Properties

Label 1110.2.l.b.697.7
Level $1110$
Weight $2$
Character 1110.697
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 697.7
Character \(\chi\) \(=\) 1110.697
Dual form 1110.2.l.b.43.7

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.325656 - 2.21223i) q^{5} +(0.707107 - 0.707107i) q^{6} +(0.597471 + 0.597471i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.325656 - 2.21223i) q^{5} +(0.707107 - 0.707107i) q^{6} +(0.597471 + 0.597471i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(2.21223 - 0.325656i) q^{10} -6.22563i q^{11} +(0.707107 + 0.707107i) q^{12} +0.986429i q^{13} +(-0.597471 + 0.597471i) q^{14} +(-1.33401 + 1.79455i) q^{15} +1.00000 q^{16} -5.73489 q^{17} -1.00000 q^{18} +(1.99420 + 1.99420i) q^{19} +(0.325656 + 2.21223i) q^{20} -0.844952i q^{21} +6.22563 q^{22} +1.91811i q^{23} +(-0.707107 + 0.707107i) q^{24} +(-4.78790 + 1.44085i) q^{25} -0.986429 q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.597471 - 0.597471i) q^{28} +(-3.12397 + 3.12397i) q^{29} +(-1.79455 - 1.33401i) q^{30} +(-0.922513 - 0.922513i) q^{31} +1.00000i q^{32} +(-4.40219 + 4.40219i) q^{33} -5.73489i q^{34} +(1.12717 - 1.51631i) q^{35} -1.00000i q^{36} +(-6.02093 - 0.865086i) q^{37} +(-1.99420 + 1.99420i) q^{38} +(0.697511 - 0.697511i) q^{39} +(-2.21223 + 0.325656i) q^{40} +1.55336i q^{41} +0.844952 q^{42} +6.23715i q^{43} +6.22563i q^{44} +(2.21223 - 0.325656i) q^{45} -1.91811 q^{46} +(-2.10291 - 2.10291i) q^{47} +(-0.707107 - 0.707107i) q^{48} -6.28606i q^{49} +(-1.44085 - 4.78790i) q^{50} +(4.05518 + 4.05518i) q^{51} -0.986429i q^{52} +(9.01816 - 9.01816i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-13.7725 + 2.02742i) q^{55} +(0.597471 - 0.597471i) q^{56} -2.82022i q^{57} +(-3.12397 - 3.12397i) q^{58} +(-5.56150 - 5.56150i) q^{59} +(1.33401 - 1.79455i) q^{60} +(-1.20352 - 1.20352i) q^{61} +(0.922513 - 0.922513i) q^{62} +(-0.597471 + 0.597471i) q^{63} -1.00000 q^{64} +(2.18221 - 0.321237i) q^{65} +(-4.40219 - 4.40219i) q^{66} +(-9.76587 + 9.76587i) q^{67} +5.73489 q^{68} +(1.35631 - 1.35631i) q^{69} +(1.51631 + 1.12717i) q^{70} -14.9453 q^{71} +1.00000 q^{72} +(-8.62767 - 8.62767i) q^{73} +(0.865086 - 6.02093i) q^{74} +(4.40439 + 2.36672i) q^{75} +(-1.99420 - 1.99420i) q^{76} +(3.71964 - 3.71964i) q^{77} +(0.697511 + 0.697511i) q^{78} +(-4.54031 - 4.54031i) q^{79} +(-0.325656 - 2.21223i) q^{80} -1.00000 q^{81} -1.55336 q^{82} +(-7.29893 + 7.29893i) q^{83} +0.844952i q^{84} +(1.86760 + 12.6869i) q^{85} -6.23715 q^{86} +4.41796 q^{87} -6.22563 q^{88} +(3.84900 - 3.84900i) q^{89} +(0.325656 + 2.21223i) q^{90} +(-0.589363 + 0.589363i) q^{91} -1.91811i q^{92} +1.30463i q^{93} +(2.10291 - 2.10291i) q^{94} +(3.76219 - 5.06103i) q^{95} +(0.707107 - 0.707107i) q^{96} +12.5351 q^{97} +6.28606 q^{98} +6.22563 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{4} - 4q^{7} + O(q^{10}) \) \( 40q - 40q^{4} - 4q^{7} + 4q^{14} + 40q^{16} + 24q^{17} - 40q^{18} + 4q^{19} + 8q^{22} + 8q^{25} + 8q^{26} + 4q^{28} + 28q^{31} - 4q^{33} + 20q^{35} + 20q^{37} - 4q^{38} + 4q^{39} + 16q^{42} - 16q^{47} + 16q^{51} + 20q^{53} + 16q^{55} - 4q^{56} - 4q^{59} - 8q^{61} - 28q^{62} + 4q^{63} - 40q^{64} - 4q^{65} - 4q^{66} + 16q^{67} - 24q^{68} - 8q^{69} + 12q^{70} + 40q^{71} + 40q^{72} + 8q^{73} - 8q^{74} + 16q^{75} - 4q^{76} - 24q^{77} + 4q^{78} - 12q^{79} - 40q^{81} - 24q^{82} - 8q^{83} - 8q^{85} + 8q^{87} - 8q^{88} + 12q^{89} - 24q^{91} + 16q^{94} - 28q^{95} + 40q^{97} - 56q^{98} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) −1.00000 −0.500000
\(5\) −0.325656 2.21223i −0.145638 0.989338i
\(6\) 0.707107 0.707107i 0.288675 0.288675i
\(7\) 0.597471 + 0.597471i 0.225823 + 0.225823i 0.810945 0.585122i \(-0.198953\pi\)
−0.585122 + 0.810945i \(0.698953\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) 2.21223 0.325656i 0.699568 0.102981i
\(11\) 6.22563i 1.87710i −0.345144 0.938550i \(-0.612170\pi\)
0.345144 0.938550i \(-0.387830\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) 0.986429i 0.273586i 0.990600 + 0.136793i \(0.0436796\pi\)
−0.990600 + 0.136793i \(0.956320\pi\)
\(14\) −0.597471 + 0.597471i −0.159681 + 0.159681i
\(15\) −1.33401 + 1.79455i −0.344439 + 0.463352i
\(16\) 1.00000 0.250000
\(17\) −5.73489 −1.39092 −0.695458 0.718567i \(-0.744798\pi\)
−0.695458 + 0.718567i \(0.744798\pi\)
\(18\) −1.00000 −0.235702
\(19\) 1.99420 + 1.99420i 0.457500 + 0.457500i 0.897834 0.440334i \(-0.145140\pi\)
−0.440334 + 0.897834i \(0.645140\pi\)
\(20\) 0.325656 + 2.21223i 0.0728189 + 0.494669i
\(21\) 0.844952i 0.184384i
\(22\) 6.22563 1.32731
\(23\) 1.91811i 0.399954i 0.979801 + 0.199977i \(0.0640868\pi\)
−0.979801 + 0.199977i \(0.935913\pi\)
\(24\) −0.707107 + 0.707107i −0.144338 + 0.144338i
\(25\) −4.78790 + 1.44085i −0.957579 + 0.288170i
\(26\) −0.986429 −0.193455
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) −0.597471 0.597471i −0.112911 0.112911i
\(29\) −3.12397 + 3.12397i −0.580107 + 0.580107i −0.934932 0.354826i \(-0.884540\pi\)
0.354826 + 0.934932i \(0.384540\pi\)
\(30\) −1.79455 1.33401i −0.327639 0.243555i
\(31\) −0.922513 0.922513i −0.165688 0.165688i 0.619393 0.785081i \(-0.287379\pi\)
−0.785081 + 0.619393i \(0.787379\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −4.40219 + 4.40219i −0.766323 + 0.766323i
\(34\) 5.73489i 0.983526i
\(35\) 1.12717 1.51631i 0.190527 0.256303i
\(36\) 1.00000i 0.166667i
\(37\) −6.02093 0.865086i −0.989835 0.142219i
\(38\) −1.99420 + 1.99420i −0.323501 + 0.323501i
\(39\) 0.697511 0.697511i 0.111691 0.111691i
\(40\) −2.21223 + 0.325656i −0.349784 + 0.0514907i
\(41\) 1.55336i 0.242594i 0.992616 + 0.121297i \(0.0387053\pi\)
−0.992616 + 0.121297i \(0.961295\pi\)
\(42\) 0.844952 0.130379
\(43\) 6.23715i 0.951157i 0.879673 + 0.475578i \(0.157761\pi\)
−0.879673 + 0.475578i \(0.842239\pi\)
\(44\) 6.22563i 0.938550i
\(45\) 2.21223 0.325656i 0.329779 0.0485459i
\(46\) −1.91811 −0.282810
\(47\) −2.10291 2.10291i −0.306741 0.306741i 0.536903 0.843644i \(-0.319594\pi\)
−0.843644 + 0.536903i \(0.819594\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) 6.28606i 0.898008i
\(50\) −1.44085 4.78790i −0.203767 0.677111i
\(51\) 4.05518 + 4.05518i 0.567839 + 0.567839i
\(52\) 0.986429i 0.136793i
\(53\) 9.01816 9.01816i 1.23874 1.23874i 0.278223 0.960516i \(-0.410255\pi\)
0.960516 0.278223i \(-0.0897454\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) −13.7725 + 2.02742i −1.85709 + 0.273377i
\(56\) 0.597471 0.597471i 0.0798404 0.0798404i
\(57\) 2.82022i 0.373547i
\(58\) −3.12397 3.12397i −0.410197 0.410197i
\(59\) −5.56150 5.56150i −0.724046 0.724046i 0.245381 0.969427i \(-0.421087\pi\)
−0.969427 + 0.245381i \(0.921087\pi\)
\(60\) 1.33401 1.79455i 0.172220 0.231676i
\(61\) −1.20352 1.20352i −0.154096 0.154096i 0.625849 0.779944i \(-0.284753\pi\)
−0.779944 + 0.625849i \(0.784753\pi\)
\(62\) 0.922513 0.922513i 0.117159 0.117159i
\(63\) −0.597471 + 0.597471i −0.0752743 + 0.0752743i
\(64\) −1.00000 −0.125000
\(65\) 2.18221 0.321237i 0.270669 0.0398445i
\(66\) −4.40219 4.40219i −0.541872 0.541872i
\(67\) −9.76587 + 9.76587i −1.19309 + 1.19309i −0.216896 + 0.976195i \(0.569593\pi\)
−0.976195 + 0.216896i \(0.930407\pi\)
\(68\) 5.73489 0.695458
\(69\) 1.35631 1.35631i 0.163281 0.163281i
\(70\) 1.51631 + 1.12717i 0.181234 + 0.134723i
\(71\) −14.9453 −1.77368 −0.886842 0.462073i \(-0.847106\pi\)
−0.886842 + 0.462073i \(0.847106\pi\)
\(72\) 1.00000 0.117851
\(73\) −8.62767 8.62767i −1.00979 1.00979i −0.999952 0.00984027i \(-0.996868\pi\)
−0.00984027 0.999952i \(-0.503132\pi\)
\(74\) 0.865086 6.02093i 0.100564 0.699919i
\(75\) 4.40439 + 2.36672i 0.508575 + 0.273285i
\(76\) −1.99420 1.99420i −0.228750 0.228750i
\(77\) 3.71964 3.71964i 0.423892 0.423892i
\(78\) 0.697511 + 0.697511i 0.0789776 + 0.0789776i
\(79\) −4.54031 4.54031i −0.510825 0.510825i 0.403954 0.914779i \(-0.367635\pi\)
−0.914779 + 0.403954i \(0.867635\pi\)
\(80\) −0.325656 2.21223i −0.0364095 0.247334i
\(81\) −1.00000 −0.111111
\(82\) −1.55336 −0.171540
\(83\) −7.29893 + 7.29893i −0.801161 + 0.801161i −0.983277 0.182116i \(-0.941705\pi\)
0.182116 + 0.983277i \(0.441705\pi\)
\(84\) 0.844952i 0.0921918i
\(85\) 1.86760 + 12.6869i 0.202570 + 1.37609i
\(86\) −6.23715 −0.672569
\(87\) 4.41796 0.473655
\(88\) −6.22563 −0.663655
\(89\) 3.84900 3.84900i 0.407994 0.407994i −0.473045 0.881038i \(-0.656845\pi\)
0.881038 + 0.473045i \(0.156845\pi\)
\(90\) 0.325656 + 2.21223i 0.0343272 + 0.233189i
\(91\) −0.589363 + 0.589363i −0.0617820 + 0.0617820i
\(92\) 1.91811i 0.199977i
\(93\) 1.30463i 0.135284i
\(94\) 2.10291 2.10291i 0.216899 0.216899i
\(95\) 3.76219 5.06103i 0.385993 0.519251i
\(96\) 0.707107 0.707107i 0.0721688 0.0721688i
\(97\) 12.5351 1.27275 0.636374 0.771380i \(-0.280433\pi\)
0.636374 + 0.771380i \(0.280433\pi\)
\(98\) 6.28606 0.634988
\(99\) 6.22563 0.625700
\(100\) 4.78790 1.44085i 0.478790 0.144085i
\(101\) 9.83775i 0.978893i −0.872033 0.489447i \(-0.837199\pi\)
0.872033 0.489447i \(-0.162801\pi\)
\(102\) −4.05518 + 4.05518i −0.401523 + 0.401523i
\(103\) −11.7463 −1.15740 −0.578700 0.815540i \(-0.696440\pi\)
−0.578700 + 0.815540i \(0.696440\pi\)
\(104\) 0.986429 0.0967274
\(105\) −1.86922 + 0.275164i −0.182418 + 0.0268532i
\(106\) 9.01816 + 9.01816i 0.875921 + 0.875921i
\(107\) −0.373231 0.373231i −0.0360816 0.0360816i 0.688836 0.724917i \(-0.258122\pi\)
−0.724917 + 0.688836i \(0.758122\pi\)
\(108\) −0.707107 + 0.707107i −0.0680414 + 0.0680414i
\(109\) 7.16221 + 7.16221i 0.686015 + 0.686015i 0.961349 0.275333i \(-0.0887882\pi\)
−0.275333 + 0.961349i \(0.588788\pi\)
\(110\) −2.02742 13.7725i −0.193306 1.31316i
\(111\) 3.64573 + 4.86915i 0.346038 + 0.462159i
\(112\) 0.597471 + 0.597471i 0.0564557 + 0.0564557i
\(113\) 8.61878 0.810787 0.405393 0.914142i \(-0.367135\pi\)
0.405393 + 0.914142i \(0.367135\pi\)
\(114\) 2.82022 0.264138
\(115\) 4.24330 0.624645i 0.395690 0.0582485i
\(116\) 3.12397 3.12397i 0.290053 0.290053i
\(117\) −0.986429 −0.0911954
\(118\) 5.56150 5.56150i 0.511978 0.511978i
\(119\) −3.42643 3.42643i −0.314101 0.314101i
\(120\) 1.79455 + 1.33401i 0.163820 + 0.121778i
\(121\) −27.7585 −2.52350
\(122\) 1.20352 1.20352i 0.108962 0.108962i
\(123\) 1.09839 1.09839i 0.0990384 0.0990384i
\(124\) 0.922513 + 0.922513i 0.0828441 + 0.0828441i
\(125\) 4.74670 + 10.1227i 0.424557 + 0.905401i
\(126\) −0.597471 0.597471i −0.0532269 0.0532269i
\(127\) 6.23989 + 6.23989i 0.553701 + 0.553701i 0.927507 0.373806i \(-0.121947\pi\)
−0.373806 + 0.927507i \(0.621947\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 4.41033 4.41033i 0.388308 0.388308i
\(130\) 0.321237 + 2.18221i 0.0281743 + 0.191392i
\(131\) 13.4413 + 13.4413i 1.17437 + 1.17437i 0.981156 + 0.193215i \(0.0618915\pi\)
0.193215 + 0.981156i \(0.438109\pi\)
\(132\) 4.40219 4.40219i 0.383161 0.383161i
\(133\) 2.38295i 0.206628i
\(134\) −9.76587 9.76587i −0.843642 0.843642i
\(135\) −1.79455 1.33401i −0.154451 0.114813i
\(136\) 5.73489i 0.491763i
\(137\) −2.43423 2.43423i −0.207970 0.207970i 0.595434 0.803404i \(-0.296980\pi\)
−0.803404 + 0.595434i \(0.796980\pi\)
\(138\) 1.35631 + 1.35631i 0.115457 + 0.115457i
\(139\) −0.295024 −0.0250236 −0.0125118 0.999922i \(-0.503983\pi\)
−0.0125118 + 0.999922i \(0.503983\pi\)
\(140\) −1.12717 + 1.51631i −0.0952634 + 0.128152i
\(141\) 2.97397i 0.250453i
\(142\) 14.9453i 1.25418i
\(143\) 6.14115 0.513549
\(144\) 1.00000i 0.0833333i
\(145\) 7.92827 + 5.89359i 0.658407 + 0.489436i
\(146\) 8.62767 8.62767i 0.714031 0.714031i
\(147\) −4.44491 + 4.44491i −0.366610 + 0.366610i
\(148\) 6.02093 + 0.865086i 0.494918 + 0.0711096i
\(149\) 21.7666i 1.78319i −0.452834 0.891595i \(-0.649587\pi\)
0.452834 0.891595i \(-0.350413\pi\)
\(150\) −2.36672 + 4.40439i −0.193242 + 0.359617i
\(151\) 15.4134i 1.25432i −0.778888 0.627162i \(-0.784216\pi\)
0.778888 0.627162i \(-0.215784\pi\)
\(152\) 1.99420 1.99420i 0.161751 0.161751i
\(153\) 5.73489i 0.463639i
\(154\) 3.71964 + 3.71964i 0.299737 + 0.299737i
\(155\) −1.74039 + 2.34123i −0.139791 + 0.188052i
\(156\) −0.697511 + 0.697511i −0.0558456 + 0.0558456i
\(157\) −2.42992 2.42992i −0.193928 0.193928i 0.603463 0.797391i \(-0.293787\pi\)
−0.797391 + 0.603463i \(0.793787\pi\)
\(158\) 4.54031 4.54031i 0.361208 0.361208i
\(159\) −12.7536 −1.01143
\(160\) 2.21223 0.325656i 0.174892 0.0257454i
\(161\) −1.14602 + 1.14602i −0.0903188 + 0.0903188i
\(162\) 1.00000i 0.0785674i
\(163\) 23.0110 1.80236 0.901180 0.433445i \(-0.142702\pi\)
0.901180 + 0.433445i \(0.142702\pi\)
\(164\) 1.55336i 0.121297i
\(165\) 11.1722 + 8.30504i 0.869758 + 0.646546i
\(166\) −7.29893 7.29893i −0.566507 0.566507i
\(167\) 0.763298 0.0590657 0.0295329 0.999564i \(-0.490598\pi\)
0.0295329 + 0.999564i \(0.490598\pi\)
\(168\) −0.844952 −0.0651894
\(169\) 12.0270 0.925151
\(170\) −12.6869 + 1.86760i −0.973040 + 0.143239i
\(171\) −1.99420 + 1.99420i −0.152500 + 0.152500i
\(172\) 6.23715i 0.475578i
\(173\) 7.46496 + 7.46496i 0.567550 + 0.567550i 0.931441 0.363891i \(-0.118552\pi\)
−0.363891 + 0.931441i \(0.618552\pi\)
\(174\) 4.41796i 0.334925i
\(175\) −3.72150 1.99976i −0.281319 0.151168i
\(176\) 6.22563i 0.469275i
\(177\) 7.86515i 0.591181i
\(178\) 3.84900 + 3.84900i 0.288495 + 0.288495i
\(179\) 5.31685 5.31685i 0.397400 0.397400i −0.479915 0.877315i \(-0.659333\pi\)
0.877315 + 0.479915i \(0.159333\pi\)
\(180\) −2.21223 + 0.325656i −0.164890 + 0.0242730i
\(181\) −12.3877 −0.920770 −0.460385 0.887719i \(-0.652289\pi\)
−0.460385 + 0.887719i \(0.652289\pi\)
\(182\) −0.589363 0.589363i −0.0436865 0.0436865i
\(183\) 1.70204i 0.125819i
\(184\) 1.91811 0.141405
\(185\) 0.0469870 + 13.6014i 0.00345455 + 0.999994i
\(186\) −1.30463 −0.0956601
\(187\) 35.7033i 2.61089i
\(188\) 2.10291 + 2.10291i 0.153371 + 0.153371i
\(189\) 0.844952 0.0614612
\(190\) 5.06103 + 3.76219i 0.367166 + 0.272938i
\(191\) −3.82822 + 3.82822i −0.277000 + 0.277000i −0.831910 0.554910i \(-0.812753\pi\)
0.554910 + 0.831910i \(0.312753\pi\)
\(192\) 0.707107 + 0.707107i 0.0510310 + 0.0510310i
\(193\) 5.48394i 0.394743i 0.980329 + 0.197371i \(0.0632405\pi\)
−0.980329 + 0.197371i \(0.936760\pi\)
\(194\) 12.5351i 0.899969i
\(195\) −1.77020 1.31590i −0.126767 0.0942338i
\(196\) 6.28606i 0.449004i
\(197\) 3.31072 + 3.31072i 0.235879 + 0.235879i 0.815141 0.579262i \(-0.196659\pi\)
−0.579262 + 0.815141i \(0.696659\pi\)
\(198\) 6.22563i 0.442437i
\(199\) 6.97405 6.97405i 0.494377 0.494377i −0.415305 0.909682i \(-0.636325\pi\)
0.909682 + 0.415305i \(0.136325\pi\)
\(200\) 1.44085 + 4.78790i 0.101884 + 0.338555i
\(201\) 13.8110 0.974154
\(202\) 9.83775 0.692182
\(203\) −3.73296 −0.262003
\(204\) −4.05518 4.05518i −0.283919 0.283919i
\(205\) 3.43638 0.505860i 0.240007 0.0353308i
\(206\) 11.7463i 0.818406i
\(207\) −1.91811 −0.133318
\(208\) 0.986429i 0.0683966i
\(209\) 12.4151 12.4151i 0.858773 0.858773i
\(210\) −0.275164 1.86922i −0.0189881 0.128989i
\(211\) −4.37831 −0.301415 −0.150708 0.988578i \(-0.548155\pi\)
−0.150708 + 0.988578i \(0.548155\pi\)
\(212\) −9.01816 + 9.01816i −0.619370 + 0.619370i
\(213\) 10.5679 + 10.5679i 0.724103 + 0.724103i
\(214\) 0.373231 0.373231i 0.0255136 0.0255136i
\(215\) 13.7980 2.03117i 0.941015 0.138524i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) 1.10235i 0.0748323i
\(218\) −7.16221 + 7.16221i −0.485086 + 0.485086i
\(219\) 12.2014i 0.824492i
\(220\) 13.7725 2.02742i 0.928543 0.136688i
\(221\) 5.65707i 0.380535i
\(222\) −4.86915 + 3.64573i −0.326796 + 0.244686i
\(223\) −19.9346 + 19.9346i −1.33492 + 1.33492i −0.434010 + 0.900908i \(0.642902\pi\)
−0.900908 + 0.434010i \(0.857098\pi\)
\(224\) −0.597471 + 0.597471i −0.0399202 + 0.0399202i
\(225\) −1.44085 4.78790i −0.0960567 0.319193i
\(226\) 8.61878i 0.573313i
\(227\) −14.0813 −0.934611 −0.467306 0.884096i \(-0.654775\pi\)
−0.467306 + 0.884096i \(0.654775\pi\)
\(228\) 2.82022i 0.186774i
\(229\) 15.5420i 1.02704i 0.858076 + 0.513522i \(0.171660\pi\)
−0.858076 + 0.513522i \(0.828340\pi\)
\(230\) 0.624645 + 4.24330i 0.0411879 + 0.279795i
\(231\) −5.26036 −0.346106
\(232\) 3.12397 + 3.12397i 0.205099 + 0.205099i
\(233\) 7.25032 + 7.25032i 0.474985 + 0.474985i 0.903523 0.428539i \(-0.140971\pi\)
−0.428539 + 0.903523i \(0.640971\pi\)
\(234\) 0.986429i 0.0644849i
\(235\) −3.96729 + 5.33694i −0.258798 + 0.348144i
\(236\) 5.56150 + 5.56150i 0.362023 + 0.362023i
\(237\) 6.42097i 0.417087i
\(238\) 3.42643 3.42643i 0.222103 0.222103i
\(239\) −12.8280 12.8280i −0.829777 0.829777i 0.157709 0.987486i \(-0.449589\pi\)
−0.987486 + 0.157709i \(0.949589\pi\)
\(240\) −1.33401 + 1.79455i −0.0861098 + 0.115838i
\(241\) 9.19108 9.19108i 0.592050 0.592050i −0.346135 0.938185i \(-0.612506\pi\)
0.938185 + 0.346135i \(0.112506\pi\)
\(242\) 27.7585i 1.78438i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 1.20352 + 1.20352i 0.0770478 + 0.0770478i
\(245\) −13.9062 + 2.04709i −0.888434 + 0.130784i
\(246\) 1.09839 + 1.09839i 0.0700307 + 0.0700307i
\(247\) −1.96713 + 1.96713i −0.125166 + 0.125166i
\(248\) −0.922513 + 0.922513i −0.0585796 + 0.0585796i
\(249\) 10.3222 0.654146
\(250\) −10.1227 + 4.74670i −0.640215 + 0.300207i
\(251\) −3.26175 3.26175i −0.205880 0.205880i 0.596634 0.802514i \(-0.296504\pi\)
−0.802514 + 0.596634i \(0.796504\pi\)
\(252\) 0.597471 0.597471i 0.0376371 0.0376371i
\(253\) 11.9415 0.750754
\(254\) −6.23989 + 6.23989i −0.391526 + 0.391526i
\(255\) 7.65039 10.2916i 0.479086 0.644484i
\(256\) 1.00000 0.0625000
\(257\) −12.9116 −0.805400 −0.402700 0.915332i \(-0.631928\pi\)
−0.402700 + 0.915332i \(0.631928\pi\)
\(258\) 4.41033 + 4.41033i 0.274575 + 0.274575i
\(259\) −3.08047 4.11420i −0.191411 0.255644i
\(260\) −2.18221 + 0.321237i −0.135335 + 0.0199223i
\(261\) −3.12397 3.12397i −0.193369 0.193369i
\(262\) −13.4413 + 13.4413i −0.830406 + 0.830406i
\(263\) 7.64722 + 7.64722i 0.471548 + 0.471548i 0.902415 0.430868i \(-0.141792\pi\)
−0.430868 + 0.902415i \(0.641792\pi\)
\(264\) 4.40219 + 4.40219i 0.270936 + 0.270936i
\(265\) −22.8870 17.0134i −1.40594 1.04512i
\(266\) −2.38295 −0.146108
\(267\) −5.44331 −0.333125
\(268\) 9.76587 9.76587i 0.596545 0.596545i
\(269\) 22.1242i 1.34893i −0.738305 0.674467i \(-0.764373\pi\)
0.738305 0.674467i \(-0.235627\pi\)
\(270\) 1.33401 1.79455i 0.0811851 0.109213i
\(271\) 1.96662 0.119464 0.0597319 0.998214i \(-0.480975\pi\)
0.0597319 + 0.998214i \(0.480975\pi\)
\(272\) −5.73489 −0.347729
\(273\) 0.833485 0.0504448
\(274\) 2.43423 2.43423i 0.147057 0.147057i
\(275\) 8.97021 + 29.8077i 0.540924 + 1.79747i
\(276\) −1.35631 + 1.35631i −0.0816403 + 0.0816403i
\(277\) 10.4985i 0.630796i 0.948959 + 0.315398i \(0.102138\pi\)
−0.948959 + 0.315398i \(0.897862\pi\)
\(278\) 0.295024i 0.0176944i
\(279\) 0.922513 0.922513i 0.0552294 0.0552294i
\(280\) −1.51631 1.12717i −0.0906169 0.0673614i
\(281\) 13.8482 13.8482i 0.826114 0.826114i −0.160863 0.986977i \(-0.551428\pi\)
0.986977 + 0.160863i \(0.0514276\pi\)
\(282\) −2.97397 −0.177097
\(283\) −16.7535 −0.995893 −0.497947 0.867208i \(-0.665912\pi\)
−0.497947 + 0.867208i \(0.665912\pi\)
\(284\) 14.9453 0.886842
\(285\) −6.23896 + 0.918421i −0.369564 + 0.0544026i
\(286\) 6.14115i 0.363134i
\(287\) −0.928086 + 0.928086i −0.0547832 + 0.0547832i
\(288\) −1.00000 −0.0589256
\(289\) 15.8890 0.934647
\(290\) −5.89359 + 7.92827i −0.346083 + 0.465564i
\(291\) −8.86367 8.86367i −0.519597 0.519597i
\(292\) 8.62767 + 8.62767i 0.504896 + 0.504896i
\(293\) 3.05021 3.05021i 0.178195 0.178195i −0.612373 0.790569i \(-0.709785\pi\)
0.790569 + 0.612373i \(0.209785\pi\)
\(294\) −4.44491 4.44491i −0.259233 0.259233i
\(295\) −10.4922 + 14.1144i −0.610878 + 0.821774i
\(296\) −0.865086 + 6.02093i −0.0502821 + 0.349960i
\(297\) −4.40219 4.40219i −0.255441 0.255441i
\(298\) 21.7666 1.26091
\(299\) −1.89208 −0.109422
\(300\) −4.40439 2.36672i −0.254288 0.136643i
\(301\) −3.72652 + 3.72652i −0.214793 + 0.214793i
\(302\) 15.4134 0.886942
\(303\) −6.95634 + 6.95634i −0.399631 + 0.399631i
\(304\) 1.99420 + 1.99420i 0.114375 + 0.114375i
\(305\) −2.27054 + 3.05441i −0.130010 + 0.174895i
\(306\) 5.73489 0.327842
\(307\) 23.3606 23.3606i 1.33326 1.33326i 0.430819 0.902438i \(-0.358225\pi\)
0.902438 0.430819i \(-0.141775\pi\)
\(308\) −3.71964 + 3.71964i −0.211946 + 0.211946i
\(309\) 8.30591 + 8.30591i 0.472507 + 0.472507i
\(310\) −2.34123 1.74039i −0.132973 0.0988473i
\(311\) −18.5458 18.5458i −1.05163 1.05163i −0.998592 0.0530421i \(-0.983108\pi\)
−0.0530421 0.998592i \(-0.516892\pi\)
\(312\) −0.697511 0.697511i −0.0394888 0.0394888i
\(313\) 33.3726i 1.88633i −0.332320 0.943167i \(-0.607831\pi\)
0.332320 0.943167i \(-0.392169\pi\)
\(314\) 2.42992 2.42992i 0.137128 0.137128i
\(315\) 1.51631 + 1.12717i 0.0854345 + 0.0635089i
\(316\) 4.54031 + 4.54031i 0.255412 + 0.255412i
\(317\) 18.7269 18.7269i 1.05181 1.05181i 0.0532273 0.998582i \(-0.483049\pi\)
0.998582 0.0532273i \(-0.0169508\pi\)
\(318\) 12.7536i 0.715187i
\(319\) 19.4487 + 19.4487i 1.08892 + 1.08892i
\(320\) 0.325656 + 2.21223i 0.0182047 + 0.123667i
\(321\) 0.527829i 0.0294605i
\(322\) −1.14602 1.14602i −0.0638650 0.0638650i
\(323\) −11.4365 11.4365i −0.636344 0.636344i
\(324\) 1.00000 0.0555556
\(325\) −1.42130 4.72292i −0.0788394 0.261981i
\(326\) 23.0110i 1.27446i
\(327\) 10.1289i 0.560129i
\(328\) 1.55336 0.0857698
\(329\) 2.51286i 0.138538i
\(330\) −8.30504 + 11.1722i −0.457177 + 0.615011i
\(331\) 20.7521 20.7521i 1.14064 1.14064i 0.152304 0.988334i \(-0.451331\pi\)
0.988334 0.152304i \(-0.0486692\pi\)
\(332\) 7.29893 7.29893i 0.400581 0.400581i
\(333\) 0.865086 6.02093i 0.0474064 0.329945i
\(334\) 0.763298i 0.0417658i
\(335\) 24.7846 + 18.4240i 1.35413 + 1.00661i
\(336\) 0.844952i 0.0460959i
\(337\) −14.7056 + 14.7056i −0.801067 + 0.801067i −0.983262 0.182196i \(-0.941680\pi\)
0.182196 + 0.983262i \(0.441680\pi\)
\(338\) 12.0270i 0.654180i
\(339\) −6.09440 6.09440i −0.331002 0.331002i
\(340\) −1.86760 12.6869i −0.101285 0.688043i
\(341\) −5.74323 + 5.74323i −0.311013 + 0.311013i
\(342\) −1.99420 1.99420i −0.107834 0.107834i
\(343\) 7.93803 7.93803i 0.428614 0.428614i
\(344\) 6.23715 0.336285
\(345\) −3.44216 2.55878i −0.185320 0.137760i
\(346\) −7.46496 + 7.46496i −0.401319 + 0.401319i
\(347\) 17.2146i 0.924127i 0.886847 + 0.462063i \(0.152891\pi\)
−0.886847 + 0.462063i \(0.847109\pi\)
\(348\) −4.41796 −0.236827
\(349\) 28.4058i 1.52053i 0.649616 + 0.760263i \(0.274930\pi\)
−0.649616 + 0.760263i \(0.725070\pi\)
\(350\) 1.99976 3.72150i 0.106892 0.198922i
\(351\) 0.697511 + 0.697511i 0.0372304 + 0.0372304i
\(352\) 6.22563 0.331827
\(353\) −12.3989 −0.659929 −0.329965 0.943993i \(-0.607037\pi\)
−0.329965 + 0.943993i \(0.607037\pi\)
\(354\) −7.86515 −0.418028
\(355\) 4.86703 + 33.0624i 0.258315 + 1.75477i
\(356\) −3.84900 + 3.84900i −0.203997 + 0.203997i
\(357\) 4.84571i 0.256462i
\(358\) 5.31685 + 5.31685i 0.281004 + 0.281004i
\(359\) 6.27293i 0.331072i −0.986204 0.165536i \(-0.947065\pi\)
0.986204 0.165536i \(-0.0529355\pi\)
\(360\) −0.325656 2.21223i −0.0171636 0.116595i
\(361\) 11.0464i 0.581388i
\(362\) 12.3877i 0.651082i
\(363\) 19.6282 + 19.6282i 1.03022 + 1.03022i
\(364\) 0.589363 0.589363i 0.0308910 0.0308910i
\(365\) −16.2767 + 21.8960i −0.851962 + 1.14609i
\(366\) −1.70204 −0.0889671
\(367\) −0.228414 0.228414i −0.0119231 0.0119231i 0.701120 0.713043i \(-0.252684\pi\)
−0.713043 + 0.701120i \(0.752684\pi\)
\(368\) 1.91811i 0.0999886i
\(369\) −1.55336 −0.0808645
\(370\) −13.6014 + 0.0469870i −0.707103 + 0.00244274i
\(371\) 10.7762 0.559471
\(372\) 1.30463i 0.0676419i
\(373\) −13.8845 13.8845i −0.718910 0.718910i 0.249472 0.968382i \(-0.419743\pi\)
−0.968382 + 0.249472i \(0.919743\pi\)
\(374\) −35.7033 −1.84618
\(375\) 3.80140 10.5142i 0.196304 0.542953i
\(376\) −2.10291 + 2.10291i −0.108449 + 0.108449i
\(377\) −3.08158 3.08158i −0.158709 0.158709i
\(378\) 0.844952i 0.0434596i
\(379\) 0.247309i 0.0127034i −0.999980 0.00635171i \(-0.997978\pi\)
0.999980 0.00635171i \(-0.00202183\pi\)
\(380\) −3.76219 + 5.06103i −0.192996 + 0.259626i
\(381\) 8.82454i 0.452095i
\(382\) −3.82822 3.82822i −0.195869 0.195869i
\(383\) 7.97917i 0.407716i 0.979000 + 0.203858i \(0.0653481\pi\)
−0.979000 + 0.203858i \(0.934652\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) −9.44000 7.01736i −0.481107 0.357638i
\(386\) −5.48394 −0.279125
\(387\) −6.23715 −0.317052
\(388\) −12.5351 −0.636374
\(389\) −0.310092 0.310092i −0.0157223 0.0157223i 0.699202 0.714924i \(-0.253539\pi\)
−0.714924 + 0.699202i \(0.753539\pi\)
\(390\) 1.31590 1.77020i 0.0666334 0.0896376i
\(391\) 11.0002i 0.556303i
\(392\) −6.28606 −0.317494
\(393\) 19.0089i 0.958870i
\(394\) −3.31072 + 3.31072i −0.166791 + 0.166791i
\(395\) −8.56561 + 11.5228i −0.430983 + 0.579774i
\(396\) −6.22563 −0.312850
\(397\) 18.6543 18.6543i 0.936233 0.936233i −0.0618525 0.998085i \(-0.519701\pi\)
0.998085 + 0.0618525i \(0.0197008\pi\)
\(398\) 6.97405 + 6.97405i 0.349578 + 0.349578i
\(399\) 1.68500 1.68500i 0.0843554 0.0843554i
\(400\) −4.78790 + 1.44085i −0.239395 + 0.0720425i
\(401\) −21.5690 21.5690i −1.07710 1.07710i −0.996768 0.0803350i \(-0.974401\pi\)
−0.0803350 0.996768i \(-0.525599\pi\)
\(402\) 13.8110i 0.688831i
\(403\) 0.909994 0.909994i 0.0453300 0.0453300i
\(404\) 9.83775i 0.489447i
\(405\) 0.325656 + 2.21223i 0.0161820 + 0.109926i
\(406\) 3.73296i 0.185264i
\(407\) −5.38571 + 37.4841i −0.266960 + 1.85802i
\(408\) 4.05518 4.05518i 0.200761 0.200761i
\(409\) 22.0875 22.0875i 1.09216 1.09216i 0.0968567 0.995298i \(-0.469121\pi\)
0.995298 0.0968567i \(-0.0308789\pi\)
\(410\) 0.505860 + 3.43638i 0.0249826 + 0.169711i
\(411\) 3.44252i 0.169807i
\(412\) 11.7463 0.578700
\(413\) 6.64567i 0.327012i
\(414\) 1.91811i 0.0942701i
\(415\) 18.5238 + 13.7699i 0.909299 + 0.675940i
\(416\) −0.986429 −0.0483637
\(417\) 0.208614 + 0.208614i 0.0102159 + 0.0102159i
\(418\) 12.4151 + 12.4151i 0.607244 + 0.607244i
\(419\) 13.1035i 0.640150i 0.947392 + 0.320075i \(0.103708\pi\)
−0.947392 + 0.320075i \(0.896292\pi\)
\(420\) 1.86922 0.275164i 0.0912088 0.0134266i
\(421\) 6.69042 + 6.69042i 0.326071 + 0.326071i 0.851090 0.525019i \(-0.175942\pi\)
−0.525019 + 0.851090i \(0.675942\pi\)
\(422\) 4.37831i 0.213133i
\(423\) 2.10291 2.10291i 0.102247 0.102247i
\(424\) −9.01816 9.01816i −0.437961 0.437961i
\(425\) 27.4581 8.26312i 1.33191 0.400820i
\(426\) −10.5679 + 10.5679i −0.512018 + 0.512018i
\(427\) 1.43814i 0.0695966i
\(428\) 0.373231 + 0.373231i 0.0180408 + 0.0180408i
\(429\) −4.34245 4.34245i −0.209655 0.209655i
\(430\) 2.03117 + 13.7980i 0.0979515 + 0.665398i
\(431\) 7.79285 + 7.79285i 0.375369 + 0.375369i 0.869428 0.494059i \(-0.164488\pi\)
−0.494059 + 0.869428i \(0.664488\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) −1.28687 + 1.28687i −0.0618431 + 0.0618431i −0.737352 0.675509i \(-0.763924\pi\)
0.675509 + 0.737352i \(0.263924\pi\)
\(434\) 1.10235 0.0529145
\(435\) −1.43874 9.77353i −0.0689821 0.468605i
\(436\) −7.16221 7.16221i −0.343008 0.343008i
\(437\) −3.82509 + 3.82509i −0.182979 + 0.182979i
\(438\) −12.2014 −0.583004
\(439\) 5.61954 5.61954i 0.268206 0.268206i −0.560171 0.828377i \(-0.689265\pi\)
0.828377 + 0.560171i \(0.189265\pi\)
\(440\) 2.02742 + 13.7725i 0.0966532 + 0.656579i
\(441\) 6.28606 0.299336
\(442\) 5.65707 0.269079
\(443\) 14.2078 + 14.2078i 0.675034 + 0.675034i 0.958872 0.283838i \(-0.0916079\pi\)
−0.283838 + 0.958872i \(0.591608\pi\)
\(444\) −3.64573 4.86915i −0.173019 0.231080i
\(445\) −9.76832 7.26142i −0.463063 0.344224i
\(446\) −19.9346 19.9346i −0.943930 0.943930i
\(447\) −15.3913 + 15.3913i −0.727984 + 0.727984i
\(448\) −0.597471 0.597471i −0.0282279 0.0282279i
\(449\) −5.85112 5.85112i −0.276132 0.276132i 0.555431 0.831563i \(-0.312553\pi\)
−0.831563 + 0.555431i \(0.812553\pi\)
\(450\) 4.78790 1.44085i 0.225704 0.0679223i
\(451\) 9.67063 0.455372
\(452\) −8.61878 −0.405393
\(453\) −10.8989 + 10.8989i −0.512076 + 0.512076i
\(454\) 14.0813i 0.660870i
\(455\) 1.49573 + 1.11188i 0.0701211 + 0.0521255i
\(456\) −2.82022 −0.132069
\(457\) −0.0348084 −0.00162827 −0.000814134 1.00000i \(-0.500259\pi\)
−0.000814134 1.00000i \(0.500259\pi\)
\(458\) −15.5420 −0.726230
\(459\) −4.05518 + 4.05518i −0.189280 + 0.189280i
\(460\) −4.24330 + 0.624645i −0.197845 + 0.0291242i
\(461\) −0.163914 + 0.163914i −0.00763424 + 0.00763424i −0.710914 0.703279i \(-0.751718\pi\)
0.703279 + 0.710914i \(0.251718\pi\)
\(462\) 5.26036i 0.244734i
\(463\) 24.0434i 1.11739i −0.829373 0.558695i \(-0.811302\pi\)
0.829373 0.558695i \(-0.188698\pi\)
\(464\) −3.12397 + 3.12397i −0.145027 + 0.145027i
\(465\) 2.88614 0.424861i 0.133841 0.0197024i
\(466\) −7.25032 + 7.25032i −0.335865 + 0.335865i
\(467\) −1.37090 −0.0634376 −0.0317188 0.999497i \(-0.510098\pi\)
−0.0317188 + 0.999497i \(0.510098\pi\)
\(468\) 0.986429 0.0455977
\(469\) −11.6696 −0.538854
\(470\) −5.33694 3.96729i −0.246175 0.182998i
\(471\) 3.43642i 0.158342i
\(472\) −5.56150 + 5.56150i −0.255989 + 0.255989i
\(473\) 38.8302 1.78542
\(474\) −6.42097 −0.294925
\(475\) −12.4213 6.67466i −0.569930 0.306255i
\(476\) 3.42643 + 3.42643i 0.157050 + 0.157050i
\(477\) 9.01816 + 9.01816i 0.412913 + 0.412913i
\(478\) 12.8280 12.8280i 0.586741 0.586741i
\(479\) 18.7408 + 18.7408i 0.856290 + 0.856290i 0.990899 0.134609i \(-0.0429779\pi\)
−0.134609 + 0.990899i \(0.542978\pi\)
\(480\) −1.79455 1.33401i −0.0819098 0.0608888i
\(481\) 0.853346 5.93922i 0.0389092 0.270805i
\(482\) 9.19108 + 9.19108i 0.418642 + 0.418642i
\(483\) 1.62071 0.0737450
\(484\) 27.7585 1.26175
\(485\) −4.08214 27.7305i −0.185360 1.25918i
\(486\) −0.707107 + 0.707107i −0.0320750 + 0.0320750i
\(487\) 23.7276 1.07520 0.537599 0.843201i \(-0.319331\pi\)
0.537599 + 0.843201i \(0.319331\pi\)
\(488\) −1.20352 + 1.20352i −0.0544810 + 0.0544810i
\(489\) −16.2712 16.2712i −0.735810 0.735810i
\(490\) −2.04709 13.9062i −0.0924782 0.628217i
\(491\) −2.30518 −0.104031 −0.0520156 0.998646i \(-0.516565\pi\)
−0.0520156 + 0.998646i \(0.516565\pi\)
\(492\) −1.09839 + 1.09839i −0.0495192 + 0.0495192i
\(493\) 17.9156 17.9156i 0.806879 0.806879i
\(494\) −1.96713 1.96713i −0.0885055 0.0885055i
\(495\) −2.02742 13.7725i −0.0911255 0.619029i
\(496\) −0.922513 0.922513i −0.0414220 0.0414220i
\(497\) −8.92940 8.92940i −0.400538 0.400538i
\(498\) 10.3222i 0.462551i
\(499\) −7.87010 + 7.87010i −0.352314 + 0.352314i −0.860970 0.508656i \(-0.830143\pi\)
0.508656 + 0.860970i \(0.330143\pi\)
\(500\) −4.74670 10.1227i −0.212279 0.452701i
\(501\) −0.539733 0.539733i −0.0241135 0.0241135i
\(502\) 3.26175 3.26175i 0.145579 0.145579i
\(503\) 25.8165i 1.15110i −0.817766 0.575551i \(-0.804788\pi\)
0.817766 0.575551i \(-0.195212\pi\)
\(504\) 0.597471 + 0.597471i 0.0266135 + 0.0266135i
\(505\) −21.7633 + 3.20372i −0.968456 + 0.142564i
\(506\) 11.9415i 0.530863i
\(507\) −8.50434 8.50434i −0.377691 0.377691i
\(508\) −6.23989 6.23989i −0.276850 0.276850i
\(509\) 3.51184 0.155660 0.0778299 0.996967i \(-0.475201\pi\)
0.0778299 + 0.996967i \(0.475201\pi\)
\(510\) 10.2916 + 7.65039i 0.455719 + 0.338765i
\(511\) 10.3096i 0.456068i
\(512\) 1.00000i 0.0441942i
\(513\) 2.82022 0.124516
\(514\) 12.9116i 0.569504i
\(515\) 3.82527 + 25.9856i 0.168561 + 1.14506i
\(516\) −4.41033 + 4.41033i −0.194154 + 0.194154i
\(517\) −13.0920 + 13.0920i −0.575784 + 0.575784i
\(518\) 4.11420 3.08047i 0.180767 0.135348i
\(519\) 10.5570i 0.463403i
\(520\) −0.321237 2.18221i −0.0140872 0.0956960i
\(521\) 44.1201i 1.93294i −0.256786 0.966468i \(-0.582664\pi\)
0.256786 0.966468i \(-0.417336\pi\)
\(522\) 3.12397 3.12397i 0.136732 0.136732i
\(523\) 30.8971i 1.35104i −0.737343 0.675519i \(-0.763920\pi\)
0.737343 0.675519i \(-0.236080\pi\)
\(524\) −13.4413 13.4413i −0.587186 0.587186i
\(525\) 1.21745 + 4.04554i 0.0531338 + 0.176562i
\(526\) −7.64722 + 7.64722i −0.333434 + 0.333434i
\(527\) 5.29051 + 5.29051i 0.230458 + 0.230458i
\(528\) −4.40219 + 4.40219i −0.191581 + 0.191581i
\(529\) 19.3208 0.840037
\(530\) 17.0134 22.8870i 0.739015 0.994149i
\(531\) 5.56150 5.56150i 0.241349 0.241349i
\(532\) 2.38295i 0.103314i
\(533\) −1.53228 −0.0663703
\(534\) 5.44331i 0.235555i
\(535\) −0.704127 + 0.947217i −0.0304421 + 0.0409518i
\(536\) 9.76587 + 9.76587i 0.421821 + 0.421821i
\(537\) −7.51916 −0.324476
\(538\) 22.1242 0.953841
\(539\) −39.1347 −1.68565
\(540\) 1.79455 + 1.33401i 0.0772253 + 0.0574065i
\(541\) −27.3608 + 27.3608i −1.17633 + 1.17633i −0.195661 + 0.980672i \(0.562685\pi\)
−0.980672 + 0.195661i \(0.937315\pi\)
\(542\) 1.96662i 0.0844736i
\(543\) 8.75942 + 8.75942i 0.375903 + 0.375903i
\(544\) 5.73489i 0.245881i
\(545\) 13.5120 18.1769i 0.578791 0.778611i
\(546\) 0.833485i 0.0356699i
\(547\) 21.4614i 0.917621i 0.888534 + 0.458811i \(0.151724\pi\)
−0.888534 + 0.458811i \(0.848276\pi\)
\(548\) 2.43423 + 2.43423i 0.103985 + 0.103985i
\(549\) 1.20352 1.20352i 0.0513652 0.0513652i
\(550\) −29.8077 + 8.97021i −1.27100 + 0.382491i
\(551\) −12.4596 −0.530797
\(552\) −1.35631 1.35631i −0.0577284 0.0577284i
\(553\) 5.42541i 0.230712i
\(554\) −10.4985 −0.446040
\(555\) 9.58441 9.65086i 0.406836 0.409656i
\(556\) 0.295024 0.0125118
\(557\) 0.327825i 0.0138904i −0.999976 0.00694520i \(-0.997789\pi\)
0.999976 0.00694520i \(-0.00221074\pi\)
\(558\) 0.922513 + 0.922513i 0.0390531 + 0.0390531i
\(559\) −6.15251 −0.260223
\(560\) 1.12717 1.51631i 0.0476317 0.0640759i
\(561\) 25.2461 25.2461i 1.06589 1.06589i
\(562\) 13.8482 + 13.8482i 0.584151 + 0.584151i
\(563\) 26.8738i 1.13260i −0.824200 0.566299i \(-0.808375\pi\)
0.824200 0.566299i \(-0.191625\pi\)
\(564\) 2.97397i 0.125227i
\(565\) −2.80676 19.0667i −0.118081 0.802142i
\(566\) 16.7535i 0.704203i
\(567\) −0.597471 0.597471i −0.0250914 0.0250914i
\(568\) 14.9453i 0.627092i
\(569\) −11.2972 + 11.2972i −0.473604 + 0.473604i −0.903079 0.429475i \(-0.858699\pi\)
0.429475 + 0.903079i \(0.358699\pi\)
\(570\) −0.918421 6.23896i −0.0384684 0.261321i
\(571\) −22.8094 −0.954544 −0.477272 0.878756i \(-0.658374\pi\)
−0.477272 + 0.878756i \(0.658374\pi\)
\(572\) −6.14115 −0.256774
\(573\) 5.41392 0.226170
\(574\) −0.928086 0.928086i −0.0387375 0.0387375i
\(575\) −2.76371 9.18373i −0.115255 0.382988i
\(576\) 1.00000i 0.0416667i
\(577\) −28.9467 −1.20507 −0.602534 0.798093i \(-0.705842\pi\)
−0.602534 + 0.798093i \(0.705842\pi\)
\(578\) 15.8890i 0.660895i
\(579\) 3.87773 3.87773i 0.161153 0.161153i
\(580\) −7.92827 5.89359i −0.329203 0.244718i
\(581\) −8.72179 −0.361841
\(582\) 8.86367 8.86367i 0.367411 0.367411i
\(583\) −56.1438 56.1438i −2.32524 2.32524i
\(584\) −8.62767 + 8.62767i −0.357015 + 0.357015i
\(585\) 0.321237 + 2.18221i 0.0132815 + 0.0902231i
\(586\) 3.05021 + 3.05021i 0.126003 + 0.126003i
\(587\) 21.1277i 0.872034i −0.899938 0.436017i \(-0.856389\pi\)
0.899938 0.436017i \(-0.143611\pi\)
\(588\) 4.44491 4.44491i 0.183305 0.183305i
\(589\) 3.67934i 0.151605i
\(590\) −14.1144 10.4922i −0.581082 0.431956i
\(591\) 4.68206i 0.192594i
\(592\) −6.02093 0.865086i −0.247459 0.0355548i
\(593\) 1.60032 1.60032i 0.0657171 0.0657171i −0.673484 0.739201i \(-0.735203\pi\)
0.739201 + 0.673484i \(0.235203\pi\)
\(594\) 4.40219 4.40219i 0.180624 0.180624i
\(595\) −6.46421 + 8.69588i −0.265007 + 0.356496i
\(596\) 21.7666i 0.891595i
\(597\) −9.86280 −0.403658
\(598\) 1.89208i 0.0773730i
\(599\) 30.6306i 1.25153i 0.780011 + 0.625765i \(0.215213\pi\)
−0.780011 + 0.625765i \(0.784787\pi\)
\(600\) 2.36672 4.40439i 0.0966209 0.179808i
\(601\) 11.2697 0.459700 0.229850 0.973226i \(-0.426176\pi\)
0.229850 + 0.973226i \(0.426176\pi\)
\(602\) −3.72652 3.72652i −0.151881 0.151881i
\(603\) −9.76587 9.76587i −0.397697 0.397697i
\(604\) 15.4134i 0.627162i
\(605\) 9.03973 + 61.4081i 0.367517 + 2.49660i
\(606\) −6.95634 6.95634i −0.282582 0.282582i
\(607\) 7.13929i 0.289775i −0.989448 0.144887i \(-0.953718\pi\)
0.989448 0.144887i \(-0.0462820\pi\)
\(608\) −1.99420 + 1.99420i −0.0808753 + 0.0808753i
\(609\) 2.63960 + 2.63960i 0.106962 + 0.106962i
\(610\) −3.05441 2.27054i −0.123669 0.0919313i
\(611\) 2.07437 2.07437i 0.0839202 0.0839202i
\(612\) 5.73489i 0.231819i
\(613\) 4.20436 + 4.20436i 0.169812 + 0.169812i 0.786897 0.617084i \(-0.211686\pi\)
−0.617084 + 0.786897i \(0.711686\pi\)
\(614\) 23.3606 + 23.3606i 0.942755 + 0.942755i
\(615\) −2.78758 2.07219i −0.112406 0.0835587i
\(616\) −3.71964 3.71964i −0.149868 0.149868i
\(617\) 20.2638 20.2638i 0.815792 0.815792i −0.169703 0.985495i \(-0.554281\pi\)
0.985495 + 0.169703i \(0.0542810\pi\)
\(618\) −8.30591 + 8.30591i −0.334113 + 0.334113i
\(619\) −15.2874 −0.614452 −0.307226 0.951637i \(-0.599401\pi\)
−0.307226 + 0.951637i \(0.599401\pi\)
\(620\) 1.74039 2.34123i 0.0698956 0.0940260i
\(621\) 1.35631 + 1.35631i 0.0544269 + 0.0544269i
\(622\) 18.5458 18.5458i 0.743618 0.743618i
\(623\) 4.59934 0.184268
\(624\) 0.697511 0.697511i 0.0279228 0.0279228i
\(625\) 20.8479 13.7973i 0.833916 0.551891i
\(626\) 33.3726 1.33384
\(627\) −17.5576 −0.701185
\(628\) 2.42992 + 2.42992i 0.0969642 + 0.0969642i
\(629\) 34.5294 + 4.96117i 1.37678 + 0.197815i
\(630\) −1.12717 + 1.51631i −0.0449076 + 0.0604113i
\(631\) 14.5347 + 14.5347i 0.578616 + 0.578616i 0.934522 0.355906i \(-0.115828\pi\)
−0.355906 + 0.934522i \(0.615828\pi\)
\(632\) −4.54031 + 4.54031i −0.180604 + 0.180604i
\(633\) 3.09593 + 3.09593i 0.123052 + 0.123052i
\(634\) 18.7269 + 18.7269i 0.743742 + 0.743742i
\(635\) 11.7720 15.8361i 0.467157 0.628437i
\(636\) 12.7536 0.505713
\(637\) 6.20075 0.245683
\(638\) −19.4487 + 19.4487i −0.769981 + 0.769981i
\(639\) 14.9453i 0.591228i
\(640\) −2.21223 + 0.325656i −0.0874459 + 0.0128727i
\(641\) −10.5777 −0.417793 −0.208897 0.977938i \(-0.566987\pi\)
−0.208897 + 0.977938i \(0.566987\pi\)
\(642\) −0.527829 −0.0208317
\(643\) −30.1992 −1.19094 −0.595470 0.803378i \(-0.703034\pi\)
−0.595470 + 0.803378i \(0.703034\pi\)
\(644\) 1.14602 1.14602i 0.0451594 0.0451594i
\(645\) −11.1929 8.32040i −0.440720 0.327616i
\(646\) 11.4365 11.4365i 0.449963 0.449963i
\(647\) 16.7883i 0.660015i 0.943978 + 0.330007i \(0.107051\pi\)
−0.943978 + 0.330007i \(0.892949\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −34.6239 + 34.6239i −1.35911 + 1.35911i
\(650\) 4.72292 1.42130i 0.185248 0.0557479i
\(651\) −0.779479 + 0.779479i −0.0305502 + 0.0305502i
\(652\) −23.0110 −0.901180
\(653\) −2.45128 −0.0959259 −0.0479629 0.998849i \(-0.515273\pi\)
−0.0479629 + 0.998849i \(0.515273\pi\)
\(654\) 10.1289 0.396071
\(655\) 25.3580 34.1124i 0.990817 1.33288i
\(656\) 1.55336i 0.0606484i
\(657\) 8.62767 8.62767i 0.336597 0.336597i
\(658\) 2.51286 0.0979614
\(659\) −9.82402 −0.382690 −0.191345 0.981523i \(-0.561285\pi\)
−0.191345 + 0.981523i \(0.561285\pi\)
\(660\) −11.1722 8.30504i −0.434879 0.323273i
\(661\) −34.3200 34.3200i −1.33489 1.33489i −0.900931 0.433963i \(-0.857115\pi\)
−0.433963 0.900931i \(-0.642885\pi\)
\(662\) 20.7521 + 20.7521i 0.806553 + 0.806553i
\(663\) −4.00015 + 4.00015i −0.155353 + 0.155353i
\(664\) 7.29893 + 7.29893i 0.283253 + 0.283253i
\(665\) 5.27162 0.776021i 0.204425 0.0300928i
\(666\) 6.02093 + 0.865086i 0.233306 + 0.0335214i
\(667\) −5.99213 5.99213i −0.232016 0.232016i
\(668\) −0.763298 −0.0295329
\(669\) 28.1917 1.08996
\(670\) −18.4240 + 24.7846i −0.711781 + 0.957514i
\(671\) −7.49271 + 7.49271i −0.289253 + 0.289253i
\(672\) 0.844952 0.0325947
\(673\) 24.8554 24.8554i 0.958106 0.958106i −0.0410514 0.999157i \(-0.513071\pi\)
0.999157 + 0.0410514i \(0.0130707\pi\)
\(674\) −14.7056 14.7056i −0.566440 0.566440i
\(675\) −2.36672 + 4.40439i −0.0910951 + 0.169525i
\(676\) −12.0270 −0.462575
\(677\) −32.9033 + 32.9033i −1.26458 + 1.26458i −0.315725 + 0.948851i \(0.602248\pi\)
−0.948851 + 0.315725i \(0.897752\pi\)
\(678\) 6.09440 6.09440i 0.234054 0.234054i
\(679\) 7.48937 + 7.48937i 0.287416 + 0.287416i
\(680\) 12.6869 1.86760i 0.486520 0.0716193i
\(681\) 9.95701 + 9.95701i 0.381553 + 0.381553i
\(682\) −5.74323 5.74323i −0.219919 0.219919i
\(683\) 26.8396i 1.02699i −0.858093 0.513494i \(-0.828351\pi\)
0.858093 0.513494i \(-0.171649\pi\)
\(684\) 1.99420 1.99420i 0.0762500 0.0762500i
\(685\) −4.59235 + 6.17779i −0.175465 + 0.236041i
\(686\) 7.93803 + 7.93803i 0.303076 + 0.303076i
\(687\) 10.9899 10.9899i 0.419289 0.419289i
\(688\) 6.23715i 0.237789i
\(689\) 8.89578 + 8.89578i 0.338902 + 0.338902i
\(690\) 2.55878 3.44216i 0.0974110 0.131041i
\(691\) 5.35284i 0.203631i 0.994803 + 0.101816i \(0.0324652\pi\)
−0.994803 + 0.101816i \(0.967535\pi\)
\(692\) −7.46496 7.46496i −0.283775 0.283775i
\(693\) 3.71964 + 3.71964i 0.141297 + 0.141297i
\(694\) −17.2146 −0.653456
\(695\) 0.0960764 + 0.652660i 0.00364439 + 0.0247568i
\(696\) 4.41796i 0.167462i
\(697\) 8.90833i 0.337427i
\(698\) −28.4058 −1.07517
\(699\) 10.2535i 0.387823i
\(700\) 3.72150 + 1.99976i 0.140659 + 0.0755839i
\(701\) 22.1584 22.1584i 0.836910 0.836910i −0.151541 0.988451i \(-0.548423\pi\)
0.988451 + 0.151541i \(0.0484235\pi\)
\(702\) −0.697511 + 0.697511i −0.0263259 + 0.0263259i
\(703\) −10.2818 13.7321i −0.387784 0.517915i
\(704\) 6.22563i 0.234637i
\(705\) 6.57909 0.968490i 0.247783 0.0364755i
\(706\) 12.3989i 0.466641i
\(707\) 5.87777 5.87777i 0.221056 0.221056i
\(708\) 7.86515i 0.295590i
\(709\) 18.1716 + 18.1716i 0.682449 + 0.682449i 0.960551 0.278103i \(-0.0897055\pi\)
−0.278103 + 0.960551i \(0.589706\pi\)
\(710\) −33.0624 + 4.86703i −1.24081 + 0.182657i
\(711\) 4.54031 4.54031i 0.170275 0.170275i
\(712\) −3.84900 3.84900i −0.144247 0.144247i
\(713\) 1.76948 1.76948i 0.0662677 0.0662677i
\(714\) −4.84571 −0.181346
\(715\) −1.99990 13.5856i −0.0747921 0.508073i
\(716\) −5.31685 + 5.31685i −0.198700 + 0.198700i
\(717\) 18.1416i 0.677510i
\(718\) 6.27293 0.234104
\(719\) 2.21940i 0.0827695i −0.999143 0.0413848i \(-0.986823\pi\)
0.999143 0.0413848i \(-0.0131769\pi\)
\(720\) 2.21223 0.325656i 0.0824448 0.0121365i
\(721\) −7.01810 7.01810i −0.261368 0.261368i
\(722\) 11.0464 0.411103
\(723\) −12.9982 −0.483406
\(724\) 12.3877 0.460385
\(725\) 10.4561 19.4584i 0.388329 0.722667i
\(726\) −19.6282 + 19.6282i −0.728472 + 0.728472i
\(727\) 28.6133i 1.06121i −0.847619 0.530605i \(-0.821965\pi\)
0.847619 0.530605i \(-0.178035\pi\)
\(728\) 0.589363 + 0.589363i 0.0218432 + 0.0218432i
\(729\) 1.00000i 0.0370370i
\(730\) −21.8960 16.2767i −0.810408 0.602428i
\(731\) 35.7694i 1.32298i
\(732\) 1.70204i 0.0629093i
\(733\) −18.8456 18.8456i −0.696079 0.696079i 0.267484 0.963562i \(-0.413808\pi\)
−0.963562 + 0.267484i \(0.913808\pi\)
\(734\) 0.228414 0.228414i 0.00843090 0.00843090i
\(735\) 11.2807 + 8.38564i 0.416094 + 0.309309i
\(736\) −1.91811 −0.0707026
\(737\) 60.7987 + 60.7987i 2.23955 + 2.23955i
\(738\) 1.55336i 0.0571798i
\(739\) 22.5110 0.828079 0.414040 0.910259i \(-0.364117\pi\)
0.414040 + 0.910259i \(0.364117\pi\)
\(740\) −0.0469870 13.6014i −0.00172728 0.499997i
\(741\) 2.78195 0.102197
\(742\) 10.7762i 0.395606i
\(743\) 18.4577 + 18.4577i 0.677149 + 0.677149i 0.959354 0.282205i \(-0.0910660\pi\)
−0.282205 + 0.959354i \(0.591066\pi\)
\(744\) 1.30463 0.0478301
\(745\) −48.1527 + 7.08843i −1.76418 + 0.259700i
\(746\) 13.8845 13.8845i 0.508346 0.508346i
\(747\) −7.29893 7.29893i −0.267054 0.267054i
\(748\) 35.7033i 1.30544i
\(749\) 0.445990i 0.0162961i
\(750\) 10.5142 + 3.80140i 0.383926 + 0.138808i
\(751\) 31.7070i 1.15700i 0.815681 + 0.578502i \(0.196362\pi\)
−0.815681 + 0.578502i \(0.803638\pi\)
\(752\) −2.10291 2.10291i −0.0766853 0.0766853i
\(753\) 4.61281i 0.168100i
\(754\) 3.08158 3.08158i 0.112224 0.112224i
\(755\) −34.0979 + 5.01947i −1.24095 + 0.182677i
\(756\) −0.844952 −0.0307306
\(757\) −16.4593 −0.598224 −0.299112 0.954218i \(-0.596690\pi\)
−0.299112 + 0.954218i \(0.596690\pi\)
\(758\) 0.247309 0.00898268
\(759\) −8.44389 8.44389i −0.306494 0.306494i
\(760\) −5.06103 3.76219i −0.183583 0.136469i
\(761\) 1.08101i 0.0391865i −0.999808 0.0195933i \(-0.993763\pi\)
0.999808 0.0195933i \(-0.00623713\pi\)
\(762\) 8.82454 0.319679
\(763\) 8.55843i 0.309836i
\(764\) 3.82822 3.82822i 0.138500 0.138500i
\(765\) −12.6869 + 1.86760i −0.458695 + 0.0675233i
\(766\) −7.97917 −0.288299
\(767\) 5.48603 5.48603i 0.198089 0.198089i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) −7.99476 + 7.99476i −0.288298 + 0.288298i −0.836407 0.548109i \(-0.815348\pi\)
0.548109 + 0.836407i \(0.315348\pi\)
\(770\) 7.01736 9.44000i 0.252888 0.340194i
\(771\) 9.12984 + 9.12984i 0.328803 + 0.328803i
\(772\) 5.48394i 0.197371i
\(773\) 6.30521 6.30521i 0.226783 0.226783i −0.584564 0.811347i \(-0.698735\pi\)
0.811347 + 0.584564i \(0.198735\pi\)
\(774\) 6.23715i 0.224190i
\(775\) 5.74610 + 3.08769i 0.206406 + 0.110913i
\(776\) 12.5351i 0.449985i
\(777\) −0.730956 + 5.08740i −0.0262229 + 0.182509i
\(778\) 0.310092 0.310092i 0.0111173 0.0111173i
\(779\) −3.09770 + 3.09770i −0.110987 + 0.110987i