Properties

Label 105.2.j.a.8.2
Level 105
Weight 2
Character 105.8
Analytic conductor 0.838
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 105.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 8.2
Character \(\chi\) = 105.8
Dual form 105.2.j.a.92.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.54414 - 1.54414i) q^{2} +(-0.00622252 - 1.73204i) q^{3} +2.76875i q^{4} +(0.252500 - 2.22177i) q^{5} +(-2.66491 + 2.68412i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.18705 - 1.18705i) q^{8} +(-2.99992 + 0.0215553i) q^{9} +O(q^{10})\) \(q+(-1.54414 - 1.54414i) q^{2} +(-0.00622252 - 1.73204i) q^{3} +2.76875i q^{4} +(0.252500 - 2.22177i) q^{5} +(-2.66491 + 2.68412i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.18705 - 1.18705i) q^{8} +(-2.99992 + 0.0215553i) q^{9} +(-3.82062 + 3.04083i) q^{10} +3.38507i q^{11} +(4.79558 - 0.0172286i) q^{12} +(-0.206632 - 0.206632i) q^{13} -2.18375 q^{14} +(-3.84976 - 0.423515i) q^{15} +1.87154 q^{16} +(-0.167409 - 0.167409i) q^{17} +(4.66559 + 4.59902i) q^{18} -5.31419i q^{19} +(6.15151 + 0.699108i) q^{20} +(-1.22914 - 1.22034i) q^{21} +(5.22702 - 5.22702i) q^{22} +(5.07773 - 5.07773i) q^{23} +(-2.06341 - 2.04864i) q^{24} +(-4.87249 - 1.12199i) q^{25} +0.638138i q^{26} +(0.0560017 + 5.19585i) q^{27} +(1.95780 + 1.95780i) q^{28} +2.84268 q^{29} +(5.29060 + 6.59854i) q^{30} +9.11776 q^{31} +(-5.26402 - 5.26402i) q^{32} +(5.86307 - 0.0210636i) q^{33} +0.517005i q^{34} +(-1.39248 - 1.74957i) q^{35} +(-0.0596812 - 8.30602i) q^{36} +(-5.27013 + 5.27013i) q^{37} +(-8.20586 + 8.20586i) q^{38} +(-0.356609 + 0.359180i) q^{39} +(-2.33762 - 2.93708i) q^{40} +0.0314968i q^{41} +(0.0135884 + 3.78233i) q^{42} +(-3.76875 - 3.76875i) q^{43} -9.37239 q^{44} +(-0.709590 + 6.67057i) q^{45} -15.6815 q^{46} +(3.56639 + 3.56639i) q^{47} +(-0.0116457 - 3.24158i) q^{48} -1.00000i q^{49} +(5.79130 + 9.25632i) q^{50} +(-0.288917 + 0.291000i) q^{51} +(0.572111 - 0.572111i) q^{52} +(-3.55291 + 3.55291i) q^{53} +(7.93665 - 8.10960i) q^{54} +(7.52082 + 0.854729i) q^{55} -1.67875i q^{56} +(-9.20439 + 0.0330677i) q^{57} +(-4.38949 - 4.38949i) q^{58} +10.3168 q^{59} +(1.17261 - 10.6590i) q^{60} -6.80634 q^{61} +(-14.0791 - 14.0791i) q^{62} +(-2.10602 + 2.13651i) q^{63} +12.5137i q^{64} +(-0.511262 + 0.406913i) q^{65} +(-9.08593 - 9.02088i) q^{66} +(6.34806 - 6.34806i) q^{67} +(0.463512 - 0.463512i) q^{68} +(-8.82642 - 8.76323i) q^{69} +(-0.551396 + 4.85177i) q^{70} +3.95454i q^{71} +(-3.53548 + 3.58665i) q^{72} +(8.61099 + 8.61099i) q^{73} +16.2757 q^{74} +(-1.91302 + 8.44632i) q^{75} +14.7136 q^{76} +(2.39360 + 2.39360i) q^{77} +(1.10528 - 0.00397083i) q^{78} +11.4449i q^{79} +(0.472563 - 4.15812i) q^{80} +(8.99907 - 0.129328i) q^{81} +(0.0486356 - 0.0486356i) q^{82} +(-3.88059 + 3.88059i) q^{83} +(3.37880 - 3.40317i) q^{84} +(-0.414214 + 0.329672i) q^{85} +11.6390i q^{86} +(-0.0176886 - 4.92363i) q^{87} +(4.01825 + 4.01825i) q^{88} -2.00190 q^{89} +(11.3960 - 9.20459i) q^{90} -0.292222 q^{91} +(14.0589 + 14.0589i) q^{92} +(-0.0567354 - 15.7923i) q^{93} -11.0140i q^{94} +(-11.8069 - 1.34183i) q^{95} +(-9.08474 + 9.15025i) q^{96} +(2.26760 - 2.26760i) q^{97} +(-1.54414 + 1.54414i) q^{98} +(-0.0729661 - 10.1549i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 4q^{3} + O(q^{10}) \) \( 24q - 4q^{3} - 16q^{10} + 16q^{12} - 8q^{13} - 16q^{15} - 16q^{16} - 20q^{18} + 4q^{21} + 8q^{22} - 16q^{25} - 16q^{27} + 20q^{30} + 28q^{33} + 16q^{36} - 16q^{37} + 64q^{40} - 20q^{42} - 40q^{43} + 20q^{45} - 64q^{46} + 16q^{48} - 20q^{51} + 40q^{55} + 4q^{57} + 40q^{58} + 32q^{60} + 32q^{61} - 8q^{63} - 16q^{66} + 24q^{67} - 8q^{70} - 8q^{72} + 32q^{73} - 60q^{75} + 32q^{76} + 60q^{78} + 52q^{81} - 80q^{82} + 24q^{85} + 4q^{87} + 96q^{88} - 24q^{90} - 24q^{91} - 76q^{93} - 96q^{96} + 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.54414 1.54414i −1.09187 1.09187i −0.995329 0.0965442i \(-0.969221\pi\)
−0.0965442 0.995329i \(-0.530779\pi\)
\(3\) −0.00622252 1.73204i −0.00359257 0.999994i
\(4\) 2.76875i 1.38437i
\(5\) 0.252500 2.22177i 0.112921 0.993604i
\(6\) −2.66491 + 2.68412i −1.08794 + 1.09579i
\(7\) 0.707107 0.707107i 0.267261 0.267261i
\(8\) 1.18705 1.18705i 0.419686 0.419686i
\(9\) −2.99992 + 0.0215553i −0.999974 + 0.00718510i
\(10\) −3.82062 + 3.04083i −1.20819 + 0.961593i
\(11\) 3.38507i 1.02064i 0.859986 + 0.510318i \(0.170472\pi\)
−0.859986 + 0.510318i \(0.829528\pi\)
\(12\) 4.79558 0.0172286i 1.38436 0.00497346i
\(13\) −0.206632 0.206632i −0.0573094 0.0573094i 0.677871 0.735181i \(-0.262903\pi\)
−0.735181 + 0.677871i \(0.762903\pi\)
\(14\) −2.18375 −0.583631
\(15\) −3.84976 0.423515i −0.994003 0.109351i
\(16\) 1.87154 0.467884
\(17\) −0.167409 0.167409i −0.0406026 0.0406026i 0.686514 0.727117i \(-0.259140\pi\)
−0.727117 + 0.686514i \(0.759140\pi\)
\(18\) 4.66559 + 4.59902i 1.09969 + 1.08400i
\(19\) 5.31419i 1.21916i −0.792725 0.609579i \(-0.791338\pi\)
0.792725 0.609579i \(-0.208662\pi\)
\(20\) 6.15151 + 0.699108i 1.37552 + 0.156325i
\(21\) −1.22914 1.22034i −0.268220 0.266299i
\(22\) 5.22702 5.22702i 1.11440 1.11440i
\(23\) 5.07773 5.07773i 1.05878 1.05878i 0.0606179 0.998161i \(-0.480693\pi\)
0.998161 0.0606179i \(-0.0193071\pi\)
\(24\) −2.06341 2.04864i −0.421191 0.418176i
\(25\) −4.87249 1.12199i −0.974497 0.224398i
\(26\) 0.638138i 0.125149i
\(27\) 0.0560017 + 5.19585i 0.0107775 + 0.999942i
\(28\) 1.95780 + 1.95780i 0.369989 + 0.369989i
\(29\) 2.84268 0.527872 0.263936 0.964540i \(-0.414979\pi\)
0.263936 + 0.964540i \(0.414979\pi\)
\(30\) 5.29060 + 6.59854i 0.965928 + 1.20472i
\(31\) 9.11776 1.63760 0.818799 0.574081i \(-0.194640\pi\)
0.818799 + 0.574081i \(0.194640\pi\)
\(32\) −5.26402 5.26402i −0.930557 0.930557i
\(33\) 5.86307 0.0210636i 1.02063 0.00366671i
\(34\) 0.517005i 0.0886657i
\(35\) −1.39248 1.74957i −0.235372 0.295731i
\(36\) −0.0596812 8.30602i −0.00994686 1.38434i
\(37\) −5.27013 + 5.27013i −0.866404 + 0.866404i −0.992072 0.125668i \(-0.959893\pi\)
0.125668 + 0.992072i \(0.459893\pi\)
\(38\) −8.20586 + 8.20586i −1.33117 + 1.33117i
\(39\) −0.356609 + 0.359180i −0.0571031 + 0.0575149i
\(40\) −2.33762 2.93708i −0.369611 0.464394i
\(41\) 0.0314968i 0.00491898i 0.999997 + 0.00245949i \(0.000782881\pi\)
−0.999997 + 0.00245949i \(0.999217\pi\)
\(42\) 0.0135884 + 3.78233i 0.00209674 + 0.583627i
\(43\) −3.76875 3.76875i −0.574728 0.574728i 0.358718 0.933446i \(-0.383214\pi\)
−0.933446 + 0.358718i \(0.883214\pi\)
\(44\) −9.37239 −1.41294
\(45\) −0.709590 + 6.67057i −0.105779 + 0.994390i
\(46\) −15.6815 −2.31210
\(47\) 3.56639 + 3.56639i 0.520211 + 0.520211i 0.917635 0.397424i \(-0.130096\pi\)
−0.397424 + 0.917635i \(0.630096\pi\)
\(48\) −0.0116457 3.24158i −0.00168091 0.467881i
\(49\) 1.00000i 0.142857i
\(50\) 5.79130 + 9.25632i 0.819013 + 1.30904i
\(51\) −0.288917 + 0.291000i −0.0404564 + 0.0407482i
\(52\) 0.572111 0.572111i 0.0793376 0.0793376i
\(53\) −3.55291 + 3.55291i −0.488030 + 0.488030i −0.907684 0.419654i \(-0.862151\pi\)
0.419654 + 0.907684i \(0.362151\pi\)
\(54\) 7.93665 8.10960i 1.08004 1.10358i
\(55\) 7.52082 + 0.854729i 1.01411 + 0.115252i
\(56\) 1.67875i 0.224332i
\(57\) −9.20439 + 0.0330677i −1.21915 + 0.00437992i
\(58\) −4.38949 4.38949i −0.576369 0.576369i
\(59\) 10.3168 1.34313 0.671565 0.740946i \(-0.265622\pi\)
0.671565 + 0.740946i \(0.265622\pi\)
\(60\) 1.17261 10.6590i 0.151383 1.37607i
\(61\) −6.80634 −0.871462 −0.435731 0.900077i \(-0.643510\pi\)
−0.435731 + 0.900077i \(0.643510\pi\)
\(62\) −14.0791 14.0791i −1.78805 1.78805i
\(63\) −2.10602 + 2.13651i −0.265334 + 0.269175i
\(64\) 12.5137i 1.56422i
\(65\) −0.511262 + 0.406913i −0.0634143 + 0.0504714i
\(66\) −9.08593 9.02088i −1.11840 1.11039i
\(67\) 6.34806 6.34806i 0.775539 0.775539i −0.203530 0.979069i \(-0.565241\pi\)
0.979069 + 0.203530i \(0.0652413\pi\)
\(68\) 0.463512 0.463512i 0.0562091 0.0562091i
\(69\) −8.82642 8.76323i −1.06258 1.05497i
\(70\) −0.551396 + 4.85177i −0.0659044 + 0.579898i
\(71\) 3.95454i 0.469318i 0.972078 + 0.234659i \(0.0753973\pi\)
−0.972078 + 0.234659i \(0.924603\pi\)
\(72\) −3.53548 + 3.58665i −0.416660 + 0.422691i
\(73\) 8.61099 + 8.61099i 1.00784 + 1.00784i 0.999969 + 0.00787086i \(0.00250540\pi\)
0.00787086 + 0.999969i \(0.497495\pi\)
\(74\) 16.2757 1.89201
\(75\) −1.91302 + 8.44632i −0.220896 + 0.975297i
\(76\) 14.7136 1.68777
\(77\) 2.39360 + 2.39360i 0.272776 + 0.272776i
\(78\) 1.10528 0.00397083i 0.125148 0.000449608i
\(79\) 11.4449i 1.28766i 0.765170 + 0.643828i \(0.222655\pi\)
−0.765170 + 0.643828i \(0.777345\pi\)
\(80\) 0.472563 4.15812i 0.0528342 0.464892i
\(81\) 8.99907 0.129328i 0.999897 0.0143698i
\(82\) 0.0486356 0.0486356i 0.00537090 0.00537090i
\(83\) −3.88059 + 3.88059i −0.425951 + 0.425951i −0.887246 0.461296i \(-0.847385\pi\)
0.461296 + 0.887246i \(0.347385\pi\)
\(84\) 3.37880 3.40317i 0.368658 0.371316i
\(85\) −0.414214 + 0.329672i −0.0449278 + 0.0357580i
\(86\) 11.6390i 1.25506i
\(87\) −0.0176886 4.92363i −0.00189642 0.527868i
\(88\) 4.01825 + 4.01825i 0.428347 + 0.428347i
\(89\) −2.00190 −0.212201 −0.106100 0.994355i \(-0.533836\pi\)
−0.106100 + 0.994355i \(0.533836\pi\)
\(90\) 11.3960 9.20459i 1.20124 0.970249i
\(91\) −0.292222 −0.0306332
\(92\) 14.0589 + 14.0589i 1.46574 + 1.46574i
\(93\) −0.0567354 15.7923i −0.00588319 1.63759i
\(94\) 11.0140i 1.13601i
\(95\) −11.8069 1.34183i −1.21136 0.137669i
\(96\) −9.08474 + 9.15025i −0.927208 + 0.933894i
\(97\) 2.26760 2.26760i 0.230240 0.230240i −0.582553 0.812793i \(-0.697946\pi\)
0.812793 + 0.582553i \(0.197946\pi\)
\(98\) −1.54414 + 1.54414i −0.155982 + 0.155982i
\(99\) −0.0729661 10.1549i −0.00733337 1.02061i
\(100\) 3.10651 13.4907i 0.310651 1.34907i
\(101\) 8.63630i 0.859344i −0.902985 0.429672i \(-0.858629\pi\)
0.902985 0.429672i \(-0.141371\pi\)
\(102\) 0.895474 0.00321708i 0.0886651 0.000318538i
\(103\) 0.964332 + 0.964332i 0.0950185 + 0.0950185i 0.753018 0.658000i \(-0.228597\pi\)
−0.658000 + 0.753018i \(0.728597\pi\)
\(104\) −0.490566 −0.0481039
\(105\) −3.02166 + 2.42272i −0.294884 + 0.236433i
\(106\) 10.9724 1.06573
\(107\) 2.95847 + 2.95847i 0.286007 + 0.286007i 0.835499 0.549492i \(-0.185179\pi\)
−0.549492 + 0.835499i \(0.685179\pi\)
\(108\) −14.3860 + 0.155055i −1.38429 + 0.0149201i
\(109\) 2.82182i 0.270281i 0.990826 + 0.135141i \(0.0431486\pi\)
−0.990826 + 0.135141i \(0.956851\pi\)
\(110\) −10.2934 12.9330i −0.981436 1.23312i
\(111\) 9.16087 + 9.09528i 0.869511 + 0.863286i
\(112\) 1.32338 1.32338i 0.125047 0.125047i
\(113\) −2.01798 + 2.01798i −0.189835 + 0.189835i −0.795625 0.605790i \(-0.792857\pi\)
0.605790 + 0.795625i \(0.292857\pi\)
\(114\) 14.2639 + 14.1618i 1.33594 + 1.32638i
\(115\) −9.99939 12.5636i −0.932448 1.17157i
\(116\) 7.87065i 0.730771i
\(117\) 0.624334 + 0.615426i 0.0577197 + 0.0568961i
\(118\) −15.9306 15.9306i −1.46653 1.46653i
\(119\) −0.236752 −0.0217030
\(120\) −5.07260 + 4.06713i −0.463063 + 0.371276i
\(121\) −0.458667 −0.0416970
\(122\) 10.5099 + 10.5099i 0.951526 + 0.951526i
\(123\) 0.0545538 0.000195990i 0.00491895 1.76718e-5i
\(124\) 25.2448i 2.26705i
\(125\) −3.72311 + 10.5422i −0.333005 + 0.942925i
\(126\) 6.55107 0.0470713i 0.583616 0.00419345i
\(127\) −11.6271 + 11.6271i −1.03174 + 1.03174i −0.0322583 + 0.999480i \(0.510270\pi\)
−0.999480 + 0.0322583i \(0.989730\pi\)
\(128\) 8.79491 8.79491i 0.777367 0.777367i
\(129\) −6.50417 + 6.55107i −0.572660 + 0.576789i
\(130\) 1.41779 + 0.161130i 0.124349 + 0.0141320i
\(131\) 12.7013i 1.10972i −0.831943 0.554861i \(-0.812772\pi\)
0.831943 0.554861i \(-0.187228\pi\)
\(132\) 0.0583199 + 16.2333i 0.00507609 + 1.41293i
\(133\) −3.75770 3.75770i −0.325834 0.325834i
\(134\) −19.6046 −1.69358
\(135\) 11.5581 + 1.18753i 0.994763 + 0.102206i
\(136\) −0.397446 −0.0340807
\(137\) 5.19451 + 5.19451i 0.443797 + 0.443797i 0.893286 0.449489i \(-0.148394\pi\)
−0.449489 + 0.893286i \(0.648394\pi\)
\(138\) 0.0975782 + 27.1609i 0.00830641 + 2.31209i
\(139\) 12.3138i 1.04444i 0.852810 + 0.522221i \(0.174897\pi\)
−0.852810 + 0.522221i \(0.825103\pi\)
\(140\) 4.84412 3.85543i 0.409402 0.325843i
\(141\) 6.15493 6.19932i 0.518339 0.522077i
\(142\) 6.10637 6.10637i 0.512435 0.512435i
\(143\) 0.699463 0.699463i 0.0584920 0.0584920i
\(144\) −5.61447 + 0.0403416i −0.467872 + 0.00336180i
\(145\) 0.717776 6.31576i 0.0596080 0.524495i
\(146\) 26.5932i 2.20087i
\(147\) −1.73204 + 0.00622252i −0.142856 + 0.000513225i
\(148\) −14.5917 14.5917i −1.19943 1.19943i
\(149\) −18.9350 −1.55121 −0.775607 0.631216i \(-0.782556\pi\)
−0.775607 + 0.631216i \(0.782556\pi\)
\(150\) 15.9963 10.0884i 1.30609 0.823710i
\(151\) −1.90527 −0.155049 −0.0775243 0.996990i \(-0.524702\pi\)
−0.0775243 + 0.996990i \(0.524702\pi\)
\(152\) −6.30822 6.30822i −0.511665 0.511665i
\(153\) 0.505822 + 0.498604i 0.0408933 + 0.0403098i
\(154\) 7.39212i 0.595674i
\(155\) 2.30223 20.2575i 0.184920 1.62712i
\(156\) −0.994479 0.987359i −0.0796221 0.0790520i
\(157\) −4.31728 + 4.31728i −0.344557 + 0.344557i −0.858077 0.513521i \(-0.828341\pi\)
0.513521 + 0.858077i \(0.328341\pi\)
\(158\) 17.6726 17.6726i 1.40596 1.40596i
\(159\) 6.17589 + 6.13167i 0.489780 + 0.486273i
\(160\) −13.0246 + 10.3663i −1.02968 + 0.819525i
\(161\) 7.18099i 0.565941i
\(162\) −14.0955 13.6961i −1.10745 1.07607i
\(163\) 3.57655 + 3.57655i 0.280137 + 0.280137i 0.833164 0.553027i \(-0.186527\pi\)
−0.553027 + 0.833164i \(0.686527\pi\)
\(164\) −0.0872068 −0.00680970
\(165\) 1.43363 13.0317i 0.111608 1.01452i
\(166\) 11.9844 0.930168
\(167\) 6.39241 + 6.39241i 0.494659 + 0.494659i 0.909771 0.415111i \(-0.136257\pi\)
−0.415111 + 0.909771i \(0.636257\pi\)
\(168\) −2.90765 + 0.0104460i −0.224330 + 0.000805929i
\(169\) 12.9146i 0.993431i
\(170\) 1.14866 + 0.130544i 0.0880986 + 0.0100123i
\(171\) 0.114549 + 15.9422i 0.00875978 + 1.21913i
\(172\) 10.4347 10.4347i 0.795638 0.795638i
\(173\) −3.88791 + 3.88791i −0.295592 + 0.295592i −0.839285 0.543692i \(-0.817026\pi\)
0.543692 + 0.839285i \(0.317026\pi\)
\(174\) −7.57546 + 7.63009i −0.574294 + 0.578436i
\(175\) −4.23874 + 2.65200i −0.320418 + 0.200472i
\(176\) 6.33528i 0.477540i
\(177\) −0.0641964 17.8691i −0.00482529 1.34312i
\(178\) 3.09121 + 3.09121i 0.231696 + 0.231696i
\(179\) 14.6322 1.09366 0.546832 0.837242i \(-0.315834\pi\)
0.546832 + 0.837242i \(0.315834\pi\)
\(180\) −18.4691 1.96467i −1.37661 0.146438i
\(181\) −9.83718 −0.731192 −0.365596 0.930774i \(-0.619135\pi\)
−0.365596 + 0.930774i \(0.619135\pi\)
\(182\) 0.451232 + 0.451232i 0.0334475 + 0.0334475i
\(183\) 0.0423526 + 11.7888i 0.00313079 + 0.871456i
\(184\) 12.0551i 0.888710i
\(185\) 10.3783 + 13.0397i 0.763027 + 0.958698i
\(186\) −24.2980 + 24.4732i −1.78161 + 1.79446i
\(187\) 0.566689 0.566689i 0.0414404 0.0414404i
\(188\) −9.87442 + 9.87442i −0.720166 + 0.720166i
\(189\) 3.71362 + 3.63442i 0.270126 + 0.264365i
\(190\) 16.1595 + 20.3035i 1.17234 + 1.47297i
\(191\) 6.37886i 0.461558i −0.973006 0.230779i \(-0.925873\pi\)
0.973006 0.230779i \(-0.0741275\pi\)
\(192\) 21.6743 0.0778669i 1.56421 0.00561956i
\(193\) 7.56336 + 7.56336i 0.544422 + 0.544422i 0.924822 0.380400i \(-0.124214\pi\)
−0.380400 + 0.924822i \(0.624214\pi\)
\(194\) −7.00299 −0.502785
\(195\) 0.707971 + 0.882995i 0.0506989 + 0.0632326i
\(196\) 2.76875 0.197768
\(197\) 1.01490 + 1.01490i 0.0723090 + 0.0723090i 0.742336 0.670027i \(-0.233718\pi\)
−0.670027 + 0.742336i \(0.733718\pi\)
\(198\) −15.5680 + 15.7933i −1.10637 + 1.12238i
\(199\) 9.40041i 0.666378i −0.942860 0.333189i \(-0.891875\pi\)
0.942860 0.333189i \(-0.108125\pi\)
\(200\) −7.11576 + 4.45204i −0.503160 + 0.314806i
\(201\) −11.0346 10.9556i −0.778320 0.772748i
\(202\) −13.3357 + 13.3357i −0.938295 + 0.938295i
\(203\) 2.01007 2.01007i 0.141080 0.141080i
\(204\) −0.805705 0.799937i −0.0564107 0.0560068i
\(205\) 0.0699786 + 0.00795295i 0.00488752 + 0.000555458i
\(206\) 2.97813i 0.207496i
\(207\) −15.1233 + 15.3422i −1.05114 + 1.06636i
\(208\) −0.386719 0.386719i −0.0268142 0.0268142i
\(209\) 17.9889 1.24432
\(210\) 8.40689 + 0.924849i 0.580131 + 0.0638207i
\(211\) −8.29157 −0.570815 −0.285407 0.958406i \(-0.592129\pi\)
−0.285407 + 0.958406i \(0.592129\pi\)
\(212\) −9.83710 9.83710i −0.675615 0.675615i
\(213\) 6.84942 0.0246072i 0.469315 0.00168606i
\(214\) 9.13661i 0.624566i
\(215\) −9.32488 + 7.42166i −0.635952 + 0.506153i
\(216\) 6.23422 + 6.10127i 0.424185 + 0.415139i
\(217\) 6.44723 6.44723i 0.437666 0.437666i
\(218\) 4.35729 4.35729i 0.295113 0.295113i
\(219\) 14.8610 14.9682i 1.00421 1.01145i
\(220\) −2.36653 + 20.8232i −0.159551 + 1.40390i
\(221\) 0.0691839i 0.00465382i
\(222\) −0.101276 28.1901i −0.00679717 1.89199i
\(223\) 3.86020 + 3.86020i 0.258498 + 0.258498i 0.824443 0.565945i \(-0.191489\pi\)
−0.565945 + 0.824443i \(0.691489\pi\)
\(224\) −7.44445 −0.497404
\(225\) 14.6413 + 3.26086i 0.976085 + 0.217391i
\(226\) 6.23208 0.414552
\(227\) −1.50739 1.50739i −0.100049 0.100049i 0.655310 0.755360i \(-0.272538\pi\)
−0.755360 + 0.655310i \(0.772538\pi\)
\(228\) −0.0915560 25.4846i −0.00606344 1.68776i
\(229\) 6.26009i 0.413678i 0.978375 + 0.206839i \(0.0663177\pi\)
−0.978375 + 0.206839i \(0.933682\pi\)
\(230\) −3.95957 + 34.8405i −0.261086 + 2.29732i
\(231\) 4.13092 4.16071i 0.271795 0.273755i
\(232\) 3.37440 3.37440i 0.221541 0.221541i
\(233\) 2.67422 2.67422i 0.175194 0.175194i −0.614063 0.789257i \(-0.710466\pi\)
0.789257 + 0.614063i \(0.210466\pi\)
\(234\) −0.0137553 1.91436i −0.000899209 0.125146i
\(235\) 8.82419 7.02317i 0.575627 0.458141i
\(236\) 28.5645i 1.85939i
\(237\) 19.8231 0.0712164i 1.28765 0.00462600i
\(238\) 0.365578 + 0.365578i 0.0236969 + 0.0236969i
\(239\) −2.08521 −0.134881 −0.0674406 0.997723i \(-0.521483\pi\)
−0.0674406 + 0.997723i \(0.521483\pi\)
\(240\) −7.20497 0.792624i −0.465079 0.0511637i
\(241\) −5.43686 −0.350219 −0.175110 0.984549i \(-0.556028\pi\)
−0.175110 + 0.984549i \(0.556028\pi\)
\(242\) 0.708247 + 0.708247i 0.0455279 + 0.0455279i
\(243\) −0.279999 15.5859i −0.0179619 0.999839i
\(244\) 18.8450i 1.20643i
\(245\) −2.22177 0.252500i −0.141943 0.0161316i
\(246\) −0.0845414 0.0839361i −0.00539016 0.00535157i
\(247\) −1.09808 + 1.09808i −0.0698692 + 0.0698692i
\(248\) 10.8233 10.8233i 0.687278 0.687278i
\(249\) 6.74549 + 6.69720i 0.427478 + 0.424418i
\(250\) 22.0277 10.5297i 1.39315 0.665956i
\(251\) 23.3428i 1.47339i −0.676227 0.736693i \(-0.736386\pi\)
0.676227 0.736693i \(-0.263614\pi\)
\(252\) −5.91545 5.83104i −0.372638 0.367321i
\(253\) 17.1884 + 17.1884i 1.08063 + 1.08063i
\(254\) 35.9078 2.25305
\(255\) 0.573583 + 0.715383i 0.0359191 + 0.0447990i
\(256\) −2.13372 −0.133358
\(257\) −10.9273 10.9273i −0.681627 0.681627i 0.278740 0.960367i \(-0.410083\pi\)
−0.960367 + 0.278740i \(0.910083\pi\)
\(258\) 20.1591 0.0724236i 1.25505 0.00450890i
\(259\) 7.45309i 0.463112i
\(260\) −1.12664 1.41556i −0.0698712 0.0877890i
\(261\) −8.52781 + 0.0612747i −0.527858 + 0.00379281i
\(262\) −19.6127 + 19.6127i −1.21167 + 1.21167i
\(263\) −18.1808 + 18.1808i −1.12108 + 1.12108i −0.129497 + 0.991580i \(0.541336\pi\)
−0.991580 + 0.129497i \(0.958664\pi\)
\(264\) 6.93477 6.98477i 0.426805 0.429883i
\(265\) 6.99662 + 8.79084i 0.429799 + 0.540017i
\(266\) 11.6048i 0.711539i
\(267\) 0.0124569 + 3.46737i 0.000762347 + 0.212199i
\(268\) 17.5762 + 17.5762i 1.07364 + 1.07364i
\(269\) −28.5125 −1.73844 −0.869219 0.494428i \(-0.835378\pi\)
−0.869219 + 0.494428i \(0.835378\pi\)
\(270\) −16.0136 19.6811i −0.974559 1.19775i
\(271\) 3.12214 0.189656 0.0948282 0.995494i \(-0.469770\pi\)
0.0948282 + 0.995494i \(0.469770\pi\)
\(272\) −0.313312 0.313312i −0.0189973 0.0189973i
\(273\) 0.00181836 + 0.506139i 0.000110052 + 0.0306330i
\(274\) 16.0421i 0.969139i
\(275\) 3.79802 16.4937i 0.229029 0.994607i
\(276\) 24.2631 24.4381i 1.46047 1.47100i
\(277\) 12.2472 12.2472i 0.735861 0.735861i −0.235913 0.971774i \(-0.575808\pi\)
0.971774 + 0.235913i \(0.0758081\pi\)
\(278\) 19.0142 19.0142i 1.14040 1.14040i
\(279\) −27.3526 + 0.196536i −1.63756 + 0.0117663i
\(280\) −3.72978 0.423883i −0.222897 0.0253319i
\(281\) 12.7181i 0.758698i 0.925254 + 0.379349i \(0.123852\pi\)
−0.925254 + 0.379349i \(0.876148\pi\)
\(282\) −19.0767 + 0.0685349i −1.13600 + 0.00408120i
\(283\) −19.8271 19.8271i −1.17860 1.17860i −0.980102 0.198495i \(-0.936395\pi\)
−0.198495 0.980102i \(-0.563605\pi\)
\(284\) −10.9491 −0.649711
\(285\) −2.25064 + 20.4583i −0.133316 + 1.21185i
\(286\) −2.16014 −0.127732
\(287\) 0.0222716 + 0.0222716i 0.00131465 + 0.00131465i
\(288\) 15.9051 + 15.6782i 0.937219 + 0.923847i
\(289\) 16.9439i 0.996703i
\(290\) −10.8608 + 8.64408i −0.637767 + 0.507598i
\(291\) −3.94168 3.91346i −0.231066 0.229411i
\(292\) −23.8416 + 23.8416i −1.39523 + 1.39523i
\(293\) 6.72836 6.72836i 0.393075 0.393075i −0.482707 0.875782i \(-0.660346\pi\)
0.875782 + 0.482707i \(0.160346\pi\)
\(294\) 2.68412 + 2.66491i 0.156541 + 0.155420i
\(295\) 2.60499 22.9215i 0.151668 1.33454i
\(296\) 12.5118i 0.727236i
\(297\) −17.5883 + 0.189570i −1.02058 + 0.0109999i
\(298\) 29.2383 + 29.2383i 1.69373 + 1.69373i
\(299\) −2.09844 −0.121356
\(300\) −23.3857 5.29665i −1.35018 0.305802i
\(301\) −5.32981 −0.307205
\(302\) 2.94201 + 2.94201i 0.169293 + 0.169293i
\(303\) −14.9584 + 0.0537396i −0.859339 + 0.00308726i
\(304\) 9.94571i 0.570426i
\(305\) −1.71860 + 15.1221i −0.0984068 + 0.865888i
\(306\) −0.0111442 1.55098i −0.000637072 0.0886634i
\(307\) 10.1105 10.1105i 0.577034 0.577034i −0.357051 0.934085i \(-0.616218\pi\)
0.934085 + 0.357051i \(0.116218\pi\)
\(308\) −6.62728 + 6.62728i −0.377624 + 0.377624i
\(309\) 1.66426 1.67626i 0.0946765 0.0953592i
\(310\) −34.8355 + 27.7255i −1.97852 + 1.57470i
\(311\) 0.394155i 0.0223505i −0.999938 0.0111752i \(-0.996443\pi\)
0.999938 0.0111752i \(-0.00355726\pi\)
\(312\) 0.00305256 + 0.849680i 0.000172817 + 0.0481036i
\(313\) −10.3810 10.3810i −0.586767 0.586767i 0.349987 0.936754i \(-0.386186\pi\)
−0.936754 + 0.349987i \(0.886186\pi\)
\(314\) 13.3330 0.752424
\(315\) 4.21505 + 5.21856i 0.237491 + 0.294033i
\(316\) −31.6881 −1.78260
\(317\) 19.8075 + 19.8075i 1.11250 + 1.11250i 0.992812 + 0.119688i \(0.0381896\pi\)
0.119688 + 0.992812i \(0.461810\pi\)
\(318\) −0.0682759 19.0046i −0.00382872 1.06573i
\(319\) 9.62264i 0.538764i
\(320\) 27.8026 + 3.15971i 1.55421 + 0.176633i
\(321\) 5.10579 5.14260i 0.284977 0.287032i
\(322\) −11.0885 + 11.0885i −0.617936 + 0.617936i
\(323\) −0.889642 + 0.889642i −0.0495010 + 0.0495010i
\(324\) 0.358078 + 24.9161i 0.0198932 + 1.38423i
\(325\) 0.774972 + 1.23865i 0.0429877 + 0.0687080i
\(326\) 11.0454i 0.611748i
\(327\) 4.88750 0.0175588i 0.270279 0.000971005i
\(328\) 0.0373884 + 0.0373884i 0.00206443 + 0.00206443i
\(329\) 5.04363 0.278065
\(330\) −22.3365 + 17.9090i −1.22958 + 0.985860i
\(331\) −24.7348 −1.35955 −0.679774 0.733422i \(-0.737922\pi\)
−0.679774 + 0.733422i \(0.737922\pi\)
\(332\) −10.7444 10.7444i −0.589674 0.589674i
\(333\) 15.6964 15.9236i 0.860157 0.872607i
\(334\) 19.7416i 1.08021i
\(335\) −12.5010 15.7068i −0.683004 0.858154i
\(336\) −2.30038 2.28391i −0.125496 0.124597i
\(337\) −3.40139 + 3.40139i −0.185286 + 0.185286i −0.793655 0.608369i \(-0.791824\pi\)
0.608369 + 0.793655i \(0.291824\pi\)
\(338\) −19.9420 + 19.9420i −1.08470 + 1.08470i
\(339\) 3.50777 + 3.48266i 0.190516 + 0.189152i
\(340\) −0.912779 1.14685i −0.0495024 0.0621968i
\(341\) 30.8642i 1.67139i
\(342\) 24.4401 24.7938i 1.32157 1.34070i
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) −8.94740 −0.482411
\(345\) −21.6985 + 17.3975i −1.16821 + 0.936651i
\(346\) 12.0070 0.645498
\(347\) −24.0324 24.0324i −1.29013 1.29013i −0.934706 0.355421i \(-0.884337\pi\)
−0.355421 0.934706i \(-0.615663\pi\)
\(348\) 13.6323 0.0489753i 0.730766 0.00262535i
\(349\) 9.37078i 0.501607i −0.968038 0.250803i \(-0.919305\pi\)
0.968038 0.250803i \(-0.0806947\pi\)
\(350\) 10.6403 + 2.45015i 0.568747 + 0.130966i
\(351\) 1.06206 1.08520i 0.0566884 0.0579237i
\(352\) 17.8191 17.8191i 0.949759 0.949759i
\(353\) −14.5888 + 14.5888i −0.776481 + 0.776481i −0.979231 0.202750i \(-0.935012\pi\)
0.202750 + 0.979231i \(0.435012\pi\)
\(354\) −27.4932 + 27.6915i −1.46125 + 1.47179i
\(355\) 8.78606 + 0.998522i 0.466316 + 0.0529960i
\(356\) 5.54275i 0.293765i
\(357\) 0.00147319 + 0.410063i 7.79696e−5 + 0.0217028i
\(358\) −22.5942 22.5942i −1.19414 1.19414i
\(359\) −27.2654 −1.43901 −0.719506 0.694486i \(-0.755632\pi\)
−0.719506 + 0.694486i \(0.755632\pi\)
\(360\) 7.07599 + 8.76064i 0.372938 + 0.461726i
\(361\) −9.24062 −0.486349
\(362\) 15.1900 + 15.1900i 0.798369 + 0.798369i
\(363\) 0.00285407 + 0.794430i 0.000149800 + 0.0416968i
\(364\) 0.809088i 0.0424077i
\(365\) 21.3059 16.9573i 1.11520 0.887587i
\(366\) 18.1382 18.2690i 0.948101 0.954938i
\(367\) 15.9239 15.9239i 0.831218 0.831218i −0.156465 0.987683i \(-0.550010\pi\)
0.987683 + 0.156465i \(0.0500099\pi\)
\(368\) 9.50315 9.50315i 0.495386 0.495386i
\(369\) −0.000678924 0.0944881i −3.53434e−5 0.00491885i
\(370\) 4.10960 36.1607i 0.213648 1.87990i
\(371\) 5.02457i 0.260863i
\(372\) 43.7249 0.157086i 2.26703 0.00814453i
\(373\) 23.3283 + 23.3283i 1.20790 + 1.20790i 0.971707 + 0.236189i \(0.0758984\pi\)
0.236189 + 0.971707i \(0.424102\pi\)
\(374\) −1.75010 −0.0904954
\(375\) 18.2827 + 6.38297i 0.944115 + 0.329615i
\(376\) 8.46698 0.436651
\(377\) −0.587387 0.587387i −0.0302520 0.0302520i
\(378\) −0.122294 11.3464i −0.00629010 0.583597i
\(379\) 37.4477i 1.92356i 0.273828 + 0.961779i \(0.411710\pi\)
−0.273828 + 0.961779i \(0.588290\pi\)
\(380\) 3.71520 32.6903i 0.190586 1.67698i
\(381\) 20.2109 + 20.0662i 1.03544 + 1.02802i
\(382\) −9.84986 + 9.84986i −0.503963 + 0.503963i
\(383\) 4.95443 4.95443i 0.253159 0.253159i −0.569105 0.822265i \(-0.692710\pi\)
0.822265 + 0.569105i \(0.192710\pi\)
\(384\) −15.2879 15.1784i −0.780155 0.774570i
\(385\) 5.92241 4.71364i 0.301834 0.240229i
\(386\) 23.3578i 1.18888i
\(387\) 11.3872 + 11.2247i 0.578843 + 0.570584i
\(388\) 6.27841 + 6.27841i 0.318738 + 0.318738i
\(389\) −9.20279 −0.466600 −0.233300 0.972405i \(-0.574952\pi\)
−0.233300 + 0.972405i \(0.574952\pi\)
\(390\) 0.270261 2.45668i 0.0136852 0.124399i
\(391\) −1.70011 −0.0859783
\(392\) −1.18705 1.18705i −0.0599552 0.0599552i
\(393\) −21.9992 + 0.0790344i −1.10971 + 0.00398676i
\(394\) 3.13431i 0.157904i
\(395\) 25.4280 + 2.88985i 1.27942 + 0.145404i
\(396\) 28.1164 0.202025i 1.41290 0.0101521i
\(397\) 21.9242 21.9242i 1.10034 1.10034i 0.105976 0.994369i \(-0.466203\pi\)
0.994369 0.105976i \(-0.0337966\pi\)
\(398\) −14.5156 + 14.5156i −0.727600 + 0.727600i
\(399\) −6.48510 + 6.53187i −0.324661 + 0.327002i
\(400\) −9.11904 2.09985i −0.455952 0.104993i
\(401\) 25.7514i 1.28596i 0.765882 + 0.642982i \(0.222303\pi\)
−0.765882 + 0.642982i \(0.777697\pi\)
\(402\) 0.121990 + 33.9560i 0.00608431 + 1.69357i
\(403\) −1.88402 1.88402i −0.0938497 0.0938497i
\(404\) 23.9117 1.18965
\(405\) 1.98493 20.0265i 0.0986319 0.995124i
\(406\) −6.20768 −0.308082
\(407\) −17.8397 17.8397i −0.884283 0.884283i
\(408\) 0.00247311 + 0.688392i 0.000122437 + 0.0340805i
\(409\) 10.9496i 0.541425i 0.962660 + 0.270712i \(0.0872592\pi\)
−0.962660 + 0.270712i \(0.912741\pi\)
\(410\) −0.0957764 0.120337i −0.00473006 0.00594304i
\(411\) 8.96477 9.02942i 0.442200 0.445388i
\(412\) −2.66999 + 2.66999i −0.131541 + 0.131541i
\(413\) 7.29506 7.29506i 0.358967 0.358967i
\(414\) 47.0431 0.338019i 2.31204 0.0166127i
\(415\) 7.64192 + 9.60162i 0.375127 + 0.471325i
\(416\) 2.17543i 0.106659i
\(417\) 21.3280 0.0766229i 1.04444 0.00375224i
\(418\) −27.7774 27.7774i −1.35864 1.35864i
\(419\) 5.86958 0.286748 0.143374 0.989669i \(-0.454205\pi\)
0.143374 + 0.989669i \(0.454205\pi\)
\(420\) −6.70789 8.36621i −0.327312 0.408229i
\(421\) 26.8842 1.31026 0.655129 0.755517i \(-0.272614\pi\)
0.655129 + 0.755517i \(0.272614\pi\)
\(422\) 12.8034 + 12.8034i 0.623257 + 0.623257i
\(423\) −10.7758 10.6220i −0.523936 0.516460i
\(424\) 8.43498i 0.409639i
\(425\) 0.627865 + 1.00353i 0.0304559 + 0.0486782i
\(426\) −10.6145 10.5385i −0.514273 0.510591i
\(427\) −4.81281 + 4.81281i −0.232908 + 0.232908i
\(428\) −8.19126 + 8.19126i −0.395940 + 0.395940i
\(429\) −1.21585 1.20714i −0.0587018 0.0582815i
\(430\) 25.8590 + 2.93884i 1.24703 + 0.141723i
\(431\) 4.18118i 0.201400i 0.994917 + 0.100700i \(0.0321083\pi\)
−0.994917 + 0.100700i \(0.967892\pi\)
\(432\) 0.104809 + 9.72423i 0.00504264 + 0.467857i
\(433\) −2.20877 2.20877i −0.106146 0.106146i 0.652039 0.758185i \(-0.273914\pi\)
−0.758185 + 0.652039i \(0.773914\pi\)
\(434\) −19.9109 −0.955752
\(435\) −10.9436 1.20392i −0.524706 0.0577233i
\(436\) −7.81290 −0.374170
\(437\) −26.9840 26.9840i −1.29082 1.29082i
\(438\) −46.0604 + 0.165477i −2.20085 + 0.00790678i
\(439\) 27.6028i 1.31741i 0.752401 + 0.658706i \(0.228896\pi\)
−0.752401 + 0.658706i \(0.771104\pi\)
\(440\) 9.94222 7.91300i 0.473977 0.377238i
\(441\) 0.0215553 + 2.99992i 0.00102644 + 0.142853i
\(442\) 0.106830 0.106830i 0.00508138 0.00508138i
\(443\) −12.3040 + 12.3040i −0.584582 + 0.584582i −0.936159 0.351577i \(-0.885646\pi\)
0.351577 + 0.936159i \(0.385646\pi\)
\(444\) −25.1825 + 25.3641i −1.19511 + 1.20373i
\(445\) −0.505479 + 4.44775i −0.0239620 + 0.210843i
\(446\) 11.9214i 0.564494i
\(447\) 0.117823 + 32.7961i 0.00557285 + 1.55120i
\(448\) 8.84854 + 8.84854i 0.418054 + 0.418054i
\(449\) 34.1859 1.61333 0.806666 0.591008i \(-0.201270\pi\)
0.806666 + 0.591008i \(0.201270\pi\)
\(450\) −17.5730 27.6434i −0.828397 1.30312i
\(451\) −0.106619 −0.00502049
\(452\) −5.58726 5.58726i −0.262803 0.262803i
\(453\) 0.0118556 + 3.30000i 0.000557024 + 0.155048i
\(454\) 4.65526i 0.218482i
\(455\) −0.0737860 + 0.649248i −0.00345914 + 0.0304372i
\(456\) −10.8868 + 10.9653i −0.509823 + 0.513499i
\(457\) −9.31021 + 9.31021i −0.435513 + 0.435513i −0.890499 0.454986i \(-0.849644\pi\)
0.454986 + 0.890499i \(0.349644\pi\)
\(458\) 9.66646 9.66646i 0.451684 0.451684i
\(459\) 0.860455 0.879206i 0.0401626 0.0410378i
\(460\) 34.7855 27.6858i 1.62188 1.29086i
\(461\) 25.6579i 1.19501i 0.801865 + 0.597505i \(0.203841\pi\)
−0.801865 + 0.597505i \(0.796159\pi\)
\(462\) −12.8034 + 0.0459976i −0.595670 + 0.00214000i
\(463\) 13.2170 + 13.2170i 0.614248 + 0.614248i 0.944050 0.329802i \(-0.106982\pi\)
−0.329802 + 0.944050i \(0.606982\pi\)
\(464\) 5.32017 0.246983
\(465\) −35.1012 3.86151i −1.62778 0.179073i
\(466\) −8.25874 −0.382579
\(467\) 19.6659 + 19.6659i 0.910031 + 0.910031i 0.996274 0.0862431i \(-0.0274862\pi\)
−0.0862431 + 0.996274i \(0.527486\pi\)
\(468\) −1.70396 + 1.72862i −0.0787655 + 0.0799056i
\(469\) 8.97752i 0.414543i
\(470\) −24.4706 2.78104i −1.12874 0.128280i
\(471\) 7.50457 + 7.45084i 0.345792 + 0.343317i
\(472\) 12.2466 12.2466i 0.563693 0.563693i
\(473\) 12.7575 12.7575i 0.586588 0.586588i
\(474\) −30.7196 30.4997i −1.41100 1.40090i
\(475\) −5.96248 + 25.8933i −0.273577 + 1.18807i
\(476\) 0.655505i 0.0300450i
\(477\) 10.5819 10.7350i 0.484510 0.491524i
\(478\) 3.21986 + 3.21986i 0.147273 + 0.147273i
\(479\) 26.9725 1.23240 0.616202 0.787588i \(-0.288670\pi\)
0.616202 + 0.787588i \(0.288670\pi\)
\(480\) 18.0358 + 22.4946i 0.823219 + 1.02673i
\(481\) 2.17795 0.0993062
\(482\) 8.39528 + 8.39528i 0.382395 + 0.382395i
\(483\) −12.4378 + 0.0446838i −0.565937 + 0.00203319i
\(484\) 1.26993i 0.0577242i
\(485\) −4.46551 5.61064i −0.202768 0.254766i
\(486\) −23.6345 + 24.4993i −1.07208 + 1.11131i
\(487\) −28.6505 + 28.6505i −1.29828 + 1.29828i −0.368749 + 0.929529i \(0.620214\pi\)
−0.929529 + 0.368749i \(0.879786\pi\)
\(488\) −8.07948 + 8.07948i −0.365741 + 0.365741i
\(489\) 6.17247 6.21698i 0.279129 0.281141i
\(490\) 3.04083 + 3.82062i 0.137370 + 0.172598i
\(491\) 2.74522i 0.123890i 0.998080 + 0.0619450i \(0.0197303\pi\)
−0.998080 + 0.0619450i \(0.980270\pi\)
\(492\) 0.000542646 0.151046i 2.44644e−5 0.00680966i
\(493\) −0.475888 0.475888i −0.0214329 0.0214329i
\(494\) 3.39119 0.152577
\(495\) −22.5803 2.40201i −1.01491 0.107962i
\(496\) 17.0642 0.766206
\(497\) 2.79628 + 2.79628i 0.125430 + 0.125430i
\(498\) −0.0745730 20.7574i −0.00334170 0.930162i
\(499\) 30.3151i 1.35709i −0.734558 0.678546i \(-0.762611\pi\)
0.734558 0.678546i \(-0.237389\pi\)
\(500\) −29.1887 10.3083i −1.30536 0.461003i
\(501\) 11.0321 11.1117i 0.492879 0.496433i
\(502\) −36.0446 + 36.0446i −1.60875 + 1.60875i
\(503\) 0.331820 0.331820i 0.0147951 0.0147951i −0.699671 0.714466i \(-0.746670\pi\)
0.714466 + 0.699671i \(0.246670\pi\)
\(504\) 0.0361859 + 5.03611i 0.00161185 + 0.224326i
\(505\) −19.1878 2.18067i −0.853848 0.0970384i
\(506\) 53.0827i 2.35982i
\(507\) −22.3686 + 0.0803614i −0.993425 + 0.00356898i
\(508\) −32.1925 32.1925i −1.42831 1.42831i
\(509\) −14.6491 −0.649311 −0.324656 0.945832i \(-0.605248\pi\)
−0.324656 + 0.945832i \(0.605248\pi\)
\(510\) 0.218960 1.99035i 0.00969569 0.0881340i
\(511\) 12.1778 0.538713
\(512\) −14.2950 14.2950i −0.631758 0.631758i
\(513\) 27.6117 0.297604i 1.21909 0.0131395i
\(514\) 33.7466i 1.48850i
\(515\) 2.38601 1.89903i 0.105140 0.0836811i
\(516\) −18.1382 18.0084i −0.798492 0.792775i
\(517\) −12.0725 + 12.0725i −0.530946 + 0.530946i
\(518\) 11.5086 11.5086i 0.505660 0.505660i
\(519\) 6.75820 + 6.70982i 0.296652 + 0.294528i
\(520\) −0.123868 + 1.08992i −0.00543197 + 0.0477963i
\(521\) 24.6501i 1.07994i −0.841683 0.539971i \(-0.818435\pi\)
0.841683 0.539971i \(-0.181565\pi\)
\(522\) 13.2628 + 13.0735i 0.580495 + 0.572212i
\(523\) −23.4069 23.4069i −1.02351 1.02351i −0.999717 0.0237950i \(-0.992425\pi\)
−0.0237950 0.999717i \(-0.507575\pi\)
\(524\) 35.1668 1.53627
\(525\) 4.61975 + 7.32516i 0.201622 + 0.319696i
\(526\) 56.1475 2.44815
\(527\) −1.52639 1.52639i −0.0664907 0.0664907i
\(528\) 10.9730 0.0394214i 0.477536 0.00171560i
\(529\) 28.5666i 1.24203i
\(530\) 2.77053 24.3781i 0.120344 1.05892i
\(531\) −30.9495 + 0.222381i −1.34310 + 0.00965053i
\(532\) 10.4041 10.4041i 0.451076 0.451076i
\(533\) 0.00650825 0.00650825i 0.000281904 0.000281904i
\(534\) 5.33487 5.37334i 0.230862 0.232527i
\(535\) 7.32005 5.82602i 0.316473 0.251881i
\(536\) 15.0710i 0.650967i
\(537\) −0.0910493 25.3436i −0.00392907 1.09366i
\(538\) 44.0273 + 44.0273i 1.89815 + 1.89815i
\(539\) 3.38507 0.145805
\(540\) −3.28797 + 32.0015i −0.141492 + 1.37712i
\(541\) −27.2143 −1.17003 −0.585017 0.811021i \(-0.698912\pi\)
−0.585017 + 0.811021i \(0.698912\pi\)
\(542\) −4.82102 4.82102i −0.207081 0.207081i
\(543\) 0.0612121 + 17.0384i 0.00262686 + 0.731187i
\(544\) 1.76249i 0.0755660i
\(545\) 6.26942 + 0.712509i 0.268552 + 0.0305205i
\(546\) 0.778743 0.784359i 0.0333271 0.0335675i
\(547\) −3.63475 + 3.63475i −0.155411 + 0.155411i −0.780530 0.625119i \(-0.785051\pi\)
0.625119 + 0.780530i \(0.285051\pi\)
\(548\) −14.3823 + 14.3823i −0.614380 + 0.614380i
\(549\) 20.4185 0.146713i 0.871440 0.00626154i
\(550\) −31.3333 + 19.6039i −1.33605 + 0.835914i
\(551\) 15.1065i 0.643559i
\(552\) −20.8798 + 0.0750128i −0.888705 + 0.00319276i
\(553\) 8.09279 + 8.09279i 0.344141 + 0.344141i
\(554\) −37.8227 −1.60693
\(555\) 22.5207 18.0567i 0.955951 0.766466i
\(556\) −34.0938 −1.44590
\(557\) −5.91751 5.91751i −0.250733 0.250733i 0.570538 0.821271i \(-0.306735\pi\)
−0.821271 + 0.570538i \(0.806735\pi\)
\(558\) 42.5397 + 41.9328i 1.80085 + 1.77516i
\(559\) 1.55749i 0.0658747i
\(560\) −2.60608 3.27439i −0.110127 0.138368i
\(561\) −0.985055 0.978002i −0.0415890 0.0412913i
\(562\) 19.6385 19.6385i 0.828402 0.828402i
\(563\) 13.8267 13.8267i 0.582728 0.582728i −0.352924 0.935652i \(-0.614813\pi\)
0.935652 + 0.352924i \(0.114813\pi\)
\(564\) 17.1643 + 17.0414i 0.722749 + 0.717574i
\(565\) 3.97393 + 4.99301i 0.167185 + 0.210058i
\(566\) 61.2316i 2.57376i
\(567\) 6.27185 6.45475i 0.263393 0.271074i
\(568\) 4.69425 + 4.69425i 0.196966 + 0.196966i
\(569\) 6.82232 0.286007 0.143003 0.989722i \(-0.454324\pi\)
0.143003 + 0.989722i \(0.454324\pi\)
\(570\) 35.0659 28.1153i 1.46875 1.17762i
\(571\) 19.7545 0.826701 0.413351 0.910572i \(-0.364358\pi\)
0.413351 + 0.910572i \(0.364358\pi\)
\(572\) 1.93663 + 1.93663i 0.0809747 + 0.0809747i
\(573\) −11.0484 + 0.0396926i −0.461555 + 0.00165818i
\(574\) 0.0687811i 0.00287087i
\(575\) −30.4383 + 19.0440i −1.26937 + 0.794189i
\(576\) −0.269737 37.5402i −0.0112390 1.56417i
\(577\) 1.10727 1.10727i 0.0460964 0.0460964i −0.683683 0.729779i \(-0.739623\pi\)
0.729779 + 0.683683i \(0.239623\pi\)
\(578\) −26.1639 + 26.1639i −1.08827 + 1.08827i
\(579\) 13.0530 13.1471i 0.542463 0.546375i
\(580\) 17.4867 + 1.98734i 0.726097 + 0.0825197i
\(581\) 5.48799i 0.227680i
\(582\) 0.0435762 + 12.1295i 0.00180629 + 0.502782i
\(583\) −12.0268 12.0268i −0.498100 0.498100i
\(584\) 20.4434 0.845953
\(585\) 1.52498 1.23173i 0.0630500 0.0509257i
\(586\) −20.7791 −0.858376
\(587\) −7.76708 7.76708i −0.320582 0.320582i 0.528408 0.848990i \(-0.322789\pi\)
−0.848990 + 0.528408i \(0.822789\pi\)
\(588\) −0.0172286 4.79558i −0.000710495 0.197766i
\(589\) 48.4535i 1.99649i
\(590\) −39.4165 + 31.3715i −1.62275 + 1.29154i
\(591\) 1.75154 1.76417i 0.0720487 0.0725683i
\(592\) −9.86325 + 9.86325i −0.405377 + 0.405377i
\(593\) 8.01301 8.01301i 0.329055 0.329055i −0.523172 0.852227i \(-0.675252\pi\)
0.852227 + 0.523172i \(0.175252\pi\)
\(594\) 27.4515 + 26.8661i 1.12635 + 1.10233i
\(595\) −0.0597798 + 0.526007i −0.00245073 + 0.0215642i
\(596\) 52.4261i 2.14746i
\(597\) −16.2819 + 0.0584943i −0.666373 + 0.00239401i
\(598\) 3.24029 + 3.24029i 0.132505 + 0.132505i
\(599\) 20.3742 0.832467 0.416233 0.909258i \(-0.363350\pi\)
0.416233 + 0.909258i \(0.363350\pi\)
\(600\) 7.75538 + 12.2971i 0.316612 + 0.502026i
\(601\) −32.4833 −1.32502 −0.662511 0.749052i \(-0.730509\pi\)
−0.662511 + 0.749052i \(0.730509\pi\)
\(602\) 8.22998 + 8.22998i 0.335429 + 0.335429i
\(603\) −18.9069 + 19.1805i −0.769947 + 0.781092i
\(604\) 5.27521i 0.214645i
\(605\) −0.115814 + 1.01905i −0.00470849 + 0.0414303i
\(606\) 23.1809 + 23.0149i 0.941660 + 0.934918i
\(607\) −0.0701607 + 0.0701607i −0.00284774 + 0.00284774i −0.708529 0.705681i \(-0.750641\pi\)
0.705681 + 0.708529i \(0.250641\pi\)
\(608\) −27.9740 + 27.9740i −1.13450 + 1.13450i
\(609\) −3.49404 3.46902i −0.141586 0.140572i
\(610\) 26.0044 20.6969i 1.05289 0.837992i
\(611\) 1.47386i 0.0596260i
\(612\) −1.38051 + 1.40049i −0.0558038 + 0.0566115i
\(613\) −26.6840 26.6840i −1.07776 1.07776i −0.996710 0.0810445i \(-0.974174\pi\)
−0.0810445 0.996710i \(-0.525826\pi\)
\(614\) −31.2239 −1.26010
\(615\) 0.0133394 0.121255i 0.000537896 0.00488948i
\(616\) 5.68266 0.228961
\(617\) −6.37294 6.37294i −0.256565 0.256565i 0.567090 0.823656i \(-0.308069\pi\)
−0.823656 + 0.567090i \(0.808069\pi\)
\(618\) −5.15824 + 0.0185315i −0.207495 + 0.000745446i
\(619\) 17.7676i 0.714139i 0.934078 + 0.357070i \(0.116224\pi\)
−0.934078 + 0.357070i \(0.883776\pi\)
\(620\) 56.0879 + 6.37430i 2.25255 + 0.255998i
\(621\) 26.6675 + 26.0987i 1.07013 + 1.04731i
\(622\) −0.608631 + 0.608631i −0.0244039 + 0.0244039i
\(623\) −1.41556 + 1.41556i −0.0567130 + 0.0567130i
\(624\) −0.667407 + 0.672220i −0.0267177 + 0.0269103i
\(625\) 22.4823 + 10.9338i 0.899291 + 0.437351i
\(626\) 32.0594i 1.28135i
\(627\) −0.111936 31.1575i −0.00447030 1.24431i
\(628\) −11.9535 11.9535i −0.476995 0.476995i
\(629\) 1.76453 0.0703565
\(630\) 1.54956 14.5668i 0.0617361 0.580356i
\(631\) 17.8248 0.709592 0.354796 0.934944i \(-0.384550\pi\)
0.354796 + 0.934944i \(0.384550\pi\)
\(632\) 13.5857 + 13.5857i 0.540412 + 0.540412i
\(633\) 0.0515944 + 14.3613i 0.00205070 + 0.570811i
\(634\) 61.1712i 2.42942i
\(635\) 22.8968 + 28.7685i 0.908633 + 1.14164i
\(636\) −16.9770 + 17.0995i −0.673183 + 0.678038i
\(637\) −0.206632 + 0.206632i −0.00818705 + 0.00818705i
\(638\) 14.8587 14.8587i 0.588262 0.588262i
\(639\) −0.0852413 11.8633i −0.00337210 0.469306i
\(640\) −17.3195 21.7609i −0.684614 0.860177i
\(641\) 14.8270i 0.585630i 0.956169 + 0.292815i \(0.0945920\pi\)
−0.956169 + 0.292815i \(0.905408\pi\)
\(642\) −15.8250 + 0.0568527i −0.624562 + 0.00224380i
\(643\) −32.7229 32.7229i −1.29047 1.29047i −0.934498 0.355968i \(-0.884151\pi\)
−0.355968 0.934498i \(-0.615849\pi\)
\(644\) 19.8823 0.783474
\(645\) 12.9126 + 16.1049i 0.508435 + 0.634129i
\(646\) 2.74747 0.108098
\(647\) 27.0564 + 27.0564i 1.06370 + 1.06370i 0.997828 + 0.0658674i \(0.0209814\pi\)
0.0658674 + 0.997828i \(0.479019\pi\)
\(648\) 10.5289 10.8359i 0.413612 0.425674i
\(649\) 34.9230i 1.37085i
\(650\) 0.715985 3.10932i 0.0280833 0.121958i
\(651\) −11.2070 11.1267i −0.439236 0.436091i
\(652\) −9.90255 + 9.90255i −0.387814 + 0.387814i
\(653\) 4.04918 4.04918i 0.158457 0.158457i −0.623426 0.781883i \(-0.714260\pi\)
0.781883 + 0.623426i \(0.214260\pi\)
\(654\) −7.57410 7.51988i −0.296171 0.294050i
\(655\) −28.2194 3.20709i −1.10262 0.125311i
\(656\) 0.0589475i 0.00230151i
\(657\) −26.0179 25.6467i −1.01506 1.00057i
\(658\) −7.78809 7.78809i −0.303611 0.303611i
\(659\) −11.5870 −0.451366 −0.225683 0.974201i \(-0.572461\pi\)
−0.225683 + 0.974201i \(0.572461\pi\)
\(660\) 36.0814 + 3.96935i 1.40447 + 0.154507i
\(661\) −15.1550 −0.589462 −0.294731 0.955580i \(-0.595230\pi\)
−0.294731 + 0.955580i \(0.595230\pi\)
\(662\) 38.1940 + 38.1940i 1.48445 + 1.48445i
\(663\) 0.119829 0.000430499i 0.00465379 1.67192e-5i
\(664\) 9.21294i 0.357531i
\(665\) −9.29755 + 7.39991i −0.360544 + 0.286956i
\(666\) −48.8257 + 0.350827i −1.89196 + 0.0135943i
\(667\) 14.4343 14.4343i 0.558899 0.558899i
\(668\) −17.6990 + 17.6990i −0.684793 + 0.684793i
\(669\) 6.66199 6.71003i 0.257568 0.259425i
\(670\) −4.95017 + 43.5569i −0.191242 + 1.68275i
\(671\) 23.0399i 0.889445i
\(672\) 0.0463233 + 12.8941i 0.00178696 + 0.497400i
\(673\) −13.7667 13.7667i −0.530666 0.530666i 0.390105 0.920770i \(-0.372439\pi\)
−0.920770 + 0.390105i \(0.872439\pi\)
\(674\) 10.5045 0.404617
\(675\) 5.55683 25.3796i 0.213883 0.976859i
\(676\) 35.7573 1.37528
\(677\) −16.3594 16.3594i −0.628742 0.628742i 0.319009 0.947752i \(-0.396650\pi\)
−0.947752 + 0.319009i \(0.896650\pi\)
\(678\) −0.0387793 10.7942i −0.00148931 0.414549i
\(679\) 3.20687i 0.123068i
\(680\) −0.100355 + 0.883031i −0.00384844 + 0.0338627i
\(681\) −2.60148 + 2.62024i −0.0996891 + 0.100408i
\(682\) 47.6587 47.6587i 1.82495 1.82495i
\(683\) −5.85622 + 5.85622i −0.224082 + 0.224082i −0.810215 0.586133i \(-0.800650\pi\)
0.586133 + 0.810215i \(0.300650\pi\)
\(684\) −44.1398 + 0.317157i −1.68773 + 0.0121268i
\(685\) 12.8526 10.2294i 0.491072 0.390844i
\(686\) 2.18375i 0.0833758i
\(687\) 10.8427 0.0389535i 0.413676 0.00148617i
\(688\) −7.05335 7.05335i −0.268906 0.268906i
\(689\) 1.46829 0.0559373
\(690\) 60.3698 + 6.64133i 2.29824 + 0.252831i
\(691\) 25.9095 0.985642 0.492821 0.870131i \(-0.335966\pi\)
0.492821 + 0.870131i \(0.335966\pi\)
\(692\) −10.7646 10.7646i −0.409210 0.409210i
\(693\) −7.23222 7.12903i −0.274729 0.270809i
\(694\) 74.2189i 2.81731i
\(695\) 27.3584 + 3.10923i 1.03776 + 0.117940i
\(696\) −5.86560 5.82361i −0.222335 0.220743i
\(697\) 0.00527284 0.00527284i 0.000199723 0.000199723i
\(698\) −14.4698 + 14.4698i −0.547691 + 0.547691i
\(699\) −4.64849 4.61521i −0.175822 0.174563i
\(700\) −7.34272 11.7360i −0.277529 0.443579i
\(701\) 37.9089i 1.43180i 0.698204 + 0.715899i \(0.253983\pi\)
−0.698204 + 0.715899i \(0.746017\pi\)
\(702\) −3.31567 + 0.0357368i −0.125142 + 0.00134880i
\(703\) 28.0065 + 28.0065i 1.05628 + 1.05628i
\(704\) −42.3598 −1.59649
\(705\) −12.2193 15.2402i −0.460206 0.573977i
\(706\) 45.0542 1.69564
\(707\) −6.10679 6.10679i −0.229669 0.229669i
\(708\) 49.4749 0.177743i 1.85938 0.00668001i
\(709\) 16.6841i 0.626586i 0.949656 + 0.313293i \(0.101432\pi\)
−0.949656 + 0.313293i \(0.898568\pi\)
\(710\) −12.0251 15.1088i −0.451293 0.567023i
\(711\) −0.246699 34.3339i −0.00925194 1.28762i
\(712\) −2.37636 + 2.37636i −0.0890578 + 0.0890578i
\(713\) 46.2975 46.2975i 1.73385 1.73385i
\(714\) 0.630921 0.635470i 0.0236116 0.0237819i
\(715\) −1.37743 1.73066i −0.0515129 0.0647229i
\(716\) 40.5129i 1.51404i
\(717\) 0.0129753 + 3.61167i 0.000484570 + 0.134880i
\(718\) 42.1016 + 42.1016i 1.57122 + 1.57122i
\(719\) −13.0709 −0.487464 −0.243732 0.969843i \(-0.578372\pi\)
−0.243732 + 0.969843i \(0.578372\pi\)
\(720\) −1.32802 + 12.4842i −0.0494925 + 0.465259i
\(721\) 1.36377 0.0507895
\(722\) 14.2688 + 14.2688i 0.531031 + 0.531031i
\(723\) 0.0338310 + 9.41686i 0.00125819 + 0.350217i
\(724\) 27.2367i 1.01224i
\(725\) −13.8509 3.18946i −0.514409 0.118454i
\(726\) 1.22231 1.23112i 0.0453640 0.0456911i
\(727\) 19.4878 19.4878i 0.722761 0.722761i −0.246406 0.969167i \(-0.579250\pi\)
0.969167 + 0.246406i \(0.0792495\pi\)
\(728\) −0.346882 + 0.346882i −0.0128563 + 0.0128563i
\(729\) −26.9937 + 0.581953i −0.999768 + 0.0215538i
\(730\) −59.0838 6.71478i −2.18679 0.248525i
\(731\) 1.26184i 0.0466709i
\(732\) −32.6403 + 0.117264i −1.20642 + 0.00433418i
\(733\) 24.5624 + 24.5624i 0.907232 + 0.907232i 0.996048 0.0888162i \(-0.0283084\pi\)
−0.0888162 + 0.996048i \(0.528308\pi\)
\(734\) −49.1774 −1.81517
\(735\) −0.423515 + 3.84976i −0.0156216 + 0.142000i
\(736\) −53.4585 −1.97051
\(737\) 21.4886 + 21.4886i 0.791543 + 0.791543i
\(738\) −0.144855 + 0.146951i −0.00533217 + 0.00540935i
\(739\) 25.3925i 0.934079i 0.884236 + 0.467040i \(0.154679\pi\)
−0.884236 + 0.467040i \(0.845321\pi\)
\(740\) −36.1036 + 28.7348i −1.32720 + 1.05631i
\(741\) 1.90875 + 1.89509i 0.0701198 + 0.0696178i
\(742\) 7.75865 7.75865i 0.284829 0.284829i
\(743\) 14.4447 14.4447i 0.529923 0.529923i −0.390626 0.920549i \(-0.627742\pi\)
0.920549 + 0.390626i \(0.127742\pi\)
\(744\) −18.8137 18.6790i −0.689742 0.684804i
\(745\) −4.78108 + 42.0691i −0.175165 + 1.54129i
\(746\) 72.0445i 2.63774i
\(747\) 11.5578 11.7251i 0.422879 0.429000i
\(748\) 1.56902 + 1.56902i 0.0573690 + 0.0573690i
\(749\) 4.18391 0.152877
\(750\) −18.3749 38.0873i −0.670956 1.39075i
\(751\) 27.4358 1.00115 0.500573 0.865694i \(-0.333123\pi\)
0.500573 + 0.865694i \(0.333123\pi\)
\(752\) 6.67463 + 6.67463i 0.243399 + 0.243399i
\(753\) −40.4307 + 0.145251i −1.47338 + 0.00529325i
\(754\) 1.81402i 0.0660627i
\(755\) −0.481081 + 4.23306i −0.0175083 + 0.154057i
\(756\) −10.0628 + 10.2821i −0.365980 + 0.373955i
\(757\) −11.9760 + 11.9760i −0.435274 + 0.435274i −0.890418 0.455144i \(-0.849588\pi\)
0.455144 + 0.890418i \(0.349588\pi\)
\(758\) 57.8245 57.8245i 2.10028 2.10028i
\(759\) 29.6641 29.8780i 1.07674 1.08450i
\(760\) −15.6082 + 12.4226i −0.566170 + 0.450614i
\(761\) 41.1635i 1.49217i −0.665848 0.746087i \(-0.731930\pi\)
0.665848 0.746087i \(-0.268070\pi\)
\(762\) −0.223437 62.1937i −0.00809426 2.25304i
\(763\) 1.99533 + 1.99533i 0.0722357 + 0.0722357i
\(764\) 17.6614 0.638969
\(765\) 1.23550 0.997919i 0.0446697 0.0360799i
\(766\) −15.3007 −0.552836
\(767\) −2.13178 2.13178i −0.0769740 0.0769740i
\(768\) 0.0132771 + 3.69569i 0.000479097 + 0.133357i
\(769\) 3.96520i