Properties

Label 349.2.e.a.123.3
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 123.3
Character \(\chi\) = 349.123
Dual form 349.2.e.a.227.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.10033 + 1.21263i) q^{2} +(0.180949 - 0.313412i) q^{3} +(1.94093 - 3.36178i) q^{4} +(-1.51394 + 2.62221i) q^{5} +0.877693i q^{6} +(0.636711 - 0.367605i) q^{7} +4.56397i q^{8} +(1.43452 + 2.48465i) q^{9} +O(q^{10})\) \(q+(-2.10033 + 1.21263i) q^{2} +(0.180949 - 0.313412i) q^{3} +(1.94093 - 3.36178i) q^{4} +(-1.51394 + 2.62221i) q^{5} +0.877693i q^{6} +(0.636711 - 0.367605i) q^{7} +4.56397i q^{8} +(1.43452 + 2.48465i) q^{9} -7.34336i q^{10} -0.521449i q^{11} +(-0.702417 - 1.21662i) q^{12} +(2.12237 - 1.22535i) q^{13} +(-0.891536 + 1.54419i) q^{14} +(0.547890 + 0.948973i) q^{15} +(-1.65254 - 2.86229i) q^{16} -3.97105 q^{17} +(-6.02591 - 3.47906i) q^{18} +(-1.80811 + 3.13175i) q^{19} +(5.87688 + 10.1791i) q^{20} -0.266071i q^{21} +(0.632323 + 1.09522i) q^{22} +(1.71639 + 2.97288i) q^{23} +(1.43041 + 0.825845i) q^{24} +(-2.08401 - 3.60961i) q^{25} +(-2.97179 + 5.14729i) q^{26} +2.12399 q^{27} -2.85398i q^{28} +(-4.59276 + 7.95490i) q^{29} +(-2.30150 - 1.32877i) q^{30} -7.18488 q^{31} +(-0.963261 - 0.556139i) q^{32} +(-0.163429 - 0.0943555i) q^{33} +(8.34052 - 4.81540i) q^{34} +2.22613i q^{35} +11.1372 q^{36} -0.220912 q^{37} -8.77027i q^{38} -0.886904i q^{39} +(-11.9677 - 6.90957i) q^{40} -6.02009 q^{41} +(0.322645 + 0.558837i) q^{42} +(-3.30643 - 1.90897i) q^{43} +(-1.75300 - 1.01209i) q^{44} -8.68706 q^{45} +(-7.20998 - 4.16268i) q^{46} -11.2183i q^{47} -1.19610 q^{48} +(-3.22973 + 5.59406i) q^{49} +(8.75421 + 5.05424i) q^{50} +(-0.718556 + 1.24458i) q^{51} -9.51328i q^{52} +4.18955i q^{53} +(-4.46108 + 2.57560i) q^{54} +(1.36735 + 0.789441i) q^{55} +(1.67774 + 2.90593i) q^{56} +(0.654352 + 1.13337i) q^{57} -22.2772i q^{58} +(7.00991 + 4.04717i) q^{59} +4.25366 q^{60} +2.04793i q^{61} +(15.0906 - 8.71258i) q^{62} +(1.82674 + 1.05467i) q^{63} +9.30773 q^{64} +7.42042i q^{65} +0.457672 q^{66} +5.86487 q^{67} +(-7.70752 + 13.3498i) q^{68} +1.24232 q^{69} +(-2.69946 - 4.67560i) q^{70} +(5.57107 - 3.21646i) q^{71} +(-11.3399 + 6.54709i) q^{72} +(-2.09291 + 3.62502i) q^{73} +(0.463987 - 0.267883i) q^{74} -1.50839 q^{75} +(7.01884 + 12.1570i) q^{76} +(-0.191687 - 0.332012i) q^{77} +(1.07548 + 1.86279i) q^{78} +8.38030i q^{79} +10.0074 q^{80} +(-3.91921 + 6.78828i) q^{81} +(12.6442 - 7.30012i) q^{82} +(6.22161 + 10.7761i) q^{83} +(-0.894473 - 0.516424i) q^{84} +(6.01192 - 10.4129i) q^{85} +9.25947 q^{86} +(1.66211 + 2.87886i) q^{87} +2.37988 q^{88} +(1.77931 + 1.02729i) q^{89} +(18.2457 - 10.5342i) q^{90} +(0.900892 - 1.56039i) q^{91} +13.3256 q^{92} +(-1.30009 + 2.25183i) q^{93} +(13.6036 + 23.5621i) q^{94} +(-5.47474 - 9.48253i) q^{95} +(-0.348602 + 0.201265i) q^{96} +(-1.50118 + 0.866708i) q^{97} -15.6658i q^{98} +(1.29562 - 0.748026i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.10033 + 1.21263i −1.48516 + 0.857457i −0.999857 0.0168905i \(-0.994623\pi\)
−0.485301 + 0.874347i \(0.661290\pi\)
\(3\) 0.180949 0.313412i 0.104471 0.180949i −0.809051 0.587738i \(-0.800018\pi\)
0.913522 + 0.406790i \(0.133352\pi\)
\(4\) 1.94093 3.36178i 0.970464 1.68089i
\(5\) −1.51394 + 2.62221i −0.677053 + 1.17269i 0.298811 + 0.954312i \(0.403410\pi\)
−0.975864 + 0.218378i \(0.929923\pi\)
\(6\) 0.877693i 0.358317i
\(7\) 0.636711 0.367605i 0.240654 0.138942i −0.374823 0.927096i \(-0.622297\pi\)
0.615477 + 0.788155i \(0.288963\pi\)
\(8\) 4.56397i 1.61361i
\(9\) 1.43452 + 2.48465i 0.478172 + 0.828218i
\(10\) 7.34336i 2.32217i
\(11\) 0.521449i 0.157223i −0.996905 0.0786114i \(-0.974951\pi\)
0.996905 0.0786114i \(-0.0250486\pi\)
\(12\) −0.702417 1.21662i −0.202770 0.351208i
\(13\) 2.12237 1.22535i 0.588640 0.339852i −0.175919 0.984405i \(-0.556290\pi\)
0.764560 + 0.644553i \(0.222956\pi\)
\(14\) −0.891536 + 1.54419i −0.238273 + 0.412701i
\(15\) 0.547890 + 0.948973i 0.141464 + 0.245024i
\(16\) −1.65254 2.86229i −0.413136 0.715572i
\(17\) −3.97105 −0.963121 −0.481561 0.876413i \(-0.659930\pi\)
−0.481561 + 0.876413i \(0.659930\pi\)
\(18\) −6.02591 3.47906i −1.42032 0.820023i
\(19\) −1.80811 + 3.13175i −0.414810 + 0.718472i −0.995408 0.0957181i \(-0.969485\pi\)
0.580599 + 0.814190i \(0.302819\pi\)
\(20\) 5.87688 + 10.1791i 1.31411 + 2.27611i
\(21\) 0.266071i 0.0580614i
\(22\) 0.632323 + 1.09522i 0.134812 + 0.233501i
\(23\) 1.71639 + 2.97288i 0.357892 + 0.619888i 0.987609 0.156937i \(-0.0501621\pi\)
−0.629716 + 0.776825i \(0.716829\pi\)
\(24\) 1.43041 + 0.825845i 0.291980 + 0.168575i
\(25\) −2.08401 3.60961i −0.416801 0.721921i
\(26\) −2.97179 + 5.14729i −0.582816 + 1.00947i
\(27\) 2.12399 0.408761
\(28\) 2.85398i 0.539352i
\(29\) −4.59276 + 7.95490i −0.852855 + 1.47719i 0.0257663 + 0.999668i \(0.491797\pi\)
−0.878621 + 0.477520i \(0.841536\pi\)
\(30\) −2.30150 1.32877i −0.420194 0.242599i
\(31\) −7.18488 −1.29044 −0.645221 0.763996i \(-0.723235\pi\)
−0.645221 + 0.763996i \(0.723235\pi\)
\(32\) −0.963261 0.556139i −0.170282 0.0983125i
\(33\) −0.163429 0.0943555i −0.0284493 0.0164252i
\(34\) 8.34052 4.81540i 1.43039 0.825835i
\(35\) 2.22613i 0.376284i
\(36\) 11.1372 1.85619
\(37\) −0.220912 −0.0363176 −0.0181588 0.999835i \(-0.505780\pi\)
−0.0181588 + 0.999835i \(0.505780\pi\)
\(38\) 8.77027i 1.42273i
\(39\) 0.886904i 0.142018i
\(40\) −11.9677 6.90957i −1.89226 1.09250i
\(41\) −6.02009 −0.940180 −0.470090 0.882619i \(-0.655778\pi\)
−0.470090 + 0.882619i \(0.655778\pi\)
\(42\) 0.322645 + 0.558837i 0.0497852 + 0.0862304i
\(43\) −3.30643 1.90897i −0.504226 0.291115i 0.226231 0.974074i \(-0.427360\pi\)
−0.730457 + 0.682959i \(0.760693\pi\)
\(44\) −1.75300 1.01209i −0.264275 0.152579i
\(45\) −8.68706 −1.29499
\(46\) −7.20998 4.16268i −1.06305 0.613754i
\(47\) 11.2183i 1.63636i −0.574966 0.818178i \(-0.694985\pi\)
0.574966 0.818178i \(-0.305015\pi\)
\(48\) −1.19610 −0.172642
\(49\) −3.22973 + 5.59406i −0.461390 + 0.799152i
\(50\) 8.75421 + 5.05424i 1.23803 + 0.714778i
\(51\) −0.718556 + 1.24458i −0.100618 + 0.174276i
\(52\) 9.51328i 1.31925i
\(53\) 4.18955i 0.575479i 0.957709 + 0.287739i \(0.0929037\pi\)
−0.957709 + 0.287739i \(0.907096\pi\)
\(54\) −4.46108 + 2.57560i −0.607075 + 0.350495i
\(55\) 1.36735 + 0.789441i 0.184374 + 0.106448i
\(56\) 1.67774 + 2.90593i 0.224198 + 0.388322i
\(57\) 0.654352 + 1.13337i 0.0866710 + 0.150119i
\(58\) 22.2772i 2.92514i
\(59\) 7.00991 + 4.04717i 0.912612 + 0.526897i 0.881271 0.472612i \(-0.156689\pi\)
0.0313417 + 0.999509i \(0.490022\pi\)
\(60\) 4.25366 0.549145
\(61\) 2.04793i 0.262211i 0.991368 + 0.131105i \(0.0418526\pi\)
−0.991368 + 0.131105i \(0.958147\pi\)
\(62\) 15.0906 8.71258i 1.91651 1.10650i
\(63\) 1.82674 + 1.05467i 0.230148 + 0.132876i
\(64\) 9.30773 1.16347
\(65\) 7.42042i 0.920390i
\(66\) 0.457672 0.0563355
\(67\) 5.86487 0.716507 0.358254 0.933624i \(-0.383372\pi\)
0.358254 + 0.933624i \(0.383372\pi\)
\(68\) −7.70752 + 13.3498i −0.934674 + 1.61890i
\(69\) 1.24232 0.149557
\(70\) −2.69946 4.67560i −0.322647 0.558841i
\(71\) 5.57107 3.21646i 0.661164 0.381723i −0.131556 0.991309i \(-0.541997\pi\)
0.792720 + 0.609585i \(0.208664\pi\)
\(72\) −11.3399 + 6.54709i −1.33642 + 0.771582i
\(73\) −2.09291 + 3.62502i −0.244956 + 0.424276i −0.962119 0.272629i \(-0.912107\pi\)
0.717163 + 0.696905i \(0.245440\pi\)
\(74\) 0.463987 0.267883i 0.0539374 0.0311408i
\(75\) −1.50839 −0.174174
\(76\) 7.01884 + 12.1570i 0.805116 + 1.39450i
\(77\) −0.191687 0.332012i −0.0218448 0.0378363i
\(78\) 1.07548 + 1.86279i 0.121774 + 0.210920i
\(79\) 8.38030i 0.942857i 0.881904 + 0.471429i \(0.156261\pi\)
−0.881904 + 0.471429i \(0.843739\pi\)
\(80\) 10.0074 1.11886
\(81\) −3.91921 + 6.78828i −0.435468 + 0.754253i
\(82\) 12.6442 7.30012i 1.39632 0.806163i
\(83\) 6.22161 + 10.7761i 0.682910 + 1.18284i 0.974089 + 0.226166i \(0.0726193\pi\)
−0.291178 + 0.956669i \(0.594047\pi\)
\(84\) −0.894473 0.516424i −0.0975950 0.0563465i
\(85\) 6.01192 10.4129i 0.652084 1.12944i
\(86\) 9.25947 0.998475
\(87\) 1.66211 + 2.87886i 0.178197 + 0.308646i
\(88\) 2.37988 0.253696
\(89\) 1.77931 + 1.02729i 0.188607 + 0.108892i 0.591330 0.806430i \(-0.298603\pi\)
−0.402723 + 0.915322i \(0.631936\pi\)
\(90\) 18.2457 10.5342i 1.92327 1.11040i
\(91\) 0.900892 1.56039i 0.0944392 0.163573i
\(92\) 13.3256 1.38929
\(93\) −1.30009 + 2.25183i −0.134814 + 0.233504i
\(94\) 13.6036 + 23.5621i 1.40310 + 2.43025i
\(95\) −5.47474 9.48253i −0.561697 0.972887i
\(96\) −0.348602 + 0.201265i −0.0355790 + 0.0205416i
\(97\) −1.50118 + 0.866708i −0.152422 + 0.0880008i −0.574271 0.818665i \(-0.694714\pi\)
0.421849 + 0.906666i \(0.361381\pi\)
\(98\) 15.6658i 1.58249i
\(99\) 1.29562 0.748026i 0.130215 0.0751795i
\(100\) −16.1796 −1.61796
\(101\) 13.2211i 1.31555i −0.753216 0.657773i \(-0.771499\pi\)
0.753216 0.657773i \(-0.228501\pi\)
\(102\) 3.48536i 0.345102i
\(103\) 5.15375i 0.507814i 0.967229 + 0.253907i \(0.0817158\pi\)
−0.967229 + 0.253907i \(0.918284\pi\)
\(104\) 5.59248 + 9.68645i 0.548387 + 0.949835i
\(105\) 0.697695 + 0.402814i 0.0680881 + 0.0393107i
\(106\) −5.08036 8.79944i −0.493448 0.854677i
\(107\) 9.00541 5.19928i 0.870586 0.502633i 0.00304313 0.999995i \(-0.499031\pi\)
0.867543 + 0.497362i \(0.165698\pi\)
\(108\) 4.12250 7.14039i 0.396688 0.687084i
\(109\) 1.04215 1.80505i 0.0998196 0.172893i −0.811790 0.583949i \(-0.801507\pi\)
0.911610 + 0.411056i \(0.134840\pi\)
\(110\) −3.82919 −0.365099
\(111\) −0.0399736 + 0.0692364i −0.00379413 + 0.00657163i
\(112\) −2.10439 1.21497i −0.198846 0.114804i
\(113\) 15.0613 8.69564i 1.41685 0.818017i 0.420827 0.907141i \(-0.361740\pi\)
0.996021 + 0.0891237i \(0.0284066\pi\)
\(114\) −2.74871 1.58697i −0.257440 0.148633i
\(115\) −10.3940 −0.969248
\(116\) 17.8284 + 30.8798i 1.65533 + 2.86711i
\(117\) 6.08915 + 3.51557i 0.562942 + 0.325015i
\(118\) −19.6308 −1.80717
\(119\) −2.52841 + 1.45978i −0.231779 + 0.133818i
\(120\) −4.33109 + 2.50055i −0.395372 + 0.228268i
\(121\) 10.7281 0.975281
\(122\) −2.48338 4.30133i −0.224834 0.389424i
\(123\) −1.08933 + 1.88677i −0.0982213 + 0.170124i
\(124\) −13.9453 + 24.1540i −1.25233 + 2.16910i
\(125\) −2.51915 −0.225320
\(126\) −5.11569 −0.455742
\(127\) 3.28802i 0.291764i 0.989302 + 0.145882i \(0.0466020\pi\)
−0.989302 + 0.145882i \(0.953398\pi\)
\(128\) −17.6228 + 10.1745i −1.55765 + 0.899309i
\(129\) −1.19659 + 0.690851i −0.105354 + 0.0608261i
\(130\) −8.99820 15.5853i −0.789195 1.36693i
\(131\) 9.11661i 0.796522i −0.917272 0.398261i \(-0.869614\pi\)
0.917272 0.398261i \(-0.130386\pi\)
\(132\) −0.634406 + 0.366274i −0.0552179 + 0.0318801i
\(133\) 2.65869i 0.230538i
\(134\) −12.3182 + 7.11189i −1.06413 + 0.614374i
\(135\) −3.21558 + 5.56955i −0.276753 + 0.479350i
\(136\) 18.1238i 1.55410i
\(137\) −6.00394 3.46638i −0.512951 0.296153i 0.221095 0.975252i \(-0.429037\pi\)
−0.734046 + 0.679100i \(0.762370\pi\)
\(138\) −2.60927 + 1.50646i −0.222116 + 0.128239i
\(139\) 4.30215 0.364904 0.182452 0.983215i \(-0.441597\pi\)
0.182452 + 0.983215i \(0.441597\pi\)
\(140\) 7.48375 + 4.32075i 0.632493 + 0.365170i
\(141\) −3.51595 2.02993i −0.296096 0.170951i
\(142\) −7.80073 + 13.5113i −0.654623 + 1.13384i
\(143\) −0.638959 1.10671i −0.0534324 0.0925477i
\(144\) 4.74120 8.21199i 0.395100 0.684333i
\(145\) −13.9063 24.0864i −1.15486 2.00027i
\(146\) 10.1517i 0.840157i
\(147\) 1.16883 + 2.02448i 0.0964036 + 0.166976i
\(148\) −0.428773 + 0.742657i −0.0352449 + 0.0610460i
\(149\) −10.5014 + 6.06299i −0.860308 + 0.496699i −0.864115 0.503294i \(-0.832121\pi\)
0.00380732 + 0.999993i \(0.498788\pi\)
\(150\) 3.16812 1.82912i 0.258676 0.149347i
\(151\) −9.13473 + 15.8218i −0.743374 + 1.28756i 0.207577 + 0.978219i \(0.433442\pi\)
−0.950951 + 0.309343i \(0.899891\pi\)
\(152\) −14.2932 8.25219i −1.15933 0.669341i
\(153\) −5.69653 9.86668i −0.460537 0.797674i
\(154\) 0.805214 + 0.464891i 0.0648860 + 0.0374620i
\(155\) 10.8775 18.8403i 0.873698 1.51329i
\(156\) −2.98158 1.72142i −0.238717 0.137824i
\(157\) 11.6174 20.1219i 0.927170 1.60591i 0.139137 0.990273i \(-0.455567\pi\)
0.788033 0.615633i \(-0.211099\pi\)
\(158\) −10.1622 17.6014i −0.808459 1.40029i
\(159\) 1.31306 + 0.758093i 0.104132 + 0.0601207i
\(160\) 2.91663 1.68392i 0.230580 0.133125i
\(161\) 2.18569 + 1.26191i 0.172257 + 0.0994524i
\(162\) 19.0102i 1.49358i
\(163\) 6.19983i 0.485608i −0.970075 0.242804i \(-0.921933\pi\)
0.970075 0.242804i \(-0.0780672\pi\)
\(164\) −11.6845 + 20.2382i −0.912410 + 1.58034i
\(165\) 0.494841 0.285696i 0.0385233 0.0222414i
\(166\) −26.1349 15.0890i −2.02846 1.17113i
\(167\) 3.13488i 0.242584i −0.992617 0.121292i \(-0.961296\pi\)
0.992617 0.121292i \(-0.0387037\pi\)
\(168\) 1.21434 0.0936884
\(169\) −3.49702 + 6.05702i −0.269002 + 0.465925i
\(170\) 29.1608i 2.23653i
\(171\) −10.3751 −0.793402
\(172\) −12.8351 + 7.41034i −0.978667 + 0.565033i
\(173\) 1.11384 0.643075i 0.0846836 0.0488921i −0.457060 0.889436i \(-0.651098\pi\)
0.541744 + 0.840544i \(0.317764\pi\)
\(174\) −6.98196 4.03104i −0.529301 0.305592i
\(175\) −2.65382 1.53218i −0.200610 0.115822i
\(176\) −1.49254 + 0.861717i −0.112504 + 0.0649543i
\(177\) 2.53687 1.46466i 0.190683 0.110091i
\(178\) −4.98286 −0.373481
\(179\) 15.5840i 1.16480i 0.812901 + 0.582402i \(0.197887\pi\)
−0.812901 + 0.582402i \(0.802113\pi\)
\(180\) −16.8609 + 29.2040i −1.25674 + 2.17674i
\(181\) 21.6112 1.60635 0.803174 0.595745i \(-0.203143\pi\)
0.803174 + 0.595745i \(0.203143\pi\)
\(182\) 4.36979i 0.323910i
\(183\) 0.641847 + 0.370571i 0.0474467 + 0.0273934i
\(184\) −13.5681 + 7.83357i −1.00026 + 0.577498i
\(185\) 0.334446 0.579277i 0.0245890 0.0425893i
\(186\) 6.30612i 0.462387i
\(187\) 2.07070i 0.151425i
\(188\) −37.7135 21.7739i −2.75054 1.58802i
\(189\) 1.35237 0.780789i 0.0983702 0.0567941i
\(190\) 22.9975 + 13.2776i 1.66842 + 0.963261i
\(191\) 9.91040 + 17.1653i 0.717092 + 1.24204i 0.962147 + 0.272530i \(0.0878604\pi\)
−0.245056 + 0.969509i \(0.578806\pi\)
\(192\) 1.68422 2.91716i 0.121548 0.210528i
\(193\) 9.22880 + 5.32825i 0.664303 + 0.383536i 0.793915 0.608029i \(-0.208040\pi\)
−0.129611 + 0.991565i \(0.541373\pi\)
\(194\) 2.10199 3.64075i 0.150914 0.261390i
\(195\) 2.32565 + 1.34272i 0.166543 + 0.0961539i
\(196\) 12.5374 + 21.7153i 0.895525 + 1.55109i
\(197\) −8.39184 4.84503i −0.597894 0.345194i 0.170319 0.985389i \(-0.445520\pi\)
−0.768213 + 0.640195i \(0.778854\pi\)
\(198\) −1.81415 + 3.14221i −0.128926 + 0.223307i
\(199\) 6.82940 3.94295i 0.484123 0.279509i −0.238010 0.971263i \(-0.576495\pi\)
0.722133 + 0.691754i \(0.243162\pi\)
\(200\) 16.4741 9.51135i 1.16490 0.672554i
\(201\) 1.06124 1.83812i 0.0748541 0.129651i
\(202\) 16.0322 + 27.7686i 1.12802 + 1.95379i
\(203\) 6.75330i 0.473989i
\(204\) 2.78933 + 4.83126i 0.195292 + 0.338256i
\(205\) 9.11403 15.7860i 0.636551 1.10254i
\(206\) −6.24958 10.8246i −0.435429 0.754185i
\(207\) −4.92438 + 8.52928i −0.342268 + 0.592826i
\(208\) −7.01462 4.04989i −0.486377 0.280810i
\(209\) 1.63305 + 0.942840i 0.112960 + 0.0652176i
\(210\) −1.95385 −0.134829
\(211\) 23.0086 13.2840i 1.58398 0.914512i 0.589711 0.807615i \(-0.299242\pi\)
0.994270 0.106897i \(-0.0340915\pi\)
\(212\) 14.0844 + 8.13161i 0.967318 + 0.558481i
\(213\) 2.32806i 0.159516i
\(214\) −12.6096 + 21.8404i −0.861972 + 1.49298i
\(215\) 10.0115 5.78012i 0.682776 0.394201i
\(216\) 9.69382i 0.659581i
\(217\) −4.57469 + 2.64120i −0.310551 + 0.179296i
\(218\) 5.05494i 0.342364i
\(219\) 0.757417 + 1.31189i 0.0511815 + 0.0886490i
\(220\) 5.30786 3.06449i 0.357856 0.206608i
\(221\) −8.42805 + 4.86594i −0.566932 + 0.327318i
\(222\) 0.193892i 0.0130132i
\(223\) −16.4911 −1.10432 −0.552162 0.833737i \(-0.686197\pi\)
−0.552162 + 0.833737i \(0.686197\pi\)
\(224\) −0.817759 −0.0546388
\(225\) 5.97908 10.3561i 0.398605 0.690404i
\(226\) −21.0891 + 36.5275i −1.40283 + 2.42977i
\(227\) 6.11344 + 10.5888i 0.405763 + 0.702803i 0.994410 0.105588i \(-0.0336724\pi\)
−0.588647 + 0.808390i \(0.700339\pi\)
\(228\) 5.08020 0.336444
\(229\) −8.88316 + 5.12869i −0.587016 + 0.338914i −0.763917 0.645315i \(-0.776726\pi\)
0.176901 + 0.984229i \(0.443393\pi\)
\(230\) 21.8309 12.6041i 1.43949 0.831088i
\(231\) −0.138742 −0.00912858
\(232\) −36.3060 20.9613i −2.38360 1.37617i
\(233\) −5.22137 9.04367i −0.342063 0.592471i 0.642753 0.766074i \(-0.277792\pi\)
−0.984816 + 0.173603i \(0.944459\pi\)
\(234\) −17.0523 −1.11474
\(235\) 29.4168 + 16.9838i 1.91894 + 1.10790i
\(236\) 27.2114 15.7105i 1.77131 1.02267i
\(237\) 2.62649 + 1.51640i 0.170609 + 0.0985010i
\(238\) 3.54034 6.13204i 0.229486 0.397481i
\(239\) 9.22397 0.596649 0.298325 0.954464i \(-0.403572\pi\)
0.298325 + 0.954464i \(0.403572\pi\)
\(240\) 1.81082 3.13644i 0.116888 0.202456i
\(241\) 11.2243 19.4410i 0.723018 1.25230i −0.236767 0.971567i \(-0.576088\pi\)
0.959785 0.280737i \(-0.0905790\pi\)
\(242\) −22.5325 + 13.0092i −1.44845 + 0.836261i
\(243\) 4.60433 + 7.97494i 0.295368 + 0.511593i
\(244\) 6.88470 + 3.97489i 0.440748 + 0.254466i
\(245\) −9.77922 16.9381i −0.624771 1.08214i
\(246\) 5.28379i 0.336882i
\(247\) 8.86231i 0.563895i
\(248\) 32.7916i 2.08227i
\(249\) 4.50317 0.285377
\(250\) 5.29105 3.05479i 0.334635 0.193202i
\(251\) 6.35574i 0.401171i 0.979676 + 0.200585i \(0.0642844\pi\)
−0.979676 + 0.200585i \(0.935716\pi\)
\(252\) 7.09115 4.09408i 0.446701 0.257903i
\(253\) 1.55020 0.895011i 0.0974605 0.0562688i
\(254\) −3.98714 6.90592i −0.250175 0.433316i
\(255\) −2.17570 3.76842i −0.136247 0.235987i
\(256\) 15.3681 26.6183i 0.960504 1.66364i
\(257\) −21.2274 −1.32413 −0.662063 0.749448i \(-0.730319\pi\)
−0.662063 + 0.749448i \(0.730319\pi\)
\(258\) 1.67549 2.90203i 0.104311 0.180673i
\(259\) −0.140657 + 0.0812083i −0.00873999 + 0.00504604i
\(260\) 24.9459 + 14.4025i 1.54708 + 0.893205i
\(261\) −26.3536 −1.63124
\(262\) 11.0550 + 19.1479i 0.682983 + 1.18296i
\(263\) −22.0470 −1.35947 −0.679737 0.733456i \(-0.737906\pi\)
−0.679737 + 0.733456i \(0.737906\pi\)
\(264\) 0.430636 0.745884i 0.0265038 0.0459060i
\(265\) −10.9859 6.34271i −0.674858 0.389630i
\(266\) −3.22400 5.58413i −0.197676 0.342385i
\(267\) 0.643928 0.371772i 0.0394078 0.0227521i
\(268\) 11.3833 19.7164i 0.695344 1.20437i
\(269\) 28.4222 1.73293 0.866467 0.499234i \(-0.166385\pi\)
0.866467 + 0.499234i \(0.166385\pi\)
\(270\) 15.5972i 0.949215i
\(271\) −12.7708 22.1197i −0.775772 1.34368i −0.934360 0.356331i \(-0.884027\pi\)
0.158588 0.987345i \(-0.449306\pi\)
\(272\) 6.56233 + 11.3663i 0.397900 + 0.689182i
\(273\) −0.326031 0.564702i −0.0197323 0.0341773i
\(274\) 16.8137 1.01575
\(275\) −1.88222 + 1.08670i −0.113502 + 0.0655307i
\(276\) 2.41124 4.17640i 0.145140 0.251390i
\(277\) −22.7261 + 13.1209i −1.36548 + 0.788360i −0.990347 0.138611i \(-0.955736\pi\)
−0.375133 + 0.926971i \(0.622403\pi\)
\(278\) −9.03594 + 5.21690i −0.541940 + 0.312889i
\(279\) −10.3068 17.8519i −0.617053 1.06877i
\(280\) −10.1600 −0.607175
\(281\) −3.09788 + 5.36568i −0.184804 + 0.320090i −0.943510 0.331343i \(-0.892498\pi\)
0.758707 + 0.651433i \(0.225832\pi\)
\(282\) 9.84621 0.586333
\(283\) 25.6860 1.52688 0.763438 0.645881i \(-0.223510\pi\)
0.763438 + 0.645881i \(0.223510\pi\)
\(284\) 24.9717i 1.48179i
\(285\) −3.96259 −0.234724
\(286\) 2.68405 + 1.54964i 0.158711 + 0.0916320i
\(287\) −3.83306 + 2.21302i −0.226258 + 0.130630i
\(288\) 3.19116i 0.188041i
\(289\) −1.23076 −0.0723978
\(290\) 58.4157 + 33.7263i 3.43029 + 1.98048i
\(291\) 0.627319i 0.0367741i
\(292\) 8.12436 + 14.0718i 0.475442 + 0.823490i
\(293\) −7.60089 13.1651i −0.444049 0.769115i 0.553936 0.832559i \(-0.313125\pi\)
−0.997985 + 0.0634435i \(0.979792\pi\)
\(294\) −4.90987 2.83471i −0.286349 0.165324i
\(295\) −21.2251 + 12.2543i −1.23577 + 0.713474i
\(296\) 1.00823i 0.0586024i
\(297\) 1.10755i 0.0642666i
\(298\) 14.7043 25.4686i 0.851796 1.47535i
\(299\) 7.28565 + 4.20637i 0.421340 + 0.243261i
\(300\) −2.92768 + 5.07089i −0.169030 + 0.292768i
\(301\) −2.80699 −0.161792
\(302\) 44.3081i 2.54964i
\(303\) −4.14365 2.39234i −0.238046 0.137436i
\(304\) 11.9519 0.685491
\(305\) −5.37012 3.10044i −0.307492 0.177531i
\(306\) 23.9292 + 13.8155i 1.36794 + 0.789781i
\(307\) 10.9489 + 18.9641i 0.624887 + 1.08234i 0.988563 + 0.150811i \(0.0481885\pi\)
−0.363675 + 0.931526i \(0.618478\pi\)
\(308\) −1.48821 −0.0847984
\(309\) 1.61525 + 0.932565i 0.0918883 + 0.0530518i
\(310\) 52.7612i 2.99663i
\(311\) 13.1461i 0.745445i 0.927943 + 0.372723i \(0.121576\pi\)
−0.927943 + 0.372723i \(0.878424\pi\)
\(312\) 4.04781 0.229162
\(313\) −6.70566 −0.379026 −0.189513 0.981878i \(-0.560691\pi\)
−0.189513 + 0.981878i \(0.560691\pi\)
\(314\) 56.3503i 3.18003i
\(315\) −5.53115 + 3.19341i −0.311645 + 0.179928i
\(316\) 28.1728 + 16.2655i 1.58484 + 0.915009i
\(317\) 0.958606 + 0.553452i 0.0538407 + 0.0310849i 0.526679 0.850064i \(-0.323437\pi\)
−0.472838 + 0.881149i \(0.656770\pi\)
\(318\) −3.67714 −0.206204
\(319\) 4.14807 + 2.39489i 0.232248 + 0.134088i
\(320\) −14.0913 + 24.4069i −0.787728 + 1.36439i
\(321\) 3.76321i 0.210042i
\(322\) −6.12090 −0.341105
\(323\) 7.18011 12.4363i 0.399512 0.691975i
\(324\) 15.2138 + 26.3511i 0.845212 + 1.46395i
\(325\) −8.84608 5.10728i −0.490692 0.283301i
\(326\) 7.51808 + 13.0217i 0.416388 + 0.721205i
\(327\) −0.377150 0.653244i −0.0208565 0.0361245i
\(328\) 27.4755i 1.51708i
\(329\) −4.12390 7.14281i −0.227358 0.393796i
\(330\) −0.692886 + 1.20011i −0.0381421 + 0.0660641i
\(331\) −7.82194 4.51600i −0.429933 0.248222i 0.269385 0.963033i \(-0.413180\pi\)
−0.699318 + 0.714811i \(0.746513\pi\)
\(332\) 48.3028 2.65096
\(333\) −0.316901 0.548888i −0.0173661 0.0300789i
\(334\) 3.80143 + 6.58428i 0.208005 + 0.360276i
\(335\) −8.87903 + 15.3789i −0.485113 + 0.840241i
\(336\) −0.761572 + 0.439694i −0.0415471 + 0.0239872i
\(337\) 8.11116 + 14.0489i 0.441843 + 0.765295i 0.997826 0.0658988i \(-0.0209914\pi\)
−0.555983 + 0.831194i \(0.687658\pi\)
\(338\) 16.9623i 0.922629i
\(339\) 6.29386i 0.341836i
\(340\) −23.3374 40.4215i −1.26565 2.19217i
\(341\) 3.74655i 0.202887i
\(342\) 21.7911 12.5811i 1.17833 0.680307i
\(343\) 9.89555i 0.534309i
\(344\) 8.71249 15.0905i 0.469746 0.813624i
\(345\) −1.88079 + 3.25762i −0.101258 + 0.175384i
\(346\) −1.55962 + 2.70134i −0.0838457 + 0.145225i
\(347\) 18.4115 10.6299i 0.988380 0.570641i 0.0835902 0.996500i \(-0.473361\pi\)
0.904790 + 0.425859i \(0.140028\pi\)
\(348\) 12.9041 0.691734
\(349\) −11.6439 + 14.6089i −0.623282 + 0.781997i
\(350\) 7.43187 0.397250
\(351\) 4.50789 2.60263i 0.240613 0.138918i
\(352\) −0.289998 + 0.502292i −0.0154570 + 0.0267722i
\(353\) 3.12925 5.42003i 0.166553 0.288479i −0.770652 0.637256i \(-0.780070\pi\)
0.937206 + 0.348777i \(0.113403\pi\)
\(354\) −3.55218 + 6.15255i −0.188796 + 0.327004i
\(355\) 19.4781i 1.03379i
\(356\) 6.90703 3.98778i 0.366072 0.211352i
\(357\) 1.05658i 0.0559202i
\(358\) −18.8976 32.7316i −0.998769 1.72992i
\(359\) 31.8355i 1.68021i −0.542422 0.840106i \(-0.682493\pi\)
0.542422 0.840106i \(-0.317507\pi\)
\(360\) 39.6475i 2.08961i
\(361\) 2.96144 + 5.12937i 0.155865 + 0.269967i
\(362\) −45.3907 + 26.2063i −2.38568 + 1.37737i
\(363\) 1.94123 3.36232i 0.101888 0.176476i
\(364\) −3.49713 6.05721i −0.183300 0.317484i
\(365\) −6.33705 10.9761i −0.331697 0.574515i
\(366\) −1.79745 −0.0939545
\(367\) 7.70111 + 4.44624i 0.401995 + 0.232092i 0.687344 0.726332i \(-0.258776\pi\)
−0.285350 + 0.958424i \(0.592110\pi\)
\(368\) 5.67282 9.82561i 0.295716 0.512196i
\(369\) −8.63590 14.9578i −0.449567 0.778673i
\(370\) 1.62223i 0.0843358i
\(371\) 1.54010 + 2.66753i 0.0799580 + 0.138491i
\(372\) 5.04678 + 8.74128i 0.261663 + 0.453214i
\(373\) −22.3071 12.8790i −1.15502 0.666851i −0.204914 0.978780i \(-0.565691\pi\)
−0.950105 + 0.311929i \(0.899025\pi\)
\(374\) −2.51099 4.34916i −0.129840 0.224889i
\(375\) −0.455837 + 0.789533i −0.0235393 + 0.0407713i
\(376\) 51.2000 2.64044
\(377\) 22.5110i 1.15938i
\(378\) −1.89361 + 3.27983i −0.0973969 + 0.168696i
\(379\) 16.6729 + 9.62609i 0.856428 + 0.494459i 0.862814 0.505521i \(-0.168700\pi\)
−0.00638661 + 0.999980i \(0.502033\pi\)
\(380\) −42.5043 −2.18042
\(381\) 1.03051 + 0.594962i 0.0527944 + 0.0304808i
\(382\) −41.6303 24.0352i −2.12999 1.22975i
\(383\) −12.0088 + 6.93326i −0.613619 + 0.354273i −0.774381 0.632720i \(-0.781938\pi\)
0.160761 + 0.986993i \(0.448605\pi\)
\(384\) 7.36427i 0.375806i
\(385\) 1.16081 0.0591604
\(386\) −25.8447 −1.31546
\(387\) 10.9538i 0.556812i
\(388\) 6.72887i 0.341606i
\(389\) 31.4674 + 18.1677i 1.59546 + 0.921139i 0.992347 + 0.123483i \(0.0394065\pi\)
0.603113 + 0.797656i \(0.293927\pi\)
\(390\) −6.51285 −0.329791
\(391\) −6.81588 11.8054i −0.344694 0.597027i
\(392\) −25.5311 14.7404i −1.28952 0.744503i
\(393\) −2.85726 1.64964i −0.144130 0.0832132i
\(394\) 23.5009 1.18396
\(395\) −21.9749 12.6872i −1.10568 0.638364i
\(396\) 5.80746i 0.291836i
\(397\) 26.0140 1.30561 0.652803 0.757528i \(-0.273593\pi\)
0.652803 + 0.757528i \(0.273593\pi\)
\(398\) −9.56267 + 16.5630i −0.479333 + 0.830229i
\(399\) 0.833267 + 0.481087i 0.0417155 + 0.0240845i
\(400\) −6.88782 + 11.9301i −0.344391 + 0.596503i
\(401\) 25.0199i 1.24943i −0.780851 0.624717i \(-0.785214\pi\)
0.780851 0.624717i \(-0.214786\pi\)
\(402\) 5.14755i 0.256737i
\(403\) −15.2490 + 8.80401i −0.759607 + 0.438559i
\(404\) −44.4464 25.6611i −2.21129 1.27669i
\(405\) −11.8669 20.5540i −0.589670 1.02134i
\(406\) −8.18923 14.1842i −0.406425 0.703948i
\(407\) 0.115194i 0.00570996i
\(408\) −5.68021 3.27947i −0.281212 0.162358i
\(409\) 29.9009 1.47850 0.739252 0.673429i \(-0.235179\pi\)
0.739252 + 0.673429i \(0.235179\pi\)
\(410\) 44.2077i 2.18326i
\(411\) −2.17281 + 1.25447i −0.107177 + 0.0618786i
\(412\) 17.3258 + 10.0031i 0.853581 + 0.492815i
\(413\) 5.95105 0.292832
\(414\) 23.8857i 1.17392i
\(415\) −37.6765 −1.84947
\(416\) −2.72587 −0.133647
\(417\) 0.778469 1.34835i 0.0381218 0.0660288i
\(418\) −4.57325 −0.223685
\(419\) 1.61419 + 2.79586i 0.0788583 + 0.136587i 0.902758 0.430150i \(-0.141539\pi\)
−0.823899 + 0.566736i \(0.808206\pi\)
\(420\) 2.70835 1.56367i 0.132154 0.0762991i
\(421\) −18.3736 + 10.6080i −0.895473 + 0.517002i −0.875729 0.482804i \(-0.839619\pi\)
−0.0197442 + 0.999805i \(0.506285\pi\)
\(422\) −32.2172 + 55.8018i −1.56831 + 2.71639i
\(423\) 27.8735 16.0928i 1.35526 0.782459i
\(424\) −19.1210 −0.928597
\(425\) 8.27569 + 14.3339i 0.401430 + 0.695297i
\(426\) 2.82306 + 4.88969i 0.136778 + 0.236906i
\(427\) 0.752831 + 1.30394i 0.0364320 + 0.0631021i
\(428\) 40.3657i 1.95115i
\(429\) −0.462475 −0.0223285
\(430\) −14.0183 + 24.2803i −0.676020 + 1.17090i
\(431\) 9.42400 5.44095i 0.453938 0.262081i −0.255554 0.966795i \(-0.582258\pi\)
0.709492 + 0.704713i \(0.248924\pi\)
\(432\) −3.50998 6.07946i −0.168874 0.292498i
\(433\) 27.3923 + 15.8149i 1.31639 + 0.760018i 0.983146 0.182823i \(-0.0585235\pi\)
0.333244 + 0.942841i \(0.391857\pi\)
\(434\) 6.40558 11.0948i 0.307478 0.532567i
\(435\) −10.0653 −0.482595
\(436\) −4.04547 7.00695i −0.193743 0.335572i
\(437\) −12.4137 −0.593829
\(438\) −3.18165 1.83693i −0.152025 0.0877719i
\(439\) 21.9273 12.6597i 1.04653 0.604215i 0.124855 0.992175i \(-0.460153\pi\)
0.921676 + 0.387960i \(0.126820\pi\)
\(440\) −3.60299 + 6.24056i −0.171766 + 0.297507i
\(441\) −18.5324 −0.882495
\(442\) 11.8011 20.4402i 0.561322 0.972239i
\(443\) 19.6701 + 34.0696i 0.934554 + 1.61869i 0.775428 + 0.631436i \(0.217534\pi\)
0.159126 + 0.987258i \(0.449132\pi\)
\(444\) 0.155172 + 0.268766i 0.00736413 + 0.0127551i
\(445\) −5.38753 + 3.11049i −0.255393 + 0.147451i
\(446\) 34.6367 19.9975i 1.64010 0.946910i
\(447\) 4.38836i 0.207562i
\(448\) 5.92634 3.42157i 0.279993 0.161654i
\(449\) −1.85843 −0.0877046 −0.0438523 0.999038i \(-0.513963\pi\)
−0.0438523 + 0.999038i \(0.513963\pi\)
\(450\) 29.0016i 1.36715i
\(451\) 3.13917i 0.147818i
\(452\) 67.5104i 3.17542i
\(453\) 3.30584 + 5.72588i 0.155322 + 0.269025i
\(454\) −25.6805 14.8266i −1.20525 0.695849i
\(455\) 2.72779 + 4.72467i 0.127881 + 0.221496i
\(456\) −5.17268 + 2.98645i −0.242233 + 0.139853i
\(457\) 2.49905 4.32848i 0.116900 0.202478i −0.801637 0.597811i \(-0.796037\pi\)
0.918538 + 0.395333i \(0.129371\pi\)
\(458\) 12.4384 21.5439i 0.581207 1.00668i
\(459\) −8.43446 −0.393687
\(460\) −20.1741 + 34.9425i −0.940620 + 1.62920i
\(461\) −12.3731 7.14359i −0.576271 0.332710i 0.183379 0.983042i \(-0.441296\pi\)
−0.759650 + 0.650332i \(0.774630\pi\)
\(462\) 0.291405 0.168243i 0.0135574 0.00782736i
\(463\) −0.874914 0.505132i −0.0406607 0.0234755i 0.479532 0.877524i \(-0.340806\pi\)
−0.520193 + 0.854049i \(0.674140\pi\)
\(464\) 30.3589 1.40938
\(465\) −3.93652 6.81826i −0.182552 0.316189i
\(466\) 21.9332 + 12.6631i 1.01604 + 0.586608i
\(467\) 39.1229 1.81039 0.905195 0.424996i \(-0.139724\pi\)
0.905195 + 0.424996i \(0.139724\pi\)
\(468\) 23.6372 13.6469i 1.09263 0.630830i
\(469\) 3.73423 2.15596i 0.172431 0.0995528i
\(470\) −82.3799 −3.79990
\(471\) −4.20431 7.28208i −0.193724 0.335540i
\(472\) −18.4712 + 31.9930i −0.850206 + 1.47260i
\(473\) −0.995431 + 1.72414i −0.0457699 + 0.0792759i
\(474\) −7.35533 −0.337841
\(475\) 15.0725 0.691573
\(476\) 11.3333i 0.519461i
\(477\) −10.4096 + 6.00997i −0.476622 + 0.275178i
\(478\) −19.3734 + 11.1852i −0.886118 + 0.511601i
\(479\) −7.93792 13.7489i −0.362693 0.628202i 0.625710 0.780056i \(-0.284809\pi\)
−0.988403 + 0.151853i \(0.951476\pi\)
\(480\) 1.21881i 0.0556309i
\(481\) −0.468857 + 0.270694i −0.0213780 + 0.0123426i
\(482\) 54.4433i 2.47983i
\(483\) 0.790996 0.456682i 0.0359916 0.0207797i
\(484\) 20.8224 36.0655i 0.946475 1.63934i
\(485\) 5.24856i 0.238325i
\(486\) −19.3412 11.1667i −0.877337 0.506531i
\(487\) −22.8934 + 13.2175i −1.03740 + 0.598943i −0.919096 0.394034i \(-0.871079\pi\)
−0.118305 + 0.992977i \(0.537746\pi\)
\(488\) −9.34671 −0.423106
\(489\) −1.94310 1.12185i −0.0878702 0.0507319i
\(490\) 41.0792 + 23.7171i 1.85577 + 1.07143i
\(491\) −16.3994 + 28.4046i −0.740094 + 1.28188i 0.212359 + 0.977192i \(0.431885\pi\)
−0.952452 + 0.304688i \(0.901448\pi\)
\(492\) 4.22861 + 7.32416i 0.190640 + 0.330199i
\(493\) 18.2381 31.5893i 0.821402 1.42271i
\(494\) −10.7467 18.6138i −0.483516 0.837474i
\(495\) 4.52986i 0.203602i
\(496\) 11.8733 + 20.5652i 0.533128 + 0.923405i
\(497\) 2.36478 4.09591i 0.106075 0.183727i
\(498\) −9.45814 + 5.46066i −0.423830 + 0.244698i
\(499\) 28.7892 16.6214i 1.28878 0.744078i 0.310343 0.950624i \(-0.399556\pi\)
0.978437 + 0.206547i \(0.0662226\pi\)
\(500\) −4.88949 + 8.46884i −0.218665 + 0.378738i
\(501\) −0.982509 0.567252i −0.0438953 0.0253429i
\(502\) −7.70714 13.3492i −0.343986 0.595802i
\(503\) −23.9983 13.8554i −1.07003 0.617782i −0.141840 0.989890i \(-0.545302\pi\)
−0.928190 + 0.372107i \(0.878635\pi\)
\(504\) −4.81349 + 8.33721i −0.214410 + 0.371369i
\(505\) 34.6685 + 20.0159i 1.54273 + 0.890694i
\(506\) −2.17063 + 3.75964i −0.0964962 + 0.167136i
\(507\) 1.26556 + 2.19202i 0.0562056 + 0.0973510i
\(508\) 11.0536 + 6.38180i 0.490424 + 0.283147i
\(509\) 32.1348 18.5530i 1.42435 0.822348i 0.427682 0.903929i \(-0.359330\pi\)
0.996667 + 0.0815813i \(0.0259970\pi\)
\(510\) 9.13937 + 5.27662i 0.404698 + 0.233653i
\(511\) 3.07745i 0.136139i
\(512\) 33.8448i 1.49574i
\(513\) −3.84041 + 6.65179i −0.169558 + 0.293684i
\(514\) 44.5845 25.7409i 1.96654 1.13538i
\(515\) −13.5142 7.80245i −0.595509 0.343817i
\(516\) 5.36357i 0.236118i
\(517\) −5.84976 −0.257272
\(518\) 0.196951 0.341129i 0.00865351 0.0149883i
\(519\) 0.465455i 0.0204312i
\(520\) −33.8666 −1.48515
\(521\) −15.4685 + 8.93072i −0.677686 + 0.391262i −0.798982 0.601354i \(-0.794628\pi\)
0.121297 + 0.992616i \(0.461295\pi\)
\(522\) 55.3512 31.9570i 2.42266 1.39872i
\(523\) 2.30768 + 1.33234i 0.100908 + 0.0582590i 0.549605 0.835425i \(-0.314778\pi\)
−0.448697 + 0.893684i \(0.648112\pi\)
\(524\) −30.6481 17.6947i −1.33887 0.772995i
\(525\) −0.960411 + 0.554494i −0.0419158 + 0.0242001i
\(526\) 46.3059 26.7347i 2.01903 1.16569i
\(527\) 28.5315 1.24285
\(528\) 0.623706i 0.0271433i
\(529\) 5.60800 9.71334i 0.243826 0.422319i
\(530\) 30.7654 1.33636
\(531\) 23.2229i 1.00779i
\(532\) 8.93795 + 5.16033i 0.387509 + 0.223729i
\(533\) −12.7769 + 7.37673i −0.553428 + 0.319522i
\(534\) −0.901642 + 1.56169i −0.0390179 + 0.0675809i
\(535\) 31.4855i 1.36124i
\(536\) 26.7671i 1.15616i
\(537\) 4.88422 + 2.81991i 0.210770 + 0.121688i
\(538\) −59.6961 + 34.4656i −2.57368 + 1.48592i
\(539\) 2.91702 + 1.68414i 0.125645 + 0.0725411i
\(540\) 12.4824 + 21.6202i 0.537158 + 0.930384i
\(541\) −10.8052 + 18.7152i −0.464554 + 0.804631i −0.999181 0.0404571i \(-0.987119\pi\)
0.534628 + 0.845088i \(0.320452\pi\)
\(542\) 53.6459 + 30.9725i 2.30429 + 1.33038i
\(543\) 3.91052 6.77322i 0.167816 0.290667i
\(544\) 3.82516 + 2.20846i 0.164002 + 0.0946868i
\(545\) 3.15549 + 5.46547i 0.135166 + 0.234115i
\(546\) 1.36954 + 0.790707i 0.0586111 + 0.0338391i
\(547\) −6.75459 + 11.6993i −0.288806 + 0.500226i −0.973525 0.228581i \(-0.926591\pi\)
0.684719 + 0.728807i \(0.259925\pi\)
\(548\) −23.3064 + 13.4560i −0.995601 + 0.574811i
\(549\) −5.08840 + 2.93779i −0.217168 + 0.125382i
\(550\) 2.63553 4.56487i 0.112379 0.194647i
\(551\) −16.6085 28.7667i −0.707545 1.22550i
\(552\) 5.66990i 0.241327i
\(553\) 3.08064 + 5.33583i 0.131002 + 0.226903i
\(554\) 31.8216 55.1166i 1.35197 2.34168i
\(555\) −0.121035 0.209639i −0.00513765 0.00889868i
\(556\) 8.35016 14.4629i 0.354126 0.613364i
\(557\) 2.27924 + 1.31592i 0.0965745 + 0.0557573i 0.547509 0.836800i \(-0.315576\pi\)
−0.450935 + 0.892557i \(0.648909\pi\)
\(558\) 43.2955 + 24.9967i 1.83284 + 1.05819i
\(559\) −9.35664 −0.395744
\(560\) 6.37181 3.67877i 0.269258 0.155456i
\(561\) 0.648983 + 0.374690i 0.0274001 + 0.0158194i
\(562\) 15.0263i 0.633845i
\(563\) 2.68767 4.65518i 0.113272 0.196193i −0.803816 0.594878i \(-0.797200\pi\)
0.917088 + 0.398686i \(0.130534\pi\)
\(564\) −13.6484 + 7.87991i −0.574701 + 0.331804i
\(565\) 52.6586i 2.21536i
\(566\) −53.9492 + 31.1476i −2.26765 + 1.30923i
\(567\) 5.76290i 0.242019i
\(568\) 14.6798 + 25.4262i 0.615952 + 1.06686i
\(569\) −39.3688 + 22.7296i −1.65043 + 0.952874i −0.673531 + 0.739159i \(0.735223\pi\)
−0.976896 + 0.213715i \(0.931444\pi\)
\(570\) 8.32275 4.80514i 0.348602 0.201265i
\(571\) 45.0105i 1.88363i −0.336131 0.941815i \(-0.609118\pi\)
0.336131 0.941815i \(-0.390882\pi\)
\(572\) −4.96069 −0.207417
\(573\) 7.17310 0.299660
\(574\) 5.36713 9.29614i 0.224020 0.388013i
\(575\) 7.15394 12.3910i 0.298340 0.516740i
\(576\) 13.3521 + 23.1265i 0.556337 + 0.963603i
\(577\) −19.7927 −0.823983 −0.411991 0.911188i \(-0.635167\pi\)
−0.411991 + 0.911188i \(0.635167\pi\)
\(578\) 2.58501 1.49246i 0.107522 0.0620779i
\(579\) 3.33988 1.92828i 0.138801 0.0801365i
\(580\) −107.964 −4.48298
\(581\) 7.92274 + 4.57419i 0.328691 + 0.189770i
\(582\) −0.760703 1.31758i −0.0315322 0.0546153i
\(583\) 2.18464 0.0904784
\(584\) −16.5445 9.55197i −0.684616 0.395263i
\(585\) −18.4372 + 10.6447i −0.762283 + 0.440105i
\(586\) 31.9288 + 18.4341i 1.31897 + 0.761506i
\(587\) 11.7353 20.3262i 0.484368 0.838950i −0.515470 0.856907i \(-0.672383\pi\)
0.999839 + 0.0179569i \(0.00571616\pi\)
\(588\) 9.07447 0.374225
\(589\) 12.9911 22.5012i 0.535288 0.927147i
\(590\) 29.7198 51.4763i 1.22355 2.11924i
\(591\) −3.03699 + 1.75340i −0.124925 + 0.0721254i
\(592\) 0.365066 + 0.632312i 0.0150041 + 0.0259879i
\(593\) −1.11329 0.642757i −0.0457172 0.0263949i 0.476967 0.878921i \(-0.341736\pi\)
−0.522684 + 0.852526i \(0.675069\pi\)
\(594\) 1.34305 + 2.32622i 0.0551058 + 0.0954461i
\(595\) 8.84005i 0.362407i
\(596\) 47.0713i 1.92811i
\(597\) 2.85389i 0.116802i
\(598\) −20.4030 −0.834342
\(599\) −13.2550 + 7.65277i −0.541584 + 0.312684i −0.745721 0.666259i \(-0.767895\pi\)
0.204136 + 0.978942i \(0.434561\pi\)
\(600\) 6.88427i 0.281049i
\(601\) −29.6757 + 17.1332i −1.21050 + 0.698880i −0.962867 0.269975i \(-0.912984\pi\)
−0.247628 + 0.968855i \(0.579651\pi\)
\(602\) 5.89561 3.40383i 0.240287 0.138730i
\(603\) 8.41324 + 14.5722i 0.342614 + 0.593424i
\(604\) 35.4597 + 61.4180i 1.44283 + 2.49906i
\(605\) −16.2416 + 28.1314i −0.660317 + 1.14370i
\(606\) 11.6040 0.471382
\(607\) 15.2307 26.3803i 0.618195 1.07075i −0.371620 0.928385i \(-0.621198\pi\)
0.989815 0.142360i \(-0.0454691\pi\)
\(608\) 3.48337 2.01113i 0.141269 0.0815620i
\(609\) 2.11657 + 1.22200i 0.0857676 + 0.0495180i
\(610\) 15.0387 0.608899
\(611\) −13.7464 23.8094i −0.556118 0.963224i
\(612\) −44.2262 −1.78774
\(613\) 10.4814 18.1543i 0.423340 0.733247i −0.572924 0.819609i \(-0.694191\pi\)
0.996264 + 0.0863619i \(0.0275241\pi\)
\(614\) −45.9927 26.5539i −1.85611 1.07163i
\(615\) −3.29834 5.71290i −0.133002 0.230366i
\(616\) 1.51530 0.874857i 0.0610530 0.0352490i
\(617\) 18.5830 32.1867i 0.748122 1.29579i −0.200599 0.979673i \(-0.564289\pi\)
0.948722 0.316113i \(-0.102378\pi\)
\(618\) −4.52341 −0.181958
\(619\) 21.8856i 0.879656i −0.898082 0.439828i \(-0.855039\pi\)
0.898082 0.439828i \(-0.144961\pi\)
\(620\) −42.2247 73.1353i −1.69578 2.93718i
\(621\) 3.64559 + 6.31435i 0.146293 + 0.253386i
\(622\) −15.9413 27.6111i −0.639187 1.10710i
\(623\) 1.51054 0.0605187
\(624\) −2.53857 + 1.46565i −0.101624 + 0.0586728i
\(625\) 14.2339 24.6538i 0.569355 0.986151i
\(626\) 14.0841 8.13146i 0.562914 0.324999i
\(627\) 0.590995 0.341211i 0.0236021 0.0136267i
\(628\) −45.0971 78.1105i −1.79957 3.11695i
\(629\) 0.877251 0.0349783
\(630\) 7.74483 13.4144i 0.308561 0.534444i
\(631\) −20.1531 −0.802282 −0.401141 0.916016i \(-0.631386\pi\)
−0.401141 + 0.916016i \(0.631386\pi\)
\(632\) −38.2475 −1.52140
\(633\) 9.61493i 0.382159i
\(634\) −2.68452 −0.106616
\(635\) −8.62189 4.97785i −0.342149 0.197540i
\(636\) 5.09709 2.94281i 0.202113 0.116690i
\(637\) 15.8302i 0.627217i
\(638\) −11.6164 −0.459899
\(639\) 15.9836 + 9.22812i 0.632300 + 0.365059i
\(640\) 61.6143i 2.43552i
\(641\) 11.0077 + 19.0658i 0.434776 + 0.753054i 0.997277 0.0737420i \(-0.0234941\pi\)
−0.562501 + 0.826797i \(0.690161\pi\)
\(642\) 4.56337 + 7.90399i 0.180102 + 0.311945i
\(643\) −9.99492 5.77057i −0.394161 0.227569i 0.289800 0.957087i \(-0.406411\pi\)
−0.683962 + 0.729518i \(0.739744\pi\)
\(644\) 8.48454 4.89855i 0.334338 0.193030i
\(645\) 4.18362i 0.164730i
\(646\) 34.8272i 1.37026i
\(647\) −7.33821 + 12.7102i −0.288495 + 0.499688i −0.973451 0.228897i \(-0.926488\pi\)
0.684956 + 0.728585i \(0.259822\pi\)
\(648\) −30.9815 17.8872i −1.21707 0.702675i
\(649\) 2.11039 3.65531i 0.0828402 0.143483i
\(650\) 24.7729 0.971674
\(651\) 1.91169i 0.0749249i
\(652\) −20.8425 12.0334i −0.816255 0.471265i
\(653\) 14.3875 0.563025 0.281513 0.959557i \(-0.409164\pi\)
0.281513 + 0.959557i \(0.409164\pi\)
\(654\) 1.58428 + 0.914686i 0.0619503 + 0.0357670i
\(655\) 23.9057 + 13.8020i 0.934073 + 0.539287i
\(656\) 9.94845 + 17.2312i 0.388422 + 0.672766i
\(657\) −12.0092 −0.468524
\(658\) 17.3231 + 10.0015i 0.675326 + 0.389899i
\(659\) 20.9536i 0.816237i −0.912929 0.408118i \(-0.866185\pi\)
0.912929 0.408118i \(-0.133815\pi\)
\(660\) 2.21806i 0.0863380i
\(661\) −21.7182 −0.844741 −0.422371 0.906423i \(-0.638802\pi\)
−0.422371 + 0.906423i \(0.638802\pi\)
\(662\) 21.9049 0.851358
\(663\) 3.52194i 0.136781i
\(664\) −49.1820 + 28.3953i −1.90863 + 1.10195i
\(665\) −6.97166 4.02509i −0.270349 0.156086i
\(666\) 1.33119 + 0.768565i 0.0515827 + 0.0297813i
\(667\) −31.5319 −1.22092
\(668\) −10.5388 6.08457i −0.407758 0.235419i
\(669\) −2.98404 + 5.16851i −0.115370 + 0.199826i
\(670\) 43.0678i 1.66385i
\(671\) 1.06789 0.0412255
\(672\) −0.147972 + 0.256296i −0.00570816 + 0.00988683i
\(673\) 3.77092 + 6.53143i 0.145358 + 0.251768i 0.929507 0.368805i \(-0.120233\pi\)
−0.784148 + 0.620574i \(0.786900\pi\)
\(674\) −34.0723 19.6716i −1.31241 0.757723i
\(675\) −4.42640 7.66675i −0.170372 0.295093i
\(676\) 13.5749 + 23.5125i 0.522113 + 0.904326i
\(677\) 0.154122i 0.00592337i −0.999996 0.00296169i \(-0.999057\pi\)
0.999996 0.00296169i \(-0.000942735\pi\)
\(678\) 7.63210 + 13.2192i 0.293109 + 0.507680i
\(679\) −0.637213 + 1.10369i −0.0244540 + 0.0423556i
\(680\) 47.5244 + 27.4382i 1.82248 + 1.05221i
\(681\) 4.42488 0.169562
\(682\) −4.54317 7.86899i −0.173967 0.301319i
\(683\) 18.6919 + 32.3754i 0.715228 + 1.23881i 0.962872 + 0.269959i \(0.0870103\pi\)
−0.247644 + 0.968851i \(0.579656\pi\)
\(684\) −20.1373 + 34.8788i −0.769967 + 1.33362i
\(685\) 18.1792 10.4958i 0.694590 0.401022i
\(686\) −11.9996 20.7839i −0.458147 0.793534i
\(687\) 3.71212i 0.141626i
\(688\) 12.6186i 0.481080i
\(689\) 5.13367 + 8.89178i 0.195577 + 0.338750i
\(690\) 9.12277i 0.347298i
\(691\) −27.5523 + 15.9073i −1.04814 + 0.605143i −0.922128 0.386885i \(-0.873551\pi\)
−0.126011 + 0.992029i \(0.540218\pi\)
\(692\) 4.99265i 0.189792i
\(693\) 0.549957 0.952554i 0.0208911 0.0361845i
\(694\) −25.7801 + 44.6525i −0.978600 + 1.69499i
\(695\) −6.51318 + 11.2812i −0.247059 + 0.427919i
\(696\) −13.1390 + 7.58582i −0.498034 + 0.287540i
\(697\) 23.9061 0.905507
\(698\) 6.74080 44.8032i 0.255143 1.69583i
\(699\) −3.77920 −0.142942
\(700\) −10.3017 + 5.94772i −0.389369 + 0.224803i
\(701\) 20.3238 35.2018i 0.767619 1.32956i −0.171232 0.985231i \(-0.554775\pi\)
0.938851 0.344324i \(-0.111892\pi\)
\(702\) −6.31204 + 10.9328i −0.238233 + 0.412631i
\(703\) 0.399433 0.691839i 0.0150649 0.0260932i
\(704\) 4.85351i 0.182923i
\(705\) 10.6458 6.14638i 0.400946 0.231486i
\(706\) 15.1785i 0.571249i
\(707\) −4.86014 8.41800i −0.182784 0.316592i
\(708\) 11.3712i 0.427356i
\(709\) 9.70847i 0.364609i 0.983242 + 0.182305i \(0.0583557\pi\)
−0.983242 + 0.182305i \(0.941644\pi\)
\(710\) −23.6196 40.9104i −0.886428 1.53534i
\(711\) −20.8221 + 12.0217i −0.780891 + 0.450848i
\(712\) −4.68851 + 8.12073i −0.175709 + 0.304337i
\(713\) −12.3321 21.3598i −0.461840 0.799930i
\(714\) −1.28124 2.21917i −0.0479491 0.0830503i
\(715\) 3.86937 0.144706
\(716\) 52.3901 + 30.2474i 1.95791 + 1.13040i
\(717\) 1.66907 2.89091i 0.0623324 0.107963i
\(718\) 38.6045 + 66.8650i 1.44071 + 2.49538i
\(719\) 41.3961i 1.54381i −0.635736 0.771907i \(-0.719303\pi\)
0.635736 0.771907i \(-0.280697\pi\)
\(720\) 14.3557 + 24.8649i 0.535007 + 0.926659i
\(721\) 1.89455 + 3.28145i 0.0705566 + 0.122208i
\(722\) −12.4400 7.18225i −0.462970 0.267296i
\(723\) −4.06203 7.03564i −0.151068 0.261658i
\(724\) 41.9458 72.6522i 1.55890 2.70010i
\(725\) 38.2854 1.42188
\(726\) 9.41597i 0.349459i
\(727\) −15.6259 + 27.0648i −0.579531 + 1.00378i 0.416002 + 0.909364i \(0.363431\pi\)
−0.995533 + 0.0944133i \(0.969902\pi\)
\(728\) 7.12159 + 4.11165i 0.263944 + 0.152388i
\(729\) −20.1827 −0.747507
\(730\) 26.6198 + 15.3690i 0.985244 + 0.568831i
\(731\) 13.1300 + 7.58062i 0.485631 + 0.280379i
\(732\) 2.49156 1.43850i 0.0920906 0.0531685i
\(733\) 38.8971i 1.43670i 0.695684 + 0.718348i \(0.255102\pi\)
−0.695684 + 0.718348i \(0.744898\pi\)
\(734\) −21.5665 −0.796034
\(735\) −7.07815 −0.261081
\(736\) 3.81821i 0.140741i
\(737\) 3.05823i 0.112651i
\(738\) 36.2765 + 20.9443i 1.33536 + 0.770969i
\(739\) 27.2513 1.00246 0.501228 0.865315i \(-0.332882\pi\)
0.501228 + 0.865315i \(0.332882\pi\)
\(740\) −1.29827 2.24867i −0.0477254 0.0826628i
\(741\) 2.77756 + 1.60362i 0.102036 + 0.0589106i
\(742\) −6.46944 3.73513i −0.237501 0.137121i
\(743\) 30.3423 1.11315 0.556575 0.830797i \(-0.312115\pi\)
0.556575 + 0.830797i \(0.312115\pi\)
\(744\) −10.2773 5.93360i −0.376784 0.217536i
\(745\) 36.7159i 1.34517i
\(746\) 62.4698 2.28718
\(747\) −17.8500 + 30.9171i −0.653097 + 1.13120i
\(748\) 6.96125 + 4.01908i 0.254528 + 0.146952i
\(749\) 3.82257 6.62088i 0.139674 0.241922i
\(750\) 2.21104i 0.0807358i
\(751\) 32.8675i 1.19935i 0.800242 + 0.599677i \(0.204704\pi\)
−0.800242 + 0.599677i \(0.795296\pi\)
\(752\) −32.1100 + 18.5387i −1.17093 + 0.676037i
\(753\) 1.99197 + 1.15006i 0.0725913 + 0.0419106i
\(754\) −27.2975 47.2806i −0.994115 1.72186i
\(755\) −27.6588 47.9065i −1.00661 1.74349i
\(756\) 6.06182i 0.220466i
\(757\) −19.9983 11.5460i −0.726849 0.419647i 0.0904192 0.995904i \(-0.471179\pi\)
−0.817268 + 0.576257i \(0.804513\pi\)
\(758\) −46.6914 −1.69591
\(759\) 0.647804i 0.0235138i
\(760\) 43.2780 24.9866i 1.56986 0.906358i
\(761\) 27.4598 + 15.8539i 0.995417 + 0.574705i 0.906889 0.421369i \(-0.138450\pi\)
0.0885282 + 0.996074i \(0.471784\pi\)
\(762\) −2.88587 −0.104544
\(763\) 1.53240i 0.0554765i
\(764\) 76.9415 2.78365
\(765\) 34.4967 1.24723
\(766\) 16.8149 29.1243i 0.607548 1.05230i
\(767\)