Properties

Label 576.2.bb.d.337.1
Level $576$
Weight $2$
Character 576.337
Analytic conductor $4.599$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bb (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 337.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 576.337
Dual form 576.2.bb.d.241.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 0.866025i) q^{3} +(-0.267949 - 1.00000i) q^{5} +(2.36603 - 1.36603i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(1.50000 - 0.866025i) q^{3} +(-0.267949 - 1.00000i) q^{5} +(2.36603 - 1.36603i) q^{7} +(1.50000 - 2.59808i) q^{9} +(4.23205 + 1.13397i) q^{11} +(-3.36603 + 0.901924i) q^{13} +(-1.26795 - 1.26795i) q^{15} -5.73205 q^{17} +(2.36603 + 2.36603i) q^{19} +(2.36603 - 4.09808i) q^{21} +(-4.09808 - 2.36603i) q^{23} +(3.40192 - 1.96410i) q^{25} -5.19615i q^{27} +(-0.633975 + 2.36603i) q^{29} +(0.267949 - 0.464102i) q^{31} +(7.33013 - 1.96410i) q^{33} +(-2.00000 - 2.00000i) q^{35} +(4.73205 - 4.73205i) q^{37} +(-4.26795 + 4.26795i) q^{39} +(2.59808 + 1.50000i) q^{41} +(8.33013 + 2.23205i) q^{43} +(-3.00000 - 0.803848i) q^{45} +(-3.83013 - 6.63397i) q^{47} +(0.232051 - 0.401924i) q^{49} +(-8.59808 + 4.96410i) q^{51} +(-7.46410 + 7.46410i) q^{53} -4.53590i q^{55} +(5.59808 + 1.50000i) q^{57} +(1.96410 + 7.33013i) q^{59} +(-3.00000 + 11.1962i) q^{61} -8.19615i q^{63} +(1.80385 + 3.12436i) q^{65} +(-6.59808 + 1.76795i) q^{67} -8.19615 q^{69} -2.92820i q^{71} -6.26795i q^{73} +(3.40192 - 5.89230i) q^{75} +(11.5622 - 3.09808i) q^{77} +(6.00000 + 10.3923i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-0.366025 + 1.36603i) q^{83} +(1.53590 + 5.73205i) q^{85} +(1.09808 + 4.09808i) q^{87} -2.00000i q^{89} +(-6.73205 + 6.73205i) q^{91} -0.928203i q^{93} +(1.73205 - 3.00000i) q^{95} +(-5.86603 - 10.1603i) q^{97} +(9.29423 - 9.29423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 6q^{3} - 8q^{5} + 6q^{7} + 6q^{9} + O(q^{10}) \) \( 4q + 6q^{3} - 8q^{5} + 6q^{7} + 6q^{9} + 10q^{11} - 10q^{13} - 12q^{15} - 16q^{17} + 6q^{19} + 6q^{21} - 6q^{23} + 24q^{25} - 6q^{29} + 8q^{31} + 12q^{33} - 8q^{35} + 12q^{37} - 24q^{39} + 16q^{43} - 12q^{45} + 2q^{47} - 6q^{49} - 24q^{51} - 16q^{53} + 12q^{57} - 6q^{59} - 12q^{61} + 28q^{65} - 16q^{67} - 12q^{69} + 24q^{75} + 22q^{77} + 24q^{79} - 18q^{81} + 2q^{83} + 20q^{85} - 6q^{87} - 20q^{91} - 20q^{97} + 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.50000 0.866025i 0.866025 0.500000i
\(4\) 0 0
\(5\) −0.267949 1.00000i −0.119831 0.447214i 0.879772 0.475395i \(-0.157695\pi\)
−0.999603 + 0.0281817i \(0.991028\pi\)
\(6\) 0 0
\(7\) 2.36603 1.36603i 0.894274 0.516309i 0.0189356 0.999821i \(-0.493972\pi\)
0.875338 + 0.483512i \(0.160639\pi\)
\(8\) 0 0
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) 0 0
\(11\) 4.23205 + 1.13397i 1.27601 + 0.341906i 0.832331 0.554279i \(-0.187006\pi\)
0.443680 + 0.896185i \(0.353673\pi\)
\(12\) 0 0
\(13\) −3.36603 + 0.901924i −0.933567 + 0.250149i −0.693375 0.720577i \(-0.743877\pi\)
−0.240192 + 0.970725i \(0.577210\pi\)
\(14\) 0 0
\(15\) −1.26795 1.26795i −0.327383 0.327383i
\(16\) 0 0
\(17\) −5.73205 −1.39023 −0.695113 0.718900i \(-0.744646\pi\)
−0.695113 + 0.718900i \(0.744646\pi\)
\(18\) 0 0
\(19\) 2.36603 + 2.36603i 0.542803 + 0.542803i 0.924350 0.381546i \(-0.124608\pi\)
−0.381546 + 0.924350i \(0.624608\pi\)
\(20\) 0 0
\(21\) 2.36603 4.09808i 0.516309 0.894274i
\(22\) 0 0
\(23\) −4.09808 2.36603i −0.854508 0.493350i 0.00766135 0.999971i \(-0.497561\pi\)
−0.862169 + 0.506620i \(0.830895\pi\)
\(24\) 0 0
\(25\) 3.40192 1.96410i 0.680385 0.392820i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) −0.633975 + 2.36603i −0.117726 + 0.439360i −0.999476 0.0323566i \(-0.989699\pi\)
0.881750 + 0.471717i \(0.156365\pi\)
\(30\) 0 0
\(31\) 0.267949 0.464102i 0.0481251 0.0833551i −0.840959 0.541098i \(-0.818009\pi\)
0.889085 + 0.457743i \(0.151342\pi\)
\(32\) 0 0
\(33\) 7.33013 1.96410i 1.27601 0.341906i
\(34\) 0 0
\(35\) −2.00000 2.00000i −0.338062 0.338062i
\(36\) 0 0
\(37\) 4.73205 4.73205i 0.777944 0.777944i −0.201537 0.979481i \(-0.564594\pi\)
0.979481 + 0.201537i \(0.0645935\pi\)
\(38\) 0 0
\(39\) −4.26795 + 4.26795i −0.683419 + 0.683419i
\(40\) 0 0
\(41\) 2.59808 + 1.50000i 0.405751 + 0.234261i 0.688963 0.724797i \(-0.258066\pi\)
−0.283211 + 0.959058i \(0.591400\pi\)
\(42\) 0 0
\(43\) 8.33013 + 2.23205i 1.27033 + 0.340385i 0.830158 0.557528i \(-0.188250\pi\)
0.440174 + 0.897912i \(0.354917\pi\)
\(44\) 0 0
\(45\) −3.00000 0.803848i −0.447214 0.119831i
\(46\) 0 0
\(47\) −3.83013 6.63397i −0.558681 0.967665i −0.997607 0.0691412i \(-0.977974\pi\)
0.438925 0.898523i \(-0.355359\pi\)
\(48\) 0 0
\(49\) 0.232051 0.401924i 0.0331501 0.0574177i
\(50\) 0 0
\(51\) −8.59808 + 4.96410i −1.20397 + 0.695113i
\(52\) 0 0
\(53\) −7.46410 + 7.46410i −1.02527 + 1.02527i −0.0256010 + 0.999672i \(0.508150\pi\)
−0.999672 + 0.0256010i \(0.991850\pi\)
\(54\) 0 0
\(55\) 4.53590i 0.611620i
\(56\) 0 0
\(57\) 5.59808 + 1.50000i 0.741483 + 0.198680i
\(58\) 0 0
\(59\) 1.96410 + 7.33013i 0.255704 + 0.954301i 0.967697 + 0.252115i \(0.0811261\pi\)
−0.711993 + 0.702186i \(0.752207\pi\)
\(60\) 0 0
\(61\) −3.00000 + 11.1962i −0.384111 + 1.43352i 0.455453 + 0.890260i \(0.349477\pi\)
−0.839564 + 0.543261i \(0.817189\pi\)
\(62\) 0 0
\(63\) 8.19615i 1.03262i
\(64\) 0 0
\(65\) 1.80385 + 3.12436i 0.223740 + 0.387529i
\(66\) 0 0
\(67\) −6.59808 + 1.76795i −0.806083 + 0.215989i −0.638253 0.769827i \(-0.720343\pi\)
−0.167830 + 0.985816i \(0.553676\pi\)
\(68\) 0 0
\(69\) −8.19615 −0.986701
\(70\) 0 0
\(71\) 2.92820i 0.347514i −0.984789 0.173757i \(-0.944409\pi\)
0.984789 0.173757i \(-0.0555907\pi\)
\(72\) 0 0
\(73\) 6.26795i 0.733608i −0.930298 0.366804i \(-0.880452\pi\)
0.930298 0.366804i \(-0.119548\pi\)
\(74\) 0 0
\(75\) 3.40192 5.89230i 0.392820 0.680385i
\(76\) 0 0
\(77\) 11.5622 3.09808i 1.31763 0.353059i
\(78\) 0 0
\(79\) 6.00000 + 10.3923i 0.675053 + 1.16923i 0.976453 + 0.215728i \(0.0692125\pi\)
−0.301401 + 0.953498i \(0.597454\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 0 0
\(83\) −0.366025 + 1.36603i −0.0401765 + 0.149941i −0.983100 0.183068i \(-0.941397\pi\)
0.942924 + 0.333009i \(0.108064\pi\)
\(84\) 0 0
\(85\) 1.53590 + 5.73205i 0.166592 + 0.621728i
\(86\) 0 0
\(87\) 1.09808 + 4.09808i 0.117726 + 0.439360i
\(88\) 0 0
\(89\) 2.00000i 0.212000i −0.994366 0.106000i \(-0.966196\pi\)
0.994366 0.106000i \(-0.0338043\pi\)
\(90\) 0 0
\(91\) −6.73205 + 6.73205i −0.705711 + 0.705711i
\(92\) 0 0
\(93\) 0.928203i 0.0962502i
\(94\) 0 0
\(95\) 1.73205 3.00000i 0.177705 0.307794i
\(96\) 0 0
\(97\) −5.86603 10.1603i −0.595605 1.03162i −0.993461 0.114170i \(-0.963579\pi\)
0.397857 0.917448i \(-0.369754\pi\)
\(98\) 0 0
\(99\) 9.29423 9.29423i 0.934105 0.934105i
\(100\) 0 0
\(101\) −2.00000 0.535898i −0.199007 0.0533239i 0.157938 0.987449i \(-0.449515\pi\)
−0.356946 + 0.934125i \(0.616182\pi\)
\(102\) 0 0
\(103\) 13.0981 + 7.56218i 1.29059 + 0.745124i 0.978759 0.205014i \(-0.0657238\pi\)
0.311833 + 0.950137i \(0.399057\pi\)
\(104\) 0 0
\(105\) −4.73205 1.26795i −0.461801 0.123739i
\(106\) 0 0
\(107\) −12.4904 + 12.4904i −1.20749 + 1.20749i −0.235654 + 0.971837i \(0.575723\pi\)
−0.971837 + 0.235654i \(0.924277\pi\)
\(108\) 0 0
\(109\) 10.7321 + 10.7321i 1.02794 + 1.02794i 0.999598 + 0.0283459i \(0.00902398\pi\)
0.0283459 + 0.999598i \(0.490976\pi\)
\(110\) 0 0
\(111\) 3.00000 11.1962i 0.284747 1.06269i
\(112\) 0 0
\(113\) −6.92820 + 12.0000i −0.651751 + 1.12887i 0.330947 + 0.943649i \(0.392632\pi\)
−0.982698 + 0.185216i \(0.940702\pi\)
\(114\) 0 0
\(115\) −1.26795 + 4.73205i −0.118237 + 0.441266i
\(116\) 0 0
\(117\) −2.70577 + 10.0981i −0.250149 + 0.933567i
\(118\) 0 0
\(119\) −13.5622 + 7.83013i −1.24324 + 0.717787i
\(120\) 0 0
\(121\) 7.09808 + 4.09808i 0.645280 + 0.372552i
\(122\) 0 0
\(123\) 5.19615 0.468521
\(124\) 0 0
\(125\) −6.53590 6.53590i −0.584589 0.584589i
\(126\) 0 0
\(127\) −4.19615 −0.372348 −0.186174 0.982517i \(-0.559609\pi\)
−0.186174 + 0.982517i \(0.559609\pi\)
\(128\) 0 0
\(129\) 14.4282 3.86603i 1.27033 0.340385i
\(130\) 0 0
\(131\) 7.83013 2.09808i 0.684121 0.183310i 0.100014 0.994986i \(-0.468111\pi\)
0.584108 + 0.811676i \(0.301445\pi\)
\(132\) 0 0
\(133\) 8.83013 + 2.36603i 0.765669 + 0.205160i
\(134\) 0 0
\(135\) −5.19615 + 1.39230i −0.447214 + 0.119831i
\(136\) 0 0
\(137\) −8.25833 + 4.76795i −0.705557 + 0.407353i −0.809414 0.587239i \(-0.800215\pi\)
0.103857 + 0.994592i \(0.466882\pi\)
\(138\) 0 0
\(139\) −3.06218 11.4282i −0.259731 0.969328i −0.965397 0.260784i \(-0.916019\pi\)
0.705667 0.708544i \(-0.250648\pi\)
\(140\) 0 0
\(141\) −11.4904 6.63397i −0.967665 0.558681i
\(142\) 0 0
\(143\) −15.2679 −1.27677
\(144\) 0 0
\(145\) 2.53590 0.210595
\(146\) 0 0
\(147\) 0.803848i 0.0663002i
\(148\) 0 0
\(149\) −2.09808 7.83013i −0.171881 0.641469i −0.997062 0.0766003i \(-0.975593\pi\)
0.825181 0.564869i \(-0.191073\pi\)
\(150\) 0 0
\(151\) 0.633975 0.366025i 0.0515921 0.0297867i −0.473982 0.880534i \(-0.657184\pi\)
0.525574 + 0.850748i \(0.323851\pi\)
\(152\) 0 0
\(153\) −8.59808 + 14.8923i −0.695113 + 1.20397i
\(154\) 0 0
\(155\) −0.535898 0.143594i −0.0430444 0.0115337i
\(156\) 0 0
\(157\) −4.73205 + 1.26795i −0.377659 + 0.101193i −0.442655 0.896692i \(-0.645963\pi\)
0.0649959 + 0.997886i \(0.479297\pi\)
\(158\) 0 0
\(159\) −4.73205 + 17.6603i −0.375276 + 1.40055i
\(160\) 0 0
\(161\) −12.9282 −1.01889
\(162\) 0 0
\(163\) 7.00000 + 7.00000i 0.548282 + 0.548282i 0.925944 0.377661i \(-0.123272\pi\)
−0.377661 + 0.925944i \(0.623272\pi\)
\(164\) 0 0
\(165\) −3.92820 6.80385i −0.305810 0.529679i
\(166\) 0 0
\(167\) 6.46410 + 3.73205i 0.500207 + 0.288795i 0.728799 0.684728i \(-0.240079\pi\)
−0.228592 + 0.973522i \(0.573412\pi\)
\(168\) 0 0
\(169\) −0.741670 + 0.428203i −0.0570515 + 0.0329387i
\(170\) 0 0
\(171\) 9.69615 2.59808i 0.741483 0.198680i
\(172\) 0 0
\(173\) −0.437822 + 1.63397i −0.0332870 + 0.124229i −0.980570 0.196169i \(-0.937150\pi\)
0.947283 + 0.320398i \(0.103817\pi\)
\(174\) 0 0
\(175\) 5.36603 9.29423i 0.405633 0.702578i
\(176\) 0 0
\(177\) 9.29423 + 9.29423i 0.698597 + 0.698597i
\(178\) 0 0
\(179\) 1.92820 + 1.92820i 0.144121 + 0.144121i 0.775486 0.631365i \(-0.217505\pi\)
−0.631365 + 0.775486i \(0.717505\pi\)
\(180\) 0 0
\(181\) −7.39230 + 7.39230i −0.549466 + 0.549466i −0.926286 0.376821i \(-0.877017\pi\)
0.376821 + 0.926286i \(0.377017\pi\)
\(182\) 0 0
\(183\) 5.19615 + 19.3923i 0.384111 + 1.43352i
\(184\) 0 0
\(185\) −6.00000 3.46410i −0.441129 0.254686i
\(186\) 0 0
\(187\) −24.2583 6.50000i −1.77394 0.475327i
\(188\) 0 0
\(189\) −7.09808 12.2942i −0.516309 0.894274i
\(190\) 0 0
\(191\) 12.0263 + 20.8301i 0.870191 + 1.50722i 0.861799 + 0.507250i \(0.169338\pi\)
0.00839227 + 0.999965i \(0.497329\pi\)
\(192\) 0 0
\(193\) −10.8660 + 18.8205i −0.782154 + 1.35473i 0.148531 + 0.988908i \(0.452545\pi\)
−0.930685 + 0.365822i \(0.880788\pi\)
\(194\) 0 0
\(195\) 5.41154 + 3.12436i 0.387529 + 0.223740i
\(196\) 0 0
\(197\) 13.6603 13.6603i 0.973253 0.973253i −0.0263987 0.999651i \(-0.508404\pi\)
0.999651 + 0.0263987i \(0.00840394\pi\)
\(198\) 0 0
\(199\) 25.1244i 1.78102i −0.454965 0.890509i \(-0.650348\pi\)
0.454965 0.890509i \(-0.349652\pi\)
\(200\) 0 0
\(201\) −8.36603 + 8.36603i −0.590094 + 0.590094i
\(202\) 0 0
\(203\) 1.73205 + 6.46410i 0.121566 + 0.453691i
\(204\) 0 0
\(205\) 0.803848 3.00000i 0.0561432 0.209529i
\(206\) 0 0
\(207\) −12.2942 + 7.09808i −0.854508 + 0.493350i
\(208\) 0 0
\(209\) 7.33013 + 12.6962i 0.507035 + 0.878211i
\(210\) 0 0
\(211\) −4.09808 + 1.09808i −0.282123 + 0.0755947i −0.397106 0.917773i \(-0.629985\pi\)
0.114983 + 0.993367i \(0.463319\pi\)
\(212\) 0 0
\(213\) −2.53590 4.39230i −0.173757 0.300956i
\(214\) 0 0
\(215\) 8.92820i 0.608898i
\(216\) 0 0
\(217\) 1.46410i 0.0993897i
\(218\) 0 0
\(219\) −5.42820 9.40192i −0.366804 0.635323i
\(220\) 0 0
\(221\) 19.2942 5.16987i 1.29787 0.347763i
\(222\) 0 0
\(223\) 8.02628 + 13.9019i 0.537479 + 0.930942i 0.999039 + 0.0438324i \(0.0139568\pi\)
−0.461559 + 0.887109i \(0.652710\pi\)
\(224\) 0 0
\(225\) 11.7846i 0.785641i
\(226\) 0 0
\(227\) 0.571797 2.13397i 0.0379515 0.141637i −0.944351 0.328941i \(-0.893308\pi\)
0.982302 + 0.187304i \(0.0599750\pi\)
\(228\) 0 0
\(229\) −1.83013 6.83013i −0.120938 0.451347i 0.878724 0.477330i \(-0.158395\pi\)
−0.999662 + 0.0259823i \(0.991729\pi\)
\(230\) 0 0
\(231\) 14.6603 14.6603i 0.964574 0.964574i
\(232\) 0 0
\(233\) 3.19615i 0.209387i −0.994505 0.104693i \(-0.966614\pi\)
0.994505 0.104693i \(-0.0333861\pi\)
\(234\) 0 0
\(235\) −5.60770 + 5.60770i −0.365806 + 0.365806i
\(236\) 0 0
\(237\) 18.0000 + 10.3923i 1.16923 + 0.675053i
\(238\) 0 0
\(239\) 7.90192 13.6865i 0.511133 0.885308i −0.488784 0.872405i \(-0.662559\pi\)
0.999917 0.0129033i \(-0.00410736\pi\)
\(240\) 0 0
\(241\) −11.5981 20.0885i −0.747098 1.29401i −0.949208 0.314649i \(-0.898113\pi\)
0.202110 0.979363i \(-0.435220\pi\)
\(242\) 0 0
\(243\) −13.5000 7.79423i −0.866025 0.500000i
\(244\) 0 0
\(245\) −0.464102 0.124356i −0.0296504 0.00794479i
\(246\) 0 0
\(247\) −10.0981 5.83013i −0.642525 0.370962i
\(248\) 0 0
\(249\) 0.633975 + 2.36603i 0.0401765 + 0.149941i
\(250\) 0 0
\(251\) 5.83013 5.83013i 0.367994 0.367994i −0.498751 0.866745i \(-0.666208\pi\)
0.866745 + 0.498751i \(0.166208\pi\)
\(252\) 0 0
\(253\) −14.6603 14.6603i −0.921682 0.921682i
\(254\) 0 0
\(255\) 7.26795 + 7.26795i 0.455137 + 0.455137i
\(256\) 0 0
\(257\) 9.42820 16.3301i 0.588115 1.01865i −0.406364 0.913711i \(-0.633204\pi\)
0.994479 0.104934i \(-0.0334632\pi\)
\(258\) 0 0
\(259\) 4.73205 17.6603i 0.294035 1.09735i
\(260\) 0 0
\(261\) 5.19615 + 5.19615i 0.321634 + 0.321634i
\(262\) 0 0
\(263\) −2.49038 + 1.43782i −0.153563 + 0.0886599i −0.574813 0.818285i \(-0.694925\pi\)
0.421249 + 0.906945i \(0.361592\pi\)
\(264\) 0 0
\(265\) 9.46410 + 5.46410i 0.581375 + 0.335657i
\(266\) 0 0
\(267\) −1.73205 3.00000i −0.106000 0.183597i
\(268\) 0 0
\(269\) 1.26795 + 1.26795i 0.0773082 + 0.0773082i 0.744704 0.667395i \(-0.232591\pi\)
−0.667395 + 0.744704i \(0.732591\pi\)
\(270\) 0 0
\(271\) 0.392305 0.0238308 0.0119154 0.999929i \(-0.496207\pi\)
0.0119154 + 0.999929i \(0.496207\pi\)
\(272\) 0 0
\(273\) −4.26795 + 15.9282i −0.258308 + 0.964019i
\(274\) 0 0
\(275\) 16.6244 4.45448i 1.00249 0.268615i
\(276\) 0 0
\(277\) 25.2224 + 6.75833i 1.51547 + 0.406069i 0.918247 0.396007i \(-0.129605\pi\)
0.597222 + 0.802076i \(0.296271\pi\)
\(278\) 0 0
\(279\) −0.803848 1.39230i −0.0481251 0.0833551i
\(280\) 0 0
\(281\) 8.66025 5.00000i 0.516627 0.298275i −0.218926 0.975741i \(-0.570255\pi\)
0.735554 + 0.677466i \(0.236922\pi\)
\(282\) 0 0
\(283\) −5.24167 19.5622i −0.311585 1.16285i −0.927127 0.374747i \(-0.877730\pi\)
0.615542 0.788104i \(-0.288937\pi\)
\(284\) 0 0
\(285\) 6.00000i 0.355409i
\(286\) 0 0
\(287\) 8.19615 0.483804
\(288\) 0 0
\(289\) 15.8564 0.932730
\(290\) 0 0
\(291\) −17.5981 10.1603i −1.03162 0.595605i
\(292\) 0 0
\(293\) 1.43782 + 5.36603i 0.0839985 + 0.313487i 0.995123 0.0986454i \(-0.0314509\pi\)
−0.911124 + 0.412132i \(0.864784\pi\)
\(294\) 0 0
\(295\) 6.80385 3.92820i 0.396135 0.228709i
\(296\) 0 0
\(297\) 5.89230 21.9904i 0.341906 1.27601i
\(298\) 0 0
\(299\) 15.9282 + 4.26795i 0.921152 + 0.246822i
\(300\) 0 0
\(301\) 22.7583 6.09808i 1.31177 0.351487i
\(302\) 0 0
\(303\) −3.46410 + 0.928203i −0.199007 + 0.0533239i
\(304\) 0 0
\(305\) 12.0000 0.687118
\(306\) 0 0
\(307\) −3.02628 3.02628i −0.172719 0.172719i 0.615454 0.788173i \(-0.288973\pi\)
−0.788173 + 0.615454i \(0.788973\pi\)
\(308\) 0 0
\(309\) 26.1962 1.49025
\(310\) 0 0
\(311\) −19.0981 11.0263i −1.08295 0.625243i −0.151261 0.988494i \(-0.548333\pi\)
−0.931691 + 0.363251i \(0.881667\pi\)
\(312\) 0 0
\(313\) −18.6506 + 10.7679i −1.05420 + 0.608640i −0.923821 0.382824i \(-0.874951\pi\)
−0.130375 + 0.991465i \(0.541618\pi\)
\(314\) 0 0
\(315\) −8.19615 + 2.19615i −0.461801 + 0.123739i
\(316\) 0 0
\(317\) 5.50962 20.5622i 0.309451 1.15489i −0.619595 0.784922i \(-0.712703\pi\)
0.929046 0.369965i \(-0.120630\pi\)
\(318\) 0 0
\(319\) −5.36603 + 9.29423i −0.300440 + 0.520377i
\(320\) 0 0
\(321\) −7.91858 + 29.5526i −0.441972 + 1.64946i
\(322\) 0 0
\(323\) −13.5622 13.5622i −0.754620 0.754620i
\(324\) 0 0
\(325\) −9.67949 + 9.67949i −0.536922 + 0.536922i
\(326\) 0 0
\(327\) 25.3923 + 6.80385i 1.40420 + 0.376254i
\(328\) 0 0
\(329\) −18.1244 10.4641i −0.999228 0.576905i
\(330\) 0 0
\(331\) 0.0980762 + 0.0262794i 0.00539076 + 0.00144445i 0.261513 0.965200i \(-0.415778\pi\)
−0.256123 + 0.966644i \(0.582445\pi\)
\(332\) 0 0
\(333\) −5.19615 19.3923i −0.284747 1.06269i
\(334\) 0 0
\(335\) 3.53590 + 6.12436i 0.193187 + 0.334609i
\(336\) 0 0
\(337\) 8.89230 15.4019i 0.484395 0.838996i −0.515445 0.856923i \(-0.672373\pi\)
0.999839 + 0.0179267i \(0.00570654\pi\)
\(338\) 0 0
\(339\) 24.0000i 1.30350i
\(340\) 0 0
\(341\) 1.66025 1.66025i 0.0899078 0.0899078i
\(342\) 0 0
\(343\) 17.8564i 0.964155i
\(344\) 0 0
\(345\) 2.19615 + 8.19615i 0.118237 + 0.441266i
\(346\) 0 0
\(347\) −4.72243 17.6244i −0.253513 0.946125i −0.968911 0.247408i \(-0.920421\pi\)
0.715398 0.698717i \(-0.246245\pi\)
\(348\) 0 0
\(349\) −4.26795 + 15.9282i −0.228458 + 0.852617i 0.752531 + 0.658556i \(0.228833\pi\)
−0.980989 + 0.194061i \(0.937834\pi\)
\(350\) 0 0
\(351\) 4.68653 + 17.4904i 0.250149 + 0.933567i
\(352\) 0 0
\(353\) 7.16025 + 12.4019i 0.381102 + 0.660088i 0.991220 0.132223i \(-0.0422114\pi\)
−0.610118 + 0.792310i \(0.708878\pi\)
\(354\) 0 0
\(355\) −2.92820 + 0.784610i −0.155413 + 0.0416428i
\(356\) 0 0
\(357\) −13.5622 + 23.4904i −0.717787 + 1.24324i
\(358\) 0 0
\(359\) 11.2679i 0.594700i −0.954769 0.297350i \(-0.903897\pi\)
0.954769 0.297350i \(-0.0961028\pi\)
\(360\) 0 0
\(361\) 7.80385i 0.410729i
\(362\) 0 0
\(363\) 14.1962 0.745105
\(364\) 0 0
\(365\) −6.26795 + 1.67949i −0.328079 + 0.0879086i
\(366\) 0 0
\(367\) −14.1244 24.4641i −0.737285 1.27702i −0.953713 0.300717i \(-0.902774\pi\)
0.216428 0.976299i \(-0.430559\pi\)
\(368\) 0 0
\(369\) 7.79423 4.50000i 0.405751 0.234261i
\(370\) 0 0
\(371\) −7.46410 + 27.8564i −0.387517 + 1.44623i
\(372\) 0 0
\(373\) −7.36603 27.4904i −0.381398 1.42340i −0.843767 0.536710i \(-0.819667\pi\)
0.462368 0.886688i \(-0.347000\pi\)
\(374\) 0 0
\(375\) −15.4641 4.14359i −0.798563 0.213974i
\(376\) 0 0
\(377\) 8.53590i 0.439621i
\(378\) 0 0
\(379\) −3.75833 + 3.75833i −0.193052 + 0.193052i −0.797014 0.603961i \(-0.793588\pi\)
0.603961 + 0.797014i \(0.293588\pi\)
\(380\) 0 0
\(381\) −6.29423 + 3.63397i −0.322463 + 0.186174i
\(382\) 0 0
\(383\) 6.73205 11.6603i 0.343992 0.595811i −0.641178 0.767392i \(-0.721554\pi\)
0.985170 + 0.171581i \(0.0548874\pi\)
\(384\) 0 0
\(385\) −6.19615 10.7321i −0.315785 0.546956i
\(386\) 0 0
\(387\) 18.2942 18.2942i 0.929948 0.929948i
\(388\) 0 0
\(389\) 19.7583 + 5.29423i 1.00179 + 0.268428i 0.722194 0.691691i \(-0.243134\pi\)
0.279593 + 0.960119i \(0.409800\pi\)
\(390\) 0 0
\(391\) 23.4904 + 13.5622i 1.18796 + 0.685869i
\(392\) 0 0
\(393\) 9.92820 9.92820i 0.500812 0.500812i
\(394\) 0 0
\(395\) 8.78461 8.78461i 0.442002 0.442002i
\(396\) 0 0
\(397\) −9.26795 9.26795i −0.465145 0.465145i 0.435192 0.900337i \(-0.356680\pi\)
−0.900337 + 0.435192i \(0.856680\pi\)
\(398\) 0 0
\(399\) 15.2942 4.09808i 0.765669 0.205160i
\(400\) 0 0
\(401\) −1.79423 + 3.10770i −0.0895995 + 0.155191i −0.907342 0.420393i \(-0.861892\pi\)
0.817742 + 0.575584i \(0.195225\pi\)
\(402\) 0 0
\(403\) −0.483340 + 1.80385i −0.0240769 + 0.0898560i
\(404\) 0 0
\(405\) −6.58846 + 6.58846i −0.327383 + 0.327383i
\(406\) 0 0
\(407\) 25.3923 14.6603i 1.25865 0.726682i
\(408\) 0 0
\(409\) −27.8660 16.0885i −1.37789 0.795523i −0.385981 0.922507i \(-0.626137\pi\)
−0.991905 + 0.126984i \(0.959470\pi\)
\(410\) 0 0
\(411\) −8.25833 + 14.3038i −0.407353 + 0.705557i
\(412\) 0 0
\(413\) 14.6603 + 14.6603i 0.721384 + 0.721384i
\(414\) 0 0
\(415\) 1.46410 0.0718699
\(416\) 0 0
\(417\) −14.4904 14.4904i −0.709597 0.709597i
\(418\) 0 0
\(419\) 6.63397 1.77757i 0.324091 0.0868399i −0.0931055 0.995656i \(-0.529679\pi\)
0.417196 + 0.908816i \(0.363013\pi\)
\(420\) 0 0
\(421\) −30.5885 8.19615i −1.49079 0.399456i −0.580786 0.814056i \(-0.697255\pi\)
−0.910004 + 0.414600i \(0.863922\pi\)
\(422\) 0 0
\(423\) −22.9808 −1.11736
\(424\) 0 0
\(425\) −19.5000 + 11.2583i −0.945889 + 0.546109i
\(426\) 0 0
\(427\) 8.19615 + 30.5885i 0.396640 + 1.48028i
\(428\) 0 0
\(429\) −22.9019 + 13.2224i −1.10572 + 0.638385i
\(430\) 0 0
\(431\) 16.1962 0.780141 0.390071 0.920785i \(-0.372451\pi\)
0.390071 + 0.920785i \(0.372451\pi\)
\(432\) 0 0
\(433\) −5.73205 −0.275465 −0.137732 0.990469i \(-0.543981\pi\)
−0.137732 + 0.990469i \(0.543981\pi\)
\(434\) 0 0
\(435\) 3.80385 2.19615i 0.182381 0.105297i
\(436\) 0 0
\(437\) −4.09808 15.2942i −0.196038 0.731622i
\(438\) 0 0
\(439\) −22.8564 + 13.1962i −1.09088 + 0.629818i −0.933810 0.357770i \(-0.883537\pi\)
−0.157067 + 0.987588i \(0.550204\pi\)
\(440\) 0 0
\(441\) −0.696152 1.20577i −0.0331501 0.0574177i
\(442\) 0 0
\(443\) −17.2583 4.62436i −0.819968 0.219710i −0.175636 0.984455i \(-0.556198\pi\)
−0.644332 + 0.764745i \(0.722865\pi\)
\(444\) 0 0
\(445\) −2.00000 + 0.535898i −0.0948091 + 0.0254040i
\(446\) 0 0
\(447\) −9.92820 9.92820i −0.469588 0.469588i
\(448\) 0 0
\(449\) −3.33975 −0.157612 −0.0788062 0.996890i \(-0.525111\pi\)
−0.0788062 + 0.996890i \(0.525111\pi\)
\(450\) 0 0
\(451\) 9.29423 + 9.29423i 0.437648 + 0.437648i
\(452\) 0 0
\(453\) 0.633975 1.09808i 0.0297867 0.0515921i
\(454\) 0 0
\(455\) 8.53590 + 4.92820i 0.400169 + 0.231038i
\(456\) 0 0
\(457\) −2.25833 + 1.30385i −0.105640 + 0.0609914i −0.551889 0.833917i \(-0.686093\pi\)
0.446249 + 0.894909i \(0.352760\pi\)
\(458\) 0 0
\(459\) 29.7846i 1.39023i
\(460\) 0 0
\(461\) −9.56218 + 35.6865i −0.445355 + 1.66209i 0.269642 + 0.962961i \(0.413094\pi\)
−0.714997 + 0.699127i \(0.753572\pi\)
\(462\) 0 0
\(463\) −1.19615 + 2.07180i −0.0555899 + 0.0962846i −0.892481 0.451085i \(-0.851037\pi\)
0.836891 + 0.547369i \(0.184371\pi\)
\(464\) 0 0
\(465\) −0.928203 + 0.248711i −0.0430444 + 0.0115337i
\(466\) 0 0
\(467\) −2.63397 2.63397i −0.121886 0.121886i 0.643533 0.765419i \(-0.277468\pi\)
−0.765419 + 0.643533i \(0.777468\pi\)
\(468\) 0 0
\(469\) −13.1962 + 13.1962i −0.609342 + 0.609342i
\(470\) 0 0
\(471\) −6.00000 + 6.00000i −0.276465 + 0.276465i
\(472\) 0 0
\(473\) 32.7224 + 18.8923i 1.50458 + 0.868669i
\(474\) 0 0
\(475\) 12.6962 + 3.40192i 0.582539 + 0.156091i
\(476\) 0 0
\(477\) 8.19615 + 30.5885i 0.375276 + 1.40055i
\(478\) 0 0
\(479\) −4.16987 7.22243i −0.190526 0.330001i 0.754898 0.655842i \(-0.227686\pi\)
−0.945425 + 0.325840i \(0.894353\pi\)
\(480\) 0 0
\(481\) −11.6603 + 20.1962i −0.531662 + 0.920865i
\(482\) 0 0
\(483\) −19.3923 + 11.1962i −0.882380 + 0.509443i
\(484\) 0 0
\(485\) −8.58846 + 8.58846i −0.389982 + 0.389982i
\(486\) 0 0
\(487\) 5.80385i 0.262997i −0.991316 0.131499i \(-0.958021\pi\)
0.991316 0.131499i \(-0.0419789\pi\)
\(488\) 0 0
\(489\) 16.5622 + 4.43782i 0.748968 + 0.200685i
\(490\) 0 0
\(491\) −3.72243 13.8923i −0.167991 0.626951i −0.997640 0.0686652i \(-0.978126\pi\)
0.829649 0.558286i \(-0.188541\pi\)
\(492\) 0 0
\(493\) 3.63397 13.5622i 0.163666 0.610810i
\(494\) 0 0
\(495\) −11.7846 6.80385i −0.529679 0.305810i
\(496\) 0 0
\(497\) −4.00000 6.92820i −0.179425 0.310772i
\(498\) 0 0
\(499\) −8.69615 + 2.33013i −0.389293 + 0.104311i −0.448156 0.893955i \(-0.647919\pi\)
0.0588630 + 0.998266i \(0.481252\pi\)
\(500\) 0 0
\(501\) 12.9282 0.577590
\(502\) 0 0
\(503\) 27.7128i 1.23565i 0.786314 + 0.617827i \(0.211987\pi\)
−0.786314 + 0.617827i \(0.788013\pi\)
\(504\) 0 0
\(505\) 2.14359i 0.0953887i
\(506\) 0 0
\(507\) −0.741670 + 1.28461i −0.0329387 + 0.0570515i
\(508\) 0 0
\(509\) −11.4641 + 3.07180i −0.508137 + 0.136155i −0.503774 0.863835i \(-0.668056\pi\)
−0.00436335 + 0.999990i \(0.501389\pi\)
\(510\) 0 0
\(511\) −8.56218 14.8301i −0.378768 0.656046i
\(512\) 0 0
\(513\) 12.2942 12.2942i 0.542803 0.542803i
\(514\) 0 0
\(515\) 4.05256 15.1244i 0.178577 0.666459i
\(516\) 0 0
\(517\) −8.68653 32.4186i −0.382033 1.42577i
\(518\) 0 0
\(519\) 0.758330 + 2.83013i 0.0332870 + 0.124229i
\(520\) 0 0
\(521\) 13.0000i 0.569540i 0.958596 + 0.284770i \(0.0919173\pi\)
−0.958596 + 0.284770i \(0.908083\pi\)
\(522\) 0 0
\(523\) 7.53590 7.53590i 0.329522 0.329522i −0.522883 0.852405i \(-0.675143\pi\)
0.852405 + 0.522883i \(0.175143\pi\)
\(524\) 0 0
\(525\) 18.5885i 0.811267i
\(526\) 0 0
\(527\) −1.53590 + 2.66025i −0.0669048 + 0.115882i
\(528\) 0 0
\(529\) −0.303848 0.526279i −0.0132108 0.0228817i
\(530\) 0 0
\(531\) 21.9904 + 5.89230i 0.954301 + 0.255704i
\(532\) 0 0
\(533\) −10.0981 2.70577i −0.437396 0.117200i
\(534\) 0 0
\(535\) 15.8372 + 9.14359i 0.684701 + 0.395312i
\(536\) 0 0
\(537\) 4.56218 + 1.22243i 0.196873 + 0.0527518i
\(538\) 0 0
\(539\) 1.43782 1.43782i 0.0619314 0.0619314i
\(540\) 0 0
\(541\) 2.19615 + 2.19615i 0.0944200 + 0.0944200i 0.752739 0.658319i \(-0.228732\pi\)
−0.658319 + 0.752739i \(0.728732\pi\)
\(542\) 0 0
\(543\) −4.68653 + 17.4904i −0.201118 + 0.750584i
\(544\) 0 0
\(545\) 7.85641 13.6077i 0.336531 0.582890i
\(546\) 0 0
\(547\) 8.74167 32.6244i 0.373767 1.39492i −0.481371 0.876517i \(-0.659861\pi\)
0.855138 0.518400i \(-0.173472\pi\)
\(548\) 0 0
\(549\) 24.5885 + 24.5885i 1.04941 + 1.04941i
\(550\) 0 0
\(551\) −7.09808 + 4.09808i −0.302388 + 0.174584i
\(552\) 0 0
\(553\) 28.3923 + 16.3923i 1.20736 + 0.697072i
\(554\) 0 0
\(555\) −12.0000 −0.509372
\(556\) 0 0
\(557\) −14.8038 14.8038i −0.627259 0.627259i 0.320118 0.947378i \(-0.396277\pi\)
−0.947378 + 0.320118i \(0.896277\pi\)
\(558\) 0 0
\(559\) −30.0526 −1.27109
\(560\) 0 0
\(561\) −42.0167 + 11.2583i −1.77394 + 0.475327i
\(562\) 0 0
\(563\) −26.9904 + 7.23205i −1.13751 + 0.304795i −0.777949 0.628327i \(-0.783740\pi\)
−0.359560 + 0.933122i \(0.617073\pi\)
\(564\) 0 0
\(565\) 13.8564 + 3.71281i 0.582943 + 0.156199i
\(566\) 0 0
\(567\) −21.2942 12.2942i −0.894274 0.516309i
\(568\) 0 0
\(569\) 18.4019 10.6244i 0.771449 0.445396i −0.0619424 0.998080i \(-0.519730\pi\)
0.833391 + 0.552684i \(0.186396\pi\)
\(570\) 0 0
\(571\) −0.892305 3.33013i −0.0373418 0.139361i 0.944738 0.327825i \(-0.106316\pi\)
−0.982080 + 0.188464i \(0.939649\pi\)
\(572\) 0 0
\(573\) 36.0788 + 20.8301i 1.50722 + 0.870191i
\(574\) 0 0
\(575\) −18.5885 −0.775192
\(576\) 0 0
\(577\) −5.78461 −0.240816 −0.120408 0.992724i \(-0.538420\pi\)
−0.120408 + 0.992724i \(0.538420\pi\)
\(578\) 0 0
\(579\) 37.6410i 1.56431i
\(580\) 0 0
\(581\) 1.00000 + 3.73205i 0.0414870 + 0.154832i
\(582\) 0 0
\(583\) −40.0526 + 23.1244i −1.65881 + 0.957713i
\(584\) 0 0
\(585\) 10.8231 0.447480
\(586\) 0 0
\(587\) 26.9904 + 7.23205i 1.11401 + 0.298499i 0.768458 0.639900i \(-0.221024\pi\)
0.345554 + 0.938399i \(0.387691\pi\)
\(588\) 0 0
\(589\) 1.73205 0.464102i 0.0713679 0.0191230i
\(590\) 0 0
\(591\) 8.66025 32.3205i 0.356235 1.32949i
\(592\) 0 0
\(593\) 17.4641 0.717165 0.358582 0.933498i \(-0.383260\pi\)
0.358582 + 0.933498i \(0.383260\pi\)
\(594\) 0 0
\(595\) 11.4641 + 11.4641i 0.469982 + 0.469982i
\(596\) 0 0
\(597\) −21.7583 37.6865i −0.890509 1.54241i
\(598\) 0 0
\(599\) 11.3205 + 6.53590i 0.462543 + 0.267050i 0.713113 0.701049i \(-0.247285\pi\)
−0.250570 + 0.968099i \(0.580618\pi\)
\(600\) 0 0
\(601\) 20.5526 11.8660i 0.838356 0.484025i −0.0183488 0.999832i \(-0.505841\pi\)
0.856705 + 0.515806i \(0.172508\pi\)
\(602\) 0 0
\(603\) −5.30385 + 19.7942i −0.215989 + 0.806083i
\(604\) 0 0
\(605\) 2.19615 8.19615i 0.0892863 0.333221i
\(606\) 0 0
\(607\) 8.58846 14.8756i 0.348595 0.603784i −0.637405 0.770529i \(-0.719992\pi\)
0.986000 + 0.166745i \(0.0533256\pi\)
\(608\) 0 0
\(609\) 8.19615 + 8.19615i 0.332125 + 0.332125i
\(610\) 0 0
\(611\) 18.8756 + 18.8756i 0.763627 + 0.763627i
\(612\) 0 0
\(613\) −15.6603 + 15.6603i −0.632512 + 0.632512i −0.948697 0.316186i \(-0.897598\pi\)
0.316186 + 0.948697i \(0.397598\pi\)
\(614\) 0 0
\(615\) −1.39230 5.19615i −0.0561432 0.209529i
\(616\) 0 0
\(617\) 35.0885 + 20.2583i 1.41261 + 0.815570i 0.995633 0.0933485i \(-0.0297571\pi\)
0.416975 + 0.908918i \(0.363090\pi\)
\(618\) 0 0
\(619\) 15.5981 + 4.17949i 0.626940 + 0.167988i 0.558281 0.829652i \(-0.311461\pi\)
0.0686590 + 0.997640i \(0.478128\pi\)
\(620\) 0 0
\(621\) −12.2942 + 21.2942i −0.493350 + 0.854508i
\(622\) 0 0
\(623\) −2.73205 4.73205i −0.109457 0.189586i
\(624\) 0 0
\(625\) 5.03590 8.72243i 0.201436 0.348897i
\(626\) 0 0
\(627\) 21.9904 + 12.6962i 0.878211 + 0.507035i
\(628\) 0 0
\(629\) −27.1244 + 27.1244i −1.08152 + 1.08152i
\(630\) 0 0
\(631\) 17.6077i 0.700951i −0.936572 0.350476i \(-0.886020\pi\)
0.936572 0.350476i \(-0.113980\pi\)
\(632\) 0 0
\(633\) −5.19615 + 5.19615i −0.206529 + 0.206529i
\(634\) 0 0
\(635\) 1.12436 + 4.19615i 0.0446187 + 0.166519i
\(636\) 0 0
\(637\) −0.418584 + 1.56218i −0.0165849 + 0.0618957i
\(638\) 0 0
\(639\) −7.60770 4.39230i −0.300956 0.173757i
\(640\) 0 0
\(641\) −19.7942 34.2846i −0.781825 1.35416i −0.930878 0.365331i \(-0.880956\pi\)
0.149053 0.988829i \(-0.452378\pi\)
\(642\) 0 0
\(643\) −8.76795 + 2.34936i −0.345774 + 0.0926499i −0.427527 0.904003i \(-0.640615\pi\)
0.0817525 + 0.996653i \(0.473948\pi\)
\(644\) 0 0
\(645\) −7.73205 13.3923i −0.304449 0.527321i
\(646\) 0 0
\(647\) 16.7321i 0.657805i −0.944364 0.328902i \(-0.893321\pi\)
0.944364 0.328902i \(-0.106679\pi\)
\(648\) 0 0
\(649\) 33.2487i 1.30513i
\(650\) 0 0
\(651\) −1.26795 2.19615i −0.0496948 0.0860740i
\(652\) 0 0
\(653\) −27.4904 + 7.36603i −1.07578 + 0.288255i −0.752867 0.658173i \(-0.771329\pi\)
−0.322915 + 0.946428i \(0.604663\pi\)
\(654\) 0 0
\(655\) −4.19615 7.26795i −0.163957 0.283982i
\(656\) 0 0
\(657\) −16.2846 9.40192i −0.635323 0.366804i
\(658\) 0 0
\(659\) −4.02628 + 15.0263i −0.156842 + 0.585341i 0.842099 + 0.539323i \(0.181320\pi\)
−0.998941 + 0.0460178i \(0.985347\pi\)
\(660\) 0 0
\(661\) 2.19615 + 8.19615i 0.0854204 + 0.318793i 0.995393 0.0958740i \(-0.0305646\pi\)
−0.909973 + 0.414667i \(0.863898\pi\)
\(662\) 0 0
\(663\) 24.4641 24.4641i 0.950107 0.950107i
\(664\) 0 0
\(665\) 9.46410i 0.367002i
\(666\) 0 0
\(667\) 8.19615 8.19615i 0.317356 0.317356i
\(668\) 0 0
\(669\) 24.0788 + 13.9019i 0.930942 + 0.537479i
\(670\) 0 0
\(671\) −25.3923 + 43.9808i −0.980259 + 1.69786i
\(672\) 0 0
\(673\) 19.1962 + 33.2487i 0.739957 + 1.28164i 0.952514 + 0.304495i \(0.0984877\pi\)
−0.212557 + 0.977149i \(0.568179\pi\)
\(674\) 0 0
\(675\) −10.2058 17.6769i −0.392820 0.680385i
\(676\) 0 0
\(677\) −4.73205 1.26795i −0.181867 0.0487312i 0.166736 0.986002i \(-0.446677\pi\)
−0.348603 + 0.937270i \(0.613344\pi\)
\(678\) 0 0
\(679\) −27.7583 16.0263i −1.06527 0.615032i
\(680\) 0 0
\(681\) −0.990381 3.69615i −0.0379515 0.141637i
\(682\) 0 0
\(683\) 20.2942 20.2942i 0.776537 0.776537i −0.202703 0.979240i \(-0.564973\pi\)
0.979240 + 0.202703i \(0.0649726\pi\)
\(684\) 0 0
\(685\) 6.98076 + 6.98076i 0.266721 + 0.266721i
\(686\) 0 0
\(687\) −8.66025 8.66025i −0.330409 0.330409i
\(688\) 0 0
\(689\) 18.3923 31.8564i 0.700691 1.21363i
\(690\) 0 0
\(691\) 2.49038 9.29423i 0.0947386 0.353569i −0.902241 0.431232i \(-0.858079\pi\)
0.996980 + 0.0776628i \(0.0247457\pi\)
\(692\) 0 0
\(693\) 9.29423 34.6865i 0.353059 1.31763i
\(694\) 0 0
\(695\) −10.6077 + 6.12436i −0.402373 + 0.232310i
\(696\) 0 0
\(697\) −14.8923 8.59808i −0.564086 0.325675i
\(698\) 0 0
\(699\) −2.76795 4.79423i −0.104693 0.181334i
\(700\) 0 0
\(701\) −6.66025 6.66025i −0.251554 0.251554i 0.570053 0.821608i \(-0.306923\pi\)
−0.821608 + 0.570053i \(0.806923\pi\)
\(702\) 0 0
\(703\) 22.3923 0.844542
\(704\) 0 0
\(705\) −3.55514 + 13.2679i −0.133894 + 0.499700i
\(706\) 0 0
\(707\) −5.46410 + 1.46410i −0.205499 + 0.0550632i
\(708\) 0 0
\(709\) 36.5885 + 9.80385i 1.37411 + 0.368191i 0.868978 0.494852i \(-0.164778\pi\)
0.505131 + 0.863043i \(0.331444\pi\)
\(710\) 0 0
\(711\) 36.0000 1.35011
\(712\) 0 0
\(713\) −2.19615 + 1.26795i −0.0822466 + 0.0474851i
\(714\) 0 0
\(715\) 4.09103 + 15.2679i 0.152996 + 0.570989i
\(716\) 0 0
\(717\) 27.3731i 1.02227i
\(718\) 0 0
\(719\) −4.39230 −0.163805 −0.0819027 0.996640i \(-0.526100\pi\)
−0.0819027 + 0.996640i \(0.526100\pi\)
\(720\) 0 0
\(721\) 41.3205 1.53886
\(722\) 0 0
\(723\) −34.7942 20.0885i −1.29401 0.747098i
\(724\) 0 0
\(725\) 2.49038 + 9.29423i 0.0924904 + 0.345179i
\(726\) 0 0
\(727\) −28.8109 + 16.6340i −1.06854 + 0.616920i −0.927781 0.373124i \(-0.878286\pi\)
−0.140755 + 0.990044i \(0.544953\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −47.7487 12.7942i −1.76605 0.473212i
\(732\) 0 0
\(733\) −11.0263 + 2.95448i −0.407265 + 0.109126i −0.456635 0.889654i \(-0.650945\pi\)
0.0493698 + 0.998781i \(0.484279\pi\)
\(734\) 0 0
\(735\) −0.803848 + 0.215390i −0.0296504 + 0.00794479i
\(736\) 0 0
\(737\) −29.9282 −1.10242
\(738\) 0 0
\(739\) 8.22243 + 8.22243i 0.302467 + 0.302467i 0.841978 0.539511i \(-0.181391\pi\)
−0.539511 + 0.841978i \(0.681391\pi\)
\(740\) 0 0
\(741\) −20.1962 −0.741924
\(742\) 0 0
\(743\) 24.7583 + 14.2942i 0.908295 + 0.524404i 0.879882 0.475192i \(-0.157621\pi\)
0.0284129 + 0.999596i \(0.490955\pi\)
\(744\) 0 0
\(745\) −7.26795 + 4.19615i −0.266277 + 0.153735i
\(746\) 0 0
\(747\) 3.00000 + 3.00000i 0.109764 + 0.109764i
\(748\) 0 0
\(749\) −12.4904 + 46.6147i −0.456389 + 1.70327i
\(750\) 0 0
\(751\) 8.85641 15.3397i 0.323175 0.559755i −0.657966 0.753047i \(-0.728583\pi\)
0.981141 + 0.193292i \(0.0619165\pi\)
\(752\) 0 0
\(753\) 3.69615 13.7942i 0.134695 0.502690i
\(754\) 0 0
\(755\) −0.535898 0.535898i −0.0195033 0.0195033i
\(756\) 0 0
\(757\) −19.9282 + 19.9282i −0.724303 + 0.724303i −0.969479 0.245176i \(-0.921154\pi\)
0.245176 + 0.969479i \(0.421154\pi\)
\(758\) 0 0
\(759\) −34.6865 9.29423i −1.25904 0.337359i
\(760\) 0 0
\(761\) −45.3731 26.1962i −1.64477 0.949610i −0.979104 0.203363i \(-0.934813\pi\)
−0.665669 0.746247i \(-0.731854\pi\)
\(762\) 0 0
\(763\) 40.0526 + 10.7321i 1.45000 + 0.388526i
\(764\) 0 0
\(765\) 17.1962 + 4.60770i 0.621728 + 0.166592i
\(766\) 0 0
\(767\) −13.2224 22.9019i −0.477434 0.826941i
\(768\) 0 0
\(769\) −14.1244 + 24.4641i −0.509337 + 0.882198i 0.490604 + 0.871383i \(0.336776\pi\)
−0.999942 + 0.0108155i \(0.996557\pi\)
\(770\) 0 0
\(771\) 32.6603i 1.17623i
\(772\) 0 0
\(773\) 35.5885 35.5885i 1.28003 1.28003i 0.339378 0.940650i \(-0.389784\pi\)
0.940650 0.339378i \(-0.110216\pi\)
\(774\) 0 0
\(775\) 2.10512i 0.0756181i
\(776\) 0 0
\(777\) −8.19615 30.5885i −0.294035 1.09735i
\(778\) 0 0
\(779\) 2.59808 + 9.69615i 0.0930857 + 0.347401i
\(780\) 0 0
\(781\) 3.32051 12.3923i 0.118817 0.443432i
\(782\) 0 0
\(783\) 12.2942 + 3.29423i 0.439360 + 0.117726i
\(784\) 0 0
\(785\) 2.53590 + 4.39230i 0.0905101 + 0.156768i
\(786\) 0 0
\(787\) −40.3468 + 10.8109i −1.43821 + 0.385367i −0.891906 0.452222i \(-0.850632\pi\)
−0.546302 + 0.837588i \(0.683965\pi\)
\(788\) 0 0
\(789\) −2.49038 + 4.31347i −0.0886599 + 0.153563i
\(790\) 0 0
\(791\) 37.8564i 1.34602i
\(792\) 0 0
\(793\) 40.3923i