Properties

Label 405.4.e.s.136.2
Level $405$
Weight $4$
Character 405.136
Analytic conductor $23.896$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.148347072.2
Defining polynomial: \( x^{6} + 29x^{4} + 223x^{2} + 243 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 136.2
Root \(-3.41374i\) of defining polynomial
Character \(\chi\) \(=\) 405.136
Dual form 405.4.e.s.271.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.663404 + 1.14905i) q^{2} +(3.11979 + 5.40363i) q^{4} +(2.50000 + 4.33013i) q^{5} +(12.0521 - 20.8749i) q^{7} -18.8932 q^{8} +O(q^{10})\) \(q+(-0.663404 + 1.14905i) q^{2} +(3.11979 + 5.40363i) q^{4} +(2.50000 + 4.33013i) q^{5} +(12.0521 - 20.8749i) q^{7} -18.8932 q^{8} -6.63404 q^{10} +(4.13810 - 7.16739i) q^{11} +(-43.5573 - 75.4434i) q^{13} +(15.9909 + 27.6970i) q^{14} +(-12.4245 + 21.5198i) q^{16} -51.9166 q^{17} -88.5107 q^{19} +(-15.5989 + 27.0182i) q^{20} +(5.49046 + 9.50976i) q^{22} +(-64.6224 - 111.929i) q^{23} +(-12.5000 + 21.6506i) q^{25} +115.584 q^{26} +150.400 q^{28} +(-135.554 + 234.787i) q^{29} +(-112.273 - 194.463i) q^{31} +(-92.0577 - 159.449i) q^{32} +(34.4417 - 59.6548i) q^{34} +120.521 q^{35} -70.5268 q^{37} +(58.7184 - 101.703i) q^{38} +(-47.2330 - 81.8099i) q^{40} +(183.469 + 317.778i) q^{41} +(97.7736 - 169.349i) q^{43} +51.6399 q^{44} +171.483 q^{46} +(-179.596 + 311.069i) q^{47} +(-119.008 - 206.128i) q^{49} +(-16.5851 - 28.7262i) q^{50} +(271.779 - 470.735i) q^{52} -29.4890 q^{53} +41.3810 q^{55} +(-227.703 + 394.394i) q^{56} +(-179.855 - 311.517i) q^{58} +(-429.052 - 743.140i) q^{59} +(278.406 - 482.213i) q^{61} +297.931 q^{62} +45.4941 q^{64} +(217.786 - 377.217i) q^{65} +(20.9493 + 36.2853i) q^{67} +(-161.969 - 280.538i) q^{68} +(-79.9544 + 138.485i) q^{70} +549.163 q^{71} -185.505 q^{73} +(46.7878 - 81.0388i) q^{74} +(-276.135 - 478.279i) q^{76} +(-99.7458 - 172.765i) q^{77} +(-40.2456 + 69.7075i) q^{79} -124.245 q^{80} -486.857 q^{82} +(-288.377 + 499.483i) q^{83} +(-129.792 - 224.806i) q^{85} +(129.727 + 224.694i) q^{86} +(-78.1818 + 135.415i) q^{88} -224.516 q^{89} -2099.83 q^{91} +(403.216 - 698.391i) q^{92} +(-238.290 - 412.730i) q^{94} +(-221.277 - 383.263i) q^{95} +(277.508 - 480.658i) q^{97} +315.801 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - 5 q^{4} + 15 q^{5} + 25 q^{7} - 54 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{2} - 5 q^{4} + 15 q^{5} + 25 q^{7} - 54 q^{8} - 10 q^{10} - 58 q^{11} + 47 q^{13} - 159 q^{14} + 127 q^{16} + 68 q^{17} - 10 q^{19} + 25 q^{20} - 260 q^{22} + 51 q^{23} - 75 q^{25} + 506 q^{26} + 166 q^{28} - 350 q^{29} - 638 q^{31} - 245 q^{32} + 154 q^{34} + 250 q^{35} - 828 q^{37} - 397 q^{38} - 135 q^{40} - 179 q^{41} + 836 q^{43} + 664 q^{44} + 522 q^{46} - 235 q^{47} - 892 q^{49} - 25 q^{50} + 1335 q^{52} + 1010 q^{53} - 580 q^{55} - 15 q^{56} - 1876 q^{58} - 535 q^{59} + 104 q^{61} + 696 q^{62} - 606 q^{64} - 235 q^{65} + 40 q^{67} - 830 q^{68} + 795 q^{70} + 904 q^{71} - 1420 q^{73} - 1394 q^{74} - 849 q^{76} - 2148 q^{77} + 634 q^{79} + 1270 q^{80} + 1226 q^{82} - 1734 q^{83} + 170 q^{85} - 460 q^{86} + 768 q^{88} - 1704 q^{89} - 2458 q^{91} + 1839 q^{92} - 1751 q^{94} - 25 q^{95} + 76 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.663404 + 1.14905i −0.234549 + 0.406251i −0.959141 0.282927i \(-0.908695\pi\)
0.724593 + 0.689177i \(0.242028\pi\)
\(3\) 0 0
\(4\) 3.11979 + 5.40363i 0.389974 + 0.675454i
\(5\) 2.50000 + 4.33013i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 12.0521 20.8749i 0.650754 1.12714i −0.332186 0.943214i \(-0.607786\pi\)
0.982940 0.183925i \(-0.0588804\pi\)
\(8\) −18.8932 −0.834969
\(9\) 0 0
\(10\) −6.63404 −0.209787
\(11\) 4.13810 7.16739i 0.113426 0.196459i −0.803724 0.595003i \(-0.797151\pi\)
0.917149 + 0.398544i \(0.130484\pi\)
\(12\) 0 0
\(13\) −43.5573 75.4434i −0.929278 1.60956i −0.784533 0.620087i \(-0.787097\pi\)
−0.144745 0.989469i \(-0.546236\pi\)
\(14\) 15.9909 + 27.6970i 0.305267 + 0.528738i
\(15\) 0 0
\(16\) −12.4245 + 21.5198i −0.194133 + 0.336248i
\(17\) −51.9166 −0.740684 −0.370342 0.928895i \(-0.620760\pi\)
−0.370342 + 0.928895i \(0.620760\pi\)
\(18\) 0 0
\(19\) −88.5107 −1.06872 −0.534362 0.845256i \(-0.679448\pi\)
−0.534362 + 0.845256i \(0.679448\pi\)
\(20\) −15.5989 + 27.0182i −0.174402 + 0.302072i
\(21\) 0 0
\(22\) 5.49046 + 9.50976i 0.0532077 + 0.0921585i
\(23\) −64.6224 111.929i −0.585856 1.01473i −0.994768 0.102159i \(-0.967425\pi\)
0.408912 0.912574i \(-0.365908\pi\)
\(24\) 0 0
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) 115.584 0.871844
\(27\) 0 0
\(28\) 150.400 1.01511
\(29\) −135.554 + 234.787i −0.867993 + 1.50341i −0.00394885 + 0.999992i \(0.501257\pi\)
−0.864044 + 0.503416i \(0.832076\pi\)
\(30\) 0 0
\(31\) −112.273 194.463i −0.650481 1.12667i −0.983006 0.183571i \(-0.941234\pi\)
0.332526 0.943094i \(-0.392099\pi\)
\(32\) −92.0577 159.449i −0.508552 0.880837i
\(33\) 0 0
\(34\) 34.4417 59.6548i 0.173727 0.300903i
\(35\) 120.521 0.582052
\(36\) 0 0
\(37\) −70.5268 −0.313366 −0.156683 0.987649i \(-0.550080\pi\)
−0.156683 + 0.987649i \(0.550080\pi\)
\(38\) 58.7184 101.703i 0.250668 0.434169i
\(39\) 0 0
\(40\) −47.2330 81.8099i −0.186705 0.323382i
\(41\) 183.469 + 317.778i 0.698855 + 1.21045i 0.968864 + 0.247594i \(0.0796401\pi\)
−0.270009 + 0.962858i \(0.587027\pi\)
\(42\) 0 0
\(43\) 97.7736 169.349i 0.346752 0.600592i −0.638918 0.769274i \(-0.720618\pi\)
0.985670 + 0.168682i \(0.0539512\pi\)
\(44\) 51.6399 0.176932
\(45\) 0 0
\(46\) 171.483 0.549648
\(47\) −179.596 + 311.069i −0.557378 + 0.965407i 0.440336 + 0.897833i \(0.354859\pi\)
−0.997714 + 0.0675743i \(0.978474\pi\)
\(48\) 0 0
\(49\) −119.008 206.128i −0.346962 0.600955i
\(50\) −16.5851 28.7262i −0.0469098 0.0812501i
\(51\) 0 0
\(52\) 271.779 470.735i 0.724788 1.25537i
\(53\) −29.4890 −0.0764270 −0.0382135 0.999270i \(-0.512167\pi\)
−0.0382135 + 0.999270i \(0.512167\pi\)
\(54\) 0 0
\(55\) 41.3810 0.101451
\(56\) −227.703 + 394.394i −0.543360 + 0.941126i
\(57\) 0 0
\(58\) −179.855 311.517i −0.407174 0.705245i
\(59\) −429.052 743.140i −0.946743 1.63981i −0.752224 0.658908i \(-0.771019\pi\)
−0.194519 0.980899i \(-0.562315\pi\)
\(60\) 0 0
\(61\) 278.406 482.213i 0.584364 1.01215i −0.410591 0.911820i \(-0.634677\pi\)
0.994954 0.100328i \(-0.0319892\pi\)
\(62\) 297.931 0.610278
\(63\) 0 0
\(64\) 45.4941 0.0888557
\(65\) 217.786 377.217i 0.415586 0.719815i
\(66\) 0 0
\(67\) 20.9493 + 36.2853i 0.0381995 + 0.0661635i 0.884493 0.466553i \(-0.154504\pi\)
−0.846294 + 0.532717i \(0.821171\pi\)
\(68\) −161.969 280.538i −0.288847 0.500298i
\(69\) 0 0
\(70\) −79.9544 + 138.485i −0.136520 + 0.236459i
\(71\) 549.163 0.917939 0.458970 0.888452i \(-0.348219\pi\)
0.458970 + 0.888452i \(0.348219\pi\)
\(72\) 0 0
\(73\) −185.505 −0.297420 −0.148710 0.988881i \(-0.547512\pi\)
−0.148710 + 0.988881i \(0.547512\pi\)
\(74\) 46.7878 81.0388i 0.0734996 0.127305i
\(75\) 0 0
\(76\) −276.135 478.279i −0.416774 0.721874i
\(77\) −99.7458 172.765i −0.147624 0.255693i
\(78\) 0 0
\(79\) −40.2456 + 69.7075i −0.0573163 + 0.0992748i −0.893260 0.449541i \(-0.851588\pi\)
0.835944 + 0.548815i \(0.184921\pi\)
\(80\) −124.245 −0.173637
\(81\) 0 0
\(82\) −486.857 −0.655663
\(83\) −288.377 + 499.483i −0.381367 + 0.660547i −0.991258 0.131939i \(-0.957880\pi\)
0.609891 + 0.792485i \(0.291213\pi\)
\(84\) 0 0
\(85\) −129.792 224.806i −0.165622 0.286866i
\(86\) 129.727 + 224.694i 0.162661 + 0.281736i
\(87\) 0 0
\(88\) −78.1818 + 135.415i −0.0947070 + 0.164037i
\(89\) −224.516 −0.267401 −0.133700 0.991022i \(-0.542686\pi\)
−0.133700 + 0.991022i \(0.542686\pi\)
\(90\) 0 0
\(91\) −2099.83 −2.41893
\(92\) 403.216 698.391i 0.456937 0.791438i
\(93\) 0 0
\(94\) −238.290 412.730i −0.261465 0.452870i
\(95\) −221.277 383.263i −0.238974 0.413915i
\(96\) 0 0
\(97\) 277.508 480.658i 0.290481 0.503128i −0.683442 0.730005i \(-0.739518\pi\)
0.973924 + 0.226876i \(0.0728513\pi\)
\(98\) 315.801 0.325518
\(99\) 0 0
\(100\) −155.989 −0.155989
\(101\) 113.500 196.587i 0.111818 0.193675i −0.804685 0.593702i \(-0.797666\pi\)
0.916503 + 0.400027i \(0.130999\pi\)
\(102\) 0 0
\(103\) −191.762 332.142i −0.183446 0.317737i 0.759606 0.650383i \(-0.225392\pi\)
−0.943052 + 0.332646i \(0.892058\pi\)
\(104\) 822.936 + 1425.37i 0.775918 + 1.34393i
\(105\) 0 0
\(106\) 19.5632 33.8844i 0.0179259 0.0310485i
\(107\) 1775.32 1.60399 0.801993 0.597334i \(-0.203773\pi\)
0.801993 + 0.597334i \(0.203773\pi\)
\(108\) 0 0
\(109\) 1530.50 1.34491 0.672454 0.740139i \(-0.265240\pi\)
0.672454 + 0.740139i \(0.265240\pi\)
\(110\) −27.4523 + 47.5488i −0.0237952 + 0.0412145i
\(111\) 0 0
\(112\) 299.483 + 518.720i 0.252665 + 0.437629i
\(113\) −420.391 728.138i −0.349974 0.606173i 0.636271 0.771466i \(-0.280476\pi\)
−0.986244 + 0.165293i \(0.947143\pi\)
\(114\) 0 0
\(115\) 323.112 559.646i 0.262003 0.453802i
\(116\) −1691.60 −1.35398
\(117\) 0 0
\(118\) 1138.54 0.888230
\(119\) −625.706 + 1083.75i −0.482003 + 0.834854i
\(120\) 0 0
\(121\) 631.252 + 1093.36i 0.474269 + 0.821458i
\(122\) 369.391 + 639.804i 0.274124 + 0.474796i
\(123\) 0 0
\(124\) 700.539 1213.37i 0.507341 0.878740i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 1038.45 0.725572 0.362786 0.931873i \(-0.381826\pi\)
0.362786 + 0.931873i \(0.381826\pi\)
\(128\) 706.281 1223.31i 0.487711 0.844740i
\(129\) 0 0
\(130\) 288.961 + 500.495i 0.194950 + 0.337664i
\(131\) −401.705 695.774i −0.267917 0.464046i 0.700407 0.713744i \(-0.253002\pi\)
−0.968324 + 0.249698i \(0.919669\pi\)
\(132\) 0 0
\(133\) −1066.74 + 1847.65i −0.695476 + 1.20460i
\(134\) −55.5915 −0.0358386
\(135\) 0 0
\(136\) 980.871 0.618449
\(137\) 434.576 752.707i 0.271010 0.469402i −0.698111 0.715990i \(-0.745976\pi\)
0.969121 + 0.246587i \(0.0793091\pi\)
\(138\) 0 0
\(139\) 98.1990 + 170.086i 0.0599218 + 0.103788i 0.894430 0.447208i \(-0.147582\pi\)
−0.834508 + 0.550995i \(0.814248\pi\)
\(140\) 376.001 + 651.253i 0.226985 + 0.393150i
\(141\) 0 0
\(142\) −364.317 + 631.016i −0.215302 + 0.372913i
\(143\) −720.976 −0.421616
\(144\) 0 0
\(145\) −1355.54 −0.776357
\(146\) 123.065 213.154i 0.0697596 0.120827i
\(147\) 0 0
\(148\) −220.029 381.101i −0.122204 0.211664i
\(149\) 377.142 + 653.228i 0.207360 + 0.359158i 0.950882 0.309553i \(-0.100180\pi\)
−0.743522 + 0.668711i \(0.766846\pi\)
\(150\) 0 0
\(151\) −1028.82 + 1781.96i −0.554464 + 0.960359i 0.443481 + 0.896284i \(0.353743\pi\)
−0.997945 + 0.0640756i \(0.979590\pi\)
\(152\) 1672.25 0.892351
\(153\) 0 0
\(154\) 264.687 0.138501
\(155\) 561.367 972.316i 0.290904 0.503860i
\(156\) 0 0
\(157\) 1679.29 + 2908.62i 0.853644 + 1.47855i 0.877897 + 0.478849i \(0.158946\pi\)
−0.0242531 + 0.999706i \(0.507721\pi\)
\(158\) −53.3983 92.4885i −0.0268869 0.0465696i
\(159\) 0 0
\(160\) 460.289 797.243i 0.227431 0.393922i
\(161\) −3115.35 −1.52499
\(162\) 0 0
\(163\) −710.376 −0.341356 −0.170678 0.985327i \(-0.554596\pi\)
−0.170678 + 0.985327i \(0.554596\pi\)
\(164\) −1144.77 + 1982.80i −0.545070 + 0.944089i
\(165\) 0 0
\(166\) −382.621 662.718i −0.178898 0.309861i
\(167\) −574.134 994.430i −0.266035 0.460786i 0.701799 0.712375i \(-0.252380\pi\)
−0.967834 + 0.251589i \(0.919047\pi\)
\(168\) 0 0
\(169\) −2695.97 + 4669.56i −1.22711 + 2.12542i
\(170\) 344.417 0.155386
\(171\) 0 0
\(172\) 1220.13 0.540897
\(173\) −1462.64 + 2533.37i −0.642790 + 1.11335i 0.342017 + 0.939694i \(0.388890\pi\)
−0.984807 + 0.173652i \(0.944443\pi\)
\(174\) 0 0
\(175\) 301.303 + 521.873i 0.130151 + 0.225428i
\(176\) 102.827 + 178.102i 0.0440393 + 0.0762782i
\(177\) 0 0
\(178\) 148.945 257.980i 0.0627185 0.108632i
\(179\) −3422.02 −1.42890 −0.714452 0.699685i \(-0.753324\pi\)
−0.714452 + 0.699685i \(0.753324\pi\)
\(180\) 0 0
\(181\) −1151.58 −0.472907 −0.236454 0.971643i \(-0.575985\pi\)
−0.236454 + 0.971643i \(0.575985\pi\)
\(182\) 1393.04 2412.81i 0.567356 0.982690i
\(183\) 0 0
\(184\) 1220.92 + 2114.70i 0.489172 + 0.847271i
\(185\) −176.317 305.390i −0.0700707 0.121366i
\(186\) 0 0
\(187\) −214.836 + 372.107i −0.0840126 + 0.145514i
\(188\) −2241.21 −0.869451
\(189\) 0 0
\(190\) 587.184 0.224204
\(191\) 466.060 807.240i 0.176560 0.305811i −0.764140 0.645050i \(-0.776836\pi\)
0.940700 + 0.339240i \(0.110170\pi\)
\(192\) 0 0
\(193\) 2136.41 + 3700.36i 0.796797 + 1.38009i 0.921692 + 0.387923i \(0.126807\pi\)
−0.124894 + 0.992170i \(0.539859\pi\)
\(194\) 368.200 + 637.742i 0.136264 + 0.236016i
\(195\) 0 0
\(196\) 742.559 1286.15i 0.270612 0.468713i
\(197\) 1924.15 0.695888 0.347944 0.937515i \(-0.386880\pi\)
0.347944 + 0.937515i \(0.386880\pi\)
\(198\) 0 0
\(199\) 1738.84 0.619414 0.309707 0.950832i \(-0.399769\pi\)
0.309707 + 0.950832i \(0.399769\pi\)
\(200\) 236.165 409.050i 0.0834969 0.144621i
\(201\) 0 0
\(202\) 150.593 + 260.834i 0.0524537 + 0.0908525i
\(203\) 3267.44 + 5659.37i 1.12970 + 1.95670i
\(204\) 0 0
\(205\) −917.345 + 1588.89i −0.312537 + 0.541331i
\(206\) 508.864 0.172108
\(207\) 0 0
\(208\) 2164.71 0.721613
\(209\) −366.266 + 634.391i −0.121221 + 0.209960i
\(210\) 0 0
\(211\) −1601.17 2773.32i −0.522414 0.904848i −0.999660 0.0260782i \(-0.991698\pi\)
0.477246 0.878770i \(-0.341635\pi\)
\(212\) −91.9996 159.348i −0.0298045 0.0516229i
\(213\) 0 0
\(214\) −1177.75 + 2039.93i −0.376213 + 0.651620i
\(215\) 977.736 0.310144
\(216\) 0 0
\(217\) −5412.54 −1.69321
\(218\) −1015.34 + 1758.62i −0.315447 + 0.546370i
\(219\) 0 0
\(220\) 129.100 + 223.608i 0.0395632 + 0.0685255i
\(221\) 2261.35 + 3916.77i 0.688301 + 1.19217i
\(222\) 0 0
\(223\) 702.494 1216.76i 0.210953 0.365381i −0.741060 0.671439i \(-0.765677\pi\)
0.952013 + 0.306058i \(0.0990100\pi\)
\(224\) −4437.97 −1.32377
\(225\) 0 0
\(226\) 1115.56 0.328344
\(227\) 3119.17 5402.57i 0.912012 1.57965i 0.100794 0.994907i \(-0.467862\pi\)
0.811218 0.584744i \(-0.198805\pi\)
\(228\) 0 0
\(229\) −3315.15 5742.01i −0.956644 1.65696i −0.730560 0.682848i \(-0.760741\pi\)
−0.226084 0.974108i \(-0.572592\pi\)
\(230\) 428.708 + 742.543i 0.122905 + 0.212878i
\(231\) 0 0
\(232\) 2561.05 4435.88i 0.724747 1.25530i
\(233\) −2453.48 −0.689840 −0.344920 0.938632i \(-0.612094\pi\)
−0.344920 + 0.938632i \(0.612094\pi\)
\(234\) 0 0
\(235\) −1795.96 −0.498534
\(236\) 2677.10 4636.88i 0.738410 1.27896i
\(237\) 0 0
\(238\) −830.192 1437.94i −0.226107 0.391628i
\(239\) −3474.87 6018.65i −0.940463 1.62893i −0.764590 0.644517i \(-0.777058\pi\)
−0.175873 0.984413i \(-0.556275\pi\)
\(240\) 0 0
\(241\) −3167.60 + 5486.44i −0.846651 + 1.46644i 0.0375294 + 0.999296i \(0.488051\pi\)
−0.884180 + 0.467146i \(0.845282\pi\)
\(242\) −1675.10 −0.444957
\(243\) 0 0
\(244\) 3474.27 0.911546
\(245\) 595.039 1030.64i 0.155166 0.268755i
\(246\) 0 0
\(247\) 3855.28 + 6677.55i 0.993141 + 1.72017i
\(248\) 2121.20 + 3674.03i 0.543131 + 0.940731i
\(249\) 0 0
\(250\) 82.9255 143.631i 0.0209787 0.0363362i
\(251\) 4022.65 1.01158 0.505792 0.862656i \(-0.331200\pi\)
0.505792 + 0.862656i \(0.331200\pi\)
\(252\) 0 0
\(253\) −1069.65 −0.265805
\(254\) −688.913 + 1193.23i −0.170182 + 0.294764i
\(255\) 0 0
\(256\) 1119.08 + 1938.30i 0.273212 + 0.473217i
\(257\) −2498.87 4328.17i −0.606519 1.05052i −0.991809 0.127726i \(-0.959232\pi\)
0.385291 0.922795i \(-0.374101\pi\)
\(258\) 0 0
\(259\) −849.998 + 1472.24i −0.203924 + 0.353207i
\(260\) 2717.79 0.648270
\(261\) 0 0
\(262\) 1065.97 0.251359
\(263\) −1996.24 + 3457.58i −0.468035 + 0.810660i −0.999333 0.0365251i \(-0.988371\pi\)
0.531298 + 0.847185i \(0.321704\pi\)
\(264\) 0 0
\(265\) −73.7226 127.691i −0.0170896 0.0296000i
\(266\) −1415.36 2451.48i −0.326246 0.565075i
\(267\) 0 0
\(268\) −130.715 + 226.405i −0.0297936 + 0.0516041i
\(269\) 2188.89 0.496131 0.248065 0.968743i \(-0.420205\pi\)
0.248065 + 0.968743i \(0.420205\pi\)
\(270\) 0 0
\(271\) 4280.26 0.959437 0.479718 0.877423i \(-0.340739\pi\)
0.479718 + 0.877423i \(0.340739\pi\)
\(272\) 645.038 1117.24i 0.143791 0.249053i
\(273\) 0 0
\(274\) 576.599 + 998.699i 0.127130 + 0.220196i
\(275\) 103.452 + 179.185i 0.0226851 + 0.0392918i
\(276\) 0 0
\(277\) 1939.98 3360.15i 0.420803 0.728852i −0.575215 0.818002i \(-0.695082\pi\)
0.996018 + 0.0891502i \(0.0284151\pi\)
\(278\) −260.583 −0.0562184
\(279\) 0 0
\(280\) −2277.03 −0.485996
\(281\) −3198.72 + 5540.34i −0.679072 + 1.17619i 0.296188 + 0.955130i \(0.404284\pi\)
−0.975261 + 0.221058i \(0.929049\pi\)
\(282\) 0 0
\(283\) 171.435 + 296.933i 0.0360096 + 0.0623705i 0.883469 0.468490i \(-0.155202\pi\)
−0.847459 + 0.530861i \(0.821869\pi\)
\(284\) 1713.27 + 2967.48i 0.357972 + 0.620026i
\(285\) 0 0
\(286\) 478.299 828.438i 0.0988895 0.171282i
\(287\) 8844.78 1.81913
\(288\) 0 0
\(289\) −2217.66 −0.451387
\(290\) 899.273 1557.59i 0.182094 0.315395i
\(291\) 0 0
\(292\) −578.735 1002.40i −0.115986 0.200894i
\(293\) −3666.71 6350.94i −0.731098 1.26630i −0.956414 0.292013i \(-0.905675\pi\)
0.225316 0.974286i \(-0.427659\pi\)
\(294\) 0 0
\(295\) 2145.26 3715.70i 0.423396 0.733344i
\(296\) 1332.48 0.261651
\(297\) 0 0
\(298\) −1000.79 −0.194544
\(299\) −5629.55 + 9750.66i −1.08885 + 1.88594i
\(300\) 0 0
\(301\) −2356.76 4082.03i −0.451300 0.781675i
\(302\) −1365.04 2364.33i −0.260098 0.450502i
\(303\) 0 0
\(304\) 1099.70 1904.74i 0.207474 0.359356i
\(305\) 2784.06 0.522671
\(306\) 0 0
\(307\) −7965.33 −1.48080 −0.740399 0.672167i \(-0.765364\pi\)
−0.740399 + 0.672167i \(0.765364\pi\)
\(308\) 622.372 1077.98i 0.115139 0.199427i
\(309\) 0 0
\(310\) 744.827 + 1290.08i 0.136462 + 0.236360i
\(311\) −1093.10 1893.30i −0.199305 0.345206i 0.748998 0.662572i \(-0.230535\pi\)
−0.948303 + 0.317366i \(0.897202\pi\)
\(312\) 0 0
\(313\) −19.3152 + 33.4549i −0.00348805 + 0.00604147i −0.867764 0.496976i \(-0.834444\pi\)
0.864276 + 0.503018i \(0.167777\pi\)
\(314\) −4456.20 −0.800885
\(315\) 0 0
\(316\) −502.232 −0.0894074
\(317\) 4767.91 8258.25i 0.844770 1.46319i −0.0410499 0.999157i \(-0.513070\pi\)
0.885820 0.464028i \(-0.153596\pi\)
\(318\) 0 0
\(319\) 1121.87 + 1943.14i 0.196905 + 0.341050i
\(320\) 113.735 + 196.995i 0.0198687 + 0.0344137i
\(321\) 0 0
\(322\) 2066.74 3579.69i 0.357686 0.619530i
\(323\) 4595.18 0.791587
\(324\) 0 0
\(325\) 2177.86 0.371711
\(326\) 471.267 816.258i 0.0800645 0.138676i
\(327\) 0 0
\(328\) −3466.32 6003.84i −0.583522 1.01069i
\(329\) 4329.03 + 7498.10i 0.725432 + 1.25649i
\(330\) 0 0
\(331\) 1505.29 2607.24i 0.249964 0.432951i −0.713551 0.700603i \(-0.752914\pi\)
0.963516 + 0.267652i \(0.0862477\pi\)
\(332\) −3598.70 −0.594892
\(333\) 0 0
\(334\) 1523.53 0.249593
\(335\) −104.747 + 181.427i −0.0170833 + 0.0295892i
\(336\) 0 0
\(337\) −1406.36 2435.89i −0.227327 0.393742i 0.729688 0.683780i \(-0.239665\pi\)
−0.957015 + 0.290038i \(0.906332\pi\)
\(338\) −3577.04 6195.61i −0.575637 0.997032i
\(339\) 0 0
\(340\) 809.845 1402.69i 0.129176 0.223740i
\(341\) −1858.39 −0.295125
\(342\) 0 0
\(343\) 2530.57 0.398361
\(344\) −1847.26 + 3199.54i −0.289527 + 0.501476i
\(345\) 0 0
\(346\) −1940.65 3361.30i −0.301531 0.522268i
\(347\) −69.6769 120.684i −0.0107794 0.0186705i 0.860585 0.509306i \(-0.170098\pi\)
−0.871365 + 0.490636i \(0.836765\pi\)
\(348\) 0 0
\(349\) 2605.14 4512.24i 0.399571 0.692077i −0.594102 0.804390i \(-0.702493\pi\)
0.993673 + 0.112313i \(0.0358259\pi\)
\(350\) −799.544 −0.122107
\(351\) 0 0
\(352\) −1523.77 −0.230731
\(353\) −1705.23 + 2953.55i −0.257112 + 0.445330i −0.965467 0.260526i \(-0.916104\pi\)
0.708355 + 0.705856i \(0.249437\pi\)
\(354\) 0 0
\(355\) 1372.91 + 2377.95i 0.205257 + 0.355516i
\(356\) −700.443 1213.20i −0.104279 0.180617i
\(357\) 0 0
\(358\) 2270.18 3932.07i 0.335148 0.580493i
\(359\) −8131.85 −1.19549 −0.597747 0.801685i \(-0.703937\pi\)
−0.597747 + 0.801685i \(0.703937\pi\)
\(360\) 0 0
\(361\) 975.143 0.142170
\(362\) 763.963 1323.22i 0.110920 0.192119i
\(363\) 0 0
\(364\) −6551.03 11346.7i −0.943317 1.63387i
\(365\) −463.762 803.259i −0.0665052 0.115190i
\(366\) 0 0
\(367\) −66.0757 + 114.447i −0.00939816 + 0.0162781i −0.870686 0.491839i \(-0.836325\pi\)
0.861288 + 0.508117i \(0.169658\pi\)
\(368\) 3211.60 0.454935
\(369\) 0 0
\(370\) 467.878 0.0657400
\(371\) −355.406 + 615.581i −0.0497352 + 0.0861438i
\(372\) 0 0
\(373\) −4674.44 8096.37i −0.648883 1.12390i −0.983390 0.181505i \(-0.941903\pi\)
0.334507 0.942393i \(-0.391430\pi\)
\(374\) −285.046 493.715i −0.0394101 0.0682603i
\(375\) 0 0
\(376\) 3393.14 5877.10i 0.465394 0.806085i
\(377\) 23617.5 3.22643
\(378\) 0 0
\(379\) 6164.17 0.835441 0.417720 0.908576i \(-0.362829\pi\)
0.417720 + 0.908576i \(0.362829\pi\)
\(380\) 1380.67 2391.40i 0.186387 0.322832i
\(381\) 0 0
\(382\) 618.373 + 1071.05i 0.0828238 + 0.143455i
\(383\) −1300.64 2252.77i −0.173523 0.300551i 0.766126 0.642690i \(-0.222182\pi\)
−0.939649 + 0.342139i \(0.888849\pi\)
\(384\) 0 0
\(385\) 498.729 863.824i 0.0660197 0.114349i
\(386\) −5669.20 −0.747552
\(387\) 0 0
\(388\) 3463.07 0.453120
\(389\) −2125.29 + 3681.10i −0.277008 + 0.479793i −0.970640 0.240537i \(-0.922676\pi\)
0.693631 + 0.720330i \(0.256010\pi\)
\(390\) 0 0
\(391\) 3354.98 + 5810.99i 0.433935 + 0.751597i
\(392\) 2248.44 + 3894.41i 0.289702 + 0.501779i
\(393\) 0 0
\(394\) −1276.49 + 2210.94i −0.163220 + 0.282705i
\(395\) −402.456 −0.0512653
\(396\) 0 0
\(397\) −6088.35 −0.769687 −0.384843 0.922982i \(-0.625745\pi\)
−0.384843 + 0.922982i \(0.625745\pi\)
\(398\) −1153.56 + 1998.02i −0.145283 + 0.251637i
\(399\) 0 0
\(400\) −310.612 537.996i −0.0388265 0.0672495i
\(401\) −3862.90 6690.73i −0.481057 0.833215i 0.518707 0.854952i \(-0.326414\pi\)
−0.999764 + 0.0217370i \(0.993080\pi\)
\(402\) 0 0
\(403\) −9780.64 + 16940.6i −1.20895 + 2.09397i
\(404\) 1416.38 0.174425
\(405\) 0 0
\(406\) −8670.53 −1.05988
\(407\) −291.847 + 505.493i −0.0355437 + 0.0615635i
\(408\) 0 0
\(409\) −8160.57 14134.5i −0.986588 1.70882i −0.634657 0.772794i \(-0.718859\pi\)
−0.351930 0.936026i \(-0.614475\pi\)
\(410\) −1217.14 2108.15i −0.146611 0.253937i
\(411\) 0 0
\(412\) 1196.52 2072.43i 0.143078 0.247818i
\(413\) −20684.0 −2.46439
\(414\) 0 0
\(415\) −2883.77 −0.341105
\(416\) −8019.56 + 13890.3i −0.945172 + 1.63709i
\(417\) 0 0
\(418\) −485.964 841.715i −0.0568644 0.0984920i
\(419\) −576.228 998.055i −0.0671851 0.116368i 0.830476 0.557054i \(-0.188068\pi\)
−0.897661 + 0.440686i \(0.854735\pi\)
\(420\) 0 0
\(421\) 1765.61 3058.13i 0.204396 0.354024i −0.745544 0.666456i \(-0.767810\pi\)
0.949940 + 0.312432i \(0.101144\pi\)
\(422\) 4248.91 0.490127
\(423\) 0 0
\(424\) 557.142 0.0638142
\(425\) 648.958 1124.03i 0.0740684 0.128290i
\(426\) 0 0
\(427\) −6710.76 11623.4i −0.760554 1.31732i
\(428\) 5538.62 + 9593.17i 0.625512 + 1.08342i
\(429\) 0 0
\(430\) −648.634 + 1123.47i −0.0727440 + 0.125996i
\(431\) 10230.6 1.14337 0.571683 0.820475i \(-0.306291\pi\)
0.571683 + 0.820475i \(0.306291\pi\)
\(432\) 0 0
\(433\) −7311.31 −0.811453 −0.405726 0.913995i \(-0.632981\pi\)
−0.405726 + 0.913995i \(0.632981\pi\)
\(434\) 3590.70 6219.27i 0.397141 0.687868i
\(435\) 0 0
\(436\) 4774.83 + 8270.24i 0.524479 + 0.908424i
\(437\) 5719.77 + 9906.94i 0.626119 + 1.08447i
\(438\) 0 0
\(439\) −3526.59 + 6108.23i −0.383405 + 0.664077i −0.991547 0.129751i \(-0.958582\pi\)
0.608141 + 0.793829i \(0.291915\pi\)
\(440\) −781.818 −0.0847085
\(441\) 0 0
\(442\) −6000.75 −0.645761
\(443\) 83.8952 145.311i 0.00899770 0.0155845i −0.861491 0.507772i \(-0.830469\pi\)
0.870489 + 0.492188i \(0.163803\pi\)
\(444\) 0 0
\(445\) −561.290 972.183i −0.0597926 0.103564i
\(446\) 932.076 + 1614.40i 0.0989575 + 0.171399i
\(447\) 0 0
\(448\) 548.301 949.685i 0.0578232 0.100153i
\(449\) 3949.94 0.415165 0.207582 0.978218i \(-0.433440\pi\)
0.207582 + 0.978218i \(0.433440\pi\)
\(450\) 0 0
\(451\) 3036.85 0.317072
\(452\) 2623.06 4543.28i 0.272961 0.472783i
\(453\) 0 0
\(454\) 4138.55 + 7168.17i 0.427823 + 0.741011i
\(455\) −5249.58 9092.54i −0.540888 0.936846i
\(456\) 0 0
\(457\) 3723.80 6449.81i 0.381164 0.660195i −0.610065 0.792351i \(-0.708857\pi\)
0.991229 + 0.132156i \(0.0421900\pi\)
\(458\) 8797.15 0.897519
\(459\) 0 0
\(460\) 4032.16 0.408697
\(461\) −5443.82 + 9428.98i −0.549987 + 0.952606i 0.448287 + 0.893889i \(0.352034\pi\)
−0.998275 + 0.0587164i \(0.981299\pi\)
\(462\) 0 0
\(463\) 1585.63 + 2746.40i 0.159159 + 0.275672i 0.934566 0.355791i \(-0.115788\pi\)
−0.775407 + 0.631462i \(0.782455\pi\)
\(464\) −3368.39 5834.21i −0.337012 0.583721i
\(465\) 0 0
\(466\) 1627.65 2819.17i 0.161801 0.280248i
\(467\) −16348.5 −1.61996 −0.809978 0.586461i \(-0.800521\pi\)
−0.809978 + 0.586461i \(0.800521\pi\)
\(468\) 0 0
\(469\) 1009.94 0.0994340
\(470\) 1191.45 2063.65i 0.116931 0.202530i
\(471\) 0 0
\(472\) 8106.17 + 14040.3i 0.790501 + 1.36919i
\(473\) −809.193 1401.56i −0.0786612 0.136245i
\(474\) 0 0
\(475\) 1106.38 1916.31i 0.106872 0.185108i
\(476\) −7808.29 −0.751874
\(477\) 0 0
\(478\) 9220.98 0.882338
\(479\) −4706.84 + 8152.49i −0.448980 + 0.777655i −0.998320 0.0579433i \(-0.981546\pi\)
0.549340 + 0.835599i \(0.314879\pi\)
\(480\) 0 0
\(481\) 3071.95 + 5320.78i 0.291204 + 0.504380i
\(482\) −4202.79 7279.45i −0.397162 0.687905i
\(483\) 0 0
\(484\) −3938.75 + 6822.11i −0.369905 + 0.640694i
\(485\) 2775.08 0.259814
\(486\) 0 0
\(487\) 13482.3 1.25450 0.627250 0.778818i \(-0.284180\pi\)
0.627250 + 0.778818i \(0.284180\pi\)
\(488\) −5259.97 + 9110.54i −0.487926 + 0.845112i
\(489\) 0 0
\(490\) 789.503 + 1367.46i 0.0727880 + 0.126073i
\(491\) 4609.87 + 7984.53i 0.423708 + 0.733883i 0.996299 0.0859577i \(-0.0273950\pi\)
−0.572591 + 0.819841i \(0.694062\pi\)
\(492\) 0 0
\(493\) 7037.52 12189.3i 0.642909 1.11355i
\(494\) −10230.4 −0.931760
\(495\) 0 0
\(496\) 5579.76 0.505118
\(497\) 6618.59 11463.7i 0.597353 1.03465i
\(498\) 0 0
\(499\) −52.1731 90.3665i −0.00468054 0.00810693i 0.863676 0.504048i \(-0.168157\pi\)
−0.868356 + 0.495941i \(0.834823\pi\)
\(500\) −389.974 675.454i −0.0348803 0.0604145i
\(501\) 0 0
\(502\) −2668.64 + 4622.23i −0.237266 + 0.410956i
\(503\) 490.652 0.0434933 0.0217466 0.999764i \(-0.493077\pi\)
0.0217466 + 0.999764i \(0.493077\pi\)
\(504\) 0 0
\(505\) 1135.00 0.100013
\(506\) 709.613 1229.09i 0.0623442 0.107983i
\(507\) 0 0
\(508\) 3239.75 + 5611.41i 0.282954 + 0.490090i
\(509\) 1706.40 + 2955.58i 0.148595 + 0.257375i 0.930709 0.365762i \(-0.119192\pi\)
−0.782113 + 0.623136i \(0.785858\pi\)
\(510\) 0 0
\(511\) −2235.73 + 3872.39i −0.193547 + 0.335234i
\(512\) 8330.89 0.719095
\(513\) 0 0
\(514\) 6631.05 0.569033
\(515\) 958.811 1660.71i 0.0820393 0.142096i
\(516\) 0 0
\(517\) 1486.37 + 2574.47i 0.126442 + 0.219004i
\(518\) −1127.79 1953.38i −0.0956603 0.165688i
\(519\) 0 0
\(520\) −4114.68 + 7126.83i −0.347001 + 0.601024i
\(521\) −3486.31 −0.293163 −0.146582 0.989199i \(-0.546827\pi\)
−0.146582 + 0.989199i \(0.546827\pi\)
\(522\) 0 0
\(523\) 14465.6 1.20943 0.604717 0.796440i \(-0.293286\pi\)
0.604717 + 0.796440i \(0.293286\pi\)
\(524\) 2506.47 4341.34i 0.208961 0.361932i
\(525\) 0 0
\(526\) −2648.62 4587.55i −0.219554 0.380279i
\(527\) 5828.86 + 10095.9i 0.481801 + 0.834503i
\(528\) 0 0
\(529\) −2268.60 + 3929.34i −0.186456 + 0.322950i
\(530\) 195.632 0.0160334
\(531\) 0 0
\(532\) −13312.1 −1.08487
\(533\) 15982.8 27683.1i 1.29886 2.24969i
\(534\) 0 0
\(535\) 4438.29 + 7687.35i 0.358662 + 0.621221i
\(536\) −395.800 685.545i −0.0318954 0.0552445i
\(537\) 0 0
\(538\) −1452.12 + 2515.15i −0.116367 + 0.201553i
\(539\) −1969.86 −0.157417
\(540\) 0 0
\(541\) 6602.78 0.524724 0.262362 0.964970i \(-0.415499\pi\)
0.262362 + 0.964970i \(0.415499\pi\)
\(542\) −2839.54 + 4918.23i −0.225035 + 0.389772i
\(543\) 0 0
\(544\) 4779.33 + 8278.03i 0.376676 + 0.652422i
\(545\) 3826.24 + 6627.24i 0.300731 + 0.520881i
\(546\) 0 0
\(547\) −3179.28 + 5506.67i −0.248512 + 0.430436i −0.963113 0.269096i \(-0.913275\pi\)
0.714601 + 0.699532i \(0.246608\pi\)
\(548\) 5423.14 0.422746
\(549\) 0 0
\(550\) −274.523 −0.0212831
\(551\) 11998.0 20781.2i 0.927645 1.60673i
\(552\) 0 0
\(553\) 970.092 + 1680.25i 0.0745976 + 0.129207i
\(554\) 2573.99 + 4458.28i 0.197398 + 0.341903i
\(555\) 0 0
\(556\) −612.720 + 1061.26i −0.0467359 + 0.0809489i
\(557\) −20782.3 −1.58092 −0.790461 0.612513i \(-0.790159\pi\)
−0.790461 + 0.612513i \(0.790159\pi\)
\(558\) 0 0
\(559\) −17035.0 −1.28892
\(560\) −1497.42 + 2593.60i −0.112995 + 0.195714i
\(561\) 0 0
\(562\) −4244.08 7350.97i −0.318551 0.551747i
\(563\) −8234.98 14263.4i −0.616453 1.06773i −0.990128 0.140168i \(-0.955236\pi\)
0.373675 0.927560i \(-0.378098\pi\)
\(564\) 0 0
\(565\) 2101.95 3640.69i 0.156513 0.271089i
\(566\) −454.922 −0.0337841
\(567\) 0 0
\(568\) −10375.4 −0.766451
\(569\) −2712.69 + 4698.52i −0.199863 + 0.346173i −0.948484 0.316825i \(-0.897383\pi\)
0.748621 + 0.662998i \(0.230716\pi\)
\(570\) 0 0
\(571\) 7344.86 + 12721.7i 0.538306 + 0.932374i 0.998995 + 0.0448121i \(0.0142689\pi\)
−0.460689 + 0.887561i \(0.652398\pi\)
\(572\) −2249.29 3895.89i −0.164419 0.284782i
\(573\) 0 0
\(574\) −5867.66 + 10163.1i −0.426675 + 0.739023i
\(575\) 3231.12 0.234343
\(576\) 0 0
\(577\) −17933.1 −1.29387 −0.646935 0.762545i \(-0.723949\pi\)
−0.646935 + 0.762545i \(0.723949\pi\)
\(578\) 1471.21 2548.21i 0.105872 0.183376i
\(579\) 0 0
\(580\) −4229.01 7324.86i −0.302759 0.524393i
\(581\) 6951.11 + 12039.7i 0.496352 + 0.859707i
\(582\) 0 0
\(583\) −122.028 + 211.359i −0.00866878 + 0.0150148i
\(584\) 3504.78 0.248337
\(585\) 0 0
\(586\) 9730.06 0.685913
\(587\) −2400.58 + 4157.92i −0.168795 + 0.292361i −0.937996 0.346645i \(-0.887321\pi\)
0.769202 + 0.639006i \(0.220654\pi\)
\(588\) 0 0
\(589\) 9937.40 + 17212.1i 0.695184 + 1.20409i
\(590\) 2846.35 + 4930.02i 0.198614 + 0.344010i
\(591\) 0 0
\(592\) 876.259 1517.73i 0.0608345 0.105368i
\(593\) −16803.8 −1.16366 −0.581830 0.813311i \(-0.697663\pi\)
−0.581830 + 0.813311i \(0.697663\pi\)
\(594\) 0 0
\(595\) −6257.06 −0.431117
\(596\) −2353.20 + 4075.87i −0.161730 + 0.280124i
\(597\) 0 0
\(598\) −7469.33 12937.3i −0.510775 0.884689i
\(599\) 8610.08 + 14913.1i 0.587310 + 1.01725i 0.994583 + 0.103944i \(0.0331462\pi\)
−0.407274 + 0.913306i \(0.633520\pi\)
\(600\) 0 0
\(601\) −10768.3 + 18651.3i −0.730865 + 1.26590i 0.225649 + 0.974209i \(0.427550\pi\)
−0.956514 + 0.291687i \(0.905784\pi\)
\(602\) 6253.94 0.423408
\(603\) 0 0
\(604\) −12838.8 −0.864905
\(605\) −3156.26 + 5466.81i −0.212100 + 0.367367i
\(606\) 0 0
\(607\) 12025.5 + 20828.7i 0.804117 + 1.39277i 0.916886 + 0.399150i \(0.130695\pi\)
−0.112769 + 0.993621i \(0.535972\pi\)
\(608\) 8148.09 + 14112.9i 0.543501 + 0.941372i
\(609\) 0 0
\(610\) −1846.96 + 3199.02i −0.122592 + 0.212335i
\(611\) 31290.8 2.07184
\(612\) 0 0
\(613\) −3554.49 −0.234200 −0.117100 0.993120i \(-0.537360\pi\)
−0.117100 + 0.993120i \(0.537360\pi\)
\(614\) 5284.23 9152.56i 0.347320 0.601575i
\(615\) 0 0
\(616\) 1884.52 + 3264.08i 0.123262 + 0.213496i
\(617\) −4873.71 8441.51i −0.318003 0.550798i 0.662068 0.749444i \(-0.269679\pi\)
−0.980071 + 0.198646i \(0.936346\pi\)
\(618\) 0 0
\(619\) 10382.6 17983.2i 0.674171 1.16770i −0.302540 0.953137i \(-0.597835\pi\)
0.976711 0.214561i \(-0.0688321\pi\)
\(620\) 7005.39 0.453779
\(621\) 0 0
\(622\) 2900.66 0.186987
\(623\) −2705.90 + 4686.75i −0.174012 + 0.301398i
\(624\) 0 0
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) −25.6275 44.3882i −0.00163623 0.00283404i
\(627\) 0 0
\(628\) −10478.1 + 18148.6i −0.665797 + 1.15320i
\(629\) 3661.51 0.232105
\(630\) 0 0
\(631\) 23740.6 1.49778 0.748890 0.662694i \(-0.230587\pi\)
0.748890 + 0.662694i \(0.230587\pi\)
\(632\) 760.369 1317.00i 0.0478574 0.0828914i
\(633\) 0 0
\(634\) 6326.10 + 10957.1i 0.396280 + 0.686377i
\(635\) 2596.13 + 4496.62i 0.162243 + 0.281013i
\(636\) 0 0
\(637\) −10367.3 + 17956.7i −0.644848 + 1.11691i
\(638\) −2977.02 −0.184736
\(639\) 0 0
\(640\) 7062.81 0.436222
\(641\) 13054.4 22610.8i 0.804394 1.39325i −0.112306 0.993674i \(-0.535824\pi\)
0.916700 0.399577i \(-0.130843\pi\)
\(642\) 0 0
\(643\) 12008.9 + 20800.1i 0.736526 + 1.27570i 0.954051 + 0.299646i \(0.0968685\pi\)
−0.217525 + 0.976055i \(0.569798\pi\)
\(644\) −9719.24 16834.2i −0.594707 1.03006i
\(645\) 0 0
\(646\) −3048.46 + 5280.09i −0.185666 + 0.321582i
\(647\) −18588.3 −1.12949 −0.564747 0.825264i \(-0.691026\pi\)
−0.564747 + 0.825264i \(0.691026\pi\)
\(648\) 0 0
\(649\) −7101.83 −0.429540
\(650\) −1444.80 + 2502.47i −0.0871844 + 0.151008i
\(651\) 0 0
\(652\) −2216.22 3838.61i −0.133120 0.230570i
\(653\) 6085.97 + 10541.2i 0.364721 + 0.631714i 0.988731 0.149701i \(-0.0478312\pi\)
−0.624011 + 0.781416i \(0.714498\pi\)
\(654\) 0 0
\(655\) 2008.53 3478.87i 0.119816 0.207528i
\(656\) −9118.04 −0.542682
\(657\) 0 0
\(658\) −11487.6 −0.680597
\(659\) 4294.82 7438.84i 0.253873 0.439721i −0.710716 0.703479i \(-0.751629\pi\)
0.964589 + 0.263758i \(0.0849621\pi\)
\(660\) 0 0
\(661\) −12497.7 21646.6i −0.735405 1.27376i −0.954545 0.298066i \(-0.903659\pi\)
0.219140 0.975693i \(-0.429675\pi\)
\(662\) 1997.23 + 3459.31i 0.117258 + 0.203096i
\(663\) 0 0
\(664\) 5448.36 9436.83i 0.318430 0.551536i
\(665\) −10667.4 −0.622053
\(666\) 0 0
\(667\) 35039.4 2.03408
\(668\) 3582.36 6204.82i 0.207493 0.359389i
\(669\) 0 0
\(670\) −138.979 240.718i −0.00801376 0.0138802i
\(671\) −2304.14 3990.88i −0.132564 0.229607i
\(672\) 0 0
\(673\) 1270.08 2199.85i 0.0727461 0.126000i −0.827358 0.561675i \(-0.810157\pi\)
0.900104 + 0.435675i \(0.143490\pi\)
\(674\) 3731.94 0.213277
\(675\) 0 0
\(676\) −33643.4 −1.91417
\(677\) 2098.89 3635.39i 0.119154 0.206380i −0.800279 0.599628i \(-0.795315\pi\)
0.919433 + 0.393248i \(0.128649\pi\)
\(678\) 0 0
\(679\) −6689.13 11585.9i −0.378064 0.654826i
\(680\) 2452.18 + 4247.30i 0.138289 + 0.239524i
\(681\) 0 0
\(682\) 1232.87 2135.39i 0.0692212 0.119895i
\(683\) −8523.02 −0.477488 −0.238744 0.971083i \(-0.576736\pi\)
−0.238744 + 0.971083i \(0.576736\pi\)
\(684\) 0 0
\(685\) 4345.76 0.242398
\(686\) −1678.79 + 2907.75i −0.0934352 + 0.161834i
\(687\) 0 0
\(688\) 2429.57 + 4208.15i 0.134632 + 0.233189i
\(689\) 1284.46 + 2224.75i 0.0710219 + 0.123014i
\(690\) 0 0
\(691\) 10146.0 17573.4i 0.558571 0.967473i −0.439045 0.898465i \(-0.644683\pi\)
0.997616 0.0690084i \(-0.0219835\pi\)
\(692\) −18252.6 −1.00269
\(693\) 0 0
\(694\) 184.896 0.0101132
\(695\) −490.995 + 850.428i −0.0267978 + 0.0464152i
\(696\) 0 0
\(697\) −9525.10 16498.0i −0.517631 0.896563i
\(698\) 3456.53 + 5986.88i 0.187438 + 0.324652i
\(699\) 0 0
\(700\) −1880.01 + 3256.27i −0.101511 + 0.175822i
\(701\) −11223.6 −0.604721 −0.302361 0.953194i \(-0.597775\pi\)
−0.302361 + 0.953194i \(0.597775\pi\)
\(702\) 0 0
\(703\) 6242.38 0.334901
\(704\) 188.259 326.074i 0.0100785 0.0174565i
\(705\) 0 0
\(706\) −2262.52 3918.79i −0.120610 0.208903i
\(707\) −2735.83 4738.60i −0.145533 0.252070i
\(708\) 0 0
\(709\) 9965.49 17260.7i 0.527873 0.914302i −0.471600 0.881813i \(-0.656323\pi\)
0.999472 0.0324893i \(-0.0103435\pi\)
\(710\) −3643.17 −0.192572
\(711\) 0 0
\(712\) 4241.83 0.223271
\(713\) −14510.7 + 25133.4i −0.762177 + 1.32013i
\(714\) 0 0
\(715\) −1802.44 3121.92i −0.0942762 0.163291i
\(716\) −10676.0 18491.3i −0.557235 0.965159i
\(717\) 0 0
\(718\) 5394.70 9343.90i 0.280402 0.485670i
\(719\) −3186.13 −0.165261 −0.0826305 0.996580i \(-0.526332\pi\)
−0.0826305 + 0.996580i \(0.526332\pi\)
\(720\) 0 0
\(721\) −9244.58 −0.477512
\(722\) −646.914 + 1120.49i −0.0333458 + 0.0577566i
\(723\) 0 0
\(724\) −3592.69 6222.72i −0.184421 0.319427i
\(725\) −3388.86 5869.67i −0.173599 0.300682i
\(726\) 0 0
\(727\) 11544.1 19995.0i 0.588923 1.02004i −0.405451 0.914117i \(-0.632886\pi\)
0.994374 0.105927i \(-0.0337810\pi\)
\(728\) 39672.5 2.01973
\(729\) 0 0
\(730\) 1230.65 0.0623949
\(731\) −5076.08 + 8792.02i −0.256834 + 0.444849i
\(732\) 0 0
\(733\) 14900.7 + 25808.8i 0.750846 + 1.30050i 0.947413 + 0.320013i \(0.103687\pi\)
−0.196567 + 0.980490i \(0.562979\pi\)
\(734\) −87.6698 151.849i −0.00440866 0.00763602i
\(735\) 0 0
\(736\) −11898.0 + 20607.9i −0.595877 + 1.03209i
\(737\) 346.761 0.0173312
\(738\) 0 0
\(739\) 39741.5 1.97823 0.989117 0.147134i \(-0.0470047\pi\)
0.989117 + 0.147134i \(0.0470047\pi\)
\(740\) 1100.14 1905.50i 0.0546515 0.0946591i
\(741\) 0 0
\(742\) −471.555 816.758i −0.0233307 0.0404099i
\(743\) −4856.77 8412.17i −0.239808 0.415360i 0.720851 0.693090i \(-0.243751\pi\)
−0.960659 + 0.277730i \(0.910418\pi\)
\(744\) 0 0
\(745\) −1885.71 + 3266.14i −0.0927342 + 0.160620i
\(746\) 12404.2 0.608779
\(747\) 0 0
\(748\) −2680.97 −0.131051
\(749\) 21396.4 37059.6i 1.04380 1.80791i
\(750\) 0 0
\(751\) 1254.64 + 2173.10i 0.0609619 + 0.105589i 0.894896 0.446275i \(-0.147250\pi\)
−0.833934 + 0.551865i \(0.813917\pi\)
\(752\) −4462.78 7729.76i −0.216411 0.374834i
\(753\) 0 0
\(754\) −15667.9 + 27137.7i −0.756755 + 1.31074i
\(755\) −10288.2 −0.495927
\(756\) 0 0
\(757\) 9705.73 0.465998 0.232999 0.972477i \(-0.425146\pi\)
0.232999 + 0.972477i \(0.425146\pi\)
\(758\) −4089.34 + 7082.94i −0.195952 + 0.339398i
\(759\) 0 0
\(760\) 4180.62 + 7241.05i 0.199536 + 0.345606i
\(761\) 3889.22 + 6736.33i 0.185262 + 0.320883i 0.943665 0.330903i \(-0.107353\pi\)
−0.758403 + 0.651786i \(0.774020\pi\)
\(762\) 0 0
\(763\) 18445.7 31949.0i 0.875204 1.51590i
\(764\) 5816.04 0.275415
\(765\) 0 0
\(766\) 3451.39 0.162799
\(767\) −37376.7 + 64738.3i −1.75957 + 3.04767i
\(768\) 0 0
\(769\) −693.951 1201.96i −0.0325416 0.0563638i 0.849296 0.527917i \(-0.177027\pi\)
−0.881838 + 0.471553i \(0.843693\pi\)
\(770\) 661.718 + 1146.13i 0.0309697 + 0.0536410i
\(771\) 0 0
\(772\) −13330.3 + 23088.7i −0.621460 + 1.07640i
\(773\) 20692.0 0.962796 0.481398 0.876502i \(-0.340129\pi\)
0.481398 + 0.876502i \(0.340129\pi\)
\(774\) 0 0
\(775\) 5613.67 0.260192
\(776\) −5243.02 + 9081.17i −0.242543 + 0.420097i
\(777\) 0 0
\(778\) −2819.85 4884.12i −0.129944 0.225070i
\(779\) −16239.0 28126.7i −0.746883 1.29364i
\(780\) 0 0
\(781\) 2272.49 3936.07i 0.104118 0.180338i
\(782\) −8902.82 −0.407115
\(783\) 0 0
\(784\) 5914.45 0.269426
\(785\) −8396.46 + 14543.1i −0.381761 + 0.661230i
\(786\) 0