Properties

Label 864.2.v.b.109.16
Level $864$
Weight $2$
Character 864.109
Analytic conductor $6.899$
Analytic rank $0$
Dimension $128$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.v (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 109.16
Character \(\chi\) \(=\) 864.109
Dual form 864.2.v.b.325.16

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.239074 + 1.39386i) q^{2} +(-1.88569 - 0.666470i) q^{4} +(0.369546 - 0.153071i) q^{5} +(-1.24156 + 1.24156i) q^{7} +(1.37978 - 2.46905i) q^{8} +O(q^{10})\) \(q+(-0.239074 + 1.39386i) q^{2} +(-1.88569 - 0.666470i) q^{4} +(0.369546 - 0.153071i) q^{5} +(-1.24156 + 1.24156i) q^{7} +(1.37978 - 2.46905i) q^{8} +(0.125011 + 0.551690i) q^{10} +(-0.490552 - 1.18430i) q^{11} +(4.60261 + 1.90646i) q^{13} +(-1.43373 - 2.02738i) q^{14} +(3.11164 + 2.51351i) q^{16} +4.73651i q^{17} +(2.25236 + 0.932959i) q^{19} +(-0.798865 + 0.0423528i) q^{20} +(1.76802 - 0.400626i) q^{22} +(-4.41161 - 4.41161i) q^{23} +(-3.42240 + 3.42240i) q^{25} +(-3.75771 + 5.95961i) q^{26} +(3.16865 - 1.51373i) q^{28} +(-3.72693 + 8.99760i) q^{29} +5.82890 q^{31} +(-4.24739 + 3.73627i) q^{32} +(-6.60203 - 1.13238i) q^{34} +(-0.268766 + 0.648859i) q^{35} +(-1.91286 + 0.792332i) q^{37} +(-1.83889 + 2.91643i) q^{38} +(0.131954 - 1.12363i) q^{40} +(-3.14074 - 3.14074i) q^{41} +(1.99088 + 4.80640i) q^{43} +(0.135729 + 2.56015i) q^{44} +(7.20386 - 5.09446i) q^{46} +3.99894i q^{47} +3.91707i q^{49} +(-3.95214 - 5.58855i) q^{50} +(-7.40849 - 6.66250i) q^{52} +(0.855802 + 2.06609i) q^{53} +(-0.362563 - 0.362563i) q^{55} +(1.35239 + 4.77854i) q^{56} +(-11.6504 - 7.34590i) q^{58} +(-1.65001 + 0.683456i) q^{59} +(0.408897 - 0.987165i) q^{61} +(-1.39354 + 8.12467i) q^{62} +(-4.19240 - 6.81350i) q^{64} +1.99270 q^{65} +(-4.01800 + 9.70032i) q^{67} +(3.15674 - 8.93159i) q^{68} +(-0.840163 - 0.529747i) q^{70} +(2.17183 - 2.17183i) q^{71} +(7.91821 + 7.91821i) q^{73} +(-0.647085 - 2.85568i) q^{74} +(-3.62546 - 3.26040i) q^{76} +(2.07942 + 0.861324i) q^{77} -0.868785i q^{79} +(1.53464 + 0.452555i) q^{80} +(5.12862 - 3.62688i) q^{82} +(-5.47101 - 2.26617i) q^{83} +(0.725022 + 1.75036i) q^{85} +(-7.17541 + 1.62592i) q^{86} +(-3.60094 - 0.422876i) q^{88} +(-4.82488 + 4.82488i) q^{89} +(-8.08139 + 3.34742i) q^{91} +(5.37871 + 11.2591i) q^{92} +(-5.57396 - 0.956040i) q^{94} +0.975160 q^{95} +6.97696 q^{97} +(-5.45985 - 0.936468i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q+O(q^{10}) \) Copy content Toggle raw display \( 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.239074 + 1.39386i −0.169051 + 0.985607i
\(3\) 0 0
\(4\) −1.88569 0.666470i −0.942844 0.333235i
\(5\) 0.369546 0.153071i 0.165266 0.0684554i −0.298517 0.954404i \(-0.596492\pi\)
0.463783 + 0.885949i \(0.346492\pi\)
\(6\) 0 0
\(7\) −1.24156 + 1.24156i −0.469265 + 0.469265i −0.901676 0.432412i \(-0.857663\pi\)
0.432412 + 0.901676i \(0.357663\pi\)
\(8\) 1.37978 2.46905i 0.487827 0.872940i
\(9\) 0 0
\(10\) 0.125011 + 0.551690i 0.0395318 + 0.174460i
\(11\) −0.490552 1.18430i −0.147907 0.357079i 0.832511 0.554009i \(-0.186903\pi\)
−0.980417 + 0.196930i \(0.936903\pi\)
\(12\) 0 0
\(13\) 4.60261 + 1.90646i 1.27654 + 0.528758i 0.914945 0.403579i \(-0.132234\pi\)
0.361590 + 0.932337i \(0.382234\pi\)
\(14\) −1.43373 2.02738i −0.383181 0.541840i
\(15\) 0 0
\(16\) 3.11164 + 2.51351i 0.777909 + 0.628377i
\(17\) 4.73651i 1.14877i 0.818584 + 0.574387i \(0.194759\pi\)
−0.818584 + 0.574387i \(0.805241\pi\)
\(18\) 0 0
\(19\) 2.25236 + 0.932959i 0.516727 + 0.214035i 0.625779 0.780001i \(-0.284781\pi\)
−0.109051 + 0.994036i \(0.534781\pi\)
\(20\) −0.798865 + 0.0423528i −0.178632 + 0.00947038i
\(21\) 0 0
\(22\) 1.76802 0.400626i 0.376943 0.0854137i
\(23\) −4.41161 4.41161i −0.919884 0.919884i 0.0771364 0.997021i \(-0.475422\pi\)
−0.997021 + 0.0771364i \(0.975422\pi\)
\(24\) 0 0
\(25\) −3.42240 + 3.42240i −0.684480 + 0.684480i
\(26\) −3.75771 + 5.95961i −0.736947 + 1.16878i
\(27\) 0 0
\(28\) 3.16865 1.51373i 0.598819 0.286068i
\(29\) −3.72693 + 8.99760i −0.692073 + 1.67081i 0.0484889 + 0.998824i \(0.484559\pi\)
−0.740562 + 0.671988i \(0.765441\pi\)
\(30\) 0 0
\(31\) 5.82890 1.04690 0.523451 0.852056i \(-0.324644\pi\)
0.523451 + 0.852056i \(0.324644\pi\)
\(32\) −4.24739 + 3.73627i −0.750839 + 0.660485i
\(33\) 0 0
\(34\) −6.60203 1.13238i −1.13224 0.194201i
\(35\) −0.268766 + 0.648859i −0.0454298 + 0.109677i
\(36\) 0 0
\(37\) −1.91286 + 0.792332i −0.314472 + 0.130259i −0.534336 0.845272i \(-0.679438\pi\)
0.219865 + 0.975530i \(0.429438\pi\)
\(38\) −1.83889 + 2.91643i −0.298308 + 0.473108i
\(39\) 0 0
\(40\) 0.131954 1.12363i 0.0208637 0.177662i
\(41\) −3.14074 3.14074i −0.490501 0.490501i 0.417963 0.908464i \(-0.362744\pi\)
−0.908464 + 0.417963i \(0.862744\pi\)
\(42\) 0 0
\(43\) 1.99088 + 4.80640i 0.303606 + 0.732969i 0.999885 + 0.0151975i \(0.00483770\pi\)
−0.696279 + 0.717771i \(0.745162\pi\)
\(44\) 0.135729 + 2.56015i 0.0204620 + 0.385957i
\(45\) 0 0
\(46\) 7.20386 5.09446i 1.06215 0.751138i
\(47\) 3.99894i 0.583305i 0.956524 + 0.291652i \(0.0942051\pi\)
−0.956524 + 0.291652i \(0.905795\pi\)
\(48\) 0 0
\(49\) 3.91707i 0.559581i
\(50\) −3.95214 5.58855i −0.558917 0.790340i
\(51\) 0 0
\(52\) −7.40849 6.66250i −1.02737 0.923922i
\(53\) 0.855802 + 2.06609i 0.117553 + 0.283799i 0.971694 0.236243i \(-0.0759162\pi\)
−0.854141 + 0.520042i \(0.825916\pi\)
\(54\) 0 0
\(55\) −0.362563 0.362563i −0.0488879 0.0488879i
\(56\) 1.35239 + 4.77854i 0.180720 + 0.638560i
\(57\) 0 0
\(58\) −11.6504 7.34590i −1.52977 0.964564i
\(59\) −1.65001 + 0.683456i −0.214813 + 0.0889783i −0.487495 0.873126i \(-0.662089\pi\)
0.272682 + 0.962104i \(0.412089\pi\)
\(60\) 0 0
\(61\) 0.408897 0.987165i 0.0523539 0.126394i −0.895539 0.444984i \(-0.853209\pi\)
0.947893 + 0.318590i \(0.103209\pi\)
\(62\) −1.39354 + 8.12467i −0.176979 + 1.03183i
\(63\) 0 0
\(64\) −4.19240 6.81350i −0.524050 0.851688i
\(65\) 1.99270 0.247164
\(66\) 0 0
\(67\) −4.01800 + 9.70032i −0.490877 + 1.18508i 0.463397 + 0.886151i \(0.346630\pi\)
−0.954274 + 0.298932i \(0.903370\pi\)
\(68\) 3.15674 8.93159i 0.382811 1.08311i
\(69\) 0 0
\(70\) −0.840163 0.529747i −0.100419 0.0633169i
\(71\) 2.17183 2.17183i 0.257748 0.257748i −0.566389 0.824138i \(-0.691660\pi\)
0.824138 + 0.566389i \(0.191660\pi\)
\(72\) 0 0
\(73\) 7.91821 + 7.91821i 0.926757 + 0.926757i 0.997495 0.0707380i \(-0.0225354\pi\)
−0.0707380 + 0.997495i \(0.522535\pi\)
\(74\) −0.647085 2.85568i −0.0752222 0.331966i
\(75\) 0 0
\(76\) −3.62546 3.26040i −0.415869 0.373994i
\(77\) 2.07942 + 0.861324i 0.236972 + 0.0981570i
\(78\) 0 0
\(79\) 0.868785i 0.0977460i −0.998805 0.0488730i \(-0.984437\pi\)
0.998805 0.0488730i \(-0.0155630\pi\)
\(80\) 1.53464 + 0.452555i 0.171578 + 0.0505972i
\(81\) 0 0
\(82\) 5.12862 3.62688i 0.566361 0.400522i
\(83\) −5.47101 2.26617i −0.600521 0.248744i 0.0616485 0.998098i \(-0.480364\pi\)
−0.662170 + 0.749354i \(0.730364\pi\)
\(84\) 0 0
\(85\) 0.725022 + 1.75036i 0.0786397 + 0.189853i
\(86\) −7.17541 + 1.62592i −0.773744 + 0.175327i
\(87\) 0 0
\(88\) −3.60094 0.422876i −0.383861 0.0450788i
\(89\) −4.82488 + 4.82488i −0.511437 + 0.511437i −0.914966 0.403530i \(-0.867783\pi\)
0.403530 + 0.914966i \(0.367783\pi\)
\(90\) 0 0
\(91\) −8.08139 + 3.34742i −0.847160 + 0.350905i
\(92\) 5.37871 + 11.2591i 0.560770 + 1.17384i
\(93\) 0 0
\(94\) −5.57396 0.956040i −0.574910 0.0986080i
\(95\) 0.975160 0.100049
\(96\) 0 0
\(97\) 6.97696 0.708403 0.354201 0.935169i \(-0.384753\pi\)
0.354201 + 0.935169i \(0.384753\pi\)
\(98\) −5.45985 0.936468i −0.551528 0.0945975i
\(99\) 0 0
\(100\) 8.73450 4.17265i 0.873450 0.417265i
\(101\) 9.37354 3.88265i 0.932702 0.386338i 0.135999 0.990709i \(-0.456576\pi\)
0.796703 + 0.604371i \(0.206576\pi\)
\(102\) 0 0
\(103\) 11.8340 11.8340i 1.16604 1.16604i 0.182906 0.983130i \(-0.441450\pi\)
0.983130 0.182906i \(-0.0585504\pi\)
\(104\) 11.0578 8.73357i 1.08430 0.856397i
\(105\) 0 0
\(106\) −3.08444 + 0.698921i −0.299587 + 0.0678852i
\(107\) −5.36875 12.9613i −0.519017 1.25302i −0.938508 0.345258i \(-0.887791\pi\)
0.419491 0.907759i \(-0.362209\pi\)
\(108\) 0 0
\(109\) −17.3323 7.17926i −1.66013 0.687649i −0.662043 0.749466i \(-0.730311\pi\)
−0.998088 + 0.0618168i \(0.980311\pi\)
\(110\) 0.592040 0.418682i 0.0564488 0.0399198i
\(111\) 0 0
\(112\) −6.98394 + 0.742611i −0.659920 + 0.0701702i
\(113\) 4.58506i 0.431327i 0.976468 + 0.215663i \(0.0691913\pi\)
−0.976468 + 0.215663i \(0.930809\pi\)
\(114\) 0 0
\(115\) −2.30558 0.955003i −0.214997 0.0890545i
\(116\) 13.0244 14.4828i 1.20929 1.34469i
\(117\) 0 0
\(118\) −0.558168 2.46328i −0.0513835 0.226763i
\(119\) −5.88065 5.88065i −0.539079 0.539079i
\(120\) 0 0
\(121\) 6.61626 6.61626i 0.601478 0.601478i
\(122\) 1.27821 + 0.805950i 0.115724 + 0.0729673i
\(123\) 0 0
\(124\) −10.9915 3.88478i −0.987064 0.348864i
\(125\) −1.50622 + 3.63633i −0.134720 + 0.325244i
\(126\) 0 0
\(127\) −2.96737 −0.263311 −0.131656 0.991296i \(-0.542029\pi\)
−0.131656 + 0.991296i \(0.542029\pi\)
\(128\) 10.4994 4.21468i 0.928021 0.372529i
\(129\) 0 0
\(130\) −0.476402 + 2.77754i −0.0417832 + 0.243607i
\(131\) 4.48635 10.8310i 0.391975 0.946311i −0.597535 0.801843i \(-0.703853\pi\)
0.989510 0.144468i \(-0.0461469\pi\)
\(132\) 0 0
\(133\) −3.95476 + 1.63812i −0.342921 + 0.142043i
\(134\) −12.5603 7.91962i −1.08504 0.684151i
\(135\) 0 0
\(136\) 11.6947 + 6.53536i 1.00281 + 0.560403i
\(137\) 16.1892 + 16.1892i 1.38314 + 1.38314i 0.838991 + 0.544145i \(0.183146\pi\)
0.544145 + 0.838991i \(0.316854\pi\)
\(138\) 0 0
\(139\) 2.98923 + 7.21663i 0.253543 + 0.612106i 0.998485 0.0550224i \(-0.0175230\pi\)
−0.744942 + 0.667129i \(0.767523\pi\)
\(140\) 0.939254 1.04442i 0.0793814 0.0882696i
\(141\) 0 0
\(142\) 2.50799 + 3.54645i 0.210466 + 0.297611i
\(143\) 6.38608i 0.534031i
\(144\) 0 0
\(145\) 3.89551i 0.323504i
\(146\) −12.9299 + 9.14384i −1.07009 + 0.756750i
\(147\) 0 0
\(148\) 4.13512 0.219228i 0.339905 0.0180205i
\(149\) −4.00080 9.65879i −0.327759 0.791279i −0.998758 0.0498215i \(-0.984135\pi\)
0.671000 0.741458i \(-0.265865\pi\)
\(150\) 0 0
\(151\) 3.96565 + 3.96565i 0.322720 + 0.322720i 0.849810 0.527090i \(-0.176717\pi\)
−0.527090 + 0.849810i \(0.676717\pi\)
\(152\) 5.41129 4.27391i 0.438914 0.346660i
\(153\) 0 0
\(154\) −1.69770 + 2.69250i −0.136804 + 0.216968i
\(155\) 2.15405 0.892235i 0.173017 0.0716660i
\(156\) 0 0
\(157\) −0.375808 + 0.907280i −0.0299927 + 0.0724088i −0.938166 0.346185i \(-0.887477\pi\)
0.908174 + 0.418594i \(0.137477\pi\)
\(158\) 1.21096 + 0.207704i 0.0963391 + 0.0165240i
\(159\) 0 0
\(160\) −0.997690 + 2.03087i −0.0788743 + 0.160555i
\(161\) 10.9545 0.863338
\(162\) 0 0
\(163\) −4.94673 + 11.9425i −0.387458 + 0.935406i 0.603019 + 0.797727i \(0.293964\pi\)
−0.990477 + 0.137679i \(0.956036\pi\)
\(164\) 3.82925 + 8.01567i 0.299014 + 0.625918i
\(165\) 0 0
\(166\) 4.46669 7.08404i 0.346682 0.549828i
\(167\) 11.8590 11.8590i 0.917677 0.917677i −0.0791830 0.996860i \(-0.525231\pi\)
0.996860 + 0.0791830i \(0.0252312\pi\)
\(168\) 0 0
\(169\) 8.35705 + 8.35705i 0.642850 + 0.642850i
\(170\) −2.61309 + 0.592115i −0.200415 + 0.0454131i
\(171\) 0 0
\(172\) −0.550850 10.3902i −0.0420019 0.792247i
\(173\) 21.5118 + 8.91050i 1.63552 + 0.677453i 0.995834 0.0911875i \(-0.0290663\pi\)
0.639681 + 0.768640i \(0.279066\pi\)
\(174\) 0 0
\(175\) 8.49821i 0.642405i
\(176\) 1.45032 4.91810i 0.109322 0.370716i
\(177\) 0 0
\(178\) −5.57171 7.87871i −0.417617 0.590534i
\(179\) 17.0995 + 7.08284i 1.27808 + 0.529396i 0.915410 0.402523i \(-0.131867\pi\)
0.362666 + 0.931919i \(0.381867\pi\)
\(180\) 0 0
\(181\) −4.33210 10.4586i −0.322002 0.777383i −0.999138 0.0415238i \(-0.986779\pi\)
0.677135 0.735859i \(-0.263221\pi\)
\(182\) −2.73379 12.0646i −0.202642 0.894288i
\(183\) 0 0
\(184\) −16.9795 + 4.80541i −1.25175 + 0.354260i
\(185\) −0.585606 + 0.585606i −0.0430546 + 0.0430546i
\(186\) 0 0
\(187\) 5.60944 2.32350i 0.410203 0.169911i
\(188\) 2.66517 7.54075i 0.194378 0.549966i
\(189\) 0 0
\(190\) −0.233135 + 1.35924i −0.0169134 + 0.0986093i
\(191\) −25.8962 −1.87378 −0.936892 0.349619i \(-0.886311\pi\)
−0.936892 + 0.349619i \(0.886311\pi\)
\(192\) 0 0
\(193\) 17.1836 1.23690 0.618452 0.785822i \(-0.287760\pi\)
0.618452 + 0.785822i \(0.287760\pi\)
\(194\) −1.66801 + 9.72490i −0.119756 + 0.698207i
\(195\) 0 0
\(196\) 2.61061 7.38637i 0.186472 0.527598i
\(197\) −11.0761 + 4.58787i −0.789139 + 0.326872i −0.740597 0.671949i \(-0.765457\pi\)
−0.0485417 + 0.998821i \(0.515457\pi\)
\(198\) 0 0
\(199\) −1.73738 + 1.73738i −0.123159 + 0.123159i −0.766000 0.642841i \(-0.777756\pi\)
0.642841 + 0.766000i \(0.277756\pi\)
\(200\) 3.72790 + 13.1722i 0.263602 + 0.931418i
\(201\) 0 0
\(202\) 3.17090 + 13.9936i 0.223104 + 0.984589i
\(203\) −6.54384 15.7982i −0.459288 1.10882i
\(204\) 0 0
\(205\) −1.64140 0.679892i −0.114641 0.0474857i
\(206\) 13.6657 + 19.3241i 0.952135 + 1.34637i
\(207\) 0 0
\(208\) 9.52974 + 17.5009i 0.660769 + 1.21347i
\(209\) 3.12513i 0.216170i
\(210\) 0 0
\(211\) −4.05517 1.67971i −0.279170 0.115636i 0.238706 0.971092i \(-0.423277\pi\)
−0.517875 + 0.855456i \(0.673277\pi\)
\(212\) −0.236790 4.46637i −0.0162628 0.306751i
\(213\) 0 0
\(214\) 19.3498 4.38458i 1.32272 0.299724i
\(215\) 1.47144 + 1.47144i 0.100351 + 0.100351i
\(216\) 0 0
\(217\) −7.23691 + 7.23691i −0.491274 + 0.491274i
\(218\) 14.1506 22.4424i 0.958398 1.51999i
\(219\) 0 0
\(220\) 0.442043 + 0.925317i 0.0298025 + 0.0623848i
\(221\) −9.03000 + 21.8003i −0.607423 + 1.46645i
\(222\) 0 0
\(223\) 7.31801 0.490050 0.245025 0.969517i \(-0.421204\pi\)
0.245025 + 0.969517i \(0.421204\pi\)
\(224\) 0.634579 9.91217i 0.0423996 0.662285i
\(225\) 0 0
\(226\) −6.39093 1.09617i −0.425119 0.0729160i
\(227\) −7.10939 + 17.1636i −0.471867 + 1.13919i 0.491470 + 0.870894i \(0.336460\pi\)
−0.963337 + 0.268293i \(0.913540\pi\)
\(228\) 0 0
\(229\) 3.35015 1.38768i 0.221384 0.0917002i −0.269235 0.963075i \(-0.586771\pi\)
0.490619 + 0.871374i \(0.336771\pi\)
\(230\) 1.88234 2.98534i 0.124118 0.196847i
\(231\) 0 0
\(232\) 17.0732 + 21.6167i 1.12091 + 1.41921i
\(233\) −13.2085 13.2085i −0.865315 0.865315i 0.126634 0.991949i \(-0.459583\pi\)
−0.991949 + 0.126634i \(0.959583\pi\)
\(234\) 0 0
\(235\) 0.612121 + 1.47779i 0.0399304 + 0.0964004i
\(236\) 3.56690 0.189104i 0.232186 0.0123096i
\(237\) 0 0
\(238\) 9.60271 6.79090i 0.622451 0.440188i
\(239\) 5.06396i 0.327560i −0.986497 0.163780i \(-0.947631\pi\)
0.986497 0.163780i \(-0.0523687\pi\)
\(240\) 0 0
\(241\) 17.2330i 1.11008i 0.831825 + 0.555038i \(0.187296\pi\)
−0.831825 + 0.555038i \(0.812704\pi\)
\(242\) 7.64036 + 10.8039i 0.491141 + 0.694501i
\(243\) 0 0
\(244\) −1.42897 + 1.58897i −0.0914803 + 0.101723i
\(245\) 0.599590 + 1.44754i 0.0383064 + 0.0924798i
\(246\) 0 0
\(247\) 8.58810 + 8.58810i 0.546448 + 0.546448i
\(248\) 8.04262 14.3918i 0.510707 0.913882i
\(249\) 0 0
\(250\) −4.70844 2.96881i −0.297788 0.187764i
\(251\) 13.4329 5.56408i 0.847876 0.351202i 0.0839221 0.996472i \(-0.473255\pi\)
0.763954 + 0.645270i \(0.223255\pi\)
\(252\) 0 0
\(253\) −3.06053 + 7.38877i −0.192414 + 0.464528i
\(254\) 0.709419 4.13610i 0.0445129 0.259522i
\(255\) 0 0
\(256\) 3.36456 + 15.6422i 0.210285 + 0.977640i
\(257\) 10.0676 0.628003 0.314001 0.949423i \(-0.398330\pi\)
0.314001 + 0.949423i \(0.398330\pi\)
\(258\) 0 0
\(259\) 1.39120 3.35865i 0.0864448 0.208696i
\(260\) −3.75761 1.32807i −0.233037 0.0823637i
\(261\) 0 0
\(262\) 14.0243 + 8.84276i 0.866427 + 0.546307i
\(263\) 16.4698 16.4698i 1.01557 1.01557i 0.0156926 0.999877i \(-0.495005\pi\)
0.999877 0.0156926i \(-0.00499531\pi\)
\(264\) 0 0
\(265\) 0.632516 + 0.632516i 0.0388552 + 0.0388552i
\(266\) −1.33782 5.90401i −0.0820272 0.361998i
\(267\) 0 0
\(268\) 14.0417 15.6139i 0.857731 0.953770i
\(269\) −3.67390 1.52178i −0.224002 0.0927845i 0.267860 0.963458i \(-0.413683\pi\)
−0.491862 + 0.870673i \(0.663683\pi\)
\(270\) 0 0
\(271\) 19.6229i 1.19201i −0.802981 0.596005i \(-0.796754\pi\)
0.802981 0.596005i \(-0.203246\pi\)
\(272\) −11.9053 + 14.7383i −0.721863 + 0.893641i
\(273\) 0 0
\(274\) −26.4359 + 18.6951i −1.59705 + 1.12941i
\(275\) 5.73200 + 2.37427i 0.345653 + 0.143174i
\(276\) 0 0
\(277\) −11.4955 27.7526i −0.690699 1.66749i −0.743368 0.668882i \(-0.766773\pi\)
0.0526694 0.998612i \(-0.483227\pi\)
\(278\) −10.7736 + 2.44125i −0.646158 + 0.146417i
\(279\) 0 0
\(280\) 1.23122 + 1.55888i 0.0735797 + 0.0931609i
\(281\) −6.56486 + 6.56486i −0.391627 + 0.391627i −0.875267 0.483640i \(-0.839314\pi\)
0.483640 + 0.875267i \(0.339314\pi\)
\(282\) 0 0
\(283\) −13.0853 + 5.42010i −0.777839 + 0.322192i −0.736043 0.676935i \(-0.763308\pi\)
−0.0417960 + 0.999126i \(0.513308\pi\)
\(284\) −5.54284 + 2.64793i −0.328907 + 0.157126i
\(285\) 0 0
\(286\) 8.90129 + 1.52674i 0.526344 + 0.0902781i
\(287\) 7.79882 0.460350
\(288\) 0 0
\(289\) −5.43457 −0.319680
\(290\) −5.42979 0.931313i −0.318848 0.0546886i
\(291\) 0 0
\(292\) −9.65403 20.2085i −0.564959 1.18261i
\(293\) 9.80395 4.06093i 0.572753 0.237242i −0.0774584 0.996996i \(-0.524680\pi\)
0.650211 + 0.759754i \(0.274680\pi\)
\(294\) 0 0
\(295\) −0.505136 + 0.505136i −0.0294102 + 0.0294102i
\(296\) −0.683024 + 5.81619i −0.0397000 + 0.338059i
\(297\) 0 0
\(298\) 14.4195 3.26740i 0.835298 0.189275i
\(299\) −11.8944 28.7155i −0.687868 1.66066i
\(300\) 0 0
\(301\) −8.43921 3.49563i −0.486428 0.201485i
\(302\) −6.47564 + 4.57948i −0.372631 + 0.263519i
\(303\) 0 0
\(304\) 4.66353 + 8.56436i 0.267472 + 0.491200i
\(305\) 0.427393i 0.0244725i
\(306\) 0 0
\(307\) −23.2604 9.63475i −1.32754 0.549884i −0.397586 0.917565i \(-0.630152\pi\)
−0.929952 + 0.367680i \(0.880152\pi\)
\(308\) −3.34709 3.01006i −0.190718 0.171514i
\(309\) 0 0
\(310\) 0.728675 + 3.21575i 0.0413859 + 0.182642i
\(311\) 10.6265 + 10.6265i 0.602574 + 0.602574i 0.940995 0.338421i \(-0.109893\pi\)
−0.338421 + 0.940995i \(0.609893\pi\)
\(312\) 0 0
\(313\) 17.1006 17.1006i 0.966586 0.966586i −0.0328739 0.999460i \(-0.510466\pi\)
0.999460 + 0.0328739i \(0.0104660\pi\)
\(314\) −1.17477 0.740729i −0.0662964 0.0418018i
\(315\) 0 0
\(316\) −0.579019 + 1.63826i −0.0325724 + 0.0921592i
\(317\) 1.32310 3.19425i 0.0743128 0.179407i −0.882358 0.470579i \(-0.844045\pi\)
0.956671 + 0.291172i \(0.0940451\pi\)
\(318\) 0 0
\(319\) 12.4841 0.698974
\(320\) −2.59223 1.87617i −0.144910 0.104881i
\(321\) 0 0
\(322\) −2.61894 + 15.2691i −0.145948 + 0.850912i
\(323\) −4.41897 + 10.6683i −0.245878 + 0.593603i
\(324\) 0 0
\(325\) −22.2767 + 9.22730i −1.23569 + 0.511838i
\(326\) −15.4635 9.75017i −0.856443 0.540012i
\(327\) 0 0
\(328\) −12.0882 + 3.42110i −0.667458 + 0.188899i
\(329\) −4.96491 4.96491i −0.273724 0.273724i
\(330\) 0 0
\(331\) −6.57155 15.8651i −0.361205 0.872026i −0.995124 0.0986269i \(-0.968555\pi\)
0.633920 0.773399i \(-0.281445\pi\)
\(332\) 8.80628 + 7.91954i 0.483308 + 0.434641i
\(333\) 0 0
\(334\) 13.6946 + 19.3650i 0.749336 + 1.05960i
\(335\) 4.19975i 0.229457i
\(336\) 0 0
\(337\) 16.9321i 0.922350i −0.887309 0.461175i \(-0.847428\pi\)
0.887309 0.461175i \(-0.152572\pi\)
\(338\) −13.6465 + 9.65060i −0.742272 + 0.524924i
\(339\) 0 0
\(340\) −0.200605 3.78384i −0.0108793 0.205207i
\(341\) −2.85938 6.90314i −0.154844 0.373826i
\(342\) 0 0
\(343\) −13.5542 13.5542i −0.731856 0.731856i
\(344\) 14.6142 + 1.71622i 0.787945 + 0.0925324i
\(345\) 0 0
\(346\) −17.5629 + 27.8542i −0.944187 + 1.49745i
\(347\) −25.5167 + 10.5694i −1.36981 + 0.567393i −0.941736 0.336352i \(-0.890807\pi\)
−0.428071 + 0.903745i \(0.640807\pi\)
\(348\) 0 0
\(349\) 10.7832 26.0329i 0.577210 1.39351i −0.318096 0.948058i \(-0.603044\pi\)
0.895307 0.445450i \(-0.146956\pi\)
\(350\) 11.8453 + 2.03170i 0.633159 + 0.108599i
\(351\) 0 0
\(352\) 6.50841 + 3.19733i 0.346900 + 0.170418i
\(353\) 30.7053 1.63428 0.817140 0.576440i \(-0.195558\pi\)
0.817140 + 0.576440i \(0.195558\pi\)
\(354\) 0 0
\(355\) 0.470146 1.13503i 0.0249528 0.0602413i
\(356\) 12.3139 5.88258i 0.652633 0.311776i
\(357\) 0 0
\(358\) −13.9605 + 22.1410i −0.737836 + 1.17019i
\(359\) 11.5340 11.5340i 0.608740 0.608740i −0.333877 0.942617i \(-0.608357\pi\)
0.942617 + 0.333877i \(0.108357\pi\)
\(360\) 0 0
\(361\) −9.23231 9.23231i −0.485911 0.485911i
\(362\) 15.6135 3.53796i 0.820629 0.185951i
\(363\) 0 0
\(364\) 17.4699 0.926190i 0.915674 0.0485455i
\(365\) 4.13819 + 1.71410i 0.216603 + 0.0897198i
\(366\) 0 0
\(367\) 2.72042i 0.142005i −0.997476 0.0710024i \(-0.977380\pi\)
0.997476 0.0710024i \(-0.0226198\pi\)
\(368\) −2.63871 24.8159i −0.137552 1.29362i
\(369\) 0 0
\(370\) −0.676249 0.956255i −0.0351565 0.0497133i
\(371\) −3.62770 1.50264i −0.188341 0.0780132i
\(372\) 0 0
\(373\) 0.956551 + 2.30932i 0.0495283 + 0.119572i 0.946707 0.322095i \(-0.104387\pi\)
−0.897179 + 0.441667i \(0.854387\pi\)
\(374\) 1.89757 + 8.37425i 0.0981210 + 0.433022i
\(375\) 0 0
\(376\) 9.87357 + 5.51767i 0.509190 + 0.284552i
\(377\) −34.3072 + 34.3072i −1.76691 + 1.76691i
\(378\) 0 0
\(379\) −21.2748 + 8.81229i −1.09281 + 0.452657i −0.854986 0.518651i \(-0.826434\pi\)
−0.237825 + 0.971308i \(0.576434\pi\)
\(380\) −1.83885 0.649915i −0.0943309 0.0333399i
\(381\) 0 0
\(382\) 6.19110 36.0957i 0.316764 1.84681i
\(383\) −27.4698 −1.40364 −0.701821 0.712354i \(-0.747629\pi\)
−0.701821 + 0.712354i \(0.747629\pi\)
\(384\) 0 0
\(385\) 0.900285 0.0458827
\(386\) −4.10815 + 23.9516i −0.209099 + 1.21910i
\(387\) 0 0
\(388\) −13.1564 4.64993i −0.667913 0.236065i
\(389\) 1.59053 0.658819i 0.0806430 0.0334034i −0.341997 0.939701i \(-0.611103\pi\)
0.422640 + 0.906298i \(0.361103\pi\)
\(390\) 0 0
\(391\) 20.8956 20.8956i 1.05674 1.05674i
\(392\) 9.67144 + 5.40471i 0.488481 + 0.272979i
\(393\) 0 0
\(394\) −3.74684 16.5354i −0.188763 0.833039i
\(395\) −0.132986 0.321056i −0.00669124 0.0161541i
\(396\) 0 0
\(397\) −0.440821 0.182594i −0.0221242 0.00916414i 0.371594 0.928395i \(-0.378811\pi\)
−0.393718 + 0.919231i \(0.628811\pi\)
\(398\) −2.00630 2.83702i −0.100567 0.142207i
\(399\) 0 0
\(400\) −19.2515 + 2.04704i −0.962575 + 0.102352i
\(401\) 13.7833i 0.688307i 0.938913 + 0.344154i \(0.111834\pi\)
−0.938913 + 0.344154i \(0.888166\pi\)
\(402\) 0 0
\(403\) 26.8282 + 11.1126i 1.33641 + 0.553558i
\(404\) −20.2632 + 1.07428i −1.00813 + 0.0534474i
\(405\) 0 0
\(406\) 23.5850 5.34426i 1.17050 0.265231i
\(407\) 1.87671 + 1.87671i 0.0930251 + 0.0930251i
\(408\) 0 0
\(409\) −5.34078 + 5.34078i −0.264085 + 0.264085i −0.826711 0.562627i \(-0.809791\pi\)
0.562627 + 0.826711i \(0.309791\pi\)
\(410\) 1.34009 2.12534i 0.0661823 0.104963i
\(411\) 0 0
\(412\) −30.2022 + 14.4282i −1.48795 + 0.710826i
\(413\) 1.20003 2.89713i 0.0590496 0.142558i
\(414\) 0 0
\(415\) −2.36867 −0.116274
\(416\) −26.6721 + 9.09911i −1.30771 + 0.446121i
\(417\) 0 0
\(418\) 4.35599 + 0.747136i 0.213058 + 0.0365436i
\(419\) 4.20919 10.1619i 0.205632 0.496440i −0.787094 0.616833i \(-0.788415\pi\)
0.992726 + 0.120393i \(0.0384154\pi\)
\(420\) 0 0
\(421\) −8.39263 + 3.47634i −0.409032 + 0.169427i −0.577705 0.816245i \(-0.696052\pi\)
0.168673 + 0.985672i \(0.446052\pi\)
\(422\) 3.31076 5.25077i 0.161165 0.255603i
\(423\) 0 0
\(424\) 6.28210 + 0.737738i 0.305086 + 0.0358277i
\(425\) −16.2102 16.2102i −0.786313 0.786313i
\(426\) 0 0
\(427\) 0.717953 + 1.73329i 0.0347442 + 0.0838798i
\(428\) 1.48547 + 28.0191i 0.0718027 + 1.35435i
\(429\) 0 0
\(430\) −2.40276 + 1.69920i −0.115871 + 0.0819426i
\(431\) 36.2680i 1.74697i 0.486852 + 0.873485i \(0.338145\pi\)
−0.486852 + 0.873485i \(0.661855\pi\)
\(432\) 0 0
\(433\) 1.42391i 0.0684286i −0.999415 0.0342143i \(-0.989107\pi\)
0.999415 0.0342143i \(-0.0108929\pi\)
\(434\) −8.35708 11.8174i −0.401153 0.567253i
\(435\) 0 0
\(436\) 27.8985 + 25.0893i 1.33610 + 1.20156i
\(437\) −5.82069 14.0524i −0.278441 0.672217i
\(438\) 0 0
\(439\) −28.2959 28.2959i −1.35049 1.35049i −0.885111 0.465381i \(-0.845917\pi\)
−0.465381 0.885111i \(-0.654083\pi\)
\(440\) −1.39544 + 0.394927i −0.0665251 + 0.0188274i
\(441\) 0 0
\(442\) −28.2278 17.7984i −1.34266 0.846585i
\(443\) −33.4735 + 13.8652i −1.59037 + 0.658755i −0.990013 0.140975i \(-0.954976\pi\)
−0.600361 + 0.799729i \(0.704976\pi\)
\(444\) 0 0
\(445\) −1.04447 + 2.52156i −0.0495124 + 0.119534i
\(446\) −1.74954 + 10.2003i −0.0828432 + 0.482997i
\(447\) 0 0
\(448\) 13.6645 + 3.25425i 0.645585 + 0.153749i
\(449\) 15.1120 0.713182 0.356591 0.934261i \(-0.383939\pi\)
0.356591 + 0.934261i \(0.383939\pi\)
\(450\) 0 0
\(451\) −2.17887 + 5.26026i −0.102599 + 0.247696i
\(452\) 3.05581 8.64600i 0.143733 0.406674i
\(453\) 0 0
\(454\) −22.2240 14.0129i −1.04302 0.657656i
\(455\) −2.47405 + 2.47405i −0.115985 + 0.115985i
\(456\) 0 0
\(457\) 22.8696 + 22.8696i 1.06979 + 1.06979i 0.997374 + 0.0724182i \(0.0230716\pi\)
0.0724182 + 0.997374i \(0.476928\pi\)
\(458\) 1.13329 + 5.00139i 0.0529554 + 0.233700i
\(459\) 0 0
\(460\) 3.71113 + 3.33744i 0.173032 + 0.155609i
\(461\) 1.28205 + 0.531041i 0.0597108 + 0.0247330i 0.412339 0.911030i \(-0.364712\pi\)
−0.352628 + 0.935764i \(0.614712\pi\)
\(462\) 0 0
\(463\) 25.7372i 1.19611i −0.801455 0.598055i \(-0.795940\pi\)
0.801455 0.598055i \(-0.204060\pi\)
\(464\) −34.2124 + 18.6296i −1.58827 + 0.864857i
\(465\) 0 0
\(466\) 21.5685 15.2529i 0.999143 0.706579i
\(467\) 20.9980 + 8.69764i 0.971670 + 0.402479i 0.811333 0.584584i \(-0.198742\pi\)
0.160336 + 0.987062i \(0.448742\pi\)
\(468\) 0 0
\(469\) −7.05492 17.0321i −0.325766 0.786469i
\(470\) −2.20617 + 0.499910i −0.101763 + 0.0230591i
\(471\) 0 0
\(472\) −0.589168 + 5.01697i −0.0271187 + 0.230925i
\(473\) 4.71557 4.71557i 0.216822 0.216822i
\(474\) 0 0
\(475\) −10.9014 + 4.51553i −0.500193 + 0.207187i
\(476\) 7.16980 + 15.0084i 0.328627 + 0.687907i
\(477\) 0 0
\(478\) 7.05844 + 1.21066i 0.322846 + 0.0553742i
\(479\) −26.0170 −1.18875 −0.594373 0.804190i \(-0.702600\pi\)
−0.594373 + 0.804190i \(0.702600\pi\)
\(480\) 0 0
\(481\) −10.3147 −0.470310
\(482\) −24.0204 4.11996i −1.09410 0.187659i
\(483\) 0 0
\(484\) −16.8857 + 8.06666i −0.767533 + 0.366666i
\(485\) 2.57831 1.06797i 0.117075 0.0484940i
\(486\) 0 0
\(487\) 17.6649 17.6649i 0.800474 0.800474i −0.182695 0.983170i \(-0.558482\pi\)
0.983170 + 0.182695i \(0.0584822\pi\)
\(488\) −1.87317 2.37166i −0.0847944 0.107360i
\(489\) 0 0
\(490\) −2.16101 + 0.489676i −0.0976244 + 0.0221213i
\(491\) 15.0583 + 36.3539i 0.679571 + 1.64063i 0.764799 + 0.644269i \(0.222838\pi\)
−0.0852275 + 0.996362i \(0.527162\pi\)
\(492\) 0 0
\(493\) −42.6172 17.6526i −1.91938 0.795035i
\(494\) −14.0238 + 9.91741i −0.630960 + 0.446206i
\(495\) 0 0
\(496\) 18.1374 + 14.6510i 0.814394 + 0.657848i
\(497\) 5.39290i 0.241904i
\(498\) 0 0
\(499\) −6.96691 2.88579i −0.311882 0.129186i 0.221252 0.975217i \(-0.428986\pi\)
−0.533134 + 0.846031i \(0.678986\pi\)
\(500\) 5.26376 5.85314i 0.235403 0.261760i
\(501\) 0 0
\(502\) 4.54410 + 20.0538i 0.202813 + 0.895044i
\(503\) −10.7377 10.7377i −0.478769 0.478769i 0.425969 0.904738i \(-0.359933\pi\)
−0.904738 + 0.425969i \(0.859933\pi\)
\(504\) 0 0
\(505\) 2.86963 2.86963i 0.127697 0.127697i
\(506\) −9.56722 6.03241i −0.425315 0.268173i
\(507\) 0 0
\(508\) 5.59553 + 1.97766i 0.248262 + 0.0877445i
\(509\) −13.1996 + 31.8667i −0.585062 + 1.41247i 0.303111 + 0.952955i \(0.401975\pi\)
−0.888173 + 0.459510i \(0.848025\pi\)
\(510\) 0 0
\(511\) −19.6618 −0.869788
\(512\) −22.6075 + 0.950078i −0.999118 + 0.0419879i
\(513\) 0 0
\(514\) −2.40691 + 14.0329i −0.106164 + 0.618964i
\(515\) 2.56176 6.18463i 0.112885 0.272528i
\(516\) 0 0
\(517\) 4.73593 1.96169i 0.208286 0.0862748i
\(518\) 4.34889 + 2.74210i 0.191079 + 0.120481i
\(519\) 0 0
\(520\) 2.74949 4.92007i 0.120573 0.215760i
\(521\) −24.7770 24.7770i −1.08550 1.08550i −0.995985 0.0895150i \(-0.971468\pi\)
−0.0895150 0.995985i \(-0.528532\pi\)
\(522\) 0 0
\(523\) 8.84025 + 21.3423i 0.386557 + 0.933232i 0.990664 + 0.136328i \(0.0435302\pi\)
−0.604106 + 0.796904i \(0.706470\pi\)
\(524\) −15.6784 + 17.4339i −0.684915 + 0.761603i
\(525\) 0 0
\(526\) 19.0191 + 26.8940i 0.829270 + 1.17264i
\(527\) 27.6087i 1.20265i
\(528\) 0 0
\(529\) 15.9246i 0.692374i
\(530\) −1.03286 + 0.730421i −0.0448644 + 0.0317275i
\(531\) 0 0
\(532\) 8.54920 0.453246i 0.370655 0.0196507i
\(533\) −8.46790 20.4433i −0.366786 0.885499i
\(534\) 0 0
\(535\) −3.96800 3.96800i −0.171552 0.171552i
\(536\) 18.4066 + 23.3050i 0.795043 + 1.00662i
\(537\) 0 0
\(538\) 2.99948 4.75708i 0.129317 0.205092i
\(539\) 4.63897 1.92152i 0.199815 0.0827659i
\(540\) 0 0
\(541\) 8.50552 20.5341i 0.365681 0.882832i −0.628766 0.777594i \(-0.716440\pi\)
0.994447 0.105237i \(-0.0335602\pi\)
\(542\) 27.3516 + 4.69133i 1.17485 + 0.201510i
\(543\) 0 0
\(544\) −17.6969 20.1178i −0.758748 0.862544i
\(545\) −7.50401 −0.321436
\(546\) 0 0
\(547\) −1.76171 + 4.25314i −0.0753252 + 0.181851i −0.957057 0.289900i \(-0.906378\pi\)
0.881732 + 0.471751i \(0.156378\pi\)
\(548\) −19.7382 41.3174i −0.843172 1.76499i
\(549\) 0 0
\(550\) −4.67977 + 7.42198i −0.199546 + 0.316474i
\(551\) −16.7888 + 16.7888i −0.715226 + 0.715226i
\(552\) 0 0
\(553\) 1.07865 + 1.07865i 0.0458687 + 0.0458687i
\(554\) 41.4315 9.38822i 1.76026 0.398867i
\(555\) 0 0
\(556\) −0.827081 15.6005i −0.0350761 0.661610i
\(557\) −39.6505 16.4238i −1.68004 0.695897i −0.680716 0.732548i \(-0.738331\pi\)
−0.999328 + 0.0366506i \(0.988331\pi\)
\(558\) 0 0
\(559\) 25.9175i 1.09619i
\(560\) −2.46721 + 1.34347i −0.104259 + 0.0567718i
\(561\) 0 0
\(562\) −7.58100 10.7200i −0.319785 0.452195i
\(563\) 39.2925 + 16.2755i 1.65598 + 0.685930i 0.997760 0.0668949i \(-0.0213092\pi\)
0.658221 + 0.752825i \(0.271309\pi\)
\(564\) 0 0
\(565\) 0.701840 + 1.69439i 0.0295266 + 0.0712836i
\(566\) −4.42651 19.5348i −0.186060 0.821111i
\(567\) 0 0
\(568\) −2.36570 8.35899i −0.0992624 0.350736i
\(569\) 12.7803 12.7803i 0.535780 0.535780i −0.386507 0.922287i \(-0.626318\pi\)
0.922287 + 0.386507i \(0.126318\pi\)
\(570\) 0 0
\(571\) −27.3723 + 11.3380i −1.14550 + 0.474480i −0.873021 0.487683i \(-0.837842\pi\)
−0.272475 + 0.962163i \(0.587842\pi\)
\(572\) −4.25613 + 12.0421i −0.177958 + 0.503507i
\(573\) 0 0
\(574\) −1.86449 + 10.8705i −0.0778224 + 0.453724i
\(575\) 30.1966 1.25928
\(576\) 0 0
\(577\) 18.5299 0.771412 0.385706 0.922622i \(-0.373958\pi\)
0.385706 + 0.922622i \(0.373958\pi\)
\(578\) 1.29926 7.57502i 0.0540421 0.315079i
\(579\) 0 0
\(580\) 2.59624 7.34571i 0.107803 0.305014i
\(581\) 9.60615 3.97900i 0.398530 0.165077i
\(582\) 0 0
\(583\) 2.02705 2.02705i 0.0839517 0.0839517i
\(584\) 30.4759 8.62504i 1.26110 0.356907i
\(585\) 0 0
\(586\) 3.31650 + 14.6362i 0.137003 + 0.604615i
\(587\) −1.97372 4.76497i −0.0814640 0.196671i 0.877899 0.478845i \(-0.158945\pi\)
−0.959363 + 0.282174i \(0.908945\pi\)
\(588\) 0 0
\(589\) 13.1288 + 5.43812i 0.540962 + 0.224074i
\(590\) −0.583324 0.824854i −0.0240151 0.0339587i
\(591\) 0 0
\(592\) −7.94365 2.34254i −0.326482 0.0962776i
\(593\) 37.8468i 1.55418i −0.629387 0.777092i \(-0.716694\pi\)
0.629387 0.777092i \(-0.283306\pi\)
\(594\) 0 0
\(595\) −3.07333 1.27301i −0.125994 0.0521885i
\(596\) 1.10697 + 20.8799i 0.0453434 + 0.855273i
\(597\) 0 0
\(598\) 42.8690 9.71394i 1.75304 0.397232i
\(599\) 13.1026 + 13.1026i 0.535358 + 0.535358i 0.922162 0.386804i \(-0.126421\pi\)
−0.386804 + 0.922162i \(0.626421\pi\)
\(600\) 0 0
\(601\) −23.6421 + 23.6421i −0.964383 + 0.964383i −0.999387 0.0350039i \(-0.988856\pi\)
0.0350039 + 0.999387i \(0.488856\pi\)
\(602\) 6.89001 10.9274i 0.280816 0.445366i
\(603\) 0 0
\(604\) −4.83499 10.1210i −0.196733 0.411816i
\(605\) 1.43225 3.45777i 0.0582294 0.140578i
\(606\) 0 0
\(607\) 40.7663 1.65465 0.827327 0.561721i \(-0.189860\pi\)
0.827327 + 0.561721i \(0.189860\pi\)
\(608\) −13.0524 + 4.45280i −0.529346 + 0.180585i
\(609\) 0 0
\(610\) 0.595726 + 0.102178i 0.0241202 + 0.00413708i
\(611\) −7.62383 + 18.4056i −0.308427 + 0.744609i
\(612\) 0 0
\(613\) 26.6836 11.0527i 1.07774 0.446414i 0.228024 0.973656i \(-0.426774\pi\)
0.849716 + 0.527241i \(0.176774\pi\)
\(614\) 18.9904 30.1182i 0.766391 1.21547i
\(615\) 0 0
\(616\) 4.99580 3.94575i 0.201286 0.158979i
\(617\) −9.58241 9.58241i −0.385773 0.385773i 0.487404 0.873177i \(-0.337944\pi\)
−0.873177 + 0.487404i \(0.837944\pi\)
\(618\) 0 0
\(619\) 7.72395 + 18.6473i 0.310452 + 0.749496i 0.999688 + 0.0249603i \(0.00794594\pi\)
−0.689237 + 0.724536i \(0.742054\pi\)
\(620\) −4.65650 + 0.246870i −0.187010 + 0.00991455i
\(621\) 0 0
\(622\) −17.3524 + 12.2714i −0.695767 + 0.492036i
\(623\) 11.9807i 0.479998i
\(624\) 0 0
\(625\) 22.6257i 0.905027i
\(626\) 19.7476 + 27.9242i 0.789272 + 1.11608i
\(627\) 0 0
\(628\) 1.31333 1.46038i 0.0524076 0.0582756i
\(629\) −3.75289 9.06028i −0.149638 0.361257i
\(630\) 0 0
\(631\) 12.5702 + 12.5702i 0.500413 + 0.500413i 0.911566 0.411153i \(-0.134874\pi\)
−0.411153 + 0.911566i \(0.634874\pi\)
\(632\) −2.14507 1.19874i −0.0853264 0.0476831i
\(633\) 0 0
\(634\) 4.13602 + 2.60788i 0.164262 + 0.103572i
\(635\) −1.09658 + 0.454218i −0.0435164 + 0.0180251i
\(636\) 0 0
\(637\) −7.46776 + 18.0288i −0.295883 + 0.714325i
\(638\) −2.98461 + 17.4010i −0.118162 + 0.688914i
\(639\) 0 0
\(640\) 3.23485 3.16466i 0.127869 0.125094i
\(641\) 33.2881 1.31480 0.657401 0.753541i \(-0.271656\pi\)
0.657401 + 0.753541i \(0.271656\pi\)
\(642\) 0 0
\(643\) −17.1295 + 41.3543i −0.675521 + 1.63085i 0.0965583 + 0.995327i \(0.469217\pi\)
−0.772080 + 0.635526i \(0.780783\pi\)
\(644\) −20.6568 7.30086i −0.813993 0.287694i
\(645\) 0 0
\(646\) −13.8137 8.70995i −0.543493 0.342688i
\(647\) 17.7157 17.7157i 0.696477 0.696477i −0.267171 0.963649i \(-0.586089\pi\)
0.963649 + 0.267171i \(0.0860890\pi\)
\(648\) 0 0
\(649\) 1.61883 + 1.61883i 0.0635446 + 0.0635446i
\(650\) −7.53579 33.2565i −0.295578 1.30443i
\(651\) 0 0
\(652\) 17.2873 19.2229i 0.677022 0.752827i
\(653\) 15.9543 + 6.60849i 0.624340 + 0.258610i 0.672346 0.740237i \(-0.265287\pi\)
−0.0480060 + 0.998847i \(0.515287\pi\)
\(654\) 0 0
\(655\) 4.68929i 0.183226i
\(656\) −1.87857 17.6671i −0.0733458 0.689785i
\(657\) 0 0
\(658\) 8.10737 5.73341i 0.316058 0.223512i
\(659\) 23.0850 + 9.56212i 0.899264 + 0.372487i 0.783937 0.620840i \(-0.213208\pi\)
0.115327 + 0.993328i \(0.463208\pi\)
\(660\) 0 0
\(661\) 6.95887 + 16.8002i 0.270669 + 0.653452i 0.999512 0.0312280i \(-0.00994181\pi\)
−0.728843 + 0.684680i \(0.759942\pi\)
\(662\) 23.6848 5.36688i 0.920537 0.208590i
\(663\) 0 0
\(664\) −13.1441 + 10.3814i −0.510089 + 0.402875i
\(665\) −1.21072 + 1.21072i −0.0469496 + 0.0469496i
\(666\) 0 0
\(667\) 56.1356 23.2521i 2.17358 0.900326i
\(668\) −30.2660 + 14.4587i −1.17103 + 0.559424i
\(669\) 0 0
\(670\) −5.85386 1.00405i −0.226154 0.0387898i
\(671\) −1.36968 −0.0528759
\(672\) 0 0
\(673\) 37.1001 1.43010 0.715052 0.699072i \(-0.246403\pi\)
0.715052 + 0.699072i \(0.246403\pi\)
\(674\) 23.6009 + 4.04801i 0.909075 + 0.155924i
\(675\) 0 0
\(676\) −10.1891 21.3285i −0.391887 0.820327i
\(677\) 21.1103 8.74417i 0.811335 0.336066i 0.0618482 0.998086i \(-0.480301\pi\)
0.749486 + 0.662020i \(0.230301\pi\)
\(678\) 0 0
\(679\) −8.66230 + 8.66230i −0.332428 + 0.332428i
\(680\) 5.32209 + 0.625000i 0.204093 + 0.0239677i
\(681\) 0 0
\(682\) 10.3056 2.33521i 0.394622 0.0894198i
\(683\) −14.5245 35.0654i −0.555766 1.34174i −0.913090 0.407758i \(-0.866311\pi\)
0.357324 0.933981i \(-0.383689\pi\)
\(684\) 0 0
\(685\) 8.46074 + 3.50455i 0.323268 + 0.133902i
\(686\) 22.1330 15.6522i 0.845044 0.597602i
\(687\) 0 0
\(688\) −5.88604 + 19.9598i −0.224403 + 0.760962i
\(689\) 11.1410i 0.424437i
\(690\) 0 0
\(691\) −12.6524 5.24080i −0.481320 0.199369i 0.128812 0.991669i \(-0.458884\pi\)
−0.610132 + 0.792300i \(0.708884\pi\)
\(692\) −34.6260 31.1394i −1.31628 1.18374i
\(693\) 0 0
\(694\) −8.63183 38.0935i −0.327660 1.44601i
\(695\) 2.20931 + 2.20931i 0.0838040 + 0.0838040i
\(696\) 0 0
\(697\) 14.8762 14.8762i 0.563475 0.563475i
\(698\) 33.7082 + 21.2540i 1.27587 + 0.804476i
\(699\) 0 0
\(700\) −5.66380 + 16.0250i −0.214072 + 0.605687i
\(701\) −9.65633 + 23.3124i −0.364714 + 0.880498i 0.629883 + 0.776690i \(0.283103\pi\)
−0.994597 + 0.103808i \(0.966897\pi\)
\(702\) 0 0
\(703\) −5.04766 −0.190376
\(704\) −6.01262 + 8.30741i −0.226609 + 0.313097i
\(705\) 0 0
\(706\) −7.34083 + 42.7989i −0.276276 + 1.61076i
\(707\) −6.81726 + 16.4583i −0.256389 + 0.618979i
\(708\) 0 0
\(709\) −0.738551 + 0.305918i −0.0277369 + 0.0114890i −0.396509 0.918031i \(-0.629778\pi\)
0.368772 + 0.929520i \(0.379778\pi\)
\(710\) 1.46968 + 0.926674i 0.0551560 + 0.0347775i
\(711\) 0 0
\(712\) 5.25558 + 18.5702i 0.196961 + 0.695946i
\(713\) −25.7148 25.7148i −0.963028 0.963028i
\(714\) 0 0
\(715\) −0.977522 2.35995i −0.0365573 0.0882570i
\(716\) −27.5238 24.7523i −1.02861 0.925038i
\(717\) 0 0
\(718\) 13.3193 + 18.8342i 0.497071 + 0.702886i
\(719\) 36.8730i 1.37513i 0.726122 + 0.687566i \(0.241321\pi\)
−0.726122 + 0.687566i \(0.758679\pi\)
\(720\) 0 0
\(721\) 29.3851i 1.09436i
\(722\) 15.0757 10.6613i 0.561061 0.396774i
\(723\) 0 0
\(724\) 1.19864 + 22.6089i 0.0445470 + 0.840253i
\(725\) −18.0383 43.5484i −0.669927 1.61735i
\(726\) 0 0
\(727\) 32.3080 + 32.3080i 1.19824 + 1.19824i 0.974694 + 0.223544i \(0.0717626\pi\)
0.223544 + 0.974694i \(0.428237\pi\)
\(728\) −2.88562 + 24.5721i −0.106948 + 0.910701i
\(729\) 0 0
\(730\) −3.37854 + 5.35826i −0.125045 + 0.198318i
\(731\) −22.7656 + 9.42981i −0.842015 + 0.348774i
\(732\) 0 0
\(733\) −11.2720 + 27.2131i −0.416343 + 1.00514i 0.567056 + 0.823679i \(0.308082\pi\)
−0.983398 + 0.181460i \(0.941918\pi\)
\(734\) 3.79188 + 0.650381i 0.139961 + 0.0240060i
\(735\) 0 0
\(736\) 35.2208 + 2.25484i 1.29825 + 0.0831146i
\(737\) 13.4591 0.495772
\(738\) 0 0
\(739\) 13.5065 32.6075i 0.496843 1.19948i −0.454332 0.890832i \(-0.650122\pi\)
0.951175 0.308652i \(-0.0998780\pi\)
\(740\) 1.49456 0.713981i 0.0549411 0.0262465i
\(741\) 0 0
\(742\) 2.96176 4.69726i 0.108729 0.172442i
\(743\) 30.1102 30.1102i 1.10464 1.10464i 0.110792 0.993844i \(-0.464661\pi\)
0.993844 0.110792i \(-0.0353387\pi\)
\(744\) 0 0
\(745\) −2.95696 2.95696i −0.108335 0.108335i
\(746\) −3.44755 + 0.781201i −0.126224 + 0.0286018i
\(747\) 0 0
\(748\) −12.1262 + 0.642885i −0.443377 + 0.0235062i
\(749\) 22.7578 + 9.42660i 0.831553 + 0.344440i
\(750\) 0 0
\(751\) 3.38793i 0.123627i −0.998088 0.0618137i \(-0.980312\pi\)
0.998088 0.0618137i \(-0.0196885\pi\)
\(752\) −10.0514 + 12.4432i −0.366535 + 0.453758i
\(753\) 0 0
\(754\) −39.6175 56.0214i −1.44278 2.04018i
\(755\) 2.07252 + 0.858464i 0.0754266 + 0.0312427i
\(756\) 0 0
\(757\) 11.1514 + 26.9218i 0.405304 + 0.978491i 0.986356 + 0.164624i \(0.0526412\pi\)
−0.581052 + 0.813866i \(0.697359\pi\)
\(758\) −7.19686 31.7608i −0.261402 1.15360i
\(759\) 0 0
\(760\) 1.34551 2.40772i 0.0488068 0.0873371i
\(761\) −8.70271 + 8.70271i −0.315473 + 0.315473i −0.847025 0.531553i \(-0.821609\pi\)
0.531553 + 0.847025i \(0.321609\pi\)
\(762\) 0 0
\(763\) 30.4325 12.6055i 1.10173 0.456351i
\(764\) 48.8322 + 17.2590i 1.76669 + 0.624410i
\(765\) 0 0
\(766\) 6.56730 38.2890i 0.237286 1.38344i
\(767\) −8.89733 −0.321264
\(768\) 0 0
\(769\) −48.2614 −1.74035 −0.870175 0.492743i \(-0.835994\pi\)
−0.870175 + 0.492743i \(0.835994\pi\)
\(770\) −0.215234 + 1.25487i −0.00775650 + 0.0452224i
\(771\) 0 0
\(772\) −32.4029 11.4524i −1.16621 0.412180i
\(773\) 13.9602 5.78251i 0.502114 0.207983i −0.117226 0.993105i \(-0.537400\pi\)
0.619340 + 0.785123i \(0.287400\pi\)
\(774\) 0 0
\(775\) −19.9488 + 19.9488i −0.716583 + 0.716583i
\(776\) 9.62669 17.2265i 0.345578 0.618394i
\(777\) 0 0
\(778\) 0.538047 + 2.37448i 0.0192899 + 0.0851292i
\(779\) −4.14390 10.0043i −0.148471 0.358440i
\(780\) 0 0
\(781\) −3.63748 1.50669i −0.130159 0.0539137i
\(782\) 24.1300 + 34.1212i 0.862887 + 1.22017i
\(783\) 0 0
\(784\) −9.84559 + 12.1885i −0.351628 + 0.435304i
\(785\) 0.392807i 0.0140199i
\(786\) 0 0
\(787\) −8.99927 3.72762i −0.320789 0.132875i 0.216477 0.976288i \(-0.430543\pi\)
−0.537267 + 0.843412i \(0.680543\pi\)
\(788\) 23.9437 1.26941i 0.852960 0.0452207i