Properties

Label 432.2.y.c.37.1
Level $432$
Weight $2$
Character 432.37
Analytic conductor $3.450$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.y (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 37.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 432.37
Dual form 432.2.y.c.397.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.366025 + 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(3.73205 - 1.00000i) q^{5} +(-0.633975 + 0.366025i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})\) \(q+(-0.366025 + 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(3.73205 - 1.00000i) q^{5} +(-0.633975 + 0.366025i) q^{7} +(2.00000 - 2.00000i) q^{8} +5.46410i q^{10} +(0.767949 - 2.86603i) q^{11} +(-1.63397 - 6.09808i) q^{13} +(-0.267949 - 1.00000i) q^{14} +(2.00000 + 3.46410i) q^{16} +2.26795 q^{17} +(-0.633975 + 0.633975i) q^{19} +(-7.46410 - 2.00000i) q^{20} +(3.63397 + 2.09808i) q^{22} +(1.09808 + 0.633975i) q^{23} +(8.59808 - 4.96410i) q^{25} +8.92820 q^{26} +1.46410 q^{28} +(2.36603 + 0.633975i) q^{29} +(-3.73205 + 6.46410i) q^{31} +(-5.46410 + 1.46410i) q^{32} +(-0.830127 + 3.09808i) q^{34} +(-2.00000 + 2.00000i) q^{35} +(1.26795 + 1.26795i) q^{37} +(-0.633975 - 1.09808i) q^{38} +(5.46410 - 9.46410i) q^{40} +(2.59808 + 1.50000i) q^{41} +(0.330127 - 1.23205i) q^{43} +(-4.19615 + 4.19615i) q^{44} +(-1.26795 + 1.26795i) q^{46} +(4.83013 + 8.36603i) q^{47} +(-3.23205 + 5.59808i) q^{49} +(3.63397 + 13.5622i) q^{50} +(-3.26795 + 12.1962i) q^{52} +(0.535898 + 0.535898i) q^{53} -11.4641i q^{55} +(-0.535898 + 2.00000i) q^{56} +(-1.73205 + 3.00000i) q^{58} +(-4.96410 + 1.33013i) q^{59} +(-3.00000 - 0.803848i) q^{61} +(-7.46410 - 7.46410i) q^{62} -8.00000i q^{64} +(-12.1962 - 21.1244i) q^{65} +(1.40192 + 5.23205i) q^{67} +(-3.92820 - 2.26795i) q^{68} +(-2.00000 - 3.46410i) q^{70} -10.9282i q^{71} +9.73205i q^{73} +(-2.19615 + 1.26795i) q^{74} +(1.73205 - 0.464102i) q^{76} +(0.562178 + 2.09808i) q^{77} +(-6.00000 - 10.3923i) q^{79} +(10.9282 + 10.9282i) q^{80} +(-3.00000 + 3.00000i) q^{82} +(1.36603 + 0.366025i) q^{83} +(8.46410 - 2.26795i) q^{85} +(1.56218 + 0.901924i) q^{86} +(-4.19615 - 7.26795i) q^{88} -2.00000i q^{89} +(3.26795 + 3.26795i) q^{91} +(-1.26795 - 2.19615i) q^{92} +(-13.1962 + 3.53590i) q^{94} +(-1.73205 + 3.00000i) q^{95} +(-4.13397 - 7.16025i) q^{97} +(-6.46410 - 6.46410i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} + 8q^{5} - 6q^{7} + 8q^{8} + O(q^{10}) \) \( 4q + 2q^{2} + 8q^{5} - 6q^{7} + 8q^{8} + 10q^{11} - 10q^{13} - 8q^{14} + 8q^{16} + 16q^{17} - 6q^{19} - 16q^{20} + 18q^{22} - 6q^{23} + 24q^{25} + 8q^{26} - 8q^{28} + 6q^{29} - 8q^{31} - 8q^{32} + 14q^{34} - 8q^{35} + 12q^{37} - 6q^{38} + 8q^{40} - 16q^{43} + 4q^{44} - 12q^{46} + 2q^{47} - 6q^{49} + 18q^{50} - 20q^{52} + 16q^{53} - 16q^{56} - 6q^{59} - 12q^{61} - 16q^{62} - 28q^{65} + 16q^{67} + 12q^{68} - 8q^{70} + 12q^{74} - 22q^{77} - 24q^{79} + 16q^{80} - 12q^{82} + 2q^{83} + 20q^{85} - 18q^{86} + 4q^{88} + 20q^{91} - 12q^{92} - 32q^{94} - 20q^{97} - 12q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.366025 + 1.36603i −0.258819 + 0.965926i
\(3\) 0 0
\(4\) −1.73205 1.00000i −0.866025 0.500000i
\(5\) 3.73205 1.00000i 1.66902 0.447214i 0.704177 0.710025i \(-0.251316\pi\)
0.964847 + 0.262811i \(0.0846497\pi\)
\(6\) 0 0
\(7\) −0.633975 + 0.366025i −0.239620 + 0.138345i −0.615002 0.788526i \(-0.710845\pi\)
0.375382 + 0.926870i \(0.377511\pi\)
\(8\) 2.00000 2.00000i 0.707107 0.707107i
\(9\) 0 0
\(10\) 5.46410i 1.72790i
\(11\) 0.767949 2.86603i 0.231545 0.864139i −0.748130 0.663552i \(-0.769048\pi\)
0.979676 0.200587i \(-0.0642851\pi\)
\(12\) 0 0
\(13\) −1.63397 6.09808i −0.453183 1.69130i −0.693375 0.720577i \(-0.743877\pi\)
0.240192 0.970725i \(-0.422790\pi\)
\(14\) −0.267949 1.00000i −0.0716124 0.267261i
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 2.26795 0.550058 0.275029 0.961436i \(-0.411312\pi\)
0.275029 + 0.961436i \(0.411312\pi\)
\(18\) 0 0
\(19\) −0.633975 + 0.633975i −0.145444 + 0.145444i −0.776079 0.630635i \(-0.782794\pi\)
0.630635 + 0.776079i \(0.282794\pi\)
\(20\) −7.46410 2.00000i −1.66902 0.447214i
\(21\) 0 0
\(22\) 3.63397 + 2.09808i 0.774766 + 0.447311i
\(23\) 1.09808 + 0.633975i 0.228965 + 0.132193i 0.610094 0.792329i \(-0.291132\pi\)
−0.381130 + 0.924522i \(0.624465\pi\)
\(24\) 0 0
\(25\) 8.59808 4.96410i 1.71962 0.992820i
\(26\) 8.92820 1.75096
\(27\) 0 0
\(28\) 1.46410 0.276689
\(29\) 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
\(31\) −3.73205 + 6.46410i −0.670296 + 1.16099i 0.307524 + 0.951540i \(0.400500\pi\)
−0.977820 + 0.209447i \(0.932834\pi\)
\(32\) −5.46410 + 1.46410i −0.965926 + 0.258819i
\(33\) 0 0
\(34\) −0.830127 + 3.09808i −0.142366 + 0.531316i
\(35\) −2.00000 + 2.00000i −0.338062 + 0.338062i
\(36\) 0 0
\(37\) 1.26795 + 1.26795i 0.208450 + 0.208450i 0.803608 0.595159i \(-0.202911\pi\)
−0.595159 + 0.803608i \(0.702911\pi\)
\(38\) −0.633975 1.09808i −0.102844 0.178131i
\(39\) 0 0
\(40\) 5.46410 9.46410i 0.863950 1.49641i
\(41\) 2.59808 + 1.50000i 0.405751 + 0.234261i 0.688963 0.724797i \(-0.258066\pi\)
−0.283211 + 0.959058i \(0.591400\pi\)
\(42\) 0 0
\(43\) 0.330127 1.23205i 0.0503439 0.187886i −0.936175 0.351535i \(-0.885660\pi\)
0.986519 + 0.163649i \(0.0523265\pi\)
\(44\) −4.19615 + 4.19615i −0.632594 + 0.632594i
\(45\) 0 0
\(46\) −1.26795 + 1.26795i −0.186949 + 0.186949i
\(47\) 4.83013 + 8.36603i 0.704546 + 1.22031i 0.966855 + 0.255326i \(0.0821828\pi\)
−0.262309 + 0.964984i \(0.584484\pi\)
\(48\) 0 0
\(49\) −3.23205 + 5.59808i −0.461722 + 0.799725i
\(50\) 3.63397 + 13.5622i 0.513922 + 1.91798i
\(51\) 0 0
\(52\) −3.26795 + 12.1962i −0.453183 + 1.69130i
\(53\) 0.535898 + 0.535898i 0.0736113 + 0.0736113i 0.742954 0.669343i \(-0.233424\pi\)
−0.669343 + 0.742954i \(0.733424\pi\)
\(54\) 0 0
\(55\) 11.4641i 1.54582i
\(56\) −0.535898 + 2.00000i −0.0716124 + 0.267261i
\(57\) 0 0
\(58\) −1.73205 + 3.00000i −0.227429 + 0.393919i
\(59\) −4.96410 + 1.33013i −0.646271 + 0.173168i −0.567042 0.823689i \(-0.691912\pi\)
−0.0792287 + 0.996856i \(0.525246\pi\)
\(60\) 0 0
\(61\) −3.00000 0.803848i −0.384111 0.102922i 0.0615961 0.998101i \(-0.480381\pi\)
−0.445707 + 0.895179i \(0.647048\pi\)
\(62\) −7.46410 7.46410i −0.947942 0.947942i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) −12.1962 21.1244i −1.51275 2.62015i
\(66\) 0 0
\(67\) 1.40192 + 5.23205i 0.171272 + 0.639197i 0.997157 + 0.0753572i \(0.0240097\pi\)
−0.825884 + 0.563840i \(0.809324\pi\)
\(68\) −3.92820 2.26795i −0.476365 0.275029i
\(69\) 0 0
\(70\) −2.00000 3.46410i −0.239046 0.414039i
\(71\) 10.9282i 1.29694i −0.761241 0.648470i \(-0.775409\pi\)
0.761241 0.648470i \(-0.224591\pi\)
\(72\) 0 0
\(73\) 9.73205i 1.13905i 0.821974 + 0.569525i \(0.192873\pi\)
−0.821974 + 0.569525i \(0.807127\pi\)
\(74\) −2.19615 + 1.26795i −0.255298 + 0.147396i
\(75\) 0 0
\(76\) 1.73205 0.464102i 0.198680 0.0532361i
\(77\) 0.562178 + 2.09808i 0.0640661 + 0.239098i
\(78\) 0 0
\(79\) −6.00000 10.3923i −0.675053 1.16923i −0.976453 0.215728i \(-0.930788\pi\)
0.301401 0.953498i \(-0.402546\pi\)
\(80\) 10.9282 + 10.9282i 1.22181 + 1.22181i
\(81\) 0 0
\(82\) −3.00000 + 3.00000i −0.331295 + 0.331295i
\(83\) 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
\(85\) 8.46410 2.26795i 0.918061 0.245994i
\(86\) 1.56218 + 0.901924i 0.168454 + 0.0972569i
\(87\) 0 0
\(88\) −4.19615 7.26795i −0.447311 0.774766i
\(89\) 2.00000i 0.212000i −0.994366 0.106000i \(-0.966196\pi\)
0.994366 0.106000i \(-0.0338043\pi\)
\(90\) 0 0
\(91\) 3.26795 + 3.26795i 0.342574 + 0.342574i
\(92\) −1.26795 2.19615i −0.132193 0.228965i
\(93\) 0 0
\(94\) −13.1962 + 3.53590i −1.36108 + 0.364700i
\(95\) −1.73205 + 3.00000i −0.177705 + 0.307794i
\(96\) 0 0
\(97\) −4.13397 7.16025i −0.419742 0.727014i 0.576172 0.817329i \(-0.304546\pi\)
−0.995913 + 0.0903150i \(0.971213\pi\)
\(98\) −6.46410 6.46410i −0.652973 0.652973i
\(99\) 0 0
\(100\) −19.8564 −1.98564
\(101\) 2.00000 7.46410i 0.199007 0.742706i −0.792186 0.610280i \(-0.791057\pi\)
0.991193 0.132426i \(-0.0422765\pi\)
\(102\) 0 0
\(103\) −7.90192 4.56218i −0.778600 0.449525i 0.0573341 0.998355i \(-0.481740\pi\)
−0.835934 + 0.548830i \(0.815073\pi\)
\(104\) −15.4641 8.92820i −1.51638 0.875482i
\(105\) 0 0
\(106\) −0.928203 + 0.535898i −0.0901551 + 0.0520511i
\(107\) 13.4904 + 13.4904i 1.30416 + 1.30416i 0.925558 + 0.378607i \(0.123597\pi\)
0.378607 + 0.925558i \(0.376403\pi\)
\(108\) 0 0
\(109\) 7.26795 7.26795i 0.696143 0.696143i −0.267433 0.963576i \(-0.586175\pi\)
0.963576 + 0.267433i \(0.0861754\pi\)
\(110\) 15.6603 + 4.19615i 1.49315 + 0.400087i
\(111\) 0 0
\(112\) −2.53590 1.46410i −0.239620 0.138345i
\(113\) −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
\(116\) −3.46410 3.46410i −0.321634 0.321634i
\(117\) 0 0
\(118\) 7.26795i 0.669069i
\(119\) −1.43782 + 0.830127i −0.131805 + 0.0760976i
\(120\) 0 0
\(121\) 1.90192 + 1.09808i 0.172902 + 0.0998251i
\(122\) 2.19615 3.80385i 0.198830 0.344384i
\(123\) 0 0
\(124\) 12.9282 7.46410i 1.16099 0.670296i
\(125\) 13.4641 13.4641i 1.20427 1.20427i
\(126\) 0 0
\(127\) −6.19615 −0.549820 −0.274910 0.961470i \(-0.588648\pi\)
−0.274910 + 0.961470i \(0.588648\pi\)
\(128\) 10.9282 + 2.92820i 0.965926 + 0.258819i
\(129\) 0 0
\(130\) 33.3205 8.92820i 2.92240 0.783055i
\(131\) −0.830127 3.09808i −0.0725285 0.270680i 0.920133 0.391606i \(-0.128080\pi\)
−0.992662 + 0.120926i \(0.961414\pi\)
\(132\) 0 0
\(133\) 0.169873 0.633975i 0.0147299 0.0549726i
\(134\) −7.66025 −0.661745
\(135\) 0 0
\(136\) 4.53590 4.53590i 0.388950 0.388950i
\(137\) −14.2583 + 8.23205i −1.21817 + 0.703312i −0.964527 0.263986i \(-0.914963\pi\)
−0.253645 + 0.967297i \(0.581629\pi\)
\(138\) 0 0
\(139\) −9.06218 + 2.42820i −0.768644 + 0.205958i −0.621772 0.783198i \(-0.713587\pi\)
−0.146872 + 0.989156i \(0.546920\pi\)
\(140\) 5.46410 1.46410i 0.461801 0.123739i
\(141\) 0 0
\(142\) 14.9282 + 4.00000i 1.25275 + 0.335673i
\(143\) −18.7321 −1.56645
\(144\) 0 0
\(145\) 9.46410 0.785951
\(146\) −13.2942 3.56218i −1.10024 0.294808i
\(147\) 0 0
\(148\) −0.928203 3.46410i −0.0762978 0.284747i
\(149\) −3.09808 + 0.830127i −0.253804 + 0.0680067i −0.383478 0.923550i \(-0.625274\pi\)
0.129674 + 0.991557i \(0.458607\pi\)
\(150\) 0 0
\(151\) −2.36603 + 1.36603i −0.192544 + 0.111166i −0.593173 0.805075i \(-0.702125\pi\)
0.400629 + 0.916240i \(0.368792\pi\)
\(152\) 2.53590i 0.205689i
\(153\) 0 0
\(154\) −3.07180 −0.247532
\(155\) −7.46410 + 27.8564i −0.599531 + 2.23748i
\(156\) 0 0
\(157\) −1.26795 4.73205i −0.101193 0.377659i 0.896692 0.442655i \(-0.145963\pi\)
−0.997886 + 0.0649959i \(0.979297\pi\)
\(158\) 16.3923 4.39230i 1.30410 0.349433i
\(159\) 0 0
\(160\) −18.9282 + 10.9282i −1.49641 + 0.863950i
\(161\) −0.928203 −0.0731527
\(162\) 0 0
\(163\) −7.00000 + 7.00000i −0.548282 + 0.548282i −0.925944 0.377661i \(-0.876728\pi\)
0.377661 + 0.925944i \(0.376728\pi\)
\(164\) −3.00000 5.19615i −0.234261 0.405751i
\(165\) 0 0
\(166\) −1.00000 + 1.73205i −0.0776151 + 0.134433i
\(167\) −0.464102 0.267949i −0.0359133 0.0207345i 0.481936 0.876206i \(-0.339934\pi\)
−0.517849 + 0.855472i \(0.673267\pi\)
\(168\) 0 0
\(169\) −23.2583 + 13.4282i −1.78910 + 1.03294i
\(170\) 12.3923i 0.950446i
\(171\) 0 0
\(172\) −1.80385 + 1.80385i −0.137542 + 0.137542i
\(173\) 12.5622 + 3.36603i 0.955085 + 0.255914i 0.702519 0.711665i \(-0.252059\pi\)
0.252566 + 0.967580i \(0.418725\pi\)
\(174\) 0 0
\(175\) −3.63397 + 6.29423i −0.274703 + 0.475799i
\(176\) 11.4641 3.07180i 0.864139 0.231545i
\(177\) 0 0
\(178\) 2.73205 + 0.732051i 0.204776 + 0.0548695i
\(179\) −11.9282 + 11.9282i −0.891556 + 0.891556i −0.994670 0.103114i \(-0.967119\pi\)
0.103114 + 0.994670i \(0.467119\pi\)
\(180\) 0 0
\(181\) 13.3923 + 13.3923i 0.995442 + 0.995442i 0.999990 0.00454748i \(-0.00144751\pi\)
−0.00454748 + 0.999990i \(0.501448\pi\)
\(182\) −5.66025 + 3.26795i −0.419566 + 0.242237i
\(183\) 0 0
\(184\) 3.46410 0.928203i 0.255377 0.0684280i
\(185\) 6.00000 + 3.46410i 0.441129 + 0.254686i
\(186\) 0 0
\(187\) 1.74167 6.50000i 0.127364 0.475327i
\(188\) 19.3205i 1.40909i
\(189\) 0 0
\(190\) −3.46410 3.46410i −0.251312 0.251312i
\(191\) −7.02628 12.1699i −0.508404 0.880581i −0.999953 0.00973114i \(-0.996902\pi\)
0.491549 0.870850i \(-0.336431\pi\)
\(192\) 0 0
\(193\) −9.13397 + 15.8205i −0.657478 + 1.13879i 0.323789 + 0.946129i \(0.395043\pi\)
−0.981266 + 0.192656i \(0.938290\pi\)
\(194\) 11.2942 3.02628i 0.810878 0.217274i
\(195\) 0 0
\(196\) 11.1962 6.46410i 0.799725 0.461722i
\(197\) 3.66025 + 3.66025i 0.260782 + 0.260782i 0.825372 0.564590i \(-0.190966\pi\)
−0.564590 + 0.825372i \(0.690966\pi\)
\(198\) 0 0
\(199\) 0.875644i 0.0620728i −0.999518 0.0310364i \(-0.990119\pi\)
0.999518 0.0310364i \(-0.00988078\pi\)
\(200\) 7.26795 27.1244i 0.513922 1.91798i
\(201\) 0 0
\(202\) 9.46410 + 5.46410i 0.665892 + 0.384453i
\(203\) −1.73205 + 0.464102i −0.121566 + 0.0325735i
\(204\) 0 0
\(205\) 11.1962 + 3.00000i 0.781973 + 0.209529i
\(206\) 9.12436 9.12436i 0.635724 0.635724i
\(207\) 0 0
\(208\) 17.8564 17.8564i 1.23812 1.23812i
\(209\) 1.33013 + 2.30385i 0.0920068 + 0.159360i
\(210\) 0 0
\(211\) −1.09808 4.09808i −0.0755947 0.282123i 0.917773 0.397106i \(-0.129985\pi\)
−0.993367 + 0.114983i \(0.963319\pi\)
\(212\) −0.392305 1.46410i −0.0269436 0.100555i
\(213\) 0 0
\(214\) −23.3660 + 13.4904i −1.59727 + 0.922183i
\(215\) 4.92820i 0.336101i
\(216\) 0 0
\(217\) 5.46410i 0.370927i
\(218\) 7.26795 + 12.5885i 0.492248 + 0.852598i
\(219\) 0 0
\(220\) −11.4641 + 19.8564i −0.772910 + 1.33872i
\(221\) −3.70577 13.8301i −0.249277 0.930315i
\(222\) 0 0
\(223\) 11.0263 + 19.0981i 0.738374 + 1.27890i 0.953227 + 0.302255i \(0.0977395\pi\)
−0.214853 + 0.976646i \(0.568927\pi\)
\(224\) 2.92820 2.92820i 0.195649 0.195649i
\(225\) 0 0
\(226\) −13.8564 13.8564i −0.921714 0.921714i
\(227\) 14.4282 + 3.86603i 0.957633 + 0.256597i 0.703598 0.710598i \(-0.251575\pi\)
0.254035 + 0.967195i \(0.418242\pi\)
\(228\) 0 0
\(229\) 6.83013 1.83013i 0.451347 0.120938i −0.0259823 0.999662i \(-0.508271\pi\)
0.477330 + 0.878724i \(0.341605\pi\)
\(230\) −3.46410 + 6.00000i −0.228416 + 0.395628i
\(231\) 0 0
\(232\) 6.00000 3.46410i 0.393919 0.227429i
\(233\) 7.19615i 0.471436i 0.971822 + 0.235718i \(0.0757441\pi\)
−0.971822 + 0.235718i \(0.924256\pi\)
\(234\) 0 0
\(235\) 26.3923 + 26.3923i 1.72164 + 1.72164i
\(236\) 9.92820 + 2.66025i 0.646271 + 0.173168i
\(237\) 0 0
\(238\) −0.607695 2.26795i −0.0393910 0.147009i
\(239\) 13.0981 22.6865i 0.847244 1.46747i −0.0364139 0.999337i \(-0.511593\pi\)
0.883658 0.468133i \(-0.155073\pi\)
\(240\) 0 0
\(241\) −6.40192 11.0885i −0.412384 0.714270i 0.582766 0.812640i \(-0.301971\pi\)
−0.995150 + 0.0983699i \(0.968637\pi\)
\(242\) −2.19615 + 2.19615i −0.141174 + 0.141174i
\(243\) 0 0
\(244\) 4.39230 + 4.39230i 0.281189 + 0.281189i
\(245\) −6.46410 + 24.1244i −0.412976 + 1.54125i
\(246\) 0 0
\(247\) 4.90192 + 2.83013i 0.311902 + 0.180077i
\(248\) 5.46410 + 20.3923i 0.346971 + 1.29491i
\(249\) 0 0
\(250\) 13.4641 + 23.3205i 0.851545 + 1.47492i
\(251\) −2.83013 2.83013i −0.178636 0.178636i 0.612125 0.790761i \(-0.290315\pi\)
−0.790761 + 0.612125i \(0.790315\pi\)
\(252\) 0 0
\(253\) 2.66025 2.66025i 0.167249 0.167249i
\(254\) 2.26795 8.46410i 0.142304 0.531085i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 4.42820 7.66987i 0.276224 0.478434i −0.694219 0.719763i \(-0.744250\pi\)
0.970443 + 0.241330i \(0.0775836\pi\)
\(258\) 0 0
\(259\) −1.26795 0.339746i −0.0787865 0.0211108i
\(260\) 48.7846i 3.02549i
\(261\) 0 0
\(262\) 4.53590 0.280229
\(263\) 23.4904 13.5622i 1.44848 0.836280i 0.450088 0.892984i \(-0.351393\pi\)
0.998391 + 0.0567045i \(0.0180593\pi\)
\(264\) 0 0
\(265\) 2.53590 + 1.46410i 0.155779 + 0.0899390i
\(266\) 0.803848 + 0.464102i 0.0492871 + 0.0284559i
\(267\) 0 0
\(268\) 2.80385 10.4641i 0.171272 0.639197i
\(269\) −4.73205 + 4.73205i −0.288518 + 0.288518i −0.836494 0.547976i \(-0.815399\pi\)
0.547976 + 0.836494i \(0.315399\pi\)
\(270\) 0 0
\(271\) 20.3923 1.23874 0.619372 0.785098i \(-0.287387\pi\)
0.619372 + 0.785098i \(0.287387\pi\)
\(272\) 4.53590 + 7.85641i 0.275029 + 0.476365i
\(273\) 0 0
\(274\) −6.02628 22.4904i −0.364061 1.35869i
\(275\) −7.62436 28.4545i −0.459766 1.71587i
\(276\) 0 0
\(277\) −4.22243 + 15.7583i −0.253701 + 0.946826i 0.715107 + 0.699015i \(0.246378\pi\)
−0.968808 + 0.247811i \(0.920289\pi\)
\(278\) 13.2679i 0.795759i
\(279\) 0 0
\(280\) 8.00000i 0.478091i
\(281\) 8.66025 5.00000i 0.516627 0.298275i −0.218926 0.975741i \(-0.570255\pi\)
0.735554 + 0.677466i \(0.236922\pi\)
\(282\) 0 0
\(283\) 27.7583 7.43782i 1.65006 0.442133i 0.690431 0.723398i \(-0.257421\pi\)
0.959630 + 0.281265i \(0.0907541\pi\)
\(284\) −10.9282 + 18.9282i −0.648470 + 1.12318i
\(285\) 0 0
\(286\) 6.85641 25.5885i 0.405428 1.51308i
\(287\) −2.19615 −0.129635
\(288\) 0 0
\(289\) −11.8564 −0.697436
\(290\) −3.46410 + 12.9282i −0.203419 + 0.759170i
\(291\) 0 0
\(292\) 9.73205 16.8564i 0.569525 0.986447i
\(293\) −13.5622 + 3.63397i −0.792311 + 0.212299i −0.632205 0.774801i \(-0.717850\pi\)
−0.160106 + 0.987100i \(0.551183\pi\)
\(294\) 0 0
\(295\) −17.1962 + 9.92820i −1.00120 + 0.578042i
\(296\) 5.07180 0.294792
\(297\) 0 0
\(298\) 4.53590i 0.262758i
\(299\) 2.07180 7.73205i 0.119815 0.447156i
\(300\) 0 0
\(301\) 0.241670 + 0.901924i 0.0139296 + 0.0519860i
\(302\) −1.00000 3.73205i −0.0575435 0.214755i
\(303\) 0 0
\(304\) −3.46410 0.928203i −0.198680 0.0532361i
\(305\) −12.0000 −0.687118
\(306\) 0 0
\(307\) −16.0263 + 16.0263i −0.914668 + 0.914668i −0.996635 0.0819670i \(-0.973880\pi\)
0.0819670 + 0.996635i \(0.473880\pi\)
\(308\) 1.12436 4.19615i 0.0640661 0.239098i
\(309\) 0 0
\(310\) −35.3205 20.3923i −2.00607 1.15821i
\(311\) −13.9019 8.02628i −0.788306 0.455129i 0.0510600 0.998696i \(-0.483740\pi\)
−0.839366 + 0.543567i \(0.817073\pi\)
\(312\) 0 0
\(313\) 24.6506 14.2321i 1.39334 0.804443i 0.399653 0.916666i \(-0.369131\pi\)
0.993683 + 0.112223i \(0.0357972\pi\)
\(314\) 6.92820 0.390981
\(315\) 0 0
\(316\) 24.0000i 1.35011i
\(317\) −31.4904 8.43782i −1.76868 0.473915i −0.780231 0.625492i \(-0.784898\pi\)
−0.988445 + 0.151577i \(0.951565\pi\)
\(318\) 0 0
\(319\) 3.63397 6.29423i 0.203464 0.352409i
\(320\) −8.00000 29.8564i −0.447214 1.66902i
\(321\) 0 0
\(322\) 0.339746 1.26795i 0.0189333 0.0706600i
\(323\) −1.43782 + 1.43782i −0.0800026 + 0.0800026i
\(324\) 0 0
\(325\) −44.3205 44.3205i −2.45846 2.45846i
\(326\) −7.00000 12.1244i −0.387694 0.671506i
\(327\) 0 0
\(328\) 8.19615 2.19615i 0.452557 0.121262i
\(329\) −6.12436 3.53590i −0.337647 0.194940i
\(330\) 0 0
\(331\) 5.09808 19.0263i 0.280216 1.04578i −0.672049 0.740506i \(-0.734586\pi\)
0.952265 0.305273i \(-0.0987476\pi\)
\(332\) −2.00000 2.00000i −0.109764 0.109764i
\(333\) 0 0
\(334\) 0.535898 0.535898i 0.0293231 0.0293231i
\(335\) 10.4641 + 18.1244i 0.571715 + 0.990239i
\(336\) 0 0
\(337\) −11.8923 + 20.5981i −0.647815 + 1.12205i 0.335829 + 0.941923i \(0.390984\pi\)
−0.983644 + 0.180126i \(0.942350\pi\)
\(338\) −9.83013 36.6865i −0.534688 1.99548i
\(339\) 0 0
\(340\) −16.9282 4.53590i −0.918061 0.245994i
\(341\) 15.6603 + 15.6603i 0.848050 + 0.848050i
\(342\) 0 0
\(343\) 9.85641i 0.532196i
\(344\) −1.80385 3.12436i −0.0972569 0.168454i
\(345\) 0 0
\(346\) −9.19615 + 15.9282i −0.494388 + 0.856306i
\(347\) 24.7224 6.62436i 1.32717 0.355614i 0.475510 0.879710i \(-0.342263\pi\)
0.851659 + 0.524096i \(0.175597\pi\)
\(348\) 0 0
\(349\) −7.73205 2.07180i −0.413887 0.110901i 0.0458657 0.998948i \(-0.485395\pi\)
−0.459753 + 0.888047i \(0.652062\pi\)
\(350\) −7.26795 7.26795i −0.388488 0.388488i
\(351\) 0 0
\(352\) 16.7846i 0.894623i
\(353\) 10.1603 + 17.5981i 0.540776 + 0.936651i 0.998860 + 0.0477421i \(0.0152026\pi\)
−0.458084 + 0.888909i \(0.651464\pi\)
\(354\) 0 0
\(355\) −10.9282 40.7846i −0.580009 2.16462i
\(356\) −2.00000 + 3.46410i −0.106000 + 0.183597i
\(357\) 0 0
\(358\) −11.9282 20.6603i −0.630425 1.09193i
\(359\) 14.7321i 0.777528i 0.921337 + 0.388764i \(0.127098\pi\)
−0.921337 + 0.388764i \(0.872902\pi\)
\(360\) 0 0
\(361\) 18.1962i 0.957692i
\(362\) −23.1962 + 13.3923i −1.21916 + 0.703884i
\(363\) 0 0
\(364\) −2.39230 8.92820i −0.125391 0.467965i
\(365\) 9.73205 + 36.3205i 0.509399 + 1.90110i
\(366\) 0 0
\(367\) −10.1244 17.5359i −0.528487 0.915366i −0.999448 0.0332125i \(-0.989426\pi\)
0.470961 0.882154i \(-0.343907\pi\)
\(368\) 5.07180i 0.264386i
\(369\) 0 0
\(370\) −6.92820 + 6.92820i −0.360180 + 0.360180i
\(371\) −0.535898 0.143594i −0.0278225 0.00745501i
\(372\) 0 0
\(373\) −5.63397 + 1.50962i −0.291716 + 0.0781651i −0.401709 0.915767i \(-0.631584\pi\)
0.109993 + 0.993932i \(0.464917\pi\)
\(374\) 8.24167 + 4.75833i 0.426167 + 0.246047i
\(375\) 0 0
\(376\) 26.3923 + 7.07180i 1.36108 + 0.364700i
\(377\) 15.4641i 0.796442i
\(378\) 0 0
\(379\) −18.7583 18.7583i −0.963551 0.963551i 0.0358080 0.999359i \(-0.488600\pi\)
−0.999359 + 0.0358080i \(0.988600\pi\)
\(380\) 6.00000 3.46410i 0.307794 0.177705i
\(381\) 0 0
\(382\) 19.1962 5.14359i 0.982161 0.263169i
\(383\) 3.26795 5.66025i 0.166984 0.289225i −0.770374 0.637593i \(-0.779930\pi\)
0.937358 + 0.348367i \(0.113264\pi\)
\(384\) 0 0
\(385\) 4.19615 + 7.26795i 0.213856 + 0.370409i
\(386\) −18.2679 18.2679i −0.929814 0.929814i
\(387\) 0 0
\(388\) 16.5359i 0.839483i
\(389\) 2.75833 10.2942i 0.139853 0.521938i −0.860078 0.510163i \(-0.829585\pi\)
0.999931 0.0117752i \(-0.00374824\pi\)
\(390\) 0 0
\(391\) 2.49038 + 1.43782i 0.125944 + 0.0727138i
\(392\) 4.73205 + 17.6603i 0.239005 + 0.891978i
\(393\) 0 0
\(394\) −6.33975 + 3.66025i −0.319392 + 0.184401i
\(395\) −32.7846 32.7846i −1.64957 1.64957i
\(396\) 0 0
\(397\) −12.7321 + 12.7321i −0.639003 + 0.639003i −0.950310 0.311306i \(-0.899233\pi\)
0.311306 + 0.950310i \(0.399233\pi\)
\(398\) 1.19615 + 0.320508i 0.0599577 + 0.0160656i
\(399\) 0 0
\(400\) 34.3923 + 19.8564i 1.71962 + 0.992820i
\(401\) −13.7942 + 23.8923i −0.688851 + 1.19312i 0.283359 + 0.959014i \(0.408551\pi\)
−0.972210 + 0.234111i \(0.924782\pi\)
\(402\) 0 0
\(403\) 45.5167 + 12.1962i 2.26735 + 0.607534i
\(404\) −10.9282 + 10.9282i −0.543698 + 0.543698i
\(405\) 0 0
\(406\) 2.53590i 0.125855i
\(407\) 4.60770 2.66025i 0.228395 0.131864i
\(408\) 0 0
\(409\) −26.1340 15.0885i −1.29224 0.746076i −0.313191 0.949690i \(-0.601398\pi\)
−0.979051 + 0.203614i \(0.934731\pi\)
\(410\) −8.19615 + 14.1962i −0.404779 + 0.701098i
\(411\) 0 0
\(412\) 9.12436 + 15.8038i 0.449525 + 0.778600i
\(413\) 2.66025 2.66025i 0.130903 0.130903i
\(414\) 0 0
\(415\) 5.46410 0.268222
\(416\) 17.8564 + 30.9282i 0.875482 + 1.51638i
\(417\) 0 0
\(418\) −3.63397 + 0.973721i −0.177744 + 0.0476262i
\(419\) 8.36603 + 31.2224i 0.408707 + 1.52532i 0.797115 + 0.603828i \(0.206359\pi\)
−0.388408 + 0.921488i \(0.626975\pi\)
\(420\) 0 0
\(421\) 0.588457 2.19615i 0.0286797 0.107034i −0.950102 0.311938i \(-0.899022\pi\)
0.978782 + 0.204905i \(0.0656884\pi\)
\(422\) 6.00000 0.292075
\(423\) 0 0
\(424\) 2.14359 0.104102
\(425\) 19.5000 11.2583i 0.945889 0.546109i
\(426\) 0 0
\(427\) 2.19615 0.588457i 0.106279 0.0284774i
\(428\) −9.87564 36.8564i −0.477357 1.78152i
\(429\) 0 0
\(430\) 6.73205 + 1.80385i 0.324648 + 0.0869893i
\(431\) 5.80385 0.279562 0.139781 0.990182i \(-0.455360\pi\)
0.139781 + 0.990182i \(0.455360\pi\)
\(432\) 0 0
\(433\) −2.26795 −0.108991 −0.0544953 0.998514i \(-0.517355\pi\)
−0.0544953 + 0.998514i \(0.517355\pi\)
\(434\) 7.46410 + 2.00000i 0.358288 + 0.0960031i
\(435\) 0 0
\(436\) −19.8564 + 5.32051i −0.950949 + 0.254806i
\(437\) −1.09808 + 0.294229i −0.0525281 + 0.0140749i
\(438\) 0 0
\(439\) −4.85641 + 2.80385i −0.231784 + 0.133820i −0.611395 0.791326i \(-0.709391\pi\)
0.379611 + 0.925146i \(0.376058\pi\)
\(440\) −22.9282 22.9282i −1.09306 1.09306i
\(441\) 0 0
\(442\) 20.2487 0.963133
\(443\) 5.25833 19.6244i 0.249831 0.932381i −0.721063 0.692870i \(-0.756346\pi\)
0.970894 0.239511i \(-0.0769873\pi\)
\(444\) 0 0
\(445\) −2.00000 7.46410i −0.0948091 0.353832i
\(446\) −30.1244 + 8.07180i −1.42643 + 0.382211i
\(447\) 0 0
\(448\) 2.92820 + 5.07180i 0.138345 + 0.239620i
\(449\) 20.6603 0.975018 0.487509 0.873118i \(-0.337906\pi\)
0.487509 + 0.873118i \(0.337906\pi\)
\(450\) 0 0
\(451\) 6.29423 6.29423i 0.296384 0.296384i
\(452\) 24.0000 13.8564i 1.12887 0.651751i
\(453\) 0 0
\(454\) −10.5622 + 18.2942i −0.495708 + 0.858591i
\(455\) 15.4641 + 8.92820i 0.724968 + 0.418561i
\(456\) 0 0
\(457\) 20.2583 11.6962i 0.947645 0.547123i 0.0552962 0.998470i \(-0.482390\pi\)
0.892348 + 0.451347i \(0.149056\pi\)
\(458\) 10.0000i 0.467269i
\(459\) 0 0
\(460\) −6.92820 6.92820i −0.323029 0.323029i
\(461\) −2.56218 0.686533i −0.119333 0.0319751i 0.198659 0.980069i \(-0.436342\pi\)
−0.317991 + 0.948094i \(0.603008\pi\)
\(462\) 0 0
\(463\) −9.19615 + 15.9282i −0.427381 + 0.740246i −0.996640 0.0819125i \(-0.973897\pi\)
0.569258 + 0.822159i \(0.307231\pi\)
\(464\) 2.53590 + 9.46410i 0.117726 + 0.439360i
\(465\) 0 0
\(466\) −9.83013 2.63397i −0.455372 0.122017i
\(467\) −4.36603 + 4.36603i −0.202036 + 0.202036i −0.800872 0.598836i \(-0.795630\pi\)
0.598836 + 0.800872i \(0.295630\pi\)
\(468\) 0 0
\(469\) −2.80385 2.80385i −0.129470 0.129470i
\(470\) −45.7128 + 26.3923i −2.10857 + 1.21739i
\(471\) 0 0
\(472\) −7.26795 + 12.5885i −0.334534 + 0.579431i
\(473\) −3.27757 1.89230i −0.150703 0.0870083i
\(474\) 0 0
\(475\) −2.30385 + 8.59808i −0.105708 + 0.394507i
\(476\) 3.32051 0.152195
\(477\) 0 0
\(478\) 26.1962 + 26.1962i 1.19818 + 1.19818i
\(479\) −12.8301 22.2224i −0.586223 1.01537i −0.994722 0.102610i \(-0.967281\pi\)
0.408498 0.912759i \(-0.366053\pi\)
\(480\) 0 0
\(481\) 5.66025 9.80385i 0.258085 0.447017i
\(482\) 17.4904 4.68653i 0.796665 0.213466i
\(483\) 0 0
\(484\) −2.19615 3.80385i −0.0998251 0.172902i
\(485\) −22.5885 22.5885i −1.02569 1.02569i
\(486\) 0 0
\(487\) 16.1962i 0.733918i −0.930237 0.366959i \(-0.880399\pi\)
0.930237 0.366959i \(-0.119601\pi\)
\(488\) −7.60770 + 4.39230i −0.344384 + 0.198830i
\(489\) 0 0
\(490\) −30.5885 17.6603i −1.38185 0.797809i
\(491\) 25.7224 6.89230i 1.16084 0.311045i 0.373537 0.927615i \(-0.378145\pi\)
0.787300 + 0.616570i \(0.211478\pi\)
\(492\) 0 0
\(493\) 5.36603 + 1.43782i 0.241674 + 0.0647563i
\(494\) −5.66025 + 5.66025i −0.254667 + 0.254667i
\(495\) 0 0
\(496\) −29.8564 −1.34059
\(497\) 4.00000 + 6.92820i 0.179425 + 0.310772i
\(498\) 0 0
\(499\) −1.69615 6.33013i −0.0759302 0.283375i 0.917512 0.397707i \(-0.130194\pi\)
−0.993443 + 0.114332i \(0.963527\pi\)
\(500\) −36.7846 + 9.85641i −1.64506 + 0.440792i
\(501\) 0 0
\(502\) 4.90192 2.83013i 0.218784 0.126315i
\(503\) 27.7128i 1.23565i 0.786314 + 0.617827i \(0.211987\pi\)
−0.786314 + 0.617827i \(0.788013\pi\)
\(504\) 0 0
\(505\) 29.8564i 1.32859i
\(506\) 2.66025 + 4.60770i 0.118263 + 0.204837i
\(507\) 0 0
\(508\) 10.7321 + 6.19615i 0.476158 + 0.274910i
\(509\) 4.53590 + 16.9282i 0.201050 + 0.750329i 0.990617 + 0.136665i \(0.0436385\pi\)
−0.789567 + 0.613664i \(0.789695\pi\)
\(510\) 0 0
\(511\) −3.56218 6.16987i −0.157581 0.272939i
\(512\) −16.0000 16.0000i −0.707107 0.707107i
\(513\) 0 0
\(514\) 8.85641 + 8.85641i 0.390639 + 0.390639i
\(515\) −34.0526 9.12436i −1.50054 0.402067i
\(516\) 0 0
\(517\) 27.6865 7.41858i 1.21765 0.326269i
\(518\) 0.928203 1.60770i 0.0407829 0.0706381i
\(519\) 0 0
\(520\) −66.6410 17.8564i −2.92240 0.783055i
\(521\) 13.0000i 0.569540i 0.958596 + 0.284770i \(0.0919173\pi\)
−0.958596 + 0.284770i \(0.908083\pi\)
\(522\) 0 0
\(523\) −14.4641 14.4641i −0.632471 0.632471i 0.316216 0.948687i \(-0.397588\pi\)
−0.948687 + 0.316216i \(0.897588\pi\)
\(524\) −1.66025 + 6.19615i −0.0725285 + 0.270680i
\(525\) 0 0
\(526\) 9.92820 + 37.0526i 0.432890 + 1.61557i
\(527\) −8.46410 + 14.6603i −0.368702 + 0.638611i
\(528\) 0 0
\(529\) −10.6962 18.5263i −0.465050 0.805490i
\(530\) −2.92820 + 2.92820i −0.127193 + 0.127193i
\(531\) 0 0
\(532\) −0.928203 + 0.928203i −0.0402427 + 0.0402427i
\(533\) 4.90192 18.2942i 0.212326 0.792411i
\(534\) 0 0
\(535\) 63.8372 + 36.8564i 2.75992 + 1.59344i
\(536\) 13.2679 + 7.66025i 0.573088 + 0.330873i
\(537\) 0 0
\(538\) −4.73205 8.19615i −0.204013 0.353361i
\(539\) 13.5622 + 13.5622i 0.584164 + 0.584164i
\(540\) 0 0
\(541\) −8.19615 + 8.19615i −0.352380 + 0.352380i −0.860994 0.508614i \(-0.830158\pi\)
0.508614 + 0.860994i \(0.330158\pi\)
\(542\) −7.46410 + 27.8564i −0.320611 + 1.19654i
\(543\) 0 0
\(544\) −12.3923 + 3.32051i −0.531316 + 0.142366i
\(545\) 19.8564 34.3923i 0.850555 1.47320i
\(546\) 0 0
\(547\) −31.2583 8.37564i −1.33651 0.358117i −0.481371 0.876517i \(-0.659861\pi\)
−0.855138 + 0.518400i \(0.826528\pi\)
\(548\) 32.9282 1.40662
\(549\) 0 0
\(550\) 41.6603 1.77640
\(551\) −1.90192 + 1.09808i −0.0810247 + 0.0467796i
\(552\) 0 0
\(553\) 7.60770 + 4.39230i 0.323512 + 0.186780i
\(554\) −19.9808 11.5359i −0.848901 0.490113i
\(555\) 0 0
\(556\) 18.1244 + 4.85641i 0.768644 + 0.205958i
\(557\) 25.1962 25.1962i 1.06760 1.06760i 0.0700519 0.997543i \(-0.477684\pi\)
0.997543 0.0700519i \(-0.0223165\pi\)
\(558\) 0 0
\(559\) −8.05256 −0.340587
\(560\) −10.9282 2.92820i −0.461801 0.123739i
\(561\) 0 0
\(562\) 3.66025 + 13.6603i 0.154398 + 0.576223i
\(563\) −1.00962 3.76795i −0.0425504 0.158800i 0.941382 0.337343i \(-0.109528\pi\)
−0.983932 + 0.178543i \(0.942862\pi\)
\(564\) 0 0
\(565\) −13.8564 + 51.7128i −0.582943 + 2.17557i
\(566\) 40.6410i 1.70827i
\(567\) 0 0
\(568\) −21.8564 21.8564i −0.917074 0.917074i
\(569\) −23.5981 + 13.6244i −0.989283 + 0.571163i −0.905060 0.425284i \(-0.860174\pi\)
−0.0842230 + 0.996447i \(0.526841\pi\)
\(570\) 0 0
\(571\) −19.8923 + 5.33013i −0.832467 + 0.223059i −0.649790 0.760114i \(-0.725143\pi\)
−0.182677 + 0.983173i \(0.558476\pi\)
\(572\) 32.4449 + 18.7321i 1.35659 + 0.783226i
\(573\) 0 0
\(574\) 0.803848 3.00000i 0.0335519 0.125218i
\(575\) 12.5885 0.524975
\(576\) 0 0
\(577\) 35.7846 1.48973 0.744866 0.667214i \(-0.232513\pi\)
0.744866 + 0.667214i \(0.232513\pi\)
\(578\) 4.33975 16.1962i 0.180510 0.673671i
\(579\) 0 0
\(580\) −16.3923 9.46410i −0.680653 0.392975i
\(581\) −1.00000 + 0.267949i −0.0414870 + 0.0111164i
\(582\) 0 0
\(583\) 1.94744 1.12436i 0.0806548 0.0465661i
\(584\) 19.4641 + 19.4641i 0.805430 + 0.805430i
\(585\) 0 0
\(586\) 19.8564i 0.820261i
\(587\) 1.00962 3.76795i 0.0416714 0.155520i −0.941955 0.335739i \(-0.891014\pi\)
0.983626 + 0.180219i \(0.0576807\pi\)
\(588\) 0 0
\(589\) −1.73205 6.46410i −0.0713679 0.266349i
\(590\) −7.26795 27.1244i −0.299217 1.11669i
\(591\) 0 0
\(592\) −1.85641 + 6.92820i −0.0762978 + 0.284747i
\(593\) −10.5359 −0.432657 −0.216329 0.976321i \(-0.569408\pi\)
−0.216329 + 0.976321i \(0.569408\pi\)
\(594\) 0 0
\(595\) −4.53590 + 4.53590i −0.185954 + 0.185954i
\(596\) 6.19615 + 1.66025i 0.253804 + 0.0680067i
\(597\) 0 0
\(598\) 9.80385 + 5.66025i 0.400909 + 0.231465i
\(599\) −23.3205 13.4641i −0.952850 0.550128i −0.0588850 0.998265i \(-0.518755\pi\)
−0.893965 + 0.448136i \(0.852088\pi\)
\(600\) 0 0
\(601\) −17.5526 + 10.1340i −0.715984 + 0.413373i −0.813273 0.581883i \(-0.802316\pi\)
0.0972889 + 0.995256i \(0.468983\pi\)
\(602\) −1.32051 −0.0538199
\(603\) 0 0
\(604\) 5.46410 0.222331
\(605\) 8.19615 + 2.19615i 0.333221 + 0.0892863i
\(606\) 0 0
\(607\) 22.5885 39.1244i 0.916837 1.58801i 0.112648 0.993635i \(-0.464067\pi\)
0.804189 0.594374i \(-0.202600\pi\)
\(608\) 2.53590 4.39230i 0.102844 0.178131i
\(609\) 0 0
\(610\) 4.39230 16.3923i 0.177839 0.663705i
\(611\) 43.1244 43.1244i 1.74462 1.74462i
\(612\) 0 0
\(613\) 1.66025 + 1.66025i 0.0670570 + 0.0670570i 0.739840 0.672783i \(-0.234901\pi\)
−0.672783 + 0.739840i \(0.734901\pi\)
\(614\) −16.0263 27.7583i −0.646768 1.12024i
\(615\) 0 0
\(616\) 5.32051 + 3.07180i 0.214369 + 0.123766i
\(617\) −3.91154 2.25833i −0.157473 0.0909170i 0.419193 0.907897i \(-0.362313\pi\)
−0.576666 + 0.816980i \(0.695646\pi\)
\(618\) 0 0
\(619\) −10.4019 + 38.8205i −0.418089 + 1.56033i 0.360479 + 0.932767i \(0.382613\pi\)
−0.778568 + 0.627561i \(0.784053\pi\)
\(620\) 40.7846 40.7846i 1.63795 1.63795i
\(621\) 0 0
\(622\) 16.0526 16.0526i 0.643649 0.643649i
\(623\) 0.732051 + 1.26795i 0.0293290 + 0.0507993i
\(624\) 0 0
\(625\) 11.9641 20.7224i 0.478564 0.828897i
\(626\) 10.4186 + 38.8827i 0.416410 + 1.55406i
\(627\) 0 0
\(628\) −2.53590 + 9.46410i −0.101193 + 0.377659i
\(629\) 2.87564 + 2.87564i 0.114659 + 0.114659i
\(630\) 0 0
\(631\) 38.3923i 1.52837i −0.644995 0.764187i \(-0.723141\pi\)
0.644995 0.764187i \(-0.276859\pi\)
\(632\) −32.7846 8.78461i −1.30410 0.349433i
\(633\) 0 0
\(634\) 23.0526 39.9282i 0.915534 1.58575i
\(635\) −23.1244 + 6.19615i −0.917662 + 0.245887i
\(636\) 0 0
\(637\) 39.4186 + 10.5622i 1.56182 + 0.418489i
\(638\) 7.26795 + 7.26795i 0.287741 + 0.287741i
\(639\) 0 0
\(640\) 43.7128 1.72790
\(641\) 4.20577 + 7.28461i 0.166118 + 0.287725i 0.937052 0.349191i \(-0.113543\pi\)
−0.770934 + 0.636915i \(0.780210\pi\)
\(642\) 0 0
\(643\) 12.2321 + 45.6506i 0.482385 + 1.80029i 0.591558 + 0.806263i \(0.298513\pi\)
−0.109173 + 0.994023i \(0.534820\pi\)
\(644\) 1.60770 + 0.928203i 0.0633521 + 0.0365763i
\(645\) 0 0
\(646\) −1.43782 2.49038i −0.0565704 0.0979827i
\(647\) 13.2679i 0.521617i 0.965391 + 0.260808i \(0.0839891\pi\)
−0.965391 + 0.260808i \(0.916011\pi\)
\(648\) 0 0
\(649\) 15.2487i 0.598564i
\(650\) 76.7654 44.3205i 3.01099 1.73839i
\(651\) 0 0
\(652\) 19.1244 5.12436i 0.748968 0.200685i
\(653\) 1.50962 + 5.63397i 0.0590760 + 0.220474i 0.989153 0.146891i \(-0.0469266\pi\)
−0.930077 + 0.367365i \(0.880260\pi\)
\(654\) 0 0
\(655\) −6.19615 10.7321i −0.242104 0.419336i
\(656\) 12.0000i 0.468521i
\(657\) 0 0
\(658\) 7.07180 7.07180i 0.275687 0.275687i
\(659\) 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 \(0.469435\pi\)
\(662\) 24.1244 + 13.9282i 0.937620 + 0.541335i
\(663\) 0 0
\(664\) 3.46410 2.00000i 0.134433 0.0776151i
\(665\) 2.53590i 0.0983379i
\(666\) 0 0
\(667\) 2.19615 + 2.19615i 0.0850354 + 0.0850354i
\(668\) 0.535898 + 0.928203i 0.0207345 + 0.0359133i
\(669\) 0 0
\(670\) −28.5885 + 7.66025i −1.10447 + 0.295941i
\(671\) −4.60770 + 7.98076i −0.177878 + 0.308094i
\(672\) 0 0
\(673\) 8.80385 + 15.2487i 0.339363 + 0.587795i 0.984313 0.176430i \(-0.0564550\pi\)
−0.644950 + 0.764225i \(0.723122\pi\)
\(674\) −23.7846 23.7846i −0.916149 0.916149i
\(675\) 0 0
\(676\) 53.7128 2.06588
\(677\) 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
\(679\) 5.24167 + 3.02628i 0.201157 + 0.116138i
\(680\) 12.3923 21.4641i 0.475223 0.823111i
\(681\) 0 0
\(682\) −27.1244 + 15.6603i −1.03865 + 0.599662i
\(683\) 4.70577 + 4.70577i 0.180061 + 0.180061i 0.791383 0.611321i \(-0.209362\pi\)
−0.611321 + 0.791383i \(0.709362\pi\)
\(684\) 0 0
\(685\) −44.9808 + 44.9808i −1.71863 + 1.71863i
\(686\) 13.4641 + 3.60770i 0.514062 + 0.137742i
\(687\) 0 0
\(688\) 4.92820 1.32051i 0.187886 0.0503439i
\(689\) 2.39230 4.14359i 0.0911396 0.157858i
\(690\) 0 0
\(691\) 23.4904 + 6.29423i 0.893616 + 0.239444i 0.676273 0.736651i \(-0.263594\pi\)
0.217344 + 0.976095i \(0.430261\pi\)
\(692\) −18.3923 18.3923i −0.699171 0.699171i
\(693\) 0 0
\(694\) 36.1962i 1.37399i
\(695\) −31.3923 + 18.1244i −1.19078 + 0.687496i
\(696\) 0 0
\(697\) 5.89230 + 3.40192i 0.223187 + 0.128857i
\(698\) 5.66025 9.80385i 0.214244 0.371081i
\(699\) 0 0
\(700\) 12.5885 7.26795i 0.475799 0.274703i
\(701\) −10.6603 + 10.6603i −0.402632 + 0.402632i −0.879160 0.476527i \(-0.841895\pi\)
0.476527 + 0.879160i \(0.341895\pi\)
\(702\) 0 0
\(703\) −1.60770 −0.0606354
\(704\) −22.9282 6.14359i −0.864139 0.231545i
\(705\) 0 0
\(706\) −27.7583 + 7.43782i −1.04470 + 0.279926i
\(707\) 1.46410 + 5.46410i 0.0550632 + 0.205499i
\(708\) 0 0
\(709\) 5.41154 20.1962i 0.203235 0.758482i −0.786746 0.617277i \(-0.788236\pi\)
0.989980 0.141205i \(-0.0450977\pi\)
\(710\) 59.7128 2.24098
\(711\) 0 0
\(712\) −4.00000 4.00000i −0.149906 0.149906i
\(713\) −8.19615 + 4.73205i −0.306948 + 0.177217i
\(714\) 0 0
\(715\) −69.9090 + 18.7321i −2.61445 + 0.700539i
\(716\) 32.5885 8.73205i 1.21789 0.326332i
\(717\) 0 0
\(718\) −20.1244 5.39230i −0.751034 0.201239i
\(719\) 16.3923 0.611330 0.305665 0.952139i \(-0.401121\pi\)
0.305665 + 0.952139i \(0.401121\pi\)
\(720\) 0 0
\(721\) 6.67949 0.248757
\(722\) −24.8564 6.66025i −0.925060 0.247869i
\(723\) 0 0
\(724\) −9.80385 36.5885i −0.364357 1.35980i
\(725\) 23.4904 6.29423i 0.872411 0.233762i
\(726\) 0 0
\(727\) −31.8109 + 18.3660i −1.17980 + 0.681158i −0.955968 0.293470i \(-0.905190\pi\)
−0.223832 + 0.974628i \(0.571857\pi\)
\(728\) 13.0718 0.484473
\(729\) 0 0
\(730\) −53.1769 −1.96817
\(731\) 0.748711 2.79423i 0.0276921 0.103348i
\(732\) 0 0
\(733\) 8.02628 + 29.9545i 0.296457 + 1.10639i 0.940053 + 0.341028i \(0.110775\pi\)
−0.643596 + 0.765366i \(0.722558\pi\)
\(734\) 27.6603 7.41154i 1.02096 0.273565i
\(735\) 0 0
\(736\) −6.92820 1.85641i −0.255377 0.0684280i
\(737\) 16.0718 0.592012
\(738\) 0 0
\(739\) 21.2224 21.2224i 0.780680 0.780680i −0.199266 0.979945i \(-0.563856\pi\)
0.979945 + 0.199266i \(0.0638557\pi\)
\(740\) −6.92820 12.0000i −0.254686 0.441129i
\(741\) 0 0
\(742\) 0.392305 0.679492i 0.0144020 0.0249449i
\(743\) 2.24167 + 1.29423i 0.0822389 + 0.0474806i 0.540556 0.841308i \(-0.318214\pi\)
−0.458317 + 0.888789i \(0.651547\pi\)
\(744\) 0 0
\(745\) −10.7321 + 6.19615i −0.393192 + 0.227009i
\(746\) 8.24871i 0.302007i
\(747\) 0 0
\(748\) −9.51666 + 9.51666i −0.347964 + 0.347964i
\(749\) −13.4904 3.61474i −0.492928 0.132080i
\(750\) 0 0
\(751\) 18.8564 32.6603i 0.688080 1.19179i −0.284378 0.958712i \(-0.591787\pi\)
0.972458 0.233077i \(-0.0748796\pi\)
\(752\) −19.3205 + 33.4641i −0.704546 + 1.22031i
\(753\) 0 0
\(754\) 21.1244 + 5.66025i 0.769304 + 0.206134i
\(755\) −7.46410 + 7.46410i −0.271646 + 0.271646i
\(756\) 0 0
\(757\) −6.07180 6.07180i −0.220683 0.220683i 0.588103 0.808786i \(-0.299875\pi\)
−0.808786 + 0.588103i \(0.799875\pi\)
\(758\) 32.4904 18.7583i 1.18010 0.681333i
\(759\) 0 0
\(760\) 2.53590 + 9.46410i 0.0919867 + 0.343299i
\(761\) −27.3731 15.8038i −0.992273 0.572889i −0.0863200 0.996267i \(-0.527511\pi\)
−0.905953 + 0.423378i \(0.860844\pi\)
\(762\) 0 0
\(763\) −1.94744 + 7.26795i −0.0705021 + 0.263117i
\(764\) 28.1051i 1.01681i
\(765\) 0 0
\(766\) 6.53590 + 6.53590i 0.236152 + 0.236152i
\(767\) 16.2224 + 28.0981i 0.585758 + 1.01456i
\(768\) 0 0
\(769\) 10.1244 17.5359i 0.365094 0.632361i −0.623698 0.781666i \(-0.714370\pi\)
0.988791 + 0.149305i \(0.0477036\pi\)
\(770\) −11.4641 + 3.07180i −0.413138 + 0.110700i
\(771\) 0 0
\(772\) 31.6410 18.2679i 1.13879 0.657478i
\(773\) −4.41154 4.41154i −0.158672 0.158672i 0.623306 0.781978i \(-0.285789\pi\)
−0.781978 + 0.623306i \(0.785789\pi\)
\(774\) 0 0
\(775\) 74.1051i 2.66193i
\(776\) −22.5885 6.05256i −0.810878 0.217274i
\(777\) 0 0
\(778\) 13.0526 + 7.53590i 0.467957 + 0.270175i
\(779\) −2.59808 + 0.696152i −0.0930857 + 0.0249422i
\(780\) 0 0
\(781\) −31.3205 8.39230i −1.12074 0.300300i
\(782\) −2.87564 + 2.87564i −0.102833 + 0.102833i
\(783\) 0 0
\(784\) −25.8564 −0.923443
\(785\) −9.46410 16.3923i −0.337788 0.585066i
\(786\) 0 0