Properties

Label 216.2.q.b.97.3
Level $216$
Weight $2$
Character 216.97
Analytic conductor $1.725$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 216.q (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.72476868366\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(5\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 97.3
Character \(\chi\) \(=\) 216.97
Dual form 216.2.q.b.49.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.997080 + 1.41627i) q^{3} +(1.95510 + 0.711598i) q^{5} +(0.739573 - 4.19433i) q^{7} +(-1.01166 + 2.82428i) q^{9} +O(q^{10})\) \(q+(0.997080 + 1.41627i) q^{3} +(1.95510 + 0.711598i) q^{5} +(0.739573 - 4.19433i) q^{7} +(-1.01166 + 2.82428i) q^{9} +(2.33115 - 0.848468i) q^{11} +(-4.38271 + 3.67753i) q^{13} +(0.941573 + 3.47847i) q^{15} +(0.340351 + 0.589505i) q^{17} +(-2.58368 + 4.47506i) q^{19} +(6.67773 - 3.13464i) q^{21} +(-1.23287 - 6.99197i) q^{23} +(-0.514184 - 0.431451i) q^{25} +(-5.00866 + 1.38324i) q^{27} +(4.22836 + 3.54802i) q^{29} +(-0.787375 - 4.46543i) q^{31} +(3.52600 + 2.45555i) q^{33} +(4.43061 - 7.67405i) q^{35} +(-3.69778 - 6.40475i) q^{37} +(-9.57830 - 2.54033i) q^{39} +(-0.256172 + 0.214954i) q^{41} +(-1.61090 + 0.586320i) q^{43} +(-3.98765 + 4.80184i) q^{45} +(-0.889756 + 5.04606i) q^{47} +(-10.4676 - 3.80989i) q^{49} +(-0.495544 + 1.06981i) q^{51} +9.45353 q^{53} +5.16139 q^{55} +(-8.91404 + 0.802799i) q^{57} +(-9.52366 - 3.46633i) q^{59} +(1.36385 - 7.73479i) q^{61} +(11.0977 + 6.33201i) q^{63} +(-11.1856 + 4.07121i) q^{65} +(3.13628 - 2.63165i) q^{67} +(8.67327 - 8.71764i) q^{69} +(2.77081 + 4.79919i) q^{71} +(-4.43331 + 7.67871i) q^{73} +(0.0983709 - 1.15842i) q^{75} +(-1.83470 - 10.4051i) q^{77} +(4.53194 + 3.80275i) q^{79} +(-6.95308 - 5.71443i) q^{81} +(-6.90986 - 5.79806i) q^{83} +(0.245929 + 1.39473i) q^{85} +(-0.808948 + 9.52617i) q^{87} +(0.983567 - 1.70359i) q^{89} +(12.1834 + 21.1023i) q^{91} +(5.53919 - 5.56753i) q^{93} +(-8.23578 + 6.91064i) q^{95} +(0.443556 - 0.161441i) q^{97} +(0.0379741 + 7.44216i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 3q^{7} - 6q^{9} + O(q^{10}) \) \( 30q + 3q^{7} - 6q^{9} - 3q^{11} - 12q^{13} + 15q^{15} + 6q^{17} - 9q^{19} + 30q^{21} - 12q^{23} + 24q^{25} - 15q^{27} - 9q^{29} + 27q^{31} - 30q^{33} - 18q^{35} - 15q^{37} - 21q^{39} - 15q^{41} - 30q^{43} + 15q^{45} - 18q^{47} + 15q^{49} - 6q^{51} - 18q^{53} + 54q^{55} - 72q^{57} - 12q^{59} + 6q^{61} - 54q^{63} - 54q^{65} - 45q^{67} + 9q^{69} - 36q^{73} + 69q^{75} + 12q^{77} + 45q^{79} - 30q^{81} - 3q^{83} + 57q^{85} - 60q^{87} + 36q^{89} - 39q^{91} + 30q^{93} + 51q^{95} - 84q^{97} + 162q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).

\(n\) \(55\) \(109\) \(137\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{9}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.997080 + 1.41627i 0.575664 + 0.817686i
\(4\) 0 0
\(5\) 1.95510 + 0.711598i 0.874347 + 0.318236i 0.739926 0.672688i \(-0.234860\pi\)
0.134421 + 0.990924i \(0.457083\pi\)
\(6\) 0 0
\(7\) 0.739573 4.19433i 0.279532 1.58531i −0.444653 0.895703i \(-0.646673\pi\)
0.724186 0.689605i \(-0.242216\pi\)
\(8\) 0 0
\(9\) −1.01166 + 2.82428i −0.337221 + 0.941426i
\(10\) 0 0
\(11\) 2.33115 0.848468i 0.702867 0.255823i 0.0342324 0.999414i \(-0.489101\pi\)
0.668634 + 0.743591i \(0.266879\pi\)
\(12\) 0 0
\(13\) −4.38271 + 3.67753i −1.21555 + 1.01996i −0.216500 + 0.976283i \(0.569464\pi\)
−0.999046 + 0.0436808i \(0.986092\pi\)
\(14\) 0 0
\(15\) 0.941573 + 3.47847i 0.243113 + 0.898138i
\(16\) 0 0
\(17\) 0.340351 + 0.589505i 0.0825473 + 0.142976i 0.904343 0.426806i \(-0.140361\pi\)
−0.821796 + 0.569782i \(0.807028\pi\)
\(18\) 0 0
\(19\) −2.58368 + 4.47506i −0.592736 + 1.02665i 0.401126 + 0.916023i \(0.368619\pi\)
−0.993862 + 0.110626i \(0.964714\pi\)
\(20\) 0 0
\(21\) 6.67773 3.13464i 1.45720 0.684035i
\(22\) 0 0
\(23\) −1.23287 6.99197i −0.257072 1.45793i −0.790698 0.612206i \(-0.790282\pi\)
0.533627 0.845720i \(-0.320829\pi\)
\(24\) 0 0
\(25\) −0.514184 0.431451i −0.102837 0.0862903i
\(26\) 0 0
\(27\) −5.00866 + 1.38324i −0.963917 + 0.266204i
\(28\) 0 0
\(29\) 4.22836 + 3.54802i 0.785187 + 0.658850i 0.944549 0.328370i \(-0.106499\pi\)
−0.159362 + 0.987220i \(0.550944\pi\)
\(30\) 0 0
\(31\) −0.787375 4.46543i −0.141417 0.802014i −0.970175 0.242407i \(-0.922063\pi\)
0.828758 0.559607i \(-0.189048\pi\)
\(32\) 0 0
\(33\) 3.52600 + 2.45555i 0.613798 + 0.427456i
\(34\) 0 0
\(35\) 4.43061 7.67405i 0.748910 1.29715i
\(36\) 0 0
\(37\) −3.69778 6.40475i −0.607912 1.05293i −0.991584 0.129465i \(-0.958674\pi\)
0.383672 0.923469i \(-0.374659\pi\)
\(38\) 0 0
\(39\) −9.57830 2.54033i −1.53376 0.406778i
\(40\) 0 0
\(41\) −0.256172 + 0.214954i −0.0400074 + 0.0335702i −0.662572 0.748998i \(-0.730535\pi\)
0.622565 + 0.782568i \(0.286091\pi\)
\(42\) 0 0
\(43\) −1.61090 + 0.586320i −0.245660 + 0.0894130i −0.461916 0.886924i \(-0.652838\pi\)
0.216256 + 0.976337i \(0.430616\pi\)
\(44\) 0 0
\(45\) −3.98765 + 4.80184i −0.594444 + 0.715816i
\(46\) 0 0
\(47\) −0.889756 + 5.04606i −0.129784 + 0.736043i 0.848566 + 0.529089i \(0.177466\pi\)
−0.978351 + 0.206954i \(0.933645\pi\)
\(48\) 0 0
\(49\) −10.4676 3.80989i −1.49537 0.544270i
\(50\) 0 0
\(51\) −0.495544 + 1.06981i −0.0693900 + 0.149804i
\(52\) 0 0
\(53\) 9.45353 1.29854 0.649271 0.760557i \(-0.275074\pi\)
0.649271 + 0.760557i \(0.275074\pi\)
\(54\) 0 0
\(55\) 5.16139 0.695961
\(56\) 0 0
\(57\) −8.91404 + 0.802799i −1.18069 + 0.106333i
\(58\) 0 0
\(59\) −9.52366 3.46633i −1.23987 0.451277i −0.362906 0.931826i \(-0.618216\pi\)
−0.876968 + 0.480548i \(0.840438\pi\)
\(60\) 0 0
\(61\) 1.36385 7.73479i 0.174623 0.990338i −0.763954 0.645270i \(-0.776745\pi\)
0.938578 0.345068i \(-0.112144\pi\)
\(62\) 0 0
\(63\) 11.0977 + 6.33201i 1.39818 + 0.797758i
\(64\) 0 0
\(65\) −11.1856 + 4.07121i −1.38740 + 0.504971i
\(66\) 0 0
\(67\) 3.13628 2.63165i 0.383157 0.321507i −0.430783 0.902455i \(-0.641763\pi\)
0.813940 + 0.580948i \(0.197318\pi\)
\(68\) 0 0
\(69\) 8.67327 8.71764i 1.04414 1.04948i
\(70\) 0 0
\(71\) 2.77081 + 4.79919i 0.328835 + 0.569559i 0.982281 0.187414i \(-0.0600106\pi\)
−0.653446 + 0.756973i \(0.726677\pi\)
\(72\) 0 0
\(73\) −4.43331 + 7.67871i −0.518879 + 0.898725i 0.480880 + 0.876786i \(0.340317\pi\)
−0.999759 + 0.0219389i \(0.993016\pi\)
\(74\) 0 0
\(75\) 0.0983709 1.15842i 0.0113589 0.133762i
\(76\) 0 0
\(77\) −1.83470 10.4051i −0.209083 1.18577i
\(78\) 0 0
\(79\) 4.53194 + 3.80275i 0.509883 + 0.427842i 0.861088 0.508456i \(-0.169784\pi\)
−0.351205 + 0.936299i \(0.614228\pi\)
\(80\) 0 0
\(81\) −6.95308 5.71443i −0.772564 0.634937i
\(82\) 0 0
\(83\) −6.90986 5.79806i −0.758456 0.636420i 0.179268 0.983800i \(-0.442627\pi\)
−0.937724 + 0.347380i \(0.887071\pi\)
\(84\) 0 0
\(85\) 0.245929 + 1.39473i 0.0266748 + 0.151280i
\(86\) 0 0
\(87\) −0.808948 + 9.52617i −0.0867283 + 1.02131i
\(88\) 0 0
\(89\) 0.983567 1.70359i 0.104258 0.180580i −0.809177 0.587565i \(-0.800087\pi\)
0.913435 + 0.406985i \(0.133420\pi\)
\(90\) 0 0
\(91\) 12.1834 + 21.1023i 1.27717 + 2.21213i
\(92\) 0 0
\(93\) 5.53919 5.56753i 0.574387 0.577326i
\(94\) 0 0
\(95\) −8.23578 + 6.91064i −0.844974 + 0.709017i
\(96\) 0 0
\(97\) 0.443556 0.161441i 0.0450363 0.0163919i −0.319404 0.947619i \(-0.603483\pi\)
0.364440 + 0.931227i \(0.381260\pi\)
\(98\) 0 0
\(99\) 0.0379741 + 7.44216i 0.00381654 + 0.747965i
\(100\) 0 0
\(101\) −2.35090 + 13.3326i −0.233923 + 1.32665i 0.610946 + 0.791673i \(0.290789\pi\)
−0.844869 + 0.534973i \(0.820322\pi\)
\(102\) 0 0
\(103\) −2.63679 0.959715i −0.259811 0.0945635i 0.208831 0.977952i \(-0.433034\pi\)
−0.468642 + 0.883388i \(0.655256\pi\)
\(104\) 0 0
\(105\) 15.2862 1.37668i 1.49178 0.134350i
\(106\) 0 0
\(107\) 17.3455 1.67685 0.838426 0.545016i \(-0.183476\pi\)
0.838426 + 0.545016i \(0.183476\pi\)
\(108\) 0 0
\(109\) 10.1417 0.971398 0.485699 0.874126i \(-0.338565\pi\)
0.485699 + 0.874126i \(0.338565\pi\)
\(110\) 0 0
\(111\) 5.38389 11.6231i 0.511016 1.10322i
\(112\) 0 0
\(113\) 9.18308 + 3.34237i 0.863871 + 0.314423i 0.735683 0.677326i \(-0.236862\pi\)
0.128189 + 0.991750i \(0.459084\pi\)
\(114\) 0 0
\(115\) 2.56508 14.5473i 0.239195 1.35654i
\(116\) 0 0
\(117\) −5.95254 16.0984i −0.550312 1.48830i
\(118\) 0 0
\(119\) 2.72429 0.991562i 0.249736 0.0908964i
\(120\) 0 0
\(121\) −3.71215 + 3.11486i −0.337468 + 0.283169i
\(122\) 0 0
\(123\) −0.559858 0.148484i −0.0504807 0.0133883i
\(124\) 0 0
\(125\) −5.89969 10.2186i −0.527684 0.913976i
\(126\) 0 0
\(127\) 5.20346 9.01266i 0.461733 0.799744i −0.537315 0.843382i \(-0.680561\pi\)
0.999047 + 0.0436375i \(0.0138947\pi\)
\(128\) 0 0
\(129\) −2.43659 1.69687i −0.214529 0.149401i
\(130\) 0 0
\(131\) 2.62938 + 14.9120i 0.229730 + 1.30286i 0.853433 + 0.521202i \(0.174516\pi\)
−0.623703 + 0.781661i \(0.714373\pi\)
\(132\) 0 0
\(133\) 16.8591 + 14.1464i 1.46187 + 1.22665i
\(134\) 0 0
\(135\) −10.7767 0.859782i −0.927513 0.0739982i
\(136\) 0 0
\(137\) 14.5223 + 12.1857i 1.24073 + 1.04109i 0.997467 + 0.0711323i \(0.0226613\pi\)
0.243260 + 0.969961i \(0.421783\pi\)
\(138\) 0 0
\(139\) 1.98835 + 11.2765i 0.168650 + 0.956460i 0.945221 + 0.326431i \(0.105846\pi\)
−0.776571 + 0.630029i \(0.783043\pi\)
\(140\) 0 0
\(141\) −8.03376 + 3.77118i −0.676564 + 0.317591i
\(142\) 0 0
\(143\) −7.09647 + 12.2914i −0.593437 + 1.02786i
\(144\) 0 0
\(145\) 5.74210 + 9.94561i 0.476856 + 0.825938i
\(146\) 0 0
\(147\) −5.04117 18.6237i −0.415789 1.53606i
\(148\) 0 0
\(149\) −7.47668 + 6.27368i −0.612514 + 0.513960i −0.895440 0.445182i \(-0.853139\pi\)
0.282927 + 0.959142i \(0.408695\pi\)
\(150\) 0 0
\(151\) −8.61982 + 3.13736i −0.701471 + 0.255314i −0.668039 0.744127i \(-0.732866\pi\)
−0.0334320 + 0.999441i \(0.510644\pi\)
\(152\) 0 0
\(153\) −2.00925 + 0.364865i −0.162438 + 0.0294976i
\(154\) 0 0
\(155\) 1.63819 9.29064i 0.131583 0.746242i
\(156\) 0 0
\(157\) −0.470052 0.171085i −0.0375142 0.0136541i 0.323195 0.946332i \(-0.395243\pi\)
−0.360709 + 0.932678i \(0.617465\pi\)
\(158\) 0 0
\(159\) 9.42592 + 13.3888i 0.747524 + 1.06180i
\(160\) 0 0
\(161\) −30.2384 −2.38312
\(162\) 0 0
\(163\) −7.75047 −0.607064 −0.303532 0.952821i \(-0.598166\pi\)
−0.303532 + 0.952821i \(0.598166\pi\)
\(164\) 0 0
\(165\) 5.14632 + 7.30994i 0.400640 + 0.569078i
\(166\) 0 0
\(167\) −21.9210 7.97859i −1.69630 0.617402i −0.700902 0.713257i \(-0.747219\pi\)
−0.995395 + 0.0958557i \(0.969441\pi\)
\(168\) 0 0
\(169\) 3.42649 19.4326i 0.263576 1.49482i
\(170\) 0 0
\(171\) −10.0250 11.8243i −0.766631 0.904225i
\(172\) 0 0
\(173\) −5.74869 + 2.09235i −0.437065 + 0.159079i −0.551175 0.834389i \(-0.685820\pi\)
0.114110 + 0.993468i \(0.463598\pi\)
\(174\) 0 0
\(175\) −2.18993 + 1.83757i −0.165543 + 0.138907i
\(176\) 0 0
\(177\) −4.58658 16.9443i −0.344748 1.27361i
\(178\) 0 0
\(179\) 2.87922 + 4.98696i 0.215203 + 0.372743i 0.953335 0.301913i \(-0.0976252\pi\)
−0.738132 + 0.674656i \(0.764292\pi\)
\(180\) 0 0
\(181\) 6.87176 11.9022i 0.510774 0.884687i −0.489148 0.872201i \(-0.662692\pi\)
0.999922 0.0124858i \(-0.00397445\pi\)
\(182\) 0 0
\(183\) 12.3145 5.78062i 0.910310 0.427316i
\(184\) 0 0
\(185\) −2.67193 15.1532i −0.196444 1.11409i
\(186\) 0 0
\(187\) 1.29358 + 1.08545i 0.0945962 + 0.0793757i
\(188\) 0 0
\(189\) 2.09749 + 22.0310i 0.152570 + 1.60252i
\(190\) 0 0
\(191\) −5.96488 5.00513i −0.431604 0.362159i 0.400953 0.916099i \(-0.368679\pi\)
−0.832556 + 0.553940i \(0.813124\pi\)
\(192\) 0 0
\(193\) 0.234364 + 1.32915i 0.0168699 + 0.0956741i 0.992080 0.125606i \(-0.0400876\pi\)
−0.975210 + 0.221280i \(0.928976\pi\)
\(194\) 0 0
\(195\) −16.9188 11.7825i −1.21158 0.843761i
\(196\) 0 0
\(197\) 4.52195 7.83225i 0.322176 0.558024i −0.658761 0.752352i \(-0.728919\pi\)
0.980937 + 0.194328i \(0.0622525\pi\)
\(198\) 0 0
\(199\) 2.80907 + 4.86545i 0.199130 + 0.344903i 0.948246 0.317535i \(-0.102855\pi\)
−0.749117 + 0.662438i \(0.769522\pi\)
\(200\) 0 0
\(201\) 6.85426 + 1.81786i 0.483462 + 0.128222i
\(202\) 0 0
\(203\) 18.0087 15.1111i 1.26397 1.06059i
\(204\) 0 0
\(205\) −0.653803 + 0.237965i −0.0456636 + 0.0166202i
\(206\) 0 0
\(207\) 20.9945 + 3.59154i 1.45922 + 0.249629i
\(208\) 0 0
\(209\) −2.22598 + 12.6242i −0.153975 + 0.873233i
\(210\) 0 0
\(211\) 6.64659 + 2.41916i 0.457570 + 0.166542i 0.560513 0.828145i \(-0.310604\pi\)
−0.102943 + 0.994687i \(0.532826\pi\)
\(212\) 0 0
\(213\) −4.03424 + 8.70941i −0.276422 + 0.596759i
\(214\) 0 0
\(215\) −3.56669 −0.243246
\(216\) 0 0
\(217\) −19.3118 −1.31097
\(218\) 0 0
\(219\) −15.2955 + 1.37752i −1.03358 + 0.0930838i
\(220\) 0 0
\(221\) −3.65958 1.33198i −0.246170 0.0895987i
\(222\) 0 0
\(223\) 2.77934 15.7624i 0.186118 1.05553i −0.738392 0.674372i \(-0.764414\pi\)
0.924510 0.381157i \(-0.124474\pi\)
\(224\) 0 0
\(225\) 1.73872 1.01571i 0.115915 0.0677142i
\(226\) 0 0
\(227\) −3.95630 + 1.43997i −0.262589 + 0.0955744i −0.469960 0.882688i \(-0.655732\pi\)
0.207371 + 0.978262i \(0.433509\pi\)
\(228\) 0 0
\(229\) −10.9610 + 9.19738i −0.724324 + 0.607780i −0.928578 0.371138i \(-0.878968\pi\)
0.204253 + 0.978918i \(0.434523\pi\)
\(230\) 0 0
\(231\) 12.9071 12.9732i 0.849226 0.853571i
\(232\) 0 0
\(233\) 3.52385 + 6.10349i 0.230855 + 0.399853i 0.958060 0.286568i \(-0.0925143\pi\)
−0.727205 + 0.686421i \(0.759181\pi\)
\(234\) 0 0
\(235\) −5.33032 + 9.23239i −0.347712 + 0.602255i
\(236\) 0 0
\(237\) −0.867026 + 10.2101i −0.0563194 + 0.663218i
\(238\) 0 0
\(239\) 2.17975 + 12.3620i 0.140997 + 0.799631i 0.970495 + 0.241122i \(0.0775153\pi\)
−0.829498 + 0.558509i \(0.811374\pi\)
\(240\) 0 0
\(241\) 22.3747 + 18.7746i 1.44128 + 1.20938i 0.938649 + 0.344874i \(0.112078\pi\)
0.502629 + 0.864502i \(0.332366\pi\)
\(242\) 0 0
\(243\) 1.16042 15.5452i 0.0744412 0.997225i
\(244\) 0 0
\(245\) −17.7540 14.8974i −1.13426 0.951761i
\(246\) 0 0
\(247\) −5.13366 29.1144i −0.326647 1.85251i
\(248\) 0 0
\(249\) 1.32196 15.5674i 0.0837757 0.986543i
\(250\) 0 0
\(251\) −3.31998 + 5.75038i −0.209556 + 0.362961i −0.951575 0.307418i \(-0.900535\pi\)
0.742019 + 0.670379i \(0.233868\pi\)
\(252\) 0 0
\(253\) −8.80646 15.2532i −0.553658 0.958963i
\(254\) 0 0
\(255\) −1.73011 + 1.73896i −0.108344 + 0.108898i
\(256\) 0 0
\(257\) 16.0707 13.4849i 1.00246 0.841165i 0.0151383 0.999885i \(-0.495181\pi\)
0.987324 + 0.158720i \(0.0507367\pi\)
\(258\) 0 0
\(259\) −29.5984 + 10.7729i −1.83916 + 0.669398i
\(260\) 0 0
\(261\) −14.2983 + 8.35266i −0.885040 + 0.517017i
\(262\) 0 0
\(263\) −0.306469 + 1.73807i −0.0188977 + 0.107174i −0.992798 0.119804i \(-0.961773\pi\)
0.973900 + 0.226978i \(0.0728845\pi\)
\(264\) 0 0
\(265\) 18.4826 + 6.72711i 1.13538 + 0.413243i
\(266\) 0 0
\(267\) 3.39344 0.305613i 0.207675 0.0187032i
\(268\) 0 0
\(269\) 24.8211 1.51337 0.756684 0.653781i \(-0.226818\pi\)
0.756684 + 0.653781i \(0.226818\pi\)
\(270\) 0 0
\(271\) −13.9629 −0.848188 −0.424094 0.905618i \(-0.639407\pi\)
−0.424094 + 0.905618i \(0.639407\pi\)
\(272\) 0 0
\(273\) −17.7388 + 38.2958i −1.07360 + 2.31777i
\(274\) 0 0
\(275\) −1.56471 0.569508i −0.0943555 0.0343426i
\(276\) 0 0
\(277\) −2.70629 + 15.3481i −0.162605 + 0.922178i 0.788895 + 0.614528i \(0.210654\pi\)
−0.951500 + 0.307650i \(0.900457\pi\)
\(278\) 0 0
\(279\) 13.4082 + 2.29374i 0.802725 + 0.137323i
\(280\) 0 0
\(281\) 18.9646 6.90254i 1.13133 0.411771i 0.292556 0.956248i \(-0.405494\pi\)
0.838775 + 0.544478i \(0.183272\pi\)
\(282\) 0 0
\(283\) 11.8757 9.96486i 0.705935 0.592350i −0.217520 0.976056i \(-0.569797\pi\)
0.923455 + 0.383706i \(0.125352\pi\)
\(284\) 0 0
\(285\) −17.9991 4.77366i −1.06617 0.282767i
\(286\) 0 0
\(287\) 0.712130 + 1.23344i 0.0420357 + 0.0728079i
\(288\) 0 0
\(289\) 8.26832 14.3212i 0.486372 0.842421i
\(290\) 0 0
\(291\) 0.670906 + 0.467227i 0.0393292 + 0.0273893i
\(292\) 0 0
\(293\) 3.79392 + 21.5164i 0.221643 + 1.25700i 0.868999 + 0.494814i \(0.164764\pi\)
−0.647356 + 0.762188i \(0.724125\pi\)
\(294\) 0 0
\(295\) −16.1531 13.5540i −0.940467 0.789146i
\(296\) 0 0
\(297\) −10.5023 + 7.47421i −0.609404 + 0.433698i
\(298\) 0 0
\(299\) 31.1165 + 26.1098i 1.79951 + 1.50997i
\(300\) 0 0
\(301\) 1.26784 + 7.19028i 0.0730771 + 0.414441i
\(302\) 0 0
\(303\) −21.2267 + 9.96417i −1.21944 + 0.572427i
\(304\) 0 0
\(305\) 8.17052 14.1518i 0.467843 0.810328i
\(306\) 0 0
\(307\) −12.4443 21.5541i −0.710232 1.23016i −0.964770 0.263094i \(-0.915257\pi\)
0.254539 0.967063i \(-0.418076\pi\)
\(308\) 0 0
\(309\) −1.26988 4.69134i −0.0722407 0.266881i
\(310\) 0 0
\(311\) 1.69907 1.42569i 0.0963455 0.0808435i −0.593343 0.804950i \(-0.702192\pi\)
0.689688 + 0.724107i \(0.257748\pi\)
\(312\) 0 0
\(313\) −12.6348 + 4.59869i −0.714161 + 0.259933i −0.673445 0.739237i \(-0.735186\pi\)
−0.0407162 + 0.999171i \(0.512964\pi\)
\(314\) 0 0
\(315\) 17.1913 + 20.2768i 0.968623 + 1.14247i
\(316\) 0 0
\(317\) 4.76942 27.0487i 0.267877 1.51921i −0.492838 0.870121i \(-0.664040\pi\)
0.760715 0.649086i \(-0.224849\pi\)
\(318\) 0 0
\(319\) 12.8673 + 4.68331i 0.720430 + 0.262215i
\(320\) 0 0
\(321\) 17.2948 + 24.5660i 0.965304 + 1.37114i
\(322\) 0 0
\(323\) −3.51743 −0.195715
\(324\) 0 0
\(325\) 3.84019 0.213016
\(326\) 0 0
\(327\) 10.1121 + 14.3634i 0.559199 + 0.794299i
\(328\) 0 0
\(329\) 20.5068 + 7.46386i 1.13058 + 0.411496i
\(330\) 0 0
\(331\) −4.12868 + 23.4149i −0.226933 + 1.28700i 0.632023 + 0.774950i \(0.282225\pi\)
−0.858956 + 0.512050i \(0.828886\pi\)
\(332\) 0 0
\(333\) 21.8297 3.96412i 1.19626 0.217232i
\(334\) 0 0
\(335\) 8.00441 2.91337i 0.437327 0.159174i
\(336\) 0 0
\(337\) 15.9915 13.4184i 0.871110 0.730948i −0.0932216 0.995645i \(-0.529717\pi\)
0.964332 + 0.264697i \(0.0852721\pi\)
\(338\) 0 0
\(339\) 4.42256 + 16.3384i 0.240200 + 0.887378i
\(340\) 0 0
\(341\) −5.62426 9.74150i −0.304571 0.527532i
\(342\) 0 0
\(343\) −8.81486 + 15.2678i −0.475958 + 0.824383i
\(344\) 0 0
\(345\) 23.1605 10.8720i 1.24692 0.585327i
\(346\) 0 0
\(347\) 2.31831 + 13.1478i 0.124454 + 0.705811i 0.981631 + 0.190790i \(0.0611049\pi\)
−0.857177 + 0.515021i \(0.827784\pi\)
\(348\) 0 0
\(349\) 8.77715 + 7.36491i 0.469830 + 0.394234i 0.846733 0.532019i \(-0.178566\pi\)
−0.376902 + 0.926253i \(0.623011\pi\)
\(350\) 0 0
\(351\) 16.8646 24.4818i 0.900165 1.30674i
\(352\) 0 0
\(353\) −17.1875 14.4220i −0.914799 0.767607i 0.0582273 0.998303i \(-0.481455\pi\)
−0.973026 + 0.230696i \(0.925900\pi\)
\(354\) 0 0
\(355\) 2.00212 + 11.3546i 0.106262 + 0.602639i
\(356\) 0 0
\(357\) 4.12066 + 2.86968i 0.218089 + 0.151880i
\(358\) 0 0
\(359\) 4.41502 7.64704i 0.233016 0.403595i −0.725678 0.688034i \(-0.758474\pi\)
0.958694 + 0.284439i \(0.0918073\pi\)
\(360\) 0 0
\(361\) −3.85077 6.66974i −0.202672 0.351039i
\(362\) 0 0
\(363\) −8.11280 2.15165i −0.425812 0.112932i
\(364\) 0 0
\(365\) −14.1317 + 11.8579i −0.739687 + 0.620671i
\(366\) 0 0
\(367\) −20.3876 + 7.42050i −1.06423 + 0.387347i −0.814015 0.580844i \(-0.802723\pi\)
−0.250212 + 0.968191i \(0.580500\pi\)
\(368\) 0 0
\(369\) −0.347930 0.940962i −0.0181125 0.0489845i
\(370\) 0 0
\(371\) 6.99158 39.6512i 0.362985 2.05859i
\(372\) 0 0
\(373\) −30.1587 10.9769i −1.56156 0.568361i −0.590465 0.807063i \(-0.701056\pi\)
−0.971093 + 0.238702i \(0.923278\pi\)
\(374\) 0 0
\(375\) 8.58982 18.5443i 0.443576 0.957624i
\(376\) 0 0
\(377\) −31.5796 −1.62643
\(378\) 0 0
\(379\) 19.3500 0.993942 0.496971 0.867767i \(-0.334445\pi\)
0.496971 + 0.867767i \(0.334445\pi\)
\(380\) 0 0
\(381\) 17.9527 1.61682i 0.919743 0.0828320i
\(382\) 0 0
\(383\) 22.2072 + 8.08276i 1.13474 + 0.413010i 0.840009 0.542572i \(-0.182549\pi\)
0.294726 + 0.955582i \(0.404772\pi\)
\(384\) 0 0
\(385\) 3.81722 21.6486i 0.194544 1.10331i
\(386\) 0 0
\(387\) −0.0262414 5.14279i −0.00133392 0.261423i
\(388\) 0 0
\(389\) 5.25949 1.91430i 0.266667 0.0970587i −0.205226 0.978715i \(-0.565793\pi\)
0.471893 + 0.881656i \(0.343571\pi\)
\(390\) 0 0
\(391\) 3.70219 3.10651i 0.187228 0.157103i
\(392\) 0 0
\(393\) −18.4977 + 18.5923i −0.933086 + 0.937859i
\(394\) 0 0
\(395\) 6.15436 + 10.6597i 0.309659 + 0.536346i
\(396\) 0 0
\(397\) 4.32648 7.49368i 0.217140 0.376097i −0.736793 0.676119i \(-0.763661\pi\)
0.953932 + 0.300022i \(0.0969940\pi\)
\(398\) 0 0
\(399\) −3.22539 + 37.9822i −0.161471 + 1.90149i
\(400\) 0 0
\(401\) −5.00348 28.3761i −0.249862 1.41704i −0.808925 0.587912i \(-0.799950\pi\)
0.559063 0.829125i \(-0.311161\pi\)
\(402\) 0 0
\(403\) 19.8726 + 16.6751i 0.989924 + 0.830645i
\(404\) 0 0
\(405\) −9.52757 16.1201i −0.473429 0.801013i
\(406\) 0 0
\(407\) −14.0543 11.7930i −0.696645 0.584555i
\(408\) 0 0
\(409\) −0.223219 1.26594i −0.0110375 0.0625966i 0.978792 0.204859i \(-0.0656735\pi\)
−0.989829 + 0.142262i \(0.954562\pi\)
\(410\) 0 0
\(411\) −2.77834 + 32.7177i −0.137045 + 1.61385i
\(412\) 0 0
\(413\) −21.5824 + 37.3818i −1.06200 + 1.83944i
\(414\) 0 0
\(415\) −9.38357 16.2528i −0.460622 0.797820i
\(416\) 0 0
\(417\) −13.9881 + 14.0596i −0.684999 + 0.688503i
\(418\) 0 0
\(419\) 7.32223 6.14408i 0.357714 0.300158i −0.446165 0.894951i \(-0.647210\pi\)
0.803879 + 0.594793i \(0.202766\pi\)
\(420\) 0 0
\(421\) −28.9095 + 10.5222i −1.40896 + 0.512820i −0.930825 0.365465i \(-0.880910\pi\)
−0.478137 + 0.878285i \(0.658688\pi\)
\(422\) 0 0
\(423\) −13.3513 7.61782i −0.649164 0.370391i
\(424\) 0 0
\(425\) 0.0793399 0.449959i 0.00384855 0.0218262i
\(426\) 0 0
\(427\) −31.4336 11.4409i −1.52118 0.553664i
\(428\) 0 0
\(429\) −24.4838 + 2.20501i −1.18209 + 0.106459i
\(430\) 0 0
\(431\) −5.17147 −0.249101 −0.124551 0.992213i \(-0.539749\pi\)
−0.124551 + 0.992213i \(0.539749\pi\)
\(432\) 0 0
\(433\) 25.7835 1.23907 0.619537 0.784968i \(-0.287320\pi\)
0.619537 + 0.784968i \(0.287320\pi\)
\(434\) 0 0
\(435\) −8.36037 + 18.0490i −0.400849 + 0.865381i
\(436\) 0 0
\(437\) 34.4748 + 12.5478i 1.64915 + 0.600243i
\(438\) 0 0
\(439\) 4.28234 24.2864i 0.204385 1.15913i −0.694019 0.719956i \(-0.744162\pi\)
0.898404 0.439169i \(-0.144727\pi\)
\(440\) 0 0
\(441\) 21.3498 25.7090i 1.01666 1.22424i
\(442\) 0 0
\(443\) 3.76116 1.36895i 0.178698 0.0650409i −0.251121 0.967956i \(-0.580799\pi\)
0.429820 + 0.902915i \(0.358577\pi\)
\(444\) 0 0
\(445\) 3.13524 2.63078i 0.148625 0.124711i
\(446\) 0 0
\(447\) −16.3401 4.33367i −0.772860 0.204975i
\(448\) 0 0
\(449\) −11.9152 20.6377i −0.562312 0.973952i −0.997294 0.0735135i \(-0.976579\pi\)
0.434983 0.900439i \(-0.356755\pi\)
\(450\) 0 0
\(451\) −0.414793 + 0.718443i −0.0195318 + 0.0338301i
\(452\) 0 0
\(453\) −13.0380 9.07982i −0.612579 0.426607i
\(454\) 0 0
\(455\) 8.80345 + 49.9268i 0.412712 + 2.34061i
\(456\) 0 0
\(457\) −29.6052 24.8417i −1.38487 1.16205i −0.967370 0.253369i \(-0.918461\pi\)
−0.417502 0.908676i \(-0.637094\pi\)
\(458\) 0 0
\(459\) −2.52013 2.48184i −0.117630 0.115843i
\(460\) 0 0
\(461\) −12.4218 10.4232i −0.578542 0.485455i 0.305926 0.952055i \(-0.401034\pi\)
−0.884468 + 0.466601i \(0.845479\pi\)
\(462\) 0 0
\(463\) 2.21589 + 12.5670i 0.102981 + 0.584036i 0.992007 + 0.126180i \(0.0402716\pi\)
−0.889026 + 0.457857i \(0.848617\pi\)
\(464\) 0 0
\(465\) 14.7915 6.94339i 0.685939 0.321992i
\(466\) 0 0
\(467\) 1.29669 2.24593i 0.0600035 0.103929i −0.834463 0.551064i \(-0.814222\pi\)
0.894467 + 0.447134i \(0.147555\pi\)
\(468\) 0 0
\(469\) −8.71850 15.1009i −0.402583 0.697294i
\(470\) 0 0
\(471\) −0.226376 0.836308i −0.0104309 0.0385350i
\(472\) 0 0
\(473\) −3.25777 + 2.73359i −0.149792 + 0.125691i
\(474\) 0 0
\(475\) 3.25925 1.18627i 0.149545 0.0544299i
\(476\) 0 0
\(477\) −9.56378 + 26.6994i −0.437895 + 1.22248i
\(478\) 0 0
\(479\) −0.531048 + 3.01172i −0.0242642 + 0.137609i −0.994533 0.104419i \(-0.966702\pi\)
0.970269 + 0.242028i \(0.0778127\pi\)
\(480\) 0 0
\(481\) 39.7600 + 14.4714i 1.81290 + 0.659841i
\(482\) 0 0
\(483\) −30.1501 42.8259i −1.37188 1.94865i
\(484\) 0 0
\(485\) 0.982077 0.0445938
\(486\) 0 0
\(487\) −4.46808 −0.202468 −0.101234 0.994863i \(-0.532279\pi\)
−0.101234 + 0.994863i \(0.532279\pi\)
\(488\) 0 0
\(489\) −7.72784 10.9768i −0.349465 0.496387i
\(490\) 0 0
\(491\) −28.3262 10.3099i −1.27834 0.465278i −0.388458 0.921466i \(-0.626992\pi\)
−0.889883 + 0.456188i \(0.849214\pi\)
\(492\) 0 0
\(493\) −0.652447 + 3.70021i −0.0293847 + 0.166649i
\(494\) 0 0
\(495\) −5.22158 + 14.5772i −0.234693 + 0.655196i
\(496\) 0 0
\(497\) 22.1786 8.07235i 0.994847 0.362095i
\(498\) 0 0
\(499\) −3.92557 + 3.29394i −0.175732 + 0.147457i −0.726411 0.687260i \(-0.758813\pi\)
0.550679 + 0.834717i \(0.314369\pi\)
\(500\) 0 0
\(501\) −10.5571 39.0014i −0.471657 1.74245i
\(502\) 0 0
\(503\) −3.32680 5.76219i −0.148335 0.256923i 0.782277 0.622930i \(-0.214058\pi\)
−0.930612 + 0.366007i \(0.880725\pi\)
\(504\) 0 0
\(505\) −14.0837 + 24.3937i −0.626717 + 1.08551i
\(506\) 0 0
\(507\) 30.9384 14.5230i 1.37402 0.644989i
\(508\) 0 0
\(509\) −1.89801 10.7641i −0.0841278 0.477112i −0.997541 0.0700798i \(-0.977675\pi\)
0.913414 0.407033i \(-0.133436\pi\)
\(510\) 0 0
\(511\) 28.9283 + 24.2737i 1.27971 + 1.07381i
\(512\) 0 0
\(513\) 6.75068 25.9879i 0.298050 1.14739i
\(514\) 0 0
\(515\) −4.47226 3.75267i −0.197071 0.165363i
\(516\) 0 0
\(517\) 2.20726 + 12.5180i 0.0970754 + 0.550542i
\(518\) 0 0
\(519\) −8.69525 6.05548i −0.381679 0.265806i
\(520\) 0 0
\(521\) −11.1465 + 19.3062i −0.488335 + 0.845822i −0.999910 0.0134171i \(-0.995729\pi\)
0.511575 + 0.859239i \(0.329062\pi\)
\(522\) 0 0
\(523\) −11.2501 19.4858i −0.491933 0.852053i 0.508024 0.861343i \(-0.330376\pi\)
−0.999957 + 0.00928981i \(0.997043\pi\)
\(524\) 0 0
\(525\) −4.78603 1.26933i −0.208879 0.0553983i
\(526\) 0 0
\(527\) 2.36441 1.98397i 0.102995 0.0864233i
\(528\) 0 0
\(529\) −25.7547 + 9.37395i −1.11977 + 0.407563i
\(530\) 0 0
\(531\) 19.4246 23.3907i 0.842956 1.01507i
\(532\) 0 0
\(533\) 0.332229 1.88416i 0.0143904 0.0816121i
\(534\) 0 0
\(535\) 33.9121 + 12.3430i 1.46615 + 0.533635i
\(536\) 0 0
\(537\) −4.19209 + 9.05017i −0.180902 + 0.390544i
\(538\) 0 0
\(539\) −27.6340 −1.19028
\(540\) 0 0
\(541\) −31.6333 −1.36002 −0.680012 0.733201i \(-0.738025\pi\)
−0.680012 + 0.733201i \(0.738025\pi\)
\(542\) 0 0
\(543\) 23.7085 2.13519i 1.01743 0.0916298i
\(544\) 0 0
\(545\) 19.8280 + 7.21681i 0.849339 + 0.309134i
\(546\) 0 0
\(547\) −2.00203 + 11.3541i −0.0856006 + 0.485465i 0.911625 + 0.411024i \(0.134829\pi\)
−0.997225 + 0.0744418i \(0.976282\pi\)
\(548\) 0 0
\(549\) 20.4654 + 11.6769i 0.873443 + 0.498358i
\(550\) 0 0
\(551\) −26.8023 + 9.75524i −1.14182 + 0.415587i
\(552\) 0 0
\(553\) 19.3017 16.1960i 0.820790 0.688725i
\(554\) 0 0
\(555\) 18.7970 18.8932i 0.797889 0.801971i
\(556\) 0 0
\(557\) 4.96708 + 8.60324i 0.210462 + 0.364531i 0.951859 0.306535i \(-0.0991698\pi\)
−0.741397 + 0.671067i \(0.765836\pi\)
\(558\) 0 0
\(559\) 4.90390 8.49381i 0.207413 0.359250i
\(560\) 0 0
\(561\) −0.247482 + 2.91435i −0.0104487 + 0.123044i
\(562\) 0 0
\(563\) −4.60555 26.1193i −0.194101 1.10080i −0.913694 0.406403i \(-0.866783\pi\)
0.719593 0.694396i \(-0.244328\pi\)
\(564\) 0 0
\(565\) 15.5754 + 13.0693i 0.655262 + 0.549830i
\(566\) 0 0
\(567\) −29.1105 + 24.9373i −1.22253 + 1.04727i
\(568\) 0 0
\(569\) 27.5862 + 23.1476i 1.15647 + 0.970397i 0.999851 0.0172614i \(-0.00549475\pi\)
0.156623 + 0.987658i \(0.449939\pi\)
\(570\) 0 0
\(571\) 1.24236 + 7.04575i 0.0519910 + 0.294855i 0.999706 0.0242636i \(-0.00772411\pi\)
−0.947715 + 0.319119i \(0.896613\pi\)
\(572\) 0 0
\(573\) 1.14117 13.4384i 0.0476731 0.561398i
\(574\) 0 0
\(575\) −2.38277 + 4.12708i −0.0993684 + 0.172111i
\(576\) 0 0
\(577\) 7.83173 + 13.5650i 0.326039 + 0.564717i 0.981722 0.190320i \(-0.0609525\pi\)
−0.655683 + 0.755036i \(0.727619\pi\)
\(578\) 0 0
\(579\) −1.64876 + 1.65719i −0.0685200 + 0.0688705i
\(580\) 0 0
\(581\) −29.4293 + 24.6941i −1.22093 + 1.02449i
\(582\) 0 0
\(583\) 22.0375 8.02101i 0.912702 0.332196i
\(584\) 0 0
\(585\) −0.182211 35.7098i −0.00753351 1.47642i
\(586\) 0 0
\(587\) −1.59747 + 9.05971i −0.0659347 + 0.373934i 0.933930 + 0.357457i \(0.116356\pi\)
−0.999864 + 0.0164772i \(0.994755\pi\)
\(588\) 0 0
\(589\) 22.0174 + 8.01367i 0.907210 + 0.330197i
\(590\) 0 0
\(591\) 15.6014 1.40506i 0.641754 0.0577964i
\(592\) 0 0
\(593\) 19.8285 0.814259 0.407129 0.913370i \(-0.366530\pi\)
0.407129 + 0.913370i \(0.366530\pi\)
\(594\) 0 0
\(595\) 6.03186 0.247282
\(596\) 0 0
\(597\) −4.08994 + 8.82965i −0.167390 + 0.361374i
\(598\) 0 0
\(599\) −26.6087 9.68479i −1.08720 0.395710i −0.264619 0.964353i \(-0.585246\pi\)
−0.822584 + 0.568643i \(0.807469\pi\)
\(600\) 0 0
\(601\) −7.14558 + 40.5246i −0.291474 + 1.65303i 0.389723 + 0.920932i \(0.372571\pi\)
−0.681197 + 0.732100i \(0.738540\pi\)
\(602\) 0 0
\(603\) 4.25965 + 11.5201i 0.173466 + 0.469133i
\(604\) 0 0
\(605\) −9.47414 + 3.44831i −0.385179 + 0.140194i
\(606\) 0 0
\(607\) 9.62083 8.07283i 0.390497 0.327666i −0.426310 0.904577i \(-0.640187\pi\)
0.816807 + 0.576911i \(0.195742\pi\)
\(608\) 0 0
\(609\) 39.3576 + 10.4383i 1.59485 + 0.422981i
\(610\) 0 0
\(611\) −14.6575 25.3875i −0.592978 1.02707i
\(612\) 0 0
\(613\) 4.01692 6.95752i 0.162242 0.281011i −0.773430 0.633881i \(-0.781461\pi\)
0.935672 + 0.352870i \(0.114794\pi\)
\(614\) 0 0
\(615\) −0.988917 0.688694i −0.0398770 0.0277708i
\(616\) 0 0
\(617\) −0.677179 3.84047i −0.0272622 0.154612i 0.968138 0.250418i \(-0.0805681\pi\)
−0.995400 + 0.0958065i \(0.969457\pi\)
\(618\) 0 0
\(619\) 21.1733 + 17.7665i 0.851026 + 0.714095i 0.960015 0.279948i \(-0.0903171\pi\)
−0.108990 + 0.994043i \(0.534762\pi\)
\(620\) 0 0
\(621\) 15.8466 + 33.3150i 0.635902 + 1.33689i
\(622\) 0 0
\(623\) −6.41799 5.38533i −0.257131 0.215759i
\(624\) 0 0
\(625\) −3.68019 20.8714i −0.147208 0.834856i
\(626\) 0 0
\(627\) −20.0988 + 9.43472i −0.802668 + 0.376786i
\(628\) 0 0
\(629\) 2.51709 4.35973i 0.100363 0.173834i
\(630\) 0 0
\(631\) −6.29226 10.8985i −0.250491 0.433863i 0.713170 0.700991i \(-0.247259\pi\)
−0.963661 + 0.267128i \(0.913925\pi\)
\(632\) 0 0
\(633\) 3.20099 + 11.8255i 0.127228 + 0.470021i
\(634\) 0 0
\(635\) 16.5867 13.9179i 0.658222 0.552314i
\(636\) 0 0
\(637\) 59.8874 21.7972i 2.37282 0.863637i
\(638\) 0 0
\(639\) −16.3574 + 2.97038i −0.647088 + 0.117507i
\(640\) 0 0
\(641\) −7.12752 + 40.4222i −0.281520 + 1.59658i 0.435936 + 0.899977i \(0.356417\pi\)
−0.717457 + 0.696603i \(0.754694\pi\)
\(642\) 0 0
\(643\) 17.0607 + 6.20958i 0.672808 + 0.244882i 0.655756 0.754973i \(-0.272350\pi\)
0.0170514 + 0.999855i \(0.494572\pi\)
\(644\) 0 0
\(645\) −3.55628 5.05141i −0.140028 0.198899i
\(646\) 0 0
\(647\) 0.286590 0.0112670 0.00563350 0.999984i \(-0.498207\pi\)
0.00563350 + 0.999984i \(0.498207\pi\)
\(648\) 0 0
\(649\) −25.1421 −0.986914
\(650\) 0 0
\(651\) −19.2554 27.3508i −0.754679 1.07196i
\(652\) 0 0
\(653\) −6.82970 2.48581i −0.267267 0.0972771i 0.204911 0.978781i \(-0.434310\pi\)
−0.472177 + 0.881504i \(0.656532\pi\)
\(654\) 0 0
\(655\) −5.47061 + 31.0254i −0.213755 + 1.21226i
\(656\) 0 0
\(657\) −17.2018 20.2892i −0.671106 0.791555i
\(658\) 0 0
\(659\) −10.3014 + 3.74940i −0.401285 + 0.146056i −0.534775 0.844994i \(-0.679604\pi\)
0.133490 + 0.991050i \(0.457381\pi\)
\(660\) 0 0
\(661\) −12.9108 + 10.8334i −0.502171 + 0.421372i −0.858364 0.513041i \(-0.828519\pi\)
0.356193 + 0.934412i \(0.384075\pi\)
\(662\) 0 0
\(663\) −1.76245 6.51106i −0.0684479 0.252869i
\(664\) 0 0
\(665\) 22.8946 + 39.6545i 0.887813 + 1.53774i
\(666\) 0 0
\(667\) 19.5946 33.9388i 0.758705 1.31412i
\(668\) 0 0
\(669\) 25.0951 11.7801i 0.970233 0.455444i
\(670\) 0 0
\(671\) −3.38338 19.1881i −0.130614 0.740749i
\(672\) 0 0
\(673\) −29.7906 24.9973i −1.14834 0.963574i −0.148663 0.988888i \(-0.547497\pi\)
−0.999680 + 0.0253140i \(0.991941\pi\)
\(674\) 0 0
\(675\) 3.17217 + 1.44975i 0.122097 + 0.0558010i
\(676\) 0 0
\(677\) 10.3174 + 8.65735i 0.396531 + 0.332729i 0.819151 0.573578i \(-0.194445\pi\)
−0.422620 + 0.906307i \(0.638889\pi\)
\(678\) 0 0
\(679\) −0.349095 1.97982i −0.0133971 0.0759785i
\(680\) 0 0
\(681\) −5.98414 4.16743i −0.229313 0.159696i
\(682\) 0 0
\(683\) −13.8061 + 23.9128i −0.528275 + 0.914998i 0.471182 + 0.882036i \(0.343827\pi\)
−0.999457 + 0.0329623i \(0.989506\pi\)
\(684\) 0 0
\(685\) 19.7213 + 34.1583i 0.753512 + 1.30512i
\(686\) 0 0
\(687\) −23.9550 6.35327i −0.913941 0.242392i
\(688\) 0 0
\(689\) −41.4321 + 34.7656i −1.57844 + 1.32446i
\(690\) 0 0
\(691\) 19.5307 7.10858i 0.742982 0.270423i 0.0573322 0.998355i \(-0.481741\pi\)
0.685649 + 0.727932i \(0.259518\pi\)
\(692\) 0 0
\(693\) 31.2430 + 5.34475i 1.18682 + 0.203030i
\(694\) 0 0
\(695\) −4.13691 + 23.4616i −0.156922 + 0.889948i
\(696\) 0 0
\(697\) −0.213905 0.0778551i −0.00810223 0.00294897i
\(698\) 0 0
\(699\) −5.13065 + 11.0764i −0.194059 + 0.418948i
\(700\) 0 0
\(701\) 0.227676 0.00859920 0.00429960 0.999991i \(-0.498631\pi\)
0.00429960 + 0.999991i \(0.498631\pi\)
\(702\) 0 0
\(703\) 38.2155 1.44133
\(704\) 0 0
\(705\) −18.3903 + 1.65624i −0.692621 + 0.0623774i
\(706\) 0 0
\(707\) 54.1828 + 19.7209i 2.03775 + 0.741681i
\(708\) 0 0
\(709\) 3.26873 18.5379i 0.122760 0.696205i −0.859854 0.510541i \(-0.829445\pi\)
0.982613 0.185664i \(-0.0594436\pi\)
\(710\) 0 0
\(711\) −15.3248 + 8.95234i −0.574725 + 0.335739i
\(712\) 0 0
\(713\) −30.2514 + 11.0106i −1.13292 + 0.412350i
\(714\) 0 0
\(715\) −22.6209 + 18.9812i −0.845972 + 0.709855i
\(716\) 0 0
\(717\) −15.3346 + 15.4130i −0.572680 + 0.575610i
\(718\) 0 0
\(719\) −4.87179 8.43819i −0.181687 0.314692i 0.760768 0.649024i \(-0.224823\pi\)
−0.942455 + 0.334332i \(0.891489\pi\)
\(720\) 0 0
\(721\) −5.97546 + 10.3498i −0.222538 + 0.385447i
\(722\) 0 0
\(723\) −4.28060 + 50.4084i −0.159197 + 1.87471i
\(724\) 0 0
\(725\) −0.643358 3.64866i −0.0238937 0.135508i
\(726\) 0 0
\(727\) −18.6693 15.6654i −0.692405 0.580997i 0.227197 0.973849i \(-0.427044\pi\)
−0.919602 + 0.392852i \(0.871488\pi\)
\(728\) 0 0
\(729\) 23.1733 13.8563i 0.858270 0.513198i
\(730\) 0 0
\(731\) −0.893911 0.750080i −0.0330625 0.0277427i
\(732\) 0 0
\(733\) −2.27026 12.8753i −0.0838541 0.475560i −0.997598 0.0692695i \(-0.977933\pi\)
0.913744 0.406291i \(-0.133178\pi\)
\(734\) 0 0
\(735\) 3.39661 39.9985i 0.125286 1.47537i
\(736\) 0 0
\(737\) 5.07825 8.79579i 0.187060 0.323997i
\(738\) 0 0
\(739\) 17.9397 + 31.0725i 0.659922 + 1.14302i 0.980635 + 0.195842i \(0.0627441\pi\)
−0.320713 + 0.947176i \(0.603923\pi\)
\(740\) 0 0
\(741\) 36.1153 36.3001i 1.32673 1.33352i
\(742\) 0 0
\(743\) 39.7781 33.3778i 1.45932 1.22451i 0.533910 0.845541i \(-0.320722\pi\)
0.925408 0.378972i \(-0.123722\pi\)
\(744\) 0 0
\(745\) −19.0820 + 6.94527i −0.699110 + 0.254455i
\(746\) 0 0
\(747\) 23.3658 13.6497i 0.854909 0.499416i
\(748\) 0 0
\(749\) 12.8283 72.7527i 0.468734 2.65832i
\(750\) 0 0
\(751\) −3.08467 1.12273i −0.112561 0.0409690i 0.285125 0.958490i \(-0.407965\pi\)
−0.397687 + 0.917521i \(0.630187\pi\)
\(752\) 0 0
\(753\) −11.4544 + 1.03158i −0.417422 + 0.0375930i
\(754\) 0 0
\(755\) −19.0851 −0.694579
\(756\) 0 0
\(757\) −3.70968 −0.134831 −0.0674153 0.997725i \(-0.521475\pi\)
−0.0674153 + 0.997725i \(0.521475\pi\)
\(758\) 0 0
\(759\) 12.8220 27.6811i 0.465410 1.00476i
\(760\) 0 0
\(761\) −20.5395 7.47578i −0.744557 0.270997i −0.0582436 0.998302i \(-0.518550\pi\)
−0.686314 + 0.727306i \(0.740772\pi\)
\(762\) 0 0
\(763\) 7.50053 42.5376i 0.271537 1.53996i
\(764\) 0 0
\(765\) −4.18791 0.716428i −0.151414 0.0259025i
\(766\) 0 0
\(767\) 54.4870 19.8316i 1.96741 0.716079i
\(768\) 0 0
\(769\) −2.44362 + 2.05044i −0.0881193 + 0.0739409i −0.685783 0.727806i \(-0.740540\pi\)
0.597664 + 0.801747i \(0.296096\pi\)
\(770\) 0 0
\(771\) 35.1221 + 9.31496i 1.26489 + 0.335470i
\(772\) 0 0
\(773\) 22.7097 + 39.3344i 0.816812 + 1.41476i 0.908020 + 0.418927i \(0.137594\pi\)
−0.0912081 + 0.995832i \(0.529073\pi\)
\(774\) 0 0
\(775\) −1.52176 + 2.63576i −0.0546632 + 0.0946794i
\(776\) 0 0
\(777\) −44.7694 31.1780i −1.60609 1.11850i
\(778\) 0 0
\(779\) −0.300066 1.70176i −0.0107510 0.0609718i
\(780\) 0 0
\(781\) 10.5311 + 8.83667i 0.376833 + 0.316201i
\(782\) 0 0
\(783\) −26.0862 11.9220i −0.932243 0.426056i
\(784\) 0 0
\(785\) −0.797255 0.668976i −0.0284552 0.0238768i
\(786\) 0 0
\(787\) 0.633058 + 3.59025i 0.0225661 + 0.127979i 0.994010 0.109292i \(-0.0348583\pi\)
−0.971444 + 0.237271i \(0.923747\pi\)
\(788\) 0 0
\(789\) −2.76716 + 1.29895i −0.0985135 + 0.0462439i
\(790\) 0 0
\(791\) 20.8105 36.0449i 0.739938 1.28161i
\(792\) 0 0
\(793\) 22.4676 + 38.9150i 0.797846 + 1.38191i
\(794\) 0 0
\(795\) 8.90118 + 32.8838i 0.315692 + 1.16627i
\(796\) 0