Properties

Label 105.2.j.a.92.4
Level 105
Weight 2
Character 105.92
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 92.4
Character \(\chi\) = 105.92
Dual form 105.2.j.a.8.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.800553 + 0.800553i) q^{2} +(-1.34285 + 1.09397i) q^{3} +0.718229i q^{4} +(-2.10480 - 0.754855i) q^{5} +(0.199242 - 1.95080i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-2.17609 - 2.17609i) q^{8} +(0.606476 - 2.93806i) q^{9} +O(q^{10})\) \(q+(-0.800553 + 0.800553i) q^{2} +(-1.34285 + 1.09397i) q^{3} +0.718229i q^{4} +(-2.10480 - 0.754855i) q^{5} +(0.199242 - 1.95080i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-2.17609 - 2.17609i) q^{8} +(0.606476 - 2.93806i) q^{9} +(2.28931 - 1.08070i) q^{10} +5.20191i q^{11} +(-0.785718 - 0.964471i) q^{12} +(-3.24693 + 3.24693i) q^{13} +1.13215 q^{14} +(3.65221 - 1.28893i) q^{15} +2.04769 q^{16} +(-0.844232 + 0.844232i) q^{17} +(1.86656 + 2.83759i) q^{18} -1.32025i q^{19} +(0.542159 - 1.51173i) q^{20} +(1.72309 + 0.175985i) q^{21} +(-4.16440 - 4.16440i) q^{22} +(5.62910 + 5.62910i) q^{23} +(5.30272 + 0.541586i) q^{24} +(3.86039 + 3.17764i) q^{25} -5.19868i q^{26} +(2.39973 + 4.60883i) q^{27} +(0.507864 - 0.507864i) q^{28} -4.38282 q^{29} +(-1.89194 + 3.95565i) q^{30} -1.70499 q^{31} +(2.71289 - 2.71289i) q^{32} +(-5.69071 - 6.98536i) q^{33} -1.35170i q^{34} +(0.954557 + 2.02208i) q^{35} +(2.11020 + 0.435588i) q^{36} +(-1.71171 - 1.71171i) q^{37} +(1.05693 + 1.05693i) q^{38} +(0.808099 - 7.91217i) q^{39} +(2.93760 + 6.22286i) q^{40} +1.82176i q^{41} +(-1.52031 + 1.23854i) q^{42} +(-0.281771 + 0.281771i) q^{43} -3.73616 q^{44} +(-3.49432 + 5.72623i) q^{45} -9.01279 q^{46} +(3.39588 - 3.39588i) q^{47} +(-2.74973 + 2.24010i) q^{48} +1.00000i q^{49} +(-5.63432 + 0.546575i) q^{50} +(0.210113 - 2.05723i) q^{51} +(-2.33204 - 2.33204i) q^{52} +(-3.51059 - 3.51059i) q^{53} +(-5.61073 - 1.76850i) q^{54} +(3.92668 - 10.9490i) q^{55} +3.07745i q^{56} +(1.44431 + 1.77289i) q^{57} +(3.50868 - 3.50868i) q^{58} -1.81772 q^{59} +(0.925745 + 2.62313i) q^{60} -2.47514 q^{61} +(1.36494 - 1.36494i) q^{62} +(-2.50636 + 1.64868i) q^{63} +8.43900i q^{64} +(9.28511 - 4.38319i) q^{65} +(10.1479 + 1.03644i) q^{66} +(7.92132 + 7.92132i) q^{67} +(-0.606352 - 0.606352i) q^{68} +(-13.7171 - 1.40098i) q^{69} +(-2.38296 - 0.854612i) q^{70} -9.06358i q^{71} +(-7.71322 + 5.07373i) q^{72} +(-1.33856 + 1.33856i) q^{73} +2.74064 q^{74} +(-8.66014 - 0.0439525i) q^{75} +0.948239 q^{76} +(3.67830 - 3.67830i) q^{77} +(5.68718 + 6.98104i) q^{78} +11.5015i q^{79} +(-4.30998 - 1.54571i) q^{80} +(-8.26437 - 3.56372i) q^{81} +(-1.45841 - 1.45841i) q^{82} +(5.46196 + 5.46196i) q^{83} +(-0.126398 + 1.23757i) q^{84} +(2.41421 - 1.13967i) q^{85} -0.451146i q^{86} +(5.88546 - 4.79466i) q^{87} +(11.3198 - 11.3198i) q^{88} +9.43116 q^{89} +(-1.78676 - 7.38154i) q^{90} +4.59186 q^{91} +(-4.04298 + 4.04298i) q^{92} +(2.28954 - 1.86520i) q^{93} +5.43717i q^{94} +(-0.996595 + 2.77886i) q^{95} +(-0.675186 + 6.61080i) q^{96} +(-3.06315 - 3.06315i) q^{97} +(-0.800553 - 0.800553i) q^{98} +(15.2835 + 3.15483i) 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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.800553 + 0.800553i −0.566077 + 0.566077i −0.931027 0.364950i \(-0.881086\pi\)
0.364950 + 0.931027i \(0.381086\pi\)
\(3\) −1.34285 + 1.09397i −0.775293 + 0.631602i
\(4\) 0.718229i 0.359114i
\(5\) −2.10480 0.754855i −0.941296 0.337581i
\(6\) 0.199242 1.95080i 0.0813403 0.796410i
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) −2.17609 2.17609i −0.769363 0.769363i
\(9\) 0.606476 2.93806i 0.202159 0.979353i
\(10\) 2.28931 1.08070i 0.723943 0.341749i
\(11\) 5.20191i 1.56843i 0.620487 + 0.784217i \(0.286935\pi\)
−0.620487 + 0.784217i \(0.713065\pi\)
\(12\) −0.785718 0.964471i −0.226817 0.278419i
\(13\) −3.24693 + 3.24693i −0.900537 + 0.900537i −0.995482 0.0949456i \(-0.969732\pi\)
0.0949456 + 0.995482i \(0.469732\pi\)
\(14\) 1.13215 0.302581
\(15\) 3.65221 1.28893i 0.942997 0.332800i
\(16\) 2.04769 0.511922
\(17\) −0.844232 + 0.844232i −0.204756 + 0.204756i −0.802034 0.597278i \(-0.796249\pi\)
0.597278 + 0.802034i \(0.296249\pi\)
\(18\) 1.86656 + 2.83759i 0.439951 + 0.668826i
\(19\) 1.32025i 0.302885i −0.988466 0.151443i \(-0.951608\pi\)
0.988466 0.151443i \(-0.0483919\pi\)
\(20\) 0.542159 1.51173i 0.121230 0.338033i
\(21\) 1.72309 + 0.175985i 0.376008 + 0.0384031i
\(22\) −4.16440 4.16440i −0.887854 0.887854i
\(23\) 5.62910 + 5.62910i 1.17375 + 1.17375i 0.981309 + 0.192440i \(0.0616401\pi\)
0.192440 + 0.981309i \(0.438360\pi\)
\(24\) 5.30272 + 0.541586i 1.08241 + 0.110551i
\(25\) 3.86039 + 3.17764i 0.772078 + 0.635528i
\(26\) 5.19868i 1.01955i
\(27\) 2.39973 + 4.60883i 0.461829 + 0.886969i
\(28\) 0.507864 0.507864i 0.0959774 0.0959774i
\(29\) −4.38282 −0.813870 −0.406935 0.913457i \(-0.633402\pi\)
−0.406935 + 0.913457i \(0.633402\pi\)
\(30\) −1.89194 + 3.95565i −0.345419 + 0.722199i
\(31\) −1.70499 −0.306225 −0.153113 0.988209i \(-0.548930\pi\)
−0.153113 + 0.988209i \(0.548930\pi\)
\(32\) 2.71289 2.71289i 0.479576 0.479576i
\(33\) −5.69071 6.98536i −0.990625 1.21600i
\(34\) 1.35170i 0.231815i
\(35\) 0.954557 + 2.02208i 0.161350 + 0.341794i
\(36\) 2.11020 + 0.435588i 0.351700 + 0.0725981i
\(37\) −1.71171 1.71171i −0.281404 0.281404i 0.552265 0.833669i \(-0.313764\pi\)
−0.833669 + 0.552265i \(0.813764\pi\)
\(38\) 1.05693 + 1.05693i 0.171456 + 0.171456i
\(39\) 0.808099 7.91217i 0.129399 1.26696i
\(40\) 2.93760 + 6.22286i 0.464476 + 0.983921i
\(41\) 1.82176i 0.284511i 0.989830 + 0.142255i \(0.0454354\pi\)
−0.989830 + 0.142255i \(0.954565\pi\)
\(42\) −1.52031 + 1.23854i −0.234589 + 0.191110i
\(43\) −0.281771 + 0.281771i −0.0429697 + 0.0429697i −0.728265 0.685295i \(-0.759673\pi\)
0.685295 + 0.728265i \(0.259673\pi\)
\(44\) −3.73616 −0.563247
\(45\) −3.49432 + 5.72623i −0.520902 + 0.853616i
\(46\) −9.01279 −1.32886
\(47\) 3.39588 3.39588i 0.495340 0.495340i −0.414644 0.909984i \(-0.636094\pi\)
0.909984 + 0.414644i \(0.136094\pi\)
\(48\) −2.74973 + 2.24010i −0.396890 + 0.323331i
\(49\) 1.00000i 0.142857i
\(50\) −5.63432 + 0.546575i −0.796813 + 0.0772973i
\(51\) 0.210113 2.05723i 0.0294217 0.288071i
\(52\) −2.33204 2.33204i −0.323396 0.323396i
\(53\) −3.51059 3.51059i −0.482216 0.482216i 0.423623 0.905839i \(-0.360758\pi\)
−0.905839 + 0.423623i \(0.860758\pi\)
\(54\) −5.61073 1.76850i −0.763523 0.240662i
\(55\) 3.92668 10.9490i 0.529474 1.47636i
\(56\) 3.07745i 0.411242i
\(57\) 1.44431 + 1.77289i 0.191303 + 0.234825i
\(58\) 3.50868 3.50868i 0.460713 0.460713i
\(59\) −1.81772 −0.236647 −0.118323 0.992975i \(-0.537752\pi\)
−0.118323 + 0.992975i \(0.537752\pi\)
\(60\) 0.925745 + 2.62313i 0.119513 + 0.338644i
\(61\) −2.47514 −0.316909 −0.158455 0.987366i \(-0.550651\pi\)
−0.158455 + 0.987366i \(0.550651\pi\)
\(62\) 1.36494 1.36494i 0.173347 0.173347i
\(63\) −2.50636 + 1.64868i −0.315772 + 0.207714i
\(64\) 8.43900i 1.05488i
\(65\) 9.28511 4.38319i 1.15168 0.543668i
\(66\) 10.1479 + 1.03644i 1.24912 + 0.127577i
\(67\) 7.92132 + 7.92132i 0.967743 + 0.967743i 0.999496 0.0317530i \(-0.0101090\pi\)
−0.0317530 + 0.999496i \(0.510109\pi\)
\(68\) −0.606352 0.606352i −0.0735309 0.0735309i
\(69\) −13.7171 1.40098i −1.65134 0.168658i
\(70\) −2.38296 0.854612i −0.284818 0.102146i
\(71\) 9.06358i 1.07565i −0.843057 0.537825i \(-0.819246\pi\)
0.843057 0.537825i \(-0.180754\pi\)
\(72\) −7.71322 + 5.07373i −0.909011 + 0.597944i
\(73\) −1.33856 + 1.33856i −0.156666 + 0.156666i −0.781088 0.624422i \(-0.785335\pi\)
0.624422 + 0.781088i \(0.285335\pi\)
\(74\) 2.74064 0.318592
\(75\) −8.66014 0.0439525i −0.999987 0.00507520i
\(76\) 0.948239 0.108771
\(77\) 3.67830 3.67830i 0.419182 0.419182i
\(78\) 5.68718 + 6.98104i 0.643947 + 0.790447i
\(79\) 11.5015i 1.29402i 0.762481 + 0.647011i \(0.223981\pi\)
−0.762481 + 0.647011i \(0.776019\pi\)
\(80\) −4.30998 1.54571i −0.481871 0.172815i
\(81\) −8.26437 3.56372i −0.918264 0.395969i
\(82\) −1.45841 1.45841i −0.161055 0.161055i
\(83\) 5.46196 + 5.46196i 0.599528 + 0.599528i 0.940187 0.340659i \(-0.110650\pi\)
−0.340659 + 0.940187i \(0.610650\pi\)
\(84\) −0.126398 + 1.23757i −0.0137911 + 0.135030i
\(85\) 2.41421 1.13967i 0.261858 0.123614i
\(86\) 0.451146i 0.0486483i
\(87\) 5.88546 4.79466i 0.630988 0.514041i
\(88\) 11.3198 11.3198i 1.20669 1.20669i
\(89\) 9.43116 0.999701 0.499850 0.866112i \(-0.333388\pi\)
0.499850 + 0.866112i \(0.333388\pi\)
\(90\) −1.78676 7.38154i −0.188341 0.778083i
\(91\) 4.59186 0.481357
\(92\) −4.04298 + 4.04298i −0.421510 + 0.421510i
\(93\) 2.28954 1.86520i 0.237414 0.193412i
\(94\) 5.43717i 0.560801i
\(95\) −0.996595 + 2.77886i −0.102248 + 0.285105i
\(96\) −0.675186 + 6.61080i −0.0689109 + 0.674712i
\(97\) −3.06315 3.06315i −0.311016 0.311016i 0.534287 0.845303i \(-0.320580\pi\)
−0.845303 + 0.534287i \(0.820580\pi\)
\(98\) −0.800553 0.800553i −0.0808681 0.0808681i
\(99\) 15.2835 + 3.15483i 1.53605 + 0.317072i
\(100\) −2.28227 + 2.77264i −0.228227 + 0.277264i
\(101\) 3.71640i 0.369796i 0.982758 + 0.184898i \(0.0591954\pi\)
−0.982758 + 0.184898i \(0.940805\pi\)
\(102\) 1.47872 + 1.81513i 0.146415 + 0.179725i
\(103\) 1.18049 1.18049i 0.116317 0.116317i −0.646553 0.762869i \(-0.723790\pi\)
0.762869 + 0.646553i \(0.223790\pi\)
\(104\) 14.1312 1.38568
\(105\) −3.49391 1.67110i −0.340971 0.163082i
\(106\) 5.62082 0.545943
\(107\) 1.38009 1.38009i 0.133418 0.133418i −0.637244 0.770662i \(-0.719926\pi\)
0.770662 + 0.637244i \(0.219926\pi\)
\(108\) −3.31019 + 1.72356i −0.318523 + 0.165849i
\(109\) 5.93506i 0.568475i −0.958754 0.284238i \(-0.908260\pi\)
0.958754 0.284238i \(-0.0917405\pi\)
\(110\) 5.62173 + 11.9088i 0.536011 + 1.13546i
\(111\) 4.17113 + 0.426013i 0.395906 + 0.0404353i
\(112\) −1.44794 1.44794i −0.136817 0.136817i
\(113\) −0.240664 0.240664i −0.0226398 0.0226398i 0.695696 0.718336i \(-0.255096\pi\)
−0.718336 + 0.695696i \(0.755096\pi\)
\(114\) −2.57554 0.263049i −0.241221 0.0246368i
\(115\) −7.59899 16.0973i −0.708610 1.50108i
\(116\) 3.14787i 0.292272i
\(117\) 7.57049 + 11.5089i 0.699892 + 1.06399i
\(118\) 1.45518 1.45518i 0.133960 0.133960i
\(119\) 1.19392 0.109447
\(120\) −10.7524 5.14271i −0.981551 0.469463i
\(121\) −16.0598 −1.45998
\(122\) 1.98148 1.98148i 0.179395 0.179395i
\(123\) −1.99294 2.44634i −0.179697 0.220579i
\(124\) 1.22457i 0.109970i
\(125\) −5.72670 9.60234i −0.512211 0.858860i
\(126\) 0.686624 3.32633i 0.0611693 0.296333i
\(127\) −4.55939 4.55939i −0.404581 0.404581i 0.475263 0.879844i \(-0.342353\pi\)
−0.879844 + 0.475263i \(0.842353\pi\)
\(128\) −1.33009 1.33009i −0.117565 0.117565i
\(129\) 0.0701274 0.686624i 0.00617437 0.0604538i
\(130\) −3.92425 + 10.9422i −0.344180 + 0.959695i
\(131\) 13.6784i 1.19509i 0.801837 + 0.597543i \(0.203856\pi\)
−0.801837 + 0.597543i \(0.796144\pi\)
\(132\) 5.01709 4.08723i 0.436682 0.355748i
\(133\) −0.933556 + 0.933556i −0.0809495 + 0.0809495i
\(134\) −12.6829 −1.09563
\(135\) −1.57197 11.5121i −0.135293 0.990806i
\(136\) 3.67424 0.315064
\(137\) −10.0232 + 10.0232i −0.856337 + 0.856337i −0.990904 0.134567i \(-0.957036\pi\)
0.134567 + 0.990904i \(0.457036\pi\)
\(138\) 12.1028 9.85969i 1.03026 0.839313i
\(139\) 15.8262i 1.34236i 0.741292 + 0.671182i \(0.234213\pi\)
−0.741292 + 0.671182i \(0.765787\pi\)
\(140\) −1.45232 + 0.685590i −0.122743 + 0.0579430i
\(141\) −0.845170 + 8.27513i −0.0711761 + 0.696892i
\(142\) 7.25588 + 7.25588i 0.608900 + 0.608900i
\(143\) −16.8902 16.8902i −1.41243 1.41243i
\(144\) 1.24187 6.01623i 0.103490 0.501353i
\(145\) 9.22498 + 3.30840i 0.766093 + 0.274747i
\(146\) 2.14317i 0.177370i
\(147\) −1.09397 1.34285i −0.0902288 0.110756i
\(148\) 1.22940 1.22940i 0.101056 0.101056i
\(149\) −9.30594 −0.762373 −0.381186 0.924498i \(-0.624484\pi\)
−0.381186 + 0.924498i \(0.624484\pi\)
\(150\) 6.96809 6.89772i 0.568942 0.563196i
\(151\) −16.8274 −1.36939 −0.684697 0.728827i \(-0.740066\pi\)
−0.684697 + 0.728827i \(0.740066\pi\)
\(152\) −2.87297 + 2.87297i −0.233029 + 0.233029i
\(153\) 1.96840 + 2.99241i 0.159135 + 0.241922i
\(154\) 5.88936i 0.474578i
\(155\) 3.58867 + 1.28702i 0.288249 + 0.103376i
\(156\) 5.68275 + 0.580400i 0.454984 + 0.0464692i
\(157\) 6.80647 + 6.80647i 0.543216 + 0.543216i 0.924470 0.381255i \(-0.124508\pi\)
−0.381255 + 0.924470i \(0.624508\pi\)
\(158\) −9.20757 9.20757i −0.732515 0.732515i
\(159\) 8.55464 + 0.873717i 0.678427 + 0.0692903i
\(160\) −7.75793 + 3.66226i −0.613319 + 0.289527i
\(161\) 7.96075i 0.627395i
\(162\) 9.46902 3.76312i 0.743957 0.295659i
\(163\) 8.77966 8.77966i 0.687676 0.687676i −0.274042 0.961718i \(-0.588361\pi\)
0.961718 + 0.274042i \(0.0883607\pi\)
\(164\) −1.30844 −0.102172
\(165\) 6.70488 + 18.9985i 0.521974 + 1.47903i
\(166\) −8.74519 −0.678758
\(167\) −12.4516 + 12.4516i −0.963532 + 0.963532i −0.999358 0.0358258i \(-0.988594\pi\)
0.0358258 + 0.999358i \(0.488594\pi\)
\(168\) −3.36663 4.13255i −0.259741 0.318833i
\(169\) 8.08513i 0.621933i
\(170\) −1.02034 + 2.84507i −0.0782566 + 0.218207i
\(171\) −3.87896 0.800698i −0.296632 0.0612309i
\(172\) −0.202376 0.202376i −0.0154310 0.0154310i
\(173\) 13.7966 + 13.7966i 1.04894 + 1.04894i 0.998739 + 0.0501977i \(0.0159851\pi\)
0.0501977 + 0.998739i \(0.484015\pi\)
\(174\) −0.873244 + 8.55000i −0.0662004 + 0.648174i
\(175\) −0.482774 4.97664i −0.0364943 0.376198i
\(176\) 10.6519i 0.802916i
\(177\) 2.44092 1.98852i 0.183471 0.149466i
\(178\) −7.55015 + 7.55015i −0.565907 + 0.565907i
\(179\) −7.03160 −0.525567 −0.262783 0.964855i \(-0.584640\pi\)
−0.262783 + 0.964855i \(0.584640\pi\)
\(180\) −4.11274 2.50972i −0.306546 0.187064i
\(181\) 14.1873 1.05454 0.527268 0.849699i \(-0.323216\pi\)
0.527268 + 0.849699i \(0.323216\pi\)
\(182\) −3.67602 + 3.67602i −0.272485 + 0.272485i
\(183\) 3.32374 2.70772i 0.245698 0.200161i
\(184\) 24.4988i 1.80608i
\(185\) 2.31072 + 4.89492i 0.169888 + 0.359881i
\(186\) −0.339706 + 3.32609i −0.0249085 + 0.243881i
\(187\) −4.39161 4.39161i −0.321147 0.321147i
\(188\) 2.43902 + 2.43902i 0.177884 + 0.177884i
\(189\) 1.56207 4.95580i 0.113624 0.360481i
\(190\) −1.42680 3.02245i −0.103511 0.219272i
\(191\) 15.6450i 1.13203i −0.824394 0.566017i \(-0.808484\pi\)
0.824394 0.566017i \(-0.191516\pi\)
\(192\) −9.23199 11.3323i −0.666261 0.817838i
\(193\) 9.00959 9.00959i 0.648525 0.648525i −0.304112 0.952636i \(-0.598360\pi\)
0.952636 + 0.304112i \(0.0983596\pi\)
\(194\) 4.90443 0.352118
\(195\) −7.67343 + 16.0436i −0.549506 + 1.14890i
\(196\) −0.718229 −0.0513021
\(197\) −2.78986 + 2.78986i −0.198769 + 0.198769i −0.799472 0.600703i \(-0.794887\pi\)
0.600703 + 0.799472i \(0.294887\pi\)
\(198\) −14.7609 + 9.70965i −1.04901 + 0.690035i
\(199\) 14.4320i 1.02306i 0.859266 + 0.511528i \(0.170920\pi\)
−0.859266 + 0.511528i \(0.829080\pi\)
\(200\) −1.48572 15.3154i −0.105056 1.08296i
\(201\) −19.3028 1.97146i −1.36151 0.139056i
\(202\) −2.97518 2.97518i −0.209333 0.209333i
\(203\) 3.09912 + 3.09912i 0.217516 + 0.217516i
\(204\) 1.47757 + 0.150909i 0.103450 + 0.0105658i
\(205\) 1.37516 3.83444i 0.0960455 0.267809i
\(206\) 1.89009i 0.131689i
\(207\) 19.9525 13.1247i 1.38680 0.912231i
\(208\) −6.64871 + 6.64871i −0.461005 + 0.461005i
\(209\) 6.86780 0.475056
\(210\) 4.13487 1.45926i 0.285333 0.100699i
\(211\) 11.9845 0.825049 0.412524 0.910947i \(-0.364647\pi\)
0.412524 + 0.910947i \(0.364647\pi\)
\(212\) 2.52140 2.52140i 0.173171 0.173171i
\(213\) 9.91525 + 12.1710i 0.679382 + 0.833943i
\(214\) 2.20967i 0.151050i
\(215\) 0.805769 0.380376i 0.0549530 0.0259414i
\(216\) 4.80718 15.2512i 0.327087 1.03772i
\(217\) 1.20561 + 1.20561i 0.0818422 + 0.0818422i
\(218\) 4.75133 + 4.75133i 0.321801 + 0.321801i
\(219\) 0.333141 3.26181i 0.0225116 0.220413i
\(220\) 7.86388 + 2.82026i 0.530182 + 0.190142i
\(221\) 5.48233i 0.368781i
\(222\) −3.68025 + 2.99816i −0.247003 + 0.201224i
\(223\) −12.1834 + 12.1834i −0.815858 + 0.815858i −0.985505 0.169647i \(-0.945737\pi\)
0.169647 + 0.985505i \(0.445737\pi\)
\(224\) −3.83661 −0.256344
\(225\) 11.6773 9.41488i 0.778489 0.627659i
\(226\) 0.385328 0.0256317
\(227\) −4.17335 + 4.17335i −0.276995 + 0.276995i −0.831908 0.554913i \(-0.812751\pi\)
0.554913 + 0.831908i \(0.312751\pi\)
\(228\) −1.27334 + 1.03734i −0.0843290 + 0.0686996i
\(229\) 27.2705i 1.80209i −0.433730 0.901043i \(-0.642803\pi\)
0.433730 0.901043i \(-0.357197\pi\)
\(230\) 18.9701 + 6.80335i 1.25085 + 0.448600i
\(231\) −0.915459 + 8.96334i −0.0602328 + 0.589744i
\(232\) 9.53740 + 9.53740i 0.626161 + 0.626161i
\(233\) −1.96791 1.96791i −0.128922 0.128922i 0.639701 0.768624i \(-0.279058\pi\)
−0.768624 + 0.639701i \(0.779058\pi\)
\(234\) −15.2740 3.15288i −0.998495 0.206110i
\(235\) −9.71106 + 4.58426i −0.633480 + 0.299044i
\(236\) 1.30554i 0.0849832i
\(237\) −12.5823 15.4448i −0.817306 1.00325i
\(238\) −0.955800 + 0.955800i −0.0619553 + 0.0619553i
\(239\) 1.42942 0.0924613 0.0462307 0.998931i \(-0.485279\pi\)
0.0462307 + 0.998931i \(0.485279\pi\)
\(240\) 7.47860 2.63932i 0.482742 0.170368i
\(241\) 29.1319 1.87655 0.938274 0.345893i \(-0.112424\pi\)
0.938274 + 0.345893i \(0.112424\pi\)
\(242\) 12.8567 12.8567i 0.826463 0.826463i
\(243\) 14.9964 4.25541i 0.962018 0.272985i
\(244\) 1.77772i 0.113807i
\(245\) 0.754855 2.10480i 0.0482259 0.134471i
\(246\) 3.55388 + 0.362971i 0.226587 + 0.0231422i
\(247\) 4.28675 + 4.28675i 0.272759 + 0.272759i
\(248\) 3.71021 + 3.71021i 0.235598 + 0.235598i
\(249\) −13.3098 1.35938i −0.843473 0.0861470i
\(250\) 12.2717 + 3.10266i 0.776131 + 0.196230i
\(251\) 12.3977i 0.782538i 0.920276 + 0.391269i \(0.127964\pi\)
−0.920276 + 0.391269i \(0.872036\pi\)
\(252\) −1.18413 1.80014i −0.0745931 0.113398i
\(253\) −29.2821 + 29.2821i −1.84095 + 1.84095i
\(254\) 7.30007 0.458047
\(255\) −1.99516 + 4.17147i −0.124942 + 0.261227i
\(256\) −14.7484 −0.921774
\(257\) 13.8717 13.8717i 0.865290 0.865290i −0.126657 0.991947i \(-0.540425\pi\)
0.991947 + 0.126657i \(0.0404246\pi\)
\(258\) 0.493538 + 0.605820i 0.0307263 + 0.0377167i
\(259\) 2.42073i 0.150417i
\(260\) 3.14813 + 6.66884i 0.195239 + 0.413584i
\(261\) −2.65808 + 12.8770i −0.164531 + 0.797066i
\(262\) −10.9503 10.9503i −0.676511 0.676511i
\(263\) 12.2912 + 12.2912i 0.757909 + 0.757909i 0.975942 0.218032i \(-0.0699639\pi\)
−0.218032 + 0.975942i \(0.569964\pi\)
\(264\) −2.81728 + 27.5842i −0.173392 + 1.69769i
\(265\) 4.73911 + 10.0391i 0.291121 + 0.616695i
\(266\) 1.49472i 0.0916473i
\(267\) −12.6646 + 10.3174i −0.775061 + 0.631413i
\(268\) −5.68932 + 5.68932i −0.347530 + 0.347530i
\(269\) 19.1535 1.16781 0.583906 0.811822i \(-0.301524\pi\)
0.583906 + 0.811822i \(0.301524\pi\)
\(270\) 10.4745 + 7.95762i 0.637458 + 0.484286i
\(271\) 18.4629 1.12154 0.560771 0.827971i \(-0.310505\pi\)
0.560771 + 0.827971i \(0.310505\pi\)
\(272\) −1.72872 + 1.72872i −0.104819 + 0.104819i
\(273\) −6.16616 + 5.02333i −0.373193 + 0.304026i
\(274\) 16.0482i 0.969505i
\(275\) −16.5298 + 20.0814i −0.996784 + 1.21095i
\(276\) 1.00622 9.85200i 0.0605674 0.593020i
\(277\) −7.66076 7.66076i −0.460290 0.460290i 0.438460 0.898751i \(-0.355524\pi\)
−0.898751 + 0.438460i \(0.855524\pi\)
\(278\) −12.6698 12.6698i −0.759881 0.759881i
\(279\) −1.03404 + 5.00936i −0.0619061 + 0.299903i
\(280\) 2.32303 6.47743i 0.138828 0.387100i
\(281\) 20.4646i 1.22082i −0.792087 0.610408i \(-0.791005\pi\)
0.792087 0.610408i \(-0.208995\pi\)
\(282\) −5.94808 7.30129i −0.354203 0.434785i
\(283\) 8.24528 8.24528i 0.490131 0.490131i −0.418216 0.908347i \(-0.637345\pi\)
0.908347 + 0.418216i \(0.137345\pi\)
\(284\) 6.50972 0.386281
\(285\) −1.70170 4.82182i −0.100800 0.285620i
\(286\) 27.0431 1.59909
\(287\) 1.28818 1.28818i 0.0760387 0.0760387i
\(288\) −6.32533 9.61593i −0.372723 0.566624i
\(289\) 15.5745i 0.916150i
\(290\) −10.0336 + 4.73654i −0.589195 + 0.278139i
\(291\) 7.46433 + 0.762360i 0.437567 + 0.0446903i
\(292\) −0.961389 0.961389i −0.0562610 0.0562610i
\(293\) −19.7225 19.7225i −1.15220 1.15220i −0.986111 0.166088i \(-0.946886\pi\)
−0.166088 0.986111i \(-0.553114\pi\)
\(294\) 1.95080 + 0.199242i 0.113773 + 0.0116200i
\(295\) 3.82594 + 1.37211i 0.222755 + 0.0798875i
\(296\) 7.44968i 0.433004i
\(297\) −23.9747 + 12.4832i −1.39115 + 0.724348i
\(298\) 7.44990 7.44990i 0.431561 0.431561i
\(299\) −36.5546 −2.11401
\(300\) 0.0315680 6.21996i 0.00182258 0.359110i
\(301\) 0.398485 0.0229683
\(302\) 13.4712 13.4712i 0.775182 0.775182i
\(303\) −4.06562 4.99056i −0.233564 0.286700i
\(304\) 2.70346i 0.155054i
\(305\) 5.20968 + 1.86837i 0.298306 + 0.106983i
\(306\) −3.97139 0.819776i −0.227029 0.0468635i
\(307\) −13.2997 13.2997i −0.759057 0.759057i 0.217094 0.976151i \(-0.430342\pi\)
−0.976151 + 0.217094i \(0.930342\pi\)
\(308\) 2.64186 + 2.64186i 0.150534 + 0.150534i
\(309\) −0.293801 + 2.87663i −0.0167137 + 0.163646i
\(310\) −3.90325 + 1.84259i −0.221690 + 0.104652i
\(311\) 23.8049i 1.34985i −0.737885 0.674926i \(-0.764176\pi\)
0.737885 0.674926i \(-0.235824\pi\)
\(312\) −18.9761 + 15.4591i −1.07431 + 0.875197i
\(313\) −18.9352 + 18.9352i −1.07028 + 1.07028i −0.0729475 + 0.997336i \(0.523241\pi\)
−0.997336 + 0.0729475i \(0.976759\pi\)
\(314\) −10.8979 −0.615003
\(315\) 6.51991 1.57820i 0.367356 0.0889215i
\(316\) −8.26072 −0.464702
\(317\) 11.6929 11.6929i 0.656739 0.656739i −0.297868 0.954607i \(-0.596275\pi\)
0.954607 + 0.297868i \(0.0962755\pi\)
\(318\) −7.54790 + 6.14899i −0.423265 + 0.344818i
\(319\) 22.7990i 1.27650i
\(320\) 6.37022 17.7624i 0.356106 0.992950i
\(321\) −0.343478 + 3.36302i −0.0191711 + 0.187706i
\(322\) 6.37301 + 6.37301i 0.355154 + 0.355154i
\(323\) 1.11459 + 1.11459i 0.0620177 + 0.0620177i
\(324\) 2.55957 5.93571i 0.142198 0.329762i
\(325\) −22.8520 + 2.21683i −1.26760 + 0.122968i
\(326\) 14.0572i 0.778555i
\(327\) 6.49275 + 7.96987i 0.359050 + 0.440735i
\(328\) 3.96430 3.96430i 0.218892 0.218892i
\(329\) −4.80250 −0.264771
\(330\) −20.5769 9.84167i −1.13272 0.541766i
\(331\) −11.5898 −0.637031 −0.318516 0.947918i \(-0.603184\pi\)
−0.318516 + 0.947918i \(0.603184\pi\)
\(332\) −3.92294 + 3.92294i −0.215299 + 0.215299i
\(333\) −6.06723 + 3.99100i −0.332482 + 0.218706i
\(334\) 19.9363i 1.09087i
\(335\) −10.6934 22.6523i −0.584241 1.23762i
\(336\) 3.52835 + 0.360363i 0.192487 + 0.0196594i
\(337\) −5.46127 5.46127i −0.297494 0.297494i 0.542537 0.840032i \(-0.317464\pi\)
−0.840032 + 0.542537i \(0.817464\pi\)
\(338\) 6.47258 + 6.47258i 0.352062 + 0.352062i
\(339\) 0.586453 + 0.0598966i 0.0318517 + 0.00325314i
\(340\) 0.818543 + 1.73396i 0.0443917 + 0.0940371i
\(341\) 8.86920i 0.480294i
\(342\) 3.74632 2.46431i 0.202578 0.133255i
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) 1.22632 0.0661186
\(345\) 27.8142 + 13.3032i 1.49747 + 0.716219i
\(346\) −22.0898 −1.18756
\(347\) −20.1982 + 20.1982i −1.08430 + 1.08430i −0.0881938 + 0.996103i \(0.528109\pi\)
−0.996103 + 0.0881938i \(0.971891\pi\)
\(348\) 3.44366 + 4.22711i 0.184600 + 0.226597i
\(349\) 11.9748i 0.640997i −0.947249 0.320498i \(-0.896150\pi\)
0.947249 0.320498i \(-0.103850\pi\)
\(350\) 4.37055 + 3.59758i 0.233616 + 0.192299i
\(351\) −22.7563 7.17278i −1.21464 0.382855i
\(352\) 14.1122 + 14.1122i 0.752183 + 0.752183i
\(353\) 24.3423 + 24.3423i 1.29561 + 1.29561i 0.931264 + 0.364345i \(0.118707\pi\)
0.364345 + 0.931264i \(0.381293\pi\)
\(354\) −0.362166 + 3.54600i −0.0192489 + 0.188468i
\(355\) −6.84169 + 19.0770i −0.363119 + 1.01250i
\(356\) 6.77373i 0.359007i
\(357\) −1.60326 + 1.30611i −0.0848534 + 0.0691268i
\(358\) 5.62917 5.62917i 0.297511 0.297511i
\(359\) 14.2164 0.750314 0.375157 0.926961i \(-0.377589\pi\)
0.375157 + 0.926961i \(0.377589\pi\)
\(360\) 20.0647 4.85683i 1.05750 0.255978i
\(361\) 17.2569 0.908260
\(362\) −11.3577 + 11.3577i −0.596948 + 0.596948i
\(363\) 21.5659 17.5689i 1.13192 0.922129i
\(364\) 3.29800i 0.172862i
\(365\) 3.82781 1.80698i 0.200357 0.0945816i
\(366\) −0.493153 + 4.82850i −0.0257775 + 0.252390i
\(367\) 16.7024 + 16.7024i 0.871859 + 0.871859i 0.992675 0.120816i \(-0.0385512\pi\)
−0.120816 + 0.992675i \(0.538551\pi\)
\(368\) 11.5267 + 11.5267i 0.600868 + 0.600868i
\(369\) 5.35243 + 1.10485i 0.278636 + 0.0575163i
\(370\) −5.76850 2.06878i −0.299890 0.107551i
\(371\) 4.96472i 0.257755i
\(372\) 1.33964 + 1.64441i 0.0694572 + 0.0852589i
\(373\) 4.57877 4.57877i 0.237080 0.237080i −0.578560 0.815640i \(-0.696385\pi\)
0.815640 + 0.578560i \(0.196385\pi\)
\(374\) 7.03144 0.363587
\(375\) 18.1947 + 6.62966i 0.939571 + 0.342354i
\(376\) −14.7795 −0.762193
\(377\) 14.2307 14.2307i 0.732920 0.732920i
\(378\) 2.71686 + 5.21790i 0.139740 + 0.268380i
\(379\) 12.6506i 0.649816i 0.945746 + 0.324908i \(0.105333\pi\)
−0.945746 + 0.324908i \(0.894667\pi\)
\(380\) −1.99586 0.715783i −0.102385 0.0367189i
\(381\) 11.1104 + 1.13474i 0.569202 + 0.0581347i
\(382\) 12.5247 + 12.5247i 0.640818 + 0.640818i
\(383\) −18.0165 18.0165i −0.920601 0.920601i 0.0764705 0.997072i \(-0.475635\pi\)
−0.997072 + 0.0764705i \(0.975635\pi\)
\(384\) 3.24119 + 0.331035i 0.165401 + 0.0168930i
\(385\) −10.5187 + 4.96552i −0.536082 + 0.253066i
\(386\) 14.4253i 0.734229i
\(387\) 0.656973 + 0.998748i 0.0333958 + 0.0507692i
\(388\) 2.20004 2.20004i 0.111690 0.111690i
\(389\) 17.7215 0.898517 0.449259 0.893402i \(-0.351688\pi\)
0.449259 + 0.893402i \(0.351688\pi\)
\(390\) −6.70073 18.9867i −0.339305 0.961429i
\(391\) −9.50453 −0.480665
\(392\) 2.17609 2.17609i 0.109909 0.109909i
\(393\) −14.9637 18.3680i −0.754819 0.926543i
\(394\) 4.46686i 0.225037i
\(395\) 8.68197 24.2084i 0.436838 1.21806i
\(396\) −2.26589 + 10.9771i −0.113865 + 0.551618i
\(397\) 4.43035 + 4.43035i 0.222353 + 0.222353i 0.809489 0.587136i \(-0.199745\pi\)
−0.587136 + 0.809489i \(0.699745\pi\)
\(398\) −11.5536 11.5536i −0.579128 0.579128i
\(399\) 0.232344 2.27490i 0.0116317 0.113887i
\(400\) 7.90488 + 6.50682i 0.395244 + 0.325341i
\(401\) 34.4780i 1.72175i 0.508818 + 0.860874i \(0.330082\pi\)
−0.508818 + 0.860874i \(0.669918\pi\)
\(402\) 17.0312 13.8746i 0.849437 0.692004i
\(403\) 5.53599 5.53599i 0.275767 0.275767i
\(404\) −2.66923 −0.132799
\(405\) 14.7048 + 13.7393i 0.730686 + 0.682713i
\(406\) −4.96203 −0.246261
\(407\) 8.90417 8.90417i 0.441364 0.441364i
\(408\) −4.93395 + 4.01950i −0.244267 + 0.198995i
\(409\) 19.5663i 0.967490i −0.875209 0.483745i \(-0.839276\pi\)
0.875209 0.483745i \(-0.160724\pi\)
\(410\) 1.96878 + 4.17056i 0.0972312 + 0.205969i
\(411\) 2.49457 24.4246i 0.123048 1.20478i
\(412\) 0.847860 + 0.847860i 0.0417711 + 0.0417711i
\(413\) 1.28532 + 1.28532i 0.0632465 + 0.0632465i
\(414\) −5.46604 + 26.4801i −0.268641 + 1.30143i
\(415\) −7.37336 15.6193i −0.361944 0.766723i
\(416\) 17.6171i 0.863751i
\(417\) −17.3134 21.2522i −0.847840 1.04073i
\(418\) −5.49804 + 5.49804i −0.268918 + 0.268918i
\(419\) 17.0209 0.831524 0.415762 0.909474i \(-0.363515\pi\)
0.415762 + 0.909474i \(0.363515\pi\)
\(420\) 1.20023 2.50943i 0.0585652 0.122448i
\(421\) 21.7474 1.05990 0.529951 0.848028i \(-0.322210\pi\)
0.529951 + 0.848028i \(0.322210\pi\)
\(422\) −9.59425 + 9.59425i −0.467041 + 0.467041i
\(423\) −7.91778 12.0368i −0.384976 0.585250i
\(424\) 15.2787i 0.741998i
\(425\) −5.94173 + 0.576396i −0.288216 + 0.0279593i
\(426\) −17.6812 1.80585i −0.856658 0.0874936i
\(427\) 1.75019 + 1.75019i 0.0846976 + 0.0846976i
\(428\) 0.991221 + 0.991221i 0.0479125 + 0.0479125i
\(429\) 41.1583 + 4.20365i 1.98714 + 0.202954i
\(430\) −0.340550 + 0.949573i −0.0164228 + 0.0457925i
\(431\) 10.7912i 0.519796i 0.965636 + 0.259898i \(0.0836889\pi\)
−0.965636 + 0.259898i \(0.916311\pi\)
\(432\) 4.91391 + 9.43745i 0.236420 + 0.454059i
\(433\) 0.466927 0.466927i 0.0224391 0.0224391i −0.695798 0.718237i \(-0.744949\pi\)
0.718237 + 0.695798i \(0.244949\pi\)
\(434\) −1.93031 −0.0926579
\(435\) −16.0070 + 5.64914i −0.767477 + 0.270856i
\(436\) 4.26273 0.204148
\(437\) 7.43180 7.43180i 0.355511 0.355511i
\(438\) 2.34456 + 2.87795i 0.112027 + 0.137514i
\(439\) 9.43662i 0.450385i 0.974314 + 0.225193i \(0.0723011\pi\)
−0.974314 + 0.225193i \(0.927699\pi\)
\(440\) −32.3708 + 15.2811i −1.54322 + 0.728500i
\(441\) 2.93806 + 0.606476i 0.139908 + 0.0288798i
\(442\) 4.38889 + 4.38889i 0.208758 + 0.208758i
\(443\) −16.8956 16.8956i −0.802734 0.802734i 0.180788 0.983522i \(-0.442135\pi\)
−0.983522 + 0.180788i \(0.942135\pi\)
\(444\) −0.305975 + 2.99582i −0.0145209 + 0.142175i
\(445\) −19.8507 7.11916i −0.941015 0.337480i
\(446\) 19.5068i 0.923676i
\(447\) 12.4965 10.1804i 0.591062 0.481516i
\(448\) 5.96728 5.96728i 0.281927 0.281927i
\(449\) 11.5643 0.545753 0.272876 0.962049i \(-0.412025\pi\)
0.272876 + 0.962049i \(0.412025\pi\)
\(450\) −1.81121 + 16.8854i −0.0853812 + 0.795987i
\(451\) −9.47661 −0.446236
\(452\) 0.172852 0.172852i 0.00813026 0.00813026i
\(453\) 22.5966 18.4086i 1.06168 0.864912i
\(454\) 6.68197i 0.313601i
\(455\) −9.66495 3.46618i −0.453100 0.162497i
\(456\) 0.715027 7.00090i 0.0334842 0.327847i
\(457\) −17.8413 17.8413i −0.834580 0.834580i 0.153560 0.988139i \(-0.450926\pi\)
−0.988139 + 0.153560i \(0.950926\pi\)
\(458\) 21.8315 + 21.8315i 1.02012 + 1.02012i
\(459\) −5.91685 1.86499i −0.276175 0.0870502i
\(460\) 11.5615 5.45782i 0.539060 0.254472i
\(461\) 13.0571i 0.608129i −0.952651 0.304064i \(-0.901656\pi\)
0.952651 0.304064i \(-0.0983438\pi\)
\(462\) −6.44276 7.90850i −0.299744 0.367937i
\(463\) 17.3925 17.3925i 0.808298 0.808298i −0.176079 0.984376i \(-0.556341\pi\)
0.984376 + 0.176079i \(0.0563413\pi\)
\(464\) −8.97466 −0.416638
\(465\) −6.22699 + 2.19761i −0.288770 + 0.101912i
\(466\) 3.15084 0.145960
\(467\) −9.40605 + 9.40605i −0.435260 + 0.435260i −0.890413 0.455153i \(-0.849585\pi\)
0.455153 + 0.890413i \(0.349585\pi\)
\(468\) −8.26600 + 5.43734i −0.382096 + 0.251341i
\(469\) 11.2024i 0.517280i
\(470\) 4.10427 11.4442i 0.189316 0.527880i
\(471\) −16.5861 1.69400i −0.764247 0.0780554i
\(472\) 3.95551 + 3.95551i 0.182067 + 0.182067i
\(473\) −1.46575 1.46575i −0.0673951 0.0673951i
\(474\) 22.4371 + 2.29159i 1.03057 + 0.105256i
\(475\) 4.19527 5.09667i 0.192492 0.233851i
\(476\) 0.857511i 0.0393039i
\(477\) −12.4434 + 8.18522i −0.569744 + 0.374776i
\(478\) −1.14432 + 1.14432i −0.0523402 + 0.0523402i
\(479\) −38.8689 −1.77596 −0.887982 0.459879i \(-0.847893\pi\)
−0.887982 + 0.459879i \(0.847893\pi\)
\(480\) 6.41133 13.4048i 0.292636 0.611841i
\(481\) 11.1156 0.506829
\(482\) −23.3216 + 23.3216i −1.06227 + 1.06227i
\(483\) 8.70879 + 10.6901i 0.396264 + 0.486415i
\(484\) 11.5346i 0.524301i
\(485\) 4.13509 + 8.75957i 0.187765 + 0.397751i
\(486\) −8.59872 + 15.4121i −0.390046 + 0.699106i
\(487\) 23.9549 + 23.9549i 1.08550 + 1.08550i 0.995985 + 0.0895148i \(0.0285316\pi\)
0.0895148 + 0.995985i \(0.471468\pi\)
\(488\) 5.38612 + 5.38612i 0.243818 + 0.243818i
\(489\) −2.18509 + 21.3944i −0.0988131 + 0.967488i
\(490\) 1.08070 + 2.28931i 0.0488213 + 0.103420i
\(491\) 25.6453i 1.15736i 0.815556 + 0.578678i \(0.196431\pi\)
−0.815556 + 0.578678i \(0.803569\pi\)
\(492\) 1.75703 1.43139i 0.0792132 0.0645319i
\(493\) 3.70012 3.70012i 0.166645 0.166645i
\(494\) −6.86355 −0.308806
\(495\) −29.7873 18.1771i −1.33884 0.817001i
\(496\) −3.49129 −0.156764
\(497\) −6.40892 + 6.40892i −0.287479 + 0.287479i
\(498\) 11.7434 9.56694i 0.526236 0.428705i
\(499\) 29.1057i 1.30295i 0.758669 + 0.651476i \(0.225850\pi\)
−0.758669 + 0.651476i \(0.774150\pi\)
\(500\) 6.89668 4.11308i 0.308429 0.183942i
\(501\) 3.09896 30.3422i 0.138451 1.35559i
\(502\) −9.92505 9.92505i −0.442976 0.442976i
\(503\) 10.1763 + 10.1763i 0.453738 + 0.453738i 0.896593 0.442855i \(-0.146035\pi\)
−0.442855 + 0.896593i \(0.646035\pi\)
\(504\) 9.04173 + 1.86640i 0.402751 + 0.0831361i
\(505\) 2.80534 7.82229i 0.124836 0.348087i
\(506\) 46.8837i 2.08423i
\(507\) 8.84486 + 10.8571i 0.392814 + 0.482181i
\(508\) 3.27469 3.27469i 0.145291 0.145291i
\(509\) −31.2970 −1.38721 −0.693607 0.720354i \(-0.743979\pi\)
−0.693607 + 0.720354i \(0.743979\pi\)
\(510\) −1.74225 4.93672i −0.0771481 0.218601i
\(511\) 1.89300 0.0837415
\(512\) 14.4671 14.4671i 0.639360 0.639360i
\(513\) 6.08479 3.16824i 0.268650 0.139881i
\(514\) 22.2100i 0.979641i
\(515\) −3.37579 + 1.59360i −0.148755 + 0.0702222i
\(516\) 0.493153 + 0.0503675i 0.0217098 + 0.00221731i
\(517\) 17.6651 + 17.6651i 0.776908 + 0.776908i
\(518\) −1.93792 1.93792i −0.0851474 0.0851474i
\(519\) −33.6198 3.43371i −1.47574 0.150723i
\(520\) −29.7434 10.6670i −1.30433 0.467780i
\(521\) 24.4644i 1.07180i 0.844280 + 0.535902i \(0.180028\pi\)
−0.844280 + 0.535902i \(0.819972\pi\)
\(522\) −8.18078 12.4366i −0.358063 0.544337i
\(523\) 1.82790 1.82790i 0.0799284 0.0799284i −0.666012 0.745941i \(-0.732000\pi\)
0.745941 + 0.666012i \(0.232000\pi\)
\(524\) −9.82422 −0.429173
\(525\) 6.09257 + 6.15472i 0.265901 + 0.268614i
\(526\) −19.6796 −0.858069
\(527\) 1.43941 1.43941i 0.0627015 0.0627015i
\(528\) −11.6528 14.3039i −0.507123 0.622495i
\(529\) 40.3736i 1.75537i
\(530\) −11.8307 4.24291i −0.513894 0.184300i
\(531\) −1.10240 + 5.34056i −0.0478402 + 0.231761i
\(532\) −0.670507 0.670507i −0.0290701 0.0290701i
\(533\) −5.91512 5.91512i −0.256212 0.256212i
\(534\) 1.87909 18.3983i 0.0813160 0.796172i
\(535\) −3.94659 + 1.86305i −0.170626 + 0.0805467i
\(536\) 34.4749i 1.48909i
\(537\) 9.44237 7.69234i 0.407468 0.331949i
\(538\) −15.3334 + 15.3334i −0.661071 + 0.661071i
\(539\) −5.20191 −0.224062
\(540\) 8.26834 1.12903i 0.355813 0.0485858i
\(541\) 41.8839 1.80073 0.900364 0.435137i \(-0.143300\pi\)
0.900364 + 0.435137i \(0.143300\pi\)
\(542\) −14.7805 + 14.7805i −0.634879 + 0.634879i
\(543\) −19.0514 + 15.5205i −0.817575 + 0.666047i
\(544\) 4.58061i 0.196392i
\(545\) −4.48011 + 12.4921i −0.191907 + 0.535104i
\(546\) 0.914892 8.95779i 0.0391538 0.383358i
\(547\) −21.6813 21.6813i −0.927024 0.927024i 0.0704885 0.997513i \(-0.477544\pi\)
−0.997513 + 0.0704885i \(0.977544\pi\)
\(548\) −7.19893 7.19893i −0.307523 0.307523i
\(549\) −1.50111 + 7.27211i −0.0640660 + 0.310366i
\(550\) −2.84323 29.3092i −0.121236 1.24975i
\(551\) 5.78641i 0.246509i
\(552\) 26.8009 + 32.8982i 1.14072 + 1.40024i
\(553\) 8.13280 8.13280i 0.345842 0.345842i
\(554\) 12.2657 0.521119
\(555\) −8.45782 4.04527i −0.359014 0.171712i
\(556\) −11.3669 −0.482063
\(557\) 13.1204 13.1204i 0.555929 0.555929i −0.372217 0.928146i \(-0.621402\pi\)
0.928146 + 0.372217i \(0.121402\pi\)
\(558\) −3.18246 4.83806i −0.134724 0.204811i
\(559\) 1.82978i 0.0773916i
\(560\) 1.95464 + 4.14060i 0.0825985 + 0.174972i
\(561\) 10.7015 + 1.09299i 0.451819 + 0.0461460i
\(562\) 16.3830 + 16.3830i 0.691076 + 0.691076i
\(563\) −15.9166 15.9166i −0.670804 0.670804i 0.287097 0.957901i \(-0.407310\pi\)
−0.957901 + 0.287097i \(0.907310\pi\)
\(564\) −5.94344 0.607025i −0.250264 0.0255604i
\(565\) 0.324884 + 0.688216i 0.0136680 + 0.0289535i
\(566\) 13.2016i 0.554903i
\(567\) 3.32386 + 8.36373i 0.139589 + 0.351244i
\(568\) −19.7231 + 19.7231i −0.827565 + 0.827565i
\(569\) −27.8303 −1.16671 −0.583354 0.812218i \(-0.698260\pi\)
−0.583354 + 0.812218i \(0.698260\pi\)
\(570\) 5.22243 + 2.49782i 0.218744 + 0.104622i
\(571\) −4.11555 −0.172230 −0.0861151 0.996285i \(-0.527445\pi\)
−0.0861151 + 0.996285i \(0.527445\pi\)
\(572\) 12.1311 12.1311i 0.507225 0.507225i
\(573\) 17.1151 + 21.0089i 0.714994 + 0.877658i
\(574\) 2.06251i 0.0860874i
\(575\) 3.84325 + 39.6178i 0.160275 + 1.65218i
\(576\) 24.7943 + 5.11805i 1.03310 + 0.213252i
\(577\) −15.3143 15.3143i −0.637542 0.637542i 0.312406 0.949949i \(-0.398865\pi\)
−0.949949 + 0.312406i \(0.898865\pi\)
\(578\) −12.4683 12.4683i −0.518611 0.518611i
\(579\) −2.24231 + 21.9547i −0.0931874 + 0.912406i
\(580\) −2.37619 + 6.62564i −0.0986657 + 0.275115i
\(581\) 7.72438i 0.320461i
\(582\) −6.58590 + 5.36528i −0.272994 + 0.222398i
\(583\) 18.2617 18.2617i 0.756324 0.756324i
\(584\) 5.82563 0.241066
\(585\) −7.24686 29.9385i −0.299621 1.23780i
\(586\) 31.5778 1.30447
\(587\) 23.2211 23.2211i 0.958439 0.958439i −0.0407314 0.999170i \(-0.512969\pi\)
0.999170 + 0.0407314i \(0.0129688\pi\)
\(588\) 0.964471 0.785718i 0.0397741 0.0324025i
\(589\) 2.25101i 0.0927512i
\(590\) −4.16132 + 1.96442i −0.171319 + 0.0808737i
\(591\) 0.694342 6.79837i 0.0285614 0.279647i
\(592\) −3.50506 3.50506i −0.144057 0.144057i
\(593\) 24.2941 + 24.2941i 0.997641 + 0.997641i 0.999997 0.00235668i \(-0.000750155\pi\)
−0.00235668 + 0.999997i \(0.500750\pi\)
\(594\) 9.19956 29.1865i 0.377463 1.19754i
\(595\) −2.51297 0.901239i −0.103022 0.0369472i
\(596\) 6.68380i 0.273779i
\(597\) −15.7881 19.3799i −0.646164 0.793169i
\(598\) 29.2639 29.2639i 1.19669 1.19669i
\(599\) 22.7865 0.931029 0.465515 0.885040i \(-0.345869\pi\)
0.465515 + 0.885040i \(0.345869\pi\)
\(600\) 18.7496 + 18.9409i 0.765448 + 0.773258i
\(601\) −41.7276 −1.70210 −0.851052 0.525082i \(-0.824035\pi\)
−0.851052 + 0.525082i \(0.824035\pi\)
\(602\) −0.319008 + 0.319008i −0.0130018 + 0.0130018i
\(603\) 28.0774 18.4692i 1.14340 0.752124i
\(604\) 12.0859i 0.491769i
\(605\) 33.8028 + 12.1228i 1.37428 + 0.492864i
\(606\) 7.24995 + 0.740464i 0.294509 + 0.0300793i
\(607\) −17.5164 17.5164i −0.710968 0.710968i 0.255770 0.966738i \(-0.417671\pi\)
−0.966738 + 0.255770i \(0.917671\pi\)
\(608\) −3.58168 3.58168i −0.145256 0.145256i
\(609\) −7.55198 0.771312i −0.306022 0.0312551i
\(610\) −5.66636 + 2.67490i −0.229424 + 0.108303i
\(611\) 22.0524i 0.892144i
\(612\) −2.14923 + 1.41376i −0.0868776 + 0.0571478i
\(613\) −25.9860 + 25.9860i −1.04956 + 1.04956i −0.0508591 + 0.998706i \(0.516196\pi\)
−0.998706 + 0.0508591i \(0.983804\pi\)
\(614\) 21.2943 0.859369
\(615\) 2.34811 + 6.65345i 0.0946851 + 0.268293i
\(616\) −16.0086 −0.645005
\(617\) −8.12737 + 8.12737i −0.327196 + 0.327196i −0.851519 0.524323i \(-0.824318\pi\)
0.524323 + 0.851519i \(0.324318\pi\)
\(618\) −2.06769 2.53810i −0.0831747 0.102097i
\(619\) 7.20599i 0.289633i −0.989459 0.144817i \(-0.953741\pi\)
0.989459 0.144817i \(-0.0462592\pi\)
\(620\) −0.924375 + 2.57748i −0.0371238 + 0.103514i
\(621\) −12.4352 + 39.4519i −0.499008 + 1.58315i
\(622\) 19.0571 + 19.0571i 0.764120 + 0.764120i
\(623\) −6.66884 6.66884i −0.267181 0.267181i
\(624\) 1.65474 16.2017i 0.0662424 0.648586i
\(625\) 4.80519 + 24.5339i 0.192208 + 0.981354i
\(626\) 30.3173i 1.21172i
\(627\) −9.22241 + 7.51314i −0.368307 + 0.300046i
\(628\) −4.88860 + 4.88860i −0.195077 + 0.195077i
\(629\) 2.89017 0.115238
\(630\) −3.95611 + 6.48297i −0.157615 + 0.258288i
\(631\) −29.8770 −1.18938 −0.594692 0.803954i \(-0.702726\pi\)
−0.594692 + 0.803954i \(0.702726\pi\)
\(632\) 25.0283 25.0283i 0.995572 0.995572i
\(633\) −16.0934 + 13.1107i −0.639655 + 0.521102i
\(634\) 18.7216i 0.743530i
\(635\) 6.15494 + 13.0383i 0.244251 + 0.517409i
\(636\) −0.627529 + 6.14419i −0.0248831 + 0.243633i
\(637\) −3.24693 3.24693i −0.128648 0.128648i
\(638\) 18.2518 + 18.2518i 0.722597 + 0.722597i
\(639\) −26.6293 5.49684i −1.05344 0.217452i
\(640\) 1.79556 + 3.80361i 0.0709756 + 0.150351i
\(641\) 19.3661i 0.764917i 0.923973 + 0.382458i \(0.124922\pi\)
−0.923973 + 0.382458i \(0.875078\pi\)
\(642\) −2.41731 2.96725i −0.0954035 0.117108i
\(643\) 11.6091 11.6091i 0.457819 0.457819i −0.440120 0.897939i \(-0.645064\pi\)
0.897939 + 0.440120i \(0.145064\pi\)
\(644\) 5.71764 0.225307
\(645\) −0.665906 + 1.39227i −0.0262200 + 0.0548206i
\(646\) −1.78458 −0.0702135
\(647\) 10.6517 10.6517i 0.418760 0.418760i −0.466016 0.884776i \(-0.654311\pi\)
0.884776 + 0.466016i \(0.154311\pi\)
\(648\) 10.2290 + 25.7390i 0.401834 + 1.01112i
\(649\) 9.45560i 0.371165i
\(650\) 16.5196 20.0689i 0.647950 0.787168i
\(651\) −2.93785 0.300053i −0.115143 0.0117600i
\(652\) 6.30580 + 6.30580i 0.246954 + 0.246954i
\(653\) 3.67307 + 3.67307i 0.143738 + 0.143738i 0.775314 0.631576i \(-0.217592\pi\)
−0.631576 + 0.775314i \(0.717592\pi\)
\(654\) −11.5781 1.18251i −0.452740 0.0462400i
\(655\) 10.3252 28.7903i 0.403439 1.12493i
\(656\) 3.73039i 0.145647i
\(657\) 3.12095 + 4.74456i 0.121760 + 0.185103i
\(658\) 3.84466 3.84466i 0.149880 0.149880i
\(659\) 45.6844 1.77961 0.889807 0.456338i \(-0.150839\pi\)
0.889807 + 0.456338i \(0.150839\pi\)
\(660\) −13.6453 + 4.81564i −0.531141 + 0.187449i
\(661\) −21.8518 −0.849935 −0.424968 0.905209i \(-0.639715\pi\)
−0.424968 + 0.905209i \(0.639715\pi\)
\(662\) 9.27823 9.27823i 0.360609 0.360609i
\(663\) 5.99748 + 7.36192i 0.232923 + 0.285913i
\(664\) 23.7714i 0.922510i
\(665\) 2.66965 1.26025i 0.103525 0.0488704i
\(666\) 1.66213 8.05215i 0.0644062 0.312014i
\(667\) −24.6714 24.6714i −0.955279 0.955279i
\(668\) −8.94308 8.94308i −0.346018 0.346018i
\(669\) 3.03220 29.6886i 0.117232 1.14783i
\(670\) 26.6949 + 9.57373i 1.03132 + 0.369865i
\(671\) 12.8755i 0.497051i
\(672\) 5.15197 4.19712i 0.198742 0.161907i
\(673\) 12.1963 12.1963i 0.470132 0.470132i −0.431825 0.901957i \(-0.642130\pi\)
0.901957 + 0.431825i \(0.142130\pi\)
\(674\) 8.74408 0.336809
\(675\) −5.38130 + 25.4173i −0.207126 + 0.978314i
\(676\) 5.80698 0.223345
\(677\) −30.0858 + 30.0858i −1.15629 + 1.15629i −0.171025 + 0.985267i \(0.554708\pi\)
−0.985267 + 0.171025i \(0.945292\pi\)
\(678\) −0.517437 + 0.421536i −0.0198721 + 0.0161890i
\(679\) 4.33195i 0.166245i
\(680\) −7.73356 2.77352i −0.296568 0.106360i
\(681\) 1.03867 10.1697i 0.0398018 0.389703i
\(682\) 7.10027 + 7.10027i 0.271883 + 0.271883i
\(683\) 1.48486 + 1.48486i 0.0568166 + 0.0568166i 0.734944 0.678128i \(-0.237208\pi\)
−0.678128 + 0.734944i \(0.737208\pi\)
\(684\) 0.575084 2.78598i 0.0219889 0.106525i
\(685\) 28.6628 13.5308i 1.09515 0.516984i
\(686\) 1.13215i 0.0432258i
\(687\) 29.8330 + 36.6201i 1.13820 + 1.39714i
\(688\) −0.576980 + 0.576980i −0.0219972 + 0.0219972i
\(689\) 22.7973 0.868507
\(690\) −32.9166 + 11.6168i −1.25312 + 0.442246i
\(691\) 42.2833 1.60853 0.804267 0.594269i \(-0.202558\pi\)
0.804267 + 0.594269i \(0.202558\pi\)
\(692\) −9.90912 + 9.90912i −0.376688 + 0.376688i
\(693\) −8.57627 13.0379i −0.325785 0.495268i
\(694\) 32.3395i 1.22759i
\(695\) 11.9465 33.3111i 0.453157 1.26356i
\(696\) −23.2409 2.37368i −0.880943 0.0899740i
\(697\) −1.53799 1.53799i −0.0582553 0.0582553i
\(698\) 9.58647 + 9.58647i 0.362853 + 0.362853i
\(699\) 4.79544 + 0.489776i 0.181380 + 0.0185250i
\(700\) 3.57437 0.346743i 0.135098 0.0131056i
\(701\) 42.8399i 1.61804i −0.587781 0.809020i \(-0.699998\pi\)
0.587781 0.809020i \(-0.300002\pi\)
\(702\) 23.9598 12.4755i 0.904306 0.470856i
\(703\) −2.25988 + 2.25988i −0.0852332 + 0.0852332i
\(704\) −43.8989 −1.65450
\(705\) 8.02544 16.7795i 0.302255 0.631954i
\(706\) −38.9746 −1.46683
\(707\) 2.62789 2.62789i 0.0988320 0.0988320i
\(708\) 1.42821 + 1.75314i 0.0536756 + 0.0658869i
\(709\) 21.7856i 0.818175i 0.912495 + 0.409087i \(0.134153\pi\)
−0.912495 + 0.409087i \(0.865847\pi\)
\(710\) −9.79506 20.7493i −0.367602 0.778708i
\(711\) 33.7921 + 6.97539i 1.26730 + 0.261598i
\(712\) −20.5230 20.5230i −0.769133 0.769133i
\(713\) −9.59756 9.59756i −0.359432 0.359432i
\(714\) 0.237880 2.32911i 0.00890244 0.0871646i
\(715\) 22.8009 + 48.3003i 0.852706 + 1.80633i
\(716\) 5.05030i 0.188739i
\(717\) −1.91949 + 1.56373i −0.0716846 + 0.0583987i
\(718\) −11.3810 + 11.3810i −0.424735 + 0.424735i
\(719\) 45.9617 1.71408 0.857041 0.515249i \(-0.172301\pi\)
0.857041 + 0.515249i \(0.172301\pi\)
\(720\) −7.15528 + 11.7255i −0.266662 + 0.436985i
\(721\) −1.66946 −0.0621740
\(722\) −13.8151 + 13.8151i −0.514145 + 0.514145i
\(723\) −39.1196 + 31.8693i −1.45487 + 1.18523i
\(724\) 10.1898i 0.378699i
\(725\) −16.9194 13.9270i −0.628371 0.517237i
\(726\) −3.19980 + 31.3295i −0.118756 + 1.16275i
\(727\) −4.37251 4.37251i −0.162168 0.162168i 0.621359 0.783526i \(-0.286581\pi\)
−0.783526 + 0.621359i \(0.786581\pi\)
\(728\) −9.99228 9.99228i −0.370338 0.370338i
\(729\) −15.4826 + 22.1199i −0.573428 + 0.819256i
\(730\) −1.61778 + 4.51095i −0.0598768 + 0.166958i
\(731\) 0.475760i 0.0175966i
\(732\) 1.94476 + 2.38720i 0.0718805 + 0.0882336i
\(733\) −32.0267 + 32.0267i −1.18293 + 1.18293i −0.203952 + 0.978981i \(0.565379\pi\)
−0.978981 + 0.203952i \(0.934621\pi\)
\(734\) −26.7423 −0.987078
\(735\) 1.28893 + 3.65221i 0.0475428 + 0.134714i
\(736\) 30.5423 1.12580
\(737\) −41.2059 + 41.2059i −1.51784 + 1.51784i
\(738\) −5.16940 + 3.40041i −0.190288 + 0.125171i
\(739\) 19.8100i 0.728722i 0.931258 + 0.364361i \(0.118713\pi\)
−0.931258 + 0.364361i \(0.881287\pi\)
\(740\) −3.51567 + 1.65963i −0.129239 + 0.0610092i
\(741\) −10.4460 1.06689i −0.383744 0.0391932i
\(742\) −3.97452 3.97452i −0.145909 0.145909i
\(743\) 14.6828 + 14.6828i 0.538660 + 0.538660i 0.923135 0.384475i \(-0.125618\pi\)
−0.384475 + 0.923135i \(0.625618\pi\)
\(744\) −9.04108 0.923399i −0.331462 0.0338535i
\(745\) 19.5872 + 7.02464i 0.717619 + 0.257363i
\(746\) 7.33110i 0.268411i
\(747\) 19.3601 12.7350i 0.708350 0.465950i
\(748\) 3.15418 3.15418i 0.115328 0.115328i
\(749\) −1.95174 −0.0713151
\(750\) −19.8732 + 9.25844i −0.725668 + 0.338070i
\(751\) −26.6832 −0.973682 −0.486841 0.873491i \(-0.661851\pi\)
−0.486841 + 0.873491i \(0.661851\pi\)
\(752\) 6.95371 6.95371i 0.253576 0.253576i
\(753\) −13.5627 16.6483i −0.494252 0.606696i
\(754\) 22.7849i 0.829777i
\(755\) 35.4184 + 12.7023i 1.28901 + 0.462282i
\(756\) 3.55940 + 1.12192i 0.129454 + 0.0408039i
\(757\) −4.11078 4.11078i −0.149409 0.149409i 0.628445 0.777854i \(-0.283692\pi\)
−0.777854 + 0.628445i \(0.783692\pi\)
\(758\) −10.1275 10.1275i −0.367846 0.367846i
\(759\) 7.28774 71.3549i 0.264528 2.59002i
\(760\) 8.21572 3.87836i 0.298015 0.140683i
\(761\) 22.2859i 0.807862i 0.914789 + 0.403931i \(0.132356\pi\)
−0.914789 + 0.403931i \(0.867644\pi\)
\(762\) −9.80288 + 7.98603i −0.355121 + 0.289303i
\(763\) −4.19672 + 4.19672i −0.151931 + 0.151931i
\(764\) 11.2367 0.406530
\(765\) −1.88425 7.78428i −0.0681252 0.281441i
\(766\) 28.8464 1.04226
\(767\) 5.90201 5.90201i 0.213109 0.213109i
\(768\) 19.8048 16.1342i 0.714645 0.582194i
\(769\) 37.7021i 1.35957i −0.733410 0.6