Properties

Label 4020.2.q.k.3781.4
Level 4020
Weight 2
Character 4020.3781
Analytic conductor 32.100
Analytic rank 0
Dimension 14
CM No
Inner twists 2

Related objects

Downloads

Learn more about

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 3781.4
Root \(0.150493 + 0.260662i\)
Character \(\chi\) = 4020.3781
Dual form 4020.2.q.k.841.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.00000 q^{5} +(0.827889 + 1.43395i) q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +1.00000 q^{5} +(0.827889 + 1.43395i) q^{7} +1.00000 q^{9} +(-2.81310 - 4.87244i) q^{11} +(0.800986 - 1.38735i) q^{13} -1.00000 q^{15} +(-1.35601 + 2.34868i) q^{17} +(-0.454704 + 0.787570i) q^{19} +(-0.827889 - 1.43395i) q^{21} +(-3.02247 + 5.23507i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-1.34683 - 2.33278i) q^{29} +(5.11431 + 8.85825i) q^{31} +(2.81310 + 4.87244i) q^{33} +(0.827889 + 1.43395i) q^{35} +(-0.237490 + 0.411344i) q^{37} +(-0.800986 + 1.38735i) q^{39} +(0.573228 + 0.992859i) q^{41} +5.46671 q^{43} +1.00000 q^{45} +(1.69934 + 2.94334i) q^{47} +(2.12920 - 3.68788i) q^{49} +(1.35601 - 2.34868i) q^{51} -5.97455 q^{53} +(-2.81310 - 4.87244i) q^{55} +(0.454704 - 0.787570i) q^{57} +8.25736 q^{59} +(5.07988 - 8.79861i) q^{61} +(0.827889 + 1.43395i) q^{63} +(0.800986 - 1.38735i) q^{65} +(8.03367 - 1.56851i) q^{67} +(3.02247 - 5.23507i) q^{69} +(1.81642 + 3.14614i) q^{71} +(-0.751860 + 1.30226i) q^{73} -1.00000 q^{75} +(4.65787 - 8.06767i) q^{77} +(4.38601 + 7.59678i) q^{79} +1.00000 q^{81} +(-5.96714 + 10.3354i) q^{83} +(-1.35601 + 2.34868i) q^{85} +(1.34683 + 2.33278i) q^{87} +10.1310 q^{89} +2.65251 q^{91} +(-5.11431 - 8.85825i) q^{93} +(-0.454704 + 0.787570i) q^{95} +(2.33139 - 4.03809i) q^{97} +(-2.81310 - 4.87244i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{3} + 14q^{5} + 3q^{7} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{3} + 14q^{5} + 3q^{7} + 14q^{9} + 6q^{11} + 9q^{13} - 14q^{15} - 12q^{17} + 14q^{19} - 3q^{21} + 6q^{23} + 14q^{25} - 14q^{27} - q^{29} + 7q^{31} - 6q^{33} + 3q^{35} - 2q^{37} - 9q^{39} - 18q^{41} - 6q^{43} + 14q^{45} + 7q^{47} + 12q^{51} - 12q^{53} + 6q^{55} - 14q^{57} - 2q^{59} + 3q^{63} + 9q^{65} + 25q^{67} - 6q^{69} + 22q^{71} - 15q^{73} - 14q^{75} + q^{77} + 9q^{79} + 14q^{81} - q^{83} - 12q^{85} + q^{87} - 12q^{89} - 38q^{91} - 7q^{93} + 14q^{95} + 16q^{97} + 6q^{99} + O(q^{100}) \)

Character Values

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

\(n\) \(1141\) \(2011\) \(2681\) \(3217\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(1\)

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
\(7\) 0.827889 + 1.43395i 0.312913 + 0.541981i 0.978992 0.203901i \(-0.0653620\pi\)
−0.666079 + 0.745881i \(0.732029\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −2.81310 4.87244i −0.848182 1.46909i −0.882829 0.469695i \(-0.844364\pi\)
0.0346464 0.999400i \(-0.488970\pi\)
\(12\) 0 0
\(13\) 0.800986 1.38735i 0.222154 0.384781i −0.733308 0.679897i \(-0.762025\pi\)
0.955462 + 0.295115i \(0.0953580\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) −1.35601 + 2.34868i −0.328882 + 0.569640i −0.982290 0.187366i \(-0.940005\pi\)
0.653409 + 0.757005i \(0.273338\pi\)
\(18\) 0 0
\(19\) −0.454704 + 0.787570i −0.104316 + 0.180681i −0.913459 0.406932i \(-0.866599\pi\)
0.809142 + 0.587613i \(0.199932\pi\)
\(20\) 0 0
\(21\) −0.827889 1.43395i −0.180660 0.312913i
\(22\) 0 0
\(23\) −3.02247 + 5.23507i −0.630228 + 1.09159i 0.357277 + 0.933999i \(0.383705\pi\)
−0.987505 + 0.157588i \(0.949628\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −1.34683 2.33278i −0.250100 0.433186i 0.713453 0.700703i \(-0.247130\pi\)
−0.963553 + 0.267517i \(0.913797\pi\)
\(30\) 0 0
\(31\) 5.11431 + 8.85825i 0.918558 + 1.59099i 0.801608 + 0.597850i \(0.203978\pi\)
0.116950 + 0.993138i \(0.462688\pi\)
\(32\) 0 0
\(33\) 2.81310 + 4.87244i 0.489698 + 0.848182i
\(34\) 0 0
\(35\) 0.827889 + 1.43395i 0.139939 + 0.242381i
\(36\) 0 0
\(37\) −0.237490 + 0.411344i −0.0390430 + 0.0676245i −0.884887 0.465806i \(-0.845764\pi\)
0.845844 + 0.533431i \(0.179098\pi\)
\(38\) 0 0
\(39\) −0.800986 + 1.38735i −0.128260 + 0.222154i
\(40\) 0 0
\(41\) 0.573228 + 0.992859i 0.0895231 + 0.155059i 0.907310 0.420463i \(-0.138132\pi\)
−0.817787 + 0.575522i \(0.804799\pi\)
\(42\) 0 0
\(43\) 5.46671 0.833665 0.416833 0.908983i \(-0.363140\pi\)
0.416833 + 0.908983i \(0.363140\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) 1.69934 + 2.94334i 0.247874 + 0.429330i 0.962936 0.269731i \(-0.0869348\pi\)
−0.715062 + 0.699061i \(0.753601\pi\)
\(48\) 0 0
\(49\) 2.12920 3.68788i 0.304171 0.526840i
\(50\) 0 0
\(51\) 1.35601 2.34868i 0.189880 0.328882i
\(52\) 0 0
\(53\) −5.97455 −0.820667 −0.410334 0.911935i \(-0.634588\pi\)
−0.410334 + 0.911935i \(0.634588\pi\)
\(54\) 0 0
\(55\) −2.81310 4.87244i −0.379319 0.656999i
\(56\) 0 0
\(57\) 0.454704 0.787570i 0.0602270 0.104316i
\(58\) 0 0
\(59\) 8.25736 1.07502 0.537509 0.843258i \(-0.319366\pi\)
0.537509 + 0.843258i \(0.319366\pi\)
\(60\) 0 0
\(61\) 5.07988 8.79861i 0.650412 1.12655i −0.332611 0.943064i \(-0.607930\pi\)
0.983023 0.183482i \(-0.0587371\pi\)
\(62\) 0 0
\(63\) 0.827889 + 1.43395i 0.104304 + 0.180660i
\(64\) 0 0
\(65\) 0.800986 1.38735i 0.0993501 0.172079i
\(66\) 0 0
\(67\) 8.03367 1.56851i 0.981469 0.191623i
\(68\) 0 0
\(69\) 3.02247 5.23507i 0.363862 0.630228i
\(70\) 0 0
\(71\) 1.81642 + 3.14614i 0.215570 + 0.373378i 0.953449 0.301555i \(-0.0975058\pi\)
−0.737879 + 0.674933i \(0.764172\pi\)
\(72\) 0 0
\(73\) −0.751860 + 1.30226i −0.0879985 + 0.152418i −0.906665 0.421851i \(-0.861380\pi\)
0.818667 + 0.574269i \(0.194714\pi\)
\(74\) 0 0
\(75\) −1.00000 −0.115470
\(76\) 0 0
\(77\) 4.65787 8.06767i 0.530814 0.919397i
\(78\) 0 0
\(79\) 4.38601 + 7.59678i 0.493464 + 0.854705i 0.999972 0.00753058i \(-0.00239708\pi\)
−0.506507 + 0.862236i \(0.669064\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −5.96714 + 10.3354i −0.654979 + 1.13446i 0.326920 + 0.945052i \(0.393989\pi\)
−0.981899 + 0.189405i \(0.939344\pi\)
\(84\) 0 0
\(85\) −1.35601 + 2.34868i −0.147080 + 0.254751i
\(86\) 0 0
\(87\) 1.34683 + 2.33278i 0.144395 + 0.250100i
\(88\) 0 0
\(89\) 10.1310 1.07389 0.536943 0.843619i \(-0.319579\pi\)
0.536943 + 0.843619i \(0.319579\pi\)
\(90\) 0 0
\(91\) 2.65251 0.278059
\(92\) 0 0
\(93\) −5.11431 8.85825i −0.530329 0.918558i
\(94\) 0 0
\(95\) −0.454704 + 0.787570i −0.0466516 + 0.0808030i
\(96\) 0 0
\(97\) 2.33139 4.03809i 0.236717 0.410006i −0.723053 0.690792i \(-0.757262\pi\)
0.959770 + 0.280786i \(0.0905952\pi\)
\(98\) 0 0
\(99\) −2.81310 4.87244i −0.282727 0.489698i
\(100\) 0 0
\(101\) −4.05606 7.02530i −0.403593 0.699043i 0.590564 0.806991i \(-0.298905\pi\)
−0.994157 + 0.107948i \(0.965572\pi\)
\(102\) 0 0
\(103\) −0.101231 0.175338i −0.00997461 0.0172765i 0.860995 0.508613i \(-0.169842\pi\)
−0.870970 + 0.491337i \(0.836508\pi\)
\(104\) 0 0
\(105\) −0.827889 1.43395i −0.0807937 0.139939i
\(106\) 0 0
\(107\) −7.09586 −0.685983 −0.342991 0.939339i \(-0.611440\pi\)
−0.342991 + 0.939339i \(0.611440\pi\)
\(108\) 0 0
\(109\) −9.42556 −0.902805 −0.451402 0.892321i \(-0.649076\pi\)
−0.451402 + 0.892321i \(0.649076\pi\)
\(110\) 0 0
\(111\) 0.237490 0.411344i 0.0225415 0.0390430i
\(112\) 0 0
\(113\) 5.20764 + 9.01990i 0.489894 + 0.848520i 0.999932 0.0116309i \(-0.00370232\pi\)
−0.510039 + 0.860151i \(0.670369\pi\)
\(114\) 0 0
\(115\) −3.02247 + 5.23507i −0.281847 + 0.488173i
\(116\) 0 0
\(117\) 0.800986 1.38735i 0.0740512 0.128260i
\(118\) 0 0
\(119\) −4.49051 −0.411645
\(120\) 0 0
\(121\) −10.3271 + 17.8870i −0.938826 + 1.62610i
\(122\) 0 0
\(123\) −0.573228 0.992859i −0.0516862 0.0895231i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 8.57825 + 14.8580i 0.761196 + 1.31843i 0.942234 + 0.334955i \(0.108721\pi\)
−0.181038 + 0.983476i \(0.557946\pi\)
\(128\) 0 0
\(129\) −5.46671 −0.481317
\(130\) 0 0
\(131\) −4.43412 −0.387411 −0.193705 0.981060i \(-0.562051\pi\)
−0.193705 + 0.981060i \(0.562051\pi\)
\(132\) 0 0
\(133\) −1.50578 −0.130567
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) 13.6451 1.16578 0.582890 0.812551i \(-0.301922\pi\)
0.582890 + 0.812551i \(0.301922\pi\)
\(138\) 0 0
\(139\) 3.07755 0.261034 0.130517 0.991446i \(-0.458336\pi\)
0.130517 + 0.991446i \(0.458336\pi\)
\(140\) 0 0
\(141\) −1.69934 2.94334i −0.143110 0.247874i
\(142\) 0 0
\(143\) −9.01303 −0.753707
\(144\) 0 0
\(145\) −1.34683 2.33278i −0.111848 0.193727i
\(146\) 0 0
\(147\) −2.12920 + 3.68788i −0.175613 + 0.304171i
\(148\) 0 0
\(149\) 8.71209 0.713722 0.356861 0.934158i \(-0.383847\pi\)
0.356861 + 0.934158i \(0.383847\pi\)
\(150\) 0 0
\(151\) 11.4966 19.9127i 0.935582 1.62048i 0.161989 0.986793i \(-0.448209\pi\)
0.773593 0.633683i \(-0.218458\pi\)
\(152\) 0 0
\(153\) −1.35601 + 2.34868i −0.109627 + 0.189880i
\(154\) 0 0
\(155\) 5.11431 + 8.85825i 0.410791 + 0.711512i
\(156\) 0 0
\(157\) 10.0754 17.4511i 0.804106 1.39275i −0.112786 0.993619i \(-0.535978\pi\)
0.916893 0.399134i \(-0.130689\pi\)
\(158\) 0 0
\(159\) 5.97455 0.473812
\(160\) 0 0
\(161\) −10.0091 −0.788825
\(162\) 0 0
\(163\) 4.52114 + 7.83085i 0.354123 + 0.613359i 0.986968 0.160920i \(-0.0514460\pi\)
−0.632844 + 0.774279i \(0.718113\pi\)
\(164\) 0 0
\(165\) 2.81310 + 4.87244i 0.219000 + 0.379319i
\(166\) 0 0
\(167\) 3.20616 + 5.55323i 0.248100 + 0.429722i 0.962999 0.269506i \(-0.0868606\pi\)
−0.714899 + 0.699228i \(0.753527\pi\)
\(168\) 0 0
\(169\) 5.21684 + 9.03584i 0.401296 + 0.695064i
\(170\) 0 0
\(171\) −0.454704 + 0.787570i −0.0347721 + 0.0602270i
\(172\) 0 0
\(173\) −9.45972 + 16.3847i −0.719209 + 1.24571i 0.242104 + 0.970250i \(0.422162\pi\)
−0.961313 + 0.275457i \(0.911171\pi\)
\(174\) 0 0
\(175\) 0.827889 + 1.43395i 0.0625825 + 0.108396i
\(176\) 0 0
\(177\) −8.25736 −0.620661
\(178\) 0 0
\(179\) 5.01635 0.374939 0.187470 0.982270i \(-0.439971\pi\)
0.187470 + 0.982270i \(0.439971\pi\)
\(180\) 0 0
\(181\) −4.71426 8.16533i −0.350408 0.606924i 0.635913 0.771761i \(-0.280624\pi\)
−0.986321 + 0.164836i \(0.947290\pi\)
\(182\) 0 0
\(183\) −5.07988 + 8.79861i −0.375516 + 0.650412i
\(184\) 0 0
\(185\) −0.237490 + 0.411344i −0.0174606 + 0.0302426i
\(186\) 0 0
\(187\) 15.2584 1.11581
\(188\) 0 0
\(189\) −0.827889 1.43395i −0.0602201 0.104304i
\(190\) 0 0
\(191\) 3.77371 6.53626i 0.273056 0.472947i −0.696587 0.717473i \(-0.745299\pi\)
0.969643 + 0.244525i \(0.0786322\pi\)
\(192\) 0 0
\(193\) 9.80997 0.706137 0.353068 0.935597i \(-0.385138\pi\)
0.353068 + 0.935597i \(0.385138\pi\)
\(194\) 0 0
\(195\) −0.800986 + 1.38735i −0.0573598 + 0.0993501i
\(196\) 0 0
\(197\) 7.16415 + 12.4087i 0.510425 + 0.884082i 0.999927 + 0.0120795i \(0.00384513\pi\)
−0.489502 + 0.872002i \(0.662822\pi\)
\(198\) 0 0
\(199\) −12.8696 + 22.2908i −0.912304 + 1.58016i −0.101502 + 0.994835i \(0.532365\pi\)
−0.810802 + 0.585321i \(0.800969\pi\)
\(200\) 0 0
\(201\) −8.03367 + 1.56851i −0.566651 + 0.110634i
\(202\) 0 0
\(203\) 2.23005 3.86256i 0.156519 0.271099i
\(204\) 0 0
\(205\) 0.573228 + 0.992859i 0.0400360 + 0.0693443i
\(206\) 0 0
\(207\) −3.02247 + 5.23507i −0.210076 + 0.363862i
\(208\) 0 0
\(209\) 5.11651 0.353917
\(210\) 0 0
\(211\) −12.5115 + 21.6706i −0.861329 + 1.49187i 0.00931696 + 0.999957i \(0.497034\pi\)
−0.870646 + 0.491910i \(0.836299\pi\)
\(212\) 0 0
\(213\) −1.81642 3.14614i −0.124459 0.215570i
\(214\) 0 0
\(215\) 5.46671 0.372826
\(216\) 0 0
\(217\) −8.46816 + 14.6673i −0.574856 + 0.995681i
\(218\) 0 0
\(219\) 0.751860 1.30226i 0.0508060 0.0879985i
\(220\) 0 0
\(221\) 2.17230 + 3.76253i 0.146124 + 0.253095i
\(222\) 0 0
\(223\) 16.9045 1.13201 0.566004 0.824402i \(-0.308489\pi\)
0.566004 + 0.824402i \(0.308489\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) −5.58831 9.67924i −0.370909 0.642434i 0.618796 0.785551i \(-0.287621\pi\)
−0.989706 + 0.143118i \(0.954287\pi\)
\(228\) 0 0
\(229\) 7.62535 13.2075i 0.503897 0.872776i −0.496092 0.868270i \(-0.665232\pi\)
0.999990 0.00450622i \(-0.00143438\pi\)
\(230\) 0 0
\(231\) −4.65787 + 8.06767i −0.306466 + 0.530814i
\(232\) 0 0
\(233\) −1.94446 3.36790i −0.127386 0.220639i 0.795277 0.606246i \(-0.207325\pi\)
−0.922663 + 0.385607i \(0.873992\pi\)
\(234\) 0 0
\(235\) 1.69934 + 2.94334i 0.110853 + 0.192002i
\(236\) 0 0
\(237\) −4.38601 7.59678i −0.284902 0.493464i
\(238\) 0 0
\(239\) −4.86697 8.42984i −0.314818 0.545281i 0.664581 0.747217i \(-0.268610\pi\)
−0.979399 + 0.201935i \(0.935277\pi\)
\(240\) 0 0
\(241\) 18.8478 1.21409 0.607047 0.794666i \(-0.292354\pi\)
0.607047 + 0.794666i \(0.292354\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 2.12920 3.68788i 0.136030 0.235610i
\(246\) 0 0
\(247\) 0.728423 + 1.26167i 0.0463484 + 0.0802778i
\(248\) 0 0
\(249\) 5.96714 10.3354i 0.378152 0.654979i
\(250\) 0 0
\(251\) 2.50889 4.34552i 0.158360 0.274287i −0.775918 0.630834i \(-0.782713\pi\)
0.934277 + 0.356547i \(0.116046\pi\)
\(252\) 0 0
\(253\) 34.0100 2.13819
\(254\) 0 0
\(255\) 1.35601 2.34868i 0.0849169 0.147080i
\(256\) 0 0
\(257\) −0.989493 1.71385i −0.0617229 0.106907i 0.833513 0.552500i \(-0.186326\pi\)
−0.895236 + 0.445593i \(0.852993\pi\)
\(258\) 0 0
\(259\) −0.786460 −0.0488682
\(260\) 0 0
\(261\) −1.34683 2.33278i −0.0833667 0.144395i
\(262\) 0 0
\(263\) 6.03457 0.372107 0.186054 0.982540i \(-0.440430\pi\)
0.186054 + 0.982540i \(0.440430\pi\)
\(264\) 0 0
\(265\) −5.97455 −0.367014
\(266\) 0 0
\(267\) −10.1310 −0.620008
\(268\) 0 0
\(269\) 22.0260 1.34295 0.671474 0.741028i \(-0.265662\pi\)
0.671474 + 0.741028i \(0.265662\pi\)
\(270\) 0 0
\(271\) −16.3255 −0.991705 −0.495852 0.868407i \(-0.665144\pi\)
−0.495852 + 0.868407i \(0.665144\pi\)
\(272\) 0 0
\(273\) −2.65251 −0.160537
\(274\) 0 0
\(275\) −2.81310 4.87244i −0.169636 0.293819i
\(276\) 0 0
\(277\) −21.6875 −1.30307 −0.651537 0.758617i \(-0.725875\pi\)
−0.651537 + 0.758617i \(0.725875\pi\)
\(278\) 0 0
\(279\) 5.11431 + 8.85825i 0.306186 + 0.530329i
\(280\) 0 0
\(281\) −11.1094 + 19.2421i −0.662733 + 1.14789i 0.317161 + 0.948372i \(0.397270\pi\)
−0.979895 + 0.199516i \(0.936063\pi\)
\(282\) 0 0
\(283\) 18.8268 1.11914 0.559568 0.828784i \(-0.310967\pi\)
0.559568 + 0.828784i \(0.310967\pi\)
\(284\) 0 0
\(285\) 0.454704 0.787570i 0.0269343 0.0466516i
\(286\) 0 0
\(287\) −0.949138 + 1.64395i −0.0560258 + 0.0970396i
\(288\) 0 0
\(289\) 4.82245 + 8.35274i 0.283674 + 0.491337i
\(290\) 0 0
\(291\) −2.33139 + 4.03809i −0.136669 + 0.236717i
\(292\) 0 0
\(293\) 31.2928 1.82814 0.914072 0.405552i \(-0.132921\pi\)
0.914072 + 0.405552i \(0.132921\pi\)
\(294\) 0 0
\(295\) 8.25736 0.480762
\(296\) 0 0
\(297\) 2.81310 + 4.87244i 0.163233 + 0.282727i
\(298\) 0 0
\(299\) 4.84191 + 8.38643i 0.280015 + 0.485000i
\(300\) 0 0
\(301\) 4.52583 + 7.83896i 0.260864 + 0.451830i
\(302\) 0 0
\(303\) 4.05606 + 7.02530i 0.233014 + 0.403593i
\(304\) 0 0
\(305\) 5.07988 8.79861i 0.290873 0.503807i
\(306\) 0 0
\(307\) −1.74426 + 3.02115i −0.0995503 + 0.172426i −0.911499 0.411303i \(-0.865074\pi\)
0.811948 + 0.583729i \(0.198407\pi\)
\(308\) 0 0
\(309\) 0.101231 + 0.175338i 0.00575884 + 0.00997461i
\(310\) 0 0
\(311\) −14.1487 −0.802300 −0.401150 0.916012i \(-0.631389\pi\)
−0.401150 + 0.916012i \(0.631389\pi\)
\(312\) 0 0
\(313\) 11.0740 0.625941 0.312971 0.949763i \(-0.398676\pi\)
0.312971 + 0.949763i \(0.398676\pi\)
\(314\) 0 0
\(315\) 0.827889 + 1.43395i 0.0466463 + 0.0807937i
\(316\) 0 0
\(317\) 14.1965 24.5890i 0.797353 1.38106i −0.123981 0.992285i \(-0.539566\pi\)
0.921334 0.388772i \(-0.127101\pi\)
\(318\) 0 0
\(319\) −7.57754 + 13.1247i −0.424261 + 0.734842i
\(320\) 0 0
\(321\) 7.09586 0.396052
\(322\) 0 0
\(323\) −1.23317 2.13591i −0.0686153 0.118845i
\(324\) 0 0
\(325\) 0.800986 1.38735i 0.0444307 0.0769563i
\(326\) 0 0
\(327\) 9.42556 0.521235
\(328\) 0 0
\(329\) −2.81373 + 4.87352i −0.155126 + 0.268686i
\(330\) 0 0
\(331\) −12.0830 20.9283i −0.664140 1.15032i −0.979518 0.201358i \(-0.935465\pi\)
0.315378 0.948966i \(-0.397869\pi\)
\(332\) 0 0
\(333\) −0.237490 + 0.411344i −0.0130143 + 0.0225415i
\(334\) 0 0
\(335\) 8.03367 1.56851i 0.438926 0.0856966i
\(336\) 0 0
\(337\) −5.35191 + 9.26977i −0.291537 + 0.504957i −0.974173 0.225801i \(-0.927500\pi\)
0.682636 + 0.730758i \(0.260833\pi\)
\(338\) 0 0
\(339\) −5.20764 9.01990i −0.282840 0.489894i
\(340\) 0 0
\(341\) 28.7742 49.8383i 1.55821 2.69890i
\(342\) 0 0
\(343\) 18.6414 1.00654
\(344\) 0 0
\(345\) 3.02247 5.23507i 0.162724 0.281847i
\(346\) 0 0
\(347\) 7.40314 + 12.8226i 0.397421 + 0.688354i 0.993407 0.114641i \(-0.0365718\pi\)
−0.595986 + 0.802995i \(0.703238\pi\)
\(348\) 0 0
\(349\) 10.5221 0.563236 0.281618 0.959527i \(-0.409129\pi\)
0.281618 + 0.959527i \(0.409129\pi\)
\(350\) 0 0
\(351\) −0.800986 + 1.38735i −0.0427535 + 0.0740512i
\(352\) 0 0
\(353\) 11.7966 20.4324i 0.627872 1.08751i −0.360106 0.932911i \(-0.617259\pi\)
0.987978 0.154595i \(-0.0494072\pi\)
\(354\) 0 0
\(355\) 1.81642 + 3.14614i 0.0964057 + 0.166980i
\(356\) 0 0
\(357\) 4.49051 0.237663
\(358\) 0 0
\(359\) −20.4751 −1.08063 −0.540317 0.841461i \(-0.681696\pi\)
−0.540317 + 0.841461i \(0.681696\pi\)
\(360\) 0 0
\(361\) 9.08649 + 15.7383i 0.478236 + 0.828330i
\(362\) 0 0
\(363\) 10.3271 17.8870i 0.542032 0.938826i
\(364\) 0 0
\(365\) −0.751860 + 1.30226i −0.0393541 + 0.0681633i
\(366\) 0 0
\(367\) 15.3612 + 26.6064i 0.801848 + 1.38884i 0.918398 + 0.395657i \(0.129483\pi\)
−0.116550 + 0.993185i \(0.537184\pi\)
\(368\) 0 0
\(369\) 0.573228 + 0.992859i 0.0298410 + 0.0516862i
\(370\) 0 0
\(371\) −4.94626 8.56718i −0.256797 0.444786i
\(372\) 0 0
\(373\) 13.9993 + 24.2476i 0.724859 + 1.25549i 0.959032 + 0.283297i \(0.0914283\pi\)
−0.234173 + 0.972195i \(0.575238\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) −4.31517 −0.222243
\(378\) 0 0
\(379\) −13.3276 + 23.0841i −0.684594 + 1.18575i 0.288970 + 0.957338i \(0.406687\pi\)
−0.973564 + 0.228413i \(0.926646\pi\)
\(380\) 0 0
\(381\) −8.57825 14.8580i −0.439477 0.761196i
\(382\) 0 0
\(383\) 8.54153 14.7944i 0.436452 0.755957i −0.560961 0.827842i \(-0.689568\pi\)
0.997413 + 0.0718855i \(0.0229016\pi\)
\(384\) 0 0
\(385\) 4.65787 8.06767i 0.237387 0.411167i
\(386\) 0 0
\(387\) 5.46671 0.277888
\(388\) 0 0
\(389\) 1.45917 2.52735i 0.0739828 0.128142i −0.826661 0.562701i \(-0.809762\pi\)
0.900643 + 0.434559i \(0.143096\pi\)
\(390\) 0 0
\(391\) −8.19701 14.1976i −0.414541 0.718006i
\(392\) 0 0
\(393\) 4.43412 0.223672
\(394\) 0 0
\(395\) 4.38601 + 7.59678i 0.220684 + 0.382236i
\(396\) 0 0
\(397\) −35.6606 −1.78976 −0.894878 0.446312i \(-0.852737\pi\)
−0.894878 + 0.446312i \(0.852737\pi\)
\(398\) 0 0
\(399\) 1.50578 0.0753831
\(400\) 0 0
\(401\) −34.4152 −1.71861 −0.859306 0.511462i \(-0.829104\pi\)
−0.859306 + 0.511462i \(0.829104\pi\)
\(402\) 0 0
\(403\) 16.3860 0.816243
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 2.67233 0.132462
\(408\) 0 0
\(409\) −0.883687 1.53059i −0.0436955 0.0756829i 0.843350 0.537364i \(-0.180580\pi\)
−0.887046 + 0.461681i \(0.847246\pi\)
\(410\) 0 0
\(411\) −13.6451 −0.673064
\(412\) 0 0
\(413\) 6.83618 + 11.8406i 0.336386 + 0.582638i
\(414\) 0 0
\(415\) −5.96714 + 10.3354i −0.292916 + 0.507345i
\(416\) 0 0
\(417\) −3.07755 −0.150708
\(418\) 0 0
\(419\) −0.414007 + 0.717081i −0.0202256 + 0.0350317i −0.875961 0.482382i \(-0.839772\pi\)
0.855735 + 0.517414i \(0.173105\pi\)
\(420\) 0 0
\(421\) −2.38387 + 4.12898i −0.116183 + 0.201234i −0.918252 0.395997i \(-0.870399\pi\)
0.802069 + 0.597231i \(0.203732\pi\)
\(422\) 0 0
\(423\) 1.69934 + 2.94334i 0.0826247 + 0.143110i
\(424\) 0 0
\(425\) −1.35601 + 2.34868i −0.0657763 + 0.113928i
\(426\) 0 0
\(427\) 16.8223 0.814088
\(428\) 0 0
\(429\) 9.01303 0.435153
\(430\) 0 0
\(431\) −5.53658 9.58964i −0.266688 0.461917i 0.701317 0.712850i \(-0.252596\pi\)
−0.968004 + 0.250933i \(0.919263\pi\)
\(432\) 0 0
\(433\) 0.740009 + 1.28173i 0.0355626 + 0.0615962i 0.883259 0.468886i \(-0.155344\pi\)
−0.847696 + 0.530482i \(0.822011\pi\)
\(434\) 0 0
\(435\) 1.34683 + 2.33278i 0.0645756 + 0.111848i
\(436\) 0 0
\(437\) −2.74865 4.76081i −0.131486 0.227740i
\(438\) 0 0
\(439\) 10.4870 18.1641i 0.500519 0.866924i −0.499481 0.866325i \(-0.666476\pi\)
1.00000 0.000598899i \(-0.000190636\pi\)
\(440\) 0 0
\(441\) 2.12920 3.68788i 0.101390 0.175613i
\(442\) 0 0
\(443\) 15.1526 + 26.2450i 0.719921 + 1.24694i 0.961031 + 0.276441i \(0.0891551\pi\)
−0.241110 + 0.970498i \(0.577512\pi\)
\(444\) 0 0
\(445\) 10.1310 0.480256
\(446\) 0 0
\(447\) −8.71209 −0.412068
\(448\) 0 0
\(449\) 14.1124 + 24.4433i 0.666004 + 1.15355i 0.979012 + 0.203802i \(0.0653298\pi\)
−0.313008 + 0.949750i \(0.601337\pi\)
\(450\) 0 0
\(451\) 3.22510 5.58603i 0.151864 0.263036i
\(452\) 0 0
\(453\) −11.4966 + 19.9127i −0.540158 + 0.935582i
\(454\) 0 0
\(455\) 2.65251 0.124352
\(456\) 0 0
\(457\) 0.527111 + 0.912983i 0.0246572 + 0.0427076i 0.878091 0.478494i \(-0.158817\pi\)
−0.853433 + 0.521202i \(0.825484\pi\)
\(458\) 0 0
\(459\) 1.35601 2.34868i 0.0632933 0.109627i
\(460\) 0 0
\(461\) −37.0052 −1.72350 −0.861751 0.507331i \(-0.830632\pi\)
−0.861751 + 0.507331i \(0.830632\pi\)
\(462\) 0 0
\(463\) 2.62376 4.54448i 0.121936 0.211200i −0.798595 0.601869i \(-0.794423\pi\)
0.920531 + 0.390669i \(0.127756\pi\)
\(464\) 0 0
\(465\) −5.11431 8.85825i −0.237171 0.410791i
\(466\) 0 0
\(467\) −15.8832 + 27.5106i −0.734989 + 1.27304i 0.219740 + 0.975559i \(0.429479\pi\)
−0.954728 + 0.297479i \(0.903854\pi\)
\(468\) 0 0
\(469\) 8.90013 + 10.2213i 0.410970 + 0.471975i
\(470\) 0 0
\(471\) −10.0754 + 17.4511i −0.464251 + 0.804106i
\(472\) 0 0
\(473\) −15.3784 26.6362i −0.707100 1.22473i
\(474\) 0 0
\(475\) −0.454704 + 0.787570i −0.0208632 + 0.0361362i
\(476\) 0 0
\(477\) −5.97455 −0.273556
\(478\) 0 0
\(479\) −17.6079 + 30.4978i −0.804527 + 1.39348i 0.112084 + 0.993699i \(0.464248\pi\)
−0.916610 + 0.399782i \(0.869086\pi\)
\(480\) 0 0
\(481\) 0.380452 + 0.658962i 0.0173471 + 0.0300461i
\(482\) 0 0
\(483\) 10.0091 0.455428
\(484\) 0 0
\(485\) 2.33139 4.03809i 0.105863 0.183360i
\(486\) 0 0
\(487\) −0.935906 + 1.62104i −0.0424100 + 0.0734562i −0.886451 0.462822i \(-0.846837\pi\)
0.844041 + 0.536278i \(0.180170\pi\)
\(488\) 0 0
\(489\) −4.52114 7.83085i −0.204453 0.354123i
\(490\) 0 0
\(491\) 4.81111 0.217122 0.108561 0.994090i \(-0.465376\pi\)
0.108561 + 0.994090i \(0.465376\pi\)
\(492\) 0 0
\(493\) 7.30528 0.329013
\(494\) 0 0
\(495\) −2.81310 4.87244i −0.126440 0.219000i
\(496\) 0 0
\(497\) −3.00759 + 5.20930i −0.134909 + 0.233669i
\(498\) 0 0
\(499\) 2.88805 5.00226i 0.129287 0.223932i −0.794114 0.607769i \(-0.792064\pi\)
0.923401 + 0.383838i \(0.125398\pi\)
\(500\) 0 0
\(501\) −3.20616 5.55323i −0.143241 0.248100i
\(502\) 0 0
\(503\) −7.34561 12.7230i −0.327525 0.567289i 0.654495 0.756066i \(-0.272881\pi\)
−0.982020 + 0.188777i \(0.939548\pi\)
\(504\) 0 0
\(505\) −4.05606 7.02530i −0.180492 0.312622i
\(506\) 0 0
\(507\) −5.21684 9.03584i −0.231688 0.401296i
\(508\) 0 0
\(509\) −39.1868 −1.73692 −0.868462 0.495756i \(-0.834891\pi\)
−0.868462 + 0.495756i \(0.834891\pi\)
\(510\) 0 0
\(511\) −2.48982 −0.110143
\(512\) 0 0
\(513\) 0.454704 0.787570i 0.0200757 0.0347721i
\(514\) 0 0
\(515\) −0.101231 0.175338i −0.00446078 0.00772630i
\(516\) 0 0
\(517\) 9.56083 16.5598i 0.420485 0.728301i
\(518\) 0 0
\(519\) 9.45972 16.3847i 0.415236 0.719209i
\(520\) 0 0
\(521\) −15.0438 −0.659080 −0.329540 0.944142i \(-0.606894\pi\)
−0.329540 + 0.944142i \(0.606894\pi\)
\(522\) 0 0
\(523\) −17.6705 + 30.6062i −0.772677 + 1.33832i 0.163413 + 0.986558i \(0.447750\pi\)
−0.936091 + 0.351759i \(0.885584\pi\)
\(524\) 0 0
\(525\) −0.827889 1.43395i −0.0361320 0.0625825i
\(526\) 0 0
\(527\) −27.7403 −1.20839
\(528\) 0 0
\(529\) −6.77062 11.7271i −0.294375 0.509872i
\(530\) 0 0
\(531\) 8.25736 0.358339
\(532\) 0 0
\(533\) 1.83659 0.0795515
\(534\) 0 0
\(535\) −7.09586 −0.306781
\(536\) 0 0
\(537\) −5.01635 −0.216471
\(538\) 0 0
\(539\) −23.9586 −1.03197
\(540\) 0 0
\(541\) 6.01368 0.258548 0.129274 0.991609i \(-0.458735\pi\)
0.129274 + 0.991609i \(0.458735\pi\)
\(542\) 0 0
\(543\) 4.71426 + 8.16533i 0.202308 + 0.350408i
\(544\) 0 0
\(545\) −9.42556 −0.403747
\(546\) 0 0
\(547\) 7.04360 + 12.1999i 0.301163 + 0.521629i 0.976400 0.215972i \(-0.0692920\pi\)
−0.675237 + 0.737601i \(0.735959\pi\)
\(548\) 0 0
\(549\) 5.07988 8.79861i 0.216804 0.375516i
\(550\) 0 0
\(551\) 2.44963 0.104358
\(552\) 0 0
\(553\) −7.26225 + 12.5786i −0.308822 + 0.534896i
\(554\) 0 0
\(555\) 0.237490 0.411344i 0.0100809 0.0174606i
\(556\) 0 0
\(557\) −18.4614 31.9761i −0.782235 1.35487i −0.930637 0.365944i \(-0.880746\pi\)
0.148401 0.988927i \(-0.452587\pi\)
\(558\) 0 0
\(559\) 4.37876 7.58423i 0.185202 0.320779i
\(560\) 0 0
\(561\) −15.2584 −0.644211
\(562\) 0 0
\(563\) −19.4229 −0.818578 −0.409289 0.912405i \(-0.634223\pi\)
−0.409289 + 0.912405i \(0.634223\pi\)
\(564\) 0 0
\(565\) 5.20764 + 9.01990i 0.219087 + 0.379470i
\(566\) 0 0
\(567\) 0.827889 + 1.43395i 0.0347681 + 0.0602201i
\(568\) 0 0
\(569\) 5.90660 + 10.2305i 0.247617 + 0.428886i 0.962864 0.269986i \(-0.0870191\pi\)
−0.715247 + 0.698872i \(0.753686\pi\)
\(570\) 0 0
\(571\) −10.0988 17.4916i −0.422620 0.731999i 0.573575 0.819153i \(-0.305556\pi\)
−0.996195 + 0.0871539i \(0.972223\pi\)
\(572\) 0 0
\(573\) −3.77371 + 6.53626i −0.157649 + 0.273056i
\(574\) 0 0
\(575\) −3.02247 + 5.23507i −0.126046 + 0.218317i
\(576\) 0 0
\(577\) −14.2372 24.6596i −0.592703 1.02659i −0.993867 0.110585i \(-0.964728\pi\)
0.401164 0.916006i \(-0.368606\pi\)
\(578\) 0 0
\(579\) −9.80997 −0.407688
\(580\) 0 0
\(581\) −19.7605 −0.819805
\(582\) 0 0
\(583\) 16.8070 + 29.1106i 0.696075 + 1.20564i
\(584\) 0 0
\(585\) 0.800986 1.38735i 0.0331167 0.0573598i
\(586\) 0 0
\(587\) −8.22117 + 14.2395i −0.339324 + 0.587726i −0.984306 0.176472i \(-0.943532\pi\)
0.644982 + 0.764198i \(0.276865\pi\)
\(588\) 0 0
\(589\) −9.30198 −0.383282
\(590\) 0 0
\(591\) −7.16415 12.4087i −0.294694 0.510425i
\(592\) 0 0
\(593\) 0.417897 0.723819i 0.0171610 0.0297237i −0.857317 0.514788i \(-0.827871\pi\)
0.874478 + 0.485065i \(0.161204\pi\)
\(594\) 0 0
\(595\) −4.49051 −0.184093
\(596\) 0 0
\(597\) 12.8696 22.2908i 0.526719 0.912304i
\(598\) 0 0
\(599\) −13.8672 24.0187i −0.566599 0.981378i −0.996899 0.0786922i \(-0.974926\pi\)
0.430300 0.902686i \(-0.358408\pi\)
\(600\) 0 0
\(601\) 3.10975 5.38625i 0.126850 0.219710i −0.795605 0.605816i \(-0.792847\pi\)
0.922454 + 0.386106i \(0.126180\pi\)
\(602\) 0 0
\(603\) 8.03367 1.56851i 0.327156 0.0638745i
\(604\) 0 0
\(605\) −10.3271 + 17.8870i −0.419856 + 0.727212i
\(606\) 0 0
\(607\) 18.3997 + 31.8692i 0.746822 + 1.29353i 0.949339 + 0.314254i \(0.101754\pi\)
−0.202517 + 0.979279i \(0.564912\pi\)
\(608\) 0 0
\(609\) −2.23005 + 3.86256i −0.0903663 + 0.156519i
\(610\) 0 0
\(611\) 5.44459 0.220264
\(612\) 0 0
\(613\) −15.2977 + 26.4965i −0.617870 + 1.07018i 0.372004 + 0.928231i \(0.378671\pi\)
−0.989874 + 0.141951i \(0.954663\pi\)
\(614\) 0 0
\(615\) −0.573228 0.992859i −0.0231148 0.0400360i
\(616\) 0 0
\(617\) 19.4967 0.784906 0.392453 0.919772i \(-0.371627\pi\)
0.392453 + 0.919772i \(0.371627\pi\)
\(618\) 0 0
\(619\) 6.62543 11.4756i 0.266298 0.461242i −0.701605 0.712567i \(-0.747533\pi\)
0.967903 + 0.251324i \(0.0808660\pi\)
\(620\) 0 0
\(621\) 3.02247 5.23507i 0.121287 0.210076i
\(622\) 0 0
\(623\) 8.38736 + 14.5273i 0.336032 + 0.582025i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −5.11651 −0.204334
\(628\) 0 0
\(629\) −0.644078 1.11558i −0.0256811 0.0444809i
\(630\) 0 0
\(631\) 18.9734 32.8629i 0.755320 1.30825i −0.189896 0.981804i \(-0.560815\pi\)
0.945215 0.326448i \(-0.105852\pi\)
\(632\) 0 0
\(633\) 12.5115 21.6706i 0.497289 0.861329i
\(634\) 0 0
\(635\) 8.57825 + 14.8580i 0.340417 + 0.589620i
\(636\) 0 0
\(637\) −3.41092 5.90789i −0.135146 0.234079i
\(638\) 0 0
\(639\) 1.81642 + 3.14614i 0.0718566 + 0.124459i
\(640\) 0 0
\(641\) −17.2803 29.9304i −0.682531 1.18218i −0.974206 0.225660i \(-0.927546\pi\)
0.291675 0.956517i \(-0.405787\pi\)
\(642\) 0 0
\(643\) −14.3668 −0.566570 −0.283285 0.959036i \(-0.591424\pi\)
−0.283285 + 0.959036i \(0.591424\pi\)
\(644\) 0 0
\(645\) −5.46671 −0.215251
\(646\) 0 0
\(647\) 14.3641 24.8794i 0.564712 0.978110i −0.432364 0.901699i \(-0.642321\pi\)
0.997076 0.0764108i \(-0.0243461\pi\)
\(648\) 0 0
\(649\) −23.2288 40.2335i −0.911811 1.57930i
\(650\) 0 0
\(651\) 8.46816 14.6673i 0.331894 0.574856i
\(652\) 0 0
\(653\) 3.76966 6.52924i 0.147518 0.255509i −0.782791 0.622284i \(-0.786205\pi\)
0.930310 + 0.366775i \(0.119538\pi\)
\(654\) 0 0
\(655\) −4.43412 −0.173255
\(656\) 0 0
\(657\) −0.751860 + 1.30226i −0.0293328 + 0.0508060i
\(658\) 0 0
\(659\) 8.82506 + 15.2854i 0.343775 + 0.595437i 0.985131 0.171808i \(-0.0549608\pi\)
−0.641355 + 0.767244i \(0.721627\pi\)
\(660\) 0 0
\(661\) 0.732720 0.0284995 0.0142498 0.999898i \(-0.495464\pi\)
0.0142498 + 0.999898i \(0.495464\pi\)
\(662\) 0 0
\(663\) −2.17230 3.76253i −0.0843650 0.146124i
\(664\) 0 0
\(665\) −1.50578 −0.0583915
\(666\) 0 0
\(667\) 16.2830 0.630480
\(668\) 0 0
\(669\) −16.9045 −0.653565
\(670\) 0 0
\(671\) −57.1609 −2.20667
\(672\) 0 0
\(673\) 44.2787 1.70682 0.853409 0.521242i \(-0.174531\pi\)
0.853409 + 0.521242i \(0.174531\pi\)
\(674\) 0 0
\(675\) −1.00000 −0.0384900
\(676\) 0 0
\(677\) −17.6334 30.5420i −0.677708 1.17383i −0.975669 0.219247i \(-0.929640\pi\)
0.297961 0.954578i \(-0.403693\pi\)
\(678\) 0 0
\(679\) 7.72054 0.296287
\(680\) 0 0
\(681\) 5.58831 + 9.67924i 0.214145 + 0.370909i
\(682\) 0 0
\(683\) 2.93772 5.08828i 0.112409 0.194698i −0.804332 0.594180i \(-0.797477\pi\)
0.916741 + 0.399482i \(0.130810\pi\)
\(684\) 0 0
\(685\) 13.6451 0.521353
\(686\) 0 0
\(687\) −7.62535 + 13.2075i −0.290925 + 0.503897i
\(688\) 0 0
\(689\) −4.78553 + 8.28878i −0.182314 + 0.315777i
\(690\) 0 0
\(691\) 15.1951 + 26.3186i 0.578048 + 1.00121i 0.995703 + 0.0926028i \(0.0295187\pi\)
−0.417655 + 0.908606i \(0.637148\pi\)
\(692\) 0 0
\(693\) 4.65787 8.06767i 0.176938 0.306466i
\(694\) 0 0
\(695\) 3.07755 0.116738
\(696\) 0 0
\(697\) −3.10922 −0.117770
\(698\) 0 0
\(699\) 1.94446 + 3.36790i 0.0735462 + 0.127386i
\(700\) 0 0
\(701\) 17.7302 + 30.7097i 0.669661 + 1.15989i 0.977999 + 0.208611i \(0.0668941\pi\)
−0.308337 + 0.951277i \(0.599773\pi\)
\(702\) 0 0
\(703\) −0.215975 0.374079i −0.00814564 0.0141087i
\(704\) 0 0
\(705\) −1.69934 2.94334i −0.0640008 0.110853i
\(706\) 0 0
\(707\) 6.71593 11.6323i 0.252578 0.437479i
\(708\) 0 0
\(709\) −12.5341 + 21.7097i −0.470727 + 0.815324i −0.999439 0.0334774i \(-0.989342\pi\)
0.528712 + 0.848801i \(0.322675\pi\)
\(710\) 0 0
\(711\) 4.38601 + 7.59678i 0.164488 + 0.284902i
\(712\) 0 0
\(713\) −61.8314 −2.31560
\(714\) 0 0
\(715\) −9.01303 −0.337068
\(716\) 0 0
\(717\) 4.86697 + 8.42984i 0.181760 + 0.314818i
\(718\) 0 0
\(719\) 12.9619 22.4507i 0.483397 0.837269i −0.516421 0.856335i \(-0.672736\pi\)
0.999818 + 0.0190661i \(0.00606931\pi\)
\(720\) 0 0
\(721\) 0.167616 0.290320i 0.00624236 0.0108121i
\(722\) 0 0
\(723\) −18.8478 −0.700958
\(724\) 0 0
\(725\) −1.34683 2.33278i −0.0500200 0.0866372i
\(726\) 0 0
\(727\) 19.5361 33.8375i 0.724555 1.25497i −0.234603 0.972091i \(-0.575379\pi\)
0.959157 0.282874i \(-0.0912878\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −7.41293 + 12.8396i −0.274177 + 0.474889i
\(732\) 0 0
\(733\) 4.97287 + 8.61326i 0.183677 + 0.318138i 0.943130 0.332424i \(-0.107867\pi\)
−0.759453 + 0.650562i \(0.774533\pi\)
\(734\) 0 0
\(735\) −2.12920 + 3.68788i −0.0785367 + 0.136030i
\(736\) 0 0
\(737\) −30.2420 34.7312i −1.11398 1.27934i
\(738\) 0 0
\(739\) 18.5996 32.2155i 0.684197 1.18506i −0.289491 0.957181i \(-0.593486\pi\)
0.973688 0.227884i \(-0.0731807\pi\)
\(740\) 0 0
\(741\) −0.728423 1.26167i −0.0267593 0.0463484i
\(742\) 0 0
\(743\) 4.37068 7.57024i 0.160345 0.277725i −0.774648 0.632393i \(-0.782073\pi\)
0.934992 + 0.354668i \(0.115406\pi\)
\(744\) 0 0
\(745\) 8.71209 0.319186
\(746\) 0 0
\(747\) −5.96714 + 10.3354i −0.218326 + 0.378152i
\(748\) 0 0
\(749\) −5.87458 10.1751i −0.214653 0.371789i
\(750\) 0 0
\(751\) −44.5269 −1.62481 −0.812405 0.583094i \(-0.801842\pi\)
−0.812405 + 0.583094i \(0.801842\pi\)
\(752\) 0 0
\(753\) −2.50889 + 4.34552i −0.0914290 + 0.158360i
\(754\) 0 0
\(755\) 11.4966 19.9127i 0.418405 0.724699i
\(756\) 0 0
\(757\) −20.1417 34.8865i −0.732064 1.26797i −0.956000 0.293368i \(-0.905224\pi\)
0.223936 0.974604i \(-0.428109\pi\)
\(758\) 0 0
\(759\) −34.0100 −1.23449
\(760\) 0 0
\(761\) −20.5812 −0.746068 −0.373034 0.927818i \(-0.621682\pi\)
−0.373034 + 0.927818i \(0.621682\pi\)
\(762\) 0 0
\(763\) −7.80331 13.5157i −0.282499 0.489303i
\(764\) 0 0
\(765\) −1.35601 + 2.34868i −0.0490268 + 0.0849169i
\(766\) 0 0
\(767\) 6.61403 11.4558i 0.238819 0.413647i
\(768\) 0 0
\(769\) 0.892739 + 1.54627i 0.0321930 + 0.0557599i 0.881673 0.471861i \(-0.156418\pi\)
−0.849480 + 0.527621i \(0.823084\pi\)
\(770\) 0 0
\(771\) 0.989493 + 1.71385i 0.0356357 + 0.0617229i
\(772\) 0 0
\(773\) −1.82765 3.16558i −0.0657359 0.113858i 0.831284 0.555848i \(-0.187606\pi\)
−0.897020 + 0.441990i \(0.854273\pi\)
\(774\) 0 0
\(775\) 5.11431 + 8.85825i 0.183712 + 0.318198i
\(776\) 0 0
\(777\) 0.786460 0.0282141
\(778\) 0 0
\(779\) −1.04259 −0.0373548
\(780\) 0 0
\(781\) 10.2196 17.7008i 0.365685 0.633385i
\(782\) 0 0
\(783\) 1.34683 + 2.33278i 0.0481318 + 0.0833667i
\(784\) 0 0
\(785\) 10.0754 17.4511i 0.359607 0.622858i
\(786\) 0 0
\(787\) −9.99119 + 17.3053i −0.356148 + 0.616866i −0.987314 0.158782i \(-0.949243\pi\)
0.631166 + 0.775648i \(0.282577\pi\)
\(788\) 0 0
\(789\) −6.03457 −0.214836
\(790\) 0 0
\(791\) −8.62269 + 14.9349i −0.306588 + 0.531025i
\(792\) 0 0
\(793\) −8.13783 14.0951i −0.288983 0.500533i