Properties

Label 804.2.e.a.535.20
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 535.20
Character \(\chi\) = 804.535
Dual form 804.2.e.a.535.19

$q$-expansion

\(f(q)\) \(=\) \(q+(0.338334 + 1.37315i) q^{2} -1.00000 q^{3} +(-1.77106 + 0.929165i) q^{4} -0.0609697i q^{5} +(-0.338334 - 1.37315i) q^{6} +3.75704 q^{7} +(-1.87509 - 2.11755i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(0.338334 + 1.37315i) q^{2} -1.00000 q^{3} +(-1.77106 + 0.929165i) q^{4} -0.0609697i q^{5} +(-0.338334 - 1.37315i) q^{6} +3.75704 q^{7} +(-1.87509 - 2.11755i) q^{8} +1.00000 q^{9} +(0.0837203 - 0.0206282i) q^{10} -1.10283 q^{11} +(1.77106 - 0.929165i) q^{12} -4.93979i q^{13} +(1.27114 + 5.15897i) q^{14} +0.0609697i q^{15} +(2.27330 - 3.29121i) q^{16} +6.72065 q^{17} +(0.338334 + 1.37315i) q^{18} +1.13293i q^{19} +(0.0566509 + 0.107981i) q^{20} -3.75704 q^{21} +(-0.373126 - 1.51435i) q^{22} +2.63987i q^{23} +(1.87509 + 2.11755i) q^{24} +4.99628 q^{25} +(6.78305 - 1.67130i) q^{26} -1.00000 q^{27} +(-6.65395 + 3.49091i) q^{28} -1.58868 q^{29} +(-0.0837203 + 0.0206282i) q^{30} -0.470277 q^{31} +(5.28845 + 2.00805i) q^{32} +1.10283 q^{33} +(2.27383 + 9.22844i) q^{34} -0.229066i q^{35} +(-1.77106 + 0.929165i) q^{36} +4.49393 q^{37} +(-1.55567 + 0.383308i) q^{38} +4.93979i q^{39} +(-0.129107 + 0.114324i) q^{40} -1.53098i q^{41} +(-1.27114 - 5.15897i) q^{42} -3.78361 q^{43} +(1.95318 - 1.02471i) q^{44} -0.0609697i q^{45} +(-3.62493 + 0.893161i) q^{46} +8.21552i q^{47} +(-2.27330 + 3.29121i) q^{48} +7.11537 q^{49} +(1.69041 + 6.86063i) q^{50} -6.72065 q^{51} +(4.58988 + 8.74866i) q^{52} -2.81313i q^{53} +(-0.338334 - 1.37315i) q^{54} +0.0672393i q^{55} +(-7.04479 - 7.95574i) q^{56} -1.13293i q^{57} +(-0.537506 - 2.18149i) q^{58} +8.36670i q^{59} +(-0.0566509 - 0.107981i) q^{60} +4.04264i q^{61} +(-0.159111 - 0.645759i) q^{62} +3.75704 q^{63} +(-0.968076 + 7.94121i) q^{64} -0.301178 q^{65} +(0.373126 + 1.51435i) q^{66} +(6.62825 - 4.80274i) q^{67} +(-11.9027 + 6.24460i) q^{68} -2.63987i q^{69} +(0.314541 - 0.0775009i) q^{70} +8.01796i q^{71} +(-1.87509 - 2.11755i) q^{72} +11.0563 q^{73} +(1.52045 + 6.17082i) q^{74} -4.99628 q^{75} +(-1.05268 - 2.00648i) q^{76} -4.14339 q^{77} +(-6.78305 + 1.67130i) q^{78} +4.16494 q^{79} +(-0.200664 - 0.138603i) q^{80} +1.00000 q^{81} +(2.10226 - 0.517983i) q^{82} -0.0220613i q^{83} +(6.65395 - 3.49091i) q^{84} -0.409756i q^{85} +(-1.28013 - 5.19545i) q^{86} +1.58868 q^{87} +(2.06791 + 2.33531i) q^{88} -10.1973 q^{89} +(0.0837203 - 0.0206282i) q^{90} -18.5590i q^{91} +(-2.45288 - 4.67537i) q^{92} +0.470277 q^{93} +(-11.2811 + 2.77959i) q^{94} +0.0690742 q^{95} +(-5.28845 - 2.00805i) q^{96} +3.14310i q^{97} +(2.40738 + 9.77045i) q^{98} -1.10283 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.338334 + 1.37315i 0.239239 + 0.970961i
\(3\) −1.00000 −0.577350
\(4\) −1.77106 + 0.929165i −0.885530 + 0.464583i
\(5\) 0.0609697i 0.0272665i −0.999907 0.0136332i \(-0.995660\pi\)
0.999907 0.0136332i \(-0.00433973\pi\)
\(6\) −0.338334 1.37315i −0.138124 0.560584i
\(7\) 3.75704 1.42003 0.710014 0.704187i \(-0.248688\pi\)
0.710014 + 0.704187i \(0.248688\pi\)
\(8\) −1.87509 2.11755i −0.662944 0.748669i
\(9\) 1.00000 0.333333
\(10\) 0.0837203 0.0206282i 0.0264747 0.00652319i
\(11\) −1.10283 −0.332516 −0.166258 0.986082i \(-0.553169\pi\)
−0.166258 + 0.986082i \(0.553169\pi\)
\(12\) 1.77106 0.929165i 0.511261 0.268227i
\(13\) 4.93979i 1.37005i −0.728519 0.685026i \(-0.759791\pi\)
0.728519 0.685026i \(-0.240209\pi\)
\(14\) 1.27114 + 5.15897i 0.339726 + 1.37879i
\(15\) 0.0609697i 0.0157423i
\(16\) 2.27330 3.29121i 0.568326 0.822803i
\(17\) 6.72065 1.63000 0.814999 0.579462i \(-0.196737\pi\)
0.814999 + 0.579462i \(0.196737\pi\)
\(18\) 0.338334 + 1.37315i 0.0797462 + 0.323654i
\(19\) 1.13293i 0.259911i 0.991520 + 0.129956i \(0.0414835\pi\)
−0.991520 + 0.129956i \(0.958517\pi\)
\(20\) 0.0566509 + 0.107981i 0.0126675 + 0.0241453i
\(21\) −3.75704 −0.819854
\(22\) −0.373126 1.51435i −0.0795507 0.322860i
\(23\) 2.63987i 0.550452i 0.961380 + 0.275226i \(0.0887527\pi\)
−0.961380 + 0.275226i \(0.911247\pi\)
\(24\) 1.87509 + 2.11755i 0.382751 + 0.432244i
\(25\) 4.99628 0.999257
\(26\) 6.78305 1.67130i 1.33027 0.327769i
\(27\) −1.00000 −0.192450
\(28\) −6.65395 + 3.49091i −1.25748 + 0.659721i
\(29\) −1.58868 −0.295011 −0.147505 0.989061i \(-0.547124\pi\)
−0.147505 + 0.989061i \(0.547124\pi\)
\(30\) −0.0837203 + 0.0206282i −0.0152852 + 0.00376617i
\(31\) −0.470277 −0.0844643 −0.0422322 0.999108i \(-0.513447\pi\)
−0.0422322 + 0.999108i \(0.513447\pi\)
\(32\) 5.28845 + 2.00805i 0.934875 + 0.354976i
\(33\) 1.10283 0.191978
\(34\) 2.27383 + 9.22844i 0.389958 + 1.58266i
\(35\) 0.229066i 0.0387192i
\(36\) −1.77106 + 0.929165i −0.295177 + 0.154861i
\(37\) 4.49393 0.738797 0.369399 0.929271i \(-0.379564\pi\)
0.369399 + 0.929271i \(0.379564\pi\)
\(38\) −1.55567 + 0.383308i −0.252363 + 0.0621808i
\(39\) 4.93979i 0.791000i
\(40\) −0.129107 + 0.114324i −0.0204136 + 0.0180762i
\(41\) 1.53098i 0.239099i −0.992828 0.119549i \(-0.961855\pi\)
0.992828 0.119549i \(-0.0381450\pi\)
\(42\) −1.27114 5.15897i −0.196141 0.796046i
\(43\) −3.78361 −0.576995 −0.288498 0.957481i \(-0.593156\pi\)
−0.288498 + 0.957481i \(0.593156\pi\)
\(44\) 1.95318 1.02471i 0.294453 0.154481i
\(45\) 0.0609697i 0.00908883i
\(46\) −3.62493 + 0.893161i −0.534467 + 0.131689i
\(47\) 8.21552i 1.19836i 0.800616 + 0.599178i \(0.204506\pi\)
−0.800616 + 0.599178i \(0.795494\pi\)
\(48\) −2.27330 + 3.29121i −0.328123 + 0.475046i
\(49\) 7.11537 1.01648
\(50\) 1.69041 + 6.86063i 0.239061 + 0.970239i
\(51\) −6.72065 −0.941080
\(52\) 4.58988 + 8.74866i 0.636502 + 1.21322i
\(53\) 2.81313i 0.386414i −0.981158 0.193207i \(-0.938111\pi\)
0.981158 0.193207i \(-0.0618888\pi\)
\(54\) −0.338334 1.37315i −0.0460415 0.186861i
\(55\) 0.0672393i 0.00906655i
\(56\) −7.04479 7.95574i −0.941400 1.06313i
\(57\) 1.13293i 0.150060i
\(58\) −0.537506 2.18149i −0.0705779 0.286444i
\(59\) 8.36670i 1.08925i 0.838679 + 0.544626i \(0.183328\pi\)
−0.838679 + 0.544626i \(0.816672\pi\)
\(60\) −0.0566509 0.107981i −0.00731360 0.0139403i
\(61\) 4.04264i 0.517607i 0.965930 + 0.258803i \(0.0833281\pi\)
−0.965930 + 0.258803i \(0.916672\pi\)
\(62\) −0.159111 0.645759i −0.0202071 0.0820115i
\(63\) 3.75704 0.473343
\(64\) −0.968076 + 7.94121i −0.121009 + 0.992651i
\(65\) −0.301178 −0.0373565
\(66\) 0.373126 + 1.51435i 0.0459286 + 0.186403i
\(67\) 6.62825 4.80274i 0.809770 0.586747i
\(68\) −11.9027 + 6.24460i −1.44341 + 0.757269i
\(69\) 2.63987i 0.317804i
\(70\) 0.314541 0.0775009i 0.0375948 0.00926312i
\(71\) 8.01796i 0.951556i 0.879565 + 0.475778i \(0.157833\pi\)
−0.879565 + 0.475778i \(0.842167\pi\)
\(72\) −1.87509 2.11755i −0.220981 0.249556i
\(73\) 11.0563 1.29405 0.647023 0.762471i \(-0.276014\pi\)
0.647023 + 0.762471i \(0.276014\pi\)
\(74\) 1.52045 + 6.17082i 0.176749 + 0.717343i
\(75\) −4.99628 −0.576921
\(76\) −1.05268 2.00648i −0.120750 0.230159i
\(77\) −4.14339 −0.472183
\(78\) −6.78305 + 1.67130i −0.768030 + 0.189238i
\(79\) 4.16494 0.468592 0.234296 0.972165i \(-0.424722\pi\)
0.234296 + 0.972165i \(0.424722\pi\)
\(80\) −0.200664 0.138603i −0.0224350 0.0154963i
\(81\) 1.00000 0.111111
\(82\) 2.10226 0.517983i 0.232156 0.0572017i
\(83\) 0.0220613i 0.00242154i −0.999999 0.00121077i \(-0.999615\pi\)
0.999999 0.00121077i \(-0.000385401\pi\)
\(84\) 6.65395 3.49091i 0.726005 0.380890i
\(85\) 0.409756i 0.0444443i
\(86\) −1.28013 5.19545i −0.138040 0.560240i
\(87\) 1.58868 0.170324
\(88\) 2.06791 + 2.33531i 0.220440 + 0.248945i
\(89\) −10.1973 −1.08091 −0.540455 0.841373i \(-0.681748\pi\)
−0.540455 + 0.841373i \(0.681748\pi\)
\(90\) 0.0837203 0.0206282i 0.00882489 0.00217440i
\(91\) 18.5590i 1.94551i
\(92\) −2.45288 4.67537i −0.255730 0.487442i
\(93\) 0.470277 0.0487655
\(94\) −11.2811 + 2.77959i −1.16356 + 0.286693i
\(95\) 0.0690742 0.00708686
\(96\) −5.28845 2.00805i −0.539751 0.204945i
\(97\) 3.14310i 0.319133i 0.987187 + 0.159567i \(0.0510096\pi\)
−0.987187 + 0.159567i \(0.948990\pi\)
\(98\) 2.40738 + 9.77045i 0.243182 + 0.986964i
\(99\) −1.10283 −0.110839
\(100\) −8.84871 + 4.64237i −0.884871 + 0.464237i
\(101\) 7.96684i 0.792730i 0.918093 + 0.396365i \(0.129729\pi\)
−0.918093 + 0.396365i \(0.870271\pi\)
\(102\) −2.27383 9.22844i −0.225143 0.913752i
\(103\) 16.4526i 1.62112i −0.585655 0.810561i \(-0.699163\pi\)
0.585655 0.810561i \(-0.300837\pi\)
\(104\) −10.4603 + 9.26255i −1.02571 + 0.908268i
\(105\) 0.229066i 0.0223545i
\(106\) 3.86284 0.951780i 0.375192 0.0924450i
\(107\) 7.61778i 0.736439i −0.929739 0.368219i \(-0.879968\pi\)
0.929739 0.368219i \(-0.120032\pi\)
\(108\) 1.77106 0.929165i 0.170420 0.0894090i
\(109\) 15.1979i 1.45570i −0.685737 0.727849i \(-0.740520\pi\)
0.685737 0.727849i \(-0.259480\pi\)
\(110\) −0.0923294 + 0.0227494i −0.00880326 + 0.00216907i
\(111\) −4.49393 −0.426545
\(112\) 8.54090 12.3652i 0.807039 1.16840i
\(113\) 18.0077i 1.69402i −0.531574 0.847012i \(-0.678399\pi\)
0.531574 0.847012i \(-0.321601\pi\)
\(114\) 1.55567 0.383308i 0.145702 0.0359001i
\(115\) 0.160952 0.0150089
\(116\) 2.81365 1.47615i 0.261241 0.137057i
\(117\) 4.93979i 0.456684i
\(118\) −11.4887 + 2.83074i −1.05762 + 0.260591i
\(119\) 25.2498 2.31464
\(120\) 0.129107 0.114324i 0.0117858 0.0104363i
\(121\) −9.78376 −0.889433
\(122\) −5.55113 + 1.36776i −0.502576 + 0.123831i
\(123\) 1.53098i 0.138044i
\(124\) 0.832889 0.436965i 0.0747957 0.0392406i
\(125\) 0.609470i 0.0545127i
\(126\) 1.27114 + 5.15897i 0.113242 + 0.459597i
\(127\) 13.1675i 1.16843i −0.811600 0.584213i \(-0.801403\pi\)
0.811600 0.584213i \(-0.198597\pi\)
\(128\) −11.2320 + 1.35748i −0.992776 + 0.119985i
\(129\) 3.78361 0.333128
\(130\) −0.101899 0.413561i −0.00893711 0.0362717i
\(131\) 13.2574i 1.15831i −0.815219 0.579153i \(-0.803383\pi\)
0.815219 0.579153i \(-0.196617\pi\)
\(132\) −1.95318 + 1.02471i −0.170003 + 0.0891898i
\(133\) 4.25645i 0.369081i
\(134\) 8.83742 + 7.47663i 0.763437 + 0.645882i
\(135\) 0.0609697i 0.00524744i
\(136\) −12.6018 14.2314i −1.08060 1.22033i
\(137\) 0.299850i 0.0256179i −0.999918 0.0128090i \(-0.995923\pi\)
0.999918 0.0128090i \(-0.00407733\pi\)
\(138\) 3.62493 0.893161i 0.308575 0.0760309i
\(139\) −4.27209 −0.362354 −0.181177 0.983451i \(-0.557991\pi\)
−0.181177 + 0.983451i \(0.557991\pi\)
\(140\) 0.212840 + 0.405689i 0.0179883 + 0.0342870i
\(141\) 8.21552i 0.691871i
\(142\) −11.0098 + 2.71275i −0.923924 + 0.227649i
\(143\) 5.44776i 0.455565i
\(144\) 2.27330 3.29121i 0.189442 0.274268i
\(145\) 0.0968614i 0.00804390i
\(146\) 3.74074 + 15.1820i 0.309586 + 1.25647i
\(147\) −7.11537 −0.586866
\(148\) −7.95901 + 4.17560i −0.654227 + 0.343232i
\(149\) 11.3899 0.933096 0.466548 0.884496i \(-0.345497\pi\)
0.466548 + 0.884496i \(0.345497\pi\)
\(150\) −1.69041 6.86063i −0.138022 0.560168i
\(151\) 5.92062i 0.481814i 0.970548 + 0.240907i \(0.0774448\pi\)
−0.970548 + 0.240907i \(0.922555\pi\)
\(152\) 2.39903 2.12434i 0.194587 0.172307i
\(153\) 6.72065 0.543333
\(154\) −1.40185 5.68948i −0.112964 0.458471i
\(155\) 0.0286727i 0.00230304i
\(156\) −4.58988 8.74866i −0.367485 0.700454i
\(157\) 5.21451 0.416163 0.208082 0.978111i \(-0.433278\pi\)
0.208082 + 0.978111i \(0.433278\pi\)
\(158\) 1.40914 + 5.71907i 0.112105 + 0.454984i
\(159\) 2.81313i 0.223096i
\(160\) 0.122430 0.322435i 0.00967894 0.0254908i
\(161\) 9.91812i 0.781658i
\(162\) 0.338334 + 1.37315i 0.0265821 + 0.107885i
\(163\) 0.859050i 0.0672860i −0.999434 0.0336430i \(-0.989289\pi\)
0.999434 0.0336430i \(-0.0107109\pi\)
\(164\) 1.42253 + 2.71146i 0.111081 + 0.211729i
\(165\) 0.0672393i 0.00523458i
\(166\) 0.0302934 0.00746411i 0.00235122 0.000579327i
\(167\) 13.4828i 1.04333i 0.853149 + 0.521667i \(0.174690\pi\)
−0.853149 + 0.521667i \(0.825310\pi\)
\(168\) 7.04479 + 7.95574i 0.543518 + 0.613799i
\(169\) −11.4015 −0.877041
\(170\) 0.562655 0.138635i 0.0431537 0.0106328i
\(171\) 1.13293i 0.0866370i
\(172\) 6.70100 3.51560i 0.510947 0.268062i
\(173\) 3.37315 0.256456 0.128228 0.991745i \(-0.459071\pi\)
0.128228 + 0.991745i \(0.459071\pi\)
\(174\) 0.537506 + 2.18149i 0.0407482 + 0.165378i
\(175\) 18.7713 1.41897
\(176\) −2.50707 + 3.62966i −0.188978 + 0.273596i
\(177\) 8.36670i 0.628880i
\(178\) −3.45010 14.0024i −0.258596 1.04952i
\(179\) 19.8446 1.48326 0.741629 0.670810i \(-0.234053\pi\)
0.741629 + 0.670810i \(0.234053\pi\)
\(180\) 0.0566509 + 0.107981i 0.00422251 + 0.00804843i
\(181\) −12.1020 −0.899535 −0.449767 0.893146i \(-0.648493\pi\)
−0.449767 + 0.893146i \(0.648493\pi\)
\(182\) 25.4842 6.27915i 1.88902 0.465442i
\(183\) 4.04264i 0.298840i
\(184\) 5.59008 4.95000i 0.412106 0.364919i
\(185\) 0.273993i 0.0201444i
\(186\) 0.159111 + 0.645759i 0.0116666 + 0.0473494i
\(187\) −7.41175 −0.542001
\(188\) −7.63357 14.5502i −0.556736 1.06118i
\(189\) −3.75704 −0.273285
\(190\) 0.0233702 + 0.0948489i 0.00169545 + 0.00688106i
\(191\) −19.4833 −1.40976 −0.704882 0.709325i \(-0.749000\pi\)
−0.704882 + 0.709325i \(0.749000\pi\)
\(192\) 0.968076 7.94121i 0.0698648 0.573108i
\(193\) −16.3459 −1.17661 −0.588303 0.808641i \(-0.700204\pi\)
−0.588303 + 0.808641i \(0.700204\pi\)
\(194\) −4.31593 + 1.06342i −0.309866 + 0.0763489i
\(195\) 0.301178 0.0215678
\(196\) −12.6018 + 6.61136i −0.900125 + 0.472240i
\(197\) 17.6850i 1.26000i 0.776594 + 0.630001i \(0.216946\pi\)
−0.776594 + 0.630001i \(0.783054\pi\)
\(198\) −0.373126 1.51435i −0.0265169 0.107620i
\(199\) 0.273537i 0.0193905i 0.999953 + 0.00969525i \(0.00308614\pi\)
−0.999953 + 0.00969525i \(0.996914\pi\)
\(200\) −9.36848 10.5799i −0.662452 0.748112i
\(201\) −6.62825 + 4.80274i −0.467521 + 0.338759i
\(202\) −10.9396 + 2.69546i −0.769710 + 0.189652i
\(203\) −5.96874 −0.418924
\(204\) 11.9027 6.24460i 0.833354 0.437209i
\(205\) −0.0933434 −0.00651939
\(206\) 22.5918 5.56648i 1.57405 0.387835i
\(207\) 2.63987i 0.183484i
\(208\) −16.2579 11.2296i −1.12728 0.778636i
\(209\) 1.24943i 0.0864247i
\(210\) −0.314541 + 0.0775009i −0.0217054 + 0.00534807i
\(211\) 23.0337i 1.58570i 0.609415 + 0.792852i \(0.291405\pi\)
−0.609415 + 0.792852i \(0.708595\pi\)
\(212\) 2.61387 + 4.98223i 0.179521 + 0.342181i
\(213\) 8.01796i 0.549381i
\(214\) 10.4603 2.57736i 0.715053 0.176185i
\(215\) 0.230686i 0.0157326i
\(216\) 1.87509 + 2.11755i 0.127584 + 0.144081i
\(217\) −1.76685 −0.119942
\(218\) 20.8690 5.14199i 1.41343 0.348259i
\(219\) −11.0563 −0.747117
\(220\) −0.0624764 0.119085i −0.00421216 0.00802870i
\(221\) 33.1986i 2.23318i
\(222\) −1.52045 6.17082i −0.102046 0.414158i
\(223\) 0.306864i 0.0205491i 0.999947 + 0.0102746i \(0.00327055\pi\)
−0.999947 + 0.0102746i \(0.996729\pi\)
\(224\) 19.8690 + 7.54432i 1.32755 + 0.504076i
\(225\) 4.99628 0.333086
\(226\) 24.7272 6.09263i 1.64483 0.405276i
\(227\) 25.5455i 1.69552i 0.530383 + 0.847758i \(0.322048\pi\)
−0.530383 + 0.847758i \(0.677952\pi\)
\(228\) 1.05268 + 2.00648i 0.0697151 + 0.132882i
\(229\) 0.674492i 0.0445717i −0.999752 0.0222858i \(-0.992906\pi\)
0.999752 0.0222858i \(-0.00709439\pi\)
\(230\) 0.0544557 + 0.221011i 0.00359070 + 0.0145730i
\(231\) 4.14339 0.272615
\(232\) 2.97892 + 3.36412i 0.195576 + 0.220865i
\(233\) 26.4164i 1.73059i 0.501259 + 0.865297i \(0.332870\pi\)
−0.501259 + 0.865297i \(0.667130\pi\)
\(234\) 6.78305 1.67130i 0.443422 0.109256i
\(235\) 0.500898 0.0326750
\(236\) −7.77405 14.8179i −0.506047 0.964565i
\(237\) −4.16494 −0.270542
\(238\) 8.54287 + 34.6716i 0.553752 + 2.24743i
\(239\) −14.5374 −0.940348 −0.470174 0.882574i \(-0.655809\pi\)
−0.470174 + 0.882574i \(0.655809\pi\)
\(240\) 0.200664 + 0.138603i 0.0129528 + 0.00894676i
\(241\) 25.6937 1.65507 0.827537 0.561411i \(-0.189741\pi\)
0.827537 + 0.561411i \(0.189741\pi\)
\(242\) −3.31018 13.4345i −0.212787 0.863604i
\(243\) −1.00000 −0.0641500
\(244\) −3.75628 7.15975i −0.240471 0.458356i
\(245\) 0.433822i 0.0277159i
\(246\) −2.10226 + 0.517983i −0.134035 + 0.0330254i
\(247\) 5.59642 0.356092
\(248\) 0.881812 + 0.995838i 0.0559951 + 0.0632358i
\(249\) 0.0220613i 0.00139808i
\(250\) 0.836892 0.206205i 0.0529297 0.0130415i
\(251\) −10.6671 −0.673298 −0.336649 0.941630i \(-0.609294\pi\)
−0.336649 + 0.941630i \(0.609294\pi\)
\(252\) −6.65395 + 3.49091i −0.419159 + 0.219907i
\(253\) 2.91134i 0.183034i
\(254\) 18.0809 4.45502i 1.13450 0.279533i
\(255\) 0.409756i 0.0256599i
\(256\) −5.66418 14.9639i −0.354011 0.935241i
\(257\) −19.2696 −1.20200 −0.601002 0.799248i \(-0.705232\pi\)
−0.601002 + 0.799248i \(0.705232\pi\)
\(258\) 1.28013 + 5.19545i 0.0796972 + 0.323455i
\(259\) 16.8839 1.04911
\(260\) 0.533404 0.279844i 0.0330803 0.0173552i
\(261\) −1.58868 −0.0983369
\(262\) 18.2044 4.48544i 1.12467 0.277112i
\(263\) 5.69061i 0.350898i −0.984489 0.175449i \(-0.943862\pi\)
0.984489 0.175449i \(-0.0561377\pi\)
\(264\) −2.06791 2.33531i −0.127271 0.143728i
\(265\) −0.171516 −0.0105361
\(266\) −5.84473 + 1.44010i −0.358363 + 0.0882985i
\(267\) 10.1973 0.624064
\(268\) −7.27650 + 14.6647i −0.444483 + 0.895787i
\(269\) −28.6783 −1.74854 −0.874272 0.485436i \(-0.838661\pi\)
−0.874272 + 0.485436i \(0.838661\pi\)
\(270\) −0.0837203 + 0.0206282i −0.00509506 + 0.00125539i
\(271\) −3.65752 −0.222179 −0.111089 0.993810i \(-0.535434\pi\)
−0.111089 + 0.993810i \(0.535434\pi\)
\(272\) 15.2781 22.1191i 0.926370 1.34117i
\(273\) 18.5590i 1.12324i
\(274\) 0.411738 0.101450i 0.0248740 0.00612880i
\(275\) −5.51006 −0.332269
\(276\) 2.45288 + 4.67537i 0.147646 + 0.281424i
\(277\) −24.8319 −1.49200 −0.746002 0.665943i \(-0.768029\pi\)
−0.746002 + 0.665943i \(0.768029\pi\)
\(278\) −1.44540 5.86620i −0.0866891 0.351831i
\(279\) −0.470277 −0.0281548
\(280\) −0.485059 + 0.429519i −0.0289878 + 0.0256687i
\(281\) 27.2668i 1.62660i −0.581845 0.813300i \(-0.697669\pi\)
0.581845 0.813300i \(-0.302331\pi\)
\(282\) 11.2811 2.77959i 0.671780 0.165522i
\(283\) 29.4074i 1.74809i −0.485845 0.874045i \(-0.661488\pi\)
0.485845 0.874045i \(-0.338512\pi\)
\(284\) −7.45001 14.2003i −0.442077 0.842632i
\(285\) −0.0690742 −0.00409160
\(286\) −7.48057 + 1.84316i −0.442335 + 0.108989i
\(287\) 5.75196i 0.339527i
\(288\) 5.28845 + 2.00805i 0.311625 + 0.118325i
\(289\) 28.1672 1.65689
\(290\) −0.133005 + 0.0327716i −0.00781031 + 0.00192441i
\(291\) 3.14310i 0.184252i
\(292\) −19.5814 + 10.2732i −1.14592 + 0.601191i
\(293\) 3.91718 0.228844 0.114422 0.993432i \(-0.463498\pi\)
0.114422 + 0.993432i \(0.463498\pi\)
\(294\) −2.40738 9.77045i −0.140401 0.569824i
\(295\) 0.510115 0.0297001
\(296\) −8.42652 9.51614i −0.489781 0.553114i
\(297\) 1.10283 0.0639928
\(298\) 3.85359 + 15.6400i 0.223233 + 0.906000i
\(299\) 13.0404 0.754147
\(300\) 8.84871 4.64237i 0.510881 0.268027i
\(301\) −14.2152 −0.819350
\(302\) −8.12988 + 2.00315i −0.467822 + 0.115268i
\(303\) 7.96684i 0.457683i
\(304\) 3.72870 + 2.57549i 0.213856 + 0.147714i
\(305\) 0.246478 0.0141133
\(306\) 2.27383 + 9.22844i 0.129986 + 0.527555i
\(307\) 19.0966i 1.08990i −0.838468 0.544951i \(-0.816548\pi\)
0.838468 0.544951i \(-0.183452\pi\)
\(308\) 7.33819 3.84989i 0.418132 0.219368i
\(309\) 16.4526i 0.935955i
\(310\) −0.0393718 + 0.00970095i −0.00223617 + 0.000550977i
\(311\) −16.1088 −0.913448 −0.456724 0.889609i \(-0.650977\pi\)
−0.456724 + 0.889609i \(0.650977\pi\)
\(312\) 10.4603 9.26255i 0.592197 0.524389i
\(313\) 25.0638i 1.41669i 0.705868 + 0.708344i \(0.250557\pi\)
−0.705868 + 0.708344i \(0.749443\pi\)
\(314\) 1.76425 + 7.16028i 0.0995623 + 0.404078i
\(315\) 0.229066i 0.0129064i
\(316\) −7.37635 + 3.86991i −0.414952 + 0.217700i
\(317\) 5.89851 0.331293 0.165647 0.986185i \(-0.447029\pi\)
0.165647 + 0.986185i \(0.447029\pi\)
\(318\) −3.86284 + 0.951780i −0.216617 + 0.0533732i
\(319\) 1.75205 0.0980959
\(320\) 0.484173 + 0.0590233i 0.0270661 + 0.00329950i
\(321\) 7.61778i 0.425183i
\(322\) −13.6190 + 3.35564i −0.758959 + 0.187003i
\(323\) 7.61400i 0.423654i
\(324\) −1.77106 + 0.929165i −0.0983922 + 0.0516203i
\(325\) 24.6806i 1.36903i
\(326\) 1.17960 0.290646i 0.0653321 0.0160974i
\(327\) 15.1979i 0.840448i
\(328\) −3.24193 + 2.87073i −0.179006 + 0.158509i
\(329\) 30.8661i 1.70170i
\(330\) 0.0923294 0.0227494i 0.00508257 0.00125231i
\(331\) 9.35027 0.513937 0.256969 0.966420i \(-0.417276\pi\)
0.256969 + 0.966420i \(0.417276\pi\)
\(332\) 0.0204986 + 0.0390719i 0.00112501 + 0.00214435i
\(333\) 4.49393 0.246266
\(334\) −18.5139 + 4.56171i −1.01304 + 0.249606i
\(335\) −0.292821 0.404123i −0.0159985 0.0220796i
\(336\) −8.54090 + 12.3652i −0.465944 + 0.674579i
\(337\) 26.5945i 1.44869i 0.689436 + 0.724346i \(0.257858\pi\)
−0.689436 + 0.724346i \(0.742142\pi\)
\(338\) −3.85753 15.6560i −0.209822 0.851573i
\(339\) 18.0077i 0.978045i
\(340\) 0.380731 + 0.725703i 0.0206481 + 0.0393568i
\(341\) 0.518637 0.0280858
\(342\) −1.55567 + 0.383308i −0.0841211 + 0.0207269i
\(343\) 0.433469 0.0234051
\(344\) 7.09461 + 8.01200i 0.382516 + 0.431978i
\(345\) −0.160952 −0.00866538
\(346\) 1.14125 + 4.63183i 0.0613542 + 0.249009i
\(347\) 3.83875 0.206075 0.103038 0.994677i \(-0.467144\pi\)
0.103038 + 0.994677i \(0.467144\pi\)
\(348\) −2.81365 + 1.47615i −0.150827 + 0.0791298i
\(349\) −1.32332 −0.0708355 −0.0354178 0.999373i \(-0.511276\pi\)
−0.0354178 + 0.999373i \(0.511276\pi\)
\(350\) 6.35096 + 25.7757i 0.339473 + 1.37777i
\(351\) 4.93979i 0.263667i
\(352\) −5.83228 2.21454i −0.310861 0.118035i
\(353\) 21.3119i 1.13432i 0.823608 + 0.567160i \(0.191958\pi\)
−0.823608 + 0.567160i \(0.808042\pi\)
\(354\) 11.4887 2.83074i 0.610618 0.150452i
\(355\) 0.488852 0.0259456
\(356\) 18.0600 9.47497i 0.957179 0.502172i
\(357\) −25.2498 −1.33636
\(358\) 6.71413 + 27.2496i 0.354853 + 1.44019i
\(359\) 33.0334i 1.74344i −0.490005 0.871719i \(-0.663005\pi\)
0.490005 0.871719i \(-0.336995\pi\)
\(360\) −0.129107 + 0.114324i −0.00680452 + 0.00602539i
\(361\) 17.7165 0.932446
\(362\) −4.09452 16.6178i −0.215203 0.873413i
\(363\) 9.78376 0.513514
\(364\) 17.2444 + 32.8691i 0.903851 + 1.72281i
\(365\) 0.674101i 0.0352841i
\(366\) 5.55113 1.36776i 0.290162 0.0714941i
\(367\) −21.1961 −1.10643 −0.553215 0.833039i \(-0.686599\pi\)
−0.553215 + 0.833039i \(0.686599\pi\)
\(368\) 8.68839 + 6.00124i 0.452914 + 0.312836i
\(369\) 1.53098i 0.0796996i
\(370\) 0.376233 0.0927014i 0.0195594 0.00481932i
\(371\) 10.5691i 0.548718i
\(372\) −0.832889 + 0.436965i −0.0431833 + 0.0226556i
\(373\) 35.8774i 1.85766i 0.370507 + 0.928830i \(0.379184\pi\)
−0.370507 + 0.928830i \(0.620816\pi\)
\(374\) −2.50765 10.1774i −0.129668 0.526262i
\(375\) 0.609470i 0.0314729i
\(376\) 17.3968 15.4048i 0.897172 0.794444i
\(377\) 7.84775i 0.404180i
\(378\) −1.27114 5.15897i −0.0653802 0.265349i
\(379\) −30.5273 −1.56808 −0.784041 0.620710i \(-0.786845\pi\)
−0.784041 + 0.620710i \(0.786845\pi\)
\(380\) −0.122334 + 0.0641813i −0.00627563 + 0.00329243i
\(381\) 13.1675i 0.674591i
\(382\) −6.59188 26.7534i −0.337270 1.36882i
\(383\) −15.2134 −0.777368 −0.388684 0.921371i \(-0.627070\pi\)
−0.388684 + 0.921371i \(0.627070\pi\)
\(384\) 11.2320 1.35748i 0.573179 0.0692734i
\(385\) 0.252621i 0.0128748i
\(386\) −5.53039 22.4453i −0.281489 1.14244i
\(387\) −3.78361 −0.192332
\(388\) −2.92046 5.56661i −0.148264 0.282602i
\(389\) −1.67565 −0.0849590 −0.0424795 0.999097i \(-0.513526\pi\)
−0.0424795 + 0.999097i \(0.513526\pi\)
\(390\) 0.101899 + 0.413561i 0.00515984 + 0.0209415i
\(391\) 17.7417i 0.897235i
\(392\) −13.3420 15.0672i −0.673871 0.761008i
\(393\) 13.2574i 0.668748i
\(394\) −24.2841 + 5.98344i −1.22341 + 0.301441i
\(395\) 0.253935i 0.0127769i
\(396\) 1.95318 1.02471i 0.0981510 0.0514938i
\(397\) −25.6396 −1.28681 −0.643407 0.765524i \(-0.722480\pi\)
−0.643407 + 0.765524i \(0.722480\pi\)
\(398\) −0.375606 + 0.0925469i −0.0188274 + 0.00463896i
\(399\) 4.25645i 0.213089i
\(400\) 11.3581 16.4438i 0.567903 0.822192i
\(401\) 19.3773i 0.967657i −0.875163 0.483829i \(-0.839246\pi\)
0.875163 0.483829i \(-0.160754\pi\)
\(402\) −8.83742 7.47663i −0.440771 0.372900i
\(403\) 2.32307i 0.115720i
\(404\) −7.40251 14.1097i −0.368289 0.701986i
\(405\) 0.0609697i 0.00302961i
\(406\) −2.01943 8.19596i −0.100223 0.406758i
\(407\) −4.95605 −0.245662
\(408\) 12.6018 + 14.2314i 0.623884 + 0.704557i
\(409\) 15.0648i 0.744904i −0.928051 0.372452i \(-0.878517\pi\)
0.928051 0.372452i \(-0.121483\pi\)
\(410\) −0.0315813 0.128174i −0.00155969 0.00633007i
\(411\) 0.299850i 0.0147905i
\(412\) 15.2872 + 29.1385i 0.753145 + 1.43555i
\(413\) 31.4341i 1.54677i
\(414\) −3.62493 + 0.893161i −0.178156 + 0.0438964i
\(415\) −0.00134507 −6.60270e−5
\(416\) 9.91933 26.1239i 0.486335 1.28083i
\(417\) 4.27209 0.209205
\(418\) 1.71565 0.422724i 0.0839150 0.0206761i
\(419\) 9.77867i 0.477720i 0.971054 + 0.238860i \(0.0767736\pi\)
−0.971054 + 0.238860i \(0.923226\pi\)
\(420\) −0.212840 0.405689i −0.0103855 0.0197956i
\(421\) 4.19368 0.204388 0.102194 0.994765i \(-0.467414\pi\)
0.102194 + 0.994765i \(0.467414\pi\)
\(422\) −31.6286 + 7.79309i −1.53966 + 0.379361i
\(423\) 8.21552i 0.399452i
\(424\) −5.95696 + 5.27488i −0.289296 + 0.256171i
\(425\) 33.5783 1.62879
\(426\) 11.0098 2.71275i 0.533428 0.131433i
\(427\) 15.1884i 0.735016i
\(428\) 7.07818 + 13.4915i 0.342137 + 0.652138i
\(429\) 5.44776i 0.263020i
\(430\) −0.316765 + 0.0780489i −0.0152758 + 0.00376385i
\(431\) 29.5680i 1.42424i −0.702057 0.712121i \(-0.747735\pi\)
0.702057 0.712121i \(-0.252265\pi\)
\(432\) −2.27330 + 3.29121i −0.109374 + 0.158349i
\(433\) 24.4560i 1.17528i 0.809122 + 0.587641i \(0.199943\pi\)
−0.809122 + 0.587641i \(0.800057\pi\)
\(434\) −0.597787 2.42615i −0.0286947 0.116459i
\(435\) 0.0968614i 0.00464415i
\(436\) 14.1214 + 26.9165i 0.676292 + 1.28906i
\(437\) −2.99078 −0.143069
\(438\) −3.74074 15.1820i −0.178739 0.725422i
\(439\) 2.81752i 0.134473i −0.997737 0.0672364i \(-0.978582\pi\)
0.997737 0.0672364i \(-0.0214182\pi\)
\(440\) 0.142383 0.126080i 0.00678784 0.00601062i
\(441\) 7.11537 0.338827
\(442\) 45.5866 11.2322i 2.16833 0.534263i
\(443\) −20.3857 −0.968555 −0.484278 0.874914i \(-0.660918\pi\)
−0.484278 + 0.874914i \(0.660918\pi\)
\(444\) 7.95901 4.17560i 0.377718 0.198165i
\(445\) 0.621726i 0.0294726i
\(446\) −0.421369 + 0.103823i −0.0199524 + 0.00491614i
\(447\) −11.3899 −0.538723
\(448\) −3.63710 + 29.8355i −0.171837 + 1.40959i
\(449\) 15.7872 0.745046 0.372523 0.928023i \(-0.378493\pi\)
0.372523 + 0.928023i \(0.378493\pi\)
\(450\) 1.69041 + 6.86063i 0.0796869 + 0.323413i
\(451\) 1.68841i 0.0795043i
\(452\) 16.7321 + 31.8927i 0.787014 + 1.50011i
\(453\) 5.92062i 0.278175i
\(454\) −35.0777 + 8.64293i −1.64628 + 0.405633i
\(455\) −1.13154 −0.0530473
\(456\) −2.39903 + 2.12434i −0.112345 + 0.0994812i
\(457\) −15.0733 −0.705098 −0.352549 0.935793i \(-0.614685\pi\)
−0.352549 + 0.935793i \(0.614685\pi\)
\(458\) 0.926175 0.228204i 0.0432773 0.0106633i
\(459\) −6.72065 −0.313693
\(460\) −0.285056 + 0.149551i −0.0132908 + 0.00697287i
\(461\) −6.00665 −0.279758 −0.139879 0.990169i \(-0.544671\pi\)
−0.139879 + 0.990169i \(0.544671\pi\)
\(462\) 1.40185 + 5.68948i 0.0652200 + 0.264698i
\(463\) 27.9282 1.29793 0.648966 0.760817i \(-0.275202\pi\)
0.648966 + 0.760817i \(0.275202\pi\)
\(464\) −3.61155 + 5.22869i −0.167662 + 0.242736i
\(465\) 0.0286727i 0.00132966i
\(466\) −36.2735 + 8.93757i −1.68034 + 0.414025i
\(467\) 8.56204i 0.396204i −0.980181 0.198102i \(-0.936522\pi\)
0.980181 0.198102i \(-0.0634778\pi\)
\(468\) 4.58988 + 8.74866i 0.212167 + 0.404407i
\(469\) 24.9026 18.0441i 1.14990 0.833198i
\(470\) 0.169471 + 0.687806i 0.00781711 + 0.0317261i
\(471\) −5.21451 −0.240272
\(472\) 17.7170 15.6883i 0.815489 0.722113i
\(473\) 4.17269 0.191860
\(474\) −1.40914 5.71907i −0.0647240 0.262685i
\(475\) 5.66042i 0.259718i
\(476\) −44.7189 + 23.4612i −2.04969 + 1.07534i
\(477\) 2.81313i 0.128805i
\(478\) −4.91851 19.9620i −0.224968 0.913041i
\(479\) 4.26200i 0.194736i 0.995248 + 0.0973679i \(0.0310424\pi\)
−0.995248 + 0.0973679i \(0.968958\pi\)
\(480\) −0.122430 + 0.322435i −0.00558814 + 0.0147171i
\(481\) 22.1991i 1.01219i
\(482\) 8.69305 + 35.2811i 0.395957 + 1.60701i
\(483\) 9.91812i 0.451290i
\(484\) 17.3276 9.09073i 0.787619 0.413215i
\(485\) 0.191634 0.00870164
\(486\) −0.338334 1.37315i −0.0153472 0.0622872i
\(487\) −27.6700 −1.25385 −0.626924 0.779080i \(-0.715686\pi\)
−0.626924 + 0.779080i \(0.715686\pi\)
\(488\) 8.56050 7.58031i 0.387516 0.343144i
\(489\) 0.859050i 0.0388476i
\(490\) 0.595701 0.146777i 0.0269110 0.00663071i
\(491\) 37.3820i 1.68702i 0.537110 + 0.843512i \(0.319516\pi\)
−0.537110 + 0.843512i \(0.680484\pi\)
\(492\) −1.42253 2.71146i −0.0641328 0.122242i
\(493\) −10.6770 −0.480867
\(494\) 1.89346 + 7.68470i 0.0851908 + 0.345751i
\(495\) 0.0672393i 0.00302218i
\(496\) −1.06908 + 1.54778i −0.0480033 + 0.0694975i
\(497\) 30.1238i 1.35124i
\(498\) −0.0302934 + 0.00746411i −0.00135748 + 0.000334475i
\(499\) −5.40037 −0.241754 −0.120877 0.992668i \(-0.538571\pi\)
−0.120877 + 0.992668i \(0.538571\pi\)
\(500\) 0.566299 + 1.07941i 0.0253256 + 0.0482726i
\(501\) 13.4828i 0.602369i
\(502\) −3.60903 14.6474i −0.161079 0.653746i
\(503\) −32.7304 −1.45938 −0.729689 0.683779i \(-0.760335\pi\)
−0.729689 + 0.683779i \(0.760335\pi\)
\(504\) −7.04479 7.95574i −0.313800 0.354377i
\(505\) 0.485736 0.0216150
\(506\) 3.99769 0.985006i 0.177719 0.0437889i
\(507\) 11.4015 0.506360
\(508\) 12.2348 + 23.3204i 0.542830 + 1.03468i
\(509\) 0.765912 0.0339485 0.0169742 0.999856i \(-0.494597\pi\)
0.0169742 + 0.999856i \(0.494597\pi\)
\(510\) −0.562655 + 0.138635i −0.0249148 + 0.00613885i
\(511\) 41.5391 1.83758
\(512\) 18.6312 12.8405i 0.823389 0.567477i
\(513\) 1.13293i 0.0500199i
\(514\) −6.51957 26.4600i −0.287566 1.16710i
\(515\) −1.00311 −0.0442023
\(516\) −6.70100 + 3.51560i −0.294995 + 0.154766i
\(517\) 9.06033i 0.398473i
\(518\) 5.71240 + 23.1840i 0.250988 + 1.01865i
\(519\) −3.37315 −0.148065
\(520\) 0.564735 + 0.637760i 0.0247653 + 0.0279676i
\(521\) 33.7198i 1.47729i −0.674094 0.738646i \(-0.735466\pi\)
0.674094 0.738646i \(-0.264534\pi\)
\(522\) −0.537506 2.18149i −0.0235260 0.0954813i
\(523\) 9.44525i 0.413012i −0.978445 0.206506i \(-0.933791\pi\)
0.978445 0.206506i \(-0.0662093\pi\)
\(524\) 12.3183 + 23.4797i 0.538129 + 1.02571i
\(525\) −18.7713 −0.819245
\(526\) 7.81404 1.92533i 0.340708 0.0839483i
\(527\) −3.16057 −0.137677
\(528\) 2.50707 3.62966i 0.109106 0.157960i
\(529\) 16.0311 0.697003
\(530\) −0.0580297 0.235516i −0.00252065 0.0102302i
\(531\) 8.36670i 0.363084i
\(532\) −3.95495 7.53843i −0.171469 0.326832i
\(533\) −7.56272 −0.327578
\(534\) 3.45010 + 14.0024i 0.149300 + 0.605942i
\(535\) −0.464454 −0.0200801
\(536\) −22.5986 5.03013i −0.976112 0.217268i
\(537\) −19.8446 −0.856360
\(538\) −9.70285 39.3794i −0.418319 1.69777i
\(539\) −7.84706 −0.337997
\(540\) −0.0566509 0.107981i −0.00243787 0.00464676i
\(541\) 34.1061i 1.46634i 0.680047 + 0.733169i \(0.261959\pi\)
−0.680047 + 0.733169i \(0.738041\pi\)
\(542\) −1.23747 5.02231i −0.0531537 0.215727i
\(543\) 12.1020 0.519347
\(544\) 35.5419 + 13.4954i 1.52385 + 0.578610i
\(545\) −0.926614 −0.0396918
\(546\) −25.4842 + 6.27915i −1.09062 + 0.268723i
\(547\) 42.8293 1.83125 0.915624 0.402036i \(-0.131697\pi\)
0.915624 + 0.402036i \(0.131697\pi\)
\(548\) 0.278610 + 0.531053i 0.0119016 + 0.0226854i
\(549\) 4.04264i 0.172536i
\(550\) −1.86424 7.56612i −0.0794916 0.322620i
\(551\) 1.79986i 0.0766765i
\(552\) −5.59008 + 4.95000i −0.237930 + 0.210686i
\(553\) 15.6478 0.665414
\(554\) −8.40149 34.0978i −0.356945 1.44868i
\(555\) 0.273993i 0.0116304i
\(556\) 7.56613 3.96948i 0.320875 0.168343i
\(557\) −10.7291 −0.454607 −0.227303 0.973824i \(-0.572991\pi\)
−0.227303 + 0.973824i \(0.572991\pi\)
\(558\) −0.159111 0.645759i −0.00673571 0.0273372i
\(559\) 18.6902i 0.790513i
\(560\) −0.753905 0.520736i −0.0318583 0.0220051i
\(561\) 7.41175 0.312924
\(562\) 37.4413 9.22529i 1.57936 0.389145i
\(563\) 27.9704 1.17881 0.589405 0.807837i \(-0.299362\pi\)
0.589405 + 0.807837i \(0.299362\pi\)
\(564\) 7.63357 + 14.5502i 0.321431 + 0.612673i
\(565\) −1.09792 −0.0461901
\(566\) 40.3807 9.94955i 1.69733 0.418211i
\(567\) 3.75704 0.157781
\(568\) 16.9785 15.0344i 0.712400 0.630829i
\(569\) −6.81343 −0.285634 −0.142817 0.989749i \(-0.545616\pi\)
−0.142817 + 0.989749i \(0.545616\pi\)
\(570\) −0.0233702 0.0948489i −0.000978869 0.00397278i
\(571\) 4.24888i 0.177810i −0.996040 0.0889050i \(-0.971663\pi\)
0.996040 0.0889050i \(-0.0283368\pi\)
\(572\) −5.06187 9.64831i −0.211647 0.403416i
\(573\) 19.4833 0.813927
\(574\) 7.89828 1.94609i 0.329668 0.0812281i
\(575\) 13.1896i 0.550043i
\(576\) −0.968076 + 7.94121i −0.0403365 + 0.330884i
\(577\) 33.8937i 1.41101i 0.708704 + 0.705506i \(0.249280\pi\)
−0.708704 + 0.705506i \(0.750720\pi\)
\(578\) 9.52993 + 38.6777i 0.396393 + 1.60878i
\(579\) 16.3459 0.679314
\(580\) −0.0900003 0.171547i −0.00373706 0.00712312i
\(581\) 0.0828853i 0.00343866i
\(582\) 4.31593 1.06342i 0.178901 0.0440801i
\(583\) 3.10241i 0.128489i
\(584\) −20.7316 23.4124i −0.857880 0.968811i
\(585\) −0.301178 −0.0124522
\(586\) 1.32532 + 5.37887i 0.0547484 + 0.222199i
\(587\) −20.6867 −0.853831 −0.426915 0.904292i \(-0.640400\pi\)
−0.426915 + 0.904292i \(0.640400\pi\)
\(588\) 12.6018 6.61136i 0.519688 0.272648i
\(589\) 0.532789i 0.0219532i
\(590\) 0.172590 + 0.700463i 0.00710540 + 0.0288376i
\(591\) 17.6850i 0.727463i
\(592\) 10.2161 14.7905i 0.419878 0.607885i
\(593\) 33.6914i 1.38354i −0.722118 0.691770i \(-0.756831\pi\)
0.722118 0.691770i \(-0.243169\pi\)
\(594\) 0.373126 + 1.51435i 0.0153095 + 0.0621345i
\(595\) 1.53947i 0.0631122i
\(596\) −20.1722 + 10.5831i −0.826284 + 0.433500i
\(597\) 0.273537i 0.0111951i
\(598\) 4.41203 + 17.9064i 0.180421 + 0.732248i
\(599\) 34.3230 1.40240 0.701199 0.712966i \(-0.252648\pi\)
0.701199 + 0.712966i \(0.252648\pi\)
\(600\) 9.36848 + 10.5799i 0.382467 + 0.431923i
\(601\) −11.6051 −0.473383 −0.236691 0.971585i \(-0.576063\pi\)
−0.236691 + 0.971585i \(0.576063\pi\)
\(602\) −4.80949 19.5195i −0.196020 0.795557i
\(603\) 6.62825 4.80274i 0.269923 0.195582i
\(604\) −5.50124 10.4858i −0.223842 0.426660i
\(605\) 0.596513i 0.0242517i
\(606\) 10.9396 2.69546i 0.444392 0.109495i
\(607\) 36.1180i 1.46599i −0.680236 0.732993i \(-0.738123\pi\)
0.680236 0.732993i \(-0.261877\pi\)
\(608\) −2.27497 + 5.99143i −0.0922622 + 0.242984i
\(609\) 5.96874 0.241866
\(610\) 0.0833921 + 0.338451i 0.00337645 + 0.0137035i
\(611\) 40.5829 1.64181
\(612\) −11.9027 + 6.24460i −0.481137 + 0.252423i
\(613\) −22.2211 −0.897501 −0.448750 0.893657i \(-0.648131\pi\)
−0.448750 + 0.893657i \(0.648131\pi\)
\(614\) 26.2224 6.46104i 1.05825 0.260746i
\(615\) 0.0933434 0.00376397
\(616\) 7.76922 + 8.77385i 0.313031 + 0.353508i
\(617\) 1.45070 0.0584028 0.0292014 0.999574i \(-0.490704\pi\)
0.0292014 + 0.999574i \(0.490704\pi\)
\(618\) −22.5918 + 5.56648i −0.908775 + 0.223917i
\(619\) 45.2790i 1.81992i −0.414699 0.909958i \(-0.636113\pi\)
0.414699 0.909958i \(-0.363887\pi\)
\(620\) −0.0266416 0.0507810i −0.00106995 0.00203941i
\(621\) 2.63987i 0.105935i
\(622\) −5.45017 22.1198i −0.218532 0.886922i
\(623\) −38.3117 −1.53492
\(624\) 16.2579 + 11.2296i 0.650837 + 0.449546i
\(625\) 24.9443 0.997770
\(626\) −34.4162 + 8.47994i −1.37555 + 0.338926i
\(627\) 1.24943i 0.0498973i
\(628\) −9.23521 + 4.84514i −0.368525 + 0.193342i
\(629\) 30.2021 1.20424
\(630\) 0.314541 0.0775009i 0.0125316 0.00308771i
\(631\) 43.0310 1.71304 0.856518 0.516118i \(-0.172623\pi\)
0.856518 + 0.516118i \(0.172623\pi\)
\(632\) −7.80963 8.81948i −0.310650 0.350820i
\(633\) 23.0337i 0.915506i
\(634\) 1.99567 + 8.09951i 0.0792581 + 0.321673i
\(635\) −0.802818 −0.0318589
\(636\) −2.61387 4.98223i −0.103647 0.197558i
\(637\) 35.1485i 1.39263i
\(638\) 0.592778 + 2.40582i 0.0234683 + 0.0952472i
\(639\) 8.01796i 0.317185i
\(640\) 0.0827649 + 0.684810i 0.00327157 + 0.0270695i
\(641\) 8.27565i 0.326869i −0.986554 0.163434i \(-0.947743\pi\)
0.986554 0.163434i \(-0.0522572\pi\)
\(642\) −10.4603 + 2.57736i −0.412836 + 0.101720i
\(643\) 44.9629i 1.77317i 0.462570 + 0.886583i \(0.346927\pi\)
−0.462570 + 0.886583i \(0.653073\pi\)
\(644\) −9.21557 17.5656i −0.363145 0.692181i
\(645\) 0.230686i 0.00908324i
\(646\) −10.4551 + 2.57608i −0.411352 + 0.101355i
\(647\) −16.8929 −0.664127 −0.332063 0.943257i \(-0.607745\pi\)
−0.332063 + 0.943257i \(0.607745\pi\)
\(648\) −1.87509 2.11755i −0.0736605 0.0831854i
\(649\) 9.22707i 0.362194i
\(650\) 33.8901 8.35030i 1.32928 0.327526i
\(651\) 1.76685 0.0692484
\(652\) 0.798200 + 1.52143i 0.0312599 + 0.0595838i
\(653\) 14.8987i 0.583033i −0.956566 0.291516i \(-0.905840\pi\)
0.956566 0.291516i \(-0.0941598\pi\)
\(654\) −20.8690 + 5.14199i −0.816042 + 0.201068i
\(655\) −0.808301 −0.0315829
\(656\) −5.03878 3.48038i −0.196731 0.135886i
\(657\) 11.0563 0.431348
\(658\) −42.3836 + 10.4431i −1.65228 + 0.407112i
\(659\) 11.9371i 0.465003i −0.972596 0.232502i \(-0.925309\pi\)
0.972596 0.232502i \(-0.0746911\pi\)
\(660\) 0.0624764 + 0.119085i 0.00243189 + 0.00463537i
\(661\) 27.4833i 1.06898i 0.845176 + 0.534488i \(0.179496\pi\)
−0.845176 + 0.534488i \(0.820504\pi\)
\(662\) 3.16352 + 12.8393i 0.122954 + 0.499013i
\(663\) 33.1986i 1.28933i
\(664\) −0.0467161 + 0.0413670i −0.00181293 + 0.00160535i
\(665\) 0.259515 0.0100635
\(666\) 1.52045 + 6.17082i 0.0589163 + 0.239114i
\(667\) 4.19392i 0.162389i
\(668\) −12.5278 23.8789i −0.484715 0.923903i
\(669\) 0.306864i 0.0118640i
\(670\) 0.455848 0.538815i 0.0176109 0.0208162i
\(671\) 4.45835i 0.172113i
\(672\) −19.8690 7.54432i −0.766461 0.291028i
\(673\) 39.3560i 1.51706i 0.651638 + 0.758530i \(0.274082\pi\)
−0.651638 + 0.758530i \(0.725918\pi\)
\(674\) −36.5181 + 8.99782i −1.40662 + 0.346583i
\(675\) −4.99628 −0.192307
\(676\) 20.1928 10.5939i 0.776646 0.407458i
\(677\) 30.4168i 1.16901i −0.811390 0.584505i \(-0.801289\pi\)
0.811390 0.584505i \(-0.198711\pi\)
\(678\) −24.7272 + 6.09263i −0.949643 + 0.233986i
\(679\) 11.8087i 0.453178i
\(680\) −0.867681 + 0.768330i −0.0332741 + 0.0294641i
\(681\) 25.5455i 0.978907i
\(682\) 0.175473 + 0.712164i 0.00671920 + 0.0272702i
\(683\) 35.5098 1.35874 0.679372 0.733794i \(-0.262252\pi\)
0.679372 + 0.733794i \(0.262252\pi\)
\(684\) −1.05268 2.00648i −0.0402500 0.0767197i
\(685\) −0.0182818 −0.000698511
\(686\) 0.146657 + 0.595216i 0.00559941 + 0.0227255i
\(687\) 0.674492i 0.0257335i
\(688\) −8.60130 + 12.4527i −0.327921 + 0.474754i
\(689\) −13.8963 −0.529407
\(690\) −0.0544557 0.221011i −0.00207309 0.00841375i
\(691\) 5.77351i 0.219635i 0.993952 + 0.109817i \(0.0350266\pi\)
−0.993952 + 0.109817i \(0.964973\pi\)
\(692\) −5.97406 + 3.13422i −0.227100 + 0.119145i
\(693\) −4.14339 −0.157394
\(694\) 1.29878 + 5.27117i 0.0493011 + 0.200091i
\(695\) 0.260468i 0.00988012i
\(696\) −2.97892 3.36412i −0.112916 0.127517i
\(697\) 10.2892i 0.389731i
\(698\) −0.447724 1.81711i −0.0169466 0.0687785i
\(699\) 26.4164i 0.999159i
\(700\) −33.2450 + 17.4416i −1.25654 + 0.659230i
\(701\) 38.6943i 1.46146i −0.682666 0.730731i \(-0.739179\pi\)
0.682666 0.730731i \(-0.260821\pi\)
\(702\) −6.78305 + 1.67130i −0.256010 + 0.0630792i
\(703\) 5.09129i 0.192021i
\(704\) 1.06762 8.75782i 0.0402376 0.330073i
\(705\) −0.500898 −0.0188649
\(706\) −29.2644 + 7.21056i −1.10138 + 0.271373i
\(707\) 29.9318i 1.12570i
\(708\) 7.77405 + 14.8179i 0.292167 + 0.556892i
\(709\) −6.14543 −0.230797 −0.115398 0.993319i \(-0.536814\pi\)
−0.115398 + 0.993319i \(0.536814\pi\)
\(710\) 0.165396 + 0.671266i 0.00620719 + 0.0251922i
\(711\) 4.16494 0.156197
\(712\) 19.1208 + 21.5933i 0.716584 + 0.809244i
\(713\) 1.24147i 0.0464935i
\(714\) −8.54287 34.6716i −0.319709 1.29755i
\(715\) 0.332148 0.0124216
\(716\) −35.1460 + 18.4390i −1.31347 + 0.689096i
\(717\) 14.5374 0.542910
\(718\) 45.3597 11.1764i 1.69281 0.417098i
\(719\) 27.3015i 1.01817i −0.860715 0.509087i \(-0.829983\pi\)
0.860715 0.509087i \(-0.170017\pi\)
\(720\) −0.200664 0.138603i −0.00747832 0.00516542i
\(721\) 61.8131i 2.30204i
\(722\) 5.99410 + 24.3273i 0.223077 + 0.905369i
\(723\) −25.6937 −0.955557
\(724\) 21.4334 11.2448i 0.796565 0.417908i
\(725\) −7.93750 −0.294791
\(726\) 3.31018 + 13.4345i 0.122852 + 0.498602i
\(727\) −28.2755 −1.04868 −0.524340 0.851509i \(-0.675688\pi\)
−0.524340 + 0.851509i \(0.675688\pi\)
\(728\) −39.2997 + 34.7998i −1.45654 + 1.28977i
\(729\) 1.00000 0.0370370
\(730\) 0.925639 0.228072i 0.0342594 0.00844131i
\(731\) −25.4283 −0.940501
\(732\) 3.75628 + 7.15975i 0.138836 + 0.264632i
\(733\) 4.28232i 0.158171i 0.996868 + 0.0790855i \(0.0252000\pi\)
−0.996868 + 0.0790855i \(0.974800\pi\)
\(734\) −7.17139 29.1054i −0.264701 1.07430i
\(735\) 0.433822i 0.0160018i
\(736\) −5.30099 + 13.9609i −0.195397 + 0.514604i
\(737\) −7.30985 + 5.29661i −0.269262 + 0.195103i
\(738\) 2.10226 0.517983i 0.0773852 0.0190672i
\(739\) −50.2060 −1.84686 −0.923429 0.383769i \(-0.874626\pi\)
−0.923429 + 0.383769i \(0.874626\pi\)
\(740\) 0.254585 + 0.485259i 0.00935874 + 0.0178385i
\(741\) −5.59642 −0.205590
\(742\) 14.5129 3.57588i 0.532784 0.131275i
\(743\) 45.7389i 1.67800i −0.544134 0.838998i \(-0.683142\pi\)
0.544134 0.838998i \(-0.316858\pi\)
\(744\) −0.881812 0.995838i −0.0323288 0.0365092i
\(745\) 0.694438i 0.0254422i
\(746\) −49.2649 + 12.1386i −1.80371 + 0.444424i
\(747\) 0.0220613i 0.000807182i
\(748\) 13.1267 6.88674i 0.479958 0.251804i
\(749\) 28.6203i 1.04576i
\(750\) −0.836892 + 0.206205i −0.0305590 + 0.00752954i
\(751\) 23.7461i 0.866507i 0.901272 + 0.433253i \(0.142634\pi\)
−0.901272 + 0.433253i \(0.857366\pi\)
\(752\) 27.0390 + 18.6764i 0.986012 + 0.681057i
\(753\) 10.6671 0.388729
\(754\) −10.7761 + 2.65517i −0.392443 + 0.0966954i
\(755\) 0.360979 0.0131374
\(756\) 6.65395 3.49091i 0.242002 0.126963i
\(757\) 49.3512i 1.79370i −0.442334 0.896850i \(-0.645850\pi\)
0.442334 0.896850i \(-0.354150\pi\)
\(758\) −10.3284 41.9184i −0.375146 1.52255i
\(759\) 2.91134i 0.105675i
\(760\) −0.129520 0.146268i −0.00469819 0.00530571i
\(761\) 27.3276 0.990624 0.495312 0.868715i \(-0.335054\pi\)
0.495312 + 0.868715i \(0.335054\pi\)
\(762\) −18.0809 + 4.45502i −0.655002 + 0.161388i
\(763\) 57.0993i 2.06713i
\(764\) 34.5061 18.1032i 1.24839 0.654951i
\(765\) 0.409756i 0.0148148i
\(766\) −5.14721 20.8902i −0.185976 0.754793i
\(767\) 41.3298 1.49233
\(768\) 5.66418 + 14.9639i 0.204388 + 0.539962i
\(769\) 39.0002i 1.40638i 0.711000 + 0.703192i \(0.248243\pi\)
−0.711000 + 0.703192i \(0.751757\pi\)
\(770\) −0.346886 + 0.0854704i −0.0125009 + 0.00308014i
\(771\)