Properties

Label 300.2.o.a.109.1
Level $300$
Weight $2$
Character 300.109
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 109.1
Character \(\chi\) \(=\) 300.109
Dual form 300.2.o.a.289.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.951057 + 0.309017i) q^{3} +(-2.10592 + 0.751722i) q^{5} +0.595901i q^{7} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.951057 + 0.309017i) q^{3} +(-2.10592 + 0.751722i) q^{5} +0.595901i q^{7} +(0.809017 - 0.587785i) q^{9} +(-2.71474 - 1.97238i) q^{11} +(-2.80319 - 3.85825i) q^{13} +(1.77056 - 1.36570i) q^{15} +(-7.11384 - 2.31143i) q^{17} +(-1.91242 + 5.88583i) q^{19} +(-0.184143 - 0.566735i) q^{21} +(-2.59154 + 3.56694i) q^{23} +(3.86983 - 3.16614i) q^{25} +(-0.587785 + 0.809017i) q^{27} +(0.853035 + 2.62537i) q^{29} +(1.38708 - 4.26899i) q^{31} +(3.19137 + 1.03694i) q^{33} +(-0.447952 - 1.25492i) q^{35} +(-0.764512 - 1.05226i) q^{37} +(3.85825 + 2.80319i) q^{39} +(7.61184 - 5.53032i) q^{41} +7.59854i q^{43} +(-1.26188 + 1.84599i) q^{45} +(-4.18645 + 1.36026i) q^{47} +6.64490 q^{49} +7.47993 q^{51} +(-7.80561 + 2.53620i) q^{53} +(7.19972 + 2.11294i) q^{55} -6.18873i q^{57} +(-1.80309 + 1.31002i) q^{59} +(-10.2014 - 7.41175i) q^{61} +(0.350262 + 0.482094i) q^{63} +(8.80363 + 6.01797i) q^{65} +(7.94930 + 2.58288i) q^{67} +(1.36245 - 4.19319i) q^{69} +(2.09986 + 6.46271i) q^{71} +(4.29801 - 5.91570i) q^{73} +(-2.70203 + 4.20702i) q^{75} +(1.17534 - 1.61772i) q^{77} +(3.26546 + 10.0500i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-3.97694 - 1.29219i) q^{83} +(16.7188 - 0.479942i) q^{85} +(-1.62257 - 2.23328i) q^{87} +(3.43862 + 2.49830i) q^{89} +(2.29914 - 1.67042i) q^{91} +4.48868i q^{93} +(-0.397094 - 13.8327i) q^{95} +(-11.6744 + 3.79326i) q^{97} -3.35561 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 2q^{5} + 6q^{9} + O(q^{10}) \) \( 24q - 2q^{5} + 6q^{9} - 6q^{11} + 4q^{15} + 10q^{17} + 10q^{19} - 4q^{21} + 40q^{23} - 4q^{25} + 4q^{29} + 6q^{31} + 10q^{33} - 6q^{35} - 10q^{41} + 2q^{45} - 40q^{47} - 56q^{49} + 16q^{51} - 60q^{53} - 62q^{55} - 36q^{59} - 12q^{61} - 10q^{63} + 20q^{67} + 4q^{69} + 40q^{71} + 60q^{73} + 8q^{75} - 40q^{77} + 8q^{79} - 6q^{81} - 50q^{83} + 34q^{85} - 20q^{87} - 30q^{91} - 60q^{95} - 40q^{97} - 4q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\)

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
\(3\) −0.951057 + 0.309017i −0.549093 + 0.178411i
\(4\) 0 0
\(5\) −2.10592 + 0.751722i −0.941798 + 0.336180i
\(6\) 0 0
\(7\) 0.595901i 0.225229i 0.993639 + 0.112615i \(0.0359225\pi\)
−0.993639 + 0.112615i \(0.964077\pi\)
\(8\) 0 0
\(9\) 0.809017 0.587785i 0.269672 0.195928i
\(10\) 0 0
\(11\) −2.71474 1.97238i −0.818526 0.594694i 0.0977636 0.995210i \(-0.468831\pi\)
−0.916290 + 0.400515i \(0.868831\pi\)
\(12\) 0 0
\(13\) −2.80319 3.85825i −0.777464 1.07009i −0.995557 0.0941591i \(-0.969984\pi\)
0.218094 0.975928i \(-0.430016\pi\)
\(14\) 0 0
\(15\) 1.77056 1.36570i 0.457156 0.352621i
\(16\) 0 0
\(17\) −7.11384 2.31143i −1.72536 0.560603i −0.732593 0.680667i \(-0.761690\pi\)
−0.992766 + 0.120064i \(0.961690\pi\)
\(18\) 0 0
\(19\) −1.91242 + 5.88583i −0.438740 + 1.35030i 0.450466 + 0.892794i \(0.351258\pi\)
−0.889205 + 0.457508i \(0.848742\pi\)
\(20\) 0 0
\(21\) −0.184143 0.566735i −0.0401834 0.123672i
\(22\) 0 0
\(23\) −2.59154 + 3.56694i −0.540373 + 0.743759i −0.988667 0.150127i \(-0.952032\pi\)
0.448294 + 0.893886i \(0.352032\pi\)
\(24\) 0 0
\(25\) 3.86983 3.16614i 0.773966 0.633228i
\(26\) 0 0
\(27\) −0.587785 + 0.809017i −0.113119 + 0.155695i
\(28\) 0 0
\(29\) 0.853035 + 2.62537i 0.158405 + 0.487519i 0.998490 0.0549349i \(-0.0174951\pi\)
−0.840085 + 0.542454i \(0.817495\pi\)
\(30\) 0 0
\(31\) 1.38708 4.26899i 0.249127 0.766734i −0.745803 0.666166i \(-0.767934\pi\)
0.994930 0.100567i \(-0.0320658\pi\)
\(32\) 0 0
\(33\) 3.19137 + 1.03694i 0.555547 + 0.180508i
\(34\) 0 0
\(35\) −0.447952 1.25492i −0.0757176 0.212120i
\(36\) 0 0
\(37\) −0.764512 1.05226i −0.125685 0.172991i 0.741537 0.670912i \(-0.234097\pi\)
−0.867222 + 0.497921i \(0.834097\pi\)
\(38\) 0 0
\(39\) 3.85825 + 2.80319i 0.617815 + 0.448869i
\(40\) 0 0
\(41\) 7.61184 5.53032i 1.18877 0.863691i 0.195636 0.980677i \(-0.437323\pi\)
0.993134 + 0.116985i \(0.0373230\pi\)
\(42\) 0 0
\(43\) 7.59854i 1.15877i 0.815055 + 0.579383i \(0.196706\pi\)
−0.815055 + 0.579383i \(0.803294\pi\)
\(44\) 0 0
\(45\) −1.26188 + 1.84599i −0.188109 + 0.275183i
\(46\) 0 0
\(47\) −4.18645 + 1.36026i −0.610656 + 0.198414i −0.597987 0.801506i \(-0.704033\pi\)
−0.0126688 + 0.999920i \(0.504033\pi\)
\(48\) 0 0
\(49\) 6.64490 0.949272
\(50\) 0 0
\(51\) 7.47993 1.04740
\(52\) 0 0
\(53\) −7.80561 + 2.53620i −1.07218 + 0.348373i −0.791338 0.611379i \(-0.790615\pi\)
−0.280846 + 0.959753i \(0.590615\pi\)
\(54\) 0 0
\(55\) 7.19972 + 2.11294i 0.970811 + 0.284909i
\(56\) 0 0
\(57\) 6.18873i 0.819717i
\(58\) 0 0
\(59\) −1.80309 + 1.31002i −0.234743 + 0.170550i −0.698938 0.715182i \(-0.746344\pi\)
0.464195 + 0.885733i \(0.346344\pi\)
\(60\) 0 0
\(61\) −10.2014 7.41175i −1.30615 0.948977i −0.306159 0.951980i \(-0.599044\pi\)
−0.999995 + 0.00300353i \(0.999044\pi\)
\(62\) 0 0
\(63\) 0.350262 + 0.482094i 0.0441288 + 0.0607381i
\(64\) 0 0
\(65\) 8.80363 + 6.01797i 1.09196 + 0.746437i
\(66\) 0 0
\(67\) 7.94930 + 2.58288i 0.971161 + 0.315549i 0.751285 0.659978i \(-0.229435\pi\)
0.219877 + 0.975528i \(0.429435\pi\)
\(68\) 0 0
\(69\) 1.36245 4.19319i 0.164020 0.504801i
\(70\) 0 0
\(71\) 2.09986 + 6.46271i 0.249208 + 0.766983i 0.994916 + 0.100710i \(0.0321114\pi\)
−0.745708 + 0.666273i \(0.767889\pi\)
\(72\) 0 0
\(73\) 4.29801 5.91570i 0.503044 0.692381i −0.479683 0.877442i \(-0.659248\pi\)
0.982727 + 0.185061i \(0.0592483\pi\)
\(74\) 0 0
\(75\) −2.70203 + 4.20702i −0.312004 + 0.485785i
\(76\) 0 0
\(77\) 1.17534 1.61772i 0.133943 0.184356i
\(78\) 0 0
\(79\) 3.26546 + 10.0500i 0.367393 + 1.13072i 0.948469 + 0.316870i \(0.102632\pi\)
−0.581076 + 0.813849i \(0.697368\pi\)
\(80\) 0 0
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 0 0
\(83\) −3.97694 1.29219i −0.436526 0.141836i 0.0825062 0.996591i \(-0.473708\pi\)
−0.519032 + 0.854755i \(0.673708\pi\)
\(84\) 0 0
\(85\) 16.7188 0.479942i 1.81340 0.0520571i
\(86\) 0 0
\(87\) −1.62257 2.23328i −0.173958 0.239432i
\(88\) 0 0
\(89\) 3.43862 + 2.49830i 0.364493 + 0.264819i 0.754924 0.655813i \(-0.227674\pi\)
−0.390431 + 0.920632i \(0.627674\pi\)
\(90\) 0 0
\(91\) 2.29914 1.67042i 0.241015 0.175108i
\(92\) 0 0
\(93\) 4.48868i 0.465455i
\(94\) 0 0
\(95\) −0.397094 13.8327i −0.0407409 1.41921i
\(96\) 0 0
\(97\) −11.6744 + 3.79326i −1.18536 + 0.385147i −0.834355 0.551227i \(-0.814160\pi\)
−0.351004 + 0.936374i \(0.614160\pi\)
\(98\) 0 0
\(99\) −3.35561 −0.337251
\(100\) 0 0
\(101\) −8.00835 −0.796860 −0.398430 0.917199i \(-0.630445\pi\)
−0.398430 + 0.917199i \(0.630445\pi\)
\(102\) 0 0
\(103\) −5.34989 + 1.73829i −0.527141 + 0.171278i −0.560484 0.828166i \(-0.689385\pi\)
0.0333428 + 0.999444i \(0.489385\pi\)
\(104\) 0 0
\(105\) 0.813819 + 1.05508i 0.0794206 + 0.102965i
\(106\) 0 0
\(107\) 13.7701i 1.33120i −0.746308 0.665601i \(-0.768175\pi\)
0.746308 0.665601i \(-0.231825\pi\)
\(108\) 0 0
\(109\) −10.3566 + 7.52450i −0.991981 + 0.720716i −0.960354 0.278784i \(-0.910069\pi\)
−0.0316266 + 0.999500i \(0.510069\pi\)
\(110\) 0 0
\(111\) 1.05226 + 0.764512i 0.0998761 + 0.0725643i
\(112\) 0 0
\(113\) 6.84147 + 9.41647i 0.643591 + 0.885827i 0.998801 0.0489597i \(-0.0155906\pi\)
−0.355210 + 0.934787i \(0.615591\pi\)
\(114\) 0 0
\(115\) 2.77623 9.45983i 0.258885 0.882133i
\(116\) 0 0
\(117\) −4.53565 1.47372i −0.419321 0.136246i
\(118\) 0 0
\(119\) 1.37738 4.23914i 0.126264 0.388601i
\(120\) 0 0
\(121\) 0.0803793 + 0.247382i 0.00730721 + 0.0224893i
\(122\) 0 0
\(123\) −5.53032 + 7.61184i −0.498652 + 0.686336i
\(124\) 0 0
\(125\) −5.76951 + 9.57668i −0.516040 + 0.856564i
\(126\) 0 0
\(127\) 1.56452 2.15338i 0.138829 0.191081i −0.733941 0.679213i \(-0.762321\pi\)
0.872770 + 0.488132i \(0.162321\pi\)
\(128\) 0 0
\(129\) −2.34808 7.22664i −0.206737 0.636270i
\(130\) 0 0
\(131\) 3.00070 9.23520i 0.262172 0.806883i −0.730159 0.683277i \(-0.760554\pi\)
0.992331 0.123606i \(-0.0394458\pi\)
\(132\) 0 0
\(133\) −3.50737 1.13961i −0.304128 0.0988170i
\(134\) 0 0
\(135\) 0.629675 2.14558i 0.0541938 0.184662i
\(136\) 0 0
\(137\) −2.25823 3.10819i −0.192934 0.265551i 0.701580 0.712591i \(-0.252478\pi\)
−0.894514 + 0.447040i \(0.852478\pi\)
\(138\) 0 0
\(139\) −3.98655 2.89640i −0.338135 0.245670i 0.405740 0.913989i \(-0.367014\pi\)
−0.743875 + 0.668319i \(0.767014\pi\)
\(140\) 0 0
\(141\) 3.56121 2.58737i 0.299908 0.217896i
\(142\) 0 0
\(143\) 16.0031i 1.33825i
\(144\) 0 0
\(145\) −3.76998 4.88759i −0.313080 0.405892i
\(146\) 0 0
\(147\) −6.31968 + 2.05339i −0.521238 + 0.169361i
\(148\) 0 0
\(149\) 6.59040 0.539907 0.269953 0.962873i \(-0.412992\pi\)
0.269953 + 0.962873i \(0.412992\pi\)
\(150\) 0 0
\(151\) −19.5433 −1.59041 −0.795207 0.606338i \(-0.792638\pi\)
−0.795207 + 0.606338i \(0.792638\pi\)
\(152\) 0 0
\(153\) −7.11384 + 2.31143i −0.575120 + 0.186868i
\(154\) 0 0
\(155\) 0.288012 + 10.0329i 0.0231337 + 0.805859i
\(156\) 0 0
\(157\) 0.341995i 0.0272942i −0.999907 0.0136471i \(-0.995656\pi\)
0.999907 0.0136471i \(-0.00434414\pi\)
\(158\) 0 0
\(159\) 6.63985 4.82413i 0.526574 0.382579i
\(160\) 0 0
\(161\) −2.12554 1.54430i −0.167516 0.121708i
\(162\) 0 0
\(163\) −13.2347 18.2161i −1.03663 1.42679i −0.899855 0.436190i \(-0.856328\pi\)
−0.136770 0.990603i \(-0.543672\pi\)
\(164\) 0 0
\(165\) −7.50028 + 0.215309i −0.583896 + 0.0167618i
\(166\) 0 0
\(167\) 4.10375 + 1.33339i 0.317557 + 0.103181i 0.463459 0.886118i \(-0.346608\pi\)
−0.145901 + 0.989299i \(0.546608\pi\)
\(168\) 0 0
\(169\) −3.01105 + 9.26706i −0.231619 + 0.712851i
\(170\) 0 0
\(171\) 1.91242 + 5.88583i 0.146247 + 0.450101i
\(172\) 0 0
\(173\) 10.0916 13.8898i 0.767247 1.05602i −0.229330 0.973349i \(-0.573653\pi\)
0.996577 0.0826755i \(-0.0263465\pi\)
\(174\) 0 0
\(175\) 1.88670 + 2.30603i 0.142621 + 0.174320i
\(176\) 0 0
\(177\) 1.31002 1.80309i 0.0984674 0.135529i
\(178\) 0 0
\(179\) −0.328670 1.01154i −0.0245659 0.0756062i 0.938022 0.346576i \(-0.112656\pi\)
−0.962588 + 0.270970i \(0.912656\pi\)
\(180\) 0 0
\(181\) −3.71645 + 11.4380i −0.276241 + 0.850183i 0.712647 + 0.701523i \(0.247496\pi\)
−0.988888 + 0.148660i \(0.952504\pi\)
\(182\) 0 0
\(183\) 11.9925 + 3.89659i 0.886508 + 0.288044i
\(184\) 0 0
\(185\) 2.40101 + 1.64128i 0.176526 + 0.120669i
\(186\) 0 0
\(187\) 14.7533 + 20.3061i 1.07886 + 1.48493i
\(188\) 0 0
\(189\) −0.482094 0.350262i −0.0350672 0.0254778i
\(190\) 0 0
\(191\) 17.7737 12.9134i 1.28606 0.934379i 0.286344 0.958127i \(-0.407560\pi\)
0.999718 + 0.0237480i \(0.00755992\pi\)
\(192\) 0 0
\(193\) 20.4002i 1.46844i −0.678912 0.734220i \(-0.737548\pi\)
0.678912 0.734220i \(-0.262452\pi\)
\(194\) 0 0
\(195\) −10.2324 3.00296i −0.732758 0.215046i
\(196\) 0 0
\(197\) −3.90410 + 1.26852i −0.278155 + 0.0903781i −0.444773 0.895644i \(-0.646716\pi\)
0.166617 + 0.986022i \(0.446716\pi\)
\(198\) 0 0
\(199\) −25.5940 −1.81431 −0.907156 0.420795i \(-0.861751\pi\)
−0.907156 + 0.420795i \(0.861751\pi\)
\(200\) 0 0
\(201\) −8.35839 −0.589555
\(202\) 0 0
\(203\) −1.56446 + 0.508324i −0.109804 + 0.0356774i
\(204\) 0 0
\(205\) −11.8727 + 17.3684i −0.829224 + 1.21306i
\(206\) 0 0
\(207\) 4.40898i 0.306446i
\(208\) 0 0
\(209\) 16.8008 12.2065i 1.16214 0.844342i
\(210\) 0 0
\(211\) −15.7826 11.4667i −1.08652 0.789402i −0.107710 0.994182i \(-0.534352\pi\)
−0.978808 + 0.204781i \(0.934352\pi\)
\(212\) 0 0
\(213\) −3.99418 5.49751i −0.273676 0.376683i
\(214\) 0 0
\(215\) −5.71199 16.0019i −0.389554 1.09132i
\(216\) 0 0
\(217\) 2.54389 + 0.826561i 0.172691 + 0.0561106i
\(218\) 0 0
\(219\) −2.25960 + 6.95433i −0.152689 + 0.469930i
\(220\) 0 0
\(221\) 11.0233 + 33.9263i 0.741510 + 2.28213i
\(222\) 0 0
\(223\) 1.30975 1.80271i 0.0877071 0.120718i −0.762909 0.646506i \(-0.776229\pi\)
0.850616 + 0.525788i \(0.176229\pi\)
\(224\) 0 0
\(225\) 1.26975 4.83609i 0.0846498 0.322406i
\(226\) 0 0
\(227\) −2.67322 + 3.67938i −0.177428 + 0.244209i −0.888463 0.458947i \(-0.848227\pi\)
0.711035 + 0.703156i \(0.248227\pi\)
\(228\) 0 0
\(229\) −1.05533 3.24796i −0.0697380 0.214631i 0.910113 0.414359i \(-0.135994\pi\)
−0.979851 + 0.199728i \(0.935994\pi\)
\(230\) 0 0
\(231\) −0.617913 + 1.90174i −0.0406557 + 0.125125i
\(232\) 0 0
\(233\) 15.9202 + 5.17279i 1.04297 + 0.338881i 0.779905 0.625898i \(-0.215267\pi\)
0.263063 + 0.964779i \(0.415267\pi\)
\(234\) 0 0
\(235\) 7.79380 6.01165i 0.508412 0.392157i
\(236\) 0 0
\(237\) −6.21127 8.54908i −0.403465 0.555323i
\(238\) 0 0
\(239\) −18.0931 13.1454i −1.17035 0.850306i −0.179295 0.983795i \(-0.557382\pi\)
−0.991050 + 0.133490i \(0.957382\pi\)
\(240\) 0 0
\(241\) −0.214678 + 0.155973i −0.0138286 + 0.0100471i −0.594678 0.803964i \(-0.702720\pi\)
0.580849 + 0.814011i \(0.302720\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) −13.9937 + 4.99512i −0.894022 + 0.319126i
\(246\) 0 0
\(247\) 28.0699 9.12046i 1.78604 0.580321i
\(248\) 0 0
\(249\) 4.18160 0.264998
\(250\) 0 0
\(251\) 29.0694 1.83484 0.917422 0.397915i \(-0.130266\pi\)
0.917422 + 0.397915i \(0.130266\pi\)
\(252\) 0 0
\(253\) 14.0707 4.57185i 0.884619 0.287430i
\(254\) 0 0
\(255\) −15.7522 + 5.62283i −0.986439 + 0.352115i
\(256\) 0 0
\(257\) 7.05952i 0.440361i 0.975459 + 0.220180i \(0.0706646\pi\)
−0.975459 + 0.220180i \(0.929335\pi\)
\(258\) 0 0
\(259\) 0.627043 0.455573i 0.0389625 0.0283079i
\(260\) 0 0
\(261\) 2.23328 + 1.62257i 0.138236 + 0.100435i
\(262\) 0 0
\(263\) −0.814961 1.12170i −0.0502527 0.0691669i 0.783151 0.621831i \(-0.213611\pi\)
−0.833404 + 0.552665i \(0.813611\pi\)
\(264\) 0 0
\(265\) 14.5315 11.2087i 0.892663 0.688544i
\(266\) 0 0
\(267\) −4.04234 1.31343i −0.247387 0.0803809i
\(268\) 0 0
\(269\) 4.38039 13.4815i 0.267077 0.821979i −0.724130 0.689663i \(-0.757759\pi\)
0.991208 0.132316i \(-0.0422414\pi\)
\(270\) 0 0
\(271\) 4.64795 + 14.3049i 0.282343 + 0.868963i 0.987182 + 0.159596i \(0.0510191\pi\)
−0.704839 + 0.709367i \(0.748981\pi\)
\(272\) 0 0
\(273\) −1.67042 + 2.29914i −0.101098 + 0.139150i
\(274\) 0 0
\(275\) −16.7504 + 0.962496i −1.01009 + 0.0580407i
\(276\) 0 0
\(277\) −7.51973 + 10.3500i −0.451817 + 0.621873i −0.972787 0.231703i \(-0.925570\pi\)
0.520970 + 0.853575i \(0.325570\pi\)
\(278\) 0 0
\(279\) −1.38708 4.26899i −0.0830423 0.255578i
\(280\) 0 0
\(281\) −4.72976 + 14.5567i −0.282154 + 0.868380i 0.705084 + 0.709124i \(0.250909\pi\)
−0.987237 + 0.159256i \(0.949091\pi\)
\(282\) 0 0
\(283\) 22.2073 + 7.21559i 1.32009 + 0.428923i 0.882525 0.470265i \(-0.155842\pi\)
0.437563 + 0.899188i \(0.355842\pi\)
\(284\) 0 0
\(285\) 4.65220 + 13.0330i 0.275573 + 0.772008i
\(286\) 0 0
\(287\) 3.29552 + 4.53590i 0.194529 + 0.267746i
\(288\) 0 0
\(289\) 31.5107 + 22.8939i 1.85357 + 1.34670i
\(290\) 0 0
\(291\) 9.93087 7.21520i 0.582158 0.422963i
\(292\) 0 0
\(293\) 6.36651i 0.371936i 0.982556 + 0.185968i \(0.0595420\pi\)
−0.982556 + 0.185968i \(0.940458\pi\)
\(294\) 0 0
\(295\) 2.81240 4.11423i 0.163744 0.239540i
\(296\) 0 0
\(297\) 3.19137 1.03694i 0.185182 0.0601694i
\(298\) 0 0
\(299\) 21.0267 1.21601
\(300\) 0 0
\(301\) −4.52797 −0.260988
\(302\) 0 0
\(303\) 7.61639 2.47472i 0.437550 0.142169i
\(304\) 0 0
\(305\) 27.0549 + 7.93996i 1.54916 + 0.454641i
\(306\) 0 0
\(307\) 27.2317i 1.55419i 0.629382 + 0.777096i \(0.283308\pi\)
−0.629382 + 0.777096i \(0.716692\pi\)
\(308\) 0 0
\(309\) 4.55089 3.30642i 0.258891 0.188095i
\(310\) 0 0
\(311\) −13.8814 10.0854i −0.787142 0.571892i 0.119972 0.992777i \(-0.461719\pi\)
−0.907114 + 0.420885i \(0.861719\pi\)
\(312\) 0 0
\(313\) −11.9120 16.3955i −0.673307 0.926728i 0.326523 0.945189i \(-0.394123\pi\)
−0.999830 + 0.0184618i \(0.994123\pi\)
\(314\) 0 0
\(315\) −1.10002 0.751953i −0.0619794 0.0423678i
\(316\) 0 0
\(317\) 19.9868 + 6.49409i 1.12257 + 0.364745i 0.810747 0.585396i \(-0.199061\pi\)
0.311821 + 0.950141i \(0.399061\pi\)
\(318\) 0 0
\(319\) 2.86245 8.80972i 0.160267 0.493250i
\(320\) 0 0
\(321\) 4.25518 + 13.0961i 0.237501 + 0.730953i
\(322\) 0 0
\(323\) 27.2093 37.4504i 1.51397 2.08380i
\(324\) 0 0
\(325\) −23.0636 6.05550i −1.27934 0.335899i
\(326\) 0 0
\(327\) 7.52450 10.3566i 0.416106 0.572720i
\(328\) 0 0
\(329\) −0.810579 2.49471i −0.0446887 0.137538i
\(330\) 0 0
\(331\) −3.93765 + 12.1188i −0.216433 + 0.666111i 0.782616 + 0.622505i \(0.213885\pi\)
−0.999049 + 0.0436066i \(0.986115\pi\)
\(332\) 0 0
\(333\) −1.23701 0.401928i −0.0677875 0.0220255i
\(334\) 0 0
\(335\) −18.6822 + 0.536308i −1.02072 + 0.0293016i
\(336\) 0 0
\(337\) 7.25720 + 9.98868i 0.395325 + 0.544118i 0.959563 0.281494i \(-0.0908300\pi\)
−0.564238 + 0.825612i \(0.690830\pi\)
\(338\) 0 0
\(339\) −9.41647 6.84147i −0.511432 0.371577i
\(340\) 0 0
\(341\) −12.1856 + 8.85338i −0.659889 + 0.479437i
\(342\) 0 0
\(343\) 8.13100i 0.439033i
\(344\) 0 0
\(345\) 0.282898 + 9.85473i 0.0152307 + 0.530561i
\(346\) 0 0
\(347\) 12.5175 4.06718i 0.671974 0.218337i 0.0468956 0.998900i \(-0.485067\pi\)
0.625078 + 0.780562i \(0.285067\pi\)
\(348\) 0 0
\(349\) −20.8060 −1.11372 −0.556861 0.830606i \(-0.687994\pi\)
−0.556861 + 0.830606i \(0.687994\pi\)
\(350\) 0 0
\(351\) 4.76906 0.254554
\(352\) 0 0
\(353\) −27.3852 + 8.89800i −1.45757 + 0.473593i −0.927326 0.374254i \(-0.877899\pi\)
−0.530242 + 0.847846i \(0.677899\pi\)
\(354\) 0 0
\(355\) −9.28031 12.0315i −0.492548 0.638564i
\(356\) 0 0
\(357\) 4.45730i 0.235905i
\(358\) 0 0
\(359\) −26.9627 + 19.5896i −1.42304 + 1.03390i −0.431779 + 0.901979i \(0.642114\pi\)
−0.991260 + 0.131919i \(0.957886\pi\)
\(360\) 0 0
\(361\) −15.6143 11.3445i −0.821806 0.597077i
\(362\) 0 0
\(363\) −0.152891 0.210436i −0.00802468 0.0110450i
\(364\) 0 0
\(365\) −4.60432 + 15.6889i −0.241001 + 0.821196i
\(366\) 0 0
\(367\) 1.80441 + 0.586288i 0.0941894 + 0.0306040i 0.355733 0.934588i \(-0.384231\pi\)
−0.261543 + 0.965192i \(0.584231\pi\)
\(368\) 0 0
\(369\) 2.90746 8.94825i 0.151356 0.465827i
\(370\) 0 0
\(371\) −1.51132 4.65137i −0.0784639 0.241487i
\(372\) 0 0
\(373\) 18.1572 24.9912i 0.940143 1.29400i −0.0156262 0.999878i \(-0.504974\pi\)
0.955769 0.294118i \(-0.0950258\pi\)
\(374\) 0 0
\(375\) 2.52777 10.8908i 0.130533 0.562401i
\(376\) 0 0
\(377\) 7.73814 10.6506i 0.398534 0.548535i
\(378\) 0 0
\(379\) −6.96979 21.4508i −0.358014 1.10185i −0.954241 0.299038i \(-0.903334\pi\)
0.596227 0.802816i \(-0.296666\pi\)
\(380\) 0 0
\(381\) −0.822516 + 2.53145i −0.0421388 + 0.129690i
\(382\) 0 0
\(383\) −4.13113 1.34229i −0.211091 0.0685877i 0.201563 0.979476i \(-0.435398\pi\)
−0.412654 + 0.910888i \(0.635398\pi\)
\(384\) 0 0
\(385\) −1.25910 + 4.29032i −0.0641699 + 0.218655i
\(386\) 0 0
\(387\) 4.46631 + 6.14735i 0.227035 + 0.312487i
\(388\) 0 0
\(389\) −15.0039 10.9010i −0.760729 0.552702i 0.138405 0.990376i \(-0.455802\pi\)
−0.899134 + 0.437674i \(0.855802\pi\)
\(390\) 0 0
\(391\) 26.6805 19.3845i 1.34929 0.980317i
\(392\) 0 0
\(393\) 9.71046i 0.489828i
\(394\) 0 0
\(395\) −14.4317 18.7099i −0.726135 0.941398i
\(396\) 0 0
\(397\) 0.672391 0.218473i 0.0337463 0.0109648i −0.292095 0.956389i \(-0.594352\pi\)
0.325842 + 0.945424i \(0.394352\pi\)
\(398\) 0 0
\(399\) 3.68787 0.184624
\(400\) 0 0
\(401\) −24.8304 −1.23997 −0.619986 0.784613i \(-0.712862\pi\)
−0.619986 + 0.784613i \(0.712862\pi\)
\(402\) 0 0
\(403\) −20.3591 + 6.61507i −1.01416 + 0.329520i
\(404\) 0 0
\(405\) 0.0641640 + 2.23515i 0.00318833 + 0.111065i
\(406\) 0 0
\(407\) 4.36453i 0.216341i
\(408\) 0 0
\(409\) −0.590588 + 0.429087i −0.0292027 + 0.0212170i −0.602291 0.798277i \(-0.705745\pi\)
0.573088 + 0.819494i \(0.305745\pi\)
\(410\) 0 0
\(411\) 3.10819 + 2.25823i 0.153316 + 0.111390i
\(412\) 0 0
\(413\) −0.780643 1.07446i −0.0384130 0.0528709i
\(414\) 0 0
\(415\) 9.34650 0.268308i 0.458802 0.0131707i
\(416\) 0 0
\(417\) 4.68647 + 1.52273i 0.229498 + 0.0745683i
\(418\) 0 0
\(419\) 3.98923 12.2776i 0.194887 0.599799i −0.805091 0.593151i \(-0.797884\pi\)
0.999978 0.00664830i \(-0.00211623\pi\)
\(420\) 0 0
\(421\) 11.7828 + 36.2639i 0.574261 + 1.76739i 0.638683 + 0.769470i \(0.279480\pi\)
−0.0644219 + 0.997923i \(0.520520\pi\)
\(422\) 0 0
\(423\) −2.58737 + 3.56121i −0.125802 + 0.173152i
\(424\) 0 0
\(425\) −34.8476 + 13.5786i −1.69036 + 0.658658i
\(426\) 0 0
\(427\) 4.41666 6.07902i 0.213737 0.294184i
\(428\) 0 0
\(429\) −4.94523 15.2199i −0.238758 0.734822i
\(430\) 0 0
\(431\) −11.1829 + 34.4175i −0.538663 + 1.65783i 0.196936 + 0.980416i \(0.436901\pi\)
−0.735599 + 0.677418i \(0.763099\pi\)
\(432\) 0 0
\(433\) 20.6842 + 6.72071i 0.994021 + 0.322977i 0.760474 0.649369i \(-0.224967\pi\)
0.233547 + 0.972346i \(0.424967\pi\)
\(434\) 0 0
\(435\) 5.09581 + 3.48339i 0.244325 + 0.167016i
\(436\) 0 0
\(437\) −16.0383 22.0748i −0.767217 1.05598i
\(438\) 0 0
\(439\) −31.8418 23.1344i −1.51973 1.10415i −0.961623 0.274374i \(-0.911529\pi\)
−0.558103 0.829772i \(-0.688471\pi\)
\(440\) 0 0
\(441\) 5.37584 3.90578i 0.255992 0.185989i
\(442\) 0 0
\(443\) 27.4919i 1.30618i 0.757281 + 0.653089i \(0.226527\pi\)
−0.757281 + 0.653089i \(0.773473\pi\)
\(444\) 0 0
\(445\) −9.11949 2.67635i −0.432305 0.126871i
\(446\) 0 0
\(447\) −6.26784 + 2.03655i −0.296459 + 0.0963253i
\(448\) 0 0
\(449\) −3.51087 −0.165688 −0.0828441 0.996563i \(-0.526400\pi\)
−0.0828441 + 0.996563i \(0.526400\pi\)
\(450\) 0 0
\(451\) −31.5721 −1.48667
\(452\) 0 0
\(453\) 18.5868 6.03923i 0.873285 0.283748i
\(454\) 0 0
\(455\) −3.58611 + 5.24609i −0.168120 + 0.245940i
\(456\) 0 0
\(457\) 10.1677i 0.475624i −0.971311 0.237812i \(-0.923570\pi\)
0.971311 0.237812i \(-0.0764302\pi\)
\(458\) 0 0
\(459\) 6.05139 4.39659i 0.282455 0.205215i
\(460\) 0 0
\(461\) −0.755758 0.549090i −0.0351992 0.0255737i 0.570047 0.821612i \(-0.306925\pi\)
−0.605246 + 0.796039i \(0.706925\pi\)
\(462\) 0 0
\(463\) 2.87183 + 3.95274i 0.133465 + 0.183699i 0.870519 0.492135i \(-0.163783\pi\)
−0.737053 + 0.675835i \(0.763783\pi\)
\(464\) 0 0
\(465\) −3.37424 9.45282i −0.156477 0.438364i
\(466\) 0 0
\(467\) −24.5416 7.97406i −1.13565 0.368996i −0.319931 0.947441i \(-0.603660\pi\)
−0.815721 + 0.578445i \(0.803660\pi\)
\(468\) 0 0
\(469\) −1.53914 + 4.73699i −0.0710710 + 0.218734i
\(470\) 0 0
\(471\) 0.105682 + 0.325257i 0.00486958 + 0.0149870i
\(472\) 0 0
\(473\) 14.9872 20.6281i 0.689111 0.948480i
\(474\) 0 0
\(475\) 11.2346 + 28.8321i 0.515479 + 1.32291i
\(476\) 0 0
\(477\) −4.82413 + 6.63985i −0.220882 + 0.304018i
\(478\) 0 0
\(479\) 5.22721 + 16.0877i 0.238837 + 0.735065i 0.996589 + 0.0825225i \(0.0262976\pi\)
−0.757752 + 0.652543i \(0.773702\pi\)
\(480\) 0 0
\(481\) −1.91682 + 5.89936i −0.0873994 + 0.268988i
\(482\) 0 0
\(483\) 2.49873 + 0.811885i 0.113696 + 0.0369421i
\(484\) 0 0
\(485\) 21.7340 16.7642i 0.986890 0.761225i
\(486\) 0 0
\(487\) −9.63237 13.2578i −0.436484 0.600769i 0.532942 0.846152i \(-0.321086\pi\)
−0.969426 + 0.245383i \(0.921086\pi\)
\(488\) 0 0
\(489\) 18.2161 + 13.2347i 0.823759 + 0.598496i
\(490\) 0 0
\(491\) 8.30972 6.03737i 0.375013 0.272463i −0.384274 0.923219i \(-0.625548\pi\)
0.759286 + 0.650757i \(0.225548\pi\)
\(492\) 0 0
\(493\) 20.6482i 0.929948i
\(494\) 0 0
\(495\) 7.06666 2.52249i 0.317623 0.113377i
\(496\) 0 0
\(497\) −3.85113 + 1.25131i −0.172747 + 0.0561289i
\(498\) 0 0
\(499\) 16.5015 0.738707 0.369354 0.929289i \(-0.379579\pi\)
0.369354 + 0.929289i \(0.379579\pi\)
\(500\) 0 0
\(501\) −4.31493 −0.192777
\(502\) 0 0
\(503\) −7.22834 + 2.34863i −0.322296 + 0.104720i −0.465697 0.884944i \(-0.654196\pi\)
0.143401 + 0.989665i \(0.454196\pi\)
\(504\) 0 0
\(505\) 16.8650 6.02005i 0.750481 0.267889i
\(506\) 0 0
\(507\) 9.74397i 0.432745i
\(508\) 0 0
\(509\) −17.7590 + 12.9027i −0.787154 + 0.571901i −0.907118 0.420877i \(-0.861722\pi\)
0.119963 + 0.992778i \(0.461722\pi\)
\(510\) 0 0
\(511\) 3.52517 + 2.56119i 0.155944 + 0.113300i
\(512\) 0 0
\(513\) −3.63764 5.00679i −0.160606 0.221055i
\(514\) 0 0
\(515\) 9.95976 7.68233i 0.438879 0.338524i
\(516\) 0 0
\(517\) 14.0481 + 4.56450i 0.617834 + 0.200746i
\(518\) 0 0
\(519\) −5.30544 + 16.3285i −0.232883 + 0.716741i
\(520\) 0 0
\(521\) −11.3835 35.0349i −0.498722 1.53491i −0.811075 0.584942i \(-0.801117\pi\)
0.312353 0.949966i \(-0.398883\pi\)
\(522\) 0 0
\(523\) −24.4517 + 33.6548i −1.06920 + 1.47162i −0.198310 + 0.980139i \(0.563545\pi\)
−0.870887 + 0.491484i \(0.836455\pi\)
\(524\) 0 0
\(525\) −2.50696 1.61014i −0.109413 0.0702724i
\(526\) 0 0
\(527\) −19.7349 + 27.1628i −0.859667 + 1.18323i
\(528\) 0 0
\(529\) 1.10036 + 3.38657i 0.0478419 + 0.147242i
\(530\) 0 0
\(531\) −0.688720 + 2.11966i −0.0298879 + 0.0919855i
\(532\) 0 0
\(533\) −42.6748 13.8659i −1.84845 0.600598i
\(534\) 0 0
\(535\) 10.3513 + 28.9987i 0.447524 + 1.25372i
\(536\) 0 0
\(537\) 0.625167 + 0.860469i 0.0269779 + 0.0371320i
\(538\) 0 0
\(539\) −18.0392 13.1063i −0.777004 0.564526i
\(540\) 0 0
\(541\) 12.5570 9.12319i 0.539867 0.392237i −0.284168 0.958774i \(-0.591717\pi\)
0.824036 + 0.566538i \(0.191717\pi\)
\(542\) 0 0
\(543\) 12.0267i 0.516114i
\(544\) 0 0
\(545\) 16.1538 23.6313i 0.691954 1.01225i
\(546\) 0 0
\(547\) 22.1633 7.20130i 0.947636 0.307906i 0.205881 0.978577i \(-0.433994\pi\)
0.741755 + 0.670671i \(0.233994\pi\)
\(548\) 0 0
\(549\) −12.6096 −0.538165
\(550\) 0 0
\(551\) −17.0839 −0.727797
\(552\) 0 0
\(553\) −5.98883 + 1.94589i −0.254671 + 0.0827476i
\(554\) 0 0
\(555\) −2.79068 0.818996i −0.118458 0.0347645i
\(556\) 0 0
\(557\) 11.0914i 0.469959i 0.972000 + 0.234979i \(0.0755023\pi\)
−0.972000 + 0.234979i \(0.924498\pi\)
\(558\) 0 0
\(559\) 29.3171 21.3001i 1.23998 0.900898i
\(560\) 0 0
\(561\) −20.3061 14.7533i −0.857325 0.622883i
\(562\) 0 0
\(563\) 8.40836 + 11.5731i 0.354370 + 0.487749i 0.948569 0.316569i \(-0.102531\pi\)
−0.594199 + 0.804318i \(0.702531\pi\)
\(564\) 0 0
\(565\) −21.4862 14.6875i −0.903930 0.617907i
\(566\) 0 0
\(567\) 0.566735 + 0.184143i 0.0238006 + 0.00773330i
\(568\) 0 0
\(569\) 8.89176 27.3660i 0.372762 1.14724i −0.572214 0.820104i \(-0.693915\pi\)
0.944976 0.327139i \(-0.106085\pi\)
\(570\) 0 0
\(571\) −4.02941 12.4012i −0.168625 0.518976i 0.830660 0.556780i \(-0.187963\pi\)
−0.999285 + 0.0378048i \(0.987963\pi\)
\(572\) 0 0
\(573\) −12.9134 + 17.7737i −0.539464 + 0.742508i
\(574\) 0 0
\(575\) 1.26464 + 22.0086i 0.0527390 + 0.917823i
\(576\) 0 0
\(577\) 1.05786 1.45601i 0.0440391 0.0606147i −0.786430 0.617680i \(-0.788073\pi\)
0.830469 + 0.557065i \(0.188073\pi\)
\(578\) 0 0
\(579\) 6.30401 + 19.4018i 0.261986 + 0.806309i
\(580\) 0 0
\(581\) 0.770015 2.36986i 0.0319456 0.0983184i
\(582\) 0 0
\(583\) 26.1926 + 8.51049i 1.08479 + 0.352468i
\(584\) 0 0
\(585\) 10.6596 0.306002i 0.440719 0.0126516i
\(586\) 0 0
\(587\) 23.8620 + 32.8432i 0.984889 + 1.35558i 0.934153 + 0.356872i \(0.116157\pi\)
0.0507360 + 0.998712i \(0.483843\pi\)
\(588\) 0 0
\(589\) 22.4739 + 16.3282i 0.926020 + 0.672793i
\(590\) 0 0
\(591\) 3.32102 2.41286i 0.136609 0.0992519i
\(592\) 0 0
\(593\) 29.4991i 1.21138i 0.795700 + 0.605690i \(0.207103\pi\)
−0.795700 + 0.605690i \(0.792897\pi\)
\(594\) 0 0
\(595\) 0.285998 + 9.96271i 0.0117248 + 0.408431i
\(596\) 0 0
\(597\) 24.3413 7.90898i 0.996225 0.323693i
\(598\) 0 0
\(599\) 8.91418 0.364224 0.182112 0.983278i \(-0.441707\pi\)
0.182112 + 0.983278i \(0.441707\pi\)
\(600\) 0 0
\(601\) 16.6757 0.680217 0.340109 0.940386i \(-0.389536\pi\)
0.340109 + 0.940386i \(0.389536\pi\)
\(602\) 0 0
\(603\) 7.94930 2.58288i 0.323720 0.105183i
\(604\) 0 0
\(605\) −0.355235 0.460545i −0.0144424 0.0187238i
\(606\) 0 0
\(607\) 26.9626i 1.09438i −0.837008 0.547190i \(-0.815698\pi\)
0.837008 0.547190i \(-0.184302\pi\)
\(608\) 0 0
\(609\) 1.33081 0.966890i 0.0539271 0.0391804i
\(610\) 0 0
\(611\) 16.9836 + 12.3393i 0.687083 + 0.499195i
\(612\) 0 0
\(613\) −9.71195 13.3673i −0.392262 0.539902i 0.566519 0.824049i \(-0.308290\pi\)
−0.958781 + 0.284147i \(0.908290\pi\)
\(614\) 0 0
\(615\) 5.92445 20.1872i 0.238897 0.814027i
\(616\) 0 0
\(617\) −21.8628 7.10364i −0.880161 0.285982i −0.166137 0.986103i \(-0.553129\pi\)
−0.714024 + 0.700121i \(0.753129\pi\)
\(618\) 0 0
\(619\) −15.2396 + 46.9028i −0.612533 + 1.88518i −0.179658 + 0.983729i \(0.557499\pi\)
−0.432875 + 0.901454i \(0.642501\pi\)
\(620\) 0 0
\(621\) −1.36245 4.19319i −0.0546733 0.168267i
\(622\) 0 0
\(623\) −1.48874 + 2.04907i −0.0596451 + 0.0820944i
\(624\) 0 0
\(625\) 4.95114 24.5048i 0.198045 0.980193i
\(626\) 0 0
\(627\) −12.2065 + 16.8008i −0.487481 + 0.670960i
\(628\) 0 0
\(629\) 3.00639 + 9.25273i 0.119873 + 0.368930i
\(630\) 0 0
\(631\) 7.47148 22.9948i 0.297435 0.915410i −0.684958 0.728583i \(-0.740179\pi\)
0.982393 0.186828i \(-0.0598206\pi\)
\(632\) 0 0
\(633\) 18.5535 + 6.02841i 0.737437 + 0.239608i
\(634\) 0 0
\(635\) −1.67602 + 5.71093i −0.0665107 + 0.226631i
\(636\) 0 0
\(637\) −18.6269 25.6377i −0.738024 1.01580i
\(638\) 0 0
\(639\) 5.49751 + 3.99418i 0.217478 + 0.158007i
\(640\) 0 0
\(641\) 39.9382 29.0168i 1.57746 1.14610i 0.657935 0.753075i \(-0.271430\pi\)
0.919530 0.393020i \(-0.128570\pi\)
\(642\) 0 0
\(643\) 3.97743i 0.156854i 0.996920 + 0.0784272i \(0.0249898\pi\)
−0.996920 + 0.0784272i \(0.975010\pi\)
\(644\) 0 0
\(645\) 10.3773 + 13.4536i 0.408606 + 0.529737i
\(646\) 0 0
\(647\) 0.964765 0.313471i 0.0379288 0.0123238i −0.289991 0.957029i \(-0.593652\pi\)
0.327920 + 0.944706i \(0.393652\pi\)
\(648\) 0 0
\(649\) 7.47879 0.293568
\(650\) 0 0
\(651\) −2.67481 −0.104834
\(652\) 0 0
\(653\) 7.77161 2.52515i 0.304127 0.0988167i −0.152978 0.988230i \(-0.548886\pi\)
0.457105 + 0.889413i \(0.348886\pi\)
\(654\) 0 0
\(655\) 0.623062 + 21.7043i 0.0243450 + 0.848057i
\(656\) 0 0
\(657\) 7.31221i 0.285277i
\(658\) 0 0
\(659\) 6.22020 4.51924i 0.242305 0.176045i −0.460005 0.887916i \(-0.652152\pi\)
0.702309 + 0.711872i \(0.252152\pi\)
\(660\) 0 0
\(661\) 29.2864 + 21.2778i 1.13911 + 0.827611i 0.986995 0.160752i \(-0.0513919\pi\)
0.152114 + 0.988363i \(0.451392\pi\)
\(662\) 0 0
\(663\) −20.9676 28.8595i −0.814316 1.12081i
\(664\) 0 0
\(665\) 8.24292 0.236628i 0.319647 0.00917605i
\(666\) 0 0
\(667\) −11.5752 3.76102i −0.448195 0.145627i
\(668\) 0 0
\(669\) −0.688574 + 2.11921i −0.0266218 + 0.0819335i
\(670\) 0 0
\(671\) 13.0754 + 40.2420i 0.504771 + 1.55353i
\(672\) 0 0
\(673\) −17.7405 + 24.4177i −0.683845 + 0.941233i −0.999972 0.00748451i \(-0.997618\pi\)
0.316127 + 0.948717i \(0.397618\pi\)
\(674\) 0 0
\(675\) 0.286832 + 4.99177i 0.0110402 + 0.192133i
\(676\) 0 0
\(677\) 27.6349 38.0362i 1.06210 1.46185i 0.184268 0.982876i \(-0.441009\pi\)
0.877829 0.478975i \(-0.158991\pi\)
\(678\) 0 0
\(679\) −2.26040 6.95680i −0.0867463 0.266978i
\(680\) 0 0
\(681\) 1.40540 4.32537i 0.0538549 0.165748i
\(682\) 0 0
\(683\) 2.08476 + 0.677379i 0.0797710 + 0.0259192i 0.348631 0.937260i \(-0.386647\pi\)
−0.268860 + 0.963179i \(0.586647\pi\)
\(684\) 0 0
\(685\) 7.09217 + 4.84805i 0.270978 + 0.185235i
\(686\) 0 0
\(687\) 2.00735 + 2.76288i 0.0765852 + 0.105411i
\(688\) 0 0
\(689\) 31.6659 + 23.0066i 1.20637 + 0.876482i
\(690\) 0 0
\(691\) −1.44427 + 1.04932i −0.0549425 + 0.0399181i −0.614918 0.788591i \(-0.710811\pi\)
0.559975 + 0.828509i \(0.310811\pi\)
\(692\) 0 0
\(693\) 1.99961i 0.0759589i
\(694\) 0 0
\(695\) 10.5727 + 3.10282i 0.401044 + 0.117697i
\(696\) 0 0
\(697\) −66.9323 + 21.7476i −2.53524 + 0.823750i
\(698\) 0 0
\(699\) −16.7395 −0.633146
\(700\) 0 0
\(701\) −11.0728 −0.418215 −0.209107 0.977893i \(-0.567056\pi\)
−0.209107 + 0.977893i \(0.567056\pi\)
\(702\) 0 0
\(703\) 7.65550 2.48742i 0.288733 0.0938149i
\(704\) 0 0
\(705\) −5.55464 + 8.12583i −0.209200 + 0.306037i
\(706\) 0 0
\(707\) 4.77218i 0.179476i
\(708\) 0 0
\(709\) 16.1099 11.7045i 0.605020 0.439573i −0.242637 0.970117i \(-0.578012\pi\)
0.847657 + 0.530544i \(0.178012\pi\)
\(710\) 0 0
\(711\) 8.54908 + 6.21127i 0.320616 + 0.232941i
\(712\) 0 0
\(713\) 11.6326 + 16.0109i 0.435644 + 0.599612i
\(714\) 0 0
\(715\) −12.0299 33.7013i −0.449892 1.26036i
\(716\) 0 0
\(717\) 21.2697 + 6.91095i 0.794332 + 0.258094i
\(718\) 0 0
\(719\) −10.7477 + 33.0782i −0.400823 + 1.23361i 0.523509 + 0.852020i \(0.324623\pi\)
−0.924333 + 0.381587i \(0.875377\pi\)
\(720\) 0 0
\(721\) −1.03585 3.18801i −0.0385769 0.118728i
\(722\) 0 0
\(723\) 0.155973 0.214678i 0.00580068 0.00798395i
\(724\) 0 0
\(725\) 11.6134 + 7.45891i 0.431311 + 0.277017i
\(726\) 0 0
\(727\) −9.38558 + 12.9181i −0.348092 + 0.479107i −0.946783 0.321873i \(-0.895688\pi\)
0.598691 + 0.800980i \(0.295688\pi\)
\(728\) 0 0
\(729\) −0.309017 0.951057i −0.0114451 0.0352243i
\(730\) 0 0
\(731\) 17.5635 54.0548i 0.649608 1.99929i
\(732\) 0 0
\(733\) 9.64606 + 3.13420i 0.356286 + 0.115764i 0.481690 0.876341i \(-0.340023\pi\)
−0.125405 + 0.992106i \(0.540023\pi\)
\(734\) 0 0
\(735\) 11.7652 9.07492i 0.433965 0.334733i
\(736\) 0 0
\(737\) −16.4859 22.6909i −0.607266 0.835830i
\(738\) 0 0
\(739\) 2.65234 + 1.92704i 0.0975681 + 0.0708873i 0.635500 0.772101i \(-0.280794\pi\)
−0.537932 + 0.842988i \(0.680794\pi\)
\(740\) 0 0
\(741\) −23.8777 + 17.3482i −0.877169 + 0.637300i
\(742\) 0 0
\(743\) 38.7278i 1.42078i −0.703806 0.710392i \(-0.748518\pi\)
0.703806 0.710392i \(-0.251482\pi\)
\(744\) 0 0
\(745\) −13.8789 + 4.95415i −0.508483 + 0.181506i
\(746\) 0 0
\(747\) −3.97694 + 1.29219i −0.145509 + 0.0472786i
\(748\) 0 0
\(749\) 8.20559 0.299826
\(750\) 0 0
\(751\) 13.0211 0.475146 0.237573 0.971370i \(-0.423648\pi\)
0.237573 + 0.971370i \(0.423648\pi\)
\(752\) 0 0
\(753\) −27.6466 + 8.98294i −1.00750 + 0.327357i
\(754\) 0 0
\(755\) 41.1568 14.6912i 1.49785 0.534666i
\(756\) 0 0
\(757\) 33.4057i 1.21415i 0.794645 + 0.607075i \(0.207657\pi\)
−0.794645 + 0.607075i \(0.792343\pi\)
\(758\) 0 0
\(759\) −11.9693 + 8.69618i −0.434457 + 0.315651i
\(760\) 0 0
\(761\) −24.0536 17.4760i −0.871943 0.633504i 0.0591647 0.998248i \(-0.481156\pi\)
−0.931108 + 0.364745i \(0.881156\pi\)
\(762\) 0 0
\(763\) −4.48385 6.17149i −0.162326 0.223423i
\(764\) 0 0
\(765\) 13.2437 10.2153i 0.478825 0.369336i
\(766\) 0 0
\(767\) 10.1088 + 3.28455i 0.365008 + 0.118598i
\(768\) 0 0
\(769\) 1.68546 5.18732i 0.0607794 0.187060i −0.916057 0.401049i \(-0.868646\pi\)
0.976836 + 0.213989i \(0.0686458\pi\)
\(770\) 0 0
\(771\) −2.18151 6.71400i −0.0785652 0.241799i
\(772\) 0 0
\(773\) 17.0953 23.5297i 0.614875 0.846303i −0.382092 0.924124i \(-0.624796\pi\)
0.996967 + 0.0778211i \(0.0247963\pi\)
\(774\) 0 0
\(775\) −8.14846 20.9119i −0.292701 0.751179i
\(776\) 0 0
\(777\) −0.455573 + 0.627043i −0.0163436 + 0.0224950i
\(778\) 0 0
\(779\) 17.9935 + 55.3783i 0.644684 + 1.98413i
\(780\) 0 0
\(781\) 7.04632 21.6863i 0.252137 0.775998i
\(782\) 0 0
\(783\) −2.62537 0.853035i −0.0938232 0.0304850i
\(784\) 0 0
\(785\) 0.257085 + 0.720216i 0.00917577 + 0.0257056i
\(786\) 0 0
\(787\) −20.0518 27.5989i −0.714768 0.983794i −0.999681 0.0252406i \(-0.991965\pi\)
0.284913 0.958553i \(-0.408035\pi\)
\(788\) 0 0
\(789\) 1.12170 + 0.814961i 0.0399335 + 0.0290134i
\(790\) 0 0
\(791\) −5.61128 + 4.07683i −0.199514 + 0.144955i
\(792\) 0 0
\(793\) 60.1361i 2.13549i
\(794\) 0 0
\(795\) −10.3566 + 15.1506i −0.367311 + 0.537336i
\(796\) 0 0
\(797\) 23.2590 7.55732i 0.823877 0.267694i 0.133413 0.991061i