Properties

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

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Newspace parameters

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

Newform invariants

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

Embedding invariants

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

$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.366025 + 1.36603i −0.258819 + 0.965926i
\(3\) 0 0
\(4\) −1.73205 1.00000i −0.866025 0.500000i
\(5\) −1.00000 + 0.267949i −0.447214 + 0.119831i −0.475395 0.879772i \(-0.657695\pi\)
0.0281817 + 0.999603i \(0.491028\pi\)
\(6\) 0 0
\(7\) 2.36603 1.36603i 0.894274 0.516309i 0.0189356 0.999821i \(-0.493972\pi\)
0.875338 + 0.483512i \(0.160639\pi\)
\(8\) 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 0.554279 + 0.832331i \(0.312994\pi\)
−0.896185 + 0.443680i \(0.853673\pi\)
\(12\) 0 0
\(13\) 0.901924 + 3.36603i 0.250149 + 0.933567i 0.970725 + 0.240192i \(0.0772105\pi\)
−0.720577 + 0.693375i \(0.756123\pi\)
\(14\) 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 −0.924350 0.381546i \(-0.875392\pi\)
0.381546 + 0.924350i \(0.375392\pi\)
\(20\) 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 0.862169 0.506620i \(-0.169105\pi\)
−0.00766135 + 0.999971i \(0.502439\pi\)
\(24\) 0 0
\(25\) −3.40192 + 1.96410i −0.680385 + 0.392820i
\(26\) −4.92820 −0.966500
\(27\) 0 0
\(28\) −5.46410 −1.03262
\(29\) −2.36603 0.633975i −0.439360 0.117726i 0.0323566 0.999476i \(-0.489699\pi\)
−0.471717 + 0.881750i \(0.656365\pi\)
\(30\) 0 0
\(31\) −0.267949 + 0.464102i −0.0481251 + 0.0833551i −0.889085 0.457743i \(-0.848658\pi\)
0.840959 + 0.541098i \(0.181991\pi\)
\(32\) −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 0.979481 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 \(-0.258066\pi\)
−0.283211 + 0.959058i \(0.591400\pi\)
\(42\) 0 0
\(43\) 2.23205 8.33013i 0.340385 1.27033i −0.557528 0.830158i \(-0.688250\pi\)
0.897912 0.440174i \(-0.145083\pi\)
\(44\) 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 −0.997607 0.0691412i \(-0.977974\pi\)
0.438925 0.898523i \(-0.355359\pi\)
\(48\) 0 0
\(49\) 0.232051 0.401924i 0.0331501 0.0574177i
\(50\) −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 0.999672 + 0.0256010i \(0.00814993\pi\)
0.0256010 + 0.999672i \(0.491850\pi\)
\(54\) 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 −0.702186 0.711993i \(-0.747793\pi\)
−0.252115 + 0.967697i \(0.581126\pi\)
\(60\) 0 0
\(61\) 11.1962 + 3.00000i 1.43352 + 0.384111i 0.890260 0.455453i \(-0.150523\pi\)
0.543261 + 0.839564i \(0.317189\pi\)
\(62\) −0.535898 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 −0.985816 0.167830i \(-0.946324\pi\)
0.769827 0.638253i \(-0.220343\pi\)
\(68\) −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
\(76\) 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 −0.976453 0.215728i \(-0.930788\pi\)
0.301401 0.953498i \(-0.402546\pi\)
\(80\) −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 0.333009 0.942924i \(-0.391936\pi\)
−0.183068 + 0.983100i \(0.558603\pi\)
\(84\) 0 0
\(85\) −5.73205 + 1.53590i −0.621728 + 0.166592i
\(86\) 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
\(94\) 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 −0.993461 0.114170i \(-0.963579\pi\)
0.397857 0.917448i \(-0.369754\pi\)
\(98\) 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 −0.987449 0.157938i \(-0.949515\pi\)
0.934125 + 0.356946i \(0.116182\pi\)
\(102\) 0 0
\(103\) 13.0981 + 7.56218i 1.29059 + 0.745124i 0.978759 0.205014i \(-0.0657238\pi\)
0.311833 + 0.950137i \(0.399057\pi\)
\(104\) 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 \(-0.00902398\pi\)
\(110\) 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 −0.330947 0.943649i \(-0.607368\pi\)
0.982698 0.185216i \(-0.0592984\pi\)
\(114\) 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 −0.994986 0.100014i \(-0.968111\pi\)
0.811676 0.584108i \(-0.198555\pi\)
\(132\) 0 0
\(133\) −2.36603 + 8.83013i −0.205160 + 0.765669i
\(134\) 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 \(-0.800215\pi\)
0.103857 + 0.994592i \(0.466882\pi\)
\(138\) 0 0
\(139\) −11.4282 + 3.06218i −0.969328 + 0.259731i −0.708544 0.705667i \(-0.750648\pi\)
−0.260784 + 0.965397i \(0.583981\pi\)
\(140\) 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 −0.564869 0.825181i \(-0.691073\pi\)
−0.0766003 + 0.997062i \(0.524407\pi\)
\(150\) 0 0
\(151\) 0.633975 0.366025i 0.0515921 0.0297867i −0.473982 0.880534i \(-0.657184\pi\)
0.525574 + 0.850748i \(0.323851\pi\)
\(152\) 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 0.997886 0.0649959i \(-0.0207034\pi\)
−0.896692 + 0.442655i \(0.854037\pi\)
\(158\) 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 −0.925944 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 \(-0.426588\pi\)
−0.728799 + 0.684728i \(0.759921\pi\)
\(168\) 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 0.196169 0.980570i \(-0.437150\pi\)
−0.320398 + 0.947283i \(0.603817\pi\)
\(174\) 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 −0.631365 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
\(184\) 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 0.861799 + 0.507250i \(0.169338\pi\)
0.00839227 + 0.999965i \(0.497329\pi\)
\(192\) 0 0
\(193\) −10.8660 + 18.8205i −0.782154 + 1.35473i 0.148531 + 0.988908i \(0.452545\pi\)
−0.930685 + 0.365822i \(0.880788\pi\)
\(194\) 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 0.0263987 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 \(-0.349652\pi\)
\(200\) −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 0.917773 0.397106i \(-0.129985\pi\)
−0.993367 + 0.114983i \(0.963319\pi\)
\(212\) −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 −0.999039 0.0438324i \(-0.986043\pi\)
0.461559 0.887109i \(-0.347290\pi\)
\(224\) −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 0.187304 0.982302i \(-0.440025\pi\)
−0.328941 + 0.944351i \(0.606692\pi\)
\(228\) 0 0
\(229\) 6.83013 1.83013i 0.451347 0.120938i −0.0259823 0.999662i \(-0.508271\pi\)
0.477330 + 0.878724i \(0.341605\pi\)
\(230\) 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
\(236\) 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 −0.488784 0.872405i \(-0.662559\pi\)
0.999917 0.0129033i \(-0.00410736\pi\)
\(240\) 0 0
\(241\) −11.5981 20.0885i −0.747098 1.29401i −0.949208 0.314649i \(-0.898113\pi\)
0.202110 0.979363i \(-0.435220\pi\)
\(242\) 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 0.866745 0.498751i \(-0.166208\pi\)
−0.498751 + 0.866745i \(0.666208\pi\)
\(252\) 0 0
\(253\) −14.6603 + 14.6603i −0.921682 + 0.921682i
\(254\) −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 0.406364 + 0.913711i \(0.366796\pi\)
−0.994479 + 0.104934i \(0.966537\pi\)
\(258\) 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 −0.421249 0.906945i \(-0.638408\pi\)
0.574813 + 0.818285i \(0.305075\pi\)
\(264\) 0 0
\(265\) −9.46410 5.46410i −0.581375 0.335657i
\(266\) −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 −0.744704 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
\(274\) −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 0.396007 + 0.918247i \(0.370395\pi\)
−0.802076 + 0.597222i \(0.796271\pi\)
\(278\) 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 \(-0.570255\pi\)
0.735554 + 0.677466i \(0.236922\pi\)
\(282\) 0 0
\(283\) −19.5622 + 5.24167i −1.16285 + 0.311585i −0.788104 0.615542i \(-0.788937\pi\)
−0.374747 + 0.927127i \(0.622270\pi\)
\(284\) 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 −0.0986454 0.995123i \(-0.531451\pi\)
0.412132 + 0.911124i \(0.364784\pi\)
\(294\) 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 −0.615454 0.788173i \(-0.711027\pi\)
0.788173 + 0.615454i \(0.211027\pi\)
\(308\) 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 0.931691 0.363251i \(-0.118333\pi\)
0.151261 + 0.988494i \(0.451667\pi\)
\(312\) 0 0
\(313\) 18.6506 10.7679i 1.05420 0.608640i 0.130375 0.991465i \(-0.458382\pi\)
0.923821 + 0.382824i \(0.125049\pi\)
\(314\) −6.92820 −0.390981
\(315\) 0 0
\(316\) 24.0000i 1.35011i
\(317\) 20.5622 + 5.50962i 1.15489 + 0.309451i 0.784922 0.619595i \(-0.212703\pi\)
0.369965 + 0.929046i \(0.379370\pi\)
\(318\) 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 −0.965200 0.261513i \(-0.915778\pi\)
0.966644 + 0.256123i \(0.0824451\pi\)
\(332\) −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 −0.515445 0.856923i \(-0.672373\pi\)
0.999839 + 0.0179267i \(0.00570654\pi\)
\(338\) 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 0.247408 0.968911i \(-0.420421\pi\)
0.698717 + 0.715398i \(0.253755\pi\)
\(348\) 0 0
\(349\) 15.9282 + 4.26795i 0.852617 + 0.228458i 0.658556 0.752531i \(-0.271167\pi\)
0.194061 + 0.980989i \(0.437834\pi\)
\(350\) −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 0.610118 0.792310i \(-0.291122\pi\)
−0.991220 + 0.132223i \(0.957789\pi\)
\(354\) 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 \(0.0961028\pi\)
−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
\(364\) −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 0.953713 + 0.300717i \(0.0972260\pi\)
−0.216428 + 0.976299i \(0.569441\pi\)
\(368\) 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 0.536710 0.843767i \(-0.319667\pi\)
0.886688 + 0.462368i \(0.153000\pi\)
\(374\) −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 0.797014 0.603961i \(-0.206412\pi\)
−0.603961 + 0.797014i \(0.706412\pi\)
\(380\) −6.00000 + 3.46410i −0.307794 + 0.177705i
\(381\) 0 0
\(382\) −32.8564 + 8.80385i −1.68108 + 0.450444i
\(383\) 6.73205 11.6603i 0.343992 0.595811i −0.641178 0.767392i \(-0.721554\pi\)
0.985170 + 0.171581i \(0.0548874\pi\)
\(384\) 0 0
\(385\) −6.19615 10.7321i −0.315785 0.546956i
\(386\) −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 −0.691691 0.722194i \(-0.743134\pi\)
0.960119 0.279593i \(-0.0901996\pi\)
\(390\) 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 −0.900337 0.435192i \(-0.856680\pi\)
0.435192 + 0.900337i \(0.356680\pi\)
\(398\) 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 −0.817742 0.575584i \(-0.804775\pi\)
0.907342 + 0.420393i \(0.138108\pi\)
\(402\) 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 0.991905 0.126984i \(-0.0405295\pi\)
0.385981 + 0.922507i \(0.373863\pi\)
\(410\) 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 0.908816 0.417196i \(-0.136987\pi\)
−0.995656 + 0.0931055i \(0.970321\pi\)
\(420\) 0 0
\(421\) 8.19615 30.5885i 0.399456 1.49079i −0.414600 0.910004i \(-0.636078\pi\)
0.814056 0.580786i \(-0.197255\pi\)
\(422\) 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 −0.933810 0.357770i \(-0.883537\pi\)
−0.157067 + 0.987588i \(0.550204\pi\)
\(440\) −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 −0.764745 0.644332i \(-0.777135\pi\)
0.984455 0.175636i \(-0.0561980\pi\)
\(444\) 0 0
\(445\) 0.535898 + 2.00000i 0.0254040 + 0.0948091i
\(446\) 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 −0.446249 0.894909i \(-0.647240\pi\)
0.551889 + 0.833917i \(0.313907\pi\)
\(458\) 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 −0.699127 0.714997i \(-0.746428\pi\)
−0.962961 + 0.269642i \(0.913094\pi\)
\(462\) 0 0
\(463\) 1.19615 2.07180i 0.0555899 0.0962846i −0.836891 0.547369i \(-0.815629\pi\)
0.892481 + 0.451085i \(0.148963\pi\)
\(464\) −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 −0.765419 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
\(475\) 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 0.754898 0.655842i \(-0.227686\pi\)
−0.945425 + 0.325840i \(0.894353\pi\)
\(480\) 0 0
\(481\) −11.6603 + 20.1962i −0.531662 + 0.920865i
\(482\) 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 \(-0.958021\pi\)
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
\(491\) 13.8923 3.72243i 0.626951 0.167991i 0.0686652 0.997640i \(-0.478126\pi\)
0.558286 + 0.829649i \(0.311459\pi\)
\(492\) 0 0
\(493\) −13.5622 3.63397i −0.610810 0.163666i
\(494\) 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 0.893955 0.448156i \(-0.147919\pi\)
−0.998266 + 0.0588630i \(0.981252\pi\)
\(500\) −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 \(-0.788013\pi\)
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
\(509\) −3.07180 11.4641i −0.136155 0.508137i −0.999990 0.00436335i \(-0.998611\pi\)
0.863835 0.503774i \(-0.168056\pi\)
\(510\) 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 \(0.0919173\pi\)
−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 \(0.824857\pi\)
\(524\) −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 −0.658319 0.752739i \(-0.728732\pi\)
0.752739 + 0.658319i \(0.228732\pi\)
\(542\) 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 0.876517 0.481371i \(-0.159861\pi\)
0.518400 + 0.855138i \(0.326528\pi\)
\(548\) 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 −0.320118 0.947378i \(-0.603723\pi\)
0.947378 + 0.320118i \(0.103723\pi\)
\(558\) 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 0.933122 + 0.359560i \(0.117073\pi\)
−0.628327 + 0.777949i \(0.716260\pi\)
\(564\) 0 0
\(565\) −3.71281 + 13.8564i −0.156199 + 0.582943i
\(566\) 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 \(-0.519730\pi\)
0.833391 + 0.552684i \(0.186396\pi\)
\(570\) 0 0
\(571\) −3.33013 + 0.892305i −0.139361 + 0.0373418i −0.327825 0.944738i \(-0.606316\pi\)
0.188464 + 0.982080i \(0.439649\pi\)
\(572\) 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 0.639900 + 0.768458i \(0.278976\pi\)
−0.938399 + 0.345554i \(0.887691\pi\)
\(588\) 0 0
\(589\) −0.464102 1.73205i −0.0191230 0.0713679i
\(590\) 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 0.250570 0.968099i \(-0.419382\pi\)
−0.713113 + 0.701049i \(0.752715\pi\)
\(600\) 0 0
\(601\) −20.5526 + 11.8660i −0.838356 + 0.484025i −0.856705 0.515806i \(-0.827492\pi\)
0.0183488 + 0.999832i \(0.494159\pi\)
\(602\) 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 −0.986000 0.166745i \(-0.946674\pi\)
0.637405 + 0.770529i \(0.280008\pi\)
\(608\) 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 0.316186 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 \(-0.0297571\pi\)
0.416975 + 0.908918i \(0.363090\pi\)
\(618\) 0 0
\(619\) 4.17949 15.5981i 0.167988 0.626940i −0.829652 0.558281i \(-0.811461\pi\)
0.997640 0.0686590i \(-0.0218721\pi\)
\(620\) −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 \(-0.886020\pi\)
0.936572 0.350476i \(-0.113980\pi\)
\(632\) −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 0.930878 + 0.365331i \(0.119044\pi\)
−0.149053 + 0.988829i \(0.547622\pi\)
\(642\) 0 0
\(643\) −2.34936 8.76795i −0.0926499 0.345774i 0.904003 0.427527i \(-0.140615\pi\)
−0.996653 + 0.0817525i \(0.973948\pi\)
\(644\) −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
\(652\) 19.1244 5.12436i 0.748968 0.200685i
\(653\) −7.36603 27.4904i −0.288255 1.07578i −0.946428 0.322915i \(-0.895337\pi\)
0.658173 0.752867i \(-0.271329\pi\)
\(654\) 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 0.539323 0.842099i \(-0.318680\pi\)
0.0460178 + 0.998941i \(0.485347\pi\)
\(660\) 0 0
\(661\) −8.19615 + 2.19615i −0.318793 + 0.0854204i −0.414667 0.909973i \(-0.636102\pi\)
0.0958740 + 0.995393i \(0.469435\pi\)
\(662\) 0.124356 + 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 0.952514 + 0.304495i \(0.0984877\pi\)
−0.212557 + 0.977149i \(0.568179\pi\)
\(674\) 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 −0.986002 0.166736i \(-0.946677\pi\)
0.937270 + 0.348603i \(0.113344\pi\)
\(678\) 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
\(686\) −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 0.431232 0.902241i \(-0.358079\pi\)
−0.0776628 + 0.996980i \(0.524746\pi\)
\(692\) 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
\(704\) 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 0.494852 + 0.868978i \(0.335222\pi\)
−0.863043 + 0.505131i \(0.831444\pi\)
\(710\) 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 −0.927781 0.373124i \(-0.878286\pi\)
−0.140755 + 0.990044i \(0.544953\pi\)
\(728\) 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 0.998781 0.0493698i \(-0.0157213\pi\)
−0.889654 + 0.456635i \(0.849055\pi\)
\(734\) −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 −0.841978 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 \(-0.509045\pi\)
−0.879882 + 0.475192i \(0.842379\pi\)
\(744\) 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 −0.981141 0.193292i \(-0.938084\pi\)
0.657966 + 0.753047i \(0.271417\pi\)
\(752\) 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 0.245176 0.969479i \(-0.421154\pi\)
−0.969479 + 0.245176i \(0.921154\pi\)
\(758\) −6.50962 + 3.75833i −0.236440 + 0.136509i
\(759\) 0 0
\(760\) −2.53590 9.46410i −0.0919867 0.343299i
\(761\) −45.3731 26.1962i −1.64477 0.949610i −0.979104 0.203363i \(-0.934813\pi\)
−0.665669 0.746247i \(-0.731854\pi\)
\(762\) 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 0.490604 + 0.871383i \(0.336776\pi\)
−0.999942 + 0.0108155i \(0.996557\pi\)
\(770\) 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 −0.940650 0.339378i \(-0.889784\pi\)
−0.339378 0.940650i \(-0.610216\pi\)
\(774\) 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