Properties

Label 525.2.j.b.218.4
Level 525
Weight 2
Character 525.218
Analytic conductor 4.192
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 218.4
Character \(\chi\) \(=\) 525.218
Dual form 525.2.j.b.407.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.800553 - 0.800553i) q^{2} +(1.09397 + 1.34285i) q^{3} -0.718229i q^{4} +(0.199242 - 1.95080i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.17609 + 2.17609i) q^{8} +(-0.606476 + 2.93806i) q^{9} +O(q^{10})\) \(q+(-0.800553 - 0.800553i) q^{2} +(1.09397 + 1.34285i) q^{3} -0.718229i q^{4} +(0.199242 - 1.95080i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.17609 + 2.17609i) q^{8} +(-0.606476 + 2.93806i) q^{9} +5.20191i q^{11} +(0.964471 - 0.785718i) q^{12} +(3.24693 + 3.24693i) q^{13} -1.13215 q^{14} +2.04769 q^{16} +(-0.844232 - 0.844232i) q^{17} +(2.83759 - 1.86656i) q^{18} +1.32025i q^{19} +(1.72309 + 0.175985i) q^{21} +(4.16440 - 4.16440i) q^{22} +(5.62910 - 5.62910i) q^{23} +(-5.30272 - 0.541586i) q^{24} -5.19868i q^{26} +(-4.60883 + 2.39973i) q^{27} +(-0.507864 - 0.507864i) q^{28} +4.38282 q^{29} -1.70499 q^{31} +(2.71289 + 2.71289i) q^{32} +(-6.98536 + 5.69071i) q^{33} +1.35170i q^{34} +(2.11020 + 0.435588i) q^{36} +(1.71171 - 1.71171i) q^{37} +(1.05693 - 1.05693i) q^{38} +(-0.808099 + 7.91217i) q^{39} +1.82176i q^{41} +(-1.23854 - 1.52031i) q^{42} +(0.281771 + 0.281771i) q^{43} +3.73616 q^{44} -9.01279 q^{46} +(3.39588 + 3.39588i) q^{47} +(2.24010 + 2.74973i) q^{48} -1.00000i q^{49} +(0.210113 - 2.05723i) q^{51} +(2.33204 - 2.33204i) q^{52} +(-3.51059 + 3.51059i) q^{53} +(5.61073 + 1.76850i) q^{54} +3.07745i q^{56} +(-1.77289 + 1.44431i) q^{57} +(-3.50868 - 3.50868i) q^{58} +1.81772 q^{59} -2.47514 q^{61} +(1.36494 + 1.36494i) q^{62} +(1.64868 + 2.50636i) q^{63} -8.43900i q^{64} +(10.1479 + 1.03644i) q^{66} +(-7.92132 + 7.92132i) q^{67} +(-0.606352 + 0.606352i) q^{68} +(13.7171 + 1.40098i) q^{69} -9.06358i q^{71} +(-5.07373 - 7.71322i) q^{72} +(1.33856 + 1.33856i) q^{73} -2.74064 q^{74} +0.948239 q^{76} +(3.67830 + 3.67830i) q^{77} +(6.98104 - 5.68718i) q^{78} -11.5015i q^{79} +(-8.26437 - 3.56372i) q^{81} +(1.45841 - 1.45841i) q^{82} +(5.46196 - 5.46196i) q^{83} +(0.126398 - 1.23757i) q^{84} -0.451146i q^{86} +(4.79466 + 5.88546i) q^{87} +(-11.3198 - 11.3198i) q^{88} -9.43116 q^{89} +4.59186 q^{91} +(-4.04298 - 4.04298i) q^{92} +(-1.86520 - 2.28954i) q^{93} -5.43717i q^{94} +(-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 4q^{3} + O(q^{10}) \) \( 24q + 4q^{3} - 16q^{12} + 8q^{13} - 16q^{16} + 20q^{18} + 4q^{21} - 8q^{22} + 16q^{27} - 28q^{33} + 16q^{36} + 16q^{37} + 20q^{42} + 40q^{43} - 64q^{46} - 16q^{48} - 20q^{51} - 4q^{57} - 40q^{58} + 32q^{61} + 8q^{63} - 16q^{66} - 24q^{67} + 8q^{72} - 32q^{73} + 32q^{76} - 60q^{78} + 52q^{81} + 80q^{82} - 4q^{87} - 96q^{88} - 24q^{91} + 76q^{93} - 96q^{96} - 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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 0.364950 0.931027i \(-0.381086\pi\)
−0.931027 + 0.364950i \(0.881086\pi\)
\(3\) 1.09397 + 1.34285i 0.631602 + 0.775293i
\(4\) 0.718229i 0.359114i
\(5\) 0 0
\(6\) 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
\(10\) 0 0
\(11\) 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 0.995482 0.0949456i \(-0.0302677\pi\)
−0.0949456 + 0.995482i \(0.530268\pi\)
\(14\) −1.13215 −0.302581
\(15\) 0 0
\(16\) 2.04769 0.511922
\(17\) −0.844232 0.844232i −0.204756 0.204756i 0.597278 0.802034i \(-0.296249\pi\)
−0.802034 + 0.597278i \(0.796249\pi\)
\(18\) 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 0
\(21\) 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 \(-0.438360\pi\)
0.981309 0.192440i \(-0.0616401\pi\)
\(24\) −5.30272 0.541586i −1.08241 0.110551i
\(25\) 0 0
\(26\) 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 \(0.366598\pi\)
\(30\) 0 0
\(31\) −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 0
\(36\) 2.11020 + 0.435588i 0.351700 + 0.0725981i
\(37\) 1.71171 1.71171i 0.281404 0.281404i −0.552265 0.833669i \(-0.686236\pi\)
0.833669 + 0.552265i \(0.186236\pi\)
\(38\) 1.05693 1.05693i 0.171456 0.171456i
\(39\) −0.808099 + 7.91217i −0.129399 + 1.26696i
\(40\) 0 0
\(41\) 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 0.728265 0.685295i \(-0.240327\pi\)
−0.685295 + 0.728265i \(0.740327\pi\)
\(44\) 3.73616 0.563247
\(45\) 0 0
\(46\) −9.01279 −1.32886
\(47\) 3.39588 + 3.39588i 0.495340 + 0.495340i 0.909984 0.414644i \(-0.136094\pi\)
−0.414644 + 0.909984i \(0.636094\pi\)
\(48\) 2.24010 + 2.74973i 0.323331 + 0.396890i
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 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 −0.905839 0.423623i \(-0.860758\pi\)
0.423623 + 0.905839i \(0.360758\pi\)
\(54\) 5.61073 + 1.76850i 0.763523 + 0.240662i
\(55\) 0 0
\(56\) 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 \(0.462248\pi\)
\(60\) 0 0
\(61\) −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
\(65\) 0 0
\(66\) 10.1479 + 1.03644i 1.24912 + 0.127577i
\(67\) −7.92132 + 7.92132i −0.967743 + 0.967743i −0.999496 0.0317530i \(-0.989891\pi\)
0.0317530 + 0.999496i \(0.489891\pi\)
\(68\) −0.606352 + 0.606352i −0.0735309 + 0.0735309i
\(69\) 13.7171 + 1.40098i 1.65134 + 0.168658i
\(70\) 0 0
\(71\) 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 0.781088 0.624422i \(-0.214665\pi\)
−0.624422 + 0.781088i \(0.714665\pi\)
\(74\) −2.74064 −0.318592
\(75\) 0 0
\(76\) 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 \(-0.223981\pi\)
\(80\) 0 0
\(81\) −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 −0.340659 0.940187i \(-0.610650\pi\)
0.940187 + 0.340659i \(0.110650\pi\)
\(84\) 0.126398 1.23757i 0.0137911 0.135030i
\(85\) 0 0
\(86\) 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 \(0.666612\pi\)
\(90\) 0 0
\(91\) 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 0
\(96\) −0.675186 + 6.61080i −0.0689109 + 0.674712i
\(97\) 3.06315 3.06315i 0.311016 0.311016i −0.534287 0.845303i \(-0.679420\pi\)
0.845303 + 0.534287i \(0.179420\pi\)
\(98\) −0.800553 + 0.800553i −0.0808681 + 0.0808681i
\(99\) −15.2835 3.15483i −1.53605 0.317072i
\(100\) 0 0
\(101\) 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 0.646553 0.762869i \(-0.276210\pi\)
−0.762869 + 0.646553i \(0.776210\pi\)
\(104\) −14.1312 −1.38568
\(105\) 0 0
\(106\) 5.62082 0.545943
\(107\) 1.38009 + 1.38009i 0.133418 + 0.133418i 0.770662 0.637244i \(-0.219926\pi\)
−0.637244 + 0.770662i \(0.719926\pi\)
\(108\) 1.72356 + 3.31019i 0.165849 + 0.318523i
\(109\) 5.93506i 0.568475i 0.958754 + 0.284238i \(0.0917405\pi\)
−0.958754 + 0.284238i \(0.908260\pi\)
\(110\) 0 0
\(111\) 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 −0.718336 0.695696i \(-0.755096\pi\)
0.695696 + 0.718336i \(0.255096\pi\)
\(114\) 2.57554 + 0.263049i 0.241221 + 0.0246368i
\(115\) 0 0
\(116\) 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
\(120\) 0 0
\(121\) −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
\(125\) 0 0
\(126\) 0.686624 3.32633i 0.0611693 0.296333i
\(127\) 4.55939 4.55939i 0.404581 0.404581i −0.475263 0.879844i \(-0.657647\pi\)
0.879844 + 0.475263i \(0.157647\pi\)
\(128\) −1.33009 + 1.33009i −0.117565 + 0.117565i
\(129\) −0.0701274 + 0.686624i −0.00617437 + 0.0604538i
\(130\) 0 0
\(131\) 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
\(135\) 0 0
\(136\) 3.67424 0.315064
\(137\) −10.0232 10.0232i −0.856337 0.856337i 0.134567 0.990904i \(-0.457036\pi\)
−0.990904 + 0.134567i \(0.957036\pi\)
\(138\) −9.85969 12.1028i −0.839313 1.03026i
\(139\) 15.8262i 1.34236i −0.741292 0.671182i \(-0.765787\pi\)
0.741292 0.671182i \(-0.234213\pi\)
\(140\) 0 0
\(141\) −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
\(145\) 0 0
\(146\) 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 \(0.375516\pi\)
\(150\) 0 0
\(151\) −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
\(155\) 0 0
\(156\) 5.68275 + 0.580400i 0.454984 + 0.0464692i
\(157\) −6.80647 + 6.80647i −0.543216 + 0.543216i −0.924470 0.381255i \(-0.875492\pi\)
0.381255 + 0.924470i \(0.375492\pi\)
\(158\) −9.20757 + 9.20757i −0.732515 + 0.732515i
\(159\) −8.55464 0.873717i −0.678427 0.0692903i
\(160\) 0 0
\(161\) 7.96075i 0.627395i
\(162\) 3.76312 + 9.46902i 0.295659 + 0.743957i
\(163\) −8.77966 8.77966i −0.687676 0.687676i 0.274042 0.961718i \(-0.411639\pi\)
−0.961718 + 0.274042i \(0.911639\pi\)
\(164\) 1.30844 0.102172
\(165\) 0 0
\(166\) −8.74519 −0.678758
\(167\) −12.4516 12.4516i −0.963532 0.963532i 0.0358258 0.999358i \(-0.488594\pi\)
−0.999358 + 0.0358258i \(0.988594\pi\)
\(168\) −4.13255 + 3.36663i −0.318833 + 0.259741i
\(169\) 8.08513i 0.621933i
\(170\) 0 0
\(171\) −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 \(-0.484015\pi\)
0.998739 0.0501977i \(-0.0159851\pi\)
\(174\) 0.873244 8.55000i 0.0662004 0.648174i
\(175\) 0 0
\(176\) 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 \(0.415360\pi\)
\(180\) 0 0
\(181\) 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
\(185\) 0 0
\(186\) −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
\(190\) 0 0
\(191\) 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 0.304112 0.952636i \(-0.401640\pi\)
−0.952636 + 0.304112i \(0.901640\pi\)
\(194\) −4.90443 −0.352118
\(195\) 0 0
\(196\) −0.718229 −0.0513021
\(197\) −2.78986 2.78986i −0.198769 0.198769i 0.600703 0.799472i \(-0.294887\pi\)
−0.799472 + 0.600703i \(0.794887\pi\)
\(198\) 9.70965 + 14.7609i 0.690035 + 1.04901i
\(199\) 14.4320i 1.02306i −0.859266 0.511528i \(-0.829080\pi\)
0.859266 0.511528i \(-0.170920\pi\)
\(200\) 0 0
\(201\) −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
\(205\) 0 0
\(206\) 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
\(210\) 0 0
\(211\) 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 0
\(216\) 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
\(220\) 0 0
\(221\) 5.48233i 0.368781i
\(222\) −2.99816 3.68025i −0.201224 0.247003i
\(223\) 12.1834 + 12.1834i 0.815858 + 0.815858i 0.985505 0.169647i \(-0.0542628\pi\)
−0.169647 + 0.985505i \(0.554263\pi\)
\(224\) 3.83661 0.256344
\(225\) 0 0
\(226\) 0.385328 0.0256317
\(227\) −4.17335 4.17335i −0.276995 0.276995i 0.554913 0.831908i \(-0.312751\pi\)
−0.831908 + 0.554913i \(0.812751\pi\)
\(228\) 1.03734 + 1.27334i 0.0686996 + 0.0843290i
\(229\) 27.2705i 1.80209i 0.433730 + 0.901043i \(0.357197\pi\)
−0.433730 + 0.901043i \(0.642803\pi\)
\(230\) 0 0
\(231\) −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 −0.768624 0.639701i \(-0.779058\pi\)
0.639701 + 0.768624i \(0.279058\pi\)
\(234\) 15.2740 + 3.15288i 0.998495 + 0.206110i
\(235\) 0 0
\(236\) 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 \(0.514721\pi\)
\(240\) 0 0
\(241\) 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 0
\(246\) 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
\(250\) 0 0
\(251\) 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
\(255\) 0 0
\(256\) −14.7484 −0.921774
\(257\) 13.8717 + 13.8717i 0.865290 + 0.865290i 0.991947 0.126657i \(-0.0404246\pi\)
−0.126657 + 0.991947i \(0.540425\pi\)
\(258\) 0.605820 0.493538i 0.0377167 0.0307263i
\(259\) 2.42073i 0.150417i
\(260\) 0 0
\(261\) −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 −0.218032 0.975942i \(-0.569964\pi\)
0.975942 + 0.218032i \(0.0699639\pi\)
\(264\) 2.81728 27.5842i 0.173392 1.69769i
\(265\) 0 0
\(266\) 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 \(0.698476\pi\)
\(270\) 0 0
\(271\) 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
\(275\) 0 0
\(276\) 1.00622 9.85200i 0.0605674 0.593020i
\(277\) 7.66076 7.66076i 0.460290 0.460290i −0.438460 0.898751i \(-0.644476\pi\)
0.898751 + 0.438460i \(0.144476\pi\)
\(278\) −12.6698 + 12.6698i −0.759881 + 0.759881i
\(279\) 1.03404 5.00936i 0.0619061 0.299903i
\(280\) 0 0
\(281\) 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 0.418216 0.908347i \(-0.362655\pi\)
−0.908347 + 0.418216i \(0.862655\pi\)
\(284\) −6.50972 −0.386281
\(285\) 0 0
\(286\) 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
\(290\) 0 0
\(291\) 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 \(0.553114\pi\)
−0.986111 + 0.166088i \(0.946886\pi\)
\(294\) −1.95080 0.199242i −0.113773 0.0116200i
\(295\) 0 0
\(296\) 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
\(300\) 0 0
\(301\) 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
\(305\) 0 0
\(306\) −3.97139 0.819776i −0.227029 0.0468635i
\(307\) 13.2997 13.2997i 0.759057 0.759057i −0.217094 0.976151i \(-0.569658\pi\)
0.976151 + 0.217094i \(0.0696578\pi\)
\(308\) 2.64186 2.64186i 0.150534 0.150534i
\(309\) 0.293801 2.87663i 0.0167137 0.163646i
\(310\) 0 0
\(311\) 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 \(0.0232406\pi\)
0.0729475 + 0.997336i \(0.476759\pi\)
\(314\) 10.8979 0.615003
\(315\) 0 0
\(316\) −8.26072 −0.464702
\(317\) 11.6929 + 11.6929i 0.656739 + 0.656739i 0.954607 0.297868i \(-0.0962755\pi\)
−0.297868 + 0.954607i \(0.596275\pi\)
\(318\) 6.14899 + 7.54790i 0.344818 + 0.423265i
\(319\) 22.7990i 1.27650i
\(320\) 0 0
\(321\) −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
\(325\) 0 0
\(326\) 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
\(330\) 0 0
\(331\) −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
\(335\) 0 0
\(336\) 3.52835 + 0.360363i 0.192487 + 0.0196594i
\(337\) 5.46127 5.46127i 0.297494 0.297494i −0.542537 0.840032i \(-0.682536\pi\)
0.840032 + 0.542537i \(0.182536\pi\)
\(338\) 6.47258 6.47258i 0.352062 0.352062i
\(339\) −0.586453 0.0598966i −0.0318517 0.00325314i
\(340\) 0 0
\(341\) 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
\(345\) 0 0
\(346\) −22.0898 −1.18756
\(347\) −20.1982 20.1982i −1.08430 1.08430i −0.996103 0.0881938i \(-0.971891\pi\)
−0.0881938 0.996103i \(-0.528109\pi\)
\(348\) 4.22711 3.44366i 0.226597 0.184600i
\(349\) 11.9748i 0.640997i 0.947249 + 0.320498i \(0.103850\pi\)
−0.947249 + 0.320498i \(0.896150\pi\)
\(350\) 0 0
\(351\) −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 \(-0.381293\pi\)
0.931264 0.364345i \(-0.118707\pi\)
\(354\) 0.362166 3.54600i 0.0192489 0.188468i
\(355\) 0 0
\(356\) 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 \(0.622411\pi\)
\(360\) 0 0
\(361\) 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
\(365\) 0 0
\(366\) −0.493153 + 4.82850i −0.0257775 + 0.252390i
\(367\) −16.7024 + 16.7024i −0.871859 + 0.871859i −0.992675 0.120816i \(-0.961449\pi\)
0.120816 + 0.992675i \(0.461449\pi\)
\(368\) 11.5267 11.5267i 0.600868 0.600868i
\(369\) −5.35243 1.10485i −0.278636 0.0575163i
\(370\) 0 0
\(371\) 4.96472i 0.257755i
\(372\) −1.64441 + 1.33964i −0.0852589 + 0.0694572i
\(373\) −4.57877 4.57877i −0.237080 0.237080i 0.578560 0.815640i \(-0.303615\pi\)
−0.815640 + 0.578560i \(0.803615\pi\)
\(374\) −7.03144 −0.363587
\(375\) 0 0
\(376\) −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 \(-0.105333\pi\)
\(380\) 0 0
\(381\) 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 −0.997072 0.0764705i \(-0.975635\pi\)
0.0764705 + 0.997072i \(0.475635\pi\)
\(384\) −3.24119 0.331035i −0.165401 0.0168930i
\(385\) 0 0
\(386\) 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 \(0.648312\pi\)
\(390\) 0 0
\(391\) −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
\(395\) 0 0
\(396\) −2.26589 + 10.9771i −0.113865 + 0.551618i
\(397\) −4.43035 + 4.43035i −0.222353 + 0.222353i −0.809489 0.587136i \(-0.800255\pi\)
0.587136 + 0.809489i \(0.300255\pi\)
\(398\) −11.5536 + 11.5536i −0.579128 + 0.579128i
\(399\) −0.232344 + 2.27490i −0.0116317 + 0.113887i
\(400\) 0 0
\(401\) 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
\(405\) 0 0
\(406\) −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 \(0.839276\pi\)
\(410\) 0 0
\(411\) 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
\(415\) 0 0
\(416\) 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 0
\(421\) 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
\(425\) 0 0
\(426\) −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 0
\(431\) 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 0.695798 0.718237i \(-0.255051\pi\)
−0.718237 + 0.695798i \(0.755051\pi\)
\(434\) 1.93031 0.0926579
\(435\) 0 0
\(436\) 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 \(-0.0723011\pi\)
\(440\) 0 0
\(441\) 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 −0.983522 0.180788i \(-0.942135\pi\)
0.180788 + 0.983522i \(0.442135\pi\)
\(444\) 0.305975 2.99582i 0.0145209 0.142175i
\(445\) 0 0
\(446\) 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 \(0.587975\pi\)
\(450\) 0 0
\(451\) −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
\(455\) 0 0
\(456\) 0.715027 7.00090i 0.0334842 0.327847i
\(457\) 17.8413 17.8413i 0.834580 0.834580i −0.153560 0.988139i \(-0.549074\pi\)
0.988139 + 0.153560i \(0.0490737\pi\)
\(458\) 21.8315 21.8315i 1.02012 1.02012i
\(459\) 5.91685 + 1.86499i 0.276175 + 0.0870502i
\(460\) 0 0
\(461\) 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 0.176079 0.984376i \(-0.443659\pi\)
−0.984376 + 0.176079i \(0.943659\pi\)
\(464\) 8.97466 0.416638
\(465\) 0 0
\(466\) 3.15084 0.145960
\(467\) −9.40605 9.40605i −0.435260 0.435260i 0.455153 0.890413i \(-0.349585\pi\)
−0.890413 + 0.455153i \(0.849585\pi\)
\(468\) 5.43734 + 8.26600i 0.251341 + 0.382096i
\(469\) 11.2024i 0.517280i
\(470\) 0 0
\(471\) −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
\(475\) 0 0
\(476\) 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 \(0.152107\pi\)
\(480\) 0 0
\(481\) 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
\(485\) 0 0
\(486\) −8.59872 + 15.4121i −0.390046 + 0.699106i
\(487\) −23.9549 + 23.9549i −1.08550 + 1.08550i −0.0895148 + 0.995985i \(0.528532\pi\)
−0.995985 + 0.0895148i \(0.971468\pi\)
\(488\) 5.38612 5.38612i 0.243818 0.243818i
\(489\) 2.18509 21.3944i 0.0988131 0.967488i
\(490\) 0 0
\(491\) 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
\(495\) 0 0
\(496\) −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 \(-0.225850\pi\)
\(500\) 0 0
\(501\) 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 −0.442855 0.896593i \(-0.646035\pi\)
0.896593 + 0.442855i \(0.146035\pi\)
\(504\) −9.04173 1.86640i −0.402751 0.0831361i
\(505\) 0 0
\(506\) 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 \(0.256021\pi\)
\(510\) 0 0
\(511\) 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
\(515\) 0 0
\(516\) 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
\(520\) 0 0
\(521\) 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 0.666012 0.745941i \(-0.268000\pi\)
−0.745941 + 0.666012i \(0.768000\pi\)
\(524\) 9.82422 0.429173
\(525\) 0 0
\(526\) −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
\(530\) 0 0
\(531\) −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
\(535\) 0 0
\(536\) 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
\(540\) 0 0
\(541\) 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
\(545\) 0 0
\(546\) 0.914892 8.95779i 0.0391538 0.383358i
\(547\) 21.6813 21.6813i 0.927024 0.927024i −0.0704885 0.997513i \(-0.522456\pi\)
0.997513 + 0.0704885i \(0.0224558\pi\)
\(548\) −7.19893 + 7.19893i −0.307523 + 0.307523i
\(549\) 1.50111 7.27211i 0.0640660 0.310366i
\(550\) 0 0
\(551\) 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
\(555\) 0 0
\(556\) −11.3669 −0.482063
\(557\) 13.1204 + 13.1204i 0.555929 + 0.555929i 0.928146 0.372217i \(-0.121402\pi\)
−0.372217 + 0.928146i \(0.621402\pi\)
\(558\) −4.83806 + 3.18246i −0.204811 + 0.134724i
\(559\) 1.82978i 0.0773916i
\(560\) 0 0
\(561\) 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 −0.957901 0.287097i \(-0.907310\pi\)
0.287097 + 0.957901i \(0.407310\pi\)
\(564\) 5.94344 + 0.607025i 0.250264 + 0.0255604i
\(565\) 0 0
\(566\) 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 \(0.301740\pi\)
\(570\) 0 0
\(571\) −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
\(575\) 0 0
\(576\) 24.7943 + 5.11805i 1.03310 + 0.213252i
\(577\) 15.3143 15.3143i 0.637542 0.637542i −0.312406 0.949949i \(-0.601135\pi\)
0.949949 + 0.312406i \(0.101135\pi\)
\(578\) −12.4683 + 12.4683i −0.518611 + 0.518611i
\(579\) 2.24231 21.9547i 0.0931874 0.912406i
\(580\) 0 0
\(581\) 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
\(585\) 0 0
\(586\) 31.5778 1.30447
\(587\) 23.2211 + 23.2211i 0.958439 + 0.958439i 0.999170 0.0407314i \(-0.0129688\pi\)
−0.0407314 + 0.999170i \(0.512969\pi\)
\(588\) −0.785718 0.964471i −0.0324025 0.0397741i
\(589\) 2.25101i 0.0927512i
\(590\) 0 0
\(591\) 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 −0.00235668 0.999997i \(-0.500750\pi\)
0.999997 + 0.00235668i \(0.000750155\pi\)
\(594\) −9.19956 + 29.1865i −0.377463 + 1.19754i
\(595\) 0 0
\(596\) 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 \(0.654131\pi\)
\(600\) 0 0
\(601\) −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
\(605\) 0 0
\(606\) 7.24995 + 0.740464i 0.294509 + 0.0300793i
\(607\) 17.5164 17.5164i 0.710968 0.710968i −0.255770 0.966738i \(-0.582329\pi\)
0.966738 + 0.255770i \(0.0823289\pi\)
\(608\) −3.58168 + 3.58168i −0.145256 + 0.145256i
\(609\) 7.55198 + 0.771312i 0.306022 + 0.0312551i
\(610\) 0 0
\(611\) 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 \(0.0161959\pi\)
0.0508591 + 0.998706i \(0.483804\pi\)
\(614\) −21.2943 −0.859369
\(615\) 0 0
\(616\) −16.0086 −0.645005
\(617\) −8.12737 8.12737i −0.327196 0.327196i 0.524323 0.851519i \(-0.324318\pi\)
−0.851519 + 0.524323i \(0.824318\pi\)
\(618\) −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 0
\(621\) −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
\(625\) 0 0
\(626\) 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
\(630\) 0 0
\(631\) −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
\(635\) 0 0
\(636\) −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
\(640\) 0 0
\(641\) 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 0.440120 0.897939i \(-0.354936\pi\)
−0.897939 + 0.440120i \(0.854936\pi\)
\(644\) −5.71764 −0.225307
\(645\) 0 0
\(646\) −1.78458 −0.0702135
\(647\) 10.6517 + 10.6517i 0.418760 + 0.418760i 0.884776 0.466016i \(-0.154311\pi\)
−0.466016 + 0.884776i \(0.654311\pi\)
\(648\) 25.7390 10.2290i 1.01112 0.401834i
\(649\) 9.45560i 0.371165i
\(650\) 0 0
\(651\) −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 −0.631576 0.775314i \(-0.717592\pi\)
0.775314 + 0.631576i \(0.217592\pi\)
\(654\) 11.5781 + 1.18251i 0.452740 + 0.0462400i
\(655\) 0 0
\(656\) 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 \(0.849161\pi\)
\(660\) 0 0
\(661\) −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
\(665\) 0 0
\(666\) 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
\(670\) 0 0
\(671\) 12.8755i 0.497051i
\(672\) 4.19712 + 5.15197i 0.161907 + 0.198742i
\(673\) −12.1963 12.1963i −0.470132 0.470132i 0.431825 0.901957i \(-0.357870\pi\)
−0.901957 + 0.431825i \(0.857870\pi\)
\(674\) −8.74408 −0.336809
\(675\) 0 0
\(676\) 5.80698 0.223345
\(677\) −30.0858 30.0858i −1.15629 1.15629i −0.985267 0.171025i \(-0.945292\pi\)
−0.171025 0.985267i \(-0.554708\pi\)
\(678\) 0.421536 + 0.517437i 0.0161890 + 0.0198721i
\(679\) 4.33195i 0.166245i
\(680\) 0 0
\(681\) 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 −0.678128 0.734944i \(-0.737208\pi\)
0.734944 + 0.678128i \(0.237208\pi\)
\(684\) −0.575084 + 2.78598i −0.0219889 + 0.106525i
\(685\) 0 0
\(686\) 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
\(690\) 0 0
\(691\) 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
\(695\) 0 0
\(696\) −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
\(700\) 0 0
\(701\) 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
\(705\) 0 0
\(706\) −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 \(-0.134153\pi\)
\(710\) 0 0
\(711\) 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
\(715\) 0 0
\(716\) 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 \(0.827699\pi\)
\(720\) 0 0
\(721\) −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
\(725\) 0 0
\(726\) −3.19980 + 31.3295i −0.118756 + 1.16275i
\(727\) 4.37251 4.37251i 0.162168 0.162168i −0.621359 0.783526i \(-0.713419\pi\)
0.783526 + 0.621359i \(0.213419\pi\)
\(728\) −9.99228 + 9.99228i −0.370338 + 0.370338i
\(729\) 15.4826 22.1199i 0.573428 0.819256i
\(730\) 0 0
\(731\) 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 \(0.0653787\pi\)
0.203952 + 0.978981i \(0.434621\pi\)
\(734\) 26.7423 0.987078
\(735\) 0 0
\(736\) 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 \(-0.118713\pi\)
\(740\) 0 0
\(741\) −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 −0.384475 0.923135i \(-0.625618\pi\)
0.923135 + 0.384475i \(0.125618\pi\)
\(744\) 9.04108 + 0.923399i 0.331462 + 0.0338535i
\(745\) 0 0
\(746\) 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
\(750\) 0 0
\(751\) −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
\(755\) 0 0
\(756\) 3.55940 + 1.12192i 0.129454 + 0.0408039i
\(757\) 4.11078 4.11078i 0.149409 0.149409i −0.628445 0.777854i \(-0.716308\pi\)
0.777854 + 0.628445i \(0.216308\pi\)
\(758\) −10.1275 + 10.1275i −0.367846 + 0.367846i
\(759\) −7.28774 + 71.3549i −0.264528 + 2.59002i
\(760\) 0 0
\(761\) 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
\(765\) 0 0
\(766\) 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 0.733410 + 0.679786i \(0.237927\pi\)
−0.733410 + 0.679786i \(0.762073\pi\)
\(770\) 0 0
\(771\) −3.45239 + 33.8026i −0.124335 + 1.21737i
\(772\) −6.47095 + 6.47095i −0.232895 + 0.232895i
\(773\) −20.5564 + 20.5564i −0.739362 + 0.739362i −0.972455 0.233093i \(-0.925116\pi\)
0.233093 + 0.972455i \(0.425116\pi\)
\(774\) 1.32549 + 0.273609i 0.0476438 + 0.00983467i
\(775\) 0 0
\(776\) 13.3314i 0.478568i
\(777\) 3.25067 2.64820i 0.116617 0.0950035i
\(778\) 14.1870 +