Properties

Label 624.2.cn.f.353.4
Level $624$
Weight $2$
Character 624.353
Analytic conductor $4.983$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.cn (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.98266508613\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 312)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 353.4
Character \(\chi\) \(=\) 624.353
Dual form 624.2.cn.f.449.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.49406 + 0.876234i) q^{3} +(1.23702 + 1.23702i) q^{5} +(-0.738861 + 0.197977i) q^{7} +(1.46443 - 2.61829i) q^{9} +O(q^{10})\) \(q+(-1.49406 + 0.876234i) q^{3} +(1.23702 + 1.23702i) q^{5} +(-0.738861 + 0.197977i) q^{7} +(1.46443 - 2.61829i) q^{9} +(2.29872 + 0.615941i) q^{11} +(3.60547 - 0.0237240i) q^{13} +(-2.93209 - 0.764261i) q^{15} +(-3.05255 + 5.28717i) q^{17} +(-0.372377 - 1.38973i) q^{19} +(0.930427 - 0.943204i) q^{21} +(2.40599 + 4.16730i) q^{23} -1.93958i q^{25} +(0.106292 + 5.19507i) q^{27} +(-0.864314 + 0.499012i) q^{29} +(-4.61745 + 4.61745i) q^{31} +(-3.97414 + 1.09397i) q^{33} +(-1.15888 - 0.669082i) q^{35} +(-1.22221 + 4.56134i) q^{37} +(-5.36600 + 3.19468i) q^{39} +(-2.42071 + 9.03420i) q^{41} +(6.80661 + 3.92980i) q^{43} +(5.05039 - 1.42735i) q^{45} +(2.43647 - 2.43647i) q^{47} +(-5.55546 + 3.20745i) q^{49} +(-0.0721073 - 10.5741i) q^{51} -7.28014i q^{53} +(2.08163 + 3.60549i) q^{55} +(1.77408 + 1.75005i) q^{57} +(-1.72558 - 6.43995i) q^{59} +(-1.32559 + 2.29599i) q^{61} +(-0.563647 + 2.22448i) q^{63} +(4.48938 + 4.43068i) q^{65} +(8.12377 + 2.17676i) q^{67} +(-7.24623 - 4.11798i) q^{69} +(-0.399558 + 0.107061i) q^{71} +(10.0014 + 10.0014i) q^{73} +(1.69953 + 2.89785i) q^{75} -1.82038 q^{77} +8.40805 q^{79} +(-4.71090 - 7.66860i) q^{81} +(2.95883 + 2.95883i) q^{83} +(-10.3164 + 2.76426i) q^{85} +(0.854085 - 1.50289i) q^{87} +(-11.6548 - 3.12290i) q^{89} +(-2.65925 + 0.731330i) q^{91} +(2.85278 - 10.9447i) q^{93} +(1.25848 - 2.17976i) q^{95} +(0.595155 + 2.22115i) q^{97} +(4.97903 - 5.11672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 4q^{7} + O(q^{10}) \) \( 56q - 4q^{7} + 8q^{13} + 8q^{15} - 4q^{19} + 16q^{21} - 24q^{27} + 36q^{31} + 28q^{33} + 20q^{37} - 16q^{39} + 84q^{43} + 12q^{45} - 12q^{49} + 24q^{55} - 36q^{57} - 24q^{61} + 12q^{63} + 32q^{67} - 36q^{69} - 20q^{73} + 60q^{75} + 32q^{79} - 88q^{85} + 16q^{87} - 28q^{91} - 88q^{93} - 36q^{97} - 44q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.49406 + 0.876234i −0.862596 + 0.505894i
\(4\) 0 0
\(5\) 1.23702 + 1.23702i 0.553211 + 0.553211i 0.927366 0.374155i \(-0.122067\pi\)
−0.374155 + 0.927366i \(0.622067\pi\)
\(6\) 0 0
\(7\) −0.738861 + 0.197977i −0.279263 + 0.0748283i −0.395732 0.918366i \(-0.629509\pi\)
0.116469 + 0.993194i \(0.462842\pi\)
\(8\) 0 0
\(9\) 1.46443 2.61829i 0.488143 0.872764i
\(10\) 0 0
\(11\) 2.29872 + 0.615941i 0.693091 + 0.185713i 0.588134 0.808764i \(-0.299863\pi\)
0.104957 + 0.994477i \(0.466530\pi\)
\(12\) 0 0
\(13\) 3.60547 0.0237240i 0.999978 0.00657985i
\(14\) 0 0
\(15\) −2.93209 0.764261i −0.757063 0.197331i
\(16\) 0 0
\(17\) −3.05255 + 5.28717i −0.740352 + 1.28233i 0.211983 + 0.977273i \(0.432008\pi\)
−0.952335 + 0.305054i \(0.901326\pi\)
\(18\) 0 0
\(19\) −0.372377 1.38973i −0.0854292 0.318826i 0.909966 0.414683i \(-0.136108\pi\)
−0.995395 + 0.0958570i \(0.969441\pi\)
\(20\) 0 0
\(21\) 0.930427 0.943204i 0.203036 0.205824i
\(22\) 0 0
\(23\) 2.40599 + 4.16730i 0.501684 + 0.868942i 0.999998 + 0.00194568i \(0.000619330\pi\)
−0.498314 + 0.866997i \(0.666047\pi\)
\(24\) 0 0
\(25\) 1.93958i 0.387916i
\(26\) 0 0
\(27\) 0.106292 + 5.19507i 0.0204560 + 0.999791i
\(28\) 0 0
\(29\) −0.864314 + 0.499012i −0.160499 + 0.0926642i −0.578098 0.815967i \(-0.696205\pi\)
0.417599 + 0.908631i \(0.362872\pi\)
\(30\) 0 0
\(31\) −4.61745 + 4.61745i −0.829318 + 0.829318i −0.987422 0.158104i \(-0.949462\pi\)
0.158104 + 0.987422i \(0.449462\pi\)
\(32\) 0 0
\(33\) −3.97414 + 1.09397i −0.691808 + 0.190435i
\(34\) 0 0
\(35\) −1.15888 0.669082i −0.195887 0.113095i
\(36\) 0 0
\(37\) −1.22221 + 4.56134i −0.200930 + 0.749880i 0.789722 + 0.613465i \(0.210225\pi\)
−0.990652 + 0.136415i \(0.956442\pi\)
\(38\) 0 0
\(39\) −5.36600 + 3.19468i −0.859248 + 0.511559i
\(40\) 0 0
\(41\) −2.42071 + 9.03420i −0.378051 + 1.41090i 0.470785 + 0.882248i \(0.343971\pi\)
−0.848836 + 0.528657i \(0.822696\pi\)
\(42\) 0 0
\(43\) 6.80661 + 3.92980i 1.03800 + 0.599289i 0.919266 0.393638i \(-0.128784\pi\)
0.118733 + 0.992926i \(0.462117\pi\)
\(44\) 0 0
\(45\) 5.05039 1.42735i 0.752868 0.212776i
\(46\) 0 0
\(47\) 2.43647 2.43647i 0.355395 0.355395i −0.506717 0.862112i \(-0.669141\pi\)
0.862112 + 0.506717i \(0.169141\pi\)
\(48\) 0 0
\(49\) −5.55546 + 3.20745i −0.793637 + 0.458206i
\(50\) 0 0
\(51\) −0.0721073 10.5741i −0.0100970 1.48067i
\(52\) 0 0
\(53\) 7.28014i 1.00000i −0.866024 0.500002i \(-0.833333\pi\)
0.866024 0.500002i \(-0.166667\pi\)
\(54\) 0 0
\(55\) 2.08163 + 3.60549i 0.280687 + 0.486164i
\(56\) 0 0
\(57\) 1.77408 + 1.75005i 0.234983 + 0.231800i
\(58\) 0 0
\(59\) −1.72558 6.43995i −0.224651 0.838410i −0.982544 0.186031i \(-0.940438\pi\)
0.757893 0.652379i \(-0.226229\pi\)
\(60\) 0 0
\(61\) −1.32559 + 2.29599i −0.169724 + 0.293971i −0.938323 0.345760i \(-0.887621\pi\)
0.768599 + 0.639731i \(0.220954\pi\)
\(62\) 0 0
\(63\) −0.563647 + 2.22448i −0.0710128 + 0.280258i
\(64\) 0 0
\(65\) 4.48938 + 4.43068i 0.556839 + 0.549559i
\(66\) 0 0
\(67\) 8.12377 + 2.17676i 0.992476 + 0.265933i 0.718290 0.695744i \(-0.244925\pi\)
0.274186 + 0.961677i \(0.411592\pi\)
\(68\) 0 0
\(69\) −7.24623 4.11798i −0.872343 0.495747i
\(70\) 0 0
\(71\) −0.399558 + 0.107061i −0.0474188 + 0.0127058i −0.282450 0.959282i \(-0.591147\pi\)
0.235032 + 0.971988i \(0.424481\pi\)
\(72\) 0 0
\(73\) 10.0014 + 10.0014i 1.17057 + 1.17057i 0.982073 + 0.188501i \(0.0603630\pi\)
0.188501 + 0.982073i \(0.439637\pi\)
\(74\) 0 0
\(75\) 1.69953 + 2.89785i 0.196244 + 0.334615i
\(76\) 0 0
\(77\) −1.82038 −0.207451
\(78\) 0 0
\(79\) 8.40805 0.945979 0.472990 0.881068i \(-0.343175\pi\)
0.472990 + 0.881068i \(0.343175\pi\)
\(80\) 0 0
\(81\) −4.71090 7.66860i −0.523433 0.852067i
\(82\) 0 0
\(83\) 2.95883 + 2.95883i 0.324774 + 0.324774i 0.850595 0.525821i \(-0.176242\pi\)
−0.525821 + 0.850595i \(0.676242\pi\)
\(84\) 0 0
\(85\) −10.3164 + 2.76426i −1.11897 + 0.299826i
\(86\) 0 0
\(87\) 0.854085 1.50289i 0.0915675 0.161127i
\(88\) 0 0
\(89\) −11.6548 3.12290i −1.23541 0.331027i −0.418725 0.908113i \(-0.637523\pi\)
−0.816683 + 0.577087i \(0.804190\pi\)
\(90\) 0 0
\(91\) −2.65925 + 0.731330i −0.278765 + 0.0766642i
\(92\) 0 0
\(93\) 2.85278 10.9447i 0.295819 1.13491i
\(94\) 0 0
\(95\) 1.25848 2.17976i 0.129118 0.223638i
\(96\) 0 0
\(97\) 0.595155 + 2.22115i 0.0604288 + 0.225523i 0.989536 0.144288i \(-0.0460891\pi\)
−0.929107 + 0.369811i \(0.879422\pi\)
\(98\) 0 0
\(99\) 4.97903 5.11672i 0.500411 0.514250i
\(100\) 0 0
\(101\) −3.28558 5.69079i −0.326928 0.566255i 0.654973 0.755652i \(-0.272680\pi\)
−0.981901 + 0.189397i \(0.939347\pi\)
\(102\) 0 0
\(103\) 18.3695i 1.81000i −0.425412 0.905000i \(-0.639871\pi\)
0.425412 0.905000i \(-0.360129\pi\)
\(104\) 0 0
\(105\) 2.31771 0.0158050i 0.226186 0.00154241i
\(106\) 0 0
\(107\) −7.06155 + 4.07699i −0.682666 + 0.394137i −0.800859 0.598853i \(-0.795623\pi\)
0.118193 + 0.992991i \(0.462290\pi\)
\(108\) 0 0
\(109\) 13.3774 13.3774i 1.28133 1.28133i 0.341414 0.939913i \(-0.389094\pi\)
0.939913 0.341414i \(-0.110906\pi\)
\(110\) 0 0
\(111\) −2.17075 7.88585i −0.206038 0.748492i
\(112\) 0 0
\(113\) 1.19839 + 0.691891i 0.112735 + 0.0650876i 0.555307 0.831645i \(-0.312601\pi\)
−0.442572 + 0.896733i \(0.645934\pi\)
\(114\) 0 0
\(115\) −2.17877 + 8.13127i −0.203171 + 0.758245i
\(116\) 0 0
\(117\) 5.21784 9.47492i 0.482390 0.875957i
\(118\) 0 0
\(119\) 1.20867 4.51082i 0.110799 0.413506i
\(120\) 0 0
\(121\) −4.62154 2.66825i −0.420140 0.242568i
\(122\) 0 0
\(123\) −4.29939 15.6187i −0.387663 1.40829i
\(124\) 0 0
\(125\) 8.58438 8.58438i 0.767810 0.767810i
\(126\) 0 0
\(127\) 4.03037 2.32693i 0.357637 0.206482i −0.310406 0.950604i \(-0.600465\pi\)
0.668044 + 0.744122i \(0.267132\pi\)
\(128\) 0 0
\(129\) −13.6129 + 0.0928296i −1.19855 + 0.00817319i
\(130\) 0 0
\(131\) 16.2778i 1.42219i −0.703094 0.711097i \(-0.748199\pi\)
0.703094 0.711097i \(-0.251801\pi\)
\(132\) 0 0
\(133\) 0.550269 + 0.953095i 0.0477144 + 0.0826438i
\(134\) 0 0
\(135\) −6.29490 + 6.55787i −0.541778 + 0.564411i
\(136\) 0 0
\(137\) −1.44910 5.40813i −0.123805 0.462048i 0.875989 0.482331i \(-0.160210\pi\)
−0.999794 + 0.0202834i \(0.993543\pi\)
\(138\) 0 0
\(139\) −10.9170 + 18.9088i −0.925965 + 1.60382i −0.135964 + 0.990714i \(0.543413\pi\)
−0.790001 + 0.613106i \(0.789920\pi\)
\(140\) 0 0
\(141\) −1.50531 + 5.77514i −0.126770 + 0.486354i
\(142\) 0 0
\(143\) 8.30259 + 2.16622i 0.694298 + 0.181149i
\(144\) 0 0
\(145\) −1.68646 0.451885i −0.140053 0.0375270i
\(146\) 0 0
\(147\) 5.48971 9.65999i 0.452784 0.796743i
\(148\) 0 0
\(149\) 19.5294 5.23289i 1.59991 0.428695i 0.654896 0.755719i \(-0.272713\pi\)
0.945016 + 0.327024i \(0.106046\pi\)
\(150\) 0 0
\(151\) −9.38092 9.38092i −0.763408 0.763408i 0.213529 0.976937i \(-0.431504\pi\)
−0.976937 + 0.213529i \(0.931504\pi\)
\(152\) 0 0
\(153\) 9.37311 + 15.7351i 0.757771 + 1.27211i
\(154\) 0 0
\(155\) −11.4237 −0.917575
\(156\) 0 0
\(157\) 13.2462 1.05716 0.528582 0.848882i \(-0.322724\pi\)
0.528582 + 0.848882i \(0.322724\pi\)
\(158\) 0 0
\(159\) 6.37911 + 10.8770i 0.505896 + 0.862600i
\(160\) 0 0
\(161\) −2.60272 2.60272i −0.205123 0.205123i
\(162\) 0 0
\(163\) −4.26909 + 1.14390i −0.334381 + 0.0895970i −0.422103 0.906548i \(-0.638708\pi\)
0.0877222 + 0.996145i \(0.472041\pi\)
\(164\) 0 0
\(165\) −6.26932 3.56282i −0.488066 0.277365i
\(166\) 0 0
\(167\) −18.1775 4.87064i −1.40661 0.376901i −0.525899 0.850547i \(-0.676271\pi\)
−0.880715 + 0.473646i \(0.842938\pi\)
\(168\) 0 0
\(169\) 12.9989 0.171072i 0.999913 0.0131594i
\(170\) 0 0
\(171\) −4.18404 1.06017i −0.319961 0.0810731i
\(172\) 0 0
\(173\) 9.53096 16.5081i 0.724625 1.25509i −0.234503 0.972116i \(-0.575346\pi\)
0.959128 0.282973i \(-0.0913205\pi\)
\(174\) 0 0
\(175\) 0.383992 + 1.43308i 0.0290271 + 0.108331i
\(176\) 0 0
\(177\) 8.22102 + 8.10966i 0.617930 + 0.609559i
\(178\) 0 0
\(179\) 7.17177 + 12.4219i 0.536043 + 0.928454i 0.999112 + 0.0421314i \(0.0134148\pi\)
−0.463069 + 0.886322i \(0.653252\pi\)
\(180\) 0 0
\(181\) 8.03070i 0.596917i 0.954423 + 0.298459i \(0.0964725\pi\)
−0.954423 + 0.298459i \(0.903527\pi\)
\(182\) 0 0
\(183\) −0.0313130 4.59187i −0.00231473 0.339441i
\(184\) 0 0
\(185\) −7.15434 + 4.13056i −0.525998 + 0.303685i
\(186\) 0 0
\(187\) −10.2735 + 10.2735i −0.751276 + 0.751276i
\(188\) 0 0
\(189\) −1.10704 3.81739i −0.0805252 0.277674i
\(190\) 0 0
\(191\) −2.75509 1.59065i −0.199351 0.115096i 0.397001 0.917818i \(-0.370051\pi\)
−0.596353 + 0.802722i \(0.703384\pi\)
\(192\) 0 0
\(193\) 0.700163 2.61304i 0.0503988 0.188091i −0.936137 0.351635i \(-0.885626\pi\)
0.986536 + 0.163544i \(0.0522925\pi\)
\(194\) 0 0
\(195\) −10.5897 2.68596i −0.758345 0.192346i
\(196\) 0 0
\(197\) 1.61535 6.02855i 0.115089 0.429516i −0.884205 0.467099i \(-0.845299\pi\)
0.999294 + 0.0375827i \(0.0119658\pi\)
\(198\) 0 0
\(199\) 23.2863 + 13.4443i 1.65072 + 0.953044i 0.976777 + 0.214261i \(0.0687342\pi\)
0.673943 + 0.738783i \(0.264599\pi\)
\(200\) 0 0
\(201\) −14.0447 + 3.86612i −0.990640 + 0.272695i
\(202\) 0 0
\(203\) 0.539814 0.539814i 0.0378875 0.0378875i
\(204\) 0 0
\(205\) −14.1699 + 8.18100i −0.989669 + 0.571386i
\(206\) 0 0
\(207\) 14.4346 0.196875i 1.00327 0.0136838i
\(208\) 0 0
\(209\) 3.42396i 0.236841i
\(210\) 0 0
\(211\) 1.53625 + 2.66086i 0.105760 + 0.183181i 0.914048 0.405605i \(-0.132939\pi\)
−0.808289 + 0.588786i \(0.799606\pi\)
\(212\) 0 0
\(213\) 0.503153 0.510062i 0.0344755 0.0349489i
\(214\) 0 0
\(215\) 3.55866 + 13.2811i 0.242699 + 0.905764i
\(216\) 0 0
\(217\) 2.49750 4.32580i 0.169541 0.293654i
\(218\) 0 0
\(219\) −23.7062 6.17912i −1.60192 0.417546i
\(220\) 0 0
\(221\) −10.8805 + 19.1352i −0.731898 + 1.28717i
\(222\) 0 0
\(223\) −19.1565 5.13296i −1.28281 0.343728i −0.447886 0.894091i \(-0.647823\pi\)
−0.834926 + 0.550362i \(0.814490\pi\)
\(224\) 0 0
\(225\) −5.07839 2.84038i −0.338559 0.189358i
\(226\) 0 0
\(227\) 17.9885 4.82001i 1.19394 0.319915i 0.393498 0.919325i \(-0.371265\pi\)
0.800442 + 0.599410i \(0.204598\pi\)
\(228\) 0 0
\(229\) −2.35000 2.35000i −0.155292 0.155292i 0.625185 0.780477i \(-0.285024\pi\)
−0.780477 + 0.625185i \(0.785024\pi\)
\(230\) 0 0
\(231\) 2.71975 1.59508i 0.178947 0.104948i
\(232\) 0 0
\(233\) 13.2959 0.871042 0.435521 0.900178i \(-0.356564\pi\)
0.435521 + 0.900178i \(0.356564\pi\)
\(234\) 0 0
\(235\) 6.02790 0.393217
\(236\) 0 0
\(237\) −12.5621 + 7.36742i −0.815998 + 0.478565i
\(238\) 0 0
\(239\) 4.96197 + 4.96197i 0.320963 + 0.320963i 0.849137 0.528173i \(-0.177123\pi\)
−0.528173 + 0.849137i \(0.677123\pi\)
\(240\) 0 0
\(241\) −15.1218 + 4.05187i −0.974079 + 0.261004i −0.710549 0.703648i \(-0.751553\pi\)
−0.263530 + 0.964651i \(0.584887\pi\)
\(242\) 0 0
\(243\) 13.7579 + 7.32950i 0.882567 + 0.470187i
\(244\) 0 0
\(245\) −10.8399 2.90453i −0.692533 0.185564i
\(246\) 0 0
\(247\) −1.37557 5.00180i −0.0875251 0.318257i
\(248\) 0 0
\(249\) −7.01329 1.82804i −0.444449 0.115847i
\(250\) 0 0
\(251\) −12.5280 + 21.6991i −0.790760 + 1.36964i 0.134736 + 0.990881i \(0.456981\pi\)
−0.925497 + 0.378756i \(0.876352\pi\)
\(252\) 0 0
\(253\) 2.96390 + 11.0614i 0.186339 + 0.695425i
\(254\) 0 0
\(255\) 12.9911 13.1695i 0.813536 0.824708i
\(256\) 0 0
\(257\) 10.2962 + 17.8336i 0.642262 + 1.11243i 0.984927 + 0.172972i \(0.0553371\pi\)
−0.342665 + 0.939458i \(0.611330\pi\)
\(258\) 0 0
\(259\) 3.61216i 0.224449i
\(260\) 0 0
\(261\) 0.0408327 + 2.99379i 0.00252748 + 0.185311i
\(262\) 0 0
\(263\) −11.1344 + 6.42842i −0.686574 + 0.396394i −0.802327 0.596884i \(-0.796405\pi\)
0.115753 + 0.993278i \(0.463072\pi\)
\(264\) 0 0
\(265\) 9.00566 9.00566i 0.553213 0.553213i
\(266\) 0 0
\(267\) 20.1494 5.54655i 1.23312 0.339443i
\(268\) 0 0
\(269\) 3.56613 + 2.05891i 0.217431 + 0.125534i 0.604760 0.796408i \(-0.293269\pi\)
−0.387329 + 0.921941i \(0.626602\pi\)
\(270\) 0 0
\(271\) 8.04182 30.0125i 0.488506 1.82313i −0.0752219 0.997167i \(-0.523967\pi\)
0.563727 0.825961i \(-0.309367\pi\)
\(272\) 0 0
\(273\) 3.33225 3.42277i 0.201677 0.207156i
\(274\) 0 0
\(275\) 1.19467 4.45855i 0.0720411 0.268861i
\(276\) 0 0
\(277\) −8.31478 4.80054i −0.499587 0.288437i 0.228956 0.973437i \(-0.426469\pi\)
−0.728543 + 0.685000i \(0.759802\pi\)
\(278\) 0 0
\(279\) 5.32790 + 18.8517i 0.318973 + 1.12862i
\(280\) 0 0
\(281\) 16.1257 16.1257i 0.961980 0.961980i −0.0373236 0.999303i \(-0.511883\pi\)
0.999303 + 0.0373236i \(0.0118832\pi\)
\(282\) 0 0
\(283\) 8.54607 4.93408i 0.508011 0.293300i −0.224005 0.974588i \(-0.571913\pi\)
0.732016 + 0.681288i \(0.238580\pi\)
\(284\) 0 0
\(285\) 0.0297279 + 4.35941i 0.00176093 + 0.258229i
\(286\) 0 0
\(287\) 7.15426i 0.422302i
\(288\) 0 0
\(289\) −10.1361 17.5563i −0.596242 1.03272i
\(290\) 0 0
\(291\) −2.83544 2.79703i −0.166216 0.163965i
\(292\) 0 0
\(293\) 1.43585 + 5.35866i 0.0838831 + 0.313056i 0.995100 0.0988701i \(-0.0315228\pi\)
−0.911217 + 0.411926i \(0.864856\pi\)
\(294\) 0 0
\(295\) 5.83176 10.1009i 0.339538 0.588097i
\(296\) 0 0
\(297\) −2.95552 + 12.0075i −0.171496 + 0.696745i
\(298\) 0 0
\(299\) 8.77361 + 14.9680i 0.507391 + 0.865622i
\(300\) 0 0
\(301\) −5.80715 1.55602i −0.334718 0.0896875i
\(302\) 0 0
\(303\) 9.89532 + 5.62345i 0.568471 + 0.323059i
\(304\) 0 0
\(305\) −4.47995 + 1.20040i −0.256521 + 0.0687346i
\(306\) 0 0
\(307\) 4.51728 + 4.51728i 0.257815 + 0.257815i 0.824165 0.566350i \(-0.191645\pi\)
−0.566350 + 0.824165i \(0.691645\pi\)
\(308\) 0 0
\(309\) 16.0960 + 27.4451i 0.915668 + 1.56130i
\(310\) 0 0
\(311\) −32.9339 −1.86751 −0.933755 0.357912i \(-0.883489\pi\)
−0.933755 + 0.357912i \(0.883489\pi\)
\(312\) 0 0
\(313\) −25.7601 −1.45605 −0.728024 0.685552i \(-0.759561\pi\)
−0.728024 + 0.685552i \(0.759561\pi\)
\(314\) 0 0
\(315\) −3.44895 + 2.05447i −0.194326 + 0.115756i
\(316\) 0 0
\(317\) −1.05776 1.05776i −0.0594098 0.0594098i 0.676778 0.736187i \(-0.263376\pi\)
−0.736187 + 0.676778i \(0.763376\pi\)
\(318\) 0 0
\(319\) −2.29418 + 0.614723i −0.128449 + 0.0344179i
\(320\) 0 0
\(321\) 6.97798 12.2788i 0.389473 0.685337i
\(322\) 0 0
\(323\) 8.48444 + 2.27340i 0.472087 + 0.126495i
\(324\) 0 0
\(325\) −0.0460146 6.99310i −0.00255243 0.387908i
\(326\) 0 0
\(327\) −8.26493 + 31.7085i −0.457052 + 1.75348i
\(328\) 0 0
\(329\) −1.31784 + 2.28257i −0.0726551 + 0.125842i
\(330\) 0 0
\(331\) −5.08912 18.9929i −0.279723 1.04394i −0.952610 0.304196i \(-0.901612\pi\)
0.672886 0.739746i \(-0.265054\pi\)
\(332\) 0 0
\(333\) 10.1531 + 9.87985i 0.556385 + 0.541413i
\(334\) 0 0
\(335\) 7.35655 + 12.7419i 0.401931 + 0.696165i
\(336\) 0 0
\(337\) 18.5533i 1.01066i 0.862925 + 0.505331i \(0.168630\pi\)
−0.862925 + 0.505331i \(0.831370\pi\)
\(338\) 0 0
\(339\) −2.39672 + 0.0163438i −0.130172 + 0.000887675i
\(340\) 0 0
\(341\) −13.4583 + 7.77015i −0.728808 + 0.420777i
\(342\) 0 0
\(343\) 7.25589 7.25589i 0.391781 0.391781i
\(344\) 0 0
\(345\) −3.86969 14.0577i −0.208337 0.756842i
\(346\) 0 0
\(347\) −24.8498 14.3470i −1.33401 0.770189i −0.348096 0.937459i \(-0.613172\pi\)
−0.985911 + 0.167269i \(0.946505\pi\)
\(348\) 0 0
\(349\) 6.28760 23.4657i 0.336568 1.25609i −0.565592 0.824685i \(-0.691352\pi\)
0.902160 0.431402i \(-0.141981\pi\)
\(350\) 0 0
\(351\) 0.506482 + 18.7281i 0.0270340 + 0.999635i
\(352\) 0 0
\(353\) −3.66157 + 13.6652i −0.194886 + 0.727324i 0.797411 + 0.603437i \(0.206203\pi\)
−0.992296 + 0.123887i \(0.960464\pi\)
\(354\) 0 0
\(355\) −0.626697 0.361823i −0.0332616 0.0192036i
\(356\) 0 0
\(357\) 2.14671 + 7.79851i 0.113616 + 0.412741i
\(358\) 0 0
\(359\) 4.37863 4.37863i 0.231095 0.231095i −0.582055 0.813150i \(-0.697751\pi\)
0.813150 + 0.582055i \(0.197751\pi\)
\(360\) 0 0
\(361\) 14.6618 8.46499i 0.771674 0.445526i
\(362\) 0 0
\(363\) 9.24287 0.0630293i 0.485125 0.00330818i
\(364\) 0 0
\(365\) 24.7438i 1.29515i
\(366\) 0 0
\(367\) −0.770224 1.33407i −0.0402054 0.0696377i 0.845222 0.534415i \(-0.179468\pi\)
−0.885428 + 0.464777i \(0.846135\pi\)
\(368\) 0 0
\(369\) 20.1092 + 19.5680i 1.04684 + 1.01867i
\(370\) 0 0
\(371\) 1.44130 + 5.37901i 0.0748286 + 0.279264i
\(372\) 0 0
\(373\) −7.95264 + 13.7744i −0.411772 + 0.713210i −0.995084 0.0990385i \(-0.968423\pi\)
0.583312 + 0.812248i \(0.301757\pi\)
\(374\) 0 0
\(375\) −5.30365 + 20.3475i −0.273879 + 1.05074i
\(376\) 0 0
\(377\) −3.10442 + 1.81968i −0.159886 + 0.0937182i
\(378\) 0 0
\(379\) 21.0724 + 5.64632i 1.08241 + 0.290032i 0.755585 0.655051i \(-0.227353\pi\)
0.326830 + 0.945083i \(0.394020\pi\)
\(380\) 0 0
\(381\) −3.98267 + 7.00813i −0.204039 + 0.359037i
\(382\) 0 0
\(383\) 35.4395 9.49599i 1.81087 0.485222i 0.815286 0.579058i \(-0.196580\pi\)
0.995588 + 0.0938358i \(0.0299129\pi\)
\(384\) 0 0
\(385\) −2.25184 2.25184i −0.114764 0.114764i
\(386\) 0 0
\(387\) 20.2571 12.0668i 1.02973 0.613389i
\(388\) 0 0
\(389\) −16.4110 −0.832073 −0.416036 0.909348i \(-0.636581\pi\)
−0.416036 + 0.909348i \(0.636581\pi\)
\(390\) 0 0
\(391\) −29.3776 −1.48569
\(392\) 0 0
\(393\) 14.2631 + 24.3199i 0.719479 + 1.22678i
\(394\) 0 0
\(395\) 10.4009 + 10.4009i 0.523326 + 0.523326i
\(396\) 0 0
\(397\) 11.8439 3.17357i 0.594429 0.159277i 0.0509523 0.998701i \(-0.483774\pi\)
0.543476 + 0.839424i \(0.317108\pi\)
\(398\) 0 0
\(399\) −1.65727 0.941815i −0.0829672 0.0471497i
\(400\) 0 0
\(401\) −28.9636 7.76078i −1.44638 0.387555i −0.551614 0.834100i \(-0.685988\pi\)
−0.894761 + 0.446545i \(0.852654\pi\)
\(402\) 0 0
\(403\) −16.5385 + 16.7576i −0.823843 + 0.834757i
\(404\) 0 0
\(405\) 3.65872 15.3136i 0.181804 0.760941i
\(406\) 0 0
\(407\) −5.61903 + 9.73244i −0.278525 + 0.482419i
\(408\) 0 0
\(409\) −4.70449 17.5574i −0.232622 0.868157i −0.979206 0.202867i \(-0.934974\pi\)
0.746584 0.665291i \(-0.231692\pi\)
\(410\) 0 0
\(411\) 6.90384 + 6.81032i 0.340541 + 0.335928i
\(412\) 0 0
\(413\) 2.54993 + 4.41660i 0.125474 + 0.217327i
\(414\) 0 0
\(415\) 7.32024i 0.359336i
\(416\) 0 0
\(417\) −0.257881 37.8166i −0.0126285 1.85189i
\(418\) 0 0
\(419\) 9.43496 5.44727i 0.460928 0.266117i −0.251507 0.967856i \(-0.580926\pi\)
0.712434 + 0.701739i \(0.247593\pi\)
\(420\) 0 0
\(421\) 1.33998 1.33998i 0.0653068 0.0653068i −0.673699 0.739006i \(-0.735296\pi\)
0.739006 + 0.673699i \(0.235296\pi\)
\(422\) 0 0
\(423\) −2.81135 9.94741i −0.136692 0.483659i
\(424\) 0 0
\(425\) 10.2549 + 5.92066i 0.497435 + 0.287194i
\(426\) 0 0
\(427\) 0.524872 1.95885i 0.0254003 0.0947954i
\(428\) 0 0
\(429\) −14.3027 + 4.03855i −0.690540 + 0.194983i
\(430\) 0 0
\(431\) 6.86458 25.6190i 0.330655 1.23402i −0.577848 0.816144i \(-0.696107\pi\)
0.908503 0.417878i \(-0.137226\pi\)
\(432\) 0 0
\(433\) 19.7093 + 11.3792i 0.947169 + 0.546849i 0.892201 0.451640i \(-0.149161\pi\)
0.0549690 + 0.998488i \(0.482494\pi\)
\(434\) 0 0
\(435\) 2.91562 0.802588i 0.139793 0.0384811i
\(436\) 0 0
\(437\) 4.89549 4.89549i 0.234183 0.234183i
\(438\) 0 0
\(439\) −23.4222 + 13.5228i −1.11788 + 0.645409i −0.940859 0.338798i \(-0.889980\pi\)
−0.177022 + 0.984207i \(0.556646\pi\)
\(440\) 0 0
\(441\) 0.262456 + 19.2429i 0.0124979 + 0.916328i
\(442\) 0 0
\(443\) 3.11751i 0.148117i −0.997254 0.0740586i \(-0.976405\pi\)
0.997254 0.0740586i \(-0.0235952\pi\)
\(444\) 0 0
\(445\) −10.5541 18.2803i −0.500313 0.866568i
\(446\) 0 0
\(447\) −24.5929 + 24.9306i −1.16320 + 1.17918i
\(448\) 0 0
\(449\) −6.65092 24.8216i −0.313876 1.17140i −0.925031 0.379891i \(-0.875961\pi\)
0.611155 0.791511i \(-0.290705\pi\)
\(450\) 0 0
\(451\) −11.1291 + 19.2761i −0.524047 + 0.907676i
\(452\) 0 0
\(453\) 22.2355 + 5.79577i 1.04472 + 0.272309i
\(454\) 0 0
\(455\) −4.19420 2.38486i −0.196627 0.111804i
\(456\) 0 0
\(457\) 8.26681 + 2.21508i 0.386705 + 0.103617i 0.446933 0.894567i \(-0.352516\pi\)
−0.0602282 + 0.998185i \(0.519183\pi\)
\(458\) 0 0
\(459\) −27.7917 15.2962i −1.29720 0.713966i
\(460\) 0 0
\(461\) 5.16716 1.38454i 0.240659 0.0644843i −0.136474 0.990644i \(-0.543577\pi\)
0.377132 + 0.926159i \(0.376910\pi\)
\(462\) 0 0
\(463\) −19.3714 19.3714i −0.900264 0.900264i 0.0951945 0.995459i \(-0.469653\pi\)
−0.995459 + 0.0951945i \(0.969653\pi\)
\(464\) 0 0
\(465\) 17.0677 10.0098i 0.791496 0.464196i
\(466\) 0 0
\(467\) −20.0260 −0.926692 −0.463346 0.886177i \(-0.653351\pi\)
−0.463346 + 0.886177i \(0.653351\pi\)
\(468\) 0 0
\(469\) −6.43328 −0.297061
\(470\) 0 0
\(471\) −19.7907 + 11.6068i −0.911906 + 0.534813i
\(472\) 0 0
\(473\) 13.2260 + 13.2260i 0.608131 + 0.608131i
\(474\) 0 0
\(475\) −2.69549 + 0.722255i −0.123678 + 0.0331393i
\(476\) 0 0
\(477\) −19.0615 10.6612i −0.872768 0.488145i
\(478\) 0 0
\(479\) −2.93031 0.785175i −0.133889 0.0358755i 0.191252 0.981541i \(-0.438745\pi\)
−0.325141 + 0.945665i \(0.605412\pi\)
\(480\) 0 0
\(481\) −4.29842 + 16.4748i −0.195991 + 0.751186i
\(482\) 0 0
\(483\) 6.16922 + 1.60803i 0.280709 + 0.0731679i
\(484\) 0 0
\(485\) −2.01138 + 3.48381i −0.0913320 + 0.158192i
\(486\) 0 0
\(487\) −1.32878 4.95906i −0.0602126 0.224716i 0.929262 0.369420i \(-0.120444\pi\)
−0.989475 + 0.144704i \(0.953777\pi\)
\(488\) 0 0
\(489\) 5.37595 5.44977i 0.243109 0.246447i
\(490\) 0 0
\(491\) 6.20757 + 10.7518i 0.280144 + 0.485223i 0.971420 0.237368i \(-0.0762846\pi\)
−0.691276 + 0.722590i \(0.742951\pi\)
\(492\) 0 0
\(493\) 6.09303i 0.274416i
\(494\) 0 0
\(495\) 12.4886 0.170334i 0.561321 0.00765592i
\(496\) 0 0
\(497\) 0.274022 0.158207i 0.0122916 0.00709654i
\(498\) 0 0
\(499\) 20.0749 20.0749i 0.898675 0.898675i −0.0966444 0.995319i \(-0.530811\pi\)
0.995319 + 0.0966444i \(0.0308109\pi\)
\(500\) 0 0
\(501\) 31.4260 8.65069i 1.40401 0.386484i
\(502\) 0 0
\(503\) 12.6957 + 7.32987i 0.566074 + 0.326823i 0.755580 0.655057i \(-0.227355\pi\)
−0.189506 + 0.981880i \(0.560689\pi\)
\(504\) 0 0
\(505\) 2.97529 11.1039i 0.132399 0.494118i
\(506\) 0 0
\(507\) −19.2712 + 11.6456i −0.855864 + 0.517201i
\(508\) 0 0
\(509\) −8.71003 + 32.5063i −0.386065 + 1.44081i 0.450416 + 0.892819i \(0.351276\pi\)
−0.836481 + 0.547996i \(0.815391\pi\)
\(510\) 0 0
\(511\) −9.36968 5.40959i −0.414490 0.239306i
\(512\) 0 0
\(513\) 7.18016 2.08224i 0.317012 0.0919332i
\(514\) 0 0
\(515\) 22.7234 22.7234i 1.00131 1.00131i
\(516\) 0 0
\(517\) 7.10147 4.10004i 0.312322 0.180319i
\(518\) 0 0
\(519\) 0.225140 + 33.0154i 0.00988256 + 1.44922i
\(520\) 0 0
\(521\) 38.9045i 1.70444i −0.523185 0.852219i \(-0.675256\pi\)
0.523185 0.852219i \(-0.324744\pi\)
\(522\) 0 0
\(523\) −10.4524 18.1040i −0.457050 0.791634i 0.541754 0.840537i \(-0.317761\pi\)
−0.998803 + 0.0489038i \(0.984427\pi\)
\(524\) 0 0
\(525\) −1.82942 1.80464i −0.0798424 0.0787609i
\(526\) 0 0
\(527\) −10.3182 38.5082i −0.449470 1.67744i
\(528\) 0 0
\(529\) −0.0775974 + 0.134403i −0.00337380 + 0.00584359i
\(530\) 0 0
\(531\) −19.3887 4.91278i −0.841396 0.213196i
\(532\) 0 0
\(533\) −8.51346 + 32.6300i −0.368759 + 1.41336i
\(534\) 0 0
\(535\) −13.7786 3.69195i −0.595699 0.159617i
\(536\) 0 0
\(537\) −21.5995 12.2749i −0.932087 0.529699i
\(538\) 0 0
\(539\) −14.7460 + 3.95119i −0.635157 + 0.170190i
\(540\) 0 0
\(541\) −11.4929 11.4929i −0.494117 0.494117i 0.415483 0.909601i \(-0.363612\pi\)
−0.909601 + 0.415483i \(0.863612\pi\)
\(542\) 0 0
\(543\) −7.03677 11.9983i −0.301977 0.514898i
\(544\) 0 0
\(545\) 33.0962 1.41769
\(546\) 0 0
\(547\) −11.2755 −0.482104 −0.241052 0.970512i \(-0.577492\pi\)
−0.241052 + 0.970512i \(0.577492\pi\)
\(548\) 0 0
\(549\) 4.07033 + 6.83308i 0.173718 + 0.291629i
\(550\) 0 0
\(551\) 1.01534 + 1.01534i 0.0432550 + 0.0432550i
\(552\) 0 0
\(553\) −6.21238 + 1.66460i −0.264177 + 0.0707860i
\(554\) 0 0
\(555\) 7.06968 12.4402i 0.300091 0.528056i
\(556\) 0 0
\(557\) −13.7737 3.69064i −0.583609 0.156378i −0.0450785 0.998983i \(-0.514354\pi\)
−0.538531 + 0.842606i \(0.681020\pi\)
\(558\) 0 0
\(559\) 24.6343 + 14.0073i 1.04192 + 0.592446i
\(560\) 0 0
\(561\) 6.34726 24.3513i 0.267982 1.02811i
\(562\) 0 0
\(563\) 15.4189 26.7063i 0.649828 1.12554i −0.333336 0.942808i \(-0.608174\pi\)
0.983164 0.182727i \(-0.0584925\pi\)
\(564\) 0 0
\(565\) 0.626548 + 2.33831i 0.0263591 + 0.0983734i
\(566\) 0 0
\(567\) 4.99890 + 4.73338i 0.209934 + 0.198783i
\(568\) 0 0
\(569\) −16.1979 28.0557i −0.679053 1.17615i −0.975266 0.221033i \(-0.929057\pi\)
0.296213 0.955122i \(-0.404276\pi\)
\(570\) 0 0
\(571\) 22.4605i 0.939942i 0.882682 + 0.469971i \(0.155736\pi\)
−0.882682 + 0.469971i \(0.844264\pi\)
\(572\) 0 0
\(573\) 5.51006 0.0375744i 0.230186 0.00156969i
\(574\) 0 0
\(575\) 8.08281 4.66661i 0.337077 0.194611i
\(576\) 0 0
\(577\) −9.61220 + 9.61220i −0.400161 + 0.400161i −0.878290 0.478129i \(-0.841315\pi\)
0.478129 + 0.878290i \(0.341315\pi\)
\(578\) 0 0
\(579\) 1.24355 + 4.51755i 0.0516803 + 0.187743i
\(580\) 0 0
\(581\) −2.77194 1.60038i −0.115000 0.0663950i
\(582\) 0 0
\(583\) 4.48414 16.7350i 0.185714 0.693094i
\(584\) 0 0
\(585\) 18.1752 5.26608i 0.751452 0.217726i
\(586\) 0 0
\(587\) 2.04380 7.62756i 0.0843566 0.314823i −0.910835 0.412771i \(-0.864561\pi\)
0.995192 + 0.0979476i \(0.0312278\pi\)
\(588\) 0 0
\(589\) 8.13644 + 4.69757i 0.335256 + 0.193560i
\(590\) 0 0
\(591\) 2.86900 + 10.4224i 0.118015 + 0.428722i
\(592\) 0 0
\(593\) 19.1065 19.1065i 0.784610 0.784610i −0.195995 0.980605i \(-0.562793\pi\)
0.980605 + 0.195995i \(0.0627935\pi\)
\(594\) 0 0
\(595\) 7.07510 4.08481i 0.290051 0.167461i
\(596\) 0 0
\(597\) −46.5715 + 0.317582i −1.90604 + 0.0129978i
\(598\) 0 0
\(599\) 6.13152i 0.250527i −0.992123 0.125264i \(-0.960022\pi\)
0.992123 0.125264i \(-0.0399777\pi\)
\(600\) 0 0
\(601\) −0.933390 1.61668i −0.0380738 0.0659457i 0.846361 0.532610i \(-0.178789\pi\)
−0.884434 + 0.466665i \(0.845456\pi\)
\(602\) 0 0
\(603\) 17.5961 18.0827i 0.716567 0.736384i
\(604\) 0 0
\(605\) −2.41626 9.01759i −0.0982348 0.366617i
\(606\) 0 0
\(607\) 16.0665 27.8280i 0.652119 1.12950i −0.330489 0.943810i \(-0.607214\pi\)
0.982608 0.185693i \(-0.0594530\pi\)
\(608\) 0 0
\(609\) −0.333511 + 1.27952i −0.0135146 + 0.0518487i
\(610\) 0 0
\(611\) 8.72681 8.84241i 0.353049 0.357726i
\(612\) 0 0
\(613\) 29.0703 + 7.78936i 1.17414 + 0.314609i 0.792599 0.609743i \(-0.208727\pi\)
0.381539 + 0.924353i \(0.375394\pi\)
\(614\) 0 0
\(615\) 14.0022 24.6390i 0.564624 0.993542i
\(616\) 0 0
\(617\) 9.28297 2.48737i 0.373718 0.100138i −0.0670707 0.997748i \(-0.521365\pi\)
0.440789 + 0.897611i \(0.354699\pi\)
\(618\) 0 0
\(619\) −1.32964 1.32964i −0.0534429 0.0534429i 0.679880 0.733323i \(-0.262032\pi\)
−0.733323 + 0.679880i \(0.762032\pi\)
\(620\) 0 0
\(621\) −21.3937 + 12.9422i −0.858498 + 0.519354i
\(622\) 0 0
\(623\) 9.22954 0.369774
\(624\) 0 0
\(625\) 11.5401 0.461605
\(626\) 0 0
\(627\) 3.00019 + 5.11561i 0.119816 + 0.204298i
\(628\) 0 0
\(629\) −20.3857 20.3857i −0.812833 0.812833i
\(630\) 0 0
\(631\) 25.1993 6.75212i 1.00317 0.268798i 0.280395 0.959885i \(-0.409534\pi\)
0.722772 + 0.691087i \(0.242868\pi\)
\(632\) 0 0
\(633\) −4.62678 2.62937i −0.183898 0.104508i
\(634\) 0 0
\(635\) 7.86409 + 2.10718i 0.312077 + 0.0836208i
\(636\) 0 0
\(637\) −19.9540 + 11.6962i −0.790605 + 0.463419i
\(638\) 0 0
\(639\) −0.304807 + 1.20294i −0.0120580 + 0.0475877i
\(640\) 0 0
\(641\) −0.831687 + 1.44052i −0.0328497 + 0.0568973i −0.881983 0.471282i \(-0.843792\pi\)
0.849133 + 0.528179i \(0.177125\pi\)
\(642\) 0 0
\(643\) 9.12962 + 34.0722i 0.360037 + 1.34368i 0.874026 + 0.485879i \(0.161501\pi\)
−0.513989 + 0.857797i \(0.671833\pi\)
\(644\) 0 0
\(645\) −16.9542 16.7246i −0.667572 0.658529i
\(646\) 0 0
\(647\) 19.6110 + 33.9672i 0.770986 + 1.33539i 0.937023 + 0.349268i \(0.113570\pi\)
−0.166037 + 0.986120i \(0.553097\pi\)
\(648\) 0 0
\(649\) 15.8665i 0.622815i
\(650\) 0 0
\(651\) 0.0589959 + 8.65140i 0.00231223 + 0.339075i
\(652\) 0 0
\(653\) 13.5902 7.84630i 0.531826 0.307050i −0.209934 0.977716i \(-0.567325\pi\)
0.741760 + 0.670666i \(0.233992\pi\)
\(654\) 0 0
\(655\) 20.1359 20.1359i 0.786773 0.786773i
\(656\) 0 0
\(657\) 40.8329 11.5402i 1.59304 0.450227i
\(658\) 0 0
\(659\) −7.77507 4.48894i −0.302874 0.174864i 0.340859 0.940114i \(-0.389282\pi\)
−0.643733 + 0.765250i \(0.722615\pi\)
\(660\) 0 0
\(661\) 2.39828 8.95050i 0.0932823 0.348134i −0.903471 0.428649i \(-0.858990\pi\)
0.996753 + 0.0805148i \(0.0256564\pi\)
\(662\) 0 0
\(663\) −0.510840 38.1229i −0.0198394 1.48057i
\(664\) 0 0
\(665\) −0.498301 + 1.85969i −0.0193233 + 0.0721155i
\(666\) 0 0
\(667\) −4.15906 2.40124i −0.161040 0.0929763i
\(668\) 0 0
\(669\) 33.1186 9.11660i 1.28044 0.352468i
\(670\) 0 0
\(671\) −4.46135 + 4.46135i −0.172229 + 0.172229i
\(672\) 0 0
\(673\) −20.6348 + 11.9135i −0.795415 + 0.459233i −0.841865 0.539688i \(-0.818542\pi\)
0.0464506 + 0.998921i \(0.485209\pi\)
\(674\) 0 0
\(675\) 10.0762 0.206163i 0.387835 0.00793520i
\(676\) 0 0
\(677\) 36.4474i 1.40079i 0.713756 + 0.700394i \(0.246992\pi\)
−0.713756 + 0.700394i \(0.753008\pi\)
\(678\) 0 0
\(679\) −0.879472 1.52329i −0.0337511 0.0584585i
\(680\) 0 0
\(681\) −22.6525 + 22.9635i −0.868045 + 0.879965i
\(682\) 0 0
\(683\) −7.27470 27.1495i −0.278359 1.03885i −0.953557 0.301212i \(-0.902609\pi\)
0.675198 0.737636i \(-0.264058\pi\)
\(684\) 0 0
\(685\) 4.89738 8.48251i 0.187119 0.324100i
\(686\) 0 0
\(687\) 5.57019 + 1.45189i 0.212516 + 0.0553931i
\(688\) 0 0
\(689\) −0.172714 26.2484i −0.00657988 0.999983i
\(690\) 0 0
\(691\) 20.8059 + 5.57492i 0.791493 + 0.212080i 0.631846 0.775094i \(-0.282298\pi\)
0.159647 + 0.987174i \(0.448964\pi\)
\(692\) 0 0
\(693\) −2.66581 + 4.76628i −0.101266 + 0.181056i
\(694\) 0 0
\(695\) −36.8949 + 9.88596i −1.39950 + 0.374996i
\(696\) 0 0
\(697\) −40.3760 40.3760i −1.52935 1.52935i
\(698\) 0 0
\(699\) −19.8648 + 11.6503i −0.751357 + 0.440655i
\(700\) 0 0
\(701\) −26.6772 −1.00758 −0.503792 0.863825i \(-0.668062\pi\)
−0.503792 + 0.863825i \(0.668062\pi\)
\(702\) 0 0
\(703\) 6.79415 0.256246
\(704\) 0 0
\(705\) −9.00604 + 5.28185i −0.339187 + 0.198926i
\(706\) 0 0
\(707\) 3.55423 + 3.55423i 0.133671 + 0.133671i
\(708\) 0 0
\(709\) −21.4498 + 5.74745i −0.805563 + 0.215850i −0.638025 0.770016i \(-0.720248\pi\)
−0.167538 + 0.985866i \(0.553582\pi\)
\(710\) 0 0
\(711\) 12.3130 22.0147i 0.461773 0.825617i
\(712\) 0 0
\(713\) −30.3518 8.13275i −1.13669 0.304574i
\(714\) 0 0
\(715\) 7.59079 + 12.9501i 0.283879 + 0.484306i
\(716\) 0 0
\(717\) −11.7613 3.06563i −0.439235 0.114488i
\(718\) 0 0
\(719\) −9.24099 + 16.0059i −0.344631 + 0.596918i −0.985287 0.170910i \(-0.945329\pi\)
0.640656 + 0.767828i \(0.278663\pi\)
\(720\) 0 0
\(721\) 3.63674 + 13.5725i 0.135439 + 0.505466i
\(722\) 0 0
\(723\) 19.0424 19.3039i 0.708196 0.717921i
\(724\) 0 0
\(725\) 0.967873 + 1.67641i 0.0359459 + 0.0622601i
\(726\) 0 0
\(727\) 19.7224i 0.731462i 0.930721 + 0.365731i \(0.119181\pi\)
−0.930721 + 0.365731i \(0.880819\pi\)
\(728\) 0 0
\(729\) −26.9774 + 1.10439i −0.999163 + 0.0409034i
\(730\) 0 0
\(731\) −41.5550 + 23.9918i −1.53697 + 0.887369i
\(732\) 0 0
\(733\) −24.0041 + 24.0041i −0.886613 + 0.886613i −0.994196 0.107583i \(-0.965689\pi\)
0.107583 + 0.994196i \(0.465689\pi\)
\(734\) 0 0
\(735\) 18.7404 5.15871i 0.691252 0.190282i
\(736\) 0 0
\(737\) 17.3335 + 10.0075i 0.638489 + 0.368632i
\(738\) 0 0
\(739\) 5.29170 19.7489i 0.194658 0.726475i −0.797697 0.603059i \(-0.793948\pi\)
0.992355 0.123416i \(-0.0393850\pi\)
\(740\) 0 0
\(741\) 6.43792 + 6.26767i 0.236503 + 0.230249i
\(742\) 0 0
\(743\) 3.04508 11.3644i 0.111713 0.416920i −0.887307 0.461180i \(-0.847426\pi\)
0.999020 + 0.0442600i \(0.0140930\pi\)
\(744\) 0 0
\(745\) 30.6314 + 17.6850i 1.12225 + 0.647929i
\(746\) 0 0
\(747\) 12.0801 3.41408i 0.441987 0.124915i
\(748\) 0 0
\(749\) 4.41035 4.41035i 0.161151 0.161151i
\(750\) 0 0
\(751\) −21.4873 + 12.4057i −0.784082 + 0.452690i −0.837875 0.545862i \(-0.816202\pi\)
0.0537931 + 0.998552i \(0.482869\pi\)
\(752\) 0 0
\(753\) −0.295936 43.3973i −0.0107845 1.58148i
\(754\) 0 0
\(755\) 23.2087i 0.844651i
\(756\) 0 0
\(757\) 20.6305 + 35.7331i 0.749828 + 1.29874i 0.947905 + 0.318554i \(0.103197\pi\)
−0.198077 + 0.980187i \(0.563469\pi\)
\(758\) 0 0
\(759\) −14.1206 13.9293i −0.512546 0.505603i
\(760\) 0 0
\(761\) 4.78578 + 17.8608i 0.173484 + 0.647453i 0.996805 + 0.0798759i \(0.0254524\pi\)
−0.823320 + 0.567577i \(0.807881\pi\)
\(762\) 0 0
\(763\) −7.23564 + 12.5325i −0.261948 + 0.453707i
\(764\) 0 0
\(765\) −7.86994 + 31.0593i −0.284538 + 1.12295i
\(766\) 0 0
\(767\) −6.37431 23.1781i −0.230163 0.836914i
\(768\) 0 0
\(769\) 8.53913 + 2.28805i 0.307929 + 0.0825093i 0.409474 0.912322i \(-0.365712\pi\)
−0.101545 + 0.994831i \(0.532379\pi\)
\(770\) 0 0
\(771\) −31.0096 17.6226i −1.11678 0.634661i
\(772\) 0 0
\(773\) 30.7940 8.25123i 1.10758 0.296776i 0.341735 0.939796i \(-0.388986\pi\)
0.765849 + 0.643020i \(0.222319\pi\)
\(774\) 0 0
\(775\) 8.95591 + 8.95591i 0.321706 + 0.321706i
\(776\) 0 0
\(777\) 3.16510 + 5.39679i 0.113547 + 0.193609i
\(778\) 0 0
\(779\) 13.4565 0.482129
\(780\) 0 0
\(781\) −0.984416 −0.0352252
\(782\) 0 0
\(783\) −2.68427 4.43712i −0.0959279 0.158570i
\(784\) 0 0
\(785\) 16.3858 + 16.3858i 0.584835 + 0.584835i
\(786\) 0 0
\(787\) −41.6411 + 11.1577i −1.48434 + 0.397729i −0.907823 0.419353i \(-0.862257\pi\)
−0.576521 + 0.817082i \(0.695590\pi\)
\(788\) 0 0
\(789\) 11.0026 19.3607i 0.391703 0.689261i
\(790\) 0 0
\(791\) −1.02242 0.273957i −0.0363531 0.00974079i
\(792\) 0 0
\(793\) −4.72490 + 8.30957i −0.167786 + 0.295081i
\(794\) 0 0
\(795\) −5.56393 + 21.3460i −0.197332 + 0.757066i
\(796\) 0 0
\(797\)