Properties

Label 825.2.n.b.526.1
Level $825$
Weight $2$
Character 825.526
Analytic conductor $6.588$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.n (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \(x^{4} - x^{3} + x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 526.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 825.526
Dual form 825.2.n.b.676.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 1.53884i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(0.500000 + 1.53884i) q^{6} +(4.23607 + 3.07768i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 1.53884i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(0.500000 + 1.53884i) q^{6} +(4.23607 + 3.07768i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-1.23607 + 3.07768i) q^{11} -0.618034 q^{12} +(1.00000 - 3.07768i) q^{13} +(-6.85410 + 4.97980i) q^{14} +(-1.50000 - 4.61653i) q^{16} +(0.618034 + 1.90211i) q^{17} +(1.30902 + 0.951057i) q^{18} +(-4.04508 + 2.93893i) q^{19} +5.23607 q^{21} +(-4.11803 - 3.44095i) q^{22} +4.61803 q^{23} +(-0.690983 + 2.12663i) q^{24} +(4.23607 + 3.07768i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-1.00000 - 3.07768i) q^{28} +(-0.690983 - 0.502029i) q^{29} +(2.16312 - 6.65740i) q^{31} +3.38197 q^{32} +(0.809017 + 3.21644i) q^{33} -3.23607 q^{34} +(-0.500000 + 0.363271i) q^{36} +(-1.19098 - 0.865300i) q^{37} +(-2.50000 - 7.69421i) q^{38} +(-1.00000 - 3.07768i) q^{39} +(-9.28115 + 6.74315i) q^{41} +(-2.61803 + 8.05748i) q^{42} +9.09017 q^{43} +(1.73607 - 1.08981i) q^{44} +(-2.30902 + 7.10642i) q^{46} +(4.92705 - 3.57971i) q^{47} +(-3.92705 - 2.85317i) q^{48} +(6.30902 + 19.4172i) q^{49} +(1.61803 + 1.17557i) q^{51} +(-1.61803 + 1.17557i) q^{52} +(-1.66312 + 5.11855i) q^{53} +1.61803 q^{54} -11.7082 q^{56} +(-1.54508 + 4.75528i) q^{57} +(1.11803 - 0.812299i) q^{58} +(-5.42705 - 3.94298i) q^{59} +(2.16312 + 6.65740i) q^{61} +(9.16312 + 6.65740i) q^{62} +(4.23607 - 3.07768i) q^{63} +(1.30902 - 4.02874i) q^{64} +(-5.35410 - 0.363271i) q^{66} -11.6180 q^{67} +(0.381966 - 1.17557i) q^{68} +(3.73607 - 2.71441i) q^{69} +(-2.47214 - 7.60845i) q^{71} +(0.690983 + 2.12663i) q^{72} +(3.66312 + 2.66141i) q^{73} +(1.92705 - 1.40008i) q^{74} +3.09017 q^{76} +(-14.7082 + 9.23305i) q^{77} +5.23607 q^{78} +(0.954915 - 2.93893i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-5.73607 - 17.6538i) q^{82} +(2.38197 + 7.33094i) q^{83} +(-2.61803 - 1.90211i) q^{84} +(-4.54508 + 13.9883i) q^{86} -0.854102 q^{87} +(-1.80902 - 7.19218i) q^{88} +4.14590 q^{89} +(13.7082 - 9.95959i) q^{91} +(-2.30902 - 1.67760i) q^{92} +(-2.16312 - 6.65740i) q^{93} +(3.04508 + 9.37181i) q^{94} +(2.73607 - 1.98787i) q^{96} +(0.781153 - 2.40414i) q^{97} -33.0344 q^{98} +(2.54508 + 2.12663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{6} + 8 q^{7} - 5 q^{8} - q^{9} + O(q^{10}) \) \( 4 q - 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{6} + 8 q^{7} - 5 q^{8} - q^{9} + 4 q^{11} + 2 q^{12} + 4 q^{13} - 14 q^{14} - 6 q^{16} - 2 q^{17} + 3 q^{18} - 5 q^{19} + 12 q^{21} - 12 q^{22} + 14 q^{23} - 5 q^{24} + 8 q^{26} + q^{27} - 4 q^{28} - 5 q^{29} - 7 q^{31} + 18 q^{32} + q^{33} - 4 q^{34} - 2 q^{36} - 7 q^{37} - 10 q^{38} - 4 q^{39} - 17 q^{41} - 6 q^{42} + 14 q^{43} - 2 q^{44} - 7 q^{46} + 13 q^{47} - 9 q^{48} + 23 q^{49} + 2 q^{51} - 2 q^{52} + 9 q^{53} + 2 q^{54} - 20 q^{56} + 5 q^{57} - 15 q^{59} - 7 q^{61} + 21 q^{62} + 8 q^{63} + 3 q^{64} - 8 q^{66} - 42 q^{67} + 6 q^{68} + 6 q^{69} + 8 q^{71} + 5 q^{72} - q^{73} + q^{74} - 10 q^{76} - 32 q^{77} + 12 q^{78} + 15 q^{79} - q^{81} - 14 q^{82} + 14 q^{83} - 6 q^{84} - 7 q^{86} + 10 q^{87} - 5 q^{88} + 30 q^{89} + 28 q^{91} - 7 q^{92} + 7 q^{93} + q^{94} + 2 q^{96} - 17 q^{97} - 74 q^{98} - q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 1.53884i −0.353553 + 1.08813i 0.603290 + 0.797522i \(0.293856\pi\)
−0.956844 + 0.290604i \(0.906144\pi\)
\(3\) 0.809017 0.587785i 0.467086 0.339358i
\(4\) −0.500000 0.363271i −0.250000 0.181636i
\(5\) 0 0
\(6\) 0.500000 + 1.53884i 0.204124 + 0.628230i
\(7\) 4.23607 + 3.07768i 1.60108 + 1.16326i 0.885400 + 0.464830i \(0.153885\pi\)
0.715683 + 0.698425i \(0.246115\pi\)
\(8\) −1.80902 + 1.31433i −0.639584 + 0.464685i
\(9\) 0.309017 0.951057i 0.103006 0.317019i
\(10\) 0 0
\(11\) −1.23607 + 3.07768i −0.372689 + 0.927957i
\(12\) −0.618034 −0.178411
\(13\) 1.00000 3.07768i 0.277350 0.853596i −0.711238 0.702951i \(-0.751865\pi\)
0.988588 0.150644i \(-0.0481349\pi\)
\(14\) −6.85410 + 4.97980i −1.83184 + 1.33091i
\(15\) 0 0
\(16\) −1.50000 4.61653i −0.375000 1.15413i
\(17\) 0.618034 + 1.90211i 0.149895 + 0.461330i 0.997608 0.0691254i \(-0.0220209\pi\)
−0.847713 + 0.530456i \(0.822021\pi\)
\(18\) 1.30902 + 0.951057i 0.308538 + 0.224166i
\(19\) −4.04508 + 2.93893i −0.928006 + 0.674236i −0.945504 0.325611i \(-0.894430\pi\)
0.0174977 + 0.999847i \(0.494430\pi\)
\(20\) 0 0
\(21\) 5.23607 1.14260
\(22\) −4.11803 3.44095i −0.877968 0.733614i
\(23\) 4.61803 0.962927 0.481463 0.876466i \(-0.340105\pi\)
0.481463 + 0.876466i \(0.340105\pi\)
\(24\) −0.690983 + 2.12663i −0.141046 + 0.434096i
\(25\) 0 0
\(26\) 4.23607 + 3.07768i 0.830761 + 0.603583i
\(27\) −0.309017 0.951057i −0.0594703 0.183031i
\(28\) −1.00000 3.07768i −0.188982 0.581628i
\(29\) −0.690983 0.502029i −0.128312 0.0932244i 0.521778 0.853081i \(-0.325269\pi\)
−0.650090 + 0.759857i \(0.725269\pi\)
\(30\) 0 0
\(31\) 2.16312 6.65740i 0.388508 1.19570i −0.545396 0.838179i \(-0.683621\pi\)
0.933904 0.357525i \(-0.116379\pi\)
\(32\) 3.38197 0.597853
\(33\) 0.809017 + 3.21644i 0.140832 + 0.559910i
\(34\) −3.23607 −0.554981
\(35\) 0 0
\(36\) −0.500000 + 0.363271i −0.0833333 + 0.0605452i
\(37\) −1.19098 0.865300i −0.195796 0.142254i 0.485568 0.874199i \(-0.338613\pi\)
−0.681364 + 0.731945i \(0.738613\pi\)
\(38\) −2.50000 7.69421i −0.405554 1.24817i
\(39\) −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 \(0.946587\pi\)
\(42\) −2.61803 + 8.05748i −0.403971 + 1.24330i
\(43\) 9.09017 1.38624 0.693119 0.720823i \(-0.256236\pi\)
0.693119 + 0.720823i \(0.256236\pi\)
\(44\) 1.73607 1.08981i 0.261722 0.164296i
\(45\) 0 0
\(46\) −2.30902 + 7.10642i −0.340446 + 1.04778i
\(47\) 4.92705 3.57971i 0.718684 0.522155i −0.167279 0.985910i \(-0.553498\pi\)
0.885964 + 0.463755i \(0.153498\pi\)
\(48\) −3.92705 2.85317i −0.566821 0.411820i
\(49\) 6.30902 + 19.4172i 0.901288 + 2.77388i
\(50\) 0 0
\(51\) 1.61803 + 1.17557i 0.226570 + 0.164613i
\(52\) −1.61803 + 1.17557i −0.224381 + 0.163022i
\(53\) −1.66312 + 5.11855i −0.228447 + 0.703087i 0.769476 + 0.638675i \(0.220517\pi\)
−0.997923 + 0.0644122i \(0.979483\pi\)
\(54\) 1.61803 0.220187
\(55\) 0 0
\(56\) −11.7082 −1.56457
\(57\) −1.54508 + 4.75528i −0.204652 + 0.629853i
\(58\) 1.11803 0.812299i 0.146805 0.106660i
\(59\) −5.42705 3.94298i −0.706542 0.513333i 0.175514 0.984477i \(-0.443841\pi\)
−0.882056 + 0.471144i \(0.843841\pi\)
\(60\) 0 0
\(61\) 2.16312 + 6.65740i 0.276959 + 0.852392i 0.988694 + 0.149945i \(0.0479095\pi\)
−0.711735 + 0.702448i \(0.752090\pi\)
\(62\) 9.16312 + 6.65740i 1.16372 + 0.845490i
\(63\) 4.23607 3.07768i 0.533694 0.387752i
\(64\) 1.30902 4.02874i 0.163627 0.503593i
\(65\) 0 0
\(66\) −5.35410 0.363271i −0.659044 0.0447156i
\(67\) −11.6180 −1.41937 −0.709684 0.704520i \(-0.751162\pi\)
−0.709684 + 0.704520i \(0.751162\pi\)
\(68\) 0.381966 1.17557i 0.0463202 0.142559i
\(69\) 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 \(-0.257448\pi\)
\(72\) 0.690983 + 2.12663i 0.0814331 + 0.250625i
\(73\) 3.66312 + 2.66141i 0.428736 + 0.311495i 0.781143 0.624352i \(-0.214637\pi\)
−0.352408 + 0.935847i \(0.614637\pi\)
\(74\) 1.92705 1.40008i 0.224015 0.162757i
\(75\) 0 0
\(76\) 3.09017 0.354467
\(77\) −14.7082 + 9.23305i −1.67616 + 1.05220i
\(78\) 5.23607 0.592868
\(79\) 0.954915 2.93893i 0.107436 0.330655i −0.882858 0.469640i \(-0.844384\pi\)
0.990295 + 0.138985i \(0.0443839\pi\)
\(80\) 0 0
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) −5.73607 17.6538i −0.633443 1.94954i
\(83\) 2.38197 + 7.33094i 0.261455 + 0.804675i 0.992489 + 0.122334i \(0.0390380\pi\)
−0.731034 + 0.682341i \(0.760962\pi\)
\(84\) −2.61803 1.90211i −0.285651 0.207538i
\(85\) 0 0
\(86\) −4.54508 + 13.9883i −0.490109 + 1.50840i
\(87\) −0.854102 −0.0915693
\(88\) −1.80902 7.19218i −0.192842 0.766689i
\(89\) 4.14590 0.439464 0.219732 0.975560i \(-0.429482\pi\)
0.219732 + 0.975560i \(0.429482\pi\)
\(90\) 0 0
\(91\) 13.7082 9.95959i 1.43701 1.04405i
\(92\) −2.30902 1.67760i −0.240732 0.174902i
\(93\) −2.16312 6.65740i −0.224305 0.690340i
\(94\) 3.04508 + 9.37181i 0.314077 + 0.966628i
\(95\) 0 0
\(96\) 2.73607 1.98787i 0.279249 0.202886i
\(97\) 0.781153 2.40414i 0.0793141 0.244104i −0.903535 0.428514i \(-0.859037\pi\)
0.982849 + 0.184410i \(0.0590374\pi\)
\(98\) −33.0344 −3.33698
\(99\) 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 \(-0.326225\pi\)
\(102\) −2.61803 + 1.90211i −0.259224 + 0.188337i
\(103\) −3.73607 2.71441i −0.368126 0.267459i 0.388308 0.921530i \(-0.373060\pi\)
−0.756433 + 0.654071i \(0.773060\pi\)
\(104\) 2.23607 + 6.88191i 0.219265 + 0.674827i
\(105\) 0 0
\(106\) −7.04508 5.11855i −0.684279 0.497158i
\(107\) 3.11803 2.26538i 0.301432 0.219003i −0.426780 0.904356i \(-0.640352\pi\)
0.728211 + 0.685353i \(0.240352\pi\)
\(108\) −0.190983 + 0.587785i −0.0183773 + 0.0565597i
\(109\) 10.8541 1.03963 0.519817 0.854278i \(-0.326000\pi\)
0.519817 + 0.854278i \(0.326000\pi\)
\(110\) 0 0
\(111\) −1.47214 −0.139729
\(112\) 7.85410 24.1724i 0.742143 2.28408i
\(113\) 2.80902 2.04087i 0.264250 0.191989i −0.447769 0.894150i \(-0.647781\pi\)
0.712019 + 0.702161i \(0.247781\pi\)
\(114\) −6.54508 4.75528i −0.613003 0.445373i
\(115\) 0 0
\(116\) 0.163119 + 0.502029i 0.0151452 + 0.0466122i
\(117\) −2.61803 1.90211i −0.242037 0.175850i
\(118\) 8.78115 6.37988i 0.808371 0.587316i
\(119\) −3.23607 + 9.95959i −0.296650 + 0.912994i
\(120\) 0 0
\(121\) −7.94427 7.60845i −0.722207 0.691677i
\(122\) −11.3262 −1.02543
\(123\) −3.54508 + 10.9106i −0.319650 + 0.983780i
\(124\) −3.50000 + 2.54290i −0.314309 + 0.228359i
\(125\) 0 0
\(126\) 2.61803 + 8.05748i 0.233233 + 0.717817i
\(127\) −0.600813 1.84911i −0.0533135 0.164082i 0.920855 0.389906i \(-0.127493\pi\)
−0.974168 + 0.225824i \(0.927493\pi\)
\(128\) 11.0172 + 8.00448i 0.973794 + 0.707503i
\(129\) 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 \(0.631353\pi\)
\(132\) 0.763932 1.90211i 0.0664917 0.165558i
\(133\) −26.1803 −2.27012
\(134\) 5.80902 17.8783i 0.501823 1.54445i
\(135\) 0 0
\(136\) −3.61803 2.62866i −0.310244 0.225405i
\(137\) 1.63525 + 5.03280i 0.139709 + 0.429981i 0.996293 0.0860276i \(-0.0274173\pi\)
−0.856584 + 0.516008i \(0.827417\pi\)
\(138\) 2.30902 + 7.10642i 0.196557 + 0.604939i
\(139\) 0.954915 + 0.693786i 0.0809948 + 0.0588462i 0.627546 0.778580i \(-0.284060\pi\)
−0.546551 + 0.837426i \(0.684060\pi\)
\(140\) 0 0
\(141\) 1.88197 5.79210i 0.158490 0.487782i
\(142\) 12.9443 1.08626
\(143\) 8.23607 + 6.88191i 0.688735 + 0.575494i
\(144\) −4.85410 −0.404508
\(145\) 0 0
\(146\) −5.92705 + 4.30625i −0.490526 + 0.356388i
\(147\) 16.5172 + 12.0005i 1.36232 + 0.989782i
\(148\) 0.281153 + 0.865300i 0.0231106 + 0.0711272i
\(149\) −6.21885 19.1396i −0.509468 1.56798i −0.793127 0.609056i \(-0.791549\pi\)
0.283660 0.958925i \(-0.408451\pi\)
\(150\) 0 0
\(151\) 12.3262 8.95554i 1.00310 0.728791i 0.0403454 0.999186i \(-0.487154\pi\)
0.962750 + 0.270395i \(0.0871542\pi\)
\(152\) 3.45492 10.6331i 0.280231 0.862461i
\(153\) 2.00000 0.161690
\(154\) −6.85410 27.2501i −0.552319 2.19588i
\(155\) 0 0
\(156\) −0.618034 + 1.90211i −0.0494823 + 0.152291i
\(157\) −9.97214 + 7.24518i −0.795863 + 0.578228i −0.909698 0.415271i \(-0.863687\pi\)
0.113835 + 0.993500i \(0.463687\pi\)
\(158\) 4.04508 + 2.93893i 0.321810 + 0.233808i
\(159\) 1.66312 + 5.11855i 0.131894 + 0.405928i
\(160\) 0 0
\(161\) 19.5623 + 14.2128i 1.54173 + 1.12013i
\(162\) 1.30902 0.951057i 0.102846 0.0747221i
\(163\) −2.02786 + 6.24112i −0.158835 + 0.488843i −0.998529 0.0542163i \(-0.982734\pi\)
0.839695 + 0.543059i \(0.182734\pi\)
\(164\) 7.09017 0.553649
\(165\) 0 0
\(166\) −12.4721 −0.968025
\(167\) 2.79180 8.59226i 0.216036 0.664889i −0.783043 0.621968i \(-0.786333\pi\)
0.999078 0.0429216i \(-0.0136666\pi\)
\(168\) −9.47214 + 6.88191i −0.730791 + 0.530951i
\(169\) 2.04508 + 1.48584i 0.157314 + 0.114295i
\(170\) 0 0
\(171\) 1.54508 + 4.75528i 0.118156 + 0.363646i
\(172\) −4.54508 3.30220i −0.346559 0.251790i
\(173\) 13.3992 9.73508i 1.01872 0.740144i 0.0527010 0.998610i \(-0.483217\pi\)
0.966020 + 0.258466i \(0.0832170\pi\)
\(174\) 0.427051 1.31433i 0.0323747 0.0996389i
\(175\) 0 0
\(176\) 16.0623 + 1.08981i 1.21074 + 0.0821478i
\(177\) −6.70820 −0.504219
\(178\) −2.07295 + 6.37988i −0.155374 + 0.478192i
\(179\) 8.51722 6.18812i 0.636607 0.462522i −0.222076 0.975029i \(-0.571283\pi\)
0.858683 + 0.512507i \(0.171283\pi\)
\(180\) 0 0
\(181\) −0.236068 0.726543i −0.0175468 0.0540035i 0.941900 0.335894i \(-0.109038\pi\)
−0.959447 + 0.281891i \(0.909038\pi\)
\(182\) 8.47214 + 26.0746i 0.627996 + 1.93277i
\(183\) 5.66312 + 4.11450i 0.418630 + 0.304152i
\(184\) −8.35410 + 6.06961i −0.615873 + 0.447458i
\(185\) 0 0
\(186\) 11.3262 0.830480
\(187\) −6.61803 0.449028i −0.483959 0.0328362i
\(188\) −3.76393 −0.274513
\(189\) 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 \(0.497578\pi\)
\(192\) −1.30902 4.02874i −0.0944702 0.290749i
\(193\) 2.48278 + 7.64121i 0.178714 + 0.550026i 0.999784 0.0208024i \(-0.00662208\pi\)
−0.821069 + 0.570829i \(0.806622\pi\)
\(194\) 3.30902 + 2.40414i 0.237574 + 0.172607i
\(195\) 0 0
\(196\) 3.89919 12.0005i 0.278513 0.857176i
\(197\) 9.76393 0.695651 0.347826 0.937559i \(-0.386920\pi\)
0.347826 + 0.937559i \(0.386920\pi\)
\(198\) −4.54508 + 2.85317i −0.323005 + 0.202766i
\(199\) −4.79837 −0.340148 −0.170074 0.985431i \(-0.554401\pi\)
−0.170074 + 0.985431i \(0.554401\pi\)
\(200\) 0 0
\(201\) −9.39919 + 6.82891i −0.662968 + 0.481674i
\(202\) 25.6074 + 18.6049i 1.80173 + 1.30903i
\(203\) −1.38197 4.25325i −0.0969950 0.298520i
\(204\) −0.381966 1.17557i −0.0267430 0.0823064i
\(205\) 0 0
\(206\) 6.04508 4.39201i 0.421181 0.306006i
\(207\) 1.42705 4.39201i 0.0991869 0.305266i
\(208\) −15.7082 −1.08917
\(209\) −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 \(0.0686780\pi\)
\(212\) 2.69098 1.95511i 0.184817 0.134278i
\(213\) −6.47214 4.70228i −0.443463 0.322195i
\(214\) 1.92705 + 5.93085i 0.131730 + 0.405425i
\(215\) 0 0
\(216\) 1.80902 + 1.31433i 0.123088 + 0.0894287i
\(217\) 29.6525 21.5438i 2.01294 1.46249i
\(218\) −5.42705 + 16.7027i −0.367566 + 1.13125i
\(219\) 4.52786 0.305965
\(220\) 0 0
\(221\) 6.47214 0.435363
\(222\) 0.736068 2.26538i 0.0494016 0.152043i
\(223\) 17.0172 12.3637i 1.13956 0.827937i 0.152500 0.988303i \(-0.451268\pi\)
0.987058 + 0.160367i \(0.0512676\pi\)
\(224\) 14.3262 + 10.4086i 0.957212 + 0.695455i
\(225\) 0 0
\(226\) 1.73607 + 5.34307i 0.115482 + 0.355416i
\(227\) −6.51722 4.73504i −0.432563 0.314276i 0.350110 0.936709i \(-0.386144\pi\)
−0.782673 + 0.622433i \(0.786144\pi\)
\(228\) 2.50000 1.81636i 0.165567 0.120291i
\(229\) 2.13525 6.57164i 0.141102 0.434266i −0.855387 0.517989i \(-0.826681\pi\)
0.996489 + 0.0837225i \(0.0266809\pi\)
\(230\) 0 0
\(231\) −6.47214 + 16.1150i −0.425835 + 1.06029i
\(232\) 1.90983 0.125386
\(233\) 3.17376 9.76784i 0.207920 0.639912i −0.791661 0.610961i \(-0.790783\pi\)
0.999581 0.0289512i \(-0.00921676\pi\)
\(234\) 4.23607 3.07768i 0.276920 0.201194i
\(235\) 0 0
\(236\) 1.28115 + 3.94298i 0.0833960 + 0.256666i
\(237\) −0.954915 2.93893i −0.0620284 0.190904i
\(238\) −13.7082 9.95959i −0.888571 0.645585i
\(239\) −17.8262 + 12.9515i −1.15308 + 0.837764i −0.988888 0.148664i \(-0.952503\pi\)
−0.164196 + 0.986428i \(0.552503\pi\)
\(240\) 0 0
\(241\) 0.618034 0.0398111 0.0199055 0.999802i \(-0.493663\pi\)
0.0199055 + 0.999802i \(0.493663\pi\)
\(242\) 15.6803 8.42075i 1.00797 0.541306i
\(243\) −1.00000 −0.0641500
\(244\) 1.33688 4.11450i 0.0855850 0.263404i
\(245\) 0 0
\(246\) −15.0172 10.9106i −0.957463 0.695638i
\(247\) 5.00000 + 15.3884i 0.318142 + 0.979142i
\(248\) 4.83688 + 14.8864i 0.307142 + 0.945287i
\(249\) 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 \(-0.0740144\pi\)
\(252\) −3.23607 −0.203853
\(253\) −5.70820 + 14.2128i −0.358872 + 0.893554i
\(254\) 3.14590 0.197391
\(255\) 0 0
\(256\) −10.9721 + 7.97172i −0.685758 + 0.498233i
\(257\) −7.73607 5.62058i −0.482563 0.350602i 0.319754 0.947500i \(-0.396400\pi\)
−0.802317 + 0.596898i \(0.796400\pi\)
\(258\) 4.54508 + 13.9883i 0.282965 + 0.870876i
\(259\) −2.38197 7.33094i −0.148008 0.455522i
\(260\) 0 0
\(261\) −0.690983 + 0.502029i −0.0427708 + 0.0310748i
\(262\) 4.59017 14.1271i 0.283582 0.872775i
\(263\) 24.2148 1.49315 0.746574 0.665303i \(-0.231698\pi\)
0.746574 + 0.665303i \(0.231698\pi\)
\(264\) −5.69098 4.75528i −0.350256 0.292667i
\(265\) 0 0
\(266\) 13.0902 40.2874i 0.802610 2.47018i
\(267\) 3.35410 2.43690i 0.205268 0.149136i
\(268\) 5.80902 + 4.22050i 0.354842 + 0.257808i
\(269\) 0.263932 + 0.812299i 0.0160922 + 0.0495268i 0.958780 0.284149i \(-0.0917110\pi\)
−0.942688 + 0.333676i \(0.891711\pi\)
\(270\) 0 0
\(271\) −14.8713 10.8046i −0.903369 0.656336i 0.0359605 0.999353i \(-0.488551\pi\)
−0.939329 + 0.343018i \(0.888551\pi\)
\(272\) 7.85410 5.70634i 0.476225 0.345998i
\(273\) 5.23607 16.1150i 0.316901 0.975322i
\(274\) −8.56231 −0.517268
\(275\) 0 0
\(276\) −2.85410 −0.171797
\(277\) 7.00000 21.5438i 0.420589 1.29444i −0.486566 0.873644i \(-0.661751\pi\)
0.907155 0.420797i \(-0.138249\pi\)
\(278\) −1.54508 + 1.12257i −0.0926680 + 0.0673273i
\(279\) −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 \(0.910352\pi\)
\(282\) 7.97214 + 5.79210i 0.474734 + 0.344914i
\(283\) 12.9721 9.42481i 0.771113 0.560247i −0.131185 0.991358i \(-0.541878\pi\)
0.902299 + 0.431111i \(0.141878\pi\)
\(284\) −1.52786 + 4.70228i −0.0906621 + 0.279029i
\(285\) 0 0
\(286\) −14.7082 + 9.23305i −0.869714 + 0.545962i
\(287\) −60.0689 −3.54575
\(288\) 1.04508 3.21644i 0.0615822 0.189531i
\(289\) 10.5172 7.64121i 0.618660 0.449483i
\(290\) 0 0
\(291\) −0.781153 2.40414i −0.0457920 0.140933i
\(292\) −0.864745 2.66141i −0.0506054 0.155747i
\(293\) −20.6074 14.9721i −1.20390 0.874682i −0.209234 0.977866i \(-0.567097\pi\)
−0.994662 + 0.103183i \(0.967097\pi\)
\(294\) −26.7254 + 19.4172i −1.55866 + 1.13243i
\(295\) 0 0
\(296\) 3.29180 0.191332
\(297\) 3.30902 + 0.224514i 0.192009 + 0.0130276i
\(298\) 32.5623 1.88628
\(299\) 4.61803 14.2128i 0.267068 0.821950i
\(300\) 0 0
\(301\) 38.5066 + 27.9767i 2.21948 + 1.61255i
\(302\) 7.61803 + 23.4459i 0.438369 + 1.34916i
\(303\) −6.04508 18.6049i −0.347281 1.06882i
\(304\) 19.6353 + 14.2658i 1.12616 + 0.818202i
\(305\) 0 0
\(306\) −1.00000 + 3.07768i −0.0571662 + 0.175939i
\(307\) −28.1246 −1.60516 −0.802578 0.596547i \(-0.796539\pi\)
−0.802578 + 0.596547i \(0.796539\pi\)
\(308\) 10.7082 + 0.726543i 0.610157 + 0.0413986i
\(309\) −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 \(0.415586\pi\)
\(312\) 5.85410 + 4.25325i 0.331423 + 0.240793i
\(313\) −2.61803 8.05748i −0.147980 0.455436i 0.849402 0.527746i \(-0.176963\pi\)
−0.997382 + 0.0723104i \(0.976963\pi\)
\(314\) −6.16312 18.9681i −0.347805 1.07043i
\(315\) 0 0
\(316\) −1.54508 + 1.12257i −0.0869178 + 0.0631495i
\(317\) 1.10739 3.40820i 0.0621973 0.191424i −0.915130 0.403160i \(-0.867912\pi\)
0.977327 + 0.211736i \(0.0679118\pi\)
\(318\) −8.70820 −0.488332
\(319\) 2.39919 1.50609i 0.134329 0.0843246i
\(320\) 0 0
\(321\) 1.19098 3.66547i 0.0664742 0.204587i
\(322\) −31.6525 + 22.9969i −1.76392 + 1.28157i
\(323\) −8.09017 5.87785i −0.450149 0.327052i
\(324\) 0.190983 + 0.587785i 0.0106102 + 0.0326547i
\(325\) 0 0
\(326\) −8.59017 6.24112i −0.475766 0.345664i
\(327\) 8.78115 6.37988i 0.485599 0.352808i
\(328\) 7.92705 24.3970i 0.437698 1.34710i
\(329\) 31.8885 1.75807
\(330\) 0 0
\(331\) −27.5967 −1.51685 −0.758427 0.651758i \(-0.774032\pi\)
−0.758427 + 0.651758i \(0.774032\pi\)
\(332\) 1.47214 4.53077i 0.0807940 0.248658i
\(333\) −1.19098 + 0.865300i −0.0652655 + 0.0474181i
\(334\) 11.8262 + 8.59226i 0.647103 + 0.470148i
\(335\) 0 0
\(336\) −7.85410 24.1724i −0.428476 1.31871i
\(337\) 23.3435 + 16.9600i 1.27160 + 0.923871i 0.999265 0.0383318i \(-0.0122044\pi\)
0.272334 + 0.962203i \(0.412204\pi\)
\(338\) −3.30902 + 2.40414i −0.179987 + 0.130768i
\(339\) 1.07295 3.30220i 0.0582746 0.179351i
\(340\) 0 0
\(341\) 17.8156 + 14.8864i 0.964769 + 0.806143i
\(342\) −8.09017 −0.437466
\(343\) −21.7082 + 66.8110i −1.17213 + 3.60745i
\(344\) −16.4443 + 11.9475i −0.886616 + 0.644164i
\(345\) 0 0
\(346\) 8.28115 + 25.4868i 0.445198 + 1.37018i
\(347\) 8.70820 + 26.8011i 0.467481 + 1.43876i 0.855835 + 0.517248i \(0.173044\pi\)
−0.388355 + 0.921510i \(0.626956\pi\)
\(348\) 0.427051 + 0.310271i 0.0228923 + 0.0166323i
\(349\) −26.0795 + 18.9479i −1.39601 + 1.01426i −0.400829 + 0.916153i \(0.631278\pi\)
−0.995176 + 0.0981041i \(0.968722\pi\)
\(350\) 0 0
\(351\) −3.23607 −0.172729
\(352\) −4.18034 + 10.4086i −0.222813 + 0.554781i
\(353\) 17.8328 0.949145 0.474573 0.880216i \(-0.342603\pi\)
0.474573 + 0.880216i \(0.342603\pi\)
\(354\) 3.35410 10.3229i 0.178269 0.548654i
\(355\) 0 0
\(356\) −2.07295 1.50609i −0.109866 0.0798224i
\(357\) 3.23607 + 9.95959i 0.171271 + 0.527118i
\(358\) 5.26393 + 16.2007i 0.278207 + 0.856234i
\(359\) −2.66312 1.93487i −0.140554 0.102118i 0.515286 0.857018i \(-0.327686\pi\)
−0.655840 + 0.754900i \(0.727686\pi\)
\(360\) 0 0
\(361\) 1.85410 5.70634i 0.0975843 0.300334i
\(362\) 1.23607 0.0649663
\(363\) −10.8992 1.48584i −0.572059 0.0779864i
\(364\) −10.4721 −0.548889
\(365\) 0 0
\(366\) −9.16312 + 6.65740i −0.478964 + 0.347988i
\(367\) −17.8992 13.0045i −0.934330 0.678830i 0.0127192 0.999919i \(-0.495951\pi\)
−0.947049 + 0.321089i \(0.895951\pi\)
\(368\) −6.92705 21.3193i −0.361097 1.11134i
\(369\) 3.54508 + 10.9106i 0.184550 + 0.567986i
\(370\) 0 0
\(371\) −22.7984 + 16.5640i −1.18363 + 0.859959i
\(372\) −1.33688 + 4.11450i −0.0693141 + 0.213327i
\(373\) −32.7426 −1.69535 −0.847675 0.530516i \(-0.821998\pi\)
−0.847675 + 0.530516i \(0.821998\pi\)
\(374\) 4.00000 9.95959i 0.206835 0.514998i
\(375\) 0 0
\(376\) −4.20820 + 12.9515i −0.217022 + 0.667924i
\(377\) −2.23607 + 1.62460i −0.115163 + 0.0836711i
\(378\) 6.85410 + 4.97980i 0.352537 + 0.256133i
\(379\) −1.54508 4.75528i −0.0793657 0.244262i 0.903499 0.428590i \(-0.140989\pi\)
−0.982865 + 0.184327i \(0.940989\pi\)
\(380\) 0 0
\(381\) −1.57295 1.14281i −0.0805846 0.0585482i
\(382\) −21.4894 + 15.6129i −1.09949 + 0.798827i
\(383\) 4.12868 12.7068i 0.210966 0.649285i −0.788450 0.615099i \(-0.789116\pi\)
0.999415 0.0341862i \(-0.0108839\pi\)
\(384\) 13.6180 0.694942
\(385\) 0 0
\(386\) −13.0000 −0.661683
\(387\) 2.80902 8.64527i 0.142790 0.439464i
\(388\) −1.26393 + 0.918300i −0.0641664 + 0.0466196i
\(389\) 17.0344 + 12.3762i 0.863680 + 0.627501i 0.928884 0.370371i \(-0.120770\pi\)
−0.0652033 + 0.997872i \(0.520770\pi\)
\(390\) 0 0
\(391\) 2.85410 + 8.78402i 0.144338 + 0.444227i
\(392\) −36.9336 26.8339i −1.86543 1.35531i
\(393\) −7.42705 + 5.39607i −0.374645 + 0.272196i
\(394\) −4.88197 + 15.0251i −0.245950 + 0.756956i
\(395\) 0 0
\(396\) −0.500000 1.98787i −0.0251259 0.0998942i
\(397\) 2.72949 0.136989 0.0684946 0.997651i \(-0.478180\pi\)
0.0684946 + 0.997651i \(0.478180\pi\)
\(398\) 2.39919 7.38394i 0.120260 0.370123i
\(399\) −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 \(-0.380368\pi\)
\(402\) −5.80902 17.8783i −0.289727 0.891689i
\(403\) −18.3262 13.3148i −0.912895 0.663257i
\(404\) −9.78115 + 7.10642i −0.486631 + 0.353558i
\(405\) 0 0
\(406\) 7.23607 0.359120
\(407\) 4.13525 2.59590i 0.204977 0.128674i
\(408\) −4.47214 −0.221404
\(409\) −8.12868 + 25.0175i −0.401937 + 1.23704i 0.521488 + 0.853258i \(0.325377\pi\)
−0.923426 + 0.383777i \(0.874623\pi\)
\(410\) 0 0
\(411\) 4.28115 + 3.11044i 0.211174 + 0.153427i
\(412\) 0.881966 + 2.71441i 0.0434513 + 0.133729i
\(413\) −10.8541 33.4055i −0.534095 1.64378i
\(414\) 6.04508 + 4.39201i 0.297100 + 0.215856i
\(415\) 0 0
\(416\) 3.38197 10.4086i 0.165815 0.510325i
\(417\) 1.18034 0.0578015
\(418\) 26.7705 + 1.81636i 1.30939 + 0.0888409i
\(419\) −24.5967 −1.20163 −0.600815 0.799388i \(-0.705157\pi\)
−0.600815 + 0.799388i \(0.705157\pi\)
\(420\) 0 0
\(421\) 3.11803 2.26538i 0.151964 0.110408i −0.509205 0.860645i \(-0.670061\pi\)
0.661169 + 0.750237i \(0.270061\pi\)
\(422\) 3.73607 + 2.71441i 0.181869 + 0.132136i
\(423\) −1.88197 5.79210i −0.0915043 0.281621i
\(424\) −3.71885 11.4454i −0.180603 0.555839i
\(425\) 0 0
\(426\) 10.4721 7.60845i 0.507377 0.368631i
\(427\) −11.3262 + 34.8586i −0.548115 + 1.68692i
\(428\) −2.38197 −0.115137
\(429\) 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 \(0.975007\pi\)
\(432\) −3.92705 + 2.85317i −0.188940 + 0.137273i
\(433\) 0.836881 + 0.608030i 0.0402179 + 0.0292200i 0.607713 0.794157i \(-0.292087\pi\)
−0.567495 + 0.823377i \(0.692087\pi\)
\(434\) 18.3262 + 56.4024i 0.879688 + 2.70740i
\(435\) 0 0
\(436\) −5.42705 3.94298i −0.259909 0.188835i
\(437\) −18.6803 + 13.5721i −0.893602 + 0.649240i
\(438\) −2.26393 + 6.96767i −0.108175 + 0.332928i
\(439\) 25.3262 1.20876 0.604378 0.796698i \(-0.293422\pi\)
0.604378 + 0.796698i \(0.293422\pi\)
\(440\) 0 0
\(441\) 20.4164 0.972210
\(442\) −3.23607 + 9.95959i −0.153924 + 0.473730i
\(443\) 6.69098 4.86128i 0.317898 0.230967i −0.417380 0.908732i \(-0.637052\pi\)
0.735278 + 0.677766i \(0.237052\pi\)
\(444\) 0.736068 + 0.534785i 0.0349322 + 0.0253798i
\(445\) 0 0
\(446\) 10.5172 + 32.3687i 0.498005 + 1.53270i
\(447\) −16.2812 11.8290i −0.770072 0.559490i
\(448\) 17.9443 13.0373i 0.847787 0.615953i
\(449\) −10.5902 + 32.5932i −0.499781 + 1.53817i 0.309590 + 0.950870i \(0.399808\pi\)
−0.809371 + 0.587298i \(0.800192\pi\)
\(450\) 0 0
\(451\) −9.28115 36.8994i −0.437032 1.73753i
\(452\) −2.14590 −0.100935
\(453\) 4.70820 14.4904i 0.221211 0.680817i
\(454\) 10.5451 7.66145i 0.494905 0.359570i
\(455\) 0 0
\(456\) −3.45492 10.6331i −0.161791 0.497942i
\(457\) −2.30902 7.10642i −0.108011 0.332424i 0.882414 0.470473i \(-0.155917\pi\)
−0.990425 + 0.138049i \(0.955917\pi\)
\(458\) 9.04508 + 6.57164i 0.422649 + 0.307073i
\(459\) 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 \(0.439930\pi\)
\(462\) −21.5623 18.0171i −1.00317 0.838230i
\(463\) 0.270510 0.0125717 0.00628583 0.999980i \(-0.497999\pi\)
0.00628583 + 0.999980i \(0.497999\pi\)
\(464\) −1.28115 + 3.94298i −0.0594760 + 0.183048i
\(465\) 0 0
\(466\) 13.4443 + 9.76784i 0.622794 + 0.452486i
\(467\) −9.54508 29.3768i −0.441694 1.35939i −0.886069 0.463553i \(-0.846574\pi\)
0.444375 0.895841i \(-0.353426\pi\)
\(468\) 0.618034 + 1.90211i 0.0285686 + 0.0879252i
\(469\) −49.2148 35.7566i −2.27253 1.65109i
\(470\) 0 0
\(471\) −3.80902 + 11.7229i −0.175510 + 0.540165i
\(472\) 15.0000 0.690431
\(473\) −11.2361 + 27.9767i −0.516635 + 1.28637i
\(474\) 5.00000 0.229658
\(475\) 0 0
\(476\) 5.23607 3.80423i 0.239995 0.174366i
\(477\) 4.35410 + 3.16344i 0.199361 + 0.144844i
\(478\) −11.0172 33.9075i −0.503916 1.55089i
\(479\) 2.03444 + 6.26137i 0.0929560 + 0.286089i 0.986716 0.162457i \(-0.0519419\pi\)
−0.893760 + 0.448546i \(0.851942\pi\)
\(480\) 0 0
\(481\) −3.85410 + 2.80017i −0.175732 + 0.127677i
\(482\) −0.309017 + 0.951057i −0.0140753 + 0.0433194i
\(483\) 24.1803 1.10024
\(484\) 1.20820 + 6.69015i 0.0549184 + 0.304098i
\(485\) 0 0
\(486\) 0.500000 1.53884i 0.0226805 0.0698033i
\(487\) −6.61803 + 4.80828i −0.299892 + 0.217884i −0.727547 0.686058i \(-0.759340\pi\)
0.427655 + 0.903942i \(0.359340\pi\)
\(488\) −12.6631 9.20029i −0.573232 0.416478i
\(489\) 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 \(0.751957\pi\)
\(492\) 5.73607 4.16750i 0.258602 0.187885i
\(493\) 0.527864 1.62460i 0.0237738 0.0731682i
\(494\) −26.1803 −1.17791
\(495\) 0 0
\(496\) −33.9787 −1.52569
\(497\) 12.9443 39.8384i 0.580630 1.78700i
\(498\) −10.0902 + 7.33094i −0.452151 + 0.328507i
\(499\) −9.04508 6.57164i −0.404914 0.294187i 0.366626 0.930368i \(-0.380513\pi\)
−0.771539 + 0.636182i \(0.780513\pi\)
\(500\) 0 0
\(501\) −2.79180 8.59226i −0.124728 0.383874i
\(502\) 21.5623 + 15.6659i 0.962373 + 0.699205i
\(503\) −11.2361 + 8.16348i −0.500992 + 0.363992i −0.809396 0.587264i \(-0.800205\pi\)
0.308404 + 0.951255i \(0.400205\pi\)
\(504\) −3.61803 + 11.1352i −0.161160 + 0.496000i
\(505\) 0 0
\(506\) −19.0172 15.8904i −0.845419 0.706416i
\(507\) 2.52786 0.112266
\(508\) −0.371323 + 1.14281i −0.0164748 + 0.0507042i
\(509\) −7.66312 + 5.56758i −0.339662 + 0.246779i −0.744519 0.667601i \(-0.767321\pi\)
0.404857 + 0.914380i \(0.367321\pi\)
\(510\) 0 0
\(511\) 7.32624 + 22.5478i 0.324094 + 0.997458i
\(512\) 1.63525 + 5.03280i 0.0722687 + 0.222420i
\(513\) 4.04508 + 2.93893i 0.178595 + 0.129757i
\(514\) 12.5172 9.09429i 0.552111 0.401132i
\(515\) 0 0
\(516\) −5.61803 −0.247320
\(517\) 4.92705 + 19.5887i 0.216691 + 0.861509i
\(518\) 12.4721 0.547994
\(519\) 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 \(0.922376\pi\)
\(522\) −0.427051 1.31433i −0.0186915 0.0575266i
\(523\) 1.16312 + 3.57971i 0.0508596 + 0.156530i 0.973261 0.229704i \(-0.0737758\pi\)
−0.922401 + 0.386234i \(0.873776\pi\)
\(524\) 4.59017 + 3.33495i 0.200523 + 0.145688i
\(525\) 0 0
\(526\) −12.1074 + 37.2627i −0.527907 + 1.62473i
\(527\) 14.0000 0.609850
\(528\) 13.6353 8.55951i 0.593398 0.372505i
\(529\) −1.67376 −0.0727723
\(530\) 0 0
\(531\) −5.42705 + 3.94298i −0.235514 + 0.171111i
\(532\) 13.0902 + 9.51057i 0.567531 + 0.412335i
\(533\) 11.4721 + 35.3076i 0.496913 + 1.52934i
\(534\) 2.07295 + 6.37988i 0.0897053 + 0.276084i
\(535\) 0 0
\(536\) 21.0172 15.2699i 0.907806 0.659559i
\(537\) 3.25329 10.0126i 0.140390 0.432075i
\(538\) −1.38197 −0.0595808
\(539\) −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 \(0.111074\pi\)
\(542\) 24.0623 17.4823i 1.03356 0.750929i
\(543\) −0.618034 0.449028i −0.0265224 0.0192696i
\(544\) 2.09017 + 6.43288i 0.0896153 + 0.275808i
\(545\) 0 0
\(546\) 22.1803 + 16.1150i 0.949231 + 0.689657i
\(547\) −15.6631 + 11.3799i −0.669707 + 0.486570i −0.869927 0.493181i \(-0.835834\pi\)
0.200220 + 0.979751i \(0.435834\pi\)
\(548\) 1.01064 3.11044i 0.0431725 0.132871i
\(549\) 7.00000 0.298753
\(550\) 0 0
\(551\) 4.27051 0.181930
\(552\) −3.19098 + 9.82084i −0.135817 + 0.418003i
\(553\) 13.0902 9.51057i 0.556651 0.404430i
\(554\) 29.6525 + 21.5438i 1.25981 + 0.915308i
\(555\) 0 0
\(556\) −0.225425 0.693786i −0.00956014 0.0294231i
\(557\) 34.2984 + 24.9192i 1.45327 + 1.05586i 0.985054 + 0.172247i \(0.0551027\pi\)
0.468215 + 0.883615i \(0.344897\pi\)
\(558\) 9.16312 6.65740i 0.387906 0.281830i
\(559\) 9.09017 27.9767i 0.384473 1.18329i
\(560\) 0 0
\(561\) −5.61803 + 3.52671i −0.237194 + 0.148898i
\(562\) 1.76393 0.0744070
\(563\) 6.38854 19.6619i 0.269245 0.828651i −0.721440 0.692477i \(-0.756519\pi\)
0.990685 0.136174i \(-0.0434806\pi\)
\(564\) −3.04508 + 2.21238i −0.128221 + 0.0931582i
\(565\) 0 0
\(566\) 8.01722 + 24.6745i 0.336989 + 1.03715i
\(567\) −1.61803 4.97980i −0.0679510 0.209132i
\(568\) 14.4721 + 10.5146i 0.607237 + 0.441184i
\(569\) 18.2533 13.2618i 0.765218 0.555963i −0.135289 0.990806i \(-0.543196\pi\)
0.900506 + 0.434843i \(0.143196\pi\)
\(570\) 0 0
\(571\) −11.0902 −0.464109 −0.232055 0.972703i \(-0.574545\pi\)
−0.232055 + 0.972703i \(0.574545\pi\)
\(572\) −1.61803 6.43288i −0.0676534 0.268972i
\(573\) 16.4164 0.685805
\(574\) 30.0344 92.4365i 1.25361 3.85823i
\(575\) 0 0
\(576\) −3.42705 2.48990i −0.142794 0.103746i
\(577\) 9.27458 + 28.5442i 0.386106 + 1.18831i 0.935675 + 0.352863i \(0.114792\pi\)
−0.549569 + 0.835448i \(0.685208\pi\)
\(578\) 6.50000 + 20.0049i 0.270364 + 0.832096i
\(579\) 6.50000 + 4.72253i 0.270131 + 0.196262i
\(580\) 0 0
\(581\) −12.4721 + 38.3853i −0.517431 + 1.59249i
\(582\) 4.09017 0.169543
\(583\) −13.6976 11.4454i −0.567295 0.474021i
\(584\) −10.1246 −0.418959
\(585\) 0 0
\(586\) 33.3435 24.2254i 1.37741 1.00074i
\(587\) 17.4894 + 12.7068i 0.721863 + 0.524464i 0.886979 0.461810i \(-0.152800\pi\)
−0.165116 + 0.986274i \(0.552800\pi\)
\(588\) −3.89919 12.0005i −0.160800 0.494891i
\(589\) 10.8156 + 33.2870i 0.445649 + 1.37157i
\(590\) 0 0
\(591\) 7.89919 5.73910i 0.324929 0.236075i
\(592\) −2.20820 + 6.79615i −0.0907566 + 0.279320i
\(593\) 3.11146 0.127772 0.0638861 0.997957i \(-0.479651\pi\)
0.0638861 + 0.997957i \(0.479651\pi\)
\(594\) −2.00000 + 4.97980i −0.0820610 + 0.204324i
\(595\) 0 0
\(596\) −3.84346 + 11.8290i −0.157434 + 0.484533i
\(597\) −3.88197 + 2.82041i −0.158878 + 0.115432i
\(598\) 19.5623 + 14.2128i 0.799962 + 0.581207i
\(599\) −5.48936 16.8945i −0.224289 0.690291i −0.998363 0.0571955i \(-0.981784\pi\)
0.774074 0.633095i \(-0.218216\pi\)
\(600\) 0 0
\(601\) 8.38197 + 6.08985i 0.341908 + 0.248410i 0.745466 0.666543i \(-0.232227\pi\)
−0.403559 + 0.914954i \(0.632227\pi\)
\(602\) −62.3050 + 45.2672i −2.53936 + 1.84495i
\(603\) −3.59017 + 11.0494i −0.146203 + 0.449967i
\(604\) −9.41641 −0.383148
\(605\) 0 0
\(606\) 31.6525 1.28579
\(607\) −10.1976 + 31.3849i −0.413906 + 1.27387i 0.499319 + 0.866418i \(0.333583\pi\)
−0.913226 + 0.407454i \(0.866417\pi\)
\(608\) −13.6803 + 9.93935i −0.554811 + 0.403094i
\(609\) −3.61803 2.62866i −0.146610 0.106518i
\(610\) 0 0
\(611\) −6.09017 18.7436i −0.246382 0.758286i
\(612\) −1.00000 0.726543i −0.0404226 0.0293687i
\(613\) −3.04508 + 2.21238i −0.122990 + 0.0893573i −0.647580 0.761998i \(-0.724219\pi\)
0.524590 + 0.851355i \(0.324219\pi\)
\(614\) 14.0623 43.2793i 0.567508 1.74661i
\(615\) 0 0
\(616\) 14.4721 36.0341i 0.583099 1.45186i
\(617\) 42.2492 1.70089 0.850445 0.526064i \(-0.176333\pi\)
0.850445 + 0.526064i \(0.176333\pi\)
\(618\) 2.30902 7.10642i 0.0928823 0.285862i
\(619\) −34.6976 + 25.2093i −1.39461 + 1.01325i −0.399271 + 0.916833i \(0.630737\pi\)
−0.995341 + 0.0964126i \(0.969263\pi\)
\(620\) 0 0
\(621\) −1.42705 4.39201i −0.0572656 0.176245i
\(622\) −6.26393 19.2784i −0.251161 0.772993i
\(623\) 17.5623 + 12.7598i 0.703619 + 0.511209i
\(624\) −12.7082 + 9.23305i −0.508735 + 0.369618i
\(625\) 0 0
\(626\) 13.7082 0.547890
\(627\) −12.7254 10.6331i −0.508205 0.424647i
\(628\) 7.61803 0.303993
\(629\) 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 \(0.410679\pi\)
\(632\) 2.13525 + 6.57164i 0.0849359 + 0.261406i
\(633\) −0.881966 2.71441i −0.0350550 0.107888i
\(634\) 4.69098 + 3.40820i 0.186303 + 0.135357i
\(635\) 0 0
\(636\) 1.02786 3.16344i 0.0407575 0.125439i
\(637\) 66.0689 2.61774
\(638\) 1.11803 + 4.44501i 0.0442634 + 0.175980i
\(639\) −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 \(0.326660\pi\)
\(642\) 5.04508 + 3.66547i 0.199114 + 0.144665i
\(643\) −4.22542 13.0045i −0.166634 0.512848i 0.832519 0.553997i \(-0.186898\pi\)
−0.999153 + 0.0411490i \(0.986898\pi\)
\(644\) −4.61803 14.2128i −0.181976 0.560065i
\(645\) 0 0
\(646\) 13.0902 9.51057i 0.515026 0.374188i
\(647\) 9.76393 30.0503i 0.383860 1.18140i −0.553444 0.832886i \(-0.686687\pi\)
0.937304 0.348513i \(-0.113313\pi\)
\(648\) 2.23607 0.0878410
\(649\) 18.8435 11.8290i 0.739670 0.464327i
\(650\) 0 0
\(651\) 11.3262 34.8586i 0.443910 1.36622i
\(652\) 3.28115 2.38390i 0.128500 0.0933606i
\(653\) −35.2426 25.6053i −1.37915 1.00201i −0.996959 0.0779293i \(-0.975169\pi\)
−0.382192 0.924083i \(-0.624831\pi\)
\(654\) 5.42705 + 16.7027i 0.212214 + 0.653129i
\(655\) 0 0
\(656\) 45.0517 + 32.7319i 1.75897 + 1.27797i
\(657\) 3.66312 2.66141i 0.142912 0.103832i
\(658\) −15.9443 + 49.0714i −0.621572 + 1.91300i
\(659\) 42.0344 1.63743 0.818715 0.574201i \(-0.194687\pi\)
0.818715 + 0.574201i \(0.194687\pi\)
\(660\) 0 0
\(661\) 15.0902 0.586940 0.293470 0.955968i \(-0.405190\pi\)
0.293470 + 0.955968i \(0.405190\pi\)
\(662\) 13.7984 42.4670i 0.536289 1.65053i
\(663\) 5.23607 3.80423i 0.203352 0.147744i
\(664\) −13.9443 10.1311i −0.541143 0.393163i
\(665\) 0 0
\(666\) −0.736068 2.26538i −0.0285221 0.0877819i
\(667\) −3.19098 2.31838i −0.123555 0.0897682i
\(668\) −4.51722 + 3.28195i −0.174777 + 0.126983i
\(669\) 6.50000 20.0049i 0.251305 0.773436i
\(670\) 0 0
\(671\) −23.1631 1.57160i −0.894202 0.0606709i
\(672\) 17.7082 0.683109
\(673\) −10.9098 + 33.5770i −0.420543 + 1.29430i 0.486655 + 0.873594i \(0.338217\pi\)
−0.907198 + 0.420704i \(0.861783\pi\)
\(674\) −37.7705 + 27.4419i −1.45487 + 1.05702i
\(675\) 0 0
\(676\) −0.482779 1.48584i −0.0185684 0.0571477i
\(677\) 1.83688 + 5.65334i 0.0705971 + 0.217275i 0.980130 0.198357i \(-0.0635604\pi\)
−0.909533 + 0.415632i \(0.863560\pi\)
\(678\) 4.54508 + 3.30220i 0.174553 + 0.126820i
\(679\) 10.7082 7.77997i 0.410943 0.298568i
\(680\) 0 0
\(681\) −8.05573 −0.308696
\(682\) −31.8156 + 19.9722i −1.21828 + 0.764775i
\(683\) −15.7082 −0.601058 −0.300529 0.953773i \(-0.597163\pi\)
−0.300529 + 0.953773i \(0.597163\pi\)
\(684\) 0.954915 2.93893i 0.0365121 0.112373i
\(685\) 0 0
\(686\) −91.9574 66.8110i −3.51095 2.55086i
\(687\) −2.13525 6.57164i −0.0814651 0.250724i
\(688\) −13.6353 41.9650i −0.519839 1.59990i
\(689\) 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 \(0.911797\pi\)
\(692\) −10.2361 −0.389117
\(693\) 4.23607 + 16.8415i 0.160915 + 0.639756i
\(694\) −45.5967 −1.73083
\(695\) 0 0
\(696\) 1.54508 1.12257i 0.0585663 0.0425509i
\(697\) −18.5623 13.4863i −0.703097 0.510830i
\(698\) −16.1180 49.6062i −0.610077 1.87762i
\(699\) −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 \(0.576399\pi\)
\(702\) 1.61803 4.97980i 0.0610688 0.187950i
\(703\) 7.36068 0.277613
\(704\) 10.7812 + 9.00854i 0.406330 + 0.339522i
\(705\) 0 0
\(706\) −8.91641 + 27.4419i −0.335573 + 1.03279i
\(707\) 82.8673 60.2066i 3.11654 2.26430i
\(708\) 3.35410 + 2.43690i 0.126055 + 0.0915842i
\(709\) 5.81559 + 17.8986i 0.218409 + 0.672195i 0.998894 + 0.0470197i \(0.0149724\pi\)
−0.780485 + 0.625175i \(0.785028\pi\)
\(710\) 0 0
\(711\) −2.50000 1.81636i −0.0937573 0.0681187i
\(712\) −7.50000 + 5.44907i −0.281074 + 0.204212i
\(713\) 9.98936 30.7441i 0.374104 1.15137i
\(714\) −16.9443 −0.634123
\(715\) 0 0
\(716\) −6.50658 −0.243162
\(717\) −6.80902 + 20.9560i −0.254287 + 0.782616i
\(718\) 4.30902 3.13068i 0.160811 0.116836i
\(719\) −21.7705 15.8172i −0.811903 0.589882i 0.102479 0.994735i \(-0.467323\pi\)
−0.914382 + 0.404853i \(0.867323\pi\)
\(720\) 0 0
\(721\) −7.47214 22.9969i −0.278277 0.856448i
\(722\) 7.85410 + 5.70634i 0.292299 + 0.212368i
\(723\) 0.500000 0.363271i 0.0185952 0.0135102i
\(724\) −0.145898 + 0.449028i −0.00542226 + 0.0166880i
\(725\) 0 0
\(726\) 7.73607 16.0292i 0.287112 0.594900i
\(727\) 21.6738 0.803835 0.401918 0.915676i \(-0.368344\pi\)
0.401918 + 0.915676i \(0.368344\pi\)
\(728\) −11.7082 + 36.0341i −0.433935 + 1.33551i
\(729\) −0.809017 + 0.587785i −0.0299636 + 0.0217698i
\(730\) 0 0
\(731\) 5.61803 + 17.2905i 0.207790 + 0.639513i
\(732\) −1.33688 4.11450i −0.0494125 0.152076i
\(733\) 3.92705 + 2.85317i 0.145049 + 0.105384i 0.657943 0.753068i \(-0.271427\pi\)
−0.512894 + 0.858452i \(0.671427\pi\)
\(734\) 28.9615 21.0418i 1.06899 0.776665i
\(735\) 0 0
\(736\) 15.6180 0.575688
\(737\) 14.3607 35.7566i 0.528982 1.31711i
\(738\) −18.5623 −0.683288
\(739\) −6.18034 + 19.0211i −0.227347 + 0.699704i 0.770697 + 0.637201i \(0.219908\pi\)
−0.998045 + 0.0625022i \(0.980092\pi\)
\(740\) 0 0
\(741\) 13.0902 + 9.51057i 0.480879 + 0.349379i
\(742\) −14.0902 43.3651i −0.517266 1.59198i
\(743\) 9.78115 + 30.1033i 0.358836 + 1.10438i 0.953752 + 0.300595i \(0.0971852\pi\)
−0.594916 + 0.803788i \(0.702815\pi\)
\(744\) 12.6631 + 9.20029i 0.464252 + 0.337299i
\(745\) 0 0
\(746\) 16.3713 50.3858i 0.599397 1.84475i
\(747\) 7.70820 0.282028
\(748\) 3.14590 + 2.62866i 0.115025 + 0.0961132i
\(749\) 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 \(0.240938\pi\)
\(752\) −23.9164 17.3763i −0.872142 0.633648i
\(753\) −5.09017 15.6659i −0.185496 0.570898i
\(754\) −1.38197 4.25325i −0.0503282 0.154894i
\(755\) 0 0
\(756\) −2.61803 + 1.90211i −0.0952170 + 0.0691792i
\(757\) −0.562306 + 1.73060i −0.0204374 + 0.0628997i −0.960755 0.277398i \(-0.910528\pi\)
0.940318 + 0.340298i \(0.110528\pi\)
\(758\) 8.09017 0.293848
\(759\) 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 \(0.0421878\pi\)
\(762\) 2.54508 1.84911i 0.0921987 0.0669863i
\(763\) 45.9787 + 33.4055i 1.66454 + 1.20936i
\(764\) −3.13525 9.64932i −0.113430 0.349100i
\(765\) 0 0
\(766\) 17.4894 + 12.7068i 0.631916 + 0.459114i
\(767\) −17.5623 + 12.7598i −0.634138 + 0.460728i
\(768\) −4.19098 + 12.8985i −0.151229 + 0.465435i
\(769\) 17.2361 0.621549 0.310774 0.950484i \(-0.399412\pi\)
0.310774 + 0.950484i \(0.399412\pi\)
\(770\) 0 0
\(771\) −9.56231 −0.344378
\(772\) 1.53444 4.72253i 0.0552258 0.169967i
\(773\) −22.2533 + 16.1680i −0.800395 + 0.581521i −0.911030 0.412340i \(-0.864712\pi\)
0.110635 + 0.993861i \(0.464712\pi\)
\(774\) 11.8992 + 8.64527i 0.427707 + 0.310748i
\(775\) 0 0
\(776\) 1.74671 + 5.37582i 0.0627033 + 0.192981i
\(777\) −6.23607 4.53077i −0.223718 0.162540i
\(778\) −27.5623 + 20.0252i −0.988157 + 0.717938i
\(779\) 17.7254 54.5532i 0.635079 1.95457i
\(780\) 0 0
\(781\) 26.4721 + 1.79611i 0.947247 + 0.0642699i
\(782\) −14.9443 −0.534406