Properties

Label 441.2.bg.a.395.17
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 395.17
Character \(\chi\) \(=\) 441.395
Dual form 441.2.bg.a.278.17

$q$-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 0.981129 0.193352i \(-0.0619360\pi\)
0.587706 + 0.809075i \(0.300031\pi\)
\(3\) 0 0
\(4\) 2.69816 + 2.50352i 1.34908 + 1.25176i
\(5\) 1.55712 + 1.06163i 0.696367 + 0.474775i 0.859042 0.511904i \(-0.171060\pi\)
−0.162675 + 0.986680i \(0.552012\pi\)
\(6\) 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 0.998697 0.0510342i \(-0.0162517\pi\)
−0.969370 + 0.245604i \(0.921014\pi\)
\(12\) 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 −0.468677 0.883369i \(-0.655269\pi\)
−0.884859 + 0.465859i \(0.845746\pi\)
\(18\) 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 \(0.190109\pi\)
−0.366415 + 0.930451i \(0.619415\pi\)
\(24\) 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 0.189491 0.981883i \(-0.439316\pi\)
0.596748 + 0.802429i \(0.296459\pi\)
\(30\) 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 −0.141403 0.989952i \(-0.545161\pi\)
0.685813 + 0.727778i \(0.259447\pi\)
\(42\) 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 −0.808275 0.588805i \(-0.799599\pi\)
0.992997 + 0.118142i \(0.0376938\pi\)
\(48\) 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 \(-0.513824\pi\)
0.999508 0.0313660i \(-0.00998575\pi\)
\(54\) 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 −0.657601 0.753366i \(-0.728429\pi\)
0.461040 + 0.887379i \(0.347476\pi\)
\(60\) 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 0.986948 0.161042i \(-0.0514855\pi\)
0.819335 + 0.573314i \(0.194343\pi\)
\(72\) 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 −0.993008 0.118044i \(-0.962338\pi\)
0.336050 + 0.941844i \(0.390909\pi\)
\(84\) 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 −0.111283 0.993789i \(-0.535496\pi\)
−0.399263 + 0.916836i \(0.630734\pi\)
\(90\) 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 \(0.400406\pi\)
−0.446172 + 0.894947i \(0.647213\pi\)
\(102\) 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 \(0.205935\pi\)
−0.940137 + 0.340798i \(0.889303\pi\)
\(108\) 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 0.0261316 0.999659i \(-0.491681\pi\)
−0.968780 + 0.247921i \(0.920253\pi\)
\(114\) 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 \(-0.981745\pi\)
0.978663 0.205474i \(-0.0658737\pi\)
\(132\) 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 0.879272 0.476320i \(-0.158030\pi\)
−0.764628 + 0.644472i \(0.777077\pi\)
\(138\) 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 0.771025 0.636805i \(-0.219744\pi\)
0.132064 + 0.991241i \(0.457839\pi\)
\(150\) 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 \(0.133157\pi\)
−0.647021 + 0.762472i \(0.723986\pi\)
\(168\) 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 −0.383114 0.923701i \(-0.625148\pi\)
0.203796 + 0.979013i \(0.434672\pi\)
\(174\) 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 −0.981620 0.190848i \(-0.938876\pi\)
0.918561 + 0.395280i \(0.129352\pi\)
\(180\) 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 −0.938911 0.344160i \(-0.888164\pi\)
0.663393 + 0.748272i \(0.269116\pi\)
\(192\) 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 \(0.0518332\pi\)
−0.986771 + 0.162120i \(0.948167\pi\)
\(198\) 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 −0.999303 0.0373231i \(-0.988117\pi\)
0.531974 + 0.846760i \(0.321450\pi\)
\(228\) 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 0.449015 0.893524i \(-0.351775\pi\)
−0.924581 + 0.380987i \(0.875584\pi\)
\(234\) 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 \(0.379494\pi\)
−0.956913 + 0.290374i \(0.906220\pi\)
\(240\) 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 0.533918 0.845536i \(-0.320719\pi\)
−0.328174 + 0.944617i \(0.606433\pi\)
\(252\) 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 −0.410375 0.911917i \(-0.634602\pi\)
0.878700 + 0.477375i \(0.158412\pi\)
\(258\) 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 0.389411 0.921064i \(-0.372679\pi\)
−0.602960 + 0.797772i \(0.706012\pi\)
\(264\) 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 0.835013 0.550230i \(-0.185460\pi\)
−0.986359 + 0.164606i \(0.947365\pi\)
\(270\) 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 −0.128051 0.991768i \(-0.540872\pi\)
0.938408 + 0.345530i \(0.112301\pi\)
\(282\) 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 \(-0.639549\pi\)
−0.424496 + 0.905430i \(0.639549\pi\)
\(294\) 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 0.216409 0.976303i \(-0.430565\pi\)
−0.371165 + 0.928567i \(0.621042\pi\)
\(312\) 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 0.924757 0.380558i \(-0.124268\pi\)
−0.978446 + 0.206503i \(0.933792\pi\)
\(318\) 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 −0.918504 0.395411i \(-0.870602\pi\)
0.462945 + 0.886387i \(0.346793\pi\)
\(348\) 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 0.182363 0.983231i \(-0.441626\pi\)
0.981889 + 0.189458i \(0.0606732\pi\)
\(354\) 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 0.150089 0.988673i \(-0.452044\pi\)
0.295766 + 0.955260i \(0.404425\pi\)
\(360\) 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 0.625337 0.780355i \(-0.284962\pi\)
0.367541 + 0.930007i \(0.380200\pi\)
\(384\) 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 −0.106443 0.994319i \(-0.533946\pi\)
−0.253449 + 0.967349i \(0.581565\pi\)
\(390\) 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 \(0.458409\pi\)
−0.416745 + 0.909023i \(0.636829\pi\)
\(402\) 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 \(-0.829609\pi\)
0.996261 0.0863937i \(-0.0275343\pi\)
\(420\) 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 \(-0.773629\pi\)
−0.330816 0.943695i \(-0.607324\pi\)
\(432\) 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 0.655541 0.755159i \(-0.272441\pi\)
−0.0330932 + 0.999452i \(0.510536\pi\)
\(444\) 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 0.777131 0.629339i \(-0.216674\pi\)
−0.976570 + 0.215199i \(0.930960\pi\)
\(450\) 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 \(-0.867179\pi\)
0.647826 0.761789i \(-0.275679\pi\)
\(462\) 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 0.0732575 0.997313i \(-0.476660\pi\)
0.622335 + 0.782751i \(0.286184\pi\)
\(468\) 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 −0.762406 0.647100i \(-0.775982\pi\)
−0.537798 + 0.843074i \(0.680744\pi\)
\(480\) 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 \(-0.901011\pi\)
0.952034 0.305994i \(-0.0989886\pi\)
\(492\) 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 0.989488 0.144616i \(-0.0461948\pi\)
−0.361172 + 0.932499i \(0.617623\pi\)
\(504\) 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 0.625685 0.780076i \(-0.284819\pi\)
−0.988408 + 0.151821i \(0.951486\pi\)
\(510\) 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 −0.948412 0.317040i \(-0.897311\pi\)
0.748770 + 0.662829i \(0.230645\pi\)
\(522\) 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 0.827396 0.561620i \(-0.189822\pi\)
−0.0726790 + 0.997355i \(0.523155\pi\)
\(558\) 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 \(0.0428214\pi\)
−0.635203 + 0.772346i \(0.719083\pi\)
\(564\) 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 −0.210486 0.977597i \(-0.567505\pi\)
0.741381 + 0.671084i \(0.234171\pi\)
\(570\) 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 \(-0.303250\pi\)
0.579495 + 0.814976i \(0.303250\pi\)
\(588\) 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 0.0263324 0.999653i \(-0.491617\pi\)
−0.920931 + 0.389727i \(0.872570\pi\)
\(594\) 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 \(0.0479091\pi\)
−0.900573 + 0.434704i \(0.856853\pi\)
\(600\) 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 −0.527376 0.849632i \(-0.676824\pi\)
−0.106508 + 0.994312i \(0.533967\pi\)
\(618\) 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 −0.981097 0.193515i \(-0.938011\pi\)
0.266292 + 0.963892i \(0.414202\pi\)
\(642\) 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 \(0.694397\pi\)
−0.972113 + 0.234512i \(0.924651\pi\)
\(648\) 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 −0.0126721 0.999920i \(-0.504034\pi\)
0.136500 + 0.990640i \(0.456415\pi\)
\(654\) 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 −0.244338 0.969690i \(-0.578571\pi\)
−0.640874 + 0.767646i \(0.721428\pi\)
\(660\) 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 −0.600628 0.799529i \(-0.705083\pi\)
−0.809609 + 0.586970i \(0.800321\pi\)
\(678\) 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 −0.275892 0.961189i \(-0.588973\pi\)
−0.416069 + 0.909333i \(0.636592\pi\)
\(684\) 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 0.934746 0.355317i \(-0.115627\pi\)
−0.138408 + 0.990375i \(0.544198\pi\)
\(702\) 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 \(-0.966590\pi\)
0.967774 0.251821i \(-0.0810293\pi\)
\(720\) 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 0.995674 0.0929122i \(-0.0296176\pi\)
−0.693434 + 0.720520i \(0.743903\pi\)
\(744\) 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 −0.158614 0.987341i \(-0.550703\pi\)
0.425135 + 0.905130i \(0.360226\pi\)
\(762\) 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 0.568058 0.822988i \(-0.307695\pi\)
0.785401 + 0.618987i \(0.212457\pi\)
\(774\) 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