Properties

Label 403.2.h.b.118.12
Level 403
Weight 2
Character 403.118
Analytic conductor 3.218
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.h (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 118.12
Character \(\chi\) \(=\) 403.118
Dual form 403.2.h.b.222.12

$q$-expansion

\(f(q)\) \(=\) \(q+1.35626 q^{2} +(0.0933728 + 0.161726i) q^{3} -0.160553 q^{4} +(1.08899 - 1.88618i) q^{5} +(0.126638 + 0.219343i) q^{6} +(-1.43912 - 2.49263i) q^{7} -2.93028 q^{8} +(1.48256 - 2.56787i) q^{9} +O(q^{10})\) \(q+1.35626 q^{2} +(0.0933728 + 0.161726i) q^{3} -0.160553 q^{4} +(1.08899 - 1.88618i) q^{5} +(0.126638 + 0.219343i) q^{6} +(-1.43912 - 2.49263i) q^{7} -2.93028 q^{8} +(1.48256 - 2.56787i) q^{9} +(1.47695 - 2.55816i) q^{10} +(1.47628 - 2.55699i) q^{11} +(-0.0149913 - 0.0259657i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-1.95182 - 3.38066i) q^{14} +0.406727 q^{15} -3.65312 q^{16} +(0.832376 + 1.44172i) q^{17} +(2.01074 - 3.48271i) q^{18} +(3.39325 + 5.87729i) q^{19} +(-0.174840 + 0.302832i) q^{20} +(0.268749 - 0.465488i) q^{21} +(2.00222 - 3.46795i) q^{22} +4.72909 q^{23} +(-0.273608 - 0.473903i) q^{24} +(0.128215 + 0.222075i) q^{25} +(-0.678131 + 1.17456i) q^{26} +1.11396 q^{27} +(0.231056 + 0.400200i) q^{28} -1.93062 q^{29} +0.551628 q^{30} +(-4.88752 - 2.66686i) q^{31} +0.905970 q^{32} +0.551377 q^{33} +(1.12892 + 1.95535i) q^{34} -6.26873 q^{35} +(-0.238030 + 0.412281i) q^{36} +(-0.166256 - 0.287964i) q^{37} +(4.60214 + 7.97114i) q^{38} -0.186746 q^{39} +(-3.19103 + 5.52703i) q^{40} +(-0.561667 + 0.972836i) q^{41} +(0.364495 - 0.631323i) q^{42} +(2.62471 + 4.54613i) q^{43} +(-0.237022 + 0.410533i) q^{44} +(-3.22898 - 5.59276i) q^{45} +6.41388 q^{46} -8.43721 q^{47} +(-0.341102 - 0.590805i) q^{48} +(-0.642137 + 1.11221i) q^{49} +(0.173893 + 0.301192i) q^{50} +(-0.155443 + 0.269234i) q^{51} +(0.0802766 - 0.139043i) q^{52} +(5.94060 - 10.2894i) q^{53} +1.51082 q^{54} +(-3.21530 - 5.56906i) q^{55} +(4.21702 + 7.30410i) q^{56} +(-0.633675 + 1.09756i) q^{57} -2.61843 q^{58} +(3.23067 + 5.59568i) q^{59} -0.0653013 q^{60} +5.91690 q^{61} +(-6.62876 - 3.61696i) q^{62} -8.53435 q^{63} +8.53497 q^{64} +(1.08899 + 1.88618i) q^{65} +0.747812 q^{66} +(-5.73764 + 9.93788i) q^{67} +(-0.133641 - 0.231472i) q^{68} +(0.441568 + 0.764819i) q^{69} -8.50205 q^{70} +(-0.218153 + 0.377852i) q^{71} +(-4.34432 + 7.52458i) q^{72} +(2.33501 - 4.04435i) q^{73} +(-0.225487 - 0.390554i) q^{74} +(-0.0239436 + 0.0414715i) q^{75} +(-0.544798 - 0.943617i) q^{76} -8.49818 q^{77} -0.253276 q^{78} +(6.84557 + 11.8569i) q^{79} +(-3.97820 + 6.89044i) q^{80} +(-4.34368 - 7.52347i) q^{81} +(-0.761767 + 1.31942i) q^{82} +(-3.91140 + 6.77474i) q^{83} +(-0.0431486 + 0.0747356i) q^{84} +3.62579 q^{85} +(3.55979 + 6.16574i) q^{86} +(-0.180267 - 0.312232i) q^{87} +(-4.32591 + 7.49269i) q^{88} +4.45512 q^{89} +(-4.37935 - 7.58525i) q^{90} +2.87824 q^{91} -0.759271 q^{92} +(-0.0250597 - 1.03945i) q^{93} -11.4431 q^{94} +14.7808 q^{95} +(0.0845929 + 0.146519i) q^{96} -1.02000 q^{97} +(-0.870906 + 1.50845i) q^{98} +(-4.37736 - 7.58180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q + 6q^{2} - 2q^{3} + 34q^{4} - 5q^{5} - 2q^{7} + 36q^{8} - 23q^{9} + O(q^{10}) \) \( 34q + 6q^{2} - 2q^{3} + 34q^{4} - 5q^{5} - 2q^{7} + 36q^{8} - 23q^{9} - 7q^{10} - 5q^{11} - 28q^{12} - 17q^{13} - 7q^{14} + 8q^{15} + 18q^{16} - 8q^{17} + 6q^{18} + 3q^{19} - 8q^{20} + 13q^{21} + 12q^{22} - 14q^{23} - 6q^{24} - 26q^{25} - 3q^{26} + 28q^{27} - 7q^{28} - 18q^{29} - 60q^{30} - 9q^{31} + 58q^{32} - 14q^{33} - 15q^{34} + 50q^{35} - 49q^{36} - 6q^{37} + 2q^{38} + 4q^{39} - 29q^{40} - 5q^{41} + 8q^{42} - q^{43} - 22q^{44} + 13q^{45} + 34q^{46} + 16q^{47} - 49q^{48} + 3q^{49} - 35q^{51} - 17q^{52} + 30q^{53} - 2q^{54} + 21q^{55} - 7q^{56} + 34q^{58} - 9q^{59} - 38q^{60} - 28q^{61} - 62q^{62} + 88q^{63} + 56q^{64} - 5q^{65} + 140q^{66} - 31q^{67} - 39q^{68} + 5q^{69} + 56q^{70} + q^{71} - 32q^{72} - 10q^{73} - 39q^{74} - 2q^{75} - 16q^{76} + 76q^{77} - 23q^{79} - 22q^{80} - 29q^{81} - 10q^{82} + 3q^{83} + 52q^{84} - 32q^{85} + 4q^{86} + 18q^{87} - 10q^{88} + 26q^{89} + 35q^{90} + 4q^{91} - 94q^{92} - 41q^{93} + 70q^{94} + 28q^{95} - 23q^{96} + 32q^{97} - 38q^{98} - 70q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.35626 0.959022 0.479511 0.877536i \(-0.340814\pi\)
0.479511 + 0.877536i \(0.340814\pi\)
\(3\) 0.0933728 + 0.161726i 0.0539088 + 0.0933728i 0.891720 0.452587i \(-0.149499\pi\)
−0.837812 + 0.545959i \(0.816165\pi\)
\(4\) −0.160553 −0.0802766
\(5\) 1.08899 1.88618i 0.487010 0.843526i −0.512879 0.858461i \(-0.671421\pi\)
0.999888 + 0.0149354i \(0.00475427\pi\)
\(6\) 0.126638 + 0.219343i 0.0516997 + 0.0895466i
\(7\) −1.43912 2.49263i −0.543936 0.942126i −0.998673 0.0514996i \(-0.983600\pi\)
0.454737 0.890626i \(-0.349733\pi\)
\(8\) −2.93028 −1.03601
\(9\) 1.48256 2.56787i 0.494188 0.855958i
\(10\) 1.47695 2.55816i 0.467053 0.808960i
\(11\) 1.47628 2.55699i 0.445115 0.770962i −0.552945 0.833218i \(-0.686496\pi\)
0.998060 + 0.0622557i \(0.0198294\pi\)
\(12\) −0.0149913 0.0259657i −0.00432762 0.00749565i
\(13\) −0.500000 + 0.866025i −0.138675 + 0.240192i
\(14\) −1.95182 3.38066i −0.521647 0.903519i
\(15\) 0.406727 0.105016
\(16\) −3.65312 −0.913279
\(17\) 0.832376 + 1.44172i 0.201881 + 0.349668i 0.949134 0.314871i \(-0.101961\pi\)
−0.747254 + 0.664539i \(0.768628\pi\)
\(18\) 2.01074 3.48271i 0.473937 0.820883i
\(19\) 3.39325 + 5.87729i 0.778465 + 1.34834i 0.932826 + 0.360327i \(0.117335\pi\)
−0.154360 + 0.988015i \(0.549332\pi\)
\(20\) −0.174840 + 0.302832i −0.0390955 + 0.0677154i
\(21\) 0.268749 0.465488i 0.0586459 0.101578i
\(22\) 2.00222 3.46795i 0.426875 0.739370i
\(23\) 4.72909 0.986083 0.493042 0.870006i \(-0.335885\pi\)
0.493042 + 0.870006i \(0.335885\pi\)
\(24\) −0.273608 0.473903i −0.0558500 0.0967351i
\(25\) 0.128215 + 0.222075i 0.0256430 + 0.0444149i
\(26\) −0.678131 + 1.17456i −0.132992 + 0.230350i
\(27\) 1.11396 0.214382
\(28\) 0.231056 + 0.400200i 0.0436654 + 0.0756307i
\(29\) −1.93062 −0.358507 −0.179254 0.983803i \(-0.557368\pi\)
−0.179254 + 0.983803i \(0.557368\pi\)
\(30\) 0.551628 0.100713
\(31\) −4.88752 2.66686i −0.877825 0.478982i
\(32\) 0.905970 0.160154
\(33\) 0.551377 0.0959825
\(34\) 1.12892 + 1.95535i 0.193608 + 0.335339i
\(35\) −6.26873 −1.05961
\(36\) −0.238030 + 0.412281i −0.0396717 + 0.0687134i
\(37\) −0.166256 0.287964i −0.0273323 0.0473410i 0.852036 0.523484i \(-0.175368\pi\)
−0.879368 + 0.476143i \(0.842035\pi\)
\(38\) 4.60214 + 7.97114i 0.746566 + 1.29309i
\(39\) −0.186746 −0.0299032
\(40\) −3.19103 + 5.52703i −0.504547 + 0.873900i
\(41\) −0.561667 + 0.972836i −0.0877176 + 0.151931i −0.906546 0.422107i \(-0.861291\pi\)
0.818828 + 0.574038i \(0.194624\pi\)
\(42\) 0.364495 0.631323i 0.0562427 0.0974153i
\(43\) 2.62471 + 4.54613i 0.400264 + 0.693278i 0.993758 0.111561i \(-0.0355849\pi\)
−0.593493 + 0.804839i \(0.702252\pi\)
\(44\) −0.237022 + 0.410533i −0.0357323 + 0.0618902i
\(45\) −3.22898 5.59276i −0.481348 0.833720i
\(46\) 6.41388 0.945676
\(47\) −8.43721 −1.23069 −0.615347 0.788256i \(-0.710984\pi\)
−0.615347 + 0.788256i \(0.710984\pi\)
\(48\) −0.341102 0.590805i −0.0492338 0.0852754i
\(49\) −0.642137 + 1.11221i −0.0917338 + 0.158888i
\(50\) 0.173893 + 0.301192i 0.0245922 + 0.0425949i
\(51\) −0.155443 + 0.269234i −0.0217663 + 0.0377003i
\(52\) 0.0802766 0.139043i 0.0111324 0.0192818i
\(53\) 5.94060 10.2894i 0.816004 1.41336i −0.0926012 0.995703i \(-0.529518\pi\)
0.908605 0.417657i \(-0.137148\pi\)
\(54\) 1.51082 0.205597
\(55\) −3.21530 5.56906i −0.433551 0.750932i
\(56\) 4.21702 + 7.30410i 0.563523 + 0.976051i
\(57\) −0.633675 + 1.09756i −0.0839323 + 0.145375i
\(58\) −2.61843 −0.343816
\(59\) 3.23067 + 5.59568i 0.420597 + 0.728495i 0.995998 0.0893762i \(-0.0284873\pi\)
−0.575401 + 0.817871i \(0.695154\pi\)
\(60\) −0.0653013 −0.00843037
\(61\) 5.91690 0.757581 0.378790 0.925482i \(-0.376340\pi\)
0.378790 + 0.925482i \(0.376340\pi\)
\(62\) −6.62876 3.61696i −0.841853 0.459355i
\(63\) −8.53435 −1.07523
\(64\) 8.53497 1.06687
\(65\) 1.08899 + 1.88618i 0.135072 + 0.233952i
\(66\) 0.747812 0.0920493
\(67\) −5.73764 + 9.93788i −0.700964 + 1.21411i 0.267164 + 0.963651i \(0.413913\pi\)
−0.968128 + 0.250454i \(0.919420\pi\)
\(68\) −0.133641 0.231472i −0.0162063 0.0280702i
\(69\) 0.441568 + 0.764819i 0.0531586 + 0.0920733i
\(70\) −8.50205 −1.01619
\(71\) −0.218153 + 0.377852i −0.0258900 + 0.0448428i −0.878680 0.477411i \(-0.841575\pi\)
0.852790 + 0.522254i \(0.174909\pi\)
\(72\) −4.34432 + 7.52458i −0.511983 + 0.886781i
\(73\) 2.33501 4.04435i 0.273292 0.473356i −0.696411 0.717644i \(-0.745221\pi\)
0.969703 + 0.244288i \(0.0785541\pi\)
\(74\) −0.225487 0.390554i −0.0262123 0.0454010i
\(75\) −0.0239436 + 0.0414715i −0.00276477 + 0.00478871i
\(76\) −0.544798 0.943617i −0.0624926 0.108240i
\(77\) −8.49818 −0.968457
\(78\) −0.253276 −0.0286779
\(79\) 6.84557 + 11.8569i 0.770187 + 1.33400i 0.937460 + 0.348092i \(0.113170\pi\)
−0.167274 + 0.985910i \(0.553496\pi\)
\(80\) −3.97820 + 6.89044i −0.444776 + 0.770374i
\(81\) −4.34368 7.52347i −0.482631 0.835941i
\(82\) −0.761767 + 1.31942i −0.0841231 + 0.145706i
\(83\) −3.91140 + 6.77474i −0.429331 + 0.743624i −0.996814 0.0797616i \(-0.974584\pi\)
0.567483 + 0.823385i \(0.307917\pi\)
\(84\) −0.0431486 + 0.0747356i −0.00470790 + 0.00815432i
\(85\) 3.62579 0.393272
\(86\) 3.55979 + 6.16574i 0.383862 + 0.664869i
\(87\) −0.180267 0.312232i −0.0193267 0.0334748i
\(88\) −4.32591 + 7.49269i −0.461143 + 0.798724i
\(89\) 4.45512 0.472242 0.236121 0.971724i \(-0.424124\pi\)
0.236121 + 0.971724i \(0.424124\pi\)
\(90\) −4.37935 7.58525i −0.461624 0.799556i
\(91\) 2.87824 0.301722
\(92\) −0.759271 −0.0791594
\(93\) −0.0250597 1.03945i −0.00259857 0.107786i
\(94\) −11.4431 −1.18026
\(95\) 14.7808 1.51648
\(96\) 0.0845929 + 0.146519i 0.00863373 + 0.0149541i
\(97\) −1.02000 −0.103565 −0.0517826 0.998658i \(-0.516490\pi\)
−0.0517826 + 0.998658i \(0.516490\pi\)
\(98\) −0.870906 + 1.50845i −0.0879748 + 0.152377i
\(99\) −4.37736 7.58180i −0.439941 0.762000i
\(100\) −0.0205853 0.0356548i −0.00205853 0.00356548i
\(101\) 11.5844 1.15269 0.576347 0.817205i \(-0.304478\pi\)
0.576347 + 0.817205i \(0.304478\pi\)
\(102\) −0.210821 + 0.365152i −0.0208744 + 0.0361555i
\(103\) −3.20893 + 5.55803i −0.316185 + 0.547649i −0.979689 0.200524i \(-0.935735\pi\)
0.663503 + 0.748173i \(0.269069\pi\)
\(104\) 1.46514 2.53769i 0.143669 0.248841i
\(105\) −0.585329 1.01382i −0.0571223 0.0989387i
\(106\) 8.05701 13.9551i 0.782566 1.35544i
\(107\) −6.84343 11.8532i −0.661580 1.14589i −0.980201 0.198007i \(-0.936553\pi\)
0.318621 0.947882i \(-0.396780\pi\)
\(108\) −0.178850 −0.0172099
\(109\) −6.09277 −0.583582 −0.291791 0.956482i \(-0.594251\pi\)
−0.291791 + 0.956482i \(0.594251\pi\)
\(110\) −4.36079 7.55311i −0.415785 0.720160i
\(111\) 0.0310476 0.0537760i 0.00294691 0.00510419i
\(112\) 5.25727 + 9.10587i 0.496766 + 0.860424i
\(113\) 2.97561 5.15390i 0.279922 0.484838i −0.691443 0.722431i \(-0.743025\pi\)
0.971365 + 0.237592i \(0.0763582\pi\)
\(114\) −0.859429 + 1.48857i −0.0804929 + 0.139418i
\(115\) 5.14992 8.91992i 0.480232 0.831786i
\(116\) 0.309967 0.0287798
\(117\) 1.48256 + 2.56787i 0.137063 + 0.237400i
\(118\) 4.38163 + 7.58921i 0.403362 + 0.698643i
\(119\) 2.39578 4.14961i 0.219621 0.380394i
\(120\) −1.19182 −0.108798
\(121\) 1.14120 + 1.97661i 0.103745 + 0.179692i
\(122\) 8.02486 0.726537
\(123\) −0.209778 −0.0189150
\(124\) 0.784707 + 0.428173i 0.0704688 + 0.0384511i
\(125\) 11.4484 1.02397
\(126\) −11.5748 −1.03117
\(127\) −3.92779 6.80314i −0.348535 0.603681i 0.637454 0.770488i \(-0.279988\pi\)
−0.985990 + 0.166807i \(0.946654\pi\)
\(128\) 9.76371 0.862998
\(129\) −0.490153 + 0.848970i −0.0431556 + 0.0747476i
\(130\) 1.47695 + 2.55816i 0.129537 + 0.224365i
\(131\) 6.23032 + 10.7912i 0.544346 + 0.942835i 0.998648 + 0.0519869i \(0.0165554\pi\)
−0.454302 + 0.890848i \(0.650111\pi\)
\(132\) −0.0885255 −0.00770515
\(133\) 9.76660 16.9162i 0.846872 1.46682i
\(134\) −7.78174 + 13.4784i −0.672240 + 1.16435i
\(135\) 1.21309 2.10113i 0.104406 0.180837i
\(136\) −2.43909 4.22463i −0.209150 0.362259i
\(137\) −3.34706 + 5.79728i −0.285959 + 0.495295i −0.972841 0.231473i \(-0.925645\pi\)
0.686882 + 0.726769i \(0.258979\pi\)
\(138\) 0.598882 + 1.03729i 0.0509802 + 0.0883004i
\(139\) −1.57378 −0.133486 −0.0667432 0.997770i \(-0.521261\pi\)
−0.0667432 + 0.997770i \(0.521261\pi\)
\(140\) 1.00647 0.0850619
\(141\) −0.787806 1.36452i −0.0663453 0.114913i
\(142\) −0.295873 + 0.512466i −0.0248291 + 0.0430052i
\(143\) 1.47628 + 2.55699i 0.123453 + 0.213826i
\(144\) −5.41597 + 9.38074i −0.451331 + 0.781729i
\(145\) −2.10242 + 3.64150i −0.174597 + 0.302410i
\(146\) 3.16688 5.48521i 0.262093 0.453959i
\(147\) −0.239832 −0.0197810
\(148\) 0.0266929 + 0.0462335i 0.00219415 + 0.00380037i
\(149\) 7.20311 + 12.4762i 0.590102 + 1.02209i 0.994218 + 0.107379i \(0.0342458\pi\)
−0.404116 + 0.914708i \(0.632421\pi\)
\(150\) −0.0324738 + 0.0562462i −0.00265147 + 0.00459248i
\(151\) −11.9734 −0.974385 −0.487193 0.873295i \(-0.661979\pi\)
−0.487193 + 0.873295i \(0.661979\pi\)
\(152\) −9.94317 17.2221i −0.806497 1.39689i
\(153\) 4.93620 0.399068
\(154\) −11.5258 −0.928772
\(155\) −10.3526 + 6.31457i −0.831543 + 0.507199i
\(156\) 0.0299826 0.00240053
\(157\) −9.19658 −0.733967 −0.366983 0.930227i \(-0.619609\pi\)
−0.366983 + 0.930227i \(0.619609\pi\)
\(158\) 9.28438 + 16.0810i 0.738626 + 1.27934i
\(159\) 2.21876 0.175959
\(160\) 0.986590 1.70882i 0.0779968 0.135094i
\(161\) −6.80573 11.7879i −0.536367 0.929014i
\(162\) −5.89116 10.2038i −0.462853 0.801686i
\(163\) 0.327869 0.0256807 0.0128404 0.999918i \(-0.495913\pi\)
0.0128404 + 0.999918i \(0.495913\pi\)
\(164\) 0.0901775 0.156192i 0.00704168 0.0121965i
\(165\) 0.600443 1.04000i 0.0467444 0.0809637i
\(166\) −5.30488 + 9.18832i −0.411738 + 0.713152i
\(167\) 0.259404 + 0.449301i 0.0200733 + 0.0347680i 0.875888 0.482515i \(-0.160277\pi\)
−0.855814 + 0.517283i \(0.826943\pi\)
\(168\) −0.787510 + 1.36401i −0.0607577 + 0.105235i
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) 4.91752 0.377156
\(171\) 20.1228 1.53883
\(172\) −0.421406 0.729896i −0.0321319 0.0556541i
\(173\) −3.54626 + 6.14231i −0.269617 + 0.466991i −0.968763 0.247988i \(-0.920231\pi\)
0.699146 + 0.714979i \(0.253564\pi\)
\(174\) −0.244490 0.423469i −0.0185347 0.0321031i
\(175\) 0.369033 0.639185i 0.0278963 0.0483178i
\(176\) −5.39302 + 9.34099i −0.406514 + 0.704103i
\(177\) −0.603313 + 1.04497i −0.0453478 + 0.0785446i
\(178\) 6.04231 0.452890
\(179\) −9.91972 17.1815i −0.741435 1.28420i −0.951842 0.306589i \(-0.900812\pi\)
0.210408 0.977614i \(-0.432521\pi\)
\(180\) 0.518424 + 0.897936i 0.0386410 + 0.0669282i
\(181\) 6.83259 11.8344i 0.507862 0.879643i −0.492096 0.870541i \(-0.663769\pi\)
0.999959 0.00910261i \(-0.00289749\pi\)
\(182\) 3.90365 0.289358
\(183\) 0.552477 + 0.956918i 0.0408403 + 0.0707374i
\(184\) −13.8575 −1.02159
\(185\) −0.724203 −0.0532444
\(186\) −0.0339875 1.40977i −0.00249208 0.103369i
\(187\) 4.91528 0.359441
\(188\) 1.35462 0.0987960
\(189\) −1.60312 2.77669i −0.116610 0.201975i
\(190\) 20.0467 1.45434
\(191\) −12.0453 + 20.8630i −0.871566 + 1.50960i −0.0111903 + 0.999937i \(0.503562\pi\)
−0.860376 + 0.509660i \(0.829771\pi\)
\(192\) 0.796933 + 1.38033i 0.0575137 + 0.0996167i
\(193\) −0.0996204 0.172548i −0.00717083 0.0124202i 0.862418 0.506197i \(-0.168949\pi\)
−0.869589 + 0.493777i \(0.835616\pi\)
\(194\) −1.38339 −0.0993214
\(195\) −0.203363 + 0.352236i −0.0145632 + 0.0252241i
\(196\) 0.103097 0.178570i 0.00736408 0.0127550i
\(197\) −0.331896 + 0.574860i −0.0236466 + 0.0409571i −0.877607 0.479382i \(-0.840861\pi\)
0.853960 + 0.520339i \(0.174194\pi\)
\(198\) −5.93684 10.2829i −0.421913 0.730775i
\(199\) 8.60620 14.9064i 0.610077 1.05668i −0.381150 0.924513i \(-0.624472\pi\)
0.991227 0.132172i \(-0.0421950\pi\)
\(200\) −0.375705 0.650740i −0.0265664 0.0460143i
\(201\) −2.14296 −0.151153
\(202\) 15.7115 1.10546
\(203\) 2.77840 + 4.81232i 0.195005 + 0.337759i
\(204\) 0.0249568 0.0432265i 0.00174733 0.00302646i
\(205\) 1.22330 + 2.11881i 0.0854387 + 0.147984i
\(206\) −4.35215 + 7.53815i −0.303229 + 0.525208i
\(207\) 7.01117 12.1437i 0.487310 0.844046i
\(208\) 1.82656 3.16369i 0.126649 0.219363i
\(209\) 20.0376 1.38603
\(210\) −0.793860 1.37501i −0.0547815 0.0948844i
\(211\) −9.17204 15.8864i −0.631429 1.09367i −0.987260 0.159117i \(-0.949135\pi\)
0.355830 0.934551i \(-0.384198\pi\)
\(212\) −0.953782 + 1.65200i −0.0655060 + 0.113460i
\(213\) −0.0814782 −0.00558280
\(214\) −9.28149 16.0760i −0.634469 1.09893i
\(215\) 11.4331 0.779731
\(216\) −3.26421 −0.222102
\(217\) 0.386236 + 16.0207i 0.0262194 + 1.08756i
\(218\) −8.26340 −0.559668
\(219\) 0.872105 0.0589314
\(220\) 0.516227 + 0.894131i 0.0348040 + 0.0602823i
\(221\) −1.66475 −0.111983
\(222\) 0.0421086 0.0729343i 0.00282615 0.00489503i
\(223\) −6.51339 11.2815i −0.436169 0.755467i 0.561221 0.827666i \(-0.310332\pi\)
−0.997390 + 0.0721990i \(0.976998\pi\)
\(224\) −1.30380 2.25825i −0.0871138 0.150886i
\(225\) 0.760347 0.0506898
\(226\) 4.03570 6.99004i 0.268451 0.464971i
\(227\) −11.1974 + 19.3944i −0.743195 + 1.28725i 0.207838 + 0.978163i \(0.433357\pi\)
−0.951033 + 0.309088i \(0.899976\pi\)
\(228\) 0.101739 0.176216i 0.00673780 0.0116702i
\(229\) −13.0652 22.6296i −0.863374 1.49541i −0.868652 0.495422i \(-0.835013\pi\)
0.00527771 0.999986i \(-0.498320\pi\)
\(230\) 6.98464 12.0977i 0.460553 0.797702i
\(231\) −0.793499 1.37438i −0.0522084 0.0904276i
\(232\) 5.65725 0.371417
\(233\) 10.7839 0.706474 0.353237 0.935534i \(-0.385081\pi\)
0.353237 + 0.935534i \(0.385081\pi\)
\(234\) 2.01074 + 3.48271i 0.131446 + 0.227672i
\(235\) −9.18802 + 15.9141i −0.599360 + 1.03812i
\(236\) −0.518694 0.898404i −0.0337641 0.0584811i
\(237\) −1.27838 + 2.21422i −0.0830397 + 0.143829i
\(238\) 3.24930 5.62796i 0.210621 0.364806i
\(239\) 11.0239 19.0939i 0.713075 1.23508i −0.250622 0.968085i \(-0.580635\pi\)
0.963697 0.266998i \(-0.0860316\pi\)
\(240\) −1.48582 −0.0959093
\(241\) −4.49832 7.79132i −0.289762 0.501883i 0.683991 0.729491i \(-0.260243\pi\)
−0.973753 + 0.227608i \(0.926910\pi\)
\(242\) 1.54776 + 2.68080i 0.0994938 + 0.172328i
\(243\) 2.48210 4.29913i 0.159227 0.275789i
\(244\) −0.949977 −0.0608160
\(245\) 1.39856 + 2.42237i 0.0893505 + 0.154760i
\(246\) −0.284513 −0.0181399
\(247\) −6.78650 −0.431815
\(248\) 14.3218 + 7.81464i 0.909434 + 0.496230i
\(249\) −1.46087 −0.0925790
\(250\) 15.5270 0.982013
\(251\) 14.4953 + 25.1067i 0.914937 + 1.58472i 0.806993 + 0.590561i \(0.201093\pi\)
0.107944 + 0.994157i \(0.465573\pi\)
\(252\) 1.37022 0.0863156
\(253\) 6.98146 12.0922i 0.438921 0.760233i
\(254\) −5.32712 9.22684i −0.334253 0.578943i
\(255\) 0.338550 + 0.586385i 0.0212008 + 0.0367209i
\(256\) −3.82778 −0.239236
\(257\) −8.68613 + 15.0448i −0.541826 + 0.938470i 0.456973 + 0.889480i \(0.348934\pi\)
−0.998799 + 0.0489898i \(0.984400\pi\)
\(258\) −0.664776 + 1.15143i −0.0413871 + 0.0716846i
\(259\) −0.478525 + 0.828830i −0.0297341 + 0.0515010i
\(260\) −0.174840 0.302832i −0.0108431 0.0187809i
\(261\) −2.86227 + 4.95759i −0.177170 + 0.306867i
\(262\) 8.44995 + 14.6357i 0.522040 + 0.904199i
\(263\) −7.59299 −0.468204 −0.234102 0.972212i \(-0.575215\pi\)
−0.234102 + 0.972212i \(0.575215\pi\)
\(264\) −1.61569 −0.0994387
\(265\) −12.9385 22.4101i −0.794804 1.37664i
\(266\) 13.2461 22.9429i 0.812169 1.40672i
\(267\) 0.415987 + 0.720511i 0.0254580 + 0.0440945i
\(268\) 0.921197 1.59556i 0.0562710 0.0974643i
\(269\) −12.7968 + 22.1646i −0.780232 + 1.35140i 0.151575 + 0.988446i \(0.451565\pi\)
−0.931807 + 0.362955i \(0.881768\pi\)
\(270\) 1.64527 2.84968i 0.100128 0.173426i
\(271\) −16.6475 −1.01127 −0.505633 0.862749i \(-0.668741\pi\)
−0.505633 + 0.862749i \(0.668741\pi\)
\(272\) −3.04077 5.26676i −0.184373 0.319344i
\(273\) 0.268749 + 0.465488i 0.0162655 + 0.0281726i
\(274\) −4.53949 + 7.86263i −0.274241 + 0.474999i
\(275\) 0.757124 0.0456563
\(276\) −0.0708952 0.122794i −0.00426739 0.00739134i
\(277\) −7.37235 −0.442961 −0.221481 0.975165i \(-0.571089\pi\)
−0.221481 + 0.975165i \(0.571089\pi\)
\(278\) −2.13446 −0.128016
\(279\) −14.0942 + 8.59675i −0.843799 + 0.514674i
\(280\) 18.3691 1.09777
\(281\) 15.1665 0.904757 0.452379 0.891826i \(-0.350576\pi\)
0.452379 + 0.891826i \(0.350576\pi\)
\(282\) −1.06847 1.85065i −0.0636266 0.110204i
\(283\) 20.4765 1.21720 0.608602 0.793476i \(-0.291731\pi\)
0.608602 + 0.793476i \(0.291731\pi\)
\(284\) 0.0350252 0.0606654i 0.00207836 0.00359983i
\(285\) 1.38013 + 2.39045i 0.0817517 + 0.141598i
\(286\) 2.00222 + 3.46795i 0.118394 + 0.205064i
\(287\) 3.23323 0.190851
\(288\) 1.34316 2.32642i 0.0791463 0.137085i
\(289\) 7.11430 12.3223i 0.418488 0.724843i
\(290\) −2.85143 + 4.93883i −0.167442 + 0.290018i
\(291\) −0.0952402 0.164961i −0.00558308 0.00967018i
\(292\) −0.374893 + 0.649334i −0.0219390 + 0.0379994i
\(293\) −8.59044 14.8791i −0.501859 0.869245i −0.999998 0.00214776i \(-0.999316\pi\)
0.498139 0.867097i \(-0.334017\pi\)
\(294\) −0.325276 −0.0189705
\(295\) 14.0726 0.819339
\(296\) 0.487176 + 0.843814i 0.0283165 + 0.0490457i
\(297\) 1.64452 2.84839i 0.0954246 0.165280i
\(298\) 9.76931 + 16.9209i 0.565921 + 0.980204i
\(299\) −2.36454 + 4.09551i −0.136745 + 0.236850i
\(300\) 0.00384422 0.00665838i 0.000221946 0.000384422i
\(301\) 7.55455 13.0849i 0.435437 0.754199i
\(302\) −16.2391 −0.934457
\(303\) 1.08167 + 1.87351i 0.0621403 + 0.107630i
\(304\) −12.3959 21.4704i −0.710956 1.23141i
\(305\) 6.44342 11.1603i 0.368949 0.639039i
\(306\) 6.69478 0.382715
\(307\) 13.7596 + 23.8323i 0.785301 + 1.36018i 0.928819 + 0.370534i \(0.120825\pi\)
−0.143518 + 0.989648i \(0.545841\pi\)
\(308\) 1.36441 0.0777445
\(309\) −1.19851 −0.0681807
\(310\) −14.0409 + 8.56421i −0.797468 + 0.486415i
\(311\) 24.0241 1.36228 0.681140 0.732154i \(-0.261485\pi\)
0.681140 + 0.732154i \(0.261485\pi\)
\(312\) 0.547216 0.0309800
\(313\) −5.24145 9.07846i −0.296264 0.513145i 0.679014 0.734125i \(-0.262408\pi\)
−0.975278 + 0.220981i \(0.929074\pi\)
\(314\) −12.4730 −0.703890
\(315\) −9.29379 + 16.0973i −0.523646 + 0.906981i
\(316\) −1.09908 1.90366i −0.0618280 0.107089i
\(317\) −15.8580 27.4669i −0.890676 1.54270i −0.839067 0.544029i \(-0.816898\pi\)
−0.0516094 0.998667i \(-0.516435\pi\)
\(318\) 3.00922 0.168749
\(319\) −2.85014 + 4.93658i −0.159577 + 0.276395i
\(320\) 9.29447 16.0985i 0.519576 0.899933i
\(321\) 1.27798 2.21353i 0.0713299 0.123547i
\(322\) −9.23035 15.9874i −0.514387 0.890945i
\(323\) −5.64892 + 9.78422i −0.314314 + 0.544409i
\(324\) 0.697391 + 1.20792i 0.0387440 + 0.0671065i
\(325\) −0.256430 −0.0142242
\(326\) 0.444677 0.0246284
\(327\) −0.568899 0.985362i −0.0314602 0.0544907i
\(328\) 1.64584 2.85068i 0.0908763 0.157402i
\(329\) 12.1422 + 21.0309i 0.669420 + 1.15947i
\(330\) 0.814358 1.41051i 0.0448289 0.0776460i
\(331\) −4.08321 + 7.07233i −0.224433 + 0.388730i −0.956149 0.292880i \(-0.905386\pi\)
0.731716 + 0.681610i \(0.238720\pi\)
\(332\) 0.627987 1.08771i 0.0344653 0.0596956i
\(333\) −0.985940 −0.0540292
\(334\) 0.351820 + 0.609370i 0.0192507 + 0.0333433i
\(335\) 12.4964 + 21.6444i 0.682753 + 1.18256i
\(336\) −0.981773 + 1.70048i −0.0535601 + 0.0927688i
\(337\) −19.9688 −1.08777 −0.543884 0.839160i \(-0.683047\pi\)
−0.543884 + 0.839160i \(0.683047\pi\)
\(338\) −0.678131 1.17456i −0.0368855 0.0638875i
\(339\) 1.11136 0.0603609
\(340\) −0.582132 −0.0315705
\(341\) −14.0345 + 8.56032i −0.760010 + 0.463567i
\(342\) 27.2918 1.47577
\(343\) −16.4512 −0.888283
\(344\) −7.69113 13.3214i −0.414678 0.718243i
\(345\) 1.92345 0.103555
\(346\) −4.80966 + 8.33058i −0.258569 + 0.447855i
\(347\) −7.61368 13.1873i −0.408724 0.707930i 0.586023 0.810294i \(-0.300693\pi\)
−0.994747 + 0.102364i \(0.967359\pi\)
\(348\) 0.0289425 + 0.0501299i 0.00155148 + 0.00268725i
\(349\) −26.7180 −1.43018 −0.715092 0.699030i \(-0.753615\pi\)
−0.715092 + 0.699030i \(0.753615\pi\)
\(350\) 0.500506 0.866902i 0.0267532 0.0463379i
\(351\) −0.556980 + 0.964718i −0.0297294 + 0.0514929i
\(352\) 1.33747 2.31656i 0.0712871 0.123473i
\(353\) 9.27936 + 16.0723i 0.493891 + 0.855443i 0.999975 0.00704033i \(-0.00224102\pi\)
−0.506085 + 0.862484i \(0.668908\pi\)
\(354\) −0.818250 + 1.41725i −0.0434895 + 0.0753260i
\(355\) 0.475132 + 0.822952i 0.0252174 + 0.0436778i
\(356\) −0.715284 −0.0379100
\(357\) 0.894802 0.0473579
\(358\) −13.4537 23.3026i −0.711052 1.23158i
\(359\) −6.03482 + 10.4526i −0.318505 + 0.551668i −0.980176 0.198127i \(-0.936514\pi\)
0.661671 + 0.749794i \(0.269848\pi\)
\(360\) 9.46181 + 16.3883i 0.498681 + 0.863742i
\(361\) −13.5283 + 23.4317i −0.712017 + 1.23325i
\(362\) 9.26678 16.0505i 0.487051 0.843597i
\(363\) −0.213113 + 0.369123i −0.0111855 + 0.0193739i
\(364\) −0.462111 −0.0242212
\(365\) −5.08559 8.80850i −0.266192 0.461058i
\(366\) 0.749304 + 1.29783i 0.0391667 + 0.0678388i
\(367\) −17.9960 + 31.1699i −0.939382 + 1.62706i −0.172754 + 0.984965i \(0.555267\pi\)
−0.766628 + 0.642092i \(0.778067\pi\)
\(368\) −17.2759 −0.900569
\(369\) 1.66541 + 2.88458i 0.0866979 + 0.150165i
\(370\) −0.982208 −0.0510626
\(371\) −34.1969 −1.77542
\(372\) 0.00402341 + 0.166888i 0.000208604 + 0.00865272i
\(373\) 31.3883 1.62523 0.812613 0.582803i \(-0.198044\pi\)
0.812613 + 0.582803i \(0.198044\pi\)
\(374\) 6.66641 0.344712
\(375\) 1.06897 + 1.85150i 0.0552012 + 0.0956112i
\(376\) 24.7234 1.27501
\(377\) 0.965310 1.67197i 0.0497160 0.0861106i
\(378\) −2.17426 3.76592i −0.111832 0.193698i
\(379\) −13.8879 24.0546i −0.713375 1.23560i −0.963583 0.267409i \(-0.913832\pi\)
0.250208 0.968192i \(-0.419501\pi\)
\(380\) −2.37311 −0.121738
\(381\) 0.733498 1.27046i 0.0375782 0.0650874i
\(382\) −16.3366 + 28.2958i −0.835851 + 1.44774i
\(383\) −5.60038 + 9.70015i −0.286166 + 0.495654i −0.972891 0.231263i \(-0.925714\pi\)
0.686725 + 0.726917i \(0.259048\pi\)
\(384\) 0.911665 + 1.57905i 0.0465232 + 0.0805805i
\(385\) −9.25441 + 16.0291i −0.471648 + 0.816919i
\(386\) −0.135111 0.234020i −0.00687699 0.0119113i
\(387\) 15.5652 0.791223
\(388\) 0.163764 0.00831387
\(389\) 17.3718 + 30.0888i 0.880784 + 1.52556i 0.850471 + 0.526022i \(0.176317\pi\)
0.0303128 + 0.999540i \(0.490350\pi\)
\(390\) −0.275814 + 0.477724i −0.0139664 + 0.0241905i
\(391\) 3.93638 + 6.81801i 0.199071 + 0.344802i
\(392\) 1.88164 3.25909i 0.0950371 0.164609i
\(393\) −1.16349 + 2.01522i −0.0586901 + 0.101654i
\(394\) −0.450138 + 0.779661i −0.0226776 + 0.0392788i
\(395\) 29.8189 1.50035
\(396\) 0.702799 + 1.21728i 0.0353170 + 0.0611708i
\(397\) −3.55656 6.16015i −0.178499 0.309169i 0.762868 0.646555i \(-0.223791\pi\)
−0.941367 + 0.337386i \(0.890457\pi\)
\(398\) 11.6723 20.2170i 0.585078 1.01338i
\(399\) 3.64774 0.182615
\(400\) −0.468384 0.811265i −0.0234192 0.0405632i
\(401\) 8.14388 0.406686 0.203343 0.979108i \(-0.434819\pi\)
0.203343 + 0.979108i \(0.434819\pi\)
\(402\) −2.90641 −0.144959
\(403\) 4.75333 2.89929i 0.236780 0.144424i
\(404\) −1.85992 −0.0925344
\(405\) −18.9208 −0.940183
\(406\) 3.76823 + 6.52677i 0.187014 + 0.323918i
\(407\) −0.981762 −0.0486641
\(408\) 0.455490 0.788931i 0.0225501 0.0390579i
\(409\) 13.7112 + 23.7485i 0.677975 + 1.17429i 0.975590 + 0.219601i \(0.0704756\pi\)
−0.297615 + 0.954686i \(0.596191\pi\)
\(410\) 1.65911 + 2.87366i 0.0819376 + 0.141920i
\(411\) −1.25010 −0.0616628
\(412\) 0.515204 0.892360i 0.0253823 0.0439634i
\(413\) 9.29864 16.1057i 0.457556 0.792510i
\(414\) 9.50899 16.4700i 0.467341 0.809459i
\(415\) 8.51892 + 14.7552i 0.418177 + 0.724304i
\(416\) −0.452985 + 0.784593i −0.0222094 + 0.0384678i
\(417\) −0.146948 0.254522i −0.00719610 0.0124640i
\(418\) 27.1762 1.32923
\(419\) −9.57344 −0.467693 −0.233847 0.972273i \(-0.575131\pi\)
−0.233847 + 0.972273i \(0.575131\pi\)
\(420\) 0.0939765 + 0.162772i 0.00458558 + 0.00794247i
\(421\) −11.7265 + 20.3108i −0.571513 + 0.989890i 0.424898 + 0.905241i \(0.360310\pi\)
−0.996411 + 0.0846482i \(0.973023\pi\)
\(422\) −12.4397 21.5462i −0.605555 1.04885i
\(423\) −12.5087 + 21.6657i −0.608194 + 1.05342i
\(424\) −17.4076 + 30.1508i −0.845387 + 1.46425i
\(425\) −0.213446 + 0.369699i −0.0103537 + 0.0179331i
\(426\) −0.110506 −0.00535402
\(427\) −8.51513 14.7486i −0.412076 0.713736i
\(428\) 1.09874 + 1.90307i 0.0531094 + 0.0919881i
\(429\) −0.275689 + 0.477507i −0.0133104 + 0.0230542i
\(430\) 15.5063 0.747779
\(431\) 10.4062 + 18.0241i 0.501251 + 0.868192i 0.999999 + 0.00144499i \(0.000459954\pi\)
−0.498748 + 0.866747i \(0.666207\pi\)
\(432\) −4.06943 −0.195790
\(433\) −30.7389 −1.47722 −0.738609 0.674134i \(-0.764517\pi\)
−0.738609 + 0.674134i \(0.764517\pi\)
\(434\) 0.523837 + 21.7283i 0.0251450 + 1.04299i
\(435\) −0.785235 −0.0376492
\(436\) 0.978215 0.0468480
\(437\) 16.0470 + 27.7942i 0.767632 + 1.32958i
\(438\) 1.18280 0.0565165
\(439\) −0.576157 + 0.997933i −0.0274985 + 0.0476287i −0.879447 0.475997i \(-0.842087\pi\)
0.851949 + 0.523625i \(0.175421\pi\)
\(440\) 9.42171 + 16.3189i 0.449163 + 0.777972i
\(441\) 1.90402 + 3.29785i 0.0906675 + 0.157041i
\(442\) −2.25784 −0.107394
\(443\) −9.80273 + 16.9788i −0.465742 + 0.806689i −0.999235 0.0391161i \(-0.987546\pi\)
0.533493 + 0.845805i \(0.320879\pi\)
\(444\) −0.00498479 + 0.00863391i −0.000236568 + 0.000409747i
\(445\) 4.85157 8.40316i 0.229986 0.398348i
\(446\) −8.83387 15.3007i −0.418296 0.724509i
\(447\) −1.34515 + 2.32987i −0.0636234 + 0.110199i
\(448\) −12.2828 21.2745i −0.580310 1.00513i
\(449\) −2.59800 −0.122607 −0.0613035 0.998119i \(-0.519526\pi\)
−0.0613035 + 0.998119i \(0.519526\pi\)
\(450\) 1.03123 0.0486126
\(451\) 1.65835 + 2.87236i 0.0780889 + 0.135254i
\(452\) −0.477743 + 0.827476i −0.0224712 + 0.0389212i
\(453\) −1.11799 1.93642i −0.0525279 0.0909811i
\(454\) −15.1866 + 26.3039i −0.712740 + 1.23450i
\(455\) 3.13437 5.42888i 0.146941 0.254510i
\(456\) 1.85684 3.21615i 0.0869546 0.150610i
\(457\) −36.8522 −1.72387 −0.861936 0.507018i \(-0.830748\pi\)
−0.861936 + 0.507018i \(0.830748\pi\)
\(458\) −17.7199 30.6917i −0.827995 1.43413i
\(459\) 0.927234 + 1.60602i 0.0432796 + 0.0749624i
\(460\) −0.826836 + 1.43212i −0.0385514 + 0.0667730i
\(461\) 31.8251 1.48224 0.741121 0.671371i \(-0.234294\pi\)
0.741121 + 0.671371i \(0.234294\pi\)
\(462\) −1.07619 1.86402i −0.0500690 0.0867220i
\(463\) −6.89236 −0.320315 −0.160158 0.987091i \(-0.551200\pi\)
−0.160158 + 0.987091i \(0.551200\pi\)
\(464\) 7.05278 0.327417
\(465\) −1.98789 1.08468i −0.0921860 0.0503010i
\(466\) 14.6257 0.677524
\(467\) −32.8087 −1.51821 −0.759104 0.650970i \(-0.774362\pi\)
−0.759104 + 0.650970i \(0.774362\pi\)
\(468\) −0.238030 0.412281i −0.0110030 0.0190577i
\(469\) 33.0286 1.52512
\(470\) −12.4614 + 21.5837i −0.574800 + 0.995582i
\(471\) −0.858710 1.48733i −0.0395673 0.0685325i
\(472\) −9.46674 16.3969i −0.435742 0.754728i
\(473\) 15.4992 0.712655
\(474\) −1.73382 + 3.00306i −0.0796369 + 0.137935i
\(475\) −0.870131 + 1.50711i −0.0399244 + 0.0691510i
\(476\) −0.384650 + 0.666234i −0.0176304 + 0.0305368i
\(477\) −17.6146 30.5094i −0.806518 1.39693i
\(478\) 14.9513 25.8964i 0.683855 1.18447i
\(479\) −9.12652 15.8076i −0.417001 0.722267i 0.578635 0.815587i \(-0.303586\pi\)
−0.995636 + 0.0933193i \(0.970252\pi\)
\(480\) 0.368482 0.0168188
\(481\) 0.332512 0.0151612
\(482\) −6.10090 10.5671i −0.277888 0.481317i
\(483\) 1.27094 2.20133i 0.0578298 0.100164i
\(484\) −0.183223 0.317351i −0.00832831 0.0144250i
\(485\) −1.11077 + 1.92390i −0.0504373 + 0.0873600i
\(486\) 3.36638 5.83075i 0.152702 0.264488i
\(487\) 8.01984 13.8908i 0.363414 0.629451i −0.625106 0.780539i \(-0.714944\pi\)
0.988520 + 0.151088i \(0.0482778\pi\)
\(488\) −17.3381 −0.784861
\(489\) 0.0306141 + 0.0530251i 0.00138442 + 0.00239788i
\(490\) 1.89681 + 3.28537i 0.0856891 + 0.148418i
\(491\) −6.84390 + 11.8540i −0.308861 + 0.534962i −0.978113 0.208072i \(-0.933281\pi\)
0.669253 + 0.743035i \(0.266614\pi\)
\(492\) 0.0336805 0.00151843
\(493\) −1.60700 2.78341i −0.0723757 0.125358i
\(494\) −9.20428 −0.414120
\(495\) −19.0675 −0.857022
\(496\) 17.8547 + 9.74235i 0.801699 + 0.437444i
\(497\) 1.25579 0.0563301
\(498\) −1.98132 −0.0887853
\(499\) −3.55686 6.16065i −0.159227 0.275789i 0.775363 0.631515i \(-0.217567\pi\)
−0.934590 + 0.355727i \(0.884233\pi\)
\(500\) −1.83807 −0.0822011
\(501\) −0.0484426 + 0.0839050i −0.00216426 + 0.00374860i
\(502\) 19.6595 + 34.0512i 0.877445 + 1.51978i
\(503\) 18.5050 + 32.0516i 0.825097 + 1.42911i 0.901845 + 0.432060i \(0.142213\pi\)
−0.0767478 + 0.997051i \(0.524454\pi\)
\(504\) 25.0080 1.11394
\(505\) 12.6153 21.8503i 0.561373 0.972327i
\(506\) 9.46869 16.4002i 0.420934 0.729080i
\(507\) 0.0933728 0.161726i 0.00414683 0.00718252i
\(508\) 0.630620 + 1.09227i 0.0279792 + 0.0484615i
\(509\) 15.0910 26.1384i 0.668896 1.15856i −0.309317 0.950959i \(-0.600100\pi\)
0.978213 0.207603i \(-0.0665663\pi\)
\(510\) 0.459162 + 0.795292i 0.0203320 + 0.0352161i
\(511\) −13.4414 −0.594614
\(512\) −24.7189 −1.09243
\(513\) 3.77995 + 6.54707i 0.166889 + 0.289060i
\(514\) −11.7807 + 20.4047i −0.519623 + 0.900014i
\(515\) 6.98897 + 12.1052i 0.307971 + 0.533421i
\(516\) 0.0786957 0.136305i 0.00346438 0.00600049i
\(517\) −12.4557 + 21.5739i −0.547801 + 0.948818i
\(518\) −0.649005 + 1.12411i −0.0285157 + 0.0493906i
\(519\) −1.32450 −0.0581390
\(520\) −3.19103 5.52703i −0.139936 0.242376i
\(521\) 1.91968 + 3.32498i 0.0841025 + 0.145670i 0.905008 0.425394i \(-0.139864\pi\)
−0.820906 + 0.571063i \(0.806531\pi\)
\(522\) −3.88198 + 6.72379i −0.169910 + 0.294292i
\(523\) 38.3566 1.67722 0.838609 0.544734i \(-0.183370\pi\)
0.838609 + 0.544734i \(0.183370\pi\)
\(524\) −1.00030 1.73257i −0.0436983 0.0756876i
\(525\) 0.137831 0.00601543
\(526\) −10.2981 −0.449018
\(527\) −0.223396 9.26625i −0.00973127 0.403644i
\(528\) −2.01425 −0.0876588
\(529\) −0.635718 −0.0276399
\(530\) −17.5479 30.3939i −0.762234 1.32023i
\(531\) 19.1587 0.831415
\(532\) −1.56806 + 2.71596i −0.0679840 + 0.117752i
\(533\) −0.561667 0.972836i −0.0243285 0.0421382i
\(534\) 0.564187 + 0.977201i 0.0244148 + 0.0422876i
\(535\) −29.8096 −1.28878
\(536\) 16.8129 29.1207i 0.726205 1.25782i
\(537\) 1.85246 3.20856i 0.0799397 0.138460i
\(538\) −17.3557 + 30.0610i −0.748259 + 1.29602i
\(539\) 1.89595 + 3.28388i 0.0816642 + 0.141447i
\(540\) −0.194765 + 0.337344i −0.00838137 + 0.0145170i
\(541\) −12.8613 22.2765i −0.552952 0.957741i −0.998060 0.0622638i \(-0.980168\pi\)
0.445108 0.895477i \(-0.353165\pi\)
\(542\) −22.5784 −0.969826
\(543\) 2.55191 0.109513
\(544\) 0.754108 + 1.30615i 0.0323321 + 0.0560008i
\(545\) −6.63495 + 11.4921i −0.284210 + 0.492266i
\(546\) 0.364495 + 0.631323i 0.0155989 + 0.0270181i
\(547\) 2.50748 4.34309i 0.107212 0.185697i −0.807428 0.589967i \(-0.799141\pi\)
0.914640 + 0.404270i \(0.132474\pi\)
\(548\) 0.537382 0.930773i 0.0229558 0.0397606i
\(549\) 8.77217 15.1938i 0.374387 0.648457i
\(550\) 1.02686 0.0437854
\(551\) −6.55108 11.3468i −0.279085 0.483390i
\(552\) −1.29392 2.24113i −0.0550728 0.0953888i
\(553\) 19.7032 34.1269i 0.837865 1.45123i
\(554\) −9.99883 −0.424810
\(555\) −0.0676208 0.117123i −0.00287034 0.00497158i
\(556\) 0.252676 0.0107158
\(557\) 0.0641080 0.00271634 0.00135817 0.999999i \(-0.499568\pi\)
0.00135817 + 0.999999i \(0.499568\pi\)
\(558\) −19.1155 + 11.6594i −0.809222 + 0.493584i
\(559\) −5.24942 −0.222027
\(560\) 22.9004 0.967719
\(561\) 0.458953 + 0.794930i 0.0193770 + 0.0335620i
\(562\) 20.5697 0.867682
\(563\) 3.22100 5.57894i 0.135749 0.235124i −0.790134 0.612934i \(-0.789989\pi\)
0.925883 + 0.377809i \(0.123323\pi\)
\(564\) 0.126485 + 0.219078i 0.00532597 + 0.00922486i
\(565\) −6.48079 11.2251i −0.272649 0.472242i
\(566\) 27.7715 1.16732
\(567\) −12.5021 + 21.6544i −0.525041 + 0.909397i
\(568\) 0.639249 1.10721i 0.0268223 0.0464575i
\(569\) 6.00352 10.3984i 0.251680 0.435923i −0.712308 0.701867i \(-0.752350\pi\)
0.963989 + 0.265943i \(0.0856835\pi\)
\(570\) 1.87181 + 3.24208i 0.0784017 + 0.135796i
\(571\) 18.8128 32.5848i 0.787293 1.36363i −0.140327 0.990105i \(-0.544815\pi\)
0.927620 0.373526i \(-0.121851\pi\)
\(572\) −0.237022 0.410533i −0.00991037 0.0171653i
\(573\) −4.49881 −0.187940
\(574\) 4.38510 0.183031
\(575\) 0.606340 + 1.05021i 0.0252861 + 0.0437968i
\(576\) 12.6536 21.9167i 0.527234 0.913197i
\(577\) −4.10675 7.11310i −0.170966 0.296122i 0.767792 0.640700i \(-0.221356\pi\)
−0.938758 + 0.344577i \(0.888022\pi\)
\(578\) 9.64886 16.7123i 0.401340 0.695140i
\(579\) 0.0186037 0.0322225i 0.000773142 0.00133912i
\(580\) 0.337550 0.584655i 0.0140160 0.0242765i
\(581\) 22.5159 0.934116
\(582\) −0.129171 0.223730i −0.00535430 0.00927391i
\(583\) −17.5400 30.3801i −0.726431 1.25822i
\(584\) −6.84222 + 11.8511i −0.283133 + 0.490401i
\(585\) 6.45797 0.267004
\(586\) −11.6509 20.1799i −0.481294 0.833625i
\(587\) 8.54422 0.352658 0.176329 0.984331i \(-0.443578\pi\)
0.176329 + 0.984331i \(0.443578\pi\)
\(588\) 0.0385059 0.00158796
\(589\) −0.910692 37.7747i −0.0375244 1.55648i
\(590\) 19.0862 0.785764
\(591\) −0.123960 −0.00509904
\(592\) 0.607353 + 1.05197i 0.0249620 + 0.0432355i
\(593\) 20.7398 0.851681 0.425840 0.904798i \(-0.359978\pi\)
0.425840 + 0.904798i \(0.359978\pi\)
\(594\) 2.23040 3.86316i 0.0915143 0.158507i
\(595\) −5.21794 9.03774i −0.213915 0.370511i
\(596\) −1.15648 2.00309i −0.0473714 0.0820497i
\(597\) 3.21434 0.131554
\(598\) −3.20694 + 5.55459i −0.131142 + 0.227144i
\(599\) −3.84848 + 6.66576i −0.157245 + 0.272356i −0.933874 0.357602i \(-0.883594\pi\)
0.776630 + 0.629958i \(0.216928\pi\)
\(600\) 0.0701613 0.121523i 0.00286432 0.00496115i
\(601\) 23.1095 + 40.0269i 0.942658 + 1.63273i 0.760374 + 0.649486i \(0.225016\pi\)
0.182285 + 0.983246i \(0.441651\pi\)
\(602\) 10.2459 17.7465i 0.417594 0.723293i
\(603\) 17.0128 + 29.4671i 0.692816 + 1.19999i
\(604\) 1.92238 0.0782204
\(605\) 4.97099 0.202099
\(606\) 1.46703 + 2.54097i 0.0595940 + 0.103220i
\(607\) −3.63460 + 6.29531i −0.147524 + 0.255519i −0.930312 0.366770i \(-0.880464\pi\)
0.782788 + 0.622289i \(0.213797\pi\)
\(608\) 3.07419 + 5.32464i 0.124675 + 0.215943i
\(609\) −0.518853 + 0.898680i −0.0210250 + 0.0364163i
\(610\) 8.73897 15.1363i 0.353830 0.612852i
\(611\) 4.21861 7.30684i 0.170667 0.295603i
\(612\) −0.792523 −0.0320358
\(613\) −21.2675 36.8364i −0.858985 1.48781i −0.872898 0.487903i \(-0.837762\pi\)
0.0139125 0.999903i \(-0.495571\pi\)
\(614\) 18.6616 + 32.3229i 0.753121 + 1.30444i
\(615\) −0.228445 + 0.395678i −0.00921179 + 0.0159553i
\(616\) 24.9020 1.00333
\(617\) −0.984131 1.70456i −0.0396196 0.0686232i 0.845536 0.533919i \(-0.179281\pi\)
−0.885155 + 0.465296i \(0.845948\pi\)
\(618\) −1.62549 −0.0653868
\(619\) 43.9663 1.76716 0.883578 0.468285i \(-0.155128\pi\)
0.883578 + 0.468285i \(0.155128\pi\)
\(620\) 1.66215 1.01383i 0.0667535 0.0407162i
\(621\) 5.26802 0.211398
\(622\) 32.5829 1.30646
\(623\) −6.41146 11.1050i −0.256870 0.444911i
\(624\) 0.682203 0.0273100
\(625\) 11.8260 20.4833i 0.473042 0.819333i
\(626\) −7.10878 12.3128i −0.284124 0.492117i
\(627\) 1.87096 + 3.24060i 0.0747191 + 0.129417i
\(628\) 1.47654 0.0589204
\(629\) 0.276775 0.479388i 0.0110357 0.0191145i
\(630\) −12.6048 + 21.8322i −0.502188 + 0.869815i
\(631\) 15.7299 27.2450i 0.626197 1.08461i −0.362111 0.932135i \(-0.617944\pi\)
0.988308 0.152470i \(-0.0487228\pi\)
\(632\) −20.0594 34.7439i −0.797920 1.38204i
\(633\) 1.71284 2.96672i 0.0680792 0.117917i
\(634\) −21.5077 37.2523i −0.854178 1.47948i
\(635\) −17.1093 −0.678960
\(636\) −0.356229 −0.0141254
\(637\) −0.642137 1.11221i −0.0254424 0.0440675i
\(638\) −3.86553 + 6.69530i −0.153038 + 0.265069i
\(639\) 0.646851 + 1.12038i 0.0255890 + 0.0443215i
\(640\) 10.6326 18.4161i 0.420289 0.727961i
\(641\) 1.03194 1.78737i 0.0407592 0.0705971i −0.844926 0.534883i \(-0.820356\pi\)
0.885685 + 0.464286i \(0.153689\pi\)
\(642\) 1.73328 3.00212i 0.0684070 0.118484i
\(643\) −15.7954 −0.622910 −0.311455 0.950261i \(-0.600816\pi\)
−0.311455 + 0.950261i \(0.600816\pi\)
\(644\) 1.09268 + 1.89258i 0.0430577 + 0.0745781i
\(645\) 1.06754 + 1.84903i 0.0420344 + 0.0728056i
\(646\) −7.66142 + 13.2700i −0.301435 + 0.522100i
\(647\) 9.03423 0.355172 0.177586 0.984105i \(-0.443171\pi\)
0.177586 + 0.984105i \(0.443171\pi\)
\(648\) 12.7282 + 22.0458i 0.500010 + 0.866042i
\(649\) 19.0775 0.748856
\(650\) −0.347786 −0.0136413
\(651\) −2.55491 + 1.55836i −0.100135 + 0.0610771i
\(652\) −0.0526405 −0.00206156
\(653\) −2.31286 −0.0905092 −0.0452546 0.998975i \(-0.514410\pi\)
−0.0452546 + 0.998975i \(0.514410\pi\)
\(654\) −0.771576 1.33641i −0.0301710 0.0522577i
\(655\) 27.1390 1.06041
\(656\) 2.05183 3.55388i 0.0801107 0.138756i
\(657\) −6.92360 11.9920i −0.270115 0.467853i
\(658\) 16.4680 + 28.5234i 0.641988 + 1.11196i
\(659\) −13.3775 −0.521113 −0.260557 0.965459i \(-0.583906\pi\)
−0.260557 + 0.965459i \(0.583906\pi\)
\(660\) −0.0964031 + 0.166975i −0.00375248 + 0.00649949i
\(661\) −8.35346 + 14.4686i −0.324912 + 0.562764i −0.981495 0.191490i \(-0.938668\pi\)
0.656582 + 0.754254i \(0.272001\pi\)
\(662\) −5.53790 + 9.59193i −0.215237 + 0.372801i
\(663\) −0.155443 0.269234i −0.00603689 0.0104562i
\(664\) 11.4615 19.8518i 0.444791 0.770401i
\(665\) −21.2714 36.8431i −0.824869 1.42872i
\(666\) −1.33719 −0.0518152
\(667\) −9.13008 −0.353518
\(668\) −0.0416482 0.0721368i −0.00161142 0.00279106i
\(669\) 1.21635 2.10677i 0.0470267 0.0814526i
\(670\) 16.9484 + 29.3555i 0.654775 + 1.13410i
\(671\) 8.73499 15.1295i 0.337211 0.584066i
\(672\) 0.243479 0.421718i 0.00939240 0.0162681i
\(673\) −25.4022 + 43.9979i −0.979182 + 1.69599i −0.313803 + 0.949488i \(0.601603\pi\)
−0.665380 + 0.746505i \(0.731730\pi\)
\(674\) −27.0829 −1.04319
\(675\) 0.142826 + 0.247383i 0.00549739 + 0.00952176i
\(676\) 0.0802766 + 0.139043i 0.00308756 + 0.00534782i
\(677\) 11.8003 20.4387i 0.453523 0.785524i −0.545079 0.838384i \(-0.683500\pi\)
0.998602 + 0.0528604i \(0.0168338\pi\)
\(678\) 1.50730 0.0578875
\(679\) 1.46790 + 2.54248i 0.0563329 + 0.0975715i
\(680\) −10.6246 −0.407433
\(681\) −4.18212 −0.160259
\(682\) −19.0344 + 11.6100i −0.728866 + 0.444571i
\(683\) −46.6744 −1.78594 −0.892972 0.450111i \(-0.851384\pi\)
−0.892972 + 0.450111i \(0.851384\pi\)
\(684\) −3.23079 −0.123532
\(685\) 7.28981 + 12.6263i 0.278530 + 0.482427i
\(686\) −22.3122 −0.851883
\(687\) 2.43987 4.22598i 0.0930870 0.161231i
\(688\) −9.58837 16.6075i −0.365553 0.633157i
\(689\) 5.94060 + 10.2894i 0.226319 + 0.391996i
\(690\) 2.60870 0.0993115
\(691\) −3.43710 + 5.95323i −0.130753 + 0.226471i −0.923967 0.382472i \(-0.875073\pi\)
0.793214 + 0.608943i \(0.208406\pi\)
\(692\) 0.569364 0.986168i 0.0216440 0.0374885i
\(693\) −12.5991 + 21.8223i −0.478600 + 0.828959i
\(694\) −10.3261 17.8854i −0.391975 0.678921i
\(695\) −1.71383 + 2.96844i −0.0650092 + 0.112599i
\(696\) 0.528233 + 0.914927i 0.0200226 + 0.0346802i
\(697\) −1.87007 −0.0708340
\(698\) −36.2367 −1.37158
\(699\) 1.00692 + 1.74403i 0.0380851 + 0.0659654i
\(700\) −0.0592495 + 0.102623i −0.00223942 + 0.00387879i
\(701\) −21.7566 37.6835i −0.821736 1.42329i −0.904389 0.426710i \(-0.859673\pi\)
0.0826530 0.996578i \(-0.473661\pi\)
\(702\) −0.755411 + 1.30841i −0.0285112 + 0.0493828i
\(703\) 1.12830 1.95427i 0.0425545 0.0737066i
\(704\) 12.6000 21.8238i 0.474880 0.822517i
\(705\) −3.43164 −0.129243
\(706\) 12.5852 + 21.7983i 0.473652 + 0.820389i
\(707\) −16.6714 28.8757i −0.626992 1.08598i
\(708\) 0.0968638 0.167773i 0.00364036 0.00630530i
\(709\) 9.78000 0.367296 0.183648 0.982992i \(-0.441209\pi\)
0.183648 + 0.982992i \(0.441209\pi\)
\(710\) 0.644403 + 1.11614i 0.0241840 + 0.0418879i
\(711\) 40.5959 1.52247
\(712\) −13.0547 −0.489247
\(713\) −23.1135 12.6118i −0.865608 0.472316i
\(714\) 1.21359 0.0454173
\(715\) 6.43060 0.240491
\(716\) 1.59264 + 2.75854i 0.0595199 + 0.103091i
\(717\) 4.11732 0.153764
\(718\) −8.18479 + 14.1765i −0.305454 + 0.529061i
\(719\) −11.4743 19.8740i −0.427918 0.741175i 0.568770 0.822496i \(-0.307419\pi\)
−0.996688 + 0.0813213i \(0.974086\pi\)
\(720\) 11.7959 + 20.4310i 0.439605 + 0.761419i
\(721\) 18.4722 0.687939
\(722\) −18.3480 + 31.7796i −0.682840 + 1.18271i
\(723\) 0.840041 1.45499i 0.0312415 0.0541118i
\(724\) −1.09699 + 1.90005i −0.0407695 + 0.0706148i
\(725\) −0.247534 0.428742i −0.00919319 0.0159231i
\(726\) −0.289037 + 0.500628i −0.0107272 + 0.0185800i
\(727\) −11.3168 19.6013i −0.419717 0.726972i 0.576194 0.817313i \(-0.304537\pi\)
−0.995911 + 0.0903416i \(0.971204\pi\)
\(728\) −8.43404 −0.312586
\(729\) −25.1350 −0.930926
\(730\) −6.89739 11.9466i −0.255284 0.442165i
\(731\) −4.36949 + 7.56818i −0.161611 + 0.279919i
\(732\) −0.0887020 0.153636i −0.00327852 0.00567856i
\(733\) −3.75883 + 6.51048i −0.138835 + 0.240470i −0.927056 0.374923i \(-0.877669\pi\)
0.788221 + 0.615393i \(0.211003\pi\)
\(734\) −24.4072 + 42.2746i −0.900888 + 1.56038i
\(735\) −0.261174 + 0.452367i −0.00963356 + 0.0166858i
\(736\) 4.28441 0.157926
\(737\) 16.9407 + 29.3422i 0.624019 + 1.08083i
\(738\) 2.25874 + 3.91225i 0.0831452 + 0.144012i
\(739\) 17.6005 30.4849i 0.647445 1.12141i −0.336287 0.941760i \(-0.609171\pi\)
0.983731 0.179647i \(-0.0574956\pi\)
\(740\) 0.116273 0.00427428
\(741\) −0.633675 1.09756i −0.0232786 0.0403198i
\(742\) −46.3800 −1.70266
\(743\) 17.9335 0.657915 0.328957 0.944345i \(-0.393303\pi\)
0.328957 + 0.944345i \(0.393303\pi\)
\(744\) 0.0734318 + 3.04589i 0.00269214 + 0.111668i
\(745\) 31.3764 1.14954
\(746\) 42.5708 1.55863
\(747\) 11.5978 + 20.0879i 0.424341 + 0.734979i
\(748\) −0.789164 −0.0288547
\(749\) −19.6970 + 34.1163i −0.719714 + 1.24658i
\(750\) 1.44980 + 2.51112i 0.0529391 + 0.0916933i
\(751\) 15.0065 + 25.9921i 0.547596 + 0.948465i 0.998439 + 0.0558611i \(0.0177904\pi\)
−0.450842 + 0.892604i \(0.648876\pi\)
\(752\) 30.8221 1.12397
\(753\) −2.70694 + 4.68856i −0.0986463 + 0.170860i
\(754\) 1.30921 2.26762i 0.0476787 0.0825820i
\(755\) −13.0389 + 22.5841i −0.474535 + 0.821919i
\(756\) 0.257387 + 0.445807i 0.00936107 + 0.0162138i
\(757\) −0.495280 + 0.857850i −0.0180012 + 0.0311791i −0.874886 0.484329i \(-0.839064\pi\)
0.856884 + 0.515509i \(0.172397\pi\)
\(758\) −18.8357 32.6243i −0.684142 1.18497i
\(759\) 2.60751 0.0946467
\(760\) −43.3119 −1.57109
\(761\) −21.9233 37.9723i −0.794720 1.37650i −0.923017 0.384760i \(-0.874284\pi\)
0.128296 0.991736i \(-0.459049\pi\)
\(762\) 0.994816 1.72307i 0.0360384 0.0624203i
\(763\) 8.76823 + 15.1870i 0.317431 + 0.549807i
\(764\) 1.93391 3.34963i 0.0699664 0.121185i
\(765\) 5.37546 9.31056i 0.194350 0.336624i
\(766\) −7.59559 + 13.1559i −0.274440 + 0.475343i
\(767\) −6.46133 −0.233305
\(768\) −0.357411 0.619053i −0.0128969 0.0223382i
\(769\) 20.8735 + 36.1540i 0.752719 + 1.30375i 0.946500 + 0.322703i \(0.104591\pi\)
−0.193781 + 0.981045i \(0.562075\pi\)
\(770\) −12.5514 + 21.7397i −0.452321 + 0.783443i