Properties

Label 804.2.q.b.241.1
Level 804
Weight 2
Character 804.241
Analytic conductor 6.420
Analytic rank 0
Dimension 60
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.q (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(6\) over \(\Q(\zeta_{11})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 241.1
Character \(\chi\) = 804.241
Dual form 804.2.q.b.397.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.415415 + 0.909632i) q^{3} +(-3.70609 - 1.08821i) q^{5} +(1.46290 + 1.68828i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\) \(q+(-0.415415 + 0.909632i) q^{3} +(-3.70609 - 1.08821i) q^{5} +(1.46290 + 1.68828i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(2.70614 + 0.794594i) q^{11} +(-3.84882 - 2.47349i) q^{13} +(2.52943 - 2.91912i) q^{15} +(-0.224262 - 1.55978i) q^{17} +(-0.859532 + 0.991952i) q^{19} +(-2.14342 + 0.629366i) q^{21} +(2.93332 - 6.42308i) q^{23} +(8.34463 + 5.36277i) q^{25} +(0.959493 - 0.281733i) q^{27} -4.81587 q^{29} +(8.94623 - 5.74939i) q^{31} +(-1.84696 + 2.13150i) q^{33} +(-3.58445 - 7.84885i) q^{35} +7.46743 q^{37} +(3.84882 - 2.47349i) q^{39} +(-1.66891 - 11.6075i) q^{41} +(1.12343 + 7.81364i) q^{43} +(1.60456 + 3.51350i) q^{45} +(3.36046 - 7.35838i) q^{47} +(0.286000 - 1.98918i) q^{49} +(1.51198 + 0.443959i) q^{51} +(1.29234 - 8.98844i) q^{53} +(-9.16450 - 5.88967i) q^{55} +(-0.545249 - 1.19393i) q^{57} +(-6.82652 + 4.38714i) q^{59} +(10.3720 - 3.04550i) q^{61} +(0.317919 - 2.21118i) q^{63} +(11.5724 + 13.3553i) q^{65} +(-8.11668 + 1.05805i) q^{67} +(4.62409 + 5.33649i) q^{69} +(-0.502245 + 3.49319i) q^{71} +(-1.12043 + 0.328988i) q^{73} +(-8.34463 + 5.36277i) q^{75} +(2.61732 + 5.73113i) q^{77} +(0.447096 + 0.287331i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(-3.13511 - 0.920552i) q^{83} +(-0.866223 + 6.02471i) q^{85} +(2.00058 - 4.38067i) q^{87} +(1.58594 + 3.47273i) q^{89} +(-1.45451 - 10.1164i) q^{91} +(1.51343 + 10.5262i) q^{93} +(4.26495 - 2.74092i) q^{95} -9.59493 q^{97} +(-1.17163 - 2.56551i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} + O(q^{10}) \) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} - 11q^{11} - 2q^{13} + 9q^{15} + 21q^{17} + 10q^{19} - 2q^{21} - 10q^{23} - 36q^{25} + 6q^{27} + 4q^{29} - 24q^{31} - 32q^{35} + 2q^{37} + 2q^{39} + 10q^{41} + 23q^{43} + 2q^{45} + 66q^{47} + 34q^{49} + 23q^{51} - 13q^{53} + 27q^{55} + q^{57} + 35q^{59} + 56q^{61} - 9q^{63} + 48q^{65} + 13q^{67} + 10q^{69} + 76q^{71} - q^{73} + 36q^{75} - 38q^{77} - 46q^{79} - 6q^{81} - 26q^{83} + 42q^{85} + 7q^{87} + 58q^{89} - 40q^{91} - 9q^{93} - 29q^{95} - 46q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{11}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.415415 + 0.909632i −0.239840 + 0.525176i
\(4\) 0 0
\(5\) −3.70609 1.08821i −1.65741 0.486660i −0.686708 0.726934i \(-0.740945\pi\)
−0.970705 + 0.240273i \(0.922763\pi\)
\(6\) 0 0
\(7\) 1.46290 + 1.68828i 0.552925 + 0.638110i 0.961562 0.274587i \(-0.0885413\pi\)
−0.408637 + 0.912697i \(0.633996\pi\)
\(8\) 0 0
\(9\) −0.654861 0.755750i −0.218287 0.251917i
\(10\) 0 0
\(11\) 2.70614 + 0.794594i 0.815931 + 0.239579i 0.662963 0.748652i \(-0.269299\pi\)
0.152968 + 0.988231i \(0.451117\pi\)
\(12\) 0 0
\(13\) −3.84882 2.47349i −1.06747 0.686022i −0.115841 0.993268i \(-0.536956\pi\)
−0.951630 + 0.307246i \(0.900593\pi\)
\(14\) 0 0
\(15\) 2.52943 2.91912i 0.653096 0.753713i
\(16\) 0 0
\(17\) −0.224262 1.55978i −0.0543915 0.378301i −0.998776 0.0494586i \(-0.984250\pi\)
0.944385 0.328843i \(-0.106659\pi\)
\(18\) 0 0
\(19\) −0.859532 + 0.991952i −0.197190 + 0.227569i −0.845730 0.533611i \(-0.820835\pi\)
0.648540 + 0.761181i \(0.275380\pi\)
\(20\) 0 0
\(21\) −2.14342 + 0.629366i −0.467734 + 0.137339i
\(22\) 0 0
\(23\) 2.93332 6.42308i 0.611640 1.33930i −0.309807 0.950800i \(-0.600264\pi\)
0.921447 0.388505i \(-0.127008\pi\)
\(24\) 0 0
\(25\) 8.34463 + 5.36277i 1.66893 + 1.07255i
\(26\) 0 0
\(27\) 0.959493 0.281733i 0.184655 0.0542195i
\(28\) 0 0
\(29\) −4.81587 −0.894285 −0.447142 0.894463i \(-0.647558\pi\)
−0.447142 + 0.894463i \(0.647558\pi\)
\(30\) 0 0
\(31\) 8.94623 5.74939i 1.60679 1.03262i 0.643033 0.765838i \(-0.277676\pi\)
0.963757 0.266783i \(-0.0859606\pi\)
\(32\) 0 0
\(33\) −1.84696 + 2.13150i −0.321514 + 0.371047i
\(34\) 0 0
\(35\) −3.58445 7.84885i −0.605882 1.32670i
\(36\) 0 0
\(37\) 7.46743 1.22764 0.613819 0.789447i \(-0.289633\pi\)
0.613819 + 0.789447i \(0.289633\pi\)
\(38\) 0 0
\(39\) 3.84882 2.47349i 0.616305 0.396075i
\(40\) 0 0
\(41\) −1.66891 11.6075i −0.260640 1.81279i −0.528055 0.849210i \(-0.677079\pi\)
0.267415 0.963581i \(-0.413831\pi\)
\(42\) 0 0
\(43\) 1.12343 + 7.81364i 0.171322 + 1.19157i 0.876096 + 0.482137i \(0.160139\pi\)
−0.704774 + 0.709432i \(0.748952\pi\)
\(44\) 0 0
\(45\) 1.60456 + 3.51350i 0.239194 + 0.523761i
\(46\) 0 0
\(47\) 3.36046 7.35838i 0.490173 1.07333i −0.489367 0.872078i \(-0.662772\pi\)
0.979540 0.201251i \(-0.0645008\pi\)
\(48\) 0 0
\(49\) 0.286000 1.98918i 0.0408572 0.284168i
\(50\) 0 0
\(51\) 1.51198 + 0.443959i 0.211720 + 0.0621667i
\(52\) 0 0
\(53\) 1.29234 8.98844i 0.177517 1.23466i −0.684967 0.728574i \(-0.740184\pi\)
0.862484 0.506084i \(-0.168907\pi\)
\(54\) 0 0
\(55\) −9.16450 5.88967i −1.23574 0.794163i
\(56\) 0 0
\(57\) −0.545249 1.19393i −0.0722200 0.158140i
\(58\) 0 0
\(59\) −6.82652 + 4.38714i −0.888738 + 0.571157i −0.903430 0.428735i \(-0.858959\pi\)
0.0146926 + 0.999892i \(0.495323\pi\)
\(60\) 0 0
\(61\) 10.3720 3.04550i 1.32800 0.389937i 0.460628 0.887593i \(-0.347624\pi\)
0.867374 + 0.497657i \(0.165806\pi\)
\(62\) 0 0
\(63\) 0.317919 2.21118i 0.0400540 0.278582i
\(64\) 0 0
\(65\) 11.5724 + 13.3553i 1.43538 + 1.65652i
\(66\) 0 0
\(67\) −8.11668 + 1.05805i −0.991611 + 0.129262i
\(68\) 0 0
\(69\) 4.62409 + 5.33649i 0.556675 + 0.642437i
\(70\) 0 0
\(71\) −0.502245 + 3.49319i −0.0596055 + 0.414565i 0.938071 + 0.346442i \(0.112610\pi\)
−0.997677 + 0.0681233i \(0.978299\pi\)
\(72\) 0 0
\(73\) −1.12043 + 0.328988i −0.131136 + 0.0385051i −0.346642 0.937997i \(-0.612678\pi\)
0.215506 + 0.976503i \(0.430860\pi\)
\(74\) 0 0
\(75\) −8.34463 + 5.36277i −0.963555 + 0.619239i
\(76\) 0 0
\(77\) 2.61732 + 5.73113i 0.298271 + 0.653123i
\(78\) 0 0
\(79\) 0.447096 + 0.287331i 0.0503022 + 0.0323273i 0.565550 0.824714i \(-0.308664\pi\)
−0.515248 + 0.857041i \(0.672300\pi\)
\(80\) 0 0
\(81\) −0.142315 + 0.989821i −0.0158128 + 0.109980i
\(82\) 0 0
\(83\) −3.13511 0.920552i −0.344123 0.101044i 0.105104 0.994461i \(-0.466482\pi\)
−0.449227 + 0.893418i \(0.648301\pi\)
\(84\) 0 0
\(85\) −0.866223 + 6.02471i −0.0939551 + 0.653472i
\(86\) 0 0
\(87\) 2.00058 4.38067i 0.214485 0.469657i
\(88\) 0 0
\(89\) 1.58594 + 3.47273i 0.168109 + 0.368108i 0.974871 0.222768i \(-0.0715093\pi\)
−0.806762 + 0.590876i \(0.798782\pi\)
\(90\) 0 0
\(91\) −1.45451 10.1164i −0.152474 1.06048i
\(92\) 0 0
\(93\) 1.51343 + 10.5262i 0.156936 + 1.09151i
\(94\) 0 0
\(95\) 4.26495 2.74092i 0.437574 0.281212i
\(96\) 0 0
\(97\) −9.59493 −0.974218 −0.487109 0.873341i \(-0.661949\pi\)
−0.487109 + 0.873341i \(0.661949\pi\)
\(98\) 0 0
\(99\) −1.17163 2.56551i −0.117753 0.257843i
\(100\) 0 0
\(101\) −2.50416 + 2.88995i −0.249173 + 0.287561i −0.866533 0.499120i \(-0.833657\pi\)
0.617360 + 0.786681i \(0.288202\pi\)
\(102\) 0 0
\(103\) −8.52782 + 5.48050i −0.840271 + 0.540009i −0.888526 0.458826i \(-0.848270\pi\)
0.0482553 + 0.998835i \(0.484634\pi\)
\(104\) 0 0
\(105\) 8.62860 0.842065
\(106\) 0 0
\(107\) 5.36715 1.57594i 0.518862 0.152352i −0.0118079 0.999930i \(-0.503759\pi\)
0.530670 + 0.847579i \(0.321940\pi\)
\(108\) 0 0
\(109\) 5.95760 + 3.82872i 0.570635 + 0.366725i 0.793914 0.608030i \(-0.208040\pi\)
−0.223279 + 0.974755i \(0.571676\pi\)
\(110\) 0 0
\(111\) −3.10208 + 6.79261i −0.294436 + 0.644726i
\(112\) 0 0
\(113\) 0.342349 0.100523i 0.0322055 0.00945639i −0.265590 0.964086i \(-0.585567\pi\)
0.297796 + 0.954630i \(0.403749\pi\)
\(114\) 0 0
\(115\) −17.8608 + 20.6124i −1.66553 + 1.92212i
\(116\) 0 0
\(117\) 0.651105 + 4.52854i 0.0601947 + 0.418663i
\(118\) 0 0
\(119\) 2.30527 2.66042i 0.211323 0.243880i
\(120\) 0 0
\(121\) −2.56199 1.64649i −0.232908 0.149681i
\(122\) 0 0
\(123\) 11.2519 + 3.30385i 1.01455 + 0.297898i
\(124\) 0 0
\(125\) −12.4430 14.3600i −1.11293 1.28439i
\(126\) 0 0
\(127\) −10.6519 12.2929i −0.945202 1.09082i −0.995750 0.0920992i \(-0.970642\pi\)
0.0505482 0.998722i \(-0.483903\pi\)
\(128\) 0 0
\(129\) −7.57423 2.22399i −0.666874 0.195812i
\(130\) 0 0
\(131\) 7.72816 16.9223i 0.675212 1.47851i −0.192426 0.981312i \(-0.561635\pi\)
0.867638 0.497197i \(-0.165637\pi\)
\(132\) 0 0
\(133\) −2.93210 −0.254246
\(134\) 0 0
\(135\) −3.86255 −0.332435
\(136\) 0 0
\(137\) −8.50368 + 18.6205i −0.726518 + 1.59085i 0.0780203 + 0.996952i \(0.475140\pi\)
−0.804538 + 0.593901i \(0.797587\pi\)
\(138\) 0 0
\(139\) 1.51730 + 0.445520i 0.128696 + 0.0377885i 0.345446 0.938439i \(-0.387728\pi\)
−0.216750 + 0.976227i \(0.569546\pi\)
\(140\) 0 0
\(141\) 5.29743 + 6.11356i 0.446124 + 0.514855i
\(142\) 0 0
\(143\) −8.45002 9.75185i −0.706626 0.815490i
\(144\) 0 0
\(145\) 17.8480 + 5.24066i 1.48220 + 0.435213i
\(146\) 0 0
\(147\) 1.69061 + 1.08649i 0.139439 + 0.0896120i
\(148\) 0 0
\(149\) −1.93779 + 2.23633i −0.158750 + 0.183207i −0.829552 0.558429i \(-0.811404\pi\)
0.670802 + 0.741636i \(0.265950\pi\)
\(150\) 0 0
\(151\) −1.85852 12.9263i −0.151244 1.05193i −0.914138 0.405402i \(-0.867132\pi\)
0.762895 0.646523i \(-0.223778\pi\)
\(152\) 0 0
\(153\) −1.03194 + 1.19092i −0.0834274 + 0.0962804i
\(154\) 0 0
\(155\) −39.4120 + 11.5724i −3.16565 + 0.929519i
\(156\) 0 0
\(157\) 9.14669 20.0284i 0.729985 1.59844i −0.0693742 0.997591i \(-0.522100\pi\)
0.799359 0.600853i \(-0.205172\pi\)
\(158\) 0 0
\(159\) 7.63932 + 4.90949i 0.605837 + 0.389348i
\(160\) 0 0
\(161\) 15.1351 4.44407i 1.19281 0.350242i
\(162\) 0 0
\(163\) 2.52199 0.197538 0.0987689 0.995110i \(-0.468510\pi\)
0.0987689 + 0.995110i \(0.468510\pi\)
\(164\) 0 0
\(165\) 9.16450 5.88967i 0.713455 0.458510i
\(166\) 0 0
\(167\) 3.75480 4.33327i 0.290555 0.335319i −0.591640 0.806202i \(-0.701519\pi\)
0.882195 + 0.470883i \(0.156065\pi\)
\(168\) 0 0
\(169\) 3.29489 + 7.21481i 0.253453 + 0.554985i
\(170\) 0 0
\(171\) 1.31254 0.100373
\(172\) 0 0
\(173\) −6.49736 + 4.17560i −0.493985 + 0.317465i −0.763806 0.645446i \(-0.776672\pi\)
0.269821 + 0.962910i \(0.413035\pi\)
\(174\) 0 0
\(175\) 3.15353 + 21.9333i 0.238384 + 1.65800i
\(176\) 0 0
\(177\) −1.15484 8.03211i −0.0868033 0.603730i
\(178\) 0 0
\(179\) −7.35712 16.1099i −0.549897 1.20411i −0.956830 0.290649i \(-0.906129\pi\)
0.406933 0.913458i \(-0.366598\pi\)
\(180\) 0 0
\(181\) −0.718335 + 1.57293i −0.0533934 + 0.116915i −0.934448 0.356099i \(-0.884107\pi\)
0.881055 + 0.473014i \(0.156834\pi\)
\(182\) 0 0
\(183\) −1.53841 + 10.6999i −0.113723 + 0.790957i
\(184\) 0 0
\(185\) −27.6749 8.12609i −2.03470 0.597442i
\(186\) 0 0
\(187\) 0.632505 4.39917i 0.0462533 0.321699i
\(188\) 0 0
\(189\) 1.87929 + 1.20774i 0.136698 + 0.0878505i
\(190\) 0 0
\(191\) 11.0573 + 24.2121i 0.800077 + 1.75193i 0.645232 + 0.763986i \(0.276761\pi\)
0.154845 + 0.987939i \(0.450512\pi\)
\(192\) 0 0
\(193\) −0.526924 + 0.338633i −0.0379288 + 0.0243754i −0.559468 0.828852i \(-0.688994\pi\)
0.521539 + 0.853227i \(0.325358\pi\)
\(194\) 0 0
\(195\) −16.9557 + 4.97865i −1.21423 + 0.356529i
\(196\) 0 0
\(197\) −1.96423 + 13.6615i −0.139945 + 0.973341i 0.791943 + 0.610595i \(0.209070\pi\)
−0.931888 + 0.362746i \(0.881839\pi\)
\(198\) 0 0
\(199\) −3.30373 3.81271i −0.234195 0.270276i 0.626472 0.779444i \(-0.284498\pi\)
−0.860667 + 0.509169i \(0.829953\pi\)
\(200\) 0 0
\(201\) 2.40935 7.82272i 0.169943 0.551772i
\(202\) 0 0
\(203\) −7.04515 8.13053i −0.494472 0.570652i
\(204\) 0 0
\(205\) −6.44625 + 44.8346i −0.450225 + 3.13139i
\(206\) 0 0
\(207\) −6.77516 + 1.98937i −0.470906 + 0.138270i
\(208\) 0 0
\(209\) −3.11421 + 2.00138i −0.215414 + 0.138438i
\(210\) 0 0
\(211\) 7.53334 + 16.4957i 0.518616 + 1.13561i 0.969961 + 0.243262i \(0.0782174\pi\)
−0.451344 + 0.892350i \(0.649055\pi\)
\(212\) 0 0
\(213\) −2.96888 1.90798i −0.203424 0.130733i
\(214\) 0 0
\(215\) 4.33931 30.1806i 0.295939 2.05830i
\(216\) 0 0
\(217\) 22.7940 + 6.69293i 1.54736 + 0.454346i
\(218\) 0 0
\(219\) 0.166185 1.15584i 0.0112298 0.0781047i
\(220\) 0 0
\(221\) −2.99494 + 6.55801i −0.201462 + 0.441140i
\(222\) 0 0
\(223\) −5.46061 11.9571i −0.365670 0.800705i −0.999626 0.0273365i \(-0.991297\pi\)
0.633956 0.773369i \(-0.281430\pi\)
\(224\) 0 0
\(225\) −1.41166 9.81831i −0.0941107 0.654554i
\(226\) 0 0
\(227\) −1.52228 10.5877i −0.101037 0.702729i −0.975878 0.218318i \(-0.929943\pi\)
0.874840 0.484411i \(-0.160966\pi\)
\(228\) 0 0
\(229\) −10.8476 + 6.97135i −0.716832 + 0.460680i −0.847534 0.530742i \(-0.821913\pi\)
0.130702 + 0.991422i \(0.458277\pi\)
\(230\) 0 0
\(231\) −6.30049 −0.414542
\(232\) 0 0
\(233\) 3.36593 + 7.37036i 0.220510 + 0.482848i 0.987264 0.159092i \(-0.0508568\pi\)
−0.766754 + 0.641941i \(0.778129\pi\)
\(234\) 0 0
\(235\) −20.4616 + 23.6139i −1.33477 + 1.54040i
\(236\) 0 0
\(237\) −0.447096 + 0.287331i −0.0290420 + 0.0186642i
\(238\) 0 0
\(239\) 21.1887 1.37058 0.685290 0.728270i \(-0.259675\pi\)
0.685290 + 0.728270i \(0.259675\pi\)
\(240\) 0 0
\(241\) 25.0770 7.36328i 1.61535 0.474310i 0.655589 0.755118i \(-0.272421\pi\)
0.959764 + 0.280808i \(0.0906023\pi\)
\(242\) 0 0
\(243\) −0.841254 0.540641i −0.0539664 0.0346821i
\(244\) 0 0
\(245\) −3.22457 + 7.06083i −0.206010 + 0.451100i
\(246\) 0 0
\(247\) 5.76177 1.69181i 0.366612 0.107647i
\(248\) 0 0
\(249\) 2.13974 2.46939i 0.135600 0.156491i
\(250\) 0 0
\(251\) 3.18299 + 22.1382i 0.200909 + 1.39735i 0.801596 + 0.597866i \(0.203984\pi\)
−0.600688 + 0.799484i \(0.705106\pi\)
\(252\) 0 0
\(253\) 13.0417 15.0509i 0.819925 0.946244i
\(254\) 0 0
\(255\) −5.12043 3.29070i −0.320654 0.206072i
\(256\) 0 0
\(257\) −9.49217 2.78715i −0.592106 0.173858i −0.0280666 0.999606i \(-0.508935\pi\)
−0.564039 + 0.825748i \(0.690753\pi\)
\(258\) 0 0
\(259\) 10.9241 + 12.6071i 0.678791 + 0.783367i
\(260\) 0 0
\(261\) 3.15372 + 3.63959i 0.195211 + 0.225285i
\(262\) 0 0
\(263\) 0.869082 + 0.255186i 0.0535899 + 0.0157354i 0.308418 0.951251i \(-0.400201\pi\)
−0.254828 + 0.966986i \(0.582019\pi\)
\(264\) 0 0
\(265\) −14.5708 + 31.9056i −0.895078 + 1.95995i
\(266\) 0 0
\(267\) −3.81773 −0.233641
\(268\) 0 0
\(269\) 1.32037 0.0805046 0.0402523 0.999190i \(-0.487184\pi\)
0.0402523 + 0.999190i \(0.487184\pi\)
\(270\) 0 0
\(271\) −2.64695 + 5.79601i −0.160791 + 0.352082i −0.972830 0.231520i \(-0.925630\pi\)
0.812039 + 0.583603i \(0.198357\pi\)
\(272\) 0 0
\(273\) 9.80639 + 2.87942i 0.593510 + 0.174270i
\(274\) 0 0
\(275\) 18.3205 + 21.1430i 1.10477 + 1.27497i
\(276\) 0 0
\(277\) −15.6771 18.0924i −0.941948 1.08707i −0.996073 0.0885319i \(-0.971782\pi\)
0.0541252 0.998534i \(-0.482763\pi\)
\(278\) 0 0
\(279\) −10.2036 2.99606i −0.610875 0.179369i
\(280\) 0 0
\(281\) 23.2569 + 14.9463i 1.38739 + 0.891621i 0.999547 0.0301039i \(-0.00958383\pi\)
0.387843 + 0.921725i \(0.373220\pi\)
\(282\) 0 0
\(283\) −3.88353 + 4.48183i −0.230852 + 0.266417i −0.859343 0.511399i \(-0.829127\pi\)
0.628491 + 0.777817i \(0.283673\pi\)
\(284\) 0 0
\(285\) 0.721501 + 5.01815i 0.0427380 + 0.297250i
\(286\) 0 0
\(287\) 17.1553 19.7983i 1.01265 1.16865i
\(288\) 0 0
\(289\) 13.9288 4.08986i 0.819339 0.240580i
\(290\) 0 0
\(291\) 3.98588 8.72786i 0.233656 0.511636i
\(292\) 0 0
\(293\) −9.95748 6.39928i −0.581722 0.373850i 0.216437 0.976297i \(-0.430556\pi\)
−0.798159 + 0.602447i \(0.794193\pi\)
\(294\) 0 0
\(295\) 30.0738 8.83047i 1.75096 0.514130i
\(296\) 0 0
\(297\) 2.82038 0.163655
\(298\) 0 0
\(299\) −27.1772 + 17.4657i −1.57170 + 1.01007i
\(300\) 0 0
\(301\) −11.5481 + 13.3273i −0.665624 + 0.768171i
\(302\) 0 0
\(303\) −1.58853 3.47839i −0.0912585 0.199828i
\(304\) 0 0
\(305\) −41.7538 −2.39081
\(306\) 0 0
\(307\) 8.09919 5.20503i 0.462245 0.297067i −0.288714 0.957415i \(-0.593228\pi\)
0.750959 + 0.660348i \(0.229591\pi\)
\(308\) 0 0
\(309\) −1.44265 10.0339i −0.0820696 0.570806i
\(310\) 0 0
\(311\) 0.329020 + 2.28838i 0.0186570 + 0.129762i 0.997021 0.0771276i \(-0.0245749\pi\)
−0.978364 + 0.206890i \(0.933666\pi\)
\(312\) 0 0
\(313\) −2.92198 6.39825i −0.165160 0.361651i 0.808898 0.587950i \(-0.200065\pi\)
−0.974058 + 0.226299i \(0.927337\pi\)
\(314\) 0 0
\(315\) −3.58445 + 7.84885i −0.201961 + 0.442233i
\(316\) 0 0
\(317\) 2.79376 19.4310i 0.156913 1.09136i −0.747366 0.664413i \(-0.768682\pi\)
0.904279 0.426942i \(-0.140409\pi\)
\(318\) 0 0
\(319\) −13.0324 3.82666i −0.729675 0.214252i
\(320\) 0 0
\(321\) −0.796071 + 5.53680i −0.0444324 + 0.309034i
\(322\) 0 0
\(323\) 1.73998 + 1.11822i 0.0968153 + 0.0622194i
\(324\) 0 0
\(325\) −18.8522 41.2807i −1.04573 2.28984i
\(326\) 0 0
\(327\) −5.95760 + 3.82872i −0.329456 + 0.211729i
\(328\) 0 0
\(329\) 17.3390 5.09119i 0.955931 0.280687i
\(330\) 0 0
\(331\) 1.95108 13.5700i 0.107241 0.745876i −0.863257 0.504765i \(-0.831579\pi\)
0.970498 0.241111i \(-0.0775118\pi\)
\(332\) 0 0
\(333\) −4.89012 5.64350i −0.267977 0.309262i
\(334\) 0 0
\(335\) 31.2325 + 4.91138i 1.70641 + 0.268338i
\(336\) 0 0
\(337\) −16.8573 19.4544i −0.918277 1.05975i −0.998018 0.0629328i \(-0.979955\pi\)
0.0797405 0.996816i \(-0.474591\pi\)
\(338\) 0 0
\(339\) −0.0507783 + 0.353171i −0.00275790 + 0.0191816i
\(340\) 0 0
\(341\) 28.7781 8.45003i 1.55842 0.457595i
\(342\) 0 0
\(343\) 16.9317 10.8813i 0.914225 0.587537i
\(344\) 0 0
\(345\) −11.3301 24.8094i −0.609992 1.33570i
\(346\) 0 0
\(347\) 16.2621 + 10.4510i 0.872994 + 0.561039i 0.898667 0.438631i \(-0.144537\pi\)
−0.0256730 + 0.999670i \(0.508173\pi\)
\(348\) 0 0
\(349\) 4.23410 29.4488i 0.226646 1.57636i −0.485442 0.874269i \(-0.661341\pi\)
0.712088 0.702090i \(-0.247750\pi\)
\(350\) 0 0
\(351\) −4.38978 1.28896i −0.234309 0.0687994i
\(352\) 0 0
\(353\) 3.78430 26.3204i 0.201418 1.40089i −0.598663 0.801001i \(-0.704301\pi\)
0.800081 0.599892i \(-0.204790\pi\)
\(354\) 0 0
\(355\) 5.66267 12.3995i 0.300543 0.658098i
\(356\) 0 0
\(357\) 1.46236 + 3.20212i 0.0773963 + 0.169474i
\(358\) 0 0
\(359\) −3.39838 23.6362i −0.179360 1.24747i −0.858249 0.513233i \(-0.828448\pi\)
0.678890 0.734240i \(-0.262461\pi\)
\(360\) 0 0
\(361\) 2.45881 + 17.1014i 0.129411 + 0.900073i
\(362\) 0 0
\(363\) 2.56199 1.64649i 0.134470 0.0864183i
\(364\) 0 0
\(365\) 4.51041 0.236086
\(366\) 0 0
\(367\) −0.995541 2.17993i −0.0519668 0.113791i 0.881867 0.471497i \(-0.156286\pi\)
−0.933834 + 0.357706i \(0.883559\pi\)
\(368\) 0 0
\(369\) −7.67948 + 8.86259i −0.399778 + 0.461368i
\(370\) 0 0
\(371\) 17.0656 10.9674i 0.886000 0.569398i
\(372\) 0 0
\(373\) 1.56322 0.0809406 0.0404703 0.999181i \(-0.487114\pi\)
0.0404703 + 0.999181i \(0.487114\pi\)
\(374\) 0 0
\(375\) 18.2313 5.35318i 0.941459 0.276437i
\(376\) 0 0
\(377\) 18.5354 + 11.9120i 0.954623 + 0.613499i
\(378\) 0 0
\(379\) 11.1574 24.4312i 0.573115 1.25495i −0.372007 0.928230i \(-0.621330\pi\)
0.945122 0.326717i \(-0.105942\pi\)
\(380\) 0 0
\(381\) 15.6070 4.58263i 0.799570 0.234775i
\(382\) 0 0
\(383\) −14.8343 + 17.1197i −0.757999 + 0.874777i −0.995318 0.0966544i \(-0.969186\pi\)
0.237319 + 0.971432i \(0.423731\pi\)
\(384\) 0 0
\(385\) −3.46337 24.0882i −0.176509 1.22765i
\(386\) 0 0
\(387\) 5.16947 5.96588i 0.262779 0.303263i
\(388\) 0 0
\(389\) −2.09988 1.34951i −0.106468 0.0684229i 0.486323 0.873779i \(-0.338338\pi\)
−0.592791 + 0.805356i \(0.701974\pi\)
\(390\) 0 0
\(391\) −10.6764 3.13487i −0.539929 0.158537i
\(392\) 0 0
\(393\) 12.1827 + 14.0596i 0.614535 + 0.709211i
\(394\) 0 0
\(395\) −1.34430 1.55141i −0.0676391 0.0780597i
\(396\) 0 0
\(397\) −27.7887 8.15951i −1.39468 0.409514i −0.503824 0.863806i \(-0.668074\pi\)
−0.890853 + 0.454292i \(0.849892\pi\)
\(398\) 0 0
\(399\) 1.21804 2.66713i 0.0609783 0.133524i
\(400\) 0 0
\(401\) −11.6944 −0.583988 −0.291994 0.956420i \(-0.594319\pi\)
−0.291994 + 0.956420i \(0.594319\pi\)
\(402\) 0 0
\(403\) −48.6535 −2.42360
\(404\) 0 0
\(405\) 1.60456 3.51350i 0.0797312 0.174587i
\(406\) 0 0
\(407\) 20.2079 + 5.93357i 1.00167 + 0.294116i
\(408\) 0 0
\(409\) 23.9216 + 27.6070i 1.18285 + 1.36508i 0.915918 + 0.401364i \(0.131464\pi\)
0.266930 + 0.963716i \(0.413991\pi\)
\(410\) 0 0
\(411\) −13.4052 15.4704i −0.661230 0.763100i
\(412\) 0 0
\(413\) −17.3933 5.10712i −0.855866 0.251305i
\(414\) 0 0
\(415\) 10.6173 + 6.82329i 0.521180 + 0.334942i
\(416\) 0 0
\(417\) −1.03557 + 1.19511i −0.0507120 + 0.0585248i
\(418\) 0 0
\(419\) 1.55757 + 10.8331i 0.0760922 + 0.529233i 0.991841 + 0.127482i \(0.0406894\pi\)
−0.915749 + 0.401752i \(0.868402\pi\)
\(420\) 0 0
\(421\) −6.15145 + 7.09915i −0.299803 + 0.345992i −0.885585 0.464477i \(-0.846242\pi\)
0.585782 + 0.810469i \(0.300788\pi\)
\(422\) 0 0
\(423\) −7.76172 + 2.27905i −0.377388 + 0.110811i
\(424\) 0 0
\(425\) 6.49334 14.2184i 0.314973 0.689695i
\(426\) 0 0
\(427\) 20.3149 + 13.0556i 0.983108 + 0.631805i
\(428\) 0 0
\(429\) 12.3809 3.63535i 0.597753 0.175516i
\(430\) 0 0
\(431\) −11.4577 −0.551900 −0.275950 0.961172i \(-0.588992\pi\)
−0.275950 + 0.961172i \(0.588992\pi\)
\(432\) 0 0
\(433\) −24.2352 + 15.5750i −1.16467 + 0.748488i −0.972507 0.232875i \(-0.925187\pi\)
−0.192163 + 0.981363i \(0.561550\pi\)
\(434\) 0 0
\(435\) −12.1814 + 14.0581i −0.584054 + 0.674034i
\(436\) 0 0
\(437\) 3.85011 + 8.43055i 0.184176 + 0.403288i
\(438\) 0 0
\(439\) 10.1104 0.482545 0.241272 0.970457i \(-0.422435\pi\)
0.241272 + 0.970457i \(0.422435\pi\)
\(440\) 0 0
\(441\) −1.69061 + 1.08649i −0.0805052 + 0.0517375i
\(442\) 0 0
\(443\) −2.34920 16.3390i −0.111614 0.776291i −0.966350 0.257229i \(-0.917191\pi\)
0.854737 0.519062i \(-0.173719\pi\)
\(444\) 0 0
\(445\) −2.09860 14.5961i −0.0994830 0.691919i
\(446\) 0 0
\(447\) −1.22925 2.69168i −0.0581415 0.127312i
\(448\) 0 0
\(449\) −11.4663 + 25.1077i −0.541128 + 1.18491i 0.419675 + 0.907674i \(0.362144\pi\)
−0.960803 + 0.277231i \(0.910583\pi\)
\(450\) 0 0
\(451\) 4.70697 32.7377i 0.221642 1.54156i
\(452\) 0 0
\(453\) 12.5302 + 3.67920i 0.588720 + 0.172864i
\(454\) 0 0
\(455\) −5.61812 + 39.0749i −0.263382 + 1.83186i
\(456\) 0 0
\(457\) 29.5824 + 19.0114i 1.38381 + 0.889318i 0.999427 0.0338572i \(-0.0107791\pi\)
0.384379 + 0.923175i \(0.374416\pi\)
\(458\) 0 0
\(459\) −0.654618 1.43341i −0.0305549 0.0669060i
\(460\) 0 0
\(461\) −10.1460 + 6.52045i −0.472547 + 0.303687i −0.755153 0.655549i \(-0.772437\pi\)
0.282606 + 0.959236i \(0.408801\pi\)
\(462\) 0 0
\(463\) 20.8419 6.11974i 0.968607 0.284409i 0.241093 0.970502i \(-0.422494\pi\)
0.727514 + 0.686093i \(0.240676\pi\)
\(464\) 0 0
\(465\) 5.84571 40.6578i 0.271088 1.88546i
\(466\) 0 0
\(467\) 15.1904 + 17.5307i 0.702930 + 0.811224i 0.989145 0.146941i \(-0.0469427\pi\)
−0.286215 + 0.958165i \(0.592397\pi\)
\(468\) 0 0
\(469\) −13.6602 12.1554i −0.630769 0.561284i
\(470\) 0 0
\(471\) 14.4188 + 16.6402i 0.664385 + 0.766742i
\(472\) 0 0
\(473\) −3.16851 + 22.0375i −0.145688 + 1.01328i
\(474\) 0 0
\(475\) −12.4921 + 3.66801i −0.573176 + 0.168300i
\(476\) 0 0
\(477\) −7.63932 + 4.90949i −0.349780 + 0.224790i
\(478\) 0 0
\(479\) 5.13549 + 11.2452i 0.234647 + 0.513804i 0.989924 0.141601i \(-0.0452250\pi\)
−0.755277 + 0.655405i \(0.772498\pi\)
\(480\) 0 0
\(481\) −28.7408 18.4706i −1.31047 0.842186i
\(482\) 0 0
\(483\) −2.24488 + 15.6135i −0.102146 + 0.710440i
\(484\) 0 0
\(485\) 35.5597 + 10.4413i 1.61468 + 0.474113i
\(486\) 0 0
\(487\) −2.25712 + 15.6986i −0.102280 + 0.711372i 0.872567 + 0.488495i \(0.162454\pi\)
−0.974847 + 0.222877i \(0.928455\pi\)
\(488\) 0 0
\(489\) −1.04767 + 2.29409i −0.0473774 + 0.103742i
\(490\) 0 0
\(491\) −12.3347 27.0091i −0.556655 1.21890i −0.953604 0.301064i \(-0.902658\pi\)
0.396949 0.917841i \(-0.370069\pi\)
\(492\) 0 0
\(493\) 1.08002 + 7.51168i 0.0486415 + 0.338309i
\(494\) 0 0
\(495\) 1.55036 + 10.7830i 0.0696834 + 0.484659i
\(496\) 0 0
\(497\) −6.63221 + 4.26226i −0.297495 + 0.191189i
\(498\) 0 0
\(499\) 0.913315 0.0408856 0.0204428 0.999791i \(-0.493492\pi\)
0.0204428 + 0.999791i \(0.493492\pi\)
\(500\) 0 0
\(501\) 2.38188 + 5.21560i 0.106415 + 0.233016i
\(502\) 0 0
\(503\) −26.2797 + 30.3284i −1.17175 + 1.35227i −0.248244 + 0.968698i \(0.579853\pi\)
−0.923509 + 0.383577i \(0.874692\pi\)
\(504\) 0 0
\(505\) 12.4255 7.98537i 0.552927 0.355344i
\(506\) 0 0
\(507\) −7.93157 −0.352253
\(508\) 0 0
\(509\) 24.9511 7.32630i 1.10594 0.324733i 0.322729 0.946491i \(-0.395400\pi\)
0.783209 + 0.621759i \(0.213582\pi\)
\(510\) 0 0
\(511\) −2.19450 1.41032i −0.0970790 0.0623889i
\(512\) 0 0
\(513\) −0.545249 + 1.19393i −0.0240733 + 0.0527133i
\(514\) 0 0
\(515\) 37.5688 11.0312i 1.65548 0.486092i
\(516\) 0 0
\(517\) 14.9408 17.2426i 0.657095 0.758328i
\(518\) 0 0
\(519\) −1.09916 7.64481i −0.0482477 0.335570i
\(520\) 0 0
\(521\) −6.16976 + 7.12028i −0.270302 + 0.311945i −0.874631 0.484790i \(-0.838896\pi\)
0.604328 + 0.796735i \(0.293441\pi\)
\(522\) 0 0
\(523\) 5.07812 + 3.26351i 0.222051 + 0.142703i 0.646937 0.762543i \(-0.276050\pi\)
−0.424886 + 0.905247i \(0.639686\pi\)
\(524\) 0 0
\(525\) −21.2612 6.24286i −0.927916 0.272461i
\(526\) 0 0
\(527\) −10.9741 12.6647i −0.478038 0.551685i
\(528\) 0 0
\(529\) −17.5898 20.2997i −0.764772 0.882594i
\(530\) 0 0
\(531\) 7.78600 + 2.28618i 0.337884 + 0.0992116i
\(532\) 0 0
\(533\) −22.2877 + 48.8033i −0.965389 + 2.11391i
\(534\) 0 0
\(535\) −21.6061 −0.934112
\(536\) 0 0
\(537\) 17.7103 0.764256
\(538\) 0 0
\(539\) 2.35454 5.15573i 0.101417 0.222073i
\(540\) 0 0
\(541\) 20.4412 + 6.00208i 0.878837 + 0.258050i 0.689870 0.723934i \(-0.257668\pi\)
0.188967 + 0.981983i \(0.439486\pi\)
\(542\) 0 0
\(543\) −1.13238 1.30684i −0.0485952 0.0560819i
\(544\) 0 0
\(545\) −17.9130 20.6727i −0.767307 0.885520i
\(546\) 0 0
\(547\) −19.4371 5.70725i −0.831071 0.244024i −0.161594 0.986857i \(-0.551663\pi\)
−0.669477 + 0.742833i \(0.733482\pi\)
\(548\) 0 0
\(549\) −9.09387 5.84427i −0.388117 0.249428i
\(550\) 0 0
\(551\) 4.13939 4.77711i 0.176344 0.203512i
\(552\) 0 0
\(553\) 0.168962 + 1.17516i 0.00718502 + 0.0499729i
\(554\) 0 0
\(555\) 18.8883 21.7983i 0.801765 0.925286i
\(556\) 0 0
\(557\) 5.39961 1.58547i 0.228789 0.0671785i −0.165329 0.986239i \(-0.552868\pi\)
0.394118 + 0.919060i \(0.371050\pi\)
\(558\) 0 0
\(559\) 15.0031 32.8521i 0.634562 1.38950i
\(560\) 0 0
\(561\) 3.73887 + 2.40283i 0.157855 + 0.101447i
\(562\) 0 0
\(563\) 41.1431 12.0807i 1.73397 0.509141i 0.746292 0.665619i \(-0.231832\pi\)
0.987681 + 0.156478i \(0.0500141\pi\)
\(564\) 0 0
\(565\) −1.37817 −0.0579799
\(566\) 0 0
\(567\) −1.87929 + 1.20774i −0.0789227 + 0.0507205i
\(568\) 0 0
\(569\) 11.1474 12.8648i 0.467324 0.539321i −0.472341 0.881416i \(-0.656591\pi\)
0.939665 + 0.342095i \(0.111136\pi\)
\(570\) 0 0
\(571\) −7.04016 15.4158i −0.294622 0.645131i 0.703208 0.710984i \(-0.251750\pi\)
−0.997829 + 0.0658531i \(0.979023\pi\)
\(572\) 0 0
\(573\) −26.6175 −1.11196
\(574\) 0 0
\(575\) 58.9229 37.8675i 2.45726 1.57918i
\(576\) 0 0
\(577\) −4.84442 33.6937i −0.201676 1.40269i −0.799310 0.600918i \(-0.794802\pi\)
0.597634 0.801769i \(-0.296107\pi\)
\(578\) 0 0
\(579\) −0.0891397 0.619980i −0.00370452 0.0257655i
\(580\) 0 0
\(581\) −3.03221 6.63962i −0.125797 0.275458i
\(582\) 0 0
\(583\) 10.6394 23.2971i 0.440640 0.964866i
\(584\) 0 0
\(585\) 2.51492 17.4917i 0.103979 0.723192i
\(586\) 0 0
\(587\) −0.520857 0.152937i −0.0214981 0.00631241i 0.270966 0.962589i \(-0.412657\pi\)
−0.292464 + 0.956277i \(0.594475\pi\)
\(588\) 0 0
\(589\) −1.98644 + 13.8160i −0.0818500 + 0.569279i
\(590\) 0 0
\(591\) −11.6110 7.46191i −0.477611 0.306942i
\(592\) 0 0
\(593\) 5.13485 + 11.2437i 0.210863 + 0.461725i 0.985280 0.170951i \(-0.0546838\pi\)
−0.774417 + 0.632676i \(0.781957\pi\)
\(594\) 0 0
\(595\) −11.4386 + 7.35114i −0.468937 + 0.301367i
\(596\) 0 0
\(597\) 4.84058 1.42132i 0.198112 0.0581709i
\(598\) 0 0
\(599\) 1.56693 10.8982i 0.0640228 0.445289i −0.932445 0.361312i \(-0.882329\pi\)
0.996468 0.0839765i \(-0.0267621\pi\)
\(600\) 0 0
\(601\) 16.1811 + 18.6740i 0.660042 + 0.761729i 0.982784 0.184758i \(-0.0591500\pi\)
−0.322742 + 0.946487i \(0.604605\pi\)
\(602\) 0 0
\(603\) 6.11492 + 5.44130i 0.249019 + 0.221587i
\(604\) 0 0
\(605\) 7.70324 + 8.89001i 0.313181 + 0.361430i
\(606\) 0 0
\(607\) −2.33356 + 16.2302i −0.0947161 + 0.658765i 0.886052 + 0.463587i \(0.153438\pi\)
−0.980768 + 0.195179i \(0.937471\pi\)
\(608\) 0 0
\(609\) 10.3225 3.03095i 0.418287 0.122820i
\(610\) 0 0
\(611\) −31.1347 + 20.0090i −1.25957 + 0.809479i
\(612\) 0 0
\(613\) 2.33435 + 5.11152i 0.0942837 + 0.206452i 0.950898 0.309505i \(-0.100163\pi\)
−0.856614 + 0.515958i \(0.827436\pi\)
\(614\) 0 0
\(615\) −38.1052 24.4887i −1.53655 0.987480i
\(616\) 0 0
\(617\) −4.32193 + 30.0597i −0.173994 + 1.21016i 0.696346 + 0.717706i \(0.254808\pi\)
−0.870340 + 0.492451i \(0.836101\pi\)
\(618\) 0 0
\(619\) −13.6599 4.01091i −0.549038 0.161212i −0.00456385 0.999990i \(-0.501453\pi\)
−0.544475 + 0.838777i \(0.683271\pi\)
\(620\) 0 0
\(621\) 1.00491 6.98931i 0.0403257 0.280471i
\(622\) 0 0
\(623\) −3.54285 + 7.75777i −0.141941 + 0.310808i
\(624\) 0 0
\(625\) 9.88508 + 21.6453i 0.395403 + 0.865812i
\(626\) 0 0
\(627\) −0.526831 3.66419i −0.0210396 0.146334i
\(628\) 0 0
\(629\) −1.67466 11.6475i −0.0667731 0.464417i
\(630\) 0 0
\(631\) 20.7581 13.3404i 0.826368 0.531074i −0.0577540 0.998331i \(-0.518394\pi\)
0.884122 + 0.467257i \(0.154758\pi\)
\(632\) 0 0
\(633\) −18.1345 −0.720781
\(634\) 0 0
\(635\) 26.0996 + 57.1501i 1.03573 + 2.26793i
\(636\) 0 0
\(637\) −6.02096 + 6.94856i −0.238559 + 0.275312i
\(638\) 0 0
\(639\) 2.96888 1.90798i 0.117447 0.0754785i
\(640\) 0 0
\(641\) 2.05916 0.0813317 0.0406659 0.999173i \(-0.487052\pi\)
0.0406659 + 0.999173i \(0.487052\pi\)
\(642\) 0 0
\(643\) 4.09442 1.20223i 0.161468 0.0474113i −0.199999 0.979796i \(-0.564094\pi\)
0.361467 + 0.932385i \(0.382276\pi\)
\(644\) 0 0
\(645\) 25.6506 + 16.4846i 1.00999 + 0.649082i
\(646\) 0 0
\(647\) −11.6707 + 25.5552i −0.458821 + 1.00468i 0.528934 + 0.848663i \(0.322592\pi\)
−0.987755 + 0.156015i \(0.950135\pi\)
\(648\) 0 0
\(649\) −21.9595 + 6.44789i −0.861986 + 0.253102i
\(650\) 0 0
\(651\) −15.5571 + 17.9538i −0.609730 + 0.703666i
\(652\) 0 0
\(653\) 2.72694 + 18.9663i 0.106713 + 0.742209i 0.970978 + 0.239170i \(0.0768754\pi\)
−0.864264 + 0.503038i \(0.832215\pi\)
\(654\) 0 0
\(655\) −47.0562 + 54.3057i −1.83864 + 2.12190i
\(656\) 0 0
\(657\) 0.982357 + 0.631323i 0.0383254 + 0.0246302i
\(658\) 0 0
\(659\) −22.9231 6.73082i −0.892955 0.262195i −0.197105 0.980382i \(-0.563154\pi\)
−0.695850 + 0.718187i \(0.744972\pi\)
\(660\) 0 0
\(661\) 26.2191 + 30.2585i 1.01981 + 1.17692i 0.984111 + 0.177556i \(0.0568189\pi\)
0.0356947 + 0.999363i \(0.488636\pi\)
\(662\) 0 0
\(663\) −4.72123 5.44859i −0.183358 0.211606i
\(664\) 0 0
\(665\) 10.8666 + 3.19073i 0.421390 + 0.123731i
\(666\) 0 0
\(667\) −14.1265 + 30.9327i −0.546980 + 1.19772i
\(668\) 0 0
\(669\) 13.1450 0.508214
\(670\) 0 0
\(671\) 30.4881 1.17698
\(672\) 0 0
\(673\) −3.24482 + 7.10517i −0.125079 + 0.273884i −0.961804 0.273739i \(-0.911740\pi\)
0.836726 + 0.547622i \(0.184467\pi\)
\(674\) 0 0
\(675\) 9.51748 + 2.79458i 0.366328 + 0.107564i
\(676\) 0 0
\(677\) −24.6370 28.4326i −0.946875 1.09275i −0.995578 0.0939391i \(-0.970054\pi\)
0.0487026 0.998813i \(-0.484491\pi\)
\(678\) 0 0
\(679\) −14.0364 16.1989i −0.538670 0.621658i
\(680\) 0 0
\(681\) 10.2633 + 3.01357i 0.393289 + 0.115480i
\(682\) 0 0
\(683\) −15.9586 10.2560i −0.610638 0.392433i 0.198458 0.980109i \(-0.436407\pi\)
−0.809096 + 0.587676i \(0.800043\pi\)
\(684\) 0 0
\(685\) 51.7782 59.7553i 1.97834 2.28313i
\(686\) 0 0
\(687\) −1.83509 12.7634i −0.0700132 0.486953i
\(688\) 0 0
\(689\) −27.2068 + 31.3983i −1.03650 + 1.19618i
\(690\) 0 0
\(691\) 28.5952 8.39632i 1.08781 0.319411i 0.311813 0.950143i \(-0.399064\pi\)
0.776000 + 0.630732i \(0.217245\pi\)
\(692\) 0 0
\(693\) 2.61732 5.73113i 0.0994237 0.217708i
\(694\) 0 0
\(695\) −5.13844 3.30227i −0.194912 0.125262i
\(696\) 0 0
\(697\) −17.7309 + 5.20626i −0.671605 + 0.197201i
\(698\) 0 0
\(699\) −8.10258 −0.306468
\(700\) 0 0
\(701\) 1.12058 0.720150i 0.0423236 0.0271997i −0.519308 0.854587i \(-0.673810\pi\)
0.561632 + 0.827387i \(0.310174\pi\)
\(702\) 0 0
\(703\) −6.41849 + 7.40733i −0.242078 + 0.279373i
\(704\) 0 0
\(705\) −12.9799 28.4221i −0.488852 1.07044i
\(706\) 0 0
\(707\) −8.54238 −0.321269
\(708\) 0 0
\(709\) 10.1651 6.53273i 0.381759 0.245342i −0.335660 0.941983i \(-0.608959\pi\)
0.717420 + 0.696641i \(0.245323\pi\)
\(710\) 0 0
\(711\) −0.0756352 0.526054i −0.00283654 0.0197286i
\(712\) 0 0
\(713\) −10.6866 74.3271i −0.400217 2.78357i
\(714\) 0 0
\(715\) 20.7045 + 45.3366i 0.774305 + 1.69549i
\(716\) 0 0
\(717\) −8.80209 + 19.2739i −0.328720 + 0.719797i
\(718\) 0 0
\(719\) −3.04229 + 21.1596i −0.113458 + 0.789119i 0.851053 + 0.525079i \(0.175964\pi\)
−0.964512 + 0.264040i \(0.914945\pi\)
\(720\) 0 0
\(721\) −21.7280 6.37991i −0.809192 0.237600i
\(722\) 0 0
\(723\) −3.71950 + 25.8697i −0.138330 + 0.962104i
\(724\) 0 0
\(725\) −40.1866 25.8264i −1.49249 0.959168i
\(726\) 0 0
\(727\) −6.95721 15.2342i −0.258028 0.565004i 0.735638 0.677375i \(-0.236883\pi\)
−0.993666 + 0.112372i \(0.964155\pi\)
\(728\) 0 0
\(729\) 0.841254 0.540641i 0.0311575 0.0200237i
\(730\) 0 0
\(731\) 11.9356 3.50461i 0.441454 0.129623i
\(732\) 0 0
\(733\) −7.08049 + 49.2459i −0.261524 + 1.81894i 0.259895 + 0.965637i \(0.416312\pi\)
−0.521419 + 0.853301i \(0.674597\pi\)
\(734\) 0 0
\(735\) −5.08322 5.86635i −0.187497 0.216384i
\(736\) 0 0
\(737\) −22.8056 3.58623i −0.840054 0.132100i
\(738\) 0 0
\(739\) −22.5597 26.0353i −0.829873 0.957725i 0.169741 0.985489i \(-0.445707\pi\)
−0.999615 + 0.0277641i \(0.991161\pi\)
\(740\) 0 0
\(741\) −0.854602 + 5.94389i −0.0313946 + 0.218354i
\(742\) 0 0
\(743\) 2.17746 0.639359i 0.0798831 0.0234558i −0.241547 0.970389i \(-0.577655\pi\)
0.321430 + 0.946933i \(0.395837\pi\)
\(744\) 0 0
\(745\) 9.61521 6.17932i 0.352274 0.226393i
\(746\) 0 0
\(747\) 1.35736 + 2.97219i 0.0496630 + 0.108747i
\(748\) 0 0
\(749\) 10.5122 + 6.75580i 0.384109 + 0.246852i
\(750\) 0 0
\(751\) −5.52216 + 38.4075i −0.201507 + 1.40151i 0.598310 + 0.801264i \(0.295839\pi\)
−0.799817 + 0.600244i \(0.795070\pi\)
\(752\) 0 0
\(753\) −21.4599 6.30118i −0.782041 0.229628i
\(754\) 0 0
\(755\) −7.17861 + 49.9283i −0.261256 + 1.81708i
\(756\) 0 0
\(757\) 10.1371 22.1972i 0.368439 0.806769i −0.631079 0.775719i \(-0.717387\pi\)
0.999518 0.0310505i \(-0.00988527\pi\)
\(758\) 0 0
\(759\) 8.27309 + 18.1155i 0.300294 + 0.657552i
\(760\) 0 0
\(761\) 0.0984397 + 0.684663i 0.00356844 + 0.0248190i 0.991528 0.129894i \(-0.0414637\pi\)
−0.987959 + 0.154713i \(0.950555\pi\)
\(762\) 0 0
\(763\) 2.25144 + 15.6591i 0.0815078 + 0.566899i
\(764\) 0 0
\(765\) 5.12043 3.29070i 0.185130 0.118976i
\(766\) 0 0
\(767\) 37.1256 1.34053
\(768\) 0 0
\(769\) 20.1128 + 44.0410i 0.725287 + 1.58816i 0.806343 + 0.591448i \(0.201444\pi\)
−0.0810554 + 0.996710i \(0.525829\pi\)
\(770\) 0 0
\(771\) 6.47848 7.47656i 0.233317 0.269262i
\(772\) 0 0
\(773\) −36.5387 + 23.4820i −1.31420 + 0.844588i −0.994682 0.102991i \(-0.967159\pi\)
−0.319522 + 0.947579i \(0.603522\pi\)
\(774\) 0 0
\(775\) 105.486 3.78915
\(776\) 0 0
\(777\) −16.0059 + 4.69974i −0.574207 + 0.168602i
\(778\) 0 0
\(779\) 12.9486 + 8.32156i 0.463932 + 0.298151i
\(780\) 0 0
\(781\) −4.13481 + 9.05397i −0.147955 + 0.323976i