Properties

Label 950.2.e.n.201.2
Level $950$
Weight $2$
Character 950.201
Analytic conductor $7.586$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \(x^{10} + 10 x^{8} - 12 x^{7} + 85 x^{6} - 70 x^{5} + 186 x^{4} - 110 x^{3} + 285 x^{2} - 150 x + 100\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.2
Root \(-0.664633 + 1.15118i\) of defining polynomial
Character \(\chi\) \(=\) 950.201
Dual form 950.2.e.n.501.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.664633 + 1.15118i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.664633 - 1.15118i) q^{6} -2.32927 q^{7} +1.00000 q^{8} +(0.616527 + 1.06786i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.664633 + 1.15118i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.664633 - 1.15118i) q^{6} -2.32927 q^{7} +1.00000 q^{8} +(0.616527 + 1.06786i) q^{9} +6.39380 q^{11} +1.32927 q^{12} +(-0.429320 - 0.743604i) q^{13} +(1.16463 - 2.01720i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.34506 - 4.06176i) q^{17} -1.23305 q^{18} +(3.75178 - 2.21903i) q^{19} +(1.54811 - 2.68140i) q^{21} +(-3.19690 + 5.53719i) q^{22} +(1.73531 + 3.00565i) q^{23} +(-0.664633 + 1.15118i) q^{24} +0.858640 q^{26} -5.62685 q^{27} +(1.16463 + 2.01720i) q^{28} +(2.21048 + 3.82866i) q^{29} -8.25244 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.24953 + 7.36040i) q^{33} +(2.34506 + 4.06176i) q^{34} +(0.616527 - 1.06786i) q^{36} +9.76821 q^{37} +(0.0458469 + 4.35866i) q^{38} +1.14136 q^{39} +(-1.84506 + 3.19574i) q^{41} +(1.54811 + 2.68140i) q^{42} +(-3.56232 + 6.17012i) q^{43} +(-3.19690 - 5.53719i) q^{44} -3.47063 q^{46} +(3.59684 + 6.22992i) q^{47} +(-0.664633 - 1.15118i) q^{48} -1.57452 q^{49} +(3.11721 + 5.39916i) q^{51} +(-0.429320 + 0.743604i) q^{52} +(3.10295 + 5.37446i) q^{53} +(2.81343 - 4.87300i) q^{54} -2.32927 q^{56} +(0.0609427 + 5.79381i) q^{57} -4.42096 q^{58} +(3.09395 - 5.35888i) q^{59} +(4.01037 + 6.94616i) q^{61} +(4.12622 - 7.14682i) q^{62} +(-1.43605 - 2.48732i) q^{63} +1.00000 q^{64} +(-4.24953 - 7.36040i) q^{66} +(2.45257 + 4.24798i) q^{67} -4.69012 q^{68} -4.61338 q^{69} +(-1.10005 + 1.90535i) q^{71} +(0.616527 + 1.06786i) q^{72} +(2.32859 - 4.03323i) q^{73} +(-4.88411 + 8.45952i) q^{74} +(-3.79763 - 2.13962i) q^{76} -14.8928 q^{77} +(-0.570680 + 0.988447i) q^{78} +(-5.79153 + 10.0312i) q^{79} +(1.89021 - 3.27394i) q^{81} +(-1.84506 - 3.19574i) q^{82} +6.07809 q^{83} -3.09621 q^{84} +(-3.56232 - 6.17012i) q^{86} -5.87663 q^{87} +6.39380 q^{88} +(-5.64947 - 9.78517i) q^{89} +(1.00000 + 1.73205i) q^{91} +(1.73531 - 3.00565i) q^{92} +(5.48484 - 9.50002i) q^{93} -7.19369 q^{94} +1.32927 q^{96} +(5.67500 - 9.82939i) q^{97} +(0.787262 - 1.36358i) q^{98} +(3.94195 + 6.82766i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 5q^{2} - 5q^{4} - 10q^{7} + 10q^{8} - 5q^{9} + O(q^{10}) \) \( 10q - 5q^{2} - 5q^{4} - 10q^{7} + 10q^{8} - 5q^{9} - 6q^{11} - 2q^{13} + 5q^{14} - 5q^{16} + 4q^{17} + 10q^{18} + 11q^{19} + 20q^{21} + 3q^{22} + 13q^{23} + 4q^{26} + 36q^{27} + 5q^{28} + 2q^{29} - 8q^{31} - 5q^{32} + 2q^{33} + 4q^{34} - 5q^{36} + 10q^{37} - 13q^{38} + 16q^{39} + q^{41} + 20q^{42} + 3q^{44} - 26q^{46} - 10q^{47} - 20q^{49} + 4q^{51} - 2q^{52} + 5q^{53} - 18q^{54} - 10q^{56} - 10q^{57} - 4q^{58} + 22q^{59} - 2q^{61} + 4q^{62} + 23q^{63} + 10q^{64} + 2q^{66} + 4q^{67} - 8q^{68} - 24q^{69} - 22q^{71} - 5q^{72} + 26q^{73} - 5q^{74} + 2q^{76} + 10q^{77} - 8q^{78} + 2q^{79} - 5q^{81} + q^{82} + 12q^{83} - 40q^{84} - 20q^{87} - 6q^{88} - q^{89} + 10q^{91} + 13q^{92} + 6q^{93} + 20q^{94} + 8q^{97} + 10q^{98} + 13q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.664633 + 1.15118i −0.383726 + 0.664633i −0.991592 0.129407i \(-0.958693\pi\)
0.607866 + 0.794040i \(0.292026\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) −0.664633 1.15118i −0.271335 0.469966i
\(7\) −2.32927 −0.880379 −0.440190 0.897905i \(-0.645089\pi\)
−0.440190 + 0.897905i \(0.645089\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.616527 + 1.06786i 0.205509 + 0.355952i
\(10\) 0 0
\(11\) 6.39380 1.92780 0.963901 0.266260i \(-0.0857880\pi\)
0.963901 + 0.266260i \(0.0857880\pi\)
\(12\) 1.32927 0.383726
\(13\) −0.429320 0.743604i −0.119072 0.206239i 0.800328 0.599562i \(-0.204659\pi\)
−0.919400 + 0.393324i \(0.871325\pi\)
\(14\) 1.16463 2.01720i 0.311261 0.539120i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.34506 4.06176i 0.568760 0.985122i −0.427929 0.903813i \(-0.640757\pi\)
0.996689 0.0813093i \(-0.0259102\pi\)
\(18\) −1.23305 −0.290634
\(19\) 3.75178 2.21903i 0.860718 0.509081i
\(20\) 0 0
\(21\) 1.54811 2.68140i 0.337824 0.585129i
\(22\) −3.19690 + 5.53719i −0.681581 + 1.18053i
\(23\) 1.73531 + 3.00565i 0.361838 + 0.626721i 0.988263 0.152760i \(-0.0488161\pi\)
−0.626426 + 0.779481i \(0.715483\pi\)
\(24\) −0.664633 + 1.15118i −0.135668 + 0.234983i
\(25\) 0 0
\(26\) 0.858640 0.168393
\(27\) −5.62685 −1.08289
\(28\) 1.16463 + 2.01720i 0.220095 + 0.381216i
\(29\) 2.21048 + 3.82866i 0.410476 + 0.710965i 0.994942 0.100453i \(-0.0320293\pi\)
−0.584466 + 0.811418i \(0.698696\pi\)
\(30\) 0 0
\(31\) −8.25244 −1.48218 −0.741091 0.671405i \(-0.765691\pi\)
−0.741091 + 0.671405i \(0.765691\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −4.24953 + 7.36040i −0.739748 + 1.28128i
\(34\) 2.34506 + 4.06176i 0.402174 + 0.696586i
\(35\) 0 0
\(36\) 0.616527 1.06786i 0.102754 0.177976i
\(37\) 9.76821 1.60588 0.802942 0.596057i \(-0.203267\pi\)
0.802942 + 0.596057i \(0.203267\pi\)
\(38\) 0.0458469 + 4.35866i 0.00743735 + 0.707068i
\(39\) 1.14136 0.182764
\(40\) 0 0
\(41\) −1.84506 + 3.19574i −0.288150 + 0.499090i −0.973368 0.229248i \(-0.926373\pi\)
0.685218 + 0.728338i \(0.259707\pi\)
\(42\) 1.54811 + 2.68140i 0.238878 + 0.413749i
\(43\) −3.56232 + 6.17012i −0.543249 + 0.940934i 0.455466 + 0.890253i \(0.349473\pi\)
−0.998715 + 0.0506811i \(0.983861\pi\)
\(44\) −3.19690 5.53719i −0.481951 0.834763i
\(45\) 0 0
\(46\) −3.47063 −0.511716
\(47\) 3.59684 + 6.22992i 0.524654 + 0.908727i 0.999588 + 0.0287055i \(0.00913849\pi\)
−0.474934 + 0.880021i \(0.657528\pi\)
\(48\) −0.664633 1.15118i −0.0959315 0.166158i
\(49\) −1.57452 −0.224932
\(50\) 0 0
\(51\) 3.11721 + 5.39916i 0.436496 + 0.756033i
\(52\) −0.429320 + 0.743604i −0.0595360 + 0.103119i
\(53\) 3.10295 + 5.37446i 0.426222 + 0.738239i 0.996534 0.0831897i \(-0.0265108\pi\)
−0.570311 + 0.821429i \(0.693177\pi\)
\(54\) 2.81343 4.87300i 0.382859 0.663131i
\(55\) 0 0
\(56\) −2.32927 −0.311261
\(57\) 0.0609427 + 5.79381i 0.00807206 + 0.767409i
\(58\) −4.42096 −0.580500
\(59\) 3.09395 5.35888i 0.402798 0.697667i −0.591264 0.806478i \(-0.701371\pi\)
0.994062 + 0.108811i \(0.0347043\pi\)
\(60\) 0 0
\(61\) 4.01037 + 6.94616i 0.513475 + 0.889365i 0.999878 + 0.0156304i \(0.00497553\pi\)
−0.486403 + 0.873735i \(0.661691\pi\)
\(62\) 4.12622 7.14682i 0.524030 0.907647i
\(63\) −1.43605 2.48732i −0.180926 0.313373i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −4.24953 7.36040i −0.523081 0.906002i
\(67\) 2.45257 + 4.24798i 0.299629 + 0.518973i 0.976051 0.217541i \(-0.0698036\pi\)
−0.676422 + 0.736515i \(0.736470\pi\)
\(68\) −4.69012 −0.568760
\(69\) −4.61338 −0.555386
\(70\) 0 0
\(71\) −1.10005 + 1.90535i −0.130552 + 0.226124i −0.923890 0.382659i \(-0.875008\pi\)
0.793337 + 0.608782i \(0.208342\pi\)
\(72\) 0.616527 + 1.06786i 0.0726584 + 0.125848i
\(73\) 2.32859 4.03323i 0.272540 0.472054i −0.696971 0.717099i \(-0.745469\pi\)
0.969512 + 0.245045i \(0.0788028\pi\)
\(74\) −4.88411 + 8.45952i −0.567766 + 0.983399i
\(75\) 0 0
\(76\) −3.79763 2.13962i −0.435618 0.245432i
\(77\) −14.8928 −1.69720
\(78\) −0.570680 + 0.988447i −0.0646168 + 0.111920i
\(79\) −5.79153 + 10.0312i −0.651598 + 1.12860i 0.331137 + 0.943583i \(0.392568\pi\)
−0.982735 + 0.185018i \(0.940766\pi\)
\(80\) 0 0
\(81\) 1.89021 3.27394i 0.210023 0.363771i
\(82\) −1.84506 3.19574i −0.203753 0.352910i
\(83\) 6.07809 0.667157 0.333579 0.942722i \(-0.391744\pi\)
0.333579 + 0.942722i \(0.391744\pi\)
\(84\) −3.09621 −0.337824
\(85\) 0 0
\(86\) −3.56232 6.17012i −0.384135 0.665341i
\(87\) −5.87663 −0.630041
\(88\) 6.39380 0.681581
\(89\) −5.64947 9.78517i −0.598843 1.03723i −0.992992 0.118180i \(-0.962294\pi\)
0.394149 0.919046i \(-0.371039\pi\)
\(90\) 0 0
\(91\) 1.00000 + 1.73205i 0.104828 + 0.181568i
\(92\) 1.73531 3.00565i 0.180919 0.313361i
\(93\) 5.48484 9.50002i 0.568751 0.985106i
\(94\) −7.19369 −0.741972
\(95\) 0 0
\(96\) 1.32927 0.135668
\(97\) 5.67500 9.82939i 0.576209 0.998024i −0.419700 0.907663i \(-0.637865\pi\)
0.995909 0.0903607i \(-0.0288020\pi\)
\(98\) 0.787262 1.36358i 0.0795254 0.137742i
\(99\) 3.94195 + 6.82766i 0.396181 + 0.686205i
\(100\) 0 0
\(101\) −1.11042 1.92331i −0.110491 0.191377i 0.805477 0.592627i \(-0.201909\pi\)
−0.915968 + 0.401250i \(0.868576\pi\)
\(102\) −6.23441 −0.617299
\(103\) −3.26464 −0.321675 −0.160837 0.986981i \(-0.551419\pi\)
−0.160837 + 0.986981i \(0.551419\pi\)
\(104\) −0.429320 0.743604i −0.0420983 0.0729164i
\(105\) 0 0
\(106\) −6.20589 −0.602770
\(107\) −10.0000 −0.966736 −0.483368 0.875417i \(-0.660587\pi\)
−0.483368 + 0.875417i \(0.660587\pi\)
\(108\) 2.81343 + 4.87300i 0.270722 + 0.468904i
\(109\) 1.51717 2.62782i 0.145319 0.251699i −0.784173 0.620542i \(-0.786913\pi\)
0.929492 + 0.368843i \(0.120246\pi\)
\(110\) 0 0
\(111\) −6.49227 + 11.2449i −0.616219 + 1.06732i
\(112\) 1.16463 2.01720i 0.110047 0.190608i
\(113\) −4.97420 −0.467933 −0.233966 0.972245i \(-0.575171\pi\)
−0.233966 + 0.972245i \(0.575171\pi\)
\(114\) −5.04806 2.84413i −0.472794 0.266377i
\(115\) 0 0
\(116\) 2.21048 3.82866i 0.205238 0.355482i
\(117\) 0.529375 0.916904i 0.0489407 0.0847678i
\(118\) 3.09395 + 5.35888i 0.284821 + 0.493325i
\(119\) −5.46226 + 9.46092i −0.500725 + 0.867281i
\(120\) 0 0
\(121\) 29.8806 2.71642
\(122\) −8.02074 −0.726164
\(123\) −2.45257 4.24798i −0.221141 0.383028i
\(124\) 4.12622 + 7.14682i 0.370545 + 0.641803i
\(125\) 0 0
\(126\) 2.87211 0.255868
\(127\) 7.14949 + 12.3833i 0.634415 + 1.09884i 0.986639 + 0.162923i \(0.0520922\pi\)
−0.352224 + 0.935916i \(0.614574\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −4.73527 8.20172i −0.416917 0.722121i
\(130\) 0 0
\(131\) −1.18947 + 2.06022i −0.103924 + 0.180002i −0.913298 0.407292i \(-0.866473\pi\)
0.809374 + 0.587294i \(0.199807\pi\)
\(132\) 8.49905 0.739748
\(133\) −8.73890 + 5.16872i −0.757759 + 0.448185i
\(134\) −4.90515 −0.423740
\(135\) 0 0
\(136\) 2.34506 4.06176i 0.201087 0.348293i
\(137\) 4.54585 + 7.87364i 0.388378 + 0.672690i 0.992232 0.124405i \(-0.0397022\pi\)
−0.603854 + 0.797095i \(0.706369\pi\)
\(138\) 2.30669 3.99531i 0.196359 0.340103i
\(139\) 10.5329 + 18.2435i 0.893389 + 1.54739i 0.835786 + 0.549055i \(0.185012\pi\)
0.0576028 + 0.998340i \(0.481654\pi\)
\(140\) 0 0
\(141\) −9.56232 −0.805293
\(142\) −1.10005 1.90535i −0.0923145 0.159893i
\(143\) −2.74498 4.75445i −0.229547 0.397587i
\(144\) −1.23305 −0.102754
\(145\) 0 0
\(146\) 2.32859 + 4.03323i 0.192715 + 0.333793i
\(147\) 1.04648 1.81256i 0.0863122 0.149497i
\(148\) −4.88411 8.45952i −0.401471 0.695368i
\(149\) 3.17889 5.50600i 0.260425 0.451069i −0.705930 0.708282i \(-0.749471\pi\)
0.966355 + 0.257212i \(0.0828040\pi\)
\(150\) 0 0
\(151\) −3.05559 −0.248660 −0.124330 0.992241i \(-0.539678\pi\)
−0.124330 + 0.992241i \(0.539678\pi\)
\(152\) 3.75178 2.21903i 0.304310 0.179987i
\(153\) 5.78317 0.467541
\(154\) 7.44642 12.8976i 0.600050 1.03932i
\(155\) 0 0
\(156\) −0.570680 0.988447i −0.0456910 0.0791391i
\(157\) 4.07136 7.05180i 0.324930 0.562795i −0.656568 0.754267i \(-0.727993\pi\)
0.981498 + 0.191472i \(0.0613260\pi\)
\(158\) −5.79153 10.0312i −0.460749 0.798041i
\(159\) −8.24928 −0.654210
\(160\) 0 0
\(161\) −4.04200 7.00096i −0.318554 0.551753i
\(162\) 1.89021 + 3.27394i 0.148509 + 0.257225i
\(163\) 13.4100 1.05035 0.525177 0.850993i \(-0.323999\pi\)
0.525177 + 0.850993i \(0.323999\pi\)
\(164\) 3.69012 0.288150
\(165\) 0 0
\(166\) −3.03905 + 5.26378i −0.235876 + 0.408549i
\(167\) −6.49232 11.2450i −0.502391 0.870166i −0.999996 0.00276265i \(-0.999121\pi\)
0.497606 0.867403i \(-0.334213\pi\)
\(168\) 1.54811 2.68140i 0.119439 0.206874i
\(169\) 6.13137 10.6198i 0.471644 0.816911i
\(170\) 0 0
\(171\) 4.68269 + 2.63827i 0.358094 + 0.201754i
\(172\) 7.12464 0.543249
\(173\) 1.05780 1.83216i 0.0804228 0.139296i −0.823009 0.568029i \(-0.807706\pi\)
0.903432 + 0.428732i \(0.141040\pi\)
\(174\) 2.93831 5.08931i 0.222753 0.385819i
\(175\) 0 0
\(176\) −3.19690 + 5.53719i −0.240975 + 0.417381i
\(177\) 4.11268 + 7.12338i 0.309128 + 0.535426i
\(178\) 11.2989 0.846892
\(179\) −9.87938 −0.738420 −0.369210 0.929346i \(-0.620372\pi\)
−0.369210 + 0.929346i \(0.620372\pi\)
\(180\) 0 0
\(181\) −7.53974 13.0592i −0.560425 0.970684i −0.997459 0.0712395i \(-0.977305\pi\)
0.437034 0.899445i \(-0.356029\pi\)
\(182\) −2.00000 −0.148250
\(183\) −10.6617 −0.788135
\(184\) 1.73531 + 3.00565i 0.127929 + 0.221579i
\(185\) 0 0
\(186\) 5.48484 + 9.50002i 0.402168 + 0.696575i
\(187\) 14.9938 25.9701i 1.09646 1.89912i
\(188\) 3.59684 6.22992i 0.262327 0.454363i
\(189\) 13.1064 0.953352
\(190\) 0 0
\(191\) 8.84192 0.639779 0.319889 0.947455i \(-0.396354\pi\)
0.319889 + 0.947455i \(0.396354\pi\)
\(192\) −0.664633 + 1.15118i −0.0479657 + 0.0830791i
\(193\) 9.34642 16.1885i 0.672770 1.16527i −0.304346 0.952562i \(-0.598438\pi\)
0.977115 0.212710i \(-0.0682289\pi\)
\(194\) 5.67500 + 9.82939i 0.407441 + 0.705709i
\(195\) 0 0
\(196\) 0.787262 + 1.36358i 0.0562330 + 0.0973984i
\(197\) −16.3169 −1.16253 −0.581267 0.813713i \(-0.697443\pi\)
−0.581267 + 0.813713i \(0.697443\pi\)
\(198\) −7.88390 −0.560284
\(199\) 1.57452 + 2.72715i 0.111615 + 0.193323i 0.916422 0.400214i \(-0.131064\pi\)
−0.804807 + 0.593537i \(0.797731\pi\)
\(200\) 0 0
\(201\) −6.52024 −0.459902
\(202\) 2.22085 0.156258
\(203\) −5.14879 8.91797i −0.361374 0.625919i
\(204\) 3.11721 5.39916i 0.218248 0.378017i
\(205\) 0 0
\(206\) 1.63232 2.82726i 0.113729 0.196985i
\(207\) −2.13973 + 3.70613i −0.148722 + 0.257594i
\(208\) 0.858640 0.0595360
\(209\) 23.9882 14.1881i 1.65930 0.981408i
\(210\) 0 0
\(211\) 3.95415 6.84879i 0.272215 0.471490i −0.697214 0.716863i \(-0.745577\pi\)
0.969429 + 0.245373i \(0.0789104\pi\)
\(212\) 3.10295 5.37446i 0.213111 0.369119i
\(213\) −1.46226 2.53272i −0.100193 0.173539i
\(214\) 5.00000 8.66025i 0.341793 0.592003i
\(215\) 0 0
\(216\) −5.62685 −0.382859
\(217\) 19.2221 1.30488
\(218\) 1.51717 + 2.62782i 0.102756 + 0.177978i
\(219\) 3.09531 + 5.36123i 0.209162 + 0.362279i
\(220\) 0 0
\(221\) −4.02712 −0.270894
\(222\) −6.49227 11.2449i −0.435733 0.754711i
\(223\) −4.16463 + 7.21336i −0.278884 + 0.483042i −0.971108 0.238641i \(-0.923298\pi\)
0.692223 + 0.721683i \(0.256631\pi\)
\(224\) 1.16463 + 2.01720i 0.0778153 + 0.134780i
\(225\) 0 0
\(226\) 2.48710 4.30778i 0.165439 0.286549i
\(227\) −11.3680 −0.754523 −0.377261 0.926107i \(-0.623134\pi\)
−0.377261 + 0.926107i \(0.623134\pi\)
\(228\) 4.98712 2.94968i 0.330280 0.195348i
\(229\) −2.25560 −0.149054 −0.0745270 0.997219i \(-0.523745\pi\)
−0.0745270 + 0.997219i \(0.523745\pi\)
\(230\) 0 0
\(231\) 9.89827 17.1443i 0.651259 1.12801i
\(232\) 2.21048 + 3.82866i 0.145125 + 0.251364i
\(233\) 7.96900 13.8027i 0.522067 0.904246i −0.477604 0.878575i \(-0.658495\pi\)
0.999670 0.0256705i \(-0.00817206\pi\)
\(234\) 0.529375 + 0.916904i 0.0346063 + 0.0599399i
\(235\) 0 0
\(236\) −6.18791 −0.402798
\(237\) −7.69848 13.3342i −0.500070 0.866147i
\(238\) −5.46226 9.46092i −0.354066 0.613260i
\(239\) 6.63412 0.429126 0.214563 0.976710i \(-0.431167\pi\)
0.214563 + 0.976710i \(0.431167\pi\)
\(240\) 0 0
\(241\) 11.0397 + 19.1213i 0.711130 + 1.23171i 0.964433 + 0.264326i \(0.0851494\pi\)
−0.253304 + 0.967387i \(0.581517\pi\)
\(242\) −14.9403 + 25.8774i −0.960400 + 1.66346i
\(243\) −5.92769 10.2671i −0.380261 0.658632i
\(244\) 4.01037 6.94616i 0.256738 0.444683i
\(245\) 0 0
\(246\) 4.90515 0.312741
\(247\) −3.26080 1.83717i −0.207480 0.116896i
\(248\) −8.25244 −0.524030
\(249\) −4.03970 + 6.99696i −0.256006 + 0.443415i
\(250\) 0 0
\(251\) −4.72558 8.18494i −0.298276 0.516629i 0.677466 0.735554i \(-0.263078\pi\)
−0.975742 + 0.218926i \(0.929745\pi\)
\(252\) −1.43605 + 2.48732i −0.0904630 + 0.156686i
\(253\) 11.0952 + 19.2175i 0.697552 + 1.20819i
\(254\) −14.2990 −0.897198
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 13.3945 + 23.1999i 0.835524 + 1.44717i 0.893603 + 0.448859i \(0.148169\pi\)
−0.0580783 + 0.998312i \(0.518497\pi\)
\(258\) 9.47053 0.589610
\(259\) −22.7528 −1.41379
\(260\) 0 0
\(261\) −2.72564 + 4.72095i −0.168713 + 0.292219i
\(262\) −1.18947 2.06022i −0.0734854 0.127281i
\(263\) −7.19364 + 12.4598i −0.443579 + 0.768301i −0.997952 0.0639670i \(-0.979625\pi\)
0.554373 + 0.832268i \(0.312958\pi\)
\(264\) −4.24953 + 7.36040i −0.261540 + 0.453001i
\(265\) 0 0
\(266\) −0.106790 10.1525i −0.00654769 0.622488i
\(267\) 15.0193 0.919166
\(268\) 2.45257 4.24798i 0.149815 0.259487i
\(269\) −6.44486 + 11.1628i −0.392950 + 0.680609i −0.992837 0.119475i \(-0.961879\pi\)
0.599887 + 0.800085i \(0.295212\pi\)
\(270\) 0 0
\(271\) −10.0907 + 17.4776i −0.612966 + 1.06169i 0.377772 + 0.925899i \(0.376690\pi\)
−0.990738 + 0.135790i \(0.956643\pi\)
\(272\) 2.34506 + 4.06176i 0.142190 + 0.246280i
\(273\) −2.65853 −0.160902
\(274\) −9.09169 −0.549249
\(275\) 0 0
\(276\) 2.30669 + 3.99531i 0.138846 + 0.240489i
\(277\) 7.40098 0.444682 0.222341 0.974969i \(-0.428630\pi\)
0.222341 + 0.974969i \(0.428630\pi\)
\(278\) −21.0658 −1.26344
\(279\) −5.08785 8.81242i −0.304602 0.527586i
\(280\) 0 0
\(281\) −1.36083 2.35703i −0.0811805 0.140609i 0.822577 0.568654i \(-0.192536\pi\)
−0.903757 + 0.428045i \(0.859202\pi\)
\(282\) 4.78116 8.28121i 0.284714 0.493139i
\(283\) 10.2721 17.7918i 0.610613 1.05761i −0.380524 0.924771i \(-0.624256\pi\)
0.991137 0.132842i \(-0.0424102\pi\)
\(284\) 2.20011 0.130552
\(285\) 0 0
\(286\) 5.48997 0.324629
\(287\) 4.29763 7.44372i 0.253681 0.439389i
\(288\) 0.616527 1.06786i 0.0363292 0.0629240i
\(289\) −2.49860 4.32771i −0.146977 0.254571i
\(290\) 0 0
\(291\) 7.54358 + 13.0659i 0.442213 + 0.765935i
\(292\) −4.65717 −0.272540
\(293\) 26.7315 1.56167 0.780836 0.624736i \(-0.214794\pi\)
0.780836 + 0.624736i \(0.214794\pi\)
\(294\) 1.04648 + 1.81256i 0.0610319 + 0.105710i
\(295\) 0 0
\(296\) 9.76821 0.567766
\(297\) −35.9769 −2.08759
\(298\) 3.17889 + 5.50600i 0.184148 + 0.318954i
\(299\) 1.49001 2.58077i 0.0861694 0.149250i
\(300\) 0 0
\(301\) 8.29759 14.3718i 0.478265 0.828379i
\(302\) 1.52779 2.64622i 0.0879147 0.152273i
\(303\) 2.95210 0.169594
\(304\) 0.0458469 + 4.35866i 0.00262950 + 0.249986i
\(305\) 0 0
\(306\) −2.89158 + 5.00837i −0.165301 + 0.286310i
\(307\) 6.38026 11.0509i 0.364141 0.630710i −0.624497 0.781027i \(-0.714696\pi\)
0.988638 + 0.150317i \(0.0480294\pi\)
\(308\) 7.44642 + 12.8976i 0.424299 + 0.734908i
\(309\) 2.16979 3.75818i 0.123435 0.213795i
\(310\) 0 0
\(311\) −6.96646 −0.395031 −0.197516 0.980300i \(-0.563287\pi\)
−0.197516 + 0.980300i \(0.563287\pi\)
\(312\) 1.14136 0.0646168
\(313\) −13.0846 22.6632i −0.739585 1.28100i −0.952682 0.303968i \(-0.901688\pi\)
0.213097 0.977031i \(-0.431645\pi\)
\(314\) 4.07136 + 7.05180i 0.229760 + 0.397956i
\(315\) 0 0
\(316\) 11.5831 0.651598
\(317\) −4.37870 7.58413i −0.245932 0.425967i 0.716461 0.697627i \(-0.245761\pi\)
−0.962393 + 0.271660i \(0.912427\pi\)
\(318\) 4.12464 7.14408i 0.231298 0.400620i
\(319\) 14.1334 + 24.4797i 0.791316 + 1.37060i
\(320\) 0 0
\(321\) 6.64633 11.5118i 0.370962 0.642525i
\(322\) 8.08401 0.450504
\(323\) −0.215028 20.4426i −0.0119645 1.13746i
\(324\) −3.78042 −0.210023
\(325\) 0 0
\(326\) −6.70501 + 11.6134i −0.371356 + 0.643208i
\(327\) 2.01672 + 3.49306i 0.111525 + 0.193167i
\(328\) −1.84506 + 3.19574i −0.101876 + 0.176455i
\(329\) −8.37800 14.5111i −0.461894 0.800024i
\(330\) 0 0
\(331\) −9.34738 −0.513779 −0.256889 0.966441i \(-0.582698\pi\)
−0.256889 + 0.966441i \(0.582698\pi\)
\(332\) −3.03905 5.26378i −0.166789 0.288888i
\(333\) 6.02237 + 10.4310i 0.330024 + 0.571618i
\(334\) 12.9846 0.710488
\(335\) 0 0
\(336\) 1.54811 + 2.68140i 0.0844561 + 0.146282i
\(337\) −4.87376 + 8.44159i −0.265490 + 0.459843i −0.967692 0.252135i \(-0.918867\pi\)
0.702202 + 0.711978i \(0.252201\pi\)
\(338\) 6.13137 + 10.6198i 0.333502 + 0.577643i
\(339\) 3.30601 5.72618i 0.179558 0.311003i
\(340\) 0 0
\(341\) −52.7644 −2.85735
\(342\) −4.62615 + 2.73619i −0.250154 + 0.147956i
\(343\) 19.9723 1.07840
\(344\) −3.56232 + 6.17012i −0.192067 + 0.332670i
\(345\) 0 0
\(346\) 1.05780 + 1.83216i 0.0568675 + 0.0984975i
\(347\) −7.38162 + 12.7853i −0.396266 + 0.686353i −0.993262 0.115891i \(-0.963028\pi\)
0.596996 + 0.802244i \(0.296361\pi\)
\(348\) 2.93831 + 5.08931i 0.157510 + 0.272816i
\(349\) 14.8315 0.793913 0.396956 0.917837i \(-0.370066\pi\)
0.396956 + 0.917837i \(0.370066\pi\)
\(350\) 0 0
\(351\) 2.41572 + 4.18415i 0.128942 + 0.223333i
\(352\) −3.19690 5.53719i −0.170395 0.295133i
\(353\) −26.8115 −1.42703 −0.713516 0.700639i \(-0.752898\pi\)
−0.713516 + 0.700639i \(0.752898\pi\)
\(354\) −8.22537 −0.437173
\(355\) 0 0
\(356\) −5.64947 + 9.78517i −0.299421 + 0.518613i
\(357\) −7.26080 12.5761i −0.384282 0.665596i
\(358\) 4.93969 8.55579i 0.261071 0.452188i
\(359\) −0.197846 + 0.342680i −0.0104419 + 0.0180859i −0.871199 0.490930i \(-0.836657\pi\)
0.860757 + 0.509016i \(0.169990\pi\)
\(360\) 0 0
\(361\) 9.15178 16.6507i 0.481673 0.876351i
\(362\) 15.0795 0.792560
\(363\) −19.8597 + 34.3979i −1.04236 + 1.80542i
\(364\) 1.00000 1.73205i 0.0524142 0.0907841i
\(365\) 0 0
\(366\) 5.33085 9.23330i 0.278648 0.482632i
\(367\) 3.49227 + 6.04879i 0.182295 + 0.315744i 0.942662 0.333750i \(-0.108314\pi\)
−0.760367 + 0.649494i \(0.774981\pi\)
\(368\) −3.47063 −0.180919
\(369\) −4.55011 −0.236870
\(370\) 0 0
\(371\) −7.22758 12.5185i −0.375237 0.649930i
\(372\) −10.9697 −0.568751
\(373\) −2.52621 −0.130802 −0.0654012 0.997859i \(-0.520833\pi\)
−0.0654012 + 0.997859i \(0.520833\pi\)
\(374\) 14.9938 + 25.9701i 0.775313 + 1.34288i
\(375\) 0 0
\(376\) 3.59684 + 6.22992i 0.185493 + 0.321283i
\(377\) 1.89801 3.28744i 0.0977523 0.169312i
\(378\) −6.55321 + 11.3505i −0.337061 + 0.583807i
\(379\) −29.3075 −1.50543 −0.752713 0.658349i \(-0.771255\pi\)
−0.752713 + 0.658349i \(0.771255\pi\)
\(380\) 0 0
\(381\) −19.0071 −0.973765
\(382\) −4.42096 + 7.65733i −0.226196 + 0.391783i
\(383\) 3.11717 5.39911i 0.159280 0.275881i −0.775329 0.631557i \(-0.782416\pi\)
0.934609 + 0.355676i \(0.115749\pi\)
\(384\) −0.664633 1.15118i −0.0339169 0.0587458i
\(385\) 0 0
\(386\) 9.34642 + 16.1885i 0.475720 + 0.823971i
\(387\) −8.78506 −0.446570
\(388\) −11.3500 −0.576209
\(389\) −13.2183 22.8947i −0.670193 1.16081i −0.977849 0.209311i \(-0.932878\pi\)
0.307656 0.951498i \(-0.400455\pi\)
\(390\) 0 0
\(391\) 16.2776 0.823196
\(392\) −1.57452 −0.0795254
\(393\) −1.58112 2.73857i −0.0797567 0.138143i
\(394\) 8.15847 14.1309i 0.411018 0.711903i
\(395\) 0 0
\(396\) 3.94195 6.82766i 0.198090 0.343103i
\(397\) −4.36575 + 7.56171i −0.219111 + 0.379511i −0.954536 0.298094i \(-0.903649\pi\)
0.735426 + 0.677606i \(0.236982\pi\)
\(398\) −3.14905 −0.157847
\(399\) −0.141952 13.4953i −0.00710648 0.675611i
\(400\) 0 0
\(401\) 1.58356 2.74281i 0.0790794 0.136969i −0.823774 0.566919i \(-0.808135\pi\)
0.902853 + 0.429949i \(0.141469\pi\)
\(402\) 3.26012 5.64669i 0.162600 0.281631i
\(403\) 3.54294 + 6.13654i 0.176486 + 0.305683i
\(404\) −1.11042 + 1.92331i −0.0552457 + 0.0956884i
\(405\) 0 0
\(406\) 10.2976 0.511061
\(407\) 62.4560 3.09583
\(408\) 3.11721 + 5.39916i 0.154325 + 0.267298i
\(409\) −8.54431 14.7992i −0.422489 0.731773i 0.573693 0.819070i \(-0.305510\pi\)
−0.996182 + 0.0872978i \(0.972177\pi\)
\(410\) 0 0
\(411\) −12.0853 −0.596123
\(412\) 1.63232 + 2.82726i 0.0804187 + 0.139289i
\(413\) −7.20664 + 12.4823i −0.354615 + 0.614212i
\(414\) −2.13973 3.70613i −0.105162 0.182146i
\(415\) 0 0
\(416\) −0.429320 + 0.743604i −0.0210491 + 0.0364582i
\(417\) −28.0020 −1.37127
\(418\) 0.293136 + 27.8684i 0.0143378 + 1.36309i
\(419\) 7.80296 0.381200 0.190600 0.981668i \(-0.438957\pi\)
0.190600 + 0.981668i \(0.438957\pi\)
\(420\) 0 0
\(421\) −16.9845 + 29.4180i −0.827773 + 1.43374i 0.0720091 + 0.997404i \(0.477059\pi\)
−0.899782 + 0.436340i \(0.856274\pi\)
\(422\) 3.95415 + 6.84879i 0.192485 + 0.333394i
\(423\) −4.43510 + 7.68182i −0.215642 + 0.373503i
\(424\) 3.10295 + 5.37446i 0.150692 + 0.261007i
\(425\) 0 0
\(426\) 2.92453 0.141694
\(427\) −9.34122 16.1795i −0.452053 0.782979i
\(428\) 5.00000 + 8.66025i 0.241684 + 0.418609i
\(429\) 7.29763 0.352333
\(430\) 0 0
\(431\) −9.07565 15.7195i −0.437158 0.757181i 0.560311 0.828283i \(-0.310682\pi\)
−0.997469 + 0.0711019i \(0.977348\pi\)
\(432\) 2.81343 4.87300i 0.135361 0.234452i
\(433\) −0.157154 0.272199i −0.00755234 0.0130810i 0.862225 0.506526i \(-0.169071\pi\)
−0.869777 + 0.493445i \(0.835737\pi\)
\(434\) −9.61106 + 16.6468i −0.461346 + 0.799074i
\(435\) 0 0
\(436\) −3.03434 −0.145319
\(437\) 13.1802 + 7.42583i 0.630492 + 0.355226i
\(438\) −6.19062 −0.295799
\(439\) −4.33220 + 7.50359i −0.206765 + 0.358127i −0.950694 0.310132i \(-0.899627\pi\)
0.743929 + 0.668259i \(0.232960\pi\)
\(440\) 0 0
\(441\) −0.970736 1.68136i −0.0462255 0.0800650i
\(442\) 2.01356 3.48759i 0.0957753 0.165888i
\(443\) 1.94419 + 3.36744i 0.0923714 + 0.159992i 0.908509 0.417866i \(-0.137222\pi\)
−0.816137 + 0.577858i \(0.803889\pi\)
\(444\) 12.9845 0.616219
\(445\) 0 0
\(446\) −4.16463 7.21336i −0.197201 0.341562i
\(447\) 4.22559 + 7.31894i 0.199864 + 0.346174i
\(448\) −2.32927 −0.110047
\(449\) 32.9375 1.55442 0.777208 0.629243i \(-0.216635\pi\)
0.777208 + 0.629243i \(0.216635\pi\)
\(450\) 0 0
\(451\) −11.7969 + 20.4329i −0.555496 + 0.962147i
\(452\) 2.48710 + 4.30778i 0.116983 + 0.202621i
\(453\) 2.03084 3.51752i 0.0954174 0.165268i
\(454\) 5.68402 9.84500i 0.266764 0.462049i
\(455\) 0 0
\(456\) 0.0609427 + 5.79381i 0.00285390 + 0.271320i
\(457\) 1.22533 0.0573184 0.0286592 0.999589i \(-0.490876\pi\)
0.0286592 + 0.999589i \(0.490876\pi\)
\(458\) 1.12780 1.95341i 0.0526986 0.0912766i
\(459\) −13.1953 + 22.8549i −0.615904 + 1.06678i
\(460\) 0 0
\(461\) 19.5927 33.9356i 0.912524 1.58054i 0.102038 0.994781i \(-0.467464\pi\)
0.810486 0.585758i \(-0.199203\pi\)
\(462\) 9.89827 + 17.1443i 0.460509 + 0.797626i
\(463\) −32.5754 −1.51391 −0.756953 0.653469i \(-0.773313\pi\)
−0.756953 + 0.653469i \(0.773313\pi\)
\(464\) −4.42096 −0.205238
\(465\) 0 0
\(466\) 7.96900 + 13.8027i 0.369157 + 0.639398i
\(467\) −16.9079 −0.782406 −0.391203 0.920304i \(-0.627941\pi\)
−0.391203 + 0.920304i \(0.627941\pi\)
\(468\) −1.05875 −0.0489407
\(469\) −5.71269 9.89467i −0.263788 0.456894i
\(470\) 0 0
\(471\) 5.41192 + 9.37371i 0.249368 + 0.431918i
\(472\) 3.09395 5.35888i 0.142411 0.246663i
\(473\) −22.7767 + 39.4505i −1.04728 + 1.81394i
\(474\) 15.3970 0.707206
\(475\) 0 0
\(476\) 10.9245 0.500725
\(477\) −3.82610 + 6.62700i −0.175185 + 0.303429i
\(478\) −3.31706 + 5.74532i −0.151719 + 0.262785i
\(479\) −1.82570 3.16220i −0.0834181 0.144484i 0.821298 0.570500i \(-0.193250\pi\)
−0.904716 + 0.426015i \(0.859917\pi\)
\(480\) 0 0
\(481\) −4.19369 7.26368i −0.191216 0.331195i
\(482\) −22.0794 −1.00569
\(483\) 10.7458 0.488950
\(484\) −14.9403 25.8774i −0.679106 1.17625i
\(485\) 0 0
\(486\) 11.8554 0.537771
\(487\) −13.7416 −0.622691 −0.311346 0.950297i \(-0.600780\pi\)
−0.311346 + 0.950297i \(0.600780\pi\)
\(488\) 4.01037 + 6.94616i 0.181541 + 0.314438i
\(489\) −8.91274 + 15.4373i −0.403048 + 0.698099i
\(490\) 0 0
\(491\) 17.3839 30.1098i 0.784525 1.35884i −0.144758 0.989467i \(-0.546240\pi\)
0.929283 0.369369i \(-0.120426\pi\)
\(492\) −2.45257 + 4.24798i −0.110571 + 0.191514i
\(493\) 20.7348 0.933849
\(494\) 3.22143 1.90535i 0.144939 0.0857258i
\(495\) 0 0
\(496\) 4.12622 7.14682i 0.185273 0.320902i
\(497\) 2.56232 4.43807i 0.114936 0.199075i
\(498\) −4.03970 6.99696i −0.181023 0.313541i
\(499\) −8.31410 + 14.4005i −0.372190 + 0.644653i −0.989902 0.141752i \(-0.954726\pi\)
0.617712 + 0.786405i \(0.288060\pi\)
\(500\) 0 0
\(501\) 17.2600 0.771121
\(502\) 9.45115 0.421825
\(503\) −2.37970 4.12176i −0.106106 0.183780i 0.808084 0.589068i \(-0.200505\pi\)
−0.914189 + 0.405287i \(0.867171\pi\)
\(504\) −1.43605 2.48732i −0.0639670 0.110794i
\(505\) 0 0
\(506\) −22.1905 −0.986487
\(507\) 8.15022 + 14.1166i 0.361964 + 0.626940i
\(508\) 7.14949 12.3833i 0.317207 0.549419i
\(509\) 1.41576 + 2.45217i 0.0627524 + 0.108690i 0.895695 0.444669i \(-0.146679\pi\)
−0.832942 + 0.553360i \(0.813345\pi\)
\(510\) 0 0
\(511\) −5.42390 + 9.39446i −0.239939 + 0.415587i
\(512\) 1.00000 0.0441942
\(513\) −21.1107 + 12.4862i −0.932062 + 0.551278i
\(514\) −26.7890 −1.18161
\(515\) 0 0
\(516\) −4.73527 + 8.20172i −0.208459 + 0.361061i
\(517\) 22.9975 + 39.8328i 1.01143 + 1.75185i
\(518\) 11.3764 19.7045i 0.499849 0.865764i
\(519\) 1.40609 + 2.43542i 0.0617206 + 0.106903i
\(520\) 0 0
\(521\) 4.92317 0.215688 0.107844 0.994168i \(-0.465605\pi\)
0.107844 + 0.994168i \(0.465605\pi\)
\(522\) −2.72564 4.72095i −0.119298 0.206630i
\(523\) 14.4447 + 25.0190i 0.631624 + 1.09400i 0.987220 + 0.159365i \(0.0509446\pi\)
−0.355596 + 0.934640i \(0.615722\pi\)
\(524\) 2.37893 0.103924
\(525\) 0 0
\(526\) −7.19364 12.4598i −0.313658 0.543271i
\(527\) −19.3525 + 33.5194i −0.843006 + 1.46013i
\(528\) −4.24953 7.36040i −0.184937 0.320320i
\(529\) 5.47738 9.48710i 0.238147 0.412483i
\(530\) 0 0
\(531\) 7.63002 0.331115
\(532\) 8.84569 + 4.98375i 0.383509 + 0.216073i
\(533\) 3.16848 0.137242
\(534\) −7.50965 + 13.0071i −0.324974 + 0.562872i
\(535\) 0 0
\(536\) 2.45257 + 4.24798i 0.105935 + 0.183485i
\(537\) 6.56616 11.3729i 0.283351 0.490778i
\(538\) −6.44486 11.1628i −0.277858 0.481264i
\(539\) −10.0672 −0.433624
\(540\) 0 0
\(541\) −2.30730 3.99637i −0.0991987 0.171817i 0.812154 0.583442i \(-0.198295\pi\)
−0.911353 + 0.411625i \(0.864961\pi\)
\(542\) −10.0907 17.4776i −0.433433 0.750727i
\(543\) 20.0446 0.860198
\(544\) −4.69012 −0.201087
\(545\) 0 0
\(546\) 1.32927 2.30235i 0.0568873 0.0985317i
\(547\) −12.1562 21.0552i −0.519763 0.900255i −0.999736 0.0229724i \(-0.992687\pi\)
0.479973 0.877283i \(-0.340646\pi\)
\(548\) 4.54585 7.87364i 0.194189 0.336345i
\(549\) −4.94500 + 8.56500i −0.211048 + 0.365545i
\(550\) 0 0
\(551\) 16.7892 + 9.45919i 0.715243 + 0.402975i
\(552\) −4.61338 −0.196359
\(553\) 13.4900 23.3654i 0.573654 0.993597i
\(554\) −3.70049 + 6.40943i −0.157219 + 0.272311i
\(555\) 0 0
\(556\) 10.5329 18.2435i 0.446694 0.773697i
\(557\) −12.2154 21.1577i −0.517582 0.896479i −0.999791 0.0204227i \(-0.993499\pi\)
0.482209 0.876056i \(-0.339835\pi\)
\(558\) 10.1757 0.430772
\(559\) 6.11750 0.258743
\(560\) 0 0
\(561\) 19.9308 + 34.5211i 0.841478 + 1.45748i
\(562\) 2.72167 0.114807
\(563\) −19.7981 −0.834390 −0.417195 0.908817i \(-0.636987\pi\)
−0.417195 + 0.908817i \(0.636987\pi\)
\(564\) 4.78116 + 8.28121i 0.201323 + 0.348702i
\(565\) 0 0
\(566\) 10.2721 + 17.7918i 0.431769 + 0.747845i
\(567\) −4.40280 + 7.62587i −0.184900 + 0.320256i
\(568\) −1.10005 + 1.90535i −0.0461573 + 0.0799467i
\(569\) −39.9935 −1.67662 −0.838308 0.545197i \(-0.816455\pi\)
−0.838308 + 0.545197i \(0.816455\pi\)
\(570\) 0 0
\(571\) −30.3255 −1.26908 −0.634542 0.772889i \(-0.718811\pi\)
−0.634542 + 0.772889i \(0.718811\pi\)
\(572\) −2.74498 + 4.75445i −0.114774 + 0.198794i
\(573\) −5.87663 + 10.1786i −0.245500 + 0.425218i
\(574\) 4.29763 + 7.44372i 0.179380 + 0.310695i
\(575\) 0 0
\(576\) 0.616527 + 1.06786i 0.0256886 + 0.0444940i
\(577\) 31.8330 1.32523 0.662613 0.748962i \(-0.269448\pi\)
0.662613 + 0.748962i \(0.269448\pi\)
\(578\) 4.99721 0.207856
\(579\) 12.4239 + 21.5188i 0.516318 + 0.894289i
\(580\) 0 0
\(581\) −14.1575 −0.587352
\(582\) −15.0872 −0.625383
\(583\) 19.8396 + 34.3632i 0.821673 + 1.42318i
\(584\) 2.32859 4.03323i 0.0963576 0.166896i
\(585\) 0 0
\(586\) −13.3658 + 23.1502i −0.552134 + 0.956324i
\(587\) −0.530771 + 0.919322i −0.0219073 + 0.0379445i −0.876771 0.480908i \(-0.840307\pi\)
0.854864 + 0.518852i \(0.173641\pi\)
\(588\) −2.09296 −0.0863122
\(589\) −30.9614 + 18.3124i −1.27574 + 0.754551i
\(590\) 0 0
\(591\) 10.8448 18.7837i 0.446094 0.772657i
\(592\) −4.88411 + 8.45952i −0.200736 + 0.347684i
\(593\) 18.7747 + 32.5188i 0.770985 + 1.33539i 0.937024 + 0.349266i \(0.113569\pi\)
−0.166039 + 0.986119i \(0.553098\pi\)
\(594\) 17.9885 31.1570i 0.738076 1.27839i
\(595\) 0 0
\(596\) −6.35778 −0.260425
\(597\) −4.18592 −0.171318
\(598\) 1.49001 + 2.58077i 0.0609310 + 0.105536i
\(599\) 5.02165 + 8.69775i 0.205179 + 0.355380i 0.950190 0.311672i \(-0.100889\pi\)
−0.745011 + 0.667052i \(0.767556\pi\)
\(600\) 0 0
\(601\) 7.56630 0.308636 0.154318 0.988021i \(-0.450682\pi\)
0.154318 + 0.988021i \(0.450682\pi\)
\(602\) 8.29759 + 14.3718i 0.338184 + 0.585753i
\(603\) −3.02415 + 5.23799i −0.123153 + 0.213307i
\(604\) 1.52779 + 2.64622i 0.0621651 + 0.107673i
\(605\) 0 0
\(606\) −1.47605 + 2.55659i −0.0599604 + 0.103854i
\(607\) 30.8174 1.25084 0.625420 0.780288i \(-0.284928\pi\)
0.625420 + 0.780288i \(0.284928\pi\)
\(608\) −3.79763 2.13962i −0.154014 0.0867732i
\(609\) 13.6882 0.554675
\(610\) 0 0
\(611\) 3.08839 5.34925i 0.124943 0.216408i
\(612\) −2.89158 5.00837i −0.116885 0.202451i
\(613\) −9.36510 + 16.2208i −0.378253 + 0.655153i −0.990808 0.135275i \(-0.956808\pi\)
0.612555 + 0.790428i \(0.290142\pi\)
\(614\) 6.38026 + 11.0509i 0.257486 + 0.445980i
\(615\) 0 0
\(616\) −14.8928 −0.600050
\(617\) −23.1741 40.1386i −0.932952 1.61592i −0.778245 0.627960i \(-0.783890\pi\)
−0.154707 0.987960i \(-0.549443\pi\)
\(618\) 2.16979 + 3.75818i 0.0872816 + 0.151176i
\(619\) 11.5591 0.464600 0.232300 0.972644i \(-0.425375\pi\)
0.232300 + 0.972644i \(0.425375\pi\)
\(620\) 0 0
\(621\) −9.76435 16.9123i −0.391830 0.678669i
\(622\) 3.48323 6.03313i 0.139665 0.241906i
\(623\) 13.1591 + 22.7923i 0.527209 + 0.913153i
\(624\) −0.570680 + 0.988447i −0.0228455 + 0.0395695i
\(625\) 0 0
\(626\) 26.1692 1.04593
\(627\) 0.389655 + 37.0445i 0.0155613 + 1.47941i
\(628\) −8.14272 −0.324930
\(629\) 22.9070 39.6761i 0.913363 1.58199i
\(630\) 0 0
\(631\) −22.4567 38.8962i −0.893989 1.54843i −0.835051 0.550173i \(-0.814562\pi\)
−0.0589383 0.998262i \(-0.518772\pi\)
\(632\) −5.79153 + 10.0312i −0.230375 + 0.399021i
\(633\) 5.25612 + 9.10386i 0.208912 + 0.361846i
\(634\) 8.75740 0.347801
\(635\) 0 0
\(636\) 4.12464 + 7.14408i 0.163553 + 0.283281i
\(637\) 0.675974 + 1.17082i 0.0267831 + 0.0463897i
\(638\) −28.2667 −1.11909
\(639\) −2.71285 −0.107319
\(640\) 0 0
\(641\) 17.3522 30.0549i 0.685371 1.18710i −0.287949 0.957646i \(-0.592973\pi\)
0.973320 0.229451i \(-0.0736932\pi\)
\(642\) 6.64633 + 11.5118i 0.262310 + 0.454333i
\(643\) 18.7485 32.4734i 0.739369 1.28062i −0.213411 0.976963i \(-0.568457\pi\)
0.952780 0.303662i \(-0.0982094\pi\)
\(644\) −4.04200 + 7.00096i −0.159277 + 0.275876i
\(645\) 0 0
\(646\) 17.8113 + 10.0351i 0.700778 + 0.394825i
\(647\) −22.6592 −0.890823 −0.445412 0.895326i \(-0.646943\pi\)
−0.445412 + 0.895326i \(0.646943\pi\)
\(648\) 1.89021 3.27394i 0.0742544 0.128612i
\(649\) 19.7821 34.2636i 0.776516 1.34496i
\(650\) 0 0
\(651\) −12.7756 + 22.1281i −0.500717 + 0.867267i
\(652\) −6.70501 11.6134i −0.262588 0.454817i
\(653\) −17.7667 −0.695266 −0.347633 0.937631i \(-0.613014\pi\)
−0.347633 + 0.937631i \(0.613014\pi\)
\(654\) −4.03344 −0.157720
\(655\) 0 0
\(656\) −1.84506 3.19574i −0.0720375 0.124773i
\(657\) 5.74255 0.224038
\(658\) 16.7560 0.653217
\(659\) −0.991869 1.71797i −0.0386377 0.0669225i 0.846060 0.533088i \(-0.178969\pi\)
−0.884698 + 0.466165i \(0.845635\pi\)
\(660\) 0 0
\(661\) −13.1253 22.7337i −0.510515 0.884237i −0.999926 0.0121841i \(-0.996122\pi\)
0.489411 0.872053i \(-0.337212\pi\)
\(662\) 4.67369 8.09507i 0.181648 0.314624i
\(663\) 2.67656 4.63593i 0.103949 0.180045i
\(664\) 6.07809 0.235876
\(665\) 0 0
\(666\) −12.0447 −0.466724
\(667\) −7.67175 + 13.2879i −0.297051 + 0.514508i
\(668\) −6.49232 + 11.2450i −0.251195 + 0.435083i
\(669\) −5.53590 9.58846i −0.214030 0.370711i
\(670\) 0 0
\(671\) 25.6415 + 44.4124i 0.989879 + 1.71452i
\(672\) −3.09621 −0.119439
\(673\) −16.0432 −0.618418 −0.309209 0.950994i \(-0.600064\pi\)
−0.309209 + 0.950994i \(0.600064\pi\)
\(674\) −4.87376 8.44159i −0.187730 0.325158i
\(675\) 0 0
\(676\) −12.2627 −0.471644
\(677\) −48.5483 −1.86586 −0.932931 0.360056i \(-0.882757\pi\)
−0.932931 + 0.360056i \(0.882757\pi\)
\(678\) 3.30601 + 5.72618i 0.126967 + 0.219913i
\(679\) −13.2186 + 22.8953i −0.507283 + 0.878640i
\(680\) 0 0
\(681\) 7.55556 13.0866i 0.289530 0.501480i
\(682\) 26.3822 45.6953i 1.01023 1.74976i
\(683\) −13.3802 −0.511981 −0.255990 0.966679i \(-0.582402\pi\)
−0.255990 + 0.966679i \(0.582402\pi\)
\(684\) −0.0565317 5.37446i −0.00216155 0.205498i
\(685\) 0 0
\(686\) −9.98617 + 17.2966i −0.381274 + 0.660385i
\(687\) 1.49914 2.59659i 0.0571959 0.0990662i
\(688\) −3.56232 6.17012i −0.135812 0.235234i
\(689\) 2.66431 4.61473i 0.101502 0.175807i
\(690\) 0 0
\(691\) −25.8354 −0.982825 −0.491413 0.870927i \(-0.663519\pi\)
−0.491413 + 0.870927i \(0.663519\pi\)
\(692\) −2.11559 −0.0804228
\(693\) −9.18184 15.9034i −0.348789 0.604121i
\(694\) −7.38162 12.7853i −0.280202 0.485325i
\(695\) 0 0
\(696\) −5.87663 −0.222753
\(697\) 8.65354 + 14.9884i 0.327776 + 0.567725i
\(698\) −7.41576 + 12.8445i −0.280691 + 0.486170i
\(699\) 10.5929 + 18.3475i 0.400661 + 0.693965i
\(700\) 0 0
\(701\) −24.6167 + 42.6373i −0.929758 + 1.61039i −0.146034 + 0.989280i \(0.546651\pi\)
−0.783724 + 0.621109i \(0.786682\pi\)
\(702\) −4.83144 −0.182351
\(703\) 36.6482 21.6760i 1.38221 0.817525i
\(704\) 6.39380 0.240975
\(705\) 0 0
\(706\) 13.4058 23.2194i 0.504532 0.873875i
\(707\) 2.58647 + 4.47990i 0.0972744 + 0.168484i
\(708\) 4.11268 7.12338i 0.154564 0.267713i
\(709\) −5.44796 9.43614i −0.204602 0.354382i 0.745404 0.666613i \(-0.232257\pi\)
−0.950006 + 0.312232i \(0.898923\pi\)
\(710\) 0 0
\(711\) −14.2825 −0.535637
\(712\) −5.64947 9.78517i −0.211723 0.366715i
\(713\) −14.3206 24.8039i −0.536309 0.928915i
\(714\) 14.5216 0.543457
\(715\) 0 0
\(716\) 4.93969 + 8.55579i 0.184605 + 0.319745i
\(717\) −4.40925 + 7.63705i −0.164667 + 0.285211i
\(718\) −0.197846 0.342680i −0.00738355 0.0127887i
\(719\) 16.9141 29.2961i 0.630789 1.09256i −0.356602 0.934257i \(-0.616065\pi\)
0.987391 0.158302i \(-0.0506020\pi\)
\(720\) 0 0
\(721\) 7.60422 0.283196
\(722\) 9.84402 + 16.2510i 0.366356 + 0.604800i
\(723\) −29.3494 −1.09152
\(724\) −7.53974 + 13.0592i −0.280212 + 0.485342i
\(725\) 0 0
\(726\) −19.8597 34.3979i −0.737061 1.27663i
\(727\) 25.4674 44.1108i 0.944533 1.63598i 0.187848 0.982198i \(-0.439849\pi\)
0.756684 0.653780i \(-0.226818\pi\)
\(728\) 1.00000 + 1.73205i 0.0370625 + 0.0641941i
\(729\) 27.1002 1.00371
\(730\) 0 0
\(731\) 16.7077 + 28.9386i 0.617957 + 1.07033i
\(732\) 5.33085 + 9.23330i 0.197034 + 0.341272i
\(733\) −30.8270 −1.13862 −0.569310 0.822123i \(-0.692790\pi\)
−0.569310 + 0.822123i \(0.692790\pi\)
\(734\) −6.98454 −0.257804
\(735\) 0 0
\(736\) 1.73531 3.00565i 0.0639645 0.110790i
\(737\) 15.6813 + 27.1607i 0.577626 + 1.00048i
\(738\) 2.27506 3.94052i 0.0837460 0.145052i
\(739\) 18.8645 32.6742i 0.693941 1.20194i −0.276596 0.960986i \(-0.589206\pi\)
0.970536 0.240954i \(-0.0774604\pi\)
\(740\) 0 0
\(741\) 4.28214 2.53272i 0.157308 0.0930417i
\(742\) 14.4552 0.530666
\(743\) 16.3990 28.4038i 0.601619 1.04204i −0.390957 0.920409i \(-0.627856\pi\)
0.992576 0.121626i \(-0.0388108\pi\)
\(744\) 5.48484 9.50002i 0.201084 0.348288i
\(745\) 0 0
\(746\) 1.26311 2.18777i 0.0462456 0.0800998i
\(747\) 3.74731 + 6.49053i 0.137107 + 0.237476i
\(748\) −29.9877 −1.09646
\(749\) 23.2927 0.851095
\(750\) 0 0
\(751\) −2.19685 3.80505i −0.0801641 0.138848i 0.823156 0.567815i \(-0.192211\pi\)
−0.903320 + 0.428967i \(0.858878\pi\)
\(752\) −7.19369 −0.262327
\(753\) 12.5631 0.457824
\(754\) 1.89801 + 3.28744i 0.0691213 + 0.119722i
\(755\) 0 0
\(756\) −6.55321 11.3505i −0.238338 0.412814i
\(757\) 25.4884 44.1472i 0.926391 1.60456i 0.137082 0.990560i \(-0.456227\pi\)
0.789309 0.613997i \(-0.210439\pi\)
\(758\) 14.6538 25.3811i 0.532248 0.921881i
\(759\) −29.4970 −1.07067
\(760\) 0 0
\(761\) 10.5364 0.381945 0.190973 0.981595i \(-0.438836\pi\)
0.190973 + 0.981595i \(0.438836\pi\)
\(762\) 9.50357 16.4607i 0.344278 0.596307i
\(763\) −3.53389 + 6.12088i −0.127935 + 0.221591i
\(764\) −4.42096 7.65733i −0.159945 0.277032i
\(765\) 0 0
\(766\) 3.11717 + 5.39911i 0.112628 + 0.195078i
\(767\) −5.31318 −0.191848
\(768\) 1.32927 0.0479657
\(769\) 22.2243 + 38.4936i 0.801429 + 1.38812i 0.918676 + 0.395013i \(0.129260\pi\)
−0.117246 + 0.993103i \(0.537407\pi\)
\(770\) 0 0
\(771\) −35.6096 −1.28245
\(772\) −18.6928 −0.672770
\(773\) −23.1902 40.1667i −0.834095 1.44469i −0.894766 0.446536i \(-0.852657\pi\)
0.0606710 0.998158i \(-0.480676\pi\)
\(774\) 4.39253 7.60809i 0.157886 0.273467i
\(775\) 0 0
\(776\) 5.67500 9.82939i 0.203721 0.352855i
\(777\) 15.1222 26.1925i 0.542507 0.939649i
\(778\) 26.4365 0.947796
\(779\) 0.169181 + 16.0840i 0.00606152 + 0.576268i
\(780\) 0 0
\(781\) −7.03353 + 12.1824i −0.251679 + 0.435921i
\(782\) −8.13882 + 14.0969i −0.291044 + 0.504102i
\(783\) −12.4380 21.5433i −0.444499 0.769895i
\(784\) 0.787262 1.36358i 0.0281165 0.0486992i
\(785\) 0 0
\(786\) 3.16223