Properties

Label 576.2.bb.d.241.1
Level $576$
Weight $2$
Character 576.241
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 241.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 576.241
Dual form 576.2.bb.d.337.1

$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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 −0.999603 0.0281817i \(-0.991028\pi\)
0.879772 + 0.475395i \(0.157695\pi\)
\(6\) 0 0
\(7\) 2.36603 + 1.36603i 0.894274 + 0.516309i 0.875338 0.483512i \(-0.160639\pi\)
0.0189356 + 0.999821i \(0.493972\pi\)
\(8\) 0 0
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 0 0
\(11\) 4.23205 1.13397i 1.27601 0.341906i 0.443680 0.896185i \(-0.353673\pi\)
0.832331 + 0.554279i \(0.187006\pi\)
\(12\) 0 0
\(13\) −3.36603 0.901924i −0.933567 0.250149i −0.240192 0.970725i \(-0.577210\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 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 −0.381546 0.924350i \(-0.624608\pi\)
0.924350 + 0.381546i \(0.124608\pi\)
\(20\) 0 0
\(21\) 2.36603 + 4.09808i 0.516309 + 0.894274i
\(22\) 0 0
\(23\) −4.09808 + 2.36603i −0.854508 + 0.493350i −0.862169 0.506620i \(-0.830895\pi\)
0.00766135 + 0.999971i \(0.497561\pi\)
\(24\) 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 0.881750 0.471717i \(-0.156365\pi\)
−0.999476 + 0.0323566i \(0.989699\pi\)
\(30\) 0 0
\(31\) 0.267949 + 0.464102i 0.0481251 + 0.0833551i 0.889085 0.457743i \(-0.151342\pi\)
−0.840959 + 0.541098i \(0.818009\pi\)
\(32\) 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 0.979481 0.201537i \(-0.0645935\pi\)
−0.201537 + 0.979481i \(0.564594\pi\)
\(38\) 0 0
\(39\) −4.26795 4.26795i −0.683419 0.683419i
\(40\) 0 0
\(41\) 2.59808 1.50000i 0.405751 0.234261i −0.283211 0.959058i \(-0.591400\pi\)
0.688963 + 0.724797i \(0.258066\pi\)
\(42\) 0 0
\(43\) 8.33013 2.23205i 1.27033 0.340385i 0.440174 0.897912i \(-0.354917\pi\)
0.830158 + 0.557528i \(0.188250\pi\)
\(44\) 0 0
\(45\) −3.00000 + 0.803848i −0.447214 + 0.119831i
\(46\) 0 0
\(47\) −3.83013 + 6.63397i −0.558681 + 0.967665i 0.438925 + 0.898523i \(0.355359\pi\)
−0.997607 + 0.0691412i \(0.977974\pi\)
\(48\) 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 −0.999672 0.0256010i \(-0.991850\pi\)
−0.0256010 0.999672i \(-0.508150\pi\)
\(54\) 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 −0.711993 0.702186i \(-0.752207\pi\)
0.967697 0.252115i \(-0.0811261\pi\)
\(60\) 0 0
\(61\) −3.00000 11.1962i −0.384111 1.43352i −0.839564 0.543261i \(-0.817189\pi\)
0.455453 0.890260i \(-0.349477\pi\)
\(62\) 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 −0.167830 0.985816i \(-0.553676\pi\)
−0.638253 + 0.769827i \(0.720343\pi\)
\(68\) 0 0
\(69\) −8.19615 −0.986701
\(70\) 0 0
\(71\) 2.92820i 0.347514i 0.984789 + 0.173757i \(0.0555907\pi\)
−0.984789 + 0.173757i \(0.944409\pi\)
\(72\) 0 0
\(73\) 6.26795i 0.733608i 0.930298 + 0.366804i \(0.119548\pi\)
−0.930298 + 0.366804i \(0.880452\pi\)
\(74\) 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 −0.301401 0.953498i \(-0.597454\pi\)
0.976453 0.215728i \(-0.0692125\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) −0.366025 1.36603i −0.0401765 0.149941i 0.942924 0.333009i \(-0.108064\pi\)
−0.983100 + 0.183068i \(0.941397\pi\)
\(84\) 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 \(0.0338043\pi\)
−0.994366 + 0.106000i \(0.966196\pi\)
\(90\) 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 0.397857 + 0.917448i \(0.369754\pi\)
−0.993461 + 0.114170i \(0.963579\pi\)
\(98\) 0 0
\(99\) 9.29423 + 9.29423i 0.934105 + 0.934105i
\(100\) 0 0
\(101\) −2.00000 + 0.535898i −0.199007 + 0.0533239i −0.356946 0.934125i \(-0.616182\pi\)
0.157938 + 0.987449i \(0.449515\pi\)
\(102\) 0 0
\(103\) 13.0981 7.56218i 1.29059 0.745124i 0.311833 0.950137i \(-0.399057\pi\)
0.978759 + 0.205014i \(0.0657238\pi\)
\(104\) 0 0
\(105\) −4.73205 + 1.26795i −0.461801 + 0.123739i
\(106\) 0 0
\(107\) −12.4904 12.4904i −1.20749 1.20749i −0.971837 0.235654i \(-0.924277\pi\)
−0.235654 0.971837i \(-0.575723\pi\)
\(108\) 0 0
\(109\) 10.7321 10.7321i 1.02794 1.02794i 0.0283459 0.999598i \(-0.490976\pi\)
0.999598 0.0283459i \(-0.00902398\pi\)
\(110\) 0 0
\(111\) 3.00000 + 11.1962i 0.284747 + 1.06269i
\(112\) 0 0
\(113\) −6.92820 12.0000i −0.651751 1.12887i −0.982698 0.185216i \(-0.940702\pi\)
0.330947 0.943649i \(-0.392632\pi\)
\(114\) 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 0.584108 0.811676i \(-0.301445\pi\)
0.100014 + 0.994986i \(0.468111\pi\)
\(132\) 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 0.103857 0.994592i \(-0.466882\pi\)
−0.809414 + 0.587239i \(0.800215\pi\)
\(138\) 0 0
\(139\) −3.06218 + 11.4282i −0.259731 + 0.969328i 0.705667 + 0.708544i \(0.250648\pi\)
−0.965397 + 0.260784i \(0.916019\pi\)
\(140\) 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 0.825181 + 0.564869i \(0.191073\pi\)
−0.997062 + 0.0766003i \(0.975593\pi\)
\(150\) 0 0
\(151\) 0.633975 + 0.366025i 0.0515921 + 0.0297867i 0.525574 0.850748i \(-0.323851\pi\)
−0.473982 + 0.880534i \(0.657184\pi\)
\(152\) 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 0.0649959 0.997886i \(-0.479297\pi\)
−0.442655 + 0.896692i \(0.645963\pi\)
\(158\) 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 −0.377661 0.925944i \(-0.623272\pi\)
0.925944 + 0.377661i \(0.123272\pi\)
\(164\) 0 0
\(165\) −3.92820 + 6.80385i −0.305810 + 0.529679i
\(166\) 0 0
\(167\) 6.46410 3.73205i 0.500207 0.288795i −0.228592 0.973522i \(-0.573412\pi\)
0.728799 + 0.684728i \(0.240079\pi\)
\(168\) 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 0.947283 0.320398i \(-0.103817\pi\)
−0.980570 + 0.196169i \(0.937150\pi\)
\(174\) 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 −0.631365 0.775486i \(-0.717505\pi\)
0.775486 + 0.631365i \(0.217505\pi\)
\(180\) 0 0
\(181\) −7.39230 7.39230i −0.549466 0.549466i 0.376821 0.926286i \(-0.377017\pi\)
−0.926286 + 0.376821i \(0.877017\pi\)
\(182\) 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 0.00839227 0.999965i \(-0.497329\pi\)
0.861799 0.507250i \(-0.169338\pi\)
\(192\) 0 0
\(193\) −10.8660 18.8205i −0.782154 1.35473i −0.930685 0.365822i \(-0.880788\pi\)
0.148531 0.988908i \(-0.452545\pi\)
\(194\) 0 0
\(195\) 5.41154 3.12436i 0.387529 0.223740i
\(196\) 0 0
\(197\) 13.6603 + 13.6603i 0.973253 + 0.973253i 0.999651 0.0263987i \(-0.00840394\pi\)
−0.0263987 + 0.999651i \(0.508404\pi\)
\(198\) 0 0
\(199\) 25.1244i 1.78102i 0.454965 + 0.890509i \(0.349652\pi\)
−0.454965 + 0.890509i \(0.650348\pi\)
\(200\) 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 0.114983 0.993367i \(-0.463319\pi\)
−0.397106 + 0.917773i \(0.629985\pi\)
\(212\) 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 −0.461559 0.887109i \(-0.652710\pi\)
0.999039 0.0438324i \(-0.0139568\pi\)
\(224\) 0 0
\(225\) 11.7846i 0.785641i
\(226\) 0 0
\(227\) 0.571797 + 2.13397i 0.0379515 + 0.141637i 0.982302 0.187304i \(-0.0599750\pi\)
−0.944351 + 0.328941i \(0.893308\pi\)
\(228\) 0 0
\(229\) −1.83013 + 6.83013i −0.120938 + 0.451347i −0.999662 0.0259823i \(-0.991729\pi\)
0.878724 + 0.477330i \(0.158395\pi\)
\(230\) 0 0
\(231\) 14.6603 + 14.6603i 0.964574 + 0.964574i
\(232\) 0 0
\(233\) 3.19615i 0.209387i 0.994505 + 0.104693i \(0.0333861\pi\)
−0.994505 + 0.104693i \(0.966614\pi\)
\(234\) 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 0.999917 + 0.0129033i \(0.00410736\pi\)
−0.488784 + 0.872405i \(0.662559\pi\)
\(240\) 0 0
\(241\) −11.5981 + 20.0885i −0.747098 + 1.29401i 0.202110 + 0.979363i \(0.435220\pi\)
−0.949208 + 0.314649i \(0.898113\pi\)
\(242\) 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 0.866745 0.498751i \(-0.166208\pi\)
−0.498751 + 0.866745i \(0.666208\pi\)
\(252\) 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 0.994479 + 0.104934i \(0.0334632\pi\)
−0.406364 + 0.913711i \(0.633204\pi\)
\(258\) 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 0.421249 0.906945i \(-0.361592\pi\)
−0.574813 + 0.818285i \(0.694925\pi\)
\(264\) 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 −0.667395 0.744704i \(-0.732591\pi\)
0.744704 + 0.667395i \(0.232591\pi\)
\(270\) 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 0.597222 0.802076i \(-0.296271\pi\)
0.918247 + 0.396007i \(0.129605\pi\)
\(278\) 0 0
\(279\) −0.803848 + 1.39230i −0.0481251 + 0.0833551i
\(280\) 0 0
\(281\) 8.66025 + 5.00000i 0.516627 + 0.298275i 0.735554 0.677466i \(-0.236922\pi\)
−0.218926 + 0.975741i \(0.570255\pi\)
\(282\) 0 0
\(283\) −5.24167 + 19.5622i −0.311585 + 1.16285i 0.615542 + 0.788104i \(0.288937\pi\)
−0.927127 + 0.374747i \(0.877730\pi\)
\(284\) 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 −0.911124 0.412132i \(-0.864784\pi\)
0.995123 + 0.0986454i \(0.0314509\pi\)
\(294\) 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 −0.788173 0.615454i \(-0.788973\pi\)
0.615454 + 0.788173i \(0.288973\pi\)
\(308\) 0 0
\(309\) 26.1962 1.49025
\(310\) 0 0
\(311\) −19.0981 + 11.0263i −1.08295 + 0.625243i −0.931691 0.363251i \(-0.881667\pi\)
−0.151261 + 0.988494i \(0.548333\pi\)
\(312\) 0 0
\(313\) −18.6506 10.7679i −1.05420 0.608640i −0.130375 0.991465i \(-0.541618\pi\)
−0.923821 + 0.382824i \(0.874951\pi\)
\(314\) 0 0
\(315\) −8.19615 2.19615i −0.461801 0.123739i
\(316\) 0 0
\(317\) 5.50962 + 20.5622i 0.309451 + 1.15489i 0.929046 + 0.369965i \(0.120630\pi\)
−0.619595 + 0.784922i \(0.712703\pi\)
\(318\) 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 −0.256123 0.966644i \(-0.582445\pi\)
0.261513 + 0.965200i \(0.415778\pi\)
\(332\) 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 0.999839 0.0179267i \(-0.00570654\pi\)
−0.515445 + 0.856923i \(0.672373\pi\)
\(338\) 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 0.715398 + 0.698717i \(0.246245\pi\)
−0.968911 + 0.247408i \(0.920421\pi\)
\(348\) 0 0
\(349\) −4.26795 15.9282i −0.228458 0.852617i −0.980989 0.194061i \(-0.937834\pi\)
0.752531 0.658556i \(-0.228833\pi\)
\(350\) 0 0
\(351\) 4.68653 17.4904i 0.250149 0.933567i
\(352\) 0 0
\(353\) 7.16025 12.4019i 0.381102 0.660088i −0.610118 0.792310i \(-0.708878\pi\)
0.991220 + 0.132223i \(0.0422114\pi\)
\(354\) 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 \(0.0961028\pi\)
−0.954769 + 0.297350i \(0.903897\pi\)
\(360\) 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 0.216428 + 0.976299i \(0.430559\pi\)
−0.953713 + 0.300717i \(0.902774\pi\)
\(368\) 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 0.462368 + 0.886688i \(0.347000\pi\)
−0.843767 + 0.536710i \(0.819667\pi\)
\(374\) 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 0.603961 0.797014i \(-0.293588\pi\)
−0.797014 + 0.603961i \(0.793588\pi\)
\(380\) 0 0
\(381\) −6.29423 3.63397i −0.322463 0.186174i
\(382\) 0 0
\(383\) 6.73205 + 11.6603i 0.343992 + 0.595811i 0.985170 0.171581i \(-0.0548874\pi\)
−0.641178 + 0.767392i \(0.721554\pi\)
\(384\) 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 0.279593 0.960119i \(-0.409800\pi\)
0.722194 + 0.691691i \(0.243134\pi\)
\(390\) 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 −0.900337 0.435192i \(-0.856680\pi\)
0.435192 + 0.900337i \(0.356680\pi\)
\(398\) 0 0
\(399\) 15.2942 + 4.09808i 0.765669 + 0.205160i
\(400\) 0 0
\(401\) −1.79423 3.10770i −0.0895995 0.155191i 0.817742 0.575584i \(-0.195225\pi\)
−0.907342 + 0.420393i \(0.861892\pi\)
\(402\) 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 −0.991905 0.126984i \(-0.959470\pi\)
−0.385981 + 0.922507i \(0.626137\pi\)
\(410\) 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 0.417196 0.908816i \(-0.363013\pi\)
−0.0931055 + 0.995656i \(0.529679\pi\)
\(420\) 0 0
\(421\) −30.5885 + 8.19615i −1.49079 + 0.399456i −0.910004 0.414600i \(-0.863922\pi\)
−0.580786 + 0.814056i \(0.697255\pi\)
\(422\) 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 −0.157067 0.987588i \(-0.550204\pi\)
−0.933810 + 0.357770i \(0.883537\pi\)
\(440\) 0 0
\(441\) −0.696152 + 1.20577i −0.0331501 + 0.0574177i
\(442\) 0 0
\(443\) −17.2583 + 4.62436i −0.819968 + 0.219710i −0.644332 0.764745i \(-0.722865\pi\)
−0.175636 + 0.984455i \(0.556198\pi\)
\(444\) 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 0.446249 0.894909i \(-0.352760\pi\)
−0.551889 + 0.833917i \(0.686093\pi\)
\(458\) 0 0
\(459\) 29.7846i 1.39023i
\(460\) 0 0
\(461\) −9.56218 35.6865i −0.445355 1.66209i −0.714997 0.699127i \(-0.753572\pi\)
0.269642 0.962961i \(-0.413094\pi\)
\(462\) 0 0
\(463\) −1.19615 2.07180i −0.0555899 0.0962846i 0.836891 0.547369i \(-0.184371\pi\)
−0.892481 + 0.451085i \(0.851037\pi\)
\(464\) 0 0
\(465\) −0.928203 0.248711i −0.0430444 0.0115337i
\(466\) 0 0
\(467\) −2.63397 + 2.63397i −0.121886 + 0.121886i −0.765419 0.643533i \(-0.777468\pi\)
0.643533 + 0.765419i \(0.277468\pi\)
\(468\) 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 −0.945425 0.325840i \(-0.894353\pi\)
0.754898 + 0.655842i \(0.227686\pi\)
\(480\) 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 \(0.0419789\pi\)
−0.991316 + 0.131499i \(0.958021\pi\)
\(488\) 0 0
\(489\) 16.5622 4.43782i 0.748968 0.200685i
\(490\) 0 0
\(491\) −3.72243 + 13.8923i −0.167991 + 0.626951i 0.829649 + 0.558286i \(0.188541\pi\)
−0.997640 + 0.0686652i \(0.978126\pi\)
\(492\) 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 0.0588630 0.998266i \(-0.481252\pi\)
−0.448156 + 0.893955i \(0.647919\pi\)
\(500\) 0 0
\(501\) 12.9282 0.577590
\(502\) 0 0
\(503\) 27.7128i 1.23565i −0.786314 0.617827i \(-0.788013\pi\)
0.786314 0.617827i \(-0.211987\pi\)
\(504\) 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 −0.00436335 0.999990i \(-0.501389\pi\)
−0.503774 + 0.863835i \(0.668056\pi\)
\(510\) 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 \(-0.908083\pi\)
0.958596 0.284770i \(-0.0919173\pi\)
\(522\) 0 0
\(523\) 7.53590 + 7.53590i 0.329522 + 0.329522i 0.852405 0.522883i \(-0.175143\pi\)
−0.522883 + 0.852405i \(0.675143\pi\)
\(524\) 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 −0.658319 0.752739i \(-0.728732\pi\)
0.752739 + 0.658319i \(0.228732\pi\)
\(542\) 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 0.855138 + 0.518400i \(0.173472\pi\)
−0.481371 + 0.876517i \(0.659861\pi\)
\(548\) 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 −0.947378 0.320118i \(-0.896277\pi\)
0.320118 + 0.947378i \(0.396277\pi\)
\(558\) 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 −0.359560 0.933122i \(-0.617073\pi\)
−0.777949 + 0.628327i \(0.783740\pi\)
\(564\) 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 0.833391 0.552684i \(-0.186396\pi\)
−0.0619424 + 0.998080i \(0.519730\pi\)
\(570\) 0 0
\(571\) −0.892305 + 3.33013i −0.0373418 + 0.139361i −0.982080 0.188464i \(-0.939649\pi\)
0.944738 + 0.327825i \(0.106316\pi\)
\(572\) 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 0.345554 0.938399i \(-0.387691\pi\)
0.768458 + 0.639900i \(0.221024\pi\)
\(588\) 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 −0.250570 0.968099i \(-0.580618\pi\)
0.713113 + 0.701049i \(0.247285\pi\)
\(600\) 0 0
\(601\) 20.5526 + 11.8660i 0.838356 + 0.484025i 0.856705 0.515806i \(-0.172508\pi\)
−0.0183488 + 0.999832i \(0.505841\pi\)
\(602\) 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 0.986000 0.166745i \(-0.0533256\pi\)
−0.637405 + 0.770529i \(0.719992\pi\)
\(608\) 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 0.316186 0.948697i \(-0.397598\pi\)
−0.948697 + 0.316186i \(0.897598\pi\)
\(614\) 0 0
\(615\) −1.39230 + 5.19615i −0.0561432 + 0.209529i
\(616\) 0 0
\(617\) 35.0885 20.2583i 1.41261 0.815570i 0.416975 0.908918i \(-0.363090\pi\)
0.995633 + 0.0933485i \(0.0297571\pi\)
\(618\) 0 0
\(619\) 15.5981 4.17949i 0.626940 0.167988i 0.0686590 0.997640i \(-0.478128\pi\)
0.558281 + 0.829652i \(0.311461\pi\)
\(620\) 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 \(0.113980\pi\)
−0.936572 + 0.350476i \(0.886020\pi\)
\(632\) 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 0.149053 + 0.988829i \(0.452378\pi\)
−0.930878 + 0.365331i \(0.880956\pi\)
\(642\) 0 0
\(643\) −8.76795 2.34936i −0.345774 0.0926499i 0.0817525 0.996653i \(-0.473948\pi\)
−0.427527 + 0.904003i \(0.640615\pi\)
\(644\) 0 0
\(645\) −7.73205 + 13.3923i −0.304449 + 0.527321i
\(646\) 0 0
\(647\) 16.7321i 0.657805i 0.944364 + 0.328902i \(0.106679\pi\)
−0.944364 + 0.328902i \(0.893321\pi\)
\(648\) 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 −0.322915 0.946428i \(-0.604663\pi\)
−0.752867 + 0.658173i \(0.771329\pi\)
\(654\) 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 −0.998941 0.0460178i \(-0.985347\pi\)
0.842099 0.539323i \(-0.181320\pi\)
\(660\) 0 0
\(661\) 2.19615 8.19615i 0.0854204 0.318793i −0.909973 0.414667i \(-0.863898\pi\)
0.995393 + 0.0958740i \(0.0305646\pi\)
\(662\) 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 −0.212557 0.977149i \(-0.568179\pi\)
0.952514 0.304495i \(-0.0984877\pi\)
\(674\) 0 0
\(675\) −10.2058 + 17.6769i −0.392820 + 0.680385i
\(676\) 0 0
\(677\) −4.73205 + 1.26795i −0.181867 + 0.0487312i −0.348603 0.937270i \(-0.613344\pi\)
0.166736 + 0.986002i \(0.446677\pi\)
\(678\) 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 0.979240 0.202703i \(-0.0649726\pi\)
−0.202703 + 0.979240i \(0.564973\pi\)
\(684\) 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 0.996980 0.0776628i \(-0.0247457\pi\)
−0.902241 + 0.431232i \(0.858079\pi\)
\(692\) 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 −0.821608 0.570053i \(-0.806923\pi\)
0.570053 + 0.821608i \(0.306923\pi\)
\(702\) 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 0.505131 0.863043i \(-0.331444\pi\)
0.868978 + 0.494852i \(0.164778\pi\)
\(710\) 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 −0.140755 0.990044i \(-0.544953\pi\)
−0.927781 + 0.373124i \(0.878286\pi\)
\(728\) 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 0.0493698 0.998781i \(-0.484279\pi\)
−0.456635 + 0.889654i \(0.650945\pi\)
\(734\) 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 −0.539511 0.841978i \(-0.681391\pi\)
0.841978 + 0.539511i \(0.181391\pi\)
\(740\) 0 0
\(741\) −20.1962 −0.741924
\(742\) 0 0
\(743\) 24.7583 14.2942i 0.908295 0.524404i 0.0284129 0.999596i \(-0.490955\pi\)
0.879882 + 0.475192i \(0.157621\pi\)
\(744\) 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 0.981141 0.193292i \(-0.0619165\pi\)
−0.657966 + 0.753047i \(0.728583\pi\)
\(752\) 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 0.245176 0.969479i \(-0.421154\pi\)
−0.969479 + 0.245176i \(0.921154\pi\)
\(758\) 0 0
\(759\) −34.6865 + 9.29423i −1.25904 + 0.337359i
\(760\) 0 0
\(761\) −45.3731 + 26.1962i −1.64477 + 0.949610i −0.665669 + 0.746247i \(0.731854\pi\)
−0.979104 + 0.203363i \(0.934813\pi\)
\(762\) 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 −0.999942 0.0108155i \(-0.996557\pi\)
0.490604 0.871383i \(-0.336776\pi\)
\(770\) 0 0
\(771\) 32.6603i 1.17623i
\(772\) 0 0
\(773\) 35.5885 + 35.5885i 1.28003 + 1.28003i 0.940650 + 0.339378i \(0.110216\pi\)
0.339378 + 0.940650i \(0.389784\pi\)
\(774\) 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 −0.546302 0.837588i \(-0.683965\pi\)
−0.891906 + 0.452222i \(0.850632\pi\)
\(788\) 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 1.43437i