Properties

Label 403.2.l.c.25.19
Level 403
Weight 2
Character 403.25
Analytic conductor 3.218
Analytic rank 0
Dimension 68
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.l (of order \(6\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(68\)
Relative dimension: \(34\) over \(\Q(\zeta_{6})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 25.19
Character \(\chi\) = 403.25
Dual form 403.2.l.c.129.16

$q$-expansion

\(f(q)\) \(=\) \(q+0.177509i q^{2} +(0.311192 + 0.539000i) q^{3} +1.96849 q^{4} +(-1.82613 - 1.05431i) q^{5} +(-0.0956771 + 0.0552392i) q^{6} +(-1.99646 + 1.15265i) q^{7} +0.704441i q^{8} +(1.30632 - 2.26261i) q^{9} +O(q^{10})\) \(q+0.177509i q^{2} +(0.311192 + 0.539000i) q^{3} +1.96849 q^{4} +(-1.82613 - 1.05431i) q^{5} +(-0.0956771 + 0.0552392i) q^{6} +(-1.99646 + 1.15265i) q^{7} +0.704441i q^{8} +(1.30632 - 2.26261i) q^{9} +(0.187150 - 0.324153i) q^{10} +(3.83942 + 2.21669i) q^{11} +(0.612578 + 1.06102i) q^{12} +(3.46062 + 1.01199i) q^{13} +(-0.204606 - 0.354388i) q^{14} -1.31238i q^{15} +3.81194 q^{16} +(3.63636 + 6.29835i) q^{17} +(0.401633 + 0.231883i) q^{18} +(5.84727 - 3.37592i) q^{19} +(-3.59471 - 2.07541i) q^{20} +(-1.24256 - 0.717393i) q^{21} +(-0.393482 + 0.681531i) q^{22} -9.13913 q^{23} +(-0.379694 + 0.219216i) q^{24} +(-0.276843 - 0.479507i) q^{25} +(-0.179638 + 0.614289i) q^{26} +3.49321 q^{27} +(-3.93001 + 2.26899i) q^{28} -0.638044 q^{29} +0.232958 q^{30} +(-4.14520 - 3.71717i) q^{31} +2.08553i q^{32} +2.75927i q^{33} +(-1.11801 + 0.645485i) q^{34} +4.86104 q^{35} +(2.57148 - 4.45393i) q^{36} +(-2.94161 + 1.69834i) q^{37} +(0.599255 + 1.03794i) q^{38} +(0.531451 + 2.18020i) q^{39} +(0.742703 - 1.28640i) q^{40} +(-1.49289 - 0.861918i) q^{41} +(0.127344 - 0.220565i) q^{42} +(-1.66436 - 2.88275i) q^{43} +(7.55787 + 4.36354i) q^{44} +(-4.77101 + 2.75454i) q^{45} -1.62227i q^{46} -9.94211i q^{47} +(1.18624 + 2.05463i) q^{48} +(-0.842774 + 1.45973i) q^{49} +(0.0851166 - 0.0491421i) q^{50} +(-2.26321 + 3.91999i) q^{51} +(6.81219 + 1.99210i) q^{52} +(-5.41936 + 9.38660i) q^{53} +0.620076i q^{54} +(-4.67418 - 8.09592i) q^{55} +(-0.811978 - 1.40639i) q^{56} +(3.63924 + 2.10112i) q^{57} -0.113258i q^{58} +(1.57839 - 0.911283i) q^{59} -2.58340i q^{60} +1.62489 q^{61} +(0.659830 - 0.735808i) q^{62} +6.02294i q^{63} +7.25367 q^{64} +(-5.25256 - 5.49661i) q^{65} -0.489793 q^{66} +(1.49673 + 0.864137i) q^{67} +(7.15813 + 12.3983i) q^{68} +(-2.84402 - 4.92599i) q^{69} +0.862877i q^{70} +(-6.34620 - 3.66398i) q^{71} +(1.59388 + 0.920225i) q^{72} +(-1.36850 - 0.790105i) q^{73} +(-0.301470 - 0.522161i) q^{74} +(0.172303 - 0.298437i) q^{75} +(11.5103 - 6.64547i) q^{76} -10.2203 q^{77} +(-0.387004 + 0.0943371i) q^{78} +(-2.85115 - 4.93834i) q^{79} +(-6.96108 - 4.01898i) q^{80} +(-2.83190 - 4.90499i) q^{81} +(0.152998 - 0.265000i) q^{82} +(-2.14235 - 1.23688i) q^{83} +(-2.44597 - 1.41218i) q^{84} -15.3354i q^{85} +(0.511714 - 0.295438i) q^{86} +(-0.198554 - 0.343906i) q^{87} +(-1.56153 + 2.70465i) q^{88} +12.4713i q^{89} +(-0.488955 - 0.846895i) q^{90} +(-8.07545 + 1.96849i) q^{91} -17.9903 q^{92} +(0.713603 - 3.39101i) q^{93} +1.76481 q^{94} -14.2371 q^{95} +(-1.12410 + 0.649001i) q^{96} -7.23658i q^{97} +(-0.259114 - 0.149600i) q^{98} +(10.0310 - 5.79142i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 68q - 6q^{3} - 76q^{4} - 40q^{9} + O(q^{10}) \) \( 68q - 6q^{3} - 76q^{4} - 40q^{9} + 8q^{10} - 10q^{12} - 3q^{13} + 10q^{14} + 84q^{16} + 6q^{17} + 4q^{22} - 44q^{23} + 30q^{25} - 3q^{26} - 12q^{27} + 48q^{29} - 4q^{30} - 48q^{35} + 40q^{36} + 60q^{38} - 14q^{39} + 20q^{40} - 10q^{42} - 12q^{43} + 32q^{48} + 58q^{49} + 20q^{51} - 27q^{52} + 8q^{53} - 36q^{55} - 50q^{56} - 12q^{61} - 74q^{62} - 15q^{65} + 164q^{66} + 4q^{68} - 34q^{69} - 4q^{74} + 20q^{75} - 200q^{77} - 58q^{78} - 80q^{79} - 82q^{81} - 66q^{82} + 52q^{87} + 16q^{88} - 14q^{90} - 70q^{91} + 108q^{92} - 4q^{94} + 76q^{95} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.177509i 0.125518i 0.998029 + 0.0627588i \(0.0199899\pi\)
−0.998029 + 0.0627588i \(0.980010\pi\)
\(3\) 0.311192 + 0.539000i 0.179667 + 0.311192i 0.941766 0.336268i \(-0.109165\pi\)
−0.762100 + 0.647460i \(0.775831\pi\)
\(4\) 1.96849 0.984245
\(5\) −1.82613 1.05431i −0.816668 0.471504i 0.0325980 0.999469i \(-0.489622\pi\)
−0.849266 + 0.527965i \(0.822955\pi\)
\(6\) −0.0956771 + 0.0552392i −0.0390600 + 0.0225513i
\(7\) −1.99646 + 1.15265i −0.754590 + 0.435663i −0.827350 0.561687i \(-0.810153\pi\)
0.0727602 + 0.997349i \(0.476819\pi\)
\(8\) 0.704441i 0.249058i
\(9\) 1.30632 2.26261i 0.435440 0.754204i
\(10\) 0.187150 0.324153i 0.0591820 0.102506i
\(11\) 3.83942 + 2.21669i 1.15763 + 0.668358i 0.950735 0.310005i \(-0.100331\pi\)
0.206895 + 0.978363i \(0.433664\pi\)
\(12\) 0.612578 + 1.06102i 0.176836 + 0.306289i
\(13\) 3.46062 + 1.01199i 0.959802 + 0.280677i
\(14\) −0.204606 0.354388i −0.0546833 0.0947143i
\(15\) 1.31238i 0.338854i
\(16\) 3.81194 0.952984
\(17\) 3.63636 + 6.29835i 0.881946 + 1.52758i 0.849175 + 0.528112i \(0.177100\pi\)
0.0327713 + 0.999463i \(0.489567\pi\)
\(18\) 0.401633 + 0.231883i 0.0946658 + 0.0546553i
\(19\) 5.84727 3.37592i 1.34146 0.774490i 0.354434 0.935081i \(-0.384673\pi\)
0.987021 + 0.160591i \(0.0513401\pi\)
\(20\) −3.59471 2.07541i −0.803802 0.464075i
\(21\) −1.24256 0.717393i −0.271149 0.156548i
\(22\) −0.393482 + 0.681531i −0.0838907 + 0.145303i
\(23\) −9.13913 −1.90564 −0.952820 0.303536i \(-0.901833\pi\)
−0.952820 + 0.303536i \(0.901833\pi\)
\(24\) −0.379694 + 0.219216i −0.0775047 + 0.0447473i
\(25\) −0.276843 0.479507i −0.0553687 0.0959014i
\(26\) −0.179638 + 0.614289i −0.0352298 + 0.120472i
\(27\) 3.49321 0.672269
\(28\) −3.93001 + 2.26899i −0.742701 + 0.428799i
\(29\) −0.638044 −0.118482 −0.0592409 0.998244i \(-0.518868\pi\)
−0.0592409 + 0.998244i \(0.518868\pi\)
\(30\) 0.232958 0.0425321
\(31\) −4.14520 3.71717i −0.744499 0.667623i
\(32\) 2.08553i 0.368674i
\(33\) 2.75927i 0.480326i
\(34\) −1.11801 + 0.645485i −0.191738 + 0.110700i
\(35\) 4.86104 0.821666
\(36\) 2.57148 4.45393i 0.428580 0.742322i
\(37\) −2.94161 + 1.69834i −0.483597 + 0.279205i −0.721914 0.691982i \(-0.756738\pi\)
0.238317 + 0.971187i \(0.423404\pi\)
\(38\) 0.599255 + 1.03794i 0.0972121 + 0.168376i
\(39\) 0.531451 + 2.18020i 0.0851002 + 0.349111i
\(40\) 0.742703 1.28640i 0.117432 0.203397i
\(41\) −1.49289 0.861918i −0.233150 0.134609i 0.378875 0.925448i \(-0.376311\pi\)
−0.612024 + 0.790839i \(0.709645\pi\)
\(42\) 0.127344 0.220565i 0.0196495 0.0340340i
\(43\) −1.66436 2.88275i −0.253812 0.439616i 0.710760 0.703435i \(-0.248351\pi\)
−0.964572 + 0.263819i \(0.915018\pi\)
\(44\) 7.55787 + 4.36354i 1.13939 + 0.657828i
\(45\) −4.77101 + 2.75454i −0.711220 + 0.410623i
\(46\) 1.62227i 0.239191i
\(47\) 9.94211i 1.45021i −0.688641 0.725103i \(-0.741792\pi\)
0.688641 0.725103i \(-0.258208\pi\)
\(48\) 1.18624 + 2.05463i 0.171219 + 0.296561i
\(49\) −0.842774 + 1.45973i −0.120396 + 0.208532i
\(50\) 0.0851166 0.0491421i 0.0120373 0.00694974i
\(51\) −2.26321 + 3.91999i −0.316912 + 0.548909i
\(52\) 6.81219 + 1.99210i 0.944681 + 0.276255i
\(53\) −5.41936 + 9.38660i −0.744406 + 1.28935i 0.206066 + 0.978538i \(0.433934\pi\)
−0.950472 + 0.310811i \(0.899399\pi\)
\(54\) 0.620076i 0.0843816i
\(55\) −4.67418 8.09592i −0.630266 1.09165i
\(56\) −0.811978 1.40639i −0.108505 0.187936i
\(57\) 3.63924 + 2.10112i 0.482030 + 0.278300i
\(58\) 0.113258i 0.0148716i
\(59\) 1.57839 0.911283i 0.205489 0.118639i −0.393724 0.919229i \(-0.628814\pi\)
0.599213 + 0.800590i \(0.295480\pi\)
\(60\) 2.58340i 0.333515i
\(61\) 1.62489 0.208045 0.104023 0.994575i \(-0.466829\pi\)
0.104023 + 0.994575i \(0.466829\pi\)
\(62\) 0.659830 0.735808i 0.0837984 0.0934477i
\(63\) 6.02294i 0.758819i
\(64\) 7.25367 0.906709
\(65\) −5.25256 5.49661i −0.651500 0.681770i
\(66\) −0.489793 −0.0602894
\(67\) 1.49673 + 0.864137i 0.182855 + 0.105571i 0.588633 0.808400i \(-0.299666\pi\)
−0.405779 + 0.913971i \(0.633000\pi\)
\(68\) 7.15813 + 12.3983i 0.868051 + 1.50351i
\(69\) −2.84402 4.92599i −0.342380 0.593019i
\(70\) 0.862877i 0.103134i
\(71\) −6.34620 3.66398i −0.753155 0.434834i 0.0736778 0.997282i \(-0.476526\pi\)
−0.826833 + 0.562448i \(0.809860\pi\)
\(72\) 1.59388 + 0.920225i 0.187840 + 0.108450i
\(73\) −1.36850 0.790105i −0.160171 0.0924748i 0.417772 0.908552i \(-0.362811\pi\)
−0.577943 + 0.816077i \(0.696144\pi\)
\(74\) −0.301470 0.522161i −0.0350451 0.0607000i
\(75\) 0.172303 0.298437i 0.0198958 0.0344606i
\(76\) 11.5103 6.64547i 1.32032 0.762288i
\(77\) −10.2203 −1.16471
\(78\) −0.387004 + 0.0943371i −0.0438195 + 0.0106816i
\(79\) −2.85115 4.93834i −0.320780 0.555607i 0.659869 0.751380i \(-0.270612\pi\)
−0.980649 + 0.195774i \(0.937278\pi\)
\(80\) −6.96108 4.01898i −0.778272 0.449336i
\(81\) −2.83190 4.90499i −0.314655 0.544999i
\(82\) 0.152998 0.265000i 0.0168958 0.0292644i
\(83\) −2.14235 1.23688i −0.235153 0.135766i 0.377794 0.925890i \(-0.376683\pi\)
−0.612947 + 0.790124i \(0.710016\pi\)
\(84\) −2.44597 1.41218i −0.266877 0.154082i
\(85\) 15.3354i 1.66336i
\(86\) 0.511714 0.295438i 0.0551795 0.0318579i
\(87\) −0.198554 0.343906i −0.0212872 0.0368706i
\(88\) −1.56153 + 2.70465i −0.166460 + 0.288317i
\(89\) 12.4713i 1.32195i 0.750407 + 0.660976i \(0.229857\pi\)
−0.750407 + 0.660976i \(0.770143\pi\)
\(90\) −0.488955 0.846895i −0.0515404 0.0892706i
\(91\) −8.07545 + 1.96849i −0.846537 + 0.206354i
\(92\) −17.9903 −1.87562
\(93\) 0.713603 3.39101i 0.0739972 0.351632i
\(94\) 1.76481 0.182026
\(95\) −14.2371 −1.46070
\(96\) −1.12410 + 0.649001i −0.114728 + 0.0662384i
\(97\) 7.23658i 0.734763i −0.930070 0.367382i \(-0.880254\pi\)
0.930070 0.367382i \(-0.119746\pi\)
\(98\) −0.259114 0.149600i −0.0261745 0.0151118i
\(99\) 10.0310 5.79142i 1.00816 0.582059i
\(100\) −0.544964 0.943905i −0.0544964 0.0943905i
\(101\) −7.19412 −0.715842 −0.357921 0.933752i \(-0.616514\pi\)
−0.357921 + 0.933752i \(0.616514\pi\)
\(102\) −0.695832 0.401739i −0.0688977 0.0397781i
\(103\) 6.73489 11.6652i 0.663608 1.14940i −0.316053 0.948742i \(-0.602358\pi\)
0.979661 0.200661i \(-0.0643090\pi\)
\(104\) −0.712890 + 2.43780i −0.0699047 + 0.239046i
\(105\) 1.51272 + 2.62010i 0.147626 + 0.255696i
\(106\) −1.66620 0.961983i −0.161836 0.0934360i
\(107\) 0.326395 + 0.565332i 0.0315538 + 0.0546527i 0.881371 0.472425i \(-0.156621\pi\)
−0.849817 + 0.527077i \(0.823288\pi\)
\(108\) 6.87636 0.661678
\(109\) 11.6385i 1.11476i 0.830256 + 0.557382i \(0.188194\pi\)
−0.830256 + 0.557382i \(0.811806\pi\)
\(110\) 1.43710 0.829707i 0.137022 0.0791095i
\(111\) −1.83081 1.05702i −0.173773 0.100328i
\(112\) −7.61037 + 4.39385i −0.719112 + 0.415180i
\(113\) 1.39270 2.41222i 0.131014 0.226923i −0.793054 0.609152i \(-0.791510\pi\)
0.924068 + 0.382229i \(0.124843\pi\)
\(114\) −0.372967 + 0.645997i −0.0349315 + 0.0605032i
\(115\) 16.6892 + 9.63551i 1.55628 + 0.898516i
\(116\) −1.25598 −0.116615
\(117\) 6.81042 6.50804i 0.629624 0.601669i
\(118\) 0.161761 + 0.280178i 0.0148913 + 0.0257924i
\(119\) −14.5197 8.38293i −1.33101 0.768462i
\(120\) 0.924491 0.0843941
\(121\) 4.32745 + 7.49537i 0.393405 + 0.681397i
\(122\) 0.288431i 0.0261133i
\(123\) 1.07289i 0.0967390i
\(124\) −8.15978 7.31721i −0.732770 0.657105i
\(125\) 11.7107i 1.04743i
\(126\) −1.06912 −0.0952452
\(127\) 3.12070 + 5.40522i 0.276918 + 0.479635i 0.970617 0.240629i \(-0.0773538\pi\)
−0.693700 + 0.720264i \(0.744020\pi\)
\(128\) 5.45866i 0.482482i
\(129\) 1.03587 1.79418i 0.0912032 0.157969i
\(130\) 0.975695 0.932375i 0.0855741 0.0817747i
\(131\) −4.85712 8.41278i −0.424369 0.735028i 0.571993 0.820259i \(-0.306171\pi\)
−0.996361 + 0.0852308i \(0.972837\pi\)
\(132\) 5.43159i 0.472759i
\(133\) −7.78255 + 13.4798i −0.674832 + 1.16884i
\(134\) −0.153392 + 0.265682i −0.0132510 + 0.0229515i
\(135\) −6.37905 3.68294i −0.549021 0.316977i
\(136\) −4.43682 + 2.56160i −0.380454 + 0.219655i
\(137\) −11.8923 6.86605i −1.01603 0.586606i −0.103080 0.994673i \(-0.532870\pi\)
−0.912952 + 0.408067i \(0.866203\pi\)
\(138\) 0.874406 0.504838i 0.0744343 0.0429747i
\(139\) −16.0370 −1.36024 −0.680119 0.733102i \(-0.738072\pi\)
−0.680119 + 0.733102i \(0.738072\pi\)
\(140\) 9.56891 0.808721
\(141\) 5.35879 3.09390i 0.451292 0.260554i
\(142\) 0.650388 1.12650i 0.0545793 0.0945342i
\(143\) 11.0435 + 11.5566i 0.923504 + 0.966411i
\(144\) 4.97961 8.62493i 0.414967 0.718744i
\(145\) 1.16515 + 0.672699i 0.0967604 + 0.0558646i
\(146\) 0.140251 0.242921i 0.0116072 0.0201043i
\(147\) −1.04906 −0.0865248
\(148\) −5.79053 + 3.34316i −0.475978 + 0.274806i
\(149\) −4.51836 + 2.60868i −0.370159 + 0.213711i −0.673528 0.739162i \(-0.735222\pi\)
0.303369 + 0.952873i \(0.401888\pi\)
\(150\) 0.0529752 + 0.0305852i 0.00432541 + 0.00249727i
\(151\) 15.8717i 1.29162i 0.763496 + 0.645812i \(0.223481\pi\)
−0.763496 + 0.645812i \(0.776519\pi\)
\(152\) 2.37814 + 4.11906i 0.192893 + 0.334100i
\(153\) 19.0010 1.53614
\(154\) 1.81420i 0.146192i
\(155\) 3.65059 + 11.1584i 0.293222 + 0.896261i
\(156\) 1.04616 + 4.29170i 0.0837595 + 0.343611i
\(157\) 12.7405 1.01680 0.508400 0.861121i \(-0.330237\pi\)
0.508400 + 0.861121i \(0.330237\pi\)
\(158\) 0.876598 0.506104i 0.0697384 0.0402635i
\(159\) −6.74584 −0.534980
\(160\) 2.19881 3.80845i 0.173831 0.301084i
\(161\) 18.2459 10.5343i 1.43798 0.830216i
\(162\) 0.870679 0.502687i 0.0684070 0.0394948i
\(163\) 4.66669i 0.365523i 0.983157 + 0.182762i \(0.0585036\pi\)
−0.983157 + 0.182762i \(0.941496\pi\)
\(164\) −2.93873 1.69668i −0.229476 0.132488i
\(165\) 2.90913 5.03877i 0.226476 0.392267i
\(166\) 0.219558 0.380285i 0.0170410 0.0295158i
\(167\) 13.0048 7.50835i 1.00634 0.581014i 0.0962255 0.995360i \(-0.469323\pi\)
0.910119 + 0.414346i \(0.135990\pi\)
\(168\) 0.505362 0.875312i 0.0389895 0.0675318i
\(169\) 10.9517 + 7.00425i 0.842441 + 0.538788i
\(170\) 2.72217 0.208781
\(171\) 17.6401i 1.34897i
\(172\) −3.27628 5.67468i −0.249814 0.432690i
\(173\) 7.62580 13.2083i 0.579779 1.00421i −0.415726 0.909490i \(-0.636472\pi\)
0.995504 0.0947160i \(-0.0301943\pi\)
\(174\) 0.0610463 0.0352451i 0.00462791 0.00267192i
\(175\) 1.10541 + 0.638210i 0.0835613 + 0.0482441i
\(176\) 14.6356 + 8.44989i 1.10320 + 0.636935i
\(177\) 0.982363 + 0.567167i 0.0738389 + 0.0426309i
\(178\) −2.21376 −0.165928
\(179\) −1.05313 1.82407i −0.0787145 0.136338i 0.823981 0.566617i \(-0.191748\pi\)
−0.902696 + 0.430280i \(0.858415\pi\)
\(180\) −9.39168 + 5.42229i −0.700015 + 0.404154i
\(181\) 10.4591 18.1157i 0.777417 1.34653i −0.156008 0.987756i \(-0.549863\pi\)
0.933426 0.358771i \(-0.116804\pi\)
\(182\) −0.349425 1.43346i −0.0259011 0.106255i
\(183\) 0.505651 + 0.875813i 0.0373788 + 0.0647420i
\(184\) 6.43798i 0.474614i
\(185\) 7.16233 0.526585
\(186\) 0.601934 + 0.126671i 0.0441359 + 0.00928794i
\(187\) 32.2427i 2.35782i
\(188\) 19.5709i 1.42736i
\(189\) −6.97405 + 4.02647i −0.507287 + 0.292883i
\(190\) 2.52721i 0.183343i
\(191\) −3.86611 + 6.69631i −0.279742 + 0.484528i −0.971321 0.237774i \(-0.923582\pi\)
0.691578 + 0.722301i \(0.256916\pi\)
\(192\) 2.25728 + 3.90973i 0.162905 + 0.282160i
\(193\) −12.0335 + 6.94756i −0.866192 + 0.500096i −0.866081 0.499904i \(-0.833369\pi\)
−0.000111226 1.00000i \(0.500035\pi\)
\(194\) 1.28456 0.0922257
\(195\) 1.32812 4.54163i 0.0951084 0.325233i
\(196\) −1.65899 + 2.87346i −0.118499 + 0.205247i
\(197\) −10.5063 6.06582i −0.748543 0.432171i 0.0766242 0.997060i \(-0.475586\pi\)
−0.825167 + 0.564889i \(0.808919\pi\)
\(198\) 1.02803 + 1.78059i 0.0730587 + 0.126541i
\(199\) 3.32950 5.76686i 0.236022 0.408802i −0.723547 0.690275i \(-0.757490\pi\)
0.959569 + 0.281473i \(0.0908230\pi\)
\(200\) 0.337785 0.195020i 0.0238850 0.0137900i
\(201\) 1.07565i 0.0758704i
\(202\) 1.27702i 0.0898507i
\(203\) 1.27383 0.735445i 0.0894052 0.0516181i
\(204\) −4.45510 + 7.71647i −0.311920 + 0.540261i
\(205\) 1.81746 + 3.14794i 0.126937 + 0.219862i
\(206\) 2.07067 + 1.19550i 0.144270 + 0.0832945i
\(207\) −11.9386 + 20.6783i −0.829791 + 1.43724i
\(208\) 13.1917 + 3.85766i 0.914677 + 0.267480i
\(209\) 29.9335 2.07055
\(210\) −0.465090 + 0.268520i −0.0320943 + 0.0185296i
\(211\) −4.33279 7.50462i −0.298282 0.516639i 0.677461 0.735558i \(-0.263080\pi\)
−0.975743 + 0.218919i \(0.929747\pi\)
\(212\) −10.6680 + 18.4774i −0.732678 + 1.26904i
\(213\) 4.56080i 0.312501i
\(214\) −0.100351 + 0.0579379i −0.00685988 + 0.00396055i
\(215\) 7.01903i 0.478694i
\(216\) 2.46076i 0.167434i
\(217\) 12.5603 + 2.64319i 0.852650 + 0.179431i
\(218\) −2.06593 −0.139922
\(219\) 0.983497i 0.0664586i
\(220\) −9.20108 15.9367i −0.620337 1.07445i
\(221\) 6.21014 + 25.4762i 0.417739 + 1.71371i
\(222\) 0.187630 0.324984i 0.0125929 0.0218115i
\(223\) −15.2966 + 8.83148i −1.02433 + 0.591400i −0.915356 0.402644i \(-0.868091\pi\)
−0.108978 + 0.994044i \(0.534758\pi\)
\(224\) −2.40390 4.16368i −0.160617 0.278198i
\(225\) −1.44658 −0.0964389
\(226\) 0.428190 + 0.247216i 0.0284828 + 0.0164445i
\(227\) −18.7353 10.8168i −1.24351 0.717939i −0.273701 0.961815i \(-0.588248\pi\)
−0.969807 + 0.243875i \(0.921581\pi\)
\(228\) 7.16382 + 4.13603i 0.474435 + 0.273915i
\(229\) 13.2127 7.62836i 0.873121 0.504096i 0.00473670 0.999989i \(-0.498492\pi\)
0.868384 + 0.495892i \(0.165159\pi\)
\(230\) −1.71039 + 2.96248i −0.112780 + 0.195340i
\(231\) −3.18048 5.50875i −0.209260 0.362449i
\(232\) 0.449465i 0.0295088i
\(233\) −11.1940 −0.733341 −0.366670 0.930351i \(-0.619502\pi\)
−0.366670 + 0.930351i \(0.619502\pi\)
\(234\) 1.15523 + 1.20891i 0.0755200 + 0.0790288i
\(235\) −10.4821 + 18.1555i −0.683777 + 1.18434i
\(236\) 3.10704 1.79385i 0.202251 0.116770i
\(237\) 1.77451 3.07354i 0.115267 0.199648i
\(238\) 1.48804 2.57736i 0.0964554 0.167066i
\(239\) 13.4528 + 7.76696i 0.870187 + 0.502403i 0.867410 0.497593i \(-0.165783\pi\)
0.00277683 + 0.999996i \(0.499116\pi\)
\(240\) 5.00269i 0.322922i
\(241\) −2.34241 + 1.35239i −0.150888 + 0.0871151i −0.573543 0.819175i \(-0.694431\pi\)
0.422655 + 0.906291i \(0.361098\pi\)
\(242\) −1.33049 + 0.768160i −0.0855273 + 0.0493792i
\(243\) 7.00235 12.1284i 0.449201 0.778039i
\(244\) 3.19857 0.204768
\(245\) 3.07802 1.77710i 0.196648 0.113535i
\(246\) 0.190447 0.0121424
\(247\) 23.6516 5.76537i 1.50491 0.366842i
\(248\) 2.61853 2.92005i 0.166277 0.185423i
\(249\) 1.53963i 0.0975702i
\(250\) −2.07874 −0.131471
\(251\) −5.56233 9.63424i −0.351091 0.608108i 0.635350 0.772225i \(-0.280856\pi\)
−0.986441 + 0.164117i \(0.947523\pi\)
\(252\) 11.8561i 0.746864i
\(253\) −35.0890 20.2586i −2.20603 1.27365i
\(254\) −0.959472 + 0.553952i −0.0602027 + 0.0347580i
\(255\) 8.26580 4.77226i 0.517625 0.298851i
\(256\) 13.5384 0.846149
\(257\) −4.82248 + 8.35277i −0.300818 + 0.521032i −0.976321 0.216325i \(-0.930593\pi\)
0.675504 + 0.737357i \(0.263926\pi\)
\(258\) 0.318482 + 0.183876i 0.0198278 + 0.0114476i
\(259\) 3.91519 6.78132i 0.243278 0.421370i
\(260\) −10.3396 10.8200i −0.641236 0.671029i
\(261\) −0.833490 + 1.44365i −0.0515917 + 0.0893595i
\(262\) 1.49334 0.862181i 0.0922589 0.0532657i
\(263\) 19.2206 1.18519 0.592597 0.805499i \(-0.298103\pi\)
0.592597 + 0.805499i \(0.298103\pi\)
\(264\) −1.94374 −0.119629
\(265\) 19.7929 11.4274i 1.21587 0.701980i
\(266\) −2.39277 1.38147i −0.146710 0.0847033i
\(267\) −6.72201 + 3.88095i −0.411380 + 0.237511i
\(268\) 2.94630 + 1.70105i 0.179974 + 0.103908i
\(269\) −2.47431 + 4.28562i −0.150861 + 0.261299i −0.931544 0.363628i \(-0.881538\pi\)
0.780683 + 0.624927i \(0.214871\pi\)
\(270\) 0.653754 1.13234i 0.0397862 0.0689118i
\(271\) 4.03105i 0.244869i 0.992477 + 0.122434i \(0.0390701\pi\)
−0.992477 + 0.122434i \(0.960930\pi\)
\(272\) 13.8616 + 24.0089i 0.840481 + 1.45576i
\(273\) −3.57403 3.74009i −0.216310 0.226360i
\(274\) 1.21878 2.11099i 0.0736294 0.127530i
\(275\) 2.45471i 0.148024i
\(276\) −5.59843 9.69676i −0.336986 0.583677i
\(277\) 11.7173 0.704027 0.352013 0.935995i \(-0.385497\pi\)
0.352013 + 0.935995i \(0.385497\pi\)
\(278\) 2.84670i 0.170734i
\(279\) −13.8255 + 4.52316i −0.827709 + 0.270795i
\(280\) 3.42432i 0.204642i
\(281\) 19.6933i 1.17480i 0.809296 + 0.587401i \(0.199849\pi\)
−0.809296 + 0.587401i \(0.800151\pi\)
\(282\) 0.549194 + 0.951232i 0.0327040 + 0.0566451i
\(283\) −15.8694 −0.943336 −0.471668 0.881776i \(-0.656348\pi\)
−0.471668 + 0.881776i \(0.656348\pi\)
\(284\) −12.4924 7.21251i −0.741289 0.427983i
\(285\) −4.43048 7.67381i −0.262439 0.454557i
\(286\) −2.05140 + 1.96032i −0.121302 + 0.115916i
\(287\) 3.97398 0.234576
\(288\) 4.71875 + 2.72437i 0.278055 + 0.160535i
\(289\) −17.9462 + 31.0837i −1.05566 + 1.82845i
\(290\) −0.119410 + 0.206824i −0.00701199 + 0.0121451i
\(291\) 3.90052 2.25196i 0.228652 0.132012i
\(292\) −2.69388 1.55531i −0.157648 0.0910179i
\(293\) 18.6240 10.7526i 1.08803 0.628172i 0.154976 0.987918i \(-0.450470\pi\)
0.933050 + 0.359746i \(0.117137\pi\)
\(294\) 0.186217i 0.0108604i
\(295\) −3.84311 −0.223755
\(296\) −1.19638 2.07219i −0.0695381 0.120444i
\(297\) 13.4119 + 7.74338i 0.778239 + 0.449316i
\(298\) −0.463063 0.802048i −0.0268245 0.0464614i
\(299\) −31.6270 9.24874i −1.82904 0.534869i
\(300\) 0.339176 0.587471i 0.0195824 0.0339176i
\(301\) 6.64564 + 3.83686i 0.383048 + 0.221153i
\(302\) −2.81737 −0.162122
\(303\) −2.23875 3.87763i −0.128613 0.222764i
\(304\) 22.2894 12.8688i 1.27839 0.738076i
\(305\) −2.96724 1.71314i −0.169904 0.0980941i
\(306\) 3.37284i 0.192812i
\(307\) 13.3403 7.70204i 0.761373 0.439579i −0.0684155 0.997657i \(-0.521794\pi\)
0.829788 + 0.558078i \(0.188461\pi\)
\(308\) −20.1186 −1.14636
\(309\) 8.38336 0.476913
\(310\) −1.98070 + 0.648011i −0.112496 + 0.0368045i
\(311\) −6.08294 −0.344932 −0.172466 0.985016i \(-0.555173\pi\)
−0.172466 + 0.985016i \(0.555173\pi\)
\(312\) −1.53582 + 0.374376i −0.0869487 + 0.0211949i
\(313\) 13.0147 + 22.5421i 0.735633 + 1.27415i 0.954445 + 0.298387i \(0.0964485\pi\)
−0.218812 + 0.975767i \(0.570218\pi\)
\(314\) 2.26154i 0.127626i
\(315\) 6.35007 10.9986i 0.357786 0.619704i
\(316\) −5.61247 9.72108i −0.315726 0.546853i
\(317\) −1.29542 + 0.747913i −0.0727582 + 0.0420070i −0.535938 0.844257i \(-0.680042\pi\)
0.463180 + 0.886264i \(0.346709\pi\)
\(318\) 1.19744i 0.0671493i
\(319\) −2.44972 1.41435i −0.137158 0.0791883i
\(320\) −13.2461 7.64765i −0.740481 0.427517i
\(321\) −0.203143 + 0.351853i −0.0113383 + 0.0196385i
\(322\) 1.86992 + 3.23880i 0.104207 + 0.180491i
\(323\) 42.5255 + 24.5521i 2.36618 + 1.36612i
\(324\) −5.57457 9.65543i −0.309698 0.536413i
\(325\) −0.472791 1.93955i −0.0262257 0.107587i
\(326\) −0.828377 −0.0458796
\(327\) −6.27314 + 3.62180i −0.346905 + 0.200286i
\(328\) 0.607171 1.05165i 0.0335254 0.0580677i
\(329\) 11.4598 + 19.8490i 0.631800 + 1.09431i
\(330\) 0.894424 + 0.516396i 0.0492364 + 0.0284267i
\(331\) −27.2646 15.7412i −1.49860 0.865215i −0.498598 0.866833i \(-0.666152\pi\)
−0.999999 + 0.00161815i \(0.999485\pi\)
\(332\) −4.21719 2.43480i −0.231448 0.133627i
\(333\) 8.87429i 0.486308i
\(334\) 1.33280 + 2.30847i 0.0729274 + 0.126314i
\(335\) −1.82214 3.15604i −0.0995543 0.172433i
\(336\) −4.73657 2.73466i −0.258401 0.149188i
\(337\) 6.70046 0.364998 0.182499 0.983206i \(-0.441581\pi\)
0.182499 + 0.983206i \(0.441581\pi\)
\(338\) −1.24331 + 1.94403i −0.0676274 + 0.105741i
\(339\) 1.73358 0.0941552
\(340\) 30.1877i 1.63716i
\(341\) −7.67535 23.4604i −0.415643 1.27045i
\(342\) 3.13128 0.169320
\(343\) 20.0229i 1.08113i
\(344\) 2.03073 1.17244i 0.109490 0.0632139i
\(345\) 11.9940i 0.645733i
\(346\) 2.34458 + 1.35364i 0.126045 + 0.0727724i
\(347\) −10.5100 18.2038i −0.564206 0.977233i −0.997123 0.0757993i \(-0.975849\pi\)
0.432917 0.901434i \(-0.357484\pi\)
\(348\) −0.390852 0.676976i −0.0209519 0.0362897i
\(349\) 21.2859i 1.13941i 0.821850 + 0.569704i \(0.192942\pi\)
−0.821850 + 0.569704i \(0.807058\pi\)
\(350\) −0.113288 + 0.196220i −0.00605549 + 0.0104884i
\(351\) 12.0887 + 3.53511i 0.645246 + 0.188690i
\(352\) −4.62299 + 8.00725i −0.246406 + 0.426788i
\(353\) −2.90376 + 1.67649i −0.154551 + 0.0892303i −0.575281 0.817956i \(-0.695107\pi\)
0.420730 + 0.907186i \(0.361774\pi\)
\(354\) −0.100677 + 0.174378i −0.00535093 + 0.00926808i
\(355\) 7.72597 + 13.3818i 0.410052 + 0.710230i
\(356\) 24.5496i 1.30112i
\(357\) 10.4348i 0.552268i
\(358\) 0.323789 0.186939i 0.0171128 0.00988006i
\(359\) 15.9483 + 9.20775i 0.841718 + 0.485966i 0.857848 0.513904i \(-0.171801\pi\)
−0.0161297 + 0.999870i \(0.505134\pi\)
\(360\) −1.94041 3.36089i −0.102269 0.177135i
\(361\) 13.2937 23.0254i 0.699668 1.21186i
\(362\) 3.21569 + 1.85658i 0.169013 + 0.0975796i
\(363\) −2.69333 + 4.66499i −0.141363 + 0.244849i
\(364\) −15.8965 + 3.87496i −0.833200 + 0.203103i
\(365\) 1.66604 + 2.88566i 0.0872044 + 0.151043i
\(366\) −0.155464 + 0.0897574i −0.00812625 + 0.00469169i
\(367\) −13.5138 + 23.4067i −0.705417 + 1.22182i 0.261124 + 0.965305i \(0.415907\pi\)
−0.966541 + 0.256513i \(0.917426\pi\)
\(368\) −34.8378 −1.81604
\(369\) −3.90037 + 2.25188i −0.203045 + 0.117228i
\(370\) 1.27137i 0.0660956i
\(371\) 24.9866i 1.29724i
\(372\) 1.40472 6.67518i 0.0728314 0.346092i
\(373\) −24.1486 −1.25037 −0.625183 0.780478i \(-0.714976\pi\)
−0.625183 + 0.780478i \(0.714976\pi\)
\(374\) −5.72336 −0.295948
\(375\) −6.31204 + 3.64426i −0.325953 + 0.188189i
\(376\) 7.00363 0.361185
\(377\) −2.20803 0.645697i −0.113719 0.0332551i
\(378\) −0.714733 1.23795i −0.0367619 0.0636735i
\(379\) −18.4380 + 10.6452i −0.947095 + 0.546806i −0.892177 0.451685i \(-0.850823\pi\)
−0.0549180 + 0.998491i \(0.517490\pi\)
\(380\) −28.0257 −1.43769
\(381\) −1.94227 + 3.36412i −0.0995057 + 0.172349i
\(382\) −1.18865 0.686269i −0.0608167 0.0351126i
\(383\) −8.11184 4.68337i −0.414496 0.239309i 0.278224 0.960516i \(-0.410254\pi\)
−0.692720 + 0.721207i \(0.743588\pi\)
\(384\) −2.94222 + 1.69869i −0.150144 + 0.0866859i
\(385\) 18.6636 + 10.7754i 0.951185 + 0.549167i
\(386\) −1.23325 2.13606i −0.0627709 0.108722i
\(387\) −8.69674 −0.442080
\(388\) 14.2451i 0.723187i
\(389\) 12.7629 + 22.1060i 0.647106 + 1.12082i 0.983811 + 0.179211i \(0.0573543\pi\)
−0.336705 + 0.941610i \(0.609312\pi\)
\(390\) 0.806178 + 0.235752i 0.0408224 + 0.0119378i
\(391\) −33.2331 57.5615i −1.68067 2.91101i
\(392\) −1.02829 0.593685i −0.0519366 0.0299856i
\(393\) 3.02299 5.23597i 0.152490 0.264120i
\(394\) 1.07673 1.86496i 0.0542451 0.0939553i
\(395\) 12.0240i 0.604995i
\(396\) 19.7460 11.4004i 0.992273 0.572889i
\(397\) 9.57746 5.52955i 0.480679 0.277520i −0.240020 0.970768i \(-0.577154\pi\)
0.720699 + 0.693248i \(0.243821\pi\)
\(398\) 1.02367 + 0.591014i 0.0513118 + 0.0296249i
\(399\) −9.68745 −0.484979
\(400\) −1.05531 1.82785i −0.0527655 0.0913925i
\(401\) 27.5214i 1.37435i −0.726490 0.687177i \(-0.758850\pi\)
0.726490 0.687177i \(-0.241150\pi\)
\(402\) −0.190937 −0.00952307
\(403\) −10.5832 17.0586i −0.527186 0.849750i
\(404\) −14.1616 −0.704564
\(405\) 11.9428i 0.593445i
\(406\) 0.130548 + 0.226116i 0.00647898 + 0.0112219i
\(407\) −15.0588 −0.746436
\(408\) −2.76140 1.59430i −0.136710 0.0789295i
\(409\) 6.83852 3.94822i 0.338143 0.195227i −0.321307 0.946975i \(-0.604122\pi\)
0.659451 + 0.751748i \(0.270789\pi\)
\(410\) −0.558787 + 0.322616i −0.0275965 + 0.0159329i
\(411\) 8.54663i 0.421574i
\(412\) 13.2576 22.9628i 0.653153 1.13129i
\(413\) −2.10079 + 3.63867i −0.103373 + 0.179047i
\(414\) −3.67058 2.11921i −0.180399 0.104153i
\(415\) 2.60813 + 4.51741i 0.128028 + 0.221751i
\(416\) −2.11055 + 7.21724i −0.103478 + 0.353854i
\(417\) −4.99057 8.64392i −0.244389 0.423295i
\(418\) 5.31346i 0.259890i
\(419\) 26.9102 1.31465 0.657324 0.753608i \(-0.271688\pi\)
0.657324 + 0.753608i \(0.271688\pi\)
\(420\) 2.97777 + 5.15764i 0.145300 + 0.251667i
\(421\) −23.0878 13.3298i −1.12523 0.649653i −0.182500 0.983206i \(-0.558419\pi\)
−0.942731 + 0.333553i \(0.891752\pi\)
\(422\) 1.33213 0.769108i 0.0648473 0.0374396i
\(423\) −22.4951 12.9876i −1.09375 0.631477i
\(424\) −6.61231 3.81762i −0.321122 0.185400i
\(425\) 2.01340 3.48732i 0.0976644 0.169160i
\(426\) 0.809581 0.0392243
\(427\) −3.24401 + 1.87293i −0.156989 + 0.0906375i
\(428\) 0.642505 + 1.11285i 0.0310566 + 0.0537917i
\(429\) −2.79236 + 9.54876i −0.134816 + 0.461018i
\(430\) −1.24594 −0.0600845
\(431\) 25.2229 14.5624i 1.21494 0.701448i 0.251111 0.967958i \(-0.419204\pi\)
0.963832 + 0.266510i \(0.0858707\pi\)
\(432\) 13.3159 0.640662
\(433\) 22.0114 1.05780 0.528899 0.848685i \(-0.322605\pi\)
0.528899 + 0.848685i \(0.322605\pi\)
\(434\) −0.469188 + 2.22957i −0.0225218 + 0.107023i
\(435\) 0.837354i 0.0401480i
\(436\) 22.9102i 1.09720i
\(437\) −53.4389 + 30.8530i −2.55633 + 1.47590i
\(438\) 0.174579 0.00834172
\(439\) −16.3497 + 28.3185i −0.780329 + 1.35157i 0.151422 + 0.988469i \(0.451615\pi\)
−0.931750 + 0.363100i \(0.881718\pi\)
\(440\) 5.70310 3.29269i 0.271885 0.156973i
\(441\) 2.20186 + 3.81374i 0.104851 + 0.181607i
\(442\) −4.52224 + 1.10235i −0.215101 + 0.0524336i
\(443\) 1.55276 2.68946i 0.0737739 0.127780i −0.826779 0.562528i \(-0.809829\pi\)
0.900552 + 0.434747i \(0.143162\pi\)
\(444\) −3.60393 2.08073i −0.171035 0.0987470i
\(445\) 13.1486 22.7741i 0.623305 1.07960i
\(446\) −1.56766 2.71527i −0.0742311 0.128572i
\(447\) −2.81215 1.62360i −0.133010 0.0767935i
\(448\) −14.4816 + 8.36098i −0.684193 + 0.395019i
\(449\) 27.4104i 1.29358i 0.762670 + 0.646788i \(0.223888\pi\)
−0.762670 + 0.646788i \(0.776112\pi\)
\(450\) 0.256781i 0.0121048i
\(451\) −3.82121 6.61854i −0.179934 0.311655i
\(452\) 2.74151 4.74843i 0.128950 0.223348i
\(453\) −8.55487 + 4.93916i −0.401943 + 0.232062i
\(454\) 1.92008 3.32568i 0.0901140 0.156082i
\(455\) 16.8222 + 4.91934i 0.788637 + 0.230622i
\(456\) −1.48011 + 2.56363i −0.0693127 + 0.120053i
\(457\) 28.3739i 1.32728i −0.748054 0.663638i \(-0.769011\pi\)
0.748054 0.663638i \(-0.230989\pi\)
\(458\) 1.35410 + 2.34537i 0.0632730 + 0.109592i
\(459\) 12.7026 + 22.0015i 0.592905 + 1.02694i
\(460\) 32.8525 + 18.9674i 1.53176 + 0.884360i
\(461\) 8.45607i 0.393838i 0.980420 + 0.196919i \(0.0630937\pi\)
−0.980420 + 0.196919i \(0.936906\pi\)
\(462\) 0.977851 0.564563i 0.0454938 0.0262658i
\(463\) 11.7725i 0.547113i −0.961856 0.273557i \(-0.911800\pi\)
0.961856 0.273557i \(-0.0882001\pi\)
\(464\) −2.43219 −0.112911
\(465\) −4.87832 + 5.44005i −0.226227 + 0.252276i
\(466\) 1.98702i 0.0920472i
\(467\) −10.9044 −0.504596 −0.252298 0.967650i \(-0.581186\pi\)
−0.252298 + 0.967650i \(0.581186\pi\)
\(468\) 13.4062 12.8110i 0.619704 0.592190i
\(469\) −3.98421 −0.183974
\(470\) −3.22277 1.86066i −0.148655 0.0858260i
\(471\) 3.96473 + 6.86711i 0.182685 + 0.316420i
\(472\) 0.641945 + 1.11188i 0.0295479 + 0.0511785i
\(473\) 14.7575i 0.678550i
\(474\) 0.545580 + 0.314991i 0.0250593 + 0.0144680i
\(475\) −3.23756 1.86920i −0.148549 0.0857650i
\(476\) −28.5818 16.5017i −1.31004 0.756355i
\(477\) 14.1588 + 24.5238i 0.648288 + 1.12287i
\(478\) −1.37870 + 2.38798i −0.0630604 + 0.109224i
\(479\) 27.5740 15.9199i 1.25989 0.727398i 0.286837 0.957979i \(-0.407396\pi\)
0.973053 + 0.230582i \(0.0740629\pi\)
\(480\) 2.73700 0.124927
\(481\) −11.8985 + 2.90041i −0.542524 + 0.132247i
\(482\) −0.240061 0.415798i −0.0109345 0.0189391i
\(483\) 11.3559 + 6.55635i 0.516713 + 0.298324i
\(484\) 8.51855 + 14.7546i 0.387207 + 0.670662i
\(485\) −7.62963 + 13.2149i −0.346444 + 0.600058i
\(486\) 2.15290 + 1.24298i 0.0976575 + 0.0563826i
\(487\) 31.0021 + 17.8991i 1.40484 + 0.811083i 0.994884 0.101023i \(-0.0322116\pi\)
0.409954 + 0.912106i \(0.365545\pi\)
\(488\) 1.14464i 0.0518153i
\(489\) −2.51534 + 1.45223i −0.113748 + 0.0656723i
\(490\) 0.315450 + 0.546375i 0.0142506 + 0.0246827i
\(491\) 8.97171 15.5395i 0.404888 0.701286i −0.589421 0.807826i \(-0.700644\pi\)
0.994308 + 0.106540i \(0.0339773\pi\)
\(492\) 2.11197i 0.0952149i
\(493\) −2.32016 4.01863i −0.104495 0.180990i
\(494\) 1.02340 + 4.19836i 0.0460451 + 0.188893i
\(495\) −24.4239 −1.09777
\(496\) −15.8012 14.1696i −0.709496 0.636234i
\(497\) 16.8932 0.757764
\(498\) 0.273298 0.0122468
\(499\) −0.917631 + 0.529795i −0.0410788 + 0.0237169i −0.520399 0.853923i \(-0.674217\pi\)
0.479320 + 0.877640i \(0.340883\pi\)
\(500\) 23.0523i 1.03093i
\(501\) 8.09400 + 4.67307i 0.361613 + 0.208777i
\(502\) 1.71016 0.987362i 0.0763282 0.0440681i
\(503\) 8.39005 + 14.5320i 0.374094 + 0.647949i 0.990191 0.139721i \(-0.0446205\pi\)
−0.616097 + 0.787670i \(0.711287\pi\)
\(504\) −4.24281 −0.188990
\(505\) 13.1374 + 7.58487i 0.584605 + 0.337522i
\(506\) 3.59608 6.22860i 0.159865 0.276895i
\(507\) −0.367199 + 8.08265i −0.0163079 + 0.358963i
\(508\) 6.14307 + 10.6401i 0.272555 + 0.472079i
\(509\) 12.0337 + 6.94766i 0.533384 + 0.307950i 0.742394 0.669964i \(-0.233691\pi\)
−0.209009 + 0.977914i \(0.567024\pi\)
\(510\) 0.847118 + 1.46725i 0.0375110 + 0.0649710i
\(511\) 3.64287 0.161151
\(512\) 13.3205i 0.588688i
\(513\) 20.4258 11.7928i 0.901819 0.520666i
\(514\) −1.48269 0.856031i −0.0653986 0.0377579i
\(515\) −24.5975 + 14.2014i −1.08390 + 0.625787i
\(516\) 2.03910 3.53182i 0.0897663 0.155480i
\(517\) 22.0386 38.1720i 0.969256 1.67880i
\(518\) 1.20374 + 0.694981i 0.0528894 + 0.0305357i
\(519\) 9.49234 0.416667
\(520\) 3.87204 3.70012i 0.169800 0.162261i
\(521\) 10.1180 + 17.5249i 0.443278 + 0.767779i 0.997930 0.0643026i \(-0.0204823\pi\)
−0.554653 + 0.832082i \(0.687149\pi\)
\(522\) −0.256260 0.147952i −0.0112162 0.00647567i
\(523\) 14.1021 0.616643 0.308321 0.951282i \(-0.400233\pi\)
0.308321 + 0.951282i \(0.400233\pi\)
\(524\) −9.56120 16.5605i −0.417683 0.723448i
\(525\) 0.794423i 0.0346714i
\(526\) 3.41183i 0.148763i
\(527\) 8.33863 39.6249i 0.363237 1.72609i
\(528\) 10.5181i 0.457744i
\(529\) 60.5237 2.63146
\(530\) 2.02846 + 3.51340i 0.0881108 + 0.152612i
\(531\) 4.76171i 0.206640i
\(532\) −15.3199 + 26.5348i −0.664201 + 1.15043i
\(533\) −4.29405 4.49356i −0.185996 0.194638i
\(534\) −0.688903 1.19321i −0.0298117 0.0516354i
\(535\) 1.37649i 0.0595109i
\(536\) −0.608734 + 1.05436i −0.0262933 + 0.0455413i
\(537\) 0.655450 1.13527i 0.0282847 0.0489906i
\(538\) −0.760735 0.439211i −0.0327976 0.0189357i
\(539\) −6.47153 + 3.73634i −0.278749 + 0.160936i
\(540\) −12.5571 7.24984i −0.540371 0.311983i
\(541\) 33.7679 19.4959i 1.45180 0.838194i 0.453212 0.891403i \(-0.350278\pi\)
0.998583 + 0.0532085i \(0.0169448\pi\)
\(542\) −0.715546 −0.0307353
\(543\) 13.0191 0.558704
\(544\) −13.1354 + 7.58375i −0.563177 + 0.325150i
\(545\) 12.2706 21.2533i 0.525615 0.910392i
\(546\) 0.663898 0.634422i 0.0284122 0.0271507i
\(547\) −16.2249 + 28.1024i −0.693727 + 1.20157i 0.276881 + 0.960904i \(0.410699\pi\)
−0.970608 + 0.240667i \(0.922634\pi\)
\(548\) −23.4100 13.5158i −1.00002 0.577364i
\(549\) 2.12262 3.67648i 0.0905912 0.156909i
\(550\) 0.435732 0.0185797
\(551\) −3.73082 + 2.15399i −0.158938 + 0.0917630i
\(552\) 3.47007 2.00345i 0.147696 0.0852723i
\(553\) 11.3844 + 6.57279i 0.484114 + 0.279503i
\(554\) 2.07993i 0.0883677i
\(555\) 2.22886 + 3.86049i 0.0946097 + 0.163869i
\(556\) −31.5686 −1.33881
\(557\) 7.40371i 0.313705i 0.987622 + 0.156853i \(0.0501347\pi\)
−0.987622 + 0.156853i \(0.949865\pi\)
\(558\) −0.802900 2.45414i −0.0339895 0.103892i
\(559\) −2.84238 11.6604i −0.120220 0.493184i
\(560\) 18.5300 0.783035
\(561\) −17.3788 + 10.0337i −0.733735 + 0.423622i
\(562\) −3.49572 −0.147458
\(563\) 17.7861 30.8064i 0.749595 1.29834i −0.198422 0.980117i \(-0.563582\pi\)
0.948017 0.318220i \(-0.103085\pi\)
\(564\) 10.5487 6.09032i 0.444182 0.256449i
\(565\) −5.08648 + 2.93668i −0.213990 + 0.123547i
\(566\) 2.81695i 0.118405i
\(567\) 11.3075 + 6.52840i 0.474872 + 0.274167i
\(568\) 2.58106 4.47052i 0.108299 0.187579i
\(569\) 2.69060 4.66026i 0.112796 0.195368i −0.804101 0.594493i \(-0.797353\pi\)
0.916896 + 0.399125i \(0.130686\pi\)
\(570\) 1.36217 0.786448i 0.0570549 0.0329407i
\(571\) −13.9447 + 24.1530i −0.583569 + 1.01077i 0.411483 + 0.911417i \(0.365011\pi\)
−0.995052 + 0.0993539i \(0.968322\pi\)
\(572\) 21.7390 + 22.7491i 0.908954 + 0.951186i
\(573\) −4.81241 −0.201041
\(574\) 0.705415i 0.0294435i
\(575\) 2.53011 + 4.38228i 0.105513 + 0.182754i
\(576\) 9.47561 16.4122i 0.394817 0.683844i
\(577\) −37.5618 + 21.6863i −1.56372 + 0.902812i −0.566841 + 0.823827i \(0.691835\pi\)
−0.996876 + 0.0789849i \(0.974832\pi\)
\(578\) −5.51762 3.18560i −0.229503 0.132504i
\(579\) −7.48947 4.32405i −0.311252 0.179701i
\(580\) 2.29359 + 1.32420i 0.0952360 + 0.0549845i
\(581\) 5.70280 0.236592
\(582\) 0.399743 + 0.692375i 0.0165699 + 0.0286999i
\(583\) −41.6144 + 24.0261i −1.72349 + 0.995059i
\(584\) 0.556583 0.964030i 0.0230316 0.0398918i
\(585\) −19.2982 + 4.70418i −0.797883 + 0.194494i
\(586\) 1.90868 + 3.30592i 0.0788467 + 0.136566i
\(587\) 27.9682i 1.15437i 0.816614 + 0.577185i \(0.195849\pi\)
−0.816614 + 0.577185i \(0.804151\pi\)
\(588\) −2.06506 −0.0851616
\(589\) −36.7870 7.74142i −1.51578 0.318980i
\(590\) 0.682186i 0.0280851i
\(591\) 7.55053i 0.310587i
\(592\) −11.2132 + 6.47396i −0.460861 + 0.266078i
\(593\) 13.4247i 0.551288i −0.961260 0.275644i \(-0.911109\pi\)
0.961260 0.275644i \(-0.0888911\pi\)
\(594\) −1.37452 + 2.38073i −0.0563971 + 0.0976827i
\(595\) 17.6765 + 30.6166i 0.724665 + 1.25516i
\(596\) −8.89436 + 5.13516i −0.364327 + 0.210344i
\(597\) 4.14445 0.169621
\(598\) 1.64173 5.61407i 0.0671354 0.229576i
\(599\) 8.84805 15.3253i 0.361522 0.626174i −0.626690 0.779269i \(-0.715591\pi\)
0.988211 + 0.153095i \(0.0489241\pi\)
\(600\) 0.210232 + 0.121377i 0.00858267 + 0.00495520i
\(601\) −7.09939 12.2965i −0.289590 0.501585i 0.684122 0.729368i \(-0.260186\pi\)
−0.973712 + 0.227783i \(0.926852\pi\)
\(602\) −0.681076 + 1.17966i −0.0277586 + 0.0480793i
\(603\) 3.91041 2.25768i 0.159244 0.0919397i
\(604\) 31.2434i 1.27128i
\(605\) 18.2500i 0.741967i
\(606\) 0.688313 0.397398i 0.0279608 0.0161432i
\(607\) −13.3328 + 23.0932i −0.541163 + 0.937322i 0.457674 + 0.889120i \(0.348683\pi\)
−0.998838 + 0.0482025i \(0.984651\pi\)
\(608\) 7.04060 + 12.1947i 0.285534 + 0.494560i
\(609\) 0.792810 + 0.457729i 0.0321263 + 0.0185481i
\(610\) 0.304097 0.526712i 0.0123125 0.0213259i
\(611\) 10.0614 34.4058i 0.407039 1.39191i
\(612\) 37.4032 1.51194
\(613\) 39.8799 23.0247i 1.61073 0.929957i 0.621533 0.783388i \(-0.286510\pi\)
0.989200 0.146570i \(-0.0468232\pi\)
\(614\) 1.36718 + 2.36802i 0.0551749 + 0.0955657i
\(615\) −1.13116 + 1.95923i −0.0456128 + 0.0790036i
\(616\) 7.19962i 0.290081i
\(617\) 1.59801 0.922614i 0.0643336 0.0371430i −0.467488 0.883999i \(-0.654841\pi\)
0.531822 + 0.846856i \(0.321508\pi\)
\(618\) 1.48812i 0.0598609i
\(619\) 1.59885i 0.0642632i 0.999484 + 0.0321316i \(0.0102296\pi\)
−0.999484 + 0.0321316i \(0.989770\pi\)
\(620\) 7.18614 + 21.9651i 0.288603 + 0.882140i
\(621\) −31.9249 −1.28110
\(622\) 1.07977i 0.0432950i
\(623\) −14.3751 24.8983i −0.575925 0.997531i
\(624\) 2.02586 + 8.31077i 0.0810992 + 0.332697i
\(625\) 10.9625 18.9876i 0.438500 0.759504i
\(626\) −4.00141 + 2.31022i −0.159929 + 0.0923349i
\(627\) 9.31507 + 16.1342i 0.372008 + 0.644337i
\(628\) 25.0795 1.00078
\(629\) −21.3935 12.3515i −0.853013 0.492487i
\(630\) 1.95236 + 1.12719i 0.0777837 + 0.0449084i
\(631\) −38.7293 22.3604i −1.54179 0.890153i −0.998726 0.0504628i \(-0.983930\pi\)
−0.543065 0.839691i \(-0.682736\pi\)
\(632\) 3.47877 2.00847i 0.138378 0.0798926i
\(633\) 2.69666 4.67075i 0.107183 0.185646i
\(634\) −0.132761 0.229949i −0.00527262 0.00913244i
\(635\) 13.1608i 0.522271i
\(636\) −13.2791 −0.526551
\(637\) −4.39375 + 4.19867i −0.174087 + 0.166358i
\(638\) 0.251059 0.434847i 0.00993952 0.0172158i
\(639\) −16.5803 + 9.57265i −0.655907 + 0.378688i
\(640\) 5.75514 9.96820i 0.227492 0.394028i
\(641\) 12.9174 22.3735i 0.510205 0.883701i −0.489725 0.871877i \(-0.662903\pi\)
0.999930 0.0118242i \(-0.00376385\pi\)
\(642\) −0.0624570 0.0360596i −0.00246498 0.00142316i
\(643\) 15.6490i 0.617137i 0.951202 + 0.308568i \(0.0998499\pi\)
−0.951202 + 0.308568i \(0.900150\pi\)
\(644\) 35.9168 20.7366i 1.41532 0.817136i
\(645\) −3.78326 + 2.18426i −0.148966 + 0.0860053i
\(646\) −4.35821 + 7.54864i −0.171472 + 0.296997i
\(647\) 2.83716 0.111540 0.0557702 0.998444i \(-0.482239\pi\)
0.0557702 + 0.998444i \(0.482239\pi\)
\(648\) 3.45528 1.99491i 0.135736 0.0783674i
\(649\) 8.08013 0.317173
\(650\) 0.344288 0.0839245i 0.0135041 0.00329179i
\(651\) 2.48399 + 7.59255i 0.0973552 + 0.297575i
\(652\) 9.18633i 0.359765i
\(653\) −19.0412 −0.745141 −0.372570 0.928004i \(-0.621524\pi\)
−0.372570 + 0.928004i \(0.621524\pi\)
\(654\) −0.642900 1.11354i −0.0251394 0.0435427i
\(655\) 20.4837i 0.800365i
\(656\) −5.69079 3.28558i −0.222188 0.128280i
\(657\) −3.57540 + 2.06426i −0.139490 + 0.0805344i
\(658\) −3.52337 + 2.03422i −0.137355 + 0.0793020i
\(659\) 3.11251 0.121246 0.0606231 0.998161i \(-0.480691\pi\)
0.0606231 + 0.998161i \(0.480691\pi\)
\(660\) 5.72660 9.91876i 0.222908 0.386087i
\(661\) 29.8334 + 17.2243i 1.16038 + 0.669948i 0.951396 0.307970i \(-0.0996496\pi\)
0.208988 + 0.977918i \(0.432983\pi\)
\(662\) 2.79420 4.83970i 0.108600 0.188100i
\(663\) −11.7991 + 11.2752i −0.458239 + 0.437894i
\(664\) 0.871313 1.50916i 0.0338135 0.0585667i
\(665\) 28.4238 16.4105i 1.10223 0.636372i
\(666\) −1.57526 −0.0610402
\(667\) 5.83117 0.225784
\(668\) 25.5999 14.7801i 0.990490 0.571860i
\(669\) −9.52034 5.49657i −0.368077 0.212510i
\(670\) 0.560225 0.323446i 0.0216434 0.0124958i
\(671\) 6.23862 + 3.60187i 0.240839 + 0.139049i
\(672\) 1.49615 2.59141i 0.0577152 0.0999656i
\(673\) −3.27940 + 5.68009i −0.126412 + 0.218951i −0.922284 0.386513i \(-0.873679\pi\)
0.795872 + 0.605465i \(0.207013\pi\)
\(674\) 1.18939i 0.0458136i
\(675\) −0.967073 1.67502i −0.0372227 0.0644716i
\(676\) 21.5584 + 13.7878i 0.829169 + 0.530300i
\(677\) 4.80721 8.32633i 0.184756 0.320007i −0.758738 0.651396i \(-0.774184\pi\)
0.943494 + 0.331389i \(0.107517\pi\)
\(678\) 0.307726i 0.0118181i
\(679\) 8.34128 + 14.4475i 0.320109 + 0.554445i
\(680\) 10.8029 0.414273
\(681\) 13.4645i 0.515959i
\(682\) 4.16443 1.36244i 0.159464 0.0521705i
\(683\) 25.7995i 0.987189i 0.869692 + 0.493595i \(0.164317\pi\)
−0.869692 + 0.493595i \(0.835683\pi\)
\(684\) 34.7244i 1.32772i
\(685\) 14.4779 + 25.0765i 0.553174 + 0.958125i
\(686\) 3.55423 0.135701
\(687\) 8.22337 + 4.74777i 0.313741 + 0.181139i
\(688\) −6.34443 10.9889i −0.241879 0.418947i
\(689\) −28.2535 + 26.9991i −1.07637 + 1.02858i
\(690\) −2.12903 −0.0810509
\(691\) 30.4991 + 17.6087i 1.16024 + 0.669865i 0.951361 0.308077i \(-0.0996855\pi\)
0.208878 + 0.977942i \(0.433019\pi\)
\(692\) 15.0113 26.0004i 0.570644 0.988385i
\(693\) −13.3510 + 23.1246i −0.507163 + 0.878432i
\(694\) 3.23134 1.86561i 0.122660 0.0708177i
\(695\) 29.2855 + 16.9080i 1.11086 + 0.641357i
\(696\) 0.242262 0.139870i 0.00918290 0.00530175i
\(697\) 12.5370i 0.474871i
\(698\) −3.77843 −0.143016
\(699\) −3.48347 6.03354i −0.131757 0.228210i
\(700\) 2.17599 + 1.25631i 0.0822448 + 0.0474841i
\(701\) −3.59467 6.22616i −0.135769 0.235159i 0.790122 0.612950i \(-0.210017\pi\)
−0.925891 + 0.377791i \(0.876684\pi\)
\(702\) −0.627513 + 2.14584i −0.0236839 + 0.0809897i
\(703\) −11.4669 + 19.8613i −0.432483 + 0.749082i
\(704\) 27.8499 + 16.0792i 1.04963 + 0.606006i
\(705\) −13.0478 −0.491408
\(706\) −0.297591 0.515442i −0.0112000 0.0193989i
\(707\) 14.3628 8.29234i 0.540167 0.311866i
\(708\) 1.93377 + 1.11646i 0.0726756 + 0.0419593i
\(709\) 24.8610i 0.933673i −0.884344 0.466837i \(-0.845394\pi\)
0.884344 0.466837i \(-0.154606\pi\)
\(710\) −2.37538 + 1.37143i −0.0891464 + 0.0514687i
\(711\) −14.8981 −0.558721
\(712\) −8.78527 −0.329242
\(713\) 37.8835 + 33.9717i 1.41875 + 1.27225i
\(714\) 1.85227 0.0693193
\(715\) −7.98253 32.7471i −0.298530 1.22467i
\(716\) −2.07307 3.59067i −0.0774744 0.134190i
\(717\) 9.66805i 0.361060i
\(718\) −1.63445 + 2.83096i −0.0609973 + 0.105650i
\(719\) 11.0930 + 19.2136i 0.413699 + 0.716547i 0.995291 0.0969334i \(-0.0309034\pi\)
−0.581592 + 0.813480i \(0.697570\pi\)
\(720\) −18.1868 + 10.5001i −0.677781 + 0.391317i
\(721\) 31.0520i 1.15644i
\(722\) 4.08720 + 2.35975i 0.152110 + 0.0878207i
\(723\) −1.45788 0.841705i −0.0542190 0.0313034i
\(724\) 20.5886 35.6605i 0.765170 1.32531i
\(725\) 0.176638 + 0.305947i 0.00656019 + 0.0113626i
\(726\) −0.828076 0.478090i −0.0307328 0.0177436i
\(727\) 2.10380 + 3.64389i 0.0780256 + 0.135144i 0.902398 0.430904i \(-0.141805\pi\)
−0.824372 + 0.566048i \(0.808472\pi\)
\(728\) −1.38669 5.68868i −0.0513941 0.210837i
\(729\) −8.27511 −0.306485
\(730\) −0.512230 + 0.295736i −0.0189585 + 0.0109457i
\(731\) 12.1044 20.9654i 0.447698 0.775435i
\(732\) 0.995369 + 1.72403i 0.0367899 + 0.0637220i
\(733\) −22.8876 13.2141i −0.845371 0.488075i 0.0137152 0.999906i \(-0.495634\pi\)
−0.859086 + 0.511831i \(0.828968\pi\)
\(734\) −4.15488 2.39882i −0.153360 0.0885422i
\(735\) 1.91571 + 1.10604i 0.0706620 + 0.0407967i
\(736\) 19.0600i 0.702560i
\(737\) 3.83105 + 6.63557i 0.141119 + 0.244425i
\(738\) −0.399728 0.692350i −0.0147142 0.0254857i
\(739\) −40.5324 23.4014i −1.49101 0.860834i −0.491061 0.871125i \(-0.663391\pi\)
−0.999947 + 0.0102910i \(0.996724\pi\)
\(740\) 14.0990 0.518289
\(741\) 10.4677 + 10.9541i 0.384541 + 0.402407i
\(742\) 4.43534 0.162826
\(743\) 5.29404i 0.194220i 0.995274 + 0.0971098i \(0.0309598\pi\)
−0.995274 + 0.0971098i \(0.969040\pi\)
\(744\) 2.38877 + 0.502691i 0.0875765 + 0.0184296i
\(745\) 11.0015 0.403062
\(746\) 4.28658i 0.156943i
\(747\) −5.59718 + 3.23153i −0.204790 + 0.118236i
\(748\) 63.4695i 2.32068i
\(749\) −1.30327 0.752441i −0.0476203 0.0274936i
\(750\) −0.646888 1.12044i −0.0236210 0.0409128i
\(751\) −8.85694 15.3407i −0.323194 0.559789i 0.657951 0.753061i \(-0.271423\pi\)
−0.981145 + 0.193272i \(0.938090\pi\)
\(752\) 37.8987i 1.38202i
\(753\) 3.46190 5.99619i 0.126159 0.218513i
\(754\) 0.114617 0.391944i 0.00417410 0.0142738i
\(755\) 16.7338 28.9838i 0.609006 1.05483i
\(756\) −13.7284 + 7.92607i −0.499295 + 0.288268i
\(757\) −24.8102 + 42.9725i −0.901740 + 1.56186i −0.0765066 + 0.997069i \(0.524377\pi\)
−0.825234 + 0.564791i \(0.808957\pi\)
\(758\) −1.88961 3.27290i −0.0686337 0.118877i
\(759\) 25.2173i 0.915329i
\(760\) 10.0292i 0.363798i
\(761\) −0.0239750 + 0.0138420i −0.000869093 + 0.000501771i −0.500434 0.865774i \(-0.666826\pi\)
0.499565 + 0.866276i \(0.333493\pi\)
\(762\) −0.597160 0.344770i −0.0216328 0.0124897i
\(763\) −13.4151 23.2357i −0.485661 0.841189i
\(764\) −7.61041 + 13.1816i −0.275335 + 0.476894i