Properties

Label 432.2.y.b.253.1
Level $432$
Weight $2$
Character 432.253
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 253.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 432.253
Dual form 432.2.y.b.181.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.36603 + 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(-1.00000 - 3.73205i) q^{5} +(0.633975 - 0.366025i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})\) \(q+(1.36603 + 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(-1.00000 - 3.73205i) q^{5} +(0.633975 - 0.366025i) q^{7} +(2.00000 + 2.00000i) q^{8} -5.46410i q^{10} +(-2.86603 - 0.767949i) q^{11} +(6.09808 - 1.63397i) q^{13} +(1.00000 - 0.267949i) q^{14} +(2.00000 + 3.46410i) q^{16} +2.26795 q^{17} +(-0.633975 - 0.633975i) q^{19} +(2.00000 - 7.46410i) q^{20} +(-3.63397 - 2.09808i) q^{22} +(-1.09808 - 0.633975i) q^{23} +(-8.59808 + 4.96410i) q^{25} +8.92820 q^{26} +1.46410 q^{28} +(-0.633975 + 2.36603i) q^{29} +(-3.73205 + 6.46410i) q^{31} +(1.46410 + 5.46410i) q^{32} +(3.09808 + 0.830127i) q^{34} +(-2.00000 - 2.00000i) q^{35} +(1.26795 - 1.26795i) q^{37} +(-0.633975 - 1.09808i) q^{38} +(5.46410 - 9.46410i) q^{40} +(-2.59808 - 1.50000i) q^{41} +(-1.23205 - 0.330127i) q^{43} +(-4.19615 - 4.19615i) q^{44} +(-1.26795 - 1.26795i) q^{46} +(4.83013 + 8.36603i) q^{47} +(-3.23205 + 5.59808i) q^{49} +(-13.5622 + 3.63397i) q^{50} +(12.1962 + 3.26795i) q^{52} +(0.535898 - 0.535898i) q^{53} +11.4641i q^{55} +(2.00000 + 0.535898i) q^{56} +(-1.73205 + 3.00000i) q^{58} +(1.33013 + 4.96410i) q^{59} +(0.803848 - 3.00000i) q^{61} +(-7.46410 + 7.46410i) q^{62} +8.00000i q^{64} +(-12.1962 - 21.1244i) q^{65} +(-5.23205 + 1.40192i) q^{67} +(3.92820 + 2.26795i) q^{68} +(-2.00000 - 3.46410i) q^{70} +10.9282i q^{71} -9.73205i q^{73} +(2.19615 - 1.26795i) q^{74} +(-0.464102 - 1.73205i) q^{76} +(-2.09808 + 0.562178i) q^{77} +(-6.00000 - 10.3923i) q^{79} +(10.9282 - 10.9282i) q^{80} +(-3.00000 - 3.00000i) q^{82} +(-0.366025 + 1.36603i) q^{83} +(-2.26795 - 8.46410i) q^{85} +(-1.56218 - 0.901924i) q^{86} +(-4.19615 - 7.26795i) q^{88} +2.00000i q^{89} +(3.26795 - 3.26795i) q^{91} +(-1.26795 - 2.19615i) q^{92} +(3.53590 + 13.1962i) q^{94} +(-1.73205 + 3.00000i) q^{95} +(-4.13397 - 7.16025i) q^{97} +(-6.46410 + 6.46410i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 4q^{5} + 6q^{7} + 8q^{8} + O(q^{10}) \) \( 4q + 2q^{2} - 4q^{5} + 6q^{7} + 8q^{8} - 8q^{11} + 14q^{13} + 4q^{14} + 8q^{16} + 16q^{17} - 6q^{19} + 8q^{20} - 18q^{22} + 6q^{23} - 24q^{25} + 8q^{26} - 8q^{28} - 6q^{29} - 8q^{31} - 8q^{32} + 2q^{34} - 8q^{35} + 12q^{37} - 6q^{38} + 8q^{40} + 2q^{43} + 4q^{44} - 12q^{46} + 2q^{47} - 6q^{49} - 30q^{50} + 28q^{52} + 16q^{53} + 8q^{56} - 12q^{59} + 24q^{61} - 16q^{62} - 28q^{65} - 14q^{67} - 12q^{68} - 8q^{70} - 12q^{74} + 12q^{76} + 2q^{77} - 24q^{79} + 16q^{80} - 12q^{82} + 2q^{83} - 16q^{85} + 18q^{86} + 4q^{88} + 20q^{91} - 12q^{92} + 28q^{94} - 20q^{97} - 12q^{98} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36603 + 0.366025i 0.965926 + 0.258819i
\(3\) 0 0
\(4\) 1.73205 + 1.00000i 0.866025 + 0.500000i
\(5\) −1.00000 3.73205i −0.447214 1.66902i −0.710025 0.704177i \(-0.751316\pi\)
0.262811 0.964847i \(-0.415350\pi\)
\(6\) 0 0
\(7\) 0.633975 0.366025i 0.239620 0.138345i −0.375382 0.926870i \(-0.622489\pi\)
0.615002 + 0.788526i \(0.289155\pi\)
\(8\) 2.00000 + 2.00000i 0.707107 + 0.707107i
\(9\) 0 0
\(10\) 5.46410i 1.72790i
\(11\) −2.86603 0.767949i −0.864139 0.231545i −0.200587 0.979676i \(-0.564285\pi\)
−0.663552 + 0.748130i \(0.730952\pi\)
\(12\) 0 0
\(13\) 6.09808 1.63397i 1.69130 0.453183i 0.720577 0.693375i \(-0.243877\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) 1.00000 0.267949i 0.267261 0.0716124i
\(15\) 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 0.630635 0.776079i \(-0.282794\pi\)
−0.776079 + 0.630635i \(0.782794\pi\)
\(20\) 2.00000 7.46410i 0.447214 1.66902i
\(21\) 0 0
\(22\) −3.63397 2.09808i −0.774766 0.447311i
\(23\) −1.09808 0.633975i −0.228965 0.132193i 0.381130 0.924522i \(-0.375535\pi\)
−0.610094 + 0.792329i \(0.708868\pi\)
\(24\) 0 0
\(25\) −8.59808 + 4.96410i −1.71962 + 0.992820i
\(26\) 8.92820 1.75096
\(27\) 0 0
\(28\) 1.46410 0.276689
\(29\) −0.633975 + 2.36603i −0.117726 + 0.439360i −0.999476 0.0323566i \(-0.989699\pi\)
0.881750 + 0.471717i \(0.156365\pi\)
\(30\) 0 0
\(31\) −3.73205 + 6.46410i −0.670296 + 1.16099i 0.307524 + 0.951540i \(0.400500\pi\)
−0.977820 + 0.209447i \(0.932834\pi\)
\(32\) 1.46410 + 5.46410i 0.258819 + 0.965926i
\(33\) 0 0
\(34\) 3.09808 + 0.830127i 0.531316 + 0.142366i
\(35\) −2.00000 2.00000i −0.338062 0.338062i
\(36\) 0 0
\(37\) 1.26795 1.26795i 0.208450 0.208450i −0.595159 0.803608i \(-0.702911\pi\)
0.803608 + 0.595159i \(0.202911\pi\)
\(38\) −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 0.283211 0.959058i \(-0.408600\pi\)
−0.688963 + 0.724797i \(0.741934\pi\)
\(42\) 0 0
\(43\) −1.23205 0.330127i −0.187886 0.0503439i 0.163649 0.986519i \(-0.447674\pi\)
−0.351535 + 0.936175i \(0.614340\pi\)
\(44\) −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
\(50\) −13.5622 + 3.63397i −1.91798 + 0.513922i
\(51\) 0 0
\(52\) 12.1962 + 3.26795i 1.69130 + 0.453183i
\(53\) 0.535898 0.535898i 0.0736113 0.0736113i −0.669343 0.742954i \(-0.733424\pi\)
0.742954 + 0.669343i \(0.233424\pi\)
\(54\) 0 0
\(55\) 11.4641i 1.54582i
\(56\) 2.00000 + 0.535898i 0.267261 + 0.0716124i
\(57\) 0 0
\(58\) −1.73205 + 3.00000i −0.227429 + 0.393919i
\(59\) 1.33013 + 4.96410i 0.173168 + 0.646271i 0.996856 + 0.0792287i \(0.0252457\pi\)
−0.823689 + 0.567042i \(0.808088\pi\)
\(60\) 0 0
\(61\) 0.803848 3.00000i 0.102922 0.384111i −0.895179 0.445707i \(-0.852952\pi\)
0.998101 + 0.0615961i \(0.0196191\pi\)
\(62\) −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
\(67\) −5.23205 + 1.40192i −0.639197 + 0.171272i −0.563840 0.825884i \(-0.690676\pi\)
−0.0753572 + 0.997157i \(0.524010\pi\)
\(68\) 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 \(0.224591\pi\)
−0.761241 + 0.648470i \(0.775409\pi\)
\(72\) 0 0
\(73\) 9.73205i 1.13905i −0.821974 0.569525i \(-0.807127\pi\)
0.821974 0.569525i \(-0.192873\pi\)
\(74\) 2.19615 1.26795i 0.255298 0.147396i
\(75\) 0 0
\(76\) −0.464102 1.73205i −0.0532361 0.198680i
\(77\) −2.09808 + 0.562178i −0.239098 + 0.0640661i
\(78\) 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
\(83\) −0.366025 + 1.36603i −0.0401765 + 0.149941i −0.983100 0.183068i \(-0.941397\pi\)
0.942924 + 0.333009i \(0.108064\pi\)
\(84\) 0 0
\(85\) −2.26795 8.46410i −0.245994 0.918061i
\(86\) −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 \(0.0338043\pi\)
−0.994366 + 0.106000i \(0.966196\pi\)
\(90\) 0 0
\(91\) 3.26795 3.26795i 0.342574 0.342574i
\(92\) −1.26795 2.19615i −0.132193 0.228965i
\(93\) 0 0
\(94\) 3.53590 + 13.1962i 0.364700 + 1.36108i
\(95\) −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
\(101\) −7.46410 2.00000i −0.742706 0.199007i −0.132426 0.991193i \(-0.542277\pi\)
−0.610280 + 0.792186i \(0.708943\pi\)
\(102\) 0 0
\(103\) 7.90192 + 4.56218i 0.778600 + 0.449525i 0.835934 0.548830i \(-0.184927\pi\)
−0.0573341 + 0.998355i \(0.518260\pi\)
\(104\) 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 0.378607 0.925558i \(-0.376403\pi\)
0.925558 0.378607i \(-0.123597\pi\)
\(108\) 0 0
\(109\) 7.26795 + 7.26795i 0.696143 + 0.696143i 0.963576 0.267433i \(-0.0861754\pi\)
−0.267433 + 0.963576i \(0.586175\pi\)
\(110\) −4.19615 + 15.6603i −0.400087 + 1.49315i
\(111\) 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
\(115\) −1.26795 + 4.73205i −0.118237 + 0.441266i
\(116\) −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 \(0.588648\pi\)
\(128\) −2.92820 + 10.9282i −0.258819 + 0.965926i
\(129\) 0 0
\(130\) −8.92820 33.3205i −0.783055 2.92240i
\(131\) 3.09808 0.830127i 0.270680 0.0725285i −0.120926 0.992662i \(-0.538586\pi\)
0.391606 + 0.920133i \(0.371920\pi\)
\(132\) 0 0
\(133\) −0.633975 0.169873i −0.0549726 0.0147299i
\(134\) −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 0.253645 0.967297i \(-0.418371\pi\)
0.964527 + 0.263986i \(0.0850372\pi\)
\(138\) 0 0
\(139\) 2.42820 + 9.06218i 0.205958 + 0.768644i 0.989156 + 0.146872i \(0.0469204\pi\)
−0.783198 + 0.621772i \(0.786413\pi\)
\(140\) −1.46410 5.46410i −0.123739 0.461801i
\(141\) 0 0
\(142\) −4.00000 + 14.9282i −0.335673 + 1.25275i
\(143\) −18.7321 −1.56645
\(144\) 0 0
\(145\) 9.46410 0.785951
\(146\) 3.56218 13.2942i 0.294808 1.10024i
\(147\) 0 0
\(148\) 3.46410 0.928203i 0.284747 0.0762978i
\(149\) 0.830127 + 3.09808i 0.0680067 + 0.253804i 0.991557 0.129674i \(-0.0413929\pi\)
−0.923550 + 0.383478i \(0.874726\pi\)
\(150\) 0 0
\(151\) 2.36603 1.36603i 0.192544 0.111166i −0.400629 0.916240i \(-0.631208\pi\)
0.593173 + 0.805075i \(0.297875\pi\)
\(152\) 2.53590i 0.205689i
\(153\) 0 0
\(154\) −3.07180 −0.247532
\(155\) 27.8564 + 7.46410i 2.23748 + 0.599531i
\(156\) 0 0
\(157\) 4.73205 1.26795i 0.377659 0.101193i −0.0649959 0.997886i \(-0.520703\pi\)
0.442655 + 0.896692i \(0.354037\pi\)
\(158\) −4.39230 16.3923i −0.349433 1.30410i
\(159\) 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 0.377661 0.925944i \(-0.376728\pi\)
−0.925944 + 0.377661i \(0.876728\pi\)
\(164\) −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 0.517849 0.855472i \(-0.326733\pi\)
−0.481936 + 0.876206i \(0.660066\pi\)
\(168\) 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
\(173\) −3.36603 + 12.5622i −0.255914 + 0.955085i 0.711665 + 0.702519i \(0.247941\pi\)
−0.967580 + 0.252566i \(0.918725\pi\)
\(174\) 0 0
\(175\) −3.63397 + 6.29423i −0.274703 + 0.475799i
\(176\) −3.07180 11.4641i −0.231545 0.864139i
\(177\) 0 0
\(178\) −0.732051 + 2.73205i −0.0548695 + 0.204776i
\(179\) −11.9282 11.9282i −0.891556 0.891556i 0.103114 0.994670i \(-0.467119\pi\)
−0.994670 + 0.103114i \(0.967119\pi\)
\(180\) 0 0
\(181\) 13.3923 13.3923i 0.995442 0.995442i −0.00454748 0.999990i \(-0.501448\pi\)
0.999990 + 0.00454748i \(0.00144751\pi\)
\(182\) 5.66025 3.26795i 0.419566 0.242237i
\(183\) 0 0
\(184\) −0.928203 3.46410i −0.0684280 0.255377i
\(185\) −6.00000 3.46410i −0.441129 0.254686i
\(186\) 0 0
\(187\) −6.50000 1.74167i −0.475327 0.127364i
\(188\) 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 \(0.938290\pi\)
\(194\) −3.02628 11.2942i −0.217274 0.810878i
\(195\) 0 0
\(196\) −11.1962 + 6.46410i −0.799725 + 0.461722i
\(197\) 3.66025 3.66025i 0.260782 0.260782i −0.564590 0.825372i \(-0.690966\pi\)
0.825372 + 0.564590i \(0.190966\pi\)
\(198\) 0 0
\(199\) 0.875644i 0.0620728i 0.999518 + 0.0310364i \(0.00988078\pi\)
−0.999518 + 0.0310364i \(0.990119\pi\)
\(200\) −27.1244 7.26795i −1.91798 0.513922i
\(201\) 0 0
\(202\) −9.46410 5.46410i −0.665892 0.384453i
\(203\) 0.464102 + 1.73205i 0.0325735 + 0.121566i
\(204\) 0 0
\(205\) −3.00000 + 11.1962i −0.209529 + 0.781973i
\(206\) 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
\(211\) 4.09808 1.09808i 0.282123 0.0755947i −0.114983 0.993367i \(-0.536681\pi\)
0.397106 + 0.917773i \(0.370015\pi\)
\(212\) 1.46410 0.392305i 0.100555 0.0269436i
\(213\) 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
\(221\) 13.8301 3.70577i 0.930315 0.249277i
\(222\) 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
\(227\) −3.86603 + 14.4282i −0.256597 + 0.957633i 0.710598 + 0.703598i \(0.248425\pi\)
−0.967195 + 0.254035i \(0.918242\pi\)
\(228\) 0 0
\(229\) −1.83013 6.83013i −0.120938 0.451347i 0.878724 0.477330i \(-0.158395\pi\)
−0.999662 + 0.0259823i \(0.991729\pi\)
\(230\) −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 \(-0.924256\pi\)
0.971822 0.235718i \(-0.0757441\pi\)
\(234\) 0 0
\(235\) 26.3923 26.3923i 1.72164 1.72164i
\(236\) −2.66025 + 9.92820i −0.173168 + 0.646271i
\(237\) 0 0
\(238\) 2.26795 0.607695i 0.147009 0.0393910i
\(239\) 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
\(245\) 24.1244 + 6.46410i 1.54125 + 0.412976i
\(246\) 0 0
\(247\) −4.90192 2.83013i −0.311902 0.180077i
\(248\) −20.3923 + 5.46410i −1.29491 + 0.346971i
\(249\) 0 0
\(250\) 13.4641 + 23.3205i 0.851545 + 1.47492i
\(251\) −2.83013 + 2.83013i −0.178636 + 0.178636i −0.790761 0.612125i \(-0.790315\pi\)
0.612125 + 0.790761i \(0.290315\pi\)
\(252\) 0 0
\(253\) 2.66025 + 2.66025i 0.167249 + 0.167249i
\(254\) −8.46410 2.26795i −0.531085 0.142304i
\(255\) 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
\(259\) 0.339746 1.26795i 0.0211108 0.0787865i
\(260\) 48.7846i 3.02549i
\(261\) 0 0
\(262\) 4.53590 0.280229
\(263\) −23.4904 + 13.5622i −1.44848 + 0.836280i −0.998391 0.0567045i \(-0.981941\pi\)
−0.450088 + 0.892984i \(0.648607\pi\)
\(264\) 0 0
\(265\) −2.53590 1.46410i −0.155779 0.0899390i
\(266\) −0.803848 0.464102i −0.0492871 0.0284559i
\(267\) 0 0
\(268\) −10.4641 2.80385i −0.639197 0.171272i
\(269\) −4.73205 4.73205i −0.288518 0.288518i 0.547976 0.836494i \(-0.315399\pi\)
−0.836494 + 0.547976i \(0.815399\pi\)
\(270\) 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
\(274\) 22.4904 6.02628i 1.35869 0.364061i
\(275\) 28.4545 7.62436i 1.71587 0.459766i
\(276\) 0 0
\(277\) 15.7583 + 4.22243i 0.946826 + 0.253701i 0.699015 0.715107i \(-0.253622\pi\)
0.247811 + 0.968808i \(0.420289\pi\)
\(278\) 13.2679i 0.795759i
\(279\) 0 0
\(280\) 8.00000i 0.478091i
\(281\) −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
\(283\) −7.43782 27.7583i −0.442133 1.65006i −0.723398 0.690431i \(-0.757421\pi\)
0.281265 0.959630i \(-0.409246\pi\)
\(284\) −10.9282 + 18.9282i −0.648470 + 1.12318i
\(285\) 0 0
\(286\) −25.5885 6.85641i −1.51308 0.405428i
\(287\) −2.19615 −0.129635
\(288\) 0 0
\(289\) −11.8564 −0.697436
\(290\) 12.9282 + 3.46410i 0.759170 + 0.203419i
\(291\) 0 0
\(292\) 9.73205 16.8564i 0.569525 0.986447i
\(293\) 3.63397 + 13.5622i 0.212299 + 0.792311i 0.987100 + 0.160106i \(0.0511834\pi\)
−0.774801 + 0.632205i \(0.782150\pi\)
\(294\) 0 0
\(295\) 17.1962 9.92820i 1.00120 0.578042i
\(296\) 5.07180 0.294792
\(297\) 0 0
\(298\) 4.53590i 0.262758i
\(299\) −7.73205 2.07180i −0.447156 0.119815i
\(300\) 0 0
\(301\) −0.901924 + 0.241670i −0.0519860 + 0.0139296i
\(302\) 3.73205 1.00000i 0.214755 0.0575435i
\(303\) 0 0
\(304\) 0.928203 3.46410i 0.0532361 0.198680i
\(305\) −12.0000 −0.687118
\(306\) 0 0
\(307\) −16.0263 16.0263i −0.914668 0.914668i 0.0819670 0.996635i \(-0.473880\pi\)
−0.996635 + 0.0819670i \(0.973880\pi\)
\(308\) −4.19615 1.12436i −0.239098 0.0640661i
\(309\) 0 0
\(310\) 35.3205 + 20.3923i 2.00607 + 1.15821i
\(311\) 13.9019 + 8.02628i 0.788306 + 0.455129i 0.839366 0.543567i \(-0.182927\pi\)
−0.0510600 + 0.998696i \(0.516260\pi\)
\(312\) 0 0
\(313\) −24.6506 + 14.2321i −1.39334 + 0.804443i −0.993683 0.112223i \(-0.964203\pi\)
−0.399653 + 0.916666i \(0.630869\pi\)
\(314\) 6.92820 0.390981
\(315\) 0 0
\(316\) 24.0000i 1.35011i
\(317\) 8.43782 31.4904i 0.473915 1.76868i −0.151577 0.988445i \(-0.548435\pi\)
0.625492 0.780231i \(-0.284898\pi\)
\(318\) 0 0
\(319\) 3.63397 6.29423i 0.203464 0.352409i
\(320\) 29.8564 8.00000i 1.66902 0.447214i
\(321\) 0 0
\(322\) −1.26795 0.339746i −0.0706600 0.0189333i
\(323\) −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
\(328\) −2.19615 8.19615i −0.121262 0.452557i
\(329\) 6.12436 + 3.53590i 0.337647 + 0.194940i
\(330\) 0 0
\(331\) −19.0263 5.09808i −1.04578 0.280216i −0.305273 0.952265i \(-0.598748\pi\)
−0.740506 + 0.672049i \(0.765414\pi\)
\(332\) −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 \(0.942350\pi\)
\(338\) 36.6865 9.83013i 1.99548 0.534688i
\(339\) 0 0
\(340\) 4.53590 16.9282i 0.245994 0.918061i
\(341\) 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
\(347\) −6.62436 24.7224i −0.355614 1.32717i −0.879710 0.475510i \(-0.842263\pi\)
0.524096 0.851659i \(-0.324403\pi\)
\(348\) 0 0
\(349\) 2.07180 7.73205i 0.110901 0.413887i −0.888047 0.459753i \(-0.847938\pi\)
0.998948 + 0.0458657i \(0.0146046\pi\)
\(350\) −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
\(355\) 40.7846 10.9282i 2.16462 0.580009i
\(356\) −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 \(-0.872902\pi\)
0.921337 0.388764i \(-0.127098\pi\)
\(360\) 0 0
\(361\) 18.1962i 0.957692i
\(362\) 23.1962 13.3923i 1.21916 0.703884i
\(363\) 0 0
\(364\) 8.92820 2.39230i 0.467965 0.125391i
\(365\) −36.3205 + 9.73205i −1.90110 + 0.509399i
\(366\) 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
\(371\) 0.143594 0.535898i 0.00745501 0.0278225i
\(372\) 0 0
\(373\) 1.50962 + 5.63397i 0.0781651 + 0.291716i 0.993932 0.109993i \(-0.0350829\pi\)
−0.915767 + 0.401709i \(0.868416\pi\)
\(374\) −8.24167 4.75833i −0.426167 0.246047i
\(375\) 0 0
\(376\) −7.07180 + 26.3923i −0.364700 + 1.36108i
\(377\) 15.4641i 0.796442i
\(378\) 0 0
\(379\) −18.7583 + 18.7583i −0.963551 + 0.963551i −0.999359 0.0358080i \(-0.988600\pi\)
0.0358080 + 0.999359i \(0.488600\pi\)
\(380\) −6.00000 + 3.46410i −0.307794 + 0.177705i
\(381\) 0 0
\(382\) −5.14359 19.1962i −0.263169 0.982161i
\(383\) 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
\(389\) −10.2942 2.75833i −0.521938 0.139853i −0.0117752 0.999931i \(-0.503748\pi\)
−0.510163 + 0.860078i \(0.670415\pi\)
\(390\) 0 0
\(391\) −2.49038 1.43782i −0.125944 0.0727138i
\(392\) −17.6603 + 4.73205i −0.891978 + 0.239005i
\(393\) 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 0.311306 0.950310i \(-0.399233\pi\)
−0.950310 + 0.311306i \(0.899233\pi\)
\(398\) −0.320508 + 1.19615i −0.0160656 + 0.0599577i
\(399\) 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
\(403\) −12.1962 + 45.5167i −0.607534 + 2.26735i
\(404\) −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 0.979051 0.203614i \(-0.0652688\pi\)
0.313191 + 0.949690i \(0.398602\pi\)
\(410\) −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
\(418\) 0.973721 + 3.63397i 0.0476262 + 0.177744i
\(419\) −31.2224 + 8.36603i −1.52532 + 0.408707i −0.921488 0.388408i \(-0.873025\pi\)
−0.603828 + 0.797115i \(0.706359\pi\)
\(420\) 0 0
\(421\) −2.19615 0.588457i −0.107034 0.0286797i 0.204905 0.978782i \(-0.434312\pi\)
−0.311938 + 0.950102i \(0.600978\pi\)
\(422\) 6.00000 0.292075
\(423\) 0 0
\(424\) 2.14359 0.104102
\(425\) −19.5000 + 11.2583i −0.945889 + 0.546109i
\(426\) 0 0
\(427\) −0.588457 2.19615i −0.0284774 0.106279i
\(428\) 36.8564 9.87564i 1.78152 0.477357i
\(429\) 0 0
\(430\) −1.80385 + 6.73205i −0.0869893 + 0.324648i
\(431\) 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 \(0.517355\pi\)
\(434\) −2.00000 + 7.46410i −0.0960031 + 0.358288i
\(435\) 0 0
\(436\) 5.32051 + 19.8564i 0.254806 + 0.950949i
\(437\) 0.294229 + 1.09808i 0.0140749 + 0.0525281i
\(438\) 0 0
\(439\) 4.85641 2.80385i 0.231784 0.133820i −0.379611 0.925146i \(-0.623942\pi\)
0.611395 + 0.791326i \(0.290609\pi\)
\(440\) −22.9282 + 22.9282i −1.09306 + 1.09306i
\(441\) 0 0
\(442\) 20.2487 0.963133
\(443\) −19.6244 5.25833i −0.932381 0.249831i −0.239511 0.970894i \(-0.576987\pi\)
−0.692870 + 0.721063i \(0.743654\pi\)
\(444\) 0 0
\(445\) 7.46410 2.00000i 0.353832 0.0948091i
\(446\) 8.07180 + 30.1244i 0.382211 + 1.42643i
\(447\) 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 −0.892348 0.451347i \(-0.850944\pi\)
−0.0552962 + 0.998470i \(0.517610\pi\)
\(458\) 10.0000i 0.467269i
\(459\) 0 0
\(460\) −6.92820 + 6.92820i −0.323029 + 0.323029i
\(461\) 0.686533 2.56218i 0.0319751 0.119333i −0.948094 0.317991i \(-0.896992\pi\)
0.980069 + 0.198659i \(0.0636585\pi\)
\(462\) 0 0
\(463\) −9.19615 + 15.9282i −0.427381 + 0.740246i −0.996640 0.0819125i \(-0.973897\pi\)
0.569258 + 0.822159i \(0.307231\pi\)
\(464\) −9.46410 + 2.53590i −0.439360 + 0.117726i
\(465\) 0 0
\(466\) 2.63397 9.83013i 0.122017 0.455372i
\(467\) −4.36603 4.36603i −0.202036 0.202036i 0.598836 0.800872i \(-0.295630\pi\)
−0.800872 + 0.598836i \(0.795630\pi\)
\(468\) 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
\(475\) 8.59808 + 2.30385i 0.394507 + 0.105708i
\(476\) 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
\(482\) −4.68653 17.4904i −0.213466 0.796665i
\(483\) 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 \(0.119601\pi\)
−0.930237 + 0.366959i \(0.880399\pi\)
\(488\) 7.60770 4.39230i 0.344384 0.198830i
\(489\) 0 0
\(490\) 30.5885 + 17.6603i 1.38185 + 0.797809i
\(491\) −6.89230 25.7224i −0.311045 1.16084i −0.927615 0.373537i \(-0.878145\pi\)
0.616570 0.787300i \(-0.288522\pi\)
\(492\) 0 0
\(493\) −1.43782 + 5.36603i −0.0647563 + 0.241674i
\(494\) −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
\(499\) 6.33013 1.69615i 0.283375 0.0759302i −0.114332 0.993443i \(-0.536473\pi\)
0.397707 + 0.917512i \(0.369806\pi\)
\(500\) 9.85641 + 36.7846i 0.440792 + 1.64506i
\(501\) 0 0
\(502\) −4.90192 + 2.83013i −0.218784 + 0.126315i
\(503\) 27.7128i 1.23565i −0.786314 0.617827i \(-0.788013\pi\)
0.786314 0.617827i \(-0.211987\pi\)
\(504\) 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
\(509\) −16.9282 + 4.53590i −0.750329 + 0.201050i −0.613664 0.789567i \(-0.710305\pi\)
−0.136665 + 0.990617i \(0.543638\pi\)
\(510\) 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
\(515\) 9.12436 34.0526i 0.402067 1.50054i
\(516\) 0 0
\(517\) −7.41858 27.6865i −0.326269 1.21765i
\(518\) 0.928203 1.60770i 0.0407829 0.0706381i
\(519\) 0 0
\(520\) 17.8564 66.6410i 0.783055 2.92240i
\(521\) 13.0000i 0.569540i −0.958596 0.284770i \(-0.908083\pi\)
0.958596 0.284770i \(-0.0919173\pi\)
\(522\) 0 0
\(523\) −14.4641 + 14.4641i −0.632471 + 0.632471i −0.948687 0.316216i \(-0.897588\pi\)
0.316216 + 0.948687i \(0.397588\pi\)
\(524\) 6.19615 + 1.66025i 0.270680 + 0.0725285i
\(525\) 0 0
\(526\) −37.0526 + 9.92820i −1.61557 + 0.432890i
\(527\) −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
\(533\) −18.2942 4.90192i −0.792411 0.212326i
\(534\) 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 0.508614 0.860994i \(-0.330158\pi\)
−0.860994 + 0.508614i \(0.830158\pi\)
\(542\) 27.8564 + 7.46410i 1.19654 + 0.320611i
\(543\) 0 0
\(544\) 3.32051 + 12.3923i 0.142366 + 0.531316i
\(545\) 19.8564 34.3923i 0.850555 1.47320i
\(546\) 0 0
\(547\) 8.37564 31.2583i 0.358117 1.33651i −0.518400 0.855138i \(-0.673472\pi\)
0.876517 0.481371i \(-0.159861\pi\)
\(548\) 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
\(556\) −4.85641 + 18.1244i −0.205958 + 0.768644i
\(557\) 25.1962 + 25.1962i 1.06760 + 1.06760i 0.997543 + 0.0700519i \(0.0223165\pi\)
0.0700519 + 0.997543i \(0.477684\pi\)
\(558\) 0 0
\(559\) −8.05256 −0.340587
\(560\) 2.92820 10.9282i 0.123739 0.461801i
\(561\) 0 0
\(562\) −13.6603 + 3.66025i −0.576223 + 0.154398i
\(563\) 3.76795 1.00962i 0.158800 0.0425504i −0.178543 0.983932i \(-0.557138\pi\)
0.337343 + 0.941382i \(0.390472\pi\)
\(564\) 0 0
\(565\) 51.7128 + 13.8564i 2.17557 + 0.582943i
\(566\) 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 0.0842230 0.996447i \(-0.473159\pi\)
0.905060 + 0.425284i \(0.139826\pi\)
\(570\) 0 0
\(571\) 5.33013 + 19.8923i 0.223059 + 0.832467i 0.983173 + 0.182677i \(0.0584764\pi\)
−0.760114 + 0.649790i \(0.774857\pi\)
\(572\) −32.4449 18.7321i −1.35659 0.783226i
\(573\) 0 0
\(574\) −3.00000 0.803848i −0.125218 0.0335519i
\(575\) 12.5885 0.524975
\(576\) 0 0
\(577\) 35.7846 1.48973 0.744866 0.667214i \(-0.232513\pi\)
0.744866 + 0.667214i \(0.232513\pi\)
\(578\) −16.1962 4.33975i −0.673671 0.180510i
\(579\) 0 0
\(580\) 16.3923 + 9.46410i 0.680653 + 0.392975i
\(581\) 0.267949 + 1.00000i 0.0111164 + 0.0414870i
\(582\) 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
\(587\) −3.76795 1.00962i −0.155520 0.0416714i 0.180219 0.983626i \(-0.442319\pi\)
−0.335739 + 0.941955i \(0.608986\pi\)
\(588\) 0 0
\(589\) 6.46410 1.73205i 0.266349 0.0713679i
\(590\) 27.1244 7.26795i 1.11669 0.299217i
\(591\) 0 0
\(592\) 6.92820 + 1.85641i 0.284747 + 0.0762978i
\(593\) −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
\(596\) −1.66025 + 6.19615i −0.0680067 + 0.253804i
\(597\) 0 0
\(598\) −9.80385 5.66025i −0.400909 0.231465i
\(599\) 23.3205 + 13.4641i 0.952850 + 0.550128i 0.893965 0.448136i \(-0.147912\pi\)
0.0588850 + 0.998265i \(0.481245\pi\)
\(600\) 0 0
\(601\) 17.5526 10.1340i 0.715984 0.413373i −0.0972889 0.995256i \(-0.531017\pi\)
0.813273 + 0.581883i \(0.197684\pi\)
\(602\) −1.32051 −0.0538199
\(603\) 0 0
\(604\) 5.46410 0.222331
\(605\) −2.19615 + 8.19615i −0.0892863 + 0.333221i
\(606\) 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
\(610\) −16.3923 4.39230i −0.663705 0.177839i
\(611\) 43.1244 + 43.1244i 1.74462 + 1.74462i
\(612\) 0 0
\(613\) 1.66025 1.66025i 0.0670570 0.0670570i −0.672783 0.739840i \(-0.734901\pi\)
0.739840 + 0.672783i \(0.234901\pi\)
\(614\) −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 0.576666 0.816980i \(-0.304354\pi\)
−0.419193 + 0.907897i \(0.637687\pi\)
\(618\) 0 0
\(619\) 38.8205 + 10.4019i 1.56033 + 0.418089i 0.932767 0.360479i \(-0.117387\pi\)
0.627561 + 0.778568i \(0.284053\pi\)
\(620\) 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
\(626\) −38.8827 + 10.4186i −1.55406 + 0.416410i
\(627\) 0 0
\(628\) 9.46410 + 2.53590i 0.377659 + 0.101193i
\(629\) 2.87564 2.87564i 0.114659 0.114659i
\(630\) 0 0
\(631\) 38.3923i 1.52837i 0.644995 + 0.764187i \(0.276859\pi\)
−0.644995 + 0.764187i \(0.723141\pi\)
\(632\) 8.78461 32.7846i 0.349433 1.30410i
\(633\) 0 0
\(634\) 23.0526 39.9282i 0.915534 1.58575i
\(635\) 6.19615 + 23.1244i 0.245887 + 0.917662i
\(636\) 0 0
\(637\) −10.5622 + 39.4186i −0.418489 + 1.56182i
\(638\) 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
\(643\) −45.6506 + 12.2321i −1.80029 + 0.482385i −0.994023 0.109173i \(-0.965180\pi\)
−0.806263 + 0.591558i \(0.798513\pi\)
\(644\) −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 \(-0.916011\pi\)
0.965391 0.260808i \(-0.0839891\pi\)
\(648\) 0 0
\(649\) 15.2487i 0.598564i
\(650\) −76.7654 + 44.3205i −3.01099 + 1.73839i
\(651\) 0 0
\(652\) −5.12436 19.1244i −0.200685 0.748968i
\(653\) −5.63397 + 1.50962i −0.220474 + 0.0590760i −0.367365 0.930077i \(-0.619740\pi\)
0.146891 + 0.989153i \(0.453073\pi\)
\(654\) 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
\(659\) −4.02628 + 15.0263i −0.156842 + 0.585341i 0.842099 + 0.539323i \(0.181320\pi\)
−0.998941 + 0.0460178i \(0.985347\pi\)
\(660\) 0 0
\(661\) 2.19615 + 8.19615i 0.0854204 + 0.318793i 0.995393 0.0958740i \(-0.0305646\pi\)
−0.909973 + 0.414667i \(0.863898\pi\)
\(662\) −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
\(670\) 7.66025 + 28.5885i 0.295941 + 1.10447i
\(671\) −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
\(677\) −4.73205 1.26795i −0.181867 0.0487312i 0.166736 0.986002i \(-0.446677\pi\)
−0.348603 + 0.937270i \(0.613344\pi\)
\(678\) 0 0
\(679\) −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 −0.611321 0.791383i \(-0.709362\pi\)
0.791383 + 0.611321i \(0.209362\pi\)
\(684\) 0 0
\(685\) −44.9808 44.9808i −1.71863 1.71863i
\(686\) −3.60770 + 13.4641i −0.137742 + 0.514062i
\(687\) 0 0
\(688\) −1.32051 4.92820i −0.0503439 0.187886i
\(689\) 2.39230 4.14359i 0.0911396 0.157858i
\(690\) 0 0
\(691\) −6.29423 + 23.4904i −0.239444 + 0.893616i 0.736651 + 0.676273i \(0.236406\pi\)
−0.976095 + 0.217344i \(0.930261\pi\)
\(692\) −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 0.476527 0.879160i \(-0.341895\pi\)
−0.879160 + 0.476527i \(0.841895\pi\)
\(702\) 0 0
\(703\) −1.60770 −0.0606354
\(704\) 6.14359 22.9282i 0.231545 0.864139i
\(705\) 0 0
\(706\) 7.43782 + 27.7583i 0.279926 + 1.04470i
\(707\) −5.46410 + 1.46410i −0.205499 + 0.0550632i
\(708\) 0 0
\(709\) −20.1962 5.41154i −0.758482 0.203235i −0.141205 0.989980i \(-0.545098\pi\)
−0.617277 + 0.786746i \(0.711764\pi\)
\(710\) 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
\(715\) 18.7321 + 69.9090i 0.700539 + 2.61445i
\(716\) −8.73205 32.5885i −0.326332 1.21789i
\(717\) 0 0
\(718\) 5.39230 20.1244i 0.201239 0.751034i
\(719\) 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
\(722\) 6.66025 24.8564i 0.247869 0.925060i
\(723\) 0 0
\(724\) 36.5885 9.80385i 1.35980 0.364357i
\(725\) −6.29423 23.4904i −0.233762 0.872411i
\(726\) 0 0
\(727\) 31.8109 18.3660i 1.17980 0.681158i 0.223832 0.974628i \(-0.428143\pi\)
0.955968 + 0.293470i \(0.0948099\pi\)
\(728\) 13.0718 0.484473
\(729\) 0 0
\(730\) −53.1769 −1.96817
\(731\) −2.79423 0.748711i −0.103348 0.0276921i
\(732\) 0 0
\(733\) −29.9545 + 8.02628i −1.10639 + 0.296457i −0.765366 0.643596i \(-0.777442\pi\)
−0.341028 + 0.940053i \(0.610775\pi\)
\(734\) −7.41154 27.6603i −0.273565 1.02096i
\(735\) 0 0
\(736\) 1.85641 6.92820i 0.0684280 0.255377i
\(737\) 16.0718 0.592012
\(738\) 0 0
\(739\) 21.2224 + 21.2224i 0.780680 + 0.780680i 0.979945 0.199266i \(-0.0638557\pi\)
−0.199266 + 0.979945i \(0.563856\pi\)
\(740\) −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 0.458317 0.888789i \(-0.348453\pi\)
−0.540556 + 0.841308i \(0.681786\pi\)
\(744\) 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
\(749\) 3.61474 13.4904i 0.132080 0.492928i
\(750\) 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
\(754\) −5.66025 + 21.1244i −0.206134 + 0.769304i
\(755\) −7.46410 7.46410i −0.271646 0.271646i
\(756\) 0 0
\(757\) −6.07180 + 6.07180i −0.220683 + 0.220683i −0.808786 0.588103i \(-0.799875\pi\)
0.588103 + 0.808786i \(0.299875\pi\)
\(758\) −32.4904 + 18.7583i −1.18010 + 0.681333i
\(759\) 0 0
\(760\) −9.46410 + 2.53590i −0.343299 + 0.0919867i
\(761\) 27.3731 + 15.8038i 0.992273 + 0.572889i 0.905953 0.423378i \(-0.139156\pi\)
0.0863200 + 0.996267i \(0.472489\pi\)
\(762\) 0 0
\(763\) 7.26795 + 1.94744i 0.263117 + 0.0705021i
\(764\) 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 \(0.0477036\pi\)
\(770\) 3.07180 + 11.4641i 0.110700 + 0.413138i
\(771\) 0 0
\(772\) −31.6410 + 18.2679i −1.13879 + 0.657478i
\(773\) −4.41154 + 4.41154i −0.158672 + 0.158672i −0.781978 0.623306i \(-0.785789\pi\)
0.623306 + 0.781978i \(0.285789\pi\)
\(774\) 0 0
\(775\) 74.1051i 2.66193i
\(776\) 6.05256 22.5885i 0.217274 0.810878i
\(777\) 0 0
\(778\) −13.0526 7.53590i −0.467957 0.270175i
\(779\) 0.696152 + 2.59808i 0.0249422 + 0.0930857i
\(780\) 0 0
\(781\) 8.39230 31.3205i 0.300300 1.12074i
\(782\) −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
\(786\)