Properties

Label 380.2.d.b.379.12
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 379.12
Character \(\chi\) \(=\) 380.379
Dual form 380.2.d.b.379.9

$q$-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} +(0.457886 - 3.12895i) 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} +(2.84869 + 3.44746i) 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} +(5.51167 + 0.806569i) 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} +(5.98386 - 1.48103i) q^{38} +1.63570i q^{39} +(-6.31834 - 0.280241i) 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} +(3.03928 + 6.38457i) 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} +(-6.07272 + 5.01798i) 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} +(-1.96548 + 13.4311i) 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} +(-4.12034 + 7.68263i) q^{76} -1.61674i q^{77} +(-1.71617 - 1.55106i) q^{78} -14.4968 q^{79} +(6.28543 - 6.36344i) 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} +(-0.0471176 + 0.321977i) 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 \(-0.801190\pi\)
−0.811209 + 0.584756i \(0.801190\pi\)
\(8\) 2.27889 + 1.67531i 0.805709 + 0.592311i
\(9\) −0.102903 −0.0343009
\(10\) 0.457886 3.12895i 0.144796 0.989461i
\(11\) 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 \(-0.742486\pi\)
0.690219 0.723601i \(-0.257514\pi\)
\(18\) 0.0975780 0.107965i 0.0229994 0.0254476i
\(19\) −3.61406 2.43692i −0.829122 0.559068i
\(20\) 2.84869 + 3.44746i 0.636986 + 0.770875i
\(21\) 7.56129i 1.65001i
\(22\) −0.395170 0.357152i −0.0842505 0.0761450i
\(23\) 0.352652 0.0735331 0.0367666 0.999324i \(-0.488294\pi\)
0.0367666 + 0.999324i \(0.488294\pi\)
\(24\) −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 \(0.117658\pi\)
−0.932459 + 0.361275i \(0.882342\pi\)
\(30\) 5.51167 + 0.806569i 1.00629 + 0.147259i
\(31\) 1.06308 0.190934 0.0954672 0.995433i \(-0.469565\pi\)
0.0954672 + 0.995433i \(0.469565\pi\)
\(32\) 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 \(0.789521\pi\)
\(38\) 5.98386 1.48103i 0.970710 0.240254i
\(39\) 1.63570i 0.261922i
\(40\) −6.31834 0.280241i −0.999018 0.0443099i
\(41\) 6.82129i 1.06531i −0.846334 0.532653i \(-0.821195\pi\)
0.846334 0.532653i \(-0.178805\pi\)
\(42\) 7.93327 + 7.17004i 1.22413 + 1.10636i
\(43\) −9.45416 −1.44175 −0.720873 0.693067i \(-0.756259\pi\)
−0.720873 + 0.693067i \(0.756259\pi\)
\(44\) 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 \(-0.559819\pi\)
−0.186823 + 0.982394i \(0.559819\pi\)
\(48\) −1.41340 6.90281i −0.204006 0.996334i
\(49\) 11.4257 1.63224
\(50\) 3.03928 + 6.38457i 0.429819 + 0.902915i
\(51\) 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 \(-0.416454\pi\)
0.259463 + 0.965753i \(0.416454\pi\)
\(60\) −6.07272 + 5.01798i −0.783985 + 0.647819i
\(61\) −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
\(70\) −1.96548 + 13.4311i −0.234920 + 1.60532i
\(71\) −10.1166 −1.20062 −0.600308 0.799769i \(-0.704956\pi\)
−0.600308 + 0.799769i \(0.704956\pi\)
\(72\) −0.234504 0.172394i −0.0276365 0.0203168i
\(73\) 5.09707i 0.596567i 0.954477 + 0.298283i \(0.0964141\pi\)
−0.954477 + 0.298283i \(0.903586\pi\)
\(74\) 9.10461 10.0738i 1.05839 1.17105i
\(75\) 8.14081 + 3.36152i 0.940019 + 0.388155i
\(76\) −4.12034 + 7.68263i −0.472636 + 0.881258i
\(77\) 1.61674i 0.184244i
\(78\) −1.71617 1.55106i −0.194318 0.175623i
\(79\) −14.4968 −1.63102 −0.815509 0.578745i \(-0.803543\pi\)
−0.815509 + 0.578745i \(0.803543\pi\)
\(80\) 6.28543 6.36344i 0.702733 0.711454i
\(81\) −9.29812 −1.03312
\(82\) 7.15687 + 6.46833i 0.790344 + 0.714307i
\(83\) 3.49815 0.383972 0.191986 0.981398i \(-0.438507\pi\)
0.191986 + 0.981398i \(0.438507\pi\)
\(84\) −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 \(0.187684\pi\)
−0.831149 + 0.556050i \(0.812316\pi\)
\(90\) −0.0471176 + 0.321977i −0.00496664 + 0.0339394i
\(91\) −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
\(100\) −9.58068 2.86541i −0.958068 0.286541i
\(101\) −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 \(0.313379\pi\)
−0.553273 + 0.833000i \(0.686621\pi\)
\(110\) 1.17849 + 0.172459i 0.112365 + 0.0164433i
\(111\) 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 \(0.692071\pi\)
\(114\) 2.60884 + 10.5406i 0.244340 + 0.987218i
\(115\) −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
\(120\) 0.493646 11.1298i 0.0450635 1.01601i
\(121\) 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
\(130\) 0.425185 2.90549i 0.0372912 0.254828i
\(131\) 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 \(0.0482095\pi\)
−0.988553 + 0.150876i \(0.951790\pi\)
\(138\) −0.651759 0.589056i −0.0554814 0.0501438i
\(139\) 7.20995i 0.611540i −0.952105 0.305770i \(-0.901086\pi\)
0.952105 0.305770i \(-0.0989139\pi\)
\(140\) −12.2280 14.7983i −1.03346 1.25068i
\(141\) 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 \(0.448725\pi\)
\(150\) −11.2465 + 5.35371i −0.918270 + 0.437129i
\(151\) 7.22811 0.588216 0.294108 0.955772i \(-0.404978\pi\)
0.294108 + 0.955772i \(0.404978\pi\)
\(152\) −4.15344 11.6081i −0.336888 0.941545i
\(153\) 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 \(-0.601510\pi\)
0.313526 0.949580i \(-0.398490\pi\)
\(158\) 13.7467 15.2100i 1.09363 1.21004i
\(159\) 5.61301i 0.445140i
\(160\) 0.716291 + 12.6288i 0.0566278 + 0.998395i
\(161\) −1.51377 −0.119301
\(162\) 8.81699 9.75554i 0.692729 0.766468i
\(163\) 15.5139 1.21514 0.607571 0.794265i \(-0.292144\pi\)
0.607571 + 0.794265i \(0.292144\pi\)
\(164\) −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
\(170\) −18.6704 2.73219i −1.43195 0.209549i
\(171\) 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 \(-0.238381\pi\)
0.732440 + 0.680832i \(0.238381\pi\)
\(180\) −0.293138 0.354752i −0.0218492 0.0264417i
\(181\) 17.6144i 1.30926i 0.755947 + 0.654632i \(0.227177\pi\)
−0.755947 + 0.654632i \(0.772823\pi\)
\(182\) 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
\(190\) −9.27984 + 10.1924i −0.673230 + 0.739433i
\(191\) 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 \(0.245395\pi\)
−0.717262 + 0.696803i \(0.754605\pi\)
\(198\) 0.0406640 + 0.0367519i 0.00288987 + 0.00261184i
\(199\) 20.7395i 1.47018i −0.677969 0.735091i \(-0.737140\pi\)
0.677969 0.735091i \(-0.262860\pi\)
\(200\) 12.0913 7.33487i 0.854984 0.518654i
\(201\) −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
\(210\) −23.6589 3.46221i −1.63262 0.238915i
\(211\) 0.0749824 0.00516200 0.00258100 0.999997i \(-0.499178\pi\)
0.00258100 + 0.999997i \(0.499178\pi\)
\(212\) −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
\(220\) −1.29845 + 1.07293i −0.0875417 + 0.0723371i
\(221\) 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 \(0.927754\pi\)
\(228\) −13.5330 7.25801i −0.896244 0.480673i
\(229\) −18.5264 −1.22426 −0.612129 0.790758i \(-0.709687\pi\)
−0.612129 + 0.790758i \(0.709687\pi\)
\(230\) 0.161475 1.10343i 0.0106473 0.0727582i
\(231\) 2.84789 0.187378
\(232\) −6.51870 + 8.86727i −0.427974 + 0.582165i
\(233\) 10.1129i 0.662519i 0.943540 + 0.331259i \(0.107473\pi\)
−0.943540 + 0.331259i \(0.892527\pi\)
\(234\) 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 \(-0.201208\pi\)
\(240\) 11.2092 + 11.0718i 0.723553 + 0.714683i
\(241\) 13.1021i 0.843981i −0.906600 0.421991i \(-0.861332\pi\)
0.906600 0.421991i \(-0.138668\pi\)
\(242\) −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
\(250\) −13.5867 8.08717i −0.859297 0.511478i
\(251\) 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
\(260\) 2.64524 + 3.20125i 0.164051 + 0.198533i
\(261\) 0.400399i 0.0247841i
\(262\) 1.02282 + 0.924417i 0.0631900 + 0.0571107i
\(263\) 18.6447 1.14968 0.574841 0.818265i \(-0.305064\pi\)
0.574841 + 0.818265i \(0.305064\pi\)
\(264\) −1.51194 1.11149i −0.0930536 0.0684076i
\(265\) −5.92220 + 3.96181i −0.363798 + 0.243372i
\(266\) −25.6858 + 6.35733i −1.57490 + 0.389793i
\(267\) −18.4809 −1.13101
\(268\) 17.4184 1.76496i 1.06400 0.107812i
\(269\) 4.51225i 0.275116i −0.990494 0.137558i \(-0.956075\pi\)
0.990494 0.137558i \(-0.0439254\pi\)
\(270\) 15.9678 + 2.33671i 0.971772 + 0.142208i
\(271\) 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 \(-0.958194\pi\)
0.991388 0.130961i \(-0.0418063\pi\)
\(278\) 7.56465 + 6.83688i 0.453697 + 0.410049i
\(279\) −0.109394 −0.00654922
\(280\) 27.1216 + 1.20294i 1.62083 + 0.0718893i
\(281\) 7.22169i 0.430810i 0.976525 + 0.215405i \(0.0691071\pi\)
−0.976525 + 0.215405i \(0.930893\pi\)
\(282\) 4.73423 + 4.27876i 0.281919 + 0.254797i
\(283\) 4.15031 0.246710 0.123355 0.992363i \(-0.460635\pi\)
0.123355 + 0.992363i \(0.460635\pi\)
\(284\) 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
\(290\) 12.1749 + 1.78166i 0.714935 + 0.104622i
\(291\) 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
\(300\) 5.04743 16.8764i 0.291413 0.974361i
\(301\) 40.5821 2.33911
\(302\) −6.85410 + 7.58370i −0.394409 + 0.436393i
\(303\) 22.6073i 1.29875i
\(304\) 16.1177 + 6.64972i 0.924415 + 0.381387i
\(305\) 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
\(310\) 0.486769 3.32632i 0.0276466 0.188922i
\(311\) 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 \(0.0861154\pi\)
−0.963627 + 0.267251i \(0.913885\pi\)
\(314\) 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
\(320\) −13.9293 11.2238i −0.778673 0.627430i
\(321\) 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
\(330\) −0.303787 + 2.07592i −0.0167229 + 0.114276i
\(331\) −17.7390 −0.975021 −0.487511 0.873117i \(-0.662095\pi\)
−0.487511 + 0.873117i \(0.662095\pi\)
\(332\) −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
\(340\) 20.5709 16.9980i 1.11561 0.921848i
\(341\) 0.400399i 0.0216828i
\(342\) −0.615755 + 0.152401i −0.0332962 + 0.00824093i
\(343\) −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 \(-0.720223\pi\)
−0.637964 + 0.770067i \(0.720223\pi\)
\(348\) 1.38194 + 13.6384i 0.0740796 + 0.731093i
\(349\) 14.9933 0.802570 0.401285 0.915953i \(-0.368564\pi\)
0.401285 + 0.915953i \(0.368564\pi\)
\(350\) −13.0462 27.4059i −0.697347 1.46491i
\(351\) 4.73879i 0.252938i
\(352\) 1.83512 + 1.08249i 0.0978124 + 0.0576971i
\(353\) 3.27604i 0.174366i −0.996192 0.0871831i \(-0.972213\pi\)
0.996192 0.0871831i \(-0.0277865\pi\)
\(354\) −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 \(0.984554\pi\)
\(360\) 0.650174 + 0.0288375i 0.0342672 + 0.00151987i
\(361\) 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 \(-0.417424\pi\)
0.256520 + 0.966539i \(0.417424\pi\)
\(368\) −1.38194 + 0.282961i −0.0720385 + 0.0147504i
\(369\) 0.701928i 0.0365409i
\(370\) −4.39636 + 30.0424i −0.228556 + 1.56183i
\(371\) −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 \(-0.816425\pi\)
−0.838256 + 0.545277i \(0.816425\pi\)
\(380\) −1.89414 19.4013i −0.0971671 0.995268i
\(381\) 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 \(0.470434\pi\)
\(390\) 5.11803 + 0.748965i 0.259162 + 0.0379253i
\(391\) 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 \(-0.726691\pi\)
0.653478 0.756946i \(-0.273309\pi\)
\(398\) 21.7597 + 19.6663i 1.09072 + 0.985783i
\(399\) −18.4263 + 27.3269i −0.922468 + 1.36806i
\(400\) −3.76994 + 19.6415i −0.188497 + 0.982074i
\(401\) 34.6456i 1.73012i 0.501670 + 0.865059i \(0.332719\pi\)
−0.501670 + 0.865059i \(0.667281\pi\)
\(402\) 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 \(-0.727770\pi\)
0.656041 0.754726i \(-0.272230\pi\)
\(410\) −21.3435 3.12337i −1.05408 0.154252i
\(411\) −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
\(418\) 0.557815 + 2.25377i 0.0272836 + 0.110235i
\(419\) 6.46767i 0.315966i −0.987442 0.157983i \(-0.949501\pi\)
0.987442 0.157983i \(-0.0504992\pi\)
\(420\) 26.0672 21.5398i 1.27195 1.05103i
\(421\) 21.2039i 1.03341i 0.856162 + 0.516707i \(0.172842\pi\)
−0.856162 + 0.516707i \(0.827158\pi\)
\(422\) −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
\(430\) −4.32893 + 29.5816i −0.208759 + 1.42655i
\(431\) −7.73794 −0.372723 −0.186362 0.982481i \(-0.559670\pi\)
−0.186362 + 0.982481i \(0.559670\pi\)
\(432\) −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 \(-0.579969\pi\)
−0.248596 + 0.968607i \(0.579969\pi\)
\(440\) 0.105550 2.37975i 0.00503190 0.113450i
\(441\) −1.17573 −0.0559873
\(442\) 5.81340 + 5.25411i 0.276515 + 0.249913i
\(443\) 5.03629 0.239282 0.119641 0.992817i \(-0.461826\pi\)
0.119641 + 0.992817i \(0.461826\pi\)
\(444\) −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 \(0.223547\pi\)
−0.763363 + 0.645970i \(0.776453\pi\)
\(450\) −0.312750 0.656989i −0.0147432 0.0309708i
\(451\) 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
\(456\) 20.4478 7.31631i 0.957556 0.342618i
\(457\) 8.86333i 0.414609i 0.978276 + 0.207305i \(0.0664691\pi\)
−0.978276 + 0.207305i \(0.933531\pi\)
\(458\) 17.5677 19.4378i 0.820887 0.908268i
\(459\) 30.4509 1.42133
\(460\) 1.00460 + 1.21575i 0.0468396 + 0.0566848i
\(461\) −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 \(-0.555293\pi\)
−0.172837 + 0.984950i \(0.555293\pi\)
\(464\) −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 \(-0.244953\pi\)
0.718228 + 0.695808i \(0.244953\pi\)
\(468\) 0.0192657 + 0.190133i 0.000890557 + 0.00878892i
\(469\) 37.5758i 1.73509i
\(470\) −1.17291 + 8.01507i −0.0541025 + 0.369708i
\(471\) 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 \(-0.159380\pi\)
\(480\) −22.2457 + 1.26175i −1.01537 + 0.0575908i
\(481\) −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
\(490\) 5.23167 35.7505i 0.236343 1.61504i
\(491\) 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
\(494\) 5.55650 1.37525i 0.249999 0.0618756i
\(495\) 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 \(0.767829\pi\)
\(500\) 21.3687 6.58636i 0.955636 0.294551i
\(501\) 7.85660 0.351007
\(502\) −13.4956 12.1972i −0.602337 0.544388i
\(503\) −24.3841 −1.08723 −0.543617 0.839333i \(-0.682946\pi\)
−0.543617 + 0.839333i \(0.682946\pi\)
\(504\) 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 \(-0.778489\pi\)
0.767478 0.641075i \(-0.221511\pi\)
\(510\) 4.81277 32.8879i 0.213113 1.45630i
\(511\) 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
\(520\) −5.86710 0.260226i −0.257289 0.0114117i
\(521\) 8.62409i 0.377828i 0.981994 + 0.188914i \(0.0604968\pi\)
−0.981994 + 0.188914i \(0.939503\pi\)
\(522\) 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
\(530\) 1.45905 9.97035i 0.0633769 0.433084i
\(531\) −0.410165 −0.0177996
\(532\) 17.6866 32.9778i 0.766813 1.42977i
\(533\) 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
\(540\) −17.5933 + 14.5376i −0.757093 + 0.625598i
\(541\) −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
\(550\) −2.40469 + 1.14472i −0.102536 + 0.0488109i
\(551\) 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 \(0.0595674\pi\)
−0.982541 + 0.186046i \(0.940433\pi\)
\(558\) 0.103733 0.114775i 0.00439137 0.00485882i
\(559\) −8.77896 −0.371310
\(560\) −26.9803 + 27.3152i −1.14013 + 1.15428i
\(561\) 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 \(-0.891177\pi\)
0.942127 0.335258i \(-0.108823\pi\)
\(570\) −17.9539 16.3465i −0.752008 0.684679i
\(571\) 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 \(-0.901241\pi\)
0.952254 0.305306i \(-0.0987589\pi\)
\(578\) 17.6420 19.5200i 0.733811 0.811923i
\(579\) 33.5472i 1.39418i
\(580\) −13.4142 + 11.0844i −0.556995 + 0.460254i
\(581\) −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 \(-0.497303\pi\)
0.00847272 + 0.999964i \(0.497303\pi\)
\(588\) 40.0478 4.05793i 1.65154 0.167346i
\(589\) −3.84203 2.59064i −0.158308 0.106745i
\(590\) 1.82511 12.4719i 0.0751387 0.513458i
\(591\) −34.4554 −1.41731
\(592\) 37.6251 7.70399i 1.54638 0.316632i
\(593\) 20.4734i 0.840742i 0.907352 + 0.420371i \(0.138100\pi\)
−0.907352 + 0.420371i \(0.861900\pi\)
\(594\) 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 \(-0.761094\pi\)
−0.731317 + 0.682038i \(0.761094\pi\)
\(600\) 12.9204 + 21.2989i 0.527474 + 0.869524i
\(601\) 36.5899i 1.49253i −0.665647 0.746267i \(-0.731844\pi\)
0.665647 0.746267i \(-0.268156\pi\)
\(602\) −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 \(-0.169176\pi\)
\(608\) −22.2606 + 10.6050i −0.902786 + 0.430090i
\(609\) 29.4213 1.19221
\(610\) −1.47587 + 10.0853i −0.0597561 + 0.408342i
\(611\) −2.37864 −0.0962295
\(612\) 1.22178 0.123799i 0.0493874 0.00500429i
\(613\) 19.7446i 0.797478i −0.917065 0.398739i \(-0.869448\pi\)
0.917065 0.398739i \(-0.130552\pi\)
\(614\) 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 \(0.225561\pi\)
−0.759259 + 0.650788i \(0.774439\pi\)
\(618\) −3.55795 + 3.93669i −0.143122 + 0.158357i
\(619\) 7.95921i 0.319908i −0.987124 0.159954i \(-0.948865\pi\)
0.987124 0.159954i \(-0.0511345\pi\)
\(620\) 3.02838 + 3.66492i 0.121623 + 0.147187i
\(621\) 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
\(630\) 0.202253 1.38209i 0.00805796 0.0550639i
\(631\) 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
\(640\) 24.9845 3.97153i 0.987600 0.156989i
\(641\) 22.7859i 0.899988i −0.893032 0.449994i \(-0.851426\pi\)
0.893032 0.449994i \(-0.148574\pi\)
\(642\) −27.4243 + 30.3436i −1.08235 + 1.19757i
\(643\) −17.9394 −0.707461 −0.353731 0.935347i \(-0.615087\pi\)
−0.353731 + 0.935347i \(0.615087\pi\)
\(644\) 0.305209 + 3.01211i 0.0120269 + 0.118694i
\(645\) 20.7057 + 30.9513i 0.815284 + 1.21870i
\(646\) −8.83723 35.7055i −0.347696 1.40481i
\(647\) 21.4626 0.843781 0.421891 0.906647i \(-0.361367\pi\)
0.421891 + 0.906647i \(0.361367\pi\)
\(648\) −21.1894 15.5772i −0.832398 0.611931i
\(649\) 1.50127i 0.0589301i
\(650\) 2.82222 + 5.92860i 0.110697 + 0.232539i
\(651\) 8.03825i 0.315044i
\(652\) −3.12794 30.8697i −0.122500 1.20895i
\(653\) 11.7812i 0.461035i 0.973068 + 0.230518i \(0.0740420\pi\)
−0.973068 + 0.230518i \(0.925958\pi\)
\(654\) 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 \(-0.342834\pi\)
0.473933 + 0.880561i \(0.342834\pi\)
\(660\) −1.88998 2.28723i −0.0735673 0.0890305i
\(661\) 7.73106i 0.300703i −0.988633 0.150352i \(-0.951959\pi\)
0.988633 0.150352i \(-0.0480406\pi\)
\(662\) 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
\(670\) 27.3902 + 4.00824i 1.05818 + 0.154852i
\(671\) 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
\(680\) −1.67219 + 37.7013i −0.0641254 + 1.44578i
\(681\) −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 \(-0.0587457\pi\)
\(684\) 0.423994 0.790562i 0.0162118 0.0302279i
\(685\) −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
\(690\) 1.94370 + 0.284438i 0.0739955 + 0.0108284i
\(691\) 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
\(700\) 41.1252 + 12.2998i 1.55439 + 0.464889i
\(701\) 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 \(0.490390\pi\)
\(710\) −4.63224 + 31.6543i −0.173845 + 1.18796i
\(711\) 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 \(0.754578\pi\)
\(720\) −0.646787 + 0.654814i −0.0241043 + 0.0244035i
\(721\) 9.14329i 0.340514i
\(722\) −25.2352 9.22969i −0.939155 0.343493i
\(723\) 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 \(-0.439878\pi\)
0.187757 + 0.982216i \(0.439878\pi\)
\(728\) −9.08355 6.67770i −0.336659 0.247492i
\(729\) −26.0114 −0.963386
\(730\) 15.9485 + 2.33388i 0.590280 + 0.0863806i
\(731\) 56.4126i 2.08650i
\(732\) −11.2976 + 1.14475i −0.417571 + 0.0423113i
\(733\) 26.6032i 0.982613i 0.870987 + 0.491307i \(0.163481\pi\)
−0.870987 + 0.491307i \(0.836519\pi\)
\(734\) −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 \(-0.0923147\pi\)
\(740\) −27.3515 33.1005i −1.00546 1.21680i
\(741\) 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
\(750\) 14.2456 23.9330i 0.520176 0.873910i
\(751\) 4.74210 0.173042 0.0865208 0.996250i \(-0.472425\pi\)
0.0865208 + 0.996250i \(0.472425\pi\)
\(752\) 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 \(0.0883992\pi\)
−0.961685 + 0.274158i \(0.911601\pi\)
\(758\) 30.9494 34.2439i 1.12413 1.24379i
\(759\) −0.233969 −0.00849254
\(760\) 22.1519 + 16.4101i 0.803535 + 0.595258i
\(761\) −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 \(0.336873\pi\)
\(770\) −5.05869 0.740281i −0.182303 0.0266779i
\(771\) 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
\(780\) −5.63902 + 4.65961i −0.201909 + 0.166841i
\(781\)