Properties

Label 750.2.l.c.143.4
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 143.4
Character \(\chi\) \(=\) 750.143
Dual form 750.2.l.c.257.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.453990 + 0.891007i) q^{2} +(0.530925 - 1.64867i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.22794 + 1.22154i) q^{6} +(-0.152718 + 0.152718i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.43624 - 1.75064i) q^{9} +O(q^{10})\) \(q+(-0.453990 + 0.891007i) q^{2} +(0.530925 - 1.64867i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.22794 + 1.22154i) q^{6} +(-0.152718 + 0.152718i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.43624 - 1.75064i) q^{9} +(4.88609 - 1.58759i) q^{11} +(-1.64587 + 0.539538i) q^{12} +(-1.32436 + 0.674795i) q^{13} +(-0.0667401 - 0.205405i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-0.762690 - 4.81543i) q^{17} +(2.66586 - 1.37593i) q^{18} +(-0.283032 + 0.389560i) q^{19} +(0.170700 + 0.332863i) q^{21} +(-0.803689 + 5.07429i) q^{22} +(-2.38239 - 1.21389i) q^{23} +(0.266479 - 1.71143i) q^{24} -1.48636i q^{26} +(-4.17969 + 3.08710i) q^{27} +(0.213317 + 0.0337860i) q^{28} +(7.59423 - 5.51753i) q^{29} +(-1.84019 - 1.33698i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.0232622 - 8.89846i) q^{33} +(4.63684 + 1.50660i) q^{34} +(0.0156850 + 2.99996i) q^{36} +(-1.95441 - 3.83574i) q^{37} +(-0.218606 - 0.429039i) q^{38} +(0.409380 + 2.54170i) q^{39} +(5.95547 + 1.93505i) q^{41} +(-0.374079 + 0.000977913i) q^{42} +(-2.72225 - 2.72225i) q^{43} +(-4.15636 - 3.01977i) q^{44} +(2.16317 - 1.57163i) q^{46} +(-10.0271 - 1.58814i) q^{47} +(1.40392 + 1.01441i) q^{48} +6.95335i q^{49} +(-8.34400 - 1.29921i) q^{51} +(1.32436 + 0.674795i) q^{52} +(1.20325 - 7.59700i) q^{53} +(-0.853081 - 5.12565i) q^{54} +(-0.126947 + 0.174728i) q^{56} +(0.491987 + 0.673453i) q^{57} +(1.46845 + 9.27141i) q^{58} +(1.54130 - 4.74363i) q^{59} +(-4.21680 - 12.9780i) q^{61} +(2.02668 - 1.03265i) q^{62} +(0.639411 - 0.104703i) q^{63} +(0.951057 - 0.309017i) q^{64} +(7.93914 + 4.01909i) q^{66} +(14.8405 - 2.35050i) q^{67} +(-3.44747 + 3.44747i) q^{68} +(-3.26618 + 3.28330i) q^{69} +(-7.13100 - 9.81498i) q^{71} +(-2.68010 - 1.34798i) q^{72} +(-4.26070 + 8.36209i) q^{73} +4.30495 q^{74} +0.481522 q^{76} +(-0.503741 + 0.988647i) q^{77} +(-2.45053 - 0.789148i) q^{78} +(1.28502 + 1.76867i) q^{79} +(2.87050 + 8.52996i) q^{81} +(-4.42787 + 4.42787i) q^{82} +(4.93895 - 0.782253i) q^{83} +(0.168957 - 0.333751i) q^{84} +(3.66142 - 1.18967i) q^{86} +(-5.06463 - 15.4498i) q^{87} +(4.57759 - 2.33240i) q^{88} +(3.38311 + 10.4121i) q^{89} +(0.0992002 - 0.305307i) q^{91} +(0.418278 + 2.64090i) q^{92} +(-3.18124 + 2.32404i) q^{93} +(5.96725 - 8.21321i) q^{94} +(-1.54121 + 0.790366i) q^{96} +(-1.57877 + 9.96799i) q^{97} +(-6.19548 - 3.15676i) q^{98} +(-14.6830 - 4.68606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q + 4q^{3} + 4q^{7} + O(q^{10}) \) \( 80q + 4q^{3} + 4q^{7} + 16q^{12} + 20q^{16} - 8q^{18} + 40q^{19} + 4q^{22} - 56q^{27} + 4q^{28} - 96q^{33} + 40q^{34} - 64q^{37} + 40q^{39} - 4q^{42} - 24q^{43} + 16q^{48} - 64q^{57} + 20q^{58} + 4q^{63} - 104q^{67} - 140q^{69} + 8q^{72} - 60q^{73} - 60q^{78} - 80q^{79} - 40q^{81} + 96q^{82} - 60q^{84} + 80q^{87} + 24q^{88} + 12q^{93} - 12q^{97} + O(q^{100}) \)

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
\(3\) 0.530925 1.64867i 0.306530 0.951861i
\(4\) −0.587785 0.809017i −0.293893 0.404508i
\(5\) 0 0
\(6\) 1.22794 + 1.22154i 0.501305 + 0.498691i
\(7\) −0.152718 + 0.152718i −0.0577219 + 0.0577219i −0.735379 0.677657i \(-0.762996\pi\)
0.677657 + 0.735379i \(0.262996\pi\)
\(8\) 0.987688 0.156434i 0.349201 0.0553079i
\(9\) −2.43624 1.75064i −0.812079 0.583547i
\(10\) 0 0
\(11\) 4.88609 1.58759i 1.47321 0.478676i 0.541136 0.840935i \(-0.317995\pi\)
0.932077 + 0.362259i \(0.117995\pi\)
\(12\) −1.64587 + 0.539538i −0.475123 + 0.155751i
\(13\) −1.32436 + 0.674795i −0.367312 + 0.187155i −0.627897 0.778296i \(-0.716084\pi\)
0.260586 + 0.965451i \(0.416084\pi\)
\(14\) −0.0667401 0.205405i −0.0178371 0.0548968i
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) −0.762690 4.81543i −0.184979 1.16791i −0.889059 0.457793i \(-0.848640\pi\)
0.704080 0.710121i \(-0.251360\pi\)
\(18\) 2.66586 1.37593i 0.628350 0.324309i
\(19\) −0.283032 + 0.389560i −0.0649319 + 0.0893711i −0.840248 0.542202i \(-0.817591\pi\)
0.775316 + 0.631574i \(0.217591\pi\)
\(20\) 0 0
\(21\) 0.170700 + 0.332863i 0.0372498 + 0.0726367i
\(22\) −0.803689 + 5.07429i −0.171347 + 1.08184i
\(23\) −2.38239 1.21389i −0.496763 0.253114i 0.187612 0.982243i \(-0.439925\pi\)
−0.684376 + 0.729130i \(0.739925\pi\)
\(24\) 0.266479 1.71143i 0.0543949 0.349344i
\(25\) 0 0
\(26\) 1.48636i 0.291500i
\(27\) −4.17969 + 3.08710i −0.804382 + 0.594112i
\(28\) 0.213317 + 0.0337860i 0.0403130 + 0.00638496i
\(29\) 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
\(33\) −0.0232622 8.89846i −0.00404943 1.54902i
\(34\) 4.63684 + 1.50660i 0.795211 + 0.258380i
\(35\) 0 0
\(36\) 0.0156850 + 2.99996i 0.00261417 + 0.499993i
\(37\) −1.95441 3.83574i −0.321303 0.630592i 0.672704 0.739912i \(-0.265133\pi\)
−0.994007 + 0.109320i \(0.965133\pi\)
\(38\) −0.218606 0.429039i −0.0354627 0.0695994i
\(39\) 0.409380 + 2.54170i 0.0655533 + 0.406998i
\(40\) 0 0
\(41\) 5.95547 + 1.93505i 0.930087 + 0.302204i 0.734598 0.678502i \(-0.237371\pi\)
0.195489 + 0.980706i \(0.437371\pi\)
\(42\) −0.374079 0.000977913i −0.0577217 0.000150895i
\(43\) −2.72225 2.72225i −0.415139 0.415139i 0.468385 0.883524i \(-0.344836\pi\)
−0.883524 + 0.468385i \(0.844836\pi\)
\(44\) −4.15636 3.01977i −0.626595 0.455248i
\(45\) 0 0
\(46\) 2.16317 1.57163i 0.318942 0.231725i
\(47\) −10.0271 1.58814i −1.46260 0.231654i −0.626154 0.779699i \(-0.715372\pi\)
−0.836448 + 0.548046i \(0.815372\pi\)
\(48\) 1.40392 + 1.01441i 0.202638 + 0.146417i
\(49\) 6.95335i 0.993336i
\(50\) 0 0
\(51\) −8.34400 1.29921i −1.16839 0.181926i
\(52\) 1.32436 + 0.674795i 0.183656 + 0.0935773i
\(53\) 1.20325 7.59700i 0.165279 1.04353i −0.755985 0.654589i \(-0.772842\pi\)
0.921264 0.388939i \(-0.127158\pi\)
\(54\) −0.853081 5.12565i −0.116090 0.697512i
\(55\) 0 0
\(56\) −0.126947 + 0.174728i −0.0169640 + 0.0233490i
\(57\) 0.491987 + 0.673453i 0.0651653 + 0.0892011i
\(58\) 1.46845 + 9.27141i 0.192817 + 1.21740i
\(59\) 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 \(-0.438211\pi\)
\(62\) 2.02668 1.03265i 0.257389 0.131146i
\(63\) 0.639411 0.104703i 0.0805582 0.0131913i
\(64\) 0.951057 0.309017i 0.118882 0.0386271i
\(65\) 0 0
\(66\) 7.93914 + 4.01909i 0.977241 + 0.494716i
\(67\) 14.8405 2.35050i 1.81305 0.287159i 0.844425 0.535673i \(-0.179942\pi\)
0.968628 + 0.248514i \(0.0799422\pi\)
\(68\) −3.44747 + 3.44747i −0.418067 + 0.418067i
\(69\) −3.26618 + 3.28330i −0.393202 + 0.395263i
\(70\) 0 0
\(71\) −7.13100 9.81498i −0.846294 1.16482i −0.984667 0.174444i \(-0.944187\pi\)
0.138373 0.990380i \(-0.455813\pi\)
\(72\) −2.68010 1.34798i −0.315853 0.158861i
\(73\) −4.26070 + 8.36209i −0.498677 + 0.978708i 0.495259 + 0.868745i \(0.335073\pi\)
−0.993936 + 0.109963i \(0.964927\pi\)
\(74\) 4.30495 0.500441
\(75\) 0 0
\(76\) 0.481522 0.0552344
\(77\) −0.503741 + 0.988647i −0.0574066 + 0.112667i
\(78\) −2.45053 0.789148i −0.277468 0.0893534i
\(79\) 1.28502 + 1.76867i 0.144576 + 0.198991i 0.875163 0.483828i \(-0.160754\pi\)
−0.730588 + 0.682819i \(0.760754\pi\)
\(80\) 0 0
\(81\) 2.87050 + 8.52996i 0.318945 + 0.947773i
\(82\) −4.42787 + 4.42787i −0.488976 + 0.488976i
\(83\) 4.93895 0.782253i 0.542120 0.0858634i 0.120632 0.992697i \(-0.461508\pi\)
0.421488 + 0.906834i \(0.361508\pi\)
\(84\) 0.168957 0.333751i 0.0184347 0.0364152i
\(85\) 0 0
\(86\) 3.66142 1.18967i 0.394821 0.128285i
\(87\) −5.06463 15.4498i −0.542985 1.65639i
\(88\) 4.57759 2.33240i 0.487972 0.248634i
\(89\) 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
\(92\) 0.418278 + 2.64090i 0.0436085 + 0.275333i
\(93\) −3.18124 + 2.32404i −0.329879 + 0.240991i
\(94\) 5.96725 8.21321i 0.615475 0.847128i
\(95\) 0 0
\(96\) −1.54121 + 0.790366i −0.157299 + 0.0806664i
\(97\) −1.57877 + 9.96799i −0.160300 + 1.01210i 0.768050 + 0.640390i \(0.221227\pi\)
−0.928350 + 0.371706i \(0.878773\pi\)
\(98\) −6.19548 3.15676i −0.625838 0.318881i
\(99\) −14.6830 4.68606i −1.47570 0.470967i
\(100\) 0 0
\(101\) 9.53700i 0.948967i 0.880264 + 0.474483i \(0.157365\pi\)
−0.880264 + 0.474483i \(0.842635\pi\)
\(102\) 4.94570 6.84473i 0.489697 0.677729i
\(103\) 9.98929 + 1.58215i 0.984274 + 0.155894i 0.627769 0.778400i \(-0.283968\pi\)
0.356505 + 0.934293i \(0.383968\pi\)
\(104\) −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 \(-0.0707659\pi\)
−0.220491 + 0.975389i \(0.570766\pi\)
\(108\) 4.95428 + 1.56689i 0.476725 + 0.150774i
\(109\) 5.83194 + 1.89491i 0.558598 + 0.181500i 0.574690 0.818371i \(-0.305123\pi\)
−0.0160921 + 0.999871i \(0.505123\pi\)
\(110\) 0 0
\(111\) −7.36152 + 1.18569i −0.698725 + 0.112540i
\(112\) −0.0980509 0.192436i −0.00926494 0.0181835i
\(113\) 4.98756 + 9.78864i 0.469190 + 0.920838i 0.997423 + 0.0717385i \(0.0228547\pi\)
−0.528233 + 0.849099i \(0.677145\pi\)
\(114\) −0.823409 + 0.132623i −0.0771193 + 0.0124212i
\(115\) 0 0
\(116\) −8.92755 2.90074i −0.828902 0.269327i
\(117\) 4.40778 + 0.674520i 0.407500 + 0.0623594i
\(118\) 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
\(122\) 13.4778 + 2.13468i 1.22023 + 0.193265i
\(123\) 6.35216 8.79124i 0.572755 0.792680i
\(124\) 2.27460i 0.204265i
\(125\) 0 0
\(126\) −0.196996 + 0.617253i −0.0175498 + 0.0549893i
\(127\) 13.3979 + 6.82658i 1.18887 + 0.605761i 0.932624 0.360850i \(-0.117513\pi\)
0.256249 + 0.966611i \(0.417513\pi\)
\(128\) −0.156434 + 0.987688i −0.0138270 + 0.0873001i
\(129\) −5.93341 + 3.04279i −0.522407 + 0.267902i
\(130\) 0 0
\(131\) −5.12870 + 7.05905i −0.448097 + 0.616752i −0.971987 0.235034i \(-0.924480\pi\)
0.523891 + 0.851785i \(0.324480\pi\)
\(132\) −7.18533 + 5.24920i −0.625403 + 0.456884i
\(133\) −0.0162687 0.102717i −0.00141068 0.00890667i
\(134\) −4.64313 + 14.2901i −0.401105 + 1.23447i
\(135\) 0 0
\(136\) −1.50660 4.63684i −0.129190 0.397605i
\(137\) 2.51567 1.28180i 0.214928 0.109511i −0.343212 0.939258i \(-0.611515\pi\)
0.558140 + 0.829747i \(0.311515\pi\)
\(138\) −1.44263 4.40077i −0.122805 0.374619i
\(139\) 6.62014 2.15102i 0.561513 0.182447i −0.0144887 0.999895i \(-0.504612\pi\)
0.576002 + 0.817448i \(0.304612\pi\)
\(140\) 0 0
\(141\) −7.94195 + 15.6882i −0.668833 + 1.32119i
\(142\) 11.9826 1.89786i 1.00556 0.159265i
\(143\) −5.39965 + 5.39965i −0.451542 + 0.451542i
\(144\) 2.41780 1.77602i 0.201483 0.148002i
\(145\) 0 0
\(146\) −5.51636 7.59261i −0.456537 0.628369i
\(147\) 11.4638 + 3.69171i 0.945518 + 0.304487i
\(148\) −1.95441 + 3.83574i −0.160651 + 0.315296i
\(149\) −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 \(0.705497\pi\)
\(152\) −0.218606 + 0.429039i −0.0177313 + 0.0347997i
\(153\) −6.57201 + 13.0667i −0.531315 + 1.05638i
\(154\) −0.652197 0.897673i −0.0525556 0.0723365i
\(155\) 0 0
\(156\) 1.81565 1.82517i 0.145369 0.146131i
\(157\) −11.5941 + 11.5941i −0.925312 + 0.925312i −0.997398 0.0720863i \(-0.977034\pi\)
0.0720863 + 0.997398i \(0.477034\pi\)
\(158\) −2.15928 + 0.341997i −0.171783 + 0.0272078i
\(159\) −11.8861 6.01719i −0.942630 0.477194i
\(160\) 0 0
\(161\) 0.549217 0.178451i 0.0432843 0.0140639i
\(162\) −8.90343 1.31488i −0.699520 0.103307i
\(163\) 3.61543 1.84215i 0.283182 0.144289i −0.306630 0.951829i \(-0.599202\pi\)
0.589813 + 0.807540i \(0.299202\pi\)
\(164\) −1.93505 5.95547i −0.151102 0.465044i
\(165\) 0 0
\(166\) −1.54524 + 4.75577i −0.119934 + 0.369119i
\(167\) −2.16520 13.6706i −0.167549 1.05786i −0.917897 0.396818i \(-0.870114\pi\)
0.750349 0.661042i \(-0.229886\pi\)
\(168\) 0.220670 + 0.302062i 0.0170250 + 0.0233046i
\(169\) −6.34263 + 8.72988i −0.487894 + 0.671529i
\(170\) 0 0
\(171\) 1.37151 0.453573i 0.104882 0.0346856i
\(172\) −0.602248 + 3.80244i −0.0459210 + 0.289934i
\(173\) −0.809140 0.412278i −0.0615178 0.0313449i 0.422961 0.906148i \(-0.360991\pi\)
−0.484479 + 0.874803i \(0.660991\pi\)
\(174\) 16.0652 + 2.50144i 1.21790 + 0.189633i
\(175\) 0 0
\(176\) 5.13754i 0.387257i
\(177\) −7.00238 5.05961i −0.526331 0.380304i
\(178\) −10.8132 1.71264i −0.810482 0.128368i
\(179\) −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
\(183\) −23.6352 + 0.0617869i −1.74717 + 0.00456742i
\(184\) −2.54296 0.826257i −0.187469 0.0609125i
\(185\) 0 0
\(186\) −0.626479 3.88960i −0.0459357 0.285199i
\(187\) −11.3715 22.3178i −0.831566 1.63204i
\(188\) 4.60895 + 9.04558i 0.336142 + 0.659716i
\(189\) 0.166859 1.10977i 0.0121372 0.0807238i
\(190\) 0 0
\(191\) −4.70151 1.52761i −0.340189 0.110534i 0.133940 0.990989i \(-0.457237\pi\)
−0.474129 + 0.880455i \(0.657237\pi\)
\(192\) −0.00452789 1.73204i −0.000326772 0.125000i
\(193\) 2.38356 + 2.38356i 0.171572 + 0.171572i 0.787670 0.616098i \(-0.211287\pi\)
−0.616098 + 0.787670i \(0.711287\pi\)
\(194\) −8.16479 5.93207i −0.586198 0.425898i
\(195\) 0 0
\(196\) 5.62538 4.08708i 0.401813 0.291934i
\(197\) 7.24145 + 1.14693i 0.515932 + 0.0817156i 0.408970 0.912548i \(-0.365888\pi\)
0.106961 + 0.994263i \(0.465888\pi\)
\(198\) 10.8412 10.9552i 0.770454 0.778553i
\(199\) 8.34182i 0.591336i −0.955291 0.295668i \(-0.904458\pi\)
0.955291 0.295668i \(-0.0955422\pi\)
\(200\) 0 0
\(201\) 4.00398 25.7150i 0.282419 1.81380i
\(202\) −8.49753 4.32971i −0.597884 0.304637i
\(203\) −0.317149 + 2.00240i −0.0222595 + 0.140541i
\(204\) 3.85340 + 7.51409i 0.269792 + 0.526092i
\(205\) 0 0
\(206\) −5.94475 + 8.18224i −0.414190 + 0.570084i
\(207\) 3.67899 + 7.12804i 0.255707 + 0.495433i
\(208\) −0.232519 1.46807i −0.0161223 0.101792i
\(209\) −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 \(0.852852\pi\)
\(212\) −6.85335 + 3.49196i −0.470690 + 0.239828i
\(213\) −19.9677 + 6.54566i −1.36817 + 0.448501i
\(214\) −10.5027 + 3.41254i −0.717951 + 0.233276i
\(215\) 0 0
\(216\) −3.64531 + 3.70294i −0.248032 + 0.251953i
\(217\) 0.485210 0.0768498i 0.0329382 0.00521690i
\(218\) −4.33602 + 4.33602i −0.293672 + 0.293672i
\(219\) 11.5242 + 11.4641i 0.778735 + 0.774674i
\(220\) 0 0
\(221\) 4.25951 + 5.86271i 0.286525 + 0.394369i
\(222\) 2.28561 7.09746i 0.153400 0.476350i
\(223\) −0.331831 + 0.651256i −0.0222211 + 0.0436113i −0.901850 0.432049i \(-0.857791\pi\)
0.879629 + 0.475660i \(0.157791\pi\)
\(224\) 0.215976 0.0144305
\(225\) 0 0
\(226\) −10.9860 −0.730781
\(227\) −1.50300 + 2.94981i −0.0997579 + 0.195786i −0.935492 0.353349i \(-0.885043\pi\)
0.835734 + 0.549135i \(0.185043\pi\)
\(228\) 0.255652 0.793872i 0.0169310 0.0525755i
\(229\) 6.20224 + 8.53665i 0.409855 + 0.564117i 0.963183 0.268846i \(-0.0866423\pi\)
−0.553328 + 0.832964i \(0.686642\pi\)
\(230\) 0 0
\(231\) 1.36251 + 1.35540i 0.0896463 + 0.0891788i
\(232\) 6.63760 6.63760i 0.435780 0.435780i
\(233\) 12.4340 1.96935i 0.814577 0.129016i 0.264774 0.964311i \(-0.414703\pi\)
0.549803 + 0.835294i \(0.314703\pi\)
\(234\) −2.60209 + 3.62114i −0.170104 + 0.236721i
\(235\) 0 0
\(236\) −4.74363 + 1.54130i −0.308784 + 0.100330i
\(237\) 3.59821 1.17954i 0.233729 0.0766192i
\(238\) −0.938212 + 0.478043i −0.0608152 + 0.0309869i
\(239\) −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 \(0.0875275\pi\)
\(242\) 2.40821 + 15.2048i 0.154805 + 0.977403i
\(243\) 15.5871 0.203749i 0.999915 0.0130705i
\(244\) −8.02083 + 11.0397i −0.513481 + 0.706746i
\(245\) 0 0
\(246\) 4.94923 + 9.65096i 0.315552 + 0.615323i
\(247\) 0.111963 0.706906i 0.00712403 0.0449793i
\(248\) −2.02668 1.03265i −0.128695 0.0655732i
\(249\) 1.33253 8.55802i 0.0844459 0.542343i
\(250\) 0 0
\(251\) 22.6123i 1.42728i 0.700515 + 0.713638i \(0.252954\pi\)
−0.700515 + 0.713638i \(0.747046\pi\)
\(252\) −0.460543 0.455752i −0.0290115 0.0287097i
\(253\) −13.5678 2.14892i −0.852998 0.135102i
\(254\) −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 \(-0.292022\pi\)
−0.794033 + 0.607874i \(0.792022\pi\)
\(258\) −0.0174316 6.66810i −0.00108525 0.415138i
\(259\) 0.884259 + 0.287313i 0.0549452 + 0.0178528i
\(260\) 0 0
\(261\) −28.1606 + 0.147235i −1.74309 + 0.00911361i
\(262\) −3.96128 7.77445i −0.244729 0.480307i
\(263\) −1.16756 2.29146i −0.0719947 0.141298i 0.852204 0.523210i \(-0.175266\pi\)
−0.924199 + 0.381912i \(0.875266\pi\)
\(264\) −1.41500 8.78526i −0.0870873 0.540696i
\(265\) 0 0
\(266\) 0.0989071 + 0.0321369i 0.00606438 + 0.00197044i
\(267\) 18.9624 0.0495712i 1.16048 0.00303371i
\(268\) −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 \(0.414354\pi\)
\(272\) 4.81543 + 0.762690i 0.291978 + 0.0462448i
\(273\) −0.450683 0.325644i −0.0272766 0.0197088i
\(274\) 2.82340i 0.170568i
\(275\) 0 0
\(276\) 4.57606 + 0.712519i 0.275446 + 0.0428886i
\(277\) −6.71461 3.42126i −0.403442 0.205564i 0.240482 0.970654i \(-0.422695\pi\)
−0.643924 + 0.765090i \(0.722695\pi\)
\(278\) −1.08891 + 6.87513i −0.0653087 + 0.412343i
\(279\) 2.14257 + 6.47871i 0.128273 + 0.387870i
\(280\) 0 0
\(281\) 13.8790 19.1028i 0.827952 1.13958i −0.160349 0.987060i \(-0.551262\pi\)
0.988301 0.152517i \(-0.0487380\pi\)
\(282\) −10.3727 14.1986i −0.617687 0.845516i
\(283\) 1.54005 + 9.72347i 0.0915463 + 0.578000i 0.990234 + 0.139412i \(0.0445213\pi\)
−0.898688 + 0.438588i \(0.855479\pi\)
\(284\) −3.74899 + 11.5382i −0.222462 + 0.684667i
\(285\) 0 0
\(286\) −2.35974 7.26252i −0.139534 0.429442i
\(287\) −1.20502 + 0.613989i −0.0711302 + 0.0362426i
\(288\) 0.484789 + 2.96057i 0.0285665 + 0.174453i
\(289\) −6.43873 + 2.09207i −0.378749 + 0.123063i
\(290\) 0 0
\(291\) 15.5957 + 7.89513i 0.914238 + 0.462821i
\(292\) 9.26944 1.46814i 0.542453 0.0859161i
\(293\) 3.33944 3.33944i 0.195092 0.195092i −0.602800 0.797892i \(-0.705948\pi\)
0.797892 + 0.602800i \(0.205948\pi\)
\(294\) −8.49379 + 8.53832i −0.495368 + 0.497965i
\(295\) 0 0
\(296\) −2.53039 3.48278i −0.147076 0.202433i
\(297\) −15.5213 + 21.7195i −0.900640 + 1.26029i
\(298\) 3.50644 6.88178i 0.203123 0.398651i
\(299\) 3.97428 0.229838
\(300\) 0 0
\(301\) 0.831472 0.0479252
\(302\) 6.71307 13.1751i 0.386294 0.758145i
\(303\) 15.7234 + 5.06343i 0.903285 + 0.290887i
\(304\) −0.283032 0.389560i −0.0162330 0.0223428i
\(305\) 0 0
\(306\) −8.65891 11.7879i −0.494997 0.673868i
\(307\) −11.8133 + 11.8133i −0.674221 + 0.674221i −0.958686 0.284465i \(-0.908184\pi\)
0.284465 + 0.958686i \(0.408184\pi\)
\(308\) 1.09592 0.173577i 0.0624460 0.00989048i
\(309\) 7.91201 15.6291i 0.450098 0.889106i
\(310\) 0 0
\(311\) 28.7239 9.33296i 1.62878 0.529224i 0.654791 0.755810i \(-0.272756\pi\)
0.973991 + 0.226586i \(0.0727564\pi\)
\(312\) 0.801950 + 2.44637i 0.0454015 + 0.138498i
\(313\) 14.8624 7.57278i 0.840073 0.428039i 0.0196580 0.999807i \(-0.493742\pi\)
0.820415 + 0.571768i \(0.193742\pi\)
\(314\) −5.06682 15.5941i −0.285937 0.880024i
\(315\) 0 0
\(316\) 0.675573 2.07920i 0.0380040 0.116964i
\(317\) 1.69675 + 10.7129i 0.0952991 + 0.601695i 0.988404 + 0.151847i \(0.0485219\pi\)
−0.893105 + 0.449848i \(0.851478\pi\)
\(318\) 10.7575 7.85886i 0.603253 0.440703i
\(319\) 28.3466 39.0157i 1.58710 2.18446i
\(320\) 0 0
\(321\) 17.0199 8.72818i 0.949957 0.487160i
\(322\) −0.0903379 + 0.570371i −0.00503433 + 0.0317855i
\(323\) 2.09176 + 1.06581i 0.116389 + 0.0593031i
\(324\) 5.21364 7.33607i 0.289647 0.407559i
\(325\) 0 0
\(326\) 4.05769i 0.224735i
\(327\) 6.22041 8.60889i 0.343989 0.476073i
\(328\) 6.18485 + 0.979584i 0.341501 + 0.0540885i
\(329\) 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
\(333\) −1.95361 + 12.7662i −0.107057 + 0.699586i
\(334\) 13.1635 + 4.27710i 0.720277 + 0.234032i
\(335\) 0 0
\(336\) −0.369321 + 0.0594848i −0.0201481 + 0.00324516i
\(337\) 12.7818 + 25.0858i 0.696272 + 1.36651i 0.920023 + 0.391864i \(0.128170\pi\)
−0.223752 + 0.974646i \(0.571830\pi\)
\(338\) −4.89888 9.61460i −0.266464 0.522965i
\(339\) 18.7863 3.02582i 1.02033 0.164340i
\(340\) 0 0
\(341\) −11.1139 3.61113i −0.601852 0.195554i
\(342\) −0.218517 + 1.42794i −0.0118161 + 0.0772143i
\(343\) −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
\(347\) −19.0736 3.02097i −1.02393 0.162174i −0.378185 0.925730i \(-0.623452\pi\)
−0.645742 + 0.763556i \(0.723452\pi\)
\(348\) −9.52222 + 13.1785i −0.510445 + 0.706443i
\(349\) 14.4119i 0.771451i 0.922614 + 0.385725i \(0.126049\pi\)
−0.922614 + 0.385725i \(0.873951\pi\)
\(350\) 0 0
\(351\) 3.45226 6.90887i 0.184268 0.368768i
\(352\) −4.57759 2.33240i −0.243986 0.124317i
\(353\) 5.47696 34.5802i 0.291509 1.84052i −0.212929 0.977068i \(-0.568300\pi\)
0.504438 0.863448i \(-0.331700\pi\)
\(354\) 7.68716 3.94215i 0.408568 0.209523i
\(355\) 0 0
\(356\) 6.43505 8.85709i 0.341057 0.469425i
\(357\) 1.47269 1.07586i 0.0779430 0.0569408i
\(358\) −1.85367 11.7036i −0.0979695 0.618555i
\(359\) 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
\(362\) −15.3170 + 7.80442i −0.805045 + 0.410191i
\(363\) −8.30583 25.3372i −0.435943 1.32986i
\(364\) −0.305307 + 0.0992002i −0.0160024 + 0.00519950i
\(365\) 0 0
\(366\) 10.6751 21.0872i 0.557997 1.10224i
\(367\) 3.18996 0.505240i 0.166514 0.0263733i −0.0726205 0.997360i \(-0.523136\pi\)
0.239135 + 0.970986i \(0.423136\pi\)
\(368\) 1.89068 1.89068i 0.0985584 0.0985584i
\(369\) −11.1214 15.1401i −0.578954 0.788163i
\(370\) 0 0
\(371\) 0.976440 + 1.34395i 0.0506942 + 0.0697746i
\(372\) 3.75007 + 1.20764i 0.194432 + 0.0626134i
\(373\) −4.91900 + 9.65408i −0.254696 + 0.499869i −0.982582 0.185829i \(-0.940503\pi\)
0.727886 + 0.685698i \(0.240503\pi\)
\(374\) 25.0479 1.29519
\(375\) 0 0
\(376\) −10.1521 −0.523554
\(377\) −6.33429 + 12.4317i −0.326233 + 0.640268i
\(378\) 0.913058 + 0.652497i 0.0469627 + 0.0335608i
\(379\) −19.6854 27.0946i −1.01117 1.39176i −0.918213 0.396087i \(-0.870368\pi\)
−0.0929573 0.995670i \(-0.529632\pi\)
\(380\) 0 0
\(381\) 18.3681 18.4644i 0.941025 0.945958i
\(382\) 3.49555 3.49555i 0.178848 0.178848i
\(383\) 16.0484 2.54182i 0.820034 0.129881i 0.267699 0.963503i \(-0.413737\pi\)
0.552335 + 0.833622i \(0.313737\pi\)
\(384\) 1.54532 + 0.782298i 0.0788592 + 0.0399215i
\(385\) 0 0
\(386\) −3.20588 + 1.04165i −0.163175 + 0.0530187i
\(387\) 1.86636 + 11.3977i 0.0948724 + 0.579379i
\(388\) 8.99225 4.58178i 0.456512 0.232605i
\(389\) 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
\(392\) 1.08774 + 6.86775i 0.0549394 + 0.346874i
\(393\) 8.91510 + 12.2034i 0.449707 + 0.615578i
\(394\) −4.30947 + 5.93148i −0.217108 + 0.298824i
\(395\) 0 0
\(396\) 4.83934 + 14.6332i 0.243186 + 0.735345i
\(397\) 0.295160 1.86357i 0.0148137 0.0935298i −0.979174 0.203024i \(-0.934923\pi\)
0.993987 + 0.109494i \(0.0349231\pi\)
\(398\) 7.43262 + 3.78711i 0.372563 + 0.189831i
\(399\) −0.177984 0.0277131i −0.00891032 0.00138739i
\(400\) 0 0
\(401\) 7.16880i 0.357993i 0.983850 + 0.178996i \(0.0572850\pi\)
−0.983850 + 0.178996i \(0.942715\pi\)
\(402\) 21.0945 + 15.2419i 1.05210 + 0.760199i
\(403\) 3.33926 + 0.528887i 0.166341 + 0.0263458i
\(404\) 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
\(408\) −8.44451 + 0.0220755i −0.418066 + 0.00109290i
\(409\) −15.2838 4.96600i −0.755734 0.245553i −0.0942874 0.995545i \(-0.530057\pi\)
−0.661447 + 0.749992i \(0.730057\pi\)
\(410\) 0 0
\(411\) −0.777631 4.82805i −0.0383577 0.238150i
\(412\) −4.59157 9.01147i −0.226211 0.443963i
\(413\) 0.489054 + 0.959822i 0.0240648 + 0.0472297i
\(414\) −8.02136 + 0.0419389i −0.394228 + 0.00206119i
\(415\) 0 0
\(416\) 1.41362 + 0.459312i 0.0693083 + 0.0225196i
\(417\) −0.0315179 12.0565i −0.00154344 0.590408i
\(418\) −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 \(0.279900\pi\)
\(422\) −4.23458 0.670692i −0.206136 0.0326488i
\(423\) 21.6481 + 21.4229i 1.05257 + 1.04162i
\(424\) 7.69169i 0.373542i
\(425\) 0 0
\(426\) 3.23292 20.7630i 0.156636 1.00597i
\(427\) 2.62595 + 1.33799i 0.127079 + 0.0647498i
\(428\) 1.72754 10.9072i 0.0835037 0.527222i
\(429\) 6.03545 + 11.7691i 0.291394 + 0.568216i
\(430\) 0 0
\(431\) −0.661426 + 0.910375i −0.0318598 + 0.0438512i −0.824650 0.565644i \(-0.808628\pi\)
0.792790 + 0.609495i \(0.208628\pi\)
\(432\) −1.64441 4.92909i −0.0791165 0.237151i
\(433\) 3.21125 + 20.2750i 0.154323 + 0.974355i 0.936339 + 0.351097i \(0.114191\pi\)
−0.782016 + 0.623258i \(0.785809\pi\)
\(434\) −0.151807 + 0.467215i −0.00728698 + 0.0224270i
\(435\) 0 0
\(436\) −1.89491 5.83194i −0.0907498 0.279299i
\(437\) 1.14718 0.584515i 0.0548768 0.0279611i
\(438\) −15.4465 + 5.06355i −0.738062 + 0.241946i
\(439\) −22.3736 + 7.26963i −1.06783 + 0.346960i −0.789644 0.613565i \(-0.789735\pi\)
−0.278191 + 0.960526i \(0.589735\pi\)
\(440\) 0 0
\(441\) 12.1728 16.9400i 0.579659 0.806668i
\(442\) −7.15749 + 1.13363i −0.340447 + 0.0539215i
\(443\) 13.6168 13.6168i 0.646952 0.646952i −0.305303 0.952255i \(-0.598758\pi\)
0.952255 + 0.305303i \(0.0987577\pi\)
\(444\) 5.28624 + 5.25867i 0.250874 + 0.249565i
\(445\) 0 0
\(446\) −0.429625 0.591328i −0.0203433 0.0280002i
\(447\) −4.10066 + 12.7337i −0.193954 + 0.602283i
\(448\) −0.0980509 + 0.192436i −0.00463247 + 0.00909173i
\(449\) −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
\(452\) 4.98756 9.78864i 0.234595 0.460419i
\(453\) −7.85069 + 24.3786i −0.368858 + 1.14541i
\(454\) −1.94595 2.67837i −0.0913281 0.125702i
\(455\) 0 0
\(456\) 0.591281 + 0.588198i 0.0276893 + 0.0275449i
\(457\) 15.9563 15.9563i 0.746405 0.746405i −0.227397 0.973802i \(-0.573021\pi\)
0.973802 + 0.227397i \(0.0730215\pi\)
\(458\) −10.4220 + 1.65068i −0.486986 + 0.0771311i
\(459\) 18.0535 + 17.7725i 0.842666 + 0.829551i
\(460\) 0 0
\(461\) 15.2184 4.94475i 0.708790 0.230300i 0.0676337 0.997710i \(-0.478455\pi\)
0.641156 + 0.767410i \(0.278455\pi\)
\(462\) −1.82624 + 0.598662i −0.0849642 + 0.0278523i
\(463\) 5.51675 2.81092i 0.256385 0.130635i −0.321075 0.947054i \(-0.604044\pi\)
0.577460 + 0.816419i \(0.304044\pi\)
\(464\) 2.90074 + 8.92755i 0.134663 + 0.414451i
\(465\) 0 0
\(466\) −3.89021 + 11.9728i −0.180210 + 0.554630i
\(467\) −3.63127 22.9270i −0.168035 1.06093i −0.917164 0.398509i \(-0.869528\pi\)
0.749129 0.662424i \(-0.230472\pi\)
\(468\) −2.04513 3.96244i −0.0945362 0.183164i
\(469\) −1.90744 + 2.62537i −0.0880775 + 0.121228i
\(470\) 0 0
\(471\) 12.9593 + 25.2705i 0.597133 + 1.16440i
\(472\) 0.780256 4.92635i 0.0359142 0.226753i
\(473\) −17.6230 8.97936i −0.810305 0.412871i
\(474\) −0.582577 + 3.74153i −0.0267587 + 0.171854i
\(475\) 0 0
\(476\) 1.05298i 0.0482633i
\(477\) −16.2310 + 16.4016i −0.743167 + 0.750979i
\(478\) 11.6007 + 1.83738i 0.530605 + 0.0840396i
\(479\) 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
\(483\) −0.00261477 1.00022i −0.000118976 0.0455117i
\(484\) −14.6409 4.75712i −0.665496 0.216233i
\(485\) 0 0
\(486\) −6.89486 + 13.9807i −0.312757 + 0.634179i
\(487\) −9.62881 18.8976i −0.436323 0.856332i −0.999549 0.0300294i \(-0.990440\pi\)
0.563226 0.826303i \(-0.309560\pi\)
\(488\) −6.19509 12.1585i −0.280438 0.550391i
\(489\) −1.11758 6.93870i −0.0505389 0.313779i
\(490\) 0 0
\(491\) −29.6177 9.62339i −1.33663 0.434297i −0.448456 0.893805i \(-0.648026\pi\)
−0.888174 + 0.459507i \(0.848026\pi\)
\(492\) −10.8460 + 0.0283534i −0.488974 + 0.00127827i
\(493\) −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
\(497\) 2.58795 + 0.409892i 0.116086 + 0.0183862i
\(498\) 7.02030 + 5.07256i 0.314587 + 0.227307i
\(499\) 1.25659i 0.0562528i 0.999604 + 0.0281264i \(0.00895410\pi\)
−0.999604 + 0.0281264i \(0.991046\pi\)
\(500\) 0 0
\(501\) −23.6878 3.68833i −1.05829 0.164783i
\(502\) −20.1477 10.2658i −0.899236 0.458184i
\(503\) −4.11407 + 25.9752i −0.183437 + 1.15818i 0.708397 + 0.705815i \(0.249419\pi\)
−0.891834 + 0.452363i \(0.850581\pi\)
\(504\) 0.615160 0.203439i 0.0274014 0.00906191i
\(505\) 0 0
\(506\) 8.07434 11.1134i 0.358948 0.494050i
\(507\) 11.0252 + 15.0918i 0.489648 + 0.670251i
\(508\) −2.35228 14.8517i −0.104366 0.658938i
\(509\) 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
\(512\) 0.891007 0.453990i 0.0393773 0.0200637i
\(513\) −0.0196223 2.50199i −0.000866347 0.110465i
\(514\) 4.01395 1.30421i 0.177048 0.0575263i
\(515\) 0 0
\(516\) 5.94923 + 3.01172i 0.261900 + 0.132584i
\(517\) −51.5147 + 8.15912i −2.26561 + 0.358838i
\(518\) −0.657443 + 0.657443i −0.0288864 + 0.0288864i
\(519\) −1.10930 + 1.11512i −0.0486930 + 0.0489483i
\(520\) 0 0
\(521\) 7.91212 + 10.8901i 0.346636 + 0.477104i 0.946365 0.323099i \(-0.104725\pi\)
−0.599729 + 0.800203i \(0.704725\pi\)
\(522\) 12.6534 25.1581i 0.553826 1.10114i
\(523\) 11.6979 22.9585i 0.511514 1.00390i −0.480407 0.877046i \(-0.659511\pi\)
0.991921 0.126858i \(-0.0404891\pi\)
\(524\) 8.72546 0.381174
\(525\) 0 0
\(526\) 2.57177 0.112134
\(527\) −5.03463 + 9.88101i −0.219312 + 0.430424i
\(528\) 8.47012 + 2.72765i 0.368615 + 0.118706i
\(529\) −9.31679 12.8235i −0.405078 0.557542i
\(530\) 0 0
\(531\) −12.0594 + 8.85835i −0.523333 + 0.384420i
\(532\) −0.0735370 + 0.0735370i −0.00318823 + 0.00318823i
\(533\) −9.19295 + 1.45602i −0.398191 + 0.0630672i
\(534\) −8.56457 + 16.9181i −0.370625 + 0.732118i
\(535\) 0 0
\(536\) 14.2901 4.64313i 0.617237 0.200553i
\(537\) 6.39325 + 19.5028i 0.275889 + 0.841607i
\(538\) −21.5305 + 10.9703i −0.928246 + 0.472965i
\(539\) 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 \(0.951304\pi\)
\(542\) −1.81078 11.4328i −0.0777797 0.491082i
\(543\) 24.0428 17.5643i 1.03177 0.753757i
\(544\) −2.86572 + 3.94433i −0.122867 + 0.169112i
\(545\) 0 0
\(546\) 0.494756 0.253722i 0.0211736 0.0108583i
\(547\) 6.82585 43.0967i 0.291852 1.84268i −0.209965 0.977709i \(-0.567335\pi\)
0.501817 0.864974i \(-0.332665\pi\)
\(548\) −2.51567 1.28180i −0.107464 0.0547557i
\(549\) −12.4467 + 38.9995i −0.531211 + 1.66446i
\(550\) 0 0
\(551\) 4.52004i 0.192560i
\(552\) −2.71235 + 3.75382i −0.115445 + 0.159773i
\(553\) −0.466353 0.0738630i −0.0198313 0.00314098i
\(554\) 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 \(-0.0358615\pi\)
−0.112424 + 0.993660i \(0.535861\pi\)
\(558\) −6.74528 1.03223i −0.285551 0.0436976i
\(559\) 5.44220 + 1.76828i 0.230181 + 0.0747902i
\(560\) 0 0
\(561\) −42.8322 + 6.89878i −1.80838 + 0.291267i
\(562\) 10.7198 + 21.0388i 0.452187 + 0.887467i
\(563\) 7.14045 + 14.0139i 0.300934 + 0.590616i 0.991113 0.133022i \(-0.0424682\pi\)
−0.690179 + 0.723639i \(0.742468\pi\)
\(564\) 17.3602 2.79613i 0.730996 0.117738i
\(565\) 0 0
\(566\) −9.36284 3.04217i −0.393550 0.127872i
\(567\) −1.74105 0.864300i −0.0731174 0.0362972i
\(568\) −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 \(0.992676\pi\)
\(572\) 7.54225 + 1.19457i 0.315357 + 0.0499477i
\(573\) −5.01468 + 6.94020i −0.209491 + 0.289931i
\(574\) 1.35243i 0.0564492i
\(575\) 0 0
\(576\) −2.85798 0.912121i −0.119082 0.0380050i
\(577\) 16.8154 + 8.56788i 0.700034 + 0.356685i 0.767511 0.641036i \(-0.221495\pi\)
−0.0674769 + 0.997721i \(0.521495\pi\)
\(578\) 1.05907 6.68673i 0.0440517 0.278131i
\(579\) 5.19519 2.66421i 0.215905 0.110721i
\(580\) 0 0
\(581\) −0.634802 + 0.873729i −0.0263360 + 0.0362484i
\(582\) −14.1149 + 10.3116i −0.585083 + 0.427429i
\(583\) −6.18173 39.0299i −0.256021 1.61645i
\(584\) −2.90012 + 8.92565i −0.120008 + 0.369346i
\(585\) 0 0
\(586\) 1.45939 + 4.49153i 0.0602867 + 0.185543i
\(587\) 4.14963 2.11434i 0.171274 0.0872683i −0.366252 0.930516i \(-0.619359\pi\)
0.537526 + 0.843247i \(0.319359\pi\)
\(588\) −3.75160 11.4443i −0.154713 0.471957i
\(589\) 1.04166 0.338457i 0.0429210 0.0139459i
\(590\) 0 0
\(591\) 5.73558 11.3298i 0.235930 0.466047i
\(592\) 4.25195 0.673443i 0.174754 0.0276783i
\(593\) −32.4687 + 32.4687i −1.33333 + 1.33333i −0.430960 + 0.902371i \(0.641825\pi\)
−0.902371 + 0.430960i \(0.858175\pi\)
\(594\) −12.3057 23.6901i −0.504907 0.972015i
\(595\) 0 0
\(596\) 4.53982 + 6.24853i 0.185958 + 0.255950i
\(597\) −13.7529 4.42888i −0.562870 0.181262i
\(598\) −1.80428 + 3.54111i −0.0737826 + 0.144807i
\(599\) −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 \(0.506374\pi\)
\(602\) −0.377480 + 0.740847i −0.0153850 + 0.0301947i
\(603\) −40.2698 20.2540i −1.63991 0.824807i
\(604\) 8.69147 + 11.9628i 0.353651 + 0.486759i
\(605\) 0 0
\(606\) −11.6498 + 11.7109i −0.473241 + 0.475722i
\(607\) −2.39455 + 2.39455i −0.0971917 + 0.0971917i −0.754031 0.656839i \(-0.771893\pi\)
0.656839 + 0.754031i \(0.271893\pi\)
\(608\) 0.475594 0.0753267i 0.0192879 0.00305490i
\(609\) 3.13292 + 1.58600i 0.126952 + 0.0642679i
\(610\) 0 0
\(611\) 14.3512 4.66298i 0.580586 0.188644i
\(612\) 14.4341 2.36357i 0.583465 0.0955415i
\(613\) −12.2470 + 6.24017i −0.494653 + 0.252038i −0.683476 0.729973i \(-0.739533\pi\)
0.188823 + 0.982011i \(0.439533\pi\)
\(614\) −5.16261 15.8889i −0.208346 0.641223i
\(615\) 0 0
\(616\) −0.342880 + 1.05528i −0.0138150 + 0.0425183i
\(617\) 1.60431 + 10.1292i 0.0645872 + 0.407787i 0.998707 + 0.0508287i \(0.0161863\pi\)
−0.934120 + 0.356959i \(0.883814\pi\)
\(618\) 10.3336 + 14.1451i 0.415679 + 0.568999i
\(619\) −27.3325 + 37.6199i −1.09859 + 1.51207i −0.261338 + 0.965247i \(0.584164\pi\)
−0.837247 + 0.546825i \(0.815836\pi\)
\(620\) 0 0
\(621\) 13.7051 2.28099i 0.549966 0.0915329i
\(622\) −4.72465 + 29.8303i −0.189441 + 1.19608i
\(623\) −2.10678 1.07346i −0.0844063 0.0430072i
\(624\) −2.54381 0.396086i −0.101834 0.0158561i
\(625\) 0 0
\(626\) 16.6805i 0.666686i
\(627\) 3.47306 + 2.50948i 0.138701 + 0.100219i
\(628\) 16.1947 + 2.56499i 0.646239 + 0.102354i
\(629\) −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
\(633\) 7.42591 0.0194127i 0.295153 0.000771586i
\(634\) −10.3155 3.35172i −0.409683 0.133114i
\(635\) 0 0
\(636\) 2.11847 + 13.1529i 0.0840030 + 0.521546i
\(637\) −4.69209 9.20875i −0.185907 0.364864i
\(638\) 21.8942 + 42.9697i 0.866798 + 1.70119i
\(639\) 0.190290 + 36.3955i 0.00752777 + 1.43978i
\(640\) 0 0
\(641\) 0.702023 + 0.228101i 0.0277282 + 0.00900945i 0.322848 0.946451i \(-0.395360\pi\)
−0.295120 + 0.955460i \(0.595360\pi\)
\(642\) 0.0500024 + 19.1273i 0.00197344 + 0.754896i
\(643\) 17.1573 + 17.1573i 0.676616 + 0.676616i 0.959233 0.282617i \(-0.0912025\pi\)
−0.282617 + 0.959233i \(0.591203\pi\)
\(644\) −0.467192 0.339435i −0.0184099 0.0133756i
\(645\) 0 0
\(646\) −1.89928 + 1.37991i −0.0747262 + 0.0542918i
\(647\) 5.95524 + 0.943217i 0.234125 + 0.0370817i 0.272394 0.962186i \(-0.412185\pi\)
−0.0382696 + 0.999267i \(0.512185\pi\)
\(648\) 4.16954 + 7.97590i 0.163795 + 0.313323i
\(649\) 25.6248i 1.00586i
\(650\) 0 0
\(651\) 0.130910 0.840754i 0.00513078 0.0329517i
\(652\) −3.61543 1.84215i −0.141591 0.0721443i
\(653\) 1.57981 9.97451i 0.0618226 0.390333i −0.937303 0.348516i \(-0.886686\pi\)
0.999125 0.0418163i \(-0.0133144\pi\)
\(654\) 4.84657 + 9.45078i 0.189516 + 0.369555i
\(655\) 0 0
\(656\) −3.68068 + 5.06602i −0.143706 + 0.197795i
\(657\) 25.0191 12.9131i 0.976087 0.503787i
\(658\) 0.342999 + 2.16561i 0.0133715 + 0.0844242i
\(659\) −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 \(0.600881\pi\)
\(662\) 8.58467 4.37411i 0.333653 0.170005i
\(663\) 11.9272 3.90987i 0.463213 0.151847i
\(664\) 4.75577 1.54524i 0.184560 0.0599671i
\(665\) 0 0
\(666\) −10.4879 7.53643i −0.406397 0.292031i
\(667\) −24.7901 + 3.92637i −0.959877 + 0.152030i
\(668\) −9.78704 + 9.78704i −0.378672 + 0.378672i
\(669\) 0.897530 + 0.892849i 0.0347005 + 0.0345195i
\(670\) 0 0
\(671\) −41.2074 56.7171i −1.59079 2.18954i
\(672\) 0.114667 0.356073i 0.00442337 0.0137358i
\(673\) 12.1800 23.9046i 0.469504 0.921454i −0.527890 0.849313i \(-0.677017\pi\)
0.997394 0.0721411i \(-0.0229832\pi\)
\(674\) −28.1544 −1.08447
\(675\) 0 0
\(676\) 10.7907 0.415028
\(677\) 10.0184 19.6621i 0.385037 0.755677i −0.614408 0.788988i \(-0.710605\pi\)
0.999445 + 0.0333112i \(0.0106052\pi\)
\(678\) −5.83277 + 18.1124i −0.224006 + 0.695602i
\(679\) −1.28118 1.76340i −0.0491673 0.0676729i
\(680\) 0 0
\(681\) 4.06529 + 4.04409i 0.155782 + 0.154970i
\(682\) 8.26315 8.26315i 0.316413 0.316413i
\(683\) −19.3379 + 3.06282i −0.739944 + 0.117196i −0.515017 0.857180i \(-0.672214\pi\)
−0.224927 + 0.974376i \(0.572214\pi\)
\(684\) −1.17310 0.842973i −0.0448547 0.0322319i
\(685\) 0 0
\(686\) 2.86609 0.931249i 0.109428 0.0355552i
\(687\) 17.3670 5.69313i 0.662594 0.217207i
\(688\) 3.43023 1.74779i 0.130776 0.0666339i
\(689\) 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 \(-0.182958\pi\)
\(692\) 0.142061 + 0.896939i 0.00540036 + 0.0340965i
\(693\) 2.95800 1.52671i 0.112365 0.0579949i
\(694\) 11.3510 15.6232i 0.430876 0.593050i
\(695\) 0 0
\(696\) −7.41915 14.4673i −0.281222 0.548381i
\(697\) 4.77592 30.1540i 0.180901 1.14216i
\(698\) −12.8411 6.54286i −0.486042 0.247651i
\(699\) 3.35470 21.5451i 0.126886 0.814912i
\(700\) 0 0
\(701\) 1.34594i 0.0508356i 0.999677 + 0.0254178i \(0.00809161\pi\)
−0.999677 + 0.0254178i \(0.991908\pi\)
\(702\) 4.58855 + 6.21255i 0.173184 + 0.234478i
\(703\) 2.04741 + 0.324278i 0.0772195 + 0.0122304i
\(704\) 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
\(708\) 0.0225840 + 8.63901i 0.000848758 + 0.324674i
\(709\) 5.99345 + 1.94739i 0.225089 + 0.0731358i 0.419390 0.907806i \(-0.362244\pi\)
−0.194301 + 0.980942i \(0.562244\pi\)
\(710\) 0 0
\(711\) −0.0342906 6.55851i −0.00128600 0.245963i
\(712\) 4.97027 + 9.75471i 0.186269 + 0.365573i
\(713\) 2.76112 + 5.41900i 0.103405 + 0.202943i
\(714\) 0.290016 + 1.80061i 0.0108536 + 0.0673861i
\(715\) 0 0
\(716\) 11.2695 + 3.66170i 0.421163 + 0.136844i
\(717\) −20.3435 + 0.0531816i −0.759740 + 0.00198610i
\(718\) 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
\(722\) −18.5371 2.93598i −0.689878 0.109266i
\(723\) −1.70755 1.23380i −0.0635043 0.0458854i
\(724\) 17.1907i 0.638888i
\(725\) 0 0
\(726\) 26.3463 + 4.10228i 0.977805 + 0.152250i
\(727\) 11.0417 + 5.62601i 0.409513 + 0.208657i 0.646597 0.762832i \(-0.276192\pi\)
−0.237084 + 0.971489i \(0.576192\pi\)
\(728\) 0.0502184 0.317066i 0.00186122 0.0117513i
\(729\) 7.93968 25.8062i 0.294062 0.955786i
\(730\) 0 0
\(731\) −11.0326 + 15.1850i −0.408055 + 0.561639i
\(732\) 13.9424 + 19.0850i 0.515327 + 0.705401i
\(733\) 1.46889 + 9.27418i 0.0542545 + 0.342550i 0.999852 + 0.0172103i \(0.00547849\pi\)
−0.945597 + 0.325339i \(0.894522\pi\)
\(734\) −0.998039 + 3.07165i −0.0368383 + 0.113377i
\(735\) 0 0
\(736\) 0.826257 + 2.54296i 0.0304562 + 0.0937346i
\(737\) 68.7804 35.0454i 2.53356 1.29091i
\(738\) 18.5389 3.03572i 0.682428 0.111746i
\(739\) 18.0916 5.87832i 0.665511 0.216238i 0.0432699 0.999063i \(-0.486222\pi\)
0.622241 + 0.782826i \(0.286222\pi\)
\(740\) 0 0
\(741\) −1.10601 0.559904i −0.0406304 0.0205686i
\(742\) −1.64077 + 0.259872i −0.0602344 + 0.00954019i
\(743\) −23.1938 + 23.1938i −0.850899 + 0.850899i −0.990244 0.139345i \(-0.955500\pi\)
0.139345 + 0.990244i \(0.455500\pi\)
\(744\) −2.77851 + 2.79308i −0.101865 + 0.102399i
\(745\) 0 0
\(746\) −6.36867 8.76572i −0.233174 0.320936i
\(747\) −13.4019 6.74058i −0.490350 0.246625i
\(748\) −11.3715 + 22.3178i −0.415783 + 0.816020i
\(749\) −2.38506 −0.0871483
\(750\) 0 0
\(751\) 35.1267 1.28179 0.640895 0.767628i \(-0.278563\pi\)
0.640895 + 0.767628i \(0.278563\pi\)
\(752\) 4.60895 9.04558i 0.168071 0.329858i
\(753\) 37.2803 + 12.0054i 1.35857 + 0.437502i
\(754\) −8.20106 11.2878i −0.298665 0.411077i
\(755\) 0 0
\(756\) −0.995899 + 0.517314i −0.0362205 + 0.0188145i
\(757\) 20.0652 20.0652i 0.729283 0.729283i −0.241194 0.970477i \(-0.577539\pi\)
0.970477 + 0.241194i \(0.0775389\pi\)
\(758\) 33.0785 5.23911i 1.20146 0.190293i
\(759\) −10.7463 + 21.2279i −0.390067 + 0.770523i
\(760\) 0 0
\(761\) −30.4666 + 9.89919i −1.10441 + 0.358845i −0.803799 0.594901i \(-0.797191\pi\)
−0.300613 + 0.953746i \(0.597191\pi\)
\(762\) 8.11294 + 24.7487i 0.293901 + 0.896552i
\(763\) −1.18003 + 0.601254i −0.0427199 + 0.0217669i
\(764\) 1.52761 + 4.70151i 0.0552671 + 0.170095i
\(765\) 0 0
\(766\) −5.02104 + 15.4532i −0.181418 + 0.558346i
\(767\) 1.15975 + 7.32235i 0.0418760 + 0.264395i
\(768\) −1.39859 + 1.02173i −0.0504674 + 0.0368686i
\(769\) 8.74366 12.0346i 0.315305 0.433980i −0.621722 0.783238i \(-0.713567\pi\)
0.937026 + 0.349259i \(0.113567\pi\)
\(770\) 0 0
\(771\) −6.50470 + 3.33576i −0.234261 + 0.120134i
\(772\) 0.527318 3.32936i 0.0189786 0.119826i
\(773\) −19.8204 10.0990i −0.712889 0.363235i 0.0596354 0.998220i \(-0.481006\pi\)
−0.772524 + 0.634985i \(0.781006\pi\)
\(774\) −11.0028 3.51152i −0.395486 0.126219i
\(775\) 0 0
\(776\) 10.0922i 0.362290i
\(777\) 0.943161 1.30531i 0.0338357 0.0468278i
\(778\) −2.57264 0.407467i −0.0922337 0.0146084i
\(779\) −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