Properties

Label 576.2.bb.c.49.1
Level $576$
Weight $2$
Character 576.49
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 49.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 576.49
Dual form 576.2.bb.c.529.1

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

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

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
\(3\) −0.866025 1.50000i −0.500000 0.866025i
\(4\) 0 0
\(5\) 1.00000 0.267949i 0.447214 0.119831i −0.0281817 0.999603i \(-0.508972\pi\)
0.475395 + 0.879772i \(0.342305\pi\)
\(6\) 0 0
\(7\) −2.36603 + 1.36603i −0.894274 + 0.516309i −0.875338 0.483512i \(-0.839361\pi\)
−0.0189356 + 0.999821i \(0.506028\pi\)
\(8\) 0 0
\(9\) −1.50000 + 2.59808i −0.500000 + 0.866025i
\(10\) 0 0
\(11\) −1.13397 + 4.23205i −0.341906 + 1.27601i 0.554279 + 0.832331i \(0.312994\pi\)
−0.896185 + 0.443680i \(0.853673\pi\)
\(12\) 0 0
\(13\) 0.901924 + 3.36603i 0.250149 + 0.933567i 0.970725 + 0.240192i \(0.0772105\pi\)
−0.720577 + 0.693375i \(0.756123\pi\)
\(14\) 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
\(21\) 4.09808 + 2.36603i 0.894274 + 0.516309i
\(22\) 0 0
\(23\) 4.09808 + 2.36603i 0.854508 + 0.493350i 0.862169 0.506620i \(-0.169105\pi\)
−0.00766135 + 0.999971i \(0.502439\pi\)
\(24\) 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 0.471717 0.881750i \(-0.343635\pi\)
−0.0323566 + 0.999476i \(0.510301\pi\)
\(30\) 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 0.979481 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 \(-0.408600\pi\)
−0.688963 + 0.724797i \(0.741934\pi\)
\(42\) 0 0
\(43\) −2.23205 + 8.33013i −0.340385 + 1.27033i 0.557528 + 0.830158i \(0.311750\pi\)
−0.897912 + 0.440174i \(0.854917\pi\)
\(44\) 0 0
\(45\) −0.803848 + 3.00000i −0.119831 + 0.447214i
\(46\) 0 0
\(47\) −3.83013 6.63397i −0.558681 0.967665i −0.997607 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
\(51\) 4.96410 + 8.59808i 0.695113 + 1.20397i
\(52\) 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
\(59\) −7.33013 + 1.96410i −0.954301 + 0.255704i −0.702186 0.711993i \(-0.747793\pi\)
−0.252115 + 0.967697i \(0.581126\pi\)
\(60\) 0 0
\(61\) 11.1962 + 3.00000i 1.43352 + 0.384111i 0.890260 0.455453i \(-0.150523\pi\)
0.543261 + 0.839564i \(0.317189\pi\)
\(62\) 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 0.985816 + 0.167830i \(0.0536760\pi\)
−0.769827 + 0.638253i \(0.779657\pi\)
\(68\) 0 0
\(69\) 8.19615i 0.986701i
\(70\) 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
\(75\) 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 0.976453 + 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
\(83\) 1.36603 + 0.366025i 0.149941 + 0.0401765i 0.333009 0.942924i \(-0.391936\pi\)
−0.183068 + 0.983100i \(0.558603\pi\)
\(84\) 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 \(0.0338043\pi\)
−0.994366 + 0.106000i \(0.966196\pi\)
\(90\) 0 0
\(91\) −6.73205 6.73205i −0.705711 0.705711i
\(92\) 0 0
\(93\) −0.928203 −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 −0.993461 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
\(101\) 0.535898 2.00000i 0.0533239 0.199007i −0.934125 0.356946i \(-0.883818\pi\)
0.987449 + 0.157938i \(0.0504847\pi\)
\(102\) 0 0
\(103\) −13.0981 7.56218i −1.29059 0.745124i −0.311833 0.950137i \(-0.600943\pi\)
−0.978759 + 0.205014i \(0.934276\pi\)
\(104\) 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 0.330947 + 0.943649i \(0.392632\pi\)
−0.982698 + 0.185216i \(0.940702\pi\)
\(114\) 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 −0.994986 0.100014i \(-0.968111\pi\)
0.811676 0.584108i \(-0.198555\pi\)
\(132\) 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 −0.103857 0.994592i \(-0.533118\pi\)
0.809414 + 0.587239i \(0.199785\pi\)
\(138\) 0 0
\(139\) 11.4282 3.06218i 0.969328 0.259731i 0.260784 0.965397i \(-0.416019\pi\)
0.708544 + 0.705667i \(0.249352\pi\)
\(140\) 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 0.0766003 0.997062i \(-0.475593\pi\)
0.564869 + 0.825181i \(0.308927\pi\)
\(150\) 0 0
\(151\) −0.633975 + 0.366025i −0.0515921 + 0.0297867i −0.525574 0.850748i \(-0.676149\pi\)
0.473982 + 0.880534i \(0.342816\pi\)
\(152\) 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 0.997886 0.0649959i \(-0.0207034\pi\)
−0.896692 + 0.442655i \(0.854037\pi\)
\(158\) 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
\(165\) 6.80385 3.92820i 0.529679 0.305810i
\(166\) 0 0
\(167\) −6.46410 3.73205i −0.500207 0.288795i 0.228592 0.973522i \(-0.426588\pi\)
−0.728799 + 0.684728i \(0.759921\pi\)
\(168\) 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 0.320398 0.947283i \(-0.396183\pi\)
−0.196169 + 0.980570i \(0.562850\pi\)
\(174\) 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
\(187\) 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 0.861799 + 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
\(195\) 3.12436 5.41154i 0.223740 0.387529i
\(196\) 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
\(203\) −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 0.993367 0.114983i \(-0.0366812\pi\)
−0.917773 + 0.397106i \(0.870015\pi\)
\(212\) 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 0.999039 + 0.0438324i \(0.0139568\pi\)
−0.461559 + 0.887109i \(0.652710\pi\)
\(224\) 0 0
\(225\) 11.7846i 0.785641i
\(226\) 0 0
\(227\) −2.13397 0.571797i −0.141637 0.0379515i 0.187304 0.982302i \(-0.440025\pi\)
−0.328941 + 0.944351i \(0.606692\pi\)
\(228\) 0 0
\(229\) 6.83013 1.83013i 0.451347 0.120938i −0.0259823 0.999662i \(-0.508271\pi\)
0.477330 + 0.878724i \(0.341605\pi\)
\(230\) 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
\(237\) 10.3923 18.0000i 0.675053 1.16923i
\(238\) 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
\(243\) −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 0.866745 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 −0.406364 0.913711i \(-0.633204\pi\)
0.994479 0.104934i \(-0.0334632\pi\)
\(258\) 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 −0.421249 0.906945i \(-0.638408\pi\)
0.574813 + 0.818285i \(0.305075\pi\)
\(264\) 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 −0.667395 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
\(275\) −4.45448 16.6244i −0.268615 1.00249i
\(276\) 0 0
\(277\) −6.75833 + 25.2224i −0.406069 + 1.51547i 0.396007 + 0.918247i \(0.370395\pi\)
−0.802076 + 0.597222i \(0.796271\pi\)
\(278\) 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 \(-0.763078\pi\)
0.218926 + 0.975741i \(0.429745\pi\)
\(282\) 0 0
\(283\) 19.5622 5.24167i 1.16285 0.311585i 0.374747 0.927127i \(-0.377730\pi\)
0.788104 + 0.615542i \(0.211063\pi\)
\(284\) 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 −0.412132 0.911124i \(-0.635216\pi\)
0.0986454 + 0.995123i \(0.468549\pi\)
\(294\) 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 −0.788173 0.615454i \(-0.788973\pi\)
0.615454 + 0.788173i \(0.288973\pi\)
\(308\) 0 0
\(309\) 26.1962i 1.49025i
\(310\) 0 0
\(311\) 19.0981 + 11.0263i 1.08295 + 0.625243i 0.931691 0.363251i \(-0.118333\pi\)
0.151261 + 0.988494i \(0.451667\pi\)
\(312\) 0 0
\(313\) 18.6506 10.7679i 1.05420 0.608640i 0.130375 0.991465i \(-0.458382\pi\)
0.923821 + 0.382824i \(0.125049\pi\)
\(314\) 0 0
\(315\) −2.19615 8.19615i −0.123739 0.461801i
\(316\) 0 0
\(317\) −20.5622 5.50962i −1.15489 0.309451i −0.369965 0.929046i \(-0.620630\pi\)
−0.784922 + 0.619595i \(0.787297\pi\)
\(318\) 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 −0.966644 0.256123i \(-0.917555\pi\)
0.965200 + 0.261513i \(0.0842216\pi\)
\(332\) 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 −0.515445 0.856923i \(-0.672373\pi\)
0.999839 + 0.0179267i \(0.00570654\pi\)
\(338\) 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 0.247408 0.968911i \(-0.420421\pi\)
0.698717 + 0.715398i \(0.253755\pi\)
\(348\) 0 0
\(349\) 15.9282 + 4.26795i 0.852617 + 0.228458i 0.658556 0.752531i \(-0.271167\pi\)
0.194061 + 0.980989i \(0.437834\pi\)
\(350\) 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
\(355\) 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 \(0.0961028\pi\)
−0.954769 + 0.297350i \(0.903897\pi\)
\(360\) 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 −0.953713 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
\(371\) 27.8564 + 7.46410i 1.44623 + 0.387517i
\(372\) 0 0
\(373\) 27.4904 7.36603i 1.42340 0.381398i 0.536710 0.843767i \(-0.319667\pi\)
0.886688 + 0.462368i \(0.153000\pi\)
\(374\) 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
\(381\) 3.63397 + 6.29423i 0.186174 + 0.322463i
\(382\) 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
\(389\) −5.29423 + 19.7583i −0.268428 + 1.00179i 0.691691 + 0.722194i \(0.256866\pi\)
−0.960119 + 0.279593i \(0.909800\pi\)
\(390\) 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 −0.907342 0.420393i \(-0.861892\pi\)
0.817742 + 0.575584i \(0.195225\pi\)
\(402\) 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 0.991905 0.126984i \(-0.0405295\pi\)
0.385981 + 0.922507i \(0.373863\pi\)
\(410\) 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 0.908816 0.417196i \(-0.136987\pi\)
−0.995656 + 0.0931055i \(0.970321\pi\)
\(420\) 0 0
\(421\) 8.19615 30.5885i 0.399456 1.49079i −0.414600 0.910004i \(-0.636078\pi\)
0.814056 0.580786i \(-0.197255\pi\)
\(422\) 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 0.157067 0.987588i \(-0.449796\pi\)
0.933810 + 0.357770i \(0.116463\pi\)
\(440\) 0 0
\(441\) 0.696152 + 1.20577i 0.0331501 + 0.0574177i
\(442\) 0 0
\(443\) 4.62436 17.2583i 0.219710 0.819968i −0.764745 0.644332i \(-0.777135\pi\)
0.984455 0.175636i \(-0.0561980\pi\)
\(444\) 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 −0.446249 0.894909i \(-0.647240\pi\)
0.551889 + 0.833917i \(0.313907\pi\)
\(458\) 0 0
\(459\) −29.7846 −1.39023
\(460\) 0 0
\(461\) 35.6865 + 9.56218i 1.66209 + 0.445355i 0.962961 0.269642i \(-0.0869055\pi\)
0.699127 + 0.714997i \(0.253572\pi\)
\(462\) 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 −0.765419 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
\(475\) −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 0.754898 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
\(483\) 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 \(0.0419789\pi\)
−0.991316 + 0.131499i \(0.958021\pi\)
\(488\) 0 0
\(489\) −16.5622 4.43782i −0.748968 0.200685i
\(490\) 0 0
\(491\) 13.8923 3.72243i 0.626951 0.167991i 0.0686652 0.997640i \(-0.478126\pi\)
0.558286 + 0.829649i \(0.311459\pi\)
\(492\) 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 0.998266 0.0588630i \(-0.0187475\pi\)
−0.893955 + 0.448156i \(0.852081\pi\)
\(500\) 0 0
\(501\) 12.9282i 0.577590i
\(502\) 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
\(507\) −1.28461 0.741670i −0.0570515 0.0329387i
\(508\) 0 0
\(509\) 3.07180 + 11.4641i 0.136155 + 0.508137i 0.999990 + 0.00436335i \(0.00138890\pi\)
−0.863835 + 0.503774i \(0.831944\pi\)
\(510\) 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 \(-0.908083\pi\)
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
\(525\) −18.5885 −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 −0.658319 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
\(547\) −32.6244 8.74167i −1.39492 0.373767i −0.518400 0.855138i \(-0.673472\pi\)
−0.876517 + 0.481371i \(0.840139\pi\)
\(548\) 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 −0.947378 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
\(563\) 7.23205 + 26.9904i 0.304795 + 1.13751i 0.933122 + 0.359560i \(0.117073\pi\)
−0.628327 + 0.777949i \(0.716260\pi\)
\(564\) 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 −0.833391 0.552684i \(-0.813604\pi\)
0.0619424 + 0.998080i \(0.480270\pi\)
\(570\) 0 0
\(571\) 3.33013 0.892305i 0.139361 0.0373418i −0.188464 0.982080i \(-0.560351\pi\)
0.327825 + 0.944738i \(0.393684\pi\)
\(572\) 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 0.639900 + 0.768458i \(0.278976\pi\)
−0.938399 + 0.345554i \(0.887691\pi\)
\(588\) 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 0.250570 0.968099i \(-0.419382\pi\)
−0.713113 + 0.701049i \(0.752715\pi\)
\(600\) 0 0
\(601\) −20.5526 + 11.8660i −0.838356 + 0.484025i −0.856705 0.515806i \(-0.827492\pi\)
0.0183488 + 0.999832i \(0.494159\pi\)
\(602\) 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 −0.637405 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 0.316186 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 \(-0.636910\pi\)
−0.995633 + 0.0933485i \(0.970243\pi\)
\(618\) 0 0
\(619\) −4.17949 + 15.5981i −0.167988 + 0.626940i 0.829652 + 0.558281i \(0.188539\pi\)
−0.997640 + 0.0686590i \(0.978128\pi\)
\(620\) 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 \(0.113980\pi\)
−0.936572 + 0.350476i \(0.886020\pi\)
\(632\) 0 0
\(633\) 5.19615 5.19615i 0.206529 0.206529i
\(634\) 0 0
\(635\) −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 −0.930878 0.365331i \(-0.880956\pi\)
0.149053 0.988829i \(-0.452378\pi\)
\(642\) 0 0
\(643\) 2.34936 + 8.76795i 0.0926499 + 0.345774i 0.996653 0.0817525i \(-0.0260517\pi\)
−0.904003 + 0.427527i \(0.859385\pi\)
\(644\) 0 0
\(645\) 13.3923 7.73205i 0.527321 0.304449i
\(646\) 0 0
\(647\) 16.7321i 0.657805i 0.944364 + 0.328902i \(0.106679\pi\)
−0.944364 + 0.328902i \(0.893321\pi\)
\(648\) 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 0.946428 + 0.322915i \(0.104663\pi\)
−0.658173 + 0.752867i \(0.728671\pi\)
\(654\) 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 0.539323 0.842099i \(-0.318680\pi\)
0.0460178 + 0.998941i \(0.485347\pi\)
\(660\) 0 0
\(661\) −8.19615 + 2.19615i −0.318793 + 0.0854204i −0.414667 0.909973i \(-0.636102\pi\)
0.0958740 + 0.995393i \(0.469435\pi\)
\(662\) 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 0.952514 + 0.304495i \(0.0984877\pi\)
−0.212557 + 0.977149i \(0.568179\pi\)
\(674\) 0 0
\(675\) −17.6769 + 10.2058i −0.680385 + 0.392820i
\(676\) 0 0
\(677\) 1.26795 4.73205i 0.0487312 0.181867i −0.937270 0.348603i \(-0.886656\pi\)
0.986002 + 0.166736i \(0.0533227\pi\)
\(678\) 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
\(691\) −9.29423 2.49038i −0.353569 0.0947386i 0.0776628 0.996980i \(-0.475254\pi\)
−0.431232 + 0.902241i \(0.641921\pi\)
\(692\) 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 −0.821608 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
\(707\) 1.46410 + 5.46410i 0.0550632 + 0.205499i
\(708\) 0 0
\(709\) −9.80385 + 36.5885i −0.368191 + 1.37411i 0.494852 + 0.868978i \(0.335222\pi\)
−0.863043 + 0.505131i \(0.831444\pi\)
\(710\) 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 0.140755 0.990044i \(-0.455047\pi\)
0.927781 + 0.373124i \(0.121714\pi\)
\(728\) 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 0.998781 0.0493698i \(-0.0157213\pi\)
−0.889654 + 0.456635i \(0.849055\pi\)
\(734\) 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
\(741\) 20.1962i 0.741924i
\(742\) 0 0
\(743\) −24.7583 14.2942i −0.908295 0.524404i −0.0284129 0.999596i \(-0.509045\pi\)
−0.879882 + 0.475192i \(0.842379\pi\)
\(744\) 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 −0.657966 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 0.245176 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 0.979104 + 0.203363i \(0.0651870\pi\)
0.665669 + 0.746247i \(0.268146\pi\)
\(762\) 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 0.490604 + 0.871383i \(0.336776\pi\)
−0.999942 + 0.0108155i \(0.996557\pi\)
\(770\) 0 0
\(771\) −32.6603 −1.17623
\(772\) 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
\(779\) −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 0.837588 + 0.546302i \(0.183965\pi\)
−0.452222 + 0.891906i \(0.649368\pi\)
\(788\) 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
\(794\)