i 0.823639 0.567114i \(-0.191940\pi\)
0.181391 + 0.983411i \(0.441940\pi\)
\(500\) −25.6182 + 61.8477i −1.14568 + 2.76591i
\(501\) 22.3642 22.3642i 0.999159 0.999159i
\(502\) 49.9665 49.9665i 2.23012 2.23012i
\(503\) 8.39859 20.2760i 0.374475 0.904061i −0.618506 0.785780i \(-0.712262\pi\)
0.992980 0.118281i \(-0.0377384\pi\)
\(504\) −1.52308 0.630879i −0.0678433 0.0281016i
\(505\) 13.7020 + 33.0796i 0.609731 + 1.47202i
\(506\) 4.75141i 0.211226i
\(507\) 3.72434 1.54267i 0.165404 0.0685124i
\(508\) 60.5105 + 60.5105i 2.68472 + 2.68472i
\(509\) 39.6020 1.75533 0.877663 0.479278i \(-0.159102\pi\)
0.877663 + 0.479278i \(0.159102\pi\)
\(510\) 15.1075 + 35.7408i 0.668973 + 1.58263i
\(511\) 1.27102 0.0562266
\(512\) −58.5961 58.5961i −2.58961 2.58961i
\(513\) 32.0922 13.2930i 1.41691 0.586901i
\(514\) 58.7243i 2.59022i
\(515\) −6.33600 15.2965i −0.279198 0.674043i
\(516\) −8.69118 3.60001i −0.382608 0.158481i
\(517\) −0.623232 + 1.50462i −0.0274097 + 0.0661729i
\(518\) −16.7779 + 16.7779i −0.737177 + 0.737177i
\(519\) −1.56295 + 1.56295i −0.0686058 + 0.0686058i
\(520\) −25.3002 + 61.0801i −1.10949 + 2.67854i
\(521\) −24.3017 10.0661i −1.06468 0.441004i −0.219568 0.975597i \(-0.570465\pi\)
−0.845109 + 0.534593i \(0.820465\pi\)
\(522\) 1.96681 + 4.74829i 0.0860848 + 0.207827i
\(523\) 35.8861i 1.56919i 0.620009 + 0.784595i \(0.287129\pi\)
−0.620009 + 0.784595i \(0.712871\pi\)
\(524\) −54.0893 + 22.4045i −2.36290 + 0.978746i
\(525\) 0.864391 + 0.864391i 0.0377251 + 0.0377251i
\(526\) −55.6852 −2.42799
\(527\) −2.94861 + 2.99149i −0.128443 + 0.130312i
\(528\) −37.2004 −1.61894
\(529\) −15.1335 15.1335i −0.657978 0.657978i
\(530\) 63.7258 26.3961i 2.76807 1.14657i
\(531\) 2.01306i 0.0873596i
\(532\) 11.8973 + 28.7227i 0.515815 + 1.24529i
\(533\) −7.38707 3.05983i −0.319970 0.132536i
\(534\) 8.37151 20.2106i 0.362271 0.874598i
\(535\) 22.3702 22.3702i 0.967147 0.967147i
\(536\) 1.74960 1.74960i 0.0755711 0.0755711i
\(537\) −0.890544 + 2.14996i −0.0384298 + 0.0927778i
\(538\) −32.8570 13.6098i −1.41657 0.586761i
\(539\) 3.26957 + 7.89345i 0.140830 + 0.339995i
\(540\) 61.1627i 2.63202i
\(541\) −5.73630 + 2.37605i −0.246623 + 0.102154i −0.502571 0.864536i \(-0.667612\pi\)
0.255948 + 0.966691i \(0.417612\pi\)
\(542\) −7.61079 7.61079i −0.326911 0.326911i
\(543\) −14.5180 −0.623027
\(544\) −95.6606 38.8172i −4.10142 1.66427i
\(545\) 14.5127 0.621654
\(546\) 9.07218 + 9.07218i 0.388254 + 0.388254i
\(547\) −34.8140 + 14.4204i −1.48854 + 0.616573i −0.970998 0.239087i \(-0.923152\pi\)
−0.517540 + 0.855659i \(0.673152\pi\)
\(548\) 12.1417i 0.518668i
\(549\) 0.253181 + 0.611234i 0.0108055 + 0.0260868i
\(550\) −2.97183 1.23097i −0.126719 0.0524888i
\(551\) 23.8810 57.6538i 1.01736 2.45613i
\(552\) 14.9409 14.9409i 0.635927 0.635927i
\(553\) −1.12455 + 1.12455i −0.0478205 + 0.0478205i
\(554\) −29.7396 + 71.7977i −1.26351 + 3.05039i
\(555\) −31.7692 13.1592i −1.34853 0.558578i
\(556\) 37.4786 + 90.4815i 1.58945 + 3.83727i
\(557\) 15.0954i 0.639611i −0.947483 0.319806i \(-0.896382\pi\)
0.947483 0.319806i \(-0.103618\pi\)
\(558\) 0.503280 0.208465i 0.0213055 0.00882505i
\(559\) −2.30148 2.30148i −0.0973420 0.0973420i
\(560\) 28.3018 1.19597
\(561\) −8.66505 + 3.66269i −0.365839 + 0.154639i
\(562\) −86.0827 −3.63118
\(563\) 29.4702 + 29.4702i 1.24202 + 1.24202i 0.959161 + 0.282861i \(0.0912834\pi\)
0.282861 + 0.959161i \(0.408717\pi\)
\(564\) −10.3922 + 4.30460i −0.437591 + 0.181256i
\(565\) 13.4575i 0.566162i
\(566\) −10.8610 26.2207i −0.456521 1.10214i
\(567\) −6.60251 2.73485i −0.277279 0.114853i
\(568\) −36.0453 + 87.0210i −1.51243 + 3.65132i
\(569\) −20.6335 + 20.6335i −0.865002 + 0.865002i −0.991914 0.126912i \(-0.959493\pi\)
0.126912 + 0.991914i \(0.459493\pi\)
\(570\) −43.2056 + 43.2056i −1.80969 + 1.80969i
\(571\) −6.19180 + 14.9483i −0.259119 + 0.625568i −0.998881 0.0473005i \(-0.984938\pi\)
0.739762 + 0.672869i \(0.234938\pi\)
\(572\) −22.9995 9.52673i −0.961659 0.398332i
\(573\) 7.95745 + 19.2110i 0.332427 + 0.802551i
\(574\) 5.78068i 0.241281i
\(575\) 0.999485 0.414000i 0.0416814 0.0172650i
\(576\) 4.99939 + 4.99939i 0.208308 + 0.208308i
\(577\) 18.5841 0.773666 0.386833 0.922150i \(-0.373569\pi\)
0.386833 + 0.922150i \(0.373569\pi\)
\(578\) −46.9092 + 0.677360i −1.95116 + 0.0281744i
\(579\) 40.5422 1.68488
\(580\) −77.6962 77.6962i −3.22616 3.22616i
\(581\) 3.07972 1.27566i 0.127768 0.0529234i
\(582\) 13.9485i 0.578185i
\(583\) 6.39950 + 15.4498i 0.265040 + 0.639864i
\(584\) −13.7411 5.69174i −0.568610 0.235526i
\(585\) 0.491310 1.18613i 0.0203132 0.0490404i
\(586\) 39.0903 39.0903i 1.61481 1.61481i
\(587\) 32.2970 32.2970i 1.33304 1.33304i 0.430399 0.902639i \(-0.358373\pi\)
0.902639 0.430399i \(-0.141627\pi\)
\(588\) −22.5826 + 54.5191i −0.931289 + 2.24833i
\(589\) −6.11083 2.53119i −0.251792 0.104296i
\(590\) −22.3356 53.9228i −0.919541 2.21997i
\(591\) 9.05222i 0.372358i
\(592\) 151.890 62.9148i 6.24263 2.58578i
\(593\) −26.1923 26.1923i −1.07559 1.07559i −0.996899 0.0786906i \(-0.974926\pi\)
−0.0786906 0.996899i \(-0.525074\pi\)
\(594\) 20.1094 0.825101
\(595\) 6.59231 2.78655i 0.270258 0.114237i
\(596\) −9.26838 −0.379648
\(597\) −0.0908975 0.0908975i −0.00372019 0.00372019i
\(598\) 10.4901 4.34513i 0.428970 0.177685i
\(599\) 15.9949i 0.653534i −0.945105 0.326767i \(-0.894041\pi\)
0.945105 0.326767i \(-0.105959\pi\)
\(600\) −5.47417 13.2158i −0.223482 0.539533i
\(601\) −29.1125 12.0588i −1.18752 0.491888i −0.300575 0.953758i \(-0.597178\pi\)
−0.886947 + 0.461870i \(0.847178\pi\)
\(602\) −0.900499 + 2.17400i −0.0367016 + 0.0886055i
\(603\) −0.0339758 + 0.0339758i −0.00138360 + 0.00138360i
\(604\) −12.5956 + 12.5956i −0.512507 + 0.512507i
\(605\) 7.12426 17.1995i 0.289642 0.699259i
\(606\) −75.1200 31.1157i −3.05154 1.26399i
\(607\) 9.20355 + 22.2193i 0.373560 + 0.901855i 0.993141 + 0.116922i \(0.0373027\pi\)
−0.619581 + 0.784933i \(0.712697\pi\)
\(608\) 162.565i 6.59288i
\(609\) −12.6841 + 5.25393i −0.513986 + 0.212900i
\(610\) −13.5637 13.5637i −0.549176 0.549176i
\(611\) −3.89180 −0.157445
\(612\) 4.15720 + 1.68691i 0.168045 + 0.0681894i
\(613\) −39.8476 −1.60943 −0.804716 0.593660i \(-0.797682\pi\)
−0.804716 + 0.593660i \(0.797682\pi\)
\(614\) 23.8868 + 23.8868i 0.963993 + 0.963993i
\(615\) −7.73986 + 3.20596i −0.312101 + 0.129277i
\(616\) 11.5881i 0.466899i
\(617\) 11.7168 + 28.2867i 0.471699 + 1.13878i 0.963412 + 0.268024i \(0.0863708\pi\)
−0.491713 + 0.870757i \(0.663629\pi\)
\(618\) 34.7366 + 14.3884i 1.39731 + 0.578785i
\(619\) −14.8962 + 35.9626i −0.598729 + 1.44546i 0.276148 + 0.961115i \(0.410942\pi\)
−0.874877 + 0.484344i \(0.839058\pi\)
\(620\) −8.23517 + 8.23517i −0.330732 + 0.330732i
\(621\) −4.78230 + 4.78230i −0.191907 + 0.191907i
\(622\) 20.5782 49.6801i 0.825110 1.99199i
\(623\) −3.72780 1.54411i −0.149351 0.0618633i
\(624\) −34.0195 82.1303i −1.36187 3.28784i
\(625\) 19.9886i 0.799544i
\(626\) 48.1091 19.9274i 1.92283 0.796461i
\(627\) −10.4748 10.4748i −0.418325 0.418325i
\(628\) −69.4822 −2.77264
\(629\) 29.1850 29.6095i 1.16368 1.18061i
\(630\) −0.928193 −0.0369801
\(631\) 24.4611 + 24.4611i 0.973779 + 0.973779i 0.999665 0.0258856i \(-0.00824055\pi\)
−0.0258856 + 0.999665i \(0.508241\pi\)
\(632\) 17.1934 7.12172i 0.683915 0.283287i
\(633\) 38.8624i 1.54464i
\(634\) 7.52040 + 18.1559i 0.298673 + 0.721061i
\(635\) 28.6602 + 11.8715i 1.13735 + 0.471104i
\(636\) −44.2007 + 106.710i −1.75267 + 4.23132i
\(637\) −14.4370 + 14.4370i −0.572014 + 0.572014i
\(638\) 25.5454 25.5454i 1.01135 1.01135i
\(639\) 0.699971 1.68988i 0.0276904 0.0668506i
\(640\) −95.2025 39.4342i −3.76321 1.55877i
\(641\) 7.38639 + 17.8323i 0.291745 + 0.704334i 0.999999 0.00162373i \(-0.000516849\pi\)
−0.708254 + 0.705958i \(0.750517\pi\)
\(642\) 71.8423i 2.83539i
\(643\) 5.87421 2.43318i 0.231656 0.0959552i −0.263836 0.964568i \(-0.584988\pi\)
0.495492 + 0.868612i \(0.334988\pi\)
\(644\) −4.28019 4.28019i −0.168663 0.168663i
\(645\) −3.41022 −0.134277
\(646\) −28.7627 68.0457i −1.13166 2.67722i
\(647\) −17.8781 −0.702860 −0.351430 0.936214i \(-0.614304\pi\)
−0.351430 + 0.936214i \(0.614304\pi\)
\(648\) 59.1333 + 59.1333i 2.32297 + 2.32297i
\(649\) 13.0731 5.41507i 0.513165 0.212560i
\(650\) 7.68686i 0.301503i
\(651\) 0.556874 + 1.34441i 0.0218256 + 0.0526917i
\(652\) −64.2560 26.6157i −2.51646 1.04235i
\(653\) −2.56117 + 6.18321i −0.100226 + 0.241968i −0.966037 0.258404i \(-0.916803\pi\)
0.865811 + 0.500372i \(0.166803\pi\)
\(654\) −23.3039 + 23.3039i −0.911253 + 0.911253i
\(655\) −15.0072 + 15.0072i −0.586380 + 0.586380i
\(656\) 15.3278 37.0046i 0.598451 1.44479i
\(657\) 0.266841 + 0.110529i 0.0104105 + 0.00431216i
\(658\) 1.07674 + 2.59949i 0.0419758 + 0.101339i
\(659\) 28.9866i 1.12916i 0.825379 + 0.564579i \(0.190962\pi\)
−0.825379 + 0.564579i \(0.809038\pi\)
\(660\) −24.0980 + 9.98170i −0.938012 + 0.388537i
\(661\) 23.0132 + 23.0132i 0.895111 + 0.895111i 0.994999 0.0998880i \(-0.0318485\pi\)
−0.0998880 + 0.994999i \(0.531848\pi\)
\(662\) 20.2186 0.785817
\(663\) −16.0105 15.7810i −0.621797 0.612884i
\(664\) −39.0076 −1.51379
\(665\) 7.96918 + 7.96918i 0.309032 + 0.309032i
\(666\) −4.98141 + 2.06337i −0.193026 + 0.0799539i
\(667\) 12.1501i 0.470454i
\(668\) 40.5740 + 97.9543i 1.56985 + 3.78996i
\(669\) −28.5462 11.8242i −1.10366 0.457151i
\(670\) 0.533119 1.28706i 0.0205962 0.0497236i
\(671\) 3.28839 3.28839i 0.126947 0.126947i
\(672\) −25.2897 + 25.2897i −0.975573 + 0.975573i
\(673\) −15.6355 + 37.7475i −0.602706 + 1.45506i 0.268079 + 0.963397i \(0.413611\pi\)
−0.870785 + 0.491664i \(0.836389\pi\)
\(674\) 73.8472 + 30.5885i 2.84449 + 1.17823i
\(675\) 1.75218 + 4.23013i 0.0674414 + 0.162818i
\(676\) 13.5137i 0.519756i
\(677\) 27.4236 11.3592i 1.05397 0.436570i 0.212665 0.977125i \(-0.431786\pi\)
0.841309 + 0.540555i \(0.181786\pi\)
\(678\) 21.6095 + 21.6095i 0.829909 + 0.829909i
\(679\) 2.57277 0.0987340
\(680\) −83.7483 + 0.604624i −3.21160 + 0.0231863i
\(681\) −19.4620 −0.745784
\(682\) −2.70761 2.70761i −0.103680 0.103680i
\(683\) 3.57206 1.47960i 0.136681 0.0566152i −0.313294 0.949656i \(-0.601433\pi\)
0.449976 + 0.893041i \(0.351433\pi\)
\(684\) 7.06473i 0.270127i
\(685\) −1.68437 4.06643i −0.0643565 0.155370i
\(686\) 28.8553 + 11.9523i 1.10170 + 0.456339i
\(687\) −10.5220 + 25.4023i −0.401439 + 0.969159i
\(688\) 11.5290 11.5290i 0.439537 0.439537i
\(689\) −28.2574 + 28.2574i −1.07652 + 1.07652i
\(690\) 4.55264 10.9910i 0.173316 0.418422i
\(691\) 17.7379 + 7.34727i 0.674780 + 0.279503i 0.693643 0.720319i \(-0.256005\pi\)
−0.0188627 + 0.999822i \(0.506005\pi\)
\(692\) −2.83556 6.84564i −0.107792 0.260232i
\(693\) 0.225032i 0.00854828i
\(694\) 2.89429 1.19886i 0.109866 0.0455079i
\(695\) 25.1043 + 25.1043i 0.952260 + 0.952260i
\(696\) 160.656 6.08966
\(697\) −0.0731236 10.1286i −0.00276976 0.383648i
\(698\) −42.5540 −1.61069
\(699\) −17.0919 17.0919i −0.646473 0.646473i
\(700\) −3.78599 + 1.56821i −0.143097 + 0.0592728i
\(701\) 35.1008i 1.32574i −0.748734 0.662870i \(-0.769338\pi\)
0.748734 0.662870i \(-0.230662\pi\)
\(702\) 18.3899 + 44.3972i 0.694083 + 1.67566i
\(703\) 60.4843 + 25.0534i 2.28121 + 0.944908i
\(704\) 19.0186 45.9150i 0.716790 1.73048i
\(705\) −2.88334 + 2.88334i −0.108593 + 0.108593i
\(706\) −45.4377 + 45.4377i −1.71007 + 1.71007i
\(707\) −5.73923 + 13.8557i −0.215846 + 0.521098i
\(708\) 90.2946 + 37.4013i 3.39348 + 1.40563i
\(709\) 6.02394 + 14.5431i 0.226234 + 0.546177i 0.995713 0.0924951i \(-0.0294842\pi\)
−0.769479 + 0.638672i \(0.779484\pi\)
\(710\) 53.0323i 1.99027i
\(711\) −0.333882 + 0.138298i −0.0125215 + 0.00518659i
\(712\) 33.3869 + 33.3869i 1.25123 + 1.25123i
\(713\) 1.28781 0.0482290
\(714\) −6.11114 + 15.0602i −0.228704 + 0.563614i
\(715\) −9.02449 −0.337497
\(716\) −5.51620 5.51620i −0.206150 0.206150i
\(717\) 2.82155 1.16872i 0.105373 0.0436468i
\(718\) 37.0423i 1.38240i
\(719\) 6.66163 + 16.0826i 0.248437 + 0.599780i 0.998072 0.0620721i \(-0.0197709\pi\)
−0.749635 + 0.661852i \(0.769771\pi\)
\(720\) 5.94176 + 2.46116i 0.221436 + 0.0917219i
\(721\) 2.65390 6.40708i 0.0988364 0.238612i
\(722\) 45.1819 45.1819i 1.68149 1.68149i
\(723\) −3.89817 + 3.89817i −0.144975 + 0.144975i
\(724\) 18.6245 44.9636i 0.692176 1.67106i
\(725\) 7.59945 + 3.14779i 0.282236 + 0.116906i
\(726\) 16.1784 + 39.0581i 0.600437 + 1.44958i
\(727\) 3.29769i 0.122305i −0.998128 0.0611523i \(-0.980522\pi\)
0.998128 0.0611523i \(-0.0194775\pi\)
\(728\) −25.5840 + 10.5972i −0.948207 + 0.392760i
\(729\) −20.1606 20.1606i −0.746687 0.746687i
\(730\) −8.37408 −0.309939
\(731\) 1.55030 3.82054i 0.0573400 0.141308i
\(732\) 32.1204 1.18720
\(733\) −7.84996 7.84996i −0.289945 0.289945i 0.547113 0.837058i \(-0.315727\pi\)
−0.837058 + 0.547113i \(0.815727\pi\)
\(734\) −43.6025 + 18.0607i −1.60940 + 0.666634i
\(735\) 21.3921i 0.789058i
\(736\) 12.1125 + 29.2422i 0.446474 + 1.07788i
\(737\) 0.312038 + 0.129250i 0.0114941 + 0.00476099i
\(738\) −0.502694 + 1.21361i −0.0185044 + 0.0446737i
\(739\) 32.0698 32.0698i 1.17971 1.17971i 0.199887 0.979819i \(-0.435943\pi\)
0.979819 0.199887i \(-0.0640574\pi\)
\(740\) 81.5108 81.5108i 2.99640 2.99640i
\(741\) 13.5470 32.7053i 0.497660 1.20146i
\(742\) 26.6922 + 11.0563i 0.979901 + 0.405888i
\(743\) 19.5303 + 47.1503i 0.716497 + 1.72978i 0.683089 + 0.730335i \(0.260636\pi\)
0.0334077 + 0.999442i \(0.489364\pi\)
\(744\) 17.0283i 0.624287i
\(745\) −3.10412 + 1.28577i −0.113726 + 0.0471069i
\(746\) −3.91366 3.91366i −0.143289 0.143289i
\(747\) 0.757498 0.0277154
\(748\) −0.227669 31.5352i −0.00832442 1.15304i
\(749\) 13.2512 0.484187
\(750\) −38.9680 38.9680i −1.42291 1.42291i
\(751\) 45.9853 19.0477i 1.67803 0.695062i 0.678799 0.734324i \(-0.262501\pi\)
0.999229 + 0.0392616i \(0.0125006\pi\)
\(752\) 19.4955i 0.710927i
\(753\) 16.4150 + 39.6294i 0.598197 + 1.44418i
\(754\) 79.7598 + 33.0376i 2.90468 + 1.20316i
\(755\) −2.47111 + 5.96578i −0.0899328 + 0.217117i
\(756\) 18.1151 18.1151i 0.658840 0.658840i
\(757\) 14.2444 14.2444i 0.517723 0.517723i −0.399159 0.916882i \(-0.630698\pi\)
0.916882 + 0.399159i \(0.130698\pi\)
\(758\) −16.5885 + 40.0482i −0.602522 + 1.45462i
\(759\) 2.66468 + 1.10375i 0.0967219 + 0.0400635i
\(760\) −50.4687 121.842i −1.83069 4.41968i
\(761\) 16.6616i 0.603983i