Properties

Label 441.2.w.a.251.2
Level $441$
Weight $2$
Character 441.251
Analytic conductor $3.521$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.w (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(20\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 251.2
Character \(\chi\) \(=\) 441.251
Dual form 441.2.w.a.188.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.12540 - 1.69495i) q^{2} +(1.19944 + 5.25507i) q^{4} +(2.70367 + 1.30202i) q^{5} +(-0.967619 + 2.46246i) q^{7} +(3.99879 - 8.30358i) q^{8} +O(q^{10})\) \(q+(-2.12540 - 1.69495i) q^{2} +(1.19944 + 5.25507i) q^{4} +(2.70367 + 1.30202i) q^{5} +(-0.967619 + 2.46246i) q^{7} +(3.99879 - 8.30358i) q^{8} +(-3.53953 - 7.34991i) q^{10} +(-1.87132 - 1.49233i) q^{11} +(1.93441 + 1.54264i) q^{13} +(6.23034 - 3.59366i) q^{14} +(-12.8604 + 6.19325i) q^{16} +(-1.15098 + 5.04278i) q^{17} +0.270871i q^{19} +(-3.59932 + 15.7697i) q^{20} +(1.44789 + 6.34361i) q^{22} +(-8.11148 + 1.85139i) q^{23} +(2.49713 + 3.13130i) q^{25} +(-1.49670 - 6.55747i) q^{26} +(-14.1010 - 2.13134i) q^{28} +(2.64195 + 0.603008i) q^{29} +8.55709i q^{31} +(19.8604 + 4.53301i) q^{32} +(10.9936 - 8.76709i) q^{34} +(-5.82229 + 5.39782i) q^{35} +(1.31758 - 5.77270i) q^{37} +(0.459113 - 0.575710i) q^{38} +(21.6228 - 17.2436i) q^{40} +(-0.862545 - 0.415380i) q^{41} +(5.37639 - 2.58913i) q^{43} +(5.59777 - 11.6239i) q^{44} +(20.3782 + 9.81363i) q^{46} +(-5.40670 + 6.77979i) q^{47} +(-5.12743 - 4.76545i) q^{49} -10.8878i q^{50} +(-5.78648 + 12.0158i) q^{52} +(1.39025 - 0.317315i) q^{53} +(-3.11640 - 6.47127i) q^{55} +(16.5779 + 17.8816i) q^{56} +(-4.59314 - 5.75962i) q^{58} +(5.63248 - 2.71246i) q^{59} +(12.1109 + 2.76423i) q^{61} +(14.5039 - 18.1873i) q^{62} +(-16.7288 - 20.9773i) q^{64} +(3.22146 + 6.68943i) q^{65} -9.18698 q^{67} -27.8807 q^{68} +(21.5238 - 1.60405i) q^{70} +(3.43876 - 0.784875i) q^{71} +(-6.58618 + 5.25231i) q^{73} +(-12.5848 + 10.0361i) q^{74} +(-1.42344 + 0.324892i) q^{76} +(5.48553 - 3.16405i) q^{77} +8.56875 q^{79} -42.8340 q^{80} +(1.12921 + 2.34483i) q^{82} +(0.701261 + 0.879353i) q^{83} +(-9.67767 + 12.1354i) q^{85} +(-15.8155 - 3.60978i) q^{86} +(-19.8747 + 9.57116i) q^{88} +(10.3983 + 13.0391i) q^{89} +(-5.67046 + 3.27072i) q^{91} +(-19.4584 - 40.4058i) q^{92} +(22.9829 - 5.24569i) q^{94} +(-0.352678 + 0.732344i) q^{95} +1.73671i q^{97} +(2.82065 + 18.8193i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q + 24q^{4} + O(q^{10}) \) \( 120q + 24q^{4} - 32q^{16} - 44q^{22} - 4q^{25} - 56q^{28} + 112q^{34} - 76q^{37} + 28q^{40} + 8q^{43} - 40q^{46} - 84q^{49} - 140q^{52} + 12q^{58} - 84q^{61} + 24q^{64} + 16q^{67} + 112q^{70} - 84q^{76} - 24q^{79} + 140q^{82} - 96q^{85} - 24q^{88} - 112q^{91} - 112q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{9}{14}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.12540 1.69495i −1.50289 1.19851i −0.923581 0.383404i \(-0.874752\pi\)
−0.579307 0.815109i \(-0.696677\pi\)
\(3\) 0 0
\(4\) 1.19944 + 5.25507i 0.599718 + 2.62753i
\(5\) 2.70367 + 1.30202i 1.20912 + 0.582280i 0.926261 0.376882i \(-0.123004\pi\)
0.282856 + 0.959162i \(0.408718\pi\)
\(6\) 0 0
\(7\) −0.967619 + 2.46246i −0.365725 + 0.930723i
\(8\) 3.99879 8.30358i 1.41379 2.93576i
\(9\) 0 0
\(10\) −3.53953 7.34991i −1.11930 2.32425i
\(11\) −1.87132 1.49233i −0.564225 0.449955i 0.299372 0.954136i \(-0.403223\pi\)
−0.863598 + 0.504182i \(0.831794\pi\)
\(12\) 0 0
\(13\) 1.93441 + 1.54264i 0.536509 + 0.427851i 0.853895 0.520445i \(-0.174234\pi\)
−0.317387 + 0.948296i \(0.602805\pi\)
\(14\) 6.23034 3.59366i 1.66513 0.960445i
\(15\) 0 0
\(16\) −12.8604 + 6.19325i −3.21510 + 1.54831i
\(17\) −1.15098 + 5.04278i −0.279154 + 1.22305i 0.619711 + 0.784830i \(0.287250\pi\)
−0.898866 + 0.438225i \(0.855607\pi\)
\(18\) 0 0
\(19\) 0.270871i 0.0621420i 0.999517 + 0.0310710i \(0.00989179\pi\)
−0.999517 + 0.0310710i \(0.990108\pi\)
\(20\) −3.59932 + 15.7697i −0.804833 + 3.52620i
\(21\) 0 0
\(22\) 1.44789 + 6.34361i 0.308691 + 1.35246i
\(23\) −8.11148 + 1.85139i −1.69136 + 0.386042i −0.956398 0.292066i \(-0.905657\pi\)
−0.734963 + 0.678108i \(0.762800\pi\)
\(24\) 0 0
\(25\) 2.49713 + 3.13130i 0.499425 + 0.626260i
\(26\) −1.49670 6.55747i −0.293527 1.28603i
\(27\) 0 0
\(28\) −14.1010 2.13134i −2.66484 0.402785i
\(29\) 2.64195 + 0.603008i 0.490598 + 0.111976i 0.460661 0.887576i \(-0.347612\pi\)
0.0299365 + 0.999552i \(0.490469\pi\)
\(30\) 0 0
\(31\) 8.55709i 1.53690i 0.639911 + 0.768449i \(0.278971\pi\)
−0.639911 + 0.768449i \(0.721029\pi\)
\(32\) 19.8604 + 4.53301i 3.51086 + 0.801331i
\(33\) 0 0
\(34\) 10.9936 8.76709i 1.88538 1.50354i
\(35\) −5.82229 + 5.39782i −0.984147 + 0.912399i
\(36\) 0 0
\(37\) 1.31758 5.77270i 0.216609 0.949026i −0.743354 0.668898i \(-0.766766\pi\)
0.959963 0.280127i \(-0.0903767\pi\)
\(38\) 0.459113 0.575710i 0.0744780 0.0933924i
\(39\) 0 0
\(40\) 21.6228 17.2436i 3.41887 2.72646i
\(41\) −0.862545 0.415380i −0.134707 0.0648715i 0.365316 0.930884i \(-0.380961\pi\)
−0.500023 + 0.866012i \(0.666675\pi\)
\(42\) 0 0
\(43\) 5.37639 2.58913i 0.819892 0.394839i 0.0235776 0.999722i \(-0.492494\pi\)
0.796315 + 0.604883i \(0.206780\pi\)
\(44\) 5.59777 11.6239i 0.843895 1.75237i
\(45\) 0 0
\(46\) 20.3782 + 9.81363i 3.00460 + 1.44694i
\(47\) −5.40670 + 6.77979i −0.788648 + 0.988934i 0.211285 + 0.977424i \(0.432235\pi\)
−0.999934 + 0.0115095i \(0.996336\pi\)
\(48\) 0 0
\(49\) −5.12743 4.76545i −0.732490 0.680778i
\(50\) 10.8878i 1.53977i
\(51\) 0 0
\(52\) −5.78648 + 12.0158i −0.802441 + 1.66629i
\(53\) 1.39025 0.317315i 0.190965 0.0435866i −0.125968 0.992034i \(-0.540204\pi\)
0.316934 + 0.948448i \(0.397347\pi\)
\(54\) 0 0
\(55\) −3.11640 6.47127i −0.420215 0.872585i
\(56\) 16.5779 + 17.8816i 2.21532 + 2.38953i
\(57\) 0 0
\(58\) −4.59314 5.75962i −0.603109 0.756275i
\(59\) 5.63248 2.71246i 0.733286 0.353132i −0.0296897 0.999559i \(-0.509452\pi\)
0.762976 + 0.646427i \(0.223738\pi\)
\(60\) 0 0
\(61\) 12.1109 + 2.76423i 1.55064 + 0.353923i 0.910227 0.414109i \(-0.135907\pi\)
0.640411 + 0.768032i \(0.278764\pi\)
\(62\) 14.5039 18.1873i 1.84199 2.30979i
\(63\) 0 0
\(64\) −16.7288 20.9773i −2.09110 2.62216i
\(65\) 3.22146 + 6.68943i 0.399573 + 0.829721i
\(66\) 0 0
\(67\) −9.18698 −1.12237 −0.561184 0.827691i \(-0.689654\pi\)
−0.561184 + 0.827691i \(0.689654\pi\)
\(68\) −27.8807 −3.38103
\(69\) 0 0
\(70\) 21.5238 1.60405i 2.57258 0.191720i
\(71\) 3.43876 0.784875i 0.408106 0.0931475i −0.0135394 0.999908i \(-0.504310\pi\)
0.421645 + 0.906761i \(0.361453\pi\)
\(72\) 0 0
\(73\) −6.58618 + 5.25231i −0.770854 + 0.614736i −0.927889 0.372857i \(-0.878378\pi\)
0.157034 + 0.987593i \(0.449807\pi\)
\(74\) −12.5848 + 10.0361i −1.46296 + 1.16667i
\(75\) 0 0
\(76\) −1.42344 + 0.324892i −0.163280 + 0.0372676i
\(77\) 5.48553 3.16405i 0.625134 0.360577i
\(78\) 0 0
\(79\) 8.56875 0.964059 0.482030 0.876155i \(-0.339900\pi\)
0.482030 + 0.876155i \(0.339900\pi\)
\(80\) −42.8340 −4.78899
\(81\) 0 0
\(82\) 1.12921 + 2.34483i 0.124700 + 0.258943i
\(83\) 0.701261 + 0.879353i 0.0769734 + 0.0965216i 0.818827 0.574040i \(-0.194625\pi\)
−0.741854 + 0.670562i \(0.766053\pi\)
\(84\) 0 0
\(85\) −9.67767 + 12.1354i −1.04969 + 1.31627i
\(86\) −15.8155 3.60978i −1.70543 0.389252i
\(87\) 0 0
\(88\) −19.8747 + 9.57116i −2.11865 + 1.02029i
\(89\) 10.3983 + 13.0391i 1.10222 + 1.38214i 0.916736 + 0.399494i \(0.130814\pi\)
0.185485 + 0.982647i \(0.440615\pi\)
\(90\) 0 0
\(91\) −5.67046 + 3.27072i −0.594426 + 0.342865i
\(92\) −19.4584 40.4058i −2.02868 4.21259i
\(93\) 0 0
\(94\) 22.9829 5.24569i 2.37050 0.541051i
\(95\) −0.352678 + 0.732344i −0.0361840 + 0.0751369i
\(96\) 0 0
\(97\) 1.73671i 0.176336i 0.996106 + 0.0881680i \(0.0281012\pi\)
−0.996106 + 0.0881680i \(0.971899\pi\)
\(98\) 2.82065 + 18.8193i 0.284929 + 1.90103i
\(99\) 0 0
\(100\) −13.4600 + 16.8784i −1.34600 + 1.68784i
\(101\) 6.02148 + 2.89979i 0.599160 + 0.288540i 0.708776 0.705434i \(-0.249248\pi\)
−0.109616 + 0.993974i \(0.534962\pi\)
\(102\) 0 0
\(103\) 0.102115 0.212045i 0.0100617 0.0208934i −0.895877 0.444301i \(-0.853452\pi\)
0.905939 + 0.423408i \(0.139166\pi\)
\(104\) 20.5447 9.89382i 2.01458 0.970169i
\(105\) 0 0
\(106\) −3.49268 1.68199i −0.339239 0.163369i
\(107\) 7.97075 6.35646i 0.770562 0.614502i −0.157247 0.987559i \(-0.550262\pi\)
0.927808 + 0.373057i \(0.121690\pi\)
\(108\) 0 0
\(109\) 1.90055 2.38321i 0.182039 0.228270i −0.682436 0.730945i \(-0.739079\pi\)
0.864475 + 0.502675i \(0.167651\pi\)
\(110\) −4.34489 + 19.0362i −0.414269 + 1.81503i
\(111\) 0 0
\(112\) −2.80666 37.6609i −0.265204 3.55863i
\(113\) −7.60077 + 6.06141i −0.715020 + 0.570210i −0.911996 0.410199i \(-0.865459\pi\)
0.196976 + 0.980408i \(0.436888\pi\)
\(114\) 0 0
\(115\) −24.3413 5.55575i −2.26984 0.518076i
\(116\) 14.6069i 1.35622i
\(117\) 0 0
\(118\) −16.5688 3.78172i −1.52528 0.348135i
\(119\) −11.3039 7.71374i −1.03623 0.707117i
\(120\) 0 0
\(121\) −1.17293 5.13894i −0.106630 0.467177i
\(122\) −21.0553 26.4025i −1.90625 2.39037i
\(123\) 0 0
\(124\) −44.9681 + 10.2637i −4.03825 + 0.921705i
\(125\) −0.664359 2.91075i −0.0594221 0.260345i
\(126\) 0 0
\(127\) −0.361736 + 1.58487i −0.0320989 + 0.140634i −0.988438 0.151624i \(-0.951550\pi\)
0.956339 + 0.292259i \(0.0944068\pi\)
\(128\) 32.1975i 2.84588i
\(129\) 0 0
\(130\) 4.49137 19.6780i 0.393919 1.72587i
\(131\) 5.01771 2.41640i 0.438399 0.211122i −0.201647 0.979458i \(-0.564629\pi\)
0.640046 + 0.768336i \(0.278915\pi\)
\(132\) 0 0
\(133\) −0.667008 0.262099i −0.0578369 0.0227269i
\(134\) 19.5261 + 15.5715i 1.68679 + 1.34517i
\(135\) 0 0
\(136\) 37.2706 + 29.7223i 3.19593 + 2.54867i
\(137\) −5.88936 12.2294i −0.503162 1.04483i −0.985631 0.168913i \(-0.945974\pi\)
0.482469 0.875913i \(-0.339740\pi\)
\(138\) 0 0
\(139\) 5.46003 11.3379i 0.463114 0.961666i −0.530378 0.847761i \(-0.677950\pi\)
0.993492 0.113905i \(-0.0363358\pi\)
\(140\) −35.3494 24.1222i −2.98757 2.03870i
\(141\) 0 0
\(142\) −8.63909 4.16037i −0.724976 0.349130i
\(143\) −1.31778 5.77356i −0.110198 0.482809i
\(144\) 0 0
\(145\) 6.35783 + 5.07020i 0.527989 + 0.421057i
\(146\) 22.9007 1.89528
\(147\) 0 0
\(148\) 31.9163 2.62350
\(149\) 13.7999 + 11.0051i 1.13053 + 0.901569i 0.996001 0.0893399i \(-0.0284757\pi\)
0.134531 + 0.990909i \(0.457047\pi\)
\(150\) 0 0
\(151\) 1.46652 + 6.42522i 0.119343 + 0.522877i 0.998892 + 0.0470678i \(0.0149877\pi\)
−0.879548 + 0.475809i \(0.842155\pi\)
\(152\) 2.24919 + 1.08316i 0.182434 + 0.0878555i
\(153\) 0 0
\(154\) −17.0219 2.57283i −1.37166 0.207324i
\(155\) −11.1415 + 23.1355i −0.894906 + 1.85829i
\(156\) 0 0
\(157\) 3.49186 + 7.25092i 0.278681 + 0.578686i 0.992584 0.121558i \(-0.0387889\pi\)
−0.713904 + 0.700244i \(0.753075\pi\)
\(158\) −18.2121 14.5236i −1.44887 1.15544i
\(159\) 0 0
\(160\) 47.7939 + 38.1144i 3.77844 + 3.01321i
\(161\) 3.28984 21.7656i 0.259275 1.71537i
\(162\) 0 0
\(163\) 1.76194 0.848503i 0.138005 0.0664599i −0.363607 0.931553i \(-0.618455\pi\)
0.501612 + 0.865093i \(0.332740\pi\)
\(164\) 1.14828 5.03096i 0.0896659 0.392852i
\(165\) 0 0
\(166\) 3.05759i 0.237315i
\(167\) 0.178441 0.781800i 0.0138082 0.0604975i −0.967554 0.252663i \(-0.918694\pi\)
0.981363 + 0.192165i \(0.0615509\pi\)
\(168\) 0 0
\(169\) −1.53057 6.70587i −0.117736 0.515836i
\(170\) 41.1379 9.38947i 3.15514 0.720139i
\(171\) 0 0
\(172\) 20.0547 + 25.1478i 1.52916 + 1.91750i
\(173\) −3.18902 13.9720i −0.242457 1.06227i −0.938773 0.344537i \(-0.888036\pi\)
0.696316 0.717736i \(-0.254821\pi\)
\(174\) 0 0
\(175\) −10.1270 + 3.11918i −0.765527 + 0.235788i
\(176\) 33.3083 + 7.60241i 2.51071 + 0.573053i
\(177\) 0 0
\(178\) 45.3380i 3.39823i
\(179\) −4.91685 1.12224i −0.367502 0.0838800i 0.0347817 0.999395i \(-0.488926\pi\)
−0.402284 + 0.915515i \(0.631784\pi\)
\(180\) 0 0
\(181\) 4.24460 3.38496i 0.315499 0.251602i −0.452917 0.891553i \(-0.649617\pi\)
0.768416 + 0.639951i \(0.221045\pi\)
\(182\) 17.5957 + 2.65956i 1.30428 + 0.197140i
\(183\) 0 0
\(184\) −17.0629 + 74.7577i −1.25790 + 5.51121i
\(185\) 11.0785 13.8920i 0.814505 1.02136i
\(186\) 0 0
\(187\) 9.67936 7.71903i 0.707825 0.564471i
\(188\) −42.1133 20.2807i −3.07142 1.47912i
\(189\) 0 0
\(190\) 1.99087 0.958755i 0.144433 0.0695554i
\(191\) −9.56076 + 19.8531i −0.691793 + 1.43652i 0.198021 + 0.980198i \(0.436549\pi\)
−0.889814 + 0.456324i \(0.849166\pi\)
\(192\) 0 0
\(193\) 9.46536 + 4.55828i 0.681331 + 0.328112i 0.742338 0.670025i \(-0.233717\pi\)
−0.0610068 + 0.998137i \(0.519431\pi\)
\(194\) 2.94364 3.69121i 0.211341 0.265013i
\(195\) 0 0
\(196\) 18.8927 32.6608i 1.34948 2.33292i
\(197\) 2.45389i 0.174833i 0.996172 + 0.0874164i \(0.0278611\pi\)
−0.996172 + 0.0874164i \(0.972139\pi\)
\(198\) 0 0
\(199\) 9.14326 18.9862i 0.648149 1.34589i −0.274997 0.961445i \(-0.588677\pi\)
0.923146 0.384450i \(-0.125609\pi\)
\(200\) 35.9865 8.21368i 2.54463 0.580795i
\(201\) 0 0
\(202\) −7.88307 16.3694i −0.554651 1.15175i
\(203\) −4.04128 + 5.92222i −0.283642 + 0.415658i
\(204\) 0 0
\(205\) −1.79121 2.24610i −0.125103 0.156874i
\(206\) −0.576442 + 0.277600i −0.0401626 + 0.0193413i
\(207\) 0 0
\(208\) −34.4312 7.85871i −2.38738 0.544903i
\(209\) 0.404228 0.506886i 0.0279611 0.0350621i
\(210\) 0 0
\(211\) −13.2934 16.6694i −0.915154 1.14757i −0.988645 0.150271i \(-0.951985\pi\)
0.0734905 0.997296i \(-0.476586\pi\)
\(212\) 3.33503 + 6.92526i 0.229051 + 0.475629i
\(213\) 0 0
\(214\) −27.7150 −1.89456
\(215\) 17.9071 1.22125
\(216\) 0 0
\(217\) −21.0715 8.28000i −1.43043 0.562083i
\(218\) −8.07886 + 1.84395i −0.547169 + 0.124888i
\(219\) 0 0
\(220\) 30.2690 24.1387i 2.04074 1.62743i
\(221\) −10.0057 + 7.97925i −0.673054 + 0.536743i
\(222\) 0 0
\(223\) −5.73095 + 1.30805i −0.383773 + 0.0875937i −0.410055 0.912061i \(-0.634490\pi\)
0.0262818 + 0.999655i \(0.491633\pi\)
\(224\) −30.3797 + 44.5193i −2.02983 + 2.97457i
\(225\) 0 0
\(226\) 26.4285 1.75800
\(227\) 1.71036 0.113520 0.0567602 0.998388i \(-0.481923\pi\)
0.0567602 + 0.998388i \(0.481923\pi\)
\(228\) 0 0
\(229\) −8.18552 16.9974i −0.540915 1.12322i −0.974970 0.222335i \(-0.928632\pi\)
0.434056 0.900886i \(-0.357082\pi\)
\(230\) 42.3184 + 53.0656i 2.79039 + 3.49904i
\(231\) 0 0
\(232\) 15.5717 19.5263i 1.02233 1.28197i
\(233\) 6.22666 + 1.42120i 0.407922 + 0.0931056i 0.421558 0.906801i \(-0.361483\pi\)
−0.0136357 + 0.999907i \(0.504341\pi\)
\(234\) 0 0
\(235\) −23.4453 + 11.2907i −1.52941 + 0.736523i
\(236\) 21.0099 + 26.3456i 1.36763 + 1.71495i
\(237\) 0 0
\(238\) 10.9510 + 35.5545i 0.709850 + 2.30465i
\(239\) 2.07872 + 4.31651i 0.134461 + 0.279212i 0.957318 0.289037i \(-0.0933352\pi\)
−0.822856 + 0.568249i \(0.807621\pi\)
\(240\) 0 0
\(241\) −14.6103 + 3.33471i −0.941134 + 0.214808i −0.665452 0.746441i \(-0.731761\pi\)
−0.275683 + 0.961249i \(0.588904\pi\)
\(242\) −6.21732 + 12.9104i −0.399664 + 0.829912i
\(243\) 0 0
\(244\) 66.9590i 4.28661i
\(245\) −7.65817 19.5602i −0.489263 1.24966i
\(246\) 0 0
\(247\) −0.417856 + 0.523975i −0.0265875 + 0.0333397i
\(248\) 71.0544 + 34.2180i 4.51196 + 2.17285i
\(249\) 0 0
\(250\) −3.52155 + 7.31257i −0.222722 + 0.462488i
\(251\) 6.93459 3.33952i 0.437707 0.210789i −0.202035 0.979378i \(-0.564755\pi\)
0.639742 + 0.768590i \(0.279041\pi\)
\(252\) 0 0
\(253\) 17.9421 + 8.64046i 1.12801 + 0.543221i
\(254\) 3.45511 2.75536i 0.216793 0.172887i
\(255\) 0 0
\(256\) 21.1156 26.4781i 1.31973 1.65488i
\(257\) 0.244069 1.06934i 0.0152246 0.0667033i −0.966745 0.255742i \(-0.917680\pi\)
0.981970 + 0.189039i \(0.0605373\pi\)
\(258\) 0 0
\(259\) 12.9401 + 8.83026i 0.804060 + 0.548686i
\(260\) −31.2895 + 24.9525i −1.94049 + 1.54749i
\(261\) 0 0
\(262\) −14.7604 3.36895i −0.911898 0.208135i
\(263\) 2.81416i 0.173529i −0.996229 0.0867643i \(-0.972347\pi\)
0.996229 0.0867643i \(-0.0276527\pi\)
\(264\) 0 0
\(265\) 4.17193 + 0.952215i 0.256279 + 0.0584941i
\(266\) 0.973416 + 1.68762i 0.0596840 + 0.103474i
\(267\) 0 0
\(268\) −11.0192 48.2782i −0.673104 2.94906i
\(269\) −17.7274 22.2294i −1.08086 1.35535i −0.930320 0.366749i \(-0.880471\pi\)
−0.150538 0.988604i \(-0.548101\pi\)
\(270\) 0 0
\(271\) 28.4023 6.48263i 1.72531 0.393792i 0.758987 0.651106i \(-0.225695\pi\)
0.966328 + 0.257314i \(0.0828374\pi\)
\(272\) −16.4291 71.9805i −0.996160 4.36446i
\(273\) 0 0
\(274\) −8.21096 + 35.9746i −0.496042 + 2.17330i
\(275\) 9.58621i 0.578070i
\(276\) 0 0
\(277\) −4.11057 + 18.0096i −0.246980 + 1.08209i 0.687531 + 0.726155i \(0.258695\pi\)
−0.934511 + 0.355935i \(0.884163\pi\)
\(278\) −30.8220 + 14.8431i −1.84858 + 0.890228i
\(279\) 0 0
\(280\) 21.5391 + 69.9306i 1.28721 + 4.17915i
\(281\) −12.2493 9.76846i −0.730729 0.582737i 0.185856 0.982577i \(-0.440494\pi\)
−0.916585 + 0.399840i \(0.869066\pi\)
\(282\) 0 0
\(283\) −15.4090 12.2882i −0.915968 0.730460i 0.0473341 0.998879i \(-0.484927\pi\)
−0.963302 + 0.268419i \(0.913499\pi\)
\(284\) 8.24915 + 17.1295i 0.489497 + 1.01645i
\(285\) 0 0
\(286\) −6.98510 + 14.5047i −0.413038 + 0.857682i
\(287\) 1.85747 1.72206i 0.109643 0.101650i
\(288\) 0 0
\(289\) −8.78842 4.23228i −0.516966 0.248958i
\(290\) −4.91921 21.5525i −0.288866 1.26560i
\(291\) 0 0
\(292\) −35.5009 28.3111i −2.07754 1.65678i
\(293\) 19.1934 1.12129 0.560645 0.828056i \(-0.310553\pi\)
0.560645 + 0.828056i \(0.310553\pi\)
\(294\) 0 0
\(295\) 18.7600 1.09225
\(296\) −42.6653 34.0245i −2.47987 1.97763i
\(297\) 0 0
\(298\) −10.6773 46.7804i −0.618521 2.70992i
\(299\) −18.5470 8.93175i −1.07260 0.516536i
\(300\) 0 0
\(301\) 1.17335 + 15.7444i 0.0676305 + 0.907495i
\(302\) 7.77352 16.1419i 0.447316 0.928861i
\(303\) 0 0
\(304\) −1.67757 3.48351i −0.0962151 0.199793i
\(305\) 29.1447 + 23.2421i 1.66882 + 1.33084i
\(306\) 0 0
\(307\) −12.3704 9.86507i −0.706016 0.563029i 0.203309 0.979115i \(-0.434830\pi\)
−0.909326 + 0.416085i \(0.863402\pi\)
\(308\) 23.2069 + 25.0318i 1.32233 + 1.42632i
\(309\) 0 0
\(310\) 62.8938 30.2881i 3.57213 1.72025i
\(311\) −7.30205 + 31.9924i −0.414061 + 1.81412i 0.150358 + 0.988632i \(0.451957\pi\)
−0.564419 + 0.825488i \(0.690900\pi\)
\(312\) 0 0
\(313\) 22.7644i 1.28672i 0.765564 + 0.643360i \(0.222460\pi\)
−0.765564 + 0.643360i \(0.777540\pi\)
\(314\) 4.86836 21.3297i 0.274737 1.20370i
\(315\) 0 0
\(316\) 10.2777 + 45.0294i 0.578163 + 2.53310i
\(317\) 22.8351 5.21197i 1.28255 0.292733i 0.473667 0.880704i \(-0.342930\pi\)
0.808882 + 0.587971i \(0.200073\pi\)
\(318\) 0 0
\(319\) −4.04405 5.07108i −0.226424 0.283926i
\(320\) −17.9164 78.4969i −1.00156 4.38811i
\(321\) 0 0
\(322\) −43.8840 + 40.6847i −2.44556 + 2.26727i
\(323\) −1.36594 0.311767i −0.0760030 0.0173472i
\(324\) 0 0
\(325\) 9.90938i 0.549674i
\(326\) −5.18300 1.18299i −0.287060 0.0655195i
\(327\) 0 0
\(328\) −6.89828 + 5.50120i −0.380894 + 0.303753i
\(329\) −11.4633 19.8740i −0.631995 1.09569i
\(330\) 0 0
\(331\) 2.82186 12.3634i 0.155103 0.679553i −0.836252 0.548346i \(-0.815258\pi\)
0.991355 0.131207i \(-0.0418852\pi\)
\(332\) −3.77995 + 4.73990i −0.207452 + 0.260136i
\(333\) 0 0
\(334\) −1.70437 + 1.35919i −0.0932592 + 0.0743717i
\(335\) −24.8386 11.9616i −1.35708 0.653533i
\(336\) 0 0
\(337\) 3.43373 1.65360i 0.187047 0.0900771i −0.338016 0.941140i \(-0.609756\pi\)
0.525063 + 0.851063i \(0.324042\pi\)
\(338\) −8.11305 + 16.8469i −0.441292 + 0.916352i
\(339\) 0 0
\(340\) −75.3802 36.3012i −4.08806 1.96871i
\(341\) 12.7700 16.0131i 0.691534 0.867157i
\(342\) 0 0
\(343\) 16.6961 8.01496i 0.901506 0.432767i
\(344\) 54.9967i 2.96522i
\(345\) 0 0
\(346\) −16.9040 + 35.1014i −0.908763 + 1.88707i
\(347\) 4.35892 0.994896i 0.233999 0.0534088i −0.103913 0.994586i \(-0.533136\pi\)
0.337912 + 0.941178i \(0.390279\pi\)
\(348\) 0 0
\(349\) −6.92086 14.3713i −0.370465 0.769278i 0.629505 0.776996i \(-0.283258\pi\)
−0.999970 + 0.00771786i \(0.997543\pi\)
\(350\) 26.8108 + 10.5352i 1.43310 + 0.563132i
\(351\) 0 0
\(352\) −30.4005 38.1210i −1.62035 2.03186i
\(353\) 13.1168 6.31673i 0.698138 0.336206i −0.0509266 0.998702i \(-0.516217\pi\)
0.749065 + 0.662497i \(0.230503\pi\)
\(354\) 0 0
\(355\) 10.3192 + 2.35529i 0.547686 + 0.125006i
\(356\) −56.0492 + 70.2835i −2.97060 + 3.72502i
\(357\) 0 0
\(358\) 8.54815 + 10.7190i 0.451784 + 0.566519i
\(359\) 1.62133 + 3.36672i 0.0855703 + 0.177688i 0.939363 0.342925i \(-0.111418\pi\)
−0.853793 + 0.520613i \(0.825703\pi\)
\(360\) 0 0
\(361\) 18.9266 0.996138
\(362\) −14.7589 −0.775708
\(363\) 0 0
\(364\) −23.9892 25.8757i −1.25738 1.35625i
\(365\) −24.6455 + 5.62517i −1.29000 + 0.294435i
\(366\) 0 0
\(367\) 8.56520 6.83052i 0.447100 0.356550i −0.373909 0.927465i \(-0.621983\pi\)
0.821009 + 0.570915i \(0.193411\pi\)
\(368\) 92.8508 74.0461i 4.84018 3.85992i
\(369\) 0 0
\(370\) −47.0924 + 10.7485i −2.44822 + 0.558790i
\(371\) −0.563854 + 3.73048i −0.0292739 + 0.193677i
\(372\) 0 0
\(373\) 32.1769 1.66605 0.833027 0.553232i \(-0.186606\pi\)
0.833027 + 0.553232i \(0.186606\pi\)
\(374\) −33.6559 −1.74031
\(375\) 0 0
\(376\) 34.6762 + 72.0059i 1.78829 + 3.71342i
\(377\) 4.18039 + 5.24204i 0.215301 + 0.269979i
\(378\) 0 0
\(379\) −2.16842 + 2.71912i −0.111384 + 0.139672i −0.834398 0.551162i \(-0.814185\pi\)
0.723014 + 0.690833i \(0.242756\pi\)
\(380\) −4.27154 0.974950i −0.219125 0.0500139i
\(381\) 0 0
\(382\) 53.9706 25.9909i 2.76138 1.32981i
\(383\) −15.1494 18.9968i −0.774100 0.970691i 0.225894 0.974152i \(-0.427470\pi\)
−0.999994 + 0.00346120i \(0.998898\pi\)
\(384\) 0 0
\(385\) 18.9507 1.41229i 0.965818 0.0719770i
\(386\) −12.3916 25.7315i −0.630718 1.30970i
\(387\) 0 0
\(388\) −9.12653 + 2.08307i −0.463329 + 0.105752i
\(389\) 11.1089 23.0679i 0.563245 1.16959i −0.403768 0.914861i \(-0.632300\pi\)
0.967013 0.254728i \(-0.0819861\pi\)
\(390\) 0 0
\(391\) 43.0354i 2.17639i
\(392\) −60.0738 + 23.5200i −3.03418 + 1.18794i
\(393\) 0 0
\(394\) 4.15924 5.21552i 0.209539 0.262754i
\(395\) 23.1671 + 11.1567i 1.16566 + 0.561353i
\(396\) 0 0
\(397\) −0.366625 + 0.761304i −0.0184004 + 0.0382088i −0.909966 0.414682i \(-0.863893\pi\)
0.891566 + 0.452891i \(0.149607\pi\)
\(398\) −51.6138 + 24.8559i −2.58717 + 1.24591i
\(399\) 0 0
\(400\) −51.5070 24.8044i −2.57535 1.24022i
\(401\) −7.59276 + 6.05502i −0.379164 + 0.302373i −0.794464 0.607311i \(-0.792248\pi\)
0.415300 + 0.909685i \(0.363677\pi\)
\(402\) 0 0
\(403\) −13.2005 + 16.5529i −0.657564 + 0.824559i
\(404\) −8.01624 + 35.1214i −0.398823 + 1.74736i
\(405\) 0 0
\(406\) 18.6272 5.73732i 0.924455 0.284738i
\(407\) −11.0804 + 8.83632i −0.549235 + 0.438000i
\(408\) 0 0
\(409\) −5.13723 1.17254i −0.254019 0.0579783i 0.0936148 0.995608i \(-0.470158\pi\)
−0.347634 + 0.937630i \(0.613015\pi\)
\(410\) 7.80988i 0.385703i
\(411\) 0 0
\(412\) 1.23679 + 0.282289i 0.0609323 + 0.0139074i
\(413\) 1.22923 + 16.4944i 0.0604866 + 0.811635i
\(414\) 0 0
\(415\) 0.751043 + 3.29054i 0.0368673 + 0.161526i
\(416\) 31.4254 + 39.4062i 1.54076 + 1.93205i
\(417\) 0 0
\(418\) −1.71830 + 0.392190i −0.0840447 + 0.0191827i
\(419\) −6.55607 28.7240i −0.320285 1.40326i −0.837047 0.547132i \(-0.815720\pi\)
0.516761 0.856129i \(-0.327137\pi\)
\(420\) 0 0
\(421\) −2.72489 + 11.9385i −0.132803 + 0.581849i 0.864108 + 0.503307i \(0.167884\pi\)
−0.996911 + 0.0785417i \(0.974974\pi\)
\(422\) 57.9608i 2.82149i
\(423\) 0 0
\(424\) 2.92447 12.8129i 0.142025 0.622251i
\(425\) −18.6646 + 8.98840i −0.905366 + 0.436001i
\(426\) 0 0
\(427\) −18.5255 + 27.1478i −0.896512 + 1.31378i
\(428\) 42.9640 + 34.2627i 2.07675 + 1.65615i
\(429\) 0 0
\(430\) −38.0598 30.3517i −1.83541 1.46369i
\(431\) −8.65432 17.9709i −0.416864 0.865626i −0.998633 0.0522725i \(-0.983354\pi\)
0.581769 0.813354i \(-0.302361\pi\)
\(432\) 0 0
\(433\) −5.39220 + 11.1970i −0.259133 + 0.538094i −0.989426 0.145039i \(-0.953669\pi\)
0.730293 + 0.683134i \(0.239383\pi\)
\(434\) 30.7512 + 53.3135i 1.47611 + 2.55913i
\(435\) 0 0
\(436\) 14.8035 + 7.12900i 0.708960 + 0.341417i
\(437\) −0.501488 2.19716i −0.0239894 0.105104i
\(438\) 0 0
\(439\) 21.4607 + 17.1144i 1.02426 + 0.816824i 0.983237 0.182334i \(-0.0583653\pi\)
0.0410281 + 0.999158i \(0.486937\pi\)
\(440\) −66.1965 −3.15579
\(441\) 0 0
\(442\) 34.7906 1.65482
\(443\) 17.9005 + 14.2752i 0.850480 + 0.678236i 0.948441 0.316955i \(-0.102660\pi\)
−0.0979602 + 0.995190i \(0.531232\pi\)
\(444\) 0 0
\(445\) 11.1365 + 48.7922i 0.527921 + 2.31297i
\(446\) 14.3977 + 6.93356i 0.681750 + 0.328314i
\(447\) 0 0
\(448\) 67.8429 20.8961i 3.20528 0.987247i
\(449\) −5.24856 + 10.8987i −0.247695 + 0.514344i −0.987333 0.158661i \(-0.949282\pi\)
0.739638 + 0.673005i \(0.234997\pi\)
\(450\) 0 0
\(451\) 0.994217 + 2.06451i 0.0468158 + 0.0972141i
\(452\) −40.9698 32.6723i −1.92706 1.53678i
\(453\) 0 0
\(454\) −3.63520 2.89898i −0.170609 0.136056i
\(455\) −19.5896 + 1.45990i −0.918374 + 0.0684413i
\(456\) 0 0
\(457\) −6.92848 + 3.33658i −0.324101 + 0.156079i −0.588858 0.808236i \(-0.700422\pi\)
0.264757 + 0.964315i \(0.414708\pi\)
\(458\) −11.4123 + 50.0005i −0.533261 + 2.33637i
\(459\) 0 0
\(460\) 134.579i 6.27478i
\(461\) −2.31255 + 10.1319i −0.107706 + 0.471891i 0.892093 + 0.451851i \(0.149236\pi\)
−0.999799 + 0.0200393i \(0.993621\pi\)
\(462\) 0 0
\(463\) 0.620618 + 2.71911i 0.0288426 + 0.126368i 0.987300 0.158869i \(-0.0507849\pi\)
−0.958457 + 0.285237i \(0.907928\pi\)
\(464\) −37.7111 + 8.60732i −1.75069 + 0.399585i
\(465\) 0 0
\(466\) −10.8253 13.5745i −0.501473 0.628828i
\(467\) 5.42836 + 23.7832i 0.251195 + 1.10056i 0.930382 + 0.366591i \(0.119475\pi\)
−0.679187 + 0.733965i \(0.737668\pi\)
\(468\) 0 0
\(469\) 8.88949 22.6226i 0.410479 1.04461i
\(470\) 68.9680 + 15.7415i 3.18126 + 0.726101i
\(471\) 0 0
\(472\) 57.6163i 2.65200i
\(473\) −13.9248 3.17825i −0.640263 0.146136i
\(474\) 0 0
\(475\) −0.848176 + 0.676398i −0.0389170 + 0.0310353i
\(476\) 26.9779 68.6551i 1.23653 3.14680i
\(477\) 0 0
\(478\) 2.89816 12.6977i 0.132559 0.580778i
\(479\) −0.244479 + 0.306568i −0.0111706 + 0.0140074i −0.787385 0.616461i \(-0.788566\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(480\) 0 0
\(481\) 11.4539 9.13421i 0.522255 0.416484i
\(482\) 36.7050 + 17.6762i 1.67187 + 0.805130i
\(483\) 0 0
\(484\) 25.5986 12.3277i 1.16357 0.560348i
\(485\) −2.26123 + 4.69549i −0.102677 + 0.213211i
\(486\) 0 0
\(487\) 15.9031 + 7.65855i 0.720640 + 0.347042i 0.757995 0.652260i \(-0.226179\pi\)
−0.0373551 + 0.999302i \(0.511893\pi\)
\(488\) 71.3818 89.5100i 3.23130 4.05193i
\(489\) 0 0
\(490\) −16.8769 + 54.5536i −0.762421 + 2.46448i
\(491\) 10.2550i 0.462802i 0.972859 + 0.231401i \(0.0743309\pi\)
−0.972859 + 0.231401i \(0.925669\pi\)
\(492\) 0 0
\(493\) −6.08167 + 12.6287i −0.273905 + 0.568769i
\(494\) 1.77623 0.405412i 0.0799162 0.0182403i
\(495\) 0 0
\(496\) −52.9961 110.048i −2.37960 4.94128i
\(497\) −1.39469 + 9.22728i −0.0625602 + 0.413900i
\(498\) 0 0
\(499\) −20.1202 25.2300i −0.900706 1.12945i −0.991044 0.133538i \(-0.957366\pi\)
0.0903377 0.995911i \(-0.471205\pi\)
\(500\) 14.4993 6.98250i 0.648429 0.312267i
\(501\) 0 0
\(502\) −20.3991 4.65597i −0.910458 0.207806i
\(503\) 10.4008 13.0422i 0.463749 0.581523i −0.493879 0.869531i \(-0.664421\pi\)
0.957628 + 0.288008i \(0.0929929\pi\)
\(504\) 0 0
\(505\) 12.5045 + 15.6802i 0.556444 + 0.697758i
\(506\) −23.4890 48.7755i −1.04422 2.16833i
\(507\) 0 0
\(508\) −8.76248 −0.388772
\(509\) 11.5471 0.511816 0.255908 0.966701i \(-0.417626\pi\)
0.255908 + 0.966701i \(0.417626\pi\)
\(510\) 0 0
\(511\) −6.56069 21.3004i −0.290228 0.942276i
\(512\) −26.9779 + 6.15754i −1.19227 + 0.272127i
\(513\) 0 0
\(514\) −2.33122 + 1.85909i −0.102826 + 0.0820007i
\(515\) 0.552172 0.440342i 0.0243316 0.0194038i
\(516\) 0 0
\(517\) 20.2354 4.61859i 0.889951 0.203125i
\(518\) −12.5361 40.7008i −0.550806 1.78829i
\(519\) 0 0
\(520\) 68.4281 3.00077
\(521\) 43.6211 1.91107 0.955537 0.294871i \(-0.0952767\pi\)
0.955537 + 0.294871i \(0.0952767\pi\)
\(522\) 0 0
\(523\) 18.3822 + 38.1710i 0.803797 + 1.66910i 0.741412 + 0.671051i \(0.234157\pi\)
0.0623858 + 0.998052i \(0.480129\pi\)
\(524\) 18.7168 + 23.4701i 0.817646 + 1.02530i
\(525\) 0 0
\(526\) −4.76987 + 5.98123i −0.207976 + 0.260794i
\(527\) −43.1515 9.84905i −1.87971 0.429031i
\(528\) 0 0
\(529\) 41.6462 20.0558i 1.81070 0.871989i
\(530\) −7.25307 9.09506i −0.315053 0.395064i
\(531\) 0 0
\(532\) 0.577317 3.81955i 0.0250299 0.165598i
\(533\) −1.02773 2.13411i −0.0445161 0.0924387i
\(534\) 0 0
\(535\) 29.8265 6.80771i 1.28951 0.294323i
\(536\) −36.7368 + 76.2848i −1.58679 + 3.29500i
\(537\) 0 0
\(538\) 77.2937i 3.33237i
\(539\) 2.48346 + 16.5695i 0.106970 + 0.713699i
\(540\) 0 0
\(541\) −21.0846 + 26.4392i −0.906496 + 1.13671i 0.0836249 + 0.996497i \(0.473350\pi\)
−0.990121 + 0.140213i \(0.955221\pi\)
\(542\) −71.3541 34.3623i −3.06492 1.47599i
\(543\) 0 0
\(544\) −45.7180 + 94.9344i −1.96014 + 4.07028i
\(545\) 8.24143 3.96886i 0.353024 0.170007i
\(546\) 0 0
\(547\) 32.6267 + 15.7122i 1.39502 + 0.671805i 0.972144 0.234384i \(-0.0753073\pi\)
0.422873 + 0.906189i \(0.361022\pi\)
\(548\) 57.2023 45.6173i 2.44356 1.94868i
\(549\) 0 0
\(550\) −16.2482 + 20.3746i −0.692825 + 0.868775i
\(551\) −0.163337 + 0.715626i −0.00695839 + 0.0304867i
\(552\) 0 0
\(553\) −8.29128 + 21.1002i −0.352581 + 0.897272i
\(554\) 39.2620 31.3104i 1.66808 1.33025i
\(555\) 0 0
\(556\) 66.1303 + 15.0938i 2.80455 + 0.640120i
\(557\) 2.84407i 0.120507i −0.998183 0.0602535i \(-0.980809\pi\)
0.998183 0.0602535i \(-0.0191909\pi\)
\(558\) 0 0
\(559\) 14.3942 + 3.28539i 0.608812 + 0.138957i
\(560\) 41.4470 105.477i 1.75145 4.45722i
\(561\) 0 0
\(562\) 9.47755 + 41.5238i 0.399786 + 1.75158i
\(563\) −5.45793 6.84403i −0.230024 0.288441i 0.653402 0.757011i \(-0.273341\pi\)
−0.883427 + 0.468569i \(0.844770\pi\)
\(564\) 0 0
\(565\) −28.4420 + 6.49171i −1.19657 + 0.273108i
\(566\) 11.9223 + 52.2350i 0.501131 + 2.19560i
\(567\) 0 0
\(568\) 7.23363 31.6926i 0.303516 1.32979i
\(569\) 12.6997i 0.532400i 0.963918 + 0.266200i \(0.0857681\pi\)
−0.963918 + 0.266200i \(0.914232\pi\)
\(570\) 0 0
\(571\) −3.77390 + 16.5345i −0.157933 + 0.691949i 0.832508 + 0.554013i \(0.186904\pi\)
−0.990441 + 0.137936i \(0.955953\pi\)
\(572\) 28.7599 13.8500i 1.20251 0.579098i
\(573\) 0 0
\(574\) −6.86668 + 0.511735i −0.286610 + 0.0213594i
\(575\) −26.0527 20.7763i −1.08647 0.866432i
\(576\) 0 0
\(577\) −22.3053 17.7879i −0.928582 0.740520i 0.0373534 0.999302i \(-0.488107\pi\)
−0.965936 + 0.258782i \(0.916679\pi\)
\(578\) 11.5054 + 23.8913i 0.478563 + 0.993746i
\(579\) 0 0
\(580\) −19.0185 + 39.4922i −0.789698 + 1.63983i
\(581\) −2.84393 + 0.875949i −0.117986 + 0.0363405i
\(582\) 0 0
\(583\) −3.07515 1.48091i −0.127360 0.0613331i
\(584\) 17.2762 + 75.6918i 0.714892 + 3.13215i
\(585\) 0 0
\(586\) −40.7938 32.5319i −1.68517 1.34388i
\(587\) 1.15074 0.0474962 0.0237481 0.999718i \(-0.492440\pi\)
0.0237481 + 0.999718i \(0.492440\pi\)
\(588\) 0 0
\(589\) −2.31786 −0.0955059
\(590\) −39.8726 31.7974i −1.64153 1.30908i
\(591\) 0 0
\(592\) 18.8071 + 82.3993i 0.772968 + 3.38659i
\(593\) 1.55219 + 0.747496i 0.0637408 + 0.0306960i 0.465483 0.885057i \(-0.345881\pi\)
−0.401742 + 0.915753i \(0.631595\pi\)
\(594\) 0 0
\(595\) −20.5187 35.5733i −0.841184 1.45836i
\(596\) −41.2803 + 85.7193i −1.69090 + 3.51120i
\(597\) 0 0
\(598\) 24.2809 + 50.4198i 0.992920 + 2.06182i
\(599\) 17.9381 + 14.3051i 0.732929 + 0.584491i 0.917220 0.398380i \(-0.130428\pi\)
−0.184291 + 0.982872i \(0.558999\pi\)
\(600\) 0 0
\(601\) 32.9543 + 26.2802i 1.34424 + 1.07199i 0.990626 + 0.136599i \(0.0436171\pi\)
0.353609 + 0.935393i \(0.384954\pi\)
\(602\) 24.1923 35.4521i 0.986004 1.44492i
\(603\) 0 0
\(604\) −32.0060 + 15.4133i −1.30231 + 0.627157i
\(605\) 3.51978 15.4212i 0.143100 0.626960i
\(606\) 0 0
\(607\) 27.4582i 1.11449i −0.830347 0.557247i \(-0.811858\pi\)
0.830347 0.557247i \(-0.188142\pi\)
\(608\) −1.22786 + 5.37960i −0.0497963 + 0.218172i
\(609\) 0 0
\(610\) −22.5500 98.7979i −0.913022 4.00021i
\(611\) −20.9176 + 4.77429i −0.846234 + 0.193147i
\(612\) 0 0
\(613\) −24.1730 30.3120i −0.976340 1.22429i −0.974522 0.224293i \(-0.927993\pi\)
−0.00181824 0.999998i \(-0.500579\pi\)
\(614\) 9.57128 + 41.9345i 0.386266 + 1.69234i
\(615\) 0 0
\(616\) −4.33746 58.2019i −0.174761 2.34502i
\(617\) −1.98842 0.453844i −0.0800508 0.0182711i 0.182308 0.983241i \(-0.441643\pi\)
−0.262359 + 0.964970i \(0.584500\pi\)
\(618\) 0 0
\(619\) 0.0855953i 0.00344037i 0.999999 + 0.00172018i \(0.000547552\pi\)
−0.999999 + 0.00172018i \(0.999452\pi\)
\(620\) −134.942 30.7997i −5.41941 1.23695i
\(621\) 0 0
\(622\) 69.7454 55.6201i 2.79653 2.23016i
\(623\) −42.1699 + 12.9886i −1.68950 + 0.520378i
\(624\) 0 0
\(625\) 6.44971 28.2580i 0.257988 1.13032i
\(626\) 38.5846 48.3835i 1.54215 1.93380i
\(627\) 0 0
\(628\) −33.9158 + 27.0470i −1.35339 + 1.07929i
\(629\) 27.5939 + 13.2885i 1.10024 + 0.529849i
\(630\) 0 0
\(631\) −35.7609 + 17.2216i −1.42362 + 0.685580i −0.977800 0.209543i \(-0.932803\pi\)
−0.445821 + 0.895122i \(0.647088\pi\)
\(632\) 34.2646 71.1513i 1.36297 2.83025i
\(633\) 0 0
\(634\) −57.3679 27.6269i −2.27837 1.09721i
\(635\) −3.04154 + 3.81397i −0.120700 + 0.151353i
\(636\) 0 0
\(637\) −2.56718 17.1281i −0.101715 0.678640i
\(638\) 17.6326i 0.698081i
\(639\) 0 0
\(640\) −41.9217 + 87.0514i −1.65710 + 3.44101i
\(641\) −38.8795 + 8.87399i −1.53565 + 0.350501i −0.904947 0.425525i \(-0.860089\pi\)
−0.630700 + 0.776027i \(0.717232\pi\)
\(642\) 0 0
\(643\) 6.45301 + 13.3998i 0.254482 + 0.528437i 0.988597 0.150588i \(-0.0481168\pi\)
−0.734115 + 0.679026i \(0.762403\pi\)
\(644\) 118.326 8.81817i 4.66270 0.347484i
\(645\) 0 0
\(646\) 2.37475 + 2.97784i 0.0934332 + 0.117161i
\(647\) −9.84255 + 4.73992i −0.386951 + 0.186346i −0.617237 0.786777i \(-0.711748\pi\)
0.230286 + 0.973123i \(0.426034\pi\)
\(648\) 0 0
\(649\) −14.5881 3.32963i −0.572632 0.130699i
\(650\) 16.7959 21.0614i 0.658791 0.826098i
\(651\) 0 0
\(652\) 6.57227 + 8.24137i 0.257390 + 0.322757i
\(653\) 13.3105 + 27.6396i 0.520881 + 1.08162i 0.981044 + 0.193786i \(0.0620769\pi\)
−0.460162 + 0.887835i \(0.652209\pi\)
\(654\) 0 0
\(655\) 16.7124 0.653009
\(656\) 13.6652 0.533538
\(657\) 0 0
\(658\) −9.32134 + 61.6702i −0.363384 + 2.40416i
\(659\) 34.5048 7.87550i 1.34412 0.306786i 0.510857 0.859666i \(-0.329328\pi\)
0.833261 + 0.552880i \(0.186471\pi\)
\(660\) 0 0
\(661\) −15.9364 + 12.7089i −0.619856 + 0.494319i −0.882337 0.470619i \(-0.844031\pi\)
0.262481 + 0.964937i \(0.415459\pi\)
\(662\) −26.9529 + 21.4943i −1.04756 + 0.835398i
\(663\) 0 0
\(664\) 10.1060 2.30662i 0.392188 0.0895144i
\(665\) −1.46211 1.57709i −0.0566982 0.0611568i
\(666\) 0 0
\(667\) −22.5465 −0.873005
\(668\) 4.32244 0.167240
\(669\) 0 0
\(670\) 32.5176 + 67.5235i 1.25626 + 2.60866i
\(671\) −18.5382 23.2462i −0.715660 0.897409i
\(672\) 0 0
\(673\) −16.9857 + 21.2993i −0.654749 + 0.821030i −0.992760 0.120113i \(-0.961674\pi\)
0.338011 + 0.941142i \(0.390246\pi\)
\(674\) −10.1008 2.30545i −0.389069 0.0888025i
\(675\) 0 0
\(676\) 33.4040 16.0865i 1.28477 0.618712i
\(677\) −3.58349 4.49355i −0.137725 0.172701i 0.708186 0.706026i \(-0.249514\pi\)
−0.845911 + 0.533325i \(0.820942\pi\)
\(678\) 0 0
\(679\) −4.27658 1.68047i −0.164120 0.0644906i
\(680\) 62.0684 + 128.886i 2.38021 + 4.94256i
\(681\) 0 0
\(682\) −54.2828 + 12.3897i −2.07860 + 0.474426i
\(683\) 8.42918 17.5034i 0.322533 0.669748i −0.675157 0.737674i \(-0.735924\pi\)
0.997690 + 0.0679266i \(0.0216384\pi\)
\(684\) 0 0
\(685\) 40.7323i 1.55630i
\(686\) −49.0710 11.2641i −1.87354 0.430066i
\(687\) 0 0
\(688\) −53.1074 + 66.5946i −2.02470 + 2.53890i
\(689\) 3.17882 + 1.53084i 0.121103 + 0.0583202i
\(690\) 0 0
\(691\) 6.06239 12.5887i 0.230624 0.478896i −0.753255 0.657728i \(-0.771518\pi\)
0.983880 + 0.178832i \(0.0572319\pi\)
\(692\) 69.5989 33.5171i 2.64575 1.27413i
\(693\) 0 0
\(694\) −10.9508 5.27362i −0.415686 0.200184i
\(695\) 29.5242 23.5448i 1.11992 0.893105i
\(696\) 0 0
\(697\) 3.08744 3.87153i 0.116945 0.146645i
\(698\) −9.64908 + 42.2754i −0.365223 + 1.60015i
\(699\) 0 0
\(700\) −28.5381 49.4767i −1.07864 1.87004i
\(701\) −8.87667 + 7.07890i −0.335267 + 0.267367i −0.776623 0.629966i \(-0.783069\pi\)
0.441356 + 0.897332i \(0.354498\pi\)
\(702\) 0 0
\(703\) 1.56365 + 0.356894i 0.0589743 + 0.0134605i
\(704\) 64.2202i 2.42039i
\(705\) 0 0
\(706\) −38.5851 8.80680i −1.45217 0.331448i
\(707\) −12.9671 + 12.0218i −0.487679 + 0.452125i
\(708\) 0 0
\(709\) −3.84875 16.8625i −0.144543 0.633284i −0.994346 0.106184i \(-0.966137\pi\)
0.849803 0.527100i \(-0.176721\pi\)
\(710\) −17.9404 22.4965i −0.673290 0.844279i
\(711\) 0 0
\(712\) 149.852 34.2027i 5.61594 1.28180i
\(713\) −15.8425 69.4106i −0.593307 2.59945i
\(714\) 0 0
\(715\) 3.95445 17.3256i 0.147888 0.647939i
\(716\) 27.1844i 1.01593i
\(717\) 0 0
\(718\) 2.26046 9.90371i 0.0843595 0.369603i
\(719\) 6.23567 3.00294i 0.232551 0.111991i −0.313980 0.949430i \(-0.601662\pi\)
0.546531 + 0.837439i \(0.315948\pi\)
\(720\) 0 0
\(721\) 0.423343 + 0.456633i 0.0157661 + 0.0170059i
\(722\) −40.2267 32.0798i −1.49708 1.19389i
\(723\) 0 0
\(724\) 22.8793 + 18.2457i 0.850303 + 0.678094i
\(725\) 4.70909 + 9.77852i 0.174891 + 0.363165i
\(726\) 0 0
\(727\) −1.33244 + 2.76683i −0.0494173 + 0.102616i −0.924215 0.381872i \(-0.875280\pi\)
0.874798 + 0.484488i \(0.160994\pi\)
\(728\) 4.48369 + 60.1641i 0.166177 + 2.22983i
\(729\) 0 0
\(730\) 61.9160 + 29.8172i 2.29161 + 1.10358i
\(731\) 6.86831 + 30.0920i 0.254034 + 1.11299i
\(732\) 0 0
\(733\) −35.6911 28.4627i −1.31828 1.05129i −0.994453 0.105177i \(-0.966459\pi\)
−0.323827 0.946116i \(-0.604970\pi\)
\(734\) −29.7819 −1.09927
\(735\) 0 0
\(736\) −169.490 −6.24748
\(737\) 17.1918 + 13.7100i 0.633268 + 0.505015i
\(738\) 0 0
\(739\) 2.36098 + 10.3441i 0.0868502 + 0.380515i 0.999608 0.0279849i \(-0.00890902\pi\)
−0.912758 + 0.408500i \(0.866052\pi\)
\(740\) 86.2911 + 41.5556i 3.17212 + 1.52761i
\(741\) 0 0
\(742\) 7.52140 6.97306i 0.276119 0.255989i
\(743\) 13.5006 28.0342i 0.495287 1.02847i −0.492157 0.870506i \(-0.663791\pi\)
0.987444 0.157968i \(-0.0504943\pi\)
\(744\) 0 0
\(745\) 22.9816 + 47.7218i 0.841980 + 1.74839i
\(746\) −68.3889 54.5383i −2.50389 1.99679i
\(747\) 0 0
\(748\) 52.1738 + 41.6072i 1.90766 + 1.52131i
\(749\) 7.93989 + 25.7783i 0.290117 + 0.941918i
\(750\) 0 0
\(751\) −21.0103 + 10.1180i −0.766677 + 0.369212i −0.775991 0.630744i \(-0.782750\pi\)
0.00931362 + 0.999957i \(0.497035\pi\)
\(752\) 27.5435 120.676i 1.00441 4.40060i
\(753\) 0 0
\(754\) 18.2270i 0.663789i
\(755\) −4.40079 + 19.2811i −0.160161 + 0.701711i
\(756\) 0 0
\(757\) −7.20955 31.5871i −0.262036 1.14805i −0.919039 0.394166i \(-0.871034\pi\)
0.657004 0.753887i \(-0.271824\pi\)
\(758\) 9.21755 2.10385i 0.334797 0.0764152i
\(759\) 0 0
\(760\) 4.67079 + 5.85699i 0.169427 + 0.212455i
\(761\) 0.723345 + 3.16918i 0.0262212 + 0.114883i 0.986345 0.164693i \(-0.0526633\pi\)
−0.960124 + 0.279576i \(0.909806\pi\)
\(762\) 0 0
\(763\) 4.02956 + 6.98606i 0.145880 + 0.252912i
\(764\) −115.797 26.4299i −4.18939 0.956201i
\(765\) 0 0
\(766\) 66.0535i 2.38661i
\(767\) 15.0799 + 3.44188i 0.544502 + 0.124279i
\(768\) 0 0
\(769\) 0.571663 0.455886i 0.0206147 0.0164397i −0.613128 0.789983i \(-0.710089\pi\)
0.633743 + 0.773544i \(0.281518\pi\)
\(770\) −42.6717 29.1189i −1.53778 1.04937i
\(771\) 0 0
\(772\) −12.6010 + 55.2085i −0.453519 + 1.98700i
\(773\) 4.27724 5.36348i 0.153841 0.192911i −0.698938 0.715182i \(-0.746344\pi\)
0.852779 + 0.522271i \(0.174915\pi\)
\(774\) 0 0
\(775\) −26.7948 + 21.3681i −0.962497 + 0.767566i
\(776\) 14.4209 + 6.94474i 0.517680 + 0.249302i
\(777\) 0 0
\(778\) −62.7100 + 30.1996i −2.24826 + 1.08271i
\(779\) 0.112514 0.233638i 0.00403124 0.00837095i
\(780\) 0 0
\(781\) −7.60633 3.66302i −0.272176 0.131073i
\(782\) −72.9429 + 91.4675i −2.60843 + 3.27087i
\(783\) 0 0
\(784\) 95.4544 + 29.5301i 3.40909 + 1.05465i
\(785\) 24.1505i 0.861970i
\(786\) 0 0
\(787\) 2.23077 4.63224i 0.0795183 0.165121i −0.857419 0.514619i \(-0.827933\pi\)
0.936937 + 0.349497i \(0.113648\pi\)
\(788\) −12.8954 + 2.94329i −0.459379 + 0.104850i
\(789\) 0 0
\(790\)