Properties

Label 804.2.c.b.671.1
Level 804
Weight 2
Character 804.671
Analytic conductor 6.420
Analytic rank 0
Dimension 128
CM no
Inner twists 4

Related objects

Downloads

Learn more about

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

$q$-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 \(-0.761160\pi\)
0.731458 0.681887i \(-0.238840\pi\)
\(6\) −2.23094 1.01138i −0.910779 0.412893i
\(7\) 0.278695i 0.105337i 0.998612 + 0.0526684i \(0.0167726\pi\)
−0.998612 + 0.0526684i \(0.983227\pi\)
\(8\) −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 \(-0.625935\pi\)
0.385395 0.922752i \(-0.374065\pi\)
\(18\) −3.03343 2.96619i −0.714986 0.699139i
\(19\) 5.91318i 1.35658i −0.734796 0.678288i \(-0.762722\pi\)
0.734796 0.678288i \(-0.237278\pi\)
\(20\) 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 \(-0.817910\pi\)
0.840792 0.541359i \(-0.182090\pi\)
\(30\) −3.08419 + 6.80324i −0.563093 + 1.24210i
\(31\) 4.34794i 0.780912i 0.920622 + 0.390456i \(0.127683\pi\)
−0.920622 + 0.390456i \(0.872317\pi\)
\(32\) −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 \(0.230462\pi\)
−0.749151 + 0.662399i \(0.769538\pi\)
\(42\) 0.281866 0.621753i 0.0434929 0.0959386i
\(43\) 2.79230i 0.425821i −0.977072 0.212911i \(-0.931706\pi\)
0.977072 0.212911i \(-0.0682943\pi\)
\(44\) −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 \(-0.878210\pi\)
0.927692 0.373347i \(-0.121790\pi\)
\(54\) −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 \(-0.755909\pi\)
0.720110 0.693860i \(-0.244091\pi\)
\(80\) 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 \(0.0285812\pi\)
−0.995972 + 0.0896698i \(0.971419\pi\)
\(90\) −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 \(-0.994362\pi\)
0.999843 0.0177114i \(-0.00563800\pi\)
\(102\) −7.69578 + 16.9757i −0.761996 + 1.68085i
\(103\) 10.6829i 1.05262i −0.850292 0.526311i \(-0.823575\pi\)
0.850292 0.526311i \(-0.176425\pi\)
\(104\) 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 \(0.267816\pi\)
−0.666443 + 0.745556i \(0.732184\pi\)
\(114\) −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 \(-0.971524\pi\)
0.996001 0.0893393i \(-0.0284755\pi\)
\(128\) −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 \(-0.876818\pi\)
0.926051 0.377399i \(-0.123182\pi\)
\(138\) −5.01844 2.27506i −0.427198 0.193666i
\(139\) 12.3675i 1.04899i 0.851412 + 0.524497i \(0.175747\pi\)
−0.851412 + 0.524497i \(0.824253\pi\)
\(140\) 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 \(0.141215\pi\)
−0.903196 + 0.429229i \(0.858785\pi\)
\(150\) 9.59170 + 4.34831i 0.783159 + 0.355038i
\(151\) 7.69810i 0.626463i −0.949677 0.313231i \(-0.898588\pi\)
0.949677 0.313231i \(-0.101412\pi\)
\(152\) −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 \(-0.879791\pi\)
0.929534 0.368736i \(-0.120209\pi\)
\(164\) −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 \(0.255486\pi\)
−0.694815 + 0.719188i \(0.744514\pi\)
\(174\) −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 \(-0.841907\pi\)
0.879177 0.476495i \(-0.158093\pi\)
\(198\) 15.4078 + 15.0662i 1.09498 + 1.07071i
\(199\) 13.1693i 0.933548i 0.884377 + 0.466774i \(0.154584\pi\)
−0.884377 + 0.466774i \(0.845416\pi\)
\(200\) 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 \(0.0539030\pi\)
−0.985696 + 0.168533i \(0.946097\pi\)
\(212\) 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 \(-0.640023\pi\)
0.425845 0.904796i \(-0.359977\pi\)
\(224\) 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 \(-0.730358\pi\)
0.662154 0.749368i \(-0.269642\pi\)
\(234\) 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 \(-0.984653\pi\)
0.998838 0.0481941i \(-0.0153466\pi\)
\(258\) −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 \(-0.887624\pi\)
0.938326 0.345752i \(-0.112376\pi\)
\(270\) −20.1973 + 9.70763i −1.22917 + 0.590788i
\(271\) 3.42034i 0.207771i −0.994589 0.103885i \(-0.966872\pi\)
0.994589 0.103885i \(-0.0331275\pi\)
\(272\) 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 \(-0.905333\pi\)
0.956101 0.293039i \(-0.0946666\pi\)
\(282\) −1.01524 0.460247i −0.0604564 0.0274073i
\(283\) 17.7063i 1.05253i −0.850320 0.526265i \(-0.823592\pi\)
0.850320 0.526265i \(-0.176408\pi\)
\(284\) −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 \(0.151920\pi\)
−0.888252 + 0.459356i \(0.848080\pi\)
\(294\) −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 \(-0.835419\pi\)
0.869282 0.494316i \(-0.164581\pi\)
\(308\) 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 \(0.165164\pi\)
−0.868376 + 0.495907i \(0.834836\pi\)
\(318\) −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 \(0.391328\pi\)
−0.334810 + 0.942286i \(0.608672\pi\)
\(332\) 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 \(0.115475\pi\)
−0.934916 + 0.354869i \(0.884525\pi\)
\(354\) 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 \(0.0164511\pi\)
−0.998665 + 0.0516596i \(0.983549\pi\)
\(368\) 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 \(0.246603\pi\)
−0.714612 + 0.699521i \(0.753397\pi\)
\(380\) −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 \(-0.936453\pi\)
0.980138 0.198316i \(-0.0635473\pi\)
\(390\) 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 \(0.0151320\pi\)
−0.998870 + 0.0475207i \(0.984868\pi\)
\(402\) −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 \(0.178531\pi\)
−0.846793 + 0.531923i \(0.821469\pi\)
\(440\) 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 \(0.200811\pi\)
−0.807516 + 0.589845i \(0.799189\pi\)
\(450\) 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 \(-0.997363\pi\)
0.999966 0.00828286i \(-0.00263655\pi\)
\(462\) −1.43169 + 3.15808i −0.0666081 + 0.146927i
\(463\) 3.72249i 0.172999i 0.996252 + 0.0864994i \(0.0275681\pi\)
−0.996252 + 0.0864994i \(0.972432\pi\)
\(464\) 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 \(-0.722213\pi\)
0.642766 0.766063i \(-0.277787\pi\)
\(488\) −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 \(-0.753172\pi\)
0.714118 0.700025i \(-0.246828\pi\)
\(500\) 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 \(-0.864980\pi\)
0.911377 0.411572i \(-0.135020\pi\)
\(510\) 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 \(-0.946472\pi\)
0.985894 0.167373i \(-0.0535284\pi\)
\(522\) −17.2947 + 17.6867i −0.756969 + 0.774128i
\(523\) 21.5819i 0.943711i −0.881676 0.471855i \(-0.843584\pi\)
0.881676 0.471855i \(-0.156416\pi\)
\(524\) −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 \(0.00101272\pi\)
−0.999995 + 0.00318155i \(0.998987\pi\)
\(548\) 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 \(-0.932088\pi\)
0.977327 0.211737i \(-0.0679120\pi\)
\(558\) 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 \(0.0309016\pi\)
−0.995291 + 0.0969279i \(0.969098\pi\)
\(570\) 40.2288 + 18.2374i 1.68500 + 0.763879i
\(571\) 0.855969i 0.0358212i −0.999840 0.0179106i \(-0.994299\pi\)
0.999840 0.0179106i \(-0.00570142\pi\)
\(572\) 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 \(-0.794817\pi\)
0.799340 0.600880i \(-0.205183\pi\)
\(594\) 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 \(-0.954565\pi\)
0.989830 0.142255i \(-0.0454351\pi\)
\(608\) −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 \(-0.821309\pi\)
0.846524 0.532350i \(-0.178691\pi\)
\(618\) −10.8045 + 23.8331i −0.434621 + 0.958707i
\(619\) 5.44867i 0.219000i 0.993987 + 0.109500i \(0.0349250\pi\)
−0.993987 + 0.109500i \(0.965075\pi\)
\(620\) 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 \(-0.829622\pi\)
0.860137 0.510063i \(-0.170378\pi\)
\(632\) −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 \(-0.982296\pi\)
0.998454 0.0555911i \(-0.0177043\pi\)
\(642\) 7.53006 + 3.41368i 0.297188 + 0.134727i
\(643\) 29.8717i 1.17802i −0.808125 0.589011i \(-0.799517\pi\)
0.808125 0.589011i \(-0.200483\pi\)
\(644\) −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 \(0.328527\pi\)
−0.513018 + 0.858378i \(0.671473\pi\)
\(654\) −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 \(0.131658\pi\)
−0.915673 + 0.401924i \(0.868342\pi\)
\(678\) 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 \(-0.942584\pi\)
0.983776 0.179401i \(-0.0574159\pi\)
\(692\) −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 \(-0.810397\pi\)
0.827780 0.561052i \(-0.189603\pi\)
\(702\) 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 \(-0.883712\pi\)
0.934006 0.357257i \(-0.116288\pi\)
\(728\) −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 \(0.317831\pi\)
−0.541568 + 0.840657i \(0.682169\pi\)
\(740\) −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 \(-0.835567\pi\)
0.869513 0.493910i \(-0.164433\pi\)
\(752\) 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 \(0.135101\pi\)
−0.911273 + 0.411803i \(0.864899\pi\)
\(762\) −2.03652 + 4.49224i −0.0737752 + 0.162737i
\(763\) 2.37619i 0.0860240i