Properties

Label 804.2.e.a.535.31
Level 804
Weight 2
Character 804.535
Analytic conductor 6.420
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(34\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 535.31
Character \(\chi\) = 804.535
Dual form 804.2.e.a.535.32

$q$-expansion

\(f(q)\) \(=\) \(q+(1.36992 - 0.351182i) q^{2} -1.00000 q^{3} +(1.75334 - 0.962180i) q^{4} -3.58679i q^{5} +(-1.36992 + 0.351182i) q^{6} +4.07396 q^{7} +(2.06403 - 1.93385i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(1.36992 - 0.351182i) q^{2} -1.00000 q^{3} +(1.75334 - 0.962180i) q^{4} -3.58679i q^{5} +(-1.36992 + 0.351182i) q^{6} +4.07396 q^{7} +(2.06403 - 1.93385i) q^{8} +1.00000 q^{9} +(-1.25962 - 4.91361i) q^{10} -4.30204 q^{11} +(-1.75334 + 0.962180i) q^{12} -0.588657i q^{13} +(5.58098 - 1.43070i) q^{14} +3.58679i q^{15} +(2.14842 - 3.37406i) q^{16} +0.330562 q^{17} +(1.36992 - 0.351182i) q^{18} +5.25211i q^{19} +(-3.45114 - 6.28888i) q^{20} -4.07396 q^{21} +(-5.89344 + 1.51080i) q^{22} -0.501468i q^{23} +(-2.06403 + 1.93385i) q^{24} -7.86509 q^{25} +(-0.206726 - 0.806411i) q^{26} -1.00000 q^{27} +(7.14304 - 3.91988i) q^{28} -5.91148 q^{29} +(1.25962 + 4.91361i) q^{30} +5.74994 q^{31} +(1.75825 - 5.37667i) q^{32} +4.30204 q^{33} +(0.452843 - 0.116088i) q^{34} -14.6124i q^{35} +(1.75334 - 0.962180i) q^{36} -1.03067 q^{37} +(1.84445 + 7.19495i) q^{38} +0.588657i q^{39} +(-6.93632 - 7.40326i) q^{40} -7.04610i q^{41} +(-5.58098 + 1.43070i) q^{42} +6.86370 q^{43} +(-7.54296 + 4.13934i) q^{44} -3.58679i q^{45} +(-0.176106 - 0.686969i) q^{46} +10.3763i q^{47} +(-2.14842 + 3.37406i) q^{48} +9.59712 q^{49} +(-10.7745 + 2.76208i) q^{50} -0.330562 q^{51} +(-0.566394 - 1.03212i) q^{52} +8.47969i q^{53} +(-1.36992 + 0.351182i) q^{54} +15.4305i q^{55} +(8.40878 - 7.87842i) q^{56} -5.25211i q^{57} +(-8.09823 + 2.07601i) q^{58} -8.93686i q^{59} +(3.45114 + 6.28888i) q^{60} -6.57062i q^{61} +(7.87693 - 2.01927i) q^{62} +4.07396 q^{63} +(0.520460 - 7.98305i) q^{64} -2.11139 q^{65} +(5.89344 - 1.51080i) q^{66} +(4.33838 - 6.94107i) q^{67} +(0.579589 - 0.318061i) q^{68} +0.501468i q^{69} +(-5.13163 - 20.0178i) q^{70} +0.0930167i q^{71} +(2.06403 - 1.93385i) q^{72} -6.32174 q^{73} +(-1.41193 + 0.361951i) q^{74} +7.86509 q^{75} +(5.05348 + 9.20875i) q^{76} -17.5263 q^{77} +(0.206726 + 0.806411i) q^{78} -1.43384 q^{79} +(-12.1021 - 7.70594i) q^{80} +1.00000 q^{81} +(-2.47446 - 9.65256i) q^{82} +12.5742i q^{83} +(-7.14304 + 3.91988i) q^{84} -1.18566i q^{85} +(9.40270 - 2.41041i) q^{86} +5.91148 q^{87} +(-8.87956 + 8.31950i) q^{88} +18.3287 q^{89} +(-1.25962 - 4.91361i) q^{90} -2.39816i q^{91} +(-0.482502 - 0.879244i) q^{92} -5.74994 q^{93} +(3.64395 + 14.2146i) q^{94} +18.8382 q^{95} +(-1.75825 + 5.37667i) q^{96} +6.83533i q^{97} +(13.1473 - 3.37034i) q^{98} -4.30204 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 34q^{3} + 2q^{4} - 4q^{7} + 6q^{8} + 34q^{9} + O(q^{10}) \) \( 34q - 34q^{3} + 2q^{4} - 4q^{7} + 6q^{8} + 34q^{9} - 6q^{10} - 2q^{12} - 4q^{14} + 2q^{16} + 12q^{20} + 4q^{21} - 8q^{22} - 6q^{24} - 34q^{25} + 10q^{26} - 34q^{27} + 8q^{28} - 16q^{29} + 6q^{30} + 4q^{31} + 2q^{36} + 12q^{37} - 26q^{38} - 18q^{40} + 4q^{42} + 4q^{43} - 26q^{44} + 4q^{46} - 2q^{48} + 46q^{49} + 18q^{50} - 32q^{52} + 14q^{56} - 4q^{58} - 12q^{60} - 2q^{62} - 4q^{63} + 26q^{64} + 8q^{66} + 18q^{67} - 34q^{68} - 56q^{70} + 6q^{72} + 12q^{73} - 22q^{74} + 34q^{75} - 32q^{76} - 8q^{77} - 10q^{78} + 12q^{79} + 2q^{80} + 34q^{81} + 26q^{82} - 8q^{84} + 6q^{86} + 16q^{87} - 28q^{88} - 6q^{90} - 46q^{92} - 4q^{93} - 32q^{94} + 40q^{95} + 40q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36992 0.351182i 0.968677 0.248323i
\(3\) −1.00000 −0.577350
\(4\) 1.75334 0.962180i 0.876671 0.481090i
\(5\) 3.58679i 1.60406i −0.597282 0.802031i \(-0.703753\pi\)
0.597282 0.802031i \(-0.296247\pi\)
\(6\) −1.36992 + 0.351182i −0.559266 + 0.143369i
\(7\) 4.07396 1.53981 0.769905 0.638158i \(-0.220303\pi\)
0.769905 + 0.638158i \(0.220303\pi\)
\(8\) 2.06403 1.93385i 0.729746 0.683719i
\(9\) 1.00000 0.333333
\(10\) −1.25962 4.91361i −0.398326 1.55382i
\(11\) −4.30204 −1.29712 −0.648558 0.761166i \(-0.724627\pi\)
−0.648558 + 0.761166i \(0.724627\pi\)
\(12\) −1.75334 + 0.962180i −0.506146 + 0.277757i
\(13\) 0.588657i 0.163264i −0.996663 0.0816321i \(-0.973987\pi\)
0.996663 0.0816321i \(-0.0260132\pi\)
\(14\) 5.58098 1.43070i 1.49158 0.382371i
\(15\) 3.58679i 0.926106i
\(16\) 2.14842 3.37406i 0.537105 0.843516i
\(17\) 0.330562 0.0801732 0.0400866 0.999196i \(-0.487237\pi\)
0.0400866 + 0.999196i \(0.487237\pi\)
\(18\) 1.36992 0.351182i 0.322892 0.0827744i
\(19\) 5.25211i 1.20492i 0.798150 + 0.602458i \(0.205812\pi\)
−0.798150 + 0.602458i \(0.794188\pi\)
\(20\) −3.45114 6.28888i −0.771699 1.40624i
\(21\) −4.07396 −0.889010
\(22\) −5.89344 + 1.51080i −1.25649 + 0.322104i
\(23\) 0.501468i 0.104563i −0.998632 0.0522816i \(-0.983351\pi\)
0.998632 0.0522816i \(-0.0166493\pi\)
\(24\) −2.06403 + 1.93385i −0.421319 + 0.394745i
\(25\) −7.86509 −1.57302
\(26\) −0.206726 0.806411i −0.0405423 0.158150i
\(27\) −1.00000 −0.192450
\(28\) 7.14304 3.91988i 1.34991 0.740788i
\(29\) −5.91148 −1.09773 −0.548867 0.835910i \(-0.684941\pi\)
−0.548867 + 0.835910i \(0.684941\pi\)
\(30\) 1.25962 + 4.91361i 0.229974 + 0.897098i
\(31\) 5.74994 1.03272 0.516359 0.856372i \(-0.327287\pi\)
0.516359 + 0.856372i \(0.327287\pi\)
\(32\) 1.75825 5.37667i 0.310817 0.950470i
\(33\) 4.30204 0.748890
\(34\) 0.452843 0.116088i 0.0776619 0.0199089i
\(35\) 14.6124i 2.46995i
\(36\) 1.75334 0.962180i 0.292224 0.160363i
\(37\) −1.03067 −0.169440 −0.0847202 0.996405i \(-0.527000\pi\)
−0.0847202 + 0.996405i \(0.527000\pi\)
\(38\) 1.84445 + 7.19495i 0.299209 + 1.16718i
\(39\) 0.588657i 0.0942606i
\(40\) −6.93632 7.40326i −1.09673 1.17056i
\(41\) 7.04610i 1.10042i −0.835028 0.550208i \(-0.814549\pi\)
0.835028 0.550208i \(-0.185451\pi\)
\(42\) −5.58098 + 1.43070i −0.861164 + 0.220762i
\(43\) 6.86370 1.04671 0.523353 0.852116i \(-0.324681\pi\)
0.523353 + 0.852116i \(0.324681\pi\)
\(44\) −7.54296 + 4.13934i −1.13714 + 0.624029i
\(45\) 3.58679i 0.534688i
\(46\) −0.176106 0.686969i −0.0259655 0.101288i
\(47\) 10.3763i 1.51353i 0.653686 + 0.756766i \(0.273222\pi\)
−0.653686 + 0.756766i \(0.726778\pi\)
\(48\) −2.14842 + 3.37406i −0.310098 + 0.487004i
\(49\) 9.59712 1.37102
\(50\) −10.7745 + 2.76208i −1.52375 + 0.390617i
\(51\) −0.330562 −0.0462880
\(52\) −0.566394 1.03212i −0.0785447 0.143129i
\(53\) 8.47969i 1.16477i 0.812911 + 0.582387i \(0.197881\pi\)
−0.812911 + 0.582387i \(0.802119\pi\)
\(54\) −1.36992 + 0.351182i −0.186422 + 0.0477898i
\(55\) 15.4305i 2.08065i
\(56\) 8.40878 7.87842i 1.12367 1.05280i
\(57\) 5.25211i 0.695659i
\(58\) −8.09823 + 2.07601i −1.06335 + 0.272593i
\(59\) 8.93686i 1.16348i −0.813375 0.581740i \(-0.802372\pi\)
0.813375 0.581740i \(-0.197628\pi\)
\(60\) 3.45114 + 6.28888i 0.445540 + 0.811891i
\(61\) 6.57062i 0.841282i −0.907227 0.420641i \(-0.861805\pi\)
0.907227 0.420641i \(-0.138195\pi\)
\(62\) 7.87693 2.01927i 1.00037 0.256448i
\(63\) 4.07396 0.513270
\(64\) 0.520460 7.98305i 0.0650574 0.997882i
\(65\) −2.11139 −0.261886
\(66\) 5.89344 1.51080i 0.725433 0.185967i
\(67\) 4.33838 6.94107i 0.530018 0.847987i
\(68\) 0.579589 0.318061i 0.0702855 0.0385705i
\(69\) 0.501468i 0.0603696i
\(70\) −5.13163 20.0178i −0.613347 2.39259i
\(71\) 0.0930167i 0.0110391i 0.999985 + 0.00551953i \(0.00175693\pi\)
−0.999985 + 0.00551953i \(0.998243\pi\)
\(72\) 2.06403 1.93385i 0.243249 0.227906i
\(73\) −6.32174 −0.739903 −0.369952 0.929051i \(-0.620626\pi\)
−0.369952 + 0.929051i \(0.620626\pi\)
\(74\) −1.41193 + 0.361951i −0.164133 + 0.0420760i
\(75\) 7.86509 0.908182
\(76\) 5.05348 + 9.20875i 0.579673 + 1.05632i
\(77\) −17.5263 −1.99731
\(78\) 0.206726 + 0.806411i 0.0234071 + 0.0913081i
\(79\) −1.43384 −0.161319 −0.0806596 0.996742i \(-0.525703\pi\)
−0.0806596 + 0.996742i \(0.525703\pi\)
\(80\) −12.1021 7.70594i −1.35305 0.861550i
\(81\) 1.00000 0.111111
\(82\) −2.47446 9.65256i −0.273259 1.06595i
\(83\) 12.5742i 1.38020i 0.723715 + 0.690099i \(0.242433\pi\)
−0.723715 + 0.690099i \(0.757567\pi\)
\(84\) −7.14304 + 3.91988i −0.779370 + 0.427694i
\(85\) 1.18566i 0.128603i
\(86\) 9.40270 2.41041i 1.01392 0.259921i
\(87\) 5.91148 0.633777
\(88\) −8.87956 + 8.31950i −0.946564 + 0.886862i
\(89\) 18.3287 1.94284 0.971420 0.237368i \(-0.0762846\pi\)
0.971420 + 0.237368i \(0.0762846\pi\)
\(90\) −1.25962 4.91361i −0.132775 0.517940i
\(91\) 2.39816i 0.251396i
\(92\) −0.482502 0.879244i −0.0503043 0.0916676i
\(93\) −5.74994 −0.596241
\(94\) 3.64395 + 14.2146i 0.375845 + 1.46612i
\(95\) 18.8382 1.93276
\(96\) −1.75825 + 5.37667i −0.179450 + 0.548754i
\(97\) 6.83533i 0.694022i 0.937861 + 0.347011i \(0.112803\pi\)
−0.937861 + 0.347011i \(0.887197\pi\)
\(98\) 13.1473 3.37034i 1.32807 0.340455i
\(99\) −4.30204 −0.432372
\(100\) −13.7902 + 7.56763i −1.37902 + 0.756763i
\(101\) 6.18058i 0.614991i 0.951550 + 0.307495i \(0.0994908\pi\)
−0.951550 + 0.307495i \(0.900509\pi\)
\(102\) −0.452843 + 0.116088i −0.0448381 + 0.0114944i
\(103\) 20.2293i 1.99325i 0.0820875 + 0.996625i \(0.473841\pi\)
−0.0820875 + 0.996625i \(0.526159\pi\)
\(104\) −1.13837 1.21501i −0.111627 0.119141i
\(105\) 14.6124i 1.42603i
\(106\) 2.97791 + 11.6165i 0.289240 + 1.12829i
\(107\) 5.29024i 0.511427i 0.966753 + 0.255713i \(0.0823103\pi\)
−0.966753 + 0.255713i \(0.917690\pi\)
\(108\) −1.75334 + 0.962180i −0.168715 + 0.0925858i
\(109\) 6.13549i 0.587673i 0.955856 + 0.293837i \(0.0949322\pi\)
−0.955856 + 0.293837i \(0.905068\pi\)
\(110\) 5.41893 + 21.1386i 0.516675 + 2.01548i
\(111\) 1.03067 0.0978264
\(112\) 8.75257 13.7458i 0.827040 1.29885i
\(113\) 4.41158i 0.415007i 0.978234 + 0.207503i \(0.0665338\pi\)
−0.978234 + 0.207503i \(0.933466\pi\)
\(114\) −1.84445 7.19495i −0.172748 0.673869i
\(115\) −1.79866 −0.167726
\(116\) −10.3648 + 5.68791i −0.962352 + 0.528109i
\(117\) 0.588657i 0.0544214i
\(118\) −3.13847 12.2428i −0.288919 1.12704i
\(119\) 1.34670 0.123452
\(120\) 6.93632 + 7.40326i 0.633196 + 0.675822i
\(121\) 7.50759 0.682508
\(122\) −2.30748 9.00121i −0.208910 0.814931i
\(123\) 7.04610i 0.635325i
\(124\) 10.0816 5.53247i 0.905355 0.496831i
\(125\) 10.2765i 0.919156i
\(126\) 5.58098 1.43070i 0.497193 0.127457i
\(127\) 14.7447i 1.30838i −0.756330 0.654190i \(-0.773010\pi\)
0.756330 0.654190i \(-0.226990\pi\)
\(128\) −2.09052 11.1189i −0.184777 0.982780i
\(129\) −6.86370 −0.604315
\(130\) −2.89243 + 0.741483i −0.253683 + 0.0650323i
\(131\) 20.6777i 1.80662i 0.428993 + 0.903308i \(0.358868\pi\)
−0.428993 + 0.903308i \(0.641132\pi\)
\(132\) 7.54296 4.13934i 0.656530 0.360283i
\(133\) 21.3969i 1.85534i
\(134\) 3.50564 11.0322i 0.302841 0.953041i
\(135\) 3.58679i 0.308702i
\(136\) 0.682292 0.639258i 0.0585060 0.0548159i
\(137\) 14.5696i 1.24477i −0.782712 0.622384i \(-0.786164\pi\)
0.782712 0.622384i \(-0.213836\pi\)
\(138\) 0.176106 + 0.686969i 0.0149912 + 0.0584787i
\(139\) −17.9896 −1.52586 −0.762930 0.646481i \(-0.776240\pi\)
−0.762930 + 0.646481i \(0.776240\pi\)
\(140\) −14.0598 25.6206i −1.18827 2.16534i
\(141\) 10.3763i 0.873838i
\(142\) 0.0326658 + 0.127425i 0.00274125 + 0.0106933i
\(143\) 2.53243i 0.211772i
\(144\) 2.14842 3.37406i 0.179035 0.281172i
\(145\) 21.2033i 1.76083i
\(146\) −8.66025 + 2.22008i −0.716727 + 0.183735i
\(147\) −9.59712 −0.791557
\(148\) −1.80711 + 0.991685i −0.148543 + 0.0815160i
\(149\) 17.7725 1.45598 0.727990 0.685588i \(-0.240455\pi\)
0.727990 + 0.685588i \(0.240455\pi\)
\(150\) 10.7745 2.76208i 0.879735 0.225523i
\(151\) 2.76841i 0.225290i 0.993635 + 0.112645i \(0.0359322\pi\)
−0.993635 + 0.112645i \(0.964068\pi\)
\(152\) 10.1568 + 10.8405i 0.823824 + 0.879283i
\(153\) 0.330562 0.0267244
\(154\) −24.0096 + 6.15494i −1.93475 + 0.495979i
\(155\) 20.6238i 1.65655i
\(156\) 0.566394 + 1.03212i 0.0453478 + 0.0826356i
\(157\) 7.09583 0.566309 0.283154 0.959074i \(-0.408619\pi\)
0.283154 + 0.959074i \(0.408619\pi\)
\(158\) −1.96424 + 0.503537i −0.156266 + 0.0400593i
\(159\) 8.47969i 0.672483i
\(160\) −19.2850 6.30646i −1.52461 0.498570i
\(161\) 2.04296i 0.161008i
\(162\) 1.36992 0.351182i 0.107631 0.0275915i
\(163\) 4.97600i 0.389751i −0.980828 0.194875i \(-0.937570\pi\)
0.980828 0.194875i \(-0.0624302\pi\)
\(164\) −6.77961 12.3542i −0.529399 0.964703i
\(165\) 15.4305i 1.20127i
\(166\) 4.41583 + 17.2256i 0.342735 + 1.33697i
\(167\) 5.01857i 0.388349i 0.980967 + 0.194174i \(0.0622028\pi\)
−0.980967 + 0.194174i \(0.937797\pi\)
\(168\) −8.40878 + 7.87842i −0.648751 + 0.607833i
\(169\) 12.6535 0.973345
\(170\) −0.416382 1.62425i −0.0319351 0.124575i
\(171\) 5.25211i 0.401639i
\(172\) 12.0344 6.60412i 0.917616 0.503559i
\(173\) −11.2641 −0.856397 −0.428199 0.903685i \(-0.640852\pi\)
−0.428199 + 0.903685i \(0.640852\pi\)
\(174\) 8.09823 2.07601i 0.613926 0.157382i
\(175\) −32.0420 −2.42215
\(176\) −9.24260 + 14.5154i −0.696687 + 1.09414i
\(177\) 8.93686i 0.671736i
\(178\) 25.1088 6.43671i 1.88198 0.482452i
\(179\) −21.4107 −1.60031 −0.800156 0.599792i \(-0.795250\pi\)
−0.800156 + 0.599792i \(0.795250\pi\)
\(180\) −3.45114 6.28888i −0.257233 0.468745i
\(181\) −5.39768 −0.401206 −0.200603 0.979673i \(-0.564290\pi\)
−0.200603 + 0.979673i \(0.564290\pi\)
\(182\) −0.842192 3.28528i −0.0624274 0.243521i
\(183\) 6.57062i 0.485714i
\(184\) −0.969762 1.03505i −0.0714918 0.0763046i
\(185\) 3.69678i 0.271793i
\(186\) −7.87693 + 2.01927i −0.577565 + 0.148060i
\(187\) −1.42209 −0.103994
\(188\) 9.98382 + 18.1931i 0.728145 + 1.32687i
\(189\) −4.07396 −0.296337
\(190\) 25.8068 6.61565i 1.87222 0.479950i
\(191\) −4.14224 −0.299722 −0.149861 0.988707i \(-0.547883\pi\)
−0.149861 + 0.988707i \(0.547883\pi\)
\(192\) −0.520460 + 7.98305i −0.0375609 + 0.576127i
\(193\) 21.8440 1.57237 0.786183 0.617994i \(-0.212054\pi\)
0.786183 + 0.617994i \(0.212054\pi\)
\(194\) 2.40044 + 9.36383i 0.172342 + 0.672284i
\(195\) 2.11139 0.151200
\(196\) 16.8270 9.23416i 1.20193 0.659583i
\(197\) 25.7830i 1.83696i −0.395464 0.918481i \(-0.629416\pi\)
0.395464 0.918481i \(-0.370584\pi\)
\(198\) −5.89344 + 1.51080i −0.418829 + 0.107368i
\(199\) 9.34594i 0.662516i 0.943540 + 0.331258i \(0.107473\pi\)
−0.943540 + 0.331258i \(0.892527\pi\)
\(200\) −16.2338 + 15.2099i −1.14790 + 1.07550i
\(201\) −4.33838 + 6.94107i −0.306006 + 0.489585i
\(202\) 2.17051 + 8.46688i 0.152716 + 0.595727i
\(203\) −24.0831 −1.69030
\(204\) −0.579589 + 0.318061i −0.0405794 + 0.0222687i
\(205\) −25.2729 −1.76514
\(206\) 7.10416 + 27.7124i 0.494970 + 1.93082i
\(207\) 0.501468i 0.0348544i
\(208\) −1.98617 1.26468i −0.137716 0.0876900i
\(209\) 22.5948i 1.56292i
\(210\) 5.13163 + 20.0178i 0.354116 + 1.38136i
\(211\) 3.95038i 0.271955i −0.990712 0.135978i \(-0.956582\pi\)
0.990712 0.135978i \(-0.0434175\pi\)
\(212\) 8.15898 + 14.8678i 0.560361 + 1.02112i
\(213\) 0.0930167i 0.00637340i
\(214\) 1.85784 + 7.24719i 0.126999 + 0.495408i
\(215\) 24.6187i 1.67898i
\(216\) −2.06403 + 1.93385i −0.140440 + 0.131582i
\(217\) 23.4250 1.59019
\(218\) 2.15467 + 8.40511i 0.145933 + 0.569266i
\(219\) 6.32174 0.427183
\(220\) 14.8470 + 27.0550i 1.00098 + 1.82405i
\(221\) 0.194588i 0.0130894i
\(222\) 1.41193 0.361951i 0.0947622 0.0242926i
\(223\) 2.38734i 0.159868i 0.996800 + 0.0799341i \(0.0254710\pi\)
−0.996800 + 0.0799341i \(0.974529\pi\)
\(224\) 7.16301 21.9043i 0.478599 1.46354i
\(225\) −7.86509 −0.524339
\(226\) 1.54927 + 6.04350i 0.103056 + 0.402008i
\(227\) 6.93501i 0.460293i −0.973156 0.230146i \(-0.926080\pi\)
0.973156 0.230146i \(-0.0739205\pi\)
\(228\) −5.05348 9.20875i −0.334675 0.609864i
\(229\) 24.0931i 1.59212i 0.605219 + 0.796059i \(0.293086\pi\)
−0.605219 + 0.796059i \(0.706914\pi\)
\(230\) −2.46402 + 0.631657i −0.162472 + 0.0416502i
\(231\) 17.5263 1.15315
\(232\) −12.2015 + 11.4319i −0.801067 + 0.750541i
\(233\) 15.1293i 0.991152i 0.868565 + 0.495576i \(0.165043\pi\)
−0.868565 + 0.495576i \(0.834957\pi\)
\(234\) −0.206726 0.806411i −0.0135141 0.0527168i
\(235\) 37.2175 2.42780
\(236\) −8.59887 15.6694i −0.559739 1.01999i
\(237\) 1.43384 0.0931376
\(238\) 1.84486 0.472936i 0.119585 0.0306559i
\(239\) −11.1501 −0.721237 −0.360619 0.932713i \(-0.617434\pi\)
−0.360619 + 0.932713i \(0.617434\pi\)
\(240\) 12.1021 + 7.70594i 0.781185 + 0.497416i
\(241\) −26.2380 −1.69014 −0.845068 0.534659i \(-0.820440\pi\)
−0.845068 + 0.534659i \(0.820440\pi\)
\(242\) 10.2848 2.63653i 0.661130 0.169483i
\(243\) −1.00000 −0.0641500
\(244\) −6.32212 11.5206i −0.404732 0.737528i
\(245\) 34.4229i 2.19920i
\(246\) 2.47446 + 9.65256i 0.157766 + 0.615425i
\(247\) 3.09169 0.196720
\(248\) 11.8681 11.1195i 0.753622 0.706089i
\(249\) 12.5742i 0.796858i
\(250\) 3.60891 + 14.0779i 0.228248 + 0.890365i
\(251\) 23.7883 1.50150 0.750752 0.660584i \(-0.229691\pi\)
0.750752 + 0.660584i \(0.229691\pi\)
\(252\) 7.14304 3.91988i 0.449969 0.246929i
\(253\) 2.15734i 0.135631i
\(254\) −5.17807 20.1990i −0.324901 1.26740i
\(255\) 1.18566i 0.0742489i
\(256\) −6.76859 14.4978i −0.423037 0.906112i
\(257\) 12.6784 0.790858 0.395429 0.918497i \(-0.370596\pi\)
0.395429 + 0.918497i \(0.370596\pi\)
\(258\) −9.40270 + 2.41041i −0.585387 + 0.150066i
\(259\) −4.19889 −0.260906
\(260\) −3.70199 + 2.03154i −0.229588 + 0.125991i
\(261\) −5.91148 −0.365911
\(262\) 7.26162 + 28.3267i 0.448624 + 1.75003i
\(263\) 3.60969i 0.222583i −0.993788 0.111292i \(-0.964501\pi\)
0.993788 0.111292i \(-0.0354988\pi\)
\(264\) 8.87956 8.31950i 0.546499 0.512030i
\(265\) 30.4149 1.86837
\(266\) 7.51420 + 29.3119i 0.460725 + 1.79723i
\(267\) −18.3287 −1.12170
\(268\) 0.928110 16.3444i 0.0566934 0.998392i
\(269\) 30.3436 1.85008 0.925041 0.379866i \(-0.124030\pi\)
0.925041 + 0.379866i \(0.124030\pi\)
\(270\) 1.25962 + 4.91361i 0.0766579 + 0.299033i
\(271\) −22.2235 −1.34998 −0.674990 0.737827i \(-0.735852\pi\)
−0.674990 + 0.737827i \(0.735852\pi\)
\(272\) 0.710187 1.11534i 0.0430614 0.0676273i
\(273\) 2.39816i 0.145143i
\(274\) −5.11659 19.9592i −0.309105 1.20578i
\(275\) 33.8360 2.04039
\(276\) 0.482502 + 0.879244i 0.0290432 + 0.0529243i
\(277\) −3.09791 −0.186135 −0.0930677 0.995660i \(-0.529667\pi\)
−0.0930677 + 0.995660i \(0.529667\pi\)
\(278\) −24.6443 + 6.31764i −1.47807 + 0.378907i
\(279\) 5.74994 0.344240
\(280\) −28.2582 30.1606i −1.68875 1.80244i
\(281\) 24.6045i 1.46778i −0.679267 0.733892i \(-0.737702\pi\)
0.679267 0.733892i \(-0.262298\pi\)
\(282\) −3.64395 14.2146i −0.216994 0.846467i
\(283\) 29.8385i 1.77372i −0.462042 0.886858i \(-0.652883\pi\)
0.462042 0.886858i \(-0.347117\pi\)
\(284\) 0.0894988 + 0.163090i 0.00531078 + 0.00967762i
\(285\) −18.8382 −1.11588
\(286\) 0.889344 + 3.46922i 0.0525880 + 0.205139i
\(287\) 28.7055i 1.69443i
\(288\) 1.75825 5.37667i 0.103606 0.316823i
\(289\) −16.8907 −0.993572
\(290\) 7.44620 + 29.0467i 0.437256 + 1.70568i
\(291\) 6.83533i 0.400694i
\(292\) −11.0842 + 6.08265i −0.648652 + 0.355960i
\(293\) 20.9178 1.22203 0.611016 0.791618i \(-0.290761\pi\)
0.611016 + 0.791618i \(0.290761\pi\)
\(294\) −13.1473 + 3.37034i −0.766764 + 0.196562i
\(295\) −32.0547 −1.86630
\(296\) −2.12733 + 1.99315i −0.123648 + 0.115850i
\(297\) 4.30204 0.249630
\(298\) 24.3468 6.24138i 1.41037 0.361553i
\(299\) −0.295193 −0.0170714
\(300\) 13.7902 7.56763i 0.796177 0.436917i
\(301\) 27.9624 1.61173
\(302\) 0.972214 + 3.79248i 0.0559446 + 0.218233i
\(303\) 6.18058i 0.355065i
\(304\) 17.7209 + 11.2837i 1.01637 + 0.647167i
\(305\) −23.5675 −1.34947
\(306\) 0.452843 0.116088i 0.0258873 0.00663629i
\(307\) 11.5339i 0.658273i 0.944282 + 0.329136i \(0.106758\pi\)
−0.944282 + 0.329136i \(0.893242\pi\)
\(308\) −30.7297 + 16.8635i −1.75099 + 0.960887i
\(309\) 20.2293i 1.15080i
\(310\) −7.24272 28.2529i −0.411359 1.60466i
\(311\) 12.2954 0.697207 0.348603 0.937270i \(-0.386656\pi\)
0.348603 + 0.937270i \(0.386656\pi\)
\(312\) 1.13837 + 1.21501i 0.0644477 + 0.0687863i
\(313\) 5.39606i 0.305004i −0.988303 0.152502i \(-0.951267\pi\)
0.988303 0.152502i \(-0.0487330\pi\)
\(314\) 9.72069 2.49193i 0.548570 0.140628i
\(315\) 14.6124i 0.823318i
\(316\) −2.51400 + 1.37961i −0.141424 + 0.0776090i
\(317\) −16.1308 −0.905995 −0.452997 0.891512i \(-0.649645\pi\)
−0.452997 + 0.891512i \(0.649645\pi\)
\(318\) −2.97791 11.6165i −0.166993 0.651419i
\(319\) 25.4315 1.42389
\(320\) −28.6336 1.86678i −1.60066 0.104356i
\(321\) 5.29024i 0.295272i
\(322\) −0.717450 2.79868i −0.0399819 0.155964i
\(323\) 1.73615i 0.0966020i
\(324\) 1.75334 0.962180i 0.0974079 0.0534544i
\(325\) 4.62984i 0.256817i
\(326\) −1.74748 6.81671i −0.0967841 0.377543i
\(327\) 6.13549i 0.339293i
\(328\) −13.6261 14.5434i −0.752375 0.803023i
\(329\) 42.2724i 2.33055i
\(330\) −5.41893 21.1386i −0.298302 1.16364i
\(331\) 12.6337 0.694410 0.347205 0.937789i \(-0.387131\pi\)
0.347205 + 0.937789i \(0.387131\pi\)
\(332\) 12.0986 + 22.0469i 0.663999 + 1.20998i
\(333\) −1.03067 −0.0564801
\(334\) 1.76243 + 6.87503i 0.0964360 + 0.376185i
\(335\) −24.8962 15.5609i −1.36022 0.850182i
\(336\) −8.75257 + 13.7458i −0.477492 + 0.749894i
\(337\) 16.8432i 0.917508i 0.888563 + 0.458754i \(0.151704\pi\)
−0.888563 + 0.458754i \(0.848296\pi\)
\(338\) 17.3342 4.44368i 0.942857 0.241704i
\(339\) 4.41158i 0.239604i
\(340\) −1.14082 2.07887i −0.0618695 0.112742i
\(341\) −24.7365 −1.33956
\(342\) 1.84445 + 7.19495i 0.0997363 + 0.389058i
\(343\) 10.5806 0.571297
\(344\) 14.1669 13.2734i 0.763828 0.715652i
\(345\) 1.79866 0.0968366
\(346\) −15.4309 + 3.95576i −0.829572 + 0.212663i
\(347\) 3.44586 0.184984 0.0924918 0.995713i \(-0.470517\pi\)
0.0924918 + 0.995713i \(0.470517\pi\)
\(348\) 10.3648 5.68791i 0.555614 0.304904i
\(349\) −4.46833 −0.239184 −0.119592 0.992823i \(-0.538159\pi\)
−0.119592 + 0.992823i \(0.538159\pi\)
\(350\) −43.8949 + 11.2526i −2.34628 + 0.601476i
\(351\) 0.588657i 0.0314202i
\(352\) −7.56405 + 23.1307i −0.403165 + 1.23287i
\(353\) 4.56092i 0.242753i 0.992607 + 0.121377i \(0.0387309\pi\)
−0.992607 + 0.121377i \(0.961269\pi\)
\(354\) 3.13847 + 12.2428i 0.166808 + 0.650695i
\(355\) 0.333632 0.0177073
\(356\) 32.1365 17.6355i 1.70323 0.934681i
\(357\) −1.34670 −0.0712748
\(358\) −29.3309 + 7.51906i −1.55019 + 0.397395i
\(359\) 20.7570i 1.09551i −0.836638 0.547756i \(-0.815482\pi\)
0.836638 0.547756i \(-0.184518\pi\)
\(360\) −6.93632 7.40326i −0.365576 0.390186i
\(361\) −8.58466 −0.451824
\(362\) −7.39437 + 1.89557i −0.388639 + 0.0996288i
\(363\) −7.50759 −0.394046
\(364\) −2.30747 4.20480i −0.120944 0.220392i
\(365\) 22.6748i 1.18685i
\(366\) 2.30748 + 9.00121i 0.120614 + 0.470501i
\(367\) −5.26708 −0.274939 −0.137470 0.990506i \(-0.543897\pi\)
−0.137470 + 0.990506i \(0.543897\pi\)
\(368\) −1.69198 1.07736i −0.0882007 0.0561614i
\(369\) 7.04610i 0.366805i
\(370\) 1.29824 + 5.06428i 0.0674925 + 0.263280i
\(371\) 34.5459i 1.79353i
\(372\) −10.0816 + 5.53247i −0.522707 + 0.286845i
\(373\) 14.5957i 0.755736i −0.925860 0.377868i \(-0.876657\pi\)
0.925860 0.377868i \(-0.123343\pi\)
\(374\) −1.94815 + 0.499414i −0.100736 + 0.0258241i
\(375\) 10.2765i 0.530675i
\(376\) 20.0661 + 21.4169i 1.03483 + 1.10449i
\(377\) 3.47984i 0.179221i
\(378\) −5.58098 + 1.43070i −0.287055 + 0.0735873i
\(379\) −26.2477 −1.34825 −0.674127 0.738615i \(-0.735480\pi\)
−0.674127 + 0.738615i \(0.735480\pi\)
\(380\) 33.0299 18.1258i 1.69440 0.929833i
\(381\) 14.7447i 0.755393i
\(382\) −5.67452 + 1.45468i −0.290334 + 0.0744279i
\(383\) −21.4139 −1.09420 −0.547098 0.837068i \(-0.684268\pi\)
−0.547098 + 0.837068i \(0.684268\pi\)
\(384\) 2.09052 + 11.1189i 0.106681 + 0.567409i
\(385\) 62.8634i 3.20381i
\(386\) 29.9245 7.67122i 1.52312 0.390455i
\(387\) 6.86370 0.348902
\(388\) 6.57681 + 11.9847i 0.333887 + 0.608429i
\(389\) 3.91720 0.198610 0.0993050 0.995057i \(-0.468338\pi\)
0.0993050 + 0.995057i \(0.468338\pi\)
\(390\) 2.89243 0.741483i 0.146464 0.0375464i
\(391\) 0.165766i 0.00838317i
\(392\) 19.8088 18.5594i 1.00049 0.937390i
\(393\) 20.6777i 1.04305i
\(394\) −9.05453 35.3206i −0.456160 1.77942i
\(395\) 5.14287i 0.258766i
\(396\) −7.54296 + 4.13934i −0.379048 + 0.208010i
\(397\) −8.71504 −0.437396 −0.218698 0.975793i \(-0.570181\pi\)
−0.218698 + 0.975793i \(0.570181\pi\)
\(398\) 3.28213 + 12.8032i 0.164518 + 0.641764i
\(399\) 21.3969i 1.07118i
\(400\) −16.8975 + 26.5373i −0.844875 + 1.32686i
\(401\) 16.8353i 0.840713i −0.907359 0.420357i \(-0.861905\pi\)
0.907359 0.420357i \(-0.138095\pi\)
\(402\) −3.50564 + 11.0322i −0.174846 + 0.550238i
\(403\) 3.38474i 0.168606i
\(404\) 5.94683 + 10.8367i 0.295866 + 0.539145i
\(405\) 3.58679i 0.178229i
\(406\) −32.9919 + 8.45756i −1.63736 + 0.419741i
\(407\) 4.43397 0.219784
\(408\) −0.682292 + 0.639258i −0.0337785 + 0.0316480i
\(409\) 14.1575i 0.700045i −0.936741 0.350022i \(-0.886174\pi\)
0.936741 0.350022i \(-0.113826\pi\)
\(410\) −34.6218 + 8.87539i −1.70985 + 0.438324i
\(411\) 14.5696i 0.718667i
\(412\) 19.4642 + 35.4689i 0.958933 + 1.74743i
\(413\) 36.4084i 1.79154i
\(414\) −0.176106 0.686969i −0.00865516 0.0337627i
\(415\) 45.1011 2.21392
\(416\) −3.16502 1.03500i −0.155178 0.0507452i
\(417\) 17.9896 0.880956
\(418\) −7.93489 30.9530i −0.388108 1.51396i
\(419\) 24.7345i 1.20836i 0.796848 + 0.604179i \(0.206499\pi\)
−0.796848 + 0.604179i \(0.793501\pi\)
\(420\) 14.0598 + 25.6206i 0.686048 + 1.25016i
\(421\) 0.0863411 0.00420801 0.00210400 0.999998i \(-0.499330\pi\)
0.00210400 + 0.999998i \(0.499330\pi\)
\(422\) −1.38730 5.41169i −0.0675328 0.263437i
\(423\) 10.3763i 0.504511i
\(424\) 16.3984 + 17.5023i 0.796378 + 0.849989i
\(425\) −2.59990 −0.126114
\(426\) −0.0326658 0.127425i −0.00158266 0.00617377i
\(427\) 26.7684i 1.29542i
\(428\) 5.09016 + 9.27560i 0.246042 + 0.448353i
\(429\) 2.53243i 0.122267i
\(430\) −8.64564 33.7255i −0.416930 1.62639i
\(431\) 13.3565i 0.643360i 0.946848 + 0.321680i \(0.104248\pi\)
−0.946848 + 0.321680i \(0.895752\pi\)
\(432\) −2.14842 + 3.37406i −0.103366 + 0.162335i
\(433\) 1.00574i 0.0483328i −0.999708 0.0241664i \(-0.992307\pi\)
0.999708 0.0241664i \(-0.00769316\pi\)
\(434\) 32.0903 8.22643i 1.54038 0.394881i
\(435\) 21.2033i 1.01662i
\(436\) 5.90345 + 10.7576i 0.282724 + 0.515196i
\(437\) 2.63376 0.125990
\(438\) 8.66025 2.22008i 0.413803 0.106080i
\(439\) 25.7975i 1.23125i 0.788040 + 0.615624i \(0.211096\pi\)
−0.788040 + 0.615624i \(0.788904\pi\)
\(440\) 29.8403 + 31.8491i 1.42258 + 1.51835i
\(441\) 9.59712 0.457006
\(442\) −0.0683358 0.266569i −0.00325040 0.0126794i
\(443\) 6.93125 0.329314 0.164657 0.986351i \(-0.447348\pi\)
0.164657 + 0.986351i \(0.447348\pi\)
\(444\) 1.80711 0.991685i 0.0857616 0.0470633i
\(445\) 65.7413i 3.11644i
\(446\) 0.838391 + 3.27046i 0.0396990 + 0.154861i
\(447\) −17.7725 −0.840610
\(448\) 2.12033 32.5226i 0.100176 1.53655i
\(449\) −28.0410 −1.32333 −0.661667 0.749798i \(-0.730151\pi\)
−0.661667 + 0.749798i \(0.730151\pi\)
\(450\) −10.7745 + 2.76208i −0.507915 + 0.130206i
\(451\) 30.3126i 1.42737i
\(452\) 4.24474 + 7.73501i 0.199656 + 0.363824i
\(453\) 2.76841i 0.130071i
\(454\) −2.43545 9.50038i −0.114301 0.445875i
\(455\) −8.60172 −0.403255
\(456\) −10.1568 10.8405i −0.475635 0.507654i
\(457\) −17.7010 −0.828016 −0.414008 0.910273i \(-0.635871\pi\)
−0.414008 + 0.910273i \(0.635871\pi\)
\(458\) 8.46107 + 33.0056i 0.395360 + 1.54225i
\(459\) −0.330562 −0.0154293
\(460\) −3.15367 + 1.73064i −0.147041 + 0.0806913i
\(461\) −25.5414 −1.18958 −0.594790 0.803881i \(-0.702765\pi\)
−0.594790 + 0.803881i \(0.702765\pi\)
\(462\) 24.0096 6.15494i 1.11703 0.286354i
\(463\) −29.6295 −1.37700 −0.688499 0.725237i \(-0.741730\pi\)
−0.688499 + 0.725237i \(0.741730\pi\)
\(464\) −12.7003 + 19.9457i −0.589598 + 0.925956i
\(465\) 20.6238i 0.956407i
\(466\) 5.31313 + 20.7258i 0.246126 + 0.960106i
\(467\) 1.83988i 0.0851395i 0.999093 + 0.0425698i \(0.0135545\pi\)
−0.999093 + 0.0425698i \(0.986446\pi\)
\(468\) −0.566394 1.03212i −0.0261816 0.0477097i
\(469\) 17.6744 28.2776i 0.816127 1.30574i
\(470\) 50.9848 13.0701i 2.35176 0.602879i
\(471\) −7.09583 −0.326959
\(472\) −17.2825 18.4460i −0.795493 0.849045i
\(473\) −29.5280 −1.35770
\(474\) 1.96424 0.503537i 0.0902203 0.0231282i
\(475\) 41.3083i 1.89536i
\(476\) 2.36122 1.29577i 0.108226 0.0593913i
\(477\) 8.47969i 0.388258i
\(478\) −15.2746 + 3.91570i −0.698646 + 0.179100i
\(479\) 29.7336i 1.35856i −0.733879 0.679281i \(-0.762292\pi\)
0.733879 0.679281i \(-0.237708\pi\)
\(480\) 19.2850 + 6.30646i 0.880236 + 0.287849i
\(481\) 0.606709i 0.0276635i
\(482\) −35.9438 + 9.21430i −1.63720 + 0.419700i
\(483\) 2.04296i 0.0929578i
\(484\) 13.1634 7.22365i 0.598335 0.328348i
\(485\) 24.5169 1.11326
\(486\) −1.36992 + 0.351182i −0.0621407 + 0.0159299i
\(487\) −32.6107 −1.47773 −0.738867 0.673852i \(-0.764639\pi\)
−0.738867 + 0.673852i \(0.764639\pi\)
\(488\) −12.7066 13.5620i −0.575200 0.613922i
\(489\) 4.97600i 0.225023i
\(490\) −12.0887 47.1565i −0.546112 2.13031i
\(491\) 39.1050i 1.76478i 0.470516 + 0.882391i \(0.344068\pi\)
−0.470516 + 0.882391i \(0.655932\pi\)
\(492\) 6.77961 + 12.3542i 0.305649 + 0.556971i
\(493\) −1.95411 −0.0880088
\(494\) 4.23536 1.08575i 0.190558 0.0488501i
\(495\) 15.4305i 0.693551i
\(496\) 12.3533 19.4006i 0.554678 0.871114i
\(497\) 0.378946i 0.0169981i
\(498\) −4.41583 17.2256i −0.197878 0.771898i
\(499\) −17.5274 −0.784634 −0.392317 0.919830i \(-0.628326\pi\)
−0.392317 + 0.919830i \(0.628326\pi\)
\(500\) 9.88782 + 18.0182i 0.442197 + 0.805798i
\(501\) 5.01857i 0.224213i
\(502\) 32.5880 8.35402i 1.45447 0.372858i
\(503\) 22.9024 1.02117 0.510583 0.859828i \(-0.329430\pi\)
0.510583 + 0.859828i \(0.329430\pi\)
\(504\) 8.40878 7.87842i 0.374557 0.350933i
\(505\) 22.1685 0.986483
\(506\) 0.757618 + 2.95537i 0.0336802 + 0.131382i
\(507\) −12.6535 −0.561961
\(508\) −14.1870 25.8525i −0.629448 1.14702i
\(509\) −29.2971 −1.29857 −0.649286 0.760545i \(-0.724932\pi\)
−0.649286 + 0.760545i \(0.724932\pi\)
\(510\) 0.416382 + 1.62425i 0.0184377 + 0.0719232i
\(511\) −25.7545 −1.13931
\(512\) −14.3638 17.4838i −0.634795 0.772681i
\(513\) 5.25211i 0.231886i
\(514\) 17.3684 4.45243i 0.766086 0.196388i
\(515\) 72.5583 3.19730
\(516\) −12.0344 + 6.60412i −0.529786 + 0.290730i
\(517\) 44.6391i 1.96323i
\(518\) −5.75212 + 1.47457i −0.252734 + 0.0647890i
\(519\) 11.2641 0.494441
\(520\) −4.35798 + 4.08311i −0.191110 + 0.179056i
\(521\) 38.8819i 1.70345i 0.523990 + 0.851724i \(0.324443\pi\)
−0.523990 + 0.851724i \(0.675557\pi\)
\(522\) −8.09823 + 2.07601i −0.354450 + 0.0908643i
\(523\) 27.8489i 1.21775i 0.793268 + 0.608873i \(0.208378\pi\)
−0.793268 + 0.608873i \(0.791622\pi\)
\(524\) 19.8956 + 36.2550i 0.869144 + 1.58381i
\(525\) 32.0420 1.39843
\(526\) −1.26766 4.94498i −0.0552726 0.215611i
\(527\) 1.90071 0.0827964
\(528\) 9.24260 14.5154i 0.402232 0.631700i
\(529\) 22.7485 0.989067
\(530\) 41.6659 10.6812i 1.80985 0.463960i
\(531\) 8.93686i 0.387827i
\(532\) 20.5876 + 37.5160i 0.892587 + 1.62653i
\(533\) −4.14774 −0.179658
\(534\) −25.1088 + 6.43671i −1.08656 + 0.278544i
\(535\) 18.9750 0.820361
\(536\) −4.46842 22.7164i −0.193006 0.981198i
\(537\) 21.4107 0.923940
\(538\) 41.5682 10.6561i 1.79213 0.459418i
\(539\) −41.2873 −1.77837
\(540\) 3.45114 + 6.28888i 0.148513 + 0.270630i
\(541\) 3.23277i 0.138987i −0.997582 0.0694937i \(-0.977862\pi\)
0.997582 0.0694937i \(-0.0221384\pi\)
\(542\) −30.4443 + 7.80449i −1.30770 + 0.335231i
\(543\) 5.39768 0.231636
\(544\) 0.581210 1.77733i 0.0249192 0.0762022i
\(545\) 22.0067 0.942665
\(546\) 0.842192 + 3.28528i 0.0360425 + 0.140597i
\(547\) 1.84336 0.0788163 0.0394082 0.999223i \(-0.487453\pi\)
0.0394082 + 0.999223i \(0.487453\pi\)
\(548\) −14.0186 25.5456i −0.598845 1.09125i
\(549\) 6.57062i 0.280427i
\(550\) 46.3524 11.8826i 1.97647 0.506675i
\(551\) 31.0477i 1.32268i
\(552\) 0.969762 + 1.03505i 0.0412758 + 0.0440545i
\(553\) −5.84138 −0.248401
\(554\) −4.24388 + 1.08793i −0.180305 + 0.0462217i
\(555\) 3.69678i 0.156920i
\(556\) −31.5420 + 17.3093i −1.33768 + 0.734076i
\(557\) −6.80158 −0.288192 −0.144096 0.989564i \(-0.546027\pi\)
−0.144096 + 0.989564i \(0.546027\pi\)
\(558\) 7.87693 2.01927i 0.333457 0.0854827i
\(559\) 4.04037i 0.170889i
\(560\) −49.3033 31.3937i −2.08344 1.32662i
\(561\) 1.42209 0.0600409
\(562\) −8.64067 33.7062i −0.364485 1.42181i
\(563\) −26.6033 −1.12119 −0.560597 0.828089i \(-0.689428\pi\)
−0.560597 + 0.828089i \(0.689428\pi\)
\(564\) −9.98382 18.1931i −0.420395 0.766069i
\(565\) 15.8234 0.665697
\(566\) −10.4788 40.8763i −0.440455 1.71816i
\(567\) 4.07396 0.171090
\(568\) 0.179880 + 0.191990i 0.00754761 + 0.00805570i
\(569\) −20.2191 −0.847629 −0.423814 0.905749i \(-0.639309\pi\)
−0.423814 + 0.905749i \(0.639309\pi\)
\(570\) −25.8068 + 6.61565i −1.08093 + 0.277099i
\(571\) 5.10883i 0.213798i −0.994270 0.106899i \(-0.965908\pi\)
0.994270 0.106899i \(-0.0340921\pi\)
\(572\) 2.43665 + 4.44022i 0.101882 + 0.185655i
\(573\) 4.14224 0.173045
\(574\) −10.0809 39.3241i −0.420767 1.64136i
\(575\) 3.94409i 0.164480i
\(576\) 0.520460 7.98305i 0.0216858 0.332627i
\(577\) 41.9636i 1.74697i −0.486852 0.873485i \(-0.661855\pi\)
0.486852 0.873485i \(-0.338145\pi\)
\(578\) −23.1389 + 5.93172i −0.962451 + 0.246727i
\(579\) −21.8440 −0.907806
\(580\) 20.4014 + 37.1766i 0.847120 + 1.54367i
\(581\) 51.2267i 2.12524i
\(582\) −2.40044 9.36383i −0.0995016 0.388143i
\(583\) 36.4800i 1.51085i
\(584\) −13.0483 + 12.2253i −0.539941 + 0.505886i
\(585\) −2.11139 −0.0872953
\(586\) 28.6557 7.34596i 1.18375 0.303459i
\(587\) −4.63536 −0.191322 −0.0956608 0.995414i \(-0.530496\pi\)
−0.0956608 + 0.995414i \(0.530496\pi\)
\(588\) −16.8270 + 9.23416i −0.693936 + 0.380810i
\(589\) 30.1993i 1.24434i
\(590\) −43.9122 + 11.2570i −1.80784 + 0.463444i
\(591\) 25.7830i 1.06057i
\(592\) −2.21430 + 3.47753i −0.0910072 + 0.142926i
\(593\) 19.5812i 0.804105i 0.915617 + 0.402053i \(0.131703\pi\)
−0.915617 + 0.402053i \(0.868297\pi\)
\(594\) 5.89344 1.51080i 0.241811 0.0619889i
\(595\) 4.83032i 0.198024i
\(596\) 31.1613 17.1003i 1.27642 0.700457i
\(597\) 9.34594i 0.382504i
\(598\) −0.404389 + 0.103666i −0.0165367 + 0.00423923i
\(599\) −13.4500 −0.549553 −0.274776 0.961508i \(-0.588604\pi\)
−0.274776 + 0.961508i \(0.588604\pi\)
\(600\) 16.2338 15.2099i 0.662742 0.620941i
\(601\) −14.6596 −0.597978 −0.298989 0.954257i \(-0.596649\pi\)
−0.298989 + 0.954257i \(0.596649\pi\)
\(602\) 38.3062 9.81990i 1.56124 0.400229i
\(603\) 4.33838 6.94107i 0.176673 0.282662i
\(604\) 2.66370 + 4.85396i 0.108385 + 0.197505i
\(605\) 26.9282i 1.09479i
\(606\) −2.17051 8.46688i −0.0881709 0.343943i
\(607\) 25.3724i 1.02983i −0.857241 0.514916i \(-0.827823\pi\)
0.857241 0.514916i \(-0.172177\pi\)
\(608\) 28.2389 + 9.23450i 1.14524 + 0.374508i
\(609\) 24.0831 0.975897
\(610\) −32.2855 + 8.27647i −1.30720 + 0.335104i
\(611\) 6.10806 0.247106
\(612\) 0.579589 0.318061i 0.0234285 0.0128568i
\(613\) 25.1012 1.01383 0.506914 0.861997i \(-0.330786\pi\)
0.506914 + 0.861997i \(0.330786\pi\)
\(614\) 4.05049 + 15.8004i 0.163464 + 0.637654i
\(615\) 25.2729 1.01910
\(616\) −36.1749 + 33.8933i −1.45753 + 1.36560i
\(617\) −44.8891 −1.80717 −0.903583 0.428413i \(-0.859073\pi\)
−0.903583 + 0.428413i \(0.859073\pi\)
\(618\) −7.10416 27.7124i −0.285771 1.11476i
\(619\) 24.7139i 0.993337i −0.867940 0.496669i \(-0.834556\pi\)
0.867940 0.496669i \(-0.165444\pi\)
\(620\) −19.8438 36.1606i −0.796948 1.45225i
\(621\) 0.501468i 0.0201232i
\(622\) 16.8436 4.31791i 0.675368 0.173133i
\(623\) 74.6704 2.99161
\(624\) 1.98617 + 1.26468i 0.0795103 + 0.0506278i
\(625\) −2.46584 −0.0986335
\(626\) −1.89500 7.39216i −0.0757394 0.295450i
\(627\) 22.5948i 0.902350i
\(628\) 12.4414 6.82746i 0.496467 0.272446i
\(629\) −0.340699 −0.0135846
\(630\) −5.13163 20.0178i −0.204449 0.797529i
\(631\) −12.7802 −0.508770 −0.254385 0.967103i \(-0.581873\pi\)
−0.254385 + 0.967103i \(0.581873\pi\)
\(632\) −2.95948 + 2.77282i −0.117722 + 0.110297i
\(633\) 3.95038i 0.157013i
\(634\) −22.0978 + 5.66484i −0.877617 + 0.224980i
\(635\) −52.8862 −2.09872
\(636\) −8.15898 14.8678i −0.323525 0.589546i
\(637\) 5.64942i 0.223838i
\(638\) 34.8390 8.93107i 1.37929 0.353584i
\(639\) 0.0930167i 0.00367968i
\(640\) −39.8812 + 7.49826i −1.57644 + 0.296395i
\(641\) 37.4738i 1.48012i 0.672538 + 0.740062i \(0.265204\pi\)
−0.672538 + 0.740062i \(0.734796\pi\)
\(642\) −1.85784 7.24719i −0.0733230 0.286024i
\(643\) 39.8345i 1.57092i −0.618914 0.785459i \(-0.712427\pi\)
0.618914 0.785459i \(-0.287573\pi\)
\(644\) −1.96569 3.58200i −0.0774591 0.141151i
\(645\) 24.6187i 0.969360i
\(646\) 0.609705 + 2.37838i 0.0239885 + 0.0935762i
\(647\) −15.4857 −0.608807 −0.304403 0.952543i \(-0.598457\pi\)
−0.304403 + 0.952543i \(0.598457\pi\)
\(648\) 2.06403 1.93385i 0.0810829 0.0759687i
\(649\) 38.4468i 1.50917i
\(650\) 1.62592 + 6.34249i 0.0637737 + 0.248773i
\(651\) −23.4250 −0.918098
\(652\) −4.78781 8.72464i −0.187505 0.341683i
\(653\) 12.2344i 0.478770i −0.970925 0.239385i \(-0.923054\pi\)
0.970925 0.239385i \(-0.0769457\pi\)
\(654\) −2.15467 8.40511i −0.0842544 0.328666i
\(655\) 74.1665 2.89792
\(656\) −23.7740 15.1380i −0.928218 0.591038i
\(657\) −6.32174 −0.246634
\(658\) 14.8453 + 57.9097i 0.578730 + 2.25755i
\(659\) 27.8274i 1.08400i −0.840377 0.542002i \(-0.817667\pi\)
0.840377 0.542002i \(-0.182333\pi\)
\(660\) −14.8470 27.0550i −0.577917 1.05312i
\(661\) 6.59513i 0.256521i 0.991741 + 0.128260i \(0.0409393\pi\)
−0.991741 + 0.128260i \(0.959061\pi\)
\(662\) 17.3071 4.43672i 0.672659 0.172438i
\(663\) 0.194588i 0.00755717i
\(664\) 24.3166 + 25.9536i 0.943667 + 1.00719i
\(665\) 76.7462 2.97609
\(666\) −1.41193 + 0.361951i −0.0547110 + 0.0140253i
\(667\) 2.96442i 0.114783i
\(668\) 4.82877 + 8.79928i 0.186831 + 0.340454i
\(669\) 2.38734i 0.0922999i
\(670\) −39.5704 12.5740i −1.52874 0.485777i
\(671\) 28.2671i 1.09124i
\(672\) −7.16301 + 21.9043i −0.276319 + 0.844977i
\(673\) 18.4436i 0.710947i 0.934686 + 0.355474i \(0.115680\pi\)
−0.934686 + 0.355474i \(0.884320\pi\)
\(674\) 5.91503 + 23.0738i 0.227839 + 0.888770i
\(675\) 7.86509 0.302727
\(676\) 22.1859 12.1749i 0.853303 0.468266i
\(677\) 1.22827i 0.0472061i 0.999721 + 0.0236030i \(0.00751378\pi\)
−0.999721 + 0.0236030i \(0.992486\pi\)
\(678\) −1.54927 6.04350i −0.0594993 0.232099i
\(679\) 27.8468i 1.06866i
\(680\) −2.29289 2.44724i −0.0879282 0.0938473i
\(681\) 6.93501i 0.265750i
\(682\) −33.8869 + 8.68701i −1.29760 + 0.332643i
\(683\) −10.5079 −0.402072 −0.201036 0.979584i \(-0.564431\pi\)
−0.201036 + 0.979584i \(0.564431\pi\)
\(684\) 5.05348 + 9.20875i 0.193224 + 0.352105i
\(685\) −52.2583 −1.99669
\(686\) 14.4945 3.71571i 0.553402 0.141866i
\(687\) 24.0931i 0.919210i
\(688\) 14.7461 23.1586i 0.562190 0.882912i
\(689\) 4.99163 0.190166
\(690\) 2.46402 0.631657i 0.0938035 0.0240468i
\(691\) 17.2718i 0.657048i 0.944496 + 0.328524i \(0.106551\pi\)
−0.944496 + 0.328524i \(0.893449\pi\)
\(692\) −19.7499 + 10.8381i −0.750779 + 0.412004i
\(693\) −17.5263 −0.665771
\(694\) 4.72054 1.21012i 0.179189 0.0459357i
\(695\) 64.5251i 2.44758i
\(696\) 12.2015 11.4319i 0.462496 0.433325i
\(697\) 2.32918i 0.0882238i
\(698\) −6.12124 + 1.56920i −0.231692 + 0.0593950i
\(699\) 15.1293i 0.572242i
\(700\) −56.1806 + 30.8302i −2.12343 + 1.16527i
\(701\) 3.01308i 0.113803i 0.998380 + 0.0569013i \(0.0181220\pi\)
−0.998380 + 0.0569013i \(0.981878\pi\)
\(702\) 0.206726 + 0.806411i 0.00780236 + 0.0304360i
\(703\) 5.41317i 0.204161i
\(704\) −2.23904 + 34.3434i −0.0843870 + 1.29437i
\(705\) −37.2175 −1.40169
\(706\) 1.60171 + 6.24808i 0.0602813 + 0.235150i
\(707\) 25.1794i 0.946969i
\(708\) 8.59887 + 15.6694i 0.323165 + 0.588891i
\(709\) 18.5087 0.695110 0.347555 0.937660i \(-0.387012\pi\)
0.347555 + 0.937660i \(0.387012\pi\)
\(710\) 0.457048 0.117165i 0.0171527 0.00439714i
\(711\) −1.43384 −0.0537730
\(712\) 37.8311 35.4450i 1.41778 1.32836i
\(713\) 2.88341i 0.107984i
\(714\) −1.84486 + 0.472936i −0.0690423 + 0.0176992i
\(715\) 9.08330 0.339696
\(716\) −37.5403 + 20.6010i −1.40295 + 0.769894i
\(717\) 11.1501 0.416407
\(718\) −7.28949 28.4354i −0.272041 1.06120i
\(719\) 43.2229i 1.61194i 0.591955 + 0.805971i \(0.298356\pi\)
−0.591955 + 0.805971i \(0.701644\pi\)
\(720\) −12.1021 7.70594i −0.451017 0.287183i
\(721\) 82.4132i 3.06923i
\(722\) −11.7603 + 3.01478i −0.437672 + 0.112198i
\(723\) 26.2380 0.975801
\(724\) −9.46398 + 5.19354i −0.351726 + 0.193016i
\(725\) 46.4943 1.72676
\(726\) −10.2848 + 2.63653i −0.381704 + 0.0978508i
\(727\) −17.3390 −0.643068 −0.321534 0.946898i \(-0.604199\pi\)
−0.321534 + 0.946898i \(0.604199\pi\)
\(728\) −4.63769 4.94989i −0.171884 0.183455i
\(729\) 1.00000 0.0370370
\(730\) 7.96297 + 31.0625i 0.294723 + 1.14968i
\(731\) 2.26888 0.0839177
\(732\) 6.32212 + 11.5206i 0.233672 + 0.425812i
\(733\) 29.9866i 1.10758i −0.832656 0.553790i \(-0.813181\pi\)
0.832656 0.553790i \(-0.186819\pi\)
\(734\) −7.21546 + 1.84970i −0.266327 + 0.0682738i
\(735\) 34.4229i 1.26971i
\(736\) −2.69623 0.881703i −0.0993842 0.0325000i
\(737\) −18.6639 + 29.8608i −0.687494 + 1.09994i
\(738\) −2.47446 9.65256i −0.0910862 0.355316i
\(739\) 44.1171 1.62287 0.811436 0.584441i \(-0.198686\pi\)
0.811436 + 0.584441i \(0.198686\pi\)
\(740\) 3.55697 + 6.48173i 0.130757 + 0.238273i
\(741\) −3.09169 −0.113576
\(742\) 12.1319 + 47.3250i 0.445376 + 1.73735i
\(743\) 4.71118i 0.172836i −0.996259 0.0864182i \(-0.972458\pi\)
0.996259 0.0864182i \(-0.0275421\pi\)
\(744\) −11.8681 + 11.1195i −0.435104 + 0.407661i
\(745\) 63.7463i 2.33548i
\(746\) −5.12574 19.9949i −0.187667 0.732064i
\(747\) 12.5742i 0.460066i
\(748\) −2.49342 + 1.36831i −0.0911684 + 0.0500304i
\(749\) 21.5522i 0.787501i
\(750\) −3.60891 14.0779i −0.131779 0.514053i
\(751\) 6.08768i 0.222143i 0.993812 + 0.111071i \(0.0354282\pi\)
−0.993812 + 0.111071i \(0.964572\pi\)
\(752\) 35.0101 + 22.2925i 1.27669 + 0.812925i
\(753\) −23.7883 −0.866894
\(754\) 1.22206 + 4.76708i 0.0445046 + 0.173607i
\(755\) 9.92970 0.361379
\(756\) −7.14304 + 3.91988i −0.259790 + 0.142565i
\(757\) 51.7396i 1.88051i −0.340474 0.940254i \(-0.610588\pi\)
0.340474 0.940254i \(-0.389412\pi\)
\(758\) −35.9572 + 9.21773i −1.30602 + 0.334803i
\(759\) 2.15734i 0.0783063i
\(760\) 38.8827 36.4303i 1.41042 1.32147i
\(761\) 34.7942 1.26129 0.630645 0.776071i \(-0.282790\pi\)
0.630645 + 0.776071i \(0.282790\pi\)
\(762\) 5.17807 + 20.1990i 0.187582 + 0.731732i
\(763\) 24.9957i 0.904906i
\(764\) −7.26276 + 3.98558i −0.262758 + 0.144193i
\(765\) 1.18566i 0.0428676i
\(766\) −29.3352 + 7.52016i −1.05992 + 0.271714i
\(767\) −5.26075 −0.189955
\(768\) 6.76859 + 14.4978i 0.244240 + 0.523144i
\(769\) 13.9823i 0.504215i 0.967699 + 0.252107i \(0.0811236\pi\)
−0.967699 + 0.252107i \(0.918876\pi\)
\(770\) 22.0765 + 86.1176i 0.795581 + 3.10346i
\(771\) −12.6784 −0.456602