Properties

Label 624.2.cn.f.353.5
Level $624$
Weight $2$
Character 624.353
Analytic conductor $4.983$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.cn (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.98266508613\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 312)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 353.5
Character \(\chi\) \(=\) 624.353
Dual form 624.2.cn.f.449.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.852797 + 1.50756i) q^{3} +(0.477579 + 0.477579i) q^{5} +(-0.988569 + 0.264886i) q^{7} +(-1.54548 - 2.57128i) q^{9} +O(q^{10})\) \(q+(-0.852797 + 1.50756i) q^{3} +(0.477579 + 0.477579i) q^{5} +(-0.988569 + 0.264886i) q^{7} +(-1.54548 - 2.57128i) q^{9} +(-5.10637 - 1.36825i) q^{11} +(-1.49059 - 3.28301i) q^{13} +(-1.12726 + 0.312701i) q^{15} +(-1.22274 + 2.11784i) q^{17} +(1.14039 + 4.25599i) q^{19} +(0.443716 - 1.71622i) q^{21} +(-2.40904 - 4.17258i) q^{23} -4.54384i q^{25} +(5.19434 - 0.137115i) q^{27} +(-3.23138 + 1.86564i) q^{29} +(2.91416 - 2.91416i) q^{31} +(6.41741 - 6.53132i) q^{33} +(-0.598623 - 0.345615i) q^{35} +(-0.898805 + 3.35438i) q^{37} +(6.22050 + 0.552587i) q^{39} +(1.25078 - 4.66796i) q^{41} +(-10.9673 - 6.33197i) q^{43} +(0.489904 - 1.96608i) q^{45} +(0.646174 - 0.646174i) q^{47} +(-5.15507 + 2.97628i) q^{49} +(-2.15003 - 3.64943i) q^{51} +6.56807i q^{53} +(-1.78525 - 3.09214i) q^{55} +(-7.38868 - 1.91029i) q^{57} +(-2.21886 - 8.28091i) q^{59} +(-3.99581 + 6.92094i) q^{61} +(2.20891 + 2.13252i) q^{63} +(0.856021 - 2.27977i) q^{65} +(-3.54515 - 0.949919i) q^{67} +(8.34484 - 0.0734109i) q^{69} +(5.34544 - 1.43231i) q^{71} +(-0.225083 - 0.225083i) q^{73} +(6.85011 + 3.87497i) q^{75} +5.41043 q^{77} +2.70428 q^{79} +(-4.22301 + 7.94772i) q^{81} +(7.41135 + 7.41135i) q^{83} +(-1.59539 + 0.427483i) q^{85} +(-0.0568517 - 6.46251i) q^{87} +(-10.0378 - 2.68962i) q^{89} +(2.34317 + 2.85064i) q^{91} +(1.90809 + 6.87846i) q^{93} +(-1.48794 + 2.57719i) q^{95} +(-2.57029 - 9.59245i) q^{97} +(4.37361 + 15.2445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 4q^{7} + O(q^{10}) \) \( 56q - 4q^{7} + 8q^{13} + 8q^{15} - 4q^{19} + 16q^{21} - 24q^{27} + 36q^{31} + 28q^{33} + 20q^{37} - 16q^{39} + 84q^{43} + 12q^{45} - 12q^{49} + 24q^{55} - 36q^{57} - 24q^{61} + 12q^{63} + 32q^{67} - 36q^{69} - 20q^{73} + 60q^{75} + 32q^{79} - 88q^{85} + 16q^{87} - 28q^{91} - 88q^{93} - 36q^{97} - 44q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.852797 + 1.50756i −0.492362 + 0.870390i
\(4\) 0 0
\(5\) 0.477579 + 0.477579i 0.213580 + 0.213580i 0.805786 0.592207i \(-0.201743\pi\)
−0.592207 + 0.805786i \(0.701743\pi\)
\(6\) 0 0
\(7\) −0.988569 + 0.264886i −0.373644 + 0.100118i −0.440754 0.897628i \(-0.645289\pi\)
0.0671099 + 0.997746i \(0.478622\pi\)
\(8\) 0 0
\(9\) −1.54548 2.57128i −0.515159 0.857095i
\(10\) 0 0
\(11\) −5.10637 1.36825i −1.53963 0.412542i −0.613482 0.789709i \(-0.710232\pi\)
−0.926145 + 0.377167i \(0.876898\pi\)
\(12\) 0 0
\(13\) −1.49059 3.28301i −0.413415 0.910543i
\(14\) 0 0
\(15\) −1.12726 + 0.312701i −0.291056 + 0.0807391i
\(16\) 0 0
\(17\) −1.22274 + 2.11784i −0.296557 + 0.513652i −0.975346 0.220682i \(-0.929172\pi\)
0.678789 + 0.734333i \(0.262505\pi\)
\(18\) 0 0
\(19\) 1.14039 + 4.25599i 0.261623 + 0.976391i 0.964285 + 0.264867i \(0.0853280\pi\)
−0.702662 + 0.711524i \(0.748005\pi\)
\(20\) 0 0
\(21\) 0.443716 1.71622i 0.0968268 0.374510i
\(22\) 0 0
\(23\) −2.40904 4.17258i −0.502320 0.870044i −0.999996 0.00268084i \(-0.999147\pi\)
0.497677 0.867363i \(-0.334187\pi\)
\(24\) 0 0
\(25\) 4.54384i 0.908767i
\(26\) 0 0
\(27\) 5.19434 0.137115i 0.999652 0.0263877i
\(28\) 0 0
\(29\) −3.23138 + 1.86564i −0.600052 + 0.346440i −0.769062 0.639174i \(-0.779276\pi\)
0.169010 + 0.985614i \(0.445943\pi\)
\(30\) 0 0
\(31\) 2.91416 2.91416i 0.523398 0.523398i −0.395198 0.918596i \(-0.629324\pi\)
0.918596 + 0.395198i \(0.129324\pi\)
\(32\) 0 0
\(33\) 6.41741 6.53132i 1.11713 1.13696i
\(34\) 0 0
\(35\) −0.598623 0.345615i −0.101186 0.0584197i
\(36\) 0 0
\(37\) −0.898805 + 3.35438i −0.147763 + 0.551457i 0.851854 + 0.523779i \(0.175478\pi\)
−0.999617 + 0.0276786i \(0.991188\pi\)
\(38\) 0 0
\(39\) 6.22050 + 0.552587i 0.996078 + 0.0884847i
\(40\) 0 0
\(41\) 1.25078 4.66796i 0.195338 0.729013i −0.796841 0.604189i \(-0.793497\pi\)
0.992179 0.124823i \(-0.0398363\pi\)
\(42\) 0 0
\(43\) −10.9673 6.33197i −1.67250 0.965616i −0.966235 0.257664i \(-0.917047\pi\)
−0.706261 0.707952i \(-0.749619\pi\)
\(44\) 0 0
\(45\) 0.489904 1.96608i 0.0730306 0.293085i
\(46\) 0 0
\(47\) 0.646174 0.646174i 0.0942541 0.0942541i −0.658408 0.752662i \(-0.728770\pi\)
0.752662 + 0.658408i \(0.228770\pi\)
\(48\) 0 0
\(49\) −5.15507 + 2.97628i −0.736439 + 0.425183i
\(50\) 0 0
\(51\) −2.15003 3.64943i −0.301064 0.511023i
\(52\) 0 0
\(53\) 6.56807i 0.902194i 0.892475 + 0.451097i \(0.148967\pi\)
−0.892475 + 0.451097i \(0.851033\pi\)
\(54\) 0 0
\(55\) −1.78525 3.09214i −0.240722 0.416944i
\(56\) 0 0
\(57\) −7.38868 1.91029i −0.978655 0.253024i
\(58\) 0 0
\(59\) −2.21886 8.28091i −0.288872 1.07808i −0.945964 0.324273i \(-0.894880\pi\)
0.657092 0.753810i \(-0.271786\pi\)
\(60\) 0 0
\(61\) −3.99581 + 6.92094i −0.511611 + 0.886136i 0.488299 + 0.872676i \(0.337618\pi\)
−0.999909 + 0.0134590i \(0.995716\pi\)
\(62\) 0 0
\(63\) 2.20891 + 2.13252i 0.278296 + 0.268672i
\(64\) 0 0
\(65\) 0.856021 2.27977i 0.106176 0.282770i
\(66\) 0 0
\(67\) −3.54515 0.949919i −0.433109 0.116051i 0.0356764 0.999363i \(-0.488641\pi\)
−0.468785 + 0.883312i \(0.655308\pi\)
\(68\) 0 0
\(69\) 8.34484 0.0734109i 1.00460 0.00883764i
\(70\) 0 0
\(71\) 5.34544 1.43231i 0.634387 0.169984i 0.0727276 0.997352i \(-0.476830\pi\)
0.561660 + 0.827368i \(0.310163\pi\)
\(72\) 0 0
\(73\) −0.225083 0.225083i −0.0263440 0.0263440i 0.693812 0.720156i \(-0.255930\pi\)
−0.720156 + 0.693812i \(0.755930\pi\)
\(74\) 0 0
\(75\) 6.85011 + 3.87497i 0.790982 + 0.447443i
\(76\) 0 0
\(77\) 5.41043 0.616575
\(78\) 0 0
\(79\) 2.70428 0.304256 0.152128 0.988361i \(-0.451387\pi\)
0.152128 + 0.988361i \(0.451387\pi\)
\(80\) 0 0
\(81\) −4.22301 + 7.94772i −0.469223 + 0.883080i
\(82\) 0 0
\(83\) 7.41135 + 7.41135i 0.813502 + 0.813502i 0.985157 0.171655i \(-0.0549115\pi\)
−0.171655 + 0.985157i \(0.554911\pi\)
\(84\) 0 0
\(85\) −1.59539 + 0.427483i −0.173044 + 0.0463670i
\(86\) 0 0
\(87\) −0.0568517 6.46251i −0.00609514 0.692853i
\(88\) 0 0
\(89\) −10.0378 2.68962i −1.06401 0.285099i −0.315978 0.948767i \(-0.602332\pi\)
−0.748028 + 0.663667i \(0.768999\pi\)
\(90\) 0 0
\(91\) 2.34317 + 2.85064i 0.245631 + 0.298829i
\(92\) 0 0
\(93\) 1.90809 + 6.87846i 0.197859 + 0.713263i
\(94\) 0 0
\(95\) −1.48794 + 2.57719i −0.152660 + 0.264415i
\(96\) 0 0
\(97\) −2.57029 9.59245i −0.260973 0.973966i −0.964669 0.263465i \(-0.915135\pi\)
0.703696 0.710502i \(-0.251532\pi\)
\(98\) 0 0
\(99\) 4.37361 + 15.2445i 0.439565 + 1.53213i
\(100\) 0 0
\(101\) 8.34245 + 14.4495i 0.830105 + 1.43778i 0.897954 + 0.440088i \(0.145053\pi\)
−0.0678495 + 0.997696i \(0.521614\pi\)
\(102\) 0 0
\(103\) 4.13601i 0.407533i 0.979020 + 0.203766i \(0.0653183\pi\)
−0.979020 + 0.203766i \(0.934682\pi\)
\(104\) 0 0
\(105\) 1.03154 0.607721i 0.100668 0.0593075i
\(106\) 0 0
\(107\) 3.57621 2.06472i 0.345725 0.199604i −0.317076 0.948400i \(-0.602701\pi\)
0.662801 + 0.748796i \(0.269368\pi\)
\(108\) 0 0
\(109\) −11.2846 + 11.2846i −1.08086 + 1.08086i −0.0844356 + 0.996429i \(0.526909\pi\)
−0.996429 + 0.0844356i \(0.973091\pi\)
\(110\) 0 0
\(111\) −4.29044 4.21561i −0.407230 0.400128i
\(112\) 0 0
\(113\) −2.46074 1.42071i −0.231487 0.133649i 0.379771 0.925081i \(-0.376003\pi\)
−0.611258 + 0.791431i \(0.709336\pi\)
\(114\) 0 0
\(115\) 0.842229 3.14324i 0.0785383 0.293109i
\(116\) 0 0
\(117\) −6.13788 + 8.90654i −0.567447 + 0.823410i
\(118\) 0 0
\(119\) 0.647772 2.41752i 0.0593811 0.221613i
\(120\) 0 0
\(121\) 14.6766 + 8.47354i 1.33424 + 0.770322i
\(122\) 0 0
\(123\) 5.97057 + 5.86644i 0.538348 + 0.528959i
\(124\) 0 0
\(125\) 4.55793 4.55793i 0.407674 0.407674i
\(126\) 0 0
\(127\) −17.1930 + 9.92638i −1.52563 + 0.880823i −0.526093 + 0.850427i \(0.676344\pi\)
−0.999538 + 0.0303965i \(0.990323\pi\)
\(128\) 0 0
\(129\) 18.8987 11.1340i 1.66394 0.980291i
\(130\) 0 0
\(131\) 5.89464i 0.515017i 0.966276 + 0.257509i \(0.0829016\pi\)
−0.966276 + 0.257509i \(0.917098\pi\)
\(132\) 0 0
\(133\) −2.25471 3.90527i −0.195508 0.338629i
\(134\) 0 0
\(135\) 2.54619 + 2.41522i 0.219141 + 0.207869i
\(136\) 0 0
\(137\) −2.47941 9.25328i −0.211830 0.790561i −0.987258 0.159125i \(-0.949133\pi\)
0.775428 0.631436i \(-0.217534\pi\)
\(138\) 0 0
\(139\) −1.60178 + 2.77436i −0.135861 + 0.235318i −0.925926 0.377705i \(-0.876713\pi\)
0.790065 + 0.613023i \(0.210047\pi\)
\(140\) 0 0
\(141\) 0.423091 + 1.52520i 0.0356307 + 0.128445i
\(142\) 0 0
\(143\) 3.11953 + 18.8037i 0.260868 + 1.57245i
\(144\) 0 0
\(145\) −2.43422 0.652249i −0.202151 0.0541663i
\(146\) 0 0
\(147\) −0.0906965 10.3097i −0.00748052 0.850334i
\(148\) 0 0
\(149\) 19.0182 5.09591i 1.55803 0.417474i 0.625993 0.779829i \(-0.284694\pi\)
0.932040 + 0.362355i \(0.118027\pi\)
\(150\) 0 0
\(151\) 13.0832 + 13.0832i 1.06470 + 1.06470i 0.997757 + 0.0669402i \(0.0213237\pi\)
0.0669402 + 0.997757i \(0.478676\pi\)
\(152\) 0 0
\(153\) 7.33528 0.129069i 0.593022 0.0104346i
\(154\) 0 0
\(155\) 2.78348 0.223574
\(156\) 0 0
\(157\) −0.0824533 −0.00658049 −0.00329025 0.999995i \(-0.501047\pi\)
−0.00329025 + 0.999995i \(0.501047\pi\)
\(158\) 0 0
\(159\) −9.90176 5.60123i −0.785261 0.444206i
\(160\) 0 0
\(161\) 3.48676 + 3.48676i 0.274795 + 0.274795i
\(162\) 0 0
\(163\) −22.9940 + 6.16123i −1.80103 + 0.482585i −0.994139 0.108112i \(-0.965520\pi\)
−0.806893 + 0.590697i \(0.798853\pi\)
\(164\) 0 0
\(165\) 6.18403 0.0544019i 0.481426 0.00423519i
\(166\) 0 0
\(167\) −21.8268 5.84848i −1.68901 0.452569i −0.718876 0.695138i \(-0.755343\pi\)
−0.970134 + 0.242569i \(0.922010\pi\)
\(168\) 0 0
\(169\) −8.55629 + 9.78723i −0.658176 + 0.752864i
\(170\) 0 0
\(171\) 9.18092 9.50979i 0.702082 0.727232i
\(172\) 0 0
\(173\) −10.6401 + 18.4292i −0.808954 + 1.40115i 0.104635 + 0.994511i \(0.466633\pi\)
−0.913589 + 0.406639i \(0.866701\pi\)
\(174\) 0 0
\(175\) 1.20360 + 4.49190i 0.0909836 + 0.339555i
\(176\) 0 0
\(177\) 14.3762 + 3.71686i 1.08058 + 0.279377i
\(178\) 0 0
\(179\) 5.21779 + 9.03748i 0.389996 + 0.675493i 0.992449 0.122662i \(-0.0391431\pi\)
−0.602453 + 0.798155i \(0.705810\pi\)
\(180\) 0 0
\(181\) 15.3678i 1.14228i −0.820852 0.571141i \(-0.806501\pi\)
0.820852 0.571141i \(-0.193499\pi\)
\(182\) 0 0
\(183\) −7.02612 11.9261i −0.519386 0.881601i
\(184\) 0 0
\(185\) −2.03123 + 1.17273i −0.149339 + 0.0862210i
\(186\) 0 0
\(187\) 9.14146 9.14146i 0.668490 0.668490i
\(188\) 0 0
\(189\) −5.09865 + 1.51146i −0.370872 + 0.109942i
\(190\) 0 0
\(191\) 17.1586 + 9.90652i 1.24155 + 0.716810i 0.969410 0.245447i \(-0.0789347\pi\)
0.272142 + 0.962257i \(0.412268\pi\)
\(192\) 0 0
\(193\) 5.30664 19.8047i 0.381980 1.42557i −0.460892 0.887456i \(-0.652470\pi\)
0.842872 0.538114i \(-0.180863\pi\)
\(194\) 0 0
\(195\) 2.70687 + 3.23468i 0.193843 + 0.231640i
\(196\) 0 0
\(197\) 4.65798 17.3838i 0.331868 1.23855i −0.575358 0.817902i \(-0.695137\pi\)
0.907225 0.420645i \(-0.138196\pi\)
\(198\) 0 0
\(199\) 15.7149 + 9.07301i 1.11400 + 0.643169i 0.939863 0.341553i \(-0.110953\pi\)
0.174138 + 0.984721i \(0.444286\pi\)
\(200\) 0 0
\(201\) 4.45535 4.53443i 0.314256 0.319834i
\(202\) 0 0
\(203\) 2.70026 2.70026i 0.189521 0.189521i
\(204\) 0 0
\(205\) 2.82666 1.63197i 0.197423 0.113982i
\(206\) 0 0
\(207\) −7.00578 + 12.6430i −0.486935 + 0.878746i
\(208\) 0 0
\(209\) 23.2930i 1.61121i
\(210\) 0 0
\(211\) −10.5719 18.3111i −0.727801 1.26059i −0.957811 0.287400i \(-0.907209\pi\)
0.230009 0.973188i \(-0.426124\pi\)
\(212\) 0 0
\(213\) −2.39929 + 9.28005i −0.164396 + 0.635858i
\(214\) 0 0
\(215\) −2.21373 8.26175i −0.150975 0.563447i
\(216\) 0 0
\(217\) −2.10893 + 3.65277i −0.143163 + 0.247966i
\(218\) 0 0
\(219\) 0.531276 0.147376i 0.0359003 0.00995876i
\(220\) 0 0
\(221\) 8.77548 + 0.857423i 0.590303 + 0.0576765i
\(222\) 0 0
\(223\) −0.931275 0.249534i −0.0623628 0.0167101i 0.227503 0.973777i \(-0.426944\pi\)
−0.289866 + 0.957067i \(0.593611\pi\)
\(224\) 0 0
\(225\) −11.6835 + 7.02239i −0.778900 + 0.468159i
\(226\) 0 0
\(227\) 9.18679 2.46159i 0.609749 0.163382i 0.0592855 0.998241i \(-0.481118\pi\)
0.550463 + 0.834859i \(0.314451\pi\)
\(228\) 0 0
\(229\) −11.7646 11.7646i −0.777428 0.777428i 0.201965 0.979393i \(-0.435267\pi\)
−0.979393 + 0.201965i \(0.935267\pi\)
\(230\) 0 0
\(231\) −4.61399 + 8.15654i −0.303578 + 0.536661i
\(232\) 0 0
\(233\) −18.2304 −1.19431 −0.597156 0.802125i \(-0.703703\pi\)
−0.597156 + 0.802125i \(0.703703\pi\)
\(234\) 0 0
\(235\) 0.617197 0.0402615
\(236\) 0 0
\(237\) −2.30621 + 4.07687i −0.149804 + 0.264821i
\(238\) 0 0
\(239\) −1.82483 1.82483i −0.118039 0.118039i 0.645620 0.763659i \(-0.276599\pi\)
−0.763659 + 0.645620i \(0.776599\pi\)
\(240\) 0 0
\(241\) 3.81149 1.02128i 0.245519 0.0657867i −0.133961 0.990987i \(-0.542770\pi\)
0.379480 + 0.925200i \(0.376103\pi\)
\(242\) 0 0
\(243\) −8.38029 13.1442i −0.537596 0.843203i
\(244\) 0 0
\(245\) −3.88336 1.04054i −0.248099 0.0664779i
\(246\) 0 0
\(247\) 12.2726 10.0878i 0.780887 0.641874i
\(248\) 0 0
\(249\) −17.4934 + 4.85269i −1.10860 + 0.307526i
\(250\) 0 0
\(251\) 9.23209 15.9904i 0.582724 1.00931i −0.412431 0.910989i \(-0.635320\pi\)
0.995155 0.0983191i \(-0.0313466\pi\)
\(252\) 0 0
\(253\) 6.59233 + 24.6029i 0.414456 + 1.54677i
\(254\) 0 0
\(255\) 0.716085 2.76970i 0.0448430 0.173445i
\(256\) 0 0
\(257\) 7.69399 + 13.3264i 0.479938 + 0.831276i 0.999735 0.0230131i \(-0.00732594\pi\)
−0.519798 + 0.854290i \(0.673993\pi\)
\(258\) 0 0
\(259\) 3.55412i 0.220842i
\(260\) 0 0
\(261\) 9.79110 + 5.42550i 0.606054 + 0.335830i
\(262\) 0 0
\(263\) −5.28088 + 3.04892i −0.325633 + 0.188004i −0.653901 0.756580i \(-0.726869\pi\)
0.328268 + 0.944585i \(0.393535\pi\)
\(264\) 0 0
\(265\) −3.13677 + 3.13677i −0.192690 + 0.192690i
\(266\) 0 0
\(267\) 12.6150 12.8389i 0.772024 0.785728i
\(268\) 0 0
\(269\) −25.7884 14.8889i −1.57234 0.907793i −0.995881 0.0906696i \(-0.971099\pi\)
−0.576463 0.817123i \(-0.695567\pi\)
\(270\) 0 0
\(271\) 3.63143 13.5527i 0.220593 0.823266i −0.763529 0.645774i \(-0.776535\pi\)
0.984122 0.177492i \(-0.0567984\pi\)
\(272\) 0 0
\(273\) −6.29577 + 1.10146i −0.381037 + 0.0666631i
\(274\) 0 0
\(275\) −6.21709 + 23.2025i −0.374905 + 1.39916i
\(276\) 0 0
\(277\) 14.7600 + 8.52167i 0.886840 + 0.512017i 0.872908 0.487886i \(-0.162232\pi\)
0.0139325 + 0.999903i \(0.495565\pi\)
\(278\) 0 0
\(279\) −11.9969 2.98937i −0.718235 0.178969i
\(280\) 0 0
\(281\) 4.61708 4.61708i 0.275432 0.275432i −0.555851 0.831282i \(-0.687607\pi\)
0.831282 + 0.555851i \(0.187607\pi\)
\(282\) 0 0
\(283\) −10.4471 + 6.03162i −0.621014 + 0.358542i −0.777264 0.629175i \(-0.783393\pi\)
0.156250 + 0.987718i \(0.450059\pi\)
\(284\) 0 0
\(285\) −2.61636 4.44099i −0.154980 0.263061i
\(286\) 0 0
\(287\) 4.94591i 0.291948i
\(288\) 0 0
\(289\) 5.50984 + 9.54332i 0.324108 + 0.561372i
\(290\) 0 0
\(291\) 16.6531 + 4.30554i 0.976224 + 0.252396i
\(292\) 0 0
\(293\) 2.06466 + 7.70541i 0.120619 + 0.450155i 0.999646 0.0266171i \(-0.00847349\pi\)
−0.879027 + 0.476772i \(0.841807\pi\)
\(294\) 0 0
\(295\) 2.89510 5.01447i 0.168560 0.291954i
\(296\) 0 0
\(297\) −26.7118 6.40698i −1.54998 0.371771i
\(298\) 0 0
\(299\) −10.1077 + 14.1285i −0.584545 + 0.817073i
\(300\) 0 0
\(301\) 12.5192 + 3.35450i 0.721593 + 0.193350i
\(302\) 0 0
\(303\) −28.8980 + 0.254220i −1.66015 + 0.0146046i
\(304\) 0 0
\(305\) −5.21360 + 1.39698i −0.298530 + 0.0799909i
\(306\) 0 0
\(307\) 2.20646 + 2.20646i 0.125929 + 0.125929i 0.767262 0.641333i \(-0.221618\pi\)
−0.641333 + 0.767262i \(0.721618\pi\)
\(308\) 0 0
\(309\) −6.23528 3.52717i −0.354713 0.200654i
\(310\) 0 0
\(311\) −1.32763 −0.0752831 −0.0376416 0.999291i \(-0.511985\pi\)
−0.0376416 + 0.999291i \(0.511985\pi\)
\(312\) 0 0
\(313\) 16.9933 0.960519 0.480260 0.877126i \(-0.340542\pi\)
0.480260 + 0.877126i \(0.340542\pi\)
\(314\) 0 0
\(315\) 0.0364824 + 2.07337i 0.00205555 + 0.116821i
\(316\) 0 0
\(317\) −18.5898 18.5898i −1.04410 1.04410i −0.998981 0.0451236i \(-0.985632\pi\)
−0.0451236 0.998981i \(-0.514368\pi\)
\(318\) 0 0
\(319\) 19.0533 5.10530i 1.06678 0.285842i
\(320\) 0 0
\(321\) 0.0629185 + 7.15213i 0.00351177 + 0.399193i
\(322\) 0 0
\(323\) −10.4079 2.78879i −0.579111 0.155172i
\(324\) 0 0
\(325\) −14.9175 + 6.77299i −0.827472 + 0.375698i
\(326\) 0 0
\(327\) −7.38872 26.6356i −0.408597 1.47295i
\(328\) 0 0
\(329\) −0.467625 + 0.809950i −0.0257810 + 0.0446540i
\(330\) 0 0
\(331\) −2.77794 10.3674i −0.152690 0.569845i −0.999292 0.0376195i \(-0.988023\pi\)
0.846603 0.532226i \(-0.178644\pi\)
\(332\) 0 0
\(333\) 10.0142 2.87304i 0.548772 0.157441i
\(334\) 0 0
\(335\) −1.23943 2.14675i −0.0677170 0.117289i
\(336\) 0 0
\(337\) 2.17912i 0.118704i −0.998237 0.0593522i \(-0.981097\pi\)
0.998237 0.0593522i \(-0.0189035\pi\)
\(338\) 0 0
\(339\) 4.24032 2.49814i 0.230303 0.135680i
\(340\) 0 0
\(341\) −18.8681 + 10.8935i −1.02176 + 0.589915i
\(342\) 0 0
\(343\) 9.37355 9.37355i 0.506124 0.506124i
\(344\) 0 0
\(345\) 4.02038 + 3.95026i 0.216450 + 0.212675i
\(346\) 0 0
\(347\) −24.6713 14.2440i −1.32443 0.764657i −0.339994 0.940428i \(-0.610425\pi\)
−0.984431 + 0.175770i \(0.943758\pi\)
\(348\) 0 0
\(349\) 8.27424 30.8799i 0.442910 1.65296i −0.278486 0.960440i \(-0.589833\pi\)
0.721396 0.692522i \(-0.243501\pi\)
\(350\) 0 0
\(351\) −8.19278 16.8487i −0.437298 0.899317i
\(352\) 0 0
\(353\) −1.25756 + 4.69329i −0.0669333 + 0.249799i −0.991283 0.131747i \(-0.957941\pi\)
0.924350 + 0.381545i \(0.124608\pi\)
\(354\) 0 0
\(355\) 3.23691 + 1.86883i 0.171797 + 0.0991872i
\(356\) 0 0
\(357\) 3.09213 + 3.03820i 0.163653 + 0.160799i
\(358\) 0 0
\(359\) 23.0189 23.0189i 1.21489 1.21489i 0.245491 0.969399i \(-0.421051\pi\)
0.969399 0.245491i \(-0.0789492\pi\)
\(360\) 0 0
\(361\) −0.358474 + 0.206965i −0.0188671 + 0.0108929i
\(362\) 0 0
\(363\) −25.2905 + 14.8997i −1.32741 + 0.782029i
\(364\) 0 0
\(365\) 0.214990i 0.0112531i
\(366\) 0 0
\(367\) 3.89669 + 6.74926i 0.203405 + 0.352308i 0.949623 0.313393i \(-0.101466\pi\)
−0.746218 + 0.665702i \(0.768132\pi\)
\(368\) 0 0
\(369\) −13.9357 + 3.99812i −0.725463 + 0.208134i
\(370\) 0 0
\(371\) −1.73979 6.49299i −0.0903255 0.337099i
\(372\) 0 0
\(373\) −2.55768 + 4.43003i −0.132432 + 0.229378i −0.924613 0.380907i \(-0.875612\pi\)
0.792182 + 0.610285i \(0.208945\pi\)
\(374\) 0 0
\(375\) 2.98437 + 10.7583i 0.154112 + 0.555559i
\(376\) 0 0
\(377\) 10.9416 + 7.82774i 0.563519 + 0.403149i
\(378\) 0 0
\(379\) 20.9755 + 5.62036i 1.07744 + 0.288699i 0.753546 0.657395i \(-0.228342\pi\)
0.323892 + 0.946094i \(0.395008\pi\)
\(380\) 0 0
\(381\) −0.302487 34.3846i −0.0154969 1.76158i
\(382\) 0 0
\(383\) −17.1403 + 4.59273i −0.875828 + 0.234677i −0.668606 0.743617i \(-0.733109\pi\)
−0.207222 + 0.978294i \(0.566442\pi\)
\(384\) 0 0
\(385\) 2.58390 + 2.58390i 0.131688 + 0.131688i
\(386\) 0 0
\(387\) 0.668388 + 37.9859i 0.0339761 + 1.93093i
\(388\) 0 0
\(389\) −22.4460 −1.13806 −0.569028 0.822318i \(-0.692680\pi\)
−0.569028 + 0.822318i \(0.692680\pi\)
\(390\) 0 0
\(391\) 11.7825 0.595866
\(392\) 0 0
\(393\) −8.88653 5.02693i −0.448266 0.253575i
\(394\) 0 0
\(395\) 1.29151 + 1.29151i 0.0649828 + 0.0649828i
\(396\) 0 0
\(397\) 7.62283 2.04253i 0.382579 0.102512i −0.0624036 0.998051i \(-0.519877\pi\)
0.444982 + 0.895539i \(0.353210\pi\)
\(398\) 0 0
\(399\) 7.81023 0.0687078i 0.391001 0.00343969i
\(400\) 0 0
\(401\) 11.4464 + 3.06705i 0.571605 + 0.153161i 0.533033 0.846095i \(-0.321052\pi\)
0.0385726 + 0.999256i \(0.487719\pi\)
\(402\) 0 0
\(403\) −13.9110 5.22340i −0.692957 0.260196i
\(404\) 0 0
\(405\) −5.81248 + 1.77884i −0.288824 + 0.0883913i
\(406\) 0 0
\(407\) 9.17925 15.8989i 0.454999 0.788081i
\(408\) 0 0
\(409\) −2.09514 7.81915i −0.103598 0.386632i 0.894585 0.446899i \(-0.147472\pi\)
−0.998182 + 0.0602665i \(0.980805\pi\)
\(410\) 0 0
\(411\) 16.0643 + 4.15331i 0.792394 + 0.204868i
\(412\) 0 0
\(413\) 4.38700 + 7.59851i 0.215870 + 0.373898i
\(414\) 0 0
\(415\) 7.07901i 0.347495i
\(416\) 0 0
\(417\) −2.81653 4.78074i −0.137926 0.234114i
\(418\) 0 0
\(419\) −19.6793 + 11.3619i −0.961398 + 0.555064i −0.896603 0.442835i \(-0.853973\pi\)
−0.0647951 + 0.997899i \(0.520639\pi\)
\(420\) 0 0
\(421\) 24.6721 24.6721i 1.20244 1.20244i 0.229023 0.973421i \(-0.426447\pi\)
0.973421 0.229023i \(-0.0735532\pi\)
\(422\) 0 0
\(423\) −2.66014 0.662851i −0.129341 0.0322289i
\(424\) 0 0
\(425\) 9.62312 + 5.55591i 0.466790 + 0.269501i
\(426\) 0 0
\(427\) 2.11687 7.90026i 0.102442 0.382320i
\(428\) 0 0
\(429\) −31.0081 11.3329i −1.49708 0.547157i
\(430\) 0 0
\(431\) 0.538030 2.00795i 0.0259160 0.0967198i −0.951756 0.306854i \(-0.900724\pi\)
0.977672 + 0.210135i \(0.0673902\pi\)
\(432\) 0 0
\(433\) −12.6016 7.27553i −0.605593 0.349639i 0.165645 0.986185i \(-0.447029\pi\)
−0.771239 + 0.636546i \(0.780363\pi\)
\(434\) 0 0
\(435\) 3.05920 3.11351i 0.146678 0.149281i
\(436\) 0 0
\(437\) 15.0112 15.0112i 0.718084 0.718084i
\(438\) 0 0
\(439\) 3.37300 1.94740i 0.160984 0.0929444i −0.417343 0.908749i \(-0.637039\pi\)
0.578328 + 0.815804i \(0.303705\pi\)
\(440\) 0 0
\(441\) 15.6199 + 8.65539i 0.743805 + 0.412161i
\(442\) 0 0
\(443\) 36.8108i 1.74894i −0.485084 0.874468i \(-0.661211\pi\)
0.485084 0.874468i \(-0.338789\pi\)
\(444\) 0 0
\(445\) −3.50934 6.07835i −0.166358 0.288141i
\(446\) 0 0
\(447\) −8.53627 + 33.0169i −0.403752 + 1.56164i
\(448\) 0 0
\(449\) 0.879334 + 3.28172i 0.0414983 + 0.154874i 0.983566 0.180549i \(-0.0577874\pi\)
−0.942068 + 0.335423i \(0.891121\pi\)
\(450\) 0 0
\(451\) −12.7738 + 22.1249i −0.601496 + 1.04182i
\(452\) 0 0
\(453\) −30.8811 + 8.56641i −1.45092 + 0.402485i
\(454\) 0 0
\(455\) −0.242357 + 2.48046i −0.0113619 + 0.116286i
\(456\) 0 0
\(457\) 1.41752 + 0.379824i 0.0663090 + 0.0177674i 0.291821 0.956473i \(-0.405739\pi\)
−0.225512 + 0.974240i \(0.572406\pi\)
\(458\) 0 0
\(459\) −6.06092 + 11.1684i −0.282899 + 0.521298i
\(460\) 0 0
\(461\) 22.1924 5.94644i 1.03360 0.276953i 0.298144 0.954521i \(-0.403633\pi\)
0.735460 + 0.677568i \(0.236966\pi\)
\(462\) 0 0
\(463\) −5.38119 5.38119i −0.250085 0.250085i 0.570920 0.821006i \(-0.306587\pi\)
−0.821006 + 0.570920i \(0.806587\pi\)
\(464\) 0 0
\(465\) −2.37374 + 4.19626i −0.110080 + 0.194597i
\(466\) 0 0
\(467\) 2.33847 0.108211 0.0541057 0.998535i \(-0.482769\pi\)
0.0541057 + 0.998535i \(0.482769\pi\)
\(468\) 0 0
\(469\) 3.75624 0.173447
\(470\) 0 0
\(471\) 0.0703159 0.124303i 0.00323999 0.00572760i
\(472\) 0 0
\(473\) 47.3393 + 47.3393i 2.17666 + 2.17666i
\(474\) 0 0
\(475\) 19.3385 5.18174i 0.887312 0.237755i
\(476\) 0 0
\(477\) 16.8884 10.1508i 0.773266 0.464773i
\(478\) 0 0
\(479\) 1.53047 + 0.410089i 0.0699292 + 0.0187375i 0.293614 0.955924i \(-0.405142\pi\)
−0.223685 + 0.974662i \(0.571809\pi\)
\(480\) 0 0
\(481\) 12.3522 2.04922i 0.563213 0.0934366i
\(482\) 0 0
\(483\) −8.23001 + 2.28301i −0.374478 + 0.103880i
\(484\) 0 0
\(485\) 3.35363 5.80866i 0.152281 0.263758i
\(486\) 0 0
\(487\) 8.73299 + 32.5920i 0.395730 + 1.47688i 0.820534 + 0.571598i \(0.193676\pi\)
−0.424804 + 0.905285i \(0.639657\pi\)
\(488\) 0 0
\(489\) 10.3208 39.9192i 0.466723 1.80521i
\(490\) 0 0
\(491\) −3.16125 5.47545i −0.142665 0.247104i 0.785834 0.618437i \(-0.212234\pi\)
−0.928499 + 0.371334i \(0.878901\pi\)
\(492\) 0 0
\(493\) 9.12472i 0.410957i
\(494\) 0 0
\(495\) −5.19171 + 9.36920i −0.233350 + 0.421114i
\(496\) 0 0
\(497\) −4.90494 + 2.83187i −0.220017 + 0.127027i
\(498\) 0 0
\(499\) −10.0492 + 10.0492i −0.449864 + 0.449864i −0.895309 0.445445i \(-0.853045\pi\)
0.445445 + 0.895309i \(0.353045\pi\)
\(500\) 0 0
\(501\) 27.4308 27.9177i 1.22552 1.24727i
\(502\) 0 0
\(503\) 22.7387 + 13.1282i 1.01387 + 0.585358i 0.912322 0.409473i \(-0.134287\pi\)
0.101547 + 0.994831i \(0.467621\pi\)
\(504\) 0 0
\(505\) −2.91662 + 10.8850i −0.129788 + 0.484375i
\(506\) 0 0
\(507\) −7.45806 21.2456i −0.331224 0.943552i
\(508\) 0 0
\(509\) 0.773870 2.88812i 0.0343012 0.128014i −0.946652 0.322257i \(-0.895558\pi\)
0.980953 + 0.194243i \(0.0622251\pi\)
\(510\) 0 0
\(511\) 0.282132 + 0.162889i 0.0124808 + 0.00720577i
\(512\) 0 0
\(513\) 6.50713 + 21.9507i 0.287297 + 0.969147i
\(514\) 0 0
\(515\) −1.97527 + 1.97527i −0.0870407 + 0.0870407i
\(516\) 0 0
\(517\) −4.18372 + 2.41547i −0.184000 + 0.106232i
\(518\) 0 0
\(519\) −18.7093 31.7570i −0.821248 1.39398i
\(520\) 0 0
\(521\) 27.3243i 1.19710i −0.801086 0.598549i \(-0.795744\pi\)
0.801086 0.598549i \(-0.204256\pi\)
\(522\) 0 0
\(523\) −12.3901 21.4602i −0.541780 0.938391i −0.998802 0.0489353i \(-0.984417\pi\)
0.457022 0.889456i \(-0.348916\pi\)
\(524\) 0 0
\(525\) −7.79823 2.01617i −0.340343 0.0879931i
\(526\) 0 0
\(527\) 2.60848 + 9.73497i 0.113627 + 0.424062i
\(528\) 0 0
\(529\) −0.106962 + 0.185264i −0.00465052 + 0.00805495i
\(530\) 0 0
\(531\) −17.8634 + 18.5033i −0.775205 + 0.802974i
\(532\) 0 0
\(533\) −17.1893 + 2.85170i −0.744553 + 0.123521i
\(534\) 0 0
\(535\) 2.69399 + 0.721852i 0.116471 + 0.0312084i
\(536\) 0 0
\(537\) −18.0743 + 0.159002i −0.779962 + 0.00686145i
\(538\) 0 0
\(539\) 30.3960 8.14458i 1.30925 0.350812i
\(540\) 0 0
\(541\) 24.7719 + 24.7719i 1.06503 + 1.06503i 0.997733 + 0.0672936i \(0.0214364\pi\)
0.0672936 + 0.997733i \(0.478564\pi\)
\(542\) 0 0
\(543\) 23.1679 + 13.1056i 0.994231 + 0.562417i
\(544\) 0 0
\(545\) −10.7785 −0.461701
\(546\) 0 0
\(547\) −1.08492 −0.0463880 −0.0231940 0.999731i \(-0.507384\pi\)
−0.0231940 + 0.999731i \(0.507384\pi\)
\(548\) 0 0
\(549\) 23.9711 0.421788i 1.02306 0.0180015i
\(550\) 0 0
\(551\) −11.6252 11.6252i −0.495248 0.495248i
\(552\) 0 0
\(553\) −2.67337 + 0.716328i −0.113683 + 0.0304614i
\(554\) 0 0
\(555\) −0.0357368 4.06231i −0.00151694 0.172435i
\(556\) 0 0
\(557\) 41.5314 + 11.1283i 1.75974 + 0.471521i 0.986661 0.162787i \(-0.0520484\pi\)
0.773080 + 0.634308i \(0.218715\pi\)
\(558\) 0 0
\(559\) −4.44019 + 45.4440i −0.187800 + 1.92208i
\(560\) 0 0
\(561\) 5.98550 + 21.5771i 0.252708 + 0.910986i
\(562\) 0 0
\(563\) 6.04323 10.4672i 0.254692 0.441139i −0.710120 0.704081i \(-0.751359\pi\)
0.964812 + 0.262941i \(0.0846926\pi\)
\(564\) 0 0
\(565\) −0.496697 1.85370i −0.0208962 0.0779857i
\(566\) 0 0
\(567\) 2.06950 8.97548i 0.0869106 0.376935i
\(568\) 0 0
\(569\) 20.9215 + 36.2370i 0.877073 + 1.51914i 0.854538 + 0.519389i \(0.173841\pi\)
0.0225354 + 0.999746i \(0.492826\pi\)
\(570\) 0 0
\(571\) 12.0755i 0.505343i 0.967552 + 0.252671i \(0.0813092\pi\)
−0.967552 + 0.252671i \(0.918691\pi\)
\(572\) 0 0
\(573\) −29.5675 + 17.4194i −1.23520 + 0.727704i
\(574\) 0 0
\(575\) −18.9595 + 10.9463i −0.790667 + 0.456492i
\(576\) 0 0
\(577\) −17.6869 + 17.6869i −0.736314 + 0.736314i −0.971863 0.235548i \(-0.924311\pi\)
0.235548 + 0.971863i \(0.424311\pi\)
\(578\) 0 0
\(579\) 25.3312 + 24.8894i 1.05273 + 1.03437i
\(580\) 0 0
\(581\) −9.28980 5.36347i −0.385406 0.222514i
\(582\) 0 0
\(583\) 8.98674 33.5390i 0.372193 1.38904i
\(584\) 0 0
\(585\) −7.18489 + 1.32225i −0.297059 + 0.0546683i
\(586\) 0 0
\(587\) −9.99047 + 37.2849i −0.412351 + 1.53891i 0.377732 + 0.925915i \(0.376704\pi\)
−0.790083 + 0.612999i \(0.789963\pi\)
\(588\) 0 0
\(589\) 15.7259 + 9.07936i 0.647975 + 0.374108i
\(590\) 0 0
\(591\) 22.2349 + 21.8471i 0.914620 + 0.898668i
\(592\) 0 0
\(593\) −18.9343 + 18.9343i −0.777538 + 0.777538i −0.979412 0.201874i \(-0.935297\pi\)
0.201874 + 0.979412i \(0.435297\pi\)
\(594\) 0 0
\(595\) 1.46392 0.845192i 0.0600147 0.0346495i
\(596\) 0 0
\(597\) −27.0797 + 15.9537i −1.10830 + 0.652944i
\(598\) 0 0
\(599\) 7.02037i 0.286845i −0.989662 0.143422i \(-0.954189\pi\)
0.989662 0.143422i \(-0.0458107\pi\)
\(600\) 0 0
\(601\) −16.1442 27.9626i −0.658536 1.14062i −0.980995 0.194034i \(-0.937843\pi\)
0.322459 0.946583i \(-0.395491\pi\)
\(602\) 0 0
\(603\) 3.03643 + 10.5837i 0.123653 + 0.431000i
\(604\) 0 0
\(605\) 2.96245 + 11.0560i 0.120441 + 0.449491i
\(606\) 0 0
\(607\) 8.03959 13.9250i 0.326317 0.565197i −0.655461 0.755229i \(-0.727526\pi\)
0.981778 + 0.190032i \(0.0608590\pi\)
\(608\) 0 0
\(609\) 1.76803 + 6.37357i 0.0716442 + 0.258270i
\(610\) 0 0
\(611\) −3.08457 1.15821i −0.124788 0.0468564i
\(612\) 0 0
\(613\) −5.01679 1.34425i −0.202626 0.0542936i 0.156078 0.987745i \(-0.450115\pi\)
−0.358705 + 0.933451i \(0.616781\pi\)
\(614\) 0 0
\(615\) 0.0497312 + 5.65310i 0.00200536 + 0.227955i
\(616\) 0 0
\(617\) −21.5594 + 5.77683i −0.867950 + 0.232567i −0.665201 0.746664i \(-0.731654\pi\)
−0.202749 + 0.979231i \(0.564988\pi\)
\(618\) 0 0
\(619\) −7.41621 7.41621i −0.298083 0.298083i 0.542180 0.840262i \(-0.317599\pi\)
−0.840262 + 0.542180i \(0.817599\pi\)
\(620\) 0 0
\(621\) −13.0855 21.3435i −0.525103 0.856486i
\(622\) 0 0
\(623\) 10.6355 0.426103
\(624\) 0 0
\(625\) −18.3656 −0.734626
\(626\) 0 0
\(627\) 35.1156 + 19.8642i 1.40238 + 0.793299i
\(628\) 0 0
\(629\) −6.00505 6.00505i −0.239437 0.239437i
\(630\) 0 0
\(631\) −21.0236 + 5.63326i −0.836937 + 0.224257i −0.651738 0.758444i \(-0.725960\pi\)
−0.185199 + 0.982701i \(0.559293\pi\)
\(632\) 0 0
\(633\) 36.6208 0.322159i 1.45555 0.0128047i
\(634\) 0 0
\(635\) −12.9516 3.47038i −0.513970 0.137718i
\(636\) 0 0
\(637\) 17.4553 + 12.4877i 0.691603 + 0.494782i
\(638\) 0 0
\(639\) −11.9441 11.5311i −0.472502 0.456162i
\(640\) 0 0
\(641\) −1.60308 + 2.77662i −0.0633179 + 0.109670i −0.895947 0.444162i \(-0.853502\pi\)
0.832629 + 0.553832i \(0.186835\pi\)
\(642\) 0 0
\(643\) −4.14972 15.4870i −0.163649 0.610746i −0.998209 0.0598284i \(-0.980945\pi\)
0.834560 0.550917i \(-0.185722\pi\)
\(644\) 0 0
\(645\) 14.3429 + 3.70826i 0.564753 + 0.146013i
\(646\) 0 0
\(647\) −3.12295 5.40911i −0.122776 0.212654i 0.798085 0.602544i \(-0.205846\pi\)
−0.920861 + 0.389890i \(0.872513\pi\)
\(648\) 0 0
\(649\) 45.3213i 1.77902i
\(650\) 0 0
\(651\) −3.70828 6.29440i −0.145339 0.246697i
\(652\) 0 0
\(653\) −4.17845 + 2.41243i −0.163515 + 0.0944057i −0.579525 0.814955i \(-0.696762\pi\)
0.416009 + 0.909360i \(0.363428\pi\)
\(654\) 0 0
\(655\) −2.81515 + 2.81515i −0.109997 + 0.109997i
\(656\) 0 0
\(657\) −0.230892 + 0.926613i −0.00900796 + 0.0361506i
\(658\) 0 0
\(659\) 32.5080 + 18.7685i 1.26633 + 0.731118i 0.974292 0.225288i \(-0.0723324\pi\)
0.292041 + 0.956406i \(0.405666\pi\)
\(660\) 0 0
\(661\) −3.47617 + 12.9732i −0.135207 + 0.504600i 0.864790 + 0.502134i \(0.167452\pi\)
−0.999997 + 0.00246616i \(0.999215\pi\)
\(662\) 0 0
\(663\) −8.77632 + 12.4984i −0.340844 + 0.485396i
\(664\) 0 0
\(665\) 0.788272 2.94187i 0.0305679 0.114081i
\(666\) 0 0
\(667\) 15.5690 + 8.98879i 0.602836 + 0.348047i
\(668\) 0 0
\(669\) 1.17038 1.19115i 0.0452494 0.0460526i
\(670\) 0 0
\(671\) 29.8736 29.8736i 1.15326 1.15326i
\(672\) 0 0
\(673\) −33.3998 + 19.2834i −1.28747 + 0.743320i −0.978202 0.207656i \(-0.933417\pi\)
−0.309266 + 0.950976i \(0.600083\pi\)
\(674\) 0 0
\(675\) −0.623027 23.6023i −0.0239803 0.908451i
\(676\) 0 0
\(677\) 20.6740i 0.794568i −0.917696 0.397284i \(-0.869953\pi\)
0.917696 0.397284i \(-0.130047\pi\)
\(678\) 0 0
\(679\) 5.08182 + 8.80197i 0.195022 + 0.337788i
\(680\) 0 0
\(681\) −4.12346 + 15.9489i −0.158012 + 0.611162i
\(682\) 0 0
\(683\) 5.94896 + 22.2018i 0.227631 + 0.849529i 0.981333 + 0.192314i \(0.0615992\pi\)
−0.753703 + 0.657215i \(0.771734\pi\)
\(684\) 0 0
\(685\) 3.23505 5.60328i 0.123605 0.214090i
\(686\) 0 0
\(687\) 27.7687 7.70304i 1.05944 0.293889i
\(688\) 0 0
\(689\) 21.5630 9.79029i 0.821486 0.372980i
\(690\) 0 0
\(691\) 13.1628 + 3.52697i 0.500738 + 0.134172i 0.500342 0.865828i \(-0.333208\pi\)
0.000395273 1.00000i \(0.499874\pi\)
\(692\) 0 0
\(693\) −8.36168 13.9117i −0.317634 0.528463i
\(694\) 0 0
\(695\) −2.08995 + 0.560001i −0.0792763 + 0.0212420i
\(696\) 0 0
\(697\) 8.35662 + 8.35662i 0.316530 + 0.316530i
\(698\) 0 0
\(699\) 15.5468 27.4834i 0.588035 1.03952i
\(700\) 0 0
\(701\) −46.1778 −1.74411 −0.872055 0.489408i \(-0.837213\pi\)
−0.872055 + 0.489408i \(0.837213\pi\)
\(702\) 0 0
\(703\) −15.3012 −0.577096
\(704\) 0 0
\(705\) −0.526344 + 0.930462i −0.0198233 + 0.0350432i
\(706\) 0 0
\(707\) −12.0746 12.0746i −0.454111 0.454111i
\(708\) 0 0
\(709\) −33.9442 + 9.09532i −1.27480 + 0.341582i −0.831868 0.554973i \(-0.812728\pi\)
−0.442932 + 0.896555i \(0.646062\pi\)
\(710\) 0 0
\(711\) −4.17941 6.95349i −0.156740 0.260776i
\(712\) 0 0
\(713\) −19.1799 5.13924i −0.718293 0.192466i
\(714\) 0 0
\(715\) −7.49044 + 10.4701i −0.280127 + 0.391559i
\(716\) 0 0
\(717\) 4.30726 1.19483i 0.160857 0.0446219i
\(718\) 0 0
\(719\) −17.7746 + 30.7866i −0.662882 + 1.14815i 0.316973 + 0.948435i \(0.397334\pi\)
−0.979855 + 0.199711i \(0.936000\pi\)
\(720\) 0 0
\(721\) −1.09557 4.08873i −0.0408012 0.152272i
\(722\) 0 0
\(723\) −1.71077 + 6.61699i −0.0636244 + 0.246089i
\(724\) 0 0
\(725\) 8.47715 + 14.6829i 0.314833 + 0.545308i
\(726\) 0 0
\(727\) 27.8304i 1.03217i −0.856537 0.516086i \(-0.827389\pi\)
0.856537 0.516086i \(-0.172611\pi\)
\(728\) 0 0
\(729\) 26.9624 1.42444i 0.998607 0.0527571i
\(730\) 0 0
\(731\) 26.8202 15.4846i 0.991980 0.572720i
\(732\) 0 0
\(733\) 37.4547 37.4547i 1.38342 1.38342i 0.544961 0.838462i \(-0.316545\pi\)
0.838462 0.544961i \(-0.183455\pi\)
\(734\) 0 0
\(735\) 4.88040 4.96703i 0.180016 0.183212i
\(736\) 0 0
\(737\) 16.8031 + 9.70127i 0.618950 + 0.357351i
\(738\) 0 0
\(739\) 5.33765 19.9204i 0.196349 0.732783i −0.795565 0.605868i \(-0.792826\pi\)
0.991914 0.126915i \(-0.0405074\pi\)
\(740\) 0 0
\(741\) 4.74199 + 27.1046i 0.174201 + 0.995711i
\(742\) 0 0
\(743\) −2.94715 + 10.9989i −0.108120 + 0.403510i −0.998680 0.0513550i \(-0.983646\pi\)
0.890560 + 0.454865i \(0.150313\pi\)
\(744\) 0 0
\(745\) 11.5164 + 6.64899i 0.421928 + 0.243600i
\(746\) 0 0
\(747\) 7.60263 30.5108i 0.278166 1.11633i
\(748\) 0 0
\(749\) −2.98841 + 2.98841i −0.109194 + 0.109194i
\(750\) 0 0
\(751\) 16.1054 9.29844i 0.587693 0.339305i −0.176492 0.984302i \(-0.556475\pi\)
0.764185 + 0.644997i \(0.223142\pi\)
\(752\) 0 0
\(753\) 16.2335 + 27.5545i 0.591580 + 1.00414i
\(754\) 0 0
\(755\) 12.4965i 0.454795i
\(756\) 0 0
\(757\) −12.1506 21.0455i −0.441622 0.764911i 0.556188 0.831056i \(-0.312263\pi\)
−0.997810 + 0.0661450i \(0.978930\pi\)
\(758\) 0 0
\(759\) −42.7123 11.0429i −1.55036 0.400833i
\(760\) 0 0
\(761\) −7.86168 29.3402i −0.284986 1.06358i −0.948850 0.315728i \(-0.897751\pi\)
0.663864 0.747853i \(-0.268915\pi\)
\(762\) 0 0
\(763\) 8.16644 14.1447i 0.295645 0.512072i
\(764\) 0 0
\(765\) 3.56481 + 3.44153i 0.128886 + 0.124429i
\(766\) 0 0
\(767\) −23.8789 + 19.6280i −0.862217 + 0.708726i
\(768\) 0 0
\(769\) 16.7832 + 4.49705i 0.605218 + 0.162168i 0.548399 0.836217i \(-0.315237\pi\)
0.0568192 + 0.998384i \(0.481904\pi\)
\(770\) 0 0
\(771\) −26.6517 + 0.234459i −0.959838 + 0.00844385i
\(772\) 0 0
\(773\) −2.97458 + 0.797037i −0.106988 + 0.0286674i −0.311916 0.950110i \(-0.600971\pi\)
0.204928 + 0.978777i \(0.434304\pi\)
\(774\) 0 0
\(775\) −13.2415 13.2415i −0.475647 0.475647i
\(776\) 0 0
\(777\) 5.35805 + 3.03094i 0.192219 + 0.108734i
\(778\) 0 0
\(779\) 21.2931 0.762906
\(780\) 0 0
\(781\) −29.2555 −1.04685
\(782\) 0 0
\(783\) −16.5291 + 10.1338i −0.590701 + 0.362153i
\(784\) 0 0
\(785\) −0.0393779 0.0393779i −0.00140546 0.00140546i
\(786\) 0 0
\(787\) −23.4451 + 6.28211i −0.835729 + 0.223933i −0.651211 0.758896i \(-0.725739\pi\)
−0.184518 + 0.982829i \(0.559072\pi\)
\(788\) 0 0
\(789\) −0.0929099 10.5614i −0.00330768 0.375994i
\(790\) 0 0
\(791\) 2.80894 + 0.752654i 0.0998745 + 0.0267613i
\(792\) 0 0
\(793\) 28.6776 + 2.80199i 1.01837 + 0.0995017i
\(794\) 0 0
\(795\) −2.05384 7.40389i −0.0728423 0.262589i
\(796\) 0 0