Properties

Label 1440.2.q.j.961.4
Level $1440$
Weight $2$
Character 1440.961
Analytic conductor $11.498$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1440.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.4984578911\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.3317760000.8
Defining polynomial: \(x^{8} + 4 x^{6} + 7 x^{4} + 36 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.4
Root \(-1.40294 + 1.01575i\) of defining polynomial
Character \(\chi\) \(=\) 1440.961
Dual form 1440.2.q.j.481.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.40294 + 1.01575i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.40294 + 2.42997i) q^{7} +(0.936492 + 2.85008i) q^{9} +O(q^{10})\) \(q+(1.40294 + 1.01575i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.40294 + 2.42997i) q^{7} +(0.936492 + 2.85008i) q^{9} +(-1.22474 + 2.12132i) q^{11} +(-2.43649 - 4.22013i) q^{13} +(0.178197 - 1.72286i) q^{15} -6.87298 q^{17} -7.34847 q^{19} +(-4.43649 + 1.98406i) q^{21} +(-1.40294 - 2.42997i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-1.58114 + 4.94975i) q^{27} +(3.37298 - 5.84218i) q^{29} +(1.93753 + 3.35591i) q^{31} +(-3.87298 + 1.73205i) q^{33} +2.80588 q^{35} +0.872983 q^{37} +(0.868351 - 8.39547i) q^{39} +(1.06351 + 1.84205i) q^{41} +(1.22474 - 2.12132i) q^{43} +(2.00000 - 2.23607i) q^{45} +(2.98408 - 5.16858i) q^{47} +(-0.436492 - 0.756026i) q^{49} +(-9.64240 - 6.98125i) q^{51} -4.00000 q^{53} +2.44949 q^{55} +(-10.3095 - 7.46423i) q^{57} +(2.80588 + 4.85993i) q^{59} +(-2.93649 + 5.08615i) q^{61} +(-8.23945 - 1.72286i) q^{63} +(-2.43649 + 4.22013i) q^{65} +(7.88306 + 13.6539i) q^{67} +(0.500000 - 4.83414i) q^{69} -3.16228 q^{71} -9.74597 q^{73} +(-1.58114 + 0.707107i) q^{75} +(-3.43649 - 5.95218i) q^{77} +(-6.32456 + 10.9545i) q^{79} +(-7.24597 + 5.33816i) q^{81} +(7.72750 - 13.3844i) q^{83} +(3.43649 + 5.95218i) q^{85} +(10.6663 - 4.77012i) q^{87} -16.7460 q^{89} +13.6730 q^{91} +(-0.690525 + 6.67619i) q^{93} +(3.67423 + 6.36396i) q^{95} +(0.872983 - 1.51205i) q^{97} +(-7.19291 - 1.50403i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{5} - 8 q^{9} + O(q^{10}) \) \( 8 q - 4 q^{5} - 8 q^{9} - 4 q^{13} - 24 q^{17} - 20 q^{21} - 4 q^{25} - 4 q^{29} - 24 q^{37} + 24 q^{41} + 16 q^{45} + 12 q^{49} - 32 q^{53} - 36 q^{57} - 8 q^{61} - 4 q^{65} + 4 q^{69} - 16 q^{73} - 12 q^{77} + 4 q^{81} + 12 q^{85} - 72 q^{89} - 52 q^{93} - 24 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(641\) \(901\) \(991\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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
\(3\) 1.40294 + 1.01575i 0.809989 + 0.586445i
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) −1.40294 + 2.42997i −0.530262 + 0.918441i 0.469114 + 0.883137i \(0.344573\pi\)
−0.999377 + 0.0353037i \(0.988760\pi\)
\(8\) 0 0
\(9\) 0.936492 + 2.85008i 0.312164 + 0.950028i
\(10\) 0 0
\(11\) −1.22474 + 2.12132i −0.369274 + 0.639602i −0.989452 0.144859i \(-0.953727\pi\)
0.620178 + 0.784461i \(0.287060\pi\)
\(12\) 0 0
\(13\) −2.43649 4.22013i −0.675761 1.17045i −0.976246 0.216666i \(-0.930482\pi\)
0.300485 0.953787i \(-0.402852\pi\)
\(14\) 0 0
\(15\) 0.178197 1.72286i 0.0460103 0.444840i
\(16\) 0 0
\(17\) −6.87298 −1.66694 −0.833472 0.552562i \(-0.813650\pi\)
−0.833472 + 0.552562i \(0.813650\pi\)
\(18\) 0 0
\(19\) −7.34847 −1.68585 −0.842927 0.538028i \(-0.819170\pi\)
−0.842927 + 0.538028i \(0.819170\pi\)
\(20\) 0 0
\(21\) −4.43649 + 1.98406i −0.968122 + 0.432957i
\(22\) 0 0
\(23\) −1.40294 2.42997i −0.292534 0.506683i 0.681875 0.731469i \(-0.261165\pi\)
−0.974408 + 0.224786i \(0.927832\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) −1.58114 + 4.94975i −0.304290 + 0.952579i
\(28\) 0 0
\(29\) 3.37298 5.84218i 0.626347 1.08487i −0.361931 0.932205i \(-0.617883\pi\)
0.988279 0.152661i \(-0.0487841\pi\)
\(30\) 0 0
\(31\) 1.93753 + 3.35591i 0.347991 + 0.602738i 0.985893 0.167380i \(-0.0535306\pi\)
−0.637901 + 0.770118i \(0.720197\pi\)
\(32\) 0 0
\(33\) −3.87298 + 1.73205i −0.674200 + 0.301511i
\(34\) 0 0
\(35\) 2.80588 0.474281
\(36\) 0 0
\(37\) 0.872983 0.143518 0.0717588 0.997422i \(-0.477139\pi\)
0.0717588 + 0.997422i \(0.477139\pi\)
\(38\) 0 0
\(39\) 0.868351 8.39547i 0.139047 1.34435i
\(40\) 0 0
\(41\) 1.06351 + 1.84205i 0.166092 + 0.287680i 0.937043 0.349215i \(-0.113552\pi\)
−0.770950 + 0.636895i \(0.780218\pi\)
\(42\) 0 0
\(43\) 1.22474 2.12132i 0.186772 0.323498i −0.757400 0.652951i \(-0.773531\pi\)
0.944172 + 0.329452i \(0.106864\pi\)
\(44\) 0 0
\(45\) 2.00000 2.23607i 0.298142 0.333333i
\(46\) 0 0
\(47\) 2.98408 5.16858i 0.435273 0.753915i −0.562045 0.827107i \(-0.689985\pi\)
0.997318 + 0.0731919i \(0.0233186\pi\)
\(48\) 0 0
\(49\) −0.436492 0.756026i −0.0623560 0.108004i
\(50\) 0 0
\(51\) −9.64240 6.98125i −1.35021 0.977571i
\(52\) 0 0
\(53\) −4.00000 −0.549442 −0.274721 0.961524i \(-0.588586\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) 0 0
\(55\) 2.44949 0.330289
\(56\) 0 0
\(57\) −10.3095 7.46423i −1.36552 0.988661i
\(58\) 0 0
\(59\) 2.80588 + 4.85993i 0.365295 + 0.632709i 0.988823 0.149091i \(-0.0476348\pi\)
−0.623529 + 0.781801i \(0.714301\pi\)
\(60\) 0 0
\(61\) −2.93649 + 5.08615i −0.375979 + 0.651215i −0.990473 0.137706i \(-0.956027\pi\)
0.614494 + 0.788922i \(0.289360\pi\)
\(62\) 0 0
\(63\) −8.23945 1.72286i −1.03807 0.217060i
\(64\) 0 0
\(65\) −2.43649 + 4.22013i −0.302210 + 0.523442i
\(66\) 0 0
\(67\) 7.88306 + 13.6539i 0.963069 + 1.66808i 0.714716 + 0.699415i \(0.246556\pi\)
0.248353 + 0.968670i \(0.420111\pi\)
\(68\) 0 0
\(69\) 0.500000 4.83414i 0.0601929 0.581963i
\(70\) 0 0
\(71\) −3.16228 −0.375293 −0.187647 0.982237i \(-0.560086\pi\)
−0.187647 + 0.982237i \(0.560086\pi\)
\(72\) 0 0
\(73\) −9.74597 −1.14068 −0.570340 0.821409i \(-0.693188\pi\)
−0.570340 + 0.821409i \(0.693188\pi\)
\(74\) 0 0
\(75\) −1.58114 + 0.707107i −0.182574 + 0.0816497i
\(76\) 0 0
\(77\) −3.43649 5.95218i −0.391625 0.678314i
\(78\) 0 0
\(79\) −6.32456 + 10.9545i −0.711568 + 1.23247i 0.252700 + 0.967545i \(0.418681\pi\)
−0.964268 + 0.264927i \(0.914652\pi\)
\(80\) 0 0
\(81\) −7.24597 + 5.33816i −0.805107 + 0.593129i
\(82\) 0 0
\(83\) 7.72750 13.3844i 0.848203 1.46913i −0.0346073 0.999401i \(-0.511018\pi\)
0.882810 0.469730i \(-0.155649\pi\)
\(84\) 0 0
\(85\) 3.43649 + 5.95218i 0.372740 + 0.645604i
\(86\) 0 0
\(87\) 10.6663 4.77012i 1.14355 0.511410i
\(88\) 0 0
\(89\) −16.7460 −1.77507 −0.887534 0.460741i \(-0.847584\pi\)
−0.887534 + 0.460741i \(0.847584\pi\)
\(90\) 0 0
\(91\) 13.6730 1.43332
\(92\) 0 0
\(93\) −0.690525 + 6.67619i −0.0716041 + 0.692289i
\(94\) 0 0
\(95\) 3.67423 + 6.36396i 0.376969 + 0.652929i
\(96\) 0 0
\(97\) 0.872983 1.51205i 0.0886380 0.153526i −0.818298 0.574795i \(-0.805082\pi\)
0.906936 + 0.421269i \(0.138415\pi\)
\(98\) 0 0
\(99\) −7.19291 1.50403i −0.722914 0.151160i
\(100\) 0 0
\(101\) −0.872983 + 1.51205i −0.0868651 + 0.150455i −0.906184 0.422883i \(-0.861018\pi\)
0.819319 + 0.573337i \(0.194352\pi\)
\(102\) 0 0
\(103\) −0.511957 0.886735i −0.0504446 0.0873726i 0.839701 0.543050i \(-0.182731\pi\)
−0.890145 + 0.455677i \(0.849397\pi\)
\(104\) 0 0
\(105\) 3.93649 + 2.85008i 0.384162 + 0.278140i
\(106\) 0 0
\(107\) 14.0294 1.35628 0.678138 0.734935i \(-0.262787\pi\)
0.678138 + 0.734935i \(0.262787\pi\)
\(108\) 0 0
\(109\) −15.8730 −1.52036 −0.760178 0.649715i \(-0.774888\pi\)
−0.760178 + 0.649715i \(0.774888\pi\)
\(110\) 0 0
\(111\) 1.22474 + 0.886735i 0.116248 + 0.0841652i
\(112\) 0 0
\(113\) 9.87298 + 17.1005i 0.928772 + 1.60868i 0.785379 + 0.619015i \(0.212468\pi\)
0.143393 + 0.989666i \(0.454199\pi\)
\(114\) 0 0
\(115\) −1.40294 + 2.42997i −0.130825 + 0.226596i
\(116\) 0 0
\(117\) 9.74597 10.8963i 0.901015 1.00737i
\(118\) 0 0
\(119\) 9.64240 16.7011i 0.883917 1.53099i
\(120\) 0 0
\(121\) 2.50000 + 4.33013i 0.227273 + 0.393648i
\(122\) 0 0
\(123\) −0.379028 + 3.66455i −0.0341758 + 0.330421i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −14.3405 −1.27252 −0.636259 0.771476i \(-0.719519\pi\)
−0.636259 + 0.771476i \(0.719519\pi\)
\(128\) 0 0
\(129\) 3.87298 1.73205i 0.340997 0.152499i
\(130\) 0 0
\(131\) 2.44949 + 4.24264i 0.214013 + 0.370681i 0.952967 0.303075i \(-0.0980132\pi\)
−0.738954 + 0.673756i \(0.764680\pi\)
\(132\) 0 0
\(133\) 10.3095 17.8565i 0.893945 1.54836i
\(134\) 0 0
\(135\) 5.07718 1.10557i 0.436974 0.0951521i
\(136\) 0 0
\(137\) 1.87298 3.24410i 0.160020 0.277162i −0.774856 0.632138i \(-0.782178\pi\)
0.934876 + 0.354976i \(0.115511\pi\)
\(138\) 0 0
\(139\) −2.44949 4.24264i −0.207763 0.359856i 0.743247 0.669018i \(-0.233285\pi\)
−0.951010 + 0.309162i \(0.899952\pi\)
\(140\) 0 0
\(141\) 9.43649 4.22013i 0.794696 0.355399i
\(142\) 0 0
\(143\) 11.9363 0.998165
\(144\) 0 0
\(145\) −6.74597 −0.560222
\(146\) 0 0
\(147\) 0.155563 1.50403i 0.0128306 0.124050i
\(148\) 0 0
\(149\) −2.93649 5.08615i −0.240567 0.416674i 0.720309 0.693653i \(-0.244000\pi\)
−0.960876 + 0.276979i \(0.910667\pi\)
\(150\) 0 0
\(151\) −9.28600 + 16.0838i −0.755684 + 1.30888i 0.189349 + 0.981910i \(0.439362\pi\)
−0.945033 + 0.326974i \(0.893971\pi\)
\(152\) 0 0
\(153\) −6.43649 19.5886i −0.520360 1.58364i
\(154\) 0 0
\(155\) 1.93753 3.35591i 0.155626 0.269553i
\(156\) 0 0
\(157\) −6.87298 11.9044i −0.548524 0.950071i −0.998376 0.0569681i \(-0.981857\pi\)
0.449852 0.893103i \(-0.351477\pi\)
\(158\) 0 0
\(159\) −5.61177 4.06301i −0.445042 0.322218i
\(160\) 0 0
\(161\) 7.87298 0.620478
\(162\) 0 0
\(163\) −15.0986 −1.18261 −0.591307 0.806447i \(-0.701388\pi\)
−0.591307 + 0.806447i \(0.701388\pi\)
\(164\) 0 0
\(165\) 3.43649 + 2.48808i 0.267531 + 0.193696i
\(166\) 0 0
\(167\) 4.36439 + 7.55934i 0.337727 + 0.584960i 0.984005 0.178142i \(-0.0570088\pi\)
−0.646278 + 0.763102i \(0.723675\pi\)
\(168\) 0 0
\(169\) −5.37298 + 9.30628i −0.413306 + 0.715868i
\(170\) 0 0
\(171\) −6.88178 20.9438i −0.526263 1.60161i
\(172\) 0 0
\(173\) 2.00000 3.46410i 0.152057 0.263371i −0.779926 0.625871i \(-0.784744\pi\)
0.931984 + 0.362500i \(0.118077\pi\)
\(174\) 0 0
\(175\) −1.40294 2.42997i −0.106052 0.183688i
\(176\) 0 0
\(177\) −1.00000 + 9.66829i −0.0751646 + 0.726713i
\(178\) 0 0
\(179\) −5.21011 −0.389422 −0.194711 0.980861i \(-0.562377\pi\)
−0.194711 + 0.980861i \(0.562377\pi\)
\(180\) 0 0
\(181\) 14.7460 1.09606 0.548030 0.836459i \(-0.315378\pi\)
0.548030 + 0.836459i \(0.315378\pi\)
\(182\) 0 0
\(183\) −9.28600 + 4.15283i −0.686441 + 0.306986i
\(184\) 0 0
\(185\) −0.436492 0.756026i −0.0320915 0.0555841i
\(186\) 0 0
\(187\) 8.41765 14.5798i 0.615560 1.06618i
\(188\) 0 0
\(189\) −9.80948 10.7863i −0.713534 0.784590i
\(190\) 0 0
\(191\) −1.58114 + 2.73861i −0.114407 + 0.198159i −0.917543 0.397637i \(-0.869830\pi\)
0.803135 + 0.595797i \(0.203164\pi\)
\(192\) 0 0
\(193\) 3.30948 + 5.73218i 0.238221 + 0.412611i 0.960204 0.279300i \(-0.0901023\pi\)
−0.721983 + 0.691911i \(0.756769\pi\)
\(194\) 0 0
\(195\) −7.70486 + 3.44572i −0.551757 + 0.246753i
\(196\) 0 0
\(197\) 23.2379 1.65563 0.827816 0.561000i \(-0.189583\pi\)
0.827816 + 0.561000i \(0.189583\pi\)
\(198\) 0 0
\(199\) 15.0986 1.07031 0.535156 0.844753i \(-0.320253\pi\)
0.535156 + 0.844753i \(0.320253\pi\)
\(200\) 0 0
\(201\) −2.80948 + 27.1628i −0.198165 + 1.91592i
\(202\) 0 0
\(203\) 9.46420 + 16.3925i 0.664257 + 1.15053i
\(204\) 0 0
\(205\) 1.06351 1.84205i 0.0742786 0.128654i
\(206\) 0 0
\(207\) 5.61177 6.27415i 0.390045 0.436083i
\(208\) 0 0
\(209\) 9.00000 15.5885i 0.622543 1.07828i
\(210\) 0 0
\(211\) 0.200831 + 0.347849i 0.0138258 + 0.0239469i 0.872856 0.487979i \(-0.162266\pi\)
−0.859030 + 0.511926i \(0.828932\pi\)
\(212\) 0 0
\(213\) −4.43649 3.21209i −0.303983 0.220089i
\(214\) 0 0
\(215\) −2.44949 −0.167054
\(216\) 0 0
\(217\) −10.8730 −0.738106
\(218\) 0 0
\(219\) −13.6730 9.89949i −0.923937 0.668946i
\(220\) 0 0
\(221\) 16.7460 + 29.0049i 1.12646 + 1.95108i
\(222\) 0 0
\(223\) −14.5640 + 25.2256i −0.975278 + 1.68923i −0.296264 + 0.955106i \(0.595741\pi\)
−0.679014 + 0.734125i \(0.737592\pi\)
\(224\) 0 0
\(225\) −2.93649 0.614017i −0.195766 0.0409345i
\(226\) 0 0
\(227\) −3.31784 + 5.74667i −0.220213 + 0.381420i −0.954872 0.297016i \(-0.904009\pi\)
0.734660 + 0.678436i \(0.237342\pi\)
\(228\) 0 0
\(229\) 9.37298 + 16.2345i 0.619384 + 1.07280i 0.989598 + 0.143858i \(0.0459510\pi\)
−0.370214 + 0.928946i \(0.620716\pi\)
\(230\) 0 0
\(231\) 1.22474 11.8412i 0.0805823 0.779093i
\(232\) 0 0
\(233\) 0.872983 0.0571910 0.0285955 0.999591i \(-0.490897\pi\)
0.0285955 + 0.999591i \(0.490897\pi\)
\(234\) 0 0
\(235\) −5.96816 −0.389320
\(236\) 0 0
\(237\) −20.0000 + 8.94427i −1.29914 + 0.580993i
\(238\) 0 0
\(239\) −5.96816 10.3372i −0.386048 0.668655i 0.605866 0.795567i \(-0.292827\pi\)
−0.991914 + 0.126912i \(0.959494\pi\)
\(240\) 0 0
\(241\) −5.68246 + 9.84231i −0.366039 + 0.633999i −0.988942 0.148300i \(-0.952620\pi\)
0.622903 + 0.782299i \(0.285953\pi\)
\(242\) 0 0
\(243\) −15.5879 + 0.129018i −0.999966 + 0.00827648i
\(244\) 0 0
\(245\) −0.436492 + 0.756026i −0.0278864 + 0.0483007i
\(246\) 0 0
\(247\) 17.9045 + 31.0115i 1.13924 + 1.97321i
\(248\) 0 0
\(249\) 24.4365 10.9283i 1.54860 0.692555i
\(250\) 0 0
\(251\) 20.7104 1.30723 0.653613 0.756829i \(-0.273252\pi\)
0.653613 + 0.756829i \(0.273252\pi\)
\(252\) 0 0
\(253\) 6.87298 0.432101
\(254\) 0 0
\(255\) −1.22474 + 11.8412i −0.0766965 + 0.741524i
\(256\) 0 0
\(257\) −8.74597 15.1485i −0.545558 0.944935i −0.998572 0.0534310i \(-0.982984\pi\)
0.453013 0.891504i \(-0.350349\pi\)
\(258\) 0 0
\(259\) −1.22474 + 2.12132i −0.0761019 + 0.131812i
\(260\) 0 0
\(261\) 19.8095 + 4.14214i 1.22618 + 0.256392i
\(262\) 0 0
\(263\) −2.24866 + 3.89479i −0.138658 + 0.240163i −0.926989 0.375089i \(-0.877612\pi\)
0.788331 + 0.615252i \(0.210946\pi\)
\(264\) 0 0
\(265\) 2.00000 + 3.46410i 0.122859 + 0.212798i
\(266\) 0 0
\(267\) −23.4936 17.0098i −1.43779 1.04098i
\(268\) 0 0
\(269\) −23.8730 −1.45556 −0.727781 0.685810i \(-0.759448\pi\)
−0.727781 + 0.685810i \(0.759448\pi\)
\(270\) 0 0
\(271\) 5.30064 0.321991 0.160996 0.986955i \(-0.448530\pi\)
0.160996 + 0.986955i \(0.448530\pi\)
\(272\) 0 0
\(273\) 19.1825 + 13.8884i 1.16098 + 0.840565i
\(274\) 0 0
\(275\) −1.22474 2.12132i −0.0738549 0.127920i
\(276\) 0 0
\(277\) 6.56351 11.3683i 0.394363 0.683057i −0.598657 0.801006i \(-0.704299\pi\)
0.993020 + 0.117949i \(0.0376319\pi\)
\(278\) 0 0
\(279\) −7.75013 + 8.66491i −0.463988 + 0.518755i
\(280\) 0 0
\(281\) −5.68246 + 9.84231i −0.338987 + 0.587143i −0.984242 0.176824i \(-0.943418\pi\)
0.645255 + 0.763967i \(0.276751\pi\)
\(282\) 0 0
\(283\) −10.8898 18.8616i −0.647330 1.12121i −0.983758 0.179499i \(-0.942552\pi\)
0.336428 0.941709i \(-0.390781\pi\)
\(284\) 0 0
\(285\) −1.30948 + 12.6604i −0.0775666 + 0.749936i
\(286\) 0 0
\(287\) −5.96816 −0.352289
\(288\) 0 0
\(289\) 30.2379 1.77870
\(290\) 0 0
\(291\) 2.76062 1.23458i 0.161830 0.0723726i
\(292\) 0 0
\(293\) −3.43649 5.95218i −0.200762 0.347730i 0.748012 0.663685i \(-0.231008\pi\)
−0.948774 + 0.315955i \(0.897675\pi\)
\(294\) 0 0
\(295\) 2.80588 4.85993i 0.163365 0.282956i
\(296\) 0 0
\(297\) −8.56351 9.41628i −0.496905 0.546388i
\(298\) 0 0
\(299\) −6.83651 + 11.8412i −0.395366 + 0.684794i
\(300\) 0 0
\(301\) 3.43649 + 5.95218i 0.198076 + 0.343078i
\(302\) 0 0
\(303\) −2.76062 + 1.23458i −0.158593 + 0.0709250i
\(304\) 0 0
\(305\) 5.87298 0.336286
\(306\) 0 0
\(307\) 2.09310 0.119459 0.0597296 0.998215i \(-0.480976\pi\)
0.0597296 + 0.998215i \(0.480976\pi\)
\(308\) 0 0
\(309\) 0.182458 1.76406i 0.0103797 0.100354i
\(310\) 0 0
\(311\) −13.8286 23.9518i −0.784147 1.35818i −0.929507 0.368804i \(-0.879767\pi\)
0.145360 0.989379i \(-0.453566\pi\)
\(312\) 0 0
\(313\) 0.309475 0.536026i 0.0174926 0.0302980i −0.857147 0.515073i \(-0.827765\pi\)
0.874639 + 0.484774i \(0.161098\pi\)
\(314\) 0 0
\(315\) 2.62769 + 7.99701i 0.148053 + 0.450580i
\(316\) 0 0
\(317\) 9.43649 16.3445i 0.530006 0.917998i −0.469381 0.882996i \(-0.655523\pi\)
0.999387 0.0350019i \(-0.0111437\pi\)
\(318\) 0 0
\(319\) 8.26209 + 14.3104i 0.462588 + 0.801226i
\(320\) 0 0
\(321\) 19.6825 + 14.2504i 1.09857 + 0.795381i
\(322\) 0 0
\(323\) 50.5059 2.81022
\(324\) 0 0
\(325\) 4.87298 0.270304
\(326\) 0 0
\(327\) −22.2689 16.1230i −1.23147 0.891606i
\(328\) 0 0
\(329\) 8.37298 + 14.5024i 0.461618 + 0.799545i
\(330\) 0 0
\(331\) −15.0533 + 26.0731i −0.827406 + 1.43311i 0.0726606 + 0.997357i \(0.476851\pi\)
−0.900067 + 0.435752i \(0.856482\pi\)
\(332\) 0 0
\(333\) 0.817542 + 2.48808i 0.0448010 + 0.136346i
\(334\) 0 0
\(335\) 7.88306 13.6539i 0.430698 0.745990i
\(336\) 0 0
\(337\) −14.7460 25.5408i −0.803264 1.39129i −0.917457 0.397835i \(-0.869761\pi\)
0.114193 0.993459i \(-0.463572\pi\)
\(338\) 0 0
\(339\) −3.51867 + 34.0195i −0.191108 + 1.84769i
\(340\) 0 0
\(341\) −9.49193 −0.514017
\(342\) 0 0
\(343\) −17.1917 −0.928264
\(344\) 0 0
\(345\) −4.43649 + 1.98406i −0.238853 + 0.106818i
\(346\) 0 0
\(347\) −2.24866 3.89479i −0.120714 0.209083i 0.799335 0.600885i \(-0.205185\pi\)
−0.920050 + 0.391802i \(0.871852\pi\)
\(348\) 0 0
\(349\) 16.1190 27.9188i 0.862828 1.49446i −0.00636054 0.999980i \(-0.502025\pi\)
0.869188 0.494481i \(-0.164642\pi\)
\(350\) 0 0
\(351\) 24.7410 5.38741i 1.32058 0.287559i
\(352\) 0 0
\(353\) 12.0000 20.7846i 0.638696 1.10625i −0.347024 0.937856i \(-0.612808\pi\)
0.985719 0.168397i \(-0.0538590\pi\)
\(354\) 0 0
\(355\) 1.58114 + 2.73861i 0.0839181 + 0.145350i
\(356\) 0 0
\(357\) 30.4919 13.6364i 1.61380 0.721715i
\(358\) 0 0
\(359\) 10.1091 0.533537 0.266769 0.963761i \(-0.414044\pi\)
0.266769 + 0.963761i \(0.414044\pi\)
\(360\) 0 0
\(361\) 35.0000 1.84211
\(362\) 0 0
\(363\) −0.890985 + 8.61430i −0.0467646 + 0.452133i
\(364\) 0 0
\(365\) 4.87298 + 8.44025i 0.255064 + 0.441783i
\(366\) 0 0
\(367\) −8.26209 + 14.3104i −0.431277 + 0.746995i −0.996984 0.0776124i \(-0.975270\pi\)
0.565706 + 0.824607i \(0.308604\pi\)
\(368\) 0 0
\(369\) −4.25403 + 4.75615i −0.221456 + 0.247595i
\(370\) 0 0
\(371\) 5.61177 9.71987i 0.291348 0.504630i
\(372\) 0 0
\(373\) 7.74597 + 13.4164i 0.401071 + 0.694675i 0.993855 0.110686i \(-0.0353047\pi\)
−0.592784 + 0.805361i \(0.701971\pi\)
\(374\) 0 0
\(375\) 1.40294 + 1.01575i 0.0724476 + 0.0524533i
\(376\) 0 0
\(377\) −32.8730 −1.69304
\(378\) 0 0
\(379\) 21.0215 1.07980 0.539901 0.841729i \(-0.318462\pi\)
0.539901 + 0.841729i \(0.318462\pi\)
\(380\) 0 0
\(381\) −20.1190 14.5665i −1.03073 0.746262i
\(382\) 0 0
\(383\) −11.4244 19.7876i −0.583758 1.01110i −0.995029 0.0995852i \(-0.968248\pi\)
0.411271 0.911513i \(-0.365085\pi\)
\(384\) 0 0
\(385\) −3.43649 + 5.95218i −0.175140 + 0.303351i
\(386\) 0 0
\(387\) 7.19291 + 1.50403i 0.365636 + 0.0764540i
\(388\) 0 0
\(389\) 2.06351 3.57410i 0.104624 0.181214i −0.808961 0.587863i \(-0.799969\pi\)
0.913585 + 0.406649i \(0.133303\pi\)
\(390\) 0 0
\(391\) 9.64240 + 16.7011i 0.487637 + 0.844612i
\(392\) 0 0
\(393\) −0.872983 + 8.44025i −0.0440362 + 0.425755i
\(394\) 0 0
\(395\) 12.6491 0.636446
\(396\) 0 0
\(397\) 17.4919 0.877895 0.438947 0.898513i \(-0.355351\pi\)
0.438947 + 0.898513i \(0.355351\pi\)
\(398\) 0 0
\(399\) 32.6014 14.5798i 1.63211 0.729903i
\(400\) 0 0
\(401\) 7.74597 + 13.4164i 0.386815 + 0.669983i 0.992019 0.126087i \(-0.0402418\pi\)
−0.605204 + 0.796070i \(0.706908\pi\)
\(402\) 0 0
\(403\) 9.44157 16.3533i 0.470318 0.814614i
\(404\) 0 0
\(405\) 8.24597 + 3.60611i 0.409745 + 0.179189i
\(406\) 0 0
\(407\) −1.06918 + 1.85188i −0.0529974 + 0.0917942i
\(408\) 0 0
\(409\) −6.12702 10.6123i −0.302961 0.524745i 0.673844 0.738874i \(-0.264642\pi\)
−0.976805 + 0.214129i \(0.931309\pi\)
\(410\) 0 0
\(411\) 5.92289 2.64880i 0.292155 0.130656i
\(412\) 0 0
\(413\) −15.7460 −0.774808
\(414\) 0 0
\(415\) −15.4550 −0.758656
\(416\) 0 0
\(417\) 0.872983 8.44025i 0.0427502 0.413321i
\(418\) 0 0
\(419\) 7.86043 + 13.6147i 0.384007 + 0.665120i 0.991631 0.129105i \(-0.0412105\pi\)
−0.607624 + 0.794225i \(0.707877\pi\)
\(420\) 0 0
\(421\) −11.6190 + 20.1246i −0.566273 + 0.980814i 0.430657 + 0.902516i \(0.358282\pi\)
−0.996930 + 0.0782979i \(0.975051\pi\)
\(422\) 0 0
\(423\) 17.5255 + 3.66455i 0.852117 + 0.178177i
\(424\) 0 0
\(425\) 3.43649 5.95218i 0.166694 0.288723i
\(426\) 0 0
\(427\) −8.23945 14.2712i −0.398735 0.690630i
\(428\) 0 0
\(429\) 16.7460 + 12.1244i 0.808503 + 0.585369i
\(430\) 0 0
\(431\) −37.9473 −1.82786 −0.913929 0.405873i \(-0.866967\pi\)
−0.913929 + 0.405873i \(0.866967\pi\)
\(432\) 0 0
\(433\) 18.8730 0.906978 0.453489 0.891262i \(-0.350179\pi\)
0.453489 + 0.891262i \(0.350179\pi\)
\(434\) 0 0
\(435\) −9.46420 6.85224i −0.453774 0.328540i
\(436\) 0 0
\(437\) 10.3095 + 17.8565i 0.493169 + 0.854194i
\(438\) 0 0
\(439\) −2.09310 + 3.62535i −0.0998980 + 0.173028i −0.911642 0.410985i \(-0.865185\pi\)
0.811744 + 0.584013i \(0.198518\pi\)
\(440\) 0 0
\(441\) 1.74597 1.95205i 0.0831413 0.0929548i
\(442\) 0 0
\(443\) 1.96017 3.39511i 0.0931303 0.161306i −0.815696 0.578480i \(-0.803646\pi\)
0.908827 + 0.417174i \(0.136979\pi\)
\(444\) 0 0
\(445\) 8.37298 + 14.5024i 0.396917 + 0.687481i
\(446\) 0 0
\(447\) 1.04655 10.1183i 0.0495000 0.478580i
\(448\) 0 0
\(449\) 30.9839 1.46222 0.731110 0.682260i \(-0.239003\pi\)
0.731110 + 0.682260i \(0.239003\pi\)
\(450\) 0 0
\(451\) −5.21011 −0.245334
\(452\) 0 0
\(453\) −29.3649 + 13.1324i −1.37968 + 0.617014i
\(454\) 0 0
\(455\) −6.83651 11.8412i −0.320501 0.555123i
\(456\) 0 0
\(457\) −2.69052 + 4.66013i −0.125857 + 0.217991i −0.922068 0.387028i \(-0.873502\pi\)
0.796210 + 0.605020i \(0.206835\pi\)
\(458\) 0 0
\(459\) 10.8671 34.0195i 0.507235 1.58790i
\(460\) 0 0
\(461\) 8.37298 14.5024i 0.389969 0.675446i −0.602476 0.798137i \(-0.705819\pi\)
0.992445 + 0.122691i \(0.0391525\pi\)
\(462\) 0 0
\(463\) −12.8047 22.1783i −0.595084 1.03072i −0.993535 0.113526i \(-0.963786\pi\)
0.398451 0.917189i \(-0.369548\pi\)
\(464\) 0 0
\(465\) 6.12702 2.74009i 0.284134 0.127068i
\(466\) 0 0
\(467\) −26.3221 −1.21804 −0.609022 0.793154i \(-0.708438\pi\)
−0.609022 + 0.793154i \(0.708438\pi\)
\(468\) 0 0
\(469\) −44.2379 −2.04272
\(470\) 0 0
\(471\) 2.44949 23.6824i 0.112867 1.09123i
\(472\) 0 0
\(473\) 3.00000 + 5.19615i 0.137940 + 0.238919i
\(474\) 0 0
\(475\) 3.67423 6.36396i 0.168585 0.291999i
\(476\) 0 0
\(477\) −3.74597 11.4003i −0.171516 0.521986i
\(478\) 0 0
\(479\) −4.89898 + 8.48528i −0.223840 + 0.387702i −0.955971 0.293462i \(-0.905193\pi\)
0.732131 + 0.681164i \(0.238526\pi\)
\(480\) 0 0
\(481\) −2.12702 3.68410i −0.0969836 0.167981i
\(482\) 0 0
\(483\) 11.0453 + 7.99701i 0.502580 + 0.363876i
\(484\) 0 0
\(485\) −1.74597 −0.0792803
\(486\) 0 0
\(487\) 15.8114 0.716482 0.358241 0.933629i \(-0.383377\pi\)
0.358241 + 0.933629i \(0.383377\pi\)
\(488\) 0 0
\(489\) −21.1825 15.3364i −0.957904 0.693538i
\(490\) 0 0
\(491\) 6.68095 + 11.5717i 0.301507 + 0.522225i 0.976478 0.215619i \(-0.0691770\pi\)
−0.674970 + 0.737845i \(0.735844\pi\)
\(492\) 0 0
\(493\) −23.1825 + 40.1532i −1.04409 + 1.80841i
\(494\) 0 0
\(495\) 2.29393 + 6.98125i 0.103104 + 0.313784i
\(496\) 0 0
\(497\) 4.43649 7.68423i 0.199004 0.344685i
\(498\) 0 0
\(499\) −4.23146 7.32910i −0.189426 0.328096i 0.755633 0.654995i \(-0.227329\pi\)
−0.945059 + 0.326900i \(0.893996\pi\)
\(500\) 0 0
\(501\) −1.55544 + 15.0385i −0.0694920 + 0.671869i
\(502\) 0 0
\(503\) 37.5004 1.67206 0.836030 0.548684i \(-0.184871\pi\)
0.836030 + 0.548684i \(0.184871\pi\)
\(504\) 0 0
\(505\) 1.74597 0.0776945
\(506\) 0 0
\(507\) −16.9909 + 7.59855i −0.754591 + 0.337463i
\(508\) 0 0
\(509\) 3.75403 + 6.50218i 0.166395 + 0.288204i 0.937150 0.348928i \(-0.113454\pi\)
−0.770755 + 0.637132i \(0.780121\pi\)
\(510\) 0 0
\(511\) 13.6730 23.6824i 0.604859 1.04765i
\(512\) 0 0
\(513\) 11.6190 36.3731i 0.512989 1.60591i
\(514\) 0 0
\(515\) −0.511957 + 0.886735i −0.0225595 + 0.0390742i
\(516\) 0 0
\(517\) 7.30948 + 12.6604i 0.321470 + 0.556803i
\(518\) 0 0
\(519\) 6.32456 2.82843i 0.277617 0.124154i
\(520\) 0 0
\(521\) −8.74597 −0.383168 −0.191584 0.981476i \(-0.561362\pi\)
−0.191584 + 0.981476i \(0.561362\pi\)
\(522\) 0 0
\(523\) 19.2395 0.841286 0.420643 0.907226i \(-0.361805\pi\)
0.420643 + 0.907226i \(0.361805\pi\)
\(524\) 0 0
\(525\) 0.500000 4.83414i 0.0218218 0.210979i
\(526\) 0 0
\(527\) −13.3166 23.0651i −0.580082 1.00473i
\(528\) 0 0
\(529\) 7.56351 13.1004i 0.328848 0.569582i
\(530\) 0 0
\(531\) −11.2235 + 12.5483i −0.487060 + 0.544550i
\(532\) 0 0
\(533\) 5.18246 8.97628i 0.224477 0.388806i
\(534\) 0 0
\(535\) −7.01471 12.1498i −0.303272 0.525283i
\(536\) 0 0
\(537\) −7.30948 5.29218i −0.315427 0.228374i
\(538\) 0 0
\(539\) 2.13836 0.0921058
\(540\) 0 0
\(541\) −43.9839 −1.89101 −0.945507 0.325602i \(-0.894433\pi\)
−0.945507 + 0.325602i \(0.894433\pi\)
\(542\) 0 0
\(543\) 20.6877 + 14.9783i 0.887796 + 0.642779i
\(544\) 0 0
\(545\) 7.93649 + 13.7464i 0.339962 + 0.588831i
\(546\) 0 0
\(547\) 10.8898 18.8616i 0.465613 0.806466i −0.533616 0.845727i \(-0.679167\pi\)
0.999229 + 0.0392614i \(0.0125005\pi\)
\(548\) 0 0
\(549\) −17.2460 3.60611i −0.736040 0.153905i
\(550\) 0 0
\(551\) −24.7863 + 42.9311i −1.05593 + 1.82893i
\(552\) 0 0
\(553\) −17.7460 30.7369i −0.754635 1.30707i
\(554\) 0 0
\(555\) 0.155563 1.50403i 0.00660328 0.0638424i
\(556\) 0 0
\(557\) −19.7460 −0.836663 −0.418332 0.908294i \(-0.637385\pi\)
−0.418332 + 0.908294i \(0.637385\pi\)
\(558\) 0 0
\(559\) −11.9363 −0.504853
\(560\) 0 0
\(561\) 26.6190 11.9044i 1.12385 0.502602i
\(562\) 0 0
\(563\) 7.17027 + 12.4193i 0.302191 + 0.523410i 0.976632 0.214919i \(-0.0689486\pi\)
−0.674441 + 0.738329i \(0.735615\pi\)
\(564\) 0 0
\(565\) 9.87298 17.1005i 0.415360 0.719424i
\(566\) 0 0
\(567\) −2.80588 25.0966i −0.117836 1.05396i
\(568\) 0 0
\(569\) 8.74597 15.1485i 0.366650 0.635056i −0.622389 0.782708i \(-0.713838\pi\)
0.989039 + 0.147651i \(0.0471713\pi\)
\(570\) 0 0
\(571\) 23.4710 + 40.6529i 0.982230 + 1.70127i 0.653651 + 0.756796i \(0.273236\pi\)
0.328579 + 0.944477i \(0.393430\pi\)
\(572\) 0 0
\(573\) −5.00000 + 2.23607i −0.208878 + 0.0934131i
\(574\) 0 0
\(575\) 2.80588 0.117013
\(576\) 0 0
\(577\) 5.74597 0.239208 0.119604 0.992822i \(-0.461838\pi\)
0.119604 + 0.992822i \(0.461838\pi\)
\(578\) 0 0
\(579\) −1.17948 + 11.4035i −0.0490174 + 0.473914i
\(580\) 0 0
\(581\) 21.6825 + 37.5551i 0.899540 + 1.55805i
\(582\) 0 0
\(583\) 4.89898 8.48528i 0.202895 0.351424i
\(584\) 0 0
\(585\) −14.3095 2.99209i −0.591624 0.123708i
\(586\) 0 0
\(587\) −20.7330 + 35.9106i −0.855743 + 1.48219i 0.0202119 + 0.999796i \(0.493566\pi\)
−0.875954 + 0.482394i \(0.839767\pi\)
\(588\) 0 0
\(589\) −14.2379 24.6608i −0.586662 1.01613i
\(590\) 0 0
\(591\) 32.6014 + 23.6040i 1.34104 + 0.970937i
\(592\) 0 0
\(593\) −16.8730 −0.692890 −0.346445 0.938070i \(-0.612611\pi\)
−0.346445 + 0.938070i \(0.612611\pi\)
\(594\) 0 0
\(595\) −19.2848 −0.790599
\(596\) 0 0
\(597\) 21.1825 + 15.3364i 0.866940 + 0.627679i
\(598\) 0 0
\(599\) 13.6730 + 23.6824i 0.558665 + 0.967636i 0.997608 + 0.0691209i \(0.0220194\pi\)
−0.438944 + 0.898515i \(0.644647\pi\)
\(600\) 0 0
\(601\) −7.25403 + 12.5644i −0.295898 + 0.512511i −0.975193 0.221354i \(-0.928952\pi\)
0.679295 + 0.733865i \(0.262286\pi\)
\(602\) 0 0
\(603\) −31.5322 + 35.2541i −1.28409 + 1.43566i
\(604\) 0 0
\(605\) 2.50000 4.33013i 0.101639 0.176045i
\(606\) 0 0
\(607\) 2.67295 + 4.62969i 0.108492 + 0.187913i 0.915159 0.403092i \(-0.132065\pi\)
−0.806668 + 0.591005i \(0.798731\pi\)
\(608\) 0 0
\(609\) −3.37298 + 32.6110i −0.136680 + 1.32146i
\(610\) 0 0
\(611\) −29.0828 −1.17656
\(612\) 0 0
\(613\) −12.6190 −0.509675 −0.254837 0.966984i \(-0.582022\pi\)
−0.254837 + 0.966984i \(0.582022\pi\)
\(614\) 0 0
\(615\) 3.36311 1.50403i 0.135614 0.0606483i
\(616\) 0 0
\(617\) 0.127017 + 0.219999i 0.00511350 + 0.00885684i 0.868571 0.495565i \(-0.165039\pi\)
−0.863457 + 0.504422i \(0.831706\pi\)
\(618\) 0 0
\(619\) 0.200831 0.347849i 0.00807208 0.0139812i −0.861961 0.506974i \(-0.830764\pi\)
0.870033 + 0.492993i \(0.164097\pi\)
\(620\) 0 0
\(621\) 14.2460 3.10209i 0.571671 0.124483i
\(622\) 0 0
\(623\) 23.4936 40.6921i 0.941252 1.63030i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 28.4605 12.7279i 1.13660 0.508304i
\(628\) 0 0
\(629\) −6.00000 −0.239236
\(630\) 0 0
\(631\) 9.88849 0.393655 0.196827 0.980438i \(-0.436936\pi\)
0.196827 + 0.980438i \(0.436936\pi\)
\(632\) 0 0
\(633\) −0.0715749 + 0.692007i −0.00284485 + 0.0275048i
\(634\) 0 0
\(635\) 7.17027 + 12.4193i 0.284544 + 0.492844i
\(636\) 0 0
\(637\) −2.12702 + 3.68410i −0.0842755 + 0.145969i
\(638\) 0 0
\(639\) −2.96145 9.01276i −0.117153 0.356539i
\(640\) 0 0
\(641\) 4.93649 8.55025i 0.194980 0.337715i −0.751914 0.659261i \(-0.770869\pi\)
0.946894 + 0.321546i \(0.104203\pi\)
\(642\) 0 0
\(643\) −11.0906 19.2095i −0.437371 0.757548i 0.560115 0.828415i \(-0.310757\pi\)
−0.997486 + 0.0708664i \(0.977424\pi\)
\(644\) 0 0
\(645\) −3.43649 2.48808i −0.135312 0.0979679i
\(646\) 0 0
\(647\) −19.9523 −0.784406 −0.392203 0.919879i \(-0.628287\pi\)
−0.392203 + 0.919879i \(0.628287\pi\)
\(648\) 0 0
\(649\) −13.7460 −0.539576
\(650\) 0 0
\(651\) −15.2542 11.0443i −0.597858 0.432859i
\(652\) 0 0
\(653\) −11.9284 20.6606i −0.466795 0.808513i 0.532485 0.846439i \(-0.321258\pi\)
−0.999281 + 0.0379261i \(0.987925\pi\)
\(654\) 0 0
\(655\) 2.44949 4.24264i 0.0957095 0.165774i
\(656\) 0 0
\(657\) −9.12702 27.7768i −0.356079 1.08368i
\(658\) 0 0
\(659\) 8.72878 15.1187i 0.340025 0.588940i −0.644412 0.764678i \(-0.722898\pi\)
0.984437 + 0.175738i \(0.0562312\pi\)
\(660\) 0 0
\(661\) 10.1270 + 17.5405i 0.393895 + 0.682247i 0.992960 0.118454i \(-0.0377939\pi\)
−0.599064 + 0.800701i \(0.704461\pi\)
\(662\) 0 0
\(663\) −5.96816 + 57.7019i −0.231784 + 2.24096i
\(664\) 0 0
\(665\) −20.6190 −0.799569
\(666\) 0 0
\(667\) −18.9284 −0.732910
\(668\) 0 0
\(669\) −46.0554 + 20.5966i −1.78061 + 0.796311i
\(670\) 0 0
\(671\) −7.19291 12.4585i −0.277679 0.480954i
\(672\) 0 0
\(673\) −6.30948 + 10.9283i −0.243212 + 0.421256i −0.961628 0.274358i \(-0.911535\pi\)
0.718415 + 0.695615i \(0.244868\pi\)
\(674\) 0 0
\(675\) −3.49604 3.84418i −0.134563 0.147963i
\(676\) 0 0
\(677\) −6.05544 + 10.4883i −0.232730 + 0.403099i −0.958610 0.284721i \(-0.908099\pi\)
0.725881 + 0.687820i \(0.241432\pi\)
\(678\) 0 0
\(679\) 2.44949 + 4.24264i 0.0940028 + 0.162818i
\(680\) 0 0
\(681\) −10.4919 + 4.69214i −0.402052 + 0.179803i
\(682\) 0 0
\(683\) −41.6413 −1.59336 −0.796681 0.604401i \(-0.793413\pi\)
−0.796681 + 0.604401i \(0.793413\pi\)
\(684\) 0 0
\(685\) −3.74597 −0.143126
\(686\) 0 0
\(687\) −3.34047 + 32.2967i −0.127447 + 1.23219i
\(688\) 0 0
\(689\) 9.74597 + 16.8805i 0.371292 + 0.643096i
\(690\) 0 0
\(691\) 1.02391 1.77347i 0.0389515 0.0674660i −0.845892 0.533354i \(-0.820932\pi\)
0.884844 + 0.465888i \(0.154265\pi\)
\(692\) 0 0
\(693\) 13.7460 15.3685i 0.522166 0.583799i
\(694\) 0 0
\(695\) −2.44949 + 4.24264i −0.0929144 + 0.160933i
\(696\) 0 0
\(697\) −7.30948 12.6604i −0.276866 0.479546i
\(698\) 0 0
\(699\) 1.22474 + 0.886735i 0.0463241 + 0.0335394i
\(700\) 0 0
\(701\) −39.8730 −1.50598 −0.752991 0.658031i \(-0.771390\pi\)
−0.752991 + 0.658031i \(0.771390\pi\)
\(702\) 0 0
\(703\) −6.41509 −0.241950
\(704\) 0 0
\(705\) −8.37298 6.06218i −0.315345 0.228315i
\(706\) 0 0
\(707\) −2.44949 4.24264i −0.0921225 0.159561i
\(708\) 0 0
\(709\) 10.5000 18.1865i 0.394336 0.683010i −0.598680 0.800988i \(-0.704308\pi\)
0.993016 + 0.117978i \(0.0376414\pi\)
\(710\) 0 0
\(711\) −37.1440 7.76677i −1.39301 0.291277i
\(712\) 0 0
\(713\) 5.43649 9.41628i 0.203598 0.352642i
\(714\) 0 0
\(715\) −5.96816 10.3372i −0.223197 0.386588i
\(716\) 0 0
\(717\) 2.12702 20.5646i 0.0794349 0.767999i
\(718\) 0 0
\(719\) −26.6333 −0.993253 −0.496627 0.867964i \(-0.665428\pi\)
−0.496627 + 0.867964i \(0.665428\pi\)
\(720\) 0 0
\(721\) 2.87298 0.106995
\(722\) 0 0
\(723\) −17.9695 + 8.03621i −0.668293 + 0.298870i
\(724\) 0 0
\(725\) 3.37298 + 5.84218i 0.125269 + 0.216973i
\(726\) 0 0
\(727\) −6.10109 + 10.5674i −0.226277 + 0.391923i −0.956702 0.291070i \(-0.905989\pi\)
0.730425 + 0.682993i \(0.239322\pi\)
\(728\) 0 0
\(729\) −22.0000 15.6525i −0.814815 0.579721i
\(730\) 0 0
\(731\) −8.41765 + 14.5798i −0.311338 + 0.539253i
\(732\) 0 0
\(733\) −13.6190 23.5887i −0.503027 0.871269i −0.999994 0.00349927i \(-0.998886\pi\)
0.496966 0.867770i \(-0.334447\pi\)
\(734\) 0 0
\(735\) −1.38031 + 0.617292i −0.0509134 + 0.0227692i
\(736\) 0 0
\(737\) −38.6190 −1.42255
\(738\) 0 0
\(739\) 18.8831 0.694627 0.347314 0.937749i \(-0.387094\pi\)
0.347314 + 0.937749i \(0.387094\pi\)
\(740\) 0 0
\(741\) −6.38105 + 61.6938i −0.234414 + 2.26638i
\(742\) 0 0
\(743\) −2.78325 4.82073i −0.102108 0.176855i 0.810445 0.585814i \(-0.199225\pi\)
−0.912553 + 0.408959i \(0.865892\pi\)
\(744\) 0 0
\(745\) −2.93649 + 5.08615i −0.107585 + 0.186342i
\(746\) 0 0
\(747\) 45.3835 + 9.48963i 1.66049 + 0.347207i
\(748\) 0 0
\(749\) −19.6825 + 34.0910i −0.719181 + 1.24566i
\(750\) 0 0
\(751\) 9.95352 + 17.2400i 0.363209 + 0.629097i 0.988487 0.151305i \(-0.0483477\pi\)
−0.625278 + 0.780402i \(0.715014\pi\)
\(752\) 0 0
\(753\) 29.0554 + 21.0366i 1.05884 + 0.766617i
\(754\) 0 0
\(755\) 18.5720 0.675904
\(756\) 0 0
\(757\) −34.6190 −1.25825 −0.629124 0.777305i \(-0.716586\pi\)
−0.629124 + 0.777305i \(0.716586\pi\)
\(758\) 0 0
\(759\) 9.64240 + 6.98125i 0.349997 + 0.253403i
\(760\) 0 0
\(761\) −11.1190 19.2586i −0.403062 0.698123i 0.591032 0.806648i \(-0.298721\pi\)
−0.994094 + 0.108525i \(0.965387\pi\)
\(762\) 0 0
\(763\) 22.2689 38.5708i 0.806187 1.39636i
\(764\) 0 0
\(765\) −13.7460 + 15.3685i −0.496986 + 0.555648i
\(766\) 0 0
\(767\) 13.6730 23.6824i 0.493704 0.855121i
\(768\) 0 0
\(769\) 7.37298 + 12.7704i 0.265877 + 0.460512i 0.967793 0.251748i \(-0.0810053\pi\)
−0.701916 + 0.712259i \(0.747672\pi\)
\(770\) 0 0
\(771\) 3.11701 30.1361i 0.112256 1.08533i
\(772\) 0 0
\(773\) 1.74597 0.0627981 0.0313990 0.999507i \(-0.490004\pi\)
0.0313990 + 0.999507i \(0.490004\pi\)
\(774\) 0 0
\(775\) −3.87507 −0.139196
\(776\) 0 0
\(777\) −3.87298 + 1.73205i −0.138943 + 0.0621370i
\(778\) 0 0
\(779\) −7.81516 13.5363i −0.280007 0.484987i
\(780\) 0 0
\(781\) 3.87298 6.70820i 0.138586 0.240038i
\(782\) 0 0
\(783\) 23.5842 + 25.9327i 0.842829 + 0.926759i
\(784\) 0 0
\(785\) −6.87298 + 11.9044i −0.245307 + 0.424885i
\(786\) 0 0
\(787\) −18.7728 32.5155i −0.669179 1.15905i −0.978134 0.207976i \(-0.933312\pi\)
0.308955 0.951077i \(-0.400021\pi\)
\(788\) 0 0
\(789\) −7.11088 + 3.18008i −0.253154 + 0.113214i
\(790\) 0 0
\(791\) −55.4049 −1.96997
\(792\) 0 0
\(793\) 28.6190 1.01629
\(794\) 0 0
\(795\) −0.712788 + 6.89144i −0.0252800 + 0.244414i
\(796\)