Properties

Label 1323.2.g.e.667.2
Level $1323$
Weight $2$
Character 1323.667
Analytic conductor $10.564$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \(x^{6} - x^{3} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.2
Root \(-0.173648 - 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 1323.667
Dual form 1323.2.g.e.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.673648 + 1.16679i) q^{2} +(0.0923963 - 0.160035i) q^{4} +2.53209 q^{5} +2.94356 q^{8} +O(q^{10})\) \(q+(0.673648 + 1.16679i) q^{2} +(0.0923963 - 0.160035i) q^{4} +2.53209 q^{5} +2.94356 q^{8} +(1.70574 + 2.95442i) q^{10} -0.467911 q^{11} +(2.91147 + 5.04282i) q^{13} +(1.79813 + 3.11446i) q^{16} +(-1.93969 - 3.35965i) q^{17} +(-1.09240 + 1.89209i) q^{19} +(0.233956 - 0.405223i) q^{20} +(-0.315207 - 0.545955i) q^{22} +0.106067 q^{23} +1.41147 q^{25} +(-3.92262 + 6.79417i) q^{26} +(4.39053 - 7.60462i) q^{29} +(-3.84002 + 6.65111i) q^{31} +(0.520945 - 0.902302i) q^{32} +(2.61334 - 4.52644i) q^{34} +(3.84002 - 6.65111i) q^{37} -2.94356 q^{38} +7.45336 q^{40} +(1.11334 + 1.92836i) q^{41} +(-0.613341 + 1.06234i) q^{43} +(-0.0432332 + 0.0748822i) q^{44} +(0.0714517 + 0.123758i) q^{46} +(2.66637 + 4.61830i) q^{47} +(0.950837 + 1.64690i) q^{50} +1.07604 q^{52} +(-0.358441 - 0.620838i) q^{53} -1.18479 q^{55} +11.8307 q^{58} +(-0.368241 + 0.637812i) q^{59} +(0.479055 + 0.829748i) q^{61} -10.3473 q^{62} +8.59627 q^{64} +(7.37211 + 12.7689i) q^{65} +(4.81908 - 8.34689i) q^{67} -0.716881 q^{68} -13.2344 q^{71} +(-5.13429 - 8.89284i) q^{73} +10.3473 q^{74} +(0.201867 + 0.349643i) q^{76} +(6.31908 + 10.9450i) q^{79} +(4.55303 + 7.88609i) q^{80} +(-1.50000 + 2.59808i) q^{82} +(1.36571 - 2.36549i) q^{83} +(-4.91147 - 8.50692i) q^{85} -1.65270 q^{86} -1.37733 q^{88} +(4.05690 - 7.02676i) q^{89} +(0.00980018 - 0.0169744i) q^{92} +(-3.59240 + 6.22221i) q^{94} +(-2.76604 + 4.79093i) q^{95} +(-6.80200 + 11.7814i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 3q^{2} - 3q^{4} + 6q^{5} - 12q^{8} + O(q^{10}) \) \( 6q + 3q^{2} - 3q^{4} + 6q^{5} - 12q^{8} - 12q^{11} - 3q^{13} - 3q^{16} - 6q^{17} - 3q^{19} + 6q^{20} - 9q^{22} - 24q^{23} - 12q^{25} + 3q^{26} + 9q^{29} - 3q^{31} + 9q^{34} + 3q^{37} + 12q^{38} + 18q^{40} + 3q^{43} + 15q^{44} - 3q^{47} - 6q^{50} + 42q^{52} + 6q^{53} - 18q^{58} + 3q^{59} + 6q^{61} - 60q^{62} + 24q^{64} + 15q^{65} + 12q^{67} + 12q^{68} - 18q^{71} - 21q^{73} + 60q^{74} + 15q^{76} + 21q^{79} + 15q^{80} - 9q^{82} + 18q^{83} - 9q^{85} - 12q^{86} + 54q^{88} - 12q^{89} + 3q^{92} - 18q^{94} - 12q^{95} - 3q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.673648 + 1.16679i 0.476341 + 0.825047i 0.999633 0.0271067i \(-0.00862938\pi\)
−0.523291 + 0.852154i \(0.675296\pi\)
\(3\) 0 0
\(4\) 0.0923963 0.160035i 0.0461981 0.0800175i
\(5\) 2.53209 1.13238 0.566192 0.824273i \(-0.308416\pi\)
0.566192 + 0.824273i \(0.308416\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.94356 1.04071
\(9\) 0 0
\(10\) 1.70574 + 2.95442i 0.539401 + 0.934271i
\(11\) −0.467911 −0.141081 −0.0705403 0.997509i \(-0.522472\pi\)
−0.0705403 + 0.997509i \(0.522472\pi\)
\(12\) 0 0
\(13\) 2.91147 + 5.04282i 0.807498 + 1.39863i 0.914592 + 0.404378i \(0.132512\pi\)
−0.107094 + 0.994249i \(0.534155\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.79813 + 3.11446i 0.449533 + 0.778615i
\(17\) −1.93969 3.35965i −0.470445 0.814834i 0.528984 0.848632i \(-0.322573\pi\)
−0.999429 + 0.0337978i \(0.989240\pi\)
\(18\) 0 0
\(19\) −1.09240 + 1.89209i −0.250613 + 0.434074i −0.963695 0.267007i \(-0.913965\pi\)
0.713082 + 0.701081i \(0.247299\pi\)
\(20\) 0.233956 0.405223i 0.0523141 0.0906106i
\(21\) 0 0
\(22\) −0.315207 0.545955i −0.0672025 0.116398i
\(23\) 0.106067 0.0221165 0.0110582 0.999939i \(-0.496480\pi\)
0.0110582 + 0.999939i \(0.496480\pi\)
\(24\) 0 0
\(25\) 1.41147 0.282295
\(26\) −3.92262 + 6.79417i −0.769289 + 1.33245i
\(27\) 0 0
\(28\) 0 0
\(29\) 4.39053 7.60462i 0.815301 1.41214i −0.0938108 0.995590i \(-0.529905\pi\)
0.909112 0.416552i \(-0.136762\pi\)
\(30\) 0 0
\(31\) −3.84002 + 6.65111i −0.689688 + 1.19458i 0.282250 + 0.959341i \(0.408919\pi\)
−0.971939 + 0.235235i \(0.924414\pi\)
\(32\) 0.520945 0.902302i 0.0920909 0.159506i
\(33\) 0 0
\(34\) 2.61334 4.52644i 0.448184 0.776278i
\(35\) 0 0
\(36\) 0 0
\(37\) 3.84002 6.65111i 0.631296 1.09344i −0.355991 0.934489i \(-0.615857\pi\)
0.987287 0.158947i \(-0.0508099\pi\)
\(38\) −2.94356 −0.477509
\(39\) 0 0
\(40\) 7.45336 1.17848
\(41\) 1.11334 + 1.92836i 0.173875 + 0.301160i 0.939771 0.341804i \(-0.111038\pi\)
−0.765897 + 0.642964i \(0.777705\pi\)
\(42\) 0 0
\(43\) −0.613341 + 1.06234i −0.0935336 + 0.162005i −0.908996 0.416806i \(-0.863150\pi\)
0.815462 + 0.578811i \(0.196483\pi\)
\(44\) −0.0432332 + 0.0748822i −0.00651766 + 0.0112889i
\(45\) 0 0
\(46\) 0.0714517 + 0.123758i 0.0105350 + 0.0182471i
\(47\) 2.66637 + 4.61830i 0.388931 + 0.673648i 0.992306 0.123810i \(-0.0395112\pi\)
−0.603375 + 0.797457i \(0.706178\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.950837 + 1.64690i 0.134469 + 0.232907i
\(51\) 0 0
\(52\) 1.07604 0.149220
\(53\) −0.358441 0.620838i −0.0492356 0.0852786i 0.840357 0.542033i \(-0.182345\pi\)
−0.889593 + 0.456754i \(0.849012\pi\)
\(54\) 0 0
\(55\) −1.18479 −0.159757
\(56\) 0 0
\(57\) 0 0
\(58\) 11.8307 1.55345
\(59\) −0.368241 + 0.637812i −0.0479409 + 0.0830360i −0.889000 0.457907i \(-0.848599\pi\)
0.841059 + 0.540943i \(0.181933\pi\)
\(60\) 0 0
\(61\) 0.479055 + 0.829748i 0.0613368 + 0.106238i 0.895063 0.445939i \(-0.147130\pi\)
−0.833726 + 0.552178i \(0.813797\pi\)
\(62\) −10.3473 −1.31411
\(63\) 0 0
\(64\) 8.59627 1.07453
\(65\) 7.37211 + 12.7689i 0.914398 + 1.58378i
\(66\) 0 0
\(67\) 4.81908 8.34689i 0.588744 1.01973i −0.405653 0.914027i \(-0.632956\pi\)
0.994397 0.105708i \(-0.0337107\pi\)
\(68\) −0.716881 −0.0869346
\(69\) 0 0
\(70\) 0 0
\(71\) −13.2344 −1.57064 −0.785318 0.619092i \(-0.787501\pi\)
−0.785318 + 0.619092i \(0.787501\pi\)
\(72\) 0 0
\(73\) −5.13429 8.89284i −0.600923 1.04083i −0.992682 0.120761i \(-0.961467\pi\)
0.391759 0.920068i \(-0.371867\pi\)
\(74\) 10.3473 1.20285
\(75\) 0 0
\(76\) 0.201867 + 0.349643i 0.0231557 + 0.0401068i
\(77\) 0 0
\(78\) 0 0
\(79\) 6.31908 + 10.9450i 0.710952 + 1.23140i 0.964500 + 0.264082i \(0.0850689\pi\)
−0.253548 + 0.967323i \(0.581598\pi\)
\(80\) 4.55303 + 7.88609i 0.509045 + 0.881691i
\(81\) 0 0
\(82\) −1.50000 + 2.59808i −0.165647 + 0.286910i
\(83\) 1.36571 2.36549i 0.149907 0.259646i −0.781286 0.624173i \(-0.785436\pi\)
0.931193 + 0.364527i \(0.118769\pi\)
\(84\) 0 0
\(85\) −4.91147 8.50692i −0.532724 0.922705i
\(86\) −1.65270 −0.178216
\(87\) 0 0
\(88\) −1.37733 −0.146823
\(89\) 4.05690 7.02676i 0.430031 0.744835i −0.566845 0.823825i \(-0.691836\pi\)
0.996875 + 0.0789894i \(0.0251693\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.00980018 0.0169744i 0.00102174 0.00176970i
\(93\) 0 0
\(94\) −3.59240 + 6.22221i −0.370527 + 0.641772i
\(95\) −2.76604 + 4.79093i −0.283790 + 0.491539i
\(96\) 0 0
\(97\) −6.80200 + 11.7814i −0.690639 + 1.19622i 0.280990 + 0.959711i \(0.409337\pi\)
−0.971629 + 0.236511i \(0.923996\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.130415 0.225885i 0.0130415 0.0225885i
\(101\) −9.57398 −0.952646 −0.476323 0.879270i \(-0.658031\pi\)
−0.476323 + 0.879270i \(0.658031\pi\)
\(102\) 0 0
\(103\) −3.04189 −0.299726 −0.149863 0.988707i \(-0.547883\pi\)
−0.149863 + 0.988707i \(0.547883\pi\)
\(104\) 8.57011 + 14.8439i 0.840368 + 1.45556i
\(105\) 0 0
\(106\) 0.482926 0.836452i 0.0469059 0.0812434i
\(107\) −3.25877 + 5.64436i −0.315037 + 0.545660i −0.979445 0.201709i \(-0.935350\pi\)
0.664408 + 0.747370i \(0.268684\pi\)
\(108\) 0 0
\(109\) −5.31908 9.21291i −0.509475 0.882437i −0.999940 0.0109759i \(-0.996506\pi\)
0.490465 0.871461i \(-0.336827\pi\)
\(110\) −0.798133 1.38241i −0.0760990 0.131807i
\(111\) 0 0
\(112\) 0 0
\(113\) 2.58853 + 4.48346i 0.243508 + 0.421768i 0.961711 0.274065i \(-0.0883684\pi\)
−0.718203 + 0.695834i \(0.755035\pi\)
\(114\) 0 0
\(115\) 0.268571 0.0250443
\(116\) −0.811337 1.40528i −0.0753308 0.130477i
\(117\) 0 0
\(118\) −0.992259 −0.0913449
\(119\) 0 0
\(120\) 0 0
\(121\) −10.7811 −0.980096
\(122\) −0.645430 + 1.11792i −0.0584345 + 0.101211i
\(123\) 0 0
\(124\) 0.709607 + 1.22908i 0.0637246 + 0.110374i
\(125\) −9.08647 −0.812718
\(126\) 0 0
\(127\) −8.88207 −0.788157 −0.394078 0.919077i \(-0.628936\pi\)
−0.394078 + 0.919077i \(0.628936\pi\)
\(128\) 4.74897 + 8.22546i 0.419754 + 0.727035i
\(129\) 0 0
\(130\) −9.93242 + 17.2035i −0.871131 + 1.50884i
\(131\) 11.3628 0.992771 0.496385 0.868102i \(-0.334660\pi\)
0.496385 + 0.868102i \(0.334660\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 12.9855 1.12177
\(135\) 0 0
\(136\) −5.70961 9.88933i −0.489595 0.848003i
\(137\) 5.72462 0.489087 0.244544 0.969638i \(-0.421362\pi\)
0.244544 + 0.969638i \(0.421362\pi\)
\(138\) 0 0
\(139\) −0.461981 0.800175i −0.0391847 0.0678700i 0.845768 0.533551i \(-0.179143\pi\)
−0.884953 + 0.465681i \(0.845809\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −8.91534 15.4418i −0.748159 1.29585i
\(143\) −1.36231 2.35959i −0.113922 0.197319i
\(144\) 0 0
\(145\) 11.1172 19.2556i 0.923234 1.59909i
\(146\) 6.91740 11.9813i 0.572488 0.991579i
\(147\) 0 0
\(148\) −0.709607 1.22908i −0.0583294 0.101029i
\(149\) −8.72462 −0.714749 −0.357374 0.933961i \(-0.616328\pi\)
−0.357374 + 0.933961i \(0.616328\pi\)
\(150\) 0 0
\(151\) 18.4270 1.49956 0.749782 0.661685i \(-0.230158\pi\)
0.749782 + 0.661685i \(0.230158\pi\)
\(152\) −3.21554 + 5.56947i −0.260815 + 0.451744i
\(153\) 0 0
\(154\) 0 0
\(155\) −9.72328 + 16.8412i −0.780992 + 1.35272i
\(156\) 0 0
\(157\) 2.46198 4.26428i 0.196488 0.340326i −0.750900 0.660416i \(-0.770380\pi\)
0.947387 + 0.320090i \(0.103713\pi\)
\(158\) −8.51367 + 14.7461i −0.677311 + 1.17314i
\(159\) 0 0
\(160\) 1.31908 2.28471i 0.104282 0.180622i
\(161\) 0 0
\(162\) 0 0
\(163\) −3.81908 + 6.61484i −0.299133 + 0.518114i −0.975938 0.218049i \(-0.930031\pi\)
0.676805 + 0.736163i \(0.263364\pi\)
\(164\) 0.411474 0.0321307
\(165\) 0 0
\(166\) 3.68004 0.285627
\(167\) 2.82770 + 4.89771i 0.218814 + 0.378996i 0.954446 0.298385i \(-0.0964480\pi\)
−0.735632 + 0.677382i \(0.763115\pi\)
\(168\) 0 0
\(169\) −10.4534 + 18.1058i −0.804105 + 1.39275i
\(170\) 6.61721 11.4613i 0.507517 0.879045i
\(171\) 0 0
\(172\) 0.113341 + 0.196312i 0.00864215 + 0.0149687i
\(173\) −10.5346 18.2465i −0.800932 1.38725i −0.919003 0.394250i \(-0.871005\pi\)
0.118071 0.993005i \(-0.462329\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.841367 1.45729i −0.0634204 0.109847i
\(177\) 0 0
\(178\) 10.9317 0.819366
\(179\) −2.56031 4.43458i −0.191366 0.331456i 0.754337 0.656487i \(-0.227959\pi\)
−0.945703 + 0.325031i \(0.894625\pi\)
\(180\) 0 0
\(181\) 0.319955 0.0237821 0.0118910 0.999929i \(-0.496215\pi\)
0.0118910 + 0.999929i \(0.496215\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.312214 0.0230168
\(185\) 9.72328 16.8412i 0.714870 1.23819i
\(186\) 0 0
\(187\) 0.907604 + 1.57202i 0.0663706 + 0.114957i
\(188\) 0.985452 0.0718715
\(189\) 0 0
\(190\) −7.45336 −0.540724
\(191\) −7.78359 13.4816i −0.563200 0.975492i −0.997215 0.0745858i \(-0.976237\pi\)
0.434014 0.900906i \(-0.357097\pi\)
\(192\) 0 0
\(193\) −3.02094 + 5.23243i −0.217452 + 0.376639i −0.954028 0.299716i \(-0.903108\pi\)
0.736576 + 0.676355i \(0.236441\pi\)
\(194\) −18.3286 −1.31592
\(195\) 0 0
\(196\) 0 0
\(197\) −25.2344 −1.79788 −0.898939 0.438074i \(-0.855661\pi\)
−0.898939 + 0.438074i \(0.855661\pi\)
\(198\) 0 0
\(199\) 1.52094 + 2.63435i 0.107817 + 0.186744i 0.914886 0.403713i \(-0.132281\pi\)
−0.807069 + 0.590458i \(0.798947\pi\)
\(200\) 4.15476 0.293786
\(201\) 0 0
\(202\) −6.44949 11.1708i −0.453785 0.785978i
\(203\) 0 0
\(204\) 0 0
\(205\) 2.81908 + 4.88279i 0.196893 + 0.341029i
\(206\) −2.04916 3.54925i −0.142772 0.247288i
\(207\) 0 0
\(208\) −10.4704 + 18.1353i −0.725994 + 1.25746i
\(209\) 0.511144 0.885328i 0.0353566 0.0612394i
\(210\) 0 0
\(211\) 2.72668 + 4.72275i 0.187713 + 0.325128i 0.944487 0.328548i \(-0.106559\pi\)
−0.756775 + 0.653676i \(0.773226\pi\)
\(212\) −0.132474 −0.00909837
\(213\) 0 0
\(214\) −8.78106 −0.600261
\(215\) −1.55303 + 2.68993i −0.105916 + 0.183452i
\(216\) 0 0
\(217\) 0 0
\(218\) 7.16637 12.4125i 0.485368 0.840682i
\(219\) 0 0
\(220\) −0.109470 + 0.189608i −0.00738049 + 0.0127834i
\(221\) 11.2947 19.5630i 0.759766 1.31595i
\(222\) 0 0
\(223\) 7.09627 12.2911i 0.475201 0.823073i −0.524395 0.851475i \(-0.675709\pi\)
0.999597 + 0.0284023i \(0.00904195\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −3.48751 + 6.04055i −0.231986 + 0.401811i
\(227\) −2.89393 −0.192077 −0.0960385 0.995378i \(-0.530617\pi\)
−0.0960385 + 0.995378i \(0.530617\pi\)
\(228\) 0 0
\(229\) −9.16756 −0.605809 −0.302905 0.953021i \(-0.597956\pi\)
−0.302905 + 0.953021i \(0.597956\pi\)
\(230\) 0.180922 + 0.313366i 0.0119297 + 0.0206628i
\(231\) 0 0
\(232\) 12.9238 22.3847i 0.848489 1.46963i
\(233\) 6.63563 11.4932i 0.434715 0.752948i −0.562558 0.826758i \(-0.690183\pi\)
0.997272 + 0.0738103i \(0.0235159\pi\)
\(234\) 0 0
\(235\) 6.75150 + 11.6939i 0.440419 + 0.762828i
\(236\) 0.0680482 + 0.117863i 0.00442956 + 0.00767222i
\(237\) 0 0
\(238\) 0 0
\(239\) 4.76857 + 8.25941i 0.308453 + 0.534257i 0.978024 0.208491i \(-0.0668553\pi\)
−0.669571 + 0.742748i \(0.733522\pi\)
\(240\) 0 0
\(241\) 8.95811 0.577043 0.288521 0.957473i \(-0.406836\pi\)
0.288521 + 0.957473i \(0.406836\pi\)
\(242\) −7.26264 12.5793i −0.466860 0.808626i
\(243\) 0 0
\(244\) 0.177052 0.0113346
\(245\) 0 0
\(246\) 0 0
\(247\) −12.7219 −0.809477
\(248\) −11.3033 + 19.5780i −0.717763 + 1.24320i
\(249\) 0 0
\(250\) −6.12108 10.6020i −0.387131 0.670531i
\(251\) −24.9982 −1.57788 −0.788938 0.614473i \(-0.789369\pi\)
−0.788938 + 0.614473i \(0.789369\pi\)
\(252\) 0 0
\(253\) −0.0496299 −0.00312020
\(254\) −5.98339 10.3635i −0.375431 0.650266i
\(255\) 0 0
\(256\) 2.19800 3.80704i 0.137375 0.237940i
\(257\) 10.8520 0.676932 0.338466 0.940979i \(-0.390092\pi\)
0.338466 + 0.940979i \(0.390092\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 2.72462 0.168974
\(261\) 0 0
\(262\) 7.65451 + 13.2580i 0.472897 + 0.819082i
\(263\) −26.0874 −1.60862 −0.804309 0.594211i \(-0.797464\pi\)
−0.804309 + 0.594211i \(0.797464\pi\)
\(264\) 0 0
\(265\) −0.907604 1.57202i −0.0557537 0.0965682i
\(266\) 0 0
\(267\) 0 0
\(268\) −0.890530 1.54244i −0.0543978 0.0942197i
\(269\) 3.81655 + 6.61046i 0.232699 + 0.403047i 0.958602 0.284751i \(-0.0919109\pi\)
−0.725902 + 0.687798i \(0.758578\pi\)
\(270\) 0 0
\(271\) 1.70187 2.94772i 0.103381 0.179061i −0.809695 0.586852i \(-0.800367\pi\)
0.913076 + 0.407790i \(0.133701\pi\)
\(272\) 6.97565 12.0822i 0.422961 0.732590i
\(273\) 0 0
\(274\) 3.85638 + 6.67945i 0.232973 + 0.403520i
\(275\) −0.660444 −0.0398263
\(276\) 0 0
\(277\) −5.72193 −0.343798 −0.171899 0.985115i \(-0.554990\pi\)
−0.171899 + 0.985115i \(0.554990\pi\)
\(278\) 0.622426 1.07807i 0.0373306 0.0646585i
\(279\) 0 0
\(280\) 0 0
\(281\) 14.1887 24.5755i 0.846425 1.46605i −0.0379535 0.999280i \(-0.512084\pi\)
0.884378 0.466771i \(-0.154583\pi\)
\(282\) 0 0
\(283\) 2.28564 3.95885i 0.135867 0.235329i −0.790061 0.613028i \(-0.789951\pi\)
0.925929 + 0.377699i \(0.123285\pi\)
\(284\) −1.22281 + 2.11797i −0.0725605 + 0.125678i
\(285\) 0 0
\(286\) 1.83544 3.17907i 0.108532 0.187982i
\(287\) 0 0
\(288\) 0 0
\(289\) 0.975185 1.68907i 0.0573638 0.0993571i
\(290\) 29.9564 1.75910
\(291\) 0 0
\(292\) −1.89756 −0.111046
\(293\) −2.16385 3.74789i −0.126413 0.218954i 0.795871 0.605466i \(-0.207013\pi\)
−0.922285 + 0.386512i \(0.873680\pi\)
\(294\) 0 0
\(295\) −0.932419 + 1.61500i −0.0542875 + 0.0940287i
\(296\) 11.3033 19.5780i 0.656994 1.13795i
\(297\) 0 0
\(298\) −5.87733 10.1798i −0.340464 0.589702i
\(299\) 0.308811 + 0.534876i 0.0178590 + 0.0309327i
\(300\) 0 0
\(301\) 0 0
\(302\) 12.4133 + 21.5004i 0.714304 + 1.23721i
\(303\) 0 0
\(304\) −7.85710 −0.450635
\(305\) 1.21301 + 2.10100i 0.0694568 + 0.120303i
\(306\) 0 0
\(307\) −12.3773 −0.706411 −0.353206 0.935546i \(-0.614908\pi\)
−0.353206 + 0.935546i \(0.614908\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −26.2003 −1.48808
\(311\) 10.9927 19.0400i 0.623340 1.07966i −0.365519 0.930804i \(-0.619108\pi\)
0.988859 0.148853i \(-0.0475582\pi\)
\(312\) 0 0
\(313\) −6.94491 12.0289i −0.392549 0.679915i 0.600236 0.799823i \(-0.295073\pi\)
−0.992785 + 0.119908i \(0.961740\pi\)
\(314\) 6.63404 0.374380
\(315\) 0 0
\(316\) 2.33544 0.131379
\(317\) −3.09105 5.35386i −0.173611 0.300703i 0.766069 0.642759i \(-0.222210\pi\)
−0.939680 + 0.342056i \(0.888877\pi\)
\(318\) 0 0
\(319\) −2.05438 + 3.55829i −0.115023 + 0.199226i
\(320\) 21.7665 1.21678
\(321\) 0 0
\(322\) 0 0
\(323\) 8.47565 0.471598
\(324\) 0 0
\(325\) 4.10947 + 7.11781i 0.227952 + 0.394825i
\(326\) −10.2909 −0.569958
\(327\) 0 0
\(328\) 3.27719 + 5.67626i 0.180952 + 0.313419i
\(329\) 0 0
\(330\) 0 0
\(331\) −5.36571 9.29369i −0.294926 0.510827i 0.680041 0.733174i \(-0.261962\pi\)
−0.974968 + 0.222346i \(0.928628\pi\)
\(332\) −0.252374 0.437124i −0.0138508 0.0239903i
\(333\) 0 0
\(334\) −3.80974 + 6.59867i −0.208460 + 0.361063i
\(335\) 12.2023 21.1351i 0.666685 1.15473i
\(336\) 0 0
\(337\) 9.29726 + 16.1033i 0.506454 + 0.877204i 0.999972 + 0.00746831i \(0.00237726\pi\)
−0.493518 + 0.869735i \(0.664289\pi\)
\(338\) −28.1676 −1.53211
\(339\) 0 0
\(340\) −1.81521 −0.0984434
\(341\) 1.79679 3.11213i 0.0973016 0.168531i
\(342\) 0 0
\(343\) 0 0
\(344\) −1.80541 + 3.12706i −0.0973410 + 0.168600i
\(345\) 0 0
\(346\) 14.1932 24.5834i 0.763034 1.32161i
\(347\) −10.2062 + 17.6777i −0.547898 + 0.948987i 0.450521 + 0.892766i \(0.351238\pi\)
−0.998418 + 0.0562207i \(0.982095\pi\)
\(348\) 0 0
\(349\) −1.78106 + 3.08489i −0.0953379 + 0.165130i −0.909750 0.415157i \(-0.863726\pi\)
0.814412 + 0.580288i \(0.197060\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.243756 + 0.422197i −0.0129922 + 0.0225032i
\(353\) 10.0223 0.533433 0.266716 0.963775i \(-0.414061\pi\)
0.266716 + 0.963775i \(0.414061\pi\)
\(354\) 0 0
\(355\) −33.5107 −1.77857
\(356\) −0.749686 1.29849i −0.0397333 0.0688200i
\(357\) 0 0
\(358\) 3.44949 5.97470i 0.182311 0.315773i
\(359\) 4.74035 8.21053i 0.250186 0.433335i −0.713391 0.700766i \(-0.752841\pi\)
0.963577 + 0.267431i \(0.0861748\pi\)
\(360\) 0 0
\(361\) 7.11334 + 12.3207i 0.374386 + 0.648456i
\(362\) 0.215537 + 0.373321i 0.0113284 + 0.0196213i
\(363\) 0 0
\(364\) 0 0
\(365\) −13.0005 22.5175i −0.680476 1.17862i
\(366\) 0 0
\(367\) −16.1334 −0.842157 −0.421079 0.907024i \(-0.638348\pi\)
−0.421079 + 0.907024i \(0.638348\pi\)
\(368\) 0.190722 + 0.330341i 0.00994209 + 0.0172202i
\(369\) 0 0
\(370\) 26.2003 1.36209
\(371\) 0 0
\(372\) 0 0
\(373\) 14.0496 0.727462 0.363731 0.931504i \(-0.381503\pi\)
0.363731 + 0.931504i \(0.381503\pi\)
\(374\) −1.22281 + 2.11797i −0.0632301 + 0.109518i
\(375\) 0 0
\(376\) 7.84864 + 13.5942i 0.404763 + 0.701070i
\(377\) 51.1317 2.63341
\(378\) 0 0
\(379\) 16.0574 0.824812 0.412406 0.911000i \(-0.364689\pi\)
0.412406 + 0.911000i \(0.364689\pi\)
\(380\) 0.511144 + 0.885328i 0.0262212 + 0.0454164i
\(381\) 0 0
\(382\) 10.4868 18.1637i 0.536551 0.929334i
\(383\) −32.0205 −1.63617 −0.818086 0.575095i \(-0.804965\pi\)
−0.818086 + 0.575095i \(0.804965\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −8.14022 −0.414326
\(387\) 0 0
\(388\) 1.25696 + 2.17712i 0.0638124 + 0.110526i
\(389\) 30.0428 1.52323 0.761616 0.648029i \(-0.224406\pi\)
0.761616 + 0.648029i \(0.224406\pi\)
\(390\) 0 0
\(391\) −0.205737 0.356347i −0.0104046 0.0180212i
\(392\) 0 0
\(393\) 0 0
\(394\) −16.9991 29.4433i −0.856403 1.48333i
\(395\) 16.0005 + 27.7136i 0.805071 + 1.39442i
\(396\) 0 0
\(397\) −6.15998 + 10.6694i −0.309160 + 0.535482i −0.978179 0.207764i \(-0.933381\pi\)
0.669019 + 0.743246i \(0.266715\pi\)
\(398\) −2.04916 + 3.54925i −0.102715 + 0.177908i
\(399\) 0 0
\(400\) 2.53802 + 4.39598i 0.126901 + 0.219799i
\(401\) −20.9760 −1.04749 −0.523745 0.851875i \(-0.675465\pi\)
−0.523745 + 0.851875i \(0.675465\pi\)
\(402\) 0 0
\(403\) −44.7205 −2.22769
\(404\) −0.884600 + 1.53217i −0.0440105 + 0.0762284i
\(405\) 0 0
\(406\) 0 0
\(407\) −1.79679 + 3.11213i −0.0890635 + 0.154263i
\(408\) 0 0
\(409\) 12.8307 22.2234i 0.634437 1.09888i −0.352197 0.935926i \(-0.614565\pi\)
0.986634 0.162951i \(-0.0521012\pi\)
\(410\) −3.79813 + 6.57856i −0.187576 + 0.324892i
\(411\) 0 0
\(412\) −0.281059 + 0.486809i −0.0138468 + 0.0239833i
\(413\) 0 0
\(414\) 0 0
\(415\) 3.45811 5.98962i 0.169752 0.294019i
\(416\) 6.06687 0.297453
\(417\) 0 0
\(418\) 1.37733 0.0673672
\(419\) 0.739885 + 1.28152i 0.0361458 + 0.0626063i 0.883532 0.468370i \(-0.155159\pi\)
−0.847387 + 0.530976i \(0.821825\pi\)
\(420\) 0 0
\(421\) −6.55350 + 11.3510i −0.319398 + 0.553214i −0.980363 0.197203i \(-0.936814\pi\)
0.660965 + 0.750417i \(0.270147\pi\)
\(422\) −3.67365 + 6.36295i −0.178830 + 0.309743i
\(423\) 0 0
\(424\) −1.05509 1.82747i −0.0512398 0.0887500i
\(425\) −2.73783 4.74205i −0.132804 0.230023i
\(426\) 0 0
\(427\) 0 0
\(428\) 0.602196 + 1.04303i 0.0291083 + 0.0504170i
\(429\) 0 0
\(430\) −4.18479 −0.201809
\(431\) 8.86349 + 15.3520i 0.426939 + 0.739481i 0.996599 0.0823997i \(-0.0262584\pi\)
−0.569660 + 0.821881i \(0.692925\pi\)
\(432\) 0 0
\(433\) 5.83843 0.280577 0.140289 0.990111i \(-0.455197\pi\)
0.140289 + 0.990111i \(0.455197\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.96585 −0.0941472
\(437\) −0.115867 + 0.200688i −0.00554267 + 0.00960019i
\(438\) 0 0
\(439\) 14.9277 + 25.8555i 0.712459 + 1.23401i 0.963931 + 0.266151i \(0.0857518\pi\)
−0.251473 + 0.967864i \(0.580915\pi\)
\(440\) −3.48751 −0.166261
\(441\) 0 0
\(442\) 30.4347 1.44763
\(443\) 5.33275 + 9.23659i 0.253367 + 0.438844i 0.964451 0.264263i \(-0.0851288\pi\)
−0.711084 + 0.703107i \(0.751795\pi\)
\(444\) 0 0
\(445\) 10.2724 17.7924i 0.486960 0.843440i
\(446\) 19.1215 0.905432
\(447\) 0 0
\(448\) 0 0
\(449\) −3.55438 −0.167741 −0.0838707 0.996477i \(-0.526728\pi\)
−0.0838707 + 0.996477i \(0.526728\pi\)
\(450\) 0 0
\(451\) −0.520945 0.902302i −0.0245303 0.0424878i
\(452\) 0.956680 0.0449985
\(453\) 0 0
\(454\) −1.94949 3.37662i −0.0914942 0.158473i
\(455\) 0 0
\(456\) 0 0
\(457\) −2.51161 4.35024i −0.117488 0.203496i 0.801283 0.598285i \(-0.204151\pi\)
−0.918772 + 0.394789i \(0.870818\pi\)
\(458\) −6.17571 10.6966i −0.288572 0.499821i
\(459\) 0 0
\(460\) 0.0248149 0.0429807i 0.00115700 0.00200399i
\(461\) −9.23055 + 15.9878i −0.429910 + 0.744625i −0.996865 0.0791233i \(-0.974788\pi\)
0.566955 + 0.823749i \(0.308121\pi\)
\(462\) 0 0
\(463\) 7.11721 + 12.3274i 0.330765 + 0.572902i 0.982662 0.185406i \(-0.0593600\pi\)
−0.651897 + 0.758307i \(0.726027\pi\)
\(464\) 31.5790 1.46602
\(465\) 0 0
\(466\) 17.8803 0.828290
\(467\) 1.68433 2.91734i 0.0779413 0.134998i −0.824420 0.565978i \(-0.808499\pi\)
0.902362 + 0.430980i \(0.141832\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −9.09627 + 15.7552i −0.419579 + 0.726733i
\(471\) 0 0
\(472\) −1.08394 + 1.87744i −0.0498924 + 0.0864162i
\(473\) 0.286989 0.497079i 0.0131958 0.0228557i
\(474\) 0 0
\(475\) −1.54189 + 2.67063i −0.0707467 + 0.122537i
\(476\) 0 0
\(477\) 0 0
\(478\) −6.42468 + 11.1279i −0.293858 + 0.508977i
\(479\) −36.7665 −1.67990 −0.839952 0.542660i \(-0.817417\pi\)
−0.839952 + 0.542660i \(0.817417\pi\)
\(480\) 0 0
\(481\) 44.7205 2.03908
\(482\) 6.03462 + 10.4523i 0.274869 + 0.476087i
\(483\) 0 0
\(484\) −0.996130 + 1.72535i −0.0452786 + 0.0784249i
\(485\) −17.2233 + 29.8316i −0.782069 + 1.35458i
\(486\) 0 0
\(487\) 18.7087 + 32.4045i 0.847773 + 1.46839i 0.883191 + 0.469014i \(0.155391\pi\)
−0.0354172 + 0.999373i \(0.511276\pi\)
\(488\) 1.41013 + 2.44242i 0.0638336 + 0.110563i
\(489\) 0 0
\(490\) 0 0
\(491\) −13.3353 23.0974i −0.601813 1.04237i −0.992547 0.121866i \(-0.961112\pi\)
0.390734 0.920504i \(-0.372221\pi\)
\(492\) 0 0
\(493\) −34.0651 −1.53422
\(494\) −8.57011 14.8439i −0.385587 0.667857i
\(495\) 0 0
\(496\) −27.6195 −1.24015
\(497\) 0 0
\(498\) 0 0
\(499\) 33.7452 1.51064 0.755320 0.655356i \(-0.227481\pi\)
0.755320 + 0.655356i \(0.227481\pi\)
\(500\) −0.839556 + 1.45415i −0.0375461 + 0.0650317i
\(501\) 0 0
\(502\) −16.8400 29.1678i −0.751607 1.30182i
\(503\) −32.0401 −1.42860 −0.714299 0.699840i \(-0.753255\pi\)
−0.714299 + 0.699840i \(0.753255\pi\)
\(504\) 0 0
\(505\) −24.2422 −1.07876
\(506\) −0.0334331 0.0579078i −0.00148628 0.00257431i
\(507\) 0 0
\(508\) −0.820670 + 1.42144i −0.0364114 + 0.0630663i
\(509\) −7.93851 −0.351868 −0.175934 0.984402i \(-0.556295\pi\)
−0.175934 + 0.984402i \(0.556295\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 24.9186 1.10126
\(513\) 0 0
\(514\) 7.31046 + 12.6621i 0.322451 + 0.558501i
\(515\) −7.70233 −0.339405
\(516\) 0 0
\(517\) −1.24763 2.16095i −0.0548705 0.0950386i
\(518\) 0 0
\(519\) 0 0
\(520\) 21.7003 + 37.5860i 0.951620 + 1.64825i
\(521\) 7.33750 + 12.7089i 0.321462 + 0.556788i 0.980790 0.195067i \(-0.0624926\pi\)
−0.659328 + 0.751855i \(0.729159\pi\)
\(522\) 0 0
\(523\) 14.1716 24.5459i 0.619680 1.07332i −0.369864 0.929086i \(-0.620596\pi\)
0.989544 0.144232i \(-0.0460711\pi\)
\(524\) 1.04988 1.81844i 0.0458641 0.0794390i
\(525\) 0 0
\(526\) −17.5737 30.4386i −0.766251 1.32719i
\(527\) 29.7939 1.29784
\(528\) 0 0
\(529\) −22.9887 −0.999511
\(530\) 1.22281 2.11797i 0.0531155 0.0919988i
\(531\) 0 0
\(532\) 0 0
\(533\) −6.48293 + 11.2288i −0.280807 + 0.486371i
\(534\) 0 0
\(535\) −8.25150 + 14.2920i −0.356743 + 0.617898i
\(536\) 14.1853 24.5696i 0.612710 1.06124i
\(537\) 0 0
\(538\) −5.14203 + 8.90625i −0.221688 + 0.383976i
\(539\) 0 0
\(540\) 0 0
\(541\) −5.64290 + 9.77380i −0.242607 + 0.420208i −0.961456 0.274958i \(-0.911336\pi\)
0.718849 + 0.695166i \(0.244669\pi\)
\(542\) 4.58584 0.196979
\(543\) 0 0
\(544\) −4.04189 −0.173295
\(545\) −13.4684 23.3279i −0.576922 0.999258i
\(546\) 0 0
\(547\) 14.6202 25.3229i 0.625115 1.08273i −0.363404 0.931632i \(-0.618385\pi\)
0.988519 0.151099i \(-0.0482812\pi\)
\(548\) 0.528934 0.916140i 0.0225949 0.0391356i
\(549\) 0 0
\(550\) −0.444907 0.770602i −0.0189709 0.0328586i
\(551\) 9.59240 + 16.6145i 0.408650 + 0.707802i
\(552\) 0 0
\(553\) 0 0
\(554\) −3.85457 6.67631i −0.163765 0.283649i
\(555\) 0 0
\(556\) −0.170741 −0.00724105
\(557\) −0.387841 0.671761i −0.0164334 0.0284634i 0.857692 0.514164i \(-0.171898\pi\)
−0.874125 + 0.485701i \(0.838564\pi\)
\(558\) 0 0
\(559\) −7.14290 −0.302113
\(560\) 0 0
\(561\) 0 0
\(562\) 38.2327 1.61275
\(563\) −12.4761 + 21.6093i −0.525806 + 0.910722i 0.473742 + 0.880663i \(0.342903\pi\)
−0.999548 + 0.0300588i \(0.990431\pi\)
\(564\) 0 0
\(565\) 6.55438 + 11.3525i 0.275745 + 0.477604i
\(566\) 6.15888 0.258877
\(567\) 0 0
\(568\) −38.9564 −1.63457
\(569\) −12.4017 21.4803i −0.519905 0.900502i −0.999732 0.0231391i \(-0.992634\pi\)
0.479827 0.877363i \(-0.340699\pi\)
\(570\) 0 0
\(571\) −4.39827 + 7.61803i −0.184062 + 0.318805i −0.943260 0.332055i \(-0.892258\pi\)
0.759198 + 0.650860i \(0.225591\pi\)
\(572\) −0.503490 −0.0210520
\(573\) 0 0
\(574\) 0 0
\(575\) 0.149711 0.00624336
\(576\) 0 0
\(577\) −6.43717 11.1495i −0.267983 0.464160i 0.700358 0.713792i \(-0.253024\pi\)
−0.968341 + 0.249632i \(0.919690\pi\)
\(578\) 2.62773 0.109299
\(579\) 0 0
\(580\) −2.05438 3.55829i −0.0853034 0.147750i
\(581\) 0 0
\(582\) 0 0
\(583\) 0.167718 + 0.290497i 0.00694619 + 0.0120311i
\(584\) −15.1131 26.1766i −0.625384 1.08320i
\(585\) 0 0
\(586\) 2.91534 5.04952i 0.120432 0.208594i
\(587\) −22.4315 + 38.8526i −0.925849 + 1.60362i −0.135658 + 0.990756i \(0.543315\pi\)
−0.790190 + 0.612861i \(0.790018\pi\)
\(588\) 0 0
\(589\) −8.38965 14.5313i −0.345690 0.598752i
\(590\) −2.51249 −0.103438
\(591\) 0 0
\(592\) 27.6195 1.13515
\(593\) −1.88026 + 3.25671i −0.0772131 + 0.133737i −0.902047 0.431639i \(-0.857936\pi\)
0.824833 + 0.565376i \(0.191269\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.806123 + 1.39625i −0.0330201 + 0.0571924i
\(597\) 0 0
\(598\) −0.416060 + 0.720637i −0.0170139 + 0.0294690i
\(599\) −1.84524 + 3.19604i −0.0753943 + 0.130587i −0.901258 0.433283i \(-0.857355\pi\)
0.825863 + 0.563870i \(0.190688\pi\)
\(600\) 0 0
\(601\) −10.9285 + 18.9288i −0.445785 + 0.772122i −0.998107 0.0615091i \(-0.980409\pi\)
0.552322 + 0.833631i \(0.313742\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.70258 2.94896i 0.0692771 0.119991i
\(605\) −27.2986 −1.10985
\(606\) 0 0
\(607\) −24.3946 −0.990145 −0.495072 0.868852i \(-0.664858\pi\)
−0.495072 + 0.868852i \(0.664858\pi\)
\(608\) 1.13816 + 1.97134i 0.0461583 + 0.0799485i
\(609\) 0 0
\(610\) −1.63429 + 2.83067i −0.0661703 + 0.114610i
\(611\) −15.5262 + 26.8921i −0.628121 + 1.08794i
\(612\) 0 0
\(613\) −21.0107 36.3917i −0.848616 1.46985i −0.882444 0.470418i \(-0.844103\pi\)
0.0338284 0.999428i \(-0.489230\pi\)
\(614\) −8.33796 14.4418i −0.336493 0.582823i
\(615\) 0 0
\(616\) 0 0
\(617\) 23.2049 + 40.1920i 0.934192 + 1.61807i 0.776068 + 0.630650i \(0.217212\pi\)
0.158125 + 0.987419i \(0.449455\pi\)
\(618\) 0 0
\(619\) 27.2094 1.09364 0.546820 0.837250i \(-0.315838\pi\)
0.546820 + 0.837250i \(0.315838\pi\)
\(620\) 1.79679 + 3.11213i 0.0721608 + 0.124986i
\(621\) 0 0
\(622\) 29.6209 1.18769
\(623\) 0 0
\(624\) 0 0
\(625\) −30.0651 −1.20260
\(626\) 9.35685 16.2065i 0.373975 0.647743i
\(627\) 0 0
\(628\) −0.454956 0.788006i −0.0181547 0.0314449i
\(629\) −29.7939 −1.18796
\(630\) 0 0
\(631\) −29.6023 −1.17845 −0.589224 0.807970i \(-0.700566\pi\)
−0.589224 + 0.807970i \(0.700566\pi\)
\(632\) 18.6006 + 32.2172i 0.739892 + 1.28153i
\(633\) 0 0
\(634\) 4.16456 7.21324i 0.165396 0.286474i
\(635\) −22.4902 −0.892496
\(636\) 0 0
\(637\) 0 0
\(638\) −5.53571 −0.219161
\(639\) 0 0
\(640\) 12.0248 + 20.8276i 0.475323 + 0.823283i
\(641\) 0.279000 0.0110198 0.00550991 0.999985i \(-0.498246\pi\)
0.00550991 + 0.999985i \(0.498246\pi\)
\(642\) 0 0
\(643\) −9.12196 15.7997i −0.359735 0.623079i 0.628181 0.778067i \(-0.283800\pi\)
−0.987916 + 0.154988i \(0.950466\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 5.70961 + 9.88933i 0.224642 + 0.389090i
\(647\) −11.2285 19.4483i −0.441438 0.764592i 0.556359 0.830942i \(-0.312198\pi\)
−0.997796 + 0.0663498i \(0.978865\pi\)
\(648\) 0 0
\(649\) 0.172304 0.298439i 0.00676352 0.0117148i
\(650\) −5.53667 + 9.58980i −0.217166 + 0.376143i
\(651\) 0 0
\(652\) 0.705737 + 1.22237i 0.0276388 + 0.0478718i
\(653\) 50.5313 1.97744 0.988721 0.149771i \(-0.0478538\pi\)
0.988721 + 0.149771i \(0.0478538\pi\)
\(654\) 0 0
\(655\) 28.7716 1.12420
\(656\) −4.00387 + 6.93491i −0.156325 + 0.270763i
\(657\) 0 0
\(658\) 0 0
\(659\) −1.33631 + 2.31456i −0.0520554 + 0.0901626i −0.890879 0.454241i \(-0.849911\pi\)
0.838824 + 0.544403i \(0.183244\pi\)
\(660\) 0 0
\(661\) −17.3050 + 29.9731i −0.673086 + 1.16582i 0.303938 + 0.952692i \(0.401698\pi\)
−0.977024 + 0.213128i \(0.931635\pi\)
\(662\) 7.22921 12.5214i 0.280971 0.486656i
\(663\) 0 0
\(664\) 4.02007 6.96296i 0.156009 0.270215i
\(665\) 0 0
\(666\) 0 0
\(667\) 0.465690 0.806598i 0.0180316 0.0312316i
\(668\) 1.04507 0.0404351
\(669\) 0 0
\(670\) 32.8803 1.27028
\(671\) −0.224155 0.388249i −0.00865342 0.0149882i
\(672\) 0 0
\(673\) −8.25624 + 14.3002i −0.318255 + 0.551234i −0.980124 0.198386i \(-0.936430\pi\)
0.661869 + 0.749619i \(0.269763\pi\)
\(674\) −12.5262 + 21.6959i −0.482490 + 0.835697i
\(675\) 0 0
\(676\) 1.93170 + 3.34581i 0.0742963 + 0.128685i
\(677\) 21.8790 + 37.8955i 0.840877 + 1.45644i 0.889154 + 0.457608i \(0.151294\pi\)
−0.0482766 + 0.998834i \(0.515373\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −14.4572 25.0407i −0.554410 0.960266i
\(681\) 0 0
\(682\) 4.84161 0.185395
\(683\) 14.1206 + 24.4576i 0.540310 + 0.935845i 0.998886 + 0.0471895i \(0.0150265\pi\)
−0.458576 + 0.888655i \(0.651640\pi\)
\(684\) 0 0
\(685\) 14.4953 0.553835
\(686\) 0 0
\(687\) 0 0
\(688\) −4.41147 −0.168186
\(689\) 2.08718 3.61510i 0.0795153 0.137725i
\(690\) 0 0
\(691\) −14.5326 25.1711i −0.552844 0.957555i −0.998068 0.0621351i \(-0.980209\pi\)
0.445223 0.895420i \(-0.353124\pi\)
\(692\) −3.89344 −0.148006
\(693\) 0 0
\(694\) −27.5016 −1.04395
\(695\) −1.16978 2.02611i −0.0443722 0.0768549i
\(696\) 0 0
\(697\) 4.31908 7.48086i 0.163597 0.283358i
\(698\) −4.79923 −0.181654
\(699\) 0 0
\(700\) 0 0
\(701\) 1.10876 0.0418771 0.0209386 0.999781i \(-0.493335\pi\)
0.0209386 + 0.999781i \(0.493335\pi\)
\(702\) 0 0
\(703\) 8.38965 + 14.5313i 0.316422 + 0.548059i
\(704\) −4.02229 −0.151596
\(705\) 0 0
\(706\) 6.75150 + 11.6939i 0.254096 + 0.440107i
\(707\) 0 0
\(708\) 0 0
\(709\) 9.23442 + 15.9945i 0.346806 + 0.600686i 0.985680 0.168626i \(-0.0539329\pi\)
−0.638874 + 0.769311i \(0.720600\pi\)
\(710\) −22.5744 39.1001i −0.847204 1.46740i
\(711\) 0 0
\(712\) 11.9418 20.6837i 0.447536 0.775155i
\(713\) −0.407299 + 0.705463i −0.0152535 + 0.0264198i
\(714\) 0 0
\(715\) −3.44949 5.97470i −0.129004 0.223441i
\(716\) −0.946251 −0.0353631
\(717\) 0 0
\(718\) 12.7733 0.476696
\(719\) 16.8885 29.2517i 0.629834 1.09090i −0.357751 0.933817i \(-0.616456\pi\)
0.987585 0.157087i \(-0.0502103\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −9.58378 + 16.5996i −0.356671 + 0.617773i
\(723\) 0 0
\(724\) 0.0295627 0.0512040i 0.00109869 0.00190298i
\(725\) 6.19712 10.7337i 0.230155 0.398641i
\(726\) 0 0
\(727\) 8.40214 14.5529i 0.311618 0.539738i −0.667095 0.744973i \(-0.732462\pi\)
0.978713 + 0.205234i \(0.0657957\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 17.5155 30.3377i 0.648277 1.12285i
\(731\) 4.75877 0.176009
\(732\) 0 0
\(733\) 13.6364 0.503672 0.251836 0.967770i \(-0.418966\pi\)
0.251836 + 0.967770i \(0.418966\pi\)
\(734\) −10.8682 18.8243i −0.401154 0.694819i
\(735\) 0 0
\(736\) 0.0552549 0.0957044i 0.00203672 0.00352771i
\(737\) −2.25490 + 3.90560i −0.0830603 + 0.143865i
\(738\) 0 0
\(739\) 16.0209 + 27.7491i 0.589340 + 1.02077i 0.994319 + 0.106441i \(0.0339455\pi\)
−0.404979 + 0.914326i \(0.632721\pi\)
\(740\) −1.79679 3.11213i −0.0660513 0.114404i
\(741\) 0 0
\(742\) 0 0
\(743\) 16.8764 + 29.2309i 0.619137 + 1.07238i 0.989644 + 0.143547i \(0.0458507\pi\)
−0.370507 + 0.928830i \(0.620816\pi\)
\(744\) 0 0
\(745\) −22.0915 −0.809371
\(746\) 9.46451 + 16.3930i 0.346520 + 0.600191i
\(747\) 0 0
\(748\) 0.335437 0.0122648
\(749\) 0 0
\(750\) 0 0
\(751\) 26.1165 0.953004 0.476502 0.879173i \(-0.341904\pi\)
0.476502 + 0.879173i \(0.341904\pi\)
\(752\) −9.58899 + 16.6086i −0.349675 + 0.605654i
\(753\) 0 0
\(754\) 34.4447 + 59.6600i 1.25440 + 2.17269i
\(755\) 46.6587 1.69808
\(756\) 0 0
\(757\) 35.6536 1.29585 0.647927 0.761703i \(-0.275636\pi\)
0.647927 + 0.761703i \(0.275636\pi\)
\(758\) 10.8170 + 18.7356i 0.392892 + 0.680509i
\(759\) 0 0
\(760\) −8.14203 + 14.1024i −0.295342 + 0.511548i
\(761\) 40.7648 1.47772 0.738861 0.673858i \(-0.235364\pi\)
0.738861 + 0.673858i \(0.235364\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −2.87670 −0.104075
\(765\) 0 0
\(766\) −21.5706 37.3613i −0.779377 1.34992i
\(767\) −4.28850 −0.154849
\(768\) 0 0
\(769\) 19.7135 + 34.1447i 0.710886 + 1.23129i 0.964525 + 0.263992i \(0.0850392\pi\)
−0.253639 + 0.967299i \(0.581627\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.558248 + 0.966914i 0.0200918 + 0.0348000i
\(773\) −12.4513 21.5663i −0.447842 0.775686i 0.550403 0.834899i \(-0.314474\pi\)
−0.998245 + 0.0592135i \(0.981141\pi\)
\(774\) 0 0
\(775\) −5.42009 + 9.38788i −0.194695 + 0.337222i
\(776\) −20.0221 + 34.6793i −0.718752 + 1.24492i
\(777\) 0 0
\(778\) 20.2383 + 35.0538i 0.725578 + 1.25674i
\(779\) −4.86484 −0.174301
\(780\) 0 0
\(781\) 6.19253 0.221586
\(782\) 0.277189 0.480105i 0.00991225 0.0171685i
\(783\) 0 0
\(784\) 0 0
\(785\) 6.23396 10.7975i 0.222499 0.385380i
\(786\) 0 0
\(787\) −15.3525 + 26.5913i −0.547258 + 0.947879i 0.451203 + 0.892421i \(0.350995\pi\)
−0.998461 + 0.0554572i \(0.982338\pi\)
\(788\) −2.33157 + 4.03839i −0.0830586 + 0.143862i
\(789\) 0 0
\(790\) −21.5574 + 37.3385i −0.766977 + 1.32844i
\(791\) 0 0
\(792\) 0 0
\(793\) −2.78952 + 4.83158i −0.0990586 + 0.171575i
\(794\) −16.5986