Properties

Label 405.4.e.u.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.u.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 −0.724593 0.689177i \(-0.757972\pi\)
0.959141 + 0.282927i \(0.0913054\pi\)
\(3\) 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 −0.917149 0.398544i \(-0.869516\pi\)
0.803724 + 0.595003i \(0.202849\pi\)
\(12\) 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 \(-0.379240\pi\)
0.370342 + 0.928895i \(0.379240\pi\)
\(18\) 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 \(0.0325751\pi\)
−0.408912 + 0.912574i \(0.634092\pi\)
\(24\) 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 \(-0.498743\pi\)
0.864044 0.503416i \(-0.167924\pi\)
\(30\) 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 \(-0.920360\pi\)
0.270009 0.962858i \(-0.412973\pi\)
\(42\) 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 \(-0.645141\pi\)
0.997714 0.0675743i \(-0.0215260\pi\)
\(48\) 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 \(-0.487833\pi\)
0.0382135 + 0.999270i \(0.487833\pi\)
\(54\) 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 \(0.228981\pi\)
0.194519 + 0.980899i \(0.437685\pi\)
\(60\) 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 \(-0.651781\pi\)
−0.458970 + 0.888452i \(0.651781\pi\)
\(72\) 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 −0.609891 0.792485i \(-0.708787\pi\)
0.991258 + 0.131939i \(0.0421201\pi\)
\(84\) 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 \(-0.457314\pi\)
0.133700 + 0.991022i \(0.457314\pi\)
\(90\) 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 −0.916503 0.400027i \(-0.869001\pi\)
0.804685 + 0.593702i \(0.202334\pi\)
\(102\) 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 \(-0.796227\pi\)
−0.801993 + 0.597334i \(0.796227\pi\)
\(108\) 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 0.986244 0.165293i \(-0.0528571\pi\)
−0.636271 + 0.771466i \(0.719524\pi\)
\(114\) 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 0.968324 0.249698i \(-0.0803313\pi\)
−0.700407 + 0.713744i \(0.746998\pi\)
\(132\) 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 −0.969121 0.246587i \(-0.920691\pi\)
0.698111 + 0.715990i \(0.254024\pi\)
\(138\) 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 0.743522 0.668711i \(-0.233154\pi\)
−0.950882 + 0.309553i \(0.899820\pi\)
\(150\) 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 0.967834 0.251589i \(-0.0809530\pi\)
−0.701799 + 0.712375i \(0.747620\pi\)
\(168\) 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 \(-0.611110\pi\)
0.984807 0.173652i \(-0.0555566\pi\)
\(174\) 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 \(-0.246676\pi\)
0.714452 + 0.699685i \(0.246676\pi\)
\(180\) 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 −0.940700 0.339240i \(-0.889830\pi\)
0.764140 + 0.645050i \(0.223164\pi\)
\(192\) 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 \(-0.613120\pi\)
−0.347944 + 0.937515i \(0.613120\pi\)
\(198\) 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 \(0.532138\pi\)
−0.811218 + 0.584744i \(0.801195\pi\)
\(228\) 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 \(-0.387906\pi\)
0.344920 + 0.938632i \(0.387906\pi\)
\(234\) 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 \(0.222942\pi\)
0.175873 + 0.984413i \(0.443725\pi\)
\(240\) 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 \(-0.668800\pi\)
−0.505792 + 0.862656i \(0.668800\pi\)
\(252\) 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 \(0.0407678\pi\)
−0.385291 + 0.922795i \(0.625899\pi\)
\(258\) 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 −0.531298 0.847185i \(-0.678296\pi\)
0.999333 + 0.0365251i \(0.0116289\pi\)
\(264\) 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 \(-0.579795\pi\)
−0.248065 + 0.968743i \(0.579795\pi\)
\(270\) 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 \(-0.595716\pi\)
0.975261 0.221058i \(-0.0709511\pi\)
\(282\) 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 \(0.0943252\pi\)
−0.225316 + 0.974286i \(0.572341\pi\)
\(294\) 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 0.948303 0.317366i \(-0.102798\pi\)
−0.748998 + 0.662572i \(0.769465\pi\)
\(312\) 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 \(0.486930\pi\)
−0.885820 + 0.464028i \(0.846404\pi\)
\(318\) 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 0.871365 0.490636i \(-0.163235\pi\)
−0.860585 + 0.509306i \(0.829902\pi\)
\(348\) 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 −0.708355 0.705856i \(-0.750563\pi\)
0.965467 + 0.260526i \(0.0838959\pi\)
\(354\) 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 \(-0.296063\pi\)
0.597747 + 0.801685i \(0.296063\pi\)
\(360\) 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 0.939649 0.342139i \(-0.111151\pi\)
−0.766126 + 0.642690i \(0.777818\pi\)
\(384\) 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 −0.693631 0.720330i \(-0.743990\pi\)
0.970640 + 0.240537i \(0.0773237\pi\)
\(390\) 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 0.999764 0.0217370i \(-0.00691965\pi\)
−0.518707 + 0.854952i \(0.673586\pi\)
\(402\) 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 0.897661 0.440686i \(-0.145265\pi\)
−0.830476 + 0.557054i \(0.811932\pi\)
\(420\) 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 \(-0.693709\pi\)
−0.571683 + 0.820475i \(0.693709\pi\)
\(432\) 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 −0.870489 0.492188i \(-0.836197\pi\)
0.861491 + 0.507772i \(0.169531\pi\)
\(444\) 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 \(-0.566560\pi\)
−0.207582 + 0.978218i \(0.566560\pi\)
\(450\) 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 \(-0.647966\pi\)
0.998275 0.0587164i \(-0.0187008\pi\)
\(462\) 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 \(-0.199479\pi\)
0.809978 + 0.586461i \(0.199479\pi\)
\(468\) 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 −0.549340 0.835599i \(-0.685121\pi\)
0.998320 + 0.0579433i \(0.0184543\pi\)
\(480\) 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 0.572591 0.819841i \(-0.305938\pi\)
−0.996299 + 0.0859577i \(0.972605\pi\)
\(492\) 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 \(-0.506923\pi\)
−0.0217466 + 0.999764i \(0.506923\pi\)
\(504\) 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 0.782113 0.623136i \(-0.214142\pi\)
−0.930709 + 0.365762i \(0.880808\pi\)
\(510\) 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 \(-0.453173\pi\)
0.146582 + 0.989199i \(0.453173\pi\)
\(522\) 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 \(-0.209841\pi\)
0.790461 + 0.612513i \(0.209841\pi\)
\(558\) 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 \(0.0447643\pi\)
−0.373675 + 0.927560i \(0.621902\pi\)
\(564\) 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 −0.748621 0.662998i \(-0.769284\pi\)
0.948484 + 0.316825i \(0.102617\pi\)
\(570\) 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 −0.769202 0.639006i \(-0.779346\pi\)
0.937996 + 0.346645i \(0.112679\pi\)
\(588\) 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 \(-0.302337\pi\)
0.581830 + 0.813311i \(0.302337\pi\)
\(594\) 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 \(-0.966854\pi\)
0.407274 0.913306i \(-0.366480\pi\)
\(600\) 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 0.980071 0.198646i \(-0.0636543\pi\)
−0.662068 + 0.749444i \(0.730321\pi\)
\(618\) 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 \(0.464176\pi\)
−0.916700 + 0.399577i \(0.869157\pi\)
\(642\) 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 \(-0.308974\pi\)
0.564747 + 0.825264i \(0.308974\pi\)
\(648\) 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 0.624011 0.781416i \(-0.285502\pi\)
−0.988731 + 0.149701i \(0.952169\pi\)
\(654\) 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 −0.964589 0.263758i \(-0.915038\pi\)
0.710716 + 0.703479i \(0.248371\pi\)
\(660\) 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 −0.919433 0.393248i \(-0.871351\pi\)
0.800279 + 0.599628i \(0.204685\pi\)
\(678\) 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 \(-0.423264\pi\)
0.238744 + 0.971083i \(0.423264\pi\)
\(684\) 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 \(-0.402225\pi\)
0.302361 + 0.953194i \(0.402225\pi\)
\(702\) 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 \(-0.473668\pi\)
0.0826305 + 0.996580i \(0.473668\pi\)
\(720\) 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 0.960659 0.277730i \(-0.0895821\pi\)
−0.720851 + 0.693090i \(0.756249\pi\)
\(744\) 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 0.758403 0.651786i \(-0.225980\pi\)
−0.943665 + 0.330903i \(0.892647\pi\)
\(762\) 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 \(-0.659871\pi\)
−0.481398 + 0.876502i \(0.659871\pi\)
\(774\) 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
\(786\)