Properties

Label 1148.2.ba.a.113.12
Level $1148$
Weight $2$
Character 1148.113
Analytic conductor $9.167$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 113.12
Character \(\chi\) \(=\) 1148.113
Dual form 1148.2.ba.a.701.9

$q$-expansion

\(f(q)\) \(=\) \(q+0.927936i q^{3} +(0.718305 + 2.21072i) q^{5} +(-0.587785 - 0.809017i) q^{7} +2.13894 q^{9} +O(q^{10})\) \(q+0.927936i q^{3} +(0.718305 + 2.21072i) q^{5} +(-0.587785 - 0.809017i) q^{7} +2.13894 q^{9} +(-2.17752 - 0.707518i) q^{11} +(2.09337 - 2.88128i) q^{13} +(-2.05140 + 0.666541i) q^{15} +(4.08898 + 1.32859i) q^{17} +(3.47829 + 4.78745i) q^{19} +(0.750716 - 0.545427i) q^{21} +(1.51889 + 1.10354i) q^{23} +(-0.326219 + 0.237012i) q^{25} +4.76860i q^{27} +(4.40009 - 1.42968i) q^{29} +(-2.17082 + 6.68111i) q^{31} +(0.656531 - 2.02060i) q^{33} +(1.36630 - 1.88055i) q^{35} +(-0.715941 - 2.20344i) q^{37} +(2.67364 + 1.94251i) q^{39} +(-6.06374 - 2.05695i) q^{41} +(0.206092 + 0.149735i) q^{43} +(1.53641 + 4.72858i) q^{45} +(-6.91235 + 9.51404i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-1.23285 + 3.79431i) q^{51} +(-13.4073 + 4.35631i) q^{53} -5.32209i q^{55} +(-4.44245 + 3.22763i) q^{57} +(-0.491392 - 0.357017i) q^{59} +(5.39061 - 3.91651i) q^{61} +(-1.25723 - 1.73044i) q^{63} +(7.87337 + 2.55821i) q^{65} +(2.80488 - 0.911362i) q^{67} +(-1.02401 + 1.40944i) q^{69} +(-2.31494 - 0.752169i) q^{71} -0.789290 q^{73} +(-0.219932 - 0.302710i) q^{75} +(0.707518 + 2.17752i) q^{77} +2.86187i q^{79} +1.99185 q^{81} -0.0274158 q^{83} +9.99390i q^{85} +(1.32665 + 4.08300i) q^{87} +(4.94716 + 6.80918i) q^{89} -3.56146 q^{91} +(-6.19964 - 2.01438i) q^{93} +(-8.08523 + 11.1284i) q^{95} +(13.0991 - 4.25615i) q^{97} +(-4.65757 - 1.51334i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

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
\(3\) 0.927936i 0.535744i 0.963455 + 0.267872i \(0.0863204\pi\)
−0.963455 + 0.267872i \(0.913680\pi\)
\(4\) 0 0
\(5\) 0.718305 + 2.21072i 0.321236 + 0.988662i 0.973111 + 0.230336i \(0.0739826\pi\)
−0.651875 + 0.758326i \(0.726017\pi\)
\(6\) 0 0
\(7\) −0.587785 0.809017i −0.222162 0.305780i
\(8\) 0 0
\(9\) 2.13894 0.712978
\(10\) 0 0
\(11\) −2.17752 0.707518i −0.656546 0.213325i −0.0382478 0.999268i \(-0.512178\pi\)
−0.618298 + 0.785944i \(0.712178\pi\)
\(12\) 0 0
\(13\) 2.09337 2.88128i 0.580597 0.799123i −0.413164 0.910657i \(-0.635576\pi\)
0.993761 + 0.111534i \(0.0355763\pi\)
\(14\) 0 0
\(15\) −2.05140 + 0.666541i −0.529670 + 0.172100i
\(16\) 0 0
\(17\) 4.08898 + 1.32859i 0.991723 + 0.322230i 0.759553 0.650445i \(-0.225418\pi\)
0.232170 + 0.972675i \(0.425418\pi\)
\(18\) 0 0
\(19\) 3.47829 + 4.78745i 0.797974 + 1.09832i 0.993069 + 0.117533i \(0.0374986\pi\)
−0.195095 + 0.980784i \(0.562501\pi\)
\(20\) 0 0
\(21\) 0.750716 0.545427i 0.163820 0.119022i
\(22\) 0 0
\(23\) 1.51889 + 1.10354i 0.316711 + 0.230104i 0.734771 0.678315i \(-0.237290\pi\)
−0.418060 + 0.908420i \(0.637290\pi\)
\(24\) 0 0
\(25\) −0.326219 + 0.237012i −0.0652438 + 0.0474024i
\(26\) 0 0
\(27\) 4.76860i 0.917718i
\(28\) 0 0
\(29\) 4.40009 1.42968i 0.817077 0.265484i 0.129485 0.991581i \(-0.458668\pi\)
0.687592 + 0.726097i \(0.258668\pi\)
\(30\) 0 0
\(31\) −2.17082 + 6.68111i −0.389891 + 1.19996i 0.542978 + 0.839747i \(0.317297\pi\)
−0.932869 + 0.360215i \(0.882703\pi\)
\(32\) 0 0
\(33\) 0.656531 2.02060i 0.114287 0.351741i
\(34\) 0 0
\(35\) 1.36630 1.88055i 0.230946 0.317871i
\(36\) 0 0
\(37\) −0.715941 2.20344i −0.117700 0.362243i 0.874801 0.484483i \(-0.160992\pi\)
−0.992501 + 0.122240i \(0.960992\pi\)
\(38\) 0 0
\(39\) 2.67364 + 1.94251i 0.428125 + 0.311051i
\(40\) 0 0
\(41\) −6.06374 2.05695i −0.946997 0.321242i
\(42\) 0 0
\(43\) 0.206092 + 0.149735i 0.0314288 + 0.0228343i 0.603389 0.797447i \(-0.293817\pi\)
−0.571960 + 0.820282i \(0.693817\pi\)
\(44\) 0 0
\(45\) 1.53641 + 4.72858i 0.229034 + 0.704895i
\(46\) 0 0
\(47\) −6.91235 + 9.51404i −1.00827 + 1.38777i −0.0881600 + 0.996106i \(0.528099\pi\)
−0.920110 + 0.391659i \(0.871901\pi\)
\(48\) 0 0
\(49\) −0.309017 + 0.951057i −0.0441453 + 0.135865i
\(50\) 0 0
\(51\) −1.23285 + 3.79431i −0.172633 + 0.531310i
\(52\) 0 0
\(53\) −13.4073 + 4.35631i −1.84164 + 0.598385i −0.843520 + 0.537098i \(0.819521\pi\)
−0.998120 + 0.0612872i \(0.980479\pi\)
\(54\) 0 0
\(55\) 5.32209i 0.717630i
\(56\) 0 0
\(57\) −4.44245 + 3.22763i −0.588417 + 0.427510i
\(58\) 0 0
\(59\) −0.491392 0.357017i −0.0639738 0.0464797i 0.555339 0.831624i \(-0.312589\pi\)
−0.619313 + 0.785145i \(0.712589\pi\)
\(60\) 0 0
\(61\) 5.39061 3.91651i 0.690197 0.501457i −0.186528 0.982450i \(-0.559723\pi\)
0.876725 + 0.480992i \(0.159723\pi\)
\(62\) 0 0
\(63\) −1.25723 1.73044i −0.158397 0.218014i
\(64\) 0 0
\(65\) 7.87337 + 2.55821i 0.976571 + 0.317307i
\(66\) 0 0
\(67\) 2.80488 0.911362i 0.342671 0.111341i −0.132626 0.991166i \(-0.542341\pi\)
0.475297 + 0.879826i \(0.342341\pi\)
\(68\) 0 0
\(69\) −1.02401 + 1.40944i −0.123277 + 0.169676i
\(70\) 0 0
\(71\) −2.31494 0.752169i −0.274733 0.0892661i 0.168410 0.985717i \(-0.446137\pi\)
−0.443143 + 0.896451i \(0.646137\pi\)
\(72\) 0 0
\(73\) −0.789290 −0.0923794 −0.0461897 0.998933i \(-0.514708\pi\)
−0.0461897 + 0.998933i \(0.514708\pi\)
\(74\) 0 0
\(75\) −0.219932 0.302710i −0.0253956 0.0349540i
\(76\) 0 0
\(77\) 0.707518 + 2.17752i 0.0806292 + 0.248151i
\(78\) 0 0
\(79\) 2.86187i 0.321986i 0.986956 + 0.160993i \(0.0514696\pi\)
−0.986956 + 0.160993i \(0.948530\pi\)
\(80\) 0 0
\(81\) 1.99185 0.221317
\(82\) 0 0
\(83\) −0.0274158 −0.00300927 −0.00150464 0.999999i \(-0.500479\pi\)
−0.00150464 + 0.999999i \(0.500479\pi\)
\(84\) 0 0
\(85\) 9.99390i 1.08399i
\(86\) 0 0
\(87\) 1.32665 + 4.08300i 0.142232 + 0.437744i
\(88\) 0 0
\(89\) 4.94716 + 6.80918i 0.524398 + 0.721772i 0.986264 0.165178i \(-0.0528199\pi\)
−0.461866 + 0.886950i \(0.652820\pi\)
\(90\) 0 0
\(91\) −3.56146 −0.373342
\(92\) 0 0
\(93\) −6.19964 2.01438i −0.642873 0.208882i
\(94\) 0 0
\(95\) −8.08523 + 11.1284i −0.829527 + 1.14175i
\(96\) 0 0
\(97\) 13.0991 4.25615i 1.33001 0.432146i 0.444089 0.895983i \(-0.353528\pi\)
0.885921 + 0.463837i \(0.153528\pi\)
\(98\) 0 0
\(99\) −4.65757 1.51334i −0.468103 0.152096i
\(100\) 0 0
\(101\) −0.0657389 0.0904818i −0.00654126 0.00900327i 0.805734 0.592278i \(-0.201771\pi\)
−0.812275 + 0.583275i \(0.801771\pi\)
\(102\) 0 0
\(103\) 12.0420 8.74903i 1.18653 0.862068i 0.193641 0.981072i \(-0.437970\pi\)
0.992894 + 0.119005i \(0.0379703\pi\)
\(104\) 0 0
\(105\) 1.74503 + 1.26784i 0.170297 + 0.123728i
\(106\) 0 0
\(107\) 5.10145 3.70642i 0.493175 0.358313i −0.313229 0.949678i \(-0.601411\pi\)
0.806404 + 0.591365i \(0.201411\pi\)
\(108\) 0 0
\(109\) 14.0228i 1.34314i −0.740942 0.671569i \(-0.765621\pi\)
0.740942 0.671569i \(-0.234379\pi\)
\(110\) 0 0
\(111\) 2.04465 0.664347i 0.194070 0.0630570i
\(112\) 0 0
\(113\) −5.71578 + 17.5914i −0.537695 + 1.65486i 0.200057 + 0.979784i \(0.435887\pi\)
−0.737752 + 0.675072i \(0.764113\pi\)
\(114\) 0 0
\(115\) −1.34859 + 4.15052i −0.125756 + 0.387038i
\(116\) 0 0
\(117\) 4.47759 6.16287i 0.413953 0.569757i
\(118\) 0 0
\(119\) −1.32859 4.08898i −0.121792 0.374836i
\(120\) 0 0
\(121\) −4.65819 3.38437i −0.423472 0.307670i
\(122\) 0 0
\(123\) 1.90872 5.62676i 0.172103 0.507348i
\(124\) 0 0
\(125\) 8.64445 + 6.28056i 0.773183 + 0.561750i
\(126\) 0 0
\(127\) 1.85636 + 5.71329i 0.164725 + 0.506973i 0.999016 0.0443523i \(-0.0141224\pi\)
−0.834291 + 0.551325i \(0.814122\pi\)
\(128\) 0 0
\(129\) −0.138944 + 0.191240i −0.0122334 + 0.0168378i
\(130\) 0 0
\(131\) 4.81926 14.8322i 0.421060 1.29589i −0.485656 0.874150i \(-0.661419\pi\)
0.906716 0.421741i \(-0.138581\pi\)
\(132\) 0 0
\(133\) 1.82865 5.62799i 0.158564 0.488009i
\(134\) 0 0
\(135\) −10.5420 + 3.42531i −0.907313 + 0.294804i
\(136\) 0 0
\(137\) 1.91000i 0.163183i −0.996666 0.0815913i \(-0.974000\pi\)
0.996666 0.0815913i \(-0.0260002\pi\)
\(138\) 0 0
\(139\) 1.08709 0.789815i 0.0922055 0.0669912i −0.540727 0.841198i \(-0.681851\pi\)
0.632933 + 0.774207i \(0.281851\pi\)
\(140\) 0 0
\(141\) −8.82842 6.41422i −0.743487 0.540175i
\(142\) 0 0
\(143\) −6.59691 + 4.79294i −0.551661 + 0.400805i
\(144\) 0 0
\(145\) 6.32122 + 8.70041i 0.524949 + 0.722530i
\(146\) 0 0
\(147\) −0.882519 0.286748i −0.0727890 0.0236506i
\(148\) 0 0
\(149\) 2.80250 0.910588i 0.229590 0.0745983i −0.191963 0.981402i \(-0.561485\pi\)
0.421553 + 0.906804i \(0.361485\pi\)
\(150\) 0 0
\(151\) −3.90234 + 5.37111i −0.317568 + 0.437094i −0.937723 0.347385i \(-0.887070\pi\)
0.620155 + 0.784479i \(0.287070\pi\)
\(152\) 0 0
\(153\) 8.74606 + 2.84177i 0.707077 + 0.229743i
\(154\) 0 0
\(155\) −16.3294 −1.31161
\(156\) 0 0
\(157\) −10.2781 14.1466i −0.820280 1.12902i −0.989655 0.143467i \(-0.954175\pi\)
0.169375 0.985552i \(-0.445825\pi\)
\(158\) 0 0
\(159\) −4.04237 12.4412i −0.320581 0.986647i
\(160\) 0 0
\(161\) 1.87746i 0.147964i
\(162\) 0 0
\(163\) −4.04965 −0.317193 −0.158596 0.987343i \(-0.550697\pi\)
−0.158596 + 0.987343i \(0.550697\pi\)
\(164\) 0 0
\(165\) 4.93855 0.384466
\(166\) 0 0
\(167\) 14.3600i 1.11121i −0.831446 0.555606i \(-0.812486\pi\)
0.831446 0.555606i \(-0.187514\pi\)
\(168\) 0 0
\(169\) 0.0976583 + 0.300561i 0.00751218 + 0.0231201i
\(170\) 0 0
\(171\) 7.43984 + 10.2401i 0.568939 + 0.783077i
\(172\) 0 0
\(173\) 17.0283 1.29464 0.647321 0.762218i \(-0.275889\pi\)
0.647321 + 0.762218i \(0.275889\pi\)
\(174\) 0 0
\(175\) 0.383494 + 0.124605i 0.0289894 + 0.00941923i
\(176\) 0 0
\(177\) 0.331289 0.455980i 0.0249012 0.0342736i
\(178\) 0 0
\(179\) 13.4952 4.38486i 1.00868 0.327740i 0.242351 0.970189i \(-0.422081\pi\)
0.766329 + 0.642449i \(0.222081\pi\)
\(180\) 0 0
\(181\) 13.6189 + 4.42504i 1.01228 + 0.328911i 0.767763 0.640734i \(-0.221370\pi\)
0.244519 + 0.969644i \(0.421370\pi\)
\(182\) 0 0
\(183\) 3.63427 + 5.00214i 0.268653 + 0.369769i
\(184\) 0 0
\(185\) 4.35692 3.16548i 0.320327 0.232731i
\(186\) 0 0
\(187\) −7.96382 5.78605i −0.582372 0.423118i
\(188\) 0 0
\(189\) 3.85788 2.80291i 0.280619 0.203882i
\(190\) 0 0
\(191\) 6.38731i 0.462170i −0.972934 0.231085i \(-0.925773\pi\)
0.972934 0.231085i \(-0.0742275\pi\)
\(192\) 0 0
\(193\) −5.97950 + 1.94286i −0.430414 + 0.139850i −0.516209 0.856463i \(-0.672657\pi\)
0.0857946 + 0.996313i \(0.472657\pi\)
\(194\) 0 0
\(195\) −2.37386 + 7.30598i −0.169995 + 0.523192i
\(196\) 0 0
\(197\) −0.604573 + 1.86068i −0.0430740 + 0.132568i −0.970281 0.241981i \(-0.922203\pi\)
0.927207 + 0.374550i \(0.122203\pi\)
\(198\) 0 0
\(199\) −9.80973 + 13.5019i −0.695393 + 0.957127i 0.304596 + 0.952482i \(0.401479\pi\)
−0.999989 + 0.00464515i \(0.998521\pi\)
\(200\) 0 0
\(201\) 0.845685 + 2.60275i 0.0596500 + 0.183584i
\(202\) 0 0
\(203\) −3.74294 2.71941i −0.262703 0.190865i
\(204\) 0 0
\(205\) 0.191720 14.8827i 0.0133903 1.03945i
\(206\) 0 0
\(207\) 3.24881 + 2.36040i 0.225808 + 0.164059i
\(208\) 0 0
\(209\) −4.18682 12.8857i −0.289609 0.891324i
\(210\) 0 0
\(211\) −2.00836 + 2.76428i −0.138262 + 0.190301i −0.872533 0.488555i \(-0.837524\pi\)
0.734271 + 0.678856i \(0.237524\pi\)
\(212\) 0 0
\(213\) 0.697965 2.14811i 0.0478237 0.147186i
\(214\) 0 0
\(215\) −0.182984 + 0.563167i −0.0124794 + 0.0384077i
\(216\) 0 0
\(217\) 6.68111 2.17082i 0.453543 0.147365i
\(218\) 0 0
\(219\) 0.732410i 0.0494917i
\(220\) 0 0
\(221\) 12.3878 9.00025i 0.833293 0.605423i
\(222\) 0 0
\(223\) −20.4162 14.8332i −1.36717 0.993307i −0.997952 0.0639641i \(-0.979626\pi\)
−0.369218 0.929343i \(-0.620374\pi\)
\(224\) 0 0
\(225\) −0.697762 + 0.506954i −0.0465175 + 0.0337969i
\(226\) 0 0
\(227\) −13.2752 18.2717i −0.881103 1.21273i −0.976114 0.217258i \(-0.930289\pi\)
0.0950113 0.995476i \(-0.469711\pi\)
\(228\) 0 0
\(229\) −14.9109 4.84486i −0.985342 0.320157i −0.228349 0.973579i \(-0.573333\pi\)
−0.756994 + 0.653422i \(0.773333\pi\)
\(230\) 0 0
\(231\) −2.02060 + 0.656531i −0.132945 + 0.0431966i
\(232\) 0 0
\(233\) 7.23281 9.95511i 0.473837 0.652181i −0.503469 0.864014i \(-0.667943\pi\)
0.977306 + 0.211832i \(0.0679431\pi\)
\(234\) 0 0
\(235\) −25.9980 8.44727i −1.69592 0.551039i
\(236\) 0 0
\(237\) −2.65563 −0.172502
\(238\) 0 0
\(239\) −2.08097 2.86421i −0.134607 0.185270i 0.736393 0.676555i \(-0.236528\pi\)
−0.870999 + 0.491284i \(0.836528\pi\)
\(240\) 0 0
\(241\) 4.95810 + 15.2594i 0.319379 + 0.982947i 0.973914 + 0.226916i \(0.0728643\pi\)
−0.654535 + 0.756031i \(0.727136\pi\)
\(242\) 0 0
\(243\) 16.1541i 1.03629i
\(244\) 0 0
\(245\) −2.32448 −0.148506
\(246\) 0 0
\(247\) 21.0753 1.34099
\(248\) 0 0
\(249\) 0.0254401i 0.00161220i
\(250\) 0 0
\(251\) 2.43021 + 7.47941i 0.153393 + 0.472096i 0.997995 0.0632996i \(-0.0201624\pi\)
−0.844601 + 0.535396i \(0.820162\pi\)
\(252\) 0 0
\(253\) −2.52664 3.47762i −0.158849 0.218636i
\(254\) 0 0
\(255\) −9.27370 −0.580742
\(256\) 0 0
\(257\) −11.5894 3.76563i −0.722927 0.234893i −0.0756353 0.997136i \(-0.524098\pi\)
−0.647292 + 0.762242i \(0.724098\pi\)
\(258\) 0 0
\(259\) −1.36180 + 1.87436i −0.0846182 + 0.116467i
\(260\) 0 0
\(261\) 9.41152 3.05799i 0.582558 0.189285i
\(262\) 0 0
\(263\) −17.1700 5.57888i −1.05875 0.344009i −0.272653 0.962112i \(-0.587901\pi\)
−0.786097 + 0.618104i \(0.787901\pi\)
\(264\) 0 0
\(265\) −19.2611 26.5107i −1.18320 1.62854i
\(266\) 0 0
\(267\) −6.31848 + 4.59065i −0.386685 + 0.280943i
\(268\) 0 0
\(269\) 7.39565 + 5.37325i 0.450921 + 0.327613i 0.789959 0.613160i \(-0.210102\pi\)
−0.339039 + 0.940772i \(0.610102\pi\)
\(270\) 0 0
\(271\) 23.7229 17.2357i 1.44107 1.04700i 0.453248 0.891384i \(-0.350265\pi\)
0.987818 0.155611i \(-0.0497348\pi\)
\(272\) 0 0
\(273\) 3.30480i 0.200016i
\(274\) 0 0
\(275\) 0.878038 0.285292i 0.0529477 0.0172038i
\(276\) 0 0
\(277\) 9.43052 29.0242i 0.566625 1.74389i −0.0964473 0.995338i \(-0.530748\pi\)
0.663073 0.748555i \(-0.269252\pi\)
\(278\) 0 0
\(279\) −4.64325 + 14.2905i −0.277984 + 0.855548i
\(280\) 0 0
\(281\) −15.2131 + 20.9390i −0.907538 + 1.24912i 0.0604624 + 0.998170i \(0.480742\pi\)
−0.968000 + 0.250948i \(0.919258\pi\)
\(282\) 0 0
\(283\) −6.86559 21.1301i −0.408117 1.25606i −0.918264 0.395968i \(-0.870409\pi\)
0.510147 0.860087i \(-0.329591\pi\)
\(284\) 0 0
\(285\) −10.3264 7.50257i −0.611684 0.444414i
\(286\) 0 0
\(287\) 1.90007 + 6.11472i 0.112157 + 0.360940i
\(288\) 0 0
\(289\) 1.20130 + 0.872799i 0.0706650 + 0.0513411i
\(290\) 0 0
\(291\) 3.94943 + 12.1551i 0.231520 + 0.712544i
\(292\) 0 0
\(293\) 1.22909 1.69170i 0.0718044 0.0988303i −0.771604 0.636103i \(-0.780545\pi\)
0.843409 + 0.537273i \(0.180545\pi\)
\(294\) 0 0
\(295\) 0.436294 1.34278i 0.0254020 0.0781794i
\(296\) 0 0
\(297\) 3.37387 10.3837i 0.195772 0.602524i
\(298\) 0 0
\(299\) 6.35922 2.06623i 0.367763 0.119493i
\(300\) 0 0
\(301\) 0.254744i 0.0146832i
\(302\) 0 0
\(303\) 0.0839613 0.0610014i 0.00482345 0.00350444i
\(304\) 0 0
\(305\) 12.5304 + 9.10386i 0.717488 + 0.521286i
\(306\) 0 0
\(307\) 14.6282 10.6280i 0.834876 0.606573i −0.0860589 0.996290i \(-0.527427\pi\)
0.920934 + 0.389717i \(0.127427\pi\)
\(308\) 0 0
\(309\) 8.11854 + 11.1742i 0.461848 + 0.635679i
\(310\) 0 0
\(311\) 1.54919 + 0.503363i 0.0878467 + 0.0285431i 0.352611 0.935770i \(-0.385294\pi\)
−0.264764 + 0.964313i \(0.585294\pi\)
\(312\) 0 0
\(313\) 1.37897 0.448054i 0.0779439 0.0253255i −0.269785 0.962920i \(-0.586953\pi\)
0.347729 + 0.937595i \(0.386953\pi\)
\(314\) 0 0
\(315\) 2.92242 4.02237i 0.164660 0.226635i
\(316\) 0 0
\(317\) −23.8274 7.74198i −1.33828 0.434833i −0.449545 0.893258i \(-0.648414\pi\)
−0.888733 + 0.458425i \(0.848414\pi\)
\(318\) 0 0
\(319\) −10.5928 −0.593083
\(320\) 0 0
\(321\) 3.43932 + 4.73381i 0.191964 + 0.264216i
\(322\) 0 0
\(323\) 7.86209 + 24.1970i 0.437458 + 1.34636i
\(324\) 0 0
\(325\) 1.43608i 0.0796596i
\(326\) 0 0
\(327\) 13.0122 0.719578
\(328\) 0 0
\(329\) 11.7600 0.648350
\(330\) 0 0
\(331\) 29.0787i 1.59831i −0.601124 0.799156i \(-0.705280\pi\)
0.601124 0.799156i \(-0.294720\pi\)
\(332\) 0 0
\(333\) −1.53135 4.71302i −0.0839176 0.258272i
\(334\) 0 0
\(335\) 4.02952 + 5.54616i 0.220156 + 0.303019i
\(336\) 0 0
\(337\) −8.95467 −0.487792 −0.243896 0.969801i \(-0.578426\pi\)
−0.243896 + 0.969801i \(0.578426\pi\)
\(338\) 0 0
\(339\) −16.3236 5.30388i −0.886579 0.288067i
\(340\) 0 0
\(341\) 9.45401 13.0123i 0.511964 0.704657i
\(342\) 0 0
\(343\) 0.951057 0.309017i 0.0513522 0.0166853i
\(344\) 0 0
\(345\) −3.85142 1.25140i −0.207353 0.0673732i
\(346\) 0 0
\(347\) 16.8230 + 23.1549i 0.903106 + 1.24302i 0.969467 + 0.245222i \(0.0788610\pi\)
−0.0663613 + 0.997796i \(0.521139\pi\)
\(348\) 0 0
\(349\) 5.96806 4.33605i 0.319463 0.232103i −0.416483 0.909143i \(-0.636738\pi\)
0.735946 + 0.677040i \(0.236738\pi\)
\(350\) 0 0
\(351\) 13.7397 + 9.98245i 0.733369 + 0.532824i
\(352\) 0 0
\(353\) 6.18363 4.49267i 0.329121 0.239121i −0.410936 0.911664i \(-0.634798\pi\)
0.740058 + 0.672543i \(0.234798\pi\)
\(354\) 0 0
\(355\) 5.65796i 0.300293i
\(356\) 0 0
\(357\) 3.79431 1.23285i 0.200816 0.0652491i
\(358\) 0 0
\(359\) −7.19235 + 22.1358i −0.379598 + 1.16828i 0.560726 + 0.828001i \(0.310522\pi\)
−0.940324 + 0.340281i \(0.889478\pi\)
\(360\) 0 0
\(361\) −4.94990 + 15.2342i −0.260521 + 0.801802i
\(362\) 0 0
\(363\) 3.14048 4.32250i 0.164832 0.226872i
\(364\) 0 0
\(365\) −0.566951 1.74490i −0.0296756 0.0913320i
\(366\) 0 0
\(367\) −18.8964 13.7291i −0.986385 0.716651i −0.0272588 0.999628i \(-0.508678\pi\)
−0.959127 + 0.282977i \(0.908678\pi\)
\(368\) 0 0
\(369\) −12.9699 4.39969i −0.675189 0.229039i
\(370\) 0 0
\(371\) 11.4050 + 8.28619i 0.592116 + 0.430198i
\(372\) 0 0
\(373\) −5.72887 17.6317i −0.296630 0.912933i −0.982669 0.185368i \(-0.940652\pi\)
0.686039 0.727564i \(-0.259348\pi\)
\(374\) 0 0
\(375\) −5.82795 + 8.02149i −0.300954 + 0.414228i
\(376\) 0 0
\(377\) 5.09173 15.6707i 0.262238 0.807084i
\(378\) 0 0
\(379\) 1.09937 3.38350i 0.0564707 0.173799i −0.918843 0.394624i \(-0.870875\pi\)
0.975313 + 0.220825i \(0.0708749\pi\)
\(380\) 0 0
\(381\) −5.30157 + 1.72258i −0.271608 + 0.0882506i
\(382\) 0 0
\(383\) 16.6699i 0.851793i −0.904772 0.425897i \(-0.859959\pi\)
0.904772 0.425897i \(-0.140041\pi\)
\(384\) 0 0
\(385\) −4.30566 + 3.12824i −0.219437 + 0.159430i
\(386\) 0 0
\(387\) 0.440818 + 0.320273i 0.0224080 + 0.0162804i
\(388\) 0 0
\(389\) −17.5979 + 12.7856i −0.892249 + 0.648257i −0.936463 0.350765i \(-0.885921\pi\)
0.0442145 + 0.999022i \(0.485921\pi\)
\(390\) 0 0
\(391\) 4.74457 + 6.53034i 0.239943 + 0.330253i
\(392\) 0 0
\(393\) 13.7633 + 4.47196i 0.694266 + 0.225581i
\(394\) 0 0
\(395\) −6.32678 + 2.05570i −0.318335 + 0.103433i
\(396\) 0 0
\(397\) −1.93140 + 2.65834i −0.0969341 + 0.133418i −0.854729 0.519074i \(-0.826277\pi\)
0.757795 + 0.652493i \(0.226277\pi\)
\(398\) 0 0
\(399\) 5.22241 + 1.69686i 0.261448 + 0.0849495i
\(400\) 0 0
\(401\) 31.0618 1.55115 0.775577 0.631253i \(-0.217459\pi\)
0.775577 + 0.631253i \(0.217459\pi\)
\(402\) 0 0
\(403\) 14.7058 + 20.2408i 0.732548 + 1.00827i
\(404\) 0 0
\(405\) 1.43076 + 4.40342i 0.0710949 + 0.218808i
\(406\) 0 0
\(407\) 5.30457i 0.262938i
\(408\) 0 0
\(409\) −31.6976 −1.56734 −0.783672 0.621175i \(-0.786656\pi\)
−0.783672 + 0.621175i \(0.786656\pi\)
\(410\) 0 0
\(411\) 1.77236 0.0874241
\(412\) 0 0
\(413\) 0.607394i 0.0298879i
\(414\) 0 0
\(415\) −0.0196929 0.0606085i −0.000966687 0.00297516i
\(416\) 0 0
\(417\) 0.732898 + 1.00875i 0.0358901 + 0.0493985i
\(418\) 0 0
\(419\) 11.9740 0.584967 0.292484 0.956271i \(-0.405518\pi\)
0.292484 + 0.956271i \(0.405518\pi\)
\(420\) 0 0
\(421\) −16.4889 5.35757i −0.803620 0.261112i −0.121727 0.992564i \(-0.538843\pi\)
−0.681893 + 0.731452i \(0.738843\pi\)
\(422\) 0 0
\(423\) −14.7851 + 20.3499i −0.718875 + 0.989447i
\(424\) 0 0
\(425\) −1.64880 + 0.535726i −0.0799783 + 0.0259865i
\(426\) 0 0
\(427\) −6.33704 2.05903i −0.306671 0.0996434i
\(428\) 0 0
\(429\) −4.44754 6.12151i −0.214729 0.295549i
\(430\) 0 0
\(431\) −12.2261 + 8.88281i −0.588913 + 0.427870i −0.841926 0.539593i \(-0.818578\pi\)
0.253014 + 0.967463i \(0.418578\pi\)
\(432\) 0 0
\(433\) 16.7707 + 12.1846i 0.805950 + 0.585557i 0.912653 0.408734i \(-0.134030\pi\)
−0.106704 + 0.994291i \(0.534030\pi\)
\(434\) 0 0
\(435\) −8.07342 + 5.86569i −0.387091 + 0.281238i
\(436\) 0 0
\(437\) 11.1101i 0.531467i
\(438\) 0 0
\(439\) 14.4008 4.67911i 0.687313 0.223322i 0.0555187 0.998458i \(-0.482319\pi\)
0.631794 + 0.775136i \(0.282319\pi\)
\(440\) 0 0
\(441\) −0.660967 + 2.03425i −0.0314746 + 0.0968690i
\(442\) 0 0
\(443\) 3.92888 12.0919i 0.186667 0.574502i −0.813306 0.581836i \(-0.802335\pi\)
0.999973 + 0.00733416i \(0.00233456\pi\)
\(444\) 0 0
\(445\) −11.4996 + 15.8278i −0.545133 + 0.750311i
\(446\) 0 0
\(447\) 0.844967 + 2.60054i 0.0399656 + 0.123001i
\(448\) 0 0
\(449\) 20.6976 + 15.0377i 0.976779 + 0.709672i 0.956987 0.290132i \(-0.0936994\pi\)
0.0197928 + 0.999804i \(0.493699\pi\)
\(450\) 0 0
\(451\) 11.7486 + 8.76926i 0.553218 + 0.412928i
\(452\) 0 0
\(453\) −4.98404 3.62112i −0.234171 0.170135i
\(454\) 0 0
\(455\) −2.55821 7.87337i −0.119931 0.369109i
\(456\) 0 0
\(457\) 13.0151 17.9138i 0.608821 0.837970i −0.387659 0.921803i \(-0.626716\pi\)
0.996480 + 0.0838328i \(0.0267162\pi\)
\(458\) 0 0
\(459\) −6.33551 + 19.4987i −0.295716 + 0.910122i
\(460\) 0 0
\(461\) 4.85336 14.9371i 0.226044 0.695691i −0.772140 0.635452i \(-0.780814\pi\)
0.998184 0.0602387i \(-0.0191862\pi\)
\(462\) 0 0
\(463\) −36.0497 + 11.7132i −1.67537 + 0.544361i −0.984004 0.178145i \(-0.942990\pi\)
−0.691365 + 0.722505i \(0.742990\pi\)
\(464\) 0 0
\(465\) 15.1526i 0.702684i
\(466\) 0 0
\(467\) 2.88590 2.09673i 0.133544 0.0970251i −0.519008 0.854769i \(-0.673699\pi\)
0.652552 + 0.757744i \(0.273699\pi\)
\(468\) 0 0
\(469\) −2.38598 1.73351i −0.110174 0.0800462i
\(470\) 0 0
\(471\) 13.1271 9.53740i 0.604865 0.439460i
\(472\) 0 0
\(473\) −0.342829 0.471864i −0.0157633 0.0216963i
\(474\) 0 0
\(475\) −2.26937 0.737363i −0.104126 0.0338325i
\(476\) 0 0
\(477\) −28.6774 + 9.31786i −1.31305 + 0.426636i
\(478\) 0 0
\(479\) −12.0651 + 16.6062i −0.551268 + 0.758755i −0.990184 0.139773i \(-0.955363\pi\)
0.438915 + 0.898528i \(0.355363\pi\)
\(480\) 0 0
\(481\) −7.84745 2.54979i −0.357813 0.116261i
\(482\) 0 0
\(483\) 1.74216 0.0792709
\(484\) 0 0
\(485\) 18.8183 + 25.9011i 0.854494 + 1.17611i
\(486\) 0 0
\(487\) 1.87756 + 5.77853i 0.0850803 + 0.261850i 0.984542 0.175150i \(-0.0560410\pi\)
−0.899461 + 0.437000i \(0.856041\pi\)
\(488\) 0 0
\(489\) 3.75781i 0.169934i
\(490\) 0 0
\(491\) −11.2978 −0.509863 −0.254931 0.966959i \(-0.582053\pi\)
−0.254931 + 0.966959i \(0.582053\pi\)
\(492\) 0 0
\(493\) 19.8913 0.895861
\(494\) 0 0
\(495\) 11.3836i 0.511655i
\(496\) 0 0
\(497\) 0.752169 + 2.31494i 0.0337394 + 0.103839i
\(498\) 0 0
\(499\) −16.4072 22.5826i −0.734488 1.01094i −0.998917 0.0465313i \(-0.985183\pi\)
0.264428 0.964405i \(-0.414817\pi\)
\(500\) 0 0
\(501\) 13.3252 0.595325
\(502\) 0 0
\(503\) −32.5023 10.5606i −1.44920 0.470875i −0.524450 0.851441i \(-0.675729\pi\)
−0.924754 + 0.380566i \(0.875729\pi\)
\(504\) 0 0
\(505\) 0.152809 0.210323i 0.00679991 0.00935927i
\(506\) 0 0
\(507\) −0.278902 + 0.0906206i −0.0123865 + 0.00402460i
\(508\) 0 0
\(509\) −16.4263 5.33722i −0.728082 0.236568i −0.0785584 0.996910i \(-0.525032\pi\)
−0.649524 + 0.760341i \(0.725032\pi\)
\(510\) 0 0
\(511\) 0.463933 + 0.638549i 0.0205232 + 0.0282477i
\(512\) 0 0
\(513\) −22.8295 + 16.5866i −1.00795 + 0.732315i
\(514\) 0 0
\(515\) 27.9915 + 20.3370i 1.23345 + 0.896155i
\(516\) 0 0
\(517\) 21.7831 15.8264i 0.958021 0.696043i
\(518\) 0 0
\(519\) 15.8012i 0.693596i
\(520\) 0 0
\(521\) 28.7877 9.35370i 1.26121 0.409793i 0.399287 0.916826i \(-0.369258\pi\)
0.861927 + 0.507033i \(0.169258\pi\)
\(522\) 0 0
\(523\) 6.69725 20.6120i 0.292850 0.901301i −0.691085 0.722774i \(-0.742867\pi\)
0.983935 0.178527i \(-0.0571332\pi\)
\(524\) 0 0
\(525\) −0.115625 + 0.355857i −0.00504629 + 0.0155309i
\(526\) 0 0
\(527\) −17.7529 + 24.4348i −0.773329 + 1.06440i
\(528\) 0 0
\(529\) −6.01816 18.5220i −0.261659 0.805303i
\(530\) 0 0
\(531\) −1.05106 0.763636i −0.0456119 0.0331390i
\(532\) 0 0
\(533\) −18.6203 + 13.1654i −0.806535 + 0.570255i
\(534\) 0 0
\(535\) 11.8582 + 8.61551i 0.512676 + 0.372481i
\(536\) 0 0
\(537\) 4.06887 + 12.5227i 0.175585 + 0.540394i
\(538\) 0 0
\(539\) 1.34578 1.85231i 0.0579668 0.0797845i
\(540\) 0 0
\(541\) −0.737024 + 2.26833i −0.0316871 + 0.0975230i −0.965649 0.259849i \(-0.916327\pi\)
0.933962 + 0.357372i \(0.116327\pi\)
\(542\) 0 0
\(543\) −4.10615 + 12.6374i −0.176212 + 0.542324i
\(544\) 0 0
\(545\) 31.0004 10.0726i 1.32791 0.431464i
\(546\) 0 0
\(547\) 37.0731i 1.58513i −0.609787 0.792565i \(-0.708745\pi\)
0.609787 0.792565i \(-0.291255\pi\)
\(548\) 0 0
\(549\) 11.5302 8.37716i 0.492096 0.357528i
\(550\) 0 0
\(551\) 22.1493 + 16.0924i 0.943593 + 0.685560i
\(552\) 0 0
\(553\) 2.31530 1.68217i 0.0984567 0.0715330i
\(554\) 0 0
\(555\) 2.93737 + 4.04294i 0.124684 + 0.171613i
\(556\) 0 0
\(557\) −39.4647 12.8228i −1.67217 0.543321i −0.688804 0.724948i \(-0.741864\pi\)
−0.983368 + 0.181626i \(0.941864\pi\)
\(558\) 0 0
\(559\) 0.862855 0.280359i 0.0364949 0.0118579i
\(560\) 0 0
\(561\) 5.36909 7.38991i 0.226683 0.312002i
\(562\) 0 0
\(563\) 9.92782 + 3.22574i 0.418408 + 0.135949i 0.510652 0.859788i \(-0.329404\pi\)
−0.0922444 + 0.995736i \(0.529404\pi\)
\(564\) 0 0
\(565\) −42.9952 −1.80882
\(566\) 0 0
\(567\) −1.17078 1.61144i −0.0491682 0.0676742i
\(568\) 0 0
\(569\) 6.24267 + 19.2130i 0.261706 + 0.805450i 0.992434 + 0.122780i \(0.0391811\pi\)
−0.730727 + 0.682669i \(0.760819\pi\)
\(570\) 0 0
\(571\) 18.2960i 0.765662i 0.923818 + 0.382831i \(0.125051\pi\)
−0.923818 + 0.382831i \(0.874949\pi\)
\(572\) 0 0
\(573\) 5.92701 0.247604
\(574\) 0 0
\(575\) −0.757045 −0.0315709
\(576\) 0 0
\(577\) 32.5111i 1.35346i 0.736233 + 0.676728i \(0.236603\pi\)
−0.736233 + 0.676728i \(0.763397\pi\)
\(578\) 0 0
\(579\) −1.80285 5.54859i −0.0749238 0.230592i
\(580\) 0 0
\(581\) 0.0161146 + 0.0221798i 0.000668546 + 0.000920175i
\(582\) 0 0
\(583\) 32.2769 1.33677
\(584\) 0 0
\(585\) 16.8406 + 5.47185i 0.696274 + 0.226233i
\(586\) 0 0
\(587\) −0.320688 + 0.441389i −0.0132362 + 0.0182181i −0.815584 0.578639i \(-0.803584\pi\)
0.802348 + 0.596857i \(0.203584\pi\)
\(588\) 0 0
\(589\) −39.5363 + 12.8461i −1.62906 + 0.529315i
\(590\) 0 0
\(591\) −1.72660 0.561005i −0.0710226 0.0230767i
\(592\) 0 0
\(593\) 18.4403 + 25.3810i 0.757254 + 1.04227i 0.997437 + 0.0715436i \(0.0227925\pi\)
−0.240183 + 0.970728i \(0.577207\pi\)
\(594\) 0 0
\(595\) 8.08524 5.87427i 0.331462 0.240822i
\(596\) 0 0
\(597\) −12.5289 9.10280i −0.512775 0.372553i
\(598\) 0 0
\(599\) 31.3307 22.7631i 1.28014 0.930074i 0.280580 0.959831i \(-0.409473\pi\)
0.999557 + 0.0297565i \(0.00947318\pi\)
\(600\) 0 0
\(601\) 36.7746i 1.50007i 0.661400 + 0.750033i \(0.269962\pi\)
−0.661400 + 0.750033i \(0.730038\pi\)
\(602\) 0 0
\(603\) 5.99946 1.94934i 0.244317 0.0793834i
\(604\) 0 0
\(605\) 4.13588 12.7289i 0.168148 0.517505i
\(606\) 0 0
\(607\) 9.02060 27.7626i 0.366135 1.12685i −0.583132 0.812377i \(-0.698173\pi\)
0.949267 0.314470i \(-0.101827\pi\)
\(608\) 0 0
\(609\) 2.52344 3.47321i 0.102255 0.140742i
\(610\) 0 0
\(611\) 12.9425 + 39.8328i 0.523596 + 1.61146i
\(612\) 0 0
\(613\) −7.07340 5.13912i −0.285692 0.207567i 0.435704 0.900090i \(-0.356499\pi\)
−0.721396 + 0.692523i \(0.756499\pi\)
\(614\) 0 0
\(615\) 13.8102 + 0.177904i 0.556882 + 0.00717379i
\(616\) 0 0
\(617\) 6.41150 + 4.65823i 0.258117 + 0.187533i 0.709317 0.704890i \(-0.249004\pi\)
−0.451199 + 0.892423i \(0.649004\pi\)
\(618\) 0 0
\(619\) 6.74574 + 20.7613i 0.271134 + 0.834465i 0.990216 + 0.139540i \(0.0445625\pi\)
−0.719082 + 0.694925i \(0.755438\pi\)
\(620\) 0 0
\(621\) −5.26235 + 7.24300i −0.211171 + 0.290651i
\(622\) 0 0
\(623\) 2.60088 8.00467i 0.104202 0.320700i
\(624\) 0 0
\(625\) −8.29820 + 25.5392i −0.331928 + 1.02157i
\(626\) 0 0
\(627\) 11.9571 3.88510i 0.477521 0.155156i
\(628\) 0 0
\(629\) 9.96101i 0.397171i
\(630\) 0 0
\(631\) 9.07496 6.59335i 0.361269 0.262477i −0.392312 0.919832i \(-0.628325\pi\)
0.753581 + 0.657355i \(0.228325\pi\)
\(632\) 0 0
\(633\) −2.56507 1.86363i −0.101952 0.0740728i
\(634\) 0 0
\(635\) −11.2970 + 8.20778i −0.448309 + 0.325716i
\(636\) 0 0
\(637\) 2.09337 + 2.88128i 0.0829424 + 0.114160i
\(638\) 0 0
\(639\) −4.95150 1.60884i −0.195878 0.0636448i
\(640\) 0 0
\(641\) −0.0931082 + 0.0302527i −0.00367755 + 0.00119491i −0.310855 0.950457i \(-0.600615\pi\)
0.307178 + 0.951652i \(0.400615\pi\)
\(642\) 0 0
\(643\) 2.25548 3.10440i 0.0889475 0.122426i −0.762224 0.647313i \(-0.775893\pi\)
0.851172 + 0.524887i \(0.175893\pi\)
\(644\) 0 0
\(645\) −0.522582 0.169797i −0.0205767 0.00668576i
\(646\) 0 0
\(647\) −0.487361 −0.0191602 −0.00958008 0.999954i \(-0.503049\pi\)
−0.00958008 + 0.999954i \(0.503049\pi\)
\(648\) 0 0
\(649\) 0.817418 + 1.12508i 0.0320865 + 0.0441632i
\(650\) 0 0
\(651\) 2.01438 + 6.19964i 0.0789500 + 0.242983i
\(652\) 0 0
\(653\) 32.0771i 1.25528i 0.778506 + 0.627638i \(0.215978\pi\)
−0.778506 + 0.627638i \(0.784022\pi\)
\(654\) 0 0
\(655\) 36.2514 1.41646
\(656\) 0 0
\(657\) −1.68824 −0.0658645
\(658\) 0 0
\(659\) 29.8372i 1.16229i 0.813800 + 0.581146i \(0.197395\pi\)
−0.813800 + 0.581146i \(0.802605\pi\)
\(660\) 0 0
\(661\) 12.5364 + 38.5830i 0.487608 + 1.50070i 0.828168 + 0.560480i \(0.189383\pi\)
−0.340560 + 0.940223i \(0.610617\pi\)
\(662\) 0 0
\(663\) 8.35166 + 11.4951i 0.324351 + 0.446432i
\(664\) 0 0
\(665\) 13.7554 0.533412
\(666\) 0 0
\(667\) 8.26098 + 2.68415i 0.319866 + 0.103931i
\(668\) 0 0
\(669\) 13.7643 18.9449i 0.532158 0.732453i
\(670\) 0 0
\(671\) −14.5091 + 4.71431i −0.560119 + 0.181994i
\(672\) 0 0
\(673\) 43.2222 + 14.0437i 1.66609 + 0.541347i 0.982136 0.188175i \(-0.0602571\pi\)
0.683958 + 0.729521i \(0.260257\pi\)
\(674\) 0 0
\(675\) −1.13022 1.55561i −0.0435021 0.0598754i
\(676\) 0 0
\(677\) 4.47672 3.25253i 0.172054 0.125005i −0.498426 0.866933i \(-0.666088\pi\)
0.670480 + 0.741928i \(0.266088\pi\)
\(678\) 0 0
\(679\) −11.1427 8.09567i −0.427619 0.310683i
\(680\) 0 0
\(681\) 16.9549 12.3185i 0.649715 0.472046i
\(682\) 0 0
\(683\) 8.33546i 0.318948i −0.987202 0.159474i \(-0.949020\pi\)
0.987202 0.159474i \(-0.0509798\pi\)
\(684\) 0 0
\(685\) 4.22248 1.37197i 0.161333 0.0524201i
\(686\) 0 0
\(687\) 4.49571 13.8364i 0.171522 0.527891i
\(688\) 0 0
\(689\) −15.5148 + 47.7497i −0.591067 + 1.81912i
\(690\) 0 0
\(691\) −19.4249 + 26.7361i −0.738959 + 1.01709i 0.259719 + 0.965684i \(0.416370\pi\)
−0.998678 + 0.0514058i \(0.983630\pi\)
\(692\) 0 0
\(693\) 1.51334 + 4.65757i 0.0574869 + 0.176926i
\(694\) 0 0
\(695\) 2.52692 + 1.83591i 0.0958514 + 0.0696401i
\(696\) 0 0
\(697\) −22.0617 16.4671i −0.835645 0.623734i
\(698\) 0 0
\(699\) 9.23771 + 6.71159i 0.349402 + 0.253856i
\(700\) 0 0
\(701\) 13.7945 + 42.4552i 0.521013 + 1.60351i 0.772068 + 0.635540i \(0.219222\pi\)
−0.251056 + 0.967973i \(0.580778\pi\)
\(702\) 0 0
\(703\) 8.05862 11.0917i 0.303937 0.418333i
\(704\) 0 0
\(705\) 7.83852 24.1245i 0.295216 0.908581i
\(706\) 0 0
\(707\) −0.0345610 + 0.106368i −0.00129980 + 0.00400037i
\(708\) 0 0
\(709\) 11.7843 3.82894i 0.442567 0.143799i −0.0792525 0.996855i \(-0.525253\pi\)
0.521820 + 0.853056i \(0.325253\pi\)
\(710\) 0 0
\(711\) 6.12136i 0.229569i
\(712\) 0 0
\(713\) −10.6701 + 7.75230i −0.399599 + 0.290326i
\(714\) 0 0
\(715\) −15.3344 11.1411i −0.573475 0.416654i
\(716\) 0 0
\(717\) 2.65780 1.93101i 0.0992575 0.0721148i
\(718\) 0 0
\(719\) −2.18707 3.01025i −0.0815640 0.112263i 0.766285 0.642500i \(-0.222103\pi\)
−0.847849 + 0.530237i \(0.822103\pi\)
\(720\) 0 0
\(721\) −14.1562 4.59964i −0.527206 0.171300i
\(722\) 0 0
\(723\) −14.1598 + 4.60079i −0.526608 + 0.171105i
\(724\) 0 0
\(725\) −1.09654 + 1.50926i −0.0407246 + 0.0560527i
\(726\) 0 0
\(727\) −23.1431 7.51967i −0.858332 0.278889i −0.153400 0.988164i \(-0.549022\pi\)
−0.704932 + 0.709275i \(0.749022\pi\)
\(728\) 0 0
\(729\) −9.01443 −0.333868
\(730\) 0 0
\(731\) 0.643771 + 0.886074i 0.0238107 + 0.0327726i
\(732\) 0 0
\(733\) 4.18628 + 12.8841i 0.154624 + 0.475883i 0.998123 0.0612478i \(-0.0195080\pi\)
−0.843499 + 0.537131i \(0.819508\pi\)
\(734\) 0 0
\(735\) 2.15697i 0.0795611i
\(736\) 0 0
\(737\) −6.75248 −0.248731
\(738\) 0 0
\(739\) −21.6946 −0.798049 −0.399025 0.916940i \(-0.630651\pi\)
−0.399025 + 0.916940i \(0.630651\pi\)
\(740\) 0 0
\(741\) 19.5566i 0.718428i
\(742\) 0 0
\(743\) −6.73798 20.7374i −0.247192 0.760780i −0.995268 0.0971666i \(-0.969022\pi\)
0.748076 0.663613i \(-0.230978\pi\)
\(744\) 0 0
\(745\) 4.02610 + 5.54146i 0.147505 + 0.203023i
\(746\) 0 0
\(747\) −0.0586406 −0.00214555
\(748\) 0 0
\(749\) −5.99711 1.94858i −0.219130 0.0711995i
\(750\) 0 0
\(751\) 21.9400 30.1978i 0.800602 1.10193i −0.192104 0.981375i \(-0.561531\pi\)
0.992706 0.120560i \(-0.0384690\pi\)
\(752\) 0 0
\(753\) −6.94042 + 2.25508i −0.252923 + 0.0821796i
\(754\) 0 0
\(755\) −14.6771 4.76887i −0.534153 0.173557i
\(756\) 0 0
\(757\) −18.7888 25.8606i −0.682891 0.939919i 0.317073 0.948401i \(-0.397300\pi\)
−0.999964 + 0.00848196i \(0.997300\pi\)
\(758\) 0 0
\(759\) 3.22701 2.34456i 0.117133 0.0851022i
\(760\) 0 0
\(761\) −0.424665 0.308537i −0.0153941 0.0111845i 0.580062 0.814573i \(-0.303028\pi\)
−0.595456 + 0.803388i \(0.703028\pi\)
\(762\) 0 0
\(763\) −11.3447 + 8.24238i −0.410704 + 0.298394i
\(764\) 0 0
\(765\) 21.3763i 0.772862i
\(766\) 0 0
\(767\) −2.05733 + 0.668467i −0.0742859 + 0.0241370i
\(768\) 0 0
\(769\) 9.45426 29.0972i 0.340929 1.04927i −0.622798 0.782383i \(-0.714004\pi\)
0.963727 0.266889i \(-0.0859959\pi\)
\(770\) 0 0
\(771\) 3.49426 10.7542i 0.125843 0.387304i
\(772\) 0 0
\(773\) 4.19030 5.76746i 0.150715 0.207441i −0.726983 0.686655i \(-0.759078\pi\)
0.877698 + 0.479214i \(0.159078\pi\)
\(774\) 0 0
\(775\) −0.875340 2.69402i −0.0314431 0.0967720i
\(776\) 0 0
\(777\) −1.73928 1.26366i −0.0623964 0.0453337i
\(778\) 0 0
\(779\) −11.2439 36.1846i −0.402854 1.29645i
\(780\) 0 0
\(781\) 4.50865 + 3.27572i 0.161332 + 0.117215i
\(782\) 0 0
\(783\) 6.81756 + 20.9823i 0.243640 + 0.749846i
\(784\) 0 0
\(785\) 23.8912 32.8835i 0.852715 1.17366i
\(786\) 0 0
\(787\) 0.633760 1.95051i 0.0225911 0.0695283i −0.939125 0.343575i \(-0.888362\pi\)
0.961716 + 0.274046i \(0.0883622\pi\)
\(788\) 0 0
\(789\) 5.17685 15.9327i 0.184301 0.567219i
\(790\) 0 0
\(791\) 17.5914 5.71578i 0.625477 0.203230i
\(792\) 0 0
\(793\) 23.7306i 0.842697i
\(794\) 0 0
\(795\) 24.6002 17.8731i 0.872479 0.633893i
\(796\) 0 0
\(797\) −28.7439 20.8836i −1.01816