Properties

Label 756.2.ck.a.5.15
Level 756
Weight 2
Character 756.5
Analytic conductor 6.037
Analytic rank 0
Dimension 144
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 756.ck (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.15
Character \(\chi\) = 756.5
Dual form 756.2.ck.a.605.15

$q$-expansion

\(f(q)\) \(=\) \(q+(0.671662 + 1.59652i) q^{3} +(-0.158784 + 0.900507i) q^{5} +(-0.241705 - 2.63469i) q^{7} +(-2.09774 + 2.14464i) q^{9} +O(q^{10})\) \(q+(0.671662 + 1.59652i) q^{3} +(-0.158784 + 0.900507i) q^{5} +(-0.241705 - 2.63469i) q^{7} +(-2.09774 + 2.14464i) q^{9} +(-3.68787 + 0.650271i) q^{11} +(-2.48376 + 2.96003i) q^{13} +(-1.54432 + 0.351336i) q^{15} -6.10539 q^{17} +5.56765i q^{19} +(4.04398 - 2.15551i) q^{21} +(-1.03164 + 1.22946i) q^{23} +(3.91276 + 1.42413i) q^{25} +(-4.83293 - 1.90860i) q^{27} +(4.21794 + 5.02674i) q^{29} +(-0.823531 - 2.26263i) q^{31} +(-3.51517 - 5.45099i) q^{33} +(2.41093 + 0.200688i) q^{35} +(1.21795 + 2.10956i) q^{37} +(-6.39400 - 1.97723i) q^{39} +(-4.95635 - 4.15887i) q^{41} +(7.68736 + 2.79797i) q^{43} +(-1.59818 - 2.22956i) q^{45} +(4.31905 + 1.57200i) q^{47} +(-6.88316 + 1.27364i) q^{49} +(-4.10076 - 9.74737i) q^{51} +(-9.92435 + 5.72983i) q^{53} -3.42420i q^{55} +(-8.88885 + 3.73958i) q^{57} +(0.682613 + 0.572780i) q^{59} +(4.21480 - 11.5801i) q^{61} +(6.15750 + 5.00852i) q^{63} +(-2.27115 - 2.70665i) q^{65} +(2.26341 - 12.8364i) q^{67} +(-2.65578 - 0.821252i) q^{69} +(11.1044 + 6.41115i) q^{71} +(-4.20689 - 2.42885i) q^{73} +(0.354408 + 7.20333i) q^{75} +(2.60464 + 9.55921i) q^{77} +(-0.979078 - 5.55263i) q^{79} +(-0.198980 - 8.99780i) q^{81} +(-6.26479 + 5.25678i) q^{83} +(0.969437 - 5.49795i) q^{85} +(-5.19226 + 10.1103i) q^{87} +4.08655 q^{89} +(8.39910 + 5.82848i) q^{91} +(3.05920 - 2.83451i) q^{93} +(-5.01371 - 0.884052i) q^{95} +(-4.13766 + 11.3681i) q^{97} +(6.34159 - 9.27326i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144q + 6q^{9} + O(q^{10}) \) \( 144q + 6q^{9} - 6q^{11} + 12q^{15} + 33q^{21} + 21q^{23} - 6q^{29} + 27q^{35} + 39q^{39} - 54q^{47} + 18q^{49} - 9q^{51} - 45q^{53} + 3q^{57} + 45q^{59} + 39q^{63} + 24q^{65} - 36q^{69} + 36q^{71} + 45q^{75} + 21q^{77} - 18q^{79} + 18q^{81} + 36q^{85} - 45q^{87} + 9q^{91} - 48q^{93} - 66q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.671662 + 1.59652i 0.387784 + 0.921750i
\(4\) 0 0
\(5\) −0.158784 + 0.900507i −0.0710102 + 0.402719i 0.928497 + 0.371339i \(0.121101\pi\)
−0.999508 + 0.0313798i \(0.990010\pi\)
\(6\) 0 0
\(7\) −0.241705 2.63469i −0.0913560 0.995818i
\(8\) 0 0
\(9\) −2.09774 + 2.14464i −0.699246 + 0.714881i
\(10\) 0 0
\(11\) −3.68787 + 0.650271i −1.11193 + 0.196064i −0.699297 0.714831i \(-0.746503\pi\)
−0.412637 + 0.910895i \(0.635392\pi\)
\(12\) 0 0
\(13\) −2.48376 + 2.96003i −0.688872 + 0.820965i −0.991219 0.132233i \(-0.957785\pi\)
0.302347 + 0.953198i \(0.402230\pi\)
\(14\) 0 0
\(15\) −1.54432 + 0.351336i −0.398743 + 0.0907145i
\(16\) 0 0
\(17\) −6.10539 −1.48078 −0.740388 0.672180i \(-0.765358\pi\)
−0.740388 + 0.672180i \(0.765358\pi\)
\(18\) 0 0
\(19\) 5.56765i 1.27731i 0.769495 + 0.638653i \(0.220508\pi\)
−0.769495 + 0.638653i \(0.779492\pi\)
\(20\) 0 0
\(21\) 4.04398 2.15551i 0.882469 0.470370i
\(22\) 0 0
\(23\) −1.03164 + 1.22946i −0.215113 + 0.256361i −0.862800 0.505545i \(-0.831292\pi\)
0.647688 + 0.761906i \(0.275736\pi\)
\(24\) 0 0
\(25\) 3.91276 + 1.42413i 0.782553 + 0.284826i
\(26\) 0 0
\(27\) −4.83293 1.90860i −0.930098 0.367311i
\(28\) 0 0
\(29\) 4.21794 + 5.02674i 0.783251 + 0.933443i 0.999076 0.0429895i \(-0.0136882\pi\)
−0.215824 + 0.976432i \(0.569244\pi\)
\(30\) 0 0
\(31\) −0.823531 2.26263i −0.147911 0.406381i 0.843506 0.537119i \(-0.180487\pi\)
−0.991417 + 0.130738i \(0.958265\pi\)
\(32\) 0 0
\(33\) −3.51517 5.45099i −0.611913 0.948895i
\(34\) 0 0
\(35\) 2.41093 + 0.200688i 0.407522 + 0.0339225i
\(36\) 0 0
\(37\) 1.21795 + 2.10956i 0.200230 + 0.346809i 0.948603 0.316470i \(-0.102498\pi\)
−0.748372 + 0.663279i \(0.769164\pi\)
\(38\) 0 0
\(39\) −6.39400 1.97723i −1.02386 0.316610i
\(40\) 0 0
\(41\) −4.95635 4.15887i −0.774052 0.649506i 0.167691 0.985840i \(-0.446369\pi\)
−0.941743 + 0.336333i \(0.890813\pi\)
\(42\) 0 0
\(43\) 7.68736 + 2.79797i 1.17231 + 0.426686i 0.853480 0.521125i \(-0.174488\pi\)
0.318831 + 0.947812i \(0.396710\pi\)
\(44\) 0 0
\(45\) −1.59818 2.22956i −0.238242 0.332364i
\(46\) 0 0
\(47\) 4.31905 + 1.57200i 0.629998 + 0.229300i 0.637230 0.770673i \(-0.280080\pi\)
−0.00723267 + 0.999974i \(0.502302\pi\)
\(48\) 0 0
\(49\) −6.88316 + 1.27364i −0.983308 + 0.181948i
\(50\) 0 0
\(51\) −4.10076 9.74737i −0.574222 1.36490i
\(52\) 0 0
\(53\) −9.92435 + 5.72983i −1.36321 + 0.787052i −0.990050 0.140713i \(-0.955060\pi\)
−0.373164 + 0.927765i \(0.621727\pi\)
\(54\) 0 0
\(55\) 3.42420i 0.461720i
\(56\) 0 0
\(57\) −8.88885 + 3.73958i −1.17736 + 0.495319i
\(58\) 0 0
\(59\) 0.682613 + 0.572780i 0.0888687 + 0.0745697i 0.686140 0.727470i \(-0.259304\pi\)
−0.597271 + 0.802039i \(0.703748\pi\)
\(60\) 0 0
\(61\) 4.21480 11.5801i 0.539650 1.48268i −0.307617 0.951510i \(-0.599531\pi\)
0.847267 0.531167i \(-0.178246\pi\)
\(62\) 0 0
\(63\) 6.15750 + 5.00852i 0.775772 + 0.631014i
\(64\) 0 0
\(65\) −2.27115 2.70665i −0.281701 0.335719i
\(66\) 0 0
\(67\) 2.26341 12.8364i 0.276520 1.56822i −0.457574 0.889172i \(-0.651281\pi\)
0.734093 0.679049i \(-0.237607\pi\)
\(68\) 0 0
\(69\) −2.65578 0.821252i −0.319718 0.0988671i
\(70\) 0 0
\(71\) 11.1044 + 6.41115i 1.31785 + 0.760864i 0.983383 0.181542i \(-0.0581089\pi\)
0.334471 + 0.942406i \(0.391442\pi\)
\(72\) 0 0
\(73\) −4.20689 2.42885i −0.492379 0.284275i 0.233182 0.972433i \(-0.425086\pi\)
−0.725561 + 0.688158i \(0.758420\pi\)
\(74\) 0 0
\(75\) 0.354408 + 7.20333i 0.0409235 + 0.831769i
\(76\) 0 0
\(77\) 2.60464 + 9.55921i 0.296826 + 1.08937i
\(78\) 0 0
\(79\) −0.979078 5.55263i −0.110155 0.624719i −0.989036 0.147678i \(-0.952820\pi\)
0.878881 0.477042i \(-0.158291\pi\)
\(80\) 0 0
\(81\) −0.198980 8.99780i −0.0221089 0.999756i
\(82\) 0 0
\(83\) −6.26479 + 5.25678i −0.687650 + 0.577006i −0.918230 0.396047i \(-0.870382\pi\)
0.230581 + 0.973053i \(0.425937\pi\)
\(84\) 0 0
\(85\) 0.969437 5.49795i 0.105150 0.596336i
\(86\) 0 0
\(87\) −5.19226 + 10.1103i −0.556668 + 1.08394i
\(88\) 0 0
\(89\) 4.08655 0.433174 0.216587 0.976263i \(-0.430508\pi\)
0.216587 + 0.976263i \(0.430508\pi\)
\(90\) 0 0
\(91\) 8.39910 + 5.82848i 0.880465 + 0.610991i
\(92\) 0 0
\(93\) 3.05920 2.83451i 0.317224 0.293925i
\(94\) 0 0
\(95\) −5.01371 0.884052i −0.514395 0.0907018i
\(96\) 0 0
\(97\) −4.13766 + 11.3681i −0.420115 + 1.15426i 0.531525 + 0.847043i \(0.321619\pi\)
−0.951640 + 0.307215i \(0.900603\pi\)
\(98\) 0 0
\(99\) 6.34159 9.27326i 0.637354 0.931998i
\(100\) 0 0
\(101\) −2.27509 + 1.90902i −0.226380 + 0.189955i −0.748922 0.662658i \(-0.769428\pi\)
0.522542 + 0.852613i \(0.324984\pi\)
\(102\) 0 0
\(103\) 8.96723 + 1.58117i 0.883568 + 0.155797i 0.596979 0.802257i \(-0.296368\pi\)
0.286589 + 0.958054i \(0.407479\pi\)
\(104\) 0 0
\(105\) 1.29893 + 3.98389i 0.126763 + 0.388788i
\(106\) 0 0
\(107\) 12.5146 + 7.22532i 1.20983 + 0.698498i 0.962723 0.270489i \(-0.0871855\pi\)
0.247111 + 0.968987i \(0.420519\pi\)
\(108\) 0 0
\(109\) 4.51287 + 7.81653i 0.432255 + 0.748688i 0.997067 0.0765319i \(-0.0243847\pi\)
−0.564812 + 0.825220i \(0.691051\pi\)
\(110\) 0 0
\(111\) −2.54989 + 3.36139i −0.242025 + 0.319049i
\(112\) 0 0
\(113\) −3.84867 10.5741i −0.362053 0.994732i −0.978303 0.207181i \(-0.933571\pi\)
0.616250 0.787551i \(-0.288651\pi\)
\(114\) 0 0
\(115\) −0.943333 1.12422i −0.0879663 0.104834i
\(116\) 0 0
\(117\) −1.13793 11.5362i −0.105201 1.06652i
\(118\) 0 0
\(119\) 1.47571 + 16.0858i 0.135278 + 1.47458i
\(120\) 0 0
\(121\) 2.84091 1.03401i 0.258264 0.0940005i
\(122\) 0 0
\(123\) 3.31072 10.7063i 0.298517 0.965351i
\(124\) 0 0
\(125\) −4.18972 + 7.25680i −0.374740 + 0.649068i
\(126\) 0 0
\(127\) 1.76290 + 3.05343i 0.156432 + 0.270948i 0.933579 0.358370i \(-0.116668\pi\)
−0.777148 + 0.629318i \(0.783334\pi\)
\(128\) 0 0
\(129\) 0.696301 + 14.1523i 0.0613059 + 1.24604i
\(130\) 0 0
\(131\) −8.87289 7.44524i −0.775228 0.650493i 0.166814 0.985988i \(-0.446652\pi\)
−0.942042 + 0.335495i \(0.891096\pi\)
\(132\) 0 0
\(133\) 14.6690 1.34573i 1.27196 0.116690i
\(134\) 0 0
\(135\) 2.48610 4.04903i 0.213969 0.348485i
\(136\) 0 0
\(137\) 1.59066 4.37031i 0.135899 0.373381i −0.853011 0.521893i \(-0.825226\pi\)
0.988911 + 0.148512i \(0.0474484\pi\)
\(138\) 0 0
\(139\) 20.6952 + 3.64913i 1.75535 + 0.309515i 0.956438 0.291935i \(-0.0942992\pi\)
0.798910 + 0.601450i \(0.205410\pi\)
\(140\) 0 0
\(141\) 0.391208 + 7.95129i 0.0329457 + 0.669619i
\(142\) 0 0
\(143\) 7.23497 12.5313i 0.605018 1.04792i
\(144\) 0 0
\(145\) −5.19636 + 3.00012i −0.431534 + 0.249146i
\(146\) 0 0
\(147\) −6.65654 10.1336i −0.549022 0.835808i
\(148\) 0 0
\(149\) 4.58792 + 12.6052i 0.375857 + 1.03266i 0.973057 + 0.230566i \(0.0740576\pi\)
−0.597200 + 0.802092i \(0.703720\pi\)
\(150\) 0 0
\(151\) −1.81633 10.3009i −0.147811 0.838279i −0.965067 0.262004i \(-0.915617\pi\)
0.817256 0.576275i \(-0.195494\pi\)
\(152\) 0 0
\(153\) 12.8075 13.0939i 1.03543 1.05858i
\(154\) 0 0
\(155\) 2.16828 0.382326i 0.174160 0.0307092i
\(156\) 0 0
\(157\) −12.7728 + 15.2220i −1.01938 + 1.21485i −0.0429337 + 0.999078i \(0.513670\pi\)
−0.976444 + 0.215770i \(0.930774\pi\)
\(158\) 0 0
\(159\) −15.8136 11.9959i −1.25410 0.951336i
\(160\) 0 0
\(161\) 3.48861 + 2.42089i 0.274941 + 0.190793i
\(162\) 0 0
\(163\) 7.01252 12.1460i 0.549263 0.951352i −0.449062 0.893501i \(-0.648242\pi\)
0.998325 0.0578512i \(-0.0184249\pi\)
\(164\) 0 0
\(165\) 5.46680 2.29991i 0.425590 0.179048i
\(166\) 0 0
\(167\) −2.12777 + 0.774444i −0.164652 + 0.0599283i −0.423031 0.906115i \(-0.639034\pi\)
0.258379 + 0.966044i \(0.416812\pi\)
\(168\) 0 0
\(169\) −0.335292 1.90154i −0.0257917 0.146272i
\(170\) 0 0
\(171\) −11.9406 11.6795i −0.913121 0.893152i
\(172\) 0 0
\(173\) −19.4358 + 16.3086i −1.47768 + 1.23992i −0.569057 + 0.822298i \(0.692692\pi\)
−0.908621 + 0.417621i \(0.862864\pi\)
\(174\) 0 0
\(175\) 2.80640 10.6531i 0.212144 0.805301i
\(176\) 0 0
\(177\) −0.455969 + 1.47452i −0.0342727 + 0.110832i
\(178\) 0 0
\(179\) 4.35026i 0.325154i 0.986696 + 0.162577i \(0.0519805\pi\)
−0.986696 + 0.162577i \(0.948019\pi\)
\(180\) 0 0
\(181\) −2.32397 + 1.34175i −0.172740 + 0.0997313i −0.583877 0.811842i \(-0.698465\pi\)
0.411137 + 0.911573i \(0.365132\pi\)
\(182\) 0 0
\(183\) 21.3187 1.04889i 1.57593 0.0775364i
\(184\) 0 0
\(185\) −2.09306 + 0.761812i −0.153885 + 0.0560095i
\(186\) 0 0
\(187\) 22.5159 3.97016i 1.64653 0.290327i
\(188\) 0 0
\(189\) −3.86043 + 13.1946i −0.280805 + 0.959765i
\(190\) 0 0
\(191\) −16.2247 + 2.86085i −1.17398 + 0.207004i −0.726419 0.687252i \(-0.758817\pi\)
−0.447557 + 0.894256i \(0.647706\pi\)
\(192\) 0 0
\(193\) −9.52163 + 3.46559i −0.685382 + 0.249459i −0.661157 0.750248i \(-0.729934\pi\)
−0.0242252 + 0.999707i \(0.507712\pi\)
\(194\) 0 0
\(195\) 2.79577 5.44389i 0.200209 0.389845i
\(196\) 0 0
\(197\) 23.3394 13.4750i 1.66286 0.960054i 0.691524 0.722353i \(-0.256939\pi\)
0.971338 0.237701i \(-0.0763939\pi\)
\(198\) 0 0
\(199\) 12.5565i 0.890107i 0.895504 + 0.445053i \(0.146815\pi\)
−0.895504 + 0.445053i \(0.853185\pi\)
\(200\) 0 0
\(201\) 22.0138 5.00818i 1.55274 0.353250i
\(202\) 0 0
\(203\) 12.2244 12.3279i 0.857985 0.865252i
\(204\) 0 0
\(205\) 4.53208 3.80287i 0.316534 0.265604i
\(206\) 0 0
\(207\) −0.472643 4.79160i −0.0328510 0.333039i
\(208\) 0 0
\(209\) −3.62048 20.5328i −0.250434 1.42028i
\(210\) 0 0
\(211\) 4.63971 1.68871i 0.319411 0.116256i −0.177339 0.984150i \(-0.556749\pi\)
0.496750 + 0.867894i \(0.334527\pi\)
\(212\) 0 0
\(213\) −2.77708 + 22.0346i −0.190283 + 1.50978i
\(214\) 0 0
\(215\) −3.74022 + 6.47825i −0.255081 + 0.441813i
\(216\) 0 0
\(217\) −5.76228 + 2.71664i −0.391169 + 0.184417i
\(218\) 0 0
\(219\) 1.05209 8.34775i 0.0710938 0.564088i
\(220\) 0 0
\(221\) 15.1643 18.0722i 1.02006 1.21567i
\(222\) 0 0
\(223\) 12.8650 2.26844i 0.861502 0.151906i 0.274595 0.961560i \(-0.411456\pi\)
0.586908 + 0.809654i \(0.300345\pi\)
\(224\) 0 0
\(225\) −11.2622 + 5.40402i −0.750814 + 0.360268i
\(226\) 0 0
\(227\) 2.66067 + 15.0894i 0.176595 + 1.00152i 0.936287 + 0.351237i \(0.114239\pi\)
−0.759692 + 0.650284i \(0.774650\pi\)
\(228\) 0 0
\(229\) 3.17798 + 8.73143i 0.210007 + 0.576989i 0.999315 0.0370081i \(-0.0117827\pi\)
−0.789308 + 0.613997i \(0.789561\pi\)
\(230\) 0 0
\(231\) −13.5120 + 10.5789i −0.889025 + 0.696041i
\(232\) 0 0
\(233\) 8.13366 4.69597i 0.532854 0.307643i −0.209324 0.977846i \(-0.567126\pi\)
0.742178 + 0.670203i \(0.233793\pi\)
\(234\) 0 0
\(235\) −2.10139 + 3.63972i −0.137080 + 0.237429i
\(236\) 0 0
\(237\) 8.20726 5.29261i 0.533119 0.343792i
\(238\) 0 0
\(239\) −8.59351 1.51527i −0.555868 0.0980145i −0.111345 0.993782i \(-0.535516\pi\)
−0.444523 + 0.895767i \(0.646627\pi\)
\(240\) 0 0
\(241\) −1.93208 + 5.30834i −0.124456 + 0.341940i −0.986236 0.165342i \(-0.947127\pi\)
0.861780 + 0.507282i \(0.169350\pi\)
\(242\) 0 0
\(243\) 14.2315 6.36116i 0.912951 0.408069i
\(244\) 0 0
\(245\) −0.0539848 6.40056i −0.00344896 0.408917i
\(246\) 0 0
\(247\) −16.4804 13.8287i −1.04862 0.879900i
\(248\) 0 0
\(249\) −12.6004 6.47106i −0.798516 0.410087i
\(250\) 0 0
\(251\) 0.593298 + 1.02762i 0.0374487 + 0.0648630i 0.884142 0.467218i \(-0.154744\pi\)
−0.846694 + 0.532081i \(0.821410\pi\)
\(252\) 0 0
\(253\) 3.00508 5.20495i 0.188928 0.327233i
\(254\) 0 0
\(255\) 9.42871 2.14504i 0.590449 0.134328i
\(256\) 0 0
\(257\) 11.3769 4.14085i 0.709672 0.258299i 0.0381371 0.999273i \(-0.487858\pi\)
0.671535 + 0.740973i \(0.265635\pi\)
\(258\) 0 0
\(259\) 5.26363 3.71882i 0.327066 0.231076i
\(260\) 0 0
\(261\) −19.6287 1.49883i −1.21499 0.0927751i
\(262\) 0 0
\(263\) −0.921965 1.09875i −0.0568508 0.0677521i 0.736870 0.676035i \(-0.236303\pi\)
−0.793720 + 0.608283i \(0.791859\pi\)
\(264\) 0 0
\(265\) −3.58392 9.84675i −0.220159 0.604881i
\(266\) 0 0
\(267\) 2.74478 + 6.52425i 0.167978 + 0.399278i
\(268\) 0 0
\(269\) 5.22031 + 9.04184i 0.318288 + 0.551291i 0.980131 0.198352i \(-0.0635588\pi\)
−0.661843 + 0.749642i \(0.730225\pi\)
\(270\) 0 0
\(271\) 11.2170 + 6.47615i 0.681386 + 0.393398i 0.800377 0.599497i \(-0.204633\pi\)
−0.118991 + 0.992895i \(0.537966\pi\)
\(272\) 0 0
\(273\) −3.66392 + 17.3241i −0.221750 + 1.04850i
\(274\) 0 0
\(275\) −15.3558 2.70765i −0.925991 0.163277i
\(276\) 0 0
\(277\) −15.4923 + 12.9996i −0.930842 + 0.781069i −0.975968 0.217912i \(-0.930075\pi\)
0.0451263 + 0.998981i \(0.485631\pi\)
\(278\) 0 0
\(279\) 6.58009 + 2.98024i 0.393940 + 0.178422i
\(280\) 0 0
\(281\) −9.35867 + 25.7127i −0.558291 + 1.53389i 0.263824 + 0.964571i \(0.415016\pi\)
−0.822115 + 0.569322i \(0.807206\pi\)
\(282\) 0 0
\(283\) −21.6032 3.80923i −1.28418 0.226435i −0.510426 0.859922i \(-0.670512\pi\)
−0.773754 + 0.633486i \(0.781623\pi\)
\(284\) 0 0
\(285\) −1.95611 8.59825i −0.115870 0.509317i
\(286\) 0 0
\(287\) −9.75935 + 14.0637i −0.576076 + 0.830151i
\(288\) 0 0
\(289\) 20.2758 1.19270
\(290\) 0 0
\(291\) −20.9285 + 1.02969i −1.22685 + 0.0603618i
\(292\) 0 0
\(293\) 2.68082 15.2037i 0.156615 0.888209i −0.800679 0.599094i \(-0.795528\pi\)
0.957294 0.289116i \(-0.0933612\pi\)
\(294\) 0 0
\(295\) −0.624181 + 0.523750i −0.0363412 + 0.0304939i
\(296\) 0 0
\(297\) 19.0643 + 3.89596i 1.10622 + 0.226067i
\(298\) 0 0
\(299\) −1.07690 6.10740i −0.0622787 0.353200i
\(300\) 0 0
\(301\) 5.51370 20.9301i 0.317804 1.20639i
\(302\) 0 0
\(303\) −4.57588 2.35000i −0.262877 0.135004i
\(304\) 0 0
\(305\) 9.75870 + 5.63419i 0.558781 + 0.322613i
\(306\) 0 0
\(307\) −22.4632 12.9691i −1.28204 0.740187i −0.304820 0.952410i \(-0.598596\pi\)
−0.977221 + 0.212223i \(0.931930\pi\)
\(308\) 0 0
\(309\) 3.49860 + 15.3784i 0.199028 + 0.874844i
\(310\) 0 0
\(311\) −0.161417 + 0.915442i −0.00915313 + 0.0519100i −0.989042 0.147633i \(-0.952835\pi\)
0.979889 + 0.199543i \(0.0639457\pi\)
\(312\) 0 0
\(313\) 3.09257 + 3.68558i 0.174802 + 0.208321i 0.846331 0.532657i \(-0.178807\pi\)
−0.671529 + 0.740978i \(0.734362\pi\)
\(314\) 0 0
\(315\) −5.48791 + 4.74960i −0.309209 + 0.267610i
\(316\) 0 0
\(317\) 4.48170 12.3134i 0.251718 0.691588i −0.747897 0.663815i \(-0.768936\pi\)
0.999614 0.0277732i \(-0.00884162\pi\)
\(318\) 0 0
\(319\) −18.8239 15.7952i −1.05394 0.884360i
\(320\) 0 0
\(321\) −3.12975 + 24.8328i −0.174686 + 1.38603i
\(322\) 0 0
\(323\) 33.9927i 1.89140i
\(324\) 0 0
\(325\) −13.9338 + 8.04471i −0.772910 + 0.446240i
\(326\) 0 0
\(327\) −9.44810 + 12.4550i −0.522481 + 0.688761i
\(328\) 0 0
\(329\) 3.09780 11.7593i 0.170787 0.648311i
\(330\) 0 0
\(331\) 17.2491 + 6.27817i 0.948098 + 0.345079i 0.769359 0.638817i \(-0.220576\pi\)
0.178739 + 0.983896i \(0.442798\pi\)
\(332\) 0 0
\(333\) −7.07919 1.81323i −0.387937 0.0993641i
\(334\) 0 0
\(335\) 11.1999 + 4.07643i 0.611916 + 0.222719i
\(336\) 0 0
\(337\) −19.7150 16.5428i −1.07394 0.901145i −0.0785390 0.996911i \(-0.525026\pi\)
−0.995404 + 0.0957659i \(0.969470\pi\)
\(338\) 0 0
\(339\) 14.2968 13.2467i 0.776496 0.719464i
\(340\) 0 0
\(341\) 4.50840 + 7.80878i 0.244144 + 0.422869i
\(342\) 0 0
\(343\) 5.01933 + 17.8271i 0.271018 + 0.962574i
\(344\) 0 0
\(345\) 1.16124 2.26115i 0.0625189 0.121736i
\(346\) 0 0
\(347\) −6.60870 18.1573i −0.354774 0.974733i −0.980815 0.194942i \(-0.937548\pi\)
0.626041 0.779790i \(-0.284674\pi\)
\(348\) 0 0
\(349\) −5.91691 7.05150i −0.316725 0.377458i 0.584070 0.811704i \(-0.301459\pi\)
−0.900795 + 0.434245i \(0.857015\pi\)
\(350\) 0 0
\(351\) 17.6534 9.56512i 0.942268 0.510548i
\(352\) 0 0
\(353\) −24.3476 8.86179i −1.29589 0.471666i −0.400234 0.916413i \(-0.631071\pi\)
−0.895656 + 0.444747i \(0.853293\pi\)
\(354\) 0 0
\(355\) −7.53649 + 8.98164i −0.399995 + 0.476696i
\(356\) 0 0
\(357\) −24.6901 + 13.1602i −1.30674 + 0.696513i
\(358\) 0 0
\(359\) 21.7705i 1.14901i 0.818503 + 0.574503i \(0.194805\pi\)
−0.818503 + 0.574503i \(0.805195\pi\)
\(360\) 0 0
\(361\) −11.9987 −0.631511
\(362\) 0 0
\(363\) 3.55894 + 3.84106i 0.186796 + 0.201603i
\(364\) 0 0
\(365\) 2.85518 3.40267i 0.149447 0.178104i
\(366\) 0 0
\(367\) −15.3983 + 2.71514i −0.803787 + 0.141729i −0.560424 0.828206i \(-0.689362\pi\)
−0.243363 + 0.969935i \(0.578251\pi\)
\(368\) 0 0
\(369\) 19.3164 1.90537i 1.00557 0.0991896i
\(370\) 0 0
\(371\) 17.4951 + 24.7626i 0.908299 + 1.28561i
\(372\) 0 0
\(373\) −4.12582 + 23.3987i −0.213627 + 1.21154i 0.669647 + 0.742680i \(0.266446\pi\)
−0.883273 + 0.468858i \(0.844666\pi\)
\(374\) 0 0
\(375\) −14.3997 1.81484i −0.743597 0.0937178i
\(376\) 0 0
\(377\) −25.3557 −1.30588
\(378\) 0 0
\(379\) −2.22199 −0.114136 −0.0570680 0.998370i \(-0.518175\pi\)
−0.0570680 + 0.998370i \(0.518175\pi\)
\(380\) 0 0
\(381\) −3.69078 + 4.86537i −0.189084 + 0.249260i
\(382\) 0 0
\(383\) −3.59378 + 20.3814i −0.183634 + 1.04144i 0.744065 + 0.668108i \(0.232895\pi\)
−0.927698 + 0.373331i \(0.878216\pi\)
\(384\) 0 0
\(385\) −9.02171 + 0.827648i −0.459789 + 0.0421809i
\(386\) 0 0
\(387\) −22.1267 + 10.6172i −1.12476 + 0.539704i
\(388\) 0 0
\(389\) −28.8767 + 5.09173i −1.46410 + 0.258161i −0.848207 0.529665i \(-0.822318\pi\)
−0.615898 + 0.787826i \(0.711207\pi\)
\(390\) 0 0
\(391\) 6.29859 7.50637i 0.318533 0.379613i
\(392\) 0 0
\(393\) 5.92687 19.1664i 0.298971 0.966817i
\(394\) 0 0
\(395\) 5.15564 0.259408
\(396\) 0 0
\(397\) 31.8885i 1.60044i 0.599707 + 0.800220i \(0.295284\pi\)
−0.599707 + 0.800220i \(0.704716\pi\)
\(398\) 0 0
\(399\) 12.0011 + 22.5155i 0.600807 + 1.12718i
\(400\) 0 0
\(401\) 6.72607 8.01582i 0.335884 0.400291i −0.571494 0.820606i \(-0.693636\pi\)
0.907378 + 0.420315i \(0.138080\pi\)
\(402\) 0 0
\(403\) 8.74293 + 3.18216i 0.435516 + 0.158515i
\(404\) 0 0
\(405\) 8.13418 + 1.24952i 0.404190 + 0.0620892i
\(406\) 0 0
\(407\) −5.86343 6.98777i −0.290640 0.346371i
\(408\) 0 0
\(409\) 0.336606 + 0.924817i 0.0166441 + 0.0457293i 0.947736 0.319054i \(-0.103365\pi\)
−0.931092 + 0.364784i \(0.881143\pi\)
\(410\) 0 0
\(411\) 8.04566 0.395851i 0.396863 0.0195259i
\(412\) 0 0
\(413\) 1.34411 1.93692i 0.0661392 0.0953094i
\(414\) 0 0
\(415\) −3.73902 6.47617i −0.183541 0.317903i
\(416\) 0 0
\(417\) 8.07432 + 35.4913i 0.395401 + 1.73802i
\(418\) 0 0
\(419\) 10.6223 + 8.91314i 0.518931 + 0.435435i 0.864259 0.503047i \(-0.167788\pi\)
−0.345328 + 0.938482i \(0.612232\pi\)
\(420\) 0 0
\(421\) 6.03019 + 2.19481i 0.293893 + 0.106968i 0.484759 0.874648i \(-0.338907\pi\)
−0.190866 + 0.981616i \(0.561130\pi\)
\(422\) 0 0
\(423\) −12.4316 + 5.96515i −0.604446 + 0.290036i
\(424\) 0 0
\(425\) −23.8890 8.69487i −1.15878 0.421763i
\(426\) 0 0
\(427\) −31.5286 8.30573i −1.52578 0.401942i
\(428\) 0 0
\(429\) 24.8660 + 3.13393i 1.20054 + 0.151308i
\(430\) 0 0
\(431\) 8.73432 5.04276i 0.420717 0.242901i −0.274667 0.961539i \(-0.588568\pi\)
0.695384 + 0.718638i \(0.255234\pi\)
\(432\) 0 0
\(433\) 15.6232i 0.750805i 0.926862 + 0.375403i \(0.122496\pi\)
−0.926862 + 0.375403i \(0.877504\pi\)
\(434\) 0 0
\(435\) −8.27994 6.28101i −0.396993 0.301151i
\(436\) 0 0
\(437\) −6.84523 5.74383i −0.327452 0.274765i
\(438\) 0 0
\(439\) −9.20653 + 25.2947i −0.439404 + 1.20725i 0.500477 + 0.865750i \(0.333158\pi\)
−0.939881 + 0.341502i \(0.889064\pi\)
\(440\) 0 0
\(441\) 11.7076 17.4337i 0.557504 0.830175i
\(442\) 0 0
\(443\) 21.9759 + 26.1899i 1.04411 + 1.24432i 0.968978 + 0.247146i \(0.0794927\pi\)
0.0751299 + 0.997174i \(0.476063\pi\)
\(444\) 0 0
\(445\) −0.648878 + 3.67997i −0.0307597 + 0.174447i
\(446\) 0 0
\(447\) −17.0429 + 15.7911i −0.806101 + 0.746895i
\(448\) 0 0
\(449\) 21.9379 + 12.6659i 1.03531 + 0.597739i 0.918502 0.395415i \(-0.129399\pi\)
0.116812 + 0.993154i \(0.462733\pi\)
\(450\) 0 0
\(451\) 20.9828 + 12.1144i 0.988040 + 0.570445i
\(452\) 0 0
\(453\) 15.2257 9.81857i 0.715365 0.461316i
\(454\) 0 0
\(455\) −6.58223 + 6.63798i −0.308580 + 0.311193i
\(456\) 0 0
\(457\) −5.22960 29.6585i −0.244630 1.38737i −0.821350 0.570425i \(-0.806779\pi\)
0.576720 0.816942i \(-0.304333\pi\)
\(458\) 0 0
\(459\) 29.5070 + 11.6528i 1.37727 + 0.543905i
\(460\) 0 0
\(461\) 16.9479 14.2210i 0.789344 0.662338i −0.156239 0.987719i \(-0.549937\pi\)
0.945583 + 0.325381i \(0.105493\pi\)
\(462\) 0 0
\(463\) −6.48204 + 36.7614i −0.301246 + 1.70845i 0.339425 + 0.940633i \(0.389768\pi\)
−0.640670 + 0.767816i \(0.721343\pi\)
\(464\) 0 0
\(465\) 2.06674 + 3.20490i 0.0958429 + 0.148624i
\(466\) 0 0
\(467\) −17.6269 −0.815678 −0.407839 0.913054i \(-0.633717\pi\)
−0.407839 + 0.913054i \(0.633717\pi\)
\(468\) 0 0
\(469\) −34.3671 2.86074i −1.58692 0.132097i
\(470\) 0 0
\(471\) −32.8812 10.1679i −1.51508 0.468513i
\(472\) 0 0
\(473\) −30.1694 5.31968i −1.38719 0.244599i
\(474\) 0 0
\(475\) −7.92905 + 21.7849i −0.363810 + 0.999559i
\(476\) 0 0
\(477\) 8.53027 33.3039i 0.390574 1.52488i
\(478\) 0 0
\(479\) 19.9841 16.7687i 0.913098 0.766180i −0.0596077 0.998222i \(-0.518985\pi\)
0.972706 + 0.232042i \(0.0745405\pi\)
\(480\) 0 0
\(481\) −9.26946 1.63446i −0.422651 0.0745248i
\(482\) 0 0
\(483\) −1.52183 + 7.19565i −0.0692455 + 0.327413i
\(484\) 0 0
\(485\) −9.58008 5.53106i −0.435009 0.251153i
\(486\) 0 0
\(487\) 1.88377 + 3.26279i 0.0853619 + 0.147851i 0.905545 0.424249i \(-0.139462\pi\)
−0.820183 + 0.572101i \(0.806129\pi\)
\(488\) 0 0
\(489\) 24.1014 + 3.03758i 1.08990 + 0.137364i
\(490\) 0 0
\(491\) −10.2584 28.1847i −0.462955 1.27196i −0.923253 0.384193i \(-0.874480\pi\)
0.460298 0.887764i \(-0.347743\pi\)
\(492\) 0 0
\(493\) −25.7522 30.6902i −1.15982 1.38222i
\(494\) 0 0
\(495\) 7.34369 + 7.18309i 0.330074 + 0.322856i
\(496\) 0 0
\(497\) 14.2074 30.8063i 0.637288 1.38185i
\(498\) 0 0
\(499\) 17.4946 6.36751i 0.783166 0.285049i 0.0806736 0.996741i \(-0.474293\pi\)
0.702492 + 0.711692i \(0.252071\pi\)
\(500\) 0 0
\(501\) −2.66555 2.87685i −0.119088 0.128528i
\(502\) 0 0
\(503\) 21.0298 36.4246i 0.937670 1.62409i 0.167869 0.985809i \(-0.446311\pi\)
0.769801 0.638284i \(-0.220355\pi\)
\(504\) 0 0
\(505\) −1.35784 2.35185i −0.0604232 0.104656i
\(506\) 0 0
\(507\) 2.81063 1.81249i 0.124825 0.0804955i
\(508\) 0 0
\(509\) −18.7068 15.6968i −0.829162 0.695750i 0.125936 0.992038i \(-0.459807\pi\)
−0.955098 + 0.296289i \(0.904251\pi\)
\(510\) 0 0
\(511\) −5.38243 + 11.6709i −0.238105 + 0.516291i
\(512\) 0 0
\(513\) 10.6264 26.9081i 0.469168 1.18802i
\(514\) 0 0
\(515\) −2.84770 + 7.82399i −0.125485 + 0.344766i
\(516\) 0 0
\(517\) −16.9503 2.98880i −0.745474 0.131447i
\(518\) 0 0
\(519\) −39.0913 20.0758i −1.71592 0.881229i
\(520\) 0 0
\(521\) 8.33631 14.4389i 0.365220 0.632580i −0.623591 0.781751i \(-0.714327\pi\)
0.988812 + 0.149170i \(0.0476603\pi\)
\(522\) 0 0
\(523\) −8.45882 + 4.88370i −0.369878 + 0.213549i −0.673405 0.739273i \(-0.735169\pi\)
0.303527 + 0.952823i \(0.401836\pi\)
\(524\) 0 0
\(525\) 18.8929 2.67484i 0.824552 0.116739i
\(526\) 0 0
\(527\) 5.02798 + 13.8143i 0.219022 + 0.601759i
\(528\) 0 0
\(529\) 3.54661 + 20.1138i 0.154201 + 0.874515i
\(530\) 0 0
\(531\) −2.66035 + 0.262417i −0.115450 + 0.0113879i
\(532\) 0 0
\(533\) 24.6208 4.34131i 1.06644 0.188043i
\(534\) 0 0
\(535\) −8.49357 + 10.1222i −0.367209 + 0.437623i
\(536\) 0 0
\(537\) −6.94527 + 2.92191i −0.299710 + 0.126090i
\(538\) 0 0
\(539\) 24.5560 9.17292i 1.05770 0.395106i
\(540\) 0 0
\(541\) 15.0773 26.1147i 0.648224 1.12276i −0.335322 0.942103i \(-0.608845\pi\)
0.983547 0.180654i \(-0.0578214\pi\)
\(542\) 0 0
\(543\) −3.70305 2.80907i −0.158913 0.120549i
\(544\) 0 0
\(545\) −7.75541 + 2.82274i −0.332205 + 0.120913i
\(546\) 0 0
\(547\) −8.06550 45.7417i −0.344856 1.95578i −0.288970 0.957338i \(-0.593313\pi\)
−0.0558860 0.998437i \(-0.517798\pi\)
\(548\) 0 0
\(549\) 15.9936 + 33.3312i 0.682589 + 1.42254i
\(550\) 0 0
\(551\) −27.9871 + 23.4840i −1.19229 + 1.00045i
\(552\) 0 0
\(553\) −14.3928 + 3.92166i −0.612044 + 0.166766i
\(554\) 0 0
\(555\) −2.62208 2.82993i −0.111301 0.120124i
\(556\) 0 0
\(557\) 34.1214i 1.44577i −0.690968 0.722886i \(-0.742815\pi\)
0.690968 0.722886i \(-0.257185\pi\)
\(558\) 0 0
\(559\) −27.3756 + 15.8053i −1.15787 + 0.668494i
\(560\) 0 0
\(561\) 21.4615 + 33.2804i 0.906106 + 1.40510i
\(562\) 0 0
\(563\) −5.11849 + 1.86298i −0.215719 + 0.0785151i −0.447619 0.894224i \(-0.647728\pi\)
0.231900 + 0.972740i \(0.425506\pi\)
\(564\) 0 0
\(565\) 10.1332 1.78676i 0.426307 0.0751694i
\(566\) 0 0
\(567\) −23.6583 + 2.69907i −0.993555 + 0.113350i
\(568\) 0 0
\(569\) 1.00282 0.176824i 0.0420403 0.00741284i −0.152588 0.988290i \(-0.548761\pi\)
0.194629 + 0.980877i \(0.437650\pi\)
\(570\) 0 0
\(571\) −3.36592 + 1.22509i −0.140859 + 0.0512686i −0.411488 0.911415i \(-0.634991\pi\)
0.270629 + 0.962684i \(0.412768\pi\)
\(572\) 0 0
\(573\) −15.4649 23.9814i −0.646055 1.00184i
\(574\) 0 0
\(575\) −5.78749 + 3.34141i −0.241355 + 0.139346i
\(576\) 0 0
\(577\) 23.0893i 0.961218i 0.876935 + 0.480609i \(0.159584\pi\)
−0.876935 + 0.480609i \(0.840416\pi\)
\(578\) 0 0
\(579\) −11.9282 12.8737i −0.495719 0.535014i
\(580\) 0 0
\(581\) 15.3642 + 15.2352i 0.637414 + 0.632061i
\(582\) 0 0
\(583\) 32.8738 27.5844i 1.36149 1.14243i
\(584\) 0 0
\(585\) 10.5691 + 0.807044i 0.436977 + 0.0333672i
\(586\) 0 0
\(587\) −0.0818717 0.464317i −0.00337921 0.0191644i 0.983072 0.183222i \(-0.0586528\pi\)
−0.986451 + 0.164058i \(0.947542\pi\)
\(588\) 0 0
\(589\) 12.5975 4.58513i 0.519073 0.188927i
\(590\) 0 0
\(591\) 37.1893 + 28.2111i 1.52976 + 1.16045i
\(592\) 0 0
\(593\) 19.0760 33.0406i 0.783357 1.35681i −0.146619 0.989193i \(-0.546839\pi\)
0.929976 0.367621i \(-0.119828\pi\)
\(594\) 0 0
\(595\) −14.7197 1.22528i −0.603449 0.0502316i
\(596\) 0 0
\(597\) −20.0467 + 8.43373i −0.820456 + 0.345170i
\(598\) 0 0
\(599\) 17.1655 20.4570i 0.701362 0.835850i −0.291318 0.956626i \(-0.594094\pi\)
0.992680 + 0.120776i \(0.0385382\pi\)
\(600\) 0 0
\(601\) 26.0201 4.58804i 1.06138 0.187150i 0.384412 0.923162i \(-0.374404\pi\)
0.676969 + 0.736012i \(0.263293\pi\)
\(602\) 0 0
\(603\) 22.7815 + 31.7817i 0.927735 + 1.29425i
\(604\) 0 0
\(605\) 0.480040 + 2.72244i 0.0195164 + 0.110683i
\(606\) 0 0
\(607\) −2.40611 6.61074i −0.0976611 0.268322i 0.881236 0.472677i \(-0.156712\pi\)
−0.978897 + 0.204356i \(0.934490\pi\)
\(608\) 0 0
\(609\) 27.8924 + 11.2363i 1.13026 + 0.455316i
\(610\) 0 0
\(611\) −15.3807 + 8.88003i −0.622235 + 0.359248i
\(612\) 0 0
\(613\) 10.6152 18.3860i 0.428743 0.742604i −0.568019 0.823015i \(-0.692290\pi\)
0.996762 + 0.0804113i \(0.0256234\pi\)
\(614\) 0 0
\(615\) 9.11537 + 4.68130i 0.367567 + 0.188768i
\(616\) 0 0
\(617\) −16.1973 2.85602i −0.652079 0.114979i −0.162184 0.986761i \(-0.551854\pi\)
−0.489895 + 0.871782i \(0.662965\pi\)
\(618\) 0 0
\(619\) 9.90984 27.2271i 0.398310 1.09435i −0.564797 0.825230i \(-0.691045\pi\)
0.963107 0.269118i \(-0.0867323\pi\)
\(620\) 0 0
\(621\) 7.33242 3.97292i 0.294240 0.159428i
\(622\) 0 0
\(623\) −0.987741 10.7668i −0.0395730 0.431362i
\(624\) 0 0
\(625\) 10.0790 + 8.45731i 0.403161 + 0.338292i
\(626\) 0 0
\(627\) 30.3492 19.5712i 1.21203 0.781600i
\(628\) 0 0
\(629\) −7.43608 12.8797i −0.296496 0.513546i
\(630\) 0 0
\(631\) −7.51188 + 13.0110i −0.299043 + 0.517958i −0.975917 0.218141i \(-0.930001\pi\)
0.676874 + 0.736099i \(0.263334\pi\)
\(632\) 0 0
\(633\) 5.81238 + 6.27313i 0.231021 + 0.249334i
\(634\) 0 0
\(635\) −3.02955 + 1.10267i −0.120224 + 0.0437580i
\(636\) 0 0
\(637\) 13.3261 23.5378i 0.528000 0.932601i
\(638\) 0 0
\(639\) −37.0438 + 10.3661i −1.46543 + 0.410078i
\(640\) 0 0
\(641\) 5.13002 + 6.11372i 0.202624 + 0.241478i 0.857781 0.514015i \(-0.171842\pi\)
−0.655158 + 0.755492i \(0.727398\pi\)
\(642\) 0 0
\(643\) −10.8529 29.8181i −0.427996 1.17591i −0.947027 0.321154i \(-0.895929\pi\)
0.519031 0.854756i \(-0.326293\pi\)
\(644\) 0 0
\(645\) −12.8548 1.62013i −0.506157 0.0637925i
\(646\) 0 0
\(647\) −0.285978 0.495329i −0.0112430 0.0194734i 0.860349 0.509705i \(-0.170245\pi\)
−0.871592 + 0.490232i \(0.836912\pi\)
\(648\) 0 0
\(649\) −2.88985 1.66846i −0.113437 0.0654926i
\(650\) 0 0
\(651\) −8.20747 7.37492i −0.321676 0.289046i
\(652\) 0 0
\(653\) 40.4916 + 7.13976i 1.58456 + 0.279400i 0.895417 0.445228i \(-0.146877\pi\)
0.689140 + 0.724628i \(0.257988\pi\)
\(654\) 0 0
\(655\) 8.11335 6.80791i 0.317015 0.266007i
\(656\) 0 0
\(657\) 14.0340 3.92718i 0.547518 0.153214i
\(658\) 0 0
\(659\) −4.33314 + 11.9052i −0.168795 + 0.463761i −0.995031 0.0995628i \(-0.968256\pi\)
0.826236 + 0.563324i \(0.190478\pi\)
\(660\) 0 0
\(661\) 8.08600 + 1.42578i 0.314509 + 0.0554564i 0.328674 0.944443i \(-0.393398\pi\)
−0.0141656 + 0.999900i \(0.504509\pi\)
\(662\) 0 0
\(663\) 39.0379 + 12.0718i 1.51610 + 0.468828i
\(664\) 0 0
\(665\) −1.11736 + 13.4232i −0.0433294 + 0.520530i
\(666\) 0 0
\(667\) −10.5316 −0.407786
\(668\) 0 0
\(669\) 12.2625 + 19.0155i 0.474097 + 0.735183i
\(670\) 0 0
\(671\) −8.01346 + 45.4466i −0.309356 + 1.75445i
\(672\) 0 0
\(673\) −33.8139 + 28.3732i −1.30343 + 1.09371i −0.313889 + 0.949460i \(0.601632\pi\)
−0.989542 + 0.144248i \(0.953924\pi\)
\(674\) 0 0
\(675\) −16.1920 14.3506i −0.623231 0.552356i
\(676\) 0 0
\(677\) −3.91905 22.2260i −0.150621 0.854216i −0.962680 0.270641i \(-0.912764\pi\)
0.812059 0.583575i \(-0.198347\pi\)
\(678\) 0 0
\(679\) 30.9515 + 8.15370i 1.18781 + 0.312910i
\(680\) 0 0
\(681\) −22.3035 + 14.3828i −0.854671 + 0.551151i
\(682\) 0 0
\(683\) 10.1811 + 5.87807i 0.389569 + 0.224918i 0.681974 0.731377i \(-0.261122\pi\)
−0.292404 + 0.956295i \(0.594455\pi\)
\(684\) 0 0
\(685\) 3.68292 + 2.12634i 0.140717 + 0.0812431i
\(686\) 0 0
\(687\) −11.8054 + 10.9383i −0.450403 + 0.417321i
\(688\) 0 0
\(689\) 7.68925 43.6079i 0.292937 1.66133i
\(690\) 0 0
\(691\) 11.6847 + 13.9253i 0.444506 + 0.529742i 0.941049 0.338270i \(-0.109842\pi\)
−0.496543 + 0.868012i \(0.665397\pi\)
\(692\) 0 0
\(693\) −25.9649 14.4667i −0.986326 0.549545i
\(694\) 0 0
\(695\) −6.57213 + 18.0568i −0.249295 + 0.684933i
\(696\) 0 0
\(697\) 30.2605 + 25.3915i 1.14620 + 0.961773i
\(698\) 0 0
\(699\) 12.9603 + 9.83142i 0.490202 + 0.371859i
\(700\) 0 0
\(701\) 10.7142i 0.404669i 0.979317 + 0.202334i \(0.0648527\pi\)
−0.979317 + 0.202334i \(0.935147\pi\)
\(702\) 0 0
\(703\) −11.7453 + 6.78113i −0.442981 + 0.255755i
\(704\) 0 0
\(705\) −7.22231 0.910250i −0.272008 0.0342820i
\(706\) 0 0
\(707\) 5.57958 + 5.53272i 0.209842 + 0.208079i
\(708\) 0 0
\(709\) −6.72909 2.44919i −0.252716 0.0919812i 0.212556 0.977149i \(-0.431821\pi\)
−0.465272 + 0.885168i \(0.654043\pi\)
\(710\) 0 0
\(711\) 13.9622 + 9.54819i 0.523625 + 0.358085i
\(712\) 0 0
\(713\) 3.63142 + 1.32173i 0.135998 + 0.0494991i
\(714\) 0 0
\(715\) 10.1358 + 8.50491i 0.379056 + 0.318066i
\(716\) 0 0
\(717\) −3.35279 14.7374i −0.125212 0.550380i
\(718\) 0 0
\(719\) 6.42531 + 11.1290i 0.239624 + 0.415040i 0.960606 0.277913i \(-0.0896426\pi\)
−0.720983 + 0.692953i \(0.756309\pi\)
\(720\) 0 0
\(721\) 1.99845 24.0080i 0.0744261 0.894106i
\(722\) 0 0
\(723\) −9.77256 + 0.480815i −0.363445 + 0.0178817i
\(724\) 0 0
\(725\) 9.34506 + 25.6753i 0.347067 + 0.953558i
\(726\) 0 0
\(727\) 25.2662 + 30.1111i 0.937071 + 1.11676i 0.992975 + 0.118322i \(0.0377514\pi\)
−0.0559043 + 0.998436i \(0.517804\pi\)
\(728\) 0 0
\(729\) 19.7145 + 18.4483i 0.730166 + 0.683270i
\(730\) 0 0
\(731\) −46.9343 17.0827i −1.73593 0.631827i
\(732\) 0 0
\(733\) 4.42383 5.27212i 0.163398 0.194730i −0.678133 0.734939i \(-0.737211\pi\)
0.841531 + 0.540209i \(0.181655\pi\)
\(734\) 0 0
\(735\) 10.1824 4.38521i 0.375582 0.161751i
\(736\) 0 0
\(737\) 48.8109i 1.79797i
\(738\) 0 0
\(739\) 16.2662 0.598360 0.299180 0.954197i \(-0.403287\pi\)
0.299180 + 0.954197i \(0.403287\pi\)
\(740\) 0 0
\(741\) 11.0085 35.5995i 0.404408 1.30778i
\(742\) 0 0
\(743\) −4.66918 + 5.56451i −0.171296 + 0.204142i −0.844862 0.534985i \(-0.820317\pi\)
0.673566 + 0.739127i \(0.264762\pi\)
\(744\) 0 0
\(745\) −12.0796 + 2.12995i −0.442561 + 0.0780354i
\(746\) 0 0
\(747\) 1.86798 24.4631i 0.0683456 0.895057i
\(748\) 0 0
\(749\) 16.0116 34.7185i 0.585051 1.26859i
\(750\) 0 0
\(751\) 5.09362 28.8874i 0.185869 1.05411i −0.738965 0.673744i \(-0.764685\pi\)
0.924834 0.380371i \(-0.124204\pi\)
\(752\) 0 0
\(753\) −1.24212 + 1.63743i −0.0452654 + 0.0596711i
\(754\) 0 0
\(755\) 9.56447 0.348087
\(756\) 0 0
\(757\) 20.1619 0.732796 0.366398 0.930458i \(-0.380591\pi\)
0.366398 + 0.930458i \(0.380591\pi\)
\(758\) 0 0
\(759\) 10.3282 + 1.30169i 0.374890 + 0.0472485i
\(760\) 0 0
\(761\) 7.77530 44.0959i 0.281855 1.59848i −0.434455 0.900694i \(-0.643059\pi\)
0.716309 0.697783i \(-0.245830\pi\)
\(762\) 0 0
\(763\) 19.5033 13.7793i 0.706068 0.498845i
\(764\) 0 0
\(765\) 9.75751 + 13.6124i 0.352783 + 0.492156i
\(766\) 0 0
\(767\) −3.39090 + 0.597907i −0.122438 + 0.0215892i
\(768\) 0 0
\(769\) −7.23057 + 8.61705i −0.260741 + 0.310739i −0.880493 0.474058i \(-0.842789\pi\)
0.619752 + 0.784797i \(0.287233\pi\)
\(770\) 0 0
\(771\) 14.2524 + 15.3822i 0.513287 + 0.553976i
\(772\) 0 0
\(773\) 20.3371 0.731475 0.365737 0.930718i \(-0.380817\pi\)
0.365737 + 0.930718i \(0.380817\pi\)
\(774\) 0 0
\(775\) 10.0260i 0.360143i
\(776\) 0 0
\(777\) 9.47254 + 5.90570i 0.339826 + 0.211866i
\(778\)