Properties

Label 819.2.fm.e.496.3
Level $819$
Weight $2$
Character 819.496
Analytic conductor $6.540$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fm (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 496.3
Character \(\chi\) \(=\) 819.496
Dual form 819.2.fm.e.748.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.34112 - 0.359352i) q^{2} +(-0.0625832 - 0.0361324i) q^{4} +(-2.52867 - 2.52867i) q^{5} +(-0.324044 + 2.62583i) q^{7} +(2.03448 + 2.03448i) q^{8} +O(q^{10})\) \(q+(-1.34112 - 0.359352i) q^{2} +(-0.0625832 - 0.0361324i) q^{4} +(-2.52867 - 2.52867i) q^{5} +(-0.324044 + 2.62583i) q^{7} +(2.03448 + 2.03448i) q^{8} +(2.48257 + 4.29993i) q^{10} +(-0.0529715 + 0.197692i) q^{11} +(-2.07540 - 2.94834i) q^{13} +(1.37818 - 3.40511i) q^{14} +(-1.92512 - 3.33441i) q^{16} +(-1.13739 + 1.97002i) q^{17} +(-1.50152 + 0.402330i) q^{19} +(0.0668853 + 0.249619i) q^{20} +(0.142082 - 0.246094i) q^{22} +(-2.59661 + 1.49915i) q^{23} +7.78835i q^{25} +(1.72386 + 4.69988i) q^{26} +(0.115157 - 0.152625i) q^{28} +(4.75430 + 8.23469i) q^{29} +(2.75209 + 2.75209i) q^{31} +(-0.105751 - 0.394667i) q^{32} +(2.23331 - 2.23331i) q^{34} +(7.45927 - 5.82046i) q^{35} +(1.17697 - 4.39250i) q^{37} +2.15829 q^{38} -10.2891i q^{40} +(1.36054 - 5.07760i) q^{41} +(1.76513 + 1.01910i) q^{43} +(0.0104582 - 0.0104582i) q^{44} +(4.02109 - 1.07745i) q^{46} +(9.42358 - 9.42358i) q^{47} +(-6.78999 - 1.70177i) q^{49} +(2.79876 - 10.4451i) q^{50} +(0.0233541 + 0.259506i) q^{52} +12.6997 q^{53} +(0.633846 - 0.365951i) q^{55} +(-6.00147 + 4.68295i) q^{56} +(-3.41693 - 12.7522i) q^{58} +(0.510631 + 1.90570i) q^{59} +(-0.850570 - 0.491077i) q^{61} +(-2.70191 - 4.67985i) q^{62} +8.26779i q^{64} +(-2.20740 + 12.7034i) q^{65} +(15.1633 + 4.06300i) q^{67} +(0.142363 - 0.0821934i) q^{68} +(-12.0954 + 5.12543i) q^{70} +(-0.00355777 - 0.0132778i) q^{71} +(2.24560 - 2.24560i) q^{73} +(-3.15691 + 5.46792i) q^{74} +(0.108507 + 0.0290743i) q^{76} +(-0.501942 - 0.203155i) q^{77} +12.7231 q^{79} +(-3.56363 + 13.2996i) q^{80} +(-3.64929 + 6.32076i) q^{82} +(-3.37812 - 3.37812i) q^{83} +(7.85762 - 2.10544i) q^{85} +(-2.00104 - 2.00104i) q^{86} +(-0.509971 + 0.294432i) q^{88} +(-11.8364 - 3.17155i) q^{89} +(8.41438 - 4.49425i) q^{91} +0.216672 q^{92} +(-16.0245 + 9.25177i) q^{94} +(4.81420 + 2.77948i) q^{95} +(-7.85674 + 2.10521i) q^{97} +(8.49465 + 4.72228i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + O(q^{10}) \) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + 2q^{10} + 4q^{11} + 6q^{13} - 34q^{14} + 14q^{16} + 8q^{17} + 2q^{19} - 44q^{20} - 4q^{22} + 18q^{23} + 28q^{26} - 32q^{28} + 18q^{29} - 14q^{31} + 8q^{32} - 66q^{34} - 22q^{35} - 24q^{37} - 24q^{38} - 6q^{43} + 20q^{44} - 58q^{46} + 28q^{47} + 8q^{49} - 70q^{50} + 28q^{52} + 80q^{53} + 60q^{55} + 54q^{56} - 4q^{58} + 42q^{59} + 36q^{61} - 52q^{62} - 14q^{65} + 26q^{67} + 72q^{68} - 116q^{70} + 4q^{71} + 12q^{73} + 18q^{74} - 48q^{76} - 28q^{77} - 4q^{79} + 98q^{80} + 20q^{82} + 36q^{83} - 10q^{85} + 40q^{86} + 96q^{88} + 54q^{89} + 148q^{91} + 4q^{92} - 60q^{95} - 40q^{97} - 36q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.34112 0.359352i −0.948315 0.254100i −0.248668 0.968589i \(-0.579993\pi\)
−0.699647 + 0.714489i \(0.746659\pi\)
\(3\) 0 0
\(4\) −0.0625832 0.0361324i −0.0312916 0.0180662i
\(5\) −2.52867 2.52867i −1.13086 1.13086i −0.990035 0.140821i \(-0.955026\pi\)
−0.140821 0.990035i \(-0.544974\pi\)
\(6\) 0 0
\(7\) −0.324044 + 2.62583i −0.122477 + 0.992471i
\(8\) 2.03448 + 2.03448i 0.719298 + 0.719298i
\(9\) 0 0
\(10\) 2.48257 + 4.29993i 0.785056 + 1.35976i
\(11\) −0.0529715 + 0.197692i −0.0159715 + 0.0596065i −0.973452 0.228893i \(-0.926490\pi\)
0.957480 + 0.288499i \(0.0931562\pi\)
\(12\) 0 0
\(13\) −2.07540 2.94834i −0.575611 0.817724i
\(14\) 1.37818 3.40511i 0.368334 0.910054i
\(15\) 0 0
\(16\) −1.92512 3.33441i −0.481281 0.833603i
\(17\) −1.13739 + 1.97002i −0.275858 + 0.477800i −0.970351 0.241699i \(-0.922295\pi\)
0.694493 + 0.719499i \(0.255629\pi\)
\(18\) 0 0
\(19\) −1.50152 + 0.402330i −0.344472 + 0.0923009i −0.426907 0.904296i \(-0.640397\pi\)
0.0824354 + 0.996596i \(0.473730\pi\)
\(20\) 0.0668853 + 0.249619i 0.0149560 + 0.0558166i
\(21\) 0 0
\(22\) 0.142082 0.246094i 0.0302920 0.0524673i
\(23\) −2.59661 + 1.49915i −0.541430 + 0.312595i −0.745658 0.666328i \(-0.767865\pi\)
0.204228 + 0.978923i \(0.434532\pi\)
\(24\) 0 0
\(25\) 7.78835i 1.55767i
\(26\) 1.72386 + 4.69988i 0.338077 + 0.921722i
\(27\) 0 0
\(28\) 0.115157 0.152625i 0.0217627 0.0288433i
\(29\) 4.75430 + 8.23469i 0.882852 + 1.52914i 0.848156 + 0.529746i \(0.177713\pi\)
0.0346955 + 0.999398i \(0.488954\pi\)
\(30\) 0 0
\(31\) 2.75209 + 2.75209i 0.494290 + 0.494290i 0.909655 0.415365i \(-0.136346\pi\)
−0.415365 + 0.909655i \(0.636346\pi\)
\(32\) −0.105751 0.394667i −0.0186943 0.0697679i
\(33\) 0 0
\(34\) 2.23331 2.23331i 0.383009 0.383009i
\(35\) 7.45927 5.82046i 1.26085 0.983838i
\(36\) 0 0
\(37\) 1.17697 4.39250i 0.193492 0.722122i −0.799160 0.601119i \(-0.794722\pi\)
0.992652 0.121004i \(-0.0386114\pi\)
\(38\) 2.15829 0.350121
\(39\) 0 0
\(40\) 10.2891i 1.62684i
\(41\) 1.36054 5.07760i 0.212480 0.792988i −0.774558 0.632503i \(-0.782028\pi\)
0.987038 0.160485i \(-0.0513058\pi\)
\(42\) 0 0
\(43\) 1.76513 + 1.01910i 0.269180 + 0.155411i 0.628515 0.777798i \(-0.283663\pi\)
−0.359335 + 0.933209i \(0.616996\pi\)
\(44\) 0.0104582 0.0104582i 0.00157664 0.00157664i
\(45\) 0 0
\(46\) 4.02109 1.07745i 0.592877 0.158861i
\(47\) 9.42358 9.42358i 1.37457 1.37457i 0.521036 0.853535i \(-0.325546\pi\)
0.853535 0.521036i \(-0.174454\pi\)
\(48\) 0 0
\(49\) −6.78999 1.70177i −0.969999 0.243110i
\(50\) 2.79876 10.4451i 0.395804 1.47716i
\(51\) 0 0
\(52\) 0.0233541 + 0.259506i 0.00323863 + 0.0359870i
\(53\) 12.6997 1.74444 0.872218 0.489117i \(-0.162681\pi\)
0.872218 + 0.489117i \(0.162681\pi\)
\(54\) 0 0
\(55\) 0.633846 0.365951i 0.0854678 0.0493449i
\(56\) −6.00147 + 4.68295i −0.801980 + 0.625785i
\(57\) 0 0
\(58\) −3.41693 12.7522i −0.448666 1.67444i
\(59\) 0.510631 + 1.90570i 0.0664785 + 0.248101i 0.991166 0.132625i \(-0.0423407\pi\)
−0.924688 + 0.380726i \(0.875674\pi\)
\(60\) 0 0
\(61\) −0.850570 0.491077i −0.108904 0.0628760i 0.444558 0.895750i \(-0.353361\pi\)
−0.553463 + 0.832874i \(0.686694\pi\)
\(62\) −2.70191 4.67985i −0.343143 0.594342i
\(63\) 0 0
\(64\) 8.26779i 1.03347i
\(65\) −2.20740 + 12.7034i −0.273794 + 1.57566i
\(66\) 0 0
\(67\) 15.1633 + 4.06300i 1.85249 + 0.496374i 0.999667 0.0258173i \(-0.00821883\pi\)
0.852828 + 0.522192i \(0.174885\pi\)
\(68\) 0.142363 0.0821934i 0.0172641 0.00996742i
\(69\) 0 0
\(70\) −12.0954 + 5.12543i −1.44567 + 0.612607i
\(71\) −0.00355777 0.0132778i −0.000422230 0.00157578i 0.965714 0.259607i \(-0.0835930\pi\)
−0.966137 + 0.258031i \(0.916926\pi\)
\(72\) 0 0
\(73\) 2.24560 2.24560i 0.262827 0.262827i −0.563374 0.826202i \(-0.690497\pi\)
0.826202 + 0.563374i \(0.190497\pi\)
\(74\) −3.15691 + 5.46792i −0.366983 + 0.635633i
\(75\) 0 0
\(76\) 0.108507 + 0.0290743i 0.0124466 + 0.00333506i
\(77\) −0.501942 0.203155i −0.0572016 0.0231517i
\(78\) 0 0
\(79\) 12.7231 1.43146 0.715732 0.698375i \(-0.246093\pi\)
0.715732 + 0.698375i \(0.246093\pi\)
\(80\) −3.56363 + 13.2996i −0.398425 + 1.48694i
\(81\) 0 0
\(82\) −3.64929 + 6.32076i −0.402997 + 0.698011i
\(83\) −3.37812 3.37812i −0.370797 0.370797i 0.496971 0.867767i \(-0.334446\pi\)
−0.867767 + 0.496971i \(0.834446\pi\)
\(84\) 0 0
\(85\) 7.85762 2.10544i 0.852278 0.228367i
\(86\) −2.00104 2.00104i −0.215777 0.215777i
\(87\) 0 0
\(88\) −0.509971 + 0.294432i −0.0543631 + 0.0313866i
\(89\) −11.8364 3.17155i −1.25466 0.336184i −0.430523 0.902580i \(-0.641671\pi\)
−0.824133 + 0.566396i \(0.808337\pi\)
\(90\) 0 0
\(91\) 8.41438 4.49425i 0.882066 0.471125i
\(92\) 0.216672 0.0225896
\(93\) 0 0
\(94\) −16.0245 + 9.25177i −1.65280 + 0.954247i
\(95\) 4.81420 + 2.77948i 0.493927 + 0.285169i
\(96\) 0 0
\(97\) −7.85674 + 2.10521i −0.797731 + 0.213751i −0.634587 0.772851i \(-0.718830\pi\)
−0.163143 + 0.986602i \(0.552163\pi\)
\(98\) 8.49465 + 4.72228i 0.858090 + 0.477022i
\(99\) 0 0
\(100\) 0.281412 0.487420i 0.0281412 0.0487420i
\(101\) 5.41672 + 9.38204i 0.538984 + 0.933548i 0.998959 + 0.0456161i \(0.0145251\pi\)
−0.459975 + 0.887932i \(0.652142\pi\)
\(102\) 0 0
\(103\) 2.40912 0.237378 0.118689 0.992931i \(-0.462131\pi\)
0.118689 + 0.992931i \(0.462131\pi\)
\(104\) 1.77600 10.2207i 0.174151 1.00222i
\(105\) 0 0
\(106\) −17.0318 4.56366i −1.65428 0.443262i
\(107\) 2.22804 + 3.85907i 0.215392 + 0.373071i 0.953394 0.301728i \(-0.0975636\pi\)
−0.738001 + 0.674799i \(0.764230\pi\)
\(108\) 0 0
\(109\) −11.9987 + 11.9987i −1.14927 + 1.14927i −0.162570 + 0.986697i \(0.551978\pi\)
−0.986697 + 0.162570i \(0.948022\pi\)
\(110\) −0.981569 + 0.263010i −0.0935889 + 0.0250771i
\(111\) 0 0
\(112\) 9.37943 3.97455i 0.886273 0.375560i
\(113\) −0.238333 + 0.412805i −0.0224205 + 0.0388334i −0.877018 0.480458i \(-0.840471\pi\)
0.854597 + 0.519291i \(0.173804\pi\)
\(114\) 0 0
\(115\) 10.3568 + 2.77510i 0.965780 + 0.258780i
\(116\) 0.687138i 0.0637992i
\(117\) 0 0
\(118\) 2.73927i 0.252170i
\(119\) −4.80438 3.62497i −0.440416 0.332301i
\(120\) 0 0
\(121\) 9.49000 + 5.47906i 0.862728 + 0.498096i
\(122\) 0.964247 + 0.964247i 0.0872988 + 0.0872988i
\(123\) 0 0
\(124\) −0.0727950 0.271675i −0.00653718 0.0243971i
\(125\) 7.05081 7.05081i 0.630643 0.630643i
\(126\) 0 0
\(127\) −1.88759 + 1.08980i −0.167496 + 0.0967041i −0.581405 0.813614i \(-0.697497\pi\)
0.413908 + 0.910319i \(0.364163\pi\)
\(128\) 2.75955 10.2988i 0.243912 0.910291i
\(129\) 0 0
\(130\) 7.52537 16.2435i 0.660019 1.42465i
\(131\) 7.17276i 0.626687i −0.949640 0.313344i \(-0.898551\pi\)
0.949640 0.313344i \(-0.101449\pi\)
\(132\) 0 0
\(133\) −0.569893 4.07310i −0.0494160 0.353183i
\(134\) −18.8758 10.8979i −1.63062 0.941438i
\(135\) 0 0
\(136\) −6.32197 + 1.69397i −0.542105 + 0.145257i
\(137\) −12.1825 + 3.26430i −1.04082 + 0.278888i −0.738455 0.674303i \(-0.764444\pi\)
−0.302369 + 0.953191i \(0.597778\pi\)
\(138\) 0 0
\(139\) 17.5612 + 10.1390i 1.48952 + 0.859975i 0.999928 0.0119768i \(-0.00381244\pi\)
0.489592 + 0.871952i \(0.337146\pi\)
\(140\) −0.677132 + 0.0947418i −0.0572281 + 0.00800715i
\(141\) 0 0
\(142\) 0.0190856i 0.00160163i
\(143\) 0.692802 0.254112i 0.0579350 0.0212499i
\(144\) 0 0
\(145\) 8.80076 32.8449i 0.730863 2.72762i
\(146\) −3.81857 + 2.20465i −0.316027 + 0.182459i
\(147\) 0 0
\(148\) −0.232370 + 0.232370i −0.0191007 + 0.0191007i
\(149\) 2.91147 + 10.8658i 0.238517 + 0.890157i 0.976532 + 0.215373i \(0.0690967\pi\)
−0.738015 + 0.674784i \(0.764237\pi\)
\(150\) 0 0
\(151\) −9.18076 9.18076i −0.747120 0.747120i 0.226818 0.973937i \(-0.427168\pi\)
−0.973937 + 0.226818i \(0.927168\pi\)
\(152\) −3.87334 2.23628i −0.314170 0.181386i
\(153\) 0 0
\(154\) 0.600160 + 0.452829i 0.0483622 + 0.0364900i
\(155\) 13.9183i 1.11794i
\(156\) 0 0
\(157\) 20.3277i 1.62232i 0.584821 + 0.811162i \(0.301165\pi\)
−0.584821 + 0.811162i \(0.698835\pi\)
\(158\) −17.0632 4.57208i −1.35748 0.363735i
\(159\) 0 0
\(160\) −0.730574 + 1.26539i −0.0577569 + 0.100038i
\(161\) −3.09511 7.30405i −0.243929 0.575640i
\(162\) 0 0
\(163\) 0.193660 0.0518911i 0.0151686 0.00406442i −0.251227 0.967928i \(-0.580834\pi\)
0.266395 + 0.963864i \(0.414167\pi\)
\(164\) −0.268613 + 0.268613i −0.0209752 + 0.0209752i
\(165\) 0 0
\(166\) 3.31653 + 5.74439i 0.257412 + 0.445852i
\(167\) 13.5813 + 3.63909i 1.05095 + 0.281602i 0.742645 0.669686i \(-0.233571\pi\)
0.308306 + 0.951287i \(0.400238\pi\)
\(168\) 0 0
\(169\) −4.38547 + 12.2380i −0.337344 + 0.941382i
\(170\) −11.2946 −0.866256
\(171\) 0 0
\(172\) −0.0736451 0.127557i −0.00561538 0.00972613i
\(173\) −6.32817 + 10.9607i −0.481122 + 0.833328i −0.999765 0.0216628i \(-0.993104\pi\)
0.518643 + 0.854991i \(0.326437\pi\)
\(174\) 0 0
\(175\) −20.4509 2.52377i −1.54594 0.190779i
\(176\) 0.761164 0.203953i 0.0573749 0.0153736i
\(177\) 0 0
\(178\) 14.7343 + 8.50687i 1.10438 + 0.637617i
\(179\) 8.90908 5.14366i 0.665896 0.384455i −0.128624 0.991693i \(-0.541056\pi\)
0.794520 + 0.607238i \(0.207723\pi\)
\(180\) 0 0
\(181\) 8.60644 0.639711 0.319856 0.947466i \(-0.396366\pi\)
0.319856 + 0.947466i \(0.396366\pi\)
\(182\) −12.8997 + 3.00360i −0.956189 + 0.222642i
\(183\) 0 0
\(184\) −8.33276 2.23276i −0.614299 0.164601i
\(185\) −14.0833 + 8.13102i −1.03543 + 0.597805i
\(186\) 0 0
\(187\) −0.329208 0.329208i −0.0240741 0.0240741i
\(188\) −0.930255 + 0.249261i −0.0678458 + 0.0181792i
\(189\) 0 0
\(190\) −5.45761 5.45761i −0.395936 0.395936i
\(191\) −8.10759 + 14.0428i −0.586645 + 1.01610i 0.408023 + 0.912971i \(0.366218\pi\)
−0.994668 + 0.103127i \(0.967115\pi\)
\(192\) 0 0
\(193\) 5.21705 19.4703i 0.375531 1.40150i −0.477035 0.878884i \(-0.658289\pi\)
0.852567 0.522618i \(-0.175045\pi\)
\(194\) 11.2933 0.810814
\(195\) 0 0
\(196\) 0.363450 + 0.351841i 0.0259607 + 0.0251315i
\(197\) −2.43284 0.651878i −0.173333 0.0464444i 0.171109 0.985252i \(-0.445265\pi\)
−0.344442 + 0.938808i \(0.611932\pi\)
\(198\) 0 0
\(199\) −8.23179 + 14.2579i −0.583536 + 1.01071i 0.411520 + 0.911401i \(0.364998\pi\)
−0.995056 + 0.0993137i \(0.968335\pi\)
\(200\) −15.8453 + 15.8453i −1.12043 + 1.12043i
\(201\) 0 0
\(202\) −3.89302 14.5289i −0.273912 1.02225i
\(203\) −23.1635 + 9.81559i −1.62576 + 0.688920i
\(204\) 0 0
\(205\) −16.2799 + 9.39922i −1.13704 + 0.656470i
\(206\) −3.23092 0.865723i −0.225109 0.0603178i
\(207\) 0 0
\(208\) −5.83560 + 12.5962i −0.404626 + 0.873386i
\(209\) 0.318150i 0.0220069i
\(210\) 0 0
\(211\) −3.66647 6.35051i −0.252410 0.437187i 0.711779 0.702404i \(-0.247890\pi\)
−0.964189 + 0.265217i \(0.914557\pi\)
\(212\) −0.794788 0.458871i −0.0545862 0.0315154i
\(213\) 0 0
\(214\) −1.60130 5.97613i −0.109463 0.408520i
\(215\) −1.88647 7.04040i −0.128656 0.480151i
\(216\) 0 0
\(217\) −8.11833 + 6.33473i −0.551108 + 0.430029i
\(218\) 20.4034 11.7799i 1.38190 0.797838i
\(219\) 0 0
\(220\) −0.0528908 −0.00356590
\(221\) 8.16883 0.735149i 0.549495 0.0494515i
\(222\) 0 0
\(223\) −0.683979 + 2.55265i −0.0458026 + 0.170938i −0.985038 0.172335i \(-0.944869\pi\)
0.939236 + 0.343273i \(0.111536\pi\)
\(224\) 1.07060 0.149794i 0.0715323 0.0100085i
\(225\) 0 0
\(226\) 0.467975 0.467975i 0.0311293 0.0311293i
\(227\) 17.7461 4.75506i 1.17785 0.315604i 0.383777 0.923426i \(-0.374623\pi\)
0.794074 + 0.607821i \(0.207956\pi\)
\(228\) 0 0
\(229\) 5.79771 5.79771i 0.383124 0.383124i −0.489103 0.872226i \(-0.662676\pi\)
0.872226 + 0.489103i \(0.162676\pi\)
\(230\) −12.8925 7.44349i −0.850107 0.490809i
\(231\) 0 0
\(232\) −7.08079 + 26.4259i −0.464877 + 1.73494i
\(233\) 21.0210i 1.37713i −0.725173 0.688567i \(-0.758240\pi\)
0.725173 0.688567i \(-0.241760\pi\)
\(234\) 0 0
\(235\) −47.6583 −3.10888
\(236\) 0.0369007 0.137715i 0.00240203 0.00896450i
\(237\) 0 0
\(238\) 5.14060 + 6.58798i 0.333216 + 0.427035i
\(239\) −10.3794 + 10.3794i −0.671386 + 0.671386i −0.958036 0.286650i \(-0.907458\pi\)
0.286650 + 0.958036i \(0.407458\pi\)
\(240\) 0 0
\(241\) −0.355487 1.32670i −0.0228989 0.0854600i 0.953531 0.301296i \(-0.0974191\pi\)
−0.976430 + 0.215836i \(0.930752\pi\)
\(242\) −10.7583 10.7583i −0.691571 0.691571i
\(243\) 0 0
\(244\) 0.0354876 + 0.0614664i 0.00227186 + 0.00393498i
\(245\) 12.8664 + 21.4729i 0.822006 + 1.37185i
\(246\) 0 0
\(247\) 4.30245 + 3.59199i 0.273758 + 0.228553i
\(248\) 11.1982i 0.711084i
\(249\) 0 0
\(250\) −11.9897 + 6.92225i −0.758295 + 0.437802i
\(251\) −1.76834 + 3.06285i −0.111616 + 0.193325i −0.916422 0.400213i \(-0.868936\pi\)
0.804806 + 0.593538i \(0.202269\pi\)
\(252\) 0 0
\(253\) −0.158825 0.592742i −0.00998523 0.0372654i
\(254\) 2.92310 0.783243i 0.183412 0.0491451i
\(255\) 0 0
\(256\) 0.866033 1.50001i 0.0541271 0.0937508i
\(257\) 10.0381 + 17.3866i 0.626163 + 1.08455i 0.988315 + 0.152426i \(0.0487087\pi\)
−0.362152 + 0.932119i \(0.617958\pi\)
\(258\) 0 0
\(259\) 11.1526 + 4.51388i 0.692987 + 0.280479i
\(260\) 0.597150 0.715260i 0.0370337 0.0443585i
\(261\) 0 0
\(262\) −2.57755 + 9.61953i −0.159241 + 0.594297i
\(263\) −10.5381 18.2526i −0.649809 1.12550i −0.983168 0.182702i \(-0.941516\pi\)
0.333360 0.942800i \(-0.391818\pi\)
\(264\) 0 0
\(265\) −32.1133 32.1133i −1.97271 1.97271i
\(266\) −0.699382 + 5.66731i −0.0428819 + 0.347485i
\(267\) 0 0
\(268\) −0.802164 0.802164i −0.0489999 0.0489999i
\(269\) 21.4982 + 12.4120i 1.31077 + 0.756773i 0.982224 0.187715i \(-0.0601081\pi\)
0.328546 + 0.944488i \(0.393441\pi\)
\(270\) 0 0
\(271\) −12.1049 3.24351i −0.735323 0.197029i −0.128325 0.991732i \(-0.540960\pi\)
−0.606999 + 0.794703i \(0.707627\pi\)
\(272\) 8.75848 0.531061
\(273\) 0 0
\(274\) 17.5113 1.05789
\(275\) −1.53970 0.412560i −0.0928472 0.0248783i
\(276\) 0 0
\(277\) 14.3673 + 8.29496i 0.863247 + 0.498396i 0.865098 0.501602i \(-0.167256\pi\)
−0.00185106 + 0.999998i \(0.500589\pi\)
\(278\) −19.9082 19.9082i −1.19401 1.19401i
\(279\) 0 0
\(280\) 27.0174 + 3.33412i 1.61460 + 0.199252i
\(281\) 5.40004 + 5.40004i 0.322140 + 0.322140i 0.849587 0.527448i \(-0.176851\pi\)
−0.527448 + 0.849587i \(0.676851\pi\)
\(282\) 0 0
\(283\) −12.4721 21.6023i −0.741390 1.28412i −0.951863 0.306525i \(-0.900834\pi\)
0.210473 0.977600i \(-0.432500\pi\)
\(284\) −0.000257102 0 0.000959517i −1.52562e−5 0 5.69369e-5i
\(285\) 0 0
\(286\) −1.02045 + 0.0918343i −0.0603402 + 0.00543028i
\(287\) 12.8921 + 5.21792i 0.760994 + 0.308004i
\(288\) 0 0
\(289\) 5.91268 + 10.2411i 0.347805 + 0.602416i
\(290\) −23.6057 + 40.8863i −1.38618 + 2.40093i
\(291\) 0 0
\(292\) −0.221676 + 0.0593978i −0.0129726 + 0.00347599i
\(293\) 3.65015 + 13.6225i 0.213244 + 0.795838i 0.986777 + 0.162082i \(0.0518209\pi\)
−0.773533 + 0.633756i \(0.781512\pi\)
\(294\) 0 0
\(295\) 3.52767 6.11011i 0.205389 0.355744i
\(296\) 11.3310 6.54195i 0.658600 0.380243i
\(297\) 0 0
\(298\) 15.6185i 0.904756i
\(299\) 9.80901 + 4.54436i 0.567270 + 0.262807i
\(300\) 0 0
\(301\) −3.24796 + 4.30471i −0.187210 + 0.248119i
\(302\) 9.01337 + 15.6116i 0.518661 + 0.898348i
\(303\) 0 0
\(304\) 4.23214 + 4.23214i 0.242730 + 0.242730i
\(305\) 0.909040 + 3.39258i 0.0520515 + 0.194259i
\(306\) 0 0
\(307\) −6.57661 + 6.57661i −0.375347 + 0.375347i −0.869420 0.494073i \(-0.835507\pi\)
0.494073 + 0.869420i \(0.335507\pi\)
\(308\) 0.0240726 + 0.0308505i 0.00137167 + 0.00175787i
\(309\) 0 0
\(310\) −5.00155 + 18.6660i −0.284069 + 1.06016i
\(311\) −6.01960 −0.341340 −0.170670 0.985328i \(-0.554593\pi\)
−0.170670 + 0.985328i \(0.554593\pi\)
\(312\) 0 0
\(313\) 4.19182i 0.236935i −0.992958 0.118468i \(-0.962202\pi\)
0.992958 0.118468i \(-0.0377982\pi\)
\(314\) 7.30479 27.2618i 0.412233 1.53847i
\(315\) 0 0
\(316\) −0.796254 0.459718i −0.0447928 0.0258611i
\(317\) 10.1411 10.1411i 0.569578 0.569578i −0.362432 0.932010i \(-0.618054\pi\)
0.932010 + 0.362432i \(0.118054\pi\)
\(318\) 0 0
\(319\) −1.87978 + 0.503685i −0.105247 + 0.0282009i
\(320\) 20.9065 20.9065i 1.16871 1.16871i
\(321\) 0 0
\(322\) 1.52618 + 10.9078i 0.0850509 + 0.607870i
\(323\) 0.915214 3.41562i 0.0509239 0.190050i
\(324\) 0 0
\(325\) 22.9627 16.1639i 1.27374 0.896612i
\(326\) −0.278368 −0.0154174
\(327\) 0 0
\(328\) 13.0983 7.56230i 0.723232 0.417558i
\(329\) 21.6911 + 27.7984i 1.19587 + 1.53258i
\(330\) 0 0
\(331\) 3.99969 + 14.9270i 0.219843 + 0.820465i 0.984405 + 0.175915i \(0.0562884\pi\)
−0.764563 + 0.644550i \(0.777045\pi\)
\(332\) 0.0893539 + 0.333473i 0.00490393 + 0.0183017i
\(333\) 0 0
\(334\) −16.9064 9.76092i −0.925077 0.534094i
\(335\) −28.0691 48.6170i −1.53358 2.65623i
\(336\) 0 0
\(337\) 32.5729i 1.77436i −0.461427 0.887178i \(-0.652662\pi\)
0.461427 0.887178i \(-0.347338\pi\)
\(338\) 10.2792 14.8366i 0.559113 0.807007i
\(339\) 0 0
\(340\) −0.567830 0.152150i −0.0307949 0.00825147i
\(341\) −0.689850 + 0.398285i −0.0373574 + 0.0215683i
\(342\) 0 0
\(343\) 6.66883 17.2779i 0.360083 0.932920i
\(344\) 1.51779 + 5.66447i 0.0818337 + 0.305408i
\(345\) 0 0
\(346\) 12.4256 12.4256i 0.668004 0.668004i
\(347\) 11.6943 20.2551i 0.627783 1.08735i −0.360213 0.932870i \(-0.617296\pi\)
0.987996 0.154481i \(-0.0493706\pi\)
\(348\) 0 0
\(349\) 21.3942 + 5.73255i 1.14520 + 0.306856i 0.781041 0.624479i \(-0.214689\pi\)
0.364162 + 0.931336i \(0.381356\pi\)
\(350\) 26.5202 + 10.7337i 1.41756 + 0.573743i
\(351\) 0 0
\(352\) 0.0836244 0.00445720
\(353\) 3.15762 11.7844i 0.168063 0.627220i −0.829566 0.558408i \(-0.811412\pi\)
0.997630 0.0688124i \(-0.0219210\pi\)
\(354\) 0 0
\(355\) −0.0245787 + 0.0425715i −0.00130450 + 0.00225946i
\(356\) 0.626164 + 0.626164i 0.0331866 + 0.0331866i
\(357\) 0 0
\(358\) −13.7965 + 3.69677i −0.729169 + 0.195380i
\(359\) −7.63230 7.63230i −0.402818 0.402818i 0.476407 0.879225i \(-0.341939\pi\)
−0.879225 + 0.476407i \(0.841939\pi\)
\(360\) 0 0
\(361\) −14.3618 + 8.29179i −0.755884 + 0.436410i
\(362\) −11.5423 3.09274i −0.606648 0.162551i
\(363\) 0 0
\(364\) −0.688987 0.0227676i −0.0361127 0.00119335i
\(365\) −11.3568 −0.594440
\(366\) 0 0
\(367\) −29.9667 + 17.3013i −1.56425 + 0.903118i −0.567427 + 0.823423i \(0.692061\pi\)
−0.996819 + 0.0796947i \(0.974605\pi\)
\(368\) 9.99759 + 5.77211i 0.521160 + 0.300892i
\(369\) 0 0
\(370\) 21.8093 5.84380i 1.13381 0.303804i
\(371\) −4.11526 + 33.3473i −0.213654 + 1.73130i
\(372\) 0 0
\(373\) 7.12384 12.3388i 0.368858 0.638881i −0.620529 0.784183i \(-0.713082\pi\)
0.989387 + 0.145302i \(0.0464154\pi\)
\(374\) 0.323206 + 0.559809i 0.0167126 + 0.0289471i
\(375\) 0 0
\(376\) 38.3442 1.97745
\(377\) 14.4117 31.1076i 0.742238 1.60212i
\(378\) 0 0
\(379\) 21.6859 + 5.81071i 1.11393 + 0.298476i 0.768424 0.639941i \(-0.221041\pi\)
0.345504 + 0.938417i \(0.387708\pi\)
\(380\) −0.200859 0.347898i −0.0103038 0.0178468i
\(381\) 0 0
\(382\) 15.9195 15.9195i 0.814515 0.814515i
\(383\) 13.1230 3.51630i 0.670554 0.179674i 0.0925494 0.995708i \(-0.470498\pi\)
0.578004 + 0.816034i \(0.303832\pi\)
\(384\) 0 0
\(385\) 0.755532 + 1.78296i 0.0385055 + 0.0908680i
\(386\) −13.9934 + 24.2372i −0.712244 + 1.23364i
\(387\) 0 0
\(388\) 0.567766 + 0.152132i 0.0288240 + 0.00772336i
\(389\) 20.6138i 1.04516i 0.852590 + 0.522581i \(0.175031\pi\)
−0.852590 + 0.522581i \(0.824969\pi\)
\(390\) 0 0
\(391\) 6.82049i 0.344927i
\(392\) −10.3519 17.2763i −0.522849 0.872587i
\(393\) 0 0
\(394\) 3.02848 + 1.74849i 0.152572 + 0.0880877i
\(395\) −32.1726 32.1726i −1.61878 1.61878i
\(396\) 0 0
\(397\) 4.36581 + 16.2934i 0.219114 + 0.817743i 0.984678 + 0.174384i \(0.0557933\pi\)
−0.765564 + 0.643360i \(0.777540\pi\)
\(398\) 16.1634 16.1634i 0.810199 0.810199i
\(399\) 0 0
\(400\) 25.9696 14.9935i 1.29848 0.749677i
\(401\) −3.52338 + 13.1494i −0.175949 + 0.656652i 0.820439 + 0.571735i \(0.193729\pi\)
−0.996388 + 0.0849175i \(0.972937\pi\)
\(402\) 0 0
\(403\) 2.40243 13.8258i 0.119674 0.688712i
\(404\) 0.782878i 0.0389496i
\(405\) 0 0
\(406\) 34.5923 4.84003i 1.71679 0.240206i
\(407\) 0.806018 + 0.465355i 0.0399528 + 0.0230668i
\(408\) 0 0
\(409\) 30.8141 8.25662i 1.52366 0.408263i 0.602715 0.797956i \(-0.294086\pi\)
0.920945 + 0.389693i \(0.127419\pi\)
\(410\) 25.2110 6.75526i 1.24508 0.333618i
\(411\) 0 0
\(412\) −0.150771 0.0870475i −0.00742794 0.00428852i
\(413\) −5.16952 + 0.723300i −0.254375 + 0.0355913i
\(414\) 0 0
\(415\) 17.0843i 0.838635i
\(416\) −0.944140 + 1.13088i −0.0462903 + 0.0554459i
\(417\) 0 0
\(418\) −0.114328 + 0.426678i −0.00559196 + 0.0208695i
\(419\) −25.3302 + 14.6244i −1.23746 + 0.714449i −0.968575 0.248722i \(-0.919989\pi\)
−0.268888 + 0.963172i \(0.586656\pi\)
\(420\) 0 0
\(421\) 19.1090 19.1090i 0.931318 0.931318i −0.0664703 0.997788i \(-0.521174\pi\)
0.997788 + 0.0664703i \(0.0211738\pi\)
\(422\) 2.63510 + 9.83434i 0.128275 + 0.478728i
\(423\) 0 0
\(424\) 25.8373 + 25.8373i 1.25477 + 1.25477i
\(425\) −15.3432 8.85840i −0.744254 0.429695i
\(426\) 0 0
\(427\) 1.56511 2.07432i 0.0757409 0.100384i
\(428\) 0.322018i 0.0155653i
\(429\) 0 0
\(430\) 10.1199i 0.488026i
\(431\) 26.6643 + 7.14467i 1.28437 + 0.344147i 0.835520 0.549460i \(-0.185166\pi\)
0.448852 + 0.893606i \(0.351833\pi\)
\(432\) 0 0
\(433\) −11.9677 + 20.7287i −0.575132 + 0.996157i 0.420896 + 0.907109i \(0.361716\pi\)
−0.996027 + 0.0890483i \(0.971617\pi\)
\(434\) 13.1640 5.57829i 0.631894 0.267767i
\(435\) 0 0
\(436\) 1.18446 0.317375i 0.0567253 0.0151995i
\(437\) 3.29570 3.29570i 0.157655 0.157655i
\(438\) 0 0
\(439\) 5.23894 + 9.07411i 0.250041 + 0.433083i 0.963537 0.267576i \(-0.0862226\pi\)
−0.713496 + 0.700659i \(0.752889\pi\)
\(440\) 2.03407 + 0.545027i 0.0969705 + 0.0259832i
\(441\) 0 0
\(442\) −11.2196 1.94956i −0.533660 0.0927312i
\(443\) 19.7645 0.939041 0.469521 0.882922i \(-0.344427\pi\)
0.469521 + 0.882922i \(0.344427\pi\)
\(444\) 0 0
\(445\) 21.9105 + 37.9502i 1.03866 + 1.79901i
\(446\) 1.83460 3.17761i 0.0868706 0.150464i
\(447\) 0 0
\(448\) −21.7098 2.67913i −1.02569 0.126577i
\(449\) −27.2909 + 7.31258i −1.28794 + 0.345102i −0.836877 0.547391i \(-0.815621\pi\)
−0.451061 + 0.892493i \(0.648954\pi\)
\(450\) 0 0
\(451\) 0.931733 + 0.537936i 0.0438736 + 0.0253304i
\(452\) 0.0298313 0.0172231i 0.00140315 0.000810107i
\(453\) 0 0
\(454\) −25.5084 −1.19717
\(455\) −32.6417 9.91272i −1.53026 0.464715i
\(456\) 0 0
\(457\) −18.9311 5.07256i −0.885558 0.237285i −0.212754 0.977106i \(-0.568243\pi\)
−0.672804 + 0.739821i \(0.734910\pi\)
\(458\) −9.85884 + 5.69201i −0.460673 + 0.265970i
\(459\) 0 0
\(460\) −0.547893 0.547893i −0.0255456 0.0255456i
\(461\) −14.1139 + 3.78182i −0.657351 + 0.176137i −0.572050 0.820218i \(-0.693852\pi\)
−0.0853010 + 0.996355i \(0.527185\pi\)
\(462\) 0 0
\(463\) 0.639781 + 0.639781i 0.0297332 + 0.0297332i 0.721817 0.692084i \(-0.243307\pi\)
−0.692084 + 0.721817i \(0.743307\pi\)
\(464\) 18.3052 31.7056i 0.849800 1.47190i
\(465\) 0 0
\(466\) −7.55395 + 28.1917i −0.349930 + 1.30596i
\(467\) −18.2232 −0.843268 −0.421634 0.906766i \(-0.638543\pi\)
−0.421634 + 0.906766i \(0.638543\pi\)
\(468\) 0 0
\(469\) −15.5823 + 38.4998i −0.719526 + 1.77775i
\(470\) 63.9154 + 17.1261i 2.94820 + 0.789967i
\(471\) 0 0
\(472\) −2.83825 + 4.91599i −0.130641 + 0.226277i
\(473\) −0.294970 + 0.294970i −0.0135627 + 0.0135627i
\(474\) 0 0
\(475\) −3.13349 11.6943i −0.143774 0.536573i
\(476\) 0.169694 + 0.400456i 0.00777792 + 0.0183549i
\(477\) 0 0
\(478\) 17.6498 10.1901i 0.807284 0.466086i
\(479\) 37.9467 + 10.1678i 1.73383 + 0.464578i 0.981060 0.193706i \(-0.0620507\pi\)
0.752770 + 0.658284i \(0.228717\pi\)
\(480\) 0 0
\(481\) −15.3933 + 5.64607i −0.701873 + 0.257439i
\(482\) 1.90700i 0.0868616i
\(483\) 0 0
\(484\) −0.395943 0.685794i −0.0179974 0.0311725i
\(485\) 25.1905 + 14.5437i 1.14384 + 0.660396i
\(486\) 0 0
\(487\) 5.80987 + 21.6827i 0.263270 + 0.982538i 0.963301 + 0.268425i \(0.0865031\pi\)
−0.700030 + 0.714113i \(0.746830\pi\)
\(488\) −0.731383 2.72956i −0.0331081 0.123561i
\(489\) 0 0
\(490\) −9.53910 33.4213i −0.430932 1.50982i
\(491\) −5.46145 + 3.15317i −0.246472 + 0.142301i −0.618148 0.786062i \(-0.712117\pi\)
0.371676 + 0.928363i \(0.378783\pi\)
\(492\) 0 0
\(493\) −21.6300 −0.974166
\(494\) −4.47931 6.36339i −0.201534 0.286302i
\(495\) 0 0
\(496\) 3.87849 14.4747i 0.174149 0.649934i
\(497\) 0.0360181 0.00503952i 0.00161563 0.000226053i
\(498\) 0 0
\(499\) −0.186545 + 0.186545i −0.00835090 + 0.00835090i −0.711270 0.702919i \(-0.751880\pi\)
0.702919 + 0.711270i \(0.251880\pi\)
\(500\) −0.696025 + 0.186499i −0.0311272 + 0.00834050i
\(501\) 0 0
\(502\) 3.47219 3.47219i 0.154971 0.154971i
\(503\) −14.8498 8.57353i −0.662119 0.382275i 0.130965 0.991387i \(-0.458193\pi\)
−0.793084 + 0.609112i \(0.791526\pi\)
\(504\) 0 0
\(505\) 10.0270 37.4212i 0.446195 1.66522i
\(506\) 0.852012i 0.0378765i
\(507\) 0 0
\(508\) 0.157509 0.00698831
\(509\) −4.12567 + 15.3972i −0.182867 + 0.682470i 0.812210 + 0.583366i \(0.198264\pi\)
−0.995077 + 0.0991045i \(0.968402\pi\)
\(510\) 0 0
\(511\) 5.16889 + 6.62424i 0.228658 + 0.293039i
\(512\) −16.7789 + 16.7789i −0.741531 + 0.741531i
\(513\) 0 0
\(514\) −7.21446 26.9247i −0.318216 1.18760i
\(515\) −6.09188 6.09188i −0.268440 0.268440i
\(516\) 0 0
\(517\) 1.36379 + 2.36215i 0.0599793 + 0.103887i
\(518\) −13.3349 10.0614i −0.585900 0.442071i
\(519\) 0 0
\(520\) −30.3357 + 21.3539i −1.33031 + 0.936430i
\(521\) 5.95318i 0.260814i −0.991461 0.130407i \(-0.958372\pi\)
0.991461 0.130407i \(-0.0416283\pi\)
\(522\) 0 0
\(523\) −7.98659 + 4.61106i −0.349229 + 0.201628i −0.664346 0.747425i \(-0.731290\pi\)
0.315116 + 0.949053i \(0.397956\pi\)
\(524\) −0.259170 + 0.448895i −0.0113219 + 0.0196101i
\(525\) 0 0
\(526\) 7.57379 + 28.2658i 0.330233 + 1.23245i
\(527\) −8.55188 + 2.29147i −0.372526 + 0.0998179i
\(528\) 0 0
\(529\) −7.00508 + 12.1332i −0.304569 + 0.527528i
\(530\) 31.5278 + 54.6078i 1.36948 + 2.37201i
\(531\) 0 0
\(532\) −0.111505 + 0.275500i −0.00483437 + 0.0119444i
\(533\) −17.7942 + 6.52669i −0.770751 + 0.282702i
\(534\) 0 0
\(535\) 4.12435 15.3923i 0.178311 0.665467i
\(536\) 22.5834 + 39.1156i 0.975455 + 1.68954i
\(537\) 0 0
\(538\) −24.3714 24.3714i −1.05073 1.05073i
\(539\) 0.696103 1.25218i 0.0299833 0.0539354i
\(540\) 0 0
\(541\) −18.1277 18.1277i −0.779369 0.779369i 0.200354 0.979723i \(-0.435791\pi\)
−0.979723 + 0.200354i \(0.935791\pi\)
\(542\) 15.0686 + 8.69987i 0.647253 + 0.373691i
\(543\) 0 0
\(544\) 0.897782 + 0.240560i 0.0384921 + 0.0103139i
\(545\) 60.6815 2.59931
\(546\) 0 0
\(547\) −9.47939 −0.405309 −0.202655 0.979250i \(-0.564957\pi\)
−0.202655 + 0.979250i \(0.564957\pi\)
\(548\) 0.880370 + 0.235894i 0.0376075 + 0.0100769i
\(549\) 0 0
\(550\) 1.91666 + 1.10659i 0.0817267 + 0.0471850i
\(551\) −10.4517 10.4517i −0.445259 0.445259i
\(552\) 0 0
\(553\) −4.12286 + 33.4088i −0.175322 + 1.42069i
\(554\) −16.2875 16.2875i −0.691988 0.691988i
\(555\) 0 0
\(556\) −0.732690 1.26906i −0.0310730 0.0538200i
\(557\) 4.20935 15.7095i 0.178356 0.665633i −0.817600 0.575787i \(-0.804696\pi\)
0.995956 0.0898459i \(-0.0286375\pi\)
\(558\) 0 0
\(559\) −0.658691 7.31925i −0.0278597 0.309571i
\(560\) −33.7678 13.6672i −1.42695 0.577543i
\(561\) 0 0
\(562\) −5.30159 9.18262i −0.223634 0.387345i
\(563\) 8.25217 14.2932i 0.347788 0.602386i −0.638068 0.769980i \(-0.720266\pi\)
0.985856 + 0.167594i \(0.0535997\pi\)
\(564\) 0 0
\(565\) 1.64651 0.441182i 0.0692693 0.0185607i
\(566\) 8.96375 + 33.4532i 0.376774 + 1.40614i
\(567\) 0 0
\(568\) 0.0197752 0.0342516i 0.000829748 0.00143717i
\(569\) 17.3607 10.0232i 0.727797 0.420194i −0.0898186 0.995958i \(-0.528629\pi\)
0.817616 + 0.575764i \(0.195295\pi\)
\(570\) 0 0
\(571\) 37.7943i 1.58164i −0.612046 0.790822i \(-0.709653\pi\)
0.612046 0.790822i \(-0.290347\pi\)
\(572\) −0.0525394 0.00912950i −0.00219678 0.000381724i
\(573\) 0 0
\(574\) −15.4147 11.6306i −0.643398 0.485453i
\(575\) −11.6759 20.2233i −0.486920 0.843370i
\(576\) 0 0
\(577\) −7.30060 7.30060i −0.303928 0.303928i 0.538621 0.842548i \(-0.318946\pi\)
−0.842548 + 0.538621i \(0.818946\pi\)
\(578\) −4.24947 15.8592i −0.176755 0.659657i
\(579\) 0 0
\(580\) −1.73755 + 1.73755i −0.0721477 + 0.0721477i
\(581\) 9.96504 7.77571i 0.413419 0.322591i
\(582\) 0 0
\(583\) −0.672722 + 2.51063i −0.0278613 + 0.103980i
\(584\) 9.13726 0.378102
\(585\) 0 0
\(586\) 19.5812i 0.808890i
\(587\) −5.01367 + 18.7113i −0.206936 + 0.772296i 0.781915 + 0.623386i \(0.214243\pi\)
−0.988851 + 0.148911i \(0.952423\pi\)
\(588\) 0 0
\(589\) −5.23956 3.02506i −0.215892 0.124645i
\(590\) −6.92671 + 6.92671i −0.285168 + 0.285168i
\(591\) 0 0
\(592\) −16.9122 + 4.53161i −0.695088 + 0.186248i
\(593\) 11.9510 11.9510i 0.490769 0.490769i −0.417780 0.908548i \(-0.637192\pi\)
0.908548 + 0.417780i \(0.137192\pi\)
\(594\) 0 0
\(595\) 2.98232 + 21.3150i 0.122263 + 0.873831i
\(596\) 0.210397 0.785213i 0.00861820 0.0321636i
\(597\) 0 0
\(598\) −11.5220 9.61942i −0.471171 0.393367i
\(599\) −14.2777 −0.583372 −0.291686 0.956514i \(-0.594216\pi\)
−0.291686 + 0.956514i \(0.594216\pi\)
\(600\) 0 0
\(601\) 20.5084 11.8405i 0.836556 0.482986i −0.0195364 0.999809i \(-0.506219\pi\)
0.856092 + 0.516824i \(0.172886\pi\)
\(602\) 5.90281 4.60596i 0.240581 0.187725i
\(603\) 0 0
\(604\) 0.242838 + 0.906285i 0.00988095 + 0.0368762i
\(605\) −10.1424 37.8518i −0.412346 1.53890i
\(606\) 0 0
\(607\) 12.8523 + 7.42026i 0.521657 + 0.301179i 0.737612 0.675224i \(-0.235953\pi\)
−0.215955 + 0.976403i \(0.569287\pi\)
\(608\) 0.317573 + 0.550052i 0.0128793 + 0.0223076i
\(609\) 0 0
\(610\) 4.87652i 0.197445i
\(611\) −47.3416 8.22630i −1.91524 0.332801i
\(612\) 0 0
\(613\) 15.9485 + 4.27337i 0.644152 + 0.172600i 0.566083 0.824348i \(-0.308458\pi\)
0.0780686 + 0.996948i \(0.475125\pi\)
\(614\) 11.1833 6.45671i 0.451323 0.260571i
\(615\) 0 0
\(616\) −0.607876 1.43451i −0.0244920 0.0577980i
\(617\) −1.60910 6.00524i −0.0647799 0.241762i 0.925942 0.377665i \(-0.123273\pi\)
−0.990722 + 0.135903i \(0.956606\pi\)
\(618\) 0 0
\(619\) 19.0180 19.0180i 0.764399 0.764399i −0.212715 0.977114i \(-0.568231\pi\)
0.977114 + 0.212715i \(0.0682306\pi\)
\(620\) −0.502901 + 0.871050i −0.0201970 + 0.0349822i
\(621\) 0 0
\(622\) 8.07300 + 2.16316i 0.323698 + 0.0867346i
\(623\) 12.1635 30.0527i 0.487320 1.20404i
\(624\) 0 0
\(625\) 3.28341 0.131336
\(626\) −1.50634 + 5.62173i −0.0602053 + 0.224689i
\(627\) 0 0
\(628\) 0.734488 1.27217i 0.0293093 0.0507652i
\(629\) 7.31464 + 7.31464i 0.291654 + 0.291654i
\(630\) 0 0
\(631\) −31.4581 + 8.42917i −1.25233 + 0.335560i −0.823235 0.567701i \(-0.807833\pi\)
−0.429092 + 0.903261i \(0.641166\pi\)
\(632\) 25.8850 + 25.8850i 1.02965 + 1.02965i
\(633\) 0 0
\(634\) −17.2446 + 9.95615i −0.684869 + 0.395409i
\(635\) 7.52884 + 2.01735i 0.298773 + 0.0800559i
\(636\) 0 0
\(637\) 9.07450 + 23.5511i 0.359545 + 0.933128i
\(638\) 2.70201 0.106973
\(639\) 0 0
\(640\) −33.0202 + 19.0642i −1.30524 + 0.753579i
\(641\) −10.6137 6.12780i −0.419214 0.242034i 0.275527 0.961293i \(-0.411148\pi\)
−0.694741 + 0.719260i \(0.744481\pi\)
\(642\) 0 0
\(643\) −10.2233 + 2.73933i −0.403169 + 0.108029i −0.454704 0.890642i \(-0.650255\pi\)
0.0515356 + 0.998671i \(0.483588\pi\)
\(644\) −0.0702114 + 0.568945i −0.00276672 + 0.0224196i
\(645\) 0 0
\(646\) −2.45482 + 4.25188i −0.0965837 + 0.167288i
\(647\) 12.5880 + 21.8030i 0.494884 + 0.857164i 0.999983 0.00589775i \(-0.00187732\pi\)
−0.505099 + 0.863061i \(0.668544\pi\)
\(648\) 0 0
\(649\) −0.403791 −0.0158502
\(650\) −36.6043 + 13.4260i −1.43574 + 0.526612i
\(651\) 0 0
\(652\) −0.0139948 0.00374990i −0.000548080 0.000146857i
\(653\) −5.72589 9.91753i −0.224071 0.388103i 0.731969 0.681338i \(-0.238602\pi\)
−0.956040 + 0.293235i \(0.905268\pi\)
\(654\) 0 0
\(655\) −18.1376 + 18.1376i −0.708693 + 0.708693i
\(656\) −19.5500 + 5.23841i −0.763300 + 0.204526i
\(657\) 0 0
\(658\) −19.1009 45.0757i −0.744632 1.75723i
\(659\) −10.2755 + 17.7977i −0.400276 + 0.693298i −0.993759 0.111548i \(-0.964419\pi\)
0.593483 + 0.804846i \(0.297752\pi\)
\(660\) 0 0
\(661\) −0.197372 0.0528857i −0.00767689 0.00205702i 0.254979 0.966947i \(-0.417932\pi\)
−0.262655 + 0.964890i \(0.584598\pi\)
\(662\) 21.4562i 0.833921i
\(663\) 0 0
\(664\) 13.7454i 0.533427i
\(665\) −8.85846 + 11.7406i −0.343517 + 0.455281i
\(666\) 0 0
\(667\) −24.6901 14.2549i −0.956006 0.551950i
\(668\) −0.718471 0.718471i −0.0277985 0.0277985i
\(669\) 0 0
\(670\) 20.1733 + 75.2879i 0.779364 + 2.90863i
\(671\) 0.142138 0.142138i 0.00548718 0.00548718i
\(672\) 0 0
\(673\) 22.6738 13.0907i 0.874010 0.504610i 0.00533138 0.999986i \(-0.498303\pi\)
0.868679 + 0.495376i \(0.164970\pi\)
\(674\) −11.7051 + 43.6841i −0.450864 + 1.68265i
\(675\) 0 0
\(676\) 0.716644 0.607434i 0.0275632 0.0233628i
\(677\) 17.3226i 0.665762i 0.942969 + 0.332881i \(0.108021\pi\)
−0.942969 + 0.332881i \(0.891979\pi\)
\(678\) 0 0
\(679\) −2.98199 21.3127i −0.114438 0.817905i
\(680\) 20.2697 + 11.7027i 0.777306 + 0.448778i
\(681\) 0 0
\(682\) 1.06830 0.286249i 0.0409071 0.0109610i
\(683\) 33.8713 9.07578i 1.29605 0.347275i 0.456094 0.889932i \(-0.349248\pi\)
0.839954 + 0.542657i \(0.182582\pi\)
\(684\) 0 0
\(685\) 39.0600 + 22.5513i 1.49240 + 0.861640i
\(686\) −15.1526 + 20.7753i −0.578527 + 0.793205i
\(687\) 0 0
\(688\) 7.84757i 0.299186i
\(689\) −26.3569 37.4431i −1.00412 1.42647i
\(690\) 0 0
\(691\) 4.51121 16.8361i 0.171614 0.640474i −0.825489 0.564418i \(-0.809101\pi\)
0.997104 0.0760557i \(-0.0242327\pi\)
\(692\) 0.792075 0.457305i 0.0301102 0.0173841i
\(693\) 0 0
\(694\) −22.9622 + 22.9622i −0.871631 + 0.871631i
\(695\) −18.7684 70.0445i −0.711925 2.65694i
\(696\) 0 0
\(697\) 8.45551 + 8.45551i 0.320275 + 0.320275i
\(698\) −26.6321 15.3761i −1.00804 0.581993i
\(699\) 0 0
\(700\) 1.18869 + 0.896886i 0.0449284 + 0.0338991i
\(701\) 18.7752i 0.709130i 0.935031 + 0.354565i \(0.115371\pi\)
−0.935031 + 0.354565i \(0.884629\pi\)
\(702\) 0 0
\(703\) 7.06894i 0.266610i
\(704\) −1.63448 0.437957i −0.0616018 0.0165061i
\(705\) 0 0
\(706\) −8.46949 + 14.6696i −0.318754 + 0.552097i
\(707\) −26.3909 + 11.1832i −0.992533 + 0.420588i
\(708\) 0 0
\(709\) −0.672100 + 0.180089i −0.0252412 + 0.00676337i −0.271418 0.962462i \(-0.587492\pi\)
0.246176 + 0.969225i \(0.420826\pi\)
\(710\) 0.0482611 0.0482611i 0.00181121 0.00181121i
\(711\) 0 0
\(712\) −17.6285 30.5334i −0.660655 1.14429i
\(713\) −11.2719 3.02030i −0.422136 0.113111i
\(714\) 0 0
\(715\) −2.39443 1.10930i −0.0895467 0.0414856i
\(716\) −0.743412 −0.0277826
\(717\) 0 0
\(718\) 7.49315 + 12.9785i 0.279642 + 0.484354i
\(719\) −15.1031 + 26.1593i −0.563249 + 0.975576i 0.433961 + 0.900931i \(0.357115\pi\)
−0.997210 + 0.0746442i \(0.976218\pi\)
\(720\) 0 0
\(721\) −0.780663 + 6.32595i −0.0290734 + 0.235591i
\(722\) 22.2406 5.95934i 0.827708 0.221784i
\(723\) 0 0
\(724\) −0.538619 0.310972i −0.0200176 0.0115572i
\(725\) −64.1346 + 37.0281i −2.38190 + 1.37519i
\(726\) 0 0
\(727\) −8.42295 −0.312390 −0.156195 0.987726i \(-0.549923\pi\)
−0.156195 + 0.987726i \(0.549923\pi\)
\(728\) 26.2624 + 7.97544i 0.973348 + 0.295589i
\(729\) 0 0
\(730\) 15.2308 + 4.08107i 0.563716 + 0.151047i
\(731\) −4.01529 + 2.31823i −0.148511 + 0.0857428i
\(732\) 0 0
\(733\) 22.1020 + 22.1020i 0.816357 + 0.816357i 0.985578 0.169221i \(-0.0541253\pi\)
−0.169221 + 0.985578i \(0.554125\pi\)
\(734\) 46.4061 12.4345i 1.71288 0.458965i
\(735\) 0 0
\(736\) 0.866260 + 0.866260i 0.0319308 + 0.0319308i
\(737\) −1.60645 + 2.78245i −0.0591743 + 0.102493i
\(738\) 0 0
\(739\) 13.4932 50.3573i 0.496356 1.85242i −0.0259454 0.999663i \(-0.508260\pi\)
0.522301 0.852761i \(-0.325074\pi\)
\(740\) 1.17517 0.0432003
\(741\) 0 0
\(742\) 17.5025 43.2438i 0.642536 1.58753i
\(743\) −39.2722 10.5230i −1.44076 0.386050i −0.547958 0.836506i \(-0.684595\pi\)
−0.892799 + 0.450456i \(0.851261\pi\)
\(744\) 0 0
\(745\) 20.1138 34.8381i 0.736911 1.27637i
\(746\) −13.9879 + 13.9879i −0.512134 + 0.512134i
\(747\) 0 0
\(748\) 0.00870782 + 0.0324980i 0.000318389 + 0.00118825i
\(749\) −10.8553 + 4.59994i −0.396643 + 0.168078i
\(750\) 0 0
\(751\) 34.2507 19.7747i 1.24983 0.721588i 0.278752 0.960363i \(-0.410079\pi\)
0.971075 + 0.238775i \(0.0767459\pi\)
\(752\) −49.5637 13.2805i −1.80740 0.484292i
\(753\) 0 0
\(754\) −30.5063 + 36.5401i −1.11097 + 1.33071i
\(755\) 46.4302i 1.68977i
\(756\) 0 0
\(757\) 10.7369 + 18.5969i 0.390241 + 0.675917i 0.992481 0.122398i \(-0.0390584\pi\)
−0.602240 + 0.798315i \(0.705725\pi\)
\(758\) −26.9953 15.5857i −0.980512 0.566099i
\(759\) 0 0
\(760\) 4.13960 + 15.4492i 0.150159 + 0.560402i
\(761\) 5.26977 + 19.6670i 0.191029 + 0.712930i 0.993259 + 0.115915i \(0.0369800\pi\)
−0.802230 + 0.597015i \(0.796353\pi\)
\(762\) 0 0
\(763\) −27.6185 35.3947i −0.999856 1.28137i
\(764\) 1.01480 0.585894i 0.0367141 0.0211969i
\(765\) 0 0
\(766\) −18.8631 −0.681551
\(767\) 4.55890 5.46060i 0.164612 0.197171i
\(768\) 0 0
\(769\) −11.7253 + 43.7592i −0.422823 + 1.57800i 0.345807 + 0.938306i \(0.387605\pi\)
−0.768631 + 0.639693i \(0.779062\pi\)
\(770\) −0.372550 2.66266i −0.0134258 0.0959557i
\(771\) 0 0
\(772\) −1.03001 + 1.03001i −0.0370708 + 0.0370708i
\(773\) 19.0521 5.10499i 0.685256 0.183614i 0.100638 0.994923i \(-0.467911\pi\)
0.584617 + 0.811309i \(0.301245\pi\)
\(774\) 0 0
\(775\) −21.4342 + 21.4342i −0.769940 + 0.769940i
\(776\) −20.2674 11.7014i −0.727557 0.420055i
\(777\) 0 0
\(778\) 7.40762 27.6456i 0.265576 0.991143i
\(779\) 8.17149i 0.292774i
\(780\) 0 0
\(781\) 0.00281338 0.000100670
\(782\) −2.45096 + 9.14710i −0.0876461 + 0.327100i
\(783\) 0 0
\(784\) 7.39716 + 25.9168i 0.264184 + 0.925598i
\(785\) 51.4020 51.4020i 1.83461 1.83461i
\(786\) 0 0
\(787\) −6.36046 23.7376i −0.226726 0.846153i −0.981706 0.190405i \(-0.939020\pi\)
0.754980 0.655748i \(-0.227647\pi\)
\(788\) 0.128701