Properties

Label 950.2.e.o.201.4
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 201.4
Root \(-0.664633 + 1.15118i\) of defining polynomial
Character \(\chi\) \(=\) 950.201
Dual form 950.2.e.o.501.4

$q$-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 −0.607866 0.794040i \(-0.707974\pi\)
0.991592 + 0.129407i \(0.0413074\pi\)
\(4\) −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 \(-0.354911\pi\)
0.440190 + 0.897905i \(0.354911\pi\)
\(8\) −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 0.919400 0.393324i \(-0.128675\pi\)
−0.800328 + 0.599562i \(0.795341\pi\)
\(14\) 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 \(0.359243\pi\)
−0.996689 + 0.0813093i \(0.974090\pi\)
\(18\) 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 0.626426 0.779481i \(-0.284517\pi\)
−0.988263 + 0.152760i \(0.951184\pi\)
\(24\) −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 \(-0.796733\pi\)
−0.802942 + 0.596057i \(0.796733\pi\)
\(38\) −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 \(-0.650527\pi\)
0.998715 0.0506811i \(-0.0161392\pi\)
\(44\) −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 \(-0.990862\pi\)
0.474934 0.880021i \(-0.342472\pi\)
\(48\) 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 0.570311 0.821429i \(-0.306823\pi\)
−0.996534 + 0.0831897i \(0.973489\pi\)
\(54\) 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 0.676422 0.736515i \(-0.263530\pi\)
−0.976051 + 0.217541i \(0.930196\pi\)
\(68\) 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 −0.969512 0.245045i \(-0.921197\pi\)
0.696971 + 0.717099i \(0.254531\pi\)
\(74\) −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 \(-0.608256\pi\)
−0.333579 + 0.942722i \(0.608256\pi\)
\(84\) −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 \(0.362135\pi\)
−0.995909 + 0.0903607i \(0.971198\pi\)
\(98\) −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 \(-0.448581\pi\)
0.160837 + 0.986981i \(0.448581\pi\)
\(104\) −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 \(-0.339413\pi\)
0.483368 + 0.875417i \(0.339413\pi\)
\(108\) −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 \(-0.424829\pi\)
0.233966 + 0.972245i \(0.424829\pi\)
\(114\) −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 \(-0.947908\pi\)
0.352224 0.935916i \(-0.385426\pi\)
\(128\) 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 0.603854 0.797095i \(-0.293631\pi\)
−0.992232 + 0.124405i \(0.960298\pi\)
\(138\) −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 −0.981498 0.191472i \(-0.938674\pi\)
0.656568 + 0.754267i \(0.272007\pi\)
\(158\) 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 \(-0.676001\pi\)
−0.525177 + 0.850993i \(0.676001\pi\)
\(164\) 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 \(0.000879380\pi\)
−0.497606 + 0.867403i \(0.665787\pi\)
\(168\) −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 −0.903432 0.428732i \(-0.858960\pi\)
0.823009 + 0.568029i \(0.192294\pi\)
\(174\) 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 \(0.401562\pi\)
−0.977115 + 0.212710i \(0.931771\pi\)
\(194\) 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 \(-0.302557\pi\)
0.581267 + 0.813713i \(0.302557\pi\)
\(198\) 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 −0.692223 0.721683i \(-0.743369\pi\)
0.971108 + 0.238641i \(0.0767020\pi\)
\(224\) 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 \(-0.376866\pi\)
0.377261 + 0.926107i \(0.376866\pi\)
\(228\) −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 \(0.341505\pi\)
−0.999670 + 0.0256705i \(0.991828\pi\)
\(234\) 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 \(-0.851831\pi\)
0.0580783 0.998312i \(-0.481503\pi\)
\(258\) −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 −0.554373 0.832268i \(-0.687042\pi\)
0.997952 + 0.0639670i \(0.0203752\pi\)
\(264\) −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 \(-0.571370\pi\)
−0.222341 + 0.974969i \(0.571370\pi\)
\(278\) 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 \(0.375744\pi\)
−0.991137 + 0.132842i \(0.957590\pi\)
\(284\) 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 \(-0.785206\pi\)
−0.780836 + 0.624736i \(0.785206\pi\)
\(294\) 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 −0.988638 0.150317i \(-0.951971\pi\)
0.624497 + 0.781027i \(0.285304\pi\)
\(308\) −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 \(0.0983115\pi\)
−0.213097 + 0.977031i \(0.568355\pi\)
\(314\) 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 0.962393 0.271660i \(-0.0875725\pi\)
−0.716461 + 0.697627i \(0.754239\pi\)
\(318\) −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 −0.702202 0.711978i \(-0.747799\pi\)
0.967692 + 0.252135i \(0.0811328\pi\)
\(338\) −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 −0.596996 0.802244i \(-0.703639\pi\)
0.993262 + 0.115891i \(0.0369724\pi\)
\(348\) −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 \(-0.247102\pi\)
0.713516 + 0.700639i \(0.247102\pi\)
\(354\) −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 0.760367 0.649494i \(-0.225019\pi\)
−0.942662 + 0.333750i \(0.891686\pi\)
\(368\) 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 \(-0.479167\pi\)
0.0654012 + 0.997859i \(0.479167\pi\)
\(374\) 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 −0.934609 0.355676i \(-0.884251\pi\)
0.775329 + 0.631557i \(0.217584\pi\)
\(384\) −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 −0.735426 0.677606i \(-0.763018\pi\)
0.954536 + 0.298094i \(0.0963510\pi\)
\(398\) 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 0.869777 0.493445i \(-0.164263\pi\)
−0.862225 + 0.506526i \(0.830929\pi\)
\(434\) −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 0.816137 0.577858i \(-0.196111\pi\)
−0.908509 + 0.417866i \(0.862778\pi\)
\(444\) 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 \(-0.509124\pi\)
−0.0286592 + 0.999589i \(0.509124\pi\)
\(458\) −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 \(-0.226687\pi\)
0.756953 + 0.653469i \(0.226687\pi\)
\(464\) −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 \(-0.372059\pi\)
0.391203 + 0.920304i \(0.372059\pi\)
\(468\) 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 \(-0.399220\pi\)
0.311346 + 0.950297i \(0.399220\pi\)
\(488\) −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 0.914189 0.405287i \(-0.132829\pi\)
−0.808084 + 0.589068i \(0.799495\pi\)
\(504\) −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 \(-0.949055\pi\)
0.355596 0.934640i \(-0.384278\pi\)
\(524\) 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 \(0.00731297\pi\)
−0.479973 + 0.877283i \(0.659354\pi\)
\(548\) −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 \(0.00650119\pi\)
−0.482209 + 0.876056i \(0.660165\pi\)
\(558\) −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 \(-0.363013\pi\)
0.417195 + 0.908817i \(0.363013\pi\)
\(564\) 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 \(-0.730552\pi\)
−0.662613 + 0.748962i \(0.730552\pi\)
\(578\) −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 −0.854864 0.518852i \(-0.826359\pi\)
0.876771 + 0.480908i \(0.159693\pi\)
\(588\) 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 \(-0.886431\pi\)
0.166039 0.986119i \(-0.446902\pi\)
\(594\) 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 \(-0.715072\pi\)
−0.625420 + 0.780288i \(0.715072\pi\)
\(608\) 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 −0.612555 0.790428i \(-0.709858\pi\)
0.990808 + 0.135275i \(0.0431916\pi\)
\(614\) 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 \(0.216110\pi\)
0.154707 + 0.987960i \(0.450557\pi\)
\(618\) −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 \(0.431543\pi\)
−0.952780 + 0.303662i \(0.901791\pi\)
\(644\) −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 \(-0.353057\pi\)
0.445412 + 0.895326i \(0.353057\pi\)
\(648\) −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 \(-0.386986\pi\)
0.347633 + 0.937631i \(0.386986\pi\)
\(654\) −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 \(-0.399936\pi\)
0.309209 + 0.950994i \(0.399936\pi\)
\(674\) −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 \(-0.117243\pi\)
0.932931 + 0.360056i \(0.117243\pi\)
\(678\) −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 \(-0.417598\pi\)
0.255990 + 0.966679i \(0.417598\pi\)
\(684\) −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 \(0.560151\pi\)
−0.756684 + 0.653780i \(0.773182\pi\)
\(728\) −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 \(-0.307210\pi\)
0.569310 + 0.822123i \(0.307210\pi\)
\(734\) −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 \(0.372144\pi\)
−0.992576 + 0.121626i \(0.961189\pi\)
\(744\) 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 \(0.543773\pi\)
−0.789309 + 0.613997i \(0.789561\pi\)
\(758\) −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 \(0.147343\pi\)
−0.0606710 + 0.998158i \(0.519324\pi\)
\(774\) 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 0.112793