Properties

Label 784.2.m.k.197.10
Level $784$
Weight $2$
Character 784.197
Analytic conductor $6.260$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26027151847\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 112)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 197.10
Character \(\chi\) \(=\) 784.197
Dual form 784.2.m.k.589.10

$q$-expansion

\(f(q)\) \(=\) \(q+(1.19460 + 0.756916i) q^{2} +(1.42954 - 1.42954i) q^{3} +(0.854157 + 1.80843i) q^{4} +(0.702089 + 0.702089i) q^{5} +(2.78978 - 0.625694i) q^{6} +(-0.348448 + 2.80688i) q^{8} -1.08719i q^{9} +O(q^{10})\) \(q+(1.19460 + 0.756916i) q^{2} +(1.42954 - 1.42954i) q^{3} +(0.854157 + 1.80843i) q^{4} +(0.702089 + 0.702089i) q^{5} +(2.78978 - 0.625694i) q^{6} +(-0.348448 + 2.80688i) q^{8} -1.08719i q^{9} +(0.307296 + 1.37014i) q^{10} +(-1.38191 - 1.38191i) q^{11} +(3.80628 + 1.36417i) q^{12} +(2.10314 - 2.10314i) q^{13} +2.00733 q^{15} +(-2.54083 + 3.08937i) q^{16} +5.67771 q^{17} +(0.822907 - 1.29876i) q^{18} +(0.451363 - 0.451363i) q^{19} +(-0.669984 + 1.86937i) q^{20} +(-0.604848 - 2.69683i) q^{22} +6.84381i q^{23} +(3.51444 + 4.51068i) q^{24} -4.01414i q^{25} +(4.10432 - 0.920521i) q^{26} +(2.73445 + 2.73445i) q^{27} +(-0.207295 + 0.207295i) q^{29} +(2.39797 + 1.51938i) q^{30} -7.89385 q^{31} +(-5.37368 + 1.76737i) q^{32} -3.95101 q^{33} +(6.78261 + 4.29755i) q^{34} +(1.96610 - 0.928627i) q^{36} +(-7.03159 - 7.03159i) q^{37} +(0.880843 - 0.197556i) q^{38} -6.01306i q^{39} +(-2.21532 + 1.72604i) q^{40} -2.40202i q^{41} +(3.65586 + 3.65586i) q^{43} +(1.31872 - 3.67947i) q^{44} +(0.763301 - 0.763301i) q^{45} +(-5.18019 + 8.17564i) q^{46} -0.289185 q^{47} +(0.784155 + 8.04861i) q^{48} +(3.03837 - 4.79531i) q^{50} +(8.11653 - 8.11653i) q^{51} +(5.59980 + 2.00697i) q^{52} +(-5.58365 - 5.58365i) q^{53} +(1.19684 + 5.33633i) q^{54} -1.94045i q^{55} -1.29048i q^{57} +(-0.404540 + 0.0907305i) q^{58} +(-9.84923 - 9.84923i) q^{59} +(1.71458 + 3.63012i) q^{60} +(2.64783 - 2.64783i) q^{61} +(-9.43003 - 5.97498i) q^{62} +(-7.75717 - 1.95611i) q^{64} +2.95319 q^{65} +(-4.71989 - 2.99058i) q^{66} +(-7.35474 + 7.35474i) q^{67} +(4.84966 + 10.2677i) q^{68} +(9.78352 + 9.78352i) q^{69} +11.5947i q^{71} +(3.05160 + 0.378828i) q^{72} +0.358849i q^{73} +(-3.07764 - 13.7223i) q^{74} +(-5.73839 - 5.73839i) q^{75} +(1.20179 + 0.430722i) q^{76} +(4.55138 - 7.18323i) q^{78} +7.69906 q^{79} +(-3.95290 + 0.385121i) q^{80} +11.0796 q^{81} +(1.81812 - 2.86946i) q^{82} +(0.424001 - 0.424001i) q^{83} +(3.98626 + 3.98626i) q^{85} +(1.60013 + 7.13449i) q^{86} +0.592673i q^{87} +(4.36039 - 3.39734i) q^{88} -17.5887i q^{89} +(1.48960 - 0.334088i) q^{90} +(-12.3765 + 5.84569i) q^{92} +(-11.2846 + 11.2846i) q^{93} +(-0.345462 - 0.218889i) q^{94} +0.633794 q^{95} +(-5.15536 + 10.2084i) q^{96} -12.2678 q^{97} +(-1.50240 + 1.50240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{8} + O(q^{10}) \) \( 24 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{8} - 2 q^{10} + 4 q^{11} + 2 q^{12} + 12 q^{13} - 20 q^{15} - 16 q^{16} + 8 q^{17} - 18 q^{18} - 4 q^{19} + 8 q^{20} + 18 q^{24} - 10 q^{26} + 12 q^{27} + 12 q^{29} + 4 q^{30} + 28 q^{31} - 16 q^{32} + 16 q^{33} + 22 q^{34} - 36 q^{36} + 24 q^{37} + 20 q^{38} + 26 q^{40} - 20 q^{43} - 6 q^{44} - 28 q^{45} + 14 q^{46} - 20 q^{47} - 28 q^{48} + 28 q^{50} - 24 q^{51} - 16 q^{52} + 16 q^{53} + 64 q^{54} + 6 q^{58} - 20 q^{59} - 46 q^{60} + 8 q^{61} - 12 q^{62} + 40 q^{64} - 8 q^{65} - 20 q^{66} - 48 q^{67} + 20 q^{69} + 32 q^{72} + 8 q^{74} - 4 q^{75} + 18 q^{76} + 58 q^{78} + 36 q^{79} - 28 q^{80} + 2 q^{82} + 4 q^{83} + 20 q^{86} + 42 q^{88} + 10 q^{90} + 38 q^{92} - 8 q^{93} - 72 q^{94} + 4 q^{95} - 120 q^{96} + 24 q^{97} - 12 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.19460 + 0.756916i 0.844713 + 0.535220i
\(3\) 1.42954 1.42954i 0.825347 0.825347i −0.161522 0.986869i \(-0.551640\pi\)
0.986869 + 0.161522i \(0.0516403\pi\)
\(4\) 0.854157 + 1.80843i 0.427079 + 0.904214i
\(5\) 0.702089 + 0.702089i 0.313984 + 0.313984i 0.846451 0.532467i \(-0.178735\pi\)
−0.532467 + 0.846451i \(0.678735\pi\)
\(6\) 2.78978 0.625694i 1.13892 0.255439i
\(7\) 0 0
\(8\) −0.348448 + 2.80688i −0.123195 + 0.992382i
\(9\) 1.08719i 0.362395i
\(10\) 0.307296 + 1.37014i 0.0971756 + 0.433277i
\(11\) −1.38191 1.38191i −0.416663 0.416663i 0.467389 0.884052i \(-0.345195\pi\)
−0.884052 + 0.467389i \(0.845195\pi\)
\(12\) 3.80628 + 1.36417i 1.09878 + 0.393803i
\(13\) 2.10314 2.10314i 0.583307 0.583307i −0.352504 0.935810i \(-0.614670\pi\)
0.935810 + 0.352504i \(0.114670\pi\)
\(14\) 0 0
\(15\) 2.00733 0.518291
\(16\) −2.54083 + 3.08937i −0.635208 + 0.772341i
\(17\) 5.67771 1.37705 0.688523 0.725214i \(-0.258259\pi\)
0.688523 + 0.725214i \(0.258259\pi\)
\(18\) 0.822907 1.29876i 0.193961 0.306120i
\(19\) 0.451363 0.451363i 0.103550 0.103550i −0.653434 0.756984i \(-0.726672\pi\)
0.756984 + 0.653434i \(0.226672\pi\)
\(20\) −0.669984 + 1.86937i −0.149813 + 0.418005i
\(21\) 0 0
\(22\) −0.604848 2.69683i −0.128954 0.574967i
\(23\) 6.84381i 1.42703i 0.700639 + 0.713516i \(0.252899\pi\)
−0.700639 + 0.713516i \(0.747101\pi\)
\(24\) 3.51444 + 4.51068i 0.717381 + 0.920738i
\(25\) 4.01414i 0.802828i
\(26\) 4.10432 0.920521i 0.804924 0.180529i
\(27\) 2.73445 + 2.73445i 0.526245 + 0.526245i
\(28\) 0 0
\(29\) −0.207295 + 0.207295i −0.0384937 + 0.0384937i −0.726092 0.687598i \(-0.758665\pi\)
0.687598 + 0.726092i \(0.258665\pi\)
\(30\) 2.39797 + 1.51938i 0.437807 + 0.277400i
\(31\) −7.89385 −1.41778 −0.708889 0.705320i \(-0.750803\pi\)
−0.708889 + 0.705320i \(0.750803\pi\)
\(32\) −5.37368 + 1.76737i −0.949941 + 0.312431i
\(33\) −3.95101 −0.687783
\(34\) 6.78261 + 4.29755i 1.16321 + 0.737023i
\(35\) 0 0
\(36\) 1.96610 0.928627i 0.327683 0.154771i
\(37\) −7.03159 7.03159i −1.15599 1.15599i −0.985331 0.170655i \(-0.945412\pi\)
−0.170655 0.985331i \(-0.554588\pi\)
\(38\) 0.880843 0.197556i 0.142892 0.0320478i
\(39\) 6.01306i 0.962861i
\(40\) −2.21532 + 1.72604i −0.350273 + 0.272911i
\(41\) 2.40202i 0.375132i −0.982252 0.187566i \(-0.939940\pi\)
0.982252 0.187566i \(-0.0600599\pi\)
\(42\) 0 0
\(43\) 3.65586 + 3.65586i 0.557514 + 0.557514i 0.928599 0.371085i \(-0.121014\pi\)
−0.371085 + 0.928599i \(0.621014\pi\)
\(44\) 1.31872 3.67947i 0.198805 0.554700i
\(45\) 0.763301 0.763301i 0.113786 0.113786i
\(46\) −5.18019 + 8.17564i −0.763777 + 1.20543i
\(47\) −0.289185 −0.0421820 −0.0210910 0.999778i \(-0.506714\pi\)
−0.0210910 + 0.999778i \(0.506714\pi\)
\(48\) 0.784155 + 8.04861i 0.113183 + 1.16172i
\(49\) 0 0
\(50\) 3.03837 4.79531i 0.429690 0.678159i
\(51\) 8.11653 8.11653i 1.13654 1.13654i
\(52\) 5.59980 + 2.00697i 0.776552 + 0.278316i
\(53\) −5.58365 5.58365i −0.766973 0.766973i 0.210599 0.977572i \(-0.432458\pi\)
−0.977572 + 0.210599i \(0.932458\pi\)
\(54\) 1.19684 + 5.33633i 0.162869 + 0.726183i
\(55\) 1.94045i 0.261651i
\(56\) 0 0
\(57\) 1.29048i 0.170929i
\(58\) −0.404540 + 0.0907305i −0.0531187 + 0.0119135i
\(59\) −9.84923 9.84923i −1.28226 1.28226i −0.939378 0.342883i \(-0.888597\pi\)
−0.342883 0.939378i \(-0.611403\pi\)
\(60\) 1.71458 + 3.63012i 0.221351 + 0.468646i
\(61\) 2.64783 2.64783i 0.339020 0.339020i −0.516978 0.855999i \(-0.672943\pi\)
0.855999 + 0.516978i \(0.172943\pi\)
\(62\) −9.43003 5.97498i −1.19761 0.758823i
\(63\) 0 0
\(64\) −7.75717 1.95611i −0.969646 0.244513i
\(65\) 2.95319 0.366298
\(66\) −4.71989 2.99058i −0.580979 0.368115i
\(67\) −7.35474 + 7.35474i −0.898525 + 0.898525i −0.995306 0.0967807i \(-0.969145\pi\)
0.0967807 + 0.995306i \(0.469145\pi\)
\(68\) 4.84966 + 10.2677i 0.588107 + 1.24515i
\(69\) 9.78352 + 9.78352i 1.17780 + 1.17780i
\(70\) 0 0
\(71\) 11.5947i 1.37603i 0.725695 + 0.688017i \(0.241518\pi\)
−0.725695 + 0.688017i \(0.758482\pi\)
\(72\) 3.05160 + 0.378828i 0.359634 + 0.0446453i
\(73\) 0.358849i 0.0420001i 0.999779 + 0.0210000i \(0.00668501\pi\)
−0.999779 + 0.0210000i \(0.993315\pi\)
\(74\) −3.07764 13.7223i −0.357769 1.59518i
\(75\) −5.73839 5.73839i −0.662612 0.662612i
\(76\) 1.20179 + 0.430722i 0.137855 + 0.0494073i
\(77\) 0 0
\(78\) 4.55138 7.18323i 0.515342 0.813341i
\(79\) 7.69906 0.866211 0.433106 0.901343i \(-0.357418\pi\)
0.433106 + 0.901343i \(0.357418\pi\)
\(80\) −3.95290 + 0.385121i −0.441948 + 0.0430578i
\(81\) 11.0796 1.23106
\(82\) 1.81812 2.86946i 0.200778 0.316879i
\(83\) 0.424001 0.424001i 0.0465402 0.0465402i −0.683454 0.729994i \(-0.739523\pi\)
0.729994 + 0.683454i \(0.239523\pi\)
\(84\) 0 0
\(85\) 3.98626 + 3.98626i 0.432371 + 0.432371i
\(86\) 1.60013 + 7.13449i 0.172546 + 0.769332i
\(87\) 0.592673i 0.0635412i
\(88\) 4.36039 3.39734i 0.464820 0.362158i
\(89\) 17.5887i 1.86440i −0.361940 0.932201i \(-0.617885\pi\)
0.361940 0.932201i \(-0.382115\pi\)
\(90\) 1.48960 0.334088i 0.157017 0.0352160i
\(91\) 0 0
\(92\) −12.3765 + 5.84569i −1.29034 + 0.609455i
\(93\) −11.2846 + 11.2846i −1.17016 + 1.17016i
\(94\) −0.345462 0.218889i −0.0356317 0.0225767i
\(95\) 0.633794 0.0650259
\(96\) −5.15536 + 10.2084i −0.526167 + 1.04189i
\(97\) −12.2678 −1.24560 −0.622802 0.782379i \(-0.714006\pi\)
−0.622802 + 0.782379i \(0.714006\pi\)
\(98\) 0 0
\(99\) −1.50240 + 1.50240i −0.150997 + 0.150997i
\(100\) 7.25929 3.42871i 0.725929 0.342871i
\(101\) 0.855455 + 0.855455i 0.0851209 + 0.0851209i 0.748385 0.663264i \(-0.230829\pi\)
−0.663264 + 0.748385i \(0.730829\pi\)
\(102\) 15.8396 3.55251i 1.56835 0.351751i
\(103\) 5.84488i 0.575913i 0.957643 + 0.287956i \(0.0929759\pi\)
−0.957643 + 0.287956i \(0.907024\pi\)
\(104\) 5.17043 + 6.63611i 0.507003 + 0.650724i
\(105\) 0 0
\(106\) −2.44390 10.8966i −0.237372 1.05837i
\(107\) −2.65363 2.65363i −0.256536 0.256536i 0.567108 0.823644i \(-0.308062\pi\)
−0.823644 + 0.567108i \(0.808062\pi\)
\(108\) −2.60941 + 7.28071i −0.251090 + 0.700587i
\(109\) −7.08373 + 7.08373i −0.678499 + 0.678499i −0.959660 0.281162i \(-0.909280\pi\)
0.281162 + 0.959660i \(0.409280\pi\)
\(110\) 1.46876 2.31807i 0.140041 0.221020i
\(111\) −20.1039 −1.90818
\(112\) 0 0
\(113\) 5.07461 0.477379 0.238689 0.971096i \(-0.423282\pi\)
0.238689 + 0.971096i \(0.423282\pi\)
\(114\) 0.976788 1.54162i 0.0914846 0.144386i
\(115\) −4.80496 + 4.80496i −0.448065 + 0.448065i
\(116\) −0.551940 0.197815i −0.0512463 0.0183667i
\(117\) −2.28650 2.28650i −0.211387 0.211387i
\(118\) −4.31089 19.2210i −0.396850 1.76943i
\(119\) 0 0
\(120\) −0.699452 + 5.63435i −0.0638509 + 0.514343i
\(121\) 7.18063i 0.652784i
\(122\) 5.16730 1.15893i 0.467825 0.104924i
\(123\) −3.43379 3.43379i −0.309614 0.309614i
\(124\) −6.74259 14.2755i −0.605503 1.28197i
\(125\) 6.32873 6.32873i 0.566059 0.566059i
\(126\) 0 0
\(127\) −11.1710 −0.991270 −0.495635 0.868531i \(-0.665065\pi\)
−0.495635 + 0.868531i \(0.665065\pi\)
\(128\) −7.78614 8.20829i −0.688204 0.725518i
\(129\) 10.4524 0.920285
\(130\) 3.52789 + 2.23531i 0.309416 + 0.196050i
\(131\) 8.91555 8.91555i 0.778956 0.778956i −0.200698 0.979653i \(-0.564321\pi\)
0.979653 + 0.200698i \(0.0643209\pi\)
\(132\) −3.37478 7.14512i −0.293737 0.621903i
\(133\) 0 0
\(134\) −14.3529 + 3.21909i −1.23990 + 0.278087i
\(135\) 3.83966i 0.330465i
\(136\) −1.97839 + 15.9367i −0.169645 + 1.36656i
\(137\) 16.2033i 1.38434i 0.721733 + 0.692172i \(0.243346\pi\)
−0.721733 + 0.692172i \(0.756654\pi\)
\(138\) 4.28213 + 19.0927i 0.364519 + 1.62528i
\(139\) −10.5018 10.5018i −0.890748 0.890748i 0.103846 0.994593i \(-0.466885\pi\)
−0.994593 + 0.103846i \(0.966885\pi\)
\(140\) 0 0
\(141\) −0.413403 + 0.413403i −0.0348148 + 0.0348148i
\(142\) −8.77618 + 13.8510i −0.736481 + 1.16235i
\(143\) −5.81272 −0.486084
\(144\) 3.35871 + 2.76235i 0.279893 + 0.230196i
\(145\) −0.291079 −0.0241728
\(146\) −0.271618 + 0.428682i −0.0224793 + 0.0354780i
\(147\) 0 0
\(148\) 6.71005 18.7222i 0.551562 1.53896i
\(149\) 7.04183 + 7.04183i 0.576889 + 0.576889i 0.934045 0.357156i \(-0.116254\pi\)
−0.357156 + 0.934045i \(0.616254\pi\)
\(150\) −2.51162 11.1986i −0.205073 0.914360i
\(151\) 10.3650i 0.843494i 0.906713 + 0.421747i \(0.138583\pi\)
−0.906713 + 0.421747i \(0.861417\pi\)
\(152\) 1.10964 + 1.42420i 0.0900041 + 0.115518i
\(153\) 6.17272i 0.499035i
\(154\) 0 0
\(155\) −5.54219 5.54219i −0.445159 0.445159i
\(156\) 10.8742 5.13610i 0.870633 0.411217i
\(157\) 2.91731 2.91731i 0.232827 0.232827i −0.581045 0.813872i \(-0.697356\pi\)
0.813872 + 0.581045i \(0.197356\pi\)
\(158\) 9.19732 + 5.82754i 0.731700 + 0.463614i
\(159\) −15.9641 −1.26604
\(160\) −5.01366 2.53195i −0.396364 0.200168i
\(161\) 0 0
\(162\) 13.2357 + 8.38631i 1.03990 + 0.658891i
\(163\) 5.84382 5.84382i 0.457723 0.457723i −0.440184 0.897907i \(-0.645087\pi\)
0.897907 + 0.440184i \(0.145087\pi\)
\(164\) 4.34388 2.05170i 0.339200 0.160211i
\(165\) −2.77396 2.77396i −0.215953 0.215953i
\(166\) 0.827446 0.185580i 0.0642223 0.0144038i
\(167\) 8.92669i 0.690768i 0.938462 + 0.345384i \(0.112251\pi\)
−0.938462 + 0.345384i \(0.887749\pi\)
\(168\) 0 0
\(169\) 4.15359i 0.319507i
\(170\) 1.74474 + 7.77926i 0.133815 + 0.596642i
\(171\) −0.490715 0.490715i −0.0375259 0.0375259i
\(172\) −3.48869 + 9.73405i −0.266010 + 0.742214i
\(173\) −3.85339 + 3.85339i −0.292968 + 0.292968i −0.838252 0.545284i \(-0.816422\pi\)
0.545284 + 0.838252i \(0.316422\pi\)
\(174\) −0.448604 + 0.708010i −0.0340086 + 0.0536741i
\(175\) 0 0
\(176\) 7.78045 0.758029i 0.586473 0.0571386i
\(177\) −28.1598 −2.11662
\(178\) 13.3132 21.0116i 0.997866 1.57488i
\(179\) 6.89914 6.89914i 0.515666 0.515666i −0.400591 0.916257i \(-0.631195\pi\)
0.916257 + 0.400591i \(0.131195\pi\)
\(180\) 2.03235 + 0.728396i 0.151483 + 0.0542915i
\(181\) 8.42976 + 8.42976i 0.626579 + 0.626579i 0.947206 0.320627i \(-0.103894\pi\)
−0.320627 + 0.947206i \(0.603894\pi\)
\(182\) 0 0
\(183\) 7.57038i 0.559619i
\(184\) −19.2098 2.38471i −1.41616 0.175803i
\(185\) 9.87361i 0.725922i
\(186\) −22.0221 + 4.93914i −1.61474 + 0.362155i
\(187\) −7.84611 7.84611i −0.573764 0.573764i
\(188\) −0.247010 0.522971i −0.0180150 0.0381416i
\(189\) 0 0
\(190\) 0.757132 + 0.479728i 0.0549282 + 0.0348032i
\(191\) −4.93044 −0.356754 −0.178377 0.983962i \(-0.557085\pi\)
−0.178377 + 0.983962i \(0.557085\pi\)
\(192\) −13.8855 + 8.29286i −1.00210 + 0.598486i
\(193\) 21.9087 1.57702 0.788510 0.615022i \(-0.210853\pi\)
0.788510 + 0.615022i \(0.210853\pi\)
\(194\) −14.6551 9.28568i −1.05218 0.666673i
\(195\) 4.22171 4.22171i 0.302323 0.302323i
\(196\) 0 0
\(197\) 7.61984 + 7.61984i 0.542891 + 0.542891i 0.924375 0.381484i \(-0.124587\pi\)
−0.381484 + 0.924375i \(0.624587\pi\)
\(198\) −2.93196 + 0.657581i −0.208365 + 0.0467323i
\(199\) 3.57622i 0.253511i 0.991934 + 0.126756i \(0.0404564\pi\)
−0.991934 + 0.126756i \(0.959544\pi\)
\(200\) 11.2672 + 1.39872i 0.796713 + 0.0989045i
\(201\) 21.0278i 1.48319i
\(202\) 0.374422 + 1.66944i 0.0263443 + 0.117461i
\(203\) 0 0
\(204\) 21.6110 + 7.74537i 1.51307 + 0.542285i
\(205\) 1.68643 1.68643i 0.117785 0.117785i
\(206\) −4.42408 + 6.98232i −0.308240 + 0.486481i
\(207\) 7.44049 0.517149
\(208\) 1.15365 + 11.8411i 0.0799911 + 0.821033i
\(209\) −1.24749 −0.0862906
\(210\) 0 0
\(211\) 7.33737 7.33737i 0.505126 0.505126i −0.407901 0.913026i \(-0.633739\pi\)
0.913026 + 0.407901i \(0.133739\pi\)
\(212\) 5.32832 14.8669i 0.365950 1.02107i
\(213\) 16.5751 + 16.5751i 1.13570 + 1.13570i
\(214\) −1.16146 5.17861i −0.0793959 0.354002i
\(215\) 5.13349i 0.350101i
\(216\) −8.62809 + 6.72246i −0.587067 + 0.457406i
\(217\) 0 0
\(218\) −13.8240 + 3.10047i −0.936283 + 0.209990i
\(219\) 0.512990 + 0.512990i 0.0346646 + 0.0346646i
\(220\) 3.50917 1.65745i 0.236588 0.111745i
\(221\) 11.9410 11.9410i 0.803241 0.803241i
\(222\) −24.0162 15.2170i −1.61186 1.02130i
\(223\) −4.26037 −0.285295 −0.142648 0.989774i \(-0.545562\pi\)
−0.142648 + 0.989774i \(0.545562\pi\)
\(224\) 0 0
\(225\) −4.36411 −0.290941
\(226\) 6.06214 + 3.84105i 0.403248 + 0.255503i
\(227\) −3.42116 + 3.42116i −0.227071 + 0.227071i −0.811468 0.584397i \(-0.801331\pi\)
0.584397 + 0.811468i \(0.301331\pi\)
\(228\) 2.33375 1.10228i 0.154556 0.0730001i
\(229\) 13.8716 + 13.8716i 0.916663 + 0.916663i 0.996785 0.0801224i \(-0.0255311\pi\)
−0.0801224 + 0.996785i \(0.525531\pi\)
\(230\) −9.37698 + 2.10308i −0.618300 + 0.138673i
\(231\) 0 0
\(232\) −0.509620 0.654083i −0.0334582 0.0429427i
\(233\) 5.06546i 0.331849i −0.986138 0.165925i \(-0.946939\pi\)
0.986138 0.165925i \(-0.0530608\pi\)
\(234\) −1.00078 4.46216i −0.0654228 0.291700i
\(235\) −0.203034 0.203034i −0.0132445 0.0132445i
\(236\) 9.39884 26.2244i 0.611813 1.70707i
\(237\) 11.0061 11.0061i 0.714925 0.714925i
\(238\) 0 0
\(239\) −9.32494 −0.603181 −0.301590 0.953438i \(-0.597517\pi\)
−0.301590 + 0.953438i \(0.597517\pi\)
\(240\) −5.10029 + 6.20139i −0.329223 + 0.400298i
\(241\) −25.7325 −1.65758 −0.828789 0.559562i \(-0.810969\pi\)
−0.828789 + 0.559562i \(0.810969\pi\)
\(242\) 5.43513 8.57801i 0.349383 0.551415i
\(243\) 7.63539 7.63539i 0.489810 0.489810i
\(244\) 7.05008 + 2.52675i 0.451335 + 0.161759i
\(245\) 0 0
\(246\) −1.50293 6.70110i −0.0958232 0.427247i
\(247\) 1.89856i 0.120802i
\(248\) 2.75060 22.1571i 0.174663 1.40698i
\(249\) 1.21226i 0.0768236i
\(250\) 12.3506 2.77001i 0.781123 0.175191i
\(251\) 3.64372 + 3.64372i 0.229990 + 0.229990i 0.812688 0.582699i \(-0.198003\pi\)
−0.582699 + 0.812688i \(0.698003\pi\)
\(252\) 0 0
\(253\) 9.45755 9.45755i 0.594591 0.594591i
\(254\) −13.3450 8.45554i −0.837338 0.530548i
\(255\) 11.3971 0.713711
\(256\) −3.08836 15.6991i −0.193023 0.981194i
\(257\) 3.75548 0.234260 0.117130 0.993117i \(-0.462631\pi\)
0.117130 + 0.993117i \(0.462631\pi\)
\(258\) 12.4865 + 7.91160i 0.777376 + 0.492555i
\(259\) 0 0
\(260\) 2.52249 + 5.34063i 0.156438 + 0.331212i
\(261\) 0.225368 + 0.225368i 0.0139499 + 0.0139499i
\(262\) 17.3989 3.90223i 1.07491 0.241081i
\(263\) 18.8507i 1.16238i −0.813767 0.581191i \(-0.802587\pi\)
0.813767 0.581191i \(-0.197413\pi\)
\(264\) 1.37672 11.0900i 0.0847315 0.682543i
\(265\) 7.84044i 0.481634i
\(266\) 0 0
\(267\) −25.1439 25.1439i −1.53878 1.53878i
\(268\) −19.5826 7.01842i −1.19620 0.428718i
\(269\) 12.1259 12.1259i 0.739330 0.739330i −0.233118 0.972448i \(-0.574893\pi\)
0.972448 + 0.233118i \(0.0748930\pi\)
\(270\) −2.90630 + 4.58687i −0.176872 + 0.279148i
\(271\) −5.31215 −0.322690 −0.161345 0.986898i \(-0.551583\pi\)
−0.161345 + 0.986898i \(0.551583\pi\)
\(272\) −14.4261 + 17.5405i −0.874711 + 1.06355i
\(273\) 0 0
\(274\) −12.2646 + 19.3566i −0.740929 + 1.16937i
\(275\) −5.54720 + 5.54720i −0.334509 + 0.334509i
\(276\) −9.33613 + 26.0495i −0.561969 + 1.56799i
\(277\) −10.7488 10.7488i −0.645834 0.645834i 0.306149 0.951984i \(-0.400959\pi\)
−0.951984 + 0.306149i \(0.900959\pi\)
\(278\) −4.59650 20.4944i −0.275680 1.22917i
\(279\) 8.58208i 0.513795i
\(280\) 0 0
\(281\) 3.15786i 0.188382i −0.995554 0.0941910i \(-0.969974\pi\)
0.995554 0.0941910i \(-0.0300264\pi\)
\(282\) −0.806763 + 0.180941i −0.0480420 + 0.0107749i
\(283\) 9.98203 + 9.98203i 0.593370 + 0.593370i 0.938540 0.345170i \(-0.112179\pi\)
−0.345170 + 0.938540i \(0.612179\pi\)
\(284\) −20.9681 + 9.90367i −1.24423 + 0.587674i
\(285\) 0.906035 0.906035i 0.0536689 0.0536689i
\(286\) −6.94390 4.39974i −0.410602 0.260162i
\(287\) 0 0
\(288\) 1.92146 + 5.84218i 0.113223 + 0.344254i
\(289\) 15.2364 0.896258
\(290\) −0.347724 0.220322i −0.0204190 0.0129378i
\(291\) −17.5373 + 17.5373i −1.02806 + 1.02806i
\(292\) −0.648952 + 0.306513i −0.0379771 + 0.0179373i
\(293\) 10.9335 + 10.9335i 0.638743 + 0.638743i 0.950245 0.311502i \(-0.100832\pi\)
−0.311502 + 0.950245i \(0.600832\pi\)
\(294\) 0 0
\(295\) 13.8301i 0.805219i
\(296\) 22.1870 17.2867i 1.28959 1.00477i
\(297\) 7.55755i 0.438534i
\(298\) 3.08213 + 13.7423i 0.178543 + 0.796068i
\(299\) 14.3935 + 14.3935i 0.832398 + 0.832398i
\(300\) 5.47598 15.2789i 0.316156 0.882131i
\(301\) 0 0
\(302\) −7.84545 + 12.3821i −0.451455 + 0.712510i
\(303\) 2.44582 0.140509
\(304\) 0.247588 + 2.54126i 0.0142002 + 0.145751i
\(305\) 3.71803 0.212894
\(306\) 4.67223 7.37396i 0.267094 0.421541i
\(307\) 14.7735 14.7735i 0.843170 0.843170i −0.146100 0.989270i \(-0.546672\pi\)
0.989270 + 0.146100i \(0.0466721\pi\)
\(308\) 0 0
\(309\) 8.35550 + 8.35550i 0.475328 + 0.475328i
\(310\) −2.42575 10.8157i −0.137773 0.614290i
\(311\) 8.73588i 0.495366i 0.968841 + 0.247683i \(0.0796692\pi\)
−0.968841 + 0.247683i \(0.920331\pi\)
\(312\) 16.8780 + 2.09524i 0.955526 + 0.118620i
\(313\) 4.11784i 0.232754i 0.993205 + 0.116377i \(0.0371281\pi\)
−0.993205 + 0.116377i \(0.962872\pi\)
\(314\) 5.69319 1.27687i 0.321285 0.0720581i
\(315\) 0 0
\(316\) 6.57621 + 13.9232i 0.369940 + 0.783241i
\(317\) 17.2736 17.2736i 0.970182 0.970182i −0.0293866 0.999568i \(-0.509355\pi\)
0.999568 + 0.0293866i \(0.00935539\pi\)
\(318\) −19.0708 12.0835i −1.06944 0.677609i
\(319\) 0.572927 0.0320777
\(320\) −4.07286 6.81959i −0.227680 0.381226i
\(321\) −7.58695 −0.423462
\(322\) 0 0
\(323\) 2.56271 2.56271i 0.142593 0.142593i
\(324\) 9.46371 + 20.0366i 0.525762 + 1.11315i
\(325\) −8.44231 8.44231i −0.468295 0.468295i
\(326\) 11.4043 2.55777i 0.631627 0.141662i
\(327\) 20.2530i 1.11999i
\(328\) 6.74218 + 0.836979i 0.372274 + 0.0462144i
\(329\) 0 0
\(330\) −1.21413 5.41344i −0.0668357 0.298000i
\(331\) 5.16464 + 5.16464i 0.283874 + 0.283874i 0.834652 0.550778i \(-0.185669\pi\)
−0.550778 + 0.834652i \(0.685669\pi\)
\(332\) 1.12894 + 0.404612i 0.0619586 + 0.0222060i
\(333\) −7.64464 + 7.64464i −0.418924 + 0.418924i
\(334\) −6.75675 + 10.6639i −0.369713 + 0.583500i
\(335\) −10.3274 −0.564245
\(336\) 0 0
\(337\) −9.53985 −0.519669 −0.259834 0.965653i \(-0.583668\pi\)
−0.259834 + 0.965653i \(0.583668\pi\)
\(338\) −3.14392 + 4.96189i −0.171006 + 0.269891i
\(339\) 7.25436 7.25436i 0.394003 0.394003i
\(340\) −3.80397 + 10.6138i −0.206299 + 0.575612i
\(341\) 10.9086 + 10.9086i 0.590735 + 0.590735i
\(342\) −0.214780 0.957639i −0.0116140 0.0517832i
\(343\) 0 0
\(344\) −11.5355 + 8.98769i −0.621950 + 0.484584i
\(345\) 13.7378i 0.739619i
\(346\) −7.51997 + 1.68658i −0.404276 + 0.0906714i
\(347\) 6.46084 + 6.46084i 0.346836 + 0.346836i 0.858930 0.512094i \(-0.171130\pi\)
−0.512094 + 0.858930i \(0.671130\pi\)
\(348\) −1.07181 + 0.506236i −0.0574549 + 0.0271371i
\(349\) −24.4862 + 24.4862i −1.31072 + 1.31072i −0.389831 + 0.920887i \(0.627467\pi\)
−0.920887 + 0.389831i \(0.872533\pi\)
\(350\) 0 0
\(351\) 11.5019 0.613925
\(352\) 9.86832 + 4.98360i 0.525983 + 0.265627i
\(353\) 26.0704 1.38759 0.693793 0.720175i \(-0.255938\pi\)
0.693793 + 0.720175i \(0.255938\pi\)
\(354\) −33.6398 21.3146i −1.78794 1.13286i
\(355\) −8.14049 + 8.14049i −0.432052 + 0.432052i
\(356\) 31.8080 15.0236i 1.68582 0.796247i
\(357\) 0 0
\(358\) 13.4638 3.01967i 0.711584 0.159595i
\(359\) 3.48419i 0.183889i 0.995764 + 0.0919443i \(0.0293082\pi\)
−0.995764 + 0.0919443i \(0.970692\pi\)
\(360\) 1.87652 + 2.40847i 0.0989015 + 0.126937i
\(361\) 18.5925i 0.978555i
\(362\) 3.68961 + 16.4508i 0.193921 + 0.864637i
\(363\) −10.2650 10.2650i −0.538773 0.538773i
\(364\) 0 0
\(365\) −0.251944 + 0.251944i −0.0131873 + 0.0131873i
\(366\) 5.73014 9.04361i 0.299519 0.472717i
\(367\) −24.4561 −1.27660 −0.638298 0.769789i \(-0.720361\pi\)
−0.638298 + 0.769789i \(0.720361\pi\)
\(368\) −21.1430 17.3890i −1.10216 0.906462i
\(369\) −2.61144 −0.135946
\(370\) 7.47349 11.7951i 0.388528 0.613196i
\(371\) 0 0
\(372\) −30.0462 10.7686i −1.55782 0.558324i
\(373\) 25.9873 + 25.9873i 1.34557 + 1.34557i 0.890410 + 0.455160i \(0.150418\pi\)
0.455160 + 0.890410i \(0.349582\pi\)
\(374\) −3.43415 15.3118i −0.177576 0.791756i
\(375\) 18.0944i 0.934390i
\(376\) 0.100766 0.811708i 0.00519661 0.0418607i
\(377\) 0.871940i 0.0449072i
\(378\) 0 0
\(379\) 18.5183 + 18.5183i 0.951222 + 0.951222i 0.998864 0.0476420i \(-0.0151707\pi\)
−0.0476420 + 0.998864i \(0.515171\pi\)
\(380\) 0.541360 + 1.14617i 0.0277712 + 0.0587973i
\(381\) −15.9695 + 15.9695i −0.818142 + 0.818142i
\(382\) −5.88992 3.73193i −0.301355 0.190942i
\(383\) 15.7957 0.807123 0.403562 0.914953i \(-0.367772\pi\)
0.403562 + 0.914953i \(0.367772\pi\)
\(384\) −22.8647 0.603494i −1.16681 0.0307969i
\(385\) 0 0
\(386\) 26.1722 + 16.5830i 1.33213 + 0.844053i
\(387\) 3.97460 3.97460i 0.202040 0.202040i
\(388\) −10.4786 22.1854i −0.531971 1.12629i
\(389\) 4.03146 + 4.03146i 0.204403 + 0.204403i 0.801883 0.597481i \(-0.203831\pi\)
−0.597481 + 0.801883i \(0.703831\pi\)
\(390\) 8.23875 1.84779i 0.417185 0.0935666i
\(391\) 38.8572i 1.96509i
\(392\) 0 0
\(393\) 25.4903i 1.28582i
\(394\) 3.33512 + 14.8703i 0.168021 + 0.749154i
\(395\) 5.40543 + 5.40543i 0.271976 + 0.271976i
\(396\) −4.00026 1.43369i −0.201021 0.0720458i
\(397\) −0.711500 + 0.711500i −0.0357092 + 0.0357092i −0.724736 0.689027i \(-0.758038\pi\)
0.689027 + 0.724736i \(0.258038\pi\)
\(398\) −2.70690 + 4.27216i −0.135684 + 0.214144i
\(399\) 0 0
\(400\) 12.4012 + 10.1993i 0.620058 + 0.509963i
\(401\) −17.4064 −0.869232 −0.434616 0.900616i \(-0.643116\pi\)
−0.434616 + 0.900616i \(0.643116\pi\)
\(402\) −15.9163 + 25.1199i −0.793833 + 1.25287i
\(403\) −16.6019 + 16.6019i −0.826999 + 0.826999i
\(404\) −0.816336 + 2.27772i −0.0406142 + 0.113321i
\(405\) 7.77886 + 7.77886i 0.386535 + 0.386535i
\(406\) 0 0
\(407\) 19.4341i 0.963313i
\(408\) 19.9539 + 25.6103i 0.987867 + 1.26790i
\(409\) 38.1750i 1.88763i 0.330474 + 0.943815i \(0.392792\pi\)
−0.330474 + 0.943815i \(0.607208\pi\)
\(410\) 3.29110 0.738131i 0.162536 0.0364537i
\(411\) 23.1633 + 23.1633i 1.14256 + 1.14256i
\(412\) −10.5700 + 4.99245i −0.520749 + 0.245960i
\(413\) 0 0
\(414\) 8.88843 + 5.63182i 0.436843 + 0.276789i
\(415\) 0.595373 0.0292257
\(416\) −7.58456 + 15.0186i −0.371864 + 0.736350i
\(417\) −30.0254 −1.47035
\(418\) −1.49025 0.944244i −0.0728907 0.0461845i
\(419\) 27.0004 27.0004i 1.31905 1.31905i 0.404529 0.914525i \(-0.367435\pi\)
0.914525 0.404529i \(-0.132565\pi\)
\(420\) 0 0
\(421\) −19.1472 19.1472i −0.933175 0.933175i 0.0647277 0.997903i \(-0.479382\pi\)
−0.997903 + 0.0647277i \(0.979382\pi\)
\(422\) 14.3190 3.21148i 0.697039 0.156333i
\(423\) 0.314398i 0.0152865i
\(424\) 17.6182 13.7270i 0.855618 0.666643i
\(425\) 22.7911i 1.10553i
\(426\) 7.25471 + 32.3466i 0.351492 + 1.56720i
\(427\) 0 0
\(428\) 2.53228 7.06551i 0.122402 0.341524i
\(429\) −8.30954 + 8.30954i −0.401188 + 0.401188i
\(430\) −3.88562 + 6.13248i −0.187381 + 0.295735i
\(431\) 1.25711 0.0605528 0.0302764 0.999542i \(-0.490361\pi\)
0.0302764 + 0.999542i \(0.490361\pi\)
\(432\) −15.3955 + 1.49994i −0.740716 + 0.0721660i
\(433\) 9.16885 0.440627 0.220313 0.975429i \(-0.429292\pi\)
0.220313 + 0.975429i \(0.429292\pi\)
\(434\) 0 0
\(435\) −0.416110 + 0.416110i −0.0199509 + 0.0199509i
\(436\) −18.8611 6.75981i −0.903281 0.323736i
\(437\) 3.08904 + 3.08904i 0.147769 + 0.147769i
\(438\) 0.224530 + 1.00111i 0.0107284 + 0.0478349i
\(439\) 7.96586i 0.380190i −0.981766 0.190095i \(-0.939120\pi\)
0.981766 0.190095i \(-0.0608796\pi\)
\(440\) 5.44663 + 0.676148i 0.259658 + 0.0322341i
\(441\) 0 0
\(442\) 23.3032 5.22645i 1.10842 0.248597i
\(443\) 17.6930 + 17.6930i 0.840621 + 0.840621i 0.988940 0.148319i \(-0.0473861\pi\)
−0.148319 + 0.988940i \(0.547386\pi\)
\(444\) −17.1719 36.3565i −0.814943 1.72540i
\(445\) 12.3489 12.3489i 0.585393 0.585393i
\(446\) −5.08945 3.22474i −0.240992 0.152696i
\(447\) 20.1332 0.952267
\(448\) 0 0
\(449\) −8.33038 −0.393135 −0.196567 0.980490i \(-0.562979\pi\)
−0.196567 + 0.980490i \(0.562979\pi\)
\(450\) −5.21339 3.30327i −0.245761 0.155717i
\(451\) −3.31938 + 3.31938i −0.156304 + 0.156304i
\(452\) 4.33451 + 9.17706i 0.203878 + 0.431653i
\(453\) 14.8173 + 14.8173i 0.696175 + 0.696175i
\(454\) −6.67647 + 1.49740i −0.313342 + 0.0702766i
\(455\) 0 0
\(456\) 3.62224 + 0.449667i 0.169627 + 0.0210576i
\(457\) 14.4728i 0.677010i 0.940965 + 0.338505i \(0.109921\pi\)
−0.940965 + 0.338505i \(0.890079\pi\)
\(458\) 6.07145 + 27.0707i 0.283700 + 1.26493i
\(459\) 15.5254 + 15.5254i 0.724664 + 0.724664i
\(460\) −12.7936 4.58524i −0.596506 0.213788i
\(461\) 4.23021 4.23021i 0.197020 0.197020i −0.601701 0.798721i \(-0.705510\pi\)
0.798721 + 0.601701i \(0.205510\pi\)
\(462\) 0 0
\(463\) −25.1987 −1.17108 −0.585542 0.810642i \(-0.699118\pi\)
−0.585542 + 0.810642i \(0.699118\pi\)
\(464\) −0.113708 1.16711i −0.00527878 0.0541817i
\(465\) −15.8456 −0.734822
\(466\) 3.83412 6.05121i 0.177612 0.280317i
\(467\) −10.8645 + 10.8645i −0.502747 + 0.502747i −0.912291 0.409543i \(-0.865688\pi\)
0.409543 + 0.912291i \(0.365688\pi\)
\(468\) 2.18195 6.08802i 0.100860 0.281419i
\(469\) 0 0
\(470\) −0.0888655 0.396224i −0.00409906 0.0182765i
\(471\) 8.34085i 0.384326i
\(472\) 31.0776 24.2137i 1.43046 1.11453i
\(473\) 10.1042i 0.464591i
\(474\) 21.4787 4.81725i 0.986548 0.221264i
\(475\) −1.81183 1.81183i −0.0831326 0.0831326i
\(476\) 0 0
\(477\) −6.07046 + 6.07046i −0.277947 + 0.277947i
\(478\) −11.1396 7.05820i −0.509514 0.322834i
\(479\) 20.8293 0.951717 0.475859 0.879522i \(-0.342137\pi\)
0.475859 + 0.879522i \(0.342137\pi\)
\(480\) −10.7868 + 3.54771i −0.492346 + 0.161930i
\(481\) −29.5769 −1.34859
\(482\) −30.7402 19.4773i −1.40018 0.887169i
\(483\) 0 0
\(484\) 12.9857 6.13339i 0.590257 0.278790i
\(485\) −8.61308 8.61308i −0.391100 0.391100i
\(486\) 14.9006 3.34192i 0.675905 0.151593i
\(487\) 0.222431i 0.0100793i −0.999987 0.00503966i \(-0.998396\pi\)
0.999987 0.00503966i \(-0.00160418\pi\)
\(488\) 6.50952 + 8.35479i 0.294672 + 0.378203i
\(489\) 16.7080i 0.755561i
\(490\) 0 0
\(491\) 18.1586 + 18.1586i 0.819486 + 0.819486i 0.986033 0.166547i \(-0.0532618\pi\)
−0.166547 + 0.986033i \(0.553262\pi\)
\(492\) 3.27676 9.14275i 0.147728 0.412187i
\(493\) −1.17696 + 1.17696i −0.0530076 + 0.0530076i
\(494\) 1.43705 2.26803i 0.0646559 0.102043i
\(495\) −2.10963 −0.0948209
\(496\) 20.0569 24.3870i 0.900583 1.09501i
\(497\) 0 0
\(498\) 0.917575 1.44816i 0.0411175 0.0648938i
\(499\) 2.48274 2.48274i 0.111143 0.111143i −0.649348 0.760491i \(-0.724958\pi\)
0.760491 + 0.649348i \(0.224958\pi\)
\(500\) 16.8508 + 6.03933i 0.753591 + 0.270087i
\(501\) 12.7611 + 12.7611i 0.570123 + 0.570123i
\(502\) 1.59481 + 7.11079i 0.0711800 + 0.317370i
\(503\) 7.65278i 0.341220i 0.985339 + 0.170610i \(0.0545739\pi\)
−0.985339 + 0.170610i \(0.945426\pi\)
\(504\) 0 0
\(505\) 1.20121i 0.0534532i
\(506\) 18.4566 4.13946i 0.820496 0.184021i
\(507\) 5.93773 + 5.93773i 0.263704 + 0.263704i
\(508\) −9.54183 20.2020i −0.423350 0.896321i
\(509\) 22.6006 22.6006i 1.00175 1.00175i 0.00175431 0.999998i \(-0.499442\pi\)
0.999998 0.00175431i \(-0.000558414\pi\)
\(510\) 13.6150 + 8.62661i 0.602881 + 0.381993i
\(511\) 0 0
\(512\) 8.19353 21.0918i 0.362106 0.932137i
\(513\) 2.46846 0.108985
\(514\) 4.48631 + 2.84258i 0.197883 + 0.125381i
\(515\) −4.10363 + 4.10363i −0.180827 + 0.180827i
\(516\) 8.92802 + 18.9025i 0.393034 + 0.832135i
\(517\) 0.399629 + 0.399629i 0.0175757 + 0.0175757i
\(518\) 0 0
\(519\) 11.0172i 0.483600i
\(520\) −1.02903 + 8.28925i −0.0451261 + 0.363508i
\(521\) 2.76916i 0.121319i −0.998159 0.0606595i \(-0.980680\pi\)
0.998159 0.0606595i \(-0.0193204\pi\)
\(522\) 0.0986408 + 0.439809i 0.00431739 + 0.0192499i
\(523\) −15.6353 15.6353i −0.683686 0.683686i 0.277143 0.960829i \(-0.410612\pi\)
−0.960829 + 0.277143i \(0.910612\pi\)
\(524\) 23.7384 + 8.50786i 1.03702 + 0.371668i
\(525\) 0 0
\(526\) 14.2684 22.5191i 0.622131 0.981879i
\(527\) −44.8190 −1.95235
\(528\) 10.0388 12.2061i 0.436885 0.531203i
\(529\) −23.8377 −1.03642
\(530\) 5.93455 9.36622i 0.257780 0.406843i
\(531\) −10.7079 + 10.7079i −0.464685 + 0.464685i
\(532\) 0 0
\(533\) −5.05178 5.05178i −0.218817 0.218817i
\(534\) −11.0052 49.0687i −0.476240 2.12341i
\(535\) 3.72617i 0.161096i
\(536\) −18.0811 23.2066i −0.780987 1.00237i
\(537\) 19.7252i 0.851207i
\(538\) 23.6640 5.30737i 1.02023 0.228817i
\(539\) 0 0
\(540\) −6.94375 + 3.27967i −0.298811 + 0.141135i
\(541\) 23.6185 23.6185i 1.01544 1.01544i 0.0155590 0.999879i \(-0.495047\pi\)
0.999879 0.0155590i \(-0.00495280\pi\)
\(542\) −6.34592 4.02085i −0.272580 0.172710i
\(543\) 24.1014 1.03429
\(544\) −30.5102 + 10.0346i −1.30811 + 0.430232i
\(545\) −9.94683 −0.426075
\(546\) 0 0
\(547\) 3.45137 3.45137i 0.147570 0.147570i −0.629462 0.777032i \(-0.716724\pi\)
0.777032 + 0.629462i \(0.216724\pi\)
\(548\) −29.3026 + 13.8402i −1.25174 + 0.591224i
\(549\) −2.87868 2.87868i −0.122859 0.122859i
\(550\) −10.8255 + 2.42794i −0.461599 + 0.103528i
\(551\) 0.187130i 0.00797201i
\(552\) −30.8702 + 24.0521i −1.31392 + 1.02373i
\(553\) 0 0
\(554\) −4.70464 20.9765i −0.199881 0.891208i
\(555\) −14.1147 14.1147i −0.599138 0.599138i
\(556\) 10.0215 27.9618i 0.425008 1.18585i
\(557\) −15.5967 + 15.5967i −0.660853 + 0.660853i −0.955581 0.294728i \(-0.904771\pi\)
0.294728 + 0.955581i \(0.404771\pi\)
\(558\) −6.49591 + 10.2522i −0.274994 + 0.434009i
\(559\) 15.3776 0.650403
\(560\) 0 0
\(561\) −22.4327 −0.947109
\(562\) 2.39023 3.77239i 0.100826 0.159129i
\(563\) 19.5230 19.5230i 0.822798 0.822798i −0.163710 0.986508i \(-0.552346\pi\)
0.986508 + 0.163710i \(0.0523462\pi\)
\(564\) −1.10072 0.394498i −0.0463487 0.0166114i
\(565\) 3.56283 + 3.56283i 0.149889 + 0.149889i
\(566\) 4.36902 + 19.4801i 0.183644 + 0.818811i
\(567\) 0 0
\(568\) −32.5448 4.04014i −1.36555 0.169521i
\(569\) 35.0633i 1.46993i −0.678105 0.734965i \(-0.737198\pi\)
0.678105 0.734965i \(-0.262802\pi\)
\(570\) 1.76815 0.396561i 0.0740595 0.0166101i
\(571\) −0.913269 0.913269i −0.0382191 0.0382191i 0.687739 0.725958i \(-0.258603\pi\)
−0.725958 + 0.687739i \(0.758603\pi\)
\(572\) −4.96498 10.5119i −0.207596 0.439524i
\(573\) −7.04827 + 7.04827i −0.294446 + 0.294446i
\(574\) 0 0
\(575\) 27.4720 1.14566
\(576\) −2.12665 + 8.43348i −0.0886104 + 0.351395i
\(577\) −15.3294 −0.638171 −0.319086 0.947726i \(-0.603376\pi\)
−0.319086 + 0.947726i \(0.603376\pi\)
\(578\) 18.2014 + 11.5327i 0.757080 + 0.479695i
\(579\) 31.3194 31.3194i 1.30159 1.30159i
\(580\) −0.248627 0.526395i −0.0103237 0.0218574i
\(581\) 0 0
\(582\) −34.2244 + 7.67588i −1.41865 + 0.318176i
\(583\) 15.4322i 0.639138i
\(584\) −1.00725 0.125040i −0.0416801 0.00517420i
\(585\) 3.21066i 0.132744i
\(586\) 4.78547 + 21.3370i 0.197686 + 0.881423i
\(587\) 27.8270 + 27.8270i 1.14854 + 1.14854i 0.986840 + 0.161702i \(0.0516982\pi\)
0.161702 + 0.986840i \(0.448302\pi\)
\(588\) 0 0
\(589\) −3.56299 + 3.56299i −0.146810 + 0.146810i
\(590\) 10.4682 16.5215i 0.430969 0.680178i
\(591\) 21.7858 0.896148
\(592\) 39.5892 3.85708i 1.62711 0.158525i
\(593\) −17.7962 −0.730803 −0.365401 0.930850i \(-0.619068\pi\)
−0.365401 + 0.930850i \(0.619068\pi\)
\(594\) 5.72043 9.02828i 0.234712 0.370435i
\(595\) 0 0
\(596\) −6.71981 + 18.7495i −0.275254 + 0.768008i
\(597\) 5.11236 + 5.11236i 0.209235 + 0.209235i
\(598\) 6.29987 + 28.0892i 0.257621 + 1.14865i
\(599\) 19.1935i 0.784226i −0.919917 0.392113i \(-0.871744\pi\)
0.919917 0.392113i \(-0.128256\pi\)
\(600\) 18.1065 14.1074i 0.739195 0.575934i
\(601\) 26.9530i 1.09944i 0.835351 + 0.549718i \(0.185265\pi\)
−0.835351 + 0.549718i \(0.814735\pi\)
\(602\) 0 0
\(603\) 7.99597 + 7.99597i 0.325621 + 0.325621i
\(604\) −18.7444 + 8.85337i −0.762700 + 0.360238i
\(605\) 5.04144 5.04144i 0.204964 0.204964i
\(606\) 2.92178 + 1.85128i 0.118689 + 0.0752030i
\(607\) 29.4551 1.19555 0.597773 0.801665i \(-0.296052\pi\)
0.597773 + 0.801665i \(0.296052\pi\)
\(608\) −1.62775 + 3.22320i −0.0660140 + 0.130718i
\(609\) 0 0
\(610\) 4.44157 + 2.81424i 0.179834 + 0.113945i
\(611\) −0.608197 + 0.608197i −0.0246050 + 0.0246050i
\(612\) 11.1629 5.27247i 0.451235 0.213127i
\(613\) −17.6491 17.6491i −0.712839 0.712839i 0.254289 0.967128i \(-0.418159\pi\)
−0.967128 + 0.254289i \(0.918159\pi\)
\(614\) 28.8308 6.46620i 1.16352 0.260955i
\(615\) 4.82165i 0.194428i
\(616\) 0 0
\(617\) 10.8407i 0.436431i 0.975901 + 0.218216i \(0.0700236\pi\)
−0.975901 + 0.218216i \(0.929976\pi\)
\(618\) 3.65711 + 16.3059i 0.147110 + 0.655921i
\(619\) −14.1990 14.1990i −0.570707 0.570707i 0.361619 0.932326i \(-0.382224\pi\)
−0.932326 + 0.361619i \(0.882224\pi\)
\(620\) 5.28875 14.7566i 0.212401 0.592638i
\(621\) −18.7141 + 18.7141i −0.750969 + 0.750969i
\(622\) −6.61232 + 10.4359i −0.265130 + 0.418442i
\(623\) 0 0
\(624\) 18.5766 + 15.2782i 0.743657 + 0.611616i
\(625\) −11.1840 −0.447361
\(626\) −3.11686 + 4.91919i −0.124575 + 0.196610i
\(627\) −1.78334 + 1.78334i −0.0712197 + 0.0712197i
\(628\) 7.76760 + 2.78391i 0.309961 + 0.111090i
\(629\) −39.9233 39.9233i −1.59185 1.59185i
\(630\) 0 0
\(631\) 5.71697i 0.227589i −0.993504 0.113794i \(-0.963699\pi\)
0.993504 0.113794i \(-0.0363005\pi\)
\(632\) −2.68272 + 21.6103i −0.106713 + 0.859613i
\(633\) 20.9782i 0.833808i
\(634\) 33.7098 7.56045i 1.33879 0.300264i
\(635\) −7.84307 7.84307i −0.311243 0.311243i
\(636\) −13.6359 28.8700i −0.540698 1.14477i
\(637\) 0 0
\(638\) 0.684421 + 0.433657i 0.0270965 + 0.0171687i
\(639\) 12.6055 0.498668
\(640\) 0.296393 11.2295i 0.0117160 0.443886i
\(641\) 29.6950 1.17288 0.586441 0.809992i \(-0.300528\pi\)
0.586441 + 0.809992i \(0.300528\pi\)
\(642\) −9.06340 5.74268i −0.357704 0.226646i
\(643\) −3.53512 + 3.53512i −0.139412 + 0.139412i −0.773368 0.633957i \(-0.781430\pi\)
0.633957 + 0.773368i \(0.281430\pi\)
\(644\) 0 0
\(645\) 7.33854 + 7.33854i 0.288955 + 0.288955i
\(646\) 5.00117 1.12167i 0.196768 0.0441314i
\(647\) 14.7556i 0.580104i −0.957011 0.290052i \(-0.906327\pi\)
0.957011 0.290052i \(-0.0936726\pi\)
\(648\) −3.86066 + 31.0991i −0.151661 + 1.22169i
\(649\) 27.2216i 1.06854i
\(650\) −3.69510 16.4753i −0.144934 0.646216i
\(651\) 0 0
\(652\) 15.5597 + 5.57659i 0.609364 + 0.218396i
\(653\) −7.00360 + 7.00360i −0.274072 + 0.274072i −0.830737 0.556665i \(-0.812081\pi\)
0.556665 + 0.830737i \(0.312081\pi\)
\(654\) −15.3298 + 24.1943i −0.599443 + 0.946073i
\(655\) 12.5190 0.489159
\(656\) 7.42071 + 6.10312i 0.289730 + 0.238287i
\(657\) 0.390135 0.0152206
\(658\) 0 0
\(659\) 5.68205 5.68205i 0.221341 0.221341i −0.587722 0.809063i \(-0.699975\pi\)
0.809063 + 0.587722i \(0.199975\pi\)
\(660\) 2.64711 7.38591i 0.103039 0.287496i
\(661\) 6.78275 + 6.78275i 0.263819 + 0.263819i 0.826603 0.562785i \(-0.190270\pi\)
−0.562785 + 0.826603i \(0.690270\pi\)
\(662\) 2.26050 + 10.0789i 0.0878569 + 0.391727i
\(663\) 34.1404i 1.32590i
\(664\) 1.04238 + 1.33786i 0.0404521 + 0.0519192i
\(665\) 0 0
\(666\) −14.9187 + 3.34597i −0.578086 + 0.129654i
\(667\) −1.41869 1.41869i −0.0549317 0.0549317i
\(668\) −16.1433 + 7.62479i −0.624602 + 0.295012i
\(669\) −6.09037 + 6.09037i −0.235467 + 0.235467i
\(670\) −12.3371 7.81695i −0.476625 0.301995i
\(671\) −7.31815 −0.282514
\(672\) 0 0
\(673\) 3.24280 0.125001 0.0625004 0.998045i \(-0.480093\pi\)
0.0625004 + 0.998045i \(0.480093\pi\)
\(674\) −11.3963 7.22086i −0.438971 0.278137i
\(675\) 10.9765 10.9765i 0.422485 0.422485i
\(676\) −7.51147 + 3.54782i −0.288903 + 0.136454i
\(677\) −23.7096 23.7096i −0.911234 0.911234i 0.0851352 0.996369i \(-0.472868\pi\)
−0.996369 + 0.0851352i \(0.972868\pi\)
\(678\) 14.1570 3.17515i 0.543698 0.121941i
\(679\) 0 0
\(680\) −12.5780 + 9.79995i −0.482343 + 0.375811i
\(681\) 9.78140i 0.374824i
\(682\) 4.77458 + 21.2884i 0.182828 + 0.815175i
\(683\) 13.1530 + 13.1530i 0.503284 + 0.503284i 0.912457 0.409173i \(-0.134183\pi\)
−0.409173 + 0.912457i \(0.634183\pi\)
\(684\) 0.468275 1.30657i 0.0179049 0.0499580i
\(685\) −11.3762 + 11.3762i −0.434662 + 0.434662i
\(686\) 0 0
\(687\) 39.6602 1.51313
\(688\) −20.5832 + 2.00537i −0.784728 + 0.0764540i
\(689\) −23.4864 −0.894761
\(690\) −10.3984 + 16.4112i −0.395859 + 0.624765i
\(691\) −15.3221 + 15.3221i −0.582878 + 0.582878i −0.935693 0.352815i \(-0.885225\pi\)
0.352815 + 0.935693i \(0.385225\pi\)
\(692\) −10.2600 3.67718i −0.390026 0.139786i
\(693\) 0 0
\(694\) 2.82783 + 12.6085i 0.107343 + 0.478611i
\(695\) 14.7463i 0.559361i
\(696\) −1.66356 0.206516i −0.0630572 0.00782797i
\(697\) 13.6380i 0.516574i
\(698\) −47.7853 + 10.7173i −1.80870 + 0.405657i
\(699\) −7.24128 7.24128i −0.273891 0.273891i
\(700\) 0 0
\(701\) 4.96023 4.96023i 0.187345 0.187345i −0.607202 0.794547i \(-0.707708\pi\)
0.794547 + 0.607202i \(0.207708\pi\)
\(702\) 13.7402 + 8.70595i 0.518590 + 0.328585i
\(703\) −6.34759 −0.239404
\(704\) 8.01657 + 13.4229i 0.302136 + 0.505895i
\(705\) −0.580491 −0.0218626
\(706\) 31.1438 + 19.7331i 1.17211 + 0.742664i
\(707\) 0 0
\(708\) −24.0529 50.9250i −0.903963 1.91388i
\(709\) −10.2322 10.2322i −0.384277 0.384277i 0.488363 0.872640i \(-0.337594\pi\)
−0.872640 + 0.488363i \(0.837594\pi\)
\(710\) −15.8863 + 3.56300i −0.596203 + 0.133717i
\(711\) 8.37030i 0.313911i
\(712\) 49.3695 + 6.12877i 1.85020 + 0.229685i
\(713\) 54.0240i 2.02321i
\(714\) 0 0
\(715\) −4.08105 4.08105i −0.152623 0.152623i
\(716\) 18.3696 + 6.58365i 0.686503 + 0.246043i
\(717\) −13.3304 + 13.3304i −0.497833 + 0.497833i
\(718\) −2.63724 + 4.16223i −0.0984209 + 0.155333i
\(719\) −33.1292 −1.23551 −0.617756 0.786370i \(-0.711958\pi\)
−0.617756 + 0.786370i \(0.711958\pi\)
\(720\) 0.418698 + 4.29753i 0.0156039 + 0.160160i
\(721\) 0 0
\(722\) −14.0730 + 22.2107i −0.523742 + 0.826598i
\(723\) −36.7857 + 36.7857i −1.36808 + 1.36808i
\(724\) −8.04428 + 22.4450i −0.298963 + 0.834160i
\(725\) 0.832110 + 0.832110i 0.0309038 + 0.0309038i
\(726\) −4.49288 20.0324i −0.166746 0.743471i
\(727\) 23.5496i 0.873406i −0.899606 0.436703i \(-0.856146\pi\)
0.899606 0.436703i \(-0.143854\pi\)
\(728\) 0 0
\(729\) 11.4085i 0.422538i
\(730\) −0.491673 + 0.110273i −0.0181977 + 0.00408138i
\(731\) 20.7569 + 20.7569i 0.767723 + 0.767723i
\(732\) 13.6905 6.46630i 0.506015 0.239001i
\(733\) −1.26479 + 1.26479i −0.0467162 + 0.0467162i −0.730079 0.683363i \(-0.760517\pi\)
0.683363 + 0.730079i \(0.260517\pi\)
\(734\) −29.2153 18.5112i −1.07836 0.683260i
\(735\) 0 0
\(736\) −12.0956 36.7764i −0.445849 1.35560i
\(737\) 20.3272 0.748764
\(738\) −3.11963 1.97664i −0.114835 0.0727610i
\(739\) 16.5610 16.5610i 0.609206 0.609206i −0.333532 0.942739i \(-0.608241\pi\)
0.942739 + 0.333532i \(0.108241\pi\)
\(740\) 17.8557 8.43362i 0.656389 0.310026i
\(741\) −2.71407 2.71407i −0.0997039 0.0997039i
\(742\) 0 0
\(743\) 13.9219i 0.510747i −0.966843 0.255373i \(-0.917802\pi\)
0.966843 0.255373i \(-0.0821984\pi\)
\(744\) −27.7424 35.6066i −1.01709 1.30540i
\(745\) 9.88798i 0.362268i
\(746\) 11.3743 + 50.7147i 0.416444 + 1.85680i
\(747\) −0.460968 0.460968i −0.0168659 0.0168659i
\(748\) 7.48732 20.8909i 0.273763 0.763848i
\(749\) 0 0
\(750\) 13.6959 21.6156i 0.500104 0.789291i
\(751\) −9.07708 −0.331227 −0.165614 0.986191i \(-0.552960\pi\)
−0.165614 + 0.986191i \(0.552960\pi\)
\(752\) 0.734770 0.893399i 0.0267943 0.0325789i
\(753\) 10.4177 0.379642
\(754\) −0.659985 + 1.04162i −0.0240352 + 0.0379337i
\(755\) −7.27718 + 7.27718i −0.264844 + 0.264844i
\(756\) 0 0
\(757\) −1.14043 1.14043i −0.0414496 0.0414496i 0.686078 0.727528i \(-0.259331\pi\)
−0.727528 + 0.686078i \(0.759331\pi\)
\(758\) 8.10525 + 36.1389i 0.294396 + 1.31262i
\(759\) 27.0400i 0.981488i
\(760\) −0.220844 + 1.77898i −0.00801087 + 0.0645305i
\(761\) 8.78122i 0.318319i −0.987253 0.159159i \(-0.949122\pi\)
0.987253 0.159159i \(-0.0508784\pi\)
\(762\) −31.1648 + 6.98966i −1.12898 + 0.253209i
\(763\) 0 0
\(764\) −4.21137 8.91635i −0.152362 0.322582i
\(765\) 4.33380 4.33380i 0.156689 0.156689i
\(766\) 18.8696 + 11.9560i 0.681787 + 0.431989i
\(767\) −41.4287 −1.49590
\(768\) −26.8575 18.0276i −0.969136 0.650515i
\(769\) −29.8204 −1.07535 −0.537676 0.843152i \(-0.680697\pi\)
−0.537676 + 0.843152i \(0.680697\pi\)
\(770\) 0 0
\(771\) 5.36862 5.36862i 0.193346 0.193346i
\(772\) 18.7134 + 39.6202i 0.673511 + 1.42596i
\(773\) −32.6111 32.6111i −1.17294 1.17294i −0.981505 0.191435i \(-0.938686\pi\)
−0.191435 0.981505i \(-0.561314\pi\)
\(774\) 7.75651 1.73964i 0.278802 0.0625299i
\(775\) 31.6870i 1.13823i
\(776\) 4.27469 34.4342i 0.153452 1.23612i
\(777\) 0 0
\(778\) 1.76452 + 7.86746i 0.0632611 + 0.282062i
\(779\) −1.08418 1.08418i −0.0388448 0.0388448i
\(780\) 11.2407 + 4.02866i 0.402480 + 0.144249i
\(781\) 16.0228 16.0228i 0.573342 0.573342i
\(782\) −29.4116 + 46.4189i −1.05176 + 1.65994i