Properties

Label 1323.2.g.f.361.2
Level $1323$
Weight $2$
Character 1323.361
Analytic conductor $10.564$
Analytic rank $0$
Dimension $10$
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: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
Defining polynomial: \(x^{10} - 2 x^{9} + 9 x^{8} - 8 x^{7} + 40 x^{6} - 36 x^{5} + 90 x^{4} - 3 x^{3} + 36 x^{2} - 9 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.2
Root \(0.920620 - 1.59456i\) of defining polynomial
Character \(\chi\) \(=\) 1323.361
Dual form 1323.2.g.f.667.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.920620 + 1.59456i) q^{2} +(-0.695084 - 1.20392i) q^{4} +1.33475 q^{5} -1.12285 q^{8} +O(q^{10})\) \(q+(-0.920620 + 1.59456i) q^{2} +(-0.695084 - 1.20392i) q^{4} +1.33475 q^{5} -1.12285 q^{8} +(-1.22880 + 2.12835i) q^{10} -1.51302 q^{11} +(2.58800 - 4.48254i) q^{13} +(2.42388 - 4.19829i) q^{16} +(0.774463 - 1.34141i) q^{17} +(1.25211 + 2.16872i) q^{19} +(-0.927765 - 1.60694i) q^{20} +(1.39291 - 2.41260i) q^{22} +7.36079 q^{23} -3.21843 q^{25} +(4.76513 + 8.25344i) q^{26} +(0.0309713 + 0.0536439i) q^{29} +(-1.92388 - 3.33227i) q^{31} +(3.34011 + 5.78523i) q^{32} +(1.42597 + 2.46986i) q^{34} +(-0.281608 - 0.487760i) q^{37} -4.61087 q^{38} -1.49873 q^{40} +(4.51188 - 7.81481i) q^{41} +(5.09988 + 8.83325i) q^{43} +(1.05167 + 1.82155i) q^{44} +(-6.77649 + 11.7372i) q^{46} +(4.75925 - 8.24327i) q^{47} +(2.96296 - 5.13199i) q^{50} -7.19550 q^{52} +(-0.755374 + 1.30835i) q^{53} -2.01950 q^{55} -0.114051 q^{58} +(4.22166 + 7.31212i) q^{59} +(1.61958 - 2.80520i) q^{61} +7.08467 q^{62} -2.60434 q^{64} +(3.45434 - 5.98309i) q^{65} +(-3.46670 - 6.00449i) q^{67} -2.15327 q^{68} +12.3304 q^{71} +(1.37936 - 2.38912i) q^{73} +1.03702 q^{74} +(1.74064 - 3.01488i) q^{76} +(2.95969 - 5.12633i) q^{79} +(3.23529 - 5.60368i) q^{80} +(8.30746 + 14.3889i) q^{82} +(2.80111 + 4.85167i) q^{83} +(1.03372 - 1.79045i) q^{85} -18.7802 q^{86} +1.69889 q^{88} +(0.703287 + 1.21813i) q^{89} +(-5.11636 - 8.86180i) q^{92} +(8.76293 + 15.1778i) q^{94} +(1.67126 + 2.89470i) q^{95} +(6.09713 + 10.5605i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 2q^{2} - 4q^{4} - 8q^{5} + 6q^{8} + O(q^{10}) \) \( 10q - 2q^{2} - 4q^{4} - 8q^{5} + 6q^{8} + 7q^{10} + 8q^{11} + 8q^{13} + 2q^{16} + 12q^{17} - q^{19} + 5q^{20} - q^{22} + 6q^{23} + 2q^{25} + 11q^{26} - 7q^{29} + 3q^{31} + 2q^{32} - 3q^{34} - 40q^{38} - 6q^{40} + 5q^{41} - 7q^{43} + 10q^{44} + 3q^{46} + 27q^{47} - 19q^{50} - 20q^{52} + 21q^{53} - 4q^{55} + 20q^{58} + 30q^{59} + 14q^{61} - 12q^{62} - 50q^{64} + 11q^{65} - 2q^{67} - 54q^{68} + 6q^{71} - 15q^{73} - 72q^{74} - 5q^{76} - 4q^{79} + 20q^{80} + 5q^{82} + 9q^{83} - 6q^{85} - 16q^{86} + 36q^{88} + 28q^{89} - 27q^{92} + 3q^{94} + 14q^{95} + 12q^{97} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.920620 + 1.59456i −0.650977 + 1.12753i 0.331909 + 0.943311i \(0.392307\pi\)
−0.982886 + 0.184214i \(0.941026\pi\)
\(3\) 0 0
\(4\) −0.695084 1.20392i −0.347542 0.601960i
\(5\) 1.33475 0.596920 0.298460 0.954422i \(-0.403527\pi\)
0.298460 + 0.954422i \(0.403527\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.12285 −0.396987
\(9\) 0 0
\(10\) −1.22880 + 2.12835i −0.388581 + 0.673042i
\(11\) −1.51302 −0.456192 −0.228096 0.973639i \(-0.573250\pi\)
−0.228096 + 0.973639i \(0.573250\pi\)
\(12\) 0 0
\(13\) 2.58800 4.48254i 0.717781 1.24323i −0.244096 0.969751i \(-0.578491\pi\)
0.961877 0.273482i \(-0.0881755\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.42388 4.19829i 0.605971 1.04957i
\(17\) 0.774463 1.34141i 0.187835 0.325340i −0.756693 0.653770i \(-0.773186\pi\)
0.944528 + 0.328430i \(0.106520\pi\)
\(18\) 0 0
\(19\) 1.25211 + 2.16872i 0.287254 + 0.497538i 0.973153 0.230158i \(-0.0739244\pi\)
−0.685900 + 0.727696i \(0.740591\pi\)
\(20\) −0.927765 1.60694i −0.207455 0.359322i
\(21\) 0 0
\(22\) 1.39291 2.41260i 0.296970 0.514367i
\(23\) 7.36079 1.53483 0.767415 0.641151i \(-0.221543\pi\)
0.767415 + 0.641151i \(0.221543\pi\)
\(24\) 0 0
\(25\) −3.21843 −0.643687
\(26\) 4.76513 + 8.25344i 0.934518 + 1.61863i
\(27\) 0 0
\(28\) 0 0
\(29\) 0.0309713 + 0.0536439i 0.00575123 + 0.00996143i 0.868887 0.495011i \(-0.164836\pi\)
−0.863135 + 0.504972i \(0.831503\pi\)
\(30\) 0 0
\(31\) −1.92388 3.33227i −0.345540 0.598493i 0.639912 0.768448i \(-0.278971\pi\)
−0.985452 + 0.169956i \(0.945638\pi\)
\(32\) 3.34011 + 5.78523i 0.590453 + 1.02269i
\(33\) 0 0
\(34\) 1.42597 + 2.46986i 0.244552 + 0.423577i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.281608 0.487760i −0.0462961 0.0801872i 0.841949 0.539557i \(-0.181408\pi\)
−0.888245 + 0.459370i \(0.848075\pi\)
\(38\) −4.61087 −0.747982
\(39\) 0 0
\(40\) −1.49873 −0.236969
\(41\) 4.51188 7.81481i 0.704638 1.22047i −0.262185 0.965018i \(-0.584443\pi\)
0.966822 0.255450i \(-0.0822237\pi\)
\(42\) 0 0
\(43\) 5.09988 + 8.83325i 0.777724 + 1.34706i 0.933251 + 0.359226i \(0.116959\pi\)
−0.155526 + 0.987832i \(0.549707\pi\)
\(44\) 1.05167 + 1.82155i 0.158546 + 0.274609i
\(45\) 0 0
\(46\) −6.77649 + 11.7372i −0.999139 + 1.73056i
\(47\) 4.75925 8.24327i 0.694209 1.20240i −0.276238 0.961089i \(-0.589088\pi\)
0.970447 0.241315i \(-0.0775788\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 2.96296 5.13199i 0.419025 0.725773i
\(51\) 0 0
\(52\) −7.19550 −0.997836
\(53\) −0.755374 + 1.30835i −0.103759 + 0.179715i −0.913230 0.407444i \(-0.866420\pi\)
0.809472 + 0.587159i \(0.199754\pi\)
\(54\) 0 0
\(55\) −2.01950 −0.272310
\(56\) 0 0
\(57\) 0 0
\(58\) −0.114051 −0.0149757
\(59\) 4.22166 + 7.31212i 0.549613 + 0.951957i 0.998301 + 0.0582689i \(0.0185581\pi\)
−0.448688 + 0.893688i \(0.648109\pi\)
\(60\) 0 0
\(61\) 1.61958 2.80520i 0.207367 0.359169i −0.743518 0.668716i \(-0.766844\pi\)
0.950884 + 0.309547i \(0.100177\pi\)
\(62\) 7.08467 0.899754
\(63\) 0 0
\(64\) −2.60434 −0.325543
\(65\) 3.45434 5.98309i 0.428458 0.742111i
\(66\) 0 0
\(67\) −3.46670 6.00449i −0.423524 0.733566i 0.572757 0.819725i \(-0.305874\pi\)
−0.996281 + 0.0861595i \(0.972541\pi\)
\(68\) −2.15327 −0.261122
\(69\) 0 0
\(70\) 0 0
\(71\) 12.3304 1.46335 0.731673 0.681656i \(-0.238740\pi\)
0.731673 + 0.681656i \(0.238740\pi\)
\(72\) 0 0
\(73\) 1.37936 2.38912i 0.161442 0.279625i −0.773944 0.633254i \(-0.781719\pi\)
0.935386 + 0.353629i \(0.115052\pi\)
\(74\) 1.03702 0.120551
\(75\) 0 0
\(76\) 1.74064 3.01488i 0.199665 0.345830i
\(77\) 0 0
\(78\) 0 0
\(79\) 2.95969 5.12633i 0.332991 0.576758i −0.650106 0.759844i \(-0.725275\pi\)
0.983097 + 0.183086i \(0.0586087\pi\)
\(80\) 3.23529 5.60368i 0.361716 0.626511i
\(81\) 0 0
\(82\) 8.30746 + 14.3889i 0.917406 + 1.58899i
\(83\) 2.80111 + 4.85167i 0.307462 + 0.532540i 0.977806 0.209510i \(-0.0671870\pi\)
−0.670344 + 0.742050i \(0.733854\pi\)
\(84\) 0 0
\(85\) 1.03372 1.79045i 0.112122 0.194202i
\(86\) −18.7802 −2.02512
\(87\) 0 0
\(88\) 1.69889 0.181102
\(89\) 0.703287 + 1.21813i 0.0745483 + 0.129121i 0.900890 0.434048i \(-0.142915\pi\)
−0.826341 + 0.563169i \(0.809582\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −5.11636 8.86180i −0.533418 0.923906i
\(93\) 0 0
\(94\) 8.76293 + 15.1778i 0.903827 + 1.56548i
\(95\) 1.67126 + 2.89470i 0.171467 + 0.296990i
\(96\) 0 0
\(97\) 6.09713 + 10.5605i 0.619070 + 1.07226i 0.989656 + 0.143462i \(0.0458236\pi\)
−0.370586 + 0.928798i \(0.620843\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 2.23708 + 3.87474i 0.223708 + 0.387474i
\(101\) 1.11867 0.111312 0.0556560 0.998450i \(-0.482275\pi\)
0.0556560 + 0.998450i \(0.482275\pi\)
\(102\) 0 0
\(103\) −1.93045 −0.190213 −0.0951063 0.995467i \(-0.530319\pi\)
−0.0951063 + 0.995467i \(0.530319\pi\)
\(104\) −2.90593 + 5.03322i −0.284950 + 0.493548i
\(105\) 0 0
\(106\) −1.39082 2.40898i −0.135089 0.233981i
\(107\) −2.88969 5.00509i −0.279357 0.483860i 0.691868 0.722024i \(-0.256788\pi\)
−0.971225 + 0.238163i \(0.923455\pi\)
\(108\) 0 0
\(109\) −4.12106 + 7.13788i −0.394726 + 0.683685i −0.993066 0.117557i \(-0.962494\pi\)
0.598340 + 0.801242i \(0.295827\pi\)
\(110\) 1.85920 3.22022i 0.177267 0.307036i
\(111\) 0 0
\(112\) 0 0
\(113\) −7.25105 + 12.5592i −0.682121 + 1.18147i 0.292211 + 0.956354i \(0.405609\pi\)
−0.974332 + 0.225115i \(0.927724\pi\)
\(114\) 0 0
\(115\) 9.82483 0.916170
\(116\) 0.0430553 0.0745740i 0.00399759 0.00692403i
\(117\) 0 0
\(118\) −15.5462 −1.43114
\(119\) 0 0
\(120\) 0 0
\(121\) −8.71078 −0.791889
\(122\) 2.98204 + 5.16505i 0.269982 + 0.467622i
\(123\) 0 0
\(124\) −2.67452 + 4.63241i −0.240179 + 0.416002i
\(125\) −10.9696 −0.981149
\(126\) 0 0
\(127\) 8.50004 0.754257 0.377128 0.926161i \(-0.376912\pi\)
0.377128 + 0.926161i \(0.376912\pi\)
\(128\) −4.28260 + 7.41769i −0.378532 + 0.655637i
\(129\) 0 0
\(130\) 6.36027 + 11.0163i 0.557832 + 0.966194i
\(131\) −2.01346 −0.175917 −0.0879585 0.996124i \(-0.528034\pi\)
−0.0879585 + 0.996124i \(0.528034\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 12.7660 1.10282
\(135\) 0 0
\(136\) −0.869605 + 1.50620i −0.0745680 + 0.129156i
\(137\) −2.21740 −0.189445 −0.0947225 0.995504i \(-0.530196\pi\)
−0.0947225 + 0.995504i \(0.530196\pi\)
\(138\) 0 0
\(139\) −0.377669 + 0.654143i −0.0320335 + 0.0554836i −0.881598 0.472002i \(-0.843532\pi\)
0.849564 + 0.527485i \(0.176865\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −11.3516 + 19.6615i −0.952604 + 1.64996i
\(143\) −3.91568 + 6.78216i −0.327446 + 0.567153i
\(144\) 0 0
\(145\) 0.0413391 + 0.0716014i 0.00343303 + 0.00594618i
\(146\) 2.53973 + 4.39894i 0.210189 + 0.364059i
\(147\) 0 0
\(148\) −0.391482 + 0.678068i −0.0321797 + 0.0557368i
\(149\) −6.58499 −0.539463 −0.269732 0.962936i \(-0.586935\pi\)
−0.269732 + 0.962936i \(0.586935\pi\)
\(150\) 0 0
\(151\) 12.6671 1.03083 0.515417 0.856939i \(-0.327637\pi\)
0.515417 + 0.856939i \(0.327637\pi\)
\(152\) −1.40593 2.43514i −0.114036 0.197516i
\(153\) 0 0
\(154\) 0 0
\(155\) −2.56791 4.44775i −0.206260 0.357252i
\(156\) 0 0
\(157\) −8.65372 14.9887i −0.690642 1.19623i −0.971628 0.236515i \(-0.923995\pi\)
0.280986 0.959712i \(-0.409338\pi\)
\(158\) 5.44950 + 9.43882i 0.433539 + 0.750912i
\(159\) 0 0
\(160\) 4.45822 + 7.72186i 0.352453 + 0.610467i
\(161\) 0 0
\(162\) 0 0
\(163\) 6.10963 + 10.5822i 0.478543 + 0.828861i 0.999697 0.0246014i \(-0.00783167\pi\)
−0.521154 + 0.853463i \(0.674498\pi\)
\(164\) −12.5445 −0.979564
\(165\) 0 0
\(166\) −10.3150 −0.800602
\(167\) 1.76248 3.05270i 0.136385 0.236225i −0.789741 0.613440i \(-0.789785\pi\)
0.926126 + 0.377215i \(0.123118\pi\)
\(168\) 0 0
\(169\) −6.89546 11.9433i −0.530420 0.918714i
\(170\) 1.90332 + 3.29665i 0.145978 + 0.252842i
\(171\) 0 0
\(172\) 7.08968 12.2797i 0.540583 0.936318i
\(173\) −5.07046 + 8.78229i −0.385500 + 0.667705i −0.991838 0.127502i \(-0.959304\pi\)
0.606339 + 0.795206i \(0.292638\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −3.66738 + 6.35208i −0.276439 + 0.478806i
\(177\) 0 0
\(178\) −2.58984 −0.194117
\(179\) −0.850579 + 1.47325i −0.0635752 + 0.110116i −0.896061 0.443931i \(-0.853584\pi\)
0.832486 + 0.554046i \(0.186917\pi\)
\(180\) 0 0
\(181\) 16.9941 1.26316 0.631581 0.775310i \(-0.282406\pi\)
0.631581 + 0.775310i \(0.282406\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −8.26505 −0.609308
\(185\) −0.375877 0.651039i −0.0276351 0.0478653i
\(186\) 0 0
\(187\) −1.17178 + 2.02957i −0.0856887 + 0.148417i
\(188\) −13.2323 −0.965066
\(189\) 0 0
\(190\) −6.15437 −0.446485
\(191\) 11.3470 19.6535i 0.821038 1.42208i −0.0838717 0.996477i \(-0.526729\pi\)
0.904910 0.425603i \(-0.139938\pi\)
\(192\) 0 0
\(193\) −3.09349 5.35808i −0.222674 0.385683i 0.732945 0.680288i \(-0.238145\pi\)
−0.955619 + 0.294605i \(0.904812\pi\)
\(194\) −22.4526 −1.61200
\(195\) 0 0
\(196\) 0 0
\(197\) −9.77010 −0.696091 −0.348045 0.937478i \(-0.613154\pi\)
−0.348045 + 0.937478i \(0.613154\pi\)
\(198\) 0 0
\(199\) 4.33973 7.51664i 0.307636 0.532840i −0.670209 0.742172i \(-0.733796\pi\)
0.977845 + 0.209332i \(0.0671289\pi\)
\(200\) 3.61381 0.255535
\(201\) 0 0
\(202\) −1.02987 + 1.78379i −0.0724615 + 0.125507i
\(203\) 0 0
\(204\) 0 0
\(205\) 6.02225 10.4308i 0.420612 0.728522i
\(206\) 1.77721 3.07822i 0.123824 0.214470i
\(207\) 0 0
\(208\) −12.5460 21.7303i −0.869909 1.50673i
\(209\) −1.89446 3.28130i −0.131043 0.226973i
\(210\) 0 0
\(211\) −2.84219 + 4.92283i −0.195665 + 0.338901i −0.947118 0.320885i \(-0.896020\pi\)
0.751453 + 0.659786i \(0.229353\pi\)
\(212\) 2.10019 0.144242
\(213\) 0 0
\(214\) 10.6412 0.727420
\(215\) 6.80708 + 11.7902i 0.464239 + 0.804086i
\(216\) 0 0
\(217\) 0 0
\(218\) −7.58786 13.1426i −0.513915 0.890126i
\(219\) 0 0
\(220\) 1.40372 + 2.43132i 0.0946390 + 0.163920i
\(221\) −4.00862 6.94313i −0.269649 0.467045i
\(222\) 0 0
\(223\) −5.86133 10.1521i −0.392503 0.679836i 0.600276 0.799793i \(-0.295058\pi\)
−0.992779 + 0.119957i \(0.961724\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −13.3509 23.1245i −0.888091 1.53822i
\(227\) 11.1831 0.742247 0.371123 0.928584i \(-0.378973\pi\)
0.371123 + 0.928584i \(0.378973\pi\)
\(228\) 0 0
\(229\) 9.65647 0.638118 0.319059 0.947735i \(-0.396633\pi\)
0.319059 + 0.947735i \(0.396633\pi\)
\(230\) −9.04494 + 15.6663i −0.596406 + 1.03301i
\(231\) 0 0
\(232\) −0.0347761 0.0602340i −0.00228317 0.00395456i
\(233\) 9.64492 + 16.7055i 0.631860 + 1.09441i 0.987171 + 0.159666i \(0.0510416\pi\)
−0.355311 + 0.934748i \(0.615625\pi\)
\(234\) 0 0
\(235\) 6.35243 11.0027i 0.414387 0.717739i
\(236\) 5.86881 10.1651i 0.382027 0.661690i
\(237\) 0 0
\(238\) 0 0
\(239\) 0.194641 0.337128i 0.0125903 0.0218070i −0.859662 0.510864i \(-0.829326\pi\)
0.872252 + 0.489057i \(0.162659\pi\)
\(240\) 0 0
\(241\) −10.6361 −0.685134 −0.342567 0.939493i \(-0.611296\pi\)
−0.342567 + 0.939493i \(0.611296\pi\)
\(242\) 8.01932 13.8899i 0.515502 0.892875i
\(243\) 0 0
\(244\) −4.50299 −0.288274
\(245\) 0 0
\(246\) 0 0
\(247\) 12.9618 0.824741
\(248\) 2.16023 + 3.74163i 0.137175 + 0.237594i
\(249\) 0 0
\(250\) 10.0988 17.4917i 0.638705 1.10627i
\(251\) −3.26628 −0.206166 −0.103083 0.994673i \(-0.532871\pi\)
−0.103083 + 0.994673i \(0.532871\pi\)
\(252\) 0 0
\(253\) −11.1370 −0.700176
\(254\) −7.82531 + 13.5538i −0.491004 + 0.850443i
\(255\) 0 0
\(256\) −10.4896 18.1686i −0.655603 1.13554i
\(257\) −4.69573 −0.292912 −0.146456 0.989217i \(-0.546787\pi\)
−0.146456 + 0.989217i \(0.546787\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −9.60421 −0.595628
\(261\) 0 0
\(262\) 1.85363 3.21059i 0.114518 0.198351i
\(263\) −19.5498 −1.20549 −0.602747 0.797932i \(-0.705927\pi\)
−0.602747 + 0.797932i \(0.705927\pi\)
\(264\) 0 0
\(265\) −1.00824 + 1.74632i −0.0619355 + 0.107276i
\(266\) 0 0
\(267\) 0 0
\(268\) −4.81929 + 8.34725i −0.294385 + 0.509890i
\(269\) 7.88365 13.6549i 0.480675 0.832553i −0.519079 0.854726i \(-0.673725\pi\)
0.999754 + 0.0221730i \(0.00705846\pi\)
\(270\) 0 0
\(271\) −7.39882 12.8151i −0.449446 0.778464i 0.548904 0.835886i \(-0.315045\pi\)
−0.998350 + 0.0574218i \(0.981712\pi\)
\(272\) −3.75442 6.50285i −0.227645 0.394293i
\(273\) 0 0
\(274\) 2.04138 3.53578i 0.123324 0.213604i
\(275\) 4.86954 0.293644
\(276\) 0 0
\(277\) −7.45122 −0.447701 −0.223850 0.974624i \(-0.571863\pi\)
−0.223850 + 0.974624i \(0.571863\pi\)
\(278\) −0.695380 1.20443i −0.0417061 0.0722371i
\(279\) 0 0
\(280\) 0 0
\(281\) 12.9938 + 22.5060i 0.775146 + 1.34259i 0.934712 + 0.355406i \(0.115657\pi\)
−0.159566 + 0.987187i \(0.551009\pi\)
\(282\) 0 0
\(283\) 9.37768 + 16.2426i 0.557445 + 0.965524i 0.997709 + 0.0676550i \(0.0215517\pi\)
−0.440263 + 0.897869i \(0.645115\pi\)
\(284\) −8.57064 14.8448i −0.508574 0.880876i
\(285\) 0 0
\(286\) −7.20971 12.4876i −0.426319 0.738406i
\(287\) 0 0
\(288\) 0 0
\(289\) 7.30041 + 12.6447i 0.429436 + 0.743805i
\(290\) −0.152230 −0.00893928
\(291\) 0 0
\(292\) −3.83507 −0.224431
\(293\) −1.23089 + 2.13196i −0.0719093 + 0.124551i −0.899738 0.436430i \(-0.856243\pi\)
0.827829 + 0.560981i \(0.189576\pi\)
\(294\) 0 0
\(295\) 5.63487 + 9.75988i 0.328075 + 0.568242i
\(296\) 0.316203 + 0.547680i 0.0183790 + 0.0318333i
\(297\) 0 0
\(298\) 6.06227 10.5002i 0.351178 0.608258i
\(299\) 19.0497 32.9950i 1.10167 1.90815i
\(300\) 0 0
\(301\) 0 0
\(302\) −11.6616 + 20.1985i −0.671050 + 1.16229i
\(303\) 0 0
\(304\) 12.1399 0.696270
\(305\) 2.16175 3.74425i 0.123781 0.214395i
\(306\) 0 0
\(307\) 4.66277 0.266118 0.133059 0.991108i \(-0.457520\pi\)
0.133059 + 0.991108i \(0.457520\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 9.45629 0.537081
\(311\) −13.7410 23.8002i −0.779183 1.34958i −0.932413 0.361393i \(-0.882301\pi\)
0.153231 0.988190i \(-0.451032\pi\)
\(312\) 0 0
\(313\) 2.74666 4.75735i 0.155250 0.268901i −0.777900 0.628388i \(-0.783715\pi\)
0.933150 + 0.359487i \(0.117048\pi\)
\(314\) 31.8671 1.79837
\(315\) 0 0
\(316\) −8.22893 −0.462914
\(317\) 4.93879 8.55424i 0.277390 0.480454i −0.693345 0.720606i \(-0.743864\pi\)
0.970735 + 0.240152i \(0.0771972\pi\)
\(318\) 0 0
\(319\) −0.0468601 0.0811641i −0.00262366 0.00454432i
\(320\) −3.47615 −0.194323
\(321\) 0 0
\(322\) 0 0
\(323\) 3.87885 0.215825
\(324\) 0 0
\(325\) −8.32930 + 14.4268i −0.462026 + 0.800253i
\(326\) −22.4986 −1.24608
\(327\) 0 0
\(328\) −5.06616 + 8.77485i −0.279732 + 0.484510i
\(329\) 0 0
\(330\) 0 0
\(331\) 10.3471 17.9217i 0.568729 0.985067i −0.427963 0.903796i \(-0.640769\pi\)
0.996692 0.0812710i \(-0.0258979\pi\)
\(332\) 3.89401 6.74463i 0.213712 0.370160i
\(333\) 0 0
\(334\) 3.24514 + 5.62076i 0.177566 + 0.307554i
\(335\) −4.62718 8.01452i −0.252810 0.437880i
\(336\) 0 0
\(337\) 0.748747 1.29687i 0.0407869 0.0706449i −0.844911 0.534906i \(-0.820347\pi\)
0.885698 + 0.464261i \(0.153680\pi\)
\(338\) 25.3924 1.38116
\(339\) 0 0
\(340\) −2.87408 −0.155869
\(341\) 2.91087 + 5.04177i 0.157632 + 0.273027i
\(342\) 0 0
\(343\) 0 0
\(344\) −5.72639 9.91840i −0.308746 0.534764i
\(345\) 0 0
\(346\) −9.33593 16.1703i −0.501903 0.869321i
\(347\) −14.7694 25.5813i −0.792862 1.37328i −0.924188 0.381938i \(-0.875257\pi\)
0.131326 0.991339i \(-0.458077\pi\)
\(348\) 0 0
\(349\) −18.0006 31.1780i −0.963551 1.66892i −0.713458 0.700698i \(-0.752872\pi\)
−0.250094 0.968222i \(-0.580461\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −5.05363 8.75315i −0.269360 0.466545i
\(353\) −29.4930 −1.56975 −0.784877 0.619652i \(-0.787274\pi\)
−0.784877 + 0.619652i \(0.787274\pi\)
\(354\) 0 0
\(355\) 16.4580 0.873500
\(356\) 0.977687 1.69340i 0.0518173 0.0897502i
\(357\) 0 0
\(358\) −1.56612 2.71260i −0.0827720 0.143365i
\(359\) −2.70535 4.68580i −0.142783 0.247307i 0.785761 0.618531i \(-0.212272\pi\)
−0.928544 + 0.371224i \(0.878938\pi\)
\(360\) 0 0
\(361\) 6.36444 11.0235i 0.334971 0.580186i
\(362\) −15.6451 + 27.0981i −0.822289 + 1.42425i
\(363\) 0 0
\(364\) 0 0
\(365\) 1.84110 3.18888i 0.0963676 0.166914i
\(366\) 0 0
\(367\) 23.0843 1.20499 0.602496 0.798122i \(-0.294173\pi\)
0.602496 + 0.798122i \(0.294173\pi\)
\(368\) 17.8417 30.9027i 0.930063 1.61092i
\(369\) 0 0
\(370\) 1.38416 0.0719591
\(371\) 0 0
\(372\) 0 0
\(373\) 21.5030 1.11338 0.556692 0.830719i \(-0.312070\pi\)
0.556692 + 0.830719i \(0.312070\pi\)
\(374\) −2.15752 3.73694i −0.111563 0.193232i
\(375\) 0 0
\(376\) −5.34392 + 9.25595i −0.275592 + 0.477339i
\(377\) 0.320615 0.0165125
\(378\) 0 0
\(379\) 5.72168 0.293903 0.146952 0.989144i \(-0.453054\pi\)
0.146952 + 0.989144i \(0.453054\pi\)
\(380\) 2.32333 4.02412i 0.119184 0.206433i
\(381\) 0 0
\(382\) 20.8925 + 36.1869i 1.06895 + 1.85148i
\(383\) −34.9209 −1.78437 −0.892187 0.451666i \(-0.850830\pi\)
−0.892187 + 0.451666i \(0.850830\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 11.3917 0.579823
\(387\) 0 0
\(388\) 8.47603 14.6809i 0.430305 0.745311i
\(389\) 28.8822 1.46438 0.732192 0.681098i \(-0.238497\pi\)
0.732192 + 0.681098i \(0.238497\pi\)
\(390\) 0 0
\(391\) 5.70066 9.87383i 0.288295 0.499341i
\(392\) 0 0
\(393\) 0 0
\(394\) 8.99455 15.5790i 0.453139 0.784860i
\(395\) 3.95046 6.84239i 0.198769 0.344278i
\(396\) 0 0
\(397\) −5.59226 9.68607i −0.280667 0.486130i 0.690882 0.722968i \(-0.257222\pi\)
−0.971549 + 0.236838i \(0.923889\pi\)
\(398\) 7.99049 + 13.8399i 0.400527 + 0.693734i
\(399\) 0 0
\(400\) −7.80111 + 13.5119i −0.390056 + 0.675596i
\(401\) 1.08212 0.0540386 0.0270193 0.999635i \(-0.491398\pi\)
0.0270193 + 0.999635i \(0.491398\pi\)
\(402\) 0 0
\(403\) −19.9160 −0.992088
\(404\) −0.777570 1.34679i −0.0386856 0.0670054i
\(405\) 0 0
\(406\) 0 0
\(407\) 0.426078 + 0.737988i 0.0211199 + 0.0365807i
\(408\) 0 0
\(409\) −10.8674 18.8229i −0.537360 0.930735i −0.999045 0.0436908i \(-0.986088\pi\)
0.461685 0.887044i \(-0.347245\pi\)
\(410\) 11.0884 + 19.2057i 0.547618 + 0.948501i
\(411\) 0 0
\(412\) 1.34182 + 2.32410i 0.0661069 + 0.114500i
\(413\) 0 0
\(414\) 0 0
\(415\) 3.73879 + 6.47578i 0.183530 + 0.317884i
\(416\) 34.5767 1.69526
\(417\) 0 0
\(418\) 6.97632 0.341223
\(419\) 12.5906 21.8075i 0.615090 1.06537i −0.375279 0.926912i \(-0.622453\pi\)
0.990369 0.138455i \(-0.0442135\pi\)
\(420\) 0 0
\(421\) −14.8304 25.6869i −0.722788 1.25191i −0.959878 0.280418i \(-0.909527\pi\)
0.237090 0.971488i \(-0.423806\pi\)
\(422\) −5.23316 9.06411i −0.254746 0.441234i
\(423\) 0 0
\(424\) 0.848171 1.46907i 0.0411908 0.0713446i
\(425\) −2.49256 + 4.31724i −0.120907 + 0.209417i
\(426\) 0 0
\(427\) 0 0
\(428\) −4.01715 + 6.95791i −0.194176 + 0.336323i
\(429\) 0 0
\(430\) −25.0669 −1.20884
\(431\) −2.44517 + 4.23516i −0.117780 + 0.204000i −0.918887 0.394520i \(-0.870911\pi\)
0.801108 + 0.598520i \(0.204244\pi\)
\(432\) 0 0
\(433\) −9.71430 −0.466839 −0.233420 0.972376i \(-0.574992\pi\)
−0.233420 + 0.972376i \(0.574992\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 11.4579 0.548735
\(437\) 9.21651 + 15.9635i 0.440885 + 0.763636i
\(438\) 0 0
\(439\) −7.41176 + 12.8375i −0.353744 + 0.612703i −0.986902 0.161320i \(-0.948425\pi\)
0.633158 + 0.774022i \(0.281758\pi\)
\(440\) 2.26760 0.108103
\(441\) 0 0
\(442\) 14.7617 0.702141
\(443\) −10.9510 + 18.9676i −0.520297 + 0.901180i 0.479425 + 0.877583i \(0.340845\pi\)
−0.999722 + 0.0235972i \(0.992488\pi\)
\(444\) 0 0
\(445\) 0.938715 + 1.62590i 0.0444994 + 0.0770751i
\(446\) 21.5842 1.02204
\(447\) 0 0
\(448\) 0 0
\(449\) −21.4952 −1.01442 −0.507212 0.861822i \(-0.669324\pi\)
−0.507212 + 0.861822i \(0.669324\pi\)
\(450\) 0 0
\(451\) −6.82655 + 11.8239i −0.321450 + 0.556767i
\(452\) 20.1603 0.948263
\(453\) 0 0
\(454\) −10.2954 + 17.8321i −0.483185 + 0.836902i
\(455\) 0 0
\(456\) 0 0
\(457\) −20.3128 + 35.1827i −0.950190 + 1.64578i −0.205181 + 0.978724i \(0.565778\pi\)
−0.745009 + 0.667054i \(0.767555\pi\)
\(458\) −8.88995 + 15.3978i −0.415400 + 0.719494i
\(459\) 0 0
\(460\) −6.82908 11.8283i −0.318408 0.551498i
\(461\) 1.41541 + 2.45155i 0.0659220 + 0.114180i 0.897103 0.441822i \(-0.145668\pi\)
−0.831181 + 0.556003i \(0.812334\pi\)
\(462\) 0 0
\(463\) −13.9324 + 24.1317i −0.647494 + 1.12149i 0.336225 + 0.941782i \(0.390850\pi\)
−0.983719 + 0.179711i \(0.942484\pi\)
\(464\) 0.300284 0.0139403
\(465\) 0 0
\(466\) −35.5173 −1.64531
\(467\) −13.3219 23.0742i −0.616464 1.06775i −0.990126 0.140182i \(-0.955231\pi\)
0.373661 0.927565i \(-0.378102\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 11.6964 + 20.2587i 0.539513 + 0.934463i
\(471\) 0 0
\(472\) −4.74028 8.21041i −0.218189 0.377915i
\(473\) −7.71620 13.3648i −0.354791 0.614516i
\(474\) 0 0
\(475\) −4.02983 6.97987i −0.184901 0.320258i
\(476\) 0 0
\(477\) 0 0
\(478\) 0.358381 + 0.620734i 0.0163920 + 0.0283917i
\(479\) −31.5791 −1.44289 −0.721443 0.692474i \(-0.756521\pi\)
−0.721443 + 0.692474i \(0.756521\pi\)
\(480\) 0 0
\(481\) −2.91520 −0.132922
\(482\) 9.79185 16.9600i 0.446007 0.772506i
\(483\) 0 0
\(484\) 6.05472 + 10.4871i 0.275215 + 0.476686i
\(485\) 8.13817 + 14.0957i 0.369535 + 0.640054i
\(486\) 0 0
\(487\) −0.153087 + 0.265154i −0.00693703 + 0.0120153i −0.869473 0.493980i \(-0.835541\pi\)
0.862536 + 0.505996i \(0.168875\pi\)
\(488\) −1.81855 + 3.14982i −0.0823218 + 0.142586i
\(489\) 0 0
\(490\) 0 0
\(491\) 9.06981 15.7094i 0.409315 0.708954i −0.585498 0.810674i \(-0.699101\pi\)
0.994813 + 0.101720i \(0.0324345\pi\)
\(492\) 0 0
\(493\) 0.0959447 0.00432113
\(494\) −11.9329 + 20.6684i −0.536887 + 0.929916i
\(495\) 0 0
\(496\) −18.6531 −0.837549
\(497\) 0 0
\(498\) 0 0
\(499\) −21.3091 −0.953928 −0.476964 0.878923i \(-0.658263\pi\)
−0.476964 + 0.878923i \(0.658263\pi\)
\(500\) 7.62478 + 13.2065i 0.340990 + 0.590613i
\(501\) 0 0
\(502\) 3.00701 5.20829i 0.134209 0.232457i
\(503\) −17.0738 −0.761285 −0.380642 0.924722i \(-0.624297\pi\)
−0.380642 + 0.924722i \(0.624297\pi\)
\(504\) 0 0
\(505\) 1.49315 0.0664443
\(506\) 10.2529 17.7586i 0.455799 0.789466i
\(507\) 0 0
\(508\) −5.90824 10.2334i −0.262136 0.454032i
\(509\) 36.7735 1.62996 0.814979 0.579490i \(-0.196748\pi\)
0.814979 + 0.579490i \(0.196748\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 21.4975 0.950065
\(513\) 0 0
\(514\) 4.32299 7.48764i 0.190679 0.330265i
\(515\) −2.57667 −0.113542
\(516\) 0 0
\(517\) −7.20083 + 12.4722i −0.316692 + 0.548527i
\(518\) 0 0
\(519\) 0 0
\(520\) −3.87870 + 6.71810i −0.170092 + 0.294608i
\(521\) −9.57535 + 16.5850i −0.419504 + 0.726602i −0.995890 0.0905758i \(-0.971129\pi\)
0.576386 + 0.817178i \(0.304463\pi\)
\(522\) 0 0
\(523\) 20.9715 + 36.3236i 0.917018 + 1.58832i 0.803920 + 0.594737i \(0.202744\pi\)
0.113097 + 0.993584i \(0.463923\pi\)
\(524\) 1.39952 + 2.42405i 0.0611385 + 0.105895i
\(525\) 0 0
\(526\) 17.9980 31.1734i 0.784749 1.35922i
\(527\) −5.95991 −0.259618
\(528\) 0 0
\(529\) 31.1812 1.35570
\(530\) −1.85641 3.21539i −0.0806372 0.139668i
\(531\) 0 0
\(532\) 0 0
\(533\) −23.3535 40.4494i −1.01155 1.75206i
\(534\) 0 0
\(535\) −3.85702 6.68056i −0.166754 0.288826i
\(536\) 3.89258 + 6.74214i 0.168134 + 0.291216i
\(537\) 0 0
\(538\) 14.5157 + 25.1419i 0.625816 + 1.08395i
\(539\) 0 0
\(540\) 0 0
\(541\) −1.44272 2.49886i −0.0620273 0.107434i 0.833344 0.552754i \(-0.186423\pi\)
−0.895371 + 0.445320i \(0.853090\pi\)
\(542\) 27.2460 1.17032
\(543\) 0 0
\(544\) 10.3472 0.443631
\(545\) −5.50059 + 9.52731i −0.235620 + 0.408105i
\(546\) 0 0
\(547\) 1.38738 + 2.40301i 0.0593201 + 0.102745i 0.894160 0.447747i \(-0.147773\pi\)
−0.834840 + 0.550492i \(0.814440\pi\)
\(548\) 1.54128 + 2.66957i 0.0658401 + 0.114038i
\(549\) 0 0
\(550\) −4.48300 + 7.76478i −0.191156 + 0.331091i
\(551\) −0.0775590 + 0.134336i −0.00330413 + 0.00572291i
\(552\) 0 0
\(553\) 0 0
\(554\) 6.85975 11.8814i 0.291443 0.504794i
\(555\) 0 0
\(556\) 1.05005 0.0445319
\(557\) −15.5344 + 26.9064i −0.658214 + 1.14006i 0.322864 + 0.946445i \(0.395354\pi\)
−0.981078 + 0.193614i \(0.937979\pi\)
\(558\) 0 0
\(559\) 52.7939 2.23294
\(560\) 0 0
\(561\) 0 0
\(562\) −47.8495 −2.01841
\(563\) −0.144020 0.249451i −0.00606973 0.0105131i 0.862975 0.505247i \(-0.168599\pi\)
−0.869044 + 0.494734i \(0.835265\pi\)
\(564\) 0 0
\(565\) −9.67836 + 16.7634i −0.407172 + 0.705242i
\(566\) −34.5331 −1.45154
\(567\) 0 0
\(568\) −13.8451 −0.580929
\(569\) −8.04004 + 13.9258i −0.337056 + 0.583798i −0.983878 0.178843i \(-0.942765\pi\)
0.646821 + 0.762641i \(0.276098\pi\)
\(570\) 0 0
\(571\) 7.64289 + 13.2379i 0.319845 + 0.553988i 0.980456 0.196741i \(-0.0630358\pi\)
−0.660610 + 0.750729i \(0.729702\pi\)
\(572\) 10.8869 0.455204
\(573\) 0 0
\(574\) 0 0
\(575\) −23.6902 −0.987950
\(576\) 0 0
\(577\) −12.0812 + 20.9253i −0.502949 + 0.871133i 0.497045 + 0.867725i \(0.334418\pi\)
−0.999994 + 0.00340833i \(0.998915\pi\)
\(578\) −26.8836 −1.11821
\(579\) 0 0
\(580\) 0.0574683 0.0995380i 0.00238624 0.00413309i
\(581\) 0 0
\(582\) 0 0
\(583\) 1.14289 1.97955i 0.0473338 0.0819845i
\(584\) −1.54881 + 2.68262i −0.0640902 + 0.111007i
\(585\) 0 0
\(586\) −2.26636 3.92546i −0.0936226 0.162159i
\(587\) 18.0145 + 31.2020i 0.743537 + 1.28784i 0.950875 + 0.309574i \(0.100186\pi\)
−0.207339 + 0.978269i \(0.566480\pi\)
\(588\) 0 0
\(589\) 4.81783 8.34472i 0.198515 0.343838i
\(590\) −20.7503 −0.854276
\(591\) 0 0
\(592\) −2.73034 −0.112216
\(593\) 12.4668 + 21.5932i 0.511951 + 0.886726i 0.999904 + 0.0138558i \(0.00441057\pi\)
−0.487953 + 0.872870i \(0.662256\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 4.57712 + 7.92780i 0.187486 + 0.324735i
\(597\) 0 0
\(598\) 35.0751 + 60.7518i 1.43433 + 2.48433i
\(599\) 19.7642 + 34.2325i 0.807542 + 1.39870i 0.914561 + 0.404447i \(0.132536\pi\)
−0.107019 + 0.994257i \(0.534131\pi\)
\(600\) 0 0
\(601\) −1.86447 3.22936i −0.0760534 0.131728i 0.825490 0.564416i \(-0.190899\pi\)
−0.901544 + 0.432688i \(0.857565\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −8.80470 15.2502i −0.358258 0.620521i
\(605\) −11.6267 −0.472694
\(606\) 0 0
\(607\) −23.6528 −0.960036 −0.480018 0.877259i \(-0.659370\pi\)
−0.480018 + 0.877259i \(0.659370\pi\)
\(608\) −8.36436 + 14.4875i −0.339219 + 0.587545i
\(609\) 0 0
\(610\) 3.98029 + 6.89407i 0.161157 + 0.279133i
\(611\) −24.6339 42.6671i −0.996580 1.72613i
\(612\) 0 0
\(613\) 1.89952 3.29006i 0.0767208 0.132884i −0.825113 0.564968i \(-0.808888\pi\)
0.901833 + 0.432084i \(0.142222\pi\)
\(614\) −4.29264 + 7.43507i −0.173237 + 0.300055i
\(615\) 0 0
\(616\) 0 0
\(617\) 17.5615 30.4174i 0.706999 1.22456i −0.258966 0.965886i \(-0.583382\pi\)
0.965965 0.258672i \(-0.0832849\pi\)
\(618\) 0 0
\(619\) 21.1632 0.850622 0.425311 0.905047i \(-0.360165\pi\)
0.425311 + 0.905047i \(0.360165\pi\)
\(620\) −3.56983 + 6.18312i −0.143368 + 0.248320i
\(621\) 0 0
\(622\) 50.6011 2.02892
\(623\) 0 0
\(624\) 0 0
\(625\) 1.45048 0.0580192
\(626\) 5.05726 + 8.75943i 0.202129 + 0.350097i
\(627\) 0 0
\(628\) −12.0301 + 20.8368i −0.480054 + 0.831477i
\(629\) −0.872381 −0.0347841
\(630\) 0 0
\(631\) 4.74845 0.189033 0.0945164 0.995523i \(-0.469870\pi\)
0.0945164 + 0.995523i \(0.469870\pi\)
\(632\) −3.32329 + 5.75610i −0.132193 + 0.228965i
\(633\) 0 0
\(634\) 9.09350 + 15.7504i 0.361149 + 0.625529i
\(635\) 11.3455 0.450231
\(636\) 0 0
\(637\) 0 0
\(638\) 0.172562 0.00683178
\(639\) 0 0
\(640\) −5.71622 + 9.90078i −0.225953 + 0.391363i
\(641\) 9.87469 0.390027 0.195013 0.980801i \(-0.437525\pi\)
0.195013 + 0.980801i \(0.437525\pi\)
\(642\) 0 0
\(643\) −21.9748 + 38.0615i −0.866602 + 1.50100i −0.00115462 + 0.999999i \(0.500368\pi\)
−0.865448 + 0.501000i \(0.832966\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −3.57095 + 6.18507i −0.140497 + 0.243348i
\(647\) 22.1936 38.4404i 0.872521 1.51125i 0.0131398 0.999914i \(-0.495817\pi\)
0.859381 0.511336i \(-0.170849\pi\)
\(648\) 0 0
\(649\) −6.38743 11.0634i −0.250729 0.434275i
\(650\) −15.3362 26.5631i −0.601537 1.04189i
\(651\) 0 0
\(652\) 8.49341 14.7110i 0.332628 0.576128i
\(653\) −41.9912 −1.64324 −0.821622 0.570033i \(-0.806930\pi\)
−0.821622 + 0.570033i \(0.806930\pi\)
\(654\) 0 0
\(655\) −2.68748 −0.105008
\(656\) −21.8726 37.8844i −0.853980 1.47914i
\(657\) 0 0
\(658\) 0 0
\(659\) 19.6365 + 34.0114i 0.764928 + 1.32489i 0.940284 + 0.340390i \(0.110559\pi\)
−0.175356 + 0.984505i \(0.556108\pi\)
\(660\) 0 0
\(661\) −0.0933694 0.161721i −0.00363165 0.00629020i 0.864204 0.503142i \(-0.167823\pi\)
−0.867836 + 0.496852i \(0.834489\pi\)
\(662\) 19.0515 + 32.9982i 0.740459 + 1.28251i
\(663\) 0 0
\(664\) −3.14522 5.44769i −0.122058 0.211411i
\(665\) 0 0
\(666\) 0 0
\(667\) 0.227973 + 0.394862i 0.00882717 + 0.0152891i
\(668\) −4.90028 −0.189597
\(669\) 0 0
\(670\) 17.0395 0.658294
\(671\) −2.45046 + 4.24432i −0.0945989 + 0.163850i
\(672\) 0 0
\(673\) −5.43382 9.41166i −0.209458 0.362793i 0.742086 0.670305i \(-0.233837\pi\)
−0.951544 + 0.307512i \(0.900503\pi\)
\(674\) 1.37862 + 2.38785i 0.0531026 + 0.0919764i
\(675\) 0 0
\(676\) −9.58584 + 16.6032i −0.368686 + 0.638583i
\(677\) −14.1950 + 24.5865i −0.545560 + 0.944937i 0.453012 + 0.891505i \(0.350350\pi\)
−0.998571 + 0.0534326i \(0.982984\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −1.16071 + 2.01041i −0.0445111 + 0.0770956i
\(681\) 0 0
\(682\) −10.7192 −0.410460
\(683\) −5.92034 + 10.2543i −0.226536 + 0.392371i −0.956779 0.290816i \(-0.906073\pi\)
0.730243 + 0.683187i \(0.239407\pi\)
\(684\) 0 0
\(685\) −2.95968 −0.113083
\(686\) 0 0
\(687\) 0 0
\(688\) 49.4461 1.88511
\(689\) 3.90981 + 6.77199i 0.148952 + 0.257992i
\(690\) 0 0
\(691\) 5.95416 10.3129i 0.226507 0.392321i −0.730264 0.683165i \(-0.760603\pi\)
0.956770 + 0.290844i \(0.0939361\pi\)
\(692\) 14.0976 0.535909
\(693\) 0 0
\(694\) 54.3880 2.06454
\(695\) −0.504096 + 0.873119i −0.0191214 + 0.0331193i
\(696\) 0 0
\(697\) −6.98857 12.1046i −0.264711 0.458493i
\(698\) 66.2870 2.50900
\(699\) 0 0
\(700\) 0 0
\(701\) 31.3902 1.18559 0.592795 0.805353i \(-0.298024\pi\)
0.592795 + 0.805353i \(0.298024\pi\)
\(702\) 0 0
\(703\) 0.705208 1.22146i 0.0265974 0.0460681i
\(704\) 3.94041 0.148510
\(705\) 0 0
\(706\) 27.1518 47.0284i 1.02187 1.76994i
\(707\) 0 0
\(708\) 0 0
\(709\) −0.312609 + 0.541455i −0.0117403 + 0.0203348i −0.871836 0.489798i \(-0.837070\pi\)
0.860096 + 0.510133i \(0.170404\pi\)
\(710\) −15.1516 + 26.2433i −0.568628 + 0.984893i
\(711\) 0 0
\(712\) −0.789685 1.36777i −0.0295947 0.0512595i
\(713\) −14.1613 24.5281i −0.530345 0.918584i
\(714\) 0 0
\(715\) −5.22647 + 9.05251i −0.195459 + 0.338545i
\(716\) 2.36489 0.0883802
\(717\) 0 0
\(718\) 9.96239 0.371793
\(719\) 12.1969 + 21.1257i 0.454869 + 0.787857i 0.998681 0.0513506i \(-0.0163526\pi\)
−0.543811 + 0.839208i \(0.683019\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 11.7185 + 20.2970i 0.436116 + 0.755376i
\(723\) 0 0
\(724\) −11.8123 20.4595i −0.439002 0.760373i
\(725\) −0.0996792 0.172649i −0.00370199 0.00641204i
\(726\) 0 0
\(727\) 18.9253 + 32.7796i 0.701900 + 1.21573i 0.967799 + 0.251726i \(0.0809980\pi\)
−0.265899 + 0.964001i \(0.585669\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 3.38991 + 5.87150i 0.125466 + 0.217314i
\(731\) 15.7987 0.584335
\(732\) 0 0
\(733\) −2.40155 −0.0887033 −0.0443516 0.999016i \(-0.514122\pi\)
−0.0443516 + 0.999016i \(0.514122\pi\)
\(734\) −21.2519 + 36.8093i −0.784421 + 1.35866i
\(735\) 0 0
\(736\) 24.5858 + 42.5839i 0.906245 + 1.56966i
\(737\) 5.24517 + 9.08490i 0.193208 + 0.334646i
\(738\) 0 0
\(739\) −15.1940 + 26.3167i −0.558920 + 0.968077i 0.438667 + 0.898650i \(0.355451\pi\)
−0.997587 + 0.0694277i \(0.977883\pi\)
\(740\) −0.522533 + 0.905053i −0.0192087 + 0.0332704i
\(741\) 0 0
\(742\) 0 0
\(743\) 2.54785 4.41300i 0.0934715 0.161897i −0.815498 0.578760i \(-0.803537\pi\)
0.908970 + 0.416862i \(0.136870\pi\)
\(744\) 0 0
\(745\) −8.78934 −0.322016
\(746\) −19.7961 + 34.2879i −0.724787 + 1.25537i
\(747\) 0 0
\(748\) 3.25793 0.119122
\(749\) 0 0
\(750\) 0 0
\(751\) −0.975011 −0.0355787 −0.0177893 0.999842i \(-0.505663\pi\)
−0.0177893 + 0.999842i \(0.505663\pi\)
\(752\) −23.0718 39.9615i −0.841341 1.45724i
\(753\) 0 0
\(754\) −0.295165 + 0.511240i −0.0107493 + 0.0186183i
\(755\) 16.9075 0.615326
\(756\) 0 0
\(757\) 11.6346 0.422865 0.211433 0.977393i \(-0.432187\pi\)
0.211433 + 0.977393i \(0.432187\pi\)
\(758\) −5.26750 + 9.12357i −0.191324 + 0.331383i
\(759\) 0 0
\(760\) −1.87657 3.25031i −0.0680703 0.117901i
\(761\) −54.1749 −1.96384 −0.981920 0.189298i \(-0.939379\pi\)
−0.981920 + 0.189298i \(0.939379\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −31.5484 −1.14138
\(765\) 0 0
\(766\) 32.1489 55.6835i 1.16159 2.01193i
\(767\) 43.7025 1.57801
\(768\) 0 0
\(769\) 10.4326 18.0698i 0.376208 0.651612i −0.614299 0.789074i \(-0.710561\pi\)
0.990507 + 0.137462i \(0.0438943\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −4.30047 + 7.44863i −0.154777 + 0.268082i
\(773\) −27.4972 + 47.6266i −0.989007 + 1.71301i −0.366447 + 0.930439i \(0.619426\pi\)
−0.622561 + 0.782572i \(0.713908\pi\)
\(774\) 0 0
\(775\) 6.19189 + 10.7247i 0.222419 + 0.385242i
\(776\) −6.84616 11.8579i −0.245763 0.425674i
\(777\) 0 0
\(778\) −26.5895 + 46.0544i −0.953281 + 1.65113i
\(779\) 22.5975 0.809639
\(780\) 0 0
\(781\) −18.6560 −0.667566
\(782\) 10.4963 + 18.1801i 0.375346 + 0.650119i
\(783\) 0 0
\(784\) 0 0
\(785\) −11.5506 20.0062i −0.412258 0.714051i
\(786\) 0 0
\(787\) 4.59475 + 7.95833i 0.163785 + 0.283684i 0.936223 0.351406i \(-0.114296\pi\)
−0.772438 + 0.635090i \(0.780963\pi\)
\(788\) 6.79103 + 11.7624i 0.241921 + 0.419019i
\(789\) 0 0
\(790\) 7.27374 + 12.5985i 0.258788 + 0.448234i
\(791\) 0 0
\(792\) 0 0
\(793\) −8.38296 14.5197i −0.297688 0.515610i
\(794\) 20.5934 0.730832
\(795\) 0 0
\(796\)