Properties

Label 1323.2.g.d.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.d.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 \(-0.691584\pi\)
−0.566192 + 0.824273i \(0.691584\pi\)
\(6\) 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 \(-0.867488\pi\)
0.107094 0.994249i \(-0.465845\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.79813 + 3.11446i 0.449533 + 0.778615i
\(17\) 1.93969 + 3.35965i 0.470445 + 0.814834i 0.999429 0.0337978i \(-0.0107602\pi\)
−0.528984 + 0.848632i \(0.677427\pi\)
\(18\) 0 0
\(19\) 1.09240 1.89209i 0.250613 0.434074i −0.713082 0.701081i \(-0.752701\pi\)
0.963695 + 0.267007i \(0.0860345\pi\)
\(20\) −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 \(-0.591081\pi\)
0.971939 0.235235i \(-0.0755858\pi\)
\(32\) 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 0.765897 0.642964i \(-0.222295\pi\)
−0.939771 + 0.341804i \(0.888962\pi\)
\(42\) 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 0.603375 0.797457i \(-0.293822\pi\)
−0.992306 + 0.123810i \(0.960489\pi\)
\(48\) 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 −0.841059 0.540943i \(-0.818067\pi\)
0.889000 + 0.457907i \(0.151401\pi\)
\(60\) 0 0
\(61\) −0.479055 0.829748i −0.0613368 0.106238i 0.833726 0.552178i \(-0.186203\pi\)
−0.895063 + 0.445939i \(0.852870\pi\)
\(62\) 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 \(0.0385334\pi\)
−0.391759 + 0.920068i \(0.628133\pi\)
\(74\) 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 −0.931193 0.364527i \(-0.881231\pi\)
0.781286 + 0.624173i \(0.214564\pi\)
\(84\) 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 −0.996875 0.0789894i \(-0.974831\pi\)
0.566845 + 0.823825i \(0.308164\pi\)
\(90\) 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 \(-0.590663\pi\)
0.971629 0.236511i \(-0.0760039\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.130415 0.225885i 0.0130415 0.0225885i
\(101\) 9.57398 0.952646 0.476323 0.879270i \(-0.341969\pi\)
0.476323 + 0.879270i \(0.341969\pi\)
\(102\) 0 0
\(103\) 3.04189 0.299726 0.149863 0.988707i \(-0.452117\pi\)
0.149863 + 0.988707i \(0.452117\pi\)
\(104\) −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 \(-0.665340\pi\)
−0.496385 + 0.868102i \(0.665340\pi\)
\(132\) 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 0.884953 0.465681i \(-0.154191\pi\)
−0.845768 + 0.533551i \(0.820857\pi\)
\(140\) 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 −0.947387 0.320090i \(-0.896287\pi\)
0.750900 + 0.660416i \(0.229620\pi\)
\(158\) −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 0.735632 0.677382i \(-0.236885\pi\)
−0.954446 + 0.298385i \(0.903552\pi\)
\(168\) 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 \(0.128995\pi\)
−0.118071 + 0.993005i \(0.537671\pi\)
\(174\) 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 \(-0.503785\pi\)
−0.0118910 + 0.999929i \(0.503785\pi\)
\(182\) 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 0.807069 0.590458i \(-0.201053\pi\)
−0.914886 + 0.403713i \(0.867719\pi\)
\(200\) 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 −0.999597 0.0284023i \(-0.990958\pi\)
0.524395 + 0.851475i \(0.324291\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −3.48751 + 6.04055i −0.231986 + 0.401811i
\(227\) 2.89393 0.192077 0.0960385 0.995378i \(-0.469383\pi\)
0.0960385 + 0.995378i \(0.469383\pi\)
\(228\) 0 0
\(229\) 9.16756 0.605809 0.302905 0.953021i \(-0.402044\pi\)
0.302905 + 0.953021i \(0.402044\pi\)
\(230\) −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 \(-0.593164\pi\)
−0.288521 + 0.957473i \(0.593164\pi\)
\(242\) −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 \(-0.210631\pi\)
0.788938 + 0.614473i \(0.210631\pi\)
\(252\) 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 \(-0.609908\pi\)
−0.338466 + 0.940979i \(0.609908\pi\)
\(258\) 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 0.725902 0.687798i \(-0.241422\pi\)
−0.958602 + 0.284751i \(0.908089\pi\)
\(270\) 0 0
\(271\) −1.70187 + 2.94772i −0.103381 + 0.179061i −0.913076 0.407790i \(-0.866299\pi\)
0.809695 + 0.586852i \(0.199633\pi\)
\(272\) −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 −0.925929 0.377699i \(-0.876715\pi\)
0.790061 + 0.613028i \(0.210049\pi\)
\(284\) −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 0.922285 0.386512i \(-0.126320\pi\)
−0.795871 + 0.605466i \(0.792987\pi\)
\(294\) 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 \(-0.385092\pi\)
0.353206 + 0.935546i \(0.385092\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −26.2003 −1.48808
\(311\) −10.9927 + 19.0400i −0.623340 + 1.07966i 0.365519 + 0.930804i \(0.380892\pi\)
−0.988859 + 0.148853i \(0.952442\pi\)
\(312\) 0 0
\(313\) 6.94491 + 12.0289i 0.392549 + 0.679915i 0.992785 0.119908i \(-0.0382599\pi\)
−0.600236 + 0.799823i \(0.704927\pi\)
\(314\) −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 −0.814412 0.580288i \(-0.802940\pi\)
0.909750 + 0.415157i \(0.136274\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.243756 + 0.422197i −0.0129922 + 0.0225032i
\(353\) −10.0223 −0.533433 −0.266716 0.963775i \(-0.585939\pi\)
−0.266716 + 0.963775i \(0.585939\pi\)
\(354\) 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 \(-0.361652\pi\)
0.421079 + 0.907024i \(0.361652\pi\)
\(368\) 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 \(-0.195035\pi\)
0.818086 + 0.575095i \(0.195035\pi\)
\(384\) 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 −0.669019 0.743246i \(-0.733285\pi\)
0.978179 + 0.207764i \(0.0666187\pi\)
\(398\) 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 \(0.385435\pi\)
−0.986634 + 0.162951i \(0.947899\pi\)
\(410\) −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 0.847387 0.530976i \(-0.178175\pi\)
−0.883532 + 0.468370i \(0.844841\pi\)
\(420\) 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 \(-0.544803\pi\)
−0.140289 + 0.990111i \(0.544803\pi\)
\(434\) 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 \(-0.914248\pi\)
0.251473 0.967864i \(-0.419085\pi\)
\(440\) 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 −0.566955 0.823749i \(-0.691879\pi\)
0.996865 + 0.0791233i \(0.0252121\pi\)
\(462\) 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 −0.902362 0.430980i \(-0.858168\pi\)
0.824420 + 0.565978i \(0.191501\pi\)
\(468\) 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 \(-0.182583\pi\)
0.839952 + 0.542660i \(0.182583\pi\)
\(480\) 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 \(-0.246745\pi\)
0.714299 + 0.699840i \(0.246745\pi\)
\(504\) 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 \(-0.443705\pi\)
0.175934 + 0.984402i \(0.443705\pi\)
\(510\) 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 0.659328 0.751855i \(-0.270841\pi\)
−0.980790 + 0.195067i \(0.937507\pi\)
\(522\) 0 0
\(523\) −14.1716 + 24.5459i −0.619680 + 1.07332i 0.369864 + 0.929086i \(0.379404\pi\)
−0.989544 + 0.144232i \(0.953929\pi\)
\(524\) −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 \(-0.657097\pi\)
0.999548 0.0300588i \(-0.00956944\pi\)
\(564\) 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 0.968341 0.249632i \(-0.0803096\pi\)
−0.700358 + 0.713792i \(0.746976\pi\)
\(578\) 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 \(-0.456685\pi\)
0.790190 0.612861i \(-0.209982\pi\)
\(588\) 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 −0.824833 0.565376i \(-0.808731\pi\)
0.902047 + 0.431639i \(0.142064\pi\)
\(594\) 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 −0.552322 0.833631i \(-0.686258\pi\)
0.998107 + 0.0615091i \(0.0195913\pi\)
\(602\) 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 \(-0.335142\pi\)
0.495072 + 0.868852i \(0.335142\pi\)
\(608\) −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 \(-0.684162\pi\)
−0.546820 + 0.837250i \(0.684162\pi\)
\(620\) 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 0.987916 0.154988i \(-0.0495338\pi\)
−0.628181 + 0.778067i \(0.716200\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 5.70961 + 9.88933i 0.224642 + 0.389090i
\(647\) 11.2285 + 19.4483i 0.441438 + 0.764592i 0.997796 0.0663498i \(-0.0211353\pi\)
−0.556359 + 0.830942i \(0.687802\pi\)
\(648\) 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 \(-0.598302\pi\)
0.977024 0.213128i \(-0.0683651\pi\)
\(662\) 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 \(-0.848706\pi\)
0.0482766 0.998834i \(-0.484627\pi\)
\(678\) 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 \(0.0197910\pi\)
−0.445223 + 0.895420i \(0.646876\pi\)
\(692\) 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 \(0.383544\pi\)
−0.987585 + 0.157087i \(0.949790\pi\)
\(720\) 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 −0.978713 0.205234i \(-0.934204\pi\)
0.667095 + 0.744973i \(0.267538\pi\)
\(728\) 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 \(-0.581034\pi\)
−0.251836 + 0.967770i \(0.581034\pi\)
\(734\) 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 \(-0.764636\pi\)
−0.738861 + 0.673858i \(0.764636\pi\)
\(762\) 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 \(-0.914961\pi\)
0.253639 0.967299i \(-0.418373\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.558248 + 0.966914i 0.0200918 + 0.0348000i
\(773\) 12.4513 + 21.5663i 0.447842 + 0.775686i 0.998245 0.0592135i \(-0.0188593\pi\)
−0.550403 + 0.834899i \(0.685526\pi\)
\(774\) 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 \(-0.649005\pi\)
0.998461 0.0554572i \(-0.0176616\pi\)
\(788\) −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 0.589063