Properties

Label 300.2.o.a.169.5
Level $300$
Weight $2$
Character 300.169
Analytic conductor $2.396$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.o (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 169.5
Character \(\chi\) \(=\) 300.169
Dual form 300.2.o.a.229.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.587785 + 0.809017i) q^{3} +(0.892889 - 2.05006i) q^{5} -4.13266i q^{7} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(0.587785 + 0.809017i) q^{3} +(0.892889 - 2.05006i) q^{5} -4.13266i q^{7} +(-0.309017 + 0.951057i) q^{9} +(-1.16386 - 3.58198i) q^{11} +(0.664470 + 0.215899i) q^{13} +(2.18336 - 0.482633i) q^{15} +(-3.11086 + 4.28173i) q^{17} +(4.63966 + 3.37091i) q^{19} +(3.34339 - 2.42912i) q^{21} +(5.19894 - 1.68924i) q^{23} +(-3.40550 - 3.66095i) q^{25} +(-0.951057 + 0.309017i) q^{27} +(-5.68284 + 4.12883i) q^{29} +(8.16460 + 5.93193i) q^{31} +(2.21379 - 3.04701i) q^{33} +(-8.47220 - 3.69001i) q^{35} +(5.50175 + 1.78763i) q^{37} +(0.215899 + 0.664470i) q^{39} +(-2.03813 + 6.27271i) q^{41} -4.79668i q^{43} +(1.67381 + 1.48269i) q^{45} +(-5.68611 - 7.82626i) q^{47} -10.0789 q^{49} -5.29251 q^{51} +(-1.99634 - 2.74773i) q^{53} +(-8.38247 - 0.812336i) q^{55} +5.73494i q^{57} +(-0.230309 + 0.708820i) q^{59} +(3.64886 + 11.2300i) q^{61} +(3.93039 + 1.27706i) q^{63} +(1.03591 - 1.16943i) q^{65} +(-2.81995 + 3.88133i) q^{67} +(4.42248 + 3.21312i) q^{69} +(2.54239 - 1.84715i) q^{71} +(10.2213 - 3.32110i) q^{73} +(0.960072 - 4.90696i) q^{75} +(-14.8031 + 4.80982i) q^{77} +(-7.38222 + 5.36349i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-4.96148 + 6.82889i) q^{83} +(6.00015 + 10.2006i) q^{85} +(-6.68058 - 2.17065i) q^{87} +(1.04690 + 3.22202i) q^{89} +(0.892239 - 2.74603i) q^{91} +10.0920i q^{93} +(11.0533 - 6.50174i) q^{95} +(-6.13358 - 8.44215i) q^{97} +3.76632 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 2q^{5} + 6q^{9} + O(q^{10}) \) \( 24q - 2q^{5} + 6q^{9} - 6q^{11} + 4q^{15} + 10q^{17} + 10q^{19} - 4q^{21} + 40q^{23} - 4q^{25} + 4q^{29} + 6q^{31} + 10q^{33} - 6q^{35} - 10q^{41} + 2q^{45} - 40q^{47} - 56q^{49} + 16q^{51} - 60q^{53} - 62q^{55} - 36q^{59} - 12q^{61} - 10q^{63} + 20q^{67} + 4q^{69} + 40q^{71} + 60q^{73} + 8q^{75} - 40q^{77} + 8q^{79} - 6q^{81} - 50q^{83} + 34q^{85} - 20q^{87} - 30q^{91} - 60q^{95} - 40q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{9}{10}\right)\)

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
\(3\) 0.587785 + 0.809017i 0.339358 + 0.467086i
\(4\) 0 0
\(5\) 0.892889 2.05006i 0.399312 0.916815i
\(6\) 0 0
\(7\) 4.13266i 1.56200i −0.624532 0.780999i \(-0.714710\pi\)
0.624532 0.780999i \(-0.285290\pi\)
\(8\) 0 0
\(9\) −0.309017 + 0.951057i −0.103006 + 0.317019i
\(10\) 0 0
\(11\) −1.16386 3.58198i −0.350916 1.08001i −0.958340 0.285630i \(-0.907797\pi\)
0.607424 0.794378i \(-0.292203\pi\)
\(12\) 0 0
\(13\) 0.664470 + 0.215899i 0.184291 + 0.0598797i 0.399709 0.916642i \(-0.369111\pi\)
−0.215418 + 0.976522i \(0.569111\pi\)
\(14\) 0 0
\(15\) 2.18336 0.482633i 0.563741 0.124615i
\(16\) 0 0
\(17\) −3.11086 + 4.28173i −0.754494 + 1.03847i 0.243159 + 0.969987i \(0.421816\pi\)
−0.997652 + 0.0684847i \(0.978184\pi\)
\(18\) 0 0
\(19\) 4.63966 + 3.37091i 1.06441 + 0.773340i 0.974899 0.222646i \(-0.0714692\pi\)
0.0895120 + 0.995986i \(0.471469\pi\)
\(20\) 0 0
\(21\) 3.34339 2.42912i 0.729588 0.530077i
\(22\) 0 0
\(23\) 5.19894 1.68924i 1.08405 0.352231i 0.288108 0.957598i \(-0.406974\pi\)
0.795946 + 0.605367i \(0.206974\pi\)
\(24\) 0 0
\(25\) −3.40550 3.66095i −0.681100 0.732191i
\(26\) 0 0
\(27\) −0.951057 + 0.309017i −0.183031 + 0.0594703i
\(28\) 0 0
\(29\) −5.68284 + 4.12883i −1.05528 + 0.766704i −0.973209 0.229923i \(-0.926153\pi\)
−0.0820685 + 0.996627i \(0.526153\pi\)
\(30\) 0 0
\(31\) 8.16460 + 5.93193i 1.46641 + 1.06541i 0.981636 + 0.190764i \(0.0610964\pi\)
0.484769 + 0.874642i \(0.338904\pi\)
\(32\) 0 0
\(33\) 2.21379 3.04701i 0.385371 0.530417i
\(34\) 0 0
\(35\) −8.47220 3.69001i −1.43206 0.623725i
\(36\) 0 0
\(37\) 5.50175 + 1.78763i 0.904482 + 0.293884i 0.724086 0.689710i \(-0.242262\pi\)
0.180396 + 0.983594i \(0.442262\pi\)
\(38\) 0 0
\(39\) 0.215899 + 0.664470i 0.0345716 + 0.106400i
\(40\) 0 0
\(41\) −2.03813 + 6.27271i −0.318302 + 0.979633i 0.656072 + 0.754698i \(0.272217\pi\)
−0.974374 + 0.224935i \(0.927783\pi\)
\(42\) 0 0
\(43\) 4.79668i 0.731488i −0.930716 0.365744i \(-0.880815\pi\)
0.930716 0.365744i \(-0.119185\pi\)
\(44\) 0 0
\(45\) 1.67381 + 1.48269i 0.249516 + 0.221027i
\(46\) 0 0
\(47\) −5.68611 7.82626i −0.829405 1.14158i −0.988033 0.154239i \(-0.950707\pi\)
0.158629 0.987338i \(-0.449293\pi\)
\(48\) 0 0
\(49\) −10.0789 −1.43984
\(50\) 0 0
\(51\) −5.29251 −0.741099
\(52\) 0 0
\(53\) −1.99634 2.74773i −0.274219 0.377429i 0.649590 0.760285i \(-0.274941\pi\)
−0.923808 + 0.382856i \(0.874941\pi\)
\(54\) 0 0
\(55\) −8.38247 0.812336i −1.13029 0.109535i
\(56\) 0 0
\(57\) 5.73494i 0.759611i
\(58\) 0 0
\(59\) −0.230309 + 0.708820i −0.0299837 + 0.0922804i −0.964928 0.262513i \(-0.915449\pi\)
0.934945 + 0.354793i \(0.115449\pi\)
\(60\) 0 0
\(61\) 3.64886 + 11.2300i 0.467188 + 1.43786i 0.856210 + 0.516629i \(0.172813\pi\)
−0.389021 + 0.921229i \(0.627187\pi\)
\(62\) 0 0
\(63\) 3.93039 + 1.27706i 0.495183 + 0.160895i
\(64\) 0 0
\(65\) 1.03591 1.16943i 0.128488 0.145050i
\(66\) 0 0
\(67\) −2.81995 + 3.88133i −0.344512 + 0.474180i −0.945752 0.324888i \(-0.894673\pi\)
0.601241 + 0.799068i \(0.294673\pi\)
\(68\) 0 0
\(69\) 4.42248 + 3.21312i 0.532405 + 0.386815i
\(70\) 0 0
\(71\) 2.54239 1.84715i 0.301726 0.219217i −0.426612 0.904435i \(-0.640293\pi\)
0.728338 + 0.685218i \(0.240293\pi\)
\(72\) 0 0
\(73\) 10.2213 3.32110i 1.19631 0.388706i 0.357910 0.933756i \(-0.383490\pi\)
0.838403 + 0.545051i \(0.183490\pi\)
\(74\) 0 0
\(75\) 0.960072 4.90696i 0.110860 0.566607i
\(76\) 0 0
\(77\) −14.8031 + 4.80982i −1.68697 + 0.548130i
\(78\) 0 0
\(79\) −7.38222 + 5.36349i −0.830564 + 0.603440i −0.919719 0.392578i \(-0.871583\pi\)
0.0891546 + 0.996018i \(0.471583\pi\)
\(80\) 0 0
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) 0 0
\(83\) −4.96148 + 6.82889i −0.544593 + 0.749569i −0.989266 0.146125i \(-0.953320\pi\)
0.444673 + 0.895693i \(0.353320\pi\)
\(84\) 0 0
\(85\) 6.00015 + 10.2006i 0.650808 + 1.10641i
\(86\) 0 0
\(87\) −6.68058 2.17065i −0.716234 0.232718i
\(88\) 0 0
\(89\) 1.04690 + 3.22202i 0.110971 + 0.341533i 0.991085 0.133228i \(-0.0425343\pi\)
−0.880114 + 0.474761i \(0.842534\pi\)
\(90\) 0 0
\(91\) 0.892239 2.74603i 0.0935321 0.287862i
\(92\) 0 0
\(93\) 10.0920i 1.04649i
\(94\) 0 0
\(95\) 11.0533 6.50174i 1.13404 0.667064i
\(96\) 0 0
\(97\) −6.13358 8.44215i −0.622771 0.857170i 0.374780 0.927114i \(-0.377718\pi\)
−0.997551 + 0.0699435i \(0.977718\pi\)
\(98\) 0 0
\(99\) 3.76632 0.378529
\(100\) 0 0
\(101\) 7.10799 0.707272 0.353636 0.935383i \(-0.384945\pi\)
0.353636 + 0.935383i \(0.384945\pi\)
\(102\) 0 0
\(103\) −7.17630 9.87733i −0.707102 0.973243i −0.999855 0.0170543i \(-0.994571\pi\)
0.292752 0.956188i \(-0.405429\pi\)
\(104\) 0 0
\(105\) −1.99456 9.02309i −0.194649 0.880563i
\(106\) 0 0
\(107\) 4.04303i 0.390855i 0.980718 + 0.195427i \(0.0626094\pi\)
−0.980718 + 0.195427i \(0.937391\pi\)
\(108\) 0 0
\(109\) 0.239122 0.735942i 0.0229037 0.0704904i −0.938951 0.344050i \(-0.888201\pi\)
0.961855 + 0.273560i \(0.0882010\pi\)
\(110\) 0 0
\(111\) 1.78763 + 5.50175i 0.169674 + 0.522203i
\(112\) 0 0
\(113\) −1.08366 0.352104i −0.101943 0.0331231i 0.257602 0.966251i \(-0.417068\pi\)
−0.359544 + 0.933128i \(0.617068\pi\)
\(114\) 0 0
\(115\) 1.17904 12.1665i 0.109946 1.13453i
\(116\) 0 0
\(117\) −0.410665 + 0.565232i −0.0379660 + 0.0522557i
\(118\) 0 0
\(119\) 17.6949 + 12.8561i 1.62209 + 1.17852i
\(120\) 0 0
\(121\) −2.57684 + 1.87218i −0.234258 + 0.170198i
\(122\) 0 0
\(123\) −6.27271 + 2.03813i −0.565591 + 0.183772i
\(124\) 0 0
\(125\) −10.5459 + 3.71265i −0.943255 + 0.332070i
\(126\) 0 0
\(127\) 0.511543 0.166210i 0.0453921 0.0147488i −0.286233 0.958160i \(-0.592403\pi\)
0.331625 + 0.943411i \(0.392403\pi\)
\(128\) 0 0
\(129\) 3.88060 2.81942i 0.341668 0.248236i
\(130\) 0 0
\(131\) 5.43855 + 3.95134i 0.475169 + 0.345230i 0.799452 0.600730i \(-0.205123\pi\)
−0.324284 + 0.945960i \(0.605123\pi\)
\(132\) 0 0
\(133\) 13.9308 19.1741i 1.20796 1.66261i
\(134\) 0 0
\(135\) −0.215684 + 2.22564i −0.0185632 + 0.191553i
\(136\) 0 0
\(137\) −0.174404 0.0566672i −0.0149003 0.00484140i 0.301557 0.953448i \(-0.402494\pi\)
−0.316458 + 0.948607i \(0.602494\pi\)
\(138\) 0 0
\(139\) −2.54014 7.81775i −0.215452 0.663093i −0.999121 0.0419144i \(-0.986654\pi\)
0.783669 0.621178i \(-0.213346\pi\)
\(140\) 0 0
\(141\) 2.98937 9.20032i 0.251750 0.774807i
\(142\) 0 0
\(143\) 2.63140i 0.220048i
\(144\) 0 0
\(145\) 3.39020 + 15.3368i 0.281541 + 1.27365i
\(146\) 0 0
\(147\) −5.92421 8.15398i −0.488621 0.672529i
\(148\) 0 0
\(149\) −5.53790 −0.453682 −0.226841 0.973932i \(-0.572840\pi\)
−0.226841 + 0.973932i \(0.572840\pi\)
\(150\) 0 0
\(151\) 12.8736 1.04764 0.523821 0.851828i \(-0.324506\pi\)
0.523821 + 0.851828i \(0.324506\pi\)
\(152\) 0 0
\(153\) −3.11086 4.28173i −0.251498 0.346157i
\(154\) 0 0
\(155\) 19.4509 11.4414i 1.56233 0.918993i
\(156\) 0 0
\(157\) 14.6395i 1.16836i 0.811625 + 0.584179i \(0.198583\pi\)
−0.811625 + 0.584179i \(0.801417\pi\)
\(158\) 0 0
\(159\) 1.04954 3.23015i 0.0832338 0.256167i
\(160\) 0 0
\(161\) −6.98105 21.4855i −0.550184 1.69329i
\(162\) 0 0
\(163\) −4.22672 1.37334i −0.331062 0.107569i 0.138769 0.990325i \(-0.455685\pi\)
−0.469832 + 0.882756i \(0.655685\pi\)
\(164\) 0 0
\(165\) −4.26990 7.25904i −0.332411 0.565116i
\(166\) 0 0
\(167\) 13.9690 19.2267i 1.08095 1.48780i 0.222487 0.974936i \(-0.428583\pi\)
0.858467 0.512869i \(-0.171417\pi\)
\(168\) 0 0
\(169\) −10.1223 7.35429i −0.778639 0.565715i
\(170\) 0 0
\(171\) −4.63966 + 3.37091i −0.354804 + 0.257780i
\(172\) 0 0
\(173\) 14.3484 4.66207i 1.09089 0.354451i 0.292298 0.956327i \(-0.405580\pi\)
0.798589 + 0.601877i \(0.205580\pi\)
\(174\) 0 0
\(175\) −15.1295 + 14.0738i −1.14368 + 1.06388i
\(176\) 0 0
\(177\) −0.708820 + 0.230309i −0.0532781 + 0.0173111i
\(178\) 0 0
\(179\) 13.5238 9.82561i 1.01082 0.734401i 0.0464356 0.998921i \(-0.485214\pi\)
0.964380 + 0.264521i \(0.0852138\pi\)
\(180\) 0 0
\(181\) −8.40755 6.10844i −0.624928 0.454037i 0.229711 0.973259i \(-0.426222\pi\)
−0.854639 + 0.519222i \(0.826222\pi\)
\(182\) 0 0
\(183\) −6.94054 + 9.55283i −0.513059 + 0.706166i
\(184\) 0 0
\(185\) 8.57720 9.68277i 0.630608 0.711892i
\(186\) 0 0
\(187\) 18.9576 + 6.15971i 1.38632 + 0.450443i
\(188\) 0 0
\(189\) 1.27706 + 3.93039i 0.0928926 + 0.285894i
\(190\) 0 0
\(191\) −6.10485 + 18.7888i −0.441732 + 1.35951i 0.444297 + 0.895880i \(0.353454\pi\)
−0.886029 + 0.463631i \(0.846546\pi\)
\(192\) 0 0
\(193\) 2.23549i 0.160914i −0.996758 0.0804571i \(-0.974362\pi\)
0.996758 0.0804571i \(-0.0256380\pi\)
\(194\) 0 0
\(195\) 1.55498 + 0.150691i 0.111354 + 0.0107912i
\(196\) 0 0
\(197\) 13.3761 + 18.4106i 0.953008 + 1.31170i 0.950178 + 0.311706i \(0.100901\pi\)
0.00282909 + 0.999996i \(0.499099\pi\)
\(198\) 0 0
\(199\) −22.8171 −1.61746 −0.808731 0.588179i \(-0.799845\pi\)
−0.808731 + 0.588179i \(0.799845\pi\)
\(200\) 0 0
\(201\) −4.79759 −0.338396
\(202\) 0 0
\(203\) 17.0630 + 23.4853i 1.19759 + 1.64834i
\(204\) 0 0
\(205\) 11.0396 + 9.77912i 0.771040 + 0.683003i
\(206\) 0 0
\(207\) 5.46649i 0.379947i
\(208\) 0 0
\(209\) 6.67464 20.5424i 0.461695 1.42095i
\(210\) 0 0
\(211\) 6.21019 + 19.1130i 0.427527 + 1.31579i 0.900554 + 0.434745i \(0.143161\pi\)
−0.473027 + 0.881048i \(0.656839\pi\)
\(212\) 0 0
\(213\) 2.98875 + 0.971105i 0.204786 + 0.0665390i
\(214\) 0 0
\(215\) −9.83349 4.28291i −0.670639 0.292092i
\(216\) 0 0
\(217\) 24.5146 33.7415i 1.66416 2.29052i
\(218\) 0 0
\(219\) 8.69476 + 6.31711i 0.587537 + 0.426871i
\(220\) 0 0
\(221\) −2.99149 + 2.17345i −0.201230 + 0.146202i
\(222\) 0 0
\(223\) −12.7621 + 4.14665i −0.854612 + 0.277680i −0.703377 0.710817i \(-0.748325\pi\)
−0.151236 + 0.988498i \(0.548325\pi\)
\(224\) 0 0
\(225\) 4.53413 2.10752i 0.302275 0.140502i
\(226\) 0 0
\(227\) −17.5862 + 5.71411i −1.16724 + 0.379259i −0.827612 0.561301i \(-0.810301\pi\)
−0.339628 + 0.940560i \(0.610301\pi\)
\(228\) 0 0
\(229\) −15.7050 + 11.4104i −1.03782 + 0.754017i −0.969858 0.243671i \(-0.921648\pi\)
−0.0679579 + 0.997688i \(0.521648\pi\)
\(230\) 0 0
\(231\) −12.5923 9.14882i −0.828511 0.601948i
\(232\) 0 0
\(233\) −7.16114 + 9.85646i −0.469142 + 0.645718i −0.976373 0.216092i \(-0.930669\pi\)
0.507231 + 0.861810i \(0.330669\pi\)
\(234\) 0 0
\(235\) −21.1214 + 4.66889i −1.37781 + 0.304565i
\(236\) 0 0
\(237\) −8.67832 2.81976i −0.563717 0.183163i
\(238\) 0 0
\(239\) −1.39823 4.30330i −0.0904438 0.278357i 0.895596 0.444869i \(-0.146750\pi\)
−0.986040 + 0.166512i \(0.946750\pi\)
\(240\) 0 0
\(241\) 2.78479 8.57071i 0.179384 0.552088i −0.820422 0.571758i \(-0.806262\pi\)
0.999807 + 0.0196702i \(0.00626163\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) −8.99932 + 20.6623i −0.574945 + 1.32007i
\(246\) 0 0
\(247\) 2.35514 + 3.24157i 0.149854 + 0.206256i
\(248\) 0 0
\(249\) −8.44098 −0.534925
\(250\) 0 0
\(251\) 3.16965 0.200066 0.100033 0.994984i \(-0.468105\pi\)
0.100033 + 0.994984i \(0.468105\pi\)
\(252\) 0 0
\(253\) −12.1016 16.6565i −0.760824 1.04718i
\(254\) 0 0
\(255\) −4.72562 + 10.8500i −0.295930 + 0.679451i
\(256\) 0 0
\(257\) 3.25241i 0.202880i −0.994842 0.101440i \(-0.967655\pi\)
0.994842 0.101440i \(-0.0323450\pi\)
\(258\) 0 0
\(259\) 7.38766 22.7369i 0.459047 1.41280i
\(260\) 0 0
\(261\) −2.17065 6.68058i −0.134360 0.413518i
\(262\) 0 0
\(263\) −10.5187 3.41774i −0.648612 0.210747i −0.0338097 0.999428i \(-0.510764\pi\)
−0.614802 + 0.788682i \(0.710764\pi\)
\(264\) 0 0
\(265\) −7.41552 + 1.63920i −0.455532 + 0.100696i
\(266\) 0 0
\(267\) −1.99132 + 2.74081i −0.121867 + 0.167735i
\(268\) 0 0
\(269\) 20.0279 + 14.5511i 1.22112 + 0.887197i 0.996193 0.0871780i \(-0.0277849\pi\)
0.224929 + 0.974375i \(0.427785\pi\)
\(270\) 0 0
\(271\) −0.202420 + 0.147067i −0.0122962 + 0.00893369i −0.593916 0.804527i \(-0.702419\pi\)
0.581620 + 0.813460i \(0.302419\pi\)
\(272\) 0 0
\(273\) 2.74603 0.892239i 0.166197 0.0540008i
\(274\) 0 0
\(275\) −9.14996 + 16.4593i −0.551763 + 0.992530i
\(276\) 0 0
\(277\) 8.43658 2.74121i 0.506905 0.164703i −0.0443894 0.999014i \(-0.514134\pi\)
0.551294 + 0.834311i \(0.314134\pi\)
\(278\) 0 0
\(279\) −8.16460 + 5.93193i −0.488802 + 0.355135i
\(280\) 0 0
\(281\) −15.9683 11.6016i −0.952588 0.692096i −0.00117050 0.999999i \(-0.500373\pi\)
−0.951418 + 0.307904i \(0.900373\pi\)
\(282\) 0 0
\(283\) −15.5421 + 21.3919i −0.923882 + 1.27162i 0.0383159 + 0.999266i \(0.487801\pi\)
−0.962198 + 0.272349i \(0.912199\pi\)
\(284\) 0 0
\(285\) 11.7570 + 5.12066i 0.696423 + 0.303322i
\(286\) 0 0
\(287\) 25.9230 + 8.42289i 1.53019 + 0.497187i
\(288\) 0 0
\(289\) −3.40247 10.4717i −0.200145 0.615983i
\(290\) 0 0
\(291\) 3.22461 9.92434i 0.189030 0.581775i
\(292\) 0 0
\(293\) 19.1882i 1.12099i 0.828158 + 0.560494i \(0.189389\pi\)
−0.828158 + 0.560494i \(0.810611\pi\)
\(294\) 0 0
\(295\) 1.24748 + 1.10505i 0.0726312 + 0.0643382i
\(296\) 0 0
\(297\) 2.21379 + 3.04701i 0.128457 + 0.176806i
\(298\) 0 0
\(299\) 3.81925 0.220873
\(300\) 0 0
\(301\) −19.8231 −1.14258
\(302\) 0 0
\(303\) 4.17797 + 5.75049i 0.240018 + 0.330357i
\(304\) 0 0
\(305\) 26.2803 + 2.54679i 1.50480 + 0.145829i
\(306\) 0 0
\(307\) 9.26979i 0.529055i 0.964378 + 0.264527i \(0.0852160\pi\)
−0.964378 + 0.264527i \(0.914784\pi\)
\(308\) 0 0
\(309\) 3.77281 11.6115i 0.214627 0.660555i
\(310\) 0 0
\(311\) −7.69255 23.6752i −0.436204 1.34250i −0.891847 0.452336i \(-0.850591\pi\)
0.455643 0.890163i \(-0.349409\pi\)
\(312\) 0 0
\(313\) 5.75115 + 1.86866i 0.325074 + 0.105623i 0.467008 0.884253i \(-0.345332\pi\)
−0.141934 + 0.989876i \(0.545332\pi\)
\(314\) 0 0
\(315\) 6.12746 6.91727i 0.345243 0.389744i
\(316\) 0 0
\(317\) −8.45614 + 11.6389i −0.474944 + 0.653705i −0.977523 0.210827i \(-0.932384\pi\)
0.502579 + 0.864531i \(0.332384\pi\)
\(318\) 0 0
\(319\) 21.4034 + 15.5505i 1.19836 + 0.870659i
\(320\) 0 0
\(321\) −3.27088 + 2.37644i −0.182563 + 0.132640i
\(322\) 0 0
\(323\) −28.8666 + 9.37934i −1.60618 + 0.521881i
\(324\) 0 0
\(325\) −1.47245 3.16784i −0.0816771 0.175720i
\(326\) 0 0
\(327\) 0.735942 0.239122i 0.0406977 0.0132235i
\(328\) 0 0
\(329\) −32.3433 + 23.4988i −1.78314 + 1.29553i
\(330\) 0 0
\(331\) −0.863126 0.627098i −0.0474417 0.0344684i 0.563812 0.825903i \(-0.309334\pi\)
−0.611253 + 0.791435i \(0.709334\pi\)
\(332\) 0 0
\(333\) −3.40027 + 4.68007i −0.186334 + 0.256466i
\(334\) 0 0
\(335\) 5.43906 + 9.24667i 0.297168 + 0.505200i
\(336\) 0 0
\(337\) −13.8873 4.51226i −0.756490 0.245799i −0.0947186 0.995504i \(-0.530195\pi\)
−0.661772 + 0.749705i \(0.730195\pi\)
\(338\) 0 0
\(339\) −0.352104 1.08366i −0.0191236 0.0588565i
\(340\) 0 0
\(341\) 11.7456 36.1493i 0.636062 1.95760i
\(342\) 0 0
\(343\) 12.7239i 0.687029i
\(344\) 0 0
\(345\) 10.5359 6.19740i 0.567233 0.333657i
\(346\) 0 0
\(347\) −9.48995 13.0618i −0.509447 0.701194i 0.474379 0.880321i \(-0.342673\pi\)
−0.983826 + 0.179127i \(0.942673\pi\)
\(348\) 0 0
\(349\) 22.2622 1.19167 0.595834 0.803108i \(-0.296822\pi\)
0.595834 + 0.803108i \(0.296822\pi\)
\(350\) 0 0
\(351\) −0.698665 −0.0372920
\(352\) 0 0
\(353\) −5.60158 7.70991i −0.298142 0.410357i 0.633496 0.773746i \(-0.281619\pi\)
−0.931637 + 0.363389i \(0.881619\pi\)
\(354\) 0 0
\(355\) −1.51670 6.86135i −0.0804983 0.364162i
\(356\) 0 0
\(357\) 21.8721i 1.15760i
\(358\) 0 0
\(359\) 5.18753 15.9656i 0.273788 0.842632i −0.715750 0.698357i \(-0.753915\pi\)
0.989538 0.144275i \(-0.0460850\pi\)
\(360\) 0 0
\(361\) 4.29210 + 13.2097i 0.225900 + 0.695248i
\(362\) 0 0
\(363\) −3.02925 0.984264i −0.158995 0.0516604i
\(364\) 0 0
\(365\) 2.31803 23.9197i 0.121331 1.25201i
\(366\) 0 0
\(367\) 19.0893 26.2741i 0.996452 1.37150i 0.0689751 0.997618i \(-0.478027\pi\)
0.927477 0.373880i \(-0.121973\pi\)
\(368\) 0 0
\(369\) −5.33589 3.87675i −0.277775 0.201815i
\(370\) 0 0
\(371\) −11.3554 + 8.25020i −0.589544 + 0.428329i
\(372\) 0 0
\(373\) −13.5918 + 4.41623i −0.703755 + 0.228664i −0.638966 0.769235i \(-0.720637\pi\)
−0.0647890 + 0.997899i \(0.520637\pi\)
\(374\) 0 0
\(375\) −9.20233 6.34958i −0.475206 0.327891i
\(376\) 0 0
\(377\) −4.66749 + 1.51656i −0.240388 + 0.0781068i
\(378\) 0 0
\(379\) −2.60155 + 1.89014i −0.133633 + 0.0970897i −0.652593 0.757708i \(-0.726319\pi\)
0.518961 + 0.854798i \(0.326319\pi\)
\(380\) 0 0
\(381\) 0.435145 + 0.316151i 0.0222931 + 0.0161969i
\(382\) 0 0
\(383\) 7.26491 9.99929i 0.371220 0.510940i −0.582012 0.813180i \(-0.697734\pi\)
0.953232 + 0.302240i \(0.0977344\pi\)
\(384\) 0 0
\(385\) −3.35711 + 34.6419i −0.171094 + 1.76551i
\(386\) 0 0
\(387\) 4.56192 + 1.48226i 0.231895 + 0.0753474i
\(388\) 0 0
\(389\) −7.14594 21.9930i −0.362314 1.11509i −0.951646 0.307196i \(-0.900609\pi\)
0.589332 0.807891i \(-0.299391\pi\)
\(390\) 0 0
\(391\) −8.94031 + 27.5154i −0.452131 + 1.39152i
\(392\) 0 0
\(393\) 6.72242i 0.339101i
\(394\) 0 0
\(395\) 4.40399 + 19.9230i 0.221589 + 1.00243i
\(396\) 0 0
\(397\) −1.25095 1.72179i −0.0627834 0.0864140i 0.776471 0.630153i \(-0.217008\pi\)
−0.839254 + 0.543739i \(0.817008\pi\)
\(398\) 0 0
\(399\) 23.7005 1.18651
\(400\) 0 0
\(401\) −33.8250 −1.68914 −0.844569 0.535447i \(-0.820143\pi\)
−0.844569 + 0.535447i \(0.820143\pi\)
\(402\) 0 0
\(403\) 4.14443 + 5.70432i 0.206449 + 0.284153i
\(404\) 0 0
\(405\) −1.92736 + 1.13371i −0.0957712 + 0.0563344i
\(406\) 0 0
\(407\) 21.7877i 1.07998i
\(408\) 0 0
\(409\) 10.7434 33.0647i 0.531226 1.63495i −0.220439 0.975401i \(-0.570749\pi\)
0.751665 0.659545i \(-0.229251\pi\)
\(410\) 0 0
\(411\) −0.0566672 0.174404i −0.00279518 0.00860269i
\(412\) 0 0
\(413\) 2.92931 + 0.951790i 0.144142 + 0.0468345i
\(414\) 0 0
\(415\) 9.56960 + 16.2688i 0.469753 + 0.798603i
\(416\) 0 0
\(417\) 4.83163 6.65017i 0.236606 0.325660i
\(418\) 0 0
\(419\) −5.49925 3.99544i −0.268656 0.195190i 0.445298 0.895382i \(-0.353098\pi\)
−0.713954 + 0.700192i \(0.753098\pi\)
\(420\) 0 0
\(421\) 8.75730 6.36255i 0.426805 0.310092i −0.353565 0.935410i \(-0.615031\pi\)
0.780370 + 0.625318i \(0.215031\pi\)
\(422\) 0 0
\(423\) 9.20032 2.98937i 0.447335 0.145348i
\(424\) 0 0
\(425\) 26.2692 3.19271i 1.27424 0.154869i
\(426\) 0 0
\(427\) 46.4099 15.0795i 2.24593 0.729747i
\(428\) 0 0
\(429\) 2.12884 1.54670i 0.102782 0.0746752i
\(430\) 0 0
\(431\) 8.40317 + 6.10526i 0.404767 + 0.294080i 0.771480 0.636254i \(-0.219517\pi\)
−0.366713 + 0.930334i \(0.619517\pi\)
\(432\) 0 0
\(433\) 9.20630 12.6714i 0.442427 0.608948i −0.528323 0.849044i \(-0.677179\pi\)
0.970749 + 0.240096i \(0.0771789\pi\)
\(434\) 0 0
\(435\) −10.4150 + 11.7574i −0.499361 + 0.563726i
\(436\) 0 0
\(437\) 29.8156 + 9.68768i 1.42627 + 0.463425i
\(438\) 0 0
\(439\) −6.80071 20.9304i −0.324580 0.998955i −0.971630 0.236507i \(-0.923997\pi\)
0.647050 0.762448i \(-0.276003\pi\)
\(440\) 0 0
\(441\) 3.11454 9.58558i 0.148312 0.456456i
\(442\) 0 0
\(443\) 29.4447i 1.39896i −0.714652 0.699480i \(-0.753415\pi\)
0.714652 0.699480i \(-0.246585\pi\)
\(444\) 0 0
\(445\) 7.54010 + 0.730702i 0.357435 + 0.0346386i
\(446\) 0 0
\(447\) −3.25509 4.48025i −0.153961 0.211909i
\(448\) 0 0
\(449\) −27.3445 −1.29047 −0.645234 0.763985i \(-0.723240\pi\)
−0.645234 + 0.763985i \(0.723240\pi\)
\(450\) 0 0
\(451\) 24.8408 1.16971
\(452\) 0 0
\(453\) 7.56693 + 10.4150i 0.355526 + 0.489339i
\(454\) 0 0
\(455\) −4.83286 4.28104i −0.226568 0.200698i
\(456\) 0 0
\(457\) 33.6394i 1.57359i 0.617217 + 0.786793i \(0.288260\pi\)
−0.617217 + 0.786793i \(0.711740\pi\)
\(458\) 0 0
\(459\) 1.63547 5.03347i 0.0763374 0.234942i
\(460\) 0 0
\(461\) 7.86199 + 24.1967i 0.366169 + 1.12695i 0.949246 + 0.314536i \(0.101849\pi\)
−0.583076 + 0.812417i \(0.698151\pi\)
\(462\) 0 0
\(463\) −7.45749 2.42308i −0.346579 0.112610i 0.130555 0.991441i \(-0.458324\pi\)
−0.477134 + 0.878831i \(0.658324\pi\)
\(464\) 0 0
\(465\) 20.6892 + 9.01104i 0.959439 + 0.417877i
\(466\) 0 0
\(467\) −6.34847 + 8.73792i −0.293772 + 0.404343i −0.930235 0.366965i \(-0.880397\pi\)
0.636463 + 0.771307i \(0.280397\pi\)
\(468\) 0 0
\(469\) 16.0402 + 11.6539i 0.740668 + 0.538127i
\(470\) 0 0
\(471\) −11.8436 + 8.60487i −0.545724 + 0.396491i
\(472\) 0 0
\(473\) −17.1816 + 5.58265i −0.790012 + 0.256691i
\(474\) 0 0
\(475\) −3.45961 28.4652i −0.158738 1.30607i
\(476\) 0 0
\(477\) 3.23015 1.04954i 0.147898 0.0480551i
\(478\) 0 0
\(479\) 18.3447 13.3282i 0.838191 0.608981i −0.0836740 0.996493i \(-0.526665\pi\)
0.921865 + 0.387512i \(0.126665\pi\)
\(480\) 0 0
\(481\) 3.26980 + 2.37565i 0.149090 + 0.108320i
\(482\) 0 0
\(483\) 13.2787 18.2766i 0.604204 0.831615i
\(484\) 0 0
\(485\) −22.7835 + 5.03631i −1.03455 + 0.228687i
\(486\) 0 0
\(487\) 4.74184 + 1.54072i 0.214873 + 0.0698166i 0.414476 0.910060i \(-0.363965\pi\)
−0.199602 + 0.979877i \(0.563965\pi\)
\(488\) 0 0
\(489\) −1.37334 4.22672i −0.0621048 0.191139i
\(490\) 0 0
\(491\) −8.17443 + 25.1583i −0.368907 + 1.13538i 0.578592 + 0.815617i \(0.303603\pi\)
−0.947498 + 0.319761i \(0.896397\pi\)
\(492\) 0 0
\(493\) 37.1766i 1.67435i
\(494\) 0 0
\(495\) 3.36290 7.72118i 0.151151 0.347041i
\(496\) 0 0
\(497\) −7.63365 10.5068i −0.342416 0.471295i
\(498\) 0 0
\(499\) −38.0875 −1.70503 −0.852516 0.522702i \(-0.824924\pi\)
−0.852516 + 0.522702i \(0.824924\pi\)
\(500\) 0 0
\(501\) 23.7655 1.06176
\(502\) 0 0
\(503\) −1.38481 1.90603i −0.0617456 0.0849856i 0.777027 0.629467i \(-0.216727\pi\)
−0.838773 + 0.544481i \(0.816727\pi\)
\(504\) 0 0
\(505\) 6.34665 14.5718i 0.282422 0.648438i
\(506\) 0 0
\(507\) 12.5119i 0.555672i
\(508\) 0 0
\(509\) 9.02282 27.7694i 0.399929 1.23086i −0.525126 0.851024i \(-0.675982\pi\)
0.925056 0.379832i \(-0.124018\pi\)
\(510\) 0 0
\(511\) −13.7250 42.2412i −0.607158 1.86864i
\(512\) 0 0
\(513\) −5.45425 1.77219i −0.240811 0.0782442i
\(514\) 0 0
\(515\) −26.6568 + 5.89249i −1.17464 + 0.259654i
\(516\) 0 0
\(517\) −21.4157 + 29.4762i −0.941862 + 1.29636i
\(518\) 0 0
\(519\) 12.2055 + 8.86778i 0.535760 + 0.389252i
\(520\) 0 0
\(521\) 34.4787 25.0503i 1.51054 1.09747i 0.544604 0.838693i \(-0.316680\pi\)
0.965937 0.258779i \(-0.0833200\pi\)
\(522\) 0 0
\(523\) 19.6631 6.38893i 0.859808 0.279368i 0.154259 0.988030i \(-0.450701\pi\)
0.705548 + 0.708662i \(0.250701\pi\)
\(524\) 0 0
\(525\) −20.2788 3.96765i −0.885039 0.173163i
\(526\) 0 0
\(527\) −50.7978 + 16.5052i −2.21279 + 0.718978i
\(528\) 0 0
\(529\) 5.56809 4.04545i 0.242091 0.175889i
\(530\) 0 0
\(531\) −0.602958 0.438075i −0.0261661 0.0190108i
\(532\) 0 0
\(533\) −2.70855 + 3.72800i −0.117320 + 0.161478i
\(534\) 0 0
\(535\) 8.28846 + 3.60998i 0.358342 + 0.156073i
\(536\) 0 0
\(537\) 15.8982 + 5.16563i 0.686057 + 0.222913i
\(538\) 0 0
\(539\) 11.7304 + 36.1023i 0.505262 + 1.55504i
\(540\) 0 0
\(541\) 3.69426 11.3698i 0.158829 0.488824i −0.839700 0.543050i \(-0.817269\pi\)
0.998529 + 0.0542264i \(0.0172693\pi\)
\(542\) 0 0
\(543\) 10.3923i 0.445976i
\(544\) 0 0
\(545\) −1.29522 1.14733i −0.0554810 0.0491462i
\(546\) 0 0
\(547\) −15.6366 21.5220i −0.668575 0.920214i 0.331152 0.943577i \(-0.392563\pi\)
−0.999727 + 0.0233630i \(0.992563\pi\)
\(548\) 0 0
\(549\) −11.8079 −0.503951
\(550\) 0 0
\(551\) −40.2844 −1.71617
\(552\) 0 0
\(553\) 22.1655 + 30.5082i 0.942573 + 1.29734i
\(554\) 0 0
\(555\) 12.8751 + 1.24771i 0.546517 + 0.0529623i
\(556\) 0 0
\(557\) 28.3420i 1.20089i −0.799667 0.600444i \(-0.794990\pi\)
0.799667 0.600444i \(-0.205010\pi\)
\(558\) 0 0
\(559\) 1.03560 3.18725i 0.0438013 0.134806i
\(560\) 0 0
\(561\) 6.15971 + 18.9576i 0.260063 + 0.800393i
\(562\) 0 0
\(563\) −3.85764 1.25342i −0.162580 0.0528255i 0.226596 0.973989i \(-0.427240\pi\)
−0.389176 + 0.921163i \(0.627240\pi\)
\(564\) 0 0
\(565\) −1.68943 + 1.90719i −0.0710747 + 0.0802360i
\(566\) 0 0
\(567\) −2.42912 + 3.34339i −0.102013 + 0.140409i
\(568\) 0 0
\(569\) 1.59124 + 1.15610i 0.0667081 + 0.0484663i 0.620640 0.784096i \(-0.286873\pi\)
−0.553931 + 0.832562i \(0.686873\pi\)
\(570\) 0 0
\(571\) −4.17273 + 3.03167i −0.174623 + 0.126871i −0.671664 0.740856i \(-0.734420\pi\)
0.497040 + 0.867727i \(0.334420\pi\)
\(572\) 0 0
\(573\) −18.7888 + 6.10485i −0.784914 + 0.255034i
\(574\) 0 0
\(575\) −23.8892 13.2804i −0.996249 0.553831i
\(576\) 0 0
\(577\) −36.7286 + 11.9338i −1.52903 + 0.496812i −0.948325 0.317301i \(-0.897224\pi\)
−0.580706 + 0.814113i \(0.697224\pi\)
\(578\) 0 0
\(579\) 1.80855 1.31399i 0.0751608 0.0546075i
\(580\) 0 0
\(581\) 28.2215 + 20.5041i 1.17083 + 0.850654i
\(582\) 0 0
\(583\) −7.51885 + 10.3488i −0.311399 + 0.428604i
\(584\) 0 0
\(585\) 0.792082 + 1.34658i 0.0327486 + 0.0556742i
\(586\) 0 0
\(587\) 25.8420 + 8.39659i 1.06662 + 0.346564i 0.789168 0.614177i \(-0.210512\pi\)
0.277447 + 0.960741i \(0.410512\pi\)
\(588\) 0 0
\(589\) 17.8850 + 55.0443i 0.736937 + 2.26806i
\(590\) 0 0
\(591\) −7.03223 + 21.6430i −0.289267 + 0.890273i
\(592\) 0 0
\(593\) 30.3486i 1.24627i 0.782114 + 0.623135i \(0.214141\pi\)
−0.782114 + 0.623135i \(0.785859\pi\)
\(594\) 0 0
\(595\) 42.1554 24.7966i 1.72820 1.01656i
\(596\) 0 0
\(597\) −13.4116 18.4594i −0.548899 0.755494i
\(598\) 0 0
\(599\) 26.9205 1.09994 0.549971 0.835184i \(-0.314639\pi\)
0.549971 + 0.835184i \(0.314639\pi\)
\(600\) 0 0
\(601\) −16.9133 −0.689910 −0.344955 0.938619i \(-0.612106\pi\)
−0.344955 + 0.938619i \(0.612106\pi\)
\(602\) 0 0
\(603\) −2.81995 3.88133i −0.114837 0.158060i
\(604\) 0 0
\(605\) 1.53726 + 6.95432i 0.0624983 + 0.282733i
\(606\) 0 0
\(607\) 18.9715i 0.770028i 0.922911 + 0.385014i \(0.125803\pi\)
−0.922911 + 0.385014i \(0.874197\pi\)
\(608\) 0 0
\(609\) −8.97057 + 27.6086i −0.363506 + 1.11876i
\(610\) 0 0
\(611\) −2.08857 6.42795i −0.0844944 0.260047i
\(612\) 0 0
\(613\) −5.19102 1.68666i −0.209663 0.0681237i 0.202302 0.979323i \(-0.435158\pi\)
−0.411966 + 0.911199i \(0.635158\pi\)
\(614\) 0 0
\(615\) −1.42255 + 14.6793i −0.0573628 + 0.591925i
\(616\) 0 0
\(617\) 6.99287 9.62485i 0.281522 0.387482i −0.644715 0.764423i \(-0.723024\pi\)
0.926237 + 0.376941i \(0.123024\pi\)
\(618\) 0 0
\(619\) −10.6888 7.76586i −0.429619 0.312136i 0.351878 0.936046i \(-0.385543\pi\)
−0.781496 + 0.623910i \(0.785543\pi\)
\(620\) 0 0
\(621\) −4.42248 + 3.21312i −0.177468 + 0.128938i
\(622\) 0 0
\(623\) 13.3155 4.32647i 0.533475 0.173336i
\(624\) 0 0
\(625\) −1.80517 + 24.9347i −0.0722066 + 0.997390i
\(626\) 0 0
\(627\) 20.5424 6.67464i 0.820386 0.266560i
\(628\) 0 0
\(629\) −24.7693 + 17.9959i −0.987616 + 0.717545i
\(630\) 0 0
\(631\) 9.39932 + 6.82900i 0.374181 + 0.271858i 0.758943 0.651158i \(-0.225716\pi\)
−0.384762 + 0.923016i \(0.625716\pi\)
\(632\) 0 0
\(633\) −11.8125 + 16.2585i −0.469504 + 0.646217i
\(634\) 0 0
\(635\) 0.116010 1.19710i 0.00460371 0.0475055i
\(636\) 0 0
\(637\) −6.69711 2.17602i −0.265349 0.0862172i
\(638\) 0 0
\(639\) 0.971105 + 2.98875i 0.0384163 + 0.118233i
\(640\) 0 0
\(641\) −10.7784 + 33.1725i −0.425721 + 1.31023i 0.476582 + 0.879130i \(0.341876\pi\)
−0.902303 + 0.431103i \(0.858124\pi\)
\(642\) 0 0
\(643\) 2.90629i 0.114613i 0.998357 + 0.0573065i \(0.0182512\pi\)
−0.998357 + 0.0573065i \(0.981749\pi\)
\(644\) 0 0
\(645\) −2.31504 10.4729i −0.0911545 0.412370i
\(646\) 0 0
\(647\) 7.13583 + 9.82163i 0.280538 + 0.386128i 0.925912 0.377739i \(-0.123298\pi\)
−0.645374 + 0.763867i \(0.723298\pi\)
\(648\) 0 0
\(649\) 2.80702 0.110185
\(650\) 0 0
\(651\) 41.7068 1.63462
\(652\) 0 0
\(653\) −15.3404 21.1143i −0.600318 0.826266i 0.395420 0.918500i \(-0.370599\pi\)
−0.995737 + 0.0922343i \(0.970599\pi\)
\(654\) 0 0
\(655\) 12.9565 7.62126i 0.506253 0.297787i
\(656\) 0 0
\(657\) 10.7473i 0.419293i
\(658\) 0 0
\(659\) −6.59035 + 20.2830i −0.256724 + 0.790114i 0.736761 + 0.676153i \(0.236354\pi\)
−0.993485 + 0.113962i \(0.963646\pi\)
\(660\) 0 0
\(661\) −9.79161 30.1355i −0.380850 1.17213i −0.939447 0.342695i \(-0.888660\pi\)
0.558597 0.829439i \(-0.311340\pi\)
\(662\) 0 0
\(663\) −3.51671 1.14265i −0.136578 0.0443768i
\(664\) 0 0
\(665\) −26.8695 45.6794i −1.04195 1.77137i
\(666\) 0 0
\(667\) −22.5702 + 31.0652i −0.873922 + 1.20285i
\(668\) 0 0
\(669\) −10.8561 7.88740i −0.419720 0.304945i
\(670\) 0 0
\(671\) 35.9790 26.1403i 1.38895 1.00913i
\(672\) 0 0
\(673\) −1.88857 + 0.613635i −0.0727992 + 0.0236539i −0.345190 0.938533i \(-0.612186\pi\)
0.272391 + 0.962187i \(0.412186\pi\)
\(674\) 0 0
\(675\) 4.37012 + 2.42942i 0.168206 + 0.0935083i
\(676\) 0 0
\(677\) −37.5057 + 12.1864i −1.44146 + 0.468360i −0.922353 0.386348i \(-0.873736\pi\)
−0.519110 + 0.854708i \(0.673736\pi\)
\(678\) 0 0
\(679\) −34.8885 + 25.3480i −1.33890 + 0.972767i
\(680\) 0 0
\(681\) −14.9597 10.8689i −0.573259 0.416497i
\(682\) 0 0
\(683\) 7.22768 9.94805i 0.276559 0.380651i −0.648031 0.761614i \(-0.724407\pi\)
0.924590 + 0.380962i \(0.124407\pi\)
\(684\) 0 0
\(685\) −0.271894 + 0.306940i −0.0103885 + 0.0117276i
\(686\) 0 0
\(687\) −18.4623 5.99878i −0.704382 0.228868i
\(688\) 0 0
\(689\) −0.733276 2.25679i −0.0279356 0.0859769i
\(690\) 0 0
\(691\) 4.85334 14.9371i 0.184630 0.568232i −0.815312 0.579022i \(-0.803435\pi\)
0.999942 + 0.0107896i \(0.00343451\pi\)
\(692\) 0 0
\(693\) 15.5649i 0.591262i
\(694\) 0 0
\(695\) −18.2949 1.77294i −0.693966 0.0672514i
\(696\) 0 0
\(697\) −20.5177 28.2402i −0.777164 1.06967i
\(698\) 0 0
\(699\) −12.1833 −0.460813
\(700\) 0 0
\(701\) −26.4222 −0.997953 −0.498976 0.866616i \(-0.666291\pi\)
−0.498976 + 0.866616i \(0.666291\pi\)
\(702\) 0 0
\(703\) 19.5003 + 26.8399i 0.735469 + 1.01229i
\(704\) 0 0
\(705\) −16.1921 14.3433i −0.609828 0.540198i
\(706\) 0 0
\(707\) 29.3749i 1.10476i
\(708\) 0 0
\(709\) −15.0638 + 46.3616i −0.565733 + 1.74115i 0.100030 + 0.994984i \(0.468106\pi\)
−0.665763 + 0.746163i \(0.731894\pi\)
\(710\) 0 0
\(711\) −2.81976 8.67832i −0.105749 0.325462i
\(712\) 0 0
\(713\) 52.4677 + 17.0478i 1.96493 + 0.638445i
\(714\) 0 0
\(715\) −5.39452 2.34954i −0.201744 0.0878680i
\(716\) 0 0
\(717\) 2.65959 3.66061i 0.0993241 0.136708i
\(718\) 0 0
\(719\) −27.7117 20.1337i −1.03347 0.750861i −0.0644713 0.997920i \(-0.520536\pi\)
−0.969001 + 0.247058i \(0.920536\pi\)
\(720\) 0 0
\(721\) −40.8197 + 29.6572i −1.52020 + 1.10449i
\(722\) 0 0
\(723\) 8.57071 2.78479i 0.318748 0.103568i
\(724\) 0 0
\(725\) 34.4684 + 6.74391i 1.28012 + 0.250463i
\(726\) 0 0
\(727\) −20.3168 + 6.60134i −0.753510 + 0.244830i −0.660491 0.750834i \(-0.729652\pi\)
−0.0930190 + 0.995664i \(0.529652\pi\)
\(728\) 0 0
\(729\) 0.809017 0.587785i 0.0299636 0.0217698i
\(730\) 0 0
\(731\) 20.5381 + 14.9218i 0.759629 + 0.551903i
\(732\) 0 0
\(733\) 18.3875 25.3083i 0.679159 0.934782i −0.320765 0.947159i \(-0.603940\pi\)
0.999923 + 0.0123772i \(0.00393990\pi\)
\(734\) 0 0
\(735\) −22.0058 + 4.86440i −0.811697 + 0.179426i
\(736\) 0 0
\(737\) 17.1849 + 5.58370i 0.633013 + 0.205678i
\(738\) 0 0
\(739\) −0.406330 1.25056i −0.0149471 0.0460025i 0.943305 0.331928i \(-0.107699\pi\)
−0.958252 + 0.285925i \(0.907699\pi\)
\(740\) 0 0
\(741\) −1.23817 + 3.81070i −0.0454853 + 0.139989i
\(742\) 0 0
\(743\) 8.76431i 0.321531i 0.986993 + 0.160766i \(0.0513963\pi\)
−0.986993 + 0.160766i \(0.948604\pi\)
\(744\) 0 0
\(745\) −4.94473 + 11.3530i −0.181161 + 0.415943i
\(746\) 0 0
\(747\) −4.96148 6.82889i −0.181531 0.249856i
\(748\) 0 0
\(749\) 16.7085 0.610515
\(750\) 0 0
\(751\) 44.6570 1.62956 0.814779 0.579772i \(-0.196858\pi\)
0.814779 + 0.579772i \(0.196858\pi\)
\(752\) 0 0
\(753\) 1.86307 + 2.56430i 0.0678941 + 0.0934482i
\(754\) 0 0
\(755\) 11.4947 26.3917i 0.418336 0.960494i
\(756\) 0 0
\(757\) 7.70729i 0.280126i −0.990143 0.140063i \(-0.955269\pi\)
0.990143 0.140063i \(-0.0447305\pi\)
\(758\) 0 0
\(759\) 6.36221 19.5809i 0.230934 0.710740i
\(760\) 0 0
\(761\) 12.2344 + 37.6537i 0.443498 + 1.36495i 0.884123 + 0.467254i \(0.154757\pi\)
−0.440625 + 0.897691i \(0.645243\pi\)
\(762\) 0 0
\(763\) −3.04140 0.988210i −0.110106 0.0357756i
\(764\) 0 0
\(765\) −11.5554 + 2.55434i −0.417788 + 0.0923523i
\(766\) 0 0
\(767\) −0.306068 + 0.421266i −0.0110515 + 0.0152110i
\(768\) 0 0
\(769\) 23.7336 + 17.2435i 0.855855 + 0.621815i 0.926754 0.375668i \(-0.122587\pi\)
−0.0708991 + 0.997483i \(0.522587\pi\)
\(770\) 0 0
\(771\) 2.63126 1.91172i 0.0947624 0.0688489i
\(772\) 0 0
\(773\) 10.3762 3.37142i 0.373205 0.121262i −0.116408 0.993201i \(-0.537138\pi\)
0.489613 + 0.871940i \(0.337138\pi\)
\(774\) 0 0
\(775\) −6.08801 50.0914i −0.218688 1.79934i
\(776\) 0 0
\(777\) 22.7369 7.38766i 0.815681 0.265031i
\(778\) 0 0
\(779\) −30.6010 + 22.2329i −1.09639 + 0.796577i
\(780\) 0 0
\(781\) −9.57543 6.95696i −0.342636 0.248940i
\(782\) 0 0
\(783\) 4.12883 5.68284i 0.147552 0.203088i
\(784\) 0 0
\(785\) 30.0118 + 13.0714i 1.07117 + 0.466539i
\(786\) 0 0
\(787\) −35.8619 11.6522i −1.27834 0.415358i −0.410344 0.911931i \(-0.634591\pi\)
−0.867995 + 0.496573i \(0.834591\pi\)
\(788\) 0 0
\(789\) −3.41774 10.5187i −0.121675 0.374476i
\(790\) 0 0
\(791\) −1.45512 + 4.47841i −0.0517383 + 0.159234i
\(792\) 0 0
\(793\) 8.24980i 0.292959i
\(794\) 0 0
\(795\) −5.68488 5.03578i −0.201622 0.178601i
\(796\) 0 0
\(797\) 28.9432 + 39.8369i 1.02522 + 1.41110i 0.908477 +