Properties

Label 380.2.d.b.379.11
Level $380$
Weight $2$
Character 380.379
Analytic conductor $3.034$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 379.11
Character \(\chi\) \(=\) 380.379
Dual form 380.2.d.b.379.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.948256 + 1.04920i) q^{2} +1.76151i q^{3} +(-0.201622 - 1.98981i) q^{4} +(-1.85854 - 1.24332i) q^{5} +(-1.84816 - 1.67036i) q^{6} +4.29252 q^{7} +(2.27889 + 1.67531i) q^{8} -0.102903 q^{9} +O(q^{10})\) \(q+(-0.948256 + 1.04920i) q^{2} +1.76151i q^{3} +(-0.201622 - 1.98981i) q^{4} +(-1.85854 - 1.24332i) q^{5} +(-1.84816 - 1.67036i) q^{6} +4.29252 q^{7} +(2.27889 + 1.67531i) q^{8} -0.102903 q^{9} +(3.06685 - 0.770986i) q^{10} +0.376641i q^{11} +(3.50506 - 0.355158i) q^{12} +0.928582 q^{13} +(-4.07040 + 4.50369i) q^{14} +(2.19011 - 3.27382i) q^{15} +(-3.91870 + 0.802380i) q^{16} +5.96697i q^{17} +(0.0975780 - 0.107965i) q^{18} +(3.61406 - 2.43692i) q^{19} +(-2.09924 + 3.94882i) q^{20} +7.56129i q^{21} +(-0.395170 - 0.357152i) q^{22} -0.352652 q^{23} +(-2.95107 + 4.01428i) q^{24} +(1.90832 + 4.62150i) q^{25} +(-0.880533 + 0.974264i) q^{26} +5.10325i q^{27} +(-0.865466 - 8.54130i) q^{28} -3.89105i q^{29} +(1.35810 + 5.40228i) q^{30} -1.06308 q^{31} +(2.87407 - 4.87234i) q^{32} -0.663455 q^{33} +(-6.26051 - 5.65821i) q^{34} +(-7.97780 - 5.33696i) q^{35} +(0.0207474 + 0.204757i) q^{36} -9.60143 q^{37} +(-0.870242 + 6.10268i) q^{38} +1.63570i q^{39} +(-2.15246 - 5.94701i) q^{40} +6.82129i q^{41} +(-7.93327 - 7.17004i) q^{42} +9.45416 q^{43} +(0.749444 - 0.0759391i) q^{44} +(0.191248 + 0.127941i) q^{45} +(0.334405 - 0.370001i) q^{46} +2.56158 q^{47} +(-1.41340 - 6.90281i) q^{48} +11.4257 q^{49} +(-6.65844 - 2.38016i) q^{50} -10.5108 q^{51} +(-0.187223 - 1.84770i) q^{52} +3.18648 q^{53} +(-5.35431 - 4.83919i) q^{54} +(0.468284 - 0.700001i) q^{55} +(9.78217 + 7.19129i) q^{56} +(4.29265 + 6.36618i) q^{57} +(4.08247 + 3.68971i) q^{58} -3.98595 q^{59} +(-6.95587 - 3.69783i) q^{60} -3.22322 q^{61} +(1.00807 - 1.11538i) q^{62} -0.441711 q^{63} +(2.38668 + 7.63569i) q^{64} +(-1.72580 - 1.15452i) q^{65} +(0.629125 - 0.696094i) q^{66} +8.75380i q^{67} +(11.8731 - 1.20307i) q^{68} -0.621199i q^{69} +(13.1645 - 3.30947i) q^{70} +10.1166 q^{71} +(-0.234504 - 0.172394i) q^{72} -5.09707i q^{73} +(9.10461 - 10.0738i) q^{74} +(-8.14081 + 3.36152i) q^{75} +(-5.57769 - 6.69995i) q^{76} +1.61674i q^{77} +(-1.71617 - 1.55106i) q^{78} +14.4968 q^{79} +(8.28066 + 3.38093i) q^{80} -9.29812 q^{81} +(-7.15687 - 6.46833i) q^{82} -3.49815 q^{83} +(15.0455 - 1.52452i) q^{84} +(7.41883 - 11.0898i) q^{85} +(-8.96496 + 9.91926i) q^{86} +6.85410 q^{87} +(-0.630990 + 0.858323i) q^{88} -10.4915i q^{89} +(-0.315587 + 0.0793365i) q^{90} +3.98595 q^{91} +(0.0711025 + 0.701712i) q^{92} -1.87262i q^{93} +(-2.42904 + 2.68760i) q^{94} +(-9.74673 + 0.0356921i) q^{95} +(8.58266 + 5.06270i) q^{96} -9.74137 q^{97} +(-10.8345 + 11.9878i) q^{98} -0.0387573i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 4q^{5} + 8q^{6} - 8q^{9} + O(q^{10}) \) \( 40q - 4q^{5} + 8q^{6} - 8q^{9} - 8q^{16} - 20q^{20} - 40q^{24} - 84q^{25} - 24q^{26} + 24q^{30} + 24q^{36} - 40q^{44} - 12q^{45} + 128q^{49} - 120q^{54} + 24q^{61} + 72q^{64} + 112q^{66} + 32q^{74} + 56q^{76} + 96q^{80} - 72q^{81} + 44q^{85} - 40q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.948256 + 1.04920i −0.670518 + 0.741893i
\(3\) 1.76151i 1.01701i 0.861060 + 0.508503i \(0.169801\pi\)
−0.861060 + 0.508503i \(0.830199\pi\)
\(4\) −0.201622 1.98981i −0.100811 0.994906i
\(5\) −1.85854 1.24332i −0.831163 0.556028i
\(6\) −1.84816 1.67036i −0.754510 0.681921i
\(7\) 4.29252 1.62242 0.811209 0.584756i \(-0.198810\pi\)
0.811209 + 0.584756i \(0.198810\pi\)
\(8\) 2.27889 + 1.67531i 0.805709 + 0.592311i
\(9\) −0.102903 −0.0343009
\(10\) 3.06685 0.770986i 0.969824 0.243807i
\(11\) 0.376641i 0.113562i 0.998387 + 0.0567808i \(0.0180836\pi\)
−0.998387 + 0.0567808i \(0.981916\pi\)
\(12\) 3.50506 0.355158i 1.01182 0.102525i
\(13\) 0.928582 0.257542 0.128771 0.991674i \(-0.458897\pi\)
0.128771 + 0.991674i \(0.458897\pi\)
\(14\) −4.07040 + 4.50369i −1.08786 + 1.20366i
\(15\) 2.19011 3.27382i 0.565484 0.845298i
\(16\) −3.91870 + 0.802380i −0.979674 + 0.200595i
\(17\) 5.96697i 1.44720i 0.690219 + 0.723601i \(0.257514\pi\)
−0.690219 + 0.723601i \(0.742486\pi\)
\(18\) 0.0975780 0.107965i 0.0229994 0.0254476i
\(19\) 3.61406 2.43692i 0.829122 0.559068i
\(20\) −2.09924 + 3.94882i −0.469405 + 0.882983i
\(21\) 7.56129i 1.65001i
\(22\) −0.395170 0.357152i −0.0842505 0.0761450i
\(23\) −0.352652 −0.0735331 −0.0367666 0.999324i \(-0.511706\pi\)
−0.0367666 + 0.999324i \(0.511706\pi\)
\(24\) −2.95107 + 4.01428i −0.602384 + 0.819411i
\(25\) 1.90832 + 4.62150i 0.381665 + 0.924301i
\(26\) −0.880533 + 0.974264i −0.172687 + 0.191069i
\(27\) 5.10325i 0.982122i
\(28\) −0.865466 8.54130i −0.163558 1.61415i
\(29\) 3.89105i 0.722549i −0.932459 0.361275i \(-0.882342\pi\)
0.932459 0.361275i \(-0.117658\pi\)
\(30\) 1.35810 + 5.40228i 0.247953 + 0.986316i
\(31\) −1.06308 −0.190934 −0.0954672 0.995433i \(-0.530435\pi\)
−0.0954672 + 0.995433i \(0.530435\pi\)
\(32\) 2.87407 4.87234i 0.508069 0.861316i
\(33\) −0.663455 −0.115493
\(34\) −6.26051 5.65821i −1.07367 0.970375i
\(35\) −7.97780 5.33696i −1.34849 0.902111i
\(36\) 0.0207474 + 0.204757i 0.00345791 + 0.0341261i
\(37\) −9.60143 −1.57846 −0.789232 0.614095i \(-0.789521\pi\)
−0.789232 + 0.614095i \(0.789521\pi\)
\(38\) −0.870242 + 6.10268i −0.141172 + 0.989985i
\(39\) 1.63570i 0.261922i
\(40\) −2.15246 5.94701i −0.340334 0.940305i
\(41\) 6.82129i 1.06531i 0.846334 + 0.532653i \(0.178805\pi\)
−0.846334 + 0.532653i \(0.821195\pi\)
\(42\) −7.93327 7.17004i −1.22413 1.10636i
\(43\) 9.45416 1.44175 0.720873 0.693067i \(-0.243741\pi\)
0.720873 + 0.693067i \(0.243741\pi\)
\(44\) 0.749444 0.0759391i 0.112983 0.0114483i
\(45\) 0.191248 + 0.127941i 0.0285096 + 0.0190723i
\(46\) 0.334405 0.370001i 0.0493053 0.0545537i
\(47\) 2.56158 0.373645 0.186823 0.982394i \(-0.440181\pi\)
0.186823 + 0.982394i \(0.440181\pi\)
\(48\) −1.41340 6.90281i −0.204006 0.996334i
\(49\) 11.4257 1.63224
\(50\) −6.65844 2.38016i −0.941646 0.336606i
\(51\) −10.5108 −1.47181
\(52\) −0.187223 1.84770i −0.0259631 0.256230i
\(53\) 3.18648 0.437697 0.218848 0.975759i \(-0.429770\pi\)
0.218848 + 0.975759i \(0.429770\pi\)
\(54\) −5.35431 4.83919i −0.728629 0.658530i
\(55\) 0.468284 0.700001i 0.0631434 0.0943882i
\(56\) 9.78217 + 7.19129i 1.30720 + 0.960977i
\(57\) 4.29265 + 6.36618i 0.568576 + 0.843221i
\(58\) 4.08247 + 3.68971i 0.536054 + 0.484482i
\(59\) −3.98595 −0.518927 −0.259463 0.965753i \(-0.583546\pi\)
−0.259463 + 0.965753i \(0.583546\pi\)
\(60\) −6.95587 3.69783i −0.897999 0.477388i
\(61\) −3.22322 −0.412691 −0.206346 0.978479i \(-0.566157\pi\)
−0.206346 + 0.978479i \(0.566157\pi\)
\(62\) 1.00807 1.11538i 0.128025 0.141653i
\(63\) −0.441711 −0.0556504
\(64\) 2.38668 + 7.63569i 0.298335 + 0.954461i
\(65\) −1.72580 1.15452i −0.214060 0.143201i
\(66\) 0.629125 0.696094i 0.0774400 0.0856833i
\(67\) 8.75380i 1.06945i 0.845027 + 0.534723i \(0.179584\pi\)
−0.845027 + 0.534723i \(0.820416\pi\)
\(68\) 11.8731 1.20307i 1.43983 0.145894i
\(69\) 0.621199i 0.0747836i
\(70\) 13.1645 3.30947i 1.57346 0.395557i
\(71\) 10.1166 1.20062 0.600308 0.799769i \(-0.295044\pi\)
0.600308 + 0.799769i \(0.295044\pi\)
\(72\) −0.234504 0.172394i −0.0276365 0.0203168i
\(73\) 5.09707i 0.596567i −0.954477 0.298283i \(-0.903586\pi\)
0.954477 0.298283i \(-0.0964141\pi\)
\(74\) 9.10461 10.0738i 1.05839 1.17105i
\(75\) −8.14081 + 3.36152i −0.940019 + 0.388155i
\(76\) −5.57769 6.69995i −0.639805 0.768537i
\(77\) 1.61674i 0.184244i
\(78\) −1.71617 1.55106i −0.194318 0.175623i
\(79\) 14.4968 1.63102 0.815509 0.578745i \(-0.196457\pi\)
0.815509 + 0.578745i \(0.196457\pi\)
\(80\) 8.28066 + 3.38093i 0.925806 + 0.378000i
\(81\) −9.29812 −1.03312
\(82\) −7.15687 6.46833i −0.790344 0.714307i
\(83\) −3.49815 −0.383972 −0.191986 0.981398i \(-0.561493\pi\)
−0.191986 + 0.981398i \(0.561493\pi\)
\(84\) 15.0455 1.52452i 1.64160 0.166339i
\(85\) 7.41883 11.0898i 0.804686 1.20286i
\(86\) −8.96496 + 9.91926i −0.966716 + 1.06962i
\(87\) 6.85410 0.734837
\(88\) −0.630990 + 0.858323i −0.0672638 + 0.0914976i
\(89\) 10.4915i 1.11210i −0.831149 0.556050i \(-0.812316\pi\)
0.831149 0.556050i \(-0.187684\pi\)
\(90\) −0.315587 + 0.0793365i −0.0332658 + 0.00836280i
\(91\) 3.98595 0.417841
\(92\) 0.0711025 + 0.701712i 0.00741295 + 0.0731585i
\(93\) 1.87262i 0.194181i
\(94\) −2.42904 + 2.68760i −0.250536 + 0.277205i
\(95\) −9.74673 + 0.0356921i −0.999993 + 0.00366193i
\(96\) 8.58266 + 5.06270i 0.875964 + 0.516709i
\(97\) −9.74137 −0.989086 −0.494543 0.869153i \(-0.664665\pi\)
−0.494543 + 0.869153i \(0.664665\pi\)
\(98\) −10.8345 + 11.9878i −1.09445 + 1.21095i
\(99\) 0.0387573i 0.00389526i
\(100\) 8.81116 4.72900i 0.881116 0.472900i
\(101\) −12.8341 −1.27704 −0.638519 0.769606i \(-0.720452\pi\)
−0.638519 + 0.769606i \(0.720452\pi\)
\(102\) 9.96697 11.0279i 0.986877 1.09193i
\(103\) 2.13005i 0.209881i −0.994479 0.104940i \(-0.966535\pi\)
0.994479 0.104940i \(-0.0334651\pi\)
\(104\) 2.11614 + 1.55566i 0.207504 + 0.152545i
\(105\) 9.40109 14.0529i 0.917452 1.37143i
\(106\) −3.02160 + 3.34324i −0.293484 + 0.324724i
\(107\) 16.4182i 1.58721i −0.608433 0.793606i \(-0.708201\pi\)
0.608433 0.793606i \(-0.291799\pi\)
\(108\) 10.1545 1.02893i 0.977118 0.0990087i
\(109\) 17.3936i 1.66600i −0.553273 0.833000i \(-0.686621\pi\)
0.553273 0.833000i \(-0.313379\pi\)
\(110\) 0.290385 + 1.15510i 0.0276871 + 0.110135i
\(111\) 16.9130i 1.60531i
\(112\) −16.8211 + 3.44423i −1.58944 + 0.325449i
\(113\) −12.0642 −1.13490 −0.567452 0.823406i \(-0.692071\pi\)
−0.567452 + 0.823406i \(0.692071\pi\)
\(114\) −10.7499 1.53294i −1.00682 0.143573i
\(115\) 0.655418 + 0.438459i 0.0611180 + 0.0408865i
\(116\) −7.74245 + 0.784521i −0.718868 + 0.0728409i
\(117\) −0.0955535 −0.00883392
\(118\) 3.77970 4.18204i 0.347950 0.384988i
\(119\) 25.6133i 2.34797i
\(120\) 10.4757 3.79157i 0.956295 0.346122i
\(121\) 10.8581 0.987104
\(122\) 3.05644 3.38179i 0.276717 0.306173i
\(123\) −12.0157 −1.08342
\(124\) 0.214340 + 2.11533i 0.0192483 + 0.189962i
\(125\) 2.19931 10.9619i 0.196712 0.980461i
\(126\) 0.418855 0.463441i 0.0373146 0.0412866i
\(127\) 4.18189i 0.371083i −0.982636 0.185541i \(-0.940596\pi\)
0.982636 0.185541i \(-0.0594039\pi\)
\(128\) −10.2745 4.73649i −0.908147 0.418651i
\(129\) 16.6536i 1.46626i
\(130\) 2.84782 0.715924i 0.249771 0.0627907i
\(131\) 0.974860i 0.0851740i −0.999093 0.0425870i \(-0.986440\pi\)
0.999093 0.0425870i \(-0.0135600\pi\)
\(132\) 0.133767 + 1.32015i 0.0116429 + 0.114904i
\(133\) 15.5134 10.4605i 1.34518 0.907043i
\(134\) −9.18445 8.30084i −0.793415 0.717083i
\(135\) 6.34496 9.48459i 0.546088 0.816303i
\(136\) −9.99651 + 13.5981i −0.857194 + 1.16602i
\(137\) 3.53192i 0.301753i −0.988553 0.150876i \(-0.951790\pi\)
0.988553 0.150876i \(-0.0482095\pi\)
\(138\) 0.651759 + 0.589056i 0.0554814 + 0.0501438i
\(139\) 7.20995i 0.611540i −0.952105 0.305770i \(-0.901086\pi\)
0.952105 0.305770i \(-0.0989139\pi\)
\(140\) −9.01104 + 16.9504i −0.761572 + 1.43257i
\(141\) 4.51225i 0.380000i
\(142\) −9.59310 + 10.6143i −0.805035 + 0.890729i
\(143\) 0.349742i 0.0292469i
\(144\) 0.403244 0.0825670i 0.0336037 0.00688058i
\(145\) −4.83781 + 7.23166i −0.401758 + 0.600556i
\(146\) 5.34782 + 4.83333i 0.442589 + 0.400009i
\(147\) 20.1264i 1.66000i
\(148\) 1.93586 + 19.1050i 0.159127 + 1.57042i
\(149\) 3.91562 0.320780 0.160390 0.987054i \(-0.448725\pi\)
0.160390 + 0.987054i \(0.448725\pi\)
\(150\) 4.19267 11.7289i 0.342330 0.957659i
\(151\) −7.22811 −0.588216 −0.294108 0.955772i \(-0.595022\pi\)
−0.294108 + 0.955772i \(0.595022\pi\)
\(152\) 12.3186 + 0.501183i 0.999173 + 0.0406513i
\(153\) 0.614016i 0.0496403i
\(154\) −1.69627 1.53308i −0.136690 0.123539i
\(155\) 1.97577 + 1.32174i 0.158698 + 0.106165i
\(156\) 3.25474 0.329794i 0.260588 0.0264046i
\(157\) 23.7964i 1.89916i 0.313526 + 0.949580i \(0.398490\pi\)
−0.313526 + 0.949580i \(0.601510\pi\)
\(158\) −13.7467 + 15.2100i −1.09363 + 1.21004i
\(159\) 5.61301i 0.445140i
\(160\) −11.3994 + 5.48204i −0.901205 + 0.433393i
\(161\) −1.51377 −0.119301
\(162\) 8.81699 9.75554i 0.692729 0.766468i
\(163\) −15.5139 −1.21514 −0.607571 0.794265i \(-0.707856\pi\)
−0.607571 + 0.794265i \(0.707856\pi\)
\(164\) 13.5731 1.37532i 1.05988 0.107395i
\(165\) 1.23306 + 0.824885i 0.0959933 + 0.0642172i
\(166\) 3.31714 3.67025i 0.257460 0.284866i
\(167\) 4.46016i 0.345138i −0.984997 0.172569i \(-0.944793\pi\)
0.984997 0.172569i \(-0.0552067\pi\)
\(168\) −12.6675 + 17.2314i −0.977319 + 1.32943i
\(169\) −12.1377 −0.933672
\(170\) 4.60045 + 18.2998i 0.352838 + 1.40353i
\(171\) −0.371896 + 0.250766i −0.0284396 + 0.0191765i
\(172\) −1.90617 18.8120i −0.145344 1.43440i
\(173\) 21.0522 1.60057 0.800283 0.599622i \(-0.204682\pi\)
0.800283 + 0.599622i \(0.204682\pi\)
\(174\) −6.49944 + 7.19129i −0.492721 + 0.545170i
\(175\) 8.19151 + 19.8379i 0.619220 + 1.49960i
\(176\) −0.302209 1.47594i −0.0227799 0.111253i
\(177\) 7.02128i 0.527752i
\(178\) 11.0077 + 9.94866i 0.825060 + 0.745684i
\(179\) −19.5988 −1.46488 −0.732440 0.680832i \(-0.761619\pi\)
−0.732440 + 0.680832i \(0.761619\pi\)
\(180\) 0.216018 0.406344i 0.0161010 0.0302871i
\(181\) 17.6144i 1.30926i −0.755947 0.654632i \(-0.772823\pi\)
0.755947 0.654632i \(-0.227177\pi\)
\(182\) −3.77970 + 4.18204i −0.280170 + 0.309994i
\(183\) 5.67772i 0.419709i
\(184\) −0.803656 0.590802i −0.0592463 0.0435545i
\(185\) 17.8446 + 11.9376i 1.31196 + 0.877671i
\(186\) 1.96474 + 1.77572i 0.144062 + 0.130202i
\(187\) −2.24740 −0.164346
\(188\) −0.516472 5.09707i −0.0376676 0.371742i
\(189\) 21.9058i 1.59341i
\(190\) 9.20494 10.2601i 0.667797 0.744344i
\(191\) 23.4244i 1.69493i 0.530849 + 0.847467i \(0.321873\pi\)
−0.530849 + 0.847467i \(0.678127\pi\)
\(192\) −13.4503 + 4.20415i −0.970693 + 0.303408i
\(193\) −19.0446 −1.37086 −0.685431 0.728137i \(-0.740386\pi\)
−0.685431 + 0.728137i \(0.740386\pi\)
\(194\) 9.23731 10.2206i 0.663200 0.733796i
\(195\) 2.03370 3.04001i 0.145636 0.217700i
\(196\) −2.30367 22.7350i −0.164548 1.62393i
\(197\) 19.5602i 1.39361i −0.717262 0.696803i \(-0.754605\pi\)
0.717262 0.696803i \(-0.245395\pi\)
\(198\) 0.0406640 + 0.0367519i 0.00288987 + 0.00261184i
\(199\) 20.7395i 1.47018i −0.677969 0.735091i \(-0.737140\pi\)
0.677969 0.735091i \(-0.262860\pi\)
\(200\) −3.39359 + 13.7289i −0.239963 + 0.970782i
\(201\) −15.4199 −1.08763
\(202\) 12.1700 13.4654i 0.856276 0.947425i
\(203\) 16.7024i 1.17228i
\(204\) 2.11922 + 20.9146i 0.148375 + 1.46431i
\(205\) 8.48103 12.6776i 0.592341 0.885444i
\(206\) 2.23484 + 2.01984i 0.155709 + 0.140729i
\(207\) 0.0362888 0.00252225
\(208\) −3.63883 + 0.745075i −0.252308 + 0.0516617i
\(209\) 0.917845 + 1.36120i 0.0634887 + 0.0941563i
\(210\) 5.82965 + 23.1894i 0.402284 + 1.60022i
\(211\) −0.0749824 −0.00516200 −0.00258100 0.999997i \(-0.500822\pi\)
−0.00258100 + 0.999997i \(0.500822\pi\)
\(212\) −0.642465 6.34050i −0.0441247 0.435467i
\(213\) 17.8204i 1.22103i
\(214\) 17.2259 + 15.5687i 1.17754 + 1.06425i
\(215\) −17.5709 11.7545i −1.19833 0.801651i
\(216\) −8.54953 + 11.6298i −0.581722 + 0.791305i
\(217\) −4.56328 −0.309776
\(218\) 18.2492 + 16.4935i 1.23599 + 1.11708i
\(219\) 8.97852 0.606712
\(220\) −1.48729 0.790662i −0.100273 0.0533064i
\(221\) 5.54082i 0.372716i
\(222\) 17.7450 + 16.0378i 1.19097 + 1.07639i
\(223\) 1.00367i 0.0672104i −0.999435 0.0336052i \(-0.989301\pi\)
0.999435 0.0336052i \(-0.0106989\pi\)
\(224\) 12.3370 20.9146i 0.824301 1.39742i
\(225\) −0.196371 0.475565i −0.0130914 0.0317043i
\(226\) 11.4399 12.6577i 0.760974 0.841978i
\(227\) 6.78069i 0.450050i 0.974353 + 0.225025i \(0.0722464\pi\)
−0.974353 + 0.225025i \(0.927754\pi\)
\(228\) 11.8020 9.82513i 0.781607 0.650685i
\(229\) −18.5264 −1.22426 −0.612129 0.790758i \(-0.709687\pi\)
−0.612129 + 0.790758i \(0.709687\pi\)
\(230\) −1.08153 + 0.271890i −0.0713142 + 0.0179279i
\(231\) −2.84789 −0.187378
\(232\) 6.51870 8.86727i 0.427974 0.582165i
\(233\) 10.1129i 0.662519i −0.943540 0.331259i \(-0.892527\pi\)
0.943540 0.331259i \(-0.107473\pi\)
\(234\) 0.0906091 0.100254i 0.00592331 0.00655383i
\(235\) −4.76080 3.18486i −0.310560 0.207758i
\(236\) 0.803656 + 7.93129i 0.0523136 + 0.516283i
\(237\) 25.5362i 1.65875i
\(238\) −26.8734 24.2880i −1.74194 1.57435i
\(239\) 18.2687i 1.18171i −0.806780 0.590853i \(-0.798792\pi\)
0.806780 0.590853i \(-0.201208\pi\)
\(240\) −5.95553 + 14.5864i −0.384428 + 0.941550i
\(241\) 13.1021i 0.843981i 0.906600 + 0.421991i \(0.138668\pi\)
−0.906600 + 0.421991i \(0.861332\pi\)
\(242\) −10.2963 + 11.3923i −0.661871 + 0.732326i
\(243\) 1.06893i 0.0685718i
\(244\) 0.649873 + 6.41360i 0.0416038 + 0.410589i
\(245\) −21.2351 14.2058i −1.35666 0.907573i
\(246\) 11.3940 12.6069i 0.726455 0.803784i
\(247\) 3.35595 2.26288i 0.213534 0.143984i
\(248\) −2.42264 1.78098i −0.153838 0.113093i
\(249\) 6.16202i 0.390502i
\(250\) 9.41566 + 12.7022i 0.595499 + 0.803356i
\(251\) 12.8628i 0.811891i 0.913897 + 0.405946i \(0.133058\pi\)
−0.913897 + 0.405946i \(0.866942\pi\)
\(252\) 0.0890587 + 0.878922i 0.00561017 + 0.0553669i
\(253\) 0.132823i 0.00835053i
\(254\) 4.38762 + 3.96550i 0.275304 + 0.248818i
\(255\) 19.5348 + 13.0683i 1.22332 + 0.818370i
\(256\) 14.7124 6.28857i 0.919523 0.393035i
\(257\) 27.1520 1.69369 0.846847 0.531836i \(-0.178498\pi\)
0.846847 + 0.531836i \(0.178498\pi\)
\(258\) −17.4728 15.7918i −1.08781 0.983156i
\(259\) −41.2143 −2.56093
\(260\) −1.94932 + 3.66680i −0.120892 + 0.227405i
\(261\) 0.400399i 0.0247841i
\(262\) 1.02282 + 0.924417i 0.0631900 + 0.0571107i
\(263\) −18.6447 −1.14968 −0.574841 0.818265i \(-0.694936\pi\)
−0.574841 + 0.818265i \(0.694936\pi\)
\(264\) −1.51194 1.11149i −0.0930536 0.0684076i
\(265\) −5.92220 3.96181i −0.363798 0.243372i
\(266\) −3.73553 + 26.1958i −0.229040 + 1.60617i
\(267\) 18.4809 1.13101
\(268\) 17.4184 1.76496i 1.06400 0.107812i
\(269\) 4.51225i 0.275116i 0.990494 + 0.137558i \(0.0439254\pi\)
−0.990494 + 0.137558i \(0.956075\pi\)
\(270\) 3.93454 + 15.6509i 0.239448 + 0.952485i
\(271\) 12.8691i 0.781741i 0.920446 + 0.390871i \(0.127826\pi\)
−0.920446 + 0.390871i \(0.872174\pi\)
\(272\) −4.78777 23.3827i −0.290301 1.41779i
\(273\) 7.02128i 0.424947i
\(274\) 3.70568 + 3.34917i 0.223868 + 0.202331i
\(275\) −1.74065 + 0.718753i −0.104965 + 0.0433424i
\(276\) −1.23607 + 0.125247i −0.0744026 + 0.00753901i
\(277\) 4.35925i 0.261922i 0.991388 + 0.130961i \(0.0418063\pi\)
−0.991388 + 0.130961i \(0.958194\pi\)
\(278\) 7.56465 + 6.83688i 0.453697 + 0.410049i
\(279\) 0.109394 0.00654922
\(280\) −9.23948 25.5276i −0.552164 1.52557i
\(281\) 7.22169i 0.430810i −0.976525 0.215405i \(-0.930893\pi\)
0.976525 0.215405i \(-0.0691071\pi\)
\(282\) −4.73423 4.27876i −0.281919 0.254797i
\(283\) −4.15031 −0.246710 −0.123355 0.992363i \(-0.539365\pi\)
−0.123355 + 0.992363i \(0.539365\pi\)
\(284\) −2.03973 20.1301i −0.121035 1.19450i
\(285\) −0.0628719 17.1689i −0.00372421 1.01700i
\(286\) −0.366948 0.331645i −0.0216981 0.0196106i
\(287\) 29.2805i 1.72837i
\(288\) −0.295750 + 0.501376i −0.0174272 + 0.0295439i
\(289\) −18.6047 −1.09439
\(290\) −2.99994 11.9333i −0.176163 0.700745i
\(291\) 17.1595i 1.00591i
\(292\) −10.1422 + 1.02768i −0.593528 + 0.0601405i
\(293\) 4.82841 0.282079 0.141039 0.990004i \(-0.454956\pi\)
0.141039 + 0.990004i \(0.454956\pi\)
\(294\) −21.1166 19.0850i −1.23154 1.11306i
\(295\) 7.40804 + 4.95580i 0.431313 + 0.288538i
\(296\) −21.8806 16.0854i −1.27178 0.934942i
\(297\) −1.92209 −0.111531
\(298\) −3.71301 + 4.10825i −0.215089 + 0.237985i
\(299\) −0.327467 −0.0189379
\(300\) 8.33016 + 15.5209i 0.480942 + 0.896100i
\(301\) 40.5821 2.33911
\(302\) 6.85410 7.58370i 0.394409 0.436393i
\(303\) 22.6073i 1.29875i
\(304\) −12.2071 + 12.4494i −0.700123 + 0.714023i
\(305\) 5.99048 + 4.00749i 0.343014 + 0.229468i
\(306\) 0.644223 + 0.582245i 0.0368278 + 0.0332847i
\(307\) 0.488437i 0.0278766i −0.999903 0.0139383i \(-0.995563\pi\)
0.999903 0.0139383i \(-0.00443684\pi\)
\(308\) 3.21700 0.325970i 0.183306 0.0185739i
\(309\) 3.75210 0.213450
\(310\) −3.26030 + 0.819619i −0.185173 + 0.0465512i
\(311\) 2.59142i 0.146946i −0.997297 0.0734730i \(-0.976592\pi\)
0.997297 0.0734730i \(-0.0234083\pi\)
\(312\) −2.74031 + 3.72759i −0.155139 + 0.211033i
\(313\) 9.45632i 0.534503i −0.963627 0.267251i \(-0.913885\pi\)
0.963627 0.267251i \(-0.0861154\pi\)
\(314\) −24.9671 22.5651i −1.40897 1.27342i
\(315\) 0.820937 + 0.549187i 0.0462545 + 0.0309432i
\(316\) −2.92287 28.8459i −0.164425 1.62271i
\(317\) −23.7528 −1.33409 −0.667045 0.745018i \(-0.732441\pi\)
−0.667045 + 0.745018i \(0.732441\pi\)
\(318\) −5.88914 5.32257i −0.330247 0.298475i
\(319\) 1.46553 0.0820538
\(320\) 5.05785 17.1586i 0.282743 0.959196i
\(321\) 28.9208 1.61420
\(322\) 1.43544 1.58824i 0.0799938 0.0885090i
\(323\) 14.5410 + 21.5650i 0.809085 + 1.19991i
\(324\) 1.87471 + 18.5015i 0.104150 + 1.02786i
\(325\) 1.77203 + 4.29145i 0.0982948 + 0.238047i
\(326\) 14.7111 16.2771i 0.814775 0.901506i
\(327\) 30.6388 1.69433
\(328\) −11.4278 + 15.5450i −0.630993 + 0.858327i
\(329\) 10.9956 0.606209
\(330\) −2.03472 + 0.511515i −0.112008 + 0.0281580i
\(331\) 17.7390 0.975021 0.487511 0.873117i \(-0.337905\pi\)
0.487511 + 0.873117i \(0.337905\pi\)
\(332\) 0.705305 + 6.96066i 0.0387086 + 0.382016i
\(333\) 0.988012 0.0541427
\(334\) 4.67958 + 4.22938i 0.256055 + 0.231421i
\(335\) 10.8838 16.2693i 0.594643 0.888885i
\(336\) −6.06703 29.6304i −0.330983 1.61647i
\(337\) −4.34489 −0.236681 −0.118341 0.992973i \(-0.537757\pi\)
−0.118341 + 0.992973i \(0.537757\pi\)
\(338\) 11.5097 12.7349i 0.626044 0.692685i
\(339\) 21.2512i 1.15420i
\(340\) −23.5625 12.5261i −1.27785 0.679324i
\(341\) 0.400399i 0.0216828i
\(342\) 0.0895502 0.627981i 0.00484232 0.0339573i
\(343\) 18.9974 1.02576
\(344\) 21.5450 + 15.8386i 1.16163 + 0.853962i
\(345\) −0.772348 + 1.15452i −0.0415818 + 0.0621574i
\(346\) −19.9628 + 22.0878i −1.07321 + 1.18745i
\(347\) 23.7679 1.27593 0.637964 0.770067i \(-0.279777\pi\)
0.637964 + 0.770067i \(0.279777\pi\)
\(348\) −1.38194 13.6384i −0.0740796 0.731093i
\(349\) 14.9933 0.802570 0.401285 0.915953i \(-0.368564\pi\)
0.401285 + 0.915953i \(0.368564\pi\)
\(350\) −28.5815 10.2169i −1.52774 0.546116i
\(351\) 4.73879i 0.252938i
\(352\) 1.83512 + 1.08249i 0.0978124 + 0.0576971i
\(353\) 3.27604i 0.174366i 0.996192 + 0.0871831i \(0.0277865\pi\)
−0.996192 + 0.0871831i \(0.972213\pi\)
\(354\) 7.36669 + 6.65797i 0.391535 + 0.353867i
\(355\) −18.8020 12.5781i −0.997909 0.667577i
\(356\) −20.8762 + 2.11533i −1.10644 + 0.112112i
\(357\) −45.1180 −2.38790
\(358\) 18.5846 20.5629i 0.982228 1.08678i
\(359\) 1.83814i 0.0970133i 0.998823 + 0.0485067i \(0.0154462\pi\)
−0.998823 + 0.0485067i \(0.984554\pi\)
\(360\) 0.221494 + 0.611963i 0.0116738 + 0.0322533i
\(361\) 7.12282 17.6144i 0.374885 0.927071i
\(362\) 18.4809 + 16.7029i 0.971335 + 0.877886i
\(363\) 19.1267i 1.00389i
\(364\) −0.803656 7.93129i −0.0421230 0.415713i
\(365\) −6.33728 + 9.47309i −0.331708 + 0.495844i
\(366\) 5.95704 + 5.38393i 0.311380 + 0.281423i
\(367\) −9.82842 −0.513040 −0.256520 0.966539i \(-0.582576\pi\)
−0.256520 + 0.966539i \(0.582576\pi\)
\(368\) 1.38194 0.282961i 0.0720385 0.0147504i
\(369\) 0.701928i 0.0365409i
\(370\) −29.4462 + 7.40257i −1.53083 + 0.384841i
\(371\) 13.6780 0.710128
\(372\) −3.72616 + 0.377561i −0.193192 + 0.0195756i
\(373\) −8.37248 −0.433510 −0.216755 0.976226i \(-0.569547\pi\)
−0.216755 + 0.976226i \(0.569547\pi\)
\(374\) 2.13111 2.35797i 0.110197 0.121928i
\(375\) 19.3094 + 3.87409i 0.997135 + 0.200057i
\(376\) 5.83757 + 4.29145i 0.301050 + 0.221314i
\(377\) 3.61316i 0.186087i
\(378\) −22.9835 20.7723i −1.18214 1.06841i
\(379\) 32.6382 1.67651 0.838256 0.545277i \(-0.183575\pi\)
0.838256 + 0.545277i \(0.183575\pi\)
\(380\) 2.03618 + 19.3870i 0.104454 + 0.994530i
\(381\) 7.36642 0.377393
\(382\) −24.5768 22.2124i −1.25746 1.13648i
\(383\) 6.10267i 0.311832i 0.987770 + 0.155916i \(0.0498329\pi\)
−0.987770 + 0.155916i \(0.950167\pi\)
\(384\) 8.34336 18.0986i 0.425770 0.923591i
\(385\) 2.01012 3.00477i 0.102445 0.153137i
\(386\) 18.0592 19.9815i 0.919188 1.01703i
\(387\) −0.972857 −0.0494531
\(388\) 1.96407 + 19.3835i 0.0997108 + 0.984047i
\(389\) 3.65867 0.185502 0.0927510 0.995689i \(-0.470434\pi\)
0.0927510 + 0.995689i \(0.470434\pi\)
\(390\) 1.26110 + 5.01646i 0.0638585 + 0.254018i
\(391\) 2.10427i 0.106417i
\(392\) 26.0379 + 19.1416i 1.31511 + 0.966795i
\(393\) 1.71722 0.0866224
\(394\) 20.5225 + 18.5481i 1.03391 + 0.934439i
\(395\) −26.9428 18.0241i −1.35564 0.906892i
\(396\) −0.0771198 + 0.00781433i −0.00387541 + 0.000392685i
\(397\) 30.1641i 1.51389i 0.653478 + 0.756946i \(0.273309\pi\)
−0.653478 + 0.756946i \(0.726691\pi\)
\(398\) 21.7597 + 19.6663i 1.09072 + 0.985783i
\(399\) 18.4263 + 27.3269i 0.922468 + 1.36806i
\(400\) −11.1863 16.5791i −0.559317 0.828954i
\(401\) 34.6456i 1.73012i −0.501670 0.865059i \(-0.667281\pi\)
0.501670 0.865059i \(-0.332719\pi\)
\(402\) 14.6220 16.1785i 0.729278 0.806908i
\(403\) −0.987155 −0.0491737
\(404\) 2.58763 + 25.5374i 0.128739 + 1.27053i
\(405\) 17.2809 + 11.5605i 0.858695 + 0.574447i
\(406\) 17.5241 + 15.8381i 0.869705 + 0.786033i
\(407\) 3.61629i 0.179253i
\(408\) −23.9531 17.6089i −1.18585 0.871771i
\(409\) 30.5268i 1.50945i 0.656041 + 0.754726i \(0.272230\pi\)
−0.656041 + 0.754726i \(0.727770\pi\)
\(410\) 5.25912 + 20.9199i 0.259729 + 1.03316i
\(411\) 6.22150 0.306884
\(412\) −4.23841 + 0.429466i −0.208811 + 0.0211583i
\(413\) −17.1098 −0.841917
\(414\) −0.0344111 + 0.0380741i −0.00169121 + 0.00187124i
\(415\) 6.50145 + 4.34931i 0.319144 + 0.213499i
\(416\) 2.66881 4.52437i 0.130849 0.221825i
\(417\) 12.7004 0.621940
\(418\) −2.29852 0.327769i −0.112424 0.0160317i
\(419\) 6.46767i 0.315966i −0.987442 0.157983i \(-0.949501\pi\)
0.987442 0.157983i \(-0.0504992\pi\)
\(420\) −29.8582 15.8730i −1.45693 0.774523i
\(421\) 21.2039i 1.03341i −0.856162 0.516707i \(-0.827158\pi\)
0.856162 0.516707i \(-0.172842\pi\)
\(422\) 0.0711025 0.0786712i 0.00346122 0.00382965i
\(423\) −0.263594 −0.0128164
\(424\) 7.26164 + 5.33834i 0.352656 + 0.259253i
\(425\) −27.5764 + 11.3869i −1.33765 + 0.552346i
\(426\) −18.6971 16.8983i −0.905877 0.818726i
\(427\) −13.8357 −0.669558
\(428\) −32.6692 + 3.31028i −1.57913 + 0.160008i
\(429\) −0.616072 −0.0297443
\(430\) 28.9945 7.28902i 1.39824 0.351508i
\(431\) 7.73794 0.372723 0.186362 0.982481i \(-0.440330\pi\)
0.186362 + 0.982481i \(0.440330\pi\)
\(432\) −4.09475 19.9981i −0.197009 0.962159i
\(433\) −23.8336 −1.14537 −0.572684 0.819776i \(-0.694098\pi\)
−0.572684 + 0.819776i \(0.694098\pi\)
\(434\) 4.32716 4.78777i 0.207710 0.229820i
\(435\) −12.7386 8.52182i −0.610769 0.408590i
\(436\) −34.6099 + 3.50692i −1.65751 + 0.167951i
\(437\) −1.27451 + 0.859387i −0.0609679 + 0.0411100i
\(438\) −8.51393 + 9.42022i −0.406811 + 0.450115i
\(439\) 10.4173 0.497193 0.248596 0.968607i \(-0.420031\pi\)
0.248596 + 0.968607i \(0.420031\pi\)
\(440\) 2.23989 0.810705i 0.106782 0.0386489i
\(441\) −1.17573 −0.0559873
\(442\) −5.81340 5.25411i −0.276515 0.249913i
\(443\) −5.03629 −0.239282 −0.119641 0.992817i \(-0.538174\pi\)
−0.119641 + 0.992817i \(0.538174\pi\)
\(444\) −33.6536 + 3.41003i −1.59713 + 0.161833i
\(445\) −13.0443 + 19.4989i −0.618360 + 0.924337i
\(446\) 1.05304 + 0.951732i 0.0498630 + 0.0450658i
\(447\) 6.89739i 0.326235i
\(448\) 10.2449 + 32.7763i 0.484024 + 1.54854i
\(449\) 27.3757i 1.29194i −0.763363 0.645970i \(-0.776453\pi\)
0.763363 0.645970i \(-0.223547\pi\)
\(450\) 0.685171 + 0.244925i 0.0322993 + 0.0115459i
\(451\) −2.56918 −0.120978
\(452\) 2.43241 + 24.0055i 0.114411 + 1.12912i
\(453\) 12.7324i 0.598219i
\(454\) −7.11427 6.42983i −0.333889 0.301767i
\(455\) −7.40804 4.95580i −0.347294 0.232332i
\(456\) −0.882837 + 21.6994i −0.0413426 + 1.01617i
\(457\) 8.86333i 0.414609i −0.978276 0.207305i \(-0.933531\pi\)
0.978276 0.207305i \(-0.0664691\pi\)
\(458\) 17.5677 19.4378i 0.820887 0.908268i
\(459\) −30.4509 −1.42133
\(460\) 0.740304 1.39256i 0.0345168 0.0649285i
\(461\) −6.71485 −0.312742 −0.156371 0.987698i \(-0.549980\pi\)
−0.156371 + 0.987698i \(0.549980\pi\)
\(462\) 2.70053 2.98800i 0.125640 0.139014i
\(463\) 7.43802 0.345674 0.172837 0.984950i \(-0.444707\pi\)
0.172837 + 0.984950i \(0.444707\pi\)
\(464\) 3.12210 + 15.2478i 0.144940 + 0.707863i
\(465\) −2.32826 + 3.48033i −0.107970 + 0.161397i
\(466\) 10.6104 + 9.58962i 0.491518 + 0.444231i
\(467\) −31.0421 −1.43646 −0.718228 0.695808i \(-0.755047\pi\)
−0.718228 + 0.695808i \(0.755047\pi\)
\(468\) 0.0192657 + 0.190133i 0.000890557 + 0.00878892i
\(469\) 37.5758i 1.73509i
\(470\) 7.85600 1.97495i 0.362370 0.0910975i
\(471\) −41.9175 −1.93146
\(472\) −9.08355 6.67770i −0.418104 0.307366i
\(473\) 3.56082i 0.163727i
\(474\) −26.7925 24.2148i −1.23062 1.11222i
\(475\) 18.1590 + 12.0519i 0.833194 + 0.552981i
\(476\) 50.9656 5.16421i 2.33601 0.236701i
\(477\) −0.327897 −0.0150134
\(478\) 19.1675 + 17.3234i 0.876699 + 0.792355i
\(479\) 21.0127i 0.960093i −0.877243 0.480046i \(-0.840620\pi\)
0.877243 0.480046i \(-0.159380\pi\)
\(480\) −9.65665 20.0802i −0.440764 0.916531i
\(481\) −8.91571 −0.406521
\(482\) −13.7467 12.4242i −0.626144 0.565905i
\(483\) 2.66651i 0.121330i
\(484\) −2.18924 21.6057i −0.0995110 0.982075i
\(485\) 18.1047 + 12.1116i 0.822092 + 0.549960i
\(486\) 1.12152 + 1.01362i 0.0508730 + 0.0459786i
\(487\) 23.9504i 1.08530i −0.839960 0.542648i \(-0.817422\pi\)
0.839960 0.542648i \(-0.182578\pi\)
\(488\) −7.34537 5.39989i −0.332509 0.244442i
\(489\) 27.3278i 1.23581i
\(490\) 35.0409 8.80905i 1.58299 0.397952i
\(491\) 31.9941i 1.44387i −0.691959 0.721937i \(-0.743252\pi\)
0.691959 0.721937i \(-0.256748\pi\)
\(492\) 2.42264 + 23.9091i 0.109221 + 1.07790i
\(493\) 23.2177 1.04567
\(494\) −0.808091 + 5.66684i −0.0363577 + 0.254963i
\(495\) −0.0481877 + 0.0720320i −0.00216587 + 0.00323760i
\(496\) 4.16588 0.852992i 0.187054 0.0383005i
\(497\) 43.4256 1.94790
\(498\) 6.46516 + 5.84317i 0.289711 + 0.261839i
\(499\) 29.7730i 1.33282i 0.745584 + 0.666412i \(0.232171\pi\)
−0.745584 + 0.666412i \(0.767829\pi\)
\(500\) −22.2555 2.16605i −0.995297 0.0968685i
\(501\) 7.85660 0.351007
\(502\) −13.4956 12.1972i −0.602337 0.544388i
\(503\) 24.3841 1.08723 0.543617 0.839333i \(-0.317054\pi\)
0.543617 + 0.839333i \(0.317054\pi\)
\(504\) −1.00661 0.740003i −0.0448380 0.0329623i
\(505\) 23.8526 + 15.9568i 1.06143 + 0.710069i
\(506\) 0.139358 + 0.125950i 0.00619520 + 0.00559918i
\(507\) 21.3807i 0.949550i
\(508\) −8.32117 + 0.843161i −0.369192 + 0.0374092i
\(509\) 28.9266i 1.28215i 0.767478 + 0.641075i \(0.221511\pi\)
−0.767478 + 0.641075i \(0.778489\pi\)
\(510\) −32.2352 + 8.10372i −1.42740 + 0.358839i
\(511\) 21.8793i 0.967881i
\(512\) −7.35316 + 21.3993i −0.324967 + 0.945725i
\(513\) 12.4362 + 18.4434i 0.549073 + 0.814298i
\(514\) −25.7470 + 28.4877i −1.13565 + 1.25654i
\(515\) −2.64833 + 3.95879i −0.116700 + 0.174445i
\(516\) 33.1374 3.35772i 1.45879 0.147816i
\(517\) 0.964797i 0.0424317i
\(518\) 39.0817 43.2418i 1.71715 1.89994i
\(519\) 37.0835i 1.62779i
\(520\) −1.99874 5.52228i −0.0876504 0.242168i
\(521\) 8.62409i 0.377828i −0.981994 0.188914i \(-0.939503\pi\)
0.981994 0.188914i \(-0.0604968\pi\)
\(522\) −0.420097 0.379680i −0.0183871 0.0166182i
\(523\) 33.0172i 1.44374i 0.692028 + 0.721870i \(0.256717\pi\)
−0.692028 + 0.721870i \(0.743283\pi\)
\(524\) −1.93979 + 0.196553i −0.0847400 + 0.00858647i
\(525\) −34.9445 + 14.4294i −1.52510 + 0.629750i
\(526\) 17.6800 19.5620i 0.770883 0.852942i
\(527\) 6.34335i 0.276321i
\(528\) 2.59988 0.532343i 0.113145 0.0231673i
\(529\) −22.8756 −0.994593
\(530\) 9.77247 2.45673i 0.424489 0.106714i
\(531\) 0.410165 0.0177996
\(532\) −23.9423 28.7597i −1.03803 1.24689i
\(533\) 6.33413i 0.274361i
\(534\) −17.5246 + 19.3901i −0.758364 + 0.839091i
\(535\) −20.4131 + 30.5139i −0.882535 + 1.31923i
\(536\) −14.6653 + 19.9489i −0.633445 + 0.861663i
\(537\) 34.5233i 1.48979i
\(538\) −4.73423 4.27876i −0.204107 0.184471i
\(539\) 4.30338i 0.185360i
\(540\) −20.1518 10.7130i −0.867196 0.461013i
\(541\) −31.2615 −1.34404 −0.672018 0.740535i \(-0.734572\pi\)
−0.672018 + 0.740535i \(0.734572\pi\)
\(542\) −13.5022 12.2032i −0.579969 0.524172i
\(543\) 31.0278 1.33153
\(544\) 29.0731 + 17.1495i 1.24650 + 0.735279i
\(545\) −21.6257 + 32.3266i −0.926344 + 1.38472i
\(546\) −7.36669 6.65797i −0.315265 0.284935i
\(547\) 21.1292i 0.903419i 0.892165 + 0.451709i \(0.149186\pi\)
−0.892165 + 0.451709i \(0.850814\pi\)
\(548\) −7.02786 + 0.712114i −0.300215 + 0.0304200i
\(549\) 0.331678 0.0141557
\(550\) 0.896467 2.50784i 0.0382255 0.106935i
\(551\) −9.48218 14.0625i −0.403954 0.599081i
\(552\) 1.04070 1.41564i 0.0442952 0.0602538i
\(553\) 62.2277 2.64619
\(554\) −4.57371 4.13369i −0.194318 0.175624i
\(555\) −21.0282 + 31.4334i −0.892597 + 1.33427i
\(556\) −14.3464 + 1.45369i −0.608425 + 0.0616500i
\(557\) 8.78169i 0.372092i −0.982541 0.186046i \(-0.940433\pi\)
0.982541 0.186046i \(-0.0595674\pi\)
\(558\) −0.103733 + 0.114775i −0.00439137 + 0.00485882i
\(559\) 8.77896 0.371310
\(560\) 35.5449 + 14.5127i 1.50204 + 0.613274i
\(561\) 3.95881i 0.167141i
\(562\) 7.57696 + 6.84801i 0.319615 + 0.288866i
\(563\) 17.0044i 0.716649i 0.933597 + 0.358325i \(0.116652\pi\)
−0.933597 + 0.358325i \(0.883348\pi\)
\(564\) 8.97852 0.909768i 0.378064 0.0383082i
\(565\) 22.4218 + 14.9996i 0.943291 + 0.631039i
\(566\) 3.93556 4.35449i 0.165424 0.183033i
\(567\) −39.9123 −1.67616
\(568\) 23.0546 + 16.9484i 0.967348 + 0.711139i
\(569\) 15.9943i 0.670515i 0.942127 + 0.335258i \(0.108823\pi\)
−0.942127 + 0.335258i \(0.891177\pi\)
\(570\) 18.0732 + 16.2146i 0.757002 + 0.679153i
\(571\) 40.0149i 1.67457i 0.546765 + 0.837286i \(0.315859\pi\)
−0.546765 + 0.837286i \(0.684141\pi\)
\(572\) 0.695920 0.0705157i 0.0290979 0.00294841i
\(573\) −41.2623 −1.72376
\(574\) −30.7210 27.7654i −1.28227 1.15891i
\(575\) −0.672975 1.62978i −0.0280650 0.0679667i
\(576\) −0.245596 0.785732i −0.0102331 0.0327388i
\(577\) 14.6674i 0.610613i 0.952254 + 0.305306i \(0.0987589\pi\)
−0.952254 + 0.305306i \(0.901241\pi\)
\(578\) 17.6420 19.5200i 0.733811 0.811923i
\(579\) 33.5472i 1.39418i
\(580\) 15.3650 + 8.16826i 0.637998 + 0.339168i
\(581\) −15.0159 −0.622964
\(582\) 18.0036 + 16.2716i 0.746275 + 0.674478i
\(583\) 1.20016i 0.0497055i
\(584\) 8.53917 11.6157i 0.353353 0.480659i
\(585\) 0.177590 + 0.118803i 0.00734243 + 0.00491191i
\(586\) −4.57857 + 5.06594i −0.189139 + 0.209272i
\(587\) −0.410556 −0.0169454 −0.00847272 0.999964i \(-0.502697\pi\)
−0.00847272 + 0.999964i \(0.502697\pi\)
\(588\) 40.0478 4.05793i 1.65154 0.167346i
\(589\) −3.84203 + 2.59064i −0.158308 + 0.106745i
\(590\) −12.2243 + 3.07311i −0.503268 + 0.126518i
\(591\) 34.4554 1.41731
\(592\) 37.6251 7.70399i 1.54638 0.316632i
\(593\) 20.4734i 0.840742i −0.907352 0.420371i \(-0.861900\pi\)
0.907352 0.420371i \(-0.138100\pi\)
\(594\) 1.82264 2.01665i 0.0747837 0.0827443i
\(595\) 31.8455 47.6033i 1.30554 1.95154i
\(596\) −0.789476 7.79135i −0.0323382 0.319146i
\(597\) 36.5327 1.49518
\(598\) 0.310522 0.343576i 0.0126982 0.0140499i
\(599\) 35.7972 1.46263 0.731317 0.682038i \(-0.238906\pi\)
0.731317 + 0.682038i \(0.238906\pi\)
\(600\) −24.1836 5.97783i −0.987291 0.244044i
\(601\) 36.5899i 1.49253i 0.665647 + 0.746267i \(0.268156\pi\)
−0.665647 + 0.746267i \(0.731844\pi\)
\(602\) −38.4822 + 42.5786i −1.56842 + 1.73537i
\(603\) 0.900789i 0.0366830i
\(604\) 1.45735 + 14.3826i 0.0592986 + 0.585219i
\(605\) −20.1803 13.5001i −0.820444 0.548858i
\(606\) 23.7195 + 21.4375i 0.963537 + 0.870838i
\(607\) 24.9730i 1.01362i −0.862057 0.506812i \(-0.830824\pi\)
0.862057 0.506812i \(-0.169176\pi\)
\(608\) −1.48645 24.6128i −0.0602835 0.998181i
\(609\) 29.4213 1.19221
\(610\) −9.88514 + 2.48506i −0.400238 + 0.100617i
\(611\) 2.37864 0.0962295
\(612\) −1.22178 + 0.123799i −0.0493874 + 0.00500429i
\(613\) 19.7446i 0.797478i 0.917065 + 0.398739i \(0.130552\pi\)
−0.917065 + 0.398739i \(0.869448\pi\)
\(614\) 0.512466 + 0.463163i 0.0206814 + 0.0186917i
\(615\) 22.3317 + 14.9394i 0.900501 + 0.602414i
\(616\) −2.70853 + 3.68437i −0.109130 + 0.148447i
\(617\) 32.3305i 1.30158i −0.759259 0.650788i \(-0.774439\pi\)
0.759259 0.650788i \(-0.225561\pi\)
\(618\) −3.55795 + 3.93669i −0.143122 + 0.158357i
\(619\) 7.95921i 0.319908i −0.987124 0.159954i \(-0.948865\pi\)
0.987124 0.159954i \(-0.0511345\pi\)
\(620\) 2.23166 4.19790i 0.0896257 0.168592i
\(621\) 1.79967i 0.0722185i
\(622\) 2.71891 + 2.45733i 0.109018 + 0.0985300i
\(623\) 45.0351i 1.80429i
\(624\) −1.31245 6.40982i −0.0525402 0.256598i
\(625\) −17.7166 + 17.6386i −0.708664 + 0.705546i
\(626\) 9.92153 + 8.96701i 0.396544 + 0.358394i
\(627\) −2.39776 + 1.61679i −0.0957575 + 0.0645683i
\(628\) 47.3503 4.79788i 1.88948 0.191456i
\(629\) 57.2914i 2.28436i
\(630\) −1.35466 + 0.340553i −0.0539710 + 0.0135680i
\(631\) 37.9642i 1.51133i −0.654957 0.755666i \(-0.727313\pi\)
0.654957 0.755666i \(-0.272687\pi\)
\(632\) 33.0366 + 24.2866i 1.31413 + 0.966070i
\(633\) 0.132082i 0.00524979i
\(634\) 22.5237 24.9213i 0.894531 0.989752i
\(635\) −5.19942 + 7.77220i −0.206333 + 0.308430i
\(636\) 11.1688 1.13171i 0.442873 0.0448751i
\(637\) 10.6097 0.420371
\(638\) −1.38969 + 1.53762i −0.0550185 + 0.0608751i
\(639\) −1.04102 −0.0411822
\(640\) 13.2066 + 21.5774i 0.522037 + 0.852923i
\(641\) 22.7859i 0.899988i 0.893032 + 0.449994i \(0.148574\pi\)
−0.893032 + 0.449994i \(0.851426\pi\)
\(642\) −27.4243 + 30.3436i −1.08235 + 1.19757i
\(643\) 17.9394 0.707461 0.353731 0.935347i \(-0.384913\pi\)
0.353731 + 0.935347i \(0.384913\pi\)
\(644\) 0.305209 + 3.01211i 0.0120269 + 0.118694i
\(645\) 20.7057 30.9513i 0.815284 1.21870i
\(646\) −36.4145 5.19271i −1.43271 0.204304i
\(647\) −21.4626 −0.843781 −0.421891 0.906647i \(-0.638633\pi\)
−0.421891 + 0.906647i \(0.638633\pi\)
\(648\) −21.1894 15.5772i −0.832398 0.611931i
\(649\) 1.50127i 0.0589301i
\(650\) −6.18291 2.21018i −0.242514 0.0866903i
\(651\) 8.03825i 0.315044i
\(652\) 3.12794 + 30.8697i 0.122500 + 1.20895i
\(653\) 11.7812i 0.461035i −0.973068 0.230518i \(-0.925958\pi\)
0.973068 0.230518i \(-0.0740420\pi\)
\(654\) −29.0535 + 32.1461i −1.13608 + 1.25701i
\(655\) −1.21206 + 1.81181i −0.0473591 + 0.0707935i
\(656\) −5.47326 26.7306i −0.213695 1.04365i
\(657\) 0.524502i 0.0204628i
\(658\) −10.4267 + 11.5366i −0.406474 + 0.449743i
\(659\) −24.3327 −0.947866 −0.473933 0.880561i \(-0.657166\pi\)
−0.473933 + 0.880561i \(0.657166\pi\)
\(660\) 1.39275 2.61986i 0.0542129 0.101978i
\(661\) 7.73106i 0.300703i 0.988633 + 0.150352i \(0.0480406\pi\)
−0.988633 + 0.150352i \(0.951959\pi\)
\(662\) −16.8211 + 18.6116i −0.653769 + 0.723362i
\(663\) −9.76018 −0.379054
\(664\) −7.97191 5.86049i −0.309370 0.227431i
\(665\) −41.8380 + 0.153209i −1.62241 + 0.00594119i
\(666\) −0.936888 + 1.03662i −0.0363037 + 0.0401681i
\(667\) 1.37219i 0.0531313i
\(668\) −8.87488 + 0.899267i −0.343380 + 0.0347937i
\(669\) 1.76796 0.0683534
\(670\) 6.74906 + 26.8466i 0.260739 + 1.03717i
\(671\) 1.21400i 0.0468658i
\(672\) 36.8412 + 21.7317i 1.42118 + 0.838319i
\(673\) 4.63946 0.178838 0.0894190 0.995994i \(-0.471499\pi\)
0.0894190 + 0.995994i \(0.471499\pi\)
\(674\) 4.12007 4.55864i 0.158699 0.175592i
\(675\) −23.5847 + 9.73866i −0.907776 + 0.374841i
\(676\) 2.44724 + 24.1518i 0.0941244 + 0.928915i
\(677\) −3.39362 −0.130427 −0.0652137 0.997871i \(-0.520773\pi\)
−0.0652137 + 0.997871i \(0.520773\pi\)
\(678\) 22.2966 + 20.1515i 0.856296 + 0.773915i
\(679\) −41.8150 −1.60471
\(680\) 35.4856 12.8437i 1.36081 0.492532i
\(681\) −11.9442 −0.457704
\(682\) 0.420097 + 0.379680i 0.0160863 + 0.0145387i
\(683\) 9.59176i 0.367018i −0.983018 0.183509i \(-0.941254\pi\)
0.983018 0.183509i \(-0.0587457\pi\)
\(684\) 0.573959 + 0.689443i 0.0219459 + 0.0263615i
\(685\) −4.39130 + 6.56421i −0.167783 + 0.250806i
\(686\) −18.0144 + 19.9320i −0.687792 + 0.761006i
\(687\) 32.6343i 1.24508i
\(688\) −37.0480 + 7.58582i −1.41244 + 0.289207i
\(689\) 2.95891 0.112725
\(690\) −0.478936 1.90513i −0.0182328 0.0725269i
\(691\) 21.3675i 0.812856i 0.913683 + 0.406428i \(0.133226\pi\)
−0.913683 + 0.406428i \(0.866774\pi\)
\(692\) −4.24458 41.8898i −0.161355 1.59241i
\(693\) 0.166366i 0.00631974i
\(694\) −22.5380 + 24.9372i −0.855532 + 0.946602i
\(695\) −8.96426 + 13.4000i −0.340034 + 0.508290i
\(696\) 15.6197 + 11.4827i 0.592065 + 0.435252i
\(697\) −40.7024 −1.54171
\(698\) −14.2174 + 15.7308i −0.538138 + 0.595421i
\(699\) 17.8139 0.673785
\(700\) 37.8221 20.2993i 1.42954 0.767242i
\(701\) 17.7323 0.669739 0.334869 0.942265i \(-0.391308\pi\)
0.334869 + 0.942265i \(0.391308\pi\)
\(702\) −4.97192 4.49358i −0.187653 0.169599i
\(703\) −34.7001 + 23.3979i −1.30874 + 0.882470i
\(704\) −2.87591 + 0.898921i −0.108390 + 0.0338794i
\(705\) 5.61015 8.38618i 0.211291 0.315842i
\(706\) −3.43721 3.10653i −0.129361 0.116916i
\(707\) −55.0904 −2.07189
\(708\) −13.9710 + 1.41564i −0.525063 + 0.0532032i
\(709\) 1.60751 0.0603715 0.0301857 0.999544i \(-0.490390\pi\)
0.0301857 + 0.999544i \(0.490390\pi\)
\(710\) 31.0260 7.79974i 1.16439 0.292719i
\(711\) −1.49176 −0.0559453
\(712\) 17.5766 23.9091i 0.658710 0.896030i
\(713\) 0.374897 0.0140400
\(714\) 42.7834 47.3376i 1.60113 1.77156i
\(715\) 0.434840 0.650009i 0.0162621 0.0243089i
\(716\) 3.95154 + 38.9978i 0.147676 + 1.45742i
\(717\) 32.1804 1.20180
\(718\) −1.92857 1.74303i −0.0719735 0.0650492i
\(719\) 37.3717i 1.39373i 0.717203 + 0.696864i \(0.245422\pi\)
−0.717203 + 0.696864i \(0.754578\pi\)
\(720\) −0.852101 0.347907i −0.0317559 0.0129657i
\(721\) 9.14329i 0.340514i
\(722\) 11.7266 + 24.1761i 0.436421 + 0.899743i
\(723\) −23.0794 −0.858334
\(724\) −35.0492 + 3.55144i −1.30259 + 0.131988i
\(725\) 17.9825 7.42537i 0.667853 0.275771i
\(726\) −20.0676 18.1370i −0.744779 0.673127i
\(727\) −10.1249 −0.375514 −0.187757 0.982216i \(-0.560122\pi\)
−0.187757 + 0.982216i \(0.560122\pi\)
\(728\) 9.08355 + 6.67770i 0.336659 + 0.247492i
\(729\) −26.0114 −0.963386
\(730\) −3.92977 15.6320i −0.145447 0.578565i
\(731\) 56.4126i 2.08650i
\(732\) −11.2976 + 1.14475i −0.417571 + 0.0423113i
\(733\) 26.6032i 0.982613i −0.870987 0.491307i \(-0.836519\pi\)
0.870987 0.491307i \(-0.163481\pi\)
\(734\) 9.31986 10.3119i 0.344002 0.380621i
\(735\) 25.0235 37.4057i 0.923007 1.37973i
\(736\) −1.01355 + 1.71824i −0.0373599 + 0.0633353i
\(737\) −3.29704 −0.121448
\(738\) 0.736460 + 0.665608i 0.0271095 + 0.0245014i
\(739\) 15.5478i 0.571934i −0.958239 0.285967i \(-0.907685\pi\)
0.958239 0.285967i \(-0.0923147\pi\)
\(740\) 20.1557 37.9143i 0.740940 1.39376i
\(741\) 3.98608 + 5.91152i 0.146432 + 0.217165i
\(742\) −12.9703 + 14.3509i −0.476153 + 0.526839i
\(743\) 37.6670i 1.38187i 0.722918 + 0.690934i \(0.242801\pi\)
−0.722918 + 0.690934i \(0.757199\pi\)
\(744\) 3.13721 4.26749i 0.115016 0.156454i
\(745\) −7.27733 4.86836i −0.266621 0.178363i
\(746\) 7.93925 8.78436i 0.290677 0.321618i
\(747\) 0.359969 0.0131706
\(748\) 0.453126 + 4.47191i 0.0165679 + 0.163509i
\(749\) 70.4756i 2.57512i
\(750\) −22.3750 + 16.5857i −0.817018 + 0.605626i
\(751\) −4.74210 −0.173042 −0.0865208 0.996250i \(-0.527575\pi\)
−0.0865208 + 0.996250i \(0.527575\pi\)
\(752\) −10.0381 + 2.05536i −0.366051 + 0.0749514i
\(753\) −22.6579 −0.825698
\(754\) 3.79091 + 3.42620i 0.138057 + 0.124775i
\(755\) 13.4337 + 8.98684i 0.488903 + 0.327065i
\(756\) 43.5884 4.41669i 1.58529 0.160634i
\(757\) 15.0862i 0.548316i −0.961685 0.274158i \(-0.911601\pi\)
0.961685 0.274158i \(-0.0883992\pi\)
\(758\) −30.9494 + 34.2439i −1.12413 + 1.24379i
\(759\) 0.233969 0.00849254
\(760\) −22.2715 16.2474i −0.807873 0.589357i
\(761\) −24.9280 −0.903638 −0.451819 0.892110i \(-0.649225\pi\)
−0.451819 + 0.892110i \(0.649225\pi\)
\(762\) −6.98525 + 7.72882i −0.253049 + 0.279986i
\(763\) 74.6621i 2.70295i
\(764\) 46.6102 4.72288i 1.68630 0.170868i
\(765\) −0.763417 + 1.14117i −0.0276014 + 0.0412592i
\(766\) −6.40289 5.78689i −0.231346 0.209089i
\(767\) −3.70128 −0.133646
\(768\) 11.0773 + 25.9159i 0.399719 + 0.935161i
\(769\) 27.1950 0.980678 0.490339 0.871532i \(-0.336873\pi\)
0.490339 + 0.871532i \(0.336873\pi\)
\(770\) 1.24648 + 4.95829i 0.0449201 + 0.178685i
\(771\) 47.8284i 1.72250i
\(772\) 3.83982 + 37.8952i 0.138198 + 1.36388i
\(773\) −11.1297 −0.400308 −0.200154 0.979764i \(-0.564144\pi\)
−0.200154 + 0.979764i \(0.564144\pi\)
\(774\) 0.922518 1.02072i 0.0331592 0.0366889i
\(775\) −2.02870 4.91302i −0.0728730 0.176481i
\(776\) −22.1995 16.3198i −0.796916 0.585847i
\(777\) 72.5992i 2.60448i
\(778\) −3.46936 + 3.83866i −0.124382 + 0.137623i
\(779\) 16.6230 + 24.6525i 0.595579 + 0.883269i
\(780\) −6.45909 3.43374i −0.231273 0.122948i