Properties

Label 370.2.h.e.253.9
Level $370$
Weight $2$
Character 370.253
Analytic conductor $2.954$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.h (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} - 7362 x^{11} + 13826 x^{10} + 4848 x^{9} + 13544 x^{8} - 44248 x^{7} + 76384 x^{6} + 24512 x^{5} + 28432 x^{4} - 61952 x^{3} + 61952 x^{2} - 5632 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 253.9
Root \(1.82785 + 1.82785i\) of defining polynomial
Character \(\chi\) \(=\) 370.253
Dual form 370.2.h.e.117.9

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(1.82785 - 1.82785i) q^{3} +1.00000 q^{4} +(-1.23698 - 1.86276i) q^{5} +(-1.82785 + 1.82785i) q^{6} +(3.41332 - 3.41332i) q^{7} -1.00000 q^{8} -3.68208i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(1.82785 - 1.82785i) q^{3} +1.00000 q^{4} +(-1.23698 - 1.86276i) q^{5} +(-1.82785 + 1.82785i) q^{6} +(3.41332 - 3.41332i) q^{7} -1.00000 q^{8} -3.68208i q^{9} +(1.23698 + 1.86276i) q^{10} +3.97950i q^{11} +(1.82785 - 1.82785i) q^{12} -4.28763 q^{13} +(-3.41332 + 3.41332i) q^{14} +(-5.66587 - 1.14383i) q^{15} +1.00000 q^{16} -2.57516i q^{17} +3.68208i q^{18} +(5.24415 + 5.24415i) q^{19} +(-1.23698 - 1.86276i) q^{20} -12.4781i q^{21} -3.97950i q^{22} -2.21783 q^{23} +(-1.82785 + 1.82785i) q^{24} +(-1.93975 + 4.60840i) q^{25} +4.28763 q^{26} +(-1.24674 - 1.24674i) q^{27} +(3.41332 - 3.41332i) q^{28} +(-2.03524 + 2.03524i) q^{29} +(5.66587 + 1.14383i) q^{30} +(-3.23732 - 3.23732i) q^{31} -1.00000 q^{32} +(7.27394 + 7.27394i) q^{33} +2.57516i q^{34} +(-10.5804 - 2.13598i) q^{35} -3.68208i q^{36} +(5.60171 - 2.37084i) q^{37} +(-5.24415 - 5.24415i) q^{38} +(-7.83714 + 7.83714i) q^{39} +(1.23698 + 1.86276i) q^{40} -2.50763i q^{41} +12.4781i q^{42} +9.00337 q^{43} +3.97950i q^{44} +(-6.85883 + 4.55467i) q^{45} +2.21783 q^{46} +(-0.943466 + 0.943466i) q^{47} +(1.82785 - 1.82785i) q^{48} -16.3015i q^{49} +(1.93975 - 4.60840i) q^{50} +(-4.70702 - 4.70702i) q^{51} -4.28763 q^{52} +(2.84055 + 2.84055i) q^{53} +(1.24674 + 1.24674i) q^{54} +(7.41286 - 4.92258i) q^{55} +(-3.41332 + 3.41332i) q^{56} +19.1710 q^{57} +(2.03524 - 2.03524i) q^{58} +(-2.91109 - 2.91109i) q^{59} +(-5.66587 - 1.14383i) q^{60} +(-5.71266 - 5.71266i) q^{61} +(3.23732 + 3.23732i) q^{62} +(-12.5681 - 12.5681i) q^{63} +1.00000 q^{64} +(5.30372 + 7.98682i) q^{65} +(-7.27394 - 7.27394i) q^{66} +(-1.28531 - 1.28531i) q^{67} -2.57516i q^{68} +(-4.05387 + 4.05387i) q^{69} +(10.5804 + 2.13598i) q^{70} +8.40334 q^{71} +3.68208i q^{72} +(-5.32492 + 5.32492i) q^{73} +(-5.60171 + 2.37084i) q^{74} +(4.87791 + 11.9690i) q^{75} +(5.24415 + 5.24415i) q^{76} +(13.5833 + 13.5833i) q^{77} +(7.83714 - 7.83714i) q^{78} +(9.77118 + 9.77118i) q^{79} +(-1.23698 - 1.86276i) q^{80} +6.48853 q^{81} +2.50763i q^{82} +(2.57398 + 2.57398i) q^{83} -12.4781i q^{84} +(-4.79691 + 3.18543i) q^{85} -9.00337 q^{86} +7.44024i q^{87} -3.97950i q^{88} +(-9.42876 + 9.42876i) q^{89} +(6.85883 - 4.55467i) q^{90} +(-14.6350 + 14.6350i) q^{91} -2.21783 q^{92} -11.8347 q^{93} +(0.943466 - 0.943466i) q^{94} +(3.28166 - 16.2555i) q^{95} +(-1.82785 + 1.82785i) q^{96} -5.92246i q^{97} +16.3015i q^{98} +14.6528 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 20q^{2} + 4q^{3} + 20q^{4} - 4q^{5} - 4q^{6} - 2q^{7} - 20q^{8} + O(q^{10}) \) \( 20q - 20q^{2} + 4q^{3} + 20q^{4} - 4q^{5} - 4q^{6} - 2q^{7} - 20q^{8} + 4q^{10} + 4q^{12} + 2q^{14} - 4q^{15} + 20q^{16} + 6q^{19} - 4q^{20} - 4q^{23} - 4q^{24} + 10q^{25} - 20q^{27} - 2q^{28} + 18q^{29} + 4q^{30} + 12q^{31} - 20q^{32} + 4q^{33} - 12q^{35} - 32q^{37} - 6q^{38} + 6q^{39} + 4q^{40} + 16q^{43} + 22q^{45} + 4q^{46} - 22q^{47} + 4q^{48} - 10q^{50} + 8q^{51} - 4q^{53} + 20q^{54} + 16q^{55} + 2q^{56} + 24q^{57} - 18q^{58} - 10q^{59} - 4q^{60} + 10q^{61} - 12q^{62} - 2q^{63} + 20q^{64} + 20q^{65} - 4q^{66} + 8q^{67} - 34q^{69} + 12q^{70} + 16q^{71} - 6q^{73} + 32q^{74} - 26q^{75} + 6q^{76} - 4q^{77} - 6q^{78} + 12q^{79} - 4q^{80} - 28q^{81} + 6q^{83} + 10q^{85} - 16q^{86} - 44q^{89} - 22q^{90} - 40q^{91} - 4q^{92} - 40q^{93} + 22q^{94} + 50q^{95} - 4q^{96} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.82785 1.82785i 1.05531 1.05531i 0.0569322 0.998378i \(-0.481868\pi\)
0.998378 0.0569322i \(-0.0181319\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.23698 1.86276i −0.553196 0.833051i
\(6\) −1.82785 + 1.82785i −0.746217 + 0.746217i
\(7\) 3.41332 3.41332i 1.29011 1.29011i 0.355399 0.934715i \(-0.384345\pi\)
0.934715 0.355399i \(-0.115655\pi\)
\(8\) −1.00000 −0.353553
\(9\) 3.68208i 1.22736i
\(10\) 1.23698 + 1.86276i 0.391168 + 0.589056i
\(11\) 3.97950i 1.19987i 0.800051 + 0.599933i \(0.204806\pi\)
−0.800051 + 0.599933i \(0.795194\pi\)
\(12\) 1.82785 1.82785i 0.527655 0.527655i
\(13\) −4.28763 −1.18917 −0.594587 0.804031i \(-0.702684\pi\)
−0.594587 + 0.804031i \(0.702684\pi\)
\(14\) −3.41332 + 3.41332i −0.912248 + 0.912248i
\(15\) −5.66587 1.14383i −1.46292 0.295335i
\(16\) 1.00000 0.250000
\(17\) 2.57516i 0.624569i −0.949989 0.312284i \(-0.898906\pi\)
0.949989 0.312284i \(-0.101094\pi\)
\(18\) 3.68208i 0.867874i
\(19\) 5.24415 + 5.24415i 1.20309 + 1.20309i 0.973222 + 0.229868i \(0.0738296\pi\)
0.229868 + 0.973222i \(0.426170\pi\)
\(20\) −1.23698 1.86276i −0.276598 0.416526i
\(21\) 12.4781i 2.72294i
\(22\) 3.97950i 0.848433i
\(23\) −2.21783 −0.462451 −0.231225 0.972900i \(-0.574273\pi\)
−0.231225 + 0.972900i \(0.574273\pi\)
\(24\) −1.82785 + 1.82785i −0.373109 + 0.373109i
\(25\) −1.93975 + 4.60840i −0.387949 + 0.921681i
\(26\) 4.28763 0.840873
\(27\) −1.24674 1.24674i −0.239935 0.239935i
\(28\) 3.41332 3.41332i 0.645057 0.645057i
\(29\) −2.03524 + 2.03524i −0.377935 + 0.377935i −0.870357 0.492422i \(-0.836112\pi\)
0.492422 + 0.870357i \(0.336112\pi\)
\(30\) 5.66587 + 1.14383i 1.03444 + 0.208833i
\(31\) −3.23732 3.23732i −0.581439 0.581439i 0.353859 0.935299i \(-0.384869\pi\)
−0.935299 + 0.353859i \(0.884869\pi\)
\(32\) −1.00000 −0.176777
\(33\) 7.27394 + 7.27394i 1.26623 + 1.26623i
\(34\) 2.57516i 0.441637i
\(35\) −10.5804 2.13598i −1.78842 0.361046i
\(36\) 3.68208i 0.613680i
\(37\) 5.60171 2.37084i 0.920915 0.389764i
\(38\) −5.24415 5.24415i −0.850713 0.850713i
\(39\) −7.83714 + 7.83714i −1.25495 + 1.25495i
\(40\) 1.23698 + 1.86276i 0.195584 + 0.294528i
\(41\) 2.50763i 0.391627i −0.980641 0.195813i \(-0.937265\pi\)
0.980641 0.195813i \(-0.0627347\pi\)
\(42\) 12.4781i 1.92541i
\(43\) 9.00337 1.37300 0.686501 0.727129i \(-0.259146\pi\)
0.686501 + 0.727129i \(0.259146\pi\)
\(44\) 3.97950i 0.599933i
\(45\) −6.85883 + 4.55467i −1.02245 + 0.678970i
\(46\) 2.21783 0.327002
\(47\) −0.943466 + 0.943466i −0.137619 + 0.137619i −0.772560 0.634942i \(-0.781024\pi\)
0.634942 + 0.772560i \(0.281024\pi\)
\(48\) 1.82785 1.82785i 0.263828 0.263828i
\(49\) 16.3015i 2.32879i
\(50\) 1.93975 4.60840i 0.274321 0.651727i
\(51\) −4.70702 4.70702i −0.659114 0.659114i
\(52\) −4.28763 −0.594587
\(53\) 2.84055 + 2.84055i 0.390180 + 0.390180i 0.874751 0.484572i \(-0.161025\pi\)
−0.484572 + 0.874751i \(0.661025\pi\)
\(54\) 1.24674 + 1.24674i 0.169660 + 0.169660i
\(55\) 7.41286 4.92258i 0.999549 0.663760i
\(56\) −3.41332 + 3.41332i −0.456124 + 0.456124i
\(57\) 19.1710 2.53927
\(58\) 2.03524 2.03524i 0.267240 0.267240i
\(59\) −2.91109 2.91109i −0.378991 0.378991i 0.491747 0.870738i \(-0.336359\pi\)
−0.870738 + 0.491747i \(0.836359\pi\)
\(60\) −5.66587 1.14383i −0.731460 0.147667i
\(61\) −5.71266 5.71266i −0.731431 0.731431i 0.239472 0.970903i \(-0.423026\pi\)
−0.970903 + 0.239472i \(0.923026\pi\)
\(62\) 3.23732 + 3.23732i 0.411140 + 0.411140i
\(63\) −12.5681 12.5681i −1.58343 1.58343i
\(64\) 1.00000 0.125000
\(65\) 5.30372 + 7.98682i 0.657846 + 0.990643i
\(66\) −7.27394 7.27394i −0.895360 0.895360i
\(67\) −1.28531 1.28531i −0.157026 0.157026i 0.624222 0.781247i \(-0.285416\pi\)
−0.781247 + 0.624222i \(0.785416\pi\)
\(68\) 2.57516i 0.312284i
\(69\) −4.05387 + 4.05387i −0.488029 + 0.488029i
\(70\) 10.5804 + 2.13598i 1.26460 + 0.255298i
\(71\) 8.40334 0.997293 0.498646 0.866806i \(-0.333831\pi\)
0.498646 + 0.866806i \(0.333831\pi\)
\(72\) 3.68208i 0.433937i
\(73\) −5.32492 + 5.32492i −0.623235 + 0.623235i −0.946357 0.323123i \(-0.895267\pi\)
0.323123 + 0.946357i \(0.395267\pi\)
\(74\) −5.60171 + 2.37084i −0.651185 + 0.275605i
\(75\) 4.87791 + 11.9690i 0.563253 + 1.38207i
\(76\) 5.24415 + 5.24415i 0.601545 + 0.601545i
\(77\) 13.5833 + 13.5833i 1.54796 + 1.54796i
\(78\) 7.83714 7.83714i 0.887382 0.887382i
\(79\) 9.77118 + 9.77118i 1.09934 + 1.09934i 0.994487 + 0.104856i \(0.0334382\pi\)
0.104856 + 0.994487i \(0.466562\pi\)
\(80\) −1.23698 1.86276i −0.138299 0.208263i
\(81\) 6.48853 0.720948
\(82\) 2.50763i 0.276922i
\(83\) 2.57398 + 2.57398i 0.282531 + 0.282531i 0.834117 0.551587i \(-0.185977\pi\)
−0.551587 + 0.834117i \(0.685977\pi\)
\(84\) 12.4781i 1.36147i
\(85\) −4.79691 + 3.18543i −0.520298 + 0.345509i
\(86\) −9.00337 −0.970859
\(87\) 7.44024i 0.797678i
\(88\) 3.97950i 0.424216i
\(89\) −9.42876 + 9.42876i −0.999447 + 0.999447i −1.00000 0.000552868i \(-0.999824\pi\)
0.000552868 1.00000i \(0.499824\pi\)
\(90\) 6.85883 4.55467i 0.722984 0.480104i
\(91\) −14.6350 + 14.6350i −1.53417 + 1.53417i
\(92\) −2.21783 −0.231225
\(93\) −11.8347 −1.22720
\(94\) 0.943466 0.943466i 0.0973111 0.0973111i
\(95\) 3.28166 16.2555i 0.336692 1.66778i
\(96\) −1.82785 + 1.82785i −0.186554 + 0.186554i
\(97\) 5.92246i 0.601335i −0.953729 0.300668i \(-0.902791\pi\)
0.953729 0.300668i \(-0.0972095\pi\)
\(98\) 16.3015i 1.64670i
\(99\) 14.6528 1.47267
\(100\) −1.93975 + 4.60840i −0.193975 + 0.460840i
\(101\) 1.64079i 0.163265i 0.996663 + 0.0816323i \(0.0260133\pi\)
−0.996663 + 0.0816323i \(0.973987\pi\)
\(102\) 4.70702 + 4.70702i 0.466064 + 0.466064i
\(103\) 2.79089i 0.274994i −0.990502 0.137497i \(-0.956094\pi\)
0.990502 0.137497i \(-0.0439058\pi\)
\(104\) 4.28763 0.420436
\(105\) −23.2437 + 15.4352i −2.26835 + 1.50632i
\(106\) −2.84055 2.84055i −0.275899 0.275899i
\(107\) −3.77209 + 3.77209i −0.364662 + 0.364662i −0.865526 0.500864i \(-0.833016\pi\)
0.500864 + 0.865526i \(0.333016\pi\)
\(108\) −1.24674 1.24674i −0.119967 0.119967i
\(109\) 11.9302 + 11.9302i 1.14271 + 1.14271i 0.987953 + 0.154756i \(0.0494590\pi\)
0.154756 + 0.987953i \(0.450541\pi\)
\(110\) −7.41286 + 4.92258i −0.706788 + 0.469349i
\(111\) 5.90554 14.5726i 0.560529 1.38317i
\(112\) 3.41332 3.41332i 0.322528 0.322528i
\(113\) 15.5469i 1.46253i 0.682091 + 0.731267i \(0.261071\pi\)
−0.682091 + 0.731267i \(0.738929\pi\)
\(114\) −19.1710 −1.79553
\(115\) 2.74342 + 4.13129i 0.255826 + 0.385245i
\(116\) −2.03524 + 2.03524i −0.188968 + 0.188968i
\(117\) 15.7874i 1.45954i
\(118\) 2.91109 + 2.91109i 0.267987 + 0.267987i
\(119\) −8.78986 8.78986i −0.805765 0.805765i
\(120\) 5.66587 + 1.14383i 0.517221 + 0.104417i
\(121\) −4.83644 −0.439676
\(122\) 5.71266 + 5.71266i 0.517200 + 0.517200i
\(123\) −4.58358 4.58358i −0.413288 0.413288i
\(124\) −3.23732 3.23732i −0.290720 0.290720i
\(125\) 10.9838 2.08724i 0.982419 0.186688i
\(126\) 12.5681 + 12.5681i 1.11966 + 1.11966i
\(127\) 0.0553748 0.0553748i 0.00491372 0.00491372i −0.704646 0.709559i \(-0.748894\pi\)
0.709559 + 0.704646i \(0.248894\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 16.4568 16.4568i 1.44894 1.44894i
\(130\) −5.30372 7.98682i −0.465167 0.700490i
\(131\) 3.08937 + 3.08937i 0.269920 + 0.269920i 0.829068 0.559148i \(-0.188872\pi\)
−0.559148 + 0.829068i \(0.688872\pi\)
\(132\) 7.27394 + 7.27394i 0.633115 + 0.633115i
\(133\) 35.7999 3.10425
\(134\) 1.28531 + 1.28531i 0.111034 + 0.111034i
\(135\) −0.780179 + 3.86457i −0.0671471 + 0.332609i
\(136\) 2.57516i 0.220818i
\(137\) −1.84871 + 1.84871i −0.157946 + 0.157946i −0.781656 0.623710i \(-0.785625\pi\)
0.623710 + 0.781656i \(0.285625\pi\)
\(138\) 4.05387 4.05387i 0.345088 0.345088i
\(139\) −10.9433 −0.928195 −0.464097 0.885784i \(-0.653621\pi\)
−0.464097 + 0.885784i \(0.653621\pi\)
\(140\) −10.5804 2.13598i −0.894208 0.180523i
\(141\) 3.44903i 0.290461i
\(142\) −8.40334 −0.705192
\(143\) 17.0626i 1.42685i
\(144\) 3.68208i 0.306840i
\(145\) 6.30873 + 1.27361i 0.523911 + 0.105767i
\(146\) 5.32492 5.32492i 0.440693 0.440693i
\(147\) −29.7967 29.7967i −2.45759 2.45759i
\(148\) 5.60171 2.37084i 0.460457 0.194882i
\(149\) 13.0913i 1.07248i −0.844066 0.536240i \(-0.819844\pi\)
0.844066 0.536240i \(-0.180156\pi\)
\(150\) −4.87791 11.9690i −0.398280 0.977268i
\(151\) 9.37187i 0.762672i −0.924437 0.381336i \(-0.875464\pi\)
0.924437 0.381336i \(-0.124536\pi\)
\(152\) −5.24415 5.24415i −0.425357 0.425357i
\(153\) −9.48196 −0.766571
\(154\) −13.5833 13.5833i −1.09457 1.09457i
\(155\) −2.02584 + 10.0349i −0.162719 + 0.806019i
\(156\) −7.83714 + 7.83714i −0.627474 + 0.627474i
\(157\) −16.2868 + 16.2868i −1.29983 + 1.29983i −0.371321 + 0.928504i \(0.621095\pi\)
−0.928504 + 0.371321i \(0.878905\pi\)
\(158\) −9.77118 9.77118i −0.777353 0.777353i
\(159\) 10.3842 0.823521
\(160\) 1.23698 + 1.86276i 0.0977921 + 0.147264i
\(161\) −7.57018 + 7.57018i −0.596614 + 0.596614i
\(162\) −6.48853 −0.509787
\(163\) 2.14382i 0.167917i −0.996469 0.0839586i \(-0.973244\pi\)
0.996469 0.0839586i \(-0.0267564\pi\)
\(164\) 2.50763i 0.195813i
\(165\) 4.55186 22.5473i 0.354362 1.75531i
\(166\) −2.57398 2.57398i −0.199779 0.199779i
\(167\) 20.3382i 1.57382i −0.617071 0.786908i \(-0.711681\pi\)
0.617071 0.786908i \(-0.288319\pi\)
\(168\) 12.4781i 0.962705i
\(169\) 5.38374 0.414134
\(170\) 4.79691 3.18543i 0.367906 0.244312i
\(171\) 19.3094 19.3094i 1.47662 1.47662i
\(172\) 9.00337 0.686501
\(173\) 13.7435 13.7435i 1.04490 1.04490i 0.0459570 0.998943i \(-0.485366\pi\)
0.998943 0.0459570i \(-0.0146337\pi\)
\(174\) 7.44024i 0.564043i
\(175\) 9.10899 + 22.3509i 0.688575 + 1.68957i
\(176\) 3.97950i 0.299966i
\(177\) −10.6421 −0.799907
\(178\) 9.42876 9.42876i 0.706716 0.706716i
\(179\) 13.4168 13.4168i 1.00282 1.00282i 0.00281938 0.999996i \(-0.499103\pi\)
0.999996 0.00281938i \(-0.000897436\pi\)
\(180\) −6.85883 + 4.55467i −0.511227 + 0.339485i
\(181\) −15.3711 −1.14252 −0.571261 0.820768i \(-0.693546\pi\)
−0.571261 + 0.820768i \(0.693546\pi\)
\(182\) 14.6350 14.6350i 1.08482 1.08482i
\(183\) −20.8838 −1.54377
\(184\) 2.21783 0.163501
\(185\) −11.3455 7.50194i −0.834139 0.551554i
\(186\) 11.8347 0.867760
\(187\) 10.2479 0.749398
\(188\) −0.943466 + 0.943466i −0.0688093 + 0.0688093i
\(189\) −8.51103 −0.619087
\(190\) −3.28166 + 16.2555i −0.238077 + 1.17930i
\(191\) −16.9686 + 16.9686i −1.22781 + 1.22781i −0.263016 + 0.964791i \(0.584717\pi\)
−0.964791 + 0.263016i \(0.915283\pi\)
\(192\) 1.82785 1.82785i 0.131914 0.131914i
\(193\) −5.70785 −0.410860 −0.205430 0.978672i \(-0.565859\pi\)
−0.205430 + 0.978672i \(0.565859\pi\)
\(194\) 5.92246i 0.425208i
\(195\) 24.2931 + 4.90430i 1.73967 + 0.351204i
\(196\) 16.3015i 1.16439i
\(197\) 9.14763 9.14763i 0.651742 0.651742i −0.301670 0.953412i \(-0.597544\pi\)
0.953412 + 0.301670i \(0.0975442\pi\)
\(198\) −14.6528 −1.04133
\(199\) −6.66896 + 6.66896i −0.472750 + 0.472750i −0.902803 0.430053i \(-0.858495\pi\)
0.430053 + 0.902803i \(0.358495\pi\)
\(200\) 1.93975 4.60840i 0.137161 0.325863i
\(201\) −4.69872 −0.331422
\(202\) 1.64079i 0.115445i
\(203\) 13.8939i 0.975159i
\(204\) −4.70702 4.70702i −0.329557 0.329557i
\(205\) −4.67112 + 3.10190i −0.326245 + 0.216646i
\(206\) 2.79089i 0.194450i
\(207\) 8.16624i 0.567593i
\(208\) −4.28763 −0.297293
\(209\) −20.8691 + 20.8691i −1.44355 + 1.44355i
\(210\) 23.2437 15.4352i 1.60397 1.06513i
\(211\) 15.1553 1.04334 0.521668 0.853149i \(-0.325310\pi\)
0.521668 + 0.853149i \(0.325310\pi\)
\(212\) 2.84055 + 2.84055i 0.195090 + 0.195090i
\(213\) 15.3600 15.3600i 1.05245 1.05245i
\(214\) 3.77209 3.77209i 0.257855 0.257855i
\(215\) −11.1370 16.7711i −0.759539 1.14378i
\(216\) 1.24674 + 1.24674i 0.0848298 + 0.0848298i
\(217\) −22.1000 −1.50025
\(218\) −11.9302 11.9302i −0.808017 0.808017i
\(219\) 19.4663i 1.31541i
\(220\) 7.41286 4.92258i 0.499775 0.331880i
\(221\) 11.0413i 0.742721i
\(222\) −5.90554 + 14.5726i −0.396354 + 0.978051i
\(223\) −6.25546 6.25546i −0.418896 0.418896i 0.465927 0.884823i \(-0.345721\pi\)
−0.884823 + 0.465927i \(0.845721\pi\)
\(224\) −3.41332 + 3.41332i −0.228062 + 0.228062i
\(225\) 16.9685 + 7.14229i 1.13123 + 0.476153i
\(226\) 15.5469i 1.03417i
\(227\) 9.87949i 0.655725i −0.944725 0.327862i \(-0.893672\pi\)
0.944725 0.327862i \(-0.106328\pi\)
\(228\) 19.1710 1.26963
\(229\) 21.9472i 1.45031i 0.688586 + 0.725155i \(0.258232\pi\)
−0.688586 + 0.725155i \(0.741768\pi\)
\(230\) −2.74342 4.13129i −0.180896 0.272409i
\(231\) 49.6566 3.26716
\(232\) 2.03524 2.03524i 0.133620 0.133620i
\(233\) −8.96601 + 8.96601i −0.587383 + 0.587383i −0.936922 0.349539i \(-0.886338\pi\)
0.349539 + 0.936922i \(0.386338\pi\)
\(234\) 15.7874i 1.03205i
\(235\) 2.92450 + 0.590399i 0.190773 + 0.0385134i
\(236\) −2.91109 2.91109i −0.189496 0.189496i
\(237\) 35.7205 2.32030
\(238\) 8.78986 + 8.78986i 0.569762 + 0.569762i
\(239\) −13.0815 13.0815i −0.846174 0.846174i 0.143479 0.989653i \(-0.454171\pi\)
−0.989653 + 0.143479i \(0.954171\pi\)
\(240\) −5.66587 1.14383i −0.365730 0.0738336i
\(241\) 5.41196 5.41196i 0.348615 0.348615i −0.510978 0.859594i \(-0.670717\pi\)
0.859594 + 0.510978i \(0.170717\pi\)
\(242\) 4.83644 0.310898
\(243\) 15.6003 15.6003i 1.00076 1.00076i
\(244\) −5.71266 5.71266i −0.365716 0.365716i
\(245\) −30.3658 + 20.1647i −1.94000 + 1.28828i
\(246\) 4.58358 + 4.58358i 0.292239 + 0.292239i
\(247\) −22.4849 22.4849i −1.43068 1.43068i
\(248\) 3.23732 + 3.23732i 0.205570 + 0.205570i
\(249\) 9.40969 0.596315
\(250\) −10.9838 + 2.08724i −0.694675 + 0.132009i
\(251\) 2.34715 + 2.34715i 0.148151 + 0.148151i 0.777292 0.629141i \(-0.216593\pi\)
−0.629141 + 0.777292i \(0.716593\pi\)
\(252\) −12.5681 12.5681i −0.791717 0.791717i
\(253\) 8.82588i 0.554878i
\(254\) −0.0553748 + 0.0553748i −0.00347453 + 0.00347453i
\(255\) −2.94554 + 14.5905i −0.184457 + 0.913695i
\(256\) 1.00000 0.0625000
\(257\) 5.80813i 0.362301i 0.983455 + 0.181151i \(0.0579822\pi\)
−0.983455 + 0.181151i \(0.942018\pi\)
\(258\) −16.4568 + 16.4568i −1.02456 + 1.02456i
\(259\) 11.0280 27.2129i 0.685245 1.69092i
\(260\) 5.30372 + 7.98682i 0.328923 + 0.495321i
\(261\) 7.49392 + 7.49392i 0.463862 + 0.463862i
\(262\) −3.08937 3.08937i −0.190862 0.190862i
\(263\) −15.2944 + 15.2944i −0.943090 + 0.943090i −0.998466 0.0553752i \(-0.982365\pi\)
0.0553752 + 0.998466i \(0.482365\pi\)
\(264\) −7.27394 7.27394i −0.447680 0.447680i
\(265\) 1.77755 8.80497i 0.109194 0.540885i
\(266\) −35.7999 −2.19503
\(267\) 34.4688i 2.10945i
\(268\) −1.28531 1.28531i −0.0785129 0.0785129i
\(269\) 18.2273i 1.11134i 0.831404 + 0.555668i \(0.187537\pi\)
−0.831404 + 0.555668i \(0.812463\pi\)
\(270\) 0.780179 3.86457i 0.0474802 0.235190i
\(271\) −26.6096 −1.61642 −0.808208 0.588898i \(-0.799562\pi\)
−0.808208 + 0.588898i \(0.799562\pi\)
\(272\) 2.57516i 0.156142i
\(273\) 53.5014i 3.23805i
\(274\) 1.84871 1.84871i 0.111685 0.111685i
\(275\) −18.3392 7.71922i −1.10589 0.465487i
\(276\) −4.05387 + 4.05387i −0.244014 + 0.244014i
\(277\) 0.845623 0.0508086 0.0254043 0.999677i \(-0.491913\pi\)
0.0254043 + 0.999677i \(0.491913\pi\)
\(278\) 10.9433 0.656333
\(279\) −11.9201 + 11.9201i −0.713635 + 0.713635i
\(280\) 10.5804 + 2.13598i 0.632301 + 0.127649i
\(281\) 11.3809 11.3809i 0.678927 0.678927i −0.280830 0.959757i \(-0.590610\pi\)
0.959757 + 0.280830i \(0.0906098\pi\)
\(282\) 3.44903i 0.205387i
\(283\) 6.37857i 0.379167i 0.981865 + 0.189583i \(0.0607137\pi\)
−0.981865 + 0.189583i \(0.939286\pi\)
\(284\) 8.40334 0.498646
\(285\) −23.7143 35.7110i −1.40471 2.11534i
\(286\) 17.0626i 1.00893i
\(287\) −8.55936 8.55936i −0.505243 0.505243i
\(288\) 3.68208i 0.216969i
\(289\) 10.3685 0.609914
\(290\) −6.30873 1.27361i −0.370461 0.0747888i
\(291\) −10.8254 10.8254i −0.634595 0.634595i
\(292\) −5.32492 + 5.32492i −0.311617 + 0.311617i
\(293\) −6.47894 6.47894i −0.378504 0.378504i 0.492058 0.870562i \(-0.336245\pi\)
−0.870562 + 0.492058i \(0.836245\pi\)
\(294\) 29.7967 + 29.7967i 1.73778 + 1.73778i
\(295\) −1.82169 + 9.02362i −0.106063 + 0.525376i
\(296\) −5.60171 + 2.37084i −0.325593 + 0.137802i
\(297\) 4.96140 4.96140i 0.287889 0.287889i
\(298\) 13.0913i 0.758358i
\(299\) 9.50925 0.549934
\(300\) 4.87791 + 11.9690i 0.281626 + 0.691033i
\(301\) 30.7314 30.7314i 1.77133 1.77133i
\(302\) 9.37187i 0.539290i
\(303\) 2.99912 + 2.99912i 0.172295 + 0.172295i
\(304\) 5.24415 + 5.24415i 0.300773 + 0.300773i
\(305\) −3.57485 + 17.7078i −0.204695 + 1.01394i
\(306\) 9.48196 0.542047
\(307\) 3.64587 + 3.64587i 0.208081 + 0.208081i 0.803451 0.595371i \(-0.202995\pi\)
−0.595371 + 0.803451i \(0.702995\pi\)
\(308\) 13.5833 + 13.5833i 0.773981 + 0.773981i
\(309\) −5.10132 5.10132i −0.290204 0.290204i
\(310\) 2.02584 10.0349i 0.115060 0.569941i
\(311\) −0.480637 0.480637i −0.0272545 0.0272545i 0.693348 0.720603i \(-0.256135\pi\)
−0.720603 + 0.693348i \(0.756135\pi\)
\(312\) 7.83714 7.83714i 0.443691 0.443691i
\(313\) −18.2772 −1.03309 −0.516543 0.856261i \(-0.672781\pi\)
−0.516543 + 0.856261i \(0.672781\pi\)
\(314\) 16.2868 16.2868i 0.919116 0.919116i
\(315\) −7.86483 + 38.9579i −0.443133 + 2.19503i
\(316\) 9.77118 + 9.77118i 0.549672 + 0.549672i
\(317\) −4.85997 4.85997i −0.272963 0.272963i 0.557329 0.830292i \(-0.311826\pi\)
−0.830292 + 0.557329i \(0.811826\pi\)
\(318\) −10.3842 −0.582317
\(319\) −8.09925 8.09925i −0.453471 0.453471i
\(320\) −1.23698 1.86276i −0.0691495 0.104131i
\(321\) 13.7896i 0.769662i
\(322\) 7.57018 7.57018i 0.421870 0.421870i
\(323\) 13.5045 13.5045i 0.751413 0.751413i
\(324\) 6.48853 0.360474
\(325\) 8.31690 19.7591i 0.461339 1.09604i
\(326\) 2.14382i 0.118735i
\(327\) 43.6134 2.41182
\(328\) 2.50763i 0.138461i
\(329\) 6.44070i 0.355088i
\(330\) −4.55186 + 22.5473i −0.250571 + 1.24119i
\(331\) −20.7472 + 20.7472i −1.14037 + 1.14037i −0.151986 + 0.988383i \(0.548567\pi\)
−0.988383 + 0.151986i \(0.951433\pi\)
\(332\) 2.57398 + 2.57398i 0.141265 + 0.141265i
\(333\) −8.72962 20.6259i −0.478380 1.13029i
\(334\) 20.3382i 1.11286i
\(335\) −0.804317 + 3.98413i −0.0439446 + 0.217677i
\(336\) 12.4781i 0.680735i
\(337\) 6.47001 + 6.47001i 0.352444 + 0.352444i 0.861018 0.508574i \(-0.169827\pi\)
−0.508574 + 0.861018i \(0.669827\pi\)
\(338\) −5.38374 −0.292837
\(339\) 28.4175 + 28.4175i 1.54343 + 1.54343i
\(340\) −4.79691 + 3.18543i −0.260149 + 0.172754i
\(341\) 12.8829 12.8829i 0.697649 0.697649i
\(342\) −19.3094 + 19.3094i −1.04413 + 1.04413i
\(343\) −31.7491 31.7491i −1.71429 1.71429i
\(344\) −9.00337 −0.485429
\(345\) 12.5660 + 2.53682i 0.676528 + 0.136578i
\(346\) −13.7435 + 13.7435i −0.738856 + 0.738856i
\(347\) −6.44807 −0.346151 −0.173075 0.984909i \(-0.555370\pi\)
−0.173075 + 0.984909i \(0.555370\pi\)
\(348\) 7.44024i 0.398839i
\(349\) 4.70014i 0.251593i −0.992056 0.125796i \(-0.959851\pi\)
0.992056 0.125796i \(-0.0401486\pi\)
\(350\) −9.10899 22.3509i −0.486896 1.19471i
\(351\) 5.34555 + 5.34555i 0.285324 + 0.285324i
\(352\) 3.97950i 0.212108i
\(353\) 19.6162i 1.04406i −0.852926 0.522031i \(-0.825174\pi\)
0.852926 0.522031i \(-0.174826\pi\)
\(354\) 10.6421 0.565620
\(355\) −10.3948 15.6534i −0.551698 0.830796i
\(356\) −9.42876 + 9.42876i −0.499723 + 0.499723i
\(357\) −32.1331 −1.70066
\(358\) −13.4168 + 13.4168i −0.709098 + 0.709098i
\(359\) 7.60520i 0.401387i −0.979654 0.200694i \(-0.935680\pi\)
0.979654 0.200694i \(-0.0643196\pi\)
\(360\) 6.85883 4.55467i 0.361492 0.240052i
\(361\) 36.0022i 1.89485i
\(362\) 15.3711 0.807885
\(363\) −8.84029 + 8.84029i −0.463995 + 0.463995i
\(364\) −14.6350 + 14.6350i −0.767085 + 0.767085i
\(365\) 16.5059 + 3.33221i 0.863957 + 0.174416i
\(366\) 20.8838 1.09161
\(367\) −10.3061 + 10.3061i −0.537975 + 0.537975i −0.922934 0.384959i \(-0.874216\pi\)
0.384959 + 0.922934i \(0.374216\pi\)
\(368\) −2.21783 −0.115613
\(369\) −9.23331 −0.480667
\(370\) 11.3455 + 7.50194i 0.589826 + 0.390007i
\(371\) 19.3914 1.00675
\(372\) −11.8347 −0.613599
\(373\) 0.690871 0.690871i 0.0357719 0.0357719i −0.688995 0.724767i \(-0.741948\pi\)
0.724767 + 0.688995i \(0.241948\pi\)
\(374\) −10.2479 −0.529905
\(375\) 16.2616 23.8919i 0.839743 1.23377i
\(376\) 0.943466 0.943466i 0.0486555 0.0486555i
\(377\) 8.72636 8.72636i 0.449430 0.449430i
\(378\) 8.51103 0.437760
\(379\) 0.266778i 0.0137035i 0.999977 + 0.00685174i \(0.00218099\pi\)
−0.999977 + 0.00685174i \(0.997819\pi\)
\(380\) 3.28166 16.2555i 0.168346 0.833890i
\(381\) 0.202434i 0.0103710i
\(382\) 16.9686 16.9686i 0.868191 0.868191i
\(383\) 32.6980 1.67079 0.835395 0.549650i \(-0.185239\pi\)
0.835395 + 0.549650i \(0.185239\pi\)
\(384\) −1.82785 + 1.82785i −0.0932771 + 0.0932771i
\(385\) 8.50012 42.1048i 0.433206 2.14586i
\(386\) 5.70785 0.290522
\(387\) 33.1511i 1.68517i
\(388\) 5.92246i 0.300668i
\(389\) 24.7831 + 24.7831i 1.25655 + 1.25655i 0.952728 + 0.303825i \(0.0982639\pi\)
0.303825 + 0.952728i \(0.401736\pi\)
\(390\) −24.2931 4.90430i −1.23013 0.248339i
\(391\) 5.71129i 0.288832i
\(392\) 16.3015i 0.823351i
\(393\) 11.2938 0.569698
\(394\) −9.14763 + 9.14763i −0.460851 + 0.460851i
\(395\) 6.11457 30.2881i 0.307658 1.52396i
\(396\) 14.6528 0.736333
\(397\) −11.3967 11.3967i −0.571984 0.571984i 0.360698 0.932683i \(-0.382538\pi\)
−0.932683 + 0.360698i \(0.882538\pi\)
\(398\) 6.66896 6.66896i 0.334285 0.334285i
\(399\) 65.4369 65.4369i 3.27594 3.27594i
\(400\) −1.93975 + 4.60840i −0.0969873 + 0.230420i
\(401\) −14.6783 14.6783i −0.733000 0.733000i 0.238213 0.971213i \(-0.423438\pi\)
−0.971213 + 0.238213i \(0.923438\pi\)
\(402\) 4.69872 0.234351
\(403\) 13.8804 + 13.8804i 0.691432 + 0.691432i
\(404\) 1.64079i 0.0816323i
\(405\) −8.02621 12.0866i −0.398825 0.600587i
\(406\) 13.8939i 0.689541i
\(407\) 9.43477 + 22.2920i 0.467664 + 1.10497i
\(408\) 4.70702 + 4.70702i 0.233032 + 0.233032i
\(409\) −10.7756 + 10.7756i −0.532819 + 0.532819i −0.921410 0.388591i \(-0.872962\pi\)
0.388591 + 0.921410i \(0.372962\pi\)
\(410\) 4.67112 3.10190i 0.230690 0.153192i
\(411\) 6.75833i 0.333364i
\(412\) 2.79089i 0.137497i
\(413\) −19.8730 −0.977884
\(414\) 8.16624i 0.401349i
\(415\) 1.61073 7.97866i 0.0790678 0.391657i
\(416\) 4.28763 0.210218
\(417\) −20.0026 + 20.0026i −0.979533 + 0.979533i
\(418\) 20.8691 20.8691i 1.02074 1.02074i
\(419\) 24.0943i 1.17709i 0.808466 + 0.588543i \(0.200298\pi\)
−0.808466 + 0.588543i \(0.799702\pi\)
\(420\) −23.2437 + 15.4352i −1.13417 + 0.753160i
\(421\) 21.6407 + 21.6407i 1.05470 + 1.05470i 0.998415 + 0.0562888i \(0.0179267\pi\)
0.0562888 + 0.998415i \(0.482073\pi\)
\(422\) −15.1553 −0.737750
\(423\) 3.47392 + 3.47392i 0.168908 + 0.168908i
\(424\) −2.84055 2.84055i −0.137949 0.137949i
\(425\) 11.8674 + 4.99516i 0.575653 + 0.242301i
\(426\) −15.3600 + 15.3600i −0.744197 + 0.744197i
\(427\) −38.9983 −1.88726
\(428\) −3.77209 + 3.77209i −0.182331 + 0.182331i
\(429\) −31.1879 31.1879i −1.50577 1.50577i
\(430\) 11.1370 + 16.7711i 0.537075 + 0.808775i
\(431\) 1.23281 + 1.23281i 0.0593825 + 0.0593825i 0.736174 0.676792i \(-0.236630\pi\)
−0.676792 + 0.736174i \(0.736630\pi\)
\(432\) −1.24674 1.24674i −0.0599837 0.0599837i
\(433\) −12.5825 12.5825i −0.604678 0.604678i 0.336872 0.941550i \(-0.390631\pi\)
−0.941550 + 0.336872i \(0.890631\pi\)
\(434\) 22.1000 1.06083
\(435\) 13.8594 9.20345i 0.664506 0.441272i
\(436\) 11.9302 + 11.9302i 0.571354 + 0.571354i
\(437\) −11.6307 11.6307i −0.556370 0.556370i
\(438\) 19.4663i 0.930137i
\(439\) −13.6362 + 13.6362i −0.650822 + 0.650822i −0.953191 0.302369i \(-0.902223\pi\)
0.302369 + 0.953191i \(0.402223\pi\)
\(440\) −7.41286 + 4.92258i −0.353394 + 0.234675i
\(441\) −60.0235 −2.85826
\(442\) 11.0413i 0.525183i
\(443\) −23.2157 + 23.2157i −1.10301 + 1.10301i −0.108963 + 0.994046i \(0.534753\pi\)
−0.994046 + 0.108963i \(0.965247\pi\)
\(444\) 5.90554 14.5726i 0.280265 0.691586i
\(445\) 29.2267 + 5.90030i 1.38548 + 0.279701i
\(446\) 6.25546 + 6.25546i 0.296204 + 0.296204i
\(447\) −23.9289 23.9289i −1.13180 1.13180i
\(448\) 3.41332 3.41332i 0.161264 0.161264i
\(449\) 16.0955 + 16.0955i 0.759594 + 0.759594i 0.976248 0.216654i \(-0.0695144\pi\)
−0.216654 + 0.976248i \(0.569514\pi\)
\(450\) −16.9685 7.14229i −0.799903 0.336691i
\(451\) 9.97914 0.469899
\(452\) 15.5469i 0.731267i
\(453\) −17.1304 17.1304i −0.804855 0.804855i
\(454\) 9.87949i 0.463668i
\(455\) 45.3649 + 9.15826i 2.12674 + 0.429346i
\(456\) −19.1710 −0.897766
\(457\) 3.34685i 0.156559i −0.996931 0.0782794i \(-0.975057\pi\)
0.996931 0.0782794i \(-0.0249426\pi\)
\(458\) 21.9472i 1.02552i
\(459\) −3.21055 + 3.21055i −0.149856 + 0.149856i
\(460\) 2.74342 + 4.13129i 0.127913 + 0.192623i
\(461\) 22.0325 22.0325i 1.02616 1.02616i 0.0265068 0.999649i \(-0.491562\pi\)
0.999649 0.0265068i \(-0.00843837\pi\)
\(462\) −49.6566 −2.31023
\(463\) −10.8598 −0.504696 −0.252348 0.967637i \(-0.581203\pi\)
−0.252348 + 0.967637i \(0.581203\pi\)
\(464\) −2.03524 + 2.03524i −0.0944838 + 0.0944838i
\(465\) 14.6393 + 22.0451i 0.678881 + 1.02232i
\(466\) 8.96601 8.96601i 0.415342 0.415342i
\(467\) 12.9597i 0.599702i 0.953986 + 0.299851i \(0.0969371\pi\)
−0.953986 + 0.299851i \(0.903063\pi\)
\(468\) 15.7874i 0.729772i
\(469\) −8.77436 −0.405162
\(470\) −2.92450 0.590399i −0.134897 0.0272331i
\(471\) 59.5396i 2.74344i
\(472\) 2.91109 + 2.91109i 0.133994 + 0.133994i
\(473\) 35.8289i 1.64742i
\(474\) −35.7205 −1.64070
\(475\) −34.3395 + 13.9948i −1.57560 + 0.642127i
\(476\) −8.78986 8.78986i −0.402883 0.402883i
\(477\) 10.4591 10.4591i 0.478891 0.478891i
\(478\) 13.0815 + 13.0815i 0.598335 + 0.598335i
\(479\) −2.98032 2.98032i −0.136174 0.136174i 0.635734 0.771908i \(-0.280698\pi\)
−0.771908 + 0.635734i \(0.780698\pi\)
\(480\) 5.66587 + 1.14383i 0.258610 + 0.0522083i
\(481\) −24.0180 + 10.1653i −1.09513 + 0.463497i
\(482\) −5.41196 + 5.41196i −0.246508 + 0.246508i
\(483\) 27.6743i 1.25923i
\(484\) −4.83644 −0.219838
\(485\) −11.0321 + 7.32599i −0.500943 + 0.332656i
\(486\) −15.6003 + 15.6003i −0.707643 + 0.707643i
\(487\) 4.69219i 0.212624i −0.994333 0.106312i \(-0.966096\pi\)
0.994333 0.106312i \(-0.0339042\pi\)
\(488\) 5.71266 + 5.71266i 0.258600 + 0.258600i
\(489\) −3.91859 3.91859i −0.177205 0.177205i
\(490\) 30.3658 20.1647i 1.37179 0.910948i
\(491\) −4.44735 −0.200706 −0.100353 0.994952i \(-0.531997\pi\)
−0.100353 + 0.994952i \(0.531997\pi\)
\(492\) −4.58358 4.58358i −0.206644 0.206644i
\(493\) 5.24108 + 5.24108i 0.236047 + 0.236047i
\(494\) 22.4849 + 22.4849i 1.01165 + 1.01165i
\(495\) −18.1253 27.2947i −0.814672 1.22681i
\(496\) −3.23732 3.23732i −0.145360 0.145360i
\(497\) 28.6833 28.6833i 1.28662 1.28662i
\(498\) −9.40969 −0.421658
\(499\) −24.3133 + 24.3133i −1.08841 + 1.08841i −0.0927210 + 0.995692i \(0.529556\pi\)
−0.995692 + 0.0927210i \(0.970444\pi\)
\(500\) 10.9838 2.08724i 0.491210 0.0933442i
\(501\) −37.1752 37.1752i −1.66086 1.66086i
\(502\) −2.34715 2.34715i −0.104759 0.104759i
\(503\) 15.7435 0.701968 0.350984 0.936381i \(-0.385847\pi\)
0.350984 + 0.936381i \(0.385847\pi\)
\(504\) 12.5681 + 12.5681i 0.559828 + 0.559828i
\(505\) 3.05639 2.02963i 0.136008 0.0903173i
\(506\) 8.82588i 0.392358i
\(507\) 9.84067 9.84067i 0.437040 0.437040i
\(508\) 0.0553748 0.0553748i 0.00245686 0.00245686i
\(509\) −32.8974 −1.45815 −0.729077 0.684432i \(-0.760050\pi\)
−0.729077 + 0.684432i \(0.760050\pi\)
\(510\) 2.94554 14.5905i 0.130431 0.646080i
\(511\) 36.3513i 1.60809i
\(512\) −1.00000 −0.0441942
\(513\) 13.0762i 0.577327i
\(514\) 5.80813i 0.256186i
\(515\) −5.19875 + 3.45228i −0.229084 + 0.152126i
\(516\) 16.4568 16.4568i 0.724471 0.724471i
\(517\) −3.75453 3.75453i −0.165124 0.165124i
\(518\) −11.0280 + 27.2129i −0.484542 + 1.19566i
\(519\) 50.2422i 2.20539i
\(520\) −5.30372 7.98682i −0.232584 0.350245i
\(521\) 21.7965i 0.954920i −0.878653 0.477460i \(-0.841558\pi\)
0.878653 0.477460i \(-0.158442\pi\)
\(522\) −7.49392 7.49392i −0.328000 0.328000i
\(523\) −20.7364 −0.906739 −0.453369 0.891323i \(-0.649778\pi\)
−0.453369 + 0.891323i \(0.649778\pi\)
\(524\) 3.08937 + 3.08937i 0.134960 + 0.134960i
\(525\) 57.5040 + 24.2043i 2.50968 + 1.05636i
\(526\) 15.2944 15.2944i 0.666866 0.666866i
\(527\) −8.33662 + 8.33662i −0.363149 + 0.363149i
\(528\) 7.27394 + 7.27394i 0.316557 + 0.316557i
\(529\) −18.0812 −0.786140
\(530\) −1.77755 + 8.80497i −0.0772118 + 0.382464i
\(531\) −10.7189 + 10.7189i −0.465159 + 0.465159i
\(532\) 35.7999 1.55212
\(533\) 10.7518i 0.465712i
\(534\) 34.4688i 1.49161i
\(535\) 11.6925 + 2.36048i 0.505511 + 0.102053i
\(536\) 1.28531 + 1.28531i 0.0555170 + 0.0555170i
\(537\) 49.0477i 2.11656i
\(538\) 18.2273i 0.785833i
\(539\) 64.8719 2.79423
\(540\) −0.780179 + 3.86457i −0.0335736 + 0.166304i
\(541\) 3.55548 3.55548i 0.152862 0.152862i −0.626533 0.779395i \(-0.715527\pi\)
0.779395 + 0.626533i \(0.215527\pi\)
\(542\) 26.6096 1.14298
\(543\) −28.0960 + 28.0960i −1.20572 + 1.20572i
\(544\) 2.57516i 0.110409i
\(545\) 7.46565 36.9806i 0.319793 1.58408i
\(546\) 53.5014i 2.28965i
\(547\) 10.3831 0.443950 0.221975 0.975052i \(-0.428750\pi\)
0.221975 + 0.975052i \(0.428750\pi\)
\(548\) −1.84871 + 1.84871i −0.0789729 + 0.0789729i
\(549\) −21.0345 + 21.0345i −0.897729 + 0.897729i
\(550\) 18.3392 + 7.71922i 0.781984 + 0.329149i
\(551\) −21.3462 −0.909380
\(552\) 4.05387 4.05387i 0.172544 0.172544i
\(553\) 66.7043 2.83656
\(554\) −0.845623 −0.0359271
\(555\) −34.4504 + 7.02549i −1.46234 + 0.298216i
\(556\) −10.9433 −0.464097
\(557\) −4.73501 −0.200629 −0.100314 0.994956i \(-0.531985\pi\)
−0.100314 + 0.994956i \(0.531985\pi\)
\(558\) 11.9201 11.9201i 0.504616 0.504616i
\(559\) −38.6031 −1.63274
\(560\) −10.5804 2.13598i −0.447104 0.0902614i
\(561\) 18.7316 18.7316i 0.790848 0.790848i
\(562\) −11.3809 + 11.3809i −0.480074 + 0.480074i
\(563\) 3.05563 0.128779 0.0643897 0.997925i \(-0.479490\pi\)
0.0643897 + 0.997925i \(0.479490\pi\)
\(564\) 3.44903i 0.145230i
\(565\) 28.9602 19.2313i 1.21837 0.809068i
\(566\) 6.37857i 0.268111i
\(567\) 22.1474 22.1474i 0.930105 0.930105i
\(568\) −8.40334 −0.352596
\(569\) 29.4912 29.4912i 1.23633 1.23633i 0.274845 0.961488i \(-0.411373\pi\)
0.961488 0.274845i \(-0.0886266\pi\)
\(570\) 23.7143 + 35.7110i 0.993281 + 1.49577i
\(571\) 14.8841 0.622881 0.311440 0.950266i \(-0.399189\pi\)
0.311440 + 0.950266i \(0.399189\pi\)
\(572\) 17.0626i 0.713424i
\(573\) 62.0323i 2.59144i
\(574\) 8.55936 + 8.55936i 0.357261 + 0.357261i
\(575\) 4.30203 10.2207i 0.179407 0.426232i
\(576\) 3.68208i 0.153420i
\(577\) 9.65939i 0.402126i −0.979578 0.201063i \(-0.935560\pi\)
0.979578 0.201063i \(-0.0644395\pi\)
\(578\) −10.3685 −0.431274
\(579\) −10.4331 + 10.4331i −0.433584 + 0.433584i
\(580\) 6.30873 + 1.27361i 0.261956 + 0.0528836i
\(581\) 17.5716 0.728993
\(582\) 10.8254 + 10.8254i 0.448726 + 0.448726i
\(583\) −11.3040 + 11.3040i −0.468163 + 0.468163i
\(584\) 5.32492 5.32492i 0.220347 0.220347i
\(585\) 29.4081 19.5287i 1.21587 0.807413i
\(586\) 6.47894 + 6.47894i 0.267643 + 0.267643i
\(587\) −0.789320 −0.0325787 −0.0162894 0.999867i \(-0.505185\pi\)
−0.0162894 + 0.999867i \(0.505185\pi\)
\(588\) −29.7967 29.7967i −1.22880 1.22880i
\(589\) 33.9539i 1.39905i
\(590\) 1.82169 9.02362i 0.0749978 0.371497i
\(591\) 33.4410i 1.37558i
\(592\) 5.60171 2.37084i 0.230229 0.0974410i
\(593\) 4.13138 + 4.13138i 0.169656 + 0.169656i 0.786828 0.617172i \(-0.211722\pi\)
−0.617172 + 0.786828i \(0.711722\pi\)
\(594\) −4.96140 + 4.96140i −0.203569 + 0.203569i
\(595\) −5.50049 + 27.2463i −0.225498 + 1.11699i
\(596\) 13.0913i 0.536240i
\(597\) 24.3797i 0.997796i
\(598\) −9.50925 −0.388862
\(599\) 38.0949i 1.55652i −0.627944 0.778258i \(-0.716104\pi\)
0.627944 0.778258i \(-0.283896\pi\)
\(600\) −4.87791 11.9690i −0.199140 0.488634i
\(601\) −43.6207 −1.77933 −0.889663 0.456617i \(-0.849061\pi\)
−0.889663 + 0.456617i \(0.849061\pi\)
\(602\) −30.7314 + 30.7314i −1.25252 + 1.25252i
\(603\) −4.73262 + 4.73262i −0.192727 + 0.192727i
\(604\) 9.37187i 0.381336i
\(605\) 5.98259 + 9.00912i 0.243227 + 0.366273i
\(606\) −2.99912 2.99912i −0.121831 0.121831i
\(607\) −4.59751 −0.186607 −0.0933036 0.995638i \(-0.529743\pi\)
−0.0933036 + 0.995638i \(0.529743\pi\)
\(608\) −5.24415 5.24415i −0.212678 0.212678i
\(609\) 25.3959 + 25.3959i 1.02909 + 1.02909i
\(610\) 3.57485 17.7078i 0.144741 0.716967i
\(611\) 4.04523 4.04523i 0.163652 0.163652i
\(612\) −9.48196 −0.383285
\(613\) 9.19983 9.19983i 0.371578 0.371578i −0.496474 0.868052i \(-0.665372\pi\)
0.868052 + 0.496474i \(0.165372\pi\)
\(614\) −3.64587 3.64587i −0.147135 0.147135i
\(615\) −2.86830 + 14.2079i −0.115661 + 0.572919i
\(616\) −13.5833 13.5833i −0.547287 0.547287i
\(617\) 8.47786 + 8.47786i 0.341306 + 0.341306i 0.856858 0.515552i \(-0.172413\pi\)
−0.515552 + 0.856858i \(0.672413\pi\)
\(618\) 5.10132 + 5.10132i 0.205205 + 0.205205i
\(619\) −12.3858 −0.497827 −0.248914 0.968526i \(-0.580074\pi\)
−0.248914 + 0.968526i \(0.580074\pi\)
\(620\) −2.02584 + 10.0349i −0.0813596 + 0.403009i
\(621\) 2.76506 + 2.76506i 0.110958 + 0.110958i
\(622\) 0.480637 + 0.480637i 0.0192718 + 0.0192718i
\(623\) 64.3668i 2.57880i
\(624\) −7.83714 + 7.83714i −0.313737 + 0.313737i
\(625\) −17.4748 17.8783i −0.698991 0.715130i
\(626\) 18.2772 0.730502
\(627\) 76.2912i 3.04678i
\(628\) −16.2868 + 16.2868i −0.649913 + 0.649913i
\(629\) −6.10530 14.4253i −0.243434 0.575175i
\(630\) 7.86483 38.9579i 0.313342 1.55212i
\(631\) −19.2781 19.2781i −0.767448 0.767448i 0.210208 0.977657i \(-0.432586\pi\)
−0.977657 + 0.210208i \(0.932586\pi\)
\(632\) −9.77118 9.77118i −0.388677 0.388677i
\(633\) 27.7017 27.7017i 1.10104 1.10104i
\(634\) 4.85997 + 4.85997i 0.193014 + 0.193014i
\(635\) −0.171648 0.0346523i −0.00681163 0.00137513i
\(636\) 10.3842 0.411761
\(637\) 69.8948i 2.76933i
\(638\) 8.09925 + 8.09925i 0.320653 + 0.320653i
\(639\) 30.9417i 1.22404i
\(640\) 1.23698 + 1.86276i 0.0488961 + 0.0736320i
\(641\) 0.616340 0.0243440 0.0121720 0.999926i \(-0.496125\pi\)
0.0121720 + 0.999926i \(0.496125\pi\)
\(642\) 13.7896i 0.544233i
\(643\) 42.0640i 1.65884i −0.558622 0.829422i \(-0.688670\pi\)
0.558622 0.829422i \(-0.311330\pi\)
\(644\) −7.57018 + 7.57018i −0.298307 + 0.298307i
\(645\) −51.0119 10.2983i −2.00859 0.405495i
\(646\) −13.5045 + 13.5045i −0.531329 + 0.531329i
\(647\) −35.3320 −1.38904 −0.694521 0.719472i \(-0.744384\pi\)
−0.694521 + 0.719472i \(0.744384\pi\)
\(648\) −6.48853 −0.254894
\(649\) 11.5847 11.5847i 0.454738 0.454738i
\(650\) −8.31690 + 19.7591i −0.326216 + 0.775016i
\(651\) −40.3955 + 40.3955i −1.58323 + 1.58323i
\(652\) 2.14382i 0.0839586i
\(653\) 12.3601i 0.483687i −0.970315 0.241844i \(-0.922248\pi\)
0.970315 0.241844i \(-0.0777521\pi\)
\(654\) −43.6134 −1.70542
\(655\) 1.93326 9.57626i 0.0755385 0.374175i
\(656\) 2.50763i 0.0979067i
\(657\) 19.6068 + 19.6068i 0.764933 + 0.764933i
\(658\) 6.44070i 0.251085i
\(659\) −37.7706 −1.47133 −0.735667 0.677344i \(-0.763131\pi\)
−0.735667 + 0.677344i \(0.763131\pi\)
\(660\) 4.55186 22.5473i 0.177181 0.877654i
\(661\) 25.3521 + 25.3521i 0.986082 + 0.986082i 0.999904 0.0138228i \(-0.00440006\pi\)
−0.0138228 + 0.999904i \(0.504400\pi\)
\(662\) 20.7472 20.7472i 0.806362 0.806362i
\(663\) 20.1819 + 20.1819i 0.783801 + 0.783801i
\(664\) −2.57398 2.57398i −0.0998896 0.0998896i
\(665\) −44.2839 66.6866i −1.71726 2.58600i
\(666\) 8.72962 + 20.6259i 0.338266 + 0.799238i
\(667\) 4.51383 4.51383i 0.174776 0.174776i
\(668\) 20.3382i 0.786908i
\(669\) −22.8681 −0.884131
\(670\) 0.804317 3.98413i 0.0310735 0.153921i
\(671\) 22.7335 22.7335i 0.877619 0.877619i
\(672\) 12.4781i 0.481353i
\(673\) −0.303990 0.303990i −0.0117180 0.0117180i 0.701224 0.712941i \(-0.252637\pi\)
−0.712941 + 0.701224i \(0.752637\pi\)
\(674\) −6.47001 6.47001i −0.249215 0.249215i
\(675\) 8.16383 3.32712i 0.314226 0.128061i
\(676\) 5.38374 0.207067
\(677\) 19.2022 + 19.2022i 0.738000 + 0.738000i 0.972191 0.234191i \(-0.0752440\pi\)
−0.234191 + 0.972191i \(0.575244\pi\)
\(678\) −28.4175 28.4175i −1.09137 1.09137i
\(679\) −20.2153 20.2153i −0.775791 0.775791i
\(680\) 4.79691 3.18543i 0.183953 0.122156i
\(681\) −18.0582 18.0582i −0.691993 0.691993i
\(682\) −12.8829 + 12.8829i −0.493312 + 0.493312i
\(683\) −16.4834 −0.630719 −0.315359 0.948972i \(-0.602125\pi\)
−0.315359 + 0.948972i \(0.602125\pi\)
\(684\) 19.3094 19.3094i 0.738312 0.738312i
\(685\) 5.73052 + 1.15688i 0.218952 + 0.0442020i
\(686\) 31.7491 + 31.7491i 1.21218 + 1.21218i
\(687\) 40.1161 + 40.1161i 1.53053 + 1.53053i
\(688\) 9.00337 0.343250
\(689\) −12.1792 12.1792i −0.463991 0.463991i
\(690\) −12.5660 2.53682i −0.478378 0.0965750i
\(691\) 27.8853i 1.06081i 0.847745 + 0.530403i \(0.177959\pi\)
−0.847745 + 0.530403i \(0.822041\pi\)
\(692\) 13.7435 13.7435i 0.522450 0.522450i
\(693\) 50.0148 50.0148i 1.89991 1.89991i
\(694\) 6.44807 0.244765
\(695\) 13.5366 + 20.3846i 0.513473 + 0.773234i
\(696\) 7.44024i 0.282022i
\(697\) −6.45757 −0.244598
\(698\) 4.70014i 0.177903i
\(699\) 32.7771i 1.23974i
\(700\) 9.10899 + 22.3509i 0.344287 + 0.844786i
\(701\) 5.25849 5.25849i 0.198610 0.198610i −0.600794 0.799404i \(-0.705149\pi\)
0.799404 + 0.600794i \(0.205149\pi\)
\(702\) −5.34555 5.34555i −0.201755 0.201755i
\(703\) 41.8092 + 16.9431i 1.57686 + 0.639023i
\(704\) 3.97950i 0.149983i
\(705\) 6.42471 4.26639i 0.241969 0.160682i
\(706\) 19.6162i 0.738264i
\(707\) 5.60054 + 5.60054i 0.210630 + 0.210630i
\(708\) −10.6421 −0.399953
\(709\) 25.3783 + 25.3783i 0.953101 + 0.953101i 0.998948 0.0458470i \(-0.0145987\pi\)
−0.0458470 + 0.998948i \(0.514599\pi\)
\(710\) 10.3948 + 15.6534i 0.390109 + 0.587461i
\(711\) 35.9783 35.9783i 1.34929 1.34929i
\(712\) 9.42876 9.42876i 0.353358 0.353358i
\(713\) 7.17984 + 7.17984i 0.268887 + 0.268887i
\(714\) 32.1331 1.20255
\(715\) −31.7836 + 21.1062i −1.18864 + 0.789326i
\(716\) 13.4168 13.4168i 0.501408 0.501408i
\(717\) −47.8222 −1.78595
\(718\) 7.60520i 0.283824i
\(719\) 0.372987i 0.0139101i −0.999976 0.00695503i \(-0.997786\pi\)
0.999976 0.00695503i \(-0.00221387\pi\)
\(720\) −6.85883 + 4.55467i −0.255613 + 0.169743i
\(721\) −9.52619 9.52619i −0.354774 0.354774i
\(722\) 36.0022i 1.33986i
\(723\) 19.7845i 0.735794i
\(724\) −15.3711 −0.571261
\(725\) −5.43137 13.3271i −0.201716 0.494955i
\(726\) 8.84029 8.84029i 0.328094 0.328094i
\(727\) −14.7295 −0.546286 −0.273143 0.961973i \(-0.588063\pi\)
−0.273143 + 0.961973i \(0.588063\pi\)
\(728\) 14.6350 14.6350i 0.542411 0.542411i
\(729\) 37.5644i 1.39127i
\(730\) −16.5059 3.33221i −0.610910 0.123331i
\(731\) 23.1852i 0.857534i
\(732\) −20.8838 −0.771887
\(733\) 10.6225 10.6225i 0.392351 0.392351i −0.483173 0.875525i \(-0.660516\pi\)
0.875525 + 0.483173i \(0.160516\pi\)
\(734\) 10.3061 10.3061i 0.380406 0.380406i
\(735\) −18.6461 + 92.3622i −0.687772 + 3.40683i
\(736\) 2.21783 0.0817505
\(737\) 5.11490 5.11490i 0.188410 0.188410i
\(738\) 9.23331 0.339883
\(739\) 27.4110 1.00833 0.504165 0.863608i \(-0.331800\pi\)
0.504165 + 0.863608i \(0.331800\pi\)
\(740\) −11.3455 7.50194i −0.417070 0.275777i
\(741\) −82.1983 −3.01963
\(742\) −19.3914 −0.711881
\(743\) 31.6154 31.6154i 1.15986 1.15986i 0.175349 0.984506i \(-0.443895\pi\)
0.984506 0.175349i \(-0.0561053\pi\)
\(744\) 11.8347 0.433880
\(745\) −24.3859 + 16.1937i −0.893431 + 0.593291i
\(746\) −0.690871 + 0.690871i −0.0252946 + 0.0252946i
\(747\) 9.47758 9.47758i 0.346767 0.346767i
\(748\) 10.2479 0.374699
\(749\) 25.7507i 0.940910i
\(750\) −16.2616 + 23.8919i −0.593788 + 0.872408i
\(751\) 25.5768i 0.933311i 0.884439 + 0.466655i \(0.154541\pi\)
−0.884439 + 0.466655i \(0.845459\pi\)
\(752\) −0.943466 + 0.943466i −0.0344047 + 0.0344047i
\(753\) 8.58049 0.312690
\(754\) −8.72636 + 8.72636i −0.317795 + 0.317795i
\(755\) −17.4575 + 11.5928i −0.635345 + 0.421907i
\(756\) −8.51103 −0.309543
\(757\) 14.8725i 0.540552i −0.962783 0.270276i \(-0.912885\pi\)
0.962783 0.270276i \(-0.0871149\pi\)
\(758\) 0.266778i 0.00968982i
\(759\) −16.1324 16.1324i −0.585569 0.585569i
\(760\) −3.28166 + 16.2555i −0.119038 + 0.589649i
\(761\) 41.3732i 1.49978i −0.661564 0.749888i \(-0.730107\pi\)
0.661564 0.749888i \(-0.269893\pi\)
\(762\) 0.202434i 0.00733341i
\(763\) 81.4434 2.94845
\(764\) −16.9686 + 16.9686i −0.613904 + 0.613904i
\(765\) 11.7290 + 17.6626i 0.424064 + 0.638593i
\(766\) −32.6980 −1.18143
\(767\) 12.4817 + 12.4817i 0.450686 + 0.450686i
\(768\) 1.82785 1.82785i 0.0659569 0.0659569i
\(769\) 0.831140 0.831140i 0.0299717 0.0299717i −0.691962 0.721934i \(-0.743253\pi\)
0.721934 + 0.691962i \(0.243253\pi\)
\(770\) −8.50012 + 42.1048i −0.306323 + 1.51735i
\(771\) 10.6164 + 10.6164i 0.382340 + 0.382340i
\(772\) −5.70785 −0.205430
\(773\) −24.1870 24.1870i −0.869946 0.869946i 0.122520 0.992466i \(-0.460903\pi\)
−0.992466 + 0.122520i \(0.960903\pi\)
\(774\) 33.1511i 1.19159i
\(775\) 21.1984 8.63930i 0.761470 0.310333i
\(776\) 5.92246i 0.212604i
\(777\) −29.5835 69.8986i −1.06130 2.50760i
\(778\) −24.7831