Properties

Label 756.2.ba.a.71.14
Level $756$
Weight $2$
Character 756.71
Analytic conductor $6.037$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.ba (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 71.14
Character \(\chi\) \(=\) 756.71
Dual form 756.2.ba.a.575.14

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.498620 - 1.32340i) q^{2} +(-1.50276 + 1.31974i) q^{4} +(-2.06874 - 1.19439i) q^{5} +(0.866025 - 0.500000i) q^{7} +(2.49585 + 1.33069i) q^{8} +O(q^{10})\) \(q+(-0.498620 - 1.32340i) q^{2} +(-1.50276 + 1.31974i) q^{4} +(-2.06874 - 1.19439i) q^{5} +(0.866025 - 0.500000i) q^{7} +(2.49585 + 1.33069i) q^{8} +(-0.549133 + 3.33330i) q^{10} +(3.21792 + 5.57360i) q^{11} +(2.15010 - 3.72408i) q^{13} +(-1.09352 - 0.896785i) q^{14} +(0.516556 - 3.96651i) q^{16} -1.89547i q^{17} +0.529348i q^{19} +(4.68509 - 0.935330i) q^{20} +(5.77157 - 7.03770i) q^{22} +(2.64942 - 4.58894i) q^{23} +(0.353115 + 0.611613i) q^{25} +(-6.00052 - 0.988535i) q^{26} +(-0.641554 + 1.89431i) q^{28} +(0.301871 - 0.174285i) q^{29} +(-5.09757 - 2.94308i) q^{31} +(-5.50683 + 1.29417i) q^{32} +(-2.50846 + 0.945118i) q^{34} -2.38877 q^{35} +0.842466 q^{37} +(0.700537 - 0.263943i) q^{38} +(-3.57389 - 5.73386i) q^{40} +(-4.58530 - 2.64733i) q^{41} +(7.38095 - 4.26140i) q^{43} +(-12.1915 - 4.12894i) q^{44} +(-7.39404 - 1.21810i) q^{46} +(2.04252 + 3.53774i) q^{47} +(0.500000 - 0.866025i) q^{49} +(0.633336 - 0.772273i) q^{50} +(1.68376 + 8.43397i) q^{52} -12.5979i q^{53} -15.3738i q^{55} +(2.82681 - 0.0955095i) q^{56} +(-0.381168 - 0.312593i) q^{58} +(2.66171 - 4.61021i) q^{59} +(-3.49882 - 6.06013i) q^{61} +(-1.35312 + 8.21358i) q^{62} +(4.45851 + 6.64242i) q^{64} +(-8.89599 + 5.13610i) q^{65} +(9.32818 + 5.38563i) q^{67} +(2.50153 + 2.84843i) q^{68} +(1.19109 + 3.16129i) q^{70} +6.12137 q^{71} +5.07942 q^{73} +(-0.420070 - 1.11492i) q^{74} +(-0.698603 - 0.795481i) q^{76} +(5.57360 + 3.21792i) q^{77} +(2.87851 - 1.66191i) q^{79} +(-5.80616 + 7.58869i) q^{80} +(-1.21714 + 7.38818i) q^{82} +(-3.23597 - 5.60486i) q^{83} +(-2.26392 + 3.92122i) q^{85} +(-9.31981 - 7.64311i) q^{86} +(0.614684 + 18.1929i) q^{88} +14.4170i q^{89} -4.30020i q^{91} +(2.07478 + 10.3926i) q^{92} +(3.66340 - 4.46705i) q^{94} +(0.632246 - 1.09508i) q^{95} +(-3.86625 - 6.69654i) q^{97} +(-1.39540 - 0.229881i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + O(q^{10}) \) \( 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.498620 1.32340i −0.352577 0.935783i
\(3\) 0 0
\(4\) −1.50276 + 1.31974i −0.751378 + 0.659872i
\(5\) −2.06874 1.19439i −0.925167 0.534146i −0.0398874 0.999204i \(-0.512700\pi\)
−0.885280 + 0.465059i \(0.846033\pi\)
\(6\) 0 0
\(7\) 0.866025 0.500000i 0.327327 0.188982i
\(8\) 2.49585 + 1.33069i 0.882415 + 0.470471i
\(9\) 0 0
\(10\) −0.549133 + 3.33330i −0.173651 + 1.05408i
\(11\) 3.21792 + 5.57360i 0.970240 + 1.68050i 0.694824 + 0.719180i \(0.255482\pi\)
0.275416 + 0.961325i \(0.411184\pi\)
\(12\) 0 0
\(13\) 2.15010 3.72408i 0.596331 1.03288i −0.397027 0.917807i \(-0.629958\pi\)
0.993358 0.115068i \(-0.0367086\pi\)
\(14\) −1.09352 0.896785i −0.292254 0.239676i
\(15\) 0 0
\(16\) 0.516556 3.96651i 0.129139 0.991626i
\(17\) 1.89547i 0.459718i −0.973224 0.229859i \(-0.926173\pi\)
0.973224 0.229859i \(-0.0738266\pi\)
\(18\) 0 0
\(19\) 0.529348i 0.121441i 0.998155 + 0.0607204i \(0.0193398\pi\)
−0.998155 + 0.0607204i \(0.980660\pi\)
\(20\) 4.68509 0.935330i 1.04762 0.209146i
\(21\) 0 0
\(22\) 5.77157 7.03770i 1.23050 1.50044i
\(23\) 2.64942 4.58894i 0.552443 0.956859i −0.445655 0.895205i \(-0.647029\pi\)
0.998098 0.0616543i \(-0.0196376\pi\)
\(24\) 0 0
\(25\) 0.353115 + 0.611613i 0.0706230 + 0.122323i
\(26\) −6.00052 0.988535i −1.17680 0.193868i
\(27\) 0 0
\(28\) −0.641554 + 1.89431i −0.121242 + 0.357991i
\(29\) 0.301871 0.174285i 0.0560561 0.0323640i −0.471710 0.881754i \(-0.656363\pi\)
0.527766 + 0.849390i \(0.323030\pi\)
\(30\) 0 0
\(31\) −5.09757 2.94308i −0.915550 0.528593i −0.0333376 0.999444i \(-0.510614\pi\)
−0.882213 + 0.470851i \(0.843947\pi\)
\(32\) −5.50683 + 1.29417i −0.973478 + 0.228779i
\(33\) 0 0
\(34\) −2.50846 + 0.945118i −0.430197 + 0.162086i
\(35\) −2.38877 −0.403776
\(36\) 0 0
\(37\) 0.842466 0.138501 0.0692503 0.997599i \(-0.477939\pi\)
0.0692503 + 0.997599i \(0.477939\pi\)
\(38\) 0.700537 0.263943i 0.113642 0.0428173i
\(39\) 0 0
\(40\) −3.57389 5.73386i −0.565082 0.906603i
\(41\) −4.58530 2.64733i −0.716104 0.413443i 0.0972131 0.995264i \(-0.469007\pi\)
−0.813317 + 0.581821i \(0.802340\pi\)
\(42\) 0 0
\(43\) 7.38095 4.26140i 1.12559 0.649857i 0.182764 0.983157i \(-0.441496\pi\)
0.942821 + 0.333300i \(0.108162\pi\)
\(44\) −12.1915 4.12894i −1.83793 0.622461i
\(45\) 0 0
\(46\) −7.39404 1.21810i −1.09019 0.179600i
\(47\) 2.04252 + 3.53774i 0.297932 + 0.516033i 0.975663 0.219277i \(-0.0703699\pi\)
−0.677731 + 0.735310i \(0.737037\pi\)
\(48\) 0 0
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) 0.633336 0.772273i 0.0895673 0.109216i
\(51\) 0 0
\(52\) 1.68376 + 8.43397i 0.233495 + 1.16958i
\(53\) 12.5979i 1.73046i −0.501376 0.865230i \(-0.667173\pi\)
0.501376 0.865230i \(-0.332827\pi\)
\(54\) 0 0
\(55\) 15.3738i 2.07300i
\(56\) 2.82681 0.0955095i 0.377749 0.0127630i
\(57\) 0 0
\(58\) −0.381168 0.312593i −0.0500497 0.0410455i
\(59\) 2.66171 4.61021i 0.346524 0.600198i −0.639105 0.769119i \(-0.720695\pi\)
0.985630 + 0.168921i \(0.0540284\pi\)
\(60\) 0 0
\(61\) −3.49882 6.06013i −0.447978 0.775920i 0.550277 0.834982i \(-0.314522\pi\)
−0.998254 + 0.0590625i \(0.981189\pi\)
\(62\) −1.35312 + 8.21358i −0.171846 + 1.04313i
\(63\) 0 0
\(64\) 4.45851 + 6.64242i 0.557314 + 0.830302i
\(65\) −8.89599 + 5.13610i −1.10341 + 0.637055i
\(66\) 0 0
\(67\) 9.32818 + 5.38563i 1.13962 + 0.657959i 0.946336 0.323184i \(-0.104753\pi\)
0.193282 + 0.981143i \(0.438087\pi\)
\(68\) 2.50153 + 2.84843i 0.303355 + 0.345423i
\(69\) 0 0
\(70\) 1.19109 + 3.16129i 0.142362 + 0.377847i
\(71\) 6.12137 0.726473 0.363236 0.931697i \(-0.381672\pi\)
0.363236 + 0.931697i \(0.381672\pi\)
\(72\) 0 0
\(73\) 5.07942 0.594501 0.297251 0.954799i \(-0.403930\pi\)
0.297251 + 0.954799i \(0.403930\pi\)
\(74\) −0.420070 1.11492i −0.0488322 0.129606i
\(75\) 0 0
\(76\) −0.698603 0.795481i −0.0801353 0.0912480i
\(77\) 5.57360 + 3.21792i 0.635171 + 0.366716i
\(78\) 0 0
\(79\) 2.87851 1.66191i 0.323858 0.186979i −0.329253 0.944242i \(-0.606797\pi\)
0.653111 + 0.757262i \(0.273464\pi\)
\(80\) −5.80616 + 7.58869i −0.649148 + 0.848441i
\(81\) 0 0
\(82\) −1.21714 + 7.38818i −0.134411 + 0.815888i
\(83\) −3.23597 5.60486i −0.355193 0.615213i 0.631958 0.775003i \(-0.282252\pi\)
−0.987151 + 0.159790i \(0.948918\pi\)
\(84\) 0 0
\(85\) −2.26392 + 3.92122i −0.245557 + 0.425317i
\(86\) −9.31981 7.64311i −1.00498 0.824178i
\(87\) 0 0
\(88\) 0.614684 + 18.1929i 0.0655256 + 1.93937i
\(89\) 14.4170i 1.52820i 0.645099 + 0.764099i \(0.276816\pi\)
−0.645099 + 0.764099i \(0.723184\pi\)
\(90\) 0 0
\(91\) 4.30020i 0.450784i
\(92\) 2.07478 + 10.3926i 0.216310 + 1.08350i
\(93\) 0 0
\(94\) 3.66340 4.46705i 0.377851 0.460741i
\(95\) 0.632246 1.09508i 0.0648670 0.112353i
\(96\) 0 0
\(97\) −3.86625 6.69654i −0.392558 0.679931i 0.600228 0.799829i \(-0.295077\pi\)
−0.992786 + 0.119898i \(0.961743\pi\)
\(98\) −1.39540 0.229881i −0.140957 0.0232215i
\(99\) 0 0
\(100\) −1.33782 0.453085i −0.133782 0.0453085i
\(101\) 14.7999 8.54473i 1.47265 0.850233i 0.473119 0.880998i \(-0.343128\pi\)
0.999527 + 0.0307657i \(0.00979457\pi\)
\(102\) 0 0
\(103\) −10.0362 5.79440i −0.988896 0.570939i −0.0839517 0.996470i \(-0.526754\pi\)
−0.904944 + 0.425531i \(0.860087\pi\)
\(104\) 10.3219 6.43362i 1.01215 0.630868i
\(105\) 0 0
\(106\) −16.6721 + 6.28158i −1.61933 + 0.610121i
\(107\) −1.66184 −0.160656 −0.0803278 0.996768i \(-0.525597\pi\)
−0.0803278 + 0.996768i \(0.525597\pi\)
\(108\) 0 0
\(109\) −8.21513 −0.786867 −0.393434 0.919353i \(-0.628713\pi\)
−0.393434 + 0.919353i \(0.628713\pi\)
\(110\) −20.3456 + 7.66566i −1.93988 + 0.730892i
\(111\) 0 0
\(112\) −1.53590 3.69337i −0.145129 0.348991i
\(113\) 7.87513 + 4.54671i 0.740830 + 0.427718i 0.822371 0.568952i \(-0.192651\pi\)
−0.0815410 + 0.996670i \(0.525984\pi\)
\(114\) 0 0
\(115\) −10.9619 + 6.32887i −1.02220 + 0.590170i
\(116\) −0.223627 + 0.660301i −0.0207632 + 0.0613074i
\(117\) 0 0
\(118\) −7.42831 1.22375i −0.683832 0.112655i
\(119\) −0.947734 1.64152i −0.0868786 0.150478i
\(120\) 0 0
\(121\) −15.2100 + 26.3446i −1.38273 + 2.39496i
\(122\) −6.27537 + 7.65202i −0.568146 + 0.692781i
\(123\) 0 0
\(124\) 11.5445 2.30474i 1.03673 0.206972i
\(125\) 10.2568i 0.917399i
\(126\) 0 0
\(127\) 17.0630i 1.51409i 0.653360 + 0.757047i \(0.273359\pi\)
−0.653360 + 0.757047i \(0.726641\pi\)
\(128\) 6.56745 9.21242i 0.580486 0.814270i
\(129\) 0 0
\(130\) 11.2328 + 9.21196i 0.985183 + 0.807942i
\(131\) 5.58971 9.68166i 0.488375 0.845890i −0.511536 0.859262i \(-0.670923\pi\)
0.999911 + 0.0133718i \(0.00425652\pi\)
\(132\) 0 0
\(133\) 0.264674 + 0.458429i 0.0229501 + 0.0397508i
\(134\) 2.47611 15.0303i 0.213903 1.29842i
\(135\) 0 0
\(136\) 2.52229 4.73080i 0.216284 0.405663i
\(137\) −4.30543 + 2.48574i −0.367838 + 0.212371i −0.672513 0.740085i \(-0.734785\pi\)
0.304676 + 0.952456i \(0.401452\pi\)
\(138\) 0 0
\(139\) 7.46366 + 4.30915i 0.633060 + 0.365497i 0.781936 0.623359i \(-0.214232\pi\)
−0.148876 + 0.988856i \(0.547566\pi\)
\(140\) 3.58974 3.15256i 0.303389 0.266440i
\(141\) 0 0
\(142\) −3.05223 8.10100i −0.256138 0.679821i
\(143\) 27.6754 2.31434
\(144\) 0 0
\(145\) −0.832656 −0.0691483
\(146\) −2.53270 6.72209i −0.209608 0.556324i
\(147\) 0 0
\(148\) −1.26602 + 1.11184i −0.104066 + 0.0913926i
\(149\) −2.18247 1.26005i −0.178795 0.103227i 0.407931 0.913013i \(-0.366250\pi\)
−0.586727 + 0.809785i \(0.699584\pi\)
\(150\) 0 0
\(151\) −0.331047 + 0.191130i −0.0269402 + 0.0155539i −0.513410 0.858144i \(-0.671618\pi\)
0.486469 + 0.873698i \(0.338285\pi\)
\(152\) −0.704400 + 1.32117i −0.0571344 + 0.107161i
\(153\) 0 0
\(154\) 1.47948 8.98061i 0.119220 0.723678i
\(155\) 7.03035 + 12.1769i 0.564691 + 0.978074i
\(156\) 0 0
\(157\) 4.39885 7.61904i 0.351067 0.608065i −0.635370 0.772208i \(-0.719152\pi\)
0.986437 + 0.164143i \(0.0524857\pi\)
\(158\) −3.63465 2.98075i −0.289157 0.237136i
\(159\) 0 0
\(160\) 12.9379 + 3.89998i 1.02283 + 0.308320i
\(161\) 5.29885i 0.417608i
\(162\) 0 0
\(163\) 10.7694i 0.843521i −0.906707 0.421760i \(-0.861412\pi\)
0.906707 0.421760i \(-0.138588\pi\)
\(164\) 10.3844 2.07313i 0.810884 0.161885i
\(165\) 0 0
\(166\) −5.80393 + 7.07716i −0.450473 + 0.549294i
\(167\) −3.92462 + 6.79765i −0.303697 + 0.526018i −0.976970 0.213375i \(-0.931554\pi\)
0.673274 + 0.739393i \(0.264888\pi\)
\(168\) 0 0
\(169\) −2.74587 4.75598i −0.211221 0.365845i
\(170\) 6.31817 + 1.04086i 0.484582 + 0.0798306i
\(171\) 0 0
\(172\) −5.46783 + 16.1448i −0.416918 + 1.23103i
\(173\) 16.5653 9.56396i 1.25943 0.727134i 0.286469 0.958089i \(-0.407518\pi\)
0.972964 + 0.230955i \(0.0741850\pi\)
\(174\) 0 0
\(175\) 0.611613 + 0.353115i 0.0462336 + 0.0266930i
\(176\) 23.7700 9.88483i 1.79173 0.745097i
\(177\) 0 0
\(178\) 19.0794 7.18860i 1.43006 0.538808i
\(179\) −26.1468 −1.95431 −0.977153 0.212538i \(-0.931827\pi\)
−0.977153 + 0.212538i \(0.931827\pi\)
\(180\) 0 0
\(181\) 18.9172 1.40610 0.703052 0.711139i \(-0.251820\pi\)
0.703052 + 0.711139i \(0.251820\pi\)
\(182\) −5.69087 + 2.14417i −0.421836 + 0.158936i
\(183\) 0 0
\(184\) 12.7190 7.92771i 0.937659 0.584439i
\(185\) −1.74284 1.00623i −0.128136 0.0739795i
\(186\) 0 0
\(187\) 10.5646 6.09947i 0.772559 0.446037i
\(188\) −7.73832 2.62077i −0.564375 0.191139i
\(189\) 0 0
\(190\) −1.76448 0.290682i −0.128009 0.0210883i
\(191\) 4.70709 + 8.15291i 0.340593 + 0.589924i 0.984543 0.175143i \(-0.0560389\pi\)
−0.643950 + 0.765068i \(0.722706\pi\)
\(192\) 0 0
\(193\) −0.658744 + 1.14098i −0.0474174 + 0.0821294i −0.888760 0.458373i \(-0.848432\pi\)
0.841343 + 0.540502i \(0.181766\pi\)
\(194\) −6.93439 + 8.45561i −0.497860 + 0.607078i
\(195\) 0 0
\(196\) 0.391553 + 1.96130i 0.0279680 + 0.140093i
\(197\) 3.56413i 0.253933i 0.991907 + 0.126967i \(0.0405241\pi\)
−0.991907 + 0.126967i \(0.959476\pi\)
\(198\) 0 0
\(199\) 15.9739i 1.13236i 0.824282 + 0.566179i \(0.191579\pi\)
−0.824282 + 0.566179i \(0.808421\pi\)
\(200\) 0.0674517 + 1.99638i 0.00476955 + 0.141165i
\(201\) 0 0
\(202\) −18.6876 15.3256i −1.31485 1.07830i
\(203\) 0.174285 0.301871i 0.0122324 0.0211872i
\(204\) 0 0
\(205\) 6.32386 + 10.9532i 0.441677 + 0.765007i
\(206\) −2.66404 + 16.1711i −0.185613 + 1.12669i
\(207\) 0 0
\(208\) −13.6610 10.4521i −0.947217 0.724722i
\(209\) −2.95038 + 1.70340i −0.204082 + 0.117827i
\(210\) 0 0
\(211\) 3.39401 + 1.95953i 0.233653 + 0.134900i 0.612256 0.790659i \(-0.290262\pi\)
−0.378603 + 0.925559i \(0.623595\pi\)
\(212\) 16.6260 + 18.9316i 1.14188 + 1.30023i
\(213\) 0 0
\(214\) 0.828624 + 2.19927i 0.0566436 + 0.150339i
\(215\) −20.3590 −1.38847
\(216\) 0 0
\(217\) −5.88617 −0.399579
\(218\) 4.09623 + 10.8719i 0.277432 + 0.736337i
\(219\) 0 0
\(220\) 20.2894 + 23.1030i 1.36791 + 1.55761i
\(221\) −7.05888 4.07545i −0.474832 0.274144i
\(222\) 0 0
\(223\) −2.25600 + 1.30250i −0.151073 + 0.0872218i −0.573631 0.819114i \(-0.694466\pi\)
0.422558 + 0.906336i \(0.361132\pi\)
\(224\) −4.12197 + 3.87420i −0.275410 + 0.258856i
\(225\) 0 0
\(226\) 2.09040 12.6890i 0.139052 0.844060i
\(227\) 1.56505 + 2.71075i 0.103876 + 0.179919i 0.913278 0.407336i \(-0.133542\pi\)
−0.809402 + 0.587254i \(0.800209\pi\)
\(228\) 0 0
\(229\) −3.33583 + 5.77783i −0.220438 + 0.381809i −0.954941 0.296796i \(-0.904082\pi\)
0.734503 + 0.678605i \(0.237415\pi\)
\(230\) 13.8414 + 11.3513i 0.912677 + 0.748481i
\(231\) 0 0
\(232\) 0.985345 0.0332918i 0.0646910 0.00218572i
\(233\) 15.0197i 0.983971i 0.870603 + 0.491985i \(0.163729\pi\)
−0.870603 + 0.491985i \(0.836271\pi\)
\(234\) 0 0
\(235\) 9.75821i 0.636556i
\(236\) 2.08440 + 10.4408i 0.135683 + 0.679637i
\(237\) 0 0
\(238\) −1.69983 + 2.07272i −0.110183 + 0.134355i
\(239\) −1.10101 + 1.90701i −0.0712185 + 0.123354i −0.899436 0.437053i \(-0.856022\pi\)
0.828217 + 0.560407i \(0.189355\pi\)
\(240\) 0 0
\(241\) −9.28440 16.0811i −0.598061 1.03587i −0.993107 0.117211i \(-0.962605\pi\)
0.395046 0.918661i \(-0.370729\pi\)
\(242\) 42.4483 + 6.99300i 2.72868 + 0.449527i
\(243\) 0 0
\(244\) 13.2557 + 4.48936i 0.848608 + 0.287402i
\(245\) −2.06874 + 1.19439i −0.132167 + 0.0763065i
\(246\) 0 0
\(247\) 1.97134 + 1.13815i 0.125433 + 0.0724188i
\(248\) −8.80641 14.1288i −0.559208 0.897179i
\(249\) 0 0
\(250\) 13.5739 5.11426i 0.858486 0.323454i
\(251\) −6.18166 −0.390183 −0.195092 0.980785i \(-0.562500\pi\)
−0.195092 + 0.980785i \(0.562500\pi\)
\(252\) 0 0
\(253\) 34.1026 2.14401
\(254\) 22.5811 8.50794i 1.41686 0.533836i
\(255\) 0 0
\(256\) −15.4663 4.09785i −0.966646 0.256115i
\(257\) −6.98685 4.03386i −0.435828 0.251625i 0.265998 0.963973i \(-0.414298\pi\)
−0.701826 + 0.712348i \(0.747632\pi\)
\(258\) 0 0
\(259\) 0.729597 0.421233i 0.0453350 0.0261741i
\(260\) 6.59017 19.4587i 0.408705 1.20678i
\(261\) 0 0
\(262\) −15.5998 2.56993i −0.963759 0.158771i
\(263\) 0.0757144 + 0.131141i 0.00466875 + 0.00808651i 0.868350 0.495951i \(-0.165181\pi\)
−0.863682 + 0.504038i \(0.831847\pi\)
\(264\) 0 0
\(265\) −15.0468 + 26.0618i −0.924317 + 1.60096i
\(266\) 0.474711 0.578850i 0.0291064 0.0354916i
\(267\) 0 0
\(268\) −21.1256 + 4.21751i −1.29045 + 0.257626i
\(269\) 2.18065i 0.132957i −0.997788 0.0664784i \(-0.978824\pi\)
0.997788 0.0664784i \(-0.0211763\pi\)
\(270\) 0 0
\(271\) 3.08448i 0.187369i −0.995602 0.0936844i \(-0.970136\pi\)
0.995602 0.0936844i \(-0.0298645\pi\)
\(272\) −7.51838 0.979116i −0.455869 0.0593676i
\(273\) 0 0
\(274\) 5.43639 + 4.45835i 0.328425 + 0.269339i
\(275\) −2.27259 + 3.93624i −0.137042 + 0.237364i
\(276\) 0 0
\(277\) −8.31095 14.3950i −0.499357 0.864911i 0.500643 0.865654i \(-0.333097\pi\)
−1.00000 0.000742657i \(0.999764\pi\)
\(278\) 1.98118 12.0260i 0.118823 0.721272i
\(279\) 0 0
\(280\) −5.96201 3.17872i −0.356298 0.189965i
\(281\) −8.93878 + 5.16081i −0.533243 + 0.307868i −0.742336 0.670028i \(-0.766282\pi\)
0.209093 + 0.977896i \(0.432949\pi\)
\(282\) 0 0
\(283\) 12.3659 + 7.13943i 0.735074 + 0.424395i 0.820275 0.571969i \(-0.193820\pi\)
−0.0852016 + 0.996364i \(0.527153\pi\)
\(284\) −9.19893 + 8.07863i −0.545856 + 0.479379i
\(285\) 0 0
\(286\) −13.7995 36.6256i −0.815982 2.16572i
\(287\) −5.29465 −0.312533
\(288\) 0 0
\(289\) 13.4072 0.788659
\(290\) 0.415179 + 1.10193i 0.0243801 + 0.0647078i
\(291\) 0 0
\(292\) −7.63314 + 6.70353i −0.446696 + 0.392295i
\(293\) 2.10270 + 1.21399i 0.122841 + 0.0709223i 0.560161 0.828383i \(-0.310739\pi\)
−0.437320 + 0.899306i \(0.644072\pi\)
\(294\) 0 0
\(295\) −11.0127 + 6.35821i −0.641186 + 0.370189i
\(296\) 2.10267 + 1.12106i 0.122215 + 0.0651605i
\(297\) 0 0
\(298\) −0.579324 + 3.51657i −0.0335593 + 0.203709i
\(299\) −11.3931 19.7334i −0.658877 1.14121i
\(300\) 0 0
\(301\) 4.26140 7.38095i 0.245623 0.425431i
\(302\) 0.418007 + 0.342805i 0.0240536 + 0.0197262i
\(303\) 0 0
\(304\) 2.09966 + 0.273438i 0.120424 + 0.0156827i
\(305\) 16.7157i 0.957141i
\(306\) 0 0
\(307\) 8.87237i 0.506373i 0.967417 + 0.253187i \(0.0814787\pi\)
−0.967417 + 0.253187i \(0.918521\pi\)
\(308\) −12.6226 + 2.51997i −0.719240 + 0.143589i
\(309\) 0 0
\(310\) 12.6094 15.3756i 0.716168 0.873275i
\(311\) −3.03771 + 5.26147i −0.172253 + 0.298350i −0.939207 0.343351i \(-0.888438\pi\)
0.766954 + 0.641702i \(0.221771\pi\)
\(312\) 0 0
\(313\) −10.3245 17.8825i −0.583575 1.01078i −0.995051 0.0993607i \(-0.968320\pi\)
0.411477 0.911420i \(-0.365013\pi\)
\(314\) −12.2764 2.02242i −0.692795 0.114132i
\(315\) 0 0
\(316\) −2.13241 + 6.29634i −0.119957 + 0.354197i
\(317\) −21.2581 + 12.2734i −1.19397 + 0.689341i −0.959205 0.282710i \(-0.908767\pi\)
−0.234769 + 0.972051i \(0.575433\pi\)
\(318\) 0 0
\(319\) 1.94280 + 1.12167i 0.108776 + 0.0628017i
\(320\) −1.28988 19.0666i −0.0721064 1.06585i
\(321\) 0 0
\(322\) −7.01248 + 2.64211i −0.390790 + 0.147239i
\(323\) 1.00336 0.0558286
\(324\) 0 0
\(325\) 3.03693 0.168459
\(326\) −14.2521 + 5.36981i −0.789352 + 0.297406i
\(327\) 0 0
\(328\) −7.92144 12.7090i −0.437388 0.701734i
\(329\) 3.53774 + 2.04252i 0.195042 + 0.112608i
\(330\) 0 0
\(331\) −25.9866 + 15.0034i −1.42835 + 0.824660i −0.996991 0.0775195i \(-0.975300\pi\)
−0.431362 + 0.902179i \(0.641967\pi\)
\(332\) 12.2598 + 4.15210i 0.672846 + 0.227876i
\(333\) 0 0
\(334\) 10.9529 + 1.80439i 0.599315 + 0.0987320i
\(335\) −12.8650 22.2829i −0.702892 1.21744i
\(336\) 0 0
\(337\) −5.27401 + 9.13486i −0.287294 + 0.497608i −0.973163 0.230117i \(-0.926089\pi\)
0.685869 + 0.727725i \(0.259422\pi\)
\(338\) −4.92491 + 6.00530i −0.267880 + 0.326645i
\(339\) 0 0
\(340\) −1.77289 8.88044i −0.0961483 0.481609i
\(341\) 37.8824i 2.05145i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 24.0924 0.814008i 1.29897 0.0438884i
\(345\) 0 0
\(346\) −20.9167 17.1536i −1.12449 0.922185i
\(347\) 4.55660 7.89227i 0.244611 0.423679i −0.717411 0.696650i \(-0.754673\pi\)
0.962022 + 0.272971i \(0.0880063\pi\)
\(348\) 0 0
\(349\) 11.2978 + 19.5684i 0.604760 + 1.04747i 0.992089 + 0.125533i \(0.0400642\pi\)
−0.387330 + 0.921941i \(0.626602\pi\)
\(350\) 0.162349 0.985476i 0.00867791 0.0526759i
\(351\) 0 0
\(352\) −24.9337 26.5283i −1.32897 1.41396i
\(353\) 5.76564 3.32879i 0.306874 0.177174i −0.338653 0.940911i \(-0.609971\pi\)
0.645527 + 0.763738i \(0.276638\pi\)
\(354\) 0 0
\(355\) −12.6635 7.31128i −0.672109 0.388042i
\(356\) −19.0267 21.6652i −1.00841 1.14826i
\(357\) 0 0
\(358\) 13.0373 + 34.6026i 0.689044 + 1.82881i
\(359\) −8.03334 −0.423984 −0.211992 0.977271i \(-0.567995\pi\)
−0.211992 + 0.977271i \(0.567995\pi\)
\(360\) 0 0
\(361\) 18.7198 0.985252
\(362\) −9.43248 25.0349i −0.495760 1.31581i
\(363\) 0 0
\(364\) 5.67516 + 6.46216i 0.297459 + 0.338709i
\(365\) −10.5080 6.06679i −0.550013 0.317550i
\(366\) 0 0
\(367\) −14.9220 + 8.61523i −0.778923 + 0.449712i −0.836049 0.548656i \(-0.815140\pi\)
0.0571254 + 0.998367i \(0.481807\pi\)
\(368\) −16.8335 12.8794i −0.877505 0.671385i
\(369\) 0 0
\(370\) −0.462626 + 2.80820i −0.0240508 + 0.145991i
\(371\) −6.29897 10.9101i −0.327026 0.566426i
\(372\) 0 0
\(373\) −0.260742 + 0.451618i −0.0135007 + 0.0233839i −0.872697 0.488262i \(-0.837631\pi\)
0.859196 + 0.511646i \(0.170964\pi\)
\(374\) −13.3397 10.9398i −0.689781 0.565685i
\(375\) 0 0
\(376\) 0.390160 + 11.5476i 0.0201209 + 0.595524i
\(377\) 1.49892i 0.0771985i
\(378\) 0 0
\(379\) 22.8440i 1.17342i 0.809797 + 0.586710i \(0.199577\pi\)
−0.809797 + 0.586710i \(0.800423\pi\)
\(380\) 0.495115 + 2.48004i 0.0253989 + 0.127224i
\(381\) 0 0
\(382\) 8.44249 10.2945i 0.431956 0.526715i
\(383\) −12.4781 + 21.6128i −0.637603 + 1.10436i 0.348354 + 0.937363i \(0.386741\pi\)
−0.985957 + 0.166998i \(0.946593\pi\)
\(384\) 0 0
\(385\) −7.68688 13.3141i −0.391760 0.678548i
\(386\) 1.83843 + 0.302865i 0.0935736 + 0.0154154i
\(387\) 0 0
\(388\) 14.6478 + 4.96082i 0.743627 + 0.251847i
\(389\) 22.0002 12.7018i 1.11545 0.644007i 0.175216 0.984530i \(-0.443938\pi\)
0.940236 + 0.340523i \(0.110604\pi\)
\(390\) 0 0
\(391\) −8.69818 5.02190i −0.439886 0.253968i
\(392\) 2.40034 1.49612i 0.121235 0.0755655i
\(393\) 0 0
\(394\) 4.71675 1.77714i 0.237627 0.0895312i
\(395\) −7.93985 −0.399497
\(396\) 0 0
\(397\) 5.32969 0.267489 0.133745 0.991016i \(-0.457300\pi\)
0.133745 + 0.991016i \(0.457300\pi\)
\(398\) 21.1398 7.96489i 1.05964 0.399244i
\(399\) 0 0
\(400\) 2.60837 1.08470i 0.130418 0.0542350i
\(401\) −20.2109 11.6688i −1.00928 0.582710i −0.0983016 0.995157i \(-0.531341\pi\)
−0.910982 + 0.412447i \(0.864674\pi\)
\(402\) 0 0
\(403\) −21.9206 + 12.6558i −1.09194 + 0.630433i
\(404\) −10.9638 + 32.3727i −0.545470 + 1.61060i
\(405\) 0 0
\(406\) −0.486397 0.0801298i −0.0241395 0.00397677i
\(407\) 2.71099 + 4.69557i 0.134379 + 0.232751i
\(408\) 0 0
\(409\) 15.5599 26.9506i 0.769389 1.33262i −0.168506 0.985701i \(-0.553894\pi\)
0.937895 0.346920i \(-0.112772\pi\)
\(410\) 11.3423 13.8305i 0.560155 0.683038i
\(411\) 0 0
\(412\) 22.7291 4.53763i 1.11978 0.223553i
\(413\) 5.32341i 0.261948i
\(414\) 0 0
\(415\) 15.4600i 0.758900i
\(416\) −7.02064 + 23.2905i −0.344215 + 1.14191i
\(417\) 0 0
\(418\) 3.72539 + 3.05517i 0.182215 + 0.149433i
\(419\) −13.4133 + 23.2325i −0.655283 + 1.13498i 0.326540 + 0.945183i \(0.394117\pi\)
−0.981823 + 0.189800i \(0.939216\pi\)
\(420\) 0 0
\(421\) 4.00100 + 6.92994i 0.194997 + 0.337744i 0.946899 0.321530i \(-0.104197\pi\)
−0.751903 + 0.659274i \(0.770864\pi\)
\(422\) 0.900918 5.46868i 0.0438560 0.266211i
\(423\) 0 0
\(424\) 16.7640 31.4425i 0.814131 1.52698i
\(425\) 1.15929 0.669318i 0.0562339 0.0324667i
\(426\) 0 0
\(427\) −6.06013 3.49882i −0.293270 0.169320i
\(428\) 2.49733 2.19320i 0.120713 0.106012i
\(429\) 0 0
\(430\) 10.1514 + 26.9430i 0.489544 + 1.29931i
\(431\) 23.2635 1.12056 0.560282 0.828302i \(-0.310693\pi\)
0.560282 + 0.828302i \(0.310693\pi\)
\(432\) 0 0
\(433\) −40.4077 −1.94187 −0.970936 0.239340i \(-0.923069\pi\)
−0.970936 + 0.239340i \(0.923069\pi\)
\(434\) 2.93496 + 7.78973i 0.140882 + 0.373919i
\(435\) 0 0
\(436\) 12.3453 10.8419i 0.591235 0.519231i
\(437\) 2.42914 + 1.40247i 0.116202 + 0.0670891i
\(438\) 0 0
\(439\) 4.54218 2.62243i 0.216786 0.125162i −0.387675 0.921796i \(-0.626722\pi\)
0.604461 + 0.796634i \(0.293388\pi\)
\(440\) 20.4578 38.3706i 0.975286 1.82924i
\(441\) 0 0
\(442\) −1.87374 + 11.3738i −0.0891245 + 0.540996i
\(443\) −4.84903 8.39876i −0.230384 0.399037i 0.727537 0.686068i \(-0.240665\pi\)
−0.957921 + 0.287031i \(0.907332\pi\)
\(444\) 0 0
\(445\) 17.2195 29.8250i 0.816280 1.41384i
\(446\) 2.84861 + 2.33613i 0.134885 + 0.110619i
\(447\) 0 0
\(448\) 7.18239 + 3.52325i 0.339336 + 0.166458i
\(449\) 38.7800i 1.83014i −0.403294 0.915071i \(-0.632135\pi\)
0.403294 0.915071i \(-0.367865\pi\)
\(450\) 0 0
\(451\) 34.0755i 1.60455i
\(452\) −17.8349 + 3.56055i −0.838883 + 0.167474i
\(453\) 0 0
\(454\) 2.80703 3.42282i 0.131740 0.160641i
\(455\) −5.13610 + 8.89599i −0.240784 + 0.417050i
\(456\) 0 0
\(457\) 11.3244 + 19.6145i 0.529735 + 0.917528i 0.999398 + 0.0346824i \(0.0110420\pi\)
−0.469663 + 0.882846i \(0.655625\pi\)
\(458\) 9.30966 + 1.53369i 0.435012 + 0.0716645i
\(459\) 0 0
\(460\) 8.12062 23.9777i 0.378626 1.11796i
\(461\) −32.0052 + 18.4782i −1.49063 + 0.860617i −0.999943 0.0107183i \(-0.996588\pi\)
−0.490689 + 0.871335i \(0.663255\pi\)
\(462\) 0 0
\(463\) 8.93748 + 5.16006i 0.415360 + 0.239808i 0.693090 0.720851i \(-0.256249\pi\)
−0.277730 + 0.960659i \(0.589582\pi\)
\(464\) −0.535370 1.28740i −0.0248540 0.0597661i
\(465\) 0 0
\(466\) 19.8770 7.48910i 0.920783 0.346926i
\(467\) 0.900019 0.0416479 0.0208239 0.999783i \(-0.493371\pi\)
0.0208239 + 0.999783i \(0.493371\pi\)
\(468\) 0 0
\(469\) 10.7713 0.497370
\(470\) −12.9140 + 4.86564i −0.595678 + 0.224435i
\(471\) 0 0
\(472\) 12.7780 7.96446i 0.588154 0.366594i
\(473\) 47.5027 + 27.4257i 2.18418 + 1.26103i
\(474\) 0 0
\(475\) −0.323756 + 0.186921i −0.0148549 + 0.00857651i
\(476\) 3.59060 + 1.21605i 0.164575 + 0.0557373i
\(477\) 0 0
\(478\) 3.07271 + 0.506203i 0.140543 + 0.0231532i
\(479\) −15.9460 27.6192i −0.728590 1.26195i −0.957479 0.288502i \(-0.906843\pi\)
0.228889 0.973452i \(-0.426491\pi\)
\(480\) 0 0
\(481\) 1.81139 3.13741i 0.0825921 0.143054i
\(482\) −16.6522 + 20.3053i −0.758488 + 0.924880i
\(483\) 0 0
\(484\) −11.9111 59.6628i −0.541412 2.71195i
\(485\) 18.4712i 0.838733i
\(486\) 0 0
\(487\) 7.65522i 0.346891i 0.984843 + 0.173446i \(0.0554901\pi\)
−0.984843 + 0.173446i \(0.944510\pi\)
\(488\) −0.668341 19.7810i −0.0302544 0.895444i
\(489\) 0 0
\(490\) 2.61216 + 2.14221i 0.118005 + 0.0967754i
\(491\) −1.59570 + 2.76383i −0.0720128 + 0.124730i −0.899783 0.436337i \(-0.856276\pi\)
0.827771 + 0.561067i \(0.189609\pi\)
\(492\) 0 0
\(493\) −0.330352 0.572187i −0.0148783 0.0257700i
\(494\) 0.523279 3.17636i 0.0235434 0.142911i
\(495\) 0 0
\(496\) −14.3069 + 18.6993i −0.642400 + 0.839622i
\(497\) 5.30126 3.06068i 0.237794 0.137290i
\(498\) 0 0
\(499\) −9.07585 5.23995i −0.406291 0.234572i 0.282904 0.959148i \(-0.408702\pi\)
−0.689195 + 0.724576i \(0.742036\pi\)
\(500\) −13.5364 15.4135i −0.605366 0.689314i
\(501\) 0 0
\(502\) 3.08230 + 8.18079i 0.137570 + 0.365127i
\(503\) 12.6421 0.563685 0.281843 0.959461i \(-0.409054\pi\)
0.281843 + 0.959461i \(0.409054\pi\)
\(504\) 0 0
\(505\) −40.8228 −1.81659
\(506\) −17.0042 45.1312i −0.755929 2.00633i
\(507\) 0 0
\(508\) −22.5188 25.6415i −0.999108 1.13766i
\(509\) 23.8125 + 13.7481i 1.05547 + 0.609376i 0.924176 0.381968i \(-0.124753\pi\)
0.131294 + 0.991343i \(0.458087\pi\)
\(510\) 0 0
\(511\) 4.39891 2.53971i 0.194596 0.112350i
\(512\) 2.28874 + 22.5114i 0.101149 + 0.994871i
\(513\) 0 0
\(514\) −1.85462 + 11.2577i −0.0818036 + 0.496558i
\(515\) 13.8415 + 23.9742i 0.609929 + 1.05643i
\(516\) 0 0
\(517\) −13.1453 + 22.7684i −0.578130 + 1.00135i
\(518\) −0.921250 0.755511i −0.0404774 0.0331953i
\(519\) 0 0
\(520\) −29.0376 + 0.981093i −1.27338 + 0.0430238i
\(521\) 16.7533i 0.733975i 0.930226 + 0.366988i \(0.119611\pi\)
−0.930226 + 0.366988i \(0.880389\pi\)
\(522\) 0 0
\(523\) 39.1120i 1.71025i 0.518424 + 0.855124i \(0.326519\pi\)
−0.518424 + 0.855124i \(0.673481\pi\)
\(524\) 4.37733 + 21.9262i 0.191224 + 0.957848i
\(525\) 0 0
\(526\) 0.135799 0.165590i 0.00592112 0.00722006i
\(527\) −5.57852 + 9.66228i −0.243004 + 0.420895i
\(528\) 0 0
\(529\) −2.53889 4.39749i −0.110387 0.191195i
\(530\) 41.9927 + 6.91794i 1.82405 + 0.300496i
\(531\) 0 0
\(532\) −1.00275 0.339605i −0.0434747 0.0147238i
\(533\) −19.7177 + 11.3840i −0.854069 + 0.493097i
\(534\) 0 0
\(535\) 3.43790 + 1.98487i 0.148633 + 0.0858135i
\(536\) 16.1151 + 25.8546i 0.696066 + 1.11675i
\(537\) 0 0
\(538\) −2.88587 + 1.08732i −0.124419 + 0.0468775i
\(539\) 6.43584 0.277211
\(540\) 0 0
\(541\) −11.1182 −0.478010 −0.239005 0.971018i \(-0.576821\pi\)
−0.239005 + 0.971018i \(0.576821\pi\)
\(542\) −4.08199 + 1.53798i −0.175337 + 0.0660620i
\(543\) 0 0
\(544\) 2.45306 + 10.4380i 0.105174 + 0.447526i
\(545\) 16.9950 + 9.81204i 0.727984 + 0.420302i
\(546\) 0 0
\(547\) 24.1315 13.9323i 1.03179 0.595703i 0.114291 0.993447i \(-0.463540\pi\)
0.917496 + 0.397745i \(0.130207\pi\)
\(548\) 3.18948 9.41753i 0.136248 0.402297i
\(549\) 0 0
\(550\) 6.34237 + 1.04485i 0.270440 + 0.0445526i
\(551\) 0.0922576 + 0.159795i 0.00393031 + 0.00680749i
\(552\) 0 0
\(553\) 1.66191 2.87851i 0.0706716 0.122407i
\(554\) −14.9063 + 18.1763i −0.633307 + 0.772237i
\(555\) 0 0
\(556\) −16.9030 + 3.37452i −0.716848 + 0.143111i
\(557\) 23.5098i 0.996142i −0.867136 0.498071i \(-0.834042\pi\)
0.867136 0.498071i \(-0.165958\pi\)
\(558\) 0 0
\(559\) 36.6497i 1.55012i
\(560\) −1.23394 + 9.47508i −0.0521433 + 0.400395i
\(561\) 0 0
\(562\) 11.2868 + 9.25627i 0.476107 + 0.390452i
\(563\) −16.5569 + 28.6774i −0.697790 + 1.20861i 0.271442 + 0.962455i \(0.412500\pi\)
−0.969231 + 0.246152i \(0.920834\pi\)
\(564\) 0 0
\(565\) −10.8610 18.8119i −0.456928 0.791422i
\(566\) 3.28244 19.9248i 0.137971 0.837501i
\(567\) 0 0
\(568\) 15.2780 + 8.14566i 0.641051 + 0.341784i
\(569\) −16.2900 + 9.40502i −0.682911 + 0.394279i −0.800951 0.598730i \(-0.795672\pi\)
0.118040 + 0.993009i \(0.462339\pi\)
\(570\) 0 0
\(571\) 18.0636 + 10.4290i 0.755937 + 0.436440i 0.827835 0.560972i \(-0.189572\pi\)
−0.0718982 + 0.997412i \(0.522906\pi\)
\(572\) −41.5894 + 36.5245i −1.73894 + 1.52716i
\(573\) 0 0
\(574\) 2.64002 + 7.00692i 0.110192 + 0.292463i
\(575\) 3.74220 0.156061
\(576\) 0 0
\(577\) −34.3394 −1.42957 −0.714783 0.699346i \(-0.753475\pi\)
−0.714783 + 0.699346i \(0.753475\pi\)
\(578\) −6.68509 17.7430i −0.278063 0.738013i
\(579\) 0 0
\(580\) 1.25128 1.09889i 0.0519565 0.0456290i
\(581\) −5.60486 3.23597i −0.232529 0.134251i
\(582\) 0 0
\(583\) 70.2159 40.5392i 2.90805 1.67896i
\(584\) 12.6775 + 6.75915i 0.524597 + 0.279696i
\(585\) 0 0
\(586\) 0.558148 3.38803i 0.0230569 0.139958i
\(587\) 18.1996 + 31.5226i 0.751177 + 1.30108i 0.947253 + 0.320487i \(0.103847\pi\)
−0.196076 + 0.980589i \(0.562820\pi\)
\(588\) 0 0
\(589\) 1.55791 2.69839i 0.0641928 0.111185i
\(590\) 13.9056 + 11.4039i 0.572484 + 0.469491i
\(591\) 0 0
\(592\) 0.435181 3.34165i 0.0178858 0.137341i
\(593\) 2.74882i 0.112880i 0.998406 + 0.0564402i \(0.0179750\pi\)
−0.998406 + 0.0564402i \(0.982025\pi\)
\(594\) 0 0
\(595\) 4.52784i 0.185623i
\(596\) 4.94267 0.986753i 0.202460 0.0404190i
\(597\) 0 0
\(598\) −20.4342 + 24.9170i −0.835619 + 1.01893i
\(599\) 13.1712 22.8132i 0.538162 0.932124i −0.460841 0.887483i \(-0.652452\pi\)
0.999003 0.0446413i \(-0.0142145\pi\)
\(600\) 0 0
\(601\) 10.6251 + 18.4032i 0.433406 + 0.750682i 0.997164 0.0752583i \(-0.0239781\pi\)
−0.563758 + 0.825940i \(0.690645\pi\)
\(602\) −11.8927 1.95923i −0.484712 0.0798522i
\(603\) 0 0
\(604\) 0.245240 0.724119i 0.00997869 0.0294640i
\(605\) 62.9312 36.3333i 2.55852 1.47716i
\(606\) 0 0
\(607\) −12.9081 7.45251i −0.523924 0.302488i 0.214614 0.976699i \(-0.431151\pi\)
−0.738539 + 0.674211i \(0.764484\pi\)
\(608\) −0.685066 2.91503i −0.0277831 0.118220i
\(609\) 0 0
\(610\) 22.1216 8.33480i 0.895676 0.337466i
\(611\) 17.5665 0.710663
\(612\) 0 0
\(613\) 0.497742 0.0201036 0.0100518 0.999949i \(-0.496800\pi\)
0.0100518 + 0.999949i \(0.496800\pi\)
\(614\) 11.7417 4.42394i 0.473855 0.178536i
\(615\) 0 0
\(616\) 9.62880 + 15.4482i 0.387955 + 0.622426i
\(617\) 13.3288 + 7.69541i 0.536599 + 0.309806i 0.743700 0.668514i \(-0.233069\pi\)
−0.207100 + 0.978320i \(0.566403\pi\)
\(618\) 0 0
\(619\) −6.09500 + 3.51895i −0.244979 + 0.141439i −0.617463 0.786600i \(-0.711839\pi\)
0.372484 + 0.928039i \(0.378506\pi\)
\(620\) −26.6353 9.02070i −1.06970 0.362280i
\(621\) 0 0
\(622\) 8.47767 + 1.39662i 0.339924 + 0.0559995i
\(623\) 7.20850 + 12.4855i 0.288802 + 0.500220i
\(624\) 0 0
\(625\) 14.0162 24.2768i 0.560648 0.971070i
\(626\) −18.5177 + 22.5800i −0.740116 + 0.902478i
\(627\) 0 0
\(628\) 3.44476 + 17.2549i 0.137461 + 0.688546i
\(629\) 1.59687i 0.0636713i
\(630\) 0 0
\(631\) 0.297508i 0.0118436i −0.999982 0.00592180i \(-0.998115\pi\)
0.999982 0.00592180i \(-0.00188498\pi\)
\(632\) 9.39582 0.317456i 0.373746 0.0126277i
\(633\) 0 0
\(634\) 26.8423 + 22.0132i 1.06604 + 0.874254i
\(635\) 20.3798 35.2988i 0.808747 1.40079i
\(636\) 0 0
\(637\) −2.15010 3.72408i −0.0851901 0.147554i
\(638\) 0.515703 3.13038i 0.0204169 0.123933i
\(639\) 0 0
\(640\) −24.5895 + 11.2140i −0.971985 + 0.443272i
\(641\) −8.18111 + 4.72337i −0.323134 + 0.186562i −0.652789 0.757540i \(-0.726401\pi\)
0.329654 + 0.944102i \(0.393068\pi\)
\(642\) 0 0
\(643\) 29.2594 + 16.8929i 1.15388 + 0.666193i 0.949830 0.312768i \(-0.101256\pi\)
0.204050 + 0.978960i \(0.434590\pi\)
\(644\) 6.99312 + 7.96288i 0.275567 + 0.313781i
\(645\) 0 0
\(646\) −0.500296 1.32785i −0.0196839 0.0522434i
\(647\) −8.81904 −0.346712 −0.173356 0.984859i \(-0.555461\pi\)
−0.173356 + 0.984859i \(0.555461\pi\)
\(648\) 0 0
\(649\) 34.2606 1.34485
\(650\) −1.51427 4.01906i −0.0593947 0.157641i
\(651\) 0 0
\(652\) 14.2128 + 16.1837i 0.556615 + 0.633803i
\(653\) −26.1332 15.0880i −1.02267 0.590440i −0.107795 0.994173i \(-0.534379\pi\)
−0.914877 + 0.403733i \(0.867712\pi\)
\(654\) 0 0
\(655\) −23.1273 + 13.3525i −0.903657 + 0.521727i
\(656\) −12.8692 + 16.8201i −0.502458 + 0.656716i
\(657\) 0 0
\(658\) 0.939071 5.70028i 0.0366088 0.222220i
\(659\) −4.08576 7.07674i −0.159158 0.275671i 0.775407 0.631462i \(-0.217545\pi\)
−0.934565 + 0.355791i \(0.884211\pi\)
\(660\) 0 0
\(661\) −22.1468 + 38.3593i −0.861409 + 1.49200i 0.00916009 + 0.999958i \(0.497084\pi\)
−0.870569 + 0.492046i \(0.836249\pi\)
\(662\) 32.8128 + 26.9096i 1.27531 + 1.04587i
\(663\) 0 0
\(664\) −0.618131 18.2950i −0.0239881 0.709982i
\(665\) 1.26449i 0.0490349i
\(666\) 0 0
\(667\) 1.84702i 0.0715170i
\(668\) −3.07339 15.3947i −0.118913 0.595639i
\(669\) 0 0
\(670\) −23.0743 + 28.1362i −0.891439 + 1.08700i
\(671\) 22.5178 39.0020i 0.869291 1.50566i
\(672\) 0 0
\(673\) 6.17994 + 10.7040i 0.238219 + 0.412608i 0.960203 0.279302i \(-0.0901030\pi\)
−0.721984 + 0.691910i \(0.756770\pi\)
\(674\) 14.7188 + 2.42479i 0.566946 + 0.0933995i
\(675\) 0 0
\(676\) 10.4030 + 3.52325i 0.400117 + 0.135509i
\(677\) 2.57177 1.48481i 0.0988412 0.0570660i −0.449765 0.893147i \(-0.648492\pi\)
0.548606 + 0.836081i \(0.315159\pi\)
\(678\) 0 0
\(679\) −6.69654 3.86625i −0.256990 0.148373i
\(680\) −10.8683 + 6.77420i −0.416782 + 0.259779i
\(681\) 0 0
\(682\) −50.1335 + 18.8889i −1.91971 + 0.723294i
\(683\) 13.3131 0.509413 0.254707 0.967018i \(-0.418021\pi\)
0.254707 + 0.967018i \(0.418021\pi\)
\(684\) 0 0
\(685\) 11.8757 0.453749
\(686\) −1.32340 + 0.498620i −0.0505275 + 0.0190374i
\(687\) 0 0
\(688\) −13.0902 31.4779i −0.499058 1.20008i
\(689\) −46.9158 27.0868i −1.78735 1.03193i
\(690\) 0 0
\(691\) 35.4607 20.4733i 1.34899 0.778840i 0.360884 0.932611i \(-0.382475\pi\)
0.988107 + 0.153771i \(0.0491417\pi\)
\(692\) −12.2716 + 36.2342i −0.466496 + 1.37742i
\(693\) 0 0
\(694\) −12.7166 2.09495i −0.482716 0.0795233i
\(695\) −10.2936 17.8290i −0.390457 0.676292i
\(696\) 0 0
\(697\) −5.01792 + 8.69129i −0.190067 + 0.329206i
\(698\) 20.2635 24.7087i 0.766984 0.935239i
\(699\) 0 0
\(700\) −1.38513 + 0.276526i −0.0523529 + 0.0104517i
\(701\) 18.8087i 0.710396i −0.934791 0.355198i \(-0.884413\pi\)
0.934791 0.355198i \(-0.115587\pi\)
\(702\) 0 0
\(703\) 0.445958i 0.0168196i
\(704\) −22.6751 + 46.2247i −0.854598 + 1.74216i
\(705\) 0 0
\(706\) −7.28018 5.97043i −0.273993 0.224700i
\(707\) 8.54473 14.7999i 0.321358 0.556608i
\(708\) 0 0
\(709\) 19.3884 + 33.5818i 0.728148 + 1.26119i 0.957665 + 0.287885i \(0.0929520\pi\)
−0.229517 + 0.973305i \(0.573715\pi\)
\(710\) −3.36145 + 20.4044i −0.126153 + 0.765763i
\(711\) 0 0
\(712\) −19.1846 + 35.9826i −0.718973 + 1.34851i
\(713\) −27.0112 + 15.5949i −1.01158 + 0.584035i
\(714\) 0 0
\(715\) −57.2532 33.0551i −2.14115 1.23619i
\(716\) 39.2923 34.5071i 1.46842 1.28959i
\(717\) 0 0
\(718\) 4.00558 + 10.6313i 0.149487 + 0.396757i
\(719\) 27.9873 1.04375 0.521875 0.853022i \(-0.325233\pi\)
0.521875 + 0.853022i \(0.325233\pi\)
\(720\) 0 0
\(721\) −11.5888 −0.431589
\(722\) −9.33406 24.7737i −0.347378 0.921982i
\(723\) 0 0
\(724\) −28.4279 + 24.9658i −1.05652 + 0.927848i
\(725\) 0.213190 + 0.123085i 0.00791769 + 0.00457128i
\(726\) 0 0
\(727\) −11.9395 + 6.89330i −0.442813 + 0.255658i −0.704790 0.709416i \(-0.748959\pi\)
0.261977 + 0.965074i \(0.415626\pi\)
\(728\) 5.72225 10.7326i 0.212081 0.397778i
\(729\) 0 0
\(730\) −2.78928 + 16.9313i −0.103236 + 0.626654i
\(731\) −8.07734 13.9904i −0.298751 0.517452i
\(732\) 0 0
\(733\) 20.9012 36.2020i 0.772005 1.33715i −0.164458 0.986384i \(-0.552588\pi\)
0.936463 0.350767i \(-0.114079\pi\)
\(734\) 18.8418 + 15.4520i 0.695463 + 0.570345i
\(735\) 0 0
\(736\) −8.65105 + 28.6993i −0.318882 + 1.05787i
\(737\) 69.3221i 2.55351i
\(738\) 0 0
\(739\) 47.3413i 1.74148i −0.491746 0.870739i \(-0.663641\pi\)
0.491746 0.870739i \(-0.336359\pi\)
\(740\) 3.94703 0.787984i 0.145096 0.0289669i
\(741\) 0 0
\(742\) −11.2976 + 13.7760i −0.414749 + 0.505734i
\(743\) 1.10160 1.90802i 0.0404136 0.0699984i −0.845111 0.534591i \(-0.820466\pi\)
0.885525 + 0.464592i \(0.153799\pi\)
\(744\) 0 0
\(745\) 3.00998 + 5.21343i 0.110277 + 0.191005i
\(746\) 0.727681 + 0.119879i 0.0266423 + 0.00438909i
\(747\) 0 0
\(748\) −7.82628 + 23.1086i −0.286157 + 0.844933i
\(749\) −1.43919 + 0.830918i −0.0525869 + 0.0303611i
\(750\) 0 0
\(751\) −9.02644 5.21142i −0.329379 0.190167i 0.326186 0.945306i \(-0.394236\pi\)
−0.655566 + 0.755138i \(0.727570\pi\)
\(752\) 15.0876 6.27421i 0.550186 0.228797i
\(753\) 0 0
\(754\) −1.98367 + 0.747393i −0.0722411 + 0.0272185i
\(755\) 0.913132 0.0332323
\(756\) 0 0
\(757\) 14.0656 0.511224 0.255612 0.966779i \(-0.417723\pi\)
0.255612 + 0.966779i \(0.417723\pi\)
\(758\) 30.2317 11.3905i 1.09807 0.413721i
\(759\) 0 0
\(760\) 3.03521 1.89183i 0.110099 0.0686239i
\(761\) 23.2533 + 13.4253i 0.842931 + 0.486667i 0.858260 0.513216i \(-0.171546\pi\)
−0.0153283 + 0.999883i \(0.504879\pi\)
\(762\) 0 0
\(763\) −7.11451 + 4.10757i −0.257563 + 0.148704i
\(764\) −17.8334 6.03970i −0.645188 0.218509i
\(765\) 0 0
\(766\) 34.8241 + 5.73697i 1.25825 + 0.207285i
\(767\) −11.4459 19.8248i −0.413286 0.715833i
\(768\) 0 0
\(769\) 18.9397 32.8045i 0.682983 1.18296i −0.291083 0.956698i \(-0.594016\pi\)
0.974066 0.226263i \(-0.0726510\pi\)
\(770\) −13.7870 + 16.8114i −0.496848 + 0.605842i
\(771\) 0 0
\(772\) −0.515866 2.58399i −0.0185664 0.0929997i
\(773\) 26.0697i 0.937662i 0.883288 + 0.468831i \(0.155325\pi\)
−0.883288 + 0.468831i \(0.844675\pi\)
\(774\) 0 0
\(775\) 4.15698i 0.149323i
\(776\) −0.738528 21.8583i −0.0265116 0.784669i
\(777\) 0 0
\(778\) −27.7792 22.7816i −0.995934 0.816759i
\(779\) 1.40136 2.42722i 0.0502088 0.0869642i
\(780\) 0 0
\(781\) 19.6981 + 34.1181i 0.704853 + 1.22084i
\(782\) −2.30888 + 14.0152i −0.0825653 + 0.501181i
\(783\) 0 0
\(784\) −3.17682 2.43060i −0.113458 0.0868073i
\(785\) −18.2001 + 10.5079i −0.649591 + 0.375041i
\(786\) 0 0
\(787\) 43.3071 + 25.0034i 1.54373 + 0.891275i 0.998598 + 0.0529261i \(0.0168548\pi\)
0.545135 + 0.838349i \(0.316479\pi\)
\(788\) −4.70373 5.35601i −0.167563 0.190800i
\(789\) 0 0
\(790\) 3.95896 +