Properties

Label 804.2.e.b.535.8
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 535.8
Character \(\chi\) = 804.535
Dual form 804.2.e.b.535.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.16630 + 0.799841i) q^{2} +1.00000 q^{3} +(0.720507 - 1.86571i) q^{4} +0.864540i q^{5} +(-1.16630 + 0.799841i) q^{6} -1.73467 q^{7} +(0.651944 + 2.75227i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-1.16630 + 0.799841i) q^{2} +1.00000 q^{3} +(0.720507 - 1.86571i) q^{4} +0.864540i q^{5} +(-1.16630 + 0.799841i) q^{6} -1.73467 q^{7} +(0.651944 + 2.75227i) q^{8} +1.00000 q^{9} +(-0.691495 - 1.00831i) q^{10} -5.29746 q^{11} +(0.720507 - 1.86571i) q^{12} -1.41228i q^{13} +(2.02315 - 1.38746i) q^{14} +0.864540i q^{15} +(-2.96174 - 2.68851i) q^{16} -4.82537 q^{17} +(-1.16630 + 0.799841i) q^{18} -4.26064i q^{19} +(1.61298 + 0.622907i) q^{20} -1.73467 q^{21} +(6.17843 - 4.23713i) q^{22} -1.92153i q^{23} +(0.651944 + 2.75227i) q^{24} +4.25257 q^{25} +(1.12960 + 1.64714i) q^{26} +1.00000 q^{27} +(-1.24984 + 3.23639i) q^{28} -2.13848 q^{29} +(-0.691495 - 1.00831i) q^{30} -5.52447 q^{31} +(5.60466 + 0.766689i) q^{32} -5.29746 q^{33} +(5.62783 - 3.85953i) q^{34} -1.49969i q^{35} +(0.720507 - 1.86571i) q^{36} -7.24325 q^{37} +(3.40783 + 4.96918i) q^{38} -1.41228i q^{39} +(-2.37944 + 0.563632i) q^{40} +0.306352i q^{41} +(2.02315 - 1.38746i) q^{42} +1.13429 q^{43} +(-3.81686 + 9.88352i) q^{44} +0.864540i q^{45} +(1.53692 + 2.24107i) q^{46} -11.9232i q^{47} +(-2.96174 - 2.68851i) q^{48} -3.99091 q^{49} +(-4.95977 + 3.40138i) q^{50} -4.82537 q^{51} +(-2.63490 - 1.01756i) q^{52} +8.91687i q^{53} +(-1.16630 + 0.799841i) q^{54} -4.57987i q^{55} +(-1.13091 - 4.77428i) q^{56} -4.26064i q^{57} +(2.49411 - 1.71044i) q^{58} +14.4219i q^{59} +(1.61298 + 0.622907i) q^{60} -12.4421i q^{61} +(6.44318 - 4.41870i) q^{62} -1.73467 q^{63} +(-7.14994 + 3.58865i) q^{64} +1.22097 q^{65} +(6.17843 - 4.23713i) q^{66} +(-7.97425 - 1.84697i) q^{67} +(-3.47672 + 9.00274i) q^{68} -1.92153i q^{69} +(1.19952 + 1.74909i) q^{70} +8.13841i q^{71} +(0.651944 + 2.75227i) q^{72} +12.8776 q^{73} +(8.44779 - 5.79345i) q^{74} +4.25257 q^{75} +(-7.94910 - 3.06982i) q^{76} +9.18937 q^{77} +(1.12960 + 1.64714i) q^{78} -8.20011 q^{79} +(2.32433 - 2.56054i) q^{80} +1.00000 q^{81} +(-0.245033 - 0.357299i) q^{82} -0.390864i q^{83} +(-1.24984 + 3.23639i) q^{84} -4.17173i q^{85} +(-1.32292 + 0.907249i) q^{86} -2.13848 q^{87} +(-3.45365 - 14.5800i) q^{88} -5.73285 q^{89} +(-0.691495 - 1.00831i) q^{90} +2.44984i q^{91} +(-3.58501 - 1.38447i) q^{92} -5.52447 q^{93} +(9.53668 + 13.9060i) q^{94} +3.68349 q^{95} +(5.60466 + 0.766689i) q^{96} -14.5334i q^{97} +(4.65459 - 3.19209i) q^{98} -5.29746 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.16630 + 0.799841i −0.824698 + 0.565573i
\(3\) 1.00000 0.577350
\(4\) 0.720507 1.86571i 0.360254 0.932854i
\(5\) 0.864540i 0.386634i 0.981136 + 0.193317i \(0.0619246\pi\)
−0.981136 + 0.193317i \(0.938075\pi\)
\(6\) −1.16630 + 0.799841i −0.476140 + 0.326534i
\(7\) −1.73467 −0.655645 −0.327822 0.944739i \(-0.606315\pi\)
−0.327822 + 0.944739i \(0.606315\pi\)
\(8\) 0.651944 + 2.75227i 0.230497 + 0.973073i
\(9\) 1.00000 0.333333
\(10\) −0.691495 1.00831i −0.218670 0.318856i
\(11\) −5.29746 −1.59725 −0.798623 0.601832i \(-0.794438\pi\)
−0.798623 + 0.601832i \(0.794438\pi\)
\(12\) 0.720507 1.86571i 0.207993 0.538584i
\(13\) 1.41228i 0.391696i −0.980634 0.195848i \(-0.937254\pi\)
0.980634 0.195848i \(-0.0627459\pi\)
\(14\) 2.02315 1.38746i 0.540709 0.370815i
\(15\) 0.864540i 0.223223i
\(16\) −2.96174 2.68851i −0.740435 0.672128i
\(17\) −4.82537 −1.17033 −0.585163 0.810916i \(-0.698969\pi\)
−0.585163 + 0.810916i \(0.698969\pi\)
\(18\) −1.16630 + 0.799841i −0.274899 + 0.188524i
\(19\) 4.26064i 0.977457i −0.872436 0.488728i \(-0.837461\pi\)
0.872436 0.488728i \(-0.162539\pi\)
\(20\) 1.61298 + 0.622907i 0.360673 + 0.139286i
\(21\) −1.73467 −0.378537
\(22\) 6.17843 4.23713i 1.31724 0.903359i
\(23\) 1.92153i 0.400666i −0.979728 0.200333i \(-0.935798\pi\)
0.979728 0.200333i \(-0.0642024\pi\)
\(24\) 0.651944 + 2.75227i 0.133078 + 0.561804i
\(25\) 4.25257 0.850514
\(26\) 1.12960 + 1.64714i 0.221533 + 0.323031i
\(27\) 1.00000 0.192450
\(28\) −1.24984 + 3.23639i −0.236198 + 0.611621i
\(29\) −2.13848 −0.397106 −0.198553 0.980090i \(-0.563624\pi\)
−0.198553 + 0.980090i \(0.563624\pi\)
\(30\) −0.691495 1.00831i −0.126249 0.184092i
\(31\) −5.52447 −0.992223 −0.496112 0.868259i \(-0.665239\pi\)
−0.496112 + 0.868259i \(0.665239\pi\)
\(32\) 5.60466 + 0.766689i 0.990773 + 0.135533i
\(33\) −5.29746 −0.922170
\(34\) 5.62783 3.85953i 0.965165 0.661905i
\(35\) 1.49969i 0.253495i
\(36\) 0.720507 1.86571i 0.120085 0.310951i
\(37\) −7.24325 −1.19078 −0.595391 0.803436i \(-0.703003\pi\)
−0.595391 + 0.803436i \(0.703003\pi\)
\(38\) 3.40783 + 4.96918i 0.552823 + 0.806107i
\(39\) 1.41228i 0.226146i
\(40\) −2.37944 + 0.563632i −0.376223 + 0.0891181i
\(41\) 0.306352i 0.0478442i 0.999714 + 0.0239221i \(0.00761537\pi\)
−0.999714 + 0.0239221i \(0.992385\pi\)
\(42\) 2.02315 1.38746i 0.312178 0.214090i
\(43\) 1.13429 0.172977 0.0864885 0.996253i \(-0.472435\pi\)
0.0864885 + 0.996253i \(0.472435\pi\)
\(44\) −3.81686 + 9.88352i −0.575413 + 1.49000i
\(45\) 0.864540i 0.128878i
\(46\) 1.53692 + 2.24107i 0.226606 + 0.330428i
\(47\) 11.9232i 1.73918i −0.493775 0.869590i \(-0.664383\pi\)
0.493775 0.869590i \(-0.335617\pi\)
\(48\) −2.96174 2.68851i −0.427490 0.388053i
\(49\) −3.99091 −0.570130
\(50\) −4.95977 + 3.40138i −0.701417 + 0.481028i
\(51\) −4.82537 −0.675687
\(52\) −2.63490 1.01756i −0.365395 0.141110i
\(53\) 8.91687i 1.22483i 0.790538 + 0.612413i \(0.209801\pi\)
−0.790538 + 0.612413i \(0.790199\pi\)
\(54\) −1.16630 + 0.799841i −0.158713 + 0.108845i
\(55\) 4.57987i 0.617550i
\(56\) −1.13091 4.77428i −0.151124 0.637990i
\(57\) 4.26064i 0.564335i
\(58\) 2.49411 1.71044i 0.327492 0.224592i
\(59\) 14.4219i 1.87757i 0.344508 + 0.938784i \(0.388046\pi\)
−0.344508 + 0.938784i \(0.611954\pi\)
\(60\) 1.61298 + 0.622907i 0.208235 + 0.0804170i
\(61\) 12.4421i 1.59305i −0.604606 0.796525i \(-0.706669\pi\)
0.604606 0.796525i \(-0.293331\pi\)
\(62\) 6.44318 4.41870i 0.818285 0.561175i
\(63\) −1.73467 −0.218548
\(64\) −7.14994 + 3.58865i −0.893742 + 0.448581i
\(65\) 1.22097 0.151443
\(66\) 6.17843 4.23713i 0.760512 0.521555i
\(67\) −7.97425 1.84697i −0.974210 0.225644i
\(68\) −3.47672 + 9.00274i −0.421614 + 1.09174i
\(69\) 1.92153i 0.231324i
\(70\) 1.19952 + 1.74909i 0.143370 + 0.209057i
\(71\) 8.13841i 0.965852i 0.875661 + 0.482926i \(0.160426\pi\)
−0.875661 + 0.482926i \(0.839574\pi\)
\(72\) 0.651944 + 2.75227i 0.0768324 + 0.324358i
\(73\) 12.8776 1.50720 0.753602 0.657331i \(-0.228315\pi\)
0.753602 + 0.657331i \(0.228315\pi\)
\(74\) 8.44779 5.79345i 0.982036 0.673475i
\(75\) 4.25257 0.491045
\(76\) −7.94910 3.06982i −0.911825 0.352132i
\(77\) 9.18937 1.04723
\(78\) 1.12960 + 1.64714i 0.127902 + 0.186502i
\(79\) −8.20011 −0.922584 −0.461292 0.887248i \(-0.652614\pi\)
−0.461292 + 0.887248i \(0.652614\pi\)
\(80\) 2.32433 2.56054i 0.259868 0.286277i
\(81\) 1.00000 0.111111
\(82\) −0.245033 0.357299i −0.0270594 0.0394570i
\(83\) 0.390864i 0.0429029i −0.999770 0.0214514i \(-0.993171\pi\)
0.999770 0.0214514i \(-0.00682873\pi\)
\(84\) −1.24984 + 3.23639i −0.136369 + 0.353120i
\(85\) 4.17173i 0.452488i
\(86\) −1.32292 + 0.907249i −0.142654 + 0.0978312i
\(87\) −2.13848 −0.229269
\(88\) −3.45365 14.5800i −0.368160 1.55424i
\(89\) −5.73285 −0.607681 −0.303840 0.952723i \(-0.598269\pi\)
−0.303840 + 0.952723i \(0.598269\pi\)
\(90\) −0.691495 1.00831i −0.0728900 0.106285i
\(91\) 2.44984i 0.256813i
\(92\) −3.58501 1.38447i −0.373763 0.144341i
\(93\) −5.52447 −0.572860
\(94\) 9.53668 + 13.9060i 0.983634 + 1.43430i
\(95\) 3.68349 0.377918
\(96\) 5.60466 + 0.766689i 0.572023 + 0.0782499i
\(97\) 14.5334i 1.47564i −0.674998 0.737820i \(-0.735856\pi\)
0.674998 0.737820i \(-0.264144\pi\)
\(98\) 4.65459 3.19209i 0.470185 0.322450i
\(99\) −5.29746 −0.532415
\(100\) 3.06401 7.93406i 0.306401 0.793406i
\(101\) 13.9988i 1.39293i −0.717591 0.696465i \(-0.754755\pi\)
0.717591 0.696465i \(-0.245245\pi\)
\(102\) 5.62783 3.85953i 0.557238 0.382151i
\(103\) 13.2752i 1.30805i 0.756474 + 0.654024i \(0.226920\pi\)
−0.756474 + 0.654024i \(0.773080\pi\)
\(104\) 3.88697 0.920728i 0.381149 0.0902848i
\(105\) 1.49969i 0.146355i
\(106\) −7.13209 10.3997i −0.692729 1.01011i
\(107\) 18.1278i 1.75248i −0.481871 0.876242i \(-0.660043\pi\)
0.481871 0.876242i \(-0.339957\pi\)
\(108\) 0.720507 1.86571i 0.0693308 0.179528i
\(109\) 0.269146i 0.0257795i 0.999917 + 0.0128897i \(0.00410304\pi\)
−0.999917 + 0.0128897i \(0.995897\pi\)
\(110\) 3.66317 + 5.34150i 0.349270 + 0.509292i
\(111\) −7.24325 −0.687499
\(112\) 5.13765 + 4.66369i 0.485462 + 0.440677i
\(113\) 8.30424i 0.781198i −0.920561 0.390599i \(-0.872268\pi\)
0.920561 0.390599i \(-0.127732\pi\)
\(114\) 3.40783 + 4.96918i 0.319173 + 0.465406i
\(115\) 1.66124 0.154911
\(116\) −1.54079 + 3.98978i −0.143059 + 0.370442i
\(117\) 1.41228i 0.130565i
\(118\) −11.5352 16.8202i −1.06190 1.54843i
\(119\) 8.37045 0.767317
\(120\) −2.37944 + 0.563632i −0.217213 + 0.0514523i
\(121\) 17.0631 1.55119
\(122\) 9.95172 + 14.5112i 0.900986 + 1.31378i
\(123\) 0.306352i 0.0276229i
\(124\) −3.98042 + 10.3070i −0.357452 + 0.925600i
\(125\) 7.99922i 0.715472i
\(126\) 2.02315 1.38746i 0.180236 0.123605i
\(127\) 5.90821i 0.524269i 0.965031 + 0.262135i \(0.0844265\pi\)
−0.965031 + 0.262135i \(0.915574\pi\)
\(128\) 5.46862 9.90425i 0.483362 0.875421i
\(129\) 1.13429 0.0998683
\(130\) −1.42402 + 0.976585i −0.124895 + 0.0856522i
\(131\) 6.08889i 0.531989i 0.963975 + 0.265994i \(0.0857003\pi\)
−0.963975 + 0.265994i \(0.914300\pi\)
\(132\) −3.81686 + 9.88352i −0.332215 + 0.860250i
\(133\) 7.39081i 0.640864i
\(134\) 10.7776 4.22401i 0.931047 0.364899i
\(135\) 0.864540i 0.0744078i
\(136\) −3.14587 13.2807i −0.269757 1.13881i
\(137\) 15.3658i 1.31279i 0.754418 + 0.656394i \(0.227919\pi\)
−0.754418 + 0.656394i \(0.772081\pi\)
\(138\) 1.53692 + 2.24107i 0.130831 + 0.190773i
\(139\) 5.86116 0.497137 0.248569 0.968614i \(-0.420040\pi\)
0.248569 + 0.968614i \(0.420040\pi\)
\(140\) −2.79799 1.08054i −0.236474 0.0913224i
\(141\) 11.9232i 1.00412i
\(142\) −6.50944 9.49182i −0.546260 0.796536i
\(143\) 7.48150i 0.625635i
\(144\) −2.96174 2.68851i −0.246812 0.224043i
\(145\) 1.84880i 0.153535i
\(146\) −15.0191 + 10.3000i −1.24299 + 0.852434i
\(147\) −3.99091 −0.329165
\(148\) −5.21881 + 13.5138i −0.428984 + 1.11083i
\(149\) −6.79582 −0.556735 −0.278368 0.960475i \(-0.589793\pi\)
−0.278368 + 0.960475i \(0.589793\pi\)
\(150\) −4.95977 + 3.40138i −0.404963 + 0.277722i
\(151\) 7.39573i 0.601856i 0.953647 + 0.300928i \(0.0972964\pi\)
−0.953647 + 0.300928i \(0.902704\pi\)
\(152\) 11.7264 2.77770i 0.951137 0.225301i
\(153\) −4.82537 −0.390108
\(154\) −10.7175 + 7.35004i −0.863645 + 0.592283i
\(155\) 4.77612i 0.383627i
\(156\) −2.63490 1.01756i −0.210961 0.0814699i
\(157\) −0.0538536 −0.00429799 −0.00214899 0.999998i \(-0.500684\pi\)
−0.00214899 + 0.999998i \(0.500684\pi\)
\(158\) 9.56378 6.55879i 0.760853 0.521789i
\(159\) 8.91687i 0.707154i
\(160\) −0.662834 + 4.84545i −0.0524016 + 0.383067i
\(161\) 3.33322i 0.262694i
\(162\) −1.16630 + 0.799841i −0.0916331 + 0.0628415i
\(163\) 12.2858i 0.962295i 0.876640 + 0.481148i \(0.159780\pi\)
−0.876640 + 0.481148i \(0.840220\pi\)
\(164\) 0.571564 + 0.220729i 0.0446317 + 0.0172361i
\(165\) 4.57987i 0.356542i
\(166\) 0.312629 + 0.455864i 0.0242647 + 0.0353819i
\(167\) 4.12074i 0.318873i 0.987208 + 0.159436i \(0.0509677\pi\)
−0.987208 + 0.159436i \(0.949032\pi\)
\(168\) −1.13091 4.77428i −0.0872516 0.368344i
\(169\) 11.0055 0.846574
\(170\) 3.33672 + 4.86548i 0.255915 + 0.373166i
\(171\) 4.26064i 0.325819i
\(172\) 0.817261 2.11625i 0.0623156 0.161362i
\(173\) −7.30908 −0.555699 −0.277850 0.960625i \(-0.589622\pi\)
−0.277850 + 0.960625i \(0.589622\pi\)
\(174\) 2.49411 1.71044i 0.189078 0.129668i
\(175\) −7.37682 −0.557635
\(176\) 15.6897 + 14.2423i 1.18266 + 1.07355i
\(177\) 14.4219i 1.08401i
\(178\) 6.68621 4.58537i 0.501153 0.343688i
\(179\) 0.730284 0.0545840 0.0272920 0.999628i \(-0.491312\pi\)
0.0272920 + 0.999628i \(0.491312\pi\)
\(180\) 1.61298 + 0.622907i 0.120224 + 0.0464288i
\(181\) −12.7461 −0.947412 −0.473706 0.880683i \(-0.657084\pi\)
−0.473706 + 0.880683i \(0.657084\pi\)
\(182\) −1.95949 2.85725i −0.145247 0.211794i
\(183\) 12.4421i 0.919747i
\(184\) 5.28855 1.25273i 0.389877 0.0923523i
\(185\) 6.26208i 0.460397i
\(186\) 6.44318 4.41870i 0.472437 0.323995i
\(187\) 25.5622 1.86930
\(188\) −22.2452 8.59076i −1.62240 0.626546i
\(189\) −1.73467 −0.126179
\(190\) −4.29605 + 2.94621i −0.311668 + 0.213740i
\(191\) −22.8704 −1.65484 −0.827420 0.561583i \(-0.810192\pi\)
−0.827420 + 0.561583i \(0.810192\pi\)
\(192\) −7.14994 + 3.58865i −0.516002 + 0.258988i
\(193\) 17.6675 1.27173 0.635866 0.771800i \(-0.280643\pi\)
0.635866 + 0.771800i \(0.280643\pi\)
\(194\) 11.6244 + 16.9502i 0.834582 + 1.21696i
\(195\) 1.22097 0.0874357
\(196\) −2.87548 + 7.44587i −0.205391 + 0.531848i
\(197\) 8.79635i 0.626714i 0.949635 + 0.313357i \(0.101454\pi\)
−0.949635 + 0.313357i \(0.898546\pi\)
\(198\) 6.17843 4.23713i 0.439082 0.301120i
\(199\) 12.5962i 0.892921i 0.894803 + 0.446461i \(0.147316\pi\)
−0.894803 + 0.446461i \(0.852684\pi\)
\(200\) 2.77244 + 11.7042i 0.196041 + 0.827612i
\(201\) −7.97425 1.84697i −0.562460 0.130275i
\(202\) 11.1968 + 16.3268i 0.787804 + 1.14875i
\(203\) 3.70956 0.260360
\(204\) −3.47672 + 9.00274i −0.243419 + 0.630318i
\(205\) −0.264854 −0.0184982
\(206\) −10.6181 15.4829i −0.739797 1.07874i
\(207\) 1.92153i 0.133555i
\(208\) −3.79693 + 4.18280i −0.263270 + 0.290025i
\(209\) 22.5706i 1.56124i
\(210\) 1.19952 + 1.74909i 0.0827746 + 0.120699i
\(211\) 22.3042i 1.53549i 0.640757 + 0.767744i \(0.278621\pi\)
−0.640757 + 0.767744i \(0.721379\pi\)
\(212\) 16.6363 + 6.42467i 1.14259 + 0.441248i
\(213\) 8.13841i 0.557635i
\(214\) 14.4994 + 21.1425i 0.991158 + 1.44527i
\(215\) 0.980636i 0.0668788i
\(216\) 0.651944 + 2.75227i 0.0443592 + 0.187268i
\(217\) 9.58314 0.650546
\(218\) −0.215274 0.313904i −0.0145802 0.0212603i
\(219\) 12.8776 0.870184
\(220\) −8.54470 3.29983i −0.576084 0.222474i
\(221\) 6.81478i 0.458412i
\(222\) 8.44779 5.79345i 0.566979 0.388831i
\(223\) 7.97926i 0.534331i 0.963651 + 0.267165i \(0.0860870\pi\)
−0.963651 + 0.267165i \(0.913913\pi\)
\(224\) −9.72225 1.32996i −0.649595 0.0888614i
\(225\) 4.25257 0.283505
\(226\) 6.64208 + 9.68523i 0.441825 + 0.644252i
\(227\) 2.50636i 0.166353i −0.996535 0.0831765i \(-0.973493\pi\)
0.996535 0.0831765i \(-0.0265065\pi\)
\(228\) −7.94910 3.06982i −0.526442 0.203304i
\(229\) 14.1223i 0.933226i 0.884462 + 0.466613i \(0.154526\pi\)
−0.884462 + 0.466613i \(0.845474\pi\)
\(230\) −1.93750 + 1.32873i −0.127755 + 0.0876136i
\(231\) 9.18937 0.604616
\(232\) −1.39417 5.88567i −0.0915317 0.386413i
\(233\) 19.5570i 1.28122i −0.767866 0.640610i \(-0.778682\pi\)
0.767866 0.640610i \(-0.221318\pi\)
\(234\) 1.12960 + 1.64714i 0.0738443 + 0.107677i
\(235\) 10.3081 0.672426
\(236\) 26.9070 + 10.3911i 1.75150 + 0.676400i
\(237\) −8.20011 −0.532654
\(238\) −9.76244 + 6.69503i −0.632805 + 0.433974i
\(239\) −2.10620 −0.136239 −0.0681193 0.997677i \(-0.521700\pi\)
−0.0681193 + 0.997677i \(0.521700\pi\)
\(240\) 2.32433 2.56054i 0.150035 0.165282i
\(241\) 6.84337 0.440821 0.220410 0.975407i \(-0.429260\pi\)
0.220410 + 0.975407i \(0.429260\pi\)
\(242\) −19.9007 + 13.6478i −1.27927 + 0.877313i
\(243\) 1.00000 0.0641500
\(244\) −23.2134 8.96463i −1.48608 0.573902i
\(245\) 3.45030i 0.220432i
\(246\) −0.245033 0.357299i −0.0156228 0.0227805i
\(247\) −6.01721 −0.382866
\(248\) −3.60164 15.2048i −0.228705 0.965506i
\(249\) 0.390864i 0.0247700i
\(250\) −6.39811 9.32948i −0.404652 0.590048i
\(251\) 23.8453 1.50510 0.752551 0.658534i \(-0.228823\pi\)
0.752551 + 0.658534i \(0.228823\pi\)
\(252\) −1.24984 + 3.23639i −0.0787328 + 0.203874i
\(253\) 10.1792i 0.639961i
\(254\) −4.72564 6.89075i −0.296513 0.432364i
\(255\) 4.17173i 0.261244i
\(256\) 1.54379 + 15.9253i 0.0964870 + 0.995334i
\(257\) 9.09968 0.567623 0.283811 0.958880i \(-0.408401\pi\)
0.283811 + 0.958880i \(0.408401\pi\)
\(258\) −1.32292 + 0.907249i −0.0823612 + 0.0564829i
\(259\) 12.5647 0.780731
\(260\) 0.879720 2.27798i 0.0545579 0.141274i
\(261\) −2.13848 −0.132369
\(262\) −4.87015 7.10147i −0.300879 0.438730i
\(263\) 27.3721i 1.68783i −0.536474 0.843917i \(-0.680244\pi\)
0.536474 0.843917i \(-0.319756\pi\)
\(264\) −3.45365 14.5800i −0.212558 0.897339i
\(265\) −7.70900 −0.473560
\(266\) −5.91148 8.61989i −0.362456 0.528520i
\(267\) −5.73285 −0.350845
\(268\) −9.19142 + 13.5469i −0.561455 + 0.827507i
\(269\) 6.06672 0.369894 0.184947 0.982748i \(-0.440789\pi\)
0.184947 + 0.982748i \(0.440789\pi\)
\(270\) −0.691495 1.00831i −0.0420831 0.0613639i
\(271\) −0.0167864 −0.00101970 −0.000509850 1.00000i \(-0.500162\pi\)
−0.000509850 1.00000i \(0.500162\pi\)
\(272\) 14.2915 + 12.9731i 0.866549 + 0.786609i
\(273\) 2.44984i 0.148271i
\(274\) −12.2902 17.9211i −0.742478 1.08265i
\(275\) −22.5278 −1.35848
\(276\) −3.58501 1.38447i −0.215792 0.0833355i
\(277\) 2.17332 0.130582 0.0652911 0.997866i \(-0.479202\pi\)
0.0652911 + 0.997866i \(0.479202\pi\)
\(278\) −6.83587 + 4.68800i −0.409988 + 0.281168i
\(279\) −5.52447 −0.330741
\(280\) 4.12756 0.977717i 0.246669 0.0584298i
\(281\) 12.9816i 0.774419i 0.921992 + 0.387210i \(0.126561\pi\)
−0.921992 + 0.387210i \(0.873439\pi\)
\(282\) 9.53668 + 13.9060i 0.567901 + 0.828092i
\(283\) 21.6115i 1.28467i −0.766423 0.642336i \(-0.777965\pi\)
0.766423 0.642336i \(-0.222035\pi\)
\(284\) 15.1839 + 5.86378i 0.900999 + 0.347952i
\(285\) 3.68349 0.218191
\(286\) −5.98402 8.72567i −0.353842 0.515960i
\(287\) 0.531421i 0.0313688i
\(288\) 5.60466 + 0.766689i 0.330258 + 0.0451776i
\(289\) 6.28423 0.369661
\(290\) 1.47875 + 2.15626i 0.0868351 + 0.126620i
\(291\) 14.5334i 0.851961i
\(292\) 9.27837 24.0258i 0.542976 1.40600i
\(293\) −20.3556 −1.18919 −0.594594 0.804026i \(-0.702687\pi\)
−0.594594 + 0.804026i \(0.702687\pi\)
\(294\) 4.65459 3.19209i 0.271461 0.186167i
\(295\) −12.4683 −0.725932
\(296\) −4.72219 19.9353i −0.274472 1.15872i
\(297\) −5.29746 −0.307390
\(298\) 7.92596 5.43558i 0.459139 0.314875i
\(299\) −2.71373 −0.156939
\(300\) 3.06401 7.93406i 0.176901 0.458073i
\(301\) −1.96762 −0.113411
\(302\) −5.91541 8.62564i −0.340394 0.496350i
\(303\) 13.9988i 0.804209i
\(304\) −11.4548 + 12.6189i −0.656976 + 0.723743i
\(305\) 10.7567 0.615927
\(306\) 5.62783 3.85953i 0.321722 0.220635i
\(307\) 19.9608i 1.13922i −0.821914 0.569612i \(-0.807093\pi\)
0.821914 0.569612i \(-0.192907\pi\)
\(308\) 6.62101 17.1447i 0.377267 0.976909i
\(309\) 13.2752i 0.755202i
\(310\) 3.82014 + 5.57039i 0.216969 + 0.316377i
\(311\) 5.81890 0.329960 0.164980 0.986297i \(-0.447244\pi\)
0.164980 + 0.986297i \(0.447244\pi\)
\(312\) 3.88697 0.920728i 0.220056 0.0521260i
\(313\) 6.55868i 0.370719i −0.982671 0.185359i \(-0.940655\pi\)
0.982671 0.185359i \(-0.0593449\pi\)
\(314\) 0.0628094 0.0430744i 0.00354454 0.00243083i
\(315\) 1.49969i 0.0844982i
\(316\) −5.90824 + 15.2990i −0.332364 + 0.860637i
\(317\) −31.6370 −1.77691 −0.888455 0.458963i \(-0.848221\pi\)
−0.888455 + 0.458963i \(0.848221\pi\)
\(318\) −7.13209 10.3997i −0.399948 0.583189i
\(319\) 11.3285 0.634275
\(320\) −3.10253 6.18141i −0.173437 0.345551i
\(321\) 18.1278i 1.01180i
\(322\) −2.66605 3.88753i −0.148573 0.216644i
\(323\) 20.5592i 1.14394i
\(324\) 0.720507 1.86571i 0.0400282 0.103650i
\(325\) 6.00582i 0.333143i
\(326\) −9.82666 14.3289i −0.544248 0.793603i
\(327\) 0.269146i 0.0148838i
\(328\) −0.843163 + 0.199725i −0.0465559 + 0.0110280i
\(329\) 20.6829i 1.14028i
\(330\) 3.66317 + 5.34150i 0.201651 + 0.294040i
\(331\) 10.0039 0.549863 0.274932 0.961464i \(-0.411345\pi\)
0.274932 + 0.961464i \(0.411345\pi\)
\(332\) −0.729238 0.281620i −0.0400221 0.0154559i
\(333\) −7.24325 −0.396928
\(334\) −3.29594 4.80602i −0.180346 0.262974i
\(335\) 1.59678 6.89406i 0.0872415 0.376663i
\(336\) 5.13765 + 4.66369i 0.280282 + 0.254425i
\(337\) 6.57449i 0.358135i 0.983837 + 0.179068i \(0.0573081\pi\)
−0.983837 + 0.179068i \(0.942692\pi\)
\(338\) −12.8357 + 8.80263i −0.698168 + 0.478800i
\(339\) 8.30424i 0.451025i
\(340\) −7.78323 3.00576i −0.422105 0.163010i
\(341\) 29.2657 1.58482
\(342\) 3.40783 + 4.96918i 0.184274 + 0.268702i
\(343\) 19.0656 1.02945
\(344\) 0.739491 + 3.12186i 0.0398707 + 0.168319i
\(345\) 1.66124 0.0894379
\(346\) 8.52458 5.84611i 0.458284 0.314289i
\(347\) 16.0583 0.862053 0.431026 0.902339i \(-0.358152\pi\)
0.431026 + 0.902339i \(0.358152\pi\)
\(348\) −1.54079 + 3.98978i −0.0825950 + 0.213875i
\(349\) −7.85175 −0.420294 −0.210147 0.977670i \(-0.567394\pi\)
−0.210147 + 0.977670i \(0.567394\pi\)
\(350\) 8.60358 5.90029i 0.459881 0.315384i
\(351\) 1.41228i 0.0753819i
\(352\) −29.6905 4.06151i −1.58251 0.216479i
\(353\) 8.89900i 0.473646i −0.971553 0.236823i \(-0.923894\pi\)
0.971553 0.236823i \(-0.0761061\pi\)
\(354\) −11.5352 16.8202i −0.613089 0.893984i
\(355\) −7.03598 −0.373431
\(356\) −4.13056 + 10.6958i −0.218919 + 0.566877i
\(357\) 8.37045 0.443011
\(358\) −0.851729 + 0.584111i −0.0450153 + 0.0308712i
\(359\) 14.9369i 0.788339i −0.919038 0.394169i \(-0.871032\pi\)
0.919038 0.394169i \(-0.128968\pi\)
\(360\) −2.37944 + 0.563632i −0.125408 + 0.0297060i
\(361\) 0.846986 0.0445782
\(362\) 14.8658 10.1949i 0.781329 0.535831i
\(363\) 17.0631 0.895581
\(364\) 4.57070 + 1.76513i 0.239570 + 0.0925180i
\(365\) 11.1332i 0.582736i
\(366\) 9.95172 + 14.5112i 0.520185 + 0.758514i
\(367\) 26.5010 1.38334 0.691672 0.722212i \(-0.256875\pi\)
0.691672 + 0.722212i \(0.256875\pi\)
\(368\) −5.16605 + 5.69106i −0.269299 + 0.296667i
\(369\) 0.306352i 0.0159481i
\(370\) 5.00867 + 7.30346i 0.260388 + 0.379689i
\(371\) 15.4679i 0.803051i
\(372\) −3.98042 + 10.3070i −0.206375 + 0.534395i
\(373\) 20.8471i 1.07942i −0.841850 0.539711i \(-0.818533\pi\)
0.841850 0.539711i \(-0.181467\pi\)
\(374\) −29.8132 + 20.4457i −1.54160 + 1.05722i
\(375\) 7.99922i 0.413078i
\(376\) 32.8159 7.77327i 1.69235 0.400876i
\(377\) 3.02013i 0.155545i
\(378\) 2.02315 1.38746i 0.104059 0.0713634i
\(379\) −26.9070 −1.38212 −0.691059 0.722799i \(-0.742855\pi\)
−0.691059 + 0.722799i \(0.742855\pi\)
\(380\) 2.65398 6.87232i 0.136146 0.352543i
\(381\) 5.90821i 0.302687i
\(382\) 26.6737 18.2927i 1.36474 0.935934i
\(383\) −10.2607 −0.524299 −0.262149 0.965027i \(-0.584431\pi\)
−0.262149 + 0.965027i \(0.584431\pi\)
\(384\) 5.46862 9.90425i 0.279069 0.505424i
\(385\) 7.94458i 0.404893i
\(386\) −20.6055 + 14.1312i −1.04879 + 0.719258i
\(387\) 1.13429 0.0576590
\(388\) −27.1150 10.4714i −1.37656 0.531604i
\(389\) 6.96170 0.352972 0.176486 0.984303i \(-0.443527\pi\)
0.176486 + 0.984303i \(0.443527\pi\)
\(390\) −1.42402 + 0.976585i −0.0721080 + 0.0494513i
\(391\) 9.27208i 0.468909i
\(392\) −2.60185 10.9840i −0.131413 0.554778i
\(393\) 6.08889i 0.307144i
\(394\) −7.03568 10.2592i −0.354453 0.516850i
\(395\) 7.08932i 0.356703i
\(396\) −3.81686 + 9.88352i −0.191804 + 0.496666i
\(397\) 6.12220 0.307265 0.153632 0.988128i \(-0.450903\pi\)
0.153632 + 0.988128i \(0.450903\pi\)
\(398\) −10.0750 14.6909i −0.505013 0.736391i
\(399\) 7.39081i 0.370003i
\(400\) −12.5950 11.4331i −0.629750 0.571655i
\(401\) 27.0636i 1.35149i −0.737134 0.675747i \(-0.763821\pi\)
0.737134 0.675747i \(-0.236179\pi\)
\(402\) 10.7776 4.22401i 0.537540 0.210675i
\(403\) 7.80209i 0.388650i
\(404\) −26.1176 10.0862i −1.29940 0.501808i
\(405\) 0.864540i 0.0429593i
\(406\) −4.32646 + 2.96706i −0.214719 + 0.147253i
\(407\) 38.3708 1.90197
\(408\) −3.14587 13.2807i −0.155744 0.657493i
\(409\) 20.7912i 1.02806i 0.857773 + 0.514028i \(0.171847\pi\)
−0.857773 + 0.514028i \(0.828153\pi\)
\(410\) 0.308899 0.211841i 0.0152554 0.0104621i
\(411\) 15.3658i 0.757939i
\(412\) 24.7677 + 9.56490i 1.22022 + 0.471229i
\(413\) 25.0172i 1.23102i
\(414\) 1.53692 + 2.24107i 0.0755353 + 0.110143i
\(415\) 0.337917 0.0165877
\(416\) 1.08278 7.91535i 0.0530877 0.388082i
\(417\) 5.86116 0.287022
\(418\) −18.0529 26.3240i −0.882995 1.28755i
\(419\) 14.1385i 0.690710i −0.938472 0.345355i \(-0.887759\pi\)
0.938472 0.345355i \(-0.112241\pi\)
\(420\) −2.79799 1.08054i −0.136528 0.0527250i
\(421\) −17.8438 −0.869652 −0.434826 0.900515i \(-0.643190\pi\)
−0.434826 + 0.900515i \(0.643190\pi\)
\(422\) −17.8399 26.0134i −0.868431 1.26631i
\(423\) 11.9232i 0.579726i
\(424\) −24.5416 + 5.81331i −1.19185 + 0.282319i
\(425\) −20.5202 −0.995378
\(426\) −6.50944 9.49182i −0.315383 0.459880i
\(427\) 21.5830i 1.04447i
\(428\) −33.8213 13.0612i −1.63481 0.631339i
\(429\) 7.48150i 0.361210i
\(430\) −0.784353 1.14371i −0.0378249 0.0551548i
\(431\) 8.97477i 0.432300i −0.976360 0.216150i \(-0.930650\pi\)
0.976360 0.216150i \(-0.0693500\pi\)
\(432\) −2.96174 2.68851i −0.142497 0.129351i
\(433\) 33.9473i 1.63140i −0.578473 0.815701i \(-0.696351\pi\)
0.578473 0.815701i \(-0.303649\pi\)
\(434\) −11.1768 + 7.66499i −0.536504 + 0.367931i
\(435\) 1.84880i 0.0886433i
\(436\) 0.502147 + 0.193921i 0.0240485 + 0.00928715i
\(437\) −8.18692 −0.391633
\(438\) −15.0191 + 10.3000i −0.717639 + 0.492153i
\(439\) 5.66649i 0.270447i −0.990815 0.135223i \(-0.956825\pi\)
0.990815 0.135223i \(-0.0431752\pi\)
\(440\) 12.6050 2.98582i 0.600921 0.142343i
\(441\) −3.99091 −0.190043
\(442\) −5.45074 7.94807i −0.259265 0.378051i
\(443\) −1.87188 −0.0889358 −0.0444679 0.999011i \(-0.514159\pi\)
−0.0444679 + 0.999011i \(0.514159\pi\)
\(444\) −5.21881 + 13.5138i −0.247674 + 0.641336i
\(445\) 4.95628i 0.234950i
\(446\) −6.38215 9.30621i −0.302203 0.440662i
\(447\) −6.79582 −0.321431
\(448\) 12.4028 6.22513i 0.585977 0.294110i
\(449\) 4.44786 0.209907 0.104954 0.994477i \(-0.466531\pi\)
0.104954 + 0.994477i \(0.466531\pi\)
\(450\) −4.95977 + 3.40138i −0.233806 + 0.160343i
\(451\) 1.62289i 0.0764189i
\(452\) −15.4933 5.98327i −0.728744 0.281429i
\(453\) 7.39573i 0.347482i
\(454\) 2.00469 + 2.92317i 0.0940848 + 0.137191i
\(455\) −2.11799 −0.0992929
\(456\) 11.7264 2.77770i 0.549139 0.130078i
\(457\) −2.77148 −0.129644 −0.0648221 0.997897i \(-0.520648\pi\)
−0.0648221 + 0.997897i \(0.520648\pi\)
\(458\) −11.2956 16.4708i −0.527808 0.769629i
\(459\) −4.82537 −0.225229
\(460\) 1.19693 3.09938i 0.0558073 0.144509i
\(461\) −13.1624 −0.613033 −0.306517 0.951865i \(-0.599163\pi\)
−0.306517 + 0.951865i \(0.599163\pi\)
\(462\) −10.7175 + 7.35004i −0.498626 + 0.341955i
\(463\) 39.7716 1.84834 0.924170 0.381980i \(-0.124758\pi\)
0.924170 + 0.381980i \(0.124758\pi\)
\(464\) 6.33362 + 5.74933i 0.294031 + 0.266906i
\(465\) 4.77612i 0.221487i
\(466\) 15.6425 + 22.8093i 0.724624 + 1.05662i
\(467\) 7.56735i 0.350175i 0.984553 + 0.175088i \(0.0560209\pi\)
−0.984553 + 0.175088i \(0.943979\pi\)
\(468\) −2.63490 1.01756i −0.121798 0.0470366i
\(469\) 13.8327 + 3.20389i 0.638736 + 0.147942i
\(470\) −12.0223 + 8.24484i −0.554549 + 0.380306i
\(471\) −0.0538536 −0.00248144
\(472\) −39.6928 + 9.40225i −1.82701 + 0.432774i
\(473\) −6.00884 −0.276287
\(474\) 9.56378 6.55879i 0.439279 0.301255i
\(475\) 18.1187i 0.831341i
\(476\) 6.03097 15.6168i 0.276429 0.715795i
\(477\) 8.91687i 0.408276i
\(478\) 2.45646 1.68462i 0.112356 0.0770529i
\(479\) 2.91534i 0.133205i 0.997780 + 0.0666027i \(0.0212160\pi\)
−0.997780 + 0.0666027i \(0.978784\pi\)
\(480\) −0.662834 + 4.84545i −0.0302541 + 0.221164i
\(481\) 10.2295i 0.466425i
\(482\) −7.98142 + 5.47361i −0.363544 + 0.249316i
\(483\) 3.33322i 0.151667i
\(484\) 12.2941 31.8348i 0.558823 1.44704i
\(485\) 12.5647 0.570532
\(486\) −1.16630 + 0.799841i −0.0529044 + 0.0362815i
\(487\) −39.0862 −1.77116 −0.885582 0.464483i \(-0.846240\pi\)
−0.885582 + 0.464483i \(0.846240\pi\)
\(488\) 34.2440 8.11156i 1.55015 0.367193i
\(489\) 12.2858i 0.555581i
\(490\) 2.75969 + 4.02408i 0.124670 + 0.181790i
\(491\) 9.17446i 0.414037i 0.978337 + 0.207019i \(0.0663761\pi\)
−0.978337 + 0.207019i \(0.933624\pi\)
\(492\) 0.571564 + 0.220729i 0.0257681 + 0.00995124i
\(493\) 10.3190 0.464743
\(494\) 7.01787 4.81281i 0.315749 0.216539i
\(495\) 4.57987i 0.205850i
\(496\) 16.3620 + 14.8526i 0.734677 + 0.666901i
\(497\) 14.1175i 0.633256i
\(498\) 0.312629 + 0.455864i 0.0140092 + 0.0204278i
\(499\) −22.8786 −1.02419 −0.512093 0.858930i \(-0.671130\pi\)
−0.512093 + 0.858930i \(0.671130\pi\)
\(500\) 14.9242 + 5.76350i 0.667431 + 0.257751i
\(501\) 4.12074i 0.184101i
\(502\) −27.8108 + 19.0725i −1.24126 + 0.851246i
\(503\) −1.07299 −0.0478422 −0.0239211 0.999714i \(-0.507615\pi\)
−0.0239211 + 0.999714i \(0.507615\pi\)
\(504\) −1.13091 4.77428i −0.0503747 0.212663i
\(505\) 12.1025 0.538554
\(506\) −8.14175 11.8720i −0.361945 0.527775i
\(507\) 11.0055 0.488770
\(508\) 11.0230 + 4.25691i 0.489067 + 0.188870i
\(509\) −40.6639 −1.80239 −0.901197 0.433410i \(-0.857310\pi\)
−0.901197 + 0.433410i \(0.857310\pi\)
\(510\) 3.33672 + 4.86548i 0.147753 + 0.215447i
\(511\) −22.3383 −0.988190
\(512\) −14.5383 17.3389i −0.642507 0.766280i
\(513\) 4.26064i 0.188112i
\(514\) −10.6130 + 7.27830i −0.468117 + 0.321032i
\(515\) −11.4770 −0.505736
\(516\) 0.817261 2.11625i 0.0359779 0.0931626i
\(517\) 63.1628i 2.77790i
\(518\) −14.6542 + 10.0497i −0.643867 + 0.441560i
\(519\) −7.30908 −0.320833
\(520\) 0.796006 + 3.36044i 0.0349072 + 0.147365i
\(521\) 3.99748i 0.175133i 0.996159 + 0.0875663i \(0.0279090\pi\)
−0.996159 + 0.0875663i \(0.972091\pi\)
\(522\) 2.49411 1.71044i 0.109164 0.0748641i
\(523\) 0.0484445i 0.00211833i −0.999999 0.00105916i \(-0.999663\pi\)
0.999999 0.00105916i \(-0.000337143\pi\)
\(524\) 11.3601 + 4.38709i 0.496268 + 0.191651i
\(525\) −7.37682 −0.321951
\(526\) 21.8933 + 31.9240i 0.954594 + 1.39195i
\(527\) 26.6576 1.16122
\(528\) 15.6897 + 14.2423i 0.682807 + 0.619817i
\(529\) 19.3077 0.839467
\(530\) 8.99100 6.16598i 0.390544 0.267833i
\(531\) 14.4219i 0.625856i
\(532\) 13.7891 + 5.32513i 0.597833 + 0.230874i
\(533\) 0.432656 0.0187404
\(534\) 6.68621 4.58537i 0.289341 0.198428i
\(535\) 15.6722 0.677570
\(536\) −0.115408 23.1514i −0.00498488 0.999988i
\(537\) 0.730284 0.0315141
\(538\) −7.07561 + 4.85241i −0.305051 + 0.209202i
\(539\) 21.1417 0.910637
\(540\) 1.61298 + 0.622907i 0.0694116 + 0.0268057i
\(541\) 1.19504i 0.0513788i 0.999670 + 0.0256894i \(0.00817809\pi\)
−0.999670 + 0.0256894i \(0.991822\pi\)
\(542\) 0.0195779 0.0134264i 0.000840945 0.000576715i
\(543\) −12.7461 −0.546988
\(544\) −27.0446 3.69956i −1.15953 0.158617i
\(545\) −0.232687 −0.00996722
\(546\) −1.95949 2.85725i −0.0838583 0.122279i
\(547\) 8.81373 0.376848 0.188424 0.982088i \(-0.439662\pi\)
0.188424 + 0.982088i \(0.439662\pi\)
\(548\) 28.6681 + 11.0712i 1.22464 + 0.472937i
\(549\) 12.4421i 0.531016i
\(550\) 26.2742 18.0187i 1.12034 0.768320i
\(551\) 9.11128i 0.388154i
\(552\) 5.28855 1.25273i 0.225096 0.0533196i
\(553\) 14.2245 0.604888
\(554\) −2.53474 + 1.73831i −0.107691 + 0.0738538i
\(555\) 6.26208i 0.265810i
\(556\) 4.22301 10.9352i 0.179096 0.463757i
\(557\) −10.9826 −0.465349 −0.232675 0.972555i \(-0.574748\pi\)
−0.232675 + 0.972555i \(0.574748\pi\)
\(558\) 6.44318 4.41870i 0.272762 0.187058i
\(559\) 1.60193i 0.0677544i
\(560\) −4.03195 + 4.44170i −0.170381 + 0.187696i
\(561\) 25.5622 1.07924
\(562\) −10.3833 15.1405i −0.437991 0.638662i
\(563\) −38.0350 −1.60298 −0.801491 0.598006i \(-0.795960\pi\)
−0.801491 + 0.598006i \(0.795960\pi\)
\(564\) −22.2452 8.59076i −0.936694 0.361736i
\(565\) 7.17935 0.302038
\(566\) 17.2858 + 25.2055i 0.726576 + 1.05947i
\(567\) −1.73467 −0.0728494
\(568\) −22.3991 + 5.30579i −0.939844 + 0.222626i
\(569\) 25.6937 1.07714 0.538569 0.842582i \(-0.318965\pi\)
0.538569 + 0.842582i \(0.318965\pi\)
\(570\) −4.29605 + 2.94621i −0.179942 + 0.123403i
\(571\) 0.476282i 0.0199318i 0.999950 + 0.00996588i \(0.00317229\pi\)
−0.999950 + 0.00996588i \(0.996828\pi\)
\(572\) 13.9583 + 5.39048i 0.583626 + 0.225387i
\(573\) −22.8704 −0.955423
\(574\) 0.425053 + 0.619796i 0.0177414 + 0.0258698i
\(575\) 8.17142i 0.340772i
\(576\) −7.14994 + 3.58865i −0.297914 + 0.149527i
\(577\) 33.5594i 1.39710i 0.715563 + 0.698549i \(0.246170\pi\)
−0.715563 + 0.698549i \(0.753830\pi\)
\(578\) −7.32929 + 5.02639i −0.304858 + 0.209070i
\(579\) 17.6675 0.734235
\(580\) −3.44933 1.33208i −0.143225 0.0553114i
\(581\) 0.678021i 0.0281290i
\(582\) 11.6244 + 16.9502i 0.481846 + 0.702610i
\(583\) 47.2368i 1.95635i
\(584\) 8.39545 + 35.4425i 0.347406 + 1.46662i
\(585\) 1.22097 0.0504810
\(586\) 23.7407 16.2813i 0.980721 0.672573i
\(587\) −30.0349 −1.23967 −0.619837 0.784731i \(-0.712801\pi\)
−0.619837 + 0.784731i \(0.712801\pi\)
\(588\) −2.87548 + 7.44587i −0.118583 + 0.307063i
\(589\) 23.5377i 0.969855i
\(590\) 14.5417 9.97265i 0.598674 0.410568i
\(591\) 8.79635i 0.361833i
\(592\) 21.4526 + 19.4736i 0.881697 + 0.800359i
\(593\) 24.2923i 0.997565i −0.866727 0.498783i \(-0.833781\pi\)
0.866727 0.498783i \(-0.166219\pi\)
\(594\) 6.17843 4.23713i 0.253504 0.173852i
\(595\) 7.23659i 0.296671i
\(596\) −4.89644 + 12.6790i −0.200566 + 0.519353i
\(597\) 12.5962i 0.515528i
\(598\) 3.16502 2.17056i 0.129427 0.0887606i
\(599\) 19.6921 0.804599 0.402300 0.915508i \(-0.368211\pi\)
0.402300 + 0.915508i \(0.368211\pi\)
\(600\) 2.77244 + 11.7042i 0.113184 + 0.477822i
\(601\) −38.9082 −1.58710 −0.793549 0.608506i \(-0.791769\pi\)
−0.793549 + 0.608506i \(0.791769\pi\)
\(602\) 2.29483 1.57378i 0.0935302 0.0641425i
\(603\) −7.97425 1.84697i −0.324737 0.0752145i
\(604\) 13.7983 + 5.32868i 0.561444 + 0.216821i
\(605\) 14.7517i 0.599744i
\(606\) 11.1968 + 16.3268i 0.454839 + 0.663229i
\(607\) 40.9177i 1.66080i −0.557169 0.830399i \(-0.688112\pi\)
0.557169 0.830399i \(-0.311888\pi\)
\(608\) 3.26658 23.8794i 0.132477 0.968438i
\(609\) 3.70956 0.150319
\(610\) −12.5455 + 8.60366i −0.507954 + 0.348352i
\(611\) −16.8389 −0.681230
\(612\) −3.47672 + 9.00274i −0.140538 + 0.363914i
\(613\) −16.6415 −0.672143 −0.336072 0.941836i \(-0.609098\pi\)
−0.336072 + 0.941836i \(0.609098\pi\)
\(614\) 15.9655 + 23.2803i 0.644315 + 0.939516i
\(615\) −0.264854 −0.0106799
\(616\) 5.99096 + 25.2916i 0.241382 + 1.01903i
\(617\) 22.4008 0.901823 0.450911 0.892569i \(-0.351099\pi\)
0.450911 + 0.892569i \(0.351099\pi\)
\(618\) −10.6181 15.4829i −0.427122 0.622813i
\(619\) 12.4972i 0.502307i 0.967947 + 0.251153i \(0.0808098\pi\)
−0.967947 + 0.251153i \(0.919190\pi\)
\(620\) −8.91085 3.44123i −0.357869 0.138203i
\(621\) 1.92153i 0.0771082i
\(622\) −6.78658 + 4.65420i −0.272117 + 0.186616i
\(623\) 9.94462 0.398423
\(624\) −3.79693 + 4.18280i −0.151999 + 0.167446i
\(625\) 14.3472 0.573888
\(626\) 5.24590 + 7.64938i 0.209668 + 0.305731i
\(627\) 22.5706i 0.901381i
\(628\) −0.0388019 + 0.100475i −0.00154837 + 0.00400940i
\(629\) 34.9514 1.39360
\(630\) 1.19952 + 1.74909i 0.0477899 + 0.0696855i
\(631\) 24.8311 0.988509 0.494255 0.869317i \(-0.335441\pi\)
0.494255 + 0.869317i \(0.335441\pi\)
\(632\) −5.34601 22.5689i −0.212653 0.897742i
\(633\) 22.3042i 0.886514i
\(634\) 36.8982 25.3046i 1.46541 1.00497i
\(635\) −5.10789 −0.202700
\(636\) 16.6363 + 6.42467i 0.659672 + 0.254755i
\(637\) 5.63628i 0.223318i
\(638\) −13.2124 + 9.06102i −0.523085 + 0.358729i
\(639\) 8.13841i 0.321951i
\(640\) 8.56263 + 4.72784i 0.338468 + 0.186884i
\(641\) 41.9807i 1.65814i −0.559146 0.829069i \(-0.688871\pi\)
0.559146 0.829069i \(-0.311129\pi\)
\(642\) 14.4994 + 21.1425i 0.572246 + 0.834427i
\(643\) 29.9711i 1.18194i −0.806692 0.590972i \(-0.798744\pi\)
0.806692 0.590972i \(-0.201256\pi\)
\(644\) 6.21881 + 2.40161i 0.245056 + 0.0946366i
\(645\) 0.980636i 0.0386125i
\(646\) −16.4441 23.9781i −0.646983 0.943407i
\(647\) 1.75809 0.0691176 0.0345588 0.999403i \(-0.488997\pi\)
0.0345588 + 0.999403i \(0.488997\pi\)
\(648\) 0.651944 + 2.75227i 0.0256108 + 0.108119i
\(649\) 76.3993i 2.99893i
\(650\) 4.80370 + 7.00458i 0.188417 + 0.274742i
\(651\) 9.58314 0.375593
\(652\) 22.9217 + 8.85198i 0.897681 + 0.346670i
\(653\) 44.5874i 1.74484i −0.488756 0.872420i \(-0.662549\pi\)
0.488756 0.872420i \(-0.337451\pi\)
\(654\) −0.215274 0.313904i −0.00841787 0.0122746i
\(655\) −5.26409 −0.205685
\(656\) 0.823633 0.907336i 0.0321575 0.0354255i
\(657\) 12.8776 0.502401
\(658\) −16.5430 24.1224i −0.644914 0.940390i
\(659\) 18.8246i 0.733301i 0.930359 + 0.366650i \(0.119495\pi\)
−0.930359 + 0.366650i \(0.880505\pi\)
\(660\) −8.54470 3.29983i −0.332602 0.128446i
\(661\) 12.7361i 0.495376i 0.968840 + 0.247688i \(0.0796708\pi\)
−0.968840 + 0.247688i \(0.920329\pi\)
\(662\) −11.6675 + 8.00152i −0.453471 + 0.310988i
\(663\) 6.81478i 0.264664i
\(664\) 1.07576 0.254821i 0.0417476 0.00988899i
\(665\) −6.38965 −0.247780
\(666\) 8.44779 5.79345i 0.327345 0.224492i
\(667\) 4.10914i 0.159107i
\(668\) 7.68811 + 2.96903i 0.297462 + 0.114875i
\(669\) 7.97926i 0.308496i
\(670\) 3.65183 + 9.31771i 0.141083 + 0.359975i
\(671\) 65.9116i 2.54449i
\(672\) −9.72225 1.32996i −0.375044 0.0513041i
\(673\) 47.3870i 1.82664i 0.407247 + 0.913318i \(0.366489\pi\)
−0.407247 + 0.913318i \(0.633511\pi\)
\(674\) −5.25855 7.66782i −0.202552 0.295354i
\(675\) 4.25257 0.163682
\(676\) 7.92952 20.5330i 0.304981 0.789730i
\(677\) 46.0441i 1.76962i −0.465954 0.884809i \(-0.654289\pi\)
0.465954 0.884809i \(-0.345711\pi\)
\(678\) 6.64208 + 9.68523i 0.255088 + 0.371959i
\(679\) 25.2106i 0.967495i
\(680\) 11.4817 2.71974i 0.440303 0.104297i
\(681\) 2.50636i 0.0960440i
\(682\) −34.1325 + 23.4079i −1.30700 + 0.896334i
\(683\) −38.9088 −1.48880 −0.744402 0.667732i \(-0.767265\pi\)
−0.744402 + 0.667732i \(0.767265\pi\)
\(684\) −7.94910 3.06982i −0.303942 0.117377i
\(685\) −13.2844 −0.507569
\(686\) −22.2362 + 15.2495i −0.848983 + 0.582228i
\(687\) 14.1223i 0.538798i
\(688\) −3.35946 3.04954i −0.128078 0.116263i
\(689\) 12.5931 0.479760
\(690\) −1.93750 + 1.32873i −0.0737593 + 0.0505837i
\(691\) 25.1098i 0.955222i −0.878571 0.477611i \(-0.841503\pi\)
0.878571 0.477611i \(-0.158497\pi\)
\(692\) −5.26625 + 13.6366i −0.200193 + 0.518386i
\(693\) 9.18937 0.349075
\(694\) −18.7287 + 12.8441i −0.710933 + 0.487554i
\(695\) 5.06721i 0.192210i
\(696\) −1.39417 5.88567i −0.0528459 0.223096i
\(697\) 1.47827i 0.0559933i
\(698\) 9.15749 6.28015i 0.346616 0.237707i
\(699\) 19.5570i 0.739713i
\(700\) −5.31505 + 13.7630i −0.200890 + 0.520192i
\(701\) 6.51175i 0.245945i 0.992410 + 0.122973i \(0.0392427\pi\)
−0.992410 + 0.122973i \(0.960757\pi\)
\(702\) 1.12960 + 1.64714i 0.0426340 + 0.0621673i
\(703\) 30.8608i 1.16394i
\(704\) 37.8765 19.0107i 1.42753 0.716494i
\(705\) 10.3081 0.388225
\(706\) 7.11779 + 10.3789i 0.267882 + 0.390615i
\(707\) 24.2833i 0.913267i
\(708\) 26.9070 + 10.3911i 1.01123 + 0.390520i
\(709\) −18.8407 −0.707579 −0.353790 0.935325i \(-0.615107\pi\)
−0.353790 + 0.935325i \(0.615107\pi\)
\(710\) 8.20606 5.62767i 0.307968 0.211203i
\(711\) −8.20011 −0.307528
\(712\) −3.73750 15.7783i −0.140069 0.591318i
\(713\) 10.6154i 0.397550i
\(714\) −9.76244 + 6.69503i −0.365350 + 0.250555i
\(715\) −6.46806 −0.241892
\(716\) 0.526175 1.36250i 0.0196641 0.0509189i
\(717\) −2.10620 −0.0786574
\(718\) 11.9471 + 17.4209i 0.445863 + 0.650141i
\(719\) 38.2761i 1.42746i 0.700423 + 0.713728i \(0.252995\pi\)
−0.700423 + 0.713728i \(0.747005\pi\)
\(720\) 2.32433 2.56054i 0.0866226 0.0954258i
\(721\) 23.0282i 0.857615i
\(722\) −0.987839 + 0.677454i −0.0367636 + 0.0252122i
\(723\) 6.84337 0.254508
\(724\) −9.18367 + 23.7806i −0.341309 + 0.883797i
\(725\) −9.09404 −0.337744
\(726\) −19.9007 + 13.6478i −0.738584 + 0.506517i
\(727\) −19.4592 −0.721703 −0.360851 0.932623i \(-0.617514\pi\)
−0.360851 + 0.932623i \(0.617514\pi\)
\(728\) −6.74262 + 1.59716i −0.249898 + 0.0591948i
\(729\) 1.00000 0.0370370
\(730\) −8.90477 12.9846i −0.329580 0.480582i
\(731\) −5.47335 −0.202439
\(732\) −23.2134 8.96463i −0.857990 0.331342i
\(733\) 21.9331i 0.810118i 0.914291 + 0.405059i \(0.132749\pi\)
−0.914291 + 0.405059i \(0.867251\pi\)
\(734\) −30.9082 + 21.1966i −1.14084 + 0.782382i
\(735\) 3.45030i 0.127266i
\(736\) 1.47321 10.7695i 0.0543034 0.396969i
\(737\) 42.2433 + 9.78427i 1.55605 + 0.360408i
\(738\) −0.245033 0.357299i −0.00901980 0.0131523i
\(739\) −9.41137 −0.346203 −0.173101 0.984904i \(-0.555379\pi\)
−0.173101 + 0.984904i \(0.555379\pi\)
\(740\) −11.6832 4.51187i −0.429484 0.165860i
\(741\) −6.01721 −0.221048
\(742\) 12.3718 + 18.0402i 0.454184 + 0.662275i
\(743\) 8.39736i 0.308069i −0.988065 0.154035i \(-0.950773\pi\)
0.988065 0.154035i \(-0.0492268\pi\)
\(744\) −3.60164 15.2048i −0.132043 0.557435i
\(745\) 5.87526i 0.215253i
\(746\) 16.6744 + 24.3140i 0.610492 + 0.890197i
\(747\) 0.390864i 0.0143010i
\(748\) 18.4178 47.6917i 0.673421 1.74378i
\(749\) 31.4459i 1.14901i
\(750\) −6.39811 9.32948i −0.233626 0.340665i
\(751\) 29.6677i 1.08259i −0.840833 0.541295i \(-0.817934\pi\)
0.840833 0.541295i \(-0.182066\pi\)
\(752\) −32.0557 + 35.3134i −1.16895 + 1.28775i
\(753\) 23.8453 0.868971
\(754\) −2.41563 3.52238i −0.0879720 0.128277i
\(755\) −6.39391 −0.232698
\(756\) −1.24984 + 3.23639i −0.0454564 + 0.117707i
\(757\) 29.9328i 1.08793i −0.839109 0.543963i \(-0.816923\pi\)
0.839109 0.543963i \(-0.183077\pi\)
\(758\) 31.3816 21.5213i 1.13983 0.781689i
\(759\) 10.1792i 0.369482i
\(760\) 2.40143 + 10.1379i 0.0871090 + 0.367742i
\(761\) 7.91305 0.286848 0.143424 0.989661i \(-0.454189\pi\)
0.143424 + 0.989661i \(0.454189\pi\)
\(762\) −4.72564 6.89075i −0.171192 0.249625i
\(763\) 0.466880i 0.0169022i
\(764\) −16.4783 + 42.6694i −0.596162 + 1.54373i
\(765\) 4.17173i 0.150829i
\(766\) 11.9671 8.20695i 0.432388 0.296529i
\(767\) 20.3677 0.735436
\(768\) 1.54379 + 15.9253i 0.0557068 + 0.574656i
\(769\) 12.1581i 0.438433i 0.975676 + 0.219216i \(0.0703500\pi\)
−0.975676 + 0.219216i \(0.929650\pi\)
\(770\) −6.35440 9.26575i −0.228997 0.333915i
\(771\) 9.09968 0.327717
\(772\) 12.7295 32.9623i 0.458146 1.18634i