Properties

Label 450.2.h.e.91.2
Level $450$
Weight $2$
Character 450.91
Analytic conductor $3.593$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.58140625.2
Defining polynomial: \(x^{8} - 3 x^{7} + 4 x^{6} - 7 x^{5} + 11 x^{4} + 5 x^{3} - 10 x^{2} - 25 x + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 50)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 91.2
Root \(-0.357358 - 1.86824i\) of defining polynomial
Character \(\chi\) \(=\) 450.91
Dual form 450.2.h.e.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(2.02373 + 0.951057i) q^{5} +3.77447 q^{7} +(-0.309017 + 0.951057i) q^{8} +O(q^{10})\) \(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(2.02373 + 0.951057i) q^{5} +3.77447 q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.07822 + 1.95894i) q^{10} +(-3.05361 - 2.21858i) q^{11} +(-2.56969 + 1.86699i) q^{13} +(3.05361 + 2.21858i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.430307 - 1.32435i) q^{17} +(1.20945 - 3.72230i) q^{19} +(-0.279141 + 2.21858i) q^{20} +(-1.16637 - 3.58973i) q^{22} +(0.720859 + 0.523735i) q^{23} +(3.19098 + 3.84937i) q^{25} -3.17632 q^{26} +(1.16637 + 3.58973i) q^{28} +(-0.0152089 - 0.0468081i) q^{29} +(-1.72466 + 5.30795i) q^{31} -1.00000 q^{32} +(1.12656 - 0.818492i) q^{34} +(7.63851 + 3.58973i) q^{35} +(-5.70152 + 4.14240i) q^{37} +(3.16637 - 2.30051i) q^{38} +(-1.52988 + 1.63079i) q^{40} +(-1.20477 + 0.875319i) q^{41} +2.69767 q^{43} +(1.16637 - 3.58973i) q^{44} +(0.275344 + 0.847421i) q^{46} +(-1.16637 - 3.58973i) q^{47} +7.24660 q^{49} +(0.318958 + 4.98982i) q^{50} +(-2.56969 - 1.86699i) q^{52} +(-3.58963 - 11.0477i) q^{53} +(-4.06969 - 7.39396i) q^{55} +(-1.16637 + 3.58973i) q^{56} +(0.0152089 - 0.0468081i) q^{58} +(-0.558282 + 0.405615i) q^{59} +(-8.38168 - 6.08965i) q^{61} +(-4.51521 + 3.28049i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(-6.97599 + 1.33437i) q^{65} +(4.73519 - 14.5734i) q^{67} +1.39250 q^{68} +(4.06969 + 7.39396i) q^{70} +(2.06969 + 6.36986i) q^{71} +(-4.18158 - 3.03810i) q^{73} -7.04746 q^{74} +3.91385 q^{76} +(-11.5257 - 8.37394i) q^{77} +(-0.558282 - 1.71821i) q^{79} +(-2.19625 + 0.420099i) q^{80} -1.48918 q^{82} +(3.08023 - 9.47997i) q^{83} +(2.13035 - 2.27088i) q^{85} +(2.18246 + 1.58565i) q^{86} +(3.05361 - 2.21858i) q^{88} +(11.7390 + 8.52891i) q^{89} +(-9.69922 + 7.04690i) q^{91} +(-0.275344 + 0.847421i) q^{92} +(1.16637 - 3.58973i) q^{94} +(5.98771 - 6.38268i) q^{95} +(-0.0278640 - 0.0857567i) q^{97} +(5.86263 + 4.25945i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 2q^{4} + 4q^{7} + 2q^{8} + O(q^{10}) \) \( 8q + 2q^{2} - 2q^{4} + 4q^{7} + 2q^{8} - q^{11} - 13q^{13} + q^{14} - 2q^{16} + 11q^{17} + 20q^{19} - 5q^{20} + q^{22} + 3q^{23} + 30q^{25} - 22q^{26} - q^{28} + 15q^{29} - 9q^{31} - 8q^{32} - q^{34} + 15q^{35} - 6q^{37} + 15q^{38} - 5q^{40} + 9q^{41} + 12q^{43} - q^{44} + 7q^{46} + q^{47} - 4q^{49} + 5q^{50} - 13q^{52} - 7q^{53} - 25q^{55} + q^{56} - 15q^{58} - 10q^{59} + 6q^{61} - 21q^{62} - 2q^{64} + 10q^{65} - 11q^{67} - 24q^{68} + 25q^{70} + 9q^{71} - 8q^{73} - 24q^{74} - 10q^{76} - 33q^{77} - 10q^{79} + 26q^{82} - 27q^{83} + 5q^{85} + 23q^{86} + q^{88} + 15q^{89} + q^{91} - 7q^{92} - q^{94} + 30q^{95} - 36q^{97} + 19q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 + 0.587785i 0.572061 + 0.415627i
\(3\) 0 0
\(4\) 0.309017 + 0.951057i 0.154508 + 0.475528i
\(5\) 2.02373 + 0.951057i 0.905040 + 0.425325i
\(6\) 0 0
\(7\) 3.77447 1.42661 0.713307 0.700851i \(-0.247196\pi\)
0.713307 + 0.700851i \(0.247196\pi\)
\(8\) −0.309017 + 0.951057i −0.109254 + 0.336249i
\(9\) 0 0
\(10\) 1.07822 + 1.95894i 0.340962 + 0.619471i
\(11\) −3.05361 2.21858i −0.920698 0.668926i 0.0230000 0.999735i \(-0.492678\pi\)
−0.943698 + 0.330810i \(0.892678\pi\)
\(12\) 0 0
\(13\) −2.56969 + 1.86699i −0.712705 + 0.517810i −0.884045 0.467402i \(-0.845190\pi\)
0.171340 + 0.985212i \(0.445190\pi\)
\(14\) 3.05361 + 2.21858i 0.816111 + 0.592939i
\(15\) 0 0
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) 0.430307 1.32435i 0.104365 0.321201i −0.885216 0.465180i \(-0.845990\pi\)
0.989581 + 0.143979i \(0.0459896\pi\)
\(18\) 0 0
\(19\) 1.20945 3.72230i 0.277466 0.853953i −0.711090 0.703101i \(-0.751798\pi\)
0.988556 0.150852i \(-0.0482018\pi\)
\(20\) −0.279141 + 2.21858i −0.0624178 + 0.496089i
\(21\) 0 0
\(22\) −1.16637 3.58973i −0.248672 0.765333i
\(23\) 0.720859 + 0.523735i 0.150310 + 0.109206i 0.660398 0.750916i \(-0.270387\pi\)
−0.510089 + 0.860122i \(0.670387\pi\)
\(24\) 0 0
\(25\) 3.19098 + 3.84937i 0.638197 + 0.769873i
\(26\) −3.17632 −0.622927
\(27\) 0 0
\(28\) 1.16637 + 3.58973i 0.220424 + 0.678396i
\(29\) −0.0152089 0.0468081i −0.00282422 0.00869205i 0.949634 0.313360i \(-0.101455\pi\)
−0.952459 + 0.304668i \(0.901455\pi\)
\(30\) 0 0
\(31\) −1.72466 + 5.30795i −0.309757 + 0.953335i 0.668102 + 0.744070i \(0.267107\pi\)
−0.977859 + 0.209265i \(0.932893\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 1.12656 0.818492i 0.193203 0.140370i
\(35\) 7.63851 + 3.58973i 1.29114 + 0.606775i
\(36\) 0 0
\(37\) −5.70152 + 4.14240i −0.937324 + 0.681006i −0.947775 0.318940i \(-0.896673\pi\)
0.0104512 + 0.999945i \(0.496673\pi\)
\(38\) 3.16637 2.30051i 0.513654 0.373191i
\(39\) 0 0
\(40\) −1.52988 + 1.63079i −0.241895 + 0.257851i
\(41\) −1.20477 + 0.875319i −0.188154 + 0.136702i −0.677875 0.735178i \(-0.737099\pi\)
0.489721 + 0.871879i \(0.337099\pi\)
\(42\) 0 0
\(43\) 2.69767 0.411391 0.205695 0.978616i \(-0.434054\pi\)
0.205695 + 0.978616i \(0.434054\pi\)
\(44\) 1.16637 3.58973i 0.175838 0.541172i
\(45\) 0 0
\(46\) 0.275344 + 0.847421i 0.0405972 + 0.124945i
\(47\) −1.16637 3.58973i −0.170133 0.523616i 0.829245 0.558886i \(-0.188771\pi\)
−0.999378 + 0.0352696i \(0.988771\pi\)
\(48\) 0 0
\(49\) 7.24660 1.03523
\(50\) 0.318958 + 4.98982i 0.0451075 + 0.705667i
\(51\) 0 0
\(52\) −2.56969 1.86699i −0.356352 0.258905i
\(53\) −3.58963 11.0477i −0.493073 1.51752i −0.819938 0.572453i \(-0.805992\pi\)
0.326864 0.945071i \(-0.394008\pi\)
\(54\) 0 0
\(55\) −4.06969 7.39396i −0.548757 0.997001i
\(56\) −1.16637 + 3.58973i −0.155863 + 0.479698i
\(57\) 0 0
\(58\) 0.0152089 0.0468081i 0.00199702 0.00614620i
\(59\) −0.558282 + 0.405615i −0.0726821 + 0.0528066i −0.623533 0.781797i \(-0.714303\pi\)
0.550851 + 0.834604i \(0.314303\pi\)
\(60\) 0 0
\(61\) −8.38168 6.08965i −1.07316 0.779700i −0.0966862 0.995315i \(-0.530824\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(62\) −4.51521 + 3.28049i −0.573432 + 0.416623i
\(63\) 0 0
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) −6.97599 + 1.33437i −0.865265 + 0.165508i
\(66\) 0 0
\(67\) 4.73519 14.5734i 0.578496 1.78043i −0.0454589 0.998966i \(-0.514475\pi\)
0.623955 0.781461i \(-0.285525\pi\)
\(68\) 1.39250 0.168866
\(69\) 0 0
\(70\) 4.06969 + 7.39396i 0.486421 + 0.883747i
\(71\) 2.06969 + 6.36986i 0.245627 + 0.755963i 0.995533 + 0.0944182i \(0.0300991\pi\)
−0.749905 + 0.661545i \(0.769901\pi\)
\(72\) 0 0
\(73\) −4.18158 3.03810i −0.489417 0.355582i 0.315543 0.948911i \(-0.397813\pi\)
−0.804960 + 0.593329i \(0.797813\pi\)
\(74\) −7.04746 −0.819251
\(75\) 0 0
\(76\) 3.91385 0.448950
\(77\) −11.5257 8.37394i −1.31348 0.954299i
\(78\) 0 0
\(79\) −0.558282 1.71821i −0.0628116 0.193314i 0.914726 0.404074i \(-0.132406\pi\)
−0.977538 + 0.210760i \(0.932406\pi\)
\(80\) −2.19625 + 0.420099i −0.245548 + 0.0469685i
\(81\) 0 0
\(82\) −1.48918 −0.164453
\(83\) 3.08023 9.47997i 0.338099 1.04056i −0.627076 0.778958i \(-0.715749\pi\)
0.965175 0.261604i \(-0.0842514\pi\)
\(84\) 0 0
\(85\) 2.13035 2.27088i 0.231069 0.246311i
\(86\) 2.18246 + 1.58565i 0.235341 + 0.170985i
\(87\) 0 0
\(88\) 3.05361 2.21858i 0.325516 0.236501i
\(89\) 11.7390 + 8.52891i 1.24434 + 0.904063i 0.997879 0.0650909i \(-0.0207337\pi\)
0.246457 + 0.969154i \(0.420734\pi\)
\(90\) 0 0
\(91\) −9.69922 + 7.04690i −1.01675 + 0.738716i
\(92\) −0.275344 + 0.847421i −0.0287066 + 0.0883497i
\(93\) 0 0
\(94\) 1.16637 3.58973i 0.120302 0.370253i
\(95\) 5.98771 6.38268i 0.614326 0.654849i
\(96\) 0 0
\(97\) −0.0278640 0.0857567i −0.00282917 0.00870727i 0.949632 0.313367i \(-0.101457\pi\)
−0.952461 + 0.304660i \(0.901457\pi\)
\(98\) 5.86263 + 4.25945i 0.592215 + 0.430269i
\(99\) 0 0
\(100\) −2.67490 + 4.22433i −0.267490 + 0.422433i
\(101\) −16.3785 −1.62972 −0.814859 0.579659i \(-0.803186\pi\)
−0.814859 + 0.579659i \(0.803186\pi\)
\(102\) 0 0
\(103\) −0.375822 1.15666i −0.0370308 0.113969i 0.930832 0.365446i \(-0.119084\pi\)
−0.967863 + 0.251477i \(0.919084\pi\)
\(104\) −0.981536 3.02086i −0.0962475 0.296219i
\(105\) 0 0
\(106\) 3.58963 11.0477i 0.348656 1.07305i
\(107\) 10.8125 1.04528 0.522641 0.852553i \(-0.324947\pi\)
0.522641 + 0.852553i \(0.324947\pi\)
\(108\) 0 0
\(109\) −9.23519 + 6.70976i −0.884571 + 0.642678i −0.934457 0.356077i \(-0.884114\pi\)
0.0498859 + 0.998755i \(0.484114\pi\)
\(110\) 1.05361 8.37394i 0.100458 0.798424i
\(111\) 0 0
\(112\) −3.05361 + 2.21858i −0.288539 + 0.209636i
\(113\) −8.43232 + 6.12644i −0.793246 + 0.576327i −0.908925 0.416960i \(-0.863096\pi\)
0.115679 + 0.993287i \(0.463096\pi\)
\(114\) 0 0
\(115\) 0.960724 + 1.74548i 0.0895880 + 0.162767i
\(116\) 0.0398173 0.0289290i 0.00369695 0.00268599i
\(117\) 0 0
\(118\) −0.690074 −0.0635265
\(119\) 1.62418 4.99871i 0.148888 0.458231i
\(120\) 0 0
\(121\) 1.00326 + 3.08770i 0.0912051 + 0.280700i
\(122\) −3.20152 9.85326i −0.289852 0.892072i
\(123\) 0 0
\(124\) −5.58111 −0.501198
\(125\) 2.79673 + 10.8249i 0.250147 + 0.968208i
\(126\) 0 0
\(127\) 2.87115 + 2.08601i 0.254773 + 0.185104i 0.707840 0.706373i \(-0.249670\pi\)
−0.453066 + 0.891477i \(0.649670\pi\)
\(128\) −0.309017 0.951057i −0.0273135 0.0840623i
\(129\) 0 0
\(130\) −6.42801 3.02086i −0.563774 0.264947i
\(131\) −1.25252 + 3.85486i −0.109433 + 0.336801i −0.990745 0.135734i \(-0.956661\pi\)
0.881312 + 0.472535i \(0.156661\pi\)
\(132\) 0 0
\(133\) 4.56502 14.0497i 0.395837 1.21826i
\(134\) 12.3969 9.00687i 1.07093 0.778075i
\(135\) 0 0
\(136\) 1.12656 + 0.818492i 0.0966015 + 0.0701851i
\(137\) −2.88636 + 2.09706i −0.246598 + 0.179164i −0.704218 0.709984i \(-0.748702\pi\)
0.457620 + 0.889148i \(0.348702\pi\)
\(138\) 0 0
\(139\) 8.04650 + 5.84613i 0.682495 + 0.495862i 0.874185 0.485594i \(-0.161397\pi\)
−0.191689 + 0.981456i \(0.561397\pi\)
\(140\) −1.05361 + 8.37394i −0.0890461 + 0.707727i
\(141\) 0 0
\(142\) −2.06969 + 6.36986i −0.173685 + 0.534547i
\(143\) 11.9889 1.00256
\(144\) 0 0
\(145\) 0.0137385 0.109192i 0.00114092 0.00906786i
\(146\) −1.59722 4.91575i −0.132187 0.406830i
\(147\) 0 0
\(148\) −5.70152 4.14240i −0.468662 0.340503i
\(149\) 19.5103 1.59834 0.799171 0.601104i \(-0.205272\pi\)
0.799171 + 0.601104i \(0.205272\pi\)
\(150\) 0 0
\(151\) −18.4324 −1.50001 −0.750003 0.661435i \(-0.769948\pi\)
−0.750003 + 0.661435i \(0.769948\pi\)
\(152\) 3.16637 + 2.30051i 0.256827 + 0.186596i
\(153\) 0 0
\(154\) −4.40244 13.5493i −0.354759 1.09184i
\(155\) −8.53840 + 9.10162i −0.685821 + 0.731059i
\(156\) 0 0
\(157\) 10.1564 0.810572 0.405286 0.914190i \(-0.367172\pi\)
0.405286 + 0.914190i \(0.367172\pi\)
\(158\) 0.558282 1.71821i 0.0444145 0.136694i
\(159\) 0 0
\(160\) −2.02373 0.951057i −0.159990 0.0751876i
\(161\) 2.72086 + 1.97682i 0.214434 + 0.155795i
\(162\) 0 0
\(163\) 15.0481 10.9331i 1.17865 0.856343i 0.186636 0.982429i \(-0.440242\pi\)
0.992019 + 0.126086i \(0.0402416\pi\)
\(164\) −1.20477 0.875319i −0.0940770 0.0683510i
\(165\) 0 0
\(166\) 8.06414 5.85894i 0.625899 0.454742i
\(167\) −0.671048 + 2.06527i −0.0519273 + 0.159816i −0.973657 0.228016i \(-0.926776\pi\)
0.921730 + 0.387832i \(0.126776\pi\)
\(168\) 0 0
\(169\) −0.899554 + 2.76854i −0.0691965 + 0.212965i
\(170\) 3.05828 0.584988i 0.234560 0.0448666i
\(171\) 0 0
\(172\) 0.833625 + 2.56564i 0.0635633 + 0.195628i
\(173\) −5.17306 3.75845i −0.393300 0.285750i 0.373506 0.927628i \(-0.378155\pi\)
−0.766807 + 0.641878i \(0.778155\pi\)
\(174\) 0 0
\(175\) 12.0443 + 14.5293i 0.910461 + 1.09831i
\(176\) 3.77447 0.284511
\(177\) 0 0
\(178\) 4.48391 + 13.8001i 0.336084 + 1.03436i
\(179\) −2.47630 7.62127i −0.185087 0.569640i 0.814862 0.579654i \(-0.196812\pi\)
−0.999950 + 0.0100140i \(0.996812\pi\)
\(180\) 0 0
\(181\) −3.35682 + 10.3312i −0.249510 + 0.767913i 0.745352 + 0.666671i \(0.232282\pi\)
−0.994862 + 0.101242i \(0.967718\pi\)
\(182\) −11.9889 −0.888676
\(183\) 0 0
\(184\) −0.720859 + 0.523735i −0.0531424 + 0.0386102i
\(185\) −15.4780 + 2.96063i −1.13797 + 0.217670i
\(186\) 0 0
\(187\) −4.25215 + 3.08937i −0.310948 + 0.225917i
\(188\) 3.05361 2.21858i 0.222707 0.161806i
\(189\) 0 0
\(190\) 8.59580 1.64421i 0.623605 0.119283i
\(191\) −6.62243 + 4.81147i −0.479182 + 0.348146i −0.801009 0.598652i \(-0.795703\pi\)
0.321827 + 0.946798i \(0.395703\pi\)
\(192\) 0 0
\(193\) −17.5576 −1.26382 −0.631912 0.775040i \(-0.717730\pi\)
−0.631912 + 0.775040i \(0.717730\pi\)
\(194\) 0.0278640 0.0857567i 0.00200052 0.00615697i
\(195\) 0 0
\(196\) 2.23932 + 6.89193i 0.159952 + 0.492281i
\(197\) −1.47012 4.52458i −0.104742 0.322363i 0.884928 0.465728i \(-0.154208\pi\)
−0.989670 + 0.143365i \(0.954208\pi\)
\(198\) 0 0
\(199\) 14.5320 1.03015 0.515073 0.857146i \(-0.327765\pi\)
0.515073 + 0.857146i \(0.327765\pi\)
\(200\) −4.64703 + 1.84529i −0.328595 + 0.130481i
\(201\) 0 0
\(202\) −13.2505 9.62702i −0.932299 0.677355i
\(203\) −0.0574054 0.176676i −0.00402907 0.0124002i
\(204\) 0 0
\(205\) −3.27062 + 0.625604i −0.228430 + 0.0436941i
\(206\) 0.375822 1.15666i 0.0261848 0.0805884i
\(207\) 0 0
\(208\) 0.981536 3.02086i 0.0680572 0.209459i
\(209\) −11.9514 + 8.68318i −0.826694 + 0.600628i
\(210\) 0 0
\(211\) 11.4362 + 8.30886i 0.787298 + 0.572006i 0.907160 0.420785i \(-0.138245\pi\)
−0.119862 + 0.992791i \(0.538245\pi\)
\(212\) 9.39777 6.82788i 0.645441 0.468941i
\(213\) 0 0
\(214\) 8.74748 + 6.35542i 0.597965 + 0.434447i
\(215\) 5.45936 + 2.56564i 0.372325 + 0.174975i
\(216\) 0 0
\(217\) −6.50966 + 20.0347i −0.441904 + 1.36004i
\(218\) −11.4153 −0.773143
\(219\) 0 0
\(220\) 5.77447 6.15537i 0.389315 0.414995i
\(221\) 1.36679 + 4.20655i 0.0919402 + 0.282963i
\(222\) 0 0
\(223\) −3.73139 2.71102i −0.249873 0.181543i 0.455798 0.890083i \(-0.349354\pi\)
−0.705670 + 0.708540i \(0.749354\pi\)
\(224\) −3.77447 −0.252192
\(225\) 0 0
\(226\) −10.4229 −0.693322
\(227\) −5.08578 3.69503i −0.337555 0.245248i 0.406075 0.913840i \(-0.366897\pi\)
−0.743630 + 0.668592i \(0.766897\pi\)
\(228\) 0 0
\(229\) 5.48103 + 16.8689i 0.362196 + 1.11473i 0.951718 + 0.306973i \(0.0993163\pi\)
−0.589522 + 0.807753i \(0.700684\pi\)
\(230\) −0.248723 + 1.97682i −0.0164003 + 0.130348i
\(231\) 0 0
\(232\) 0.0492169 0.00323125
\(233\) −0.792338 + 2.43856i −0.0519078 + 0.159756i −0.973650 0.228047i \(-0.926766\pi\)
0.921742 + 0.387803i \(0.126766\pi\)
\(234\) 0 0
\(235\) 1.05361 8.37394i 0.0687298 0.546256i
\(236\) −0.558282 0.405615i −0.0363410 0.0264033i
\(237\) 0 0
\(238\) 4.25215 3.08937i 0.275626 0.200254i
\(239\) 7.63851 + 5.54970i 0.494094 + 0.358980i 0.806757 0.590884i \(-0.201221\pi\)
−0.312662 + 0.949864i \(0.601221\pi\)
\(240\) 0 0
\(241\) 23.8131 17.3012i 1.53394 1.11447i 0.579940 0.814659i \(-0.303076\pi\)
0.953998 0.299812i \(-0.0969240\pi\)
\(242\) −1.00326 + 3.08770i −0.0644917 + 0.198485i
\(243\) 0 0
\(244\) 3.20152 9.85326i 0.204956 0.630790i
\(245\) 14.6652 + 6.89193i 0.936924 + 0.440309i
\(246\) 0 0
\(247\) 3.84159 + 11.8232i 0.244434 + 0.752292i
\(248\) −4.51521 3.28049i −0.286716 0.208311i
\(249\) 0 0
\(250\) −4.10011 + 10.4014i −0.259314 + 0.657842i
\(251\) 6.00759 0.379196 0.189598 0.981862i \(-0.439282\pi\)
0.189598 + 0.981862i \(0.439282\pi\)
\(252\) 0 0
\(253\) −1.03928 3.19856i −0.0653387 0.201092i
\(254\) 1.09668 + 3.37524i 0.0688119 + 0.211781i
\(255\) 0 0
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) 13.6286 0.850127 0.425063 0.905164i \(-0.360252\pi\)
0.425063 + 0.905164i \(0.360252\pi\)
\(258\) 0 0
\(259\) −21.5202 + 15.6353i −1.33720 + 0.971533i
\(260\) −3.42476 6.22221i −0.212394 0.385885i
\(261\) 0 0
\(262\) −3.27914 + 2.38244i −0.202586 + 0.147187i
\(263\) −7.41298 + 5.38584i −0.457104 + 0.332105i −0.792394 0.610010i \(-0.791166\pi\)
0.335290 + 0.942115i \(0.391166\pi\)
\(264\) 0 0
\(265\) 3.24258 25.7716i 0.199190 1.58314i
\(266\) 11.9514 8.68318i 0.732786 0.532400i
\(267\) 0 0
\(268\) 15.3234 0.936026
\(269\) −8.68419 + 26.7272i −0.529484 + 1.62959i 0.225790 + 0.974176i \(0.427504\pi\)
−0.755274 + 0.655409i \(0.772496\pi\)
\(270\) 0 0
\(271\) −2.81162 8.65329i −0.170794 0.525650i 0.828623 0.559808i \(-0.189125\pi\)
−0.999416 + 0.0341581i \(0.989125\pi\)
\(272\) 0.430307 + 1.32435i 0.0260912 + 0.0803004i
\(273\) 0 0
\(274\) −3.56773 −0.215535
\(275\) −1.20390 18.8339i −0.0725977 1.13573i
\(276\) 0 0
\(277\) −15.2006 11.0439i −0.913318 0.663564i 0.0285338 0.999593i \(-0.490916\pi\)
−0.941852 + 0.336028i \(0.890916\pi\)
\(278\) 3.07349 + 9.45923i 0.184336 + 0.567327i
\(279\) 0 0
\(280\) −5.77447 + 6.15537i −0.345090 + 0.367854i
\(281\) −2.43554 + 7.49583i −0.145292 + 0.447164i −0.997048 0.0767748i \(-0.975538\pi\)
0.851756 + 0.523938i \(0.175538\pi\)
\(282\) 0 0
\(283\) −5.65496 + 17.4042i −0.336153 + 1.03457i 0.629999 + 0.776596i \(0.283055\pi\)
−0.966151 + 0.257975i \(0.916945\pi\)
\(284\) −5.41853 + 3.93679i −0.321530 + 0.233606i
\(285\) 0 0
\(286\) 9.69922 + 7.04690i 0.573527 + 0.416692i
\(287\) −4.54738 + 3.30386i −0.268423 + 0.195021i
\(288\) 0 0
\(289\) 12.1846 + 8.85260i 0.716739 + 0.520741i
\(290\) 0.0752958 0.0802625i 0.00442152 0.00471318i
\(291\) 0 0
\(292\) 1.59722 4.91575i 0.0934704 0.287672i
\(293\) 29.4990 1.72335 0.861675 0.507461i \(-0.169416\pi\)
0.861675 + 0.507461i \(0.169416\pi\)
\(294\) 0 0
\(295\) −1.51558 + 0.289899i −0.0882402 + 0.0168786i
\(296\) −2.17779 6.70254i −0.126581 0.389577i
\(297\) 0 0
\(298\) 15.7841 + 11.4678i 0.914350 + 0.664314i
\(299\) −2.83020 −0.163674
\(300\) 0 0
\(301\) 10.1823 0.586896
\(302\) −14.9121 10.8343i −0.858095 0.623443i
\(303\) 0 0
\(304\) 1.20945 + 3.72230i 0.0693666 + 0.213488i
\(305\) −11.1707 20.2953i −0.639631 1.16210i
\(306\) 0 0
\(307\) 13.9131 0.794064 0.397032 0.917805i \(-0.370040\pi\)
0.397032 + 0.917805i \(0.370040\pi\)
\(308\) 4.40244 13.5493i 0.250852 0.772044i
\(309\) 0 0
\(310\) −12.2575 + 2.34462i −0.696180 + 0.133165i
\(311\) 21.0050 + 15.2610i 1.19108 + 0.865373i 0.993378 0.114889i \(-0.0366512\pi\)
0.197705 + 0.980262i \(0.436651\pi\)
\(312\) 0 0
\(313\) −7.66454 + 5.56861i −0.433225 + 0.314757i −0.782937 0.622101i \(-0.786279\pi\)
0.349712 + 0.936857i \(0.386279\pi\)
\(314\) 8.21673 + 5.96980i 0.463697 + 0.336895i
\(315\) 0 0
\(316\) 1.46160 1.06192i 0.0822215 0.0597374i
\(317\) −7.57321 + 23.3079i −0.425354 + 1.30910i 0.477301 + 0.878740i \(0.341615\pi\)
−0.902655 + 0.430365i \(0.858385\pi\)
\(318\) 0 0
\(319\) −0.0574054 + 0.176676i −0.00321408 + 0.00989194i
\(320\) −1.07822 1.95894i −0.0602741 0.109508i
\(321\) 0 0
\(322\) 1.03928 + 3.19856i 0.0579166 + 0.178249i
\(323\) −4.40918 3.20346i −0.245333 0.178245i
\(324\) 0 0
\(325\) −15.3866 3.93416i −0.853494 0.218228i
\(326\) 18.6004 1.03018
\(327\) 0 0
\(328\) −0.460183 1.41630i −0.0254093 0.0782019i
\(329\) −4.40244 13.5493i −0.242715 0.746998i
\(330\) 0 0
\(331\) −3.06247 + 9.42530i −0.168328 + 0.518061i −0.999266 0.0383039i \(-0.987804\pi\)
0.830938 + 0.556365i \(0.187804\pi\)
\(332\) 9.96783 0.547056
\(333\) 0 0
\(334\) −1.75683 + 1.27641i −0.0961293 + 0.0698420i
\(335\) 23.4429 24.9893i 1.28082 1.36531i
\(336\) 0 0
\(337\) 8.03812 5.84003i 0.437864 0.318127i −0.346922 0.937894i \(-0.612773\pi\)
0.784786 + 0.619767i \(0.212773\pi\)
\(338\) −2.35506 + 1.71105i −0.128099 + 0.0930690i
\(339\) 0 0
\(340\) 2.81805 + 1.32435i 0.152830 + 0.0718228i
\(341\) 17.0425 12.3821i 0.922904 0.670529i
\(342\) 0 0
\(343\) 0.930796 0.0502583
\(344\) −0.833625 + 2.56564i −0.0449461 + 0.138330i
\(345\) 0 0
\(346\) −1.97593 6.08130i −0.106227 0.326933i
\(347\) 6.06757 + 18.6741i 0.325724 + 1.00248i 0.971113 + 0.238622i \(0.0766956\pi\)
−0.645388 + 0.763855i \(0.723304\pi\)
\(348\) 0 0
\(349\) 1.48432 0.0794538 0.0397269 0.999211i \(-0.487351\pi\)
0.0397269 + 0.999211i \(0.487351\pi\)
\(350\) 1.20390 + 18.8339i 0.0643510 + 1.00671i
\(351\) 0 0
\(352\) 3.05361 + 2.21858i 0.162758 + 0.118251i
\(353\) −3.17632 9.77569i −0.169058 0.520308i 0.830254 0.557385i \(-0.188195\pi\)
−0.999312 + 0.0370772i \(0.988195\pi\)
\(354\) 0 0
\(355\) −1.86959 + 14.8593i −0.0992277 + 0.788649i
\(356\) −4.48391 + 13.8001i −0.237647 + 0.731402i
\(357\) 0 0
\(358\) 2.47630 7.62127i 0.130877 0.402797i
\(359\) −8.39154 + 6.09681i −0.442889 + 0.321777i −0.786782 0.617231i \(-0.788254\pi\)
0.343893 + 0.939009i \(0.388254\pi\)
\(360\) 0 0
\(361\) 2.97859 + 2.16408i 0.156768 + 0.113899i
\(362\) −8.78826 + 6.38504i −0.461901 + 0.335590i
\(363\) 0 0
\(364\) −9.69922 7.04690i −0.508377 0.369358i
\(365\) −5.57300 10.1252i −0.291704 0.529978i
\(366\) 0 0
\(367\) 8.05741 24.7981i 0.420593 1.29445i −0.486558 0.873648i \(-0.661748\pi\)
0.907151 0.420804i \(-0.138252\pi\)
\(368\) −0.891031 −0.0464482
\(369\) 0 0
\(370\) −14.2622 6.70254i −0.741455 0.348448i
\(371\) −13.5489 41.6993i −0.703426 2.16492i
\(372\) 0 0
\(373\) −7.65001 5.55806i −0.396102 0.287785i 0.371849 0.928293i \(-0.378724\pi\)
−0.767952 + 0.640508i \(0.778724\pi\)
\(374\) −5.25595 −0.271779
\(375\) 0 0
\(376\) 3.77447 0.194653
\(377\) 0.126472 + 0.0918876i 0.00651366 + 0.00473245i
\(378\) 0 0
\(379\) −10.9163 33.5968i −0.560731 1.72575i −0.680307 0.732927i \(-0.738154\pi\)
0.119576 0.992825i \(-0.461846\pi\)
\(380\) 7.92059 + 3.72230i 0.406318 + 0.190950i
\(381\) 0 0
\(382\) −8.18577 −0.418820
\(383\) −9.21407 + 28.3580i −0.470817 + 1.44902i 0.380700 + 0.924698i \(0.375683\pi\)
−0.851517 + 0.524327i \(0.824317\pi\)
\(384\) 0 0
\(385\) −15.3609 27.9083i −0.782865 1.42234i
\(386\) −14.2044 10.3201i −0.722985 0.525280i
\(387\) 0 0
\(388\) 0.0729490 0.0530006i 0.00370343 0.00269070i
\(389\) −17.2942 12.5649i −0.876848 0.637068i 0.0555675 0.998455i \(-0.482303\pi\)
−0.932416 + 0.361387i \(0.882303\pi\)
\(390\) 0 0
\(391\) 1.00380 0.729301i 0.0507642 0.0368824i
\(392\) −2.23932 + 6.89193i −0.113103 + 0.348095i
\(393\) 0 0
\(394\) 1.47012 4.52458i 0.0740638 0.227945i
\(395\) 0.504306 4.00816i 0.0253744 0.201673i
\(396\) 0 0
\(397\) 6.49555 + 19.9913i 0.326002 + 1.00333i 0.970986 + 0.239136i \(0.0768642\pi\)
−0.644984 + 0.764196i \(0.723136\pi\)
\(398\) 11.7566 + 8.54169i 0.589307 + 0.428156i
\(399\) 0 0
\(400\) −4.84416 1.23859i −0.242208 0.0619295i
\(401\) −16.7820 −0.838053 −0.419026 0.907974i \(-0.637629\pi\)
−0.419026 + 0.907974i \(0.637629\pi\)
\(402\) 0 0
\(403\) −5.47805 16.8597i −0.272881 0.839842i
\(404\) −5.06122 15.5768i −0.251805 0.774977i
\(405\) 0 0
\(406\) 0.0574054 0.176676i 0.00284898 0.00876826i
\(407\) 26.6004 1.31853
\(408\) 0 0
\(409\) −29.4165 + 21.3723i −1.45455 + 1.05679i −0.469809 + 0.882768i \(0.655677\pi\)
−0.984741 + 0.174025i \(0.944323\pi\)
\(410\) −3.01371 1.41630i −0.148836 0.0699459i
\(411\) 0 0
\(412\) 0.983915 0.714856i 0.0484740 0.0352184i
\(413\) −2.10722 + 1.53098i −0.103689 + 0.0753347i
\(414\) 0 0
\(415\) 15.2495 16.2554i 0.748571 0.797948i
\(416\) 2.56969 1.86699i 0.125990 0.0915368i
\(417\) 0 0
\(418\) −14.7727 −0.722557
\(419\) 10.6731 32.8484i 0.521415 1.60475i −0.249884 0.968276i \(-0.580392\pi\)
0.771298 0.636474i \(-0.219608\pi\)
\(420\) 0 0
\(421\) 3.00798 + 9.25762i 0.146600 + 0.451189i 0.997213 0.0746033i \(-0.0237691\pi\)
−0.850613 + 0.525792i \(0.823769\pi\)
\(422\) 4.36823 + 13.4440i 0.212642 + 0.654445i
\(423\) 0 0
\(424\) 11.6163 0.564136
\(425\) 6.47100 2.56956i 0.313890 0.124642i
\(426\) 0 0
\(427\) −31.6364 22.9852i −1.53099 1.11233i
\(428\) 3.34124 + 10.2833i 0.161505 + 0.497061i
\(429\) 0 0
\(430\) 2.90867 + 5.28457i 0.140269 + 0.254845i
\(431\) 0.956560 2.94399i 0.0460759 0.141807i −0.925372 0.379061i \(-0.876247\pi\)
0.971448 + 0.237254i \(0.0762472\pi\)
\(432\) 0 0
\(433\) −5.63542 + 17.3440i −0.270821 + 0.833501i 0.719474 + 0.694519i \(0.244383\pi\)
−0.990295 + 0.138981i \(0.955617\pi\)
\(434\) −17.0425 + 12.3821i −0.818067 + 0.594360i
\(435\) 0 0
\(436\) −9.23519 6.70976i −0.442285 0.321339i
\(437\) 2.82134 2.04982i 0.134963 0.0980563i
\(438\) 0 0
\(439\) 21.4595 + 15.5912i 1.02421 + 0.744129i 0.967141 0.254242i \(-0.0818259\pi\)
0.0570645 + 0.998370i \(0.481826\pi\)
\(440\) 8.28968 1.58565i 0.395195 0.0755929i
\(441\) 0 0
\(442\) −1.36679 + 4.20655i −0.0650115 + 0.200085i
\(443\) −35.5267 −1.68793 −0.843963 0.536401i \(-0.819783\pi\)
−0.843963 + 0.536401i \(0.819783\pi\)
\(444\) 0 0
\(445\) 15.6452 + 28.4247i 0.741653 + 1.34746i
\(446\) −1.42527 4.38652i −0.0674883 0.207708i
\(447\) 0 0
\(448\) −3.05361 2.21858i −0.144269 0.104818i
\(449\) −16.1841 −0.763776 −0.381888 0.924209i \(-0.624726\pi\)
−0.381888 + 0.924209i \(0.624726\pi\)
\(450\) 0 0
\(451\) 5.62087 0.264676
\(452\) −8.43232 6.12644i −0.396623 0.288163i
\(453\) 0 0
\(454\) −1.94259 5.97869i −0.0911705 0.280594i
\(455\) −26.3306 + 5.03652i −1.23440 + 0.236116i
\(456\) 0 0
\(457\) 23.7205 1.10960 0.554799 0.831984i \(-0.312795\pi\)
0.554799 + 0.831984i \(0.312795\pi\)
\(458\) −5.48103 + 16.8689i −0.256112 + 0.788230i
\(459\) 0 0
\(460\) −1.36317 + 1.45309i −0.0635580 + 0.0677504i
\(461\) −6.36936 4.62761i −0.296651 0.215529i 0.429497 0.903068i \(-0.358691\pi\)
−0.726147 + 0.687539i \(0.758691\pi\)
\(462\) 0 0
\(463\) −12.4775 + 9.06543i −0.579878 + 0.421306i −0.838680 0.544624i \(-0.816672\pi\)
0.258802 + 0.965930i \(0.416672\pi\)
\(464\) 0.0398173 + 0.0289290i 0.00184847 + 0.00134299i
\(465\) 0 0
\(466\) −2.07437 + 1.50712i −0.0960932 + 0.0698158i
\(467\) 5.26481 16.2034i 0.243626 0.749805i −0.752233 0.658897i \(-0.771023\pi\)
0.995859 0.0909075i \(-0.0289768\pi\)
\(468\) 0 0
\(469\) 17.8728 55.0069i 0.825290 2.53998i
\(470\) 5.77447 6.15537i 0.266356 0.283926i
\(471\) 0 0
\(472\) −0.213245 0.656300i −0.00981538 0.0302086i
\(473\) −8.23762 5.98498i −0.378766 0.275190i
\(474\) 0 0
\(475\) 18.1878 7.22218i 0.834514 0.331376i
\(476\) 5.25595 0.240906
\(477\) 0 0
\(478\) 2.91765 + 8.97961i 0.133450 + 0.410718i
\(479\) 7.75544 + 23.8688i 0.354355 + 1.09059i 0.956382 + 0.292118i \(0.0943598\pi\)
−0.602027 + 0.798476i \(0.705640\pi\)
\(480\) 0 0
\(481\) 6.91734 21.2894i 0.315403 0.970712i
\(482\) 29.4346 1.34071
\(483\) 0 0
\(484\) −2.62656 + 1.90831i −0.119389 + 0.0867412i
\(485\) 0.0251701 0.200049i 0.00114292 0.00908375i
\(486\) 0 0
\(487\) 11.0735 8.04536i 0.501788 0.364570i −0.307912 0.951415i \(-0.599630\pi\)
0.809699 + 0.586845i \(0.199630\pi\)
\(488\) 8.38168 6.08965i 0.379421 0.275665i
\(489\) 0 0
\(490\) 7.81341 + 14.1957i 0.352974 + 0.641295i
\(491\) −2.08733 + 1.51654i −0.0942001 + 0.0684403i −0.633888 0.773425i \(-0.718542\pi\)
0.539688 + 0.841865i \(0.318542\pi\)
\(492\) 0 0
\(493\) −0.0685347 −0.00308665
\(494\) −3.84159 + 11.8232i −0.172841 + 0.531950i
\(495\) 0 0
\(496\) −1.72466 5.30795i −0.0774394 0.238334i
\(497\) 7.81199 + 24.0428i 0.350416 + 1.07847i
\(498\) 0 0
\(499\) −39.0539 −1.74829 −0.874146 0.485664i \(-0.838578\pi\)
−0.874146 + 0.485664i \(0.838578\pi\)
\(500\) −9.43085 + 6.00492i −0.421760 + 0.268548i
\(501\) 0 0
\(502\) 4.86025 + 3.53118i 0.216923 + 0.157604i
\(503\) −3.69387 11.3686i −0.164702 0.506899i 0.834313 0.551292i \(-0.185865\pi\)
−0.999014 + 0.0443923i \(0.985865\pi\)
\(504\) 0 0
\(505\) −33.1456 15.5768i −1.47496 0.693160i
\(506\) 1.03928 3.19856i 0.0462014 0.142193i
\(507\) 0 0
\(508\) −1.09668 + 3.37524i −0.0486574 + 0.149752i
\(509\) −3.94254 + 2.86442i −0.174750 + 0.126963i −0.671722 0.740803i \(-0.734445\pi\)
0.496972 + 0.867767i \(0.334445\pi\)
\(510\) 0 0
\(511\) −15.7832 11.4672i −0.698210 0.507279i
\(512\) 0.809017 0.587785i 0.0357538 0.0259767i
\(513\) 0 0
\(514\) 11.0257 + 8.01067i 0.486325 + 0.353336i
\(515\) 0.339487 2.69820i 0.0149596 0.118897i
\(516\) 0 0
\(517\) −4.40244 + 13.5493i −0.193619 + 0.595899i
\(518\) −26.6004 −1.16876
\(519\) 0 0
\(520\) 0.886640 7.04690i 0.0388817 0.309027i
\(521\) 2.70131 + 8.31378i 0.118347 + 0.364233i 0.992630 0.121182i \(-0.0386684\pi\)
−0.874284 + 0.485415i \(0.838668\pi\)
\(522\) 0 0
\(523\) 17.0534 + 12.3900i 0.745694 + 0.541778i 0.894489 0.447090i \(-0.147540\pi\)
−0.148795 + 0.988868i \(0.547540\pi\)
\(524\) −4.05324 −0.177067
\(525\) 0 0
\(526\) −9.16294 −0.399523
\(527\) 6.28743 + 4.56809i 0.273885 + 0.198989i
\(528\) 0 0
\(529\) −6.86205 21.1192i −0.298350 0.918227i
\(530\) 17.7715 18.9437i 0.771943 0.822863i
\(531\) 0 0
\(532\) 14.7727 0.640478
\(533\) 1.46169 4.49861i 0.0633126 0.194856i
\(534\) 0 0
\(535\) 21.8816 + 10.2833i 0.946022 + 0.444585i
\(536\) 12.3969 + 9.00687i 0.535464 + 0.389038i
\(537\) 0 0
\(538\) −22.7355 + 16.5183i −0.980197 + 0.712155i
\(539\) −22.1283 16.0771i −0.953133 0.692492i
\(540\) 0 0
\(541\) −26.5406 + 19.2829i −1.14107 + 0.829036i −0.987268 0.159066i \(-0.949152\pi\)
−0.153802 + 0.988102i \(0.549152\pi\)
\(542\) 2.81162 8.65329i 0.120770 0.371690i
\(543\) 0 0
\(544\) −0.430307 + 1.32435i −0.0184492 + 0.0567809i
\(545\) −25.0709 + 4.79557i −1.07392 + 0.205419i
\(546\) 0 0
\(547\) −1.69044 5.20264i −0.0722781 0.222449i 0.908391 0.418121i \(-0.137311\pi\)
−0.980669 + 0.195672i \(0.937311\pi\)
\(548\) −2.88636 2.09706i −0.123299 0.0895820i
\(549\) 0 0
\(550\) 10.0963 15.9446i 0.430508 0.679879i
\(551\) −0.192628 −0.00820623
\(552\) 0 0
\(553\) −2.10722 6.48535i −0.0896080 0.275785i
\(554\) −5.80613 17.8694i −0.246679 0.759199i
\(555\) 0 0
\(556\) −3.07349 + 9.45923i −0.130345 + 0.401161i
\(557\) 5.19840 0.220263 0.110132 0.993917i \(-0.464873\pi\)
0.110132 + 0.993917i \(0.464873\pi\)
\(558\) 0 0
\(559\) −6.93218 + 5.03652i −0.293200 + 0.213022i
\(560\) −8.28968 + 1.58565i −0.350303 + 0.0670059i
\(561\) 0 0
\(562\) −6.37633 + 4.63268i −0.268969 + 0.195418i
\(563\) −4.05741 + 2.94788i −0.170999 + 0.124238i −0.669993 0.742367i \(-0.733703\pi\)
0.498994 + 0.866605i \(0.333703\pi\)
\(564\) 0 0
\(565\) −22.8913 + 4.37866i −0.963046 + 0.184212i
\(566\) −14.8049 + 10.7564i −0.622296 + 0.452124i
\(567\) 0 0
\(568\) −6.69767 −0.281028
\(569\) 12.9303 39.7952i 0.542064 1.66830i −0.185805 0.982587i \(-0.559489\pi\)
0.727869 0.685716i \(-0.240511\pi\)
\(570\) 0 0
\(571\) −13.7723 42.3869i −0.576355 1.77384i −0.631519 0.775360i \(-0.717568\pi\)
0.0551642 0.998477i \(-0.482432\pi\)
\(572\) 3.70477 + 11.4021i 0.154904 + 0.476747i
\(573\) 0 0
\(574\) −5.62087 −0.234611
\(575\) 0.284202 + 4.44608i 0.0118520 + 0.185414i
\(576\) 0 0
\(577\) 20.3401 + 14.7779i 0.846769 + 0.615213i 0.924253 0.381780i \(-0.124689\pi\)
−0.0774845 + 0.996994i \(0.524689\pi\)
\(578\) 4.65409 + 14.3238i 0.193584 + 0.595792i
\(579\) 0 0
\(580\) 0.108093 0.0206760i 0.00448831 0.000858524i
\(581\) 11.6262 35.7818i 0.482337 1.48448i
\(582\) 0 0
\(583\) −13.5489 + 41.6993i −0.561140 + 1.72701i
\(584\) 4.18158 3.03810i 0.173035 0.125717i
\(585\) 0 0
\(586\) 23.8652 + 17.3391i 0.985861 + 0.716270i
\(587\) 17.2770 12.5525i 0.713099 0.518097i −0.171073 0.985258i \(-0.554723\pi\)
0.884172 + 0.467162i \(0.154723\pi\)
\(588\) 0 0
\(589\) 17.6719 + 12.8394i 0.728157 + 0.529037i
\(590\) −1.39653 0.656300i −0.0574940 0.0270194i
\(591\) 0 0
\(592\) 2.17779 6.70254i 0.0895065 0.275473i
\(593\) 33.4430 1.37334 0.686669 0.726970i \(-0.259072\pi\)
0.686669 + 0.726970i \(0.259072\pi\)
\(594\) 0 0
\(595\) 8.04095 8.57136i 0.329647 0.351391i
\(596\) 6.02900 + 18.5554i 0.246957 + 0.760057i
\(597\) 0 0
\(598\) −2.28968 1.66355i −0.0936318 0.0680275i
\(599\) −26.3174 −1.07530 −0.537650 0.843168i \(-0.680688\pi\)
−0.537650 + 0.843168i \(0.680688\pi\)
\(600\) 0 0
\(601\) 20.9964 0.856462 0.428231 0.903669i \(-0.359137\pi\)
0.428231 + 0.903669i \(0.359137\pi\)
\(602\) 8.23762 + 5.98498i 0.335740 + 0.243930i
\(603\) 0 0
\(604\) −5.69592 17.5302i −0.231764 0.713295i
\(605\) −0.906260 + 7.20284i −0.0368447 + 0.292837i
\(606\) 0 0
\(607\) 9.32822 0.378621 0.189310 0.981917i \(-0.439375\pi\)
0.189310 + 0.981917i \(0.439375\pi\)
\(608\) −1.20945 + 3.72230i −0.0490496 + 0.150959i
\(609\) 0 0
\(610\) 2.89199 22.9852i 0.117093 0.930643i
\(611\) 9.69922 + 7.04690i 0.392389 + 0.285087i
\(612\) 0 0
\(613\) 25.9724 18.8700i 1.04902 0.762154i 0.0769902 0.997032i \(-0.475469\pi\)
0.972025 + 0.234878i \(0.0754690\pi\)
\(614\) 11.2560 + 8.17793i 0.454253 + 0.330034i
\(615\) 0 0
\(616\) 11.5257 8.37394i 0.464385 0.337396i
\(617\) 9.86557 30.3631i 0.397173 1.22237i −0.530084 0.847945i \(-0.677840\pi\)
0.927257 0.374427i \(-0.122160\pi\)
\(618\) 0 0
\(619\) −1.40420 + 4.32167i −0.0564394 + 0.173703i −0.975302 0.220875i \(-0.929109\pi\)
0.918863 + 0.394577i \(0.129109\pi\)
\(620\) −11.2947 5.30795i −0.453605 0.213172i
\(621\) 0 0
\(622\) 8.02319 + 24.6928i 0.321701 + 0.990093i
\(623\) 44.3086 + 32.1921i 1.77519 + 1.28975i
\(624\) 0 0
\(625\) −4.63525 + 24.5665i −0.185410 + 0.982661i
\(626\) −9.47389 −0.378653
\(627\) 0 0
\(628\) 3.13851 + 9.65934i 0.125240 + 0.385450i
\(629\) 3.03257 + 9.33329i 0.120916 + 0.372143i
\(630\) 0 0
\(631\) −8.31756 + 25.5988i −0.331117 + 1.01907i 0.637486 + 0.770462i \(0.279974\pi\)
−0.968603 + 0.248611i \(0.920026\pi\)
\(632\) 1.80664 0.0718642
\(633\) 0 0
\(634\) −19.8269 + 14.4051i −0.787427 + 0.572100i
\(635\) 3.82652 + 6.95215i 0.151851 + 0.275888i
\(636\) 0 0
\(637\) −18.6215 + 13.5293i −0.737813 + 0.536052i
\(638\) −0.150289 + 0.109192i −0.00595001 + 0.00432293i
\(639\) 0 0
\(640\) 0.279141 2.21858i 0.0110340 0.0876969i
\(641\) 28.9303 21.0191i 1.14268 0.830205i 0.155189 0.987885i \(-0.450401\pi\)
0.987490 + 0.157679i \(0.0504013\pi\)
\(642\) 0 0
\(643\) 28.2255 1.11311 0.556553 0.830812i \(-0.312124\pi\)
0.556553 + 0.830812i \(0.312124\pi\)
\(644\) −1.03928 + 3.19856i −0.0409532 + 0.126041i
\(645\) 0 0
\(646\) −1.68416 5.18330i −0.0662623 0.203934i
\(647\) −0.394848 1.21522i −0.0155231 0.0477751i 0.942995 0.332807i \(-0.107996\pi\)
−0.958518 + 0.285032i \(0.907996\pi\)
\(648\) 0 0
\(649\) 2.60466 0.102242
\(650\) −10.1356 12.2268i −0.397550 0.479575i
\(651\) 0 0
\(652\) 15.0481 + 10.9331i 0.589327 + 0.428171i
\(653\) 8.47040 + 26.0692i 0.331472 + 1.02017i 0.968434 + 0.249272i \(0.0801912\pi\)
−0.636961 + 0.770896i \(0.719809\pi\)
\(654\) 0 0
\(655\) −6.20096 + 6.60999i −0.242291 + 0.258274i
\(656\) 0.460183 1.41630i 0.0179671 0.0552971i
\(657\) 0 0
\(658\) 4.40244 13.5493i 0.171625 0.528208i
\(659\) −33.3535 + 24.2327i −1.29927 + 0.943972i −0.999948 0.0101814i \(-0.996759\pi\)
−0.299318 + 0.954153i \(0.596759\pi\)
\(660\) 0 0
\(661\) 21.4653 + 15.5955i 0.834904 + 0.606593i 0.920942 0.389699i \(-0.127421\pi\)
−0.0860388 + 0.996292i \(0.527421\pi\)
\(662\) −8.01764 + 5.82516i −0.311614 + 0.226401i
\(663\) 0 0
\(664\) 8.06414 + 5.85894i 0.312949 + 0.227371i
\(665\) 22.6004 24.0912i 0.876407 0.934217i
\(666\) 0 0
\(667\) 0.0135516 0.0417075i 0.000524719 0.00161492i
\(668\) −2.17156 −0.0840201
\(669\) 0 0
\(670\) 33.6540 6.43735i 1.30017 0.248696i
\(671\) 12.0840 + 37.1908i 0.466499 + 1.43574i
\(672\) 0 0
\(673\) 6.42142 + 4.66543i 0.247527 + 0.179839i 0.704630 0.709575i \(-0.251113\pi\)
−0.457103 + 0.889414i \(0.651113\pi\)
\(674\) 9.93566 0.382707
\(675\) 0 0
\(676\) −2.91102 −0.111962
\(677\) 23.8667 + 17.3402i 0.917271 + 0.666436i 0.942843 0.333237i \(-0.108141\pi\)
−0.0255722 + 0.999673i \(0.508141\pi\)
\(678\) 0 0
\(679\) −0.105172 0.323686i −0.00403613 0.0124219i
\(680\) 1.50142 + 2.72783i 0.0575768 + 0.104607i
\(681\) 0 0
\(682\) 21.0657 0.806647
\(683\) −11.6650 + 35.9012i −0.446349 + 1.37372i 0.434648 + 0.900600i \(0.356873\pi\)
−0.880997 + 0.473121i \(0.843127\pi\)
\(684\) 0 0
\(685\) −7.83564 + 1.49880i −0.299384 + 0.0572663i
\(686\) 0.753030 + 0.547108i 0.0287508 + 0.0208887i
\(687\) 0 0
\(688\) −2.18246 + 1.58565i −0.0832055 + 0.0604523i
\(689\) 29.8503 + 21.6875i 1.13721 + 0.826228i
\(690\) 0 0
\(691\) −14.2843 + 10.3782i −0.543401 + 0.394804i −0.825347 0.564626i \(-0.809020\pi\)
0.281945 + 0.959430i \(0.409020\pi\)
\(692\) 1.97593 6.08130i 0.0751137 0.231176i
\(693\) 0 0
\(694\) −6.06757 + 18.6741i −0.230322 + 0.708858i
\(695\) 10.7240 + 19.4837i 0.406783 + 0.739058i
\(696\) 0 0
\(697\) 0.640805 + 1.97219i 0.0242722 + 0.0747022i
\(698\) 1.20084 + 0.872461i 0.0454524 + 0.0330231i
\(699\) 0 0
\(700\) −10.0963 + 15.9446i −0.381605 + 0.602648i
\(701\) 16.8372 0.635931 0.317965 0.948102i \(-0.397000\pi\)
0.317965 + 0.948102i \(0.397000\pi\)
\(702\) 0 0
\(703\) 8.52354 + 26.2328i 0.321471 + 0.989387i
\(704\) 1.16637 + 3.58973i 0.0439594 + 0.135293i
\(705\) 0 0
\(706\) 3.17632 9.77569i 0.119542 0.367913i
\(707\) −61.8200 −2.32498
\(708\) 0 0
\(709\) 23.1615 16.8278i 0.869849 0.631982i −0.0606978 0.998156i \(-0.519333\pi\)
0.930546 + 0.366174i \(0.119333\pi\)
\(710\) −10.2466 + 10.9225i −0.384548 + 0.409914i
\(711\) 0 0
\(712\) −11.7390 + 8.52891i −0.439939 + 0.319635i
\(713\) −4.02319 + 2.92302i −0.150670 + 0.109468i
\(714\) 0 0
\(715\) 24.2623 + 11.4021i 0.907359 + 0.426415i
\(716\) 6.48304 4.71020i 0.242283 0.176029i
\(717\) 0 0
\(718\) −10.3725 −0.387099
\(719\) 2.54857 7.84368i 0.0950455 0.292520i −0.892220 0.451601i \(-0.850853\pi\)
0.987266 + 0.159081i \(0.0508531\pi\)
\(720\) 0 0
\(721\) −1.41853 4.36578i −0.0528287 0.162590i
\(722\) 1.13772 + 3.50155i 0.0423416 + 0.130314i
\(723\) 0 0
\(724\) −10.8629 −0.403716
\(725\) 0.131650 0.207908i 0.00488937 0.00772152i
\(726\) 0 0
\(727\) 1.71013 + 1.24248i 0.0634251 + 0.0460810i 0.619046 0.785355i \(-0.287519\pi\)
−0.555621 + 0.831436i \(0.687519\pi\)
\(728\) −3.70477 11.4021i −0.137308 0.422591i
\(729\) 0 0
\(730\) 1.44280 11.4672i 0.0534005 0.424420i
\(731\) 1.16082 3.57265i 0.0429346 0.132139i
\(732\) 0 0
\(733\) 13.9537 42.9451i 0.515393 1.58622i −0.267174 0.963648i \(-0.586090\pi\)
0.782567 0.622567i \(-0.213910\pi\)
\(734\) 21.0946 15.3261i 0.778614 0.565697i
\(735\) 0 0
\(736\) −0.720859 0.523735i −0.0265712 0.0193051i
\(737\) −46.7917 + 33.9961i −1.72359 + 1.25226i
\(738\) 0 0
\(739\) −24.2478 17.6171i −0.891969 0.648054i 0.0444213 0.999013i \(-0.485856\pi\)
−0.936391 + 0.350959i \(0.885856\pi\)
\(740\) −7.59869 13.8056i −0.279334 0.507503i
\(741\) 0 0
\(742\) 13.5489 41.6993i 0.497397 1.53083i
\(743\) −17.6562 −0.647741 −0.323871 0.946101i \(-0.604984\pi\)
−0.323871 + 0.946101i \(0.604984\pi\)
\(744\) 0 0
\(745\) 39.4835 + 18.5554i 1.44656 + 0.679816i
\(746\) −2.92204 8.99312i −0.106984 0.329262i
\(747\) 0 0
\(748\) −4.25215 3.08937i −0.155474 0.112959i
\(749\) 40.8113 1.49121
\(750\) 0 0
\(751\) 30.1342 1.09961 0.549806 0.835293i \(-0.314702\pi\)
0.549806 + 0.835293i \(0.314702\pi\)
\(752\) 3.05361 + 2.21858i 0.111354 + 0.0809031i
\(753\) 0 0
\(754\) 0.0483082 + 0.148677i 0.00175928 + 0.00541451i
\(755\) −37.3022 17.5302i −1.35757 0.637990i
\(756\) 0 0
\(757\) −4.90706 −0.178350 −0.0891750 0.996016i \(-0.528423\pi\)
−0.0891750 + 0.996016i \(0.528423\pi\)
\(758\) 10.9163 33.5968i 0.396497 1.22029i
\(759\) 0 0
\(760\) 4.21998 + 7.66701i 0.153075 + 0.278112i
\(761\) 10.7466 + 7.80786i 0.389564 + 0.283035i 0.765277 0.643701i \(-0.222602\pi\)
−0.375713 + 0.926736i \(0.622602\pi\)
\(762\) 0 0
\(763\) −34.8579 + 25.3258i −1.26194 + 0.916854i
\(764\) −6.62243 4.81147i −0.239591 0.174073i
\(765\) 0 0
\(766\) −24.1227 + 17.5262i −0.871590 + 0.633247i
\(767\) 0.677332 2.08461i 0.0244571 0.0752711i
\(768\) 0 0
\(769\) −8.83716 + 27.1980i −0.318676 + 0.980784i 0.655539 + 0.755162i \(0.272442\pi\)
−0.974215 + 0.225623i \(0.927558\pi\)
\(770\) 3.97681 31.6072i 0.143314 1.13904i
\(771\) 0 0
\(772\) −5.42560 16.6983i −0.195272 0.600984i
\(773\) −36.4564 26.4871i −1.31124 0.952675i −0.999997 0.00234562i \(-0.999253\pi\)
−0.311247 0.950329i \(-0.600747\pi\)
\(774\) 0 0
\(775\) −25.9356 + 10.2987i −0.931634 + 0.369941i
\(776\) 0.0901699 0.00323691
\(777\) 0 0
\(778\) −6.60578 20.3305i −0.236829 0.728884i
\(779\) 1.80109 + 5.54318i 0.0645307 + 0.198605i
\(780\) 0 0
\(781\) 7.81199 24.0428i 0.279535 0.860320i
\(782\) 1.24076 0.0443695
\(783\) 0 0
\(784\) −5.86263 + 4.25945i −0.209379 + 0.152123i
\(785\) 20.5539 + 9.65934i 0.733600 + 0.344757i
\(786\) 0 0
\(787\) −20.8458 + 15.1454i −0.743074 + 0.539875i −0.893672 0.448720i \(-0.851880\pi\)
0.150598 + 0.988595i \(0.451880\pi\)
\(788\) 3.84883