Properties

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

$q$-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 \(-0.974993\pi\)
0.996916 0.0784815i \(-0.0250072\pi\)
\(6\) 1.74615 + 1.71784i 0.712861 + 0.701305i
\(7\) 2.98214i 1.12714i 0.826068 + 0.563571i \(0.190573\pi\)
−0.826068 + 0.563571i \(0.809427\pi\)
\(8\) −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 \(0.0781091\pi\)
−0.970043 + 0.242932i \(0.921891\pi\)
\(18\) −1.90161 3.79261i −0.448214 0.893926i
\(19\) 1.45165i 0.333032i −0.986039 0.166516i \(-0.946748\pi\)
0.986039 0.166516i \(-0.0532517\pi\)
\(20\) 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 \(-0.908943\pi\)
0.959362 0.282180i \(-0.0910574\pi\)
\(30\) 0.602928 0.612862i 0.110079 0.111893i
\(31\) 10.5902i 1.90206i −0.309104 0.951028i \(-0.600029\pi\)
0.309104 0.951028i \(-0.399971\pi\)
\(32\) 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 \(-0.976744\pi\)
0.997332 0.0729968i \(-0.0232563\pi\)
\(42\) −5.12284 + 5.20725i −0.790471 + 0.803496i
\(43\) 2.28333i 0.348205i −0.984728 0.174103i \(-0.944298\pi\)
0.984728 0.174103i \(-0.0557024\pi\)
\(44\) −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 \(0.0337149\pi\)
−0.994396 + 0.105720i \(0.966285\pi\)
\(54\) 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 \(-0.608757\pi\)
0.335062 0.942196i \(-0.391243\pi\)
\(80\) 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 \(0.0960908\pi\)
−0.954780 + 0.297314i \(0.903909\pi\)
\(90\) −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 \(-0.785892\pi\)
0.782180 0.623052i \(-0.214108\pi\)
\(102\) −3.44129 + 3.49799i −0.340739 + 0.346353i
\(103\) 3.32384i 0.327508i −0.986501 0.163754i \(-0.947640\pi\)
0.986501 0.163754i \(-0.0523603\pi\)
\(104\) 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 \(-0.731524\pi\)
0.664895 0.746937i \(-0.268476\pi\)
\(114\) 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 \(0.0773335\pi\)
−0.970632 + 0.240567i \(0.922666\pi\)
\(128\) 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 \(-0.991800\pi\)
0.999668 0.0257589i \(-0.00820021\pi\)
\(138\) 6.08534 + 5.98670i 0.518018 + 0.509621i
\(139\) 16.3980i 1.39086i 0.718595 + 0.695429i \(0.244786\pi\)
−0.718595 + 0.695429i \(0.755214\pi\)
\(140\) 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 \(0.0159523\pi\)
−0.998744 + 0.0500945i \(0.984048\pi\)
\(150\) 8.51562 + 8.37759i 0.695298 + 0.684027i
\(151\) 13.9947i 1.13887i −0.822037 0.569435i \(-0.807162\pi\)
0.822037 0.569435i \(-0.192838\pi\)
\(152\) −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 \(0.0133307\pi\)
−0.999123 + 0.0418673i \(0.986669\pi\)
\(164\) 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 \(-0.857540\pi\)
0.901509 0.432761i \(-0.142460\pi\)
\(174\) 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 \(0.0810278\pi\)
−0.967775 + 0.251816i \(0.918972\pi\)
\(198\) 3.22465 + 6.43131i 0.229166 + 0.457054i
\(199\) 13.5499i 0.960530i −0.877124 0.480265i \(-0.840541\pi\)
0.877124 0.480265i \(-0.159459\pi\)
\(200\) −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 \(-0.929041\pi\)
0.975255 0.221082i \(-0.0709587\pi\)
\(212\) −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 \(0.392492\pi\)
−0.331362 + 0.943504i \(0.607508\pi\)
\(224\) 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 \(-0.719797\pi\)
0.636932 0.770920i \(-0.280203\pi\)
\(234\) 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 \(0.0385293\pi\)
−0.992683 + 0.120748i \(0.961471\pi\)
\(258\) 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 \(0.290686\pi\)
−0.611203 + 0.791474i \(0.709314\pi\)
\(270\) 2.55536 0.349592i 0.155514 0.0212755i
\(271\) 3.87398i 0.235328i 0.993053 + 0.117664i \(0.0375405\pi\)
−0.993053 + 0.117664i \(0.962459\pi\)
\(272\) −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 \(0.0968354\pi\)
−0.954082 + 0.299547i \(0.903165\pi\)
\(282\) −20.4967 20.1644i −1.22056 1.20077i
\(283\) 13.7073i 0.814814i −0.913247 0.407407i \(-0.866433\pi\)
0.913247 0.407407i \(-0.133567\pi\)
\(284\) 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 \(-0.705313\pi\)
0.601207 0.799094i \(-0.294687\pi\)
\(294\) −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 \(0.191435\pi\)
−0.824538 + 0.565806i \(0.808565\pi\)
\(308\) 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 \(0.00882934\pi\)
−0.999615 + 0.0277346i \(0.991171\pi\)
\(318\) −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 \(0.111449\pi\)
−0.939329 + 0.343018i \(0.888551\pi\)
\(332\) −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 \(0.0961663\pi\)
−0.954709 + 0.297541i \(0.903834\pi\)
\(354\) −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 \(-0.867718\pi\)
0.914884 0.403717i \(-0.132282\pi\)
\(368\) −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 \(0.242630\pi\)
−0.723288 + 0.690547i \(0.757370\pi\)
\(380\) −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 \(-0.733323\pi\)
0.669107 0.743166i \(-0.266677\pi\)
\(390\) −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 \(0.0944583\pi\)
−0.956292 + 0.292413i \(0.905542\pi\)
\(402\) −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 \(0.190011\pi\)
−0.827061 + 0.562112i \(0.809989\pi\)
\(440\) 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 \(-0.809022\pi\)
0.825350 0.564621i \(-0.190978\pi\)
\(450\) −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 \(-0.816863\pi\)
0.839007 0.544121i \(-0.183137\pi\)
\(462\) 8.68705 8.83019i 0.404158 0.410818i
\(463\) 11.3756i 0.528667i −0.964431 0.264334i \(-0.914848\pi\)
0.964431 0.264334i \(-0.0851520\pi\)
\(464\) 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 \(-0.982823\pi\)
0.998544 0.0539369i \(-0.0171770\pi\)
\(488\) 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 \(0.186407\pi\)
−0.833373 + 0.552711i \(0.813593\pi\)
\(500\) 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 \(-0.660246\pi\)
0.482432 0.875934i \(-0.339754\pi\)
\(510\) 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 \(-0.998558\pi\)
0.999990 0.00452946i \(-0.00144178\pi\)
\(522\) −11.5264 + 5.77931i −0.504496 + 0.252954i
\(523\) 26.7093i 1.16792i −0.811784 0.583958i \(-0.801503\pi\)
0.811784 0.583958i \(-0.198497\pi\)
\(524\) 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 \(-0.843518\pi\)
0.881578 0.472038i \(-0.156482\pi\)
\(548\) 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 \(-0.672127\pi\)
0.514783 0.857321i \(-0.327873\pi\)
\(558\) −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 \(0.209471\pi\)
−0.791172 + 0.611594i \(0.790529\pi\)
\(570\) −0.889663 0.875241i −0.0372639 0.0366598i
\(571\) 29.1656i 1.22054i 0.792193 + 0.610270i \(0.208939\pi\)
−0.792193 + 0.610270i \(0.791061\pi\)
\(572\) 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 \(0.268810\pi\)
−0.664110 + 0.747635i \(0.731190\pi\)
\(594\) −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 \(0.228074\pi\)
−0.754099 + 0.656761i \(0.771926\pi\)
\(608\) −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 \(0.261128\pi\)
−0.681958 + 0.731391i \(0.738872\pi\)
\(618\) 5.70983 5.80391i 0.229683 0.233467i
\(619\) 15.1003i 0.606934i −0.952842 0.303467i \(-0.901856\pi\)
0.952842 0.303467i \(-0.0981442\pi\)
\(620\) −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 \(-0.924029\pi\)
0.971653 0.236411i \(-0.0759712\pi\)
\(632\) −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 \(0.256059\pi\)
−0.693520 + 0.720438i \(0.743941\pi\)
\(642\) −0.912258 0.897470i −0.0360039 0.0354203i
\(643\) 32.3140i 1.27434i 0.770724 + 0.637170i \(0.219895\pi\)
−0.770724 + 0.637170i \(0.780105\pi\)
\(644\) −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 \(0.125562\pi\)
−0.923203 + 0.384314i \(0.874438\pi\)
\(654\) −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 \(0.339481\pi\)
−0.483183 + 0.875519i \(0.660519\pi\)
\(678\) 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 \(-0.923920\pi\)
0.971572 0.236744i \(-0.0760804\pi\)
\(692\) 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 \(0.255975\pi\)
−0.693710 + 0.720255i \(0.744025\pi\)
\(702\) −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 \(-0.650190\pi\)
0.454522 0.890736i \(-0.349810\pi\)
\(728\) −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 \(0.228862\pi\)
−0.752470 + 0.658627i \(0.771138\pi\)
\(740\) −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 \(-0.999143\pi\)
0.999996 0.00269166i \(-0.000856783\pi\)
\(752\) 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 \(0.114940\pi\)
−0.935510 + 0.353299i \(0.885060\pi\)
\(762\) −9.31433 + 9.46780i −0.337423 + 0.342982i
\(763\) 31.7172i 1.14824i