Properties

Label 750.2.l.b.107.8
Level $750$
Weight $2$
Character 750.107
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 107.8
Character \(\chi\) \(=\) 750.107
Dual form 750.2.l.b.743.8

$q$-expansion

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

Character values

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

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{13}{20}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.891007 + 0.453990i 0.630037 + 0.321020i
\(3\) 0.322239 + 1.70181i 0.186045 + 0.982541i
\(4\) 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 \(-0.254734\pi\)
−0.717545 + 0.696512i \(0.754734\pi\)
\(8\) 0.156434 + 0.987688i 0.0553079 + 0.349201i
\(9\) −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 \(0.453099\pi\)
\(12\) −1.18739 + 1.26100i −0.342769 + 0.364018i
\(13\) 2.31368 + 4.54086i 0.641700 + 1.25941i 0.951220 + 0.308514i \(0.0998317\pi\)
−0.309520 + 0.950893i \(0.600168\pi\)
\(14\) −0.0243189 0.0748459i −0.00649950 0.0200034i
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) −3.10226 + 0.491350i −0.752408 + 0.119170i −0.520846 0.853650i \(-0.674384\pi\)
−0.231562 + 0.972820i \(0.574384\pi\)
\(18\) −2.98591 0.290452i −0.703785 0.0684602i
\(19\) −0.824223 + 1.13445i −0.189090 + 0.260260i −0.893028 0.450002i \(-0.851423\pi\)
0.703938 + 0.710262i \(0.251423\pi\)
\(20\) 0 0
\(21\) 0.0767699 0.112634i 0.0167526 0.0245787i
\(22\) −1.08784 0.172297i −0.231928 0.0367338i
\(23\) −1.13408 + 2.22575i −0.236472 + 0.464102i −0.978495 0.206273i \(-0.933867\pi\)
0.742023 + 0.670375i \(0.233867\pi\)
\(24\) −1.63045 + 0.584493i −0.332814 + 0.119309i
\(25\) 0 0
\(26\) 5.09632i 0.999471i
\(27\) −2.76630 4.39859i −0.532376 0.846508i
\(28\) 0.0123110 0.0777287i 0.00232656 0.0146893i
\(29\) 5.66803 4.11807i 1.05253 0.764705i 0.0798355 0.996808i \(-0.474560\pi\)
0.972691 + 0.232103i \(0.0745605\pi\)
\(30\) 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
\(33\) −0.916756 1.67296i −0.159587 0.291225i
\(34\) −2.98720 0.970601i −0.512301 0.166457i
\(35\) 0 0
\(36\) −2.52860 1.61437i −0.421433 0.269061i
\(37\) −9.23065 + 4.70325i −1.51751 + 0.773210i −0.996755 0.0804961i \(-0.974350\pi\)
−0.520755 + 0.853706i \(0.674350\pi\)
\(38\) −1.24942 + 0.636609i −0.202682 + 0.103272i
\(39\) −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 \(0.505797\pi\)
\(42\) 0.119537 0.0655044i 0.0184450 0.0101075i
\(43\) 1.00563 1.00563i 0.153357 0.153357i −0.626258 0.779616i \(-0.715414\pi\)
0.779616 + 0.626258i \(0.215414\pi\)
\(44\) −0.891050 0.647386i −0.134331 0.0975971i
\(45\) 0 0
\(46\) −2.02094 + 1.46830i −0.297972 + 0.216489i
\(47\) 1.98797 12.5515i 0.289975 1.83083i −0.225883 0.974154i \(-0.572527\pi\)
0.515858 0.856674i \(-0.327473\pi\)
\(48\) −1.71810 0.219422i −0.247986 0.0316708i
\(49\) 6.99381i 0.999115i
\(50\) 0 0
\(51\) −1.83585 5.12113i −0.257071 0.717101i
\(52\) −2.31368 + 4.54086i −0.320850 + 0.629704i
\(53\) 6.70559 + 1.06206i 0.921083 + 0.145885i 0.598929 0.800802i \(-0.295593\pi\)
0.322154 + 0.946687i \(0.395593\pi\)
\(54\) −0.467880 5.17504i −0.0636704 0.704234i
\(55\) 0 0
\(56\) 0.0462573 0.0636677i 0.00618139 0.00850795i
\(57\) −2.19621 1.03711i −0.290895 0.137369i
\(58\) 6.91981 1.09599i 0.908616 0.143911i
\(59\) 2.03647 6.26761i 0.265126 0.815974i −0.726538 0.687126i \(-0.758872\pi\)
0.991664 0.128848i \(-0.0411279\pi\)
\(60\) 0 0
\(61\) 1.23324 + 3.79553i 0.157901 + 0.485968i 0.998443 0.0557774i \(-0.0177637\pi\)
−0.840543 + 0.541745i \(0.817764\pi\)
\(62\) 4.33774 + 8.51329i 0.550894 + 1.08119i
\(63\) 0.216419 + 0.0943531i 0.0272663 + 0.0118874i
\(64\) −0.951057 + 0.309017i −0.118882 + 0.0386271i
\(65\) 0 0
\(66\) −0.0573270 1.90682i −0.00705647 0.234713i
\(67\) 1.04169 + 6.57696i 0.127263 + 0.803504i 0.965919 + 0.258844i \(0.0833414\pi\)
−0.838657 + 0.544660i \(0.816659\pi\)
\(68\) −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 \(-0.473950\pi\)
\(72\) −1.52009 2.58637i −0.179144 0.304807i
\(73\) −1.18329 0.602914i −0.138493 0.0705658i 0.383371 0.923595i \(-0.374763\pi\)
−0.521864 + 0.853029i \(0.674763\pi\)
\(74\) −10.3598 −1.20430
\(75\) 0 0
\(76\) −1.40225 −0.160849
\(77\) 0.0772302 + 0.0393507i 0.00880119 + 0.00448443i
\(78\) −8.67298 + 1.64223i −0.982022 + 0.185946i
\(79\) 5.85354 + 8.05671i 0.658575 + 0.906451i 0.999433 0.0336639i \(-0.0107176\pi\)
−0.340858 + 0.940115i \(0.610718\pi\)
\(80\) 0 0
\(81\) 6.59415 6.12512i 0.732684 0.680569i
\(82\) 2.64098 + 2.64098i 0.291647 + 0.291647i
\(83\) 0.137997 + 0.871279i 0.0151471 + 0.0956353i 0.994104 0.108433i \(-0.0345834\pi\)
−0.978957 + 0.204069i \(0.934583\pi\)
\(84\) 0.136247 0.00409615i 0.0148657 0.000446927i
\(85\) 0 0
\(86\) 1.35257 0.439477i 0.145851 0.0473900i
\(87\) 8.83463 + 8.31892i 0.947172 + 0.891882i
\(88\) −0.500025 0.981353i −0.0533028 0.104613i
\(89\) 1.01326 + 3.11850i 0.107406 + 0.330560i 0.990288 0.139035i \(-0.0444000\pi\)
−0.882882 + 0.469595i \(0.844400\pi\)
\(90\) 0 0
\(91\) 0.123937 0.381439i 0.0129921 0.0399856i
\(92\) −2.46727 + 0.390777i −0.257230 + 0.0407413i
\(93\) −7.06668 + 14.9646i −0.732781 + 1.55175i
\(94\) 7.46957 10.2810i 0.770427 1.06040i
\(95\) 0 0
\(96\) −1.43122 0.975505i −0.146073 0.0995621i
\(97\) 10.2531 + 1.62393i 1.04104 + 0.164885i 0.653469 0.756953i \(-0.273313\pi\)
0.387575 + 0.921838i \(0.373313\pi\)
\(98\) 3.17512 6.23153i 0.320736 0.629479i
\(99\) 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 \(0.753896\pi\)
\(102\) 0.689188 5.39642i 0.0682398 0.534325i
\(103\) 2.06559 13.0416i 0.203529 1.28503i −0.648371 0.761324i \(-0.724549\pi\)
0.851900 0.523705i \(-0.175451\pi\)
\(104\) −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 0.425413 0.904999i \(-0.360129\pi\)
0.904999 0.425413i \(-0.139871\pi\)
\(108\) 1.93254 4.82341i 0.185958 0.464133i
\(109\) 11.7044 + 3.80299i 1.12108 + 0.364260i 0.810178 0.586183i \(-0.199370\pi\)
0.310898 + 0.950443i \(0.399370\pi\)
\(110\) 0 0
\(111\) −10.9785 14.1933i −1.04204 1.34716i
\(112\) 0.0701201 0.0357280i 0.00662572 0.00337598i
\(113\) −6.80204 + 3.46581i −0.639882 + 0.326036i −0.743654 0.668565i \(-0.766909\pi\)
0.103771 + 0.994601i \(0.466909\pi\)
\(114\) −1.48600 1.92113i −0.139177 0.179930i
\(115\) 0 0
\(116\) 6.66317 + 2.16499i 0.618660 + 0.201015i
\(117\) −11.4409 10.1420i −1.05771 0.937624i
\(118\) 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
\(122\) −0.624308 + 3.94172i −0.0565222 + 0.356867i
\(123\) −0.819518 + 6.41692i −0.0738935 + 0.578594i
\(124\) 9.55469i 0.858037i
\(125\) 0 0
\(126\) 0.149996 + 0.182322i 0.0133627 + 0.0162425i
\(127\) 1.46280 2.87091i 0.129803 0.254752i −0.816954 0.576703i \(-0.804339\pi\)
0.946756 + 0.321952i \(0.104339\pi\)
\(128\) −0.987688 0.156434i −0.0873001 0.0138270i
\(129\) 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 \(0.125366\pi\)
\(132\) 0.814598 1.72501i 0.0709017 0.150143i
\(133\) 0.108995 0.0172632i 0.00945109 0.00149690i
\(134\) −2.05773 + 6.33303i −0.177761 + 0.547091i
\(135\) 0 0
\(136\) −0.970601 2.98720i −0.0832283 0.256150i
\(137\) 5.21451 + 10.2341i 0.445506 + 0.874354i 0.999135 + 0.0415907i \(0.0132426\pi\)
−0.553629 + 0.832763i \(0.686757\pi\)
\(138\) −3.15000 2.96612i −0.268146 0.252493i
\(139\) 10.3684 3.36891i 0.879440 0.285747i 0.165715 0.986174i \(-0.447007\pi\)
0.713725 + 0.700426i \(0.247007\pi\)
\(140\) 0 0
\(141\) 22.0009 0.661442i 1.85281 0.0557034i
\(142\) −1.99898 12.6211i −0.167751 1.05914i
\(143\) −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
\(147\) 11.9021 2.25367i 0.981672 0.185880i
\(148\) −9.23065 4.70325i −0.758755 0.386605i
\(149\) 14.3679 1.17707 0.588534 0.808472i \(-0.299705\pi\)
0.588534 + 0.808472i \(0.299705\pi\)
\(150\) 0 0
\(151\) −0.326435 −0.0265649 −0.0132824 0.999912i \(-0.504228\pi\)
−0.0132824 + 0.999912i \(0.504228\pi\)
\(152\) −1.24942 0.636609i −0.101341 0.0516358i
\(153\) 8.12361 4.77450i 0.656755 0.385995i
\(154\) 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 \(-0.187160\pi\)
−0.554682 + 0.832062i \(0.687160\pi\)
\(158\) 1.55788 + 9.83604i 0.123938 + 0.782513i
\(159\) 0.353372 + 11.7539i 0.0280242 + 0.932144i
\(160\) 0 0
\(161\) 0.186967 0.0607491i 0.0147350 0.00478770i
\(162\) 8.65618 2.46384i 0.680094 0.193578i
\(163\) 0.695961 + 1.36590i 0.0545119 + 0.106986i 0.916655 0.399679i \(-0.130878\pi\)
−0.862143 + 0.506664i \(0.830878\pi\)
\(164\) 1.15415 + 3.55210i 0.0901239 + 0.277373i
\(165\) 0 0
\(166\) −0.272596 + 0.838964i −0.0211576 + 0.0651163i
\(167\) −22.1072 + 3.50144i −1.71071 + 0.270949i −0.933573 0.358387i \(-0.883327\pi\)
−0.777133 + 0.629336i \(0.783327\pi\)
\(168\) 0.123256 + 0.0582050i 0.00950943 + 0.00449061i
\(169\) −7.62505 + 10.4950i −0.586542 + 0.807306i
\(170\) 0 0
\(171\) 1.05726 4.07173i 0.0808509 0.311373i
\(172\) 1.40467 + 0.222477i 0.107105 + 0.0169637i
\(173\) 6.43491 12.6292i 0.489237 0.960182i −0.505985 0.862542i \(-0.668871\pi\)
0.995222 0.0976395i \(-0.0311292\pi\)
\(174\) 4.09500 + 11.4230i 0.310441 + 0.865979i
\(175\) 0 0
\(176\) 1.10140i 0.0830211i
\(177\) 11.3225 + 1.44602i 0.851053 + 0.108690i
\(178\) −0.512946 + 3.23861i −0.0384469 + 0.242744i
\(179\) −12.2896 + 8.92889i −0.918565 + 0.667377i −0.943167 0.332320i \(-0.892168\pi\)
0.0246011 + 0.999697i \(0.492168\pi\)
\(180\) 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
\(183\) −6.06188 + 3.32181i −0.448107 + 0.245556i
\(184\) −2.37576 0.771931i −0.175143 0.0569075i
\(185\) 0 0
\(186\) −13.0902 + 10.1253i −0.959823 + 0.742425i
\(187\) 3.08236 1.57054i 0.225405 0.114849i
\(188\) 11.3229 5.76930i 0.825807 0.420770i
\(189\) −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 \(0.728553\pi\)
\(192\) −0.832356 1.51894i −0.0600701 0.109620i
\(193\) 13.7241 13.7241i 0.987880 0.987880i −0.0120476 0.999927i \(-0.503835\pi\)
0.999927 + 0.0120476i \(0.00383498\pi\)
\(194\) 8.39833 + 6.10174i 0.602965 + 0.438080i
\(195\) 0 0
\(196\) 5.65811 4.11086i 0.404151 0.293633i
\(197\) −1.91320 + 12.0795i −0.136310 + 0.860625i 0.820867 + 0.571120i \(0.193491\pi\)
−0.957176 + 0.289506i \(0.906509\pi\)
\(198\) 3.22657 0.712010i 0.229302 0.0506003i
\(199\) 15.9356i 1.12965i −0.825212 0.564823i \(-0.808944\pi\)
0.825212 0.564823i \(-0.191056\pi\)
\(200\) 0 0
\(201\) −10.8571 + 3.89211i −0.765799 + 0.274528i
\(202\) −6.37296 + 12.5076i −0.448400 + 0.880034i
\(203\) −0.544573 0.0862519i −0.0382215 0.00605369i
\(204\) 3.06399 4.49536i 0.214522 0.314738i
\(205\) 0 0
\(206\) 7.76123 10.6824i 0.540750 0.744279i
\(207\) 0.725556 7.45886i 0.0504296 0.518427i
\(208\) −5.03358 + 0.797241i −0.349016 + 0.0552787i
\(209\) 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 \(-0.224311\pi\)
\(212\) 3.08222 + 6.04920i 0.211688 + 0.415461i
\(213\) 15.1729 16.1135i 1.03963 1.10408i
\(214\) 18.5097 6.01417i 1.26530 0.411120i
\(215\) 0 0
\(216\) 3.91169 3.42034i 0.266157 0.232724i
\(217\) −0.117628 0.742674i −0.00798511 0.0504160i
\(218\) 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
\(222\) −3.33833 17.6304i −0.224054 1.18328i
\(223\) −4.89460 2.49393i −0.327767 0.167006i 0.282362 0.959308i \(-0.408882\pi\)
−0.610129 + 0.792302i \(0.708882\pi\)
\(224\) 0.0786976 0.00525820
\(225\) 0 0
\(226\) −7.63411 −0.507814
\(227\) −6.02606 3.07043i −0.399964 0.203792i 0.242426 0.970170i \(-0.422057\pi\)
−0.642390 + 0.766378i \(0.722057\pi\)
\(228\) −0.451860 2.38637i −0.0299251 0.158041i
\(229\) −1.78525 2.45719i −0.117973 0.162376i 0.745947 0.666006i \(-0.231997\pi\)
−0.863919 + 0.503630i \(0.831997\pi\)
\(230\) 0 0
\(231\) −0.0420810 + 0.144111i −0.00276873 + 0.00948184i
\(232\) 4.95404 + 4.95404i 0.325249 + 0.325249i
\(233\) 0.216297 + 1.36565i 0.0141701 + 0.0894666i 0.993760 0.111541i \(-0.0355785\pi\)
−0.979590 + 0.201007i \(0.935579\pi\)
\(234\) −5.58954 14.2306i −0.365400 0.930283i
\(235\) 0 0
\(236\) 6.26761 2.03647i 0.407987 0.132563i
\(237\) −11.8248 + 12.5578i −0.768101 + 0.815717i
\(238\) 0.112219 + 0.220242i 0.00727408 + 0.0142762i
\(239\) −3.51376 10.8143i −0.227287 0.699516i −0.998051 0.0623963i \(-0.980126\pi\)
0.770765 0.637120i \(-0.219874\pi\)
\(240\) 0 0
\(241\) −2.72661 + 8.39163i −0.175636 + 0.540552i −0.999662 0.0259998i \(-0.991723\pi\)
0.824026 + 0.566552i \(0.191723\pi\)
\(242\) −9.66643 + 1.53101i −0.621382 + 0.0984172i
\(243\) 12.5487 + 9.24826i 0.804999 + 0.593276i
\(244\) −2.34577 + 3.22867i −0.150172 + 0.206695i
\(245\) 0 0
\(246\) −3.64342 + 5.34547i −0.232296 + 0.340814i
\(247\) −7.05835 1.11793i −0.449112 0.0711323i
\(248\) −4.33774 + 8.51329i −0.275447 + 0.540595i
\(249\) −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 \(0.847455\pi\)
\(252\) 0.0508748 + 0.230546i 0.00320481 + 0.0145230i
\(253\) 0.430401 2.71745i 0.0270591 0.170844i
\(254\) 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 −0.656366 0.754443i \(-0.727907\pi\)
0.754443 + 0.656366i \(0.227907\pi\)
\(258\) 1.18376 + 2.16020i 0.0736975 + 0.134488i
\(259\) 0.775389 + 0.251939i 0.0481803 + 0.0156547i
\(260\) 0 0
\(261\) −11.3104 + 17.7155i −0.700095 + 1.09656i
\(262\) 4.73859 2.41443i 0.292751 0.149164i
\(263\) −17.2650 + 8.79695i −1.06460 + 0.542443i −0.896371 0.443304i \(-0.853806\pi\)
−0.168233 + 0.985747i \(0.553806\pi\)
\(264\) 1.50895 1.16718i 0.0928695 0.0718348i
\(265\) 0 0
\(266\) 0.104953 + 0.0341012i 0.00643507 + 0.00209088i
\(267\) −4.98058 + 2.72928i −0.304807 + 0.167029i
\(268\) −4.70859 + 4.70859i −0.287623 + 0.287623i
\(269\) 4.44596 + 3.23018i 0.271075 + 0.196948i 0.715015 0.699109i \(-0.246420\pi\)
−0.443940 + 0.896056i \(0.646420\pi\)
\(270\) 0 0
\(271\) 6.02194 4.37520i 0.365807 0.265774i −0.389663 0.920957i \(-0.627409\pi\)
0.755470 + 0.655183i \(0.227409\pi\)
\(272\) 0.491350 3.10226i 0.0297924 0.188102i
\(273\) 0.689074 + 0.0880031i 0.0417047 + 0.00532619i
\(274\) 11.4859i 0.693891i
\(275\) 0 0
\(276\) −1.46008 4.07290i −0.0878863 0.245160i
\(277\) 8.66928 17.0144i 0.520886 1.02230i −0.469365 0.883004i \(-0.655517\pi\)
0.990251 0.139293i \(-0.0444830\pi\)
\(278\) 10.7678 + 1.70545i 0.645810 + 0.102286i
\(279\) −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 \(0.186623\pi\)
\(282\) 19.9033 + 9.39887i 1.18522 + 0.559694i
\(283\) −9.41786 + 1.49164i −0.559834 + 0.0886689i −0.429937 0.902859i \(-0.641464\pi\)
−0.129896 + 0.991528i \(0.541464\pi\)
\(284\) 3.94874 12.1530i 0.234315 0.721147i
\(285\) 0 0
\(286\) −1.73454 5.33836i −0.102565 0.315664i
\(287\) −0.133440 0.261892i −0.00787674 0.0154590i
\(288\) 1.19893 2.75001i 0.0706478 0.162046i
\(289\) −6.78537 + 2.20470i −0.399139 + 0.129688i
\(290\) 0 0
\(291\) 0.540319 + 17.9721i 0.0316740 + 1.05355i
\(292\) −0.207750 1.31168i −0.0121577 0.0767604i
\(293\) −22.0266 22.0266i −1.28681 1.28681i −0.936716 0.350091i \(-0.886151\pi\)
−0.350091 0.936716i \(-0.613849\pi\)
\(294\) 11.6280 + 3.39542i 0.678161 + 0.198025i
\(295\) 0 0
\(296\) −6.08934 8.38126i −0.353936 0.487151i
\(297\) 4.39475 + 3.66597i 0.255009 + 0.212721i
\(298\) 12.8019 + 6.52291i 0.741596 + 0.377862i
\(299\) −12.7307 −0.736237
\(300\) 0 0
\(301\) −0.111922 −0.00645107
\(302\) −0.290856 0.148198i −0.0167369 0.00852785i
\(303\) −23.8894 + 4.52347i −1.37241 + 0.259867i
\(304\) −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 \(-0.270111\pi\)
−0.750341 + 0.661050i \(0.770111\pi\)
\(308\) 0.0135593 + 0.0856103i 0.000772615 + 0.00487810i
\(309\) 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 \(0.273688\pi\)
\(312\) −6.42644 6.05131i −0.363826 0.342588i
\(313\) 8.67043 + 17.0167i 0.490082 + 0.961839i 0.995113 + 0.0987386i \(0.0314808\pi\)
−0.505032 + 0.863101i \(0.668519\pi\)
\(314\) 1.51888 + 4.67462i 0.0857152 + 0.263804i
\(315\) 0 0
\(316\) −3.07739 + 9.47123i −0.173117 + 0.532798i
\(317\) −8.97408 + 1.42135i −0.504034 + 0.0798312i −0.403274 0.915079i \(-0.632128\pi\)
−0.100761 + 0.994911i \(0.532128\pi\)
\(318\) −5.02130 + 10.6332i −0.281580 + 0.596281i
\(319\) −4.53563 + 6.24276i −0.253947 + 0.349528i
\(320\) 0 0
\(321\) 27.8548 + 18.9855i 1.55470 + 1.05967i
\(322\) 0.194168 + 0.0307532i 0.0108206 + 0.00171381i
\(323\) 1.99954 3.92433i 0.111258 0.218355i
\(324\) 8.83128 + 1.73453i 0.490626 + 0.0963625i
\(325\) 0 0
\(326\) 1.53299i 0.0849043i
\(327\) −2.70036 + 21.1441i −0.149330 + 1.16927i
\(328\) −0.584268 + 3.68892i −0.0322608 + 0.203687i
\(329\) −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
\(333\) 20.6166 23.2570i 1.12978 1.27448i
\(334\) −21.2873 6.91666i −1.16479 0.378463i
\(335\) 0 0
\(336\) 0.0833977 + 0.107818i 0.00454971 + 0.00588197i
\(337\) −15.4169 + 7.85531i −0.839813 + 0.427906i −0.820321 0.571904i \(-0.806205\pi\)
−0.0194923 + 0.999810i \(0.506205\pi\)
\(338\) −11.5586 + 5.88940i −0.628705 + 0.320341i
\(339\) −8.09004 10.4590i −0.439391 0.568054i
\(340\) 0 0
\(341\) −10.0085 3.25195i −0.541989 0.176103i
\(342\) 2.79056 3.14795i 0.150896 0.170222i
\(343\) −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
\(347\) 2.33923 14.7693i 0.125576 0.792857i −0.841851 0.539709i \(-0.818534\pi\)
0.967428 0.253148i \(-0.0814658\pi\)
\(348\) −1.53728 + 12.0371i −0.0824070 + 0.645256i
\(349\) 0.345103i 0.0184729i −0.999957 0.00923647i \(-0.997060\pi\)
0.999957 0.00923647i \(-0.00294010\pi\)
\(350\) 0 0
\(351\) 13.5730 22.7383i 0.724473 1.21368i
\(352\) 0.500025 0.981353i 0.0266514 0.0523063i
\(353\) −19.7879 3.13409i −1.05320 0.166811i −0.394256 0.919001i \(-0.628998\pi\)
−0.658947 + 0.752190i \(0.728998\pi\)
\(354\) 9.43196 + 6.42874i 0.501303 + 0.341683i
\(355\) 0 0
\(356\) −1.92734 + 2.65275i −0.102149 + 0.140596i
\(357\) −0.182818 + 0.387139i −0.00967574 + 0.0204896i
\(358\) −15.0037 + 2.37636i −0.792971 + 0.125594i
\(359\) −5.66877 + 17.4467i −0.299186 + 0.920800i 0.682597 + 0.730795i \(0.260850\pi\)
−0.981783 + 0.190005i \(0.939150\pi\)
\(360\) 0 0
\(361\) 5.26370 + 16.2000i 0.277037 + 0.852632i
\(362\) −4.66289 9.15143i −0.245076 0.480989i
\(363\) −12.3413 11.6209i −0.647749 0.609937i
\(364\) 0.381439 0.123937i 0.0199928 0.00649606i
\(365\) 0 0
\(366\) −6.90925 + 0.207721i −0.361152 + 0.0108578i
\(367\) −0.00304877 0.0192492i −0.000159144 0.00100480i 0.987609 0.156937i \(-0.0501619\pi\)
−0.987768 + 0.155932i \(0.950162\pi\)
\(368\) −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
\(372\) −16.2603 + 3.07889i −0.843057 + 0.159633i
\(373\) 6.23329 + 3.17602i 0.322748 + 0.164448i 0.607856 0.794047i \(-0.292030\pi\)
−0.285109 + 0.958495i \(0.592030\pi\)
\(374\) 3.45942 0.178882
\(375\) 0 0
\(376\) 12.7080 0.655364
\(377\) 31.8136 + 16.2098i 1.63848 + 0.834848i
\(378\) −0.261942 + 0.314015i −0.0134729 + 0.0161512i
\(379\) −7.15293 9.84516i −0.367421 0.505712i 0.584776 0.811194i \(-0.301182\pi\)
−0.952198 + 0.305483i \(0.901182\pi\)
\(380\) 0 0
\(381\) 5.35711 + 1.56429i 0.274453 + 0.0801412i
\(382\) −7.68054 7.68054i −0.392971 0.392971i
\(383\) 0.148258 + 0.936062i 0.00757561 + 0.0478305i 0.991187 0.132473i \(-0.0422919\pi\)
−0.983611 + 0.180304i \(0.942292\pi\)
\(384\) −0.0520493 1.73127i −0.00265613 0.0883484i
\(385\) 0 0
\(386\) 18.4588 5.99764i 0.939530 0.305272i
\(387\) −1.70509 + 3.91100i −0.0866748 + 0.198807i
\(388\) 4.71283 + 9.24945i 0.239258 + 0.469570i
\(389\) −6.14102 18.9001i −0.311362 0.958273i −0.977226 0.212200i \(-0.931937\pi\)
0.665864 0.746073i \(-0.268063\pi\)
\(390\) 0 0
\(391\) 2.42458 7.46210i 0.122616 0.377374i
\(392\) 6.90770 1.09407i 0.348892 0.0552590i
\(393\) 8.32944 + 3.93339i 0.420164 + 0.198413i
\(394\) −7.18863 + 9.89430i −0.362158 + 0.498468i
\(395\) 0 0
\(396\) 3.19814 + 0.830427i 0.160713 + 0.0417305i
\(397\) −26.6394 4.21926i −1.33699 0.211759i −0.553338 0.832957i \(-0.686646\pi\)
−0.783654 + 0.621198i \(0.786646\pi\)
\(398\) 7.23462 14.1987i 0.362639 0.711719i
\(399\) 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 \(0.678151\pi\)
\(402\) −11.4407 1.46112i −0.570611 0.0728739i
\(403\) −7.61739 + 48.0943i −0.379449 + 2.39575i
\(404\) −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
\(408\) 4.77089 2.61437i 0.236194 0.129431i
\(409\) −15.1218 4.91338i −0.747726 0.242951i −0.0897236 0.995967i \(-0.528598\pi\)
−0.658002 + 0.753016i \(0.728598\pi\)
\(410\) 0 0
\(411\) −15.7361 + 12.1719i −0.776205 + 0.600396i
\(412\) 11.7650 5.99458i 0.579621 0.295332i
\(413\) −0.462102 + 0.235453i −0.0227386 + 0.0115859i
\(414\) 4.03273 6.31650i 0.198198 0.310439i
\(415\) 0 0
\(416\) −4.84689 1.57485i −0.237638 0.0772134i
\(417\) 9.07436 + 16.5595i 0.444373 + 0.810924i
\(418\) 1.09208 1.09208i 0.0534155 0.0534155i
\(419\) −22.2455 16.1623i −1.08677 0.789582i −0.107916 0.994160i \(-0.534418\pi\)
−0.978850 + 0.204578i \(0.934418\pi\)
\(420\) 0 0
\(421\) 25.8507 18.7816i 1.25988 0.915359i 0.261132 0.965303i \(-0.415904\pi\)
0.998752 + 0.0499438i \(0.0159042\pi\)
\(422\) 1.73009 10.9234i 0.0842194 0.531741i
\(423\) 8.21520 + 37.2283i 0.399437 + 1.81010i
\(424\) 6.78917i 0.329711i
\(425\) 0 0
\(426\) 20.8346 7.46889i 1.00944 0.361869i
\(427\) 0.142585 0.279839i 0.00690018 0.0135424i
\(428\) 19.2226 + 3.04457i 0.929162 + 0.147165i
\(429\) 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 \(0.266891\pi\)
\(432\) 5.03814 1.27167i 0.242398 0.0611835i
\(433\) −10.6490 + 1.68664i −0.511760 + 0.0810548i −0.406974 0.913440i \(-0.633416\pi\)
−0.104786 + 0.994495i \(0.533416\pi\)
\(434\) 0.232360 0.715129i 0.0111536 0.0343273i
\(435\) 0 0
\(436\) 3.80299 + 11.7044i 0.182130 + 0.560538i
\(437\) −1.59026 3.12107i −0.0760726 0.149301i
\(438\) 1.57689 1.67464i 0.0753467 0.0800176i
\(439\) −32.6251 + 10.6006i −1.55711 + 0.505937i −0.956035 0.293253i \(-0.905262\pi\)
−0.601078 + 0.799190i \(0.705262\pi\)
\(440\) 0 0
\(441\) 7.67066 + 19.5290i 0.365269 + 0.929951i
\(442\) −2.50408 15.8101i −0.119107 0.752011i
\(443\) 4.58214 + 4.58214i 0.217704 + 0.217704i 0.807530 0.589826i \(-0.200804\pi\)
−0.589826 + 0.807530i \(0.700804\pi\)
\(444\) 5.02958 17.2244i 0.238693 0.817434i
\(445\) 0 0
\(446\) −3.22891 4.44421i −0.152893 0.210439i
\(447\) 4.62991 + 24.4515i 0.218987 + 1.15652i
\(448\) 0.0701201 + 0.0357280i 0.00331286 + 0.00168799i
\(449\) 22.7460 1.07345 0.536726 0.843756i \(-0.319661\pi\)
0.536726 + 0.843756i \(0.319661\pi\)
\(450\) 0 0
\(451\) −4.11362 −0.193703
\(452\) −6.80204 3.46581i −0.319941 0.163018i
\(453\) −0.105190 0.555530i −0.00494225 0.0261011i
\(454\) −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 \(-0.183386\pi\)
−0.544778 + 0.838580i \(0.683386\pi\)
\(458\) −0.475131 2.99986i −0.0222014 0.140174i
\(459\) 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 \(0.575007\pi\)
\(462\) −0.102920 + 0.109300i −0.00478826 + 0.00508509i
\(463\) −10.9916 21.5722i −0.510823 1.00255i −0.992037 0.125944i \(-0.959804\pi\)
0.481214 0.876603i \(-0.340196\pi\)
\(464\) 2.16499 + 6.66317i 0.100507 + 0.309330i
\(465\) 0 0
\(466\) −0.427269 + 1.31500i −0.0197929 + 0.0609161i
\(467\) 13.3049 2.10730i 0.615679 0.0975140i 0.159197 0.987247i \(-0.449109\pi\)
0.456482 + 0.889733i \(0.349109\pi\)
\(468\) 1.48024 15.2171i 0.0684240 0.703413i
\(469\) 0.308025 0.423960i 0.0142233 0.0195766i
\(470\) 0 0
\(471\) −4.79479 + 7.03472i −0.220932 + 0.324143i
\(472\) 6.50902 + 1.03093i 0.299602 + 0.0474523i
\(473\) −0.711123 + 1.39566i −0.0326975 + 0.0641724i
\(474\) −16.2371 + 5.82076i −0.745793 + 0.267356i
\(475\) 0 0
\(476\) 0.247184i 0.0113296i
\(477\) −19.8890 + 4.38893i −0.910656 + 0.200955i
\(478\) 1.77878 11.2308i 0.0813596 0.513684i
\(479\) 13.9808 10.1576i 0.638797 0.464113i −0.220639 0.975355i \(-0.570814\pi\)
0.859437 + 0.511242i \(0.170814\pi\)
\(480\) 0 0
\(481\) −42.7136 31.0332i −1.94757 1.41499i
\(482\) −6.23914 + 6.23914i −0.284185 + 0.284185i
\(483\) 0.163631 + 0.298606i 0.00744549 + 0.0135871i
\(484\) −9.30791 3.02432i −0.423087 0.137469i
\(485\) 0 0
\(486\) 6.98235 + 13.9372i 0.316726 + 0.632206i
\(487\) −3.22789 + 1.64469i −0.146270 + 0.0745281i −0.525593 0.850736i \(-0.676157\pi\)
0.379324 + 0.925264i \(0.376157\pi\)
\(488\) −3.55588 + 1.81181i −0.160967 + 0.0820169i
\(489\) −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 \(0.641576\pi\)
\(492\) −5.67310 + 3.10877i −0.255763 + 0.140154i
\(493\) −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
\(497\) −0.157315 + 0.993249i −0.00705655 + 0.0445533i
\(498\) −1.51560 0.193560i −0.0679157 0.00867365i
\(499\) 28.5582i 1.27844i −0.769024 0.639220i \(-0.779257\pi\)
0.769024 0.639220i \(-0.220743\pi\)
\(500\) 0 0
\(501\) −13.0826 36.4940i −0.584486 1.63043i
\(502\) −6.63296 + 13.0179i −0.296044 + 0.581018i
\(503\) 23.7938 + 3.76856i 1.06091 + 0.168032i 0.662414 0.749138i \(-0.269532\pi\)
0.398497 + 0.917170i \(0.369532\pi\)
\(504\) −0.0593360 + 0.228515i −0.00264304 + 0.0101789i
\(505\) 0 0
\(506\) 1.61718 2.22586i 0.0718926 0.0989517i
\(507\) −20.3176 9.59451i −0.902335 0.426107i
\(508\) 3.18243 0.504047i 0.141197 0.0223635i
\(509\) −1.35722 + 4.17708i −0.0601576 + 0.185146i −0.976619 0.214977i \(-0.931032\pi\)
0.916462 + 0.400123i \(0.131032\pi\)
\(510\) 0 0
\(511\) 0.0322963 + 0.0993978i 0.00142870 + 0.00439710i
\(512\) −0.453990 0.891007i −0.0200637 0.0393773i
\(513\) 7.27001 + 0.487193i 0.320979 + 0.0215101i
\(514\) 2.11472 0.687116i 0.0932765 0.0303074i
\(515\) 0 0
\(516\) 0.0740233 + 2.46217i 0.00325869 + 0.108391i
\(517\) 2.18954 + 13.8242i 0.0962960 + 0.607989i
\(518\) 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 \(0.754145\pi\)
\(522\) −18.1203 + 10.6499i −0.793104 + 0.466132i
\(523\) −7.96973 4.06078i −0.348492 0.177566i 0.270979 0.962585i \(-0.412653\pi\)
−0.619471 + 0.785020i \(0.712653\pi\)
\(524\) 5.31824 0.232328
\(525\) 0 0
\(526\) −19.3769 −0.844875
\(527\) −26.7397 13.6245i −1.16480 0.593494i
\(528\) 1.87437 0.354913i 0.0815716 0.0154456i
\(529\) 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
\(533\) 2.97762 + 18.7999i 0.128975 + 0.814315i
\(534\) −5.67680 + 0.170669i −0.245659 + 0.00738556i
\(535\) 0 0
\(536\) −6.33303 + 2.05773i −0.273545 + 0.0888803i
\(537\) −19.1555 18.0373i −0.826619 0.778367i
\(538\) 2.49491 + 4.89653i 0.107563 + 0.211105i
\(539\) 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 \(-0.0126369\pi\)
\(542\) 7.35189 1.16442i 0.315791 0.0500163i
\(543\) 7.59639 16.0863i 0.325992 0.690329i
\(544\) 1.84619 2.54107i 0.0791548 0.108947i
\(545\) 0 0
\(546\) 0.574017 + 0.391244i 0.0245657 + 0.0167437i
\(547\) 23.3625 + 3.70025i 0.998907 + 0.158211i 0.634413 0.772994i \(-0.281242\pi\)
0.364494 + 0.931206i \(0.381242\pi\)
\(548\) −5.21451 + 10.2341i −0.222753 + 0.437177i
\(549\) −7.60647 9.24576i −0.324636 0.394599i
\(550\) 0 0
\(551\) 9.82428i 0.418528i
\(552\) 0.548120 4.29184i 0.0233295 0.182673i
\(553\) 0.122601 0.774072i 0.00521353 0.0329169i
\(554\) 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 −0.182634 + 0.983181i \(0.558462\pi\)
−0.983181 + 0.182634i \(0.941538\pi\)
\(558\) −21.4496 19.0143i −0.908033 0.804941i
\(559\) 6.89314 + 2.23972i 0.291549 + 0.0947299i
\(560\) 0 0
\(561\) 3.66602 + 4.73951i 0.154780 + 0.200102i
\(562\) 1.25504 0.639477i 0.0529408 0.0269747i
\(563\) 22.1789 11.3007i 0.934728 0.476267i 0.0808412 0.996727i \(-0.474239\pi\)
0.853886 + 0.520460i \(0.174239\pi\)
\(564\) 13.4669 + 17.4103i 0.567061 + 0.733108i
\(565\) 0 0
\(566\) −9.06857 2.94656i −0.381180 0.123853i
\(567\) −0.707797 0.0261004i −0.0297247 0.00109611i
\(568\) 9.03570 9.03570i 0.379129 0.379129i
\(569\) 25.9540 + 18.8567i 1.08805 + 0.790515i 0.979069 0.203529i \(-0.0652412\pi\)
0.108981 + 0.994044i \(0.465241\pi\)
\(570\) 0 0
\(571\) −34.1170 + 24.7874i −1.42775 + 1.03732i −0.437322 + 0.899305i \(0.644073\pi\)
−0.990430 + 0.138017i \(0.955927\pi\)
\(572\) 0.878080 5.54398i 0.0367144 0.231805i
\(573\) 2.38334 18.6618i 0.0995655 0.779609i
\(574\) 0.293928i 0.0122683i
\(575\) 0 0
\(576\) 2.31674 1.90597i 0.0965306 0.0794156i
\(577\) 10.0150 19.6556i 0.416931 0.818274i −0.583052 0.812435i \(-0.698141\pi\)
0.999983 0.00583873i \(-0.00185853\pi\)
\(578\) −7.04672 1.11609i −0.293105 0.0464233i
\(579\) 27.7782 + 18.9333i 1.15442 + 0.786843i
\(580\) 0 0
\(581\) 0.0408054 0.0561638i 0.00169289 0.00233007i
\(582\) −7.67775 + 16.2586i −0.318253 + 0.673940i
\(583\) −7.38553 + 1.16975i −0.305877 + 0.0484462i
\(584\) 0.410385 1.26303i 0.0169818 0.0522647i
\(585\) 0 0
\(586\) −9.62597 29.6257i −0.397645 1.22383i
\(587\) −5.85750 11.4960i −0.241765 0.474490i 0.737958 0.674846i \(-0.235790\pi\)
−0.979723 + 0.200356i \(0.935790\pi\)
\(588\) 8.81916 + 8.30436i 0.363696 + 0.342466i
\(589\) −12.7423 + 4.14024i −0.525039 + 0.170596i
\(590\) 0 0
\(591\) −21.1735 + 0.636564i −0.870960 + 0.0261848i
\(592\) −1.62063 10.2323i −0.0666075 0.420543i
\(593\) 3.75033 + 3.75033i 0.154007 + 0.154007i 0.779905 0.625898i \(-0.215267\pi\)
−0.625898 + 0.779905i \(0.715267\pi\)
\(594\) 2.25143 + 5.26158i 0.0923774 + 0.215885i
\(595\) 0 0
\(596\) 8.44527 + 11.6239i 0.345932 + 0.476134i
\(597\) 27.1194 5.13507i 1.10992 0.210165i
\(598\) −11.3432 5.77963i −0.463856 0.236347i
\(599\) −29.8620 −1.22013 −0.610065 0.792352i \(-0.708857\pi\)
−0.610065 + 0.792352i \(0.708857\pi\)
\(600\) 0 0
\(601\) 19.0008 0.775058 0.387529 0.921858i \(-0.373329\pi\)
0.387529 + 0.921858i \(0.373329\pi\)
\(602\) −0.0997231 0.0508115i −0.00406441 0.00207092i
\(603\) −10.1222 17.2225i −0.412208 0.701355i
\(604\) −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 −0.971165 0.238406i \(-0.923375\pi\)
−0.238406 0.971165i \(-0.576625\pi\)
\(608\) −0.219361 1.38499i −0.00889625 0.0561687i
\(609\) −0.0286980 0.954554i −0.00116290 0.0386805i
\(610\) 0 0
\(611\) 61.5942 20.0132i 2.49184 0.809646i
\(612\) 8.63759 + 3.76576i 0.349154 + 0.152222i
\(613\) −0.600877 1.17929i −0.0242692 0.0476310i 0.878554 0.477644i \(-0.158509\pi\)
−0.902823 + 0.430013i \(0.858509\pi\)
\(614\) −0.683714 2.10425i −0.0275924 0.0849208i
\(615\) 0 0
\(616\) −0.0267848 + 0.0824351i −0.00107919 + 0.00332141i
\(617\) 41.5066 6.57400i 1.67099 0.264659i 0.752067 0.659087i \(-0.229057\pi\)
0.918927 + 0.394428i \(0.129057\pi\)
\(618\) 20.6804 + 9.76586i 0.831889 + 0.392841i
\(619\) −9.51877 + 13.1015i −0.382592 + 0.526592i −0.956269 0.292489i \(-0.905516\pi\)
0.573677 + 0.819082i \(0.305516\pi\)
\(620\) 0 0
\(621\) 12.9274 1.16877i 0.518758 0.0469013i
\(622\) 13.4638 + 2.13245i 0.539848 + 0.0855036i
\(623\) 0.117151 0.229923i 0.00469357 0.00921165i
\(624\) −2.97877 8.30930i −0.119246 0.332638i
\(625\) 0 0
\(626\) 19.0983i 0.763320i
\(627\) 2.65349 + 0.338883i 0.105970 + 0.0135337i
\(628\) −0.768905 + 4.85468i −0.0306827 + 0.193723i
\(629\) 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
\(633\) 16.7988 9.20545i 0.667691 0.365884i
\(634\) −8.64124 2.80771i −0.343188 0.111508i
\(635\) 0 0
\(636\) −9.30139 + 7.19464i −0.368824 + 0.285286i
\(637\) 31.7579 16.1814i 1.25829 0.641132i
\(638\) −6.87543 + 3.50321i −0.272201 + 0.138693i
\(639\) 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 \(0.704369\pi\)
\(642\) 16.1995 + 29.5620i 0.639344 + 1.16672i
\(643\) 12.8296 12.8296i 0.505952 0.505952i −0.407330 0.913281i \(-0.633540\pi\)
0.913281 + 0.407330i \(0.133540\pi\)
\(644\) 0.159043 + 0.115552i 0.00626719 + 0.00455338i
\(645\) 0 0
\(646\) 3.56321 2.58883i 0.140193 0.101856i
\(647\) −3.97829 + 25.1179i −0.156403 + 0.987488i 0.777220 + 0.629229i \(0.216629\pi\)
−0.933622 + 0.358259i \(0.883371\pi\)
\(648\) 7.08127 + 5.55479i 0.278178 + 0.218213i
\(649\) 7.25839i 0.284917i
\(650\) 0 0
\(651\) 1.22599 0.439499i 0.0480502 0.0172253i
\(652\) −0.695961 + 1.36590i −0.0272559 + 0.0534928i
\(653\) 30.0615 + 4.76127i 1.17640 + 0.186323i 0.713867 0.700281i \(-0.246942\pi\)
0.462529 + 0.886604i \(0.346942\pi\)
\(654\) −12.0053 + 17.6136i −0.469443 + 0.688747i
\(655\) 0 0
\(656\) −2.19532 + 3.02160i −0.0857129 + 0.117974i
\(657\) 3.96538 + 0.385730i 0.154704 + 0.0150488i
\(658\) −0.987775 + 0.156448i −0.0385075 + 0.00609899i
\(659\) 3.19473 9.83236i 0.124449 0.383014i −0.869351 0.494195i \(-0.835463\pi\)
0.993800 + 0.111180i \(0.0354631\pi\)
\(660\) 0 0
\(661\) 3.97825 + 12.2438i 0.154736 + 0.476229i 0.998134 0.0610606i \(-0.0194483\pi\)
−0.843398 + 0.537289i \(0.819448\pi\)
\(662\) 5.01952 + 9.85137i 0.195089 + 0.382884i
\(663\) 19.0067 20.1850i 0.738161 0.783921i
\(664\) −0.838964 + 0.272596i −0.0325581 + 0.0105788i
\(665\) 0 0
\(666\) 28.9279 11.3624i 1.12093 0.440284i
\(667\) 2.73781 + 17.2859i 0.106008 + 0.669311i
\(668\) −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
\(672\) 0.0253594 + 0.133928i 0.000978260 + 0.00516640i
\(673\) −30.0291 15.3006i −1.15754 0.589794i −0.233596 0.972334i \(-0.575049\pi\)
−0.923939 + 0.382540i \(0.875049\pi\)
\(674\) −17.3028 −0.666479
\(675\) 0 0
\(676\) −12.9725 −0.498943
\(677\) −13.8891 7.07682i −0.533800 0.271984i 0.166244 0.986085i \(-0.446836\pi\)
−0.700044 + 0.714100i \(0.746836\pi\)
\(678\) −2.46001 12.9918i −0.0944759 0.498948i
\(679\) −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
\(683\) 4.20549 + 26.5524i 0.160919 + 1.01600i 0.927492 + 0.373844i \(0.121960\pi\)
−0.766573 + 0.642157i \(0.778040\pi\)
\(684\) 3.91554 1.53796i 0.149715 0.0588054i
\(685\) 0 0
\(686\) −1.04738 + 0.340314i −0.0399891 + 0.0129932i
\(687\) 3.60640 3.82996i 0.137593 0.146122i
\(688\) 0.645655 + 1.26717i 0.0246154 + 0.0483104i
\(689\) 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 \(-0.0418212\pi\)
\(692\) 13.9996 2.21732i 0.532185 0.0842898i
\(693\) −0.258811 0.0251756i −0.00983141 0.000956343i
\(694\) 8.78938 12.0975i 0.333640 0.459217i
\(695\) 0 0
\(696\) −6.83446 + 10.0272i −0.259060 + 0.380081i
\(697\) −11.5866 1.83514i −0.438875 0.0695110i
\(698\) 0.156673 0.307489i 0.00593018 0.0116386i
\(699\) −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 \(-0.253161\pi\)
\(702\) 22.4166 14.0980i 0.846061 0.532094i
\(703\) 2.27253 14.3482i 0.0857102 0.541153i
\(704\) 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
\(708\) 5.48536 + 10.0101i 0.206152 + 0.376201i
\(709\) 37.7779 + 12.2748i 1.41878 + 0.460989i 0.915214 0.402968i \(-0.132022\pi\)
0.503565 + 0.863958i \(0.332022\pi\)
\(710\) 0 0
\(711\) −25.1814 16.0769i −0.944377 0.602931i
\(712\) −2.92160 + 1.48863i −0.109491 + 0.0557887i
\(713\) −21.2664 + 10.8358i −0.796433 + 0.405803i
\(714\) −0.338649 + 0.261946i −0.0126736 + 0.00980309i
\(715\) 0 0
\(716\) −14.4473 4.69420i −0.539919 0.175430i
\(717\) 17.2716 9.46453i 0.645018 0.353459i
\(718\) −12.9715 + 12.9715i −0.484093 + 0.484093i
\(719\) −25.6075 18.6049i −0.954998 0.693847i −0.00301445 0.999995i \(-0.500960\pi\)
−0.951984 + 0.306149i \(0.900960\pi\)
\(720\) 0 0
\(721\) −0.840680 + 0.610790i −0.0313086 + 0.0227470i
\(722\) −2.66466 + 16.8240i −0.0991682 + 0.626124i
\(723\) −15.1596 1.93606i −0.563791 0.0720029i
\(724\) 10.2709i 0.381715i
\(725\) 0 0
\(726\) −5.72039 15.9571i −0.212304 0.592223i
\(727\) 23.4214 45.9671i 0.868652 1.70483i 0.174934 0.984580i \(-0.444029\pi\)
0.693719 0.720246i \(-0.255971\pi\)
\(728\) 0.396131 + 0.0627409i 0.0146816 + 0.00232533i
\(729\) −11.6951 + 24.3357i −0.433152 + 0.901321i
\(730\) 0 0
\(731\) −2.62561 + 3.61384i −0.0971117 + 0.133663i
\(732\) −6.25049 2.95165i −0.231025 0.109096i
\(733\) 20.9008 3.31036i 0.771988 0.122271i 0.242000 0.970276i \(-0.422197\pi\)
0.529988 + 0.848005i \(0.322197\pi\)
\(734\) 0.00602247 0.0185352i 0.000222293 0.000684148i
\(735\) 0 0
\(736\) −0.771931 2.37576i −0.0284538 0.0875717i
\(737\) −3.32964 6.53478i −0.122649 0.240712i
\(738\) −10.2710 4.47789i −0.378082 0.164834i
\(739\) 11.8537 3.85150i 0.436046 0.141680i −0.0827648 0.996569i \(-0.526375\pi\)
0.518811 + 0.854889i \(0.326375\pi\)
\(740\) 0 0
\(741\) −0.371961 12.3722i −0.0136643 0.454505i
\(742\) −0.0835816 0.527714i −0.00306838 0.0193730i
\(743\) 2.30237 + 2.30237i 0.0844658 + 0.0844658i 0.748077 0.663612i \(-0.230977\pi\)
−0.663612 + 0.748077i \(0.730977\pi\)
\(744\) −15.8858 4.63870i −0.582402 0.170063i
\(745\) 0 0
\(746\) 4.11202 + 5.65971i 0.150552 + 0.207217i
\(747\) −1.34093 2.28154i −0.0490621 0.0834772i
\(748\) 3.08236 + 1.57054i 0.112702 + 0.0574247i
\(749\) −1.53163 −0.0559646
\(750\) 0 0
\(751\) 18.7652 0.684751 0.342375 0.939563i \(-0.388769\pi\)
0.342375 + 0.939563i \(0.388769\pi\)
\(752\) 11.3229 + 5.76930i 0.412904 + 0.210385i
\(753\) −24.8641 + 4.70802i −0.906097 + 0.171570i
\(754\) 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 \(-0.192200\pi\)
−0.567787 + 0.823176i \(0.692200\pi\)
\(758\) −1.90370 12.0195i −0.0691453 0.436567i
\(759\) 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 \(0.0301584\pi\)
\(762\) 4.06305 + 3.82587i 0.147189 + 0.138597i
\(763\) −0.439694 0.862948i −0.0159180 0.0312408i
\(764\) −3.35652 10.3303i −0.121435 0.373737i
\(765\) 0 0
\(766\) −0.292865 + 0.901344i −0.0105816 + 0.0325669i
\(767\) 33.1721 5.25394i 1.19777 0.189709i
\(768\) 0.739603 1.56620i 0.0266881 0.0565154i
\(769\) 21.2813 29.2912i 0.767422 1.05627i −0.229138 0.973394i \(-0.573591\pi\)
0.996560 0.0828721i \(-0.0264093\pi\)
\(770\) 0 0
\(771\) 3.18239 + 2.16909i 0.114611 + 0.0781178i
\(772\) 19.1698 + 3.03620i 0.689936 + 0.109275i
\(773\) 10.6768 20.9544i 0.384019 0.753679i −0.615384 0.788227i \(-0.710999\pi\)
0.999403 + 0.0345481i \(0.0109992\pi\)
\(774\) −3.29481 + 2.71063i −0.118429 + 0.0974317i
\(775\) 0 0
\(776\) 10.3809i 0.372653i
\(777\) −0.178893 + 1.40075i −0.00641774 + 0.0502516i
\(778\) 3.10878 19.6281i 0.111455 0.703701i
\(779\) −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 0.198397