Properties

Label 750.2.l.c.143.5
Level $750$
Weight $2$
Character 750.143
Analytic conductor $5.989$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 750.l (of order \(20\), degree \(8\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.98878015160\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 143.5
Character \(\chi\) \(=\) 750.143
Dual form 750.2.l.c.257.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.453990 + 0.891007i) q^{2} +(1.70181 - 0.322239i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.485490 + 1.66262i) q^{6} +(0.0556476 - 0.0556476i) q^{7} +(0.987688 - 0.156434i) q^{8} +(2.79232 - 1.09678i) q^{9} +O(q^{10})\) \(q+(-0.453990 + 0.891007i) q^{2} +(1.70181 - 0.322239i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.485490 + 1.66262i) q^{6} +(0.0556476 - 0.0556476i) q^{7} +(0.987688 - 0.156434i) q^{8} +(2.79232 - 1.09678i) q^{9} +(-1.04749 + 0.340351i) q^{11} +(-1.26100 - 1.18739i) q^{12} +(4.54086 - 2.31368i) q^{13} +(0.0243189 + 0.0748459i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-0.491350 - 3.10226i) q^{17} +(-0.290452 + 2.98591i) q^{18} +(0.824223 - 1.13445i) q^{19} +(0.0767699 - 0.112634i) q^{21} +(0.172297 - 1.08784i) q^{22} +(2.22575 + 1.13408i) q^{23} +(1.63045 - 0.584493i) q^{24} +5.09632i q^{26} +(4.39859 - 2.76630i) q^{27} +(-0.0777287 - 0.0123110i) q^{28} +(-5.66803 + 4.11807i) q^{29} +(7.72991 + 5.61611i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.67296 + 0.916756i) q^{33} +(2.98720 + 0.970601i) q^{34} +(-2.52860 - 1.61437i) q^{36} +(-4.70325 - 9.23065i) q^{37} +(0.636609 + 1.24942i) q^{38} +(6.98213 - 5.40069i) q^{39} +(3.55210 + 1.15415i) q^{41} +(0.0655044 + 0.119537i) q^{42} +(-1.00563 - 1.00563i) q^{43} +(0.891050 + 0.647386i) q^{44} +(-2.02094 + 1.46830i) q^{46} +(12.5515 + 1.98797i) q^{47} +(-0.219422 + 1.71810i) q^{48} +6.99381i q^{49} +(-1.83585 - 5.12113i) q^{51} +(-4.54086 - 2.31368i) q^{52} +(1.06206 - 6.70559i) q^{53} +(0.467880 + 5.17504i) q^{54} +(0.0462573 - 0.0636677i) q^{56} +(1.03711 - 2.19621i) q^{57} +(-1.09599 - 6.91981i) q^{58} +(-2.03647 + 6.26761i) q^{59} +(1.23324 + 3.79553i) q^{61} +(-8.51329 + 4.33774i) q^{62} +(0.0943531 - 0.216419i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-0.0573270 - 1.90682i) q^{66} +(-6.57696 + 1.04169i) q^{67} +(-2.22097 + 2.22097i) q^{68} +(4.15326 + 1.21276i) q^{69} +(-7.51096 - 10.3379i) q^{71} +(2.58637 - 1.52009i) q^{72} +(-0.602914 + 1.18329i) q^{73} +10.3598 q^{74} -1.40225 q^{76} +(-0.0393507 + 0.0772302i) q^{77} +(1.64223 + 8.67298i) q^{78} +(-5.85354 - 8.05671i) q^{79} +(6.59415 - 6.12512i) q^{81} +(-2.64098 + 2.64098i) q^{82} +(0.871279 - 0.137997i) q^{83} +(-0.136247 + 0.00409615i) q^{84} +(1.35257 - 0.439477i) q^{86} +(-8.31892 + 8.83463i) q^{87} +(-0.981353 + 0.500025i) q^{88} +(-1.01326 - 3.11850i) q^{89} +(0.123937 - 0.381439i) q^{91} +(-0.390777 - 2.46727i) q^{92} +(14.9646 + 7.06668i) q^{93} +(-7.46957 + 10.2810i) q^{94} +(-1.43122 - 0.975505i) q^{96} +(-1.62393 + 10.2531i) q^{97} +(-6.23153 - 3.17512i) q^{98} +(-2.55165 + 2.09924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q + 4q^{3} + 4q^{7} + O(q^{10}) \) \( 80q + 4q^{3} + 4q^{7} + 16q^{12} + 20q^{16} - 8q^{18} + 40q^{19} + 4q^{22} - 56q^{27} + 4q^{28} - 96q^{33} + 40q^{34} - 64q^{37} + 40q^{39} - 4q^{42} - 24q^{43} + 16q^{48} - 64q^{57} + 20q^{58} + 4q^{63} - 104q^{67} - 140q^{69} + 8q^{72} - 60q^{73} - 60q^{78} - 80q^{79} - 40q^{81} + 96q^{82} - 60q^{84} + 80q^{87} + 24q^{88} + 12q^{93} - 12q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{3}{20}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.453990 + 0.891007i −0.321020 + 0.630037i
\(3\) 1.70181 0.322239i 0.982541 0.186045i
\(4\) −0.587785 0.809017i −0.293893 0.404508i
\(5\) 0 0
\(6\) −0.485490 + 1.66262i −0.198200 + 0.678761i
\(7\) 0.0556476 0.0556476i 0.0210328 0.0210328i −0.696512 0.717545i \(-0.745266\pi\)
0.717545 + 0.696512i \(0.245266\pi\)
\(8\) 0.987688 0.156434i 0.349201 0.0553079i
\(9\) 2.79232 1.09678i 0.930775 0.365593i
\(10\) 0 0
\(11\) −1.04749 + 0.340351i −0.315831 + 0.102620i −0.462643 0.886545i \(-0.653099\pi\)
0.146812 + 0.989164i \(0.453099\pi\)
\(12\) −1.26100 1.18739i −0.364018 0.342769i
\(13\) 4.54086 2.31368i 1.25941 0.641700i 0.308514 0.951220i \(-0.400168\pi\)
0.950893 + 0.309520i \(0.100168\pi\)
\(14\) 0.0243189 + 0.0748459i 0.00649950 + 0.0200034i
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) −0.491350 3.10226i −0.119170 0.752408i −0.972820 0.231562i \(-0.925616\pi\)
0.853650 0.520846i \(-0.174384\pi\)
\(18\) −0.290452 + 2.98591i −0.0684602 + 0.703785i
\(19\) 0.824223 1.13445i 0.189090 0.260260i −0.703938 0.710262i \(-0.748577\pi\)
0.893028 + 0.450002i \(0.148577\pi\)
\(20\) 0 0
\(21\) 0.0767699 0.112634i 0.0167526 0.0245787i
\(22\) 0.172297 1.08784i 0.0367338 0.231928i
\(23\) 2.22575 + 1.13408i 0.464102 + 0.236472i 0.670375 0.742023i \(-0.266133\pi\)
−0.206273 + 0.978495i \(0.566133\pi\)
\(24\) 1.63045 0.584493i 0.332814 0.119309i
\(25\) 0 0
\(26\) 5.09632i 0.999471i
\(27\) 4.39859 2.76630i 0.846508 0.532376i
\(28\) −0.0777287 0.0123110i −0.0146893 0.00232656i
\(29\) −5.66803 + 4.11807i −1.05253 + 0.764705i −0.972691 0.232103i \(-0.925440\pi\)
−0.0798355 + 0.996808i \(0.525440\pi\)
\(30\) 0 0
\(31\) 7.72991 + 5.61611i 1.38833 + 1.00868i 0.996046 + 0.0888399i \(0.0283160\pi\)
0.392287 + 0.919843i \(0.371684\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) −1.67296 + 0.916756i −0.291225 + 0.159587i
\(34\) 2.98720 + 0.970601i 0.512301 + 0.166457i
\(35\) 0 0
\(36\) −2.52860 1.61437i −0.421433 0.269061i
\(37\) −4.70325 9.23065i −0.773210 1.51751i −0.853706 0.520755i \(-0.825650\pi\)
0.0804961 0.996755i \(-0.474350\pi\)
\(38\) 0.636609 + 1.24942i 0.103272 + 0.202682i
\(39\) 6.98213 5.40069i 1.11803 0.864803i
\(40\) 0 0
\(41\) 3.55210 + 1.15415i 0.554745 + 0.180248i 0.572956 0.819586i \(-0.305797\pi\)
−0.0182101 + 0.999834i \(0.505797\pi\)
\(42\) 0.0655044 + 0.119537i 0.0101075 + 0.0184450i
\(43\) −1.00563 1.00563i −0.153357 0.153357i 0.626258 0.779616i \(-0.284586\pi\)
−0.779616 + 0.626258i \(0.784586\pi\)
\(44\) 0.891050 + 0.647386i 0.134331 + 0.0975971i
\(45\) 0 0
\(46\) −2.02094 + 1.46830i −0.297972 + 0.216489i
\(47\) 12.5515 + 1.98797i 1.83083 + 0.289975i 0.974154 0.225883i \(-0.0725268\pi\)
0.856674 + 0.515858i \(0.172527\pi\)
\(48\) −0.219422 + 1.71810i −0.0316708 + 0.247986i
\(49\) 6.99381i 0.999115i
\(50\) 0 0
\(51\) −1.83585 5.12113i −0.257071 0.717101i
\(52\) −4.54086 2.31368i −0.629704 0.320850i
\(53\) 1.06206 6.70559i 0.145885 0.921083i −0.800802 0.598929i \(-0.795593\pi\)
0.946687 0.322154i \(-0.104407\pi\)
\(54\) 0.467880 + 5.17504i 0.0636704 + 0.704234i
\(55\) 0 0
\(56\) 0.0462573 0.0636677i 0.00618139 0.00850795i
\(57\) 1.03711 2.19621i 0.137369 0.290895i
\(58\) −1.09599 6.91981i −0.143911 0.908616i
\(59\) −2.03647 + 6.26761i −0.265126 + 0.815974i 0.726538 + 0.687126i \(0.241128\pi\)
−0.991664 + 0.128848i \(0.958872\pi\)
\(60\) 0 0
\(61\) 1.23324 + 3.79553i 0.157901 + 0.485968i 0.998443 0.0557774i \(-0.0177637\pi\)
−0.840543 + 0.541745i \(0.817764\pi\)
\(62\) −8.51329 + 4.33774i −1.08119 + 0.550894i
\(63\) 0.0943531 0.216419i 0.0118874 0.0272663i
\(64\) 0.951057 0.309017i 0.118882 0.0386271i
\(65\) 0 0
\(66\) −0.0573270 1.90682i −0.00705647 0.234713i
\(67\) −6.57696 + 1.04169i −0.803504 + 0.127263i −0.544660 0.838657i \(-0.683341\pi\)
−0.258844 + 0.965919i \(0.583341\pi\)
\(68\) −2.22097 + 2.22097i −0.269332 + 0.269332i
\(69\) 4.15326 + 1.21276i 0.499993 + 0.146000i
\(70\) 0 0
\(71\) −7.51096 10.3379i −0.891387 1.22689i −0.973135 0.230236i \(-0.926050\pi\)
0.0817481 0.996653i \(-0.473950\pi\)
\(72\) 2.58637 1.52009i 0.304807 0.179144i
\(73\) −0.602914 + 1.18329i −0.0705658 + 0.138493i −0.923595 0.383371i \(-0.874763\pi\)
0.853029 + 0.521864i \(0.174763\pi\)
\(74\) 10.3598 1.20430
\(75\) 0 0
\(76\) −1.40225 −0.160849
\(77\) −0.0393507 + 0.0772302i −0.00448443 + 0.00880119i
\(78\) 1.64223 + 8.67298i 0.185946 + 0.982022i
\(79\) −5.85354 8.05671i −0.658575 0.906451i 0.340858 0.940115i \(-0.389282\pi\)
−0.999433 + 0.0336639i \(0.989282\pi\)
\(80\) 0 0
\(81\) 6.59415 6.12512i 0.732684 0.680569i
\(82\) −2.64098 + 2.64098i −0.291647 + 0.291647i
\(83\) 0.871279 0.137997i 0.0956353 0.0151471i −0.108433 0.994104i \(-0.534583\pi\)
0.204069 + 0.978957i \(0.434583\pi\)
\(84\) −0.136247 + 0.00409615i −0.0148657 + 0.000446927i
\(85\) 0 0
\(86\) 1.35257 0.439477i 0.145851 0.0473900i
\(87\) −8.31892 + 8.83463i −0.891882 + 0.947172i
\(88\) −0.981353 + 0.500025i −0.104613 + 0.0533028i
\(89\) −1.01326 3.11850i −0.107406 0.330560i 0.882882 0.469595i \(-0.155600\pi\)
−0.990288 + 0.139035i \(0.955600\pi\)
\(90\) 0 0
\(91\) 0.123937 0.381439i 0.0129921 0.0399856i
\(92\) −0.390777 2.46727i −0.0407413 0.257230i
\(93\) 14.9646 + 7.06668i 1.55175 + 0.732781i
\(94\) −7.46957 + 10.2810i −0.770427 + 1.06040i
\(95\) 0 0
\(96\) −1.43122 0.975505i −0.146073 0.0995621i
\(97\) −1.62393 + 10.2531i −0.164885 + 1.04104i 0.756953 + 0.653469i \(0.226687\pi\)
−0.921838 + 0.387575i \(0.873313\pi\)
\(98\) −6.23153 3.17512i −0.629479 0.320736i
\(99\) −2.55165 + 2.09924i −0.256450 + 0.210981i
\(100\) 0 0
\(101\) 14.0377i 1.39680i 0.715708 + 0.698399i \(0.246104\pi\)
−0.715708 + 0.698399i \(0.753896\pi\)
\(102\) 5.39642 + 0.689188i 0.534325 + 0.0682398i
\(103\) −13.0416 2.06559i −1.28503 0.203529i −0.523705 0.851900i \(-0.675451\pi\)
−0.761324 + 0.648371i \(0.775451\pi\)
\(104\) 4.12301 2.99554i 0.404295 0.293737i
\(105\) 0 0
\(106\) 5.49256 + 3.99058i 0.533484 + 0.387599i
\(107\) 13.7619 + 13.7619i 1.33041 + 1.33041i 0.904999 + 0.425413i \(0.139871\pi\)
0.425413 + 0.904999i \(0.360129\pi\)
\(108\) −4.82341 1.93254i −0.464133 0.185958i
\(109\) −11.7044 3.80299i −1.12108 0.364260i −0.310898 0.950443i \(-0.600630\pi\)
−0.810178 + 0.586183i \(0.800630\pi\)
\(110\) 0 0
\(111\) −10.9785 14.1933i −1.04204 1.34716i
\(112\) 0.0357280 + 0.0701201i 0.00337598 + 0.00662572i
\(113\) 3.46581 + 6.80204i 0.326036 + 0.639882i 0.994601 0.103771i \(-0.0330911\pi\)
−0.668565 + 0.743654i \(0.733091\pi\)
\(114\) 1.48600 + 1.92113i 0.139177 + 0.179930i
\(115\) 0 0
\(116\) 6.66317 + 2.16499i 0.618660 + 0.201015i
\(117\) 10.1420 11.4409i 0.937624 1.05771i
\(118\) −4.65995 4.65995i −0.428983 0.428983i
\(119\) −0.199976 0.145291i −0.0183317 0.0133188i
\(120\) 0 0
\(121\) −7.91779 + 5.75261i −0.719799 + 0.522964i
\(122\) −3.94172 0.624308i −0.356867 0.0565222i
\(123\) 6.41692 + 0.819518i 0.578594 + 0.0738935i
\(124\) 9.55469i 0.858037i
\(125\) 0 0
\(126\) 0.149996 + 0.182322i 0.0133627 + 0.0162425i
\(127\) 2.87091 + 1.46280i 0.254752 + 0.129803i 0.576703 0.816954i \(-0.304339\pi\)
−0.321952 + 0.946756i \(0.604339\pi\)
\(128\) −0.156434 + 0.987688i −0.0138270 + 0.0873001i
\(129\) −2.03545 1.38734i −0.179211 0.122149i
\(130\) 0 0
\(131\) 3.12598 4.30255i 0.273118 0.375915i −0.650321 0.759660i \(-0.725366\pi\)
0.923439 + 0.383744i \(0.125366\pi\)
\(132\) 1.72501 + 0.814598i 0.150143 + 0.0709017i
\(133\) −0.0172632 0.108995i −0.00149690 0.00945109i
\(134\) 2.05773 6.33303i 0.177761 0.547091i
\(135\) 0 0
\(136\) −0.970601 2.98720i −0.0832283 0.256150i
\(137\) −10.2341 + 5.21451i −0.874354 + 0.445506i −0.832763 0.553629i \(-0.813243\pi\)
−0.0415907 + 0.999135i \(0.513243\pi\)
\(138\) −2.96612 + 3.15000i −0.252493 + 0.268146i
\(139\) −10.3684 + 3.36891i −0.879440 + 0.285747i −0.713725 0.700426i \(-0.752993\pi\)
−0.165715 + 0.986174i \(0.552993\pi\)
\(140\) 0 0
\(141\) 22.0009 0.661442i 1.85281 0.0557034i
\(142\) 12.6211 1.99898i 1.05914 0.167751i
\(143\) −3.96905 + 3.96905i −0.331909 + 0.331909i
\(144\) 0.180223 + 2.99458i 0.0150186 + 0.249548i
\(145\) 0 0
\(146\) −0.780598 1.07440i −0.0646028 0.0889181i
\(147\) 2.25367 + 11.9021i 0.185880 + 0.981672i
\(148\) −4.70325 + 9.23065i −0.386605 + 0.758755i
\(149\) −14.3679 −1.17707 −0.588534 0.808472i \(-0.700295\pi\)
−0.588534 + 0.808472i \(0.700295\pi\)
\(150\) 0 0
\(151\) −0.326435 −0.0265649 −0.0132824 0.999912i \(-0.504228\pi\)
−0.0132824 + 0.999912i \(0.504228\pi\)
\(152\) 0.636609 1.24942i 0.0516358 0.101341i
\(153\) −4.77450 8.12361i −0.385995 0.656755i
\(154\) −0.0509477 0.0701235i −0.00410548 0.00565071i
\(155\) 0 0
\(156\) −8.47324 2.47421i −0.678402 0.198096i
\(157\) −3.47556 + 3.47556i −0.277380 + 0.277380i −0.832062 0.554682i \(-0.812840\pi\)
0.554682 + 0.832062i \(0.312840\pi\)
\(158\) 9.83604 1.55788i 0.782513 0.123938i
\(159\) −0.353372 11.7539i −0.0280242 0.932144i
\(160\) 0 0
\(161\) 0.186967 0.0607491i 0.0147350 0.00478770i
\(162\) 2.46384 + 8.65618i 0.193578 + 0.680094i
\(163\) 1.36590 0.695961i 0.106986 0.0545119i −0.399679 0.916655i \(-0.630878\pi\)
0.506664 + 0.862143i \(0.330878\pi\)
\(164\) −1.15415 3.55210i −0.0901239 0.277373i
\(165\) 0 0
\(166\) −0.272596 + 0.838964i −0.0211576 + 0.0651163i
\(167\) −3.50144 22.1072i −0.270949 1.71071i −0.629336 0.777133i \(-0.716673\pi\)
0.358387 0.933573i \(-0.383327\pi\)
\(168\) 0.0582050 0.123256i 0.00449061 0.00950943i
\(169\) 7.62505 10.4950i 0.586542 0.807306i
\(170\) 0 0
\(171\) 1.05726 4.07173i 0.0808509 0.311373i
\(172\) −0.222477 + 1.40467i −0.0169637 + 0.107105i
\(173\) −12.6292 6.43491i −0.960182 0.489237i −0.0976395 0.995222i \(-0.531129\pi\)
−0.862542 + 0.505985i \(0.831129\pi\)
\(174\) −4.09500 11.4230i −0.310441 0.865979i
\(175\) 0 0
\(176\) 1.10140i 0.0830211i
\(177\) −1.44602 + 11.3225i −0.108690 + 0.851053i
\(178\) 3.23861 + 0.512946i 0.242744 + 0.0384469i
\(179\) 12.2896 8.92889i 0.918565 0.667377i −0.0246011 0.999697i \(-0.507832\pi\)
0.943167 + 0.332320i \(0.107832\pi\)
\(180\) 0 0
\(181\) −8.30933 6.03708i −0.617627 0.448733i 0.234465 0.972125i \(-0.424666\pi\)
−0.852092 + 0.523392i \(0.824666\pi\)
\(182\) 0.283598 + 0.283598i 0.0210217 + 0.0210217i
\(183\) 3.32181 + 6.06188i 0.245556 + 0.448107i
\(184\) 2.37576 + 0.771931i 0.175143 + 0.0569075i
\(185\) 0 0
\(186\) −13.0902 + 10.1253i −0.959823 + 0.742425i
\(187\) 1.57054 + 3.08236i 0.114849 + 0.225405i
\(188\) −5.76930 11.3229i −0.420770 0.825807i
\(189\) 0.0908325 0.398709i 0.00660709 0.0290018i
\(190\) 0 0
\(191\) −10.3303 3.35652i −0.747475 0.242869i −0.0895805 0.995980i \(-0.528553\pi\)
−0.657894 + 0.753110i \(0.728553\pi\)
\(192\) 1.51894 0.832356i 0.109620 0.0600701i
\(193\) −13.7241 13.7241i −0.987880 0.987880i 0.0120476 0.999927i \(-0.496165\pi\)
−0.999927 + 0.0120476i \(0.996165\pi\)
\(194\) −8.39833 6.10174i −0.602965 0.438080i
\(195\) 0 0
\(196\) 5.65811 4.11086i 0.404151 0.293633i
\(197\) −12.0795 1.91320i −0.860625 0.136310i −0.289506 0.957176i \(-0.593491\pi\)
−0.571120 + 0.820867i \(0.693491\pi\)
\(198\) −0.712010 3.22657i −0.0506003 0.229302i
\(199\) 15.9356i 1.12965i 0.825212 + 0.564823i \(0.191056\pi\)
−0.825212 + 0.564823i \(0.808944\pi\)
\(200\) 0 0
\(201\) −10.8571 + 3.89211i −0.765799 + 0.274528i
\(202\) −12.5076 6.37296i −0.880034 0.448400i
\(203\) −0.0862519 + 0.544573i −0.00605369 + 0.0382215i
\(204\) −3.06399 + 4.49536i −0.214522 + 0.314738i
\(205\) 0 0
\(206\) 7.76123 10.6824i 0.540750 0.744279i
\(207\) 7.45886 + 0.725556i 0.518427 + 0.0504296i
\(208\) 0.797241 + 5.03358i 0.0552787 + 0.349016i
\(209\) −0.477258 + 1.46885i −0.0330126 + 0.101602i
\(210\) 0 0
\(211\) −3.41758 10.5182i −0.235276 0.724104i −0.997085 0.0763026i \(-0.975689\pi\)
0.761809 0.647802i \(-0.224311\pi\)
\(212\) −6.04920 + 3.08222i −0.415461 + 0.211688i
\(213\) −16.1135 15.1729i −1.10408 1.03963i
\(214\) −18.5097 + 6.01417i −1.26530 + 0.411120i
\(215\) 0 0
\(216\) 3.91169 3.42034i 0.266157 0.232724i
\(217\) 0.742674 0.117628i 0.0504160 0.00798511i
\(218\) 8.70216 8.70216i 0.589385 0.589385i
\(219\) −0.644746 + 2.20801i −0.0435679 + 0.149204i
\(220\) 0 0
\(221\) −9.40879 12.9501i −0.632904 0.871117i
\(222\) 17.6304 3.33833i 1.18328 0.224054i
\(223\) −2.49393 + 4.89460i −0.167006 + 0.327767i −0.959308 0.282362i \(-0.908882\pi\)
0.792302 + 0.610129i \(0.208882\pi\)
\(224\) −0.0786976 −0.00525820
\(225\) 0 0
\(226\) −7.63411 −0.507814
\(227\) 3.07043 6.02606i 0.203792 0.399964i −0.766378 0.642390i \(-0.777943\pi\)
0.970170 + 0.242426i \(0.0779432\pi\)
\(228\) −2.38637 + 0.451860i −0.158041 + 0.0299251i
\(229\) 1.78525 + 2.45719i 0.117973 + 0.162376i 0.863919 0.503630i \(-0.168003\pi\)
−0.745947 + 0.666006i \(0.768003\pi\)
\(230\) 0 0
\(231\) −0.0420810 + 0.144111i −0.00276873 + 0.00948184i
\(232\) −4.95404 + 4.95404i −0.325249 + 0.325249i
\(233\) 1.36565 0.216297i 0.0894666 0.0141701i −0.111541 0.993760i \(-0.535579\pi\)
0.201007 + 0.979590i \(0.435579\pi\)
\(234\) 5.58954 + 14.2306i 0.365400 + 0.930283i
\(235\) 0 0
\(236\) 6.26761 2.03647i 0.407987 0.132563i
\(237\) −12.5578 11.8248i −0.815717 0.768101i
\(238\) 0.220242 0.112219i 0.0142762 0.00727408i
\(239\) 3.51376 + 10.8143i 0.227287 + 0.699516i 0.998051 + 0.0623963i \(0.0198743\pi\)
−0.770765 + 0.637120i \(0.780126\pi\)
\(240\) 0 0
\(241\) −2.72661 + 8.39163i −0.175636 + 0.540552i −0.999662 0.0259998i \(-0.991723\pi\)
0.824026 + 0.566552i \(0.191723\pi\)
\(242\) −1.53101 9.66643i −0.0984172 0.621382i
\(243\) 9.24826 12.5487i 0.593276 0.804999i
\(244\) 2.34577 3.22867i 0.150172 0.206695i
\(245\) 0 0
\(246\) −3.64342 + 5.34547i −0.232296 + 0.340814i
\(247\) 1.11793 7.05835i 0.0711323 0.449112i
\(248\) 8.51329 + 4.33774i 0.540595 + 0.275447i
\(249\) 1.43828 0.515604i 0.0911475 0.0326751i
\(250\) 0 0
\(251\) 14.6104i 0.922197i 0.887349 + 0.461099i \(0.152545\pi\)
−0.887349 + 0.461099i \(0.847455\pi\)
\(252\) −0.230546 + 0.0508748i −0.0145230 + 0.00320481i
\(253\) −2.71745 0.430401i −0.170844 0.0270591i
\(254\) −2.60673 + 1.89390i −0.163561 + 0.118834i
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) 1.57229 + 1.57229i 0.0980767 + 0.0980767i 0.754443 0.656366i \(-0.227907\pi\)
−0.656366 + 0.754443i \(0.727907\pi\)
\(258\) 2.16020 1.18376i 0.134488 0.0736975i
\(259\) −0.775389 0.251939i −0.0481803 0.0156547i
\(260\) 0 0
\(261\) −11.3104 + 17.7155i −0.700095 + 1.09656i
\(262\) 2.41443 + 4.73859i 0.149164 + 0.292751i
\(263\) 8.79695 + 17.2650i 0.542443 + 1.06460i 0.985747 + 0.168233i \(0.0538061\pi\)
−0.443304 + 0.896371i \(0.646194\pi\)
\(264\) −1.50895 + 1.16718i −0.0928695 + 0.0718348i
\(265\) 0 0
\(266\) 0.104953 + 0.0341012i 0.00643507 + 0.00209088i
\(267\) −2.72928 4.98058i −0.167029 0.304807i
\(268\) 4.70859 + 4.70859i 0.287623 + 0.287623i
\(269\) −4.44596 3.23018i −0.271075 0.196948i 0.443940 0.896056i \(-0.353580\pi\)
−0.715015 + 0.699109i \(0.753580\pi\)
\(270\) 0 0
\(271\) 6.02194 4.37520i 0.365807 0.265774i −0.389663 0.920957i \(-0.627409\pi\)
0.755470 + 0.655183i \(0.227409\pi\)
\(272\) 3.10226 + 0.491350i 0.188102 + 0.0297924i
\(273\) 0.0880031 0.689074i 0.00532619 0.0417047i
\(274\) 11.4859i 0.693891i
\(275\) 0 0
\(276\) −1.46008 4.07290i −0.0878863 0.245160i
\(277\) 17.0144 + 8.66928i 1.02230 + 0.520886i 0.883004 0.469365i \(-0.155517\pi\)
0.139293 + 0.990251i \(0.455517\pi\)
\(278\) 1.70545 10.7678i 0.102286 0.645810i
\(279\) 27.7440 + 7.20400i 1.66099 + 0.431292i
\(280\) 0 0
\(281\) 0.827936 1.13956i 0.0493905 0.0679802i −0.783607 0.621256i \(-0.786623\pi\)
0.832998 + 0.553276i \(0.186623\pi\)
\(282\) −9.39887 + 19.9033i −0.559694 + 1.18522i
\(283\) 1.49164 + 9.41786i 0.0886689 + 0.559834i 0.991528 + 0.129896i \(0.0414644\pi\)
−0.902859 + 0.429937i \(0.858536\pi\)
\(284\) −3.94874 + 12.1530i −0.234315 + 0.721147i
\(285\) 0 0
\(286\) −1.73454 5.33836i −0.102565 0.315664i
\(287\) 0.261892 0.133440i 0.0154590 0.00787674i
\(288\) −2.75001 1.19893i −0.162046 0.0706478i
\(289\) 6.78537 2.20470i 0.399139 0.129688i
\(290\) 0 0
\(291\) 0.540319 + 17.9721i 0.0316740 + 1.05355i
\(292\) 1.31168 0.207750i 0.0767604 0.0121577i
\(293\) −22.0266 + 22.0266i −1.28681 + 1.28681i −0.350091 + 0.936716i \(0.613849\pi\)
−0.936716 + 0.350091i \(0.886151\pi\)
\(294\) −11.6280 3.39542i −0.678161 0.198025i
\(295\) 0 0
\(296\) −6.08934 8.38126i −0.353936 0.487151i
\(297\) −3.66597 + 4.39475i −0.212721 + 0.255009i
\(298\) 6.52291 12.8019i 0.377862 0.741596i
\(299\) 12.7307 0.736237
\(300\) 0 0
\(301\) −0.111922 −0.00645107
\(302\) 0.148198 0.290856i 0.00852785 0.0167369i
\(303\) 4.52347 + 23.8894i 0.259867 + 1.37241i
\(304\) 0.824223 + 1.13445i 0.0472724 + 0.0650649i
\(305\) 0 0
\(306\) 9.40577 0.566067i 0.537692 0.0323599i
\(307\) 1.56450 1.56450i 0.0892910 0.0892910i −0.661050 0.750341i \(-0.729889\pi\)
0.750341 + 0.661050i \(0.229889\pi\)
\(308\) 0.0856103 0.0135593i 0.00487810 0.000772615i
\(309\) −22.8600 + 0.687269i −1.30046 + 0.0390974i
\(310\) 0 0
\(311\) 12.9644 4.21240i 0.735145 0.238863i 0.0825681 0.996585i \(-0.473688\pi\)
0.652577 + 0.757722i \(0.273688\pi\)
\(312\) 6.05131 6.42644i 0.342588 0.363826i
\(313\) 17.0167 8.67043i 0.961839 0.490082i 0.0987386 0.995113i \(-0.468519\pi\)
0.863101 + 0.505032i \(0.168519\pi\)
\(314\) −1.51888 4.67462i −0.0857152 0.263804i
\(315\) 0 0
\(316\) −3.07739 + 9.47123i −0.173117 + 0.532798i
\(317\) −1.42135 8.97408i −0.0798312 0.504034i −0.994911 0.100761i \(-0.967872\pi\)
0.915079 0.403274i \(-0.132128\pi\)
\(318\) 10.6332 + 5.02130i 0.596281 + 0.281580i
\(319\) 4.53563 6.24276i 0.253947 0.349528i
\(320\) 0 0
\(321\) 27.8548 + 18.9855i 1.55470 + 1.05967i
\(322\) −0.0307532 + 0.194168i −0.00171381 + 0.0108206i
\(323\) −3.92433 1.99954i −0.218355 0.111258i
\(324\) −8.83128 1.73453i −0.490626 0.0963625i
\(325\) 0 0
\(326\) 1.53299i 0.0849043i
\(327\) −21.1441 2.70036i −1.16927 0.149330i
\(328\) 3.68892 + 0.584268i 0.203687 + 0.0322608i
\(329\) 0.809088 0.587837i 0.0446065 0.0324085i
\(330\) 0 0
\(331\) 8.94485 + 6.49882i 0.491654 + 0.357207i 0.805820 0.592161i \(-0.201725\pi\)
−0.314166 + 0.949368i \(0.601725\pi\)
\(332\) −0.623767 0.623767i −0.0342336 0.0342336i
\(333\) −23.2570 20.6166i −1.27448 1.12978i
\(334\) 21.2873 + 6.91666i 1.16479 + 0.378463i
\(335\) 0 0
\(336\) 0.0833977 + 0.107818i 0.00454971 + 0.00588197i
\(337\) −7.85531 15.4169i −0.427906 0.839813i −0.999810 0.0194923i \(-0.993795\pi\)
0.571904 0.820321i \(-0.306205\pi\)
\(338\) 5.88940 + 11.5586i 0.320341 + 0.628705i
\(339\) 8.09004 + 10.4590i 0.439391 + 0.568054i
\(340\) 0 0
\(341\) −10.0085 3.25195i −0.541989 0.176103i
\(342\) 3.14795 + 2.79056i 0.170222 + 0.150896i
\(343\) 0.778722 + 0.778722i 0.0420470 + 0.0420470i
\(344\) −1.15057 0.835934i −0.0620343 0.0450706i
\(345\) 0 0
\(346\) 11.4671 8.33133i 0.616475 0.447895i
\(347\) 14.7693 + 2.33923i 0.792857 + 0.125576i 0.539709 0.841851i \(-0.318534\pi\)
0.253148 + 0.967428i \(0.418534\pi\)
\(348\) 12.0371 + 1.53728i 0.645256 + 0.0824070i
\(349\) 0.345103i 0.0184729i 0.999957 + 0.00923647i \(0.00294010\pi\)
−0.999957 + 0.00923647i \(0.997060\pi\)
\(350\) 0 0
\(351\) 13.5730 22.7383i 0.724473 1.21368i
\(352\) 0.981353 + 0.500025i 0.0523063 + 0.0266514i
\(353\) −3.13409 + 19.7879i −0.166811 + 1.05320i 0.752190 + 0.658947i \(0.228998\pi\)
−0.919001 + 0.394256i \(0.871002\pi\)
\(354\) −9.43196 6.42874i −0.501303 0.341683i
\(355\) 0 0
\(356\) −1.92734 + 2.65275i −0.102149 + 0.140596i
\(357\) −0.387139 0.182818i −0.0204896 0.00967574i
\(358\) 2.37636 + 15.0037i 0.125594 + 0.792971i
\(359\) 5.66877 17.4467i 0.299186 0.920800i −0.682597 0.730795i \(-0.739150\pi\)
0.981783 0.190005i \(-0.0608505\pi\)
\(360\) 0 0
\(361\) 5.26370 + 16.2000i 0.277037 + 0.852632i
\(362\) 9.15143 4.66289i 0.480989 0.245076i
\(363\) −11.6209 + 12.3413i −0.609937 + 0.647749i
\(364\) −0.381439 + 0.123937i −0.0199928 + 0.00649606i
\(365\) 0 0
\(366\) −6.90925 + 0.207721i −0.361152 + 0.0108578i
\(367\) 0.0192492 0.00304877i 0.00100480 0.000159144i −0.155932 0.987768i \(-0.549838\pi\)
0.156937 + 0.987609i \(0.449838\pi\)
\(368\) −1.76637 + 1.76637i −0.0920783 + 0.0920783i
\(369\) 11.1845 0.673114i 0.582240 0.0350409i
\(370\) 0 0
\(371\) −0.314049 0.432251i −0.0163046 0.0224414i
\(372\) −3.07889 16.2603i −0.159633 0.843057i
\(373\) 3.17602 6.23329i 0.164448 0.322748i −0.794047 0.607856i \(-0.792030\pi\)
0.958495 + 0.285109i \(0.0920297\pi\)
\(374\) −3.45942 −0.178882
\(375\) 0 0
\(376\) 12.7080 0.655364
\(377\) −16.2098 + 31.8136i −0.834848 + 1.63848i
\(378\) 0.314015 + 0.261942i 0.0161512 + 0.0134729i
\(379\) 7.15293 + 9.84516i 0.367421 + 0.505712i 0.952198 0.305483i \(-0.0988178\pi\)
−0.584776 + 0.811194i \(0.698818\pi\)
\(380\) 0 0
\(381\) 5.35711 + 1.56429i 0.274453 + 0.0801412i
\(382\) 7.68054 7.68054i 0.392971 0.392971i
\(383\) 0.936062 0.148258i 0.0478305 0.00757561i −0.132473 0.991187i \(-0.542292\pi\)
0.180304 + 0.983611i \(0.442292\pi\)
\(384\) 0.0520493 + 1.73127i 0.00265613 + 0.0883484i
\(385\) 0 0
\(386\) 18.4588 5.99764i 0.939530 0.305272i
\(387\) −3.91100 1.70509i −0.198807 0.0866748i
\(388\) 9.24945 4.71283i 0.469570 0.239258i
\(389\) 6.14102 + 18.9001i 0.311362 + 0.958273i 0.977226 + 0.212200i \(0.0680630\pi\)
−0.665864 + 0.746073i \(0.731937\pi\)
\(390\) 0 0
\(391\) 2.42458 7.46210i 0.122616 0.377374i
\(392\) 1.09407 + 6.90770i 0.0552590 + 0.348892i
\(393\) 3.93339 8.32944i 0.198413 0.420164i
\(394\) 7.18863 9.89430i 0.362158 0.498468i
\(395\) 0 0
\(396\) 3.19814 + 0.830427i 0.160713 + 0.0417305i
\(397\) 4.21926 26.6394i 0.211759 1.33699i −0.621198 0.783654i \(-0.713354\pi\)
0.832957 0.553338i \(-0.186646\pi\)
\(398\) −14.1987 7.23462i −0.711719 0.362639i
\(399\) −0.0645011 0.179927i −0.00322909 0.00900759i
\(400\) 0 0
\(401\) 33.9394i 1.69485i 0.530912 + 0.847427i \(0.321849\pi\)
−0.530912 + 0.847427i \(0.678151\pi\)
\(402\) 1.46112 11.4407i 0.0728739 0.570611i
\(403\) 48.0943 + 7.61739i 2.39575 + 0.379449i
\(404\) 11.3567 8.25112i 0.565017 0.410509i
\(405\) 0 0
\(406\) −0.446060 0.324082i −0.0221376 0.0160839i
\(407\) 8.06828 + 8.06828i 0.399930 + 0.399930i
\(408\) −2.61437 4.77089i −0.129431 0.236194i
\(409\) 15.1218 + 4.91338i 0.747726 + 0.242951i 0.658002 0.753016i \(-0.271402\pi\)
0.0897236 + 0.995967i \(0.471402\pi\)
\(410\) 0 0
\(411\) −15.7361 + 12.1719i −0.776205 + 0.600396i
\(412\) 5.99458 + 11.7650i 0.295332 + 0.579621i
\(413\) 0.235453 + 0.462102i 0.0115859 + 0.0227386i
\(414\) −4.03273 + 6.31650i −0.198198 + 0.310439i
\(415\) 0 0
\(416\) −4.84689 1.57485i −0.237638 0.0772134i
\(417\) −16.5595 + 9.07436i −0.810924 + 0.444373i
\(418\) −1.09208 1.09208i −0.0534155 0.0534155i
\(419\) 22.2455 + 16.1623i 1.08677 + 0.789582i 0.978850 0.204578i \(-0.0655823\pi\)
0.107916 + 0.994160i \(0.465582\pi\)
\(420\) 0 0
\(421\) 25.8507 18.7816i 1.25988 0.915359i 0.261132 0.965303i \(-0.415904\pi\)
0.998752 + 0.0499438i \(0.0159042\pi\)
\(422\) 10.9234 + 1.73009i 0.531741 + 0.0842194i
\(423\) 37.2283 8.21520i 1.81010 0.399437i
\(424\) 6.78917i 0.329711i
\(425\) 0 0
\(426\) 20.8346 7.46889i 1.00944 0.361869i
\(427\) 0.279839 + 0.142585i 0.0135424 + 0.00690018i
\(428\) 3.04457 19.2226i 0.147165 0.929162i
\(429\) −5.47559 + 8.03356i −0.264364 + 0.387864i
\(430\) 0 0
\(431\) −5.09101 + 7.00718i −0.245225 + 0.337524i −0.913832 0.406093i \(-0.866891\pi\)
0.668607 + 0.743616i \(0.266891\pi\)
\(432\) 1.27167 + 5.03814i 0.0611835 + 0.242398i
\(433\) 1.68664 + 10.6490i 0.0810548 + 0.511760i 0.994495 + 0.104786i \(0.0334159\pi\)
−0.913440 + 0.406974i \(0.866584\pi\)
\(434\) −0.232360 + 0.715129i −0.0111536 + 0.0343273i
\(435\) 0 0
\(436\) 3.80299 + 11.7044i 0.182130 + 0.560538i
\(437\) 3.12107 1.59026i 0.149301 0.0760726i
\(438\) −1.67464 1.57689i −0.0800176 0.0753467i
\(439\) 32.6251 10.6006i 1.55711 0.505937i 0.601078 0.799190i \(-0.294738\pi\)
0.956035 + 0.293253i \(0.0947379\pi\)
\(440\) 0 0
\(441\) 7.67066 + 19.5290i 0.365269 + 0.929951i
\(442\) 15.8101 2.50408i 0.752011 0.119107i
\(443\) 4.58214 4.58214i 0.217704 0.217704i −0.589826 0.807530i \(-0.700804\pi\)
0.807530 + 0.589826i \(0.200804\pi\)
\(444\) −5.02958 + 17.2244i −0.238693 + 0.817434i
\(445\) 0 0
\(446\) −3.22891 4.44421i −0.152893 0.210439i
\(447\) −24.4515 + 4.62991i −1.15652 + 0.218987i
\(448\) 0.0357280 0.0701201i 0.00168799 0.00331286i
\(449\) −22.7460 −1.07345 −0.536726 0.843756i \(-0.680339\pi\)
−0.536726 + 0.843756i \(0.680339\pi\)
\(450\) 0 0
\(451\) −4.11362 −0.193703
\(452\) 3.46581 6.80204i 0.163018 0.319941i
\(453\) −0.555530 + 0.105190i −0.0261011 + 0.00494225i
\(454\) 3.97531 + 5.47155i 0.186571 + 0.256792i
\(455\) 0 0
\(456\) 0.680779 2.33141i 0.0318804 0.109178i
\(457\) −6.28077 + 6.28077i −0.293802 + 0.293802i −0.838580 0.544778i \(-0.816614\pi\)
0.544778 + 0.838580i \(0.316614\pi\)
\(458\) −2.99986 + 0.475131i −0.140174 + 0.0222014i
\(459\) −10.7430 12.2863i −0.501442 0.573477i
\(460\) 0 0
\(461\) −21.3397 + 6.93369i −0.993889 + 0.322934i −0.760421 0.649430i \(-0.775007\pi\)
−0.233468 + 0.972364i \(0.575007\pi\)
\(462\) −0.109300 0.102920i −0.00508509 0.00478826i
\(463\) −21.5722 + 10.9916i −1.00255 + 0.510823i −0.876603 0.481214i \(-0.840196\pi\)
−0.125944 + 0.992037i \(0.540196\pi\)
\(464\) −2.16499 6.66317i −0.100507 0.309330i
\(465\) 0 0
\(466\) −0.427269 + 1.31500i −0.0197929 + 0.0609161i
\(467\) 2.10730 + 13.3049i 0.0975140 + 0.615679i 0.987247 + 0.159197i \(0.0508906\pi\)
−0.889733 + 0.456482i \(0.849109\pi\)
\(468\) −15.2171 1.48024i −0.703413 0.0684240i
\(469\) −0.308025 + 0.423960i −0.0142233 + 0.0195766i
\(470\) 0 0
\(471\) −4.79479 + 7.03472i −0.220932 + 0.324143i
\(472\) −1.03093 + 6.50902i −0.0474523 + 0.299602i
\(473\) 1.39566 + 0.711123i 0.0641724 + 0.0326975i
\(474\) 16.2371 5.82076i 0.745793 0.267356i
\(475\) 0 0
\(476\) 0.247184i 0.0113296i
\(477\) −4.38893 19.8890i −0.200955 0.910656i
\(478\) −11.2308 1.77878i −0.513684 0.0813596i
\(479\) −13.9808 + 10.1576i −0.638797 + 0.464113i −0.859437 0.511242i \(-0.829186\pi\)
0.220639 + 0.975355i \(0.429186\pi\)
\(480\) 0 0
\(481\) −42.7136 31.0332i −1.94757 1.41499i
\(482\) −6.23914 6.23914i −0.284185 0.284185i
\(483\) 0.298606 0.163631i 0.0135871 0.00744549i
\(484\) 9.30791 + 3.02432i 0.423087 + 0.137469i
\(485\) 0 0
\(486\) 6.98235 + 13.9372i 0.316726 + 0.632206i
\(487\) −1.64469 3.22789i −0.0745281 0.146270i 0.850736 0.525593i \(-0.176157\pi\)
−0.925264 + 0.379324i \(0.876157\pi\)
\(488\) 1.81181 + 3.55588i 0.0820169 + 0.160967i
\(489\) 2.10024 1.62454i 0.0949761 0.0734643i
\(490\) 0 0
\(491\) −5.48953 1.78366i −0.247739 0.0804953i 0.182515 0.983203i \(-0.441576\pi\)
−0.430254 + 0.902708i \(0.641576\pi\)
\(492\) −3.10877 5.67310i −0.140154 0.255763i
\(493\) 15.5603 + 15.5603i 0.700800 + 0.700800i
\(494\) 5.78150 + 4.20051i 0.260122 + 0.188990i
\(495\) 0 0
\(496\) −7.72991 + 5.61611i −0.347083 + 0.252171i
\(497\) −0.993249 0.157315i −0.0445533 0.00705655i
\(498\) −0.193560 + 1.51560i −0.00867365 + 0.0679157i
\(499\) 28.5582i 1.27844i 0.769024 + 0.639220i \(0.220743\pi\)
−0.769024 + 0.639220i \(0.779257\pi\)
\(500\) 0 0
\(501\) −13.0826 36.4940i −0.584486 1.63043i
\(502\) −13.0179 6.63296i −0.581018 0.296044i
\(503\) 3.76856 23.7938i 0.168032 1.06091i −0.749138 0.662414i \(-0.769532\pi\)
0.917170 0.398497i \(-0.130468\pi\)
\(504\) 0.0593360 0.228515i 0.00264304 0.0101789i
\(505\) 0 0
\(506\) 1.61718 2.22586i 0.0718926 0.0989517i
\(507\) 9.59451 20.3176i 0.426107 0.902335i
\(508\) −0.504047 3.18243i −0.0223635 0.141197i
\(509\) 1.35722 4.17708i 0.0601576 0.185146i −0.916462 0.400123i \(-0.868968\pi\)
0.976619 + 0.214977i \(0.0689675\pi\)
\(510\) 0 0
\(511\) 0.0322963 + 0.0993978i 0.00142870 + 0.00439710i
\(512\) 0.891007 0.453990i 0.0393773 0.0200637i
\(513\) 0.487193 7.27001i 0.0215101 0.320979i
\(514\) −2.11472 + 0.687116i −0.0932765 + 0.0303074i
\(515\) 0 0
\(516\) 0.0740233 + 2.46217i 0.00325869 + 0.108391i
\(517\) −13.8242 + 2.18954i −0.607989 + 0.0962960i
\(518\) 0.576498 0.576498i 0.0253299 0.0253299i
\(519\) −23.5661 6.88138i −1.03444 0.302059i
\(520\) 0 0
\(521\) 3.85216 + 5.30205i 0.168766 + 0.232287i 0.885020 0.465553i \(-0.154145\pi\)
−0.716254 + 0.697840i \(0.754145\pi\)
\(522\) −10.6499 18.1203i −0.466132 0.793104i
\(523\) −4.06078 + 7.96973i −0.177566 + 0.348492i −0.962585 0.270979i \(-0.912653\pi\)
0.785020 + 0.619471i \(0.212653\pi\)
\(524\) −5.31824 −0.232328
\(525\) 0 0
\(526\) −19.3769 −0.844875
\(527\) 13.6245 26.7397i 0.593494 1.16480i
\(528\) −0.354913 1.87437i −0.0154456 0.0815716i
\(529\) −9.85121 13.5590i −0.428314 0.589523i
\(530\) 0 0
\(531\) 1.18770 + 19.7348i 0.0515416 + 0.856416i
\(532\) −0.0780320 + 0.0780320i −0.00338312 + 0.00338312i
\(533\) 18.7999 2.97762i 0.814315 0.128975i
\(534\) 5.67680 0.170669i 0.245659 0.00738556i
\(535\) 0 0
\(536\) −6.33303 + 2.05773i −0.273545 + 0.0888803i
\(537\) 18.0373 19.1555i 0.778367 0.826619i
\(538\) 4.89653 2.49491i 0.211105 0.107563i
\(539\) −2.38035 7.32596i −0.102529 0.315551i
\(540\) 0 0
\(541\) 4.98127 15.3308i 0.214161 0.659121i −0.785051 0.619432i \(-0.787363\pi\)
0.999212 0.0396896i \(-0.0126369\pi\)
\(542\) 1.16442 + 7.35189i 0.0500163 + 0.315791i
\(543\) −16.0863 7.59639i −0.690329 0.325992i
\(544\) −1.84619 + 2.54107i −0.0791548 + 0.108947i
\(545\) 0 0
\(546\) 0.574017 + 0.391244i 0.0245657 + 0.0167437i
\(547\) −3.70025 + 23.3625i −0.158211 + 0.998907i 0.772994 + 0.634413i \(0.218758\pi\)
−0.931206 + 0.364494i \(0.881242\pi\)
\(548\) 10.2341 + 5.21451i 0.437177 + 0.222753i
\(549\) 7.60647 + 9.24576i 0.324636 + 0.394599i
\(550\) 0 0
\(551\) 9.82428i 0.418528i
\(552\) 4.29184 + 0.548120i 0.182673 + 0.0233295i
\(553\) −0.774072 0.122601i −0.0329169 0.00521353i
\(554\) −15.4488 + 11.2242i −0.656355 + 0.476870i
\(555\) 0 0
\(556\) 8.81992 + 6.40805i 0.374048 + 0.271762i
\(557\) −27.5142 27.5142i −1.16581 1.16581i −0.983181 0.182634i \(-0.941538\pi\)
−0.182634 0.983181i \(-0.558462\pi\)
\(558\) −19.0143 + 21.4496i −0.804941 + 0.908033i
\(559\) −6.89314 2.23972i −0.291549 0.0947299i
\(560\) 0 0
\(561\) 3.66602 + 4.73951i 0.154780 + 0.200102i
\(562\) 0.639477 + 1.25504i 0.0269747 + 0.0529408i
\(563\) −11.3007 22.1789i −0.476267 0.934728i −0.996727 0.0808412i \(-0.974239\pi\)
0.520460 0.853886i \(-0.325761\pi\)
\(564\) −13.4669 17.4103i −0.567061 0.733108i
\(565\) 0 0
\(566\) −9.06857 2.94656i −0.381180 0.123853i
\(567\) 0.0261004 0.707797i 0.00109611 0.0297247i
\(568\) −9.03570 9.03570i −0.379129 0.379129i
\(569\) −25.9540 18.8567i −1.08805 0.790515i −0.108981 0.994044i \(-0.534759\pi\)
−0.979069 + 0.203529i \(0.934759\pi\)
\(570\) 0 0
\(571\) −34.1170 + 24.7874i −1.42775 + 1.03732i −0.437322 + 0.899305i \(0.644073\pi\)
−0.990430 + 0.138017i \(0.955927\pi\)
\(572\) 5.54398 + 0.878080i 0.231805 + 0.0367144i
\(573\) −18.6618 2.38334i −0.779609 0.0995655i
\(574\) 0.293928i 0.0122683i
\(575\) 0 0
\(576\) 2.31674 1.90597i 0.0965306 0.0794156i
\(577\) 19.6556 + 10.0150i 0.818274 + 0.416931i 0.812435 0.583052i \(-0.198141\pi\)
0.00583873 + 0.999983i \(0.498141\pi\)
\(578\) −1.11609 + 7.04672i −0.0464233 + 0.293105i
\(579\) −27.7782 18.9333i −1.15442 0.786843i
\(580\) 0 0
\(581\) 0.0408054 0.0561638i 0.00169289 0.00233007i
\(582\) −16.2586 7.67775i −0.673940 0.318253i
\(583\) 1.16975 + 7.38553i 0.0484462 + 0.305877i
\(584\) −0.410385 + 1.26303i −0.0169818 + 0.0522647i
\(585\) 0 0
\(586\) −9.62597 29.6257i −0.397645 1.22383i
\(587\) 11.4960 5.85750i 0.474490 0.241765i −0.200356 0.979723i \(-0.564210\pi\)
0.674846 + 0.737958i \(0.264210\pi\)
\(588\) 8.30436 8.81916i 0.342466 0.363696i
\(589\) 12.7423 4.14024i 0.525039 0.170596i
\(590\) 0 0
\(591\) −21.1735 + 0.636564i −0.870960 + 0.0261848i
\(592\) 10.2323 1.62063i 0.420543 0.0666075i
\(593\) 3.75033 3.75033i 0.154007 0.154007i −0.625898 0.779905i \(-0.715267\pi\)
0.779905 + 0.625898i \(0.215267\pi\)
\(594\) −2.25143 5.26158i −0.0923774 0.215885i
\(595\) 0 0
\(596\) 8.44527 + 11.6239i 0.345932 + 0.476134i
\(597\) 5.13507 + 27.1194i 0.210165 + 1.10992i
\(598\) −5.77963 + 11.3432i −0.236347 + 0.463856i
\(599\) 29.8620 1.22013 0.610065 0.792352i \(-0.291143\pi\)
0.610065 + 0.792352i \(0.291143\pi\)
\(600\) 0 0
\(601\) 19.0008 0.775058 0.387529 0.921858i \(-0.373329\pi\)
0.387529 + 0.921858i \(0.373329\pi\)
\(602\) 0.0508115 0.0997231i 0.00207092 0.00406441i
\(603\) −17.2225 + 10.1222i −0.701355 + 0.412208i
\(604\) 0.191874 + 0.264091i 0.00780722 + 0.0107457i
\(605\) 0 0
\(606\) −23.3393 6.81513i −0.948092 0.276846i
\(607\) 29.8007 29.8007i 1.20957 1.20957i 0.238406 0.971165i \(-0.423375\pi\)
0.971165 0.238406i \(-0.0766250\pi\)
\(608\) −1.38499 + 0.219361i −0.0561687 + 0.00889625i
\(609\) 0.0286980 + 0.954554i 0.00116290 + 0.0386805i
\(610\) 0 0
\(611\) 61.5942 20.0132i 2.49184 0.809646i
\(612\) −3.76576 + 8.63759i −0.152222 + 0.349154i
\(613\) −1.17929 + 0.600877i −0.0476310 + 0.0242692i −0.477644 0.878554i \(-0.658509\pi\)
0.430013 + 0.902823i \(0.358509\pi\)
\(614\) 0.683714 + 2.10425i 0.0275924 + 0.0849208i
\(615\) 0 0
\(616\) −0.0267848 + 0.0824351i −0.00107919 + 0.00332141i
\(617\) 6.57400 + 41.5066i 0.264659 + 1.67099i 0.659087 + 0.752067i \(0.270943\pi\)
−0.394428 + 0.918927i \(0.629057\pi\)
\(618\) 9.76586 20.6804i 0.392841 0.831889i
\(619\) 9.51877 13.1015i 0.382592 0.526592i −0.573677 0.819082i \(-0.694484\pi\)
0.956269 + 0.292489i \(0.0944836\pi\)
\(620\) 0 0
\(621\) 12.9274 1.16877i 0.518758 0.0469013i
\(622\) −2.13245 + 13.4638i −0.0855036 + 0.539848i
\(623\) −0.229923 0.117151i −0.00921165 0.00469357i
\(624\) 2.97877 + 8.30930i 0.119246 + 0.332638i
\(625\) 0 0
\(626\) 19.0983i 0.763320i
\(627\) −0.338883 + 2.65349i −0.0135337 + 0.105970i
\(628\) 4.85468 + 0.768905i 0.193723 + 0.0306827i
\(629\) −26.3249 + 19.1262i −1.04964 + 0.762611i
\(630\) 0 0
\(631\) −9.33690 6.78365i −0.371696 0.270053i 0.386218 0.922408i \(-0.373781\pi\)
−0.757914 + 0.652355i \(0.773781\pi\)
\(632\) −7.04182 7.04182i −0.280109 0.280109i
\(633\) −9.20545 16.7988i −0.365884 0.667691i
\(634\) 8.64124 + 2.80771i 0.343188 + 0.111508i
\(635\) 0 0
\(636\) −9.30139 + 7.19464i −0.368824 + 0.285286i
\(637\) 16.1814 + 31.7579i 0.641132 + 1.25829i
\(638\) 3.50321 + 6.87543i 0.138693 + 0.272201i
\(639\) −32.3115 20.6290i −1.27822 0.816073i
\(640\) 0 0
\(641\) −15.5088 5.03912i −0.612561 0.199033i −0.0137264 0.999906i \(-0.504369\pi\)
−0.598835 + 0.800873i \(0.704369\pi\)
\(642\) −29.5620 + 16.1995i −1.16672 + 0.639344i
\(643\) −12.8296 12.8296i −0.505952 0.505952i 0.407330 0.913281i \(-0.366460\pi\)
−0.913281 + 0.407330i \(0.866460\pi\)
\(644\) −0.159043 0.115552i −0.00626719 0.00455338i
\(645\) 0 0
\(646\) 3.56321 2.58883i 0.140193 0.101856i
\(647\) −25.1179 3.97829i −0.987488 0.156403i −0.358259 0.933622i \(-0.616629\pi\)
−0.629229 + 0.777220i \(0.716629\pi\)
\(648\) 5.55479 7.08127i 0.218213 0.278178i
\(649\) 7.25839i 0.284917i
\(650\) 0 0
\(651\) 1.22599 0.439499i 0.0480502 0.0172253i
\(652\) −1.36590 0.695961i −0.0534928 0.0272559i
\(653\) 4.76127 30.0615i 0.186323 1.17640i −0.700281 0.713867i \(-0.746942\pi\)
0.886604 0.462529i \(-0.153058\pi\)
\(654\) 12.0053 17.6136i 0.469443 0.688747i
\(655\) 0 0
\(656\) −2.19532 + 3.02160i −0.0857129 + 0.117974i
\(657\) −0.385730 + 3.96538i −0.0150488 + 0.154704i
\(658\) 0.156448 + 0.987775i 0.00609899 + 0.0385075i
\(659\) −3.19473 + 9.83236i −0.124449 + 0.383014i −0.993800 0.111180i \(-0.964537\pi\)
0.869351 + 0.494195i \(0.164537\pi\)
\(660\) 0 0
\(661\) 3.97825 + 12.2438i 0.154736 + 0.476229i 0.998134 0.0610606i \(-0.0194483\pi\)
−0.843398 + 0.537289i \(0.819448\pi\)
\(662\) −9.85137 + 5.01952i −0.382884 + 0.195089i
\(663\) −20.1850 19.0067i −0.783921 0.738161i
\(664\) 0.838964 0.272596i 0.0325581 0.0105788i
\(665\) 0 0
\(666\) 28.9279 11.3624i 1.12093 0.440284i
\(667\) −17.2859 + 2.73781i −0.669311 + 0.106008i
\(668\) −15.8270 + 15.8270i −0.612365 + 0.612365i
\(669\) −2.66696 + 9.13333i −0.103111 + 0.353115i
\(670\) 0 0
\(671\) −2.58363 3.55605i −0.0997397 0.137280i
\(672\) −0.133928 + 0.0253594i −0.00516640 + 0.000978260i
\(673\) −15.3006 + 30.0291i −0.589794 + 1.15754i 0.382540 + 0.923939i \(0.375049\pi\)
−0.972334 + 0.233596i \(0.924951\pi\)
\(674\) 17.3028 0.666479
\(675\) 0 0
\(676\) −12.9725 −0.498943
\(677\) 7.07682 13.8891i 0.271984 0.533800i −0.714100 0.700044i \(-0.753164\pi\)
0.986085 + 0.166244i \(0.0531639\pi\)
\(678\) −12.9918 + 2.46001i −0.498948 + 0.0944759i
\(679\) 0.480192 + 0.660928i 0.0184281 + 0.0253641i
\(680\) 0 0
\(681\) 3.28346 11.2446i 0.125823 0.430895i
\(682\) 7.44126 7.44126i 0.284940 0.284940i
\(683\) 26.5524 4.20549i 1.01600 0.160919i 0.373844 0.927492i \(-0.378040\pi\)
0.642157 + 0.766573i \(0.278040\pi\)
\(684\) −3.91554 + 1.53796i −0.149715 + 0.0588054i
\(685\) 0 0
\(686\) −1.04738 + 0.340314i −0.0399891 + 0.0129932i
\(687\) 3.82996 + 3.60640i 0.146122 + 0.137593i
\(688\) 1.26717 0.645655i 0.0483104 0.0246154i
\(689\) −10.6919 32.9064i −0.407330 1.25363i
\(690\) 0 0
\(691\) 7.00128 21.5477i 0.266341 0.819714i −0.725040 0.688707i \(-0.758179\pi\)
0.991381 0.131007i \(-0.0418212\pi\)
\(692\) 2.21732 + 13.9996i 0.0842898 + 0.532185i
\(693\) −0.0251756 + 0.258811i −0.000956343 + 0.00983141i
\(694\) −8.78938 + 12.0975i −0.333640 + 0.459217i
\(695\) 0 0
\(696\) −6.83446 + 10.0272i −0.259060 + 0.380081i
\(697\) 1.83514 11.5866i 0.0695110 0.438875i
\(698\) −0.307489 0.156673i −0.0116386 0.00593018i
\(699\) 2.25438 0.808162i 0.0852684 0.0305675i
\(700\) 0 0
\(701\) 37.8133i 1.42819i −0.700049 0.714095i \(-0.746839\pi\)
0.700049 0.714095i \(-0.253161\pi\)
\(702\) 14.0980 + 22.4166i 0.532094 + 0.846061i
\(703\) −14.3482 2.27253i −0.541153 0.0857102i
\(704\) −0.891050 + 0.647386i −0.0335827 + 0.0243993i
\(705\) 0 0
\(706\) −16.2083 11.7760i −0.610007 0.443196i
\(707\) 0.781162 + 0.781162i 0.0293786 + 0.0293786i
\(708\) 10.0101 5.48536i 0.376201 0.206152i
\(709\) −37.7779 12.2748i −1.41878 0.460989i −0.503565 0.863958i \(-0.667978\pi\)
−0.915214 + 0.402968i \(0.867978\pi\)
\(710\) 0 0
\(711\) −25.1814 16.0769i −0.944377 0.602931i
\(712\) −1.48863 2.92160i −0.0557887 0.109491i
\(713\) 10.8358 + 21.2664i 0.405803 + 0.796433i
\(714\) 0.338649 0.261946i 0.0126736 0.00980309i
\(715\) 0 0
\(716\) −14.4473 4.69420i −0.539919 0.175430i
\(717\) 9.46453 + 17.2716i 0.353459 + 0.645018i
\(718\) 12.9715 + 12.9715i 0.484093 + 0.484093i
\(719\) 25.6075 + 18.6049i 0.954998 + 0.693847i 0.951984 0.306149i \(-0.0990405\pi\)
0.00301445 + 0.999995i \(0.499040\pi\)
\(720\) 0 0
\(721\) −0.840680 + 0.610790i −0.0313086 + 0.0227470i
\(722\) −16.8240 2.66466i −0.626124 0.0991682i
\(723\) −1.93606 + 15.1596i −0.0720029 + 0.563791i
\(724\) 10.2709i 0.381715i
\(725\) 0 0
\(726\) −5.72039 15.9571i −0.212304 0.592223i
\(727\) 45.9671 + 23.4214i 1.70483 + 0.868652i 0.984580 + 0.174934i \(0.0559711\pi\)
0.720246 + 0.693719i \(0.244029\pi\)
\(728\) 0.0627409 0.396131i 0.00232533 0.0146816i
\(729\) 11.6951 24.3357i 0.433152 0.901321i
\(730\) 0 0
\(731\) −2.62561 + 3.61384i −0.0971117 + 0.133663i
\(732\) 2.95165 6.25049i 0.109096 0.231025i
\(733\) −3.31036 20.9008i −0.122271 0.771988i −0.970276 0.242000i \(-0.922197\pi\)
0.848005 0.529988i \(-0.177803\pi\)
\(734\) −0.00602247 + 0.0185352i −0.000222293 + 0.000684148i
\(735\) 0 0
\(736\) −0.771931 2.37576i −0.0284538 0.0875717i
\(737\) 6.53478 3.32964i 0.240712 0.122649i
\(738\) −4.47789 + 10.2710i −0.164834 + 0.378082i
\(739\) −11.8537 + 3.85150i −0.436046 + 0.141680i −0.518811 0.854889i \(-0.673625\pi\)
0.0827648 + 0.996569i \(0.473625\pi\)
\(740\) 0 0
\(741\) −0.371961 12.3722i −0.0136643 0.454505i
\(742\) 0.527714 0.0835816i 0.0193730 0.00306838i
\(743\) 2.30237 2.30237i 0.0844658 0.0844658i −0.663612 0.748077i \(-0.730977\pi\)
0.748077 + 0.663612i \(0.230977\pi\)
\(744\) 15.8858 + 4.63870i 0.582402 + 0.170063i
\(745\) 0 0
\(746\) 4.11202 + 5.65971i 0.150552 + 0.207217i
\(747\) 2.28154 1.34093i 0.0834772 0.0490621i
\(748\) 1.57054 3.08236i 0.0574247 0.112702i
\(749\) 1.53163 0.0559646
\(750\) 0 0
\(751\) 18.7652 0.684751 0.342375 0.939563i \(-0.388769\pi\)
0.342375 + 0.939563i \(0.388769\pi\)
\(752\) −5.76930 + 11.3229i −0.210385 + 0.412904i
\(753\) 4.70802 + 24.8641i 0.171570 + 0.906097i
\(754\) −20.9870 28.8861i −0.764301 1.05197i
\(755\) 0 0
\(756\) −0.375952 + 0.160870i −0.0136733 + 0.00585079i
\(757\) −7.02667 + 7.02667i −0.255389 + 0.255389i −0.823176 0.567787i \(-0.807800\pi\)
0.567787 + 0.823176i \(0.307800\pi\)
\(758\) −12.0195 + 1.90370i −0.436567 + 0.0691453i
\(759\) −4.76327 + 0.143204i −0.172896 + 0.00519798i
\(760\) 0 0
\(761\) 48.1462 15.6436i 1.74530 0.567081i 0.749782 0.661685i \(-0.230158\pi\)
0.995515 + 0.0946038i \(0.0301584\pi\)
\(762\) −3.82587 + 4.06305i −0.138597 + 0.147189i
\(763\) −0.862948 + 0.439694i −0.0312408 + 0.0159180i
\(764\) 3.35652 + 10.3303i 0.121435 + 0.373737i
\(765\) 0 0
\(766\) −0.292865 + 0.901344i −0.0105816 + 0.0325669i
\(767\) 5.25394 + 33.1721i 0.189709 + 1.19777i
\(768\) −1.56620 0.739603i −0.0565154 0.0266881i
\(769\) −21.2813 + 29.2912i −0.767422 + 1.05627i 0.229138 + 0.973394i \(0.426409\pi\)
−0.996560 + 0.0828721i \(0.973591\pi\)
\(770\) 0 0
\(771\) 3.18239 + 2.16909i 0.114611 + 0.0781178i
\(772\) −3.03620 + 19.1698i −0.109275 + 0.689936i
\(773\) −20.9544 10.6768i −0.753679 0.384019i 0.0345481 0.999403i \(-0.489001\pi\)
−0.788227 + 0.615384i \(0.789001\pi\)
\(774\) 3.29481 2.71063i 0.118429 0.0974317i
\(775\) 0 0
\(776\) 10.3809i 0.372653i
\(777\) −1.40075 0.178893i −0.0502516 0.00641774i
\(778\) −19.6281 3.10878i −0.703701 0.111455i
\(779\) 4.23704 3.07839i 0.151808 0.110295i
\(780\) 0 0
\(781\) 11.3862 + 8.27256i 0.407430 + 0.296015i
\(782\) 5.54804 + 5.54804i