Properties

Label 105.2.j.a.8.9
Level 105
Weight 2
Character 105.8
Analytic conductor 0.838
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 8.9
Character \(\chi\) \(=\) 105.8
Dual form 105.2.j.a.92.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.800553 + 0.800553i) q^{2} +(-1.09397 - 1.34285i) q^{3} -0.718229i q^{4} +(2.10480 - 0.754855i) q^{5} +(0.199242 - 1.95080i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.17609 - 2.17609i) q^{8} +(-0.606476 + 2.93806i) q^{9} +O(q^{10})\) \(q+(0.800553 + 0.800553i) q^{2} +(-1.09397 - 1.34285i) 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} +(-0.964471 + 0.785718i) q^{12} +(-3.24693 - 3.24693i) q^{13} -1.13215 q^{14} +(-3.31624 - 2.00064i) q^{15} +2.04769 q^{16} +(0.844232 + 0.844232i) q^{17} +(-2.83759 + 1.86656i) 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} +(4.60883 - 2.39973i) q^{27} +(0.507864 + 0.507864i) q^{28} +4.38282 q^{29} +(-1.05320 - 4.25645i) q^{30} -1.70499 q^{31} +(-2.71289 - 2.71289i) q^{32} +(6.98536 - 5.69071i) 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} +(1.23854 + 1.52031i) q^{42} +(-0.281771 - 0.281771i) q^{43} +3.73616 q^{44} +(0.941296 + 6.64183i) q^{45} -9.01279 q^{46} +(-3.39588 - 3.39588i) q^{47} +(-2.24010 - 2.74973i) 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} +(1.77289 - 1.44431i) q^{57} +(3.50868 + 3.50868i) q^{58} +1.81772 q^{59} +(-1.43692 + 2.38182i) q^{60} -2.47514 q^{61} +(-1.36494 - 1.36494i) q^{62} +(-1.64868 - 2.50636i) 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} +(5.07373 + 7.71322i) q^{72} +(-1.33856 - 1.33856i) q^{73} -2.74064 q^{74} +(-8.49022 - 1.70768i) q^{75} +0.948239 q^{76} +(-3.67830 - 3.67830i) q^{77} +(-6.98104 + 5.68718i) 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} +(-4.79466 - 5.88546i) q^{87} +(11.3198 + 11.3198i) q^{88} -9.43116 q^{89} +(-4.56358 + 6.07070i) q^{90} +4.59186 q^{91} +(4.04298 + 4.04298i) q^{92} +(1.86520 + 2.28954i) 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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.800553 + 0.800553i 0.566077 + 0.566077i 0.931027 0.364950i \(-0.118914\pi\)
−0.364950 + 0.931027i \(0.618914\pi\)
\(3\) −1.09397 1.34285i −0.631602 0.775293i
\(4\) 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 \(0.713065\pi\)
\(12\) −0.964471 + 0.785718i −0.278419 + 0.226817i
\(13\) −3.24693 3.24693i −0.900537 0.900537i 0.0949456 0.995482i \(-0.469732\pi\)
−0.995482 + 0.0949456i \(0.969732\pi\)
\(14\) −1.13215 −0.302581
\(15\) −3.31624 2.00064i −0.856249 0.516563i
\(16\) 2.04769 0.511922
\(17\) 0.844232 + 0.844232i 0.204756 + 0.204756i 0.802034 0.597278i \(-0.203751\pi\)
−0.597278 + 0.802034i \(0.703751\pi\)
\(18\) −2.83759 + 1.86656i −0.668826 + 0.439951i
\(19\) 1.32025i 0.302885i 0.988466 + 0.151443i \(0.0483919\pi\)
−0.988466 + 0.151443i \(0.951608\pi\)
\(20\) −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 −0.192440 + 0.981309i \(0.561640\pi\)
−0.981309 + 0.192440i \(0.938360\pi\)
\(24\) −5.30272 0.541586i −1.08241 0.110551i
\(25\) 3.86039 3.17764i 0.772078 0.635528i
\(26\) 5.19868i 1.01955i
\(27\) 4.60883 2.39973i 0.886969 0.461829i
\(28\) 0.507864 + 0.507864i 0.0959774 + 0.0959774i
\(29\) 4.38282 0.813870 0.406935 0.913457i \(-0.366598\pi\)
0.406935 + 0.913457i \(0.366598\pi\)
\(30\) −1.05320 4.25645i −0.192288 0.777117i
\(31\) −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
\(33\) 6.98536 5.69071i 1.21600 0.990625i
\(34\) 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 −0.833669 0.552265i \(-0.813764\pi\)
0.552265 + 0.833669i \(0.313764\pi\)
\(38\) −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 \(0.954565\pi\)
\(42\) 1.23854 + 1.52031i 0.191110 + 0.234589i
\(43\) −0.281771 0.281771i −0.0429697 0.0429697i 0.685295 0.728265i \(-0.259673\pi\)
−0.728265 + 0.685295i \(0.759673\pi\)
\(44\) 3.73616 0.563247
\(45\) 0.941296 + 6.64183i 0.140320 + 0.990106i
\(46\) −9.01279 −1.32886
\(47\) −3.39588 3.39588i −0.495340 0.495340i 0.414644 0.909984i \(-0.363906\pi\)
−0.909984 + 0.414644i \(0.863906\pi\)
\(48\) −2.24010 2.74973i −0.323331 0.396890i
\(49\) 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 \(-0.639242\pi\)
0.905839 + 0.423623i \(0.139242\pi\)
\(54\) 5.61073 + 1.76850i 0.763523 + 0.240662i
\(55\) 3.92668 + 10.9490i 0.529474 + 1.47636i
\(56\) 3.07745i 0.411242i
\(57\) 1.77289 1.44431i 0.234825 0.191303i
\(58\) 3.50868 + 3.50868i 0.460713 + 0.460713i
\(59\) 1.81772 0.236647 0.118323 0.992975i \(-0.462248\pi\)
0.118323 + 0.992975i \(0.462248\pi\)
\(60\) −1.43692 + 2.38182i −0.185505 + 0.307491i
\(61\) −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
\(63\) −1.64868 2.50636i −0.207714 0.315772i
\(64\) 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 −0.0317530 0.999496i \(-0.510109\pi\)
0.999496 + 0.0317530i \(0.0101090\pi\)
\(68\) 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 \(-0.180754\pi\)
\(72\) 5.07373 + 7.71322i 0.597944 + 0.909011i
\(73\) −1.33856 1.33856i −0.156666 0.156666i 0.624422 0.781088i \(-0.285335\pi\)
−0.781088 + 0.624422i \(0.785335\pi\)
\(74\) −2.74064 −0.318592
\(75\) −8.49022 1.70768i −0.980366 0.197186i
\(76\) 0.948239 0.108771
\(77\) −3.67830 3.67830i −0.419182 0.419182i
\(78\) −6.98104 + 5.68718i −0.790447 + 0.643947i
\(79\) 11.5015i 1.29402i −0.762481 0.647011i \(-0.776019\pi\)
0.762481 0.647011i \(-0.223981\pi\)
\(80\) 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 \(-0.889350\pi\)
0.340659 + 0.940187i \(0.389350\pi\)
\(84\) 0.126398 1.23757i 0.0137911 0.135030i
\(85\) 2.41421 + 1.13967i 0.261858 + 0.123614i
\(86\) 0.451146i 0.0486483i
\(87\) −4.79466 5.88546i −0.514041 0.630988i
\(88\) 11.3198 + 11.3198i 1.20669 + 1.20669i
\(89\) −9.43116 −0.999701 −0.499850 0.866112i \(-0.666612\pi\)
−0.499850 + 0.866112i \(0.666612\pi\)
\(90\) −4.56358 + 6.07070i −0.481044 + 0.639908i
\(91\) 4.59186 0.481357
\(92\) 4.04298 + 4.04298i 0.421510 + 0.421510i
\(93\) 1.86520 + 2.28954i 0.193412 + 0.237414i
\(94\) 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 −0.845303 0.534287i \(-0.820580\pi\)
0.534287 + 0.845303i \(0.320580\pi\)
\(98\) 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 \(0.940805\pi\)
\(102\) 1.81513 1.47872i 0.179725 0.146415i
\(103\) 1.18049 + 1.18049i 0.116317 + 0.116317i 0.762869 0.646553i \(-0.223790\pi\)
−0.646553 + 0.762869i \(0.723790\pi\)
\(104\) −14.1312 −1.38568
\(105\) 3.75960 0.930267i 0.366900 0.0907847i
\(106\) 5.62082 0.545943
\(107\) −1.38009 1.38009i −0.133418 0.133418i 0.637244 0.770662i \(-0.280074\pi\)
−0.770662 + 0.637244i \(0.780074\pi\)
\(108\) −1.72356 3.31019i −0.165849 0.318523i
\(109\) 5.93506i 0.568475i 0.958754 + 0.284238i \(0.0917405\pi\)
−0.958754 + 0.284238i \(0.908260\pi\)
\(110\) −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 \(-0.744904\pi\)
0.718336 + 0.695696i \(0.244904\pi\)
\(114\) 2.57554 + 0.263049i 0.241221 + 0.0246368i
\(115\) −7.59899 + 16.0973i −0.708610 + 1.50108i
\(116\) 3.14787i 0.292272i
\(117\) 11.5089 7.57049i 1.06399 0.699892i
\(118\) 1.45518 + 1.45518i 0.133960 + 0.133960i
\(119\) −1.19392 −0.109447
\(120\) −11.5700 + 2.86285i −1.05619 + 0.261341i
\(121\) −16.0598 −1.45998
\(122\) −1.98148 1.98148i −0.179395 0.179395i
\(123\) 2.44634 1.99294i 0.220579 0.179697i
\(124\) 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 −0.879844 0.475263i \(-0.842353\pi\)
0.475263 + 0.879844i \(0.342353\pi\)
\(128\) 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 \(0.796144\pi\)
\(132\) −4.08723 5.01709i −0.355748 0.436682i
\(133\) −0.933556 0.933556i −0.0809495 0.0809495i
\(134\) 12.6829 1.09563
\(135\) 7.88922 8.52996i 0.678996 0.734142i
\(136\) 3.67424 0.315064
\(137\) 10.0232 + 10.0232i 0.856337 + 0.856337i 0.990904 0.134567i \(-0.0429643\pi\)
−0.134567 + 0.990904i \(0.542964\pi\)
\(138\) 9.85969 + 12.1028i 0.839313 + 1.03026i
\(139\) 15.8262i 1.34236i −0.741292 0.671182i \(-0.765787\pi\)
0.741292 0.671182i \(-0.234213\pi\)
\(140\) 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
\(147\) −1.34285 + 1.09397i −0.110756 + 0.0902288i
\(148\) 1.22940 + 1.22940i 0.101056 + 0.101056i
\(149\) 9.30594 0.762373 0.381186 0.924498i \(-0.375516\pi\)
0.381186 + 0.924498i \(0.375516\pi\)
\(150\) −5.42979 8.16396i −0.443340 0.666585i
\(151\) −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
\(153\) −2.99241 + 1.96840i −0.241922 + 0.159135i
\(154\) 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 −0.381255 0.924470i \(-0.624508\pi\)
0.924470 + 0.381255i \(0.124508\pi\)
\(158\) 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
\(162\) −3.76312 9.46902i −0.295659 0.743957i
\(163\) 8.77966 + 8.77966i 0.687676 + 0.687676i 0.961718 0.274042i \(-0.0883607\pi\)
−0.274042 + 0.961718i \(0.588361\pi\)
\(164\) 1.30844 0.102172
\(165\) 10.4072 17.2508i 0.810196 1.34297i
\(166\) −8.74519 −0.678758
\(167\) 12.4516 + 12.4516i 0.963532 + 0.963532i 0.999358 0.0358258i \(-0.0114062\pi\)
−0.0358258 + 0.999358i \(0.511406\pi\)
\(168\) 4.13255 3.36663i 0.318833 0.259741i
\(169\) 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 −0.0501977 + 0.998739i \(0.515985\pi\)
−0.998739 + 0.0501977i \(0.984015\pi\)
\(174\) 0.873244 8.55000i 0.0662004 0.648174i
\(175\) −0.482774 + 4.97664i −0.0364943 + 0.376198i
\(176\) 10.6519i 0.802916i
\(177\) −1.98852 2.44092i −0.149466 0.183471i
\(178\) −7.55015 7.55015i −0.565907 0.565907i
\(179\) 7.03160 0.525567 0.262783 0.964855i \(-0.415360\pi\)
0.262783 + 0.964855i \(0.415360\pi\)
\(180\) 4.77036 0.676066i 0.355561 0.0503910i
\(181\) 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
\(183\) 2.70772 + 3.32374i 0.200161 + 0.245698i
\(184\) 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 \(-0.191516\pi\)
\(192\) −11.3323 + 9.23199i −0.817838 + 0.666261i
\(193\) 9.00959 + 9.00959i 0.648525 + 0.648525i 0.952636 0.304112i \(-0.0983596\pi\)
−0.304112 + 0.952636i \(0.598360\pi\)
\(194\) −4.90443 −0.352118
\(195\) 4.27165 + 17.2635i 0.305899 + 1.23627i
\(196\) −0.718229 −0.0513021
\(197\) 2.78986 + 2.78986i 0.198769 + 0.198769i 0.799472 0.600703i \(-0.205113\pi\)
−0.600703 + 0.799472i \(0.705113\pi\)
\(198\) −9.70965 14.7609i −0.690035 1.04901i
\(199\) 14.4320i 1.02306i −0.859266 0.511528i \(-0.829080\pi\)
0.859266 0.511528i \(-0.170920\pi\)
\(200\) 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
\(207\) −13.1247 19.9525i −0.912231 1.38680i
\(208\) −6.64871 6.64871i −0.461005 0.461005i
\(209\) −6.86780 −0.475056
\(210\) 3.75449 + 2.26503i 0.259084 + 0.156302i
\(211\) 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
\(213\) −12.1710 + 9.91525i −0.833943 + 0.679382i
\(214\) 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
\(222\) 2.99816 + 3.68025i 0.201224 + 0.247003i
\(223\) −12.1834 12.1834i −0.815858 0.815858i 0.169647 0.985505i \(-0.445737\pi\)
−0.985505 + 0.169647i \(0.945737\pi\)
\(224\) 3.83661 0.256344
\(225\) 6.99486 + 13.2692i 0.466324 + 0.884614i
\(226\) 0.385328 0.0256317
\(227\) 4.17335 + 4.17335i 0.276995 + 0.276995i 0.831908 0.554913i \(-0.187249\pi\)
−0.554913 + 0.831908i \(0.687249\pi\)
\(228\) −1.03734 1.27334i −0.0686996 0.0843290i
\(229\) 27.2705i 1.80209i 0.433730 + 0.901043i \(0.357197\pi\)
−0.433730 + 0.901043i \(0.642803\pi\)
\(230\) −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 \(-0.720942\pi\)
0.768624 + 0.639701i \(0.220942\pi\)
\(234\) 15.2740 + 3.15288i 0.998495 + 0.206110i
\(235\) −9.71106 4.58426i −0.633480 0.299044i
\(236\) 1.30554i 0.0849832i
\(237\) −15.4448 + 12.5823i −1.00325 + 0.817306i
\(238\) −0.955800 0.955800i −0.0619553 0.0619553i
\(239\) −1.42942 −0.0924613 −0.0462307 0.998931i \(-0.514721\pi\)
−0.0462307 + 0.998931i \(0.514721\pi\)
\(240\) −6.79063 4.09669i −0.438333 0.264440i
\(241\) 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
\(243\) 4.25541 + 14.9964i 0.272985 + 0.962018i
\(244\) 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 \(0.872036\pi\)
\(252\) −1.80014 + 1.18413i −0.113398 + 0.0745931i
\(253\) −29.2821 29.2821i −1.84095 1.84095i
\(254\) −7.30007 −0.458047
\(255\) −1.11067 4.48868i −0.0695527 0.281092i
\(256\) −14.7484 −0.921774
\(257\) −13.8717 13.8717i −0.865290 0.865290i 0.126657 0.991947i \(-0.459575\pi\)
−0.991947 + 0.126657i \(0.959575\pi\)
\(258\) −0.605820 + 0.493538i −0.0377167 + 0.0307263i
\(259\) 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 \(-0.930036\pi\)
0.218032 + 0.975942i \(0.430036\pi\)
\(264\) 2.81728 27.5842i 0.173392 1.69769i
\(265\) 4.73911 10.0391i 0.291121 0.616695i
\(266\) 1.49472i 0.0916473i
\(267\) 10.3174 + 12.6646i 0.631413 + 0.775061i
\(268\) −5.68932 5.68932i −0.347530 0.347530i
\(269\) −19.1535 −1.16781 −0.583906 0.811822i \(-0.698476\pi\)
−0.583906 + 0.811822i \(0.698476\pi\)
\(270\) 13.1444 0.512945i 0.799944 0.0312169i
\(271\) 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
\(273\) −5.02333 6.16616i −0.304026 0.373193i
\(274\) 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 −0.898751 0.438460i \(-0.855524\pi\)
0.438460 + 0.898751i \(0.355524\pi\)
\(278\) 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 \(-0.208995\pi\)
\(282\) −7.30129 + 5.94808i −0.434785 + 0.354203i
\(283\) 8.24528 + 8.24528i 0.490131 + 0.490131i 0.908347 0.418216i \(-0.137345\pi\)
−0.418216 + 0.908347i \(0.637345\pi\)
\(284\) −6.50972 −0.386281
\(285\) 2.64134 4.37825i 0.156460 0.259345i
\(286\) 27.0431 1.59909
\(287\) −1.28818 1.28818i −0.0760387 0.0760387i
\(288\) 9.61593 6.32533i 0.566624 0.372723i
\(289\) 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 0.166088 0.986111i \(-0.446886\pi\)
0.986111 0.166088i \(-0.0531135\pi\)
\(294\) −1.95080 0.199242i −0.113773 0.0116200i
\(295\) 3.82594 1.37211i 0.222755 0.0798875i
\(296\) 7.44968i 0.433004i
\(297\) 12.4832 + 23.9747i 0.724348 + 1.39115i
\(298\) 7.44990 + 7.44990i 0.431561 + 0.431561i
\(299\) 36.5546 2.11401
\(300\) −1.22650 + 6.09792i −0.0708122 + 0.352064i
\(301\) 0.398485 0.0229683
\(302\) −13.4712 13.4712i −0.775182 0.775182i
\(303\) 4.99056 4.06562i 0.286700 0.233564i
\(304\) 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 −0.976151 0.217094i \(-0.930342\pi\)
0.217094 + 0.976151i \(0.430342\pi\)
\(308\) −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 \(-0.235824\pi\)
\(312\) 15.4591 + 18.9761i 0.875197 + 1.07431i
\(313\) −18.9352 18.9352i −1.07028 1.07028i −0.997336 0.0729475i \(-0.976759\pi\)
−0.0729475 0.997336i \(-0.523241\pi\)
\(314\) 10.8979 0.615003
\(315\) −5.36208 4.03089i −0.302119 0.227115i
\(316\) −8.26072 −0.464702
\(317\) −11.6929 11.6929i −0.656739 0.656739i 0.297868 0.954607i \(-0.403725\pi\)
−0.954607 + 0.297868i \(0.903725\pi\)
\(318\) −6.14899 7.54790i −0.344818 0.423265i
\(319\) 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
\(327\) 7.96987 6.49275i 0.440735 0.359050i
\(328\) 3.96430 + 3.96430i 0.218892 + 0.218892i
\(329\) 4.80250 0.264771
\(330\) 22.1416 5.47867i 1.21886 0.301591i
\(331\) −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
\(333\) −3.99100 6.06723i −0.218706 0.332482i
\(334\) 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 −0.840032 0.542537i \(-0.817464\pi\)
0.542537 + 0.840032i \(0.317464\pi\)
\(338\) −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
\(342\) −2.46431 3.74632i −0.133255 0.202578i
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) −1.22632 −0.0661186
\(345\) 29.9293 7.40562i 1.61134 0.398705i
\(346\) −22.0898 −1.18756
\(347\) 20.1982 + 20.1982i 1.08430 + 1.08430i 0.996103 + 0.0881938i \(0.0281095\pi\)
0.0881938 + 0.996103i \(0.471891\pi\)
\(348\) −4.22711 + 3.44366i −0.226597 + 0.184600i
\(349\) 11.9748i 0.640997i 0.947249 + 0.320498i \(0.103850\pi\)
−0.947249 + 0.320498i \(0.896150\pi\)
\(350\) −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 −0.364345 + 0.931264i \(0.618707\pi\)
−0.931264 + 0.364345i \(0.881293\pi\)
\(354\) 0.362166 3.54600i 0.0192489 0.188468i
\(355\) −6.84169 19.0770i −0.363119 1.01250i
\(356\) 6.77373i 0.359007i
\(357\) 1.30611 + 1.60326i 0.0691268 + 0.0848534i
\(358\) 5.62917 + 5.62917i 0.297511 + 0.297511i
\(359\) −14.2164 −0.750314 −0.375157 0.926961i \(-0.622411\pi\)
−0.375157 + 0.926961i \(0.622411\pi\)
\(360\) 16.5016 + 12.4049i 0.869708 + 0.653794i
\(361\) 17.2569 0.908260
\(362\) 11.3577 + 11.3577i 0.596948 + 0.596948i
\(363\) 17.5689 + 21.5659i 0.922129 + 1.13192i
\(364\) 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 −0.120816 0.992675i \(-0.538551\pi\)
0.992675 + 0.120816i \(0.0385512\pi\)
\(368\) −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
\(372\) 1.64441 1.33964i 0.0852589 0.0694572i
\(373\) 4.57877 + 4.57877i 0.237080 + 0.237080i 0.815640 0.578560i \(-0.196385\pi\)
−0.578560 + 0.815640i \(0.696385\pi\)
\(374\) −7.03144 −0.363587
\(375\) −19.1593 + 2.81456i −0.989381 + 0.145343i
\(376\) −14.7795 −0.762193
\(377\) −14.2307 14.2307i −0.732920 0.732920i
\(378\) −5.21790 + 2.71686i −0.268380 + 0.139740i
\(379\) 12.6506i 0.649816i −0.945746 0.324908i \(-0.894667\pi\)
0.945746 0.324908i \(-0.105333\pi\)
\(380\) 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 \(-0.524365\pi\)
0.997072 + 0.0764705i \(0.0243651\pi\)
\(384\) −3.24119 0.331035i −0.165401 0.0168930i
\(385\) −10.5187 4.96552i −0.536082 0.253066i
\(386\) 14.4253i 0.734229i
\(387\) 0.998748 0.656973i 0.0507692 0.0333958i
\(388\) 2.20004 + 2.20004i 0.111690 + 0.111690i
\(389\) −17.7215 −0.898517 −0.449259 0.893402i \(-0.648312\pi\)
−0.449259 + 0.893402i \(0.648312\pi\)
\(390\) −10.4007 + 17.2401i −0.526660 + 0.872985i
\(391\) −9.50453 −0.480665
\(392\) −2.17609 2.17609i −0.109909 0.109909i
\(393\) 18.3680 14.9637i 0.926543 0.754819i
\(394\) 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 −0.587136 0.809489i \(-0.699745\pi\)
0.809489 + 0.587136i \(0.199745\pi\)
\(398\) 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 \(0.669918\pi\)
\(402\) −13.8746 17.0312i −0.692004 0.849437i
\(403\) 5.53599 + 5.53599i 0.275767 + 0.275767i
\(404\) 2.66923 0.132799
\(405\) −20.0850 1.26253i −0.998030 0.0627356i
\(406\) −4.96203 −0.246261
\(407\) −8.90417 8.90417i −0.441364 0.441364i
\(408\) −4.01950 4.93395i −0.198995 0.244267i
\(409\) 19.5663i 0.967490i 0.875209 + 0.483745i \(0.160724\pi\)
−0.875209 + 0.483745i \(0.839276\pi\)
\(410\) −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
\(417\) −21.2522 + 17.3134i −1.04073 + 0.847840i
\(418\) −5.49804 5.49804i −0.268918 0.268918i
\(419\) −17.0209 −0.831524 −0.415762 0.909474i \(-0.636485\pi\)
−0.415762 + 0.909474i \(0.636485\pi\)
\(420\) −0.668144 2.70025i −0.0326021 0.131759i
\(421\) 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
\(423\) 12.0368 7.91778i 0.585250 0.384976i
\(424\) 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 \(0.916311\pi\)
\(432\) 9.43745 4.91391i 0.454059 0.236420i
\(433\) 0.466927 + 0.466927i 0.0224391 + 0.0224391i 0.718237 0.695798i \(-0.244949\pi\)
−0.695798 + 0.718237i \(0.744949\pi\)
\(434\) 1.93031 0.0926579
\(435\) −14.5345 8.76846i −0.696875 0.420415i
\(436\) 4.26273 0.204148
\(437\) −7.43180 7.43180i −0.355511 0.355511i
\(438\) −2.87795 + 2.34456i −0.137514 + 0.112027i
\(439\) 9.43662i 0.450385i −0.974314 0.225193i \(-0.927699\pi\)
0.974314 0.225193i \(-0.0723011\pi\)
\(440\) 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 \(-0.557865\pi\)
0.983522 + 0.180788i \(0.0578647\pi\)
\(444\) 0.305975 2.99582i 0.0145209 0.142175i
\(445\) −19.8507 + 7.11916i −0.941015 + 0.337480i
\(446\) 19.5068i 0.923676i
\(447\) −10.1804 12.4965i −0.481516 0.591062i
\(448\) 5.96728 + 5.96728i 0.281927 + 0.281927i
\(449\) −11.5643 −0.545753 −0.272876 0.962049i \(-0.587975\pi\)
−0.272876 + 0.962049i \(0.587975\pi\)
\(450\) −5.02295 + 16.2225i −0.236784 + 0.764735i
\(451\) −9.47661 −0.446236
\(452\) −0.172852 0.172852i −0.00813026 0.00813026i
\(453\) 18.4086 + 22.5966i 0.864912 + 1.06168i
\(454\) 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 −0.988139 0.153560i \(-0.950926\pi\)
0.153560 + 0.988139i \(0.450926\pi\)
\(458\) −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 \(-0.0983438\pi\)
\(462\) −7.90850 + 6.44276i −0.367937 + 0.299744i
\(463\) 17.3925 + 17.3925i 0.808298 + 0.808298i 0.984376 0.176079i \(-0.0563413\pi\)
−0.176079 + 0.984376i \(0.556341\pi\)
\(464\) 8.97466 0.416638
\(465\) 5.65415 + 3.41107i 0.262205 + 0.158185i
\(466\) 3.15084 0.145960
\(467\) 9.40605 + 9.40605i 0.435260 + 0.435260i 0.890413 0.455153i \(-0.150415\pi\)
−0.455153 + 0.890413i \(0.650415\pi\)
\(468\) −5.43734 8.26600i −0.251341 0.382096i
\(469\) 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
\(477\) 8.18522 + 12.4434i 0.374776 + 0.569744i
\(478\) −1.14432 1.14432i −0.0523402 0.0523402i
\(479\) 38.8689 1.77596 0.887982 0.459879i \(-0.152107\pi\)
0.887982 + 0.459879i \(0.152107\pi\)
\(480\) 3.56907 + 14.4241i 0.162905 + 0.658367i
\(481\) 11.1156 0.506829
\(482\) 23.3216 + 23.3216i 1.06227 + 1.06227i
\(483\) −10.6901 + 8.70879i −0.486415 + 0.396264i
\(484\) 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 0.0895148 0.995985i \(-0.471468\pi\)
0.995985 0.0895148i \(-0.0285316\pi\)
\(488\) −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 \(0.803569\pi\)
\(492\) −1.43139 1.75703i −0.0645319 0.0792132i
\(493\) 3.70012 + 3.70012i 0.166645 + 0.166645i
\(494\) 6.86355 0.308806
\(495\) −34.5502 + 4.89653i −1.55292 + 0.220083i
\(496\) −3.49129 −0.156764
\(497\) 6.40892 + 6.40892i 0.287479 + 0.287479i
\(498\) 9.56694 + 11.7434i 0.428705 + 0.526236i
\(499\) 29.1057i 1.30295i −0.758669 0.651476i \(-0.774150\pi\)
0.758669 0.651476i \(-0.225850\pi\)
\(500\) −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 \(-0.853965\pi\)
0.442855 + 0.896593i \(0.353965\pi\)
\(504\) −9.04173 1.86640i −0.402751 0.0831361i
\(505\) 2.80534 + 7.82229i 0.124836 + 0.348087i
\(506\) 46.8837i 2.08423i
\(507\) 10.8571 8.84486i 0.482181 0.392814i
\(508\) 3.27469 + 3.27469i 0.145291 + 0.145291i
\(509\) 31.2970 1.38721 0.693607 0.720354i \(-0.256021\pi\)
0.693607 + 0.720354i \(0.256021\pi\)
\(510\) 2.70428 4.48257i 0.119747 0.198492i
\(511\) 1.89300 0.0837415
\(512\) −14.4671 14.4671i −0.639360 0.639360i
\(513\) 3.16824 + 6.08479i 0.139881 + 0.268650i
\(514\) 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 \(0.819972\pi\)
\(522\) −12.4366 + 8.18078i −0.544337 + 0.358063i
\(523\) 1.82790 + 1.82790i 0.0799284 + 0.0799284i 0.745941 0.666012i \(-0.232000\pi\)
−0.666012 + 0.745941i \(0.732000\pi\)
\(524\) 9.82422 0.429173
\(525\) 7.21100 4.79598i 0.314714 0.209314i
\(526\) −19.6796 −0.858069
\(527\) −1.43941 1.43941i −0.0627015 0.0627015i
\(528\) 14.3039 11.6528i 0.622495 0.507123i
\(529\) 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
\(537\) −7.69234 9.44237i −0.331949 0.407468i
\(538\) −15.3334 15.3334i −0.661071 0.661071i
\(539\) 5.20191 0.224062
\(540\) −6.12646 5.66627i −0.263641 0.243837i
\(541\) 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
\(543\) −15.5205 19.0514i −0.666047 0.817575i
\(544\) 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 −0.997513 0.0704885i \(-0.977544\pi\)
0.0704885 + 0.997513i \(0.477544\pi\)
\(548\) 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
\(552\) 32.8982 26.8009i 1.40024 1.14072i
\(553\) 8.13280 + 8.13280i 0.345842 + 0.345842i
\(554\) −12.2657 −0.521119
\(555\) 9.10098 2.25192i 0.386315 0.0955888i
\(556\) −11.3669 −0.482063
\(557\) −13.1204 13.1204i −0.555929 0.555929i 0.372217 0.928146i \(-0.378598\pi\)
−0.928146 + 0.372217i \(0.878598\pi\)
\(558\) 4.83806 3.18246i 0.204811 0.134724i
\(559\) 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 \(-0.592690\pi\)
0.957901 + 0.287097i \(0.0926903\pi\)
\(564\) 5.94344 + 0.607025i 0.250264 + 0.0255604i
\(565\) 0.324884 0.688216i 0.0136680 0.0289535i
\(566\) 13.2016i 0.554903i
\(567\) 8.36373 3.32386i 0.351244 0.139589i
\(568\) −19.7231 19.7231i −0.827565 0.827565i
\(569\) 27.8303 1.16671 0.583354 0.812218i \(-0.301740\pi\)
0.583354 + 0.812218i \(0.301740\pi\)
\(570\) 5.61956 1.39049i 0.235377 0.0582412i
\(571\) −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
\(573\) −21.0089 + 17.1151i −0.877658 + 0.714994i
\(574\) 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 −0.949949 0.312406i \(-0.898865\pi\)
0.312406 + 0.949949i \(0.398865\pi\)
\(578\) 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
\(582\) 5.36528 + 6.58590i 0.222398 + 0.272994i
\(583\) 18.2617 + 18.2617i 0.756324 + 0.756324i
\(584\) −5.82563 −0.241066
\(585\) 18.5093 24.6219i 0.765264 1.01799i
\(586\) 31.5778 1.30447
\(587\) −23.2211 23.2211i −0.958439 0.958439i 0.0407314 0.999170i \(-0.487031\pi\)
−0.999170 + 0.0407314i \(0.987031\pi\)
\(588\) 0.785718 + 0.964471i 0.0324025 + 0.0397741i
\(589\) 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 \(-0.999250\pi\)
0.00235668 + 0.999997i \(0.499250\pi\)
\(594\) −9.19956 + 29.1865i −0.377463 + 1.19754i
\(595\) −2.51297 + 0.901239i −0.103022 + 0.0369472i
\(596\) 6.68380i 0.273779i
\(597\) −19.3799 + 15.7881i −0.793169 + 0.646164i
\(598\) 29.2639 + 29.2639i 1.19669 + 1.19669i
\(599\) −22.7865 −0.931029 −0.465515 0.885040i \(-0.654131\pi\)
−0.465515 + 0.885040i \(0.654131\pi\)
\(600\) −22.1915 + 14.7594i −0.905965 + 0.602550i
\(601\) −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
\(603\) 18.4692 + 28.0774i 0.752124 + 1.14340i
\(604\) 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 −0.966738 0.255770i \(-0.917671\pi\)
0.255770 + 0.966738i \(0.417671\pi\)
\(608\) 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
\(612\) 1.41376 + 2.14923i 0.0571478 + 0.0868776i
\(613\) −25.9860 25.9860i −1.04956 1.04956i −0.998706 0.0508591i \(-0.983804\pi\)
−0.0508591 0.998706i \(-0.516196\pi\)
\(614\) −21.2943 −0.859369
\(615\) 3.64468 6.04138i 0.146968 0.243612i
\(616\) −16.0086 −0.645005
\(617\) 8.12737 + 8.12737i 0.327196 + 0.327196i 0.851519 0.524323i \(-0.175682\pi\)
−0.524323 + 0.851519i \(0.675682\pi\)
\(618\) 2.53810 2.06769i 0.102097 0.0831747i
\(619\) 7.20599i 0.289633i 0.989459 + 0.144817i \(0.0462592\pi\)
−0.989459 + 0.144817i \(0.953741\pi\)
\(620\) 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
\(627\) 7.51314 + 9.22241i 0.300046 + 0.368307i
\(628\) −4.88860 4.88860i −0.195077 0.195077i
\(629\) −2.89017 −0.115238
\(630\) −1.06569 7.51957i −0.0424582 0.299587i
\(631\) −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
\(633\) −13.1107 16.0934i −0.521102 0.639655i
\(634\) 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 \(0.875078\pi\)
\(642\) −2.96725 + 2.41731i −0.117108 + 0.0954035i
\(643\) 11.6091 + 11.6091i 0.457819 + 0.457819i 0.897939 0.440120i \(-0.145064\pi\)
−0.440120 + 0.897939i \(0.645064\pi\)
\(644\) −5.71764 −0.225307
\(645\) 0.370697 + 1.49814i 0.0145962 + 0.0589893i
\(646\) −1.78458 −0.0702135
\(647\) −10.6517 10.6517i −0.418760 0.418760i 0.466016 0.884776i \(-0.345689\pi\)
−0.884776 + 0.466016i \(0.845689\pi\)
\(648\) −25.7390 + 10.2290i −1.01112 + 0.401834i
\(649\) 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 \(-0.782408\pi\)
0.631576 + 0.775314i \(0.282408\pi\)
\(654\) 11.5781 + 1.18251i 0.452740 + 0.0462400i
\(655\) 10.3252 + 28.7903i 0.403439 + 1.12493i
\(656\) 3.73039i 0.145647i
\(657\) 4.74456 3.12095i 0.185103 0.121760i
\(658\) 3.84466 + 3.84466i 0.149880 + 0.149880i
\(659\) −45.6844 −1.77961 −0.889807 0.456338i \(-0.849161\pi\)
−0.889807 + 0.456338i \(0.849161\pi\)
\(660\) −12.3900 7.47472i −0.482280 0.290953i
\(661\) −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
\(663\) −7.36192 + 5.99748i −0.285913 + 0.232923i
\(664\) 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
\(672\) −4.19712 5.15197i −0.161907 0.198742i
\(673\) 12.1963 + 12.1963i 0.470132 + 0.470132i 0.901957 0.431825i \(-0.142130\pi\)
−0.431825 + 0.901957i \(0.642130\pi\)
\(674\) −8.74408 −0.336809
\(675\) 10.1664 23.9091i 0.391304 0.920262i
\(676\) 5.80698 0.223345
\(677\) 30.0858 + 30.0858i 1.15629 + 1.15629i 0.985267 + 0.171025i \(0.0547080\pi\)
0.171025 + 0.985267i \(0.445292\pi\)
\(678\) −0.421536 0.517437i −0.0161890 0.0198721i
\(679\) 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 \(-0.762792\pi\)
0.678128 + 0.734944i \(0.262792\pi\)
\(684\) −0.575084 + 2.78598i −0.0219889 + 0.106525i
\(685\) 28.6628 + 13.5308i 1.09515 + 0.516984i
\(686\) 1.13215i 0.0432258i
\(687\) 36.6201 29.8330i 1.39714 1.13820i
\(688\) −0.576980 0.576980i −0.0219972 0.0219972i
\(689\) −22.7973 −0.868507
\(690\) 29.8886 + 18.0314i 1.13784 + 0.686442i
\(691\) 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
\(693\) 13.0379 8.57627i 0.495268 0.325785i
\(694\) 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 \(-0.300002\pi\)
\(702\) −12.4755 23.9598i −0.470856 0.904306i
\(703\) −2.25988 2.25988i −0.0852332 0.0852332i
\(704\) 43.8989 1.65450
\(705\) 4.46761 + 18.0555i 0.168260 + 0.680009i
\(706\) −38.9746 −1.46683
\(707\) −2.62789 2.62789i −0.0988320 0.0988320i
\(708\) −1.75314 + 1.42821i −0.0658869 + 0.0536756i
\(709\) 21.7856i 0.818175i −0.912495 0.409087i \(-0.865847\pi\)
0.912495 0.409087i \(-0.134153\pi\)
\(710\) 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
\(717\) 1.56373 + 1.91949i 0.0583987 + 0.0716846i
\(718\) −11.3810 11.3810i −0.424735 0.424735i
\(719\) −45.9617 −1.71408 −0.857041 0.515249i \(-0.827699\pi\)
−0.857041 + 0.515249i \(0.827699\pi\)
\(720\) 1.92748 + 13.6004i 0.0718330 + 0.506858i
\(721\) −1.66946 −0.0621740
\(722\) 13.8151 + 13.8151i 0.514145 + 0.514145i
\(723\) −31.8693 39.1196i −1.18523 1.45487i
\(724\) 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 −0.783526 0.621359i \(-0.786581\pi\)
0.621359 + 0.783526i \(0.286581\pi\)
\(728\) 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
\(732\) 2.38720 1.94476i 0.0882336 0.0718805i
\(733\) −32.0267 32.0267i −1.18293 1.18293i −0.978981 0.203952i \(-0.934621\pi\)
−0.203952 0.978981i \(-0.565379\pi\)
\(734\) 26.7423 0.987078
\(735\) −2.00064 + 3.31624i −0.0737948 + 0.122321i
\(736\) 30.5423 1.12580
\(737\) 41.2059 + 41.2059i 1.51784 + 1.51784i
\(738\) −3.40041 5.16940i −0.125171 0.190288i
\(739\) 19.8100i 0.728722i −0.931258 0.364361i \(-0.881287\pi\)
0.931258 0.364361i \(-0.118713\pi\)
\(740\) 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 \(-0.874382\pi\)
0.384475 + 0.923135i \(0.374382\pi\)
\(744\) 9.04108 + 0.923399i 0.331462 + 0.0338535i
\(745\) 19.5872 7.02464i 0.717619 0.257363i
\(746\) 7.33110i 0.268411i
\(747\) −12.7350 19.3601i −0.465950 0.708350i
\(748\) 3.15418 + 3.15418i 0.115328 + 0.115328i
\(749\) 1.95174 0.0713151
\(750\) −17.5912 13.0848i −0.642341 0.477790i
\(751\) −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
\(753\) 16.6483 13.5627i 0.606696 0.494252i
\(754\) 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 −0.777854 0.628445i \(-0.783692\pi\)
0.628445 + 0.777854i \(0.283692\pi\)
\(758\) 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 \(0.867644\pi\)
\(762\) 7.98603 + 9.80288i 0.289303 + 0.355121i
\(763\) −4.19672 4.19672i −0.151931 0.151931i
\(764\) −11.2367 −0.406530
\(765\) −4.81257 + 6.40192i −0.173999 + 0.231462i
\(766\) 28.8464 1.04226
\(767\) −5.90201 5.90201i −0.213109 0.213109i
\(768\) 16.1342 + 19.8048i 0.582194 + 0.714645i
\(769\) 37.7021i 1.35957i