Properties

Label 720.2.u.a.179.2
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 179.2
Character \(\chi\) \(=\) 720.179
Dual form 720.2.u.a.539.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.41373 + 0.0371259i) q^{2} +(1.99724 - 0.104972i) q^{4} +(1.31281 + 1.81012i) q^{5} -1.40695i q^{7} +(-2.81966 + 0.222551i) q^{8} +O(q^{10})\) \(q+(-1.41373 + 0.0371259i) q^{2} +(1.99724 - 0.104972i) q^{4} +(1.31281 + 1.81012i) q^{5} -1.40695i q^{7} +(-2.81966 + 0.222551i) q^{8} +(-1.92316 - 2.51027i) q^{10} +(-0.176123 + 0.176123i) q^{11} +(1.72742 - 1.72742i) q^{13} +(0.0522343 + 1.98904i) q^{14} +(3.97796 - 0.419308i) q^{16} +3.15721 q^{17} +(3.47385 - 3.47385i) q^{19} +(2.81201 + 3.47744i) q^{20} +(0.242451 - 0.255528i) q^{22} +1.97613 q^{23} +(-1.55305 + 4.75269i) q^{25} +(-2.37796 + 2.50623i) q^{26} +(-0.147690 - 2.81002i) q^{28} +(-2.62046 + 2.62046i) q^{29} -5.95492i q^{31} +(-5.60818 + 0.740472i) q^{32} +(-4.46342 + 0.117214i) q^{34} +(2.54675 - 1.84706i) q^{35} +(5.72522 + 5.72522i) q^{37} +(-4.78211 + 5.04005i) q^{38} +(-4.10452 - 4.81175i) q^{40} -0.159470 q^{41} +(-6.63058 + 6.63058i) q^{43} +(-0.333273 + 0.370248i) q^{44} +(-2.79371 + 0.0733658i) q^{46} +1.15223i q^{47} +5.02049 q^{49} +(2.01915 - 6.77665i) q^{50} +(3.26874 - 3.63141i) q^{52} +(5.35087 - 5.35087i) q^{53} +(-0.550020 - 0.0875872i) q^{55} +(0.313118 + 3.96712i) q^{56} +(3.60733 - 3.80190i) q^{58} +(4.48547 - 4.48547i) q^{59} +(6.80718 + 6.80718i) q^{61} +(0.221082 + 8.41862i) q^{62} +(7.90094 - 1.25503i) q^{64} +(5.39461 + 0.859057i) q^{65} +(9.97278 + 9.97278i) q^{67} +(6.30571 - 0.331417i) q^{68} +(-3.53183 + 2.70579i) q^{70} -0.0951463i q^{71} -7.99125 q^{73} +(-8.30645 - 7.88134i) q^{74} +(6.57347 - 7.30278i) q^{76} +(0.247796 + 0.247796i) q^{77} -5.66620i q^{79} +(5.98131 + 6.65011i) q^{80} +(0.225446 - 0.00592045i) q^{82} +(12.2672 - 12.2672i) q^{83} +(4.14481 + 5.71492i) q^{85} +(9.12765 - 9.61998i) q^{86} +(0.457410 - 0.535803i) q^{88} -10.9299 q^{89} +(-2.43039 - 2.43039i) q^{91} +(3.94682 - 0.207438i) q^{92} +(-0.0427774 - 1.62893i) q^{94} +(10.8486 + 1.72757i) q^{95} +10.4415i q^{97} +(-7.09760 + 0.186390i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96q + O(q^{10}) \) \( 96q - 8q^{16} - 16q^{19} + 72q^{34} + 8q^{40} + 8q^{46} - 96q^{49} + 64q^{55} - 32q^{61} + 48q^{64} + 24q^{70} + 40q^{76} - 88q^{94} + O(q^{100}) \)

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
\(5\) 1.31281 + 1.81012i 0.587107 + 0.809509i
\(6\) 0 0
\(7\) 1.40695i 0.531777i −0.964004 0.265889i \(-0.914335\pi\)
0.964004 0.265889i \(-0.0856653\pi\)
\(8\) −2.81966 + 0.222551i −0.996900 + 0.0786836i
\(9\) 0 0
\(10\) −1.92316 2.51027i −0.608156 0.793818i
\(11\) −0.176123 + 0.176123i −0.0531031 + 0.0531031i −0.733160 0.680057i \(-0.761955\pi\)
0.680057 + 0.733160i \(0.261955\pi\)
\(12\) 0 0
\(13\) 1.72742 1.72742i 0.479100 0.479100i −0.425744 0.904844i \(-0.639988\pi\)
0.904844 + 0.425744i \(0.139988\pi\)
\(14\) 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 \(0.0594417\pi\)
\(20\) 2.81201 + 3.47744i 0.628786 + 0.777579i
\(21\) 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 −0.907234 0.420627i \(-0.861810\pi\)
0.420627 + 0.907234i \(0.361810\pi\)
\(30\) 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
\(35\) 2.54675 1.84706i 0.430479 0.312210i
\(36\) 0 0
\(37\) 5.72522 + 5.72522i 0.941221 + 0.941221i 0.998366 0.0571453i \(-0.0181998\pi\)
−0.0571453 + 0.998366i \(0.518200\pi\)
\(38\) −4.78211 + 5.04005i −0.775760 + 0.817603i
\(39\) 0 0
\(40\) −4.10452 4.81175i −0.648982 0.760804i
\(41\) −0.159470 −0.0249050 −0.0124525 0.999922i \(-0.503964\pi\)
−0.0124525 + 0.999922i \(0.503964\pi\)
\(42\) 0 0
\(43\) −6.63058 + 6.63058i −1.01115 + 1.01115i −0.0112162 + 0.999937i \(0.503570\pi\)
−0.999937 + 0.0112162i \(0.996430\pi\)
\(44\) −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
\(50\) 2.01915 6.77665i 0.285550 0.958364i
\(51\) 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 −0.352030 0.935989i \(-0.614508\pi\)
0.935989 + 0.352030i \(0.114508\pi\)
\(60\) 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 \(0.0804851\pi\)
0.250166 + 0.968203i \(0.419515\pi\)
\(68\) 6.30571 0.331417i 0.764679 0.0401903i
\(69\) 0 0
\(70\) −3.53183 + 2.70579i −0.422134 + 0.323403i
\(71\) 0.0951463i 0.0112918i −0.999984 0.00564589i \(-0.998203\pi\)
0.999984 0.00564589i \(-0.00179715\pi\)
\(72\) 0 0
\(73\) −7.99125 −0.935305 −0.467653 0.883912i \(-0.654900\pi\)
−0.467653 + 0.883912i \(0.654900\pi\)
\(74\) −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 \(-0.103263\pi\)
\(80\) 5.98131 + 6.65011i 0.668731 + 0.743505i
\(81\) 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
\(85\) 4.14481 + 5.71492i 0.449568 + 0.619870i
\(86\) 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 \(-0.696668\pi\)
−0.579284 + 0.815126i \(0.696668\pi\)
\(90\) 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 \(0.177840\pi\)
−0.847944 + 0.530086i \(0.822160\pi\)
\(98\) −7.09760 + 0.186390i −0.716966 + 0.0188283i
\(99\) 0 0
\(100\) −2.60293 + 9.65530i −0.260293 + 0.965530i
\(101\) −4.54532 4.54532i −0.452276 0.452276i 0.443833 0.896109i \(-0.353618\pi\)
−0.896109 + 0.443833i \(0.853618\pi\)
\(102\) 0 0
\(103\) 7.65680i 0.754447i −0.926122 0.377224i \(-0.876879\pi\)
0.926122 0.377224i \(-0.123121\pi\)
\(104\) −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 \(0.746101\pi\)
\(110\) 0.780829 + 0.103404i 0.0744491 + 0.00985921i
\(111\) 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
\(115\) 2.59429 + 3.57703i 0.241919 + 0.333560i
\(116\) −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
\(125\) −10.6418 + 3.42817i −0.951831 + 0.306625i
\(126\) 0 0
\(127\) −3.18115 −0.282281 −0.141141 0.989990i \(-0.545077\pi\)
−0.141141 + 0.989990i \(0.545077\pi\)
\(128\) −11.1232 + 2.06760i −0.983159 + 0.182752i
\(129\) 0 0
\(130\) −7.65839 1.01419i −0.671685 0.0889505i
\(131\) 8.49459 + 8.49459i 0.742175 + 0.742175i 0.972996 0.230821i \(-0.0741411\pi\)
−0.230821 + 0.972996i \(0.574141\pi\)
\(132\) 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 \(0.996608\pi\)
\(140\) 4.89258 3.95636i 0.413499 0.334374i
\(141\) 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 0.0847561 0.996402i \(-0.472989\pi\)
−0.996402 + 0.0847561i \(0.972989\pi\)
\(150\) 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
\(155\) 10.7791 7.81768i 0.865798 0.627931i
\(156\) 0 0
\(157\) 15.3928 15.3928i 1.22848 1.22848i 0.263935 0.964541i \(-0.414980\pi\)
0.964541 0.263935i \(-0.0850204\pi\)
\(158\) 0.210363 + 8.01045i 0.0167356 + 0.637277i
\(159\) 0 0
\(160\) −8.70283 9.17937i −0.688019 0.725693i
\(161\) 2.78032i 0.219120i
\(162\) 0 0
\(163\) −4.90113 4.90113i −0.383886 0.383886i 0.488614 0.872500i \(-0.337503\pi\)
−0.872500 + 0.488614i \(0.837503\pi\)
\(164\) −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
\(170\) −6.07180 7.92544i −0.465686 0.607854i
\(171\) 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 0.0662383 0.997804i \(-0.478900\pi\)
−0.997804 + 0.0662383i \(0.978900\pi\)
\(180\) 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
\(190\) −15.4011 2.03955i −1.11731 0.147964i
\(191\) 12.6011 0.911781 0.455891 0.890036i \(-0.349321\pi\)
0.455891 + 0.890036i \(0.349321\pi\)
\(192\) 0 0
\(193\) 5.15723i 0.371226i −0.982623 0.185613i \(-0.940573\pi\)
0.982623 0.185613i \(-0.0594270\pi\)
\(194\) −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 \(0.413352\pi\)
\(200\) 3.32137 13.7466i 0.234856 0.972030i
\(201\) 0 0
\(202\) 6.59458 + 6.25708i 0.463993 + 0.440247i
\(203\) 3.68686 + 3.68686i 0.258767 + 0.258767i
\(204\) 0 0
\(205\) −0.209353 0.288659i −0.0146219 0.0201608i
\(206\) 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
\(220\) −1.10772 0.117196i −0.0746823 0.00790138i
\(221\) 5.45382 5.45382i 0.366863 0.366863i
\(222\) 0 0
\(223\) −25.2652 −1.69188 −0.845940 0.533278i \(-0.820960\pi\)
−0.845940 + 0.533278i \(0.820960\pi\)
\(224\) 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 \(0.250665\pi\)
\(230\) −3.80042 4.96063i −0.250592 0.327094i
\(231\) 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
\(235\) −2.08566 + 1.51265i −0.136054 + 0.0986747i
\(236\) 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 \(-0.557773\pi\)
−0.180504 + 0.983574i \(0.557773\pi\)
\(240\) 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
\(245\) 6.59096 + 9.08768i 0.421081 + 0.580591i
\(246\) 0 0
\(247\) 12.0016i 0.763643i
\(248\) 1.32527 + 16.7908i 0.0841548 + 1.06622i
\(249\) 0 0
\(250\) 14.9173 5.24158i 0.943453 0.331506i
\(251\) −10.5401 + 10.5401i −0.665287 + 0.665287i −0.956621 0.291334i \(-0.905901\pi\)
0.291334 + 0.956621i \(0.405901\pi\)
\(252\) 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
\(260\) 10.8645 + 1.14946i 0.673789 + 0.0712868i
\(261\) 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 −0.988243 0.152894i \(-0.951141\pi\)
0.152894 + 0.988243i \(0.451141\pi\)
\(270\) 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
\(275\) −0.563529 1.11059i −0.0339821 0.0669708i
\(276\) 0 0
\(277\) −10.7023 10.7023i −0.643041 0.643041i 0.308261 0.951302i \(-0.400253\pi\)
−0.951302 + 0.308261i \(0.900253\pi\)
\(278\) 16.9220 + 16.0560i 1.01492 + 0.962974i
\(279\) 0 0
\(280\) −6.76989 + 5.77486i −0.404578 + 0.345114i
\(281\) 23.3237 1.39138 0.695688 0.718344i \(-0.255100\pi\)
0.695688 + 0.718344i \(0.255100\pi\)
\(282\) 0 0
\(283\) 7.39967 7.39967i 0.439865 0.439865i −0.452102 0.891966i \(-0.649326\pi\)
0.891966 + 0.452102i \(0.149326\pi\)
\(284\) −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
\(290\) 11.6176 + 1.53851i 0.682210 + 0.0903444i
\(291\) 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 0.961818 0.273689i \(-0.0882437\pi\)
−0.273689 + 0.961818i \(0.588244\pi\)
\(308\) 0.520921 + 0.468898i 0.0296822 + 0.0267179i
\(309\) 0 0
\(310\) −14.9485 + 11.4522i −0.849016 + 0.650444i
\(311\) 31.3243i 1.77624i 0.459615 + 0.888118i \(0.347988\pi\)
−0.459615 + 0.888118i \(0.652012\pi\)
\(312\) 0 0
\(313\) −24.0690 −1.36046 −0.680230 0.732999i \(-0.738120\pi\)
−0.680230 + 0.732999i \(0.738120\pi\)
\(314\) −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
\(320\) 12.6442 + 12.6540i 0.706833 + 0.707381i
\(321\) 0 0
\(322\) 0.103222 + 3.93061i 0.00575233 + 0.219044i
\(323\) 10.9677 10.9677i 0.610257 0.610257i
\(324\) 0 0
\(325\) 5.52710 + 10.8927i 0.306589 + 0.604216i
\(326\) 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 \(0.157129\pi\)
−0.880616 + 0.473830i \(0.842871\pi\)
\(338\) −0.261071 9.94139i −0.0142004 0.540741i
\(339\) 0 0
\(340\) 8.87811 + 10.9790i 0.481483 + 0.595419i
\(341\) 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 \(0.794253\pi\)
\(350\) −9.53441 2.84084i −0.509636 0.151849i
\(351\) 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
\(355\) 0.172226 0.124909i 0.00914081 0.00662949i
\(356\) −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 \(-0.926111\pi\)
0.973178 0.230051i \(-0.0738894\pi\)
\(360\) 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
\(365\) −10.4910 14.4651i −0.549124 0.757138i
\(366\) 0 0
\(367\) −28.0501 −1.46420 −0.732101 0.681196i \(-0.761460\pi\)
−0.732101 + 0.681196i \(0.761460\pi\)
\(368\) 7.86098 0.828609i 0.409782 0.0431942i
\(369\) 0 0
\(370\) 3.36136 25.3824i 0.174749 1.31957i
\(371\) −7.52841 7.52841i −0.390856 0.390856i
\(372\) 0 0
\(373\) −4.90740 4.90740i −0.254096 0.254096i 0.568552 0.822647i \(-0.307504\pi\)
−0.822647 + 0.568552i \(0.807504\pi\)
\(374\) 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 \(0.354478\pi\)
\(380\) 21.8486 + 2.31158i 1.12081 + 0.118582i
\(381\) 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 0.971860 0.235558i \(-0.0756918\pi\)
−0.235558 + 0.971860i \(0.575692\pi\)
\(390\) 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
\(395\) 10.2565 7.43864i 0.516060 0.374279i
\(396\) 0 0
\(397\) 18.3367 18.3367i 0.920291 0.920291i −0.0767588 0.997050i \(-0.524457\pi\)
0.997050 + 0.0767588i \(0.0244571\pi\)
\(398\) −10.7239 + 0.281620i −0.537540 + 0.0141163i
\(399\) 0 0
\(400\) −4.18515 + 19.5572i −0.209257 + 0.977861i
\(401\) 33.5380i 1.67481i −0.546585 0.837404i \(-0.684073\pi\)
0.546585 0.837404i \(-0.315927\pi\)
\(402\) 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 \(-0.146842\pi\)
\(410\) 0.306685 + 0.400312i 0.0151461 + 0.0197700i
\(411\) 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 0.985981 0.166856i \(-0.0533614\pi\)
−0.166856 + 0.985981i \(0.553361\pi\)
\(420\) 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
\(430\) 29.3962 + 3.89290i 1.41761 + 0.187733i
\(431\) −36.6726 −1.76646 −0.883228 0.468943i \(-0.844635\pi\)
−0.883228 + 0.468943i \(0.844635\pi\)
\(432\) 0 0
\(433\) 28.1455i 1.35259i −0.736633 0.676293i \(-0.763586\pi\)
0.736633 0.676293i \(-0.236414\pi\)
\(434\) 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 \(0.525296\pi\)
\(440\) 1.57036 + 0.124559i 0.0748640 + 0.00593810i
\(441\) 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
\(445\) −14.3489 19.7844i −0.680203 0.937871i
\(446\) 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 \(0.109311\pi\)
−0.941612 + 0.336701i \(0.890689\pi\)
\(450\) 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 \(-0.699359\pi\)
−0.586154 + 0.810200i \(0.699359\pi\)
\(458\) 0.0615201 0.0648384i 0.00287464 0.00302970i
\(459\) 0 0
\(460\) 5.55692 + 6.87188i 0.259093 + 0.320403i
\(461\) 11.6030 11.6030i 0.540407 0.540407i −0.383241 0.923648i \(-0.625192\pi\)
0.923648 + 0.383241i \(0.125192\pi\)
\(462\) 0 0
\(463\) 8.74913 0.406607 0.203303 0.979116i \(-0.434832\pi\)
0.203303 + 0.979116i \(0.434832\pi\)
\(464\) −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
\(470\) 2.89240 2.21591i 0.133416 0.102212i
\(471\) 0 0
\(472\) −11.6493 + 13.6458i −0.536201 + 0.628097i
\(473\) 2.33559i 0.107391i
\(474\) 0 0
\(475\) 11.1150 + 21.9052i 0.509993 + 1.00508i
\(476\) −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 \(-0.349205\pi\)
0.456215 + 0.889869i \(0.349205\pi\)
\(480\) 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
\(485\) −18.9003 + 13.7077i −0.858219 + 0.622434i
\(486\) 0 0
\(487\) 34.8592i 1.57962i −0.613351 0.789811i \(-0.710179\pi\)
0.613351 0.789811i \(-0.289821\pi\)
\(488\) −20.7089 17.6790i −0.937446 0.800289i
\(489\) 0 0
\(490\) −9.65520 12.6028i −0.436177 0.569336i
\(491\) −21.4659 + 21.4659i −0.968743 + 0.968743i −0.999526 0.0307829i \(-0.990200\pi\)
0.0307829 + 0.999526i \(0.490200\pi\)
\(492\) 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 \(0.443930\pi\)
\(500\) −20.8944 + 7.96397i −0.934425 + 0.356160i
\(501\) 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 −0.417612 0.908626i \(-0.637133\pi\)
0.908626 + 0.417612i \(0.137133\pi\)
\(510\) 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
\(515\) 13.8597 10.0519i 0.610732 0.442941i
\(516\) 0 0
\(517\) −0.202933 0.202933i −0.00892500 0.00892500i
\(518\) −11.0887 + 11.6868i −0.487207 + 0.513487i
\(519\) 0 0
\(520\) −15.4021 1.22167i −0.675428 0.0535739i
\(521\) 2.61052 0.114369 0.0571844 0.998364i \(-0.481788\pi\)
0.0571844 + 0.998364i \(0.481788\pi\)
\(522\) 0 0
\(523\) −21.2735 + 21.2735i −0.930226 + 0.930226i −0.997720 0.0674935i \(-0.978500\pi\)
0.0674935 + 0.997720i \(0.478500\pi\)
\(524\) 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
\(530\) −23.7227 3.14157i −1.03045 0.136461i
\(531\) 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 \(0.00909983\pi\)
0.0285840 + 0.999591i \(0.490900\pi\)
\(548\) 1.58521 + 30.1610i 0.0677168 + 1.28841i
\(549\) 0 0
\(550\) 0.837907 + 1.54914i 0.0357285 + 0.0660557i
\(551\) 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
\(560\) 9.35637 8.41540i 0.395379 0.355616i
\(561\) 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
\(565\) 9.04353 + 12.4693i 0.380464 + 0.524588i
\(566\) −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 \(-0.467664\pi\)
0.101411 + 0.994845i \(0.467664\pi\)
\(570\) 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 \(0.122432\pi\)
−0.926936 + 0.375219i \(0.877568\pi\)
\(578\) 9.94139 0.261071i 0.413508 0.0108591i
\(579\) 0 0
\(580\) −16.4813 1.74372i −0.684347 0.0724039i
\(581\) −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
\(590\) −19.8860 2.63349i −0.818695 0.108419i
\(591\) 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
\(595\) 8.04060 5.83155i 0.329632 0.239070i
\(596\) −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 \(0.0541868\pi\)
−0.985545 + 0.169412i \(0.945813\pi\)
\(600\) 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
\(605\) −19.7990 + 14.3595i −0.804944 + 0.583796i
\(606\) 0 0
\(607\) −22.0548 −0.895178 −0.447589 0.894239i \(-0.647717\pi\)
−0.447589 + 0.894239i \(0.647717\pi\)
\(608\) −16.9097 + 22.0543i −0.685779 + 0.894419i
\(609\) 0 0
\(610\) 3.99659 30.1791i 0.161817 1.22192i
\(611\) 1.99038 + 1.99038i 0.0805220 + 0.0805220i
\(612\) 0 0
\(613\) 14.9250 + 14.9250i 0.602816 + 0.602816i 0.941059 0.338243i \(-0.109832\pi\)
−0.338243 + 0.941059i \(0.609832\pi\)
\(614\) −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 \(0.687262\pi\)
\(620\) 20.7079 16.7453i 0.831647 0.672508i
\(621\) 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
\(635\) −4.17625 5.75825i −0.165729 0.228509i
\(636\) 0 0
\(637\) 8.67249 8.67249i 0.343617 0.343617i
\(638\) 0.0342689 + 1.30493i 0.00135672 + 0.0516629i
\(639\) 0 0
\(640\) −18.3452 17.4199i −0.725159 0.688581i
\(641\) 28.3921i 1.12142i −0.828013 0.560710i \(-0.810528\pi\)
0.828013 0.560710i \(-0.189472\pi\)
\(642\) 0 0
\(643\) −2.71547 2.71547i −0.107088 0.107088i 0.651533 0.758621i \(-0.274126\pi\)
−0.758621 + 0.651533i \(0.774126\pi\)
\(644\) −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
\(650\) −8.21821 15.1940i −0.322345 0.595959i
\(651\) 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 0.115005 0.993365i \(-0.463311\pi\)
−0.993365 + 0.115005i \(0.963311\pi\)
\(660\) 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
\(670\) 5.85516 44.2136i 0.226205 1.70812i
\(671\) −2.39780 −0.0925661
\(672\) 0 0
\(673\) 20.2889i 0.782080i 0.920374 + 0.391040i \(0.127885\pi\)
−0.920374 + 0.391040i \(0.872115\pi\)
\(674\) −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
\(680\) −12.9588 15.1917i −0.496948 0.582574i
\(681\) 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
\(685\) −27.3351 + 19.8252i −1.04442 + 0.757480i
\(686\) 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
\(700\) 13.5845 + 3.66219i 0.513447 + 0.138418i
\(701\) 34.9589 34.9589i 1.32038 1.32038i 0.406913 0.913467i \(-0.366605\pi\)
0.913467 0.406913i \(-0.133395\pi\)
\(702\) 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 \(0.435922\pi\)
\(710\) −0.238843 + 0.182981i −0.00896362 + 0.00686716i
\(711\) 0 0
\(712\) 30.8186 2.43246i 1.15498 0.0911602i
\(713\) 11.7677i 0.440704i
\(714\) 0 0
\(715\) −1.10141 + 0.798814i −0.0411905 + 0.0298740i
\(716\) −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 \(-0.556593\pi\)
−0.176857 + 0.984237i \(0.556593\pi\)
\(720\) 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
\(725\) −8.38451 16.5239i −0.311393 0.613684i
\(726\) 0 0
\(727\) 29.4631i 1.09272i 0.837549 + 0.546362i \(0.183988\pi\)
−0.837549 + 0.546362i \(0.816012\pi\)
\(728\) 7.39376 + 6.31199i 0.274031 + 0.233938i
\(729\) 0 0
\(730\) 15.3684 + 20.0602i 0.568811 + 0.742462i
\(731\) −20.9341 + 20.9341i −0.774275 + 0.774275i
\(732\) 0 0
\(733\) −13.5703 + 13.5703i −0.501231 + 0.501231i −0.911820 0.410590i \(-0.865323\pi\)
0.410590 + 0.911820i \(0.365323\pi\)
\(734\) 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 \(0.259903\pi\)
\(740\) −3.80970 + 36.0085i −0.140047 + 1.32370i
\(741\) 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
\(755\) −28.7199 39.5993i −1.04522 1.44117i
\(756\) 0 0
\(757\) 19.7676 + 19.7676i 0.718467 + 0.718467i 0.968291 0.249824i \(-0.0803728\pi\)
−0.249824 + 0.968291i \(0.580373\pi\)
\(758\) −37.8121 35.8770i −1.37340 1.30311i
\(759\) 0 0
\(760\) −30.9738 2.45680i −1.12354 0.0891173i
\(761\) 3.72357 0.134979 0.0674896 0.997720i \(-0.478501\pi\)
0.0674896 + 0.997720i \(0.478501\pi\)
\(762\) 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 \(0.605174\pi\)
\(770\) 0.145485 1.09859i 0.00524290 0.0395903i
\(771\) 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 0.999772 0.0213618i \(-0.00680019\pi\)
−0.0213618 + 0.999772i \(0.506800\pi\)
\(788\) 6.80820 7.56356i 0.242532 0.269441i
\(789\) 0 0
\(790\) −14.2237 + 10.8970i −0.506056 + 0.387697i
\(791\)