Properties

Label 576.2.bb.c.529.1
Level $576$
Weight $2$
Character 576.529
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 529.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 576.529
Dual form 576.2.bb.c.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 1.50000i) q^{3} +(1.00000 + 0.267949i) q^{5} +(-2.36603 - 1.36603i) q^{7} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 1.50000i) q^{3} +(1.00000 + 0.267949i) q^{5} +(-2.36603 - 1.36603i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(-1.13397 - 4.23205i) q^{11} +(0.901924 - 3.36603i) q^{13} +(-1.26795 + 1.26795i) q^{15} -5.73205 q^{17} +(2.36603 + 2.36603i) q^{19} +(4.09808 - 2.36603i) q^{21} +(4.09808 - 2.36603i) q^{23} +(-3.40192 - 1.96410i) q^{25} +5.19615 q^{27} +(2.36603 - 0.633975i) q^{29} +(0.267949 + 0.464102i) q^{31} +(7.33013 + 1.96410i) q^{33} +(-2.00000 - 2.00000i) q^{35} +(4.73205 - 4.73205i) q^{37} +(4.26795 + 4.26795i) q^{39} +(-2.59808 + 1.50000i) q^{41} +(-2.23205 - 8.33013i) q^{43} +(-0.803848 - 3.00000i) q^{45} +(-3.83013 + 6.63397i) q^{47} +(0.232051 + 0.401924i) q^{49} +(4.96410 - 8.59808i) q^{51} +(-7.46410 + 7.46410i) q^{53} -4.53590i q^{55} +(-5.59808 + 1.50000i) q^{57} +(-7.33013 - 1.96410i) q^{59} +(11.1962 - 3.00000i) q^{61} +8.19615i q^{63} +(1.80385 - 3.12436i) q^{65} +(1.76795 - 6.59808i) q^{67} +8.19615i q^{69} -2.92820i q^{71} -6.26795i q^{73} +(5.89230 - 3.40192i) q^{75} +(-3.09808 + 11.5622i) q^{77} +(6.00000 - 10.3923i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(1.36603 - 0.366025i) q^{83} +(-5.73205 - 1.53590i) q^{85} +(-1.09808 + 4.09808i) q^{87} -2.00000i q^{89} +(-6.73205 + 6.73205i) q^{91} -0.928203 q^{93} +(1.73205 + 3.00000i) q^{95} +(-5.86603 + 10.1603i) q^{97} +(-9.29423 + 9.29423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{5} - 6q^{7} - 6q^{9} + O(q^{10}) \) \( 4q + 4q^{5} - 6q^{7} - 6q^{9} - 8q^{11} + 14q^{13} - 12q^{15} - 16q^{17} + 6q^{19} + 6q^{21} + 6q^{23} - 24q^{25} + 6q^{29} + 8q^{31} + 12q^{33} - 8q^{35} + 12q^{37} + 24q^{39} - 2q^{43} - 24q^{45} + 2q^{47} - 6q^{49} + 6q^{51} - 16q^{53} - 12q^{57} - 12q^{59} + 24q^{61} + 28q^{65} + 14q^{67} - 18q^{75} - 2q^{77} + 24q^{79} - 18q^{81} + 2q^{83} - 16q^{85} + 6q^{87} - 20q^{91} + 24q^{93} - 20q^{97} - 6q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) −0.866025 + 1.50000i −0.500000 + 0.866025i
\(4\) 0 0
\(5\) 1.00000 + 0.267949i 0.447214 + 0.119831i 0.475395 0.879772i \(-0.342305\pi\)
−0.0281817 + 0.999603i \(0.508972\pi\)
\(6\) 0 0
\(7\) −2.36603 1.36603i −0.894274 0.516309i −0.0189356 0.999821i \(-0.506028\pi\)
−0.875338 + 0.483512i \(0.839361\pi\)
\(8\) 0 0
\(9\) −1.50000 2.59808i −0.500000 0.866025i
\(10\) 0 0
\(11\) −1.13397 4.23205i −0.341906 1.27601i −0.896185 0.443680i \(-0.853673\pi\)
0.554279 0.832331i \(-0.312994\pi\)
\(12\) 0 0
\(13\) 0.901924 3.36603i 0.250149 0.933567i −0.720577 0.693375i \(-0.756123\pi\)
0.970725 0.240192i \(-0.0772105\pi\)
\(14\) 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
\(21\) 4.09808 2.36603i 0.894274 0.516309i
\(22\) 0 0
\(23\) 4.09808 2.36603i 0.854508 0.493350i −0.00766135 0.999971i \(-0.502439\pi\)
0.862169 + 0.506620i \(0.169105\pi\)
\(24\) 0 0
\(25\) −3.40192 1.96410i −0.680385 0.392820i
\(26\) 0 0
\(27\) 5.19615 1.00000
\(28\) 0 0
\(29\) 2.36603 0.633975i 0.439360 0.117726i −0.0323566 0.999476i \(-0.510301\pi\)
0.471717 + 0.881750i \(0.343635\pi\)
\(30\) 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 −0.201537 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 \(-0.741934\pi\)
0.283211 + 0.959058i \(0.408600\pi\)
\(42\) 0 0
\(43\) −2.23205 8.33013i −0.340385 1.27033i −0.897912 0.440174i \(-0.854917\pi\)
0.557528 0.830158i \(-0.311750\pi\)
\(44\) 0 0
\(45\) −0.803848 3.00000i −0.119831 0.447214i
\(46\) 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
\(51\) 4.96410 8.59808i 0.695113 1.20397i
\(52\) 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
\(59\) −7.33013 1.96410i −0.954301 0.255704i −0.252115 0.967697i \(-0.581126\pi\)
−0.702186 + 0.711993i \(0.747793\pi\)
\(60\) 0 0
\(61\) 11.1962 3.00000i 1.43352 0.384111i 0.543261 0.839564i \(-0.317189\pi\)
0.890260 + 0.455453i \(0.150523\pi\)
\(62\) 0 0
\(63\) 8.19615i 1.03262i
\(64\) 0 0
\(65\) 1.80385 3.12436i 0.223740 0.387529i
\(66\) 0 0
\(67\) 1.76795 6.59808i 0.215989 0.806083i −0.769827 0.638253i \(-0.779657\pi\)
0.985816 0.167830i \(-0.0536760\pi\)
\(68\) 0 0
\(69\) 8.19615i 0.986701i
\(70\) 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
\(75\) 5.89230 3.40192i 0.680385 0.392820i
\(76\) 0 0
\(77\) −3.09808 + 11.5622i −0.353059 + 1.31763i
\(78\) 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
\(83\) 1.36603 0.366025i 0.149941 0.0401765i −0.183068 0.983100i \(-0.558603\pi\)
0.333009 + 0.942924i \(0.391936\pi\)
\(84\) 0 0
\(85\) −5.73205 1.53590i −0.621728 0.166592i
\(86\) 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
\(93\) −0.928203 −0.0962502
\(94\) 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
\(101\) 0.535898 + 2.00000i 0.0533239 + 0.199007i 0.987449 0.157938i \(-0.0504847\pi\)
−0.934125 + 0.356946i \(0.883818\pi\)
\(102\) 0 0
\(103\) −13.0981 + 7.56218i −1.29059 + 0.745124i −0.978759 0.205014i \(-0.934276\pi\)
−0.311833 + 0.950137i \(0.600943\pi\)
\(104\) 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 −0.982698 0.185216i \(-0.940702\pi\)
0.330947 0.943649i \(-0.392632\pi\)
\(114\) 0 0
\(115\) 4.73205 1.26795i 0.441266 0.118237i
\(116\) 0 0
\(117\) −10.0981 + 2.70577i −0.933567 + 0.250149i
\(118\) 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
\(123\) 5.19615i 0.468521i
\(124\) 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
\(131\) −2.09808 + 7.83013i −0.183310 + 0.684121i 0.811676 + 0.584108i \(0.198555\pi\)
−0.994986 + 0.100014i \(0.968111\pi\)
\(132\) 0 0
\(133\) −2.36603 8.83013i −0.205160 0.765669i
\(134\) 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 \(-0.199785\pi\)
−0.103857 + 0.994592i \(0.533118\pi\)
\(138\) 0 0
\(139\) 11.4282 + 3.06218i 0.969328 + 0.259731i 0.708544 0.705667i \(-0.249352\pi\)
0.260784 + 0.965397i \(0.416019\pi\)
\(140\) 0 0
\(141\) −6.63397 11.4904i −0.558681 0.967665i
\(142\) 0 0
\(143\) −15.2679 −1.27677
\(144\) 0 0
\(145\) 2.53590 0.210595
\(146\) 0 0
\(147\) −0.803848 −0.0663002
\(148\) 0 0
\(149\) 7.83013 + 2.09808i 0.641469 + 0.171881i 0.564869 0.825181i \(-0.308927\pi\)
0.0766003 + 0.997062i \(0.475593\pi\)
\(150\) 0 0
\(151\) −0.633975 0.366025i −0.0515921 0.0297867i 0.473982 0.880534i \(-0.342816\pi\)
−0.525574 + 0.850748i \(0.676149\pi\)
\(152\) 0 0
\(153\) 8.59808 + 14.8923i 0.695113 + 1.20397i
\(154\) 0 0
\(155\) 0.143594 + 0.535898i 0.0115337 + 0.0430444i
\(156\) 0 0
\(157\) 1.26795 4.73205i 0.101193 0.377659i −0.896692 0.442655i \(-0.854037\pi\)
0.997886 + 0.0649959i \(0.0207034\pi\)
\(158\) 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
\(165\) 6.80385 + 3.92820i 0.529679 + 0.305810i
\(166\) 0 0
\(167\) −6.46410 + 3.73205i −0.500207 + 0.288795i −0.728799 0.684728i \(-0.759921\pi\)
0.228592 + 0.973522i \(0.426588\pi\)
\(168\) 0 0
\(169\) 0.741670 + 0.428203i 0.0570515 + 0.0329387i
\(170\) 0 0
\(171\) 2.59808 9.69615i 0.198680 0.741483i
\(172\) 0 0
\(173\) 1.63397 0.437822i 0.124229 0.0332870i −0.196169 0.980570i \(-0.562850\pi\)
0.320398 + 0.947283i \(0.396183\pi\)
\(174\) 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
\(187\) 6.50000 + 24.2583i 0.475327 + 1.77394i
\(188\) 0 0
\(189\) −12.2942 7.09808i −0.894274 0.516309i
\(190\) 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
\(195\) 3.12436 + 5.41154i 0.223740 + 0.387529i
\(196\) 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
\(203\) −6.46410 1.73205i −0.453691 0.121566i
\(204\) 0 0
\(205\) −3.00000 + 0.803848i −0.209529 + 0.0561432i
\(206\) 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
\(211\) 1.09808 4.09808i 0.0755947 0.282123i −0.917773 0.397106i \(-0.870015\pi\)
0.993367 + 0.114983i \(0.0366812\pi\)
\(212\) 0 0
\(213\) 4.39230 + 2.53590i 0.300956 + 0.173757i
\(214\) 0 0
\(215\) 8.92820i 0.608898i
\(216\) 0 0
\(217\) 1.46410i 0.0993897i
\(218\) 0 0
\(219\) 9.40192 + 5.42820i 0.635323 + 0.366804i
\(220\) 0 0
\(221\) −5.16987 + 19.2942i −0.347763 + 1.29787i
\(222\) 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
\(227\) −2.13397 + 0.571797i −0.141637 + 0.0379515i −0.328941 0.944351i \(-0.606692\pi\)
0.187304 + 0.982302i \(0.440025\pi\)
\(228\) 0 0
\(229\) 6.83013 + 1.83013i 0.451347 + 0.120938i 0.477330 0.878724i \(-0.341605\pi\)
−0.0259823 + 0.999662i \(0.508271\pi\)
\(230\) 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
\(237\) 10.3923 + 18.0000i 0.675053 + 1.16923i
\(238\) 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
\(243\) −7.79423 13.5000i −0.500000 0.866025i
\(244\) 0 0
\(245\) 0.124356 + 0.464102i 0.00794479 + 0.0296504i
\(246\) 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 0.994479 + 0.104934i \(0.0334632\pi\)
−0.406364 + 0.913711i \(0.633204\pi\)
\(258\) 0 0
\(259\) −17.6603 + 4.73205i −1.09735 + 0.294035i
\(260\) 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 \(-0.305075\pi\)
−0.421249 + 0.906945i \(0.638408\pi\)
\(264\) 0 0
\(265\) −9.46410 + 5.46410i −0.581375 + 0.335657i
\(266\) 0 0
\(267\) 3.00000 + 1.73205i 0.183597 + 0.106000i
\(268\) 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
\(275\) −4.45448 + 16.6244i −0.268615 + 1.00249i
\(276\) 0 0
\(277\) −6.75833 25.2224i −0.406069 1.51547i −0.802076 0.597222i \(-0.796271\pi\)
0.396007 0.918247i \(-0.370395\pi\)
\(278\) 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 \(-0.429745\pi\)
−0.735554 + 0.677466i \(0.763078\pi\)
\(282\) 0 0
\(283\) 19.5622 + 5.24167i 1.16285 + 0.311585i 0.788104 0.615542i \(-0.211063\pi\)
0.374747 + 0.927127i \(0.377730\pi\)
\(284\) 0 0
\(285\) −6.00000 −0.355409
\(286\) 0 0
\(287\) 8.19615 0.483804
\(288\) 0 0
\(289\) 15.8564 0.932730
\(290\) 0 0
\(291\) −10.1603 17.5981i −0.595605 1.03162i
\(292\) 0 0
\(293\) −5.36603 1.43782i −0.313487 0.0839985i 0.0986454 0.995123i \(-0.468549\pi\)
−0.412132 + 0.911124i \(0.635216\pi\)
\(294\) 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
\(299\) −4.26795 15.9282i −0.246822 0.921152i
\(300\) 0 0
\(301\) −6.09808 + 22.7583i −0.351487 + 1.31177i
\(302\) 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
\(309\) 26.1962i 1.49025i
\(310\) 0 0
\(311\) 19.0981 11.0263i 1.08295 0.625243i 0.151261 0.988494i \(-0.451667\pi\)
0.931691 + 0.363251i \(0.118333\pi\)
\(312\) 0 0
\(313\) 18.6506 + 10.7679i 1.05420 + 0.608640i 0.923821 0.382824i \(-0.125049\pi\)
0.130375 + 0.991465i \(0.458382\pi\)
\(314\) 0 0
\(315\) −2.19615 + 8.19615i −0.123739 + 0.461801i
\(316\) 0 0
\(317\) −20.5622 + 5.50962i −1.15489 + 0.309451i −0.784922 0.619595i \(-0.787297\pi\)
−0.369965 + 0.929046i \(0.620630\pi\)
\(318\) 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
\(331\) −0.0262794 0.0980762i −0.00144445 0.00539076i 0.965200 0.261513i \(-0.0842216\pi\)
−0.966644 + 0.256123i \(0.917555\pi\)
\(332\) 0 0
\(333\) −19.3923 5.19615i −1.06269 0.284747i
\(334\) 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
\(339\) 24.0000 1.30350
\(340\) 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
\(347\) 17.6244 + 4.72243i 0.946125 + 0.253513i 0.698717 0.715398i \(-0.253755\pi\)
0.247408 + 0.968911i \(0.420421\pi\)
\(348\) 0 0
\(349\) 15.9282 4.26795i 0.852617 0.228458i 0.194061 0.980989i \(-0.437834\pi\)
0.658556 + 0.752531i \(0.271167\pi\)
\(350\) 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
\(355\) 0.784610 2.92820i 0.0416428 0.155413i
\(356\) 0 0
\(357\) −23.4904 + 13.5622i −1.24324 + 0.717787i
\(358\) 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
\(363\) 14.1962i 0.745105i
\(364\) 0 0
\(365\) 1.67949 6.26795i 0.0879086 0.328079i
\(366\) 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
\(371\) 27.8564 7.46410i 1.44623 0.387517i
\(372\) 0 0
\(373\) 27.4904 + 7.36603i 1.42340 + 0.381398i 0.886688 0.462368i \(-0.153000\pi\)
0.536710 + 0.843767i \(0.319667\pi\)
\(374\) 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
\(381\) 3.63397 6.29423i 0.186174 0.322463i
\(382\) 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
\(389\) −5.29423 19.7583i −0.268428 1.00179i −0.960119 0.279593i \(-0.909800\pi\)
0.691691 0.722194i \(-0.256866\pi\)
\(390\) 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 0.817742 0.575584i \(-0.195225\pi\)
−0.907342 + 0.420393i \(0.861892\pi\)
\(402\) 0 0
\(403\) 1.80385 0.483340i 0.0898560 0.0240769i
\(404\) 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 \(-0.373863\pi\)
0.991905 + 0.126984i \(0.0405295\pi\)
\(410\) 0 0
\(411\) −14.3038 + 8.25833i −0.705557 + 0.407353i
\(412\) 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
\(419\) −1.77757 + 6.63397i −0.0868399 + 0.324091i −0.995656 0.0931055i \(-0.970321\pi\)
0.908816 + 0.417196i \(0.136987\pi\)
\(420\) 0 0
\(421\) 8.19615 + 30.5885i 0.399456 + 1.49079i 0.814056 + 0.580786i \(0.197255\pi\)
−0.414600 + 0.910004i \(0.636078\pi\)
\(422\) 0 0
\(423\) 22.9808 1.11736
\(424\) 0 0
\(425\) 19.5000 + 11.2583i 0.945889 + 0.546109i
\(426\) 0 0
\(427\) −30.5885 8.19615i −1.48028 0.396640i
\(428\) 0 0
\(429\) 13.2224 22.9019i 0.638385 1.10572i
\(430\) 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
\(435\) −2.19615 + 3.80385i −0.105297 + 0.182381i
\(436\) 0 0
\(437\) 15.2942 + 4.09808i 0.731622 + 0.196038i
\(438\) 0 0
\(439\) 22.8564 + 13.1962i 1.09088 + 0.629818i 0.933810 0.357770i \(-0.116463\pi\)
0.157067 + 0.987588i \(0.449796\pi\)
\(440\) 0 0
\(441\) 0.696152 1.20577i 0.0331501 0.0574177i
\(442\) 0 0
\(443\) 4.62436 + 17.2583i 0.219710 + 0.819968i 0.984455 + 0.175636i \(0.0561980\pi\)
−0.764745 + 0.644332i \(0.777135\pi\)
\(444\) 0 0
\(445\) 0.535898 2.00000i 0.0254040 0.0948091i
\(446\) 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
\(453\) 1.09808 0.633975i 0.0515921 0.0297867i
\(454\) 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 \(-0.313907\pi\)
−0.446249 + 0.894909i \(0.647240\pi\)
\(458\) 0 0
\(459\) −29.7846 −1.39023
\(460\) 0 0
\(461\) 35.6865 9.56218i 1.66209 0.445355i 0.699127 0.714997i \(-0.253572\pi\)
0.962961 + 0.269642i \(0.0869055\pi\)
\(462\) 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 0.643533 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
\(475\) −3.40192 12.6962i −0.156091 0.582539i
\(476\) 0 0
\(477\) 30.5885 + 8.19615i 1.40055 + 0.375276i
\(478\) 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
\(483\) 11.1962 19.3923i 0.509443 0.882380i
\(484\) 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
\(491\) 13.8923 + 3.72243i 0.626951 + 0.167991i 0.558286 0.829649i \(-0.311459\pi\)
0.0686652 + 0.997640i \(0.478126\pi\)
\(492\) 0 0
\(493\) −13.5622 + 3.63397i −0.610810 + 0.163666i
\(494\) 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
\(499\) 2.33013 8.69615i 0.104311 0.389293i −0.893955 0.448156i \(-0.852081\pi\)
0.998266 + 0.0588630i \(0.0187475\pi\)
\(500\) 0 0
\(501\) 12.9282i 0.577590i
\(502\) 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
\(507\) −1.28461 + 0.741670i −0.0570515 + 0.0329387i
\(508\) 0 0
\(509\) 3.07180 11.4641i 0.136155 0.508137i −0.863835 0.503774i \(-0.831944\pi\)
0.999990 0.00436335i \(-0.00138890\pi\)
\(510\) 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
\(515\) −15.1244 + 4.05256i −0.666459 + 0.178577i
\(516\) 0 0
\(517\) 32.4186 + 8.68653i 1.42577 + 0.382033i
\(518\) 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
\(525\) −18.5885 −0.811267
\(526\) 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
\(531\) 5.89230 + 21.9904i 0.255704 + 0.954301i
\(532\) 0 0
\(533\) 2.70577 + 10.0981i 0.117200 + 0.437396i
\(534\) 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
\(547\) −32.6244 + 8.74167i −1.39492 + 0.373767i −0.876517 0.481371i \(-0.840139\pi\)
−0.518400 + 0.855138i \(0.673472\pi\)
\(548\) 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
\(555\) 12.0000i 0.509372i
\(556\) 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
\(563\) 7.23205 26.9904i 0.304795 1.13751i −0.628327 0.777949i \(-0.716260\pi\)
0.933122 0.359560i \(-0.117073\pi\)
\(564\) 0 0
\(565\) −3.71281 13.8564i −0.156199 0.582943i
\(566\) 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 \(-0.480270\pi\)
−0.833391 + 0.552684i \(0.813604\pi\)
\(570\) 0 0
\(571\) 3.33013 + 0.892305i 0.139361 + 0.0373418i 0.327825 0.944738i \(-0.393684\pi\)
−0.188464 + 0.982080i \(0.560351\pi\)
\(572\) 0 0
\(573\) 20.8301 + 36.0788i 0.870191 + 1.50722i
\(574\) 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
\(579\) 37.6410 1.56431
\(580\) 0 0
\(581\) −3.73205 1.00000i −0.154832 0.0414870i
\(582\) 0 0
\(583\) 40.0526 + 23.1244i 1.65881 + 0.957713i
\(584\) 0 0
\(585\) −10.8231 −0.447480
\(586\) 0 0
\(587\) −7.23205 26.9904i −0.298499 1.11401i −0.938399 0.345554i \(-0.887691\pi\)
0.639900 0.768458i \(-0.278976\pi\)
\(588\) 0 0
\(589\) −0.464102 + 1.73205i −0.0191230 + 0.0713679i
\(590\) 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
\(597\) 37.6865 + 21.7583i 1.54241 + 0.890509i
\(598\) 0 0
\(599\) −11.3205 + 6.53590i −0.462543 + 0.267050i −0.713113 0.701049i \(-0.752715\pi\)
0.250570 + 0.968099i \(0.419382\pi\)
\(600\) 0 0
\(601\) −20.5526 11.8660i −0.838356 0.484025i 0.0183488 0.999832i \(-0.494159\pi\)
−0.856705 + 0.515806i \(0.827492\pi\)
\(602\) 0 0
\(603\) −19.7942 + 5.30385i −0.806083 + 0.215989i
\(604\) 0 0
\(605\) −8.19615 + 2.19615i −0.333221 + 0.0892863i
\(606\) 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 −0.948697 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 \(-0.970243\pi\)
−0.416975 + 0.908918i \(0.636910\pi\)
\(618\) 0 0
\(619\) −4.17949 15.5981i −0.167988 0.626940i −0.997640 0.0686590i \(-0.978128\pi\)
0.829652 0.558281i \(-0.188539\pi\)
\(620\) 0 0
\(621\) 21.2942 12.2942i 0.854508 0.493350i
\(622\) 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
\(627\) 12.6962 + 21.9904i 0.507035 + 0.878211i
\(628\) 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
\(635\) −4.19615 1.12436i −0.166519 0.0446187i
\(636\) 0 0
\(637\) 1.56218 0.418584i 0.0618957 0.0165849i
\(638\) 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
\(643\) 2.34936 8.76795i 0.0926499 0.345774i −0.904003 0.427527i \(-0.859385\pi\)
0.996653 + 0.0817525i \(0.0260517\pi\)
\(644\) 0 0
\(645\) 13.3923 + 7.73205i 0.527321 + 0.304449i
\(646\) 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
\(651\) 2.19615 + 1.26795i 0.0860740 + 0.0496948i
\(652\) 0 0
\(653\) 7.36603 27.4904i 0.288255 1.07578i −0.658173 0.752867i \(-0.728671\pi\)
0.946428 0.322915i \(-0.104663\pi\)
\(654\) 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
\(659\) 15.0263 4.02628i 0.585341 0.156842i 0.0460178 0.998941i \(-0.485347\pi\)
0.539323 + 0.842099i \(0.318680\pi\)
\(660\) 0 0
\(661\) −8.19615 2.19615i −0.318793 0.0854204i 0.0958740 0.995393i \(-0.469435\pi\)
−0.414667 + 0.909973i \(0.636102\pi\)
\(662\) 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
\(669\) 13.9019 + 24.0788i 0.537479 + 0.930942i
\(670\) 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
\(675\) −17.6769 10.2058i −0.680385 0.392820i
\(676\) 0 0
\(677\) 1.26795 + 4.73205i 0.0487312 + 0.181867i 0.986002 0.166736i \(-0.0533227\pi\)
−0.937270 + 0.348603i \(0.886656\pi\)
\(678\) 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
\(691\) −9.29423 + 2.49038i −0.353569 + 0.0947386i −0.431232 0.902241i \(-0.641921\pi\)
0.0776628 + 0.996980i \(0.475254\pi\)
\(692\) 0 0
\(693\) 34.6865 9.29423i 1.31763 0.353059i
\(694\) 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
\(699\) 4.79423 + 2.76795i 0.181334 + 0.104693i
\(700\) 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
\(707\) 1.46410 5.46410i 0.0550632 0.205499i
\(708\) 0 0
\(709\) −9.80385 36.5885i −0.368191 1.37411i −0.863043 0.505131i \(-0.831444\pi\)
0.494852 0.868978i \(-0.335222\pi\)
\(710\) 0 0
\(711\) −36.0000 −1.35011
\(712\) 0 0
\(713\) 2.19615 + 1.26795i 0.0822466 + 0.0474851i
\(714\) 0 0
\(715\) −15.2679 4.09103i −0.570989 0.152996i
\(716\) 0 0
\(717\) −27.3731 −1.02227
\(718\) 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
\(723\) −20.0885 34.7942i −0.747098 1.29401i
\(724\) 0 0
\(725\) −9.29423 2.49038i −0.345179 0.0924904i
\(726\) 0 0
\(727\) 28.8109 + 16.6340i 1.06854 + 0.616920i 0.927781 0.373124i \(-0.121714\pi\)
0.140755 + 0.990044i \(0.455047\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) 12.7942 + 47.7487i 0.473212 + 1.76605i
\(732\) 0 0
\(733\) 2.95448 11.0263i 0.109126 0.407265i −0.889654 0.456635i \(-0.849055\pi\)
0.998781 + 0.0493698i \(0.0157213\pi\)
\(734\) 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
\(741\) 20.1962i 0.741924i
\(742\) 0 0
\(743\) −24.7583 + 14.2942i −0.908295 + 0.524404i −0.879882 0.475192i \(-0.842379\pi\)
−0.0284129 + 0.999596i \(0.509045\pi\)
\(744\) 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
\(749\) 46.6147 12.4904i 1.70327 0.456389i
\(750\) 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 −0.969479 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 0.665669 0.746247i \(-0.268146\pi\)
0.979104 0.203363i \(-0.0651870\pi\)
\(762\) 0 0
\(763\) −10.7321 40.0526i −0.388526 1.45000i
\(764\) 0 0
\(765\) 4.60770 + 17.1962i 0.166592 + 0.621728i
\(766\) 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
\(771\) −32.6603 −1.17623
\(772\) 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
\(779\) −9.69615 2.59808i −0.347401 0.0930857i
\(780\) 0 0
\(781\) −12.3923 + 3.32051i −0.443432 + 0.118817i
\(782\) 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
\(787\) 10.8109 40.3468i 0.385367 1.43821i −0.452222 0.891906i \(-0.649368\pi\)
0.837588 0.546302i \(-0.183965\pi\)
\(788\) 0 0
\(789\) −4.31347 + 2.49038i −0.153563 + 0.0886599i
\(790\) 0 0
\(791\) 37.8564i 1.34602i
\(792\) 0 0
\(793\) 40.3923i 1.43437i