Properties

Label 735.2.v.a.313.5
Level 735
Weight 2
Character 735.313
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 313.5
Character \(\chi\) \(=\) 735.313
Dual form 735.2.v.a.472.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.197706 + 0.737849i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(1.22672 - 0.708245i) q^{4} +(2.23413 + 0.0930365i) q^{5} -0.763878i q^{6} +(1.84539 + 1.84539i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(0.197706 + 0.737849i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(1.22672 - 0.708245i) q^{4} +(2.23413 + 0.0930365i) q^{5} -0.763878i q^{6} +(1.84539 + 1.84539i) q^{8} +(0.866025 + 0.500000i) q^{9} +(0.373055 + 1.66685i) q^{10} +(1.92568 + 3.33538i) q^{11} +(-1.36822 + 0.366615i) q^{12} +(-3.66816 + 3.66816i) q^{13} +(-2.13393 - 0.668102i) q^{15} +(0.419714 - 0.726965i) q^{16} +(0.545404 - 2.03548i) q^{17} +(-0.197706 + 0.737849i) q^{18} +(-0.0348837 + 0.0604203i) q^{19} +(2.80654 - 1.46818i) q^{20} +(-2.08029 + 2.08029i) q^{22} +(0.729698 - 0.195522i) q^{23} +(-1.30489 - 2.26014i) q^{24} +(4.98269 + 0.415712i) q^{25} +(-3.43177 - 1.98133i) q^{26} +(-0.707107 - 0.707107i) q^{27} -2.77107i q^{29} +(0.0710685 - 1.70660i) q^{30} +(2.07564 - 1.19837i) q^{31} +(5.66108 + 1.51688i) q^{32} +(-0.996806 - 3.72013i) q^{33} +1.60970 q^{34} +1.41649 q^{36} +(2.26481 + 8.45237i) q^{37} +(-0.0514778 - 0.0137934i) q^{38} +(4.49256 - 2.59378i) q^{39} +(3.95116 + 4.29454i) q^{40} -8.68077i q^{41} +(-2.77107 - 2.77107i) q^{43} +(4.72453 + 2.72771i) q^{44} +(1.88830 + 1.19764i) q^{45} +(0.288532 + 0.499752i) q^{46} +(-7.50006 + 2.00963i) q^{47} +(-0.593565 + 0.593565i) q^{48} +(0.678376 + 3.75866i) q^{50} +(-1.05364 + 1.82496i) q^{51} +(-1.90184 + 7.09776i) q^{52} +(2.24675 - 8.38498i) q^{53} +(0.381939 - 0.661538i) q^{54} +(3.99191 + 7.63083i) q^{55} +(0.0493330 - 0.0493330i) q^{57} +(2.04464 - 0.547858i) q^{58} +(3.48720 + 6.04001i) q^{59} +(-3.09090 + 0.691771i) q^{60} +(12.3935 + 7.15536i) q^{61} +(1.29458 + 1.29458i) q^{62} +2.79807i q^{64} +(-8.53643 + 7.85389i) q^{65} +(2.54782 - 1.47098i) q^{66} +(-0.568937 - 0.152446i) q^{67} +(-0.772560 - 2.88323i) q^{68} -0.755439 q^{69} -8.12783 q^{71} +(0.675461 + 2.52086i) q^{72} +(-13.0484 - 3.49631i) q^{73} +(-5.78881 + 3.34217i) q^{74} +(-4.70531 - 1.69116i) q^{75} +0.0988248i q^{76} +(2.80203 + 2.80203i) q^{78} +(-8.54186 - 4.93165i) q^{79} +(1.00533 - 1.58509i) q^{80} +(0.500000 + 0.866025i) q^{81} +(6.40510 - 1.71624i) q^{82} +(1.63570 - 1.63570i) q^{83} +(1.40788 - 4.49678i) q^{85} +(1.49678 - 2.59249i) q^{86} +(-0.717207 + 2.67665i) q^{87} +(-2.60144 + 9.70872i) q^{88} +(2.52657 - 4.37614i) q^{89} +(-0.510348 + 1.63006i) q^{90} +(0.756656 - 0.756656i) q^{92} +(-2.31507 + 0.620321i) q^{93} +(-2.96561 - 5.13659i) q^{94} +(-0.0835560 + 0.131741i) 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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.197706 + 0.737849i 0.139799 + 0.521738i 0.999932 + 0.0116677i \(0.00371404\pi\)
−0.860133 + 0.510071i \(0.829619\pi\)
\(3\) −0.965926 0.258819i −0.557678 0.149429i
\(4\) 1.22672 0.708245i 0.613358 0.354123i
\(5\) 2.23413 + 0.0930365i 0.999134 + 0.0416072i
\(6\) 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
\(10\) 0.373055 + 1.66685i 0.117970 + 0.527103i
\(11\) 1.92568 + 3.33538i 0.580615 + 1.00565i 0.995407 + 0.0957376i \(0.0305210\pi\)
−0.414792 + 0.909916i \(0.636146\pi\)
\(12\) −1.36822 + 0.366615i −0.394973 + 0.105833i
\(13\) −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
\(17\) 0.545404 2.03548i 0.132280 0.493675i −0.867714 0.497063i \(-0.834412\pi\)
0.999994 + 0.00338789i \(0.00107840\pi\)
\(18\) −0.197706 + 0.737849i −0.0465998 + 0.173913i
\(19\) −0.0348837 + 0.0604203i −0.00800286 + 0.0138614i −0.869999 0.493053i \(-0.835881\pi\)
0.861996 + 0.506915i \(0.169214\pi\)
\(20\) 2.80654 1.46818i 0.627561 0.328296i
\(21\) 0 0
\(22\) −2.08029 + 2.08029i −0.443519 + 0.443519i
\(23\) 0.729698 0.195522i 0.152153 0.0407692i −0.181939 0.983310i \(-0.558237\pi\)
0.334091 + 0.942541i \(0.391571\pi\)
\(24\) −1.30489 2.26014i −0.266360 0.461349i
\(25\) 4.98269 + 0.415712i 0.996538 + 0.0831423i
\(26\) −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 \(-0.0828288\pi\)
\(30\) 0.0710685 1.70660i 0.0129753 0.311582i
\(31\) 2.07564 1.19837i 0.372795 0.215233i −0.301884 0.953345i \(-0.597615\pi\)
0.674679 + 0.738111i \(0.264282\pi\)
\(32\) 5.66108 + 1.51688i 1.00075 + 0.268149i
\(33\) −0.996806 3.72013i −0.173522 0.647591i
\(34\) 1.60970 0.276062
\(35\) 0 0
\(36\) 1.41649 0.236082
\(37\) 2.26481 + 8.45237i 0.372332 + 1.38956i 0.857204 + 0.514976i \(0.172199\pi\)
−0.484872 + 0.874585i \(0.661134\pi\)
\(38\) −0.0514778 0.0137934i −0.00835080 0.00223759i
\(39\) 4.49256 2.59378i 0.719386 0.415338i
\(40\) 3.95116 + 4.29454i 0.624734 + 0.679027i
\(41\) 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
\(45\) 1.88830 + 1.19764i 0.281491 + 0.178533i
\(46\) 0.288532 + 0.499752i 0.0425417 + 0.0736843i
\(47\) −7.50006 + 2.00963i −1.09400 + 0.293135i −0.760317 0.649552i \(-0.774957\pi\)
−0.333678 + 0.942687i \(0.608290\pi\)
\(48\) −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
\(52\) −1.90184 + 7.09776i −0.263737 + 0.984282i
\(53\) 2.24675 8.38498i 0.308615 1.15177i −0.621174 0.783673i \(-0.713344\pi\)
0.929789 0.368093i \(-0.119989\pi\)
\(54\) 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
\(58\) 2.04464 0.547858i 0.268474 0.0719373i
\(59\) 3.48720 + 6.04001i 0.453995 + 0.786342i 0.998630 0.0523310i \(-0.0166651\pi\)
−0.544635 + 0.838673i \(0.683332\pi\)
\(60\) −3.09090 + 0.691771i −0.399034 + 0.0893072i
\(61\) 12.3935 + 7.15536i 1.58682 + 0.916150i 0.993827 + 0.110942i \(0.0353869\pi\)
0.592992 + 0.805208i \(0.297946\pi\)
\(62\) 1.29458 + 1.29458i 0.164412 + 0.164412i
\(63\) 0 0
\(64\) 2.79807i 0.349758i
\(65\) −8.53643 + 7.85389i −1.05881 + 0.974155i
\(66\) 2.54782 1.47098i 0.313615 0.181066i
\(67\) −0.568937 0.152446i −0.0695067 0.0186243i 0.223898 0.974613i \(-0.428122\pi\)
−0.293405 + 0.955988i \(0.594788\pi\)
\(68\) −0.772560 2.88323i −0.0936866 0.349643i
\(69\) −0.755439 −0.0909442
\(70\) 0 0
\(71\) −8.12783 −0.964595 −0.482298 0.876007i \(-0.660198\pi\)
−0.482298 + 0.876007i \(0.660198\pi\)
\(72\) 0.675461 + 2.52086i 0.0796039 + 0.297086i
\(73\) −13.0484 3.49631i −1.52720 0.409212i −0.605096 0.796152i \(-0.706865\pi\)
−0.922105 + 0.386940i \(0.873532\pi\)
\(74\) −5.78881 + 3.34217i −0.672936 + 0.388520i
\(75\) −4.70531 1.69116i −0.543323 0.195278i
\(76\) 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 \(-0.520559\pi\)
−0.896491 + 0.443061i \(0.853892\pi\)
\(80\) 1.00533 1.58509i 0.112399 0.177218i
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) 6.40510 1.71624i 0.707325 0.189527i
\(83\) 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
\(87\) −0.717207 + 2.67665i −0.0768926 + 0.286967i
\(88\) −2.60144 + 9.70872i −0.277315 + 1.03495i
\(89\) 2.52657 4.37614i 0.267815 0.463870i −0.700482 0.713670i \(-0.747032\pi\)
0.968297 + 0.249800i \(0.0803649\pi\)
\(90\) −0.510348 + 1.63006i −0.0537954 + 0.171823i
\(91\) 0 0
\(92\) 0.756656 0.756656i 0.0788868 0.0788868i
\(93\) −2.31507 + 0.620321i −0.240062 + 0.0643243i
\(94\) −2.96561 5.13659i −0.305880 0.529799i
\(95\) −0.0835560 + 0.131741i −0.00857267 + 0.0135164i
\(96\) −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
\(100\) 6.40677 3.01901i 0.640677 0.301901i
\(101\) 16.6236 9.59763i 1.65411 0.955000i 0.678752 0.734368i \(-0.262521\pi\)
0.975357 0.220632i \(-0.0708121\pi\)
\(102\) −1.55485 0.416622i −0.153954 0.0412517i
\(103\) 0.855857 + 3.19410i 0.0843301 + 0.314724i 0.995186 0.0979992i \(-0.0312443\pi\)
−0.910856 + 0.412723i \(0.864578\pi\)
\(104\) −13.5384 −1.32755
\(105\) 0 0
\(106\) 6.63105 0.644064
\(107\) −2.34164 8.73911i −0.226375 0.844841i −0.981849 0.189663i \(-0.939260\pi\)
0.755475 0.655178i \(-0.227406\pi\)
\(108\) −1.36822 0.366615i −0.131658 0.0352775i
\(109\) 1.87111 1.08029i 0.179220 0.103473i −0.407706 0.913113i \(-0.633671\pi\)
0.586926 + 0.809641i \(0.300338\pi\)
\(110\) −4.84118 + 4.45409i −0.461588 + 0.424681i
\(111\) 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
\(115\) 1.64843 0.368934i 0.153717 0.0344032i
\(116\) −1.96260 3.39932i −0.182223 0.315619i
\(117\) −5.01080 + 1.34264i −0.463249 + 0.124127i
\(118\) −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
\(122\) −2.82932 + 10.5592i −0.256154 + 0.955981i
\(123\) −2.24675 + 8.38498i −0.202583 + 0.756048i
\(124\) 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 \(0.348071\pi\)
\(128\) 9.25761 2.48057i 0.818265 0.219253i
\(129\) 1.95945 + 3.39386i 0.172520 + 0.298813i
\(130\) −7.48269 4.74584i −0.656275 0.416238i
\(131\) 0.560750 + 0.323749i 0.0489930 + 0.0282861i 0.524296 0.851536i \(-0.324328\pi\)
−0.475303 + 0.879822i \(0.657662\pi\)
\(132\) −3.85756 3.85756i −0.335758 0.335758i
\(133\) 0 0
\(134\) 0.449929i 0.0388680i
\(135\) −1.51398 1.64556i −0.130303 0.141627i
\(136\) 4.76274 2.74977i 0.408402 0.235791i
\(137\) −13.9839 3.74696i −1.19472 0.320125i −0.393971 0.919123i \(-0.628899\pi\)
−0.800751 + 0.598998i \(0.795566\pi\)
\(138\) −0.149355 0.557400i −0.0127139 0.0474491i
\(139\) −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
\(142\) −1.60692 5.99711i −0.134850 0.503266i
\(143\) −19.2984 5.17099i −1.61381 0.432420i
\(144\) 0.726965 0.419714i 0.0605804 0.0349761i
\(145\) 0.257811 6.19095i 0.0214100 0.514130i
\(146\) 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 \(-0.482810\pi\)
−0.837774 + 0.546017i \(0.816143\pi\)
\(150\) 0.317553 3.80617i 0.0259281 0.310772i
\(151\) −9.19950 15.9340i −0.748645 1.29669i −0.948472 0.316859i \(-0.897372\pi\)
0.199828 0.979831i \(-0.435962\pi\)
\(152\) −0.175873 + 0.0471251i −0.0142652 + 0.00382235i
\(153\) 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
\(157\) −0.384306 + 1.43425i −0.0306709 + 0.114465i −0.979564 0.201132i \(-0.935538\pi\)
0.948893 + 0.315597i \(0.102205\pi\)
\(158\) 1.95003 7.27763i 0.155136 0.578977i
\(159\) −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
\(163\) −7.52050 + 2.01511i −0.589051 + 0.157836i −0.541020 0.841010i \(-0.681962\pi\)
−0.0480317 + 0.998846i \(0.515295\pi\)
\(164\) −6.14812 10.6488i −0.480087 0.831535i
\(165\) −1.88089 8.40400i −0.146427 0.654250i
\(166\) 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
\(170\) 3.59629 + 0.149761i 0.275823 + 0.0114862i
\(171\) −0.0604203 + 0.0348837i −0.00462046 + 0.00266762i
\(172\) −5.36192 1.43672i −0.408843 0.109549i
\(173\) −1.79627 6.70378i −0.136568 0.509679i −0.999987 0.00519041i \(-0.998348\pi\)
0.863419 0.504488i \(-0.168319\pi\)
\(174\) −2.11676 −0.160471
\(175\) 0 0
\(176\) 3.23294 0.243692
\(177\) −1.80511 6.73676i −0.135680 0.506366i
\(178\) 3.72845 + 0.999035i 0.279459 + 0.0748808i
\(179\) −16.0957 + 9.29284i −1.20305 + 0.694579i −0.961231 0.275743i \(-0.911076\pi\)
−0.241815 + 0.970322i \(0.577743\pi\)
\(180\) 3.16463 + 0.131785i 0.235877 + 0.00982270i
\(181\) 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
\(185\) 4.27350 + 19.0944i 0.314194 + 1.40385i
\(186\) −0.915407 1.58553i −0.0671209 0.116257i
\(187\) 7.83935 2.10055i 0.573270 0.153607i
\(188\) −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 −0.751813 0.659377i \(-0.770820\pi\)
0.946943 + 0.321401i \(0.104154\pi\)
\(192\) 0.724193 2.70273i 0.0522641 0.195052i
\(193\) −1.75911 + 6.56510i −0.126624 + 0.472566i −0.999892 0.0146728i \(-0.995329\pi\)
0.873269 + 0.487239i \(0.161996\pi\)
\(194\) −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 \(0.0295537\pi\)
\(198\) −2.84172 + 0.761438i −0.201953 + 0.0541130i
\(199\) 1.33556 + 2.31325i 0.0946750 + 0.163982i 0.909473 0.415763i \(-0.136485\pi\)
−0.814798 + 0.579745i \(0.803152\pi\)
\(200\) 8.42787 + 9.96218i 0.595941 + 0.704432i
\(201\) 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
\(205\) 0.807629 19.3940i 0.0564072 1.35453i
\(206\) −2.18756 + 1.26299i −0.152414 + 0.0879965i
\(207\) 0.729698 + 0.195522i 0.0507175 + 0.0135897i
\(208\) 1.12705 + 4.20621i 0.0781468 + 0.291648i
\(209\) −0.268699 −0.0185863
\(210\) 0 0
\(211\) −12.0239 −0.827757 −0.413879 0.910332i \(-0.635826\pi\)
−0.413879 + 0.910332i \(0.635826\pi\)
\(212\) −3.18250 11.8772i −0.218575 0.815733i
\(213\) 7.85088 + 2.10364i 0.537933 + 0.144139i
\(214\) 5.98519 3.45555i 0.409139 0.236217i
\(215\) −5.93313 6.44876i −0.404636 0.439802i
\(216\) 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
\(220\) 10.3014 + 6.53361i 0.694523 + 0.440496i
\(221\) 5.46582 + 9.46708i 0.367671 + 0.636825i
\(222\) 6.45658 1.73004i 0.433337 0.116112i
\(223\) −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
\(227\) 0.404524 1.50971i 0.0268492 0.100203i −0.951201 0.308572i \(-0.900149\pi\)
0.978050 + 0.208369i \(0.0668156\pi\)
\(228\) 0.0255777 0.0954574i 0.00169393 0.00632182i
\(229\) −3.91654 + 6.78365i −0.258812 + 0.448276i −0.965924 0.258826i \(-0.916664\pi\)
0.707112 + 0.707102i \(0.249998\pi\)
\(230\) 0.598123 + 1.14335i 0.0394390 + 0.0753906i
\(231\) 0 0
\(232\) 5.11372 5.11372i 0.335732 0.335732i
\(233\) −1.37692 + 0.368944i −0.0902048 + 0.0241703i −0.303639 0.952787i \(-0.598202\pi\)
0.213434 + 0.976957i \(0.431535\pi\)
\(234\) −1.98133 3.43177i −0.129524 0.224342i
\(235\) −16.9431 + 3.79201i −1.10524 + 0.247363i
\(236\) 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 \(0.772282\pi\)
\(240\) −1.38132 + 1.27088i −0.0891641 + 0.0820349i
\(241\) −2.39883 + 1.38497i −0.154522 + 0.0892136i −0.575268 0.817965i \(-0.695102\pi\)
0.420745 + 0.907179i \(0.361769\pi\)
\(242\) −2.82816 0.757804i −0.181801 0.0487135i
\(243\) −0.258819 0.965926i −0.0166032 0.0619642i
\(244\) 20.2710 1.29772
\(245\) 0 0
\(246\) −6.63105 −0.422780
\(247\) −0.0936725 0.349590i −0.00596024 0.0222439i
\(248\) 6.04183 + 1.61890i 0.383656 + 0.102800i
\(249\) −2.00331 + 1.15661i −0.126955 + 0.0732973i
\(250\) 1.16589 + 8.46046i 0.0737372 + 0.535086i
\(251\) 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
\(255\) −2.52376 + 3.97917i −0.158044 + 0.249185i
\(256\) 6.45864 + 11.1867i 0.403665 + 0.699168i
\(257\) 2.75722 0.738795i 0.171991 0.0460848i −0.171796 0.985133i \(-0.554957\pi\)
0.343787 + 0.939048i \(0.388290\pi\)
\(258\) −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
\(262\) −0.128014 + 0.477756i −0.00790876 + 0.0295159i
\(263\) 6.13773 22.9063i 0.378469 1.41246i −0.469741 0.882804i \(-0.655653\pi\)
0.848210 0.529660i \(-0.177681\pi\)
\(264\) 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
\(268\) −0.805894 + 0.215939i −0.0492278 + 0.0131905i
\(269\) −12.3676 21.4213i −0.754064 1.30608i −0.945838 0.324638i \(-0.894758\pi\)
0.191774 0.981439i \(-0.438576\pi\)
\(270\) 0.914849 1.44243i 0.0556759 0.0877834i
\(271\) 3.58076 + 2.06735i 0.217515 + 0.125583i 0.604799 0.796378i \(-0.293253\pi\)
−0.387284 + 0.921961i \(0.626587\pi\)
\(272\) −1.25081 1.25081i −0.0758413 0.0758413i
\(273\) 0 0
\(274\) 11.0588i 0.668085i
\(275\) 8.20851 + 17.4197i 0.494992 + 1.05045i
\(276\) −0.926710 + 0.535036i −0.0557814 + 0.0322054i
\(277\) 16.5463 + 4.43358i 0.994174 + 0.266388i 0.719003 0.695007i \(-0.244599\pi\)
0.275171 + 0.961395i \(0.411266\pi\)
\(278\) −4.38241 16.3554i −0.262840 0.980931i
\(279\) 2.39674 0.143489
\(280\) 0 0
\(281\) 5.25279 0.313355 0.156678 0.987650i \(-0.449922\pi\)
0.156678 + 0.987650i \(0.449922\pi\)
\(282\) 1.53511 + 5.72913i 0.0914147 + 0.341164i
\(283\) 2.27756 + 0.610271i 0.135387 + 0.0362768i 0.325876 0.945412i \(-0.394341\pi\)
−0.190489 + 0.981689i \(0.561007\pi\)
\(284\) −9.97054 + 5.75649i −0.591643 + 0.341585i
\(285\) 0.114806 0.105627i 0.00680053 0.00625678i
\(286\) 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
\(290\) 4.61896 1.03376i 0.271234 0.0607046i
\(291\) −4.84970 8.39993i −0.284294 0.492412i
\(292\) −18.4830 + 4.95249i −1.08163 + 0.289823i
\(293\) −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
\(297\) 0.996806 3.72013i 0.0578405 0.215864i
\(298\) 2.18417 8.15142i 0.126525 0.472199i
\(299\) −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
\(303\) −18.5412 + 4.96810i −1.06516 + 0.285410i
\(304\) 0.0292823 + 0.0507184i 0.00167946 + 0.00290890i
\(305\) 27.0229 + 17.1391i 1.54733 + 0.981380i
\(306\) 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
\(310\) 2.77182 + 3.01271i 0.157429 + 0.171110i
\(311\) −2.47872 + 1.43109i −0.140555 + 0.0811497i −0.568629 0.822594i \(-0.692526\pi\)
0.428073 + 0.903744i \(0.359193\pi\)
\(312\) 13.0771 + 3.50400i 0.740345 + 0.198375i
\(313\) −3.44732 12.8656i −0.194854 0.727204i −0.992305 0.123820i \(-0.960485\pi\)
0.797451 0.603384i \(-0.206181\pi\)
\(314\) −1.13424 −0.0640088
\(315\) 0 0
\(316\) −13.9713 −0.785945
\(317\) 2.70240 + 10.0855i 0.151782 + 0.566459i 0.999359 + 0.0357866i \(0.0113937\pi\)
−0.847577 + 0.530672i \(0.821940\pi\)
\(318\) −6.40510 1.71624i −0.359180 0.0962421i
\(319\) 9.24258 5.33620i 0.517485 0.298770i
\(320\) −0.260322 + 6.25125i −0.0145525 + 0.349456i
\(321\) 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
\(325\) −19.8022 + 16.7524i −1.09843 + 0.929257i
\(326\) −2.97370 5.15060i −0.164698 0.285265i
\(327\) −2.08695 + 0.559197i −0.115409 + 0.0309237i
\(328\) 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 0.334193 + 0.942505i \(0.391536\pi\)
−0.983330 + 0.181833i \(0.941797\pi\)
\(332\) 0.848062 3.16501i 0.0465435 0.173703i
\(333\) −2.26481 + 8.45237i −0.124111 + 0.463187i
\(334\) −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 \(0.310916\pi\)
\(338\) 10.2641 2.75026i 0.558293 0.149594i
\(339\) 2.92617 + 5.06828i 0.158928 + 0.275271i
\(340\) −1.45775 6.51340i −0.0790578 0.353238i
\(341\) 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
\(345\) −1.68775 0.0702834i −0.0908655 0.00378393i
\(346\) 4.59124 2.65076i 0.246827 0.142505i
\(347\) −7.97341 2.13647i −0.428035 0.114692i 0.0383685 0.999264i \(-0.487784\pi\)
−0.466404 + 0.884572i \(0.654451\pi\)
\(348\) 1.01592 + 3.79145i 0.0544589 + 0.203243i
\(349\) −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
\(352\) 5.84206 + 21.8029i 0.311383 + 1.16210i
\(353\) 15.1990 + 4.07257i 0.808963 + 0.216761i 0.639516 0.768778i \(-0.279135\pi\)
0.169448 + 0.985539i \(0.445802\pi\)
\(354\) 4.61383 2.66380i 0.245222 0.141579i
\(355\) −18.1586 0.756184i −0.963760 0.0401341i
\(356\) 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 \(-0.402320\pi\)
−0.674528 + 0.738249i \(0.735653\pi\)
\(360\) 1.27454 + 5.69477i 0.0671740 + 0.300140i
\(361\) 9.49757 + 16.4503i 0.499872 + 0.865804i
\(362\) 6.26086 1.67759i 0.329063 0.0881723i
\(363\) 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
\(367\) 5.39815 20.1462i 0.281781 1.05162i −0.669378 0.742922i \(-0.733439\pi\)
0.951160 0.308700i \(-0.0998938\pi\)
\(368\) 0.164127 0.612529i 0.00855569 0.0319303i
\(369\) 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
\(373\) −2.04168 + 0.547065i −0.105714 + 0.0283260i −0.311288 0.950316i \(-0.600760\pi\)
0.205574 + 0.978642i \(0.434094\pi\)
\(374\) 3.09977 + 5.36897i 0.160286 + 0.277623i
\(375\) −10.3549 4.21604i −0.534727 0.217716i
\(376\) −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 \(0.840410\pi\)
\(380\) −0.00919431 + 0.220788i −0.000471658 + 0.0113262i
\(381\) 5.91917 3.41743i 0.303248 0.175080i
\(382\) 3.97960 + 1.06633i 0.203614 + 0.0545582i
\(383\) 7.66288 + 28.5983i 0.391555 + 1.46130i 0.827569 + 0.561364i \(0.189723\pi\)
−0.436014 + 0.899940i \(0.643610\pi\)
\(384\) −9.58418 −0.489091
\(385\) 0 0
\(386\) −5.19184 −0.264258
\(387\) −1.01428 3.78536i −0.0515589 0.192421i
\(388\) 13.2710 + 3.55594i 0.673731 + 0.180526i
\(389\) 22.2232 12.8305i 1.12676 0.650535i 0.183641 0.982993i \(-0.441212\pi\)
0.943118 + 0.332459i \(0.107878\pi\)
\(390\) 5.99941 + 6.52079i 0.303792 + 0.330193i
\(391\) 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
\(395\) −18.6248 11.8127i −0.937117 0.594359i
\(396\) 2.72771 + 4.72453i 0.137073 + 0.237417i
\(397\) −9.20135 + 2.46549i −0.461802 + 0.123740i −0.482217 0.876052i \(-0.660168\pi\)
0.0204142 + 0.999792i \(0.493502\pi\)
\(398\) −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 −0.989299 0.145900i \(-0.953392\pi\)
0.621003 + 0.783808i \(0.286726\pi\)
\(402\) −0.116450 + 0.434598i −0.00580801 + 0.0216758i
\(403\) −3.21796 + 12.0096i −0.160298 + 0.598240i
\(404\) 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
\(408\) −5.31215 + 1.42339i −0.262990 + 0.0704681i
\(409\) −5.28021 9.14560i −0.261090 0.452221i 0.705442 0.708768i \(-0.250749\pi\)
−0.966532 + 0.256547i \(0.917415\pi\)
\(410\) 14.4695 3.23840i 0.714598 0.159933i
\(411\) 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
\(415\) 3.80654 3.50218i 0.186856 0.171915i
\(416\) −26.3299 + 15.2016i −1.29093 + 0.745320i
\(417\) 21.4110 + 5.73706i 1.04850 + 0.280945i
\(418\) −0.0531235 0.198260i −0.00259835 0.00969719i
\(419\) 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 \(0.474384\pi\)
\(422\) −2.37719 8.87180i −0.115720 0.431873i
\(423\) −7.50006 2.00963i −0.364665 0.0977117i
\(424\) 19.6197 11.3275i 0.952818 0.550110i
\(425\) 3.56375 9.91541i 0.172867 0.480968i
\(426\) 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
\(430\) 3.58519 5.65272i 0.172893 0.272598i
\(431\) 7.04553 + 12.2032i 0.339371 + 0.587809i 0.984315 0.176422i \(-0.0564523\pi\)
−0.644943 + 0.764230i \(0.723119\pi\)
\(432\) −0.810825 + 0.217260i −0.0390108 + 0.0104529i
\(433\) −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
\(437\) −0.0136411 + 0.0509091i −0.000652540 + 0.00243531i
\(438\) −2.67075 + 9.96739i −0.127614 + 0.476260i
\(439\) 13.5586 23.4841i 0.647116 1.12084i −0.336693 0.941615i \(-0.609308\pi\)
0.983809 0.179223i \(-0.0573582\pi\)
\(440\) −6.71524 + 21.4485i −0.320136 + 1.02252i
\(441\) 0 0
\(442\) −5.90465 + 5.90465i −0.280856 + 0.280856i
\(443\) 32.9897 8.83957i 1.56739 0.419981i 0.632396 0.774645i \(-0.282072\pi\)
0.934994 + 0.354664i \(0.115405\pi\)
\(444\) −6.19753 10.7344i −0.294122 0.509434i
\(445\) 6.05182 9.54181i 0.286884 0.452325i
\(446\) −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 \(-0.0743006\pi\)
\(450\) −1.29184 + 3.59428i −0.0608979 + 0.169436i
\(451\) 28.9536 16.7164i 1.36337 0.787144i
\(452\) −8.00732 2.14556i −0.376633 0.100918i
\(453\) 4.76201 + 17.7721i 0.223739 + 0.835005i
\(454\) 1.19391 0.0560331
\(455\) 0 0
\(456\) 0.182078 0.00852656
\(457\) 0.201340 + 0.751411i 0.00941828 + 0.0351495i 0.970475 0.241201i \(-0.0775415\pi\)
−0.961057 + 0.276351i \(0.910875\pi\)
\(458\) −5.77964 1.54865i −0.270065 0.0723636i
\(459\) −1.82496 + 1.05364i −0.0851817 + 0.0491797i
\(460\) 1.76087 1.62007i 0.0821008 0.0755363i
\(461\) 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
\(465\) −5.22988 + 1.17049i −0.242530 + 0.0542803i
\(466\) −0.544450 0.943015i −0.0252211 0.0436843i
\(467\) 31.8048 8.52208i 1.47175 0.394355i 0.568220 0.822876i \(-0.307632\pi\)
0.903531 + 0.428522i \(0.140965\pi\)
\(468\) −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
\(472\) −4.71094 + 17.5815i −0.216838 + 0.809252i
\(473\) 3.90637 14.5788i 0.179615 0.670333i
\(474\) −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
\(478\) −14.9639 + 4.00957i −0.684434 + 0.183394i
\(479\) 20.2160 + 35.0151i 0.923691 + 1.59988i 0.793653 + 0.608371i \(0.208177\pi\)
0.130038 + 0.991509i \(0.458490\pi\)
\(480\) −11.0669 7.01909i −0.505132 0.320376i
\(481\) −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
\(485\) 14.6847 + 15.9609i 0.666799 + 0.724748i
\(486\) 0.661538 0.381939i 0.0300080 0.0173251i
\(487\) 9.87490 + 2.64597i 0.447474 + 0.119900i 0.475517 0.879706i \(-0.342261\pi\)
−0.0280431 + 0.999607i \(0.508928\pi\)
\(488\) 9.66634 + 36.0753i 0.437575 + 1.63305i
\(489\) 7.78580 0.352086
\(490\) 0 0
\(491\) 20.1040 0.907279 0.453639 0.891185i \(-0.350125\pi\)
0.453639 + 0.891185i \(0.350125\pi\)
\(492\) 3.18250 + 11.8772i 0.143478 + 0.535468i
\(493\) −5.64045 1.51135i −0.254033 0.0680680i
\(494\) 0.239425 0.138232i 0.0107723 0.00621937i
\(495\) −0.358317 + 8.60445i −0.0161052 + 0.386741i
\(496\) 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 \(-0.445525\pi\)
−0.768221 + 0.640185i \(0.778858\pi\)
\(500\) 14.5945 6.14879i 0.652684 0.274982i
\(501\) −1.33620 2.31437i −0.0596972 0.103399i
\(502\) −4.50075 + 1.20597i −0.200878 + 0.0538252i
\(503\) 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
\(507\) −3.60039 + 13.4368i −0.159899 + 0.596751i
\(508\) −2.50576 + 9.35164i −0.111175 + 0.414912i
\(509\) −18.5636 + 32.1530i −0.822816 + 1.42516i 0.0807619 + 0.996733i \(0.474265\pi\)
−0.903577 + 0.428425i \(0.859069\pi\)
\(510\) −3.43499 1.07545i −0.152104 0.0476216i
\(511\) 0 0
\(512\) 6.57690 6.57690i 0.290661 0.290661i
\(513\) 0.0673901 0.0180571i 0.00297535 0.000797241i
\(514\) 1.09024 + 1.88835i 0.0480884 + 0.0832915i
\(515\) 1.61493 + 7.21567i 0.0711623 + 0.317960i
\(516\) 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
\(520\) −30.2466 1.25957i −1.32640 0.0552356i
\(521\) 2.24415 1.29566i 0.0983180 0.0567639i −0.450035 0.893011i \(-0.648588\pi\)
0.548353 + 0.836247i \(0.315255\pi\)
\(522\) 2.04464 + 0.547858i 0.0894913 + 0.0239791i
\(523\) −2.22856 8.31711i −0.0974482 0.363682i 0.899931 0.436032i \(-0.143617\pi\)
−0.997379 + 0.0723506i \(0.976950\pi\)
\(524\) 0.917176 0.0400670
\(525\) 0 0
\(526\) 18.1149 0.789846
\(527\) −1.30719 4.87850i −0.0569421 0.212511i
\(528\) −3.12278 0.836746i −0.135901 0.0364147i
\(529\) −19.4244 + 11.2147i −0.844537 + 0.487594i
\(530\) 14.8146 + 0.616930i 0.643507 + 0.0267977i
\(531\) 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
\(535\) −4.41847 19.7422i −0.191027 0.853529i
\(536\) −0.768589 1.33124i −0.0331980 0.0575006i
\(537\) 17.9524 4.81033i 0.774703 0.207581i
\(538\) 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 −0.241894 0.970303i \(-0.577769\pi\)
0.961254 0.275665i \(-0.0888980\pi\)
\(542\) −0.817456 + 3.05079i −0.0351127 + 0.131042i
\(543\) −2.19615 + 8.19615i −0.0942459 + 0.351731i
\(544\) 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 \(0.257973\pi\)
\(548\) −19.8080 + 5.30754i −0.846156 + 0.226727i
\(549\) 7.15536 + 12.3935i 0.305383 + 0.528940i
\(550\) −11.2302 + 9.50062i −0.478858 + 0.405108i
\(551\) 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
\(555\) 0.814119 19.5499i 0.0345574 0.829845i
\(556\) −27.1918 + 15.6992i −1.15319 + 0.665793i
\(557\) −20.0969 5.38496i −0.851534 0.228168i −0.193448 0.981111i \(-0.561967\pi\)
−0.658086 + 0.752943i \(0.728634\pi\)
\(558\) 0.473850 + 1.76843i 0.0200597 + 0.0748636i
\(559\) 20.3295 0.859846
\(560\) 0 0
\(561\) −8.11589 −0.342653
\(562\) 1.03851 + 3.87577i 0.0438069 + 0.163489i
\(563\) 32.7427 + 8.77338i 1.37994 + 0.369754i 0.871100 0.491106i \(-0.163407\pi\)
0.508841 + 0.860860i \(0.330074\pi\)
\(564\) 9.52500 5.49926i 0.401075 0.231561i
\(565\) −8.86035 9.63036i −0.372758 0.405152i
\(566\) 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 \(-0.439835\pi\)
−0.756655 + 0.653814i \(0.773168\pi\)
\(570\) 0.100634 + 0.0638266i 0.00421511 + 0.00267340i
\(571\) −18.4943 32.0331i −0.773964 1.34055i −0.935375 0.353658i \(-0.884938\pi\)
0.161411 0.986887i \(-0.448396\pi\)
\(572\) −27.3360 + 7.32466i −1.14298 + 0.306260i
\(573\) −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
\(577\) 5.69488 21.2536i 0.237081 0.884798i −0.740119 0.672476i \(-0.765231\pi\)
0.977200 0.212322i \(-0.0681025\pi\)
\(578\) −2.48307 + 9.26693i −0.103282 + 0.385453i
\(579\) 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
\(583\) 32.2936 8.65304i 1.33746 0.358372i
\(584\) −17.6274 30.5315i −0.729427 1.26340i
\(585\) −11.3197 + 2.53345i −0.468012 + 0.104745i
\(586\) −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
\(590\) −8.76685 + 8.06588i −0.360926 + 0.332067i
\(591\) −15.5223 + 8.96183i −0.638504 + 0.368640i
\(592\) 7.09515 + 1.90114i 0.291609 + 0.0781364i
\(593\) −0.677877 2.52987i −0.0278371 0.103889i 0.950610 0.310389i \(-0.100459\pi\)
−0.978447 + 0.206500i \(0.933793\pi\)
\(594\) 2.94197 0.120710
\(595\) 0 0
\(596\) −15.6487 −0.640997
\(597\) −0.691334 2.58009i −0.0282944 0.105596i
\(598\) −2.89155 0.774789i −0.118244 0.0316835i
\(599\) −40.9761 + 23.6576i −1.67424 + 0.966622i −0.709015 + 0.705193i \(0.750860\pi\)
−0.965223 + 0.261429i \(0.915806\pi\)
\(600\) −5.56230 11.8040i −0.227080 0.481897i
\(601\) 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
\(605\) −4.59052 + 7.23781i −0.186631 + 0.294259i
\(606\) −7.33142 12.6984i −0.297819 0.515837i
\(607\) −10.3088 + 2.76222i −0.418419 + 0.112115i −0.461885 0.886940i \(-0.652827\pi\)
0.0434656 + 0.999055i \(0.486160\pi\)
\(608\) −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
\(612\) 0.772560 2.88323i 0.0312289 0.116548i
\(613\) −0.960769 + 3.58564i −0.0388051 + 0.144823i −0.982610 0.185679i \(-0.940551\pi\)
0.943805 + 0.330502i \(0.107218\pi\)
\(614\) 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 \(0.145550\pi\)
\(618\) 2.43990 0.653770i 0.0981473 0.0262985i
\(619\) 4.53385 + 7.85287i 0.182231 + 0.315633i 0.942640 0.333811i \(-0.108335\pi\)
−0.760409 + 0.649445i \(0.775001\pi\)
\(620\) 4.06593 6.41068i 0.163292 0.257459i
\(621\) −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
\(625\) 24.6544 + 4.14272i 0.986175 + 0.165709i
\(626\) 8.81129 5.08720i 0.352170 0.203325i
\(627\) 0.259544 + 0.0695445i 0.0103652 + 0.00277734i
\(628\) 0.544366 + 2.03160i 0.0217225 + 0.0810697i
\(629\) 18.4398 0.735244
\(630\) 0 0
\(631\) −9.67260 −0.385060 −0.192530 0.981291i \(-0.561669\pi\)
−0.192530 + 0.981291i \(0.561669\pi\)
\(632\) −6.66227 24.8639i −0.265011 0.989034i
\(633\) 11.6142 + 3.11201i 0.461622 + 0.123691i
\(634\) −6.90730 + 3.98793i −0.274324 + 0.158381i
\(635\) −11.2472 + 10.3479i −0.446330 + 0.410643i
\(636\) 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
\(640\) 20.9135 4.68062i 0.826679 0.185018i
\(641\) 20.2924 + 35.1474i 0.801500 + 1.38824i 0.918629 + 0.395122i \(0.129298\pi\)
−0.117129 + 0.993117i \(0.537369\pi\)
\(642\) −6.67561 + 1.78872i −0.263465 + 0.0705953i
\(643\) 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
\(647\) 6.16438 23.0058i 0.242347 0.904450i −0.732352 0.680927i \(-0.761577\pi\)
0.974698 0.223524i \(-0.0717561\pi\)
\(648\) −0.675461 + 2.52086i −0.0265346 + 0.0990285i
\(649\) −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
\(653\) 31.4119 8.41678i 1.22924 0.329374i 0.414957 0.909841i \(-0.363797\pi\)
0.814284 + 0.580467i \(0.197130\pi\)
\(654\) −0.825207 1.42930i −0.0322681 0.0558901i
\(655\) 1.22267 + 0.775469i 0.0477737 + 0.0303001i
\(656\) −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 \(-0.220223\pi\)
\(660\) −8.25941 8.97720i −0.321497 0.349437i
\(661\) −28.1609 + 16.2587i −1.09533 + 0.632391i −0.934991 0.354671i \(-0.884593\pi\)
−0.160341 + 0.987062i \(0.551260\pi\)
\(662\) −17.4280 4.66982i −0.677359 0.181498i
\(663\) −2.82932 10.5592i −0.109882 0.410084i
\(664\) 6.03701 0.234281
\(665\) 0 0
\(666\) −6.68434 −0.259013
\(667\) −0.541806 2.02205i −0.0209788 0.0782940i
\(668\) 3.65646 + 0.979744i 0.141473 + 0.0379075i
\(669\) 14.3203 8.26785i 0.553656 0.319654i
\(670\) 0.0418598 1.00520i 0.00161719 0.0388343i
\(671\) 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
\(675\) −3.22934 3.81725i −0.124297 0.146926i
\(676\) −9.85228 17.0647i −0.378934 0.656333i
\(677\) 9.36503 2.50935i 0.359927 0.0964422i −0.0743237 0.997234i \(-0.523680\pi\)
0.434251 + 0.900792i \(0.357013\pi\)
\(678\) −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
\(682\) −1.82497 + 6.81087i −0.0698816 + 0.260802i
\(683\) 8.50440 31.7389i 0.325412 1.21445i −0.588485 0.808508i \(-0.700275\pi\)
0.913897 0.405946i \(-0.133058\pi\)
\(684\) −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
\(688\) −3.17753 + 0.851417i −0.121142 + 0.0324600i
\(689\) 22.5160 + 38.9989i 0.857793 + 1.48574i
\(690\) −0.281820 1.25920i −0.0107287 0.0479370i
\(691\) 36.7813 + 21.2357i 1.39923 + 0.807845i 0.994312 0.106509i \(-0.0339673\pi\)
0.404916 + 0.914354i \(0.367301\pi\)
\(692\) −6.95144 6.95144i −0.264254 0.264254i
\(693\) 0 0
\(694\) 6.30557i 0.239356i
\(695\) −49.5224 2.06227i −1.87849 0.0782265i
\(696\) −6.26301 + 3.61595i −0.237399 + 0.137062i
\(697\) −17.6695 4.73453i −0.669280 0.179333i
\(698\) −3.34362 12.4786i −0.126558 0.472320i
\(699\) 1.42549 0.0539169
\(700\) 0 0
\(701\) 17.0793 0.645077 0.322539 0.946556i \(-0.395464\pi\)
0.322539 + 0.946556i \(0.395464\pi\)
\(702\) 1.02561 + 3.82764i 0.0387093 + 0.144465i
\(703\) −0.589700 0.158010i −0.0222409 0.00595944i
\(704\) −9.33261 + 5.38818i −0.351736 + 0.203075i
\(705\) 17.3472 + 0.722394i 0.653333 + 0.0272069i
\(706\) 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 \(-0.123073\pi\)
0.136525 + 0.990637i \(0.456407\pi\)
\(710\) −3.03212 13.5478i −0.113794 0.508441i
\(711\) −4.93165 8.54186i −0.184951 0.320345i
\(712\) 12.7382 3.41319i 0.477385 0.127915i
\(713\) 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
\(717\) 5.24897 19.5894i 0.196027 0.731581i
\(718\) 1.61104 6.01247i 0.0601233 0.224383i
\(719\) 9.66239 16.7357i 0.360346 0.624138i −0.627671 0.778478i \(-0.715992\pi\)
0.988018 + 0.154340i \(0.0493252\pi\)
\(720\) 1.66319 0.870061i 0.0619832 0.0324253i
\(721\) 0 0
\(722\) −10.2601 + 10.2601i −0.381841 + 0.381841i
\(723\) 2.67555 0.716912i 0.0995048 0.0266622i
\(724\) −6.00966 10.4090i −0.223347 0.386849i
\(725\) 1.15197 13.8074i 0.0427830 0.512794i
\(726\) 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
\(730\) 0.960044 23.0540i 0.0355328 0.853267i
\(731\) −7.15181 + 4.12910i −0.264519 + 0.152720i
\(732\) −19.5803 5.24652i −0.723709 0.193917i
\(733\) −0.872739 3.25711i −0.0322354 0.120304i 0.947933 0.318469i \(-0.103169\pi\)
−0.980169 + 0.198165i \(0.936502\pi\)
\(734\) 15.9321 0.588064
\(735\) 0 0
\(736\) 4.42747 0.163199
\(737\) −0.587125 2.19118i −0.0216270 0.0807132i
\(738\) 6.40510 + 1.71624i 0.235775 + 0.0631757i
\(739\) −4.29271 + 2.47840i −0.157910 + 0.0911693i −0.576873 0.816834i \(-0.695727\pi\)
0.418963 + 0.908003i \(0.362394\pi\)
\(740\) 18.7659 + 20.3968i 0.689848 + 0.749800i
\(741\) 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
\(745\) −20.8610 13.2310i −0.764289 0.484745i
\(746\) −0.807303 1.39829i −0.0295575 0.0511950i
\(747\) 2.23440 0.598706i 0.0817525 0.0219055i
\(748\) 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 −0.745691 0.666292i \(-0.767880\pi\)
0.949871 + 0.312641i \(0.101214\pi\)
\(752\) −1.68694 + 6.29575i −0.0615164 + 0.229582i
\(753\) 1.57875 5.89197i 0.0575328 0.214715i
\(754\) −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 \(-0.0238706\pi\)
\(758\) −13.8077 + 3.69977i −0.501520 + 0.134382i
\(759\) −1.45473 2.51967i −0.0528035 0.0914584i
\(760\) −0.397309 + 0.0889211i −0.0144119 + 0.00322551i
\(761\) 24.3504 + 14.0587i 0.882703 + 0.509629i 0.871549 0.490309i \(-0.163116\pi\)
0.0111541 + 0.999938i \(0.496449\pi\)
\(762\) 3.69181 + 3.69181i 0.133740 + 0.133740i
\(763\) 0 0
\(764\) 7.63986i 0.276400i
\(765\) 3.46765 3.19038i 0.125373 0.115349i
\(766\) −19.5862 + 11.3081i −0.707679 + 0.408579i
\(767\) −34.9474 9.36412i −1.26188 0.338119i
\(768\) −3.34324 12.4771i −0.120639 0.450230i
\(769\) 6.61248 0.238452 0.119226 0.992867i \(-0.461959\pi\)
0.119226 + 0.992867i \(0.461959\pi\)