Properties

Label 450.2.p.c.407.1
Level 450
Weight 2
Character 450.407
Analytic conductor 3.593
Analytic rank 0
Dimension 8
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.p (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 407.1
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 450.407
Dual form 450.2.p.c.293.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.258819 - 0.965926i) q^{2} +(1.22474 + 1.22474i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.866025 - 1.50000i) q^{6} +(1.22474 - 0.328169i) q^{7} +(0.707107 + 0.707107i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(-0.258819 - 0.965926i) q^{2} +(1.22474 + 1.22474i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.866025 - 1.50000i) q^{6} +(1.22474 - 0.328169i) q^{7} +(0.707107 + 0.707107i) q^{8} +3.00000i q^{9} +(3.00000 + 1.73205i) q^{11} +(-1.67303 - 0.448288i) q^{12} +(-1.22474 - 0.328169i) q^{13} +(-0.633975 - 1.09808i) q^{14} +(0.500000 - 0.866025i) q^{16} +(2.89778 - 0.776457i) q^{18} +7.19615i q^{19} +(1.90192 + 1.09808i) q^{21} +(0.896575 - 3.34607i) q^{22} +(2.12132 - 7.91688i) q^{23} +1.73205i q^{24} +1.26795i q^{26} +(-3.67423 + 3.67423i) q^{27} +(-0.896575 + 0.896575i) q^{28} +(3.63397 - 6.29423i) q^{29} +(5.09808 + 8.83013i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(1.55291 + 5.79555i) q^{33} +(-1.50000 - 2.59808i) q^{36} +(1.55291 + 1.55291i) q^{37} +(6.95095 - 1.86250i) q^{38} +(-1.09808 - 1.90192i) q^{39} +(-1.50000 + 0.866025i) q^{41} +(0.568406 - 2.12132i) q^{42} +(-1.67303 - 6.24384i) q^{43} -3.46410 q^{44} -8.19615 q^{46} +(1.55291 + 5.79555i) q^{47} +(1.67303 - 0.448288i) q^{48} +(-4.66987 + 2.69615i) q^{49} +(1.22474 - 0.328169i) q^{52} +(-1.55291 - 1.55291i) q^{53} +(4.50000 + 2.59808i) q^{54} +(1.09808 + 0.633975i) q^{56} +(-8.81345 + 8.81345i) q^{57} +(-7.02030 - 1.88108i) q^{58} +(-6.23205 - 10.7942i) q^{59} +(2.00000 - 3.46410i) q^{61} +(7.20977 - 7.20977i) q^{62} +(0.984508 + 3.67423i) q^{63} +1.00000i q^{64} +(5.19615 - 3.00000i) q^{66} +(3.22595 - 12.0394i) q^{67} +(12.2942 - 7.09808i) q^{69} -10.7321i q^{71} +(-2.12132 + 2.12132i) q^{72} +(-3.67423 + 3.67423i) q^{73} +(1.09808 - 1.90192i) q^{74} +(-3.59808 - 6.23205i) q^{76} +(4.24264 + 1.13681i) q^{77} +(-1.55291 + 1.55291i) q^{78} +(-8.66025 - 5.00000i) q^{79} -9.00000 q^{81} +(1.22474 + 1.22474i) q^{82} +(-6.57201 + 1.76097i) q^{83} -2.19615 q^{84} +(-5.59808 + 3.23205i) q^{86} +(12.1595 - 3.25813i) q^{87} +(0.896575 + 3.34607i) q^{88} +8.66025 q^{89} -1.60770 q^{91} +(2.12132 + 7.91688i) q^{92} +(-4.57081 + 17.0585i) q^{93} +(5.19615 - 3.00000i) q^{94} +(-0.866025 - 1.50000i) q^{96} +(-14.1607 + 3.79435i) q^{97} +(3.81294 + 3.81294i) q^{98} +(-5.19615 + 9.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q + 24q^{11} - 12q^{14} + 4q^{16} + 36q^{21} + 36q^{29} + 20q^{31} - 12q^{36} + 12q^{39} - 12q^{41} - 24q^{46} - 72q^{49} + 36q^{54} - 12q^{56} - 36q^{59} + 16q^{61} + 36q^{69} - 12q^{74} - 8q^{76} - 72q^{81} + 24q^{84} - 24q^{86} - 96q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.258819 0.965926i −0.183013 0.683013i
\(3\) 1.22474 + 1.22474i 0.707107 + 0.707107i
\(4\) −0.866025 + 0.500000i −0.433013 + 0.250000i
\(5\) 0 0
\(6\) 0.866025 1.50000i 0.353553 0.612372i
\(7\) 1.22474 0.328169i 0.462910 0.124036i −0.0198238 0.999803i \(-0.506311\pi\)
0.482734 + 0.875767i \(0.339644\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 3.00000i 1.00000i
\(10\) 0 0
\(11\) 3.00000 + 1.73205i 0.904534 + 0.522233i 0.878668 0.477432i \(-0.158432\pi\)
0.0258656 + 0.999665i \(0.491766\pi\)
\(12\) −1.67303 0.448288i −0.482963 0.129410i
\(13\) −1.22474 0.328169i −0.339683 0.0910178i 0.0849451 0.996386i \(-0.472929\pi\)
−0.424628 + 0.905368i \(0.639595\pi\)
\(14\) −0.633975 1.09808i −0.169437 0.293473i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(18\) 2.89778 0.776457i 0.683013 0.183013i
\(19\) 7.19615i 1.65091i 0.564467 + 0.825455i \(0.309082\pi\)
−0.564467 + 0.825455i \(0.690918\pi\)
\(20\) 0 0
\(21\) 1.90192 + 1.09808i 0.415034 + 0.239620i
\(22\) 0.896575 3.34607i 0.191151 0.713384i
\(23\) 2.12132 7.91688i 0.442326 1.65078i −0.280576 0.959832i \(-0.590525\pi\)
0.722902 0.690951i \(-0.242808\pi\)
\(24\) 1.73205i 0.353553i
\(25\) 0 0
\(26\) 1.26795i 0.248665i
\(27\) −3.67423 + 3.67423i −0.707107 + 0.707107i
\(28\) −0.896575 + 0.896575i −0.169437 + 0.169437i
\(29\) 3.63397 6.29423i 0.674812 1.16881i −0.301712 0.953399i \(-0.597558\pi\)
0.976524 0.215410i \(-0.0691087\pi\)
\(30\) 0 0
\(31\) 5.09808 + 8.83013i 0.915642 + 1.58594i 0.805959 + 0.591971i \(0.201650\pi\)
0.109682 + 0.993967i \(0.465017\pi\)
\(32\) −0.965926 0.258819i −0.170753 0.0457532i
\(33\) 1.55291 + 5.79555i 0.270328 + 1.00888i
\(34\) 0 0
\(35\) 0 0
\(36\) −1.50000 2.59808i −0.250000 0.433013i
\(37\) 1.55291 + 1.55291i 0.255298 + 0.255298i 0.823138 0.567841i \(-0.192221\pi\)
−0.567841 + 0.823138i \(0.692221\pi\)
\(38\) 6.95095 1.86250i 1.12759 0.302138i
\(39\) −1.09808 1.90192i −0.175833 0.304552i
\(40\) 0 0
\(41\) −1.50000 + 0.866025i −0.234261 + 0.135250i −0.612536 0.790443i \(-0.709851\pi\)
0.378275 + 0.925693i \(0.376517\pi\)
\(42\) 0.568406 2.12132i 0.0877070 0.327327i
\(43\) −1.67303 6.24384i −0.255135 0.952177i −0.968015 0.250891i \(-0.919276\pi\)
0.712880 0.701286i \(-0.247390\pi\)
\(44\) −3.46410 −0.522233
\(45\) 0 0
\(46\) −8.19615 −1.20846
\(47\) 1.55291 + 5.79555i 0.226516 + 0.845369i 0.981792 + 0.189961i \(0.0608363\pi\)
−0.755276 + 0.655407i \(0.772497\pi\)
\(48\) 1.67303 0.448288i 0.241481 0.0647048i
\(49\) −4.66987 + 2.69615i −0.667125 + 0.385165i
\(50\) 0 0
\(51\) 0 0
\(52\) 1.22474 0.328169i 0.169842 0.0455089i
\(53\) −1.55291 1.55291i −0.213309 0.213309i 0.592362 0.805672i \(-0.298195\pi\)
−0.805672 + 0.592362i \(0.798195\pi\)
\(54\) 4.50000 + 2.59808i 0.612372 + 0.353553i
\(55\) 0 0
\(56\) 1.09808 + 0.633975i 0.146737 + 0.0847184i
\(57\) −8.81345 + 8.81345i −1.16737 + 1.16737i
\(58\) −7.02030 1.88108i −0.921811 0.246998i
\(59\) −6.23205 10.7942i −0.811344 1.40529i −0.911924 0.410360i \(-0.865403\pi\)
0.100580 0.994929i \(-0.467930\pi\)
\(60\) 0 0
\(61\) 2.00000 3.46410i 0.256074 0.443533i −0.709113 0.705095i \(-0.750904\pi\)
0.965187 + 0.261562i \(0.0842377\pi\)
\(62\) 7.20977 7.20977i 0.915642 0.915642i
\(63\) 0.984508 + 3.67423i 0.124036 + 0.462910i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 5.19615 3.00000i 0.639602 0.369274i
\(67\) 3.22595 12.0394i 0.394112 1.47085i −0.429175 0.903221i \(-0.641196\pi\)
0.823287 0.567625i \(-0.192138\pi\)
\(68\) 0 0
\(69\) 12.2942 7.09808i 1.48005 0.854508i
\(70\) 0 0
\(71\) 10.7321i 1.27366i −0.771004 0.636830i \(-0.780245\pi\)
0.771004 0.636830i \(-0.219755\pi\)
\(72\) −2.12132 + 2.12132i −0.250000 + 0.250000i
\(73\) −3.67423 + 3.67423i −0.430037 + 0.430037i −0.888641 0.458604i \(-0.848350\pi\)
0.458604 + 0.888641i \(0.348350\pi\)
\(74\) 1.09808 1.90192i 0.127649 0.221094i
\(75\) 0 0
\(76\) −3.59808 6.23205i −0.412728 0.714865i
\(77\) 4.24264 + 1.13681i 0.483494 + 0.129552i
\(78\) −1.55291 + 1.55291i −0.175833 + 0.175833i
\(79\) −8.66025 5.00000i −0.974355 0.562544i −0.0737937 0.997274i \(-0.523511\pi\)
−0.900561 + 0.434730i \(0.856844\pi\)
\(80\) 0 0
\(81\) −9.00000 −1.00000
\(82\) 1.22474 + 1.22474i 0.135250 + 0.135250i
\(83\) −6.57201 + 1.76097i −0.721372 + 0.193291i −0.600784 0.799412i \(-0.705145\pi\)
−0.120588 + 0.992703i \(0.538478\pi\)
\(84\) −2.19615 −0.239620
\(85\) 0 0
\(86\) −5.59808 + 3.23205i −0.603656 + 0.348521i
\(87\) 12.1595 3.25813i 1.30364 0.349308i
\(88\) 0.896575 + 3.34607i 0.0955753 + 0.356692i
\(89\) 8.66025 0.917985 0.458993 0.888440i \(-0.348210\pi\)
0.458993 + 0.888440i \(0.348210\pi\)
\(90\) 0 0
\(91\) −1.60770 −0.168532
\(92\) 2.12132 + 7.91688i 0.221163 + 0.825391i
\(93\) −4.57081 + 17.0585i −0.473971 + 1.76888i
\(94\) 5.19615 3.00000i 0.535942 0.309426i
\(95\) 0 0
\(96\) −0.866025 1.50000i −0.0883883 0.153093i
\(97\) −14.1607 + 3.79435i −1.43780 + 0.385258i −0.891764 0.452501i \(-0.850532\pi\)
−0.546039 + 0.837760i \(0.683865\pi\)
\(98\) 3.81294 + 3.81294i 0.385165 + 0.385165i
\(99\) −5.19615 + 9.00000i −0.522233 + 0.904534i
\(100\) 0 0
\(101\) −9.29423 5.36603i −0.924810 0.533939i −0.0396438 0.999214i \(-0.512622\pi\)
−0.885167 + 0.465274i \(0.845956\pi\)
\(102\) 0 0
\(103\) −10.0382 2.68973i −0.989093 0.265027i −0.272223 0.962234i \(-0.587759\pi\)
−0.716869 + 0.697207i \(0.754426\pi\)
\(104\) −0.633975 1.09808i −0.0621663 0.107675i
\(105\) 0 0
\(106\) −1.09808 + 1.90192i −0.106655 + 0.184731i
\(107\) 0.568406 0.568406i 0.0549499 0.0549499i −0.679098 0.734048i \(-0.737629\pi\)
0.734048 + 0.679098i \(0.237629\pi\)
\(108\) 1.34486 5.01910i 0.129410 0.482963i
\(109\) 12.1962i 1.16818i 0.811689 + 0.584090i \(0.198548\pi\)
−0.811689 + 0.584090i \(0.801452\pi\)
\(110\) 0 0
\(111\) 3.80385i 0.361045i
\(112\) 0.328169 1.22474i 0.0310091 0.115728i
\(113\) 1.91327 7.14042i 0.179985 0.671714i −0.815663 0.578527i \(-0.803628\pi\)
0.995649 0.0931872i \(-0.0297055\pi\)
\(114\) 10.7942 + 6.23205i 1.01097 + 0.583685i
\(115\) 0 0
\(116\) 7.26795i 0.674812i
\(117\) 0.984508 3.67423i 0.0910178 0.339683i
\(118\) −8.81345 + 8.81345i −0.811344 + 0.811344i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.500000 + 0.866025i 0.0454545 + 0.0787296i
\(122\) −3.86370 1.03528i −0.349803 0.0937295i
\(123\) −2.89778 0.776457i −0.261284 0.0700108i
\(124\) −8.83013 5.09808i −0.792969 0.457821i
\(125\) 0 0
\(126\) 3.29423 1.90192i 0.293473 0.169437i
\(127\) 1.55291 + 1.55291i 0.137799 + 0.137799i 0.772641 0.634843i \(-0.218935\pi\)
−0.634843 + 0.772641i \(0.718935\pi\)
\(128\) 0.965926 0.258819i 0.0853766 0.0228766i
\(129\) 5.59808 9.69615i 0.492883 0.853699i
\(130\) 0 0
\(131\) −6.00000 + 3.46410i −0.524222 + 0.302660i −0.738661 0.674078i \(-0.764541\pi\)
0.214438 + 0.976738i \(0.431208\pi\)
\(132\) −4.24264 4.24264i −0.369274 0.369274i
\(133\) 2.36156 + 8.81345i 0.204773 + 0.764223i
\(134\) −12.4641 −1.07673
\(135\) 0 0
\(136\) 0 0
\(137\) 1.91327 + 7.14042i 0.163462 + 0.610047i 0.998231 + 0.0594480i \(0.0189340\pi\)
−0.834770 + 0.550599i \(0.814399\pi\)
\(138\) −10.0382 10.0382i −0.854508 0.854508i
\(139\) 6.92820 4.00000i 0.587643 0.339276i −0.176522 0.984297i \(-0.556485\pi\)
0.764165 + 0.645021i \(0.223151\pi\)
\(140\) 0 0
\(141\) −5.19615 + 9.00000i −0.437595 + 0.757937i
\(142\) −10.3664 + 2.77766i −0.869926 + 0.233096i
\(143\) −3.10583 3.10583i −0.259722 0.259722i
\(144\) 2.59808 + 1.50000i 0.216506 + 0.125000i
\(145\) 0 0
\(146\) 4.50000 + 2.59808i 0.372423 + 0.215018i
\(147\) −9.02150 2.41730i −0.744081 0.199376i
\(148\) −2.12132 0.568406i −0.174371 0.0467227i
\(149\) 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i \(0.0972370\pi\)
−0.216394 + 0.976306i \(0.569430\pi\)
\(150\) 0 0
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) −5.08845 + 5.08845i −0.412728 + 0.412728i
\(153\) 0 0
\(154\) 4.39230i 0.353942i
\(155\) 0 0
\(156\) 1.90192 + 1.09808i 0.152276 + 0.0879165i
\(157\) 2.03339 7.58871i 0.162282 0.605645i −0.836089 0.548593i \(-0.815163\pi\)
0.998371 0.0570512i \(-0.0181698\pi\)
\(158\) −2.58819 + 9.65926i −0.205905 + 0.768449i
\(159\) 3.80385i 0.301665i
\(160\) 0 0
\(161\) 10.3923i 0.819028i
\(162\) 2.32937 + 8.69333i 0.183013 + 0.683013i
\(163\) 14.3688 14.3688i 1.12545 1.12545i 0.134541 0.990908i \(-0.457044\pi\)
0.990908 0.134541i \(-0.0429559\pi\)
\(164\) 0.866025 1.50000i 0.0676252 0.117130i
\(165\) 0 0
\(166\) 3.40192 + 5.89230i 0.264040 + 0.457332i
\(167\) −4.24264 1.13681i −0.328305 0.0879692i 0.0909015 0.995860i \(-0.471025\pi\)
−0.419207 + 0.907891i \(0.637692\pi\)
\(168\) 0.568406 + 2.12132i 0.0438535 + 0.163663i
\(169\) −9.86603 5.69615i −0.758925 0.438166i
\(170\) 0 0
\(171\) −21.5885 −1.65091
\(172\) 4.57081 + 4.57081i 0.348521 + 0.348521i
\(173\) −4.24264 + 1.13681i −0.322562 + 0.0864302i −0.416467 0.909151i \(-0.636732\pi\)
0.0939047 + 0.995581i \(0.470065\pi\)
\(174\) −6.29423 10.9019i −0.477164 0.826473i
\(175\) 0 0
\(176\) 3.00000 1.73205i 0.226134 0.130558i
\(177\) 5.58750 20.8528i 0.419983 1.56740i
\(178\) −2.24144 8.36516i −0.168003 0.626995i
\(179\) −4.85641 −0.362985 −0.181492 0.983392i \(-0.558093\pi\)
−0.181492 + 0.983392i \(0.558093\pi\)
\(180\) 0 0
\(181\) 8.39230 0.623795 0.311898 0.950116i \(-0.399035\pi\)
0.311898 + 0.950116i \(0.399035\pi\)
\(182\) 0.416102 + 1.55291i 0.0308435 + 0.115110i
\(183\) 6.69213 1.79315i 0.494697 0.132554i
\(184\) 7.09808 4.09808i 0.523277 0.302114i
\(185\) 0 0
\(186\) 17.6603 1.29491
\(187\) 0 0
\(188\) −4.24264 4.24264i −0.309426 0.309426i
\(189\) −3.29423 + 5.70577i −0.239620 + 0.415034i
\(190\) 0 0
\(191\) 3.00000 + 1.73205i 0.217072 + 0.125327i 0.604594 0.796534i \(-0.293335\pi\)
−0.387522 + 0.921861i \(0.626669\pi\)
\(192\) −1.22474 + 1.22474i −0.0883883 + 0.0883883i
\(193\) 24.0788 + 6.45189i 1.73323 + 0.464417i 0.980923 0.194396i \(-0.0622746\pi\)
0.752306 + 0.658813i \(0.228941\pi\)
\(194\) 7.33013 + 12.6962i 0.526272 + 0.911531i
\(195\) 0 0
\(196\) 2.69615 4.66987i 0.192582 0.333562i
\(197\) −2.68973 + 2.68973i −0.191635 + 0.191635i −0.796402 0.604767i \(-0.793266\pi\)
0.604767 + 0.796402i \(0.293266\pi\)
\(198\) 10.0382 + 2.68973i 0.713384 + 0.191151i
\(199\) 0.392305i 0.0278098i −0.999903 0.0139049i \(-0.995574\pi\)
0.999903 0.0139049i \(-0.00442620\pi\)
\(200\) 0 0
\(201\) 18.6962 10.7942i 1.31872 0.761366i
\(202\) −2.77766 + 10.3664i −0.195435 + 0.729375i
\(203\) 2.38512 8.90138i 0.167403 0.624755i
\(204\) 0 0
\(205\) 0 0
\(206\) 10.3923i 0.724066i
\(207\) 23.7506 + 6.36396i 1.65078 + 0.442326i
\(208\) −0.896575 + 0.896575i −0.0621663 + 0.0621663i
\(209\) −12.4641 + 21.5885i −0.862160 + 1.49330i
\(210\) 0 0
\(211\) 4.59808 + 7.96410i 0.316545 + 0.548271i 0.979765 0.200153i \(-0.0641440\pi\)
−0.663220 + 0.748424i \(0.730811\pi\)
\(212\) 2.12132 + 0.568406i 0.145693 + 0.0390383i
\(213\) 13.1440 13.1440i 0.900614 0.900614i
\(214\) −0.696152 0.401924i −0.0475880 0.0274749i
\(215\) 0 0
\(216\) −5.19615 −0.353553
\(217\) 9.14162 + 9.14162i 0.620574 + 0.620574i
\(218\) 11.7806 3.15660i 0.797881 0.213792i
\(219\) −9.00000 −0.608164
\(220\) 0 0
\(221\) 0 0
\(222\) 3.67423 0.984508i 0.246598 0.0660759i
\(223\) 2.44949 + 9.14162i 0.164030 + 0.612168i 0.998162 + 0.0606032i \(0.0193024\pi\)
−0.834132 + 0.551565i \(0.814031\pi\)
\(224\) −1.26795 −0.0847184
\(225\) 0 0
\(226\) −7.39230 −0.491729
\(227\) −6.00361 22.4058i −0.398473 1.48712i −0.815783 0.578358i \(-0.803694\pi\)
0.417310 0.908764i \(-0.362973\pi\)
\(228\) 3.22595 12.0394i 0.213644 0.797329i
\(229\) 14.0263 8.09808i 0.926883 0.535136i 0.0410583 0.999157i \(-0.486927\pi\)
0.885824 + 0.464021i \(0.153594\pi\)
\(230\) 0 0
\(231\) 3.80385 + 6.58846i 0.250275 + 0.433489i
\(232\) 7.02030 1.88108i 0.460905 0.123499i
\(233\) 17.9551 + 17.9551i 1.17628 + 1.17628i 0.980686 + 0.195590i \(0.0626622\pi\)
0.195590 + 0.980686i \(0.437338\pi\)
\(234\) −3.80385 −0.248665
\(235\) 0 0
\(236\) 10.7942 + 6.23205i 0.702644 + 0.405672i
\(237\) −4.48288 16.7303i −0.291194 1.08675i
\(238\) 0 0
\(239\) −7.09808 12.2942i −0.459136 0.795248i 0.539779 0.841807i \(-0.318508\pi\)
−0.998916 + 0.0465591i \(0.985174\pi\)
\(240\) 0 0
\(241\) 5.69615 9.86603i 0.366921 0.635527i −0.622161 0.782889i \(-0.713745\pi\)
0.989083 + 0.147363i \(0.0470785\pi\)
\(242\) 0.707107 0.707107i 0.0454545 0.0454545i
\(243\) −11.0227 11.0227i −0.707107 0.707107i
\(244\) 4.00000i 0.256074i
\(245\) 0 0
\(246\) 3.00000i 0.191273i
\(247\) 2.36156 8.81345i 0.150262 0.560786i
\(248\) −2.63896 + 9.84873i −0.167574 + 0.625395i
\(249\) −10.2058 5.89230i −0.646764 0.373410i
\(250\) 0 0
\(251\) 9.00000i 0.568075i −0.958813 0.284037i \(-0.908326\pi\)
0.958813 0.284037i \(-0.0916740\pi\)
\(252\) −2.68973 2.68973i −0.169437 0.169437i
\(253\) 20.0764 20.0764i 1.26219 1.26219i
\(254\) 1.09808 1.90192i 0.0688994 0.119337i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 4.45069 + 1.19256i 0.277627 + 0.0743898i 0.394946 0.918704i \(-0.370763\pi\)
−0.117319 + 0.993094i \(0.537430\pi\)
\(258\) −10.8147 2.89778i −0.673291 0.180408i
\(259\) 2.41154 + 1.39230i 0.149846 + 0.0865136i
\(260\) 0 0
\(261\) 18.8827 + 10.9019i 1.16881 + 0.674812i
\(262\) 4.89898 + 4.89898i 0.302660 + 0.302660i
\(263\) −17.9551 + 4.81105i −1.10716 + 0.296662i −0.765676 0.643227i \(-0.777595\pi\)
−0.341481 + 0.939889i \(0.610929\pi\)
\(264\) −3.00000 + 5.19615i −0.184637 + 0.319801i
\(265\) 0 0
\(266\) 7.90192 4.56218i 0.484498 0.279725i
\(267\) 10.6066 + 10.6066i 0.649113 + 0.649113i
\(268\) 3.22595 + 12.0394i 0.197056 + 0.735423i
\(269\) 28.0526 1.71039 0.855197 0.518303i \(-0.173436\pi\)
0.855197 + 0.518303i \(0.173436\pi\)
\(270\) 0 0
\(271\) −4.58846 −0.278729 −0.139364 0.990241i \(-0.544506\pi\)
−0.139364 + 0.990241i \(0.544506\pi\)
\(272\) 0 0
\(273\) −1.96902 1.96902i −0.119170 0.119170i
\(274\) 6.40192 3.69615i 0.386754 0.223293i
\(275\) 0 0
\(276\) −7.09808 + 12.2942i −0.427254 + 0.740026i
\(277\) −24.6472 + 6.60420i −1.48091 + 0.396808i −0.906656 0.421871i \(-0.861373\pi\)
−0.574251 + 0.818679i \(0.694707\pi\)
\(278\) −5.65685 5.65685i −0.339276 0.339276i
\(279\) −26.4904 + 15.2942i −1.58594 + 0.915642i
\(280\) 0 0
\(281\) 9.00000 + 5.19615i 0.536895 + 0.309976i 0.743820 0.668380i \(-0.233012\pi\)
−0.206925 + 0.978357i \(0.566345\pi\)
\(282\) 10.0382 + 2.68973i 0.597766 + 0.160171i
\(283\) 9.58991 + 2.56961i 0.570061 + 0.152747i 0.532325 0.846540i \(-0.321319\pi\)
0.0377364 + 0.999288i \(0.487985\pi\)
\(284\) 5.36603 + 9.29423i 0.318415 + 0.551511i
\(285\) 0 0
\(286\) −2.19615 + 3.80385i −0.129861 + 0.224926i
\(287\) −1.55291 + 1.55291i −0.0916656 + 0.0916656i
\(288\) 0.776457 2.89778i 0.0457532 0.170753i
\(289\) 17.0000i 1.00000i
\(290\) 0 0
\(291\) −21.9904 12.6962i −1.28910 0.744262i
\(292\) 1.34486 5.01910i 0.0787022 0.293720i
\(293\) −3.67423 + 13.7124i −0.214651 + 0.801089i 0.771638 + 0.636062i \(0.219438\pi\)
−0.986289 + 0.165027i \(0.947229\pi\)
\(294\) 9.33975i 0.544705i
\(295\) 0 0
\(296\) 2.19615i 0.127649i
\(297\) −17.3867 + 4.65874i −1.00888 + 0.270328i
\(298\) 12.7279 12.7279i 0.737309 0.737309i
\(299\) −5.19615 + 9.00000i −0.300501 + 0.520483i
\(300\) 0 0
\(301\) −4.09808 7.09808i −0.236209 0.409126i
\(302\) −7.72741 2.07055i −0.444662 0.119147i
\(303\) −4.81105 17.9551i −0.276387 1.03149i
\(304\) 6.23205 + 3.59808i 0.357433 + 0.206364i
\(305\) 0 0
\(306\) 0 0
\(307\) 2.44949 + 2.44949i 0.139800 + 0.139800i 0.773543 0.633743i \(-0.218483\pi\)
−0.633743 + 0.773543i \(0.718483\pi\)
\(308\) −4.24264 + 1.13681i −0.241747 + 0.0647759i
\(309\) −9.00000 15.5885i −0.511992 0.886796i
\(310\) 0 0
\(311\) 21.5885 12.4641i 1.22417 0.706774i 0.258365 0.966047i \(-0.416816\pi\)
0.965804 + 0.259273i \(0.0834829\pi\)
\(312\) 0.568406 2.12132i 0.0321797 0.120096i
\(313\) 0.864390 + 3.22595i 0.0488582 + 0.182341i 0.986043 0.166493i \(-0.0532443\pi\)
−0.937184 + 0.348834i \(0.886578\pi\)
\(314\) −7.85641 −0.443363
\(315\) 0 0
\(316\) 10.0000 0.562544
\(317\) −6.36396 23.7506i −0.357436 1.33397i −0.877392 0.479775i \(-0.840718\pi\)
0.519956 0.854193i \(-0.325948\pi\)
\(318\) −3.67423 + 0.984508i −0.206041 + 0.0552085i
\(319\) 21.8038 12.5885i 1.22078 0.704818i
\(320\) 0 0
\(321\) 1.39230 0.0777109
\(322\) −10.0382 + 2.68973i −0.559407 + 0.149893i
\(323\) 0 0
\(324\) 7.79423 4.50000i 0.433013 0.250000i
\(325\) 0 0
\(326\) −17.5981 10.1603i −0.974667 0.562724i
\(327\) −14.9372 + 14.9372i −0.826028 + 0.826028i
\(328\) −1.67303 0.448288i −0.0923778 0.0247525i
\(329\) 3.80385 + 6.58846i 0.209713 + 0.363233i
\(330\) 0 0
\(331\) −8.79423 + 15.2321i −0.483375 + 0.837229i −0.999818 0.0190922i \(-0.993922\pi\)
0.516443 + 0.856321i \(0.327256\pi\)
\(332\) 4.81105 4.81105i 0.264040 0.264040i
\(333\) −4.65874 + 4.65874i −0.255298 + 0.255298i
\(334\) 4.39230i 0.240336i
\(335\) 0 0
\(336\) 1.90192 1.09808i 0.103758 0.0599050i
\(337\) −7.10823 + 26.5283i −0.387210 + 1.44509i 0.447443 + 0.894312i \(0.352335\pi\)
−0.834653 + 0.550775i \(0.814332\pi\)
\(338\) −2.94855 + 11.0041i −0.160380 + 0.598545i
\(339\) 11.0885 6.40192i 0.602242 0.347705i
\(340\) 0 0
\(341\) 35.3205i 1.91271i
\(342\) 5.58750 + 20.8528i 0.302138 + 1.12759i
\(343\) −11.1106 + 11.1106i −0.599918 + 0.599918i
\(344\) 3.23205 5.59808i 0.174261 0.301828i
\(345\) 0 0
\(346\) 2.19615 + 3.80385i 0.118066 + 0.204496i
\(347\) −31.6675 8.48528i −1.70000 0.455514i −0.727061 0.686573i \(-0.759114\pi\)
−0.972940 + 0.231059i \(0.925781\pi\)
\(348\) −8.90138 + 8.90138i −0.477164 + 0.477164i
\(349\) −1.73205 1.00000i −0.0927146 0.0535288i 0.452926 0.891548i \(-0.350380\pi\)
−0.545640 + 0.838019i \(0.683714\pi\)
\(350\) 0 0
\(351\) 5.70577 3.29423i 0.304552 0.175833i
\(352\) −2.44949 2.44949i −0.130558 0.130558i
\(353\) −14.4889 + 3.88229i −0.771166 + 0.206633i −0.622886 0.782312i \(-0.714040\pi\)
−0.148279 + 0.988946i \(0.547373\pi\)
\(354\) −21.5885 −1.14741
\(355\) 0 0
\(356\) −7.50000 + 4.33013i −0.397499 + 0.229496i
\(357\) 0 0
\(358\) 1.25693 + 4.69093i 0.0664308 + 0.247923i
\(359\) −0.679492 −0.0358622 −0.0179311 0.999839i \(-0.505708\pi\)
−0.0179311 + 0.999839i \(0.505708\pi\)
\(360\) 0 0
\(361\) −32.7846 −1.72551
\(362\) −2.17209 8.10634i −0.114162 0.426060i
\(363\) −0.448288 + 1.67303i −0.0235290 + 0.0878114i
\(364\) 1.39230 0.803848i 0.0729766 0.0421331i
\(365\) 0 0
\(366\) −3.46410 6.00000i −0.181071 0.313625i
\(367\) 30.7709 8.24504i 1.60623 0.430388i 0.659313 0.751868i \(-0.270847\pi\)
0.946916 + 0.321481i \(0.104181\pi\)
\(368\) −5.79555 5.79555i −0.302114 0.302114i
\(369\) −2.59808 4.50000i −0.135250 0.234261i
\(370\) 0 0
\(371\) −2.41154 1.39230i −0.125201 0.0722849i
\(372\) −4.57081 17.0585i −0.236985 0.884442i
\(373\) −10.9348 2.92996i −0.566181 0.151708i −0.0356365 0.999365i \(-0.511346\pi\)
−0.530545 + 0.847657i \(0.678013\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) −6.51626 + 6.51626i −0.335605 + 0.335605i
\(378\) 6.36396 + 1.70522i 0.327327 + 0.0877070i
\(379\) 20.3923i 1.04748i −0.851877 0.523741i \(-0.824536\pi\)
0.851877 0.523741i \(-0.175464\pi\)
\(380\) 0 0
\(381\) 3.80385i 0.194877i
\(382\) 0.896575 3.34607i 0.0458728 0.171200i
\(383\) −9.46979 + 35.3417i −0.483884 + 1.80588i 0.101152 + 0.994871i \(0.467747\pi\)
−0.585036 + 0.811007i \(0.698920\pi\)
\(384\) 1.50000 + 0.866025i 0.0765466 + 0.0441942i
\(385\) 0 0
\(386\) 24.9282i 1.26881i
\(387\) 18.7315 5.01910i 0.952177 0.255135i
\(388\) 10.3664 10.3664i 0.526272 0.526272i
\(389\) −5.19615 + 9.00000i −0.263455 + 0.456318i −0.967158 0.254177i \(-0.918196\pi\)
0.703702 + 0.710495i \(0.251529\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −5.20857 1.39563i −0.263072 0.0704900i
\(393\) −11.5911 3.10583i −0.584694 0.156668i
\(394\) 3.29423 + 1.90192i 0.165961 + 0.0958175i
\(395\) 0 0
\(396\) 10.3923i 0.522233i
\(397\) 6.03579 + 6.03579i 0.302928 + 0.302928i 0.842158 0.539231i \(-0.181285\pi\)
−0.539231 + 0.842158i \(0.681285\pi\)
\(398\) −0.378937 + 0.101536i −0.0189944 + 0.00508954i
\(399\) −7.90192 + 13.6865i −0.395591 + 0.685184i
\(400\) 0 0
\(401\) 9.00000 5.19615i 0.449439 0.259483i −0.258154 0.966104i \(-0.583114\pi\)
0.707593 + 0.706620i \(0.249781\pi\)
\(402\) −15.2653 15.2653i −0.761366 0.761366i
\(403\) −3.34607 12.4877i −0.166679 0.622056i
\(404\) 10.7321 0.533939
\(405\) 0 0
\(406\) −9.21539 −0.457352
\(407\) 1.96902 + 7.34847i 0.0976005 + 0.364250i
\(408\) 0 0
\(409\) 0.526279 0.303848i 0.0260228 0.0150243i −0.486932 0.873440i \(-0.661884\pi\)
0.512955 + 0.858416i \(0.328551\pi\)
\(410\) 0 0
\(411\) −6.40192 + 11.0885i −0.315784 + 0.546953i
\(412\) 10.0382 2.68973i 0.494546 0.132513i
\(413\) −11.1750 11.1750i −0.549886 0.549886i
\(414\) 24.5885i 1.20846i
\(415\) 0 0
\(416\) 1.09808 + 0.633975i 0.0538376 + 0.0310832i
\(417\) 13.3843 + 3.58630i 0.655430 + 0.175622i
\(418\) 24.0788 + 6.45189i 1.17773 + 0.315572i
\(419\) −4.50000 7.79423i −0.219839 0.380773i 0.734919 0.678155i \(-0.237220\pi\)
−0.954759 + 0.297382i \(0.903887\pi\)
\(420\) 0 0
\(421\) 4.29423 7.43782i 0.209288 0.362497i −0.742203 0.670176i \(-0.766219\pi\)
0.951490 + 0.307678i \(0.0995521\pi\)
\(422\) 6.50266 6.50266i 0.316545 0.316545i
\(423\) −17.3867 + 4.65874i −0.845369 + 0.226516i
\(424\) 2.19615i 0.106655i
\(425\) 0 0
\(426\) −16.0981 9.29423i −0.779954 0.450307i
\(427\) 1.31268 4.89898i 0.0635249 0.237078i
\(428\) −0.208051 + 0.776457i −0.0100565 + 0.0375315i
\(429\) 7.60770i 0.367303i
\(430\) 0 0
\(431\) 3.12436i 0.150495i −0.997165 0.0752475i \(-0.976025\pi\)
0.997165 0.0752475i \(-0.0239747\pi\)
\(432\) 1.34486 + 5.01910i 0.0647048 + 0.241481i
\(433\) −21.8695 + 21.8695i −1.05098 + 1.05098i −0.0523546 + 0.998629i \(0.516673\pi\)
−0.998629 + 0.0523546i \(0.983327\pi\)
\(434\) 6.46410 11.1962i 0.310287 0.537433i
\(435\) 0 0
\(436\) −6.09808 10.5622i −0.292045 0.505837i
\(437\) 56.9710 + 15.2653i 2.72529 + 0.730240i
\(438\) 2.32937 + 8.69333i 0.111302 + 0.415383i
\(439\) 28.2224 + 16.2942i 1.34698 + 0.777681i 0.987821 0.155594i \(-0.0497292\pi\)
0.359162 + 0.933275i \(0.383063\pi\)
\(440\) 0 0
\(441\) −8.08846 14.0096i −0.385165 0.667125i
\(442\) 0 0
\(443\) 10.0382 2.68973i 0.476929 0.127793i −0.0123433 0.999924i \(-0.503929\pi\)
0.489272 + 0.872131i \(0.337262\pi\)
\(444\) −1.90192 3.29423i −0.0902613 0.156337i
\(445\) 0 0
\(446\) 8.19615 4.73205i 0.388099 0.224069i
\(447\) −8.06918 + 30.1146i −0.381659 + 1.42437i
\(448\) 0.328169 + 1.22474i 0.0155045 + 0.0578638i
\(449\) 5.87564 0.277289 0.138644 0.990342i \(-0.455725\pi\)
0.138644 + 0.990342i \(0.455725\pi\)
\(450\) 0 0
\(451\) −6.00000 −0.282529
\(452\) 1.91327 + 7.14042i 0.0899926 + 0.335857i
\(453\) 13.3843 3.58630i 0.628847 0.168499i
\(454\) −20.0885 + 11.5981i −0.942798 + 0.544325i
\(455\) 0 0
\(456\) −12.4641 −0.583685
\(457\) 3.46618 0.928761i 0.162141 0.0434456i −0.176835 0.984240i \(-0.556586\pi\)
0.338976 + 0.940795i \(0.389919\pi\)
\(458\) −11.4524 11.4524i −0.535136 0.535136i
\(459\) 0 0
\(460\) 0 0
\(461\) −24.2942 14.0263i −1.13150 0.653269i −0.187185 0.982325i \(-0.559936\pi\)
−0.944310 + 0.329056i \(0.893270\pi\)
\(462\) 5.37945 5.37945i 0.250275 0.250275i
\(463\) −7.91688 2.12132i −0.367928 0.0985861i 0.0701175 0.997539i \(-0.477663\pi\)
−0.438046 + 0.898953i \(0.644329\pi\)
\(464\) −3.63397 6.29423i −0.168703 0.292202i
\(465\) 0 0
\(466\) 12.6962 21.9904i 0.588138 1.01868i
\(467\) −15.2653 + 15.2653i −0.706396 + 0.706396i −0.965775 0.259380i \(-0.916482\pi\)
0.259380 + 0.965775i \(0.416482\pi\)
\(468\) 0.984508 + 3.67423i 0.0455089 + 0.169842i
\(469\) 15.8038i 0.729754i
\(470\) 0 0
\(471\) 11.7846 6.80385i 0.543006 0.313505i
\(472\) 3.22595 12.0394i 0.148486 0.554158i
\(473\) 5.79555 21.6293i 0.266480 0.994517i
\(474\) −15.0000 + 8.66025i −0.688973 + 0.397779i
\(475\) 0 0
\(476\) 0 0
\(477\) 4.65874 4.65874i 0.213309 0.213309i
\(478\) −10.0382 + 10.0382i −0.459136 + 0.459136i
\(479\) 10.5622 18.2942i 0.482598 0.835885i −0.517202 0.855863i \(-0.673026\pi\)
0.999800 + 0.0199786i \(0.00635981\pi\)
\(480\) 0 0
\(481\) −1.39230 2.41154i −0.0634836 0.109957i
\(482\) −11.0041 2.94855i −0.501224 0.134303i
\(483\) 12.7279 12.7279i 0.579141 0.579141i
\(484\) −0.866025 0.500000i −0.0393648 0.0227273i
\(485\) 0 0
\(486\) −7.79423 + 13.5000i −0.353553 + 0.612372i
\(487\) 15.5935 + 15.5935i 0.706610 + 0.706610i 0.965821 0.259211i \(-0.0834625\pi\)
−0.259211 + 0.965821i \(0.583463\pi\)
\(488\) 3.86370 1.03528i 0.174902 0.0468648i
\(489\) 35.1962 1.59163
\(490\) 0 0
\(491\) −31.7942 + 18.3564i −1.43485 + 0.828413i −0.997486 0.0708697i \(-0.977423\pi\)
−0.437368 + 0.899283i \(0.644089\pi\)
\(492\) 2.89778 0.776457i 0.130642 0.0350054i
\(493\) 0 0
\(494\) −9.12436 −0.410524
\(495\) 0 0
\(496\) 10.1962 0.457821
\(497\) −3.52193 13.1440i −0.157980 0.589590i
\(498\) −3.05008 + 11.3831i −0.136677 + 0.510087i
\(499\) 16.9641 9.79423i 0.759417 0.438450i −0.0696691 0.997570i \(-0.522194\pi\)
0.829087 + 0.559120i \(0.188861\pi\)
\(500\) 0 0
\(501\) −3.80385 6.58846i −0.169943 0.294351i
\(502\) −8.69333 + 2.32937i −0.388002 + 0.103965i
\(503\) 25.8719 + 25.8719i 1.15357 + 1.15357i 0.985831 + 0.167742i \(0.0536476\pi\)
0.167742 + 0.985831i \(0.446352\pi\)
\(504\) −1.90192 + 3.29423i −0.0847184 + 0.146737i
\(505\) 0 0
\(506\) −24.5885 14.1962i −1.09309 0.631096i
\(507\) −5.10703 19.0597i −0.226811 0.846471i
\(508\) −2.12132 0.568406i −0.0941184 0.0252189i
\(509\) −10.3923 18.0000i −0.460631 0.797836i 0.538362 0.842714i \(-0.319043\pi\)
−0.998992 + 0.0448779i \(0.985710\pi\)
\(510\) 0 0
\(511\) −3.29423 + 5.70577i −0.145728 + 0.252408i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −26.4404 26.4404i −1.16737 1.16737i
\(514\) 4.60770i 0.203237i
\(515\) 0 0
\(516\) 11.1962i 0.492883i
\(517\) −5.37945 + 20.0764i −0.236588 + 0.882959i
\(518\) 0.720710 2.68973i 0.0316662 0.118180i
\(519\) −6.58846 3.80385i −0.289201 0.166970i
\(520\) 0 0
\(521\) 38.7846i 1.69918i 0.527440 + 0.849592i \(0.323152\pi\)
−0.527440 + 0.849592i \(0.676848\pi\)
\(522\) 5.64325 21.0609i 0.246998 0.921811i
\(523\) −14.1929 + 14.1929i −0.620612 + 0.620612i −0.945688 0.325076i \(-0.894610\pi\)
0.325076 + 0.945688i \(0.394610\pi\)
\(524\) 3.46410 6.00000i 0.151330 0.262111i
\(525\) 0 0
\(526\) 9.29423 + 16.0981i 0.405248 + 0.701909i
\(527\) 0 0
\(528\) 5.79555 + 1.55291i 0.252219 + 0.0675819i
\(529\) −38.2583 22.0885i −1.66341 0.960368i
\(530\) 0 0
\(531\) 32.3827 18.6962i 1.40529 0.811344i
\(532\) −6.45189 6.45189i −0.279725 0.279725i
\(533\) 2.12132 0.568406i 0.0918846 0.0246204i
\(534\) 7.50000 12.9904i 0.324557 0.562149i
\(535\) 0 0
\(536\) 10.7942 6.23205i 0.466240 0.269184i
\(537\) −5.94786 5.94786i −0.256669 0.256669i
\(538\) −7.26054 27.0967i −0.313024 1.16822i
\(539\) −18.6795 −0.804583
\(540\) 0 0
\(541\) 12.3923 0.532787 0.266393 0.963864i \(-0.414168\pi\)
0.266393 + 0.963864i \(0.414168\pi\)
\(542\) 1.18758 + 4.43211i 0.0510109 + 0.190375i
\(543\) 10.2784 + 10.2784i 0.441090 + 0.441090i
\(544\) 0 0
\(545\) 0 0
\(546\) −1.39230 + 2.41154i −0.0595851 + 0.103205i
\(547\) −21.4213 + 5.73981i −0.915907 + 0.245416i −0.685835 0.727757i \(-0.740563\pi\)
−0.230072 + 0.973174i \(0.573896\pi\)
\(548\) −5.22715 5.22715i −0.223293 0.223293i
\(549\) 10.3923 + 6.00000i 0.443533 + 0.256074i
\(550\) 0 0
\(551\) 45.2942 + 26.1506i 1.92960 + 1.11405i
\(552\) 13.7124 + 3.67423i 0.583640 + 0.156386i
\(553\) −12.2474 3.28169i −0.520814 0.139552i
\(554\) 12.7583 + 22.0981i 0.542050 + 0.938857i
\(555\) 0 0
\(556\) −4.00000 + 6.92820i −0.169638 + 0.293821i
\(557\) −11.5911 + 11.5911i −0.491131 + 0.491131i −0.908662 0.417531i \(-0.862895\pi\)
0.417531 + 0.908662i \(0.362895\pi\)
\(558\) 21.6293 + 21.6293i 0.915642 + 0.915642i
\(559\) 8.19615i 0.346660i
\(560\) 0 0
\(561\) 0 0
\(562\) 2.68973 10.0382i 0.113459 0.423436i
\(563\) 8.69333 32.4440i 0.366380 1.36735i −0.499160 0.866510i \(-0.666358\pi\)
0.865540 0.500840i \(-0.166975\pi\)
\(564\) 10.3923i 0.437595i
\(565\) 0 0
\(566\) 9.92820i 0.417314i
\(567\) −11.0227 + 2.95352i −0.462910 + 0.124036i
\(568\) 7.58871 7.58871i 0.318415 0.318415i
\(569\) −5.53590 + 9.58846i −0.232077 + 0.401969i −0.958419 0.285364i \(-0.907885\pi\)
0.726342 + 0.687333i \(0.241219\pi\)
\(570\) 0 0
\(571\) −4.40192 7.62436i −0.184215 0.319069i 0.759097 0.650978i \(-0.225641\pi\)
−0.943312 + 0.331908i \(0.892308\pi\)
\(572\) 4.24264 + 1.13681i 0.177394 + 0.0475325i
\(573\) 1.55291 + 5.79555i 0.0648739 + 0.242113i
\(574\) 1.90192 + 1.09808i 0.0793848 + 0.0458328i
\(575\) 0 0
\(576\) −3.00000 −0.125000
\(577\) −15.9217 15.9217i −0.662828 0.662828i 0.293217 0.956046i \(-0.405274\pi\)
−0.956046 + 0.293217i \(0.905274\pi\)
\(578\) 16.4207 4.39992i 0.683013 0.183013i
\(579\) 21.5885 + 37.3923i 0.897186 + 1.55397i
\(580\) 0 0
\(581\) −7.47114 + 4.31347i −0.309955 + 0.178953i
\(582\) −6.57201 + 24.5271i −0.272419 + 1.01668i
\(583\) −1.96902 7.34847i −0.0815483 0.304342i
\(584\) −5.19615 −0.215018
\(585\) 0 0
\(586\) 14.1962 0.586438
\(587\) 4.24264 + 15.8338i 0.175113 + 0.653529i 0.996532 + 0.0832050i \(0.0265156\pi\)
−0.821420 + 0.570324i \(0.806818\pi\)
\(588\) 9.02150 2.41730i 0.372040 0.0996879i
\(589\) −63.5429 + 36.6865i −2.61824 + 1.51164i
\(590\) 0 0
\(591\) −6.58846 −0.271013
\(592\) 2.12132 0.568406i 0.0871857 0.0233613i
\(593\) −14.8492 14.8492i −0.609785 0.609785i 0.333105 0.942890i \(-0.391904\pi\)
−0.942890 + 0.333105i \(0.891904\pi\)
\(594\) 9.00000 + 15.5885i 0.369274 + 0.639602i
\(595\) 0 0
\(596\) −15.5885 9.00000i −0.638528 0.368654i
\(597\) 0.480473 0.480473i 0.0196645 0.0196645i
\(598\) 10.0382 + 2.68973i 0.410492 + 0.109991i
\(599\) −5.36603 9.29423i −0.219250 0.379752i 0.735329 0.677710i \(-0.237028\pi\)
−0.954579 + 0.297958i \(0.903694\pi\)
\(600\) 0 0
\(601\) −6.39230 + 11.0718i −0.260748 + 0.451628i −0.966441 0.256890i \(-0.917302\pi\)
0.705693 + 0.708518i \(0.250636\pi\)
\(602\) −5.79555 + 5.79555i −0.236209 + 0.236209i
\(603\) 36.1182 + 9.67784i 1.47085 + 0.394112i
\(604\) 8.00000i 0.325515i
\(605\) 0 0
\(606\) −16.0981 + 9.29423i −0.653940 + 0.377552i
\(607\) 4.50644 16.8183i 0.182911 0.682632i −0.812157 0.583438i \(-0.801707\pi\)
0.995068 0.0991937i \(-0.0316264\pi\)
\(608\) 1.86250 6.95095i 0.0755344 0.281898i
\(609\) 13.8231 7.98076i 0.560140 0.323397i
\(610\) 0 0
\(611\) 7.60770i 0.307774i
\(612\) 0 0
\(613\) −2.68973 + 2.68973i −0.108637 + 0.108637i −0.759336 0.650699i \(-0.774476\pi\)
0.650699 + 0.759336i \(0.274476\pi\)
\(614\) 1.73205 3.00000i 0.0698999 0.121070i
\(615\) 0 0
\(616\) 2.19615 + 3.80385i 0.0884855 + 0.153261i
\(617\) 28.7697 + 7.70882i 1.15823 + 0.310346i 0.786257 0.617900i \(-0.212016\pi\)
0.371969 + 0.928245i \(0.378683\pi\)
\(618\) −12.7279 + 12.7279i −0.511992 + 0.511992i
\(619\) 14.2128 + 8.20577i 0.571261 + 0.329818i 0.757653 0.652658i \(-0.226346\pi\)
−0.186392 + 0.982476i \(0.559679\pi\)
\(620\) 0 0
\(621\) 21.2942 + 36.8827i 0.854508 + 1.48005i
\(622\) −17.6269 17.6269i −0.706774 0.706774i
\(623\) 10.6066 2.84203i 0.424945 0.113864i
\(624\) −2.19615 −0.0879165
\(625\) 0 0
\(626\) 2.89230 1.66987i 0.115600 0.0667415i
\(627\) −41.7057 + 11.1750i −1.66557 + 0.446287i
\(628\) 2.03339 + 7.58871i 0.0811410 + 0.302822i
\(629\) 0 0
\(630\) 0 0
\(631\) 40.7846 1.62361 0.811805 0.583929i \(-0.198485\pi\)
0.811805 + 0.583929i \(0.198485\pi\)
\(632\) −2.58819 9.65926i −0.102953 0.384225i
\(633\) −4.12252 + 15.3855i −0.163856 + 0.611517i
\(634\) −21.2942 + 12.2942i −0.845702 + 0.488266i
\(635\) 0 0
\(636\) 1.90192 + 3.29423i 0.0754162 + 0.130625i
\(637\) 6.60420 1.76959i 0.261668 0.0701137i
\(638\) −17.8028 17.8028i −0.704818 0.704818i
\(639\) 32.1962 1.27366
\(640\) 0 0
\(641\) −0.911543 0.526279i −0.0360038 0.0207868i 0.481890 0.876232i \(-0.339950\pi\)
−0.517894 + 0.855445i \(0.673284\pi\)
\(642\) −0.360355 1.34486i −0.0142221 0.0530775i
\(643\) −16.0418 4.29839i −0.632627 0.169512i −0.0717654 0.997422i \(-0.522863\pi\)
−0.560861 + 0.827910i \(0.689530\pi\)
\(644\) 5.19615 + 9.00000i 0.204757 + 0.354650i
\(645\) 0 0
\(646\) 0 0
\(647\) 2.68973 2.68973i 0.105744 0.105744i −0.652255 0.757999i \(-0.726177\pi\)
0.757999 + 0.652255i \(0.226177\pi\)
\(648\) −6.36396 6.36396i −0.250000 0.250000i
\(649\) 43.1769i 1.69484i
\(650\) 0 0
\(651\) 22.3923i 0.877624i
\(652\) −5.25933 + 19.6281i −0.205971 + 0.768696i
\(653\) −0.568406 + 2.12132i −0.0222434 + 0.0830137i −0.976155 0.217073i \(-0.930349\pi\)
0.953912 + 0.300087i \(0.0970157\pi\)
\(654\) 18.2942 + 10.5622i 0.715361 + 0.413014i
\(655\) 0 0
\(656\) 1.73205i 0.0676252i
\(657\) −11.0227 11.0227i −0.430037 0.430037i
\(658\) 5.37945 5.37945i 0.209713 0.209713i
\(659\) −11.0885 + 19.2058i −0.431945 + 0.748151i −0.997041 0.0768747i \(-0.975506\pi\)
0.565096 + 0.825025i \(0.308839\pi\)
\(660\) 0 0
\(661\) −11.5885 20.0718i −0.450739 0.780702i 0.547693 0.836679i \(-0.315506\pi\)
−0.998432 + 0.0559768i \(0.982173\pi\)
\(662\) 16.9891 + 4.55223i 0.660302 + 0.176927i
\(663\) 0 0
\(664\) −5.89230 3.40192i −0.228666 0.132020i
\(665\) 0 0
\(666\) 5.70577 + 3.29423i 0.221094 + 0.127649i
\(667\) −42.1218 42.1218i −1.63096 1.63096i
\(668\) 4.24264 1.13681i 0.164153 0.0439846i
\(669\) −8.19615 + 14.1962i −0.316882 + 0.548855i
\(670\) 0 0
\(671\) 12.0000 6.92820i 0.463255 0.267460i
\(672\) −1.55291 1.55291i −0.0599050 0.0599050i
\(673\) 0.416102 + 1.55291i 0.0160396 + 0.0598604i 0.973482 0.228765i \(-0.0734686\pi\)
−0.957442 + 0.288625i \(0.906802\pi\)
\(674\) 27.4641 1.05788
\(675\) 0 0
\(676\) 11.3923 0.438166
\(677\) 1.70522 + 6.36396i 0.0655369 + 0.244587i 0.990921 0.134443i \(-0.0429245\pi\)
−0.925384 + 0.379030i \(0.876258\pi\)
\(678\) −9.05369 9.05369i −0.347705 0.347705i
\(679\) −16.0981 + 9.29423i −0.617787 + 0.356680i
\(680\) 0 0
\(681\) 20.0885 34.7942i 0.769791 1.33332i
\(682\) 34.1170 9.14162i 1.30641 0.350051i
\(683\) 27.9933 + 27.9933i 1.07113 + 1.07113i 0.997268 + 0.0738643i \(0.0235332\pi\)
0.0738643 + 0.997268i \(0.476467\pi\)
\(684\) 18.6962 10.7942i 0.714865 0.412728i
\(685\) 0 0
\(686\) 13.6077 + 7.85641i 0.519544 + 0.299959i
\(687\) 27.0967 + 7.26054i 1.03380 + 0.277007i
\(688\) −6.24384 1.67303i −0.238044 0.0637838i
\(689\) 1.39230 + 2.41154i 0.0530426 + 0.0918725i
\(690\) 0 0
\(691\) −6.20577 + 10.7487i −0.236079 + 0.408900i −0.959586 0.281417i \(-0.909196\pi\)
0.723507 + 0.690317i \(0.242529\pi\)
\(692\) 3.10583 3.10583i 0.118066 0.118066i
\(693\) −3.41044 + 12.7279i −0.129552 + 0.483494i
\(694\) 32.7846i 1.24449i
\(695\) 0 0
\(696\) 10.9019 + 6.29423i 0.413236 + 0.238582i
\(697\) 0 0
\(698\) −0.517638 + 1.93185i −0.0195929 + 0.0731217i
\(699\) 43.9808i 1.66351i
\(700\) 0 0
\(701\) 21.4641i 0.810688i −0.914164 0.405344i \(-0.867152\pi\)
0.914164 0.405344i \(-0.132848\pi\)
\(702\) −4.65874 4.65874i −0.175833 0.175833i
\(703\) −11.1750 + 11.1750i −0.421473 + 0.421473i
\(704\) −1.73205 + 3.00000i −0.0652791 + 0.113067i
\(705\) 0 0
\(706\) 7.50000 + 12.9904i 0.282266 + 0.488899i
\(707\) −13.1440 3.52193i −0.494332 0.132456i
\(708\) 5.58750 + 20.8528i 0.209991 + 0.783698i
\(709\) 22.3468 + 12.9019i 0.839251 + 0.484542i 0.857010 0.515300i \(-0.172320\pi\)
−0.0177584 + 0.999842i \(0.505653\pi\)
\(710\) 0 0
\(711\) 15.0000 25.9808i 0.562544 0.974355i
\(712\) 6.12372 + 6.12372i 0.229496 + 0.229496i
\(713\) 80.7217 21.6293i 3.02305 0.810024i
\(714\) 0 0
\(715\) 0 0
\(716\) 4.20577 2.42820i 0.157177 0.0907462i
\(717\) 6.36396 23.7506i 0.237666 0.886983i
\(718\) 0.175865 + 0.656339i 0.00656324 + 0.0244943i
\(719\) −39.1244 −1.45909 −0.729546 0.683932i \(-0.760269\pi\)
−0.729546 + 0.683932i \(0.760269\pi\)
\(720\) 0 0
\(721\) −13.1769 −0.490734
\(722\) 8.48528 + 31.6675i 0.315789 + 1.17854i
\(723\) 19.0597 5.10703i 0.708838 0.189933i
\(724\) −7.26795 + 4.19615i −0.270111 + 0.155949i
\(725\) 0 0
\(726\) 1.73205 0.0642824
\(727\) 6.69213 1.79315i 0.248197 0.0665043i −0.132575 0.991173i \(-0.542325\pi\)
0.380773 + 0.924669i \(0.375658\pi\)
\(728\) −1.13681 1.13681i −0.0421331 0.0421331i
\(729\) 27.0000i 1.00000i
\(730\) 0 0
\(731\) 0 0
\(732\) −4.89898 + 4.89898i −0.181071 + 0.181071i
\(733\) −33.2204 8.90138i −1.22702 0.328780i −0.413604 0.910457i \(-0.635730\pi\)
−0.813420 + 0.581677i \(0.802397\pi\)
\(734\) −15.9282 27.5885i −0.587921 1.01831i
\(735\) 0 0
\(736\) −4.09808 + 7.09808i −0.151057 + 0.261639i
\(737\) 30.5307 30.5307i 1.12461 1.12461i
\(738\) −3.67423 + 3.67423i −0.135250 + 0.135250i
\(739\) 11.5885i 0.426288i 0.977021 + 0.213144i \(0.0683704\pi\)
−0.977021 + 0.213144i \(0.931630\pi\)
\(740\) 0 0
\(741\) 13.6865 7.90192i 0.502787 0.290284i
\(742\) −0.720710 + 2.68973i −0.0264581 + 0.0987430i
\(743\) 10.1905 38.0315i 0.373853 1.39524i −0.481160 0.876633i \(-0.659784\pi\)
0.855013 0.518606i \(-0.173549\pi\)
\(744\) −15.2942 + 8.83013i −0.560714 + 0.323728i
\(745\) 0 0
\(746\) 11.3205i 0.414473i
\(747\) −5.28290 19.7160i −0.193291 0.721372i
\(748\) 0 0
\(749\) 0.509619 0.882686i 0.0186211 0.0322526i
\(750\) 0 0
\(751\) 10.2942 + 17.8301i 0.375642 + 0.650631i 0.990423 0.138067i \(-0.0440890\pi\)
−0.614781 + 0.788698i \(0.710756\pi\)
\(752\) 5.79555 + 1.55291i 0.211342 + 0.0566290i
\(753\) 11.0227 11.0227i 0.401690 0.401690i
\(754\) 7.98076 + 4.60770i 0.290642 + 0.167802i
\(755\) 0 0
\(756\) 6.58846i 0.239620i
\(757\) −10.5187 10.5187i −0.382308 0.382308i 0.489625 0.871933i \(-0.337134\pi\)
−0.871933 + 0.489625i \(0.837134\pi\)
\(758\) −19.6975 + 5.27792i −0.715444 + 0.191703i
\(759\) 49.1769 1.78501
\(760\) 0 0
\(761\) −9.91154 + 5.72243i −0.359293 + 0.207438i −0.668771 0.743469i \(-0.733179\pi\)
0.309478 + 0.950907i \(0.399846\pi\)
\(762\) 3.67423 0.984508i 0.133103 0.0356650i
\(763\) 4.00240 + 14.9372i 0.144897 + 0.540762i
\(764\) −3.46410 −0.125327
\(765\) 0 0
\(766\) 36.5885 1.32199
\(767\) 4.09034 + 15.2653i 0.147693 + 0.551200i
\(768\) 0.448288 1.67303i 0.0161762 0.0603704i
\(769\) −28.9186 + 16.6962i −1.04283 + 0.602079i −0.920634 0.390427i \(-0.872327\pi\)
−0.122197 + 0.992506i \(0.538994\pi\)
\(770\) 0 0
\(771\) 3.99038 + 6.91154i 0.143710 + 0.248913i
\(772\) −24.0788 + 6.45189i −0.866615 + 0.232209i
\(773\) 6.51626 + 6.51626i 0.234374 + 0.234374i 0.814516 0.580142i \(-0.197003\pi\)
−0.580142 + 0.814516i \(0.697003\pi\)
\(774\) −9.69615 16.7942i −0.348521 0.603656i
\(775\) 0 0
\(776\) −12.6962 7.33013i −0.455765 0.263136i
\(777\) 1.24831 + 4.65874i 0.0447827 + 0.167131i
\(778\) 10.0382 + 2.68973i 0.359887 + 0.0964314i
\(779\) −6.23205 10.7942i −0.223286 0.386743i
\(780\) 0 0
\(781\) 18.5885 32.1962i 0.665147 1.15207i
\(782\) 0 0
\(783\) 9.77440 + 36.4785i 0.349308 + 1.30364i
\(784\) 5.39230i 0.192582i
\(785\) 0 0
\(786\) 12.0000i