Properties

Label 804.2.q.b.241.5
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 241.5
Character \(\chi\) = 804.241
Dual form 804.2.q.b.397.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.415415 + 0.909632i) q^{3} +(1.77448 + 0.521035i) q^{5} +(-3.02047 - 3.48581i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\) \(q+(-0.415415 + 0.909632i) q^{3} +(1.77448 + 0.521035i) q^{5} +(-3.02047 - 3.48581i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(3.93894 + 1.15658i) q^{11} +(-0.415421 - 0.266975i) q^{13} +(-1.21110 + 1.39768i) q^{15} +(0.225401 + 1.56770i) q^{17} +(4.53068 - 5.22868i) q^{19} +(4.42555 - 1.29946i) q^{21} +(2.63191 - 5.76307i) q^{23} +(-1.32896 - 0.854071i) q^{25} +(0.959493 - 0.281733i) q^{27} +1.63223 q^{29} +(-2.78213 + 1.78796i) q^{31} +(-2.68836 + 3.10253i) q^{33} +(-3.54354 - 7.75928i) q^{35} +11.4300 q^{37} +(0.415421 - 0.266975i) q^{39} +(0.221415 + 1.53997i) q^{41} +(0.132442 + 0.921155i) q^{43} +(-0.768266 - 1.68227i) q^{45} +(2.43938 - 5.34151i) q^{47} +(-2.03142 + 14.1288i) q^{49} +(-1.51966 - 0.446213i) q^{51} +(-1.20219 + 8.36144i) q^{53} +(6.38696 + 4.10465i) q^{55} +(2.87406 + 6.29332i) q^{57} +(9.70533 - 6.23724i) q^{59} +(8.90205 - 2.61388i) q^{61} +(-0.656411 + 4.56544i) q^{63} +(-0.598053 - 0.690190i) q^{65} +(-6.25848 + 5.27554i) q^{67} +(4.14894 + 4.78813i) q^{69} +(0.873940 - 6.07838i) q^{71} +(-8.77361 + 2.57616i) q^{73} +(1.32896 - 0.854071i) q^{75} +(-7.86585 - 17.2238i) q^{77} +(2.48884 + 1.59948i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(-12.3072 - 3.61371i) q^{83} +(-0.416855 + 2.89929i) q^{85} +(-0.678052 + 1.48473i) q^{87} +(-1.56063 - 3.41731i) q^{89} +(0.324143 + 2.25447i) q^{91} +(-0.470652 - 3.27346i) q^{93} +(10.7639 - 6.91755i) q^{95} +8.12305 q^{97} +(-1.70538 - 3.73425i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} + O(q^{10}) \) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} - 11q^{11} - 2q^{13} + 9q^{15} + 21q^{17} + 10q^{19} - 2q^{21} - 10q^{23} - 36q^{25} + 6q^{27} + 4q^{29} - 24q^{31} - 32q^{35} + 2q^{37} + 2q^{39} + 10q^{41} + 23q^{43} + 2q^{45} + 66q^{47} + 34q^{49} + 23q^{51} - 13q^{53} + 27q^{55} + q^{57} + 35q^{59} + 56q^{61} - 9q^{63} + 48q^{65} + 13q^{67} + 10q^{69} + 76q^{71} - q^{73} + 36q^{75} - 38q^{77} - 46q^{79} - 6q^{81} - 26q^{83} + 42q^{85} + 7q^{87} + 58q^{89} - 40q^{91} - 9q^{93} - 29q^{95} - 46q^{97} + O(q^{100}) \)

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
\(5\) 1.77448 + 0.521035i 0.793572 + 0.233014i 0.653300 0.757099i \(-0.273384\pi\)
0.140272 + 0.990113i \(0.455202\pi\)
\(6\) 0 0
\(7\) −3.02047 3.48581i −1.14163 1.31751i −0.941218 0.337801i \(-0.890317\pi\)
−0.200413 0.979711i \(-0.564228\pi\)
\(8\) 0 0
\(9\) −0.654861 0.755750i −0.218287 0.251917i
\(10\) 0 0
\(11\) 3.93894 + 1.15658i 1.18764 + 0.348721i 0.815113 0.579302i \(-0.196675\pi\)
0.372522 + 0.928023i \(0.378493\pi\)
\(12\) 0 0
\(13\) −0.415421 0.266975i −0.115217 0.0740454i 0.481763 0.876301i \(-0.339997\pi\)
−0.596980 + 0.802256i \(0.703633\pi\)
\(14\) 0 0
\(15\) −1.21110 + 1.39768i −0.312704 + 0.360879i
\(16\) 0 0
\(17\) 0.225401 + 1.56770i 0.0546677 + 0.380222i 0.998727 + 0.0504459i \(0.0160642\pi\)
−0.944059 + 0.329776i \(0.893027\pi\)
\(18\) 0 0
\(19\) 4.53068 5.22868i 1.03941 1.19954i 0.0598862 0.998205i \(-0.480926\pi\)
0.979522 0.201336i \(-0.0645283\pi\)
\(20\) 0 0
\(21\) 4.42555 1.29946i 0.965735 0.283565i
\(22\) 0 0
\(23\) 2.63191 5.76307i 0.548790 1.20168i −0.408554 0.912734i \(-0.633967\pi\)
0.957344 0.288949i \(-0.0933059\pi\)
\(24\) 0 0
\(25\) −1.32896 0.854071i −0.265792 0.170814i
\(26\) 0 0
\(27\) 0.959493 0.281733i 0.184655 0.0542195i
\(28\) 0 0
\(29\) 1.63223 0.303097 0.151549 0.988450i \(-0.451574\pi\)
0.151549 + 0.988450i \(0.451574\pi\)
\(30\) 0 0
\(31\) −2.78213 + 1.78796i −0.499685 + 0.321128i −0.766090 0.642733i \(-0.777800\pi\)
0.266405 + 0.963861i \(0.414164\pi\)
\(32\) 0 0
\(33\) −2.68836 + 3.10253i −0.467983 + 0.540081i
\(34\) 0 0
\(35\) −3.54354 7.75928i −0.598968 1.31156i
\(36\) 0 0
\(37\) 11.4300 1.87908 0.939540 0.342440i \(-0.111253\pi\)
0.939540 + 0.342440i \(0.111253\pi\)
\(38\) 0 0
\(39\) 0.415421 0.266975i 0.0665205 0.0427502i
\(40\) 0 0
\(41\) 0.221415 + 1.53997i 0.0345792 + 0.240503i 0.999779 0.0210090i \(-0.00668786\pi\)
−0.965200 + 0.261512i \(0.915779\pi\)
\(42\) 0 0
\(43\) 0.132442 + 0.921155i 0.0201972 + 0.140475i 0.997425 0.0717187i \(-0.0228484\pi\)
−0.977228 + 0.212194i \(0.931939\pi\)
\(44\) 0 0
\(45\) −0.768266 1.68227i −0.114526 0.250778i
\(46\) 0 0
\(47\) 2.43938 5.34151i 0.355821 0.779139i −0.644079 0.764959i \(-0.722759\pi\)
0.999899 0.0141796i \(-0.00451366\pi\)
\(48\) 0 0
\(49\) −2.03142 + 14.1288i −0.290203 + 2.01840i
\(50\) 0 0
\(51\) −1.51966 0.446213i −0.212795 0.0624823i
\(52\) 0 0
\(53\) −1.20219 + 8.36144i −0.165134 + 1.14853i 0.723637 + 0.690181i \(0.242469\pi\)
−0.888771 + 0.458351i \(0.848440\pi\)
\(54\) 0 0
\(55\) 6.38696 + 4.10465i 0.861218 + 0.553471i
\(56\) 0 0
\(57\) 2.87406 + 6.29332i 0.380679 + 0.833571i
\(58\) 0 0
\(59\) 9.70533 6.23724i 1.26353 0.812019i 0.274763 0.961512i \(-0.411400\pi\)
0.988763 + 0.149493i \(0.0477641\pi\)
\(60\) 0 0
\(61\) 8.90205 2.61388i 1.13979 0.334673i 0.343242 0.939247i \(-0.388475\pi\)
0.796549 + 0.604574i \(0.206657\pi\)
\(62\) 0 0
\(63\) −0.656411 + 4.56544i −0.0827000 + 0.575191i
\(64\) 0 0
\(65\) −0.598053 0.690190i −0.0741794 0.0856076i
\(66\) 0 0
\(67\) −6.25848 + 5.27554i −0.764596 + 0.644510i
\(68\) 0 0
\(69\) 4.14894 + 4.78813i 0.499474 + 0.576423i
\(70\) 0 0
\(71\) 0.873940 6.07838i 0.103718 0.721371i −0.869907 0.493216i \(-0.835821\pi\)
0.973625 0.228156i \(-0.0732696\pi\)
\(72\) 0 0
\(73\) −8.77361 + 2.57616i −1.02687 + 0.301517i −0.751439 0.659803i \(-0.770640\pi\)
−0.275435 + 0.961320i \(0.588822\pi\)
\(74\) 0 0
\(75\) 1.32896 0.854071i 0.153455 0.0986196i
\(76\) 0 0
\(77\) −7.86585 17.2238i −0.896397 1.96284i
\(78\) 0 0
\(79\) 2.48884 + 1.59948i 0.280017 + 0.179956i 0.673109 0.739543i \(-0.264958\pi\)
−0.393092 + 0.919499i \(0.628595\pi\)
\(80\) 0 0
\(81\) −0.142315 + 0.989821i −0.0158128 + 0.109980i
\(82\) 0 0
\(83\) −12.3072 3.61371i −1.35089 0.396656i −0.475345 0.879799i \(-0.657677\pi\)
−0.875541 + 0.483143i \(0.839495\pi\)
\(84\) 0 0
\(85\) −0.416855 + 2.89929i −0.0452143 + 0.314472i
\(86\) 0 0
\(87\) −0.678052 + 1.48473i −0.0726948 + 0.159179i
\(88\) 0 0
\(89\) −1.56063 3.41731i −0.165427 0.362234i 0.808705 0.588214i \(-0.200169\pi\)
−0.974132 + 0.225980i \(0.927442\pi\)
\(90\) 0 0
\(91\) 0.324143 + 2.25447i 0.0339795 + 0.236332i
\(92\) 0 0
\(93\) −0.470652 3.27346i −0.0488044 0.339442i
\(94\) 0 0
\(95\) 10.7639 6.91755i 1.10436 0.709726i
\(96\) 0 0
\(97\) 8.12305 0.824771 0.412386 0.911009i \(-0.364696\pi\)
0.412386 + 0.911009i \(0.364696\pi\)
\(98\) 0 0
\(99\) −1.70538 3.73425i −0.171397 0.375306i
\(100\) 0 0
\(101\) 6.39442 7.37956i 0.636269 0.734293i −0.342442 0.939539i \(-0.611254\pi\)
0.978710 + 0.205246i \(0.0657993\pi\)
\(102\) 0 0
\(103\) −2.16340 + 1.39033i −0.213166 + 0.136994i −0.642867 0.765978i \(-0.722255\pi\)
0.429701 + 0.902971i \(0.358619\pi\)
\(104\) 0 0
\(105\) 8.53013 0.832455
\(106\) 0 0
\(107\) 9.41534 2.76459i 0.910216 0.267263i 0.207084 0.978323i \(-0.433603\pi\)
0.703132 + 0.711060i \(0.251784\pi\)
\(108\) 0 0
\(109\) −0.366325 0.235423i −0.0350876 0.0225494i 0.522979 0.852345i \(-0.324820\pi\)
−0.558067 + 0.829796i \(0.688457\pi\)
\(110\) 0 0
\(111\) −4.74819 + 10.3971i −0.450678 + 0.986848i
\(112\) 0 0
\(113\) −17.6966 + 5.19619i −1.66476 + 0.488816i −0.972513 0.232849i \(-0.925195\pi\)
−0.692242 + 0.721665i \(0.743377\pi\)
\(114\) 0 0
\(115\) 7.67303 8.85515i 0.715514 0.825747i
\(116\) 0 0
\(117\) 0.0702767 + 0.488785i 0.00649708 + 0.0451882i
\(118\) 0 0
\(119\) 4.78387 5.52089i 0.438537 0.506099i
\(120\) 0 0
\(121\) 4.92380 + 3.16433i 0.447618 + 0.287667i
\(122\) 0 0
\(123\) −1.49279 0.438322i −0.134600 0.0395222i
\(124\) 0 0
\(125\) −7.96870 9.19636i −0.712742 0.822548i
\(126\) 0 0
\(127\) −7.87392 9.08699i −0.698697 0.806340i 0.289879 0.957063i \(-0.406385\pi\)
−0.988576 + 0.150724i \(0.951840\pi\)
\(128\) 0 0
\(129\) −0.892931 0.262188i −0.0786182 0.0230844i
\(130\) 0 0
\(131\) −6.13035 + 13.4236i −0.535611 + 1.17283i 0.427572 + 0.903981i \(0.359369\pi\)
−0.963184 + 0.268844i \(0.913358\pi\)
\(132\) 0 0
\(133\) −31.9110 −2.76703
\(134\) 0 0
\(135\) 1.84940 0.159171
\(136\) 0 0
\(137\) −6.23726 + 13.6577i −0.532885 + 1.16686i 0.431442 + 0.902141i \(0.358005\pi\)
−0.964327 + 0.264714i \(0.914722\pi\)
\(138\) 0 0
\(139\) 4.84302 + 1.42204i 0.410780 + 0.120616i 0.480592 0.876944i \(-0.340422\pi\)
−0.0698123 + 0.997560i \(0.522240\pi\)
\(140\) 0 0
\(141\) 3.84545 + 4.43788i 0.323845 + 0.373737i
\(142\) 0 0
\(143\) −1.32754 1.53206i −0.111015 0.128118i
\(144\) 0 0
\(145\) 2.89636 + 0.850448i 0.240530 + 0.0706259i
\(146\) 0 0
\(147\) −12.0081 7.71717i −0.990415 0.636501i
\(148\) 0 0
\(149\) 2.46350 2.84303i 0.201818 0.232910i −0.645814 0.763495i \(-0.723482\pi\)
0.847632 + 0.530584i \(0.178027\pi\)
\(150\) 0 0
\(151\) 1.67536 + 11.6524i 0.136339 + 0.948259i 0.937047 + 0.349204i \(0.113548\pi\)
−0.800708 + 0.599055i \(0.795543\pi\)
\(152\) 0 0
\(153\) 1.03718 1.19697i 0.0838510 0.0967692i
\(154\) 0 0
\(155\) −5.86842 + 1.72312i −0.471363 + 0.138405i
\(156\) 0 0
\(157\) −7.34411 + 16.0813i −0.586123 + 1.28343i 0.351633 + 0.936138i \(0.385626\pi\)
−0.937757 + 0.347293i \(0.887101\pi\)
\(158\) 0 0
\(159\) −7.10642 4.56702i −0.563576 0.362188i
\(160\) 0 0
\(161\) −28.0386 + 8.23287i −2.20975 + 0.648841i
\(162\) 0 0
\(163\) −19.4711 −1.52510 −0.762548 0.646932i \(-0.776052\pi\)
−0.762548 + 0.646932i \(0.776052\pi\)
\(164\) 0 0
\(165\) −6.38696 + 4.10465i −0.497224 + 0.319547i
\(166\) 0 0
\(167\) −2.18599 + 2.52277i −0.169157 + 0.195217i −0.833998 0.551767i \(-0.813954\pi\)
0.664841 + 0.746985i \(0.268499\pi\)
\(168\) 0 0
\(169\) −5.29910 11.6034i −0.407623 0.892569i
\(170\) 0 0
\(171\) −6.91853 −0.529074
\(172\) 0 0
\(173\) 7.50499 4.82316i 0.570594 0.366698i −0.223305 0.974749i \(-0.571684\pi\)
0.793898 + 0.608050i \(0.208048\pi\)
\(174\) 0 0
\(175\) 1.03696 + 7.21220i 0.0783866 + 0.545191i
\(176\) 0 0
\(177\) 1.64185 + 11.4193i 0.123409 + 0.858329i
\(178\) 0 0
\(179\) 8.46433 + 18.5343i 0.632653 + 1.38532i 0.905949 + 0.423388i \(0.139159\pi\)
−0.273295 + 0.961930i \(0.588114\pi\)
\(180\) 0 0
\(181\) −4.97945 + 10.9035i −0.370120 + 0.810449i 0.629325 + 0.777142i \(0.283331\pi\)
−0.999445 + 0.0333072i \(0.989396\pi\)
\(182\) 0 0
\(183\) −1.32038 + 9.18344i −0.0976052 + 0.678859i
\(184\) 0 0
\(185\) 20.2823 + 5.95543i 1.49119 + 0.437852i
\(186\) 0 0
\(187\) −0.925322 + 6.43576i −0.0676663 + 0.470629i
\(188\) 0 0
\(189\) −3.88019 2.49364i −0.282242 0.181386i
\(190\) 0 0
\(191\) −0.748511 1.63901i −0.0541604 0.118595i 0.880617 0.473829i \(-0.157128\pi\)
−0.934777 + 0.355234i \(0.884401\pi\)
\(192\) 0 0
\(193\) −3.47383 + 2.23249i −0.250052 + 0.160698i −0.659663 0.751562i \(-0.729301\pi\)
0.409611 + 0.912260i \(0.365664\pi\)
\(194\) 0 0
\(195\) 0.876259 0.257293i 0.0627502 0.0184251i
\(196\) 0 0
\(197\) 3.22256 22.4134i 0.229598 1.59689i −0.470208 0.882556i \(-0.655821\pi\)
0.699806 0.714333i \(-0.253270\pi\)
\(198\) 0 0
\(199\) −6.09750 7.03689i −0.432240 0.498832i 0.497287 0.867586i \(-0.334330\pi\)
−0.929527 + 0.368755i \(0.879784\pi\)
\(200\) 0 0
\(201\) −2.19894 7.88446i −0.155101 0.556127i
\(202\) 0 0
\(203\) −4.93010 5.68964i −0.346025 0.399334i
\(204\) 0 0
\(205\) −0.409483 + 2.84802i −0.0285996 + 0.198914i
\(206\) 0 0
\(207\) −6.07897 + 1.78495i −0.422518 + 0.124062i
\(208\) 0 0
\(209\) 23.8934 15.3554i 1.65274 1.06215i
\(210\) 0 0
\(211\) 3.50792 + 7.68126i 0.241495 + 0.528800i 0.991105 0.133079i \(-0.0424864\pi\)
−0.749611 + 0.661879i \(0.769759\pi\)
\(212\) 0 0
\(213\) 5.16604 + 3.32002i 0.353972 + 0.227484i
\(214\) 0 0
\(215\) −0.244938 + 1.70358i −0.0167046 + 0.116183i
\(216\) 0 0
\(217\) 14.6358 + 4.29747i 0.993545 + 0.291731i
\(218\) 0 0
\(219\) 1.30133 9.05094i 0.0879356 0.611606i
\(220\) 0 0
\(221\) 0.324899 0.711430i 0.0218551 0.0478559i
\(222\) 0 0
\(223\) −5.08626 11.1374i −0.340601 0.745813i 0.659381 0.751809i \(-0.270819\pi\)
−0.999982 + 0.00599632i \(0.998091\pi\)
\(224\) 0 0
\(225\) 0.224820 + 1.56366i 0.0149880 + 0.104244i
\(226\) 0 0
\(227\) −3.88689 27.0339i −0.257982 1.79430i −0.547160 0.837028i \(-0.684291\pi\)
0.289178 0.957275i \(-0.406618\pi\)
\(228\) 0 0
\(229\) −9.84033 + 6.32399i −0.650267 + 0.417901i −0.823764 0.566933i \(-0.808130\pi\)
0.173497 + 0.984834i \(0.444493\pi\)
\(230\) 0 0
\(231\) 18.9349 1.24583
\(232\) 0 0
\(233\) 9.28928 + 20.3407i 0.608561 + 1.33256i 0.923554 + 0.383469i \(0.125271\pi\)
−0.314993 + 0.949094i \(0.602002\pi\)
\(234\) 0 0
\(235\) 7.11175 8.20740i 0.463920 0.535392i
\(236\) 0 0
\(237\) −2.48884 + 1.59948i −0.161668 + 0.103898i
\(238\) 0 0
\(239\) −15.6819 −1.01438 −0.507189 0.861835i \(-0.669315\pi\)
−0.507189 + 0.861835i \(0.669315\pi\)
\(240\) 0 0
\(241\) 17.5003 5.13854i 1.12729 0.331003i 0.335649 0.941987i \(-0.391044\pi\)
0.791643 + 0.610985i \(0.209226\pi\)
\(242\) 0 0
\(243\) −0.841254 0.540641i −0.0539664 0.0346821i
\(244\) 0 0
\(245\) −10.9663 + 24.0129i −0.700613 + 1.53413i
\(246\) 0 0
\(247\) −3.27806 + 0.962526i −0.208578 + 0.0612440i
\(248\) 0 0
\(249\) 8.39973 9.69380i 0.532311 0.614320i
\(250\) 0 0
\(251\) 3.56712 + 24.8099i 0.225155 + 1.56599i 0.718109 + 0.695930i \(0.245008\pi\)
−0.492954 + 0.870055i \(0.664083\pi\)
\(252\) 0 0
\(253\) 17.0324 19.6564i 1.07082 1.23579i
\(254\) 0 0
\(255\) −2.46412 1.58359i −0.154309 0.0991685i
\(256\) 0 0
\(257\) 12.5970 + 3.69881i 0.785778 + 0.230725i 0.649919 0.760003i \(-0.274803\pi\)
0.135858 + 0.990728i \(0.456621\pi\)
\(258\) 0 0
\(259\) −34.5240 39.8428i −2.14522 2.47571i
\(260\) 0 0
\(261\) −1.06888 1.23356i −0.0661622 0.0763552i
\(262\) 0 0
\(263\) −14.5251 4.26494i −0.895654 0.262988i −0.198663 0.980068i \(-0.563660\pi\)
−0.696991 + 0.717080i \(0.745478\pi\)
\(264\) 0 0
\(265\) −6.48987 + 14.2108i −0.398670 + 0.872965i
\(266\) 0 0
\(267\) 3.75680 0.229913
\(268\) 0 0
\(269\) −10.9118 −0.665302 −0.332651 0.943050i \(-0.607943\pi\)
−0.332651 + 0.943050i \(0.607943\pi\)
\(270\) 0 0
\(271\) 6.62936 14.5163i 0.402705 0.881801i −0.594284 0.804256i \(-0.702564\pi\)
0.996989 0.0775458i \(-0.0247084\pi\)
\(272\) 0 0
\(273\) −2.18539 0.641688i −0.132266 0.0388367i
\(274\) 0 0
\(275\) −4.24690 4.90118i −0.256097 0.295552i
\(276\) 0 0
\(277\) 14.4193 + 16.6407i 0.866369 + 0.999843i 0.999961 + 0.00880696i \(0.00280338\pi\)
−0.133592 + 0.991036i \(0.542651\pi\)
\(278\) 0 0
\(279\) 3.17316 + 0.931724i 0.189972 + 0.0557808i
\(280\) 0 0
\(281\) −14.7827 9.50024i −0.881859 0.566737i 0.0194993 0.999810i \(-0.493793\pi\)
−0.901359 + 0.433073i \(0.857429\pi\)
\(282\) 0 0
\(283\) −7.70210 + 8.88869i −0.457842 + 0.528378i −0.936990 0.349356i \(-0.886400\pi\)
0.479148 + 0.877734i \(0.340946\pi\)
\(284\) 0 0
\(285\) 1.82093 + 12.6649i 0.107863 + 0.750202i
\(286\) 0 0
\(287\) 4.69928 5.42325i 0.277390 0.320125i
\(288\) 0 0
\(289\) 13.9045 4.08273i 0.817913 0.240161i
\(290\) 0 0
\(291\) −3.37444 + 7.38899i −0.197813 + 0.433150i
\(292\) 0 0
\(293\) 19.5937 + 12.5921i 1.14468 + 0.735639i 0.968572 0.248733i \(-0.0800140\pi\)
0.176104 + 0.984372i \(0.443650\pi\)
\(294\) 0 0
\(295\) 20.4717 6.01105i 1.19191 0.349977i
\(296\) 0 0
\(297\) 4.10523 0.238210
\(298\) 0 0
\(299\) −2.63194 + 1.69145i −0.152209 + 0.0978189i
\(300\) 0 0
\(301\) 2.81093 3.24399i 0.162020 0.186981i
\(302\) 0 0
\(303\) 4.05634 + 8.88215i 0.233031 + 0.510266i
\(304\) 0 0
\(305\) 17.1585 0.982490
\(306\) 0 0
\(307\) −15.0816 + 9.69236i −0.860753 + 0.553172i −0.894911 0.446244i \(-0.852761\pi\)
0.0341585 + 0.999416i \(0.489125\pi\)
\(308\) 0 0
\(309\) −0.365983 2.54547i −0.0208200 0.144807i
\(310\) 0 0
\(311\) 0.00768065 + 0.0534201i 0.000435530 + 0.00302918i 0.990038 0.140800i \(-0.0449675\pi\)
−0.989603 + 0.143829i \(0.954058\pi\)
\(312\) 0 0
\(313\) 3.64685 + 7.98548i 0.206132 + 0.451366i 0.984257 0.176743i \(-0.0565563\pi\)
−0.778125 + 0.628109i \(0.783829\pi\)
\(314\) 0 0
\(315\) −3.54354 + 7.75928i −0.199656 + 0.437186i
\(316\) 0 0
\(317\) 1.38885 9.65969i 0.0780058 0.542542i −0.912921 0.408137i \(-0.866179\pi\)
0.990926 0.134405i \(-0.0429123\pi\)
\(318\) 0 0
\(319\) 6.42925 + 1.88780i 0.359969 + 0.105696i
\(320\) 0 0
\(321\) −1.39651 + 9.71295i −0.0779457 + 0.542124i
\(322\) 0 0
\(323\) 9.21820 + 5.92418i 0.512914 + 0.329630i
\(324\) 0 0
\(325\) 0.324062 + 0.709597i 0.0179757 + 0.0393614i
\(326\) 0 0
\(327\) 0.366325 0.235423i 0.0202578 0.0130189i
\(328\) 0 0
\(329\) −25.9876 + 7.63064i −1.43274 + 0.420691i
\(330\) 0 0
\(331\) −3.54626 + 24.6648i −0.194920 + 1.35570i 0.623836 + 0.781555i \(0.285573\pi\)
−0.818756 + 0.574142i \(0.805336\pi\)
\(332\) 0 0
\(333\) −7.48506 8.63821i −0.410179 0.473371i
\(334\) 0 0
\(335\) −13.8543 + 6.10047i −0.756942 + 0.333304i
\(336\) 0 0
\(337\) −6.81542 7.86541i −0.371259 0.428456i 0.539121 0.842228i \(-0.318757\pi\)
−0.910381 + 0.413772i \(0.864211\pi\)
\(338\) 0 0
\(339\) 2.62481 18.2560i 0.142560 0.991528i
\(340\) 0 0
\(341\) −13.0266 + 3.82494i −0.705427 + 0.207132i
\(342\) 0 0
\(343\) 28.2249 18.1391i 1.52400 0.979417i
\(344\) 0 0
\(345\) 4.86743 + 10.6582i 0.262054 + 0.573818i
\(346\) 0 0
\(347\) −12.2066 7.84470i −0.655284 0.421125i 0.170310 0.985391i \(-0.445523\pi\)
−0.825594 + 0.564265i \(0.809160\pi\)
\(348\) 0 0
\(349\) −2.48399 + 17.2766i −0.132965 + 0.924793i 0.808695 + 0.588228i \(0.200174\pi\)
−0.941660 + 0.336565i \(0.890735\pi\)
\(350\) 0 0
\(351\) −0.473809 0.139123i −0.0252900 0.00742582i
\(352\) 0 0
\(353\) 0.962906 6.69716i 0.0512503 0.356454i −0.948018 0.318216i \(-0.896916\pi\)
0.999269 0.0382381i \(-0.0121745\pi\)
\(354\) 0 0
\(355\) 4.71784 10.3306i 0.250397 0.548293i
\(356\) 0 0
\(357\) 3.03468 + 6.64502i 0.160612 + 0.351692i
\(358\) 0 0
\(359\) 1.81395 + 12.6163i 0.0957366 + 0.665862i 0.980018 + 0.198908i \(0.0637396\pi\)
−0.884282 + 0.466954i \(0.845351\pi\)
\(360\) 0 0
\(361\) −4.10808 28.5723i −0.216215 1.50381i
\(362\) 0 0
\(363\) −4.92380 + 3.16433i −0.258432 + 0.166084i
\(364\) 0 0
\(365\) −16.9109 −0.885156
\(366\) 0 0
\(367\) 2.26465 + 4.95888i 0.118214 + 0.258852i 0.959484 0.281763i \(-0.0909191\pi\)
−0.841271 + 0.540614i \(0.818192\pi\)
\(368\) 0 0
\(369\) 1.01884 1.17580i 0.0530386 0.0612098i
\(370\) 0 0
\(371\) 32.7776 21.0649i 1.70173 1.09363i
\(372\) 0 0
\(373\) 1.09455 0.0566735 0.0283367 0.999598i \(-0.490979\pi\)
0.0283367 + 0.999598i \(0.490979\pi\)
\(374\) 0 0
\(375\) 11.6756 3.42827i 0.602927 0.177035i
\(376\) 0 0
\(377\) −0.678062 0.435764i −0.0349219 0.0224430i
\(378\) 0 0
\(379\) −9.66924 + 21.1727i −0.496675 + 1.08757i 0.480860 + 0.876797i \(0.340324\pi\)
−0.977536 + 0.210770i \(0.932403\pi\)
\(380\) 0 0
\(381\) 11.5368 3.38750i 0.591046 0.173547i
\(382\) 0 0
\(383\) 7.50660 8.66307i 0.383569 0.442662i −0.530829 0.847479i \(-0.678119\pi\)
0.914398 + 0.404817i \(0.132665\pi\)
\(384\) 0 0
\(385\) −4.98360 34.6617i −0.253988 1.76652i
\(386\) 0 0
\(387\) 0.609432 0.703322i 0.0309791 0.0357518i
\(388\) 0 0
\(389\) 15.8095 + 10.1602i 0.801576 + 0.515141i 0.876130 0.482076i \(-0.160117\pi\)
−0.0745540 + 0.997217i \(0.523753\pi\)
\(390\) 0 0
\(391\) 9.62798 + 2.82703i 0.486908 + 0.142969i
\(392\) 0 0
\(393\) −9.66390 11.1527i −0.487479 0.562581i
\(394\) 0 0
\(395\) 3.58302 + 4.13503i 0.180281 + 0.208056i
\(396\) 0 0
\(397\) 18.7418 + 5.50310i 0.940626 + 0.276193i 0.715879 0.698225i \(-0.246026\pi\)
0.224747 + 0.974417i \(0.427844\pi\)
\(398\) 0 0
\(399\) 13.2563 29.0272i 0.663645 1.45318i
\(400\) 0 0
\(401\) 8.91856 0.445372 0.222686 0.974890i \(-0.428518\pi\)
0.222686 + 0.974890i \(0.428518\pi\)
\(402\) 0 0
\(403\) 1.63309 0.0813502
\(404\) 0 0
\(405\) −0.768266 + 1.68227i −0.0381755 + 0.0835926i
\(406\) 0 0
\(407\) 45.0221 + 13.2197i 2.23166 + 0.655275i
\(408\) 0 0
\(409\) 5.63197 + 6.49964i 0.278483 + 0.321387i 0.877710 0.479193i \(-0.159071\pi\)
−0.599227 + 0.800579i \(0.704525\pi\)
\(410\) 0 0
\(411\) −9.83242 11.3472i −0.484998 0.559717i
\(412\) 0 0
\(413\) −51.0565 14.9915i −2.51233 0.737685i
\(414\) 0 0
\(415\) −19.9560 12.8249i −0.979600 0.629551i
\(416\) 0 0
\(417\) −3.30540 + 3.81463i −0.161866 + 0.186803i
\(418\) 0 0
\(419\) 5.38137 + 37.4282i 0.262897 + 1.82849i 0.510796 + 0.859702i \(0.329351\pi\)
−0.247899 + 0.968786i \(0.579740\pi\)
\(420\) 0 0
\(421\) −14.8157 + 17.0982i −0.722074 + 0.833317i −0.991555 0.129688i \(-0.958602\pi\)
0.269481 + 0.963006i \(0.413148\pi\)
\(422\) 0 0
\(423\) −5.63430 + 1.65438i −0.273949 + 0.0804387i
\(424\) 0 0
\(425\) 1.03937 2.27591i 0.0504171 0.110398i
\(426\) 0 0
\(427\) −35.9999 23.1357i −1.74216 1.11962i
\(428\) 0 0
\(429\) 1.94509 0.571131i 0.0939100 0.0275745i
\(430\) 0 0
\(431\) 34.3651 1.65531 0.827653 0.561240i \(-0.189675\pi\)
0.827653 + 0.561240i \(0.189675\pi\)
\(432\) 0 0
\(433\) 24.4773 15.7306i 1.17630 0.755964i 0.201600 0.979468i \(-0.435386\pi\)
0.974703 + 0.223503i \(0.0717494\pi\)
\(434\) 0 0
\(435\) −1.97679 + 2.28133i −0.0947796 + 0.109382i
\(436\) 0 0
\(437\) −18.2089 39.8720i −0.871051 1.90734i
\(438\) 0 0
\(439\) 33.7667 1.61159 0.805797 0.592191i \(-0.201737\pi\)
0.805797 + 0.592191i \(0.201737\pi\)
\(440\) 0 0
\(441\) 12.0081 7.71717i 0.571817 0.367484i
\(442\) 0 0
\(443\) 2.29650 + 15.9725i 0.109110 + 0.758877i 0.968761 + 0.247996i \(0.0797719\pi\)
−0.859651 + 0.510882i \(0.829319\pi\)
\(444\) 0 0
\(445\) −0.988777 6.87710i −0.0468725 0.326006i
\(446\) 0 0
\(447\) 1.56274 + 3.42192i 0.0739150 + 0.161851i
\(448\) 0 0
\(449\) 7.83955 17.1662i 0.369971 0.810124i −0.629481 0.777016i \(-0.716732\pi\)
0.999452 0.0331077i \(-0.0105404\pi\)
\(450\) 0 0
\(451\) −0.908959 + 6.32195i −0.0428012 + 0.297689i
\(452\) 0 0
\(453\) −11.2954 3.31662i −0.530702 0.155828i
\(454\) 0 0
\(455\) −0.599469 + 4.16940i −0.0281035 + 0.195464i
\(456\) 0 0
\(457\) −1.44648 0.929595i −0.0676634 0.0434846i 0.506372 0.862315i \(-0.330986\pi\)
−0.574035 + 0.818831i \(0.694623\pi\)
\(458\) 0 0
\(459\) 0.657941 + 1.44069i 0.0307101 + 0.0672457i
\(460\) 0 0
\(461\) 18.2495 11.7282i 0.849963 0.546238i −0.0416002 0.999134i \(-0.513246\pi\)
0.891563 + 0.452896i \(0.149609\pi\)
\(462\) 0 0
\(463\) −11.6258 + 3.41366i −0.540299 + 0.158646i −0.540485 0.841354i \(-0.681759\pi\)
0.000185625 1.00000i \(0.499941\pi\)
\(464\) 0 0
\(465\) 0.870422 6.05392i 0.0403649 0.280744i
\(466\) 0 0
\(467\) −0.0328409 0.0379004i −0.00151969 0.00175382i 0.754989 0.655737i \(-0.227642\pi\)
−0.756509 + 0.653983i \(0.773097\pi\)
\(468\) 0 0
\(469\) 37.2931 + 5.88126i 1.72204 + 0.271571i
\(470\) 0 0
\(471\) −11.5773 13.3609i −0.533452 0.615636i
\(472\) 0 0
\(473\) −0.543706 + 3.78156i −0.0249996 + 0.173876i
\(474\) 0 0
\(475\) −10.4867 + 3.07919i −0.481165 + 0.141283i
\(476\) 0 0
\(477\) 7.10642 4.56702i 0.325381 0.209110i
\(478\) 0 0
\(479\) 10.8701 + 23.8022i 0.496667 + 1.08755i 0.977538 + 0.210757i \(0.0675930\pi\)
−0.480872 + 0.876791i \(0.659680\pi\)
\(480\) 0 0
\(481\) −4.74826 3.05152i −0.216502 0.139137i
\(482\) 0 0
\(483\) 4.15876 28.9248i 0.189230 1.31613i
\(484\) 0 0
\(485\) 14.4142 + 4.23239i 0.654516 + 0.192183i
\(486\) 0 0
\(487\) 0.575244 4.00091i 0.0260668 0.181298i −0.972628 0.232366i \(-0.925353\pi\)
0.998695 + 0.0510676i \(0.0162624\pi\)
\(488\) 0 0
\(489\) 8.08859 17.7115i 0.365779 0.800944i
\(490\) 0 0
\(491\) 16.2832 + 35.6553i 0.734852 + 1.60910i 0.791842 + 0.610726i \(0.209122\pi\)
−0.0569906 + 0.998375i \(0.518151\pi\)
\(492\) 0 0
\(493\) 0.367906 + 2.55884i 0.0165696 + 0.115244i
\(494\) 0 0
\(495\) −1.08048 7.51492i −0.0485641 0.337770i
\(496\) 0 0
\(497\) −23.8278 + 15.3132i −1.06882 + 0.686891i
\(498\) 0 0
\(499\) −3.36150 −0.150481 −0.0752406 0.997165i \(-0.523972\pi\)
−0.0752406 + 0.997165i \(0.523972\pi\)
\(500\) 0 0
\(501\) −1.38670 3.03644i −0.0619530 0.135658i
\(502\) 0 0
\(503\) 23.3166 26.9088i 1.03963 1.19980i 0.0601692 0.998188i \(-0.480836\pi\)
0.979465 0.201614i \(-0.0646186\pi\)
\(504\) 0 0
\(505\) 15.1918 9.76317i 0.676026 0.434455i
\(506\) 0 0
\(507\) 12.7562 0.566521
\(508\) 0 0
\(509\) −24.8060 + 7.28369i −1.09950 + 0.322844i −0.780655 0.624962i \(-0.785115\pi\)
−0.318849 + 0.947805i \(0.603296\pi\)
\(510\) 0 0
\(511\) 35.4805 + 22.8019i 1.56956 + 1.00870i
\(512\) 0 0
\(513\) 2.87406 6.29332i 0.126893 0.277857i
\(514\) 0 0
\(515\) −4.56333 + 1.33992i −0.201084 + 0.0590437i
\(516\) 0 0
\(517\) 15.7865 18.2185i 0.694288 0.801251i
\(518\) 0 0
\(519\) 1.26962 + 8.83039i 0.0557301 + 0.387611i
\(520\) 0 0
\(521\) −2.95775 + 3.41343i −0.129581 + 0.149545i −0.816832 0.576875i \(-0.804272\pi\)
0.687251 + 0.726420i \(0.258817\pi\)
\(522\) 0 0
\(523\) −6.32057 4.06198i −0.276379 0.177618i 0.395107 0.918635i \(-0.370707\pi\)
−0.671486 + 0.741017i \(0.734344\pi\)
\(524\) 0 0
\(525\) −6.99121 2.05281i −0.305122 0.0895918i
\(526\) 0 0
\(527\) −3.43008 3.95852i −0.149417 0.172436i
\(528\) 0 0
\(529\) −11.2243 12.9535i −0.488011 0.563195i
\(530\) 0 0
\(531\) −11.0694 3.25028i −0.480372 0.141050i
\(532\) 0 0
\(533\) 0.319154 0.698849i 0.0138241 0.0302705i
\(534\) 0 0
\(535\) 18.1478 0.784598
\(536\) 0 0
\(537\) −20.3756 −0.879272
\(538\) 0 0
\(539\) −24.3427 + 53.3031i −1.04852 + 2.29593i
\(540\) 0 0
\(541\) 14.0683 + 4.13082i 0.604842 + 0.177598i 0.569793 0.821788i \(-0.307023\pi\)
0.0350487 + 0.999386i \(0.488841\pi\)
\(542\) 0 0
\(543\) −7.84961 9.05894i −0.336859 0.388756i
\(544\) 0 0
\(545\) −0.527374 0.608622i −0.0225902 0.0260705i
\(546\) 0 0
\(547\) 25.5091 + 7.49015i 1.09069 + 0.320256i 0.777148 0.629318i \(-0.216666\pi\)
0.313543 + 0.949574i \(0.398484\pi\)
\(548\) 0 0
\(549\) −7.80504 5.01600i −0.333111 0.214078i
\(550\) 0 0
\(551\) 7.39510 8.53440i 0.315042 0.363578i
\(552\) 0 0
\(553\) −1.94199 13.5068i −0.0825818 0.574369i
\(554\) 0 0
\(555\) −13.8428 + 15.9755i −0.587595 + 0.678121i
\(556\) 0 0
\(557\) 1.08920 0.319819i 0.0461510 0.0135512i −0.258576 0.965991i \(-0.583253\pi\)
0.304727 + 0.952440i \(0.401435\pi\)
\(558\) 0 0
\(559\) 0.190906 0.418026i 0.00807446 0.0176806i
\(560\) 0 0
\(561\) −5.46978 3.51521i −0.230934 0.148412i
\(562\) 0 0
\(563\) 33.8986 9.95352i 1.42865 0.419491i 0.526231 0.850341i \(-0.323605\pi\)
0.902423 + 0.430850i \(0.141786\pi\)
\(564\) 0 0
\(565\) −34.1097 −1.43500
\(566\) 0 0
\(567\) 3.88019 2.49364i 0.162953 0.104723i
\(568\) 0 0
\(569\) −23.3991 + 27.0040i −0.980941 + 1.13207i 0.0102926 + 0.999947i \(0.496724\pi\)
−0.991234 + 0.132119i \(0.957822\pi\)
\(570\) 0 0
\(571\) −16.5013 36.1328i −0.690557 1.51211i −0.851057 0.525074i \(-0.824038\pi\)
0.160499 0.987036i \(-0.448690\pi\)
\(572\) 0 0
\(573\) 1.80184 0.0752729
\(574\) 0 0
\(575\) −8.41977 + 5.41106i −0.351129 + 0.225657i
\(576\) 0 0
\(577\) 1.00560 + 6.99407i 0.0418635 + 0.291167i 0.999988 + 0.00481642i \(0.00153312\pi\)
−0.958125 + 0.286351i \(0.907558\pi\)
\(578\) 0 0
\(579\) −0.587667 4.08732i −0.0244226 0.169863i
\(580\) 0 0
\(581\) 24.5767 + 53.8155i 1.01961 + 2.23264i
\(582\) 0 0
\(583\) −14.4060 + 31.5448i −0.596636 + 1.30645i
\(584\) 0 0
\(585\) −0.129969 + 0.903957i −0.00537357 + 0.0373740i
\(586\) 0 0
\(587\) 32.1613 + 9.44342i 1.32744 + 0.389772i 0.867172 0.498008i \(-0.165935\pi\)
0.460268 + 0.887780i \(0.347753\pi\)
\(588\) 0 0
\(589\) −3.25622 + 22.6475i −0.134170 + 0.933175i
\(590\) 0 0
\(591\) 19.0493 + 12.2422i 0.783581 + 0.503577i
\(592\) 0 0
\(593\) −8.81490 19.3019i −0.361985 0.792636i −0.999749 0.0224043i \(-0.992868\pi\)
0.637764 0.770232i \(-0.279859\pi\)
\(594\) 0 0
\(595\) 11.3655 7.30414i 0.465939 0.299441i
\(596\) 0 0
\(597\) 8.93397 2.62325i 0.365643 0.107362i
\(598\) 0 0
\(599\) −4.89689 + 34.0586i −0.200081 + 1.39160i 0.603956 + 0.797018i \(0.293590\pi\)
−0.804037 + 0.594579i \(0.797319\pi\)
\(600\) 0 0
\(601\) −24.8307 28.6562i −1.01287 1.16891i −0.985568 0.169282i \(-0.945855\pi\)
−0.0272976 0.999627i \(-0.508690\pi\)
\(602\) 0 0
\(603\) 8.08543 + 1.27510i 0.329264 + 0.0519261i
\(604\) 0 0
\(605\) 7.08846 + 8.18052i 0.288187 + 0.332585i
\(606\) 0 0
\(607\) −3.35391 + 23.3270i −0.136131 + 0.946813i 0.801206 + 0.598389i \(0.204192\pi\)
−0.937337 + 0.348424i \(0.886717\pi\)
\(608\) 0 0
\(609\) 7.22351 2.12102i 0.292712 0.0859479i
\(610\) 0 0
\(611\) −2.43942 + 1.56772i −0.0986883 + 0.0634231i
\(612\) 0 0
\(613\) −1.42453 3.11929i −0.0575363 0.125987i 0.878680 0.477411i \(-0.158425\pi\)
−0.936216 + 0.351424i \(0.885697\pi\)
\(614\) 0 0
\(615\) −2.42054 1.55559i −0.0976057 0.0627274i
\(616\) 0 0
\(617\) −6.05846 + 42.1375i −0.243904 + 1.69639i 0.388254 + 0.921552i \(0.373078\pi\)
−0.632158 + 0.774839i \(0.717831\pi\)
\(618\) 0 0
\(619\) −41.1031 12.0690i −1.65207 0.485093i −0.682703 0.730696i \(-0.739196\pi\)
−0.969370 + 0.245603i \(0.921014\pi\)
\(620\) 0 0
\(621\) 0.901651 6.27112i 0.0361820 0.251651i
\(622\) 0 0
\(623\) −7.19824 + 15.7620i −0.288391 + 0.631489i
\(624\) 0 0
\(625\) −6.06744 13.2858i −0.242698 0.531434i
\(626\) 0 0
\(627\) 4.04205 + 28.1131i 0.161424 + 1.12273i
\(628\) 0 0
\(629\) 2.57633 + 17.9188i 0.102725 + 0.714468i
\(630\) 0 0
\(631\) −28.4121 + 18.2593i −1.13107 + 0.726892i −0.965782 0.259354i \(-0.916490\pi\)
−0.165284 + 0.986246i \(0.552854\pi\)
\(632\) 0 0
\(633\) −8.44437 −0.335633
\(634\) 0 0
\(635\) −9.23749 20.2273i −0.366579 0.802695i
\(636\) 0 0
\(637\) 4.61593 5.32707i 0.182890 0.211066i
\(638\) 0 0
\(639\) −5.16604 + 3.32002i −0.204366 + 0.131338i
\(640\) 0 0
\(641\) 5.58754 0.220695 0.110347 0.993893i \(-0.464804\pi\)
0.110347 + 0.993893i \(0.464804\pi\)
\(642\) 0 0
\(643\) −39.4820 + 11.5929i −1.55702 + 0.457181i −0.943188 0.332258i \(-0.892189\pi\)
−0.613828 + 0.789440i \(0.710371\pi\)
\(644\) 0 0
\(645\) −1.44788 0.930496i −0.0570102 0.0366382i
\(646\) 0 0
\(647\) 16.0446 35.1328i 0.630779 1.38121i −0.276635 0.960975i \(-0.589219\pi\)
0.907414 0.420238i \(-0.138053\pi\)
\(648\) 0 0
\(649\) 45.4426 13.3431i 1.78378 0.523764i
\(650\) 0 0
\(651\) −9.98906 + 11.5280i −0.391502 + 0.451818i
\(652\) 0 0
\(653\) 0.138287 + 0.961807i 0.00541159 + 0.0376384i 0.992348 0.123470i \(-0.0394022\pi\)
−0.986937 + 0.161108i \(0.948493\pi\)
\(654\) 0 0
\(655\) −17.8724 + 20.6258i −0.698331 + 0.805917i
\(656\) 0 0
\(657\) 7.69243 + 4.94362i 0.300110 + 0.192869i
\(658\) 0 0
\(659\) −33.8671 9.94428i −1.31928 0.387374i −0.455044 0.890469i \(-0.650377\pi\)
−0.864231 + 0.503095i \(0.832195\pi\)
\(660\) 0 0
\(661\) −15.9115 18.3628i −0.618885 0.714232i 0.356610 0.934253i \(-0.383933\pi\)
−0.975495 + 0.220022i \(0.929387\pi\)
\(662\) 0 0
\(663\) 0.512171 + 0.591077i 0.0198911 + 0.0229555i
\(664\) 0 0
\(665\) −56.6254 16.6267i −2.19584 0.644757i
\(666\) 0 0
\(667\) 4.29587 9.40665i 0.166337 0.364227i
\(668\) 0 0
\(669\) 12.2438 0.473373
\(670\) 0 0
\(671\) 38.0878 1.47036
\(672\) 0 0
\(673\) −17.5316 + 38.3890i −0.675795 + 1.47979i 0.191242 + 0.981543i \(0.438748\pi\)
−0.867038 + 0.498243i \(0.833979\pi\)
\(674\) 0 0
\(675\) −1.51575 0.445064i −0.0583411 0.0171305i
\(676\) 0 0
\(677\) −14.8448 17.1319i −0.570533 0.658431i 0.395009 0.918677i \(-0.370742\pi\)
−0.965542 + 0.260247i \(0.916196\pi\)
\(678\) 0 0
\(679\) −24.5354 28.3154i −0.941584 1.08665i
\(680\) 0 0
\(681\) 26.2056 + 7.69465i 1.00420 + 0.294860i
\(682\) 0 0
\(683\) −31.5462 20.2735i −1.20708 0.775744i −0.226914 0.973915i \(-0.572864\pi\)
−0.980168 + 0.198171i \(0.936500\pi\)
\(684\) 0 0
\(685\) −18.1840 + 20.9855i −0.694776 + 0.801814i
\(686\) 0 0
\(687\) −1.66469 11.5782i −0.0635118 0.441734i
\(688\) 0 0
\(689\) 2.73171 3.15256i 0.104070 0.120103i
\(690\) 0 0
\(691\) 16.5198 4.85066i 0.628445 0.184528i 0.0480258 0.998846i \(-0.484707\pi\)
0.580419 + 0.814318i \(0.302889\pi\)
\(692\) 0 0
\(693\) −7.86585 + 17.2238i −0.298799 + 0.654278i
\(694\) 0 0
\(695\) 7.85292 + 5.04676i 0.297878 + 0.191435i
\(696\) 0 0
\(697\) −2.36430 + 0.694222i −0.0895544 + 0.0262955i
\(698\) 0 0
\(699\) −22.3614 −0.845788
\(700\) 0 0
\(701\) 29.1690 18.7458i 1.10170 0.708019i 0.142230 0.989834i \(-0.454573\pi\)
0.959469 + 0.281815i \(0.0909365\pi\)
\(702\) 0 0
\(703\) 51.7856 59.7638i 1.95313 2.25403i
\(704\) 0 0
\(705\) 4.51139 + 9.87856i 0.169909 + 0.372048i
\(706\) 0 0
\(707\) −45.0379 −1.69382
\(708\) 0 0
\(709\) 15.7435 10.1177i 0.591259 0.379979i −0.210529 0.977588i \(-0.567519\pi\)
0.801788 + 0.597608i \(0.203882\pi\)
\(710\) 0 0
\(711\) −0.421038 2.92838i −0.0157901 0.109823i
\(712\) 0 0
\(713\) 2.98187 + 20.7393i 0.111672 + 0.776695i
\(714\) 0 0
\(715\) −1.55744 3.41031i −0.0582449 0.127539i
\(716\) 0 0
\(717\) 6.51450 14.2648i 0.243288 0.532727i
\(718\) 0 0
\(719\) 0.115861 0.805828i 0.00432087 0.0300523i −0.987547 0.157325i \(-0.949713\pi\)
0.991868 + 0.127272i \(0.0406222\pi\)
\(720\) 0 0
\(721\) 11.3809 + 3.34175i 0.423848 + 0.124453i
\(722\) 0 0
\(723\) −2.59569 + 18.0534i −0.0965348 + 0.671414i
\(724\) 0 0
\(725\) −2.16917 1.39404i −0.0805608 0.0517733i
\(726\) 0 0
\(727\) 9.69537 + 21.2299i 0.359581 + 0.787373i 0.999816 + 0.0191937i \(0.00610993\pi\)
−0.640234 + 0.768180i \(0.721163\pi\)
\(728\) 0 0
\(729\) 0.841254 0.540641i 0.0311575 0.0200237i
\(730\) 0 0
\(731\) −1.41424 + 0.415258i −0.0523075 + 0.0153589i
\(732\) 0 0
\(733\) 7.05196 49.0475i 0.260470 1.81161i −0.268845 0.963184i \(-0.586642\pi\)
0.529315 0.848425i \(-0.322449\pi\)
\(734\) 0 0
\(735\) −17.2873 19.9506i −0.637653 0.735890i
\(736\) 0 0
\(737\) −30.7534 + 13.5416i −1.13282 + 0.498813i
\(738\) 0 0
\(739\) −5.93306 6.84712i −0.218251 0.251875i 0.636057 0.771642i \(-0.280564\pi\)
−0.854308 + 0.519767i \(0.826019\pi\)
\(740\) 0 0
\(741\) 0.486212 3.38168i 0.0178614 0.124229i
\(742\) 0 0
\(743\) −5.38620 + 1.58153i −0.197600 + 0.0580207i −0.379035 0.925382i \(-0.623744\pi\)
0.181435 + 0.983403i \(0.441926\pi\)
\(744\) 0 0
\(745\) 5.85276 3.76134i 0.214429 0.137805i
\(746\) 0 0
\(747\) 5.32842 + 11.6676i 0.194957 + 0.426896i
\(748\) 0 0
\(749\) −38.0756 24.4697i −1.39125 0.894104i
\(750\) 0 0
\(751\) −2.55729 + 17.7864i −0.0933169 + 0.649033i 0.888454 + 0.458966i \(0.151780\pi\)
−0.981771 + 0.190068i \(0.939129\pi\)
\(752\) 0 0
\(753\) −24.0497 7.06163i −0.876420 0.257340i
\(754\) 0 0
\(755\) −3.09841 + 21.5499i −0.112763 + 0.784281i
\(756\) 0 0
\(757\) 1.19822 2.62374i 0.0435501 0.0953614i −0.886606 0.462525i \(-0.846944\pi\)
0.930157 + 0.367163i \(0.119671\pi\)
\(758\) 0 0
\(759\) 10.8046 + 23.6587i 0.392182 + 0.858758i
\(760\) 0 0
\(761\) −3.84810 26.7641i −0.139493 0.970198i −0.932548 0.361047i \(-0.882419\pi\)
0.793054 0.609151i \(-0.208490\pi\)
\(762\) 0 0
\(763\) 0.285835 + 1.98803i 0.0103479 + 0.0719714i
\(764\) 0 0
\(765\) 2.46412 1.58359i 0.0890904 0.0572549i
\(766\) 0 0
\(767\) −5.69698 −0.205706
\(768\) 0 0
\(769\) 4.59671 + 10.0654i 0.165762 + 0.362967i 0.974225 0.225580i \(-0.0724276\pi\)
−0.808463 + 0.588547i \(0.799700\pi\)
\(770\) 0 0
\(771\) −8.59752 + 9.92207i −0.309632 + 0.357335i
\(772\) 0 0
\(773\) 12.4522 8.00256i 0.447876 0.287832i −0.297196 0.954816i \(-0.596052\pi\)
0.745072 + 0.666984i \(0.232415\pi\)
\(774\) 0 0
\(775\) 5.22438 0.187665
\(776\) 0 0
\(777\) 50.5841 14.8528i 1.81469 0.532842i
\(778\) 0 0
\(779\) 9.05518 + 5.81941i 0.324436 + 0.208502i
\(780\) 0 0
\(781\) 10.4725 22.9316i 0.374736 0.820558i