Properties

Label 864.2.v.b.109.17
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 109.17
Character \(\chi\) \(=\) 864.109
Dual form 864.2.v.b.325.17

$q$-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 −0.463783 0.885949i \(-0.653508\pi\)
0.298517 + 0.954404i \(0.403508\pi\)
\(6\) 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 0.980417 0.196930i \(-0.0630973\pi\)
−0.832511 + 0.554009i \(0.813097\pi\)
\(12\) 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 \(-0.805241\pi\)
0.818584 0.574387i \(-0.194759\pi\)
\(18\) 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 0.997021 0.0771364i \(-0.0245777\pi\)
−0.0771364 + 0.997021i \(0.524578\pi\)
\(24\) 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 \(-0.515441\pi\)
0.740562 0.671988i \(-0.234559\pi\)
\(30\) 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 0.908464 0.417963i \(-0.137256\pi\)
−0.417963 + 0.908464i \(0.637256\pi\)
\(42\) 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 \(-0.905795\pi\)
0.956524 0.291652i \(-0.0942051\pi\)
\(48\) 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 0.854141 0.520042i \(-0.174084\pi\)
−0.971694 + 0.236243i \(0.924084\pi\)
\(54\) 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 −0.272682 0.962104i \(-0.587911\pi\)
0.487495 + 0.873126i \(0.337911\pi\)
\(60\) 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 −0.824138 0.566389i \(-0.808340\pi\)
0.566389 + 0.824138i \(0.308340\pi\)
\(72\) 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 0.662170 0.749354i \(-0.269636\pi\)
−0.0616485 + 0.998098i \(0.519636\pi\)
\(84\) 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 −0.403530 0.914966i \(-0.632217\pi\)
0.914966 + 0.403530i \(0.132217\pi\)
\(90\) 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 −0.796703 0.604371i \(-0.793424\pi\)
−0.135999 + 0.990709i \(0.543424\pi\)
\(102\) 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 \(0.112209\pi\)
−0.419491 + 0.907759i \(0.637791\pi\)
\(108\) 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 \(-0.930809\pi\)
0.976468 0.215663i \(-0.0691913\pi\)
\(114\) 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 \(0.296147\pi\)
−0.989510 + 0.144468i \(0.953853\pi\)
\(132\) 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 \(-0.816854\pi\)
−0.544145 0.838991i \(-0.683146\pi\)
\(138\) 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 \(0.0158652\pi\)
−0.671000 + 0.741458i \(0.734135\pi\)
\(150\) 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 −0.996860 0.0791830i \(-0.974769\pi\)
0.0791830 + 0.996860i \(0.474769\pi\)
\(168\) 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 −0.639681 0.768640i \(-0.720934\pi\)
−0.995834 + 0.0911875i \(0.970934\pi\)
\(174\) 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 −0.362666 0.931919i \(-0.618133\pi\)
−0.915410 + 0.402523i \(0.868133\pi\)
\(180\) 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 \(-0.113689\pi\)
0.936892 + 0.349619i \(0.113689\pi\)
\(192\) 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 0.0485417 0.998821i \(-0.484543\pi\)
0.740597 + 0.671949i \(0.234543\pi\)
\(198\) 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 \(-0.663540\pi\)
0.963337 0.268293i \(-0.0864596\pi\)
\(228\) 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 0.991949 0.126634i \(-0.0404174\pi\)
−0.126634 + 0.991949i \(0.540417\pi\)
\(234\) 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 \(0.0523687\pi\)
−0.986497 + 0.163780i \(0.947631\pi\)
\(240\) 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 −0.763954 0.645270i \(-0.776745\pi\)
−0.0839221 + 0.996472i \(0.526745\pi\)
\(252\) 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 \(-0.601670\pi\)
−0.314001 + 0.949423i \(0.601670\pi\)
\(258\) 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 \(0.504995\pi\)
−0.999877 + 0.0156926i \(0.995005\pi\)
\(264\) 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 0.491862 0.870673i \(-0.336317\pi\)
−0.267860 + 0.963458i \(0.586317\pi\)
\(270\) 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 −0.483640 0.875267i \(-0.660686\pi\)
0.875267 + 0.483640i \(0.160686\pi\)
\(282\) 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 −0.650211 0.759754i \(-0.725320\pi\)
0.0774584 + 0.996996i \(0.475320\pi\)
\(294\) 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 0.338421 0.940995i \(-0.390107\pi\)
−0.940995 + 0.338421i \(0.890107\pi\)
\(312\) 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 −0.956671 0.291172i \(-0.905955\pi\)
0.882358 + 0.470579i \(0.155955\pi\)
\(318\) 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 0.428071 0.903745i \(-0.359193\pi\)
0.941736 + 0.336352i \(0.109193\pi\)
\(348\) 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 \(-0.804442\pi\)
−0.817140 + 0.576440i \(0.804442\pi\)
\(354\) 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 −0.942617 0.333877i \(-0.891643\pi\)
0.333877 + 0.942617i \(0.391643\pi\)
\(360\) 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 \(-0.252371\pi\)
0.701821 + 0.712354i \(0.252371\pi\)
\(384\) 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 −0.422640 0.906298i \(-0.638897\pi\)
0.341997 + 0.939701i \(0.388897\pi\)
\(390\) 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 \(-0.888166\pi\)
0.938913 0.344154i \(-0.111834\pi\)
\(402\) 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 −0.992726 0.120393i \(-0.961585\pi\)
0.787094 + 0.616833i \(0.211585\pi\)
\(420\) 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 \(-0.661855\pi\)
0.486852 0.873485i \(-0.338145\pi\)
\(432\) 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 0.600361 0.799729i \(-0.295024\pi\)
0.990013 + 0.140975i \(0.0450236\pi\)
\(444\) 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 \(-0.616061\pi\)
−0.356591 + 0.934261i \(0.616061\pi\)
\(450\) 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 0.352628 0.935764i \(-0.385288\pi\)
−0.412339 + 0.911030i \(0.635288\pi\)
\(462\) 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 −0.160336 0.987062i \(-0.551258\pi\)
−0.811333 + 0.584584i \(0.801258\pi\)
\(468\) 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 \(-0.297400\pi\)
0.594373 + 0.804190i \(0.297400\pi\)
\(480\) 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 \(-0.777162\pi\)
0.0852275 0.996362i \(-0.472838\pi\)
\(492\) 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 0.904738 0.425969i \(-0.140067\pi\)
−0.425969 + 0.904738i \(0.640067\pi\)
\(504\) 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 \(-0.598025\pi\)
0.888173 0.459510i \(-0.151975\pi\)
\(510\) 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 \(0.0285317\pi\)
0.0895150 + 0.995985i \(0.471468\pi\)
\(522\) 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 0.999328 0.0366506i \(-0.0116689\pi\)
0.680716 + 0.732548i \(0.261669\pi\)
\(558\) 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 −0.658221 0.752825i \(-0.728691\pi\)
−0.997760 + 0.0668949i \(0.978691\pi\)
\(564\) 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 −0.922287 0.386507i \(-0.873682\pi\)
0.386507 + 0.922287i \(0.373682\pi\)
\(570\) 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 0.959363 0.282174i \(-0.0910555\pi\)
−0.877899 + 0.478845i \(0.841055\pi\)
\(588\) 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 \(0.283306\pi\)
−0.629387 + 0.777092i \(0.716694\pi\)
\(594\) 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 0.386804 0.922162i \(-0.373579\pi\)
−0.922162 + 0.386804i \(0.873579\pi\)
\(600\) 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 0.873177 0.487404i \(-0.162056\pi\)
−0.487404 + 0.873177i \(0.662056\pi\)
\(618\) 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 \(-0.728344\pi\)
−0.657401 + 0.753541i \(0.728344\pi\)
\(642\) 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 −0.963649 0.267171i \(-0.913911\pi\)
0.267171 + 0.963649i \(0.413911\pi\)
\(648\) 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 0.0480060 0.998847i \(-0.484713\pi\)
−0.672346 + 0.740237i \(0.734713\pi\)
\(654\) 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 −0.115327 0.993328i \(-0.536792\pi\)
−0.783937 + 0.620840i \(0.786792\pi\)
\(660\) 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 −0.749486 0.662020i \(-0.769699\pi\)
−0.0618482 + 0.998086i \(0.519699\pi\)
\(678\) 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 \(0.133689\pi\)
−0.357324 + 0.933981i \(0.616311\pi\)
\(684\) 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 \(-0.716897\pi\)
0.994597 0.103808i \(-0.0331028\pi\)
\(702\) 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 \(-0.758679\pi\)
0.726122 0.687566i \(-0.241321\pi\)
\(720\) 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 \(0.535339\pi\)
−0.993844 + 0.110792i \(0.964661\pi\)
\(744\) 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 −0.531553 0.847025i \(-0.678391\pi\)
0.847025 + 0.531553i \(0.178391\pi\)
\(762\) 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 −0.619340 0.785123i \(-0.712600\pi\)
0.117226 + 0.993105i \(0.462600\pi\)
\(774\) 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