Properties

Label 1148.2.ba.a.113.11
Level $1148$
Weight $2$
Character 1148.113
Analytic conductor $9.167$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.ba (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 113.11
Character \(\chi\) \(=\) 1148.113
Dual form 1148.2.ba.a.701.10

$q$-expansion

\(f(q)\) \(=\) \(q+0.304900i q^{3} +(-0.420940 - 1.29552i) q^{5} +(0.587785 + 0.809017i) q^{7} +2.90704 q^{9} +O(q^{10})\) \(q+0.304900i q^{3} +(-0.420940 - 1.29552i) q^{5} +(0.587785 + 0.809017i) q^{7} +2.90704 q^{9} +(-1.66104 - 0.539703i) q^{11} +(-3.66120 + 5.03921i) q^{13} +(0.395004 - 0.128344i) q^{15} +(1.26941 + 0.412455i) q^{17} +(1.99499 + 2.74587i) q^{19} +(-0.246669 + 0.179216i) q^{21} +(2.91110 + 2.11504i) q^{23} +(2.54391 - 1.84826i) q^{25} +1.80105i q^{27} +(5.01259 - 1.62869i) q^{29} +(-0.893181 + 2.74893i) q^{31} +(0.164555 - 0.506449i) q^{33} +(0.800675 - 1.10203i) q^{35} +(-0.584605 - 1.79923i) q^{37} +(-1.53646 - 1.11630i) q^{39} +(3.76696 + 5.17784i) q^{41} +(-2.46586 - 1.79155i) q^{43} +(-1.22369 - 3.76612i) q^{45} +(2.78819 - 3.83762i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-0.125757 + 0.387042i) q^{51} +(3.78028 - 1.22829i) q^{53} +2.37908i q^{55} +(-0.837214 + 0.608272i) q^{57} +(11.2426 + 8.16822i) q^{59} +(-0.00534477 + 0.00388320i) q^{61} +(1.70871 + 2.35184i) q^{63} +(8.06954 + 2.62195i) q^{65} +(-7.38761 + 2.40038i) q^{67} +(-0.644874 + 0.887594i) q^{69} +(-1.97400 - 0.641391i) q^{71} +7.16197 q^{73} +(0.563533 + 0.775637i) q^{75} +(-0.539703 - 1.66104i) q^{77} +14.2442i q^{79} +8.17197 q^{81} -6.99080 q^{83} -1.81816i q^{85} +(0.496588 + 1.52834i) q^{87} +(8.41339 + 11.5800i) q^{89} -6.22881 q^{91} +(-0.838148 - 0.272331i) q^{93} +(2.71755 - 3.74039i) q^{95} +(10.1824 - 3.30846i) q^{97} +(-4.82869 - 1.56894i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\)

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
\(3\) 0.304900i 0.176034i 0.996119 + 0.0880170i \(0.0280530\pi\)
−0.996119 + 0.0880170i \(0.971947\pi\)
\(4\) 0 0
\(5\) −0.420940 1.29552i −0.188250 0.579374i 0.811739 0.584020i \(-0.198521\pi\)
−0.999989 + 0.00464630i \(0.998521\pi\)
\(6\) 0 0
\(7\) 0.587785 + 0.809017i 0.222162 + 0.305780i
\(8\) 0 0
\(9\) 2.90704 0.969012
\(10\) 0 0
\(11\) −1.66104 0.539703i −0.500821 0.162727i 0.0477028 0.998862i \(-0.484810\pi\)
−0.548524 + 0.836135i \(0.684810\pi\)
\(12\) 0 0
\(13\) −3.66120 + 5.03921i −1.01543 + 1.39763i −0.100079 + 0.994979i \(0.531910\pi\)
−0.915356 + 0.402647i \(0.868090\pi\)
\(14\) 0 0
\(15\) 0.395004 0.128344i 0.101989 0.0331384i
\(16\) 0 0
\(17\) 1.26941 + 0.412455i 0.307876 + 0.100035i 0.458880 0.888498i \(-0.348251\pi\)
−0.151004 + 0.988533i \(0.548251\pi\)
\(18\) 0 0
\(19\) 1.99499 + 2.74587i 0.457682 + 0.629945i 0.974026 0.226436i \(-0.0727075\pi\)
−0.516344 + 0.856381i \(0.672707\pi\)
\(20\) 0 0
\(21\) −0.246669 + 0.179216i −0.0538276 + 0.0391081i
\(22\) 0 0
\(23\) 2.91110 + 2.11504i 0.607006 + 0.441016i 0.848359 0.529422i \(-0.177591\pi\)
−0.241353 + 0.970437i \(0.577591\pi\)
\(24\) 0 0
\(25\) 2.54391 1.84826i 0.508781 0.369651i
\(26\) 0 0
\(27\) 1.80105i 0.346613i
\(28\) 0 0
\(29\) 5.01259 1.62869i 0.930815 0.302440i 0.195919 0.980620i \(-0.437231\pi\)
0.734896 + 0.678180i \(0.237231\pi\)
\(30\) 0 0
\(31\) −0.893181 + 2.74893i −0.160420 + 0.493722i −0.998670 0.0515647i \(-0.983579\pi\)
0.838250 + 0.545287i \(0.183579\pi\)
\(32\) 0 0
\(33\) 0.164555 0.506449i 0.0286454 0.0881615i
\(34\) 0 0
\(35\) 0.800675 1.10203i 0.135339 0.186278i
\(36\) 0 0
\(37\) −0.584605 1.79923i −0.0961085 0.295792i 0.891432 0.453154i \(-0.149701\pi\)
−0.987541 + 0.157362i \(0.949701\pi\)
\(38\) 0 0
\(39\) −1.53646 1.11630i −0.246030 0.178751i
\(40\) 0 0
\(41\) 3.76696 + 5.17784i 0.588301 + 0.808642i
\(42\) 0 0
\(43\) −2.46586 1.79155i −0.376041 0.273209i 0.383671 0.923470i \(-0.374660\pi\)
−0.759711 + 0.650261i \(0.774660\pi\)
\(44\) 0 0
\(45\) −1.22369 3.76612i −0.182416 0.561420i
\(46\) 0 0
\(47\) 2.78819 3.83762i 0.406700 0.559774i −0.555710 0.831376i \(-0.687554\pi\)
0.962410 + 0.271602i \(0.0875535\pi\)
\(48\) 0 0
\(49\) −0.309017 + 0.951057i −0.0441453 + 0.135865i
\(50\) 0 0
\(51\) −0.125757 + 0.387042i −0.0176096 + 0.0541967i
\(52\) 0 0
\(53\) 3.78028 1.22829i 0.519262 0.168718i −0.0376485 0.999291i \(-0.511987\pi\)
0.556910 + 0.830573i \(0.311987\pi\)
\(54\) 0 0
\(55\) 2.37908i 0.320796i
\(56\) 0 0
\(57\) −0.837214 + 0.608272i −0.110892 + 0.0805676i
\(58\) 0 0
\(59\) 11.2426 + 8.16822i 1.46366 + 1.06341i 0.982391 + 0.186839i \(0.0598243\pi\)
0.481270 + 0.876572i \(0.340176\pi\)
\(60\) 0 0
\(61\) −0.00534477 + 0.00388320i −0.000684327 + 0.000497193i −0.588127 0.808768i \(-0.700135\pi\)
0.587443 + 0.809266i \(0.300135\pi\)
\(62\) 0 0
\(63\) 1.70871 + 2.35184i 0.215278 + 0.296304i
\(64\) 0 0
\(65\) 8.06954 + 2.62195i 1.00090 + 0.325213i
\(66\) 0 0
\(67\) −7.38761 + 2.40038i −0.902541 + 0.293253i −0.723285 0.690549i \(-0.757369\pi\)
−0.179255 + 0.983803i \(0.557369\pi\)
\(68\) 0 0
\(69\) −0.644874 + 0.887594i −0.0776338 + 0.106854i
\(70\) 0 0
\(71\) −1.97400 0.641391i −0.234270 0.0761191i 0.189529 0.981875i \(-0.439304\pi\)
−0.423799 + 0.905756i \(0.639304\pi\)
\(72\) 0 0
\(73\) 7.16197 0.838245 0.419123 0.907930i \(-0.362338\pi\)
0.419123 + 0.907930i \(0.362338\pi\)
\(74\) 0 0
\(75\) 0.563533 + 0.775637i 0.0650712 + 0.0895628i
\(76\) 0 0
\(77\) −0.539703 1.66104i −0.0615049 0.189293i
\(78\) 0 0
\(79\) 14.2442i 1.60260i 0.598264 + 0.801299i \(0.295858\pi\)
−0.598264 + 0.801299i \(0.704142\pi\)
\(80\) 0 0
\(81\) 8.17197 0.907996
\(82\) 0 0
\(83\) −6.99080 −0.767340 −0.383670 0.923470i \(-0.625340\pi\)
−0.383670 + 0.923470i \(0.625340\pi\)
\(84\) 0 0
\(85\) 1.81816i 0.197207i
\(86\) 0 0
\(87\) 0.496588 + 1.52834i 0.0532398 + 0.163855i
\(88\) 0 0
\(89\) 8.41339 + 11.5800i 0.891818 + 1.22748i 0.973005 + 0.230783i \(0.0741288\pi\)
−0.0811874 + 0.996699i \(0.525871\pi\)
\(90\) 0 0
\(91\) −6.22881 −0.652957
\(92\) 0 0
\(93\) −0.838148 0.272331i −0.0869119 0.0282394i
\(94\) 0 0
\(95\) 2.71755 3.74039i 0.278815 0.383756i
\(96\) 0 0
\(97\) 10.1824 3.30846i 1.03386 0.335923i 0.257548 0.966266i \(-0.417086\pi\)
0.776317 + 0.630343i \(0.217086\pi\)
\(98\) 0 0
\(99\) −4.82869 1.56894i −0.485301 0.157684i
\(100\) 0 0
\(101\) −4.35754 5.99764i −0.433591 0.596787i 0.535182 0.844737i \(-0.320243\pi\)
−0.968773 + 0.247950i \(0.920243\pi\)
\(102\) 0 0
\(103\) −0.513837 + 0.373325i −0.0506299 + 0.0367848i −0.612812 0.790228i \(-0.709962\pi\)
0.562182 + 0.827013i \(0.309962\pi\)
\(104\) 0 0
\(105\) 0.336010 + 0.244126i 0.0327912 + 0.0238242i
\(106\) 0 0
\(107\) −0.00186821 + 0.00135734i −0.000180607 + 0.000131219i −0.587876 0.808951i \(-0.700036\pi\)
0.587695 + 0.809083i \(0.300036\pi\)
\(108\) 0 0
\(109\) 0.358508i 0.0343389i −0.999853 0.0171694i \(-0.994535\pi\)
0.999853 0.0171694i \(-0.00546547\pi\)
\(110\) 0 0
\(111\) 0.548585 0.178246i 0.0520694 0.0169184i
\(112\) 0 0
\(113\) −1.09455 + 3.36867i −0.102966 + 0.316898i −0.989248 0.146249i \(-0.953280\pi\)
0.886281 + 0.463147i \(0.153280\pi\)
\(114\) 0 0
\(115\) 1.51467 4.66169i 0.141244 0.434704i
\(116\) 0 0
\(117\) −10.6432 + 14.6492i −0.983968 + 1.35432i
\(118\) 0 0
\(119\) 0.412455 + 1.26941i 0.0378097 + 0.116366i
\(120\) 0 0
\(121\) −6.43143 4.67271i −0.584675 0.424792i
\(122\) 0 0
\(123\) −1.57872 + 1.14855i −0.142349 + 0.103561i
\(124\) 0 0
\(125\) −8.97545 6.52105i −0.802789 0.583260i
\(126\) 0 0
\(127\) −6.58029 20.2520i −0.583906 1.79708i −0.603620 0.797273i \(-0.706275\pi\)
0.0197134 0.999806i \(-0.493725\pi\)
\(128\) 0 0
\(129\) 0.546245 0.751841i 0.0480942 0.0661959i
\(130\) 0 0
\(131\) −4.64085 + 14.2831i −0.405473 + 1.24792i 0.515026 + 0.857174i \(0.327782\pi\)
−0.920499 + 0.390744i \(0.872218\pi\)
\(132\) 0 0
\(133\) −1.04883 + 3.22796i −0.0909449 + 0.279900i
\(134\) 0 0
\(135\) 2.33330 0.758135i 0.200819 0.0652499i
\(136\) 0 0
\(137\) 15.6782i 1.33948i −0.742595 0.669741i \(-0.766405\pi\)
0.742595 0.669741i \(-0.233595\pi\)
\(138\) 0 0
\(139\) 6.66357 4.84136i 0.565196 0.410639i −0.268161 0.963374i \(-0.586416\pi\)
0.833357 + 0.552735i \(0.186416\pi\)
\(140\) 0 0
\(141\) 1.17009 + 0.850119i 0.0985393 + 0.0715930i
\(142\) 0 0
\(143\) 8.80106 6.39435i 0.735982 0.534722i
\(144\) 0 0
\(145\) −4.22000 5.80833i −0.350452 0.482356i
\(146\) 0 0
\(147\) −0.289977 0.0942193i −0.0239169 0.00777107i
\(148\) 0 0
\(149\) −5.31914 + 1.72829i −0.435761 + 0.141587i −0.518679 0.854969i \(-0.673576\pi\)
0.0829179 + 0.996556i \(0.473576\pi\)
\(150\) 0 0
\(151\) −9.84354 + 13.5485i −0.801056 + 1.10256i 0.191587 + 0.981476i \(0.438637\pi\)
−0.992642 + 0.121083i \(0.961363\pi\)
\(152\) 0 0
\(153\) 3.69021 + 1.19902i 0.298336 + 0.0969351i
\(154\) 0 0
\(155\) 3.93726 0.316249
\(156\) 0 0
\(157\) −10.4234 14.3466i −0.831882 1.14499i −0.987570 0.157181i \(-0.949759\pi\)
0.155688 0.987806i \(-0.450241\pi\)
\(158\) 0 0
\(159\) 0.374505 + 1.15261i 0.0297002 + 0.0914078i
\(160\) 0 0
\(161\) 3.59832i 0.283587i
\(162\) 0 0
\(163\) −8.03055 −0.629001 −0.314500 0.949257i \(-0.601837\pi\)
−0.314500 + 0.949257i \(0.601837\pi\)
\(164\) 0 0
\(165\) −0.725383 −0.0564710
\(166\) 0 0
\(167\) 11.8793i 0.919250i 0.888113 + 0.459625i \(0.152016\pi\)
−0.888113 + 0.459625i \(0.847984\pi\)
\(168\) 0 0
\(169\) −7.97204 24.5354i −0.613234 1.88734i
\(170\) 0 0
\(171\) 5.79950 + 7.98233i 0.443499 + 0.610424i
\(172\) 0 0
\(173\) −12.5516 −0.954282 −0.477141 0.878827i \(-0.658327\pi\)
−0.477141 + 0.878827i \(0.658327\pi\)
\(174\) 0 0
\(175\) 2.99054 + 0.971686i 0.226064 + 0.0734525i
\(176\) 0 0
\(177\) −2.49049 + 3.42786i −0.187197 + 0.257654i
\(178\) 0 0
\(179\) 12.9244 4.19939i 0.966014 0.313877i 0.216808 0.976214i \(-0.430435\pi\)
0.749206 + 0.662337i \(0.230435\pi\)
\(180\) 0 0
\(181\) 10.9217 + 3.54867i 0.811801 + 0.263770i 0.685360 0.728204i \(-0.259645\pi\)
0.126441 + 0.991974i \(0.459645\pi\)
\(182\) 0 0
\(183\) −0.00118399 0.00162962i −8.75229e−5 0.000120465i
\(184\) 0 0
\(185\) −2.08485 + 1.51473i −0.153281 + 0.111366i
\(186\) 0 0
\(187\) −1.88592 1.37020i −0.137912 0.100199i
\(188\) 0 0
\(189\) −1.45708 + 1.05863i −0.105987 + 0.0770043i
\(190\) 0 0
\(191\) 9.47925i 0.685895i 0.939355 + 0.342947i \(0.111425\pi\)
−0.939355 + 0.342947i \(0.888575\pi\)
\(192\) 0 0
\(193\) 1.58648 0.515480i 0.114198 0.0371050i −0.251361 0.967893i \(-0.580878\pi\)
0.365558 + 0.930788i \(0.380878\pi\)
\(194\) 0 0
\(195\) −0.799433 + 2.46040i −0.0572486 + 0.176193i
\(196\) 0 0
\(197\) 4.00402 12.3231i 0.285275 0.877985i −0.701042 0.713120i \(-0.747281\pi\)
0.986316 0.164864i \(-0.0527187\pi\)
\(198\) 0 0
\(199\) −2.42193 + 3.33350i −0.171686 + 0.236305i −0.886186 0.463330i \(-0.846654\pi\)
0.714500 + 0.699636i \(0.246654\pi\)
\(200\) 0 0
\(201\) −0.731876 2.25248i −0.0516226 0.158878i
\(202\) 0 0
\(203\) 4.26397 + 3.09795i 0.299272 + 0.217434i
\(204\) 0 0
\(205\) 5.12232 7.05973i 0.357759 0.493073i
\(206\) 0 0
\(207\) 8.46267 + 6.14849i 0.588196 + 0.427349i
\(208\) 0 0
\(209\) −1.83179 5.63768i −0.126708 0.389967i
\(210\) 0 0
\(211\) 0.771638 1.06207i 0.0531217 0.0731158i −0.781630 0.623743i \(-0.785611\pi\)
0.834751 + 0.550627i \(0.185611\pi\)
\(212\) 0 0
\(213\) 0.195560 0.601872i 0.0133996 0.0412396i
\(214\) 0 0
\(215\) −1.28301 + 3.94871i −0.0875008 + 0.269300i
\(216\) 0 0
\(217\) −2.74893 + 0.893181i −0.186609 + 0.0606331i
\(218\) 0 0
\(219\) 2.18368i 0.147560i
\(220\) 0 0
\(221\) −6.72600 + 4.88672i −0.452440 + 0.328717i
\(222\) 0 0
\(223\) −6.10117 4.43276i −0.408565 0.296840i 0.364456 0.931221i \(-0.381255\pi\)
−0.773021 + 0.634381i \(0.781255\pi\)
\(224\) 0 0
\(225\) 7.39523 5.37295i 0.493015 0.358196i
\(226\) 0 0
\(227\) −5.57278 7.67027i −0.369878 0.509094i 0.582990 0.812480i \(-0.301883\pi\)
−0.952868 + 0.303386i \(0.901883\pi\)
\(228\) 0 0
\(229\) 7.18979 + 2.33611i 0.475115 + 0.154374i 0.536779 0.843723i \(-0.319641\pi\)
−0.0616643 + 0.998097i \(0.519641\pi\)
\(230\) 0 0
\(231\) 0.506449 0.164555i 0.0333219 0.0108270i
\(232\) 0 0
\(233\) 6.63009 9.12554i 0.434352 0.597834i −0.534594 0.845109i \(-0.679535\pi\)
0.968945 + 0.247276i \(0.0795353\pi\)
\(234\) 0 0
\(235\) −6.14537 1.99675i −0.400879 0.130254i
\(236\) 0 0
\(237\) −4.34306 −0.282112
\(238\) 0 0
\(239\) −2.07817 2.86036i −0.134426 0.185021i 0.736497 0.676440i \(-0.236478\pi\)
−0.870923 + 0.491419i \(0.836478\pi\)
\(240\) 0 0
\(241\) −9.33757 28.7381i −0.601486 1.85118i −0.519349 0.854562i \(-0.673826\pi\)
−0.0821367 0.996621i \(-0.526174\pi\)
\(242\) 0 0
\(243\) 7.89480i 0.506451i
\(244\) 0 0
\(245\) 1.36219 0.0870271
\(246\) 0 0
\(247\) −21.1411 −1.34517
\(248\) 0 0
\(249\) 2.13149i 0.135078i
\(250\) 0 0
\(251\) −1.12878 3.47404i −0.0712481 0.219279i 0.909092 0.416596i \(-0.136777\pi\)
−0.980340 + 0.197317i \(0.936777\pi\)
\(252\) 0 0
\(253\) −3.69394 5.08428i −0.232236 0.319646i
\(254\) 0 0
\(255\) 0.554356 0.0347151
\(256\) 0 0
\(257\) 0.289332 + 0.0940098i 0.0180481 + 0.00586417i 0.318027 0.948082i \(-0.396980\pi\)
−0.299979 + 0.953946i \(0.596980\pi\)
\(258\) 0 0
\(259\) 1.11199 1.53052i 0.0690954 0.0951017i
\(260\) 0 0
\(261\) 14.5718 4.73466i 0.901971 0.293068i
\(262\) 0 0
\(263\) −13.4049 4.35551i −0.826581 0.268572i −0.134976 0.990849i \(-0.543096\pi\)
−0.691605 + 0.722276i \(0.743096\pi\)
\(264\) 0 0
\(265\) −3.18254 4.38039i −0.195502 0.269085i
\(266\) 0 0
\(267\) −3.53075 + 2.56524i −0.216079 + 0.156990i
\(268\) 0 0
\(269\) −12.2365 8.89036i −0.746075 0.542055i 0.148533 0.988907i \(-0.452545\pi\)
−0.894608 + 0.446853i \(0.852545\pi\)
\(270\) 0 0
\(271\) 15.1230 10.9875i 0.918655 0.667442i −0.0245336 0.999699i \(-0.507810\pi\)
0.943189 + 0.332257i \(0.107810\pi\)
\(272\) 0 0
\(273\) 1.89916i 0.114943i
\(274\) 0 0
\(275\) −5.22303 + 1.69706i −0.314960 + 0.102337i
\(276\) 0 0
\(277\) −0.302293 + 0.930363i −0.0181630 + 0.0559001i −0.959727 0.280933i \(-0.909356\pi\)
0.941564 + 0.336834i \(0.109356\pi\)
\(278\) 0 0
\(279\) −2.59651 + 7.99123i −0.155449 + 0.478422i
\(280\) 0 0
\(281\) 13.7816 18.9688i 0.822142 1.13158i −0.167193 0.985924i \(-0.553470\pi\)
0.989335 0.145658i \(-0.0465298\pi\)
\(282\) 0 0
\(283\) −5.74089 17.6687i −0.341261 1.05029i −0.963555 0.267509i \(-0.913799\pi\)
0.622295 0.782783i \(-0.286201\pi\)
\(284\) 0 0
\(285\) 1.14044 + 0.828581i 0.0675541 + 0.0490809i
\(286\) 0 0
\(287\) −1.97479 + 6.09099i −0.116568 + 0.359540i
\(288\) 0 0
\(289\) −12.3120 8.94520i −0.724236 0.526188i
\(290\) 0 0
\(291\) 1.00875 + 3.10461i 0.0591339 + 0.181995i
\(292\) 0 0
\(293\) −7.93196 + 10.9174i −0.463390 + 0.637802i −0.975207 0.221293i \(-0.928972\pi\)
0.511817 + 0.859094i \(0.328972\pi\)
\(294\) 0 0
\(295\) 5.84963 18.0033i 0.340579 1.04819i
\(296\) 0 0
\(297\) 0.972035 2.99162i 0.0564032 0.173591i
\(298\) 0 0
\(299\) −21.3162 + 6.92606i −1.23275 + 0.400545i
\(300\) 0 0
\(301\) 3.04797i 0.175682i
\(302\) 0 0
\(303\) 1.82868 1.32861i 0.105055 0.0763268i
\(304\) 0 0
\(305\) 0.00728058 + 0.00528965i 0.000416885 + 0.000302885i
\(306\) 0 0
\(307\) −16.4123 + 11.9243i −0.936702 + 0.680554i −0.947624 0.319387i \(-0.896523\pi\)
0.0109228 + 0.999940i \(0.496523\pi\)
\(308\) 0 0
\(309\) −0.113827 0.156669i −0.00647537 0.00891259i
\(310\) 0 0
\(311\) −11.3741 3.69566i −0.644964 0.209562i −0.0317719 0.999495i \(-0.510115\pi\)
−0.613193 + 0.789934i \(0.710115\pi\)
\(312\) 0 0
\(313\) −5.20427 + 1.69097i −0.294163 + 0.0955793i −0.452381 0.891825i \(-0.649425\pi\)
0.158218 + 0.987404i \(0.449425\pi\)
\(314\) 0 0
\(315\) 2.32759 3.20365i 0.131145 0.180505i
\(316\) 0 0
\(317\) 3.54156 + 1.15072i 0.198914 + 0.0646310i 0.406780 0.913526i \(-0.366652\pi\)
−0.207866 + 0.978157i \(0.566652\pi\)
\(318\) 0 0
\(319\) −9.20510 −0.515387
\(320\) 0 0
\(321\) −0.000413852 0 0.000569618i −2.30990e−5 0 3.17930e-5i
\(322\) 0 0
\(323\) 1.39990 + 4.30846i 0.0778927 + 0.239729i
\(324\) 0 0
\(325\) 19.5861i 1.08644i
\(326\) 0 0
\(327\) 0.109309 0.00604481
\(328\) 0 0
\(329\) 4.74356 0.261521
\(330\) 0 0
\(331\) 31.4717i 1.72984i 0.501907 + 0.864922i \(0.332632\pi\)
−0.501907 + 0.864922i \(0.667368\pi\)
\(332\) 0 0
\(333\) −1.69947 5.23043i −0.0931303 0.286626i
\(334\) 0 0
\(335\) 6.21948 + 8.56038i 0.339806 + 0.467703i
\(336\) 0 0
\(337\) 7.36661 0.401285 0.200642 0.979665i \(-0.435697\pi\)
0.200642 + 0.979665i \(0.435697\pi\)
\(338\) 0 0
\(339\) −1.02711 0.333727i −0.0557848 0.0181256i
\(340\) 0 0
\(341\) 2.96721 4.08401i 0.160683 0.221162i
\(342\) 0 0
\(343\) −0.951057 + 0.309017i −0.0513522 + 0.0166853i
\(344\) 0 0
\(345\) 1.42135 + 0.461824i 0.0765228 + 0.0248638i
\(346\) 0 0
\(347\) 3.55338 + 4.89081i 0.190756 + 0.262553i 0.893673 0.448719i \(-0.148120\pi\)
−0.702917 + 0.711272i \(0.748120\pi\)
\(348\) 0 0
\(349\) −26.0309 + 18.9126i −1.39340 + 1.01237i −0.397922 + 0.917419i \(0.630269\pi\)
−0.995482 + 0.0949482i \(0.969731\pi\)
\(350\) 0 0
\(351\) −9.07590 6.59403i −0.484436 0.351963i
\(352\) 0 0
\(353\) −4.66229 + 3.38736i −0.248149 + 0.180291i −0.704906 0.709301i \(-0.749011\pi\)
0.456757 + 0.889591i \(0.349011\pi\)
\(354\) 0 0
\(355\) 2.82734i 0.150060i
\(356\) 0 0
\(357\) −0.387042 + 0.125757i −0.0204844 + 0.00665579i
\(358\) 0 0
\(359\) −5.60427 + 17.2482i −0.295782 + 0.910324i 0.687175 + 0.726492i \(0.258850\pi\)
−0.982958 + 0.183832i \(0.941150\pi\)
\(360\) 0 0
\(361\) 2.31152 7.11413i 0.121659 0.374428i
\(362\) 0 0
\(363\) 1.42471 1.96094i 0.0747778 0.102923i
\(364\) 0 0
\(365\) −3.01476 9.27847i −0.157800 0.485657i
\(366\) 0 0
\(367\) −11.4485 8.31784i −0.597608 0.434188i 0.247421 0.968908i \(-0.420417\pi\)
−0.845029 + 0.534720i \(0.820417\pi\)
\(368\) 0 0
\(369\) 10.9507 + 15.0522i 0.570070 + 0.783584i
\(370\) 0 0
\(371\) 3.21570 + 2.33634i 0.166951 + 0.121297i
\(372\) 0 0
\(373\) 3.76037 + 11.5732i 0.194704 + 0.599238i 0.999980 + 0.00633771i \(0.00201737\pi\)
−0.805276 + 0.592901i \(0.797983\pi\)
\(374\) 0 0
\(375\) 1.98827 2.73661i 0.102674 0.141318i
\(376\) 0 0
\(377\) −10.1448 + 31.2225i −0.522484 + 1.60804i
\(378\) 0 0
\(379\) 6.63217 20.4117i 0.340672 1.04848i −0.623189 0.782072i \(-0.714163\pi\)
0.963860 0.266408i \(-0.0858369\pi\)
\(380\) 0 0
\(381\) 6.17485 2.00633i 0.316347 0.102787i
\(382\) 0 0
\(383\) 4.87601i 0.249153i 0.992210 + 0.124576i \(0.0397572\pi\)
−0.992210 + 0.124576i \(0.960243\pi\)
\(384\) 0 0
\(385\) −1.92472 + 1.39839i −0.0980928 + 0.0712686i
\(386\) 0 0
\(387\) −7.16835 5.20811i −0.364388 0.264743i
\(388\) 0 0
\(389\) 20.4976 14.8924i 1.03927 0.755073i 0.0691262 0.997608i \(-0.477979\pi\)
0.970143 + 0.242535i \(0.0779789\pi\)
\(390\) 0 0
\(391\) 2.82301 + 3.88554i 0.142766 + 0.196500i
\(392\) 0 0
\(393\) −4.35491 1.41500i −0.219676 0.0713771i
\(394\) 0 0
\(395\) 18.4536 5.99595i 0.928503 0.301689i
\(396\) 0 0
\(397\) 1.84939 2.54547i 0.0928182 0.127753i −0.760082 0.649827i \(-0.774841\pi\)
0.852900 + 0.522074i \(0.174841\pi\)
\(398\) 0 0
\(399\) −0.984204 0.319787i −0.0492718 0.0160094i
\(400\) 0 0
\(401\) 21.3830 1.06782 0.533909 0.845542i \(-0.320723\pi\)
0.533909 + 0.845542i \(0.320723\pi\)
\(402\) 0 0
\(403\) −10.5823 14.5653i −0.527143 0.725550i
\(404\) 0 0
\(405\) −3.43990 10.5869i −0.170930 0.526069i
\(406\) 0 0
\(407\) 3.30410i 0.163778i
\(408\) 0 0
\(409\) −8.40686 −0.415692 −0.207846 0.978162i \(-0.566645\pi\)
−0.207846 + 0.978162i \(0.566645\pi\)
\(410\) 0 0
\(411\) 4.78029 0.235794
\(412\) 0 0
\(413\) 13.8966i 0.683807i
\(414\) 0 0
\(415\) 2.94270 + 9.05671i 0.144452 + 0.444577i
\(416\) 0 0
\(417\) 1.47613 + 2.03172i 0.0722865 + 0.0994938i
\(418\) 0 0
\(419\) 10.5515 0.515477 0.257738 0.966215i \(-0.417023\pi\)
0.257738 + 0.966215i \(0.417023\pi\)
\(420\) 0 0
\(421\) −4.29222 1.39463i −0.209190 0.0679699i 0.202548 0.979272i \(-0.435078\pi\)
−0.411737 + 0.911303i \(0.635078\pi\)
\(422\) 0 0
\(423\) 8.10537 11.1561i 0.394097 0.542428i
\(424\) 0 0
\(425\) 3.99157 1.29694i 0.193620 0.0629108i
\(426\) 0 0
\(427\) −0.00628315 0.00204152i −0.000304063 9.87960e-5i
\(428\) 0 0
\(429\) 1.94964 + 2.68344i 0.0941293 + 0.129558i
\(430\) 0 0
\(431\) −3.08384 + 2.24054i −0.148543 + 0.107923i −0.659575 0.751639i \(-0.729264\pi\)
0.511031 + 0.859562i \(0.329264\pi\)
\(432\) 0 0
\(433\) 27.8317 + 20.2209i 1.33751 + 0.971756i 0.999532 + 0.0306012i \(0.00974218\pi\)
0.337976 + 0.941155i \(0.390258\pi\)
\(434\) 0 0
\(435\) 1.77096 1.28668i 0.0849110 0.0616915i
\(436\) 0 0
\(437\) 12.2130i 0.584225i
\(438\) 0 0
\(439\) −27.1009 + 8.80561i −1.29345 + 0.420269i −0.873300 0.487183i \(-0.838024\pi\)
−0.420155 + 0.907452i \(0.638024\pi\)
\(440\) 0 0
\(441\) −0.898324 + 2.76476i −0.0427773 + 0.131655i
\(442\) 0 0
\(443\) 11.2211 34.5349i 0.533130 1.64080i −0.214527 0.976718i \(-0.568821\pi\)
0.747656 0.664086i \(-0.231179\pi\)
\(444\) 0 0
\(445\) 11.4606 15.7742i 0.543286 0.747769i
\(446\) 0 0
\(447\) −0.526957 1.62181i −0.0249242 0.0767088i
\(448\) 0 0
\(449\) −23.1445 16.8155i −1.09226 0.793572i −0.112479 0.993654i \(-0.535879\pi\)
−0.979779 + 0.200082i \(0.935879\pi\)
\(450\) 0 0
\(451\) −3.46256 10.6336i −0.163046 0.500717i
\(452\) 0 0
\(453\) −4.13093 3.00129i −0.194088 0.141013i
\(454\) 0 0
\(455\) 2.62195 + 8.06954i 0.122919 + 0.378306i
\(456\) 0 0
\(457\) −5.26117 + 7.24138i −0.246107 + 0.338738i −0.914143 0.405391i \(-0.867135\pi\)
0.668036 + 0.744129i \(0.267135\pi\)
\(458\) 0 0
\(459\) −0.742854 + 2.28627i −0.0346735 + 0.106714i
\(460\) 0 0
\(461\) 1.11097 3.41922i 0.0517431 0.159249i −0.921846 0.387557i \(-0.873319\pi\)
0.973589 + 0.228308i \(0.0733192\pi\)
\(462\) 0 0
\(463\) 39.5953 12.8653i 1.84015 0.597902i 0.841846 0.539718i \(-0.181469\pi\)
0.998306 0.0581835i \(-0.0185308\pi\)
\(464\) 0 0
\(465\) 1.20047i 0.0556705i
\(466\) 0 0
\(467\) −15.1387 + 10.9989i −0.700533 + 0.508967i −0.880106 0.474777i \(-0.842529\pi\)
0.179573 + 0.983745i \(0.442529\pi\)
\(468\) 0 0
\(469\) −6.28428 4.56580i −0.290181 0.210829i
\(470\) 0 0
\(471\) 4.37429 3.17811i 0.201557 0.146440i
\(472\) 0 0
\(473\) 3.12898 + 4.30667i 0.143871 + 0.198021i
\(474\) 0 0
\(475\) 10.1501 + 3.29798i 0.465720 + 0.151321i
\(476\) 0 0
\(477\) 10.9894 3.57068i 0.503171 0.163490i
\(478\) 0 0
\(479\) −16.2719 + 22.3963i −0.743481 + 1.02331i 0.254929 + 0.966960i \(0.417948\pi\)
−0.998411 + 0.0563548i \(0.982052\pi\)
\(480\) 0 0
\(481\) 11.2071 + 3.64140i 0.510998 + 0.166033i
\(482\) 0 0
\(483\) −1.09713 −0.0499210
\(484\) 0 0
\(485\) −8.57234 11.7988i −0.389250 0.535756i
\(486\) 0 0
\(487\) −2.26211 6.96206i −0.102506 0.315481i 0.886631 0.462478i \(-0.153039\pi\)
−0.989137 + 0.146996i \(0.953039\pi\)
\(488\) 0 0
\(489\) 2.44851i 0.110726i
\(490\) 0 0
\(491\) 37.0346 1.67135 0.835674 0.549226i \(-0.185078\pi\)
0.835674 + 0.549226i \(0.185078\pi\)
\(492\) 0 0
\(493\) 7.03478 0.316830
\(494\) 0 0
\(495\) 6.91609i 0.310855i
\(496\) 0 0
\(497\) −0.641391 1.97400i −0.0287703 0.0885459i
\(498\) 0 0
\(499\) −10.7527 14.7999i −0.481359 0.662534i 0.497406 0.867518i \(-0.334286\pi\)
−0.978765 + 0.204984i \(0.934286\pi\)
\(500\) 0 0
\(501\) −3.62201 −0.161819
\(502\) 0 0
\(503\) 3.16317 + 1.02777i 0.141039 + 0.0458262i 0.378686 0.925525i \(-0.376376\pi\)
−0.237647 + 0.971352i \(0.576376\pi\)
\(504\) 0 0
\(505\) −5.93579 + 8.16991i −0.264139 + 0.363556i
\(506\) 0 0
\(507\) 7.48085 2.43067i 0.332236 0.107950i
\(508\) 0 0
\(509\) 33.8651 + 11.0035i 1.50105 + 0.487719i 0.940323 0.340284i \(-0.110523\pi\)
0.560723 + 0.828003i \(0.310523\pi\)
\(510\) 0 0
\(511\) 4.20970 + 5.79416i 0.186226 + 0.256318i
\(512\) 0 0
\(513\) −4.94545 + 3.59308i −0.218347 + 0.158639i
\(514\) 0 0
\(515\) 0.699944 + 0.508539i 0.0308432 + 0.0224089i
\(516\) 0 0
\(517\) −6.70246 + 4.86962i −0.294774 + 0.214166i
\(518\) 0 0
\(519\) 3.82699i 0.167986i
\(520\) 0 0
\(521\) 29.2063 9.48971i 1.27955 0.415752i 0.411130 0.911577i \(-0.365134\pi\)
0.868422 + 0.495825i \(0.165134\pi\)
\(522\) 0 0
\(523\) 1.21648 3.74395i 0.0531930 0.163711i −0.920931 0.389726i \(-0.872570\pi\)
0.974124 + 0.226015i \(0.0725697\pi\)
\(524\) 0 0
\(525\) −0.296267 + 0.911816i −0.0129301 + 0.0397949i
\(526\) 0 0
\(527\) −2.26762 + 3.12111i −0.0987790 + 0.135958i
\(528\) 0 0
\(529\) −3.10628 9.56014i −0.135056 0.415658i
\(530\) 0 0
\(531\) 32.6826 + 23.7453i 1.41830 + 1.03046i
\(532\) 0 0
\(533\) −39.8838 + 0.0254083i −1.72756 + 0.00110055i
\(534\) 0 0
\(535\) 0.00254486 + 0.00184895i 0.000110024 + 7.99371e-5i
\(536\) 0 0
\(537\) 1.28039 + 3.94064i 0.0552530 + 0.170051i
\(538\) 0 0
\(539\) 1.02658 1.41296i 0.0442178 0.0608605i
\(540\) 0 0
\(541\) −10.2293 + 31.4826i −0.439793 + 1.35354i 0.448301 + 0.893882i \(0.352029\pi\)
−0.888094 + 0.459661i \(0.847971\pi\)
\(542\) 0 0
\(543\) −1.08199 + 3.33002i −0.0464325 + 0.142905i
\(544\) 0 0
\(545\) −0.464454 + 0.150910i −0.0198950 + 0.00646429i
\(546\) 0 0
\(547\) 40.7582i 1.74269i 0.490668 + 0.871346i \(0.336753\pi\)
−0.490668 + 0.871346i \(0.663247\pi\)
\(548\) 0 0
\(549\) −0.0155374 + 0.0112886i −0.000663121 + 0.000481786i
\(550\) 0 0
\(551\) 14.4722 + 10.5147i 0.616538 + 0.447941i
\(552\) 0 0
\(553\) −11.5238 + 8.37254i −0.490042 + 0.356036i
\(554\) 0 0
\(555\) −0.461843 0.635672i −0.0196041 0.0269828i
\(556\) 0 0
\(557\) −19.9626 6.48625i −0.845844 0.274831i −0.146140 0.989264i \(-0.546685\pi\)
−0.699704 + 0.714433i \(0.746685\pi\)
\(558\) 0 0
\(559\) 18.0560 5.86676i 0.763689 0.248138i
\(560\) 0 0
\(561\) 0.417775 0.575018i 0.0176385 0.0242773i
\(562\) 0 0
\(563\) −4.08245 1.32647i −0.172055 0.0559040i 0.221723 0.975110i \(-0.428832\pi\)
−0.393778 + 0.919206i \(0.628832\pi\)
\(564\) 0 0
\(565\) 4.82492 0.202986
\(566\) 0 0
\(567\) 4.80336 + 6.61126i 0.201722 + 0.277647i
\(568\) 0 0
\(569\) 6.71404 + 20.6637i 0.281467 + 0.866267i 0.987435 + 0.158023i \(0.0505121\pi\)
−0.705968 + 0.708243i \(0.749488\pi\)
\(570\) 0 0
\(571\) 40.4748i 1.69382i −0.531739 0.846908i \(-0.678461\pi\)
0.531739 0.846908i \(-0.321539\pi\)
\(572\) 0 0
\(573\) −2.89022 −0.120741
\(574\) 0 0
\(575\) 11.3147 0.471855
\(576\) 0 0
\(577\) 11.0980i 0.462017i 0.972952 + 0.231009i \(0.0742026\pi\)
−0.972952 + 0.231009i \(0.925797\pi\)
\(578\) 0 0
\(579\) 0.157170 + 0.483719i 0.00653175 + 0.0201027i
\(580\) 0 0
\(581\) −4.10909 5.65568i −0.170474 0.234637i
\(582\) 0 0
\(583\) −6.94209 −0.287512
\(584\) 0 0
\(585\) 23.4584 + 7.62211i 0.969887 + 0.315135i
\(586\) 0 0
\(587\) 15.9989 22.0206i 0.660346 0.908888i −0.339147 0.940733i \(-0.610138\pi\)
0.999493 + 0.0318454i \(0.0101384\pi\)
\(588\) 0 0
\(589\) −9.33007 + 3.03152i −0.384439 + 0.124912i
\(590\) 0 0
\(591\) 3.75731 + 1.22082i 0.154555 + 0.0502180i
\(592\) 0 0
\(593\) 13.8639 + 19.0820i 0.569322 + 0.783605i 0.992474 0.122454i \(-0.0390764\pi\)
−0.423152 + 0.906059i \(0.639076\pi\)
\(594\) 0 0
\(595\) 1.47092 1.06869i 0.0603019 0.0438119i
\(596\) 0 0
\(597\) −1.01638 0.738445i −0.0415978 0.0302226i
\(598\) 0 0
\(599\) −13.8266 + 10.0456i −0.564939 + 0.410452i −0.833263 0.552877i \(-0.813530\pi\)
0.268325 + 0.963329i \(0.413530\pi\)
\(600\) 0 0
\(601\) 2.20274i 0.0898516i −0.998990 0.0449258i \(-0.985695\pi\)
0.998990 0.0449258i \(-0.0143051\pi\)
\(602\) 0 0
\(603\) −21.4761 + 6.97800i −0.874573 + 0.284166i
\(604\) 0 0
\(605\) −3.34634 + 10.2990i −0.136048 + 0.418712i
\(606\) 0 0
\(607\) 11.1705 34.3792i 0.453395 1.39541i −0.419613 0.907703i \(-0.637834\pi\)
0.873009 0.487705i \(-0.162166\pi\)
\(608\) 0 0
\(609\) −0.944566 + 1.30008i −0.0382757 + 0.0526820i
\(610\) 0 0
\(611\) 9.13043 + 28.1006i 0.369378 + 1.13683i
\(612\) 0 0
\(613\) 20.2963 + 14.7461i 0.819759 + 0.595589i 0.916643 0.399706i \(-0.130888\pi\)
−0.0968848 + 0.995296i \(0.530888\pi\)
\(614\) 0 0
\(615\) 2.15251 + 1.56180i 0.0867976 + 0.0629777i
\(616\) 0 0
\(617\) 37.6480 + 27.3529i 1.51565 + 1.10119i 0.963591 + 0.267381i \(0.0861583\pi\)
0.552061 + 0.833804i \(0.313842\pi\)
\(618\) 0 0
\(619\) −6.77254 20.8437i −0.272211 0.837780i −0.989944 0.141461i \(-0.954820\pi\)
0.717733 0.696319i \(-0.245180\pi\)
\(620\) 0 0
\(621\) −3.80930 + 5.24305i −0.152862 + 0.210396i
\(622\) 0 0
\(623\) −4.42318 + 13.6132i −0.177211 + 0.545400i
\(624\) 0 0
\(625\) 0.188410 0.579868i 0.00753642 0.0231947i
\(626\) 0 0
\(627\) 1.71893 0.558514i 0.0686474 0.0223049i
\(628\) 0 0
\(629\) 2.52508i 0.100681i
\(630\) 0 0
\(631\) 6.54436 4.75475i 0.260527 0.189284i −0.449852 0.893103i \(-0.648523\pi\)
0.710379 + 0.703819i \(0.248523\pi\)
\(632\) 0 0
\(633\) 0.323825 + 0.235272i 0.0128709 + 0.00935123i
\(634\) 0 0
\(635\) −23.4670 + 17.0498i −0.931260 + 0.676600i
\(636\) 0 0
\(637\) −3.66120 5.03921i −0.145062 0.199661i
\(638\) 0 0
\(639\) −5.73848 1.86455i −0.227011 0.0737603i
\(640\) 0 0
\(641\) 36.8141 11.9616i 1.45407 0.472456i 0.527816 0.849359i \(-0.323011\pi\)
0.926253 + 0.376903i \(0.123011\pi\)
\(642\) 0 0
\(643\) 2.83101 3.89655i 0.111644 0.153665i −0.749538 0.661961i \(-0.769724\pi\)
0.861182 + 0.508296i \(0.169724\pi\)
\(644\) 0 0
\(645\) −1.20396 0.391191i −0.0474059 0.0154031i
\(646\) 0 0
\(647\) 20.9467 0.823500 0.411750 0.911297i \(-0.364918\pi\)
0.411750 + 0.911297i \(0.364918\pi\)
\(648\) 0 0
\(649\) −14.2659 19.6354i −0.559986 0.770755i
\(650\) 0 0
\(651\) −0.272331 0.838148i −0.0106735 0.0328496i
\(652\) 0 0
\(653\) 8.39614i 0.328566i −0.986413 0.164283i \(-0.947469\pi\)
0.986413 0.164283i \(-0.0525311\pi\)
\(654\) 0 0
\(655\) 20.4575 0.799341
\(656\) 0 0
\(657\) 20.8201 0.812270
\(658\) 0 0
\(659\) 31.4971i 1.22695i −0.789714 0.613476i \(-0.789771\pi\)
0.789714 0.613476i \(-0.210229\pi\)
\(660\) 0 0
\(661\) −3.78362 11.6448i −0.147166 0.452930i 0.850117 0.526593i \(-0.176531\pi\)
−0.997283 + 0.0736636i \(0.976531\pi\)
\(662\) 0 0
\(663\) −1.48996 2.05076i −0.0578653 0.0796448i
\(664\) 0 0
\(665\) 4.62338 0.179287
\(666\) 0 0
\(667\) 18.0369 + 5.86054i 0.698391 + 0.226921i
\(668\) 0 0
\(669\) 1.35155 1.86025i 0.0522539 0.0719213i
\(670\) 0 0
\(671\) 0.0109736 0.00356555i 0.000423632 0.000137646i
\(672\) 0 0
\(673\) −19.5233 6.34350i −0.752567 0.244524i −0.0924818 0.995714i \(-0.529480\pi\)
−0.660086 + 0.751190i \(0.729480\pi\)
\(674\) 0 0
\(675\) 3.32881 + 4.58171i 0.128126 + 0.176350i
\(676\) 0 0
\(677\) −3.35299 + 2.43609i −0.128866 + 0.0936264i −0.650351 0.759634i \(-0.725378\pi\)
0.521485 + 0.853260i \(0.325378\pi\)
\(678\) 0 0
\(679\) 8.66165 + 6.29306i 0.332404 + 0.241505i
\(680\) 0 0
\(681\) 2.33866 1.69914i 0.0896178 0.0651112i
\(682\) 0 0
\(683\) 43.9663i 1.68233i 0.540782 + 0.841163i \(0.318128\pi\)
−0.540782 + 0.841163i \(0.681872\pi\)
\(684\) 0 0
\(685\) −20.3115 + 6.59959i −0.776061 + 0.252157i
\(686\) 0 0
\(687\) −0.712278 + 2.19217i −0.0271751 + 0.0836364i
\(688\) 0 0
\(689\) −7.65077 + 23.5467i −0.291471 + 0.897056i
\(690\) 0 0
\(691\) −6.85511 + 9.43525i −0.260781 + 0.358934i −0.919250 0.393673i \(-0.871204\pi\)
0.658470 + 0.752607i \(0.271204\pi\)
\(692\) 0 0
\(693\) −1.56894 4.82869i −0.0595990 0.183427i
\(694\) 0 0
\(695\) −9.07704 6.59485i −0.344312 0.250157i
\(696\) 0 0
\(697\) 2.64618 + 8.12648i 0.100231 + 0.307812i
\(698\) 0 0
\(699\) 2.78238 + 2.02151i 0.105239 + 0.0764607i
\(700\) 0 0
\(701\) 1.90017 + 5.84812i 0.0717683 + 0.220880i 0.980507 0.196486i \(-0.0629531\pi\)
−0.908738 + 0.417367i \(0.862953\pi\)
\(702\) 0 0
\(703\) 3.77417 5.19469i 0.142345 0.195922i
\(704\) 0 0
\(705\) 0.608809 1.87372i 0.0229291 0.0705684i
\(706\) 0 0
\(707\) 2.29089 7.05064i 0.0861579 0.265167i
\(708\) 0 0
\(709\) −43.5449 + 14.1486i −1.63536 + 0.531361i −0.975495 0.220022i \(-0.929387\pi\)
−0.659866 + 0.751383i \(0.729387\pi\)
\(710\) 0 0
\(711\) 41.4084i 1.55294i
\(712\) 0 0
\(713\) −8.41422 + 6.11329i −0.315115 + 0.228944i
\(714\) 0 0
\(715\) −11.9887 8.71031i −0.448352 0.325747i
\(716\) 0 0
\(717\) 0.872123 0.633635i 0.0325700 0.0236635i
\(718\) 0 0
\(719\) 12.2056 + 16.7996i 0.455192 + 0.626518i 0.973503 0.228674i \(-0.0734391\pi\)
−0.518311 + 0.855192i \(0.673439\pi\)
\(720\) 0 0
\(721\) −0.604052 0.196268i −0.0224961 0.00730942i
\(722\) 0 0
\(723\) 8.76224 2.84702i 0.325871 0.105882i
\(724\) 0 0
\(725\) 9.74133 13.4078i 0.361784 0.497953i
\(726\) 0 0
\(727\) −15.8818 5.16032i −0.589025 0.191386i −0.000685263 1.00000i \(-0.500218\pi\)
−0.588340 + 0.808614i \(0.700218\pi\)
\(728\) 0 0
\(729\) 22.1088 0.818844
\(730\) 0 0
\(731\) −2.39124 3.29127i −0.0884434 0.121732i
\(732\) 0 0
\(733\) 5.70851 + 17.5690i 0.210849 + 0.648925i 0.999422 + 0.0339850i \(0.0108198\pi\)
−0.788574 + 0.614940i \(0.789180\pi\)
\(734\) 0 0
\(735\) 0.415331i 0.0153197i
\(736\) 0 0
\(737\) 13.5666 0.499731
\(738\) 0 0
\(739\) −4.80997 −0.176937 −0.0884687 0.996079i \(-0.528197\pi\)
−0.0884687 + 0.996079i \(0.528197\pi\)
\(740\) 0 0
\(741\) 6.44591i 0.236796i
\(742\) 0 0
\(743\) −15.6615 48.2011i −0.574564 1.76833i −0.637659 0.770319i \(-0.720097\pi\)
0.0630952 0.998008i \(-0.479903\pi\)
\(744\) 0 0
\(745\) 4.47808 + 6.16354i 0.164064 + 0.225815i
\(746\) 0 0
\(747\) −20.3225 −0.743562
\(748\) 0 0
\(749\) −0.00219622 0.000713594i −8.02480e−5 2.60742e-5i
\(750\) 0 0
\(751\) 12.7475 17.5454i 0.465162 0.640240i −0.510408 0.859933i \(-0.670505\pi\)
0.975569 + 0.219693i \(0.0705054\pi\)
\(752\) 0 0
\(753\) 1.05923 0.344166i 0.0386006 0.0125421i
\(754\) 0 0
\(755\) 21.6958 + 7.04940i 0.789592 + 0.256554i
\(756\) 0 0
\(757\) −28.2308 38.8564i −1.02607 1.41226i −0.907861 0.419271i \(-0.862286\pi\)
−0.118206 0.992989i \(-0.537714\pi\)
\(758\) 0 0
\(759\) 1.55020 1.12628i 0.0562685 0.0408815i
\(760\) 0 0
\(761\) 35.6279 + 25.8852i 1.29151 + 0.938337i 0.999835 0.0181803i \(-0.00578730\pi\)
0.291675 + 0.956517i \(0.405787\pi\)
\(762\) 0 0
\(763\) 0.290039 0.210726i 0.0105001 0.00762879i
\(764\) 0 0
\(765\) 5.28545i 0.191096i
\(766\) 0 0
\(767\) −82.3228 + 26.7483i −2.97250 + 0.965825i
\(768\) 0 0
\(769\) 0.737876 2.27095i 0.0266085 0.0818925i −0.936870 0.349677i \(-0.886291\pi\)
0.963479 + 0.267784i \(0.0862914\pi\)
\(770\) 0 0
\(771\) −0.0286636 + 0.0882175i −0.00103229 + 0.00317707i
\(772\) 0 0
\(773\) 16.7091 22.9981i 0.600984 0.827184i −0.394814 0.918761i \(-0.629191\pi\)
0.995798 + 0.0915776i \(0.0291909\pi\)
\(774\) 0 0
\(775\) 2.80855 + 8.64384i 0.100886 + 0.310496i
\(776\) 0 0
\(777\) 0.466655 + 0.339044i 0.0167411 + 0.0121631i
\(778\) 0 0
\(779\) −6.70260 + 20.6733i −0.240146 + 0.740698i
\(780\) 0 0
\(781\) 2.93272 + 2.13075i 0.104941 + 0.0762441i
\(782\) 0 0
\(783\) 2.93336 + 9.02796i 0.104830 + 0.322633i
\(784\) 0 0
\(785\) −14.1987 + 19.5428i −0.506774 + 0.697514i
\(786\) 0 0
\(787\) 5.92971 18.2498i 0.211371 0.650534i −0.788020 0.615649i \(-0.788894\pi\)
0.999391 0.0348843i \(-0.0111063\pi\)
\(788\) 0 0
\(789\) 1.32800 4.08715i 0.0472779 0.145506i
\(790\) 0 0
\(791\) −3.36867 + 1.09455i −0.119776 + 0.0389176i
\(792\) 0 0
\(793\) 0.0411506i 0.00146130i
\(794\) 0 0
\(795\) 1.33558 0.970357i 0.0473682 0.0344150i
\(796\) 0 0
\(797\) −30.7617 22.3497i −1.08963