Properties

Label 825.2.bx.c.724.1
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 724.1
Root \(0.587785 - 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 825.724
Dual form 825.2.bx.c.49.1

$q$-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 −0.290604 0.956844i \(-0.593856\pi\)
−0.797522 + 0.603290i \(0.793856\pi\)
\(3\) −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 \(0.653885\pi\)
−0.698425 + 0.715683i \(0.746115\pi\)
\(8\) 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 −0.150644 0.988588i \(-0.548135\pi\)
−0.702951 + 0.711238i \(0.748135\pi\)
\(14\) 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 −0.530456 0.847713i \(-0.677979\pi\)
0.0691254 + 0.997608i \(0.477979\pi\)
\(18\) 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 \(-0.840105\pi\)
0.876466 0.481463i \(-0.159895\pi\)
\(24\) 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 −0.731945 0.681364i \(-0.761387\pi\)
0.874199 + 0.485568i \(0.161387\pi\)
\(38\) −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 \(-0.756236\pi\)
0.720823 0.693119i \(-0.243764\pi\)
\(44\) −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 0.985910 0.167279i \(-0.0534982\pi\)
−0.463755 + 0.885964i \(0.653498\pi\)
\(48\) −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 0.638675 0.769476i \(-0.279483\pi\)
0.0644122 + 0.997923i \(0.479483\pi\)
\(54\) −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 \(-0.748838\pi\)
0.704520 0.709684i \(-0.251162\pi\)
\(68\) −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 −0.624352 0.781143i \(-0.714637\pi\)
0.935847 + 0.352408i \(0.114637\pi\)
\(74\) −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 0.122334 0.992489i \(-0.460962\pi\)
0.682341 + 0.731034i \(0.260962\pi\)
\(84\) 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 0.428514 0.903535i \(-0.359037\pi\)
−0.184410 + 0.982849i \(0.559037\pi\)
\(98\) 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 −0.921530 0.388308i \(-0.873060\pi\)
0.654071 + 0.756433i \(0.273060\pi\)
\(104\) −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 0.904356 0.426780i \(-0.140352\pi\)
−0.685353 + 0.728211i \(0.740352\pi\)
\(108\) 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 0.702161 0.712019i \(-0.252219\pi\)
−0.894150 + 0.447769i \(0.852219\pi\)
\(114\) 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 −0.225824 0.974168i \(-0.572507\pi\)
0.389906 + 0.920855i \(0.372507\pi\)
\(128\) 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 −0.516008 0.856584i \(-0.672583\pi\)
0.0860276 + 0.996293i \(0.472583\pi\)
\(138\) 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 0.415271 0.909698i \(-0.363687\pi\)
−0.993500 + 0.113835i \(0.963687\pi\)
\(158\) 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 0.543059 0.839695i \(-0.317266\pi\)
−0.0542163 + 0.998529i \(0.517266\pi\)
\(164\) −7.09017 −0.553649
\(165\) 0 0
\(166\) −12.4721 −0.968025
\(167\) 8.59226 + 2.79180i 0.664889 + 0.216036i 0.621968 0.783043i \(-0.286333\pi\)
0.0429216 + 0.999078i \(0.486333\pi\)
\(168\) 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 \(-0.983217\pi\)
0.258466 0.966020i \(-0.416783\pi\)
\(174\) −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 −0.0208024 0.999784i \(-0.506622\pi\)
0.570829 + 0.821069i \(0.306622\pi\)
\(194\) −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 \(0.113080\pi\)
−0.937559 + 0.347826i \(0.886920\pi\)
\(198\) 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 \(-0.951268\pi\)
0.160367 0.987058i \(-0.448732\pi\)
\(224\) −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 −0.622433 0.782673i \(-0.713856\pi\)
0.936709 + 0.350110i \(0.113856\pi\)
\(228\) −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 −0.0289512 0.999581i \(-0.509217\pi\)
−0.610961 + 0.791661i \(0.709217\pi\)
\(234\) −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 −0.596898 0.802317i \(-0.703600\pi\)
0.947500 + 0.319754i \(0.103600\pi\)
\(258\) 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 \(-0.731698\pi\)
0.665303 0.746574i \(-0.268302\pi\)
\(264\) 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 0.873644 0.486566i \(-0.161751\pi\)
0.420797 + 0.907155i \(0.361751\pi\)
\(278\) 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 0.431111 0.902299i \(-0.358122\pi\)
−0.991358 + 0.131185i \(0.958122\pi\)
\(284\) 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 \(0.467097\pi\)
−0.977866 + 0.209234i \(0.932903\pi\)
\(294\) 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 \(-0.703461\pi\)
0.596547 0.802578i \(-0.296539\pi\)
\(308\) 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 −0.527746 0.849402i \(-0.676963\pi\)
0.0723104 + 0.997382i \(0.476963\pi\)
\(314\) 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 0.403160 0.915130i \(-0.367912\pi\)
−0.211736 + 0.977327i \(0.567912\pi\)
\(318\) 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 \(0.487796\pi\)
−0.962203 + 0.272334i \(0.912204\pi\)
\(338\) 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 −0.921510 0.388355i \(-0.873044\pi\)
−0.517248 + 0.855835i \(0.673044\pi\)
\(348\) 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 \(-0.842603\pi\)
0.880216 0.474573i \(-0.157397\pi\)
\(354\) −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 −0.321089 0.947049i \(-0.604049\pi\)
0.999919 + 0.0127192i \(0.00404875\pi\)
\(368\) −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 \(0.321998\pi\)
−0.530516 + 0.847675i \(0.678002\pi\)
\(374\) −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 −0.0341862 0.999415i \(-0.510884\pi\)
−0.615099 + 0.788450i \(0.710884\pi\)
\(384\) −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 \(0.0218196\pi\)
−0.997651 + 0.0684946i \(0.978180\pi\)
\(398\) −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 −0.794157 0.607713i \(-0.792087\pi\)
0.823377 + 0.567495i \(0.192087\pi\)
\(434\) −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 0.677766 0.735278i \(-0.262948\pi\)
−0.908732 + 0.417380i \(0.862948\pi\)
\(444\) −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 −0.138049 0.990425i \(-0.544083\pi\)
0.470473 + 0.882414i \(0.344083\pi\)
\(458\) 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 \(-0.997999\pi\)
0.999980 0.00628583i \(-0.00200085\pi\)
\(464\) 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 0.463553 0.886069i \(-0.346574\pi\)
0.895841 + 0.444375i \(0.146574\pi\)
\(468\) 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 0.686058 0.727547i \(-0.259340\pi\)
−0.903942 + 0.427655i \(0.859340\pi\)
\(488\) −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 0.951255 0.308404i \(-0.0997949\pi\)
−0.587264 + 0.809396i \(0.699795\pi\)
\(504\) 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 −0.229704 0.973261i \(-0.573776\pi\)
0.386234 + 0.922401i \(0.373776\pi\)
\(524\) −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 0.493181 0.869927i \(-0.335834\pi\)
−0.979751 + 0.200220i \(0.935834\pi\)
\(548\) −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 \(0.555103\pi\)
−0.883615 + 0.468215i \(0.844897\pi\)
\(558\) −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 −0.136174 0.990685i \(-0.543481\pi\)
−0.692477 + 0.721440i \(0.743481\pi\)
\(564\) 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 −0.835448 0.549569i \(-0.814792\pi\)
−0.352863 + 0.935675i \(0.614792\pi\)
\(578\) 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 −0.986274 0.165116i \(-0.947200\pi\)
0.461810 + 0.886979i \(0.347200\pi\)
\(588\) −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 \(-0.979651\pi\)
0.997957 0.0638861i \(-0.0203494\pi\)
\(594\) 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 −0.407454 0.913226i \(-0.633583\pi\)
−0.866418 + 0.499319i \(0.833583\pi\)
\(608\) 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 0.851355 0.524590i \(-0.175781\pi\)
−0.761998 + 0.647580i \(0.775781\pi\)
\(614\) −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 \(0.323667\pi\)
−0.526064 + 0.850445i \(0.676333\pi\)
\(618\) −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 −0.553997 0.832519i \(-0.686898\pi\)
0.0411490 + 0.999153i \(0.486898\pi\)
\(644\) 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 0.832886 0.553444i \(-0.186687\pi\)
0.348513 + 0.937304i \(0.386687\pi\)
\(648\) 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 \(0.524831\pi\)
−0.924083 + 0.382192i \(0.875169\pi\)
\(654\) −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 0.873594 0.486655i \(-0.161783\pi\)
0.420704 + 0.907198i \(0.361783\pi\)
\(674\) 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 −0.415632 0.909533i \(-0.636440\pi\)
0.198357 + 0.980130i \(0.436440\pi\)
\(678\) 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 \(0.0971632\pi\)
−0.953773 + 0.300529i \(0.902837\pi\)
\(684\) −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 \(0.131656\pi\)
−0.915676 + 0.401918i \(0.868344\pi\)
\(728\) 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 −0.753068 0.657943i \(-0.771427\pi\)
0.858452 + 0.512894i \(0.171427\pi\)
\(734\) −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 0.300595 0.953752i \(-0.402815\pi\)
0.803788 + 0.594916i \(0.202815\pi\)
\(744\) −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 0.277398 0.960755i \(-0.410528\pi\)
−0.340298 + 0.940318i \(0.610528\pi\)
\(758\) 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 0.993861 0.110635i \(-0.0352884\pi\)
−0.412340 + 0.911030i \(0.635288\pi\)
\(774\) −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
\(781\) 26.4721