Properties

Label 804.2.c.b.671.2
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 671.2
Character \(\chi\) = 804.671
Dual form 804.2.c.b.671.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.41002 + 0.108878i) q^{2} +(1.62789 - 0.591579i) q^{3} +(1.97629 - 0.307041i) q^{4} +3.04949i q^{5} +(-2.23094 + 1.01138i) q^{6} -0.278695i q^{7} +(-2.75317 + 0.648108i) q^{8} +(2.30007 - 1.92605i) q^{9} +O(q^{10})\) \(q+(-1.41002 + 0.108878i) q^{2} +(1.62789 - 0.591579i) q^{3} +(1.97629 - 0.307041i) q^{4} +3.04949i q^{5} +(-2.23094 + 1.01138i) q^{6} -0.278695i q^{7} +(-2.75317 + 0.648108i) q^{8} +(2.30007 - 1.92605i) q^{9} +(-0.332024 - 4.29983i) q^{10} -5.07932 q^{11} +(3.03555 - 1.66896i) q^{12} -5.86045 q^{13} +(0.0303439 + 0.392964i) q^{14} +(1.80401 + 4.96424i) q^{15} +(3.81145 - 1.21360i) q^{16} +7.60921i q^{17} +(-3.03343 + 2.96619i) q^{18} +5.91318i q^{19} +(0.936317 + 6.02668i) q^{20} +(-0.164870 - 0.453686i) q^{21} +(7.16192 - 0.553028i) q^{22} +2.24947 q^{23} +(-4.09846 + 2.68377i) q^{24} -4.29939 q^{25} +(8.26333 - 0.638076i) q^{26} +(2.60486 - 4.49608i) q^{27} +(-0.0855707 - 0.550782i) q^{28} +5.83061i q^{29} +(-3.08419 - 6.80324i) q^{30} -4.34794i q^{31} +(-5.24207 + 2.12618i) q^{32} +(-8.26859 + 3.00482i) q^{33} +(-0.828478 - 10.7291i) q^{34} +0.849878 q^{35} +(3.95423 - 4.51266i) q^{36} -6.86393 q^{37} +(-0.643818 - 8.33768i) q^{38} +(-9.54018 + 3.46692i) q^{39} +(-1.97640 - 8.39577i) q^{40} -8.48285i q^{41} +(0.281866 + 0.621753i) q^{42} +2.79230i q^{43} +(-10.0382 + 1.55956i) q^{44} +(5.87348 + 7.01404i) q^{45} +(-3.17179 + 0.244919i) q^{46} +0.455070 q^{47} +(5.48669 - 4.23039i) q^{48} +6.92233 q^{49} +(6.06221 - 0.468111i) q^{50} +(4.50144 + 12.3870i) q^{51} +(-11.5820 + 1.79940i) q^{52} +5.43602i q^{53} +(-3.18336 + 6.62316i) q^{54} -15.4893i q^{55} +(0.180624 + 0.767295i) q^{56} +(3.49811 + 9.62603i) q^{57} +(-0.634828 - 8.22125i) q^{58} -0.908582 q^{59} +(5.08948 + 9.25688i) q^{60} +1.16382 q^{61} +(0.473396 + 6.13066i) q^{62} +(-0.536781 - 0.641018i) q^{63} +(7.15991 - 3.56870i) q^{64} -17.8714i q^{65} +(11.3317 - 5.13711i) q^{66} +1.00000i q^{67} +(2.33634 + 15.0380i) q^{68} +(3.66190 - 1.33074i) q^{69} +(-1.19834 + 0.0925333i) q^{70} -4.54985 q^{71} +(-5.08420 + 6.79345i) q^{72} +13.5119 q^{73} +(9.67825 - 0.747333i) q^{74} +(-6.99894 + 2.54343i) q^{75} +(1.81559 + 11.6862i) q^{76} +1.41558i q^{77} +(13.0743 - 5.92713i) q^{78} +12.3343i q^{79} +(3.70087 + 11.6230i) q^{80} +(1.58064 - 8.86011i) q^{81} +(0.923599 + 11.9610i) q^{82} +2.79368 q^{83} +(-0.465131 - 0.845993i) q^{84} -23.2042 q^{85} +(-0.304021 - 3.93718i) q^{86} +(3.44926 + 9.49161i) q^{87} +(13.9842 - 3.29194i) q^{88} -1.69189i q^{89} +(-9.04538 - 9.25041i) q^{90} +1.63328i q^{91} +(4.44561 - 0.690679i) q^{92} +(-2.57215 - 7.07797i) q^{93} +(-0.641656 + 0.0495473i) q^{94} -18.0322 q^{95} +(-7.27573 + 6.56230i) q^{96} +4.26115 q^{97} +(-9.76060 + 0.753692i) q^{98} +(-11.6828 + 9.78304i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41002 + 0.108878i −0.997032 + 0.0769887i
\(3\) 1.62789 0.591579i 0.939864 0.341548i
\(4\) 1.97629 0.307041i 0.988145 0.153520i
\(5\) 3.04949i 1.36377i 0.731458 + 0.681887i \(0.238840\pi\)
−0.731458 + 0.681887i \(0.761160\pi\)
\(6\) −2.23094 + 1.01138i −0.910779 + 0.412893i
\(7\) 0.278695i 0.105337i −0.998612 0.0526684i \(-0.983227\pi\)
0.998612 0.0526684i \(-0.0167726\pi\)
\(8\) −2.75317 + 0.648108i −0.973393 + 0.229141i
\(9\) 2.30007 1.92605i 0.766690 0.642018i
\(10\) −0.332024 4.29983i −0.104995 1.35973i
\(11\) −5.07932 −1.53147 −0.765736 0.643155i \(-0.777625\pi\)
−0.765736 + 0.643155i \(0.777625\pi\)
\(12\) 3.03555 1.66896i 0.876288 0.481787i
\(13\) −5.86045 −1.62540 −0.812698 0.582685i \(-0.802002\pi\)
−0.812698 + 0.582685i \(0.802002\pi\)
\(14\) 0.0303439 + 0.392964i 0.00810974 + 0.105024i
\(15\) 1.80401 + 4.96424i 0.465794 + 1.28176i
\(16\) 3.81145 1.21360i 0.952863 0.303401i
\(17\) 7.60921i 1.84550i 0.385395 + 0.922752i \(0.374065\pi\)
−0.385395 + 0.922752i \(0.625935\pi\)
\(18\) −3.03343 + 2.96619i −0.714986 + 0.699139i
\(19\) 5.91318i 1.35658i 0.734796 + 0.678288i \(0.237278\pi\)
−0.734796 + 0.678288i \(0.762722\pi\)
\(20\) 0.936317 + 6.02668i 0.209367 + 1.34761i
\(21\) −0.164870 0.453686i −0.0359776 0.0990023i
\(22\) 7.16192 0.553028i 1.52693 0.117906i
\(23\) 2.24947 0.469047 0.234523 0.972110i \(-0.424647\pi\)
0.234523 + 0.972110i \(0.424647\pi\)
\(24\) −4.09846 + 2.68377i −0.836595 + 0.547822i
\(25\) −4.29939 −0.859878
\(26\) 8.26333 0.638076i 1.62057 0.125137i
\(27\) 2.60486 4.49608i 0.501305 0.865271i
\(28\) −0.0855707 0.550782i −0.0161713 0.104088i
\(29\) 5.83061i 1.08272i 0.840792 + 0.541359i \(0.182090\pi\)
−0.840792 + 0.541359i \(0.817910\pi\)
\(30\) −3.08419 6.80324i −0.563093 1.24210i
\(31\) 4.34794i 0.780912i −0.920622 0.390456i \(-0.872317\pi\)
0.920622 0.390456i \(-0.127683\pi\)
\(32\) −5.24207 + 2.12618i −0.926676 + 0.375860i
\(33\) −8.26859 + 3.00482i −1.43938 + 0.523071i
\(34\) −0.828478 10.7291i −0.142083 1.84003i
\(35\) 0.849878 0.143656
\(36\) 3.95423 4.51266i 0.659038 0.752109i
\(37\) −6.86393 −1.12842 −0.564211 0.825630i \(-0.690820\pi\)
−0.564211 + 0.825630i \(0.690820\pi\)
\(38\) −0.643818 8.33768i −0.104441 1.35255i
\(39\) −9.54018 + 3.46692i −1.52765 + 0.555151i
\(40\) −1.97640 8.39577i −0.312496 1.32749i
\(41\) 8.48285i 1.32480i −0.749151 0.662399i \(-0.769538\pi\)
0.749151 0.662399i \(-0.230462\pi\)
\(42\) 0.281866 + 0.621753i 0.0434929 + 0.0959386i
\(43\) 2.79230i 0.425821i 0.977072 + 0.212911i \(0.0682943\pi\)
−0.977072 + 0.212911i \(0.931706\pi\)
\(44\) −10.0382 + 1.55956i −1.51332 + 0.235112i
\(45\) 5.87348 + 7.01404i 0.875567 + 1.04559i
\(46\) −3.17179 + 0.244919i −0.467655 + 0.0361113i
\(47\) 0.455070 0.0663787 0.0331894 0.999449i \(-0.489434\pi\)
0.0331894 + 0.999449i \(0.489434\pi\)
\(48\) 5.48669 4.23039i 0.791936 0.610604i
\(49\) 6.92233 0.988904
\(50\) 6.06221 0.468111i 0.857326 0.0662008i
\(51\) 4.50144 + 12.3870i 0.630328 + 1.73452i
\(52\) −11.5820 + 1.79940i −1.60613 + 0.249531i
\(53\) 5.43602i 0.746694i 0.927692 + 0.373347i \(0.121790\pi\)
−0.927692 + 0.373347i \(0.878210\pi\)
\(54\) −3.18336 + 6.62316i −0.433201 + 0.901297i
\(55\) 15.4893i 2.08858i
\(56\) 0.180624 + 0.767295i 0.0241369 + 0.102534i
\(57\) 3.49811 + 9.62603i 0.463336 + 1.27500i
\(58\) −0.634828 8.22125i −0.0833569 1.07950i
\(59\) −0.908582 −0.118287 −0.0591436 0.998249i \(-0.518837\pi\)
−0.0591436 + 0.998249i \(0.518837\pi\)
\(60\) 5.08948 + 9.25688i 0.657049 + 1.19506i
\(61\) 1.16382 0.149012 0.0745059 0.997221i \(-0.476262\pi\)
0.0745059 + 0.997221i \(0.476262\pi\)
\(62\) 0.473396 + 6.13066i 0.0601214 + 0.778594i
\(63\) −0.536781 0.641018i −0.0676281 0.0807607i
\(64\) 7.15991 3.56870i 0.894989 0.446088i
\(65\) 17.8714i 2.21667i
\(66\) 11.3317 5.13711i 1.39483 0.632334i
\(67\) 1.00000i 0.122169i
\(68\) 2.33634 + 15.0380i 0.283322 + 1.82363i
\(69\) 3.66190 1.33074i 0.440841 0.160202i
\(70\) −1.19834 + 0.0925333i −0.143229 + 0.0110598i
\(71\) −4.54985 −0.539967 −0.269984 0.962865i \(-0.587018\pi\)
−0.269984 + 0.962865i \(0.587018\pi\)
\(72\) −5.08420 + 6.79345i −0.599178 + 0.800615i
\(73\) 13.5119 1.58145 0.790726 0.612171i \(-0.209704\pi\)
0.790726 + 0.612171i \(0.209704\pi\)
\(74\) 9.67825 0.747333i 1.12507 0.0868757i
\(75\) −6.99894 + 2.54343i −0.808168 + 0.293690i
\(76\) 1.81559 + 11.6862i 0.208262 + 1.34050i
\(77\) 1.41558i 0.161320i
\(78\) 13.0743 5.92713i 1.48038 0.671115i
\(79\) 12.3343i 1.38772i 0.720110 + 0.693860i \(0.244091\pi\)
−0.720110 + 0.693860i \(0.755909\pi\)
\(80\) 3.70087 + 11.6230i 0.413770 + 1.29949i
\(81\) 1.58064 8.86011i 0.175627 0.984457i
\(82\) 0.923599 + 11.9610i 0.101994 + 1.32087i
\(83\) 2.79368 0.306646 0.153323 0.988176i \(-0.451003\pi\)
0.153323 + 0.988176i \(0.451003\pi\)
\(84\) −0.465131 0.845993i −0.0507499 0.0923054i
\(85\) −23.2042 −2.51685
\(86\) −0.304021 3.93718i −0.0327834 0.424557i
\(87\) 3.44926 + 9.49161i 0.369800 + 1.01761i
\(88\) 13.9842 3.29194i 1.49072 0.350923i
\(89\) 1.69189i 0.179340i −0.995972 0.0896698i \(-0.971419\pi\)
0.995972 0.0896698i \(-0.0285812\pi\)
\(90\) −9.04538 9.25041i −0.953466 0.975079i
\(91\) 1.63328i 0.171214i
\(92\) 4.44561 0.690679i 0.463487 0.0720082i
\(93\) −2.57215 7.07797i −0.266719 0.733952i
\(94\) −0.641656 + 0.0495473i −0.0661817 + 0.00511041i
\(95\) −18.0322 −1.85006
\(96\) −7.27573 + 6.56230i −0.742576 + 0.669762i
\(97\) 4.26115 0.432654 0.216327 0.976321i \(-0.430592\pi\)
0.216327 + 0.976321i \(0.430592\pi\)
\(98\) −9.76060 + 0.753692i −0.985969 + 0.0761344i
\(99\) −11.6828 + 9.78304i −1.17416 + 0.983232i
\(100\) −8.49684 + 1.32009i −0.849684 + 0.132009i
\(101\) 0.355994i 0.0354227i 0.999843 + 0.0177114i \(0.00563800\pi\)
−0.999843 + 0.0177114i \(0.994362\pi\)
\(102\) −7.69578 16.9757i −0.761996 1.68085i
\(103\) 10.6829i 1.05262i 0.850292 + 0.526311i \(0.176425\pi\)
−0.850292 + 0.526311i \(0.823575\pi\)
\(104\) 16.1348 3.79820i 1.58215 0.372444i
\(105\) 1.38351 0.502769i 0.135017 0.0490653i
\(106\) −0.591865 7.66487i −0.0574870 0.744478i
\(107\) −3.37528 −0.326300 −0.163150 0.986601i \(-0.552166\pi\)
−0.163150 + 0.986601i \(0.552166\pi\)
\(108\) 3.76747 9.68536i 0.362525 0.931974i
\(109\) 8.52614 0.816656 0.408328 0.912835i \(-0.366112\pi\)
0.408328 + 0.912835i \(0.366112\pi\)
\(110\) 1.68645 + 21.8402i 0.160797 + 2.08238i
\(111\) −11.1737 + 4.06055i −1.06056 + 0.385411i
\(112\) −0.338225 1.06223i −0.0319593 0.100372i
\(113\) 15.8507i 1.49111i −0.666443 0.745556i \(-0.732184\pi\)
0.666443 0.745556i \(-0.267816\pi\)
\(114\) −5.98046 13.1920i −0.560121 1.23554i
\(115\) 6.85974i 0.639674i
\(116\) 1.79023 + 11.5230i 0.166219 + 1.06988i
\(117\) −13.4794 + 11.2875i −1.24617 + 1.04353i
\(118\) 1.28111 0.0989249i 0.117936 0.00910678i
\(119\) 2.12065 0.194399
\(120\) −8.18412 12.4982i −0.747105 1.14093i
\(121\) 14.7995 1.34541
\(122\) −1.64100 + 0.126715i −0.148569 + 0.0114722i
\(123\) −5.01827 13.8092i −0.452482 1.24513i
\(124\) −1.33499 8.59278i −0.119886 0.771655i
\(125\) 2.13651i 0.191095i
\(126\) 0.826663 + 0.845402i 0.0736450 + 0.0753144i
\(127\) 2.01361i 0.178679i 0.996001 + 0.0893393i \(0.0284755\pi\)
−0.996001 + 0.0893393i \(0.971524\pi\)
\(128\) −9.70704 + 5.81149i −0.857989 + 0.513668i
\(129\) 1.65186 + 4.54556i 0.145438 + 0.400214i
\(130\) 1.94581 + 25.1989i 0.170659 + 2.21009i
\(131\) −3.98147 −0.347862 −0.173931 0.984758i \(-0.555647\pi\)
−0.173931 + 0.984758i \(0.555647\pi\)
\(132\) −15.4185 + 8.47718i −1.34201 + 0.737844i
\(133\) 1.64797 0.142897
\(134\) −0.108878 1.41002i −0.00940566 0.121807i
\(135\) 13.7107 + 7.94348i 1.18003 + 0.683666i
\(136\) −4.93158 20.9495i −0.422880 1.79640i
\(137\) 8.83469i 0.754798i 0.926051 + 0.377399i \(0.123182\pi\)
−0.926051 + 0.377399i \(0.876818\pi\)
\(138\) −5.01844 + 2.27506i −0.427198 + 0.193666i
\(139\) 12.3675i 1.04899i −0.851412 0.524497i \(-0.824253\pi\)
0.851412 0.524497i \(-0.175747\pi\)
\(140\) 1.67961 0.260947i 0.141953 0.0220540i
\(141\) 0.740805 0.269209i 0.0623870 0.0226715i
\(142\) 6.41535 0.495380i 0.538365 0.0415714i
\(143\) 29.7671 2.48925
\(144\) 6.42914 10.1324i 0.535762 0.844369i
\(145\) −17.7804 −1.47658
\(146\) −19.0520 + 1.47116i −1.57676 + 0.121754i
\(147\) 11.2688 4.09510i 0.929436 0.337758i
\(148\) −13.5651 + 2.10750i −1.11505 + 0.173236i
\(149\) 10.4788i 0.858457i −0.903196 0.429229i \(-0.858785\pi\)
0.903196 0.429229i \(-0.141215\pi\)
\(150\) 9.59170 4.34831i 0.783159 0.355038i
\(151\) 7.69810i 0.626463i 0.949677 + 0.313231i \(0.101412\pi\)
−0.949677 + 0.313231i \(0.898588\pi\)
\(152\) −3.83238 16.2800i −0.310847 1.32048i
\(153\) 14.6557 + 17.5017i 1.18485 + 1.41493i
\(154\) −0.154126 1.99599i −0.0124198 0.160842i
\(155\) 13.2590 1.06499
\(156\) −17.7897 + 9.78086i −1.42432 + 0.783095i
\(157\) −12.0712 −0.963384 −0.481692 0.876340i \(-0.659978\pi\)
−0.481692 + 0.876340i \(0.659978\pi\)
\(158\) −1.34294 17.3916i −0.106839 1.38360i
\(159\) 3.21583 + 8.84925i 0.255032 + 0.701791i
\(160\) −6.48378 15.9857i −0.512588 1.26378i
\(161\) 0.626916i 0.0494079i
\(162\) −1.26405 + 12.6650i −0.0993135 + 0.995056i
\(163\) 9.41541i 0.737472i 0.929534 + 0.368736i \(0.120209\pi\)
−0.929534 + 0.368736i \(0.879791\pi\)
\(164\) −2.60458 16.7646i −0.203384 1.30909i
\(165\) −9.16316 25.2150i −0.713351 1.96298i
\(166\) −3.93913 + 0.304171i −0.305736 + 0.0236082i
\(167\) −21.0838 −1.63151 −0.815756 0.578396i \(-0.803679\pi\)
−0.815756 + 0.578396i \(0.803679\pi\)
\(168\) 0.747953 + 1.14222i 0.0577058 + 0.0881243i
\(169\) 21.3449 1.64191
\(170\) 32.7183 2.52644i 2.50938 0.193769i
\(171\) 11.3891 + 13.6007i 0.870946 + 1.04007i
\(172\) 0.857348 + 5.51839i 0.0653722 + 0.420773i
\(173\) 18.9189i 1.43838i −0.694815 0.719188i \(-0.744514\pi\)
0.694815 0.719188i \(-0.255486\pi\)
\(174\) −5.89695 13.0078i −0.447047 0.986117i
\(175\) 1.19822i 0.0905768i
\(176\) −19.3596 + 6.16428i −1.45928 + 0.464650i
\(177\) −1.47907 + 0.537497i −0.111174 + 0.0404008i
\(178\) 0.184210 + 2.38559i 0.0138071 + 0.178807i
\(179\) 25.3930 1.89796 0.948982 0.315331i \(-0.102115\pi\)
0.948982 + 0.315331i \(0.102115\pi\)
\(180\) 13.7613 + 12.0584i 1.02571 + 0.898779i
\(181\) −9.38501 −0.697582 −0.348791 0.937200i \(-0.613408\pi\)
−0.348791 + 0.937200i \(0.613408\pi\)
\(182\) −0.177829 2.30295i −0.0131815 0.170706i
\(183\) 1.89457 0.688490i 0.140051 0.0508947i
\(184\) −6.19318 + 1.45790i −0.456567 + 0.107478i
\(185\) 20.9315i 1.53891i
\(186\) 4.39740 + 9.70000i 0.322433 + 0.711239i
\(187\) 38.6496i 2.82634i
\(188\) 0.899350 0.139725i 0.0655918 0.0101905i
\(189\) −1.25303 0.725960i −0.0911449 0.0528058i
\(190\) 25.4257 1.96332i 1.84457 0.142434i
\(191\) −4.93877 −0.357357 −0.178678 0.983908i \(-0.557182\pi\)
−0.178678 + 0.983908i \(0.557182\pi\)
\(192\) 9.54440 10.0451i 0.688808 0.724944i
\(193\) 20.3135 1.46220 0.731099 0.682271i \(-0.239008\pi\)
0.731099 + 0.682271i \(0.239008\pi\)
\(194\) −6.00829 + 0.463947i −0.431370 + 0.0333094i
\(195\) −10.5723 29.0927i −0.757100 2.08337i
\(196\) 13.6805 2.12544i 0.977181 0.151817i
\(197\) 13.3758i 0.952990i 0.879177 + 0.476495i \(0.158093\pi\)
−0.879177 + 0.476495i \(0.841907\pi\)
\(198\) 15.4078 15.0662i 1.09498 1.07071i
\(199\) 13.1693i 0.933548i −0.884377 0.466774i \(-0.845416\pi\)
0.884377 0.466774i \(-0.154584\pi\)
\(200\) 11.8370 2.78647i 0.836999 0.197033i
\(201\) 0.591579 + 1.62789i 0.0417267 + 0.114823i
\(202\) −0.0387601 0.501957i −0.00272715 0.0353176i
\(203\) 1.62496 0.114050
\(204\) 12.6995 + 23.0981i 0.889140 + 1.61719i
\(205\) 25.8684 1.80673
\(206\) −1.16314 15.0631i −0.0810400 1.04950i
\(207\) 5.17394 4.33260i 0.359614 0.301136i
\(208\) −22.3368 + 7.11226i −1.54878 + 0.493147i
\(209\) 30.0349i 2.07756i
\(210\) −1.89603 + 0.859547i −0.130839 + 0.0593144i
\(211\) 4.89617i 0.337066i −0.985696 0.168533i \(-0.946097\pi\)
0.985696 0.168533i \(-0.0539030\pi\)
\(212\) 1.66908 + 10.7431i 0.114633 + 0.737843i
\(213\) −7.40666 + 2.69159i −0.507496 + 0.184425i
\(214\) 4.75920 0.367495i 0.325332 0.0251214i
\(215\) −8.51508 −0.580723
\(216\) −4.25767 + 14.0667i −0.289698 + 0.957118i
\(217\) −1.21175 −0.0822588
\(218\) −12.0220 + 0.928313i −0.814233 + 0.0628733i
\(219\) 21.9960 7.99336i 1.48635 0.540141i
\(220\) −4.75585 30.6114i −0.320640 2.06382i
\(221\) 44.5934i 2.99967i
\(222\) 15.3130 6.94202i 1.02774 0.465918i
\(223\) 27.0230i 1.80959i 0.425845 + 0.904796i \(0.359977\pi\)
−0.425845 + 0.904796i \(0.640023\pi\)
\(224\) 0.592557 + 1.46094i 0.0395919 + 0.0976131i
\(225\) −9.88889 + 8.28085i −0.659260 + 0.552057i
\(226\) 1.72580 + 22.3498i 0.114799 + 1.48669i
\(227\) −0.0417672 −0.00277218 −0.00138609 0.999999i \(-0.500441\pi\)
−0.00138609 + 0.999999i \(0.500441\pi\)
\(228\) 9.86887 + 17.9498i 0.653582 + 1.18875i
\(229\) 14.7269 0.973180 0.486590 0.873631i \(-0.338241\pi\)
0.486590 + 0.873631i \(0.338241\pi\)
\(230\) −0.746877 9.67234i −0.0492476 0.637775i
\(231\) 0.837427 + 2.30441i 0.0550987 + 0.151619i
\(232\) −3.77886 16.0527i −0.248094 1.05391i
\(233\) 22.8772i 1.49874i 0.662154 + 0.749368i \(0.269642\pi\)
−0.662154 + 0.749368i \(0.730358\pi\)
\(234\) 17.7773 17.3832i 1.16214 1.13638i
\(235\) 1.38773i 0.0905255i
\(236\) −1.79562 + 0.278971i −0.116885 + 0.0181595i
\(237\) 7.29672 + 20.0789i 0.473973 + 1.30427i
\(238\) −2.99015 + 0.230893i −0.193822 + 0.0149666i
\(239\) −6.80444 −0.440142 −0.220071 0.975484i \(-0.570629\pi\)
−0.220071 + 0.975484i \(0.570629\pi\)
\(240\) 12.9005 + 16.7316i 0.832726 + 1.08002i
\(241\) −0.959498 −0.0618067 −0.0309034 0.999522i \(-0.509838\pi\)
−0.0309034 + 0.999522i \(0.509838\pi\)
\(242\) −20.8675 + 1.61134i −1.34141 + 0.103581i
\(243\) −2.66834 15.3584i −0.171174 0.985241i
\(244\) 2.30004 0.357340i 0.147245 0.0228763i
\(245\) 21.1096i 1.34864i
\(246\) 8.57937 + 18.9248i 0.547000 + 1.20660i
\(247\) 34.6539i 2.20498i
\(248\) 2.81793 + 11.9706i 0.178939 + 0.760135i
\(249\) 4.54780 1.65268i 0.288205 0.104734i
\(250\) −0.232619 3.01251i −0.0147121 0.190528i
\(251\) −11.7116 −0.739227 −0.369613 0.929186i \(-0.620510\pi\)
−0.369613 + 0.929186i \(0.620510\pi\)
\(252\) −1.25765 1.10202i −0.0792248 0.0694210i
\(253\) −11.4258 −0.718332
\(254\) −0.219238 2.83922i −0.0137562 0.178148i
\(255\) −37.7739 + 13.7271i −2.36550 + 0.859625i
\(256\) 13.0543 9.25118i 0.815896 0.578199i
\(257\) 1.54522i 0.0963883i 0.998838 + 0.0481941i \(0.0153466\pi\)
−0.998838 + 0.0481941i \(0.984653\pi\)
\(258\) −2.82407 6.22946i −0.175819 0.387829i
\(259\) 1.91294i 0.118864i
\(260\) −5.48724 35.3191i −0.340304 2.19039i
\(261\) 11.2301 + 13.4108i 0.695123 + 0.830108i
\(262\) 5.61393 0.433496i 0.346830 0.0267815i
\(263\) 25.4945 1.57206 0.786029 0.618190i \(-0.212134\pi\)
0.786029 + 0.618190i \(0.212134\pi\)
\(264\) 20.8174 13.6317i 1.28122 0.838974i
\(265\) −16.5771 −1.01832
\(266\) −2.32367 + 0.179429i −0.142473 + 0.0110015i
\(267\) −1.00088 2.75421i −0.0612531 0.168555i
\(268\) 0.307041 + 1.97629i 0.0187555 + 0.120721i
\(269\) 11.3415i 0.691505i 0.938326 + 0.345752i \(0.112376\pi\)
−0.938326 + 0.345752i \(0.887624\pi\)
\(270\) −20.1973 9.70763i −1.22917 0.590788i
\(271\) 3.42034i 0.207771i 0.994589 + 0.103885i \(0.0331275\pi\)
−0.994589 + 0.103885i \(0.966872\pi\)
\(272\) 9.23456 + 29.0021i 0.559927 + 1.75851i
\(273\) 0.966212 + 2.65880i 0.0584778 + 0.160918i
\(274\) −0.961907 12.4571i −0.0581109 0.752558i
\(275\) 21.8380 1.31688
\(276\) 6.82838 3.75428i 0.411020 0.225981i
\(277\) 11.3806 0.683793 0.341897 0.939738i \(-0.388931\pi\)
0.341897 + 0.939738i \(0.388931\pi\)
\(278\) 1.34655 + 17.4383i 0.0807607 + 1.04588i
\(279\) −8.37435 10.0006i −0.501359 0.598717i
\(280\) −2.33986 + 0.550812i −0.139833 + 0.0329173i
\(281\) 9.82446i 0.586078i 0.956101 + 0.293039i \(0.0946666\pi\)
−0.956101 + 0.293039i \(0.905333\pi\)
\(282\) −1.01524 + 0.460247i −0.0604564 + 0.0274073i
\(283\) 17.7063i 1.05253i 0.850320 + 0.526265i \(0.176408\pi\)
−0.850320 + 0.526265i \(0.823592\pi\)
\(284\) −8.99182 + 1.39699i −0.533566 + 0.0828959i
\(285\) −29.3545 + 10.6675i −1.73881 + 0.631886i
\(286\) −41.9721 + 3.24099i −2.48186 + 0.191644i
\(287\) −2.36413 −0.139550
\(288\) −7.96199 + 14.9869i −0.469165 + 0.883111i
\(289\) −40.9000 −2.40588
\(290\) 25.0706 1.93590i 1.47220 0.113680i
\(291\) 6.93669 2.52080i 0.406636 0.147772i
\(292\) 26.7035 4.14871i 1.56270 0.242785i
\(293\) 15.7258i 0.918712i −0.888252 0.459356i \(-0.848080\pi\)
0.888252 0.459356i \(-0.151920\pi\)
\(294\) −15.4433 + 7.00109i −0.900674 + 0.408312i
\(295\) 2.77071i 0.161317i
\(296\) 18.8976 4.44856i 1.09840 0.258567i
\(297\) −13.2309 + 22.8370i −0.767734 + 1.32514i
\(298\) 1.14092 + 14.7753i 0.0660915 + 0.855909i
\(299\) −13.1829 −0.762387
\(300\) −13.0510 + 7.17551i −0.753501 + 0.414278i
\(301\) 0.778199 0.0448546
\(302\) −0.838157 10.8544i −0.0482305 0.624603i
\(303\) 0.210598 + 0.579520i 0.0120986 + 0.0332926i
\(304\) 7.17626 + 22.5378i 0.411587 + 1.29263i
\(305\) 3.54905i 0.203218i
\(306\) −22.5704 23.0820i −1.29026 1.31951i
\(307\) 17.3222i 0.988632i 0.869282 + 0.494316i \(0.164581\pi\)
−0.869282 + 0.494316i \(0.835419\pi\)
\(308\) 0.434641 + 2.79760i 0.0247660 + 0.159408i
\(309\) 6.31980 + 17.3907i 0.359521 + 0.989322i
\(310\) −18.6954 + 1.44362i −1.06183 + 0.0819919i
\(311\) 16.1322 0.914776 0.457388 0.889267i \(-0.348785\pi\)
0.457388 + 0.889267i \(0.348785\pi\)
\(312\) 24.0188 15.7281i 1.35980 0.890427i
\(313\) 16.6044 0.938535 0.469267 0.883056i \(-0.344518\pi\)
0.469267 + 0.883056i \(0.344518\pi\)
\(314\) 17.0205 1.31429i 0.960525 0.0741697i
\(315\) 1.95478 1.63691i 0.110139 0.0922294i
\(316\) 3.78714 + 24.3762i 0.213043 + 1.37127i
\(317\) 17.6587i 0.991813i −0.868376 0.495907i \(-0.834836\pi\)
0.868376 0.495907i \(-0.165164\pi\)
\(318\) −5.49786 12.1275i −0.308305 0.680074i
\(319\) 29.6155i 1.65815i
\(320\) 10.8827 + 21.8341i 0.608363 + 1.22056i
\(321\) −5.49459 + 1.99674i −0.306678 + 0.111447i
\(322\) 0.0682576 + 0.883962i 0.00380385 + 0.0492613i
\(323\) −44.9946 −2.50357
\(324\) 0.403393 17.9955i 0.0224107 0.999749i
\(325\) 25.1964 1.39764
\(326\) −1.02513 13.2759i −0.0567770 0.735283i
\(327\) 13.8796 5.04388i 0.767546 0.278927i
\(328\) 5.49780 + 23.3547i 0.303565 + 1.28955i
\(329\) 0.126826i 0.00699212i
\(330\) 15.6656 + 34.5558i 0.862361 + 1.90224i
\(331\) 34.2868i 1.88457i −0.334810 0.942286i \(-0.608672\pi\)
0.334810 0.942286i \(-0.391328\pi\)
\(332\) 5.52112 0.857772i 0.303011 0.0470763i
\(333\) −15.7875 + 13.2203i −0.865150 + 0.724467i
\(334\) 29.7285 2.29557i 1.62667 0.125608i
\(335\) −3.04949 −0.166611
\(336\) −1.17899 1.52911i −0.0643191 0.0834200i
\(337\) 6.16304 0.335722 0.167861 0.985811i \(-0.446314\pi\)
0.167861 + 0.985811i \(0.446314\pi\)
\(338\) −30.0966 + 2.32400i −1.63704 + 0.126409i
\(339\) −9.37695 25.8033i −0.509286 1.40144i
\(340\) −45.8582 + 7.12463i −2.48701 + 0.386387i
\(341\) 22.0845i 1.19595i
\(342\) −17.5396 17.9372i −0.948435 0.969934i
\(343\) 3.88008i 0.209505i
\(344\) −1.80971 7.68767i −0.0975729 0.414491i
\(345\) 4.05807 + 11.1669i 0.218479 + 0.601207i
\(346\) 2.05986 + 26.6759i 0.110739 + 1.43411i
\(347\) −7.81789 −0.419686 −0.209843 0.977735i \(-0.567295\pi\)
−0.209843 + 0.977735i \(0.567295\pi\)
\(348\) 9.73106 + 17.6991i 0.521639 + 0.948772i
\(349\) −21.3355 −1.14206 −0.571031 0.820929i \(-0.693456\pi\)
−0.571031 + 0.820929i \(0.693456\pi\)
\(350\) −0.130460 1.68951i −0.00697338 0.0903079i
\(351\) −15.2656 + 26.3490i −0.814819 + 1.40641i
\(352\) 26.6262 10.7996i 1.41918 0.575619i
\(353\) 13.3348i 0.709739i −0.934916 0.354869i \(-0.884525\pi\)
0.934916 0.354869i \(-0.115475\pi\)
\(354\) 2.02700 0.918919i 0.107734 0.0488400i
\(355\) 13.8747i 0.736393i
\(356\) −0.519478 3.34366i −0.0275323 0.177214i
\(357\) 3.45219 1.25453i 0.182709 0.0663968i
\(358\) −35.8046 + 2.76475i −1.89233 + 0.146122i
\(359\) 19.0196 1.00381 0.501907 0.864922i \(-0.332632\pi\)
0.501907 + 0.864922i \(0.332632\pi\)
\(360\) −20.7165 15.5042i −1.09186 0.817144i
\(361\) −15.9657 −0.840301
\(362\) 13.2330 1.02182i 0.695512 0.0537059i
\(363\) 24.0920 8.75505i 1.26450 0.459521i
\(364\) 0.501483 + 3.22783i 0.0262848 + 0.169184i
\(365\) 41.2045i 2.15674i
\(366\) −2.59642 + 1.17706i −0.135717 + 0.0615259i
\(367\) 1.97931i 0.103319i −0.998665 0.0516596i \(-0.983549\pi\)
0.998665 0.0516596i \(-0.0164511\pi\)
\(368\) 8.57375 2.72996i 0.446938 0.142309i
\(369\) −16.3384 19.5111i −0.850544 1.01571i
\(370\) 2.27899 + 29.5137i 0.118479 + 1.53435i
\(371\) 1.51499 0.0786544
\(372\) −7.25653 13.1984i −0.376234 0.684304i
\(373\) 16.1265 0.834998 0.417499 0.908677i \(-0.362907\pi\)
0.417499 + 0.908677i \(0.362907\pi\)
\(374\) 4.20810 + 54.4965i 0.217596 + 2.81795i
\(375\) 1.26391 + 3.47800i 0.0652681 + 0.179603i
\(376\) −1.25289 + 0.294934i −0.0646126 + 0.0152101i
\(377\) 34.1700i 1.75984i
\(378\) 1.84584 + 0.887187i 0.0949398 + 0.0456320i
\(379\) 27.2364i 1.39904i −0.714612 0.699521i \(-0.753397\pi\)
0.714612 0.699521i \(-0.246603\pi\)
\(380\) −35.6369 + 5.53661i −1.82813 + 0.284022i
\(381\) 1.19121 + 3.27793i 0.0610273 + 0.167934i
\(382\) 6.96374 0.537725i 0.356296 0.0275124i
\(383\) −31.3840 −1.60365 −0.801825 0.597560i \(-0.796137\pi\)
−0.801825 + 0.597560i \(0.796137\pi\)
\(384\) −12.3641 + 15.2030i −0.630951 + 0.775823i
\(385\) −4.31680 −0.220004
\(386\) −28.6424 + 2.21170i −1.45786 + 0.112573i
\(387\) 5.37811 + 6.42247i 0.273385 + 0.326473i
\(388\) 8.42127 1.30835i 0.427525 0.0664212i
\(389\) 7.82281i 0.396632i 0.980138 + 0.198316i \(0.0635473\pi\)
−0.980138 + 0.198316i \(0.936453\pi\)
\(390\) 18.0747 + 39.8701i 0.915249 + 2.01890i
\(391\) 17.1167i 0.865628i
\(392\) −19.0584 + 4.48641i −0.962593 + 0.226598i
\(393\) −6.48140 + 2.35535i −0.326944 + 0.118812i
\(394\) −1.45634 18.8602i −0.0733694 0.950161i
\(395\) −37.6134 −1.89253
\(396\) −20.0848 + 22.9212i −1.00930 + 1.15183i
\(397\) −25.8514 −1.29744 −0.648721 0.761026i \(-0.724696\pi\)
−0.648721 + 0.761026i \(0.724696\pi\)
\(398\) 1.43385 + 18.5689i 0.0718726 + 0.930777i
\(399\) 2.68273 0.974906i 0.134304 0.0488064i
\(400\) −16.3869 + 5.21775i −0.819346 + 0.260888i
\(401\) 1.90320i 0.0950413i −0.998870 0.0475207i \(-0.984868\pi\)
0.998870 0.0475207i \(-0.0151320\pi\)
\(402\) −1.01138 2.23094i −0.0504429 0.111269i
\(403\) 25.4809i 1.26929i
\(404\) 0.109305 + 0.703548i 0.00543811 + 0.0350028i
\(405\) 27.0188 + 4.82015i 1.34258 + 0.239515i
\(406\) −2.29122 + 0.176923i −0.113711 + 0.00878055i
\(407\) 34.8641 1.72815
\(408\) −20.4213 31.1860i −1.01101 1.54394i
\(409\) −18.6244 −0.920917 −0.460459 0.887681i \(-0.652315\pi\)
−0.460459 + 0.887681i \(0.652315\pi\)
\(410\) −36.4748 + 2.81651i −1.80136 + 0.139097i
\(411\) 5.22641 + 14.3819i 0.257800 + 0.709408i
\(412\) 3.28010 + 21.1126i 0.161599 + 1.04014i
\(413\) 0.253217i 0.0124600i
\(414\) −6.82361 + 6.67236i −0.335362 + 0.327929i
\(415\) 8.51929i 0.418195i
\(416\) 30.7209 12.4604i 1.50622 0.610921i
\(417\) −7.31633 20.1329i −0.358282 0.985913i
\(418\) 3.27016 + 42.3497i 0.159949 + 2.07139i
\(419\) 20.4330 0.998217 0.499109 0.866539i \(-0.333661\pi\)
0.499109 + 0.866539i \(0.333661\pi\)
\(420\) 2.57985 1.41841i 0.125884 0.0692114i
\(421\) 15.8138 0.770716 0.385358 0.922767i \(-0.374078\pi\)
0.385358 + 0.922767i \(0.374078\pi\)
\(422\) 0.533087 + 6.90368i 0.0259503 + 0.336066i
\(423\) 1.04669 0.876488i 0.0508919 0.0426163i
\(424\) −3.52312 14.9663i −0.171098 0.726827i
\(425\) 32.7149i 1.58691i
\(426\) 10.1505 4.60161i 0.491791 0.222949i
\(427\) 0.324350i 0.0156964i
\(428\) −6.67053 + 1.03635i −0.322432 + 0.0500937i
\(429\) 48.4576 17.6096i 2.33956 0.850198i
\(430\) 12.0064 0.927108i 0.579000 0.0447091i
\(431\) 20.0667 0.966578 0.483289 0.875461i \(-0.339442\pi\)
0.483289 + 0.875461i \(0.339442\pi\)
\(432\) 4.47183 20.2979i 0.215151 0.976581i
\(433\) −13.1719 −0.633003 −0.316501 0.948592i \(-0.602508\pi\)
−0.316501 + 0.948592i \(0.602508\pi\)
\(434\) 1.70858 0.131933i 0.0820147 0.00633299i
\(435\) −28.9446 + 10.5185i −1.38779 + 0.504323i
\(436\) 16.8501 2.61787i 0.806975 0.125373i
\(437\) 13.3015i 0.636298i
\(438\) −30.1444 + 13.6657i −1.44035 + 0.652970i
\(439\) 22.2901i 1.06385i −0.846793 0.531923i \(-0.821469\pi\)
0.846793 0.531923i \(-0.178531\pi\)
\(440\) 10.0388 + 42.6448i 0.478579 + 2.03301i
\(441\) 15.9218 13.3328i 0.758183 0.634894i
\(442\) 4.85525 + 62.8774i 0.230941 + 2.99077i
\(443\) 15.4580 0.734430 0.367215 0.930136i \(-0.380311\pi\)
0.367215 + 0.930136i \(0.380311\pi\)
\(444\) −20.8358 + 11.4556i −0.988823 + 0.543660i
\(445\) 5.15939 0.244579
\(446\) −2.94222 38.1028i −0.139318 1.80422i
\(447\) −6.19904 17.0584i −0.293204 0.806833i
\(448\) −0.994580 1.99543i −0.0469895 0.0942753i
\(449\) 24.9972i 1.17969i −0.807516 0.589845i \(-0.799189\pi\)
0.807516 0.589845i \(-0.200811\pi\)
\(450\) 13.0419 12.7528i 0.614801 0.601174i
\(451\) 43.0871i 2.02889i
\(452\) −4.86682 31.3257i −0.228916 1.47344i
\(453\) 4.55403 + 12.5317i 0.213967 + 0.588790i
\(454\) 0.0588924 0.00454754i 0.00276396 0.000213427i
\(455\) −4.98066 −0.233497
\(456\) −15.8696 24.2350i −0.743162 1.13491i
\(457\) −13.8327 −0.647064 −0.323532 0.946217i \(-0.604870\pi\)
−0.323532 + 0.946217i \(0.604870\pi\)
\(458\) −20.7651 + 1.60344i −0.970291 + 0.0749238i
\(459\) 34.2116 + 19.8209i 1.59686 + 0.925160i
\(460\) 2.10622 + 13.5568i 0.0982029 + 0.632091i
\(461\) 0.355681i 0.0165657i 0.999966 + 0.00828286i \(0.00263655\pi\)
−0.999966 + 0.00828286i \(0.997363\pi\)
\(462\) −1.43169 3.15808i −0.0666081 0.146927i
\(463\) 3.72249i 0.172999i −0.996252 0.0864994i \(-0.972432\pi\)
0.996252 0.0864994i \(-0.0275681\pi\)
\(464\) 7.07605 + 22.2231i 0.328497 + 1.03168i
\(465\) 21.5842 7.84373i 1.00094 0.363744i
\(466\) −2.49083 32.2572i −0.115386 1.49429i
\(467\) 33.9317 1.57017 0.785086 0.619387i \(-0.212619\pi\)
0.785086 + 0.619387i \(0.212619\pi\)
\(468\) −23.1736 + 26.4462i −1.07120 + 1.22248i
\(469\) 0.278695 0.0128689
\(470\) −0.151094 1.95672i −0.00696944 0.0902569i
\(471\) −19.6506 + 7.14105i −0.905451 + 0.329042i
\(472\) 2.50148 0.588859i 0.115140 0.0271044i
\(473\) 14.1830i 0.652133i
\(474\) −12.4747 27.5172i −0.572980 1.26391i
\(475\) 25.4231i 1.16649i
\(476\) 4.19102 0.651125i 0.192095 0.0298443i
\(477\) 10.4701 + 12.5032i 0.479391 + 0.572483i
\(478\) 9.59436 0.740856i 0.438836 0.0338860i
\(479\) 7.68288 0.351040 0.175520 0.984476i \(-0.443839\pi\)
0.175520 + 0.984476i \(0.443839\pi\)
\(480\) −20.0117 22.1873i −0.913403 1.01271i
\(481\) 40.2257 1.83413
\(482\) 1.35291 0.104469i 0.0616233 0.00475842i
\(483\) −0.370870 1.02055i −0.0168752 0.0464367i
\(484\) 29.2481 4.54404i 1.32946 0.206547i
\(485\) 12.9943i 0.590042i
\(486\) 5.43460 + 21.3650i 0.246518 + 0.969138i
\(487\) 33.8111i 1.53213i 0.642766 + 0.766063i \(0.277787\pi\)
−0.642766 + 0.766063i \(0.722213\pi\)
\(488\) −3.20419 + 0.754280i −0.145047 + 0.0341446i
\(489\) 5.56995 + 15.3273i 0.251882 + 0.693123i
\(490\) −2.29838 29.7648i −0.103830 1.34464i
\(491\) 43.0765 1.94401 0.972007 0.234952i \(-0.0754932\pi\)
0.972007 + 0.234952i \(0.0754932\pi\)
\(492\) −14.1575 25.7501i −0.638271 1.16091i
\(493\) −44.3663 −1.99816
\(494\) 3.77306 + 48.8626i 0.169758 + 2.19843i
\(495\) −29.8333 35.6265i −1.34091 1.60129i
\(496\) −5.27667 16.5719i −0.236929 0.744102i
\(497\) 1.26802i 0.0568784i
\(498\) −6.23254 + 2.82546i −0.279287 + 0.126612i
\(499\) 31.2747i 1.40005i 0.714118 + 0.700025i \(0.246828\pi\)
−0.714118 + 0.700025i \(0.753172\pi\)
\(500\) 0.655994 + 4.22236i 0.0293370 + 0.188830i
\(501\) −34.3222 + 12.4727i −1.53340 + 0.557240i
\(502\) 16.5135 1.27514i 0.737033 0.0569121i
\(503\) 11.9246 0.531690 0.265845 0.964016i \(-0.414349\pi\)
0.265845 + 0.964016i \(0.414349\pi\)
\(504\) 1.89330 + 1.41694i 0.0843343 + 0.0631156i
\(505\) −1.08560 −0.0483086
\(506\) 16.1105 1.24402i 0.716200 0.0553034i
\(507\) 34.7472 12.6272i 1.54318 0.560792i
\(508\) 0.618259 + 3.97947i 0.0274308 + 0.176560i
\(509\) 18.5710i 0.823145i 0.911377 + 0.411572i \(0.135020\pi\)
−0.911377 + 0.411572i \(0.864980\pi\)
\(510\) 51.7673 23.4682i 2.29229 1.03919i
\(511\) 3.76571i 0.166585i
\(512\) −17.3996 + 14.4656i −0.768960 + 0.639297i
\(513\) 26.5861 + 15.4030i 1.17381 + 0.680058i
\(514\) −0.168241 2.17879i −0.00742080 0.0961022i
\(515\) −32.5775 −1.43554
\(516\) 4.66023 + 8.47616i 0.205155 + 0.373142i
\(517\) −2.31144 −0.101657
\(518\) −0.208278 2.69728i −0.00915121 0.118512i
\(519\) −11.1920 30.7979i −0.491275 1.35188i
\(520\) 11.5826 + 49.2030i 0.507930 + 2.15769i
\(521\) 7.64072i 0.334746i 0.985894 + 0.167373i \(0.0535284\pi\)
−0.985894 + 0.167373i \(0.946472\pi\)
\(522\) −17.2947 17.6867i −0.756969 0.774128i
\(523\) 21.5819i 0.943711i 0.881676 + 0.471855i \(0.156416\pi\)
−0.881676 + 0.471855i \(0.843584\pi\)
\(524\) −7.86854 + 1.22247i −0.343739 + 0.0534040i
\(525\) 0.708840 + 1.95057i 0.0309363 + 0.0851299i
\(526\) −35.9476 + 2.77580i −1.56739 + 0.121031i
\(527\) 33.0843 1.44118
\(528\) −27.8687 + 21.4875i −1.21283 + 0.935123i
\(529\) −17.9399 −0.779995
\(530\) 23.3739 1.80489i 1.01530 0.0783992i
\(531\) −2.08980 + 1.74998i −0.0906896 + 0.0759425i
\(532\) 3.25688 0.505995i 0.141204 0.0219377i
\(533\) 49.7133i 2.15332i
\(534\) 1.71114 + 3.77451i 0.0740481 + 0.163339i
\(535\) 10.2929i 0.445000i
\(536\) −0.648108 2.75317i −0.0279940 0.118919i
\(537\) 41.3371 15.0220i 1.78383 0.648246i
\(538\) −1.23485 15.9917i −0.0532380 0.689452i
\(539\) −35.1607 −1.51448
\(540\) 29.5354 + 11.4889i 1.27100 + 0.494402i
\(541\) −18.2680 −0.785402 −0.392701 0.919666i \(-0.628459\pi\)
−0.392701 + 0.919666i \(0.628459\pi\)
\(542\) −0.372401 4.82274i −0.0159960 0.207154i
\(543\) −15.2778 + 5.55197i −0.655633 + 0.238258i
\(544\) −16.1786 39.8880i −0.693651 1.71018i
\(545\) 26.0004i 1.11373i
\(546\) −1.65186 3.64375i −0.0706931 0.155938i
\(547\) 0.148820i 0.00636309i −0.999995 0.00318155i \(-0.998987\pi\)
0.999995 0.00318155i \(-0.00101272\pi\)
\(548\) 2.71261 + 17.4599i 0.115877 + 0.745851i
\(549\) 2.67686 2.24158i 0.114246 0.0956681i
\(550\) −30.7919 + 2.37768i −1.31297 + 0.101385i
\(551\) −34.4775 −1.46879
\(552\) −9.21937 + 6.03705i −0.392402 + 0.256954i
\(553\) 3.43751 0.146178
\(554\) −16.0468 + 1.23910i −0.681764 + 0.0526443i
\(555\) −12.3826 34.0742i −0.525613 1.44637i
\(556\) −3.79731 24.4417i −0.161042 1.03656i
\(557\) 9.99434i 0.423474i 0.977327 + 0.211737i \(0.0679120\pi\)
−0.977327 + 0.211737i \(0.932088\pi\)
\(558\) 12.8968 + 13.1892i 0.545966 + 0.558341i
\(559\) 16.3641i 0.692128i
\(560\) 3.23927 1.03141i 0.136884 0.0435852i
\(561\) −22.8643 62.9174i −0.965330 2.65637i
\(562\) −1.06967 13.8526i −0.0451213 0.584338i
\(563\) −21.6148 −0.910954 −0.455477 0.890247i \(-0.650531\pi\)
−0.455477 + 0.890247i \(0.650531\pi\)
\(564\) 1.38139 0.759493i 0.0581669 0.0319804i
\(565\) 48.3367 2.03354
\(566\) −1.92783 24.9662i −0.0810329 1.04941i
\(567\) −2.46927 0.440517i −0.103700 0.0185000i
\(568\) 12.5265 2.94879i 0.525601 0.123728i
\(569\) 4.62418i 0.193856i −0.995291 0.0969279i \(-0.969098\pi\)
0.995291 0.0969279i \(-0.0309016\pi\)
\(570\) 40.2288 18.2374i 1.68500 0.763879i
\(571\) 0.855969i 0.0358212i 0.999840 + 0.0179106i \(0.00570142\pi\)
−0.999840 + 0.0179106i \(0.994299\pi\)
\(572\) 58.8284 9.13971i 2.45974 0.382150i
\(573\) −8.03979 + 2.92167i −0.335867 + 0.122054i
\(574\) 3.33346 0.257403i 0.139136 0.0107438i
\(575\) −9.67135 −0.403323
\(576\) 9.59479 21.9986i 0.399783 0.916610i
\(577\) 16.9778 0.706796 0.353398 0.935473i \(-0.385026\pi\)
0.353398 + 0.935473i \(0.385026\pi\)
\(578\) 57.6697 4.45313i 2.39874 0.185226i
\(579\) 33.0682 12.0170i 1.37427 0.499411i
\(580\) −35.1392 + 5.45930i −1.45908 + 0.226685i
\(581\) 0.778583i 0.0323011i
\(582\) −9.50638 + 4.30963i −0.394052 + 0.178640i
\(583\) 27.6113i 1.14354i
\(584\) −37.2007 + 8.75718i −1.53937 + 0.362375i
\(585\) −34.4212 41.1054i −1.42314 1.69950i
\(586\) 1.71220 + 22.1737i 0.0707304 + 0.915985i
\(587\) 11.4625 0.473108 0.236554 0.971618i \(-0.423982\pi\)
0.236554 + 0.971618i \(0.423982\pi\)
\(588\) 21.0131 11.5531i 0.866565 0.476442i
\(589\) 25.7101 1.05937
\(590\) 0.301671 + 3.90675i 0.0124196 + 0.160838i
\(591\) 7.91286 + 21.7744i 0.325492 + 0.895681i
\(592\) −26.1615 + 8.33008i −1.07523 + 0.342364i
\(593\) 29.2647i 1.20176i 0.799340 + 0.600880i \(0.205183\pi\)
−0.799340 + 0.600880i \(0.794817\pi\)
\(594\) 16.1693 33.6411i 0.663435 1.38031i
\(595\) 6.46689i 0.265117i
\(596\) −3.21742 20.7092i −0.131791 0.848281i
\(597\) −7.79068 21.4382i −0.318851 0.877408i
\(598\) 18.5881 1.43533i 0.760124 0.0586952i
\(599\) 43.1247 1.76203 0.881014 0.473090i \(-0.156861\pi\)
0.881014 + 0.473090i \(0.156861\pi\)
\(600\) 17.6209 11.5386i 0.719370 0.471060i
\(601\) −9.96034 −0.406291 −0.203145 0.979149i \(-0.565116\pi\)
−0.203145 + 0.979149i \(0.565116\pi\)
\(602\) −1.09727 + 0.0847290i −0.0447215 + 0.00345330i
\(603\) 1.92605 + 2.30007i 0.0784349 + 0.0936661i
\(604\) 2.36363 + 15.2137i 0.0961747 + 0.619036i
\(605\) 45.1309i 1.83483i
\(606\) −0.360044 0.794203i −0.0146258 0.0322623i
\(607\) 7.00955i 0.284509i 0.989830 + 0.142255i \(0.0454351\pi\)
−0.989830 + 0.142255i \(0.954565\pi\)
\(608\) −12.5725 30.9973i −0.509883 1.25711i
\(609\) 2.64526 0.961293i 0.107191 0.0389535i
\(610\) −0.386415 5.00422i −0.0156455 0.202615i
\(611\) −2.66691 −0.107892
\(612\) 34.3377 + 30.0886i 1.38802 + 1.21626i
\(613\) 4.42637 0.178779 0.0893897 0.995997i \(-0.471508\pi\)
0.0893897 + 0.995997i \(0.471508\pi\)
\(614\) −1.88602 24.4246i −0.0761134 0.985698i
\(615\) 42.1109 15.3032i 1.69808 0.617083i
\(616\) −0.917449 3.89734i −0.0369651 0.157028i
\(617\) 26.4466i 1.06470i 0.846524 + 0.532350i \(0.178691\pi\)
−0.846524 + 0.532350i \(0.821309\pi\)
\(618\) −10.8045 23.8331i −0.434621 0.958707i
\(619\) 5.44867i 0.219000i −0.993987 0.109500i \(-0.965075\pi\)
0.993987 0.109500i \(-0.0349250\pi\)
\(620\) 26.2036 4.07105i 1.05236 0.163497i
\(621\) 5.85954 10.1138i 0.235135 0.405853i
\(622\) −22.7467 + 1.75645i −0.912061 + 0.0704274i
\(623\) −0.471520 −0.0188911
\(624\) −32.1545 + 24.7920i −1.28721 + 0.992474i
\(625\) −28.0122 −1.12049
\(626\) −23.4124 + 1.80786i −0.935749 + 0.0722565i
\(627\) −17.7680 48.8937i −0.709586 1.95262i
\(628\) −23.8561 + 3.70634i −0.951964 + 0.147899i
\(629\) 52.2290i 2.08251i
\(630\) −2.57804 + 2.52090i −0.102712 + 0.100435i
\(631\) 25.6253i 1.02013i 0.860137 + 0.510063i \(0.170378\pi\)
−0.860137 + 0.510063i \(0.829622\pi\)
\(632\) −7.99397 33.9585i −0.317983 1.35080i
\(633\) −2.89647 7.97044i −0.115124 0.316797i
\(634\) 1.92265 + 24.8991i 0.0763584 + 0.988870i
\(635\) −6.14047 −0.243677
\(636\) 9.07250 + 16.5013i 0.359748 + 0.654319i
\(637\) −40.5680 −1.60736
\(638\) 3.22449 + 41.7584i 0.127659 + 1.65323i
\(639\) −10.4650 + 8.76324i −0.413987 + 0.346668i
\(640\) −17.7221 29.6015i −0.700527 1.17010i
\(641\) 2.81491i 0.111182i 0.998454 + 0.0555911i \(0.0177043\pi\)
−0.998454 + 0.0555911i \(0.982296\pi\)
\(642\) 7.53006 3.41368i 0.297188 0.134727i
\(643\) 29.8717i 1.17802i 0.808125 + 0.589011i \(0.200483\pi\)
−0.808125 + 0.589011i \(0.799517\pi\)
\(644\) −0.192489 1.23897i −0.00758512 0.0488222i
\(645\) −13.8616 + 5.03734i −0.545801 + 0.198345i
\(646\) 63.4431 4.89894i 2.49614 0.192746i
\(647\) −42.3369 −1.66443 −0.832217 0.554450i \(-0.812929\pi\)
−0.832217 + 0.554450i \(0.812929\pi\)
\(648\) 1.39053 + 25.4178i 0.0546251 + 0.998507i
\(649\) 4.61498 0.181154
\(650\) −35.5273 + 2.74334i −1.39349 + 0.107603i
\(651\) −1.97260 + 0.716844i −0.0773121 + 0.0280953i
\(652\) 2.89091 + 18.6076i 0.113217 + 0.728729i
\(653\) 43.8697i 1.71676i −0.513018 0.858378i \(-0.671473\pi\)
0.513018 0.858378i \(-0.328527\pi\)
\(654\) −19.0214 + 8.62315i −0.743794 + 0.337192i
\(655\) 12.1414i 0.474406i
\(656\) −10.2948 32.3320i −0.401945 1.26235i
\(657\) 31.0784 26.0247i 1.21248 1.01532i
\(658\) 0.0138086 + 0.178826i 0.000538314 + 0.00697137i
\(659\) −30.2207 −1.17723 −0.588616 0.808413i \(-0.700327\pi\)
−0.588616 + 0.808413i \(0.700327\pi\)
\(660\) −25.8511 47.0187i −1.00625 1.83020i
\(661\) 9.40563 0.365837 0.182918 0.983128i \(-0.441446\pi\)
0.182918 + 0.983128i \(0.441446\pi\)
\(662\) 3.73309 + 48.3449i 0.145091 + 1.87898i
\(663\) −26.3805 72.5932i −1.02453 2.81929i
\(664\) −7.69147 + 1.81060i −0.298487 + 0.0702650i
\(665\) 5.02548i 0.194880i
\(666\) 20.8212 20.3597i 0.806807 0.788924i
\(667\) 13.1158i 0.507845i
\(668\) −41.6677 + 6.47358i −1.61217 + 0.250470i
\(669\) 15.9862 + 43.9905i 0.618063 + 1.70077i
\(670\) 4.29983 0.332024i 0.166117 0.0128272i
\(671\) −5.91141 −0.228207
\(672\) 1.82888 + 2.02771i 0.0705506 + 0.0782206i
\(673\) −50.0563 −1.92953 −0.964764 0.263117i \(-0.915249\pi\)
−0.964764 + 0.263117i \(0.915249\pi\)
\(674\) −8.68998 + 0.671021i −0.334725 + 0.0258468i
\(675\) −11.1993 + 19.3304i −0.431061 + 0.744027i
\(676\) 42.1837 6.55374i 1.62245 0.252067i
\(677\) 20.9155i 0.803848i −0.915673 0.401924i \(-0.868342\pi\)
0.915673 0.401924i \(-0.131658\pi\)
\(678\) 16.0311 + 35.3621i 0.615670 + 1.35807i
\(679\) 1.18756i 0.0455744i
\(680\) 63.8852 15.0388i 2.44988 0.576712i
\(681\) −0.0679925 + 0.0247086i −0.00260548 + 0.000946834i
\(682\) −2.40453 31.1396i −0.0920742 1.19240i
\(683\) −15.8548 −0.606666 −0.303333 0.952885i \(-0.598099\pi\)
−0.303333 + 0.952885i \(0.598099\pi\)
\(684\) 26.6842 + 23.3821i 1.02029 + 0.894036i
\(685\) −26.9413 −1.02937
\(686\) 0.422457 + 5.47098i 0.0161295 + 0.208883i
\(687\) 23.9738 8.71211i 0.914657 0.332388i
\(688\) 3.38874 + 10.6427i 0.129194 + 0.405749i
\(689\) 31.8575i 1.21367i
\(690\) −6.93778 15.3037i −0.264117 0.582602i
\(691\) 9.43178i 0.358802i 0.983776 + 0.179401i \(0.0574159\pi\)
−0.983776 + 0.179401i \(0.942584\pi\)
\(692\) −5.80887 37.3892i −0.220820 1.42132i
\(693\) 2.72648 + 3.25593i 0.103571 + 0.123683i
\(694\) 11.0234 0.851200i 0.418441 0.0323111i
\(695\) 37.7145 1.43059
\(696\) −15.6480 23.8965i −0.593136 0.905796i
\(697\) 64.5478 2.44492
\(698\) 30.0834 2.32297i 1.13867 0.0879258i
\(699\) 13.5337 + 37.2416i 0.511890 + 1.40861i
\(700\) 0.367902 + 2.36803i 0.0139054 + 0.0895030i
\(701\) 29.7093i 1.12210i 0.827780 + 0.561052i \(0.189603\pi\)
−0.827780 + 0.561052i \(0.810397\pi\)
\(702\) 18.6559 38.8147i 0.704123 1.46497i
\(703\) 40.5876i 1.53079i
\(704\) −36.3675 + 18.1266i −1.37065 + 0.683171i
\(705\) 0.820951 + 2.25908i 0.0309188 + 0.0850817i
\(706\) 1.45187 + 18.8023i 0.0546418 + 0.707632i
\(707\) 0.0992138 0.00373132
\(708\) −2.75805 + 1.51639i −0.103654 + 0.0569893i
\(709\) 35.4570 1.33162 0.665808 0.746123i \(-0.268087\pi\)
0.665808 + 0.746123i \(0.268087\pi\)
\(710\) 1.51066 + 19.5636i 0.0566939 + 0.734207i
\(711\) 23.7565 + 28.3698i 0.890940 + 1.06395i
\(712\) 1.09652 + 4.65806i 0.0410940 + 0.174568i
\(713\) 9.78055i 0.366285i
\(714\) −4.73105 + 2.14478i −0.177055 + 0.0802662i
\(715\) 90.7744i 3.39477i
\(716\) 50.1840 7.79669i 1.87546 0.291376i
\(717\) −11.0769 + 4.02536i −0.413674 + 0.150330i
\(718\) −26.8179 + 2.07082i −1.00083 + 0.0772823i
\(719\) 30.8444 1.15030 0.575152 0.818047i \(-0.304943\pi\)
0.575152 + 0.818047i \(0.304943\pi\)
\(720\) 30.8987 + 19.6056i 1.15153 + 0.730658i
\(721\) 2.97728 0.110880
\(722\) 22.5119 1.73832i 0.837807 0.0646936i
\(723\) −1.56196 + 0.567619i −0.0580899 + 0.0211100i
\(724\) −18.5475 + 2.88158i −0.689313 + 0.107093i
\(725\) 25.0681i 0.931004i
\(726\) −33.0168 + 14.9679i −1.22537 + 0.555509i
\(727\) 19.2654i 0.714513i 0.934006 + 0.357257i \(0.116288\pi\)
−0.934006 + 0.357257i \(0.883712\pi\)
\(728\) −1.05854 4.49670i −0.0392321 0.166659i
\(729\) −13.4295 23.4233i −0.497387 0.867529i
\(730\) −4.48628 58.0990i −0.166045 2.15034i
\(731\) −21.2472 −0.785854
\(732\) 3.53283 1.94237i 0.130577 0.0717920i
\(733\) −12.3277 −0.455334 −0.227667 0.973739i \(-0.573110\pi\)
−0.227667 + 0.973739i \(0.573110\pi\)
\(734\) 0.215504 + 2.79086i 0.00795440 + 0.103013i
\(735\) 12.4880 + 34.3641i 0.460626 + 1.26754i
\(736\) −11.7919 + 4.78279i −0.434655 + 0.176296i
\(737\) 5.07932i 0.187099i
\(738\) 25.1618 + 25.7321i 0.926218 + 0.947213i
\(739\) 45.7058i 1.68131i −0.541568 0.840657i \(-0.682169\pi\)
0.541568 0.840657i \(-0.317831\pi\)
\(740\) −6.42681 41.3667i −0.236254 1.52067i
\(741\) −20.5005 56.4128i −0.753105 2.07238i
\(742\) −2.13616 + 0.164950i −0.0784209 + 0.00605550i
\(743\) −42.4107 −1.55590 −0.777948 0.628328i \(-0.783739\pi\)
−0.777948 + 0.628328i \(0.783739\pi\)
\(744\) 11.6688 + 17.8198i 0.427801 + 0.653307i
\(745\) 31.9550 1.17074
\(746\) −22.7386 + 1.75583i −0.832520 + 0.0642854i
\(747\) 6.42565 5.38077i 0.235102 0.196872i
\(748\) −11.8670 76.3828i −0.433900 2.79283i
\(749\) 0.940673i 0.0343714i
\(750\) −2.16082 4.76643i −0.0789018 0.174045i
\(751\) 27.0706i 0.987819i 0.869513 + 0.493910i \(0.164433\pi\)
−0.869513 + 0.493910i \(0.835567\pi\)
\(752\) 1.73448 0.552274i 0.0632498 0.0201394i
\(753\) −19.0652 + 6.92831i −0.694773 + 0.252482i
\(754\) 3.72037 + 48.1802i 0.135488 + 1.75462i
\(755\) −23.4753 −0.854353
\(756\) −2.69926 1.04998i −0.0981712 0.0381873i
\(757\) −6.61541 −0.240441 −0.120221 0.992747i \(-0.538360\pi\)
−0.120221 + 0.992747i \(0.538360\pi\)
\(758\) 2.96546 + 38.4038i 0.107710 + 1.39489i
\(759\) −18.5999 + 6.75924i −0.675135 + 0.245345i
\(760\) 49.6457 11.6868i 1.80084 0.423925i
\(761\) 22.7202i 0.823606i −0.911273 0.411803i \(-0.864899\pi\)
0.911273 0.411803i \(-0.135101\pi\)
\(762\) −2.03652 4.49224i −0.0737752 0.162737i
\(763\) 2.37619i 0.0860240i