Properties

Label 441.2.bg.a.395.2
Level $441$
Weight $2$
Character 441.395
Analytic conductor $3.521$
Analytic rank $0$
Dimension $216$
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.bg (of order \(42\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(216\)
Relative dimension: \(18\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 395.2
Character \(\chi\) \(=\) 441.395
Dual form 441.2.bg.a.278.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.21867 - 0.870763i) q^{2} +(2.69816 + 2.50352i) q^{4} +(-1.55712 - 1.06163i) q^{5} +(0.00333353 - 2.64575i) q^{7} +(-1.73808 - 3.60916i) q^{8} +O(q^{10})\) \(q+(-2.21867 - 0.870763i) q^{2} +(2.69816 + 2.50352i) q^{4} +(-1.55712 - 1.06163i) q^{5} +(0.00333353 - 2.64575i) q^{7} +(-1.73808 - 3.60916i) q^{8} +(2.53032 + 3.71129i) q^{10} +(-0.0972657 - 0.645316i) q^{11} +(0.531850 - 0.424136i) q^{13} +(-2.31122 + 5.86714i) q^{14} +(0.163378 + 2.18013i) q^{16} +(5.58077 + 1.72144i) q^{17} +(-5.58665 + 3.22545i) q^{19} +(-1.54355 - 6.76274i) q^{20} +(-0.346117 + 1.51644i) q^{22} +(-2.20835 - 7.15930i) q^{23} +(-0.529125 - 1.34819i) q^{25} +(-1.54932 + 0.477902i) q^{26} +(6.63269 - 7.13030i) q^{28} +(-4.23402 + 0.966388i) q^{29} +(-2.43240 - 1.40435i) q^{31} +(-0.825605 + 2.67654i) q^{32} +(-10.8829 - 8.67884i) q^{34} +(-2.81400 + 4.11622i) q^{35} +(-2.42947 + 2.25422i) q^{37} +(15.2035 - 2.29156i) q^{38} +(-1.12518 + 7.46510i) q^{40} +(-3.48592 + 1.67873i) q^{41} +(-2.03931 - 0.982079i) q^{43} +(1.35313 - 1.98467i) q^{44} +(-1.33445 + 17.8071i) q^{46} +(-1.26639 + 3.22670i) q^{47} +(-6.99998 - 0.0176394i) q^{49} +3.45192i q^{50} +(2.49685 + 0.187113i) q^{52} +(-6.96046 + 7.50159i) q^{53} +(-0.533632 + 1.10810i) q^{55} +(-9.55472 + 4.58649i) q^{56} +(10.2354 + 1.54274i) q^{58} +(1.50981 - 1.02937i) q^{59} +(-6.85694 - 7.39003i) q^{61} +(4.17384 + 5.23382i) q^{62} +(6.88858 - 8.63800i) q^{64} +(-1.27843 + 0.0958053i) q^{65} +(-5.80262 + 10.0504i) q^{67} +(10.7481 + 18.6163i) q^{68} +(9.82758 - 6.68221i) q^{70} +(-15.2200 - 3.47387i) q^{71} +(8.21602 - 3.22455i) q^{73} +(7.35308 - 2.88587i) q^{74} +(-23.1486 - 5.28353i) q^{76} +(-1.70767 + 0.255190i) q^{77} +(4.60480 + 7.97575i) q^{79} +(2.06009 - 3.56818i) q^{80} +(9.19589 - 0.689136i) q^{82} +(5.98518 - 7.50517i) q^{83} +(-6.86243 - 8.60521i) q^{85} +(3.66939 + 3.95466i) q^{86} +(-2.15999 + 1.47266i) q^{88} +(4.81648 + 0.725967i) q^{89} +(-1.12039 - 1.40856i) q^{91} +(11.9650 - 24.8456i) q^{92} +(5.61939 - 6.05626i) q^{94} +(12.1233 + 0.908519i) q^{95} -8.08055i q^{97} +(15.5153 + 6.13446i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q - 16q^{4} + 2q^{7} + O(q^{10}) \) \( 216q - 16q^{4} + 2q^{7} + 12q^{10} + 12q^{16} - 6q^{19} + 44q^{22} + 26q^{25} + 84q^{28} - 6q^{31} - 112q^{34} + 60q^{37} - 304q^{40} + 20q^{43} - 20q^{46} - 86q^{49} - 168q^{52} - 84q^{55} - 120q^{58} - 2q^{61} + 32q^{64} + 22q^{67} - 136q^{70} - 6q^{73} + 84q^{76} + 2q^{79} - 104q^{82} + 96q^{85} - 12q^{88} + 58q^{91} + 52q^{94} + O(q^{100}) \)

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{42}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.21867 0.870763i −1.56884 0.615722i −0.587706 0.809075i \(-0.699969\pi\)
−0.981129 + 0.193352i \(0.938064\pi\)
\(3\) 0 0
\(4\) 2.69816 + 2.50352i 1.34908 + 1.25176i
\(5\) −1.55712 1.06163i −0.696367 0.474775i 0.162675 0.986680i \(-0.447988\pi\)
−0.859042 + 0.511904i \(0.828940\pi\)
\(6\) 0 0
\(7\) 0.00333353 2.64575i 0.00125996 0.999999i
\(8\) −1.73808 3.60916i −0.614503 1.27603i
\(9\) 0 0
\(10\) 2.53032 + 3.71129i 0.800156 + 1.17361i
\(11\) −0.0972657 0.645316i −0.0293267 0.194570i 0.969370 0.245604i \(-0.0789864\pi\)
−0.998697 + 0.0510342i \(0.983748\pi\)
\(12\) 0 0
\(13\) 0.531850 0.424136i 0.147509 0.117634i −0.546955 0.837162i \(-0.684213\pi\)
0.694464 + 0.719528i \(0.255642\pi\)
\(14\) −2.31122 + 5.86714i −0.617699 + 1.56806i
\(15\) 0 0
\(16\) 0.163378 + 2.18013i 0.0408445 + 0.545032i
\(17\) 5.58077 + 1.72144i 1.35354 + 0.417511i 0.884859 0.465859i \(-0.154254\pi\)
0.468677 + 0.883369i \(0.344731\pi\)
\(18\) 0 0
\(19\) −5.58665 + 3.22545i −1.28167 + 0.739970i −0.977153 0.212539i \(-0.931827\pi\)
−0.304513 + 0.952508i \(0.598494\pi\)
\(20\) −1.54355 6.76274i −0.345149 1.51219i
\(21\) 0 0
\(22\) −0.346117 + 1.51644i −0.0737924 + 0.323305i
\(23\) −2.20835 7.15930i −0.460473 1.49282i −0.826889 0.562366i \(-0.809891\pi\)
0.366415 0.930451i \(-0.380585\pi\)
\(24\) 0 0
\(25\) −0.529125 1.34819i −0.105825 0.269638i
\(26\) −1.54932 + 0.477902i −0.303847 + 0.0937244i
\(27\) 0 0
\(28\) 6.63269 7.13030i 1.25346 1.34750i
\(29\) −4.23402 + 0.966388i −0.786239 + 0.179454i −0.596748 0.802429i \(-0.703541\pi\)
−0.189491 + 0.981883i \(0.560684\pi\)
\(30\) 0 0
\(31\) −2.43240 1.40435i −0.436872 0.252228i 0.265398 0.964139i \(-0.414497\pi\)
−0.702270 + 0.711911i \(0.747830\pi\)
\(32\) −0.825605 + 2.67654i −0.145948 + 0.473151i
\(33\) 0 0
\(34\) −10.8829 8.67884i −1.86641 1.48841i
\(35\) −2.81400 + 4.11622i −0.475652 + 0.695769i
\(36\) 0 0
\(37\) −2.42947 + 2.25422i −0.399403 + 0.370592i −0.854148 0.520030i \(-0.825921\pi\)
0.454745 + 0.890622i \(0.349730\pi\)
\(38\) 15.2035 2.29156i 2.46634 0.371741i
\(39\) 0 0
\(40\) −1.12518 + 7.46510i −0.177907 + 1.18034i
\(41\) −3.48592 + 1.67873i −0.544410 + 0.262174i −0.685813 0.727778i \(-0.740553\pi\)
0.141403 + 0.989952i \(0.454839\pi\)
\(42\) 0 0
\(43\) −2.03931 0.982079i −0.310991 0.149766i 0.271877 0.962332i \(-0.412356\pi\)
−0.582869 + 0.812566i \(0.698070\pi\)
\(44\) 1.35313 1.98467i 0.203991 0.299200i
\(45\) 0 0
\(46\) −1.33445 + 17.8071i −0.196755 + 2.62551i
\(47\) −1.26639 + 3.22670i −0.184722 + 0.470663i −0.992997 0.118142i \(-0.962306\pi\)
0.808275 + 0.588805i \(0.200401\pi\)
\(48\) 0 0
\(49\) −6.99998 0.0176394i −0.999997 0.00251991i
\(50\) 3.45192i 0.488176i
\(51\) 0 0
\(52\) 2.49685 + 0.187113i 0.346251 + 0.0259479i
\(53\) −6.96046 + 7.50159i −0.956093 + 1.03042i 0.0434150 + 0.999057i \(0.486176\pi\)
−0.999508 + 0.0313660i \(0.990014\pi\)
\(54\) 0 0
\(55\) −0.533632 + 1.10810i −0.0719549 + 0.149416i
\(56\) −9.55472 + 4.58649i −1.27680 + 0.612895i
\(57\) 0 0
\(58\) 10.2354 + 1.54274i 1.34397 + 0.202571i
\(59\) 1.50981 1.02937i 0.196561 0.134013i −0.461040 0.887379i \(-0.652524\pi\)
0.657601 + 0.753366i \(0.271571\pi\)
\(60\) 0 0
\(61\) −6.85694 7.39003i −0.877942 0.946196i 0.120978 0.992655i \(-0.461397\pi\)
−0.998920 + 0.0464590i \(0.985206\pi\)
\(62\) 4.17384 + 5.23382i 0.530078 + 0.664696i
\(63\) 0 0
\(64\) 6.88858 8.63800i 0.861072 1.07975i
\(65\) −1.27843 + 0.0958053i −0.158570 + 0.0118832i
\(66\) 0 0
\(67\) −5.80262 + 10.0504i −0.708903 + 1.22786i 0.256361 + 0.966581i \(0.417476\pi\)
−0.965264 + 0.261275i \(0.915857\pi\)
\(68\) 10.7481 + 18.6163i 1.30340 + 2.25756i
\(69\) 0 0
\(70\) 9.82758 6.68221i 1.17462 0.798677i
\(71\) −15.2200 3.47387i −1.80628 0.412272i −0.819335 0.573314i \(-0.805657\pi\)
−0.986948 + 0.161042i \(0.948514\pi\)
\(72\) 0 0
\(73\) 8.21602 3.22455i 0.961612 0.377405i 0.167971 0.985792i \(-0.446278\pi\)
0.793641 + 0.608387i \(0.208183\pi\)
\(74\) 7.35308 2.88587i 0.854779 0.335476i
\(75\) 0 0
\(76\) −23.1486 5.28353i −2.65533 0.606062i
\(77\) −1.70767 + 0.255190i −0.194607 + 0.0290815i
\(78\) 0 0
\(79\) 4.60480 + 7.97575i 0.518080 + 0.897342i 0.999779 + 0.0210049i \(0.00668657\pi\)
−0.481699 + 0.876337i \(0.659980\pi\)
\(80\) 2.06009 3.56818i 0.230325 0.398934i
\(81\) 0 0
\(82\) 9.19589 0.689136i 1.01552 0.0761024i
\(83\) 5.98518 7.50517i 0.656959 0.823800i −0.336050 0.941844i \(-0.609091\pi\)
0.993008 + 0.118044i \(0.0376625\pi\)
\(84\) 0 0
\(85\) −6.86243 8.60521i −0.744335 0.933367i
\(86\) 3.66939 + 3.95466i 0.395680 + 0.426442i
\(87\) 0 0
\(88\) −2.15999 + 1.47266i −0.230256 + 0.156986i
\(89\) 4.81648 + 0.725967i 0.510545 + 0.0769524i 0.399263 0.916836i \(-0.369266\pi\)
0.111283 + 0.993789i \(0.464504\pi\)
\(90\) 0 0
\(91\) −1.12039 1.40856i −0.117448 0.147657i
\(92\) 11.9650 24.8456i 1.24744 2.59033i
\(93\) 0 0
\(94\) 5.61939 6.05626i 0.579596 0.624656i
\(95\) 12.1233 + 0.908519i 1.24383 + 0.0932121i
\(96\) 0 0
\(97\) 8.08055i 0.820455i −0.911983 0.410228i \(-0.865449\pi\)
0.911983 0.410228i \(-0.134551\pi\)
\(98\) 15.5153 + 6.13446i 1.56728 + 0.619674i
\(99\) 0 0
\(100\) 1.94756 4.96230i 0.194756 0.496230i
\(101\) 1.39058 18.5561i 0.138368 1.84640i −0.307803 0.951450i \(-0.599594\pi\)
0.446172 0.894947i \(-0.352787\pi\)
\(102\) 0 0
\(103\) 5.51061 8.08258i 0.542977 0.796400i −0.452464 0.891783i \(-0.649455\pi\)
0.995441 + 0.0953822i \(0.0304073\pi\)
\(104\) −2.45517 1.18235i −0.240749 0.115939i
\(105\) 0 0
\(106\) 21.9751 10.5826i 2.13441 1.02788i
\(107\) 1.47113 9.76031i 0.142220 0.943565i −0.797917 0.602767i \(-0.794065\pi\)
0.940137 0.340798i \(-0.110697\pi\)
\(108\) 0 0
\(109\) −6.35767 + 0.958265i −0.608955 + 0.0917852i −0.446278 0.894894i \(-0.647251\pi\)
−0.162677 + 0.986679i \(0.552013\pi\)
\(110\) 2.14884 1.99383i 0.204884 0.190105i
\(111\) 0 0
\(112\) 5.76861 0.424989i 0.545083 0.0401577i
\(113\) 10.0205 + 7.99108i 0.942649 + 0.751737i 0.968780 0.247921i \(-0.0797475\pi\)
−0.0261316 + 0.999659i \(0.508319\pi\)
\(114\) 0 0
\(115\) −4.16185 + 13.4924i −0.388094 + 1.25817i
\(116\) −13.8434 7.99251i −1.28533 0.742086i
\(117\) 0 0
\(118\) −4.24611 + 0.969146i −0.390886 + 0.0892171i
\(119\) 4.57310 14.7596i 0.419216 1.35301i
\(120\) 0 0
\(121\) 10.1043 3.11677i 0.918575 0.283343i
\(122\) 8.77832 + 22.3668i 0.794752 + 2.02499i
\(123\) 0 0
\(124\) −3.04718 9.87872i −0.273645 0.887135i
\(125\) −2.70417 + 11.8478i −0.241868 + 1.05970i
\(126\) 0 0
\(127\) −1.96619 8.61442i −0.174471 0.764406i −0.984122 0.177495i \(-0.943201\pi\)
0.809651 0.586912i \(-0.199656\pi\)
\(128\) −17.9537 + 10.3656i −1.58689 + 0.916194i
\(129\) 0 0
\(130\) 2.91984 + 0.900652i 0.256087 + 0.0789924i
\(131\) 0.225403 + 3.00779i 0.0196935 + 0.262792i 0.998356 + 0.0573173i \(0.0182547\pi\)
−0.978663 + 0.205474i \(0.934126\pi\)
\(132\) 0 0
\(133\) 8.51512 + 14.7916i 0.738354 + 1.28260i
\(134\) 21.6256 17.2459i 1.86817 1.48982i
\(135\) 0 0
\(136\) −3.48687 23.1339i −0.298997 1.98371i
\(137\) −1.34187 1.96816i −0.114644 0.168151i 0.764628 0.644472i \(-0.222923\pi\)
−0.879272 + 0.476320i \(0.841970\pi\)
\(138\) 0 0
\(139\) 9.71304 + 20.1693i 0.823849 + 1.71074i 0.694921 + 0.719086i \(0.255439\pi\)
0.128928 + 0.991654i \(0.458846\pi\)
\(140\) −17.8977 + 4.06131i −1.51263 + 0.343243i
\(141\) 0 0
\(142\) 30.7432 + 20.9604i 2.57992 + 1.75896i
\(143\) −0.325433 0.301957i −0.0272141 0.0252510i
\(144\) 0 0
\(145\) 7.61885 + 2.99018i 0.632711 + 0.248321i
\(146\) −21.0364 −1.74099
\(147\) 0 0
\(148\) −12.1986 −1.00272
\(149\) −11.0236 4.32645i −0.903089 0.354436i −0.132064 0.991241i \(-0.542161\pi\)
−0.771025 + 0.636805i \(0.780256\pi\)
\(150\) 0 0
\(151\) −15.9225 14.7740i −1.29576 1.20229i −0.966094 0.258190i \(-0.916874\pi\)
−0.329664 0.944098i \(-0.606936\pi\)
\(152\) 21.3512 + 14.5570i 1.73181 + 1.18073i
\(153\) 0 0
\(154\) 4.01096 + 0.920794i 0.323212 + 0.0741997i
\(155\) 2.29665 + 4.76905i 0.184472 + 0.383060i
\(156\) 0 0
\(157\) 13.5566 + 19.8839i 1.08194 + 1.58691i 0.771401 + 0.636350i \(0.219556\pi\)
0.310537 + 0.950561i \(0.399491\pi\)
\(158\) −3.27154 21.7052i −0.260269 1.72678i
\(159\) 0 0
\(160\) 4.12707 3.29123i 0.326273 0.260194i
\(161\) −18.9491 + 5.81888i −1.49340 + 0.458592i
\(162\) 0 0
\(163\) −1.41529 18.8857i −0.110854 1.47924i −0.724289 0.689497i \(-0.757832\pi\)
0.613435 0.789745i \(-0.289787\pi\)
\(164\) −13.6083 4.19761i −1.06263 0.327778i
\(165\) 0 0
\(166\) −19.8144 + 11.4398i −1.53789 + 0.887902i
\(167\) −3.44716 15.1030i −0.266749 1.16870i −0.913770 0.406231i \(-0.866843\pi\)
0.647021 0.762472i \(-0.276014\pi\)
\(168\) 0 0
\(169\) −2.78980 + 12.2229i −0.214600 + 0.940224i
\(170\) 7.73235 + 25.0677i 0.593044 + 1.92260i
\(171\) 0 0
\(172\) −3.04371 7.75525i −0.232081 0.591332i
\(173\) 2.35855 0.727517i 0.179318 0.0553121i −0.203796 0.979013i \(-0.565328\pi\)
0.383114 + 0.923701i \(0.374852\pi\)
\(174\) 0 0
\(175\) −3.56873 + 1.39544i −0.269771 + 0.105485i
\(176\) 1.39098 0.317482i 0.104849 0.0239311i
\(177\) 0 0
\(178\) −10.0540 5.80469i −0.753580 0.435080i
\(179\) 0.843671 2.73511i 0.0630589 0.204432i −0.918561 0.395280i \(-0.870648\pi\)
0.981620 + 0.190848i \(0.0611238\pi\)
\(180\) 0 0
\(181\) 11.8568 + 9.45547i 0.881308 + 0.702819i 0.955679 0.294411i \(-0.0951235\pi\)
−0.0743711 + 0.997231i \(0.523695\pi\)
\(182\) 1.25925 + 4.10071i 0.0933415 + 0.303965i
\(183\) 0 0
\(184\) −22.0007 + 20.4137i −1.62192 + 1.50492i
\(185\) 6.17614 0.930903i 0.454079 0.0684414i
\(186\) 0 0
\(187\) 0.568055 3.76880i 0.0415403 0.275602i
\(188\) −11.4950 + 5.53572i −0.838362 + 0.403734i
\(189\) 0 0
\(190\) −26.1066 12.5723i −1.89397 0.912088i
\(191\) 3.80774 5.58493i 0.275518 0.404111i −0.663393 0.748272i \(-0.730884\pi\)
0.938911 + 0.344160i \(0.111836\pi\)
\(192\) 0 0
\(193\) 0.511397 6.82411i 0.0368111 0.491210i −0.948080 0.318033i \(-0.896978\pi\)
0.984891 0.173177i \(-0.0554033\pi\)
\(194\) −7.03624 + 17.9281i −0.505173 + 1.28716i
\(195\) 0 0
\(196\) −18.8429 17.5722i −1.34592 1.25516i
\(197\) 4.55093i 0.324240i −0.986771 0.162120i \(-0.948167\pi\)
0.986771 0.162120i \(-0.0518332\pi\)
\(198\) 0 0
\(199\) −5.37432 0.402750i −0.380975 0.0285502i −0.117134 0.993116i \(-0.537371\pi\)
−0.263842 + 0.964566i \(0.584990\pi\)
\(200\) −3.94616 + 4.25295i −0.279036 + 0.300729i
\(201\) 0 0
\(202\) −19.2432 + 39.9589i −1.35395 + 2.81150i
\(203\) 2.54271 + 11.2054i 0.178463 + 0.786464i
\(204\) 0 0
\(205\) 7.21021 + 1.08676i 0.503583 + 0.0759029i
\(206\) −19.2642 + 13.1341i −1.34220 + 0.915098i
\(207\) 0 0
\(208\) 1.01156 + 1.09021i 0.0701393 + 0.0755922i
\(209\) 2.62483 + 3.29143i 0.181563 + 0.227673i
\(210\) 0 0
\(211\) −3.02491 + 3.79311i −0.208243 + 0.261129i −0.874974 0.484170i \(-0.839122\pi\)
0.666731 + 0.745299i \(0.267693\pi\)
\(212\) −37.5608 + 2.81479i −2.57969 + 0.193321i
\(213\) 0 0
\(214\) −11.7629 + 20.3739i −0.804093 + 1.39273i
\(215\) 2.13285 + 3.69421i 0.145459 + 0.251943i
\(216\) 0 0
\(217\) −3.72366 + 6.43084i −0.252778 + 0.436554i
\(218\) 14.9400 + 3.40996i 1.01186 + 0.230951i
\(219\) 0 0
\(220\) −4.21397 + 1.65386i −0.284106 + 0.111503i
\(221\) 3.69826 1.45146i 0.248772 0.0976358i
\(222\) 0 0
\(223\) 8.69380 + 1.98430i 0.582180 + 0.132879i 0.503461 0.864018i \(-0.332060\pi\)
0.0787193 + 0.996897i \(0.474917\pi\)
\(224\) 7.07871 + 2.19327i 0.472966 + 0.146544i
\(225\) 0 0
\(226\) −15.2738 26.4550i −1.01600 1.75976i
\(227\) 7.04102 12.1954i 0.467329 0.809437i −0.531974 0.846760i \(-0.678550\pi\)
0.999303 + 0.0373231i \(0.0118831\pi\)
\(228\) 0 0
\(229\) 18.1348 1.35902i 1.19838 0.0898063i 0.539456 0.842014i \(-0.318630\pi\)
0.658926 + 0.752208i \(0.271011\pi\)
\(230\) 20.9824 26.3111i 1.38354 1.73490i
\(231\) 0 0
\(232\) 10.8469 + 13.6016i 0.712135 + 0.892989i
\(233\) 7.25919 + 7.82354i 0.475565 + 0.512537i 0.924581 0.380987i \(-0.124416\pi\)
−0.449015 + 0.893524i \(0.648225\pi\)
\(234\) 0 0
\(235\) 5.39749 3.67995i 0.352093 0.240053i
\(236\) 6.65076 + 1.00244i 0.432928 + 0.0652533i
\(237\) 0 0
\(238\) −22.9983 + 28.7645i −1.49076 + 1.86453i
\(239\) 9.07961 18.8540i 0.587311 1.21956i −0.369602 0.929190i \(-0.620506\pi\)
0.956913 0.290374i \(-0.0937799\pi\)
\(240\) 0 0
\(241\) −14.5707 + 15.7035i −0.938582 + 1.01155i 0.0613279 + 0.998118i \(0.480466\pi\)
−0.999910 + 0.0134331i \(0.995724\pi\)
\(242\) −25.1321 1.88339i −1.61555 0.121069i
\(243\) 0 0
\(244\) 37.1060i 2.37547i
\(245\) 10.8811 + 7.45885i 0.695169 + 0.476529i
\(246\) 0 0
\(247\) −1.60323 + 4.08496i −0.102011 + 0.259920i
\(248\) −0.840806 + 11.2198i −0.0533913 + 0.712457i
\(249\) 0 0
\(250\) 16.3162 23.9315i 1.03193 1.51356i
\(251\) −3.25960 1.56974i −0.205744 0.0990812i 0.328174 0.944617i \(-0.393567\pi\)
−0.533918 + 0.845536i \(0.679281\pi\)
\(252\) 0 0
\(253\) −4.40521 + 2.12144i −0.276953 + 0.133374i
\(254\) −3.13881 + 20.8246i −0.196946 + 1.30665i
\(255\) 0 0
\(256\) 27.0091 4.07097i 1.68807 0.254436i
\(257\) −7.50781 + 6.96623i −0.468324 + 0.434542i −0.878700 0.477375i \(-0.841588\pi\)
0.410375 + 0.911917i \(0.365398\pi\)
\(258\) 0 0
\(259\) 5.95600 + 6.43529i 0.370088 + 0.399869i
\(260\) −3.68926 2.94209i −0.228798 0.182461i
\(261\) 0 0
\(262\) 2.11898 6.86956i 0.130911 0.424403i
\(263\) 3.46319 + 1.99947i 0.213549 + 0.123293i 0.602960 0.797772i \(-0.293988\pi\)
−0.389411 + 0.921064i \(0.627321\pi\)
\(264\) 0 0
\(265\) 18.8022 4.29148i 1.15501 0.263624i
\(266\) −6.01222 40.2324i −0.368633 2.46680i
\(267\) 0 0
\(268\) −40.8179 + 12.5906i −2.49335 + 0.769096i
\(269\) 2.48226 + 6.32470i 0.151346 + 0.385624i 0.986359 0.164606i \(-0.0526353\pi\)
−0.835013 + 0.550230i \(0.814540\pi\)
\(270\) 0 0
\(271\) −6.74647 21.8715i −0.409819 1.32860i −0.891805 0.452421i \(-0.850561\pi\)
0.481986 0.876179i \(-0.339916\pi\)
\(272\) −2.84118 + 12.4480i −0.172272 + 0.754773i
\(273\) 0 0
\(274\) 1.26336 + 5.53515i 0.0763225 + 0.334391i
\(275\) −0.818542 + 0.472585i −0.0493599 + 0.0284980i
\(276\) 0 0
\(277\) −8.19644 2.52827i −0.492476 0.151909i 0.0385627 0.999256i \(-0.487722\pi\)
−0.531039 + 0.847347i \(0.678198\pi\)
\(278\) −3.98730 53.2068i −0.239142 3.19113i
\(279\) 0 0
\(280\) 19.7470 + 3.00184i 1.18011 + 0.179394i
\(281\) −13.5840 + 10.8329i −0.810356 + 0.646238i −0.938408 0.345530i \(-0.887699\pi\)
0.128051 + 0.991768i \(0.459128\pi\)
\(282\) 0 0
\(283\) −4.82901 32.0384i −0.287055 1.90449i −0.410024 0.912075i \(-0.634480\pi\)
0.122969 0.992411i \(-0.460758\pi\)
\(284\) −32.3691 47.4767i −1.92075 2.81722i
\(285\) 0 0
\(286\) 0.459094 + 0.953318i 0.0271468 + 0.0563709i
\(287\) 4.42988 + 9.22848i 0.261488 + 0.544740i
\(288\) 0 0
\(289\) 14.1356 + 9.63750i 0.831507 + 0.566912i
\(290\) −14.3000 13.2684i −0.839723 0.779149i
\(291\) 0 0
\(292\) 30.2408 + 11.8686i 1.76971 + 0.694560i
\(293\) 14.5324 0.848993 0.424496 0.905430i \(-0.360451\pi\)
0.424496 + 0.905430i \(0.360451\pi\)
\(294\) 0 0
\(295\) −3.44377 −0.200504
\(296\) 12.3584 + 4.85033i 0.718320 + 0.281920i
\(297\) 0 0
\(298\) 20.6904 + 19.1979i 1.19856 + 1.11210i
\(299\) −4.21103 2.87103i −0.243530 0.166036i
\(300\) 0 0
\(301\) −2.60513 + 5.39222i −0.150157 + 0.310802i
\(302\) 22.4622 + 46.6433i 1.29256 + 2.68402i
\(303\) 0 0
\(304\) −7.94463 11.6526i −0.455656 0.668324i
\(305\) 2.83164 + 18.7867i 0.162139 + 1.07573i
\(306\) 0 0
\(307\) 4.07997 3.25367i 0.232856 0.185697i −0.500109 0.865962i \(-0.666707\pi\)
0.732966 + 0.680265i \(0.238135\pi\)
\(308\) −5.24643 3.58665i −0.298943 0.204368i
\(309\) 0 0
\(310\) −0.942800 12.5808i −0.0535474 0.714541i
\(311\) 2.72915 + 0.841833i 0.154756 + 0.0477359i 0.371165 0.928567i \(-0.378958\pi\)
−0.216409 + 0.976303i \(0.569435\pi\)
\(312\) 0 0
\(313\) 15.4116 8.89791i 0.871117 0.502940i 0.00339768 0.999994i \(-0.498918\pi\)
0.867719 + 0.497055i \(0.165585\pi\)
\(314\) −12.7635 55.9205i −0.720285 3.15578i
\(315\) 0 0
\(316\) −7.54300 + 33.0480i −0.424327 + 1.85910i
\(317\) 0.955904 + 3.09897i 0.0536889 + 0.174055i 0.978446 0.206503i \(-0.0662082\pi\)
−0.924757 + 0.380558i \(0.875732\pi\)
\(318\) 0 0
\(319\) 1.03545 + 2.63829i 0.0579741 + 0.147716i
\(320\) −19.8967 + 6.13733i −1.11226 + 0.343087i
\(321\) 0 0
\(322\) 47.1086 + 3.58999i 2.62526 + 0.200062i
\(323\) −36.7303 + 8.38344i −2.04373 + 0.466467i
\(324\) 0 0
\(325\) −0.853231 0.492613i −0.0473287 0.0273253i
\(326\) −13.3049 + 43.1335i −0.736891 + 2.38894i
\(327\) 0 0
\(328\) 12.1176 + 9.66348i 0.669083 + 0.533576i
\(329\) 8.53283 + 3.36130i 0.470430 + 0.185315i
\(330\) 0 0
\(331\) −13.3975 + 12.4310i −0.736392 + 0.683272i −0.956346 0.292238i \(-0.905600\pi\)
0.219953 + 0.975510i \(0.429409\pi\)
\(332\) 34.9383 5.26610i 1.91749 0.289015i
\(333\) 0 0
\(334\) −5.50302 + 36.5101i −0.301112 + 1.99775i
\(335\) 19.7053 9.48955i 1.07661 0.518470i
\(336\) 0 0
\(337\) −12.9190 6.22147i −0.703743 0.338905i 0.0475542 0.998869i \(-0.484857\pi\)
−0.751297 + 0.659964i \(0.770572\pi\)
\(338\) 16.8329 24.6893i 0.915589 1.34292i
\(339\) 0 0
\(340\) 3.02745 40.3985i 0.164186 2.19091i
\(341\) −0.669658 + 1.70626i −0.0362640 + 0.0923992i
\(342\) 0 0
\(343\) −0.0700040 + 18.5201i −0.00377986 + 0.999993i
\(344\) 9.06711i 0.488866i
\(345\) 0 0
\(346\) −5.86634 0.439622i −0.315377 0.0236342i
\(347\) 8.48613 9.14588i 0.455560 0.490976i −0.462945 0.886387i \(-0.653207\pi\)
0.918504 + 0.395411i \(0.129398\pi\)
\(348\) 0 0
\(349\) −5.62020 + 11.6705i −0.300843 + 0.624706i −0.995513 0.0946218i \(-0.969836\pi\)
0.694671 + 0.719328i \(0.255550\pi\)
\(350\) 9.13293 + 0.0115071i 0.488176 + 0.000615081i
\(351\) 0 0
\(352\) 1.80752 + 0.272440i 0.0963411 + 0.0145211i
\(353\) −21.8743 + 14.9136i −1.16425 + 0.793773i −0.981889 0.189458i \(-0.939327\pi\)
−0.182363 + 0.983231i \(0.558374\pi\)
\(354\) 0 0
\(355\) 20.0115 + 21.5673i 1.06210 + 1.14467i
\(356\) 11.1781 + 14.0169i 0.592440 + 0.742896i
\(357\) 0 0
\(358\) −4.25346 + 5.33367i −0.224802 + 0.281893i
\(359\) −8.44775 + 0.633071i −0.445855 + 0.0334122i −0.295766 0.955260i \(-0.595575\pi\)
−0.150089 + 0.988673i \(0.547956\pi\)
\(360\) 0 0
\(361\) 11.3071 19.5845i 0.595111 1.03076i
\(362\) −18.0728 31.3030i −0.949885 1.64525i
\(363\) 0 0
\(364\) 0.503378 6.60542i 0.0263842 0.346218i
\(365\) −16.2166 3.70134i −0.848818 0.193737i
\(366\) 0 0
\(367\) 4.17842 1.63991i 0.218112 0.0856025i −0.253769 0.967265i \(-0.581670\pi\)
0.471881 + 0.881662i \(0.343575\pi\)
\(368\) 15.2474 5.98416i 0.794825 0.311946i
\(369\) 0 0
\(370\) −14.5134 3.31259i −0.754516 0.172213i
\(371\) 19.8241 + 18.4406i 1.02922 + 0.957390i
\(372\) 0 0
\(373\) −13.0224 22.5554i −0.674274 1.16788i −0.976681 0.214697i \(-0.931123\pi\)
0.302407 0.953179i \(-0.402210\pi\)
\(374\) −4.54206 + 7.86707i −0.234864 + 0.406797i
\(375\) 0 0
\(376\) 13.8468 1.03767i 0.714092 0.0535138i
\(377\) −1.84199 + 2.30978i −0.0948671 + 0.118960i
\(378\) 0 0
\(379\) −10.1826 12.7685i −0.523044 0.655876i 0.448209 0.893929i \(-0.352062\pi\)
−0.971252 + 0.238053i \(0.923491\pi\)
\(380\) 30.4362 + 32.8024i 1.56134 + 1.68273i
\(381\) 0 0
\(382\) −13.3113 + 9.07546i −0.681063 + 0.464341i
\(383\) −19.4310 2.92875i −0.992878 0.149652i −0.367541 0.930007i \(-0.619800\pi\)
−0.625337 + 0.780355i \(0.715038\pi\)
\(384\) 0 0
\(385\) 2.92997 + 1.41555i 0.149325 + 0.0721431i
\(386\) −7.07680 + 14.6951i −0.360200 + 0.747963i
\(387\) 0 0
\(388\) 20.2298 21.8026i 1.02701 1.10686i
\(389\) 7.09818 + 0.531935i 0.359892 + 0.0269702i 0.253449 0.967349i \(-0.418435\pi\)
0.106443 + 0.994319i \(0.466054\pi\)
\(390\) 0 0
\(391\) 43.7560i 2.21283i
\(392\) 12.1028 + 25.2947i 0.611286 + 1.27757i
\(393\) 0 0
\(394\) −3.96278 + 10.0970i −0.199642 + 0.508679i
\(395\) 1.29704 17.3078i 0.0652613 0.870851i
\(396\) 0 0
\(397\) 14.4992 21.2664i 0.727693 1.06733i −0.266925 0.963717i \(-0.586008\pi\)
0.994618 0.103612i \(-0.0330399\pi\)
\(398\) 11.5731 + 5.57333i 0.580109 + 0.279366i
\(399\) 0 0
\(400\) 2.85277 1.37382i 0.142639 0.0686912i
\(401\) 5.73624 38.0575i 0.286454 1.90050i −0.130291 0.991476i \(-0.541591\pi\)
0.416745 0.909023i \(-0.363171\pi\)
\(402\) 0 0
\(403\) −1.88931 + 0.284767i −0.0941131 + 0.0141853i
\(404\) 50.2075 46.5858i 2.49792 2.31773i
\(405\) 0 0
\(406\) 4.11581 27.0751i 0.204264 1.34372i
\(407\) 1.69099 + 1.34852i 0.0838192 + 0.0668436i
\(408\) 0 0
\(409\) 7.66146 24.8378i 0.378835 1.22815i −0.542724 0.839911i \(-0.682607\pi\)
0.921558 0.388240i \(-0.126917\pi\)
\(410\) −15.0508 8.68956i −0.743304 0.429147i
\(411\) 0 0
\(412\) 35.1034 8.01213i 1.72942 0.394729i
\(413\) −2.71843 3.99801i −0.133765 0.196729i
\(414\) 0 0
\(415\) −17.2874 + 5.33245i −0.848604 + 0.261760i
\(416\) 0.696122 + 1.77369i 0.0341302 + 0.0869623i
\(417\) 0 0
\(418\) −2.95756 9.58819i −0.144659 0.468974i
\(419\) −2.78683 + 12.2099i −0.136146 + 0.596493i 0.860115 + 0.510099i \(0.170391\pi\)
−0.996261 + 0.0863937i \(0.972466\pi\)
\(420\) 0 0
\(421\) 0.571227 + 2.50271i 0.0278399 + 0.121975i 0.986938 0.161098i \(-0.0515035\pi\)
−0.959099 + 0.283072i \(0.908646\pi\)
\(422\) 10.0142 5.78168i 0.487482 0.281448i
\(423\) 0 0
\(424\) 39.1723 + 12.0830i 1.90237 + 0.586804i
\(425\) −0.632100 8.43479i −0.0306614 0.409147i
\(426\) 0 0
\(427\) −19.5750 + 18.1171i −0.947302 + 0.876749i
\(428\) 28.4045 22.6518i 1.37298 1.09492i
\(429\) 0 0
\(430\) −1.51531 10.0534i −0.0730748 0.484819i
\(431\) 22.5961 + 33.1424i 1.08842 + 1.59641i 0.757601 + 0.652718i \(0.226371\pi\)
0.330816 + 0.943695i \(0.392676\pi\)
\(432\) 0 0
\(433\) 11.9382 + 24.7899i 0.573713 + 1.19133i 0.962822 + 0.270135i \(0.0870684\pi\)
−0.389110 + 0.921191i \(0.627217\pi\)
\(434\) 13.8613 11.0255i 0.665364 0.529240i
\(435\) 0 0
\(436\) −19.5530 13.3310i −0.936421 0.638441i
\(437\) 35.4293 + 32.8736i 1.69481 + 1.57256i
\(438\) 0 0
\(439\) −37.4380 14.6933i −1.78682 0.701274i −0.996013 0.0892056i \(-0.971567\pi\)
−0.790805 0.612069i \(-0.790338\pi\)
\(440\) 4.92679 0.234876
\(441\) 0 0
\(442\) −9.46909 −0.450399
\(443\) −13.1010 5.14177i −0.622448 0.244293i 0.0330932 0.999452i \(-0.489464\pi\)
−0.655541 + 0.755159i \(0.727559\pi\)
\(444\) 0 0
\(445\) −6.72915 6.24374i −0.318992 0.295981i
\(446\) −17.5608 11.9728i −0.831528 0.566926i
\(447\) 0 0
\(448\) −22.8310 18.2542i −1.07866 0.862432i
\(449\) 4.22605 + 8.77548i 0.199439 + 0.414140i 0.976570 0.215199i \(-0.0690400\pi\)
−0.777131 + 0.629339i \(0.783326\pi\)
\(450\) 0 0
\(451\) 1.42237 + 2.08624i 0.0669770 + 0.0982372i
\(452\) 7.03101 + 46.6477i 0.330711 + 2.19412i
\(453\) 0 0
\(454\) −26.2410 + 20.9265i −1.23155 + 0.982129i
\(455\) 0.249215 + 3.38273i 0.0116834 + 0.158585i
\(456\) 0 0
\(457\) −1.07114 14.2933i −0.0501057 0.668614i −0.964550 0.263901i \(-0.914991\pi\)
0.914444 0.404712i \(-0.132628\pi\)
\(458\) −41.4185 12.7759i −1.93536 0.596979i
\(459\) 0 0
\(460\) −45.0078 + 25.9853i −2.09850 + 1.21157i
\(461\) 5.71927 + 25.0577i 0.266373 + 1.16706i 0.914198 + 0.405267i \(0.132821\pi\)
−0.647826 + 0.761789i \(0.724321\pi\)
\(462\) 0 0
\(463\) −1.45321 + 6.36694i −0.0675365 + 0.295897i −0.997405 0.0719954i \(-0.977063\pi\)
0.929868 + 0.367892i \(0.119920\pi\)
\(464\) −2.79860 9.07282i −0.129922 0.421195i
\(465\) 0 0
\(466\) −9.29327 23.6789i −0.430503 1.09690i
\(467\) −15.0319 + 4.63672i −0.695592 + 0.214562i −0.622335 0.782751i \(-0.713816\pi\)
−0.0732575 + 0.997313i \(0.523340\pi\)
\(468\) 0 0
\(469\) 26.5716 + 15.3858i 1.22696 + 0.710450i
\(470\) −15.1796 + 3.46464i −0.700183 + 0.159812i
\(471\) 0 0
\(472\) −6.33933 3.66001i −0.291791 0.168466i
\(473\) −0.435396 + 1.41152i −0.0200195 + 0.0649018i
\(474\) 0 0
\(475\) 7.30455 + 5.82519i 0.335156 + 0.267278i
\(476\) 49.2899 28.3748i 2.25920 1.30056i
\(477\) 0 0
\(478\) −36.5620 + 33.9246i −1.67231 + 1.55168i
\(479\) 28.4563 4.28910i 1.30020 0.195974i 0.537798 0.843074i \(-0.319256\pi\)
0.762406 + 0.647100i \(0.224018\pi\)
\(480\) 0 0
\(481\) −0.336018 + 2.22934i −0.0153211 + 0.101649i
\(482\) 46.0016 22.1532i 2.09531 1.00905i
\(483\) 0 0
\(484\) 35.0660 + 16.8869i 1.59391 + 0.767585i
\(485\) −8.57855 + 12.5824i −0.389532 + 0.571338i
\(486\) 0 0
\(487\) 0.958609 12.7918i 0.0434387 0.579650i −0.932438 0.361329i \(-0.882323\pi\)
0.975877 0.218321i \(-0.0700579\pi\)
\(488\) −14.7539 + 37.5922i −0.667876 + 1.70172i
\(489\) 0 0
\(490\) −17.6467 26.0236i −0.797196 1.17563i
\(491\) 13.5607i 0.611987i 0.952034 + 0.305994i \(0.0989886\pi\)
−0.952034 + 0.305994i \(0.901011\pi\)
\(492\) 0 0
\(493\) −25.2927 1.89543i −1.13913 0.0853657i
\(494\) 7.11406 7.66714i 0.320077 0.344961i
\(495\) 0 0
\(496\) 2.66425 5.53238i 0.119629 0.248411i
\(497\) −9.24172 + 40.2568i −0.414548 + 1.80576i
\(498\) 0 0
\(499\) −6.55494 0.987999i −0.293440 0.0442289i 0.000672682 1.00000i \(-0.499786\pi\)
−0.294112 + 0.955771i \(0.595024\pi\)
\(500\) −36.9574 + 25.1971i −1.65278 + 1.12685i
\(501\) 0 0
\(502\) 5.86510 + 6.32108i 0.261772 + 0.282123i
\(503\) −14.0917 17.6704i −0.628316 0.787883i 0.361172 0.932499i \(-0.382377\pi\)
−0.989488 + 0.144616i \(0.953805\pi\)
\(504\) 0 0
\(505\) −21.8650 + 27.4178i −0.972979 + 1.22008i
\(506\) 11.6210 0.870872i 0.516615 0.0387150i
\(507\) 0 0
\(508\) 16.2613 28.1654i 0.721480 1.24964i
\(509\) 8.18340 + 14.1741i 0.362723 + 0.628254i 0.988408 0.151821i \(-0.0485139\pi\)
−0.625685 + 0.780076i \(0.715181\pi\)
\(510\) 0 0
\(511\) −8.50396 21.7483i −0.376193 0.962087i
\(512\) −23.0465 5.26021i −1.01852 0.232471i
\(513\) 0 0
\(514\) 22.7233 8.91823i 1.00228 0.393366i
\(515\) −17.1614 + 6.73536i −0.756222 + 0.296795i
\(516\) 0 0
\(517\) 2.20542 + 0.503373i 0.0969943 + 0.0221383i
\(518\) −7.61078 19.4640i −0.334399 0.855201i
\(519\) 0 0
\(520\) 2.56779 + 4.44755i 0.112605 + 0.195038i
\(521\) 4.55691 7.89280i 0.199642 0.345790i −0.748770 0.662829i \(-0.769355\pi\)
0.948412 + 0.317040i \(0.102689\pi\)
\(522\) 0 0
\(523\) −1.57530 + 0.118053i −0.0688831 + 0.00516208i −0.109127 0.994028i \(-0.534806\pi\)
0.0402439 + 0.999190i \(0.487186\pi\)
\(524\) −6.92189 + 8.67978i −0.302384 + 0.379178i
\(525\) 0 0
\(526\) −5.94259 7.45178i −0.259109 0.324913i
\(527\) −11.1572 12.0246i −0.486014 0.523799i
\(528\) 0 0
\(529\) −27.3753 + 18.6641i −1.19023 + 0.811484i
\(530\) −45.4528 6.85090i −1.97434 0.297584i
\(531\) 0 0
\(532\) −14.0561 + 61.2279i −0.609407 + 2.65457i
\(533\) −1.14198 + 2.37134i −0.0494646 + 0.102714i
\(534\) 0 0
\(535\) −12.6526 + 13.6362i −0.547019 + 0.589546i
\(536\) 46.3590 + 3.47413i 2.00240 + 0.150059i
\(537\) 0 0
\(538\) 16.1939i 0.698167i
\(539\) 0.669475 + 4.51891i 0.0288363 + 0.194643i
\(540\) 0 0
\(541\) 13.8278 35.2327i 0.594505 1.51477i −0.243942 0.969790i \(-0.578441\pi\)
0.838446 0.544984i \(-0.183464\pi\)
\(542\) −4.07673 + 54.4002i −0.175111 + 2.33669i
\(543\) 0 0
\(544\) −9.21503 + 13.5160i −0.395091 + 0.579492i
\(545\) 10.9170 + 5.25736i 0.467634 + 0.225200i
\(546\) 0 0
\(547\) 24.3589 11.7306i 1.04151 0.501566i 0.166690 0.986009i \(-0.446692\pi\)
0.874823 + 0.484443i \(0.160978\pi\)
\(548\) 1.30676 8.66981i 0.0558222 0.370356i
\(549\) 0 0
\(550\) 2.22758 0.335754i 0.0949844 0.0143166i
\(551\) 20.5370 19.0555i 0.874904 0.811793i
\(552\) 0 0
\(553\) 21.1172 12.1566i 0.897994 0.516949i
\(554\) 15.9837 + 12.7465i 0.679080 + 0.541549i
\(555\) 0 0
\(556\) −24.2871 + 78.7368i −1.03000 + 3.33918i
\(557\) −17.8120 10.2837i −0.754717 0.435736i 0.0726790 0.997355i \(-0.476845\pi\)
−0.827396 + 0.561620i \(0.810178\pi\)
\(558\) 0 0
\(559\) −1.50114 + 0.342626i −0.0634915 + 0.0144915i
\(560\) −9.43363 5.46237i −0.398644 0.230827i
\(561\) 0 0
\(562\) 39.5714 12.2062i 1.66922 0.514886i
\(563\) −8.44139 21.5083i −0.355762 0.906468i −0.990965 0.134122i \(-0.957179\pi\)
0.635203 0.772346i \(-0.280917\pi\)
\(564\) 0 0
\(565\) −7.11959 23.0812i −0.299524 0.971032i
\(566\) −17.1839 + 75.2875i −0.722292 + 3.16457i
\(567\) 0 0
\(568\) 13.9158 + 60.9693i 0.583895 + 2.55821i
\(569\) −12.6638 + 7.31147i −0.530895 + 0.306513i −0.741381 0.671084i \(-0.765829\pi\)
0.210486 + 0.977597i \(0.432495\pi\)
\(570\) 0 0
\(571\) 24.5887 + 7.58460i 1.02900 + 0.317406i 0.762885 0.646535i \(-0.223782\pi\)
0.266119 + 0.963940i \(0.414259\pi\)
\(572\) −0.122111 1.62946i −0.00510571 0.0681310i
\(573\) 0 0
\(574\) −1.79263 24.3323i −0.0748228 1.01561i
\(575\) −8.48359 + 6.76544i −0.353790 + 0.282138i
\(576\) 0 0
\(577\) 5.85704 + 38.8589i 0.243832 + 1.61772i 0.690717 + 0.723126i \(0.257295\pi\)
−0.446885 + 0.894591i \(0.647467\pi\)
\(578\) −22.9703 33.6912i −0.955437 1.40137i
\(579\) 0 0
\(580\) 13.0709 + 27.1419i 0.542738 + 1.12701i
\(581\) −19.8369 15.8603i −0.822972 0.657996i
\(582\) 0 0
\(583\) 5.51791 + 3.76205i 0.228529 + 0.155808i
\(584\) −25.9180 24.0484i −1.07249 0.995129i
\(585\) 0 0
\(586\) −32.2426 12.6543i −1.33193 0.522744i
\(587\) −28.0801 −1.15899 −0.579495 0.814976i \(-0.696750\pi\)
−0.579495 + 0.814976i \(0.696750\pi\)
\(588\) 0 0
\(589\) 18.1186 0.746565
\(590\) 7.64059 + 2.99871i 0.314558 + 0.123455i
\(591\) 0 0
\(592\) −5.31141 4.92827i −0.218297 0.202550i
\(593\) 21.7849 + 14.8527i 0.894598 + 0.609927i 0.920931 0.389727i \(-0.127430\pi\)
−0.0263324 + 0.999653i \(0.508383\pi\)
\(594\) 0 0
\(595\) −22.7901 + 18.1276i −0.934304 + 0.743158i
\(596\) −18.9121 39.2713i −0.774668 1.60861i
\(597\) 0 0
\(598\) 6.84289 + 10.0367i 0.279827 + 0.410430i
\(599\) −2.15673 14.3089i −0.0881215 0.584648i −0.988695 0.149943i \(-0.952091\pi\)
0.900573 0.434704i \(-0.143147\pi\)
\(600\) 0 0
\(601\) 17.2316 13.7417i 0.702890 0.560536i −0.205502 0.978657i \(-0.565883\pi\)
0.908391 + 0.418121i \(0.137311\pi\)
\(602\) 10.4753 9.69510i 0.426940 0.395143i
\(603\) 0 0
\(604\) −5.97456 79.7249i −0.243101 3.24396i
\(605\) −19.0426 5.87385i −0.774190 0.238806i
\(606\) 0 0
\(607\) 20.0654 11.5848i 0.814429 0.470211i −0.0340628 0.999420i \(-0.510845\pi\)
0.848491 + 0.529209i \(0.177511\pi\)
\(608\) −4.02071 17.6159i −0.163061 0.714418i
\(609\) 0 0
\(610\) 10.0763 44.1472i 0.407978 1.78747i
\(611\) 0.695034 + 2.25324i 0.0281181 + 0.0911565i
\(612\) 0 0
\(613\) 1.46128 + 3.72327i 0.0590204 + 0.150381i 0.957342 0.288957i \(-0.0933083\pi\)
−0.898322 + 0.439338i \(0.855213\pi\)
\(614\) −11.8853 + 3.66612i −0.479651 + 0.147953i
\(615\) 0 0
\(616\) 3.88908 + 5.71970i 0.156696 + 0.230453i
\(617\) 15.7453 3.59377i 0.633884 0.144680i 0.106508 0.994312i \(-0.466033\pi\)
0.527376 + 0.849632i \(0.323176\pi\)
\(618\) 0 0
\(619\) −18.0870 10.4425i −0.726977 0.419720i 0.0903385 0.995911i \(-0.471205\pi\)
−0.817315 + 0.576191i \(0.804538\pi\)
\(620\) −5.74270 + 18.6174i −0.230632 + 0.747692i
\(621\) 0 0
\(622\) −5.32205 4.24419i −0.213395 0.170177i
\(623\) 1.93678 12.7408i 0.0775956 0.510448i
\(624\) 0 0
\(625\) 11.4802 10.6521i 0.459210 0.426085i
\(626\) −41.9413 + 6.32163i −1.67631 + 0.252663i
\(627\) 0 0
\(628\) −13.2020 + 87.5893i −0.526816 + 3.49519i
\(629\) −17.4388 + 8.39810i −0.695332 + 0.334854i
\(630\) 0 0
\(631\) 31.5757 + 15.2061i 1.25701 + 0.605343i 0.939382 0.342872i \(-0.111400\pi\)
0.317627 + 0.948216i \(0.397114\pi\)
\(632\) 20.7822 30.4819i 0.826672 1.21251i
\(633\) 0 0
\(634\) 0.577630 7.70794i 0.0229406 0.306122i
\(635\) −6.08373 + 15.5011i −0.241426 + 0.615142i
\(636\) 0 0
\(637\) −3.73042 + 2.95956i −0.147805 + 0.117262i
\(638\) 6.75512i 0.267438i
\(639\) 0 0
\(640\) 38.9605 + 2.91968i 1.54005 + 0.115411i
\(641\) 18.0974 19.5044i 0.714806 0.770377i −0.266292 0.963892i \(-0.585798\pi\)
0.981097 + 0.193515i \(0.0619889\pi\)
\(642\) 0 0
\(643\) −5.79296 + 12.0292i −0.228452 + 0.474386i −0.983412 0.181385i \(-0.941942\pi\)
0.754960 + 0.655771i \(0.227656\pi\)
\(644\) −65.6952 31.7392i −2.58876 1.25070i
\(645\) 0 0
\(646\) 88.7922 + 13.3833i 3.49348 + 0.526558i
\(647\) 39.3133 26.8034i 1.54557 1.05375i 0.573454 0.819238i \(-0.305603\pi\)
0.972113 0.234512i \(-0.0753492\pi\)
\(648\) 0 0
\(649\) −0.811122 0.874182i −0.0318393 0.0343147i
\(650\) 1.46409 + 1.83591i 0.0574262 + 0.0720102i
\(651\) 0 0
\(652\) 43.4621 54.4998i 1.70211 2.13438i
\(653\) −3.16428 + 0.237130i −0.123828 + 0.00927961i −0.136500 0.990640i \(-0.543585\pi\)
0.0126721 + 0.999920i \(0.495966\pi\)
\(654\) 0 0
\(655\) 2.84218 4.92280i 0.111053 0.192350i
\(656\) −4.22937 7.32549i −0.165129 0.286012i
\(657\) 0 0
\(658\) −16.0046 14.8877i −0.623925 0.580382i
\(659\) 22.7243 + 5.18667i 0.885213 + 0.202044i 0.640874 0.767646i \(-0.278572\pi\)
0.244338 + 0.969690i \(0.421429\pi\)
\(660\) 0 0
\(661\) −2.60493 + 1.02236i −0.101320 + 0.0397652i −0.415460 0.909612i \(-0.636379\pi\)
0.314140 + 0.949377i \(0.398284\pi\)
\(662\) 40.5491 15.9143i 1.57598 0.618528i
\(663\) 0 0
\(664\) −37.4901 8.55686i −1.45490 0.332071i
\(665\) 2.44413 32.0723i 0.0947792 1.24371i
\(666\) 0 0
\(667\) 16.2689 + 28.1785i 0.629933 + 1.09108i
\(668\) 28.5097 49.3802i 1.10307 1.91058i
\(669\) 0 0
\(670\) −51.9826 + 3.89555i −2.00826 + 0.150498i
\(671\) −4.10196 + 5.14369i −0.158354 + 0.198570i
\(672\) 0 0
\(673\) −2.74477 3.44183i −0.105803 0.132673i 0.726111 0.687578i \(-0.241326\pi\)
−0.831914 + 0.554905i \(0.812755\pi\)
\(674\) 23.2456 + 25.0528i 0.895386 + 0.964996i
\(675\) 0 0
\(676\) −38.1276 + 25.9950i −1.46645 + 0.999807i
\(677\) 36.6933 + 5.53062i 1.41024 + 0.212559i 0.809609 0.586970i \(-0.199679\pi\)
0.600628 + 0.799529i \(0.294917\pi\)
\(678\) 0 0
\(679\) −21.3791 0.0269368i −0.820455 0.00103374i
\(680\) −19.1301 + 39.7241i −0.733607 + 1.52335i
\(681\) 0 0
\(682\) 2.97150 3.20251i 0.113785 0.122631i
\(683\) 18.0839 + 1.35520i 0.691961 + 0.0518553i 0.416069 0.909333i \(-0.363408\pi\)
0.275892 + 0.961189i \(0.411027\pi\)
\(684\) 0 0
\(685\) 4.48924i 0.171525i
\(686\) 16.2820 41.0291i 0.621648 1.56650i
\(687\) 0 0
\(688\) 1.80788 4.60640i 0.0689247 0.175617i
\(689\) −0.520224 + 6.94191i −0.0198190 + 0.264466i
\(690\) 0 0
\(691\) 3.01327 4.41965i 0.114630 0.168131i −0.764636 0.644462i \(-0.777081\pi\)
0.879266 + 0.476331i \(0.158034\pi\)
\(692\) 8.18510 + 3.94174i 0.311151 + 0.149842i
\(693\) 0 0
\(694\) −26.7918 + 12.9023i −1.01700 + 0.489763i
\(695\) 6.28795 41.7178i 0.238515 1.58245i
\(696\) 0 0
\(697\) −22.3440 + 3.36782i −0.846339 + 0.127565i
\(698\) 22.6316 20.9990i 0.856618 0.794825i
\(699\) 0 0
\(700\) −13.1225 5.16929i −0.495984 0.195381i
\(701\) −21.0842 16.8141i −0.796338 0.635059i 0.138408 0.990375i \(-0.455802\pi\)
−0.934746 + 0.355317i \(0.884373\pi\)
\(702\) 0 0
\(703\) 6.30172 20.4297i 0.237674 0.770520i
\(704\) −6.24426 3.60513i −0.235339 0.135873i
\(705\) 0 0
\(706\) 61.5181 14.0411i 2.31526 0.528444i
\(707\) −49.0901 3.74100i −1.84622 0.140695i
\(708\) 0 0
\(709\) −31.3445 + 9.66851i −1.17717 + 0.363108i −0.820788 0.571233i \(-0.806465\pi\)
−0.356380 + 0.934341i \(0.615989\pi\)
\(710\) −25.6189 65.2759i −0.961460 2.44976i
\(711\) 0 0
\(712\) −5.75128 18.6452i −0.215538 0.698759i
\(713\) −4.68255 + 20.5156i −0.175363 + 0.768314i
\(714\) 0 0
\(715\) 0.186172 + 0.815675i 0.00696245 + 0.0305045i
\(716\) 9.12377 5.26761i 0.340971 0.196860i
\(717\) 0 0
\(718\) 19.2940 + 5.95141i 0.720046 + 0.222105i
\(719\) 0.716547 + 9.56166i 0.0267227 + 0.356590i 0.994497 + 0.104769i \(0.0334103\pi\)
−0.967774 + 0.251821i \(0.918971\pi\)
\(720\) 0 0
\(721\) −21.3661 14.6066i −0.795716 0.543980i
\(722\) −42.1401 + 33.6056i −1.56829 + 1.25067i
\(723\) 0 0
\(724\) 8.31947 + 55.1961i 0.309191 + 2.05135i
\(725\) 3.54320 + 5.19692i 0.131591 + 0.193009i
\(726\) 0 0
\(727\) 6.28579 + 13.0526i 0.233127 + 0.484093i 0.984410 0.175887i \(-0.0562792\pi\)
−0.751284 + 0.659980i \(0.770565\pi\)
\(728\) −3.13638 + 6.49183i −0.116242 + 0.240603i
\(729\) 0 0
\(730\) 32.7563 + 22.3329i 1.21237 + 0.826578i
\(731\) −9.69032 8.99130i −0.358410 0.332555i
\(732\) 0 0
\(733\) 8.26480 + 3.24370i 0.305267 + 0.119809i 0.513030 0.858371i \(-0.328523\pi\)
−0.207763 + 0.978179i \(0.566618\pi\)
\(734\) −10.6985 −0.394889
\(735\) 0 0
\(736\) 20.9854 0.773532
\(737\) 7.05010 + 2.76696i 0.259694 + 0.101922i
\(738\) 0 0
\(739\) 12.6949 + 11.7791i 0.466988 + 0.433302i 0.878240 0.478220i \(-0.158718\pi\)
−0.411252 + 0.911522i \(0.634908\pi\)
\(740\) 18.9947 + 12.9504i 0.698260 + 0.476066i
\(741\) 0 0
\(742\) −27.9257 58.1758i −1.02519 2.13570i
\(743\) −8.23846 17.1073i −0.302240 0.627608i 0.693434 0.720520i \(-0.256097\pi\)
−0.995674 + 0.0929122i \(0.970382\pi\)
\(744\) 0 0
\(745\) 12.5721 + 18.4398i 0.460604 + 0.675583i
\(746\) 9.25192 + 61.3824i 0.338737 + 2.24737i
\(747\) 0 0
\(748\) 10.9680 8.74667i 0.401029 0.319810i
\(749\) −25.8184 3.92478i −0.943385 0.143408i
\(750\) 0 0
\(751\) 0.437249 + 5.83469i 0.0159555 + 0.212911i 0.999483 + 0.0321523i \(0.0102362\pi\)
−0.983528 + 0.180758i \(0.942145\pi\)
\(752\) −7.24152 2.23371i −0.264071 0.0814552i
\(753\) 0 0
\(754\) 6.09803 3.52070i 0.222077 0.128216i
\(755\) 9.10891 + 39.9088i 0.331507 + 1.45243i
\(756\) 0 0
\(757\) 7.60558 33.3222i 0.276429 1.21112i −0.625843 0.779949i \(-0.715245\pi\)
0.902272 0.431167i \(-0.141898\pi\)
\(758\) 11.4734 + 37.1958i 0.416732 + 1.35101i
\(759\) 0 0
\(760\) −17.7923 45.3341i −0.645396 1.64444i
\(761\) −7.35231 + 2.26789i −0.266521 + 0.0822108i −0.425135 0.905130i \(-0.639774\pi\)
0.158614 + 0.987341i \(0.449297\pi\)
\(762\) 0 0
\(763\) 2.51414 + 16.8240i 0.0910178 + 0.609070i
\(764\) 24.2559 5.53624i 0.877546 0.200294i
\(765\) 0 0
\(766\) 40.5607 + 23.4177i 1.46552 + 0.846117i
\(767\) 0.366399 1.18784i 0.0132299 0.0428903i
\(768\) 0 0
\(769\) −19.9737 15.9285i −0.720272 0.574397i 0.193269 0.981146i \(-0.438091\pi\)
−0.913540 + 0.406749i \(0.866663\pi\)
\(770\) −5.26802 5.69194i −0.189846 0.205123i
\(771\) 0 0
\(772\) 18.4642 17.1322i 0.664539 0.616602i
\(773\) −37.6301 + 5.67182i −1.35346 + 0.204001i −0.785401 0.618987i \(-0.787543\pi\)
−0.568058 + 0.822988i \(0.692305\pi\)
\(774\) 0 0
\(775\) −0.606281 + 4.02241i −0.0217782 + 0.144489i
\(776\) −29.1640 + 14.0446i −1.04693 + 0.504173i
\(777\) 0 0
\(778\) −15.2853 7.36102i −0.548005 0.263905i
\(779\) 14.0600 20.6222i 0.503750 0.738866i
\(780\) 0 0
\(781\) −0.761357 + 10.1596i −0.0272435 + 0.363539i
\(782\) −38.1011 + 97.0800i −1.36249 + 3.47157i
\(783\) 0 0
\(784\) −1.10519 15.2637i −0.0394709 0.545133i
\(785\) 45.3539i 1.61875i
\(786\) 0 0
\(787\) 13.7268 + 1.02868i 0.489307 + 0.0366685i 0.317100 0.948392i \(-0.397291\pi\)
0.172208 + 0.985061i \(0.444910\pi\)
\(788\) 11.3934 12.2791i