Properties

Label 405.4.e.w.136.6
Level $405$
Weight $4$
Character 405.136
Analytic conductor $23.896$
Analytic rank $0$
Dimension $12$
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: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 2 x^{11} + 2 x^{10} + 32 x^{9} + 583 x^{8} - 624 x^{7} + 594 x^{6} + 9450 x^{5} + 90513 x^{4} - 20304 x^{3} + 10368 x^{2} + 124416 x + 746496\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 136.6
Root \(-2.61824 + 2.61824i\) of defining polynomial
Character \(\chi\) \(=\) 405.136
Dual form 405.4.e.w.271.6

$q$-expansion

\(f(q)\) \(=\) \(q+(2.05867 - 3.56572i) q^{2} +(-4.47625 - 7.75309i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(10.0115 - 17.3404i) q^{7} -3.92177 q^{8} +O(q^{10})\) \(q+(2.05867 - 3.56572i) q^{2} +(-4.47625 - 7.75309i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(10.0115 - 17.3404i) q^{7} -3.92177 q^{8} -20.5867 q^{10} +(0.839133 - 1.45342i) q^{11} +(-5.55615 - 9.62353i) q^{13} +(-41.2206 - 71.3962i) q^{14} +(27.7364 - 48.0408i) q^{16} +8.98682 q^{17} -50.6419 q^{19} +(-22.3812 + 38.7655i) q^{20} +(-3.45500 - 5.98423i) q^{22} +(-107.246 - 185.755i) q^{23} +(-12.5000 + 21.6506i) q^{25} -45.7531 q^{26} -179.255 q^{28} +(38.4544 - 66.6050i) q^{29} +(136.769 + 236.890i) q^{31} +(-129.887 - 224.971i) q^{32} +(18.5009 - 32.0445i) q^{34} -100.115 q^{35} -137.283 q^{37} +(-104.255 + 180.575i) q^{38} +(9.80442 + 16.9818i) q^{40} +(26.6729 + 46.1987i) q^{41} +(-147.635 + 255.711i) q^{43} -15.0247 q^{44} -883.134 q^{46} +(97.4916 - 168.860i) q^{47} +(-28.9587 - 50.1579i) q^{49} +(51.4668 + 89.1431i) q^{50} +(-49.7414 + 86.1547i) q^{52} -450.173 q^{53} -8.39133 q^{55} +(-39.2626 + 68.0048i) q^{56} +(-158.330 - 274.236i) q^{58} +(-240.572 - 416.684i) q^{59} +(-337.927 + 585.307i) q^{61} +1126.25 q^{62} -625.798 q^{64} +(-27.7807 + 48.1177i) q^{65} +(-447.295 - 774.737i) q^{67} +(-40.2273 - 69.6757i) q^{68} +(-206.103 + 356.981i) q^{70} +721.947 q^{71} +915.175 q^{73} +(-282.621 + 489.513i) q^{74} +(226.686 + 392.632i) q^{76} +(-16.8019 - 29.1017i) q^{77} +(-29.8321 + 51.6707i) q^{79} -277.364 q^{80} +219.643 q^{82} +(-371.438 + 643.349i) q^{83} +(-22.4671 - 38.9141i) q^{85} +(607.863 + 1052.85i) q^{86} +(-3.29089 + 5.69998i) q^{88} +1540.72 q^{89} -222.501 q^{91} +(-960.116 + 1662.97i) q^{92} +(-401.406 - 695.256i) q^{94} +(126.605 + 219.286i) q^{95} +(560.783 - 971.305i) q^{97} -238.465 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 4 q^{2} - 34 q^{4} - 30 q^{5} - 40 q^{7} + 132 q^{8} + O(q^{10}) \) \( 12 q - 4 q^{2} - 34 q^{4} - 30 q^{5} - 40 q^{7} + 132 q^{8} + 40 q^{10} - 88 q^{11} - 20 q^{13} - 180 q^{14} - 58 q^{16} + 248 q^{17} - 92 q^{19} - 170 q^{20} + 74 q^{22} - 210 q^{23} - 150 q^{25} + 8 q^{26} + 704 q^{28} - 296 q^{29} + 104 q^{31} - 722 q^{32} + 428 q^{34} + 400 q^{35} - 408 q^{37} + 20 q^{38} - 330 q^{40} - 344 q^{41} - 512 q^{43} + 1432 q^{44} - 372 q^{46} - 238 q^{47} - 68 q^{49} - 100 q^{50} + 468 q^{52} + 1700 q^{53} + 880 q^{55} - 2316 q^{56} - 890 q^{58} - 1840 q^{59} + 364 q^{61} + 2076 q^{62} - 1980 q^{64} - 100 q^{65} - 88 q^{67} - 236 q^{68} - 900 q^{70} + 2728 q^{71} + 1672 q^{73} - 1316 q^{74} + 2106 q^{76} - 840 q^{77} + 680 q^{79} + 580 q^{80} + 3484 q^{82} - 2148 q^{83} - 620 q^{85} - 2872 q^{86} - 1296 q^{88} + 6000 q^{89} - 6116 q^{91} - 1002 q^{92} + 3662 q^{94} + 230 q^{95} + 612 q^{97} + 3964 q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.05867 3.56572i 0.727850 1.26067i −0.229940 0.973205i \(-0.573853\pi\)
0.957790 0.287468i \(-0.0928136\pi\)
\(3\) 0 0
\(4\) −4.47625 7.75309i −0.559531 0.969137i
\(5\) −2.50000 4.33013i −0.223607 0.387298i
\(6\) 0 0
\(7\) 10.0115 17.3404i 0.540568 0.936291i −0.458303 0.888796i \(-0.651543\pi\)
0.998871 0.0474955i \(-0.0151240\pi\)
\(8\) −3.92177 −0.173319
\(9\) 0 0
\(10\) −20.5867 −0.651009
\(11\) 0.839133 1.45342i 0.0230007 0.0398385i −0.854296 0.519787i \(-0.826011\pi\)
0.877297 + 0.479948i \(0.159345\pi\)
\(12\) 0 0
\(13\) −5.55615 9.62353i −0.118538 0.205314i 0.800650 0.599132i \(-0.204488\pi\)
−0.919189 + 0.393818i \(0.871154\pi\)
\(14\) −41.2206 71.3962i −0.786905 1.36296i
\(15\) 0 0
\(16\) 27.7364 48.0408i 0.433381 0.750638i
\(17\) 8.98682 0.128213 0.0641066 0.997943i \(-0.479580\pi\)
0.0641066 + 0.997943i \(0.479580\pi\)
\(18\) 0 0
\(19\) −50.6419 −0.611477 −0.305738 0.952116i \(-0.598903\pi\)
−0.305738 + 0.952116i \(0.598903\pi\)
\(20\) −22.3812 + 38.7655i −0.250230 + 0.433411i
\(21\) 0 0
\(22\) −3.45500 5.98423i −0.0334822 0.0579928i
\(23\) −107.246 185.755i −0.972272 1.68402i −0.688658 0.725086i \(-0.741800\pi\)
−0.283614 0.958939i \(-0.591533\pi\)
\(24\) 0 0
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) −45.7531 −0.345113
\(27\) 0 0
\(28\) −179.255 −1.20986
\(29\) 38.4544 66.6050i 0.246235 0.426491i −0.716243 0.697851i \(-0.754140\pi\)
0.962478 + 0.271360i \(0.0874733\pi\)
\(30\) 0 0
\(31\) 136.769 + 236.890i 0.792399 + 1.37247i 0.924478 + 0.381236i \(0.124501\pi\)
−0.132079 + 0.991239i \(0.542165\pi\)
\(32\) −129.887 224.971i −0.717532 1.24280i
\(33\) 0 0
\(34\) 18.5009 32.0445i 0.0933200 0.161635i
\(35\) −100.115 −0.483499
\(36\) 0 0
\(37\) −137.283 −0.609978 −0.304989 0.952356i \(-0.598653\pi\)
−0.304989 + 0.952356i \(0.598653\pi\)
\(38\) −104.255 + 180.575i −0.445063 + 0.770872i
\(39\) 0 0
\(40\) 9.80442 + 16.9818i 0.0387554 + 0.0671263i
\(41\) 26.6729 + 46.1987i 0.101600 + 0.175976i 0.912344 0.409424i \(-0.134270\pi\)
−0.810744 + 0.585401i \(0.800937\pi\)
\(42\) 0 0
\(43\) −147.635 + 255.711i −0.523584 + 0.906874i 0.476039 + 0.879424i \(0.342072\pi\)
−0.999623 + 0.0274502i \(0.991261\pi\)
\(44\) −15.0247 −0.0514785
\(45\) 0 0
\(46\) −883.134 −2.83067
\(47\) 97.4916 168.860i 0.302566 0.524060i −0.674150 0.738594i \(-0.735490\pi\)
0.976716 + 0.214534i \(0.0688234\pi\)
\(48\) 0 0
\(49\) −28.9587 50.1579i −0.0844276 0.146233i
\(50\) 51.4668 + 89.1431i 0.145570 + 0.252135i
\(51\) 0 0
\(52\) −49.7414 + 86.1547i −0.132652 + 0.229760i
\(53\) −450.173 −1.16672 −0.583359 0.812214i \(-0.698262\pi\)
−0.583359 + 0.812214i \(0.698262\pi\)
\(54\) 0 0
\(55\) −8.39133 −0.0205725
\(56\) −39.2626 + 68.0048i −0.0936909 + 0.162277i
\(57\) 0 0
\(58\) −158.330 274.236i −0.358444 0.620843i
\(59\) −240.572 416.684i −0.530845 0.919451i −0.999352 0.0359910i \(-0.988541\pi\)
0.468507 0.883460i \(-0.344792\pi\)
\(60\) 0 0
\(61\) −337.927 + 585.307i −0.709297 + 1.22854i 0.255821 + 0.966724i \(0.417654\pi\)
−0.965118 + 0.261814i \(0.915679\pi\)
\(62\) 1126.25 2.30699
\(63\) 0 0
\(64\) −625.798 −1.22226
\(65\) −27.7807 + 48.1177i −0.0530120 + 0.0918194i
\(66\) 0 0
\(67\) −447.295 774.737i −0.815608 1.41267i −0.908890 0.417035i \(-0.863069\pi\)
0.0932823 0.995640i \(-0.470264\pi\)
\(68\) −40.2273 69.6757i −0.0717393 0.124256i
\(69\) 0 0
\(70\) −206.103 + 356.981i −0.351915 + 0.609534i
\(71\) 721.947 1.20675 0.603376 0.797457i \(-0.293822\pi\)
0.603376 + 0.797457i \(0.293822\pi\)
\(72\) 0 0
\(73\) 915.175 1.46730 0.733651 0.679526i \(-0.237815\pi\)
0.733651 + 0.679526i \(0.237815\pi\)
\(74\) −282.621 + 489.513i −0.443973 + 0.768983i
\(75\) 0 0
\(76\) 226.686 + 392.632i 0.342140 + 0.592604i
\(77\) −16.8019 29.1017i −0.0248669 0.0430708i
\(78\) 0 0
\(79\) −29.8321 + 51.6707i −0.0424858 + 0.0735875i −0.886486 0.462755i \(-0.846861\pi\)
0.844001 + 0.536342i \(0.180194\pi\)
\(80\) −277.364 −0.387628
\(81\) 0 0
\(82\) 219.643 0.295798
\(83\) −371.438 + 643.349i −0.491212 + 0.850803i −0.999949 0.0101184i \(-0.996779\pi\)
0.508737 + 0.860922i \(0.330112\pi\)
\(84\) 0 0
\(85\) −22.4671 38.9141i −0.0286693 0.0496568i
\(86\) 607.863 + 1052.85i 0.762181 + 1.32014i
\(87\) 0 0
\(88\) −3.29089 + 5.69998i −0.00398647 + 0.00690477i
\(89\) 1540.72 1.83501 0.917505 0.397723i \(-0.130200\pi\)
0.917505 + 0.397723i \(0.130200\pi\)
\(90\) 0 0
\(91\) −222.501 −0.256312
\(92\) −960.116 + 1662.97i −1.08803 + 1.88453i
\(93\) 0 0
\(94\) −401.406 695.256i −0.440445 0.762874i
\(95\) 126.605 + 219.286i 0.136730 + 0.236824i
\(96\) 0 0
\(97\) 560.783 971.305i 0.586999 1.01671i −0.407624 0.913150i \(-0.633643\pi\)
0.994623 0.103562i \(-0.0330240\pi\)
\(98\) −238.465 −0.245802
\(99\) 0 0
\(100\) 223.812 0.223812
\(101\) 879.236 1522.88i 0.866211 1.50032i 0.000370864 1.00000i \(-0.499882\pi\)
0.865840 0.500321i \(-0.166785\pi\)
\(102\) 0 0
\(103\) −528.242 914.941i −0.505332 0.875261i −0.999981 0.00616773i \(-0.998037\pi\)
0.494649 0.869093i \(-0.335297\pi\)
\(104\) 21.7899 + 37.7413i 0.0205450 + 0.0355850i
\(105\) 0 0
\(106\) −926.759 + 1605.19i −0.849196 + 1.47085i
\(107\) 1470.03 1.32816 0.664081 0.747661i \(-0.268823\pi\)
0.664081 + 0.747661i \(0.268823\pi\)
\(108\) 0 0
\(109\) 918.889 0.807464 0.403732 0.914877i \(-0.367713\pi\)
0.403732 + 0.914877i \(0.367713\pi\)
\(110\) −17.2750 + 29.9212i −0.0149737 + 0.0259352i
\(111\) 0 0
\(112\) −555.363 961.917i −0.468544 0.811541i
\(113\) −493.609 854.955i −0.410927 0.711747i 0.584064 0.811708i \(-0.301462\pi\)
−0.994991 + 0.0999606i \(0.968128\pi\)
\(114\) 0 0
\(115\) −536.228 + 928.774i −0.434813 + 0.753119i
\(116\) −688.526 −0.551104
\(117\) 0 0
\(118\) −1981.04 −1.54550
\(119\) 89.9712 155.835i 0.0693080 0.120045i
\(120\) 0 0
\(121\) 664.092 + 1150.24i 0.498942 + 0.864193i
\(122\) 1391.36 + 2409.91i 1.03252 + 1.78838i
\(123\) 0 0
\(124\) 1224.42 2120.76i 0.886744 1.53589i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 1480.10 1.03415 0.517077 0.855939i \(-0.327020\pi\)
0.517077 + 0.855939i \(0.327020\pi\)
\(128\) −249.214 + 431.651i −0.172091 + 0.298070i
\(129\) 0 0
\(130\) 114.383 + 198.117i 0.0771695 + 0.133662i
\(131\) 253.298 + 438.724i 0.168937 + 0.292607i 0.938046 0.346510i \(-0.112633\pi\)
−0.769110 + 0.639117i \(0.779300\pi\)
\(132\) 0 0
\(133\) −507.000 + 878.149i −0.330545 + 0.572520i
\(134\) −3683.33 −2.37456
\(135\) 0 0
\(136\) −35.2442 −0.0222218
\(137\) −487.861 + 845.001i −0.304240 + 0.526958i −0.977092 0.212819i \(-0.931736\pi\)
0.672852 + 0.739777i \(0.265069\pi\)
\(138\) 0 0
\(139\) 944.413 + 1635.77i 0.576288 + 0.998160i 0.995900 + 0.0904566i \(0.0288327\pi\)
−0.419612 + 0.907703i \(0.637834\pi\)
\(140\) 448.138 + 776.198i 0.270533 + 0.468576i
\(141\) 0 0
\(142\) 1486.25 2574.26i 0.878334 1.52132i
\(143\) −18.6494 −0.0109059
\(144\) 0 0
\(145\) −384.544 −0.220239
\(146\) 1884.04 3263.26i 1.06798 1.84979i
\(147\) 0 0
\(148\) 614.513 + 1064.37i 0.341302 + 0.591152i
\(149\) −1291.15 2236.33i −0.709898 1.22958i −0.964895 0.262637i \(-0.915408\pi\)
0.254997 0.966942i \(-0.417926\pi\)
\(150\) 0 0
\(151\) −1268.96 + 2197.91i −0.683885 + 1.18452i 0.289901 + 0.957057i \(0.406378\pi\)
−0.973786 + 0.227467i \(0.926956\pi\)
\(152\) 198.606 0.105981
\(153\) 0 0
\(154\) −138.358 −0.0723976
\(155\) 683.843 1184.45i 0.354372 0.613789i
\(156\) 0 0
\(157\) −52.5175 90.9630i −0.0266965 0.0462397i 0.852368 0.522942i \(-0.175165\pi\)
−0.879065 + 0.476702i \(0.841832\pi\)
\(158\) 122.829 + 212.746i 0.0618465 + 0.107121i
\(159\) 0 0
\(160\) −649.436 + 1124.86i −0.320890 + 0.555798i
\(161\) −4294.74 −2.10232
\(162\) 0 0
\(163\) 2228.88 1.07104 0.535519 0.844523i \(-0.320116\pi\)
0.535519 + 0.844523i \(0.320116\pi\)
\(164\) 238.789 413.594i 0.113697 0.196929i
\(165\) 0 0
\(166\) 1529.34 + 2648.89i 0.715057 + 1.23851i
\(167\) −1406.90 2436.82i −0.651911 1.12914i −0.982659 0.185424i \(-0.940634\pi\)
0.330748 0.943719i \(-0.392699\pi\)
\(168\) 0 0
\(169\) 1036.76 1795.72i 0.471897 0.817350i
\(170\) −185.009 −0.0834679
\(171\) 0 0
\(172\) 2643.40 1.17185
\(173\) 1642.22 2844.41i 0.721711 1.25004i −0.238603 0.971117i \(-0.576689\pi\)
0.960314 0.278922i \(-0.0899772\pi\)
\(174\) 0 0
\(175\) 250.286 + 433.509i 0.108114 + 0.187258i
\(176\) −46.5490 80.6253i −0.0199362 0.0345304i
\(177\) 0 0
\(178\) 3171.83 5493.78i 1.33561 2.31335i
\(179\) 1268.62 0.529726 0.264863 0.964286i \(-0.414673\pi\)
0.264863 + 0.964286i \(0.414673\pi\)
\(180\) 0 0
\(181\) 1080.10 0.443554 0.221777 0.975097i \(-0.428814\pi\)
0.221777 + 0.975097i \(0.428814\pi\)
\(182\) −458.056 + 793.376i −0.186557 + 0.323126i
\(183\) 0 0
\(184\) 420.592 + 728.487i 0.168513 + 0.291874i
\(185\) 343.208 + 594.453i 0.136395 + 0.236243i
\(186\) 0 0
\(187\) 7.54114 13.0616i 0.00294900 0.00510782i
\(188\) −1745.59 −0.677181
\(189\) 0 0
\(190\) 1042.55 0.398077
\(191\) −143.357 + 248.302i −0.0543087 + 0.0940654i −0.891902 0.452229i \(-0.850629\pi\)
0.837593 + 0.546295i \(0.183962\pi\)
\(192\) 0 0
\(193\) 2325.35 + 4027.63i 0.867267 + 1.50215i 0.864779 + 0.502153i \(0.167459\pi\)
0.00248836 + 0.999997i \(0.499208\pi\)
\(194\) −2308.93 3999.19i −0.854494 1.48003i
\(195\) 0 0
\(196\) −259.252 + 449.038i −0.0944797 + 0.163644i
\(197\) 1694.82 0.612947 0.306474 0.951879i \(-0.400851\pi\)
0.306474 + 0.951879i \(0.400851\pi\)
\(198\) 0 0
\(199\) −3249.77 −1.15764 −0.578819 0.815456i \(-0.696486\pi\)
−0.578819 + 0.815456i \(0.696486\pi\)
\(200\) 49.0221 84.9088i 0.0173319 0.0300198i
\(201\) 0 0
\(202\) −3620.12 6270.23i −1.26094 2.18402i
\(203\) −769.970 1333.63i −0.266213 0.461095i
\(204\) 0 0
\(205\) 133.364 230.994i 0.0454369 0.0786990i
\(206\) −4349.90 −1.47122
\(207\) 0 0
\(208\) −616.430 −0.205489
\(209\) −42.4953 + 73.6041i −0.0140644 + 0.0243603i
\(210\) 0 0
\(211\) 539.279 + 934.059i 0.175950 + 0.304755i 0.940490 0.339822i \(-0.110367\pi\)
−0.764539 + 0.644577i \(0.777034\pi\)
\(212\) 2015.09 + 3490.24i 0.652815 + 1.13071i
\(213\) 0 0
\(214\) 3026.31 5241.72i 0.966702 1.67438i
\(215\) 1476.35 0.468308
\(216\) 0 0
\(217\) 5477.01 1.71338
\(218\) 1891.69 3276.50i 0.587713 1.01795i
\(219\) 0 0
\(220\) 37.5617 + 65.0588i 0.0115110 + 0.0199376i
\(221\) −49.9321 86.4850i −0.0151982 0.0263240i
\(222\) 0 0
\(223\) 2571.64 4454.21i 0.772241 1.33756i −0.164091 0.986445i \(-0.552469\pi\)
0.936332 0.351115i \(-0.114197\pi\)
\(224\) −5201.44 −1.55150
\(225\) 0 0
\(226\) −4064.71 −1.19637
\(227\) −1454.83 + 2519.84i −0.425377 + 0.736774i −0.996456 0.0841209i \(-0.973192\pi\)
0.571079 + 0.820895i \(0.306525\pi\)
\(228\) 0 0
\(229\) −862.910 1494.60i −0.249007 0.431293i 0.714243 0.699897i \(-0.246771\pi\)
−0.963251 + 0.268604i \(0.913438\pi\)
\(230\) 2207.83 + 3824.08i 0.632958 + 1.09631i
\(231\) 0 0
\(232\) −150.809 + 261.209i −0.0426772 + 0.0739191i
\(233\) 1087.48 0.305765 0.152882 0.988244i \(-0.451144\pi\)
0.152882 + 0.988244i \(0.451144\pi\)
\(234\) 0 0
\(235\) −974.916 −0.270623
\(236\) −2153.72 + 3730.36i −0.594049 + 1.02892i
\(237\) 0 0
\(238\) −370.442 641.625i −0.100892 0.174749i
\(239\) 159.672 + 276.561i 0.0432149 + 0.0748504i 0.886824 0.462108i \(-0.152907\pi\)
−0.843609 + 0.536958i \(0.819573\pi\)
\(240\) 0 0
\(241\) −1822.91 + 3157.38i −0.487238 + 0.843920i −0.999892 0.0146745i \(-0.995329\pi\)
0.512655 + 0.858595i \(0.328662\pi\)
\(242\) 5468.58 1.45262
\(243\) 0 0
\(244\) 6050.58 1.58750
\(245\) −144.793 + 250.789i −0.0377572 + 0.0653973i
\(246\) 0 0
\(247\) 281.374 + 487.354i 0.0724834 + 0.125545i
\(248\) −536.375 929.028i −0.137338 0.237876i
\(249\) 0 0
\(250\) 257.334 445.715i 0.0651009 0.112758i
\(251\) −572.874 −0.144062 −0.0720309 0.997402i \(-0.522948\pi\)
−0.0720309 + 0.997402i \(0.522948\pi\)
\(252\) 0 0
\(253\) −359.973 −0.0894519
\(254\) 3047.04 5277.62i 0.752709 1.30373i
\(255\) 0 0
\(256\) −1477.09 2558.40i −0.360618 0.624609i
\(257\) 1838.83 + 3184.94i 0.446315 + 0.773040i 0.998143 0.0609179i \(-0.0194028\pi\)
−0.551828 + 0.833958i \(0.686069\pi\)
\(258\) 0 0
\(259\) −1374.40 + 2380.54i −0.329735 + 0.571117i
\(260\) 497.414 0.118647
\(261\) 0 0
\(262\) 2085.83 0.491842
\(263\) −1000.86 + 1733.53i −0.234659 + 0.406442i −0.959174 0.282818i \(-0.908731\pi\)
0.724514 + 0.689260i \(0.242064\pi\)
\(264\) 0 0
\(265\) 1125.43 + 1949.31i 0.260886 + 0.451868i
\(266\) 2087.49 + 3615.64i 0.481174 + 0.833418i
\(267\) 0 0
\(268\) −4004.41 + 6935.83i −0.912716 + 1.58087i
\(269\) −20.1629 −0.00457009 −0.00228504 0.999997i \(-0.500727\pi\)
−0.00228504 + 0.999997i \(0.500727\pi\)
\(270\) 0 0
\(271\) 4733.12 1.06095 0.530474 0.847701i \(-0.322014\pi\)
0.530474 + 0.847701i \(0.322014\pi\)
\(272\) 249.262 431.734i 0.0555651 0.0962416i
\(273\) 0 0
\(274\) 2008.69 + 3479.16i 0.442881 + 0.767093i
\(275\) 20.9783 + 36.3355i 0.00460015 + 0.00796769i
\(276\) 0 0
\(277\) −2514.56 + 4355.34i −0.545434 + 0.944719i 0.453146 + 0.891436i \(0.350302\pi\)
−0.998579 + 0.0532826i \(0.983032\pi\)
\(278\) 7776.94 1.67780
\(279\) 0 0
\(280\) 392.626 0.0837996
\(281\) −2904.16 + 5030.14i −0.616539 + 1.06788i 0.373574 + 0.927600i \(0.378132\pi\)
−0.990112 + 0.140276i \(0.955201\pi\)
\(282\) 0 0
\(283\) −106.512 184.483i −0.0223726 0.0387505i 0.854622 0.519250i \(-0.173789\pi\)
−0.876995 + 0.480500i \(0.840455\pi\)
\(284\) −3231.62 5597.32i −0.675215 1.16951i
\(285\) 0 0
\(286\) −38.3930 + 66.4986i −0.00793785 + 0.0137488i
\(287\) 1068.14 0.219687
\(288\) 0 0
\(289\) −4832.24 −0.983561
\(290\) −791.650 + 1371.18i −0.160301 + 0.277649i
\(291\) 0 0
\(292\) −4096.55 7095.43i −0.821002 1.42202i
\(293\) 1796.55 + 3111.71i 0.358210 + 0.620437i 0.987662 0.156602i \(-0.0500540\pi\)
−0.629452 + 0.777039i \(0.716721\pi\)
\(294\) 0 0
\(295\) −1202.86 + 2083.42i −0.237401 + 0.411191i
\(296\) 538.392 0.105721
\(297\) 0 0
\(298\) −10632.2 −2.06680
\(299\) −1191.75 + 2064.16i −0.230503 + 0.399243i
\(300\) 0 0
\(301\) 2956.08 + 5120.09i 0.566066 + 0.980455i
\(302\) 5224.75 + 9049.53i 0.995531 + 1.72431i
\(303\) 0 0
\(304\) −1404.62 + 2432.88i −0.265002 + 0.458997i
\(305\) 3379.27 0.634415
\(306\) 0 0
\(307\) 2403.23 0.446774 0.223387 0.974730i \(-0.428289\pi\)
0.223387 + 0.974730i \(0.428289\pi\)
\(308\) −150.419 + 260.533i −0.0278277 + 0.0481989i
\(309\) 0 0
\(310\) −2815.61 4876.79i −0.515859 0.893493i
\(311\) 804.080 + 1392.71i 0.146608 + 0.253933i 0.929972 0.367631i \(-0.119831\pi\)
−0.783363 + 0.621564i \(0.786498\pi\)
\(312\) 0 0
\(313\) −1390.27 + 2408.02i −0.251063 + 0.434855i −0.963819 0.266558i \(-0.914114\pi\)
0.712755 + 0.701413i \(0.247447\pi\)
\(314\) −432.465 −0.0777242
\(315\) 0 0
\(316\) 534.144 0.0950885
\(317\) −2767.85 + 4794.05i −0.490403 + 0.849403i −0.999939 0.0110461i \(-0.996484\pi\)
0.509536 + 0.860449i \(0.329817\pi\)
\(318\) 0 0
\(319\) −64.5368 111.781i −0.0113272 0.0196192i
\(320\) 1564.49 + 2709.78i 0.273306 + 0.473380i
\(321\) 0 0
\(322\) −8841.46 + 15313.9i −1.53017 + 2.65033i
\(323\) −455.110 −0.0783994
\(324\) 0 0
\(325\) 277.807 0.0474153
\(326\) 4588.53 7947.56i 0.779555 1.35023i
\(327\) 0 0
\(328\) −104.605 181.181i −0.0176092 0.0305001i
\(329\) −1952.07 3381.08i −0.327115 0.566580i
\(330\) 0 0
\(331\) 4808.37 8328.35i 0.798466 1.38298i −0.122149 0.992512i \(-0.538979\pi\)
0.920615 0.390471i \(-0.127688\pi\)
\(332\) 6650.59 1.09939
\(333\) 0 0
\(334\) −11585.4 −1.89797
\(335\) −2236.47 + 3873.69i −0.364751 + 0.631767i
\(336\) 0 0
\(337\) 1042.23 + 1805.19i 0.168468 + 0.291795i 0.937881 0.346956i \(-0.112785\pi\)
−0.769413 + 0.638751i \(0.779451\pi\)
\(338\) −4268.69 7393.58i −0.686941 1.18982i
\(339\) 0 0
\(340\) −201.136 + 348.378i −0.0320828 + 0.0555690i
\(341\) 459.068 0.0729030
\(342\) 0 0
\(343\) 5708.19 0.898581
\(344\) 578.990 1002.84i 0.0907472 0.157179i
\(345\) 0 0
\(346\) −6761.59 11711.4i −1.05059 1.81968i
\(347\) 3056.71 + 5294.38i 0.472890 + 0.819070i 0.999519 0.0310257i \(-0.00987737\pi\)
−0.526628 + 0.850096i \(0.676544\pi\)
\(348\) 0 0
\(349\) −1094.53 + 1895.78i −0.167877 + 0.290771i −0.937673 0.347519i \(-0.887024\pi\)
0.769797 + 0.638289i \(0.220358\pi\)
\(350\) 2061.03 0.314762
\(351\) 0 0
\(352\) −435.971 −0.0660151
\(353\) 1250.10 2165.24i 0.188488 0.326471i −0.756258 0.654273i \(-0.772975\pi\)
0.944746 + 0.327802i \(0.106308\pi\)
\(354\) 0 0
\(355\) −1804.87 3126.12i −0.269838 0.467373i
\(356\) −6896.65 11945.3i −1.02675 1.77838i
\(357\) 0 0
\(358\) 2611.67 4523.54i 0.385561 0.667812i
\(359\) 841.607 0.123728 0.0618639 0.998085i \(-0.480296\pi\)
0.0618639 + 0.998085i \(0.480296\pi\)
\(360\) 0 0
\(361\) −4294.40 −0.626096
\(362\) 2223.57 3851.34i 0.322841 0.559176i
\(363\) 0 0
\(364\) 995.969 + 1725.07i 0.143415 + 0.248402i
\(365\) −2287.94 3962.82i −0.328099 0.568284i
\(366\) 0 0
\(367\) 2807.21 4862.23i 0.399278 0.691571i −0.594359 0.804200i \(-0.702594\pi\)
0.993637 + 0.112630i \(0.0359273\pi\)
\(368\) −11898.4 −1.68546
\(369\) 0 0
\(370\) 2826.21 0.397101
\(371\) −4506.89 + 7806.17i −0.630691 + 1.09239i
\(372\) 0 0
\(373\) −659.587 1142.44i −0.0915607 0.158588i 0.816607 0.577194i \(-0.195852\pi\)
−0.908168 + 0.418606i \(0.862519\pi\)
\(374\) −31.0495 53.7792i −0.00429286 0.00743545i
\(375\) 0 0
\(376\) −382.339 + 662.231i −0.0524405 + 0.0908297i
\(377\) −854.634 −0.116753
\(378\) 0 0
\(379\) −5002.07 −0.677939 −0.338970 0.940797i \(-0.610078\pi\)
−0.338970 + 0.940797i \(0.610078\pi\)
\(380\) 1133.43 1963.16i 0.153010 0.265021i
\(381\) 0 0
\(382\) 590.251 + 1022.34i 0.0790572 + 0.136931i
\(383\) −1121.22 1942.02i −0.149587 0.259092i 0.781488 0.623920i \(-0.214461\pi\)
−0.931075 + 0.364828i \(0.881128\pi\)
\(384\) 0 0
\(385\) −84.0095 + 145.509i −0.0111208 + 0.0192618i
\(386\) 19148.5 2.52496
\(387\) 0 0
\(388\) −10040.8 −1.31378
\(389\) −5696.89 + 9867.30i −0.742529 + 1.28610i 0.208811 + 0.977956i \(0.433041\pi\)
−0.951340 + 0.308142i \(0.900293\pi\)
\(390\) 0 0
\(391\) −963.797 1669.35i −0.124658 0.215914i
\(392\) 113.569 + 196.707i 0.0146329 + 0.0253450i
\(393\) 0 0
\(394\) 3489.07 6043.24i 0.446134 0.772726i
\(395\) 298.321 0.0380004
\(396\) 0 0
\(397\) −14926.0 −1.88694 −0.943472 0.331454i \(-0.892461\pi\)
−0.943472 + 0.331454i \(0.892461\pi\)
\(398\) −6690.20 + 11587.8i −0.842586 + 1.45940i
\(399\) 0 0
\(400\) 693.409 + 1201.02i 0.0866762 + 0.150128i
\(401\) −3582.82 6205.62i −0.446178 0.772803i 0.551955 0.833874i \(-0.313882\pi\)
−0.998133 + 0.0610707i \(0.980548\pi\)
\(402\) 0 0
\(403\) 1519.81 2632.39i 0.187859 0.325382i
\(404\) −15742.7 −1.93869
\(405\) 0 0
\(406\) −6340.46 −0.775053
\(407\) −115.199 + 199.530i −0.0140299 + 0.0243006i
\(408\) 0 0
\(409\) 5662.05 + 9806.96i 0.684524 + 1.18563i 0.973586 + 0.228321i \(0.0733234\pi\)
−0.289062 + 0.957310i \(0.593343\pi\)
\(410\) −549.106 951.080i −0.0661425 0.114562i
\(411\) 0 0
\(412\) −4729.08 + 8191.01i −0.565498 + 0.979471i
\(413\) −9633.93 −1.14783
\(414\) 0 0
\(415\) 3714.38 0.439353
\(416\) −1443.35 + 2499.95i −0.170110 + 0.294639i
\(417\) 0 0
\(418\) 174.968 + 303.053i 0.0204736 + 0.0354613i
\(419\) −6349.90 10998.4i −0.740365 1.28235i −0.952329 0.305072i \(-0.901319\pi\)
0.211964 0.977277i \(-0.432014\pi\)
\(420\) 0 0
\(421\) 8581.39 14863.4i 0.993424 1.72066i 0.397557 0.917577i \(-0.369858\pi\)
0.595867 0.803083i \(-0.296809\pi\)
\(422\) 4440.79 0.512261
\(423\) 0 0
\(424\) 1765.48 0.202215
\(425\) −112.335 + 194.570i −0.0128213 + 0.0222072i
\(426\) 0 0
\(427\) 6766.29 + 11719.6i 0.766847 + 1.32822i
\(428\) −6580.23 11397.3i −0.743148 1.28717i
\(429\) 0 0
\(430\) 3039.32 5264.25i 0.340858 0.590383i
\(431\) 11130.9 1.24399 0.621994 0.783022i \(-0.286323\pi\)
0.621994 + 0.783022i \(0.286323\pi\)
\(432\) 0 0
\(433\) 7675.55 0.851878 0.425939 0.904752i \(-0.359944\pi\)
0.425939 + 0.904752i \(0.359944\pi\)
\(434\) 11275.4 19529.5i 1.24708 2.16001i
\(435\) 0 0
\(436\) −4113.17 7124.23i −0.451801 0.782543i
\(437\) 5431.12 + 9406.98i 0.594522 + 1.02974i
\(438\) 0 0
\(439\) −1681.90 + 2913.13i −0.182853 + 0.316711i −0.942851 0.333214i \(-0.891867\pi\)
0.759998 + 0.649926i \(0.225200\pi\)
\(440\) 32.9089 0.00356561
\(441\) 0 0
\(442\) −411.175 −0.0442480
\(443\) 3947.03 6836.46i 0.423316 0.733205i −0.572945 0.819594i \(-0.694199\pi\)
0.996262 + 0.0863883i \(0.0275326\pi\)
\(444\) 0 0
\(445\) −3851.80 6671.51i −0.410321 0.710697i
\(446\) −10588.3 18339.5i −1.12415 1.94709i
\(447\) 0 0
\(448\) −6265.15 + 10851.6i −0.660715 + 1.14439i
\(449\) −2244.52 −0.235914 −0.117957 0.993019i \(-0.537634\pi\)
−0.117957 + 0.993019i \(0.537634\pi\)
\(450\) 0 0
\(451\) 89.5283 0.00934750
\(452\) −4419.03 + 7653.99i −0.459853 + 0.796489i
\(453\) 0 0
\(454\) 5990.04 + 10375.1i 0.619221 + 1.07252i
\(455\) 556.252 + 963.456i 0.0573131 + 0.0992693i
\(456\) 0 0
\(457\) −7374.65 + 12773.3i −0.754862 + 1.30746i 0.190581 + 0.981671i \(0.438963\pi\)
−0.945443 + 0.325787i \(0.894371\pi\)
\(458\) −7105.79 −0.724960
\(459\) 0 0
\(460\) 9601.16 0.973166
\(461\) 6239.75 10807.6i 0.630400 1.09188i −0.357070 0.934078i \(-0.616224\pi\)
0.987470 0.157807i \(-0.0504424\pi\)
\(462\) 0 0
\(463\) 4839.56 + 8382.37i 0.485774 + 0.841386i 0.999866 0.0163492i \(-0.00520436\pi\)
−0.514092 + 0.857735i \(0.671871\pi\)
\(464\) −2133.17 3694.76i −0.213427 0.369666i
\(465\) 0 0
\(466\) 2238.76 3877.65i 0.222551 0.385469i
\(467\) −6714.33 −0.665315 −0.332658 0.943048i \(-0.607945\pi\)
−0.332658 + 0.943048i \(0.607945\pi\)
\(468\) 0 0
\(469\) −17912.3 −1.76357
\(470\) −2007.03 + 3476.28i −0.196973 + 0.341168i
\(471\) 0 0
\(472\) 943.469 + 1634.14i 0.0920057 + 0.159359i
\(473\) 247.771 + 429.152i 0.0240857 + 0.0417176i
\(474\) 0 0
\(475\) 633.024 1096.43i 0.0611477 0.105911i
\(476\) −1610.93 −0.155120
\(477\) 0 0
\(478\) 1314.85 0.125816
\(479\) 1063.74 1842.45i 0.101469 0.175749i −0.810821 0.585294i \(-0.800979\pi\)
0.912290 + 0.409545i \(0.134313\pi\)
\(480\) 0 0
\(481\) 762.765 + 1321.15i 0.0723058 + 0.125237i
\(482\) 7505.56 + 13000.0i 0.709272 + 1.22849i
\(483\) 0 0
\(484\) 5945.28 10297.5i 0.558347 0.967086i
\(485\) −5607.83 −0.525028
\(486\) 0 0
\(487\) −6549.04 −0.609375 −0.304687 0.952452i \(-0.598552\pi\)
−0.304687 + 0.952452i \(0.598552\pi\)
\(488\) 1325.27 2295.44i 0.122935 0.212929i
\(489\) 0 0
\(490\) 596.163 + 1032.59i 0.0549631 + 0.0951989i
\(491\) 6466.86 + 11200.9i 0.594389 + 1.02951i 0.993633 + 0.112668i \(0.0359396\pi\)
−0.399243 + 0.916845i \(0.630727\pi\)
\(492\) 0 0
\(493\) 345.583 598.567i 0.0315705 0.0546818i
\(494\) 2317.03 0.211028
\(495\) 0 0
\(496\) 15173.9 1.37364
\(497\) 7227.74 12518.8i 0.652331 1.12987i
\(498\) 0 0
\(499\) −2560.33 4434.62i −0.229692 0.397837i 0.728025 0.685550i \(-0.240438\pi\)
−0.957717 + 0.287713i \(0.907105\pi\)
\(500\) −559.531 969.137i −0.0500460 0.0866822i
\(501\) 0 0
\(502\) −1179.36 + 2042.71i −0.104855 + 0.181615i
\(503\) −10809.6 −0.958204 −0.479102 0.877759i \(-0.659038\pi\)
−0.479102 + 0.877759i \(0.659038\pi\)
\(504\) 0 0
\(505\) −8792.36 −0.774762
\(506\) −741.067 + 1283.57i −0.0651076 + 0.112770i
\(507\) 0 0
\(508\) −6625.29 11475.3i −0.578642 1.00224i
\(509\) 7378.46 + 12779.9i 0.642524 + 1.11288i 0.984868 + 0.173309i \(0.0554459\pi\)
−0.342344 + 0.939575i \(0.611221\pi\)
\(510\) 0 0
\(511\) 9162.24 15869.5i 0.793177 1.37382i
\(512\) −16150.8 −1.39409
\(513\) 0 0
\(514\) 15142.2 1.29940
\(515\) −2641.21 + 4574.71i −0.225991 + 0.391428i
\(516\) 0 0
\(517\) −163.617 283.393i −0.0139185 0.0241075i
\(518\) 5658.89 + 9801.48i 0.479995 + 0.831375i
\(519\) 0 0
\(520\) 108.950 188.706i 0.00918800 0.0159141i
\(521\) 1742.68 0.146542 0.0732709 0.997312i \(-0.476656\pi\)
0.0732709 + 0.997312i \(0.476656\pi\)
\(522\) 0 0
\(523\) 10304.8 0.861565 0.430782 0.902456i \(-0.358238\pi\)
0.430782 + 0.902456i \(0.358238\pi\)
\(524\) 2267.65 3927.68i 0.189051 0.327446i
\(525\) 0 0
\(526\) 4120.87 + 7137.55i 0.341594 + 0.591658i
\(527\) 1229.11 + 2128.89i 0.101596 + 0.175969i
\(528\) 0 0
\(529\) −16919.7 + 29305.9i −1.39063 + 2.40863i
\(530\) 9267.59 0.759544
\(531\) 0 0
\(532\) 9077.83 0.739800
\(533\) 296.397 513.374i 0.0240870 0.0417199i
\(534\) 0 0
\(535\) −3675.08 6365.42i −0.296986 0.514395i
\(536\) 1754.19 + 3038.34i 0.141361 + 0.244844i
\(537\) 0 0
\(538\) −41.5087 + 71.8953i −0.00332634 + 0.00576138i
\(539\) −97.2007 −0.00776759
\(540\) 0 0
\(541\) 3966.86 0.315247 0.157623 0.987499i \(-0.449617\pi\)
0.157623 + 0.987499i \(0.449617\pi\)
\(542\) 9743.94 16877.0i 0.772211 1.33751i
\(543\) 0 0
\(544\) −1167.27 2021.78i −0.0919971 0.159344i
\(545\) −2297.22 3978.90i −0.180554 0.312729i
\(546\) 0 0
\(547\) 2904.36 5030.50i 0.227023 0.393215i −0.729902 0.683552i \(-0.760434\pi\)
0.956924 + 0.290337i \(0.0937675\pi\)
\(548\) 8735.16 0.680926
\(549\) 0 0
\(550\) 172.750 0.0133929
\(551\) −1947.41 + 3373.01i −0.150567 + 0.260789i
\(552\) 0 0
\(553\) 597.326 + 1034.60i 0.0459329 + 0.0795581i
\(554\) 10353.3 + 17932.4i 0.793988 + 1.37523i
\(555\) 0 0
\(556\) 8454.85 14644.2i 0.644902 1.11700i
\(557\) 3563.91 0.271109 0.135554 0.990770i \(-0.456718\pi\)
0.135554 + 0.990770i \(0.456718\pi\)
\(558\) 0 0
\(559\) 3281.13 0.248259
\(560\) −2776.82 + 4809.59i −0.209539 + 0.362932i
\(561\) 0 0
\(562\) 11957.4 + 20710.8i 0.897495 + 1.55451i
\(563\) 255.772 + 443.010i 0.0191466 + 0.0331628i 0.875440 0.483327i \(-0.160572\pi\)
−0.856293 + 0.516490i \(0.827238\pi\)
\(564\) 0 0
\(565\) −2468.04 + 4274.78i −0.183772 + 0.318303i
\(566\) −877.089 −0.0651357
\(567\) 0 0
\(568\) −2831.31 −0.209153
\(569\) −4058.27 + 7029.13i −0.299001 + 0.517885i −0.975908 0.218184i \(-0.929987\pi\)
0.676907 + 0.736069i \(0.263320\pi\)
\(570\) 0 0
\(571\) −7539.06 13058.0i −0.552539 0.957026i −0.998090 0.0617692i \(-0.980326\pi\)
0.445551 0.895256i \(-0.353008\pi\)
\(572\) 83.4794 + 144.591i 0.00610218 + 0.0105693i
\(573\) 0 0
\(574\) 2198.94 3808.68i 0.159899 0.276953i
\(575\) 5362.28 0.388909
\(576\) 0 0
\(577\) 27101.5 1.95537 0.977685 0.210077i \(-0.0673716\pi\)
0.977685 + 0.210077i \(0.0673716\pi\)
\(578\) −9947.98 + 17230.4i −0.715885 + 1.23995i
\(579\) 0 0
\(580\) 1721.32 + 2981.41i 0.123231 + 0.213442i
\(581\) 7437.26 + 12881.7i 0.531067 + 0.919834i
\(582\) 0 0
\(583\) −377.755 + 654.292i −0.0268354 + 0.0464803i
\(584\) −3589.10 −0.254312
\(585\) 0 0
\(586\) 14794.0 1.04289
\(587\) −51.0411 + 88.4057i −0.00358891 + 0.00621617i −0.867814 0.496889i \(-0.834476\pi\)
0.864225 + 0.503105i \(0.167809\pi\)
\(588\) 0 0
\(589\) −6926.22 11996.6i −0.484533 0.839236i
\(590\) 4952.59 + 8578.15i 0.345585 + 0.598571i
\(591\) 0 0
\(592\) −3807.73 + 6595.19i −0.264353 + 0.457872i
\(593\) 16467.2 1.14035 0.570174 0.821524i \(-0.306876\pi\)
0.570174 + 0.821524i \(0.306876\pi\)
\(594\) 0 0
\(595\) −899.712 −0.0619909
\(596\) −11559.0 + 20020.7i −0.794420 + 1.37598i
\(597\) 0 0
\(598\) 4906.82 + 8498.87i 0.335543 + 0.581178i
\(599\) −11608.1 20105.8i −0.791809 1.37145i −0.924846 0.380342i \(-0.875806\pi\)
0.133038 0.991111i \(-0.457527\pi\)
\(600\) 0 0
\(601\) 839.147 1453.45i 0.0569543 0.0986477i −0.836143 0.548512i \(-0.815194\pi\)
0.893097 + 0.449865i \(0.148528\pi\)
\(602\) 24342.4 1.64804
\(603\) 0 0
\(604\) 22720.8 1.53062
\(605\) 3320.46 5751.20i 0.223134 0.386479i
\(606\) 0 0
\(607\) −9653.64 16720.6i −0.645517 1.11807i −0.984182 0.177162i \(-0.943308\pi\)
0.338664 0.940907i \(-0.390025\pi\)
\(608\) 6577.74 + 11393.0i 0.438754 + 0.759944i
\(609\) 0 0
\(610\) 6956.80 12049.5i 0.461759 0.799789i
\(611\) −2166.71 −0.143463
\(612\) 0 0
\(613\) 13659.9 0.900032 0.450016 0.893020i \(-0.351418\pi\)
0.450016 + 0.893020i \(0.351418\pi\)
\(614\) 4947.46 8569.26i 0.325185 0.563236i
\(615\) 0 0
\(616\) 65.8931 + 114.130i 0.00430992 + 0.00746500i
\(617\) 7301.84 + 12647.2i 0.476436 + 0.825211i 0.999635 0.0269990i \(-0.00859510\pi\)
−0.523200 + 0.852210i \(0.675262\pi\)
\(618\) 0 0
\(619\) 13194.1 22852.9i 0.856732 1.48390i −0.0182965 0.999833i \(-0.505824\pi\)
0.875029 0.484071i \(-0.160842\pi\)
\(620\) −12244.2 −0.793128
\(621\) 0 0
\(622\) 6621.35 0.426836
\(623\) 15424.9 26716.6i 0.991948 1.71810i
\(624\) 0 0
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) 5724.23 + 9914.65i 0.365473 + 0.633018i
\(627\) 0 0
\(628\) −470.163 + 814.346i −0.0298751 + 0.0517451i
\(629\) −1233.74 −0.0782072
\(630\) 0 0
\(631\) 14241.1 0.898459 0.449229 0.893416i \(-0.351699\pi\)
0.449229 + 0.893416i \(0.351699\pi\)
\(632\) 116.995 202.641i 0.00736360 0.0127541i
\(633\) 0 0
\(634\) 11396.2 + 19738.8i 0.713880 + 1.23648i
\(635\) −3700.25 6409.02i −0.231244 0.400526i
\(636\) 0 0
\(637\) −321.797 + 557.369i −0.0200158 + 0.0346684i
\(638\) −531.440 −0.0329779
\(639\) 0 0
\(640\) 2492.14 0.153923
\(641\) −9480.23 + 16420.2i −0.584160 + 1.01180i 0.410819 + 0.911717i \(0.365243\pi\)
−0.994980 + 0.100078i \(0.968091\pi\)
\(642\) 0 0
\(643\) −5527.13 9573.26i −0.338987 0.587143i 0.645256 0.763967i \(-0.276751\pi\)
−0.984242 + 0.176824i \(0.943418\pi\)
\(644\) 19224.3 + 33297.5i 1.17631 + 2.03743i
\(645\) 0 0
\(646\) −936.922 + 1622.80i −0.0570630 + 0.0988360i
\(647\) −19310.1 −1.17335 −0.586677 0.809821i \(-0.699564\pi\)
−0.586677 + 0.809821i \(0.699564\pi\)
\(648\) 0 0
\(649\) −807.489 −0.0488393
\(650\) 571.914 990.584i 0.0345113 0.0597753i
\(651\) 0 0
\(652\) −9977.02 17280.7i −0.599280 1.03798i
\(653\) 3467.13 + 6005.24i 0.207778 + 0.359883i 0.951014 0.309147i \(-0.100043\pi\)
−0.743236 + 0.669029i \(0.766710\pi\)
\(654\) 0 0
\(655\) 1266.49 2193.62i 0.0755508 0.130858i
\(656\) 2959.23 0.176126
\(657\) 0 0
\(658\) −16074.6 −0.952363
\(659\) −7939.35 + 13751.4i −0.469307 + 0.812863i −0.999384 0.0350862i \(-0.988829\pi\)
0.530078 + 0.847949i \(0.322163\pi\)
\(660\) 0 0
\(661\) 4709.16 + 8156.51i 0.277103 + 0.479957i 0.970664 0.240442i \(-0.0772923\pi\)
−0.693561 + 0.720398i \(0.743959\pi\)
\(662\) −19797.7 34290.7i −1.16233 2.01321i
\(663\) 0 0
\(664\) 1456.69 2523.06i 0.0851364 0.147461i
\(665\) 5070.00 0.295648
\(666\) 0 0
\(667\) −16496.3 −0.957628
\(668\) −12595.3 + 21815.6i −0.729529 + 1.26358i
\(669\) 0 0
\(670\) 9208.32 + 15949.3i 0.530968 + 0.919664i
\(671\) 567.132 + 982.301i 0.0326287 + 0.0565146i
\(672\) 0 0
\(673\) 9196.17 15928.2i 0.526726 0.912316i −0.472789 0.881176i \(-0.656753\pi\)
0.999515 0.0311403i \(-0.00991387\pi\)
\(674\) 8582.41 0.490478
\(675\) 0 0
\(676\) −18563.2 −1.05617
\(677\) 5285.34 9154.49i 0.300048 0.519698i −0.676099 0.736811i \(-0.736331\pi\)
0.976146 + 0.217113i \(0.0696641\pi\)
\(678\) 0 0
\(679\) −11228.5 19448.4i −0.634626 1.09920i
\(680\) 88.1106 + 152.612i 0.00496895 + 0.00860647i
\(681\) 0 0
\(682\) 945.070 1636.91i 0.0530625 0.0919069i
\(683\) 23975.0 1.34316 0.671579 0.740933i \(-0.265616\pi\)
0.671579 + 0.740933i \(0.265616\pi\)
\(684\) 0 0
\(685\) 4878.61 0.272120
\(686\) 11751.3 20353.8i 0.654032 1.13282i
\(687\) 0 0
\(688\) 8189.72 + 14185.0i 0.453823 + 0.786044i
\(689\) 2501.23 + 4332.26i 0.138301 + 0.239544i
\(690\) 0 0
\(691\) −9820.49 + 17009.6i −0.540650 + 0.936433i 0.458217 + 0.888840i \(0.348488\pi\)
−0.998867 + 0.0475927i \(0.984845\pi\)
\(692\) −29404.0 −1.61528
\(693\) 0 0
\(694\) 25171.1 1.37677
\(695\) 4722.06 8178.85i 0.257724 0.446391i
\(696\) 0 0
\(697\) 239.704 + 415.180i 0.0130265 + 0.0225625i
\(698\) 4506.56 + 7805.59i 0.244378 + 0.423275i
\(699\) 0 0
\(700\) 2240.69 3880.99i 0.120986 0.209554i
\(701\) −36098.2 −1.94495 −0.972475 0.233007i \(-0.925143\pi\)
−0.972475 + 0.233007i \(0.925143\pi\)
\(702\) 0 0
\(703\) 6952.28 0.372987
\(704\) −525.128 + 909.548i −0.0281129 + 0.0486930i
\(705\) 0 0
\(706\) −5147.10 8915.04i −0.274382 0.475243i
\(707\) −17604.9 30492.5i −0.936492 1.62205i
\(708\) 0 0
\(709\) −17617.1 + 30513.6i −0.933177 + 1.61631i −0.155323 + 0.987864i \(0.549642\pi\)
−0.777853 + 0.628446i \(0.783691\pi\)
\(710\) −14862.5 −0.785606
\(711\) 0 0
\(712\) −6042.34 −0.318043
\(713\) 29335.7 50810.9i 1.54085 2.66884i
\(714\) 0 0
\(715\) 46.6235 + 80.7543i 0.00243863 + 0.00422383i
\(716\) −5678.65 9835.71i −0.296398 0.513377i
\(717\) 0 0
\(718\) 1732.59 3000.94i 0.0900553 0.155980i
\(719\) 22089.7 1.14577 0.572885 0.819636i \(-0.305824\pi\)
0.572885 + 0.819636i \(0.305824\pi\)
\(720\) 0 0
\(721\) −21153.9 −1.09267
\(722\) −8840.75 + 15312.6i −0.455704 + 0.789303i
\(723\) 0 0
\(724\) −4834.80 8374.12i −0.248182 0.429864i
\(725\) 961.360 + 1665.13i 0.0492469 + 0.0852982i
\(726\) 0 0
\(727\) 9717.61 16831.4i 0.495744 0.858654i −0.504244 0.863561i \(-0.668229\pi\)
0.999988 + 0.00490721i \(0.00156202\pi\)
\(728\) 872.596 0.0444238
\(729\) 0 0
\(730\) −18840.4 −0.955227
\(731\) −1326.77 + 2298.03i −0.0671304 + 0.116273i
\(732\) 0 0
\(733\) −7487.10 12968.0i −0.377275 0.653459i 0.613390 0.789780i \(-0.289805\pi\)
−0.990665 + 0.136321i \(0.956472\pi\)
\(734\) −11558.2 20019.5i −0.581230 1.00672i
\(735\) 0 0
\(736\) −27859.7 + 48254.3i −1.39527 + 2.41668i
\(737\) −1501.36 −0.0750384
\(738\) 0 0
\(739\) −30663.4 −1.52635 −0.763174 0.646193i \(-0.776360\pi\)
−0.763174 + 0.646193i \(0.776360\pi\)
\(740\) 3072.57 5321.84i 0.152635 0.264371i
\(741\) 0 0
\(742\) 18556.4 + 32140.7i 0.918096 + 1.59019i
\(743\) 1707.34 + 2957.20i 0.0843018 + 0.146015i 0.905093 0.425213i \(-0.139801\pi\)
−0.820792 + 0.571228i \(0.806467\pi\)
\(744\) 0 0
\(745\) −6455.73 + 11181.6i −0.317476 + 0.549884i
\(746\) −5431.49 −0.266570
\(747\) 0 0
\(748\) −135.024 −0.00660023
\(749\) 14717.2 25490.9i 0.717962 1.24355i
\(750\) 0 0
\(751\) 373.129 + 646.279i 0.0181301 + 0.0314022i 0.874948 0.484217i \(-0.160895\pi\)
−0.856818 + 0.515619i \(0.827562\pi\)
\(752\) −5408.12 9367.15i −0.262253 0.454235i
\(753\) 0 0
\(754\) −1759.41 + 3047.39i −0.0849787 + 0.147187i
\(755\) 12689.6 0.611685
\(756\) 0 0
\(757\) −22929.5 −1.10091 −0.550454 0.834865i \(-0.685546\pi\)
−0.550454 + 0.834865i \(0.685546\pi\)
\(758\) −10297.6 + 17836.0i −0.493438 + 0.854660i
\(759\) 0 0
\(760\) −496.515 859.989i −0.0236980 0.0410461i
\(761\) −10588.3 18339.5i −0.504370 0.873595i −0.999987 0.00505384i \(-0.998391\pi\)
0.495617 0.868541i \(-0.334942\pi\)
\(762\) 0 0
\(763\) 9199.42 15933.9i 0.436489 0.756021i
\(764\) 2566.81 0.121550
\(765\) 0 0
\(766\) −9232.92 −0.435508
\(767\) −2673.31 + 4630.31i −0.125851 + 0.217980i
\(768\) 0 0
\(769\) −1387.09 2402.51i −0.0650453 0.112662i 0.831669 0.555272i \(-0.187386\pi\)
−0.896714 + 0.442610i \(0.854053\pi\)
\(770\) 345.896 + 599.109i 0.0161886 + 0.0280395i
\(771\) 0 0
\(772\) 20817.7 36057.3i 0.970526 1.68100i
\(773\) −28891.7 −1.34433 −0.672163 0.740403i \(-0.734635\pi\)
−0.672163 + 0.740403i \(0.734635\pi\)
\(774\) 0 0
\(775\) −6838.43 −0.316960
\(776\) −2199.26 + 3809.23i −0.101738 + 0.176216i
\(777\) 0 0
\(778\) 23456.0 + 40627.1i 1.08090 + 1.87217i
\(779\) −1350.76 2339.59i −0.0621260 0.107605i
\(780\) 0 0
\(781\) 605.810 1049.29i 0.0277562 0.0480751i
\(782\) −7936.56 −0.362930
\(783\) 0 0
\(784\) −3212.83 −0.146357
\(785\) −262.588 + 454.815i −0.0119390 + 0.0206790i
\(786\) 0 0
\(787\) −4404.37 7628.60i −0.199490 0.345527i