Properties

Label 735.2.v.a.178.4
Level 735
Weight 2
Character 735.178
Analytic conductor 5.869
Analytic rank 0
Dimension 32
CM no
Inner twists 8

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Newspace parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.v (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.86900454856\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 178.4
Character \(\chi\) \(=\) 735.178
Dual form 735.2.v.a.607.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.737849 - 0.197706i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-1.22672 - 0.708245i) q^{4} +(-1.19764 + 1.88830i) q^{5} -0.763878i q^{6} +(1.84539 + 1.84539i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.737849 - 0.197706i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-1.22672 - 0.708245i) q^{4} +(-1.19764 + 1.88830i) q^{5} -0.763878i q^{6} +(1.84539 + 1.84539i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(1.25700 - 1.15650i) q^{10} +(1.92568 - 3.33538i) q^{11} +(0.366615 - 1.36822i) q^{12} +(-3.66816 + 3.66816i) q^{13} +(-2.13393 - 0.668102i) q^{15} +(0.419714 + 0.726965i) q^{16} +(-2.03548 + 0.545404i) q^{17} +(0.737849 - 0.197706i) q^{18} +(-0.0348837 - 0.0604203i) q^{19} +(2.80654 - 1.46818i) q^{20} +(-2.08029 + 2.08029i) q^{22} +(-0.195522 + 0.729698i) q^{23} +(-1.30489 + 2.26014i) q^{24} +(-2.13133 - 4.52299i) q^{25} +(3.43177 - 1.98133i) q^{26} +(-0.707107 - 0.707107i) q^{27} -2.77107i q^{29} +(1.44243 + 0.914849i) q^{30} +(-2.07564 - 1.19837i) q^{31} +(-1.51688 - 5.66108i) q^{32} +(3.72013 + 0.996806i) q^{33} +1.60970 q^{34} +1.41649 q^{36} +(-8.45237 - 2.26481i) q^{37} +(0.0137934 + 0.0514778i) q^{38} +(-4.49256 - 2.59378i) q^{39} +(-5.69477 + 1.27454i) q^{40} -8.68077i q^{41} +(-2.77107 - 2.77107i) q^{43} +(-4.72453 + 2.72771i) q^{44} +(0.0930365 - 2.23413i) q^{45} +(0.288532 - 0.499752i) q^{46} +(2.00963 - 7.50006i) q^{47} +(-0.593565 + 0.593565i) q^{48} +(0.678376 + 3.75866i) q^{50} +(-1.05364 - 1.82496i) q^{51} +(7.09776 - 1.90184i) q^{52} +(-8.38498 + 2.24675i) q^{53} +(0.381939 + 0.661538i) q^{54} +(3.99191 + 7.63083i) q^{55} +(0.0493330 - 0.0493330i) q^{57} +(-0.547858 + 2.04464i) q^{58} +(3.48720 - 6.04001i) q^{59} +(2.14454 + 2.33092i) q^{60} +(-12.3935 + 7.15536i) q^{61} +(1.29458 + 1.29458i) q^{62} +2.79807i q^{64} +(-2.53345 - 11.3197i) q^{65} +(-2.54782 - 1.47098i) q^{66} +(0.152446 + 0.568937i) q^{67} +(2.88323 + 0.772560i) q^{68} -0.755439 q^{69} -8.12783 q^{71} +(-2.52086 - 0.675461i) q^{72} +(3.49631 + 13.0484i) q^{73} +(5.78881 + 3.34217i) q^{74} +(3.81725 - 3.22934i) q^{75} +0.0988248i q^{76} +(2.80203 + 2.80203i) q^{78} +(8.54186 - 4.93165i) q^{79} +(-1.87539 - 0.0780974i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-1.71624 + 6.40510i) q^{82} +(1.63570 - 1.63570i) q^{83} +(1.40788 - 4.49678i) q^{85} +(1.49678 + 2.59249i) q^{86} +(2.67665 - 0.717207i) q^{87} +(9.70872 - 2.60144i) q^{88} +(2.52657 + 4.37614i) q^{89} +(-0.510348 + 1.63006i) q^{90} +(0.756656 - 0.756656i) q^{92} +(0.620321 - 2.31507i) q^{93} +(-2.96561 + 5.13659i) q^{94} +(0.155869 + 0.00649091i) q^{95} +(5.07559 - 2.93039i) q^{96} +(6.85851 + 6.85851i) q^{97} +3.85136i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 48q^{8} + O(q^{10}) \) \( 32q + 48q^{8} + 16q^{11} + 16q^{15} + 48q^{16} - 32q^{22} + 40q^{23} + 8q^{30} - 48q^{32} - 32q^{36} - 32q^{37} - 32q^{43} - 64q^{46} - 144q^{50} + 16q^{51} - 24q^{53} + 16q^{57} - 32q^{58} - 40q^{60} - 40q^{65} + 32q^{67} + 128q^{71} - 24q^{72} - 16q^{78} + 16q^{81} + 96q^{85} - 64q^{86} + 64q^{88} - 80q^{92} - 24q^{93} + 72q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.737849 0.197706i −0.521738 0.139799i −0.0116677 0.999932i \(-0.503714\pi\)
−0.510071 + 0.860133i \(0.670381\pi\)
\(3\) 0.258819 + 0.965926i 0.149429 + 0.557678i
\(4\) −1.22672 0.708245i −0.613358 0.354123i
\(5\) −1.19764 + 1.88830i −0.535600 + 0.844472i
\(6\) 0.763878i 0.311852i
\(7\) 0 0
\(8\) 1.84539 + 1.84539i 0.652445 + 0.652445i
\(9\) −0.866025 + 0.500000i −0.288675 + 0.166667i
\(10\) 1.25700 1.15650i 0.397500 0.365717i
\(11\) 1.92568 3.33538i 0.580615 1.00565i −0.414792 0.909916i \(-0.636146\pi\)
0.995407 0.0957376i \(-0.0305210\pi\)
\(12\) 0.366615 1.36822i 0.105833 0.394973i
\(13\) −3.66816 + 3.66816i −1.01737 + 1.01737i −0.0175187 + 0.999847i \(0.505577\pi\)
−0.999847 + 0.0175187i \(0.994423\pi\)
\(14\) 0 0
\(15\) −2.13393 0.668102i −0.550977 0.172503i
\(16\) 0.419714 + 0.726965i 0.104928 + 0.181741i
\(17\) −2.03548 + 0.545404i −0.493675 + 0.132280i −0.497063 0.867714i \(-0.665588\pi\)
0.00338789 + 0.999994i \(0.498922\pi\)
\(18\) 0.737849 0.197706i 0.173913 0.0465998i
\(19\) −0.0348837 0.0604203i −0.00800286 0.0138614i 0.861996 0.506915i \(-0.169214\pi\)
−0.869999 + 0.493053i \(0.835881\pi\)
\(20\) 2.80654 1.46818i 0.627561 0.328296i
\(21\) 0 0
\(22\) −2.08029 + 2.08029i −0.443519 + 0.443519i
\(23\) −0.195522 + 0.729698i −0.0407692 + 0.152153i −0.983310 0.181939i \(-0.941763\pi\)
0.942541 + 0.334091i \(0.108429\pi\)
\(24\) −1.30489 + 2.26014i −0.266360 + 0.461349i
\(25\) −2.13133 4.52299i −0.426265 0.904598i
\(26\) 3.43177 1.98133i 0.673025 0.388571i
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 0 0
\(29\) 2.77107i 0.514576i −0.966335 0.257288i \(-0.917171\pi\)
0.966335 0.257288i \(-0.0828288\pi\)
\(30\) 1.44243 + 0.914849i 0.263350 + 0.167028i
\(31\) −2.07564 1.19837i −0.372795 0.215233i 0.301884 0.953345i \(-0.402385\pi\)
−0.674679 + 0.738111i \(0.735718\pi\)
\(32\) −1.51688 5.66108i −0.268149 1.00075i
\(33\) 3.72013 + 0.996806i 0.647591 + 0.173522i
\(34\) 1.60970 0.276062
\(35\) 0 0
\(36\) 1.41649 0.236082
\(37\) −8.45237 2.26481i −1.38956 0.372332i −0.514976 0.857204i \(-0.672199\pi\)
−0.874585 + 0.484872i \(0.838866\pi\)
\(38\) 0.0137934 + 0.0514778i 0.00223759 + 0.00835080i
\(39\) −4.49256 2.59378i −0.719386 0.415338i
\(40\) −5.69477 + 1.27454i −0.900421 + 0.201522i
\(41\) 8.68077i 1.35571i −0.735196 0.677854i \(-0.762910\pi\)
0.735196 0.677854i \(-0.237090\pi\)
\(42\) 0 0
\(43\) −2.77107 2.77107i −0.422585 0.422585i 0.463508 0.886093i \(-0.346591\pi\)
−0.886093 + 0.463508i \(0.846591\pi\)
\(44\) −4.72453 + 2.72771i −0.712250 + 0.411218i
\(45\) 0.0930365 2.23413i 0.0138691 0.333045i
\(46\) 0.288532 0.499752i 0.0425417 0.0736843i
\(47\) 2.00963 7.50006i 0.293135 1.09400i −0.649552 0.760317i \(-0.725043\pi\)
0.942687 0.333678i \(-0.108290\pi\)
\(48\) −0.593565 + 0.593565i −0.0856737 + 0.0856737i
\(49\) 0 0
\(50\) 0.678376 + 3.75866i 0.0959368 + 0.531555i
\(51\) −1.05364 1.82496i −0.147539 0.255545i
\(52\) 7.09776 1.90184i 0.984282 0.263737i
\(53\) −8.38498 + 2.24675i −1.15177 + 0.308615i −0.783673 0.621174i \(-0.786656\pi\)
−0.368093 + 0.929789i \(0.619989\pi\)
\(54\) 0.381939 + 0.661538i 0.0519753 + 0.0900239i
\(55\) 3.99191 + 7.63083i 0.538269 + 1.02894i
\(56\) 0 0
\(57\) 0.0493330 0.0493330i 0.00653431 0.00653431i
\(58\) −0.547858 + 2.04464i −0.0719373 + 0.268474i
\(59\) 3.48720 6.04001i 0.453995 0.786342i −0.544635 0.838673i \(-0.683332\pi\)
0.998630 + 0.0523310i \(0.0166651\pi\)
\(60\) 2.14454 + 2.33092i 0.276859 + 0.300920i
\(61\) −12.3935 + 7.15536i −1.58682 + 0.916150i −0.592992 + 0.805208i \(0.702054\pi\)
−0.993827 + 0.110942i \(0.964613\pi\)
\(62\) 1.29458 + 1.29458i 0.164412 + 0.164412i
\(63\) 0 0
\(64\) 2.79807i 0.349758i
\(65\) −2.53345 11.3197i −0.314236 1.40404i
\(66\) −2.54782 1.47098i −0.313615 0.181066i
\(67\) 0.152446 + 0.568937i 0.0186243 + 0.0695067i 0.974613 0.223898i \(-0.0718783\pi\)
−0.955988 + 0.293405i \(0.905212\pi\)
\(68\) 2.88323 + 0.772560i 0.349643 + 0.0936866i
\(69\) −0.755439 −0.0909442
\(70\) 0 0
\(71\) −8.12783 −0.964595 −0.482298 0.876007i \(-0.660198\pi\)
−0.482298 + 0.876007i \(0.660198\pi\)
\(72\) −2.52086 0.675461i −0.297086 0.0796039i
\(73\) 3.49631 + 13.0484i 0.409212 + 1.52720i 0.796152 + 0.605096i \(0.206865\pi\)
−0.386940 + 0.922105i \(0.626468\pi\)
\(74\) 5.78881 + 3.34217i 0.672936 + 0.388520i
\(75\) 3.81725 3.22934i 0.440778 0.372892i
\(76\) 0.0988248i 0.0113360i
\(77\) 0 0
\(78\) 2.80203 + 2.80203i 0.317267 + 0.317267i
\(79\) 8.54186 4.93165i 0.961035 0.554854i 0.0645434 0.997915i \(-0.479441\pi\)
0.896491 + 0.443061i \(0.146108\pi\)
\(80\) −1.87539 0.0780974i −0.209675 0.00873155i
\(81\) 0.500000 0.866025i 0.0555556 0.0962250i
\(82\) −1.71624 + 6.40510i −0.189527 + 0.707325i
\(83\) 1.63570 1.63570i 0.179541 0.179541i −0.611615 0.791156i \(-0.709480\pi\)
0.791156 + 0.611615i \(0.209480\pi\)
\(84\) 0 0
\(85\) 1.40788 4.49678i 0.152706 0.487744i
\(86\) 1.49678 + 2.59249i 0.161402 + 0.279556i
\(87\) 2.67665 0.717207i 0.286967 0.0768926i
\(88\) 9.70872 2.60144i 1.03495 0.277315i
\(89\) 2.52657 + 4.37614i 0.267815 + 0.463870i 0.968297 0.249800i \(-0.0803649\pi\)
−0.700482 + 0.713670i \(0.747032\pi\)
\(90\) −0.510348 + 1.63006i −0.0537954 + 0.171823i
\(91\) 0 0
\(92\) 0.756656 0.756656i 0.0788868 0.0788868i
\(93\) 0.620321 2.31507i 0.0643243 0.240062i
\(94\) −2.96561 + 5.13659i −0.305880 + 0.529799i
\(95\) 0.155869 + 0.00649091i 0.0159919 + 0.000665953i
\(96\) 5.07559 2.93039i 0.518025 0.299082i
\(97\) 6.85851 + 6.85851i 0.696376 + 0.696376i 0.963627 0.267251i \(-0.0861152\pi\)
−0.267251 + 0.963627i \(0.586115\pi\)
\(98\) 0 0
\(99\) 3.85136i 0.387076i
\(100\) −0.588852 + 7.05793i −0.0588852 + 0.705793i
\(101\) −16.6236 9.59763i −1.65411 0.955000i −0.975357 0.220632i \(-0.929188\pi\)
−0.678752 0.734368i \(-0.737479\pi\)
\(102\) 0.416622 + 1.55485i 0.0412517 + 0.153954i
\(103\) −3.19410 0.855857i −0.314724 0.0843301i 0.0979992 0.995186i \(-0.468756\pi\)
−0.412723 + 0.910856i \(0.635422\pi\)
\(104\) −13.5384 −1.32755
\(105\) 0 0
\(106\) 6.63105 0.644064
\(107\) 8.73911 + 2.34164i 0.844841 + 0.226375i 0.655178 0.755475i \(-0.272594\pi\)
0.189663 + 0.981849i \(0.439260\pi\)
\(108\) 0.366615 + 1.36822i 0.0352775 + 0.131658i
\(109\) −1.87111 1.08029i −0.179220 0.103473i 0.407706 0.913113i \(-0.366329\pi\)
−0.586926 + 0.809641i \(0.699662\pi\)
\(110\) −1.43677 6.41963i −0.136990 0.612087i
\(111\) 8.75054i 0.830564i
\(112\) 0 0
\(113\) −4.13823 4.13823i −0.389292 0.389292i 0.485143 0.874435i \(-0.338768\pi\)
−0.874435 + 0.485143i \(0.838768\pi\)
\(114\) −0.0461537 + 0.0266469i −0.00432269 + 0.00249571i
\(115\) −1.14372 1.24312i −0.106653 0.115921i
\(116\) −1.96260 + 3.39932i −0.182223 + 0.315619i
\(117\) 1.34264 5.01080i 0.124127 0.463249i
\(118\) −3.76718 + 3.76718i −0.346797 + 0.346797i
\(119\) 0 0
\(120\) −2.70502 5.17085i −0.246934 0.472032i
\(121\) −1.91649 3.31946i −0.174226 0.301769i
\(122\) 10.5592 2.82932i 0.955981 0.256154i
\(123\) 8.38498 2.24675i 0.756048 0.202583i
\(124\) 1.69748 + 2.94012i 0.152438 + 0.264030i
\(125\) 11.0933 + 1.39233i 0.992215 + 0.124533i
\(126\) 0 0
\(127\) −4.83298 + 4.83298i −0.428858 + 0.428858i −0.888239 0.459381i \(-0.848071\pi\)
0.459381 + 0.888239i \(0.348071\pi\)
\(128\) −2.48057 + 9.25761i −0.219253 + 0.818265i
\(129\) 1.95945 3.39386i 0.172520 0.298813i
\(130\) −0.368673 + 8.85312i −0.0323347 + 0.776470i
\(131\) −0.560750 + 0.323749i −0.0489930 + 0.0282861i −0.524296 0.851536i \(-0.675672\pi\)
0.475303 + 0.879822i \(0.342338\pi\)
\(132\) −3.85756 3.85756i −0.335758 0.335758i
\(133\) 0 0
\(134\) 0.449929i 0.0388680i
\(135\) 2.18209 0.488369i 0.187804 0.0420322i
\(136\) −4.76274 2.74977i −0.408402 0.235791i
\(137\) 3.74696 + 13.9839i 0.320125 + 1.19472i 0.919123 + 0.393971i \(0.128899\pi\)
−0.598998 + 0.800751i \(0.704434\pi\)
\(138\) 0.557400 + 0.149355i 0.0474491 + 0.0127139i
\(139\) −22.1663 −1.88012 −0.940060 0.341009i \(-0.889231\pi\)
−0.940060 + 0.341009i \(0.889231\pi\)
\(140\) 0 0
\(141\) 7.76463 0.653900
\(142\) 5.99711 + 1.60692i 0.503266 + 0.134850i
\(143\) 5.17099 + 19.2984i 0.432420 + 1.61381i
\(144\) −0.726965 0.419714i −0.0605804 0.0349761i
\(145\) 5.23261 + 3.31874i 0.434545 + 0.275607i
\(146\) 10.3190i 0.854007i
\(147\) 0 0
\(148\) 8.76463 + 8.76463i 0.720448 + 0.720448i
\(149\) 9.56745 5.52377i 0.783796 0.452525i −0.0539779 0.998542i \(-0.517190\pi\)
0.837774 + 0.546017i \(0.183857\pi\)
\(150\) −3.45501 + 1.62807i −0.282101 + 0.132932i
\(151\) −9.19950 + 15.9340i −0.748645 + 1.29669i 0.199828 + 0.979831i \(0.435962\pi\)
−0.948472 + 0.316859i \(0.897372\pi\)
\(152\) 0.0471251 0.175873i 0.00382235 0.0142652i
\(153\) 1.49007 1.49007i 0.120465 0.120465i
\(154\) 0 0
\(155\) 4.74873 2.48420i 0.381428 0.199536i
\(156\) 3.67407 + 6.36367i 0.294161 + 0.509502i
\(157\) 1.43425 0.384306i 0.114465 0.0306709i −0.201132 0.979564i \(-0.564462\pi\)
0.315597 + 0.948893i \(0.397795\pi\)
\(158\) −7.27763 + 1.95003i −0.578977 + 0.155136i
\(159\) −4.34039 7.51777i −0.344215 0.596198i
\(160\) 12.5065 + 3.91560i 0.988724 + 0.309555i
\(161\) 0 0
\(162\) −0.540143 + 0.540143i −0.0424377 + 0.0424377i
\(163\) 2.01511 7.52050i 0.157836 0.589051i −0.841010 0.541020i \(-0.818038\pi\)
0.998846 0.0480317i \(-0.0152948\pi\)
\(164\) −6.14812 + 10.6488i −0.480087 + 0.831535i
\(165\) −6.33763 + 5.83089i −0.493384 + 0.453935i
\(166\) −1.53028 + 0.883510i −0.118773 + 0.0685737i
\(167\) 1.88968 + 1.88968i 0.146228 + 0.146228i 0.776431 0.630203i \(-0.217028\pi\)
−0.630203 + 0.776431i \(0.717028\pi\)
\(168\) 0 0
\(169\) 13.9108i 1.07006i
\(170\) −1.92784 + 3.03960i −0.147859 + 0.233127i
\(171\) 0.0604203 + 0.0348837i 0.00462046 + 0.00266762i
\(172\) 1.43672 + 5.36192i 0.109549 + 0.408843i
\(173\) 6.70378 + 1.79627i 0.509679 + 0.136568i 0.504488 0.863419i \(-0.331681\pi\)
0.00519041 + 0.999987i \(0.498348\pi\)
\(174\) −2.11676 −0.160471
\(175\) 0 0
\(176\) 3.23294 0.243692
\(177\) 6.73676 + 1.80511i 0.506366 + 0.135680i
\(178\) −0.999035 3.72845i −0.0748808 0.279459i
\(179\) 16.0957 + 9.29284i 1.20305 + 0.694579i 0.961231 0.275743i \(-0.0889239\pi\)
0.241815 + 0.970322i \(0.422257\pi\)
\(180\) −1.69644 + 2.67475i −0.126445 + 0.199364i
\(181\) 8.48528i 0.630706i −0.948974 0.315353i \(-0.897877\pi\)
0.948974 0.315353i \(-0.102123\pi\)
\(182\) 0 0
\(183\) −10.1192 10.1192i −0.748034 0.748034i
\(184\) −1.70740 + 0.985766i −0.125871 + 0.0726716i
\(185\) 14.3995 13.2482i 1.05867 0.974025i
\(186\) −0.915407 + 1.58553i −0.0671209 + 0.116257i
\(187\) −2.10055 + 7.83935i −0.153607 + 0.573270i
\(188\) −7.77713 + 7.77713i −0.567206 + 0.567206i
\(189\) 0 0
\(190\) −0.113725 0.0356057i −0.00825047 0.00258311i
\(191\) 2.69676 + 4.67092i 0.195130 + 0.337976i 0.946943 0.321401i \(-0.104154\pi\)
−0.751813 + 0.659377i \(0.770820\pi\)
\(192\) −2.70273 + 0.724193i −0.195052 + 0.0522641i
\(193\) 6.56510 1.75911i 0.472566 0.126624i −0.0146728 0.999892i \(-0.504671\pi\)
0.487239 + 0.873269i \(0.338004\pi\)
\(194\) −3.70458 6.41652i −0.265973 0.460679i
\(195\) 10.2783 5.37688i 0.736044 0.385046i
\(196\) 0 0
\(197\) 12.6739 12.6739i 0.902981 0.902981i −0.0927124 0.995693i \(-0.529554\pi\)
0.995693 + 0.0927124i \(0.0295537\pi\)
\(198\) 0.761438 2.84172i 0.0541130 0.201953i
\(199\) 1.33556 2.31325i 0.0946750 0.163982i −0.814798 0.579745i \(-0.803152\pi\)
0.909473 + 0.415763i \(0.136485\pi\)
\(200\) 4.41356 12.2798i 0.312086 0.868316i
\(201\) −0.510095 + 0.294503i −0.0359793 + 0.0207727i
\(202\) 10.3682 + 10.3682i 0.729503 + 0.729503i
\(203\) 0 0
\(204\) 2.98494i 0.208988i
\(205\) 16.3919 + 10.3964i 1.14486 + 0.726117i
\(206\) 2.18756 + 1.26299i 0.152414 + 0.0879965i
\(207\) −0.195522 0.729698i −0.0135897 0.0507175i
\(208\) −4.20621 1.12705i −0.291648 0.0781468i
\(209\) −0.268699 −0.0185863
\(210\) 0 0
\(211\) −12.0239 −0.827757 −0.413879 0.910332i \(-0.635826\pi\)
−0.413879 + 0.910332i \(0.635826\pi\)
\(212\) 11.8772 + 3.18250i 0.815733 + 0.218575i
\(213\) −2.10364 7.85088i −0.144139 0.537933i
\(214\) −5.98519 3.45555i −0.409139 0.236217i
\(215\) 8.55135 1.91387i 0.583198 0.130525i
\(216\) 2.60978i 0.177573i
\(217\) 0 0
\(218\) 1.16702 + 1.16702i 0.0790405 + 0.0790405i
\(219\) −11.6989 + 6.75436i −0.790538 + 0.456417i
\(220\) 0.507553 12.1881i 0.0342192 0.821723i
\(221\) 5.46582 9.46708i 0.367671 0.636825i
\(222\) −1.73004 + 6.45658i −0.116112 + 0.433337i
\(223\) −11.6925 + 11.6925i −0.782988 + 0.782988i −0.980334 0.197346i \(-0.936768\pi\)
0.197346 + 0.980334i \(0.436768\pi\)
\(224\) 0 0
\(225\) 4.10728 + 2.85136i 0.273819 + 0.190091i
\(226\) 2.23524 + 3.87155i 0.148686 + 0.257531i
\(227\) −1.50971 + 0.404524i −0.100203 + 0.0268492i −0.308572 0.951201i \(-0.599851\pi\)
0.208369 + 0.978050i \(0.433184\pi\)
\(228\) −0.0954574 + 0.0255777i −0.00632182 + 0.00169393i
\(229\) −3.91654 6.78365i −0.258812 0.448276i 0.707112 0.707102i \(-0.249998\pi\)
−0.965924 + 0.258826i \(0.916664\pi\)
\(230\) 0.598123 + 1.14335i 0.0394390 + 0.0753906i
\(231\) 0 0
\(232\) 5.11372 5.11372i 0.335732 0.335732i
\(233\) 0.368944 1.37692i 0.0241703 0.0902048i −0.952787 0.303639i \(-0.901798\pi\)
0.976957 + 0.213434i \(0.0684649\pi\)
\(234\) −1.98133 + 3.43177i −0.129524 + 0.224342i
\(235\) 11.7555 + 12.7771i 0.766845 + 0.833488i
\(236\) −8.55562 + 4.93959i −0.556923 + 0.321540i
\(237\) 6.97440 + 6.97440i 0.453036 + 0.453036i
\(238\) 0 0
\(239\) 20.2805i 1.31183i 0.754833 + 0.655917i \(0.227718\pi\)
−0.754833 + 0.655917i \(0.772282\pi\)
\(240\) −0.409951 1.83170i −0.0264622 0.118236i
\(241\) 2.39883 + 1.38497i 0.154522 + 0.0892136i 0.575268 0.817965i \(-0.304898\pi\)
−0.420745 + 0.907179i \(0.638231\pi\)
\(242\) 0.757804 + 2.82816i 0.0487135 + 0.181801i
\(243\) 0.965926 + 0.258819i 0.0619642 + 0.0166032i
\(244\) 20.2710 1.29772
\(245\) 0 0
\(246\) −6.63105 −0.422780
\(247\) 0.349590 + 0.0936725i 0.0222439 + 0.00596024i
\(248\) −1.61890 6.04183i −0.102800 0.383656i
\(249\) 2.00331 + 1.15661i 0.126955 + 0.0732973i
\(250\) −7.90992 3.22054i −0.500267 0.203685i
\(251\) 6.09982i 0.385017i 0.981295 + 0.192509i \(0.0616623\pi\)
−0.981295 + 0.192509i \(0.938338\pi\)
\(252\) 0 0
\(253\) 2.05731 + 2.05731i 0.129342 + 0.129342i
\(254\) 4.52152 2.61050i 0.283706 0.163797i
\(255\) 4.70794 + 0.196054i 0.294823 + 0.0122774i
\(256\) 6.45864 11.1867i 0.403665 0.699168i
\(257\) −0.738795 + 2.75722i −0.0460848 + 0.171991i −0.985133 0.171796i \(-0.945043\pi\)
0.939048 + 0.343787i \(0.111710\pi\)
\(258\) −2.11676 + 2.11676i −0.131784 + 0.131784i
\(259\) 0 0
\(260\) −4.90931 + 15.6804i −0.304462 + 0.972456i
\(261\) 1.38554 + 2.39982i 0.0857626 + 0.148545i
\(262\) 0.477756 0.128014i 0.0295159 0.00790876i
\(263\) −22.9063 + 6.13773i −1.41246 + 0.378469i −0.882804 0.469741i \(-0.844347\pi\)
−0.529660 + 0.848210i \(0.677681\pi\)
\(264\) 5.02561 + 8.70460i 0.309305 + 0.535731i
\(265\) 5.79964 18.5241i 0.356269 1.13793i
\(266\) 0 0
\(267\) −3.57310 + 3.57310i −0.218670 + 0.218670i
\(268\) 0.215939 0.805894i 0.0131905 0.0492278i
\(269\) −12.3676 + 21.4213i −0.754064 + 1.30608i 0.191774 + 0.981439i \(0.438576\pi\)
−0.945838 + 0.324638i \(0.894758\pi\)
\(270\) −1.70660 0.0710685i −0.103861 0.00432509i
\(271\) −3.58076 + 2.06735i −0.217515 + 0.125583i −0.604799 0.796378i \(-0.706747\pi\)
0.387284 + 0.921961i \(0.373413\pi\)
\(272\) −1.25081 1.25081i −0.0758413 0.0758413i
\(273\) 0 0
\(274\) 11.0588i 0.668085i
\(275\) −19.1901 1.60106i −1.15721 0.0965473i
\(276\) 0.926710 + 0.535036i 0.0557814 + 0.0322054i
\(277\) −4.43358 16.5463i −0.266388 0.994174i −0.961395 0.275171i \(-0.911266\pi\)
0.695007 0.719003i \(-0.255401\pi\)
\(278\) 16.3554 + 4.38241i 0.980931 + 0.262840i
\(279\) 2.39674 0.143489
\(280\) 0 0
\(281\) 5.25279 0.313355 0.156678 0.987650i \(-0.449922\pi\)
0.156678 + 0.987650i \(0.449922\pi\)
\(282\) −5.72913 1.53511i −0.341164 0.0914147i
\(283\) −0.610271 2.27756i −0.0362768 0.135387i 0.945412 0.325876i \(-0.105659\pi\)
−0.981689 + 0.190489i \(0.938993\pi\)
\(284\) 9.97054 + 5.75649i 0.591643 + 0.341585i
\(285\) 0.0340722 + 0.152238i 0.00201827 + 0.00901782i
\(286\) 15.2617i 0.902441i
\(287\) 0 0
\(288\) 4.14420 + 4.14420i 0.244199 + 0.244199i
\(289\) −10.8767 + 6.27969i −0.639808 + 0.369393i
\(290\) −3.20474 3.48325i −0.188189 0.204544i
\(291\) −4.84970 + 8.39993i −0.284294 + 0.492412i
\(292\) 4.95249 18.4830i 0.289823 1.08163i
\(293\) −15.2556 + 15.2556i −0.891240 + 0.891240i −0.994640 0.103400i \(-0.967028\pi\)
0.103400 + 0.994640i \(0.467028\pi\)
\(294\) 0 0
\(295\) 7.22893 + 13.8186i 0.420884 + 0.804551i
\(296\) −11.4185 19.7774i −0.663687 1.14954i
\(297\) −3.72013 + 0.996806i −0.215864 + 0.0578405i
\(298\) −8.15142 + 2.18417i −0.472199 + 0.126525i
\(299\) −1.95945 3.39386i −0.113318 0.196272i
\(300\) −6.96984 + 1.25794i −0.402404 + 0.0726272i
\(301\) 0 0
\(302\) 9.93809 9.93809i 0.571873 0.571873i
\(303\) 4.96810 18.5412i 0.285410 1.06516i
\(304\) 0.0292823 0.0507184i 0.00167946 0.00290890i
\(305\) 1.33142 31.9720i 0.0762369 1.83071i
\(306\) −1.39404 + 0.804852i −0.0796922 + 0.0460103i
\(307\) −14.6198 14.6198i −0.834394 0.834394i 0.153721 0.988114i \(-0.450874\pi\)
−0.988114 + 0.153721i \(0.950874\pi\)
\(308\) 0 0
\(309\) 3.30678i 0.188116i
\(310\) −3.99499 + 0.894114i −0.226900 + 0.0507823i
\(311\) 2.47872 + 1.43109i 0.140555 + 0.0811497i 0.568629 0.822594i \(-0.307474\pi\)
−0.428073 + 0.903744i \(0.640807\pi\)
\(312\) −3.50400 13.0771i −0.198375 0.740345i
\(313\) 12.8656 + 3.44732i 0.727204 + 0.194854i 0.603384 0.797451i \(-0.293819\pi\)
0.123820 + 0.992305i \(0.460485\pi\)
\(314\) −1.13424 −0.0640088
\(315\) 0 0
\(316\) −13.9713 −0.785945
\(317\) −10.0855 2.70240i −0.566459 0.151782i −0.0357866 0.999359i \(-0.511394\pi\)
−0.530672 + 0.847577i \(0.678060\pi\)
\(318\) 1.71624 + 6.40510i 0.0962421 + 0.359180i
\(319\) −9.24258 5.33620i −0.517485 0.298770i
\(320\) −5.28358 3.35107i −0.295361 0.187331i
\(321\) 9.04739i 0.504976i
\(322\) 0 0
\(323\) 0.103958 + 0.103958i 0.00578440 + 0.00578440i
\(324\) −1.22672 + 0.708245i −0.0681509 + 0.0393470i
\(325\) 24.4091 + 8.77301i 1.35397 + 0.486639i
\(326\) −2.97370 + 5.15060i −0.164698 + 0.285265i
\(327\) 0.559197 2.08695i 0.0309237 0.115409i
\(328\) 16.0194 16.0194i 0.884526 0.884526i
\(329\) 0 0
\(330\) 5.82902 3.04933i 0.320877 0.167860i
\(331\) −11.8100 20.4555i −0.649136 1.12434i −0.983330 0.181833i \(-0.941797\pi\)
0.334193 0.942505i \(-0.391536\pi\)
\(332\) −3.16501 + 0.848062i −0.173703 + 0.0465435i
\(333\) 8.45237 2.26481i 0.463187 0.124111i
\(334\) −1.02070 1.76790i −0.0558500 0.0967351i
\(335\) −1.25690 0.393517i −0.0686716 0.0215001i
\(336\) 0 0
\(337\) −4.93809 + 4.93809i −0.268995 + 0.268995i −0.828695 0.559700i \(-0.810916\pi\)
0.559700 + 0.828695i \(0.310916\pi\)
\(338\) −2.75026 + 10.2641i −0.149594 + 0.558293i
\(339\) 2.92617 5.06828i 0.158928 0.275271i
\(340\) −4.91189 + 4.51915i −0.266385 + 0.245085i
\(341\) −7.99402 + 4.61535i −0.432900 + 0.249935i
\(342\) −0.0376844 0.0376844i −0.00203774 0.00203774i
\(343\) 0 0
\(344\) 10.2274i 0.551427i
\(345\) 0.904743 1.42649i 0.0487097 0.0767998i
\(346\) −4.59124 2.65076i −0.246827 0.142505i
\(347\) 2.13647 + 7.97341i 0.114692 + 0.428035i 0.999264 0.0383685i \(-0.0122161\pi\)
−0.884572 + 0.466404i \(0.845549\pi\)
\(348\) −3.79145 1.01592i −0.203243 0.0544589i
\(349\) −16.9121 −0.905282 −0.452641 0.891693i \(-0.649518\pi\)
−0.452641 + 0.891693i \(0.649518\pi\)
\(350\) 0 0
\(351\) 5.18757 0.276892
\(352\) −21.8029 5.84206i −1.16210 0.311383i
\(353\) −4.07257 15.1990i −0.216761 0.808963i −0.985539 0.169448i \(-0.945802\pi\)
0.768778 0.639516i \(-0.220865\pi\)
\(354\) −4.61383 2.66380i −0.245222 0.141579i
\(355\) 9.73419 15.3477i 0.516637 0.814574i
\(356\) 7.15771i 0.379358i
\(357\) 0 0
\(358\) −10.0389 10.0389i −0.530574 0.530574i
\(359\) 7.05693 4.07432i 0.372450 0.215034i −0.302078 0.953283i \(-0.597680\pi\)
0.674528 + 0.738249i \(0.264347\pi\)
\(360\) 4.29454 3.95116i 0.226342 0.208245i
\(361\) 9.49757 16.4503i 0.499872 0.865804i
\(362\) −1.67759 + 6.26086i −0.0881723 + 0.329063i
\(363\) 2.71033 2.71033i 0.142255 0.142255i
\(364\) 0 0
\(365\) −28.8266 9.02520i −1.50885 0.472401i
\(366\) 5.46582 + 9.46708i 0.285703 + 0.494852i
\(367\) −20.1462 + 5.39815i −1.05162 + 0.281781i −0.742922 0.669378i \(-0.766561\pi\)
−0.308700 + 0.951160i \(0.599894\pi\)
\(368\) −0.612529 + 0.164127i −0.0319303 + 0.00855569i
\(369\) 4.34039 + 7.51777i 0.225951 + 0.391359i
\(370\) −13.2439 + 6.92828i −0.688518 + 0.360184i
\(371\) 0 0
\(372\) −2.40060 + 2.40060i −0.124465 + 0.124465i
\(373\) 0.547065 2.04168i 0.0283260 0.105714i −0.950316 0.311288i \(-0.899240\pi\)
0.978642 + 0.205574i \(0.0659062\pi\)
\(374\) 3.09977 5.36897i 0.160286 0.277623i
\(375\) 1.52627 + 11.0757i 0.0788165 + 0.571945i
\(376\) 17.5491 10.1320i 0.905027 0.522518i
\(377\) 10.1648 + 10.1648i 0.523511 + 0.523511i
\(378\) 0 0
\(379\) 18.7135i 0.961248i 0.876927 + 0.480624i \(0.159590\pi\)
−0.876927 + 0.480624i \(0.840410\pi\)
\(380\) −0.186611 0.118356i −0.00957292 0.00607155i
\(381\) −5.91917 3.41743i −0.303248 0.175080i
\(382\) −1.06633 3.97960i −0.0545582 0.203614i
\(383\) −28.5983 7.66288i −1.46130 0.391555i −0.561364 0.827569i \(-0.689723\pi\)
−0.899940 + 0.436014i \(0.856390\pi\)
\(384\) −9.58418 −0.489091
\(385\) 0 0
\(386\) −5.19184 −0.264258
\(387\) 3.78536 + 1.01428i 0.192421 + 0.0515589i
\(388\) −3.55594 13.2710i −0.180526 0.673731i
\(389\) −22.2232 12.8305i −1.12676 0.650535i −0.183641 0.982993i \(-0.558788\pi\)
−0.943118 + 0.332459i \(0.892122\pi\)
\(390\) −8.64687 + 1.93525i −0.437852 + 0.0979949i
\(391\) 1.59192i 0.0805069i
\(392\) 0 0
\(393\) −0.457851 0.457851i −0.0230955 0.0230955i
\(394\) −11.8572 + 6.84574i −0.597356 + 0.344883i
\(395\) −0.917646 + 22.0359i −0.0461718 + 1.10875i
\(396\) 2.72771 4.72453i 0.137073 0.237417i
\(397\) 2.46549 9.20135i 0.123740 0.461802i −0.876052 0.482217i \(-0.839832\pi\)
0.999792 + 0.0204142i \(0.00649848\pi\)
\(398\) −1.44278 + 1.44278i −0.0723201 + 0.0723201i
\(399\) 0 0
\(400\) 2.39351 3.44776i 0.119676 0.172388i
\(401\) −7.37513 12.7741i −0.368296 0.637908i 0.621003 0.783808i \(-0.286726\pi\)
−0.989299 + 0.145900i \(0.953392\pi\)
\(402\) 0.434598 0.116450i 0.0216758 0.00580801i
\(403\) 12.0096 3.21796i 0.598240 0.160298i
\(404\) 13.5950 + 23.5472i 0.676374 + 1.17151i
\(405\) 1.03649 + 1.98133i 0.0515038 + 0.0984532i
\(406\) 0 0
\(407\) −23.8305 + 23.8305i −1.18124 + 1.18124i
\(408\) 1.42339 5.31215i 0.0704681 0.262990i
\(409\) −5.28021 + 9.14560i −0.261090 + 0.452221i −0.966532 0.256547i \(-0.917415\pi\)
0.705442 + 0.708768i \(0.250749\pi\)
\(410\) −10.0393 10.9118i −0.495805 0.538894i
\(411\) −12.5376 + 7.23858i −0.618434 + 0.357053i
\(412\) 3.31210 + 3.31210i 0.163176 + 0.163176i
\(413\) 0 0
\(414\) 0.577063i 0.0283611i
\(415\) 1.12971 + 5.04765i 0.0554552 + 0.247779i
\(416\) 26.3299 + 15.2016i 1.29093 + 0.745320i
\(417\) −5.73706 21.4110i −0.280945 1.04850i
\(418\) 0.198260 + 0.0531235i 0.00969719 + 0.00259835i
\(419\) 15.5472 0.759532 0.379766 0.925083i \(-0.376004\pi\)
0.379766 + 0.925083i \(0.376004\pi\)
\(420\) 0 0
\(421\) 3.29886 0.160776 0.0803882 0.996764i \(-0.474384\pi\)
0.0803882 + 0.996764i \(0.474384\pi\)
\(422\) 8.87180 + 2.37719i 0.431873 + 0.115720i
\(423\) 2.00963 + 7.50006i 0.0977117 + 0.364665i
\(424\) −19.6197 11.3275i −0.952818 0.550110i
\(425\) 6.80512 + 8.04400i 0.330097 + 0.390191i
\(426\) 6.20867i 0.300811i
\(427\) 0 0
\(428\) −9.06196 9.06196i −0.438026 0.438026i
\(429\) −17.3025 + 9.98959i −0.835372 + 0.482302i
\(430\) −6.68799 0.278510i −0.322524 0.0134309i
\(431\) 7.04553 12.2032i 0.339371 0.587809i −0.644943 0.764230i \(-0.723119\pi\)
0.984315 + 0.176422i \(0.0564523\pi\)
\(432\) 0.217260 0.810825i 0.0104529 0.0390108i
\(433\) −1.72650 + 1.72650i −0.0829702 + 0.0829702i −0.747374 0.664404i \(-0.768686\pi\)
0.664404 + 0.747374i \(0.268686\pi\)
\(434\) 0 0
\(435\) −1.85136 + 5.91327i −0.0887660 + 0.283519i
\(436\) 1.53022 + 2.65041i 0.0732840 + 0.126932i
\(437\) 0.0509091 0.0136411i 0.00243531 0.000652540i
\(438\) 9.96739 2.67075i 0.476260 0.127614i
\(439\) 13.5586 + 23.4841i 0.647116 + 1.12084i 0.983809 + 0.179223i \(0.0573582\pi\)
−0.336693 + 0.941615i \(0.609308\pi\)
\(440\) −6.71524 + 21.4485i −0.320136 + 1.02252i
\(441\) 0 0
\(442\) −5.90465 + 5.90465i −0.280856 + 0.280856i
\(443\) −8.83957 + 32.9897i −0.419981 + 1.56739i 0.354664 + 0.934994i \(0.384595\pi\)
−0.774645 + 0.632396i \(0.782072\pi\)
\(444\) −6.19753 + 10.7344i −0.294122 + 0.509434i
\(445\) −11.2894 0.470126i −0.535167 0.0222861i
\(446\) 10.9390 6.31563i 0.517976 0.299054i
\(447\) 7.81179 + 7.81179i 0.369485 + 0.369485i
\(448\) 0 0
\(449\) 9.80267i 0.462617i −0.972881 0.231308i \(-0.925699\pi\)
0.972881 0.231308i \(-0.0743006\pi\)
\(450\) −2.46682 2.91591i −0.116287 0.137457i
\(451\) −28.9536 16.7164i −1.36337 0.787144i
\(452\) 2.14556 + 8.00732i 0.100918 + 0.376633i
\(453\) −17.7721 4.76201i −0.835005 0.223739i
\(454\) 1.19391 0.0560331
\(455\) 0 0
\(456\) 0.182078 0.00852656
\(457\) −0.751411 0.201340i −0.0351495 0.00941828i 0.241201 0.970475i \(-0.422459\pi\)
−0.276351 + 0.961057i \(0.589125\pi\)
\(458\) 1.54865 + 5.77964i 0.0723636 + 0.270065i
\(459\) 1.82496 + 1.05364i 0.0851817 + 0.0491797i
\(460\) 0.522591 + 2.33499i 0.0243659 + 0.108869i
\(461\) 0.831786i 0.0387401i −0.999812 0.0193701i \(-0.993834\pi\)
0.999812 0.0193701i \(-0.00616607\pi\)
\(462\) 0 0
\(463\) 5.45140 + 5.45140i 0.253348 + 0.253348i 0.822342 0.568994i \(-0.192667\pi\)
−0.568994 + 0.822342i \(0.692667\pi\)
\(464\) 2.01448 1.16306i 0.0935197 0.0539936i
\(465\) 3.62862 + 3.94397i 0.168273 + 0.182897i
\(466\) −0.544450 + 0.943015i −0.0252211 + 0.0436843i
\(467\) −8.52208 + 31.8048i −0.394355 + 1.47175i 0.428522 + 0.903531i \(0.359035\pi\)
−0.822876 + 0.568220i \(0.807632\pi\)
\(468\) −5.19592 + 5.19592i −0.240181 + 0.240181i
\(469\) 0 0
\(470\) −6.14768 11.7517i −0.283571 0.542067i
\(471\) 0.742422 + 1.28591i 0.0342090 + 0.0592517i
\(472\) 17.5815 4.71094i 0.809252 0.216838i
\(473\) −14.5788 + 3.90637i −0.670333 + 0.179615i
\(474\) −3.76718 6.52494i −0.173032 0.299700i
\(475\) −0.198932 + 0.286554i −0.00912762 + 0.0131480i
\(476\) 0 0
\(477\) 6.13823 6.13823i 0.281050 0.281050i
\(478\) 4.00957 14.9639i 0.183394 0.684434i
\(479\) 20.2160 35.0151i 0.923691 1.59988i 0.130038 0.991509i \(-0.458490\pi\)
0.793653 0.608371i \(-0.208177\pi\)
\(480\) −0.545267 + 13.0938i −0.0248879 + 0.597646i
\(481\) 39.3123 22.6970i 1.79249 1.03489i
\(482\) −1.49616 1.49616i −0.0681483 0.0681483i
\(483\) 0 0
\(484\) 5.42938i 0.246790i
\(485\) −21.1649 + 4.73689i −0.961049 + 0.215091i
\(486\) −0.661538 0.381939i −0.0300080 0.0173251i
\(487\) −2.64597 9.87490i −0.119900 0.447474i 0.879706 0.475517i \(-0.157739\pi\)
−0.999607 + 0.0280431i \(0.991072\pi\)
\(488\) −36.0753 9.66634i −1.63305 0.437575i
\(489\) 7.78580 0.352086
\(490\) 0 0
\(491\) 20.1040 0.907279 0.453639 0.891185i \(-0.350125\pi\)
0.453639 + 0.891185i \(0.350125\pi\)
\(492\) −11.8772 3.18250i −0.535468 0.143478i
\(493\) 1.51135 + 5.64045i 0.0680680 + 0.254033i
\(494\) −0.239425 0.138232i −0.0107723 0.00621937i
\(495\) −7.27251 4.61254i −0.326875 0.207318i
\(496\) 2.01189i 0.0903364i
\(497\) 0 0
\(498\) −1.24947 1.24947i −0.0559902 0.0559902i
\(499\) 13.3564 7.71133i 0.597916 0.345207i −0.170306 0.985391i \(-0.554475\pi\)
0.768221 + 0.640185i \(0.221142\pi\)
\(500\) −12.6222 9.56477i −0.564484 0.427750i
\(501\) −1.33620 + 2.31437i −0.0596972 + 0.103399i
\(502\) 1.20597 4.50075i 0.0538252 0.200878i
\(503\) 25.9985 25.9985i 1.15922 1.15922i 0.174573 0.984644i \(-0.444145\pi\)
0.984644 0.174573i \(-0.0558546\pi\)
\(504\) 0 0
\(505\) 38.0322 19.8958i 1.69241 0.885350i
\(506\) −1.11124 1.92472i −0.0494006 0.0855644i
\(507\) 13.4368 3.60039i 0.596751 0.159899i
\(508\) 9.35164 2.50576i 0.414912 0.111175i
\(509\) −18.5636 32.1530i −0.822816 1.42516i −0.903577 0.428425i \(-0.859069\pi\)
0.0807619 0.996733i \(-0.474265\pi\)
\(510\) −3.43499 1.07545i −0.152104 0.0476216i
\(511\) 0 0
\(512\) 6.57690 6.57690i 0.290661 0.290661i
\(513\) −0.0180571 + 0.0673901i −0.000797241 + 0.00297535i
\(514\) 1.09024 1.88835i 0.0480884 0.0832915i
\(515\) 5.44149 5.00641i 0.239781 0.220609i
\(516\) −4.80737 + 2.77554i −0.211633 + 0.122186i
\(517\) −21.1456 21.1456i −0.929982 0.929982i
\(518\) 0 0
\(519\) 6.94026i 0.304644i
\(520\) 16.2141 25.5645i 0.711036 1.12108i
\(521\) −2.24415 1.29566i −0.0983180 0.0567639i 0.450035 0.893011i \(-0.351412\pi\)
−0.548353 + 0.836247i \(0.684745\pi\)
\(522\) −0.547858 2.04464i −0.0239791 0.0894913i
\(523\) 8.31711 + 2.22856i 0.363682 + 0.0974482i 0.436032 0.899931i \(-0.356383\pi\)
−0.0723506 + 0.997379i \(0.523050\pi\)
\(524\) 0.917176 0.0400670
\(525\) 0 0
\(526\) 18.1149 0.789846
\(527\) 4.87850 + 1.30719i 0.212511 + 0.0569421i
\(528\) 0.836746 + 3.12278i 0.0364147 + 0.135901i
\(529\) 19.4244 + 11.2147i 0.844537 + 0.487594i
\(530\) −7.94159 + 12.5214i −0.344961 + 0.543894i
\(531\) 6.97440i 0.302663i
\(532\) 0 0
\(533\) 31.8425 + 31.8425i 1.37925 + 1.37925i
\(534\) 3.34284 1.92999i 0.144659 0.0835187i
\(535\) −14.8880 + 13.6976i −0.643664 + 0.592199i
\(536\) −0.768589 + 1.33124i −0.0331980 + 0.0575006i
\(537\) −4.81033 + 17.9524i −0.207581 + 0.774703i
\(538\) 13.3605 13.3605i 0.576013 0.576013i
\(539\) 0 0
\(540\) −3.02269 0.946361i −0.130076 0.0407249i
\(541\) 16.7319 + 28.9805i 0.719360 + 1.24597i 0.961254 + 0.275665i \(0.0888980\pi\)
−0.241894 + 0.970303i \(0.577769\pi\)
\(542\) 3.05079 0.817456i 0.131042 0.0351127i
\(543\) 8.19615 2.19615i 0.351731 0.0942459i
\(544\) 6.17515 + 10.6957i 0.264757 + 0.458573i
\(545\) 4.28081 2.23942i 0.183370 0.0959262i
\(546\) 0 0
\(547\) −0.828381 + 0.828381i −0.0354190 + 0.0354190i −0.724594 0.689175i \(-0.757973\pi\)
0.689175 + 0.724594i \(0.257973\pi\)
\(548\) 5.30754 19.8080i 0.226727 0.846156i
\(549\) 7.15536 12.3935i 0.305383 0.528940i
\(550\) 13.8429 + 4.97534i 0.590263 + 0.212149i
\(551\) −0.167429 + 0.0966653i −0.00713272 + 0.00411808i
\(552\) −1.39408 1.39408i −0.0593361 0.0593361i
\(553\) 0 0
\(554\) 13.0853i 0.555939i
\(555\) 16.5236 + 10.4800i 0.701388 + 0.444850i
\(556\) 27.1918 + 15.6992i 1.15319 + 0.665793i
\(557\) 5.38496 + 20.0969i 0.228168 + 0.851534i 0.981111 + 0.193448i \(0.0619671\pi\)
−0.752943 + 0.658086i \(0.771366\pi\)
\(558\) −1.76843 0.473850i −0.0748636 0.0200597i
\(559\) 20.3295 0.859846
\(560\) 0 0
\(561\) −8.11589 −0.342653
\(562\) −3.87577 1.03851i −0.163489 0.0438069i
\(563\) −8.77338 32.7427i −0.369754 1.37994i −0.860860 0.508841i \(-0.830074\pi\)
0.491106 0.871100i \(-0.336593\pi\)
\(564\) −9.52500 5.49926i −0.401075 0.231561i
\(565\) 12.7703 2.85811i 0.537251 0.120241i
\(566\) 1.80115i 0.0757080i
\(567\) 0 0
\(568\) −14.9990 14.9990i −0.629346 0.629346i
\(569\) 13.5671 7.83298i 0.568763 0.328376i −0.187892 0.982190i \(-0.560165\pi\)
0.756655 + 0.653814i \(0.226832\pi\)
\(570\) 0.00495826 0.119065i 0.000207679 0.00498709i
\(571\) −18.4943 + 32.0331i −0.773964 + 1.34055i 0.161411 + 0.986887i \(0.448396\pi\)
−0.935375 + 0.353658i \(0.884938\pi\)
\(572\) 7.32466 27.3360i 0.306260 1.14298i
\(573\) −3.81379 + 3.81379i −0.159323 + 0.159323i
\(574\) 0 0
\(575\) 3.71714 0.670882i 0.155015 0.0279777i
\(576\) −1.39903 2.42320i −0.0582931 0.100967i
\(577\) −21.2536 + 5.69488i −0.884798 + 0.237081i −0.672476 0.740119i \(-0.734769\pi\)
−0.212322 + 0.977200i \(0.568103\pi\)
\(578\) 9.26693 2.48307i 0.385453 0.103282i
\(579\) 3.39835 + 5.88611i 0.141230 + 0.244618i
\(580\) −4.06845 7.77713i −0.168933 0.322928i
\(581\) 0 0
\(582\) 5.23907 5.23907i 0.217166 0.217166i
\(583\) −8.65304 + 32.2936i −0.358372 + 1.33746i
\(584\) −17.6274 + 30.5315i −0.729427 + 1.26340i
\(585\) 7.85389 + 8.53643i 0.324718 + 0.352938i
\(586\) 14.2724 8.24019i 0.589589 0.340399i
\(587\) −15.7111 15.7111i −0.648468 0.648468i 0.304155 0.952623i \(-0.401626\pi\)
−0.952623 + 0.304155i \(0.901626\pi\)
\(588\) 0 0
\(589\) 0.167214i 0.00688993i
\(590\) −2.60183 11.6253i −0.107116 0.478604i
\(591\) 15.5223 + 8.96183i 0.638504 + 0.368640i
\(592\) −1.90114 7.09515i −0.0781364 0.291609i
\(593\) 2.52987 + 0.677877i 0.103889 + 0.0278371i 0.310389 0.950610i \(-0.399541\pi\)
−0.206500 + 0.978447i \(0.566207\pi\)
\(594\) 2.94197 0.120710
\(595\) 0 0
\(596\) −15.6487 −0.640997
\(597\) 2.58009 + 0.691334i 0.105596 + 0.0282944i
\(598\) 0.774789 + 2.89155i 0.0316835 + 0.118244i
\(599\) 40.9761 + 23.6576i 1.67424 + 0.966622i 0.965223 + 0.261429i \(0.0841936\pi\)
0.709015 + 0.705193i \(0.249140\pi\)
\(600\) 13.0037 + 1.08492i 0.530875 + 0.0442915i
\(601\) 11.0819i 0.452041i 0.974123 + 0.226021i \(0.0725717\pi\)
−0.974123 + 0.226021i \(0.927428\pi\)
\(602\) 0 0
\(603\) −0.416491 0.416491i −0.0169608 0.0169608i
\(604\) 22.5704 13.0310i 0.918375 0.530224i
\(605\) 8.56339 + 0.356607i 0.348151 + 0.0144981i
\(606\) −7.33142 + 12.6984i −0.297819 + 0.515837i
\(607\) 2.76222 10.3088i 0.112115 0.418419i −0.886940 0.461885i \(-0.847173\pi\)
0.999055 + 0.0434656i \(0.0138399\pi\)
\(608\) −0.289130 + 0.289130i −0.0117258 + 0.0117258i
\(609\) 0 0
\(610\) −7.30346 + 23.3273i −0.295708 + 0.944496i
\(611\) 20.1398 + 34.8831i 0.814767 + 1.41122i
\(612\) −2.88323 + 0.772560i −0.116548 + 0.0312289i
\(613\) 3.58564 0.960769i 0.144823 0.0388051i −0.185679 0.982610i \(-0.559449\pi\)
0.330502 + 0.943805i \(0.392782\pi\)
\(614\) 7.89676 + 13.6776i 0.318687 + 0.551983i
\(615\) −5.79964 + 18.5241i −0.233864 + 0.746965i
\(616\) 0 0
\(617\) 11.3212 11.3212i 0.455774 0.455774i −0.441491 0.897266i \(-0.645550\pi\)
0.897266 + 0.441491i \(0.145550\pi\)
\(618\) −0.653770 + 2.43990i −0.0262985 + 0.0981473i
\(619\) 4.53385 7.85287i 0.182231 0.315633i −0.760409 0.649445i \(-0.775001\pi\)
0.942640 + 0.333811i \(0.108335\pi\)
\(620\) −7.58478 0.315855i −0.304612 0.0126850i
\(621\) 0.654230 0.377720i 0.0262533 0.0151574i
\(622\) −1.54599 1.54599i −0.0619884 0.0619884i
\(623\) 0 0
\(624\) 4.35458i 0.174323i
\(625\) −15.9149 + 19.2799i −0.636595 + 0.771198i
\(626\) −8.81129 5.08720i −0.352170 0.203325i
\(627\) −0.0695445 0.259544i −0.00277734 0.0103652i
\(628\) −2.03160 0.544366i −0.0810697 0.0217225i
\(629\) 18.4398 0.735244
\(630\) 0 0
\(631\) −9.67260 −0.385060 −0.192530 0.981291i \(-0.561669\pi\)
−0.192530 + 0.981291i \(0.561669\pi\)
\(632\) 24.8639 + 6.66227i 0.989034 + 0.265011i
\(633\) −3.11201 11.6142i −0.123691 0.461622i
\(634\) 6.90730 + 3.98793i 0.274324 + 0.158381i
\(635\) −3.33794 14.9143i −0.132462 0.591854i
\(636\) 12.2962i 0.487577i
\(637\) 0 0
\(638\) 5.76463 + 5.76463i 0.228224 + 0.228224i
\(639\) 7.03890 4.06391i 0.278455 0.160766i
\(640\) −14.5103 15.7713i −0.573570 0.623416i
\(641\) 20.2924 35.1474i 0.801500 1.38824i −0.117129 0.993117i \(-0.537369\pi\)
0.918629 0.395122i \(-0.129298\pi\)
\(642\) 1.78872 6.67561i 0.0705953 0.263465i
\(643\) 3.89544 3.89544i 0.153621 0.153621i −0.626112 0.779733i \(-0.715355\pi\)
0.779733 + 0.626112i \(0.215355\pi\)
\(644\) 0 0
\(645\) 4.06191 + 7.76463i 0.159937 + 0.305732i
\(646\) −0.0561524 0.0972588i −0.00220929 0.00382660i
\(647\) −23.0058 + 6.16438i −0.904450 + 0.242347i −0.680927 0.732352i \(-0.738423\pi\)
−0.223524 + 0.974698i \(0.571756\pi\)
\(648\) 2.52086 0.675461i 0.0990285 0.0265346i
\(649\) −13.4305 23.2623i −0.527192 0.913123i
\(650\) −16.2758 11.2990i −0.638388 0.443183i
\(651\) 0 0
\(652\) −7.79833 + 7.79833i −0.305406 + 0.305406i
\(653\) −8.41678 + 31.4119i −0.329374 + 1.22924i 0.580467 + 0.814284i \(0.302870\pi\)
−0.909841 + 0.414957i \(0.863797\pi\)
\(654\) −0.825207 + 1.42930i −0.0322681 + 0.0558901i
\(655\) 0.0602410 1.44660i 0.00235381 0.0565232i
\(656\) 6.31062 3.64344i 0.246388 0.142252i
\(657\) −9.55210 9.55210i −0.372663 0.372663i
\(658\) 0 0
\(659\) 32.7543i 1.27593i −0.770067 0.637963i \(-0.779777\pi\)
0.770067 0.637963i \(-0.220223\pi\)
\(660\) 11.9042 2.66426i 0.463370 0.103706i
\(661\) 28.1609 + 16.2587i 1.09533 + 0.632391i 0.934991 0.354671i \(-0.115407\pi\)
0.160341 + 0.987062i \(0.448740\pi\)
\(662\) 4.66982 + 17.4280i 0.181498 + 0.677359i
\(663\) 10.5592 + 2.82932i 0.410084 + 0.109882i
\(664\) 6.03701 0.234281
\(665\) 0 0
\(666\) −6.68434 −0.259013
\(667\) 2.02205 + 0.541806i 0.0782940 + 0.0209788i
\(668\) −0.979744 3.65646i −0.0379075 0.141473i
\(669\) −14.3203 8.26785i −0.553656 0.319654i
\(670\) 0.849600 + 0.538852i 0.0328229 + 0.0208177i
\(671\) 55.1158i 2.12772i
\(672\) 0 0
\(673\) −16.7534 16.7534i −0.645796 0.645796i 0.306179 0.951974i \(-0.400950\pi\)
−0.951974 + 0.306179i \(0.900950\pi\)
\(674\) 4.61986 2.66728i 0.177950 0.102740i
\(675\) −1.69116 + 4.70531i −0.0650928 + 0.181108i
\(676\) −9.85228 + 17.0647i −0.378934 + 0.656333i
\(677\) −2.50935 + 9.36503i −0.0964422 + 0.359927i −0.997234 0.0743237i \(-0.976320\pi\)
0.900792 + 0.434251i \(0.142987\pi\)
\(678\) −3.16110 + 3.16110i −0.121401 + 0.121401i
\(679\) 0 0
\(680\) 10.8964 5.70024i 0.417858 0.218594i
\(681\) −0.781481 1.35357i −0.0299464 0.0518687i
\(682\) 6.81087 1.82497i 0.260802 0.0698816i
\(683\) −31.7389 + 8.50440i −1.21445 + 0.325412i −0.808508 0.588485i \(-0.799725\pi\)
−0.405946 + 0.913897i \(0.633058\pi\)
\(684\) −0.0494124 0.0855848i −0.00188933 0.00327242i
\(685\) −30.8932 9.67222i −1.18037 0.369557i
\(686\) 0 0
\(687\) 5.53883 5.53883i 0.211319 0.211319i
\(688\) 0.851417 3.17753i 0.0324600 0.121142i
\(689\) 22.5160 38.9989i 0.857793 1.48574i
\(690\) −0.949590 + 0.873664i −0.0361503 + 0.0332598i
\(691\) −36.7813 + 21.2357i −1.39923 + 0.807845i −0.994312 0.106509i \(-0.966033\pi\)
−0.404916 + 0.914354i \(0.632699\pi\)
\(692\) −6.95144 6.95144i −0.264254 0.264254i
\(693\) 0 0
\(694\) 6.30557i 0.239356i
\(695\) 26.5472 41.8565i 1.00699 1.58771i
\(696\) 6.26301 + 3.61595i 0.237399 + 0.137062i
\(697\) 4.73453 + 17.6695i 0.179333 + 0.669280i
\(698\) 12.4786 + 3.34362i 0.472320 + 0.126558i
\(699\) 1.42549 0.0539169
\(700\) 0 0
\(701\) 17.0793 0.645077 0.322539 0.946556i \(-0.395464\pi\)
0.322539 + 0.946556i \(0.395464\pi\)
\(702\) −3.82764 1.02561i −0.144465 0.0387093i
\(703\) 0.158010 + 0.589700i 0.00595944 + 0.0222409i
\(704\) 9.33261 + 5.38818i 0.351736 + 0.203075i
\(705\) −9.29921 + 14.6619i −0.350229 + 0.552200i
\(706\) 12.0198i 0.452370i
\(707\) 0 0
\(708\) −6.98563 6.98563i −0.262536 0.262536i
\(709\) −28.2967 + 16.3371i −1.06270 + 0.613552i −0.926179 0.377084i \(-0.876927\pi\)
−0.136525 + 0.990637i \(0.543593\pi\)
\(710\) −10.2167 + 9.39981i −0.383426 + 0.352769i
\(711\) −4.93165 + 8.54186i −0.184951 + 0.320345i
\(712\) −3.41319 + 12.7382i −0.127915 + 0.477385i
\(713\) 1.28028 1.28028i 0.0479469 0.0479469i
\(714\) 0 0
\(715\) −42.6341 13.3481i −1.59443 0.499192i
\(716\) −13.1632 22.7994i −0.491933 0.852052i
\(717\) −19.5894 + 5.24897i −0.731581 + 0.196027i
\(718\) −6.01247 + 1.61104i −0.224383 + 0.0601233i
\(719\) 9.66239 + 16.7357i 0.360346 + 0.624138i 0.988018 0.154340i \(-0.0493252\pi\)
−0.627671 + 0.778478i \(0.715992\pi\)
\(720\) 1.66319 0.870061i 0.0619832 0.0324253i
\(721\) 0 0
\(722\) −10.2601 + 10.2601i −0.381841 + 0.381841i
\(723\) −0.716912 + 2.67555i −0.0266622 + 0.0995048i
\(724\) −6.00966 + 10.4090i −0.223347 + 0.386849i
\(725\) −12.5335 + 5.90607i −0.465484 + 0.219346i
\(726\) −2.53566 + 1.46396i −0.0941072 + 0.0543328i
\(727\) 2.71795 + 2.71795i 0.100803 + 0.100803i 0.755710 0.654907i \(-0.227292\pi\)
−0.654907 + 0.755710i \(0.727292\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) 19.4853 + 12.3584i 0.721185 + 0.457406i
\(731\) 7.15181 + 4.12910i 0.264519 + 0.152720i
\(732\) 5.24652 + 19.5803i 0.193917 + 0.723709i
\(733\) 3.25711 + 0.872739i 0.120304 + 0.0322354i 0.318469 0.947933i \(-0.396831\pi\)
−0.198165 + 0.980169i \(0.563498\pi\)
\(734\) 15.9321 0.588064
\(735\) 0 0
\(736\) 4.42747 0.163199
\(737\) 2.19118 + 0.587125i 0.0807132 + 0.0216270i
\(738\) −1.71624 6.40510i −0.0631757 0.235775i
\(739\) 4.29271 + 2.47840i 0.157910 + 0.0911693i 0.576873 0.816834i \(-0.304273\pi\)
−0.418963 + 0.908003i \(0.637606\pi\)
\(740\) −27.0471 + 6.05337i −0.994270 + 0.222526i
\(741\) 0.361923i 0.0132956i
\(742\) 0 0
\(743\) 15.6556 + 15.6556i 0.574347 + 0.574347i 0.933340 0.358993i \(-0.116880\pi\)
−0.358993 + 0.933340i \(0.616880\pi\)
\(744\) 5.41695 3.12748i 0.198595 0.114659i
\(745\) −1.02782 + 24.6817i −0.0376566 + 0.904266i
\(746\) −0.807303 + 1.39829i −0.0295575 + 0.0511950i
\(747\) −0.598706 + 2.23440i −0.0219055 + 0.0817525i
\(748\) 8.12896 8.12896i 0.297224 0.297224i
\(749\) 0 0
\(750\) 1.06357 8.47393i 0.0388360 0.309424i
\(751\) 5.59544 + 9.69159i 0.204181 + 0.353651i 0.949871 0.312641i \(-0.101214\pi\)
−0.745691 + 0.666292i \(0.767880\pi\)
\(752\) 6.29575 1.68694i 0.229582 0.0615164i
\(753\) −5.89197 + 1.57875i −0.214715 + 0.0575328i
\(754\) −5.49042 9.50969i −0.199949 0.346322i
\(755\) −19.0704 36.4545i −0.694045 1.32672i
\(756\) 0 0
\(757\) 29.4977 29.4977i 1.07211 1.07211i 0.0749214 0.997189i \(-0.476129\pi\)
0.997189 0.0749214i \(-0.0238706\pi\)
\(758\) 3.69977 13.8077i 0.134382 0.501520i
\(759\) −1.45473 + 2.51967i −0.0528035 + 0.0914584i
\(760\) 0.275662 + 0.299619i 0.00999932 + 0.0108683i
\(761\) −24.3504 + 14.0587i −0.882703 + 0.509629i −0.871549 0.490309i \(-0.836884\pi\)
−0.0111541 + 0.999938i \(0.503551\pi\)
\(762\) 3.69181 + 3.69181i 0.133740 + 0.133740i
\(763\) 0 0
\(764\) 7.63986i 0.276400i
\(765\) 1.02913 + 4.59826i 0.0372083 + 0.166251i
\(766\) 19.5862 + 11.3081i 0.707679 + 0.408579i
\(767\) 9.36412 + 34.9474i 0.338119 + 1.26188i
\(768\) 12.4771 + 3.34324i 0.450230 + 0.120639i
\(769\) 6.61248 0.238452 0.119226 0.992867i \(-0.461959\pi\)
0.119226 + 0.992867i \(0.461959\pi\)