Properties

Label 210.3.l.b.127.1
Level 210
Weight 3
Character 210.127
Analytic conductor 5.722
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 127.1
Root \(-0.394902 - 0.394902i\) of \(x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + 1093889 x^{8} - 4595248 x^{7} + 18837632 x^{6} + 86081152 x^{5} + 178889856 x^{4} + 70149120 x^{3} + 10035200 x^{2} - 7168000 x + 2560000\)
Character \(\chi\) \(=\) 210.127
Dual form 210.3.l.b.43.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.93066 + 0.829843i) q^{5} +2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.93066 + 0.829843i) q^{5} +2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(5.76050 + 4.10081i) q^{10} -5.74922 q^{11} +(-2.44949 - 2.44949i) q^{12} +(15.0034 - 15.0034i) q^{13} -3.74166i q^{14} +(5.02245 - 7.05514i) q^{15} -4.00000 q^{16} +(-4.78821 - 4.78821i) q^{17} +(-3.00000 + 3.00000i) q^{18} -17.4017i q^{19} +(-1.65969 - 9.86131i) q^{20} -4.58258 q^{21} +(5.74922 + 5.74922i) q^{22} +(13.2261 - 13.2261i) q^{23} +4.89898i q^{24} +(23.6227 - 8.18334i) q^{25} -30.0069 q^{26} +(3.67423 + 3.67423i) q^{27} +(-3.74166 + 3.74166i) q^{28} -37.7271i q^{29} +(-12.0776 + 2.03269i) q^{30} -27.0130 q^{31} +(4.00000 + 4.00000i) q^{32} +(7.04132 - 7.04132i) q^{33} +9.57642i q^{34} +(-10.7769 - 7.67192i) q^{35} +6.00000 q^{36} +(11.3640 + 11.3640i) q^{37} +(-17.4017 + 17.4017i) q^{38} +36.7508i q^{39} +(-8.20163 + 11.5210i) q^{40} -53.0897 q^{41} +(4.58258 + 4.58258i) q^{42} +(37.1052 - 37.1052i) q^{43} -11.4984i q^{44} +(2.48953 + 14.7920i) q^{45} -26.4522 q^{46} +(-9.39190 - 9.39190i) q^{47} +(4.89898 - 4.89898i) q^{48} +7.00000i q^{49} +(-31.8061 - 15.4394i) q^{50} +11.7287 q^{51} +(30.0069 + 30.0069i) q^{52} +(43.8996 - 43.8996i) q^{53} -7.34847i q^{54} +(28.3474 - 4.77095i) q^{55} +7.48331 q^{56} +(21.3126 + 21.3126i) q^{57} +(-37.7271 + 37.7271i) q^{58} +62.9694i q^{59} +(14.1103 + 10.0449i) q^{60} -1.67492 q^{61} +(27.0130 + 27.0130i) q^{62} +(5.61249 - 5.61249i) q^{63} -8.00000i q^{64} +(-61.5263 + 86.4273i) q^{65} -14.0826 q^{66} +(28.4909 + 28.4909i) q^{67} +(9.57642 - 9.57642i) q^{68} +32.3972i q^{69} +(3.10499 + 18.4488i) q^{70} +47.2039 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-31.2071 + 31.2071i) q^{73} -22.7281i q^{74} +(-18.9093 + 38.9543i) q^{75} +34.8033 q^{76} +(-10.7558 - 10.7558i) q^{77} +(36.7508 - 36.7508i) q^{78} +107.134i q^{79} +(19.7226 - 3.31937i) q^{80} -9.00000 q^{81} +(53.0897 + 53.0897i) q^{82} +(18.2365 - 18.2365i) q^{83} -9.16515i q^{84} +(27.5825 + 19.6356i) q^{85} -74.2105 q^{86} +(46.2061 + 46.2061i) q^{87} +(-11.4984 + 11.4984i) q^{88} -174.675i q^{89} +(12.3024 - 17.2815i) q^{90} +56.1378 q^{91} +(26.4522 + 26.4522i) q^{92} +(33.0840 - 33.0840i) q^{93} +18.7838i q^{94} +(14.4406 + 85.8016i) q^{95} -9.79796 q^{96} +(-91.5084 - 91.5084i) q^{97} +(7.00000 - 7.00000i) q^{98} +17.2477i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{2} - 16q^{5} + 32q^{8} + O(q^{10}) \) \( 16q - 16q^{2} - 16q^{5} + 32q^{8} + 24q^{10} + 8q^{11} - 32q^{13} - 12q^{15} - 64q^{16} + 56q^{17} - 48q^{18} - 16q^{20} - 8q^{22} + 24q^{23} + 40q^{25} + 64q^{26} - 112q^{31} + 64q^{32} + 24q^{33} + 28q^{35} + 96q^{36} - 152q^{37} - 16q^{40} + 24q^{45} - 48q^{46} + 80q^{47} - 72q^{50} - 72q^{51} - 64q^{52} + 48q^{53} - 24q^{55} + 24q^{57} + 96q^{58} + 24q^{60} + 96q^{61} + 112q^{62} + 16q^{65} - 48q^{66} - 80q^{67} - 112q^{68} + 536q^{71} - 96q^{72} - 288q^{75} - 168q^{77} - 48q^{78} + 64q^{80} - 144q^{81} - 256q^{83} + 40q^{85} - 144q^{87} + 16q^{88} + 24q^{90} + 48q^{92} + 192q^{93} + 360q^{95} + 688q^{97} + 112q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.500000 0.500000i
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) −4.93066 + 0.829843i −0.986131 + 0.165969i
\(6\) 2.44949 0.408248
\(7\) 1.87083 + 1.87083i 0.267261 + 0.267261i
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 5.76050 + 4.10081i 0.576050 + 0.410081i
\(11\) −5.74922 −0.522656 −0.261328 0.965250i \(-0.584160\pi\)
−0.261328 + 0.965250i \(0.584160\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) 15.0034 15.0034i 1.15411 1.15411i 0.168391 0.985720i \(-0.446143\pi\)
0.985720 0.168391i \(-0.0538571\pi\)
\(14\) 3.74166i 0.267261i
\(15\) 5.02245 7.05514i 0.334830 0.470343i
\(16\) −4.00000 −0.250000
\(17\) −4.78821 4.78821i −0.281659 0.281659i 0.552111 0.833771i \(-0.313822\pi\)
−0.833771 + 0.552111i \(0.813822\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 17.4017i 0.915877i −0.888984 0.457938i \(-0.848588\pi\)
0.888984 0.457938i \(-0.151412\pi\)
\(20\) −1.65969 9.86131i −0.0829843 0.493066i
\(21\) −4.58258 −0.218218
\(22\) 5.74922 + 5.74922i 0.261328 + 0.261328i
\(23\) 13.2261 13.2261i 0.575048 0.575048i −0.358487 0.933535i \(-0.616707\pi\)
0.933535 + 0.358487i \(0.116707\pi\)
\(24\) 4.89898i 0.204124i
\(25\) 23.6227 8.18334i 0.944909 0.327333i
\(26\) −30.0069 −1.15411
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) −3.74166 + 3.74166i −0.133631 + 0.133631i
\(29\) 37.7271i 1.30093i −0.759534 0.650467i \(-0.774573\pi\)
0.759534 0.650467i \(-0.225427\pi\)
\(30\) −12.0776 + 2.03269i −0.402586 + 0.0677564i
\(31\) −27.0130 −0.871386 −0.435693 0.900095i \(-0.643497\pi\)
−0.435693 + 0.900095i \(0.643497\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 7.04132 7.04132i 0.213373 0.213373i
\(34\) 9.57642i 0.281659i
\(35\) −10.7769 7.67192i −0.307912 0.219198i
\(36\) 6.00000 0.166667
\(37\) 11.3640 + 11.3640i 0.307136 + 0.307136i 0.843798 0.536661i \(-0.180315\pi\)
−0.536661 + 0.843798i \(0.680315\pi\)
\(38\) −17.4017 + 17.4017i −0.457938 + 0.457938i
\(39\) 36.7508i 0.942328i
\(40\) −8.20163 + 11.5210i −0.205041 + 0.288025i
\(41\) −53.0897 −1.29487 −0.647435 0.762121i \(-0.724158\pi\)
−0.647435 + 0.762121i \(0.724158\pi\)
\(42\) 4.58258 + 4.58258i 0.109109 + 0.109109i
\(43\) 37.1052 37.1052i 0.862912 0.862912i −0.128763 0.991675i \(-0.541101\pi\)
0.991675 + 0.128763i \(0.0411007\pi\)
\(44\) 11.4984i 0.261328i
\(45\) 2.48953 + 14.7920i 0.0553228 + 0.328710i
\(46\) −26.4522 −0.575048
\(47\) −9.39190 9.39190i −0.199828 0.199828i 0.600098 0.799926i \(-0.295128\pi\)
−0.799926 + 0.600098i \(0.795128\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 7.00000i 0.142857i
\(50\) −31.8061 15.4394i −0.636121 0.308788i
\(51\) 11.7287 0.229974
\(52\) 30.0069 + 30.0069i 0.577056 + 0.577056i
\(53\) 43.8996 43.8996i 0.828294 0.828294i −0.158987 0.987281i \(-0.550823\pi\)
0.987281 + 0.158987i \(0.0508228\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 28.3474 4.77095i 0.515407 0.0867445i
\(56\) 7.48331 0.133631
\(57\) 21.3126 + 21.3126i 0.373905 + 0.373905i
\(58\) −37.7271 + 37.7271i −0.650467 + 0.650467i
\(59\) 62.9694i 1.06728i 0.845713 + 0.533639i \(0.179176\pi\)
−0.845713 + 0.533639i \(0.820824\pi\)
\(60\) 14.1103 + 10.0449i 0.235171 + 0.167415i
\(61\) −1.67492 −0.0274577 −0.0137288 0.999906i \(-0.504370\pi\)
−0.0137288 + 0.999906i \(0.504370\pi\)
\(62\) 27.0130 + 27.0130i 0.435693 + 0.435693i
\(63\) 5.61249 5.61249i 0.0890871 0.0890871i
\(64\) 8.00000i 0.125000i
\(65\) −61.5263 + 86.4273i −0.946559 + 1.32965i
\(66\) −14.0826 −0.213373
\(67\) 28.4909 + 28.4909i 0.425238 + 0.425238i 0.887003 0.461765i \(-0.152784\pi\)
−0.461765 + 0.887003i \(0.652784\pi\)
\(68\) 9.57642 9.57642i 0.140830 0.140830i
\(69\) 32.3972i 0.469525i
\(70\) 3.10499 + 18.4488i 0.0443570 + 0.263555i
\(71\) 47.2039 0.664844 0.332422 0.943131i \(-0.392134\pi\)
0.332422 + 0.943131i \(0.392134\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) −31.2071 + 31.2071i −0.427495 + 0.427495i −0.887774 0.460279i \(-0.847749\pi\)
0.460279 + 0.887774i \(0.347749\pi\)
\(74\) 22.7281i 0.307136i
\(75\) −18.9093 + 38.9543i −0.252124 + 0.519391i
\(76\) 34.8033 0.457938
\(77\) −10.7558 10.7558i −0.139686 0.139686i
\(78\) 36.7508 36.7508i 0.471164 0.471164i
\(79\) 107.134i 1.35612i 0.735006 + 0.678061i \(0.237179\pi\)
−0.735006 + 0.678061i \(0.762821\pi\)
\(80\) 19.7226 3.31937i 0.246533 0.0414921i
\(81\) −9.00000 −0.111111
\(82\) 53.0897 + 53.0897i 0.647435 + 0.647435i
\(83\) 18.2365 18.2365i 0.219716 0.219716i −0.588662 0.808379i \(-0.700345\pi\)
0.808379 + 0.588662i \(0.200345\pi\)
\(84\) 9.16515i 0.109109i
\(85\) 27.5825 + 19.6356i 0.324500 + 0.231007i
\(86\) −74.2105 −0.862912
\(87\) 46.2061 + 46.2061i 0.531104 + 0.531104i
\(88\) −11.4984 + 11.4984i −0.130664 + 0.130664i
\(89\) 174.675i 1.96265i −0.192368 0.981323i \(-0.561617\pi\)
0.192368 0.981323i \(-0.438383\pi\)
\(90\) 12.3024 17.2815i 0.136694 0.192017i
\(91\) 56.1378 0.616898
\(92\) 26.4522 + 26.4522i 0.287524 + 0.287524i
\(93\) 33.0840 33.0840i 0.355742 0.355742i
\(94\) 18.7838i 0.199828i
\(95\) 14.4406 + 85.8016i 0.152007 + 0.903175i
\(96\) −9.79796 −0.102062
\(97\) −91.5084 91.5084i −0.943385 0.943385i 0.0550959 0.998481i \(-0.482454\pi\)
−0.998481 + 0.0550959i \(0.982454\pi\)
\(98\) 7.00000 7.00000i 0.0714286 0.0714286i
\(99\) 17.2477i 0.174219i
\(100\) 16.3667 + 47.2454i 0.163667 + 0.472454i
\(101\) −182.855 −1.81045 −0.905223 0.424937i \(-0.860296\pi\)
−0.905223 + 0.424937i \(0.860296\pi\)
\(102\) −11.7287 11.7287i −0.114987 0.114987i
\(103\) −46.6226 + 46.6226i −0.452647 + 0.452647i −0.896232 0.443586i \(-0.853706\pi\)
0.443586 + 0.896232i \(0.353706\pi\)
\(104\) 60.0138i 0.577056i
\(105\) 22.5951 3.80282i 0.215191 0.0362173i
\(106\) −87.7991 −0.828294
\(107\) 57.5651 + 57.5651i 0.537992 + 0.537992i 0.922939 0.384947i \(-0.125780\pi\)
−0.384947 + 0.922939i \(0.625780\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 205.254i 1.88307i −0.336920 0.941533i \(-0.609385\pi\)
0.336920 0.941533i \(-0.390615\pi\)
\(110\) −33.1184 23.5765i −0.301076 0.214331i
\(111\) −27.8361 −0.250776
\(112\) −7.48331 7.48331i −0.0668153 0.0668153i
\(113\) 32.6037 32.6037i 0.288528 0.288528i −0.547970 0.836498i \(-0.684599\pi\)
0.836498 + 0.547970i \(0.184599\pi\)
\(114\) 42.6252i 0.373905i
\(115\) −54.2378 + 76.1890i −0.471633 + 0.662513i
\(116\) 75.4542 0.650467
\(117\) −45.0103 45.0103i −0.384704 0.384704i
\(118\) 62.9694 62.9694i 0.533639 0.533639i
\(119\) 17.9158i 0.150553i
\(120\) −4.06538 24.1552i −0.0338782 0.201293i
\(121\) −87.9465 −0.726831
\(122\) 1.67492 + 1.67492i 0.0137288 + 0.0137288i
\(123\) 65.0213 65.0213i 0.528629 0.528629i
\(124\) 54.0259i 0.435693i
\(125\) −109.685 + 59.9524i −0.877477 + 0.479619i
\(126\) −11.2250 −0.0890871
\(127\) −103.735 103.735i −0.816814 0.816814i 0.168831 0.985645i \(-0.446001\pi\)
−0.985645 + 0.168831i \(0.946001\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 90.8889i 0.704565i
\(130\) 147.954 24.9010i 1.13810 0.191546i
\(131\) 157.999 1.20610 0.603049 0.797704i \(-0.293952\pi\)
0.603049 + 0.797704i \(0.293952\pi\)
\(132\) 14.0826 + 14.0826i 0.106687 + 0.106687i
\(133\) 32.5555 32.5555i 0.244778 0.244778i
\(134\) 56.9819i 0.425238i
\(135\) −21.1654 15.0673i −0.156781 0.111610i
\(136\) −19.1528 −0.140830
\(137\) −36.9574 36.9574i −0.269762 0.269762i 0.559242 0.829004i \(-0.311092\pi\)
−0.829004 + 0.559242i \(0.811092\pi\)
\(138\) 32.3972 32.3972i 0.234762 0.234762i
\(139\) 132.183i 0.950960i −0.879727 0.475480i \(-0.842274\pi\)
0.879727 0.475480i \(-0.157726\pi\)
\(140\) 15.3438 21.5538i 0.109599 0.153956i
\(141\) 23.0054 0.163159
\(142\) −47.2039 47.2039i −0.332422 0.332422i
\(143\) −86.2581 + 86.2581i −0.603203 + 0.603203i
\(144\) 12.0000i 0.0833333i
\(145\) 31.3076 + 186.019i 0.215914 + 1.28289i
\(146\) 62.4143 0.427495
\(147\) −8.57321 8.57321i −0.0583212 0.0583212i
\(148\) −22.7281 + 22.7281i −0.153568 + 0.153568i
\(149\) 255.329i 1.71362i 0.515634 + 0.856809i \(0.327556\pi\)
−0.515634 + 0.856809i \(0.672444\pi\)
\(150\) 57.8636 20.0450i 0.385757 0.133633i
\(151\) −210.524 −1.39420 −0.697098 0.716976i \(-0.745526\pi\)
−0.697098 + 0.716976i \(0.745526\pi\)
\(152\) −34.8033 34.8033i −0.228969 0.228969i
\(153\) −14.3646 + 14.3646i −0.0938865 + 0.0938865i
\(154\) 21.5116i 0.139686i
\(155\) 133.192 22.4165i 0.859301 0.144623i
\(156\) −73.5016 −0.471164
\(157\) −181.671 181.671i −1.15714 1.15714i −0.985088 0.172052i \(-0.944960\pi\)
−0.172052 0.985088i \(-0.555040\pi\)
\(158\) 107.134 107.134i 0.678061 0.678061i
\(159\) 107.532i 0.676299i
\(160\) −23.0420 16.4033i −0.144012 0.102520i
\(161\) 49.4876 0.307376
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) 155.563 155.563i 0.954376 0.954376i −0.0446274 0.999004i \(-0.514210\pi\)
0.999004 + 0.0446274i \(0.0142101\pi\)
\(164\) 106.179i 0.647435i
\(165\) −28.8751 + 40.5615i −0.175001 + 0.245827i
\(166\) −36.4729 −0.219716
\(167\) 76.0788 + 76.0788i 0.455562 + 0.455562i 0.897195 0.441634i \(-0.145601\pi\)
−0.441634 + 0.897195i \(0.645601\pi\)
\(168\) −9.16515 + 9.16515i −0.0545545 + 0.0545545i
\(169\) 281.207i 1.66395i
\(170\) −7.94692 47.2180i −0.0467466 0.277753i
\(171\) −52.2050 −0.305292
\(172\) 74.2105 + 74.2105i 0.431456 + 0.431456i
\(173\) 28.9323 28.9323i 0.167239 0.167239i −0.618526 0.785765i \(-0.712270\pi\)
0.785765 + 0.618526i \(0.212270\pi\)
\(174\) 92.4121i 0.531104i
\(175\) 59.5037 + 28.8844i 0.340021 + 0.165054i
\(176\) 22.9969 0.130664
\(177\) −77.1214 77.1214i −0.435714 0.435714i
\(178\) −174.675 + 174.675i −0.981323 + 0.981323i
\(179\) 126.849i 0.708653i −0.935122 0.354327i \(-0.884710\pi\)
0.935122 0.354327i \(-0.115290\pi\)
\(180\) −29.5839 + 4.97906i −0.164355 + 0.0276614i
\(181\) 307.681 1.69989 0.849947 0.526867i \(-0.176634\pi\)
0.849947 + 0.526867i \(0.176634\pi\)
\(182\) −56.1378 56.1378i −0.308449 0.308449i
\(183\) 2.05135 2.05135i 0.0112096 0.0112096i
\(184\) 52.9044i 0.287524i
\(185\) −65.4626 46.6018i −0.353852 0.251902i
\(186\) −66.1680 −0.355742
\(187\) 27.5285 + 27.5285i 0.147211 + 0.147211i
\(188\) 18.7838 18.7838i 0.0999139 0.0999139i
\(189\) 13.7477i 0.0727393i
\(190\) 71.3609 100.242i 0.375584 0.527591i
\(191\) 71.4969 0.374329 0.187165 0.982329i \(-0.440070\pi\)
0.187165 + 0.982329i \(0.440070\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) −155.347 + 155.347i −0.804908 + 0.804908i −0.983858 0.178950i \(-0.942730\pi\)
0.178950 + 0.983858i \(0.442730\pi\)
\(194\) 183.017i 0.943385i
\(195\) −30.4974 181.205i −0.156397 0.929259i
\(196\) −14.0000 −0.0714286
\(197\) 190.520 + 190.520i 0.967107 + 0.967107i 0.999476 0.0323691i \(-0.0103052\pi\)
−0.0323691 + 0.999476i \(0.510305\pi\)
\(198\) 17.2477 17.2477i 0.0871093 0.0871093i
\(199\) 173.246i 0.870582i 0.900290 + 0.435291i \(0.143354\pi\)
−0.900290 + 0.435291i \(0.856646\pi\)
\(200\) 30.8788 63.6121i 0.154394 0.318061i
\(201\) −69.7883 −0.347205
\(202\) 182.855 + 182.855i 0.905223 + 0.905223i
\(203\) 70.5809 70.5809i 0.347689 0.347689i
\(204\) 23.4573i 0.114987i
\(205\) 261.767 44.0561i 1.27691 0.214908i
\(206\) 93.2452 0.452647
\(207\) −39.6783 39.6783i −0.191683 0.191683i
\(208\) −60.0138 + 60.0138i −0.288528 + 0.288528i
\(209\) 100.046i 0.478689i
\(210\) −26.3979 18.7923i −0.125704 0.0894871i
\(211\) 53.9193 0.255542 0.127771 0.991804i \(-0.459218\pi\)
0.127771 + 0.991804i \(0.459218\pi\)
\(212\) 87.7991 + 87.7991i 0.414147 + 0.414147i
\(213\) −57.8128 + 57.8128i −0.271422 + 0.271422i
\(214\) 115.130i 0.537992i
\(215\) −152.162 + 213.745i −0.707728 + 0.994161i
\(216\) 14.6969 0.0680414
\(217\) −50.5366 50.5366i −0.232888 0.232888i
\(218\) −205.254 + 205.254i −0.941533 + 0.941533i
\(219\) 76.4415i 0.349048i
\(220\) 9.54189 + 56.6948i 0.0433722 + 0.257704i
\(221\) −143.679 −0.650133
\(222\) 27.8361 + 27.8361i 0.125388 + 0.125388i
\(223\) −146.512 + 146.512i −0.657006 + 0.657006i −0.954671 0.297664i \(-0.903792\pi\)
0.297664 + 0.954671i \(0.403792\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) −24.5500 70.8682i −0.109111 0.314970i
\(226\) −65.2073 −0.288528
\(227\) 162.897 + 162.897i 0.717607 + 0.717607i 0.968115 0.250508i \(-0.0805975\pi\)
−0.250508 + 0.968115i \(0.580598\pi\)
\(228\) −42.6252 + 42.6252i −0.186953 + 0.186953i
\(229\) 176.209i 0.769470i 0.923027 + 0.384735i \(0.125707\pi\)
−0.923027 + 0.384735i \(0.874293\pi\)
\(230\) 130.427 21.9512i 0.567073 0.0954399i
\(231\) 26.3462 0.114053
\(232\) −75.4542 75.4542i −0.325234 0.325234i
\(233\) −18.3615 + 18.3615i −0.0788049 + 0.0788049i −0.745411 0.666606i \(-0.767747\pi\)
0.666606 + 0.745411i \(0.267747\pi\)
\(234\) 90.0207i 0.384704i
\(235\) 54.1020 + 38.5144i 0.230221 + 0.163891i
\(236\) −125.939 −0.533639
\(237\) −131.211 131.211i −0.553634 0.553634i
\(238\) −17.9158 + 17.9158i −0.0752767 + 0.0752767i
\(239\) 275.093i 1.15102i 0.817795 + 0.575509i \(0.195196\pi\)
−0.817795 + 0.575509i \(0.804804\pi\)
\(240\) −20.0898 + 28.2206i −0.0837075 + 0.117586i
\(241\) 338.925 1.40633 0.703164 0.711028i \(-0.251770\pi\)
0.703164 + 0.711028i \(0.251770\pi\)
\(242\) 87.9465 + 87.9465i 0.363415 + 0.363415i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 3.34984i 0.0137288i
\(245\) −5.80890 34.5146i −0.0237098 0.140876i
\(246\) −130.043 −0.528629
\(247\) −261.085 261.085i −1.05702 1.05702i
\(248\) −54.0259 + 54.0259i −0.217846 + 0.217846i
\(249\) 44.6700i 0.179398i
\(250\) 169.637 + 49.7323i 0.678548 + 0.198929i
\(251\) 72.1187 0.287326 0.143663 0.989627i \(-0.454112\pi\)
0.143663 + 0.989627i \(0.454112\pi\)
\(252\) 11.2250 + 11.2250i 0.0445435 + 0.0445435i
\(253\) −76.0397 + 76.0397i −0.300552 + 0.300552i
\(254\) 207.471i 0.816814i
\(255\) −57.8301 + 9.73296i −0.226785 + 0.0381685i
\(256\) 16.0000 0.0625000
\(257\) −12.2256 12.2256i −0.0475703 0.0475703i 0.682921 0.730492i \(-0.260709\pi\)
−0.730492 + 0.682921i \(0.760709\pi\)
\(258\) 90.8889 90.8889i 0.352282 0.352282i
\(259\) 42.5204i 0.164171i
\(260\) −172.855 123.053i −0.664826 0.473279i
\(261\) −113.181 −0.433645
\(262\) −157.999 157.999i −0.603049 0.603049i
\(263\) 275.733 275.733i 1.04842 1.04842i 0.0496495 0.998767i \(-0.484190\pi\)
0.998767 0.0496495i \(-0.0158104\pi\)
\(264\) 28.1653i 0.106687i
\(265\) −180.024 + 252.883i −0.679335 + 0.954277i
\(266\) −65.1110 −0.244778
\(267\) 213.933 + 213.933i 0.801247 + 0.801247i
\(268\) −56.9819 + 56.9819i −0.212619 + 0.212619i
\(269\) 275.988i 1.02598i −0.858395 0.512989i \(-0.828538\pi\)
0.858395 0.512989i \(-0.171462\pi\)
\(270\) 6.09807 + 36.2328i 0.0225855 + 0.134195i
\(271\) 295.698 1.09114 0.545568 0.838067i \(-0.316314\pi\)
0.545568 + 0.838067i \(0.316314\pi\)
\(272\) 19.1528 + 19.1528i 0.0704149 + 0.0704149i
\(273\) −68.7544 + 68.7544i −0.251848 + 0.251848i
\(274\) 73.9148i 0.269762i
\(275\) −135.812 + 47.0478i −0.493862 + 0.171083i
\(276\) −64.7944 −0.234762
\(277\) −21.4676 21.4676i −0.0775005 0.0775005i 0.667294 0.744794i \(-0.267452\pi\)
−0.744794 + 0.667294i \(0.767452\pi\)
\(278\) −132.183 + 132.183i −0.475480 + 0.475480i
\(279\) 81.0389i 0.290462i
\(280\) −36.8976 + 6.20997i −0.131777 + 0.0221785i
\(281\) 74.2011 0.264061 0.132030 0.991246i \(-0.457850\pi\)
0.132030 + 0.991246i \(0.457850\pi\)
\(282\) −23.0054 23.0054i −0.0815793 0.0815793i
\(283\) −322.473 + 322.473i −1.13948 + 1.13948i −0.150937 + 0.988543i \(0.548229\pi\)
−0.988543 + 0.150937i \(0.951771\pi\)
\(284\) 94.4079i 0.332422i
\(285\) −122.771 87.3989i −0.430776 0.306663i
\(286\) 172.516 0.603203
\(287\) −99.3217 99.3217i −0.346069 0.346069i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 243.146i 0.841336i
\(290\) 154.712 217.327i 0.533489 0.749403i
\(291\) 224.149 0.770271
\(292\) −62.4143 62.4143i −0.213747 0.213747i
\(293\) −145.754 + 145.754i −0.497456 + 0.497456i −0.910645 0.413189i \(-0.864415\pi\)
0.413189 + 0.910645i \(0.364415\pi\)
\(294\) 17.1464i 0.0583212i
\(295\) −52.2547 310.480i −0.177134 1.05248i
\(296\) 45.4562 0.153568
\(297\) −21.1240 21.1240i −0.0711245 0.0711245i
\(298\) 255.329 255.329i 0.856809 0.856809i
\(299\) 396.874i 1.32734i
\(300\) −77.9086 37.8186i −0.259695 0.126062i
\(301\) 138.835 0.461246
\(302\) 210.524 + 210.524i 0.697098 + 0.697098i
\(303\) 223.951 223.951i 0.739111 0.739111i
\(304\) 69.6066i 0.228969i
\(305\) 8.25845 1.38992i 0.0270769 0.00455711i
\(306\) 28.7293 0.0938865
\(307\) −308.104 308.104i −1.00360 1.00360i −0.999994 0.00360237i \(-0.998853\pi\)
−0.00360237 0.999994i \(-0.501147\pi\)
\(308\) 21.5116 21.5116i 0.0698429 0.0698429i
\(309\) 114.202i 0.369584i
\(310\) −155.608 110.775i −0.501962 0.357339i
\(311\) −29.1191 −0.0936304 −0.0468152 0.998904i \(-0.514907\pi\)
−0.0468152 + 0.998904i \(0.514907\pi\)
\(312\) 73.5016 + 73.5016i 0.235582 + 0.235582i
\(313\) 12.1714 12.1714i 0.0388863 0.0388863i −0.687396 0.726283i \(-0.741246\pi\)
0.726283 + 0.687396i \(0.241246\pi\)
\(314\) 363.342i 1.15714i
\(315\) −23.0158 + 32.3307i −0.0730659 + 0.102637i
\(316\) −214.267 −0.678061
\(317\) 219.192 + 219.192i 0.691456 + 0.691456i 0.962552 0.271096i \(-0.0873862\pi\)
−0.271096 + 0.962552i \(0.587386\pi\)
\(318\) 107.532 107.532i 0.338150 0.338150i
\(319\) 216.901i 0.679941i
\(320\) 6.63874 + 39.4452i 0.0207461 + 0.123266i
\(321\) −141.005 −0.439269
\(322\) −49.4876 49.4876i −0.153688 0.153688i
\(323\) −83.3228 + 83.3228i −0.257965 + 0.257965i
\(324\) 18.0000i 0.0555556i
\(325\) 231.644 477.201i 0.712751 1.46831i
\(326\) −311.127 −0.954376
\(327\) 251.384 + 251.384i 0.768759 + 0.768759i
\(328\) −106.179 + 106.179i −0.323718 + 0.323718i
\(329\) 35.1413i 0.106812i
\(330\) 69.4367 11.6864i 0.210414 0.0354133i
\(331\) 276.111 0.834171 0.417086 0.908867i \(-0.363052\pi\)
0.417086 + 0.908867i \(0.363052\pi\)
\(332\) 36.4729 + 36.4729i 0.109858 + 0.109858i
\(333\) 34.0921 34.0921i 0.102379 0.102379i
\(334\) 152.158i 0.455562i
\(335\) −164.122 116.836i −0.489916 0.348764i
\(336\) 18.3303 0.0545545
\(337\) 276.393 + 276.393i 0.820157 + 0.820157i 0.986130 0.165973i \(-0.0530766\pi\)
−0.165973 + 0.986130i \(0.553077\pi\)
\(338\) −281.207 + 281.207i −0.831973 + 0.831973i
\(339\) 79.8623i 0.235582i
\(340\) −39.2711 + 55.1650i −0.115503 + 0.162250i
\(341\) 155.303 0.455435
\(342\) 52.2050 + 52.2050i 0.152646 + 0.152646i
\(343\) −13.0958 + 13.0958i −0.0381802 + 0.0381802i
\(344\) 148.421i 0.431456i
\(345\) −26.8846 159.739i −0.0779263 0.463013i
\(346\) −57.8647 −0.167239
\(347\) −158.084 158.084i −0.455573 0.455573i 0.441626 0.897199i \(-0.354402\pi\)
−0.897199 + 0.441626i \(0.854402\pi\)
\(348\) −92.4121 + 92.4121i −0.265552 + 0.265552i
\(349\) 452.412i 1.29631i 0.761508 + 0.648155i \(0.224459\pi\)
−0.761508 + 0.648155i \(0.775541\pi\)
\(350\) −30.6192 88.3881i −0.0874835 0.252538i
\(351\) 110.252 0.314109
\(352\) −22.9969 22.9969i −0.0653320 0.0653320i
\(353\) 481.681 481.681i 1.36453 1.36453i 0.496495 0.868039i \(-0.334620\pi\)
0.868039 0.496495i \(-0.165380\pi\)
\(354\) 154.243i 0.435714i
\(355\) −232.746 + 39.1718i −0.655624 + 0.110343i
\(356\) 349.351 0.981323
\(357\) 21.9423 + 21.9423i 0.0614631 + 0.0614631i
\(358\) −126.849 + 126.849i −0.354327 + 0.354327i
\(359\) 485.514i 1.35241i 0.736716 + 0.676203i \(0.236376\pi\)
−0.736716 + 0.676203i \(0.763624\pi\)
\(360\) 34.5630 + 24.6049i 0.0960083 + 0.0683469i
\(361\) 58.1823 0.161170
\(362\) −307.681 307.681i −0.849947 0.849947i
\(363\) 107.712 107.712i 0.296727 0.296727i
\(364\) 112.276i 0.308449i
\(365\) 127.975 179.769i 0.350615 0.492517i
\(366\) −4.10270 −0.0112096
\(367\) 205.331 + 205.331i 0.559486 + 0.559486i 0.929161 0.369675i \(-0.120531\pi\)
−0.369675 + 0.929161i \(0.620531\pi\)
\(368\) −52.9044 + 52.9044i −0.143762 + 0.143762i
\(369\) 159.269i 0.431623i
\(370\) 18.8607 + 112.064i 0.0509750 + 0.302877i
\(371\) 164.257 0.442742
\(372\) 66.1680 + 66.1680i 0.177871 + 0.177871i
\(373\) −24.9803 + 24.9803i −0.0669714 + 0.0669714i −0.739799 0.672828i \(-0.765079\pi\)
0.672828 + 0.739799i \(0.265079\pi\)
\(374\) 55.0569i 0.147211i
\(375\) 60.9093 207.762i 0.162425 0.554032i
\(376\) −37.5676 −0.0999139
\(377\) −566.037 566.037i −1.50142 1.50142i
\(378\) 13.7477 13.7477i 0.0363696 0.0363696i
\(379\) 356.423i 0.940429i −0.882552 0.470215i \(-0.844177\pi\)
0.882552 0.470215i \(-0.155823\pi\)
\(380\) −171.603 + 28.8813i −0.451587 + 0.0760034i
\(381\) 254.099 0.666926
\(382\) −71.4969 71.4969i −0.187165 0.187165i
\(383\) 480.677 480.677i 1.25503 1.25503i 0.301596 0.953436i \(-0.402481\pi\)
0.953436 0.301596i \(-0.0975194\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 61.9588 + 44.1075i 0.160932 + 0.114565i
\(386\) 310.695 0.804908
\(387\) −111.316 111.316i −0.287637 0.287637i
\(388\) 183.017 183.017i 0.471693 0.471693i
\(389\) 169.784i 0.436461i −0.975897 0.218231i \(-0.929971\pi\)
0.975897 0.218231i \(-0.0700285\pi\)
\(390\) −150.708 + 211.703i −0.386431 + 0.542828i
\(391\) −126.659 −0.323935
\(392\) 14.0000 + 14.0000i 0.0357143 + 0.0357143i
\(393\) −193.508 + 193.508i −0.492387 + 0.492387i
\(394\) 381.040i 0.967107i
\(395\) −88.9040 528.239i −0.225073 1.33731i
\(396\) −34.4953 −0.0871093
\(397\) −66.1208 66.1208i −0.166551 0.166551i 0.618910 0.785462i \(-0.287574\pi\)
−0.785462 + 0.618910i \(0.787574\pi\)
\(398\) 173.246 173.246i 0.435291 0.435291i
\(399\) 79.7444i 0.199861i
\(400\) −94.4909 + 32.7333i −0.236227 + 0.0818334i
\(401\) −213.860 −0.533318 −0.266659 0.963791i \(-0.585920\pi\)
−0.266659 + 0.963791i \(0.585920\pi\)
\(402\) 69.7883 + 69.7883i 0.173603 + 0.173603i
\(403\) −405.288 + 405.288i −1.00568 + 1.00568i
\(404\) 365.710i 0.905223i
\(405\) 44.3759 7.46858i 0.109570 0.0184409i
\(406\) −141.162 −0.347689
\(407\) −65.3344 65.3344i −0.160527 0.160527i
\(408\) 23.4573 23.4573i 0.0574935 0.0574935i
\(409\) 300.366i 0.734391i −0.930144 0.367196i \(-0.880318\pi\)
0.930144 0.367196i \(-0.119682\pi\)
\(410\) −305.823 217.711i −0.745910 0.531002i
\(411\) 90.5267 0.220260
\(412\) −93.2452 93.2452i −0.226323 0.226323i
\(413\) −117.805 + 117.805i −0.285242 + 0.285242i
\(414\) 79.3566i 0.191683i
\(415\) −74.7843 + 105.051i −0.180203 + 0.253135i
\(416\) 120.028 0.288528
\(417\) 161.891 + 161.891i 0.388228 + 0.388228i
\(418\) 100.046 100.046i 0.239344 0.239344i
\(419\) 696.907i 1.66326i 0.555328 + 0.831632i \(0.312593\pi\)
−0.555328 + 0.831632i \(0.687407\pi\)
\(420\) 7.60563 + 45.1902i 0.0181087 + 0.107596i
\(421\) −114.980 −0.273111 −0.136555 0.990632i \(-0.543603\pi\)
−0.136555 + 0.990632i \(0.543603\pi\)
\(422\) −53.9193 53.9193i −0.127771 0.127771i
\(423\) −28.1757 + 28.1757i −0.0666092 + 0.0666092i
\(424\) 175.598i 0.414147i
\(425\) −152.294 73.9270i −0.358339 0.173946i
\(426\) 115.626 0.271422
\(427\) −3.13349 3.13349i −0.00733838 0.00733838i
\(428\) −115.130 + 115.130i −0.268996 + 0.268996i
\(429\) 211.288i 0.492513i
\(430\) 365.906 61.5830i 0.850945 0.143216i
\(431\) −724.694 −1.68143 −0.840713 0.541481i \(-0.817864\pi\)
−0.840713 + 0.541481i \(0.817864\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) 100.327 100.327i 0.231703 0.231703i −0.581700 0.813403i \(-0.697612\pi\)
0.813403 + 0.581700i \(0.197612\pi\)
\(434\) 101.073i 0.232888i
\(435\) −266.170 189.482i −0.611885 0.435592i
\(436\) 410.509 0.941533
\(437\) −230.156 230.156i −0.526673 0.526673i
\(438\) −76.4415 + 76.4415i −0.174524 + 0.174524i
\(439\) 685.890i 1.56239i 0.624286 + 0.781195i \(0.285390\pi\)
−0.624286 + 0.781195i \(0.714610\pi\)
\(440\) 47.1529 66.2367i 0.107166 0.150538i
\(441\) 21.0000 0.0476190
\(442\) 143.679 + 143.679i 0.325066 + 0.325066i
\(443\) 339.752 339.752i 0.766935 0.766935i −0.210631 0.977566i \(-0.567552\pi\)
0.977566 + 0.210631i \(0.0675517\pi\)
\(444\) 55.6722i 0.125388i
\(445\) 144.953 + 861.264i 0.325737 + 1.93543i
\(446\) 293.025 0.657006
\(447\) −312.713 312.713i −0.699581 0.699581i
\(448\) 14.9666 14.9666i 0.0334077 0.0334077i
\(449\) 226.637i 0.504758i 0.967628 + 0.252379i \(0.0812130\pi\)
−0.967628 + 0.252379i \(0.918787\pi\)
\(450\) −46.3182 + 95.4182i −0.102929 + 0.212040i
\(451\) 305.224 0.676772
\(452\) 65.2073 + 65.2073i 0.144264 + 0.144264i
\(453\) 257.838 257.838i 0.569178 0.569178i
\(454\) 325.794i 0.717607i
\(455\) −276.796 + 46.5855i −0.608343 + 0.102386i
\(456\) 85.2504 0.186953
\(457\) −266.282 266.282i −0.582675 0.582675i 0.352963 0.935637i \(-0.385174\pi\)
−0.935637 + 0.352963i \(0.885174\pi\)
\(458\) 176.209 176.209i 0.384735 0.384735i
\(459\) 35.1860i 0.0766580i
\(460\) −152.378 108.476i −0.331256 0.235816i
\(461\) −121.199 −0.262905 −0.131453 0.991322i \(-0.541964\pi\)
−0.131453 + 0.991322i \(0.541964\pi\)
\(462\) −26.3462 26.3462i −0.0570265 0.0570265i
\(463\) −565.604 + 565.604i −1.22161 + 1.22161i −0.254547 + 0.967061i \(0.581926\pi\)
−0.967061 + 0.254547i \(0.918074\pi\)
\(464\) 150.908i 0.325234i
\(465\) −135.671 + 190.580i −0.291766 + 0.409850i
\(466\) 36.7231 0.0788049
\(467\) −279.536 279.536i −0.598578 0.598578i 0.341356 0.939934i \(-0.389114\pi\)
−0.939934 + 0.341356i \(0.889114\pi\)
\(468\) 90.0207 90.0207i 0.192352 0.192352i
\(469\) 106.603i 0.227299i
\(470\) −15.5876 92.6165i −0.0331651 0.197056i
\(471\) 445.001 0.944801
\(472\) 125.939 + 125.939i 0.266819 + 0.266819i
\(473\) −213.326 + 213.326i −0.451006 + 0.451006i
\(474\) 262.423i 0.553634i
\(475\) −142.404 411.075i −0.299797 0.865420i
\(476\) 35.8317 0.0752767
\(477\) −131.699 131.699i −0.276098 0.276098i
\(478\) 275.093 275.093i 0.575509 0.575509i
\(479\) 101.987i 0.212916i 0.994317 + 0.106458i \(0.0339510\pi\)
−0.994317 + 0.106458i \(0.966049\pi\)
\(480\) 48.3104 8.13076i 0.100647 0.0169391i
\(481\) 341.000 0.708939
\(482\) −338.925 338.925i −0.703164 0.703164i
\(483\) −60.6096 + 60.6096i −0.125486 + 0.125486i
\(484\) 175.893i 0.363415i
\(485\) 527.134 + 375.259i 1.08687 + 0.773729i
\(486\) −22.0454 −0.0453609
\(487\) 250.272 + 250.272i 0.513907 + 0.513907i 0.915721 0.401815i \(-0.131620\pi\)
−0.401815 + 0.915721i \(0.631620\pi\)
\(488\) −3.34984 + 3.34984i −0.00686442 + 0.00686442i
\(489\) 381.051i 0.779245i
\(490\) −28.7057 + 40.3235i −0.0585830 + 0.0822928i
\(491\) −648.021 −1.31980 −0.659899 0.751355i \(-0.729401\pi\)
−0.659899 + 0.751355i \(0.729401\pi\)
\(492\) 130.043 + 130.043i 0.264314 + 0.264314i
\(493\) −180.645 + 180.645i −0.366421 + 0.366421i
\(494\) 522.170i 1.05702i
\(495\) −14.3128 85.0422i −0.0289148 0.171802i
\(496\) 108.052 0.217846
\(497\) 88.3105 + 88.3105i 0.177687 + 0.177687i
\(498\) 44.6700 44.6700i 0.0896989 0.0896989i
\(499\) 377.798i 0.757110i 0.925579 + 0.378555i \(0.123579\pi\)
−0.925579 + 0.378555i \(0.876421\pi\)
\(500\) −119.905 219.369i −0.239809 0.438738i
\(501\) −186.354 −0.371965
\(502\) −72.1187 72.1187i −0.143663 0.143663i
\(503\) −221.145 + 221.145i −0.439651 + 0.439651i −0.891895 0.452243i \(-0.850624\pi\)
0.452243 + 0.891895i \(0.350624\pi\)
\(504\) 22.4499i 0.0445435i
\(505\) 901.595 151.741i 1.78534 0.300477i
\(506\) 152.079 0.300552
\(507\) 344.407 + 344.407i 0.679303 + 0.679303i
\(508\) 207.471 207.471i 0.408407 0.408407i
\(509\) 586.753i 1.15276i −0.817183 0.576378i \(-0.804465\pi\)
0.817183 0.576378i \(-0.195535\pi\)
\(510\) 67.5630 + 48.0971i 0.132476 + 0.0943080i
\(511\) −116.766 −0.228506
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) 63.9378 63.9378i 0.124635 0.124635i
\(514\) 24.4511i 0.0475703i
\(515\) 191.191 268.569i 0.371244 0.521494i
\(516\) −181.778 −0.352282
\(517\) 53.9961 + 53.9961i 0.104441 + 0.104441i
\(518\) 42.5204 42.5204i 0.0820857 0.0820857i
\(519\) 70.8694i 0.136550i
\(520\) 49.8020 + 295.907i 0.0957731 + 0.569052i
\(521\) −466.427 −0.895253 −0.447626 0.894221i \(-0.647731\pi\)
−0.447626 + 0.894221i \(0.647731\pi\)
\(522\) 113.181 + 113.181i 0.216822 + 0.216822i
\(523\) 303.656 303.656i 0.580604 0.580604i −0.354465 0.935069i \(-0.615337\pi\)
0.935069 + 0.354465i \(0.115337\pi\)
\(524\) 315.998i 0.603049i
\(525\) −108.253 + 37.5008i −0.206196 + 0.0714300i
\(526\) −551.467 −1.04842
\(527\) 129.344 + 129.344i 0.245434 + 0.245434i
\(528\) −28.1653 + 28.1653i −0.0533434 + 0.0533434i
\(529\) 179.140i 0.338639i
\(530\) 432.907 72.8595i 0.816806 0.137471i
\(531\) 188.908 0.355759
\(532\) 65.1110 + 65.1110i 0.122389 + 0.122389i
\(533\) −796.528 + 796.528i −1.49442 + 1.49442i
\(534\) 427.866i 0.801247i
\(535\) −331.604 236.064i −0.619820 0.441241i
\(536\) 113.964 0.212619
\(537\) 155.358 + 155.358i 0.289307 + 0.289307i
\(538\) −275.988 + 275.988i −0.512989 + 0.512989i
\(539\) 40.2445i 0.0746652i
\(540\) 30.1347 42.3308i 0.0558050 0.0783904i
\(541\) 465.245 0.859973 0.429986 0.902835i \(-0.358518\pi\)
0.429986 + 0.902835i \(0.358518\pi\)
\(542\) −295.698 295.698i −0.545568 0.545568i
\(543\) −376.831 + 376.831i −0.693979 + 0.693979i
\(544\) 38.3057i 0.0704149i
\(545\) 170.329 + 1012.04i 0.312530 + 1.85695i
\(546\) 137.509 0.251848
\(547\) 492.529 + 492.529i 0.900419 + 0.900419i 0.995472 0.0950533i \(-0.0303021\pi\)
−0.0950533 + 0.995472i \(0.530302\pi\)
\(548\) 73.9148 73.9148i 0.134881 0.134881i
\(549\) 5.02476i 0.00915257i
\(550\) 182.860 + 88.7644i 0.332473 + 0.161390i
\(551\) −656.514 −1.19150
\(552\) 64.7944 + 64.7944i 0.117381 + 0.117381i
\(553\) −200.429 + 200.429i −0.362439 + 0.362439i
\(554\) 42.9353i 0.0775005i
\(555\) 137.250 23.0996i 0.247298 0.0416209i
\(556\) 264.367 0.475480
\(557\) 395.342 + 395.342i 0.709771 + 0.709771i 0.966487 0.256716i \(-0.0826405\pi\)
−0.256716 + 0.966487i \(0.582641\pi\)
\(558\) 81.0389 81.0389i 0.145231 0.145231i
\(559\) 1113.41i 1.99179i
\(560\) 43.1076 + 30.6877i 0.0769779 + 0.0547994i
\(561\) −67.4307 −0.120197
\(562\) −74.2011 74.2011i −0.132030 0.132030i
\(563\) 447.005 447.005i 0.793971 0.793971i −0.188167 0.982137i \(-0.560254\pi\)
0.982137 + 0.188167i \(0.0602545\pi\)
\(564\) 46.0107i 0.0815793i
\(565\) −133.701 + 187.813i −0.236640 + 0.332413i
\(566\) 644.946 1.13948
\(567\) −16.8375 16.8375i −0.0296957 0.0296957i
\(568\) 94.4079 94.4079i 0.166211 0.166211i
\(569\) 39.2969i 0.0690631i −0.999404 0.0345316i \(-0.989006\pi\)
0.999404 0.0345316i \(-0.0109939\pi\)
\(570\) 35.3722 + 210.170i 0.0620565 + 0.368719i
\(571\) −824.326 −1.44365 −0.721826 0.692074i \(-0.756697\pi\)
−0.721826 + 0.692074i \(0.756697\pi\)
\(572\) −172.516 172.516i −0.301602 0.301602i
\(573\) −87.5654 + 87.5654i −0.152819 + 0.152819i
\(574\) 198.643i 0.346069i
\(575\) 204.203 420.670i 0.355136 0.731600i
\(576\) −24.0000 −0.0416667
\(577\) 645.287 + 645.287i 1.11835 + 1.11835i 0.991984 + 0.126365i \(0.0403311\pi\)
0.126365 + 0.991984i \(0.459669\pi\)
\(578\) −243.146 + 243.146i −0.420668 + 0.420668i
\(579\) 380.522i 0.657205i
\(580\) −372.039 + 62.6151i −0.641446 + 0.107957i
\(581\) 68.2346 0.117443
\(582\) −224.149 224.149i −0.385135 0.385135i
\(583\) −252.388 + 252.388i −0.432913 + 0.432913i
\(584\) 124.829i 0.213747i
\(585\) 259.282 + 184.579i 0.443217 + 0.315520i
\(586\) 291.509 0.497456
\(587\) 512.978 + 512.978i 0.873898 + 0.873898i 0.992895 0.118997i \(-0.0379679\pi\)
−0.118997 + 0.992895i \(0.537968\pi\)
\(588\) 17.1464 17.1464i 0.0291606 0.0291606i
\(589\) 470.070i 0.798082i
\(590\) −258.226 + 362.735i −0.437670 + 0.614805i
\(591\) −466.677 −0.789639
\(592\) −45.4562 45.4562i −0.0767841 0.0767841i
\(593\) −379.753 + 379.753i −0.640393 + 0.640393i −0.950652 0.310259i \(-0.899584\pi\)
0.310259 + 0.950652i \(0.399584\pi\)
\(594\) 42.2479i 0.0711245i
\(595\) 14.8673 + 88.3369i 0.0249871 + 0.148465i
\(596\) −510.658 −0.856809
\(597\) −212.182 212.182i −0.355414 0.355414i
\(598\) −396.874 + 396.874i −0.663669 + 0.663669i
\(599\) 167.160i 0.279065i −0.990218 0.139532i \(-0.955440\pi\)
0.990218 0.139532i \(-0.0445599\pi\)
\(600\) 40.0900 + 115.727i 0.0668167 + 0.192879i
\(601\) 649.442 1.08060 0.540302 0.841472i \(-0.318310\pi\)
0.540302 + 0.841472i \(0.318310\pi\)
\(602\) −138.835 138.835i −0.230623 0.230623i
\(603\) 85.4728 85.4728i 0.141746 0.141746i
\(604\) 421.047i 0.697098i
\(605\) 433.634 72.9818i 0.716750 0.120631i
\(606\) −447.901 −0.739111
\(607\) −342.997 342.997i −0.565069 0.565069i 0.365674 0.930743i \(-0.380839\pi\)
−0.930743 + 0.365674i \(0.880839\pi\)
\(608\) 69.6066 69.6066i 0.114485 0.114485i
\(609\) 172.887i 0.283887i
\(610\) −9.64837 6.86853i −0.0158170 0.0112599i
\(611\) −281.822 −0.461247
\(612\) −28.7293 28.7293i −0.0469432 0.0469432i
\(613\) −311.569 + 311.569i −0.508270 + 0.508270i −0.913995 0.405725i \(-0.867019\pi\)
0.405725 + 0.913995i \(0.367019\pi\)
\(614\) 616.208i 1.00360i
\(615\) −266.640 + 374.555i −0.433561 + 0.609033i
\(616\) −43.0232 −0.0698429
\(617\) 442.165 + 442.165i 0.716636 + 0.716636i 0.967915 0.251279i \(-0.0808510\pi\)
−0.251279 + 0.967915i \(0.580851\pi\)
\(618\) −114.202 + 114.202i −0.184792 + 0.184792i
\(619\) 375.146i 0.606052i −0.952982 0.303026i \(-0.902003\pi\)
0.952982 0.303026i \(-0.0979968\pi\)
\(620\) 44.8330 + 266.383i 0.0723113 + 0.429650i
\(621\) 97.1916 0.156508
\(622\) 29.1191 + 29.1191i 0.0468152 + 0.0468152i
\(623\) 326.788 326.788i 0.524539 0.524539i
\(624\) 147.003i 0.235582i
\(625\) 491.066 386.625i 0.785706 0.618601i
\(626\) −24.3428 −0.0388863
\(627\) −122.531 122.531i −0.195424 0.195424i
\(628\) 363.342 363.342i 0.578570 0.578570i
\(629\) 108.827i 0.173016i
\(630\) 55.3465 9.31496i 0.0878515 0.0147857i
\(631\) −973.951 −1.54350 −0.771752 0.635924i \(-0.780619\pi\)
−0.771752 + 0.635924i \(0.780619\pi\)
\(632\) 214.267 + 214.267i 0.339030 + 0.339030i
\(633\) −66.0374 + 66.0374i −0.104324 + 0.104324i
\(634\) 438.383i 0.691456i
\(635\) 597.568 + 425.400i 0.941051 + 0.669921i
\(636\) −215.063 −0.338150
\(637\) 105.024 + 105.024i 0.164873 + 0.164873i
\(638\) 216.901 216.901i 0.339971 0.339971i
\(639\) 141.612i 0.221615i
\(640\) 32.8065 46.0840i 0.0512602 0.0720062i
\(641\) 487.398 0.760371 0.380185 0.924910i \(-0.375860\pi\)
0.380185 + 0.924910i \(0.375860\pi\)
\(642\) 141.005 + 141.005i 0.219634 + 0.219634i
\(643\) 554.739 554.739i 0.862736 0.862736i −0.128919 0.991655i \(-0.541151\pi\)
0.991655 + 0.128919i \(0.0411509\pi\)
\(644\) 98.9751i 0.153688i
\(645\) −75.4235 448.142i −0.116936 0.694793i
\(646\) 166.646 0.257965
\(647\) 337.971 + 337.971i 0.522367 + 0.522367i 0.918285 0.395919i \(-0.129574\pi\)
−0.395919 + 0.918285i \(0.629574\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 362.025i 0.557819i
\(650\) −708.845 + 245.557i −1.09053 + 0.377779i
\(651\) 123.789 0.190152
\(652\) 311.127 + 311.127i 0.477188 + 0.477188i
\(653\) 379.091 379.091i 0.580537 0.580537i −0.354514 0.935051i \(-0.615354\pi\)
0.935051 + 0.354514i \(0.115354\pi\)
\(654\) 502.768i 0.768759i
\(655\) −779.038 + 131.114i −1.18937 + 0.200174i
\(656\) 212.359 0.323718
\(657\) 93.6214 + 93.6214i 0.142498 + 0.142498i
\(658\) −35.1413 + 35.1413i −0.0534062 + 0.0534062i
\(659\) 932.566i 1.41512i −0.706652 0.707561i \(-0.749795\pi\)
0.706652 0.707561i \(-0.250205\pi\)
\(660\) −81.1231 57.7503i −0.122914 0.0875005i
\(661\) 435.268 0.658500 0.329250 0.944243i \(-0.393204\pi\)
0.329250 + 0.944243i \(0.393204\pi\)
\(662\) −276.111 276.111i −0.417086 0.417086i
\(663\) 175.971 175.971i 0.265416 0.265416i
\(664\) 72.9459i 0.109858i
\(665\) −133.504 + 187.536i −0.200758 + 0.282009i
\(666\) −68.1843 −0.102379
\(667\) −498.983 498.983i −0.748100 0.748100i
\(668\) −152.158 + 152.158i −0.227781 + 0.227781i
\(669\) 358.881i 0.536443i
\(670\) 47.2860 + 280.958i 0.0705761 + 0.419340i
\(671\) 9.62948 0.0143509
\(672\) −18.3303 18.3303i −0.0272772 0.0272772i
\(673\) 268.394 268.394i 0.398803 0.398803i −0.479008 0.877811i \(-0.659003\pi\)
0.877811 + 0.479008i \(0.159003\pi\)
\(674\) 552.786i 0.820157i
\(675\) 116.863 + 56.7279i 0.173130 + 0.0840414i
\(676\) 562.414 0.831973
\(677\) −317.565 317.565i −0.469076 0.469076i 0.432539 0.901615i \(-0.357618\pi\)
−0.901615 + 0.432539i \(0.857618\pi\)
\(678\) 79.8623 79.8623i 0.117791 0.117791i
\(679\) 342.393i 0.504261i
\(680\) 94.4361 15.8938i 0.138877 0.0233733i
\(681\) −399.014 −0.585924
\(682\) −155.303 155.303i −0.227718 0.227718i
\(683\) 750.781 750.781i 1.09924 1.09924i 0.104741 0.994500i \(-0.466599\pi\)
0.994500 0.104741i \(-0.0334012\pi\)
\(684\) 104.410i 0.152646i
\(685\) 212.893 + 151.555i 0.310793 + 0.221249i
\(686\) 26.1916 0.0381802
\(687\) −215.811 215.811i −0.314135 0.314135i
\(688\) −148.421 + 148.421i −0.215728 + 0.215728i
\(689\) 1317.29i 1.91189i
\(690\) −132.855 + 186.624i −0.192543 + 0.270470i
\(691\) −630.352 −0.912231 −0.456116 0.889921i \(-0.650760\pi\)
−0.456116 + 0.889921i \(0.650760\pi\)
\(692\) 57.8647 + 57.8647i 0.0836194 + 0.0836194i
\(693\) −32.2674 + 32.2674i −0.0465619 + 0.0465619i
\(694\) 316.168i 0.455573i
\(695\) 109.691 + 651.751i 0.157829 + 0.937771i
\(696\) 184.824 0.265552
\(697\) 254.205 + 254.205i 0.364712 + 0.364712i
\(698\) 452.412 452.412i 0.648155 0.648155i
\(699\) 44.9764i 0.0643440i
\(700\) −57.7689 + 119.007i −0.0825270 + 0.170011i
\(701\) −1143.23 −1.63085 −0.815425 0.578863i \(-0.803497\pi\)
−0.815425 + 0.578863i \(0.803497\pi\)
\(702\) −110.252 110.252i −0.157055 0.157055i
\(703\) 197.753 197.753i 0.281299 0.281299i
\(704\) 45.9937i 0.0653320i
\(705\) −113.432 + 19.0908i −0.160896 + 0.0270792i
\(706\) −963.362 −1.36453
\(707\) −342.090 342.090i −0.483862 0.483862i
\(708\) 154.243 154.243i 0.217857 0.217857i
\(709\) 120.909i 0.170535i 0.996358 + 0.0852674i \(0.0271745\pi\)
−0.996358 + 0.0852674i \(0.972826\pi\)
\(710\) 271.918 + 193.575i 0.382983 + 0.272640i
\(711\) 321.401 0.452040
\(712\) −349.351 349.351i −0.490661 0.490661i
\(713\) −357.276 + 357.276i −0.501089 + 0.501089i
\(714\) 43.8847i 0.0614631i
\(715\) 353.728 496.889i 0.494725 0.694950i
\(716\) 253.698 0.354327
\(717\) −336.919 336.919i −0.469901 0.469901i
\(718\) 485.514 485.514i 0.676203 0.676203i
\(719\) 157.658i 0.219274i −0.993972 0.109637i \(-0.965031\pi\)
0.993972 0.109637i \(-0.0349688\pi\)
\(720\) −9.95811 59.1679i −0.0138307 0.0821776i
\(721\) −174.446 −0.241950
\(722\) −58.1823 58.1823i −0.0805849 0.0805849i
\(723\) −415.097 + 415.097i −0.574131 + 0.574131i
\(724\) 615.362i 0.849947i
\(725\) −308.734 891.217i −0.425839 1.22926i
\(726\) −215.424 −0.296727
\(727\) 45.5944 + 45.5944i 0.0627159 + 0.0627159i 0.737769 0.675053i \(-0.235879\pi\)
−0.675053 + 0.737769i \(0.735879\pi\)
\(728\) 112.276 112.276i 0.154225 0.154225i
\(729\) 27.0000i 0.0370370i
\(730\) −307.743 + 51.7940i −0.421566 + 0.0709507i
\(731\) −355.335 −0.486095
\(732\) 4.10270 + 4.10270i 0.00560478 + 0.00560478i
\(733\) 5.02444 5.02444i 0.00685462 0.00685462i −0.703671 0.710526i \(-0.748457\pi\)
0.710526 + 0.703671i \(0.248457\pi\)
\(734\) 410.663i 0.559486i
\(735\) 49.3860 + 35.1571i 0.0671918 + 0.0478328i
\(736\) 105.809 0.143762
\(737\) −163.801 163.801i −0.222253 0.222253i
\(738\) 159.269 159.269i 0.215812 0.215812i
\(739\) 1207.29i 1.63368i −0.576865 0.816839i \(-0.695724\pi\)
0.576865 0.816839i \(-0.304276\pi\)
\(740\) 93.2037 130.925i 0.125951 0.176926i
\(741\) 639.525 0.863056
\(742\) −164.257 164.257i −0.221371 0.221371i
\(743\) −162.402 + 162.402i −0.218577 + 0.218577i −0.807898 0.589322i \(-0.799395\pi\)
0.589322 + 0.807898i \(0.299395\pi\)
\(744\) 132.336i 0.177871i
\(745\) −211.883 1258.94i −0.284407 1.68985i
\(746\) 49.9606 0.0669714
\(747\) −54.7094 54.7094i −0.0732388 0.0732388i
\(748\) −55.0569 + 55.0569i −0.0736055 + 0.0736055i
\(749\) 215.389i 0.287569i
\(750\) −268.671 + 146.853i −0.358228 + 0.195804i
\(751\) −1054.43 −1.40404 −0.702020 0.712157i \(-0.747718\pi\)
−0.702020 + 0.712157i \(0.747718\pi\)
\(752\) 37.5676 + 37.5676i 0.0499569 + 0.0499569i
\(753\) −88.3270 + 88.3270i −0.117300 + 0.117300i
\(754\) 1132.07i 1.50142i
\(755\) 1038.02 174.701i 1.37486 0.231393i
\(756\) −27.4955 −0.0363696
\(757\) 166.416 + 166.416i 0.219836 + 0.219836i 0.808429 0.588593i \(-0.200318\pi\)
−0.588593 + 0.808429i \(0.700318\pi\)
\(758\) −356.423 + 356.423i −0.470215 + 0.470215i
\(759\) 186.259i 0.245400i
\(760\) 200.484 + 142.722i 0.263795 + 0.187792i
\(761\) 1422.52 1.86928 0.934640 0.355596i \(-0.115722\pi\)
0.934640 + 0.355596i \(0.115722\pi\)
\(762\) −254.099 254.099i −0.333463 0.333463i
\(763\) 383.996 383.996i 0.503271 0.503271i
\(764\) 142.994i 0.187165i
\(765\) 58.9067 82.7474i 0.0770022 0.108167i
\(766\) −961.354 −1.25503
\(767\) 944.758 + 944.758i 1.23176 + 1.23176i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 502.250i 0.653121i −0.945176 0.326560i \(-0.894110\pi\)
0.945176 0.326560i \(-0.105890\pi\)
\(770\) −17.8512 106.066i −0.0231834 0.137748i
\(771\) 29.9464 0.0388410
\(772\) −310.695 310.695i −0.402454 0.402454i