Properties

Label 576.2.bb.e.49.13
Level $576$
Weight $2$
Character 576.49
Analytic conductor $4.599$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bb (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 49.13
Character \(\chi\) \(=\) 576.49
Dual form 576.2.bb.e.529.13

$q$-expansion

\(f(q)\) \(=\) \(q+(1.15652 + 1.28937i) q^{3} +(1.21694 - 0.326078i) q^{5} +(0.707732 - 0.408609i) q^{7} +(-0.324925 + 2.98235i) q^{9} +O(q^{10})\) \(q+(1.15652 + 1.28937i) q^{3} +(1.21694 - 0.326078i) q^{5} +(0.707732 - 0.408609i) q^{7} +(-0.324925 + 2.98235i) q^{9} +(-0.497094 + 1.85518i) q^{11} +(0.116336 + 0.434170i) q^{13} +(1.82785 + 1.19196i) q^{15} +6.62002 q^{17} +(-1.18421 + 1.18421i) q^{19} +(1.34535 + 0.439960i) q^{21} +(-2.66201 - 1.53691i) q^{23} +(-2.95551 + 1.70637i) q^{25} +(-4.22112 + 3.03020i) q^{27} +(8.65622 + 2.31943i) q^{29} +(4.61440 - 7.99238i) q^{31} +(-2.96690 + 1.50462i) q^{33} +(0.728028 - 0.728028i) q^{35} +(-2.14134 - 2.14134i) q^{37} +(-0.425259 + 0.652125i) q^{39} +(-9.15868 - 5.28777i) q^{41} +(-1.66072 + 6.19791i) q^{43} +(0.577065 + 3.73529i) q^{45} +(0.140916 + 0.244074i) q^{47} +(-3.16608 + 5.48381i) q^{49} +(7.65618 + 8.53562i) q^{51} +(4.83822 + 4.83822i) q^{53} +2.41973i q^{55} +(-2.89645 - 0.157317i) q^{57} +(7.15823 - 1.91804i) q^{59} +(-9.87829 - 2.64688i) q^{61} +(0.988656 + 2.24347i) q^{63} +(0.283147 + 0.490424i) q^{65} +(-1.39968 - 5.22368i) q^{67} +(-1.09702 - 5.20977i) q^{69} -3.27174i q^{71} -4.92262i q^{73} +(-5.61824 - 1.83729i) q^{75} +(0.406234 + 1.51609i) q^{77} +(-7.70232 - 13.3408i) q^{79} +(-8.78885 - 1.93808i) q^{81} +(10.9241 + 2.92711i) q^{83} +(8.05616 - 2.15864i) q^{85} +(7.02050 + 13.8435i) q^{87} -3.44143i q^{89} +(0.259740 + 0.259740i) q^{91} +(15.6417 - 3.29369i) q^{93} +(-1.05497 + 1.82726i) q^{95} +(-4.46939 - 7.74121i) q^{97} +(-5.37128 - 2.08530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q - 2q^{3} + 4q^{5} + O(q^{10}) \) \( 72q - 2q^{3} + 4q^{5} + 2q^{11} - 16q^{13} + 20q^{15} - 16q^{17} - 28q^{19} - 16q^{21} - 8q^{27} + 4q^{29} - 28q^{31} - 32q^{33} + 16q^{35} + 16q^{37} + 10q^{43} + 40q^{45} + 56q^{47} + 4q^{49} + 54q^{51} - 8q^{53} + 14q^{59} - 32q^{61} + 108q^{63} - 64q^{65} + 18q^{67} + 32q^{69} - 86q^{75} - 36q^{77} - 44q^{79} - 44q^{81} - 20q^{83} - 8q^{85} + 80q^{91} - 4q^{93} - 48q^{95} + 40q^{97} - 28q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.15652 + 1.28937i 0.667717 + 0.744415i
\(4\) 0 0
\(5\) 1.21694 0.326078i 0.544232 0.145827i 0.0237796 0.999717i \(-0.492430\pi\)
0.520452 + 0.853891i \(0.325763\pi\)
\(6\) 0 0
\(7\) 0.707732 0.408609i 0.267497 0.154440i −0.360252 0.932855i \(-0.617309\pi\)
0.627750 + 0.778415i \(0.283976\pi\)
\(8\) 0 0
\(9\) −0.324925 + 2.98235i −0.108308 + 0.994117i
\(10\) 0 0
\(11\) −0.497094 + 1.85518i −0.149879 + 0.559357i 0.849610 + 0.527411i \(0.176837\pi\)
−0.999490 + 0.0319463i \(0.989829\pi\)
\(12\) 0 0
\(13\) 0.116336 + 0.434170i 0.0322657 + 0.120417i 0.980180 0.198107i \(-0.0634794\pi\)
−0.947915 + 0.318524i \(0.896813\pi\)
\(14\) 0 0
\(15\) 1.82785 + 1.19196i 0.471948 + 0.307764i
\(16\) 0 0
\(17\) 6.62002 1.60559 0.802795 0.596255i \(-0.203345\pi\)
0.802795 + 0.596255i \(0.203345\pi\)
\(18\) 0 0
\(19\) −1.18421 + 1.18421i −0.271677 + 0.271677i −0.829775 0.558098i \(-0.811531\pi\)
0.558098 + 0.829775i \(0.311531\pi\)
\(20\) 0 0
\(21\) 1.34535 + 0.439960i 0.293580 + 0.0960072i
\(22\) 0 0
\(23\) −2.66201 1.53691i −0.555067 0.320468i 0.196096 0.980585i \(-0.437174\pi\)
−0.751163 + 0.660117i \(0.770507\pi\)
\(24\) 0 0
\(25\) −2.95551 + 1.70637i −0.591102 + 0.341273i
\(26\) 0 0
\(27\) −4.22112 + 3.03020i −0.812356 + 0.583163i
\(28\) 0 0
\(29\) 8.65622 + 2.31943i 1.60742 + 0.430707i 0.947272 0.320430i \(-0.103827\pi\)
0.660147 + 0.751136i \(0.270494\pi\)
\(30\) 0 0
\(31\) 4.61440 7.99238i 0.828771 1.43547i −0.0702316 0.997531i \(-0.522374\pi\)
0.899003 0.437943i \(-0.144293\pi\)
\(32\) 0 0
\(33\) −2.96690 + 1.50462i −0.516471 + 0.261920i
\(34\) 0 0
\(35\) 0.728028 0.728028i 0.123059 0.123059i
\(36\) 0 0
\(37\) −2.14134 2.14134i −0.352035 0.352035i 0.508831 0.860866i \(-0.330078\pi\)
−0.860866 + 0.508831i \(0.830078\pi\)
\(38\) 0 0
\(39\) −0.425259 + 0.652125i −0.0680960 + 0.104424i
\(40\) 0 0
\(41\) −9.15868 5.28777i −1.43035 0.825810i −0.433199 0.901299i \(-0.642615\pi\)
−0.997147 + 0.0754884i \(0.975948\pi\)
\(42\) 0 0
\(43\) −1.66072 + 6.19791i −0.253258 + 0.945172i 0.715793 + 0.698312i \(0.246065\pi\)
−0.969051 + 0.246860i \(0.920601\pi\)
\(44\) 0 0
\(45\) 0.577065 + 3.73529i 0.0860238 + 0.556825i
\(46\) 0 0
\(47\) 0.140916 + 0.244074i 0.0205547 + 0.0356018i 0.876120 0.482093i \(-0.160123\pi\)
−0.855565 + 0.517695i \(0.826790\pi\)
\(48\) 0 0
\(49\) −3.16608 + 5.48381i −0.452297 + 0.783401i
\(50\) 0 0
\(51\) 7.65618 + 8.53562i 1.07208 + 1.19523i
\(52\) 0 0
\(53\) 4.83822 + 4.83822i 0.664580 + 0.664580i 0.956456 0.291876i \(-0.0942794\pi\)
−0.291876 + 0.956456i \(0.594279\pi\)
\(54\) 0 0
\(55\) 2.41973i 0.326277i
\(56\) 0 0
\(57\) −2.89645 0.157317i −0.383644 0.0208372i
\(58\) 0 0
\(59\) 7.15823 1.91804i 0.931923 0.249708i 0.239248 0.970958i \(-0.423099\pi\)
0.692674 + 0.721251i \(0.256432\pi\)
\(60\) 0 0
\(61\) −9.87829 2.64688i −1.26479 0.338898i −0.436755 0.899581i \(-0.643872\pi\)
−0.828031 + 0.560682i \(0.810539\pi\)
\(62\) 0 0
\(63\) 0.988656 + 2.24347i 0.124559 + 0.282651i
\(64\) 0 0
\(65\) 0.283147 + 0.490424i 0.0351200 + 0.0608296i
\(66\) 0 0
\(67\) −1.39968 5.22368i −0.170998 0.638175i −0.997199 0.0747982i \(-0.976169\pi\)
0.826200 0.563376i \(-0.190498\pi\)
\(68\) 0 0
\(69\) −1.09702 5.20977i −0.132066 0.627182i
\(70\) 0 0
\(71\) 3.27174i 0.388284i −0.980973 0.194142i \(-0.937808\pi\)
0.980973 0.194142i \(-0.0621922\pi\)
\(72\) 0 0
\(73\) 4.92262i 0.576150i −0.957608 0.288075i \(-0.906985\pi\)
0.957608 0.288075i \(-0.0930152\pi\)
\(74\) 0 0
\(75\) −5.61824 1.83729i −0.648738 0.212152i
\(76\) 0 0
\(77\) 0.406234 + 1.51609i 0.0462947 + 0.172774i
\(78\) 0 0
\(79\) −7.70232 13.3408i −0.866578 1.50096i −0.865472 0.500958i \(-0.832981\pi\)
−0.00110666 0.999999i \(-0.500352\pi\)
\(80\) 0 0
\(81\) −8.78885 1.93808i −0.976539 0.215342i
\(82\) 0 0
\(83\) 10.9241 + 2.92711i 1.19908 + 0.321292i 0.802468 0.596695i \(-0.203520\pi\)
0.396610 + 0.917987i \(0.370187\pi\)
\(84\) 0 0
\(85\) 8.05616 2.15864i 0.873813 0.234138i
\(86\) 0 0
\(87\) 7.02050 + 13.8435i 0.752676 + 1.48418i
\(88\) 0 0
\(89\) 3.44143i 0.364790i −0.983225 0.182395i \(-0.941615\pi\)
0.983225 0.182395i \(-0.0583850\pi\)
\(90\) 0 0
\(91\) 0.259740 + 0.259740i 0.0272282 + 0.0272282i
\(92\) 0 0
\(93\) 15.6417 3.29369i 1.62197 0.341540i
\(94\) 0 0
\(95\) −1.05497 + 1.82726i −0.108238 + 0.187473i
\(96\) 0 0
\(97\) −4.46939 7.74121i −0.453798 0.786001i 0.544820 0.838553i \(-0.316598\pi\)
−0.998618 + 0.0525516i \(0.983265\pi\)
\(98\) 0 0
\(99\) −5.37128 2.08530i −0.539834 0.209581i
\(100\) 0 0
\(101\) 1.78073 6.64577i 0.177189 0.661278i −0.818979 0.573823i \(-0.805460\pi\)
0.996168 0.0874556i \(-0.0278736\pi\)
\(102\) 0 0
\(103\) −5.76134 3.32631i −0.567681 0.327751i 0.188541 0.982065i \(-0.439624\pi\)
−0.756223 + 0.654314i \(0.772957\pi\)
\(104\) 0 0
\(105\) 1.78067 + 0.0967154i 0.173776 + 0.00943845i
\(106\) 0 0
\(107\) 4.06262 + 4.06262i 0.392748 + 0.392748i 0.875666 0.482918i \(-0.160423\pi\)
−0.482918 + 0.875666i \(0.660423\pi\)
\(108\) 0 0
\(109\) −7.19802 + 7.19802i −0.689445 + 0.689445i −0.962109 0.272664i \(-0.912095\pi\)
0.272664 + 0.962109i \(0.412095\pi\)
\(110\) 0 0
\(111\) 0.284468 5.23748i 0.0270005 0.497119i
\(112\) 0 0
\(113\) 6.45739 11.1845i 0.607460 1.05215i −0.384197 0.923251i \(-0.625522\pi\)
0.991657 0.128901i \(-0.0411450\pi\)
\(114\) 0 0
\(115\) −3.74066 1.00231i −0.348818 0.0934655i
\(116\) 0 0
\(117\) −1.33265 + 0.205881i −0.123203 + 0.0190337i
\(118\) 0 0
\(119\) 4.68520 2.70500i 0.429491 0.247967i
\(120\) 0 0
\(121\) 6.33169 + 3.65560i 0.575608 + 0.332328i
\(122\) 0 0
\(123\) −3.77433 17.9243i −0.340320 1.61618i
\(124\) 0 0
\(125\) −7.49458 + 7.49458i −0.670336 + 0.670336i
\(126\) 0 0
\(127\) −14.6917 −1.30368 −0.651838 0.758358i \(-0.726002\pi\)
−0.651838 + 0.758358i \(0.726002\pi\)
\(128\) 0 0
\(129\) −9.91202 + 5.02672i −0.872705 + 0.442578i
\(130\) 0 0
\(131\) −2.59556 9.68678i −0.226775 0.846338i −0.981685 0.190509i \(-0.938986\pi\)
0.754910 0.655828i \(-0.227681\pi\)
\(132\) 0 0
\(133\) −0.354225 + 1.32198i −0.0307152 + 0.114631i
\(134\) 0 0
\(135\) −4.14877 + 5.06399i −0.357069 + 0.435839i
\(136\) 0 0
\(137\) 2.37032 1.36850i 0.202510 0.116919i −0.395316 0.918545i \(-0.629365\pi\)
0.597826 + 0.801626i \(0.296031\pi\)
\(138\) 0 0
\(139\) −8.46230 + 2.26747i −0.717763 + 0.192324i −0.599173 0.800619i \(-0.704504\pi\)
−0.118590 + 0.992943i \(0.537837\pi\)
\(140\) 0 0
\(141\) −0.151728 + 0.463968i −0.0127778 + 0.0390732i
\(142\) 0 0
\(143\) −0.863293 −0.0721922
\(144\) 0 0
\(145\) 11.2904 0.937617
\(146\) 0 0
\(147\) −10.7323 + 2.25990i −0.885182 + 0.186393i
\(148\) 0 0
\(149\) −8.25990 + 2.21323i −0.676678 + 0.181315i −0.580761 0.814074i \(-0.697245\pi\)
−0.0959167 + 0.995389i \(0.530578\pi\)
\(150\) 0 0
\(151\) 20.2738 11.7051i 1.64986 0.952546i 0.672732 0.739886i \(-0.265121\pi\)
0.977126 0.212660i \(-0.0682126\pi\)
\(152\) 0 0
\(153\) −2.15101 + 19.7432i −0.173899 + 1.59614i
\(154\) 0 0
\(155\) 3.00931 11.2309i 0.241714 0.902087i
\(156\) 0 0
\(157\) −5.60365 20.9131i −0.447220 1.66905i −0.710008 0.704194i \(-0.751309\pi\)
0.262788 0.964854i \(-0.415358\pi\)
\(158\) 0 0
\(159\) −0.642736 + 11.8337i −0.0509723 + 0.938475i
\(160\) 0 0
\(161\) −2.51198 −0.197972
\(162\) 0 0
\(163\) −1.39858 + 1.39858i −0.109545 + 0.109545i −0.759755 0.650210i \(-0.774681\pi\)
0.650210 + 0.759755i \(0.274681\pi\)
\(164\) 0 0
\(165\) −3.11992 + 2.79847i −0.242885 + 0.217860i
\(166\) 0 0
\(167\) −20.0385 11.5692i −1.55063 0.895254i −0.998091 0.0617643i \(-0.980327\pi\)
−0.552535 0.833490i \(-0.686339\pi\)
\(168\) 0 0
\(169\) 11.0834 6.39898i 0.852566 0.492229i
\(170\) 0 0
\(171\) −3.14696 3.91652i −0.240654 0.299504i
\(172\) 0 0
\(173\) 4.95697 + 1.32822i 0.376871 + 0.100982i 0.442282 0.896876i \(-0.354169\pi\)
−0.0654105 + 0.997858i \(0.520836\pi\)
\(174\) 0 0
\(175\) −1.39447 + 2.41530i −0.105412 + 0.182579i
\(176\) 0 0
\(177\) 10.7517 + 7.01132i 0.808147 + 0.527003i
\(178\) 0 0
\(179\) −3.14784 + 3.14784i −0.235281 + 0.235281i −0.814893 0.579612i \(-0.803204\pi\)
0.579612 + 0.814893i \(0.303204\pi\)
\(180\) 0 0
\(181\) −2.82816 2.82816i −0.210216 0.210216i 0.594143 0.804359i \(-0.297491\pi\)
−0.804359 + 0.594143i \(0.797491\pi\)
\(182\) 0 0
\(183\) −8.01164 15.7979i −0.592238 1.16781i
\(184\) 0 0
\(185\) −3.30413 1.90764i −0.242924 0.140253i
\(186\) 0 0
\(187\) −3.29077 + 12.2813i −0.240645 + 0.898099i
\(188\) 0 0
\(189\) −1.74925 + 3.86936i −0.127240 + 0.281454i
\(190\) 0 0
\(191\) 8.50375 + 14.7289i 0.615310 + 1.06575i 0.990330 + 0.138732i \(0.0443025\pi\)
−0.375020 + 0.927017i \(0.622364\pi\)
\(192\) 0 0
\(193\) −2.70970 + 4.69334i −0.195049 + 0.337834i −0.946916 0.321480i \(-0.895820\pi\)
0.751868 + 0.659314i \(0.229153\pi\)
\(194\) 0 0
\(195\) −0.304871 + 0.932265i −0.0218323 + 0.0667609i
\(196\) 0 0
\(197\) −8.03915 8.03915i −0.572766 0.572766i 0.360135 0.932900i \(-0.382731\pi\)
−0.932900 + 0.360135i \(0.882731\pi\)
\(198\) 0 0
\(199\) 11.2258i 0.795773i 0.917435 + 0.397886i \(0.130256\pi\)
−0.917435 + 0.397886i \(0.869744\pi\)
\(200\) 0 0
\(201\) 5.11648 7.84599i 0.360888 0.553414i
\(202\) 0 0
\(203\) 7.07402 1.89548i 0.496499 0.133036i
\(204\) 0 0
\(205\) −12.8698 3.44845i −0.898865 0.240850i
\(206\) 0 0
\(207\) 5.44856 7.43966i 0.378701 0.517092i
\(208\) 0 0
\(209\) −1.60826 2.78559i −0.111246 0.192683i
\(210\) 0 0
\(211\) 3.84526 + 14.3507i 0.264718 + 0.987942i 0.962423 + 0.271556i \(0.0875383\pi\)
−0.697704 + 0.716386i \(0.745795\pi\)
\(212\) 0 0
\(213\) 4.21846 3.78383i 0.289044 0.259264i
\(214\) 0 0
\(215\) 8.08400i 0.551324i
\(216\) 0 0
\(217\) 7.54195i 0.511981i
\(218\) 0 0
\(219\) 6.34706 5.69311i 0.428895 0.384705i
\(220\) 0 0
\(221\) 0.770143 + 2.87421i 0.0518054 + 0.193340i
\(222\) 0 0
\(223\) 8.28003 + 14.3414i 0.554472 + 0.960373i 0.997944 + 0.0640854i \(0.0204130\pi\)
−0.443473 + 0.896288i \(0.646254\pi\)
\(224\) 0 0
\(225\) −4.12866 9.36882i −0.275244 0.624588i
\(226\) 0 0
\(227\) −7.88725 2.11338i −0.523495 0.140270i −0.0126123 0.999920i \(-0.504015\pi\)
−0.510883 + 0.859650i \(0.670681\pi\)
\(228\) 0 0
\(229\) −4.33776 + 1.16230i −0.286647 + 0.0768068i −0.399278 0.916830i \(-0.630739\pi\)
0.112631 + 0.993637i \(0.464072\pi\)
\(230\) 0 0
\(231\) −1.48497 + 2.27717i −0.0977039 + 0.149827i
\(232\) 0 0
\(233\) 7.33128i 0.480288i 0.970737 + 0.240144i \(0.0771947\pi\)
−0.970737 + 0.240144i \(0.922805\pi\)
\(234\) 0 0
\(235\) 0.251073 + 0.251073i 0.0163782 + 0.0163782i
\(236\) 0 0
\(237\) 8.29329 25.3600i 0.538707 1.64731i
\(238\) 0 0
\(239\) −3.40305 + 5.89425i −0.220125 + 0.381268i −0.954846 0.297102i \(-0.903980\pi\)
0.734721 + 0.678370i \(0.237313\pi\)
\(240\) 0 0
\(241\) 2.98687 + 5.17340i 0.192401 + 0.333248i 0.946045 0.324034i \(-0.105039\pi\)
−0.753644 + 0.657282i \(0.771706\pi\)
\(242\) 0 0
\(243\) −7.66558 13.5735i −0.491747 0.870738i
\(244\) 0 0
\(245\) −2.06478 + 7.70585i −0.131914 + 0.492309i
\(246\) 0 0
\(247\) −0.651915 0.376383i −0.0414804 0.0239487i
\(248\) 0 0
\(249\) 8.85985 + 17.4704i 0.561470 + 1.10714i
\(250\) 0 0
\(251\) 16.1412 + 16.1412i 1.01882 + 1.01882i 0.999819 + 0.0190030i \(0.00604922\pi\)
0.0190030 + 0.999819i \(0.493951\pi\)
\(252\) 0 0
\(253\) 4.17451 4.17451i 0.262449 0.262449i
\(254\) 0 0
\(255\) 12.1004 + 7.89082i 0.757755 + 0.494142i
\(256\) 0 0
\(257\) −0.172522 + 0.298817i −0.0107616 + 0.0186397i −0.871356 0.490651i \(-0.836759\pi\)
0.860594 + 0.509291i \(0.170092\pi\)
\(258\) 0 0
\(259\) −2.39047 0.640524i −0.148536 0.0398002i
\(260\) 0 0
\(261\) −9.72997 + 25.0623i −0.602270 + 1.55131i
\(262\) 0 0
\(263\) 4.43128 2.55840i 0.273244 0.157758i −0.357117 0.934060i \(-0.616240\pi\)
0.630361 + 0.776302i \(0.282907\pi\)
\(264\) 0 0
\(265\) 7.46546 + 4.31018i 0.458599 + 0.264772i
\(266\) 0 0
\(267\) 4.43726 3.98008i 0.271556 0.243577i
\(268\) 0 0
\(269\) −15.4613 + 15.4613i −0.942692 + 0.942692i −0.998445 0.0557529i \(-0.982244\pi\)
0.0557529 + 0.998445i \(0.482244\pi\)
\(270\) 0 0
\(271\) 12.4048 0.753538 0.376769 0.926307i \(-0.377035\pi\)
0.376769 + 0.926307i \(0.377035\pi\)
\(272\) 0 0
\(273\) −0.0345053 + 0.635294i −0.00208836 + 0.0384498i
\(274\) 0 0
\(275\) −1.69645 6.33123i −0.102300 0.381787i
\(276\) 0 0
\(277\) −5.42920 + 20.2621i −0.326209 + 1.21743i 0.586881 + 0.809673i \(0.300356\pi\)
−0.913091 + 0.407757i \(0.866311\pi\)
\(278\) 0 0
\(279\) 22.3368 + 16.3587i 1.33727 + 0.979370i
\(280\) 0 0
\(281\) 10.9537 6.32414i 0.653445 0.377266i −0.136330 0.990663i \(-0.543531\pi\)
0.789775 + 0.613397i \(0.210197\pi\)
\(282\) 0 0
\(283\) 21.2483 5.69346i 1.26308 0.338441i 0.435703 0.900090i \(-0.356500\pi\)
0.827375 + 0.561650i \(0.189833\pi\)
\(284\) 0 0
\(285\) −3.57610 + 0.753021i −0.211830 + 0.0446051i
\(286\) 0 0
\(287\) −8.64252 −0.510152
\(288\) 0 0
\(289\) 26.8246 1.57792
\(290\) 0 0
\(291\) 4.81231 14.7155i 0.282103 0.862641i
\(292\) 0 0
\(293\) −0.111616 + 0.0299075i −0.00652069 + 0.00174721i −0.262078 0.965047i \(-0.584408\pi\)
0.255557 + 0.966794i \(0.417741\pi\)
\(294\) 0 0
\(295\) 8.08571 4.66828i 0.470768 0.271798i
\(296\) 0 0
\(297\) −3.52327 9.33723i −0.204441 0.541801i
\(298\) 0 0
\(299\) 0.357595 1.33456i 0.0206802 0.0771797i
\(300\) 0 0
\(301\) 1.35717 + 5.06504i 0.0782262 + 0.291944i
\(302\) 0 0
\(303\) 10.6283 5.38995i 0.610578 0.309645i
\(304\) 0 0
\(305\) −12.8844 −0.737757
\(306\) 0 0
\(307\) 12.4426 12.4426i 0.710135 0.710135i −0.256428 0.966563i \(-0.582546\pi\)
0.966563 + 0.256428i \(0.0825456\pi\)
\(308\) 0 0
\(309\) −2.37427 11.2754i −0.135068 0.641436i
\(310\) 0 0
\(311\) 2.03115 + 1.17269i 0.115176 + 0.0664969i 0.556481 0.830860i \(-0.312151\pi\)
−0.441305 + 0.897357i \(0.645484\pi\)
\(312\) 0 0
\(313\) 8.62293 4.97845i 0.487397 0.281399i −0.236097 0.971729i \(-0.575868\pi\)
0.723494 + 0.690331i \(0.242535\pi\)
\(314\) 0 0
\(315\) 1.93468 + 2.40779i 0.109007 + 0.135664i
\(316\) 0 0
\(317\) 4.42985 + 1.18698i 0.248805 + 0.0666672i 0.381066 0.924548i \(-0.375557\pi\)
−0.132261 + 0.991215i \(0.542224\pi\)
\(318\) 0 0
\(319\) −8.60590 + 14.9059i −0.481838 + 0.834568i
\(320\) 0 0
\(321\) −0.539701 + 9.93669i −0.0301232 + 0.554612i
\(322\) 0 0
\(323\) −7.83950 + 7.83950i −0.436202 + 0.436202i
\(324\) 0 0
\(325\) −1.08468 1.08468i −0.0601674 0.0601674i
\(326\) 0 0
\(327\) −17.6055 0.956225i −0.973588 0.0528794i
\(328\) 0 0
\(329\) 0.199461 + 0.115159i 0.0109967 + 0.00634892i
\(330\) 0 0
\(331\) −4.49465 + 16.7743i −0.247048 + 0.921997i 0.725294 + 0.688439i \(0.241704\pi\)
−0.972343 + 0.233558i \(0.924963\pi\)
\(332\) 0 0
\(333\) 7.08202 5.69046i 0.388092 0.311835i
\(334\) 0 0
\(335\) −3.40666 5.90050i −0.186126 0.322379i
\(336\) 0 0
\(337\) −14.8424 + 25.7078i −0.808517 + 1.40039i 0.105375 + 0.994433i \(0.466396\pi\)
−0.913891 + 0.405959i \(0.866937\pi\)
\(338\) 0 0
\(339\) 21.8890 4.60919i 1.18885 0.250337i
\(340\) 0 0
\(341\) 12.5335 + 12.5335i 0.678727 + 0.678727i
\(342\) 0 0
\(343\) 10.8953i 0.588290i
\(344\) 0 0
\(345\) −3.03380 5.98226i −0.163334 0.322074i
\(346\) 0 0
\(347\) −1.94185 + 0.520318i −0.104244 + 0.0279321i −0.310564 0.950552i \(-0.600518\pi\)
0.206320 + 0.978485i \(0.433851\pi\)
\(348\) 0 0
\(349\) 26.6321 + 7.13604i 1.42558 + 0.381984i 0.887461 0.460883i \(-0.152467\pi\)
0.538122 + 0.842867i \(0.319134\pi\)
\(350\) 0 0
\(351\) −1.80669 1.48017i −0.0964339 0.0790054i
\(352\) 0 0
\(353\) 1.58657 + 2.74801i 0.0844444 + 0.146262i 0.905154 0.425083i \(-0.139755\pi\)
−0.820710 + 0.571345i \(0.806422\pi\)
\(354\) 0 0
\(355\) −1.06684 3.98150i −0.0566220 0.211316i
\(356\) 0 0
\(357\) 8.90625 + 2.91254i 0.471369 + 0.154148i
\(358\) 0 0
\(359\) 22.6997i 1.19804i 0.800732 + 0.599022i \(0.204444\pi\)
−0.800732 + 0.599022i \(0.795556\pi\)
\(360\) 0 0
\(361\) 16.1953i 0.852383i
\(362\) 0 0
\(363\) 2.60932 + 12.3916i 0.136954 + 0.650393i
\(364\) 0 0
\(365\) −1.60516 5.99054i −0.0840179 0.313559i
\(366\) 0 0
\(367\) 1.94141 + 3.36261i 0.101341 + 0.175527i 0.912237 0.409662i \(-0.134354\pi\)
−0.810897 + 0.585189i \(0.801020\pi\)
\(368\) 0 0
\(369\) 18.7459 25.5963i 0.975871 1.33249i
\(370\) 0 0
\(371\) 5.40110 + 1.44722i 0.280411 + 0.0751359i
\(372\) 0 0
\(373\) 4.36176 1.16873i 0.225843 0.0605145i −0.144123 0.989560i \(-0.546036\pi\)
0.369966 + 0.929045i \(0.379369\pi\)
\(374\) 0 0
\(375\) −18.3309 0.995622i −0.946602 0.0514137i
\(376\) 0 0
\(377\) 4.02810i 0.207458i
\(378\) 0 0
\(379\) −14.6109 14.6109i −0.750509 0.750509i 0.224065 0.974574i \(-0.428067\pi\)
−0.974574 + 0.224065i \(0.928067\pi\)
\(380\) 0 0
\(381\) −16.9912 18.9429i −0.870487 0.970476i
\(382\) 0 0
\(383\) −14.4164 + 24.9699i −0.736643 + 1.27590i 0.217355 + 0.976093i \(0.430257\pi\)
−0.953999 + 0.299811i \(0.903076\pi\)
\(384\) 0 0
\(385\) 0.988724 + 1.71252i 0.0503901 + 0.0872781i
\(386\) 0 0
\(387\) −17.9447 6.96672i −0.912182 0.354138i
\(388\) 0 0
\(389\) 0.0510254 0.190429i 0.00258709 0.00965514i −0.964620 0.263643i \(-0.915076\pi\)
0.967207 + 0.253988i \(0.0817425\pi\)
\(390\) 0 0
\(391\) −17.6225 10.1744i −0.891210 0.514540i
\(392\) 0 0
\(393\) 9.48797 14.5496i 0.478605 0.733929i
\(394\) 0 0
\(395\) −13.7234 13.7234i −0.690499 0.690499i
\(396\) 0 0
\(397\) −9.98504 + 9.98504i −0.501135 + 0.501135i −0.911791 0.410656i \(-0.865300\pi\)
0.410656 + 0.911791i \(0.365300\pi\)
\(398\) 0 0
\(399\) −2.11419 + 1.07218i −0.105842 + 0.0536759i
\(400\) 0 0
\(401\) 0.396741 0.687175i 0.0198123 0.0343159i −0.855949 0.517060i \(-0.827026\pi\)
0.875762 + 0.482744i \(0.160360\pi\)
\(402\) 0 0
\(403\) 4.00687 + 1.07364i 0.199596 + 0.0534817i
\(404\) 0 0
\(405\) −11.3275 + 0.507321i −0.562866 + 0.0252090i
\(406\) 0 0
\(407\) 5.03702 2.90813i 0.249676 0.144150i
\(408\) 0 0
\(409\) −0.225551 0.130222i −0.0111528 0.00643907i 0.494413 0.869227i \(-0.335383\pi\)
−0.505566 + 0.862788i \(0.668716\pi\)
\(410\) 0 0
\(411\) 4.50582 + 1.47350i 0.222256 + 0.0726826i
\(412\) 0 0
\(413\) 4.28238 4.28238i 0.210722 0.210722i
\(414\) 0 0
\(415\) 14.2485 0.699429
\(416\) 0 0
\(417\) −12.7104 8.28863i −0.622431 0.405896i
\(418\) 0 0
\(419\) 0.985334 + 3.67732i 0.0481367 + 0.179649i 0.985809 0.167873i \(-0.0536899\pi\)
−0.937672 + 0.347522i \(0.887023\pi\)
\(420\) 0 0
\(421\) −0.208895 + 0.779608i −0.0101809 + 0.0379958i −0.970829 0.239771i \(-0.922928\pi\)
0.960649 + 0.277767i \(0.0895943\pi\)
\(422\) 0 0
\(423\) −0.773700 + 0.340955i −0.0376186 + 0.0165778i
\(424\) 0 0
\(425\) −19.5655 + 11.2962i −0.949068 + 0.547945i
\(426\) 0 0
\(427\) −8.07272 + 2.16308i −0.390666 + 0.104679i
\(428\) 0 0
\(429\) −0.998415 1.11310i −0.0482039 0.0537409i
\(430\) 0 0
\(431\) −25.6515 −1.23559 −0.617796 0.786339i \(-0.711974\pi\)
−0.617796 + 0.786339i \(0.711974\pi\)
\(432\) 0 0
\(433\) −23.0987 −1.11005 −0.555026 0.831833i \(-0.687292\pi\)
−0.555026 + 0.831833i \(0.687292\pi\)
\(434\) 0 0
\(435\) 13.0576 + 14.5575i 0.626063 + 0.697977i
\(436\) 0 0
\(437\) 4.97241 1.33235i 0.237863 0.0637351i
\(438\) 0 0
\(439\) 7.88493 4.55237i 0.376327 0.217273i −0.299892 0.953973i \(-0.596951\pi\)
0.676219 + 0.736701i \(0.263617\pi\)
\(440\) 0 0
\(441\) −15.3259 11.2242i −0.729805 0.534485i
\(442\) 0 0
\(443\) 7.31445 27.2979i 0.347520 1.29696i −0.542120 0.840301i \(-0.682378\pi\)
0.889640 0.456662i \(-0.150955\pi\)
\(444\) 0 0
\(445\) −1.12217 4.18801i −0.0531961 0.198531i
\(446\) 0 0
\(447\) −12.4064 8.09038i −0.586803 0.382662i
\(448\) 0 0
\(449\) 5.90915 0.278870 0.139435 0.990231i \(-0.455471\pi\)
0.139435 + 0.990231i \(0.455471\pi\)
\(450\) 0 0
\(451\) 14.3625 14.3625i 0.676302 0.676302i
\(452\) 0 0
\(453\) 38.5392 + 12.6032i 1.81073 + 0.592149i
\(454\) 0 0
\(455\) 0.400784 + 0.231393i 0.0187890 + 0.0108478i
\(456\) 0 0
\(457\) −4.70096 + 2.71410i −0.219902 + 0.126960i −0.605905 0.795537i \(-0.707189\pi\)
0.386003 + 0.922497i \(0.373855\pi\)
\(458\) 0 0
\(459\) −27.9439 + 20.0600i −1.30431 + 0.936320i
\(460\) 0 0
\(461\) −25.1830 6.74777i −1.17289 0.314275i −0.380787 0.924663i \(-0.624347\pi\)
−0.792103 + 0.610388i \(0.791014\pi\)
\(462\) 0 0
\(463\) 9.87708 17.1076i 0.459027 0.795057i −0.539883 0.841740i \(-0.681532\pi\)
0.998910 + 0.0466825i \(0.0148649\pi\)
\(464\) 0 0
\(465\) 17.9611 9.10865i 0.832924 0.422404i
\(466\) 0 0
\(467\) −16.1348 + 16.1348i −0.746628 + 0.746628i −0.973844 0.227217i \(-0.927037\pi\)
0.227217 + 0.973844i \(0.427037\pi\)
\(468\) 0 0
\(469\) −3.12504 3.12504i −0.144301 0.144301i
\(470\) 0 0
\(471\) 20.4839 31.4116i 0.943848 1.44737i
\(472\) 0 0
\(473\) −10.6727 6.16188i −0.490731 0.283324i
\(474\) 0 0
\(475\) 1.47925 5.52065i 0.0678728 0.253305i
\(476\) 0 0
\(477\) −16.0013 + 12.8572i −0.732650 + 0.588691i
\(478\) 0 0
\(479\) −11.1996 19.3982i −0.511721 0.886327i −0.999908 0.0135877i \(-0.995675\pi\)
0.488187 0.872739i \(-0.337659\pi\)
\(480\) 0 0
\(481\) 0.680593 1.17882i 0.0310324 0.0537496i
\(482\) 0 0
\(483\) −2.90516 3.23886i −0.132189 0.147373i
\(484\) 0 0
\(485\) −7.96322 7.96322i −0.361591 0.361591i
\(486\) 0 0
\(487\) 8.27717i 0.375074i −0.982258 0.187537i \(-0.939950\pi\)
0.982258 0.187537i \(-0.0600505\pi\)
\(488\) 0 0
\(489\) −3.42076 0.185795i −0.154692 0.00840194i
\(490\) 0 0
\(491\) −34.7589 + 9.31362i −1.56865 + 0.420318i −0.935388 0.353622i \(-0.884950\pi\)
−0.633259 + 0.773940i \(0.718283\pi\)
\(492\) 0 0
\(493\) 57.3043 + 15.3546i 2.58086 + 0.691538i
\(494\) 0 0
\(495\) −7.21649 0.786232i −0.324357 0.0353385i
\(496\) 0 0
\(497\) −1.33686 2.31551i −0.0599664 0.103865i
\(498\) 0 0
\(499\) 7.44528 + 27.7862i 0.333297 + 1.24388i 0.905704 + 0.423911i \(0.139343\pi\)
−0.572407 + 0.819969i \(0.693990\pi\)
\(500\) 0 0
\(501\) −8.25795 39.2170i −0.368938 1.75209i
\(502\) 0 0
\(503\) 15.6106i 0.696044i −0.937486 0.348022i \(-0.886854\pi\)
0.937486 0.348022i \(-0.113146\pi\)
\(504\) 0 0
\(505\) 8.66815i 0.385728i
\(506\) 0 0
\(507\) 21.0687 + 6.88995i 0.935696 + 0.305994i
\(508\) 0 0
\(509\) 2.65858 + 9.92195i 0.117839 + 0.439783i 0.999484 0.0321319i \(-0.0102297\pi\)
−0.881644 + 0.471915i \(0.843563\pi\)
\(510\) 0 0
\(511\) −2.01143 3.48390i −0.0889804 0.154119i
\(512\) 0 0
\(513\) 1.41030 8.58710i 0.0622664 0.379130i
\(514\) 0 0
\(515\) −8.09583 2.16927i −0.356745 0.0955896i
\(516\) 0 0
\(517\) −0.522849 + 0.140097i −0.0229949 + 0.00616145i
\(518\) 0 0
\(519\) 4.02028 + 7.92745i 0.176471 + 0.347977i
\(520\) 0 0
\(521\) 21.2775i 0.932185i 0.884736 + 0.466092i \(0.154339\pi\)
−0.884736 + 0.466092i \(0.845661\pi\)
\(522\) 0 0
\(523\) 2.96994 + 2.96994i 0.129867 + 0.129867i 0.769052 0.639186i \(-0.220729\pi\)
−0.639186 + 0.769052i \(0.720729\pi\)
\(524\) 0 0
\(525\) −4.72694 + 0.995354i −0.206300 + 0.0434408i
\(526\) 0 0
\(527\) 30.5474 52.9097i 1.33067 2.30478i
\(528\) 0 0
\(529\) −6.77581 11.7360i −0.294600 0.510263i
\(530\) 0 0
\(531\) 3.39439 + 21.9716i 0.147304 + 0.953486i
\(532\) 0 0
\(533\) 1.23031 4.59158i 0.0532906 0.198883i
\(534\) 0 0
\(535\) 6.26869 + 3.61923i 0.271019 + 0.156473i
\(536\) 0 0
\(537\) −7.69926 0.418177i −0.332248 0.0180457i
\(538\) 0 0
\(539\) −8.59960 8.59960i −0.370411 0.370411i
\(540\) 0 0
\(541\) −15.1934 + 15.1934i −0.653214 + 0.653214i −0.953765 0.300552i \(-0.902829\pi\)
0.300552 + 0.953765i \(0.402829\pi\)
\(542\) 0 0
\(543\) 0.375709 6.91736i 0.0161232 0.296853i
\(544\) 0 0
\(545\) −6.41244 + 11.1067i −0.274679 + 0.475757i
\(546\) 0 0
\(547\) −33.6172 9.00771i −1.43737 0.385142i −0.545757 0.837943i \(-0.683758\pi\)
−0.891611 + 0.452802i \(0.850425\pi\)
\(548\) 0 0
\(549\) 11.1036 28.6005i 0.473892 1.22064i
\(550\) 0 0
\(551\) −12.9975 + 7.50410i −0.553712 + 0.319686i
\(552\) 0 0
\(553\) −10.9023 6.29447i −0.463615 0.267668i
\(554\) 0 0
\(555\) −1.36165 6.46645i −0.0577987 0.274486i
\(556\) 0 0
\(557\) 15.3686 15.3686i 0.651189 0.651189i −0.302091 0.953279i \(-0.597685\pi\)
0.953279 + 0.302091i \(0.0976845\pi\)
\(558\) 0 0
\(559\) −2.88415 −0.121986
\(560\) 0 0
\(561\) −19.6409 + 9.96058i −0.829241 + 0.420536i
\(562\) 0 0
\(563\) 4.11840 + 15.3701i 0.173570 + 0.647772i 0.996791 + 0.0800506i \(0.0255082\pi\)
−0.823221 + 0.567721i \(0.807825\pi\)
\(564\) 0 0
\(565\) 4.21123 15.7165i 0.177168 0.661199i
\(566\) 0 0
\(567\) −7.01206 + 2.21956i −0.294479 + 0.0932128i
\(568\) 0 0
\(569\) 36.4673 21.0544i 1.52879 0.882647i 0.529376 0.848387i \(-0.322426\pi\)
0.999413 0.0342597i \(-0.0109073\pi\)
\(570\) 0 0
\(571\) 37.8497 10.1418i 1.58396 0.424421i 0.643813 0.765183i \(-0.277352\pi\)
0.940150 + 0.340762i \(0.110685\pi\)
\(572\) 0 0
\(573\) −9.15622 + 27.9987i −0.382506 + 1.16966i
\(574\) 0 0
\(575\) 10.4901 0.437469
\(576\) 0 0
\(577\) 13.5220 0.562927 0.281463 0.959572i \(-0.409180\pi\)
0.281463 + 0.959572i \(0.409180\pi\)
\(578\) 0 0
\(579\) −9.18525 + 1.93414i −0.381726 + 0.0803803i
\(580\) 0 0
\(581\) 8.92739 2.39209i 0.370371 0.0992405i
\(582\) 0 0
\(583\) −11.3808 + 6.57071i −0.471345 + 0.272131i
\(584\) 0 0
\(585\) −1.55462 + 0.685092i −0.0642756 + 0.0283251i
\(586\) 0 0
\(587\) −8.32769 + 31.0793i −0.343720 + 1.28278i 0.550380 + 0.834915i \(0.314483\pi\)
−0.894100 + 0.447867i \(0.852184\pi\)
\(588\) 0 0
\(589\) 4.00024 + 14.9291i 0.164827 + 0.615143i
\(590\) 0 0
\(591\) 1.06797 19.6628i 0.0439303 0.808821i
\(592\) 0 0
\(593\) −24.2071 −0.994066 −0.497033 0.867732i \(-0.665577\pi\)
−0.497033 + 0.867732i \(0.665577\pi\)
\(594\) 0 0
\(595\) 4.81956 4.81956i 0.197583 0.197583i
\(596\) 0 0
\(597\) −14.4741 + 12.9828i −0.592386 + 0.531351i
\(598\) 0 0
\(599\) 33.5549 + 19.3729i 1.37102 + 0.791557i 0.991056 0.133445i \(-0.0426041\pi\)
0.379961 + 0.925003i \(0.375937\pi\)
\(600\) 0 0
\(601\) −21.4630 + 12.3917i −0.875493 + 0.505466i −0.869170 0.494514i \(-0.835346\pi\)
−0.00632336 + 0.999980i \(0.502013\pi\)
\(602\) 0 0
\(603\) 16.0337 2.47704i 0.652941 0.100873i
\(604\) 0 0
\(605\) 8.89730 + 2.38402i 0.361727 + 0.0969244i
\(606\) 0 0
\(607\) −5.85399 + 10.1394i −0.237606 + 0.411546i −0.960027 0.279908i \(-0.909696\pi\)
0.722421 + 0.691454i \(0.243029\pi\)
\(608\) 0 0
\(609\) 10.6252 + 6.92884i 0.430555 + 0.280771i
\(610\) 0 0
\(611\) −0.0895759 + 0.0895759i −0.00362385 + 0.00362385i
\(612\) 0 0
\(613\) −24.6378 24.6378i −0.995112 0.995112i 0.00487577 0.999988i \(-0.498448\pi\)
−0.999988 + 0.00487577i \(0.998448\pi\)
\(614\) 0 0
\(615\) −10.4378 20.5820i −0.420895 0.829948i
\(616\) 0 0
\(617\) 4.72698 + 2.72912i 0.190301 + 0.109870i 0.592123 0.805847i \(-0.298290\pi\)
−0.401822 + 0.915718i \(0.631623\pi\)
\(618\) 0 0
\(619\) 4.43389 16.5475i 0.178213 0.665101i −0.817769 0.575547i \(-0.804789\pi\)
0.995982 0.0895538i \(-0.0285441\pi\)
\(620\) 0 0
\(621\) 15.8938 1.57893i 0.637797 0.0633602i
\(622\) 0 0
\(623\) −1.40620 2.43561i −0.0563381 0.0975805i
\(624\) 0 0
\(625\) 1.85520 3.21329i 0.0742078 0.128532i
\(626\) 0 0
\(627\) 1.73166 5.29522i 0.0691557 0.211471i
\(628\) 0 0
\(629\) −14.1757 14.1757i −0.565223 0.565223i
\(630\) 0 0
\(631\) 5.04281i 0.200751i 0.994950 + 0.100376i \(0.0320045\pi\)
−0.994950 + 0.100376i \(0.967996\pi\)
\(632\) 0 0
\(633\) −14.0562 + 21.5548i −0.558682 + 0.856726i
\(634\) 0 0
\(635\) −17.8789 + 4.79063i −0.709502 + 0.190111i
\(636\) 0 0
\(637\) −2.74923 0.736654i −0.108929 0.0291873i
\(638\) 0 0
\(639\) 9.75747 + 1.06307i 0.385999 + 0.0420544i
\(640\) 0 0
\(641\) 10.2406 + 17.7373i 0.404480 + 0.700579i 0.994261 0.106984i \(-0.0341193\pi\)
−0.589781 + 0.807563i \(0.700786\pi\)
\(642\) 0 0
\(643\) 10.7731 + 40.2059i 0.424851 + 1.58557i 0.764248 + 0.644922i \(0.223110\pi\)
−0.339397 + 0.940643i \(0.610223\pi\)
\(644\) 0 0
\(645\) −10.4232 + 9.34931i −0.410414 + 0.368129i
\(646\) 0 0
\(647\) 9.07428i 0.356747i −0.983963 0.178373i \(-0.942917\pi\)
0.983963 0.178373i \(-0.0570835\pi\)
\(648\) 0 0
\(649\) 14.2332i 0.558704i
\(650\) 0 0
\(651\) 9.72432 8.72241i 0.381126 0.341858i
\(652\) 0 0
\(653\) −8.05224 30.0514i −0.315109 1.17600i −0.923888 0.382662i \(-0.875007\pi\)
0.608780 0.793339i \(-0.291659\pi\)
\(654\) 0 0
\(655\) −6.31729 10.9419i −0.246837 0.427534i
\(656\) 0 0
\(657\) 14.6810 + 1.59948i 0.572760 + 0.0624018i
\(658\) 0 0
\(659\) 12.3336 + 3.30479i 0.480450 + 0.128736i 0.490912 0.871209i \(-0.336664\pi\)
−0.0104620 + 0.999945i \(0.503330\pi\)
\(660\) 0 0
\(661\) 42.7191 11.4466i 1.66158 0.445219i 0.698759 0.715357i \(-0.253736\pi\)
0.962822 + 0.270137i \(0.0870692\pi\)
\(662\) 0 0
\(663\) −2.81522 + 4.31708i −0.109334 + 0.167661i
\(664\) 0 0
\(665\) 1.72428i 0.0668647i
\(666\) 0 0
\(667\) −19.4782 19.4782i −0.754198 0.754198i
\(668\) 0 0
\(669\) −8.91533 + 27.2621i −0.344686 + 1.05401i
\(670\) 0 0
\(671\) 9.82087 17.0102i 0.379131 0.656673i
\(672\) 0 0
\(673\) −16.9683 29.3899i −0.654079 1.13290i −0.982124 0.188236i \(-0.939723\pi\)
0.328045 0.944662i \(-0.393610\pi\)
\(674\) 0 0
\(675\) 7.30495 16.1586i 0.281168 0.621944i
\(676\) 0 0
\(677\) 10.7072 39.9599i 0.411512 1.53578i −0.380210 0.924900i \(-0.624148\pi\)
0.791721 0.610882i \(-0.209185\pi\)
\(678\) 0 0
\(679\) −6.32626 3.65247i −0.242780 0.140169i
\(680\) 0 0
\(681\) −6.39684 12.6137i −0.245127 0.483359i
\(682\) 0 0
\(683\) −0.0872426 0.0872426i −0.00333824 0.00333824i 0.705436 0.708774i \(-0.250751\pi\)
−0.708774 + 0.705436i \(0.750751\pi\)
\(684\) 0 0
\(685\) 2.43830 2.43830i 0.0931625 0.0931625i
\(686\) 0 0
\(687\) −6.51533 4.24873i −0.248575 0.162099i
\(688\) 0 0
\(689\) −1.53775 + 2.66347i −0.0585837 + 0.101470i
\(690\) 0 0
\(691\) 13.5322 + 3.62594i 0.514789 + 0.137937i 0.506855 0.862031i \(-0.330808\pi\)
0.00793395 + 0.999969i \(0.497475\pi\)
\(692\) 0 0
\(693\) −4.65350 + 0.718918i −0.176772 + 0.0273094i
\(694\) 0 0
\(695\) −9.55874 + 5.51874i −0.362584 + 0.209338i
\(696\) 0 0
\(697\) −60.6306 35.0051i −2.29655 1.32591i
\(698\) 0 0
\(699\) −9.45270 + 8.47877i −0.357534 + 0.320696i
\(700\) 0 0
\(701\) 10.7257 10.7257i 0.405103 0.405103i −0.474924 0.880027i \(-0.657525\pi\)
0.880027 + 0.474924i \(0.157525\pi\)
\(702\) 0 0
\(703\) 5.07161 0.191279
\(704\) 0 0
\(705\) −0.0333540 + 0.614096i −0.00125618 + 0.0231282i
\(706\) 0 0
\(707\) −1.45524 5.43104i −0.0547300 0.204255i
\(708\) 0 0
\(709\) −10.7081 + 39.9633i −0.402153 + 1.50085i 0.407095 + 0.913386i \(0.366542\pi\)
−0.809247 + 0.587468i \(0.800125\pi\)
\(710\) 0 0
\(711\) 42.2896 18.6363i 1.58599 0.698914i
\(712\) 0 0
\(713\) −24.5671 + 14.1839i −0.920047 + 0.531189i
\(714\) 0 0
\(715\) −1.05057 + 0.281501i −0.0392893 + 0.0105275i
\(716\) 0 0
\(717\) −11.5355 + 2.42905i −0.430802 + 0.0907144i
\(718\) 0 0
\(719\) 34.2734 1.27818 0.639091 0.769131i \(-0.279311\pi\)
0.639091 + 0.769131i \(0.279311\pi\)
\(720\) 0 0
\(721\) −5.43664 −0.202471
\(722\) 0 0
\(723\) −3.21604 + 9.83430i −0.119606 + 0.365742i
\(724\) 0 0
\(725\) −29.5413 + 7.91558i −1.09714 + 0.293977i
\(726\) 0 0
\(727\) −28.8380 + 16.6496i −1.06954 + 0.617501i −0.928057 0.372439i \(-0.878522\pi\)
−0.141487 + 0.989940i \(0.545188\pi\)
\(728\) 0 0
\(729\) 8.63576 25.5817i 0.319843 0.947471i
\(730\) 0 0
\(731\) −10.9940 + 41.0302i −0.406629 + 1.51756i
\(732\) 0 0
\(733\) −9.71001 36.2382i −0.358647 1.33849i −0.875832 0.482616i \(-0.839687\pi\)
0.517185 0.855874i \(-0.326980\pi\)
\(734\) 0 0
\(735\) −12.3236 + 6.24972i −0.454563 + 0.230524i
\(736\) 0 0
\(737\) 10.3866 0.382597
\(738\) 0 0
\(739\) 8.57380 8.57380i 0.315392 0.315392i −0.531602 0.846994i \(-0.678410\pi\)
0.846994 + 0.531602i \(0.178410\pi\)
\(740\) 0 0
\(741\) −0.268657 1.27585i −0.00986936 0.0468696i
\(742\) 0 0
\(743\) 10.3476 + 5.97418i 0.379616 + 0.219172i 0.677651 0.735383i \(-0.262998\pi\)
−0.298035 + 0.954555i \(0.596331\pi\)
\(744\) 0 0
\(745\) −9.33012 + 5.38674i −0.341829 + 0.197355i
\(746\) 0 0
\(747\) −12.2792 + 31.6285i −0.449272 + 1.15723i
\(748\) 0 0
\(749\) 4.53526 + 1.21522i 0.165715 + 0.0444032i
\(750\) 0 0
\(751\) −12.2293 + 21.1818i −0.446254 + 0.772934i −0.998139 0.0609863i \(-0.980575\pi\)
0.551885 + 0.833920i \(0.313909\pi\)
\(752\) 0 0
\(753\) −2.14429 + 39.4795i −0.0781421 + 1.43871i
\(754\) 0 0
\(755\) 20.8552 20.8552i 0.758999 0.758999i
\(756\) 0 0
\(757\) 5.77221 + 5.77221i 0.209794 + 0.209794i 0.804180 0.594386i \(-0.202605\pi\)
−0.594386 + 0.804180i \(0.702605\pi\)
\(758\) 0 0
\(759\) 10.2104 + 0.554566i 0.370613 + 0.0201295i
\(760\) 0 0
\(761\) 35.8368 + 20.6904i 1.29908 + 0.750025i 0.980246 0.197784i \(-0.0633746\pi\)
0.318836 + 0.947810i \(0.396708\pi\)
\(762\) 0 0
\(763\) −2.15309 + 8.03544i −0.0779471 + 0.290902i
\(764\) 0 0
\(765\) 3.82018 + 24.7277i 0.138119 + 0.894032i
\(766\) 0 0
\(767\) 1.66551 + 2.88475i 0.0601382 + 0.104162i
\(768\) 0 0
\(769\) 19.7893 34.2761i 0.713622 1.23603i −0.249867 0.968280i \(-0.580387\pi\)
0.963489 0.267749i \(-0.0862798\pi\)
\(770\) 0 0
\(771\) −0.584809 + 0.123144i −0.0210614 + 0.00443491i
\(772\) 0 0
\(773\) 34.1627 + 34.1627i 1.22875 + 1.22875i 0.964439 + 0.264307i \(0.0851433\pi\)
0.264307 + 0.964439i \(0.414857\pi\)
\(774\) 0 0
\(775\) 31.4954i 1.13135i
\(776\) 0 0
\(777\) −1.93875 3.82297i −0.0695524 0.137148i
\(778\) 0 0
\(779\) 17.1076 4.58398i 0.612945 0.164238i
\(780\) 0 0
\(781\) 6.06965 + 1.62636i 0.217189 + 0.0581957i
\(782\) 0 0
\(783\) −43.5673 + 16.4395i −1.55697 + 0.587500i
\(784\) 0 0
\(785\) −13.6386 23.6228i −0.486783 0.843132i
\(786\) 0 0
\(787\) −10.0877 37.6477i −0.359586 1.34199i −0.874614 0.484820i \(-0.838885\pi\)
0.515028 0.857174i \(-0.327782\pi\)
\(788\) 0 0
\(789\) 8.42357 + 2.75470i 0.299887 + 0.0980698i
\(790\) 0 0
\(791\) 10.5542i 0.375264i
\(792\) 0 0
\(793\) 4.59678i 0.163237i
\(794\) 0 0
\(795\) 3.07655 + 14.6105i 0.109114 + 0.518181i
\(796\) 0 0