Properties

Label 4020.2.q.k.841.3
Level 4020
Weight 2
Character 4020.841
Analytic conductor 32.100
Analytic rank 0
Dimension 14
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4020.q (of order \(3\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(32.0998616126\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 841.3
Root \(1.10425 - 1.91261i\)
Character \(\chi\) = 4020.841
Dual form 4020.2.q.k.3781.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.00000 q^{5} +(-0.952306 + 1.64944i) q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +1.00000 q^{5} +(-0.952306 + 1.64944i) q^{7} +1.00000 q^{9} +(-1.50261 + 2.60259i) q^{11} +(2.70849 + 4.69125i) q^{13} -1.00000 q^{15} +(-2.26869 - 3.92948i) q^{17} +(1.93872 + 3.35797i) q^{19} +(0.952306 - 1.64944i) q^{21} +(1.94438 + 3.36777i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(4.12189 - 7.13932i) q^{29} +(-3.48804 + 6.04146i) q^{31} +(1.50261 - 2.60259i) q^{33} +(-0.952306 + 1.64944i) q^{35} +(0.725995 + 1.25746i) q^{37} +(-2.70849 - 4.69125i) q^{39} +(0.0559598 - 0.0969252i) q^{41} +2.08087 q^{43} +1.00000 q^{45} +(-0.778456 + 1.34832i) q^{47} +(1.68623 + 2.92063i) q^{49} +(2.26869 + 3.92948i) q^{51} -8.39503 q^{53} +(-1.50261 + 2.60259i) q^{55} +(-1.93872 - 3.35797i) q^{57} -2.69514 q^{59} +(-0.711547 - 1.23244i) q^{61} +(-0.952306 + 1.64944i) q^{63} +(2.70849 + 4.69125i) q^{65} +(-7.90197 - 2.13517i) q^{67} +(-1.94438 - 3.36777i) q^{69} +(2.11366 - 3.66096i) q^{71} +(-2.91448 - 5.04802i) q^{73} -1.00000 q^{75} +(-2.86188 - 4.95693i) q^{77} +(3.12853 - 5.41877i) q^{79} +1.00000 q^{81} +(0.214571 + 0.371649i) q^{83} +(-2.26869 - 3.92948i) q^{85} +(-4.12189 + 7.13932i) q^{87} -7.70404 q^{89} -10.3173 q^{91} +(3.48804 - 6.04146i) q^{93} +(1.93872 + 3.35797i) q^{95} +(-1.52705 - 2.64493i) q^{97} +(-1.50261 + 2.60259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{3} + 14q^{5} + 3q^{7} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{3} + 14q^{5} + 3q^{7} + 14q^{9} + 6q^{11} + 9q^{13} - 14q^{15} - 12q^{17} + 14q^{19} - 3q^{21} + 6q^{23} + 14q^{25} - 14q^{27} - q^{29} + 7q^{31} - 6q^{33} + 3q^{35} - 2q^{37} - 9q^{39} - 18q^{41} - 6q^{43} + 14q^{45} + 7q^{47} + 12q^{51} - 12q^{53} + 6q^{55} - 14q^{57} - 2q^{59} + 3q^{63} + 9q^{65} + 25q^{67} - 6q^{69} + 22q^{71} - 15q^{73} - 14q^{75} + q^{77} + 9q^{79} + 14q^{81} - q^{83} - 12q^{85} + q^{87} - 12q^{89} - 38q^{91} - 7q^{93} + 14q^{95} + 16q^{97} + 6q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).

\(n\) \(1141\) \(2011\) \(2681\) \(3217\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(1\)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −0.952306 + 1.64944i −0.359938 + 0.623431i −0.987950 0.154773i \(-0.950535\pi\)
0.628012 + 0.778204i \(0.283869\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −1.50261 + 2.60259i −0.453053 + 0.784710i −0.998574 0.0533866i \(-0.982998\pi\)
0.545521 + 0.838097i \(0.316332\pi\)
\(12\) 0 0
\(13\) 2.70849 + 4.69125i 0.751201 + 1.30112i 0.947241 + 0.320522i \(0.103858\pi\)
−0.196040 + 0.980596i \(0.562808\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) −2.26869 3.92948i −0.550237 0.953039i −0.998257 0.0590155i \(-0.981204\pi\)
0.448020 0.894024i \(-0.352129\pi\)
\(18\) 0 0
\(19\) 1.93872 + 3.35797i 0.444773 + 0.770370i 0.998036 0.0626366i \(-0.0199509\pi\)
−0.553263 + 0.833007i \(0.686618\pi\)
\(20\) 0 0
\(21\) 0.952306 1.64944i 0.207810 0.359938i
\(22\) 0 0
\(23\) 1.94438 + 3.36777i 0.405432 + 0.702228i 0.994372 0.105949i \(-0.0337879\pi\)
−0.588940 + 0.808177i \(0.700455\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 4.12189 7.13932i 0.765415 1.32574i −0.174612 0.984637i \(-0.555867\pi\)
0.940027 0.341100i \(-0.110800\pi\)
\(30\) 0 0
\(31\) −3.48804 + 6.04146i −0.626470 + 1.08508i 0.361784 + 0.932262i \(0.382168\pi\)
−0.988255 + 0.152817i \(0.951166\pi\)
\(32\) 0 0
\(33\) 1.50261 2.60259i 0.261570 0.453053i
\(34\) 0 0
\(35\) −0.952306 + 1.64944i −0.160969 + 0.278807i
\(36\) 0 0
\(37\) 0.725995 + 1.25746i 0.119353 + 0.206725i 0.919511 0.393063i \(-0.128585\pi\)
−0.800159 + 0.599788i \(0.795251\pi\)
\(38\) 0 0
\(39\) −2.70849 4.69125i −0.433706 0.751201i
\(40\) 0 0
\(41\) 0.0559598 0.0969252i 0.00873945 0.0151372i −0.861623 0.507549i \(-0.830551\pi\)
0.870362 + 0.492412i \(0.163885\pi\)
\(42\) 0 0
\(43\) 2.08087 0.317330 0.158665 0.987332i \(-0.449281\pi\)
0.158665 + 0.987332i \(0.449281\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) −0.778456 + 1.34832i −0.113549 + 0.196673i −0.917199 0.398429i \(-0.869555\pi\)
0.803650 + 0.595103i \(0.202889\pi\)
\(48\) 0 0
\(49\) 1.68623 + 2.92063i 0.240889 + 0.417233i
\(50\) 0 0
\(51\) 2.26869 + 3.92948i 0.317680 + 0.550237i
\(52\) 0 0
\(53\) −8.39503 −1.15315 −0.576573 0.817046i \(-0.695610\pi\)
−0.576573 + 0.817046i \(0.695610\pi\)
\(54\) 0 0
\(55\) −1.50261 + 2.60259i −0.202611 + 0.350933i
\(56\) 0 0
\(57\) −1.93872 3.35797i −0.256790 0.444773i
\(58\) 0 0
\(59\) −2.69514 −0.350877 −0.175438 0.984490i \(-0.556134\pi\)
−0.175438 + 0.984490i \(0.556134\pi\)
\(60\) 0 0
\(61\) −0.711547 1.23244i −0.0911043 0.157797i 0.816872 0.576819i \(-0.195706\pi\)
−0.907976 + 0.419022i \(0.862373\pi\)
\(62\) 0 0
\(63\) −0.952306 + 1.64944i −0.119979 + 0.207810i
\(64\) 0 0
\(65\) 2.70849 + 4.69125i 0.335947 + 0.581878i
\(66\) 0 0
\(67\) −7.90197 2.13517i −0.965379 0.260852i
\(68\) 0 0
\(69\) −1.94438 3.36777i −0.234076 0.405432i
\(70\) 0 0
\(71\) 2.11366 3.66096i 0.250845 0.434476i −0.712914 0.701252i \(-0.752625\pi\)
0.963759 + 0.266776i \(0.0859582\pi\)
\(72\) 0 0
\(73\) −2.91448 5.04802i −0.341114 0.590826i 0.643526 0.765424i \(-0.277471\pi\)
−0.984640 + 0.174598i \(0.944137\pi\)
\(74\) 0 0
\(75\) −1.00000 −0.115470
\(76\) 0 0
\(77\) −2.86188 4.95693i −0.326142 0.564894i
\(78\) 0 0
\(79\) 3.12853 5.41877i 0.351987 0.609659i −0.634611 0.772832i \(-0.718839\pi\)
0.986597 + 0.163173i \(0.0521728\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 0.214571 + 0.371649i 0.0235523 + 0.0407937i 0.877561 0.479464i \(-0.159169\pi\)
−0.854009 + 0.520258i \(0.825836\pi\)
\(84\) 0 0
\(85\) −2.26869 3.92948i −0.246074 0.426212i
\(86\) 0 0
\(87\) −4.12189 + 7.13932i −0.441913 + 0.765415i
\(88\) 0 0
\(89\) −7.70404 −0.816626 −0.408313 0.912842i \(-0.633883\pi\)
−0.408313 + 0.912842i \(0.633883\pi\)
\(90\) 0 0
\(91\) −10.3173 −1.08154
\(92\) 0 0
\(93\) 3.48804 6.04146i 0.361693 0.626470i
\(94\) 0 0
\(95\) 1.93872 + 3.35797i 0.198909 + 0.344520i
\(96\) 0 0
\(97\) −1.52705 2.64493i −0.155048 0.268552i 0.778028 0.628229i \(-0.216220\pi\)
−0.933077 + 0.359678i \(0.882887\pi\)
\(98\) 0 0
\(99\) −1.50261 + 2.60259i −0.151018 + 0.261570i
\(100\) 0 0
\(101\) −3.83823 + 6.64801i −0.381918 + 0.661502i −0.991336 0.131347i \(-0.958070\pi\)
0.609418 + 0.792849i \(0.291403\pi\)
\(102\) 0 0
\(103\) −8.08233 + 13.9990i −0.796376 + 1.37936i 0.125586 + 0.992083i \(0.459919\pi\)
−0.921962 + 0.387281i \(0.873414\pi\)
\(104\) 0 0
\(105\) 0.952306 1.64944i 0.0929356 0.160969i
\(106\) 0 0
\(107\) 8.41550 0.813557 0.406779 0.913527i \(-0.366652\pi\)
0.406779 + 0.913527i \(0.366652\pi\)
\(108\) 0 0
\(109\) −4.00738 −0.383837 −0.191919 0.981411i \(-0.561471\pi\)
−0.191919 + 0.981411i \(0.561471\pi\)
\(110\) 0 0
\(111\) −0.725995 1.25746i −0.0689084 0.119353i
\(112\) 0 0
\(113\) −0.127891 + 0.221514i −0.0120310 + 0.0208383i −0.871978 0.489545i \(-0.837163\pi\)
0.859947 + 0.510383i \(0.170496\pi\)
\(114\) 0 0
\(115\) 1.94438 + 3.36777i 0.181315 + 0.314046i
\(116\) 0 0
\(117\) 2.70849 + 4.69125i 0.250400 + 0.433706i
\(118\) 0 0
\(119\) 8.64194 0.792205
\(120\) 0 0
\(121\) 0.984349 + 1.70494i 0.0894863 + 0.154995i
\(122\) 0 0
\(123\) −0.0559598 + 0.0969252i −0.00504573 + 0.00873945i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −1.91787 + 3.32185i −0.170184 + 0.294767i −0.938484 0.345323i \(-0.887769\pi\)
0.768300 + 0.640090i \(0.221103\pi\)
\(128\) 0 0
\(129\) −2.08087 −0.183211
\(130\) 0 0
\(131\) 20.6597 1.80504 0.902521 0.430645i \(-0.141714\pi\)
0.902521 + 0.430645i \(0.141714\pi\)
\(132\) 0 0
\(133\) −7.38503 −0.640363
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) −6.37529 −0.544678 −0.272339 0.962201i \(-0.587797\pi\)
−0.272339 + 0.962201i \(0.587797\pi\)
\(138\) 0 0
\(139\) 6.06502 0.514429 0.257214 0.966354i \(-0.417195\pi\)
0.257214 + 0.966354i \(0.417195\pi\)
\(140\) 0 0
\(141\) 0.778456 1.34832i 0.0655578 0.113549i
\(142\) 0 0
\(143\) −16.2792 −1.36133
\(144\) 0 0
\(145\) 4.12189 7.13932i 0.342304 0.592888i
\(146\) 0 0
\(147\) −1.68623 2.92063i −0.139078 0.240889i
\(148\) 0 0
\(149\) −19.0684 −1.56215 −0.781073 0.624440i \(-0.785327\pi\)
−0.781073 + 0.624440i \(0.785327\pi\)
\(150\) 0 0
\(151\) −3.80844 6.59641i −0.309926 0.536808i 0.668420 0.743784i \(-0.266971\pi\)
−0.978346 + 0.206976i \(0.933638\pi\)
\(152\) 0 0
\(153\) −2.26869 3.92948i −0.183412 0.317680i
\(154\) 0 0
\(155\) −3.48804 + 6.04146i −0.280166 + 0.485262i
\(156\) 0 0
\(157\) 2.20493 + 3.81905i 0.175973 + 0.304793i 0.940497 0.339801i \(-0.110360\pi\)
−0.764525 + 0.644594i \(0.777026\pi\)
\(158\) 0 0
\(159\) 8.39503 0.665769
\(160\) 0 0
\(161\) −7.40659 −0.583721
\(162\) 0 0
\(163\) −3.43242 + 5.94512i −0.268848 + 0.465658i −0.968564 0.248763i \(-0.919976\pi\)
0.699717 + 0.714420i \(0.253309\pi\)
\(164\) 0 0
\(165\) 1.50261 2.60259i 0.116978 0.202611i
\(166\) 0 0
\(167\) −9.03170 + 15.6434i −0.698894 + 1.21052i 0.269957 + 0.962872i \(0.412991\pi\)
−0.968850 + 0.247647i \(0.920343\pi\)
\(168\) 0 0
\(169\) −8.17188 + 14.1541i −0.628606 + 1.08878i
\(170\) 0 0
\(171\) 1.93872 + 3.35797i 0.148258 + 0.256790i
\(172\) 0 0
\(173\) 2.91255 + 5.04469i 0.221437 + 0.383541i 0.955245 0.295817i \(-0.0955918\pi\)
−0.733807 + 0.679358i \(0.762258\pi\)
\(174\) 0 0
\(175\) −0.952306 + 1.64944i −0.0719876 + 0.124686i
\(176\) 0 0
\(177\) 2.69514 0.202579
\(178\) 0 0
\(179\) 8.32860 0.622509 0.311254 0.950327i \(-0.399251\pi\)
0.311254 + 0.950327i \(0.399251\pi\)
\(180\) 0 0
\(181\) 4.40709 7.63330i 0.327576 0.567378i −0.654454 0.756102i \(-0.727102\pi\)
0.982030 + 0.188723i \(0.0604349\pi\)
\(182\) 0 0
\(183\) 0.711547 + 1.23244i 0.0525991 + 0.0911043i
\(184\) 0 0
\(185\) 0.725995 + 1.25746i 0.0533762 + 0.0924503i
\(186\) 0 0
\(187\) 13.6358 0.997147
\(188\) 0 0
\(189\) 0.952306 1.64944i 0.0692701 0.119979i
\(190\) 0 0
\(191\) −2.58985 4.48576i −0.187395 0.324578i 0.756986 0.653431i \(-0.226671\pi\)
−0.944381 + 0.328853i \(0.893338\pi\)
\(192\) 0 0
\(193\) −11.1088 −0.799629 −0.399814 0.916596i \(-0.630925\pi\)
−0.399814 + 0.916596i \(0.630925\pi\)
\(194\) 0 0
\(195\) −2.70849 4.69125i −0.193959 0.335947i
\(196\) 0 0
\(197\) 0.822256 1.42419i 0.0585833 0.101469i −0.835246 0.549876i \(-0.814675\pi\)
0.893830 + 0.448407i \(0.148008\pi\)
\(198\) 0 0
\(199\) 6.25750 + 10.8383i 0.443582 + 0.768307i 0.997952 0.0639631i \(-0.0203740\pi\)
−0.554370 + 0.832270i \(0.687041\pi\)
\(200\) 0 0
\(201\) 7.90197 + 2.13517i 0.557362 + 0.150603i
\(202\) 0 0
\(203\) 7.85060 + 13.5976i 0.551004 + 0.954367i
\(204\) 0 0
\(205\) 0.0559598 0.0969252i 0.00390840 0.00676955i
\(206\) 0 0
\(207\) 1.94438 + 3.36777i 0.135144 + 0.234076i
\(208\) 0 0
\(209\) −11.6525 −0.806023
\(210\) 0 0
\(211\) −6.16577 10.6794i −0.424469 0.735202i 0.571902 0.820322i \(-0.306206\pi\)
−0.996371 + 0.0851205i \(0.972872\pi\)
\(212\) 0 0
\(213\) −2.11366 + 3.66096i −0.144825 + 0.250845i
\(214\) 0 0
\(215\) 2.08087 0.141914
\(216\) 0 0
\(217\) −6.64337 11.5066i −0.450981 0.781122i
\(218\) 0 0
\(219\) 2.91448 + 5.04802i 0.196942 + 0.341114i
\(220\) 0 0
\(221\) 12.2894 21.2860i 0.826678 1.43185i
\(222\) 0 0
\(223\) −14.1142 −0.945159 −0.472579 0.881288i \(-0.656677\pi\)
−0.472579 + 0.881288i \(0.656677\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) −9.17609 + 15.8935i −0.609039 + 1.05489i 0.382361 + 0.924013i \(0.375111\pi\)
−0.991399 + 0.130873i \(0.958222\pi\)
\(228\) 0 0
\(229\) 11.3960 + 19.7385i 0.753071 + 1.30436i 0.946327 + 0.323210i \(0.104762\pi\)
−0.193256 + 0.981148i \(0.561905\pi\)
\(230\) 0 0
\(231\) 2.86188 + 4.95693i 0.188298 + 0.326142i
\(232\) 0 0
\(233\) −8.00903 + 13.8721i −0.524689 + 0.908789i 0.474897 + 0.880041i \(0.342485\pi\)
−0.999587 + 0.0287474i \(0.990848\pi\)
\(234\) 0 0
\(235\) −0.778456 + 1.34832i −0.0507808 + 0.0879550i
\(236\) 0 0
\(237\) −3.12853 + 5.41877i −0.203220 + 0.351987i
\(238\) 0 0
\(239\) −10.3235 + 17.8809i −0.667774 + 1.15662i 0.310752 + 0.950491i \(0.399419\pi\)
−0.978525 + 0.206127i \(0.933914\pi\)
\(240\) 0 0
\(241\) 3.17862 0.204753 0.102376 0.994746i \(-0.467355\pi\)
0.102376 + 0.994746i \(0.467355\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 1.68623 + 2.92063i 0.107729 + 0.186592i
\(246\) 0 0
\(247\) −10.5020 + 18.1901i −0.668228 + 1.15741i
\(248\) 0 0
\(249\) −0.214571 0.371649i −0.0135979 0.0235523i
\(250\) 0 0
\(251\) −5.34236 9.25324i −0.337207 0.584059i 0.646699 0.762745i \(-0.276149\pi\)
−0.983906 + 0.178686i \(0.942815\pi\)
\(252\) 0 0
\(253\) −11.6866 −0.734728
\(254\) 0 0
\(255\) 2.26869 + 3.92948i 0.142071 + 0.246074i
\(256\) 0 0
\(257\) 8.37861 14.5122i 0.522643 0.905244i −0.477010 0.878898i \(-0.658279\pi\)
0.999653 0.0263465i \(-0.00838731\pi\)
\(258\) 0 0
\(259\) −2.76548 −0.171838
\(260\) 0 0
\(261\) 4.12189 7.13932i 0.255138 0.441913i
\(262\) 0 0
\(263\) −8.51186 −0.524864 −0.262432 0.964951i \(-0.584525\pi\)
−0.262432 + 0.964951i \(0.584525\pi\)
\(264\) 0 0
\(265\) −8.39503 −0.515703
\(266\) 0 0
\(267\) 7.70404 0.471479
\(268\) 0 0
\(269\) −5.08990 −0.310337 −0.155168 0.987888i \(-0.549592\pi\)
−0.155168 + 0.987888i \(0.549592\pi\)
\(270\) 0 0
\(271\) 6.32399 0.384155 0.192078 0.981380i \(-0.438477\pi\)
0.192078 + 0.981380i \(0.438477\pi\)
\(272\) 0 0
\(273\) 10.3173 0.624429
\(274\) 0 0
\(275\) −1.50261 + 2.60259i −0.0906106 + 0.156942i
\(276\) 0 0
\(277\) −21.2318 −1.27569 −0.637847 0.770163i \(-0.720175\pi\)
−0.637847 + 0.770163i \(0.720175\pi\)
\(278\) 0 0
\(279\) −3.48804 + 6.04146i −0.208823 + 0.361693i
\(280\) 0 0
\(281\) −5.94374 10.2949i −0.354574 0.614139i 0.632471 0.774584i \(-0.282041\pi\)
−0.987045 + 0.160444i \(0.948707\pi\)
\(282\) 0 0
\(283\) −17.9152 −1.06495 −0.532473 0.846447i \(-0.678737\pi\)
−0.532473 + 0.846447i \(0.678737\pi\)
\(284\) 0 0
\(285\) −1.93872 3.35797i −0.114840 0.198909i
\(286\) 0 0
\(287\) 0.106582 + 0.184605i 0.00629132 + 0.0108969i
\(288\) 0 0
\(289\) −1.79388 + 3.10710i −0.105523 + 0.182770i
\(290\) 0 0
\(291\) 1.52705 + 2.64493i 0.0895172 + 0.155048i
\(292\) 0 0
\(293\) 8.98886 0.525135 0.262567 0.964914i \(-0.415431\pi\)
0.262567 + 0.964914i \(0.415431\pi\)
\(294\) 0 0
\(295\) −2.69514 −0.156917
\(296\) 0 0
\(297\) 1.50261 2.60259i 0.0871901 0.151018i
\(298\) 0 0
\(299\) −10.5327 + 18.2432i −0.609121 + 1.05503i
\(300\) 0 0
\(301\) −1.98163 + 3.43228i −0.114219 + 0.197833i
\(302\) 0 0
\(303\) 3.83823 6.64801i 0.220501 0.381918i
\(304\) 0 0
\(305\) −0.711547 1.23244i −0.0407431 0.0705691i
\(306\) 0 0
\(307\) −8.11191 14.0502i −0.462971 0.801890i 0.536136 0.844132i \(-0.319883\pi\)
−0.999107 + 0.0422417i \(0.986550\pi\)
\(308\) 0 0
\(309\) 8.08233 13.9990i 0.459788 0.796376i
\(310\) 0 0
\(311\) −7.88048 −0.446861 −0.223430 0.974720i \(-0.571726\pi\)
−0.223430 + 0.974720i \(0.571726\pi\)
\(312\) 0 0
\(313\) 20.1030 1.13629 0.568143 0.822930i \(-0.307662\pi\)
0.568143 + 0.822930i \(0.307662\pi\)
\(314\) 0 0
\(315\) −0.952306 + 1.64944i −0.0536564 + 0.0929356i
\(316\) 0 0
\(317\) 3.36681 + 5.83149i 0.189099 + 0.327529i 0.944950 0.327214i \(-0.106110\pi\)
−0.755851 + 0.654744i \(0.772777\pi\)
\(318\) 0 0
\(319\) 12.3871 + 21.4552i 0.693547 + 1.20126i
\(320\) 0 0
\(321\) −8.41550 −0.469708
\(322\) 0 0
\(323\) 8.79671 15.2363i 0.489462 0.847773i
\(324\) 0 0
\(325\) 2.70849 + 4.69125i 0.150240 + 0.260224i
\(326\) 0 0
\(327\) 4.00738 0.221609
\(328\) 0 0
\(329\) −1.48266 2.56804i −0.0817415 0.141580i
\(330\) 0 0
\(331\) −8.62257 + 14.9347i −0.473939 + 0.820887i −0.999555 0.0298355i \(-0.990502\pi\)
0.525616 + 0.850722i \(0.323835\pi\)
\(332\) 0 0
\(333\) 0.725995 + 1.25746i 0.0397843 + 0.0689084i
\(334\) 0 0
\(335\) −7.90197 2.13517i −0.431731 0.116657i
\(336\) 0 0
\(337\) −3.60167 6.23828i −0.196196 0.339821i 0.751096 0.660193i \(-0.229525\pi\)
−0.947292 + 0.320372i \(0.896192\pi\)
\(338\) 0 0
\(339\) 0.127891 0.221514i 0.00694610 0.0120310i
\(340\) 0 0
\(341\) −10.4823 18.1559i −0.567648 0.983196i
\(342\) 0 0
\(343\) −19.7555 −1.06670
\(344\) 0 0
\(345\) −1.94438 3.36777i −0.104682 0.181315i
\(346\) 0 0
\(347\) 11.3596 19.6754i 0.609815 1.05623i −0.381455 0.924387i \(-0.624577\pi\)
0.991270 0.131844i \(-0.0420898\pi\)
\(348\) 0 0
\(349\) −4.33225 −0.231900 −0.115950 0.993255i \(-0.536991\pi\)
−0.115950 + 0.993255i \(0.536991\pi\)
\(350\) 0 0
\(351\) −2.70849 4.69125i −0.144569 0.250400i
\(352\) 0 0
\(353\) 11.7645 + 20.3768i 0.626163 + 1.08455i 0.988315 + 0.152427i \(0.0487090\pi\)
−0.362151 + 0.932119i \(0.617958\pi\)
\(354\) 0 0
\(355\) 2.11366 3.66096i 0.112181 0.194304i
\(356\) 0 0
\(357\) −8.64194 −0.457380
\(358\) 0 0
\(359\) 16.6177 0.877048 0.438524 0.898719i \(-0.355501\pi\)
0.438524 + 0.898719i \(0.355501\pi\)
\(360\) 0 0
\(361\) 1.98271 3.43416i 0.104353 0.180745i
\(362\) 0 0
\(363\) −0.984349 1.70494i −0.0516649 0.0894863i
\(364\) 0 0
\(365\) −2.91448 5.04802i −0.152551 0.264226i
\(366\) 0 0
\(367\) −16.6017 + 28.7549i −0.866600 + 1.50100i −0.00115093 + 0.999999i \(0.500366\pi\)
−0.865449 + 0.500996i \(0.832967\pi\)
\(368\) 0 0
\(369\) 0.0559598 0.0969252i 0.00291315 0.00504573i
\(370\) 0 0
\(371\) 7.99464 13.8471i 0.415061 0.718907i
\(372\) 0 0
\(373\) −14.4803 + 25.0807i −0.749763 + 1.29863i 0.198173 + 0.980167i \(0.436499\pi\)
−0.947936 + 0.318461i \(0.896834\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) 44.6564 2.29992
\(378\) 0 0
\(379\) 1.44016 + 2.49444i 0.0739763 + 0.128131i 0.900641 0.434565i \(-0.143098\pi\)
−0.826664 + 0.562695i \(0.809764\pi\)
\(380\) 0 0
\(381\) 1.91787 3.32185i 0.0982556 0.170184i
\(382\) 0 0
\(383\) −5.91934 10.2526i −0.302464 0.523883i 0.674229 0.738522i \(-0.264476\pi\)
−0.976694 + 0.214639i \(0.931143\pi\)
\(384\) 0 0
\(385\) −2.86188 4.95693i −0.145855 0.252628i
\(386\) 0 0
\(387\) 2.08087 0.105777
\(388\) 0 0
\(389\) −14.4580 25.0421i −0.733051 1.26968i −0.955573 0.294755i \(-0.904762\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(390\) 0 0
\(391\) 8.82239 15.2808i 0.446167 0.772785i
\(392\) 0 0
\(393\) −20.6597 −1.04214
\(394\) 0 0
\(395\) 3.12853 5.41877i 0.157413 0.272648i
\(396\) 0 0
\(397\) −27.7710 −1.39379 −0.696894 0.717174i \(-0.745435\pi\)
−0.696894 + 0.717174i \(0.745435\pi\)
\(398\) 0 0
\(399\) 7.38503 0.369714
\(400\) 0 0
\(401\) 31.0164 1.54889 0.774443 0.632644i \(-0.218030\pi\)
0.774443 + 0.632644i \(0.218030\pi\)
\(402\) 0 0
\(403\) −37.7893 −1.88242
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) −4.36354 −0.216292
\(408\) 0 0
\(409\) −12.7849 + 22.1442i −0.632174 + 1.09496i 0.354932 + 0.934892i \(0.384504\pi\)
−0.987106 + 0.160066i \(0.948829\pi\)
\(410\) 0 0
\(411\) 6.37529 0.314470
\(412\) 0 0
\(413\) 2.56660 4.44548i 0.126294 0.218748i
\(414\) 0 0
\(415\) 0.214571 + 0.371649i 0.0105329 + 0.0182435i
\(416\) 0 0
\(417\) −6.06502 −0.297005
\(418\) 0 0
\(419\) 13.1209 + 22.7261i 0.641000 + 1.11024i 0.985210 + 0.171352i \(0.0548135\pi\)
−0.344210 + 0.938893i \(0.611853\pi\)
\(420\) 0 0
\(421\) 13.0050 + 22.5253i 0.633823 + 1.09781i 0.986763 + 0.162168i \(0.0518486\pi\)
−0.352940 + 0.935646i \(0.614818\pi\)
\(422\) 0 0
\(423\) −0.778456 + 1.34832i −0.0378498 + 0.0655578i
\(424\) 0 0
\(425\) −2.26869 3.92948i −0.110047 0.190608i
\(426\) 0 0
\(427\) 2.71044 0.131168
\(428\) 0 0
\(429\) 16.2792 0.785967
\(430\) 0 0
\(431\) 4.02725 6.97541i 0.193986 0.335993i −0.752582 0.658499i \(-0.771192\pi\)
0.946568 + 0.322505i \(0.104525\pi\)
\(432\) 0 0
\(433\) −7.04054 + 12.1946i −0.338347 + 0.586034i −0.984122 0.177494i \(-0.943201\pi\)
0.645775 + 0.763528i \(0.276534\pi\)
\(434\) 0 0
\(435\) −4.12189 + 7.13932i −0.197629 + 0.342304i
\(436\) 0 0
\(437\) −7.53923 + 13.0583i −0.360650 + 0.624665i
\(438\) 0 0
\(439\) −16.5384 28.6453i −0.789333 1.36717i −0.926376 0.376600i \(-0.877093\pi\)
0.137042 0.990565i \(-0.456240\pi\)
\(440\) 0 0
\(441\) 1.68623 + 2.92063i 0.0802964 + 0.139078i
\(442\) 0 0
\(443\) −2.08553 + 3.61225i −0.0990867 + 0.171623i −0.911307 0.411728i \(-0.864925\pi\)
0.812220 + 0.583351i \(0.198259\pi\)
\(444\) 0 0
\(445\) −7.70404 −0.365206
\(446\) 0 0
\(447\) 19.0684 0.901905
\(448\) 0 0
\(449\) 4.90893 8.50251i 0.231667 0.401258i −0.726632 0.687027i \(-0.758916\pi\)
0.958299 + 0.285769i \(0.0922488\pi\)
\(450\) 0 0
\(451\) 0.168171 + 0.291281i 0.00791887 + 0.0137159i
\(452\) 0 0
\(453\) 3.80844 + 6.59641i 0.178936 + 0.309926i
\(454\) 0 0
\(455\) −10.3173 −0.483681
\(456\) 0 0
\(457\) 0.154702 0.267953i 0.00723668 0.0125343i −0.862384 0.506254i \(-0.831030\pi\)
0.869621 + 0.493720i \(0.164363\pi\)
\(458\) 0 0
\(459\) 2.26869 + 3.92948i 0.105893 + 0.183412i
\(460\) 0 0
\(461\) 14.0077 0.652403 0.326202 0.945300i \(-0.394231\pi\)
0.326202 + 0.945300i \(0.394231\pi\)
\(462\) 0 0
\(463\) 14.5872 + 25.2657i 0.677923 + 1.17420i 0.975605 + 0.219532i \(0.0704530\pi\)
−0.297682 + 0.954665i \(0.596214\pi\)
\(464\) 0 0
\(465\) 3.48804 6.04146i 0.161754 0.280166i
\(466\) 0 0
\(467\) −3.69351 6.39735i −0.170915 0.296034i 0.767825 0.640660i \(-0.221339\pi\)
−0.938740 + 0.344626i \(0.888006\pi\)
\(468\) 0 0
\(469\) 11.0469 11.0005i 0.510100 0.507956i
\(470\) 0 0
\(471\) −2.20493 3.81905i −0.101598 0.175973i
\(472\) 0 0
\(473\) −3.12673 + 5.41566i −0.143767 + 0.249012i
\(474\) 0 0
\(475\) 1.93872 + 3.35797i 0.0889547 + 0.154074i
\(476\) 0 0
\(477\) −8.39503 −0.384382
\(478\) 0 0
\(479\) −17.1665 29.7333i −0.784359 1.35855i −0.929381 0.369121i \(-0.879659\pi\)
0.145023 0.989428i \(-0.453675\pi\)
\(480\) 0 0
\(481\) −3.93270 + 6.81164i −0.179316 + 0.310584i
\(482\) 0 0
\(483\) 7.40659 0.337011
\(484\) 0 0
\(485\) −1.52705 2.64493i −0.0693397 0.120100i
\(486\) 0 0
\(487\) 20.3592 + 35.2631i 0.922562 + 1.59792i 0.795436 + 0.606038i \(0.207242\pi\)
0.127126 + 0.991887i \(0.459425\pi\)
\(488\) 0 0
\(489\) 3.43242 5.94512i 0.155219 0.268848i
\(490\) 0 0
\(491\) 10.0579 0.453909 0.226954 0.973905i \(-0.427123\pi\)
0.226954 + 0.973905i \(0.427123\pi\)
\(492\) 0 0
\(493\) −37.4051 −1.68464
\(494\) 0 0
\(495\) −1.50261 + 2.60259i −0.0675371 + 0.116978i
\(496\) 0 0
\(497\) 4.02570 + 6.97271i 0.180577 + 0.312769i
\(498\) 0 0
\(499\) −7.55005 13.0771i −0.337987 0.585410i 0.646067 0.763281i \(-0.276413\pi\)
−0.984054 + 0.177870i \(0.943079\pi\)
\(500\) 0 0
\(501\) 9.03170 15.6434i 0.403506 0.698894i
\(502\) 0 0
\(503\) −9.62438 + 16.6699i −0.429130 + 0.743274i −0.996796 0.0799842i \(-0.974513\pi\)
0.567666 + 0.823259i \(0.307846\pi\)
\(504\) 0 0
\(505\) −3.83823 + 6.64801i −0.170799 + 0.295833i
\(506\) 0 0
\(507\) 8.17188 14.1541i 0.362926 0.628606i
\(508\) 0 0
\(509\) −28.0604 −1.24376 −0.621878 0.783114i \(-0.713630\pi\)
−0.621878 + 0.783114i \(0.713630\pi\)
\(510\) 0 0
\(511\) 11.1019 0.491119
\(512\) 0 0
\(513\) −1.93872 3.35797i −0.0855967 0.148258i
\(514\) 0 0
\(515\) −8.08233 + 13.9990i −0.356150 + 0.616870i
\(516\) 0 0
\(517\) −2.33942 4.05200i −0.102888 0.178207i
\(518\) 0 0
\(519\) −2.91255 5.04469i −0.127847 0.221437i
\(520\) 0 0
\(521\) 33.9781 1.48861 0.744303 0.667842i \(-0.232782\pi\)
0.744303 + 0.667842i \(0.232782\pi\)
\(522\) 0 0
\(523\) −2.30814 3.99781i −0.100928 0.174812i 0.811139 0.584853i \(-0.198848\pi\)
−0.912067 + 0.410041i \(0.865514\pi\)
\(524\) 0 0
\(525\) 0.952306 1.64944i 0.0415621 0.0719876i
\(526\) 0 0
\(527\) 31.6531 1.37883
\(528\) 0 0
\(529\) 3.93876 6.82213i 0.171250 0.296614i
\(530\) 0 0
\(531\) −2.69514 −0.116959
\(532\) 0 0
\(533\) 0.606267 0.0262603
\(534\) 0 0
\(535\) 8.41550 0.363834
\(536\) 0 0
\(537\) −8.32860 −0.359406
\(538\) 0 0
\(539\) −10.1349 −0.436542
\(540\) 0 0
\(541\) 45.1210 1.93990 0.969952 0.243295i \(-0.0782284\pi\)
0.969952 + 0.243295i \(0.0782284\pi\)
\(542\) 0 0
\(543\) −4.40709 + 7.63330i −0.189126 + 0.327576i
\(544\) 0 0
\(545\) −4.00738 −0.171657
\(546\) 0 0
\(547\) −9.41013 + 16.2988i −0.402348 + 0.696887i −0.994009 0.109300i \(-0.965139\pi\)
0.591661 + 0.806187i \(0.298472\pi\)
\(548\) 0 0
\(549\) −0.711547 1.23244i −0.0303681 0.0525991i
\(550\) 0 0
\(551\) 31.9648 1.36174
\(552\) 0 0
\(553\) 5.95863 + 10.3207i 0.253387 + 0.438879i
\(554\) 0 0
\(555\) −0.725995 1.25746i −0.0308168 0.0533762i
\(556\) 0 0
\(557\) 10.2456 17.7459i 0.434121 0.751919i −0.563103 0.826387i \(-0.690392\pi\)
0.997223 + 0.0744679i \(0.0237258\pi\)
\(558\) 0 0
\(559\) 5.63603 + 9.76189i 0.238379 + 0.412884i
\(560\) 0 0
\(561\) −13.6358 −0.575703
\(562\) 0 0
\(563\) 14.3876 0.606366 0.303183 0.952932i \(-0.401951\pi\)
0.303183 + 0.952932i \(0.401951\pi\)
\(564\) 0 0
\(565\) −0.127891 + 0.221514i −0.00538043 + 0.00931917i
\(566\) 0 0
\(567\) −0.952306 + 1.64944i −0.0399931 + 0.0692701i
\(568\) 0 0
\(569\) −15.0338 + 26.0393i −0.630249 + 1.09162i 0.357252 + 0.934008i \(0.383714\pi\)
−0.987501 + 0.157615i \(0.949620\pi\)
\(570\) 0 0
\(571\) −7.25219 + 12.5612i −0.303495 + 0.525668i −0.976925 0.213582i \(-0.931487\pi\)
0.673430 + 0.739251i \(0.264820\pi\)
\(572\) 0 0
\(573\) 2.58985 + 4.48576i 0.108193 + 0.187395i
\(574\) 0 0
\(575\) 1.94438 + 3.36777i 0.0810863 + 0.140446i
\(576\) 0 0
\(577\) 1.32727 2.29889i 0.0552548 0.0957041i −0.837075 0.547088i \(-0.815736\pi\)
0.892330 + 0.451384i \(0.149070\pi\)
\(578\) 0 0
\(579\) 11.1088 0.461666
\(580\) 0 0
\(581\) −0.817351 −0.0339094
\(582\) 0 0
\(583\) 12.6144 21.8488i 0.522436 0.904886i
\(584\) 0 0
\(585\) 2.70849 + 4.69125i 0.111982 + 0.193959i
\(586\) 0 0
\(587\) 0.111235 + 0.192665i 0.00459117 + 0.00795214i 0.868312 0.496019i \(-0.165205\pi\)
−0.863721 + 0.503971i \(0.831872\pi\)
\(588\) 0 0
\(589\) −27.0494 −1.11455
\(590\) 0 0
\(591\) −0.822256 + 1.42419i −0.0338231 + 0.0585833i
\(592\) 0 0
\(593\) −11.7261 20.3103i −0.481535 0.834043i 0.518240 0.855235i \(-0.326587\pi\)
−0.999775 + 0.0211918i \(0.993254\pi\)
\(594\) 0 0
\(595\) 8.64194 0.354285
\(596\) 0 0
\(597\) −6.25750 10.8383i −0.256102 0.443582i
\(598\) 0 0
\(599\) 18.6959 32.3823i 0.763895 1.32310i −0.176934 0.984223i \(-0.556618\pi\)
0.940829 0.338882i \(-0.110049\pi\)
\(600\) 0 0
\(601\) 0.570375 + 0.987919i 0.0232661 + 0.0402980i 0.877424 0.479716i \(-0.159260\pi\)
−0.854158 + 0.520014i \(0.825927\pi\)
\(602\) 0 0
\(603\) −7.90197 2.13517i −0.321793 0.0869507i
\(604\) 0 0
\(605\) 0.984349 + 1.70494i 0.0400195 + 0.0693158i
\(606\) 0 0
\(607\) 16.2178 28.0901i 0.658262 1.14014i −0.322804 0.946466i \(-0.604625\pi\)
0.981065 0.193677i \(-0.0620413\pi\)
\(608\) 0 0
\(609\) −7.85060 13.5976i −0.318122 0.551004i
\(610\) 0 0
\(611\) −8.43377 −0.341194
\(612\) 0 0
\(613\) −3.20790 5.55625i −0.129566 0.224415i 0.793943 0.607993i \(-0.208025\pi\)
−0.923508 + 0.383578i \(0.874692\pi\)
\(614\) 0 0
\(615\) −0.0559598 + 0.0969252i −0.00225652 + 0.00390840i
\(616\) 0 0
\(617\) 22.0259 0.886730 0.443365 0.896341i \(-0.353785\pi\)
0.443365 + 0.896341i \(0.353785\pi\)
\(618\) 0 0
\(619\) −20.7749 35.9831i −0.835012 1.44628i −0.894021 0.448026i \(-0.852127\pi\)
0.0590084 0.998257i \(-0.481206\pi\)
\(620\) 0 0
\(621\) −1.94438 3.36777i −0.0780254 0.135144i
\(622\) 0 0
\(623\) 7.33660 12.7074i 0.293935 0.509110i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 11.6525 0.465358
\(628\) 0 0
\(629\) 3.29411 5.70556i 0.131345 0.227496i
\(630\) 0 0
\(631\) 8.33335 + 14.4338i 0.331745 + 0.574600i 0.982854 0.184385i \(-0.0590292\pi\)
−0.651109 + 0.758984i \(0.725696\pi\)
\(632\) 0 0
\(633\) 6.16577 + 10.6794i 0.245067 + 0.424469i
\(634\) 0 0
\(635\) −1.91787 + 3.32185i −0.0761084 + 0.131824i
\(636\) 0 0
\(637\) −9.13426 + 15.8210i −0.361913 + 0.626851i
\(638\) 0 0
\(639\) 2.11366 3.66096i 0.0836150 0.144825i
\(640\) 0 0
\(641\) 19.4494 33.6874i 0.768206 1.33057i −0.170329 0.985387i \(-0.554483\pi\)
0.938535 0.345184i \(-0.112184\pi\)
\(642\) 0 0
\(643\) 14.0504 0.554092 0.277046 0.960857i \(-0.410644\pi\)
0.277046 + 0.960857i \(0.410644\pi\)
\(644\) 0 0
\(645\) −2.08087 −0.0819342
\(646\) 0 0
\(647\) 17.7320 + 30.7127i 0.697116 + 1.20744i 0.969462 + 0.245242i \(0.0788673\pi\)
−0.272345 + 0.962200i \(0.587799\pi\)
\(648\) 0 0
\(649\) 4.04973 7.01434i 0.158966 0.275337i
\(650\) 0 0
\(651\) 6.64337 + 11.5066i 0.260374 + 0.450981i
\(652\) 0 0
\(653\) 9.25399 + 16.0284i 0.362137 + 0.627239i 0.988312 0.152443i \(-0.0487140\pi\)
−0.626176 + 0.779682i \(0.715381\pi\)
\(654\) 0 0
\(655\) 20.6597 0.807240
\(656\) 0 0
\(657\) −2.91448 5.04802i −0.113705 0.196942i
\(658\) 0 0
\(659\) −5.16040 + 8.93807i −0.201021 + 0.348178i −0.948858 0.315705i \(-0.897759\pi\)
0.747837 + 0.663882i \(0.231092\pi\)
\(660\) 0 0
\(661\) −21.1457 −0.822471 −0.411235 0.911529i \(-0.634903\pi\)
−0.411235 + 0.911529i \(0.634903\pi\)
\(662\) 0 0
\(663\) −12.2894 + 21.2860i −0.477283 + 0.826678i
\(664\) 0 0
\(665\) −7.38503 −0.286379
\(666\) 0 0
\(667\) 32.0581 1.24129
\(668\) 0 0
\(669\) 14.1142 0.545688
\(670\) 0 0
\(671\) 4.27670 0.165100
\(672\) 0 0
\(673\) −28.5294 −1.09973 −0.549864 0.835254i \(-0.685321\pi\)
−0.549864 + 0.835254i \(0.685321\pi\)
\(674\) 0 0
\(675\) −1.00000 −0.0384900
\(676\) 0 0
\(677\) 15.2026 26.3317i 0.584285 1.01201i −0.410680 0.911780i \(-0.634709\pi\)
0.994964 0.100231i \(-0.0319581\pi\)
\(678\) 0 0
\(679\) 5.81688 0.223231
\(680\) 0 0
\(681\) 9.17609 15.8935i 0.351629 0.609039i
\(682\) 0 0
\(683\) −10.0436 17.3960i −0.384307 0.665639i 0.607366 0.794422i \(-0.292226\pi\)
−0.991673 + 0.128783i \(0.958893\pi\)
\(684\) 0 0
\(685\) −6.37529 −0.243587
\(686\) 0 0
\(687\) −11.3960 19.7385i −0.434786 0.753071i
\(688\) 0 0
\(689\) −22.7379 39.3832i −0.866245 1.50038i
\(690\) 0 0
\(691\) 0.382534 0.662568i 0.0145523 0.0252053i −0.858658 0.512550i \(-0.828701\pi\)
0.873210 + 0.487344i \(0.162034\pi\)
\(692\) 0 0
\(693\) −2.86188 4.95693i −0.108714 0.188298i
\(694\) 0 0
\(695\) 6.06502 0.230059
\(696\) 0 0
\(697\) −0.507821 −0.0192351
\(698\) 0 0
\(699\) 8.00903 13.8721i 0.302930 0.524689i
\(700\) 0 0
\(701\) 11.1887 19.3794i 0.422592 0.731951i −0.573600 0.819136i \(-0.694454\pi\)
0.996192 + 0.0871843i \(0.0277869\pi\)
\(702\) 0 0
\(703\) −2.81500 + 4.87573i −0.106170 + 0.183892i
\(704\) 0 0
\(705\) 0.778456 1.34832i 0.0293183 0.0507808i
\(706\) 0 0
\(707\) −7.31034 12.6619i −0.274934 0.476199i
\(708\) 0 0
\(709\) −13.7785 23.8651i −0.517462 0.896271i −0.999794 0.0202824i \(-0.993543\pi\)
0.482332 0.875988i \(-0.339790\pi\)
\(710\) 0 0
\(711\) 3.12853 5.41877i 0.117329 0.203220i
\(712\) 0 0
\(713\) −27.1283 −1.01596
\(714\) 0 0
\(715\) −16.2792 −0.608807
\(716\) 0 0
\(717\) 10.3235 17.8809i 0.385539 0.667774i
\(718\) 0 0
\(719\) 17.9605 + 31.1085i 0.669813 + 1.16015i 0.977956 + 0.208811i \(0.0669593\pi\)
−0.308143 + 0.951340i \(0.599707\pi\)
\(720\) 0 0
\(721\) −15.3937 26.6627i −0.573292 0.992971i
\(722\) 0 0
\(723\) −3.17862 −0.118214
\(724\) 0 0
\(725\) 4.12189 7.13932i 0.153083 0.265148i
\(726\) 0 0
\(727\) −8.61887 14.9283i −0.319656 0.553661i 0.660760 0.750597i \(-0.270234\pi\)
−0.980416 + 0.196937i \(0.936901\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −4.72085 8.17675i −0.174607 0.302428i
\(732\) 0 0
\(733\) 10.1070 17.5058i 0.373311 0.646593i −0.616762 0.787150i \(-0.711556\pi\)
0.990073 + 0.140557i \(0.0448892\pi\)
\(734\) 0 0
\(735\) −1.68623 2.92063i −0.0621974 0.107729i
\(736\) 0 0
\(737\) 17.4305 17.3573i 0.642061 0.639363i
\(738\) 0 0
\(739\) −2.29101 3.96814i −0.0842760 0.145970i 0.820806 0.571206i \(-0.193524\pi\)
−0.905082 + 0.425236i \(0.860191\pi\)
\(740\) 0 0
\(741\) 10.5020 18.1901i 0.385802 0.668228i
\(742\) 0 0
\(743\) 14.5208 + 25.1508i 0.532717 + 0.922693i 0.999270 + 0.0382000i \(0.0121624\pi\)
−0.466553 + 0.884493i \(0.654504\pi\)
\(744\) 0 0
\(745\) −19.0684 −0.698613
\(746\) 0 0
\(747\) 0.214571 + 0.371649i 0.00785076 + 0.0135979i
\(748\) 0 0
\(749\) −8.01414 + 13.8809i −0.292830 + 0.507197i
\(750\) 0 0
\(751\) 32.5475 1.18767 0.593837 0.804586i \(-0.297613\pi\)
0.593837 + 0.804586i \(0.297613\pi\)
\(752\) 0 0
\(753\) 5.34236 + 9.25324i 0.194686 + 0.337207i
\(754\) 0 0
\(755\) −3.80844 6.59641i −0.138603 0.240068i
\(756\) 0 0
\(757\) 15.9972 27.7080i 0.581428 1.00706i −0.413882 0.910330i \(-0.635827\pi\)
0.995310 0.0967327i \(-0.0308392\pi\)
\(758\) 0 0
\(759\) 11.6866 0.424195
\(760\) 0 0
\(761\) 21.4269 0.776726 0.388363 0.921507i \(-0.373041\pi\)
0.388363 + 0.921507i \(0.373041\pi\)
\(762\) 0 0
\(763\) 3.81625 6.60995i 0.138158 0.239296i
\(764\) 0 0
\(765\) −2.26869 3.92948i −0.0820246 0.142071i
\(766\) 0 0
\(767\) −7.29976 12.6436i −0.263579 0.456532i
\(768\) 0 0
\(769\) 20.6011 35.6821i 0.742893 1.28673i −0.208280 0.978069i \(-0.566786\pi\)
0.951173 0.308659i \(-0.0998802\pi\)
\(770\) 0 0
\(771\) −8.37861 + 14.5122i −0.301748 + 0.522643i
\(772\) 0 0
\(773\) 13.9889 24.2295i 0.503147 0.871476i −0.496846 0.867839i \(-0.665509\pi\)
0.999993 0.00363766i \(-0.00115790\pi\)
\(774\) 0 0
\(775\) −3.48804 + 6.04146i −0.125294 + 0.217016i
\(776\) 0 0
\(777\) 2.76548 0.0992109
\(778\) 0 0
\(779\) 0.433962 0.0155483
\(780\) 0 0
\(781\) 6.35199 + 11.0020i 0.227292 + 0.393681i
\(782\) 0 0
\(783\) −4.12189 + 7.13932i −0.147304 + 0.255138i
\(784\) 0 0
\(785\) 2.20493 + 3.81905i 0.0786973 + 0.136308i
\(786\) 0 0
\(787\) −9.55242 16.5453i −0.340507 0.589776i 0.644020 0.765009i \(-0.277265\pi\)
−0.984527 + 0.175233i \(0.943932\pi\)
\(788\) 0 0
\(789\) 8.51186 0.303030
\(790\) 0 0
\(791\) −0.243583 0.421899i −0.00866083 0.0150010i
\(792\) 0 0
\(793\) 3.85444 6.67609i 0.136875