Properties

Label 1183.2.e.i.170.8
Level $1183$
Weight $2$
Character 1183.170
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 170.8
Root \(1.14241 + 1.97871i\) of defining polynomial
Character \(\chi\) \(=\) 1183.170
Dual form 1183.2.e.i.508.8

$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

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

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 −0.106579 0.994304i \(-0.533990\pi\)
0.914382 0.404852i \(-0.132677\pi\)
\(3\) −1.57521 2.72835i −0.909448 1.57521i −0.814832 0.579697i \(-0.803171\pi\)
−0.0946163 0.995514i \(-0.530162\pi\)
\(4\) −1.61019 2.78892i −0.805093 1.39446i
\(5\) 1.06250 1.84030i 0.475162 0.823005i −0.524433 0.851452i \(-0.675723\pi\)
0.999595 + 0.0284464i \(0.00905598\pi\)
\(6\) −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 \(-0.151859\pi\)
−0.841837 + 0.539732i \(0.818526\pi\)
\(12\) −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 0.953340 0.301898i \(-0.0976204\pi\)
−0.738122 + 0.674667i \(0.764287\pi\)
\(18\) 7.91135 + 13.7029i 1.86472 + 3.22979i
\(19\) 0.890653 1.54266i 0.204330 0.353909i −0.745589 0.666406i \(-0.767832\pi\)
0.949919 + 0.312496i \(0.101165\pi\)
\(20\) −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 −0.919744 0.392520i \(-0.871603\pi\)
0.799804 + 0.600261i \(0.204937\pi\)
\(24\) 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 \(-0.302370\pi\)
−0.995273 + 0.0971205i \(0.969037\pi\)
\(32\) −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 \(-0.983874\pi\)
0.543215 + 0.839594i \(0.317207\pi\)
\(38\) −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 −0.276272 0.961079i \(-0.589099\pi\)
0.970455 0.241281i \(-0.0775675\pi\)
\(48\) −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 −0.999918 0.0127862i \(-0.995930\pi\)
0.488886 0.872348i \(-0.337403\pi\)
\(54\) 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 −0.999442 0.0333877i \(-0.989370\pi\)
0.470807 0.882236i \(-0.343963\pi\)
\(60\) 10.7796 + 18.6708i 1.39164 + 2.41039i
\(61\) 1.72037 2.97977i 0.220271 0.381521i −0.734619 0.678480i \(-0.762639\pi\)
0.954890 + 0.296959i \(0.0959725\pi\)
\(62\) −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 0.937245 + 0.348671i \(0.113367\pi\)
−0.166665 + 0.986014i \(0.553300\pi\)
\(68\) 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 0.970082 + 0.242778i \(0.0780588\pi\)
−0.274789 + 0.961505i \(0.588608\pi\)
\(74\) 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 −0.552284 0.833656i \(-0.686244\pi\)
0.998109 + 0.0614644i \(0.0195771\pi\)
\(80\) −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 −0.906638 0.421909i \(-0.861360\pi\)
0.818703 + 0.574218i \(0.194694\pi\)
\(90\) 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 0.545005 0.838433i \(-0.316528\pi\)
−0.998607 + 0.0527721i \(0.983194\pi\)
\(102\) −6.38738 11.0633i −0.632445 1.09543i
\(103\) −3.02085 + 5.23226i −0.297653 + 0.515550i −0.975599 0.219562i \(-0.929537\pi\)
0.677946 + 0.735112i \(0.262870\pi\)
\(104\) 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 0.410770 + 0.911739i \(0.365260\pi\)
−0.994974 + 0.100132i \(0.968074\pi\)
\(108\) −19.9114 34.4876i −1.91598 3.31857i
\(109\) 0.680941 + 1.17942i 0.0652223 + 0.112968i 0.896793 0.442451i \(-0.145891\pi\)
−0.831570 + 0.555420i \(0.812558\pi\)
\(110\) 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 0.409590 + 0.912270i \(0.365672\pi\)
−0.994844 + 0.101420i \(0.967662\pi\)
\(132\) −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 \(-0.159853\pi\)
−0.855125 + 0.518421i \(0.826520\pi\)
\(138\) 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 0.00420426 + 0.999991i \(0.498662\pi\)
−0.868120 + 0.496355i \(0.834672\pi\)
\(150\) −1.74344 3.01972i −0.142351 0.246559i
\(151\) −8.75211 15.1591i −0.712236 1.23363i −0.964016 0.265845i \(-0.914349\pi\)
0.251779 0.967785i \(-0.418984\pi\)
\(152\) −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 0.864514 0.502610i \(-0.167627\pi\)
−0.867529 + 0.497386i \(0.834293\pi\)
\(158\) −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 \(-0.962530\pi\)
0.598249 + 0.801310i \(0.295863\pi\)
\(164\) −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 0.338229 + 0.941064i \(0.390172\pi\)
−0.984100 + 0.177617i \(0.943161\pi\)
\(174\) −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 0.996376 + 0.0850537i \(0.0271062\pi\)
−0.424529 + 0.905414i \(0.639560\pi\)
\(180\) 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 0.275407 0.961328i \(-0.411188\pi\)
0.694831 0.719173i \(-0.255479\pi\)
\(192\) 20.4255 + 35.3780i 1.47409 + 2.55319i
\(193\) −0.106992 0.185315i −0.00770145 0.0133393i 0.862149 0.506655i \(-0.169118\pi\)
−0.869850 + 0.493316i \(0.835785\pi\)
\(194\) 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 −0.959478 0.281784i \(-0.909074\pi\)
0.235707 0.971824i \(-0.424259\pi\)
\(200\) −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 0.800032 0.599957i \(-0.204816\pi\)
−0.919594 + 0.392870i \(0.871482\pi\)
\(228\) 9.03614 + 15.6511i 0.598433 + 1.03652i
\(229\) −9.19208 + 15.9212i −0.607430 + 1.05210i 0.384232 + 0.923236i \(0.374466\pi\)
−0.991662 + 0.128863i \(0.958867\pi\)
\(230\) 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 0.315612 + 0.948888i \(0.397790\pi\)
−0.979567 + 0.201116i \(0.935543\pi\)
\(234\) 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 0.994835 0.101503i \(-0.0323651\pi\)
−0.585322 + 0.810801i \(0.699032\pi\)
\(242\) −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 −0.728678 0.684856i \(-0.759865\pi\)
0.957442 + 0.288626i \(0.0931983\pi\)
\(258\) −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 0.950425 0.310955i \(-0.100649\pi\)
−0.744507 + 0.667615i \(0.767315\pi\)
\(264\) −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 0.505345 0.862917i \(-0.331365\pi\)
−0.999981 + 0.00618287i \(0.998032\pi\)
\(270\) −30.0195 51.9953i −1.82693 3.16433i
\(271\) 9.36904 16.2277i 0.569129 0.985760i −0.427524 0.904004i \(-0.640614\pi\)
0.996652 0.0817555i \(-0.0260527\pi\)
\(272\) 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 −0.824575 0.565752i \(-0.808586\pi\)
−0.0776679 0.996979i \(-0.524747\pi\)
\(278\) 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 0.585393 0.810750i \(-0.300940\pi\)
−0.994826 + 0.101590i \(0.967607\pi\)
\(284\) −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 0.964872 0.262719i \(-0.0846192\pi\)
−0.709957 + 0.704245i \(0.751286\pi\)
\(312\) 0 0
\(313\) 7.61806 13.1949i 0.430598 0.745818i −0.566326 0.824181i \(-0.691636\pi\)
0.996925 + 0.0783626i \(0.0249692\pi\)
\(314\) −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 \(-0.894818\pi\)
0.753940 + 0.656944i \(0.228151\pi\)
\(318\) 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 \(-0.957292\pi\)
0.611354 + 0.791357i \(0.290625\pi\)
\(332\) −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 0.999773 + 0.0213132i \(0.00678472\pi\)
−0.481429 + 0.876485i \(0.659882\pi\)
\(348\) −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 0.998478 0.0551585i \(-0.0175664\pi\)
−0.547008 + 0.837128i \(0.684233\pi\)
\(354\) 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 0.392016 + 0.919959i \(0.371778\pi\)
−0.992715 + 0.120484i \(0.961555\pi\)
\(360\) −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 0.564293 0.825575i \(-0.309149\pi\)
−0.997115 + 0.0759048i \(0.975815\pi\)
\(368\) 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 0.246947 + 0.969029i \(0.420573\pi\)
−0.962677 + 0.270652i \(0.912761\pi\)
\(374\) 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 −0.751629 0.659586i \(-0.770732\pi\)
0.947033 + 0.321137i \(0.104065\pi\)
\(384\) 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 0.771185 0.636611i \(-0.219664\pi\)
−0.936914 + 0.349560i \(0.886331\pi\)
\(390\) 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 −0.232566 0.972581i \(-0.574712\pi\)
0.958563 0.284882i \(-0.0919544\pi\)
\(398\) −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 −0.310786 0.950480i \(-0.600592\pi\)
0.978533 0.206092i \(-0.0660746\pi\)
\(402\) −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 −0.872221 0.489112i \(-0.837321\pi\)
0.0125273 0.999922i \(-0.496012\pi\)
\(410\) −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 0.994539 0.104368i \(-0.0332820\pi\)
−0.587655 + 0.809112i \(0.699949\pi\)
\(432\) 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 −0.996968 0.0778096i \(-0.975207\pi\)
0.565869 + 0.824495i \(0.308541\pi\)
\(440\) −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 −0.932354 0.361546i \(-0.882249\pi\)
0.779285 + 0.626669i \(0.215582\pi\)
\(444\) −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 −0.175164 0.984539i \(-0.556046\pi\)
0.940218 0.340573i \(-0.110621\pi\)
\(458\) 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 −0.824323 0.566119i \(-0.808444\pi\)
0.902435 + 0.430825i \(0.141777\pi\)
\(468\) 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 \(-0.165611\pi\)
−0.864362 + 0.502871i \(0.832277\pi\)
\(480\) 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 \(-0.288016\pi\)
−0.989883 + 0.141887i \(0.954683\pi\)
\(488\) −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 −0.0480945 0.998843i \(-0.515315\pi\)
0.889070 0.457770i \(-0.151352\pi\)
\(500\) −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 \(-0.893207\pi\)
0.757254 + 0.653120i \(0.226540\pi\)
\(510\) −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 −0.996977 0.0776936i \(-0.975244\pi\)
0.431204 0.902254i \(-0.358089\pi\)
\(522\) 15.9059 + 27.5499i 0.696184 + 1.20583i
\(523\) 0.378202 0.655065i 0.0165376 0.0286440i −0.857638 0.514254i \(-0.828069\pi\)
0.874176 + 0.485610i \(0.161402\pi\)
\(524\) 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 \(-0.673318\pi\)
0.999782 + 0.0208936i \(0.00665111\pi\)
\(542\) −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 \(-0.107198\pi\)
−0.758084 + 0.652156i \(0.773865\pi\)
\(558\) 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 −0.934818 0.355127i \(-0.884438\pi\)
0.159860 0.987140i \(-0.448896\pi\)
\(564\) 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 −0.197726 0.980257i \(-0.563356\pi\)
0.947791 0.318893i \(-0.103311\pi\)
\(570\) 13.6234 + 23.5964i 0.570621 + 0.988344i
\(571\) −7.46920 12.9370i −0.312576 0.541398i 0.666343 0.745645i \(-0.267859\pi\)
−0.978919 + 0.204248i \(0.934525\pi\)
\(572\) 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 \(-0.0526247\pi\)
−0.635707 + 0.771930i \(0.719291\pi\)
\(578\) −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 −0.982840 0.184460i \(-0.940946\pi\)
0.651167 + 0.758934i \(0.274280\pi\)
\(594\) 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 0.890290 0.455394i \(-0.150502\pi\)
−0.839528 + 0.543317i \(0.817168\pi\)
\(600\) −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 −0.597705 0.801716i \(-0.703921\pi\)
0.993159 + 0.116770i \(0.0372540\pi\)
\(608\) −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 \(-0.0702669\pi\)
−0.677493 + 0.735529i \(0.736934\pi\)
\(614\) 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 0.704101 0.710100i \(-0.251350\pi\)
−0.967015 + 0.254719i \(0.918017\pi\)
\(620\) 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 0.995881 0.0906706i \(-0.0289010\pi\)
−0.576464 + 0.817123i \(0.695568\pi\)
\(642\) 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 0.550352 0.834933i \(-0.314494\pi\)
−0.998249 + 0.0591522i \(0.981160\pi\)
\(648\) 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 −0.980178 0.198117i \(-0.936517\pi\)
0.661664 + 0.749801i \(0.269851\pi\)
\(654\) −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 −0.998897 0.0469576i \(-0.985047\pi\)
0.458782 0.888549i \(-0.348286\pi\)
\(662\) 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 0.00834820 + 0.999965i \(0.497343\pi\)
−0.870169 + 0.492753i \(0.835991\pi\)
\(678\) 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 \(-0.0484170\pi\)
−0.625448 + 0.780266i \(0.715084\pi\)
\(684\) 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 −0.252376 0.967629i \(-0.581212\pi\)
0.964180 0.265250i \(-0.0854545\pi\)
\(692\) 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 −0.189644 + 0.981853i \(0.560733\pi\)
−0.755488 + 0.655163i \(0.772600\pi\)
\(710\) −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 0.459614 + 0.888119i \(0.347988\pi\)
−0.998940 + 0.0460219i \(0.985346\pi\)
\(720\) 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 \(-0.710693\pi\)
0.990450 + 0.137872i \(0.0440263\pi\)
\(734\) −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 \(-0.0530238\pi\)
−0.636674 + 0.771133i \(0.719690\pi\)
\(740\) 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 0.307417 + 0.951575i \(0.400535\pi\)
−0.977797 + 0.209556i \(0.932798\pi\)
\(752\) −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 \(-0.760811\pi\)
0.956580 + 0.291470i \(0.0941443\pi\)
\(762\) 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 0.999952 + 0.00981931i \(0.00312563\pi\)
−0.491472 + 0.870893i \(0.663541\pi\)
\(774\) 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 +