Properties

Label 750.2.l.b.107.1
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 107.1
Character \(\chi\) \(=\) 750.107
Dual form 750.2.l.b.743.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.891007 - 0.453990i) q^{2} +(-1.73204 - 0.00452789i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.54121 + 0.790366i) q^{6} +(0.152718 + 0.152718i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(2.99996 + 0.0156850i) q^{9} +O(q^{10})\) \(q+(-0.891007 - 0.453990i) q^{2} +(-1.73204 - 0.00452789i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.54121 + 0.790366i) q^{6} +(0.152718 + 0.152718i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(2.99996 + 0.0156850i) q^{9} +(-4.88609 + 1.58759i) q^{11} +(-1.01441 - 1.40392i) q^{12} +(-0.674795 - 1.32436i) q^{13} +(-0.0667401 - 0.205405i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(4.81543 - 0.762690i) q^{17} +(-2.66586 - 1.37593i) q^{18} +(0.283032 - 0.389560i) q^{19} +(-0.263823 - 0.265206i) q^{21} +(5.07429 + 0.803689i) q^{22} +(-1.21389 + 2.38239i) q^{23} +(0.266479 + 1.71143i) q^{24} +1.48636i q^{26} +(-5.19599 - 0.0407506i) q^{27} +(-0.0337860 + 0.213317i) q^{28} +(7.59423 - 5.51753i) q^{29} +(-1.84019 - 1.33698i) q^{31} +(0.707107 - 0.707107i) q^{32} +(8.47012 - 2.72765i) q^{33} +(-4.63684 - 1.50660i) q^{34} +(1.75064 + 2.43624i) q^{36} +(-3.83574 + 1.95441i) q^{37} +(-0.429039 + 0.218606i) q^{38} +(1.16278 + 2.29691i) q^{39} +(-5.95547 - 1.93505i) q^{41} +(0.114667 + 0.356073i) q^{42} +(2.72225 - 2.72225i) q^{43} +(-4.15636 - 3.01977i) q^{44} +(2.16317 - 1.57163i) q^{46} +(1.58814 - 10.0271i) q^{47} +(0.539538 - 1.64587i) q^{48} -6.95335i q^{49} +(-8.34400 + 1.29921i) q^{51} +(0.674795 - 1.32436i) q^{52} +(-7.59700 - 1.20325i) q^{53} +(4.61116 + 2.39524i) q^{54} +(0.126947 - 0.174728i) q^{56} +(-0.491987 + 0.673453i) q^{57} +(-9.27141 + 1.46845i) q^{58} +(1.54130 - 4.74363i) q^{59} +(-4.21680 - 12.9780i) q^{61} +(1.03265 + 2.02668i) q^{62} +(0.455752 + 0.460543i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-8.78526 - 1.41500i) q^{66} +(-2.35050 - 14.8405i) q^{67} +(3.44747 + 3.44747i) q^{68} +(2.11330 - 4.12092i) q^{69} +(7.13100 + 9.81498i) q^{71} +(-0.453805 - 2.96548i) q^{72} +(-8.36209 - 4.26070i) q^{73} +4.30495 q^{74} +0.481522 q^{76} +(-0.988647 - 0.503741i) q^{77} +(0.00673009 - 2.57445i) q^{78} +(-1.28502 - 1.76867i) q^{79} +(8.99951 + 0.0941087i) q^{81} +(4.42787 + 4.42787i) q^{82} +(-0.782253 - 4.93895i) q^{83} +(0.0594848 - 0.369321i) q^{84} +(-3.66142 + 1.18967i) q^{86} +(-13.1785 + 9.52222i) q^{87} +(2.33240 + 4.57759i) q^{88} +(3.38311 + 10.4121i) q^{89} +(0.0992002 - 0.305307i) q^{91} +(-2.64090 + 0.418278i) q^{92} +(3.18124 + 2.32404i) q^{93} +(-5.96725 + 8.21321i) q^{94} +(-1.22794 + 1.22154i) q^{96} +(9.96799 + 1.57877i) q^{97} +(-3.15676 + 6.19548i) q^{98} +(-14.6830 + 4.68606i) 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
\(3\) −1.73204 0.00452789i −0.999997 0.00261418i
\(4\) 0.587785 + 0.809017i 0.293893 + 0.404508i
\(5\) 0 0
\(6\) 1.54121 + 0.790366i 0.629195 + 0.322666i
\(7\) 0.152718 + 0.152718i 0.0577219 + 0.0577219i 0.735379 0.677657i \(-0.237004\pi\)
−0.677657 + 0.735379i \(0.737004\pi\)
\(8\) −0.156434 0.987688i −0.0553079 0.349201i
\(9\) 2.99996 + 0.0156850i 0.999986 + 0.00522833i
\(10\) 0 0
\(11\) −4.88609 + 1.58759i −1.47321 + 0.478676i −0.932077 0.362259i \(-0.882005\pi\)
−0.541136 + 0.840935i \(0.682005\pi\)
\(12\) −1.01441 1.40392i −0.292834 0.405275i
\(13\) −0.674795 1.32436i −0.187155 0.367312i 0.778296 0.627897i \(-0.216084\pi\)
−0.965451 + 0.260586i \(0.916084\pi\)
\(14\) −0.0667401 0.205405i −0.0178371 0.0548968i
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) 4.81543 0.762690i 1.16791 0.184979i 0.457793 0.889059i \(-0.348640\pi\)
0.710121 + 0.704080i \(0.248640\pi\)
\(18\) −2.66586 1.37593i −0.628350 0.324309i
\(19\) 0.283032 0.389560i 0.0649319 0.0893711i −0.775316 0.631574i \(-0.782409\pi\)
0.840248 + 0.542202i \(0.182409\pi\)
\(20\) 0 0
\(21\) −0.263823 0.265206i −0.0575708 0.0578726i
\(22\) 5.07429 + 0.803689i 1.08184 + 0.171347i
\(23\) −1.21389 + 2.38239i −0.253114 + 0.496763i −0.982243 0.187612i \(-0.939925\pi\)
0.729130 + 0.684376i \(0.239925\pi\)
\(24\) 0.266479 + 1.71143i 0.0543949 + 0.349344i
\(25\) 0 0
\(26\) 1.48636i 0.291500i
\(27\) −5.19599 0.0407506i −0.999969 0.00784246i
\(28\) −0.0337860 + 0.213317i −0.00638496 + 0.0403130i
\(29\) 7.59423 5.51753i 1.41021 1.02458i 0.416921 0.908943i \(-0.363109\pi\)
0.993292 0.115637i \(-0.0368909\pi\)
\(30\) 0 0
\(31\) −1.84019 1.33698i −0.330508 0.240128i 0.410138 0.912023i \(-0.365480\pi\)
−0.740646 + 0.671895i \(0.765480\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 8.47012 2.72765i 1.47446 0.474823i
\(34\) −4.63684 1.50660i −0.795211 0.258380i
\(35\) 0 0
\(36\) 1.75064 + 2.43624i 0.291774 + 0.406040i
\(37\) −3.83574 + 1.95441i −0.630592 + 0.321303i −0.739912 0.672704i \(-0.765133\pi\)
0.109320 + 0.994007i \(0.465133\pi\)
\(38\) −0.429039 + 0.218606i −0.0695994 + 0.0354627i
\(39\) 1.16278 + 2.29691i 0.186194 + 0.367800i
\(40\) 0 0
\(41\) −5.95547 1.93505i −0.930087 0.302204i −0.195489 0.980706i \(-0.562629\pi\)
−0.734598 + 0.678502i \(0.762629\pi\)
\(42\) 0.114667 + 0.356073i 0.0176935 + 0.0549432i
\(43\) 2.72225 2.72225i 0.415139 0.415139i −0.468385 0.883524i \(-0.655164\pi\)
0.883524 + 0.468385i \(0.155164\pi\)
\(44\) −4.15636 3.01977i −0.626595 0.455248i
\(45\) 0 0
\(46\) 2.16317 1.57163i 0.318942 0.231725i
\(47\) 1.58814 10.0271i 0.231654 1.46260i −0.548046 0.836448i \(-0.684628\pi\)
0.779699 0.626154i \(-0.215372\pi\)
\(48\) 0.539538 1.64587i 0.0778755 0.237561i
\(49\) 6.95335i 0.993336i
\(50\) 0 0
\(51\) −8.34400 + 1.29921i −1.16839 + 0.181926i
\(52\) 0.674795 1.32436i 0.0935773 0.183656i
\(53\) −7.59700 1.20325i −1.04353 0.165279i −0.388939 0.921264i \(-0.627158\pi\)
−0.654589 + 0.755985i \(0.727158\pi\)
\(54\) 4.61116 + 2.39524i 0.627500 + 0.325951i
\(55\) 0 0
\(56\) 0.126947 0.174728i 0.0169640 0.0233490i
\(57\) −0.491987 + 0.673453i −0.0651653 + 0.0892011i
\(58\) −9.27141 + 1.46845i −1.21740 + 0.192817i
\(59\) 1.54130 4.74363i 0.200660 0.617569i −0.799204 0.601061i \(-0.794745\pi\)
0.999864 0.0165081i \(-0.00525494\pi\)
\(60\) 0 0
\(61\) −4.21680 12.9780i −0.539906 1.66166i −0.732803 0.680440i \(-0.761789\pi\)
0.192898 0.981219i \(-0.438211\pi\)
\(62\) 1.03265 + 2.02668i 0.131146 + 0.257389i
\(63\) 0.455752 + 0.460543i 0.0574193 + 0.0580229i
\(64\) −0.951057 + 0.309017i −0.118882 + 0.0386271i
\(65\) 0 0
\(66\) −8.78526 1.41500i −1.08139 0.174175i
\(67\) −2.35050 14.8405i −0.287159 1.81305i −0.535673 0.844425i \(-0.679942\pi\)
0.248514 0.968628i \(-0.420058\pi\)
\(68\) 3.44747 + 3.44747i 0.418067 + 0.418067i
\(69\) 2.11330 4.12092i 0.254411 0.496100i
\(70\) 0 0
\(71\) 7.13100 + 9.81498i 0.846294 + 1.16482i 0.984667 + 0.174444i \(0.0558128\pi\)
−0.138373 + 0.990380i \(0.544187\pi\)
\(72\) −0.453805 2.96548i −0.0534814 0.349485i
\(73\) −8.36209 4.26070i −0.978708 0.498677i −0.109963 0.993936i \(-0.535073\pi\)
−0.868745 + 0.495259i \(0.835073\pi\)
\(74\) 4.30495 0.500441
\(75\) 0 0
\(76\) 0.481522 0.0552344
\(77\) −0.988647 0.503741i −0.112667 0.0574066i
\(78\) 0.00673009 2.57445i 0.000762033 0.291499i
\(79\) −1.28502 1.76867i −0.144576 0.198991i 0.730588 0.682819i \(-0.239246\pi\)
−0.875163 + 0.483828i \(0.839246\pi\)
\(80\) 0 0
\(81\) 8.99951 + 0.0941087i 0.999945 + 0.0104565i
\(82\) 4.42787 + 4.42787i 0.488976 + 0.488976i
\(83\) −0.782253 4.93895i −0.0858634 0.542120i −0.992697 0.120632i \(-0.961508\pi\)
0.906834 0.421488i \(-0.138492\pi\)
\(84\) 0.0594848 0.369321i 0.00649032 0.0402962i
\(85\) 0 0
\(86\) −3.66142 + 1.18967i −0.394821 + 0.128285i
\(87\) −13.1785 + 9.52222i −1.41289 + 1.02089i
\(88\) 2.33240 + 4.57759i 0.248634 + 0.487972i
\(89\) 3.38311 + 10.4121i 0.358609 + 1.10368i 0.953887 + 0.300165i \(0.0970417\pi\)
−0.595279 + 0.803519i \(0.702958\pi\)
\(90\) 0 0
\(91\) 0.0992002 0.305307i 0.0103990 0.0320048i
\(92\) −2.64090 + 0.418278i −0.275333 + 0.0436085i
\(93\) 3.18124 + 2.32404i 0.329879 + 0.240991i
\(94\) −5.96725 + 8.21321i −0.615475 + 0.847128i
\(95\) 0 0
\(96\) −1.22794 + 1.22154i −0.125326 + 0.124673i
\(97\) 9.96799 + 1.57877i 1.01210 + 0.160300i 0.640390 0.768050i \(-0.278773\pi\)
0.371706 + 0.928350i \(0.378773\pi\)
\(98\) −3.15676 + 6.19548i −0.318881 + 0.625838i
\(99\) −14.6830 + 4.68606i −1.47570 + 0.470967i
\(100\) 0 0
\(101\) 9.53700i 0.948967i −0.880264 0.474483i \(-0.842635\pi\)
0.880264 0.474483i \(-0.157365\pi\)
\(102\) 8.02438 + 2.63049i 0.794533 + 0.260458i
\(103\) −1.58215 + 9.98929i −0.155894 + 0.984274i 0.778400 + 0.627769i \(0.216032\pi\)
−0.934293 + 0.356505i \(0.883968\pi\)
\(104\) −1.20249 + 0.873663i −0.117914 + 0.0856697i
\(105\) 0 0
\(106\) 6.22271 + 4.52106i 0.604403 + 0.439125i
\(107\) −7.80873 + 7.80873i −0.754898 + 0.754898i −0.975389 0.220491i \(-0.929234\pi\)
0.220491 + 0.975389i \(0.429234\pi\)
\(108\) −3.02116 4.22760i −0.290711 0.406801i
\(109\) −5.83194 1.89491i −0.558598 0.181500i 0.0160921 0.999871i \(-0.494877\pi\)
−0.574690 + 0.818371i \(0.694877\pi\)
\(110\) 0 0
\(111\) 6.65253 3.36776i 0.631430 0.319653i
\(112\) −0.192436 + 0.0980509i −0.0181835 + 0.00926494i
\(113\) 9.78864 4.98756i 0.920838 0.469190i 0.0717385 0.997423i \(-0.477145\pi\)
0.849099 + 0.528233i \(0.177145\pi\)
\(114\) 0.744105 0.376694i 0.0696918 0.0352806i
\(115\) 0 0
\(116\) 8.92755 + 2.90074i 0.828902 + 0.269327i
\(117\) −2.00359 3.98361i −0.185232 0.368285i
\(118\) −3.52687 + 3.52687i −0.324675 + 0.324675i
\(119\) 0.851879 + 0.618926i 0.0780916 + 0.0567369i
\(120\) 0 0
\(121\) 12.4543 9.04858i 1.13221 0.822598i
\(122\) −2.13468 + 13.4778i −0.193265 + 1.22023i
\(123\) 10.3064 + 3.37856i 0.929294 + 0.304634i
\(124\) 2.27460i 0.204265i
\(125\) 0 0
\(126\) −0.196996 0.617253i −0.0175498 0.0549893i
\(127\) 6.82658 13.3979i 0.605761 1.18887i −0.360850 0.932624i \(-0.617513\pi\)
0.966611 0.256249i \(-0.0824868\pi\)
\(128\) 0.987688 + 0.156434i 0.0873001 + 0.0138270i
\(129\) −4.72738 + 4.70273i −0.416223 + 0.414052i
\(130\) 0 0
\(131\) 5.12870 7.05905i 0.448097 0.616752i −0.523891 0.851785i \(-0.675520\pi\)
0.971987 + 0.235034i \(0.0755200\pi\)
\(132\) 7.18533 + 5.24920i 0.625403 + 0.456884i
\(133\) 0.102717 0.0162687i 0.00890667 0.00141068i
\(134\) −4.64313 + 14.2901i −0.401105 + 1.23447i
\(135\) 0 0
\(136\) −1.50660 4.63684i −0.129190 0.397605i
\(137\) 1.28180 + 2.51567i 0.109511 + 0.214928i 0.939258 0.343212i \(-0.111515\pi\)
−0.829747 + 0.558140i \(0.811515\pi\)
\(138\) −3.75382 + 2.71235i −0.319546 + 0.230890i
\(139\) −6.62014 + 2.15102i −0.561513 + 0.182447i −0.576002 0.817448i \(-0.695388\pi\)
0.0144887 + 0.999895i \(0.495388\pi\)
\(140\) 0 0
\(141\) −2.79613 + 17.3602i −0.235476 + 1.46199i
\(142\) −1.89786 11.9826i −0.159265 1.00556i
\(143\) 5.39965 + 5.39965i 0.451542 + 0.451542i
\(144\) −0.941956 + 2.84828i −0.0784963 + 0.237357i
\(145\) 0 0
\(146\) 5.51636 + 7.59261i 0.456537 + 0.628369i
\(147\) −0.0314840 + 12.0435i −0.00259676 + 0.993333i
\(148\) −3.83574 1.95441i −0.315296 0.160651i
\(149\) −7.72360 −0.632742 −0.316371 0.948635i \(-0.602465\pi\)
−0.316371 + 0.948635i \(0.602465\pi\)
\(150\) 0 0
\(151\) −14.7868 −1.20333 −0.601667 0.798747i \(-0.705497\pi\)
−0.601667 + 0.798747i \(0.705497\pi\)
\(152\) −0.429039 0.218606i −0.0347997 0.0177313i
\(153\) 14.4581 2.21251i 1.16887 0.178871i
\(154\) 0.652197 + 0.897673i 0.0525556 + 0.0723365i
\(155\) 0 0
\(156\) −1.17477 + 2.29080i −0.0940571 + 0.183411i
\(157\) 11.5941 + 11.5941i 0.925312 + 0.925312i 0.997398 0.0720863i \(-0.0229657\pi\)
−0.0720863 + 0.997398i \(0.522966\pi\)
\(158\) 0.341997 + 2.15928i 0.0272078 + 0.171783i
\(159\) 13.1529 + 2.11847i 1.04309 + 0.168006i
\(160\) 0 0
\(161\) −0.549217 + 0.178451i −0.0432843 + 0.0140639i
\(162\) −7.97590 4.16954i −0.626646 0.327590i
\(163\) 1.84215 + 3.61543i 0.144289 + 0.283182i 0.951829 0.306630i \(-0.0992016\pi\)
−0.807540 + 0.589813i \(0.799202\pi\)
\(164\) −1.93505 5.95547i −0.151102 0.465044i
\(165\) 0 0
\(166\) −1.54524 + 4.75577i −0.119934 + 0.369119i
\(167\) 13.6706 2.16520i 1.05786 0.167549i 0.396818 0.917897i \(-0.370114\pi\)
0.661042 + 0.750349i \(0.270114\pi\)
\(168\) −0.220670 + 0.302062i −0.0170250 + 0.0233046i
\(169\) 6.34263 8.72988i 0.487894 0.671529i
\(170\) 0 0
\(171\) 0.855194 1.16422i 0.0653983 0.0890304i
\(172\) 3.80244 + 0.602248i 0.289934 + 0.0459210i
\(173\) −0.412278 + 0.809140i −0.0313449 + 0.0615178i −0.906148 0.422961i \(-0.860991\pi\)
0.874803 + 0.484479i \(0.160991\pi\)
\(174\) 16.0652 2.50144i 1.21790 0.189633i
\(175\) 0 0
\(176\) 5.13754i 0.387257i
\(177\) −2.69108 + 8.20921i −0.202274 + 0.617042i
\(178\) 1.71264 10.8132i 0.128368 0.810482i
\(179\) −9.58645 + 6.96496i −0.716525 + 0.520586i −0.885272 0.465074i \(-0.846028\pi\)
0.168747 + 0.985659i \(0.446028\pi\)
\(180\) 0 0
\(181\) 13.9076 + 10.1044i 1.03374 + 0.751057i 0.969054 0.246848i \(-0.0793949\pi\)
0.0646876 + 0.997906i \(0.479395\pi\)
\(182\) −0.226994 + 0.226994i −0.0168259 + 0.0168259i
\(183\) 7.24492 + 22.4975i 0.535560 + 1.66306i
\(184\) 2.54296 + 0.826257i 0.187469 + 0.0609125i
\(185\) 0 0
\(186\) −1.77942 3.51498i −0.130473 0.257731i
\(187\) −22.3178 + 11.3715i −1.63204 + 0.831566i
\(188\) 9.04558 4.60895i 0.659716 0.336142i
\(189\) −0.787297 0.799744i −0.0572675 0.0581728i
\(190\) 0 0
\(191\) 4.70151 + 1.52761i 0.340189 + 0.110534i 0.474129 0.880455i \(-0.342763\pi\)
−0.133940 + 0.990989i \(0.542763\pi\)
\(192\) 1.64867 0.530925i 0.118983 0.0383162i
\(193\) −2.38356 + 2.38356i −0.171572 + 0.171572i −0.787670 0.616098i \(-0.788713\pi\)
0.616098 + 0.787670i \(0.288713\pi\)
\(194\) −8.16479 5.93207i −0.586198 0.425898i
\(195\) 0 0
\(196\) 5.62538 4.08708i 0.401813 0.291934i
\(197\) −1.14693 + 7.24145i −0.0817156 + 0.515932i 0.912548 + 0.408970i \(0.134112\pi\)
−0.994263 + 0.106961i \(0.965888\pi\)
\(198\) 15.2101 + 2.49062i 1.08093 + 0.177001i
\(199\) 8.34182i 0.591336i 0.955291 + 0.295668i \(0.0955422\pi\)
−0.955291 + 0.295668i \(0.904458\pi\)
\(200\) 0 0
\(201\) 4.00398 + 25.7150i 0.282419 + 1.81380i
\(202\) −4.32971 + 8.49753i −0.304637 + 0.597884i
\(203\) 2.00240 + 0.317149i 0.140541 + 0.0222595i
\(204\) −5.95556 5.98678i −0.416973 0.419158i
\(205\) 0 0
\(206\) 5.94475 8.18224i 0.414190 0.570084i
\(207\) −3.67899 + 7.12804i −0.255707 + 0.495433i
\(208\) 1.46807 0.232519i 0.101792 0.0161223i
\(209\) −0.764459 + 2.35276i −0.0528787 + 0.162744i
\(210\) 0 0
\(211\) 1.32487 + 4.07753i 0.0912078 + 0.280709i 0.986247 0.165279i \(-0.0528525\pi\)
−0.895039 + 0.445988i \(0.852852\pi\)
\(212\) −3.49196 6.85335i −0.239828 0.470690i
\(213\) −12.3068 17.0323i −0.843246 1.16703i
\(214\) 10.5027 3.41254i 0.717951 0.233276i
\(215\) 0 0
\(216\) 0.772583 + 5.13840i 0.0525676 + 0.349624i
\(217\) −0.0768498 0.485210i −0.00521690 0.0329382i
\(218\) 4.33602 + 4.33602i 0.293672 + 0.293672i
\(219\) 14.4642 + 7.41758i 0.977401 + 0.501233i
\(220\) 0 0
\(221\) −4.25951 5.86271i −0.286525 0.394369i
\(222\) −7.45637 0.0194923i −0.500439 0.00130824i
\(223\) −0.651256 0.331831i −0.0436113 0.0222211i 0.432049 0.901850i \(-0.357791\pi\)
−0.475660 + 0.879629i \(0.657791\pi\)
\(224\) 0.215976 0.0144305
\(225\) 0 0
\(226\) −10.9860 −0.730781
\(227\) −2.94981 1.50300i −0.195786 0.0997579i 0.353349 0.935492i \(-0.385043\pi\)
−0.549135 + 0.835734i \(0.685043\pi\)
\(228\) −0.834018 0.00218028i −0.0552342 0.000144392i
\(229\) −6.20224 8.53665i −0.409855 0.564117i 0.553328 0.832964i \(-0.313358\pi\)
−0.963183 + 0.268846i \(0.913358\pi\)
\(230\) 0 0
\(231\) 1.71010 + 0.876978i 0.112516 + 0.0577009i
\(232\) −6.63760 6.63760i −0.435780 0.435780i
\(233\) −1.96935 12.4340i −0.129016 0.814577i −0.964311 0.264774i \(-0.914703\pi\)
0.835294 0.549803i \(-0.185297\pi\)
\(234\) −0.0233136 + 4.45903i −0.00152406 + 0.291496i
\(235\) 0 0
\(236\) 4.74363 1.54130i 0.308784 0.100330i
\(237\) 2.21770 + 3.06924i 0.144055 + 0.199369i
\(238\) −0.478043 0.938212i −0.0309869 0.0608152i
\(239\) −3.62951 11.1705i −0.234773 0.722558i −0.997151 0.0754263i \(-0.975968\pi\)
0.762378 0.647132i \(-0.224032\pi\)
\(240\) 0 0
\(241\) 0.375849 1.15675i 0.0242106 0.0745125i −0.938221 0.346036i \(-0.887527\pi\)
0.962432 + 0.271524i \(0.0875275\pi\)
\(242\) −15.2048 + 2.40821i −0.977403 + 0.154805i
\(243\) −15.5871 0.203749i −0.999915 0.0130705i
\(244\) 8.02083 11.0397i 0.513481 0.706746i
\(245\) 0 0
\(246\) −7.64921 7.68931i −0.487696 0.490253i
\(247\) −0.706906 0.111963i −0.0449793 0.00712403i
\(248\) −1.03265 + 2.02668i −0.0655732 + 0.128695i
\(249\) 1.33253 + 8.55802i 0.0844459 + 0.542343i
\(250\) 0 0
\(251\) 22.6123i 1.42728i −0.700515 0.713638i \(-0.747046\pi\)
0.700515 0.713638i \(-0.252954\pi\)
\(252\) −0.104703 + 0.639411i −0.00659564 + 0.0402791i
\(253\) 2.14892 13.5678i 0.135102 0.852998i
\(254\) −12.1651 + 8.83843i −0.763304 + 0.554573i
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) 2.98436 2.98436i 0.186159 0.186159i −0.607874 0.794033i \(-0.707978\pi\)
0.794033 + 0.607874i \(0.207978\pi\)
\(258\) 6.34713 2.04398i 0.395155 0.127252i
\(259\) −0.884259 0.287313i −0.0549452 0.0178528i
\(260\) 0 0
\(261\) 22.8689 16.4332i 1.41555 1.01719i
\(262\) −7.77445 + 3.96128i −0.480307 + 0.244729i
\(263\) −2.29146 + 1.16756i −0.141298 + 0.0719947i −0.523210 0.852204i \(-0.675266\pi\)
0.381912 + 0.924199i \(0.375266\pi\)
\(264\) −4.01909 7.93914i −0.247358 0.488621i
\(265\) 0 0
\(266\) −0.0989071 0.0321369i −0.00606438 0.00197044i
\(267\) −5.81255 18.0496i −0.355722 1.10462i
\(268\) 10.6246 10.6246i 0.649002 0.649002i
\(269\) 19.5493 + 14.2034i 1.19194 + 0.865996i 0.993468 0.114110i \(-0.0364018\pi\)
0.198473 + 0.980106i \(0.436402\pi\)
\(270\) 0 0
\(271\) −9.36464 + 6.80381i −0.568861 + 0.413302i −0.834691 0.550718i \(-0.814354\pi\)
0.265830 + 0.964020i \(0.414354\pi\)
\(272\) −0.762690 + 4.81543i −0.0462448 + 0.291978i
\(273\) −0.173202 + 0.528356i −0.0104826 + 0.0319776i
\(274\) 2.82340i 0.170568i
\(275\) 0 0
\(276\) 4.57606 0.712519i 0.275446 0.0428886i
\(277\) −3.42126 + 6.71461i −0.205564 + 0.403442i −0.970654 0.240482i \(-0.922695\pi\)
0.765090 + 0.643924i \(0.222695\pi\)
\(278\) 6.87513 + 1.08891i 0.412343 + 0.0653087i
\(279\) −5.49953 4.03974i −0.329248 0.241853i
\(280\) 0 0
\(281\) −13.8790 + 19.1028i −0.827952 + 1.13958i 0.160349 + 0.987060i \(0.448738\pi\)
−0.988301 + 0.152517i \(0.951262\pi\)
\(282\) 10.3727 14.1986i 0.617687 0.845516i
\(283\) −9.72347 + 1.54005i −0.578000 + 0.0915463i −0.438588 0.898688i \(-0.644521\pi\)
−0.139412 + 0.990234i \(0.544521\pi\)
\(284\) −3.74899 + 11.5382i −0.222462 + 0.684667i
\(285\) 0 0
\(286\) −2.35974 7.26252i −0.139534 0.429442i
\(287\) −0.613989 1.20502i −0.0362426 0.0711302i
\(288\) 2.13238 2.11020i 0.125652 0.124345i
\(289\) 6.43873 2.09207i 0.378749 0.123063i
\(290\) 0 0
\(291\) −17.2579 2.77964i −1.01167 0.162945i
\(292\) −1.46814 9.26944i −0.0859161 0.542453i
\(293\) −3.33944 3.33944i −0.195092 0.195092i 0.602800 0.797892i \(-0.294052\pi\)
−0.797892 + 0.602800i \(0.794052\pi\)
\(294\) 5.49570 10.7166i 0.320516 0.625003i
\(295\) 0 0
\(296\) 2.53039 + 3.48278i 0.147076 + 0.202433i
\(297\) 25.4528 8.04999i 1.47692 0.467108i
\(298\) 6.88178 + 3.50644i 0.398651 + 0.203123i
\(299\) 3.97428 0.229838
\(300\) 0 0
\(301\) 0.831472 0.0479252
\(302\) 13.1751 + 6.71307i 0.758145 + 0.386294i
\(303\) −0.0431824 + 16.5185i −0.00248077 + 0.948964i
\(304\) 0.283032 + 0.389560i 0.0162330 + 0.0223428i
\(305\) 0 0
\(306\) −13.8867 4.59246i −0.793849 0.262534i
\(307\) 11.8133 + 11.8133i 0.674221 + 0.674221i 0.958686 0.284465i \(-0.0918160\pi\)
−0.284465 + 0.958686i \(0.591816\pi\)
\(308\) −0.173577 1.09592i −0.00989048 0.0624460i
\(309\) 2.78558 17.2947i 0.158466 0.983863i
\(310\) 0 0
\(311\) −28.7239 + 9.33296i −1.62878 + 0.529224i −0.973991 0.226586i \(-0.927244\pi\)
−0.654791 + 0.755810i \(0.727244\pi\)
\(312\) 2.08673 1.50778i 0.118138 0.0853612i
\(313\) 7.57278 + 14.8624i 0.428039 + 0.840073i 0.999807 + 0.0196580i \(0.00625773\pi\)
−0.571768 + 0.820415i \(0.693742\pi\)
\(314\) −5.06682 15.5941i −0.285937 0.880024i
\(315\) 0 0
\(316\) 0.675573 2.07920i 0.0380040 0.116964i
\(317\) −10.7129 + 1.69675i −0.601695 + 0.0952991i −0.449848 0.893105i \(-0.648522\pi\)
−0.151847 + 0.988404i \(0.548522\pi\)
\(318\) −10.7575 7.85886i −0.603253 0.440703i
\(319\) −28.3466 + 39.0157i −1.58710 + 2.18446i
\(320\) 0 0
\(321\) 13.5604 13.4897i 0.756869 0.752922i
\(322\) 0.570371 + 0.0903379i 0.0317855 + 0.00503433i
\(323\) 1.06581 2.09176i 0.0593031 0.116389i
\(324\) 5.21364 + 7.33607i 0.289647 + 0.407559i
\(325\) 0 0
\(326\) 4.05769i 0.224735i
\(327\) 10.0926 + 3.30848i 0.558122 + 0.182959i
\(328\) −0.979584 + 6.18485i −0.0540885 + 0.341501i
\(329\) 1.77385 1.28878i 0.0977957 0.0710527i
\(330\) 0 0
\(331\) −7.79472 5.66319i −0.428436 0.311277i 0.352587 0.935779i \(-0.385302\pi\)
−0.781023 + 0.624502i \(0.785302\pi\)
\(332\) 3.53590 3.53590i 0.194058 0.194058i
\(333\) −11.5377 + 5.80298i −0.632263 + 0.318001i
\(334\) −13.1635 4.27710i −0.720277 0.234032i
\(335\) 0 0
\(336\) 0.333751 0.168957i 0.0182076 0.00921737i
\(337\) 25.0858 12.7818i 1.36651 0.696272i 0.391864 0.920023i \(-0.371830\pi\)
0.974646 + 0.223752i \(0.0718304\pi\)
\(338\) −9.61460 + 4.89888i −0.522965 + 0.266464i
\(339\) −16.9769 + 8.59436i −0.922061 + 0.466782i
\(340\) 0 0
\(341\) 11.1139 + 3.61113i 0.601852 + 0.195554i
\(342\) −1.29053 + 0.649081i −0.0697838 + 0.0350983i
\(343\) 2.13093 2.13093i 0.115059 0.115059i
\(344\) −3.11459 2.26288i −0.167927 0.122006i
\(345\) 0 0
\(346\) 0.734684 0.533779i 0.0394969 0.0286962i
\(347\) 3.02097 19.0736i 0.162174 1.02393i −0.763556 0.645742i \(-0.776548\pi\)
0.925730 0.378185i \(-0.123452\pi\)
\(348\) −15.4498 5.06463i −0.828195 0.271493i
\(349\) 14.4119i 0.771451i −0.922614 0.385725i \(-0.873951\pi\)
0.922614 0.385725i \(-0.126049\pi\)
\(350\) 0 0
\(351\) 3.45226 + 6.90887i 0.184268 + 0.368768i
\(352\) −2.33240 + 4.57759i −0.124317 + 0.243986i
\(353\) −34.5802 5.47696i −1.84052 0.291509i −0.863448 0.504438i \(-0.831700\pi\)
−0.977068 + 0.212929i \(0.931700\pi\)
\(354\) 6.12467 6.09273i 0.325523 0.323825i
\(355\) 0 0
\(356\) −6.43505 + 8.85709i −0.341057 + 0.469425i
\(357\) −1.47269 1.07586i −0.0779430 0.0569408i
\(358\) 11.7036 1.85367i 0.618555 0.0979695i
\(359\) 10.6846 32.8840i 0.563914 1.73555i −0.107242 0.994233i \(-0.534202\pi\)
0.671156 0.741316i \(-0.265798\pi\)
\(360\) 0 0
\(361\) 5.79967 + 17.8496i 0.305246 + 0.939450i
\(362\) −7.80442 15.3170i −0.410191 0.805045i
\(363\) −21.6124 + 15.6161i −1.13436 + 0.819635i
\(364\) 0.305307 0.0992002i 0.0160024 0.00519950i
\(365\) 0 0
\(366\) 3.75839 23.3346i 0.196454 1.21972i
\(367\) −0.505240 3.18996i −0.0263733 0.166514i 0.970986 0.239135i \(-0.0768638\pi\)
−0.997360 + 0.0726205i \(0.976864\pi\)
\(368\) −1.89068 1.89068i −0.0985584 0.0985584i
\(369\) −17.8358 5.89848i −0.928495 0.307062i
\(370\) 0 0
\(371\) −0.976440 1.34395i −0.0506942 0.0697746i
\(372\) −0.0102991 + 3.93971i −0.000533985 + 0.204265i
\(373\) −9.65408 4.91900i −0.499869 0.254696i 0.185829 0.982582i \(-0.440503\pi\)
−0.685698 + 0.727886i \(0.740503\pi\)
\(374\) 25.0479 1.29519
\(375\) 0 0
\(376\) −10.1521 −0.523554
\(377\) −12.4317 6.33429i −0.640268 0.326233i
\(378\) 0.338411 + 1.07000i 0.0174060 + 0.0550350i
\(379\) 19.6854 + 27.0946i 1.01117 + 1.39176i 0.918213 + 0.396087i \(0.129632\pi\)
0.0929573 + 0.995670i \(0.470368\pi\)
\(380\) 0 0
\(381\) −11.8846 + 23.1749i −0.608867 + 1.18729i
\(382\) −3.49555 3.49555i −0.178848 0.178848i
\(383\) −2.54182 16.0484i −0.129881 0.820034i −0.963503 0.267699i \(-0.913737\pi\)
0.833622 0.552335i \(-0.186263\pi\)
\(384\) −1.71001 0.275424i −0.0872637 0.0140552i
\(385\) 0 0
\(386\) 3.20588 1.04165i 0.163175 0.0530187i
\(387\) 8.20933 8.12394i 0.417304 0.412963i
\(388\) 4.58178 + 8.99225i 0.232605 + 0.456512i
\(389\) 0.804900 + 2.47723i 0.0408101 + 0.125600i 0.969386 0.245542i \(-0.0789660\pi\)
−0.928576 + 0.371143i \(0.878966\pi\)
\(390\) 0 0
\(391\) −4.02838 + 12.3981i −0.203724 + 0.626998i
\(392\) −6.86775 + 1.08774i −0.346874 + 0.0549394i
\(393\) −8.91510 + 12.2034i −0.449707 + 0.615578i
\(394\) 4.30947 5.93148i 0.217108 0.298824i
\(395\) 0 0
\(396\) −12.4215 9.12439i −0.624206 0.458518i
\(397\) −1.86357 0.295160i −0.0935298 0.0148137i 0.109494 0.993987i \(-0.465077\pi\)
−0.203024 + 0.979174i \(0.565077\pi\)
\(398\) 3.78711 7.43262i 0.189831 0.372563i
\(399\) −0.177984 + 0.0277131i −0.00891032 + 0.00138739i
\(400\) 0 0
\(401\) 7.16880i 0.357993i −0.983850 0.178996i \(-0.942715\pi\)
0.983850 0.178996i \(-0.0572850\pi\)
\(402\) 8.10681 24.7300i 0.404331 1.23342i
\(403\) −0.528887 + 3.33926i −0.0263458 + 0.166341i
\(404\) 7.71559 5.60571i 0.383865 0.278894i
\(405\) 0 0
\(406\) −1.64017 1.19165i −0.0814002 0.0591407i
\(407\) 15.6390 15.6390i 0.775197 0.775197i
\(408\) 2.58850 + 8.03803i 0.128150 + 0.397942i
\(409\) 15.2838 + 4.96600i 0.755734 + 0.245553i 0.661447 0.749992i \(-0.269943\pi\)
0.0942874 + 0.995545i \(0.469943\pi\)
\(410\) 0 0
\(411\) −2.20874 4.36305i −0.108949 0.215214i
\(412\) −9.01147 + 4.59157i −0.443963 + 0.226211i
\(413\) 0.959822 0.489054i 0.0472297 0.0240648i
\(414\) 6.51407 4.68091i 0.320149 0.230054i
\(415\) 0 0
\(416\) −1.41362 0.459312i −0.0693083 0.0225196i
\(417\) 11.4761 3.69568i 0.561988 0.180978i
\(418\) 1.74927 1.74927i 0.0855596 0.0855596i
\(419\) −1.81333 1.31746i −0.0885872 0.0643624i 0.542610 0.839985i \(-0.317436\pi\)
−0.631197 + 0.775622i \(0.717436\pi\)
\(420\) 0 0
\(421\) 2.09500 1.52210i 0.102104 0.0741828i −0.535562 0.844496i \(-0.679900\pi\)
0.637666 + 0.770313i \(0.279900\pi\)
\(422\) 0.670692 4.23458i 0.0326488 0.206136i
\(423\) 4.92162 30.0560i 0.239297 1.46137i
\(424\) 7.69169i 0.373542i
\(425\) 0 0
\(426\) 3.23292 + 20.7630i 0.156636 + 1.00597i
\(427\) 1.33799 2.62595i 0.0647498 0.127079i
\(428\) −10.9072 1.72754i −0.527222 0.0835037i
\(429\) −9.32799 9.37689i −0.450360 0.452721i
\(430\) 0 0
\(431\) 0.661426 0.910375i 0.0318598 0.0438512i −0.792790 0.609495i \(-0.791372\pi\)
0.824650 + 0.565644i \(0.191372\pi\)
\(432\) 1.64441 4.92909i 0.0791165 0.237151i
\(433\) −20.2750 + 3.21125i −0.974355 + 0.154323i −0.623258 0.782016i \(-0.714191\pi\)
−0.351097 + 0.936339i \(0.614191\pi\)
\(434\) −0.151807 + 0.467215i −0.00728698 + 0.0224270i
\(435\) 0 0
\(436\) −1.89491 5.83194i −0.0907498 0.279299i
\(437\) 0.584515 + 1.14718i 0.0279611 + 0.0548768i
\(438\) −9.52020 13.1757i −0.454893 0.629561i
\(439\) 22.3736 7.26963i 1.06783 0.346960i 0.278191 0.960526i \(-0.410265\pi\)
0.789644 + 0.613565i \(0.210265\pi\)
\(440\) 0 0
\(441\) 0.109063 20.8598i 0.00519350 0.993323i
\(442\) 1.13363 + 7.15749i 0.0539215 + 0.340447i
\(443\) −13.6168 13.6168i −0.646952 0.646952i 0.305303 0.952255i \(-0.401242\pi\)
−0.952255 + 0.305303i \(0.901242\pi\)
\(444\) 6.63483 + 3.40249i 0.314875 + 0.161475i
\(445\) 0 0
\(446\) 0.429625 + 0.591328i 0.0203433 + 0.0280002i
\(447\) 13.3776 + 0.0349716i 0.632740 + 0.00165410i
\(448\) −0.192436 0.0980509i −0.00909173 0.00463247i
\(449\) −19.2184 −0.906973 −0.453487 0.891263i \(-0.649820\pi\)
−0.453487 + 0.891263i \(0.649820\pi\)
\(450\) 0 0
\(451\) 32.1710 1.51487
\(452\) 9.78864 + 4.98756i 0.460419 + 0.234595i
\(453\) 25.6114 + 0.0669530i 1.20333 + 0.00314573i
\(454\) 1.94595 + 2.67837i 0.0913281 + 0.125702i
\(455\) 0 0
\(456\) 0.742126 + 0.380579i 0.0347532 + 0.0178222i
\(457\) −15.9563 15.9563i −0.746405 0.746405i 0.227397 0.973802i \(-0.426979\pi\)
−0.973802 + 0.227397i \(0.926979\pi\)
\(458\) 1.65068 + 10.4220i 0.0771311 + 0.486986i
\(459\) −25.0520 + 3.76670i −1.16933 + 0.175814i
\(460\) 0 0
\(461\) −15.2184 + 4.94475i −0.708790 + 0.230300i −0.641156 0.767410i \(-0.721545\pi\)
−0.0676337 + 0.997710i \(0.521545\pi\)
\(462\) −1.12557 1.55776i −0.0523663 0.0724737i
\(463\) 2.81092 + 5.51675i 0.130635 + 0.256385i 0.947054 0.321075i \(-0.104044\pi\)
−0.816419 + 0.577460i \(0.804044\pi\)
\(464\) 2.90074 + 8.92755i 0.134663 + 0.414451i
\(465\) 0 0
\(466\) −3.89021 + 11.9728i −0.180210 + 0.554630i
\(467\) 22.9270 3.63127i 1.06093 0.168035i 0.398509 0.917164i \(-0.369528\pi\)
0.662424 + 0.749129i \(0.269528\pi\)
\(468\) 2.04513 3.96244i 0.0945362 0.183164i
\(469\) 1.90744 2.62537i 0.0880775 0.121228i
\(470\) 0 0
\(471\) −20.0291 20.1340i −0.922890 0.927728i
\(472\) −4.92635 0.780256i −0.226753 0.0359142i
\(473\) −8.97936 + 17.6230i −0.412871 + 0.810305i
\(474\) −0.582577 3.74153i −0.0267587 0.171854i
\(475\) 0 0
\(476\) 1.05298i 0.0482633i
\(477\) −22.7718 3.72885i −1.04265 0.170732i
\(478\) −1.83738 + 11.6007i −0.0840396 + 0.530605i
\(479\) 18.1330 13.1744i 0.828519 0.601954i −0.0906212 0.995885i \(-0.528885\pi\)
0.919140 + 0.393931i \(0.128885\pi\)
\(480\) 0 0
\(481\) 5.17668 + 3.76108i 0.236036 + 0.171491i
\(482\) −0.860035 + 0.860035i −0.0391735 + 0.0391735i
\(483\) 0.952076 0.306599i 0.0433210 0.0139507i
\(484\) 14.6409 + 4.75712i 0.665496 + 0.216233i
\(485\) 0 0
\(486\) 13.7957 + 7.25795i 0.625787 + 0.329227i
\(487\) −18.8976 + 9.62881i −0.856332 + 0.436323i −0.826303 0.563226i \(-0.809560\pi\)
−0.0300294 + 0.999549i \(0.509560\pi\)
\(488\) −12.1585 + 6.19509i −0.550391 + 0.280438i
\(489\) −3.17432 6.27042i −0.143548 0.283558i
\(490\) 0 0
\(491\) 29.6177 + 9.62339i 1.33663 + 0.434297i 0.888174 0.459507i \(-0.151974\pi\)
0.448456 + 0.893805i \(0.351974\pi\)
\(492\) 3.32462 + 10.3239i 0.149886 + 0.465437i
\(493\) 32.3613 32.3613i 1.45748 1.45748i
\(494\) 0.579028 + 0.420688i 0.0260517 + 0.0189277i
\(495\) 0 0
\(496\) 1.84019 1.33698i 0.0826270 0.0600320i
\(497\) −0.409892 + 2.58795i −0.0183862 + 0.116086i
\(498\) 2.69796 8.23021i 0.120899 0.368805i
\(499\) 1.25659i 0.0562528i −0.999604 0.0281264i \(-0.991046\pi\)
0.999604 0.0281264i \(-0.00895410\pi\)
\(500\) 0 0
\(501\) −23.6878 + 3.68833i −1.05829 + 0.164783i
\(502\) −10.2658 + 20.1477i −0.458184 + 0.899236i
\(503\) 25.9752 + 4.11407i 1.15818 + 0.183437i 0.705815 0.708397i \(-0.250581\pi\)
0.452363 + 0.891834i \(0.350581\pi\)
\(504\) 0.383577 0.522186i 0.0170859 0.0232600i
\(505\) 0 0
\(506\) −8.07434 + 11.1134i −0.358948 + 0.494050i
\(507\) −11.0252 + 15.0918i −0.489648 + 0.670251i
\(508\) 14.8517 2.35228i 0.658938 0.104366i
\(509\) 5.31690 16.3637i 0.235668 0.725310i −0.761365 0.648324i \(-0.775470\pi\)
0.997032 0.0769863i \(-0.0245298\pi\)
\(510\) 0 0
\(511\) −0.626355 1.92772i −0.0277083 0.0852775i
\(512\) 0.453990 + 0.891007i 0.0200637 + 0.0393773i
\(513\) −1.48651 + 2.01262i −0.0656308 + 0.0888591i
\(514\) −4.01395 + 1.30421i −0.177048 + 0.0575263i
\(515\) 0 0
\(516\) −6.58328 1.06034i −0.289813 0.0466788i
\(517\) 8.15912 + 51.5147i 0.358838 + 2.26561i
\(518\) 0.657443 + 0.657443i 0.0288864 + 0.0288864i
\(519\) 0.717747 1.39960i 0.0315056 0.0614357i
\(520\) 0 0
\(521\) −7.91212 10.8901i −0.346636 0.477104i 0.599729 0.800203i \(-0.295275\pi\)
−0.946365 + 0.323099i \(0.895275\pi\)
\(522\) −27.8369 + 4.25986i −1.21839 + 0.186449i
\(523\) 22.9585 + 11.6979i 1.00390 + 0.511514i 0.877046 0.480407i \(-0.159511\pi\)
0.126858 + 0.991921i \(0.459511\pi\)
\(524\) 8.72546 0.381174
\(525\) 0 0
\(526\) 2.57177 0.112134
\(527\) −9.88101 5.03463i −0.430424 0.219312i
\(528\) −0.0232622 + 8.89846i −0.00101236 + 0.387256i
\(529\) 9.31679 + 12.8235i 0.405078 + 0.557542i
\(530\) 0 0
\(531\) 4.69824 14.2065i 0.203886 0.616511i
\(532\) 0.0735370 + 0.0735370i 0.00318823 + 0.00318823i
\(533\) 1.45602 + 9.19295i 0.0630672 + 0.398191i
\(534\) −3.01533 + 18.7212i −0.130486 + 0.810144i
\(535\) 0 0
\(536\) −14.2901 + 4.64313i −0.617237 + 0.200553i
\(537\) 16.6357 12.0202i 0.717883 0.518711i
\(538\) −10.9703 21.5305i −0.472965 0.928246i
\(539\) 11.0391 + 33.9747i 0.475486 + 1.46340i
\(540\) 0 0
\(541\) −6.47364 + 19.9238i −0.278323 + 0.856591i 0.709998 + 0.704204i \(0.248696\pi\)
−0.988321 + 0.152387i \(0.951304\pi\)
\(542\) 11.4328 1.81078i 0.491082 0.0777797i
\(543\) −24.0428 17.5643i −1.03177 0.753757i
\(544\) 2.86572 3.94433i 0.122867 0.169112i
\(545\) 0 0
\(546\) 0.394192 0.392137i 0.0168699 0.0167819i
\(547\) −43.0967 6.82585i −1.84268 0.291852i −0.864974 0.501817i \(-0.832665\pi\)
−0.977709 + 0.209965i \(0.932665\pi\)
\(548\) −1.28180 + 2.51567i −0.0547557 + 0.107464i
\(549\) −12.4467 38.9995i −0.531211 1.66446i
\(550\) 0 0
\(551\) 4.52004i 0.192560i
\(552\) −4.40077 1.44263i −0.187309 0.0614023i
\(553\) 0.0738630 0.466353i 0.00314098 0.0198313i
\(554\) 6.09674 4.42954i 0.259025 0.188193i
\(555\) 0 0
\(556\) −5.63143 4.09147i −0.238826 0.173517i
\(557\) −20.7979 + 20.7979i −0.881236 + 0.881236i −0.993660 0.112424i \(-0.964139\pi\)
0.112424 + 0.993660i \(0.464139\pi\)
\(558\) 3.06611 + 6.09617i 0.129799 + 0.258071i
\(559\) −5.44220 1.76828i −0.230181 0.0747902i
\(560\) 0 0
\(561\) 38.7070 19.5949i 1.63421 0.827297i
\(562\) 21.0388 10.7198i 0.887467 0.452187i
\(563\) 14.0139 7.14045i 0.590616 0.300934i −0.133022 0.991113i \(-0.542468\pi\)
0.723639 + 0.690179i \(0.242468\pi\)
\(564\) −15.6882 + 7.94195i −0.660593 + 0.334417i
\(565\) 0 0
\(566\) 9.36284 + 3.04217i 0.393550 + 0.127872i
\(567\) 1.36001 + 1.38876i 0.0571152 + 0.0583223i
\(568\) 8.57861 8.57861i 0.359950 0.359950i
\(569\) 3.20445 + 2.32817i 0.134338 + 0.0976021i 0.652925 0.757423i \(-0.273542\pi\)
−0.518587 + 0.855025i \(0.673542\pi\)
\(570\) 0 0
\(571\) −31.7943 + 23.0999i −1.33055 + 0.966702i −0.330815 + 0.943696i \(0.607324\pi\)
−0.999735 + 0.0230060i \(0.992676\pi\)
\(572\) −1.19457 + 7.54225i −0.0499477 + 0.315357i
\(573\) −8.13631 2.66718i −0.339899 0.111423i
\(574\) 1.35243i 0.0564492i
\(575\) 0 0
\(576\) −2.85798 + 0.912121i −0.119082 + 0.0380050i
\(577\) 8.56788 16.8154i 0.356685 0.700034i −0.641036 0.767511i \(-0.721495\pi\)
0.997721 + 0.0674769i \(0.0214949\pi\)
\(578\) −6.68673 1.05907i −0.278131 0.0440517i
\(579\) 4.13922 4.11763i 0.172020 0.171123i
\(580\) 0 0
\(581\) 0.634802 0.873729i 0.0263360 0.0362484i
\(582\) 14.1149 + 10.3116i 0.585083 + 0.427429i
\(583\) 39.0299 6.18173i 1.61645 0.256021i
\(584\) −2.90012 + 8.92565i −0.120008 + 0.369346i
\(585\) 0 0
\(586\) 1.45939 + 4.49153i 0.0602867 + 0.185543i
\(587\) 2.11434 + 4.14963i 0.0872683 + 0.171274i 0.930516 0.366252i \(-0.119359\pi\)
−0.843247 + 0.537526i \(0.819359\pi\)
\(588\) −9.76192 + 7.05353i −0.402575 + 0.290883i
\(589\) −1.04166 + 0.338457i −0.0429210 + 0.0139459i
\(590\) 0 0
\(591\) 2.01933 12.5373i 0.0830640 0.515716i
\(592\) −0.673443 4.25195i −0.0276783 0.174754i
\(593\) 32.4687 + 32.4687i 1.33333 + 1.33333i 0.902371 + 0.430960i \(0.141825\pi\)
0.430960 + 0.902371i \(0.358175\pi\)
\(594\) −26.3332 4.38274i −1.08047 0.179826i
\(595\) 0 0
\(596\) −4.53982 6.24853i −0.185958 0.255950i
\(597\) 0.0377708 14.4484i 0.00154586 0.591334i
\(598\) −3.54111 1.80428i −0.144807 0.0737826i
\(599\) −18.2921 −0.747393 −0.373697 0.927551i \(-0.621910\pi\)
−0.373697 + 0.927551i \(0.621910\pi\)
\(600\) 0 0
\(601\) −0.981781 −0.0400477 −0.0200238 0.999800i \(-0.506374\pi\)
−0.0200238 + 0.999800i \(0.506374\pi\)
\(602\) −0.740847 0.377480i −0.0301947 0.0153850i
\(603\) −6.81864 44.5577i −0.277676 1.81453i
\(604\) −8.69147 11.9628i −0.353651 0.486759i
\(605\) 0 0
\(606\) 7.53772 14.6985i 0.306199 0.597086i
\(607\) 2.39455 + 2.39455i 0.0971917 + 0.0971917i 0.754031 0.656839i \(-0.228107\pi\)
−0.656839 + 0.754031i \(0.728107\pi\)
\(608\) −0.0753267 0.475594i −0.00305490 0.0192879i
\(609\) −3.46681 0.558383i −0.140482 0.0226268i
\(610\) 0 0
\(611\) −14.3512 + 4.66298i −0.580586 + 0.188644i
\(612\) 10.2882 + 10.3963i 0.415875 + 0.420247i
\(613\) −6.24017 12.2470i −0.252038 0.494653i 0.729973 0.683476i \(-0.239533\pi\)
−0.982011 + 0.188823i \(0.939533\pi\)
\(614\) −5.16261 15.8889i −0.208346 0.641223i
\(615\) 0 0
\(616\) −0.342880 + 1.05528i −0.0138150 + 0.0425183i
\(617\) −10.1292 + 1.60431i −0.407787 + 0.0645872i −0.356959 0.934120i \(-0.616186\pi\)
−0.0508287 + 0.998707i \(0.516186\pi\)
\(618\) −10.3336 + 14.1451i −0.415679 + 0.568999i
\(619\) 27.3325 37.6199i 1.09859 1.51207i 0.261338 0.965247i \(-0.415836\pi\)
0.837247 0.546825i \(-0.184164\pi\)
\(620\) 0 0
\(621\) 6.40445 12.3294i 0.257002 0.494763i
\(622\) 29.8303 + 4.72465i 1.19608 + 0.189441i
\(623\) −1.07346 + 2.10678i −0.0430072 + 0.0844063i
\(624\) −2.54381 + 0.396086i −0.101834 + 0.0158561i
\(625\) 0 0
\(626\) 16.6805i 0.666686i
\(627\) 1.33473 4.07163i 0.0533040 0.162605i
\(628\) −2.56499 + 16.1947i −0.102354 + 0.646239i
\(629\) −16.9802 + 12.3368i −0.677043 + 0.491900i
\(630\) 0 0
\(631\) −20.6748 15.0211i −0.823051 0.597981i 0.0945340 0.995522i \(-0.469864\pi\)
−0.917585 + 0.397540i \(0.869864\pi\)
\(632\) −1.54588 + 1.54588i −0.0614917 + 0.0614917i
\(633\) −2.27627 7.06846i −0.0904736 0.280946i
\(634\) 10.3155 + 3.35172i 0.409683 + 0.133114i
\(635\) 0 0
\(636\) 6.01719 + 11.8861i 0.238597 + 0.471315i
\(637\) −9.20875 + 4.69209i −0.364864 + 0.185907i
\(638\) 42.9697 21.8942i 1.70119 0.866798i
\(639\) 21.2388 + 29.5564i 0.840193 + 1.16923i
\(640\) 0 0
\(641\) −0.702023 0.228101i −0.0277282 0.00900945i 0.295120 0.955460i \(-0.404640\pi\)
−0.322848 + 0.946451i \(0.604640\pi\)
\(642\) −18.2066 + 5.86312i −0.718558 + 0.231399i
\(643\) −17.1573 + 17.1573i −0.676616 + 0.676616i −0.959233 0.282617i \(-0.908797\pi\)
0.282617 + 0.959233i \(0.408797\pi\)
\(644\) −0.467192 0.339435i −0.0184099 0.0133756i
\(645\) 0 0
\(646\) −1.89928 + 1.37991i −0.0747262 + 0.0542918i
\(647\) −0.943217 + 5.95524i −0.0370817 + 0.234125i −0.999267 0.0382696i \(-0.987815\pi\)
0.962186 + 0.272394i \(0.0878154\pi\)
\(648\) −1.31488 8.90343i −0.0516535 0.349760i
\(649\) 25.6248i 1.00586i
\(650\) 0 0
\(651\) 0.130910 + 0.840754i 0.00513078 + 0.0329517i
\(652\) −1.84215 + 3.61543i −0.0721443 + 0.141591i
\(653\) −9.97451 1.57981i −0.390333 0.0618226i −0.0418163 0.999125i \(-0.513314\pi\)
−0.348516 + 0.937303i \(0.613314\pi\)
\(654\) −7.49055 7.52982i −0.292904 0.294439i
\(655\) 0 0
\(656\) 3.68068 5.06602i 0.143706 0.197795i
\(657\) −25.0191 12.9131i −0.976087 0.503787i
\(658\) −2.16561 + 0.342999i −0.0844242 + 0.0133715i
\(659\) −3.59331 + 11.0591i −0.139975 + 0.430800i −0.996331 0.0855871i \(-0.972723\pi\)
0.856355 + 0.516387i \(0.172723\pi\)
\(660\) 0 0
\(661\) 12.8291 + 39.4838i 0.498993 + 1.53574i 0.810641 + 0.585544i \(0.199119\pi\)
−0.311648 + 0.950197i \(0.600881\pi\)
\(662\) 4.37411 + 8.58467i 0.170005 + 0.333653i
\(663\) 7.35111 + 10.1738i 0.285494 + 0.395116i
\(664\) −4.75577 + 1.54524i −0.184560 + 0.0599671i
\(665\) 0 0
\(666\) 12.9147 + 0.0675232i 0.500434 + 0.00261647i
\(667\) 3.92637 + 24.7901i 0.152030 + 0.959877i
\(668\) 9.78704 + 9.78704i 0.378672 + 0.378672i
\(669\) 1.12650 + 0.577696i 0.0435531 + 0.0223350i
\(670\) 0 0
\(671\) 41.2074 + 56.7171i 1.59079 + 2.18954i
\(672\) −0.374079 0.000977913i −0.0144304 3.77238e-5i
\(673\) 23.9046 + 12.1800i 0.921454 + 0.469504i 0.849313 0.527890i \(-0.177017\pi\)
0.0721411 + 0.997394i \(0.477017\pi\)
\(674\) −28.1544 −1.08447
\(675\) 0 0
\(676\) 10.7907 0.415028
\(677\) 19.6621 + 10.0184i 0.755677 + 0.385037i 0.788988 0.614408i \(-0.210605\pi\)
−0.0333112 + 0.999445i \(0.510605\pi\)
\(678\) 19.0283 + 0.0497436i 0.730779 + 0.00191039i
\(679\) 1.28118 + 1.76340i 0.0491673 + 0.0676729i
\(680\) 0 0
\(681\) 5.10240 + 2.61663i 0.195524 + 0.100269i
\(682\) −8.26315 8.26315i −0.316413 0.316413i
\(683\) 3.06282 + 19.3379i 0.117196 + 0.739944i 0.974376 + 0.224927i \(0.0722144\pi\)
−0.857180 + 0.515017i \(0.827786\pi\)
\(684\) 1.44455 + 0.00755268i 0.0552336 + 0.000288784i
\(685\) 0 0
\(686\) −2.86609 + 0.931249i −0.109428 + 0.0355552i
\(687\) 10.7039 + 14.8139i 0.408379 + 0.565187i
\(688\) 1.74779 + 3.43023i 0.0666339 + 0.130776i
\(689\) 3.53289 + 10.8731i 0.134592 + 0.414232i
\(690\) 0 0
\(691\) 12.6136 38.8206i 0.479843 1.47681i −0.359469 0.933157i \(-0.617042\pi\)
0.839313 0.543649i \(-0.182958\pi\)
\(692\) −0.896939 + 0.142061i −0.0340965 + 0.00540036i
\(693\) −2.95800 1.52671i −0.112365 0.0579949i
\(694\) −11.3510 + 15.6232i −0.430876 + 0.593050i
\(695\) 0 0
\(696\) 11.4666 + 11.5267i 0.434639 + 0.436917i
\(697\) −30.1540 4.77592i −1.14216 0.180901i
\(698\) −6.54286 + 12.8411i −0.247651 + 0.486042i
\(699\) 3.35470 + 21.5451i 0.126886 + 0.814912i
\(700\) 0 0
\(701\) 1.34594i 0.0508356i −0.999677 0.0254178i \(-0.991908\pi\)
0.999677 0.0254178i \(-0.00809161\pi\)
\(702\) 0.0605703 7.72314i 0.00228608 0.291491i
\(703\) −0.324278 + 2.04741i −0.0122304 + 0.0772195i
\(704\) 4.15636 3.01977i 0.156649 0.113812i
\(705\) 0 0
\(706\) 28.3247 + 20.5791i 1.06601 + 0.774503i
\(707\) 1.45647 1.45647i 0.0547762 0.0547762i
\(708\) −8.22317 + 2.64812i −0.309046 + 0.0995225i
\(709\) −5.99345 1.94739i −0.225089 0.0731358i 0.194301 0.980942i \(-0.437756\pi\)
−0.419390 + 0.907806i \(0.637756\pi\)
\(710\) 0 0
\(711\) −3.82725 5.32610i −0.143533 0.199744i
\(712\) 9.75471 4.97027i 0.365573 0.186269i
\(713\) 5.41900 2.76112i 0.202943 0.103405i
\(714\) 0.823744 + 1.62719i 0.0308278 + 0.0608960i
\(715\) 0 0
\(716\) −11.2695 3.66170i −0.421163 0.136844i
\(717\) 6.23589 + 19.3642i 0.232884 + 0.723170i
\(718\) −24.4491 + 24.4491i −0.912432 + 0.912432i
\(719\) −15.2779 11.1001i −0.569770 0.413962i 0.265251 0.964179i \(-0.414545\pi\)
−0.835022 + 0.550217i \(0.814545\pi\)
\(720\) 0 0
\(721\) −1.76717 + 1.28392i −0.0658127 + 0.0478157i
\(722\) 2.93598 18.5371i 0.109266 0.689878i
\(723\) −0.656225 + 2.00183i −0.0244053 + 0.0744490i
\(724\) 17.1907i 0.638888i
\(725\) 0 0
\(726\) 26.3463 4.10228i 0.977805 0.152250i
\(727\) 5.62601 11.0417i 0.208657 0.409513i −0.762832 0.646597i \(-0.776192\pi\)
0.971489 + 0.237084i \(0.0761916\pi\)
\(728\) −0.317066 0.0502184i −0.0117513 0.00186122i
\(729\) 26.9967 + 0.423480i 0.999877 + 0.0156844i
\(730\) 0 0
\(731\) 11.0326 15.1850i 0.408055 0.561639i
\(732\) −13.9424 + 19.0850i −0.515327 + 0.705401i
\(733\) −9.27418 + 1.46889i −0.342550 + 0.0542545i −0.325339 0.945597i \(-0.605478\pi\)
−0.0172103 + 0.999852i \(0.505478\pi\)
\(734\) −0.998039 + 3.07165i −0.0368383 + 0.113377i
\(735\) 0 0
\(736\) 0.826257 + 2.54296i 0.0304562 + 0.0937346i
\(737\) 35.0454 + 68.7804i 1.29091 + 2.53356i
\(738\) 13.2140 + 13.3529i 0.486413 + 0.491526i
\(739\) −18.0916 + 5.87832i −0.665511 + 0.216238i −0.622241 0.782826i \(-0.713778\pi\)
−0.0432699 + 0.999063i \(0.513778\pi\)
\(740\) 0 0
\(741\) 1.22389 + 0.197126i 0.0449606 + 0.00724159i
\(742\) 0.259872 + 1.64077i 0.00954019 + 0.0602344i
\(743\) 23.1938 + 23.1938i 0.850899 + 0.850899i 0.990244 0.139345i \(-0.0444997\pi\)
−0.139345 + 0.990244i \(0.544500\pi\)
\(744\) 1.79777 3.50563i 0.0659094 0.128523i
\(745\) 0 0
\(746\) 6.36867 + 8.76572i 0.233174 + 0.320936i
\(747\) −2.26926 14.8289i −0.0830278 0.542562i
\(748\) −22.3178 11.3715i −0.816020 0.415783i
\(749\) −2.38506 −0.0871483
\(750\) 0 0
\(751\) 35.1267 1.28179 0.640895 0.767628i \(-0.278563\pi\)
0.640895 + 0.767628i \(0.278563\pi\)
\(752\) 9.04558 + 4.60895i 0.329858 + 0.168071i
\(753\) −0.102386 + 39.1655i −0.00373115 + 1.42727i
\(754\) 8.20106 + 11.2878i 0.298665 + 0.411077i
\(755\) 0 0
\(756\) 0.184245 1.10701i 0.00670092 0.0402617i
\(757\) −20.0652 20.0652i −0.729283 0.729283i 0.241194 0.970477i \(-0.422461\pi\)
−0.970477 + 0.241194i \(0.922461\pi\)
\(758\) −5.23911 33.0785i −0.190293 1.20146i
\(759\) −3.78346 + 23.4902i −0.137331 + 0.852642i
\(760\) 0 0
\(761\) 30.4666 9.89919i 1.10441 0.358845i 0.300613 0.953746i \(-0.402809\pi\)
0.803799 + 0.594901i \(0.202809\pi\)
\(762\) 21.1104 15.2535i 0.764751 0.552575i
\(763\) −0.601254 1.18003i −0.0217669 0.0427199i
\(764\) 1.52761 + 4.70151i 0.0552671 + 0.170095i
\(765\) 0 0
\(766\) −5.02104 + 15.4532i −0.181418 + 0.558346i
\(767\) −7.32235 + 1.15975i −0.264395 + 0.0418760i
\(768\) 1.39859 + 1.02173i 0.0504674 + 0.0368686i
\(769\) −8.74366 + 12.0346i −0.315305 + 0.433980i −0.937026 0.349259i \(-0.886433\pi\)
0.621722 + 0.783238i \(0.286433\pi\)
\(770\) 0 0
\(771\) −5.18256 + 5.15553i −0.186645 + 0.185672i
\(772\) −3.32936 0.527318i −0.119826 0.0189786i
\(773\) −10.0990 + 19.8204i −0.363235 + 0.712889i −0.998220 0.0596354i \(-0.981006\pi\)
0.634985 + 0.772524i \(0.281006\pi\)
\(774\) −11.0028 + 3.51152i −0.395486 + 0.126219i
\(775\) 0 0
\(776\) 10.0922i 0.362290i
\(777\) 1.53028 + 0.501643i 0.0548983 + 0.0179964i
\(778\) 0.407467 2.57264i 0.0146084 0.0922337i
\(779\) −2.43940 + 1.77233i −0.0874006 + 0.0635003i
\(780\) 0 0
\(781\) −50.4249 36.6358i −1.80435 1.31093i
\(782\) 9.21792 9.21792i 0.329632 0.329632i