Properties

Label 576.2.bb.e.49.14
Level $576$
Weight $2$
Character 576.49
Analytic conductor $4.599$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bb (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 49.14
Character \(\chi\) \(=\) 576.49
Dual form 576.2.bb.e.529.14

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22967 - 1.21980i) q^{3} +(0.174734 - 0.0468197i) q^{5} +(4.04791 - 2.33706i) q^{7} +(0.0241875 - 2.99990i) q^{9} +O(q^{10})\) \(q+(1.22967 - 1.21980i) q^{3} +(0.174734 - 0.0468197i) q^{5} +(4.04791 - 2.33706i) q^{7} +(0.0241875 - 2.99990i) q^{9} +(-0.160430 + 0.598734i) q^{11} +(1.18229 + 4.41237i) q^{13} +(0.157754 - 0.270713i) q^{15} -4.34691 q^{17} +(1.23918 - 1.23918i) q^{19} +(2.12686 - 7.81146i) q^{21} +(-3.86311 - 2.23037i) q^{23} +(-4.30179 + 2.48364i) q^{25} +(-3.62953 - 3.71840i) q^{27} +(8.64910 + 2.31752i) q^{29} +(2.25376 - 3.90364i) q^{31} +(0.533058 + 0.931939i) q^{33} +(0.597886 - 0.597886i) q^{35} +(2.79692 + 2.79692i) q^{37} +(6.83604 + 3.98362i) q^{39} +(-3.67211 - 2.12009i) q^{41} +(-0.00351694 + 0.0131254i) q^{43} +(-0.136228 - 0.525316i) q^{45} +(1.17465 + 2.03456i) q^{47} +(7.42373 - 12.8583i) q^{49} +(-5.34528 + 5.30235i) q^{51} +(-0.519418 - 0.519418i) q^{53} +0.112130i q^{55} +(0.0122364 - 3.03533i) q^{57} +(-11.0349 + 2.95679i) q^{59} +(-2.19745 - 0.588805i) q^{61} +(-6.91305 - 12.1999i) q^{63} +(0.413172 + 0.715636i) q^{65} +(1.88714 + 7.04291i) q^{67} +(-7.47096 + 1.96959i) q^{69} +7.55145i q^{71} -2.92707i q^{73} +(-2.26025 + 8.30137i) q^{75} +(0.749872 + 2.79856i) q^{77} +(-1.45885 - 2.52680i) q^{79} +(-8.99883 - 0.145120i) q^{81} +(7.44148 + 1.99394i) q^{83} +(-0.759552 + 0.203521i) q^{85} +(13.4625 - 7.70036i) q^{87} +3.18821i q^{89} +(15.0978 + 15.0978i) q^{91} +(-1.99025 - 7.54933i) q^{93} +(0.158508 - 0.274544i) q^{95} +(8.03868 + 13.9234i) q^{97} +(1.79226 + 0.495757i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q - 2q^{3} + 4q^{5} + O(q^{10}) \) \( 72q - 2q^{3} + 4q^{5} + 2q^{11} - 16q^{13} + 20q^{15} - 16q^{17} - 28q^{19} - 16q^{21} - 8q^{27} + 4q^{29} - 28q^{31} - 32q^{33} + 16q^{35} + 16q^{37} + 10q^{43} + 40q^{45} + 56q^{47} + 4q^{49} + 54q^{51} - 8q^{53} + 14q^{59} - 32q^{61} + 108q^{63} - 64q^{65} + 18q^{67} + 32q^{69} - 86q^{75} - 36q^{77} - 44q^{79} - 44q^{81} - 20q^{83} - 8q^{85} + 80q^{91} - 4q^{93} - 48q^{95} + 40q^{97} - 28q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) 1.22967 1.21980i 0.709952 0.704250i
\(4\) 0 0
\(5\) 0.174734 0.0468197i 0.0781432 0.0209384i −0.219536 0.975604i \(-0.570454\pi\)
0.297679 + 0.954666i \(0.403788\pi\)
\(6\) 0 0
\(7\) 4.04791 2.33706i 1.52997 0.883327i 0.530605 0.847619i \(-0.321965\pi\)
0.999362 0.0357075i \(-0.0113685\pi\)
\(8\) 0 0
\(9\) 0.0241875 2.99990i 0.00806251 0.999967i
\(10\) 0 0
\(11\) −0.160430 + 0.598734i −0.0483716 + 0.180525i −0.985885 0.167424i \(-0.946455\pi\)
0.937513 + 0.347949i \(0.113122\pi\)
\(12\) 0 0
\(13\) 1.18229 + 4.41237i 0.327909 + 1.22377i 0.911355 + 0.411621i \(0.135037\pi\)
−0.583446 + 0.812152i \(0.698296\pi\)
\(14\) 0 0
\(15\) 0.157754 0.270713i 0.0407320 0.0698977i
\(16\) 0 0
\(17\) −4.34691 −1.05428 −0.527141 0.849778i \(-0.676736\pi\)
−0.527141 + 0.849778i \(0.676736\pi\)
\(18\) 0 0
\(19\) 1.23918 1.23918i 0.284287 0.284287i −0.550529 0.834816i \(-0.685574\pi\)
0.834816 + 0.550529i \(0.185574\pi\)
\(20\) 0 0
\(21\) 2.12686 7.81146i 0.464119 1.70460i
\(22\) 0 0
\(23\) −3.86311 2.23037i −0.805515 0.465064i 0.0398812 0.999204i \(-0.487302\pi\)
−0.845396 + 0.534140i \(0.820635\pi\)
\(24\) 0 0
\(25\) −4.30179 + 2.48364i −0.860357 + 0.496728i
\(26\) 0 0
\(27\) −3.62953 3.71840i −0.698504 0.715607i
\(28\) 0 0
\(29\) 8.64910 + 2.31752i 1.60610 + 0.430353i 0.946877 0.321597i \(-0.104220\pi\)
0.659221 + 0.751949i \(0.270886\pi\)
\(30\) 0 0
\(31\) 2.25376 3.90364i 0.404788 0.701114i −0.589509 0.807762i \(-0.700679\pi\)
0.994297 + 0.106648i \(0.0340119\pi\)
\(32\) 0 0
\(33\) 0.533058 + 0.931939i 0.0927935 + 0.162230i
\(34\) 0 0
\(35\) 0.597886 0.597886i 0.101061 0.101061i
\(36\) 0 0
\(37\) 2.79692 + 2.79692i 0.459811 + 0.459811i 0.898593 0.438783i \(-0.144590\pi\)
−0.438783 + 0.898593i \(0.644590\pi\)
\(38\) 0 0
\(39\) 6.83604 + 3.98362i 1.09464 + 0.637889i
\(40\) 0 0
\(41\) −3.67211 2.12009i −0.573487 0.331103i 0.185054 0.982728i \(-0.440754\pi\)
−0.758541 + 0.651626i \(0.774087\pi\)
\(42\) 0 0
\(43\) −0.00351694 + 0.0131254i −0.000536329 + 0.00200161i −0.966193 0.257818i \(-0.916996\pi\)
0.965657 + 0.259820i \(0.0836631\pi\)
\(44\) 0 0
\(45\) −0.136228 0.525316i −0.0203077 0.0783095i
\(46\) 0 0
\(47\) 1.17465 + 2.03456i 0.171341 + 0.296771i 0.938889 0.344221i \(-0.111857\pi\)
−0.767548 + 0.640991i \(0.778523\pi\)
\(48\) 0 0
\(49\) 7.42373 12.8583i 1.06053 1.83690i
\(50\) 0 0
\(51\) −5.34528 + 5.30235i −0.748489 + 0.742478i
\(52\) 0 0
\(53\) −0.519418 0.519418i −0.0713476 0.0713476i 0.670533 0.741880i \(-0.266066\pi\)
−0.741880 + 0.670533i \(0.766066\pi\)
\(54\) 0 0
\(55\) 0.112130i 0.0151196i
\(56\) 0 0
\(57\) 0.0122364 3.03533i 0.00162075 0.402040i
\(58\) 0 0
\(59\) −11.0349 + 2.95679i −1.43662 + 0.384942i −0.891350 0.453317i \(-0.850241\pi\)
−0.545273 + 0.838258i \(0.683574\pi\)
\(60\) 0 0
\(61\) −2.19745 0.588805i −0.281355 0.0753887i 0.115382 0.993321i \(-0.463191\pi\)
−0.396737 + 0.917932i \(0.629857\pi\)
\(62\) 0 0
\(63\) −6.91305 12.1999i −0.870963 1.53704i
\(64\) 0 0
\(65\) 0.413172 + 0.715636i 0.0512477 + 0.0887637i
\(66\) 0 0
\(67\) 1.88714 + 7.04291i 0.230551 + 0.860428i 0.980104 + 0.198484i \(0.0636018\pi\)
−0.749553 + 0.661944i \(0.769732\pi\)
\(68\) 0 0
\(69\) −7.47096 + 1.96959i −0.899398 + 0.237111i
\(70\) 0 0
\(71\) 7.55145i 0.896193i 0.893985 + 0.448096i \(0.147898\pi\)
−0.893985 + 0.448096i \(0.852102\pi\)
\(72\) 0 0
\(73\) 2.92707i 0.342588i −0.985220 0.171294i \(-0.945205\pi\)
0.985220 0.171294i \(-0.0547948\pi\)
\(74\) 0 0
\(75\) −2.26025 + 8.30137i −0.260991 + 0.958560i
\(76\) 0 0
\(77\) 0.749872 + 2.79856i 0.0854558 + 0.318925i
\(78\) 0 0
\(79\) −1.45885 2.52680i −0.164133 0.284287i 0.772214 0.635362i \(-0.219149\pi\)
−0.936347 + 0.351076i \(0.885816\pi\)
\(80\) 0 0
\(81\) −8.99883 0.145120i −0.999870 0.0161245i
\(82\) 0 0
\(83\) 7.44148 + 1.99394i 0.816808 + 0.218863i 0.642950 0.765908i \(-0.277710\pi\)
0.173858 + 0.984771i \(0.444377\pi\)
\(84\) 0 0
\(85\) −0.759552 + 0.203521i −0.0823850 + 0.0220750i
\(86\) 0 0
\(87\) 13.4625 7.70036i 1.44333 0.825566i
\(88\) 0 0
\(89\) 3.18821i 0.337950i 0.985620 + 0.168975i \(0.0540457\pi\)
−0.985620 + 0.168975i \(0.945954\pi\)
\(90\) 0 0
\(91\) 15.0978 + 15.0978i 1.58268 + 1.58268i
\(92\) 0 0
\(93\) −1.99025 7.54933i −0.206380 0.782829i
\(94\) 0 0
\(95\) 0.158508 0.274544i 0.0162626 0.0281676i
\(96\) 0 0
\(97\) 8.03868 + 13.9234i 0.816204 + 1.41371i 0.908460 + 0.417972i \(0.137259\pi\)
−0.0922553 + 0.995735i \(0.529408\pi\)
\(98\) 0 0
\(99\) 1.79226 + 0.495757i 0.180129 + 0.0498255i
\(100\) 0 0
\(101\) −4.56339 + 17.0308i −0.454074 + 1.69463i 0.236720 + 0.971578i \(0.423928\pi\)
−0.690795 + 0.723051i \(0.742739\pi\)
\(102\) 0 0
\(103\) −8.05916 4.65296i −0.794093 0.458470i 0.0473086 0.998880i \(-0.484936\pi\)
−0.841401 + 0.540411i \(0.818269\pi\)
\(104\) 0 0
\(105\) 0.00590388 1.46450i 0.000576159 0.142921i
\(106\) 0 0
\(107\) −9.51927 9.51927i −0.920263 0.920263i 0.0767848 0.997048i \(-0.475535\pi\)
−0.997048 + 0.0767848i \(0.975535\pi\)
\(108\) 0 0
\(109\) −6.35255 + 6.35255i −0.608464 + 0.608464i −0.942544 0.334081i \(-0.891574\pi\)
0.334081 + 0.942544i \(0.391574\pi\)
\(110\) 0 0
\(111\) 6.85097 + 0.0276184i 0.650265 + 0.00262143i
\(112\) 0 0
\(113\) 5.34598 9.25951i 0.502908 0.871062i −0.497087 0.867701i \(-0.665597\pi\)
0.999994 0.00336088i \(-0.00106980\pi\)
\(114\) 0 0
\(115\) −0.779441 0.208851i −0.0726832 0.0194754i
\(116\) 0 0
\(117\) 13.2653 3.44004i 1.22638 0.318032i
\(118\) 0 0
\(119\) −17.5959 + 10.1590i −1.61302 + 0.931275i
\(120\) 0 0
\(121\) 9.19353 + 5.30789i 0.835776 + 0.482535i
\(122\) 0 0
\(123\) −7.10157 + 1.87221i −0.640327 + 0.168811i
\(124\) 0 0
\(125\) −1.27495 + 1.27495i −0.114035 + 0.114035i
\(126\) 0 0
\(127\) 11.5283 1.02297 0.511484 0.859293i \(-0.329096\pi\)
0.511484 + 0.859293i \(0.329096\pi\)
\(128\) 0 0
\(129\) 0.0116857 + 0.0204299i 0.00102886 + 0.00179875i
\(130\) 0 0
\(131\) −0.917160 3.42289i −0.0801327 0.299059i 0.914215 0.405229i \(-0.132808\pi\)
−0.994348 + 0.106169i \(0.966141\pi\)
\(132\) 0 0
\(133\) 2.12005 7.91213i 0.183832 0.686069i
\(134\) 0 0
\(135\) −0.808296 0.479796i −0.0695670 0.0412943i
\(136\) 0 0
\(137\) −13.0194 + 7.51678i −1.11233 + 0.642202i −0.939431 0.342739i \(-0.888646\pi\)
−0.172895 + 0.984940i \(0.555312\pi\)
\(138\) 0 0
\(139\) 9.76161 2.61562i 0.827969 0.221854i 0.180142 0.983641i \(-0.442344\pi\)
0.647828 + 0.761787i \(0.275678\pi\)
\(140\) 0 0
\(141\) 3.92619 + 1.06900i 0.330645 + 0.0900261i
\(142\) 0 0
\(143\) −2.83152 −0.236783
\(144\) 0 0
\(145\) 1.61979 0.134517
\(146\) 0 0
\(147\) −6.55574 24.8669i −0.540708 2.05099i
\(148\) 0 0
\(149\) −5.14811 + 1.37943i −0.421749 + 0.113007i −0.463451 0.886123i \(-0.653389\pi\)
0.0417013 + 0.999130i \(0.486722\pi\)
\(150\) 0 0
\(151\) −9.86458 + 5.69532i −0.802768 + 0.463479i −0.844438 0.535653i \(-0.820066\pi\)
0.0416699 + 0.999131i \(0.486732\pi\)
\(152\) 0 0
\(153\) −0.105141 + 13.0403i −0.00850015 + 1.05425i
\(154\) 0 0
\(155\) 0.211041 0.787617i 0.0169512 0.0632629i
\(156\) 0 0
\(157\) 1.46607 + 5.47145i 0.117005 + 0.436670i 0.999429 0.0337857i \(-0.0107564\pi\)
−0.882424 + 0.470455i \(0.844090\pi\)
\(158\) 0 0
\(159\) −1.27230 0.00512904i −0.100900 0.000406760i
\(160\) 0 0
\(161\) −20.8501 −1.64321
\(162\) 0 0
\(163\) −15.0117 + 15.0117i −1.17581 + 1.17581i −0.195004 + 0.980802i \(0.562472\pi\)
−0.980802 + 0.195004i \(0.937528\pi\)
\(164\) 0 0
\(165\) 0.136776 + 0.137884i 0.0106480 + 0.0107342i
\(166\) 0 0
\(167\) 7.81918 + 4.51441i 0.605066 + 0.349335i 0.771032 0.636796i \(-0.219741\pi\)
−0.165966 + 0.986132i \(0.553074\pi\)
\(168\) 0 0
\(169\) −6.81291 + 3.93343i −0.524070 + 0.302572i
\(170\) 0 0
\(171\) −3.68744 3.74739i −0.281986 0.286570i
\(172\) 0 0
\(173\) 5.00520 + 1.34114i 0.380539 + 0.101965i 0.444017 0.896018i \(-0.353553\pi\)
−0.0634788 + 0.997983i \(0.520220\pi\)
\(174\) 0 0
\(175\) −11.6088 + 20.1071i −0.877546 + 1.51995i
\(176\) 0 0
\(177\) −9.96263 + 17.0962i −0.748837 + 1.28503i
\(178\) 0 0
\(179\) −1.96093 + 1.96093i −0.146566 + 0.146566i −0.776582 0.630016i \(-0.783048\pi\)
0.630016 + 0.776582i \(0.283048\pi\)
\(180\) 0 0
\(181\) −0.224256 0.224256i −0.0166688 0.0166688i 0.698723 0.715392i \(-0.253752\pi\)
−0.715392 + 0.698723i \(0.753752\pi\)
\(182\) 0 0
\(183\) −3.42037 + 1.95641i −0.252841 + 0.144622i
\(184\) 0 0
\(185\) 0.619667 + 0.357765i 0.0455588 + 0.0263034i
\(186\) 0 0
\(187\) 0.697377 2.60265i 0.0509972 0.190324i
\(188\) 0 0
\(189\) −23.3822 6.56932i −1.70080 0.477847i
\(190\) 0 0
\(191\) 10.3893 + 17.9947i 0.751741 + 1.30205i 0.946978 + 0.321298i \(0.104119\pi\)
−0.195237 + 0.980756i \(0.562548\pi\)
\(192\) 0 0
\(193\) 7.69572 13.3294i 0.553950 0.959469i −0.444035 0.896010i \(-0.646453\pi\)
0.997984 0.0634596i \(-0.0202134\pi\)
\(194\) 0 0
\(195\) 1.38100 + 0.376010i 0.0988953 + 0.0269267i
\(196\) 0 0
\(197\) −0.905158 0.905158i −0.0644898 0.0644898i 0.674126 0.738616i \(-0.264520\pi\)
−0.738616 + 0.674126i \(0.764520\pi\)
\(198\) 0 0
\(199\) 16.5201i 1.17108i −0.810645 0.585538i \(-0.800883\pi\)
0.810645 0.585538i \(-0.199117\pi\)
\(200\) 0 0
\(201\) 10.9115 + 6.35854i 0.769637 + 0.448497i
\(202\) 0 0
\(203\) 40.4270 10.8324i 2.83742 0.760284i
\(204\) 0 0
\(205\) −0.740902 0.198524i −0.0517469 0.0138655i
\(206\) 0 0
\(207\) −6.78433 + 11.5350i −0.471543 + 0.801739i
\(208\) 0 0
\(209\) 0.543137 + 0.940741i 0.0375696 + 0.0650724i
\(210\) 0 0
\(211\) −6.75305 25.2027i −0.464899 1.73503i −0.657224 0.753695i \(-0.728270\pi\)
0.192325 0.981331i \(-0.438397\pi\)
\(212\) 0 0
\(213\) 9.21125 + 9.28581i 0.631144 + 0.636253i
\(214\) 0 0
\(215\) 0.00245811i 0.000167642i
\(216\) 0 0
\(217\) 21.0688i 1.43024i
\(218\) 0 0
\(219\) −3.57044 3.59934i −0.241268 0.243221i
\(220\) 0 0
\(221\) −5.13932 19.1802i −0.345708 1.29020i
\(222\) 0 0
\(223\) −6.47927 11.2224i −0.433884 0.751510i 0.563320 0.826239i \(-0.309524\pi\)
−0.997204 + 0.0747295i \(0.976191\pi\)
\(224\) 0 0
\(225\) 7.34662 + 12.9650i 0.489775 + 0.864334i
\(226\) 0 0
\(227\) 13.1401 + 3.52089i 0.872142 + 0.233690i 0.667014 0.745045i \(-0.267572\pi\)
0.205128 + 0.978735i \(0.434239\pi\)
\(228\) 0 0
\(229\) −16.2371 + 4.35071i −1.07298 + 0.287503i −0.751715 0.659488i \(-0.770773\pi\)
−0.321260 + 0.946991i \(0.604106\pi\)
\(230\) 0 0
\(231\) 4.33577 + 2.52662i 0.285273 + 0.166239i
\(232\) 0 0
\(233\) 10.0493i 0.658351i −0.944269 0.329176i \(-0.893229\pi\)
0.944269 0.329176i \(-0.106771\pi\)
\(234\) 0 0
\(235\) 0.300509 + 0.300509i 0.0196030 + 0.0196030i
\(236\) 0 0
\(237\) −4.87608 1.32763i −0.316735 0.0862390i
\(238\) 0 0
\(239\) 3.38365 5.86066i 0.218870 0.379094i −0.735593 0.677424i \(-0.763096\pi\)
0.954463 + 0.298330i \(0.0964295\pi\)
\(240\) 0 0
\(241\) −1.07804 1.86722i −0.0694428 0.120278i 0.829213 0.558932i \(-0.188789\pi\)
−0.898656 + 0.438654i \(0.855455\pi\)
\(242\) 0 0
\(243\) −11.2426 + 10.7983i −0.721215 + 0.692711i
\(244\) 0 0
\(245\) 0.695154 2.59435i 0.0444118 0.165747i
\(246\) 0 0
\(247\) 6.93279 + 4.00265i 0.441123 + 0.254683i
\(248\) 0 0
\(249\) 11.5828 6.62520i 0.734029 0.419855i
\(250\) 0 0
\(251\) −3.65289 3.65289i −0.230568 0.230568i 0.582362 0.812930i \(-0.302129\pi\)
−0.812930 + 0.582362i \(0.802129\pi\)
\(252\) 0 0
\(253\) 1.95516 1.95516i 0.122920 0.122920i
\(254\) 0 0
\(255\) −0.685745 + 1.17676i −0.0429430 + 0.0736918i
\(256\) 0 0
\(257\) −5.09689 + 8.82807i −0.317935 + 0.550680i −0.980057 0.198716i \(-0.936323\pi\)
0.662122 + 0.749396i \(0.269656\pi\)
\(258\) 0 0
\(259\) 17.8583 + 4.78511i 1.10966 + 0.297332i
\(260\) 0 0
\(261\) 7.16153 25.8904i 0.443288 1.60258i
\(262\) 0 0
\(263\) 14.5937 8.42569i 0.899888 0.519550i 0.0227239 0.999742i \(-0.492766\pi\)
0.877164 + 0.480191i \(0.159433\pi\)
\(264\) 0 0
\(265\) −0.115079 0.0664408i −0.00706924 0.00408143i
\(266\) 0 0
\(267\) 3.88897 + 3.92045i 0.238001 + 0.239928i
\(268\) 0 0
\(269\) 18.2219 18.2219i 1.11101 1.11101i 0.117993 0.993014i \(-0.462354\pi\)
0.993014 0.117993i \(-0.0376461\pi\)
\(270\) 0 0
\(271\) −9.95663 −0.604822 −0.302411 0.953178i \(-0.597792\pi\)
−0.302411 + 0.953178i \(0.597792\pi\)
\(272\) 0 0
\(273\) 36.9816 + 0.149085i 2.23823 + 0.00902302i
\(274\) 0 0
\(275\) −0.796902 2.97408i −0.0480550 0.179344i
\(276\) 0 0
\(277\) −0.706690 + 2.63740i −0.0424609 + 0.158466i −0.983901 0.178714i \(-0.942806\pi\)
0.941440 + 0.337180i \(0.109473\pi\)
\(278\) 0 0
\(279\) −11.6560 6.85549i −0.697827 0.410428i
\(280\) 0 0
\(281\) 21.8517 12.6161i 1.30356 0.752612i 0.322549 0.946553i \(-0.395460\pi\)
0.981013 + 0.193941i \(0.0621271\pi\)
\(282\) 0 0
\(283\) −8.63704 + 2.31429i −0.513419 + 0.137570i −0.506221 0.862404i \(-0.668958\pi\)
−0.00719814 + 0.999974i \(0.502291\pi\)
\(284\) 0 0
\(285\) −0.139975 0.530947i −0.00829142 0.0314506i
\(286\) 0 0
\(287\) −19.8192 −1.16989
\(288\) 0 0
\(289\) 1.89565 0.111509
\(290\) 0 0
\(291\) 26.8687 + 7.31566i 1.57507 + 0.428852i
\(292\) 0 0
\(293\) 20.1100 5.38845i 1.17484 0.314796i 0.381960 0.924179i \(-0.375249\pi\)
0.792876 + 0.609383i \(0.208583\pi\)
\(294\) 0 0
\(295\) −1.78973 + 1.03330i −0.104202 + 0.0601612i
\(296\) 0 0
\(297\) 2.80862 1.57658i 0.162973 0.0914825i
\(298\) 0 0
\(299\) 5.27390 19.6824i 0.304997 1.13827i
\(300\) 0 0
\(301\) 0.0164386 + 0.0613498i 0.000947507 + 0.00353615i
\(302\) 0 0
\(303\) 15.1627 + 26.5087i 0.871072 + 1.52289i
\(304\) 0 0
\(305\) −0.411536 −0.0235645
\(306\) 0 0
\(307\) −11.4523 + 11.4523i −0.653619 + 0.653619i −0.953863 0.300243i \(-0.902932\pi\)
0.300243 + 0.953863i \(0.402932\pi\)
\(308\) 0 0
\(309\) −15.5858 + 4.10893i −0.886645 + 0.233749i
\(310\) 0 0
\(311\) −15.6387 9.02903i −0.886792 0.511989i −0.0138999 0.999903i \(-0.504425\pi\)
−0.872892 + 0.487914i \(0.837758\pi\)
\(312\) 0 0
\(313\) 22.1825 12.8070i 1.25383 0.723897i 0.281959 0.959426i \(-0.409016\pi\)
0.971867 + 0.235529i \(0.0756823\pi\)
\(314\) 0 0
\(315\) −1.77914 1.80806i −0.100243 0.101873i
\(316\) 0 0
\(317\) 3.31301 + 0.887719i 0.186077 + 0.0498593i 0.350654 0.936505i \(-0.385959\pi\)
−0.164577 + 0.986364i \(0.552626\pi\)
\(318\) 0 0
\(319\) −2.77516 + 4.80671i −0.155379 + 0.269124i
\(320\) 0 0
\(321\) −23.3172 0.0939989i −1.30144 0.00524651i
\(322\) 0 0
\(323\) −5.38660 + 5.38660i −0.299719 + 0.299719i
\(324\) 0 0
\(325\) −16.0447 16.0447i −0.890001 0.890001i
\(326\) 0 0
\(327\) −0.0627288 + 15.5604i −0.00346891 + 0.860491i
\(328\) 0 0
\(329\) 9.50978 + 5.49047i 0.524291 + 0.302700i
\(330\) 0 0
\(331\) 4.07910 15.2234i 0.224207 0.836753i −0.758513 0.651658i \(-0.774074\pi\)
0.982721 0.185096i \(-0.0592595\pi\)
\(332\) 0 0
\(333\) 8.45813 8.32283i 0.463503 0.456088i
\(334\) 0 0
\(335\) 0.659494 + 1.14228i 0.0360320 + 0.0624093i
\(336\) 0 0
\(337\) −8.67225 + 15.0208i −0.472407 + 0.818233i −0.999501 0.0315734i \(-0.989948\pi\)
0.527094 + 0.849807i \(0.323282\pi\)
\(338\) 0 0
\(339\) −4.72093 17.9072i −0.256406 0.972585i
\(340\) 0 0
\(341\) 1.97567 + 1.97567i 0.106988 + 0.106988i
\(342\) 0 0
\(343\) 36.6800i 1.98053i
\(344\) 0 0
\(345\) −1.21321 + 0.693942i −0.0653171 + 0.0373606i
\(346\) 0 0
\(347\) −6.92193 + 1.85473i −0.371589 + 0.0995669i −0.439780 0.898105i \(-0.644944\pi\)
0.0681917 + 0.997672i \(0.478277\pi\)
\(348\) 0 0
\(349\) −1.10009 0.294768i −0.0588865 0.0157786i 0.229256 0.973366i \(-0.426371\pi\)
−0.288142 + 0.957588i \(0.593038\pi\)
\(350\) 0 0
\(351\) 12.1158 20.4111i 0.646694 1.08946i
\(352\) 0 0
\(353\) −12.2507 21.2188i −0.652037 1.12936i −0.982628 0.185587i \(-0.940581\pi\)
0.330591 0.943774i \(-0.392752\pi\)
\(354\) 0 0
\(355\) 0.353557 + 1.31949i 0.0187649 + 0.0700314i
\(356\) 0 0
\(357\) −9.24528 + 33.9557i −0.489312 + 1.79713i
\(358\) 0 0
\(359\) 11.6859i 0.616757i 0.951264 + 0.308378i \(0.0997863\pi\)
−0.951264 + 0.308378i \(0.900214\pi\)
\(360\) 0 0
\(361\) 15.9289i 0.838362i
\(362\) 0 0
\(363\) 17.7796 4.68729i 0.933186 0.246019i
\(364\) 0 0
\(365\) −0.137045 0.511458i −0.00717325 0.0267709i
\(366\) 0 0
\(367\) 5.61911 + 9.73258i 0.293315 + 0.508037i 0.974592 0.223990i \(-0.0719082\pi\)
−0.681276 + 0.732026i \(0.738575\pi\)
\(368\) 0 0
\(369\) −6.44889 + 10.9647i −0.335716 + 0.570798i
\(370\) 0 0
\(371\) −3.31647 0.888646i −0.172183 0.0461362i
\(372\) 0 0
\(373\) −11.5685 + 3.09978i −0.598996 + 0.160501i −0.545561 0.838071i \(-0.683684\pi\)
−0.0534347 + 0.998571i \(0.517017\pi\)
\(374\) 0 0
\(375\) −0.0125896 + 3.12296i −0.000650126 + 0.161269i
\(376\) 0 0
\(377\) 40.9031i 2.10661i
\(378\) 0 0
\(379\) −11.6135 11.6135i −0.596544 0.596544i 0.342847 0.939391i \(-0.388609\pi\)
−0.939391 + 0.342847i \(0.888609\pi\)
\(380\) 0 0
\(381\) 14.1760 14.0622i 0.726258 0.720426i
\(382\) 0 0
\(383\) 14.5294 25.1657i 0.742418 1.28591i −0.208973 0.977921i \(-0.567012\pi\)
0.951391 0.307985i \(-0.0996546\pi\)
\(384\) 0 0
\(385\) 0.262056 + 0.453894i 0.0133556 + 0.0231326i
\(386\) 0 0
\(387\) 0.0392899 + 0.0108680i 0.00199722 + 0.000552449i
\(388\) 0 0
\(389\) 3.65693 13.6478i 0.185414 0.691973i −0.809128 0.587632i \(-0.800060\pi\)
0.994542 0.104341i \(-0.0332732\pi\)
\(390\) 0 0
\(391\) 16.7926 + 9.69522i 0.849239 + 0.490308i
\(392\) 0 0
\(393\) −5.30304 3.09028i −0.267503 0.155884i
\(394\) 0 0
\(395\) −0.373213 0.373213i −0.0187784 0.0187784i
\(396\) 0 0
\(397\) −1.83996 + 1.83996i −0.0923450 + 0.0923450i −0.751770 0.659425i \(-0.770800\pi\)
0.659425 + 0.751770i \(0.270800\pi\)
\(398\) 0 0
\(399\) −7.04423 12.3154i −0.352653 0.616539i
\(400\) 0 0
\(401\) 14.5786 25.2509i 0.728021 1.26097i −0.229697 0.973262i \(-0.573774\pi\)
0.957718 0.287708i \(-0.0928931\pi\)
\(402\) 0 0
\(403\) 19.8889 + 5.32922i 0.990737 + 0.265467i
\(404\) 0 0
\(405\) −1.57919 + 0.395965i −0.0784707 + 0.0196757i
\(406\) 0 0
\(407\) −2.12332 + 1.22590i −0.105249 + 0.0607656i
\(408\) 0 0
\(409\) −9.18277 5.30167i −0.454059 0.262151i 0.255484 0.966813i \(-0.417765\pi\)
−0.709543 + 0.704662i \(0.751099\pi\)
\(410\) 0 0
\(411\) −6.84070 + 25.1243i −0.337427 + 1.23929i
\(412\) 0 0
\(413\) −37.7581 + 37.7581i −1.85796 + 1.85796i
\(414\) 0 0
\(415\) 1.39363 0.0684107
\(416\) 0 0
\(417\) 8.81306 15.1235i 0.431577 0.740603i
\(418\) 0 0
\(419\) −3.70507 13.8275i −0.181005 0.675519i −0.995451 0.0952792i \(-0.969626\pi\)
0.814446 0.580240i \(-0.197041\pi\)
\(420\) 0 0
\(421\) 5.16753 19.2855i 0.251850 0.939918i −0.717966 0.696079i \(-0.754926\pi\)
0.969816 0.243839i \(-0.0784068\pi\)
\(422\) 0 0
\(423\) 6.13189 3.47463i 0.298143 0.168942i
\(424\) 0 0
\(425\) 18.6995 10.7962i 0.907059 0.523691i
\(426\) 0 0
\(427\) −10.2712 + 2.75215i −0.497056 + 0.133186i
\(428\) 0 0
\(429\) −3.48184 + 3.45388i −0.168105 + 0.166755i
\(430\) 0 0
\(431\) 8.92159 0.429738 0.214869 0.976643i \(-0.431068\pi\)
0.214869 + 0.976643i \(0.431068\pi\)
\(432\) 0 0
\(433\) −29.8178 −1.43295 −0.716476 0.697612i \(-0.754246\pi\)
−0.716476 + 0.697612i \(0.754246\pi\)
\(434\) 0 0
\(435\) 1.99182 1.97582i 0.0955003 0.0947334i
\(436\) 0 0
\(437\) −7.55091 + 2.02326i −0.361209 + 0.0967857i
\(438\) 0 0
\(439\) −27.0574 + 15.6216i −1.29138 + 0.745579i −0.978899 0.204345i \(-0.934493\pi\)
−0.312481 + 0.949924i \(0.601160\pi\)
\(440\) 0 0
\(441\) −38.3940 22.5815i −1.82829 1.07531i
\(442\) 0 0
\(443\) −2.84043 + 10.6006i −0.134953 + 0.503651i 0.865045 + 0.501694i \(0.167290\pi\)
−0.999998 + 0.00195701i \(0.999377\pi\)
\(444\) 0 0
\(445\) 0.149271 + 0.557087i 0.00707613 + 0.0264085i
\(446\) 0 0
\(447\) −4.64786 + 7.97590i −0.219836 + 0.377247i
\(448\) 0 0
\(449\) 27.4967 1.29765 0.648824 0.760938i \(-0.275261\pi\)
0.648824 + 0.760938i \(0.275261\pi\)
\(450\) 0 0
\(451\) 1.85849 1.85849i 0.0875128 0.0875128i
\(452\) 0 0
\(453\) −5.18307 + 19.0362i −0.243522 + 0.894397i
\(454\) 0 0
\(455\) 3.34497 + 1.93122i 0.156815 + 0.0905370i
\(456\) 0 0
\(457\) −16.8184 + 9.71008i −0.786729 + 0.454218i −0.838810 0.544424i \(-0.816748\pi\)
0.0520805 + 0.998643i \(0.483415\pi\)
\(458\) 0 0
\(459\) 15.7773 + 16.1636i 0.736419 + 0.754451i
\(460\) 0 0
\(461\) 4.03437 + 1.08101i 0.187900 + 0.0503475i 0.351542 0.936172i \(-0.385658\pi\)
−0.163642 + 0.986520i \(0.552324\pi\)
\(462\) 0 0
\(463\) 0.773244 1.33930i 0.0359357 0.0622425i −0.847498 0.530798i \(-0.821892\pi\)
0.883434 + 0.468556i \(0.155226\pi\)
\(464\) 0 0
\(465\) −0.701222 1.22594i −0.0325184 0.0568515i
\(466\) 0 0
\(467\) 2.13196 2.13196i 0.0986553 0.0986553i −0.656056 0.754712i \(-0.727777\pi\)
0.754712 + 0.656056i \(0.227777\pi\)
\(468\) 0 0
\(469\) 24.0987 + 24.0987i 1.11277 + 1.11277i
\(470\) 0 0
\(471\) 8.47685 + 4.93978i 0.390593 + 0.227613i
\(472\) 0 0
\(473\) −0.00729441 0.00421143i −0.000335397 0.000193642i
\(474\) 0 0
\(475\) −2.25301 + 8.40836i −0.103375 + 0.385802i
\(476\) 0 0
\(477\) −1.57077 + 1.54564i −0.0719205 + 0.0707700i
\(478\) 0 0
\(479\) −14.5113 25.1343i −0.663037 1.14841i −0.979814 0.199914i \(-0.935934\pi\)
0.316777 0.948500i \(-0.397399\pi\)
\(480\) 0 0
\(481\) −9.03428 + 15.6478i −0.411928 + 0.713480i
\(482\) 0 0
\(483\) −25.6387 + 25.4328i −1.16660 + 1.15723i
\(484\) 0 0
\(485\) 2.05652 + 2.05652i 0.0933817 + 0.0933817i
\(486\) 0 0
\(487\) 3.59517i 0.162913i −0.996677 0.0814564i \(-0.974043\pi\)
0.996677 0.0814564i \(-0.0259571\pi\)
\(488\) 0 0
\(489\) −0.148234 + 36.7707i −0.00670339 + 1.66283i
\(490\) 0 0
\(491\) −19.9964 + 5.35801i −0.902424 + 0.241804i −0.680057 0.733159i \(-0.738045\pi\)
−0.222367 + 0.974963i \(0.571378\pi\)
\(492\) 0 0
\(493\) −37.5969 10.0741i −1.69328 0.453713i
\(494\) 0 0
\(495\) 0.336380 + 0.00271215i 0.0151192 + 0.000121902i
\(496\) 0 0
\(497\) 17.6482 + 30.5676i 0.791631 + 1.37115i
\(498\) 0 0
\(499\) −3.94988 14.7412i −0.176821 0.659905i −0.996234 0.0867019i \(-0.972367\pi\)
0.819413 0.573203i \(-0.194299\pi\)
\(500\) 0 0
\(501\) 15.1217 3.98658i 0.675587 0.178107i
\(502\) 0 0
\(503\) 11.1260i 0.496085i −0.968749 0.248042i \(-0.920213\pi\)
0.968749 0.248042i \(-0.0797872\pi\)
\(504\) 0 0
\(505\) 3.18951i 0.141931i
\(506\) 0 0
\(507\) −3.57965 + 13.1472i −0.158978 + 0.583888i
\(508\) 0 0
\(509\) 6.47918 + 24.1806i 0.287185 + 1.07179i 0.947228 + 0.320560i \(0.103871\pi\)
−0.660044 + 0.751227i \(0.729462\pi\)
\(510\) 0 0
\(511\) −6.84076 11.8485i −0.302617 0.524149i
\(512\) 0 0
\(513\) −9.10540 0.110125i −0.402013 0.00486214i
\(514\) 0 0
\(515\) −1.62606 0.435701i −0.0716526 0.0191993i
\(516\) 0 0
\(517\) −1.40661 + 0.376900i −0.0618626 + 0.0165760i
\(518\) 0 0
\(519\) 7.79068 4.45617i 0.341973 0.195604i
\(520\) 0 0
\(521\) 44.7974i 1.96261i −0.192458 0.981305i \(-0.561646\pi\)
0.192458 0.981305i \(-0.438354\pi\)
\(522\) 0 0
\(523\) −7.02267 7.02267i −0.307080 0.307080i 0.536696 0.843776i \(-0.319672\pi\)
−0.843776 + 0.536696i \(0.819672\pi\)
\(524\) 0 0
\(525\) 10.2515 + 38.8856i 0.447413 + 1.69711i
\(526\) 0 0
\(527\) −9.79692 + 16.9688i −0.426761 + 0.739171i
\(528\) 0 0
\(529\) −1.55091 2.68626i −0.0674309 0.116794i
\(530\) 0 0
\(531\) 8.60319 + 33.1752i 0.373347 + 1.43968i
\(532\) 0 0
\(533\) 5.01314 18.7093i 0.217143 0.810389i
\(534\) 0 0
\(535\) −2.10903 1.21765i −0.0911812 0.0526435i
\(536\) 0 0
\(537\) −0.0193633 + 4.80323i −0.000835590 + 0.207275i
\(538\) 0 0
\(539\) 6.50770 + 6.50770i 0.280306 + 0.280306i
\(540\) 0 0
\(541\) 14.9663 14.9663i 0.643452 0.643452i −0.307950 0.951402i \(-0.599643\pi\)
0.951402 + 0.307950i \(0.0996431\pi\)
\(542\) 0 0
\(543\) −0.549309 0.00221444i −0.0235731 9.50308e-5i
\(544\) 0 0
\(545\) −0.812579 + 1.40743i −0.0348071 + 0.0602876i
\(546\) 0 0
\(547\) 5.15670 + 1.38173i 0.220485 + 0.0590787i 0.367370 0.930075i \(-0.380258\pi\)
−0.146885 + 0.989154i \(0.546925\pi\)
\(548\) 0 0
\(549\) −1.81951 + 6.57789i −0.0776547 + 0.280738i
\(550\) 0 0
\(551\) 13.5896 7.84596i 0.578937 0.334249i
\(552\) 0 0
\(553\) −11.8106 6.81883i −0.502236 0.289966i
\(554\) 0 0
\(555\) 1.19839 0.315935i 0.0508687 0.0134107i
\(556\) 0 0
\(557\) 7.66230 7.66230i 0.324662 0.324662i −0.525890 0.850552i \(-0.676268\pi\)
0.850552 + 0.525890i \(0.176268\pi\)
\(558\) 0 0
\(559\) −0.0620723 −0.00262538
\(560\) 0 0
\(561\) −2.31716 4.05106i −0.0978304 0.171036i
\(562\) 0 0
\(563\) −5.71152 21.3157i −0.240712 0.898349i −0.975490 0.220042i \(-0.929381\pi\)
0.734779 0.678307i \(-0.237286\pi\)
\(564\) 0 0
\(565\) 0.500595 1.86825i 0.0210602 0.0785977i
\(566\) 0 0
\(567\) −36.7656 + 20.4434i −1.54401 + 0.858542i
\(568\) 0 0
\(569\) −38.6354 + 22.3061i −1.61968 + 0.935122i −0.632676 + 0.774416i \(0.718044\pi\)
−0.987002 + 0.160706i \(0.948623\pi\)
\(570\) 0 0
\(571\) −9.47469 + 2.53873i −0.396503 + 0.106243i −0.451561 0.892240i \(-0.649133\pi\)
0.0550573 + 0.998483i \(0.482466\pi\)
\(572\) 0 0
\(573\) 34.7253 + 9.45483i 1.45067 + 0.394981i
\(574\) 0 0
\(575\) 22.1577 0.924041
\(576\) 0 0
\(577\) −0.565932 −0.0235600 −0.0117800 0.999931i \(-0.503750\pi\)
−0.0117800 + 0.999931i \(0.503750\pi\)
\(578\) 0 0
\(579\) −6.79593 25.7780i −0.282429 1.07130i
\(580\) 0 0
\(581\) 34.7824 9.31992i 1.44302 0.386655i
\(582\) 0 0
\(583\) 0.394324 0.227663i 0.0163312 0.00942884i
\(584\) 0 0
\(585\) 2.15683 1.22217i 0.0891740 0.0505304i
\(586\) 0 0
\(587\) −10.6937 + 39.9093i −0.441375 + 1.64723i 0.283960 + 0.958836i \(0.408352\pi\)
−0.725334 + 0.688397i \(0.758315\pi\)
\(588\) 0 0
\(589\) −2.04448 7.63012i −0.0842415 0.314394i
\(590\) 0 0
\(591\) −2.21716 0.00893807i −0.0912017 0.000367663i
\(592\) 0 0
\(593\) −12.9281 −0.530893 −0.265447 0.964126i \(-0.585519\pi\)
−0.265447 + 0.964126i \(0.585519\pi\)
\(594\) 0 0
\(595\) −2.59896 + 2.59896i −0.106547 + 0.106547i
\(596\) 0 0
\(597\) −20.1511 20.3143i −0.824731 0.831408i
\(598\) 0 0
\(599\) 39.9617 + 23.0719i 1.63279 + 0.942692i 0.983227 + 0.182384i \(0.0583814\pi\)
0.649563 + 0.760308i \(0.274952\pi\)
\(600\) 0 0
\(601\) −28.4107 + 16.4029i −1.15890 + 0.669090i −0.951040 0.309069i \(-0.899983\pi\)
−0.207858 + 0.978159i \(0.566649\pi\)
\(602\) 0 0
\(603\) 21.1737 5.49089i 0.862259 0.223606i
\(604\) 0 0
\(605\) 1.85493 + 0.497028i 0.0754138 + 0.0202071i
\(606\) 0 0
\(607\) 6.36706 11.0281i 0.258431 0.447616i −0.707391 0.706823i \(-0.750128\pi\)
0.965822 + 0.259207i \(0.0834611\pi\)
\(608\) 0 0
\(609\) 36.4986 62.6330i 1.47900 2.53802i
\(610\) 0 0
\(611\) −7.58845 + 7.58845i −0.306996 + 0.306996i
\(612\) 0 0
\(613\) 29.9303 + 29.9303i 1.20888 + 1.20888i 0.971392 + 0.237483i \(0.0763225\pi\)
0.237483 + 0.971392i \(0.423677\pi\)
\(614\) 0 0
\(615\) −1.15323 + 0.659631i −0.0465026 + 0.0265989i
\(616\) 0 0
\(617\) −2.50740 1.44765i −0.100944 0.0582802i 0.448678 0.893693i \(-0.351895\pi\)
−0.549622 + 0.835413i \(0.685228\pi\)
\(618\) 0 0
\(619\) −1.48762 + 5.55188i −0.0597926 + 0.223149i −0.989356 0.145512i \(-0.953517\pi\)
0.929564 + 0.368661i \(0.120184\pi\)
\(620\) 0 0
\(621\) 5.72788 + 22.4598i 0.229852 + 0.901280i
\(622\) 0 0
\(623\) 7.45105 + 12.9056i 0.298520 + 0.517052i
\(624\) 0 0
\(625\) 12.2551 21.2265i 0.490204 0.849059i
\(626\) 0 0
\(627\) 1.81539 + 0.494286i 0.0724999 + 0.0197399i
\(628\) 0 0
\(629\) −12.1580 12.1580i −0.484770 0.484770i
\(630\) 0 0
\(631\) 33.4420i 1.33130i 0.746262 + 0.665652i \(0.231846\pi\)
−0.746262 + 0.665652i \(0.768154\pi\)
\(632\) 0 0
\(633\) −39.0462 22.7537i −1.55195 0.904379i
\(634\) 0 0
\(635\) 2.01438 0.539750i 0.0799381 0.0214193i
\(636\) 0 0
\(637\) 65.5126 + 17.5540i 2.59570 + 0.695516i
\(638\) 0 0
\(639\) 22.6536 + 0.182651i 0.896164 + 0.00722556i
\(640\) 0 0
\(641\) 9.42170 + 16.3189i 0.372135 + 0.644557i 0.989894 0.141811i \(-0.0452925\pi\)
−0.617759 + 0.786368i \(0.711959\pi\)
\(642\) 0 0
\(643\) −3.18391 11.8825i −0.125561 0.468601i 0.874298 0.485390i \(-0.161322\pi\)
−0.999859 + 0.0167890i \(0.994656\pi\)
\(644\) 0 0
\(645\) 0.00299840 + 0.00302267i 0.000118062 + 0.000119018i
\(646\) 0 0
\(647\) 8.72393i 0.342973i −0.985186 0.171487i \(-0.945143\pi\)
0.985186 0.171487i \(-0.0548570\pi\)
\(648\) 0 0
\(649\) 7.08134i 0.277967i
\(650\) 0 0
\(651\) −25.6996 25.9077i −1.00725 1.01540i
\(652\) 0 0
\(653\) −5.07099 18.9252i −0.198443 0.740600i −0.991349 0.131255i \(-0.958099\pi\)
0.792906 0.609345i \(-0.208567\pi\)
\(654\) 0 0
\(655\) −0.320517 0.555152i −0.0125237 0.0216916i
\(656\) 0 0
\(657\) −8.78094 0.0707987i −0.342577 0.00276212i
\(658\) 0 0
\(659\) −37.3628 10.0113i −1.45545 0.389986i −0.557533 0.830155i \(-0.688252\pi\)
−0.897915 + 0.440168i \(0.854919\pi\)
\(660\) 0 0
\(661\) −26.6308 + 7.13570i −1.03582 + 0.277546i −0.736379 0.676569i \(-0.763466\pi\)
−0.299438 + 0.954116i \(0.596799\pi\)
\(662\) 0 0
\(663\) −29.7157 17.3164i −1.15406 0.672515i
\(664\) 0 0
\(665\) 1.48177i 0.0574608i
\(666\) 0 0
\(667\) −28.2435 28.2435i −1.09359 1.09359i
\(668\) 0 0
\(669\) −21.6565 5.89651i −0.837288 0.227972i
\(670\) 0 0
\(671\) 0.705075 1.22123i 0.0272191 0.0471449i
\(672\) 0 0
\(673\) 10.0608 + 17.4258i 0.387815 + 0.671716i 0.992155 0.125011i \(-0.0398965\pi\)
−0.604340 + 0.796726i \(0.706563\pi\)
\(674\) 0 0
\(675\) 24.8486 + 6.98133i 0.956424 + 0.268711i
\(676\) 0 0
\(677\) −5.24998 + 19.5932i −0.201773 + 0.753027i 0.788636 + 0.614860i \(0.210788\pi\)
−0.990409 + 0.138167i \(0.955879\pi\)
\(678\) 0 0
\(679\) 65.0798 + 37.5738i 2.49753 + 1.44195i
\(680\) 0 0
\(681\) 20.4528 11.6988i 0.783755 0.448298i
\(682\) 0 0
\(683\) 18.4322 + 18.4322i 0.705287 + 0.705287i 0.965540 0.260253i \(-0.0838061\pi\)
−0.260253 + 0.965540i \(0.583806\pi\)
\(684\) 0 0
\(685\) −1.92300 + 1.92300i −0.0734741 + 0.0734741i
\(686\) 0 0
\(687\) −14.6593 + 25.1559i −0.559286 + 0.959756i
\(688\) 0 0
\(689\) 1.67776 2.90597i 0.0639177 0.110709i
\(690\) 0 0
\(691\) −15.6519 4.19392i −0.595427 0.159544i −0.0514946 0.998673i \(-0.516399\pi\)
−0.543932 + 0.839129i \(0.683065\pi\)
\(692\) 0 0
\(693\) 8.41354 2.18185i 0.319604 0.0828817i
\(694\) 0 0
\(695\) 1.58322 0.914072i 0.0600549 0.0346727i
\(696\) 0 0
\(697\) 15.9623 + 9.21585i 0.604616 + 0.349075i
\(698\) 0 0
\(699\) −12.2581 12.3573i −0.463644 0.467397i
\(700\) 0 0
\(701\) 2.97647 2.97647i 0.112420 0.112420i −0.648659 0.761079i \(-0.724670\pi\)
0.761079 + 0.648659i \(0.224670\pi\)
\(702\) 0 0
\(703\) 6.93177 0.261437
\(704\) 0 0
\(705\) 0.736087 + 0.00296740i 0.0277226 + 0.000111759i
\(706\) 0 0
\(707\) 21.3299 + 79.6042i 0.802192 + 2.99382i
\(708\) 0 0
\(709\) 10.0033 37.3329i 0.375682 1.40207i −0.476663 0.879086i \(-0.658154\pi\)
0.852345 0.522980i \(-0.175180\pi\)
\(710\) 0 0
\(711\) −7.61542 + 4.31528i −0.285601 + 0.161836i
\(712\) 0 0
\(713\) −17.4131 + 10.0535i −0.652125 + 0.376505i
\(714\) 0 0
\(715\) −0.494761 + 0.132571i −0.0185030 + 0.00495787i
\(716\) 0 0
\(717\) −2.98803 11.3341i −0.111590 0.423278i
\(718\) 0 0
\(719\) −38.3674 −1.43086 −0.715431 0.698683i \(-0.753770\pi\)
−0.715431 + 0.698683i \(0.753770\pi\)
\(720\) 0 0
\(721\) −43.4970 −1.61991
\(722\) 0 0
\(723\) −3.60327 0.981080i −0.134007 0.0364867i
\(724\) 0 0
\(725\) −42.9625 + 11.5118i −1.59559 + 0.427536i
\(726\) 0 0
\(727\) 14.8899 8.59667i 0.552235 0.318833i −0.197788 0.980245i \(-0.563376\pi\)
0.750023 + 0.661412i \(0.230042\pi\)
\(728\) 0 0
\(729\) −0.653006 + 26.9921i −0.0241854 + 0.999707i
\(730\) 0 0
\(731\) 0.0152878 0.0570550i 0.000565441 0.00211026i
\(732\) 0 0
\(733\) 3.41130 + 12.7311i 0.125999 + 0.470235i 0.999873 0.0159168i \(-0.00506670\pi\)
−0.873874 + 0.486152i \(0.838400\pi\)
\(734\) 0 0
\(735\) −2.30977 4.03815i −0.0851972 0.148949i
\(736\) 0 0
\(737\) −4.51959 −0.166481
\(738\) 0 0
\(739\) 15.2048 15.2048i 0.559316 0.559316i −0.369797 0.929113i \(-0.620573\pi\)
0.929113 + 0.369797i \(0.120573\pi\)
\(740\) 0 0
\(741\) 13.4075 3.53466i 0.492536 0.129849i
\(742\) 0 0
\(743\) −36.6127 21.1384i −1.34319 0.775491i −0.355916 0.934518i \(-0.615831\pi\)
−0.987274 + 0.159027i \(0.949164\pi\)
\(744\) 0 0
\(745\) −0.834963 + 0.482066i −0.0305907 + 0.0176615i
\(746\) 0 0
\(747\) 6.16161 22.2755i 0.225441 0.815017i
\(748\) 0 0
\(749\) −60.7803 16.2860i −2.22086 0.595079i
\(750\) 0 0
\(751\) 9.72823 16.8498i 0.354988 0.614857i −0.632128 0.774864i \(-0.717818\pi\)
0.987116 + 0.160007i \(0.0511516\pi\)
\(752\) 0 0
\(753\) −8.94764 0.0360708i −0.326070 0.00131449i
\(754\) 0 0
\(755\) −1.45702 + 1.45702i −0.0530264 + 0.0530264i
\(756\) 0 0
\(757\) 26.9716 + 26.9716i 0.980300 + 0.980300i 0.999810 0.0195093i \(-0.00621039\pi\)
−0.0195093 + 0.999810i \(0.506210\pi\)
\(758\) 0 0
\(759\) 0.0193064 4.78910i 0.000700778 0.173833i
\(760\) 0 0
\(761\) −15.0417 8.68435i −0.545263 0.314808i 0.201946 0.979397i \(-0.435273\pi\)
−0.747209 + 0.664589i \(0.768607\pi\)
\(762\) 0 0
\(763\) −10.8683 + 40.5609i −0.393457 + 1.46840i
\(764\) 0 0
\(765\) 0.592172 + 2.28350i 0.0214100 + 0.0825603i
\(766\) 0 0
\(767\) −26.0930 45.1944i −0.942163 1.63187i
\(768\) 0 0
\(769\) 15.0664 26.0957i 0.543307 0.941036i −0.455404 0.890285i \(-0.650505\pi\)
0.998711 0.0507510i \(-0.0161615\pi\)
\(770\) 0 0
\(771\) 4.50096 + 17.0728i 0.162098 + 0.614862i
\(772\) 0 0
\(773\) −9.37945 9.37945i −0.337355 0.337355i 0.518016 0.855371i \(-0.326671\pi\)
−0.855371 + 0.518016i \(0.826671\pi\)
\(774\) 0 0
\(775\) 22.3901i 0.804278i
\(776\) 0 0
\(777\) 27.7967 15.8993i 0.997200 0.570386i
\(778\) 0 0
\(779\) −7.17757 + 1.92322i −0.257163 + 0.0689067i
\(780\) 0 0
\(781\) −4.52131 1.21148i −0.161785 0.0433502i
\(782\) 0 0
\(783\) −22.7747 40.5723i −0.813902 1.44994i
\(784\) 0 0
\(785\) 0.512344 + 0.887406i 0.0182863 + 0.0316729i
\(786\) 0 0
\(787\) 3.39895 + 12.6850i 0.121159 + 0.452173i 0.999674 0.0255430i \(-0.00813148\pi\)
−0.878514 + 0.477716i \(0.841465\pi\)
\(788\) 0 0
\(789\) 7.66786 28.1622i 0.272983 1.00260i
\(790\) 0 0
\(791\) 49.9756i 1.77693i
\(792\) 0 0
\(793\) 10.3921i 0.369035i
\(794\) 0 0
\(795\) −0.222554 + 0.0586725i −0.00789316 + 0.00208090i
\(796\) 0 0