Properties

Label 720.2.u.a.179.1
Level $720$
Weight $2$
Character 720.179
Analytic conductor $5.749$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.u (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.74922894553\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(48\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 179.1
Character \(\chi\) \(=\) 720.179
Dual form 720.2.u.a.539.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.41373 + 0.0371259i) q^{2} +(1.99724 - 0.104972i) q^{4} +(-1.81012 - 1.31281i) q^{5} +1.40695i q^{7} +(-2.81966 + 0.222551i) q^{8} +O(q^{10})\) \(q+(-1.41373 + 0.0371259i) q^{2} +(1.99724 - 0.104972i) q^{4} +(-1.81012 - 1.31281i) q^{5} +1.40695i q^{7} +(-2.81966 + 0.222551i) q^{8} +(2.60775 + 1.78875i) q^{10} +(0.176123 - 0.176123i) q^{11} +(-1.72742 + 1.72742i) q^{13} +(-0.0522343 - 1.98904i) q^{14} +(3.97796 - 0.419308i) q^{16} +3.15721 q^{17} +(3.47385 - 3.47385i) q^{19} +(-3.75305 - 2.43199i) q^{20} +(-0.242451 + 0.255528i) q^{22} +1.97613 q^{23} +(1.55305 + 4.75269i) q^{25} +(2.37796 - 2.50623i) q^{26} +(0.147690 + 2.81002i) q^{28} +(2.62046 - 2.62046i) q^{29} -5.95492i q^{31} +(-5.60818 + 0.740472i) q^{32} +(-4.46342 + 0.117214i) q^{34} +(1.84706 - 2.54675i) q^{35} +(-5.72522 - 5.72522i) q^{37} +(-4.78211 + 5.04005i) q^{38} +(5.39608 + 3.29884i) q^{40} +0.159470 q^{41} +(6.63058 - 6.63058i) q^{43} +(0.333273 - 0.370248i) q^{44} +(-2.79371 + 0.0733658i) q^{46} +1.15223i q^{47} +5.02049 q^{49} +(-2.37204 - 6.66134i) q^{50} +(-3.26874 + 3.63141i) q^{52} +(5.35087 - 5.35087i) q^{53} +(-0.550020 + 0.0875872i) q^{55} +(-0.313118 - 3.96712i) q^{56} +(-3.60733 + 3.80190i) q^{58} +(-4.48547 + 4.48547i) q^{59} +(6.80718 + 6.80718i) q^{61} +(0.221082 + 8.41862i) q^{62} +(7.90094 - 1.25503i) q^{64} +(5.39461 - 0.859057i) q^{65} +(-9.97278 - 9.97278i) q^{67} +(6.30571 - 0.331417i) q^{68} +(-2.51669 + 3.66897i) q^{70} +0.0951463i q^{71} +7.99125 q^{73} +(8.30645 + 7.88134i) q^{74} +(6.57347 - 7.30278i) q^{76} +(0.247796 + 0.247796i) q^{77} -5.66620i q^{79} +(-7.75105 - 4.46332i) q^{80} +(-0.225446 + 0.00592045i) q^{82} +(12.2672 - 12.2672i) q^{83} +(-5.71492 - 4.14481i) q^{85} +(-9.12765 + 9.61998i) q^{86} +(-0.457410 + 0.535803i) q^{88} +10.9299 q^{89} +(-2.43039 - 2.43039i) q^{91} +(3.94682 - 0.207438i) q^{92} +(-0.0427774 - 1.62893i) q^{94} +(-10.8486 + 1.72757i) q^{95} -10.4415i q^{97} +(-7.09760 + 0.186390i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96q + O(q^{10}) \) \( 96q - 8q^{16} - 16q^{19} + 72q^{34} + 8q^{40} + 8q^{46} - 96q^{49} + 64q^{55} - 32q^{61} + 48q^{64} + 24q^{70} + 40q^{76} - 88q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41373 + 0.0371259i −0.999655 + 0.0262520i
\(3\) 0 0
\(4\) 1.99724 0.104972i 0.998622 0.0524859i
\(5\) −1.81012 1.31281i −0.809509 0.587107i
\(6\) 0 0
\(7\) 1.40695i 0.531777i 0.964004 + 0.265889i \(0.0856653\pi\)
−0.964004 + 0.265889i \(0.914335\pi\)
\(8\) −2.81966 + 0.222551i −0.996900 + 0.0786836i
\(9\) 0 0
\(10\) 2.60775 + 1.78875i 0.824643 + 0.565653i
\(11\) 0.176123 0.176123i 0.0531031 0.0531031i −0.680057 0.733160i \(-0.738045\pi\)
0.733160 + 0.680057i \(0.238045\pi\)
\(12\) 0 0
\(13\) −1.72742 + 1.72742i −0.479100 + 0.479100i −0.904844 0.425744i \(-0.860012\pi\)
0.425744 + 0.904844i \(0.360012\pi\)
\(14\) −0.0522343 1.98904i −0.0139602 0.531594i
\(15\) 0 0
\(16\) 3.97796 0.419308i 0.994490 0.104827i
\(17\) 3.15721 0.765735 0.382867 0.923803i \(-0.374937\pi\)
0.382867 + 0.923803i \(0.374937\pi\)
\(18\) 0 0
\(19\) 3.47385 3.47385i 0.796956 0.796956i −0.185658 0.982614i \(-0.559442\pi\)
0.982614 + 0.185658i \(0.0594417\pi\)
\(20\) −3.75305 2.43199i −0.839208 0.543810i
\(21\) 0 0
\(22\) −0.242451 + 0.255528i −0.0516907 + 0.0544788i
\(23\) 1.97613 0.412052 0.206026 0.978546i \(-0.433947\pi\)
0.206026 + 0.978546i \(0.433947\pi\)
\(24\) 0 0
\(25\) 1.55305 + 4.75269i 0.310611 + 0.950537i
\(26\) 2.37796 2.50623i 0.466357 0.491512i
\(27\) 0 0
\(28\) 0.147690 + 2.81002i 0.0279108 + 0.531044i
\(29\) 2.62046 2.62046i 0.486607 0.486607i −0.420627 0.907234i \(-0.638190\pi\)
0.907234 + 0.420627i \(0.138190\pi\)
\(30\) 0 0
\(31\) 5.95492i 1.06953i −0.844999 0.534767i \(-0.820399\pi\)
0.844999 0.534767i \(-0.179601\pi\)
\(32\) −5.60818 + 0.740472i −0.991396 + 0.130898i
\(33\) 0 0
\(34\) −4.46342 + 0.117214i −0.765471 + 0.0201021i
\(35\) 1.84706 2.54675i 0.312210 0.430479i
\(36\) 0 0
\(37\) −5.72522 5.72522i −0.941221 0.941221i 0.0571453 0.998366i \(-0.481800\pi\)
−0.998366 + 0.0571453i \(0.981800\pi\)
\(38\) −4.78211 + 5.04005i −0.775760 + 0.817603i
\(39\) 0 0
\(40\) 5.39608 + 3.29884i 0.853195 + 0.521592i
\(41\) 0.159470 0.0249050 0.0124525 0.999922i \(-0.496036\pi\)
0.0124525 + 0.999922i \(0.496036\pi\)
\(42\) 0 0
\(43\) 6.63058 6.63058i 1.01115 1.01115i 0.0112162 0.999937i \(-0.496430\pi\)
0.999937 0.0112162i \(-0.00357031\pi\)
\(44\) 0.333273 0.370248i 0.0502427 0.0558170i
\(45\) 0 0
\(46\) −2.79371 + 0.0733658i −0.411910 + 0.0108172i
\(47\) 1.15223i 0.168069i 0.996463 + 0.0840347i \(0.0267807\pi\)
−0.996463 + 0.0840347i \(0.973219\pi\)
\(48\) 0 0
\(49\) 5.02049 0.717213
\(50\) −2.37204 6.66134i −0.335457 0.942055i
\(51\) 0 0
\(52\) −3.26874 + 3.63141i −0.453293 + 0.503585i
\(53\) 5.35087 5.35087i 0.734999 0.734999i −0.236606 0.971606i \(-0.576035\pi\)
0.971606 + 0.236606i \(0.0760352\pi\)
\(54\) 0 0
\(55\) −0.550020 + 0.0875872i −0.0741646 + 0.0118103i
\(56\) −0.313118 3.96712i −0.0418421 0.530128i
\(57\) 0 0
\(58\) −3.60733 + 3.80190i −0.473665 + 0.499214i
\(59\) −4.48547 + 4.48547i −0.583959 + 0.583959i −0.935989 0.352030i \(-0.885492\pi\)
0.352030 + 0.935989i \(0.385492\pi\)
\(60\) 0 0
\(61\) 6.80718 + 6.80718i 0.871570 + 0.871570i 0.992643 0.121074i \(-0.0386338\pi\)
−0.121074 + 0.992643i \(0.538634\pi\)
\(62\) 0.221082 + 8.41862i 0.0280774 + 1.06917i
\(63\) 0 0
\(64\) 7.90094 1.25503i 0.987618 0.156879i
\(65\) 5.39461 0.859057i 0.669118 0.106553i
\(66\) 0 0
\(67\) −9.97278 9.97278i −1.21837 1.21837i −0.968203 0.250166i \(-0.919515\pi\)
−0.250166 0.968203i \(-0.580485\pi\)
\(68\) 6.30571 0.331417i 0.764679 0.0401903i
\(69\) 0 0
\(70\) −2.51669 + 3.66897i −0.300802 + 0.438526i
\(71\) 0.0951463i 0.0112918i 0.999984 + 0.00564589i \(0.00179715\pi\)
−0.999984 + 0.00564589i \(0.998203\pi\)
\(72\) 0 0
\(73\) 7.99125 0.935305 0.467653 0.883912i \(-0.345100\pi\)
0.467653 + 0.883912i \(0.345100\pi\)
\(74\) 8.30645 + 7.88134i 0.965605 + 0.916187i
\(75\) 0 0
\(76\) 6.57347 7.30278i 0.754029 0.837687i
\(77\) 0.247796 + 0.247796i 0.0282390 + 0.0282390i
\(78\) 0 0
\(79\) 5.66620i 0.637497i −0.947839 0.318748i \(-0.896737\pi\)
0.947839 0.318748i \(-0.103263\pi\)
\(80\) −7.75105 4.46332i −0.866594 0.499014i
\(81\) 0 0
\(82\) −0.225446 + 0.00592045i −0.0248964 + 0.000653804i
\(83\) 12.2672 12.2672i 1.34650 1.34650i 0.457068 0.889432i \(-0.348900\pi\)
0.889432 0.457068i \(-0.151100\pi\)
\(84\) 0 0
\(85\) −5.71492 4.14481i −0.619870 0.449568i
\(86\) −9.12765 + 9.61998i −0.984260 + 1.03735i
\(87\) 0 0
\(88\) −0.457410 + 0.535803i −0.0487601 + 0.0571168i
\(89\) 10.9299 1.15857 0.579284 0.815126i \(-0.303332\pi\)
0.579284 + 0.815126i \(0.303332\pi\)
\(90\) 0 0
\(91\) −2.43039 2.43039i −0.254774 0.254774i
\(92\) 3.94682 0.207438i 0.411484 0.0216269i
\(93\) 0 0
\(94\) −0.0427774 1.62893i −0.00441216 0.168011i
\(95\) −10.8486 + 1.72757i −1.11304 + 0.177245i
\(96\) 0 0
\(97\) 10.4415i 1.06017i −0.847944 0.530086i \(-0.822160\pi\)
0.847944 0.530086i \(-0.177840\pi\)
\(98\) −7.09760 + 0.186390i −0.716966 + 0.0188283i
\(99\) 0 0
\(100\) 3.60072 + 9.32924i 0.360072 + 0.932924i
\(101\) 4.54532 + 4.54532i 0.452276 + 0.452276i 0.896109 0.443833i \(-0.146382\pi\)
−0.443833 + 0.896109i \(0.646382\pi\)
\(102\) 0 0
\(103\) 7.65680i 0.754447i 0.926122 + 0.377224i \(0.123121\pi\)
−0.926122 + 0.377224i \(0.876879\pi\)
\(104\) 4.48629 5.25517i 0.439917 0.515312i
\(105\) 0 0
\(106\) −7.36601 + 7.76333i −0.715451 + 0.754041i
\(107\) 4.25185 + 4.25185i 0.411042 + 0.411042i 0.882102 0.471059i \(-0.156128\pi\)
−0.471059 + 0.882102i \(0.656128\pi\)
\(108\) 0 0
\(109\) 0.180834 + 0.180834i 0.0173208 + 0.0173208i 0.715714 0.698393i \(-0.246101\pi\)
−0.698393 + 0.715714i \(0.746101\pi\)
\(110\) 0.774325 0.144244i 0.0738290 0.0137532i
\(111\) 0 0
\(112\) 0.589946 + 5.59679i 0.0557446 + 0.528847i
\(113\) 6.88868 0.648032 0.324016 0.946052i \(-0.394967\pi\)
0.324016 + 0.946052i \(0.394967\pi\)
\(114\) 0 0
\(115\) −3.57703 2.59429i −0.333560 0.241919i
\(116\) 4.95862 5.50877i 0.460396 0.511476i
\(117\) 0 0
\(118\) 6.17471 6.50776i 0.568428 0.599088i
\(119\) 4.44203i 0.407200i
\(120\) 0 0
\(121\) 10.9380i 0.994360i
\(122\) −9.87621 9.37076i −0.894150 0.848389i
\(123\) 0 0
\(124\) −0.625098 11.8934i −0.0561355 1.06806i
\(125\) 3.42817 10.6418i 0.306625 0.951831i
\(126\) 0 0
\(127\) 3.18115 0.282281 0.141141 0.989990i \(-0.454923\pi\)
0.141141 + 0.989990i \(0.454923\pi\)
\(128\) −11.1232 + 2.06760i −0.983159 + 0.182752i
\(129\) 0 0
\(130\) −7.59460 + 1.41475i −0.666091 + 0.124082i
\(131\) −8.49459 8.49459i −0.742175 0.742175i 0.230821 0.972996i \(-0.425859\pi\)
−0.972996 + 0.230821i \(0.925859\pi\)
\(132\) 0 0
\(133\) 4.88754 + 4.88754i 0.423803 + 0.423803i
\(134\) 14.4690 + 13.7285i 1.24993 + 1.18596i
\(135\) 0 0
\(136\) −8.90224 + 0.702639i −0.763361 + 0.0602508i
\(137\) 15.1013i 1.29019i 0.764102 + 0.645096i \(0.223182\pi\)
−0.764102 + 0.645096i \(0.776818\pi\)
\(138\) 0 0
\(139\) −11.6635 11.6635i −0.989286 0.989286i 0.0106573 0.999943i \(-0.496608\pi\)
−0.999943 + 0.0106573i \(0.996608\pi\)
\(140\) 3.42169 5.28036i 0.289186 0.446272i
\(141\) 0 0
\(142\) −0.00353239 0.134511i −0.000296432 0.0112879i
\(143\) 0.608476i 0.0508833i
\(144\) 0 0
\(145\) −8.18351 + 1.30317i −0.679604 + 0.108223i
\(146\) −11.2974 + 0.296682i −0.934983 + 0.0245536i
\(147\) 0 0
\(148\) −12.0356 10.8337i −0.989324 0.890522i
\(149\) 11.1281 + 11.1281i 0.911646 + 0.911646i 0.996402 0.0847561i \(-0.0270111\pi\)
−0.0847561 + 0.996402i \(0.527011\pi\)
\(150\) 0 0
\(151\) −21.8766 −1.78030 −0.890148 0.455672i \(-0.849399\pi\)
−0.890148 + 0.455672i \(0.849399\pi\)
\(152\) −9.02197 + 10.5682i −0.731778 + 0.857193i
\(153\) 0 0
\(154\) −0.359516 0.341116i −0.0289706 0.0274879i
\(155\) −7.81768 + 10.7791i −0.627931 + 0.865798i
\(156\) 0 0
\(157\) −15.3928 + 15.3928i −1.22848 + 1.22848i −0.263935 + 0.964541i \(0.585020\pi\)
−0.964541 + 0.263935i \(0.914980\pi\)
\(158\) 0.210363 + 8.01045i 0.0167356 + 0.637277i
\(159\) 0 0
\(160\) 11.1236 + 6.02214i 0.879395 + 0.476092i
\(161\) 2.78032i 0.219120i
\(162\) 0 0
\(163\) 4.90113 + 4.90113i 0.383886 + 0.383886i 0.872500 0.488614i \(-0.162497\pi\)
−0.488614 + 0.872500i \(0.662497\pi\)
\(164\) 0.318499 0.0167398i 0.0248706 0.00130716i
\(165\) 0 0
\(166\) −16.8870 + 17.7979i −1.31069 + 1.38138i
\(167\) −17.4380 −1.34939 −0.674695 0.738097i \(-0.735725\pi\)
−0.674695 + 0.738097i \(0.735725\pi\)
\(168\) 0 0
\(169\) 7.03205i 0.540927i
\(170\) 8.23320 + 5.64746i 0.631458 + 0.433141i
\(171\) 0 0
\(172\) 12.5469 13.9389i 0.956688 1.06283i
\(173\) −17.4288 17.4288i −1.32509 1.32509i −0.909598 0.415490i \(-0.863610\pi\)
−0.415490 0.909598i \(-0.636390\pi\)
\(174\) 0 0
\(175\) −6.68679 + 2.18507i −0.505474 + 0.165176i
\(176\) 0.626761 0.774460i 0.0472439 0.0583771i
\(177\) 0 0
\(178\) −15.4519 + 0.405783i −1.15817 + 0.0304147i
\(179\) 12.4635 + 12.4635i 0.931565 + 0.931565i 0.997804 0.0662383i \(-0.0210998\pi\)
−0.0662383 + 0.997804i \(0.521100\pi\)
\(180\) 0 0
\(181\) −7.07994 + 7.07994i −0.526248 + 0.526248i −0.919451 0.393203i \(-0.871367\pi\)
0.393203 + 0.919451i \(0.371367\pi\)
\(182\) 3.52614 + 3.34568i 0.261375 + 0.247998i
\(183\) 0 0
\(184\) −5.57202 + 0.439790i −0.410775 + 0.0324218i
\(185\) 2.84719 + 17.8795i 0.209330 + 1.31452i
\(186\) 0 0
\(187\) 0.556057 0.556057i 0.0406629 0.0406629i
\(188\) 0.120951 + 2.30128i 0.00882127 + 0.167838i
\(189\) 0 0
\(190\) 15.2728 2.84508i 1.10801 0.206403i
\(191\) −12.6011 −0.911781 −0.455891 0.890036i \(-0.650679\pi\)
−0.455891 + 0.890036i \(0.650679\pi\)
\(192\) 0 0
\(193\) 5.15723i 0.371226i 0.982623 + 0.185613i \(0.0594270\pi\)
−0.982623 + 0.185613i \(0.940573\pi\)
\(194\) 0.387649 + 14.7614i 0.0278316 + 1.05981i
\(195\) 0 0
\(196\) 10.0271 0.527010i 0.716225 0.0376436i
\(197\) 3.59790 3.59790i 0.256340 0.256340i −0.567224 0.823564i \(-0.691983\pi\)
0.823564 + 0.567224i \(0.191983\pi\)
\(198\) 0 0
\(199\) 7.58554 0.537725 0.268862 0.963179i \(-0.413352\pi\)
0.268862 + 0.963179i \(0.413352\pi\)
\(200\) −5.43680 13.0553i −0.384439 0.923150i
\(201\) 0 0
\(202\) −6.59458 6.25708i −0.463993 0.440247i
\(203\) 3.68686 + 3.68686i 0.258767 + 0.258767i
\(204\) 0 0
\(205\) −0.288659 0.209353i −0.0201608 0.0146219i
\(206\) −0.284266 10.8246i −0.0198057 0.754187i
\(207\) 0 0
\(208\) −6.14728 + 7.59593i −0.426237 + 0.526683i
\(209\) 1.22365i 0.0846417i
\(210\) 0 0
\(211\) 0.605008 0.605008i 0.0416505 0.0416505i −0.685975 0.727625i \(-0.740624\pi\)
0.727625 + 0.685975i \(0.240624\pi\)
\(212\) 10.1253 11.2487i 0.695409 0.772563i
\(213\) 0 0
\(214\) −6.16881 5.85310i −0.421691 0.400110i
\(215\) −20.7068 + 3.29743i −1.41219 + 0.224883i
\(216\) 0 0
\(217\) 8.37827 0.568754
\(218\) −0.262363 0.248936i −0.0177695 0.0168601i
\(219\) 0 0
\(220\) −1.08933 + 0.232669i −0.0734425 + 0.0156866i
\(221\) −5.45382 + 5.45382i −0.366863 + 0.366863i
\(222\) 0 0
\(223\) 25.2652 1.69188 0.845940 0.533278i \(-0.179040\pi\)
0.845940 + 0.533278i \(0.179040\pi\)
\(224\) −1.04181 7.89043i −0.0696087 0.527202i
\(225\) 0 0
\(226\) −9.73870 + 0.255748i −0.647809 + 0.0170121i
\(227\) 6.61823 6.61823i 0.439267 0.439267i −0.452498 0.891765i \(-0.649467\pi\)
0.891765 + 0.452498i \(0.149467\pi\)
\(228\) 0 0
\(229\) −0.0446899 + 0.0446899i −0.00295319 + 0.00295319i −0.708582 0.705629i \(-0.750665\pi\)
0.705629 + 0.708582i \(0.250665\pi\)
\(230\) 5.15326 + 3.53482i 0.339796 + 0.233079i
\(231\) 0 0
\(232\) −6.80562 + 7.97199i −0.446811 + 0.523387i
\(233\) 13.5011i 0.884488i 0.896895 + 0.442244i \(0.145817\pi\)
−0.896895 + 0.442244i \(0.854183\pi\)
\(234\) 0 0
\(235\) 1.51265 2.08566i 0.0986747 0.136054i
\(236\) −8.48774 + 9.42943i −0.552505 + 0.613804i
\(237\) 0 0
\(238\) −0.164914 6.27982i −0.0106898 0.407060i
\(239\) 5.58106 0.361009 0.180504 0.983574i \(-0.442227\pi\)
0.180504 + 0.983574i \(0.442227\pi\)
\(240\) 0 0
\(241\) 15.7677 1.01569 0.507845 0.861449i \(-0.330442\pi\)
0.507845 + 0.861449i \(0.330442\pi\)
\(242\) −0.406082 15.4633i −0.0261039 0.994017i
\(243\) 0 0
\(244\) 14.3101 + 12.8810i 0.916113 + 0.824623i
\(245\) −9.08768 6.59096i −0.580591 0.421081i
\(246\) 0 0
\(247\) 12.0016i 0.763643i
\(248\) 1.32527 + 16.7908i 0.0841548 + 1.06622i
\(249\) 0 0
\(250\) −4.45140 + 15.1718i −0.281532 + 0.959552i
\(251\) 10.5401 10.5401i 0.665287 0.665287i −0.291334 0.956621i \(-0.594099\pi\)
0.956621 + 0.291334i \(0.0940992\pi\)
\(252\) 0 0
\(253\) 0.348043 0.348043i 0.0218812 0.0218812i
\(254\) −4.49727 + 0.118103i −0.282184 + 0.00741044i
\(255\) 0 0
\(256\) 15.6484 3.33598i 0.978023 0.208499i
\(257\) −20.0698 −1.25192 −0.625959 0.779856i \(-0.715292\pi\)
−0.625959 + 0.779856i \(0.715292\pi\)
\(258\) 0 0
\(259\) 8.05510 8.05510i 0.500520 0.500520i
\(260\) 10.6842 2.28203i 0.662604 0.141525i
\(261\) 0 0
\(262\) 12.3244 + 11.6937i 0.761403 + 0.722436i
\(263\) −28.6944 −1.76937 −0.884687 0.466185i \(-0.845628\pi\)
−0.884687 + 0.466185i \(0.845628\pi\)
\(264\) 0 0
\(265\) −16.7104 + 2.66103i −1.02651 + 0.163466i
\(266\) −7.09109 6.72818i −0.434783 0.412531i
\(267\) 0 0
\(268\) −20.9649 18.8712i −1.28064 1.15274i
\(269\) 13.7007 13.7007i 0.835349 0.835349i −0.152894 0.988243i \(-0.548859\pi\)
0.988243 + 0.152894i \(0.0488592\pi\)
\(270\) 0 0
\(271\) 6.47842i 0.393536i −0.980450 0.196768i \(-0.936955\pi\)
0.980450 0.196768i \(-0.0630445\pi\)
\(272\) 12.5592 1.32384i 0.761516 0.0802697i
\(273\) 0 0
\(274\) −0.560650 21.3491i −0.0338701 1.28975i
\(275\) 1.11059 + 0.563529i 0.0669708 + 0.0339821i
\(276\) 0 0
\(277\) 10.7023 + 10.7023i 0.643041 + 0.643041i 0.951302 0.308261i \(-0.0997469\pi\)
−0.308261 + 0.951302i \(0.599747\pi\)
\(278\) 16.9220 + 16.0560i 1.01492 + 0.962974i
\(279\) 0 0
\(280\) −4.64130 + 7.59202i −0.277370 + 0.453710i
\(281\) −23.3237 −1.39138 −0.695688 0.718344i \(-0.744900\pi\)
−0.695688 + 0.718344i \(0.744900\pi\)
\(282\) 0 0
\(283\) −7.39967 + 7.39967i −0.439865 + 0.439865i −0.891966 0.452102i \(-0.850674\pi\)
0.452102 + 0.891966i \(0.350674\pi\)
\(284\) 0.00998767 + 0.190030i 0.000592659 + 0.0112762i
\(285\) 0 0
\(286\) −0.0225902 0.860219i −0.00133579 0.0508658i
\(287\) 0.224366i 0.0132439i
\(288\) 0 0
\(289\) −7.03205 −0.413650
\(290\) 11.5209 2.14615i 0.676528 0.126026i
\(291\) 0 0
\(292\) 15.9605 0.838855i 0.934016 0.0490903i
\(293\) 5.94867 5.94867i 0.347525 0.347525i −0.511662 0.859187i \(-0.670970\pi\)
0.859187 + 0.511662i \(0.170970\pi\)
\(294\) 0 0
\(295\) 14.0078 2.23066i 0.815567 0.129874i
\(296\) 17.4173 + 14.8690i 1.01236 + 0.864244i
\(297\) 0 0
\(298\) −16.1452 15.3189i −0.935264 0.887399i
\(299\) −3.41361 + 3.41361i −0.197414 + 0.197414i
\(300\) 0 0
\(301\) 9.32889 + 9.32889i 0.537708 + 0.537708i
\(302\) 30.9276 0.812190i 1.77968 0.0467363i
\(303\) 0 0
\(304\) 12.3622 15.2755i 0.709023 0.876108i
\(305\) −3.38526 21.2583i −0.193839 1.21725i
\(306\) 0 0
\(307\) −12.0570 12.0570i −0.688130 0.688130i 0.273689 0.961818i \(-0.411756\pi\)
−0.961818 + 0.273689i \(0.911756\pi\)
\(308\) 0.520921 + 0.468898i 0.0296822 + 0.0267179i
\(309\) 0 0
\(310\) 10.6519 15.5289i 0.604986 0.881984i
\(311\) 31.3243i 1.77624i −0.459615 0.888118i \(-0.652012\pi\)
0.459615 0.888118i \(-0.347988\pi\)
\(312\) 0 0
\(313\) 24.0690 1.36046 0.680230 0.732999i \(-0.261880\pi\)
0.680230 + 0.732999i \(0.261880\pi\)
\(314\) 21.1897 22.3326i 1.19580 1.26030i
\(315\) 0 0
\(316\) −0.594790 11.3168i −0.0334596 0.636618i
\(317\) −10.2657 10.2657i −0.576579 0.576579i 0.357380 0.933959i \(-0.383670\pi\)
−0.933959 + 0.357380i \(0.883670\pi\)
\(318\) 0 0
\(319\) 0.923046i 0.0516807i
\(320\) −15.9493 8.10069i −0.891591 0.452842i
\(321\) 0 0
\(322\) −0.103222 3.93061i −0.00575233 0.219044i
\(323\) 10.9677 10.9677i 0.610257 0.610257i
\(324\) 0 0
\(325\) −10.8927 5.52710i −0.604216 0.306589i
\(326\) −7.11082 6.74690i −0.393832 0.373676i
\(327\) 0 0
\(328\) −0.449649 + 0.0354901i −0.0248277 + 0.00195961i
\(329\) −1.62112 −0.0893755
\(330\) 0 0
\(331\) −12.7608 12.7608i −0.701395 0.701395i 0.263315 0.964710i \(-0.415184\pi\)
−0.964710 + 0.263315i \(0.915184\pi\)
\(332\) 23.2129 25.7883i 1.27397 1.41532i
\(333\) 0 0
\(334\) 24.6525 0.647400i 1.34892 0.0354242i
\(335\) 4.95953 + 31.1443i 0.270968 + 1.70159i
\(336\) 0 0
\(337\) 17.3967i 0.947660i −0.880616 0.473830i \(-0.842871\pi\)
0.880616 0.473830i \(-0.157129\pi\)
\(338\) −0.261071 9.94139i −0.0142004 0.540741i
\(339\) 0 0
\(340\) −11.8492 7.67830i −0.642611 0.416414i
\(341\) −1.04880 1.04880i −0.0567956 0.0567956i
\(342\) 0 0
\(343\) 16.9122i 0.913175i
\(344\) −17.2203 + 20.1716i −0.928457 + 1.08758i
\(345\) 0 0
\(346\) 25.2866 + 23.9925i 1.35942 + 1.28984i
\(347\) 9.64234 + 9.64234i 0.517628 + 0.517628i 0.916853 0.399225i \(-0.130721\pi\)
−0.399225 + 0.916853i \(0.630721\pi\)
\(348\) 0 0
\(349\) −3.66120 3.66120i −0.195980 0.195980i 0.602294 0.798274i \(-0.294253\pi\)
−0.798274 + 0.602294i \(0.794253\pi\)
\(350\) 9.37217 3.33734i 0.500964 0.178388i
\(351\) 0 0
\(352\) −0.857315 + 1.11814i −0.0456951 + 0.0595973i
\(353\) 18.9960 1.01106 0.505528 0.862810i \(-0.331298\pi\)
0.505528 + 0.862810i \(0.331298\pi\)
\(354\) 0 0
\(355\) 0.124909 0.172226i 0.00662949 0.00914081i
\(356\) 21.8297 1.14733i 1.15697 0.0608084i
\(357\) 0 0
\(358\) −18.0827 17.1573i −0.955700 0.906789i
\(359\) 8.71770i 0.460103i 0.973178 + 0.230051i \(0.0738894\pi\)
−0.973178 + 0.230051i \(0.926111\pi\)
\(360\) 0 0
\(361\) 5.13530i 0.270279i
\(362\) 9.74625 10.2719i 0.512252 0.539882i
\(363\) 0 0
\(364\) −5.10921 4.59896i −0.267795 0.241051i
\(365\) −14.4651 10.4910i −0.757138 0.549124i
\(366\) 0 0
\(367\) 28.0501 1.46420 0.732101 0.681196i \(-0.238540\pi\)
0.732101 + 0.681196i \(0.238540\pi\)
\(368\) 7.86098 0.828609i 0.409782 0.0431942i
\(369\) 0 0
\(370\) −4.68894 25.1710i −0.243766 1.30858i
\(371\) 7.52841 + 7.52841i 0.390856 + 0.390856i
\(372\) 0 0
\(373\) 4.90740 + 4.90740i 0.254096 + 0.254096i 0.822647 0.568552i \(-0.192496\pi\)
−0.568552 + 0.822647i \(0.692496\pi\)
\(374\) −0.765468 + 0.806756i −0.0395814 + 0.0417163i
\(375\) 0 0
\(376\) −0.256429 3.24888i −0.0132243 0.167548i
\(377\) 9.05326i 0.466267i
\(378\) 0 0
\(379\) 26.0620 + 26.0620i 1.33872 + 1.33872i 0.897305 + 0.441412i \(0.145522\pi\)
0.441412 + 0.897305i \(0.354478\pi\)
\(380\) −21.4859 + 4.58917i −1.10221 + 0.235420i
\(381\) 0 0
\(382\) 17.8145 0.467826i 0.911467 0.0239361i
\(383\) 6.91314i 0.353245i −0.984279 0.176623i \(-0.943483\pi\)
0.984279 0.176623i \(-0.0565172\pi\)
\(384\) 0 0
\(385\) −0.123231 0.773850i −0.00628042 0.0394391i
\(386\) −0.191467 7.29091i −0.00974541 0.371098i
\(387\) 0 0
\(388\) −1.09606 20.8542i −0.0556440 1.05871i
\(389\) −14.5222 14.5222i −0.736302 0.736302i 0.235558 0.971860i \(-0.424308\pi\)
−0.971860 + 0.235558i \(0.924308\pi\)
\(390\) 0 0
\(391\) 6.23906 0.315523
\(392\) −14.1561 + 1.11731i −0.714989 + 0.0564329i
\(393\) 0 0
\(394\) −4.95287 + 5.22002i −0.249522 + 0.262981i
\(395\) −7.43864 + 10.2565i −0.374279 + 0.516060i
\(396\) 0 0
\(397\) −18.3367 + 18.3367i −0.920291 + 0.920291i −0.997050 0.0767588i \(-0.975543\pi\)
0.0767588 + 0.997050i \(0.475543\pi\)
\(398\) −10.7239 + 0.281620i −0.537540 + 0.0141163i
\(399\) 0 0
\(400\) 8.17083 + 18.2548i 0.408541 + 0.912740i
\(401\) 33.5380i 1.67481i 0.546585 + 0.837404i \(0.315927\pi\)
−0.546585 + 0.837404i \(0.684073\pi\)
\(402\) 0 0
\(403\) 10.2866 + 10.2866i 0.512414 + 0.512414i
\(404\) 9.55523 + 8.60097i 0.475391 + 0.427914i
\(405\) 0 0
\(406\) −5.34908 5.07533i −0.265471 0.251884i
\(407\) −2.01669 −0.0999634
\(408\) 0 0
\(409\) 18.0044i 0.890260i −0.895466 0.445130i \(-0.853158\pi\)
0.895466 0.445130i \(-0.146842\pi\)
\(410\) 0.415857 + 0.285252i 0.0205377 + 0.0140876i
\(411\) 0 0
\(412\) 0.803748 + 15.2925i 0.0395978 + 0.753407i
\(413\) −6.31084 6.31084i −0.310536 0.310536i
\(414\) 0 0
\(415\) −38.3096 + 6.10056i −1.88054 + 0.299465i
\(416\) 8.40857 10.9668i 0.412264 0.537691i
\(417\) 0 0
\(418\) 0.0454291 + 1.72991i 0.00222201 + 0.0846125i
\(419\) −16.7671 16.7671i −0.819126 0.819126i 0.166856 0.985981i \(-0.446639\pi\)
−0.985981 + 0.166856i \(0.946639\pi\)
\(420\) 0 0
\(421\) 9.17528 9.17528i 0.447176 0.447176i −0.447239 0.894415i \(-0.647593\pi\)
0.894415 + 0.447239i \(0.147593\pi\)
\(422\) −0.832854 + 0.877777i −0.0405427 + 0.0427295i
\(423\) 0 0
\(424\) −13.8968 + 16.2785i −0.674888 + 0.790553i
\(425\) 4.90331 + 15.0052i 0.237846 + 0.727859i
\(426\) 0 0
\(427\) −9.57736 + 9.57736i −0.463481 + 0.463481i
\(428\) 8.93831 + 8.04566i 0.432049 + 0.388902i
\(429\) 0 0
\(430\) 29.1514 5.43042i 1.40580 0.261878i
\(431\) 36.6726 1.76646 0.883228 0.468943i \(-0.155365\pi\)
0.883228 + 0.468943i \(0.155365\pi\)
\(432\) 0 0
\(433\) 28.1455i 1.35259i 0.736633 + 0.676293i \(0.236414\pi\)
−0.736633 + 0.676293i \(0.763586\pi\)
\(434\) −11.8446 + 0.311051i −0.568558 + 0.0149309i
\(435\) 0 0
\(436\) 0.380152 + 0.342187i 0.0182060 + 0.0163878i
\(437\) 6.86480 6.86480i 0.328388 0.328388i
\(438\) 0 0
\(439\) −3.32665 −0.158772 −0.0793862 0.996844i \(-0.525296\pi\)
−0.0793862 + 0.996844i \(0.525296\pi\)
\(440\) 1.53137 0.369373i 0.0730054 0.0176092i
\(441\) 0 0
\(442\) 7.50772 7.91268i 0.357106 0.376368i
\(443\) −6.03644 6.03644i −0.286800 0.286800i 0.549013 0.835814i \(-0.315004\pi\)
−0.835814 + 0.549013i \(0.815004\pi\)
\(444\) 0 0
\(445\) −19.7844 14.3489i −0.937871 0.680203i
\(446\) −35.7180 + 0.937992i −1.69130 + 0.0444152i
\(447\) 0 0
\(448\) 1.76577 + 11.1162i 0.0834248 + 0.525193i
\(449\) 14.2691i 0.673402i −0.941612 0.336701i \(-0.890689\pi\)
0.941612 0.336701i \(-0.109311\pi\)
\(450\) 0 0
\(451\) 0.0280862 0.0280862i 0.00132253 0.00132253i
\(452\) 13.7584 0.723116i 0.647139 0.0340125i
\(453\) 0 0
\(454\) −9.11065 + 9.60207i −0.427584 + 0.450647i
\(455\) 1.20865 + 7.58994i 0.0566624 + 0.355822i
\(456\) 0 0
\(457\) 25.0611 1.17231 0.586154 0.810200i \(-0.300641\pi\)
0.586154 + 0.810200i \(0.300641\pi\)
\(458\) 0.0615201 0.0648384i 0.00287464 0.00302970i
\(459\) 0 0
\(460\) −7.41654 4.80594i −0.345798 0.224078i
\(461\) −11.6030 + 11.6030i −0.540407 + 0.540407i −0.923648 0.383241i \(-0.874808\pi\)
0.383241 + 0.923648i \(0.374808\pi\)
\(462\) 0 0
\(463\) −8.74913 −0.406607 −0.203303 0.979116i \(-0.565168\pi\)
−0.203303 + 0.979116i \(0.565168\pi\)
\(464\) 9.32531 11.5229i 0.432917 0.534936i
\(465\) 0 0
\(466\) −0.501241 19.0869i −0.0232196 0.884183i
\(467\) −19.3047 + 19.3047i −0.893316 + 0.893316i −0.994834 0.101518i \(-0.967630\pi\)
0.101518 + 0.994834i \(0.467630\pi\)
\(468\) 0 0
\(469\) 14.0312 14.0312i 0.647901 0.647901i
\(470\) −2.06105 + 3.00472i −0.0950690 + 0.138597i
\(471\) 0 0
\(472\) 11.6493 13.6458i 0.536201 0.628097i
\(473\) 2.33559i 0.107391i
\(474\) 0 0
\(475\) 21.9052 + 11.1150i 1.00508 + 0.509993i
\(476\) 0.466288 + 8.87182i 0.0213723 + 0.406639i
\(477\) 0 0
\(478\) −7.89009 + 0.207202i −0.360884 + 0.00947719i
\(479\) −19.9695 −0.912431 −0.456215 0.889869i \(-0.650795\pi\)
−0.456215 + 0.889869i \(0.650795\pi\)
\(480\) 0 0
\(481\) 19.7797 0.901877
\(482\) −22.2913 + 0.585392i −1.01534 + 0.0266639i
\(483\) 0 0
\(484\) 1.14818 + 21.8458i 0.0521899 + 0.992990i
\(485\) −13.7077 + 18.9003i −0.622434 + 0.858219i
\(486\) 0 0
\(487\) 34.8592i 1.57962i 0.613351 + 0.789811i \(0.289821\pi\)
−0.613351 + 0.789811i \(0.710179\pi\)
\(488\) −20.7089 17.6790i −0.937446 0.800289i
\(489\) 0 0
\(490\) 13.0922 + 8.98042i 0.591445 + 0.405694i
\(491\) 21.4659 21.4659i 0.968743 0.968743i −0.0307829 0.999526i \(-0.509800\pi\)
0.999526 + 0.0307829i \(0.00980006\pi\)
\(492\) 0 0
\(493\) 8.27333 8.27333i 0.372612 0.372612i
\(494\) −0.445570 16.9670i −0.0200471 0.763380i
\(495\) 0 0
\(496\) −2.49695 23.6884i −0.112116 1.06364i
\(497\) −0.133866 −0.00600471
\(498\) 0 0
\(499\) −18.0781 + 18.0781i −0.809287 + 0.809287i −0.984526 0.175239i \(-0.943930\pi\)
0.175239 + 0.984526i \(0.443930\pi\)
\(500\) 5.72980 21.6141i 0.256244 0.966612i
\(501\) 0 0
\(502\) −14.5095 + 15.2922i −0.647593 + 0.682523i
\(503\) −3.90394 −0.174068 −0.0870341 0.996205i \(-0.527739\pi\)
−0.0870341 + 0.996205i \(0.527739\pi\)
\(504\) 0 0
\(505\) −2.26042 14.1947i −0.100587 0.631656i
\(506\) −0.479115 + 0.504958i −0.0212993 + 0.0224481i
\(507\) 0 0
\(508\) 6.35353 0.333931i 0.281892 0.0148158i
\(509\) −11.0778 + 11.0778i −0.491014 + 0.491014i −0.908626 0.417612i \(-0.862867\pi\)
0.417612 + 0.908626i \(0.362867\pi\)
\(510\) 0 0
\(511\) 11.2433i 0.497374i
\(512\) −21.9986 + 5.29713i −0.972212 + 0.234102i
\(513\) 0 0
\(514\) 28.3731 0.745108i 1.25149 0.0328653i
\(515\) 10.0519 13.8597i 0.442941 0.610732i
\(516\) 0 0
\(517\) 0.202933 + 0.202933i 0.00892500 + 0.00892500i
\(518\) −11.0887 + 11.6868i −0.487207 + 0.513487i
\(519\) 0 0
\(520\) −15.0198 + 3.62282i −0.658660 + 0.158871i
\(521\) −2.61052 −0.114369 −0.0571844 0.998364i \(-0.518212\pi\)
−0.0571844 + 0.998364i \(0.518212\pi\)
\(522\) 0 0
\(523\) 21.2735 21.2735i 0.930226 0.930226i −0.0674935 0.997720i \(-0.521500\pi\)
0.997720 + 0.0674935i \(0.0215002\pi\)
\(524\) −17.8574 16.0741i −0.780106 0.702199i
\(525\) 0 0
\(526\) 40.5661 1.06531i 1.76876 0.0464496i
\(527\) 18.8009i 0.818980i
\(528\) 0 0
\(529\) −19.0949 −0.830213
\(530\) 23.5251 4.38235i 1.02187 0.190357i
\(531\) 0 0
\(532\) 10.2747 + 9.24855i 0.445463 + 0.400975i
\(533\) −0.275471 + 0.275471i −0.0119320 + 0.0119320i
\(534\) 0 0
\(535\) −2.11448 13.2782i −0.0914168 0.574068i
\(536\) 30.3393 + 25.9004i 1.31046 + 1.11873i
\(537\) 0 0
\(538\) −18.8604 + 19.8777i −0.813132 + 0.856991i
\(539\) 0.884224 0.884224i 0.0380862 0.0380862i
\(540\) 0 0
\(541\) −8.92150 8.92150i −0.383565 0.383565i 0.488820 0.872385i \(-0.337428\pi\)
−0.872385 + 0.488820i \(0.837428\pi\)
\(542\) 0.240517 + 9.15871i 0.0103311 + 0.393400i
\(543\) 0 0
\(544\) −17.7062 + 2.33782i −0.759146 + 0.100233i
\(545\) −0.0899300 0.564732i −0.00385218 0.0241905i
\(546\) 0 0
\(547\) −24.0470 24.0470i −1.02818 1.02818i −0.999591 0.0285840i \(-0.990900\pi\)
−0.0285840 0.999591i \(-0.509100\pi\)
\(548\) 1.58521 + 30.1610i 0.0677168 + 1.28841i
\(549\) 0 0
\(550\) −1.59099 0.755444i −0.0678399 0.0322122i
\(551\) 18.2062i 0.775609i
\(552\) 0 0
\(553\) 7.97205 0.339006
\(554\) −15.5275 14.7328i −0.659701 0.625939i
\(555\) 0 0
\(556\) −24.5192 22.0705i −1.03985 0.935999i
\(557\) 17.5090 + 17.5090i 0.741879 + 0.741879i 0.972939 0.231060i \(-0.0742195\pi\)
−0.231060 + 0.972939i \(0.574220\pi\)
\(558\) 0 0
\(559\) 22.9076i 0.968886i
\(560\) 6.27966 10.9053i 0.265364 0.460835i
\(561\) 0 0
\(562\) 32.9733 0.865914i 1.39090 0.0365264i
\(563\) 11.2032 11.2032i 0.472157 0.472157i −0.430455 0.902612i \(-0.641647\pi\)
0.902612 + 0.430455i \(0.141647\pi\)
\(564\) 0 0
\(565\) −12.4693 9.04353i −0.524588 0.380464i
\(566\) 10.1864 10.7358i 0.428166 0.451260i
\(567\) 0 0
\(568\) −0.0211749 0.268280i −0.000888478 0.0112568i
\(569\) −4.83805 −0.202821 −0.101411 0.994845i \(-0.532336\pi\)
−0.101411 + 0.994845i \(0.532336\pi\)
\(570\) 0 0
\(571\) 9.64695 + 9.64695i 0.403712 + 0.403712i 0.879539 0.475827i \(-0.157851\pi\)
−0.475827 + 0.879539i \(0.657851\pi\)
\(572\) 0.0638728 + 1.21528i 0.00267066 + 0.0508132i
\(573\) 0 0
\(574\) −0.00832978 0.317192i −0.000347678 0.0132393i
\(575\) 3.06904 + 9.39194i 0.127988 + 0.391671i
\(576\) 0 0
\(577\) 18.0261i 0.750438i −0.926936 0.375219i \(-0.877568\pi\)
0.926936 0.375219i \(-0.122432\pi\)
\(578\) 9.94139 0.261071i 0.413508 0.0108591i
\(579\) 0 0
\(580\) −16.2077 + 3.46179i −0.672987 + 0.143743i
\(581\) 17.2593 + 17.2593i 0.716038 + 0.716038i
\(582\) 0 0
\(583\) 1.88482i 0.0780614i
\(584\) −22.5326 + 1.77846i −0.932405 + 0.0735932i
\(585\) 0 0
\(586\) −8.18894 + 8.63064i −0.338282 + 0.356528i
\(587\) −5.25140 5.25140i −0.216749 0.216749i 0.590378 0.807127i \(-0.298979\pi\)
−0.807127 + 0.590378i \(0.798979\pi\)
\(588\) 0 0
\(589\) −20.6865 20.6865i −0.852373 0.852373i
\(590\) −19.7204 + 3.67359i −0.811876 + 0.151239i
\(591\) 0 0
\(592\) −25.1753 20.3741i −1.03470 0.837369i
\(593\) −0.0811054 −0.00333060 −0.00166530 0.999999i \(-0.500530\pi\)
−0.00166530 + 0.999999i \(0.500530\pi\)
\(594\) 0 0
\(595\) 5.83155 8.04060i 0.239070 0.329632i
\(596\) 23.3936 + 21.0573i 0.958238 + 0.862541i
\(597\) 0 0
\(598\) 4.69918 4.95264i 0.192164 0.202529i
\(599\) 8.29253i 0.338824i −0.985545 0.169412i \(-0.945813\pi\)
0.985545 0.169412i \(-0.0541868\pi\)
\(600\) 0 0
\(601\) 5.82196i 0.237483i −0.992925 0.118741i \(-0.962114\pi\)
0.992925 0.118741i \(-0.0378859\pi\)
\(602\) −13.5348 12.8422i −0.551639 0.523407i
\(603\) 0 0
\(604\) −43.6930 + 2.29643i −1.77784 + 0.0934404i
\(605\) 14.3595 19.7990i 0.583796 0.804944i
\(606\) 0 0
\(607\) 22.0548 0.895178 0.447589 0.894239i \(-0.352283\pi\)
0.447589 + 0.894239i \(0.352283\pi\)
\(608\) −16.9097 + 22.0543i −0.685779 + 0.894419i
\(609\) 0 0
\(610\) 5.57506 + 29.9278i 0.225728 + 1.21174i
\(611\) −1.99038 1.99038i −0.0805220 0.0805220i
\(612\) 0 0
\(613\) −14.9250 14.9250i −0.602816 0.602816i 0.338243 0.941059i \(-0.390168\pi\)
−0.941059 + 0.338243i \(0.890168\pi\)
\(614\) 17.4929 + 16.5977i 0.705957 + 0.669828i
\(615\) 0 0
\(616\) −0.753848 0.643553i −0.0303734 0.0259295i
\(617\) 31.5403i 1.26976i −0.772609 0.634882i \(-0.781049\pi\)
0.772609 0.634882i \(-0.218951\pi\)
\(618\) 0 0
\(619\) 6.89013 + 6.89013i 0.276938 + 0.276938i 0.831885 0.554947i \(-0.187262\pi\)
−0.554947 + 0.831885i \(0.687262\pi\)
\(620\) −14.4823 + 22.3491i −0.581624 + 0.897563i
\(621\) 0 0
\(622\) 1.16294 + 44.2840i 0.0466297 + 1.77562i
\(623\) 15.3778i 0.616100i
\(624\) 0 0
\(625\) −20.1760 + 14.7624i −0.807042 + 0.590494i
\(626\) −34.0270 + 0.893583i −1.35999 + 0.0357148i
\(627\) 0 0
\(628\) −29.1273 + 32.3589i −1.16230 + 1.29126i
\(629\) −18.0757 18.0757i −0.720725 0.720725i
\(630\) 0 0
\(631\) −32.9043 −1.30990 −0.654950 0.755672i \(-0.727310\pi\)
−0.654950 + 0.755672i \(0.727310\pi\)
\(632\) 1.26102 + 15.9767i 0.0501605 + 0.635520i
\(633\) 0 0
\(634\) 14.8940 + 14.1318i 0.591517 + 0.561244i
\(635\) −5.75825 4.17625i −0.228509 0.165729i
\(636\) 0 0
\(637\) −8.67249 + 8.67249i −0.343617 + 0.343617i
\(638\) 0.0342689 + 1.30493i 0.00135672 + 0.0516629i
\(639\) 0 0
\(640\) 22.8486 + 10.8600i 0.903171 + 0.429280i
\(641\) 28.3921i 1.12142i 0.828013 + 0.560710i \(0.189472\pi\)
−0.828013 + 0.560710i \(0.810528\pi\)
\(642\) 0 0
\(643\) 2.71547 + 2.71547i 0.107088 + 0.107088i 0.758621 0.651533i \(-0.225874\pi\)
−0.651533 + 0.758621i \(0.725874\pi\)
\(644\) 0.291855 + 5.55298i 0.0115007 + 0.218818i
\(645\) 0 0
\(646\) −15.0981 + 15.9125i −0.594027 + 0.626067i
\(647\) 33.2882 1.30869 0.654346 0.756195i \(-0.272944\pi\)
0.654346 + 0.756195i \(0.272944\pi\)
\(648\) 0 0
\(649\) 1.57999i 0.0620200i
\(650\) 15.6044 + 7.40941i 0.612056 + 0.290621i
\(651\) 0 0
\(652\) 10.3032 + 9.27427i 0.403506 + 0.363208i
\(653\) 4.82719 + 4.82719i 0.188902 + 0.188902i 0.795221 0.606319i \(-0.207355\pi\)
−0.606319 + 0.795221i \(0.707355\pi\)
\(654\) 0 0
\(655\) 4.22442 + 26.5280i 0.165062 + 1.03653i
\(656\) 0.634364 0.0668669i 0.0247677 0.00261071i
\(657\) 0 0
\(658\) 2.29183 0.0601857i 0.0893447 0.00234628i
\(659\) 22.5484 + 22.5484i 0.878359 + 0.878359i 0.993365 0.115005i \(-0.0366885\pi\)
−0.115005 + 0.993365i \(0.536689\pi\)
\(660\) 0 0
\(661\) 17.3551 17.3551i 0.675035 0.675035i −0.283838 0.958872i \(-0.591608\pi\)
0.958872 + 0.283838i \(0.0916077\pi\)
\(662\) 18.5140 + 17.5665i 0.719567 + 0.682741i
\(663\) 0 0
\(664\) −31.8592 + 37.3194i −1.23638 + 1.44827i
\(665\) −2.43061 15.2634i −0.0942548 0.591890i
\(666\) 0 0
\(667\) 5.17838 5.17838i 0.200508 0.200508i
\(668\) −34.8278 + 1.83049i −1.34753 + 0.0708239i
\(669\) 0 0
\(670\) −8.16768 43.8453i −0.315545 1.69389i
\(671\) 2.39780 0.0925661
\(672\) 0 0
\(673\) 20.2889i 0.782080i −0.920374 0.391040i \(-0.872115\pi\)
0.920374 0.391040i \(-0.127885\pi\)
\(674\) 0.645869 + 24.5942i 0.0248780 + 0.947334i
\(675\) 0 0
\(676\) 0.738167 + 14.0447i 0.0283910 + 0.540181i
\(677\) −0.349388 + 0.349388i −0.0134281 + 0.0134281i −0.713789 0.700361i \(-0.753022\pi\)
0.700361 + 0.713789i \(0.253022\pi\)
\(678\) 0 0
\(679\) 14.6906 0.563775
\(680\) 17.0365 + 10.4151i 0.653321 + 0.399401i
\(681\) 0 0
\(682\) 1.52165 + 1.44378i 0.0582670 + 0.0552850i
\(683\) −4.40464 4.40464i −0.168539 0.168539i 0.617798 0.786337i \(-0.288025\pi\)
−0.786337 + 0.617798i \(0.788025\pi\)
\(684\) 0 0
\(685\) 19.8252 27.3351i 0.757480 1.04442i
\(686\) −0.627882 23.9093i −0.0239726 0.912860i
\(687\) 0 0
\(688\) 23.5959 29.1564i 0.899586 1.11158i
\(689\) 18.4864i 0.704276i
\(690\) 0 0
\(691\) −22.7615 + 22.7615i −0.865890 + 0.865890i −0.992014 0.126125i \(-0.959746\pi\)
0.126125 + 0.992014i \(0.459746\pi\)
\(692\) −36.6391 32.9800i −1.39281 1.25371i
\(693\) 0 0
\(694\) −13.9896 13.2736i −0.531038 0.503861i
\(695\) 5.80034 + 36.4243i 0.220020 + 1.38165i
\(696\) 0 0
\(697\) 0.503478 0.0190706
\(698\) 5.31186 + 5.04001i 0.201057 + 0.190767i
\(699\) 0 0
\(700\) −13.1258 + 5.06604i −0.496108 + 0.191478i
\(701\) −34.9589 + 34.9589i −1.32038 + 1.32038i −0.406913 + 0.913467i \(0.633395\pi\)
−0.913467 + 0.406913i \(0.866605\pi\)
\(702\) 0 0
\(703\) −39.7771 −1.50022
\(704\) 1.17050 1.61258i 0.0441148 0.0607763i
\(705\) 0 0
\(706\) −26.8552 + 0.705245i −1.01071 + 0.0265422i
\(707\) −6.39503 + 6.39503i −0.240510 + 0.240510i
\(708\) 0 0
\(709\) −20.7652 + 20.7652i −0.779854 + 0.779854i −0.979806 0.199952i \(-0.935922\pi\)
0.199952 + 0.979806i \(0.435922\pi\)
\(710\) −0.170193 + 0.248118i −0.00638724 + 0.00931169i
\(711\) 0 0
\(712\) −30.8186 + 2.43246i −1.15498 + 0.0911602i
\(713\) 11.7677i 0.440704i
\(714\) 0 0
\(715\) 0.798814 1.10141i 0.0298740 0.0411905i
\(716\) 26.2010 + 23.5843i 0.979175 + 0.881387i
\(717\) 0 0
\(718\) −0.323653 12.3244i −0.0120786 0.459944i
\(719\) 9.48453 0.353713 0.176857 0.984237i \(-0.443407\pi\)
0.176857 + 0.984237i \(0.443407\pi\)
\(720\) 0 0
\(721\) −10.7727 −0.401198
\(722\) 0.190653 + 7.25991i 0.00709536 + 0.270186i
\(723\) 0 0
\(724\) −13.3972 + 14.8836i −0.497902 + 0.553143i
\(725\) 16.5239 + 8.38451i 0.613684 + 0.311393i
\(726\) 0 0
\(727\) 29.4631i 1.09272i −0.837549 0.546362i \(-0.816012\pi\)
0.837549 0.546362i \(-0.183988\pi\)
\(728\) 7.39376 + 6.31199i 0.274031 + 0.233938i
\(729\) 0 0
\(730\) 20.8392 + 14.2944i 0.771293 + 0.529059i
\(731\) 20.9341 20.9341i 0.774275 0.774275i
\(732\) 0 0
\(733\) 13.5703 13.5703i 0.501231 0.501231i −0.410590 0.911820i \(-0.634677\pi\)
0.911820 + 0.410590i \(0.134677\pi\)
\(734\) −39.6551 + 1.04138i −1.46370 + 0.0384382i
\(735\) 0 0
\(736\) −11.0825 + 1.46327i −0.408507 + 0.0539369i
\(737\) −3.51287 −0.129398
\(738\) 0 0
\(739\) −1.19592 + 1.19592i −0.0439927 + 0.0439927i −0.728761 0.684768i \(-0.759903\pi\)
0.684768 + 0.728761i \(0.259903\pi\)
\(740\) 7.56337 + 35.4108i 0.278035 + 1.30173i
\(741\) 0 0
\(742\) −10.9226 10.3636i −0.400982 0.380460i
\(743\) 48.8695 1.79285 0.896424 0.443197i \(-0.146156\pi\)
0.896424 + 0.443197i \(0.146156\pi\)
\(744\) 0 0
\(745\) −5.53406 34.7521i −0.202752 1.27322i
\(746\) −7.11991 6.75553i −0.260679 0.247338i
\(747\) 0 0
\(748\) 1.05221 1.16895i 0.0384726 0.0427411i
\(749\) −5.98214 + 5.98214i −0.218583 + 0.218583i
\(750\) 0 0
\(751\) 17.8326i 0.650721i 0.945590 + 0.325360i \(0.105486\pi\)
−0.945590 + 0.325360i \(0.894514\pi\)
\(752\) 0.483138 + 4.58351i 0.0176182 + 0.167143i
\(753\) 0 0
\(754\) −0.336111 12.7988i −0.0122404 0.466106i
\(755\) 39.5993 + 28.7199i 1.44117 + 1.04522i
\(756\) 0 0
\(757\) −19.7676 19.7676i −0.718467 0.718467i 0.249824 0.968291i \(-0.419627\pi\)
−0.968291 + 0.249824i \(0.919627\pi\)
\(758\) −37.8121 35.8770i −1.37340 1.30311i
\(759\) 0 0
\(760\) 30.2049 7.28552i 1.09565 0.264274i
\(761\) −3.72357 −0.134979 −0.0674896 0.997720i \(-0.521499\pi\)
−0.0674896 + 0.997720i \(0.521499\pi\)
\(762\) 0 0
\(763\) −0.254425 + 0.254425i −0.00921079 + 0.00921079i
\(764\) −25.1674 + 1.32276i −0.910524 + 0.0478556i
\(765\) 0 0
\(766\) 0.256657 + 9.77329i 0.00927339 + 0.353123i
\(767\) 15.4966i 0.559549i
\(768\) 0 0
\(769\) −17.9937 −0.648868 −0.324434 0.945908i \(-0.605174\pi\)
−0.324434 + 0.945908i \(0.605174\pi\)
\(770\) 0.202944 + 1.08944i 0.00731361 + 0.0392606i
\(771\) 0 0
\(772\) 0.541363 + 10.3002i 0.0194841 + 0.370714i
\(773\) 14.5506 14.5506i 0.523350 0.523350i −0.395232 0.918582i \(-0.629336\pi\)
0.918582 + 0.395232i \(0.129336\pi\)
\(774\) 0 0
\(775\) 28.3019 9.24831i 1.01663 0.332209i
\(776\) 2.32376 + 29.4414i 0.0834181 + 1.05688i
\(777\) 0 0
\(778\) 21.0695 + 19.9912i 0.755378 + 0.716719i
\(779\) 0.553973 0.553973i 0.0198482 0.0198482i
\(780\) 0 0
\(781\) 0.0167574 + 0.0167574i 0.000599629 + 0.000599629i
\(782\) −8.82032 + 0.231631i −0.315414 + 0.00828310i
\(783\) 0 0
\(784\) 19.9713 2.10513i 0.713262 0.0751833i
\(785\) 48.0705 7.65492i 1.71571 0.273216i
\(786\) 0 0
\(787\) −27.4478 27.4478i −0.978410 0.978410i 0.0213618 0.999772i \(-0.493200\pi\)
−0.999772 + 0.0213618i \(0.993200\pi\)
\(788\) 6.80820 7.56356i 0.242532 0.269441i
\(789\) 0 0
\(790\) 10.1354 14.7760i 0.360602 0.525707i
\(791\) 9.69203i 0.344