Properties

Label 441.2.bg.a.395.18
Level $441$
Weight $2$
Character 441.395
Analytic conductor $3.521$
Analytic rank $0$
Dimension $216$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.bg (of order \(42\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(216\)
Relative dimension: \(18\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 395.18
Character \(\chi\) \(=\) 441.395
Dual form 441.2.bg.a.278.18

$q$-expansion

\(f(q)\) \(=\) \(q+(2.45194 + 0.962314i) q^{2} +(3.61984 + 3.35872i) q^{4} +(-1.47762 - 1.00742i) q^{5} +(2.09999 - 1.60937i) q^{7} +(3.35777 + 6.97247i) q^{8} +O(q^{10})\) \(q+(2.45194 + 0.962314i) q^{2} +(3.61984 + 3.35872i) q^{4} +(-1.47762 - 1.00742i) q^{5} +(2.09999 - 1.60937i) q^{7} +(3.35777 + 6.97247i) q^{8} +(-2.65357 - 3.89208i) q^{10} +(0.538606 + 3.57342i) q^{11} +(-2.76752 + 2.20702i) q^{13} +(6.69775 - 1.92522i) q^{14} +(0.785279 + 10.4788i) q^{16} +(-2.32943 - 0.718533i) q^{17} +(6.52328 - 3.76622i) q^{19} +(-1.96509 - 8.60964i) q^{20} +(-2.11812 + 9.28010i) q^{22} +(-1.91813 - 6.21843i) q^{23} +(-0.658247 - 1.67719i) q^{25} +(-8.90963 + 2.74826i) q^{26} +(13.0070 + 1.22762i) q^{28} +(-4.35647 + 0.994336i) q^{29} +(-5.85986 - 3.38319i) q^{31} +(-3.59633 + 11.6590i) q^{32} +(-5.02015 - 4.00344i) q^{34} +(-4.72430 + 0.262454i) q^{35} +(-4.18776 + 3.88567i) q^{37} +(19.6190 - 2.95708i) q^{38} +(2.06274 - 13.6854i) q^{40} +(-3.53525 + 1.70249i) q^{41} +(3.05468 + 1.47106i) q^{43} +(-10.0524 + 14.7442i) q^{44} +(1.28095 - 17.0930i) q^{46} +(-1.81628 + 4.62779i) q^{47} +(1.81988 - 6.75929i) q^{49} -4.74579i q^{50} +(-17.4308 - 1.30625i) q^{52} +(3.20504 - 3.45421i) q^{53} +(2.80409 - 5.82276i) q^{55} +(18.2725 + 9.23822i) q^{56} +(-11.6387 - 1.75424i) q^{58} +(-9.48163 + 6.46446i) q^{59} +(4.54073 + 4.89374i) q^{61} +(-11.1123 - 13.9344i) q^{62} +(-6.93408 + 8.69506i) q^{64} +(6.31275 - 0.473075i) q^{65} +(6.90681 - 11.9629i) q^{67} +(-6.01880 - 10.4249i) q^{68} +(-11.8362 - 3.90274i) q^{70} +(-1.21008 - 0.276193i) q^{71} +(8.19697 - 3.21707i) q^{73} +(-14.0074 + 5.49749i) q^{74} +(36.2629 + 8.27678i) q^{76} +(6.88200 + 6.63731i) q^{77} +(5.24053 + 9.07686i) q^{79} +(9.39628 - 16.2748i) q^{80} +(-10.3066 + 0.772369i) q^{82} +(8.72515 - 10.9410i) q^{83} +(2.71814 + 3.40844i) q^{85} +(6.07427 + 6.54650i) q^{86} +(-23.1070 + 15.7541i) q^{88} +(7.03212 + 1.05992i) q^{89} +(-2.25984 + 9.08866i) q^{91} +(13.9427 - 28.9522i) q^{92} +(-8.90679 + 9.59923i) q^{94} +(-13.4331 - 1.00667i) q^{95} -1.36179i q^{97} +(10.9668 - 14.8221i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q - 16q^{4} + 2q^{7} + O(q^{10}) \) \( 216q - 16q^{4} + 2q^{7} + 12q^{10} + 12q^{16} - 6q^{19} + 44q^{22} + 26q^{25} + 84q^{28} - 6q^{31} - 112q^{34} + 60q^{37} - 304q^{40} + 20q^{43} - 20q^{46} - 86q^{49} - 168q^{52} - 84q^{55} - 120q^{58} - 2q^{61} + 32q^{64} + 22q^{67} - 136q^{70} - 6q^{73} + 84q^{76} + 2q^{79} - 104q^{82} + 96q^{85} - 12q^{88} + 58q^{91} + 52q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{42}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.45194 + 0.962314i 1.73378 + 0.680459i 0.999999 + 0.00107413i \(0.000341906\pi\)
0.733782 + 0.679385i \(0.237753\pi\)
\(3\) 0 0
\(4\) 3.61984 + 3.35872i 1.80992 + 1.67936i
\(5\) −1.47762 1.00742i −0.660812 0.450534i 0.185912 0.982566i \(-0.440476\pi\)
−0.846724 + 0.532032i \(0.821428\pi\)
\(6\) 0 0
\(7\) 2.09999 1.60937i 0.793720 0.608283i
\(8\) 3.35777 + 6.97247i 1.18715 + 2.46514i
\(9\) 0 0
\(10\) −2.65357 3.89208i −0.839134 1.23078i
\(11\) 0.538606 + 3.57342i 0.162396 + 1.07743i 0.910399 + 0.413731i \(0.135774\pi\)
−0.748004 + 0.663695i \(0.768987\pi\)
\(12\) 0 0
\(13\) −2.76752 + 2.20702i −0.767571 + 0.612118i −0.926987 0.375094i \(-0.877610\pi\)
0.159415 + 0.987212i \(0.449039\pi\)
\(14\) 6.69775 1.92522i 1.79005 0.514536i
\(15\) 0 0
\(16\) 0.785279 + 10.4788i 0.196320 + 2.61970i
\(17\) −2.32943 0.718533i −0.564969 0.174270i −0.000902867 1.00000i \(-0.500287\pi\)
−0.564066 + 0.825730i \(0.690764\pi\)
\(18\) 0 0
\(19\) 6.52328 3.76622i 1.49654 0.864030i 0.496551 0.868008i \(-0.334600\pi\)
0.999992 + 0.00397809i \(0.00126627\pi\)
\(20\) −1.96509 8.60964i −0.439408 1.92517i
\(21\) 0 0
\(22\) −2.11812 + 9.28010i −0.451585 + 1.97852i
\(23\) −1.91813 6.21843i −0.399958 1.29663i −0.901980 0.431778i \(-0.857887\pi\)
0.502022 0.864855i \(-0.332590\pi\)
\(24\) 0 0
\(25\) −0.658247 1.67719i −0.131649 0.335437i
\(26\) −8.90963 + 2.74826i −1.74732 + 0.538977i
\(27\) 0 0
\(28\) 13.0070 + 1.22762i 2.45810 + 0.231999i
\(29\) −4.35647 + 0.994336i −0.808976 + 0.184644i −0.606953 0.794737i \(-0.707609\pi\)
−0.202023 + 0.979381i \(0.564751\pi\)
\(30\) 0 0
\(31\) −5.85986 3.38319i −1.05246 0.607639i −0.129124 0.991628i \(-0.541216\pi\)
−0.923337 + 0.383990i \(0.874550\pi\)
\(32\) −3.59633 + 11.6590i −0.635747 + 2.06104i
\(33\) 0 0
\(34\) −5.02015 4.00344i −0.860949 0.686584i
\(35\) −4.72430 + 0.262454i −0.798552 + 0.0443628i
\(36\) 0 0
\(37\) −4.18776 + 3.88567i −0.688464 + 0.638801i −0.944747 0.327801i \(-0.893692\pi\)
0.256283 + 0.966602i \(0.417502\pi\)
\(38\) 19.6190 2.95708i 3.18262 0.479702i
\(39\) 0 0
\(40\) 2.06274 13.6854i 0.326147 2.16385i
\(41\) −3.53525 + 1.70249i −0.552114 + 0.265884i −0.689072 0.724693i \(-0.741982\pi\)
0.136958 + 0.990577i \(0.456267\pi\)
\(42\) 0 0
\(43\) 3.05468 + 1.47106i 0.465834 + 0.224334i 0.652052 0.758175i \(-0.273909\pi\)
−0.186217 + 0.982509i \(0.559623\pi\)
\(44\) −10.0524 + 14.7442i −1.51546 + 2.22278i
\(45\) 0 0
\(46\) 1.28095 17.0930i 0.188865 2.52023i
\(47\) −1.81628 + 4.62779i −0.264931 + 0.675033i −0.999996 0.00296394i \(-0.999057\pi\)
0.735065 + 0.677997i \(0.237152\pi\)
\(48\) 0 0
\(49\) 1.81988 6.75929i 0.259983 0.965613i
\(50\) 4.74579i 0.671157i
\(51\) 0 0
\(52\) −17.4308 1.30625i −2.41721 0.181145i
\(53\) 3.20504 3.45421i 0.440247 0.474473i −0.473479 0.880805i \(-0.657002\pi\)
0.913725 + 0.406332i \(0.133192\pi\)
\(54\) 0 0
\(55\) 2.80409 5.82276i 0.378104 0.785141i
\(56\) 18.2725 + 9.23822i 2.44177 + 1.23451i
\(57\) 0 0
\(58\) −11.6387 1.75424i −1.52823 0.230344i
\(59\) −9.48163 + 6.46446i −1.23440 + 0.841601i −0.991709 0.128502i \(-0.958983\pi\)
−0.242693 + 0.970103i \(0.578031\pi\)
\(60\) 0 0
\(61\) 4.54073 + 4.89374i 0.581381 + 0.626580i 0.953423 0.301636i \(-0.0975328\pi\)
−0.372042 + 0.928216i \(0.621342\pi\)
\(62\) −11.1123 13.9344i −1.41126 1.76967i
\(63\) 0 0
\(64\) −6.93408 + 8.69506i −0.866759 + 1.08688i
\(65\) 6.31275 0.473075i 0.783000 0.0586778i
\(66\) 0 0
\(67\) 6.90681 11.9629i 0.843801 1.46151i −0.0428576 0.999081i \(-0.513646\pi\)
0.886658 0.462425i \(-0.153020\pi\)
\(68\) −6.01880 10.4249i −0.729887 1.26420i
\(69\) 0 0
\(70\) −11.8362 3.90274i −1.41470 0.466467i
\(71\) −1.21008 0.276193i −0.143610 0.0327781i 0.150112 0.988669i \(-0.452037\pi\)
−0.293722 + 0.955891i \(0.594894\pi\)
\(72\) 0 0
\(73\) 8.19697 3.21707i 0.959383 0.376530i 0.166594 0.986026i \(-0.446723\pi\)
0.792790 + 0.609495i \(0.208628\pi\)
\(74\) −14.0074 + 5.49749i −1.62832 + 0.639070i
\(75\) 0 0
\(76\) 36.2629 + 8.27678i 4.15964 + 0.949412i
\(77\) 6.88200 + 6.63731i 0.784276 + 0.756392i
\(78\) 0 0
\(79\) 5.24053 + 9.07686i 0.589606 + 1.02123i 0.994284 + 0.106768i \(0.0340502\pi\)
−0.404678 + 0.914459i \(0.632616\pi\)
\(80\) 9.39628 16.2748i 1.05054 1.81958i
\(81\) 0 0
\(82\) −10.3066 + 0.772369i −1.13817 + 0.0852939i
\(83\) 8.72515 10.9410i 0.957710 1.20093i −0.0218467 0.999761i \(-0.506955\pi\)
0.979557 0.201169i \(-0.0644740\pi\)
\(84\) 0 0
\(85\) 2.71814 + 3.40844i 0.294824 + 0.369697i
\(86\) 6.07427 + 6.54650i 0.655005 + 0.705927i
\(87\) 0 0
\(88\) −23.1070 + 15.7541i −2.46322 + 1.67939i
\(89\) 7.03212 + 1.05992i 0.745403 + 0.112351i 0.510752 0.859728i \(-0.329367\pi\)
0.234651 + 0.972080i \(0.424605\pi\)
\(90\) 0 0
\(91\) −2.25984 + 9.08866i −0.236896 + 0.952751i
\(92\) 13.9427 28.9522i 1.45362 3.01848i
\(93\) 0 0
\(94\) −8.90679 + 9.59923i −0.918665 + 0.990085i
\(95\) −13.4331 1.00667i −1.37821 0.103282i
\(96\) 0 0
\(97\) 1.36179i 0.138269i −0.997607 0.0691347i \(-0.977976\pi\)
0.997607 0.0691347i \(-0.0220238\pi\)
\(98\) 10.9668 14.8221i 1.10781 1.49725i
\(99\) 0 0
\(100\) 3.25045 8.28202i 0.325045 0.828202i
\(101\) −0.646268 + 8.62384i −0.0643060 + 0.858104i 0.868030 + 0.496512i \(0.165386\pi\)
−0.932336 + 0.361593i \(0.882233\pi\)
\(102\) 0 0
\(103\) −8.38856 + 12.3038i −0.826550 + 1.21233i 0.148185 + 0.988960i \(0.452657\pi\)
−0.974735 + 0.223366i \(0.928295\pi\)
\(104\) −24.6811 11.8858i −2.42018 1.16550i
\(105\) 0 0
\(106\) 11.1826 5.38526i 1.08615 0.523063i
\(107\) −2.23305 + 14.8153i −0.215877 + 1.43225i 0.573934 + 0.818901i \(0.305416\pi\)
−0.789811 + 0.613350i \(0.789822\pi\)
\(108\) 0 0
\(109\) −15.2528 + 2.29900i −1.46096 + 0.220204i −0.830934 0.556372i \(-0.812193\pi\)
−0.630024 + 0.776576i \(0.716955\pi\)
\(110\) 12.4788 11.5786i 1.18981 1.10398i
\(111\) 0 0
\(112\) 18.5133 + 20.7416i 1.74934 + 1.95989i
\(113\) −2.47511 1.97383i −0.232838 0.185682i 0.500120 0.865956i \(-0.333289\pi\)
−0.732958 + 0.680274i \(0.761861\pi\)
\(114\) 0 0
\(115\) −3.43033 + 11.1209i −0.319880 + 1.03703i
\(116\) −19.1094 11.0328i −1.77427 1.02437i
\(117\) 0 0
\(118\) −29.4692 + 6.72615i −2.71286 + 0.619192i
\(119\) −6.04814 + 2.23999i −0.554432 + 0.205339i
\(120\) 0 0
\(121\) −1.96790 + 0.607018i −0.178900 + 0.0551834i
\(122\) 6.42427 + 16.3688i 0.581626 + 1.48196i
\(123\) 0 0
\(124\) −9.84856 31.9283i −0.884427 2.86724i
\(125\) −2.70675 + 11.8590i −0.242099 + 1.06070i
\(126\) 0 0
\(127\) 2.81359 + 12.3271i 0.249666 + 1.09386i 0.931898 + 0.362722i \(0.118152\pi\)
−0.682232 + 0.731136i \(0.738990\pi\)
\(128\) −4.23644 + 2.44591i −0.374452 + 0.216190i
\(129\) 0 0
\(130\) 15.9337 + 4.91490i 1.39748 + 0.431065i
\(131\) −0.625833 8.35116i −0.0546793 0.729644i −0.955413 0.295272i \(-0.904590\pi\)
0.900734 0.434371i \(-0.143029\pi\)
\(132\) 0 0
\(133\) 7.63758 18.4073i 0.662262 1.59612i
\(134\) 28.4472 22.6859i 2.45746 1.95976i
\(135\) 0 0
\(136\) −2.81172 18.6545i −0.241103 1.59961i
\(137\) −3.40952 5.00085i −0.291295 0.427251i 0.652497 0.757791i \(-0.273722\pi\)
−0.943792 + 0.330540i \(0.892769\pi\)
\(138\) 0 0
\(139\) 4.97685 + 10.3345i 0.422131 + 0.876565i 0.998246 + 0.0591961i \(0.0188537\pi\)
−0.576115 + 0.817369i \(0.695432\pi\)
\(140\) −17.9827 14.9176i −1.51982 1.26076i
\(141\) 0 0
\(142\) −2.70126 1.84168i −0.226684 0.154551i
\(143\) −9.37721 8.70078i −0.784162 0.727596i
\(144\) 0 0
\(145\) 7.43893 + 2.91956i 0.617769 + 0.242457i
\(146\) 23.1943 1.91957
\(147\) 0 0
\(148\) −28.2099 −2.31884
\(149\) 11.7419 + 4.60836i 0.961934 + 0.377531i 0.793763 0.608227i \(-0.208119\pi\)
0.168171 + 0.985758i \(0.446214\pi\)
\(150\) 0 0
\(151\) 1.35780 + 1.25985i 0.110496 + 0.102525i 0.733486 0.679704i \(-0.237892\pi\)
−0.622990 + 0.782230i \(0.714082\pi\)
\(152\) 48.1635 + 32.8373i 3.90658 + 2.66346i
\(153\) 0 0
\(154\) 10.4870 + 22.8969i 0.845070 + 1.84509i
\(155\) 5.25034 + 10.9024i 0.421717 + 0.875705i
\(156\) 0 0
\(157\) −5.62320 8.24772i −0.448780 0.658240i 0.533469 0.845820i \(-0.320888\pi\)
−0.982249 + 0.187580i \(0.939936\pi\)
\(158\) 4.11465 + 27.2989i 0.327344 + 2.17179i
\(159\) 0 0
\(160\) 17.0596 13.6046i 1.34868 1.07553i
\(161\) −14.0358 9.97164i −1.10617 0.785876i
\(162\) 0 0
\(163\) 0.815078 + 10.8765i 0.0638418 + 0.851910i 0.933574 + 0.358386i \(0.116673\pi\)
−0.869732 + 0.493525i \(0.835708\pi\)
\(164\) −18.5153 5.71120i −1.44580 0.445970i
\(165\) 0 0
\(166\) 31.9222 18.4303i 2.47764 1.43047i
\(167\) 4.24385 + 18.5935i 0.328399 + 1.43881i 0.822183 + 0.569224i \(0.192756\pi\)
−0.493784 + 0.869585i \(0.664387\pi\)
\(168\) 0 0
\(169\) −0.104562 + 0.458117i −0.00804325 + 0.0352398i
\(170\) 3.38472 + 10.9730i 0.259596 + 0.841590i
\(171\) 0 0
\(172\) 6.11659 + 15.5848i 0.466386 + 1.18833i
\(173\) 17.0108 5.24713i 1.29330 0.398932i 0.429641 0.903000i \(-0.358640\pi\)
0.863664 + 0.504068i \(0.168164\pi\)
\(174\) 0 0
\(175\) −4.08151 2.46271i −0.308533 0.186163i
\(176\) −37.0222 + 8.45008i −2.79065 + 0.636949i
\(177\) 0 0
\(178\) 16.2223 + 9.36597i 1.21592 + 0.702009i
\(179\) 4.74524 15.3837i 0.354676 1.14983i −0.585939 0.810355i \(-0.699274\pi\)
0.940615 0.339476i \(-0.110250\pi\)
\(180\) 0 0
\(181\) −1.22615 0.977821i −0.0911389 0.0726809i 0.576860 0.816843i \(-0.304278\pi\)
−0.667999 + 0.744162i \(0.732849\pi\)
\(182\) −14.2871 + 20.1102i −1.05903 + 1.49066i
\(183\) 0 0
\(184\) 36.9172 34.2542i 2.72157 2.52525i
\(185\) 10.1024 1.52270i 0.742747 0.111951i
\(186\) 0 0
\(187\) 1.31297 8.71101i 0.0960142 0.637012i
\(188\) −22.1181 + 10.6515i −1.61313 + 0.776842i
\(189\) 0 0
\(190\) −31.9684 15.3952i −2.31923 1.11688i
\(191\) 4.14328 6.07708i 0.299797 0.439722i −0.646551 0.762871i \(-0.723789\pi\)
0.946348 + 0.323149i \(0.104741\pi\)
\(192\) 0 0
\(193\) 0.156219 2.08460i 0.0112449 0.150053i −0.988755 0.149545i \(-0.952219\pi\)
1.00000 0.000508213i \(-0.000161769\pi\)
\(194\) 1.31047 3.33904i 0.0940866 0.239729i
\(195\) 0 0
\(196\) 29.2903 18.3551i 2.09216 1.31108i
\(197\) 6.13583i 0.437159i −0.975819 0.218580i \(-0.929858\pi\)
0.975819 0.218580i \(-0.0701424\pi\)
\(198\) 0 0
\(199\) −24.1519 1.80994i −1.71209 0.128303i −0.817713 0.575625i \(-0.804759\pi\)
−0.894373 + 0.447322i \(0.852378\pi\)
\(200\) 9.48389 10.2212i 0.670612 0.722748i
\(201\) 0 0
\(202\) −9.88346 + 20.5232i −0.695398 + 1.44401i
\(203\) −7.54828 + 9.09924i −0.529785 + 0.638642i
\(204\) 0 0
\(205\) 6.93890 + 1.04587i 0.484633 + 0.0730467i
\(206\) −32.4083 + 22.0956i −2.25799 + 1.53947i
\(207\) 0 0
\(208\) −25.3003 27.2672i −1.75426 1.89064i
\(209\) 16.9717 + 21.2819i 1.17396 + 1.47210i
\(210\) 0 0
\(211\) 4.19892 5.26528i 0.289066 0.362477i −0.616002 0.787745i \(-0.711249\pi\)
0.905068 + 0.425268i \(0.139820\pi\)
\(212\) 23.2035 1.73886i 1.59362 0.119426i
\(213\) 0 0
\(214\) −19.7323 + 34.1773i −1.34887 + 2.33631i
\(215\) −3.03168 5.25102i −0.206759 0.358117i
\(216\) 0 0
\(217\) −17.7504 + 2.32600i −1.20498 + 0.157899i
\(218\) −39.6114 9.04104i −2.68282 0.612336i
\(219\) 0 0
\(220\) 29.7074 11.6593i 2.00287 0.786070i
\(221\) 8.03254 3.15254i 0.540327 0.212063i
\(222\) 0 0
\(223\) −7.92276 1.80832i −0.530547 0.121094i −0.0511482 0.998691i \(-0.516288\pi\)
−0.479399 + 0.877597i \(0.659145\pi\)
\(224\) 11.2114 + 30.2715i 0.749091 + 2.02260i
\(225\) 0 0
\(226\) −4.16936 7.22154i −0.277342 0.480370i
\(227\) 1.53188 2.65330i 0.101675 0.176106i −0.810700 0.585462i \(-0.800913\pi\)
0.912375 + 0.409356i \(0.134247\pi\)
\(228\) 0 0
\(229\) 0.150273 0.0112614i 0.00993034 0.000744176i −0.0697640 0.997564i \(-0.522225\pi\)
0.0796943 + 0.996819i \(0.474606\pi\)
\(230\) −19.1127 + 23.9666i −1.26026 + 1.58031i
\(231\) 0 0
\(232\) −21.5610 27.0366i −1.41555 1.77504i
\(233\) −14.6211 15.7578i −0.957860 1.03233i −0.999449 0.0331927i \(-0.989433\pi\)
0.0415891 0.999135i \(-0.486758\pi\)
\(234\) 0 0
\(235\) 7.34592 5.00836i 0.479195 0.326710i
\(236\) −56.0343 8.44582i −3.64753 0.549776i
\(237\) 0 0
\(238\) −16.9852 0.327903i −1.10099 0.0212548i
\(239\) 3.87558 8.04773i 0.250691 0.520564i −0.737208 0.675666i \(-0.763856\pi\)
0.987899 + 0.155102i \(0.0495705\pi\)
\(240\) 0 0
\(241\) −6.13948 + 6.61679i −0.395479 + 0.426225i −0.899130 0.437683i \(-0.855799\pi\)
0.503651 + 0.863907i \(0.331990\pi\)
\(242\) −5.40932 0.405372i −0.347724 0.0260583i
\(243\) 0 0
\(244\) 32.9657i 2.11041i
\(245\) −9.49858 + 8.15427i −0.606842 + 0.520957i
\(246\) 0 0
\(247\) −9.74117 + 24.8201i −0.619816 + 1.57926i
\(248\) 3.91317 52.2177i 0.248487 3.31582i
\(249\) 0 0
\(250\) −18.0489 + 26.4729i −1.14151 + 1.67429i
\(251\) −10.7491 5.17648i −0.678476 0.326737i 0.0627146 0.998031i \(-0.480024\pi\)
−0.741191 + 0.671295i \(0.765738\pi\)
\(252\) 0 0
\(253\) 21.1879 10.2036i 1.33207 0.641493i
\(254\) −4.96384 + 32.9330i −0.311459 + 2.06640i
\(255\) 0 0
\(256\) 9.25313 1.39469i 0.578321 0.0871678i
\(257\) 9.42230 8.74262i 0.587747 0.545349i −0.329251 0.944243i \(-0.606796\pi\)
0.916997 + 0.398893i \(0.130606\pi\)
\(258\) 0 0
\(259\) −2.54077 + 14.8995i −0.157876 + 0.925810i
\(260\) 24.4401 + 19.4903i 1.51571 + 1.20874i
\(261\) 0 0
\(262\) 6.50194 21.0788i 0.401691 1.30225i
\(263\) 1.45825 + 0.841921i 0.0899196 + 0.0519151i 0.544286 0.838900i \(-0.316801\pi\)
−0.454366 + 0.890815i \(0.650134\pi\)
\(264\) 0 0
\(265\) −8.21570 + 1.87518i −0.504686 + 0.115191i
\(266\) 36.4405 37.7839i 2.23431 2.31668i
\(267\) 0 0
\(268\) 65.1818 20.1059i 3.98161 1.22816i
\(269\) 7.64504 + 19.4792i 0.466126 + 1.18767i 0.949921 + 0.312489i \(0.101163\pi\)
−0.483795 + 0.875181i \(0.660742\pi\)
\(270\) 0 0
\(271\) 5.75145 + 18.6458i 0.349376 + 1.13265i 0.944361 + 0.328912i \(0.106682\pi\)
−0.594985 + 0.803737i \(0.702842\pi\)
\(272\) 5.70012 24.9739i 0.345621 1.51426i
\(273\) 0 0
\(274\) −3.54754 15.5428i −0.214315 0.938975i
\(275\) 5.63874 3.25553i 0.340029 0.196316i
\(276\) 0 0
\(277\) 4.17247 + 1.28704i 0.250700 + 0.0773306i 0.417558 0.908650i \(-0.362886\pi\)
−0.166858 + 0.985981i \(0.553362\pi\)
\(278\) 2.25785 + 30.1290i 0.135417 + 1.80701i
\(279\) 0 0
\(280\) −17.6930 32.0588i −1.05736 1.91588i
\(281\) 12.6794 10.1115i 0.756389 0.603200i −0.167495 0.985873i \(-0.553568\pi\)
0.923884 + 0.382673i \(0.124996\pi\)
\(282\) 0 0
\(283\) −2.67459 17.7447i −0.158988 1.05481i −0.915932 0.401334i \(-0.868547\pi\)
0.756944 0.653480i \(-0.226692\pi\)
\(284\) −3.45264 5.06410i −0.204877 0.300499i
\(285\) 0 0
\(286\) −14.6194 30.3576i −0.864466 1.79508i
\(287\) −4.68406 + 9.26472i −0.276491 + 0.546879i
\(288\) 0 0
\(289\) −9.13612 6.22890i −0.537419 0.366406i
\(290\) 15.4302 + 14.3172i 0.906095 + 0.840734i
\(291\) 0 0
\(292\) 40.4770 + 15.8861i 2.36874 + 0.929661i
\(293\) 32.9586 1.92546 0.962731 0.270461i \(-0.0871762\pi\)
0.962731 + 0.270461i \(0.0871762\pi\)
\(294\) 0 0
\(295\) 20.5227 1.19488
\(296\) −41.1543 16.1519i −2.39204 0.938808i
\(297\) 0 0
\(298\) 24.3557 + 22.5988i 1.41089 + 1.30911i
\(299\) 19.0327 + 12.9763i 1.10069 + 0.750436i
\(300\) 0 0
\(301\) 8.78225 1.82690i 0.506201 0.105301i
\(302\) 2.11686 + 4.39571i 0.121812 + 0.252945i
\(303\) 0 0
\(304\) 44.5881 + 65.3987i 2.55730 + 3.75087i
\(305\) −1.77940 11.8055i −0.101888 0.675983i
\(306\) 0 0
\(307\) −4.83163 + 3.85309i −0.275755 + 0.219908i −0.751596 0.659624i \(-0.770715\pi\)
0.475840 + 0.879532i \(0.342144\pi\)
\(308\) 2.61886 + 47.1408i 0.149223 + 2.68609i
\(309\) 0 0
\(310\) 2.38192 + 31.7846i 0.135284 + 1.80524i
\(311\) −8.13363 2.50889i −0.461216 0.142266i 0.0554351 0.998462i \(-0.482345\pi\)
−0.516651 + 0.856196i \(0.672822\pi\)
\(312\) 0 0
\(313\) −20.3319 + 11.7386i −1.14923 + 0.663507i −0.948699 0.316181i \(-0.897599\pi\)
−0.200529 + 0.979688i \(0.564266\pi\)
\(314\) −5.85083 25.6342i −0.330182 1.44662i
\(315\) 0 0
\(316\) −11.5168 + 50.4583i −0.647870 + 2.83850i
\(317\) −1.54066 4.99470i −0.0865322 0.280530i 0.901956 0.431828i \(-0.142131\pi\)
−0.988488 + 0.151297i \(0.951655\pi\)
\(318\) 0 0
\(319\) −5.89959 15.0319i −0.330314 0.841626i
\(320\) 19.0055 5.86244i 1.06244 0.327720i
\(321\) 0 0
\(322\) −24.8190 37.9567i −1.38311 2.11524i
\(323\) −17.9016 + 4.08593i −0.996074 + 0.227347i
\(324\) 0 0
\(325\) 5.52329 + 3.18888i 0.306377 + 0.176887i
\(326\) −8.46806 + 27.4528i −0.469002 + 1.52047i
\(327\) 0 0
\(328\) −23.7411 18.9329i −1.31088 1.04540i
\(329\) 3.63366 + 12.6414i 0.200330 + 0.696940i
\(330\) 0 0
\(331\) 2.08468 1.93430i 0.114584 0.106319i −0.620800 0.783969i \(-0.713192\pi\)
0.735384 + 0.677650i \(0.237002\pi\)
\(332\) 68.3315 10.2993i 3.75018 0.565248i
\(333\) 0 0
\(334\) −7.48715 + 49.6740i −0.409679 + 2.71804i
\(335\) −22.2574 + 10.7186i −1.21605 + 0.585620i
\(336\) 0 0
\(337\) −3.74529 1.80364i −0.204019 0.0982503i 0.329084 0.944301i \(-0.393260\pi\)
−0.533103 + 0.846050i \(0.678974\pi\)
\(338\) −0.697233 + 1.02265i −0.0379245 + 0.0556250i
\(339\) 0 0
\(340\) −1.60877 + 21.4675i −0.0872476 + 1.16424i
\(341\) 8.93339 22.7619i 0.483770 1.23263i
\(342\) 0 0
\(343\) −7.05644 17.1233i −0.381012 0.924570i
\(344\) 26.2381i 1.41467i
\(345\) 0 0
\(346\) 46.7587 + 3.50408i 2.51376 + 0.188381i
\(347\) −7.22248 + 7.78398i −0.387723 + 0.417866i −0.896508 0.443028i \(-0.853904\pi\)
0.508785 + 0.860894i \(0.330095\pi\)
\(348\) 0 0
\(349\) 3.07452 6.38430i 0.164575 0.341744i −0.802330 0.596881i \(-0.796406\pi\)
0.966905 + 0.255137i \(0.0821207\pi\)
\(350\) −7.63772 9.96610i −0.408253 0.532710i
\(351\) 0 0
\(352\) −43.5995 6.57156i −2.32386 0.350265i
\(353\) 22.5490 15.3737i 1.20016 0.818257i 0.212856 0.977084i \(-0.431724\pi\)
0.987306 + 0.158827i \(0.0507711\pi\)
\(354\) 0 0
\(355\) 1.50980 + 1.62717i 0.0801316 + 0.0863614i
\(356\) 21.8952 + 27.4557i 1.16044 + 1.45515i
\(357\) 0 0
\(358\) 26.4390 33.1534i 1.39734 1.75221i
\(359\) −13.5615 + 1.01630i −0.715750 + 0.0536380i −0.427627 0.903955i \(-0.640650\pi\)
−0.288123 + 0.957593i \(0.593031\pi\)
\(360\) 0 0
\(361\) 18.8688 32.6817i 0.993094 1.72009i
\(362\) −2.06547 3.57750i −0.108559 0.188029i
\(363\) 0 0
\(364\) −38.7066 + 25.3093i −2.02878 + 1.32657i
\(365\) −15.3530 3.50422i −0.803612 0.183419i
\(366\) 0 0
\(367\) −28.0445 + 11.0066i −1.46391 + 0.574542i −0.957675 0.287853i \(-0.907059\pi\)
−0.506235 + 0.862395i \(0.668963\pi\)
\(368\) 63.6555 24.9830i 3.31827 1.30233i
\(369\) 0 0
\(370\) 26.2359 + 5.98817i 1.36394 + 0.311310i
\(371\) 1.17145 12.4119i 0.0608187 0.644393i
\(372\) 0 0
\(373\) −3.76187 6.51575i −0.194782 0.337373i 0.752047 0.659110i \(-0.229067\pi\)
−0.946829 + 0.321737i \(0.895733\pi\)
\(374\) 11.6021 20.0954i 0.599928 1.03911i
\(375\) 0 0
\(376\) −38.3658 + 2.87512i −1.97856 + 0.148273i
\(377\) 9.86209 12.3667i 0.507923 0.636916i
\(378\) 0 0
\(379\) 2.63147 + 3.29975i 0.135169 + 0.169497i 0.844809 0.535067i \(-0.179714\pi\)
−0.709640 + 0.704564i \(0.751142\pi\)
\(380\) −45.2446 48.7621i −2.32100 2.50144i
\(381\) 0 0
\(382\) 16.0071 10.9135i 0.818996 0.558382i
\(383\) 4.24118 + 0.639255i 0.216714 + 0.0326644i 0.256502 0.966544i \(-0.417430\pi\)
−0.0397876 + 0.999208i \(0.512668\pi\)
\(384\) 0 0
\(385\) −3.48239 16.7405i −0.177479 0.853176i
\(386\) 2.38908 4.96098i 0.121601 0.252507i
\(387\) 0 0
\(388\) 4.57389 4.92948i 0.232204 0.250257i
\(389\) 13.0184 + 0.975597i 0.660061 + 0.0494647i 0.400549 0.916275i \(-0.368819\pi\)
0.259512 + 0.965740i \(0.416438\pi\)
\(390\) 0 0
\(391\) 15.8636i 0.802257i
\(392\) 53.2397 10.0070i 2.68901 0.505431i
\(393\) 0 0
\(394\) 5.90459 15.0447i 0.297469 0.757939i
\(395\) 1.40074 18.6916i 0.0704790 0.940477i
\(396\) 0 0
\(397\) 18.0630 26.4936i 0.906558 1.32968i −0.0372929 0.999304i \(-0.511873\pi\)
0.943851 0.330372i \(-0.107174\pi\)
\(398\) −57.4773 27.6796i −2.88108 1.38745i
\(399\) 0 0
\(400\) 17.0580 8.21471i 0.852901 0.410735i
\(401\) −0.0147931 + 0.0981455i −0.000738730 + 0.00490115i −0.989197 0.146591i \(-0.953170\pi\)
0.988458 + 0.151492i \(0.0484079\pi\)
\(402\) 0 0
\(403\) 23.6840 3.56979i 1.17979 0.177824i
\(404\) −31.3045 + 29.0463i −1.55746 + 1.44511i
\(405\) 0 0
\(406\) −27.2642 + 15.0470i −1.35310 + 0.746768i
\(407\) −16.1407 12.8718i −0.800064 0.638030i
\(408\) 0 0
\(409\) −1.32490 + 4.29523i −0.0655123 + 0.212386i −0.982410 0.186737i \(-0.940209\pi\)
0.916898 + 0.399122i \(0.130685\pi\)
\(410\) 16.0073 + 9.24181i 0.790543 + 0.456420i
\(411\) 0 0
\(412\) −71.6902 + 16.3628i −3.53192 + 0.806139i
\(413\) −9.50760 + 28.8347i −0.467838 + 1.41886i
\(414\) 0 0
\(415\) −23.9147 + 7.37671i −1.17393 + 0.362108i
\(416\) −15.7788 40.2037i −0.773618 1.97115i
\(417\) 0 0
\(418\) 21.1338 + 68.5140i 1.03369 + 3.35113i
\(419\) 3.03434 13.2943i 0.148237 0.649470i −0.845137 0.534549i \(-0.820481\pi\)
0.993375 0.114921i \(-0.0366615\pi\)
\(420\) 0 0
\(421\) 5.61051 + 24.5813i 0.273440 + 1.19802i 0.905923 + 0.423443i \(0.139179\pi\)
−0.632483 + 0.774574i \(0.717964\pi\)
\(422\) 15.3624 8.86946i 0.747828 0.431759i
\(423\) 0 0
\(424\) 34.8462 + 10.7486i 1.69228 + 0.522000i
\(425\) 0.328224 + 4.37985i 0.0159212 + 0.212454i
\(426\) 0 0
\(427\) 17.4113 + 2.96910i 0.842592 + 0.143685i
\(428\) −57.8439 + 46.1289i −2.79599 + 2.22973i
\(429\) 0 0
\(430\) −2.38035 15.7926i −0.114791 0.761587i
\(431\) −7.62931 11.1901i −0.367491 0.539010i 0.597303 0.802015i \(-0.296239\pi\)
−0.964794 + 0.263005i \(0.915286\pi\)
\(432\) 0 0
\(433\) −6.37412 13.2360i −0.306321 0.636081i 0.689808 0.723993i \(-0.257695\pi\)
−0.996128 + 0.0879115i \(0.971981\pi\)
\(434\) −45.7612 11.3783i −2.19661 0.546174i
\(435\) 0 0
\(436\) −62.9346 42.9081i −3.01402 2.05492i
\(437\) −35.9325 33.3405i −1.71888 1.59489i
\(438\) 0 0
\(439\) −0.572327 0.224622i −0.0273157 0.0107206i 0.351644 0.936134i \(-0.385623\pi\)
−0.378960 + 0.925413i \(0.623718\pi\)
\(440\) 50.0145 2.38435
\(441\) 0 0
\(442\) 22.7290 1.08111
\(443\) −14.0115 5.49909i −0.665704 0.261270i 0.00833484 0.999965i \(-0.497347\pi\)
−0.674039 + 0.738696i \(0.735442\pi\)
\(444\) 0 0
\(445\) −9.32302 8.65049i −0.441953 0.410073i
\(446\) −17.6859 12.0581i −0.837453 0.570966i
\(447\) 0 0
\(448\) −0.567938 + 29.4190i −0.0268326 + 1.38992i
\(449\) −2.79316 5.80005i −0.131817 0.273721i 0.824605 0.565709i \(-0.191398\pi\)
−0.956422 + 0.291988i \(0.905683\pi\)
\(450\) 0 0
\(451\) −7.98781 11.7160i −0.376131 0.551683i
\(452\) −2.32994 15.4582i −0.109591 0.727091i
\(453\) 0 0
\(454\) 6.30940 5.03157i 0.296115 0.236144i
\(455\) 12.4953 11.1530i 0.585790 0.522860i
\(456\) 0 0
\(457\) 2.37788 + 31.7305i 0.111232 + 1.48429i 0.721675 + 0.692232i \(0.243372\pi\)
−0.610443 + 0.792060i \(0.709008\pi\)
\(458\) 0.379298 + 0.116998i 0.0177234 + 0.00546695i
\(459\) 0 0
\(460\) −49.7691 + 28.7342i −2.32050 + 1.33974i
\(461\) 3.77229 + 16.5275i 0.175693 + 0.769762i 0.983587 + 0.180434i \(0.0577502\pi\)
−0.807894 + 0.589328i \(0.799393\pi\)
\(462\) 0 0
\(463\) 5.33414 23.3704i 0.247899 1.08612i −0.685725 0.727860i \(-0.740515\pi\)
0.933624 0.358255i \(-0.116628\pi\)
\(464\) −13.8405 44.8698i −0.642529 2.08303i
\(465\) 0 0
\(466\) −20.6861 52.7072i −0.958263 2.44161i
\(467\) 14.6360 4.51462i 0.677275 0.208912i 0.0630118 0.998013i \(-0.479929\pi\)
0.614263 + 0.789101i \(0.289453\pi\)
\(468\) 0 0
\(469\) −4.74855 36.2376i −0.219268 1.67330i
\(470\) 22.8314 5.21111i 1.05313 0.240370i
\(471\) 0 0
\(472\) −76.9104 44.4042i −3.54009 2.04387i
\(473\) −3.61143 + 11.7080i −0.166054 + 0.538333i
\(474\) 0 0
\(475\) −10.6106 8.46165i −0.486846 0.388247i
\(476\) −29.4168 12.2056i −1.34832 0.559444i
\(477\) 0 0
\(478\) 17.2471 16.0030i 0.788865 0.731960i
\(479\) −12.0884 + 1.82203i −0.552331 + 0.0832506i −0.419277 0.907858i \(-0.637716\pi\)
−0.133054 + 0.991109i \(0.542478\pi\)
\(480\) 0 0
\(481\) 3.01393 19.9962i 0.137424 0.911746i
\(482\) −21.4211 + 10.3158i −0.975702 + 0.469873i
\(483\) 0 0
\(484\) −9.16231 4.41233i −0.416468 0.200561i
\(485\) −1.37191 + 2.01222i −0.0622950 + 0.0913700i
\(486\) 0 0
\(487\) −1.41790 + 18.9206i −0.0642513 + 0.857374i 0.868231 + 0.496160i \(0.165257\pi\)
−0.932483 + 0.361215i \(0.882362\pi\)
\(488\) −18.8748 + 48.0922i −0.854422 + 2.17703i
\(489\) 0 0
\(490\) −31.1369 + 10.8531i −1.40662 + 0.490295i
\(491\) 40.3477i 1.82087i 0.413654 + 0.910434i \(0.364252\pi\)
−0.413654 + 0.910434i \(0.635748\pi\)
\(492\) 0 0
\(493\) 10.8625 + 0.814034i 0.489224 + 0.0366623i
\(494\) −47.7695 + 51.4832i −2.14925 + 2.31634i
\(495\) 0 0
\(496\) 30.8502 64.0611i 1.38522 2.87643i
\(497\) −2.98565 + 1.36746i −0.133925 + 0.0613390i
\(498\) 0 0
\(499\) −4.49533 0.677562i −0.201239 0.0303318i 0.0476494 0.998864i \(-0.484827\pi\)
−0.248888 + 0.968532i \(0.580065\pi\)
\(500\) −49.6292 + 33.8366i −2.21949 + 1.51322i
\(501\) 0 0
\(502\) −21.3747 23.0364i −0.953998 1.02817i
\(503\) 1.74258 + 2.18513i 0.0776980 + 0.0974302i 0.819161 0.573563i \(-0.194439\pi\)
−0.741463 + 0.670993i \(0.765868\pi\)
\(504\) 0 0
\(505\) 9.64281 12.0917i 0.429099 0.538074i
\(506\) 61.7705 4.62906i 2.74603 0.205787i
\(507\) 0 0
\(508\) −31.2187 + 54.0724i −1.38511 + 2.39908i
\(509\) −0.169361 0.293342i −0.00750680 0.0130022i 0.862248 0.506487i \(-0.169056\pi\)
−0.869754 + 0.493485i \(0.835723\pi\)
\(510\) 0 0
\(511\) 12.0361 19.9477i 0.532445 0.882436i
\(512\) 33.5686 + 7.66181i 1.48354 + 0.338607i
\(513\) 0 0
\(514\) 31.5160 12.3691i 1.39011 0.545579i
\(515\) 24.7902 9.72945i 1.09239 0.428731i
\(516\) 0 0
\(517\) −17.5153 3.99775i −0.770321 0.175821i
\(518\) −20.5678 + 34.0876i −0.903698 + 1.49772i
\(519\) 0 0
\(520\) 24.4952 + 42.4270i 1.07419 + 1.86055i
\(521\) −1.73700 + 3.00857i −0.0760994 + 0.131808i −0.901564 0.432646i \(-0.857580\pi\)
0.825464 + 0.564454i \(0.190913\pi\)
\(522\) 0 0
\(523\) 16.9196 1.26795i 0.739844 0.0554436i 0.300524 0.953774i \(-0.402839\pi\)
0.439320 + 0.898331i \(0.355219\pi\)
\(524\) 25.7838 32.3319i 1.12637 1.41242i
\(525\) 0 0
\(526\) 2.76535 + 3.46763i 0.120575 + 0.151196i
\(527\) 11.2192 + 12.0914i 0.488715 + 0.526709i
\(528\) 0 0
\(529\) −15.9862 + 10.8992i −0.695050 + 0.473877i
\(530\) −21.9489 3.30826i −0.953399 0.143702i
\(531\) 0 0
\(532\) 89.4720 40.9792i 3.87910 1.77667i
\(533\) 6.02645 12.5141i 0.261035 0.542044i
\(534\) 0 0
\(535\) 18.2249 19.6418i 0.787932 0.849189i
\(536\) 106.603 + 7.98877i 4.60454 + 0.345062i
\(537\) 0 0
\(538\) 55.1188i 2.37634i
\(539\) 25.1340 + 2.86261i 1.08260 + 0.123301i
\(540\) 0 0
\(541\) 11.8096 30.0905i 0.507736 1.29369i −0.415547 0.909572i \(-0.636410\pi\)
0.923283 0.384119i \(-0.125495\pi\)
\(542\) −3.84088 + 51.2529i −0.164980 + 2.20150i
\(543\) 0 0
\(544\) 16.7547 24.5747i 0.718354 1.05363i
\(545\) 24.8540 + 11.9690i 1.06463 + 0.512698i
\(546\) 0 0
\(547\) 6.87858 3.31255i 0.294107 0.141634i −0.281012 0.959704i \(-0.590670\pi\)
0.575119 + 0.818070i \(0.304956\pi\)
\(548\) 4.45454 29.5539i 0.190288 1.26248i
\(549\) 0 0
\(550\) 16.9587 2.55611i 0.723121 0.108993i
\(551\) −24.6736 + 22.8937i −1.05113 + 0.975306i
\(552\) 0 0
\(553\) 25.6130 + 10.6274i 1.08918 + 0.451921i
\(554\) 8.99211 + 7.17096i 0.382038 + 0.304665i
\(555\) 0 0
\(556\) −16.6954 + 54.1253i −0.708045 + 2.29542i
\(557\) −30.3332 17.5129i −1.28526 0.742044i −0.307454 0.951563i \(-0.599477\pi\)
−0.977805 + 0.209519i \(0.932810\pi\)
\(558\) 0 0
\(559\) −11.7005 + 2.67057i −0.494880 + 0.112953i
\(560\) −6.46010 49.2990i −0.272989 2.08326i
\(561\) 0 0
\(562\) 40.8195 12.5911i 1.72187 0.531125i
\(563\) 9.58141 + 24.4130i 0.403808 + 1.02889i 0.977710 + 0.209962i \(0.0673340\pi\)
−0.573901 + 0.818924i \(0.694571\pi\)
\(564\) 0 0
\(565\) 1.66878 + 5.41006i 0.0702062 + 0.227603i
\(566\) 10.5181 46.0827i 0.442108 1.93700i
\(567\) 0 0
\(568\) −2.13742 9.36464i −0.0896841 0.392932i
\(569\) −24.4831 + 14.1353i −1.02638 + 0.592583i −0.915946 0.401301i \(-0.868558\pi\)
−0.110437 + 0.993883i \(0.535225\pi\)
\(570\) 0 0
\(571\) −26.3016 8.11296i −1.10069 0.339517i −0.309381 0.950938i \(-0.600122\pi\)
−0.791305 + 0.611421i \(0.790598\pi\)
\(572\) −4.72052 62.9909i −0.197375 2.63378i
\(573\) 0 0
\(574\) −20.4006 + 18.2090i −0.851504 + 0.760028i
\(575\) −9.16686 + 7.31032i −0.382284 + 0.304862i
\(576\) 0 0
\(577\) −1.40499 9.32147i −0.0584903 0.388058i −0.998853 0.0478841i \(-0.984752\pi\)
0.940363 0.340174i \(-0.110486\pi\)
\(578\) −16.4070 24.0647i −0.682443 1.00096i
\(579\) 0 0
\(580\) 17.1217 + 35.5537i 0.710942 + 1.47629i
\(581\) 0.714637 37.0179i 0.0296481 1.53576i
\(582\) 0 0
\(583\) 14.0696 + 9.59249i 0.582703 + 0.397280i
\(584\) 49.9545 + 46.3510i 2.06713 + 1.91802i
\(585\) 0 0
\(586\) 80.8124 + 31.7165i 3.33833 + 1.31020i
\(587\) −4.59513 −0.189661 −0.0948306 0.995493i \(-0.530231\pi\)
−0.0948306 + 0.995493i \(0.530231\pi\)
\(588\) 0 0
\(589\) −50.9673 −2.10007
\(590\) 50.3204 + 19.7493i 2.07166 + 0.813066i
\(591\) 0 0
\(592\) −44.0058 40.8314i −1.80863 1.67816i
\(593\) −21.5535 14.6949i −0.885097 0.603449i 0.0331531 0.999450i \(-0.489445\pi\)
−0.918250 + 0.396002i \(0.870397\pi\)
\(594\) 0 0
\(595\) 11.1935 + 2.78320i 0.458888 + 0.114100i
\(596\) 27.0256 + 56.1193i 1.10701 + 2.29874i
\(597\) 0 0
\(598\) 34.1797 + 50.1324i 1.39771 + 2.05007i
\(599\) −4.85200 32.1909i −0.198247 1.31528i −0.837563 0.546341i \(-0.816020\pi\)
0.639316 0.768944i \(-0.279218\pi\)
\(600\) 0 0
\(601\) 1.15697 0.922654i 0.0471938 0.0376358i −0.599609 0.800293i \(-0.704677\pi\)
0.646803 + 0.762657i \(0.276106\pi\)
\(602\) 23.2916 + 3.97185i 0.949294 + 0.161880i
\(603\) 0 0
\(604\) 0.683520 + 9.12094i 0.0278120 + 0.371126i
\(605\) 3.51934 + 1.08557i 0.143081 + 0.0441348i
\(606\) 0 0
\(607\) 16.0586 9.27142i 0.651797 0.376315i −0.137347 0.990523i \(-0.543858\pi\)
0.789144 + 0.614208i \(0.210524\pi\)
\(608\) 20.4505 + 89.5995i 0.829377 + 3.63374i
\(609\) 0 0
\(610\) 6.99767 30.6588i 0.283327 1.24134i
\(611\) −5.18707 16.8161i −0.209846 0.680305i
\(612\) 0 0
\(613\) 9.73929 + 24.8153i 0.393366 + 1.00228i 0.981147 + 0.193261i \(0.0619063\pi\)
−0.587781 + 0.809020i \(0.699998\pi\)
\(614\) −15.5547 + 4.79800i −0.627738 + 0.193631i
\(615\) 0 0
\(616\) −23.1703 + 70.2711i −0.933559 + 2.83130i
\(617\) 26.1918 5.97810i 1.05444 0.240669i 0.340043 0.940410i \(-0.389558\pi\)
0.714397 + 0.699741i \(0.246701\pi\)
\(618\) 0 0
\(619\) 1.76710 + 1.02024i 0.0710259 + 0.0410068i 0.535092 0.844794i \(-0.320277\pi\)
−0.464066 + 0.885800i \(0.653610\pi\)
\(620\) −17.6129 + 57.0995i −0.707350 + 2.29317i
\(621\) 0 0
\(622\) −17.5288 13.9788i −0.702842 0.560497i
\(623\) 16.4732 9.09143i 0.659983 0.364241i
\(624\) 0 0
\(625\) 9.34282 8.66887i 0.373713 0.346755i
\(626\) −61.1488 + 9.21670i −2.44400 + 0.368374i
\(627\) 0 0
\(628\) 7.34671 48.7422i 0.293166 1.94503i
\(629\) 12.5471 6.04235i 0.500284 0.240924i
\(630\) 0 0
\(631\) −3.10135 1.49353i −0.123463 0.0594565i 0.371133 0.928580i \(-0.378969\pi\)
−0.494595 + 0.869123i \(0.664684\pi\)
\(632\) −45.6917 + 67.0174i −1.81752 + 2.66581i
\(633\) 0 0
\(634\) 1.02887 13.7293i 0.0408616 0.545260i
\(635\) 8.26125 21.0493i 0.327838 0.835317i
\(636\) 0 0
\(637\) 9.88134 + 22.7230i 0.391513 + 0.900317i
\(638\) 42.5346i 1.68396i
\(639\) 0 0
\(640\) 8.72392 + 0.653768i 0.344843 + 0.0258424i
\(641\) 10.0345 10.8146i 0.396340 0.427153i −0.503079 0.864240i \(-0.667800\pi\)
0.899419 + 0.437088i \(0.143990\pi\)
\(642\) 0 0
\(643\) 12.4660 25.8858i 0.491609 1.02084i −0.496636 0.867959i \(-0.665432\pi\)
0.988245 0.152878i \(-0.0488542\pi\)
\(644\) −17.3153 83.2381i −0.682320 3.28004i
\(645\) 0 0
\(646\) −47.8257 7.20856i −1.88168 0.283617i
\(647\) −14.3926 + 9.81273i −0.565833 + 0.385778i −0.812183 0.583403i \(-0.801721\pi\)
0.246350 + 0.969181i \(0.420769\pi\)
\(648\) 0 0
\(649\) −28.2071 30.4000i −1.10722 1.19330i
\(650\) 10.4741 + 13.1341i 0.410827 + 0.515161i
\(651\) 0 0
\(652\) −33.5806 + 42.1087i −1.31512 + 1.64910i
\(653\) 16.6668 1.24900i 0.652220 0.0488772i 0.255489 0.966812i \(-0.417763\pi\)
0.396731 + 0.917935i \(0.370144\pi\)
\(654\) 0 0
\(655\) −7.48842 + 12.9703i −0.292597 + 0.506792i
\(656\) −20.6162 35.7084i −0.804929 1.39418i
\(657\) 0 0
\(658\) −3.25545 + 34.4925i −0.126911 + 1.34466i
\(659\) −34.9386 7.97450i −1.36101 0.310643i −0.521162 0.853458i \(-0.674501\pi\)
−0.839852 + 0.542815i \(0.817358\pi\)
\(660\) 0 0
\(661\) −43.5575 + 17.0950i −1.69419 + 0.664920i −0.998568 0.0534897i \(-0.982966\pi\)
−0.695620 + 0.718410i \(0.744870\pi\)
\(662\) 6.97291 2.73666i 0.271010 0.106363i
\(663\) 0 0
\(664\) 105.583 + 24.0986i 4.09741 + 0.935207i
\(665\) −29.8295 + 19.5048i −1.15674 + 0.756363i
\(666\) 0 0
\(667\) 14.5395 + 25.1831i 0.562971 + 0.975095i
\(668\) −47.0884 + 81.5595i −1.82190 + 3.15563i
\(669\) 0 0
\(670\) −64.8884 + 4.86272i −2.50686 + 0.187863i
\(671\) −15.0417 + 18.8617i −0.580679 + 0.728149i
\(672\) 0 0
\(673\) 21.7277 + 27.2457i 0.837542 + 1.05024i 0.998001 + 0.0632019i \(0.0201312\pi\)
−0.160459 + 0.987043i \(0.551297\pi\)
\(674\) −7.44754 8.02654i −0.286869 0.309171i
\(675\) 0 0
\(676\) −1.91719 + 1.30712i −0.0737380 + 0.0502737i
\(677\) 24.5223 + 3.69615i 0.942470 + 0.142054i 0.602264 0.798297i \(-0.294265\pi\)
0.340205 + 0.940351i \(0.389503\pi\)
\(678\) 0 0
\(679\) −2.19163 2.85975i −0.0841069 0.109747i
\(680\) −14.6384 + 30.3969i −0.561356 + 1.16567i
\(681\) 0 0
\(682\) 43.8082 47.2140i 1.67750 1.80792i
\(683\) 16.4540 + 1.23306i 0.629596 + 0.0471817i 0.385707 0.922622i \(-0.373958\pi\)
0.243889 + 0.969803i \(0.421577\pi\)
\(684\) 0 0
\(685\) 10.8242i 0.413571i
\(686\) −0.823972 48.7757i −0.0314594 1.86227i
\(687\) 0 0
\(688\) −13.0162 + 33.1646i −0.496236 + 1.26439i
\(689\) −1.24649 + 16.6332i −0.0474873 + 0.633675i
\(690\) 0 0
\(691\) 1.14649 1.68159i 0.0436146 0.0639709i −0.803812 0.594883i \(-0.797198\pi\)
0.847427 + 0.530912i \(0.178151\pi\)
\(692\) 79.1999 + 38.1407i 3.01073 + 1.44989i
\(693\) 0 0
\(694\) −25.1997 + 12.1355i −0.956568 + 0.460659i
\(695\) 3.05737 20.2843i 0.115973 0.769429i
\(696\) 0 0
\(697\) 9.45841 1.42563i 0.358263 0.0539994i
\(698\) 13.6822 12.6953i 0.517880 0.480522i
\(699\) 0 0
\(700\) −6.50289 22.6233i −0.245786 0.855080i
\(701\) −24.4713 19.5152i −0.924267 0.737079i 0.0407762 0.999168i \(-0.487017\pi\)
−0.965044 + 0.262090i \(0.915588\pi\)
\(702\) 0 0
\(703\) −12.6836 + 41.1194i −0.478373 + 1.55085i
\(704\) −34.8058 20.0951i −1.31179 0.757364i
\(705\) 0 0
\(706\) 70.0830 15.9960i 2.63761 0.602017i
\(707\) 12.5218 + 19.1500i 0.470929 + 0.720211i
\(708\) 0 0
\(709\) −17.2167 + 5.31064i −0.646586 + 0.199445i −0.600666 0.799500i \(-0.705098\pi\)
−0.0459197 + 0.998945i \(0.514622\pi\)
\(710\) 2.13607 + 5.44262i 0.0801654 + 0.204258i
\(711\) 0 0
\(712\) 16.2219 + 52.5902i 0.607943 + 1.97090i
\(713\) −9.79815 + 42.9285i −0.366944 + 1.60769i
\(714\) 0 0
\(715\) 5.09058 + 22.3033i 0.190377 + 0.834095i
\(716\) 68.8466 39.7486i 2.57292 1.48548i
\(717\) 0 0
\(718\) −34.2300 10.5586i −1.27745 0.394042i
\(719\) 1.58598 + 21.1634i 0.0591471 + 0.789263i 0.945369 + 0.326002i \(0.105702\pi\)
−0.886222 + 0.463261i \(0.846679\pi\)
\(720\) 0 0
\(721\) 2.18539 + 39.3380i 0.0813880 + 1.46502i
\(722\) 77.7151 61.9758i 2.89226 2.30650i
\(723\) 0 0
\(724\) −1.15424 7.65786i −0.0428968 0.284602i
\(725\) 4.53532 + 6.65209i 0.168437 + 0.247052i
\(726\) 0 0
\(727\) −3.87602 8.04863i −0.143753 0.298507i 0.816644 0.577142i \(-0.195832\pi\)
−0.960397 + 0.278635i \(0.910118\pi\)
\(728\) −70.9585 + 14.7609i −2.62990 + 0.547076i
\(729\) 0 0
\(730\) −34.2724 23.3665i −1.26848 0.864834i
\(731\) −6.05865 5.62160i −0.224087 0.207923i
\(732\) 0 0
\(733\) −10.5663 4.14695i −0.390274 0.153171i 0.162087 0.986777i \(-0.448178\pi\)
−0.552360 + 0.833605i \(0.686273\pi\)
\(734\) −79.3552 −2.92905
\(735\) 0 0
\(736\) 79.3989 2.92668
\(737\) 46.4686 + 18.2376i 1.71169 + 0.671790i
\(738\) 0 0
\(739\) −16.4690 15.2810i −0.605823 0.562121i 0.316475 0.948601i \(-0.397501\pi\)
−0.922298 + 0.386479i \(0.873691\pi\)
\(740\) 41.6836 + 28.4194i 1.53232 + 1.04472i
\(741\) 0 0
\(742\) 14.8165 29.3059i 0.543930 1.07585i
\(743\) −15.4681 32.1198i −0.567468 1.17836i −0.965358 0.260927i \(-0.915972\pi\)
0.397890 0.917433i \(-0.369743\pi\)
\(744\) 0 0
\(745\) −12.7075 18.6385i −0.465567 0.682861i
\(746\) −2.95367 19.5963i −0.108142 0.717472i
\(747\) 0 0
\(748\) 34.0106 27.1226i 1.24355 0.991700i
\(749\) 19.1539 + 34.7058i 0.699868 + 1.26812i
\(750\) 0 0
\(751\) 2.28540 + 30.4966i 0.0833955 + 1.11283i 0.869233 + 0.494402i \(0.164613\pi\)
−0.785838 + 0.618433i \(0.787768\pi\)
\(752\) −49.9201 15.3983i −1.82040 0.561519i
\(753\) 0 0
\(754\) 36.0818 20.8319i 1.31402 0.758652i
\(755\) −0.737105 3.22947i −0.0268260 0.117532i
\(756\) 0 0
\(757\) −4.69912 + 20.5882i −0.170793 + 0.748291i 0.814881 + 0.579628i \(0.196802\pi\)
−0.985674 + 0.168663i \(0.946055\pi\)
\(758\) 3.27679 + 10.6231i 0.119018 + 0.385848i
\(759\) 0 0
\(760\) −38.0863 97.0422i −1.38153 3.52009i
\(761\) 21.1016 6.50898i 0.764932 0.235950i 0.112350 0.993669i \(-0.464162\pi\)
0.652582 + 0.757718i \(0.273686\pi\)
\(762\) 0 0
\(763\) −28.3308 + 29.3753i −1.02565 + 1.06346i
\(764\) 35.4093 8.08194i 1.28106 0.292394i
\(765\) 0 0
\(766\) 9.78395 + 5.64876i 0.353508 + 0.204098i
\(767\) 11.9734 38.8167i 0.432333 1.40159i
\(768\) 0 0
\(769\) 28.0841 + 22.3963i 1.01274 + 0.807632i 0.981419 0.191878i \(-0.0614577\pi\)
0.0313193 + 0.999509i \(0.490029\pi\)
\(770\) 7.57104 44.3979i 0.272841 1.59999i
\(771\) 0 0
\(772\) 7.56710 7.02124i 0.272346 0.252700i
\(773\) 17.7403 2.67391i 0.638072 0.0961740i 0.177964 0.984037i \(-0.443049\pi\)
0.460108 + 0.887863i \(0.347811\pi\)
\(774\) 0 0
\(775\) −1.81700 + 12.0550i −0.0652687 + 0.433030i
\(776\) 9.49508 4.57259i 0.340853 0.164146i
\(777\) 0 0
\(778\) 30.9816 + 14.9199i 1.11074 + 0.534906i
\(779\) −16.6495 + 24.4203i −0.596531 + 0.874950i
\(780\) 0 0
\(781\) 0.335196 4.47288i 0.0119943 0.160052i
\(782\) −15.2658 + 38.8966i −0.545903 + 1.39094i
\(783\) 0 0
\(784\) 72.2585 + 13.7623i 2.58066 + 0.491511i
\(785\) 17.8520i 0.637164i
\(786\) 0 0
\(787\) 15.8280 + 1.18614i 0.564206 + 0.0422814i 0.353780 0.935329i \(-0.384896\pi\)
0.210426 + 0.977610i \(0.432515\pi\)
\(788\) 20.6085 22.2107i 0.734149