Properties

Label 441.2.bg.a.278.1
Level $441$
Weight $2$
Character 441.278
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 278.1
Character \(\chi\) \(=\) 441.278
Dual form 441.2.bg.a.395.1

$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{41}{42}\right)\) \(-1\)

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 −0.733782 + 0.679385i \(0.762247\pi\)
−0.999999 + 0.00107413i \(0.999658\pi\)
\(3\) 0 0
\(4\) 3.61984 3.35872i 1.80992 1.67936i
\(5\) 1.47762 1.00742i 0.660812 0.450534i −0.185912 0.982566i \(-0.559524\pi\)
0.846724 + 0.532032i \(0.178572\pi\)
\(6\) 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 0.748004 + 0.663695i \(0.231013\pi\)
−0.910399 + 0.413731i \(0.864226\pi\)
\(12\) 0 0
\(13\) −2.76752 2.20702i −0.767571 0.612118i 0.159415 0.987212i \(-0.449039\pi\)
−0.926987 + 0.375094i \(0.877610\pi\)
\(14\) −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 \(-0.499713\pi\)
0.564066 + 0.825730i \(0.309236\pi\)
\(18\) 0 0
\(19\) 6.52328 + 3.76622i 1.49654 + 0.864030i 0.999992 0.00397809i \(-0.00126627\pi\)
0.496551 + 0.868008i \(0.334600\pi\)
\(20\) 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 −0.502022 0.864855i \(-0.667410\pi\)
0.901980 0.431778i \(-0.142113\pi\)
\(24\) 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 \(-0.292391\pi\)
0.202023 + 0.979381i \(0.435249\pi\)
\(30\) 0 0
\(31\) −5.85986 + 3.38319i −1.05246 + 0.607639i −0.923337 0.383990i \(-0.874550\pi\)
−0.129124 + 0.991628i \(0.541216\pi\)
\(32\) 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 0.256283 0.966602i \(-0.417502\pi\)
−0.944747 + 0.327801i \(0.893692\pi\)
\(38\) −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 \(-0.258018\pi\)
−0.136958 + 0.990577i \(0.543733\pi\)
\(42\) 0 0
\(43\) 3.05468 1.47106i 0.465834 0.224334i −0.186217 0.982509i \(-0.559623\pi\)
0.652052 + 0.758175i \(0.273909\pi\)
\(44\) 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 \(-0.000943454\pi\)
−0.735065 + 0.677997i \(0.762848\pi\)
\(48\) 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 \(-0.342998\pi\)
−0.913725 + 0.406332i \(0.866808\pi\)
\(54\) 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 \(-0.0410168\pi\)
0.242693 + 0.970103i \(0.421969\pi\)
\(60\) 0 0
\(61\) 4.54073 4.89374i 0.581381 0.626580i −0.372042 0.928216i \(-0.621342\pi\)
0.953423 + 0.301636i \(0.0975328\pi\)
\(62\) 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 0.886658 + 0.462425i \(0.153020\pi\)
−0.0428576 + 0.999081i \(0.513646\pi\)
\(68\) 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 \(-0.547963\pi\)
0.293722 + 0.955891i \(0.405106\pi\)
\(72\) 0 0
\(73\) 8.19697 + 3.21707i 0.959383 + 0.376530i 0.792790 0.609495i \(-0.208628\pi\)
0.166594 + 0.986026i \(0.446723\pi\)
\(74\) 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 −0.404678 0.914459i \(-0.632616\pi\)
0.994284 0.106768i \(-0.0340502\pi\)
\(80\) −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 −0.979557 0.201169i \(-0.935526\pi\)
0.0218467 0.999761i \(-0.493045\pi\)
\(84\) 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 \(-0.670633\pi\)
−0.234651 + 0.972080i \(0.575395\pi\)
\(90\) 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 \(0.0220238\pi\)
−0.997607 + 0.0691347i \(0.977976\pi\)
\(98\) −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 0.932336 + 0.361593i \(0.117767\pi\)
−0.868030 + 0.496512i \(0.834614\pi\)
\(102\) 0 0
\(103\) −8.38856 12.3038i −0.826550 1.21233i −0.974735 0.223366i \(-0.928295\pi\)
0.148185 0.988960i \(-0.452657\pi\)
\(104\) 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 0.789811 + 0.613350i \(0.210178\pi\)
−0.573934 + 0.818901i \(0.694584\pi\)
\(108\) 0 0
\(109\) −15.2528 2.29900i −1.46096 0.220204i −0.630024 0.776576i \(-0.716955\pi\)
−0.830934 + 0.556372i \(0.812193\pi\)
\(110\) −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 \(-0.666711\pi\)
0.732958 + 0.680274i \(0.238139\pi\)
\(114\) 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 −0.682232 0.731136i \(-0.738990\pi\)
0.931898 0.362722i \(-0.118152\pi\)
\(128\) 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 −0.900734 0.434371i \(-0.856971\pi\)
0.955413 0.295272i \(-0.0954104\pi\)
\(132\) 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 \(-0.726278\pi\)
0.943792 + 0.330540i \(0.107231\pi\)
\(138\) 0 0
\(139\) 4.97685 10.3345i 0.422131 0.876565i −0.576115 0.817369i \(-0.695432\pi\)
0.998246 0.0591961i \(-0.0188537\pi\)
\(140\) 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 \(-0.791881\pi\)
−0.168171 + 0.985758i \(0.553786\pi\)
\(150\) 0 0
\(151\) 1.35780 1.25985i 0.110496 0.102525i −0.622990 0.782230i \(-0.714082\pi\)
0.733486 + 0.679704i \(0.237892\pi\)
\(152\) −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 −0.982249 0.187580i \(-0.939936\pi\)
0.533469 + 0.845820i \(0.320888\pi\)
\(158\) −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 −0.869732 0.493525i \(-0.835708\pi\)
0.933574 0.358386i \(-0.116673\pi\)
\(164\) 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 0.493784 + 0.869585i \(0.335613\pi\)
−0.822183 + 0.569224i \(0.807244\pi\)
\(168\) 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 \(-0.641360\pi\)
−0.863664 + 0.504068i \(0.831836\pi\)
\(174\) 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 −0.940615 0.339476i \(-0.889750\pi\)
0.585939 0.810355i \(-0.300726\pi\)
\(180\) 0 0
\(181\) −1.22615 + 0.977821i −0.0911389 + 0.0726809i −0.667999 0.744162i \(-0.732849\pi\)
0.576860 + 0.816843i \(0.304278\pi\)
\(182\) 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 \(-0.276211\pi\)
−0.946348 + 0.323149i \(0.895259\pi\)
\(192\) 0 0
\(193\) 0.156219 + 2.08460i 0.0112449 + 0.150053i 1.00000 0.000508213i \(0.000161769\pi\)
−0.988755 + 0.149545i \(0.952219\pi\)
\(194\) −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 −0.894373 0.447322i \(-0.852378\pi\)
−0.817713 + 0.575625i \(0.804759\pi\)
\(200\) −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 0.905068 0.425268i \(-0.139820\pi\)
−0.616002 + 0.787745i \(0.711249\pi\)
\(212\) −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 −0.479399 0.877597i \(-0.659145\pi\)
−0.0511482 + 0.998691i \(0.516288\pi\)
\(224\) −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 \(-0.199087\pi\)
−0.912375 + 0.409356i \(0.865753\pi\)
\(228\) 0 0
\(229\) 0.150273 + 0.0112614i 0.00993034 + 0.000744176i 0.0796943 0.996819i \(-0.474606\pi\)
−0.0697640 + 0.997564i \(0.522225\pi\)
\(230\) 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 −0.0415891 0.999135i \(-0.513242\pi\)
0.999449 0.0331927i \(-0.0105675\pi\)
\(234\) 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 \(-0.236144\pi\)
−0.987899 + 0.155102i \(0.950430\pi\)
\(240\) 0 0
\(241\) −6.13948 6.61679i −0.395479 0.426225i 0.503651 0.863907i \(-0.331990\pi\)
−0.899130 + 0.437683i \(0.855799\pi\)
\(242\) 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 \(-0.519976\pi\)
0.741191 + 0.671295i \(0.234262\pi\)
\(252\) 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 \(-0.393204\pi\)
−0.916997 + 0.398893i \(0.869394\pi\)
\(258\) 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 \(-0.683199\pi\)
0.454366 + 0.890815i \(0.349866\pi\)
\(264\) 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 0.483795 + 0.875181i \(0.339258\pi\)
−0.949921 + 0.312489i \(0.898837\pi\)
\(270\) 0 0
\(271\) 5.75145 18.6458i 0.349376 1.13265i −0.594985 0.803737i \(-0.702842\pi\)
0.944361 0.328912i \(-0.106682\pi\)
\(272\) −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 −0.166858 0.985981i \(-0.553362\pi\)
0.417558 + 0.908650i \(0.362886\pi\)
\(278\) −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 \(-0.446432\pi\)
−0.923884 + 0.382673i \(0.875004\pi\)
\(282\) 0 0
\(283\) −2.67459 + 17.7447i −0.158988 + 1.05481i 0.756944 + 0.653480i \(0.226692\pi\)
−0.915932 + 0.401334i \(0.868547\pi\)
\(284\) 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 0.475840 0.879532i \(-0.342144\pi\)
−0.751596 + 0.659624i \(0.770715\pi\)
\(308\) −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 \(-0.517655\pi\)
0.516651 + 0.856196i \(0.327178\pi\)
\(312\) 0 0
\(313\) −20.3319 11.7386i −1.14923 0.663507i −0.200529 0.979688i \(-0.564266\pi\)
−0.948699 + 0.316181i \(0.897599\pi\)
\(314\) 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 \(-0.857869\pi\)
0.988488 + 0.151297i \(0.0483451\pi\)
\(318\) 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 0.735384 0.677650i \(-0.237002\pi\)
−0.620800 + 0.783969i \(0.713192\pi\)
\(332\) −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 −0.533103 0.846050i \(-0.678974\pi\)
0.329084 + 0.944301i \(0.393260\pi\)
\(338\) 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 \(-0.146096\pi\)
−0.508785 + 0.860894i \(0.669905\pi\)
\(348\) 0 0
\(349\) 3.07452 + 6.38430i 0.164575 + 0.341744i 0.966905 0.255137i \(-0.0821207\pi\)
−0.802330 + 0.596881i \(0.796406\pi\)
\(350\) 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 \(-0.568276\pi\)
−0.987306 + 0.158827i \(0.949229\pi\)
\(354\) 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 \(-0.359350\pi\)
0.288123 + 0.957593i \(0.406969\pi\)
\(360\) 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 −0.506235 0.862395i \(-0.668963\pi\)
−0.957675 + 0.287853i \(0.907059\pi\)
\(368\) −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 −0.946829 0.321737i \(-0.895733\pi\)
0.752047 + 0.659110i \(0.229067\pi\)
\(374\) −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 −0.709640 0.704564i \(-0.751142\pi\)
0.844809 + 0.535067i \(0.179714\pi\)
\(380\) 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 \(-0.582570\pi\)
0.0397876 + 0.999208i \(0.487332\pi\)
\(384\) 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 \(-0.631181\pi\)
−0.259512 + 0.965740i \(0.583562\pi\)
\(390\) 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 0.943851 + 0.330372i \(0.107174\pi\)
−0.0372929 + 0.999304i \(0.511873\pi\)
\(398\) 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 \(-0.0468302\pi\)
−0.988458 + 0.151492i \(0.951592\pi\)
\(402\) 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 0.916898 0.399122i \(-0.130685\pi\)
−0.982410 + 0.186737i \(0.940209\pi\)
\(410\) −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 −0.993375 0.114921i \(-0.963339\pi\)
0.845137 0.534549i \(-0.179519\pi\)
\(420\) 0 0
\(421\) 5.61051 24.5813i 0.273440 1.19802i −0.632483 0.774574i \(-0.717964\pi\)
0.905923 0.423443i \(-0.139179\pi\)
\(422\) −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 \(-0.703761\pi\)
0.964794 + 0.263005i \(0.0847135\pi\)
\(432\) 0 0
\(433\) −6.37412 + 13.2360i −0.306321 + 0.636081i −0.996128 0.0879115i \(-0.971981\pi\)
0.689808 + 0.723993i \(0.257695\pi\)
\(434\) 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 −0.378960 0.925413i \(-0.623718\pi\)
0.351644 + 0.936134i \(0.385623\pi\)
\(440\) −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 \(-0.502653\pi\)
0.674039 + 0.738696i \(0.264558\pi\)
\(444\) 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 \(-0.808602\pi\)
0.956422 + 0.291988i \(0.0943167\pi\)
\(450\) 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 −0.610443 0.792060i \(-0.709008\pi\)
0.721675 0.692232i \(-0.243372\pi\)
\(458\) −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 0.807894 + 0.589328i \(0.200607\pi\)
−0.983587 + 0.180434i \(0.942250\pi\)
\(462\) 0 0
\(463\) 5.33414 + 23.3704i 0.247899 + 1.08612i 0.933624 + 0.358255i \(0.116628\pi\)
−0.685725 + 0.727860i \(0.740515\pi\)
\(464\) 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 \(-0.520071\pi\)
−0.614263 + 0.789101i \(0.710547\pi\)
\(468\) 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 \(-0.362284\pi\)
0.133054 + 0.991109i \(0.457522\pi\)
\(480\) 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 −0.932483 0.361215i \(-0.882362\pi\)
0.868231 0.496160i \(-0.165257\pi\)
\(488\) 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 −0.248888 0.968532i \(-0.580065\pi\)
0.0476494 + 0.998864i \(0.484827\pi\)
\(500\) 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 \(-0.805561\pi\)
0.741463 + 0.670993i \(0.234132\pi\)
\(504\) 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 \(-0.830944\pi\)
0.869754 + 0.493485i \(0.164277\pi\)
\(510\) 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 \(-0.142420\pi\)
−0.825464 + 0.564454i \(0.809087\pi\)
\(522\) 0 0
\(523\) 16.9196 + 1.26795i 0.739844 + 0.0554436i 0.439320 0.898331i \(-0.355219\pi\)
0.300524 + 0.953774i \(0.402839\pi\)
\(524\) −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 0.923283 + 0.384119i \(0.125495\pi\)
−0.415547 + 0.909572i \(0.636410\pi\)
\(542\) 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 0.575119 0.818070i \(-0.304956\pi\)
−0.281012 + 0.959704i \(0.590670\pi\)
\(548\) −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 \(-0.400523\pi\)
0.977805 + 0.209519i \(0.0671898\pi\)
\(558\) 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 0.573901 + 0.818924i \(0.305429\pi\)
−0.977710 + 0.209962i \(0.932666\pi\)
\(564\) 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 \(-0.131442\pi\)
0.110437 + 0.993883i \(0.464775\pi\)
\(570\) 0 0
\(571\) −26.3016 + 8.11296i −1.10069 + 0.339517i −0.791305 0.611421i \(-0.790598\pi\)
−0.309381 + 0.950938i \(0.600122\pi\)
\(572\) 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 0.940363 + 0.340174i \(0.110486\pi\)
−0.998853 + 0.0478841i \(0.984752\pi\)
\(578\) 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 −0.0331531 0.999450i \(-0.510555\pi\)
0.918250 + 0.396002i \(0.129603\pi\)
\(594\) 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 −0.639316 0.768944i \(-0.720782\pi\)
0.837563 0.546341i \(-0.183980\pi\)
\(600\) 0 0
\(601\) 1.15697 + 0.922654i 0.0471938 + 0.0376358i 0.646803 0.762657i \(-0.276106\pi\)
−0.599609 + 0.800293i \(0.704677\pi\)
\(602\) −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 0.789144 0.614208i \(-0.210524\pi\)
−0.137347 + 0.990523i \(0.543858\pi\)
\(608\) −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 −0.587781 0.809020i \(-0.699998\pi\)
0.981147 0.193261i \(-0.0619063\pi\)
\(614\) 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 \(-0.610442\pi\)
−0.714397 + 0.699741i \(0.753299\pi\)
\(618\) 0 0
\(619\) 1.76710 1.02024i 0.0710259 0.0410068i −0.464066 0.885800i \(-0.653610\pi\)
0.535092 + 0.844794i \(0.320277\pi\)
\(620\) 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 −0.494595 0.869123i \(-0.664684\pi\)
0.371133 + 0.928580i \(0.378969\pi\)
\(632\) 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 \(-0.332200\pi\)
−0.899419 + 0.437088i \(0.856010\pi\)
\(642\) 0 0
\(643\) 12.4660 + 25.8858i 0.491609 + 1.02084i 0.988245 + 0.152878i \(0.0488542\pi\)
−0.496636 + 0.867959i \(0.665432\pi\)
\(644\) 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 \(-0.198279\pi\)
−0.246350 + 0.969181i \(0.579231\pi\)
\(648\) 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 \(-0.582237\pi\)
−0.396731 + 0.917935i \(0.629856\pi\)
\(654\) 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 \(-0.325499\pi\)
0.839852 + 0.542815i \(0.182642\pi\)
\(660\) 0 0
\(661\) −43.5575 17.0950i −1.69419 0.664920i −0.695620 0.718410i \(-0.744870\pi\)
−0.998568 + 0.0534897i \(0.982966\pi\)
\(662\) −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 −0.160459 0.987043i \(-0.551297\pi\)
0.998001 0.0632019i \(-0.0201312\pi\)
\(674\) 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 \(-0.705735\pi\)
−0.340205 + 0.940351i \(0.610497\pi\)
\(678\) 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 \(-0.626042\pi\)
−0.243889 + 0.969803i \(0.578423\pi\)
\(684\) 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 0.847427 0.530912i \(-0.178151\pi\)
−0.803812 + 0.594883i \(0.797198\pi\)
\(692\) −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 \(-0.512983\pi\)
0.965044 + 0.262090i \(0.0844116\pi\)
\(702\) 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 −0.0459197 0.998945i \(-0.514622\pi\)
−0.600666 + 0.799500i \(0.705098\pi\)
\(710\) −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 0.886222 + 0.463261i \(0.153321\pi\)
−0.945369 + 0.326002i \(0.894298\pi\)
\(720\) 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 −0.960397 0.278635i \(-0.910118\pi\)
0.816644 + 0.577142i \(0.195832\pi\)
\(728\) 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 −0.552360 0.833605i \(-0.686273\pi\)
0.162087 + 0.986777i \(0.448178\pi\)
\(734\) 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 −0.922298 0.386479i \(-0.873691\pi\)
0.316475 + 0.948601i \(0.397501\pi\)
\(740\) −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 −0.397890 0.917433i \(-0.630257\pi\)
0.965358 0.260927i \(-0.0840283\pi\)
\(744\) 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 −0.785838 0.618433i \(-0.787768\pi\)
0.869233 0.494402i \(-0.164613\pi\)
\(752\) 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 −0.985674 0.168663i \(-0.946055\pi\)
0.814881 0.579628i \(-0.196802\pi\)
\(758\) −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 \(-0.535838\pi\)
−0.652582 + 0.757718i \(0.726314\pi\)
\(762\) 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 0.0313193 0.999509i \(-0.490029\pi\)
0.981419 + 0.191878i \(0.0614577\pi\)
\(770\) −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 \(-0.556951\pi\)
−0.460108 + 0.887863i \(0.652189\pi\)
\(774\) 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 0.210426 0.977610i \(-0.432515\pi\)
0.353780 + 0.935329i \(0.384896\pi\)
\(788\) −20.6085 22.2107i