Properties

Label 441.2.bg.a.395.1
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 395.1
Character \(\chi\) \(=\) 441.395
Dual form 441.2.bg.a.278.1

$q$-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 \(-0.999658\pi\)
−0.733782 0.679385i \(-0.762247\pi\)
\(3\) 0 0
\(4\) 3.61984 + 3.35872i 1.80992 + 1.67936i
\(5\) 1.47762 + 1.00742i 0.660812 + 0.450534i 0.846724 0.532032i \(-0.178572\pi\)
−0.185912 + 0.982566i \(0.559524\pi\)
\(6\) 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 \(-0.864226\pi\)
0.748004 0.663695i \(-0.231013\pi\)
\(12\) 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 0.564066 0.825730i \(-0.309236\pi\)
0.000902867 1.00000i \(0.499713\pi\)
\(18\) 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 \(0.142113\pi\)
−0.502022 + 0.864855i \(0.667410\pi\)
\(24\) 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 0.202023 0.979381i \(-0.435249\pi\)
0.606953 + 0.794737i \(0.292391\pi\)
\(30\) 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 −0.136958 0.990577i \(-0.543733\pi\)
0.689072 + 0.724693i \(0.258018\pi\)
\(42\) 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 −0.735065 0.677997i \(-0.762848\pi\)
0.999996 + 0.00296394i \(0.000943454\pi\)
\(48\) 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 −0.913725 0.406332i \(-0.866808\pi\)
0.473479 + 0.880805i \(0.342998\pi\)
\(54\) 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 0.242693 0.970103i \(-0.421969\pi\)
0.991709 + 0.128502i \(0.0410168\pi\)
\(60\) 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 0.293722 0.955891i \(-0.405106\pi\)
−0.150112 + 0.988669i \(0.547963\pi\)
\(72\) 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 \(0.493045\pi\)
−0.979557 + 0.201169i \(0.935526\pi\)
\(84\) 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 −0.234651 0.972080i \(-0.575395\pi\)
−0.510752 + 0.859728i \(0.670633\pi\)
\(90\) 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 \(-0.834614\pi\)
0.932336 0.361593i \(-0.117767\pi\)
\(102\) 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 \(-0.694584\pi\)
0.789811 0.613350i \(-0.210178\pi\)
\(108\) 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 0.732958 0.680274i \(-0.238139\pi\)
−0.500120 + 0.865956i \(0.666711\pi\)
\(114\) 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 \(0.0954104\pi\)
−0.900734 + 0.434371i \(0.856971\pi\)
\(132\) 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 0.943792 0.330540i \(-0.107231\pi\)
−0.652497 + 0.757791i \(0.726278\pi\)
\(138\) 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 −0.168171 0.985758i \(-0.553786\pi\)
−0.793763 + 0.608227i \(0.791881\pi\)
\(150\) 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 \(-0.807244\pi\)
0.493784 0.869585i \(-0.335613\pi\)
\(168\) 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 −0.863664 0.504068i \(-0.831836\pi\)
−0.429641 + 0.903000i \(0.641360\pi\)
\(174\) 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 \(0.300726\pi\)
−0.940615 + 0.339476i \(0.889750\pi\)
\(180\) 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 −0.946348 0.323149i \(-0.895259\pi\)
0.646551 + 0.762871i \(0.276211\pi\)
\(192\) 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 \(0.0701424\pi\)
−0.975819 + 0.218580i \(0.929858\pi\)
\(198\) 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 −0.912375 0.409356i \(-0.865753\pi\)
0.810700 + 0.585462i \(0.199087\pi\)
\(228\) 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 \(0.0105675\pi\)
−0.0415891 + 0.999135i \(0.513242\pi\)
\(234\) 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 −0.987899 0.155102i \(-0.950430\pi\)
0.737208 + 0.675666i \(0.236144\pi\)
\(240\) 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 0.741191 0.671295i \(-0.234262\pi\)
−0.0627146 + 0.998031i \(0.519976\pi\)
\(252\) 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 −0.916997 0.398893i \(-0.869394\pi\)
0.329251 + 0.944243i \(0.393204\pi\)
\(258\) 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 0.454366 0.890815i \(-0.349866\pi\)
−0.544286 + 0.838900i \(0.683199\pi\)
\(264\) 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 \(-0.898837\pi\)
0.483795 0.875181i \(-0.339258\pi\)
\(270\) 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 −0.923884 0.382673i \(-0.875004\pi\)
0.167495 + 0.985873i \(0.446432\pi\)
\(282\) 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 \(-0.912824\pi\)
−0.962731 + 0.270461i \(0.912824\pi\)
\(294\) 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 0.516651 0.856196i \(-0.327178\pi\)
−0.0554351 + 0.998462i \(0.517655\pi\)
\(312\) 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 0.988488 0.151297i \(-0.0483451\pi\)
−0.901956 + 0.431828i \(0.857869\pi\)
\(318\) 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 −0.508785 0.860894i \(-0.669905\pi\)
0.896508 + 0.443028i \(0.146096\pi\)
\(348\) 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 −0.987306 0.158827i \(-0.949229\pi\)
−0.212856 + 0.977084i \(0.568276\pi\)
\(354\) 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 0.288123 0.957593i \(-0.406969\pi\)
0.427627 + 0.903955i \(0.359350\pi\)
\(360\) 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 0.0397876 0.999208i \(-0.487332\pi\)
−0.256502 + 0.966544i \(0.582570\pi\)
\(384\) 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 −0.259512 0.965740i \(-0.583562\pi\)
−0.400549 + 0.916275i \(0.631181\pi\)
\(390\) 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 −0.988458 0.151492i \(-0.951592\pi\)
0.989197 + 0.146591i \(0.0468302\pi\)
\(402\) 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 \(0.179519\pi\)
−0.993375 + 0.114921i \(0.963339\pi\)
\(420\) 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 0.964794 0.263005i \(-0.0847135\pi\)
−0.597303 + 0.802015i \(0.703761\pi\)
\(432\) 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 0.674039 0.738696i \(-0.264558\pi\)
−0.00833484 + 0.999965i \(0.502653\pi\)
\(444\) 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 0.956422 0.291988i \(-0.0943167\pi\)
−0.824605 + 0.565709i \(0.808602\pi\)
\(450\) 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 \(-0.942250\pi\)
0.807894 0.589328i \(-0.200607\pi\)
\(462\) 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 −0.614263 0.789101i \(-0.710547\pi\)
−0.0630118 + 0.998013i \(0.520071\pi\)
\(468\) 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 0.133054 0.991109i \(-0.457522\pi\)
0.419277 + 0.907858i \(0.362284\pi\)
\(480\) 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 \(-0.635748\pi\)
0.413654 0.910434i \(-0.364252\pi\)
\(492\) 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 0.741463 0.670993i \(-0.234132\pi\)
−0.819161 + 0.573563i \(0.805561\pi\)
\(504\) 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 0.869754 0.493485i \(-0.164277\pi\)
−0.862248 + 0.506487i \(0.830944\pi\)
\(510\) 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 −0.825464 0.564454i \(-0.809087\pi\)
0.901564 + 0.432646i \(0.142420\pi\)
\(522\) 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 0.977805 0.209519i \(-0.0671898\pi\)
0.307454 + 0.951563i \(0.400523\pi\)
\(558\) 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 \(-0.932666\pi\)
0.573901 0.818924i \(-0.305429\pi\)
\(564\) 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 0.110437 0.993883i \(-0.464775\pi\)
0.915946 + 0.401301i \(0.131442\pi\)
\(570\) 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 \(-0.469769\pi\)
0.0948306 + 0.995493i \(0.469769\pi\)
\(588\) 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 0.918250 0.396002i \(-0.129603\pi\)
−0.0331531 + 0.999450i \(0.510555\pi\)
\(594\) 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 \(0.183980\pi\)
−0.639316 + 0.768944i \(0.720782\pi\)
\(600\) 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 −0.714397 0.699741i \(-0.753299\pi\)
−0.340043 + 0.940410i \(0.610442\pi\)
\(618\) 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 −0.899419 0.437088i \(-0.856010\pi\)
0.503079 + 0.864240i \(0.332200\pi\)
\(642\) 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 −0.246350 0.969181i \(-0.579231\pi\)
0.812183 + 0.583403i \(0.198279\pi\)
\(648\) 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 −0.396731 0.917935i \(-0.629856\pi\)
−0.255489 + 0.966812i \(0.582237\pi\)
\(654\) 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 0.839852 0.542815i \(-0.182642\pi\)
0.521162 + 0.853458i \(0.325499\pi\)
\(660\) 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 −0.340205 0.940351i \(-0.610497\pi\)
−0.602264 + 0.798297i \(0.705735\pi\)
\(678\) 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 −0.243889 0.969803i \(-0.578423\pi\)
−0.385707 + 0.922622i \(0.626042\pi\)
\(684\) 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 0.965044 0.262090i \(-0.0844116\pi\)
−0.0407762 + 0.999168i \(0.512983\pi\)
\(702\) 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 \(-0.894298\pi\)
0.886222 0.463261i \(-0.153321\pi\)
\(720\) 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 \(0.0840283\pi\)
−0.397890 + 0.917433i \(0.630257\pi\)
\(744\) 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 −0.652582 0.757718i \(-0.726314\pi\)
−0.112350 + 0.993669i \(0.535838\pi\)
\(762\) 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 −0.460108 0.887863i \(-0.652189\pi\)
−0.177964 + 0.984037i \(0.556951\pi\)
\(774\) 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 + 0.791224i