Properties

Label 756.2.ck.a.605.15
Level 756
Weight 2
Character 756.605
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 \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 605.15
Character \(\chi\) \(=\) 756.605
Dual form 756.2.ck.a.5.15

$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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 −0.999508 0.0313798i \(-0.990010\pi\)
0.928497 0.371339i \(-0.121101\pi\)
\(6\) 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 −0.412637 0.910895i \(-0.635392\pi\)
−0.699297 + 0.714831i \(0.746503\pi\)
\(12\) 0 0
\(13\) −2.48376 2.96003i −0.688872 0.820965i 0.302347 0.953198i \(-0.402230\pi\)
−0.991219 + 0.132233i \(0.957785\pi\)
\(14\) 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 \(-0.779492\pi\)
0.769495 0.638653i \(-0.220508\pi\)
\(20\) 0 0
\(21\) 4.04398 + 2.15551i 0.882469 + 0.470370i
\(22\) 0 0
\(23\) −1.03164 1.22946i −0.215113 0.256361i 0.647688 0.761906i \(-0.275736\pi\)
−0.862800 + 0.505545i \(0.831292\pi\)
\(24\) 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 −0.215824 0.976432i \(-0.569244\pi\)
0.999076 + 0.0429895i \(0.0136882\pi\)
\(30\) 0 0
\(31\) −0.823531 + 2.26263i −0.147911 + 0.406381i −0.991417 0.130738i \(-0.958265\pi\)
0.843506 + 0.537119i \(0.180487\pi\)
\(32\) 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 −0.748372 0.663279i \(-0.769164\pi\)
0.948603 + 0.316470i \(0.102498\pi\)
\(38\) 0 0
\(39\) −6.39400 + 1.97723i −1.02386 + 0.316610i
\(40\) 0 0
\(41\) −4.95635 + 4.15887i −0.774052 + 0.649506i −0.941743 0.336333i \(-0.890813\pi\)
0.167691 + 0.985840i \(0.446369\pi\)
\(42\) 0 0
\(43\) 7.68736 2.79797i 1.17231 0.426686i 0.318831 0.947812i \(-0.396710\pi\)
0.853480 + 0.521125i \(0.174488\pi\)
\(44\) 0 0
\(45\) −1.59818 + 2.22956i −0.238242 + 0.332364i
\(46\) 0 0
\(47\) 4.31905 1.57200i 0.629998 0.229300i −0.00723267 0.999974i \(-0.502302\pi\)
0.637230 + 0.770673i \(0.280080\pi\)
\(48\) 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 −0.373164 0.927765i \(-0.621727\pi\)
−0.990050 + 0.140713i \(0.955060\pi\)
\(54\) 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 −0.597271 0.802039i \(-0.703748\pi\)
0.686140 + 0.727470i \(0.259304\pi\)
\(60\) 0 0
\(61\) 4.21480 + 11.5801i 0.539650 + 1.48268i 0.847267 + 0.531167i \(0.178246\pi\)
−0.307617 + 0.951510i \(0.599531\pi\)
\(62\) 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 0.734093 + 0.679049i \(0.237607\pi\)
−0.457574 + 0.889172i \(0.651281\pi\)
\(68\) 0 0
\(69\) −2.65578 + 0.821252i −0.319718 + 0.0988671i
\(70\) 0 0
\(71\) 11.1044 6.41115i 1.31785 0.760864i 0.334471 0.942406i \(-0.391442\pi\)
0.983383 + 0.181542i \(0.0581089\pi\)
\(72\) 0 0
\(73\) −4.20689 + 2.42885i −0.492379 + 0.284275i −0.725561 0.688158i \(-0.758420\pi\)
0.233182 + 0.972433i \(0.425086\pi\)
\(74\) 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 0.878881 + 0.477042i \(0.158291\pi\)
−0.989036 + 0.147678i \(0.952820\pi\)
\(80\) 0 0
\(81\) −0.198980 + 8.99780i −0.0221089 + 0.999756i
\(82\) 0 0
\(83\) −6.26479 5.25678i −0.687650 0.577006i 0.230581 0.973053i \(-0.425937\pi\)
−0.918230 + 0.396047i \(0.870382\pi\)
\(84\) 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 −0.951640 0.307215i \(-0.900603\pi\)
0.531525 0.847043i \(-0.321619\pi\)
\(98\) 0 0
\(99\) 6.34159 + 9.27326i 0.637354 + 0.931998i
\(100\) 0 0
\(101\) −2.27509 1.90902i −0.226380 0.189955i 0.522542 0.852613i \(-0.324984\pi\)
−0.748922 + 0.662658i \(0.769428\pi\)
\(102\) 0 0
\(103\) 8.96723 1.58117i 0.883568 0.155797i 0.286589 0.958054i \(-0.407479\pi\)
0.596979 + 0.802257i \(0.296368\pi\)
\(104\) 0 0
\(105\) 1.29893 3.98389i 0.126763 0.388788i
\(106\) 0 0
\(107\) 12.5146 7.22532i 1.20983 0.698498i 0.247111 0.968987i \(-0.420519\pi\)
0.962723 + 0.270489i \(0.0871855\pi\)
\(108\) 0 0
\(109\) 4.51287 7.81653i 0.432255 0.748688i −0.564812 0.825220i \(-0.691051\pi\)
0.997067 + 0.0765319i \(0.0243847\pi\)
\(110\) 0 0
\(111\) −2.54989 3.36139i −0.242025 0.319049i
\(112\) 0 0
\(113\) −3.84867 + 10.5741i −0.362053 + 0.994732i 0.616250 + 0.787551i \(0.288651\pi\)
−0.978303 + 0.207181i \(0.933571\pi\)
\(114\) 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 −0.777148 0.629318i \(-0.783334\pi\)
0.933579 + 0.358370i \(0.116668\pi\)
\(128\) 0 0
\(129\) 0.696301 14.1523i 0.0613059 1.24604i
\(130\) 0 0
\(131\) −8.87289 + 7.44524i −0.775228 + 0.650493i −0.942042 0.335495i \(-0.891096\pi\)
0.166814 + 0.985988i \(0.446652\pi\)
\(132\) 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 0.988911 0.148512i \(-0.0474484\pi\)
−0.853011 + 0.521893i \(0.825226\pi\)
\(138\) 0 0
\(139\) 20.6952 3.64913i 1.75535 0.309515i 0.798910 0.601450i \(-0.205410\pi\)
0.956438 + 0.291935i \(0.0942992\pi\)
\(140\) 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 −0.597200 0.802092i \(-0.703720\pi\)
0.973057 0.230566i \(-0.0740576\pi\)
\(150\) 0 0
\(151\) −1.81633 + 10.3009i −0.147811 + 0.838279i 0.817256 + 0.576275i \(0.195494\pi\)
−0.965067 + 0.262004i \(0.915617\pi\)
\(152\) 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 −0.976444 0.215770i \(-0.930774\pi\)
−0.0429337 0.999078i \(-0.513670\pi\)
\(158\) 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 0.998325 + 0.0578512i \(0.0184249\pi\)
−0.449062 + 0.893501i \(0.648242\pi\)
\(164\) 0 0
\(165\) 5.46680 + 2.29991i 0.425590 + 0.179048i
\(166\) 0 0
\(167\) −2.12777 0.774444i −0.164652 0.0599283i 0.258379 0.966044i \(-0.416812\pi\)
−0.423031 + 0.906115i \(0.639034\pi\)
\(168\) 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 −0.908621 0.417621i \(-0.862864\pi\)
−0.569057 0.822298i \(-0.692692\pi\)
\(174\) 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 \(-0.948019\pi\)
0.986696 0.162577i \(-0.0519805\pi\)
\(180\) 0 0
\(181\) −2.32397 1.34175i −0.172740 0.0997313i 0.411137 0.911573i \(-0.365132\pi\)
−0.583877 + 0.811842i \(0.698465\pi\)
\(182\) 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 −0.447557 0.894256i \(-0.647706\pi\)
−0.726419 + 0.687252i \(0.758817\pi\)
\(192\) 0 0
\(193\) −9.52163 3.46559i −0.685382 0.249459i −0.0242252 0.999707i \(-0.507712\pi\)
−0.661157 + 0.750248i \(0.729934\pi\)
\(194\) 0 0
\(195\) 2.79577 + 5.44389i 0.200209 + 0.389845i
\(196\) 0 0
\(197\) 23.3394 + 13.4750i 1.66286 + 0.960054i 0.971338 + 0.237701i \(0.0763939\pi\)
0.691524 + 0.722353i \(0.256939\pi\)
\(198\) 0 0
\(199\) 12.5565i 0.890107i −0.895504 0.445053i \(-0.853185\pi\)
0.895504 0.445053i \(-0.146815\pi\)
\(200\) 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 0.496750 0.867894i \(-0.334527\pi\)
−0.177339 + 0.984150i \(0.556749\pi\)
\(212\) 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 0.586908 0.809654i \(-0.300345\pi\)
0.274595 + 0.961560i \(0.411456\pi\)
\(224\) 0 0
\(225\) −11.2622 5.40402i −0.750814 0.360268i
\(226\) 0 0
\(227\) 2.66067 15.0894i 0.176595 1.00152i −0.759692 0.650284i \(-0.774650\pi\)
0.936287 0.351237i \(-0.114239\pi\)
\(228\) 0 0
\(229\) 3.17798 8.73143i 0.210007 0.576989i −0.789308 0.613997i \(-0.789561\pi\)
0.999315 + 0.0370081i \(0.0117827\pi\)
\(230\) 0 0
\(231\) −13.5120 10.5789i −0.889025 0.696041i
\(232\) 0 0
\(233\) 8.13366 + 4.69597i 0.532854 + 0.307643i 0.742178 0.670203i \(-0.233793\pi\)
−0.209324 + 0.977846i \(0.567126\pi\)
\(234\) 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 −0.444523 0.895767i \(-0.646627\pi\)
−0.111345 + 0.993782i \(0.535516\pi\)
\(240\) 0 0
\(241\) −1.93208 5.30834i −0.124456 0.341940i 0.861780 0.507282i \(-0.169350\pi\)
−0.986236 + 0.165342i \(0.947127\pi\)
\(242\) 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 −0.846694 0.532081i \(-0.821410\pi\)
0.884142 + 0.467218i \(0.154744\pi\)
\(252\) 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 0.671535 0.740973i \(-0.265635\pi\)
0.0381371 + 0.999273i \(0.487858\pi\)
\(258\) 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 −0.793720 0.608283i \(-0.791859\pi\)
0.736870 + 0.676035i \(0.236303\pi\)
\(264\) 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 −0.661843 0.749642i \(-0.730225\pi\)
0.980131 + 0.198352i \(0.0635588\pi\)
\(270\) 0 0
\(271\) 11.2170 6.47615i 0.681386 0.393398i −0.118991 0.992895i \(-0.537966\pi\)
0.800377 + 0.599497i \(0.204633\pi\)
\(272\) 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 0.0451263 0.998981i \(-0.485631\pi\)
−0.975968 + 0.217912i \(0.930075\pi\)
\(278\) 0 0
\(279\) 6.58009 2.98024i 0.393940 0.178422i
\(280\) 0 0
\(281\) −9.35867 25.7127i −0.558291 1.53389i −0.822115 0.569322i \(-0.807206\pi\)
0.263824 0.964571i \(-0.415016\pi\)
\(282\) 0 0
\(283\) −21.6032 + 3.80923i −1.28418 + 0.226435i −0.773754 0.633486i \(-0.781623\pi\)
−0.510426 + 0.859922i \(0.670512\pi\)
\(284\) 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 0.957294 + 0.289116i \(0.0933612\pi\)
−0.800679 + 0.599094i \(0.795528\pi\)
\(294\) 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 −0.977221 0.212223i \(-0.931930\pi\)
−0.304820 + 0.952410i \(0.598596\pi\)
\(308\) 0 0
\(309\) 3.49860 15.3784i 0.199028 0.874844i
\(310\) 0 0
\(311\) −0.161417 0.915442i −0.00915313 0.0519100i 0.979889 0.199543i \(-0.0639457\pi\)
−0.989042 + 0.147633i \(0.952835\pi\)
\(312\) 0 0
\(313\) 3.09257 3.68558i 0.174802 0.208321i −0.671529 0.740978i \(-0.734362\pi\)
0.846331 + 0.532657i \(0.178807\pi\)
\(314\) 0 0
\(315\) −5.48791 4.74960i −0.309209 0.267610i
\(316\) 0 0
\(317\) 4.48170 + 12.3134i 0.251718 + 0.691588i 0.999614 + 0.0277732i \(0.00884162\pi\)
−0.747897 + 0.663815i \(0.768936\pi\)
\(318\) 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 0.178739 0.983896i \(-0.442798\pi\)
0.769359 + 0.638817i \(0.220576\pi\)
\(332\) 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 −0.995404 0.0957659i \(-0.969470\pi\)
−0.0785390 + 0.996911i \(0.525026\pi\)
\(338\) 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 0.626041 + 0.779790i \(0.284674\pi\)
−0.980815 + 0.194942i \(0.937548\pi\)
\(348\) 0 0
\(349\) −5.91691 + 7.05150i −0.316725 + 0.377458i −0.900795 0.434245i \(-0.857015\pi\)
0.584070 + 0.811704i \(0.301459\pi\)
\(350\) 0 0
\(351\) 17.6534 + 9.56512i 0.942268 + 0.510548i
\(352\) 0 0
\(353\) −24.3476 + 8.86179i −1.29589 + 0.471666i −0.895656 0.444747i \(-0.853293\pi\)
−0.400234 + 0.916413i \(0.631071\pi\)
\(354\) 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 \(-0.805195\pi\)
0.818503 0.574503i \(-0.194805\pi\)
\(360\) 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 −0.243363 0.969935i \(-0.578251\pi\)
−0.560424 + 0.828206i \(0.689362\pi\)
\(368\) 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 −0.883273 0.468858i \(-0.844666\pi\)
0.669647 0.742680i \(-0.266446\pi\)
\(374\) 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 −0.927698 0.373331i \(-0.878216\pi\)
0.744065 0.668108i \(-0.232895\pi\)
\(384\) 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 −0.615898 0.787826i \(-0.711207\pi\)
−0.848207 + 0.529665i \(0.822318\pi\)
\(390\) 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 \(-0.704716\pi\)
0.599707 0.800220i \(-0.295284\pi\)
\(398\) 0 0
\(399\) 12.0011 22.5155i 0.600807 1.12718i
\(400\) 0 0
\(401\) 6.72607 + 8.01582i 0.335884 + 0.400291i 0.907378 0.420315i \(-0.138080\pi\)
−0.571494 + 0.820606i \(0.693636\pi\)
\(402\) 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 −0.931092 0.364784i \(-0.881143\pi\)
0.947736 + 0.319054i \(0.103365\pi\)
\(410\) 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 −0.345328 0.938482i \(-0.612232\pi\)
0.864259 + 0.503047i \(0.167788\pi\)
\(420\) 0 0
\(421\) 6.03019 2.19481i 0.293893 0.106968i −0.190866 0.981616i \(-0.561130\pi\)
0.484759 + 0.874648i \(0.338907\pi\)
\(422\) 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 0.695384 0.718638i \(-0.255234\pi\)
−0.274667 + 0.961539i \(0.588568\pi\)
\(432\) 0 0
\(433\) 15.6232i 0.750805i −0.926862 0.375403i \(-0.877504\pi\)
0.926862 0.375403i \(-0.122496\pi\)
\(434\) 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 −0.939881 0.341502i \(-0.889064\pi\)
0.500477 0.865750i \(-0.333158\pi\)
\(440\) 0 0
\(441\) 11.7076 + 17.4337i 0.557504 + 0.830175i
\(442\) 0 0
\(443\) 21.9759 26.1899i 1.04411 1.24432i 0.0751299 0.997174i \(-0.476063\pi\)
0.968978 0.247146i \(-0.0794927\pi\)
\(444\) 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 0.116812 0.993154i \(-0.462733\pi\)
0.918502 + 0.395415i \(0.129399\pi\)
\(450\) 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 0.576720 + 0.816942i \(0.304333\pi\)
−0.821350 + 0.570425i \(0.806779\pi\)
\(458\) 0 0
\(459\) 29.5070 11.6528i 1.37727 0.543905i
\(460\) 0 0
\(461\) 16.9479 + 14.2210i 0.789344 + 0.662338i 0.945583 0.325381i \(-0.105493\pi\)
−0.156239 + 0.987719i \(0.549937\pi\)
\(462\) 0 0
\(463\) −6.48204 36.7614i −0.301246 1.70845i −0.640670 0.767816i \(-0.721343\pi\)
0.339425 0.940633i \(-0.389768\pi\)
\(464\) 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 0.972706 0.232042i \(-0.0745405\pi\)
−0.0596077 + 0.998222i \(0.518985\pi\)
\(480\) 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 −0.820183 0.572101i \(-0.806129\pi\)
0.905545 + 0.424249i \(0.139462\pi\)
\(488\) 0 0
\(489\) 24.1014 3.03758i 1.08990 0.137364i
\(490\) 0 0
\(491\) −10.2584 + 28.1847i −0.462955 + 1.27196i 0.460298 + 0.887764i \(0.347743\pi\)
−0.923253 + 0.384193i \(0.874480\pi\)
\(492\) 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 0.702492 0.711692i \(-0.252071\pi\)
0.0806736 + 0.996741i \(0.474293\pi\)
\(500\) 0 0
\(501\) −2.66555 + 2.87685i −0.119088 + 0.128528i
\(502\) 0 0
\(503\) 21.0298 + 36.4246i 0.937670 + 1.62409i 0.769801 + 0.638284i \(0.220355\pi\)
0.167869 + 0.985809i \(0.446311\pi\)
\(504\) 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 −0.955098 0.296289i \(-0.904251\pi\)
0.125936 + 0.992038i \(0.459807\pi\)
\(510\) 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 0.988812 0.149170i \(-0.0476603\pi\)
−0.623591 + 0.781751i \(0.714327\pi\)
\(522\) 0 0
\(523\) −8.45882 4.88370i −0.369878 0.213549i 0.303527 0.952823i \(-0.401836\pi\)
−0.673405 + 0.739273i \(0.735169\pi\)
\(524\) 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 0.983547 + 0.180654i \(0.0578214\pi\)
−0.335322 + 0.942103i \(0.608845\pi\)
\(542\) 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 −0.0558860 + 0.998437i \(0.517798\pi\)
−0.288970 + 0.957338i \(0.593313\pi\)
\(548\) 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 \(0.257185\pi\)
−0.690968 + 0.722886i \(0.742815\pi\)
\(558\) 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 0.231900 0.972740i \(-0.425506\pi\)
−0.447619 + 0.894224i \(0.647728\pi\)
\(564\) 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 0.194629 0.980877i \(-0.437650\pi\)
−0.152588 + 0.988290i \(0.548761\pi\)
\(570\) 0 0
\(571\) −3.36592 1.22509i −0.140859 0.0512686i 0.270629 0.962684i \(-0.412768\pi\)
−0.411488 + 0.911415i \(0.634991\pi\)
\(572\) 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 \(-0.840416\pi\)
0.876935 0.480609i \(-0.159584\pi\)
\(578\) 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 −0.986451 0.164058i \(-0.947542\pi\)
0.983072 + 0.183222i \(0.0586528\pi\)
\(588\) 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 0.929976 + 0.367621i \(0.119828\pi\)
−0.146619 + 0.989193i \(0.546839\pi\)
\(594\) 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 0.992680 0.120776i \(-0.0385382\pi\)
−0.291318 + 0.956626i \(0.594094\pi\)
\(600\) 0 0
\(601\) 26.0201 + 4.58804i 1.06138 + 0.187150i 0.676969 0.736012i \(-0.263293\pi\)
0.384412 + 0.923162i \(0.374404\pi\)
\(602\) 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 −0.978897 0.204356i \(-0.934490\pi\)
0.881236 + 0.472677i \(0.156712\pi\)
\(608\) 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 0.996762 0.0804113i \(-0.0256234\pi\)
−0.568019 + 0.823015i \(0.692290\pi\)
\(614\) 0 0
\(615\) 9.11537 4.68130i 0.367567 0.188768i
\(616\) 0 0
\(617\) −16.1973 + 2.85602i −0.652079 + 0.114979i −0.489895 0.871782i \(-0.662965\pi\)
−0.162184 + 0.986761i \(0.551854\pi\)
\(618\) 0 0
\(619\) 9.90984 + 27.2271i 0.398310 + 1.09435i 0.963107 + 0.269118i \(0.0867323\pi\)
−0.564797 + 0.825230i \(0.691045\pi\)
\(620\) 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 0.676874 0.736099i \(-0.263334\pi\)
−0.975917 + 0.218141i \(0.930001\pi\)
\(632\) 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 −0.655158 0.755492i \(-0.727398\pi\)
0.857781 + 0.514015i \(0.171842\pi\)
\(642\) 0 0
\(643\) −10.8529 + 29.8181i −0.427996 + 1.17591i 0.519031 + 0.854756i \(0.326293\pi\)
−0.947027 + 0.321154i \(0.895929\pi\)
\(644\) 0 0
\(645\) −12.8548 + 1.62013i −0.506157 + 0.0637925i
\(646\) 0 0
\(647\) −0.285978 + 0.495329i −0.0112430 + 0.0194734i −0.871592 0.490232i \(-0.836912\pi\)
0.860349 + 0.509705i \(0.170245\pi\)
\(648\) 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 0.689140 0.724628i \(-0.257988\pi\)
0.895417 + 0.445228i \(0.146877\pi\)
\(654\) 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 0.826236 0.563324i \(-0.190478\pi\)
−0.995031 + 0.0995628i \(0.968256\pi\)
\(660\) 0 0
\(661\) 8.08600 1.42578i 0.314509 0.0554564i −0.0141656 0.999900i \(-0.504509\pi\)
0.328674 + 0.944443i \(0.393398\pi\)
\(662\) 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 −0.989542 0.144248i \(-0.953924\pi\)
−0.313889 0.949460i \(-0.601632\pi\)
\(674\) 0 0
\(675\) −16.1920 + 14.3506i −0.623231 + 0.552356i
\(676\) 0 0
\(677\) −3.91905 + 22.2260i −0.150621 + 0.854216i 0.812059 + 0.583575i \(0.198347\pi\)
−0.962680 + 0.270641i \(0.912764\pi\)
\(678\) 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 −0.292404 0.956295i \(-0.594455\pi\)
0.681974 + 0.731377i \(0.261122\pi\)
\(684\) 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 −0.496543 0.868012i \(-0.665397\pi\)
0.941049 + 0.338270i \(0.109842\pi\)
\(692\) 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 \(-0.935147\pi\)
0.979317 0.202334i \(-0.0648527\pi\)
\(702\) 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 −0.465272 0.885168i \(-0.654043\pi\)
0.212556 + 0.977149i \(0.431821\pi\)
\(710\) 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 −0.720983 0.692953i \(-0.756309\pi\)
0.960606 + 0.277913i \(0.0896426\pi\)
\(720\) 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 −0.0559043 0.998436i \(-0.517804\pi\)
0.992975 0.118322i \(-0.0377514\pi\)
\(728\) 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 0.841531 0.540209i \(-0.181655\pi\)
−0.678133 + 0.734939i \(0.737211\pi\)
\(734\) 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 0.673566 0.739127i \(-0.264762\pi\)
−0.844862 + 0.534985i \(0.820317\pi\)
\(744\) 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 0.924834 + 0.380371i \(0.124204\pi\)
−0.738965 + 0.673744i \(0.764685\pi\)
\(752\) 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 0.716309 + 0.697783i \(0.245830\pi\)
−0.434455 + 0.900694i \(0.643059\pi\)
\(762\) 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 0.619752 0.784797i \(-0.287233\pi\)
−0.880493 + 0.474058i \(0.842789\pi\)
\(770\) 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
\(778\)