Properties

Label 432.2.y.b.397.1
Level $432$
Weight $2$
Character 432.397
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 397.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 432.397
Dual form 432.2.y.b.37.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-1.00000 - 0.267949i) q^{5} +(2.36603 + 1.36603i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})\) \(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-1.00000 - 0.267949i) q^{5} +(2.36603 + 1.36603i) q^{7} +(2.00000 + 2.00000i) q^{8} +1.46410i q^{10} +(-1.13397 - 4.23205i) q^{11} +(0.901924 - 3.36603i) q^{13} +(1.00000 - 3.73205i) q^{14} +(2.00000 - 3.46410i) q^{16} +5.73205 q^{17} +(-2.36603 - 2.36603i) q^{19} +(2.00000 - 0.535898i) q^{20} +(-5.36603 + 3.09808i) q^{22} +(4.09808 - 2.36603i) q^{23} +(-3.40192 - 1.96410i) q^{25} -4.92820 q^{26} -5.46410 q^{28} +(-2.36603 + 0.633975i) q^{29} +(-0.267949 - 0.464102i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-2.09808 - 7.83013i) q^{34} +(-2.00000 - 2.00000i) q^{35} +(4.73205 - 4.73205i) q^{37} +(-2.36603 + 4.09808i) q^{38} +(-1.46410 - 2.53590i) q^{40} +(2.59808 - 1.50000i) q^{41} +(2.23205 + 8.33013i) q^{43} +(6.19615 + 6.19615i) q^{44} +(-4.73205 - 4.73205i) q^{46} +(-3.83013 + 6.63397i) q^{47} +(0.232051 + 0.401924i) q^{49} +(-1.43782 + 5.36603i) q^{50} +(1.80385 + 6.73205i) q^{52} +(7.46410 - 7.46410i) q^{53} +4.53590i q^{55} +(2.00000 + 7.46410i) q^{56} +(1.73205 + 3.00000i) q^{58} +(-7.33013 - 1.96410i) q^{59} +(11.1962 - 3.00000i) q^{61} +(-0.535898 + 0.535898i) q^{62} +8.00000i q^{64} +(-1.80385 + 3.12436i) q^{65} +(-1.76795 + 6.59808i) q^{67} +(-9.92820 + 5.73205i) q^{68} +(-2.00000 + 3.46410i) q^{70} -2.92820i q^{71} -6.26795i q^{73} +(-8.19615 - 4.73205i) q^{74} +(6.46410 + 1.73205i) q^{76} +(3.09808 - 11.5622i) q^{77} +(-6.00000 + 10.3923i) q^{79} +(-2.92820 + 2.92820i) q^{80} +(-3.00000 - 3.00000i) q^{82} +(1.36603 - 0.366025i) q^{83} +(-5.73205 - 1.53590i) q^{85} +(10.5622 - 6.09808i) q^{86} +(6.19615 - 10.7321i) q^{88} +2.00000i q^{89} +(6.73205 - 6.73205i) q^{91} +(-4.73205 + 8.19615i) q^{92} +(10.4641 + 2.80385i) q^{94} +(1.73205 + 3.00000i) q^{95} +(-5.86603 + 10.1603i) q^{97} +(0.464102 - 0.464102i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 4q^{5} + 6q^{7} + 8q^{8} + O(q^{10}) \) \( 4q + 2q^{2} - 4q^{5} + 6q^{7} + 8q^{8} - 8q^{11} + 14q^{13} + 4q^{14} + 8q^{16} + 16q^{17} - 6q^{19} + 8q^{20} - 18q^{22} + 6q^{23} - 24q^{25} + 8q^{26} - 8q^{28} - 6q^{29} - 8q^{31} - 8q^{32} + 2q^{34} - 8q^{35} + 12q^{37} - 6q^{38} + 8q^{40} + 2q^{43} + 4q^{44} - 12q^{46} + 2q^{47} - 6q^{49} - 30q^{50} + 28q^{52} + 16q^{53} + 8q^{56} - 12q^{59} + 24q^{61} - 16q^{62} - 28q^{65} - 14q^{67} - 12q^{68} - 8q^{70} - 12q^{74} + 12q^{76} + 2q^{77} - 24q^{79} + 16q^{80} - 12q^{82} + 2q^{83} - 16q^{85} + 18q^{86} + 4q^{88} + 20q^{91} - 12q^{92} + 28q^{94} - 20q^{97} - 12q^{98} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.366025 1.36603i −0.258819 0.965926i
\(3\) 0 0
\(4\) −1.73205 + 1.00000i −0.866025 + 0.500000i
\(5\) −1.00000 0.267949i −0.447214 0.119831i 0.0281817 0.999603i \(-0.491028\pi\)
−0.475395 + 0.879772i \(0.657695\pi\)
\(6\) 0 0
\(7\) 2.36603 + 1.36603i 0.894274 + 0.516309i 0.875338 0.483512i \(-0.160639\pi\)
0.0189356 + 0.999821i \(0.493972\pi\)
\(8\) 2.00000 + 2.00000i 0.707107 + 0.707107i
\(9\) 0 0
\(10\) 1.46410i 0.462990i
\(11\) −1.13397 4.23205i −0.341906 1.27601i −0.896185 0.443680i \(-0.853673\pi\)
0.554279 0.832331i \(-0.312994\pi\)
\(12\) 0 0
\(13\) 0.901924 3.36603i 0.250149 0.933567i −0.720577 0.693375i \(-0.756123\pi\)
0.970725 0.240192i \(-0.0772105\pi\)
\(14\) 1.00000 3.73205i 0.267261 0.997433i
\(15\) 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 0.381546 0.924350i \(-0.375392\pi\)
−0.924350 + 0.381546i \(0.875392\pi\)
\(20\) 2.00000 0.535898i 0.447214 0.119831i
\(21\) 0 0
\(22\) −5.36603 + 3.09808i −1.14404 + 0.660512i
\(23\) 4.09808 2.36603i 0.854508 0.493350i −0.00766135 0.999971i \(-0.502439\pi\)
0.862169 + 0.506620i \(0.169105\pi\)
\(24\) 0 0
\(25\) −3.40192 1.96410i −0.680385 0.392820i
\(26\) −4.92820 −0.966500
\(27\) 0 0
\(28\) −5.46410 −1.03262
\(29\) −2.36603 + 0.633975i −0.439360 + 0.117726i −0.471717 0.881750i \(-0.656365\pi\)
0.0323566 + 0.999476i \(0.489699\pi\)
\(30\) 0 0
\(31\) −0.267949 0.464102i −0.0481251 0.0833551i 0.840959 0.541098i \(-0.181991\pi\)
−0.889085 + 0.457743i \(0.848658\pi\)
\(32\) −5.46410 1.46410i −0.965926 0.258819i
\(33\) 0 0
\(34\) −2.09808 7.83013i −0.359817 1.34286i
\(35\) −2.00000 2.00000i −0.338062 0.338062i
\(36\) 0 0
\(37\) 4.73205 4.73205i 0.777944 0.777944i −0.201537 0.979481i \(-0.564594\pi\)
0.979481 + 0.201537i \(0.0645935\pi\)
\(38\) −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 −0.283211 0.959058i \(-0.591400\pi\)
0.688963 + 0.724797i \(0.258066\pi\)
\(42\) 0 0
\(43\) 2.23205 + 8.33013i 0.340385 + 1.27033i 0.897912 + 0.440174i \(0.145083\pi\)
−0.557528 + 0.830158i \(0.688250\pi\)
\(44\) 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
\(50\) −1.43782 + 5.36603i −0.203339 + 0.758871i
\(51\) 0 0
\(52\) 1.80385 + 6.73205i 0.250149 + 0.933567i
\(53\) 7.46410 7.46410i 1.02527 1.02527i 0.0256010 0.999672i \(-0.491850\pi\)
0.999672 0.0256010i \(-0.00814993\pi\)
\(54\) 0 0
\(55\) 4.53590i 0.611620i
\(56\) 2.00000 + 7.46410i 0.267261 + 0.997433i
\(57\) 0 0
\(58\) 1.73205 + 3.00000i 0.227429 + 0.393919i
\(59\) −7.33013 1.96410i −0.954301 0.255704i −0.252115 0.967697i \(-0.581126\pi\)
−0.702186 + 0.711993i \(0.747793\pi\)
\(60\) 0 0
\(61\) 11.1962 3.00000i 1.43352 0.384111i 0.543261 0.839564i \(-0.317189\pi\)
0.890260 + 0.455453i \(0.150523\pi\)
\(62\) −0.535898 + 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
\(67\) −1.76795 + 6.59808i −0.215989 + 0.806083i 0.769827 + 0.638253i \(0.220343\pi\)
−0.985816 + 0.167830i \(0.946324\pi\)
\(68\) −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 \(-0.944409\pi\)
0.984789 0.173757i \(-0.0555907\pi\)
\(72\) 0 0
\(73\) 6.26795i 0.733608i −0.930298 0.366804i \(-0.880452\pi\)
0.930298 0.366804i \(-0.119548\pi\)
\(74\) −8.19615 4.73205i −0.952783 0.550090i
\(75\) 0 0
\(76\) 6.46410 + 1.73205i 0.741483 + 0.198680i
\(77\) 3.09808 11.5622i 0.353059 1.31763i
\(78\) 0 0
\(79\) −6.00000 + 10.3923i −0.675053 + 1.16923i 0.301401 + 0.953498i \(0.402546\pi\)
−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
\(83\) 1.36603 0.366025i 0.149941 0.0401765i −0.183068 0.983100i \(-0.558603\pi\)
0.333009 + 0.942924i \(0.391936\pi\)
\(84\) 0 0
\(85\) −5.73205 1.53590i −0.621728 0.166592i
\(86\) 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 \(0.0338043\pi\)
−0.994366 + 0.106000i \(0.966196\pi\)
\(90\) 0 0
\(91\) 6.73205 6.73205i 0.705711 0.705711i
\(92\) −4.73205 + 8.19615i −0.493350 + 0.854508i
\(93\) 0 0
\(94\) 10.4641 + 2.80385i 1.07929 + 0.289195i
\(95\) 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
\(101\) −0.535898 2.00000i −0.0533239 0.199007i 0.934125 0.356946i \(-0.116182\pi\)
−0.987449 + 0.157938i \(0.949515\pi\)
\(102\) 0 0
\(103\) 13.0981 7.56218i 1.29059 0.745124i 0.311833 0.950137i \(-0.399057\pi\)
0.978759 + 0.205014i \(0.0657238\pi\)
\(104\) 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 −0.235654 + 0.971837i \(0.575723\pi\)
−0.971837 + 0.235654i \(0.924277\pi\)
\(108\) 0 0
\(109\) 10.7321 + 10.7321i 1.02794 + 1.02794i 0.999598 + 0.0283459i \(0.00902398\pi\)
0.0283459 + 0.999598i \(0.490976\pi\)
\(110\) 6.19615 1.66025i 0.590780 0.158299i
\(111\) 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
\(115\) −4.73205 + 1.26795i −0.441266 + 0.118237i
\(116\) 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 \(0.440391\pi\)
\(128\) 10.9282 2.92820i 0.965926 0.258819i
\(129\) 0 0
\(130\) 4.92820 + 1.32051i 0.432232 + 0.115816i
\(131\) −2.09808 + 7.83013i −0.183310 + 0.684121i 0.811676 + 0.584108i \(0.198555\pi\)
−0.994986 + 0.100014i \(0.968111\pi\)
\(132\) 0 0
\(133\) −2.36603 8.83013i −0.205160 0.765669i
\(134\) 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 0.103857 0.994592i \(-0.466882\pi\)
−0.809414 + 0.587239i \(0.800215\pi\)
\(138\) 0 0
\(139\) −11.4282 3.06218i −0.969328 0.259731i −0.260784 0.965397i \(-0.583981\pi\)
−0.708544 + 0.705667i \(0.750648\pi\)
\(140\) 5.46410 + 1.46410i 0.461801 + 0.123739i
\(141\) 0 0
\(142\) −4.00000 + 1.07180i −0.335673 + 0.0899432i
\(143\) −15.2679 −1.27677
\(144\) 0 0
\(145\) 2.53590 0.210595
\(146\) −8.56218 + 2.29423i −0.708611 + 0.189872i
\(147\) 0 0
\(148\) −3.46410 + 12.9282i −0.284747 + 1.06269i
\(149\) −7.83013 2.09808i −0.641469 0.171881i −0.0766003 0.997062i \(-0.524407\pi\)
−0.564869 + 0.825181i \(0.691073\pi\)
\(150\) 0 0
\(151\) 0.633975 + 0.366025i 0.0515921 + 0.0297867i 0.525574 0.850748i \(-0.323851\pi\)
−0.473982 + 0.880534i \(0.657184\pi\)
\(152\) 9.46410i 0.767640i
\(153\) 0 0
\(154\) −16.9282 −1.36411
\(155\) 0.143594 + 0.535898i 0.0115337 + 0.0430444i
\(156\) 0 0
\(157\) 1.26795 4.73205i 0.101193 0.377659i −0.896692 0.442655i \(-0.854037\pi\)
0.997886 + 0.0649959i \(0.0207034\pi\)
\(158\) 16.3923 + 4.39230i 1.30410 + 0.349433i
\(159\) 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 0.377661 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
\(167\) −6.46410 + 3.73205i −0.500207 + 0.288795i −0.728799 0.684728i \(-0.759921\pi\)
0.228592 + 0.973522i \(0.426588\pi\)
\(168\) 0 0
\(169\) 0.741670 + 0.428203i 0.0570515 + 0.0329387i
\(170\) 8.39230i 0.643660i
\(171\) 0 0
\(172\) −12.1962 12.1962i −0.929948 0.929948i
\(173\) −1.63397 + 0.437822i −0.124229 + 0.0332870i −0.320398 0.947283i \(-0.603817\pi\)
0.196169 + 0.980570i \(0.437150\pi\)
\(174\) 0 0
\(175\) −5.36603 9.29423i −0.405633 0.702578i
\(176\) −16.9282 4.53590i −1.27601 0.341906i
\(177\) 0 0
\(178\) 2.73205 0.732051i 0.204776 0.0548695i
\(179\) 1.92820 + 1.92820i 0.144121 + 0.144121i 0.775486 0.631365i \(-0.217505\pi\)
−0.631365 + 0.775486i \(0.717505\pi\)
\(180\) 0 0
\(181\) −7.39230 + 7.39230i −0.549466 + 0.549466i −0.926286 0.376821i \(-0.877017\pi\)
0.376821 + 0.926286i \(0.377017\pi\)
\(182\) −11.6603 6.73205i −0.864316 0.499013i
\(183\) 0 0
\(184\) 12.9282 + 3.46410i 0.953080 + 0.255377i
\(185\) −6.00000 + 3.46410i −0.441129 + 0.254686i
\(186\) 0 0
\(187\) −6.50000 24.2583i −0.475327 1.77394i
\(188\) 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 \(-0.452545\pi\)
\(194\) 16.0263 + 4.29423i 1.15062 + 0.308308i
\(195\) 0 0
\(196\) −0.803848 0.464102i −0.0574177 0.0331501i
\(197\) −13.6603 + 13.6603i −0.973253 + 0.973253i −0.999651 0.0263987i \(-0.991596\pi\)
0.0263987 + 0.999651i \(0.491596\pi\)
\(198\) 0 0
\(199\) 25.1244i 1.78102i 0.454965 + 0.890509i \(0.349652\pi\)
−0.454965 + 0.890509i \(0.650348\pi\)
\(200\) −2.87564 10.7321i −0.203339 0.758871i
\(201\) 0 0
\(202\) −2.53590 + 1.46410i −0.178425 + 0.103014i
\(203\) −6.46410 1.73205i −0.453691 0.121566i
\(204\) 0 0
\(205\) −3.00000 + 0.803848i −0.209529 + 0.0561432i
\(206\) −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
\(211\) −1.09808 + 4.09808i −0.0755947 + 0.282123i −0.993367 0.114983i \(-0.963319\pi\)
0.917773 + 0.397106i \(0.129985\pi\)
\(212\) −5.46410 + 20.3923i −0.375276 + 1.40055i
\(213\) 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
\(221\) 5.16987 19.2942i 0.347763 1.29787i
\(222\) 0 0
\(223\) −8.02628 + 13.9019i −0.537479 + 0.930942i 0.461559 + 0.887109i \(0.347290\pi\)
−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
\(227\) −2.13397 + 0.571797i −0.141637 + 0.0379515i −0.328941 0.944351i \(-0.606692\pi\)
0.187304 + 0.982302i \(0.440025\pi\)
\(228\) 0 0
\(229\) 6.83013 + 1.83013i 0.451347 + 0.120938i 0.477330 0.878724i \(-0.341605\pi\)
−0.0259823 + 0.999662i \(0.508271\pi\)
\(230\) 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 \(0.0333861\pi\)
−0.994505 + 0.104693i \(0.966614\pi\)
\(234\) 0 0
\(235\) 5.60770 5.60770i 0.365806 0.365806i
\(236\) 14.6603 3.92820i 0.954301 0.255704i
\(237\) 0 0
\(238\) 5.73205 21.3923i 0.371554 1.38666i
\(239\) 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
\(245\) −0.124356 0.464102i −0.00794479 0.0296504i
\(246\) 0 0
\(247\) −10.0981 + 5.83013i −0.642525 + 0.370962i
\(248\) 0.392305 1.46410i 0.0249114 0.0929705i
\(249\) 0 0
\(250\) 6.53590 11.3205i 0.413367 0.715972i
\(251\) 5.83013 5.83013i 0.367994 0.367994i −0.498751 0.866745i \(-0.666208\pi\)
0.866745 + 0.498751i \(0.166208\pi\)
\(252\) 0 0
\(253\) −14.6603 14.6603i −0.921682 0.921682i
\(254\) −1.53590 5.73205i −0.0963708 0.359661i
\(255\) 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
\(259\) 17.6603 4.73205i 1.09735 0.294035i
\(260\) 7.21539i 0.447480i
\(261\) 0 0
\(262\) 11.4641 0.708255
\(263\) 2.49038 + 1.43782i 0.153563 + 0.0886599i 0.574813 0.818285i \(-0.305075\pi\)
−0.421249 + 0.906945i \(0.638408\pi\)
\(264\) 0 0
\(265\) −9.46410 + 5.46410i −0.581375 + 0.335657i
\(266\) −11.1962 + 6.46410i −0.686480 + 0.396339i
\(267\) 0 0
\(268\) −3.53590 13.1962i −0.215989 0.806083i
\(269\) −1.26795 1.26795i −0.0773082 0.0773082i 0.667395 0.744704i \(-0.267409\pi\)
−0.744704 + 0.667395i \(0.767409\pi\)
\(270\) 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
\(274\) −3.49038 + 13.0263i −0.210862 + 0.786946i
\(275\) −4.45448 + 16.6244i −0.268615 + 1.00249i
\(276\) 0 0
\(277\) −6.75833 25.2224i −0.406069 1.51547i −0.802076 0.597222i \(-0.796271\pi\)
0.396007 0.918247i \(-0.370395\pi\)
\(278\) 16.7321i 1.00352i
\(279\) 0 0
\(280\) 8.00000i 0.478091i
\(281\) 8.66025 + 5.00000i 0.516627 + 0.298275i 0.735554 0.677466i \(-0.236922\pi\)
−0.218926 + 0.975741i \(0.570255\pi\)
\(282\) 0 0
\(283\) −19.5622 5.24167i −1.16285 0.311585i −0.374747 0.927127i \(-0.622270\pi\)
−0.788104 + 0.615542i \(0.788937\pi\)
\(284\) 2.92820 + 5.07180i 0.173757 + 0.300956i
\(285\) 0 0
\(286\) 5.58846 + 20.8564i 0.330452 + 1.23327i
\(287\) 8.19615 0.483804
\(288\) 0 0
\(289\) 15.8564 0.932730
\(290\) −0.928203 3.46410i −0.0545060 0.203419i
\(291\) 0 0
\(292\) 6.26795 + 10.8564i 0.366804 + 0.635323i
\(293\) 5.36603 + 1.43782i 0.313487 + 0.0839985i 0.412132 0.911124i \(-0.364784\pi\)
−0.0986454 + 0.995123i \(0.531451\pi\)
\(294\) 0 0
\(295\) 6.80385 + 3.92820i 0.396135 + 0.228709i
\(296\) 18.9282 1.10018
\(297\) 0 0
\(298\) 11.4641i 0.664098i
\(299\) −4.26795 15.9282i −0.246822 0.921152i
\(300\) 0 0
\(301\) −6.09808 + 22.7583i −0.351487 + 1.31177i
\(302\) 0.267949 1.00000i 0.0154187 0.0575435i
\(303\) 0 0
\(304\) −12.9282 + 3.46410i −0.741483 + 0.198680i
\(305\) −12.0000 −0.687118
\(306\) 0 0
\(307\) 3.02628 + 3.02628i 0.172719 + 0.172719i 0.788173 0.615454i \(-0.211027\pi\)
−0.615454 + 0.788173i \(0.711027\pi\)
\(308\) 6.19615 + 23.1244i 0.353059 + 1.31763i
\(309\) 0 0
\(310\) 0.679492 0.392305i 0.0385925 0.0222814i
\(311\) 19.0981 11.0263i 1.08295 0.625243i 0.151261 0.988494i \(-0.451667\pi\)
0.931691 + 0.363251i \(0.118333\pi\)
\(312\) 0 0
\(313\) 18.6506 + 10.7679i 1.05420 + 0.608640i 0.923821 0.382824i \(-0.125049\pi\)
0.130375 + 0.991465i \(0.458382\pi\)
\(314\) −6.92820 −0.390981
\(315\) 0 0
\(316\) 24.0000i 1.35011i
\(317\) 20.5622 5.50962i 1.15489 0.309451i 0.369965 0.929046i \(-0.379370\pi\)
0.784922 + 0.619595i \(0.212703\pi\)
\(318\) 0 0
\(319\) 5.36603 + 9.29423i 0.300440 + 0.520377i
\(320\) 2.14359 8.00000i 0.119831 0.447214i
\(321\) 0 0
\(322\) −4.73205 17.6603i −0.263707 0.984167i
\(323\) −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
\(328\) 8.19615 + 2.19615i 0.452557 + 0.121262i
\(329\) −18.1244 + 10.4641i −0.999228 + 0.576905i
\(330\) 0 0
\(331\) 0.0262794 + 0.0980762i 0.00144445 + 0.00539076i 0.966644 0.256123i \(-0.0824451\pi\)
−0.965200 + 0.261513i \(0.915778\pi\)
\(332\) −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 \(0.672373\pi\)
\(338\) 0.313467 1.16987i 0.0170503 0.0636327i
\(339\) 0 0
\(340\) 11.4641 3.07180i 0.621728 0.166592i
\(341\) −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
\(347\) 17.6244 + 4.72243i 0.946125 + 0.253513i 0.698717 0.715398i \(-0.253755\pi\)
0.247408 + 0.968911i \(0.420421\pi\)
\(348\) 0 0
\(349\) 15.9282 4.26795i 0.852617 0.228458i 0.194061 0.980989i \(-0.437834\pi\)
0.658556 + 0.752531i \(0.271167\pi\)
\(350\) −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
\(355\) −0.784610 + 2.92820i −0.0416428 + 0.155413i
\(356\) −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 \(-0.903897\pi\)
0.954769 0.297350i \(-0.0961028\pi\)
\(360\) 0 0
\(361\) 7.80385i 0.410729i
\(362\) 12.8038 + 7.39230i 0.672955 + 0.388531i
\(363\) 0 0
\(364\) −4.92820 + 18.3923i −0.258308 + 0.964019i
\(365\) −1.67949 + 6.26795i −0.0879086 + 0.328079i
\(366\) 0 0
\(367\) 14.1244 24.4641i 0.737285 1.27702i −0.216428 0.976299i \(-0.569441\pi\)
0.953713 0.300717i \(-0.0972260\pi\)
\(368\) 18.9282i 0.986701i
\(369\) 0 0
\(370\) 6.92820 + 6.92820i 0.360180 + 0.360180i
\(371\) 27.8564 7.46410i 1.44623 0.387517i
\(372\) 0 0
\(373\) 27.4904 + 7.36603i 1.42340 + 0.381398i 0.886688 0.462368i \(-0.153000\pi\)
0.536710 + 0.843767i \(0.319667\pi\)
\(374\) −30.7583 + 17.7583i −1.59048 + 0.918261i
\(375\) 0 0
\(376\) −20.9282 + 5.60770i −1.07929 + 0.289195i
\(377\) 8.53590i 0.439621i
\(378\) 0 0
\(379\) 3.75833 3.75833i 0.193052 0.193052i −0.603961 0.797014i \(-0.706412\pi\)
0.797014 + 0.603961i \(0.206412\pi\)
\(380\) −6.00000 3.46410i −0.307794 0.177705i
\(381\) 0 0
\(382\) −32.8564 8.80385i −1.68108 0.450444i
\(383\) 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
\(389\) 5.29423 + 19.7583i 0.268428 + 1.00179i 0.960119 + 0.279593i \(0.0901996\pi\)
−0.691691 + 0.722194i \(0.743134\pi\)
\(390\) 0 0
\(391\) 23.4904 13.5622i 1.18796 0.685869i
\(392\) −0.339746 + 1.26795i −0.0171598 + 0.0640411i
\(393\) 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 0.435192 0.900337i \(-0.356680\pi\)
−0.900337 + 0.435192i \(0.856680\pi\)
\(398\) 34.3205 9.19615i 1.72033 0.460961i
\(399\) 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
\(403\) −1.80385 + 0.483340i −0.0898560 + 0.0240769i
\(404\) 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 0.385981 0.922507i \(-0.373863\pi\)
0.991905 + 0.126984i \(0.0405295\pi\)
\(410\) 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
\(418\) 20.0263 + 5.36603i 0.979517 + 0.262461i
\(419\) −1.77757 + 6.63397i −0.0868399 + 0.324091i −0.995656 0.0931055i \(-0.970321\pi\)
0.908816 + 0.417196i \(0.136987\pi\)
\(420\) 0 0
\(421\) 8.19615 + 30.5885i 0.399456 + 1.49079i 0.814056 + 0.580786i \(0.197255\pi\)
−0.414600 + 0.910004i \(0.636078\pi\)
\(422\) 6.00000 0.292075
\(423\) 0 0
\(424\) 29.8564 1.44996
\(425\) −19.5000 11.2583i −0.945889 0.546109i
\(426\) 0 0
\(427\) 30.5885 + 8.19615i 1.48028 + 0.396640i
\(428\) 9.14359 34.1244i 0.441972 1.64946i
\(429\) 0 0
\(430\) −12.1962 + 3.26795i −0.588151 + 0.157595i
\(431\) 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 \(0.543981\pi\)
\(434\) −2.00000 + 0.535898i −0.0960031 + 0.0257239i
\(435\) 0 0
\(436\) −29.3205 7.85641i −1.40420 0.376254i
\(437\) −15.2942 4.09808i −0.731622 0.196038i
\(438\) 0 0
\(439\) −22.8564 13.1962i −1.09088 0.629818i −0.157067 0.987588i \(-0.550204\pi\)
−0.933810 + 0.357770i \(0.883537\pi\)
\(440\) −9.07180 + 9.07180i −0.432481 + 0.432481i
\(441\) 0 0
\(442\) −28.2487 −1.34365
\(443\) 4.62436 + 17.2583i 0.219710 + 0.819968i 0.984455 + 0.175636i \(0.0561980\pi\)
−0.764745 + 0.644332i \(0.777135\pi\)
\(444\) 0 0
\(445\) 0.535898 2.00000i 0.0254040 0.0948091i
\(446\) 21.9282 + 5.87564i 1.03833 + 0.278220i
\(447\) 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 0.551889 0.833917i \(-0.313907\pi\)
−0.446249 + 0.894909i \(0.647240\pi\)
\(458\) 10.0000i 0.467269i
\(459\) 0 0
\(460\) 6.92820 6.92820i 0.323029 0.323029i
\(461\) −35.6865 + 9.56218i −1.66209 + 0.445355i −0.962961 0.269642i \(-0.913094\pi\)
−0.699127 + 0.714997i \(0.746428\pi\)
\(462\) 0 0
\(463\) 1.19615 + 2.07180i 0.0555899 + 0.0962846i 0.892481 0.451085i \(-0.148963\pi\)
−0.836891 + 0.547369i \(0.815629\pi\)
\(464\) −2.53590 + 9.46410i −0.117726 + 0.439360i
\(465\) 0 0
\(466\) 4.36603 1.16987i 0.202252 0.0541933i
\(467\) −2.63397 2.63397i −0.121886 0.121886i 0.643533 0.765419i \(-0.277468\pi\)
−0.765419 + 0.643533i \(0.777468\pi\)
\(468\) 0 0
\(469\) −13.1962 + 13.1962i −0.609342 + 0.609342i
\(470\) −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
\(475\) 3.40192 + 12.6962i 0.156091 + 0.582539i
\(476\) −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
\(482\) 31.6865 + 8.49038i 1.44328 + 0.386726i
\(483\) 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 \(0.0419789\pi\)
−0.991316 + 0.131499i \(0.958021\pi\)
\(488\) 28.3923 + 16.3923i 1.28526 + 0.742045i
\(489\) 0 0
\(490\) −0.588457 + 0.339746i −0.0265838 + 0.0153482i
\(491\) 13.8923 + 3.72243i 0.626951 + 0.167991i 0.558286 0.829649i \(-0.311459\pi\)
0.0686652 + 0.997640i \(0.478126\pi\)
\(492\) 0 0
\(493\) −13.5622 + 3.63397i −0.610810 + 0.163666i
\(494\) 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
\(499\) −2.33013 + 8.69615i −0.104311 + 0.389293i −0.998266 0.0588630i \(-0.981252\pi\)
0.893955 + 0.448156i \(0.147919\pi\)
\(500\) −17.8564 4.78461i −0.798563 0.213974i
\(501\) 0 0
\(502\) −10.0981 5.83013i −0.450699 0.260211i
\(503\) 27.7128i 1.23565i 0.786314 + 0.617827i \(0.211987\pi\)
−0.786314 + 0.617827i \(0.788013\pi\)
\(504\) 0 0
\(505\) 2.14359i 0.0953887i
\(506\) −14.6603 + 25.3923i −0.651728 + 1.12883i
\(507\) 0 0
\(508\) −7.26795 + 4.19615i −0.322463 + 0.186174i
\(509\) −3.07180 + 11.4641i −0.136155 + 0.508137i 0.863835 + 0.503774i \(0.168056\pi\)
−0.999990 + 0.00436335i \(0.998611\pi\)
\(510\) 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
\(515\) −15.1244 + 4.05256i −0.666459 + 0.178577i
\(516\) 0 0
\(517\) 32.4186 + 8.68653i 1.42577 + 0.382033i
\(518\) −12.9282 22.3923i −0.568033 0.983861i
\(519\) 0 0
\(520\) −9.85641 + 2.64102i −0.432232 + 0.115816i
\(521\) 13.0000i 0.569540i −0.958596 0.284770i \(-0.908083\pi\)
0.958596 0.284770i \(-0.0919173\pi\)
\(522\) 0 0
\(523\) −7.53590 + 7.53590i −0.329522 + 0.329522i −0.852405 0.522883i \(-0.824857\pi\)
0.522883 + 0.852405i \(0.324857\pi\)
\(524\) −4.19615 15.6603i −0.183310 0.684121i
\(525\) 0 0
\(526\) 1.05256 3.92820i 0.0458937 0.171278i
\(527\) −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
\(533\) −2.70577 10.0981i −0.117200 0.437396i
\(534\) 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 0.752739 0.658319i \(-0.228732\pi\)
−0.658319 + 0.752739i \(0.728732\pi\)
\(542\) 0.143594 + 0.535898i 0.00616787 + 0.0230188i
\(543\) 0 0
\(544\) −31.3205 8.39230i −1.34286 0.359817i
\(545\) −7.85641 13.6077i −0.336531 0.582890i
\(546\) 0 0
\(547\) 32.6244 8.74167i 1.39492 0.373767i 0.518400 0.855138i \(-0.326528\pi\)
0.876517 + 0.481371i \(0.159861\pi\)
\(548\) 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
\(556\) 22.8564 6.12436i 0.969328 0.259731i
\(557\) 14.8038 + 14.8038i 0.627259 + 0.627259i 0.947378 0.320118i \(-0.103723\pi\)
−0.320118 + 0.947378i \(0.603723\pi\)
\(558\) 0 0
\(559\) 30.0526 1.27109
\(560\) −10.9282 + 2.92820i −0.461801 + 0.123739i
\(561\) 0 0
\(562\) 3.66025 13.6603i 0.154398 0.576223i
\(563\) 7.23205 26.9904i 0.304795 1.13751i −0.628327 0.777949i \(-0.716260\pi\)
0.933122 0.359560i \(-0.117073\pi\)
\(564\) 0 0
\(565\) −3.71281 13.8564i −0.156199 0.582943i
\(566\) 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 0.833391 0.552684i \(-0.186396\pi\)
−0.0619424 + 0.998080i \(0.519730\pi\)
\(570\) 0 0
\(571\) −3.33013 0.892305i −0.139361 0.0373418i 0.188464 0.982080i \(-0.439649\pi\)
−0.327825 + 0.944738i \(0.606316\pi\)
\(572\) 26.4449 15.2679i 1.10572 0.638385i
\(573\) 0 0
\(574\) −3.00000 11.1962i −0.125218 0.467318i
\(575\) −18.5885 −0.775192
\(576\) 0 0
\(577\) −5.78461 −0.240816 −0.120408 0.992724i \(-0.538420\pi\)
−0.120408 + 0.992724i \(0.538420\pi\)
\(578\) −5.80385 21.6603i −0.241408 0.900948i
\(579\) 0 0
\(580\) −4.39230 + 2.53590i −0.182381 + 0.105297i
\(581\) 3.73205 + 1.00000i 0.154832 + 0.0414870i
\(582\) 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
\(587\) −7.23205 26.9904i −0.298499 1.11401i −0.938399 0.345554i \(-0.887691\pi\)
0.639900 0.768458i \(-0.278976\pi\)
\(588\) 0 0
\(589\) −0.464102 + 1.73205i −0.0191230 + 0.0713679i
\(590\) 2.87564 10.7321i 0.118388 0.441832i
\(591\) 0 0
\(592\) −6.92820 25.8564i −0.284747 1.06269i
\(593\) −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
\(596\) 15.6603 4.19615i 0.641469 0.171881i
\(597\) 0 0
\(598\) −20.1962 + 11.6603i −0.825882 + 0.476823i
\(599\) −11.3205 + 6.53590i −0.462543 + 0.267050i −0.713113 0.701049i \(-0.752715\pi\)
0.250570 + 0.968099i \(0.419382\pi\)
\(600\) 0 0
\(601\) −20.5526 11.8660i −0.838356 0.484025i 0.0183488 0.999832i \(-0.494159\pi\)
−0.856705 + 0.515806i \(0.827492\pi\)
\(602\) 33.3205 1.35804
\(603\) 0 0
\(604\) −1.46410 −0.0595734
\(605\) 8.19615 2.19615i 0.333221 0.0892863i
\(606\) 0 0
\(607\) −8.58846 14.8756i −0.348595 0.603784i 0.637405 0.770529i \(-0.280008\pi\)
−0.986000 + 0.166745i \(0.946674\pi\)
\(608\) 9.46410 + 16.3923i 0.383820 + 0.664796i
\(609\) 0 0
\(610\) 4.39230 + 16.3923i 0.177839 + 0.663705i
\(611\) 18.8756 + 18.8756i 0.763627 + 0.763627i
\(612\) 0 0
\(613\) −15.6603 + 15.6603i −0.632512 + 0.632512i −0.948697 0.316186i \(-0.897598\pi\)
0.316186 + 0.948697i \(0.397598\pi\)
\(614\) 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 0.416975 0.908918i \(-0.363090\pi\)
0.995633 + 0.0933485i \(0.0297571\pi\)
\(618\) 0 0
\(619\) 4.17949 + 15.5981i 0.167988 + 0.626940i 0.997640 + 0.0686590i \(0.0218721\pi\)
−0.829652 + 0.558281i \(0.811461\pi\)
\(620\) −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
\(626\) 7.88269 29.4186i 0.315055 1.17580i
\(627\) 0 0
\(628\) 2.53590 + 9.46410i 0.101193 + 0.377659i
\(629\) 27.1244 27.1244i 1.08152 1.08152i
\(630\) 0 0
\(631\) 17.6077i 0.700951i 0.936572 + 0.350476i \(0.113980\pi\)
−0.936572 + 0.350476i \(0.886020\pi\)
\(632\) −32.7846 + 8.78461i −1.30410 + 0.349433i
\(633\) 0 0
\(634\) −15.0526 26.0718i −0.597813 1.03544i
\(635\) −4.19615 1.12436i −0.166519 0.0446187i
\(636\) 0 0
\(637\) 1.56218 0.418584i 0.0618957 0.0165849i
\(638\) 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
\(643\) −2.34936 + 8.76795i −0.0926499 + 0.345774i −0.996653 0.0817525i \(-0.973948\pi\)
0.904003 + 0.427527i \(0.140615\pi\)
\(644\) −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 \(-0.893321\pi\)
0.944364 0.328902i \(-0.106679\pi\)
\(648\) 0 0
\(649\) 33.2487i 1.30513i
\(650\) 16.7654 + 9.67949i 0.657592 + 0.379661i
\(651\) 0 0
\(652\) 19.1244 + 5.12436i 0.748968 + 0.200685i
\(653\) −7.36603 + 27.4904i −0.288255 + 1.07578i 0.658173 + 0.752867i \(0.271329\pi\)
−0.946428 + 0.322915i \(0.895337\pi\)
\(654\) 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
\(659\) 15.0263 4.02628i 0.585341 0.156842i 0.0460178 0.998941i \(-0.485347\pi\)
0.539323 + 0.842099i \(0.318680\pi\)
\(660\) 0 0
\(661\) −8.19615 2.19615i −0.318793 0.0854204i 0.0958740 0.995393i \(-0.469435\pi\)
−0.414667 + 0.909973i \(0.636102\pi\)
\(662\) 0.124356 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
\(670\) −9.66025 2.58846i −0.373208 0.100001i
\(671\) −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
\(677\) −1.26795 4.73205i −0.0487312 0.181867i 0.937270 0.348603i \(-0.113344\pi\)
−0.986002 + 0.166736i \(0.946677\pi\)
\(678\) 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 −0.202703 0.979240i \(-0.564973\pi\)
0.979240 + 0.202703i \(0.0649726\pi\)
\(684\) 0 0
\(685\) 6.98076 + 6.98076i 0.266721 + 0.266721i
\(686\) −24.3923 + 6.53590i −0.931303 + 0.249542i
\(687\) 0 0
\(688\) 33.3205 + 8.92820i 1.27033 + 0.340385i
\(689\) −18.3923 31.8564i −0.700691 1.21363i
\(690\) 0 0
\(691\) 9.29423 2.49038i 0.353569 0.0947386i −0.0776628 0.996980i \(-0.524746\pi\)
0.431232 + 0.902241i \(0.358079\pi\)
\(692\) 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 0.821608 0.570053i \(-0.193077\pi\)
−0.570053 + 0.821608i \(0.693077\pi\)
\(702\) 0 0
\(703\) −22.3923 −0.844542
\(704\) 33.8564 9.07180i 1.27601 0.341906i
\(705\) 0 0
\(706\) 19.5622 + 5.24167i 0.736232 + 0.197273i
\(707\) 1.46410 5.46410i 0.0550632 0.205499i
\(708\) 0 0
\(709\) −9.80385 36.5885i −0.368191 1.37411i −0.863043 0.505131i \(-0.831444\pi\)
0.494852 0.868978i \(-0.335222\pi\)
\(710\) 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
\(715\) 15.2679 + 4.09103i 0.570989 + 0.152996i
\(716\) −5.26795 1.41154i −0.196873 0.0527518i
\(717\) 0 0
\(718\) −15.3923 + 4.12436i −0.574436 + 0.153920i
\(719\) −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
\(722\) −10.6603 + 2.85641i −0.396734 + 0.106304i
\(723\) 0 0
\(724\) 5.41154 20.1962i 0.201118 0.750584i
\(725\) 9.29423 + 2.49038i 0.345179 + 0.0924904i
\(726\) 0 0
\(727\) −28.8109 16.6340i −1.06854 0.616920i −0.140755 0.990044i \(-0.544953\pi\)
−0.927781 + 0.373124i \(0.878286\pi\)
\(728\) 26.9282 0.998026
\(729\) 0 0
\(730\) 9.17691 0.339653
\(731\) 12.7942 + 47.7487i 0.473212 + 1.76605i
\(732\) 0 0
\(733\) 2.95448 11.0263i 0.109126 0.407265i −0.889654 0.456635i \(-0.849055\pi\)
0.998781 + 0.0493698i \(0.0157213\pi\)
\(734\) −38.5885 10.3397i −1.42433 0.381647i
\(735\) 0 0
\(736\) −25.8564 + 6.92820i −0.953080 + 0.255377i
\(737\) 29.9282 1.10242
\(738\) 0 0
\(739\) −8.22243 8.22243i −0.302467 0.302467i 0.539511 0.841978i \(-0.318609\pi\)
−0.841978 + 0.539511i \(0.818609\pi\)
\(740\) 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 −0.879882 0.475192i \(-0.842379\pi\)
−0.0284129 + 0.999596i \(0.509045\pi\)
\(744\) 0 0
\(745\) 7.26795 + 4.19615i 0.266277 + 0.153735i
\(746\) 40.2487i 1.47361i
\(747\) 0 0
\(748\) 35.5167 + 35.5167i 1.29862 + 1.29862i
\(749\) −46.6147 + 12.4904i −1.70327 + 0.456389i
\(750\) 0 0
\(751\) −8.85641 15.3397i −0.323175 0.559755i 0.657966 0.753047i \(-0.271417\pi\)
−0.981141 + 0.193292i \(0.938084\pi\)
\(752\) 15.3205 + 26.5359i 0.558681 + 0.967665i
\(753\) 0 0
\(754\) 11.6603 3.12436i 0.424641 0.113782i
\(755\) −0.535898 0.535898i −0.0195033 0.0195033i
\(756\) 0 0
\(757\) −19.9282 + 19.9282i −0.724303 + 0.724303i −0.969479 0.245176i \(-0.921154\pi\)
0.245176 + 0.969479i \(0.421154\pi\)
\(758\) −6.50962 3.75833i −0.236440 0.136509i
\(759\) 0 0
\(760\) −2.53590 + 9.46410i −0.0919867 + 0.343299i
\(761\) −45.3731 + 26.1962i −1.64477 + 0.949610i −0.665669 + 0.746247i \(0.731854\pi\)
−0.979104 + 0.203363i \(0.934813\pi\)
\(762\) 0 0
\(763\) 10.7321 + 40.0526i 0.388526 + 1.45000i
\(764\) 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 \(-0.336776\pi\)
\(770\) 16.9282 + 4.53590i 0.610050 + 0.163462i
\(771\) 0 0
\(772\) 37.6410 + 21.7321i 1.35473 + 0.782154i
\(773\) −35.5885 + 35.5885i −1.28003 + 1.28003i −0.339378 + 0.940650i \(0.610216\pi\)
−0.940650 + 0.339378i \(0.889784\pi\)
\(774\) 0 0
\(775\) 2.10512i 0.0756181i
\(776\) −32.0526 + 8.58846i −1.15062 + 0.308308i
\(777\) 0 0
\(778\) 25.0526 14.4641i 0.898178 0.518563i
\(779\) −9.69615 2.59808i −0.347401 0.0930857i
\(780\) 0 0
\(781\) −12.3923 + 3.32051i −0.443432 + 0.118817i
\(782\) −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