Properties

Label 1183.2.e.i.508.8
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 508.8
Root \(1.14241 - 1.97871i\) of defining polynomial
Character \(\chi\) \(=\) 1183.508
Dual form 1183.2.e.i.170.8

$q$-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 \(0.132677\pi\)
−0.106579 + 0.994304i \(0.533990\pi\)
\(3\) −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 0.999595 0.0284464i \(-0.00905598\pi\)
−0.524433 + 0.851452i \(0.675723\pi\)
\(6\) −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 −0.841837 0.539732i \(-0.818526\pi\)
0.888340 + 0.459186i \(0.151859\pi\)
\(12\) −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 0.949919 0.312496i \(-0.101165\pi\)
−0.745589 + 0.666406i \(0.767832\pi\)
\(20\) −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 −0.995273 0.0971205i \(-0.969037\pi\)
0.581745 + 0.813371i \(0.302370\pi\)
\(32\) −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 0.543215 0.839594i \(-0.317207\pi\)
−0.998717 + 0.0506410i \(0.983874\pi\)
\(38\) −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 \(-0.323874\pi\)
0.525512 + 0.850786i \(0.323874\pi\)
\(42\) 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 \(0.0775675\pi\)
−0.276272 + 0.961079i \(0.589099\pi\)
\(48\) −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 \(0.343963\pi\)
−0.999442 + 0.0333877i \(0.989370\pi\)
\(60\) 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 \(-0.553300\pi\)
0.937245 0.348671i \(-0.113367\pi\)
\(68\) 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 \(-0.474460\pi\)
0.0801494 + 0.996783i \(0.474460\pi\)
\(72\) 9.65478 + 16.7226i 1.13783 + 1.97077i
\(73\) 5.94059 10.2894i 0.695293 1.20428i −0.274789 0.961505i \(-0.588608\pi\)
0.970082 0.242778i \(-0.0780588\pi\)
\(74\) 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 \(-0.288642\pi\)
0.616273 + 0.787533i \(0.288642\pi\)
\(84\) 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 0.818703 0.574218i \(-0.194694\pi\)
−0.906638 + 0.421909i \(0.861360\pi\)
\(90\) 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 \(-0.372750\pi\)
0.389203 + 0.921152i \(0.372750\pi\)
\(98\) −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 −0.831570 0.555420i \(-0.812558\pi\)
0.896793 + 0.442451i \(0.145891\pi\)
\(110\) 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 −0.855125 0.518421i \(-0.826520\pi\)
0.876529 + 0.481349i \(0.159853\pi\)
\(138\) 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 \(-0.834672\pi\)
0.00420426 0.999991i \(-0.498662\pi\)
\(150\) −1.74344 + 3.01972i −0.142351 + 0.246559i
\(151\) −8.75211 + 15.1591i −0.712236 + 1.23363i 0.251779 + 0.967785i \(0.418984\pi\)
−0.964016 + 0.265845i \(0.914349\pi\)
\(152\) −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 0.598249 0.801310i \(-0.295863\pi\)
−0.993080 + 0.117444i \(0.962530\pi\)
\(164\) −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 \(-0.427324\pi\)
0.226339 + 0.974049i \(0.427324\pi\)
\(168\) 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 −0.869850 0.493316i \(-0.835785\pi\)
0.862149 + 0.506655i \(0.169118\pi\)
\(194\) 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 \(-0.630996\pi\)
−0.400017 + 0.916508i \(0.630996\pi\)
\(198\) −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 \(-0.650599\pi\)
−0.455666 + 0.890151i \(0.650599\pi\)
\(224\) −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 −0.919594 0.392870i \(-0.871482\pi\)
0.800032 + 0.599957i \(0.204816\pi\)
\(228\) 9.03614 15.6511i 0.598433 1.03652i
\(229\) −9.19208 15.9212i −0.607430 1.05210i −0.991662 0.128863i \(-0.958867\pi\)
0.384232 0.923236i \(-0.374466\pi\)
\(230\) 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 \(-0.264991\pi\)
0.673033 + 0.739612i \(0.264991\pi\)
\(240\) −0.234144 0.405549i −0.0151139 0.0261781i
\(241\) 6.35736 11.0113i 0.409514 0.709299i −0.585322 0.810801i \(-0.699032\pi\)
0.994835 + 0.101503i \(0.0323651\pi\)
\(242\) −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 \(0.0260527\pi\)
−0.427524 + 0.904004i \(0.640614\pi\)
\(272\) 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 \(-0.478806\pi\)
0.0665348 + 0.997784i \(0.478806\pi\)
\(282\) −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 \(-0.509414\pi\)
−0.0295700 + 0.999563i \(0.509414\pi\)
\(294\) 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 \(-0.259199\pi\)
0.686379 + 0.727244i \(0.259199\pi\)
\(308\) −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 0.753940 0.656944i \(-0.228151\pi\)
−0.945900 + 0.324459i \(0.894818\pi\)
\(318\) 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 0.611354 0.791357i \(-0.290625\pi\)
−0.991012 + 0.133770i \(0.957292\pi\)
\(332\) −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 \(-0.623701\pi\)
−0.378911 + 0.925433i \(0.623701\pi\)
\(350\) −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 −0.547008 0.837128i \(-0.684233\pi\)
0.998478 + 0.0551585i \(0.0175664\pi\)
\(354\) 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 \(-0.961555\pi\)
0.392016 0.919959i \(-0.371778\pi\)
\(360\) −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 \(-0.423714\pi\)
0.237372 + 0.971419i \(0.423714\pi\)
\(380\) −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 0.947033 0.321137i \(-0.104065\pi\)
−0.751629 + 0.659586i \(0.770732\pi\)
\(384\) 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 \(0.0919544\pi\)
−0.232566 + 0.972581i \(0.574712\pi\)
\(398\) −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 \(0.0660746\pi\)
−0.310786 + 0.950480i \(0.600592\pi\)
\(402\) −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 \(0.496012\pi\)
−0.872221 + 0.489112i \(0.837321\pi\)
\(410\) −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 \(-0.329429\pi\)
0.510584 + 0.859828i \(0.329429\pi\)
\(422\) 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 −0.587655 0.809112i \(-0.699949\pi\)
0.994539 + 0.104368i \(0.0332820\pi\)
\(432\) 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 \(-0.513171\pi\)
−0.0413661 + 0.999144i \(0.513171\pi\)
\(450\) −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 \(0.110621\pi\)
−0.175164 + 0.984539i \(0.556046\pi\)
\(458\) 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 \(-0.557134\pi\)
−0.178530 + 0.983934i \(0.557134\pi\)
\(462\) −4.67917 3.55186i −0.217695 0.165248i
\(463\) 14.4720 0.672570 0.336285 0.941760i \(-0.390829\pi\)
0.336285 + 0.941760i \(0.390829\pi\)
\(464\) 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 −0.864362 0.502871i \(-0.832277\pi\)
0.867680 + 0.497124i \(0.165611\pi\)
\(480\) 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 −0.989883 0.141887i \(-0.954683\pi\)
0.617819 + 0.786320i \(0.288016\pi\)
\(488\) −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 \(0.151352\pi\)
−0.0480945 + 0.998843i \(0.515315\pi\)
\(500\) −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 0.757254 0.653120i \(-0.226540\pi\)
−0.944246 + 0.329241i \(0.893207\pi\)
\(510\) −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 0.999782 0.0208936i \(-0.00665111\pi\)
−0.517985 + 0.855390i \(0.673318\pi\)
\(542\) −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 −0.758084 0.652156i \(-0.773865\pi\)
0.943826 + 0.330442i \(0.107198\pi\)
\(558\) 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 −0.635707 0.771930i \(-0.719291\pi\)
0.986365 + 0.164573i \(0.0526247\pi\)
\(578\) −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 \(-0.224626\pi\)
0.761168 + 0.648555i \(0.224626\pi\)
\(588\) 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 0.651167 0.758934i \(-0.274280\pi\)
−0.982840 + 0.184460i \(0.940946\pi\)
\(594\) 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 −0.677493 0.735529i \(-0.736934\pi\)
0.975733 + 0.218962i \(0.0702669\pi\)
\(614\) 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 \(-0.285932\pi\)
0.622955 + 0.782257i \(0.285932\pi\)
\(618\) 21.7444 + 37.6625i 0.874689 + 1.51501i
\(619\) −6.54123 + 11.3297i −0.262914 + 0.455380i −0.967015 0.254719i \(-0.918017\pi\)
0.704101 + 0.710100i \(0.251350\pi\)
\(620\) 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 \(-0.251480\pi\)
0.703812 + 0.710387i \(0.251480\pi\)
\(632\) −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 \(-0.667561\pi\)
−0.502432 + 0.864617i \(0.667561\pi\)
\(644\) −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 \(0.348286\pi\)
−0.998897 + 0.0469576i \(0.985047\pi\)
\(662\) 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 −0.625448 0.780266i \(-0.715084\pi\)
0.988454 + 0.151521i \(0.0484170\pi\)
\(684\) 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 \(0.0854545\pi\)
−0.252376 + 0.967629i \(0.581212\pi\)
\(692\) 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 \(-0.772600\pi\)
−0.189644 0.981853i \(-0.560733\pi\)
\(710\) −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 0.990450 0.137872i \(-0.0440263\pi\)
−0.614626 + 0.788819i \(0.710693\pi\)
\(734\) −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 −0.636674 0.771133i \(-0.719690\pi\)
0.986158 + 0.165810i \(0.0530238\pi\)
\(740\) 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 \(-0.547771\pi\)
−0.149515 + 0.988759i \(0.547771\pi\)
\(744\) 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 0.956580 0.291470i \(-0.0941443\pi\)
−0.730710 + 0.682688i \(0.760811\pi\)
\(762\) 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 \(-0.527663\pi\)
−0.0867969 + 0.996226i \(0.527663\pi\)
\(770\) −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 \(-0.663541\pi\)
0.999952 0.00981931i \(-0.00312563\pi\)
\(774\) 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 0.360825i