Properties

Label 432.2.y.c.181.1
Level $432$
Weight $2$
Character 432.181
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 181.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 432.181
Dual form 432.2.y.c.253.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(0.267949 - 1.00000i) q^{5} +(-2.36603 - 1.36603i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})\) \(q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(0.267949 - 1.00000i) q^{5} +(-2.36603 - 1.36603i) q^{7} +(2.00000 - 2.00000i) q^{8} -1.46410i q^{10} +(4.23205 - 1.13397i) q^{11} +(-3.36603 - 0.901924i) q^{13} +(-3.73205 - 1.00000i) q^{14} +(2.00000 - 3.46410i) q^{16} +5.73205 q^{17} +(-2.36603 + 2.36603i) q^{19} +(-0.535898 - 2.00000i) q^{20} +(5.36603 - 3.09808i) q^{22} +(-4.09808 + 2.36603i) q^{23} +(3.40192 + 1.96410i) q^{25} -4.92820 q^{26} -5.46410 q^{28} +(0.633975 + 2.36603i) q^{29} +(-0.267949 - 0.464102i) q^{31} +(1.46410 - 5.46410i) q^{32} +(7.83013 - 2.09808i) q^{34} +(-2.00000 + 2.00000i) q^{35} +(4.73205 + 4.73205i) q^{37} +(-2.36603 + 4.09808i) q^{38} +(-1.46410 - 2.53590i) q^{40} +(-2.59808 + 1.50000i) q^{41} +(-8.33013 + 2.23205i) q^{43} +(6.19615 - 6.19615i) q^{44} +(-4.73205 + 4.73205i) q^{46} +(-3.83013 + 6.63397i) q^{47} +(0.232051 + 0.401924i) q^{49} +(5.36603 + 1.43782i) q^{50} +(-6.73205 + 1.80385i) q^{52} +(7.46410 + 7.46410i) q^{53} -4.53590i q^{55} +(-7.46410 + 2.00000i) q^{56} +(1.73205 + 3.00000i) q^{58} +(1.96410 - 7.33013i) q^{59} +(-3.00000 - 11.1962i) q^{61} +(-0.535898 - 0.535898i) q^{62} -8.00000i q^{64} +(-1.80385 + 3.12436i) q^{65} +(6.59808 + 1.76795i) q^{67} +(9.92820 - 5.73205i) q^{68} +(-2.00000 + 3.46410i) q^{70} +2.92820i q^{71} +6.26795i q^{73} +(8.19615 + 4.73205i) q^{74} +(-1.73205 + 6.46410i) q^{76} +(-11.5622 - 3.09808i) q^{77} +(-6.00000 + 10.3923i) q^{79} +(-2.92820 - 2.92820i) q^{80} +(-3.00000 + 3.00000i) q^{82} +(-0.366025 - 1.36603i) q^{83} +(1.53590 - 5.73205i) q^{85} +(-10.5622 + 6.09808i) q^{86} +(6.19615 - 10.7321i) q^{88} -2.00000i q^{89} +(6.73205 + 6.73205i) q^{91} +(-4.73205 + 8.19615i) q^{92} +(-2.80385 + 10.4641i) q^{94} +(1.73205 + 3.00000i) q^{95} +(-5.86603 + 10.1603i) q^{97} +(0.464102 + 0.464102i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} + 8q^{5} - 6q^{7} + 8q^{8} + O(q^{10}) \) \( 4q + 2q^{2} + 8q^{5} - 6q^{7} + 8q^{8} + 10q^{11} - 10q^{13} - 8q^{14} + 8q^{16} + 16q^{17} - 6q^{19} - 16q^{20} + 18q^{22} - 6q^{23} + 24q^{25} + 8q^{26} - 8q^{28} + 6q^{29} - 8q^{31} - 8q^{32} + 14q^{34} - 8q^{35} + 12q^{37} - 6q^{38} + 8q^{40} - 16q^{43} + 4q^{44} - 12q^{46} + 2q^{47} - 6q^{49} + 18q^{50} - 20q^{52} + 16q^{53} - 16q^{56} - 6q^{59} - 12q^{61} - 16q^{62} - 28q^{65} + 16q^{67} + 12q^{68} - 8q^{70} + 12q^{74} - 22q^{77} - 24q^{79} + 16q^{80} - 12q^{82} + 2q^{83} + 20q^{85} - 18q^{86} + 4q^{88} + 20q^{91} - 12q^{92} - 32q^{94} - 20q^{97} - 12q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) 0.267949 1.00000i 0.119831 0.447214i −0.879772 0.475395i \(-0.842305\pi\)
0.999603 + 0.0281817i \(0.00897171\pi\)
\(6\) 0 0
\(7\) −2.36603 1.36603i −0.894274 0.516309i −0.0189356 0.999821i \(-0.506028\pi\)
−0.875338 + 0.483512i \(0.839361\pi\)
\(8\) 2.00000 2.00000i 0.707107 0.707107i
\(9\) 0 0
\(10\) 1.46410i 0.462990i
\(11\) 4.23205 1.13397i 1.27601 0.341906i 0.443680 0.896185i \(-0.353673\pi\)
0.832331 + 0.554279i \(0.187006\pi\)
\(12\) 0 0
\(13\) −3.36603 0.901924i −0.933567 0.250149i −0.240192 0.970725i \(-0.577210\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) −3.73205 1.00000i −0.997433 0.267261i
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) 5.73205 1.39023 0.695113 0.718900i \(-0.255354\pi\)
0.695113 + 0.718900i \(0.255354\pi\)
\(18\) 0 0
\(19\) −2.36603 + 2.36603i −0.542803 + 0.542803i −0.924350 0.381546i \(-0.875392\pi\)
0.381546 + 0.924350i \(0.375392\pi\)
\(20\) −0.535898 2.00000i −0.119831 0.447214i
\(21\) 0 0
\(22\) 5.36603 3.09808i 1.14404 0.660512i
\(23\) −4.09808 + 2.36603i −0.854508 + 0.493350i −0.862169 0.506620i \(-0.830895\pi\)
0.00766135 + 0.999971i \(0.497561\pi\)
\(24\) 0 0
\(25\) 3.40192 + 1.96410i 0.680385 + 0.392820i
\(26\) −4.92820 −0.966500
\(27\) 0 0
\(28\) −5.46410 −1.03262
\(29\) 0.633975 + 2.36603i 0.117726 + 0.439360i 0.999476 0.0323566i \(-0.0103012\pi\)
−0.881750 + 0.471717i \(0.843635\pi\)
\(30\) 0 0
\(31\) −0.267949 0.464102i −0.0481251 0.0833551i 0.840959 0.541098i \(-0.181991\pi\)
−0.889085 + 0.457743i \(0.848658\pi\)
\(32\) 1.46410 5.46410i 0.258819 0.965926i
\(33\) 0 0
\(34\) 7.83013 2.09808i 1.34286 0.359817i
\(35\) −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 \(0.564594\pi\)
\(38\) −2.36603 + 4.09808i −0.383820 + 0.664796i
\(39\) 0 0
\(40\) −1.46410 2.53590i −0.231495 0.400961i
\(41\) −2.59808 + 1.50000i −0.405751 + 0.234261i −0.688963 0.724797i \(-0.741934\pi\)
0.283211 + 0.959058i \(0.408600\pi\)
\(42\) 0 0
\(43\) −8.33013 + 2.23205i −1.27033 + 0.340385i −0.830158 0.557528i \(-0.811750\pi\)
−0.440174 + 0.897912i \(0.645083\pi\)
\(44\) 6.19615 6.19615i 0.934105 0.934105i
\(45\) 0 0
\(46\) −4.73205 + 4.73205i −0.697703 + 0.697703i
\(47\) −3.83013 + 6.63397i −0.558681 + 0.967665i 0.438925 + 0.898523i \(0.355359\pi\)
−0.997607 + 0.0691412i \(0.977974\pi\)
\(48\) 0 0
\(49\) 0.232051 + 0.401924i 0.0331501 + 0.0574177i
\(50\) 5.36603 + 1.43782i 0.758871 + 0.203339i
\(51\) 0 0
\(52\) −6.73205 + 1.80385i −0.933567 + 0.250149i
\(53\) 7.46410 + 7.46410i 1.02527 + 1.02527i 0.999672 + 0.0256010i \(0.00814993\pi\)
0.0256010 + 0.999672i \(0.491850\pi\)
\(54\) 0 0
\(55\) 4.53590i 0.611620i
\(56\) −7.46410 + 2.00000i −0.997433 + 0.267261i
\(57\) 0 0
\(58\) 1.73205 + 3.00000i 0.227429 + 0.393919i
\(59\) 1.96410 7.33013i 0.255704 0.954301i −0.711993 0.702186i \(-0.752207\pi\)
0.967697 0.252115i \(-0.0811261\pi\)
\(60\) 0 0
\(61\) −3.00000 11.1962i −0.384111 1.43352i −0.839564 0.543261i \(-0.817189\pi\)
0.455453 0.890260i \(-0.349477\pi\)
\(62\) −0.535898 0.535898i −0.0680592 0.0680592i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) −1.80385 + 3.12436i −0.223740 + 0.387529i
\(66\) 0 0
\(67\) 6.59808 + 1.76795i 0.806083 + 0.215989i 0.638253 0.769827i \(-0.279657\pi\)
0.167830 + 0.985816i \(0.446324\pi\)
\(68\) 9.92820 5.73205i 1.20397 0.695113i
\(69\) 0 0
\(70\) −2.00000 + 3.46410i −0.239046 + 0.414039i
\(71\) 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 \(0.880452\pi\)
\(74\) 8.19615 + 4.73205i 0.952783 + 0.550090i
\(75\) 0 0
\(76\) −1.73205 + 6.46410i −0.198680 + 0.741483i
\(77\) −11.5622 3.09808i −1.31763 0.353059i
\(78\) 0 0
\(79\) −6.00000 + 10.3923i −0.675053 + 1.16923i 0.301401 + 0.953498i \(0.402546\pi\)
−0.976453 + 0.215728i \(0.930788\pi\)
\(80\) −2.92820 2.92820i −0.327383 0.327383i
\(81\) 0 0
\(82\) −3.00000 + 3.00000i −0.331295 + 0.331295i
\(83\) −0.366025 1.36603i −0.0401765 0.149941i 0.942924 0.333009i \(-0.108064\pi\)
−0.983100 + 0.183068i \(0.941397\pi\)
\(84\) 0 0
\(85\) 1.53590 5.73205i 0.166592 0.621728i
\(86\) −10.5622 + 6.09808i −1.13895 + 0.657572i
\(87\) 0 0
\(88\) 6.19615 10.7321i 0.660512 1.14404i
\(89\) 2.00000i 0.212000i −0.994366 0.106000i \(-0.966196\pi\)
0.994366 0.106000i \(-0.0338043\pi\)
\(90\) 0 0
\(91\) 6.73205 + 6.73205i 0.705711 + 0.705711i
\(92\) −4.73205 + 8.19615i −0.493350 + 0.854508i
\(93\) 0 0
\(94\) −2.80385 + 10.4641i −0.289195 + 1.07929i
\(95\) 1.73205 + 3.00000i 0.177705 + 0.307794i
\(96\) 0 0
\(97\) −5.86603 + 10.1603i −0.595605 + 1.03162i 0.397857 + 0.917448i \(0.369754\pi\)
−0.993461 + 0.114170i \(0.963579\pi\)
\(98\) 0.464102 + 0.464102i 0.0468813 + 0.0468813i
\(99\) 0 0
\(100\) 7.85641 0.785641
\(101\) 2.00000 0.535898i 0.199007 0.0533239i −0.157938 0.987449i \(-0.550485\pi\)
0.356946 + 0.934125i \(0.383818\pi\)
\(102\) 0 0
\(103\) −13.0981 + 7.56218i −1.29059 + 0.745124i −0.978759 0.205014i \(-0.934276\pi\)
−0.311833 + 0.950137i \(0.600943\pi\)
\(104\) −8.53590 + 4.92820i −0.837014 + 0.483250i
\(105\) 0 0
\(106\) 12.9282 + 7.46410i 1.25570 + 0.724978i
\(107\) −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 \(-0.00902398\pi\)
\(110\) −1.66025 6.19615i −0.158299 0.590780i
\(111\) 0 0
\(112\) −9.46410 + 5.46410i −0.894274 + 0.516309i
\(113\) 6.92820 + 12.0000i 0.651751 + 1.12887i 0.982698 + 0.185216i \(0.0592984\pi\)
−0.330947 + 0.943649i \(0.607368\pi\)
\(114\) 0 0
\(115\) 1.26795 + 4.73205i 0.118237 + 0.441266i
\(116\) 3.46410 + 3.46410i 0.321634 + 0.321634i
\(117\) 0 0
\(118\) 10.7321i 0.987965i
\(119\) −13.5622 7.83013i −1.24324 0.717787i
\(120\) 0 0
\(121\) 7.09808 4.09808i 0.645280 0.372552i
\(122\) −8.19615 14.1962i −0.742045 1.28526i
\(123\) 0 0
\(124\) −0.928203 0.535898i −0.0833551 0.0481251i
\(125\) 6.53590 6.53590i 0.584589 0.584589i
\(126\) 0 0
\(127\) 4.19615 0.372348 0.186174 0.982517i \(-0.440391\pi\)
0.186174 + 0.982517i \(0.440391\pi\)
\(128\) −2.92820 10.9282i −0.258819 0.965926i
\(129\) 0 0
\(130\) −1.32051 + 4.92820i −0.115816 + 0.432232i
\(131\) 7.83013 + 2.09808i 0.684121 + 0.183310i 0.584108 0.811676i \(-0.301445\pi\)
0.100014 + 0.994986i \(0.468111\pi\)
\(132\) 0 0
\(133\) 8.83013 2.36603i 0.765669 0.205160i
\(134\) 9.66025 0.834519
\(135\) 0 0
\(136\) 11.4641 11.4641i 0.983039 0.983039i
\(137\) 8.25833 + 4.76795i 0.705557 + 0.407353i 0.809414 0.587239i \(-0.199785\pi\)
−0.103857 + 0.994592i \(0.533118\pi\)
\(138\) 0 0
\(139\) 3.06218 11.4282i 0.259731 0.969328i −0.705667 0.708544i \(-0.749352\pi\)
0.965397 0.260784i \(-0.0839809\pi\)
\(140\) −1.46410 + 5.46410i −0.123739 + 0.461801i
\(141\) 0 0
\(142\) 1.07180 + 4.00000i 0.0899432 + 0.335673i
\(143\) −15.2679 −1.27677
\(144\) 0 0
\(145\) 2.53590 0.210595
\(146\) 2.29423 + 8.56218i 0.189872 + 0.708611i
\(147\) 0 0
\(148\) 12.9282 + 3.46410i 1.06269 + 0.284747i
\(149\) 2.09808 7.83013i 0.171881 0.641469i −0.825181 0.564869i \(-0.808927\pi\)
0.997062 0.0766003i \(-0.0244065\pi\)
\(150\) 0 0
\(151\) −0.633975 0.366025i −0.0515921 0.0297867i 0.473982 0.880534i \(-0.342816\pi\)
−0.525574 + 0.850748i \(0.676149\pi\)
\(152\) 9.46410i 0.767640i
\(153\) 0 0
\(154\) −16.9282 −1.36411
\(155\) −0.535898 + 0.143594i −0.0430444 + 0.0115337i
\(156\) 0 0
\(157\) −4.73205 1.26795i −0.377659 0.101193i 0.0649959 0.997886i \(-0.479297\pi\)
−0.442655 + 0.896692i \(0.645963\pi\)
\(158\) −4.39230 + 16.3923i −0.349433 + 1.30410i
\(159\) 0 0
\(160\) −5.07180 2.92820i −0.400961 0.231495i
\(161\) 12.9282 1.01889
\(162\) 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
\(167\) 6.46410 3.73205i 0.500207 0.288795i −0.228592 0.973522i \(-0.573412\pi\)
0.728799 + 0.684728i \(0.240079\pi\)
\(168\) 0 0
\(169\) −0.741670 0.428203i −0.0570515 0.0329387i
\(170\) 8.39230i 0.643660i
\(171\) 0 0
\(172\) −12.1962 + 12.1962i −0.929948 + 0.929948i
\(173\) 0.437822 + 1.63397i 0.0332870 + 0.124229i 0.980570 0.196169i \(-0.0628501\pi\)
−0.947283 + 0.320398i \(0.896183\pi\)
\(174\) 0 0
\(175\) −5.36603 9.29423i −0.405633 0.702578i
\(176\) 4.53590 16.9282i 0.341906 1.27601i
\(177\) 0 0
\(178\) −0.732051 2.73205i −0.0548695 0.204776i
\(179\) 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 \(0.877017\pi\)
\(182\) 11.6603 + 6.73205i 0.864316 + 0.499013i
\(183\) 0 0
\(184\) −3.46410 + 12.9282i −0.255377 + 0.953080i
\(185\) 6.00000 3.46410i 0.441129 0.254686i
\(186\) 0 0
\(187\) 24.2583 6.50000i 1.77394 0.475327i
\(188\) 15.3205i 1.11736i
\(189\) 0 0
\(190\) 3.46410 + 3.46410i 0.251312 + 0.251312i
\(191\) 12.0263 20.8301i 0.870191 1.50722i 0.00839227 0.999965i \(-0.497329\pi\)
0.861799 0.507250i \(-0.169338\pi\)
\(192\) 0 0
\(193\) −10.8660 18.8205i −0.782154 1.35473i −0.930685 0.365822i \(-0.880788\pi\)
0.148531 0.988908i \(-0.452545\pi\)
\(194\) −4.29423 + 16.0263i −0.308308 + 1.15062i
\(195\) 0 0
\(196\) 0.803848 + 0.464102i 0.0574177 + 0.0331501i
\(197\) −13.6603 13.6603i −0.973253 0.973253i 0.0263987 0.999651i \(-0.491596\pi\)
−0.999651 + 0.0263987i \(0.991596\pi\)
\(198\) 0 0
\(199\) 25.1244i 1.78102i −0.454965 0.890509i \(-0.650348\pi\)
0.454965 0.890509i \(-0.349652\pi\)
\(200\) 10.7321 2.87564i 0.758871 0.203339i
\(201\) 0 0
\(202\) 2.53590 1.46410i 0.178425 0.103014i
\(203\) 1.73205 6.46410i 0.121566 0.453691i
\(204\) 0 0
\(205\) 0.803848 + 3.00000i 0.0561432 + 0.209529i
\(206\) −15.1244 + 15.1244i −1.05376 + 1.05376i
\(207\) 0 0
\(208\) −9.85641 + 9.85641i −0.683419 + 0.683419i
\(209\) −7.33013 + 12.6962i −0.507035 + 0.878211i
\(210\) 0 0
\(211\) 4.09808 + 1.09808i 0.282123 + 0.0755947i 0.397106 0.917773i \(-0.370015\pi\)
−0.114983 + 0.993367i \(0.536681\pi\)
\(212\) 20.3923 + 5.46410i 1.40055 + 0.375276i
\(213\) 0 0
\(214\) −21.6340 12.4904i −1.47887 0.853825i
\(215\) 8.92820i 0.608898i
\(216\) 0 0
\(217\) 1.46410i 0.0993897i
\(218\) 10.7321 18.5885i 0.726866 1.25897i
\(219\) 0 0
\(220\) −4.53590 7.85641i −0.305810 0.529679i
\(221\) −19.2942 5.16987i −1.29787 0.347763i
\(222\) 0 0
\(223\) −8.02628 + 13.9019i −0.537479 + 0.930942i 0.461559 + 0.887109i \(0.347290\pi\)
−0.999039 + 0.0438324i \(0.986043\pi\)
\(224\) −10.9282 + 10.9282i −0.730171 + 0.730171i
\(225\) 0 0
\(226\) 13.8564 + 13.8564i 0.921714 + 0.921714i
\(227\) 0.571797 + 2.13397i 0.0379515 + 0.141637i 0.982302 0.187304i \(-0.0599750\pi\)
−0.944351 + 0.328941i \(0.893308\pi\)
\(228\) 0 0
\(229\) −1.83013 + 6.83013i −0.120938 + 0.451347i −0.999662 0.0259823i \(-0.991729\pi\)
0.878724 + 0.477330i \(0.158395\pi\)
\(230\) 3.46410 + 6.00000i 0.228416 + 0.395628i
\(231\) 0 0
\(232\) 6.00000 + 3.46410i 0.393919 + 0.227429i
\(233\) 3.19615i 0.209387i −0.994505 0.104693i \(-0.966614\pi\)
0.994505 0.104693i \(-0.0333861\pi\)
\(234\) 0 0
\(235\) 5.60770 + 5.60770i 0.365806 + 0.365806i
\(236\) −3.92820 14.6603i −0.255704 0.954301i
\(237\) 0 0
\(238\) −21.3923 5.73205i −1.38666 0.371554i
\(239\) 7.90192 + 13.6865i 0.511133 + 0.885308i 0.999917 + 0.0129033i \(0.00410736\pi\)
−0.488784 + 0.872405i \(0.662559\pi\)
\(240\) 0 0
\(241\) −11.5981 + 20.0885i −0.747098 + 1.29401i 0.202110 + 0.979363i \(0.435220\pi\)
−0.949208 + 0.314649i \(0.898113\pi\)
\(242\) 8.19615 8.19615i 0.526869 0.526869i
\(243\) 0 0
\(244\) −16.3923 16.3923i −1.04941 1.04941i
\(245\) 0.464102 0.124356i 0.0296504 0.00794479i
\(246\) 0 0
\(247\) 10.0981 5.83013i 0.642525 0.370962i
\(248\) −1.46410 0.392305i −0.0929705 0.0249114i
\(249\) 0 0
\(250\) 6.53590 11.3205i 0.413367 0.715972i
\(251\) 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
\(254\) 5.73205 1.53590i 0.359661 0.0963708i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) −9.42820 16.3301i −0.588115 1.01865i −0.994479 0.104934i \(-0.966537\pi\)
0.406364 0.913711i \(-0.366796\pi\)
\(258\) 0 0
\(259\) −4.73205 17.6603i −0.294035 1.09735i
\(260\) 7.21539i 0.447480i
\(261\) 0 0
\(262\) 11.4641 0.708255
\(263\) −2.49038 1.43782i −0.153563 0.0886599i 0.421249 0.906945i \(-0.361592\pi\)
−0.574813 + 0.818285i \(0.694925\pi\)
\(264\) 0 0
\(265\) 9.46410 5.46410i 0.581375 0.335657i
\(266\) 11.1962 6.46410i 0.686480 0.396339i
\(267\) 0 0
\(268\) 13.1962 3.53590i 0.806083 0.215989i
\(269\) −1.26795 + 1.26795i −0.0773082 + 0.0773082i −0.744704 0.667395i \(-0.767409\pi\)
0.667395 + 0.744704i \(0.267409\pi\)
\(270\) 0 0
\(271\) −0.392305 −0.0238308 −0.0119154 0.999929i \(-0.503793\pi\)
−0.0119154 + 0.999929i \(0.503793\pi\)
\(272\) 11.4641 19.8564i 0.695113 1.20397i
\(273\) 0 0
\(274\) 13.0263 + 3.49038i 0.786946 + 0.210862i
\(275\) 16.6244 + 4.45448i 1.00249 + 0.268615i
\(276\) 0 0
\(277\) 25.2224 6.75833i 1.51547 0.406069i 0.597222 0.802076i \(-0.296271\pi\)
0.918247 + 0.396007i \(0.129605\pi\)
\(278\) 16.7321i 1.00352i
\(279\) 0 0
\(280\) 8.00000i 0.478091i
\(281\) −8.66025 5.00000i −0.516627 0.298275i 0.218926 0.975741i \(-0.429745\pi\)
−0.735554 + 0.677466i \(0.763078\pi\)
\(282\) 0 0
\(283\) 5.24167 19.5622i 0.311585 1.16285i −0.615542 0.788104i \(-0.711063\pi\)
0.927127 0.374747i \(-0.122270\pi\)
\(284\) 2.92820 + 5.07180i 0.173757 + 0.300956i
\(285\) 0 0
\(286\) −20.8564 + 5.58846i −1.23327 + 0.330452i
\(287\) 8.19615 0.483804
\(288\) 0 0
\(289\) 15.8564 0.932730
\(290\) 3.46410 0.928203i 0.203419 0.0545060i
\(291\) 0 0
\(292\) 6.26795 + 10.8564i 0.366804 + 0.635323i
\(293\) −1.43782 + 5.36603i −0.0839985 + 0.313487i −0.995123 0.0986454i \(-0.968549\pi\)
0.911124 + 0.412132i \(0.135216\pi\)
\(294\) 0 0
\(295\) −6.80385 3.92820i −0.396135 0.228709i
\(296\) 18.9282 1.10018
\(297\) 0 0
\(298\) 11.4641i 0.664098i
\(299\) 15.9282 4.26795i 0.921152 0.246822i
\(300\) 0 0
\(301\) 22.7583 + 6.09808i 1.31177 + 0.351487i
\(302\) −1.00000 0.267949i −0.0575435 0.0154187i
\(303\) 0 0
\(304\) 3.46410 + 12.9282i 0.198680 + 0.741483i
\(305\) −12.0000 −0.687118
\(306\) 0 0
\(307\) 3.02628 3.02628i 0.172719 0.172719i −0.615454 0.788173i \(-0.711027\pi\)
0.788173 + 0.615454i \(0.211027\pi\)
\(308\) −23.1244 + 6.19615i −1.31763 + 0.353059i
\(309\) 0 0
\(310\) −0.679492 + 0.392305i −0.0385925 + 0.0222814i
\(311\) −19.0981 + 11.0263i −1.08295 + 0.625243i −0.931691 0.363251i \(-0.881667\pi\)
−0.151261 + 0.988494i \(0.548333\pi\)
\(312\) 0 0
\(313\) −18.6506 10.7679i −1.05420 0.608640i −0.130375 0.991465i \(-0.541618\pi\)
−0.923821 + 0.382824i \(0.874951\pi\)
\(314\) −6.92820 −0.390981
\(315\) 0 0
\(316\) 24.0000i 1.35011i
\(317\) −5.50962 20.5622i −0.309451 1.15489i −0.929046 0.369965i \(-0.879370\pi\)
0.619595 0.784922i \(-0.287297\pi\)
\(318\) 0 0
\(319\) 5.36603 + 9.29423i 0.300440 + 0.520377i
\(320\) −8.00000 2.14359i −0.447214 0.119831i
\(321\) 0 0
\(322\) 17.6603 4.73205i 0.984167 0.263707i
\(323\) −13.5622 + 13.5622i −0.754620 + 0.754620i
\(324\) 0 0
\(325\) −9.67949 9.67949i −0.536922 0.536922i
\(326\) −7.00000 + 12.1244i −0.387694 + 0.671506i
\(327\) 0 0
\(328\) −2.19615 + 8.19615i −0.121262 + 0.452557i
\(329\) 18.1244 10.4641i 0.999228 0.576905i
\(330\) 0 0
\(331\) −0.0980762 + 0.0262794i −0.00539076 + 0.00144445i −0.261513 0.965200i \(-0.584222\pi\)
0.256123 + 0.966644i \(0.417555\pi\)
\(332\) −2.00000 2.00000i −0.109764 0.109764i
\(333\) 0 0
\(334\) 7.46410 7.46410i 0.408417 0.408417i
\(335\) 3.53590 6.12436i 0.193187 0.334609i
\(336\) 0 0
\(337\) 8.89230 + 15.4019i 0.484395 + 0.838996i 0.999839 0.0179267i \(-0.00570654\pi\)
−0.515445 + 0.856923i \(0.672373\pi\)
\(338\) −1.16987 0.313467i −0.0636327 0.0170503i
\(339\) 0 0
\(340\) −3.07180 11.4641i −0.166592 0.621728i
\(341\) −1.66025 1.66025i −0.0899078 0.0899078i
\(342\) 0 0
\(343\) 17.8564i 0.964155i
\(344\) −12.1962 + 21.1244i −0.657572 + 1.13895i
\(345\) 0 0
\(346\) 1.19615 + 2.07180i 0.0643056 + 0.111380i
\(347\) −4.72243 + 17.6244i −0.253513 + 0.946125i 0.715398 + 0.698717i \(0.246245\pi\)
−0.968911 + 0.247408i \(0.920421\pi\)
\(348\) 0 0
\(349\) −4.26795 15.9282i −0.228458 0.852617i −0.980989 0.194061i \(-0.937834\pi\)
0.752531 0.658556i \(-0.228833\pi\)
\(350\) −10.7321 10.7321i −0.573652 0.573652i
\(351\) 0 0
\(352\) 24.7846i 1.32102i
\(353\) −7.16025 + 12.4019i −0.381102 + 0.660088i −0.991220 0.132223i \(-0.957789\pi\)
0.610118 + 0.792310i \(0.291122\pi\)
\(354\) 0 0
\(355\) 2.92820 + 0.784610i 0.155413 + 0.0416428i
\(356\) −2.00000 3.46410i −0.106000 0.183597i
\(357\) 0 0
\(358\) 1.92820 3.33975i 0.101909 0.176511i
\(359\) 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
\(362\) −12.8038 7.39230i −0.672955 0.388531i
\(363\) 0 0
\(364\) 18.3923 + 4.92820i 0.964019 + 0.258308i
\(365\) 6.26795 + 1.67949i 0.328079 + 0.0879086i
\(366\) 0 0
\(367\) 14.1244 24.4641i 0.737285 1.27702i −0.216428 0.976299i \(-0.569441\pi\)
0.953713 0.300717i \(-0.0972260\pi\)
\(368\) 18.9282i 0.986701i
\(369\) 0 0
\(370\) 6.92820 6.92820i 0.360180 0.360180i
\(371\) −7.46410 27.8564i −0.387517 1.44623i
\(372\) 0 0
\(373\) −7.36603 + 27.4904i −0.381398 + 1.42340i 0.462368 + 0.886688i \(0.347000\pi\)
−0.843767 + 0.536710i \(0.819667\pi\)
\(374\) 30.7583 17.7583i 1.59048 0.918261i
\(375\) 0 0
\(376\) 5.60770 + 20.9282i 0.289195 + 1.07929i
\(377\) 8.53590i 0.439621i
\(378\) 0 0
\(379\) 3.75833 + 3.75833i 0.193052 + 0.193052i 0.797014 0.603961i \(-0.206412\pi\)
−0.603961 + 0.797014i \(0.706412\pi\)
\(380\) 6.00000 + 3.46410i 0.307794 + 0.177705i
\(381\) 0 0
\(382\) 8.80385 32.8564i 0.450444 1.68108i
\(383\) 6.73205 + 11.6603i 0.343992 + 0.595811i 0.985170 0.171581i \(-0.0548874\pi\)
−0.641178 + 0.767392i \(0.721554\pi\)
\(384\) 0 0
\(385\) −6.19615 + 10.7321i −0.315785 + 0.546956i
\(386\) −21.7321 21.7321i −1.10613 1.10613i
\(387\) 0 0
\(388\) 23.4641i 1.19121i
\(389\) −19.7583 + 5.29423i −1.00179 + 0.268428i −0.722194 0.691691i \(-0.756866\pi\)
−0.279593 + 0.960119i \(0.590200\pi\)
\(390\) 0 0
\(391\) −23.4904 + 13.5622i −1.18796 + 0.685869i
\(392\) 1.26795 + 0.339746i 0.0640411 + 0.0171598i
\(393\) 0 0
\(394\) −23.6603 13.6603i −1.19199 0.688194i
\(395\) 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 \(0.356680\pi\)
\(398\) −9.19615 34.3205i −0.460961 1.72033i
\(399\) 0 0
\(400\) 13.6077 7.85641i 0.680385 0.392820i
\(401\) 1.79423 + 3.10770i 0.0895995 + 0.155191i 0.907342 0.420393i \(-0.138108\pi\)
−0.817742 + 0.575584i \(0.804775\pi\)
\(402\) 0 0
\(403\) 0.483340 + 1.80385i 0.0240769 + 0.0898560i
\(404\) 2.92820 2.92820i 0.145684 0.145684i
\(405\) 0 0
\(406\) 9.46410i 0.469695i
\(407\) 25.3923 + 14.6603i 1.25865 + 0.726682i
\(408\) 0 0
\(409\) −27.8660 + 16.0885i −1.37789 + 0.795523i −0.991905 0.126984i \(-0.959470\pi\)
−0.385981 + 0.922507i \(0.626137\pi\)
\(410\) 2.19615 + 3.80385i 0.108460 + 0.187859i
\(411\) 0 0
\(412\) −15.1244 + 26.1962i −0.745124 + 1.29059i
\(413\) −14.6603 + 14.6603i −0.721384 + 0.721384i
\(414\) 0 0
\(415\) −1.46410 −0.0718699
\(416\) −9.85641 + 17.0718i −0.483250 + 0.837014i
\(417\) 0 0
\(418\) −5.36603 + 20.0263i −0.262461 + 0.979517i
\(419\) 6.63397 + 1.77757i 0.324091 + 0.0868399i 0.417196 0.908816i \(-0.363013\pi\)
−0.0931055 + 0.995656i \(0.529679\pi\)
\(420\) 0 0
\(421\) −30.5885 + 8.19615i −1.49079 + 0.399456i −0.910004 0.414600i \(-0.863922\pi\)
−0.580786 + 0.814056i \(0.697255\pi\)
\(422\) 6.00000 0.292075
\(423\) 0 0
\(424\) 29.8564 1.44996
\(425\) 19.5000 + 11.2583i 0.945889 + 0.546109i
\(426\) 0 0
\(427\) −8.19615 + 30.5885i −0.396640 + 1.48028i
\(428\) −34.1244 9.14359i −1.64946 0.441972i
\(429\) 0 0
\(430\) 3.26795 + 12.1962i 0.157595 + 0.588151i
\(431\) 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 \(0.543981\pi\)
\(434\) 0.535898 + 2.00000i 0.0257239 + 0.0960031i
\(435\) 0 0
\(436\) 7.85641 29.3205i 0.376254 1.40420i
\(437\) 4.09808 15.2942i 0.196038 0.731622i
\(438\) 0 0
\(439\) 22.8564 + 13.1962i 1.09088 + 0.629818i 0.933810 0.357770i \(-0.116463\pi\)
0.157067 + 0.987588i \(0.449796\pi\)
\(440\) −9.07180 9.07180i −0.432481 0.432481i
\(441\) 0 0
\(442\) −28.2487 −1.34365
\(443\) −17.2583 + 4.62436i −0.819968 + 0.219710i −0.644332 0.764745i \(-0.722865\pi\)
−0.175636 + 0.984455i \(0.556198\pi\)
\(444\) 0 0
\(445\) −2.00000 0.535898i −0.0948091 0.0254040i
\(446\) −5.87564 + 21.9282i −0.278220 + 1.03833i
\(447\) 0 0
\(448\) −10.9282 + 18.9282i −0.516309 + 0.894274i
\(449\) 3.33975 0.157612 0.0788062 0.996890i \(-0.474889\pi\)
0.0788062 + 0.996890i \(0.474889\pi\)
\(450\) 0 0
\(451\) −9.29423 + 9.29423i −0.437648 + 0.437648i
\(452\) 24.0000 + 13.8564i 1.12887 + 0.651751i
\(453\) 0 0
\(454\) 1.56218 + 2.70577i 0.0733166 + 0.126988i
\(455\) 8.53590 4.92820i 0.400169 0.231038i
\(456\) 0 0
\(457\) −2.25833 1.30385i −0.105640 0.0609914i 0.446249 0.894909i \(-0.352760\pi\)
−0.551889 + 0.833917i \(0.686093\pi\)
\(458\) 10.0000i 0.467269i
\(459\) 0 0
\(460\) 6.92820 + 6.92820i 0.323029 + 0.323029i
\(461\) 9.56218 + 35.6865i 0.445355 + 1.66209i 0.714997 + 0.699127i \(0.246428\pi\)
−0.269642 + 0.962961i \(0.586906\pi\)
\(462\) 0 0
\(463\) 1.19615 + 2.07180i 0.0555899 + 0.0962846i 0.892481 0.451085i \(-0.148963\pi\)
−0.836891 + 0.547369i \(0.815629\pi\)
\(464\) 9.46410 + 2.53590i 0.439360 + 0.117726i
\(465\) 0 0
\(466\) −1.16987 4.36603i −0.0541933 0.202252i
\(467\) −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
\(470\) 9.71281 + 5.60770i 0.448019 + 0.258664i
\(471\) 0 0
\(472\) −10.7321 18.5885i −0.493983 0.855603i
\(473\) −32.7224 + 18.8923i −1.50458 + 0.868669i
\(474\) 0 0
\(475\) −12.6962 + 3.40192i −0.582539 + 0.156091i
\(476\) −31.3205 −1.43557
\(477\) 0 0
\(478\) 15.8038 + 15.8038i 0.722851 + 0.722851i
\(479\) −4.16987 + 7.22243i −0.190526 + 0.330001i −0.945425 0.325840i \(-0.894353\pi\)
0.754898 + 0.655842i \(0.227686\pi\)
\(480\) 0 0
\(481\) −11.6603 20.1962i −0.531662 0.920865i
\(482\) −8.49038 + 31.6865i −0.386726 + 1.44328i
\(483\) 0 0
\(484\) 8.19615 14.1962i 0.372552 0.645280i
\(485\) 8.58846 + 8.58846i 0.389982 + 0.389982i
\(486\) 0 0
\(487\) 5.80385i 0.262997i −0.991316 0.131499i \(-0.958021\pi\)
0.991316 0.131499i \(-0.0419789\pi\)
\(488\) −28.3923 16.3923i −1.28526 0.742045i
\(489\) 0 0
\(490\) 0.588457 0.339746i 0.0265838 0.0153482i
\(491\) −3.72243 + 13.8923i −0.167991 + 0.626951i 0.829649 + 0.558286i \(0.188541\pi\)
−0.997640 + 0.0686652i \(0.978126\pi\)
\(492\) 0 0
\(493\) 3.63397 + 13.5622i 0.163666 + 0.610810i
\(494\) 11.6603 11.6603i 0.524620 0.524620i
\(495\) 0 0
\(496\) −2.14359 −0.0962502
\(497\) 4.00000 6.92820i 0.179425 0.310772i
\(498\) 0 0
\(499\) 8.69615 + 2.33013i 0.389293 + 0.104311i 0.448156 0.893955i \(-0.352081\pi\)
−0.0588630 + 0.998266i \(0.518748\pi\)
\(500\) 4.78461 17.8564i 0.213974 0.798563i
\(501\) 0 0
\(502\) 10.0981 + 5.83013i 0.450699 + 0.260211i
\(503\) 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
\(506\) −14.6603 + 25.3923i −0.651728 + 1.12883i
\(507\) 0 0
\(508\) 7.26795 4.19615i 0.322463 0.186174i
\(509\) 11.4641 + 3.07180i 0.508137 + 0.136155i 0.503774 0.863835i \(-0.331944\pi\)
0.00436335 + 0.999990i \(0.498611\pi\)
\(510\) 0 0
\(511\) 8.56218 14.8301i 0.378768 0.656046i
\(512\) −16.0000 16.0000i −0.707107 0.707107i
\(513\) 0 0
\(514\) −18.8564 18.8564i −0.831720 0.831720i
\(515\) 4.05256 + 15.1244i 0.178577 + 0.666459i
\(516\) 0 0
\(517\) −8.68653 + 32.4186i −0.382033 + 1.42577i
\(518\) −12.9282 22.3923i −0.568033 0.983861i
\(519\) 0 0
\(520\) 2.64102 + 9.85641i 0.115816 + 0.432232i
\(521\) 13.0000i 0.569540i 0.958596 + 0.284770i \(0.0919173\pi\)
−0.958596 + 0.284770i \(0.908083\pi\)
\(522\) 0 0
\(523\) −7.53590 7.53590i −0.329522 0.329522i 0.522883 0.852405i \(-0.324857\pi\)
−0.852405 + 0.522883i \(0.824857\pi\)
\(524\) 15.6603 4.19615i 0.684121 0.183310i
\(525\) 0 0
\(526\) −3.92820 1.05256i −0.171278 0.0458937i
\(527\) −1.53590 2.66025i −0.0669048 0.115882i
\(528\) 0 0
\(529\) −0.303848 + 0.526279i −0.0132108 + 0.0228817i
\(530\) 10.9282 10.9282i 0.474691 0.474691i
\(531\) 0 0
\(532\) 12.9282 12.9282i 0.560509 0.560509i
\(533\) 10.0981 2.70577i 0.437396 0.117200i
\(534\) 0 0
\(535\) −15.8372 + 9.14359i −0.684701 + 0.395312i
\(536\) 16.7321 9.66025i 0.722715 0.417259i
\(537\) 0 0
\(538\) −1.26795 + 2.19615i −0.0546652 + 0.0946829i
\(539\) 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 \(0.228732\pi\)
\(542\) −0.535898 + 0.143594i −0.0230188 + 0.00616787i
\(543\) 0 0
\(544\) 8.39230 31.3205i 0.359817 1.34286i
\(545\) −7.85641 13.6077i −0.336531 0.582890i
\(546\) 0 0
\(547\) −8.74167 32.6244i −0.373767 1.39492i −0.855138 0.518400i \(-0.826528\pi\)
0.481371 0.876517i \(-0.340139\pi\)
\(548\) 19.0718 0.814707
\(549\) 0 0
\(550\) 24.3397 1.03785
\(551\) −7.09808 4.09808i −0.302388 0.174584i
\(552\) 0 0
\(553\) 28.3923 16.3923i 1.20736 0.697072i
\(554\) 31.9808 18.4641i 1.35873 0.784465i
\(555\) 0 0
\(556\) −6.12436 22.8564i −0.259731 0.969328i
\(557\) 14.8038 14.8038i 0.627259 0.627259i −0.320118 0.947378i \(-0.603723\pi\)
0.947378 + 0.320118i \(0.103723\pi\)
\(558\) 0 0
\(559\) 30.0526 1.27109
\(560\) 2.92820 + 10.9282i 0.123739 + 0.461801i
\(561\) 0 0
\(562\) −13.6603 3.66025i −0.576223 0.154398i
\(563\) −26.9904 7.23205i −1.13751 0.304795i −0.359560 0.933122i \(-0.617073\pi\)
−0.777949 + 0.628327i \(0.783740\pi\)
\(564\) 0 0
\(565\) 13.8564 3.71281i 0.582943 0.156199i
\(566\) 28.6410i 1.20387i
\(567\) 0 0
\(568\) 5.85641 + 5.85641i 0.245729 + 0.245729i
\(569\) −18.4019 10.6244i −0.771449 0.445396i 0.0619424 0.998080i \(-0.480270\pi\)
−0.833391 + 0.552684i \(0.813604\pi\)
\(570\) 0 0
\(571\) 0.892305 3.33013i 0.0373418 0.139361i −0.944738 0.327825i \(-0.893684\pi\)
0.982080 + 0.188464i \(0.0603509\pi\)
\(572\) −26.4449 + 15.2679i −1.10572 + 0.638385i
\(573\) 0 0
\(574\) 11.1962 3.00000i 0.467318 0.125218i
\(575\) −18.5885 −0.775192
\(576\) 0 0
\(577\) −5.78461 −0.240816 −0.120408 0.992724i \(-0.538420\pi\)
−0.120408 + 0.992724i \(0.538420\pi\)
\(578\) 21.6603 5.80385i 0.900948 0.241408i
\(579\) 0 0
\(580\) 4.39230 2.53590i 0.182381 0.105297i
\(581\) −1.00000 + 3.73205i −0.0414870 + 0.154832i
\(582\) 0 0
\(583\) 40.0526 + 23.1244i 1.65881 + 0.957713i
\(584\) 12.5359 + 12.5359i 0.518739 + 0.518739i
\(585\) 0 0
\(586\) 7.85641i 0.324545i
\(587\) 26.9904 7.23205i 1.11401 0.298499i 0.345554 0.938399i \(-0.387691\pi\)
0.768458 + 0.639900i \(0.221024\pi\)
\(588\) 0 0
\(589\) 1.73205 + 0.464102i 0.0713679 + 0.0191230i
\(590\) −10.7321 2.87564i −0.441832 0.118388i
\(591\) 0 0
\(592\) 25.8564 6.92820i 1.06269 0.284747i
\(593\) −17.4641 −0.717165 −0.358582 0.933498i \(-0.616740\pi\)
−0.358582 + 0.933498i \(0.616740\pi\)
\(594\) 0 0
\(595\) −11.4641 + 11.4641i −0.469982 + 0.469982i
\(596\) −4.19615 15.6603i −0.171881 0.641469i
\(597\) 0 0
\(598\) 20.1962 11.6603i 0.825882 0.476823i
\(599\) 11.3205 6.53590i 0.462543 0.267050i −0.250570 0.968099i \(-0.580618\pi\)
0.713113 + 0.701049i \(0.247285\pi\)
\(600\) 0 0
\(601\) 20.5526 + 11.8660i 0.838356 + 0.484025i 0.856705 0.515806i \(-0.172508\pi\)
−0.0183488 + 0.999832i \(0.505841\pi\)
\(602\) 33.3205 1.35804
\(603\) 0 0
\(604\) −1.46410 −0.0595734
\(605\) −2.19615 8.19615i −0.0892863 0.333221i
\(606\) 0 0
\(607\) −8.58846 14.8756i −0.348595 0.603784i 0.637405 0.770529i \(-0.280008\pi\)
−0.986000 + 0.166745i \(0.946674\pi\)
\(608\) 9.46410 + 16.3923i 0.383820 + 0.664796i
\(609\) 0 0
\(610\) −16.3923 + 4.39230i −0.663705 + 0.177839i
\(611\) 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 \(0.897598\pi\)
\(614\) 3.02628 5.24167i 0.122131 0.211537i
\(615\) 0 0
\(616\) −29.3205 + 16.9282i −1.18136 + 0.682057i
\(617\) −35.0885 + 20.2583i −1.41261 + 0.815570i −0.995633 0.0933485i \(-0.970243\pi\)
−0.416975 + 0.908918i \(0.636910\pi\)
\(618\) 0 0
\(619\) −15.5981 + 4.17949i −0.626940 + 0.167988i −0.558281 0.829652i \(-0.688539\pi\)
−0.0686590 + 0.997640i \(0.521872\pi\)
\(620\) −0.784610 + 0.784610i −0.0315107 + 0.0315107i
\(621\) 0 0
\(622\) −22.0526 + 22.0526i −0.884227 + 0.884227i
\(623\) −2.73205 + 4.73205i −0.109457 + 0.189586i
\(624\) 0 0
\(625\) 5.03590 + 8.72243i 0.201436 + 0.348897i
\(626\) −29.4186 7.88269i −1.17580 0.315055i
\(627\) 0 0
\(628\) −9.46410 + 2.53590i −0.377659 + 0.101193i
\(629\) 27.1244 + 27.1244i 1.08152 + 1.08152i
\(630\) 0 0
\(631\) 17.6077i 0.700951i −0.936572 0.350476i \(-0.886020\pi\)
0.936572 0.350476i \(-0.113980\pi\)
\(632\) 8.78461 + 32.7846i 0.349433 + 1.30410i
\(633\) 0 0
\(634\) −15.0526 26.0718i −0.597813 1.03544i
\(635\) 1.12436 4.19615i 0.0446187 0.166519i
\(636\) 0 0
\(637\) −0.418584 1.56218i −0.0165849 0.0618957i
\(638\) 10.7321 + 10.7321i 0.424886 + 0.424886i
\(639\) 0 0
\(640\) −11.7128 −0.462990
\(641\) 19.7942 34.2846i 0.781825 1.35416i −0.149053 0.988829i \(-0.547622\pi\)
0.930878 0.365331i \(-0.119044\pi\)
\(642\) 0 0
\(643\) 8.76795 + 2.34936i 0.345774 + 0.0926499i 0.427527 0.904003i \(-0.359385\pi\)
−0.0817525 + 0.996653i \(0.526052\pi\)
\(644\) 22.3923 12.9282i 0.882380 0.509443i
\(645\) 0 0
\(646\) −13.5622 + 23.4904i −0.533597 + 0.924217i
\(647\) 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
\(650\) −16.7654 9.67949i −0.657592 0.379661i
\(651\) 0 0
\(652\) −5.12436 + 19.1244i −0.200685 + 0.748968i
\(653\) 27.4904 + 7.36603i 1.07578 + 0.288255i 0.752867 0.658173i \(-0.228671\pi\)
0.322915 + 0.946428i \(0.395337\pi\)
\(654\) 0 0
\(655\) 4.19615 7.26795i 0.163957 0.283982i
\(656\) 12.0000i 0.468521i
\(657\) 0 0
\(658\) 20.9282 20.9282i 0.815866 0.815866i
\(659\) −4.02628 15.0263i −0.156842 0.585341i −0.998941 0.0460178i \(-0.985347\pi\)
0.842099 0.539323i \(-0.181320\pi\)
\(660\) 0 0
\(661\) 2.19615 8.19615i 0.0854204 0.318793i −0.909973 0.414667i \(-0.863898\pi\)
0.995393 + 0.0958740i \(0.0305646\pi\)
\(662\) −0.124356 + 0.0717968i −0.00483322 + 0.00279046i
\(663\) 0 0
\(664\) −3.46410 2.00000i −0.134433 0.0776151i
\(665\) 9.46410i 0.367002i
\(666\) 0 0
\(667\) −8.19615 8.19615i −0.317356 0.317356i
\(668\) 7.46410 12.9282i 0.288795 0.500207i
\(669\) 0 0
\(670\) 2.58846 9.66025i 0.100001 0.373208i
\(671\) −25.3923 43.9808i −0.980259 1.69786i
\(672\) 0 0
\(673\) 19.1962 33.2487i 0.739957 1.28164i −0.212557 0.977149i \(-0.568179\pi\)
0.952514 0.304495i \(-0.0984877\pi\)
\(674\) 17.7846 + 17.7846i 0.685038 + 0.685038i
\(675\) 0 0
\(676\) −1.71281 −0.0658774
\(677\) 4.73205 1.26795i 0.181867 0.0487312i −0.166736 0.986002i \(-0.553323\pi\)
0.348603 + 0.937270i \(0.386656\pi\)
\(678\) 0 0
\(679\) 27.7583 16.0263i 1.06527 0.615032i
\(680\) −8.39230 14.5359i −0.321830 0.557426i
\(681\) 0 0
\(682\) −2.87564 1.66025i −0.110114 0.0635744i
\(683\) 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
\(686\) 6.53590 + 24.3923i 0.249542 + 0.931303i
\(687\) 0 0
\(688\) −8.92820 + 33.3205i −0.340385 + 1.27033i
\(689\) −18.3923 31.8564i −0.700691 1.21363i
\(690\) 0 0
\(691\) −2.49038 9.29423i −0.0947386 0.353569i 0.902241 0.431232i \(-0.141921\pi\)
−0.996980 + 0.0776628i \(0.975254\pi\)
\(692\) 2.39230 + 2.39230i 0.0909418 + 0.0909418i
\(693\) 0 0
\(694\) 25.8038i 0.979501i
\(695\) −10.6077 6.12436i −0.402373 0.232310i
\(696\) 0 0
\(697\) −14.8923 + 8.59808i −0.564086 + 0.325675i
\(698\) −11.6603 20.1962i −0.441347 0.764436i
\(699\) 0 0
\(700\) −18.5885 10.7321i −0.702578 0.405633i
\(701\) 6.66025 6.66025i 0.251554 0.251554i −0.570053 0.821608i \(-0.693077\pi\)
0.821608 + 0.570053i \(0.193077\pi\)
\(702\) 0 0
\(703\) −22.3923 −0.844542
\(704\) −9.07180 33.8564i −0.341906 1.27601i
\(705\) 0 0
\(706\) −5.24167 + 19.5622i −0.197273 + 0.736232i
\(707\) −5.46410 1.46410i −0.205499 0.0550632i
\(708\) 0 0
\(709\) 36.5885 9.80385i 1.37411 0.368191i 0.505131 0.863043i \(-0.331444\pi\)
0.868978 + 0.494852i \(0.164778\pi\)
\(710\) 4.28719 0.160895
\(711\) 0 0
\(712\) −4.00000 4.00000i −0.149906 0.149906i
\(713\) 2.19615 + 1.26795i 0.0822466 + 0.0474851i
\(714\) 0 0
\(715\) −4.09103 + 15.2679i −0.152996 + 0.570989i
\(716\) 1.41154 5.26795i 0.0527518 0.196873i
\(717\) 0 0
\(718\) 4.12436 + 15.3923i 0.153920 + 0.574436i
\(719\) −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
\(722\) 2.85641 + 10.6603i 0.106304 + 0.396734i
\(723\) 0 0
\(724\) −20.1962 5.41154i −0.750584 0.201118i
\(725\) −2.49038 + 9.29423i −0.0924904 + 0.345179i
\(726\) 0 0
\(727\) 28.8109 + 16.6340i 1.06854 + 0.616920i 0.927781 0.373124i \(-0.121714\pi\)
0.140755 + 0.990044i \(0.455047\pi\)
\(728\) 26.9282 0.998026
\(729\) 0 0
\(730\) 9.17691 0.339653
\(731\) −47.7487 + 12.7942i −1.76605 + 0.473212i
\(732\) 0 0
\(733\) −11.0263 2.95448i −0.407265 0.109126i 0.0493698 0.998781i \(-0.484279\pi\)
−0.456635 + 0.889654i \(0.650945\pi\)
\(734\) 10.3397 38.5885i 0.381647 1.42433i
\(735\) 0 0
\(736\) 6.92820 + 25.8564i 0.255377 + 0.953080i
\(737\) 29.9282 1.10242
\(738\) 0 0
\(739\) −8.22243 + 8.22243i −0.302467 + 0.302467i −0.841978 0.539511i \(-0.818609\pi\)
0.539511 + 0.841978i \(0.318609\pi\)
\(740\) 6.92820 12.0000i 0.254686 0.441129i
\(741\) 0 0
\(742\) −20.3923 35.3205i −0.748625 1.29666i
\(743\) 24.7583 14.2942i 0.908295 0.524404i 0.0284129 0.999596i \(-0.490955\pi\)
0.879882 + 0.475192i \(0.157621\pi\)
\(744\) 0 0
\(745\) −7.26795 4.19615i −0.266277 0.153735i
\(746\) 40.2487i 1.47361i
\(747\) 0 0
\(748\) 35.5167 35.5167i 1.29862 1.29862i
\(749\) 12.4904 + 46.6147i 0.456389 + 1.70327i
\(750\) 0 0
\(751\) −8.85641 15.3397i −0.323175 0.559755i 0.657966 0.753047i \(-0.271417\pi\)
−0.981141 + 0.193292i \(0.938084\pi\)
\(752\) 15.3205 + 26.5359i 0.558681 + 0.967665i
\(753\) 0 0
\(754\) −3.12436 11.6603i −0.113782 0.424641i
\(755\) −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 \(0.921154\pi\)
\(758\) 6.50962 + 3.75833i 0.236440 + 0.136509i
\(759\) 0 0
\(760\) 9.46410 + 2.53590i 0.343299 + 0.0919867i
\(761\) 45.3731 26.1962i 1.64477 0.949610i 0.665669 0.746247i \(-0.268146\pi\)
0.979104 0.203363i \(-0.0651870\pi\)
\(762\) 0 0
\(763\) −40.0526 + 10.7321i −1.45000 + 0.388526i
\(764\) 48.1051i 1.74038i
\(765\) 0 0
\(766\) 13.4641 + 13.4641i 0.486478 + 0.486478i
\(767\) −13.2224 + 22.9019i −0.477434 + 0.826941i
\(768\) 0 0
\(769\) −14.1244 24.4641i −0.509337 0.882198i −0.999942 0.0108155i \(-0.996557\pi\)
0.490604 0.871383i \(-0.336776\pi\)
\(770\) −4.53590 + 16.9282i −0.163462 + 0.610050i
\(771\) 0 0
\(772\) −37.6410 21.7321i −1.35473 0.782154i
\(773\) −35.5885 35.5885i −1.28003 1.28003i −0.940650 0.339378i \(-0.889784\pi\)
−0.339378 0.940650i \(-0.610216\pi\)
\(774\) 0 0
\(775\) 2.10512i 0.0756181i
\(776\) 8.58846 + 32.0526i 0.308308 + 1.15062i
\(777\) 0 0
\(778\) −25.0526 + 14.4641i −0.898178 + 0.518563i
\(779\) 2.59808 9.69615i 0.0930857 0.347401i
\(780\) 0 0
\(781\) 3.32051 + 12.3923i 0.118817 + 0.443432i
\(782\) −27.1244 + 27.1244i −0.969965 + 0.969965i
\(783\) 0 0
\(784\) 1.85641 0.0663002
\(785\) −2.53590 + 4.39230i −0.0905101 + 0.156768i
\(786\) 0 0