Properties

Label 1148.2.ba.a.113.1
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 113.1
Character \(\chi\) \(=\) 1148.113
Dual form 1148.2.ba.a.701.20

$q$-expansion

\(f(q)\) \(=\) \(q-3.08866i q^{3} +(-1.11364 - 3.42744i) q^{5} +(-0.587785 - 0.809017i) q^{7} -6.53981 q^{9} +O(q^{10})\) \(q-3.08866i q^{3} +(-1.11364 - 3.42744i) q^{5} +(-0.587785 - 0.809017i) q^{7} -6.53981 q^{9} +(5.51230 + 1.79105i) q^{11} +(-3.99429 + 5.49767i) q^{13} +(-10.5862 + 3.43966i) q^{15} +(-5.22070 - 1.69631i) q^{17} +(-1.80765 - 2.48802i) q^{19} +(-2.49878 + 1.81547i) q^{21} +(-1.09184 - 0.793269i) q^{23} +(-6.46203 + 4.69494i) q^{25} +10.9333i q^{27} +(9.05917 - 2.94350i) q^{29} +(1.41863 - 4.36610i) q^{31} +(5.53195 - 17.0256i) q^{33} +(-2.11827 + 2.91555i) q^{35} +(-1.00424 - 3.09074i) q^{37} +(16.9804 + 12.3370i) q^{39} +(-6.06447 + 2.05480i) q^{41} +(-0.450967 - 0.327647i) q^{43} +(7.28300 + 22.4148i) q^{45} +(-0.526001 + 0.723978i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-5.23932 + 16.1250i) q^{51} +(5.67195 - 1.84293i) q^{53} -20.8876i q^{55} +(-7.68464 + 5.58322i) q^{57} +(0.983245 + 0.714369i) q^{59} +(-1.69686 + 1.23284i) q^{61} +(3.84400 + 5.29082i) q^{63} +(23.2911 + 7.56774i) q^{65} +(-14.1189 + 4.58751i) q^{67} +(-2.45014 + 3.37232i) q^{69} +(0.947422 + 0.307836i) q^{71} +6.86712 q^{73} +(14.5011 + 19.9590i) q^{75} +(-1.79105 - 5.51230i) q^{77} -7.78933i q^{79} +14.1497 q^{81} +0.588419 q^{83} +19.7827i q^{85} +(-9.09148 - 27.9807i) q^{87} +(-7.21580 - 9.93170i) q^{89} +6.79549 q^{91} +(-13.4854 - 4.38167i) q^{93} +(-6.51445 + 8.96638i) q^{95} +(13.0390 - 4.23662i) q^{97} +(-36.0494 - 11.7132i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

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
\(3\) 3.08866i 1.78324i −0.452787 0.891619i \(-0.649570\pi\)
0.452787 0.891619i \(-0.350430\pi\)
\(4\) 0 0
\(5\) −1.11364 3.42744i −0.498036 1.53280i −0.812172 0.583418i \(-0.801715\pi\)
0.314136 0.949378i \(-0.398285\pi\)
\(6\) 0 0
\(7\) −0.587785 0.809017i −0.222162 0.305780i
\(8\) 0 0
\(9\) −6.53981 −2.17994
\(10\) 0 0
\(11\) 5.51230 + 1.79105i 1.66202 + 0.540023i 0.981294 0.192515i \(-0.0616642\pi\)
0.680726 + 0.732538i \(0.261664\pi\)
\(12\) 0 0
\(13\) −3.99429 + 5.49767i −1.10782 + 1.52478i −0.283222 + 0.959054i \(0.591403\pi\)
−0.824594 + 0.565725i \(0.808597\pi\)
\(14\) 0 0
\(15\) −10.5862 + 3.43966i −2.73334 + 0.888116i
\(16\) 0 0
\(17\) −5.22070 1.69631i −1.26621 0.411415i −0.402504 0.915418i \(-0.631860\pi\)
−0.863702 + 0.504003i \(0.831860\pi\)
\(18\) 0 0
\(19\) −1.80765 2.48802i −0.414704 0.570791i 0.549654 0.835392i \(-0.314760\pi\)
−0.964358 + 0.264601i \(0.914760\pi\)
\(20\) 0 0
\(21\) −2.49878 + 1.81547i −0.545278 + 0.396168i
\(22\) 0 0
\(23\) −1.09184 0.793269i −0.227665 0.165408i 0.468105 0.883673i \(-0.344937\pi\)
−0.695770 + 0.718265i \(0.744937\pi\)
\(24\) 0 0
\(25\) −6.46203 + 4.69494i −1.29241 + 0.938988i
\(26\) 0 0
\(27\) 10.9333i 2.10411i
\(28\) 0 0
\(29\) 9.05917 2.94350i 1.68225 0.546595i 0.696901 0.717168i \(-0.254562\pi\)
0.985345 + 0.170573i \(0.0545618\pi\)
\(30\) 0 0
\(31\) 1.41863 4.36610i 0.254794 0.784176i −0.739076 0.673622i \(-0.764738\pi\)
0.993870 0.110554i \(-0.0352624\pi\)
\(32\) 0 0
\(33\) 5.53195 17.0256i 0.962990 2.96378i
\(34\) 0 0
\(35\) −2.11827 + 2.91555i −0.358053 + 0.492818i
\(36\) 0 0
\(37\) −1.00424 3.09074i −0.165096 0.508115i 0.833947 0.551845i \(-0.186076\pi\)
−0.999043 + 0.0437299i \(0.986076\pi\)
\(38\) 0 0
\(39\) 16.9804 + 12.3370i 2.71904 + 1.97550i
\(40\) 0 0
\(41\) −6.06447 + 2.05480i −0.947111 + 0.320906i
\(42\) 0 0
\(43\) −0.450967 0.327647i −0.0687718 0.0499657i 0.552868 0.833269i \(-0.313533\pi\)
−0.621640 + 0.783303i \(0.713533\pi\)
\(44\) 0 0
\(45\) 7.28300 + 22.4148i 1.08569 + 3.34140i
\(46\) 0 0
\(47\) −0.526001 + 0.723978i −0.0767251 + 0.105603i −0.845655 0.533730i \(-0.820790\pi\)
0.768930 + 0.639334i \(0.220790\pi\)
\(48\) 0 0
\(49\) −0.309017 + 0.951057i −0.0441453 + 0.135865i
\(50\) 0 0
\(51\) −5.23932 + 16.1250i −0.733651 + 2.25795i
\(52\) 0 0
\(53\) 5.67195 1.84293i 0.779103 0.253146i 0.107646 0.994189i \(-0.465669\pi\)
0.671457 + 0.741043i \(0.265669\pi\)
\(54\) 0 0
\(55\) 20.8876i 2.81649i
\(56\) 0 0
\(57\) −7.68464 + 5.58322i −1.01786 + 0.739516i
\(58\) 0 0
\(59\) 0.983245 + 0.714369i 0.128008 + 0.0930029i 0.649947 0.759980i \(-0.274791\pi\)
−0.521939 + 0.852983i \(0.674791\pi\)
\(60\) 0 0
\(61\) −1.69686 + 1.23284i −0.217261 + 0.157849i −0.691093 0.722766i \(-0.742870\pi\)
0.473832 + 0.880615i \(0.342870\pi\)
\(62\) 0 0
\(63\) 3.84400 + 5.29082i 0.484299 + 0.666580i
\(64\) 0 0
\(65\) 23.2911 + 7.56774i 2.88891 + 0.938663i
\(66\) 0 0
\(67\) −14.1189 + 4.58751i −1.72490 + 0.560454i −0.992697 0.120633i \(-0.961508\pi\)
−0.732203 + 0.681087i \(0.761508\pi\)
\(68\) 0 0
\(69\) −2.45014 + 3.37232i −0.294962 + 0.405980i
\(70\) 0 0
\(71\) 0.947422 + 0.307836i 0.112438 + 0.0365334i 0.364696 0.931127i \(-0.381173\pi\)
−0.252257 + 0.967660i \(0.581173\pi\)
\(72\) 0 0
\(73\) 6.86712 0.803736 0.401868 0.915698i \(-0.368361\pi\)
0.401868 + 0.915698i \(0.368361\pi\)
\(74\) 0 0
\(75\) 14.5011 + 19.9590i 1.67444 + 2.30467i
\(76\) 0 0
\(77\) −1.79105 5.51230i −0.204110 0.628185i
\(78\) 0 0
\(79\) 7.78933i 0.876368i −0.898885 0.438184i \(-0.855622\pi\)
0.898885 0.438184i \(-0.144378\pi\)
\(80\) 0 0
\(81\) 14.1497 1.57219
\(82\) 0 0
\(83\) 0.588419 0.0645874 0.0322937 0.999478i \(-0.489719\pi\)
0.0322937 + 0.999478i \(0.489719\pi\)
\(84\) 0 0
\(85\) 19.7827i 2.14573i
\(86\) 0 0
\(87\) −9.09148 27.9807i −0.974708 2.99984i
\(88\) 0 0
\(89\) −7.21580 9.93170i −0.764874 1.05276i −0.996793 0.0800232i \(-0.974501\pi\)
0.231919 0.972735i \(-0.425499\pi\)
\(90\) 0 0
\(91\) 6.79549 0.712361
\(92\) 0 0
\(93\) −13.4854 4.38167i −1.39837 0.454358i
\(94\) 0 0
\(95\) −6.51445 + 8.96638i −0.668369 + 0.919931i
\(96\) 0 0
\(97\) 13.0390 4.23662i 1.32391 0.430164i 0.440073 0.897962i \(-0.354953\pi\)
0.883835 + 0.467798i \(0.154953\pi\)
\(98\) 0 0
\(99\) −36.0494 11.7132i −3.62310 1.17722i
\(100\) 0 0
\(101\) −7.80734 10.7459i −0.776859 1.06926i −0.995621 0.0934771i \(-0.970202\pi\)
0.218762 0.975778i \(-0.429798\pi\)
\(102\) 0 0
\(103\) −3.74355 + 2.71985i −0.368863 + 0.267994i −0.756739 0.653717i \(-0.773209\pi\)
0.387877 + 0.921711i \(0.373209\pi\)
\(104\) 0 0
\(105\) 9.00514 + 6.54262i 0.878812 + 0.638494i
\(106\) 0 0
\(107\) −5.40007 + 3.92338i −0.522044 + 0.379287i −0.817373 0.576108i \(-0.804571\pi\)
0.295329 + 0.955396i \(0.404571\pi\)
\(108\) 0 0
\(109\) 14.4780i 1.38675i −0.720579 0.693373i \(-0.756124\pi\)
0.720579 0.693373i \(-0.243876\pi\)
\(110\) 0 0
\(111\) −9.54624 + 3.10176i −0.906089 + 0.294406i
\(112\) 0 0
\(113\) −1.81046 + 5.57203i −0.170314 + 0.524173i −0.999389 0.0349655i \(-0.988868\pi\)
0.829074 + 0.559138i \(0.188868\pi\)
\(114\) 0 0
\(115\) −1.50296 + 4.62563i −0.140152 + 0.431343i
\(116\) 0 0
\(117\) 26.1219 35.9537i 2.41497 3.32392i
\(118\) 0 0
\(119\) 1.69631 + 5.22070i 0.155500 + 0.478581i
\(120\) 0 0
\(121\) 18.2784 + 13.2800i 1.66167 + 1.20727i
\(122\) 0 0
\(123\) 6.34657 + 18.7311i 0.572251 + 1.68892i
\(124\) 0 0
\(125\) 8.71025 + 6.32836i 0.779068 + 0.566026i
\(126\) 0 0
\(127\) −1.64879 5.07444i −0.146306 0.450284i 0.850871 0.525375i \(-0.176075\pi\)
−0.997177 + 0.0750916i \(0.976075\pi\)
\(128\) 0 0
\(129\) −1.01199 + 1.39288i −0.0891007 + 0.122637i
\(130\) 0 0
\(131\) −3.23259 + 9.94890i −0.282433 + 0.869240i 0.704723 + 0.709482i \(0.251071\pi\)
−0.987156 + 0.159757i \(0.948929\pi\)
\(132\) 0 0
\(133\) −0.950339 + 2.92484i −0.0824049 + 0.253616i
\(134\) 0 0
\(135\) 37.4731 12.1757i 3.22517 1.04792i
\(136\) 0 0
\(137\) 10.7209i 0.915945i 0.888966 + 0.457972i \(0.151424\pi\)
−0.888966 + 0.457972i \(0.848576\pi\)
\(138\) 0 0
\(139\) −0.194030 + 0.140971i −0.0164574 + 0.0119570i −0.595984 0.802997i \(-0.703238\pi\)
0.579526 + 0.814954i \(0.303238\pi\)
\(140\) 0 0
\(141\) 2.23612 + 1.62464i 0.188315 + 0.136819i
\(142\) 0 0
\(143\) −31.8643 + 23.1508i −2.66463 + 1.93597i
\(144\) 0 0
\(145\) −20.1773 27.7717i −1.67564 2.30632i
\(146\) 0 0
\(147\) 2.93749 + 0.954448i 0.242280 + 0.0787215i
\(148\) 0 0
\(149\) 8.51263 2.76592i 0.697382 0.226593i 0.0611923 0.998126i \(-0.480510\pi\)
0.636189 + 0.771533i \(0.280510\pi\)
\(150\) 0 0
\(151\) −6.28301 + 8.64782i −0.511304 + 0.703750i −0.984139 0.177402i \(-0.943231\pi\)
0.472834 + 0.881151i \(0.343231\pi\)
\(152\) 0 0
\(153\) 34.1424 + 11.0935i 2.76025 + 0.896859i
\(154\) 0 0
\(155\) −16.5444 −1.32888
\(156\) 0 0
\(157\) −5.66886 7.80252i −0.452424 0.622709i 0.520492 0.853867i \(-0.325749\pi\)
−0.972916 + 0.231158i \(0.925749\pi\)
\(158\) 0 0
\(159\) −5.69218 17.5187i −0.451419 1.38933i
\(160\) 0 0
\(161\) 1.34959i 0.106363i
\(162\) 0 0
\(163\) −6.26336 −0.490584 −0.245292 0.969449i \(-0.578884\pi\)
−0.245292 + 0.969449i \(0.578884\pi\)
\(164\) 0 0
\(165\) −64.5148 −5.02247
\(166\) 0 0
\(167\) 0.0521509i 0.00403556i −0.999998 0.00201778i \(-0.999358\pi\)
0.999998 0.00201778i \(-0.000642280\pi\)
\(168\) 0 0
\(169\) −10.2528 31.5548i −0.788676 2.42729i
\(170\) 0 0
\(171\) 11.8217 + 16.2712i 0.904028 + 1.24429i
\(172\) 0 0
\(173\) 5.63737 0.428601 0.214301 0.976768i \(-0.431253\pi\)
0.214301 + 0.976768i \(0.431253\pi\)
\(174\) 0 0
\(175\) 7.59658 + 2.46828i 0.574247 + 0.186584i
\(176\) 0 0
\(177\) 2.20644 3.03691i 0.165846 0.228268i
\(178\) 0 0
\(179\) −16.1755 + 5.25574i −1.20901 + 0.392832i −0.843069 0.537805i \(-0.819254\pi\)
−0.365944 + 0.930637i \(0.619254\pi\)
\(180\) 0 0
\(181\) 8.83006 + 2.86906i 0.656333 + 0.213256i 0.618205 0.786017i \(-0.287860\pi\)
0.0381286 + 0.999273i \(0.487860\pi\)
\(182\) 0 0
\(183\) 3.80782 + 5.24102i 0.281482 + 0.387427i
\(184\) 0 0
\(185\) −9.47495 + 6.88396i −0.696612 + 0.506118i
\(186\) 0 0
\(187\) −25.7399 18.7011i −1.88229 1.36756i
\(188\) 0 0
\(189\) 8.84519 6.42641i 0.643393 0.467453i
\(190\) 0 0
\(191\) 2.62787i 0.190146i 0.995470 + 0.0950730i \(0.0303084\pi\)
−0.995470 + 0.0950730i \(0.969692\pi\)
\(192\) 0 0
\(193\) −19.1014 + 6.20643i −1.37495 + 0.446749i −0.901006 0.433806i \(-0.857170\pi\)
−0.473945 + 0.880555i \(0.657170\pi\)
\(194\) 0 0
\(195\) 23.3742 71.9383i 1.67386 5.15161i
\(196\) 0 0
\(197\) −1.44774 + 4.45569i −0.103147 + 0.317455i −0.989291 0.145955i \(-0.953374\pi\)
0.886144 + 0.463410i \(0.153374\pi\)
\(198\) 0 0
\(199\) 7.61905 10.4867i 0.540100 0.743384i −0.448528 0.893769i \(-0.648051\pi\)
0.988627 + 0.150385i \(0.0480514\pi\)
\(200\) 0 0
\(201\) 14.1693 + 43.6085i 0.999423 + 3.07591i
\(202\) 0 0
\(203\) −7.70619 5.59888i −0.540869 0.392964i
\(204\) 0 0
\(205\) 13.7963 + 18.4973i 0.963578 + 1.29191i
\(206\) 0 0
\(207\) 7.14043 + 5.18783i 0.496294 + 0.360579i
\(208\) 0 0
\(209\) −5.50814 16.9523i −0.381006 1.17262i
\(210\) 0 0
\(211\) 9.17972 12.6348i 0.631958 0.869816i −0.366197 0.930538i \(-0.619340\pi\)
0.998155 + 0.0607217i \(0.0193402\pi\)
\(212\) 0 0
\(213\) 0.950800 2.92626i 0.0651477 0.200504i
\(214\) 0 0
\(215\) −0.620773 + 1.91054i −0.0423363 + 0.130298i
\(216\) 0 0
\(217\) −4.36610 + 1.41863i −0.296390 + 0.0963031i
\(218\) 0 0
\(219\) 21.2102i 1.43325i
\(220\) 0 0
\(221\) 30.1787 21.9261i 2.03004 1.47491i
\(222\) 0 0
\(223\) −5.61478 4.07938i −0.375994 0.273175i 0.383698 0.923459i \(-0.374650\pi\)
−0.759692 + 0.650283i \(0.774650\pi\)
\(224\) 0 0
\(225\) 42.2605 30.7040i 2.81736 2.04694i
\(226\) 0 0
\(227\) −6.24608 8.59699i −0.414567 0.570602i 0.549758 0.835324i \(-0.314720\pi\)
−0.964325 + 0.264722i \(0.914720\pi\)
\(228\) 0 0
\(229\) −5.60206 1.82022i −0.370195 0.120284i 0.118011 0.993012i \(-0.462348\pi\)
−0.488205 + 0.872729i \(0.662348\pi\)
\(230\) 0 0
\(231\) −17.0256 + 5.53195i −1.12020 + 0.363976i
\(232\) 0 0
\(233\) 16.1101 22.1737i 1.05541 1.45265i 0.171385 0.985204i \(-0.445176\pi\)
0.884024 0.467441i \(-0.154824\pi\)
\(234\) 0 0
\(235\) 3.06717 + 0.996583i 0.200080 + 0.0650099i
\(236\) 0 0
\(237\) −24.0586 −1.56277
\(238\) 0 0
\(239\) 7.49791 + 10.3200i 0.484999 + 0.667544i 0.979456 0.201658i \(-0.0646329\pi\)
−0.494457 + 0.869202i \(0.664633\pi\)
\(240\) 0 0
\(241\) 3.29045 + 10.1270i 0.211957 + 0.652336i 0.999356 + 0.0358920i \(0.0114272\pi\)
−0.787399 + 0.616444i \(0.788573\pi\)
\(242\) 0 0
\(243\) 10.9037i 0.699475i
\(244\) 0 0
\(245\) 3.60382 0.230240
\(246\) 0 0
\(247\) 20.8986 1.32975
\(248\) 0 0
\(249\) 1.81743i 0.115175i
\(250\) 0 0
\(251\) 5.03354 + 15.4916i 0.317714 + 0.977823i 0.974623 + 0.223853i \(0.0718636\pi\)
−0.656909 + 0.753970i \(0.728136\pi\)
\(252\) 0 0
\(253\) −4.59777 6.32828i −0.289059 0.397856i
\(254\) 0 0
\(255\) 61.1020 3.82635
\(256\) 0 0
\(257\) 5.42559 + 1.76288i 0.338439 + 0.109965i 0.473306 0.880898i \(-0.343061\pi\)
−0.134867 + 0.990864i \(0.543061\pi\)
\(258\) 0 0
\(259\) −1.91018 + 2.62914i −0.118693 + 0.163367i
\(260\) 0 0
\(261\) −59.2453 + 19.2499i −3.66719 + 1.19154i
\(262\) 0 0
\(263\) −6.07699 1.97453i −0.374723 0.121755i 0.115600 0.993296i \(-0.463121\pi\)
−0.490323 + 0.871541i \(0.663121\pi\)
\(264\) 0 0
\(265\) −12.6330 17.3879i −0.776042 1.06813i
\(266\) 0 0
\(267\) −30.6756 + 22.2871i −1.87732 + 1.36395i
\(268\) 0 0
\(269\) −6.12042 4.44675i −0.373169 0.271123i 0.385355 0.922768i \(-0.374079\pi\)
−0.758524 + 0.651645i \(0.774079\pi\)
\(270\) 0 0
\(271\) 25.7073 18.6774i 1.56161 1.13457i 0.626929 0.779077i \(-0.284312\pi\)
0.934678 0.355497i \(-0.115688\pi\)
\(272\) 0 0
\(273\) 20.9890i 1.27031i
\(274\) 0 0
\(275\) −44.0296 + 14.3061i −2.65508 + 0.862688i
\(276\) 0 0
\(277\) 1.57383 4.84374i 0.0945620 0.291032i −0.892577 0.450894i \(-0.851105\pi\)
0.987139 + 0.159862i \(0.0511051\pi\)
\(278\) 0 0
\(279\) −9.27759 + 28.5535i −0.555435 + 1.70945i
\(280\) 0 0
\(281\) −6.02831 + 8.29726i −0.359619 + 0.494973i −0.950043 0.312120i \(-0.898961\pi\)
0.590424 + 0.807094i \(0.298961\pi\)
\(282\) 0 0
\(283\) 4.86290 + 14.9665i 0.289069 + 0.889664i 0.985149 + 0.171700i \(0.0549259\pi\)
−0.696080 + 0.717964i \(0.745074\pi\)
\(284\) 0 0
\(285\) 27.6941 + 20.1209i 1.64046 + 1.19186i
\(286\) 0 0
\(287\) 5.22697 + 3.69848i 0.308539 + 0.218314i
\(288\) 0 0
\(289\) 10.6250 + 7.71948i 0.624997 + 0.454087i
\(290\) 0 0
\(291\) −13.0855 40.2730i −0.767085 2.36084i
\(292\) 0 0
\(293\) 6.17093 8.49355i 0.360509 0.496199i −0.589781 0.807563i \(-0.700786\pi\)
0.950291 + 0.311365i \(0.100786\pi\)
\(294\) 0 0
\(295\) 1.35347 4.16556i 0.0788022 0.242528i
\(296\) 0 0
\(297\) −19.5821 + 60.2674i −1.13627 + 3.49707i
\(298\) 0 0
\(299\) 8.72226 2.83403i 0.504421 0.163896i
\(300\) 0 0
\(301\) 0.557426i 0.0321295i
\(302\) 0 0
\(303\) −33.1904 + 24.1142i −1.90674 + 1.38533i
\(304\) 0 0
\(305\) 6.11518 + 4.44294i 0.350154 + 0.254402i
\(306\) 0 0
\(307\) 11.0682 8.04153i 0.631697 0.458955i −0.225291 0.974292i \(-0.572333\pi\)
0.856988 + 0.515337i \(0.172333\pi\)
\(308\) 0 0
\(309\) 8.40067 + 11.5625i 0.477898 + 0.657770i
\(310\) 0 0
\(311\) 13.0821 + 4.25063i 0.741818 + 0.241031i 0.655457 0.755233i \(-0.272476\pi\)
0.0863610 + 0.996264i \(0.472476\pi\)
\(312\) 0 0
\(313\) −18.8526 + 6.12558i −1.06561 + 0.346238i −0.788777 0.614679i \(-0.789285\pi\)
−0.276835 + 0.960918i \(0.589285\pi\)
\(314\) 0 0
\(315\) 13.8531 19.0671i 0.780533 1.07431i
\(316\) 0 0
\(317\) −17.4330 5.66433i −0.979136 0.318140i −0.224637 0.974442i \(-0.572120\pi\)
−0.754498 + 0.656302i \(0.772120\pi\)
\(318\) 0 0
\(319\) 55.2088 3.09110
\(320\) 0 0
\(321\) 12.1180 + 16.6790i 0.676359 + 0.930929i
\(322\) 0 0
\(323\) 5.21676 + 16.0555i 0.290268 + 0.893354i
\(324\) 0 0
\(325\) 54.2791i 3.01086i
\(326\) 0 0
\(327\) −44.7177 −2.47290
\(328\) 0 0
\(329\) 0.894886 0.0493367
\(330\) 0 0
\(331\) 10.7100i 0.588673i −0.955702 0.294336i \(-0.904901\pi\)
0.955702 0.294336i \(-0.0950986\pi\)
\(332\) 0 0
\(333\) 6.56756 + 20.2129i 0.359900 + 1.10766i
\(334\) 0 0
\(335\) 31.4468 + 43.2828i 1.71812 + 2.36479i
\(336\) 0 0
\(337\) 3.51109 0.191261 0.0956306 0.995417i \(-0.469513\pi\)
0.0956306 + 0.995417i \(0.469513\pi\)
\(338\) 0 0
\(339\) 17.2101 + 5.59190i 0.934724 + 0.303710i
\(340\) 0 0
\(341\) 15.6399 21.5264i 0.846946 1.16572i
\(342\) 0 0
\(343\) 0.951057 0.309017i 0.0513522 0.0166853i
\(344\) 0 0
\(345\) 14.2870 + 4.64213i 0.769186 + 0.249924i
\(346\) 0 0
\(347\) −14.7538 20.3069i −0.792027 1.09013i −0.993853 0.110710i \(-0.964688\pi\)
0.201826 0.979421i \(-0.435312\pi\)
\(348\) 0 0
\(349\) 5.63687 4.09543i 0.301735 0.219223i −0.426607 0.904437i \(-0.640291\pi\)
0.728342 + 0.685214i \(0.240291\pi\)
\(350\) 0 0
\(351\) −60.1074 43.6706i −3.20830 2.33096i
\(352\) 0 0
\(353\) −19.4333 + 14.1191i −1.03433 + 0.751484i −0.969171 0.246391i \(-0.920755\pi\)
−0.0651587 + 0.997875i \(0.520755\pi\)
\(354\) 0 0
\(355\) 3.59005i 0.190540i
\(356\) 0 0
\(357\) 16.1250 5.23932i 0.853423 0.277294i
\(358\) 0 0
\(359\) 8.99676 27.6892i 0.474831 1.46138i −0.371355 0.928491i \(-0.621107\pi\)
0.846186 0.532888i \(-0.178893\pi\)
\(360\) 0 0
\(361\) 2.94869 9.07512i 0.155194 0.477638i
\(362\) 0 0
\(363\) 41.0174 56.4556i 2.15286 2.96315i
\(364\) 0 0
\(365\) −7.64751 23.5366i −0.400289 1.23196i
\(366\) 0 0
\(367\) −25.8398 18.7737i −1.34882 0.979978i −0.999069 0.0431371i \(-0.986265\pi\)
−0.349755 0.936841i \(-0.613735\pi\)
\(368\) 0 0
\(369\) 39.6605 13.4380i 2.06464 0.699554i
\(370\) 0 0
\(371\) −4.82485 3.50546i −0.250494 0.181994i
\(372\) 0 0
\(373\) −10.2834 31.6489i −0.532452 1.63872i −0.749090 0.662468i \(-0.769509\pi\)
0.216638 0.976252i \(-0.430491\pi\)
\(374\) 0 0
\(375\) 19.5462 26.9030i 1.00936 1.38926i
\(376\) 0 0
\(377\) −20.0026 + 61.5615i −1.03018 + 3.17058i
\(378\) 0 0
\(379\) 1.48106 4.55822i 0.0760767 0.234140i −0.905785 0.423737i \(-0.860718\pi\)
0.981862 + 0.189597i \(0.0607181\pi\)
\(380\) 0 0
\(381\) −15.6732 + 5.09253i −0.802963 + 0.260898i
\(382\) 0 0
\(383\) 18.9334i 0.967453i 0.875219 + 0.483727i \(0.160717\pi\)
−0.875219 + 0.483727i \(0.839283\pi\)
\(384\) 0 0
\(385\) −16.8985 + 12.2774i −0.861225 + 0.625717i
\(386\) 0 0
\(387\) 2.94924 + 2.14275i 0.149918 + 0.108922i
\(388\) 0 0
\(389\) −9.70335 + 7.04990i −0.491979 + 0.357444i −0.805945 0.591990i \(-0.798342\pi\)
0.313966 + 0.949434i \(0.398342\pi\)
\(390\) 0 0
\(391\) 4.35455 + 5.99352i 0.220219 + 0.303105i
\(392\) 0 0
\(393\) 30.7288 + 9.98438i 1.55006 + 0.503645i
\(394\) 0 0
\(395\) −26.6974 + 8.67452i −1.34329 + 0.436463i
\(396\) 0 0
\(397\) −9.57860 + 13.1838i −0.480736 + 0.661677i −0.978646 0.205552i \(-0.934101\pi\)
0.497910 + 0.867229i \(0.334101\pi\)
\(398\) 0 0
\(399\) 9.03384 + 2.93527i 0.452258 + 0.146947i
\(400\) 0 0
\(401\) 18.8536 0.941506 0.470753 0.882265i \(-0.343982\pi\)
0.470753 + 0.882265i \(0.343982\pi\)
\(402\) 0 0
\(403\) 18.3370 + 25.2387i 0.913429 + 1.25723i
\(404\) 0 0
\(405\) −15.7577 48.4971i −0.783005 2.40984i
\(406\) 0 0
\(407\) 18.8357i 0.933653i
\(408\) 0 0
\(409\) 38.0194 1.87994 0.939969 0.341261i \(-0.110854\pi\)
0.939969 + 0.341261i \(0.110854\pi\)
\(410\) 0 0
\(411\) 33.1131 1.63335
\(412\) 0 0
\(413\) 1.21536i 0.0598038i
\(414\) 0 0
\(415\) −0.655288 2.01677i −0.0321668 0.0989993i
\(416\) 0 0
\(417\) 0.435411 + 0.599292i 0.0213222 + 0.0293474i
\(418\) 0 0
\(419\) −30.1308 −1.47199 −0.735994 0.676988i \(-0.763285\pi\)
−0.735994 + 0.676988i \(0.763285\pi\)
\(420\) 0 0
\(421\) 22.7417 + 7.38921i 1.10836 + 0.360128i 0.805314 0.592848i \(-0.201996\pi\)
0.303046 + 0.952976i \(0.401996\pi\)
\(422\) 0 0
\(423\) 3.43995 4.73468i 0.167256 0.230208i
\(424\) 0 0
\(425\) 41.7004 13.5493i 2.02277 0.657237i
\(426\) 0 0
\(427\) 1.99478 + 0.648143i 0.0965341 + 0.0313658i
\(428\) 0 0
\(429\) 71.5049 + 98.4181i 3.45229 + 4.75167i
\(430\) 0 0
\(431\) 21.0717 15.3095i 1.01499 0.737434i 0.0497403 0.998762i \(-0.484161\pi\)
0.965250 + 0.261329i \(0.0841606\pi\)
\(432\) 0 0
\(433\) 12.9391 + 9.40080i 0.621813 + 0.451774i 0.853554 0.521004i \(-0.174442\pi\)
−0.231741 + 0.972777i \(0.574442\pi\)
\(434\) 0 0
\(435\) −85.7774 + 62.3209i −4.11271 + 2.98806i
\(436\) 0 0
\(437\) 4.15048i 0.198544i
\(438\) 0 0
\(439\) −11.7978 + 3.83335i −0.563080 + 0.182956i −0.576706 0.816951i \(-0.695662\pi\)
0.0136267 + 0.999907i \(0.495662\pi\)
\(440\) 0 0
\(441\) 2.02091 6.21973i 0.0962339 0.296178i
\(442\) 0 0
\(443\) 12.2867 37.8147i 0.583760 1.79663i −0.0204335 0.999791i \(-0.506505\pi\)
0.604194 0.796838i \(-0.293495\pi\)
\(444\) 0 0
\(445\) −26.0044 + 35.7921i −1.23273 + 1.69671i
\(446\) 0 0
\(447\) −8.54298 26.2926i −0.404069 1.24360i
\(448\) 0 0
\(449\) −9.38106 6.81574i −0.442719 0.321654i 0.343995 0.938971i \(-0.388220\pi\)
−0.786715 + 0.617317i \(0.788220\pi\)
\(450\) 0 0
\(451\) −37.1094 + 0.464873i −1.74741 + 0.0218900i
\(452\) 0 0
\(453\) 26.7102 + 19.4061i 1.25495 + 0.911777i
\(454\) 0 0
\(455\) −7.56774 23.2911i −0.354781 1.09190i
\(456\) 0 0
\(457\) 23.0394 31.7110i 1.07774 1.48338i 0.215746 0.976450i \(-0.430782\pi\)
0.861989 0.506926i \(-0.169218\pi\)
\(458\) 0 0
\(459\) 18.5462 57.0793i 0.865662 2.66423i
\(460\) 0 0
\(461\) −11.1474 + 34.3081i −0.519185 + 1.59789i 0.256350 + 0.966584i \(0.417480\pi\)
−0.775536 + 0.631304i \(0.782520\pi\)
\(462\) 0 0
\(463\) −18.9673 + 6.16284i −0.881484 + 0.286411i −0.714573 0.699561i \(-0.753379\pi\)
−0.166911 + 0.985972i \(0.553379\pi\)
\(464\) 0 0
\(465\) 51.1000i 2.36970i
\(466\) 0 0
\(467\) 12.2415 8.89400i 0.566471 0.411565i −0.267351 0.963599i \(-0.586148\pi\)
0.833821 + 0.552034i \(0.186148\pi\)
\(468\) 0 0
\(469\) 12.0103 + 8.72597i 0.554583 + 0.402928i
\(470\) 0 0
\(471\) −24.0993 + 17.5092i −1.11044 + 0.806780i
\(472\) 0 0
\(473\) −1.89903 2.61379i −0.0873176 0.120182i
\(474\) 0 0
\(475\) 23.3622 + 7.59085i 1.07193 + 0.348292i
\(476\) 0 0
\(477\) −37.0935 + 12.0524i −1.69839 + 0.551842i
\(478\) 0 0
\(479\) 12.1346 16.7019i 0.554445 0.763128i −0.436162 0.899868i \(-0.643663\pi\)
0.990607 + 0.136740i \(0.0436626\pi\)
\(480\) 0 0
\(481\) 21.0031 + 6.82432i 0.957659 + 0.311162i
\(482\) 0 0
\(483\) 4.16842 0.189670
\(484\) 0 0
\(485\) −29.0415 39.9722i −1.31871 1.81504i
\(486\) 0 0
\(487\) −3.47164 10.6846i −0.157315 0.484165i 0.841073 0.540921i \(-0.181924\pi\)
−0.998388 + 0.0567560i \(0.981924\pi\)
\(488\) 0 0
\(489\) 19.3454i 0.874828i
\(490\) 0 0
\(491\) −35.1870 −1.58797 −0.793984 0.607939i \(-0.791997\pi\)
−0.793984 + 0.607939i \(0.791997\pi\)
\(492\) 0 0
\(493\) −52.2883 −2.35495
\(494\) 0 0
\(495\) 136.601i 6.13977i
\(496\) 0 0
\(497\) −0.307836 0.947422i −0.0138083 0.0424977i
\(498\) 0 0
\(499\) 13.7594 + 18.9382i 0.615957 + 0.847792i 0.997051 0.0767445i \(-0.0244526\pi\)
−0.381094 + 0.924536i \(0.624453\pi\)
\(500\) 0 0
\(501\) −0.161076 −0.00719636
\(502\) 0 0
\(503\) 18.2318 + 5.92387i 0.812915 + 0.264132i 0.685832 0.727760i \(-0.259439\pi\)
0.127083 + 0.991892i \(0.459439\pi\)
\(504\) 0 0
\(505\) −28.1362 + 38.7262i −1.25205 + 1.72329i
\(506\) 0 0
\(507\) −97.4621 + 31.6673i −4.32844 + 1.40640i
\(508\) 0 0
\(509\) −19.8817 6.45995i −0.881240 0.286332i −0.166768 0.985996i \(-0.553333\pi\)
−0.714472 + 0.699664i \(0.753333\pi\)
\(510\) 0 0
\(511\) −4.03639 5.55562i −0.178560 0.245766i
\(512\) 0 0
\(513\) 27.2022 19.7635i 1.20101 0.872582i
\(514\) 0 0
\(515\) 13.4911 + 9.80183i 0.594487 + 0.431920i
\(516\) 0 0
\(517\) −4.19616 + 3.04869i −0.184547 + 0.134081i
\(518\) 0 0
\(519\) 17.4119i 0.764297i
\(520\) 0 0
\(521\) −0.190173 + 0.0617910i −0.00833164 + 0.00270711i −0.313180 0.949694i \(-0.601394\pi\)
0.304848 + 0.952401i \(0.401394\pi\)
\(522\) 0 0
\(523\) −0.987891 + 3.04042i −0.0431975 + 0.132948i −0.970329 0.241787i \(-0.922266\pi\)
0.927132 + 0.374735i \(0.122266\pi\)
\(524\) 0 0
\(525\) 7.62366 23.4632i 0.332724 1.02402i
\(526\) 0 0
\(527\) −14.8125 + 20.3877i −0.645243 + 0.888101i
\(528\) 0 0
\(529\) −6.54455 20.1421i −0.284546 0.875741i
\(530\) 0 0
\(531\) −6.43023 4.67184i −0.279048 0.202741i
\(532\) 0 0
\(533\) 12.9266 41.5479i 0.559915 1.79964i
\(534\) 0 0
\(535\) 19.4609 + 14.1391i 0.841366 + 0.611289i
\(536\) 0 0
\(537\) 16.2332 + 49.9606i 0.700513 + 2.15596i
\(538\) 0 0
\(539\) −3.40679 + 4.68904i −0.146741 + 0.201971i
\(540\) 0 0
\(541\) 5.86917 18.0634i 0.252335 0.776608i −0.742008 0.670391i \(-0.766126\pi\)
0.994343 0.106217i \(-0.0338738\pi\)
\(542\) 0 0
\(543\) 8.86155 27.2730i 0.380285 1.17040i
\(544\) 0 0
\(545\) −49.6226 + 16.1234i −2.12560 + 0.690649i
\(546\) 0 0
\(547\) 18.6830i 0.798827i 0.916771 + 0.399414i \(0.130786\pi\)
−0.916771 + 0.399414i \(0.869214\pi\)
\(548\) 0 0
\(549\) 11.0971 8.06254i 0.473614 0.344101i
\(550\) 0 0
\(551\) −23.6993 17.2186i −1.00963 0.733536i
\(552\) 0 0
\(553\) −6.30170 + 4.57845i −0.267976 + 0.194696i
\(554\) 0 0
\(555\) 21.2622 + 29.2649i 0.902529 + 1.24223i
\(556\) 0 0
\(557\) 33.0912 + 10.7520i 1.40212 + 0.455576i 0.909876 0.414881i \(-0.136177\pi\)
0.492244 + 0.870457i \(0.336177\pi\)
\(558\) 0 0
\(559\) 3.60259 1.17055i 0.152373 0.0495090i
\(560\) 0 0
\(561\) −57.7613 + 79.5017i −2.43869 + 3.35656i
\(562\) 0 0
\(563\) −0.130119 0.0422783i −0.00548387 0.00178182i 0.306274 0.951943i \(-0.400918\pi\)
−0.311758 + 0.950162i \(0.600918\pi\)
\(564\) 0 0
\(565\) 21.1140 0.888272
\(566\) 0 0
\(567\) −8.31697 11.4473i −0.349280 0.480743i
\(568\) 0 0
\(569\) −6.37158 19.6097i −0.267110 0.822081i −0.991200 0.132375i \(-0.957740\pi\)
0.724089 0.689706i \(-0.242260\pi\)
\(570\) 0 0
\(571\) 12.8896i 0.539415i −0.962942 0.269707i \(-0.913073\pi\)
0.962942 0.269707i \(-0.0869269\pi\)
\(572\) 0 0
\(573\) 8.11659 0.339075
\(574\) 0 0
\(575\) 10.7799 0.449552
\(576\) 0 0
\(577\) 16.8202i 0.700232i −0.936706 0.350116i \(-0.886142\pi\)
0.936706 0.350116i \(-0.113858\pi\)
\(578\) 0 0
\(579\) 19.1695 + 58.9978i 0.796659 + 2.45186i
\(580\) 0 0
\(581\) −0.345864 0.476041i −0.0143489 0.0197495i
\(582\) 0 0
\(583\) 34.5663 1.43159
\(584\) 0 0
\(585\) −152.319 49.4916i −6.29763 2.04623i
\(586\) 0 0
\(587\) −11.8657 + 16.3318i −0.489751 + 0.674085i −0.980342 0.197305i \(-0.936781\pi\)
0.490591 + 0.871390i \(0.336781\pi\)
\(588\) 0 0
\(589\) −13.4274 + 4.36281i −0.553264 + 0.179767i
\(590\) 0 0
\(591\) 13.7621 + 4.47158i 0.566097 + 0.183936i
\(592\) 0 0
\(593\) 1.64751 + 2.26760i 0.0676550 + 0.0931192i 0.841504 0.540251i \(-0.181671\pi\)
−0.773849 + 0.633371i \(0.781671\pi\)
\(594\) 0 0
\(595\) 16.0045 11.6280i 0.656122 0.476700i
\(596\) 0 0
\(597\) −32.3899 23.5326i −1.32563 0.963126i
\(598\) 0 0
\(599\) 24.9662 18.1390i 1.02009 0.741139i 0.0537894 0.998552i \(-0.482870\pi\)
0.966302 + 0.257413i \(0.0828700\pi\)
\(600\) 0 0
\(601\) 7.74140i 0.315778i −0.987457 0.157889i \(-0.949531\pi\)
0.987457 0.157889i \(-0.0504689\pi\)
\(602\) 0 0
\(603\) 92.3350 30.0015i 3.76017 1.22175i
\(604\) 0 0
\(605\) 25.1608 77.4371i 1.02293 3.14827i
\(606\) 0 0
\(607\) 4.24158 13.0543i 0.172161 0.529856i −0.827332 0.561713i \(-0.810142\pi\)
0.999492 + 0.0318577i \(0.0101423\pi\)
\(608\) 0 0
\(609\) −17.2930 + 23.8018i −0.700748 + 0.964497i
\(610\) 0 0
\(611\) −1.87919 5.78356i −0.0760240 0.233978i
\(612\) 0 0
\(613\) −32.5332 23.6368i −1.31400 0.954679i −0.999986 0.00526211i \(-0.998325\pi\)
−0.314017 0.949417i \(-0.601675\pi\)
\(614\) 0 0
\(615\) 57.1318 42.6122i 2.30377 1.71829i
\(616\) 0 0
\(617\) 12.3053 + 8.94035i 0.495394 + 0.359925i 0.807255 0.590203i \(-0.200952\pi\)
−0.311861 + 0.950128i \(0.600952\pi\)
\(618\) 0 0
\(619\) 1.22364 + 3.76599i 0.0491824 + 0.151368i 0.972632 0.232353i \(-0.0746424\pi\)
−0.923449 + 0.383721i \(0.874642\pi\)
\(620\) 0 0
\(621\) 8.67302 11.9374i 0.348036 0.479031i
\(622\) 0 0
\(623\) −3.79357 + 11.6754i −0.151986 + 0.467766i
\(624\) 0 0
\(625\) −0.351415 + 1.08154i −0.0140566 + 0.0432617i
\(626\) 0 0
\(627\) −52.3599 + 17.0128i −2.09105 + 0.679424i
\(628\) 0 0
\(629\) 17.8393i 0.711301i
\(630\) 0 0
\(631\) −4.35000 + 3.16046i −0.173171 + 0.125816i −0.670995 0.741462i \(-0.734133\pi\)
0.497824 + 0.867278i \(0.334133\pi\)
\(632\) 0 0
\(633\) −39.0246 28.3530i −1.55109 1.12693i
\(634\) 0 0
\(635\) −15.5562 + 11.3022i −0.617327 + 0.448515i
\(636\) 0 0
\(637\) −3.99429 5.49767i −0.158260 0.217826i
\(638\) 0 0
\(639\) −6.19596 2.01319i −0.245108 0.0796405i
\(640\) 0 0
\(641\) 0.838232 0.272358i 0.0331082 0.0107575i −0.292416 0.956291i \(-0.594459\pi\)
0.325524 + 0.945534i \(0.394459\pi\)
\(642\) 0 0
\(643\) −6.28415 + 8.64939i −0.247823 + 0.341099i −0.914747 0.404027i \(-0.867610\pi\)
0.666925 + 0.745125i \(0.267610\pi\)
\(644\) 0 0
\(645\) 5.90101 + 1.91735i 0.232352 + 0.0754958i
\(646\) 0 0
\(647\) 48.0227 1.88797 0.943984 0.329991i \(-0.107046\pi\)
0.943984 + 0.329991i \(0.107046\pi\)
\(648\) 0 0
\(649\) 4.14046 + 5.69886i 0.162527 + 0.223700i
\(650\) 0 0
\(651\) 4.38167 + 13.4854i 0.171731 + 0.528535i
\(652\) 0 0
\(653\) 3.12266i 0.122199i −0.998132 0.0610995i \(-0.980539\pi\)
0.998132 0.0610995i \(-0.0194607\pi\)
\(654\) 0 0
\(655\) 37.6992 1.47303
\(656\) 0 0
\(657\) −44.9097 −1.75209
\(658\) 0 0
\(659\) 29.1705i 1.13632i 0.822918 + 0.568161i \(0.192345\pi\)
−0.822918 + 0.568161i \(0.807655\pi\)
\(660\) 0 0
\(661\) −2.21650 6.82169i −0.0862120 0.265333i 0.898652 0.438662i \(-0.144548\pi\)
−0.984864 + 0.173329i \(0.944548\pi\)
\(662\) 0 0
\(663\) −67.7223 93.2118i −2.63012 3.62005i
\(664\) 0 0
\(665\) 11.0831 0.429782
\(666\) 0 0
\(667\) −12.2262 3.97252i −0.473399 0.153817i
\(668\) 0 0
\(669\) −12.5998 + 17.3421i −0.487137 + 0.670486i
\(670\) 0 0
\(671\) −11.5617 + 3.75662i −0.446334 + 0.145023i
\(672\) 0 0
\(673\) −36.3011 11.7949i −1.39931 0.454662i −0.490339 0.871532i \(-0.663127\pi\)
−0.908966 + 0.416870i \(0.863127\pi\)
\(674\) 0 0
\(675\) −51.3310 70.6511i −1.97573 2.71936i
\(676\) 0 0
\(677\) 35.1359 25.5277i 1.35038 0.981109i 0.351389 0.936230i \(-0.385709\pi\)
0.998992 0.0448799i \(-0.0142905\pi\)
\(678\) 0 0
\(679\) −11.0916 8.05854i −0.425657 0.309258i
\(680\) 0 0
\(681\) −26.5532 + 19.2920i −1.01752 + 0.739271i
\(682\) 0 0
\(683\) 50.0871i 1.91653i 0.285880 + 0.958265i \(0.407714\pi\)
−0.285880 + 0.958265i \(0.592286\pi\)
\(684\) 0 0
\(685\) 36.7451 11.9392i 1.40396 0.456173i
\(686\) 0 0
\(687\) −5.62204 + 17.3028i −0.214494 + 0.660145i
\(688\) 0 0
\(689\) −12.5236 + 38.5437i −0.477112 + 1.46840i
\(690\) 0 0
\(691\) −11.3452 + 15.6153i −0.431592 + 0.594036i −0.968318 0.249721i \(-0.919661\pi\)
0.536726 + 0.843757i \(0.319661\pi\)
\(692\) 0 0
\(693\) 11.7132 + 36.0494i 0.444946 + 1.36940i
\(694\) 0 0
\(695\) 0.699248 + 0.508034i 0.0265240 + 0.0192708i
\(696\) 0 0
\(697\) 35.1464 0.440281i 1.33126 0.0166768i
\(698\) 0 0
\(699\) −68.4869 49.7586i −2.59041 1.88204i
\(700\) 0 0
\(701\) 7.83745 + 24.1212i 0.296016 + 0.911045i 0.982878 + 0.184257i \(0.0589878\pi\)
−0.686862 + 0.726788i \(0.741012\pi\)
\(702\) 0 0
\(703\) −5.87451 + 8.08556i −0.221561 + 0.304953i
\(704\) 0 0
\(705\) 3.07810 9.47343i 0.115928 0.356790i
\(706\) 0 0
\(707\) −4.10456 + 12.6325i −0.154368 + 0.475096i
\(708\) 0 0
\(709\) 7.05474 2.29223i 0.264946 0.0860863i −0.173531 0.984828i \(-0.555518\pi\)
0.438478 + 0.898742i \(0.355518\pi\)
\(710\) 0 0
\(711\) 50.9407i 1.91043i
\(712\) 0 0
\(713\) −5.01242 + 3.64174i −0.187717 + 0.136384i
\(714\) 0 0
\(715\) 114.833 + 83.4313i 4.29452 + 3.12015i
\(716\) 0 0
\(717\) 31.8749 23.1585i 1.19039 0.864869i
\(718\) 0 0
\(719\) 10.5848 + 14.5687i 0.394747 + 0.543323i 0.959416 0.281995i \(-0.0909961\pi\)
−0.564669 + 0.825318i \(0.690996\pi\)
\(720\) 0 0
\(721\) 4.40080 + 1.42991i 0.163894 + 0.0532525i
\(722\) 0 0
\(723\) 31.2788 10.1631i 1.16327 0.377969i
\(724\) 0 0
\(725\) −44.7211 + 61.5533i −1.66090 + 2.28603i
\(726\) 0 0
\(727\) −9.90835 3.21942i −0.367480 0.119402i 0.119455 0.992840i \(-0.461885\pi\)
−0.486935 + 0.873438i \(0.661885\pi\)
\(728\) 0 0
\(729\) 8.77112 0.324856
\(730\) 0 0
\(731\) 1.79857 + 2.47552i 0.0665227 + 0.0915606i
\(732\) 0 0
\(733\) 10.3805 + 31.9479i 0.383413 + 1.18002i 0.937625 + 0.347648i \(0.113020\pi\)
−0.554212 + 0.832375i \(0.686980\pi\)
\(734\) 0 0
\(735\) 11.1310i 0.410572i
\(736\) 0 0
\(737\) −86.0442 −3.16948
\(738\) 0 0
\(739\) −15.7297 −0.578626 −0.289313 0.957234i \(-0.593427\pi\)
−0.289313 + 0.957234i \(0.593427\pi\)
\(740\) 0 0
\(741\) 64.5486i 2.37125i
\(742\) 0 0
\(743\) 4.37989 + 13.4799i 0.160683 + 0.494531i 0.998692 0.0511250i \(-0.0162807\pi\)
−0.838010 + 0.545656i \(0.816281\pi\)
\(744\) 0 0
\(745\) −18.9600 26.0962i −0.694642 0.956092i
\(746\) 0 0
\(747\) −3.84815 −0.140796
\(748\) 0 0
\(749\) 6.34816 + 2.06264i 0.231957 + 0.0753673i
\(750\) 0 0
\(751\) −8.06974 + 11.1071i −0.294469 + 0.405302i −0.930459 0.366395i \(-0.880592\pi\)
0.635990 + 0.771697i \(0.280592\pi\)
\(752\) 0 0
\(753\) 47.8483 15.5469i 1.74369 0.566559i
\(754\) 0 0
\(755\) 36.6369 + 11.9040i 1.33335 + 0.433232i
\(756\) 0 0
\(757\) 8.09793 + 11.1458i 0.294324 + 0.405103i 0.930413 0.366513i \(-0.119449\pi\)
−0.636088 + 0.771616i \(0.719449\pi\)
\(758\) 0 0
\(759\) −19.5459 + 14.2009i −0.709471 + 0.515461i
\(760\) 0 0
\(761\) −7.97524 5.79435i −0.289102 0.210045i 0.433776 0.901021i \(-0.357181\pi\)
−0.722878 + 0.690976i \(0.757181\pi\)
\(762\) 0 0
\(763\) −11.7130 + 8.50998i −0.424039 + 0.308082i
\(764\) 0 0
\(765\) 129.375i 4.67756i
\(766\) 0 0
\(767\) −7.85473 + 2.55216i −0.283618 + 0.0921530i
\(768\) 0 0
\(769\) 9.42688 29.0130i 0.339942 1.04623i −0.624294 0.781189i \(-0.714613\pi\)
0.964236 0.265045i \(-0.0853867\pi\)
\(770\) 0 0
\(771\) 5.44493 16.7578i 0.196095 0.603517i
\(772\) 0 0
\(773\) 16.9674 23.3537i 0.610276 0.839973i −0.386324 0.922363i \(-0.626255\pi\)
0.996600 + 0.0823902i \(0.0262554\pi\)
\(774\) 0 0
\(775\) 11.3314 + 34.8743i 0.407034 + 1.25272i
\(776\) 0 0
\(777\) 8.12052 + 5.89990i 0.291322 + 0.211658i
\(778\) 0 0
\(779\) 16.0748 + 11.3742i 0.575941 + 0.407522i
\(780\) 0 0
\(781\) 4.67112 + 3.39377i 0.167146 + 0.121439i
\(782\) 0 0
\(783\) 32.1821 + 99.0463i 1.15009 + 3.53963i
\(784\) 0 0
\(785\) −20.4295 + 28.1189i −0.729162 + 1.00361i
\(786\) 0 0
\(787\) 3.10451 9.55471i 0.110664 0.340589i −0.880354 0.474317i \(-0.842695\pi\)
0.991018 + 0.133728i \(0.0426950\pi\)
\(788\) 0 0
\(789\) −6.09866 + 18.7697i −0.217118 + 0.668220i
\(790\) 0 0
\(791\) 5.57203 1.81046i 0.198119 0.0643727i
\(792\) 0 0
\(793\) 14.2531i 0.506142i
\(794\) 0 0
\(795\) −53.7053 + 39.0192i −1.90473 + 1.38387i
\(796\) 0 0
\(797\) −6.87960 4.99832i −0.243688 0.177050i 0.459237 0.888314i \(-0.348123\pi\)