Properties

Label 804.2.c.b.671.5
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 671.5
Character \(\chi\) = 804.671
Dual form 804.2.c.b.671.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.40536 - 0.157993i) q^{2} +(1.10632 + 1.33268i) q^{3} +(1.95008 + 0.444075i) q^{4} +1.25971i q^{5} +(-1.34423 - 2.04769i) q^{6} -4.86310i q^{7} +(-2.67040 - 0.932185i) q^{8} +(-0.552098 + 2.94876i) q^{9} +O(q^{10})\) \(q+(-1.40536 - 0.157993i) q^{2} +(1.10632 + 1.33268i) q^{3} +(1.95008 + 0.444075i) q^{4} +1.25971i q^{5} +(-1.34423 - 2.04769i) q^{6} -4.86310i q^{7} +(-2.67040 - 0.932185i) q^{8} +(-0.552098 + 2.94876i) q^{9} +(0.199026 - 1.77035i) q^{10} +2.77221 q^{11} +(1.56560 + 3.09013i) q^{12} -0.427783 q^{13} +(-0.768337 + 6.83441i) q^{14} +(-1.67880 + 1.39365i) q^{15} +(3.60559 + 1.73196i) q^{16} +6.13077i q^{17} +(1.24178 - 4.05684i) q^{18} -5.50865i q^{19} +(-0.559407 + 2.45653i) q^{20} +(6.48098 - 5.38016i) q^{21} +(-3.89595 - 0.437991i) q^{22} +7.85942 q^{23} +(-1.71202 - 4.59010i) q^{24} +3.41313 q^{25} +(0.601189 + 0.0675869i) q^{26} +(-4.54057 + 2.52651i) q^{27} +(2.15958 - 9.48341i) q^{28} -5.86394i q^{29} +(2.57950 - 1.69334i) q^{30} +6.21018i q^{31} +(-4.79352 - 3.00369i) q^{32} +(3.06696 + 3.69448i) q^{33} +(0.968620 - 8.61594i) q^{34} +6.12610 q^{35} +(-2.38610 + 5.50513i) q^{36} +9.87650 q^{37} +(-0.870330 + 7.74164i) q^{38} +(-0.473266 - 0.570100i) q^{39} +(1.17428 - 3.36393i) q^{40} -2.42494i q^{41} +(-9.95814 + 6.53711i) q^{42} +3.59689i q^{43} +(5.40602 + 1.23107i) q^{44} +(-3.71459 - 0.695484i) q^{45} +(-11.0453 - 1.24174i) q^{46} +2.24122 q^{47} +(1.68079 + 6.72123i) q^{48} -16.6497 q^{49} +(-4.79667 - 0.539251i) q^{50} +(-8.17038 + 6.78261i) q^{51} +(-0.834209 - 0.189968i) q^{52} +6.38222i q^{53} +(6.78031 - 2.83328i) q^{54} +3.49218i q^{55} +(-4.53331 + 12.9864i) q^{56} +(7.34129 - 6.09435i) q^{57} +(-0.926465 + 8.24096i) q^{58} -14.1971 q^{59} +(-3.89267 + 1.97221i) q^{60} +11.5337 q^{61} +(0.981168 - 8.72754i) q^{62} +(14.3401 + 2.68491i) q^{63} +(6.26206 + 4.97861i) q^{64} -0.538883i q^{65} +(-3.72648 - 5.67664i) q^{66} +1.00000i q^{67} +(-2.72252 + 11.9555i) q^{68} +(8.69506 + 10.4741i) q^{69} +(-8.60938 - 0.967883i) q^{70} -1.23130 q^{71} +(4.22311 - 7.35971i) q^{72} +1.24895 q^{73} +(-13.8800 - 1.56042i) q^{74} +(3.77602 + 4.54862i) q^{75} +(2.44626 - 10.7423i) q^{76} -13.4815i q^{77} +(0.575038 + 0.875969i) q^{78} +2.27216i q^{79} +(-2.18177 + 4.54201i) q^{80} +(-8.39038 - 3.25601i) q^{81} +(-0.383125 + 3.40792i) q^{82} +5.12319 q^{83} +(15.0276 - 7.61368i) q^{84} -7.72300 q^{85} +(0.568285 - 5.05493i) q^{86} +(7.81479 - 6.48742i) q^{87} +(-7.40291 - 2.58421i) q^{88} -7.91523i q^{89} +(5.11045 + 1.56429i) q^{90} +2.08035i q^{91} +(15.3265 + 3.49017i) q^{92} +(-8.27622 + 6.87047i) q^{93} +(-3.14972 - 0.354098i) q^{94} +6.93931 q^{95} +(-1.30021 - 9.71131i) q^{96} +10.0240 q^{97} +(23.3989 + 2.63055i) q^{98} +(-1.53053 + 8.17458i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.40536 0.157993i −0.993740 0.111718i
\(3\) 1.10632 + 1.33268i 0.638736 + 0.769426i
\(4\) 1.95008 + 0.444075i 0.975038 + 0.222038i
\(5\) 1.25971i 0.563360i 0.959508 + 0.281680i \(0.0908917\pi\)
−0.959508 + 0.281680i \(0.909108\pi\)
\(6\) −1.34423 2.04769i −0.548779 0.835968i
\(7\) 4.86310i 1.83808i −0.394166 0.919039i \(-0.628967\pi\)
0.394166 0.919039i \(-0.371033\pi\)
\(8\) −2.67040 0.932185i −0.944129 0.329577i
\(9\) −0.552098 + 2.94876i −0.184033 + 0.982920i
\(10\) 0.199026 1.77035i 0.0629376 0.559833i
\(11\) 2.77221 0.835853 0.417926 0.908481i \(-0.362757\pi\)
0.417926 + 0.908481i \(0.362757\pi\)
\(12\) 1.56560 + 3.09013i 0.451950 + 0.892043i
\(13\) −0.427783 −0.118646 −0.0593228 0.998239i \(-0.518894\pi\)
−0.0593228 + 0.998239i \(0.518894\pi\)
\(14\) −0.768337 + 6.83441i −0.205347 + 1.82657i
\(15\) −1.67880 + 1.39365i −0.433464 + 0.359838i
\(16\) 3.60559 + 1.73196i 0.901399 + 0.432990i
\(17\) 6.13077i 1.48693i 0.668775 + 0.743465i \(0.266819\pi\)
−0.668775 + 0.743465i \(0.733181\pi\)
\(18\) 1.24178 4.05684i 0.292691 0.956207i
\(19\) 5.50865i 1.26377i −0.775062 0.631885i \(-0.782281\pi\)
0.775062 0.631885i \(-0.217719\pi\)
\(20\) −0.559407 + 2.45653i −0.125087 + 0.549298i
\(21\) 6.48098 5.38016i 1.41427 1.17405i
\(22\) −3.89595 0.437991i −0.830620 0.0933799i
\(23\) 7.85942 1.63880 0.819401 0.573221i \(-0.194306\pi\)
0.819401 + 0.573221i \(0.194306\pi\)
\(24\) −1.71202 4.59010i −0.349464 0.936950i
\(25\) 3.41313 0.682625
\(26\) 0.601189 + 0.0675869i 0.117903 + 0.0132549i
\(27\) −4.54057 + 2.52651i −0.873833 + 0.486227i
\(28\) 2.15958 9.48341i 0.408123 1.79220i
\(29\) 5.86394i 1.08891i −0.838791 0.544454i \(-0.816737\pi\)
0.838791 0.544454i \(-0.183263\pi\)
\(30\) 2.57950 1.69334i 0.470951 0.309160i
\(31\) 6.21018i 1.11538i 0.830049 + 0.557691i \(0.188312\pi\)
−0.830049 + 0.557691i \(0.811688\pi\)
\(32\) −4.79352 3.00369i −0.847383 0.530982i
\(33\) 3.06696 + 3.69448i 0.533889 + 0.643127i
\(34\) 0.968620 8.61594i 0.166117 1.47762i
\(35\) 6.12610 1.03550
\(36\) −2.38610 + 5.50513i −0.397684 + 0.917522i
\(37\) 9.87650 1.62369 0.811844 0.583875i \(-0.198464\pi\)
0.811844 + 0.583875i \(0.198464\pi\)
\(38\) −0.870330 + 7.74164i −0.141186 + 1.25586i
\(39\) −0.473266 0.570100i −0.0757833 0.0912891i
\(40\) 1.17428 3.36393i 0.185671 0.531884i
\(41\) 2.42494i 0.378713i −0.981908 0.189356i \(-0.939360\pi\)
0.981908 0.189356i \(-0.0606401\pi\)
\(42\) −9.95814 + 6.53711i −1.53657 + 1.00870i
\(43\) 3.59689i 0.548521i 0.961655 + 0.274260i \(0.0884330\pi\)
−0.961655 + 0.274260i \(0.911567\pi\)
\(44\) 5.40602 + 1.23107i 0.814988 + 0.185591i
\(45\) −3.71459 0.695484i −0.553738 0.103677i
\(46\) −11.0453 1.24174i −1.62854 0.183084i
\(47\) 2.24122 0.326915 0.163458 0.986550i \(-0.447735\pi\)
0.163458 + 0.986550i \(0.447735\pi\)
\(48\) 1.68079 + 6.72123i 0.242602 + 0.970126i
\(49\) −16.6497 −2.37853
\(50\) −4.79667 0.539251i −0.678352 0.0762617i
\(51\) −8.17038 + 6.78261i −1.14408 + 0.949755i
\(52\) −0.834209 0.189968i −0.115684 0.0263438i
\(53\) 6.38222i 0.876665i 0.898813 + 0.438333i \(0.144431\pi\)
−0.898813 + 0.438333i \(0.855569\pi\)
\(54\) 6.78031 2.83328i 0.922683 0.385560i
\(55\) 3.49218i 0.470886i
\(56\) −4.53331 + 12.9864i −0.605789 + 1.73538i
\(57\) 7.34129 6.09435i 0.972378 0.807216i
\(58\) −0.926465 + 8.24096i −0.121651 + 1.08209i
\(59\) −14.1971 −1.84830 −0.924151 0.382027i \(-0.875226\pi\)
−0.924151 + 0.382027i \(0.875226\pi\)
\(60\) −3.89267 + 1.97221i −0.502542 + 0.254611i
\(61\) 11.5337 1.47674 0.738368 0.674398i \(-0.235597\pi\)
0.738368 + 0.674398i \(0.235597\pi\)
\(62\) 0.981168 8.72754i 0.124608 1.10840i
\(63\) 14.3401 + 2.68491i 1.80668 + 0.338266i
\(64\) 6.26206 + 4.97861i 0.782758 + 0.622327i
\(65\) 0.538883i 0.0668402i
\(66\) −3.72648 5.67664i −0.458698 0.698746i
\(67\) 1.00000i 0.122169i
\(68\) −2.72252 + 11.9555i −0.330154 + 1.44981i
\(69\) 8.69506 + 10.4741i 1.04676 + 1.26094i
\(70\) −8.60938 0.967883i −1.02902 0.115684i
\(71\) −1.23130 −0.146128 −0.0730639 0.997327i \(-0.523278\pi\)
−0.0730639 + 0.997327i \(0.523278\pi\)
\(72\) 4.22311 7.35971i 0.497699 0.867350i
\(73\) 1.24895 0.146179 0.0730895 0.997325i \(-0.476714\pi\)
0.0730895 + 0.997325i \(0.476714\pi\)
\(74\) −13.8800 1.56042i −1.61352 0.181395i
\(75\) 3.77602 + 4.54862i 0.436017 + 0.525230i
\(76\) 2.44626 10.7423i 0.280605 1.23222i
\(77\) 13.4815i 1.53636i
\(78\) 0.575038 + 0.875969i 0.0651102 + 0.0991839i
\(79\) 2.27216i 0.255638i 0.991797 + 0.127819i \(0.0407977\pi\)
−0.991797 + 0.127819i \(0.959202\pi\)
\(80\) −2.18177 + 4.54201i −0.243930 + 0.507812i
\(81\) −8.39038 3.25601i −0.932264 0.361779i
\(82\) −0.383125 + 3.40792i −0.0423091 + 0.376342i
\(83\) 5.12319 0.562343 0.281172 0.959657i \(-0.409277\pi\)
0.281172 + 0.959657i \(0.409277\pi\)
\(84\) 15.0276 7.61368i 1.63964 0.830720i
\(85\) −7.72300 −0.837677
\(86\) 0.568285 5.05493i 0.0612797 0.545087i
\(87\) 7.81479 6.48742i 0.837834 0.695524i
\(88\) −7.40291 2.58421i −0.789152 0.275478i
\(89\) 7.91523i 0.839012i −0.907752 0.419506i \(-0.862203\pi\)
0.907752 0.419506i \(-0.137797\pi\)
\(90\) 5.11045 + 1.56429i 0.538689 + 0.164890i
\(91\) 2.08035i 0.218080i
\(92\) 15.3265 + 3.49017i 1.59789 + 0.363876i
\(93\) −8.27622 + 6.87047i −0.858204 + 0.712434i
\(94\) −3.14972 0.354098i −0.324869 0.0365224i
\(95\) 6.93931 0.711958
\(96\) −1.30021 9.71131i −0.132702 0.991156i
\(97\) 10.0240 1.01778 0.508890 0.860831i \(-0.330056\pi\)
0.508890 + 0.860831i \(0.330056\pi\)
\(98\) 23.3989 + 2.63055i 2.36364 + 0.265725i
\(99\) −1.53053 + 8.17458i −0.153824 + 0.821576i
\(100\) 6.65586 + 1.51569i 0.665586 + 0.151569i
\(101\) 14.1039i 1.40339i 0.712478 + 0.701695i \(0.247573\pi\)
−0.712478 + 0.701695i \(0.752427\pi\)
\(102\) 12.5539 8.24114i 1.24302 0.815995i
\(103\) 10.8924i 1.07326i −0.843818 0.536629i \(-0.819697\pi\)
0.843818 0.536629i \(-0.180303\pi\)
\(104\) 1.14235 + 0.398773i 0.112017 + 0.0391029i
\(105\) 6.77745 + 8.16416i 0.661411 + 0.796741i
\(106\) 1.00835 8.96932i 0.0979395 0.871177i
\(107\) 2.87635 0.278067 0.139034 0.990288i \(-0.455600\pi\)
0.139034 + 0.990288i \(0.455600\pi\)
\(108\) −9.97641 + 2.91053i −0.959981 + 0.280066i
\(109\) −18.3966 −1.76208 −0.881038 0.473045i \(-0.843155\pi\)
−0.881038 + 0.473045i \(0.843155\pi\)
\(110\) 0.551742 4.90778i 0.0526065 0.467938i
\(111\) 10.9266 + 13.1623i 1.03711 + 1.24931i
\(112\) 8.42270 17.5344i 0.795870 1.65684i
\(113\) 6.39464i 0.601557i −0.953694 0.300779i \(-0.902753\pi\)
0.953694 0.300779i \(-0.0972466\pi\)
\(114\) −11.2800 + 7.40488i −1.05647 + 0.693530i
\(115\) 9.90060i 0.923236i
\(116\) 2.60403 11.4351i 0.241778 1.06173i
\(117\) 0.236178 1.26143i 0.0218347 0.116619i
\(118\) 19.9520 + 2.24305i 1.83673 + 0.206489i
\(119\) 29.8145 2.73309
\(120\) 5.78220 2.15665i 0.527840 0.196874i
\(121\) −3.31485 −0.301350
\(122\) −16.2090 1.82225i −1.46749 0.164978i
\(123\) 3.23169 2.68277i 0.291391 0.241897i
\(124\) −2.75779 + 12.1103i −0.247657 + 1.08754i
\(125\) 10.5981i 0.947924i
\(126\) −19.7288 6.03890i −1.75758 0.537988i
\(127\) 0.300709i 0.0266836i −0.999911 0.0133418i \(-0.995753\pi\)
0.999911 0.0133418i \(-0.00424696\pi\)
\(128\) −8.01387 7.98611i −0.708332 0.705879i
\(129\) −4.79352 + 3.97932i −0.422046 + 0.350360i
\(130\) −0.0851400 + 0.757325i −0.00746727 + 0.0664218i
\(131\) −1.25125 −0.109322 −0.0546609 0.998505i \(-0.517408\pi\)
−0.0546609 + 0.998505i \(0.517408\pi\)
\(132\) 4.34018 + 8.56648i 0.377764 + 0.745617i
\(133\) −26.7891 −2.32291
\(134\) 0.157993 1.40536i 0.0136486 0.121405i
\(135\) −3.18267 5.71981i −0.273921 0.492282i
\(136\) 5.71501 16.3716i 0.490058 1.40385i
\(137\) 1.25825i 0.107500i 0.998554 + 0.0537498i \(0.0171173\pi\)
−0.998554 + 0.0537498i \(0.982883\pi\)
\(138\) −10.5648 16.0937i −0.899339 1.36999i
\(139\) 20.8734i 1.77046i 0.465157 + 0.885228i \(0.345998\pi\)
−0.465157 + 0.885228i \(0.654002\pi\)
\(140\) 11.9464 + 2.72045i 1.00965 + 0.229920i
\(141\) 2.47951 + 2.98684i 0.208813 + 0.251537i
\(142\) 1.73041 + 0.194537i 0.145213 + 0.0163251i
\(143\) −1.18590 −0.0991703
\(144\) −7.09778 + 9.67582i −0.591482 + 0.806318i
\(145\) 7.38688 0.613447
\(146\) −1.75523 0.197326i −0.145264 0.0163309i
\(147\) −18.4200 22.1888i −1.51925 1.83010i
\(148\) 19.2599 + 4.38591i 1.58316 + 0.360520i
\(149\) 10.2635i 0.840821i −0.907334 0.420410i \(-0.861886\pi\)
0.907334 0.420410i \(-0.138114\pi\)
\(150\) −4.58802 6.98904i −0.374610 0.570653i
\(151\) 23.0493i 1.87573i −0.347004 0.937864i \(-0.612801\pi\)
0.347004 0.937864i \(-0.387199\pi\)
\(152\) −5.13508 + 14.7103i −0.416510 + 1.19316i
\(153\) −18.0782 3.38478i −1.46153 0.273644i
\(154\) −2.12999 + 18.9464i −0.171640 + 1.52674i
\(155\) −7.82304 −0.628362
\(156\) −0.669738 1.32190i −0.0536220 0.105837i
\(157\) 10.2970 0.821791 0.410895 0.911683i \(-0.365216\pi\)
0.410895 + 0.911683i \(0.365216\pi\)
\(158\) 0.358987 3.19321i 0.0285594 0.254038i
\(159\) −8.50549 + 7.06080i −0.674529 + 0.559958i
\(160\) 3.78378 6.03845i 0.299134 0.477382i
\(161\) 38.2211i 3.01225i
\(162\) 11.2771 + 5.90149i 0.886011 + 0.463665i
\(163\) 2.16912i 0.169898i −0.996385 0.0849491i \(-0.972927\pi\)
0.996385 0.0849491i \(-0.0270728\pi\)
\(164\) 1.07686 4.72883i 0.0840885 0.369259i
\(165\) −4.65398 + 3.86348i −0.362312 + 0.300772i
\(166\) −7.19993 0.809431i −0.558823 0.0628240i
\(167\) −14.9163 −1.15426 −0.577130 0.816652i \(-0.695828\pi\)
−0.577130 + 0.816652i \(0.695828\pi\)
\(168\) −22.3221 + 8.32570i −1.72219 + 0.642342i
\(169\) −12.8170 −0.985923
\(170\) 10.8536 + 1.22018i 0.832433 + 0.0935837i
\(171\) 16.2437 + 3.04131i 1.24219 + 0.232575i
\(172\) −1.59729 + 7.01421i −0.121792 + 0.534829i
\(173\) 4.41053i 0.335327i −0.985844 0.167663i \(-0.946378\pi\)
0.985844 0.167663i \(-0.0536222\pi\)
\(174\) −12.0076 + 7.88248i −0.910291 + 0.597569i
\(175\) 16.5984i 1.25472i
\(176\) 9.99546 + 4.80136i 0.753436 + 0.361916i
\(177\) −15.7066 18.9202i −1.18058 1.42213i
\(178\) −1.25055 + 11.1237i −0.0937330 + 0.833760i
\(179\) −20.9886 −1.56876 −0.784382 0.620278i \(-0.787020\pi\)
−0.784382 + 0.620278i \(0.787020\pi\)
\(180\) −6.93488 3.00580i −0.516896 0.224039i
\(181\) 1.59101 0.118259 0.0591293 0.998250i \(-0.481168\pi\)
0.0591293 + 0.998250i \(0.481168\pi\)
\(182\) 0.328682 2.92364i 0.0243635 0.216715i
\(183\) 12.7600 + 15.3708i 0.943245 + 1.13624i
\(184\) −20.9878 7.32643i −1.54724 0.540112i
\(185\) 12.4415i 0.914721i
\(186\) 12.7166 8.34790i 0.932423 0.612097i
\(187\) 16.9958i 1.24285i
\(188\) 4.37055 + 0.995270i 0.318755 + 0.0725875i
\(189\) 12.2867 + 22.0812i 0.893723 + 1.60617i
\(190\) −9.75223 1.09637i −0.707501 0.0795387i
\(191\) 3.47535 0.251467 0.125734 0.992064i \(-0.459872\pi\)
0.125734 + 0.992064i \(0.459872\pi\)
\(192\) 0.292943 + 13.8533i 0.0211413 + 0.999776i
\(193\) −5.09586 −0.366808 −0.183404 0.983038i \(-0.558712\pi\)
−0.183404 + 0.983038i \(0.558712\pi\)
\(194\) −14.0873 1.58372i −1.01141 0.113705i
\(195\) 0.718162 0.596179i 0.0514286 0.0426933i
\(196\) −32.4682 7.39373i −2.31916 0.528124i
\(197\) 2.07682i 0.147967i −0.997259 0.0739836i \(-0.976429\pi\)
0.997259 0.0739836i \(-0.0235713\pi\)
\(198\) 3.44248 11.2464i 0.244646 0.799248i
\(199\) 3.56635i 0.252812i −0.991979 0.126406i \(-0.959656\pi\)
0.991979 0.126406i \(-0.0403441\pi\)
\(200\) −9.11441 3.18167i −0.644486 0.224978i
\(201\) −1.33268 + 1.10632i −0.0940003 + 0.0780340i
\(202\) 2.22832 19.8210i 0.156784 1.39460i
\(203\) −28.5169 −2.00150
\(204\) −18.9448 + 9.59834i −1.32640 + 0.672018i
\(205\) 3.05473 0.213352
\(206\) −1.72092 + 15.3077i −0.119902 + 1.06654i
\(207\) −4.33917 + 23.1755i −0.301593 + 1.61081i
\(208\) −1.54241 0.740904i −0.106947 0.0513724i
\(209\) 15.2711i 1.05633i
\(210\) −8.23487 12.5444i −0.568260 0.865645i
\(211\) 1.25689i 0.0865278i −0.999064 0.0432639i \(-0.986224\pi\)
0.999064 0.0432639i \(-0.0137756\pi\)
\(212\) −2.83419 + 12.4458i −0.194653 + 0.854782i
\(213\) −1.36221 1.64093i −0.0933371 0.112435i
\(214\) −4.04231 0.454444i −0.276326 0.0310652i
\(215\) −4.53104 −0.309015
\(216\) 14.4803 2.51414i 0.985260 0.171065i
\(217\) 30.2007 2.05016
\(218\) 25.8539 + 2.90654i 1.75105 + 0.196856i
\(219\) 1.38175 + 1.66446i 0.0933698 + 0.112474i
\(220\) −1.55079 + 6.81003i −0.104554 + 0.459132i
\(221\) 2.62264i 0.176418i
\(222\) −13.2763 20.2241i −0.891045 1.35735i
\(223\) 1.37687i 0.0922018i −0.998937 0.0461009i \(-0.985320\pi\)
0.998937 0.0461009i \(-0.0146796\pi\)
\(224\) −14.6072 + 23.3114i −0.975987 + 1.55756i
\(225\) −1.88438 + 10.0645i −0.125625 + 0.670966i
\(226\) −1.01031 + 8.98678i −0.0672049 + 0.597792i
\(227\) 9.52868 0.632441 0.316220 0.948686i \(-0.397586\pi\)
0.316220 + 0.948686i \(0.397586\pi\)
\(228\) 17.0224 8.62435i 1.12734 0.571162i
\(229\) 7.49602 0.495351 0.247675 0.968843i \(-0.420333\pi\)
0.247675 + 0.968843i \(0.420333\pi\)
\(230\) 1.56423 13.9139i 0.103142 0.917456i
\(231\) 17.9666 14.9149i 1.18212 0.981330i
\(232\) −5.46628 + 15.6591i −0.358879 + 1.02807i
\(233\) 4.31409i 0.282625i −0.989965 0.141313i \(-0.954868\pi\)
0.989965 0.141313i \(-0.0451323\pi\)
\(234\) −0.531213 + 1.73545i −0.0347265 + 0.113450i
\(235\) 2.82329i 0.184171i
\(236\) −27.6854 6.30457i −1.80217 0.410393i
\(237\) −3.02808 + 2.51375i −0.196695 + 0.163285i
\(238\) −41.9001 4.71050i −2.71598 0.305336i
\(239\) −11.8383 −0.765755 −0.382878 0.923799i \(-0.625067\pi\)
−0.382878 + 0.923799i \(0.625067\pi\)
\(240\) −8.46681 + 2.11732i −0.546530 + 0.136672i
\(241\) −0.457915 −0.0294969 −0.0147484 0.999891i \(-0.504695\pi\)
−0.0147484 + 0.999891i \(0.504695\pi\)
\(242\) 4.65857 + 0.523725i 0.299464 + 0.0336663i
\(243\) −4.94323 14.7839i −0.317108 0.948389i
\(244\) 22.4916 + 5.12182i 1.43987 + 0.327891i
\(245\) 20.9738i 1.33997i
\(246\) −4.96555 + 3.25968i −0.316592 + 0.207829i
\(247\) 2.35651i 0.149941i
\(248\) 5.78904 16.5837i 0.367604 1.05306i
\(249\) 5.66791 + 6.82760i 0.359189 + 0.432682i
\(250\) 1.67443 14.8942i 0.105900 0.941990i
\(251\) −16.5781 −1.04640 −0.523201 0.852209i \(-0.675262\pi\)
−0.523201 + 0.852209i \(0.675262\pi\)
\(252\) 26.7720 + 11.6039i 1.68648 + 0.730975i
\(253\) 21.7879 1.36980
\(254\) −0.0475101 + 0.422605i −0.00298105 + 0.0265166i
\(255\) −8.54413 10.2923i −0.535054 0.644530i
\(256\) 10.0006 + 12.4895i 0.625039 + 0.780594i
\(257\) 0.0721774i 0.00450230i 0.999997 + 0.00225115i \(0.000716564\pi\)
−0.999997 + 0.00225115i \(0.999283\pi\)
\(258\) 7.36533 4.83504i 0.458546 0.301016i
\(259\) 48.0304i 2.98446i
\(260\) 0.239305 1.05086i 0.0148411 0.0651718i
\(261\) 17.2914 + 3.23747i 1.07031 + 0.200395i
\(262\) 1.75845 + 0.197688i 0.108637 + 0.0122132i
\(263\) −20.1693 −1.24369 −0.621846 0.783139i \(-0.713617\pi\)
−0.621846 + 0.783139i \(0.713617\pi\)
\(264\) −4.74607 12.7247i −0.292100 0.783152i
\(265\) −8.03976 −0.493878
\(266\) 37.6483 + 4.23250i 2.30837 + 0.259511i
\(267\) 10.5485 8.75680i 0.645558 0.535907i
\(268\) −0.444075 + 1.95008i −0.0271262 + 0.119120i
\(269\) 7.29380i 0.444711i 0.974966 + 0.222355i \(0.0713745\pi\)
−0.974966 + 0.222355i \(0.928625\pi\)
\(270\) 3.56911 + 8.54123i 0.217209 + 0.519803i
\(271\) 12.9899i 0.789083i −0.918878 0.394541i \(-0.870904\pi\)
0.918878 0.394541i \(-0.129096\pi\)
\(272\) −10.6182 + 22.1051i −0.643826 + 1.34032i
\(273\) −2.77245 + 2.30154i −0.167796 + 0.139296i
\(274\) 0.198795 1.76830i 0.0120097 0.106827i
\(275\) 9.46190 0.570574
\(276\) 12.3047 + 24.2866i 0.740657 + 1.46188i
\(277\) −14.0622 −0.844918 −0.422459 0.906382i \(-0.638833\pi\)
−0.422459 + 0.906382i \(0.638833\pi\)
\(278\) 3.29786 29.3346i 0.197792 1.75937i
\(279\) −18.3123 3.42863i −1.09633 0.205267i
\(280\) −16.3591 5.71066i −0.977645 0.341277i
\(281\) 19.9722i 1.19144i −0.803192 0.595720i \(-0.796867\pi\)
0.803192 0.595720i \(-0.203133\pi\)
\(282\) −3.01271 4.58933i −0.179404 0.273291i
\(283\) 3.20880i 0.190743i −0.995442 0.0953716i \(-0.969596\pi\)
0.995442 0.0953716i \(-0.0304039\pi\)
\(284\) −2.40112 0.546788i −0.142480 0.0324459i
\(285\) 7.67712 + 9.24791i 0.454753 + 0.547799i
\(286\) 1.66662 + 0.187365i 0.0985495 + 0.0110791i
\(287\) −11.7927 −0.696104
\(288\) 11.5037 12.4766i 0.677859 0.735192i
\(289\) −20.5863 −1.21096
\(290\) −10.3812 1.16708i −0.609607 0.0685332i
\(291\) 11.0898 + 13.3588i 0.650093 + 0.783107i
\(292\) 2.43556 + 0.554630i 0.142530 + 0.0324572i
\(293\) 2.12004i 0.123854i −0.998081 0.0619270i \(-0.980275\pi\)
0.998081 0.0619270i \(-0.0197246\pi\)
\(294\) 22.3810 + 34.0935i 1.30529 + 1.98838i
\(295\) 17.8842i 1.04126i
\(296\) −26.3742 9.20673i −1.53297 0.535130i
\(297\) −12.5874 + 7.00401i −0.730395 + 0.406414i
\(298\) −1.62157 + 14.4239i −0.0939350 + 0.835557i
\(299\) −3.36213 −0.194437
\(300\) 5.34360 + 10.5470i 0.308513 + 0.608931i
\(301\) 17.4920 1.00822
\(302\) −3.64164 + 32.3926i −0.209553 + 1.86399i
\(303\) −18.7960 + 15.6035i −1.07980 + 0.896395i
\(304\) 9.54077 19.8620i 0.547201 1.13916i
\(305\) 14.5291i 0.831935i
\(306\) 24.8716 + 7.61307i 1.42181 + 0.435210i
\(307\) 7.78622i 0.444383i 0.975003 + 0.222192i \(0.0713210\pi\)
−0.975003 + 0.222192i \(0.928679\pi\)
\(308\) 5.98681 26.2900i 0.341130 1.49801i
\(309\) 14.5161 12.0505i 0.825793 0.685529i
\(310\) 10.9942 + 1.23599i 0.624428 + 0.0701994i
\(311\) −9.43231 −0.534857 −0.267429 0.963578i \(-0.586174\pi\)
−0.267429 + 0.963578i \(0.586174\pi\)
\(312\) 0.732371 + 1.96357i 0.0414624 + 0.111165i
\(313\) 20.1611 1.13957 0.569786 0.821793i \(-0.307026\pi\)
0.569786 + 0.821793i \(0.307026\pi\)
\(314\) −14.4710 1.62686i −0.816646 0.0918090i
\(315\) −3.38221 + 18.0644i −0.190566 + 1.01781i
\(316\) −1.00901 + 4.43089i −0.0567613 + 0.249257i
\(317\) 10.4607i 0.587531i −0.955877 0.293766i \(-0.905091\pi\)
0.955877 0.293766i \(-0.0949085\pi\)
\(318\) 13.0688 8.57916i 0.732864 0.481095i
\(319\) 16.2561i 0.910166i
\(320\) −6.27162 + 7.88839i −0.350594 + 0.440975i
\(321\) 3.18217 + 3.83327i 0.177611 + 0.213952i
\(322\) −6.03868 + 53.7144i −0.336523 + 2.99339i
\(323\) 33.7722 1.87914
\(324\) −14.9160 10.0754i −0.828664 0.559746i
\(325\) −1.46008 −0.0809905
\(326\) −0.342706 + 3.04839i −0.0189807 + 0.168835i
\(327\) −20.3526 24.5169i −1.12550 1.35579i
\(328\) −2.26050 + 6.47557i −0.124815 + 0.357553i
\(329\) 10.8993i 0.600896i
\(330\) 7.15093 4.69429i 0.393646 0.258412i
\(331\) 1.38752i 0.0762652i −0.999273 0.0381326i \(-0.987859\pi\)
0.999273 0.0381326i \(-0.0121409\pi\)
\(332\) 9.99062 + 2.27508i 0.548306 + 0.124861i
\(333\) −5.45280 + 29.1234i −0.298812 + 1.59596i
\(334\) 20.9628 + 2.35668i 1.14704 + 0.128952i
\(335\) −1.25971 −0.0688254
\(336\) 32.6860 8.17386i 1.78317 0.445921i
\(337\) 22.9907 1.25239 0.626193 0.779668i \(-0.284612\pi\)
0.626193 + 0.779668i \(0.284612\pi\)
\(338\) 18.0125 + 2.02500i 0.979751 + 0.110146i
\(339\) 8.52204 7.07454i 0.462854 0.384236i
\(340\) −15.0604 3.42959i −0.816767 0.185996i
\(341\) 17.2159i 0.932295i
\(342\) −22.3477 6.84054i −1.20843 0.369894i
\(343\) 46.9275i 2.53385i
\(344\) 3.35297 9.60513i 0.180780 0.517874i
\(345\) −13.1944 + 10.9533i −0.710361 + 0.589704i
\(346\) −0.696835 + 6.19839i −0.0374621 + 0.333228i
\(347\) 0.285568 0.0153301 0.00766504 0.999971i \(-0.497560\pi\)
0.00766504 + 0.999971i \(0.497560\pi\)
\(348\) 18.1203 9.18060i 0.971352 0.492132i
\(349\) −33.2446 −1.77954 −0.889770 0.456409i \(-0.849136\pi\)
−0.889770 + 0.456409i \(0.849136\pi\)
\(350\) −2.62243 + 23.3267i −0.140175 + 1.24686i
\(351\) 1.94238 1.08080i 0.103676 0.0576887i
\(352\) −13.2886 8.32686i −0.708287 0.443823i
\(353\) 14.1619i 0.753762i 0.926262 + 0.376881i \(0.123003\pi\)
−0.926262 + 0.376881i \(0.876997\pi\)
\(354\) 19.0841 + 29.0713i 1.01431 + 1.54512i
\(355\) 1.55108i 0.0823226i
\(356\) 3.51496 15.4353i 0.186292 0.818069i
\(357\) 32.9845 + 39.7333i 1.74572 + 2.10291i
\(358\) 29.4966 + 3.31607i 1.55894 + 0.175260i
\(359\) 13.7325 0.724773 0.362386 0.932028i \(-0.381962\pi\)
0.362386 + 0.932028i \(0.381962\pi\)
\(360\) 9.27111 + 5.31990i 0.488630 + 0.280384i
\(361\) −11.3452 −0.597117
\(362\) −2.23594 0.251369i −0.117518 0.0132116i
\(363\) −3.66730 4.41766i −0.192483 0.231867i
\(364\) −0.923832 + 4.05684i −0.0484220 + 0.212636i
\(365\) 1.57332i 0.0823514i
\(366\) −15.5039 23.6175i −0.810402 1.23450i
\(367\) 10.3004i 0.537675i 0.963185 + 0.268838i \(0.0866395\pi\)
−0.963185 + 0.268838i \(0.913360\pi\)
\(368\) 28.3379 + 13.6122i 1.47721 + 0.709585i
\(369\) 7.15058 + 1.33881i 0.372244 + 0.0696955i
\(370\) 1.96568 17.4849i 0.102191 0.908995i
\(371\) 31.0374 1.61138
\(372\) −19.1903 + 9.72267i −0.994968 + 0.504097i
\(373\) −10.7157 −0.554836 −0.277418 0.960749i \(-0.589479\pi\)
−0.277418 + 0.960749i \(0.589479\pi\)
\(374\) 2.68522 23.8852i 0.138849 1.23507i
\(375\) −14.1239 + 11.7249i −0.729357 + 0.605473i
\(376\) −5.98495 2.08923i −0.308650 0.107744i
\(377\) 2.50850i 0.129194i
\(378\) −13.7785 32.9733i −0.708690 1.69596i
\(379\) 26.8420i 1.37878i 0.724390 + 0.689391i \(0.242122\pi\)
−0.724390 + 0.689391i \(0.757878\pi\)
\(380\) 13.5322 + 3.08158i 0.694186 + 0.158082i
\(381\) 0.400751 0.332682i 0.0205311 0.0170438i
\(382\) −4.88412 0.549082i −0.249893 0.0280935i
\(383\) 3.61111 0.184519 0.0922596 0.995735i \(-0.470591\pi\)
0.0922596 + 0.995735i \(0.470591\pi\)
\(384\) 1.77704 19.5152i 0.0906842 0.995880i
\(385\) 16.9828 0.865525
\(386\) 7.16152 + 0.805112i 0.364512 + 0.0409791i
\(387\) −10.6064 1.98584i −0.539152 0.100946i
\(388\) 19.5475 + 4.45140i 0.992375 + 0.225986i
\(389\) 28.8138i 1.46092i −0.682958 0.730458i \(-0.739307\pi\)
0.682958 0.730458i \(-0.260693\pi\)
\(390\) −1.10347 + 0.724382i −0.0558763 + 0.0366805i
\(391\) 48.1842i 2.43678i
\(392\) 44.4614 + 15.5206i 2.24564 + 0.783910i
\(393\) −1.38428 1.66752i −0.0698278 0.0841150i
\(394\) −0.328124 + 2.91868i −0.0165306 + 0.147041i
\(395\) −2.86227 −0.144016
\(396\) −6.61478 + 15.2614i −0.332405 + 0.766913i
\(397\) 12.1436 0.609471 0.304736 0.952437i \(-0.401432\pi\)
0.304736 + 0.952437i \(0.401432\pi\)
\(398\) −0.563459 + 5.01200i −0.0282437 + 0.251229i
\(399\) −29.6374 35.7014i −1.48373 1.78731i
\(400\) 12.3063 + 5.91140i 0.615317 + 0.295570i
\(401\) 34.5972i 1.72770i −0.503746 0.863852i \(-0.668045\pi\)
0.503746 0.863852i \(-0.331955\pi\)
\(402\) 2.04769 1.34423i 0.102130 0.0670440i
\(403\) 2.65661i 0.132335i
\(404\) −6.26319 + 27.5037i −0.311605 + 1.36836i
\(405\) 4.10163 10.5695i 0.203812 0.525200i
\(406\) 40.0766 + 4.50549i 1.98897 + 0.223604i
\(407\) 27.3797 1.35716
\(408\) 28.1408 10.4960i 1.39318 0.519628i
\(409\) −19.5900 −0.968663 −0.484331 0.874885i \(-0.660937\pi\)
−0.484331 + 0.874885i \(0.660937\pi\)
\(410\) −4.29300 0.482627i −0.212016 0.0238353i
\(411\) −1.67685 + 1.39203i −0.0827130 + 0.0686639i
\(412\) 4.83704 21.2410i 0.238304 1.04647i
\(413\) 69.0418i 3.39732i
\(414\) 9.75968 31.8844i 0.479662 1.56703i
\(415\) 6.45375i 0.316802i
\(416\) 2.05059 + 1.28493i 0.100538 + 0.0629988i
\(417\) −27.8176 + 23.0927i −1.36224 + 1.13085i
\(418\) −2.41274 + 21.4614i −0.118011 + 1.04971i
\(419\) −24.5940 −1.20150 −0.600748 0.799439i \(-0.705130\pi\)
−0.600748 + 0.799439i \(0.705130\pi\)
\(420\) 9.59104 + 18.9304i 0.467995 + 0.923711i
\(421\) −11.6977 −0.570112 −0.285056 0.958511i \(-0.592012\pi\)
−0.285056 + 0.958511i \(0.592012\pi\)
\(422\) −0.198580 + 1.76638i −0.00966673 + 0.0859861i
\(423\) −1.23737 + 6.60882i −0.0601631 + 0.321332i
\(424\) 5.94941 17.0431i 0.288929 0.827685i
\(425\) 20.9251i 1.01502i
\(426\) 1.65514 + 2.52132i 0.0801918 + 0.122158i
\(427\) 56.0894i 2.71436i
\(428\) 5.60910 + 1.27732i 0.271126 + 0.0617414i
\(429\) −1.31199 1.58044i −0.0633436 0.0763042i
\(430\) 6.36775 + 0.715875i 0.307080 + 0.0345226i
\(431\) 31.6932 1.52661 0.763304 0.646040i \(-0.223576\pi\)
0.763304 + 0.646040i \(0.223576\pi\)
\(432\) −20.7473 + 1.24548i −0.998203 + 0.0599232i
\(433\) −12.7355 −0.612030 −0.306015 0.952027i \(-0.598996\pi\)
−0.306015 + 0.952027i \(0.598996\pi\)
\(434\) −42.4429 4.77151i −2.03732 0.229040i
\(435\) 8.17228 + 9.84438i 0.391831 + 0.472002i
\(436\) −35.8748 8.16948i −1.71809 0.391247i
\(437\) 43.2948i 2.07107i
\(438\) −1.67888 2.55748i −0.0802199 0.122201i
\(439\) 31.4270i 1.49993i −0.661479 0.749964i \(-0.730071\pi\)
0.661479 0.749964i \(-0.269929\pi\)
\(440\) 3.25536 9.32553i 0.155193 0.444577i
\(441\) 9.19228 49.0960i 0.437727 2.33791i
\(442\) −0.414359 + 3.68575i −0.0197091 + 0.175313i
\(443\) −22.3976 −1.06414 −0.532071 0.846700i \(-0.678586\pi\)
−0.532071 + 0.846700i \(0.678586\pi\)
\(444\) 15.4627 + 30.5197i 0.733826 + 1.44840i
\(445\) 9.97090 0.472666
\(446\) −0.217536 + 1.93499i −0.0103006 + 0.0916247i
\(447\) 13.6780 11.3548i 0.646949 0.537062i
\(448\) 24.2115 30.4530i 1.14388 1.43877i
\(449\) 3.63676i 0.171629i 0.996311 + 0.0858146i \(0.0273493\pi\)
−0.996311 + 0.0858146i \(0.972651\pi\)
\(450\) 4.23836 13.8465i 0.199798 0.652731i
\(451\) 6.72245i 0.316548i
\(452\) 2.83970 12.4700i 0.133568 0.586541i
\(453\) 30.7175 25.5000i 1.44323 1.19809i
\(454\) −13.3912 1.50547i −0.628482 0.0706551i
\(455\) −2.62064 −0.122858
\(456\) −25.2852 + 9.43089i −1.18409 + 0.441642i
\(457\) −0.261403 −0.0122279 −0.00611396 0.999981i \(-0.501946\pi\)
−0.00611396 + 0.999981i \(0.501946\pi\)
\(458\) −10.5346 1.18432i −0.492250 0.0553397i
\(459\) −15.4894 27.8372i −0.722985 1.29933i
\(460\) −4.39661 + 19.3069i −0.204993 + 0.900190i
\(461\) 7.20352i 0.335501i 0.985829 + 0.167751i \(0.0536504\pi\)
−0.985829 + 0.167751i \(0.946350\pi\)
\(462\) −27.6060 + 18.1222i −1.28435 + 0.843123i
\(463\) 17.3328i 0.805522i 0.915305 + 0.402761i \(0.131949\pi\)
−0.915305 + 0.402761i \(0.868051\pi\)
\(464\) 10.1561 21.1430i 0.471486 0.981539i
\(465\) −8.65481 10.4256i −0.401357 0.483478i
\(466\) −0.681597 + 6.06285i −0.0315744 + 0.280856i
\(467\) −31.0393 −1.43633 −0.718164 0.695874i \(-0.755017\pi\)
−0.718164 + 0.695874i \(0.755017\pi\)
\(468\) 1.02074 2.35500i 0.0471835 0.108860i
\(469\) 4.86310 0.224557
\(470\) 0.446061 3.96774i 0.0205753 0.183018i
\(471\) 11.3918 + 13.7227i 0.524907 + 0.632307i
\(472\) 37.9119 + 13.2343i 1.74504 + 0.609158i
\(473\) 9.97133i 0.458482i
\(474\) 4.65269 3.05430i 0.213705 0.140289i
\(475\) 18.8017i 0.862682i
\(476\) 58.1406 + 13.2399i 2.66487 + 0.606849i
\(477\) −18.8196 3.52361i −0.861692 0.161335i
\(478\) 16.6371 + 1.87037i 0.760962 + 0.0855488i
\(479\) 11.6813 0.533731 0.266865 0.963734i \(-0.414012\pi\)
0.266865 + 0.963734i \(0.414012\pi\)
\(480\) 12.2334 1.63789i 0.558378 0.0747591i
\(481\) −4.22500 −0.192643
\(482\) 0.643535 + 0.0723475i 0.0293122 + 0.00329534i
\(483\) 50.9367 42.2849i 2.31770 1.92403i
\(484\) −6.46422 1.47205i −0.293828 0.0669112i
\(485\) 12.6273i 0.573377i
\(486\) 4.61126 + 21.5577i 0.209171 + 0.977879i
\(487\) 18.6601i 0.845569i 0.906230 + 0.422785i \(0.138947\pi\)
−0.906230 + 0.422785i \(0.861053\pi\)
\(488\) −30.7995 10.7515i −1.39423 0.486699i
\(489\) 2.89075 2.39974i 0.130724 0.108520i
\(490\) −3.31373 + 29.4758i −0.149699 + 1.33158i
\(491\) 20.4643 0.923542 0.461771 0.886999i \(-0.347214\pi\)
0.461771 + 0.886999i \(0.347214\pi\)
\(492\) 7.49339 3.79650i 0.337828 0.171159i
\(493\) 35.9505 1.61913
\(494\) 0.372313 3.31174i 0.0167511 0.149002i
\(495\) −10.2976 1.92803i −0.462843 0.0866584i
\(496\) −10.7558 + 22.3914i −0.482949 + 1.00540i
\(497\) 5.98791i 0.268594i
\(498\) −6.88674 10.4907i −0.308602 0.470101i
\(499\) 6.33076i 0.283404i 0.989909 + 0.141702i \(0.0452574\pi\)
−0.989909 + 0.141702i \(0.954743\pi\)
\(500\) −4.70636 + 20.6671i −0.210475 + 0.924262i
\(501\) −16.5023 19.8788i −0.737268 0.888118i
\(502\) 23.2983 + 2.61924i 1.03985 + 0.116902i
\(503\) 37.7123 1.68151 0.840755 0.541416i \(-0.182112\pi\)
0.840755 + 0.541416i \(0.182112\pi\)
\(504\) −35.7910 20.5374i −1.59426 0.914809i
\(505\) −17.7668 −0.790614
\(506\) −30.6199 3.44235i −1.36122 0.153031i
\(507\) −14.1797 17.0810i −0.629745 0.758595i
\(508\) 0.133538 0.586406i 0.00592477 0.0260176i
\(509\) 7.74429i 0.343260i 0.985162 + 0.171630i \(0.0549033\pi\)
−0.985162 + 0.171630i \(0.945097\pi\)
\(510\) 10.3815 + 15.8143i 0.459699 + 0.700271i
\(511\) 6.07379i 0.268688i
\(512\) −12.0812 19.1323i −0.533919 0.845535i
\(513\) 13.9177 + 25.0124i 0.614479 + 1.10432i
\(514\) 0.0114036 0.101435i 0.000502989 0.00447412i
\(515\) 13.7213 0.604631
\(516\) −11.1149 + 5.63130i −0.489304 + 0.247904i
\(517\) 6.21313 0.273253
\(518\) −7.58849 + 67.5000i −0.333419 + 2.96578i
\(519\) 5.87785 4.87948i 0.258009 0.214185i
\(520\) −0.502339 + 1.43903i −0.0220290 + 0.0631058i
\(521\) 9.29493i 0.407218i 0.979052 + 0.203609i \(0.0652672\pi\)
−0.979052 + 0.203609i \(0.934733\pi\)
\(522\) −23.7891 7.28174i −1.04122 0.318713i
\(523\) 1.17970i 0.0515845i 0.999667 + 0.0257922i \(0.00821084\pi\)
−0.999667 + 0.0257922i \(0.991789\pi\)
\(524\) −2.44002 0.555647i −0.106593 0.0242736i
\(525\) 22.1204 18.3632i 0.965413 0.801434i
\(526\) 28.3451 + 3.18662i 1.23591 + 0.138943i
\(527\) −38.0732 −1.65849
\(528\) 4.65951 + 18.6327i 0.202779 + 0.810882i
\(529\) 38.7704 1.68567
\(530\) 11.2988 + 1.27023i 0.490787 + 0.0551752i
\(531\) 7.83818 41.8638i 0.340148 1.81673i
\(532\) −52.2408 11.8964i −2.26493 0.515773i
\(533\) 1.03735i 0.0449326i
\(534\) −16.2080 + 10.6399i −0.701387 + 0.460432i
\(535\) 3.62337i 0.156652i
\(536\) 0.932185 2.67040i 0.0402643 0.115344i
\(537\) −23.2202 27.9712i −1.00203 1.20705i
\(538\) 1.15237 10.2504i 0.0496823 0.441927i
\(539\) −46.1565 −1.98810
\(540\) −3.66643 12.5674i −0.157778 0.540815i
\(541\) −6.50510 −0.279676 −0.139838 0.990174i \(-0.544658\pi\)
−0.139838 + 0.990174i \(0.544658\pi\)
\(542\) −2.05232 + 18.2555i −0.0881549 + 0.784143i
\(543\) 1.76017 + 2.12031i 0.0755360 + 0.0909913i
\(544\) 18.4149 29.3880i 0.789533 1.26000i
\(545\) 23.1744i 0.992684i
\(546\) 4.25992 2.79646i 0.182308 0.119678i
\(547\) 1.65898i 0.0709327i −0.999371 0.0354664i \(-0.988708\pi\)
0.999371 0.0354664i \(-0.0112917\pi\)
\(548\) −0.558758 + 2.45368i −0.0238690 + 0.104816i
\(549\) −6.36772 + 34.0101i −0.271768 + 1.45151i
\(550\) −13.2974 1.49492i −0.567002 0.0637435i
\(551\) −32.3024 −1.37613
\(552\) −13.4554 36.0755i −0.572702 1.53548i
\(553\) 11.0497 0.469883
\(554\) 19.7625 + 2.22174i 0.839629 + 0.0943927i
\(555\) −16.5807 + 13.7644i −0.703810 + 0.584265i
\(556\) −9.26935 + 40.7047i −0.393108 + 1.72626i
\(557\) 14.5839i 0.617942i 0.951071 + 0.308971i \(0.0999846\pi\)
−0.951071 + 0.308971i \(0.900015\pi\)
\(558\) 25.1937 + 7.71169i 1.06654 + 0.326462i
\(559\) 1.53869i 0.0650796i
\(560\) 22.0882 + 10.6102i 0.933398 + 0.448362i
\(561\) −22.6500 + 18.8028i −0.956284 + 0.793855i
\(562\) −3.15547 + 28.0681i −0.133106 + 1.18398i
\(563\) −20.4654 −0.862512 −0.431256 0.902230i \(-0.641929\pi\)
−0.431256 + 0.902230i \(0.641929\pi\)
\(564\) 3.50886 + 6.92565i 0.147750 + 0.291623i
\(565\) 8.05541 0.338893
\(566\) −0.506969 + 4.50952i −0.0213095 + 0.189549i
\(567\) −15.8343 + 40.8032i −0.664978 + 1.71357i
\(568\) 3.28805 + 1.14780i 0.137963 + 0.0481604i
\(569\) 8.56768i 0.359176i 0.983742 + 0.179588i \(0.0574764\pi\)
−0.983742 + 0.179588i \(0.942524\pi\)
\(570\) −9.32801 14.2096i −0.390707 0.595174i
\(571\) 19.2420i 0.805254i 0.915364 + 0.402627i \(0.131903\pi\)
−0.915364 + 0.402627i \(0.868097\pi\)
\(572\) −2.31260 0.526631i −0.0966948 0.0220195i
\(573\) 3.84486 + 4.63154i 0.160621 + 0.193485i
\(574\) 16.5731 + 1.86318i 0.691746 + 0.0777674i
\(575\) 26.8252 1.11869
\(576\) −18.1380 + 15.7166i −0.755750 + 0.654860i
\(577\) −24.9578 −1.03901 −0.519503 0.854469i \(-0.673883\pi\)
−0.519503 + 0.854469i \(0.673883\pi\)
\(578\) 28.9312 + 3.25250i 1.20338 + 0.135286i
\(579\) −5.63767 6.79117i −0.234293 0.282232i
\(580\) 14.4050 + 3.28033i 0.598134 + 0.136208i
\(581\) 24.9146i 1.03363i
\(582\) −13.4745 20.5260i −0.558536 0.850832i
\(583\) 17.6928i 0.732763i
\(584\) −3.33521 1.16426i −0.138012 0.0481773i
\(585\) 1.58904 + 0.297516i 0.0656986 + 0.0123008i
\(586\) −0.334952 + 2.97942i −0.0138368 + 0.123079i
\(587\) −12.7221 −0.525098 −0.262549 0.964919i \(-0.584563\pi\)
−0.262549 + 0.964919i \(0.584563\pi\)
\(588\) −26.0668 51.4498i −1.07498 2.12175i
\(589\) 34.2097 1.40959
\(590\) −2.82559 + 25.1338i −0.116328 + 1.03474i
\(591\) 2.76775 2.29763i 0.113850 0.0945120i
\(592\) 35.6107 + 17.1057i 1.46359 + 0.703041i
\(593\) 15.4614i 0.634924i 0.948271 + 0.317462i \(0.102831\pi\)
−0.948271 + 0.317462i \(0.897169\pi\)
\(594\) 18.7964 7.85444i 0.771227 0.322271i
\(595\) 37.5577i 1.53972i
\(596\) 4.55778 20.0147i 0.186694 0.819832i
\(597\) 4.75282 3.94553i 0.194520 0.161480i
\(598\) 4.72500 + 0.531194i 0.193220 + 0.0217221i
\(599\) −15.5594 −0.635740 −0.317870 0.948134i \(-0.602968\pi\)
−0.317870 + 0.948134i \(0.602968\pi\)
\(600\) −5.84333 15.6666i −0.238553 0.639586i
\(601\) −25.0477 −1.02172 −0.510858 0.859665i \(-0.670672\pi\)
−0.510858 + 0.859665i \(0.670672\pi\)
\(602\) −24.5826 2.76363i −1.00191 0.112637i
\(603\) −2.94876 0.552098i −0.120083 0.0224832i
\(604\) 10.2356 44.9479i 0.416482 1.82891i
\(605\) 4.17576i 0.169769i
\(606\) 28.8804 18.9588i 1.17319 0.770150i
\(607\) 34.6017i 1.40444i 0.711959 + 0.702221i \(0.247808\pi\)
−0.711959 + 0.702221i \(0.752192\pi\)
\(608\) −16.5463 + 26.4058i −0.671040 + 1.07090i
\(609\) −31.5489 38.0041i −1.27843 1.54000i
\(610\) 2.29550 20.4186i 0.0929422 0.826727i
\(611\) −0.958755 −0.0387871
\(612\) −33.7507 14.6286i −1.36429 0.591328i
\(613\) −38.2221 −1.54378 −0.771889 0.635758i \(-0.780688\pi\)
−0.771889 + 0.635758i \(0.780688\pi\)
\(614\) 1.23017 10.9424i 0.0496457 0.441601i
\(615\) 3.37952 + 4.07099i 0.136275 + 0.164158i
\(616\) −12.5673 + 36.0011i −0.506350 + 1.45052i
\(617\) 19.3234i 0.777930i 0.921253 + 0.388965i \(0.127167\pi\)
−0.921253 + 0.388965i \(0.872833\pi\)
\(618\) −22.3043 + 14.6418i −0.897209 + 0.588981i
\(619\) 34.2281i 1.37574i 0.725832 + 0.687872i \(0.241455\pi\)
−0.725832 + 0.687872i \(0.758545\pi\)
\(620\) −15.2555 3.47402i −0.612676 0.139520i
\(621\) −35.6862 + 19.8569i −1.43204 + 0.796830i
\(622\) 13.2558 + 1.49024i 0.531509 + 0.0597533i
\(623\) −38.4925 −1.54217
\(624\) −0.719015 2.87523i −0.0287836 0.115101i
\(625\) 3.71507 0.148603
\(626\) −28.3336 3.18532i −1.13244 0.127311i
\(627\) 20.3516 16.8948i 0.812765 0.674714i
\(628\) 20.0799 + 4.57265i 0.801277 + 0.182468i
\(629\) 60.5505i 2.41431i
\(630\) 7.60728 24.8526i 0.303081 0.990153i
\(631\) 18.3626i 0.731005i −0.930810 0.365503i \(-0.880897\pi\)
0.930810 0.365503i \(-0.119103\pi\)
\(632\) 2.11808 6.06758i 0.0842525 0.241355i
\(633\) 1.67504 1.39053i 0.0665767 0.0552684i
\(634\) −1.65272 + 14.7010i −0.0656379 + 0.583853i
\(635\) 0.378807 0.0150325
\(636\) −19.7219 + 9.99202i −0.782023 + 0.396209i
\(637\) 7.12247 0.282202
\(638\) −2.56835 + 22.8457i −0.101682 + 0.904468i
\(639\) 0.679796 3.63079i 0.0268923 0.143632i
\(640\) 10.0602 10.0952i 0.397664 0.399046i
\(641\) 37.4540i 1.47935i −0.672967 0.739673i \(-0.734980\pi\)
0.672967 0.739673i \(-0.265020\pi\)
\(642\) −3.86647 5.88988i −0.152597 0.232455i
\(643\) 4.93520i 0.194625i 0.995254 + 0.0973126i \(0.0310246\pi\)
−0.995254 + 0.0973126i \(0.968975\pi\)
\(644\) 16.9731 74.5341i 0.668832 2.93705i
\(645\) −5.01280 6.03845i −0.197379 0.237764i
\(646\) −47.4622 5.33579i −1.86737 0.209934i
\(647\) −12.0200 −0.472557 −0.236278 0.971685i \(-0.575928\pi\)
−0.236278 + 0.971685i \(0.575928\pi\)
\(648\) 19.3704 + 16.5162i 0.760943 + 0.648819i
\(649\) −39.3573 −1.54491
\(650\) 2.05194 + 0.230683i 0.0804835 + 0.00904812i
\(651\) 33.4118 + 40.2480i 1.30951 + 1.57745i
\(652\) 0.963251 4.22994i 0.0377238 0.165657i
\(653\) 18.3299i 0.717302i 0.933472 + 0.358651i \(0.116763\pi\)
−0.933472 + 0.358651i \(0.883237\pi\)
\(654\) 24.7292 + 37.6707i 0.966990 + 1.47304i
\(655\) 1.57621i 0.0615875i
\(656\) 4.19991 8.74337i 0.163979 0.341371i
\(657\) −0.689545 + 3.68287i −0.0269017 + 0.143682i
\(658\) −1.72201 + 15.3174i −0.0671310 + 0.597134i
\(659\) 28.3163 1.10305 0.551524 0.834159i \(-0.314047\pi\)
0.551524 + 0.834159i \(0.314047\pi\)
\(660\) −10.7913 + 5.46737i −0.420051 + 0.212817i
\(661\) 31.1455 1.21142 0.605710 0.795685i \(-0.292889\pi\)
0.605710 + 0.795685i \(0.292889\pi\)
\(662\) −0.219220 + 1.94997i −0.00852021 + 0.0757878i
\(663\) 3.49515 2.90148i 0.135740 0.112684i
\(664\) −13.6810 4.77576i −0.530925 0.185336i
\(665\) 33.7465i 1.30863i
\(666\) 12.2645 40.0674i 0.475238 1.55258i
\(667\) 46.0872i 1.78450i
\(668\) −29.0880 6.62398i −1.12545 0.256289i
\(669\) 1.83493 1.52326i 0.0709425 0.0588926i
\(670\) 1.77035 + 0.199026i 0.0683945 + 0.00768905i
\(671\) 31.9738 1.23433
\(672\) −47.2270 + 6.32305i −1.82182 + 0.243917i
\(673\) −22.0469 −0.849846 −0.424923 0.905230i \(-0.639699\pi\)
−0.424923 + 0.905230i \(0.639699\pi\)
\(674\) −32.3103 3.63239i −1.24455 0.139914i
\(675\) −15.4975 + 8.62330i −0.596500 + 0.331911i
\(676\) −24.9941 5.69171i −0.961313 0.218912i
\(677\) 13.9075i 0.534509i 0.963626 + 0.267255i \(0.0861165\pi\)
−0.963626 + 0.267255i \(0.913883\pi\)
\(678\) −13.0943 + 8.59586i −0.502883 + 0.330122i
\(679\) 48.7476i 1.87076i
\(680\) 20.6235 + 7.19926i 0.790874 + 0.276079i
\(681\) 10.5418 + 12.6987i 0.403963 + 0.486616i
\(682\) 2.72000 24.1946i 0.104154 0.926458i
\(683\) 2.95966 0.113248 0.0566240 0.998396i \(-0.481966\pi\)
0.0566240 + 0.998396i \(0.481966\pi\)
\(684\) 30.3259 + 13.1442i 1.15954 + 0.502582i
\(685\) −1.58503 −0.0605610
\(686\) 7.41424 65.9501i 0.283077 2.51799i
\(687\) 8.29302 + 9.98983i 0.316398 + 0.381136i
\(688\) −6.22968 + 12.9689i −0.237504 + 0.494436i
\(689\) 2.73021i 0.104013i
\(690\) 20.2734 13.3087i 0.771795 0.506652i
\(691\) 3.91167i 0.148807i 0.997228 + 0.0744035i \(0.0237053\pi\)
−0.997228 + 0.0744035i \(0.976295\pi\)
\(692\) 1.95861 8.60088i 0.0744552 0.326956i
\(693\) 39.7538 + 7.44312i 1.51012 + 0.282741i
\(694\) −0.401325 0.0451178i −0.0152341 0.00171265i
\(695\) −26.2944 −0.997405
\(696\) −26.9161 + 10.0392i −1.02025 + 0.380534i
\(697\) 14.8668 0.563119
\(698\) 46.7206 + 5.25242i 1.76840 + 0.198807i
\(699\) 5.74932 4.77277i 0.217459 0.180523i
\(700\) 7.37093 32.3681i 0.278595 1.22340i
\(701\) 19.2085i 0.725494i 0.931888 + 0.362747i \(0.118161\pi\)
−0.931888 + 0.362747i \(0.881839\pi\)
\(702\) −2.90050 + 1.21203i −0.109472 + 0.0457450i
\(703\) 54.4062i 2.05197i
\(704\) 17.3597 + 13.8018i 0.654270 + 0.520173i
\(705\) −3.76256 + 3.12347i −0.141706 + 0.117637i
\(706\) 2.23749 19.9026i 0.0842089 0.749043i
\(707\) 68.5886 2.57954
\(708\) −22.2270 43.8708i −0.835341 1.64877i
\(709\) −8.33169 −0.312903 −0.156452 0.987686i \(-0.550005\pi\)
−0.156452 + 0.987686i \(0.550005\pi\)
\(710\) −0.245060 + 2.17982i −0.00919693 + 0.0818073i
\(711\) −6.70006 1.25446i −0.251272 0.0470458i
\(712\) −7.37846 + 21.1368i −0.276519 + 0.792136i
\(713\) 48.8084i 1.82789i
\(714\) −40.0775 61.0510i −1.49986 2.28478i
\(715\) 1.49390i 0.0558686i
\(716\) −40.9295 9.32054i −1.52961 0.348325i
\(717\) −13.0970 15.7767i −0.489116 0.589192i
\(718\) −19.2991 2.16964i −0.720235 0.0809703i
\(719\) 32.2204 1.20162 0.600809 0.799393i \(-0.294845\pi\)
0.600809 + 0.799393i \(0.294845\pi\)
\(720\) −12.1887 8.94116i −0.454248 0.333217i
\(721\) −52.9707 −1.97273
\(722\) 15.9441 + 1.79247i 0.593379 + 0.0667088i
\(723\) −0.506602 0.610256i −0.0188407 0.0226957i
\(724\) 3.10259 + 0.706527i 0.115307 + 0.0262579i
\(725\) 20.0144i 0.743316i
\(726\) 4.45592 + 6.78781i 0.165375 + 0.251919i
\(727\) 36.0565i 1.33726i −0.743594 0.668632i \(-0.766880\pi\)
0.743594 0.668632i \(-0.233120\pi\)
\(728\) 1.93927 5.55537i 0.0718742 0.205896i
\(729\) 14.2335 22.9436i 0.527167 0.849762i
\(730\) 0.248574 2.21108i 0.00920015 0.0818359i
\(731\) −22.0517 −0.815611
\(732\) 18.0572 + 35.6406i 0.667412 + 1.31731i
\(733\) 1.54846 0.0571936 0.0285968 0.999591i \(-0.490896\pi\)
0.0285968 + 0.999591i \(0.490896\pi\)
\(734\) 1.62739 14.4757i 0.0600681 0.534310i
\(735\) 27.9515 23.2039i 1.03101 0.855887i
\(736\) −37.6743 23.6073i −1.38869 0.870175i
\(737\) 2.77221i 0.102116i
\(738\) −9.83762 3.01125i −0.362128 0.110846i
\(739\) 39.3655i 1.44808i 0.689756 + 0.724041i \(0.257718\pi\)
−0.689756 + 0.724041i \(0.742282\pi\)
\(740\) −5.52498 + 24.2620i −0.203102 + 0.891888i
\(741\) −3.14048 + 2.60706i −0.115368 + 0.0957727i
\(742\) −43.6187 4.90370i −1.60129 0.180020i
\(743\) −31.8855 −1.16976 −0.584882 0.811118i \(-0.698859\pi\)
−0.584882 + 0.811118i \(0.698859\pi\)
\(744\) 28.5053 10.6319i 1.04506 0.389785i
\(745\) 12.9291 0.473685
\(746\) 15.0594 + 1.69300i 0.551362 + 0.0619852i
\(747\) −2.82850 + 15.1071i −0.103490 + 0.552739i
\(748\) −7.54740 + 33.1430i −0.275960 + 1.21183i
\(749\) 13.9880i 0.511109i
\(750\) 21.7017 14.2463i 0.792434 0.520200i
\(751\) 40.4301i 1.47531i 0.675175 + 0.737657i \(0.264068\pi\)
−0.675175 + 0.737657i \(0.735932\pi\)
\(752\) 8.08093 + 3.88171i 0.294681 + 0.141551i
\(753\) −18.3408 22.0934i −0.668375 0.805130i
\(754\) 0.396326 3.52534i 0.0144333 0.128385i
\(755\) 29.0355 1.05671
\(756\) 14.1542 + 48.5163i 0.514783 + 1.76452i
\(757\) 22.6047 0.821582 0.410791 0.911729i \(-0.365253\pi\)
0.410791 + 0.911729i \(0.365253\pi\)
\(758\) 4.24086 37.7227i 0.154035 1.37015i
\(759\) 24.1045 + 29.0365i 0.874938 + 1.05396i
\(760\) −18.5307 6.46872i −0.672180 0.234645i
\(761\) 6.14774i 0.222855i 0.993773 + 0.111428i \(0.0355423\pi\)
−0.993773 + 0.111428i \(0.964458\pi\)
\(762\) −0.615761 + 0.404222i −0.0223067 + 0.0146434i
\(763\) 89.4646i 3.23883i