Properties

Label 300.2.o.a.169.6
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 169.6
Character \(\chi\) \(=\) 300.169
Dual form 300.2.o.a.229.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.587785 + 0.809017i) q^{3} +(1.28878 + 1.82730i) q^{5} +2.44380i q^{7} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(0.587785 + 0.809017i) q^{3} +(1.28878 + 1.82730i) q^{5} +2.44380i q^{7} +(-0.309017 + 0.951057i) q^{9} +(-0.178298 - 0.548744i) q^{11} +(-6.13093 - 1.99206i) q^{13} +(-0.720790 + 2.11671i) q^{15} +(1.11545 - 1.53529i) q^{17} +(6.69438 + 4.86375i) q^{19} +(-1.97708 + 1.43643i) q^{21} +(4.00298 - 1.30065i) q^{23} +(-1.67807 + 4.71000i) q^{25} +(-0.951057 + 0.309017i) q^{27} +(5.28988 - 3.84332i) q^{29} +(-3.93738 - 2.86068i) q^{31} +(0.339142 - 0.466789i) q^{33} +(-4.46557 + 3.14954i) q^{35} +(-0.207335 - 0.0673673i) q^{37} +(-1.99206 - 6.13093i) q^{39} +(1.99456 - 6.13862i) q^{41} +3.42419i q^{43} +(-2.13612 + 0.661040i) q^{45} +(5.65351 + 7.78140i) q^{47} +1.02783 q^{49} +1.89772 q^{51} +(-8.22441 - 11.3199i) q^{53} +(0.772933 - 1.03302i) q^{55} +8.27470i q^{57} +(3.72459 - 11.4631i) q^{59} +(-1.48657 - 4.57520i) q^{61} +(-2.32419 - 0.755176i) q^{63} +(-4.26136 - 13.7704i) q^{65} +(2.27528 - 3.13165i) q^{67} +(3.40513 + 2.47398i) q^{69} +(5.24443 - 3.81030i) q^{71} +(-9.55897 + 3.10590i) q^{73} +(-4.79681 + 1.41088i) q^{75} +(1.34102 - 0.435724i) q^{77} +(-3.83854 + 2.78887i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-2.01856 + 2.77831i) q^{83} +(4.24301 + 0.0596122i) q^{85} +(6.21862 + 2.02055i) q^{87} +(1.75719 + 5.40807i) q^{89} +(4.86820 - 14.9828i) q^{91} -4.86687i q^{93} +(-0.259929 + 18.5010i) q^{95} +(-3.87042 - 5.32717i) q^{97} +0.576983 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 2q^{5} + 6q^{9} + O(q^{10}) \) \( 24q - 2q^{5} + 6q^{9} - 6q^{11} + 4q^{15} + 10q^{17} + 10q^{19} - 4q^{21} + 40q^{23} - 4q^{25} + 4q^{29} + 6q^{31} + 10q^{33} - 6q^{35} - 10q^{41} + 2q^{45} - 40q^{47} - 56q^{49} + 16q^{51} - 60q^{53} - 62q^{55} - 36q^{59} - 12q^{61} - 10q^{63} + 20q^{67} + 4q^{69} + 40q^{71} + 60q^{73} + 8q^{75} - 40q^{77} + 8q^{79} - 6q^{81} - 50q^{83} + 34q^{85} - 20q^{87} - 30q^{91} - 60q^{95} - 40q^{97} - 4q^{99} + O(q^{100}) \)

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
\(5\) 1.28878 + 1.82730i 0.576362 + 0.817194i
\(6\) 0 0
\(7\) 2.44380i 0.923670i 0.886966 + 0.461835i \(0.152809\pi\)
−0.886966 + 0.461835i \(0.847191\pi\)
\(8\) 0 0
\(9\) −0.309017 + 0.951057i −0.103006 + 0.317019i
\(10\) 0 0
\(11\) −0.178298 0.548744i −0.0537588 0.165452i 0.920572 0.390572i \(-0.127723\pi\)
−0.974331 + 0.225120i \(0.927723\pi\)
\(12\) 0 0
\(13\) −6.13093 1.99206i −1.70042 0.552498i −0.711723 0.702460i \(-0.752085\pi\)
−0.988692 + 0.149962i \(0.952085\pi\)
\(14\) 0 0
\(15\) −0.720790 + 2.11671i −0.186107 + 0.546532i
\(16\) 0 0
\(17\) 1.11545 1.53529i 0.270537 0.372362i −0.652034 0.758190i \(-0.726084\pi\)
0.922571 + 0.385828i \(0.126084\pi\)
\(18\) 0 0
\(19\) 6.69438 + 4.86375i 1.53580 + 1.11582i 0.952905 + 0.303269i \(0.0980782\pi\)
0.582890 + 0.812551i \(0.301922\pi\)
\(20\) 0 0
\(21\) −1.97708 + 1.43643i −0.431434 + 0.313455i
\(22\) 0 0
\(23\) 4.00298 1.30065i 0.834678 0.271203i 0.139664 0.990199i \(-0.455398\pi\)
0.695015 + 0.718996i \(0.255398\pi\)
\(24\) 0 0
\(25\) −1.67807 + 4.71000i −0.335613 + 0.942000i
\(26\) 0 0
\(27\) −0.951057 + 0.309017i −0.183031 + 0.0594703i
\(28\) 0 0
\(29\) 5.28988 3.84332i 0.982306 0.713687i 0.0240828 0.999710i \(-0.492333\pi\)
0.958223 + 0.286023i \(0.0923335\pi\)
\(30\) 0 0
\(31\) −3.93738 2.86068i −0.707175 0.513793i 0.175086 0.984553i \(-0.443980\pi\)
−0.882261 + 0.470760i \(0.843980\pi\)
\(32\) 0 0
\(33\) 0.339142 0.466789i 0.0590371 0.0812576i
\(34\) 0 0
\(35\) −4.46557 + 3.14954i −0.754818 + 0.532369i
\(36\) 0 0
\(37\) −0.207335 0.0673673i −0.0340857 0.0110751i 0.291925 0.956441i \(-0.405704\pi\)
−0.326010 + 0.945366i \(0.605704\pi\)
\(38\) 0 0
\(39\) −1.99206 6.13093i −0.318985 0.981735i
\(40\) 0 0
\(41\) 1.99456 6.13862i 0.311498 0.958691i −0.665675 0.746242i \(-0.731856\pi\)
0.977172 0.212449i \(-0.0681439\pi\)
\(42\) 0 0
\(43\) 3.42419i 0.522184i 0.965314 + 0.261092i \(0.0840825\pi\)
−0.965314 + 0.261092i \(0.915917\pi\)
\(44\) 0 0
\(45\) −2.13612 + 0.661040i −0.318435 + 0.0985420i
\(46\) 0 0
\(47\) 5.65351 + 7.78140i 0.824650 + 1.13503i 0.988895 + 0.148614i \(0.0474811\pi\)
−0.164245 + 0.986419i \(0.552519\pi\)
\(48\) 0 0
\(49\) 1.02783 0.146833
\(50\) 0 0
\(51\) 1.89772 0.265734
\(52\) 0 0
\(53\) −8.22441 11.3199i −1.12971 1.55491i −0.788620 0.614881i \(-0.789204\pi\)
−0.341090 0.940031i \(-0.610796\pi\)
\(54\) 0 0
\(55\) 0.772933 1.03302i 0.104222 0.139292i
\(56\) 0 0
\(57\) 8.27470i 1.09601i
\(58\) 0 0
\(59\) 3.72459 11.4631i 0.484901 1.49237i −0.347224 0.937782i \(-0.612876\pi\)
0.832125 0.554589i \(-0.187124\pi\)
\(60\) 0 0
\(61\) −1.48657 4.57520i −0.190336 0.585795i 0.809663 0.586895i \(-0.199650\pi\)
−0.999999 + 0.00110016i \(0.999650\pi\)
\(62\) 0 0
\(63\) −2.32419 0.755176i −0.292821 0.0951433i
\(64\) 0 0
\(65\) −4.26136 13.7704i −0.528556 1.70801i
\(66\) 0 0
\(67\) 2.27528 3.13165i 0.277970 0.382592i −0.647090 0.762413i \(-0.724014\pi\)
0.925060 + 0.379821i \(0.124014\pi\)
\(68\) 0 0
\(69\) 3.40513 + 2.47398i 0.409930 + 0.297832i
\(70\) 0 0
\(71\) 5.24443 3.81030i 0.622399 0.452200i −0.231359 0.972868i \(-0.574317\pi\)
0.853759 + 0.520669i \(0.174317\pi\)
\(72\) 0 0
\(73\) −9.55897 + 3.10590i −1.11879 + 0.363518i −0.809307 0.587386i \(-0.800157\pi\)
−0.309486 + 0.950904i \(0.600157\pi\)
\(74\) 0 0
\(75\) −4.79681 + 1.41088i −0.553888 + 0.162915i
\(76\) 0 0
\(77\) 1.34102 0.435724i 0.152824 0.0496554i
\(78\) 0 0
\(79\) −3.83854 + 2.78887i −0.431870 + 0.313772i −0.782396 0.622781i \(-0.786003\pi\)
0.350526 + 0.936553i \(0.386003\pi\)
\(80\) 0 0
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) 0 0
\(83\) −2.01856 + 2.77831i −0.221566 + 0.304959i −0.905301 0.424772i \(-0.860354\pi\)
0.683735 + 0.729730i \(0.260354\pi\)
\(84\) 0 0
\(85\) 4.24301 + 0.0596122i 0.460220 + 0.00646585i
\(86\) 0 0
\(87\) 6.21862 + 2.02055i 0.666706 + 0.216626i
\(88\) 0 0
\(89\) 1.75719 + 5.40807i 0.186262 + 0.573254i 0.999968 0.00802201i \(-0.00255351\pi\)
−0.813706 + 0.581276i \(0.802554\pi\)
\(90\) 0 0
\(91\) 4.86820 14.9828i 0.510326 1.57062i
\(92\) 0 0
\(93\) 4.86687i 0.504671i
\(94\) 0 0
\(95\) −0.259929 + 18.5010i −0.0266682 + 1.89816i
\(96\) 0 0
\(97\) −3.87042 5.32717i −0.392982 0.540893i 0.565984 0.824416i \(-0.308497\pi\)
−0.958965 + 0.283524i \(0.908497\pi\)
\(98\) 0 0
\(99\) 0.576983 0.0579890
\(100\) 0 0
\(101\) −12.0363 −1.19766 −0.598828 0.800877i \(-0.704367\pi\)
−0.598828 + 0.800877i \(0.704367\pi\)
\(102\) 0 0
\(103\) −3.40107 4.68117i −0.335117 0.461249i 0.607890 0.794021i \(-0.292016\pi\)
−0.943007 + 0.332772i \(0.892016\pi\)
\(104\) 0 0
\(105\) −5.17282 1.76147i −0.504816 0.171902i
\(106\) 0 0
\(107\) 4.07081i 0.393540i 0.980450 + 0.196770i \(0.0630453\pi\)
−0.980450 + 0.196770i \(0.936955\pi\)
\(108\) 0 0
\(109\) 0.450471 1.38641i 0.0431473 0.132794i −0.927162 0.374660i \(-0.877759\pi\)
0.970310 + 0.241866i \(0.0777595\pi\)
\(110\) 0 0
\(111\) −0.0673673 0.207335i −0.00639422 0.0196794i
\(112\) 0 0
\(113\) 5.57114 + 1.81017i 0.524089 + 0.170287i 0.559100 0.829100i \(-0.311147\pi\)
−0.0350111 + 0.999387i \(0.511147\pi\)
\(114\) 0 0
\(115\) 7.53565 + 5.63839i 0.702703 + 0.525783i
\(116\) 0 0
\(117\) 3.78913 5.21528i 0.350305 0.482153i
\(118\) 0 0
\(119\) 3.75194 + 2.72595i 0.343940 + 0.249887i
\(120\) 0 0
\(121\) 8.62986 6.26996i 0.784532 0.569996i
\(122\) 0 0
\(123\) 6.13862 1.99456i 0.553500 0.179843i
\(124\) 0 0
\(125\) −10.7693 + 3.00384i −0.963232 + 0.268672i
\(126\) 0 0
\(127\) −14.5373 + 4.72346i −1.28998 + 0.419139i −0.872084 0.489357i \(-0.837232\pi\)
−0.417894 + 0.908496i \(0.637232\pi\)
\(128\) 0 0
\(129\) −2.77023 + 2.01269i −0.243905 + 0.177207i
\(130\) 0 0
\(131\) 3.03698 + 2.20650i 0.265343 + 0.192783i 0.712499 0.701673i \(-0.247563\pi\)
−0.447156 + 0.894456i \(0.647563\pi\)
\(132\) 0 0
\(133\) −11.8860 + 16.3597i −1.03065 + 1.41857i
\(134\) 0 0
\(135\) −1.79037 1.33961i −0.154091 0.115295i
\(136\) 0 0
\(137\) 19.2599 + 6.25793i 1.64549 + 0.534651i 0.977755 0.209751i \(-0.0672652\pi\)
0.667732 + 0.744402i \(0.267265\pi\)
\(138\) 0 0
\(139\) 0.287036 + 0.883406i 0.0243461 + 0.0749295i 0.962491 0.271312i \(-0.0874576\pi\)
−0.938145 + 0.346242i \(0.887458\pi\)
\(140\) 0 0
\(141\) −2.97223 + 9.14758i −0.250307 + 0.770365i
\(142\) 0 0
\(143\) 3.71949i 0.311040i
\(144\) 0 0
\(145\) 13.8404 + 4.71299i 1.14938 + 0.391393i
\(146\) 0 0
\(147\) 0.604143 + 0.831532i 0.0498289 + 0.0685836i
\(148\) 0 0
\(149\) −13.1432 −1.07673 −0.538364 0.842712i \(-0.680958\pi\)
−0.538364 + 0.842712i \(0.680958\pi\)
\(150\) 0 0
\(151\) 17.5864 1.43116 0.715580 0.698531i \(-0.246163\pi\)
0.715580 + 0.698531i \(0.246163\pi\)
\(152\) 0 0
\(153\) 1.11545 + 1.53529i 0.0901790 + 0.124121i
\(154\) 0 0
\(155\) 0.152881 10.8816i 0.0122797 0.874030i
\(156\) 0 0
\(157\) 8.68198i 0.692897i 0.938069 + 0.346449i \(0.112613\pi\)
−0.938069 + 0.346449i \(0.887387\pi\)
\(158\) 0 0
\(159\) 4.32383 13.3074i 0.342902 1.05534i
\(160\) 0 0
\(161\) 3.17852 + 9.78248i 0.250503 + 0.770968i
\(162\) 0 0
\(163\) 1.33900 + 0.435068i 0.104879 + 0.0340771i 0.360986 0.932571i \(-0.382440\pi\)
−0.256108 + 0.966648i \(0.582440\pi\)
\(164\) 0 0
\(165\) 1.29005 + 0.0181245i 0.100430 + 0.00141099i
\(166\) 0 0
\(167\) −5.18118 + 7.13128i −0.400932 + 0.551835i −0.960978 0.276626i \(-0.910784\pi\)
0.560046 + 0.828462i \(0.310784\pi\)
\(168\) 0 0
\(169\) 23.1028 + 16.7852i 1.77714 + 1.29117i
\(170\) 0 0
\(171\) −6.69438 + 4.86375i −0.511932 + 0.371940i
\(172\) 0 0
\(173\) −7.51629 + 2.44219i −0.571453 + 0.185676i −0.580468 0.814283i \(-0.697130\pi\)
0.00901487 + 0.999959i \(0.497130\pi\)
\(174\) 0 0
\(175\) −11.5103 4.10086i −0.870097 0.309996i
\(176\) 0 0
\(177\) 11.4631 3.72459i 0.861621 0.279958i
\(178\) 0 0
\(179\) −9.29450 + 6.75285i −0.694704 + 0.504732i −0.878203 0.478288i \(-0.841258\pi\)
0.183499 + 0.983020i \(0.441258\pi\)
\(180\) 0 0
\(181\) −3.17383 2.30592i −0.235909 0.171398i 0.463550 0.886071i \(-0.346576\pi\)
−0.699459 + 0.714673i \(0.746576\pi\)
\(182\) 0 0
\(183\) 2.82763 3.89190i 0.209024 0.287698i
\(184\) 0 0
\(185\) −0.144110 0.465686i −0.0105952 0.0342379i
\(186\) 0 0
\(187\) −1.04136 0.338359i −0.0761520 0.0247433i
\(188\) 0 0
\(189\) −0.755176 2.32419i −0.0549310 0.169060i
\(190\) 0 0
\(191\) −7.89402 + 24.2953i −0.571191 + 1.75795i 0.0776060 + 0.996984i \(0.475272\pi\)
−0.648797 + 0.760961i \(0.724728\pi\)
\(192\) 0 0
\(193\) 0.421651i 0.0303511i −0.999885 0.0151756i \(-0.995169\pi\)
0.999885 0.0151756i \(-0.00483071\pi\)
\(194\) 0 0
\(195\) 8.63573 11.5416i 0.618418 0.826508i
\(196\) 0 0
\(197\) −4.24463 5.84224i −0.302418 0.416242i 0.630580 0.776124i \(-0.282817\pi\)
−0.932998 + 0.359882i \(0.882817\pi\)
\(198\) 0 0
\(199\) −3.93505 −0.278949 −0.139474 0.990226i \(-0.544541\pi\)
−0.139474 + 0.990226i \(0.544541\pi\)
\(200\) 0 0
\(201\) 3.87094 0.273035
\(202\) 0 0
\(203\) 9.39232 + 12.9274i 0.659211 + 0.907327i
\(204\) 0 0
\(205\) 13.7877 4.26670i 0.962972 0.297999i
\(206\) 0 0
\(207\) 4.20898i 0.292544i
\(208\) 0 0
\(209\) 1.47536 4.54069i 0.102053 0.314086i
\(210\) 0 0
\(211\) −7.65156 23.5491i −0.526755 1.62119i −0.760819 0.648964i \(-0.775202\pi\)
0.234064 0.972221i \(-0.424798\pi\)
\(212\) 0 0
\(213\) 6.16520 + 2.00319i 0.422432 + 0.137257i
\(214\) 0 0
\(215\) −6.25702 + 4.41304i −0.426726 + 0.300967i
\(216\) 0 0
\(217\) 6.99093 9.62219i 0.474575 0.653197i
\(218\) 0 0
\(219\) −8.13134 5.90777i −0.549465 0.399210i
\(220\) 0 0
\(221\) −9.89715 + 7.19070i −0.665755 + 0.483699i
\(222\) 0 0
\(223\) 18.7098 6.07919i 1.25290 0.407093i 0.393942 0.919135i \(-0.371111\pi\)
0.858960 + 0.512043i \(0.171111\pi\)
\(224\) 0 0
\(225\) −3.96092 3.05141i −0.264062 0.203427i
\(226\) 0 0
\(227\) −25.0839 + 8.15025i −1.66488 + 0.540951i −0.981885 0.189476i \(-0.939321\pi\)
−0.682991 + 0.730427i \(0.739321\pi\)
\(228\) 0 0
\(229\) −12.9614 + 9.41703i −0.856515 + 0.622295i −0.926935 0.375223i \(-0.877566\pi\)
0.0704195 + 0.997517i \(0.477566\pi\)
\(230\) 0 0
\(231\) 1.14074 + 0.828797i 0.0750552 + 0.0545308i
\(232\) 0 0
\(233\) 17.2285 23.7129i 1.12867 1.55349i 0.338109 0.941107i \(-0.390213\pi\)
0.790564 0.612379i \(-0.209787\pi\)
\(234\) 0 0
\(235\) −6.93280 + 20.3592i −0.452246 + 1.32809i
\(236\) 0 0
\(237\) −4.51248 1.46619i −0.293117 0.0952395i
\(238\) 0 0
\(239\) −7.98989 24.5904i −0.516823 1.59062i −0.779940 0.625854i \(-0.784750\pi\)
0.263117 0.964764i \(-0.415250\pi\)
\(240\) 0 0
\(241\) −2.88671 + 8.88437i −0.185949 + 0.572292i −0.999963 0.00855232i \(-0.997278\pi\)
0.814014 + 0.580845i \(0.197278\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 1.32465 + 1.87816i 0.0846289 + 0.119991i
\(246\) 0 0
\(247\) −31.3539 43.1549i −1.99500 2.74588i
\(248\) 0 0
\(249\) −3.43418 −0.217632
\(250\) 0 0
\(251\) −13.5088 −0.852666 −0.426333 0.904566i \(-0.640195\pi\)
−0.426333 + 0.904566i \(0.640195\pi\)
\(252\) 0 0
\(253\) −1.42744 1.96471i −0.0897425 0.123520i
\(254\) 0 0
\(255\) 2.44575 + 3.46771i 0.153159 + 0.217156i
\(256\) 0 0
\(257\) 13.0662i 0.815044i −0.913195 0.407522i \(-0.866393\pi\)
0.913195 0.407522i \(-0.133607\pi\)
\(258\) 0 0
\(259\) 0.164632 0.506686i 0.0102298 0.0314839i
\(260\) 0 0
\(261\) 2.02055 + 6.21862i 0.125069 + 0.384923i
\(262\) 0 0
\(263\) −4.21380 1.36915i −0.259834 0.0844251i 0.176203 0.984354i \(-0.443618\pi\)
−0.436037 + 0.899929i \(0.643618\pi\)
\(264\) 0 0
\(265\) 10.0854 29.6174i 0.619543 1.81938i
\(266\) 0 0
\(267\) −3.34237 + 4.60038i −0.204550 + 0.281539i
\(268\) 0 0
\(269\) 22.6936 + 16.4879i 1.38366 + 1.00528i 0.996528 + 0.0832584i \(0.0265327\pi\)
0.387127 + 0.922026i \(0.373467\pi\)
\(270\) 0 0
\(271\) −4.84207 + 3.51797i −0.294135 + 0.213701i −0.725059 0.688687i \(-0.758188\pi\)
0.430924 + 0.902388i \(0.358188\pi\)
\(272\) 0 0
\(273\) 14.9828 4.86820i 0.906800 0.294637i
\(274\) 0 0
\(275\) 2.88378 + 0.0810472i 0.173898 + 0.00488733i
\(276\) 0 0
\(277\) 4.82254 1.56694i 0.289758 0.0941481i −0.160531 0.987031i \(-0.551321\pi\)
0.450290 + 0.892883i \(0.351321\pi\)
\(278\) 0 0
\(279\) 3.93738 2.86068i 0.235725 0.171264i
\(280\) 0 0
\(281\) 14.6885 + 10.6718i 0.876239 + 0.636625i 0.932254 0.361805i \(-0.117839\pi\)
−0.0560144 + 0.998430i \(0.517839\pi\)
\(282\) 0 0
\(283\) −2.76092 + 3.80009i −0.164120 + 0.225892i −0.883154 0.469083i \(-0.844584\pi\)
0.719034 + 0.694975i \(0.244584\pi\)
\(284\) 0 0
\(285\) −15.1204 + 10.6643i −0.895654 + 0.631699i
\(286\) 0 0
\(287\) 15.0016 + 4.87430i 0.885514 + 0.287721i
\(288\) 0 0
\(289\) 4.14041 + 12.7429i 0.243554 + 0.749581i
\(290\) 0 0
\(291\) 2.03480 6.26247i 0.119282 0.367112i
\(292\) 0 0
\(293\) 9.60771i 0.561288i 0.959812 + 0.280644i \(0.0905481\pi\)
−0.959812 + 0.280644i \(0.909452\pi\)
\(294\) 0 0
\(295\) 25.7468 7.96754i 1.49904 0.463888i
\(296\) 0 0
\(297\) 0.339142 + 0.466789i 0.0196790 + 0.0270859i
\(298\) 0 0
\(299\) −27.1329 −1.56914
\(300\) 0 0
\(301\) −8.36804 −0.482326
\(302\) 0 0
\(303\) −7.07476 9.73757i −0.406434 0.559409i
\(304\) 0 0
\(305\) 6.44441 8.61287i 0.369006 0.493172i
\(306\) 0 0
\(307\) 13.5400i 0.772771i −0.922337 0.386386i \(-0.873723\pi\)
0.922337 0.386386i \(-0.126277\pi\)
\(308\) 0 0
\(309\) 1.78805 5.50304i 0.101718 0.313057i
\(310\) 0 0
\(311\) −0.916931 2.82202i −0.0519944 0.160022i 0.921688 0.387933i \(-0.126811\pi\)
−0.973682 + 0.227910i \(0.926811\pi\)
\(312\) 0 0
\(313\) −13.3203 4.32802i −0.752906 0.244634i −0.0926747 0.995696i \(-0.529542\pi\)
−0.660231 + 0.751063i \(0.729542\pi\)
\(314\) 0 0
\(315\) −1.61545 5.22027i −0.0910203 0.294129i
\(316\) 0 0
\(317\) 15.8806 21.8577i 0.891941 1.22765i −0.0810273 0.996712i \(-0.525820\pi\)
0.972968 0.230939i \(-0.0741799\pi\)
\(318\) 0 0
\(319\) −3.05217 2.21753i −0.170889 0.124158i
\(320\) 0 0
\(321\) −3.29336 + 2.39276i −0.183817 + 0.133551i
\(322\) 0 0
\(323\) 14.9345 4.85252i 0.830979 0.270001i
\(324\) 0 0
\(325\) 19.6707 25.5339i 1.09114 1.41636i
\(326\) 0 0
\(327\) 1.38641 0.450471i 0.0766686 0.0249111i
\(328\) 0 0
\(329\) −19.0162 + 13.8161i −1.04840 + 0.761705i
\(330\) 0 0
\(331\) 5.38394 + 3.91166i 0.295928 + 0.215004i 0.725835 0.687869i \(-0.241454\pi\)
−0.429907 + 0.902873i \(0.641454\pi\)
\(332\) 0 0
\(333\) 0.128140 0.176370i 0.00702204 0.00966501i
\(334\) 0 0
\(335\) 8.65482 + 0.121596i 0.472863 + 0.00664348i
\(336\) 0 0
\(337\) −18.2629 5.93398i −0.994844 0.323245i −0.234041 0.972227i \(-0.575195\pi\)
−0.760804 + 0.648982i \(0.775195\pi\)
\(338\) 0 0
\(339\) 1.81017 + 5.57114i 0.0983152 + 0.302583i
\(340\) 0 0
\(341\) −0.867752 + 2.67067i −0.0469914 + 0.144625i
\(342\) 0 0
\(343\) 19.6184i 1.05930i
\(344\) 0 0
\(345\) −0.132214 + 9.41063i −0.00711819 + 0.506651i
\(346\) 0 0
\(347\) −9.85076 13.5584i −0.528816 0.727853i 0.458133 0.888884i \(-0.348518\pi\)
−0.986949 + 0.161030i \(0.948518\pi\)
\(348\) 0 0
\(349\) −22.9371 −1.22780 −0.613898 0.789385i \(-0.710399\pi\)
−0.613898 + 0.789385i \(0.710399\pi\)
\(350\) 0 0
\(351\) 6.44645 0.344086
\(352\) 0 0
\(353\) 4.12280 + 5.67455i 0.219434 + 0.302026i 0.904515 0.426442i \(-0.140233\pi\)
−0.685081 + 0.728467i \(0.740233\pi\)
\(354\) 0 0
\(355\) 13.7215 + 4.67250i 0.728262 + 0.247991i
\(356\) 0 0
\(357\) 4.63766i 0.245451i
\(358\) 0 0
\(359\) 4.61051 14.1897i 0.243333 0.748903i −0.752573 0.658509i \(-0.771187\pi\)
0.995906 0.0903940i \(-0.0288126\pi\)
\(360\) 0 0
\(361\) 15.2873 + 47.0494i 0.804594 + 2.47629i
\(362\) 0 0
\(363\) 10.1450 + 3.29631i 0.532475 + 0.173012i
\(364\) 0 0
\(365\) −17.9949 13.4643i −0.941894 0.704753i
\(366\) 0 0
\(367\) 0.400262 0.550914i 0.0208935 0.0287575i −0.798442 0.602071i \(-0.794342\pi\)
0.819336 + 0.573314i \(0.194342\pi\)
\(368\) 0 0
\(369\) 5.22182 + 3.79387i 0.271837 + 0.197501i
\(370\) 0 0
\(371\) 27.6637 20.0988i 1.43623 1.04348i
\(372\) 0 0
\(373\) −27.2355 + 8.84935i −1.41020 + 0.458202i −0.912475 0.409133i \(-0.865831\pi\)
−0.497725 + 0.867335i \(0.665831\pi\)
\(374\) 0 0
\(375\) −8.76017 6.94690i −0.452373 0.358736i
\(376\) 0 0
\(377\) −40.0880 + 13.0254i −2.06464 + 0.670842i
\(378\) 0 0
\(379\) −17.7191 + 12.8737i −0.910167 + 0.661275i −0.941057 0.338247i \(-0.890166\pi\)
0.0308898 + 0.999523i \(0.490166\pi\)
\(380\) 0 0
\(381\) −12.3662 8.98455i −0.633538 0.460293i
\(382\) 0 0
\(383\) 2.68378 3.69391i 0.137135 0.188750i −0.734926 0.678147i \(-0.762783\pi\)
0.872061 + 0.489397i \(0.162783\pi\)
\(384\) 0 0
\(385\) 2.52449 + 1.88890i 0.128660 + 0.0962671i
\(386\) 0 0
\(387\) −3.25660 1.05813i −0.165542 0.0537879i
\(388\) 0 0
\(389\) −6.71865 20.6779i −0.340649 1.04841i −0.963872 0.266366i \(-0.914177\pi\)
0.623223 0.782044i \(-0.285823\pi\)
\(390\) 0 0
\(391\) 2.46826 7.59653i 0.124825 0.384173i
\(392\) 0 0
\(393\) 3.75392i 0.189360i
\(394\) 0 0
\(395\) −10.0432 3.41993i −0.505326 0.172075i
\(396\) 0 0
\(397\) 9.18318 + 12.6396i 0.460891 + 0.634361i 0.974693 0.223547i \(-0.0717636\pi\)
−0.513803 + 0.857908i \(0.671764\pi\)
\(398\) 0 0
\(399\) −20.2217 −1.01235
\(400\) 0 0
\(401\) −19.9417 −0.995841 −0.497920 0.867223i \(-0.665903\pi\)
−0.497920 + 0.867223i \(0.665903\pi\)
\(402\) 0 0
\(403\) 18.4412 + 25.3821i 0.918622 + 1.26437i
\(404\) 0 0
\(405\) 0.0314125 2.23585i 0.00156090 0.111100i
\(406\) 0 0
\(407\) 0.125785i 0.00623495i
\(408\) 0 0
\(409\) 5.32001 16.3733i 0.263058 0.809608i −0.729077 0.684432i \(-0.760050\pi\)
0.992134 0.125176i \(-0.0399497\pi\)
\(410\) 0 0
\(411\) 6.25793 + 19.2599i 0.308681 + 0.950022i
\(412\) 0 0
\(413\) 28.0136 + 9.10217i 1.37846 + 0.447888i
\(414\) 0 0
\(415\) −7.67830 0.107876i −0.376913 0.00529543i
\(416\) 0 0
\(417\) −0.545975 + 0.751470i −0.0267365 + 0.0367996i
\(418\) 0 0
\(419\) 10.6230 + 7.71804i 0.518966 + 0.377051i 0.816214 0.577749i \(-0.196069\pi\)
−0.297248 + 0.954800i \(0.596069\pi\)
\(420\) 0 0
\(421\) −13.7712 + 10.0054i −0.671169 + 0.487633i −0.870416 0.492317i \(-0.836150\pi\)
0.199248 + 0.979949i \(0.436150\pi\)
\(422\) 0 0
\(423\) −9.14758 + 2.97223i −0.444770 + 0.144515i
\(424\) 0 0
\(425\) 5.35940 + 7.83010i 0.259969 + 0.379816i
\(426\) 0 0
\(427\) 11.1809 3.63289i 0.541081 0.175808i
\(428\) 0 0
\(429\) −3.00913 + 2.18626i −0.145282 + 0.105554i
\(430\) 0 0
\(431\) 10.1246 + 7.35594i 0.487684 + 0.354323i 0.804293 0.594233i \(-0.202544\pi\)
−0.316609 + 0.948556i \(0.602544\pi\)
\(432\) 0 0
\(433\) 12.1949 16.7848i 0.586048 0.806626i −0.408294 0.912850i \(-0.633876\pi\)
0.994342 + 0.106225i \(0.0338763\pi\)
\(434\) 0 0
\(435\) 4.32231 + 13.9674i 0.207239 + 0.669684i
\(436\) 0 0
\(437\) 33.1234 + 10.7625i 1.58451 + 0.514838i
\(438\) 0 0
\(439\) 10.2225 + 31.4615i 0.487891 + 1.50157i 0.827749 + 0.561098i \(0.189621\pi\)
−0.339858 + 0.940477i \(0.610379\pi\)
\(440\) 0 0
\(441\) −0.317617 + 0.977524i −0.0151246 + 0.0465488i
\(442\) 0 0
\(443\) 23.4802i 1.11558i −0.829984 0.557788i \(-0.811650\pi\)
0.829984 0.557788i \(-0.188350\pi\)
\(444\) 0 0
\(445\) −7.61754 + 10.1808i −0.361106 + 0.482614i
\(446\) 0 0
\(447\) −7.72535 10.6330i −0.365397 0.502925i
\(448\) 0 0
\(449\) 31.6965 1.49585 0.747925 0.663783i \(-0.231050\pi\)
0.747925 + 0.663783i \(0.231050\pi\)
\(450\) 0 0
\(451\) −3.72415 −0.175363
\(452\) 0 0
\(453\) 10.3370 + 14.2277i 0.485676 + 0.668475i
\(454\) 0 0
\(455\) 33.6522 10.4139i 1.57764 0.488212i
\(456\) 0 0
\(457\) 28.2267i 1.32039i 0.751094 + 0.660196i \(0.229527\pi\)
−0.751094 + 0.660196i \(0.770473\pi\)
\(458\) 0 0
\(459\) −0.586428 + 1.80484i −0.0273721 + 0.0842427i
\(460\) 0 0
\(461\) −1.52737 4.70075i −0.0711365 0.218936i 0.909167 0.416431i \(-0.136719\pi\)
−0.980304 + 0.197495i \(0.936719\pi\)
\(462\) 0 0
\(463\) 17.5435 + 5.70022i 0.815314 + 0.264912i 0.686847 0.726802i \(-0.258994\pi\)
0.128467 + 0.991714i \(0.458994\pi\)
\(464\) 0 0
\(465\) 8.89325 6.27235i 0.412415 0.290873i
\(466\) 0 0
\(467\) 10.1693 13.9969i 0.470581 0.647699i −0.506080 0.862487i \(-0.668906\pi\)
0.976661 + 0.214788i \(0.0689059\pi\)
\(468\) 0 0
\(469\) 7.65314 + 5.56033i 0.353389 + 0.256752i
\(470\) 0 0
\(471\) −7.02387 + 5.10314i −0.323643 + 0.235140i
\(472\) 0 0
\(473\) 1.87900 0.610525i 0.0863966 0.0280719i
\(474\) 0 0
\(475\) −34.1419 + 23.3688i −1.56654 + 1.07223i
\(476\) 0 0
\(477\) 13.3074 4.32383i 0.609303 0.197974i
\(478\) 0 0
\(479\) −27.8105 + 20.2055i −1.27069 + 0.923212i −0.999230 0.0392366i \(-0.987507\pi\)
−0.271463 + 0.962449i \(0.587507\pi\)
\(480\) 0 0
\(481\) 1.13696 + 0.826049i 0.0518408 + 0.0376646i
\(482\) 0 0
\(483\) −6.04591 + 8.32148i −0.275098 + 0.378640i
\(484\) 0 0
\(485\) 4.74622 13.9380i 0.215515 0.632892i
\(486\) 0 0
\(487\) −4.79530 1.55809i −0.217296 0.0706037i 0.198346 0.980132i \(-0.436443\pi\)
−0.415642 + 0.909528i \(0.636443\pi\)
\(488\) 0 0
\(489\) 0.435068 + 1.33900i 0.0196744 + 0.0605517i
\(490\) 0 0
\(491\) −8.03949 + 24.7430i −0.362817 + 1.11664i 0.588520 + 0.808483i \(0.299711\pi\)
−0.951337 + 0.308153i \(0.900289\pi\)
\(492\) 0 0
\(493\) 12.4085i 0.558852i
\(494\) 0 0
\(495\) 0.743607 + 1.05432i 0.0334227 + 0.0473883i
\(496\) 0 0
\(497\) 9.31162 + 12.8163i 0.417683 + 0.574892i
\(498\) 0 0
\(499\) −2.49658 −0.111762 −0.0558812 0.998437i \(-0.517797\pi\)
−0.0558812 + 0.998437i \(0.517797\pi\)
\(500\) 0 0
\(501\) −8.81475 −0.393814
\(502\) 0 0
\(503\) 8.38184 + 11.5366i 0.373728 + 0.514392i 0.953909 0.300095i \(-0.0970184\pi\)
−0.580181 + 0.814487i \(0.697018\pi\)
\(504\) 0 0
\(505\) −15.5122 21.9940i −0.690284 0.978718i
\(506\) 0 0
\(507\) 28.5567i 1.26825i
\(508\) 0 0
\(509\) 4.82569 14.8520i 0.213895 0.658301i −0.785335 0.619071i \(-0.787509\pi\)
0.999230 0.0392303i \(-0.0124906\pi\)
\(510\) 0 0
\(511\) −7.59020 23.3602i −0.335771 1.03340i
\(512\) 0 0
\(513\) −7.86971 2.55702i −0.347456 0.112895i
\(514\) 0 0
\(515\) 4.17067 12.2478i 0.183781 0.539703i
\(516\) 0 0
\(517\) 3.26198 4.48974i 0.143462 0.197458i
\(518\) 0 0
\(519\) −6.39374 4.64533i −0.280654 0.203907i
\(520\) 0 0
\(521\) −11.6277 + 8.44804i −0.509420 + 0.370115i −0.812604 0.582817i \(-0.801951\pi\)
0.303183 + 0.952932i \(0.401951\pi\)
\(522\) 0 0
\(523\) −4.19878 + 1.36427i −0.183600 + 0.0596552i −0.399374 0.916788i \(-0.630772\pi\)
0.215774 + 0.976443i \(0.430772\pi\)
\(524\) 0 0
\(525\) −3.44792 11.7225i −0.150480 0.511610i
\(526\) 0 0
\(527\) −8.78393 + 2.85407i −0.382634 + 0.124325i
\(528\) 0 0
\(529\) −4.27526 + 3.10615i −0.185881 + 0.135050i
\(530\) 0 0
\(531\) 9.75111 + 7.08460i 0.423162 + 0.307445i
\(532\) 0 0
\(533\) −24.4570 + 33.6622i −1.05935 + 1.45807i
\(534\) 0 0
\(535\) −7.43861 + 5.24640i −0.321599 + 0.226822i
\(536\) 0 0
\(537\) −10.9263 3.55018i −0.471507 0.153202i
\(538\) 0 0
\(539\) −0.183260 0.564015i −0.00789355 0.0242939i
\(540\) 0 0
\(541\) 11.1361 34.2734i 0.478778 1.47353i −0.362016 0.932172i \(-0.617912\pi\)
0.840794 0.541355i \(-0.182088\pi\)
\(542\) 0 0
\(543\) 3.92307i 0.168355i
\(544\) 0 0
\(545\) 3.11395 0.963635i 0.133387 0.0412776i
\(546\) 0 0
\(547\) 7.11410 + 9.79172i 0.304177 + 0.418664i 0.933554 0.358436i \(-0.116690\pi\)
−0.629377 + 0.777100i \(0.716690\pi\)
\(548\) 0 0
\(549\) 4.81065 0.205314
\(550\) 0 0
\(551\) 54.1054 2.30497
\(552\) 0 0
\(553\) −6.81544 9.38064i −0.289822 0.398906i
\(554\) 0 0
\(555\) 0.292042 0.390311i 0.0123965 0.0165678i
\(556\) 0 0
\(557\) 24.0437i 1.01876i −0.860541 0.509382i \(-0.829874\pi\)
0.860541 0.509382i \(-0.170126\pi\)
\(558\) 0 0
\(559\) 6.82119 20.9935i 0.288506 0.887929i
\(560\) 0 0
\(561\) −0.338359 1.04136i −0.0142855 0.0439664i
\(562\) 0 0
\(563\) −18.0159 5.85371i −0.759278 0.246704i −0.0963092 0.995351i \(-0.530704\pi\)
−0.662969 + 0.748647i \(0.730704\pi\)
\(564\) 0 0
\(565\) 3.87227 + 12.5131i 0.162908 + 0.526430i
\(566\) 0 0
\(567\) 1.43643 1.97708i 0.0603244 0.0830295i
\(568\) 0 0
\(569\) −25.2591 18.3518i −1.05892 0.769348i −0.0850293 0.996378i \(-0.527098\pi\)
−0.973888 + 0.227030i \(0.927098\pi\)
\(570\) 0 0
\(571\) 0.0316916 0.0230253i 0.00132625 0.000963578i −0.587122 0.809499i \(-0.699739\pi\)
0.588448 + 0.808535i \(0.299739\pi\)
\(572\) 0 0
\(573\) −24.2953 + 7.89402i −1.01495 + 0.329777i
\(574\) 0 0
\(575\) −0.591223 + 21.0366i −0.0246557 + 0.877286i
\(576\) 0 0
\(577\) −19.1443 + 6.22035i −0.796986 + 0.258957i −0.679076 0.734068i \(-0.737619\pi\)
−0.117910 + 0.993024i \(0.537619\pi\)
\(578\) 0 0
\(579\) 0.341123 0.247840i 0.0141766 0.0102999i
\(580\) 0 0
\(581\) −6.78964 4.93296i −0.281682 0.204654i
\(582\) 0 0
\(583\) −4.74535 + 6.53141i −0.196532 + 0.270503i
\(584\) 0 0
\(585\) 14.4133 + 0.202499i 0.595915 + 0.00837230i
\(586\) 0 0
\(587\) 9.48143 + 3.08070i 0.391341 + 0.127154i 0.498076 0.867133i \(-0.334040\pi\)
−0.106736 + 0.994287i \(0.534040\pi\)
\(588\) 0 0
\(589\) −12.4447 38.3009i −0.512776 1.57816i
\(590\) 0 0
\(591\) 2.23154 6.86796i 0.0917931 0.282510i
\(592\) 0 0
\(593\) 20.3619i 0.836163i −0.908410 0.418082i \(-0.862703\pi\)
0.908410 0.418082i \(-0.137297\pi\)
\(594\) 0 0
\(595\) −0.145680 + 10.3691i −0.00597231 + 0.425091i
\(596\) 0 0
\(597\) −2.31297 3.18353i −0.0946634 0.130293i
\(598\) 0 0
\(599\) 24.1075 0.985007 0.492503 0.870311i \(-0.336082\pi\)
0.492503 + 0.870311i \(0.336082\pi\)
\(600\) 0 0
\(601\) 37.2054 1.51764 0.758820 0.651300i \(-0.225776\pi\)
0.758820 + 0.651300i \(0.225776\pi\)
\(602\) 0 0
\(603\) 2.27528 + 3.13165i 0.0926565 + 0.127531i
\(604\) 0 0
\(605\) 22.5791 + 7.68873i 0.917973 + 0.312591i
\(606\) 0 0
\(607\) 40.5752i 1.64690i 0.567392 + 0.823448i \(0.307952\pi\)
−0.567392 + 0.823448i \(0.692048\pi\)
\(608\) 0 0
\(609\) −4.93783 + 15.1971i −0.200091 + 0.615817i
\(610\) 0 0
\(611\) −19.1603 58.9694i −0.775143 2.38565i
\(612\) 0 0
\(613\) 4.88423 + 1.58698i 0.197272 + 0.0640977i 0.405987 0.913879i \(-0.366928\pi\)
−0.208714 + 0.977977i \(0.566928\pi\)
\(614\) 0 0
\(615\) 11.5560 + 8.64655i 0.465983 + 0.348663i
\(616\) 0 0
\(617\) 9.62895 13.2531i 0.387647 0.533550i −0.569943 0.821684i \(-0.693035\pi\)
0.957590 + 0.288134i \(0.0930348\pi\)
\(618\) 0 0
\(619\) 14.9251 + 10.8437i 0.599892 + 0.435847i 0.845841 0.533436i \(-0.179099\pi\)
−0.245948 + 0.969283i \(0.579099\pi\)
\(620\) 0 0
\(621\) −3.40513 + 2.47398i −0.136643 + 0.0992772i
\(622\) 0 0
\(623\) −13.2163 + 4.29422i −0.529498 + 0.172044i
\(624\) 0 0
\(625\) −19.3682 15.8074i −0.774727 0.632296i
\(626\) 0 0
\(627\) 4.54069 1.47536i 0.181338 0.0589202i
\(628\) 0 0
\(629\) −0.334701 + 0.243174i −0.0133454 + 0.00969600i
\(630\) 0 0
\(631\) −31.1970 22.6659i −1.24193 0.902316i −0.244206 0.969723i \(-0.578527\pi\)
−0.997726 + 0.0674068i \(0.978527\pi\)
\(632\) 0 0
\(633\) 14.5541 20.0320i 0.578475 0.796202i
\(634\) 0 0
\(635\) −27.3667 20.4765i −1.08601 0.812587i
\(636\) 0 0
\(637\) −6.30156 2.04750i −0.249677 0.0811249i
\(638\) 0 0
\(639\) 2.00319 + 6.16520i 0.0792451 + 0.243891i
\(640\) 0 0
\(641\) 5.87099 18.0690i 0.231890 0.713684i −0.765629 0.643283i \(-0.777572\pi\)
0.997519 0.0704016i \(-0.0224281\pi\)
\(642\) 0 0
\(643\) 37.6504i 1.48479i −0.669964 0.742393i \(-0.733691\pi\)
0.669964 0.742393i \(-0.266309\pi\)
\(644\) 0 0
\(645\) −7.24801 2.46812i −0.285390 0.0971821i
\(646\) 0 0
\(647\) 3.37070 + 4.63937i 0.132516 + 0.182392i 0.870118 0.492843i \(-0.164042\pi\)
−0.737603 + 0.675235i \(0.764042\pi\)
\(648\) 0 0
\(649\) −6.95440 −0.272984
\(650\) 0 0
\(651\) 11.8937 0.466150
\(652\) 0 0
\(653\) −23.5590 32.4262i −0.921936 1.26894i −0.962923 0.269777i \(-0.913050\pi\)
0.0409866 0.999160i \(-0.486950\pi\)
\(654\) 0 0
\(655\) −0.117920 + 8.39319i −0.00460751 + 0.327949i
\(656\) 0 0
\(657\) 10.0509i 0.392123i
\(658\) 0 0
\(659\) 9.75714 30.0294i 0.380084 1.16978i −0.559900 0.828560i \(-0.689160\pi\)
0.939984 0.341218i \(-0.110840\pi\)
\(660\) 0 0
\(661\) 9.68781 + 29.8160i 0.376812 + 1.15971i 0.942248 + 0.334916i \(0.108708\pi\)
−0.565436 + 0.824792i \(0.691292\pi\)
\(662\) 0 0
\(663\) −11.6348 3.78038i −0.451858 0.146818i
\(664\) 0 0
\(665\) −45.2127 0.635215i −1.75327 0.0246326i
\(666\) 0 0
\(667\) 16.1765 22.2650i 0.626355 0.862103i
\(668\) 0 0
\(669\) 15.9155 + 11.5633i 0.615330 + 0.447063i
\(670\) 0 0
\(671\) −2.24556 + 1.63150i −0.0866889 + 0.0629832i
\(672\) 0 0
\(673\) −4.25575 + 1.38278i −0.164047 + 0.0533021i −0.389889 0.920862i \(-0.627487\pi\)
0.225842 + 0.974164i \(0.427487\pi\)
\(674\) 0 0
\(675\) 0.140467 4.99803i 0.00540658 0.192374i
\(676\) 0 0
\(677\) −13.3935 + 4.35181i −0.514754 + 0.167254i −0.554863 0.831942i \(-0.687229\pi\)
0.0401092 + 0.999195i \(0.487229\pi\)
\(678\) 0 0
\(679\) 13.0186 9.45854i 0.499607 0.362985i
\(680\) 0 0
\(681\) −21.3376 15.5027i −0.817660 0.594065i
\(682\) 0 0
\(683\) −6.95685 + 9.57528i −0.266196 + 0.366388i −0.921101 0.389324i \(-0.872709\pi\)
0.654905 + 0.755711i \(0.272709\pi\)
\(684\) 0 0
\(685\) 13.3868 + 43.2588i 0.511482 + 1.65284i
\(686\) 0 0
\(687\) −15.2371 4.95082i −0.581330 0.188886i
\(688\) 0 0
\(689\) 27.8733 + 85.7853i 1.06189 + 3.26816i
\(690\) 0 0
\(691\) −11.6676 + 35.9091i −0.443855 + 1.36605i 0.439879 + 0.898057i \(0.355021\pi\)
−0.883734 + 0.467989i \(0.844979\pi\)
\(692\) 0 0
\(693\) 1.41003i 0.0535627i
\(694\) 0 0
\(695\) −1.24432 + 1.66302i −0.0471998 + 0.0630820i
\(696\) 0 0
\(697\) −7.19971 9.90956i −0.272709 0.375351i
\(698\) 0 0
\(699\) 29.3108 1.10864
\(700\) 0 0
\(701\) −39.1678 −1.47935 −0.739674 0.672965i \(-0.765020\pi\)
−0.739674 + 0.672965i \(0.765020\pi\)
\(702\) 0 0
\(703\) −1.06032 1.45941i −0.0399908 0.0550426i
\(704\) 0 0
\(705\) −20.5460 + 6.35810i −0.773805 + 0.239460i
\(706\) 0 0
\(707\) 29.4143i 1.10624i
\(708\) 0 0
\(709\) 13.1296 40.4089i 0.493094 1.51759i −0.326812 0.945089i \(-0.605974\pi\)
0.819906 0.572498i \(-0.194026\pi\)
\(710\) 0 0
\(711\) −1.46619 4.51248i −0.0549866 0.169231i
\(712\) 0 0
\(713\) −19.4820 6.33008i −0.729606 0.237063i
\(714\) 0 0
\(715\) −6.79664 + 4.79362i −0.254180 + 0.179271i
\(716\) 0 0
\(717\) 15.1977 20.9178i 0.567568 0.781190i
\(718\) 0 0
\(719\) 24.0261 + 17.4560i 0.896022 + 0.650998i 0.937441 0.348143i \(-0.113188\pi\)
−0.0414189 + 0.999142i \(0.513188\pi\)
\(720\) 0 0
\(721\) 11.4399 8.31154i 0.426042 0.309538i
\(722\) 0 0
\(723\) −8.88437 + 2.88671i −0.330413 + 0.107358i
\(724\) 0 0
\(725\) 9.22527 + 31.3647i 0.342618 + 1.16485i
\(726\) 0 0
\(727\) 39.8796 12.9577i 1.47905 0.480573i 0.545222 0.838292i \(-0.316445\pi\)
0.933829 + 0.357719i \(0.116445\pi\)
\(728\) 0 0
\(729\) 0.809017 0.587785i 0.0299636 0.0217698i
\(730\) 0 0
\(731\) 5.25712 + 3.81952i 0.194441 + 0.141270i
\(732\) 0 0
\(733\) 17.1695 23.6317i 0.634168 0.872858i −0.364119 0.931352i \(-0.618630\pi\)
0.998288 + 0.0584945i \(0.0186300\pi\)
\(734\) 0 0
\(735\) −0.740849 + 2.17562i −0.0273266 + 0.0802489i
\(736\) 0 0
\(737\) −2.12415 0.690179i −0.0782441 0.0254231i
\(738\) 0 0
\(739\) −8.00979 24.6516i −0.294645 0.906824i −0.983340 0.181773i \(-0.941816\pi\)
0.688695 0.725051i \(-0.258184\pi\)
\(740\) 0 0
\(741\) 16.4837 50.7317i 0.605544 1.86367i
\(742\) 0 0
\(743\) 9.22935i 0.338592i −0.985565 0.169296i \(-0.945851\pi\)
0.985565 0.169296i \(-0.0541494\pi\)
\(744\) 0 0
\(745\) −16.9387 24.0165i −0.620586 0.879897i
\(746\) 0 0
\(747\) −2.01856 2.77831i −0.0738552 0.101653i
\(748\) 0 0
\(749\) −9.94826 −0.363502
\(750\) 0 0
\(751\) −37.2805 −1.36038 −0.680192 0.733034i \(-0.738103\pi\)
−0.680192 + 0.733034i \(0.738103\pi\)
\(752\) 0 0
\(753\) −7.94025 10.9288i −0.289359 0.398268i
\(754\) 0 0
\(755\) 22.6651 + 32.1356i 0.824866 + 1.16954i
\(756\) 0 0
\(757\) 27.6758i 1.00589i 0.864317 + 0.502947i \(0.167751\pi\)
−0.864317 + 0.502947i \(0.832249\pi\)
\(758\) 0 0
\(759\) 0.750451 2.30965i 0.0272396 0.0838350i
\(760\) 0 0
\(761\) −4.21264 12.9652i −0.152708 0.469988i 0.845213 0.534429i \(-0.179473\pi\)
−0.997921 + 0.0644416i \(0.979473\pi\)
\(762\) 0 0
\(763\) 3.38811 + 1.10086i 0.122658 + 0.0398539i
\(764\) 0 0
\(765\) −1.36786 + 4.01693i −0.0494550 + 0.145232i
\(766\) 0 0
\(767\) −45.6705 + 62.8600i −1.64906 + 2.26974i
\(768\) 0 0
\(769\) −24.6838 17.9339i −0.890122 0.646712i 0.0457876 0.998951i \(-0.485420\pi\)
−0.935910 + 0.352239i \(0.885420\pi\)
\(770\) 0 0
\(771\) 10.5707 7.68009i 0.380696 0.276592i
\(772\) 0 0
\(773\) 8.03172 2.60967i 0.288881 0.0938631i −0.160992 0.986956i \(-0.551469\pi\)
0.449873 + 0.893093i \(0.351469\pi\)
\(774\) 0 0
\(775\) 20.0810 13.7447i 0.721330 0.493723i
\(776\) 0 0
\(777\) 0.506686 0.164632i 0.0181773 0.00590615i
\(778\) 0 0
\(779\) 43.2090 31.3932i 1.54812 1.12478i
\(780\) 0 0
\(781\) −3.02595 2.19848i −0.108277 0.0786678i
\(782\) 0 0
\(783\) −3.84332 + 5.28988i −0.137349 + 0.189045i
\(784\) 0 0
\(785\) −15.8646 + 11.1892i −0.566232 + 0.399360i
\(786\) 0 0
\(787\) 38.8560 + 12.6251i 1.38507 + 0.450036i 0.904332 0.426829i \(-0.140369\pi\)
0.480736 + 0.876865i \(0.340369\pi\)
\(788\) 0 0
\(789\) −1.36915 4.21380i −0.0487429 0.150015i
\(790\) 0 0
\(791\) −4.42371 + 13.6148i −0.157289 + 0.484086i
\(792\) 0 0
\(793\) 31.0116i 1.10125i
\(794\) 0 0
\(795\) 29.8891 9.24940i 1.06006 0.328042i
\(796\) 0 0
\(797\) 17.3703 + 23.9082i 0.615288 + 0.846871i