Properties

Label 1183.2.e.i.508.1
Level $1183$
Weight $2$
Character 1183.508
Analytic conductor $9.446$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 11 x^{14} + 85 x^{12} + 334 x^{10} + 952 x^{8} + 1050 x^{6} + 853 x^{4} + 93 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.1
Root \(-1.14241 + 1.97871i\) of defining polynomial
Character \(\chi\) \(=\) 1183.508
Dual form 1183.2.e.i.170.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.14241 - 1.97871i) q^{2} +(-1.57521 + 2.72835i) q^{3} +(-1.61019 + 2.78892i) q^{4} +(-1.06250 - 1.84030i) q^{5} +7.19813 q^{6} +(0.331665 - 2.62488i) q^{7} +2.78832 q^{8} +(-3.46258 - 5.99736i) q^{9} +O(q^{10})\) \(q+(-1.14241 - 1.97871i) q^{2} +(-1.57521 + 2.72835i) q^{3} +(-1.61019 + 2.78892i) q^{4} +(-1.06250 - 1.84030i) q^{5} +7.19813 q^{6} +(0.331665 - 2.62488i) q^{7} +2.78832 q^{8} +(-3.46258 - 5.99736i) q^{9} +(-2.42760 + 4.20473i) q^{10} +(-0.154233 + 0.267139i) q^{11} +(-5.07276 - 8.78629i) q^{12} +(-5.57276 + 2.34241i) q^{14} +6.69462 q^{15} +(0.0349749 + 0.0605784i) q^{16} +(0.887368 - 1.53697i) q^{17} +(-7.91135 + 13.7029i) q^{18} +(-0.890653 - 1.54266i) q^{19} +6.84326 q^{20} +(6.63914 + 5.03964i) q^{21} +0.704786 q^{22} +(-0.575211 - 0.996294i) q^{23} +(-4.39219 + 7.60750i) q^{24} +(0.242207 - 0.419515i) q^{25} +12.3659 q^{27} +(6.78655 + 5.15153i) q^{28} +2.01052 q^{29} +(-7.64798 - 13.2467i) q^{30} +(2.30242 - 3.98791i) q^{31} +(2.86823 - 4.96792i) q^{32} +(-0.485898 - 0.841600i) q^{33} -4.05494 q^{34} +(-5.18295 + 2.17856i) q^{35} +22.3016 q^{36} +(2.77071 + 4.79901i) q^{37} +(-2.03497 + 3.52468i) q^{38} +(-2.96258 - 5.13134i) q^{40} -6.72984 q^{41} +(2.38737 - 18.8942i) q^{42} +1.52611 q^{43} +(-0.496686 - 0.860286i) q^{44} +(-7.35795 + 12.7443i) q^{45} +(-1.31425 + 2.27635i) q^{46} +(-4.75908 - 8.24297i) q^{47} -0.220372 q^{48} +(-6.78000 - 1.74116i) q^{49} -1.10680 q^{50} +(2.79558 + 4.84209i) q^{51} +(-3.72037 + 6.44387i) q^{53} +(-14.1269 - 24.4685i) q^{54} +0.655486 q^{55} +(0.924789 - 7.31901i) q^{56} +5.61186 q^{57} +(-2.29683 - 3.97823i) q^{58} +(4.06053 - 7.03304i) q^{59} +(-10.7796 + 18.6708i) q^{60} +(1.72037 + 2.97977i) q^{61} -10.5212 q^{62} +(-16.8908 + 7.09974i) q^{63} -12.9669 q^{64} +(-1.11019 + 1.92290i) q^{66} +(-6.30747 + 10.9249i) q^{67} +(2.85765 + 4.94960i) q^{68} +3.62431 q^{69} +(10.2318 + 7.76673i) q^{70} -1.35070 q^{71} +(-9.65478 - 16.7226i) q^{72} +(-5.94059 + 10.2894i) q^{73} +(6.33056 - 10.9648i) q^{74} +(0.763054 + 1.32165i) q^{75} +5.73646 q^{76} +(0.650054 + 0.493443i) q^{77} +(3.96258 + 6.86339i) q^{79} +(0.0743214 - 0.128728i) q^{80} +(-9.09116 + 15.7464i) q^{81} +(7.68821 + 13.3164i) q^{82} -11.2290 q^{83} +(-24.7454 + 10.4013i) q^{84} -3.77130 q^{85} +(-1.74344 - 3.01972i) q^{86} +(-3.16700 + 5.48540i) q^{87} +(-0.430050 + 0.744869i) q^{88} +(0.829583 + 1.43688i) q^{89} +33.6231 q^{90} +3.70479 q^{92} +(7.25360 + 12.5636i) q^{93} +(-10.8736 + 18.8336i) q^{94} +(-1.89263 + 3.27813i) q^{95} +(9.03614 + 15.6511i) q^{96} -7.66641 q^{97} +(4.30026 + 15.4047i) q^{98} +2.13617 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{3} - 6q^{4} - 12q^{9} + O(q^{10}) \) \( 16q - 4q^{3} - 6q^{4} - 12q^{9} + 6q^{10} - 18q^{12} - 26q^{14} + 2q^{16} - 8q^{17} - 36q^{22} + 12q^{23} + 32q^{27} - 16q^{29} - 38q^{30} + 56q^{36} - 34q^{38} - 4q^{40} + 16q^{42} - 16q^{43} + 36q^{48} - 40q^{49} - 16q^{51} - 20q^{53} + 24q^{55} + 36q^{56} - 12q^{61} - 44q^{62} - 88q^{64} + 2q^{66} - 2q^{68} + 56q^{69} + 42q^{74} - 8q^{75} + 76q^{77} + 20q^{79} - 24q^{81} + 16q^{82} - 68q^{87} - 4q^{88} + 216q^{90} + 12q^{92} - 26q^{94} + 16q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.14241 1.97871i −0.807803 1.39916i −0.914382 0.404852i \(-0.867323\pi\)
0.106579 0.994304i \(-0.466010\pi\)
\(3\) −1.57521 + 2.72835i −0.909448 + 1.57521i −0.0946163 + 0.995514i \(0.530162\pi\)
−0.814832 + 0.579697i \(0.803171\pi\)
\(4\) −1.61019 + 2.78892i −0.805093 + 1.39446i
\(5\) −1.06250 1.84030i −0.475162 0.823005i 0.524433 0.851452i \(-0.324277\pi\)
−0.999595 + 0.0284464i \(0.990944\pi\)
\(6\) 7.19813 2.93862
\(7\) 0.331665 2.62488i 0.125358 0.992112i
\(8\) 2.78832 0.985820
\(9\) −3.46258 5.99736i −1.15419 1.99912i
\(10\) −2.42760 + 4.20473i −0.767676 + 1.32965i
\(11\) −0.154233 + 0.267139i −0.0465029 + 0.0805454i −0.888340 0.459186i \(-0.848141\pi\)
0.841837 + 0.539732i \(0.181474\pi\)
\(12\) −5.07276 8.78629i −1.46438 2.53638i
\(13\) 0 0
\(14\) −5.57276 + 2.34241i −1.48938 + 0.626036i
\(15\) 6.69462 1.72854
\(16\) 0.0349749 + 0.0605784i 0.00874373 + 0.0151446i
\(17\) 0.887368 1.53697i 0.215218 0.372769i −0.738122 0.674667i \(-0.764287\pi\)
0.953340 + 0.301898i \(0.0976204\pi\)
\(18\) −7.91135 + 13.7029i −1.86472 + 3.22979i
\(19\) −0.890653 1.54266i −0.204330 0.353909i 0.745589 0.666406i \(-0.232168\pi\)
−0.949919 + 0.312496i \(0.898835\pi\)
\(20\) 6.84326 1.53020
\(21\) 6.63914 + 5.03964i 1.44878 + 1.09974i
\(22\) 0.704786 0.150261
\(23\) −0.575211 0.996294i −0.119940 0.207742i 0.799804 0.600261i \(-0.204937\pi\)
−0.919744 + 0.392520i \(0.871603\pi\)
\(24\) −4.39219 + 7.60750i −0.896553 + 1.55288i
\(25\) 0.242207 0.419515i 0.0484414 0.0839029i
\(26\) 0 0
\(27\) 12.3659 2.37982
\(28\) 6.78655 + 5.15153i 1.28254 + 0.973548i
\(29\) 2.01052 0.373345 0.186672 0.982422i \(-0.440230\pi\)
0.186672 + 0.982422i \(0.440230\pi\)
\(30\) −7.64798 13.2467i −1.39632 2.41850i
\(31\) 2.30242 3.98791i 0.413527 0.716251i −0.581745 0.813371i \(-0.697630\pi\)
0.995273 + 0.0971205i \(0.0309632\pi\)
\(32\) 2.86823 4.96792i 0.507037 0.878213i
\(33\) −0.485898 0.841600i −0.0845840 0.146504i
\(34\) −4.05494 −0.695416
\(35\) −5.18295 + 2.17856i −0.876078 + 0.368244i
\(36\) 22.3016 3.71693
\(37\) 2.77071 + 4.79901i 0.455502 + 0.788953i 0.998717 0.0506410i \(-0.0161264\pi\)
−0.543215 + 0.839594i \(0.682793\pi\)
\(38\) −2.03497 + 3.52468i −0.330117 + 0.571779i
\(39\) 0 0
\(40\) −2.96258 5.13134i −0.468425 0.811336i
\(41\) −6.72984 −1.05102 −0.525512 0.850786i \(-0.676126\pi\)
−0.525512 + 0.850786i \(0.676126\pi\)
\(42\) 2.38737 18.8942i 0.368379 2.91544i
\(43\) 1.52611 0.232729 0.116365 0.993207i \(-0.462876\pi\)
0.116365 + 0.993207i \(0.462876\pi\)
\(44\) −0.496686 0.860286i −0.0748783 0.129693i
\(45\) −7.35795 + 12.7443i −1.09686 + 1.89981i
\(46\) −1.31425 + 2.27635i −0.193776 + 0.335629i
\(47\) −4.75908 8.24297i −0.694183 1.20236i −0.970455 0.241281i \(-0.922432\pi\)
0.276272 0.961079i \(-0.410901\pi\)
\(48\) −0.220372 −0.0318079
\(49\) −6.78000 1.74116i −0.968571 0.248738i
\(50\) −1.10680 −0.156524
\(51\) 2.79558 + 4.84209i 0.391460 + 0.678028i
\(52\) 0 0
\(53\) −3.72037 + 6.44387i −0.511032 + 0.885134i 0.488886 + 0.872348i \(0.337403\pi\)
−0.999918 + 0.0127862i \(0.995930\pi\)
\(54\) −14.1269 24.4685i −1.92243 3.32974i
\(55\) 0.655486 0.0883857
\(56\) 0.924789 7.31901i 0.123580 0.978044i
\(57\) 5.61186 0.743309
\(58\) −2.29683 3.97823i −0.301589 0.522368i
\(59\) 4.06053 7.03304i 0.528636 0.915624i −0.470807 0.882236i \(-0.656037\pi\)
0.999442 0.0333877i \(-0.0106296\pi\)
\(60\) −10.7796 + 18.6708i −1.39164 + 2.41039i
\(61\) 1.72037 + 2.97977i 0.220271 + 0.381521i 0.954890 0.296959i \(-0.0959725\pi\)
−0.734619 + 0.678480i \(0.762639\pi\)
\(62\) −10.5212 −1.33620
\(63\) −16.8908 + 7.09974i −2.12804 + 0.894483i
\(64\) −12.9669 −1.62086
\(65\) 0 0
\(66\) −1.11019 + 1.92290i −0.136654 + 0.236692i
\(67\) −6.30747 + 10.9249i −0.770580 + 1.33468i 0.166665 + 0.986014i \(0.446700\pi\)
−0.937245 + 0.348671i \(0.886633\pi\)
\(68\) 2.85765 + 4.94960i 0.346541 + 0.600227i
\(69\) 3.62431 0.436316
\(70\) 10.2318 + 7.76673i 1.22293 + 0.928302i
\(71\) −1.35070 −0.160299 −0.0801494 0.996783i \(-0.525540\pi\)
−0.0801494 + 0.996783i \(0.525540\pi\)
\(72\) −9.65478 16.7226i −1.13783 1.97077i
\(73\) −5.94059 + 10.2894i −0.695293 + 1.20428i 0.274789 + 0.961505i \(0.411392\pi\)
−0.970082 + 0.242778i \(0.921941\pi\)
\(74\) 6.33056 10.9648i 0.735912 1.27464i
\(75\) 0.763054 + 1.32165i 0.0881099 + 0.152611i
\(76\) 5.73646 0.658018
\(77\) 0.650054 + 0.493443i 0.0740805 + 0.0562330i
\(78\) 0 0
\(79\) 3.96258 + 6.86339i 0.445825 + 0.772191i 0.998109 0.0614644i \(-0.0195771\pi\)
−0.552284 + 0.833656i \(0.686244\pi\)
\(80\) 0.0743214 0.128728i 0.00830939 0.0143923i
\(81\) −9.09116 + 15.7464i −1.01013 + 1.74960i
\(82\) 7.68821 + 13.3164i 0.849021 + 1.47055i
\(83\) −11.2290 −1.23255 −0.616273 0.787533i \(-0.711358\pi\)
−0.616273 + 0.787533i \(0.711358\pi\)
\(84\) −24.7454 + 10.4013i −2.69995 + 1.13487i
\(85\) −3.77130 −0.409055
\(86\) −1.74344 3.01972i −0.188000 0.325625i
\(87\) −3.16700 + 5.48540i −0.339538 + 0.588096i
\(88\) −0.430050 + 0.744869i −0.0458435 + 0.0794033i
\(89\) 0.829583 + 1.43688i 0.0879357 + 0.152309i 0.906638 0.421909i \(-0.138640\pi\)
−0.818703 + 0.574218i \(0.805306\pi\)
\(90\) 33.6231 3.54418
\(91\) 0 0
\(92\) 3.70479 0.386251
\(93\) 7.25360 + 12.5636i 0.752164 + 1.30279i
\(94\) −10.8736 + 18.8336i −1.12153 + 1.94254i
\(95\) −1.89263 + 3.27813i −0.194180 + 0.336329i
\(96\) 9.03614 + 15.6511i 0.922247 + 1.59738i
\(97\) −7.66641 −0.778406 −0.389203 0.921152i \(-0.627250\pi\)
−0.389203 + 0.921152i \(0.627250\pi\)
\(98\) 4.30026 + 15.4047i 0.434392 + 1.55611i
\(99\) 2.13617 0.214693
\(100\) 0.779996 + 1.35099i 0.0779996 + 0.135099i
\(101\) −4.55864 + 7.89579i −0.453601 + 0.785660i −0.998607 0.0527721i \(-0.983194\pi\)
0.545005 + 0.838433i \(0.316528\pi\)
\(102\) 6.38738 11.0633i 0.632445 1.09543i
\(103\) −3.02085 5.23226i −0.297653 0.515550i 0.677946 0.735112i \(-0.262870\pi\)
−0.975599 + 0.219562i \(0.929537\pi\)
\(104\) 0 0
\(105\) 2.22037 17.5726i 0.216686 1.71491i
\(106\) 17.0007 1.65125
\(107\) −6.04305 10.4669i −0.584204 1.01187i −0.994974 0.100132i \(-0.968074\pi\)
0.410770 0.911739i \(-0.365260\pi\)
\(108\) −19.9114 + 34.4876i −1.91598 + 3.31857i
\(109\) −0.680941 + 1.17942i −0.0652223 + 0.112968i −0.896793 0.442451i \(-0.854109\pi\)
0.831570 + 0.555420i \(0.187442\pi\)
\(110\) −0.748831 1.29701i −0.0713983 0.123665i
\(111\) −17.4578 −1.65702
\(112\) 0.170611 0.0717133i 0.0161212 0.00677627i
\(113\) −9.42009 −0.886168 −0.443084 0.896480i \(-0.646116\pi\)
−0.443084 + 0.896480i \(0.646116\pi\)
\(114\) −6.41103 11.1042i −0.600448 1.04001i
\(115\) −1.22232 + 2.11712i −0.113982 + 0.197422i
\(116\) −3.23731 + 5.60719i −0.300577 + 0.520615i
\(117\) 0 0
\(118\) −18.5551 −1.70814
\(119\) −3.74004 2.83899i −0.342849 0.260250i
\(120\) 18.6667 1.70403
\(121\) 5.45242 + 9.44388i 0.495675 + 0.858534i
\(122\) 3.93073 6.80822i 0.355871 0.616387i
\(123\) 10.6009 18.3613i 0.955852 1.65558i
\(124\) 7.41466 + 12.8426i 0.665856 + 1.15330i
\(125\) −11.6543 −1.04239
\(126\) 33.3444 + 25.3111i 2.97056 + 2.25489i
\(127\) −13.3998 −1.18904 −0.594519 0.804081i \(-0.702658\pi\)
−0.594519 + 0.804081i \(0.702658\pi\)
\(128\) 9.07695 + 15.7217i 0.802297 + 1.38962i
\(129\) −2.40394 + 4.16375i −0.211655 + 0.366598i
\(130\) 0 0
\(131\) −6.69854 11.6022i −0.585254 1.01369i −0.994844 0.101420i \(-0.967662\pi\)
0.409590 0.912270i \(-0.365672\pi\)
\(132\) 3.12954 0.272392
\(133\) −4.34469 + 1.82621i −0.376732 + 0.158353i
\(134\) 28.8228 2.48991
\(135\) −13.1387 22.7569i −1.13080 1.95860i
\(136\) 2.47427 4.28555i 0.212167 0.367483i
\(137\) −0.250522 + 0.433917i −0.0214036 + 0.0370720i −0.876529 0.481349i \(-0.840147\pi\)
0.855125 + 0.518421i \(0.173480\pi\)
\(138\) −4.14044 7.17145i −0.352458 0.610475i
\(139\) 1.41936 0.120388 0.0601941 0.998187i \(-0.480828\pi\)
0.0601941 + 0.998187i \(0.480828\pi\)
\(140\) 2.26967 17.9627i 0.191822 1.51813i
\(141\) 29.9862 2.52529
\(142\) 1.54305 + 2.67264i 0.129490 + 0.224283i
\(143\) 0 0
\(144\) 0.242207 0.419515i 0.0201839 0.0349596i
\(145\) −2.13617 3.69996i −0.177399 0.307265i
\(146\) 27.1463 2.24664
\(147\) 15.4304 15.7555i 1.27268 1.29949i
\(148\) −17.8454 −1.46689
\(149\) 10.5454 + 18.2652i 0.863916 + 1.49635i 0.868120 + 0.496355i \(0.165328\pi\)
−0.00420426 + 0.999991i \(0.501338\pi\)
\(150\) 1.74344 3.01972i 0.142351 0.246559i
\(151\) 8.75211 15.1591i 0.712236 1.23363i −0.251779 0.967785i \(-0.581016\pi\)
0.964016 0.265845i \(-0.0856510\pi\)
\(152\) −2.48343 4.30142i −0.201432 0.348891i
\(153\) −12.2903 −0.993614
\(154\) 0.233753 1.84998i 0.0188363 0.149075i
\(155\) −9.78526 −0.785971
\(156\) 0 0
\(157\) −0.0377894 + 0.0654532i −0.00301593 + 0.00522374i −0.867529 0.497386i \(-0.834293\pi\)
0.864514 + 0.502610i \(0.167627\pi\)
\(158\) 9.05375 15.6816i 0.720278 1.24756i
\(159\) −11.7207 20.3009i −0.929515 1.60997i
\(160\) −12.1899 −0.963699
\(161\) −2.80593 + 1.17942i −0.221138 + 0.0929516i
\(162\) 41.5432 3.26394
\(163\) 5.04086 + 8.73102i 0.394830 + 0.683866i 0.993080 0.117444i \(-0.0374701\pi\)
−0.598249 + 0.801310i \(0.704137\pi\)
\(164\) 10.8363 18.7690i 0.846172 1.46561i
\(165\) −1.03253 + 1.78839i −0.0803822 + 0.139226i
\(166\) 12.8281 + 22.2189i 0.995655 + 1.72452i
\(167\) −5.84989 −0.452678 −0.226339 0.974049i \(-0.572676\pi\)
−0.226339 + 0.974049i \(0.572676\pi\)
\(168\) 18.5120 + 14.0521i 1.42824 + 1.08415i
\(169\) 0 0
\(170\) 4.30835 + 7.46229i 0.330436 + 0.572331i
\(171\) −6.16791 + 10.6831i −0.471672 + 0.816960i
\(172\) −2.45732 + 4.25620i −0.187369 + 0.324532i
\(173\) −8.49511 14.7140i −0.645871 1.11868i −0.984100 0.177617i \(-0.943161\pi\)
0.338229 0.941064i \(-0.390172\pi\)
\(174\) 14.4720 1.09712
\(175\) −1.02084 0.774903i −0.0771686 0.0585771i
\(176\) −0.0215771 −0.00162644
\(177\) 12.7924 + 22.1570i 0.961534 + 1.66543i
\(178\) 1.89544 3.28300i 0.142069 0.246072i
\(179\) 7.65079 13.2516i 0.571847 0.990468i −0.424529 0.905414i \(-0.639560\pi\)
0.996376 0.0850537i \(-0.0271062\pi\)
\(180\) −23.6953 41.0415i −1.76615 3.05905i
\(181\) 5.84958 0.434796 0.217398 0.976083i \(-0.430243\pi\)
0.217398 + 0.976083i \(0.430243\pi\)
\(182\) 0 0
\(183\) −10.8398 −0.801301
\(184\) −1.60387 2.77799i −0.118239 0.204796i
\(185\) 5.88774 10.1979i 0.432875 0.749761i
\(186\) 16.5731 28.7055i 1.21520 2.10479i
\(187\) 0.273722 + 0.474101i 0.0200165 + 0.0346697i
\(188\) 30.6520 2.23553
\(189\) 4.10134 32.4590i 0.298329 2.36105i
\(190\) 8.64861 0.627436
\(191\) 13.4090 + 23.2250i 0.970238 + 1.68050i 0.694831 + 0.719173i \(0.255479\pi\)
0.275407 + 0.961328i \(0.411188\pi\)
\(192\) 20.4255 35.3780i 1.47409 2.55319i
\(193\) 0.106992 0.185315i 0.00770145 0.0133393i −0.862149 0.506655i \(-0.830882\pi\)
0.869850 + 0.493316i \(0.164215\pi\)
\(194\) 8.75816 + 15.1696i 0.628799 + 1.08911i
\(195\) 0 0
\(196\) 15.7730 16.1053i 1.12664 1.15038i
\(197\) 11.2290 0.800035 0.400017 0.916508i \(-0.369004\pi\)
0.400017 + 0.916508i \(0.369004\pi\)
\(198\) −2.44038 4.22685i −0.173430 0.300389i
\(199\) −10.2100 + 17.6843i −0.723771 + 1.25361i 0.235707 + 0.971824i \(0.424259\pi\)
−0.959478 + 0.281784i \(0.909074\pi\)
\(200\) 0.675351 1.16974i 0.0477545 0.0827132i
\(201\) −19.8712 34.4179i −1.40161 2.42765i
\(202\) 20.8313 1.46568
\(203\) 0.666820 5.27738i 0.0468016 0.370399i
\(204\) −18.0056 −1.26065
\(205\) 7.15042 + 12.3849i 0.499407 + 0.864999i
\(206\) −6.90207 + 11.9547i −0.480890 + 0.832926i
\(207\) −3.98343 + 6.89950i −0.276867 + 0.479548i
\(208\) 0 0
\(209\) 0.549471 0.0380077
\(210\) −37.3075 + 15.6816i −2.57446 + 1.08213i
\(211\) 8.41738 0.579476 0.289738 0.957106i \(-0.406432\pi\)
0.289738 + 0.957106i \(0.406432\pi\)
\(212\) −11.9810 20.7517i −0.822857 1.42523i
\(213\) 2.12764 3.68518i 0.145783 0.252504i
\(214\) −13.8072 + 23.9148i −0.943844 + 1.63479i
\(215\) −1.62148 2.80849i −0.110584 0.191537i
\(216\) 34.4801 2.34607
\(217\) −9.70417 7.36624i −0.658762 0.500053i
\(218\) 3.11164 0.210747
\(219\) −18.7154 32.4159i −1.26467 2.19047i
\(220\) −1.05545 + 1.82810i −0.0711587 + 0.123250i
\(221\) 0 0
\(222\) 19.9439 + 34.5439i 1.33855 + 2.31843i
\(223\) 13.6091 0.911333 0.455666 0.890151i \(-0.349401\pi\)
0.455666 + 0.890151i \(0.349401\pi\)
\(224\) −12.0889 9.17646i −0.807725 0.613128i
\(225\) −3.35464 −0.223643
\(226\) 10.7616 + 18.6396i 0.715849 + 1.23989i
\(227\) 1.80138 3.12008i 0.119562 0.207087i −0.800032 0.599957i \(-0.795184\pi\)
0.919594 + 0.392870i \(0.128518\pi\)
\(228\) −9.03614 + 15.6511i −0.598433 + 1.03652i
\(229\) 9.19208 + 15.9212i 0.607430 + 1.05210i 0.991662 + 0.128863i \(0.0411328\pi\)
−0.384232 + 0.923236i \(0.625534\pi\)
\(230\) 5.58554 0.368299
\(231\) −2.37025 + 0.996294i −0.155951 + 0.0655514i
\(232\) 5.60598 0.368051
\(233\) −10.1348 17.5541i −0.663955 1.15000i −0.979567 0.201116i \(-0.935543\pi\)
0.315612 0.948888i \(-0.397790\pi\)
\(234\) 0 0
\(235\) −10.1130 + 17.5162i −0.659699 + 1.14263i
\(236\) 13.0764 + 22.6490i 0.851202 + 1.47432i
\(237\) −24.9676 −1.62182
\(238\) −1.34488 + 10.6437i −0.0871758 + 0.689931i
\(239\) −20.8097 −1.34607 −0.673033 0.739612i \(-0.735009\pi\)
−0.673033 + 0.739612i \(0.735009\pi\)
\(240\) 0.234144 + 0.405549i 0.0151139 + 0.0261781i
\(241\) −6.35736 + 11.0113i −0.409514 + 0.709299i −0.994835 0.101503i \(-0.967635\pi\)
0.585322 + 0.810801i \(0.300968\pi\)
\(242\) 12.4578 21.5775i 0.800816 1.38705i
\(243\) −10.0922 17.4801i −0.647412 1.12135i
\(244\) −11.0805 −0.709355
\(245\) 3.99946 + 14.3272i 0.255516 + 0.915330i
\(246\) −48.4422 −3.08856
\(247\) 0 0
\(248\) 6.41990 11.1196i 0.407664 0.706094i
\(249\) 17.6881 30.6367i 1.12094 1.94152i
\(250\) 13.3140 + 23.0605i 0.842050 + 1.45847i
\(251\) 13.7436 0.867486 0.433743 0.901037i \(-0.357193\pi\)
0.433743 + 0.901037i \(0.357193\pi\)
\(252\) 7.39666 58.5390i 0.465946 3.68761i
\(253\) 0.354865 0.0223102
\(254\) 15.3080 + 26.5142i 0.960510 + 1.66365i
\(255\) 5.94059 10.2894i 0.372014 0.644347i
\(256\) 7.77229 13.4620i 0.485768 0.841375i
\(257\) 3.66736 + 6.35206i 0.228764 + 0.396231i 0.957442 0.288626i \(-0.0931983\pi\)
−0.728678 + 0.684856i \(0.759865\pi\)
\(258\) 10.9851 0.683904
\(259\) 13.5158 5.68112i 0.839830 0.353008i
\(260\) 0 0
\(261\) −6.96159 12.0578i −0.430912 0.746361i
\(262\) −15.3049 + 26.5089i −0.945540 + 1.63772i
\(263\) 3.33942 5.78405i 0.205918 0.356660i −0.744507 0.667615i \(-0.767315\pi\)
0.950425 + 0.310955i \(0.100649\pi\)
\(264\) −1.35484 2.34665i −0.0833846 0.144426i
\(265\) 15.8115 0.971293
\(266\) 8.57693 + 6.51058i 0.525886 + 0.399189i
\(267\) −5.22708 −0.319892
\(268\) −20.3124 35.1821i −1.24078 2.14909i
\(269\) −8.11263 + 14.0515i −0.494636 + 0.856735i −0.999981 0.00618287i \(-0.998032\pi\)
0.505345 + 0.862917i \(0.331365\pi\)
\(270\) −30.0195 + 51.9953i −1.82693 + 3.16433i
\(271\) −9.36904 16.2277i −0.569129 0.985760i −0.996652 0.0817555i \(-0.973947\pi\)
0.427524 0.904004i \(-0.359386\pi\)
\(272\) 0.124143 0.00752725
\(273\) 0 0
\(274\) 1.14479 0.0691595
\(275\) 0.0747124 + 0.129406i 0.00450533 + 0.00780346i
\(276\) −5.83582 + 10.1079i −0.351275 + 0.608426i
\(277\) −15.0163 + 26.0090i −0.902243 + 1.56273i −0.0776679 + 0.996979i \(0.524747\pi\)
−0.824575 + 0.565752i \(0.808586\pi\)
\(278\) −1.62148 2.80849i −0.0972501 0.168442i
\(279\) −31.8893 −1.90916
\(280\) −14.4517 + 6.07453i −0.863656 + 0.363023i
\(281\) −2.23065 −0.133070 −0.0665348 0.997784i \(-0.521194\pi\)
−0.0665348 + 0.997784i \(0.521194\pi\)
\(282\) −34.2565 59.3339i −2.03994 3.53328i
\(283\) −6.88774 + 11.9299i −0.409433 + 0.709159i −0.994826 0.101590i \(-0.967607\pi\)
0.585393 + 0.810750i \(0.300940\pi\)
\(284\) 2.17488 3.76700i 0.129055 0.223531i
\(285\) −5.96258 10.3275i −0.353193 0.611748i
\(286\) 0 0
\(287\) −2.23205 + 17.6650i −0.131754 + 1.04273i
\(288\) −39.7259 −2.34087
\(289\) 6.92516 + 11.9947i 0.407362 + 0.705572i
\(290\) −4.88075 + 8.45371i −0.286608 + 0.496419i
\(291\) 12.0762 20.9166i 0.707920 1.22615i
\(292\) −19.1309 33.1357i −1.11955 1.93912i
\(293\) 1.01231 0.0591400 0.0295700 0.999563i \(-0.490586\pi\)
0.0295700 + 0.999563i \(0.490586\pi\)
\(294\) −48.8033 12.5331i −2.84626 0.730946i
\(295\) −17.2572 −1.00475
\(296\) 7.72563 + 13.3812i 0.449043 + 0.777766i
\(297\) −1.90723 + 3.30341i −0.110668 + 0.191683i
\(298\) 24.0943 41.7326i 1.39575 2.41751i
\(299\) 0 0
\(300\) −4.91464 −0.283747
\(301\) 0.506157 4.00585i 0.0291744 0.230893i
\(302\) −39.9939 −2.30139
\(303\) −14.3616 24.8751i −0.825054 1.42904i
\(304\) 0.0623010 0.107909i 0.00357321 0.00618898i
\(305\) 3.65577 6.33199i 0.209329 0.362568i
\(306\) 14.0405 + 24.3189i 0.802645 + 1.39022i
\(307\) −24.0527 −1.37276 −0.686379 0.727244i \(-0.740801\pi\)
−0.686379 + 0.727244i \(0.740801\pi\)
\(308\) −2.42288 + 1.01842i −0.138057 + 0.0580296i
\(309\) 19.0339 1.08280
\(310\) 11.1787 + 19.3622i 0.634910 + 1.09970i
\(311\) 4.49548 7.78639i 0.254915 0.441526i −0.709957 0.704245i \(-0.751286\pi\)
0.964872 + 0.262719i \(0.0846192\pi\)
\(312\) 0 0
\(313\) 7.61806 + 13.1949i 0.430598 + 0.745818i 0.996925 0.0783626i \(-0.0249692\pi\)
−0.566326 + 0.824181i \(0.691636\pi\)
\(314\) 0.172684 0.00974510
\(315\) 31.0120 + 23.5406i 1.74733 + 1.32636i
\(316\) −25.5220 −1.43572
\(317\) 3.41775 + 5.91972i 0.191960 + 0.332484i 0.945900 0.324459i \(-0.105182\pi\)
−0.753940 + 0.656944i \(0.771849\pi\)
\(318\) −26.7797 + 46.3838i −1.50173 + 2.60107i
\(319\) −0.310088 + 0.537088i −0.0173616 + 0.0300712i
\(320\) 13.7772 + 23.8628i 0.770170 + 1.33397i
\(321\) 38.0763 2.12521
\(322\) 5.53925 + 4.20473i 0.308690 + 0.234321i
\(323\) −3.16135 −0.175902
\(324\) −29.2769 50.7091i −1.62650 2.81717i
\(325\) 0 0
\(326\) 11.5174 19.9487i 0.637890 1.10486i
\(327\) −2.14525 3.71568i −0.118633 0.205478i
\(328\) −18.7649 −1.03612
\(329\) −23.2152 + 9.75811i −1.27990 + 0.537982i
\(330\) 4.71827 0.259732
\(331\) 6.90727 + 11.9637i 0.379658 + 0.657587i 0.991012 0.133770i \(-0.0427084\pi\)
−0.611354 + 0.791357i \(0.709375\pi\)
\(332\) 18.0808 31.3169i 0.992314 1.71874i
\(333\) 19.1876 33.2339i 1.05147 1.82121i
\(334\) 6.68295 + 11.5752i 0.365675 + 0.633367i
\(335\) 26.8066 1.46460
\(336\) −0.0730896 + 0.578449i −0.00398736 + 0.0315570i
\(337\) 27.0432 1.47314 0.736568 0.676364i \(-0.236445\pi\)
0.736568 + 0.676364i \(0.236445\pi\)
\(338\) 0 0
\(339\) 14.8386 25.7013i 0.805924 1.39590i
\(340\) 6.07249 10.5179i 0.329327 0.570411i
\(341\) 0.710218 + 1.23013i 0.0384604 + 0.0666154i
\(342\) 28.1850 1.52407
\(343\) −6.81903 + 17.2192i −0.368193 + 0.929749i
\(344\) 4.25528 0.229429
\(345\) −3.85082 6.66981i −0.207321 0.359091i
\(346\) −19.4097 + 33.6186i −1.04347 + 1.80735i
\(347\) 9.65568 16.7241i 0.518344 0.897799i −0.481429 0.876485i \(-0.659882\pi\)
0.999773 0.0213132i \(-0.00678472\pi\)
\(348\) −10.1989 17.6650i −0.546719 0.946944i
\(349\) 14.1573 0.757821 0.378911 0.925433i \(-0.376299\pi\)
0.378911 + 0.925433i \(0.376299\pi\)
\(350\) −0.367085 + 2.90521i −0.0196215 + 0.155290i
\(351\) 0 0
\(352\) 0.884750 + 1.53243i 0.0471573 + 0.0816789i
\(353\) −8.48235 + 14.6919i −0.451470 + 0.781969i −0.998478 0.0551585i \(-0.982434\pi\)
0.547008 + 0.837128i \(0.315767\pi\)
\(354\) 29.2282 50.6247i 1.55346 2.69067i
\(355\) 1.43511 + 2.48569i 0.0761680 + 0.131927i
\(356\) −5.34313 −0.283186
\(357\) 13.6371 5.73212i 0.721752 0.303376i
\(358\) −34.9613 −1.84776
\(359\) 11.3816 + 19.7136i 0.600700 + 1.04044i 0.992715 + 0.120484i \(0.0384446\pi\)
−0.392016 + 0.919959i \(0.628222\pi\)
\(360\) −20.5163 + 35.5353i −1.08131 + 1.87288i
\(361\) 7.91348 13.7065i 0.416499 0.721397i
\(362\) −6.68260 11.5746i −0.351229 0.608347i
\(363\) −34.3549 −1.80316
\(364\) 0 0
\(365\) 25.2474 1.32151
\(366\) 12.3835 + 21.4488i 0.647293 + 1.12114i
\(367\) −8.29168 + 14.3616i −0.432822 + 0.749670i −0.997115 0.0759048i \(-0.975815\pi\)
0.564293 + 0.825575i \(0.309149\pi\)
\(368\) 0.0402359 0.0696907i 0.00209744 0.00363288i
\(369\) 23.3026 + 40.3613i 1.21308 + 2.10112i
\(370\) −26.9048 −1.39871
\(371\) 15.6805 + 11.9027i 0.814090 + 0.617959i
\(372\) −46.7186 −2.42225
\(373\) −13.8230 23.9422i −0.715730 1.23968i −0.962677 0.270652i \(-0.912761\pi\)
0.246947 0.969029i \(-0.420573\pi\)
\(374\) 0.625404 1.08323i 0.0323389 0.0560126i
\(375\) 18.3580 31.7970i 0.948004 1.64199i
\(376\) −13.2698 22.9840i −0.684340 1.18531i
\(377\) 0 0
\(378\) −68.9122 + 28.9660i −3.54446 + 1.48985i
\(379\) −9.24228 −0.474744 −0.237372 0.971419i \(-0.576286\pi\)
−0.237372 + 0.971419i \(0.576286\pi\)
\(380\) −6.09497 10.5568i −0.312665 0.541552i
\(381\) 21.1075 36.5592i 1.08137 1.87299i
\(382\) 30.6369 53.0648i 1.56752 2.71503i
\(383\) −3.82413 6.62358i −0.195404 0.338449i 0.751629 0.659586i \(-0.229268\pi\)
−0.947033 + 0.321137i \(0.895935\pi\)
\(384\) −57.1925 −2.91859
\(385\) 0.217402 1.72057i 0.0110798 0.0876885i
\(386\) −0.488913 −0.0248850
\(387\) −5.28427 9.15262i −0.268614 0.465254i
\(388\) 12.3443 21.3810i 0.626689 1.08546i
\(389\) −3.26868 + 5.66153i −0.165729 + 0.287051i −0.936914 0.349560i \(-0.886331\pi\)
0.771185 + 0.636611i \(0.219664\pi\)
\(390\) 0 0
\(391\) −2.04169 −0.103253
\(392\) −18.9048 4.85492i −0.954837 0.245211i
\(393\) 42.2064 2.12903
\(394\) −12.8281 22.2189i −0.646271 1.11937i
\(395\) 8.42044 14.5846i 0.423678 0.733833i
\(396\) −3.43963 + 5.95762i −0.172848 + 0.299381i
\(397\) −14.4654 25.0548i −0.725996 1.25746i −0.958563 0.284882i \(-0.908046\pi\)
0.232566 0.972581i \(-0.425288\pi\)
\(398\) 46.6561 2.33866
\(399\) 1.86126 14.7305i 0.0931795 0.737446i
\(400\) 0.0338847 0.00169423
\(401\) −13.3716 23.1603i −0.667747 1.15657i −0.978533 0.206092i \(-0.933925\pi\)
0.310786 0.950480i \(-0.399408\pi\)
\(402\) −45.4020 + 78.6385i −2.26444 + 3.92213i
\(403\) 0 0
\(404\) −14.6805 25.4274i −0.730382 1.26506i
\(405\) 38.6373 1.91990
\(406\) −11.2042 + 4.70947i −0.556053 + 0.233727i
\(407\) −1.70934 −0.0847287
\(408\) 7.79498 + 13.5013i 0.385909 + 0.668414i
\(409\) 17.3862 30.1138i 0.859694 1.48903i −0.0125273 0.999922i \(-0.503988\pi\)
0.872221 0.489112i \(-0.162679\pi\)
\(410\) 16.3374 28.2972i 0.806846 1.39750i
\(411\) −0.789250 1.36702i −0.0389309 0.0674302i
\(412\) 19.4565 0.958553
\(413\) −17.1142 12.9910i −0.842133 0.639246i
\(414\) 18.2028 0.894617
\(415\) 11.9308 + 20.6647i 0.585659 + 1.01439i
\(416\) 0 0
\(417\) −2.23579 + 3.87250i −0.109487 + 0.189637i
\(418\) −0.627719 1.08724i −0.0307027 0.0531787i
\(419\) −4.19246 −0.204815 −0.102407 0.994743i \(-0.532655\pi\)
−0.102407 + 0.994743i \(0.532655\pi\)
\(420\) 45.4333 + 34.4876i 2.21692 + 1.68282i
\(421\) −20.9526 −1.02117 −0.510584 0.859828i \(-0.670571\pi\)
−0.510584 + 0.859828i \(0.670571\pi\)
\(422\) −9.61607 16.6555i −0.468103 0.810778i
\(423\) −32.9574 + 57.0838i −1.60244 + 2.77551i
\(424\) −10.3736 + 17.9676i −0.503786 + 0.872583i
\(425\) −0.429853 0.744528i −0.0208509 0.0361149i
\(426\) −9.72252 −0.471058
\(427\) 8.39213 3.52748i 0.406124 0.170707i
\(428\) 38.9217 1.88135
\(429\) 0 0
\(430\) −3.70479 + 6.41688i −0.178661 + 0.309449i
\(431\) −8.44713 + 14.6309i −0.406884 + 0.704744i −0.994539 0.104368i \(-0.966718\pi\)
0.587655 + 0.809112i \(0.300051\pi\)
\(432\) 0.432497 + 0.749106i 0.0208085 + 0.0360414i
\(433\) −3.42241 −0.164471 −0.0822353 0.996613i \(-0.526206\pi\)
−0.0822353 + 0.996613i \(0.526206\pi\)
\(434\) −3.48952 + 27.6169i −0.167502 + 1.32566i
\(435\) 13.4597 0.645342
\(436\) −2.19288 3.79818i −0.105020 0.181900i
\(437\) −1.02463 + 1.77470i −0.0490145 + 0.0848956i
\(438\) −42.7611 + 74.0644i −2.04320 + 3.53893i
\(439\) −9.03253 15.6448i −0.431099 0.746685i 0.565869 0.824495i \(-0.308541\pi\)
−0.996968 + 0.0778096i \(0.975207\pi\)
\(440\) 1.82771 0.0871324
\(441\) 13.0339 + 46.6910i 0.620661 + 2.22338i
\(442\) 0 0
\(443\) −3.22173 5.58020i −0.153069 0.265123i 0.779285 0.626669i \(-0.215582\pi\)
−0.932354 + 0.361546i \(0.882249\pi\)
\(444\) 28.1103 48.6885i 1.33406 2.31065i
\(445\) 1.76286 3.05336i 0.0835674 0.144743i
\(446\) −15.5471 26.9284i −0.736178 1.27510i
\(447\) −66.4451 −3.14275
\(448\) −4.30065 + 34.0364i −0.203187 + 1.60807i
\(449\) 1.75306 0.0827322 0.0413661 0.999144i \(-0.486829\pi\)
0.0413661 + 0.999144i \(0.486829\pi\)
\(450\) 3.83237 + 6.63785i 0.180659 + 0.312911i
\(451\) 1.03796 1.79780i 0.0488757 0.0846551i
\(452\) 15.1681 26.2719i 0.713447 1.23573i
\(453\) 27.5728 + 47.7575i 1.29548 + 2.24385i
\(454\) −8.23163 −0.386330
\(455\) 0 0
\(456\) 15.6477 0.732770
\(457\) −16.3550 28.3277i −0.765054 1.32511i −0.940218 0.340573i \(-0.889379\pi\)
0.175164 0.984539i \(-0.443954\pi\)
\(458\) 21.0022 36.3769i 0.981368 1.69978i
\(459\) 10.9731 19.0060i 0.512180 0.887123i
\(460\) −3.93632 6.81790i −0.183532 0.317886i
\(461\) 7.66641 0.357060 0.178530 0.983934i \(-0.442866\pi\)
0.178530 + 0.983934i \(0.442866\pi\)
\(462\) 4.67917 + 3.55186i 0.217695 + 0.165248i
\(463\) −14.4720 −0.672570 −0.336285 0.941760i \(-0.609171\pi\)
−0.336285 + 0.941760i \(0.609171\pi\)
\(464\) 0.0703179 + 0.121794i 0.00326443 + 0.00565415i
\(465\) 15.4138 26.6976i 0.714800 1.23807i
\(466\) −23.1562 + 40.1077i −1.07269 + 1.85795i
\(467\) 1.68801 + 2.92373i 0.0781120 + 0.135294i 0.902435 0.430825i \(-0.141777\pi\)
−0.824323 + 0.566119i \(0.808444\pi\)
\(468\) 0 0
\(469\) 26.5845 + 20.1798i 1.22756 + 0.931815i
\(470\) 46.2126 2.13163
\(471\) −0.119053 0.206205i −0.00548566 0.00950144i
\(472\) 11.3221 19.6104i 0.521140 0.902641i
\(473\) −0.235376 + 0.407683i −0.0108226 + 0.0187453i
\(474\) 28.5231 + 49.4035i 1.31011 + 2.26918i
\(475\) −0.862889 −0.0395921
\(476\) 13.9399 5.85939i 0.638934 0.268565i
\(477\) 51.5283 2.35932
\(478\) 23.7731 + 41.1763i 1.08736 + 1.88336i
\(479\) −0.0726124 + 0.125768i −0.00331775 + 0.00574651i −0.867680 0.497124i \(-0.834389\pi\)
0.864362 + 0.502871i \(0.167723\pi\)
\(480\) 19.2017 33.2584i 0.876435 1.51803i
\(481\) 0 0
\(482\) 29.0508 1.32323
\(483\) 1.20206 9.51339i 0.0546956 0.432874i
\(484\) −35.1177 −1.59626
\(485\) 8.14553 + 14.1085i 0.369869 + 0.640633i
\(486\) −23.0587 + 39.9388i −1.04596 + 1.81166i
\(487\) 8.21073 14.2214i 0.372064 0.644433i −0.617819 0.786320i \(-0.711984\pi\)
0.989883 + 0.141887i \(0.0453169\pi\)
\(488\) 4.79695 + 8.30856i 0.217148 + 0.376111i
\(489\) −31.7616 −1.43631
\(490\) 23.7803 24.2812i 1.07428 1.09691i
\(491\) 18.2077 0.821701 0.410850 0.911703i \(-0.365232\pi\)
0.410850 + 0.911703i \(0.365232\pi\)
\(492\) 34.1389 + 59.1303i 1.53910 + 2.66580i
\(493\) 1.78407 3.09010i 0.0803506 0.139171i
\(494\) 0 0
\(495\) −2.26967 3.93119i −0.102014 0.176694i
\(496\) 0.322108 0.0144631
\(497\) −0.447981 + 3.54543i −0.0200947 + 0.159034i
\(498\) −80.8279 −3.62199
\(499\) −18.7860 32.5383i −0.840976 1.45661i −0.889070 0.457770i \(-0.848648\pi\)
0.0480945 0.998843i \(-0.484685\pi\)
\(500\) 18.7656 32.5030i 0.839225 1.45358i
\(501\) 9.21481 15.9605i 0.411687 0.713063i
\(502\) −15.7007 27.1945i −0.700758 1.21375i
\(503\) −4.20535 −0.187507 −0.0937537 0.995595i \(-0.529887\pi\)
−0.0937537 + 0.995595i \(0.529887\pi\)
\(504\) −47.0969 + 19.7964i −2.09786 + 0.881800i
\(505\) 19.3741 0.862137
\(506\) −0.405400 0.702174i −0.0180222 0.0312154i
\(507\) 0 0
\(508\) 21.5761 37.3710i 0.957287 1.65807i
\(509\) 4.21873 + 7.30705i 0.186992 + 0.323879i 0.944246 0.329241i \(-0.106793\pi\)
−0.757254 + 0.653120i \(0.773460\pi\)
\(510\) −27.1463 −1.20206
\(511\) 25.0382 + 19.0060i 1.10762 + 0.840775i
\(512\) 0.791350 0.0349731
\(513\) −11.0137 19.0763i −0.486268 0.842240i
\(514\) 8.37924 14.5133i 0.369593 0.640153i
\(515\) −6.41927 + 11.1185i −0.282867 + 0.489940i
\(516\) −7.74159 13.4088i −0.340804 0.590290i
\(517\) 2.93602 0.129126
\(518\) −26.6818 20.2536i −1.17233 0.889893i
\(519\) 53.5263 2.34955
\(520\) 0 0
\(521\) −12.9140 + 22.3677i −0.565773 + 0.979948i 0.431204 + 0.902254i \(0.358089\pi\)
−0.996977 + 0.0776936i \(0.975244\pi\)
\(522\) −15.9059 + 27.5499i −0.696184 + 1.20583i
\(523\) 0.378202 + 0.655065i 0.0165376 + 0.0286440i 0.874176 0.485610i \(-0.161402\pi\)
−0.857638 + 0.514254i \(0.828069\pi\)
\(524\) 43.1436 1.88473
\(525\) 3.72225 1.56458i 0.162452 0.0682839i
\(526\) −15.2599 −0.665364
\(527\) −4.08619 7.07749i −0.177997 0.308300i
\(528\) 0.0339885 0.0588698i 0.00147916 0.00256198i
\(529\) 10.8383 18.7724i 0.471229 0.816192i
\(530\) −18.0632 31.2863i −0.784614 1.35899i
\(531\) −56.2396 −2.44059
\(532\) 1.90259 15.0575i 0.0824876 0.652827i
\(533\) 0 0
\(534\) 5.97145 + 10.3428i 0.258410 + 0.447579i
\(535\) −12.8414 + 22.2420i −0.555183 + 0.961606i
\(536\) −17.5873 + 30.4620i −0.759654 + 1.31576i
\(537\) 24.1032 + 41.7480i 1.04013 + 1.80156i
\(538\) 37.0717 1.59827
\(539\) 1.51083 1.54266i 0.0650760 0.0664469i
\(540\) 84.6231 3.64160
\(541\) −11.2063 19.4099i −0.481797 0.834496i 0.517985 0.855390i \(-0.326682\pi\)
−0.999782 + 0.0208936i \(0.993349\pi\)
\(542\) −21.4065 + 37.0772i −0.919488 + 1.59260i
\(543\) −9.21432 + 15.9597i −0.395424 + 0.684895i
\(544\) −5.09035 8.81675i −0.218247 0.378015i
\(545\) 2.89398 0.123965
\(546\) 0 0
\(547\) −11.8059 −0.504784 −0.252392 0.967625i \(-0.581217\pi\)
−0.252392 + 0.967625i \(0.581217\pi\)
\(548\) −0.806774 1.39737i −0.0344637 0.0596929i
\(549\) 11.9138 20.6354i 0.508470 0.880697i
\(550\) 0.170704 0.295668i 0.00727884 0.0126073i
\(551\) −1.79068 3.10154i −0.0762854 0.132130i
\(552\) 10.1058 0.430129
\(553\) 19.3298 8.12495i 0.821988 0.345508i
\(554\) 68.6190 2.91534
\(555\) 18.5489 + 32.1276i 0.787355 + 1.36374i
\(556\) −2.28543 + 3.95848i −0.0969238 + 0.167877i
\(557\) −4.38366 + 7.59273i −0.185742 + 0.321714i −0.943826 0.330442i \(-0.892802\pi\)
0.758084 + 0.652156i \(0.226135\pi\)
\(558\) 36.4305 + 63.0995i 1.54223 + 2.67122i
\(559\) 0 0
\(560\) −0.313247 0.237780i −0.0132371 0.0100480i
\(561\) −1.72468 −0.0728161
\(562\) 2.54831 + 4.41380i 0.107494 + 0.186185i
\(563\) −18.3879 + 31.8488i −0.774958 + 1.34227i 0.159860 + 0.987140i \(0.448896\pi\)
−0.934818 + 0.355127i \(0.884438\pi\)
\(564\) −48.2834 + 83.6293i −2.03310 + 3.52143i
\(565\) 10.0088 + 17.3358i 0.421074 + 0.729321i
\(566\) 31.4744 1.32297
\(567\) 38.3171 + 29.0857i 1.60917 + 1.22149i
\(568\) −3.76619 −0.158026
\(569\) 17.8918 + 30.9896i 0.750065 + 1.29915i 0.947791 + 0.318893i \(0.103311\pi\)
−0.197726 + 0.980257i \(0.563356\pi\)
\(570\) −13.6234 + 23.5964i −0.570621 + 0.988344i
\(571\) −7.46920 + 12.9370i −0.312576 + 0.541398i −0.978919 0.204248i \(-0.934525\pi\)
0.666343 + 0.745645i \(0.267859\pi\)
\(572\) 0 0
\(573\) −84.4877 −3.52952
\(574\) 37.5038 15.7641i 1.56538 0.657979i
\(575\) −0.557280 −0.0232402
\(576\) 44.8987 + 77.7669i 1.87078 + 3.24029i
\(577\) −8.42309 + 14.5892i −0.350658 + 0.607357i −0.986365 0.164573i \(-0.947375\pi\)
0.635707 + 0.771930i \(0.280709\pi\)
\(578\) 15.8227 27.4057i 0.658137 1.13993i
\(579\) 0.337070 + 0.583822i 0.0140081 + 0.0242628i
\(580\) 13.7585 0.571292
\(581\) −3.72428 + 29.4748i −0.154509 + 1.22282i
\(582\) −55.1838 −2.28744
\(583\) −1.14761 1.98771i −0.0475290 0.0823226i
\(584\) −16.5643 + 28.6901i −0.685434 + 1.18721i
\(585\) 0 0
\(586\) −1.15647 2.00307i −0.0477735 0.0827461i
\(587\) −36.8833 −1.52234 −0.761168 0.648555i \(-0.775374\pi\)
−0.761168 + 0.648555i \(0.775374\pi\)
\(588\) 19.0950 + 68.4035i 0.787463 + 2.82091i
\(589\) −8.20264 −0.337984
\(590\) 19.7147 + 34.1469i 0.811642 + 1.40580i
\(591\) −17.6881 + 30.6367i −0.727590 + 1.26022i
\(592\) −0.193811 + 0.335690i −0.00796558 + 0.0137968i
\(593\) 8.07676 + 13.9894i 0.331673 + 0.574474i 0.982840 0.184460i \(-0.0590537\pi\)
−0.651167 + 0.758934i \(0.725720\pi\)
\(594\) 8.71531 0.357593
\(595\) −1.25081 + 9.89920i −0.0512781 + 0.405828i
\(596\) −67.9204 −2.78213
\(597\) −32.1660 55.7131i −1.31646 2.28018i
\(598\) 0 0
\(599\) 1.24238 2.15186i 0.0507622 0.0879227i −0.839528 0.543317i \(-0.817168\pi\)
0.890290 + 0.455394i \(0.150502\pi\)
\(600\) 2.12764 + 3.68518i 0.0868605 + 0.150447i
\(601\) 9.55999 0.389960 0.194980 0.980807i \(-0.437536\pi\)
0.194980 + 0.980807i \(0.437536\pi\)
\(602\) −8.50464 + 3.57478i −0.346623 + 0.145697i
\(603\) 87.3605 3.55759
\(604\) 28.1850 + 48.8179i 1.14683 + 1.98637i
\(605\) 11.5864 20.0682i 0.471052 0.815886i
\(606\) −32.8136 + 56.8349i −1.33296 + 2.30876i
\(607\) 9.74294 + 16.8753i 0.395454 + 0.684946i 0.993159 0.116770i \(-0.0372540\pi\)
−0.597705 + 0.801716i \(0.703921\pi\)
\(608\) −10.2184 −0.414411
\(609\) 13.3481 + 10.1323i 0.540894 + 0.410582i
\(610\) −16.7055 −0.676387
\(611\) 0 0
\(612\) 19.7897 34.2768i 0.799951 1.38556i
\(613\) −7.38409 + 12.7896i −0.298241 + 0.516568i −0.975733 0.218962i \(-0.929733\pi\)
0.677493 + 0.735529i \(0.263066\pi\)
\(614\) 27.4779 + 47.5931i 1.10892 + 1.92070i
\(615\) −45.0537 −1.81674
\(616\) 1.81256 + 1.37588i 0.0730301 + 0.0554357i
\(617\) −30.9478 −1.24591 −0.622955 0.782257i \(-0.714068\pi\)
−0.622955 + 0.782257i \(0.714068\pi\)
\(618\) −21.7444 37.6625i −0.874689 1.51501i
\(619\) 6.54123 11.3297i 0.262914 0.455380i −0.704101 0.710100i \(-0.748650\pi\)
0.967015 + 0.254719i \(0.0819831\pi\)
\(620\) 15.7561 27.2903i 0.632780 1.09601i
\(621\) −7.11300 12.3201i −0.285435 0.494388i
\(622\) −20.5426 −0.823685
\(623\) 4.04678 1.70099i 0.162131 0.0681489i
\(624\) 0 0
\(625\) 11.1716 + 19.3498i 0.446865 + 0.773994i
\(626\) 17.4059 30.1478i 0.695678 1.20495i
\(627\) −0.865532 + 1.49915i −0.0345660 + 0.0598701i
\(628\) −0.121696 0.210784i −0.00485620 0.00841119i
\(629\) 9.83456 0.392130
\(630\) 11.1516 88.2566i 0.444291 3.51623i
\(631\) −35.3591 −1.40762 −0.703812 0.710387i \(-0.748520\pi\)
−0.703812 + 0.710387i \(0.748520\pi\)
\(632\) 11.0489 + 19.1373i 0.439503 + 0.761242i
\(633\) −13.2591 + 22.9655i −0.527004 + 0.912797i
\(634\) 7.80892 13.5254i 0.310132 0.537164i
\(635\) 14.2372 + 24.6596i 0.564986 + 0.978585i
\(636\) 75.4903 2.99338
\(637\) 0 0
\(638\) 1.41699 0.0560990
\(639\) 4.67691 + 8.10065i 0.185016 + 0.320457i
\(640\) 19.2884 33.4086i 0.762443 1.32059i
\(641\) 10.6188 18.3923i 0.419417 0.726452i −0.576464 0.817123i \(-0.695568\pi\)
0.995881 + 0.0906706i \(0.0289010\pi\)
\(642\) −43.4986 75.3418i −1.71675 2.97351i
\(643\) 25.4808 1.00486 0.502432 0.864617i \(-0.332439\pi\)
0.502432 + 0.864617i \(0.332439\pi\)
\(644\) 1.22875 9.72462i 0.0484195 0.383204i
\(645\) 10.2167 0.402283
\(646\) 3.61154 + 6.25537i 0.142094 + 0.246114i
\(647\) −11.3928 + 19.7329i −0.447897 + 0.775781i −0.998249 0.0591522i \(-0.981160\pi\)
0.550352 + 0.834933i \(0.314494\pi\)
\(648\) −25.3491 + 43.9059i −0.995806 + 1.72479i
\(649\) 1.25253 + 2.16945i 0.0491662 + 0.0851583i
\(650\) 0 0
\(651\) 35.3837 14.8729i 1.38680 0.582916i
\(652\) −32.4669 −1.27150
\(653\) −8.13928 14.0976i −0.318515 0.551684i 0.661664 0.749801i \(-0.269851\pi\)
−0.980178 + 0.198117i \(0.936517\pi\)
\(654\) −4.90150 + 8.48964i −0.191664 + 0.331971i
\(655\) −14.2343 + 24.6546i −0.556181 + 0.963334i
\(656\) −0.235376 0.407683i −0.00918988 0.0159173i
\(657\) 82.2790 3.21001
\(658\) 45.8297 + 34.7884i 1.78663 + 1.35619i
\(659\) 20.5596 0.800888 0.400444 0.916321i \(-0.368856\pi\)
0.400444 + 0.916321i \(0.368856\pi\)
\(660\) −3.32513 5.75929i −0.129430 0.224180i
\(661\) 13.8863 24.0518i 0.540115 0.935507i −0.458782 0.888549i \(-0.651714\pi\)
0.998897 0.0469576i \(-0.0149526\pi\)
\(662\) 15.7818 27.3349i 0.613378 1.06240i
\(663\) 0 0
\(664\) −31.3101 −1.21507
\(665\) 7.97698 + 6.05517i 0.309334 + 0.234809i
\(666\) −87.6802 −3.39754
\(667\) −1.15647 2.00307i −0.0447789 0.0775593i
\(668\) 9.41941 16.3149i 0.364448 0.631242i
\(669\) −21.4372 + 37.1303i −0.828810 + 1.43554i
\(670\) −30.6241 53.0425i −1.18311 2.04921i
\(671\) −1.06135 −0.0409730
\(672\) 44.0791 18.5279i 1.70039 0.714729i
\(673\) −5.20337 −0.200575 −0.100288 0.994958i \(-0.531976\pi\)
−0.100288 + 0.994958i \(0.531976\pi\)
\(674\) −30.8943 53.5105i −1.19000 2.06115i
\(675\) 2.99511 5.18768i 0.115282 0.199674i
\(676\) 0 0
\(677\) −22.4239 38.8394i −0.861821 1.49272i −0.870169 0.492753i \(-0.835991\pi\)
0.00834820 0.999965i \(-0.497343\pi\)
\(678\) −67.8070 −2.60411
\(679\) −2.54268 + 20.1234i −0.0975792 + 0.772266i
\(680\) −10.5156 −0.403254
\(681\) 5.67510 + 9.82957i 0.217470 + 0.376670i
\(682\) 1.62271 2.81062i 0.0621370 0.107624i
\(683\) −9.48691 + 16.4318i −0.363006 + 0.628745i −0.988454 0.151521i \(-0.951583\pi\)
0.625448 + 0.780266i \(0.284916\pi\)
\(684\) −19.8630 34.4037i −0.759479 1.31546i
\(685\) 1.06471 0.0406807
\(686\) 41.8618 6.17846i 1.59829 0.235895i
\(687\) −57.9179 −2.20970
\(688\) 0.0533755 + 0.0924491i 0.00203492 + 0.00352459i
\(689\) 0 0
\(690\) −8.79840 + 15.2393i −0.334949 + 0.580149i
\(691\) −18.7111 32.4085i −0.711803 1.23288i −0.964180 0.265250i \(-0.914545\pi\)
0.252376 0.967629i \(-0.418788\pi\)
\(692\) 54.7148 2.07994
\(693\) 0.708493 5.60719i 0.0269134 0.213000i
\(694\) −44.1229 −1.67488
\(695\) −1.50806 2.61204i −0.0572040 0.0990802i
\(696\) −8.83060 + 15.2951i −0.334723 + 0.579757i
\(697\) −5.97184 + 10.3435i −0.226200 + 0.391789i
\(698\) −16.1734 28.0131i −0.612171 1.06031i
\(699\) 63.8580 2.41533
\(700\) 3.80489 1.59932i 0.143811 0.0604486i
\(701\) −42.5513 −1.60714 −0.803570 0.595210i \(-0.797069\pi\)
−0.803570 + 0.595210i \(0.797069\pi\)
\(702\) 0 0
\(703\) 4.93548 8.54851i 0.186145 0.322413i
\(704\) 1.99991 3.46395i 0.0753745 0.130552i
\(705\) −31.8602 55.1835i −1.19993 2.07833i
\(706\) 38.7612 1.45880
\(707\) 19.2136 + 14.5846i 0.722600 + 0.548512i
\(708\) −82.3924 −3.09650
\(709\) 25.1661 + 43.5889i 0.945131 + 1.63702i 0.755488 + 0.655163i \(0.227400\pi\)
0.189644 + 0.981853i \(0.439267\pi\)
\(710\) 3.27897 5.67934i 0.123057 0.213142i
\(711\) 27.4415 47.5300i 1.02914 1.78252i
\(712\) 2.31315 + 4.00648i 0.0866888 + 0.150149i
\(713\) −5.29752 −0.198394
\(714\) −26.9213 20.4354i −1.00750 0.764776i
\(715\) 0 0
\(716\) 24.6384 + 42.6749i 0.920780 + 1.59484i
\(717\) 32.7796 56.7760i 1.22418 2.12034i
\(718\) 26.0049 45.0418i 0.970495 1.68095i
\(719\) −14.4616 25.0482i −0.539326 0.934141i −0.998940 0.0460219i \(-0.985346\pi\)
0.459614 0.888119i \(-0.347988\pi\)
\(720\) −1.02938 −0.0383625
\(721\) −14.7360 + 6.19400i −0.548796 + 0.230677i
\(722\) −36.1616 −1.34580
\(723\) −20.0284 34.6902i −0.744863 1.29014i
\(724\) −9.41891 + 16.3140i −0.350051 + 0.606306i
\(725\) 0.486962 0.843444i 0.0180853 0.0313247i
\(726\) 39.2472 + 67.9782i 1.45660 + 2.52291i
\(727\) −19.8593 −0.736539 −0.368269 0.929719i \(-0.620050\pi\)
−0.368269 + 0.929719i \(0.620050\pi\)
\(728\) 0 0
\(729\) 9.04209 0.334892
\(730\) −28.8428 49.9572i −1.06752 1.84900i
\(731\) 1.35422 2.34558i 0.0500876 0.0867543i
\(732\) 17.4541 30.2314i 0.645121 1.11738i
\(733\) −10.1751 17.6237i −0.375824 0.650947i 0.614626 0.788819i \(-0.289307\pi\)
−0.990450 + 0.137872i \(0.955974\pi\)
\(734\) 37.8899 1.39854
\(735\) −45.3895 11.6564i −1.67422 0.429954i
\(736\) −6.59935 −0.243255
\(737\) −1.94564 3.36994i −0.0716684 0.124133i
\(738\) 53.2421 92.2180i 1.95987 3.39459i
\(739\) −9.50055 + 16.4554i −0.349483 + 0.605323i −0.986158 0.165810i \(-0.946976\pi\)
0.636674 + 0.771133i \(0.280310\pi\)
\(740\) 18.9607 + 32.8409i 0.697009 + 1.20726i
\(741\) 0 0
\(742\) 5.63854 44.6248i 0.206997 1.63823i
\(743\) 8.15098 0.299030 0.149515 0.988759i \(-0.452229\pi\)
0.149515 + 0.988759i \(0.452229\pi\)
\(744\) 20.2254 + 35.0314i 0.741498 + 1.28431i
\(745\) 22.4090 38.8134i 0.821000 1.42201i
\(746\) −31.5831 + 54.7035i −1.15634 + 2.00284i
\(747\) 38.8814 + 67.3445i 1.42260 + 2.46401i
\(748\) −1.76297 −0.0644607
\(749\) −29.4786 + 12.3908i −1.07712 + 0.452750i
\(750\) −83.8893 −3.06320
\(751\) −18.3713 31.8201i −0.670379 1.16113i −0.977797 0.209556i \(-0.932798\pi\)
0.307417 0.951575i \(-0.400535\pi\)
\(752\) 0.332897 0.576595i 0.0121395 0.0210262i
\(753\) −21.6490 + 37.4972i −0.788934 + 1.36647i
\(754\) 0 0
\(755\) −37.1963 −1.35371
\(756\) 83.9218 + 63.7034i 3.05221 + 2.31687i
\(757\) 38.3971 1.39557 0.697783 0.716310i \(-0.254170\pi\)
0.697783 + 0.716310i \(0.254170\pi\)
\(758\) 10.5584 + 18.2878i 0.383500 + 0.664241i
\(759\) −0.558987 + 0.968195i −0.0202900 + 0.0351432i
\(760\) −5.27726 + 9.14048i −0.191426 + 0.331560i
\(761\) −6.23089 10.7922i −0.225870 0.391218i 0.730710 0.682688i \(-0.239189\pi\)
−0.956580 + 0.291470i \(0.905856\pi\)
\(762\) −96.4533 −3.49414
\(763\) 2.87000 + 2.17856i 0.103901 + 0.0788692i
\(764\) −86.3636 −3.12453
\(765\) 13.0584 + 22.6178i 0.472128 + 0.817749i
\(766\) −8.73742 + 15.1336i −0.315696 + 0.546801i
\(767\) 0 0
\(768\) 24.4860 + 42.4110i 0.883562 + 1.53037i
\(769\) 4.81390 0.173594 0.0867969 0.996226i \(-0.472337\pi\)
0.0867969 + 0.996226i \(0.472337\pi\)
\(770\) −3.65287 + 1.53542i −0.131640 + 0.0553326i
\(771\) −23.1075 −0.832196
\(772\) 0.344554 + 0.596785i 0.0124008 + 0.0214787i
\(773\) −14.1372 + 24.4863i −0.508480 + 0.880713i 0.491472 + 0.870893i \(0.336459\pi\)
−0.999952 + 0.00981931i \(0.996874\pi\)
\(774\) −12.0736 + 20.9120i −0.433975 + 0.751668i
\(775\) −1.11533 1.93180i −0.0400637 0.0693923i
\(776\) −21.3764 −0.767369
\(777\) −5.79015 + 45.8247i −0.207720 + 1.64395i
\(778\) 14.9367 0.535505
\(779\) 5.99395 + 10.3818i 0.214755 + 0.371967i
\(780\) 0 0
\(781\) 0.208322 0.36