Properties

Label 825.2.bx.c.724.2
Level $825$
Weight $2$
Character 825.724
Analytic conductor $6.588$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.bx (of order \(10\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{20})\)
Defining polynomial: \(x^{8} - x^{6} + x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 724.2
Root \(-0.587785 + 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 825.724
Dual form 825.2.bx.c.49.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.53884 + 0.500000i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.500000 + 0.363271i) q^{4} +(0.500000 + 1.53884i) q^{6} +(3.07768 - 4.23607i) q^{7} +(-1.31433 - 1.80902i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(1.53884 + 0.500000i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.500000 + 0.363271i) q^{4} +(0.500000 + 1.53884i) q^{6} +(3.07768 - 4.23607i) q^{7} +(-1.31433 - 1.80902i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-1.23607 + 3.07768i) q^{11} +0.618034i q^{12} +(3.07768 + 1.00000i) q^{13} +(6.85410 - 4.97980i) q^{14} +(-1.50000 - 4.61653i) q^{16} +(1.90211 - 0.618034i) q^{17} +(-0.951057 + 1.30902i) q^{18} +(4.04508 - 2.93893i) q^{19} +5.23607 q^{21} +(-3.44095 + 4.11803i) q^{22} +4.61803i q^{23} +(0.690983 - 2.12663i) q^{24} +(4.23607 + 3.07768i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(3.07768 - 1.00000i) q^{28} +(0.690983 + 0.502029i) q^{29} +(2.16312 - 6.65740i) q^{31} -3.38197i q^{32} +(-3.21644 + 0.809017i) q^{33} +3.23607 q^{34} +(-0.500000 + 0.363271i) q^{36} +(-0.865300 + 1.19098i) q^{37} +(7.69421 - 2.50000i) q^{38} +(1.00000 + 3.07768i) q^{39} +(-9.28115 + 6.74315i) q^{41} +(8.05748 + 2.61803i) q^{42} +9.09017i q^{43} +(-1.73607 + 1.08981i) q^{44} +(-2.30902 + 7.10642i) q^{46} +(-3.57971 - 4.92705i) q^{47} +(2.85317 - 3.92705i) q^{48} +(-6.30902 - 19.4172i) q^{49} +(1.61803 + 1.17557i) q^{51} +(1.17557 + 1.61803i) q^{52} +(-5.11855 - 1.66312i) q^{53} -1.61803 q^{54} -11.7082 q^{56} +(4.75528 + 1.54508i) q^{57} +(0.812299 + 1.11803i) q^{58} +(5.42705 + 3.94298i) q^{59} +(2.16312 + 6.65740i) q^{61} +(6.65740 - 9.16312i) q^{62} +(3.07768 + 4.23607i) q^{63} +(-1.30902 + 4.02874i) q^{64} +(-5.35410 - 0.363271i) q^{66} +11.6180i q^{67} +(1.17557 + 0.381966i) q^{68} +(-3.73607 + 2.71441i) q^{69} +(-2.47214 - 7.60845i) q^{71} +(2.12663 - 0.690983i) q^{72} +(-2.66141 + 3.66312i) q^{73} +(-1.92705 + 1.40008i) q^{74} +3.09017 q^{76} +(9.23305 + 14.7082i) q^{77} +5.23607i q^{78} +(-0.954915 + 2.93893i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-17.6538 + 5.73607i) q^{82} +(-7.33094 + 2.38197i) q^{83} +(2.61803 + 1.90211i) q^{84} +(-4.54508 + 13.9883i) q^{86} +0.854102i q^{87} +(7.19218 - 1.80902i) q^{88} -4.14590 q^{89} +(13.7082 - 9.95959i) q^{91} +(-1.67760 + 2.30902i) q^{92} +(6.65740 - 2.16312i) q^{93} +(-3.04508 - 9.37181i) q^{94} +(2.73607 - 1.98787i) q^{96} +(-2.40414 - 0.781153i) q^{97} -33.0344i q^{98} +(-2.54508 - 2.12663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} + 4 q^{6} + 2 q^{9} + O(q^{10}) \) \( 8 q + 4 q^{4} + 4 q^{6} + 2 q^{9} + 8 q^{11} + 28 q^{14} - 12 q^{16} + 10 q^{19} + 24 q^{21} + 10 q^{24} + 16 q^{26} + 10 q^{29} - 14 q^{31} + 8 q^{34} - 4 q^{36} + 8 q^{39} - 34 q^{41} + 4 q^{44} - 14 q^{46} - 46 q^{49} + 4 q^{51} - 4 q^{54} - 40 q^{56} + 30 q^{59} - 14 q^{61} - 6 q^{64} - 16 q^{66} - 12 q^{69} + 16 q^{71} - 2 q^{74} - 20 q^{76} - 30 q^{79} - 2 q^{81} + 12 q^{84} - 14 q^{86} - 60 q^{89} + 56 q^{91} - 2 q^{94} + 4 q^{96} + 2 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.53884 + 0.500000i 1.08813 + 0.353553i 0.797522 0.603290i \(-0.206144\pi\)
0.290604 + 0.956844i \(0.406144\pi\)
\(3\) 0.587785 + 0.809017i 0.339358 + 0.467086i
\(4\) 0.500000 + 0.363271i 0.250000 + 0.181636i
\(5\) 0 0
\(6\) 0.500000 + 1.53884i 0.204124 + 0.628230i
\(7\) 3.07768 4.23607i 1.16326 1.60108i 0.464830 0.885400i \(-0.346115\pi\)
0.698425 0.715683i \(-0.253885\pi\)
\(8\) −1.31433 1.80902i −0.464685 0.639584i
\(9\) −0.309017 + 0.951057i −0.103006 + 0.317019i
\(10\) 0 0
\(11\) −1.23607 + 3.07768i −0.372689 + 0.927957i
\(12\) 0.618034i 0.178411i
\(13\) 3.07768 + 1.00000i 0.853596 + 0.277350i 0.702951 0.711238i \(-0.251865\pi\)
0.150644 + 0.988588i \(0.451865\pi\)
\(14\) 6.85410 4.97980i 1.83184 1.33091i
\(15\) 0 0
\(16\) −1.50000 4.61653i −0.375000 1.15413i
\(17\) 1.90211 0.618034i 0.461330 0.149895i −0.0691254 0.997608i \(-0.522021\pi\)
0.530456 + 0.847713i \(0.322021\pi\)
\(18\) −0.951057 + 1.30902i −0.224166 + 0.308538i
\(19\) 4.04508 2.93893i 0.928006 0.674236i −0.0174977 0.999847i \(-0.505570\pi\)
0.945504 + 0.325611i \(0.105570\pi\)
\(20\) 0 0
\(21\) 5.23607 1.14260
\(22\) −3.44095 + 4.11803i −0.733614 + 0.877968i
\(23\) 4.61803i 0.962927i 0.876466 + 0.481463i \(0.159895\pi\)
−0.876466 + 0.481463i \(0.840105\pi\)
\(24\) 0.690983 2.12663i 0.141046 0.434096i
\(25\) 0 0
\(26\) 4.23607 + 3.07768i 0.830761 + 0.603583i
\(27\) −0.951057 + 0.309017i −0.183031 + 0.0594703i
\(28\) 3.07768 1.00000i 0.581628 0.188982i
\(29\) 0.690983 + 0.502029i 0.128312 + 0.0932244i 0.650090 0.759857i \(-0.274731\pi\)
−0.521778 + 0.853081i \(0.674731\pi\)
\(30\) 0 0
\(31\) 2.16312 6.65740i 0.388508 1.19570i −0.545396 0.838179i \(-0.683621\pi\)
0.933904 0.357525i \(-0.116379\pi\)
\(32\) 3.38197i 0.597853i
\(33\) −3.21644 + 0.809017i −0.559910 + 0.140832i
\(34\) 3.23607 0.554981
\(35\) 0 0
\(36\) −0.500000 + 0.363271i −0.0833333 + 0.0605452i
\(37\) −0.865300 + 1.19098i −0.142254 + 0.195796i −0.874199 0.485568i \(-0.838613\pi\)
0.731945 + 0.681364i \(0.238613\pi\)
\(38\) 7.69421 2.50000i 1.24817 0.405554i
\(39\) 1.00000 + 3.07768i 0.160128 + 0.492824i
\(40\) 0 0
\(41\) −9.28115 + 6.74315i −1.44947 + 1.05310i −0.463518 + 0.886087i \(0.653413\pi\)
−0.985954 + 0.167016i \(0.946587\pi\)
\(42\) 8.05748 + 2.61803i 1.24330 + 0.403971i
\(43\) 9.09017i 1.38624i 0.720823 + 0.693119i \(0.243764\pi\)
−0.720823 + 0.693119i \(0.756236\pi\)
\(44\) −1.73607 + 1.08981i −0.261722 + 0.164296i
\(45\) 0 0
\(46\) −2.30902 + 7.10642i −0.340446 + 1.04778i
\(47\) −3.57971 4.92705i −0.522155 0.718684i 0.463755 0.885964i \(-0.346502\pi\)
−0.985910 + 0.167279i \(0.946502\pi\)
\(48\) 2.85317 3.92705i 0.411820 0.566821i
\(49\) −6.30902 19.4172i −0.901288 2.77388i
\(50\) 0 0
\(51\) 1.61803 + 1.17557i 0.226570 + 0.164613i
\(52\) 1.17557 + 1.61803i 0.163022 + 0.224381i
\(53\) −5.11855 1.66312i −0.703087 0.228447i −0.0644122 0.997923i \(-0.520517\pi\)
−0.638675 + 0.769476i \(0.720517\pi\)
\(54\) −1.61803 −0.220187
\(55\) 0 0
\(56\) −11.7082 −1.56457
\(57\) 4.75528 + 1.54508i 0.629853 + 0.204652i
\(58\) 0.812299 + 1.11803i 0.106660 + 0.146805i
\(59\) 5.42705 + 3.94298i 0.706542 + 0.513333i 0.882056 0.471144i \(-0.156159\pi\)
−0.175514 + 0.984477i \(0.556159\pi\)
\(60\) 0 0
\(61\) 2.16312 + 6.65740i 0.276959 + 0.852392i 0.988694 + 0.149945i \(0.0479095\pi\)
−0.711735 + 0.702448i \(0.752090\pi\)
\(62\) 6.65740 9.16312i 0.845490 1.16372i
\(63\) 3.07768 + 4.23607i 0.387752 + 0.533694i
\(64\) −1.30902 + 4.02874i −0.163627 + 0.503593i
\(65\) 0 0
\(66\) −5.35410 0.363271i −0.659044 0.0447156i
\(67\) 11.6180i 1.41937i 0.704520 + 0.709684i \(0.251162\pi\)
−0.704520 + 0.709684i \(0.748838\pi\)
\(68\) 1.17557 + 0.381966i 0.142559 + 0.0463202i
\(69\) −3.73607 + 2.71441i −0.449770 + 0.326777i
\(70\) 0 0
\(71\) −2.47214 7.60845i −0.293389 0.902957i −0.983758 0.179500i \(-0.942552\pi\)
0.690369 0.723457i \(-0.257448\pi\)
\(72\) 2.12663 0.690983i 0.250625 0.0814331i
\(73\) −2.66141 + 3.66312i −0.311495 + 0.428736i −0.935847 0.352408i \(-0.885363\pi\)
0.624352 + 0.781143i \(0.285363\pi\)
\(74\) −1.92705 + 1.40008i −0.224015 + 0.162757i
\(75\) 0 0
\(76\) 3.09017 0.354467
\(77\) 9.23305 + 14.7082i 1.05220 + 1.67616i
\(78\) 5.23607i 0.592868i
\(79\) −0.954915 + 2.93893i −0.107436 + 0.330655i −0.990295 0.138985i \(-0.955616\pi\)
0.882858 + 0.469640i \(0.155616\pi\)
\(80\) 0 0
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) −17.6538 + 5.73607i −1.94954 + 0.633443i
\(83\) −7.33094 + 2.38197i −0.804675 + 0.261455i −0.682341 0.731034i \(-0.739038\pi\)
−0.122334 + 0.992489i \(0.539038\pi\)
\(84\) 2.61803 + 1.90211i 0.285651 + 0.207538i
\(85\) 0 0
\(86\) −4.54508 + 13.9883i −0.490109 + 1.50840i
\(87\) 0.854102i 0.0915693i
\(88\) 7.19218 1.80902i 0.766689 0.192842i
\(89\) −4.14590 −0.439464 −0.219732 0.975560i \(-0.570518\pi\)
−0.219732 + 0.975560i \(0.570518\pi\)
\(90\) 0 0
\(91\) 13.7082 9.95959i 1.43701 1.04405i
\(92\) −1.67760 + 2.30902i −0.174902 + 0.240732i
\(93\) 6.65740 2.16312i 0.690340 0.224305i
\(94\) −3.04508 9.37181i −0.314077 0.966628i
\(95\) 0 0
\(96\) 2.73607 1.98787i 0.279249 0.202886i
\(97\) −2.40414 0.781153i −0.244104 0.0793141i 0.184410 0.982849i \(-0.440963\pi\)
−0.428514 + 0.903535i \(0.640963\pi\)
\(98\) 33.0344i 3.33698i
\(99\) −2.54508 2.12663i −0.255791 0.213734i
\(100\) 0 0
\(101\) 6.04508 18.6049i 0.601508 1.85125i 0.0822950 0.996608i \(-0.473775\pi\)
0.519213 0.854645i \(-0.326225\pi\)
\(102\) 1.90211 + 2.61803i 0.188337 + 0.259224i
\(103\) 2.71441 3.73607i 0.267459 0.368126i −0.654071 0.756433i \(-0.726940\pi\)
0.921530 + 0.388308i \(0.126940\pi\)
\(104\) −2.23607 6.88191i −0.219265 0.674827i
\(105\) 0 0
\(106\) −7.04508 5.11855i −0.684279 0.497158i
\(107\) −2.26538 3.11803i −0.219003 0.301432i 0.685353 0.728211i \(-0.259648\pi\)
−0.904356 + 0.426780i \(0.859648\pi\)
\(108\) −0.587785 0.190983i −0.0565597 0.0183773i
\(109\) −10.8541 −1.03963 −0.519817 0.854278i \(-0.674000\pi\)
−0.519817 + 0.854278i \(0.674000\pi\)
\(110\) 0 0
\(111\) −1.47214 −0.139729
\(112\) −24.1724 7.85410i −2.28408 0.742143i
\(113\) 2.04087 + 2.80902i 0.191989 + 0.264250i 0.894150 0.447769i \(-0.147781\pi\)
−0.702161 + 0.712019i \(0.747781\pi\)
\(114\) 6.54508 + 4.75528i 0.613003 + 0.445373i
\(115\) 0 0
\(116\) 0.163119 + 0.502029i 0.0151452 + 0.0466122i
\(117\) −1.90211 + 2.61803i −0.175850 + 0.242037i
\(118\) 6.37988 + 8.78115i 0.587316 + 0.808371i
\(119\) 3.23607 9.95959i 0.296650 0.912994i
\(120\) 0 0
\(121\) −7.94427 7.60845i −0.722207 0.691677i
\(122\) 11.3262i 1.02543i
\(123\) −10.9106 3.54508i −0.983780 0.319650i
\(124\) 3.50000 2.54290i 0.314309 0.228359i
\(125\) 0 0
\(126\) 2.61803 + 8.05748i 0.233233 + 0.717817i
\(127\) −1.84911 + 0.600813i −0.164082 + 0.0533135i −0.389906 0.920855i \(-0.627493\pi\)
0.225824 + 0.974168i \(0.427493\pi\)
\(128\) −8.00448 + 11.0172i −0.707503 + 0.973794i
\(129\) −7.35410 + 5.34307i −0.647493 + 0.470431i
\(130\) 0 0
\(131\) −9.18034 −0.802090 −0.401045 0.916058i \(-0.631353\pi\)
−0.401045 + 0.916058i \(0.631353\pi\)
\(132\) −1.90211 0.763932i −0.165558 0.0664917i
\(133\) 26.1803i 2.27012i
\(134\) −5.80902 + 17.8783i −0.501823 + 1.54445i
\(135\) 0 0
\(136\) −3.61803 2.62866i −0.310244 0.225405i
\(137\) 5.03280 1.63525i 0.429981 0.139709i −0.0860276 0.996293i \(-0.527417\pi\)
0.516008 + 0.856584i \(0.327417\pi\)
\(138\) −7.10642 + 2.30902i −0.604939 + 0.196557i
\(139\) −0.954915 0.693786i −0.0809948 0.0588462i 0.546551 0.837426i \(-0.315940\pi\)
−0.627546 + 0.778580i \(0.715940\pi\)
\(140\) 0 0
\(141\) 1.88197 5.79210i 0.158490 0.487782i
\(142\) 12.9443i 1.08626i
\(143\) −6.88191 + 8.23607i −0.575494 + 0.688735i
\(144\) 4.85410 0.404508
\(145\) 0 0
\(146\) −5.92705 + 4.30625i −0.490526 + 0.356388i
\(147\) 12.0005 16.5172i 0.989782 1.36232i
\(148\) −0.865300 + 0.281153i −0.0711272 + 0.0231106i
\(149\) 6.21885 + 19.1396i 0.509468 + 1.56798i 0.793127 + 0.609056i \(0.208451\pi\)
−0.283660 + 0.958925i \(0.591549\pi\)
\(150\) 0 0
\(151\) 12.3262 8.95554i 1.00310 0.728791i 0.0403454 0.999186i \(-0.487154\pi\)
0.962750 + 0.270395i \(0.0871542\pi\)
\(152\) −10.6331 3.45492i −0.862461 0.280231i
\(153\) 2.00000i 0.161690i
\(154\) 6.85410 + 27.2501i 0.552319 + 2.19588i
\(155\) 0 0
\(156\) −0.618034 + 1.90211i −0.0494823 + 0.152291i
\(157\) 7.24518 + 9.97214i 0.578228 + 0.795863i 0.993500 0.113835i \(-0.0363134\pi\)
−0.415271 + 0.909698i \(0.636313\pi\)
\(158\) −2.93893 + 4.04508i −0.233808 + 0.321810i
\(159\) −1.66312 5.11855i −0.131894 0.405928i
\(160\) 0 0
\(161\) 19.5623 + 14.2128i 1.54173 + 1.12013i
\(162\) −0.951057 1.30902i −0.0747221 0.102846i
\(163\) −6.24112 2.02786i −0.488843 0.158835i 0.0542163 0.998529i \(-0.482734\pi\)
−0.543059 + 0.839695i \(0.682734\pi\)
\(164\) −7.09017 −0.553649
\(165\) 0 0
\(166\) −12.4721 −0.968025
\(167\) −8.59226 2.79180i −0.664889 0.216036i −0.0429216 0.999078i \(-0.513667\pi\)
−0.621968 + 0.783043i \(0.713667\pi\)
\(168\) −6.88191 9.47214i −0.530951 0.730791i
\(169\) −2.04508 1.48584i −0.157314 0.114295i
\(170\) 0 0
\(171\) 1.54508 + 4.75528i 0.118156 + 0.363646i
\(172\) −3.30220 + 4.54508i −0.251790 + 0.346559i
\(173\) 9.73508 + 13.3992i 0.740144 + 1.01872i 0.998610 + 0.0527010i \(0.0167830\pi\)
−0.258466 + 0.966020i \(0.583217\pi\)
\(174\) −0.427051 + 1.31433i −0.0323747 + 0.0996389i
\(175\) 0 0
\(176\) 16.0623 + 1.08981i 1.21074 + 0.0821478i
\(177\) 6.70820i 0.504219i
\(178\) −6.37988 2.07295i −0.478192 0.155374i
\(179\) −8.51722 + 6.18812i −0.636607 + 0.462522i −0.858683 0.512507i \(-0.828717\pi\)
0.222076 + 0.975029i \(0.428717\pi\)
\(180\) 0 0
\(181\) −0.236068 0.726543i −0.0175468 0.0540035i 0.941900 0.335894i \(-0.109038\pi\)
−0.959447 + 0.281891i \(0.909038\pi\)
\(182\) 26.0746 8.47214i 1.93277 0.627996i
\(183\) −4.11450 + 5.66312i −0.304152 + 0.418630i
\(184\) 8.35410 6.06961i 0.615873 0.447458i
\(185\) 0 0
\(186\) 11.3262 0.830480
\(187\) −0.449028 + 6.61803i −0.0328362 + 0.483959i
\(188\) 3.76393i 0.274513i
\(189\) −1.61803 + 4.97980i −0.117695 + 0.362227i
\(190\) 0 0
\(191\) 13.2812 + 9.64932i 0.960991 + 0.698200i 0.953381 0.301771i \(-0.0975777\pi\)
0.00760993 + 0.999971i \(0.497578\pi\)
\(192\) −4.02874 + 1.30902i −0.290749 + 0.0944702i
\(193\) −7.64121 + 2.48278i −0.550026 + 0.178714i −0.570829 0.821069i \(-0.693378\pi\)
0.0208024 + 0.999784i \(0.493378\pi\)
\(194\) −3.30902 2.40414i −0.237574 0.172607i
\(195\) 0 0
\(196\) 3.89919 12.0005i 0.278513 0.857176i
\(197\) 9.76393i 0.695651i −0.937559 0.347826i \(-0.886920\pi\)
0.937559 0.347826i \(-0.113080\pi\)
\(198\) −2.85317 4.54508i −0.202766 0.323005i
\(199\) 4.79837 0.340148 0.170074 0.985431i \(-0.445599\pi\)
0.170074 + 0.985431i \(0.445599\pi\)
\(200\) 0 0
\(201\) −9.39919 + 6.82891i −0.662968 + 0.481674i
\(202\) 18.6049 25.6074i 1.30903 1.80173i
\(203\) 4.25325 1.38197i 0.298520 0.0969950i
\(204\) 0.381966 + 1.17557i 0.0267430 + 0.0823064i
\(205\) 0 0
\(206\) 6.04508 4.39201i 0.421181 0.306006i
\(207\) −4.39201 1.42705i −0.305266 0.0991869i
\(208\) 15.7082i 1.08917i
\(209\) 4.04508 + 16.0822i 0.279804 + 1.11243i
\(210\) 0 0
\(211\) 0.881966 2.71441i 0.0607170 0.186868i −0.916097 0.400956i \(-0.868678\pi\)
0.976814 + 0.214088i \(0.0686780\pi\)
\(212\) −1.95511 2.69098i −0.134278 0.184817i
\(213\) 4.70228 6.47214i 0.322195 0.443463i
\(214\) −1.92705 5.93085i −0.131730 0.405425i
\(215\) 0 0
\(216\) 1.80902 + 1.31433i 0.123088 + 0.0894287i
\(217\) −21.5438 29.6525i −1.46249 2.01294i
\(218\) −16.7027 5.42705i −1.13125 0.367566i
\(219\) −4.52786 −0.305965
\(220\) 0 0
\(221\) 6.47214 0.435363
\(222\) −2.26538 0.736068i −0.152043 0.0494016i
\(223\) 12.3637 + 17.0172i 0.827937 + 1.13956i 0.988303 + 0.152500i \(0.0487324\pi\)
−0.160367 + 0.987058i \(0.551268\pi\)
\(224\) −14.3262 10.4086i −0.957212 0.695455i
\(225\) 0 0
\(226\) 1.73607 + 5.34307i 0.115482 + 0.355416i
\(227\) −4.73504 + 6.51722i −0.314276 + 0.432563i −0.936709 0.350110i \(-0.886144\pi\)
0.622433 + 0.782673i \(0.286144\pi\)
\(228\) 1.81636 + 2.50000i 0.120291 + 0.165567i
\(229\) −2.13525 + 6.57164i −0.141102 + 0.434266i −0.996489 0.0837225i \(-0.973319\pi\)
0.855387 + 0.517989i \(0.173319\pi\)
\(230\) 0 0
\(231\) −6.47214 + 16.1150i −0.425835 + 1.06029i
\(232\) 1.90983i 0.125386i
\(233\) 9.76784 + 3.17376i 0.639912 + 0.207920i 0.610961 0.791661i \(-0.290783\pi\)
0.0289512 + 0.999581i \(0.490783\pi\)
\(234\) −4.23607 + 3.07768i −0.276920 + 0.201194i
\(235\) 0 0
\(236\) 1.28115 + 3.94298i 0.0833960 + 0.256666i
\(237\) −2.93893 + 0.954915i −0.190904 + 0.0620284i
\(238\) 9.95959 13.7082i 0.645585 0.888571i
\(239\) 17.8262 12.9515i 1.15308 0.837764i 0.164196 0.986428i \(-0.447497\pi\)
0.988888 + 0.148664i \(0.0474972\pi\)
\(240\) 0 0
\(241\) 0.618034 0.0398111 0.0199055 0.999802i \(-0.493663\pi\)
0.0199055 + 0.999802i \(0.493663\pi\)
\(242\) −8.42075 15.6803i −0.541306 1.00797i
\(243\) 1.00000i 0.0641500i
\(244\) −1.33688 + 4.11450i −0.0855850 + 0.263404i
\(245\) 0 0
\(246\) −15.0172 10.9106i −0.957463 0.695638i
\(247\) 15.3884 5.00000i 0.979142 0.318142i
\(248\) −14.8864 + 4.83688i −0.945287 + 0.307142i
\(249\) −6.23607 4.53077i −0.395195 0.287126i
\(250\) 0 0
\(251\) 5.09017 15.6659i 0.321289 0.988825i −0.651799 0.758391i \(-0.725986\pi\)
0.973088 0.230433i \(-0.0740144\pi\)
\(252\) 3.23607i 0.203853i
\(253\) −14.2128 5.70820i −0.893554 0.358872i
\(254\) −3.14590 −0.197391
\(255\) 0 0
\(256\) −10.9721 + 7.97172i −0.685758 + 0.498233i
\(257\) −5.62058 + 7.73607i −0.350602 + 0.482563i −0.947500 0.319754i \(-0.896400\pi\)
0.596898 + 0.802317i \(0.296400\pi\)
\(258\) −13.9883 + 4.54508i −0.870876 + 0.282965i
\(259\) 2.38197 + 7.33094i 0.148008 + 0.455522i
\(260\) 0 0
\(261\) −0.690983 + 0.502029i −0.0427708 + 0.0310748i
\(262\) −14.1271 4.59017i −0.872775 0.283582i
\(263\) 24.2148i 1.49315i 0.665303 + 0.746574i \(0.268302\pi\)
−0.665303 + 0.746574i \(0.731698\pi\)
\(264\) 5.69098 + 4.75528i 0.350256 + 0.292667i
\(265\) 0 0
\(266\) 13.0902 40.2874i 0.802610 2.47018i
\(267\) −2.43690 3.35410i −0.149136 0.205268i
\(268\) −4.22050 + 5.80902i −0.257808 + 0.354842i
\(269\) −0.263932 0.812299i −0.0160922 0.0495268i 0.942688 0.333676i \(-0.108289\pi\)
−0.958780 + 0.284149i \(0.908289\pi\)
\(270\) 0 0
\(271\) −14.8713 10.8046i −0.903369 0.656336i 0.0359605 0.999353i \(-0.488551\pi\)
−0.939329 + 0.343018i \(0.888551\pi\)
\(272\) −5.70634 7.85410i −0.345998 0.476225i
\(273\) 16.1150 + 5.23607i 0.975322 + 0.316901i
\(274\) 8.56231 0.517268
\(275\) 0 0
\(276\) −2.85410 −0.171797
\(277\) −21.5438 7.00000i −1.29444 0.420589i −0.420797 0.907155i \(-0.638249\pi\)
−0.873644 + 0.486566i \(0.838249\pi\)
\(278\) −1.12257 1.54508i −0.0673273 0.0926680i
\(279\) 5.66312 + 4.11450i 0.339042 + 0.246328i
\(280\) 0 0
\(281\) −0.336881 1.03681i −0.0200966 0.0618511i 0.940505 0.339779i \(-0.110352\pi\)
−0.960602 + 0.277928i \(0.910352\pi\)
\(282\) 5.79210 7.97214i 0.344914 0.474734i
\(283\) 9.42481 + 12.9721i 0.560247 + 0.771113i 0.991358 0.131185i \(-0.0418783\pi\)
−0.431111 + 0.902299i \(0.641878\pi\)
\(284\) 1.52786 4.70228i 0.0906621 0.279029i
\(285\) 0 0
\(286\) −14.7082 + 9.23305i −0.869714 + 0.545962i
\(287\) 60.0689i 3.54575i
\(288\) 3.21644 + 1.04508i 0.189531 + 0.0615822i
\(289\) −10.5172 + 7.64121i −0.618660 + 0.449483i
\(290\) 0 0
\(291\) −0.781153 2.40414i −0.0457920 0.140933i
\(292\) −2.66141 + 0.864745i −0.155747 + 0.0506054i
\(293\) 14.9721 20.6074i 0.874682 1.20390i −0.103183 0.994662i \(-0.532903\pi\)
0.977866 0.209234i \(-0.0670971\pi\)
\(294\) 26.7254 19.4172i 1.55866 1.13243i
\(295\) 0 0
\(296\) 3.29180 0.191332
\(297\) 0.224514 3.30902i 0.0130276 0.192009i
\(298\) 32.5623i 1.88628i
\(299\) −4.61803 + 14.2128i −0.267068 + 0.821950i
\(300\) 0 0
\(301\) 38.5066 + 27.9767i 2.21948 + 1.61255i
\(302\) 23.4459 7.61803i 1.34916 0.438369i
\(303\) 18.6049 6.04508i 1.06882 0.347281i
\(304\) −19.6353 14.2658i −1.12616 0.818202i
\(305\) 0 0
\(306\) −1.00000 + 3.07768i −0.0571662 + 0.175939i
\(307\) 28.1246i 1.60516i 0.596547 + 0.802578i \(0.296539\pi\)
−0.596547 + 0.802578i \(0.703461\pi\)
\(308\) −0.726543 + 10.7082i −0.0413986 + 0.610157i
\(309\) 4.61803 0.262711
\(310\) 0 0
\(311\) −10.1353 + 7.36369i −0.574718 + 0.417557i −0.836816 0.547484i \(-0.815586\pi\)
0.262098 + 0.965041i \(0.415586\pi\)
\(312\) 4.25325 5.85410i 0.240793 0.331423i
\(313\) 8.05748 2.61803i 0.455436 0.147980i −0.0723104 0.997382i \(-0.523037\pi\)
0.527746 + 0.849402i \(0.323037\pi\)
\(314\) 6.16312 + 18.9681i 0.347805 + 1.07043i
\(315\) 0 0
\(316\) −1.54508 + 1.12257i −0.0869178 + 0.0631495i
\(317\) −3.40820 1.10739i −0.191424 0.0621973i 0.211736 0.977327i \(-0.432088\pi\)
−0.403160 + 0.915130i \(0.632088\pi\)
\(318\) 8.70820i 0.488332i
\(319\) −2.39919 + 1.50609i −0.134329 + 0.0843246i
\(320\) 0 0
\(321\) 1.19098 3.66547i 0.0664742 0.204587i
\(322\) 22.9969 + 31.6525i 1.28157 + 1.76392i
\(323\) 5.87785 8.09017i 0.327052 0.450149i
\(324\) −0.190983 0.587785i −0.0106102 0.0326547i
\(325\) 0 0
\(326\) −8.59017 6.24112i −0.475766 0.345664i
\(327\) −6.37988 8.78115i −0.352808 0.485599i
\(328\) 24.3970 + 7.92705i 1.34710 + 0.437698i
\(329\) −31.8885 −1.75807
\(330\) 0 0
\(331\) −27.5967 −1.51685 −0.758427 0.651758i \(-0.774032\pi\)
−0.758427 + 0.651758i \(0.774032\pi\)
\(332\) −4.53077 1.47214i −0.248658 0.0807940i
\(333\) −0.865300 1.19098i −0.0474181 0.0652655i
\(334\) −11.8262 8.59226i −0.647103 0.470148i
\(335\) 0 0
\(336\) −7.85410 24.1724i −0.428476 1.31871i
\(337\) 16.9600 23.3435i 0.923871 1.27160i −0.0383318 0.999265i \(-0.512204\pi\)
0.962203 0.272334i \(-0.0877956\pi\)
\(338\) −2.40414 3.30902i −0.130768 0.179987i
\(339\) −1.07295 + 3.30220i −0.0582746 + 0.179351i
\(340\) 0 0
\(341\) 17.8156 + 14.8864i 0.964769 + 0.806143i
\(342\) 8.09017i 0.437466i
\(343\) −66.8110 21.7082i −3.60745 1.17213i
\(344\) 16.4443 11.9475i 0.886616 0.644164i
\(345\) 0 0
\(346\) 8.28115 + 25.4868i 0.445198 + 1.37018i
\(347\) 26.8011 8.70820i 1.43876 0.467481i 0.517248 0.855835i \(-0.326956\pi\)
0.921510 + 0.388355i \(0.126956\pi\)
\(348\) −0.310271 + 0.427051i −0.0166323 + 0.0228923i
\(349\) 26.0795 18.9479i 1.39601 1.01426i 0.400829 0.916153i \(-0.368722\pi\)
0.995176 0.0981041i \(-0.0312778\pi\)
\(350\) 0 0
\(351\) −3.23607 −0.172729
\(352\) 10.4086 + 4.18034i 0.554781 + 0.222813i
\(353\) 17.8328i 0.949145i 0.880216 + 0.474573i \(0.157397\pi\)
−0.880216 + 0.474573i \(0.842603\pi\)
\(354\) −3.35410 + 10.3229i −0.178269 + 0.548654i
\(355\) 0 0
\(356\) −2.07295 1.50609i −0.109866 0.0798224i
\(357\) 9.95959 3.23607i 0.527118 0.171271i
\(358\) −16.2007 + 5.26393i −0.856234 + 0.278207i
\(359\) 2.66312 + 1.93487i 0.140554 + 0.102118i 0.655840 0.754900i \(-0.272314\pi\)
−0.515286 + 0.857018i \(0.672314\pi\)
\(360\) 0 0
\(361\) 1.85410 5.70634i 0.0975843 0.300334i
\(362\) 1.23607i 0.0649663i
\(363\) 1.48584 10.8992i 0.0779864 0.572059i
\(364\) 10.4721 0.548889
\(365\) 0 0
\(366\) −9.16312 + 6.65740i −0.478964 + 0.347988i
\(367\) −13.0045 + 17.8992i −0.678830 + 0.934330i −0.999919 0.0127192i \(-0.995951\pi\)
0.321089 + 0.947049i \(0.395951\pi\)
\(368\) 21.3193 6.92705i 1.11134 0.361097i
\(369\) −3.54508 10.9106i −0.184550 0.567986i
\(370\) 0 0
\(371\) −22.7984 + 16.5640i −1.18363 + 0.859959i
\(372\) 4.11450 + 1.33688i 0.213327 + 0.0693141i
\(373\) 32.7426i 1.69535i −0.530516 0.847675i \(-0.678002\pi\)
0.530516 0.847675i \(-0.321998\pi\)
\(374\) −4.00000 + 9.95959i −0.206835 + 0.514998i
\(375\) 0 0
\(376\) −4.20820 + 12.9515i −0.217022 + 0.667924i
\(377\) 1.62460 + 2.23607i 0.0836711 + 0.115163i
\(378\) −4.97980 + 6.85410i −0.256133 + 0.352537i
\(379\) 1.54508 + 4.75528i 0.0793657 + 0.244262i 0.982865 0.184327i \(-0.0590106\pi\)
−0.903499 + 0.428590i \(0.859011\pi\)
\(380\) 0 0
\(381\) −1.57295 1.14281i −0.0805846 0.0585482i
\(382\) 15.6129 + 21.4894i 0.798827 + 1.09949i
\(383\) 12.7068 + 4.12868i 0.649285 + 0.210966i 0.615099 0.788450i \(-0.289116\pi\)
0.0341862 + 0.999415i \(0.489116\pi\)
\(384\) −13.6180 −0.694942
\(385\) 0 0
\(386\) −13.0000 −0.661683
\(387\) −8.64527 2.80902i −0.439464 0.142790i
\(388\) −0.918300 1.26393i −0.0466196 0.0641664i
\(389\) −17.0344 12.3762i −0.863680 0.627501i 0.0652033 0.997872i \(-0.479230\pi\)
−0.928884 + 0.370371i \(0.879230\pi\)
\(390\) 0 0
\(391\) 2.85410 + 8.78402i 0.144338 + 0.444227i
\(392\) −26.8339 + 36.9336i −1.35531 + 1.86543i
\(393\) −5.39607 7.42705i −0.272196 0.374645i
\(394\) 4.88197 15.0251i 0.245950 0.756956i
\(395\) 0 0
\(396\) −0.500000 1.98787i −0.0251259 0.0998942i
\(397\) 2.72949i 0.136989i −0.997651 0.0684946i \(-0.978180\pi\)
0.997651 0.0684946i \(-0.0218196\pi\)
\(398\) 7.38394 + 2.39919i 0.370123 + 0.120260i
\(399\) 21.1803 15.3884i 1.06034 0.770384i
\(400\) 0 0
\(401\) −9.54508 29.3768i −0.476659 1.46700i −0.843707 0.536803i \(-0.819632\pi\)
0.367049 0.930202i \(-0.380368\pi\)
\(402\) −17.8783 + 5.80902i −0.891689 + 0.289727i
\(403\) 13.3148 18.3262i 0.663257 0.912895i
\(404\) 9.78115 7.10642i 0.486631 0.353558i
\(405\) 0 0
\(406\) 7.23607 0.359120
\(407\) −2.59590 4.13525i −0.128674 0.204977i
\(408\) 4.47214i 0.221404i
\(409\) 8.12868 25.0175i 0.401937 1.23704i −0.521488 0.853258i \(-0.674623\pi\)
0.923426 0.383777i \(-0.125377\pi\)
\(410\) 0 0
\(411\) 4.28115 + 3.11044i 0.211174 + 0.153427i
\(412\) 2.71441 0.881966i 0.133729 0.0434513i
\(413\) 33.4055 10.8541i 1.64378 0.534095i
\(414\) −6.04508 4.39201i −0.297100 0.215856i
\(415\) 0 0
\(416\) 3.38197 10.4086i 0.165815 0.510325i
\(417\) 1.18034i 0.0578015i
\(418\) −1.81636 + 26.7705i −0.0888409 + 1.30939i
\(419\) 24.5967 1.20163 0.600815 0.799388i \(-0.294843\pi\)
0.600815 + 0.799388i \(0.294843\pi\)
\(420\) 0 0
\(421\) 3.11803 2.26538i 0.151964 0.110408i −0.509205 0.860645i \(-0.670061\pi\)
0.661169 + 0.750237i \(0.270061\pi\)
\(422\) 2.71441 3.73607i 0.132136 0.181869i
\(423\) 5.79210 1.88197i 0.281621 0.0915043i
\(424\) 3.71885 + 11.4454i 0.180603 + 0.555839i
\(425\) 0 0
\(426\) 10.4721 7.60845i 0.507377 0.368631i
\(427\) 34.8586 + 11.3262i 1.68692 + 0.548115i
\(428\) 2.38197i 0.115137i
\(429\) −10.7082 0.726543i −0.516997 0.0350778i
\(430\) 0 0
\(431\) −4.90983 + 15.1109i −0.236498 + 0.727867i 0.760421 + 0.649431i \(0.224993\pi\)
−0.996919 + 0.0784361i \(0.975007\pi\)
\(432\) 2.85317 + 3.92705i 0.137273 + 0.188940i
\(433\) −0.608030 + 0.836881i −0.0292200 + 0.0402179i −0.823377 0.567495i \(-0.807913\pi\)
0.794157 + 0.607713i \(0.207913\pi\)
\(434\) −18.3262 56.4024i −0.879688 2.70740i
\(435\) 0 0
\(436\) −5.42705 3.94298i −0.259909 0.188835i
\(437\) 13.5721 + 18.6803i 0.649240 + 0.893602i
\(438\) −6.96767 2.26393i −0.332928 0.108175i
\(439\) −25.3262 −1.20876 −0.604378 0.796698i \(-0.706578\pi\)
−0.604378 + 0.796698i \(0.706578\pi\)
\(440\) 0 0
\(441\) 20.4164 0.972210
\(442\) 9.95959 + 3.23607i 0.473730 + 0.153924i
\(443\) 4.86128 + 6.69098i 0.230967 + 0.317898i 0.908732 0.417380i \(-0.137052\pi\)
−0.677766 + 0.735278i \(0.737052\pi\)
\(444\) −0.736068 0.534785i −0.0349322 0.0253798i
\(445\) 0 0
\(446\) 10.5172 + 32.3687i 0.498005 + 1.53270i
\(447\) −11.8290 + 16.2812i −0.559490 + 0.770072i
\(448\) 13.0373 + 17.9443i 0.615953 + 0.847787i
\(449\) 10.5902 32.5932i 0.499781 1.53817i −0.309590 0.950870i \(-0.600192\pi\)
0.809371 0.587298i \(-0.199808\pi\)
\(450\) 0 0
\(451\) −9.28115 36.8994i −0.437032 1.73753i
\(452\) 2.14590i 0.100935i
\(453\) 14.4904 + 4.70820i 0.680817 + 0.221211i
\(454\) −10.5451 + 7.66145i −0.494905 + 0.359570i
\(455\) 0 0
\(456\) −3.45492 10.6331i −0.161791 0.497942i
\(457\) −7.10642 + 2.30902i −0.332424 + 0.108011i −0.470473 0.882414i \(-0.655917\pi\)
0.138049 + 0.990425i \(0.455917\pi\)
\(458\) −6.57164 + 9.04508i −0.307073 + 0.422649i
\(459\) −1.61803 + 1.17557i −0.0755234 + 0.0548709i
\(460\) 0 0
\(461\) 8.05573 0.375193 0.187596 0.982246i \(-0.439930\pi\)
0.187596 + 0.982246i \(0.439930\pi\)
\(462\) −18.0171 + 21.5623i −0.838230 + 1.00317i
\(463\) 0.270510i 0.0125717i 0.999980 + 0.00628583i \(0.00200085\pi\)
−0.999980 + 0.00628583i \(0.997999\pi\)
\(464\) 1.28115 3.94298i 0.0594760 0.183048i
\(465\) 0 0
\(466\) 13.4443 + 9.76784i 0.622794 + 0.452486i
\(467\) −29.3768 + 9.54508i −1.35939 + 0.441694i −0.895841 0.444375i \(-0.853426\pi\)
−0.463553 + 0.886069i \(0.653426\pi\)
\(468\) −1.90211 + 0.618034i −0.0879252 + 0.0285686i
\(469\) 49.2148 + 35.7566i 2.27253 + 1.65109i
\(470\) 0 0
\(471\) −3.80902 + 11.7229i −0.175510 + 0.540165i
\(472\) 15.0000i 0.690431i
\(473\) −27.9767 11.2361i −1.28637 0.516635i
\(474\) −5.00000 −0.229658
\(475\) 0 0
\(476\) 5.23607 3.80423i 0.239995 0.174366i
\(477\) 3.16344 4.35410i 0.144844 0.199361i
\(478\) 33.9075 11.0172i 1.55089 0.503916i
\(479\) −2.03444 6.26137i −0.0929560 0.286089i 0.893760 0.448546i \(-0.148058\pi\)
−0.986716 + 0.162457i \(0.948058\pi\)
\(480\) 0 0
\(481\) −3.85410 + 2.80017i −0.175732 + 0.127677i
\(482\) 0.951057 + 0.309017i 0.0433194 + 0.0140753i
\(483\) 24.1803i 1.10024i
\(484\) −1.20820 6.69015i −0.0549184 0.304098i
\(485\) 0 0
\(486\) 0.500000 1.53884i 0.0226805 0.0698033i
\(487\) 4.80828 + 6.61803i 0.217884 + 0.299892i 0.903942 0.427655i \(-0.140660\pi\)
−0.686058 + 0.727547i \(0.740660\pi\)
\(488\) 9.20029 12.6631i 0.416478 0.573232i
\(489\) −2.02786 6.24112i −0.0917032 0.282233i
\(490\) 0 0
\(491\) −5.82624 4.23301i −0.262934 0.191033i 0.448505 0.893780i \(-0.351957\pi\)
−0.711440 + 0.702747i \(0.751957\pi\)
\(492\) −4.16750 5.73607i −0.187885 0.258602i
\(493\) 1.62460 + 0.527864i 0.0731682 + 0.0237738i
\(494\) 26.1803 1.17791
\(495\) 0 0
\(496\) −33.9787 −1.52569
\(497\) −39.8384 12.9443i −1.78700 0.580630i
\(498\) −7.33094 10.0902i −0.328507 0.452151i
\(499\) 9.04508 + 6.57164i 0.404914 + 0.294187i 0.771539 0.636182i \(-0.219487\pi\)
−0.366626 + 0.930368i \(0.619487\pi\)
\(500\) 0 0
\(501\) −2.79180 8.59226i −0.124728 0.383874i
\(502\) 15.6659 21.5623i 0.699205 0.962373i
\(503\) −8.16348 11.2361i −0.363992 0.500992i 0.587264 0.809396i \(-0.300205\pi\)
−0.951255 + 0.308404i \(0.900205\pi\)
\(504\) 3.61803 11.1352i 0.161160 0.496000i
\(505\) 0 0
\(506\) −19.0172 15.8904i −0.845419 0.706416i
\(507\) 2.52786i 0.112266i
\(508\) −1.14281 0.371323i −0.0507042 0.0164748i
\(509\) 7.66312 5.56758i 0.339662 0.246779i −0.404857 0.914380i \(-0.632679\pi\)
0.744519 + 0.667601i \(0.232679\pi\)
\(510\) 0 0
\(511\) 7.32624 + 22.5478i 0.324094 + 0.997458i
\(512\) 5.03280 1.63525i 0.222420 0.0722687i
\(513\) −2.93893 + 4.04508i −0.129757 + 0.178595i
\(514\) −12.5172 + 9.09429i −0.552111 + 0.401132i
\(515\) 0 0
\(516\) −5.61803 −0.247320
\(517\) 19.5887 4.92705i 0.861509 0.216691i
\(518\) 12.4721i 0.547994i
\(519\) −5.11803 + 15.7517i −0.224657 + 0.691422i
\(520\) 0 0
\(521\) −23.7533 17.2578i −1.04065 0.756077i −0.0702381 0.997530i \(-0.522376\pi\)
−0.970412 + 0.241453i \(0.922376\pi\)
\(522\) −1.31433 + 0.427051i −0.0575266 + 0.0186915i
\(523\) −3.57971 + 1.16312i −0.156530 + 0.0508596i −0.386234 0.922401i \(-0.626224\pi\)
0.229704 + 0.973261i \(0.426224\pi\)
\(524\) −4.59017 3.33495i −0.200523 0.145688i
\(525\) 0 0
\(526\) −12.1074 + 37.2627i −0.527907 + 1.62473i
\(527\) 14.0000i 0.609850i
\(528\) 8.55951 + 13.6353i 0.372505 + 0.593398i
\(529\) 1.67376 0.0727723
\(530\) 0 0
\(531\) −5.42705 + 3.94298i −0.235514 + 0.171111i
\(532\) 9.51057 13.0902i 0.412335 0.567531i
\(533\) −35.3076 + 11.4721i −1.52934 + 0.496913i
\(534\) −2.07295 6.37988i −0.0897053 0.276084i
\(535\) 0 0
\(536\) 21.0172 15.2699i 0.907806 0.659559i
\(537\) −10.0126 3.25329i −0.432075 0.140390i
\(538\) 1.38197i 0.0595808i
\(539\) 67.5582 + 4.58377i 2.90994 + 0.197437i
\(540\) 0 0
\(541\) −0.500000 + 1.53884i −0.0214967 + 0.0661600i −0.961229 0.275750i \(-0.911074\pi\)
0.939733 + 0.341910i \(0.111074\pi\)
\(542\) −17.4823 24.0623i −0.750929 1.03356i
\(543\) 0.449028 0.618034i 0.0192696 0.0265224i
\(544\) −2.09017 6.43288i −0.0896153 0.275808i
\(545\) 0 0
\(546\) 22.1803 + 16.1150i 0.949231 + 0.689657i
\(547\) 11.3799 + 15.6631i 0.486570 + 0.669707i 0.979751 0.200220i \(-0.0641658\pi\)
−0.493181 + 0.869927i \(0.664166\pi\)
\(548\) 3.11044 + 1.01064i 0.132871 + 0.0431725i
\(549\) −7.00000 −0.298753
\(550\) 0 0
\(551\) 4.27051 0.181930
\(552\) 9.82084 + 3.19098i 0.418003 + 0.135817i
\(553\) 9.51057 + 13.0902i 0.404430 + 0.556651i
\(554\) −29.6525 21.5438i −1.25981 0.915308i
\(555\) 0 0
\(556\) −0.225425 0.693786i −0.00956014 0.0294231i
\(557\) 24.9192 34.2984i 1.05586 1.45327i 0.172247 0.985054i \(-0.444897\pi\)
0.883615 0.468215i \(-0.155103\pi\)
\(558\) 6.65740 + 9.16312i 0.281830 + 0.387906i
\(559\) −9.09017 + 27.9767i −0.384473 + 1.18329i
\(560\) 0 0
\(561\) −5.61803 + 3.52671i −0.237194 + 0.148898i
\(562\) 1.76393i 0.0744070i
\(563\) 19.6619 + 6.38854i 0.828651 + 0.269245i 0.692477 0.721440i \(-0.256519\pi\)
0.136174 + 0.990685i \(0.456519\pi\)
\(564\) 3.04508 2.21238i 0.128221 0.0931582i
\(565\) 0 0
\(566\) 8.01722 + 24.6745i 0.336989 + 1.03715i
\(567\) −4.97980 + 1.61803i −0.209132 + 0.0679510i
\(568\) −10.5146 + 14.4721i −0.441184 + 0.607237i
\(569\) −18.2533 + 13.2618i −0.765218 + 0.555963i −0.900506 0.434843i \(-0.856804\pi\)
0.135289 + 0.990806i \(0.456804\pi\)
\(570\) 0 0
\(571\) −11.0902 −0.464109 −0.232055 0.972703i \(-0.574545\pi\)
−0.232055 + 0.972703i \(0.574545\pi\)
\(572\) −6.43288 + 1.61803i −0.268972 + 0.0676534i
\(573\) 16.4164i 0.685805i
\(574\) −30.0344 + 92.4365i −1.25361 + 3.85823i
\(575\) 0 0
\(576\) −3.42705 2.48990i −0.142794 0.103746i
\(577\) 28.5442 9.27458i 1.18831 0.386106i 0.352863 0.935675i \(-0.385208\pi\)
0.835448 + 0.549569i \(0.185208\pi\)
\(578\) −20.0049 + 6.50000i −0.832096 + 0.270364i
\(579\) −6.50000 4.72253i −0.270131 0.196262i
\(580\) 0 0
\(581\) −12.4721 + 38.3853i −0.517431 + 1.59249i
\(582\) 4.09017i 0.169543i
\(583\) 11.4454 13.6976i 0.474021 0.567295i
\(584\) 10.1246 0.418959
\(585\) 0 0
\(586\) 33.3435 24.2254i 1.37741 1.00074i
\(587\) 12.7068 17.4894i 0.524464 0.721863i −0.461810 0.886979i \(-0.652800\pi\)
0.986274 + 0.165116i \(0.0527998\pi\)
\(588\) 12.0005 3.89919i 0.494891 0.160800i
\(589\) −10.8156 33.2870i −0.445649 1.37157i
\(590\) 0 0
\(591\) 7.89919 5.73910i 0.324929 0.236075i
\(592\) 6.79615 + 2.20820i 0.279320 + 0.0907566i
\(593\) 3.11146i 0.127772i 0.997957 + 0.0638861i \(0.0203494\pi\)
−0.997957 + 0.0638861i \(0.979651\pi\)
\(594\) 2.00000 4.97980i 0.0820610 0.204324i
\(595\) 0 0
\(596\) −3.84346 + 11.8290i −0.157434 + 0.484533i
\(597\) 2.82041 + 3.88197i 0.115432 + 0.158878i
\(598\) −14.2128 + 19.5623i −0.581207 + 0.799962i
\(599\) 5.48936 + 16.8945i 0.224289 + 0.690291i 0.998363 + 0.0571955i \(0.0182158\pi\)
−0.774074 + 0.633095i \(0.781784\pi\)
\(600\) 0 0
\(601\) 8.38197 + 6.08985i 0.341908 + 0.248410i 0.745466 0.666543i \(-0.232227\pi\)
−0.403559 + 0.914954i \(0.632227\pi\)
\(602\) 45.2672 + 62.3050i 1.84495 + 2.53936i
\(603\) −11.0494 3.59017i −0.449967 0.146203i
\(604\) 9.41641 0.383148
\(605\) 0 0
\(606\) 31.6525 1.28579
\(607\) 31.3849 + 10.1976i 1.27387 + 0.413906i 0.866418 0.499319i \(-0.166417\pi\)
0.407454 + 0.913226i \(0.366417\pi\)
\(608\) −9.93935 13.6803i −0.403094 0.554811i
\(609\) 3.61803 + 2.62866i 0.146610 + 0.106518i
\(610\) 0 0
\(611\) −6.09017 18.7436i −0.246382 0.758286i
\(612\) −0.726543 + 1.00000i −0.0293687 + 0.0404226i
\(613\) −2.21238 3.04508i −0.0893573 0.122990i 0.761998 0.647580i \(-0.224219\pi\)
−0.851355 + 0.524590i \(0.824219\pi\)
\(614\) −14.0623 + 43.2793i −0.567508 + 1.74661i
\(615\) 0 0
\(616\) 14.4721 36.0341i 0.583099 1.45186i
\(617\) 42.2492i 1.70089i −0.526064 0.850445i \(-0.676333\pi\)
0.526064 0.850445i \(-0.323667\pi\)
\(618\) 7.10642 + 2.30902i 0.285862 + 0.0928823i
\(619\) 34.6976 25.2093i 1.39461 1.01325i 0.399271 0.916833i \(-0.369263\pi\)
0.995341 0.0964126i \(-0.0307368\pi\)
\(620\) 0 0
\(621\) −1.42705 4.39201i −0.0572656 0.176245i
\(622\) −19.2784 + 6.26393i −0.772993 + 0.251161i
\(623\) −12.7598 + 17.5623i −0.511209 + 0.703619i
\(624\) 12.7082 9.23305i 0.508735 0.369618i
\(625\) 0 0
\(626\) 13.7082 0.547890
\(627\) −10.6331 + 12.7254i −0.424647 + 0.508205i
\(628\) 7.61803i 0.303993i
\(629\) −0.909830 + 2.80017i −0.0362773 + 0.111650i
\(630\) 0 0
\(631\) 32.0623 + 23.2946i 1.27638 + 0.927345i 0.999437 0.0335418i \(-0.0106787\pi\)
0.276943 + 0.960886i \(0.410679\pi\)
\(632\) 6.57164 2.13525i 0.261406 0.0849359i
\(633\) 2.71441 0.881966i 0.107888 0.0350550i
\(634\) −4.69098 3.40820i −0.186303 0.135357i
\(635\) 0 0
\(636\) 1.02786 3.16344i 0.0407575 0.125439i
\(637\) 66.0689i 2.61774i
\(638\) −4.44501 + 1.11803i −0.175980 + 0.0442634i
\(639\) 8.00000 0.316475
\(640\) 0 0
\(641\) −3.42705 + 2.48990i −0.135360 + 0.0983451i −0.653405 0.757009i \(-0.726660\pi\)
0.518045 + 0.855354i \(0.326660\pi\)
\(642\) 3.66547 5.04508i 0.144665 0.199114i
\(643\) 13.0045 4.22542i 0.512848 0.166634i −0.0411490 0.999153i \(-0.513102\pi\)
0.553997 + 0.832519i \(0.313102\pi\)
\(644\) 4.61803 + 14.2128i 0.181976 + 0.560065i
\(645\) 0 0
\(646\) 13.0902 9.51057i 0.515026 0.374188i
\(647\) −30.0503 9.76393i −1.18140 0.383860i −0.348513 0.937304i \(-0.613313\pi\)
−0.832886 + 0.553444i \(0.813313\pi\)
\(648\) 2.23607i 0.0878410i
\(649\) −18.8435 + 11.8290i −0.739670 + 0.464327i
\(650\) 0 0
\(651\) 11.3262 34.8586i 0.443910 1.36622i
\(652\) −2.38390 3.28115i −0.0933606 0.128500i
\(653\) 25.6053 35.2426i 1.00201 1.37915i 0.0779293 0.996959i \(-0.475169\pi\)
0.924083 0.382192i \(-0.124831\pi\)
\(654\) −5.42705 16.7027i −0.212214 0.653129i
\(655\) 0 0
\(656\) 45.0517 + 32.7319i 1.75897 + 1.27797i
\(657\) −2.66141 3.66312i −0.103832 0.142912i
\(658\) −49.0714 15.9443i −1.91300 0.621572i
\(659\) −42.0344 −1.63743 −0.818715 0.574201i \(-0.805313\pi\)
−0.818715 + 0.574201i \(0.805313\pi\)
\(660\) 0 0
\(661\) 15.0902 0.586940 0.293470 0.955968i \(-0.405190\pi\)
0.293470 + 0.955968i \(0.405190\pi\)
\(662\) −42.4670 13.7984i −1.65053 0.536289i
\(663\) 3.80423 + 5.23607i 0.147744 + 0.203352i
\(664\) 13.9443 + 10.1311i 0.541143 + 0.393163i
\(665\) 0 0
\(666\) −0.736068 2.26538i −0.0285221 0.0877819i
\(667\) −2.31838 + 3.19098i −0.0897682 + 0.123555i
\(668\) −3.28195 4.51722i −0.126983 0.174777i
\(669\) −6.50000 + 20.0049i −0.251305 + 0.773436i
\(670\) 0 0
\(671\) −23.1631 1.57160i −0.894202 0.0606709i
\(672\) 17.7082i 0.683109i
\(673\) −33.5770 10.9098i −1.29430 0.420543i −0.420704 0.907198i \(-0.638217\pi\)
−0.873594 + 0.486655i \(0.838217\pi\)
\(674\) 37.7705 27.4419i 1.45487 1.05702i
\(675\) 0 0
\(676\) −0.482779 1.48584i −0.0185684 0.0571477i
\(677\) 5.65334 1.83688i 0.217275 0.0705971i −0.198357 0.980130i \(-0.563560\pi\)
0.415632 + 0.909533i \(0.363560\pi\)
\(678\) −3.30220 + 4.54508i −0.126820 + 0.174553i
\(679\) −10.7082 + 7.77997i −0.410943 + 0.298568i
\(680\) 0 0
\(681\) −8.05573 −0.308696
\(682\) 19.9722 + 31.8156i 0.764775 + 1.21828i
\(683\) 15.7082i 0.601058i −0.953773 0.300529i \(-0.902837\pi\)
0.953773 0.300529i \(-0.0971632\pi\)
\(684\) −0.954915 + 2.93893i −0.0365121 + 0.112373i
\(685\) 0 0
\(686\) −91.9574 66.8110i −3.51095 2.55086i
\(687\) −6.57164 + 2.13525i −0.250724 + 0.0814651i
\(688\) 41.9650 13.6353i 1.59990 0.519839i
\(689\) −14.0902 10.2371i −0.536793 0.390003i
\(690\) 0 0
\(691\) −9.05573 + 27.8707i −0.344496 + 1.06025i 0.617357 + 0.786683i \(0.288203\pi\)
−0.961853 + 0.273567i \(0.911797\pi\)
\(692\) 10.2361i 0.389117i
\(693\) −16.8415 + 4.23607i −0.639756 + 0.160915i
\(694\) 45.5967 1.73083
\(695\) 0 0
\(696\) 1.54508 1.12257i 0.0585663 0.0425509i
\(697\) −13.4863 + 18.5623i −0.510830 + 0.703097i
\(698\) 49.6062 16.1180i 1.87762 0.610077i
\(699\) 3.17376 + 9.76784i 0.120043 + 0.369453i
\(700\) 0 0
\(701\) −32.6976 + 23.7562i −1.23497 + 0.897258i −0.997253 0.0740763i \(-0.976399\pi\)
−0.237717 + 0.971334i \(0.576399\pi\)
\(702\) −4.97980 1.61803i −0.187950 0.0610688i
\(703\) 7.36068i 0.277613i
\(704\) −10.7812 9.00854i −0.406330 0.339522i
\(705\) 0 0
\(706\) −8.91641 + 27.4419i −0.335573 + 1.03279i
\(707\) −60.2066 82.8673i −2.26430 3.11654i
\(708\) −2.43690 + 3.35410i −0.0915842 + 0.126055i
\(709\) −5.81559 17.8986i −0.218409 0.672195i −0.998894 0.0470197i \(-0.985028\pi\)
0.780485 0.625175i \(-0.214972\pi\)
\(710\) 0 0
\(711\) −2.50000 1.81636i −0.0937573 0.0681187i
\(712\) 5.44907 + 7.50000i 0.204212 + 0.281074i
\(713\) 30.7441 + 9.98936i 1.15137 + 0.374104i
\(714\) 16.9443 0.634123
\(715\) 0 0
\(716\) −6.50658 −0.243162
\(717\) 20.9560 + 6.80902i 0.782616 + 0.254287i
\(718\) 3.13068 + 4.30902i 0.116836 + 0.160811i
\(719\) 21.7705 + 15.8172i 0.811903 + 0.589882i 0.914382 0.404853i \(-0.132677\pi\)
−0.102479 + 0.994735i \(0.532677\pi\)
\(720\) 0 0
\(721\) −7.47214 22.9969i −0.278277 0.856448i
\(722\) 5.70634 7.85410i 0.212368 0.292299i
\(723\) 0.363271 + 0.500000i 0.0135102 + 0.0185952i
\(724\) 0.145898 0.449028i 0.00542226 0.0166880i
\(725\) 0 0
\(726\) 7.73607 16.0292i 0.287112 0.594900i
\(727\) 21.6738i 0.803835i −0.915676 0.401918i \(-0.868344\pi\)
0.915676 0.401918i \(-0.131656\pi\)
\(728\) −36.0341 11.7082i −1.33551 0.433935i
\(729\) 0.809017 0.587785i 0.0299636 0.0217698i
\(730\) 0 0
\(731\) 5.61803 + 17.2905i 0.207790 + 0.639513i
\(732\) −4.11450 + 1.33688i −0.152076 + 0.0494125i
\(733\) −2.85317 + 3.92705i −0.105384 + 0.145049i −0.858452 0.512894i \(-0.828573\pi\)
0.753068 + 0.657943i \(0.228573\pi\)
\(734\) −28.9615 + 21.0418i −1.06899 + 0.776665i
\(735\) 0 0
\(736\) 15.6180 0.575688
\(737\) −35.7566 14.3607i −1.31711 0.528982i
\(738\) 18.5623i 0.683288i
\(739\) 6.18034 19.0211i 0.227347 0.699704i −0.770697 0.637201i \(-0.780092\pi\)
0.998045 0.0625022i \(-0.0199080\pi\)
\(740\) 0 0
\(741\) 13.0902 + 9.51057i 0.480879 + 0.349379i
\(742\) −43.3651 + 14.0902i −1.59198 + 0.517266i
\(743\) −30.1033 + 9.78115i −1.10438 + 0.358836i −0.803788 0.594916i \(-0.797185\pi\)
−0.300595 + 0.953752i \(0.597185\pi\)
\(744\) −12.6631 9.20029i −0.464252 0.337299i
\(745\) 0 0
\(746\) 16.3713 50.3858i 0.599397 1.84475i
\(747\) 7.70820i 0.282028i
\(748\) −2.62866 + 3.14590i −0.0961132 + 0.115025i
\(749\) −20.1803 −0.737374
\(750\) 0 0
\(751\) 8.18034 5.94336i 0.298505 0.216876i −0.428444 0.903569i \(-0.640938\pi\)
0.726948 + 0.686692i \(0.240938\pi\)
\(752\) −17.3763 + 23.9164i −0.633648 + 0.872142i
\(753\) 15.6659 5.09017i 0.570898 0.185496i
\(754\) 1.38197 + 4.25325i 0.0503282 + 0.154894i
\(755\) 0 0
\(756\) −2.61803 + 1.90211i −0.0952170 + 0.0691792i
\(757\) 1.73060 + 0.562306i 0.0628997 + 0.0204374i 0.340298 0.940318i \(-0.389472\pi\)
−0.277398 + 0.960755i \(0.589472\pi\)
\(758\) 8.09017i 0.293848i
\(759\) −3.73607 14.8536i −0.135611 0.539153i
\(760\) 0 0
\(761\) 3.07953 9.47781i 0.111633 0.343570i −0.879597 0.475719i \(-0.842188\pi\)
0.991230 + 0.132149i \(0.0421878\pi\)
\(762\) −1.84911 2.54508i −0.0669863 0.0921987i
\(763\) −33.4055 + 45.9787i −1.20936 + 1.66454i
\(764\) 3.13525 + 9.64932i 0.113430 + 0.349100i
\(765\) 0 0
\(766\) 17.4894 + 12.7068i 0.631916 + 0.459114i
\(767\) 12.7598 + 17.5623i 0.460728 + 0.634138i
\(768\) −12.8985 4.19098i −0.465435 0.151229i
\(769\) −17.2361 −0.621549 −0.310774 0.950484i \(-0.600588\pi\)
−0.310774 + 0.950484i \(0.600588\pi\)
\(770\) 0 0
\(771\) −9.56231 −0.344378
\(772\) −4.72253 1.53444i −0.169967 0.0552258i
\(773\) −16.1680 22.2533i −0.581521 0.800395i 0.412340 0.911030i \(-0.364712\pi\)
−0.993861 + 0.110635i \(0.964712\pi\)
\(774\) −11.8992 8.64527i −0.427707 0.310748i
\(775\) 0 0
\(776\) 1.74671 + 5.37582i 0.0627033 + 0.192981i
\(777\) −4.53077 + 6.23607i −0.162540 + 0.223718i
\(778\) −20.0252 27.5623i −0.717938 0.988157i
\(779\) −17.7254 + 54.5532i −0.635079 + 1.95457i
\(780\) 0 0
\(781