Properties

Label 804.2.c.b.671.20
Level 804
Weight 2
Character 804.671
Analytic conductor 6.420
Analytic rank 0
Dimension 128
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(128\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 671.20
Character \(\chi\) = 804.671
Dual form 804.2.c.b.671.19

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.27439 + 0.613127i) q^{2} +(-1.63926 + 0.559297i) q^{3} +(1.24815 - 1.56273i) q^{4} +0.350980i q^{5} +(1.74615 - 1.71784i) q^{6} -2.98214i q^{7} +(-0.632485 + 2.75680i) q^{8} +(2.37437 - 1.83367i) q^{9} +O(q^{10})\) \(q+(-1.27439 + 0.613127i) q^{2} +(-1.63926 + 0.559297i) q^{3} +(1.24815 - 1.56273i) q^{4} +0.350980i q^{5} +(1.74615 - 1.71784i) q^{6} -2.98214i q^{7} +(-0.632485 + 2.75680i) q^{8} +(2.37437 - 1.83367i) q^{9} +(-0.215195 - 0.447286i) q^{10} -1.69575 q^{11} +(-1.17202 + 3.25981i) q^{12} -4.42815 q^{13} +(1.82843 + 3.80041i) q^{14} +(-0.196302 - 0.575349i) q^{15} +(-0.884236 - 3.90104i) q^{16} -2.00327i q^{17} +(-1.90161 + 3.79261i) q^{18} +1.45165i q^{19} +(0.548486 + 0.438076i) q^{20} +(1.66790 + 4.88851i) q^{21} +(2.16105 - 1.03971i) q^{22} +3.48501 q^{23} +(-0.505063 - 4.87288i) q^{24} +4.87681 q^{25} +(5.64319 - 2.71501i) q^{26} +(-2.86666 + 4.33385i) q^{27} +(-4.66027 - 3.72216i) q^{28} +3.03917i q^{29} +(0.602928 + 0.612862i) q^{30} +10.5902i q^{31} +(3.51870 + 4.42931i) q^{32} +(2.77978 - 0.948428i) q^{33} +(1.22826 + 2.55295i) q^{34} +1.04667 q^{35} +(0.0980481 - 5.99920i) q^{36} -6.83128 q^{37} +(-0.890047 - 1.84997i) q^{38} +(7.25890 - 2.47665i) q^{39} +(-0.967583 - 0.221989i) q^{40} +0.934816i q^{41} +(-5.12284 - 5.20725i) q^{42} +2.28333i q^{43} +(-2.11655 + 2.65000i) q^{44} +(0.643582 + 0.833358i) q^{45} +(-4.44127 + 2.13675i) q^{46} -11.7382 q^{47} +(3.63134 + 5.90029i) q^{48} -1.89315 q^{49} +(-6.21497 + 2.99010i) q^{50} +(1.12042 + 3.28388i) q^{51} +(-5.52700 + 6.91999i) q^{52} -1.53931i q^{53} +(0.996046 - 7.28065i) q^{54} -0.595174i q^{55} +(8.22117 + 1.88616i) q^{56} +(-0.811905 - 2.37964i) q^{57} +(-1.86339 - 3.87309i) q^{58} -14.8437 q^{59} +(-1.14413 - 0.411356i) q^{60} -3.43726 q^{61} +(-6.49314 - 13.4961i) q^{62} +(-5.46826 - 7.08071i) q^{63} +(-7.19993 - 3.48727i) q^{64} -1.55419i q^{65} +(-2.96103 + 2.91303i) q^{66} -1.00000i q^{67} +(-3.13056 - 2.50038i) q^{68} +(-5.71286 + 1.94916i) q^{69} +(-1.33387 + 0.641742i) q^{70} +14.0214 q^{71} +(3.55332 + 7.70545i) q^{72} -5.28996 q^{73} +(8.70573 - 4.18844i) q^{74} +(-7.99438 + 2.72759i) q^{75} +(2.26854 + 1.81188i) q^{76} +5.05696i q^{77} +(-7.73219 + 7.60685i) q^{78} +16.7488i q^{79} +(1.36919 - 0.310349i) q^{80} +(2.27530 - 8.70764i) q^{81} +(-0.573160 - 1.19132i) q^{82} -6.63054 q^{83} +(9.72121 + 3.49513i) q^{84} +0.703107 q^{85} +(-1.39997 - 2.90986i) q^{86} +(-1.69980 - 4.98200i) q^{87} +(1.07254 - 4.67485i) q^{88} -5.60971i q^{89} +(-1.33113 - 0.667427i) q^{90} +13.2053i q^{91} +(4.34982 - 5.44613i) q^{92} +(-5.92307 - 17.3601i) q^{93} +(14.9591 - 7.19702i) q^{94} -0.509501 q^{95} +(-8.24537 - 5.29281i) q^{96} -9.69599 q^{97} +(2.41261 - 1.16074i) q^{98} +(-4.02634 + 3.10945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q + 4q^{4} - 6q^{6} - 4q^{9} + O(q^{10}) \) \( 128q + 4q^{4} - 6q^{6} - 4q^{9} - 4q^{10} + 4q^{12} - 8q^{13} - 4q^{16} + 18q^{18} - 8q^{21} - 8q^{22} - 24q^{24} - 136q^{25} + 14q^{30} - 32q^{33} + 34q^{36} - 48q^{37} + 16q^{40} - 28q^{42} - 16q^{45} - 28q^{46} - 22q^{48} - 152q^{49} + 8q^{52} - 16q^{54} - 32q^{57} - 20q^{58} - 14q^{60} + 8q^{61} + 16q^{64} + 14q^{66} + 56q^{69} - 4q^{70} - 8q^{72} - 48q^{73} - 36q^{76} + 40q^{78} + 44q^{81} + 60q^{82} + 46q^{84} + 64q^{85} - 28q^{88} - 14q^{90} + 32q^{93} - 8q^{96} + 64q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.27439 + 0.613127i −0.901131 + 0.433546i
\(3\) −1.63926 + 0.559297i −0.946430 + 0.322910i
\(4\) 1.24815 1.56273i 0.624076 0.781364i
\(5\) 0.350980i 0.156963i 0.996916 + 0.0784815i \(0.0250072\pi\)
−0.996916 + 0.0784815i \(0.974993\pi\)
\(6\) 1.74615 1.71784i 0.712861 0.701305i
\(7\) 2.98214i 1.12714i −0.826068 0.563571i \(-0.809427\pi\)
0.826068 0.563571i \(-0.190573\pi\)
\(8\) −0.632485 + 2.75680i −0.223617 + 0.974677i
\(9\) 2.37437 1.83367i 0.791458 0.611224i
\(10\) −0.215195 0.447286i −0.0680507 0.141444i
\(11\) −1.69575 −0.511288 −0.255644 0.966771i \(-0.582287\pi\)
−0.255644 + 0.966771i \(0.582287\pi\)
\(12\) −1.17202 + 3.25981i −0.338333 + 0.941026i
\(13\) −4.42815 −1.22815 −0.614073 0.789249i \(-0.710470\pi\)
−0.614073 + 0.789249i \(0.710470\pi\)
\(14\) 1.82843 + 3.80041i 0.488668 + 1.01570i
\(15\) −0.196302 0.575349i −0.0506850 0.148554i
\(16\) −0.884236 3.90104i −0.221059 0.975260i
\(17\) 2.00327i 0.485863i −0.970043 0.242932i \(-0.921891\pi\)
0.970043 0.242932i \(-0.0781091\pi\)
\(18\) −1.90161 + 3.79261i −0.448214 + 0.893926i
\(19\) 1.45165i 0.333032i 0.986039 + 0.166516i \(0.0532517\pi\)
−0.986039 + 0.166516i \(0.946748\pi\)
\(20\) 0.548486 + 0.438076i 0.122645 + 0.0979568i
\(21\) 1.66790 + 4.88851i 0.363966 + 1.06676i
\(22\) 2.16105 1.03971i 0.460737 0.221667i
\(23\) 3.48501 0.726675 0.363338 0.931658i \(-0.381637\pi\)
0.363338 + 0.931658i \(0.381637\pi\)
\(24\) −0.505063 4.87288i −0.103096 0.994671i
\(25\) 4.87681 0.975363
\(26\) 5.64319 2.71501i 1.10672 0.532458i
\(27\) −2.86666 + 4.33385i −0.551689 + 0.834050i
\(28\) −4.66027 3.72216i −0.880708 0.703422i
\(29\) 3.03917i 0.564359i 0.959362 + 0.282180i \(0.0910574\pi\)
−0.959362 + 0.282180i \(0.908943\pi\)
\(30\) 0.602928 + 0.612862i 0.110079 + 0.111893i
\(31\) 10.5902i 1.90206i 0.309104 + 0.951028i \(0.399971\pi\)
−0.309104 + 0.951028i \(0.600029\pi\)
\(32\) 3.51870 + 4.42931i 0.622023 + 0.782999i
\(33\) 2.77978 0.948428i 0.483898 0.165100i
\(34\) 1.22826 + 2.55295i 0.210644 + 0.437827i
\(35\) 1.04667 0.176920
\(36\) 0.0980481 5.99920i 0.0163414 0.999866i
\(37\) −6.83128 −1.12305 −0.561527 0.827458i \(-0.689786\pi\)
−0.561527 + 0.827458i \(0.689786\pi\)
\(38\) −0.890047 1.84997i −0.144385 0.300105i
\(39\) 7.25890 2.47665i 1.16235 0.396581i
\(40\) −0.967583 0.221989i −0.152988 0.0350996i
\(41\) 0.934816i 0.145994i 0.997332 + 0.0729968i \(0.0232563\pi\)
−0.997332 + 0.0729968i \(0.976744\pi\)
\(42\) −5.12284 5.20725i −0.790471 0.803496i
\(43\) 2.28333i 0.348205i 0.984728 + 0.174103i \(0.0557024\pi\)
−0.984728 + 0.174103i \(0.944298\pi\)
\(44\) −2.11655 + 2.65000i −0.319082 + 0.399502i
\(45\) 0.643582 + 0.833358i 0.0959396 + 0.124230i
\(46\) −4.44127 + 2.13675i −0.654830 + 0.315047i
\(47\) −11.7382 −1.71220 −0.856099 0.516813i \(-0.827118\pi\)
−0.856099 + 0.516813i \(0.827118\pi\)
\(48\) 3.63134 + 5.90029i 0.524138 + 0.851633i
\(49\) −1.89315 −0.270450
\(50\) −6.21497 + 2.99010i −0.878930 + 0.422865i
\(51\) 1.12042 + 3.28388i 0.156890 + 0.459836i
\(52\) −5.52700 + 6.91999i −0.766456 + 0.959629i
\(53\) 1.53931i 0.211441i −0.994396 0.105720i \(-0.966285\pi\)
0.994396 0.105720i \(-0.0337149\pi\)
\(54\) 0.996046 7.28065i 0.135545 0.990771i
\(55\) 0.595174i 0.0802533i
\(56\) 8.22117 + 1.88616i 1.09860 + 0.252048i
\(57\) −0.811905 2.37964i −0.107539 0.315191i
\(58\) −1.86339 3.87309i −0.244676 0.508562i
\(59\) −14.8437 −1.93248 −0.966241 0.257641i \(-0.917055\pi\)
−0.966241 + 0.257641i \(0.917055\pi\)
\(60\) −1.14413 0.411356i −0.147706 0.0531058i
\(61\) −3.43726 −0.440096 −0.220048 0.975489i \(-0.570621\pi\)
−0.220048 + 0.975489i \(0.570621\pi\)
\(62\) −6.49314 13.4961i −0.824629 1.71400i
\(63\) −5.46826 7.08071i −0.688936 0.892086i
\(64\) −7.19993 3.48727i −0.899991 0.435909i
\(65\) 1.55419i 0.192774i
\(66\) −2.96103 + 2.91303i −0.364477 + 0.358569i
\(67\) 1.00000i 0.122169i
\(68\) −3.13056 2.50038i −0.379636 0.303216i
\(69\) −5.71286 + 1.94916i −0.687747 + 0.234651i
\(70\) −1.33387 + 0.641742i −0.159428 + 0.0767028i
\(71\) 14.0214 1.66403 0.832017 0.554750i \(-0.187186\pi\)
0.832017 + 0.554750i \(0.187186\pi\)
\(72\) 3.55332 + 7.70545i 0.418762 + 0.908096i
\(73\) −5.28996 −0.619143 −0.309572 0.950876i \(-0.600186\pi\)
−0.309572 + 0.950876i \(0.600186\pi\)
\(74\) 8.70573 4.18844i 1.01202 0.486896i
\(75\) −7.99438 + 2.72759i −0.923112 + 0.314955i
\(76\) 2.26854 + 1.81188i 0.260219 + 0.207837i
\(77\) 5.05696i 0.576294i
\(78\) −7.73219 + 7.60685i −0.875498 + 0.861306i
\(79\) 16.7488i 1.88439i 0.335062 + 0.942196i \(0.391243\pi\)
−0.335062 + 0.942196i \(0.608757\pi\)
\(80\) 1.36919 0.310349i 0.153080 0.0346981i
\(81\) 2.27530 8.70764i 0.252811 0.967516i
\(82\) −0.573160 1.19132i −0.0632950 0.131559i
\(83\) −6.63054 −0.727797 −0.363898 0.931439i \(-0.618554\pi\)
−0.363898 + 0.931439i \(0.618554\pi\)
\(84\) 9.72121 + 3.49513i 1.06067 + 0.381350i
\(85\) 0.703107 0.0762626
\(86\) −1.39997 2.90986i −0.150963 0.313779i
\(87\) −1.69980 4.98200i −0.182237 0.534126i
\(88\) 1.07254 4.67485i 0.114333 0.498340i
\(89\) 5.60971i 0.594628i −0.954780 0.297314i \(-0.903909\pi\)
0.954780 0.297314i \(-0.0960908\pi\)
\(90\) −1.33113 0.667427i −0.140313 0.0703530i
\(91\) 13.2053i 1.38430i
\(92\) 4.34982 5.44613i 0.453500 0.567798i
\(93\) −5.92307 17.3601i −0.614194 1.80016i
\(94\) 14.9591 7.19702i 1.54291 0.742316i
\(95\) −0.509501 −0.0522737
\(96\) −8.24537 5.29281i −0.841540 0.540195i
\(97\) −9.69599 −0.984479 −0.492239 0.870460i \(-0.663822\pi\)
−0.492239 + 0.870460i \(0.663822\pi\)
\(98\) 2.41261 1.16074i 0.243711 0.117252i
\(99\) −4.02634 + 3.10945i −0.404663 + 0.312511i
\(100\) 6.08700 7.62113i 0.608700 0.762113i
\(101\) 12.5232i 1.24610i 0.782180 + 0.623052i \(0.214108\pi\)
−0.782180 + 0.623052i \(0.785892\pi\)
\(102\) −3.44129 3.49799i −0.340739 0.346353i
\(103\) 3.32384i 0.327508i 0.986501 + 0.163754i \(0.0523603\pi\)
−0.986501 + 0.163754i \(0.947640\pi\)
\(104\) 2.80073 12.2075i 0.274635 1.19705i
\(105\) −1.71577 + 0.585400i −0.167442 + 0.0571292i
\(106\) 0.943794 + 1.96169i 0.0916694 + 0.190536i
\(107\) −0.522441 −0.0505063 −0.0252531 0.999681i \(-0.508039\pi\)
−0.0252531 + 0.999681i \(0.508039\pi\)
\(108\) 3.19461 + 9.88911i 0.307401 + 0.951580i
\(109\) −10.6357 −1.01872 −0.509358 0.860554i \(-0.670117\pi\)
−0.509358 + 0.860554i \(0.670117\pi\)
\(110\) 0.364917 + 0.758486i 0.0347935 + 0.0723188i
\(111\) 11.1983 3.82071i 1.06289 0.362646i
\(112\) −11.6334 + 2.63691i −1.09926 + 0.249165i
\(113\) 15.8801i 1.49387i 0.664895 + 0.746937i \(0.268476\pi\)
−0.664895 + 0.746937i \(0.731524\pi\)
\(114\) 2.49371 + 2.53480i 0.233557 + 0.237405i
\(115\) 1.22317i 0.114061i
\(116\) 4.74939 + 3.79334i 0.440970 + 0.352203i
\(117\) −10.5141 + 8.11976i −0.972026 + 0.750672i
\(118\) 18.9167 9.10105i 1.74142 0.837820i
\(119\) −5.97402 −0.547637
\(120\) 1.71028 0.177267i 0.156127 0.0161822i
\(121\) −8.12443 −0.738585
\(122\) 4.38041 2.10747i 0.396584 0.190802i
\(123\) −0.522840 1.53241i −0.0471429 0.138173i
\(124\) 16.5496 + 13.2182i 1.48620 + 1.18703i
\(125\) 3.46656i 0.310059i
\(126\) 11.3101 + 5.67086i 1.00758 + 0.505201i
\(127\) 5.42211i 0.481135i −0.970632 0.240567i \(-0.922666\pi\)
0.970632 0.240567i \(-0.0773335\pi\)
\(128\) 11.3137 + 0.0296842i 0.999997 + 0.00262374i
\(129\) −1.27706 3.74299i −0.112439 0.329552i
\(130\) 0.952916 + 1.98065i 0.0835762 + 0.173714i
\(131\) 9.82550 0.858458 0.429229 0.903196i \(-0.358785\pi\)
0.429229 + 0.903196i \(0.358785\pi\)
\(132\) 1.98745 5.52782i 0.172986 0.481135i
\(133\) 4.32903 0.375374
\(134\) 0.613127 + 1.27439i 0.0529661 + 0.110091i
\(135\) −1.52110 1.00614i −0.130915 0.0865947i
\(136\) 5.52261 + 1.26704i 0.473560 + 0.108647i
\(137\) 0.602999i 0.0515177i 0.999668 + 0.0257589i \(0.00820021\pi\)
−0.999668 + 0.0257589i \(0.991800\pi\)
\(138\) 6.08534 5.98670i 0.518018 0.509621i
\(139\) 16.3980i 1.39086i −0.718595 0.695429i \(-0.755214\pi\)
0.718595 0.695429i \(-0.244786\pi\)
\(140\) 1.30640 1.63566i 0.110411 0.138239i
\(141\) 19.2421 6.56516i 1.62047 0.552886i
\(142\) −17.8688 + 8.59690i −1.49951 + 0.721436i
\(143\) 7.50903 0.627936
\(144\) −9.25274 7.64113i −0.771061 0.636761i
\(145\) −1.06669 −0.0885836
\(146\) 6.74148 3.24342i 0.557929 0.268427i
\(147\) 3.10337 1.05883i 0.255962 0.0873311i
\(148\) −8.52647 + 10.6754i −0.700871 + 0.877515i
\(149\) 1.22296i 0.100189i −0.998744 0.0500945i \(-0.984048\pi\)
0.998744 0.0500945i \(-0.0159523\pi\)
\(150\) 8.51562 8.37759i 0.695298 0.684027i
\(151\) 13.9947i 1.13887i 0.822037 + 0.569435i \(0.192838\pi\)
−0.822037 + 0.569435i \(0.807162\pi\)
\(152\) −4.00192 0.918147i −0.324598 0.0744716i
\(153\) −3.67333 4.75650i −0.296971 0.384540i
\(154\) −3.10056 6.44455i −0.249850 0.519317i
\(155\) −3.71695 −0.298553
\(156\) 5.18988 14.4349i 0.415523 1.15572i
\(157\) 3.91727 0.312632 0.156316 0.987707i \(-0.450038\pi\)
0.156316 + 0.987707i \(0.450038\pi\)
\(158\) −10.2692 21.3446i −0.816971 1.69809i
\(159\) 0.860934 + 2.52334i 0.0682765 + 0.200114i
\(160\) −1.55460 + 1.23499i −0.122902 + 0.0976347i
\(161\) 10.3928i 0.819067i
\(162\) 2.43927 + 12.4920i 0.191647 + 0.981464i
\(163\) 1.06905i 0.0837345i −0.999123 0.0418673i \(-0.986669\pi\)
0.999123 0.0418673i \(-0.0133307\pi\)
\(164\) 1.46086 + 1.16679i 0.114074 + 0.0911111i
\(165\) 0.332879 + 0.975648i 0.0259146 + 0.0759541i
\(166\) 8.44991 4.06536i 0.655841 0.315533i
\(167\) 5.77658 0.447005 0.223503 0.974703i \(-0.428251\pi\)
0.223503 + 0.974703i \(0.428251\pi\)
\(168\) −14.5316 + 1.50617i −1.12114 + 0.116203i
\(169\) 6.60847 0.508344
\(170\) −0.896034 + 0.431093i −0.0687226 + 0.0330634i
\(171\) 2.66185 + 3.44676i 0.203557 + 0.263581i
\(172\) 3.56823 + 2.84995i 0.272075 + 0.217306i
\(173\) 11.3842i 0.865521i 0.901509 + 0.432761i \(0.142460\pi\)
−0.901509 + 0.432761i \(0.857540\pi\)
\(174\) 5.22080 + 5.30683i 0.395788 + 0.402310i
\(175\) 14.5433i 1.09937i
\(176\) 1.49944 + 6.61519i 0.113025 + 0.498639i
\(177\) 24.3327 8.30202i 1.82896 0.624018i
\(178\) 3.43946 + 7.14897i 0.257799 + 0.535838i
\(179\) 6.51691 0.487097 0.243548 0.969889i \(-0.421689\pi\)
0.243548 + 0.969889i \(0.421689\pi\)
\(180\) 2.10560 + 0.0344129i 0.156942 + 0.00256499i
\(181\) 16.6921 1.24071 0.620357 0.784320i \(-0.286988\pi\)
0.620357 + 0.784320i \(0.286988\pi\)
\(182\) −8.09655 16.8288i −0.600156 1.24743i
\(183\) 5.63457 1.92245i 0.416520 0.142111i
\(184\) −2.20422 + 9.60749i −0.162497 + 0.708274i
\(185\) 2.39764i 0.176278i
\(186\) 18.1923 + 18.4920i 1.33392 + 1.35590i
\(187\) 3.39704i 0.248416i
\(188\) −14.6511 + 18.3437i −1.06854 + 1.33785i
\(189\) 12.9241 + 8.54877i 0.940093 + 0.621831i
\(190\) 0.649304 0.312389i 0.0471055 0.0226631i
\(191\) 11.6575 0.843505 0.421752 0.906711i \(-0.361415\pi\)
0.421752 + 0.906711i \(0.361415\pi\)
\(192\) 13.7530 + 1.68966i 0.992537 + 0.121941i
\(193\) −18.5012 −1.33174 −0.665872 0.746066i \(-0.731940\pi\)
−0.665872 + 0.746066i \(0.731940\pi\)
\(194\) 12.3565 5.94487i 0.887145 0.426817i
\(195\) 0.869254 + 2.54773i 0.0622486 + 0.182447i
\(196\) −2.36294 + 2.95848i −0.168781 + 0.211320i
\(197\) 7.06882i 0.503632i −0.967775 0.251816i \(-0.918972\pi\)
0.967775 0.251816i \(-0.0810278\pi\)
\(198\) 3.22465 6.43131i 0.229166 0.457054i
\(199\) 13.5499i 0.960530i 0.877124 + 0.480265i \(0.159459\pi\)
−0.877124 + 0.480265i \(0.840541\pi\)
\(200\) −3.08451 + 13.4444i −0.218108 + 0.950664i
\(201\) 0.559297 + 1.63926i 0.0394498 + 0.115625i
\(202\) −7.67830 15.9595i −0.540243 1.12290i
\(203\) 9.06322 0.636113
\(204\) 6.53027 + 2.34787i 0.457210 + 0.164384i
\(205\) −0.328102 −0.0229156
\(206\) −2.03793 4.23588i −0.141990 0.295127i
\(207\) 8.27472 6.39037i 0.575133 0.444161i
\(208\) 3.91553 + 17.2744i 0.271493 + 1.19776i
\(209\) 2.46164i 0.170275i
\(210\) 1.82764 1.79801i 0.126119 0.124075i
\(211\) 6.42279i 0.442163i 0.975255 + 0.221082i \(0.0709587\pi\)
−0.975255 + 0.221082i \(0.929041\pi\)
\(212\) −2.40553 1.92130i −0.165212 0.131955i
\(213\) −22.9848 + 7.84213i −1.57489 + 0.537334i
\(214\) 0.665794 0.320322i 0.0455128 0.0218968i
\(215\) −0.801405 −0.0546553
\(216\) −10.1345 10.6439i −0.689563 0.724226i
\(217\) 31.5814 2.14389
\(218\) 13.5541 6.52104i 0.917998 0.441661i
\(219\) 8.67164 2.95866i 0.585975 0.199928i
\(220\) −0.930095 0.742868i −0.0627070 0.0500841i
\(221\) 8.87075i 0.596712i
\(222\) −11.9284 + 11.7350i −0.800582 + 0.787605i
\(223\) 28.1790i 1.88701i −0.331362 0.943504i \(-0.607508\pi\)
0.331362 0.943504i \(-0.392492\pi\)
\(224\) 13.2088 10.4932i 0.882551 0.701109i
\(225\) 11.5794 8.94247i 0.771958 0.596165i
\(226\) −9.73651 20.2375i −0.647663 1.34618i
\(227\) 4.26297 0.282943 0.141472 0.989942i \(-0.454817\pi\)
0.141472 + 0.989942i \(0.454817\pi\)
\(228\) −4.73211 1.70137i −0.313392 0.112676i
\(229\) 18.4957 1.22223 0.611114 0.791543i \(-0.290722\pi\)
0.611114 + 0.791543i \(0.290722\pi\)
\(230\) −0.749958 1.55880i −0.0494508 0.102784i
\(231\) −2.82834 8.28969i −0.186091 0.545422i
\(232\) −8.37839 1.92223i −0.550068 0.126200i
\(233\) 23.5352i 1.54184i 0.636932 + 0.770920i \(0.280203\pi\)
−0.636932 + 0.770920i \(0.719797\pi\)
\(234\) 8.42061 16.7942i 0.550472 1.09787i
\(235\) 4.11989i 0.268752i
\(236\) −18.5272 + 23.1966i −1.20601 + 1.50997i
\(237\) −9.36758 27.4558i −0.608490 1.78344i
\(238\) 7.61324 3.66283i 0.493493 0.237426i
\(239\) −9.29173 −0.601032 −0.300516 0.953777i \(-0.597159\pi\)
−0.300516 + 0.953777i \(0.597159\pi\)
\(240\) −2.07088 + 1.27453i −0.133675 + 0.0822704i
\(241\) −17.3434 −1.11719 −0.558593 0.829442i \(-0.688659\pi\)
−0.558593 + 0.829442i \(0.688659\pi\)
\(242\) 10.3537 4.98131i 0.665562 0.320211i
\(243\) 1.14035 + 15.5467i 0.0731532 + 0.997321i
\(244\) −4.29022 + 5.37150i −0.274653 + 0.343875i
\(245\) 0.664458i 0.0424506i
\(246\) 1.60586 + 1.63232i 0.102386 + 0.104073i
\(247\) 6.42813i 0.409012i
\(248\) −29.1951 6.69814i −1.85389 0.425332i
\(249\) 10.8692 3.70844i 0.688808 0.235013i
\(250\) −2.12544 4.41776i −0.134425 0.279404i
\(251\) −12.0936 −0.763344 −0.381672 0.924298i \(-0.624652\pi\)
−0.381672 + 0.924298i \(0.624652\pi\)
\(252\) −17.8904 0.292393i −1.12699 0.0184190i
\(253\) −5.90971 −0.371540
\(254\) 3.32444 + 6.90990i 0.208594 + 0.433566i
\(255\) −1.15258 + 0.393246i −0.0721772 + 0.0246260i
\(256\) −14.4363 + 6.89888i −0.902266 + 0.431180i
\(257\) 3.87147i 0.241496i −0.992683 0.120748i \(-0.961471\pi\)
0.992683 0.120748i \(-0.0385293\pi\)
\(258\) 3.92240 + 3.98703i 0.244198 + 0.248222i
\(259\) 20.3718i 1.26584i
\(260\) −2.42878 1.93987i −0.150626 0.120305i
\(261\) 5.57283 + 7.21612i 0.344950 + 0.446667i
\(262\) −12.5215 + 6.02428i −0.773584 + 0.372181i
\(263\) −20.9768 −1.29349 −0.646743 0.762708i \(-0.723869\pi\)
−0.646743 + 0.762708i \(0.723869\pi\)
\(264\) 0.856460 + 8.26318i 0.0527115 + 0.508563i
\(265\) 0.540268 0.0331884
\(266\) −5.51688 + 2.65424i −0.338262 + 0.162742i
\(267\) 3.13749 + 9.19579i 0.192012 + 0.562773i
\(268\) −1.56273 1.24815i −0.0954588 0.0762430i
\(269\) 25.9623i 1.58295i −0.611203 0.791474i \(-0.709314\pi\)
0.611203 0.791474i \(-0.290686\pi\)
\(270\) 2.55536 + 0.349592i 0.155514 + 0.0212755i
\(271\) 3.87398i 0.235328i −0.993053 0.117664i \(-0.962459\pi\)
0.993053 0.117664i \(-0.0375405\pi\)
\(272\) −7.81483 + 1.77136i −0.473843 + 0.107404i
\(273\) −7.38571 21.6470i −0.447004 1.31014i
\(274\) −0.369715 0.768458i −0.0223353 0.0464242i
\(275\) −8.26985 −0.498691
\(276\) −4.08451 + 11.3605i −0.245858 + 0.683821i
\(277\) 10.4518 0.627988 0.313994 0.949425i \(-0.398333\pi\)
0.313994 + 0.949425i \(0.398333\pi\)
\(278\) 10.0540 + 20.8974i 0.603001 + 1.25335i
\(279\) 19.4190 + 25.1451i 1.16258 + 1.50540i
\(280\) −0.662003 + 2.88547i −0.0395623 + 0.172440i
\(281\) 10.0426i 0.599093i −0.954082 0.299547i \(-0.903165\pi\)
0.954082 0.299547i \(-0.0968354\pi\)
\(282\) −20.4967 + 20.1644i −1.22056 + 1.20077i
\(283\) 13.7073i 0.814814i 0.913247 + 0.407407i \(0.133567\pi\)
−0.913247 + 0.407407i \(0.866433\pi\)
\(284\) 17.5008 21.9116i 1.03848 1.30022i
\(285\) 0.835207 0.284962i 0.0494734 0.0168797i
\(286\) −9.56944 + 4.60398i −0.565853 + 0.272239i
\(287\) 2.78775 0.164556
\(288\) 16.4766 + 4.06470i 0.970893 + 0.239515i
\(289\) 12.9869 0.763937
\(290\) 1.35938 0.654014i 0.0798254 0.0384050i
\(291\) 15.8943 5.42294i 0.931740 0.317898i
\(292\) −6.60267 + 8.26677i −0.386392 + 0.483776i
\(293\) 27.3566i 1.59819i 0.601207 + 0.799094i \(0.294687\pi\)
−0.601207 + 0.799094i \(0.705313\pi\)
\(294\) −3.30571 + 3.25213i −0.192793 + 0.189668i
\(295\) 5.20983i 0.303328i
\(296\) 4.32068 18.8325i 0.251134 1.09462i
\(297\) 4.86113 7.34913i 0.282072 0.426440i
\(298\) 0.749832 + 1.55854i 0.0434366 + 0.0902835i
\(299\) −15.4321 −0.892464
\(300\) −5.71573 + 15.8975i −0.329998 + 0.917842i
\(301\) 6.80922 0.392477
\(302\) −8.58050 17.8347i −0.493752 1.02627i
\(303\) −7.00419 20.5288i −0.402380 1.17935i
\(304\) 5.66296 1.28360i 0.324793 0.0736197i
\(305\) 1.20641i 0.0690788i
\(306\) 7.59761 + 3.80943i 0.434326 + 0.217771i
\(307\) 19.8275i 1.13161i −0.824538 0.565806i \(-0.808565\pi\)
0.824538 0.565806i \(-0.191435\pi\)
\(308\) 7.90265 + 6.31185i 0.450295 + 0.359651i
\(309\) −1.85901 5.44865i −0.105756 0.309963i
\(310\) 4.73685 2.27896i 0.269035 0.129436i
\(311\) −27.4539 −1.55677 −0.778383 0.627789i \(-0.783960\pi\)
−0.778383 + 0.627789i \(0.783960\pi\)
\(312\) 2.23649 + 21.5778i 0.126616 + 1.22160i
\(313\) −8.09384 −0.457491 −0.228745 0.973486i \(-0.573462\pi\)
−0.228745 + 0.973486i \(0.573462\pi\)
\(314\) −4.99214 + 2.40178i −0.281723 + 0.135540i
\(315\) 2.48519 1.91925i 0.140024 0.108138i
\(316\) 26.1739 + 20.9051i 1.47240 + 1.17600i
\(317\) 0.987602i 0.0554692i −0.999615 0.0277346i \(-0.991171\pi\)
0.999615 0.0277346i \(-0.00882934\pi\)
\(318\) −2.64429 2.68786i −0.148285 0.150728i
\(319\) 5.15367i 0.288550i
\(320\) 1.22396 2.52703i 0.0684216 0.141265i
\(321\) 0.856418 0.292200i 0.0478006 0.0163090i
\(322\) 6.37210 + 13.2445i 0.355103 + 0.738087i
\(323\) 2.90805 0.161808
\(324\) −10.7678 14.4241i −0.598209 0.801340i
\(325\) −21.5952 −1.19789
\(326\) 0.655463 + 1.36239i 0.0363028 + 0.0754558i
\(327\) 17.4347 5.94853i 0.964144 0.328954i
\(328\) −2.57710 0.591256i −0.142297 0.0326467i
\(329\) 35.0050i 1.92989i
\(330\) −1.02241 1.03926i −0.0562821 0.0572094i
\(331\) 12.4813i 0.686036i −0.939329 0.343018i \(-0.888551\pi\)
0.939329 0.343018i \(-0.111449\pi\)
\(332\) −8.27592 + 10.3617i −0.454200 + 0.568674i
\(333\) −16.2200 + 12.5263i −0.888851 + 0.686438i
\(334\) −7.36163 + 3.54177i −0.402810 + 0.193797i
\(335\) 0.350980 0.0191761
\(336\) 17.5955 10.8292i 0.959912 0.590779i
\(337\) −8.52881 −0.464594 −0.232297 0.972645i \(-0.574624\pi\)
−0.232297 + 0.972645i \(0.574624\pi\)
\(338\) −8.42178 + 4.05183i −0.458085 + 0.220390i
\(339\) −8.88170 26.0317i −0.482388 1.41385i
\(340\) 0.877583 1.09876i 0.0475936 0.0595889i
\(341\) 17.9583i 0.972498i
\(342\) −5.50555 2.76048i −0.297706 0.149269i
\(343\) 15.2293i 0.822307i
\(344\) −6.29470 1.44417i −0.339388 0.0778646i
\(345\) −0.684116 2.00510i −0.0368315 0.107951i
\(346\) −6.97993 14.5079i −0.375243 0.779948i
\(347\) −16.6008 −0.891179 −0.445589 0.895237i \(-0.647006\pi\)
−0.445589 + 0.895237i \(0.647006\pi\)
\(348\) −9.90711 3.56197i −0.531077 0.190941i
\(349\) 2.10653 0.112760 0.0563799 0.998409i \(-0.482044\pi\)
0.0563799 + 0.998409i \(0.482044\pi\)
\(350\) 8.91690 + 18.5339i 0.476629 + 0.990679i
\(351\) 12.6940 19.1909i 0.677554 1.02434i
\(352\) −5.96683 7.51100i −0.318033 0.400338i
\(353\) 11.1806i 0.595081i −0.954709 0.297541i \(-0.903834\pi\)
0.954709 0.297541i \(-0.0961663\pi\)
\(354\) −25.9192 + 25.4991i −1.37759 + 1.35526i
\(355\) 4.92123i 0.261192i
\(356\) −8.76645 7.00177i −0.464621 0.371093i
\(357\) 9.79299 3.34125i 0.518300 0.176838i
\(358\) −8.30510 + 3.99569i −0.438938 + 0.211179i
\(359\) 13.3649 0.705375 0.352688 0.935741i \(-0.385268\pi\)
0.352688 + 0.935741i \(0.385268\pi\)
\(360\) −2.70446 + 1.24714i −0.142538 + 0.0657302i
\(361\) 16.8927 0.889090
\(362\) −21.2723 + 10.2344i −1.11805 + 0.537907i
\(363\) 13.3181 4.54397i 0.699019 0.238497i
\(364\) 20.6364 + 16.4823i 1.08164 + 0.863905i
\(365\) 1.85667i 0.0971826i
\(366\) −6.00195 + 5.90466i −0.313727 + 0.308641i
\(367\) 15.4682i 0.807435i 0.914884 + 0.403717i \(0.132282\pi\)
−0.914884 + 0.403717i \(0.867718\pi\)
\(368\) −3.08157 13.5952i −0.160638 0.708698i
\(369\) 1.71414 + 2.21960i 0.0892348 + 0.115548i
\(370\) 1.47006 + 3.05554i 0.0764247 + 0.158850i
\(371\) −4.59044 −0.238324
\(372\) −34.5221 12.4119i −1.78989 0.643529i
\(373\) −3.08450 −0.159709 −0.0798546 0.996807i \(-0.525446\pi\)
−0.0798546 + 0.996807i \(0.525446\pi\)
\(374\) −2.08281 4.32916i −0.107700 0.223856i
\(375\) −1.93884 5.68261i −0.100121 0.293449i
\(376\) 7.42425 32.3600i 0.382876 1.66884i
\(377\) 13.4579i 0.693116i
\(378\) −21.7119 2.97035i −1.11674 0.152778i
\(379\) 26.8870i 1.38109i −0.723288 0.690547i \(-0.757370\pi\)
0.723288 0.690547i \(-0.242630\pi\)
\(380\) −0.635934 + 0.796211i −0.0326227 + 0.0408448i
\(381\) 3.03257 + 8.88828i 0.155363 + 0.455360i
\(382\) −14.8562 + 7.14750i −0.760109 + 0.365698i
\(383\) 6.19252 0.316423 0.158211 0.987405i \(-0.449427\pi\)
0.158211 + 0.987405i \(0.449427\pi\)
\(384\) −18.5627 + 6.27904i −0.947274 + 0.320426i
\(385\) −1.77489 −0.0904569
\(386\) 23.5778 11.3436i 1.20008 0.577372i
\(387\) 4.18688 + 5.42149i 0.212831 + 0.275590i
\(388\) −12.1021 + 15.1522i −0.614389 + 0.769236i
\(389\) 29.3150i 1.48633i 0.669107 + 0.743166i \(0.266677\pi\)
−0.669107 + 0.743166i \(0.733323\pi\)
\(390\) −2.66985 2.71384i −0.135193 0.137421i
\(391\) 6.98141i 0.353065i
\(392\) 1.19739 5.21904i 0.0604772 0.263601i
\(393\) −16.1066 + 5.49538i −0.812470 + 0.277205i
\(394\) 4.33408 + 9.00844i 0.218348 + 0.453839i
\(395\) −5.87851 −0.295780
\(396\) −0.166265 + 10.1731i −0.00835513 + 0.511219i
\(397\) 27.2186 1.36606 0.683030 0.730390i \(-0.260662\pi\)
0.683030 + 0.730390i \(0.260662\pi\)
\(398\) −8.30783 17.2679i −0.416434 0.865563i
\(399\) −7.09642 + 2.42121i −0.355265 + 0.121212i
\(400\) −4.31225 19.0247i −0.215613 0.951233i
\(401\) 11.7112i 0.584827i −0.956292 0.292413i \(-0.905542\pi\)
0.956292 0.292413i \(-0.0944583\pi\)
\(402\) −1.71784 1.74615i −0.0856781 0.0870898i
\(403\) 46.8950i 2.33600i
\(404\) 19.5703 + 15.6308i 0.973661 + 0.777663i
\(405\) 3.05621 + 0.798584i 0.151864 + 0.0396820i
\(406\) −11.5501 + 5.55690i −0.573222 + 0.275784i
\(407\) 11.5841 0.574204
\(408\) −9.76167 + 1.01178i −0.483275 + 0.0500904i
\(409\) −32.9181 −1.62770 −0.813848 0.581078i \(-0.802631\pi\)
−0.813848 + 0.581078i \(0.802631\pi\)
\(410\) 0.418130 0.201168i 0.0206500 0.00993497i
\(411\) −0.337256 0.988475i −0.0166356 0.0487579i
\(412\) 5.19426 + 4.14866i 0.255903 + 0.204390i
\(413\) 44.2659i 2.17818i
\(414\) −6.62714 + 13.2173i −0.325706 + 0.649594i
\(415\) 2.32719i 0.114237i
\(416\) −15.5813 19.6136i −0.763936 0.961637i
\(417\) 9.17134 + 26.8806i 0.449122 + 1.31635i
\(418\) 1.50930 + 3.13709i 0.0738221 + 0.153440i
\(419\) 16.4243 0.802382 0.401191 0.915994i \(-0.368596\pi\)
0.401191 + 0.915994i \(0.368596\pi\)
\(420\) −1.22672 + 3.41195i −0.0598578 + 0.166486i
\(421\) −16.4637 −0.802391 −0.401196 0.915992i \(-0.631405\pi\)
−0.401196 + 0.915992i \(0.631405\pi\)
\(422\) −3.93798 8.18516i −0.191698 0.398447i
\(423\) −27.8709 + 21.5241i −1.35513 + 1.04654i
\(424\) 4.24358 + 0.973592i 0.206087 + 0.0472818i
\(425\) 9.76956i 0.473893i
\(426\) 24.4834 24.0865i 1.18623 1.16700i
\(427\) 10.2504i 0.496050i
\(428\) −0.652085 + 0.816433i −0.0315197 + 0.0394638i
\(429\) −12.3093 + 4.19978i −0.594297 + 0.202767i
\(430\) 1.02130 0.491362i 0.0492516 0.0236956i
\(431\) 9.67349 0.465956 0.232978 0.972482i \(-0.425153\pi\)
0.232978 + 0.972482i \(0.425153\pi\)
\(432\) 19.4413 + 7.35080i 0.935372 + 0.353666i
\(433\) 10.5507 0.507034 0.253517 0.967331i \(-0.418413\pi\)
0.253517 + 0.967331i \(0.418413\pi\)
\(434\) −40.2472 + 19.3634i −1.93193 + 0.929474i
\(435\) 1.74858 0.596595i 0.0838381 0.0286045i
\(436\) −13.2750 + 16.6207i −0.635757 + 0.795989i
\(437\) 5.05903i 0.242006i
\(438\) −9.23704 + 9.08731i −0.441363 + 0.434208i
\(439\) 23.5551i 1.12422i −0.827061 0.562112i \(-0.809989\pi\)
0.827061 0.562112i \(-0.190011\pi\)
\(440\) 1.64078 + 0.376439i 0.0782210 + 0.0179460i
\(441\) −4.49504 + 3.47141i −0.214050 + 0.165305i
\(442\) −5.43890 11.3048i −0.258702 0.537716i
\(443\) 2.64159 0.125506 0.0627530 0.998029i \(-0.480012\pi\)
0.0627530 + 0.998029i \(0.480012\pi\)
\(444\) 8.00640 22.2687i 0.379967 1.05682i
\(445\) 1.96890 0.0933346
\(446\) 17.2773 + 35.9111i 0.818105 + 1.70044i
\(447\) 0.684000 + 2.00476i 0.0323521 + 0.0948219i
\(448\) −10.3995 + 21.4712i −0.491331 + 1.01442i
\(449\) 23.9282i 1.12924i 0.825350 + 0.564621i \(0.190978\pi\)
−0.825350 + 0.564621i \(0.809022\pi\)
\(450\) −9.27380 + 18.4958i −0.437171 + 0.871902i
\(451\) 1.58521i 0.0746448i
\(452\) 24.8163 + 19.8208i 1.16726 + 0.932291i
\(453\) −7.82717 22.9409i −0.367753 1.07786i
\(454\) −5.43269 + 2.61374i −0.254969 + 0.122669i
\(455\) −4.63481 −0.217283
\(456\) 7.07372 0.733176i 0.331257 0.0343341i
\(457\) 0.231675 0.0108373 0.00541864 0.999985i \(-0.498275\pi\)
0.00541864 + 0.999985i \(0.498275\pi\)
\(458\) −23.5707 + 11.3402i −1.10139 + 0.529892i
\(459\) 8.68186 + 5.74268i 0.405235 + 0.268045i
\(460\) 1.91148 + 1.52670i 0.0891233 + 0.0711828i
\(461\) 23.3656i 1.08824i 0.839007 + 0.544121i \(0.183137\pi\)
−0.839007 + 0.544121i \(0.816863\pi\)
\(462\) 8.68705 + 8.83019i 0.404158 + 0.410818i
\(463\) 11.3756i 0.528667i 0.964431 + 0.264334i \(0.0851520\pi\)
−0.964431 + 0.264334i \(0.914848\pi\)
\(464\) 11.8559 2.68734i 0.550397 0.124757i
\(465\) 6.09306 2.07888i 0.282559 0.0964057i
\(466\) −14.4300 29.9930i −0.668458 1.38940i
\(467\) 18.8649 0.872962 0.436481 0.899713i \(-0.356225\pi\)
0.436481 + 0.899713i \(0.356225\pi\)
\(468\) −0.434171 + 26.5653i −0.0200696 + 1.22798i
\(469\) −2.98214 −0.137702
\(470\) 2.52601 + 5.25035i 0.116516 + 0.242181i
\(471\) −6.42144 + 2.19092i −0.295884 + 0.100952i
\(472\) 9.38839 40.9211i 0.432136 1.88355i
\(473\) 3.87196i 0.178033i
\(474\) 28.7718 + 29.2459i 1.32153 + 1.34331i
\(475\) 7.07944i 0.324827i
\(476\) −7.45648 + 9.33576i −0.341767 + 0.427904i
\(477\) −2.82259 3.65490i −0.129238 0.167347i
\(478\) 11.8413 5.69701i 0.541609 0.260575i
\(479\) −42.4876 −1.94131 −0.970655 0.240476i \(-0.922697\pi\)
−0.970655 + 0.240476i \(0.922697\pi\)
\(480\) 1.85767 2.89396i 0.0847907 0.132091i
\(481\) 30.2499 1.37928
\(482\) 22.1023 10.6337i 1.00673 0.484352i
\(483\) 5.81266 + 17.0365i 0.264485 + 0.775189i
\(484\) −10.1405 + 12.6963i −0.460933 + 0.577103i
\(485\) 3.40310i 0.154527i
\(486\) −10.9853 19.1134i −0.498305 0.867002i
\(487\) 2.38057i 0.107874i 0.998544 + 0.0539369i \(0.0171770\pi\)
−0.998544 + 0.0539369i \(0.982823\pi\)
\(488\) 2.17401 9.47584i 0.0984129 0.428951i
\(489\) 0.597917 + 1.75246i 0.0270387 + 0.0792488i
\(490\) 0.407397 + 0.846780i 0.0184043 + 0.0382536i
\(491\) −4.74100 −0.213958 −0.106979 0.994261i \(-0.534118\pi\)
−0.106979 + 0.994261i \(0.534118\pi\)
\(492\) −3.04732 1.09562i −0.137384 0.0493945i
\(493\) 6.08826 0.274202
\(494\) 3.94126 + 8.19195i 0.177325 + 0.368573i
\(495\) −1.09135 1.41317i −0.0490527 0.0635171i
\(496\) 41.3128 9.36424i 1.85500 0.420467i
\(497\) 41.8138i 1.87560i
\(498\) −11.5779 + 11.3902i −0.518818 + 0.510408i
\(499\) 24.6933i 1.10542i −0.833373 0.552711i \(-0.813593\pi\)
0.833373 0.552711i \(-0.186407\pi\)
\(500\) 5.41730 + 4.32680i 0.242269 + 0.193500i
\(501\) −9.46934 + 3.23082i −0.423059 + 0.144343i
\(502\) 15.4120 7.41494i 0.687873 0.330945i
\(503\) −7.15017 −0.318810 −0.159405 0.987213i \(-0.550958\pi\)
−0.159405 + 0.987213i \(0.550958\pi\)
\(504\) 22.9787 10.5965i 1.02355 0.472005i
\(505\) −4.39539 −0.195592
\(506\) 7.53129 3.62340i 0.334807 0.161080i
\(507\) −10.8330 + 3.69610i −0.481112 + 0.164150i
\(508\) −8.47329 6.76762i −0.375941 0.300265i
\(509\) 39.5239i 1.75187i 0.482432 + 0.875934i \(0.339754\pi\)
−0.482432 + 0.875934i \(0.660246\pi\)
\(510\) 1.22773 1.20782i 0.0543646 0.0534834i
\(511\) 15.7754i 0.697862i
\(512\) 14.1676 17.6431i 0.626124 0.779724i
\(513\) −6.29125 4.16139i −0.277765 0.183730i
\(514\) 2.37370 + 4.93378i 0.104700 + 0.217619i
\(515\) −1.16660 −0.0514066
\(516\) −7.44324 2.67611i −0.327670 0.117809i
\(517\) 19.9051 0.875425
\(518\) −12.4905 25.9617i −0.548801 1.14069i
\(519\) −6.36713 18.6616i −0.279486 0.819155i
\(520\) 4.28460 + 0.983002i 0.187892 + 0.0431075i
\(521\) 0.206774i 0.00905892i 0.999990 + 0.00452946i \(0.00144178\pi\)
−0.999990 + 0.00452946i \(0.998558\pi\)
\(522\) −11.5264 5.77931i −0.504496 0.252954i
\(523\) 26.7093i 1.16792i 0.811784 + 0.583958i \(0.198497\pi\)
−0.811784 + 0.583958i \(0.801503\pi\)
\(524\) 12.2637 15.3546i 0.535743 0.670768i
\(525\) 8.13404 + 23.8404i 0.354999 + 1.04048i
\(526\) 26.7327 12.8614i 1.16560 0.560786i
\(527\) 21.2150 0.924140
\(528\) −6.15784 10.0054i −0.267986 0.435430i
\(529\) −10.8547 −0.471943
\(530\) −0.688514 + 0.331253i −0.0299071 + 0.0143887i
\(531\) −35.2444 + 27.2184i −1.52948 + 1.18118i
\(532\) 5.40328 6.76509i 0.234262 0.293304i
\(533\) 4.13950i 0.179302i
\(534\) −9.63658 9.79537i −0.417016 0.423887i
\(535\) 0.183366i 0.00792762i
\(536\) 2.75680 + 0.632485i 0.119076 + 0.0273192i
\(537\) −10.6829 + 3.64489i −0.461003 + 0.157289i
\(538\) 15.9182 + 33.0861i 0.686281 + 1.42644i
\(539\) 3.21031 0.138278
\(540\) −3.47088 + 1.12124i −0.149363 + 0.0482507i
\(541\) −6.64574 −0.285723 −0.142861 0.989743i \(-0.545630\pi\)
−0.142861 + 0.989743i \(0.545630\pi\)
\(542\) 2.37524 + 4.93697i 0.102025 + 0.212061i
\(543\) −27.3628 + 9.33584i −1.17425 + 0.400639i
\(544\) 8.87309 7.04889i 0.380430 0.302218i
\(545\) 3.73292i 0.159901i
\(546\) 22.6847 + 23.0584i 0.970814 + 0.986810i
\(547\) 22.0801i 0.944077i 0.881578 + 0.472038i \(0.156482\pi\)
−0.881578 + 0.472038i \(0.843518\pi\)
\(548\) 0.942324 + 0.752634i 0.0402541 + 0.0321510i
\(549\) −8.16133 + 6.30280i −0.348317 + 0.268997i
\(550\) 10.5390 5.07047i 0.449386 0.216205i
\(551\) −4.41181 −0.187950
\(552\) −1.76015 16.9820i −0.0749170 0.722803i
\(553\) 49.9474 2.12398
\(554\) −13.3197 + 6.40828i −0.565899 + 0.272262i
\(555\) 1.34099 + 3.93037i 0.0569220 + 0.166835i
\(556\) −25.6256 20.4671i −1.08677 0.868000i
\(557\) 40.4670i 1.71464i 0.514783 + 0.857321i \(0.327873\pi\)
−0.514783 + 0.857321i \(0.672127\pi\)
\(558\) −40.1645 20.1384i −1.70030 0.852528i
\(559\) 10.1109i 0.427647i
\(560\) −0.925504 4.08311i −0.0391097 0.172543i
\(561\) −1.89995 5.56864i −0.0802161 0.235108i
\(562\) 6.15740 + 12.7983i 0.259734 + 0.539862i
\(563\) −16.7710 −0.706814 −0.353407 0.935470i \(-0.614977\pi\)
−0.353407 + 0.935470i \(0.614977\pi\)
\(564\) 13.7574 38.2644i 0.579293 1.61122i
\(565\) −5.57360 −0.234483
\(566\) −8.40430 17.4685i −0.353259 0.734254i
\(567\) −25.9674 6.78525i −1.09053 0.284954i
\(568\) −8.86832 + 38.6543i −0.372107 + 1.62190i
\(569\) 29.1776i 1.22319i −0.791172 0.611594i \(-0.790529\pi\)
0.791172 0.611594i \(-0.209471\pi\)
\(570\) −0.889663 + 0.875241i −0.0372639 + 0.0366598i
\(571\) 29.1656i 1.22054i −0.792193 0.610270i \(-0.791061\pi\)
0.792193 0.610270i \(-0.208939\pi\)
\(572\) 9.37240 11.7346i 0.391880 0.490647i
\(573\) −19.1097 + 6.51999i −0.798318 + 0.272376i
\(574\) −3.55269 + 1.70924i −0.148286 + 0.0713424i
\(575\) 16.9958 0.708772
\(576\) −23.4898 + 4.92222i −0.978743 + 0.205092i
\(577\) 3.09196 0.128720 0.0643601 0.997927i \(-0.479499\pi\)
0.0643601 + 0.997927i \(0.479499\pi\)
\(578\) −16.5504 + 7.96263i −0.688407 + 0.331202i
\(579\) 30.3283 10.3477i 1.26040 0.430034i
\(580\) −1.33139 + 1.66694i −0.0552828 + 0.0692160i
\(581\) 19.7732i 0.820330i
\(582\) −16.9306 + 16.6562i −0.701796 + 0.690420i
\(583\) 2.61029i 0.108107i
\(584\) 3.34582 14.5834i 0.138451 0.603465i
\(585\) −2.84988 3.69023i −0.117828 0.152572i
\(586\) −16.7730 34.8630i −0.692888 1.44018i
\(587\) −3.55145 −0.146584 −0.0732921 0.997311i \(-0.523351\pi\)
−0.0732921 + 0.997311i \(0.523351\pi\)
\(588\) 2.21881 6.17131i 0.0915022 0.254500i
\(589\) −15.3733 −0.633445
\(590\) 3.19429 + 6.63937i 0.131507 + 0.273339i
\(591\) 3.95357 + 11.5877i 0.162628 + 0.476652i
\(592\) 6.04046 + 26.6491i 0.248261 + 1.09527i
\(593\) 36.4122i 1.49527i −0.664110 0.747635i \(-0.731190\pi\)
0.664110 0.747635i \(-0.268810\pi\)
\(594\) −1.68904 + 12.3462i −0.0693023 + 0.506569i
\(595\) 2.09676i 0.0859588i
\(596\) −1.91116 1.52644i −0.0782841 0.0625256i
\(597\) −7.57844 22.2119i −0.310165 0.909074i
\(598\) 19.6666 9.46186i 0.804227 0.386924i
\(599\) 2.90754 0.118799 0.0593994 0.998234i \(-0.481081\pi\)
0.0593994 + 0.998234i \(0.481081\pi\)
\(600\) −2.46310 23.7641i −0.100556 0.970165i
\(601\) 0.0252815 0.00103125 0.000515627 1.00000i \(-0.499836\pi\)
0.000515627 1.00000i \(0.499836\pi\)
\(602\) −8.67761 + 4.17491i −0.353673 + 0.170157i
\(603\) −1.83367 2.37437i −0.0746729 0.0966920i
\(604\) 21.8698 + 17.4675i 0.889871 + 0.710741i
\(605\) 2.85151i 0.115931i
\(606\) 21.5128 + 21.8673i 0.873900 + 0.888299i
\(607\) 32.3617i 1.31352i −0.754099 0.656761i \(-0.771926\pi\)
0.754099 0.656761i \(-0.228074\pi\)
\(608\) −6.42982 + 5.10792i −0.260763 + 0.207154i
\(609\) −14.8570 + 5.06903i −0.602036 + 0.205408i
\(610\) 0.739681 + 1.53744i 0.0299488 + 0.0622490i
\(611\) 51.9786 2.10283
\(612\) −12.0180 0.196417i −0.485799 0.00793967i
\(613\) 25.0972 1.01367 0.506834 0.862044i \(-0.330816\pi\)
0.506834 + 0.862044i \(0.330816\pi\)
\(614\) 12.1567 + 25.2680i 0.490606 + 1.01973i
\(615\) 0.537845 0.183506i 0.0216880 0.00739969i
\(616\) −13.9410 3.19845i −0.561701 0.128869i
\(617\) 36.3347i 1.46278i −0.681958 0.731391i \(-0.738872\pi\)
0.681958 0.731391i \(-0.261128\pi\)
\(618\) 5.70983 + 5.80391i 0.229683 + 0.233467i
\(619\) 15.1003i 0.606934i 0.952842 + 0.303467i \(0.0981442\pi\)
−0.952842 + 0.303467i \(0.901856\pi\)
\(620\) −4.63932 + 5.80858i −0.186319 + 0.233278i
\(621\) −9.99034 + 15.1035i −0.400898 + 0.606084i
\(622\) 34.9870 16.8327i 1.40285 0.674930i
\(623\) −16.7289 −0.670230
\(624\) −16.0801 26.1273i −0.643719 1.04593i
\(625\) 23.1674 0.926695
\(626\) 10.3147 4.96255i 0.412259 0.198343i
\(627\) 1.37679 + 4.03528i 0.0549836 + 0.161153i
\(628\) 4.88934 6.12162i 0.195106 0.244279i
\(629\) 13.6849i 0.545651i
\(630\) −1.99036 + 3.96961i −0.0792979 + 0.158153i
\(631\) 11.8772i 0.472822i 0.971653 + 0.236411i \(0.0759712\pi\)
−0.971653 + 0.236411i \(0.924029\pi\)
\(632\) −46.1733 10.5934i −1.83667 0.421382i
\(633\) −3.59225 10.5287i −0.142779 0.418476i
\(634\) 0.605525 + 1.25859i 0.0240485 + 0.0499851i
\(635\) 1.90305 0.0755204
\(636\) 5.01787 + 1.80411i 0.198971 + 0.0715375i
\(637\) 8.38314 0.332152
\(638\) 3.15985 + 6.56779i 0.125100 + 0.260021i
\(639\) 33.2921 25.7107i 1.31701 1.01710i
\(640\) −0.0104186 + 3.97087i −0.000411830 + 0.156963i
\(641\) 36.4801i 1.44088i −0.693520 0.720438i \(-0.743941\pi\)
0.693520 0.720438i \(-0.256059\pi\)
\(642\) −0.912258 + 0.897470i −0.0360039 + 0.0354203i
\(643\) 32.3140i 1.27434i −0.770724 0.637170i \(-0.780105\pi\)
0.770724 0.637170i \(-0.219895\pi\)
\(644\) −16.2411 12.9718i −0.639989 0.511160i
\(645\) 1.31371 0.448223i 0.0517274 0.0176488i
\(646\) −3.70599 + 1.78300i −0.145810 + 0.0701512i
\(647\) −17.8380 −0.701285 −0.350642 0.936509i \(-0.614037\pi\)
−0.350642 + 0.936509i \(0.614037\pi\)
\(648\) 22.5662 + 11.7800i 0.886483 + 0.462762i
\(649\) 25.1712 0.988054
\(650\) 27.5208 13.2406i 1.07945 0.519340i
\(651\) −51.7703 + 17.6634i −2.02904 + 0.692284i
\(652\) −1.67064 1.33434i −0.0654271 0.0522567i
\(653\) 19.6414i 0.768627i −0.923203 0.384314i \(-0.874438\pi\)
0.923203 0.384314i \(-0.125562\pi\)
\(654\) −18.5715 + 18.2705i −0.726203 + 0.714432i
\(655\) 3.44856i 0.134746i
\(656\) 3.64675 0.826598i 0.142382 0.0322732i
\(657\) −12.5603 + 9.70005i −0.490026 + 0.378435i
\(658\) −21.4625 44.6101i −0.836696 1.73908i
\(659\) −12.1305 −0.472536 −0.236268 0.971688i \(-0.575924\pi\)
−0.236268 + 0.971688i \(0.575924\pi\)
\(660\) 1.94016 + 0.697557i 0.0755205 + 0.0271524i
\(661\) −46.6603 −1.81488 −0.907439 0.420185i \(-0.861965\pi\)
−0.907439 + 0.420185i \(0.861965\pi\)
\(662\) 7.65263 + 15.9061i 0.297428 + 0.618208i
\(663\) −4.96139 14.5415i −0.192684 0.564745i
\(664\) 4.19372 18.2791i 0.162748 0.709367i
\(665\) 1.51940i 0.0589199i
\(666\) 12.9904 25.9084i 0.503369 1.00393i
\(667\) 10.5915i 0.410106i
\(668\) 7.21004 9.02722i 0.278965 0.349274i
\(669\) 15.7605 + 46.1929i 0.609334 + 1.78592i
\(670\) −0.447286 + 0.215195i −0.0172802 + 0.00831372i
\(671\) 5.82873 0.225016
\(672\) −15.7839 + 24.5888i −0.608877 + 0.948535i
\(673\) −46.2504 −1.78282 −0.891411 0.453196i \(-0.850284\pi\)
−0.891411 + 0.453196i \(0.850284\pi\)
\(674\) 10.8690 5.22924i 0.418660 0.201423i
\(675\) −13.9802 + 21.1354i −0.538096 + 0.813501i
\(676\) 8.24837 10.3272i 0.317245 0.397202i
\(677\) 45.5607i 1.75104i −0.483183 0.875519i \(-0.660519\pi\)
0.483183 0.875519i \(-0.339481\pi\)
\(678\) 27.2795 + 27.7290i 1.04766 + 1.06492i
\(679\) 28.9148i 1.10965i
\(680\) −0.444704 + 1.93833i −0.0170536 + 0.0743314i
\(681\) −6.98813 + 2.38427i −0.267786 + 0.0913653i
\(682\) 11.0107 + 22.8860i 0.421623 + 0.876349i
\(683\) 42.0262 1.60809 0.804043 0.594571i \(-0.202678\pi\)
0.804043 + 0.594571i \(0.202678\pi\)
\(684\) 8.70875 + 0.142332i 0.332987 + 0.00544219i
\(685\) −0.211641 −0.00808638
\(686\) 9.33751 + 19.4081i 0.356508 + 0.741007i
\(687\) −30.3193 + 10.3446i −1.15675 + 0.394670i
\(688\) 8.90738 2.01901i 0.339591 0.0769739i
\(689\) 6.81630i 0.259680i
\(690\) 2.10121 + 2.13583i 0.0799917 + 0.0813098i
\(691\) 12.4465i 0.473489i 0.971572 + 0.236744i \(0.0760804\pi\)
−0.971572 + 0.236744i \(0.923920\pi\)
\(692\) 17.7903 + 14.2091i 0.676287 + 0.540151i
\(693\) 9.27280 + 12.0071i 0.352245 + 0.456112i
\(694\) 21.1560 10.1784i 0.803069 0.386367i
\(695\) 5.75536 0.218313
\(696\) 14.8095 1.53497i 0.561352 0.0581829i
\(697\) 1.87268 0.0709330
\(698\) −2.68454 + 1.29157i −0.101611 + 0.0488865i
\(699\) −13.1631 38.5803i −0.497876 1.45924i
\(700\) −22.7273 18.1523i −0.859010 0.686092i
\(701\) 38.1395i 1.44051i −0.693710 0.720255i \(-0.744025\pi\)
0.693710 0.720255i \(-0.255975\pi\)
\(702\) −4.41064 + 32.2398i −0.166469 + 1.21681i
\(703\) 9.91664i 0.374013i
\(704\) 12.2093 + 5.91354i 0.460154 + 0.222875i
\(705\) 2.30424 + 6.75358i 0.0867827 + 0.254355i
\(706\) 6.85510 + 14.2484i 0.257995 + 0.536246i
\(707\) 37.3459 1.40454
\(708\) 17.3971 48.3876i 0.653823 1.81852i
\(709\) 33.0619 1.24166 0.620832 0.783943i \(-0.286795\pi\)
0.620832 + 0.783943i \(0.286795\pi\)
\(710\) −3.01734 6.27158i −0.113239 0.235368i
\(711\) 30.7119 + 39.7680i 1.15179 + 1.49142i
\(712\) 15.4649 + 3.54805i 0.579570 + 0.132969i
\(713\) 36.9070i 1.38218i
\(714\) −10.4315 + 10.2624i −0.390389 + 0.384061i
\(715\) 2.63552i 0.0985628i
\(716\) 8.13409 10.1842i 0.303985 0.380600i
\(717\) 15.2316 5.19684i 0.568835 0.194080i
\(718\) −17.0322 + 8.19441i −0.635636 + 0.305813i
\(719\) 2.64623 0.0986878 0.0493439 0.998782i \(-0.484287\pi\)
0.0493439 + 0.998782i \(0.484287\pi\)
\(720\) 2.68188 3.24753i 0.0999479 0.121028i
\(721\) 9.91215 0.369148
\(722\) −21.5279 + 10.3574i −0.801187 + 0.385461i
\(723\) 28.4304 9.70011i 1.05734 0.360751i
\(724\) 20.8343 26.0852i 0.774299 0.969449i
\(725\) 14.8215i 0.550455i
\(726\) −14.1864 + 13.9565i −0.526508 + 0.517974i
\(727\) 48.0337i 1.78147i 0.454522 + 0.890736i \(0.349810\pi\)
−0.454522 + 0.890736i \(0.650190\pi\)
\(728\) −36.4045 8.35217i −1.34924 0.309552i
\(729\) −10.5645 24.8473i −0.391280 0.920272i
\(730\) 1.13837 + 2.36613i 0.0421331 + 0.0875743i
\(731\) 4.57413 0.169180
\(732\) 4.02854 11.2048i 0.148899 0.414142i
\(733\) −26.9253 −0.994510 −0.497255 0.867605i \(-0.665659\pi\)
−0.497255 + 0.867605i \(0.665659\pi\)
\(734\) −9.48398 19.7126i −0.350060 0.727605i
\(735\) 0.371629 + 1.08922i 0.0137078 + 0.0401765i
\(736\) 12.2627 + 15.4362i 0.452009 + 0.568986i
\(737\) 1.69575i 0.0624637i
\(738\) −3.54539 1.77765i −0.130508 0.0654364i
\(739\) 35.8090i 1.31725i −0.752470 0.658627i \(-0.771138\pi\)
0.752470 0.658627i \(-0.228862\pi\)
\(740\) −3.74686 2.99262i −0.137737 0.110011i
\(741\) 3.59523 + 10.5374i 0.132074 + 0.387101i
\(742\) 5.85003 2.81452i 0.214761 0.103324i
\(743\) −22.9337 −0.841357 −0.420679 0.907210i \(-0.638208\pi\)
−0.420679 + 0.907210i \(0.638208\pi\)
\(744\) 51.6047 5.34872i 1.89192 0.196094i
\(745\) 0.429236 0.0157260
\(746\) 3.93086 1.89119i 0.143919 0.0692413i
\(747\) −15.7434 + 12.1582i −0.576020 + 0.444847i
\(748\) 5.30865 + 4.24002i 0.194103 + 0.155030i
\(749\) 1.55799i 0.0569277i
\(750\) 5.95500 + 6.05313i 0.217446 + 0.221029i
\(751\) 0.147527i 0.00538332i 0.999996 + 0.00269166i \(0.000856783\pi\)
−0.999996 + 0.00269166i \(0.999143\pi\)
\(752\) 10.3794 + 45.7913i 0.378497 + 1.66984i
\(753\) 19.8247 6.76394i 0.722451 0.246492i
\(754\) 8.25138 + 17.1506i 0.300498 + 0.624588i
\(755\) −4.91185 −0.178760
\(756\) 29.4907 9.52676i 1.07257 0.346485i
\(757\) −30.6339 −1.11341 −0.556703 0.830711i \(-0.687934\pi\)
−0.556703 + 0.830711i \(0.687934\pi\)
\(758\) 16.4851 + 34.2646i 0.598767 + 1.24455i
\(759\) 9.68757 3.30528i 0.351637 0.119974i
\(760\) 0.322251 1.40459i 0.0116893 0.0509500i
\(761\) 19.4924i 0.706599i −0.935510 0.353299i \(-0.885060\pi\)
0.935510 0.353299i \(-0.114940\pi\)
\(762\) −9.31433 9.46780i −0.337423 0.342982i
\(763\) 31.7172i 1.14824i