Properties

Label 1960.2.q.x.361.1
Level $1960$
Weight $2$
Character 1960.361
Analytic conductor $15.651$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1960.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.6506787962\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.21913473024.16
Defining polynomial: \(x^{8} - 2 x^{7} + 11 x^{6} - 2 x^{5} + 51 x^{4} + 162 x^{2} + 112 x + 196\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(1.43998 - 2.49412i\) of defining polynomial
Character \(\chi\) \(=\) 1960.361
Dual form 1960.2.q.x.961.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.43998 + 2.49412i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.64709 - 4.58489i) q^{9} +O(q^{10})\) \(q+(-1.43998 + 2.49412i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.64709 - 4.58489i) q^{9} +(-0.732874 + 1.26937i) q^{11} +2.22129 q^{13} +2.87996 q^{15} +(-3.63290 + 6.29237i) q^{17} +(2.74355 + 4.75196i) q^{19} +(-1.25773 - 2.17846i) q^{23} +(-0.500000 + 0.866025i) q^{25} +6.60713 q^{27} -7.12260 q^{29} +(3.25773 - 5.64256i) q^{31} +(-2.11065 - 3.65575i) q^{33} +(-3.45065 - 5.97671i) q^{37} +(-3.19862 + 5.54017i) q^{39} -11.3199 q^{41} +3.31733 q^{43} +(-2.64709 + 4.58489i) q^{45} +(4.18353 + 7.24608i) q^{47} +(-10.4626 - 18.1218i) q^{51} +(3.50219 - 6.06597i) q^{53} +1.46575 q^{55} -15.8026 q^{57} +(-4.53553 + 7.85578i) q^{59} +(-5.60713 - 9.71184i) q^{61} +(-1.11065 - 1.92370i) q^{65} +(3.20620 - 5.55330i) q^{67} +7.24445 q^{69} -10.5316 q^{71} +(-5.26083 + 9.11202i) q^{73} +(-1.43998 - 2.49412i) q^{75} +(-5.09555 - 8.82576i) q^{79} +(-1.57288 + 2.72431i) q^{81} +16.4186 q^{83} +7.26580 q^{85} +(10.2564 - 17.7646i) q^{87} +(-4.91512 - 8.51324i) q^{89} +(9.38215 + 16.2504i) q^{93} +(2.74355 - 4.75196i) q^{95} -2.09423 q^{97} +7.75992 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{3} - 4q^{5} - 6q^{9} + O(q^{10}) \) \( 8q - 2q^{3} - 4q^{5} - 6q^{9} - 2q^{11} + 20q^{13} + 4q^{15} - 6q^{17} + 4q^{23} - 4q^{25} + 28q^{27} - 4q^{29} + 12q^{31} - 18q^{33} - 14q^{39} + 24q^{41} - 16q^{43} - 6q^{45} + 2q^{47} - 2q^{51} + 4q^{53} + 4q^{55} - 16q^{57} - 8q^{59} - 20q^{61} - 10q^{65} + 8q^{67} + 48q^{69} + 8q^{71} - 16q^{73} - 2q^{75} - 22q^{79} + 20q^{81} + 72q^{83} + 12q^{85} + 18q^{87} - 40q^{89} + 32q^{93} + 52q^{97} + 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).

\(n\) \(981\) \(1081\) \(1177\) \(1471\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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
\(3\) −1.43998 + 2.49412i −0.831373 + 1.43998i 0.0655765 + 0.997848i \(0.479111\pi\)
−0.896950 + 0.442133i \(0.854222\pi\)
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.64709 4.58489i −0.882362 1.52830i
\(10\) 0 0
\(11\) −0.732874 + 1.26937i −0.220970 + 0.382731i −0.955103 0.296275i \(-0.904256\pi\)
0.734133 + 0.679006i \(0.237589\pi\)
\(12\) 0 0
\(13\) 2.22129 0.616076 0.308038 0.951374i \(-0.400328\pi\)
0.308038 + 0.951374i \(0.400328\pi\)
\(14\) 0 0
\(15\) 2.87996 0.743603
\(16\) 0 0
\(17\) −3.63290 + 6.29237i −0.881107 + 1.52612i −0.0309964 + 0.999519i \(0.509868\pi\)
−0.850111 + 0.526603i \(0.823465\pi\)
\(18\) 0 0
\(19\) 2.74355 + 4.75196i 0.629413 + 1.09017i 0.987670 + 0.156552i \(0.0500378\pi\)
−0.358257 + 0.933623i \(0.616629\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.25773 2.17846i −0.262256 0.454240i 0.704585 0.709619i \(-0.251133\pi\)
−0.966841 + 0.255379i \(0.917800\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 6.60713 1.27154
\(28\) 0 0
\(29\) −7.12260 −1.32263 −0.661317 0.750107i \(-0.730002\pi\)
−0.661317 + 0.750107i \(0.730002\pi\)
\(30\) 0 0
\(31\) 3.25773 5.64256i 0.585106 1.01343i −0.409756 0.912195i \(-0.634386\pi\)
0.994862 0.101239i \(-0.0322806\pi\)
\(32\) 0 0
\(33\) −2.11065 3.65575i −0.367417 0.636384i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −3.45065 5.97671i −0.567284 0.982565i −0.996833 0.0795211i \(-0.974661\pi\)
0.429549 0.903043i \(-0.358672\pi\)
\(38\) 0 0
\(39\) −3.19862 + 5.54017i −0.512189 + 0.887138i
\(40\) 0 0
\(41\) −11.3199 −1.76787 −0.883935 0.467609i \(-0.845115\pi\)
−0.883935 + 0.467609i \(0.845115\pi\)
\(42\) 0 0
\(43\) 3.31733 0.505888 0.252944 0.967481i \(-0.418601\pi\)
0.252944 + 0.967481i \(0.418601\pi\)
\(44\) 0 0
\(45\) −2.64709 + 4.58489i −0.394604 + 0.683475i
\(46\) 0 0
\(47\) 4.18353 + 7.24608i 0.610230 + 1.05695i 0.991201 + 0.132363i \(0.0422564\pi\)
−0.380971 + 0.924587i \(0.624410\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −10.4626 18.1218i −1.46506 2.53756i
\(52\) 0 0
\(53\) 3.50219 6.06597i 0.481062 0.833225i −0.518701 0.854955i \(-0.673584\pi\)
0.999764 + 0.0217309i \(0.00691771\pi\)
\(54\) 0 0
\(55\) 1.46575 0.197641
\(56\) 0 0
\(57\) −15.8026 −2.09311
\(58\) 0 0
\(59\) −4.53553 + 7.85578i −0.590476 + 1.02273i 0.403692 + 0.914895i \(0.367727\pi\)
−0.994168 + 0.107840i \(0.965607\pi\)
\(60\) 0 0
\(61\) −5.60713 9.71184i −0.717920 1.24347i −0.961823 0.273674i \(-0.911761\pi\)
0.243903 0.969800i \(-0.421572\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.11065 1.92370i −0.137759 0.238605i
\(66\) 0 0
\(67\) 3.20620 5.55330i 0.391700 0.678444i −0.600974 0.799268i \(-0.705221\pi\)
0.992674 + 0.120825i \(0.0385539\pi\)
\(68\) 0 0
\(69\) 7.24445 0.872130
\(70\) 0 0
\(71\) −10.5316 −1.24987 −0.624935 0.780677i \(-0.714875\pi\)
−0.624935 + 0.780677i \(0.714875\pi\)
\(72\) 0 0
\(73\) −5.26083 + 9.11202i −0.615733 + 1.06648i 0.374522 + 0.927218i \(0.377807\pi\)
−0.990255 + 0.139263i \(0.955527\pi\)
\(74\) 0 0
\(75\) −1.43998 2.49412i −0.166275 0.287996i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −5.09555 8.82576i −0.573295 0.992975i −0.996225 0.0868130i \(-0.972332\pi\)
0.422930 0.906162i \(-0.361002\pi\)
\(80\) 0 0
\(81\) −1.57288 + 2.72431i −0.174764 + 0.302701i
\(82\) 0 0
\(83\) 16.4186 1.80217 0.901087 0.433638i \(-0.142770\pi\)
0.901087 + 0.433638i \(0.142770\pi\)
\(84\) 0 0
\(85\) 7.26580 0.788086
\(86\) 0 0
\(87\) 10.2564 17.7646i 1.09960 1.90457i
\(88\) 0 0
\(89\) −4.91512 8.51324i −0.521002 0.902401i −0.999702 0.0244228i \(-0.992225\pi\)
0.478700 0.877978i \(-0.341108\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 9.38215 + 16.2504i 0.972883 + 1.68508i
\(94\) 0 0
\(95\) 2.74355 4.75196i 0.281482 0.487541i
\(96\) 0 0
\(97\) −2.09423 −0.212636 −0.106318 0.994332i \(-0.533906\pi\)
−0.106318 + 0.994332i \(0.533906\pi\)
\(98\) 0 0
\(99\) 7.75992 0.779901
\(100\) 0 0
\(101\) 6.83280 11.8348i 0.679889 1.17760i −0.295125 0.955459i \(-0.595361\pi\)
0.975014 0.222144i \(-0.0713054\pi\)
\(102\) 0 0
\(103\) −5.01195 8.68096i −0.493843 0.855360i 0.506132 0.862456i \(-0.331075\pi\)
−0.999975 + 0.00709551i \(0.997741\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.71020 + 8.15831i 0.455352 + 0.788693i 0.998708 0.0508091i \(-0.0161800\pi\)
−0.543356 + 0.839502i \(0.682847\pi\)
\(108\) 0 0
\(109\) 4.49280 7.78175i 0.430332 0.745356i −0.566570 0.824014i \(-0.691730\pi\)
0.996902 + 0.0786572i \(0.0250632\pi\)
\(110\) 0 0
\(111\) 19.8755 1.88650
\(112\) 0 0
\(113\) 10.9476 1.02987 0.514933 0.857231i \(-0.327817\pi\)
0.514933 + 0.857231i \(0.327817\pi\)
\(114\) 0 0
\(115\) −1.25773 + 2.17846i −0.117284 + 0.203142i
\(116\) 0 0
\(117\) −5.87996 10.1844i −0.543603 0.941547i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 4.42579 + 7.66570i 0.402345 + 0.696882i
\(122\) 0 0
\(123\) 16.3004 28.2332i 1.46976 2.54570i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −5.44696 −0.483340 −0.241670 0.970359i \(-0.577695\pi\)
−0.241670 + 0.970359i \(0.577695\pi\)
\(128\) 0 0
\(129\) −4.77689 + 8.27382i −0.420582 + 0.728469i
\(130\) 0 0
\(131\) −4.58707 7.94503i −0.400774 0.694161i 0.593046 0.805169i \(-0.297925\pi\)
−0.993820 + 0.111008i \(0.964592\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −3.30357 5.72194i −0.284326 0.492467i
\(136\) 0 0
\(137\) −5.65685 + 9.79796i −0.483298 + 0.837096i −0.999816 0.0191800i \(-0.993894\pi\)
0.516518 + 0.856276i \(0.327228\pi\)
\(138\) 0 0
\(139\) −6.83099 −0.579397 −0.289698 0.957118i \(-0.593555\pi\)
−0.289698 + 0.957118i \(0.593555\pi\)
\(140\) 0 0
\(141\) −24.0968 −2.02932
\(142\) 0 0
\(143\) −1.62793 + 2.81965i −0.136134 + 0.235791i
\(144\) 0 0
\(145\) 3.56130 + 6.16835i 0.295750 + 0.512254i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0.981216 + 1.69952i 0.0803844 + 0.139230i 0.903415 0.428767i \(-0.141052\pi\)
−0.823031 + 0.567997i \(0.807719\pi\)
\(150\) 0 0
\(151\) 3.66256 6.34373i 0.298055 0.516246i −0.677636 0.735397i \(-0.736996\pi\)
0.975691 + 0.219152i \(0.0703289\pi\)
\(152\) 0 0
\(153\) 38.4664 3.10982
\(154\) 0 0
\(155\) −6.51547 −0.523335
\(156\) 0 0
\(157\) 3.73155 6.46323i 0.297810 0.515822i −0.677825 0.735223i \(-0.737077\pi\)
0.975635 + 0.219402i \(0.0704106\pi\)
\(158\) 0 0
\(159\) 10.0862 + 17.4697i 0.799885 + 1.38544i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 6.13951 + 10.6339i 0.480883 + 0.832914i 0.999759 0.0219351i \(-0.00698273\pi\)
−0.518876 + 0.854849i \(0.673649\pi\)
\(164\) 0 0
\(165\) −2.11065 + 3.65575i −0.164314 + 0.284600i
\(166\) 0 0
\(167\) −18.2300 −1.41068 −0.705342 0.708868i \(-0.749206\pi\)
−0.705342 + 0.708868i \(0.749206\pi\)
\(168\) 0 0
\(169\) −8.06585 −0.620450
\(170\) 0 0
\(171\) 14.5248 25.1577i 1.11074 1.92386i
\(172\) 0 0
\(173\) −8.96223 15.5230i −0.681386 1.18020i −0.974558 0.224135i \(-0.928044\pi\)
0.293172 0.956060i \(-0.405289\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −13.0622 22.6243i −0.981812 1.70055i
\(178\) 0 0
\(179\) −0.0187836 + 0.0325342i −0.00140395 + 0.00243172i −0.866727 0.498784i \(-0.833780\pi\)
0.865323 + 0.501215i \(0.167114\pi\)
\(180\) 0 0
\(181\) −6.82105 −0.507004 −0.253502 0.967335i \(-0.581583\pi\)
−0.253502 + 0.967335i \(0.581583\pi\)
\(182\) 0 0
\(183\) 32.2966 2.38744
\(184\) 0 0
\(185\) −3.45065 + 5.97671i −0.253697 + 0.439416i
\(186\) 0 0
\(187\) −5.32491 9.22302i −0.389396 0.674454i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2.93101 + 5.07666i 0.212080 + 0.367334i 0.952365 0.304959i \(-0.0986428\pi\)
−0.740285 + 0.672293i \(0.765309\pi\)
\(192\) 0 0
\(193\) 2.38584 4.13239i 0.171736 0.297456i −0.767291 0.641300i \(-0.778396\pi\)
0.939027 + 0.343843i \(0.111729\pi\)
\(194\) 0 0
\(195\) 6.39724 0.458116
\(196\) 0 0
\(197\) −9.28714 −0.661682 −0.330841 0.943687i \(-0.607332\pi\)
−0.330841 + 0.943687i \(0.607332\pi\)
\(198\) 0 0
\(199\) 1.60088 2.77281i 0.113483 0.196559i −0.803689 0.595049i \(-0.797132\pi\)
0.917172 + 0.398490i \(0.130466\pi\)
\(200\) 0 0
\(201\) 9.23373 + 15.9933i 0.651297 + 1.12808i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 5.65995 + 9.80332i 0.395308 + 0.684693i
\(206\) 0 0
\(207\) −6.65867 + 11.5331i −0.462809 + 0.801609i
\(208\) 0 0
\(209\) −8.04269 −0.556325
\(210\) 0 0
\(211\) −26.1055 −1.79718 −0.898590 0.438790i \(-0.855407\pi\)
−0.898590 + 0.438790i \(0.855407\pi\)
\(212\) 0 0
\(213\) 15.1653 26.2671i 1.03911 1.79979i
\(214\) 0 0
\(215\) −1.65867 2.87289i −0.113120 0.195930i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −15.1510 26.2423i −1.02381 1.77329i
\(220\) 0 0
\(221\) −8.06974 + 13.9772i −0.542829 + 0.940208i
\(222\) 0 0
\(223\) −23.8214 −1.59520 −0.797599 0.603188i \(-0.793897\pi\)
−0.797599 + 0.603188i \(0.793897\pi\)
\(224\) 0 0
\(225\) 5.29417 0.352945
\(226\) 0 0
\(227\) 4.71100 8.15969i 0.312680 0.541577i −0.666262 0.745718i \(-0.732107\pi\)
0.978942 + 0.204141i \(0.0654400\pi\)
\(228\) 0 0
\(229\) −4.96793 8.60471i −0.328290 0.568616i 0.653882 0.756596i \(-0.273139\pi\)
−0.982173 + 0.187981i \(0.939806\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.618537 1.07134i −0.0405217 0.0701856i 0.845053 0.534682i \(-0.179569\pi\)
−0.885575 + 0.464497i \(0.846235\pi\)
\(234\) 0 0
\(235\) 4.18353 7.24608i 0.272903 0.472682i
\(236\) 0 0
\(237\) 29.3500 1.90649
\(238\) 0 0
\(239\) 1.05710 0.0683782 0.0341891 0.999415i \(-0.489115\pi\)
0.0341891 + 0.999415i \(0.489115\pi\)
\(240\) 0 0
\(241\) −2.26452 + 3.92226i −0.145870 + 0.252655i −0.929697 0.368324i \(-0.879932\pi\)
0.783827 + 0.620979i \(0.213265\pi\)
\(242\) 0 0
\(243\) 5.38087 + 9.31993i 0.345183 + 0.597874i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 6.09423 + 10.5555i 0.387766 + 0.671631i
\(248\) 0 0
\(249\) −23.6424 + 40.9499i −1.49828 + 2.59510i
\(250\) 0 0
\(251\) 4.74198 0.299311 0.149656 0.988738i \(-0.452184\pi\)
0.149656 + 0.988738i \(0.452184\pi\)
\(252\) 0 0
\(253\) 3.68704 0.231802
\(254\) 0 0
\(255\) −10.4626 + 18.1218i −0.655194 + 1.13483i
\(256\) 0 0
\(257\) −7.96484 13.7955i −0.496833 0.860540i 0.503160 0.864193i \(-0.332171\pi\)
−0.999993 + 0.00365291i \(0.998837\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 18.8541 + 32.6563i 1.16704 + 2.02138i
\(262\) 0 0
\(263\) 6.63732 11.4962i 0.409275 0.708885i −0.585534 0.810648i \(-0.699115\pi\)
0.994809 + 0.101763i \(0.0324484\pi\)
\(264\) 0 0
\(265\) −7.00437 −0.430275
\(266\) 0 0
\(267\) 28.3107 1.73259
\(268\) 0 0
\(269\) −12.4301 + 21.5295i −0.757874 + 1.31268i 0.186059 + 0.982539i \(0.440429\pi\)
−0.943933 + 0.330138i \(0.892905\pi\)
\(270\) 0 0
\(271\) 15.2143 + 26.3519i 0.924201 + 1.60076i 0.792842 + 0.609428i \(0.208601\pi\)
0.131359 + 0.991335i \(0.458066\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.732874 1.26937i −0.0441939 0.0765462i
\(276\) 0 0
\(277\) 10.8649 18.8185i 0.652807 1.13069i −0.329632 0.944109i \(-0.606925\pi\)
0.982439 0.186585i \(-0.0597419\pi\)
\(278\) 0 0
\(279\) −34.4940 −2.06510
\(280\) 0 0
\(281\) −0.285426 −0.0170271 −0.00851354 0.999964i \(-0.502710\pi\)
−0.00851354 + 0.999964i \(0.502710\pi\)
\(282\) 0 0
\(283\) −2.75731 + 4.77581i −0.163905 + 0.283892i −0.936266 0.351292i \(-0.885742\pi\)
0.772361 + 0.635184i \(0.219076\pi\)
\(284\) 0 0
\(285\) 7.90131 + 13.6855i 0.468033 + 0.810657i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −17.8959 30.9966i −1.05270 1.82333i
\(290\) 0 0
\(291\) 3.01564 5.22325i 0.176780 0.306192i
\(292\) 0 0
\(293\) 17.5777 1.02690 0.513450 0.858120i \(-0.328367\pi\)
0.513450 + 0.858120i \(0.328367\pi\)
\(294\) 0 0
\(295\) 9.07107 0.528138
\(296\) 0 0
\(297\) −4.84219 + 8.38692i −0.280973 + 0.486659i
\(298\) 0 0
\(299\) −2.79380 4.83900i −0.161570 0.279847i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 19.6782 + 34.0836i 1.13048 + 1.95805i
\(304\) 0 0
\(305\) −5.60713 + 9.71184i −0.321063 + 0.556098i
\(306\) 0 0
\(307\) −25.4771 −1.45405 −0.727026 0.686610i \(-0.759098\pi\)
−0.727026 + 0.686610i \(0.759098\pi\)
\(308\) 0 0
\(309\) 28.8685 1.64227
\(310\) 0 0
\(311\) −10.7831 + 18.6768i −0.611452 + 1.05907i 0.379544 + 0.925174i \(0.376081\pi\)
−0.990996 + 0.133893i \(0.957252\pi\)
\(312\) 0 0
\(313\) −1.48970 2.58024i −0.0842030 0.145844i 0.820848 0.571146i \(-0.193501\pi\)
−0.905051 + 0.425302i \(0.860168\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.99819 + 6.92507i 0.224561 + 0.388950i 0.956188 0.292755i \(-0.0945720\pi\)
−0.731627 + 0.681705i \(0.761239\pi\)
\(318\) 0 0
\(319\) 5.21997 9.04125i 0.292262 0.506213i
\(320\) 0 0
\(321\) −27.1304 −1.51427
\(322\) 0 0
\(323\) −39.8681 −2.21832
\(324\) 0 0
\(325\) −1.11065 + 1.92370i −0.0616076 + 0.106708i
\(326\) 0 0
\(327\) 12.9391 + 22.4111i 0.715532 + 1.23934i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −17.1483 29.7018i −0.942557 1.63256i −0.760570 0.649256i \(-0.775081\pi\)
−0.181987 0.983301i \(-0.558253\pi\)
\(332\) 0 0
\(333\) −18.2684 + 31.6417i −1.00110 + 1.73396i
\(334\) 0 0
\(335\) −6.41240 −0.350347
\(336\) 0 0
\(337\) 23.8719 1.30038 0.650192 0.759770i \(-0.274689\pi\)
0.650192 + 0.759770i \(0.274689\pi\)
\(338\) 0 0
\(339\) −15.7644 + 27.3047i −0.856203 + 1.48299i
\(340\) 0 0
\(341\) 4.77502 + 8.27057i 0.258582 + 0.447876i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −3.62223 6.27388i −0.195014 0.337774i
\(346\) 0 0
\(347\) −3.17782 + 5.50415i −0.170595 + 0.295478i −0.938628 0.344931i \(-0.887902\pi\)
0.768033 + 0.640410i \(0.221236\pi\)
\(348\) 0 0
\(349\) −9.24821 −0.495045 −0.247523 0.968882i \(-0.579616\pi\)
−0.247523 + 0.968882i \(0.579616\pi\)
\(350\) 0 0
\(351\) 14.6764 0.783368
\(352\) 0 0
\(353\) −8.98042 + 15.5545i −0.477979 + 0.827885i −0.999681 0.0252431i \(-0.991964\pi\)
0.521702 + 0.853128i \(0.325297\pi\)
\(354\) 0 0
\(355\) 5.26580 + 9.12063i 0.279480 + 0.484073i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 10.1421 + 17.5667i 0.535281 + 0.927135i 0.999150 + 0.0412304i \(0.0131278\pi\)
−0.463868 + 0.885904i \(0.653539\pi\)
\(360\) 0 0
\(361\) −5.55410 + 9.61998i −0.292321 + 0.506315i
\(362\) 0 0
\(363\) −25.4922 −1.33799
\(364\) 0 0
\(365\) 10.5217 0.550729
\(366\) 0 0
\(367\) −12.5719 + 21.7752i −0.656249 + 1.13666i 0.325330 + 0.945601i \(0.394525\pi\)
−0.981579 + 0.191056i \(0.938809\pi\)
\(368\) 0 0
\(369\) 29.9647 + 51.9005i 1.55990 + 2.70183i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −0.368866 0.638895i −0.0190992 0.0330807i 0.856318 0.516449i \(-0.172746\pi\)
−0.875417 + 0.483368i \(0.839413\pi\)
\(374\) 0 0
\(375\) −1.43998 + 2.49412i −0.0743603 + 0.128796i
\(376\) 0 0
\(377\) −15.8214 −0.814843
\(378\) 0 0
\(379\) −7.11120 −0.365278 −0.182639 0.983180i \(-0.558464\pi\)
−0.182639 + 0.983180i \(0.558464\pi\)
\(380\) 0 0
\(381\) 7.84352 13.5854i 0.401836 0.696000i
\(382\) 0 0
\(383\) −14.3421 24.8412i −0.732846 1.26933i −0.955662 0.294466i \(-0.904858\pi\)
0.222816 0.974861i \(-0.428475\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −8.78127 15.2096i −0.446377 0.773148i
\(388\) 0 0
\(389\) −6.75944 + 11.7077i −0.342717 + 0.593603i −0.984936 0.172918i \(-0.944681\pi\)
0.642219 + 0.766521i \(0.278014\pi\)
\(390\) 0 0
\(391\) 18.2769 0.924302
\(392\) 0 0
\(393\) 26.4212 1.33277
\(394\) 0 0
\(395\) −5.09555 + 8.82576i −0.256385 + 0.444072i
\(396\) 0 0
\(397\) −2.01195 3.48481i −0.100977 0.174897i 0.811110 0.584893i \(-0.198864\pi\)
−0.912087 + 0.409996i \(0.865530\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 12.1898 + 21.1133i 0.608729 + 1.05435i 0.991450 + 0.130485i \(0.0416535\pi\)
−0.382722 + 0.923864i \(0.625013\pi\)
\(402\) 0 0
\(403\) 7.23639 12.5338i 0.360470 0.624353i
\(404\) 0 0
\(405\) 3.14576 0.156314
\(406\) 0 0
\(407\) 10.1156 0.501410
\(408\) 0 0
\(409\) −4.24761 + 7.35708i −0.210031 + 0.363784i −0.951724 0.306955i \(-0.900690\pi\)
0.741693 + 0.670739i \(0.234023\pi\)
\(410\) 0 0
\(411\) −16.2915 28.2177i −0.803601 1.39188i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −8.20929 14.2189i −0.402978 0.697979i
\(416\) 0 0
\(417\) 9.83649 17.0373i 0.481695 0.834320i
\(418\) 0 0
\(419\) 3.07469 0.150209 0.0751043 0.997176i \(-0.476071\pi\)
0.0751043 + 0.997176i \(0.476071\pi\)
\(420\) 0 0
\(421\) 22.4790 1.09556 0.547780 0.836623i \(-0.315473\pi\)
0.547780 + 0.836623i \(0.315473\pi\)
\(422\) 0 0
\(423\) 22.1483 38.3620i 1.07689 1.86523i
\(424\) 0 0
\(425\) −3.63290 6.29237i −0.176221 0.305225i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −4.68837 8.12049i −0.226357 0.392061i
\(430\) 0 0
\(431\) 2.58627 4.47955i 0.124576 0.215772i −0.796991 0.603991i \(-0.793576\pi\)
0.921567 + 0.388219i \(0.126910\pi\)
\(432\) 0 0
\(433\) 1.78030 0.0855557 0.0427779 0.999085i \(-0.486379\pi\)
0.0427779 + 0.999085i \(0.486379\pi\)
\(434\) 0 0
\(435\) −20.5128 −0.983514
\(436\) 0 0
\(437\) 6.90131 11.9534i 0.330134 0.571809i
\(438\) 0 0
\(439\) 12.8932 + 22.3318i 0.615361 + 1.06584i 0.990321 + 0.138795i \(0.0443231\pi\)
−0.374960 + 0.927041i \(0.622344\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.22129 + 10.7756i 0.295583 + 0.511964i 0.975120 0.221677i \(-0.0711529\pi\)
−0.679538 + 0.733641i \(0.737820\pi\)
\(444\) 0 0
\(445\) −4.91512 + 8.51324i −0.232999 + 0.403566i
\(446\) 0 0
\(447\) −5.65173 −0.267318
\(448\) 0 0
\(449\) −25.3574 −1.19669 −0.598344 0.801239i \(-0.704174\pi\)
−0.598344 + 0.801239i \(0.704174\pi\)
\(450\) 0 0
\(451\) 8.29605 14.3692i 0.390646 0.676618i
\(452\) 0 0
\(453\) 10.5480 + 18.2697i 0.495589 + 0.858386i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 17.3520 + 30.0545i 0.811690 + 1.40589i 0.911680 + 0.410901i \(0.134786\pi\)
−0.0999897 + 0.994988i \(0.531881\pi\)
\(458\) 0 0
\(459\) −24.0030 + 41.5745i −1.12037 + 1.94053i
\(460\) 0 0
\(461\) −40.8762 −1.90380 −0.951898 0.306414i \(-0.900871\pi\)
−0.951898 + 0.306414i \(0.900871\pi\)
\(462\) 0 0
\(463\) −25.1236 −1.16759 −0.583796 0.811901i \(-0.698433\pi\)
−0.583796 + 0.811901i \(0.698433\pi\)
\(464\) 0 0
\(465\) 9.38215 16.2504i 0.435087 0.753592i
\(466\) 0 0
\(467\) 13.5883 + 23.5356i 0.628792 + 1.08910i 0.987795 + 0.155763i \(0.0497835\pi\)
−0.359003 + 0.933336i \(0.616883\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 10.7467 + 18.6138i 0.495182 + 0.857680i
\(472\) 0 0
\(473\) −2.43119 + 4.21094i −0.111786 + 0.193619i
\(474\) 0 0
\(475\) −5.48709 −0.251765
\(476\) 0 0
\(477\) −37.0824 −1.69789
\(478\) 0 0
\(479\) 1.03644 1.79517i 0.0473561 0.0820232i −0.841376 0.540451i \(-0.818254\pi\)
0.888732 + 0.458427i \(0.151587\pi\)
\(480\) 0 0
\(481\) −7.66492 13.2760i −0.349490 0.605335i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.04711 + 1.81365i 0.0475469 + 0.0823537i
\(486\) 0 0
\(487\) −16.6745 + 28.8811i −0.755594 + 1.30873i 0.189484 + 0.981884i \(0.439318\pi\)
−0.945078 + 0.326844i \(0.894015\pi\)
\(488\) 0 0
\(489\) −35.3631 −1.59917
\(490\) 0 0
\(491\) 36.4487 1.64491 0.822453 0.568833i \(-0.192605\pi\)
0.822453 + 0.568833i \(0.192605\pi\)
\(492\) 0 0
\(493\) 25.8757 44.8180i 1.16538 2.01850i
\(494\) 0 0
\(495\) −3.87996 6.72029i −0.174391 0.302055i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 3.74684 + 6.48972i 0.167732 + 0.290520i 0.937622 0.347657i \(-0.113022\pi\)
−0.769890 + 0.638176i \(0.779689\pi\)
\(500\) 0 0
\(501\) 26.2509 45.4679i 1.17280 2.03136i
\(502\) 0 0
\(503\) −15.6381 −0.697267 −0.348634 0.937259i \(-0.613354\pi\)
−0.348634 + 0.937259i \(0.613354\pi\)
\(504\) 0 0
\(505\) −13.6656 −0.608111
\(506\) 0 0
\(507\) 11.6147 20.1172i 0.515825 0.893436i
\(508\) 0 0
\(509\) −3.60525 6.24448i −0.159800 0.276782i 0.774996 0.631966i \(-0.217752\pi\)
−0.934797 + 0.355184i \(0.884418\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 18.1270 + 31.3968i 0.800326 + 1.38620i
\(514\) 0 0
\(515\) −5.01195 + 8.68096i −0.220853 + 0.382529i
\(516\) 0 0
\(517\) −12.2640 −0.539370
\(518\) 0 0
\(519\) 51.6218 2.26594
\(520\) 0 0
\(521\) −7.41181 + 12.8376i −0.324717 + 0.562426i −0.981455 0.191692i \(-0.938602\pi\)
0.656738 + 0.754119i \(0.271936\pi\)
\(522\) 0 0
\(523\) 2.13641 + 3.70038i 0.0934189 + 0.161806i 0.908948 0.416910i \(-0.136887\pi\)
−0.815529 + 0.578717i \(0.803554\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 23.6700 + 40.9977i 1.03108 + 1.78589i
\(528\) 0 0
\(529\) 8.33621 14.4387i 0.362444 0.627771i
\(530\) 0 0
\(531\) 48.0238 2.08406
\(532\) 0 0
\(533\) −25.1448 −1.08914
\(534\) 0 0
\(535\) 4.71020 8.15831i 0.203640 0.352714i
\(536\) 0 0
\(537\) −0.0540961 0.0936971i −0.00233442 0.00404333i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 0.471449 + 0.816574i 0.0202692 + 0.0351073i 0.875982 0.482344i \(-0.160214\pi\)
−0.855713 + 0.517451i \(0.826881\pi\)
\(542\) 0 0
\(543\) 9.82218 17.0125i 0.421510 0.730077i
\(544\) 0 0
\(545\) −8.98559 −0.384900
\(546\) 0 0
\(547\) −11.1871 −0.478327 −0.239164 0.970979i \(-0.576873\pi\)
−0.239164 + 0.970979i \(0.576873\pi\)
\(548\) 0 0
\(549\) −29.6851 + 51.4162i −1.26693 + 2.19439i
\(550\) 0 0
\(551\) −19.5412 33.8463i −0.832483 1.44190i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −9.93775 17.2127i −0.421834 0.730638i
\(556\) 0 0
\(557\) −14.3652 + 24.8813i −0.608675 + 1.05426i 0.382784 + 0.923838i \(0.374965\pi\)
−0.991459 + 0.130418i \(0.958368\pi\)
\(558\) 0 0
\(559\) 7.36877 0.311666
\(560\) 0 0
\(561\) 30.6711 1.29493
\(562\) 0 0
\(563\) −1.22370 + 2.11952i −0.0515729 + 0.0893270i −0.890659 0.454671i \(-0.849757\pi\)
0.839086 + 0.543998i \(0.183090\pi\)
\(564\) 0 0
\(565\) −5.47381 9.48092i −0.230285 0.398865i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −17.7529 30.7489i −0.744240 1.28906i −0.950549 0.310575i \(-0.899479\pi\)
0.206309 0.978487i \(-0.433855\pi\)
\(570\) 0 0
\(571\) −2.89437 + 5.01320i −0.121126 + 0.209796i −0.920212 0.391421i \(-0.871984\pi\)
0.799086 + 0.601216i \(0.205317\pi\)
\(572\) 0 0
\(573\) −16.8824 −0.705272
\(574\) 0 0
\(575\) 2.51547 0.104902
\(576\) 0 0
\(577\) −1.10386 + 1.91195i −0.0459545 + 0.0795955i −0.888088 0.459674i \(-0.847966\pi\)
0.842133 + 0.539270i \(0.181300\pi\)
\(578\) 0 0
\(579\) 6.87112 + 11.9011i 0.285554 + 0.494594i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 5.13332 + 8.89117i 0.212600 + 0.368235i
\(584\) 0 0
\(585\) −5.87996 + 10.1844i −0.243106 + 0.421073i
\(586\) 0 0
\(587\) 39.6719 1.63744 0.818718 0.574196i \(-0.194685\pi\)
0.818718 + 0.574196i \(0.194685\pi\)
\(588\) 0 0
\(589\) 35.7510 1.47309
\(590\) 0 0
\(591\) 13.3733 23.1632i 0.550104 0.952809i
\(592\) 0 0
\(593\) 4.46654 + 7.73628i 0.183419 + 0.317691i 0.943043 0.332672i \(-0.107950\pi\)
−0.759624 + 0.650363i \(0.774617\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 4.61047 + 7.98557i 0.188694 + 0.326828i
\(598\) 0 0
\(599\) −9.19500 + 15.9262i −0.375697 + 0.650727i −0.990431 0.138008i \(-0.955930\pi\)
0.614734 + 0.788735i \(0.289263\pi\)
\(600\) 0 0
\(601\) 17.5063 0.714096 0.357048 0.934086i \(-0.383783\pi\)
0.357048 + 0.934086i \(0.383783\pi\)
\(602\) 0 0
\(603\) −33.9484 −1.38248
\(604\) 0 0
\(605\) 4.42579 7.66570i 0.179934 0.311655i
\(606\) 0 0
\(607\) 22.5719 + 39.0957i 0.916166 + 1.58685i 0.805185 + 0.593024i \(0.202066\pi\)
0.110981 + 0.993822i \(0.464601\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 9.29285 + 16.0957i 0.375948 + 0.651162i
\(612\) 0 0
\(613\) 5.92787 10.2674i 0.239424 0.414695i −0.721125 0.692805i \(-0.756375\pi\)
0.960549 + 0.278110i \(0.0897079\pi\)
\(614\) 0 0
\(615\) −32.6009 −1.31459
\(616\) 0 0
\(617\) −20.8174 −0.838078 −0.419039 0.907968i \(-0.637633\pi\)
−0.419039 + 0.907968i \(0.637633\pi\)
\(618\) 0 0
\(619\) 4.39074 7.60499i 0.176479 0.305670i −0.764193 0.644987i \(-0.776863\pi\)
0.940672 + 0.339317i \(0.110196\pi\)
\(620\) 0 0
\(621\) −8.31002 14.3934i −0.333470 0.577586i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 11.5813 20.0594i 0.462513 0.801097i
\(628\) 0 0
\(629\) 50.1435 1.99935
\(630\) 0 0
\(631\) 22.1004 0.879803 0.439902 0.898046i \(-0.355013\pi\)
0.439902 + 0.898046i \(0.355013\pi\)
\(632\) 0 0
\(633\) 37.5915 65.1103i 1.49413 2.58790i
\(634\) 0 0
\(635\) 2.72348 + 4.71721i 0.108078 + 0.187197i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 27.8781 + 48.2862i 1.10284 + 1.91017i
\(640\) 0 0
\(641\) 21.9288 37.9819i 0.866137 1.50019i 0.000223352 1.00000i \(-0.499929\pi\)
0.865914 0.500193i \(-0.166738\pi\)
\(642\) 0 0
\(643\) 37.9895 1.49816 0.749079 0.662480i \(-0.230496\pi\)
0.749079 + 0.662480i \(0.230496\pi\)
\(644\) 0 0
\(645\) 9.55379 0.376180
\(646\) 0 0
\(647\) −16.6852 + 28.8997i −0.655964 + 1.13616i 0.325687 + 0.945478i \(0.394404\pi\)
−0.981651 + 0.190686i \(0.938929\pi\)
\(648\) 0 0
\(649\) −6.64795 11.5146i −0.260955 0.451987i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −7.53160 13.0451i −0.294734 0.510495i 0.680189 0.733037i \(-0.261898\pi\)
−0.974923 + 0.222542i \(0.928564\pi\)
\(654\) 0 0
\(655\) −4.58707 + 7.94503i −0.179232 + 0.310438i
\(656\) 0 0
\(657\) 55.7035 2.17320
\(658\) 0 0
\(659\) −0.153540 −0.00598106 −0.00299053 0.999996i \(-0.500952\pi\)
−0.00299053 + 0.999996i \(0.500952\pi\)
\(660\) 0 0
\(661\) −6.15279 + 10.6569i −0.239316 + 0.414507i −0.960518 0.278217i \(-0.910256\pi\)
0.721202 + 0.692724i \(0.243590\pi\)
\(662\) 0 0
\(663\) −23.2405 40.2538i −0.902588 1.56333i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 8.95834 + 15.5163i 0.346868 + 0.600794i
\(668\) 0 0
\(669\) 34.3023 59.4134i 1.32621 2.29705i
\(670\) 0 0
\(671\) 16.4373 0.634554
\(672\) 0 0
\(673\) 4.82480 0.185983 0.0929913 0.995667i \(-0.470357\pi\)
0.0929913 + 0.995667i \(0.470357\pi\)
\(674\) 0 0
\(675\) −3.30357 + 5.72194i −0.127154 + 0.220238i
\(676\) 0 0
\(677\) −8.25203 14.2929i −0.317151 0.549322i 0.662741 0.748849i \(-0.269393\pi\)
−0.979892 + 0.199526i \(0.936060\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 13.5675 + 23.4996i 0.519907 + 0.900506i
\(682\) 0 0
\(683\) −16.1811 + 28.0264i −0.619152 + 1.07240i 0.370489 + 0.928837i \(0.379190\pi\)
−0.989641 + 0.143565i \(0.954143\pi\)
\(684\) 0 0
\(685\) 11.3137 0.432275
\(686\) 0 0
\(687\) 28.6149 1.09173
\(688\) 0 0
\(689\) 7.77939 13.4743i 0.296371 0.513330i
\(690\) 0 0
\(691\) −1.16223 2.01304i −0.0442132 0.0765796i 0.843072 0.537801i \(-0.180745\pi\)
−0.887285 + 0.461221i \(0.847411\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3.41549 + 5.91581i 0.129557 + 0.224399i
\(696\) 0 0
\(697\) 41.1240 71.2289i 1.55768 2.69799i
\(698\) 0 0
\(699\) 3.56272 0.134755
\(700\) 0 0
\(701\) −6.77071 −0.255726 −0.127863 0.991792i \(-0.540812\pi\)
−0.127863 + 0.991792i \(0.540812\pi\)
\(702\) 0 0
\(703\) 18.9341 32.7947i 0.714111 1.23688i
\(704\) 0 0
\(705\) 12.0484 + 20.8684i 0.453769 + 0.785951i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 3.11871 + 5.40177i 0.117126 + 0.202868i 0.918627 0.395125i \(-0.129299\pi\)
−0.801502 + 0.597992i \(0.795965\pi\)
\(710\) 0 0
\(711\) −26.9767 + 46.7251i −1.01171 + 1.75233i
\(712\) 0 0
\(713\) −16.3895 −0.613790
\(714\) 0 0
\(715\) 3.25586 0.121762
\(716\) 0 0
\(717\) −1.52221 + 2.63654i −0.0568478 + 0.0984633i
\(718\) 0 0
\(719\) −2.47466 4.28623i −0.0922891 0.159849i 0.816185 0.577791i \(-0.196085\pi\)
−0.908474 + 0.417941i \(0.862752\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −6.52172 11.2960i −0.242545 0.420101i
\(724\) 0 0
\(725\) 3.56130 6.16835i 0.132263 0.229087i
\(726\) 0 0
\(727\) −18.5847 −0.689269 −0.344635 0.938737i \(-0.611997\pi\)
−0.344635 + 0.938737i \(0.611997\pi\)
\(728\) 0 0
\(729\) −40.4306 −1.49743
\(730\) 0 0
\(731\) −12.0515 + 20.8739i −0.445742 + 0.772048i
\(732\) 0 0
\(733\) 12.2848 + 21.2779i 0.453749 + 0.785916i 0.998615 0.0526068i \(-0.0167530\pi\)
−0.544867 + 0.838523i \(0.683420\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.69948 + 8.13974i 0.173108 + 0.299831i
\(738\) 0 0
\(739\) 4.21475 7.30016i 0.155042 0.268541i −0.778032 0.628224i \(-0.783782\pi\)
0.933074 + 0.359684i \(0.117115\pi\)
\(740\) 0 0
\(741\) −35.1023 −1.28951
\(742\) 0 0
\(743\) −11.4705 −0.420811 −0.210405 0.977614i \(-0.567478\pi\)
−0.210405 + 0.977614i \(0.567478\pi\)
\(744\) 0 0
\(745\) 0.981216 1.69952i 0.0359490 0.0622655i
\(746\) 0 0
\(747\) −43.4614 75.2774i −1.59017 2.75426i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 8.15146 + 14.1187i 0.297451 + 0.515200i 0.975552 0.219768i \(-0.0705302\pi\)
−0.678101 + 0.734969i \(0.737197\pi\)
\(752\) 0 0
\(753\) −6.82836 + 11.8271i −0.248839 + 0.431002i
\(754\) 0 0
\(755\) −7.32511 −0.266588
\(756\) 0 0
\(757\) 25.0875 0.911821 0.455910 0.890026i \(-0.349314\pi\)
0.455910 + 0.890026i \(0.349314\pi\)
\(758\) 0 0
\(759\) −5.30927 + 9.19592i −0.192714 + 0.333791i
\(760\) 0 0
\(761\) −24.5425 42.5088i −0.889664 1.54094i −0.840273 0.542163i \(-0.817605\pi\)
−0.0493908 0.998780i \(-0.515728\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −19.2332 33.3129i −0.695378 1.20443i
\(766\) 0 0
\(767\) −10.0748 + 17.4500i −0.363778 + 0.630083i
\(768\) 0 0
\(769\) −27.0548 −0.975619 −0.487810 0.872950i \(-0.662204\pi\)
−0.487810 + 0.872950i \(0.662204\pi\)
\(770\) 0 0
\(771\) 45.8769 1.65221
\(772\) 0 0
\(773\) 20.5414 35.5787i 0.738822 1.27968i −0.214203 0.976789i \(-0.568716\pi\)
0.953026 0.302889i \(-0.0979511\pi\)
\(774\) 0 0
\(775\) 3.25773 + 5.64256i 0.117021 + 0.202687i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −31.0567 53.7917i −1.11272 1.92729i
\(780\) 0 0
\(781\) 7.71833 13.3685i 0.276184 0.478364i
\(782\) 0 0
\(783\) −47.0600 −1.68179
\(784\) 0 0
\(785\) −7.46309 −0.266369
\(786\) 0 0
\(787\) 9.87373 17.1018i 0.351960 0.609613i −0.634632 0.772814i \(-0.718849\pi\)
0.986593 + 0.163201i \(0.0521818\pi\)
\(788\) 0 0
\(789\) 19.1152 + 33.1085i 0.680520 + 1.17870i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −12.4551 21.5729i −0.442293 0.766075i
\(794\) 0 0
\(795\) 10.0862 17.4697i 0.357719 0.619588i
\(796\) 0 0
\(797\) −35.9488 −1.27337 −0.636685 0.771124i \(-0.719695\pi\)
−0.636685 + 0.771124i \(0.719695\pi\)
\(798\) 0 0
\(799\) −60.7933 −2.15071