Properties

Label 735.2.v.a.313.6
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 313.6
Character \(\chi\) \(=\) 735.313
Dual form 735.2.v.a.472.6

$q$-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 \(-0.494423\pi\)
0.999847 0.0175187i \(-0.00557667\pi\)
\(14\) 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 −0.999994 0.00338789i \(-0.998922\pi\)
0.867714 + 0.497063i \(0.165588\pi\)
\(18\) −0.197706 + 0.737849i −0.0465998 + 0.173913i
\(19\) 0.0348837 0.0604203i 0.00800286 0.0138614i −0.861996 0.506915i \(-0.830786\pi\)
0.869999 + 0.493053i \(0.164119\pi\)
\(20\) −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 −0.674679 0.738111i \(-0.735718\pi\)
0.301884 + 0.953345i \(0.402385\pi\)
\(32\) 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 \(0.237090\pi\)
−0.735196 + 0.677854i \(0.762910\pi\)
\(42\) 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 0.333678 0.942687i \(-0.391710\pi\)
0.760317 + 0.649552i \(0.225043\pi\)
\(48\) 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 0.544635 0.838673i \(-0.316668\pi\)
−0.998630 + 0.0523310i \(0.983335\pi\)
\(60\) −3.09090 + 0.691771i −0.399034 + 0.0893072i
\(61\) −12.3935 7.15536i −1.58682 0.916150i −0.993827 0.110942i \(-0.964613\pi\)
−0.592992 0.805208i \(-0.702054\pi\)
\(62\) −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 0.922105 0.386940i \(-0.126468\pi\)
0.605096 + 0.796152i \(0.293135\pi\)
\(74\) −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 −0.791156 0.611615i \(-0.790520\pi\)
0.611615 + 0.791156i \(0.290520\pi\)
\(84\) 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 −0.968297 0.249800i \(-0.919635\pi\)
0.700482 + 0.713670i \(0.252968\pi\)
\(90\) 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 0.267251 0.963627i \(-0.413885\pi\)
−0.963627 + 0.267251i \(0.913885\pi\)
\(98\) 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 \(0.737479\pi\)
−0.975357 + 0.220632i \(0.929188\pi\)
\(102\) −1.55485 0.416622i −0.153954 0.0412517i
\(103\) −0.855857 3.19410i −0.0843301 0.314724i 0.910856 0.412723i \(-0.135422\pi\)
−0.995186 + 0.0979992i \(0.968756\pi\)
\(104\) 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 0.475303 0.879822i \(-0.342338\pi\)
−0.524296 + 0.851536i \(0.675672\pi\)
\(132\) 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 \(-0.110769\pi\)
0.940060 + 0.341009i \(0.110769\pi\)
\(140\) 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 −0.948893 0.315597i \(-0.897795\pi\)
0.979564 + 0.201132i \(0.0644619\pi\)
\(158\) 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 0.630203 0.776431i \(-0.282972\pi\)
−0.776431 + 0.630203i \(0.782972\pi\)
\(168\) 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 \(0.00165217\pi\)
−0.863419 + 0.504488i \(0.831681\pi\)
\(174\) 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 \(0.102123\pi\)
−0.948974 + 0.315353i \(0.897877\pi\)
\(182\) 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 0.814798 0.579745i \(-0.196848\pi\)
−0.909473 + 0.415763i \(0.863515\pi\)
\(200\) 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 −0.197346 0.980334i \(-0.563232\pi\)
0.980334 + 0.197346i \(0.0632321\pi\)
\(224\) 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 −0.978050 0.208369i \(-0.933184\pi\)
0.951201 + 0.308572i \(0.0998511\pi\)
\(228\) 0.0255777 0.0954574i 0.00169393 0.00632182i
\(229\) 3.91654 6.78365i 0.258812 0.448276i −0.707112 0.707102i \(-0.750002\pi\)
0.965924 + 0.258826i \(0.0833355\pi\)
\(230\) −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 −0.420745 0.907179i \(-0.638231\pi\)
0.575268 + 0.817965i \(0.304898\pi\)
\(242\) −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 \(-0.938338\pi\)
0.981295 0.192509i \(-0.0616623\pi\)
\(252\) 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 −0.343787 0.939048i \(-0.611710\pi\)
0.171796 + 0.985133i \(0.445043\pi\)
\(258\) 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 \(0.105242\pi\)
−0.191774 + 0.981439i \(0.561424\pi\)
\(270\) 0.914849 1.44243i 0.0556759 0.0877834i
\(271\) −3.58076 2.06735i −0.217515 0.125583i 0.387284 0.921961i \(-0.373413\pi\)
−0.604799 + 0.796378i \(0.706747\pi\)
\(272\) 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 0.190489 0.981689i \(-0.438993\pi\)
−0.325876 + 0.945412i \(0.605659\pi\)
\(284\) −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 −0.103400 0.994640i \(-0.532972\pi\)
0.994640 + 0.103400i \(0.0329722\pi\)
\(294\) 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 0.988114 0.153721i \(-0.0491256\pi\)
−0.153721 + 0.988114i \(0.549126\pi\)
\(308\) 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 −0.428073 0.903744i \(-0.640807\pi\)
0.568629 + 0.822594i \(0.307474\pi\)
\(312\) 13.0771 + 3.50400i 0.740345 + 0.198375i
\(313\) 3.44732 + 12.8656i 0.194854 + 0.727204i 0.992305 + 0.123820i \(0.0395146\pi\)
−0.797451 + 0.603384i \(0.793819\pi\)
\(314\) 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 \(-0.350482\pi\)
0.452641 + 0.891693i \(0.350482\pi\)
\(350\) 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 −0.169448 0.985539i \(-0.554198\pi\)
−0.639516 + 0.768778i \(0.720865\pi\)
\(354\) 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 \(0.266561\pi\)
−0.951160 + 0.308700i \(0.900106\pi\)
\(368\) 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 \(-0.810277\pi\)
0.436014 0.899940i \(-0.356390\pi\)
\(384\) 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 −0.0204142 0.999792i \(-0.506498\pi\)
0.482217 + 0.876052i \(0.339832\pi\)
\(398\) 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 0.966532 0.256547i \(-0.0825848\pi\)
−0.705442 + 0.708768i \(0.749251\pi\)
\(410\) 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 \(-0.623996\pi\)
−0.379766 + 0.925083i \(0.623996\pi\)
\(420\) 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 −0.664404 0.747374i \(-0.731314\pi\)
0.747374 + 0.664404i \(0.231314\pi\)
\(434\) 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 \(0.390692\pi\)
−0.983809 + 0.179223i \(0.942642\pi\)
\(440\) 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 \(0.00616607\pi\)
−0.999812 + 0.0193701i \(0.993834\pi\)
\(462\) 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 −0.903531 0.428522i \(-0.859035\pi\)
−0.568220 + 0.822876i \(0.692368\pi\)
\(468\) 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 \(-0.791823\pi\)
−0.130038 0.991509i \(-0.541510\pi\)
\(480\) −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 \(0.555855\pi\)
−0.984644 + 0.174573i \(0.944145\pi\)
\(504\) 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 \(-0.525735\pi\)
0.903577 0.428425i \(-0.140931\pi\)
\(510\) 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 −0.548353 0.836247i \(-0.684745\pi\)
0.450035 + 0.893011i \(0.351412\pi\)
\(522\) 2.04464 + 0.547858i 0.0894913 + 0.0239791i
\(523\) 2.22856 + 8.31711i 0.0974482 + 0.363682i 0.997379 0.0723506i \(-0.0230500\pi\)
−0.899931 + 0.436032i \(0.856383\pi\)
\(524\) −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 −0.508841 0.860860i \(-0.669926\pi\)
−0.871100 + 0.491106i \(0.836593\pi\)
\(564\) 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 \(0.234769\pi\)
−0.977200 + 0.212322i \(0.931897\pi\)
\(578\) −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 0.952623 0.304155i \(-0.0983740\pi\)
−0.304155 + 0.952623i \(0.598374\pi\)
\(588\) 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 0.978447 0.206500i \(-0.0662073\pi\)
−0.950610 + 0.310389i \(0.899541\pi\)
\(594\) −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 \(-0.927428\pi\)
0.974123 0.226021i \(-0.0725717\pi\)
\(602\) 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 −0.0434656 0.999055i \(-0.513840\pi\)
0.461885 + 0.886940i \(0.347173\pi\)
\(608\) 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 0.760409 0.649445i \(-0.224999\pi\)
−0.942640 + 0.333811i \(0.891665\pi\)
\(620\) 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 −0.779733 0.626112i \(-0.784645\pi\)
0.626112 + 0.779733i \(0.284645\pi\)
\(644\) 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 \(0.238423\pi\)
−0.974698 + 0.223524i \(0.928244\pi\)
\(648\) −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 0.160341 0.987062i \(-0.448740\pi\)
0.934991 + 0.354671i \(0.115407\pi\)
\(662\) −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 −0.434251 0.900792i \(-0.642987\pi\)
0.0743237 + 0.997234i \(0.476320\pi\)
\(678\) 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 −0.404916 0.914354i \(-0.632699\pi\)
−0.994312 + 0.106509i \(0.966033\pi\)
\(692\) 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 −0.988018 0.154340i \(-0.950675\pi\)
0.627671 + 0.778478i \(0.284008\pi\)
\(720\) −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 0.654907 0.755710i \(-0.272708\pi\)
−0.755710 + 0.654907i \(0.772708\pi\)
\(728\) 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 0.980169 0.198165i \(-0.0634981\pi\)
−0.947933 + 0.318469i \(0.896831\pi\)
\(734\) −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 −0.0111541 0.999938i \(-0.503551\pi\)
−0.871549 + 0.490309i \(0.836884\pi\)
\(762\) −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 \(-0.538041\pi\)
−0.119226 + 0.992867i \(0.538041\pi\)