Properties

Label 349.2.e.a.123.13
Level 349
Weight 2
Character 349.123
Analytic conductor 2.787
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 349.e (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.78677903054\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 123.13
Character \(\chi\) = 349.123
Dual form 349.2.e.a.227.13

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.529073 + 0.305460i) q^{2} +(0.484492 - 0.839165i) q^{3} +(-0.813388 + 1.40883i) q^{4} +(-0.0329412 + 0.0570558i) q^{5} +0.591972i q^{6} +(-3.18284 + 1.83761i) q^{7} -2.21567i q^{8} +(1.03054 + 1.78494i) q^{9} +O(q^{10})\) \(q+(-0.529073 + 0.305460i) q^{2} +(0.484492 - 0.839165i) q^{3} +(-0.813388 + 1.40883i) q^{4} +(-0.0329412 + 0.0570558i) q^{5} +0.591972i q^{6} +(-3.18284 + 1.83761i) q^{7} -2.21567i q^{8} +(1.03054 + 1.78494i) q^{9} -0.0402489i q^{10} -2.60755i q^{11} +(0.788160 + 1.36513i) q^{12} +(-3.80680 + 2.19786i) q^{13} +(1.12264 - 1.94446i) q^{14} +(0.0319195 + 0.0552861i) q^{15} +(-0.949976 - 1.64541i) q^{16} -5.89706 q^{17} +(-1.09046 - 0.629575i) q^{18} +(-1.73717 + 3.00886i) q^{19} +(-0.0535879 - 0.0928170i) q^{20} +3.56124i q^{21} +(0.796504 + 1.37959i) q^{22} +(-0.241590 - 0.418446i) q^{23} +(-1.85931 - 1.07348i) q^{24} +(2.49783 + 4.32637i) q^{25} +(1.34271 - 2.32565i) q^{26} +4.90410 q^{27} -5.97877i q^{28} +(-1.77131 + 3.06800i) q^{29} +(-0.0337754 - 0.0195003i) q^{30} +2.61433 q^{31} +(4.84287 + 2.79603i) q^{32} +(-2.18817 - 1.26334i) q^{33} +(3.11997 - 1.80132i) q^{34} -0.242133i q^{35} -3.35290 q^{36} -10.1686 q^{37} -2.12254i q^{38} +4.25937i q^{39} +(0.126417 + 0.0729868i) q^{40} +0.703340 q^{41} +(-1.08782 - 1.88415i) q^{42} +(3.36545 + 1.94304i) q^{43} +(3.67360 + 2.12095i) q^{44} -0.135788 q^{45} +(0.255637 + 0.147592i) q^{46} +6.07101i q^{47} -1.84102 q^{48} +(3.25365 - 5.63549i) q^{49} +(-2.64307 - 1.52598i) q^{50} +(-2.85708 + 4.94860i) q^{51} -7.15084i q^{52} -8.09749i q^{53} +(-2.59462 + 1.49801i) q^{54} +(0.148776 + 0.0858958i) q^{55} +(4.07155 + 7.05213i) q^{56} +(1.68329 + 2.91554i) q^{57} -2.16426i q^{58} +(5.72348 + 3.30445i) q^{59} -0.103852 q^{60} -12.7178i q^{61} +(-1.38317 + 0.798574i) q^{62} +(-6.56006 - 3.78745i) q^{63} +0.383599 q^{64} -0.289600i q^{65} +1.54360 q^{66} +0.571467 q^{67} +(4.79660 - 8.30795i) q^{68} -0.468194 q^{69} +(0.0739619 + 0.128106i) q^{70} +(6.44742 - 3.72242i) q^{71} +(3.95484 - 2.28333i) q^{72} +(-0.720077 + 1.24721i) q^{73} +(5.37990 - 3.10609i) q^{74} +4.84071 q^{75} +(-2.82598 - 4.89474i) q^{76} +(4.79168 + 8.29943i) q^{77} +(-1.30107 - 2.25352i) q^{78} +2.78194i q^{79} +0.125173 q^{80} +(-0.715611 + 1.23947i) q^{81} +(-0.372118 + 0.214842i) q^{82} +(6.64377 + 11.5073i) q^{83} +(-5.01718 - 2.89667i) q^{84} +(0.194256 - 0.336461i) q^{85} -2.37409 q^{86} +(1.71637 + 2.97284i) q^{87} -5.77748 q^{88} +(11.2523 + 6.49654i) q^{89} +(0.0718418 - 0.0414779i) q^{90} +(8.07762 - 13.9908i) q^{91} +0.786026 q^{92} +(1.26662 - 2.19385i) q^{93} +(-1.85445 - 3.21201i) q^{94} +(-0.114449 - 0.198231i) q^{95} +(4.69266 - 2.70931i) q^{96} +(2.30308 - 1.32968i) q^{97} +3.97544i q^{98} +(4.65432 - 2.68718i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} + O(q^{10}) \) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} - q^{12} - 3q^{13} - 10q^{14} + q^{15} - 29q^{16} - 10q^{17} + 15q^{18} - 9q^{19} - 3q^{22} - 17q^{23} - 48q^{24} - 29q^{25} - 4q^{26} + 18q^{27} - 2q^{29} + 9q^{30} + 32q^{31} + 9q^{32} - 12q^{33} - 63q^{34} + 24q^{36} - 16q^{37} + 54q^{40} - 10q^{41} - 15q^{42} - 45q^{43} + 18q^{44} - 2q^{45} + 27q^{46} + 6q^{48} + 35q^{49} + 6q^{50} - 14q^{51} + 27q^{54} + 24q^{55} + 11q^{56} - 29q^{57} - 18q^{59} + 116q^{60} - 9q^{62} - 21q^{63} - 132q^{64} + 130q^{66} + 58q^{67} + 42q^{69} + 40q^{70} - 24q^{71} + 72q^{72} - 6q^{73} + 30q^{74} - 58q^{75} + 37q^{76} - 4q^{77} - 33q^{78} - 40q^{80} - 81q^{81} + 21q^{82} + 12q^{83} + 18q^{84} - 11q^{85} - 126q^{86} - 42q^{87} - 50q^{88} + 3q^{89} - 12q^{90} - 28q^{91} - 120q^{92} + 31q^{93} + 29q^{94} + 60q^{95} - 120q^{96} - 15q^{97} + 39q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.529073 + 0.305460i −0.374111 + 0.215993i −0.675253 0.737586i \(-0.735966\pi\)
0.301142 + 0.953579i \(0.402632\pi\)
\(3\) 0.484492 0.839165i 0.279722 0.484492i −0.691594 0.722287i \(-0.743091\pi\)
0.971315 + 0.237795i \(0.0764245\pi\)
\(4\) −0.813388 + 1.40883i −0.406694 + 0.704415i
\(5\) −0.0329412 + 0.0570558i −0.0147317 + 0.0255161i −0.873297 0.487188i \(-0.838023\pi\)
0.858566 + 0.512704i \(0.171356\pi\)
\(6\) 0.591972i 0.241672i
\(7\) −3.18284 + 1.83761i −1.20300 + 0.694553i −0.961221 0.275778i \(-0.911064\pi\)
−0.241780 + 0.970331i \(0.577731\pi\)
\(8\) 2.21567i 0.783358i
\(9\) 1.03054 + 1.78494i 0.343512 + 0.594980i
\(10\) 0.0402489i 0.0127278i
\(11\) 2.60755i 0.786207i −0.919494 0.393103i \(-0.871401\pi\)
0.919494 0.393103i \(-0.128599\pi\)
\(12\) 0.788160 + 1.36513i 0.227522 + 0.394080i
\(13\) −3.80680 + 2.19786i −1.05582 + 0.609575i −0.924272 0.381735i \(-0.875327\pi\)
−0.131544 + 0.991310i \(0.541993\pi\)
\(14\) 1.12264 1.94446i 0.300037 0.519680i
\(15\) 0.0319195 + 0.0552861i 0.00824157 + 0.0142748i
\(16\) −0.949976 1.64541i −0.237494 0.411352i
\(17\) −5.89706 −1.43025 −0.715124 0.698998i \(-0.753630\pi\)
−0.715124 + 0.698998i \(0.753630\pi\)
\(18\) −1.09046 0.629575i −0.257023 0.148392i
\(19\) −1.73717 + 3.00886i −0.398533 + 0.690280i −0.993545 0.113437i \(-0.963814\pi\)
0.595012 + 0.803717i \(0.297147\pi\)
\(20\) −0.0535879 0.0928170i −0.0119826 0.0207545i
\(21\) 3.56124i 0.777126i
\(22\) 0.796504 + 1.37959i 0.169815 + 0.294129i
\(23\) −0.241590 0.418446i −0.0503750 0.0872521i 0.839738 0.542991i \(-0.182708\pi\)
−0.890113 + 0.455739i \(0.849375\pi\)
\(24\) −1.85931 1.07348i −0.379531 0.219122i
\(25\) 2.49783 + 4.32637i 0.499566 + 0.865274i
\(26\) 1.34271 2.32565i 0.263328 0.456098i
\(27\) 4.90410 0.943794
\(28\) 5.97877i 1.12988i
\(29\) −1.77131 + 3.06800i −0.328924 + 0.569713i −0.982299 0.187322i \(-0.940019\pi\)
0.653375 + 0.757035i \(0.273353\pi\)
\(30\) −0.0337754 0.0195003i −0.00616652 0.00356024i
\(31\) 2.61433 0.469548 0.234774 0.972050i \(-0.424565\pi\)
0.234774 + 0.972050i \(0.424565\pi\)
\(32\) 4.84287 + 2.79603i 0.856106 + 0.494273i
\(33\) −2.18817 1.26334i −0.380911 0.219919i
\(34\) 3.11997 1.80132i 0.535071 0.308923i
\(35\) 0.242133i 0.0409279i
\(36\) −3.35290 −0.558817
\(37\) −10.1686 −1.67170 −0.835850 0.548958i \(-0.815025\pi\)
−0.835850 + 0.548958i \(0.815025\pi\)
\(38\) 2.12254i 0.344322i
\(39\) 4.25937i 0.682046i
\(40\) 0.126417 + 0.0729868i 0.0199883 + 0.0115402i
\(41\) 0.703340 0.109843 0.0549216 0.998491i \(-0.482509\pi\)
0.0549216 + 0.998491i \(0.482509\pi\)
\(42\) −1.08782 1.88415i −0.167854 0.290731i
\(43\) 3.36545 + 1.94304i 0.513226 + 0.296311i 0.734159 0.678978i \(-0.237577\pi\)
−0.220933 + 0.975289i \(0.570910\pi\)
\(44\) 3.67360 + 2.12095i 0.553816 + 0.319746i
\(45\) −0.135788 −0.0202421
\(46\) 0.255637 + 0.147592i 0.0376917 + 0.0217613i
\(47\) 6.07101i 0.885548i 0.896633 + 0.442774i \(0.146006\pi\)
−0.896633 + 0.442774i \(0.853994\pi\)
\(48\) −1.84102 −0.265729
\(49\) 3.25365 5.63549i 0.464807 0.805070i
\(50\) −2.64307 1.52598i −0.373786 0.215806i
\(51\) −2.85708 + 4.94860i −0.400071 + 0.692943i
\(52\) 7.15084i 0.991643i
\(53\) 8.09749i 1.11228i −0.831090 0.556138i \(-0.812283\pi\)
0.831090 0.556138i \(-0.187717\pi\)
\(54\) −2.59462 + 1.49801i −0.353083 + 0.203853i
\(55\) 0.148776 + 0.0858958i 0.0200609 + 0.0115822i
\(56\) 4.07155 + 7.05213i 0.544084 + 0.942381i
\(57\) 1.68329 + 2.91554i 0.222957 + 0.386172i
\(58\) 2.16426i 0.284181i
\(59\) 5.72348 + 3.30445i 0.745133 + 0.430203i 0.823933 0.566688i \(-0.191775\pi\)
−0.0787994 + 0.996890i \(0.525109\pi\)
\(60\) −0.103852 −0.0134072
\(61\) 12.7178i 1.62834i −0.580623 0.814172i \(-0.697191\pi\)
0.580623 0.814172i \(-0.302809\pi\)
\(62\) −1.38317 + 0.798574i −0.175663 + 0.101419i
\(63\) −6.56006 3.78745i −0.826490 0.477174i
\(64\) 0.383599 0.0479499
\(65\) 0.289600i 0.0359204i
\(66\) 1.54360 0.190004
\(67\) 0.571467 0.0698158 0.0349079 0.999391i \(-0.488886\pi\)
0.0349079 + 0.999391i \(0.488886\pi\)
\(68\) 4.79660 8.30795i 0.581673 1.00749i
\(69\) −0.468194 −0.0563639
\(70\) 0.0739619 + 0.128106i 0.00884014 + 0.0153116i
\(71\) 6.44742 3.72242i 0.765167 0.441770i −0.0659805 0.997821i \(-0.521018\pi\)
0.831148 + 0.556051i \(0.187684\pi\)
\(72\) 3.95484 2.28333i 0.466082 0.269093i
\(73\) −0.720077 + 1.24721i −0.0842786 + 0.145975i −0.905084 0.425234i \(-0.860192\pi\)
0.820805 + 0.571209i \(0.193525\pi\)
\(74\) 5.37990 3.10609i 0.625401 0.361075i
\(75\) 4.84071 0.558957
\(76\) −2.82598 4.89474i −0.324162 0.561466i
\(77\) 4.79168 + 8.29943i 0.546062 + 0.945808i
\(78\) −1.30107 2.25352i −0.147317 0.255161i
\(79\) 2.78194i 0.312992i 0.987679 + 0.156496i \(0.0500199\pi\)
−0.987679 + 0.156496i \(0.949980\pi\)
\(80\) 0.125173 0.0139948
\(81\) −0.715611 + 1.23947i −0.0795123 + 0.137719i
\(82\) −0.372118 + 0.214842i −0.0410935 + 0.0237254i
\(83\) 6.64377 + 11.5073i 0.729248 + 1.26310i 0.957201 + 0.289423i \(0.0934634\pi\)
−0.227953 + 0.973672i \(0.573203\pi\)
\(84\) −5.01718 2.89667i −0.547419 0.316052i
\(85\) 0.194256 0.336461i 0.0210700 0.0364944i
\(86\) −2.37409 −0.256005
\(87\) 1.71637 + 2.97284i 0.184014 + 0.318722i
\(88\) −5.77748 −0.615882
\(89\) 11.2523 + 6.49654i 1.19274 + 0.688631i 0.958928 0.283649i \(-0.0915452\pi\)
0.233816 + 0.972281i \(0.424879\pi\)
\(90\) 0.0718418 0.0414779i 0.00757279 0.00437215i
\(91\) 8.07762 13.9908i 0.846765 1.46664i
\(92\) 0.786026 0.0819489
\(93\) 1.26662 2.19385i 0.131343 0.227492i
\(94\) −1.85445 3.21201i −0.191272 0.331293i
\(95\) −0.114449 0.198231i −0.0117422 0.0203380i
\(96\) 4.69266 2.70931i 0.478943 0.276518i
\(97\) 2.30308 1.32968i 0.233842 0.135009i −0.378501 0.925601i \(-0.623560\pi\)
0.612343 + 0.790592i \(0.290227\pi\)
\(98\) 3.97544i 0.401580i
\(99\) 4.65432 2.68718i 0.467777 0.270071i
\(100\) −8.12682 −0.812682
\(101\) 4.77597i 0.475227i −0.971360 0.237613i \(-0.923635\pi\)
0.971360 0.237613i \(-0.0763652\pi\)
\(102\) 3.49090i 0.345650i
\(103\) 14.0869i 1.38802i −0.719965 0.694010i \(-0.755842\pi\)
0.719965 0.694010i \(-0.244158\pi\)
\(104\) 4.86973 + 8.43461i 0.477516 + 0.827082i
\(105\) −0.203189 0.117311i −0.0198292 0.0114484i
\(106\) 2.47346 + 4.28416i 0.240244 + 0.416115i
\(107\) −6.30756 + 3.64167i −0.609774 + 0.352053i −0.772877 0.634556i \(-0.781183\pi\)
0.163103 + 0.986609i \(0.447850\pi\)
\(108\) −3.98893 + 6.90903i −0.383835 + 0.664822i
\(109\) −4.14488 + 7.17914i −0.397007 + 0.687637i −0.993355 0.115089i \(-0.963285\pi\)
0.596348 + 0.802726i \(0.296618\pi\)
\(110\) −0.104951 −0.0100067
\(111\) −4.92658 + 8.53309i −0.467610 + 0.809925i
\(112\) 6.04725 + 3.49138i 0.571411 + 0.329904i
\(113\) −6.90896 + 3.98889i −0.649941 + 0.375243i −0.788433 0.615120i \(-0.789108\pi\)
0.138493 + 0.990363i \(0.455774\pi\)
\(114\) −1.78116 1.02835i −0.166821 0.0963142i
\(115\) 0.0318330 0.00296845
\(116\) −2.88152 4.99094i −0.267543 0.463398i
\(117\) −7.84608 4.52993i −0.725370 0.418793i
\(118\) −4.03751 −0.371683
\(119\) 18.7694 10.8365i 1.72059 0.993382i
\(120\) 0.122496 0.0707230i 0.0111823 0.00645610i
\(121\) 4.20067 0.381879
\(122\) 3.88478 + 6.72863i 0.351711 + 0.609181i
\(123\) 0.340762 0.590218i 0.0307255 0.0532181i
\(124\) −2.12647 + 3.68315i −0.190962 + 0.330756i
\(125\) −0.658537 −0.0589014
\(126\) 4.62766 0.412265
\(127\) 16.2872i 1.44526i 0.691237 + 0.722628i \(0.257066\pi\)
−0.691237 + 0.722628i \(0.742934\pi\)
\(128\) −9.88869 + 5.70924i −0.874045 + 0.504630i
\(129\) 3.26107 1.88278i 0.287121 0.165769i
\(130\) 0.0884612 + 0.153219i 0.00775856 + 0.0134382i
\(131\) 12.8306i 1.12102i −0.828149 0.560508i \(-0.810606\pi\)
0.828149 0.560508i \(-0.189394\pi\)
\(132\) 3.55966 2.05517i 0.309828 0.178880i
\(133\) 12.7690i 1.10721i
\(134\) −0.302347 + 0.174560i −0.0261188 + 0.0150797i
\(135\) −0.161547 + 0.279807i −0.0139037 + 0.0240819i
\(136\) 13.0660i 1.12040i
\(137\) 7.14959 + 4.12782i 0.610831 + 0.352663i 0.773290 0.634052i \(-0.218609\pi\)
−0.162460 + 0.986715i \(0.551943\pi\)
\(138\) 0.247708 0.143015i 0.0210863 0.0121742i
\(139\) −10.6756 −0.905493 −0.452747 0.891639i \(-0.649556\pi\)
−0.452747 + 0.891639i \(0.649556\pi\)
\(140\) 0.341124 + 0.196948i 0.0288302 + 0.0166451i
\(141\) 5.09458 + 2.94136i 0.429041 + 0.247707i
\(142\) −2.27410 + 3.93886i −0.190838 + 0.330542i
\(143\) 5.73103 + 9.92643i 0.479252 + 0.830090i
\(144\) 1.95797 3.39130i 0.163164 0.282608i
\(145\) −0.116698 0.202127i −0.00969124 0.0167857i
\(146\) 0.879820i 0.0728144i
\(147\) −3.15273 5.46070i −0.260033 0.450391i
\(148\) 8.27098 14.3258i 0.679870 1.17757i
\(149\) −18.7146 + 10.8049i −1.53316 + 0.885170i −0.533946 + 0.845519i \(0.679291\pi\)
−0.999214 + 0.0396514i \(0.987375\pi\)
\(150\) −2.56109 + 1.47865i −0.209112 + 0.120731i
\(151\) 1.40691 2.43685i 0.114493 0.198308i −0.803084 0.595866i \(-0.796809\pi\)
0.917577 + 0.397558i \(0.130142\pi\)
\(152\) 6.66665 + 3.84899i 0.540737 + 0.312194i
\(153\) −6.07713 10.5259i −0.491307 0.850968i
\(154\) −5.07029 2.92733i −0.408576 0.235891i
\(155\) −0.0861191 + 0.149163i −0.00691725 + 0.0119810i
\(156\) −6.00073 3.46452i −0.480443 0.277384i
\(157\) 3.97829 6.89061i 0.317502 0.549930i −0.662464 0.749094i \(-0.730489\pi\)
0.979966 + 0.199163i \(0.0638225\pi\)
\(158\) −0.849771 1.47185i −0.0676042 0.117094i
\(159\) −6.79513 3.92317i −0.538889 0.311128i
\(160\) −0.319060 + 0.184209i −0.0252239 + 0.0145630i
\(161\) 1.53789 + 0.887898i 0.121202 + 0.0699762i
\(162\) 0.874362i 0.0686964i
\(163\) 20.9215i 1.63870i 0.573293 + 0.819351i \(0.305666\pi\)
−0.573293 + 0.819351i \(0.694334\pi\)
\(164\) −0.572088 + 0.990886i −0.0446726 + 0.0773752i
\(165\) 0.144162 0.0832317i 0.0112230 0.00647958i
\(166\) −7.03007 4.05881i −0.545639 0.315025i
\(167\) 13.1321i 1.01619i 0.861300 + 0.508096i \(0.169650\pi\)
−0.861300 + 0.508096i \(0.830350\pi\)
\(168\) 7.89053 0.608768
\(169\) 3.16114 5.47525i 0.243164 0.421173i
\(170\) 0.237350i 0.0182039i
\(171\) −7.16084 −0.547604
\(172\) −5.47483 + 3.16090i −0.417452 + 0.241016i
\(173\) −20.6719 + 11.9349i −1.57165 + 0.907395i −0.575687 + 0.817670i \(0.695265\pi\)
−0.995967 + 0.0897243i \(0.971401\pi\)
\(174\) −1.81617 1.04857i −0.137683 0.0794916i
\(175\) −15.9004 9.18009i −1.20196 0.693950i
\(176\) −4.29049 + 2.47711i −0.323408 + 0.186720i
\(177\) 5.54596 3.20196i 0.416860 0.240674i
\(178\) −7.93773 −0.594958
\(179\) 14.9034i 1.11393i −0.830535 0.556966i \(-0.811965\pi\)
0.830535 0.556966i \(-0.188035\pi\)
\(180\) 0.110448 0.191302i 0.00823234 0.0142588i
\(181\) −10.6366 −0.790615 −0.395307 0.918549i \(-0.629362\pi\)
−0.395307 + 0.918549i \(0.629362\pi\)
\(182\) 9.86957i 0.731581i
\(183\) −10.6723 6.16166i −0.788920 0.455483i
\(184\) −0.927139 + 0.535284i −0.0683496 + 0.0394617i
\(185\) 0.334964 0.580174i 0.0246270 0.0426553i
\(186\) 1.54761i 0.113476i
\(187\) 15.3769i 1.12447i
\(188\) −8.55302 4.93809i −0.623793 0.360147i
\(189\) −15.6090 + 9.01183i −1.13538 + 0.655514i
\(190\) 0.121103 + 0.0699190i 0.00878575 + 0.00507246i
\(191\) 5.70685 + 9.88456i 0.412933 + 0.715222i 0.995209 0.0977697i \(-0.0311709\pi\)
−0.582276 + 0.812991i \(0.697838\pi\)
\(192\) 0.185851 0.321903i 0.0134126 0.0232313i
\(193\) −6.52322 3.76618i −0.469552 0.271096i 0.246500 0.969143i \(-0.420719\pi\)
−0.716052 + 0.698047i \(0.754053\pi\)
\(194\) −0.812330 + 1.40700i −0.0583219 + 0.101017i
\(195\) −0.243022 0.140309i −0.0174032 0.0100477i
\(196\) 5.29296 + 9.16768i 0.378069 + 0.654834i
\(197\) −1.18484 0.684070i −0.0844166 0.0487380i 0.457197 0.889365i \(-0.348853\pi\)
−0.541614 + 0.840627i \(0.682187\pi\)
\(198\) −1.64165 + 2.84342i −0.116667 + 0.202073i
\(199\) −17.4193 + 10.0570i −1.23482 + 0.712923i −0.968031 0.250833i \(-0.919296\pi\)
−0.266788 + 0.963755i \(0.585962\pi\)
\(200\) 9.58581 5.53437i 0.677819 0.391339i
\(201\) 0.276871 0.479555i 0.0195290 0.0338252i
\(202\) 1.45887 + 2.52684i 0.102646 + 0.177788i
\(203\) 13.0199i 0.913820i
\(204\) −4.64783 8.05027i −0.325413 0.563632i
\(205\) −0.0231688 + 0.0401296i −0.00161818 + 0.00280277i
\(206\) 4.30298 + 7.45298i 0.299803 + 0.519274i
\(207\) 0.497934 0.862447i 0.0346088 0.0599442i
\(208\) 7.23274 + 4.17582i 0.501500 + 0.289541i
\(209\) 7.84577 + 4.52975i 0.542703 + 0.313330i
\(210\) 0.143336 0.00989111
\(211\) 14.8483 8.57265i 1.02220 0.590166i 0.107458 0.994210i \(-0.465729\pi\)
0.914740 + 0.404044i \(0.132396\pi\)
\(212\) 11.4080 + 6.58640i 0.783504 + 0.452356i
\(213\) 7.21392i 0.494290i
\(214\) 2.22477 3.85342i 0.152082 0.263414i
\(215\) −0.221724 + 0.128012i −0.0151214 + 0.00873036i
\(216\) 10.8659i 0.739329i
\(217\) −8.32100 + 4.80413i −0.564866 + 0.326126i
\(218\) 5.06438i 0.343003i
\(219\) 0.697743 + 1.20853i 0.0471491 + 0.0816646i
\(220\) −0.242025 + 0.139733i −0.0163173 + 0.00942082i
\(221\) 22.4489 12.9609i 1.51008 0.871843i
\(222\) 6.01950i 0.404002i
\(223\) −22.6112 −1.51416 −0.757078 0.653324i \(-0.773374\pi\)
−0.757078 + 0.653324i \(0.773374\pi\)
\(224\) −20.5521 −1.37320
\(225\) −5.14820 + 8.91695i −0.343214 + 0.594463i
\(226\) 2.43690 4.22083i 0.162100 0.280765i
\(227\) −14.8239 25.6757i −0.983895 1.70416i −0.646749 0.762703i \(-0.723872\pi\)
−0.337146 0.941453i \(-0.609461\pi\)
\(228\) −5.47666 −0.362701
\(229\) 2.89333 1.67047i 0.191197 0.110388i −0.401346 0.915927i \(-0.631457\pi\)
0.592543 + 0.805539i \(0.298124\pi\)
\(230\) −0.0168420 + 0.00972372i −0.00111053 + 0.000641163i
\(231\) 9.28611 0.610981
\(232\) 6.79768 + 3.92464i 0.446289 + 0.257665i
\(233\) 9.37841 + 16.2439i 0.614400 + 1.06417i 0.990489 + 0.137589i \(0.0439352\pi\)
−0.376089 + 0.926583i \(0.622731\pi\)
\(234\) 5.53486 0.361825
\(235\) −0.346386 0.199986i −0.0225957 0.0130457i
\(236\) −9.31082 + 5.37560i −0.606083 + 0.349922i
\(237\) 2.33450 + 1.34783i 0.151642 + 0.0875507i
\(238\) −6.62025 + 11.4666i −0.429127 + 0.743270i
\(239\) 10.7559 0.695738 0.347869 0.937543i \(-0.386905\pi\)
0.347869 + 0.937543i \(0.386905\pi\)
\(240\) 0.0606455 0.105041i 0.00391465 0.00678037i
\(241\) −7.44705 + 12.8987i −0.479707 + 0.830877i −0.999729 0.0232760i \(-0.992590\pi\)
0.520022 + 0.854153i \(0.325924\pi\)
\(242\) −2.22246 + 1.28314i −0.142865 + 0.0824831i
\(243\) 8.04956 + 13.9422i 0.516379 + 0.894395i
\(244\) 17.9172 + 10.3445i 1.14703 + 0.662238i
\(245\) 0.214358 + 0.371279i 0.0136948 + 0.0237201i
\(246\) 0.416357i 0.0265460i
\(247\) 15.2722i 0.971745i
\(248\) 5.79250i 0.367824i
\(249\) 12.8754 0.815946
\(250\) 0.348414 0.201157i 0.0220356 0.0127223i
\(251\) 10.0816i 0.636348i 0.948032 + 0.318174i \(0.103070\pi\)
−0.948032 + 0.318174i \(0.896930\pi\)
\(252\) 10.6717 6.16134i 0.672257 0.388128i
\(253\) −1.09112 + 0.629959i −0.0685982 + 0.0396052i
\(254\) −4.97510 8.61712i −0.312165 0.540686i
\(255\) −0.188231 0.326026i −0.0117875 0.0204165i
\(256\) 3.10429 5.37679i 0.194018 0.336049i
\(257\) 5.65623 0.352826 0.176413 0.984316i \(-0.443551\pi\)
0.176413 + 0.984316i \(0.443551\pi\)
\(258\) −1.15023 + 1.99225i −0.0716100 + 0.124032i
\(259\) 32.3649 18.6859i 2.01106 1.16108i
\(260\) 0.407997 + 0.235557i 0.0253029 + 0.0146086i
\(261\) −7.30159 −0.451957
\(262\) 3.91924 + 6.78832i 0.242131 + 0.419384i
\(263\) 17.7953 1.09730 0.548651 0.836051i \(-0.315141\pi\)
0.548651 + 0.836051i \(0.315141\pi\)
\(264\) −2.79914 + 4.84826i −0.172275 + 0.298390i
\(265\) 0.462009 + 0.266741i 0.0283810 + 0.0163858i
\(266\) 3.90041 + 6.75571i 0.239150 + 0.414219i
\(267\) 10.9033 6.29504i 0.667273 0.385250i
\(268\) −0.464824 + 0.805099i −0.0283937 + 0.0491792i
\(269\) −4.47779 −0.273016 −0.136508 0.990639i \(-0.543588\pi\)
−0.136508 + 0.990639i \(0.543588\pi\)
\(270\) 0.197384i 0.0120124i
\(271\) 14.1002 + 24.4222i 0.856524 + 1.48354i 0.875224 + 0.483719i \(0.160714\pi\)
−0.0186992 + 0.999825i \(0.505952\pi\)
\(272\) 5.60207 + 9.70307i 0.339675 + 0.588335i
\(273\) −7.82708 13.5569i −0.473717 0.820501i
\(274\) −5.04354 −0.304691
\(275\) 11.2812 6.51322i 0.680284 0.392762i
\(276\) 0.380823 0.659605i 0.0229229 0.0397036i
\(277\) 19.7530 11.4044i 1.18684 0.685225i 0.229257 0.973366i \(-0.426371\pi\)
0.957588 + 0.288141i \(0.0930372\pi\)
\(278\) 5.64817 3.26097i 0.338755 0.195580i
\(279\) 2.69416 + 4.66642i 0.161295 + 0.279371i
\(280\) −0.536486 −0.0320612
\(281\) −4.38624 + 7.59719i −0.261661 + 0.453210i −0.966683 0.255975i \(-0.917604\pi\)
0.705022 + 0.709185i \(0.250937\pi\)
\(282\) −3.59387 −0.214012
\(283\) −5.21469 −0.309981 −0.154991 0.987916i \(-0.549535\pi\)
−0.154991 + 0.987916i \(0.549535\pi\)
\(284\) 12.1111i 0.718660i
\(285\) −0.221798 −0.0131382
\(286\) −6.06426 3.50120i −0.358587 0.207030i
\(287\) −2.23862 + 1.29247i −0.132141 + 0.0762919i
\(288\) 11.5256i 0.679155i
\(289\) 17.7753 1.04561
\(290\) 0.123483 + 0.0712932i 0.00725120 + 0.00418648i
\(291\) 2.57688i 0.151059i
\(292\) −1.17140 2.02893i −0.0685512 0.118734i
\(293\) −8.25302 14.2946i −0.482146 0.835102i 0.517643 0.855596i \(-0.326809\pi\)
−0.999790 + 0.0204942i \(0.993476\pi\)
\(294\) 3.33605 + 1.92607i 0.194562 + 0.112331i
\(295\) −0.377076 + 0.217705i −0.0219542 + 0.0126753i
\(296\) 22.5302i 1.30954i
\(297\) 12.7877i 0.742017i
\(298\) 6.60092 11.4331i 0.382381 0.662303i
\(299\) 1.83937 + 1.06196i 0.106373 + 0.0614147i
\(300\) −3.93738 + 6.81974i −0.227325 + 0.393738i
\(301\) −14.2823 −0.823215
\(302\) 1.71903i 0.0989188i
\(303\) −4.00783 2.31392i −0.230244 0.132931i
\(304\) 6.60107 0.378597
\(305\) 0.725623 + 0.418938i 0.0415490 + 0.0239883i
\(306\) 6.43048 + 3.71264i 0.367606 + 0.212238i
\(307\) −2.01788 3.49507i −0.115167 0.199474i 0.802680 0.596410i \(-0.203407\pi\)
−0.917846 + 0.396936i \(0.870074\pi\)
\(308\) −15.5900 −0.888321
\(309\) −11.8212 6.82497i −0.672485 0.388259i
\(310\) 0.105224i 0.00597631i
\(311\) 14.2661i 0.808959i −0.914547 0.404479i \(-0.867453\pi\)
0.914547 0.404479i \(-0.132547\pi\)
\(312\) 9.43737 0.534286
\(313\) −10.8738 −0.614626 −0.307313 0.951608i \(-0.599430\pi\)
−0.307313 + 0.951608i \(0.599430\pi\)
\(314\) 4.86084i 0.274313i
\(315\) 0.432192 0.249526i 0.0243513 0.0140592i
\(316\) −3.91927 2.26279i −0.220476 0.127292i
\(317\) −1.56221 0.901942i −0.0877424 0.0506581i 0.455487 0.890243i \(-0.349465\pi\)
−0.543229 + 0.839584i \(0.682799\pi\)
\(318\) 4.79349 0.268806
\(319\) 7.99997 + 4.61878i 0.447912 + 0.258602i
\(320\) −0.0126362 + 0.0218865i −0.000706385 + 0.00122349i
\(321\) 7.05744i 0.393908i
\(322\) −1.08487 −0.0604575
\(323\) 10.2442 17.7434i 0.570001 0.987271i
\(324\) −1.16414 2.01635i −0.0646743 0.112019i
\(325\) −19.0175 10.9797i −1.05490 0.609046i
\(326\) −6.39070 11.0690i −0.353948 0.613056i
\(327\) 4.01632 + 6.95647i 0.222103 + 0.384694i
\(328\) 1.55837i 0.0860466i
\(329\) −11.1562 19.3231i −0.615060 1.06531i
\(330\) −0.0508479 + 0.0880712i −0.00279909 + 0.00484816i
\(331\) 18.9986 + 10.9689i 1.04426 + 0.602903i 0.921037 0.389476i \(-0.127344\pi\)
0.123222 + 0.992379i \(0.460677\pi\)
\(332\) −21.6158 −1.18632
\(333\) −10.4790 18.1502i −0.574248 0.994627i
\(334\) −4.01133 6.94783i −0.219490 0.380168i
\(335\) −0.0188248 + 0.0326055i −0.00102851 + 0.00178143i
\(336\) 5.85969 3.38309i 0.319672 0.184563i
\(337\) −15.1256 26.1984i −0.823946 1.42712i −0.902722 0.430224i \(-0.858435\pi\)
0.0787762 0.996892i \(-0.474899\pi\)
\(338\) 3.86241i 0.210087i
\(339\) 7.73034i 0.419855i
\(340\) 0.316011 + 0.547347i 0.0171381 + 0.0296841i
\(341\) 6.81701i 0.369162i
\(342\) 3.78861 2.18735i 0.204864 0.118279i
\(343\) 1.81078i 0.0977731i
\(344\) 4.30515 7.45673i 0.232118 0.402040i
\(345\) 0.0154228 0.0267132i 0.000830338 0.00143819i
\(346\) 7.29128 12.6289i 0.391982 0.678932i
\(347\) 13.6240 7.86580i 0.731373 0.422258i −0.0875514 0.996160i \(-0.527904\pi\)
0.818924 + 0.573902i \(0.194571\pi\)
\(348\) −5.58430 −0.299350
\(349\) −15.0052 + 11.1286i −0.803208 + 0.595698i
\(350\) 11.2166 0.599553
\(351\) −18.6689 + 10.7785i −0.996472 + 0.575313i
\(352\) 7.29080 12.6280i 0.388601 0.673077i
\(353\) 10.2244 17.7092i 0.544189 0.942563i −0.454468 0.890763i \(-0.650171\pi\)
0.998657 0.0518003i \(-0.0164959\pi\)
\(354\) −1.95614 + 3.38814i −0.103968 + 0.180078i
\(355\) 0.490483i 0.0260321i
\(356\) −18.3050 + 10.5684i −0.970164 + 0.560125i
\(357\) 21.0008i 1.11148i
\(358\) 4.55240 + 7.88498i 0.240602 + 0.416734i
\(359\) 1.88289i 0.0993753i −0.998765 0.0496877i \(-0.984177\pi\)
0.998765 0.0496877i \(-0.0158226\pi\)
\(360\) 0.300862i 0.0158568i
\(361\) 3.46450 + 6.00070i 0.182342 + 0.315826i
\(362\) 5.62755 3.24907i 0.295778 0.170767i
\(363\) 2.03519 3.52505i 0.106820 0.185017i
\(364\) 13.1405 + 22.7600i 0.688748 + 1.19295i
\(365\) −0.0474404 0.0821691i −0.00248314 0.00430093i
\(366\) 7.52857 0.393525
\(367\) −15.7224 9.07736i −0.820705 0.473834i 0.0299544 0.999551i \(-0.490464\pi\)
−0.850660 + 0.525717i \(0.823797\pi\)
\(368\) −0.459010 + 0.795028i −0.0239275 + 0.0414437i
\(369\) 0.724816 + 1.25542i 0.0377324 + 0.0653545i
\(370\) 0.409273i 0.0212771i
\(371\) 14.8801 + 25.7730i 0.772534 + 1.33807i
\(372\) 2.06051 + 3.56891i 0.106833 + 0.185039i
\(373\) 24.3582 + 14.0632i 1.26122 + 0.728165i 0.973310 0.229493i \(-0.0737067\pi\)
0.287909 + 0.957658i \(0.407040\pi\)
\(374\) −4.69703 8.13550i −0.242878 0.420677i
\(375\) −0.319056 + 0.552621i −0.0164760 + 0.0285372i
\(376\) 13.4514 0.693701
\(377\) 15.5723i 0.802016i
\(378\) 5.50551 9.53583i 0.283173 0.490470i
\(379\) 24.8881 + 14.3691i 1.27841 + 0.738093i 0.976557 0.215260i \(-0.0690598\pi\)
0.301858 + 0.953353i \(0.402393\pi\)
\(380\) 0.372364 0.0191019
\(381\) 13.6677 + 7.89102i 0.700215 + 0.404269i
\(382\) −6.03868 3.48643i −0.308966 0.178381i
\(383\) 15.6597 9.04112i 0.800172 0.461980i −0.0433591 0.999060i \(-0.513806\pi\)
0.843531 + 0.537080i \(0.180473\pi\)
\(384\) 11.0643i 0.564624i
\(385\) −0.631374 −0.0321778
\(386\) 4.60168 0.234219
\(387\) 8.00950i 0.407146i
\(388\) 4.32619i 0.219629i
\(389\) −3.45237 1.99323i −0.175042 0.101061i 0.409919 0.912122i \(-0.365557\pi\)
−0.584961 + 0.811061i \(0.698890\pi\)
\(390\) 0.171435 0.00868095
\(391\) 1.42467 + 2.46760i 0.0720487 + 0.124792i
\(392\) −12.4864 7.20902i −0.630658 0.364111i
\(393\) −10.7670 6.21632i −0.543123 0.313572i
\(394\) 0.835825 0.0421082
\(395\) −0.158726 0.0916402i −0.00798635 0.00461092i
\(396\) 8.74287i 0.439346i
\(397\) −26.6310 −1.33657 −0.668287 0.743904i \(-0.732972\pi\)
−0.668287 + 0.743904i \(0.732972\pi\)
\(398\) 6.14404 10.6418i 0.307973 0.533424i
\(399\) −10.7153 6.18646i −0.536434 0.309710i
\(400\) 4.74576 8.21990i 0.237288 0.410995i
\(401\) 24.5098i 1.22396i 0.790873 + 0.611981i \(0.209627\pi\)
−0.790873 + 0.611981i \(0.790373\pi\)
\(402\) 0.338292i 0.0168725i
\(403\) −9.95223 + 5.74592i −0.495756 + 0.286225i
\(404\) 6.72853 + 3.88472i 0.334757 + 0.193272i
\(405\) −0.0471461 0.0816594i −0.00234271 0.00405769i
\(406\) 3.97707 + 6.88849i 0.197379 + 0.341870i
\(407\) 26.5150i 1.31430i
\(408\) 10.9645 + 6.33035i 0.542823 + 0.313399i
\(409\) 20.5899 1.01811 0.509053 0.860735i \(-0.329996\pi\)
0.509053 + 0.860735i \(0.329996\pi\)
\(410\) 0.0283086i 0.00139806i
\(411\) 6.92784 3.99979i 0.341725 0.197295i
\(412\) 19.8460 + 11.4581i 0.977742 + 0.564500i
\(413\) −24.2892 −1.19519
\(414\) 0.608396i 0.0299010i
\(415\) −0.875414 −0.0429724
\(416\) −24.5811 −1.20519
\(417\) −5.17225 + 8.95859i −0.253286 + 0.438704i
\(418\) −5.53464 −0.270708
\(419\) −13.3192 23.0695i −0.650686 1.12702i −0.982957 0.183837i \(-0.941148\pi\)
0.332271 0.943184i \(-0.392185\pi\)
\(420\) 0.330543 0.190839i 0.0161289 0.00931200i
\(421\) −3.90209 + 2.25287i −0.190176 + 0.109798i −0.592065 0.805890i \(-0.701687\pi\)
0.401889 + 0.915688i \(0.368354\pi\)
\(422\) −5.23721 + 9.07111i −0.254943 + 0.441575i
\(423\) −10.8364 + 6.25639i −0.526883 + 0.304196i
\(424\) −17.9414 −0.871311
\(425\) −14.7299 25.5129i −0.714503 1.23756i
\(426\) 2.20357 + 3.81669i 0.106763 + 0.184919i
\(427\) 23.3704 + 40.4787i 1.13097 + 1.95890i
\(428\) 11.8484i 0.572712i
\(429\) 11.1065 0.536229
\(430\) 0.0782053 0.135456i 0.00377139 0.00653225i
\(431\) 21.6611 12.5060i 1.04338 0.602395i 0.122590 0.992457i \(-0.460880\pi\)
0.920788 + 0.390063i \(0.127547\pi\)
\(432\) −4.65878 8.06924i −0.224145 0.388231i
\(433\) −31.5227 18.1996i −1.51488 0.874618i −0.999848 0.0174483i \(-0.994446\pi\)
−0.515035 0.857169i \(-0.672221\pi\)
\(434\) 2.93494 5.08347i 0.140882 0.244014i
\(435\) −0.226157 −0.0108434
\(436\) −6.74279 11.6788i −0.322921 0.559315i
\(437\) 1.67873 0.0803045
\(438\) −0.738314 0.426266i −0.0352780 0.0203678i
\(439\) −25.0422 + 14.4581i −1.19520 + 0.690048i −0.959481 0.281774i \(-0.909077\pi\)
−0.235717 + 0.971822i \(0.575744\pi\)
\(440\) 0.190317 0.329639i 0.00907301 0.0157149i
\(441\) 13.4120 0.638667
\(442\) −7.91807 + 13.7145i −0.376624 + 0.652332i
\(443\) 9.11927 + 15.7950i 0.433270 + 0.750445i 0.997153 0.0754096i \(-0.0240264\pi\)
−0.563883 + 0.825855i \(0.690693\pi\)
\(444\) −8.01444 13.8814i −0.380349 0.658783i
\(445\) −0.741330 + 0.428007i −0.0351424 + 0.0202895i
\(446\) 11.9630 6.90682i 0.566462 0.327047i
\(447\) 20.9395i 0.990405i
\(448\) −1.22093 + 0.704907i −0.0576837 + 0.0333037i
\(449\) −28.2792 −1.33458 −0.667288 0.744800i \(-0.732545\pi\)
−0.667288 + 0.744800i \(0.732545\pi\)
\(450\) 6.29029i 0.296527i
\(451\) 1.83400i 0.0863595i
\(452\) 12.9781i 0.610437i
\(453\) −1.36328 2.36127i −0.0640524 0.110942i
\(454\) 15.6858 + 9.05620i 0.736171 + 0.425029i
\(455\) 0.532172 + 0.921750i 0.0249486 + 0.0432123i
\(456\) 6.45988 3.72961i 0.302511 0.174655i
\(457\) 4.76212 8.24824i 0.222763 0.385836i −0.732883 0.680355i \(-0.761826\pi\)
0.955646 + 0.294518i \(0.0951591\pi\)
\(458\) −1.02052 + 1.76760i −0.0476859 + 0.0825943i
\(459\) −28.9197 −1.34986
\(460\) −0.0258926 + 0.0448473i −0.00120725 + 0.00209102i
\(461\) 27.7864 + 16.0425i 1.29414 + 0.747173i 0.979386 0.201999i \(-0.0647438\pi\)
0.314756 + 0.949172i \(0.398077\pi\)
\(462\) −4.91303 + 2.83654i −0.228575 + 0.131968i
\(463\) 25.1154 + 14.5004i 1.16721 + 0.673889i 0.953021 0.302903i \(-0.0979560\pi\)
0.214189 + 0.976792i \(0.431289\pi\)
\(464\) 6.73081 0.312470
\(465\) 0.0834480 + 0.144536i 0.00386981 + 0.00670271i
\(466\) −9.92372 5.72946i −0.459707 0.265412i
\(467\) −9.71497 −0.449555 −0.224778 0.974410i \(-0.572166\pi\)
−0.224778 + 0.974410i \(0.572166\pi\)
\(468\) 12.7638 7.36919i 0.590007 0.340641i
\(469\) −1.81889 + 1.05014i −0.0839884 + 0.0484907i
\(470\) 0.244351 0.0112711
\(471\) −3.85490 6.67689i −0.177625 0.307655i
\(472\) 7.32158 12.6814i 0.337003 0.583706i
\(473\) 5.06659 8.77559i 0.232962 0.403502i
\(474\) −1.64683 −0.0756414
\(475\) −17.3566 −0.796375
\(476\) 35.2572i 1.61601i
\(477\) 14.4535 8.34475i 0.661782 0.382080i
\(478\) −5.69063 + 3.28549i −0.260283 + 0.150275i
\(479\) −7.05043 12.2117i −0.322143 0.557967i 0.658787 0.752329i \(-0.271070\pi\)
−0.980930 + 0.194362i \(0.937736\pi\)
\(480\) 0.356991i 0.0162943i
\(481\) 38.7096 22.3490i 1.76501 1.01903i
\(482\) 9.09912i 0.414453i
\(483\) 1.49019 0.860359i 0.0678058 0.0391477i
\(484\) −3.41677 + 5.91802i −0.155308 + 0.269001i
\(485\) 0.175205i 0.00795566i
\(486\) −8.51760 4.91764i −0.386366 0.223069i
\(487\) 1.45510 0.840105i 0.0659370 0.0380688i −0.466669 0.884432i \(-0.654546\pi\)
0.532606 + 0.846363i \(0.321213\pi\)
\(488\) −28.1784 −1.27558
\(489\) 17.5566 + 10.1363i 0.793938 + 0.458380i
\(490\) −0.226822 0.130956i −0.0102468 0.00591598i
\(491\) −0.172737 + 0.299189i −0.00779551 + 0.0135022i −0.869897 0.493234i \(-0.835815\pi\)
0.862101 + 0.506736i \(0.169148\pi\)
\(492\) 0.554344 + 0.960152i 0.0249918 + 0.0432870i
\(493\) 10.4455 18.0922i 0.470442 0.814830i
\(494\) 4.66504 + 8.08009i 0.209890 + 0.363540i
\(495\) 0.354075i 0.0159145i
\(496\) −2.48355 4.30164i −0.111515 0.193149i
\(497\) −13.6807 + 23.6957i −0.613665 + 1.06290i
\(498\) −6.81203 + 3.93293i −0.305254 + 0.176239i
\(499\) −36.1175 + 20.8525i −1.61684 + 0.933484i −0.629112 + 0.777315i \(0.716581\pi\)
−0.987730 + 0.156169i \(0.950086\pi\)
\(500\) 0.535646 0.927767i 0.0239548 0.0414910i
\(501\) 11.0200 + 6.36239i 0.492337 + 0.284251i
\(502\) −3.07954 5.33393i −0.137447 0.238065i
\(503\) 30.6297 + 17.6841i 1.36571 + 0.788494i 0.990377 0.138396i \(-0.0441947\pi\)
0.375334 + 0.926890i \(0.377528\pi\)
\(504\) −8.39175 + 14.5349i −0.373798 + 0.647438i
\(505\) 0.272497 + 0.157326i 0.0121259 + 0.00700092i
\(506\) 0.384855 0.666588i 0.0171089 0.0296335i
\(507\) −3.06309 5.30543i −0.136037 0.235622i
\(508\) −22.9459 13.2478i −1.01806 0.587777i
\(509\) 26.8662 15.5112i 1.19082 0.687521i 0.232329 0.972637i \(-0.425366\pi\)
0.958493 + 0.285116i \(0.0920322\pi\)
\(510\) 0.199176 + 0.114994i 0.00881965 + 0.00509203i
\(511\) 5.29289i 0.234144i
\(512\) 19.0440i 0.841634i
\(513\) −8.51923 + 14.7557i −0.376133 + 0.651482i
\(514\) −2.99256 + 1.72775i −0.131996 + 0.0762080i
\(515\) 0.803737 + 0.464038i 0.0354169 + 0.0204480i
\(516\) 6.12571i 0.269670i
\(517\) 15.8305 0.696224
\(518\) −11.4156 + 19.7724i −0.501572 + 0.868748i
\(519\) 23.1295i 1.01527i
\(520\) −0.641658 −0.0281386
\(521\) −29.2477 + 16.8862i −1.28137 + 0.739797i −0.977098 0.212789i \(-0.931745\pi\)
−0.304268 + 0.952586i \(0.598412\pi\)
\(522\) 3.86307 2.23034i 0.169082 0.0976195i
\(523\) 13.3663 + 7.71703i 0.584467 + 0.337442i 0.762907 0.646509i \(-0.223772\pi\)
−0.178440 + 0.983951i \(0.557105\pi\)
\(524\) 18.0761 + 10.4363i 0.789660 + 0.455910i
\(525\) −15.4072 + 8.89536i −0.672426 + 0.388225i
\(526\) −9.41499 + 5.43574i −0.410513 + 0.237010i
\(527\) −15.4169 −0.671569
\(528\) 4.80057i 0.208918i
\(529\) 11.3833 19.7164i 0.494925 0.857235i
\(530\) −0.325915 −0.0141568
\(531\) 13.6214i 0.591119i
\(532\) 17.9893 + 10.3861i 0.779935 + 0.450296i
\(533\) −2.67747 + 1.54584i −0.115974 + 0.0669577i
\(534\) −3.84577 + 6.66107i −0.166423 + 0.288252i
\(535\) 0.479843i 0.0207454i
\(536\) 1.26618i 0.0546908i
\(537\) −12.5064 7.22058i −0.539691 0.311591i
\(538\) 2.36908 1.36779i 0.102138 0.0589695i
\(539\) −14.6948 8.48407i −0.632951 0.365435i
\(540\) −0.262800 0.455183i −0.0113091 0.0195880i
\(541\) −14.5392 + 25.1827i −0.625090 + 1.08269i 0.363434 + 0.931620i \(0.381604\pi\)
−0.988524 + 0.151067i \(0.951729\pi\)
\(542\) −14.9200 8.61408i −0.640870 0.370007i
\(543\) −5.15336 + 8.92589i −0.221152 + 0.383046i
\(544\) −28.5587 16.4884i −1.22444 0.706933i
\(545\) −0.273074 0.472978i −0.0116972 0.0202602i
\(546\) 8.28219 + 4.78173i 0.354445 + 0.204639i
\(547\) 12.9096 22.3602i 0.551976 0.956051i −0.446155 0.894955i \(-0.647207\pi\)
0.998132 0.0610958i \(-0.0194595\pi\)
\(548\) −11.6308 + 6.71503i −0.496842 + 0.286852i
\(549\) 22.7005 13.1061i 0.968832 0.559355i
\(550\) −3.97906 + 6.89194i −0.169668 + 0.293873i
\(551\) −6.15412 10.6592i −0.262174 0.454099i
\(552\) 1.03736i 0.0441531i
\(553\) −5.11213 8.85446i −0.217390 0.376530i
\(554\) −6.96719 + 12.0675i −0.296008 + 0.512700i
\(555\) −0.324575 0.562180i −0.0137774 0.0238632i
\(556\) 8.68341 15.0401i 0.368259 0.637843i
\(557\) 5.98848 + 3.45745i 0.253740 + 0.146497i 0.621476 0.783433i \(-0.286533\pi\)
−0.367735 + 0.929930i \(0.619867\pi\)
\(558\) −2.85081 1.64592i −0.120685 0.0696773i
\(559\) −17.0821 −0.722496
\(560\) −0.398407 + 0.230020i −0.0168358 + 0.00972013i
\(561\) 12.9038 + 7.44998i 0.544797 + 0.314539i
\(562\) 5.35929i 0.226068i
\(563\) 15.8382 27.4326i 0.667502 1.15615i −0.311099 0.950378i \(-0.600697\pi\)
0.978601 0.205769i \(-0.0659696\pi\)
\(564\) −8.28774 + 4.78493i −0.348977 + 0.201482i
\(565\) 0.525595i 0.0221119i
\(566\) 2.75895 1.59288i 0.115967 0.0669538i
\(567\) 5.26006i 0.220902i
\(568\) −8.24765 14.2854i −0.346064 0.599400i
\(569\) 5.36889 3.09973i 0.225076 0.129948i −0.383223 0.923656i \(-0.625186\pi\)
0.608298 + 0.793709i \(0.291852\pi\)
\(570\) 0.117347 0.0677504i 0.00491513 0.00283775i
\(571\) 24.2302i 1.01400i −0.861946 0.507000i \(-0.830754\pi\)
0.861946 0.507000i \(-0.169246\pi\)
\(572\) −18.6462 −0.779636
\(573\) 11.0597 0.462026
\(574\) 0.789594 1.36762i 0.0329570 0.0570833i
\(575\) 1.20690 2.09041i 0.0503313 0.0871763i
\(576\) 0.395312 + 0.684701i 0.0164713 + 0.0285292i
\(577\) 15.1103 0.629050 0.314525 0.949249i \(-0.398155\pi\)
0.314525 + 0.949249i \(0.398155\pi\)
\(578\) −9.40443 + 5.42965i −0.391173 + 0.225844i
\(579\) −6.32089 + 3.64937i −0.262687 + 0.151663i
\(580\) 0.379683 0.0157655
\(581\) −42.2921 24.4174i −1.75457 1.01300i
\(582\) 0.787135 + 1.36336i 0.0326278 + 0.0565130i
\(583\) −21.1146 −0.874479
\(584\) 2.76341 + 1.59545i 0.114351 + 0.0660204i
\(585\) 0.516918 0.298443i 0.0213719 0.0123391i
\(586\) 8.73289 + 5.04194i 0.360752 + 0.208281i
\(587\) −16.9349 + 29.3321i −0.698979 + 1.21067i 0.269842 + 0.962904i \(0.413028\pi\)
−0.968821 + 0.247762i \(0.920305\pi\)
\(588\) 10.2576 0.423016
\(589\) −4.54153 + 7.86616i −0.187130 + 0.324119i
\(590\) 0.133000 0.230364i 0.00547554 0.00948392i
\(591\) −1.14809 + 0.662853i −0.0472263 + 0.0272661i
\(592\) 9.65988 + 16.7314i 0.397019 + 0.687657i
\(593\) −35.0640 20.2442i −1.43991 0.831331i −0.442064 0.896983i \(-0.645754\pi\)
−0.997843 + 0.0656525i \(0.979087\pi\)
\(594\) 3.90613 + 6.76562i 0.160271 + 0.277597i
\(595\) 1.42787i 0.0585370i
\(596\) 35.1542i 1.43997i
\(597\) 19.4902i 0.797679i
\(598\) −1.29755 −0.0530606
\(599\) 19.7990 11.4310i 0.808967 0.467057i −0.0376301 0.999292i \(-0.511981\pi\)
0.846597 + 0.532235i \(0.178648\pi\)
\(600\) 10.7254i 0.437864i
\(601\) −16.0598 + 9.27214i −0.655094 + 0.378218i −0.790405 0.612585i \(-0.790130\pi\)
0.135311 + 0.990803i \(0.456797\pi\)
\(602\) 7.55635 4.36266i 0.307974 0.177809i
\(603\) 0.588916 + 1.02003i 0.0239825 + 0.0415390i
\(604\) 2.28874 + 3.96421i 0.0931273 + 0.161301i
\(605\) −0.138375 + 0.239672i −0.00562574 + 0.00974406i
\(606\) 2.82724 0.114849
\(607\) 4.19724 7.26984i 0.170361 0.295074i −0.768185 0.640228i \(-0.778840\pi\)
0.938546 + 0.345154i \(0.112173\pi\)
\(608\) −16.8257 + 9.71435i −0.682374 + 0.393969i
\(609\) −10.9259 6.30805i −0.442738 0.255615i
\(610\) −0.511876 −0.0207253
\(611\) −13.3432 23.1111i −0.539808 0.934975i
\(612\) 19.7723 0.799246
\(613\) −18.9341 + 32.7949i −0.764742 + 1.32457i 0.175641 + 0.984454i \(0.443800\pi\)
−0.940383 + 0.340118i \(0.889533\pi\)
\(614\) 2.13521 + 1.23277i 0.0861701 + 0.0497504i
\(615\) 0.0224502 + 0.0388849i 0.000905280 + 0.00156799i
\(616\) 18.3888 10.6168i 0.740906 0.427762i
\(617\) −3.15799 + 5.46980i −0.127136 + 0.220206i −0.922566 0.385840i \(-0.873912\pi\)
0.795430 + 0.606045i \(0.207245\pi\)
\(618\) 8.33903 0.335445
\(619\) 18.3845i 0.738934i 0.929244 + 0.369467i \(0.120460\pi\)
−0.929244 + 0.369467i \(0.879540\pi\)
\(620\) −0.140097 0.242654i −0.00562641 0.00974523i
\(621\) −1.18478 2.05210i −0.0475436 0.0823479i
\(622\) 4.35774 + 7.54783i 0.174729 + 0.302640i
\(623\) −47.7525 −1.91316
\(624\) 7.00840 4.04630i 0.280561 0.161982i
\(625\) −12.4675 + 21.5943i −0.498698 + 0.863771i
\(626\) 5.75305 3.32153i 0.229938 0.132755i
\(627\) 7.60242 4.38926i 0.303611 0.175290i
\(628\) 6.47179 + 11.2095i 0.258253 + 0.447307i
\(629\) 59.9646 2.39094
\(630\) −0.152441 + 0.264035i −0.00607338 + 0.0105194i
\(631\) −6.38203 −0.254065 −0.127032 0.991899i \(-0.540545\pi\)
−0.127032 + 0.991899i \(0.540545\pi\)
\(632\) 6.16386 0.245185
\(633\) 16.6135i 0.660328i
\(634\) 1.10203 0.0437672
\(635\) −0.929280 0.536520i −0.0368773 0.0212911i
\(636\) 11.0542 6.38212i 0.438326 0.253067i
\(637\) 28.6042i 1.13334i
\(638\) −5.64342 −0.223425
\(639\) 13.2886 + 7.67216i 0.525688 + 0.303506i
\(640\) 0.752276i 0.0297363i
\(641\) 3.02171 + 5.23375i 0.119350 + 0.206721i 0.919510 0.393066i \(-0.128586\pi\)
−0.800160 + 0.599787i \(0.795252\pi\)
\(642\) −2.15577 3.73390i −0.0850813 0.147365i
\(643\) 5.63940 + 3.25591i 0.222396 + 0.128400i 0.607059 0.794657i \(-0.292349\pi\)
−0.384663 + 0.923057i \(0.625682\pi\)
\(644\) −2.50179 + 1.44441i −0.0985845 + 0.0569178i
\(645\) 0.248084i 0.00976828i
\(646\) 12.5168i 0.492465i
\(647\) 5.33314 9.23727i 0.209667 0.363155i −0.741942 0.670464i \(-0.766095\pi\)
0.951610 + 0.307309i \(0.0994285\pi\)
\(648\) 2.74627 + 1.58556i 0.107884 + 0.0622866i
\(649\) 8.61653 14.9243i 0.338229 0.585829i
\(650\) 13.4155 0.526199
\(651\) 9.31025i 0.364898i
\(652\) −29.4749 17.0173i −1.15433 0.666450i
\(653\) 30.6993 1.20136 0.600678 0.799491i \(-0.294898\pi\)
0.600678 + 0.799491i \(0.294898\pi\)
\(654\) −4.24985 2.45365i −0.166182 0.0959454i
\(655\) 0.732060 + 0.422655i 0.0286040 + 0.0165145i
\(656\) −0.668156 1.15728i −0.0260871 0.0451842i
\(657\) −2.96826 −0.115803
\(658\) 11.8049 + 6.81554i 0.460201 + 0.265697i
\(659\) 14.2111i 0.553586i −0.960930 0.276793i \(-0.910728\pi\)
0.960930 0.276793i \(-0.0892716\pi\)
\(660\) 0.270799i 0.0105408i
\(661\) 17.9533 0.698303 0.349152 0.937066i \(-0.386470\pi\)
0.349152 + 0.937066i \(0.386470\pi\)
\(662\) −13.4022 −0.520891
\(663\) 25.1178i 0.975494i
\(664\) 25.4965 14.7204i 0.989456 0.571263i
\(665\) 0.728543 + 0.420625i 0.0282517 + 0.0163111i
\(666\) 11.0884 + 6.40187i 0.429665 + 0.248067i
\(667\) 1.71172 0.0662782
\(668\) −18.5009 10.6815i −0.715820 0.413279i
\(669\) −10.9549 + 18.9745i −0.423542 + 0.733597i
\(670\) 0.0230009i 0.000888602i
\(671\) −33.1623 −1.28022
\(672\) −9.95733 + 17.2466i −0.384112 + 0.665302i
\(673\) 4.85546 + 8.40990i 0.187164 + 0.324178i 0.944304 0.329076i \(-0.106737\pi\)
−0.757140 + 0.653253i \(0.773404\pi\)
\(674\) 16.0051 + 9.24056i 0.616494 + 0.355933i
\(675\) 12.2496 + 21.2169i 0.471487 + 0.816640i
\(676\) 5.14246 + 8.90701i 0.197787 + 0.342577i
\(677\) 36.1255i 1.38842i 0.719775 + 0.694208i \(0.244245\pi\)
−0.719775 + 0.694208i \(0.755755\pi\)
\(678\) −2.36131 4.08991i −0.0906857 0.157072i
\(679\) −4.88689 + 8.46433i −0.187541 + 0.324831i
\(680\) −0.745488 0.430408i −0.0285882 0.0165054i
\(681\) −28.7282 −1.10087
\(682\) 2.08233 + 3.60669i 0.0797363 + 0.138107i
\(683\) −19.3319 33.4838i −0.739714 1.28122i −0.952624 0.304150i \(-0.901628\pi\)
0.212911 0.977072i \(-0.431706\pi\)
\(684\) 5.82455 10.0884i 0.222707 0.385740i
\(685\) −0.471031 + 0.271950i −0.0179972 + 0.0103907i
\(686\) 0.553122 + 0.958036i 0.0211183 + 0.0365780i
\(687\) 3.23731i 0.123511i
\(688\) 7.38338i 0.281489i
\(689\) 17.7971 + 30.8255i 0.678016 + 1.17436i
\(690\) 0.0188443i 0.000717389i
\(691\) 41.1334 23.7484i 1.56479 0.903431i 0.568028 0.823009i \(-0.307706\pi\)
0.996761 0.0804224i \(-0.0256269\pi\)
\(692\) 38.8309i 1.47613i
\(693\) −9.87598 + 17.1057i −0.375158 + 0.649792i
\(694\) −4.80538 + 8.32316i −0.182410 + 0.315943i
\(695\) 0.351667 0.609105i 0.0133395 0.0231047i
\(696\) 6.58684 3.80291i 0.249673 0.144149i
\(697\) −4.14764 −0.157103
\(698\) 4.53949 10.4713i 0.171822 0.396345i
\(699\) 18.1751 0.687444
\(700\) 25.8664 14.9340i 0.977657 0.564451i
\(701\) 10.2181 17.6983i 0.385934 0.668457i −0.605965 0.795492i \(-0.707213\pi\)
0.991898 + 0.127035i \(0.0405460\pi\)
\(702\) 6.58480 11.4052i 0.248527 0.430462i
\(703\) 17.6645 30.5958i 0.666228 1.15394i
\(704\) 1.00025i 0.0376985i
\(705\) −0.335643 + 0.193783i −0.0126410 + 0.00729830i
\(706\) 12.4926i 0.470164i
\(707\) 8.77639 + 15.2012i 0.330070 + 0.571698i
\(708\) 10.4177i 0.391523i
\(709\) 7.43814i 0.279345i −0.990198 0.139673i \(-0.955395\pi\)
0.990198 0.139673i \(-0.0446050\pi\)
\(710\) −0.149823 0.259501i −0.00562276 0.00973891i
\(711\) −4.96559 + 2.86688i −0.186224 + 0.107517i
\(712\) 14.3942 24.9315i 0.539445 0.934346i
\(713\) −0.631596 1.09396i −0.0236535 0.0409690i
\(714\) 6.41492 + 11.1110i 0.240072 + 0.415817i
\(715\) −0.755147 −0.0282409
\(716\) 20.9964 + 12.1222i 0.784671 + 0.453030i
\(717\) 5.21113 9.02593i 0.194613 0.337080i
\(718\) 0.575149 + 0.996187i 0.0214644 + 0.0371774i
\(719\) 28.0198i 1.04496i 0.852651 + 0.522481i \(0.174993\pi\)
−0.852651 + 0.522481i \(0.825007\pi\)
\(720\) 0.128995 + 0.223427i 0.00480738 + 0.00832662i
\(721\) 25.8862 + 44.8363i 0.964053 + 1.66979i
\(722\) −3.66595 2.11654i −0.136432 0.0787693i
\(723\) 7.21607 + 12.4986i 0.268369 + 0.464828i
\(724\) 8.65171 14.9852i 0.321538 0.556921i
\(725\) −17.6977 −0.657277
\(726\) 2.48668i 0.0922892i
\(727\) 8.65263 14.9868i 0.320908 0.555829i −0.659767 0.751470i \(-0.729345\pi\)
0.980676 + 0.195640i \(0.0626786\pi\)
\(728\) −30.9991 17.8974i −1.14890 0.663320i
\(729\) 11.3061 0.418745
\(730\) 0.0501988 + 0.0289823i 0.00185794 + 0.00107268i
\(731\) −19.8463 11.4582i −0.734040 0.423798i
\(732\) 17.3615 10.0236i 0.641698 0.370484i
\(733\) 5.67833i 0.209734i 0.994486 + 0.104867i \(0.0334416\pi\)
−0.994486 + 0.104867i \(0.966558\pi\)
\(734\) 11.0911 0.409380
\(735\) 0.415419 0.0153230
\(736\) 2.70197i 0.0995961i
\(737\) 1.49013i 0.0548896i
\(738\) −0.766961 0.442805i −0.0282322 0.0162999i
\(739\) 24.6857 0.908078 0.454039 0.890982i \(-0.349983\pi\)
0.454039 + 0.890982i \(0.349983\pi\)
\(740\) 0.544911 + 0.943814i 0.0200313 + 0.0346953i
\(741\) −12.8159 7.39924i −0.470802 0.271818i
\(742\) −15.7453 9.09054i −0.578027 0.333724i
\(743\) 29.2601 1.07345 0.536724 0.843758i \(-0.319662\pi\)
0.536724 + 0.843758i \(0.319662\pi\)
\(744\) −4.86086 2.80642i −0.178208 0.102888i
\(745\) 1.42370i 0.0521604i
\(746\) −17.1830 −0.629114
\(747\) −13.6933 + 23.7174i −0.501011 + 0.867776i
\(748\) −21.6634 12.5074i −0.792093 0.457315i
\(749\) 13.3840 23.1817i 0.489039 0.847041i
\(750\) 0.389836i 0.0142348i
\(751\) 16.9243i 0.617578i 0.951131 + 0.308789i \(0.0999237\pi\)
−0.951131 + 0.308789i \(0.900076\pi\)
\(752\) 9.98929 5.76732i 0.364272 0.210312i
\(753\) 8.46016 + 4.88448i 0.308306 + 0.178000i
\(754\) 4.75673 + 8.23889i 0.173230 + 0.300043i
\(755\) 0.0926908 + 0.160545i 0.00337336 + 0.00584284i
\(756\) 29.3205i 1.06638i
\(757\) 37.1940 + 21.4740i 1.35184 + 0.780485i 0.988507 0.151174i \(-0.0483053\pi\)
0.363333 + 0.931659i \(0.381639\pi\)
\(758\) −17.5568 −0.637692
\(759\) 1.22084i 0.0443137i
\(760\) −0.439214 + 0.253581i −0.0159320 + 0.00919833i
\(761\) −5.83662 3.36977i −0.211577 0.122154i 0.390467 0.920617i \(-0.372314\pi\)
−0.602044 + 0.798463i \(0.705647\pi\)
\(762\) −9.64158 −0.349277
\(763\) 30.4667i 1.10297i
\(764\) −18.5675 −0.671750
\(765\) 0.800751 0.0289512
\(766\) −5.52341 + 9.56682i −0.199569