Properties

Label 349.2.e.a.123.2
Level 349
Weight 2
Character 349.123
Analytic conductor 2.787
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 349.e (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.78677903054\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 123.2
Character \(\chi\) = 349.123
Dual form 349.2.e.a.227.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.28298 + 1.31808i) q^{2} +(-1.40419 + 2.43213i) q^{3} +(2.47467 - 4.28626i) q^{4} +(0.108819 - 0.188480i) q^{5} -7.40335i q^{6} +(3.00446 - 1.73462i) q^{7} +7.77496i q^{8} +(-2.44351 - 4.23228i) q^{9} +O(q^{10})\) \(q+(-2.28298 + 1.31808i) q^{2} +(-1.40419 + 2.43213i) q^{3} +(2.47467 - 4.28626i) q^{4} +(0.108819 - 0.188480i) q^{5} -7.40335i q^{6} +(3.00446 - 1.73462i) q^{7} +7.77496i q^{8} +(-2.44351 - 4.23228i) q^{9} +0.573727i q^{10} +6.40695i q^{11} +(6.94983 + 12.0375i) q^{12} +(3.09197 - 1.78515i) q^{13} +(-4.57275 + 7.92024i) q^{14} +(0.305605 + 0.529323i) q^{15} +(-5.29867 - 9.17757i) q^{16} +6.82681 q^{17} +(11.1570 + 6.44148i) q^{18} +(-2.30633 + 3.99469i) q^{19} +(-0.538582 - 0.932851i) q^{20} +9.74298i q^{21} +(-8.44488 - 14.6270i) q^{22} +(-1.65886 - 2.87323i) q^{23} +(-18.9097 - 10.9175i) q^{24} +(2.47632 + 4.28911i) q^{25} +(-4.70594 + 8.15093i) q^{26} +5.29945 q^{27} -17.1705i q^{28} +(3.25863 - 5.64412i) q^{29} +(-1.39538 - 0.805623i) q^{30} -2.85706 q^{31} +(10.7269 + 6.19321i) q^{32} +(-15.5825 - 8.99658i) q^{33} +(-15.5855 + 8.99829i) q^{34} -0.755039i q^{35} -24.1875 q^{36} +0.771177 q^{37} -12.1597i q^{38} +10.0268i q^{39} +(1.46542 + 0.846061i) q^{40} -4.60340 q^{41} +(-12.8420 - 22.2431i) q^{42} +(5.76174 + 3.32654i) q^{43} +(27.4619 + 15.8551i) q^{44} -1.06360 q^{45} +(7.57431 + 4.37303i) q^{46} +2.55802i q^{47} +29.7614 q^{48} +(2.51785 - 4.36104i) q^{49} +(-11.3068 - 6.52797i) q^{50} +(-9.58615 + 16.6037i) q^{51} -17.6706i q^{52} +3.79762i q^{53} +(-12.0986 + 6.98510i) q^{54} +(1.20758 + 0.697196i) q^{55} +(13.4866 + 23.3595i) q^{56} +(-6.47707 - 11.2186i) q^{57} +17.1806i q^{58} +(-7.78985 - 4.49747i) q^{59} +3.02509 q^{60} +7.60401i q^{61} +(6.52261 - 3.76583i) q^{62} +(-14.6828 - 8.47713i) q^{63} -11.4579 q^{64} -0.777030i q^{65} +47.4329 q^{66} -2.56887 q^{67} +(16.8941 - 29.2615i) q^{68} +9.31744 q^{69} +(0.995202 + 1.72374i) q^{70} +(-6.09051 + 3.51636i) q^{71} +(32.9058 - 18.9982i) q^{72} +(-0.243212 + 0.421256i) q^{73} +(-1.76058 + 1.01647i) q^{74} -13.9089 q^{75} +(11.4149 + 19.7711i) q^{76} +(11.1137 + 19.2494i) q^{77} +(-13.2161 - 22.8909i) q^{78} -3.36812i q^{79} -2.30638 q^{80} +(-0.110925 + 0.192127i) q^{81} +(10.5095 - 6.06766i) q^{82} +(6.90550 + 11.9607i) q^{83} +(41.7610 + 24.1107i) q^{84} +(0.742885 - 1.28671i) q^{85} -17.5386 q^{86} +(9.15149 + 15.8508i) q^{87} -49.8138 q^{88} +(-2.16506 - 1.25000i) q^{89} +(2.42817 - 1.40191i) q^{90} +(6.19313 - 10.7268i) q^{91} -16.4206 q^{92} +(4.01185 - 6.94874i) q^{93} +(-3.37167 - 5.83991i) q^{94} +(0.501945 + 0.869394i) q^{95} +(-30.1254 + 17.3929i) q^{96} +(-0.717554 + 0.414280i) q^{97} +13.2749i q^{98} +(27.1160 - 15.6554i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} + O(q^{10}) \) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} - q^{12} - 3q^{13} - 10q^{14} + q^{15} - 29q^{16} - 10q^{17} + 15q^{18} - 9q^{19} - 3q^{22} - 17q^{23} - 48q^{24} - 29q^{25} - 4q^{26} + 18q^{27} - 2q^{29} + 9q^{30} + 32q^{31} + 9q^{32} - 12q^{33} - 63q^{34} + 24q^{36} - 16q^{37} + 54q^{40} - 10q^{41} - 15q^{42} - 45q^{43} + 18q^{44} - 2q^{45} + 27q^{46} + 6q^{48} + 35q^{49} + 6q^{50} - 14q^{51} + 27q^{54} + 24q^{55} + 11q^{56} - 29q^{57} - 18q^{59} + 116q^{60} - 9q^{62} - 21q^{63} - 132q^{64} + 130q^{66} + 58q^{67} + 42q^{69} + 40q^{70} - 24q^{71} + 72q^{72} - 6q^{73} + 30q^{74} - 58q^{75} + 37q^{76} - 4q^{77} - 33q^{78} - 40q^{80} - 81q^{81} + 21q^{82} + 12q^{83} + 18q^{84} - 11q^{85} - 126q^{86} - 42q^{87} - 50q^{88} + 3q^{89} - 12q^{90} - 28q^{91} - 120q^{92} + 31q^{93} + 29q^{94} + 60q^{95} - 120q^{96} - 15q^{97} + 39q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.28298 + 1.31808i −1.61431 + 0.932024i −0.625958 + 0.779857i \(0.715292\pi\)
−0.988355 + 0.152167i \(0.951375\pi\)
\(3\) −1.40419 + 2.43213i −0.810710 + 1.40419i 0.101657 + 0.994819i \(0.467585\pi\)
−0.912368 + 0.409372i \(0.865748\pi\)
\(4\) 2.47467 4.28626i 1.23734 2.14313i
\(5\) 0.108819 0.188480i 0.0486652 0.0842906i −0.840667 0.541553i \(-0.817837\pi\)
0.889332 + 0.457262i \(0.151170\pi\)
\(6\) 7.40335i 3.02240i
\(7\) 3.00446 1.73462i 1.13558 0.655627i 0.190247 0.981736i \(-0.439071\pi\)
0.945332 + 0.326110i \(0.105738\pi\)
\(8\) 7.77496i 2.74886i
\(9\) −2.44351 4.23228i −0.814502 1.41076i
\(10\) 0.573727i 0.181429i
\(11\) 6.40695i 1.93177i 0.258975 + 0.965884i \(0.416615\pi\)
−0.258975 + 0.965884i \(0.583385\pi\)
\(12\) 6.94983 + 12.0375i 2.00624 + 3.47492i
\(13\) 3.09197 1.78515i 0.857558 0.495111i −0.00563602 0.999984i \(-0.501794\pi\)
0.863194 + 0.504873i \(0.168461\pi\)
\(14\) −4.57275 + 7.92024i −1.22212 + 2.11677i
\(15\) 0.305605 + 0.529323i 0.0789068 + 0.136671i
\(16\) −5.29867 9.17757i −1.32467 2.29439i
\(17\) 6.82681 1.65574 0.827872 0.560916i \(-0.189551\pi\)
0.827872 + 0.560916i \(0.189551\pi\)
\(18\) 11.1570 + 6.44148i 2.62972 + 1.51827i
\(19\) −2.30633 + 3.99469i −0.529109 + 0.916444i 0.470314 + 0.882499i \(0.344141\pi\)
−0.999424 + 0.0339454i \(0.989193\pi\)
\(20\) −0.538582 0.932851i −0.120431 0.208592i
\(21\) 9.74298i 2.12609i
\(22\) −8.44488 14.6270i −1.80045 3.11848i
\(23\) −1.65886 2.87323i −0.345897 0.599111i 0.639620 0.768692i \(-0.279092\pi\)
−0.985516 + 0.169581i \(0.945759\pi\)
\(24\) −18.9097 10.9175i −3.85993 2.22853i
\(25\) 2.47632 + 4.28911i 0.495263 + 0.857821i
\(26\) −4.70594 + 8.15093i −0.922911 + 1.59853i
\(27\) 5.29945 1.01988
\(28\) 17.1705i 3.24492i
\(29\) 3.25863 5.64412i 0.605113 1.04809i −0.386920 0.922113i \(-0.626461\pi\)
0.992034 0.125974i \(-0.0402055\pi\)
\(30\) −1.39538 0.805623i −0.254760 0.147086i
\(31\) −2.85706 −0.513143 −0.256571 0.966525i \(-0.582593\pi\)
−0.256571 + 0.966525i \(0.582593\pi\)
\(32\) 10.7269 + 6.19321i 1.89627 + 1.09481i
\(33\) −15.5825 8.99658i −2.71257 1.56610i
\(34\) −15.5855 + 8.99829i −2.67289 + 1.54319i
\(35\) 0.755039i 0.127625i
\(36\) −24.1875 −4.03125
\(37\) 0.771177 0.126781 0.0633904 0.997989i \(-0.479809\pi\)
0.0633904 + 0.997989i \(0.479809\pi\)
\(38\) 12.1597i 1.97257i
\(39\) 10.0268i 1.60557i
\(40\) 1.46542 + 0.846061i 0.231703 + 0.133774i
\(41\) −4.60340 −0.718931 −0.359465 0.933158i \(-0.617041\pi\)
−0.359465 + 0.933158i \(0.617041\pi\)
\(42\) −12.8420 22.2431i −1.98157 3.43218i
\(43\) 5.76174 + 3.32654i 0.878657 + 0.507293i 0.870215 0.492671i \(-0.163980\pi\)
0.00844180 + 0.999964i \(0.497313\pi\)
\(44\) 27.4619 + 15.8551i 4.14003 + 2.39025i
\(45\) −1.06360 −0.158552
\(46\) 7.57431 + 4.37303i 1.11677 + 0.644768i
\(47\) 2.55802i 0.373125i 0.982443 + 0.186563i \(0.0597347\pi\)
−0.982443 + 0.186563i \(0.940265\pi\)
\(48\) 29.7614 4.29569
\(49\) 2.51785 4.36104i 0.359693 0.623006i
\(50\) −11.3068 6.52797i −1.59902 0.923195i
\(51\) −9.58615 + 16.6037i −1.34233 + 2.32498i
\(52\) 17.6706i 2.45048i
\(53\) 3.79762i 0.521643i 0.965387 + 0.260822i \(0.0839934\pi\)
−0.965387 + 0.260822i \(0.916007\pi\)
\(54\) −12.0986 + 6.98510i −1.64640 + 0.950552i
\(55\) 1.20758 + 0.697196i 0.162830 + 0.0940099i
\(56\) 13.4866 + 23.3595i 1.80223 + 3.12155i
\(57\) −6.47707 11.2186i −0.857909 1.48594i
\(58\) 17.1806i 2.25592i
\(59\) −7.78985 4.49747i −1.01415 0.585521i −0.101747 0.994810i \(-0.532443\pi\)
−0.912405 + 0.409289i \(0.865777\pi\)
\(60\) 3.02509 0.390537
\(61\) 7.60401i 0.973594i 0.873515 + 0.486797i \(0.161835\pi\)
−0.873515 + 0.486797i \(0.838165\pi\)
\(62\) 6.52261 3.76583i 0.828373 0.478261i
\(63\) −14.6828 8.47713i −1.84986 1.06802i
\(64\) −11.4579 −1.43224
\(65\) 0.777030i 0.0963787i
\(66\) 47.4329 5.83859
\(67\) −2.56887 −0.313837 −0.156919 0.987612i \(-0.550156\pi\)
−0.156919 + 0.987612i \(0.550156\pi\)
\(68\) 16.8941 29.2615i 2.04871 3.54848i
\(69\) 9.31744 1.12169
\(70\) 0.995202 + 1.72374i 0.118949 + 0.206026i
\(71\) −6.09051 + 3.51636i −0.722810 + 0.417315i −0.815786 0.578354i \(-0.803695\pi\)
0.0929760 + 0.995668i \(0.470362\pi\)
\(72\) 32.9058 18.9982i 3.87798 2.23895i
\(73\) −0.243212 + 0.421256i −0.0284659 + 0.0493043i −0.879907 0.475145i \(-0.842396\pi\)
0.851442 + 0.524450i \(0.175729\pi\)
\(74\) −1.76058 + 1.01647i −0.204664 + 0.118163i
\(75\) −13.9089 −1.60606
\(76\) 11.4149 + 19.7711i 1.30937 + 2.26790i
\(77\) 11.1137 + 19.2494i 1.26652 + 2.19367i
\(78\) −13.2161 22.8909i −1.49643 2.59189i
\(79\) 3.36812i 0.378944i −0.981886 0.189472i \(-0.939322\pi\)
0.981886 0.189472i \(-0.0606776\pi\)
\(80\) −2.30638 −0.257861
\(81\) −0.110925 + 0.192127i −0.0123250 + 0.0213475i
\(82\) 10.5095 6.06766i 1.16058 0.670061i
\(83\) 6.90550 + 11.9607i 0.757977 + 1.31286i 0.943881 + 0.330287i \(0.107146\pi\)
−0.185903 + 0.982568i \(0.559521\pi\)
\(84\) 41.7610 + 24.1107i 4.55649 + 2.63069i
\(85\) 0.742885 1.28671i 0.0805772 0.139564i
\(86\) −17.5386 −1.89124
\(87\) 9.15149 + 15.8508i 0.981143 + 1.69939i
\(88\) −49.8138 −5.31017
\(89\) −2.16506 1.25000i −0.229496 0.132500i 0.380844 0.924639i \(-0.375634\pi\)
−0.610339 + 0.792140i \(0.708967\pi\)
\(90\) 2.42817 1.40191i 0.255952 0.147774i
\(91\) 6.19313 10.7268i 0.649216 1.12448i
\(92\) −16.4206 −1.71196
\(93\) 4.01185 6.94874i 0.416010 0.720550i
\(94\) −3.37167 5.83991i −0.347762 0.602341i
\(95\) 0.501945 + 0.869394i 0.0514984 + 0.0891979i
\(96\) −30.1254 + 17.3929i −3.07466 + 1.77515i
\(97\) −0.717554 + 0.414280i −0.0728566 + 0.0420638i −0.535986 0.844227i \(-0.680060\pi\)
0.463129 + 0.886291i \(0.346727\pi\)
\(98\) 13.2749i 1.34097i
\(99\) 27.1160 15.6554i 2.72526 1.57343i
\(100\) 24.5123 2.45123
\(101\) 5.46694i 0.543981i −0.962300 0.271990i \(-0.912318\pi\)
0.962300 0.271990i \(-0.0876819\pi\)
\(102\) 50.5413i 5.00433i
\(103\) 3.23464i 0.318719i 0.987221 + 0.159359i \(0.0509428\pi\)
−0.987221 + 0.159359i \(0.949057\pi\)
\(104\) 13.8795 + 24.0399i 1.36099 + 2.35731i
\(105\) 1.83635 + 1.06022i 0.179210 + 0.103467i
\(106\) −5.00557 8.66990i −0.486184 0.842095i
\(107\) 3.58817 2.07163i 0.346881 0.200272i −0.316430 0.948616i \(-0.602484\pi\)
0.663311 + 0.748344i \(0.269151\pi\)
\(108\) 13.1144 22.7148i 1.26194 2.18574i
\(109\) 0.302219 0.523458i 0.0289473 0.0501382i −0.851189 0.524860i \(-0.824118\pi\)
0.880136 + 0.474721i \(0.157451\pi\)
\(110\) −3.67584 −0.350478
\(111\) −1.08288 + 1.87560i −0.102782 + 0.178024i
\(112\) −31.8393 18.3824i −3.00853 1.73698i
\(113\) −4.74156 + 2.73754i −0.446049 + 0.257526i −0.706160 0.708052i \(-0.749574\pi\)
0.260111 + 0.965579i \(0.416241\pi\)
\(114\) 29.5741 + 17.0746i 2.76987 + 1.59918i
\(115\) −0.722061 −0.0673325
\(116\) −16.1281 27.9347i −1.49746 2.59367i
\(117\) −15.1105 8.72404i −1.39696 0.806538i
\(118\) 23.7121 2.18288
\(119\) 20.5109 11.8420i 1.88023 1.08555i
\(120\) −4.11546 + 2.37606i −0.375688 + 0.216904i
\(121\) −30.0490 −2.73173
\(122\) −10.0227 17.3598i −0.907413 1.57169i
\(123\) 6.46406 11.1961i 0.582845 1.00952i
\(124\) −7.07028 + 12.2461i −0.634930 + 1.09973i
\(125\) 2.16607 0.193739
\(126\) 44.6942 3.98167
\(127\) 7.90370i 0.701340i 0.936499 + 0.350670i \(0.114046\pi\)
−0.936499 + 0.350670i \(0.885954\pi\)
\(128\) 4.70425 2.71600i 0.415801 0.240063i
\(129\) −16.1812 + 9.34220i −1.42467 + 0.822535i
\(130\) 1.02419 + 1.77395i 0.0898273 + 0.155585i
\(131\) 9.21456i 0.805080i 0.915402 + 0.402540i \(0.131873\pi\)
−0.915402 + 0.402540i \(0.868127\pi\)
\(132\) −77.1234 + 44.5272i −6.71273 + 3.87560i
\(133\) 16.0025i 1.38759i
\(134\) 5.86469 3.38598i 0.506632 0.292504i
\(135\) 0.576679 0.998838i 0.0496327 0.0859663i
\(136\) 53.0782i 4.55142i
\(137\) 0.392816 + 0.226792i 0.0335605 + 0.0193762i 0.516686 0.856175i \(-0.327165\pi\)
−0.483126 + 0.875551i \(0.660499\pi\)
\(138\) −21.2716 + 12.2811i −1.81076 + 1.04544i
\(139\) 8.74910 0.742089 0.371044 0.928615i \(-0.379000\pi\)
0.371044 + 0.928615i \(0.379000\pi\)
\(140\) −3.23629 1.86847i −0.273517 0.157915i
\(141\) −6.22143 3.59195i −0.523939 0.302496i
\(142\) 9.26968 16.0556i 0.777894 1.34735i
\(143\) 11.4374 + 19.8101i 0.956440 + 1.65660i
\(144\) −25.8947 + 44.8509i −2.15789 + 3.73758i
\(145\) −0.709201 1.22837i −0.0588959 0.102011i
\(146\) 1.28229i 0.106123i
\(147\) 7.07108 + 12.2475i 0.583213 + 1.01015i
\(148\) 1.90841 3.30547i 0.156871 0.271708i
\(149\) −11.5649 + 6.67701i −0.947435 + 0.547002i −0.892283 0.451476i \(-0.850898\pi\)
−0.0551516 + 0.998478i \(0.517564\pi\)
\(150\) 31.7538 18.3330i 2.59268 1.49689i
\(151\) 7.74324 13.4117i 0.630136 1.09143i −0.357387 0.933956i \(-0.616332\pi\)
0.987523 0.157472i \(-0.0503343\pi\)
\(152\) −31.0585 17.9317i −2.51918 1.45445i
\(153\) −16.6814 28.8930i −1.34861 2.33586i
\(154\) −50.7446 29.2974i −4.08911 2.36085i
\(155\) −0.310901 + 0.538497i −0.0249722 + 0.0432531i
\(156\) 42.9773 + 24.8130i 3.44094 + 1.98663i
\(157\) 6.28571 10.8872i 0.501654 0.868890i −0.498344 0.866979i \(-0.666058\pi\)
0.999998 0.00191105i \(-0.000608306\pi\)
\(158\) 4.43946 + 7.68937i 0.353185 + 0.611734i
\(159\) −9.23631 5.33258i −0.732487 0.422901i
\(160\) 2.33459 1.34787i 0.184565 0.106559i
\(161\) −9.96797 5.75501i −0.785586 0.453558i
\(162\) 0.584831i 0.0459487i
\(163\) 7.85479i 0.615234i −0.951510 0.307617i \(-0.900468\pi\)
0.951510 0.307617i \(-0.0995316\pi\)
\(164\) −11.3919 + 19.7314i −0.889560 + 1.54076i
\(165\) −3.39134 + 1.95799i −0.264016 + 0.152430i
\(166\) −31.5303 18.2040i −2.44722 1.41291i
\(167\) 14.9620i 1.15780i −0.815399 0.578899i \(-0.803483\pi\)
0.815399 0.578899i \(-0.196517\pi\)
\(168\) −75.7513 −5.84434
\(169\) −0.126489 + 0.219086i −0.00972995 + 0.0168528i
\(170\) 3.91673i 0.300399i
\(171\) 22.5422 1.72384
\(172\) 28.5169 16.4642i 2.17439 1.25538i
\(173\) 13.9566 8.05787i 1.06110 0.612628i 0.135366 0.990796i \(-0.456779\pi\)
0.925737 + 0.378167i \(0.123446\pi\)
\(174\) −41.7854 24.1248i −3.16774 1.82890i
\(175\) 14.8800 + 8.59096i 1.12482 + 0.649416i
\(176\) 58.8003 33.9483i 4.43224 2.55895i
\(177\) 21.8769 12.6306i 1.64437 0.949376i
\(178\) 6.59039 0.493971
\(179\) 19.9344i 1.48996i 0.667084 + 0.744982i \(0.267542\pi\)
−0.667084 + 0.744982i \(0.732458\pi\)
\(180\) −2.63206 + 4.55885i −0.196182 + 0.339797i
\(181\) 13.8630 1.03043 0.515215 0.857061i \(-0.327712\pi\)
0.515215 + 0.857061i \(0.327712\pi\)
\(182\) 32.6522i 2.42034i
\(183\) −18.4940 10.6775i −1.36711 0.789303i
\(184\) 22.3393 12.8976i 1.64687 0.950823i
\(185\) 0.0839185 0.145351i 0.00616981 0.0106864i
\(186\) 21.1518i 1.55092i
\(187\) 43.7390i 3.19852i
\(188\) 10.9643 + 6.33026i 0.799656 + 0.461682i
\(189\) 15.9220 9.19256i 1.15815 0.668660i
\(190\) −2.29186 1.32321i −0.166269 0.0959955i
\(191\) −1.36496 2.36418i −0.0987649 0.171066i 0.812409 0.583088i \(-0.198156\pi\)
−0.911174 + 0.412022i \(0.864823\pi\)
\(192\) 16.0891 27.8671i 1.16113 2.01113i
\(193\) −20.7639 11.9880i −1.49462 0.862918i −0.494636 0.869100i \(-0.664699\pi\)
−0.999981 + 0.00618253i \(0.998032\pi\)
\(194\) 1.09211 1.89159i 0.0784089 0.135808i
\(195\) 1.88984 + 1.09110i 0.135334 + 0.0781352i
\(196\) −12.4617 21.5843i −0.890122 1.54174i
\(197\) 18.6911 + 10.7913i 1.33168 + 0.768849i 0.985558 0.169339i \(-0.0541633\pi\)
0.346127 + 0.938188i \(0.387497\pi\)
\(198\) −41.2702 + 71.4821i −2.93295 + 5.08001i
\(199\) 18.2458 10.5342i 1.29341 0.746751i 0.314154 0.949372i \(-0.398279\pi\)
0.979257 + 0.202621i \(0.0649460\pi\)
\(200\) −33.3476 + 19.2533i −2.35803 + 1.36141i
\(201\) 3.60718 6.24783i 0.254431 0.440688i
\(202\) 7.20587 + 12.4809i 0.507003 + 0.878155i
\(203\) 22.6100i 1.58691i
\(204\) 47.4452 + 82.1775i 3.32183 + 5.75357i
\(205\) −0.500937 + 0.867648i −0.0349869 + 0.0605991i
\(206\) −4.26352 7.38463i −0.297053 0.514512i
\(207\) −8.10688 + 14.0415i −0.563467 + 0.975954i
\(208\) −32.7667 18.9178i −2.27196 1.31172i
\(209\) −25.5938 14.7766i −1.77036 1.02212i
\(210\) −5.58982 −0.385734
\(211\) 4.43388 2.55990i 0.305241 0.176231i −0.339554 0.940587i \(-0.610276\pi\)
0.644795 + 0.764356i \(0.276943\pi\)
\(212\) 16.2776 + 9.39787i 1.11795 + 0.645448i
\(213\) 19.7505i 1.35328i
\(214\) −5.46115 + 9.45899i −0.373316 + 0.646603i
\(215\) 1.25397 0.723980i 0.0855201 0.0493750i
\(216\) 41.2030i 2.80351i
\(217\) −8.58391 + 4.95592i −0.582714 + 0.336430i
\(218\) 1.59339i 0.107918i
\(219\) −0.683034 1.18305i −0.0461551 0.0799430i
\(220\) 5.97673 3.45067i 0.402951 0.232644i
\(221\) 21.1083 12.1869i 1.41990 0.819778i
\(222\) 5.70930i 0.383183i
\(223\) 25.5494 1.71092 0.855459 0.517871i \(-0.173275\pi\)
0.855459 + 0.517871i \(0.173275\pi\)
\(224\) 42.9716 2.87116
\(225\) 12.1018 20.9609i 0.806786 1.39739i
\(226\) 7.21661 12.4995i 0.480042 0.831456i
\(227\) −12.5063 21.6615i −0.830070 1.43772i −0.897982 0.440032i \(-0.854967\pi\)
0.0679123 0.997691i \(-0.478366\pi\)
\(228\) −64.1145 −4.24609
\(229\) −8.26244 + 4.77032i −0.545997 + 0.315232i −0.747506 0.664255i \(-0.768749\pi\)
0.201509 + 0.979487i \(0.435416\pi\)
\(230\) 1.64845 0.951735i 0.108696 0.0627555i
\(231\) −62.4228 −4.10712
\(232\) 43.8828 + 25.3357i 2.88105 + 1.66337i
\(233\) −8.17762 14.1641i −0.535734 0.927918i −0.999127 0.0417656i \(-0.986702\pi\)
0.463394 0.886153i \(-0.346632\pi\)
\(234\) 45.9960 3.00685
\(235\) 0.482134 + 0.278360i 0.0314510 + 0.0181582i
\(236\) −38.5547 + 22.2596i −2.50970 + 1.44897i
\(237\) 8.19172 + 4.72949i 0.532109 + 0.307213i
\(238\) −31.2173 + 54.0700i −2.02352 + 3.50484i
\(239\) 23.7000 1.53303 0.766513 0.642229i \(-0.221990\pi\)
0.766513 + 0.642229i \(0.221990\pi\)
\(240\) 3.23860 5.60942i 0.209051 0.362086i
\(241\) −2.32644 + 4.02950i −0.149859 + 0.259563i −0.931175 0.364572i \(-0.881215\pi\)
0.781316 + 0.624135i \(0.214549\pi\)
\(242\) 68.6014 39.6070i 4.40986 2.54604i
\(243\) 7.63766 + 13.2288i 0.489956 + 0.848629i
\(244\) 32.5928 + 18.8175i 2.08654 + 1.20466i
\(245\) −0.547978 0.949126i −0.0350090 0.0606374i
\(246\) 34.0806i 2.17290i
\(247\) 16.4686i 1.04787i
\(248\) 22.2135i 1.41056i
\(249\) −38.7866 −2.45800
\(250\) −4.94509 + 2.85505i −0.312755 + 0.180569i
\(251\) 15.5235i 0.979834i −0.871769 0.489917i \(-0.837027\pi\)
0.871769 0.489917i \(-0.162973\pi\)
\(252\) −72.6704 + 41.9563i −4.57781 + 2.64300i
\(253\) 18.4087 10.6282i 1.15734 0.668192i
\(254\) −10.4177 18.0440i −0.653665 1.13218i
\(255\) 2.08630 + 3.61359i 0.130649 + 0.226291i
\(256\) 4.29806 7.44446i 0.268629 0.465279i
\(257\) 21.9740 1.37070 0.685350 0.728214i \(-0.259649\pi\)
0.685350 + 0.728214i \(0.259649\pi\)
\(258\) 24.6276 42.6562i 1.53324 2.65566i
\(259\) 2.31697 1.33770i 0.143970 0.0831208i
\(260\) −3.33055 1.92290i −0.206552 0.119253i
\(261\) −31.8500 −1.97146
\(262\) −12.1455 21.0367i −0.750353 1.29965i
\(263\) −18.6259 −1.14852 −0.574262 0.818671i \(-0.694711\pi\)
−0.574262 + 0.818671i \(0.694711\pi\)
\(264\) 69.9481 121.154i 4.30501 7.45649i
\(265\) 0.715774 + 0.413252i 0.0439696 + 0.0253859i
\(266\) −21.0926 36.5334i −1.29327 2.24001i
\(267\) 6.08032 3.51047i 0.372109 0.214837i
\(268\) −6.35712 + 11.0108i −0.388323 + 0.672595i
\(269\) −12.0465 −0.734488 −0.367244 0.930125i \(-0.619699\pi\)
−0.367244 + 0.930125i \(0.619699\pi\)
\(270\) 3.04044i 0.185035i
\(271\) −6.94290 12.0255i −0.421751 0.730494i 0.574360 0.818603i \(-0.305251\pi\)
−0.996111 + 0.0881086i \(0.971918\pi\)
\(272\) −36.1731 62.6536i −2.19331 3.79893i
\(273\) 17.3927 + 30.1250i 1.05265 + 1.82325i
\(274\) −1.19572 −0.0722363
\(275\) −27.4801 + 15.8656i −1.65711 + 0.956734i
\(276\) 23.0576 39.9370i 1.38791 2.40392i
\(277\) −1.64914 + 0.952131i −0.0990871 + 0.0572080i −0.548725 0.836003i \(-0.684886\pi\)
0.449638 + 0.893211i \(0.351553\pi\)
\(278\) −19.9740 + 11.5320i −1.19796 + 0.691645i
\(279\) 6.98124 + 12.0919i 0.417956 + 0.723920i
\(280\) 5.87039 0.350823
\(281\) 4.68083 8.10743i 0.279235 0.483649i −0.691960 0.721936i \(-0.743253\pi\)
0.971195 + 0.238287i \(0.0765859\pi\)
\(282\) 18.9379 1.12774
\(283\) −9.32281 −0.554184 −0.277092 0.960843i \(-0.589371\pi\)
−0.277092 + 0.960843i \(0.589371\pi\)
\(284\) 34.8073i 2.06544i
\(285\) −2.81931 −0.167001
\(286\) −52.2226 30.1507i −3.08799 1.78285i
\(287\) −13.8307 + 7.98518i −0.816403 + 0.471350i
\(288\) 60.5325i 3.56691i
\(289\) 29.6053 1.74149
\(290\) 3.23819 + 1.86957i 0.190153 + 0.109785i
\(291\) 2.32691i 0.136406i
\(292\) 1.20374 + 2.08494i 0.0704437 + 0.122012i
\(293\) −8.47896 14.6860i −0.495346 0.857965i 0.504639 0.863330i \(-0.331626\pi\)
−0.999986 + 0.00536528i \(0.998292\pi\)
\(294\) −32.2863 18.6405i −1.88298 1.08714i
\(295\) −1.69536 + 0.978818i −0.0987078 + 0.0569890i
\(296\) 5.99587i 0.348503i
\(297\) 33.9533i 1.97017i
\(298\) 17.6017 30.4870i 1.01964 1.76606i
\(299\) −10.2583 5.92263i −0.593253 0.342515i
\(300\) −34.4200 + 59.6171i −1.98724 + 3.44200i
\(301\) 23.0812 1.33038
\(302\) 40.8249i 2.34921i
\(303\) 13.2963 + 7.67663i 0.763853 + 0.441011i
\(304\) 48.8821 2.80358
\(305\) 1.43320 + 0.827459i 0.0820648 + 0.0473802i
\(306\) 76.1665 + 43.9747i 4.35415 + 2.51387i
\(307\) 0.210027 + 0.363777i 0.0119868 + 0.0207618i 0.871957 0.489583i \(-0.162851\pi\)
−0.859970 + 0.510345i \(0.829518\pi\)
\(308\) 110.011 6.26844
\(309\) −7.86707 4.54205i −0.447542 0.258388i
\(310\) 1.63917i 0.0930987i
\(311\) 32.5607i 1.84635i −0.384381 0.923175i \(-0.625585\pi\)
0.384381 0.923175i \(-0.374415\pi\)
\(312\) −77.9576 −4.41348
\(313\) −0.957373 −0.0541139 −0.0270569 0.999634i \(-0.508614\pi\)
−0.0270569 + 0.999634i \(0.508614\pi\)
\(314\) 33.1403i 1.87021i
\(315\) −3.19553 + 1.84494i −0.180048 + 0.103951i
\(316\) −14.4367 8.33501i −0.812126 0.468881i
\(317\) −3.35534 1.93721i −0.188455 0.108804i 0.402804 0.915286i \(-0.368036\pi\)
−0.591259 + 0.806482i \(0.701369\pi\)
\(318\) 28.1151 1.57662
\(319\) 36.1616 + 20.8779i 2.02466 + 1.16894i
\(320\) −1.24683 + 2.15958i −0.0697000 + 0.120724i
\(321\) 11.6359i 0.649450i
\(322\) 30.3423 1.69091
\(323\) −15.7449 + 27.2710i −0.876070 + 1.51740i
\(324\) 0.549006 + 0.950905i 0.0305003 + 0.0528281i
\(325\) 15.3134 + 8.84119i 0.849434 + 0.490421i
\(326\) 10.3532 + 17.9323i 0.573413 + 0.993181i
\(327\) 0.848745 + 1.47007i 0.0469357 + 0.0812951i
\(328\) 35.7913i 1.97624i
\(329\) 4.43720 + 7.68546i 0.244631 + 0.423713i
\(330\) 5.16159 8.94013i 0.284136 0.492138i
\(331\) −17.1985 9.92953i −0.945312 0.545776i −0.0536908 0.998558i \(-0.517099\pi\)
−0.891622 + 0.452781i \(0.850432\pi\)
\(332\) 68.3555 3.75149
\(333\) −1.88438 3.26384i −0.103263 0.178857i
\(334\) 19.7212 + 34.1581i 1.07910 + 1.86905i
\(335\) −0.279541 + 0.484179i −0.0152730 + 0.0264536i
\(336\) 89.4169 51.6249i 4.87809 2.81637i
\(337\) 7.61047 + 13.1817i 0.414569 + 0.718054i 0.995383 0.0959817i \(-0.0305990\pi\)
−0.580814 + 0.814036i \(0.697266\pi\)
\(338\) 0.666892i 0.0362742i
\(339\) 15.3761i 0.835117i
\(340\) −3.67680 6.36840i −0.199402 0.345375i
\(341\) 18.3050i 0.991272i
\(342\) −51.4634 + 29.7124i −2.78282 + 1.60666i
\(343\) 6.81466i 0.367957i
\(344\) −25.8637 + 44.7973i −1.39448 + 2.41531i
\(345\) 1.01391 1.75615i 0.0545872 0.0945478i
\(346\) −21.2418 + 36.7919i −1.14197 + 1.97795i
\(347\) 11.3854 6.57337i 0.611201 0.352877i −0.162235 0.986752i \(-0.551870\pi\)
0.773435 + 0.633875i \(0.218537\pi\)
\(348\) 90.5878 4.85602
\(349\) −14.6970 + 11.5325i −0.786713 + 0.617319i
\(350\) −45.2943 −2.42108
\(351\) 16.3857 9.46031i 0.874606 0.504954i
\(352\) −39.6796 + 68.7270i −2.11493 + 3.66316i
\(353\) 0.128539 0.222636i 0.00684143 0.0118497i −0.862584 0.505913i \(-0.831156\pi\)
0.869426 + 0.494063i \(0.164489\pi\)
\(354\) −33.2964 + 57.6710i −1.76968 + 3.06518i
\(355\) 1.53058i 0.0812348i
\(356\) −10.7156 + 6.18667i −0.567927 + 0.327893i
\(357\) 66.5135i 3.52027i
\(358\) −26.2751 45.5098i −1.38868 2.40527i
\(359\) 28.5865i 1.50874i 0.656451 + 0.754369i \(0.272057\pi\)
−0.656451 + 0.754369i \(0.727943\pi\)
\(360\) 8.26942i 0.435837i
\(361\) −1.13836 1.97169i −0.0599135 0.103773i
\(362\) −31.6491 + 18.2726i −1.66344 + 0.960386i
\(363\) 42.1946 73.0831i 2.21464 3.83587i
\(364\) −30.6519 53.0907i −1.60660 2.78271i
\(365\) 0.0529321 + 0.0916811i 0.00277059 + 0.00479881i
\(366\) 56.2952 2.94260
\(367\) 4.55133 + 2.62771i 0.237578 + 0.137166i 0.614063 0.789257i \(-0.289534\pi\)
−0.376485 + 0.926423i \(0.622867\pi\)
\(368\) −17.5795 + 30.4487i −0.916397 + 1.58725i
\(369\) 11.2484 + 19.4829i 0.585571 + 1.01424i
\(370\) 0.442446i 0.0230016i
\(371\) 6.58745 + 11.4098i 0.342003 + 0.592367i
\(372\) −19.8561 34.3917i −1.02949 1.78313i
\(373\) 16.5196 + 9.53760i 0.855353 + 0.493838i 0.862453 0.506137i \(-0.168927\pi\)
−0.00710042 + 0.999975i \(0.502260\pi\)
\(374\) −57.6516 99.8555i −2.98109 5.16340i
\(375\) −3.04157 + 5.26815i −0.157066 + 0.272046i
\(376\) −19.8885 −1.02567
\(377\) 23.2686i 1.19839i
\(378\) −24.2331 + 41.9729i −1.24641 + 2.15885i
\(379\) 6.45186 + 3.72498i 0.331410 + 0.191339i 0.656467 0.754355i \(-0.272050\pi\)
−0.325057 + 0.945694i \(0.605384\pi\)
\(380\) 4.96860 0.254884
\(381\) −19.2228 11.0983i −0.984815 0.568583i
\(382\) 6.23235 + 3.59825i 0.318875 + 0.184103i
\(383\) 10.3513 5.97634i 0.528928 0.305377i −0.211652 0.977345i \(-0.567884\pi\)
0.740580 + 0.671969i \(0.234551\pi\)
\(384\) 15.2551i 0.778486i
\(385\) 4.83750 0.246542
\(386\) 63.2048 3.21704
\(387\) 32.5137i 1.65276i
\(388\) 4.10083i 0.208188i
\(389\) 2.30430 + 1.33039i 0.116833 + 0.0674534i 0.557278 0.830326i \(-0.311846\pi\)
−0.440445 + 0.897780i \(0.645179\pi\)
\(390\) −5.75263 −0.291296
\(391\) −11.3247 19.6150i −0.572717 0.991974i
\(392\) 33.9069 + 19.5762i 1.71256 + 0.988745i
\(393\) −22.4110 12.9390i −1.13049 0.652686i
\(394\) −56.8952 −2.86634
\(395\) −0.634823 0.366515i −0.0319414 0.0184414i
\(396\) 154.968i 7.78745i
\(397\) −3.42443 −0.171867 −0.0859335 0.996301i \(-0.527387\pi\)
−0.0859335 + 0.996301i \(0.527387\pi\)
\(398\) −27.7699 + 48.0989i −1.39198 + 2.41098i
\(399\) −38.9202 22.4706i −1.94845 1.12494i
\(400\) 26.2424 45.4532i 1.31212 2.27266i
\(401\) 7.51071i 0.375067i 0.982258 + 0.187533i \(0.0600493\pi\)
−0.982258 + 0.187533i \(0.939951\pi\)
\(402\) 19.0182i 0.948544i
\(403\) −8.83393 + 5.10027i −0.440049 + 0.254063i
\(404\) −23.4327 13.5289i −1.16582 0.673088i
\(405\) 0.0241414 + 0.0418141i 0.00119960 + 0.00207776i
\(406\) 29.8018 + 51.6183i 1.47904 + 2.56177i
\(407\) 4.94089i 0.244911i
\(408\) −129.093 74.5319i −6.39106 3.68988i
\(409\) −13.8572 −0.685194 −0.342597 0.939482i \(-0.611307\pi\)
−0.342597 + 0.939482i \(0.611307\pi\)
\(410\) 2.64110i 0.130435i
\(411\) −1.10318 + 0.636920i −0.0544157 + 0.0314169i
\(412\) 13.8645 + 8.00468i 0.683056 + 0.394362i
\(413\) −31.2057 −1.53553
\(414\) 42.7421i 2.10066i
\(415\) 3.00579 0.147548
\(416\) 44.2232 2.16822
\(417\) −12.2854 + 21.2790i −0.601619 + 1.04203i
\(418\) 77.9069 3.81055
\(419\) −10.6844 18.5059i −0.521966 0.904071i −0.999673 0.0255526i \(-0.991865\pi\)
0.477708 0.878519i \(-0.341468\pi\)
\(420\) 9.08875 5.24739i 0.443485 0.256046i
\(421\) −23.4754 + 13.5535i −1.14412 + 0.660558i −0.947448 0.319911i \(-0.896347\pi\)
−0.196673 + 0.980469i \(0.563014\pi\)
\(422\) −6.74831 + 11.6884i −0.328503 + 0.568983i
\(423\) 10.8262 6.25053i 0.526390 0.303911i
\(424\) −29.5263 −1.43393
\(425\) 16.9053 + 29.2809i 0.820030 + 1.42033i
\(426\) 26.0328 + 45.0901i 1.26129 + 2.18462i
\(427\) 13.1901 + 22.8459i 0.638314 + 1.10559i
\(428\) 20.5064i 0.991216i
\(429\) −64.2410 −3.10158
\(430\) −1.90853 + 3.30567i −0.0920374 + 0.159414i
\(431\) −3.71289 + 2.14364i −0.178843 + 0.103255i −0.586749 0.809769i \(-0.699593\pi\)
0.407906 + 0.913024i \(0.366259\pi\)
\(432\) −28.0801 48.6361i −1.35100 2.34001i
\(433\) −11.4270 6.59737i −0.549146 0.317050i 0.199632 0.979871i \(-0.436025\pi\)
−0.748777 + 0.662822i \(0.769359\pi\)
\(434\) 13.0646 22.6286i 0.627121 1.08621i
\(435\) 3.98341 0.190990
\(436\) −1.49579 2.59078i −0.0716351 0.124076i
\(437\) 15.3036 0.732069
\(438\) 3.11871 + 1.80059i 0.149018 + 0.0860354i
\(439\) −31.5839 + 18.2350i −1.50742 + 0.870309i −0.507457 + 0.861677i \(0.669414\pi\)
−0.999963 + 0.00863178i \(0.997252\pi\)
\(440\) −5.42067 + 9.38888i −0.258420 + 0.447597i
\(441\) −24.6095 −1.17188
\(442\) −32.1266 + 55.6448i −1.52810 + 2.64676i
\(443\) 6.25521 + 10.8343i 0.297194 + 0.514755i 0.975493 0.220031i \(-0.0706159\pi\)
−0.678299 + 0.734786i \(0.737283\pi\)
\(444\) 5.35955 + 9.28302i 0.254353 + 0.440552i
\(445\) −0.471198 + 0.272046i −0.0223369 + 0.0128962i
\(446\) −58.3289 + 33.6762i −2.76196 + 1.59462i
\(447\) 37.5032i 1.77384i
\(448\) −34.4247 + 19.8751i −1.62642 + 0.939011i
\(449\) 19.4656 0.918640 0.459320 0.888271i \(-0.348093\pi\)
0.459320 + 0.888271i \(0.348093\pi\)
\(450\) 63.8046i 3.00778i
\(451\) 29.4938i 1.38881i
\(452\) 27.0981i 1.27459i
\(453\) 21.7460 + 37.6652i 1.02172 + 1.76966i
\(454\) 57.1032 + 32.9685i 2.67998 + 1.54729i
\(455\) −1.34786 2.33456i −0.0631885 0.109446i
\(456\) 87.2242 50.3589i 4.08465 2.35827i
\(457\) 15.1313 26.2082i 0.707812 1.22597i −0.257855 0.966184i \(-0.583016\pi\)
0.965667 0.259783i \(-0.0836511\pi\)
\(458\) 12.5753 21.7811i 0.587607 1.01776i
\(459\) 36.1783 1.68866
\(460\) −1.78687 + 3.09494i −0.0833130 + 0.144302i
\(461\) 0.828955 + 0.478597i 0.0386083 + 0.0222905i 0.519180 0.854665i \(-0.326237\pi\)
−0.480572 + 0.876955i \(0.659571\pi\)
\(462\) 142.510 82.2783i 6.63017 3.82793i
\(463\) −30.5678 17.6483i −1.42061 0.820187i −0.424255 0.905543i \(-0.639464\pi\)
−0.996351 + 0.0853553i \(0.972797\pi\)
\(464\) −69.0658 −3.20630
\(465\) −0.873130 1.51230i −0.0404904 0.0701315i
\(466\) 37.3387 + 21.5575i 1.72968 + 0.998633i
\(467\) −28.8206 −1.33366 −0.666830 0.745210i \(-0.732349\pi\)
−0.666830 + 0.745210i \(0.732349\pi\)
\(468\) −74.7870 + 43.1783i −3.45703 + 1.99592i
\(469\) −7.71806 + 4.45603i −0.356387 + 0.205760i
\(470\) −1.46760 −0.0676956
\(471\) 17.6527 + 30.5753i 0.813392 + 1.40884i
\(472\) 34.9677 60.5658i 1.60952 2.78777i
\(473\) −21.3130 + 36.9152i −0.979972 + 1.69736i
\(474\) −24.9354 −1.14532
\(475\) −22.8449 −1.04819
\(476\) 117.220i 5.37277i
\(477\) 16.0726 9.27951i 0.735913 0.424879i
\(478\) −54.1067 + 31.2385i −2.47478 + 1.42882i
\(479\) −6.73995 11.6739i −0.307956 0.533396i 0.669959 0.742398i \(-0.266312\pi\)
−0.977915 + 0.209002i \(0.932978\pi\)
\(480\) 7.57069i 0.345553i
\(481\) 2.38446 1.37667i 0.108722 0.0627706i
\(482\) 12.2657i 0.558688i
\(483\) 27.9939 16.1623i 1.27376 0.735408i
\(484\) −74.3615 + 128.798i −3.38007 + 5.85445i
\(485\) 0.180326i 0.00818817i
\(486\) −34.8733 20.1341i −1.58188 0.913301i
\(487\) 16.4234 9.48207i 0.744217 0.429674i −0.0793837 0.996844i \(-0.525295\pi\)
0.823600 + 0.567170i \(0.191962\pi\)
\(488\) −59.1209 −2.67628
\(489\) 19.1039 + 11.0296i 0.863907 + 0.498777i
\(490\) 2.50205 + 1.44456i 0.113031 + 0.0652585i
\(491\) −13.5615 + 23.4891i −0.612020 + 1.06005i 0.378879 + 0.925446i \(0.376310\pi\)
−0.990899 + 0.134604i \(0.957024\pi\)
\(492\) −31.9929 55.4133i −1.44235 2.49822i
\(493\) 22.2461 38.5313i 1.00191 1.73536i
\(494\) −21.7069 37.5975i −0.976642 1.69159i
\(495\) 6.81441i 0.306285i
\(496\) 15.1386 + 26.2209i 0.679744 + 1.17735i
\(497\) −12.1991 + 21.1295i −0.547205 + 0.947787i
\(498\) 88.5491 51.1238i 3.96798 2.29091i
\(499\) 28.2846 16.3301i 1.26619 0.731038i 0.291929 0.956440i \(-0.405703\pi\)
0.974266 + 0.225402i \(0.0723696\pi\)
\(500\) 5.36031 9.28432i 0.239720 0.415208i
\(501\) 36.3897 + 21.0096i 1.62577 + 0.938639i
\(502\) 20.4612 + 35.4399i 0.913229 + 1.58176i
\(503\) −32.1480 18.5607i −1.43341 0.827579i −0.436029 0.899933i \(-0.643616\pi\)
−0.997379 + 0.0723539i \(0.976949\pi\)
\(504\) 65.9094 114.158i 2.93584 5.08502i
\(505\) −1.03041 0.594905i −0.0458525 0.0264729i
\(506\) −28.0178 + 48.5282i −1.24554 + 2.15734i
\(507\) −0.355230 0.615277i −0.0157763 0.0273254i
\(508\) 33.8773 + 19.5591i 1.50306 + 0.867793i
\(509\) 15.7310 9.08231i 0.697265 0.402566i −0.109063 0.994035i \(-0.534785\pi\)
0.806328 + 0.591469i \(0.201452\pi\)
\(510\) −9.52599 5.49984i −0.421818 0.243537i
\(511\) 1.68753i 0.0746519i
\(512\) 33.5248i 1.48160i
\(513\) −12.2223 + 21.1697i −0.539628 + 0.934663i
\(514\) −50.1663 + 28.9635i −2.21274 + 1.27753i
\(515\) 0.609664 + 0.351989i 0.0268650 + 0.0155105i
\(516\) 92.4756i 4.07101i
\(517\) −16.3891 −0.720791
\(518\) −3.52640 + 6.10791i −0.154941 + 0.268366i
\(519\) 45.2591i 1.98666i
\(520\) 6.04138 0.264932
\(521\) 21.5970 12.4690i 0.946180 0.546277i 0.0542879 0.998525i \(-0.482711\pi\)
0.891892 + 0.452248i \(0.149378\pi\)
\(522\) 72.7129 41.9808i 3.18256 1.83745i
\(523\) −22.1910 12.8120i −0.970344 0.560229i −0.0710032 0.997476i \(-0.522620\pi\)
−0.899341 + 0.437247i \(0.855953\pi\)
\(524\) 39.4960 + 22.8030i 1.72539 + 0.996155i
\(525\) −41.7887 + 24.1267i −1.82381 + 1.05298i
\(526\) 42.5227 24.5505i 1.85408 1.07045i
\(527\) −19.5046 −0.849633
\(528\) 190.680i 8.29828i
\(529\) 5.99635 10.3860i 0.260711 0.451565i
\(530\) −2.17880 −0.0946410
\(531\) 43.9584i 1.90763i
\(532\) 68.5909 + 39.6010i 2.97379 + 1.71692i
\(533\) −14.2336 + 8.21776i −0.616525 + 0.355951i
\(534\) −9.25417 + 16.0287i −0.400467 + 0.693629i
\(535\) 0.901728i 0.0389851i
\(536\) 19.9729i 0.862696i
\(537\) −48.4830 27.9917i −2.09219 1.20793i
\(538\) 27.5020 15.8783i 1.18569 0.684560i
\(539\) 27.9410 + 16.1317i 1.20350 + 0.694843i
\(540\) −2.85419 4.94360i −0.122825 0.212739i
\(541\) 2.57521 4.46040i 0.110717 0.191767i −0.805343 0.592810i \(-0.798019\pi\)
0.916060 + 0.401042i \(0.131352\pi\)
\(542\) 31.7010 + 18.3026i 1.36168 + 0.786164i
\(543\) −19.4663 + 33.7167i −0.835381 + 1.44692i
\(544\) 73.2308 + 42.2798i 3.13975 + 1.81273i
\(545\) −0.0657741 0.113924i −0.00281745 0.00487997i
\(546\) −79.4143 45.8499i −3.39862 1.96219i
\(547\) −13.6498 + 23.6422i −0.583625 + 1.01087i 0.411421 + 0.911446i \(0.365033\pi\)
−0.995045 + 0.0994220i \(0.968301\pi\)
\(548\) 1.94418 1.12247i 0.0830514 0.0479497i
\(549\) 32.1823 18.5805i 1.37351 0.792994i
\(550\) 41.8244 72.4420i 1.78340 3.08894i
\(551\) 15.0310 + 26.0345i 0.640342 + 1.10910i
\(552\) 72.4427i 3.08337i
\(553\) −5.84243 10.1194i −0.248446 0.430320i
\(554\) 2.50997 4.34740i 0.106638 0.184703i
\(555\) 0.235675 + 0.408202i 0.0100039 + 0.0173272i
\(556\) 21.6512 37.5009i 0.918214 1.59039i
\(557\) −32.6393 18.8443i −1.38297 0.798458i −0.390460 0.920620i \(-0.627684\pi\)
−0.992510 + 0.122162i \(0.961017\pi\)
\(558\) −31.8761 18.4037i −1.34942 0.779089i
\(559\) 23.7535 1.00467
\(560\) −6.92942 + 4.00070i −0.292822 + 0.169061i
\(561\) −106.379 61.4180i −4.49133 2.59307i
\(562\) 24.6788i 1.04101i
\(563\) 12.5400 21.7199i 0.528497 0.915383i −0.470951 0.882159i \(-0.656089\pi\)
0.999448 0.0332240i \(-0.0105775\pi\)
\(564\) −30.7920 + 17.7778i −1.29658 + 0.748580i
\(565\) 1.19158i 0.0501303i
\(566\) 21.2838 12.2882i 0.894626 0.516513i
\(567\) 0.769652i 0.0323223i
\(568\) −27.3395 47.3534i −1.14714 1.98691i
\(569\) 25.3438 14.6322i 1.06247 0.613415i 0.136353 0.990660i \(-0.456462\pi\)
0.926113 + 0.377245i \(0.123129\pi\)
\(570\) 6.43643 3.71607i 0.269592 0.155649i
\(571\) 39.5659i 1.65578i −0.560889 0.827891i \(-0.689541\pi\)
0.560889 0.827891i \(-0.310459\pi\)
\(572\) 113.215 4.73375
\(573\) 7.66665 0.320279
\(574\) 21.0502 36.4601i 0.878619 1.52181i
\(575\) 8.21574 14.2301i 0.342620 0.593435i
\(576\) 27.9974 + 48.4929i 1.16656 + 2.02054i
\(577\) −0.701671 −0.0292109 −0.0146055 0.999893i \(-0.504649\pi\)
−0.0146055 + 0.999893i \(0.504649\pi\)
\(578\) −67.5885 + 39.0222i −2.81131 + 1.62311i
\(579\) 58.3129 33.6670i 2.42340 1.39915i
\(580\) −7.02016 −0.291496
\(581\) 41.4946 + 23.9569i 1.72149 + 0.993900i
\(582\) 3.06706 + 5.31230i 0.127134 + 0.220202i
\(583\) −24.3312 −1.00769
\(584\) −3.27525 1.89097i −0.135531 0.0782488i
\(585\) −3.28861 + 1.89868i −0.135967 + 0.0785007i
\(586\) 38.7147 + 22.3519i 1.59929 + 0.923349i
\(587\) 19.1966 33.2495i 0.792329 1.37235i −0.132192 0.991224i \(-0.542202\pi\)
0.924521 0.381130i \(-0.124465\pi\)
\(588\) 69.9945 2.88652
\(589\) 6.58933 11.4131i 0.271509 0.470267i
\(590\) 2.58032 4.46925i 0.106230 0.183996i
\(591\) −52.4917 + 30.3061i −2.15922 + 1.24663i
\(592\) −4.08622 7.07754i −0.167943 0.290885i
\(593\) 19.7042 + 11.3762i 0.809156 + 0.467166i 0.846663 0.532130i \(-0.178608\pi\)
−0.0375068 + 0.999296i \(0.511942\pi\)
\(594\) −44.7532 77.5149i −1.83625 3.18047i
\(595\) 5.15451i 0.211314i
\(596\) 66.0937i 2.70730i
\(597\) 59.1682i 2.42159i
\(598\) 31.2260 1.27693
\(599\) 32.6915 18.8745i 1.33574 0.771190i 0.349567 0.936911i \(-0.386329\pi\)
0.986173 + 0.165722i \(0.0529954\pi\)
\(600\) 108.141i 4.41484i
\(601\) 7.49723 4.32853i 0.305818 0.176564i −0.339235 0.940702i \(-0.610168\pi\)
0.645054 + 0.764137i \(0.276835\pi\)
\(602\) −52.6940 + 30.4229i −2.14765 + 1.23995i
\(603\) 6.27705 + 10.8722i 0.255621 + 0.442749i
\(604\) −38.3240 66.3791i −1.55938 2.70093i
\(605\) −3.26989 + 5.66362i −0.132940 + 0.230259i
\(606\) −40.4737 −1.64413
\(607\) −3.80682 + 6.59361i −0.154514 + 0.267627i −0.932882 0.360182i \(-0.882715\pi\)
0.778368 + 0.627809i \(0.216048\pi\)
\(608\) −49.4798 + 28.5672i −2.00667 + 1.15855i
\(609\) 54.9905 + 31.7488i 2.22833 + 1.28653i
\(610\) −4.36263 −0.176638
\(611\) 4.56644 + 7.90931i 0.184738 + 0.319976i
\(612\) −165.124 −6.67473
\(613\) 3.60506 6.24414i 0.145607 0.252198i −0.783992 0.620770i \(-0.786820\pi\)
0.929599 + 0.368572i \(0.120153\pi\)
\(614\) −0.958974 0.553664i −0.0387010 0.0223441i
\(615\) −1.40682 2.43669i −0.0567285 0.0982567i
\(616\) −149.663 + 86.4082i −6.03011 + 3.48149i
\(617\) 18.3661 31.8111i 0.739392 1.28067i −0.213377 0.976970i \(-0.568446\pi\)
0.952769 0.303695i \(-0.0982204\pi\)
\(618\) 23.9472 0.963297
\(619\) 6.17107i 0.248036i 0.992280 + 0.124018i \(0.0395781\pi\)
−0.992280 + 0.124018i \(0.960422\pi\)
\(620\) 1.53876 + 2.66521i 0.0617980 + 0.107037i
\(621\) −8.79106 15.2266i −0.352773 0.611021i
\(622\) 42.9177 + 74.3356i 1.72084 + 2.98058i
\(623\) −8.67311 −0.347481
\(624\) 92.0213 53.1285i 3.68380 2.12684i
\(625\) −12.1459 + 21.0373i −0.485835 + 0.841491i
\(626\) 2.18567 1.26189i 0.0873567 0.0504354i
\(627\) 71.8771 41.4983i 2.87049 1.65728i
\(628\) −31.1102 53.8844i −1.24143 2.15022i
\(629\) 5.26468 0.209917
\(630\) 4.86356 8.42394i 0.193769 0.335618i
\(631\) −25.2080 −1.00351 −0.501757 0.865009i \(-0.667313\pi\)
−0.501757 + 0.865009i \(0.667313\pi\)
\(632\) 26.1870 1.04166
\(633\) 14.3784i 0.571488i
\(634\) 10.2136 0.405633
\(635\) 1.48968 + 0.860070i 0.0591163 + 0.0341308i
\(636\) −45.7137 + 26.3928i −1.81267 + 1.04654i
\(637\) 17.9789i 0.712351i
\(638\) −110.075 −4.35791
\(639\) 29.7644 + 17.1845i 1.17746 + 0.679807i
\(640\) 1.18221i 0.0467309i
\(641\) 1.05027 + 1.81913i 0.0414834 + 0.0718513i 0.886022 0.463644i \(-0.153458\pi\)
−0.844538 + 0.535495i \(0.820125\pi\)
\(642\) −15.3370 26.5645i −0.605303 1.04842i
\(643\) 39.5176 + 22.8155i 1.55842 + 0.899756i 0.997408 + 0.0719497i \(0.0229221\pi\)
0.561014 + 0.827806i \(0.310411\pi\)
\(644\) −49.3349 + 28.4835i −1.94407 + 1.12241i
\(645\) 4.06643i 0.160115i
\(646\) 83.0122i 3.26607i
\(647\) 4.70442 8.14830i 0.184950 0.320343i −0.758610 0.651545i \(-0.774121\pi\)
0.943560 + 0.331203i \(0.107454\pi\)
\(648\) −1.49378 0.862436i −0.0586813 0.0338797i
\(649\) 28.8151 49.9092i 1.13109 1.95911i
\(650\) −46.6136 −1.82834
\(651\) 27.8362i 1.09099i
\(652\) −33.6677 19.4380i −1.31853 0.761252i
\(653\) 3.54253 0.138630 0.0693150 0.997595i \(-0.477919\pi\)
0.0693150 + 0.997595i \(0.477919\pi\)
\(654\) −3.87534 2.23743i −0.151538 0.0874904i
\(655\) 1.73676 + 1.00272i 0.0678607 + 0.0391794i
\(656\) 24.3919 + 42.2481i 0.952345 + 1.64951i
\(657\) 2.37716 0.0927420
\(658\) −20.2601 11.6972i −0.789821 0.456004i
\(659\) 28.6458i 1.11588i −0.829881 0.557941i \(-0.811592\pi\)
0.829881 0.557941i \(-0.188408\pi\)
\(660\) 19.3816i 0.754427i
\(661\) 8.95093 0.348151 0.174075 0.984732i \(-0.444306\pi\)
0.174075 + 0.984732i \(0.444306\pi\)
\(662\) 52.3517 2.03471
\(663\) 68.4508i 2.65841i
\(664\) −92.9938 + 53.6900i −3.60886 + 2.08358i
\(665\) 3.01614 + 1.74137i 0.116961 + 0.0675275i
\(666\) 8.60400 + 4.96752i 0.333398 + 0.192488i
\(667\) −21.6225 −0.837227
\(668\) −64.1312 37.0262i −2.48131 1.43259i
\(669\) −35.8763 + 62.1396i −1.38706 + 2.40246i
\(670\) 1.47383i 0.0569391i
\(671\) −48.7185 −1.88076
\(672\) −60.3403 + 104.512i −2.32768 + 4.03165i
\(673\) 2.26628 + 3.92531i 0.0873585 + 0.151309i 0.906394 0.422434i \(-0.138824\pi\)
−0.819035 + 0.573743i \(0.805491\pi\)
\(674\) −34.7492 20.0624i −1.33849 0.772776i
\(675\) 13.1231 + 22.7299i 0.505109 + 0.874875i
\(676\) 0.626040 + 1.08433i 0.0240784 + 0.0417051i
\(677\) 8.35832i 0.321236i −0.987017 0.160618i \(-0.948651\pi\)
0.987017 0.160618i \(-0.0513488\pi\)
\(678\) 20.2670 + 35.1035i 0.778349 + 1.34814i
\(679\) −1.43724 + 2.48937i −0.0551563 + 0.0955334i
\(680\) 10.0041 + 5.77590i 0.383642 + 0.221496i
\(681\) 70.2447 2.69178
\(682\) 24.1275 + 41.7901i 0.923890 + 1.60022i
\(683\) 19.3498 + 33.5149i 0.740400 + 1.28241i 0.952313 + 0.305122i \(0.0986973\pi\)
−0.211913 + 0.977289i \(0.567969\pi\)
\(684\) 55.7845 96.6216i 2.13297 3.69442i
\(685\) 0.0854915 0.0493585i 0.00326646 0.00188589i
\(686\) −8.98228 15.5578i −0.342945 0.593998i
\(687\) 26.7938i 1.02225i
\(688\) 70.5051i 2.68798i
\(689\) 6.77932 + 11.7421i 0.258271 + 0.447339i
\(690\) 5.34567i 0.203506i
\(691\) −7.88117 + 4.55020i −0.299814 + 0.173098i −0.642359 0.766404i \(-0.722044\pi\)
0.342545 + 0.939501i \(0.388711\pi\)
\(692\) 79.7624i 3.03211i
\(693\) 54.3126 94.0721i 2.06316 3.57350i
\(694\) −17.3285 + 30.0138i −0.657779 + 1.13931i
\(695\) 0.952066 1.64903i 0.0361139 0.0625511i
\(696\) −123.240 + 71.1525i −4.67139 + 2.69703i
\(697\) −31.4266 −1.19037
\(698\) 18.3523 45.7003i 0.694644 1.72978i
\(699\) 45.9318 1.73730
\(700\) 73.6462 42.5197i 2.78357 1.60709i
\(701\) 11.2972 19.5673i 0.426690 0.739049i −0.569887 0.821723i \(-0.693013\pi\)
0.996577 + 0.0826747i \(0.0263462\pi\)
\(702\) −24.9389 + 43.1954i −0.941258 + 1.63031i
\(703\) −1.77859 + 3.08061i −0.0670809 + 0.116188i
\(704\) 73.4101i 2.76675i
\(705\) −1.35402 + 0.781742i −0.0509952 + 0.0294421i
\(706\) 0.677698i 0.0255055i
\(707\) −9.48309 16.4252i −0.356648 0.617733i
\(708\) 125.027i 4.69879i
\(709\) 5.29684i 0.198927i 0.995041 + 0.0994634i \(0.0317126\pi\)
−0.995041 + 0.0994634i \(0.968287\pi\)
\(710\) −2.01743 3.49429i −0.0757128 0.131138i
\(711\) −14.2548 + 8.23003i −0.534598 + 0.308650i
\(712\) 9.71868 16.8332i 0.364223 0.630853i
\(713\) 4.73946 + 8.20899i 0.177494 + 0.307429i
\(714\) −87.6701 151.849i −3.28097 5.68281i
\(715\) 4.97839 0.186181
\(716\) 85.4439 + 49.3311i 3.19319 + 1.84359i
\(717\) −33.2793 + 57.6415i −1.24284 + 2.15266i
\(718\) −37.6793 65.2625i −1.40618 2.43557i
\(719\) 15.8281i 0.590288i −0.955453 0.295144i \(-0.904632\pi\)
0.955453 0.295144i \(-0.0953677\pi\)
\(720\) 5.63565 + 9.76124i 0.210028 + 0.363780i
\(721\) 5.61089 + 9.71834i 0.208960 + 0.361930i
\(722\) 5.19769 + 3.00089i 0.193438 + 0.111682i
\(723\) −6.53352 11.3164i −0.242984 0.420861i
\(724\) 34.3065 59.4206i 1.27499 2.20835i
\(725\) 32.2776 1.19876
\(726\) 222.463i 8.25639i
\(727\) 18.1106 31.3684i 0.671683 1.16339i −0.305743 0.952114i \(-0.598905\pi\)
0.977426 0.211276i \(-0.0677618\pi\)
\(728\) 83.4005 + 48.1513i 3.09103 + 1.78461i
\(729\) −43.5645 −1.61350
\(730\) −0.241686 0.139538i −0.00894521 0.00516452i
\(731\) 39.3343 + 22.7097i 1.45483 + 0.839948i
\(732\) −91.5330 + 52.8466i −3.38316 + 1.95327i
\(733\) 8.81140i 0.325457i −0.986671 0.162728i \(-0.947971\pi\)
0.986671 0.162728i \(-0.0520294\pi\)
\(734\) −13.8542 −0.511366
\(735\) 3.07786 0.113529
\(736\) 41.0947i 1.51477i
\(737\) 16.4586i 0.606261i
\(738\) −51.3600 29.6527i −1.89059 1.09153i
\(739\) −35.3073 −1.29880 −0.649399 0.760447i \(-0.724980\pi\)
−0.649399 + 0.760447i \(0.724980\pi\)
\(740\) −0.415342 0.719393i −0.0152683 0.0264454i
\(741\) −40.0538 23.1251i −1.47141 0.849520i
\(742\) −30.0781 17.3656i −1.10420 0.637510i
\(743\) −25.5098 −0.935864 −0.467932 0.883764i \(-0.655001\pi\)
−0.467932 + 0.883764i \(0.655001\pi\)
\(744\) 54.0261 + 31.1920i 1.98069 + 1.14355i
\(745\) 2.90633i 0.106480i
\(746\) −50.2853 −1.84108
\(747\) 33.7473 58.4520i 1.23475 2.13865i
\(748\) 187.477 + 108.240i 6.85484 + 3.95764i
\(749\) 7.18700 12.4482i 0.262607 0.454849i
\(750\) 16.0361i 0.585557i
\(751\) 46.2312i 1.68700i 0.537129 + 0.843500i \(0.319509\pi\)
−0.537129 + 0.843500i \(0.680491\pi\)
\(752\) 23.4764 13.5541i 0.856096 0.494267i
\(753\) 37.7551 + 21.7979i 1.37587 + 0.794361i
\(754\) 30.6699 + 53.1218i 1.11693 + 1.93458i
\(755\) −1.68522 2.91889i −0.0613314 0.106229i
\(756\) 90.9944i 3.30943i
\(757\) 41.1906 + 23.7814i 1.49710 + 0.864350i 0.999994 0.00334193i \(-0.00106377\pi\)
0.497103 + 0.867692i \(0.334397\pi\)
\(758\) −19.6393 −0.713332
\(759\) 59.6964i 2.16684i
\(760\) −6.75950 + 3.90260i −0.245193 + 0.141562i
\(761\) −34.2252 19.7599i −1.24066 0.716296i −0.271432 0.962458i \(-0.587497\pi\)
−0.969229 + 0.246161i \(0.920831\pi\)
\(762\) 58.5138 2.11973
\(763\) 2.09694i 0.0759145i
\(764\) −13.5113 −0.488822
\(765\) −7.26097 −0.262521
\(766\) −15.7546 + 27.2877i −0.569236 + 0.985946i
\(767\) −32.1146