Properties

Label 864.2.v.b.109.8
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 109.8
Character \(\chi\) \(=\) 864.109
Dual form 864.2.v.b.325.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.11341 + 0.871966i) q^{2} +(0.479352 - 1.94171i) q^{4} +(-2.70909 + 1.12214i) q^{5} +(0.103960 - 0.103960i) q^{7} +(1.15939 + 2.57989i) q^{8} +O(q^{10})\) \(q+(-1.11341 + 0.871966i) q^{2} +(0.479352 - 1.94171i) q^{4} +(-2.70909 + 1.12214i) q^{5} +(0.103960 - 0.103960i) q^{7} +(1.15939 + 2.57989i) q^{8} +(2.03785 - 3.61163i) q^{10} +(-2.45541 - 5.92789i) q^{11} +(5.82208 + 2.41158i) q^{13} +(-0.0251002 + 0.206399i) q^{14} +(-3.54044 - 1.86152i) q^{16} +2.21295i q^{17} +(-0.136914 - 0.0567118i) q^{19} +(0.880262 + 5.79815i) q^{20} +(7.90280 + 4.45912i) q^{22} +(4.61190 + 4.61190i) q^{23} +(2.54442 - 2.54442i) q^{25} +(-8.58516 + 2.39158i) q^{26} +(-0.152026 - 0.251692i) q^{28} +(0.234725 - 0.566675i) q^{29} -8.85403 q^{31} +(5.56514 - 1.01452i) q^{32} +(-1.92962 - 2.46392i) q^{34} +(-0.164979 + 0.398293i) q^{35} +(-4.52845 + 1.87575i) q^{37} +(0.201892 - 0.0562413i) q^{38} +(-6.03588 - 5.68815i) q^{40} +(3.66902 + 3.66902i) q^{41} +(1.55993 + 3.76601i) q^{43} +(-12.6872 + 1.92615i) q^{44} +(-9.15633 - 1.11350i) q^{46} +6.58283i q^{47} +6.97838i q^{49} +(-0.614329 + 5.05163i) q^{50} +(7.47341 - 10.1488i) q^{52} +(3.68433 + 8.89477i) q^{53} +(13.3039 + 13.3039i) q^{55} +(0.388734 + 0.147675i) q^{56} +(0.232777 + 0.835612i) q^{58} +(4.19204 - 1.73640i) q^{59} +(2.57150 - 6.20815i) q^{61} +(9.85814 - 7.72041i) q^{62} +(-5.31164 + 5.98218i) q^{64} -18.4787 q^{65} +(-2.81795 + 6.80313i) q^{67} +(4.29691 + 1.06078i) q^{68} +(-0.163610 - 0.587319i) q^{70} +(2.74210 - 2.74210i) q^{71} +(4.87325 + 4.87325i) q^{73} +(3.40642 - 6.03712i) q^{74} +(-0.175748 + 0.238663i) q^{76} +(-0.871527 - 0.360998i) q^{77} +10.4247i q^{79} +(11.6803 + 1.07014i) q^{80} +(-7.28437 - 0.885853i) q^{82} +(-6.12008 - 2.53502i) q^{83} +(-2.48325 - 5.99509i) q^{85} +(-5.02067 - 2.83289i) q^{86} +(12.4465 - 13.2074i) q^{88} +(-7.98297 + 7.98297i) q^{89} +(0.855969 - 0.354554i) q^{91} +(11.1657 - 6.74423i) q^{92} +(-5.74000 - 7.32937i) q^{94} +0.434552 q^{95} -16.1885 q^{97} +(-6.08491 - 7.76978i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.11341 + 0.871966i −0.787298 + 0.616573i
\(3\) 0 0
\(4\) 0.479352 1.94171i 0.239676 0.970853i
\(5\) −2.70909 + 1.12214i −1.21154 + 0.501837i −0.894711 0.446646i \(-0.852618\pi\)
−0.316830 + 0.948482i \(0.602618\pi\)
\(6\) 0 0
\(7\) 0.103960 0.103960i 0.0392931 0.0392931i −0.687187 0.726480i \(-0.741155\pi\)
0.726480 + 0.687187i \(0.241155\pi\)
\(8\) 1.15939 + 2.57989i 0.409905 + 0.912128i
\(9\) 0 0
\(10\) 2.03785 3.61163i 0.644425 1.14210i
\(11\) −2.45541 5.92789i −0.740335 1.78733i −0.604514 0.796594i \(-0.706633\pi\)
−0.135821 0.990733i \(-0.543367\pi\)
\(12\) 0 0
\(13\) 5.82208 + 2.41158i 1.61475 + 0.668853i 0.993403 0.114680i \(-0.0365842\pi\)
0.621351 + 0.783532i \(0.286584\pi\)
\(14\) −0.0251002 + 0.206399i −0.00670831 + 0.0551624i
\(15\) 0 0
\(16\) −3.54044 1.86152i −0.885111 0.465380i
\(17\) 2.21295i 0.536720i 0.963319 + 0.268360i \(0.0864817\pi\)
−0.963319 + 0.268360i \(0.913518\pi\)
\(18\) 0 0
\(19\) −0.136914 0.0567118i −0.0314103 0.0130106i 0.366923 0.930251i \(-0.380411\pi\)
−0.398333 + 0.917241i \(0.630411\pi\)
\(20\) 0.880262 + 5.79815i 0.196833 + 1.29651i
\(21\) 0 0
\(22\) 7.90280 + 4.45912i 1.68488 + 0.950688i
\(23\) 4.61190 + 4.61190i 0.961647 + 0.961647i 0.999291 0.0376445i \(-0.0119854\pi\)
−0.0376445 + 0.999291i \(0.511985\pi\)
\(24\) 0 0
\(25\) 2.54442 2.54442i 0.508884 0.508884i
\(26\) −8.58516 + 2.39158i −1.68369 + 0.469027i
\(27\) 0 0
\(28\) −0.152026 0.251692i −0.0287302 0.0475654i
\(29\) 0.234725 0.566675i 0.0435873 0.105229i −0.900586 0.434677i \(-0.856863\pi\)
0.944174 + 0.329448i \(0.106863\pi\)
\(30\) 0 0
\(31\) −8.85403 −1.59023 −0.795115 0.606458i \(-0.792590\pi\)
−0.795115 + 0.606458i \(0.792590\pi\)
\(32\) 5.56514 1.01452i 0.983787 0.179343i
\(33\) 0 0
\(34\) −1.92962 2.46392i −0.330927 0.422559i
\(35\) −0.164979 + 0.398293i −0.0278865 + 0.0673239i
\(36\) 0 0
\(37\) −4.52845 + 1.87575i −0.744473 + 0.308371i −0.722484 0.691387i \(-0.757000\pi\)
−0.0219887 + 0.999758i \(0.507000\pi\)
\(38\) 0.201892 0.0562413i 0.0327513 0.00912355i
\(39\) 0 0
\(40\) −6.03588 5.68815i −0.954356 0.899375i
\(41\) 3.66902 + 3.66902i 0.573004 + 0.573004i 0.932967 0.359963i \(-0.117211\pi\)
−0.359963 + 0.932967i \(0.617211\pi\)
\(42\) 0 0
\(43\) 1.55993 + 3.76601i 0.237887 + 0.574311i 0.997064 0.0765741i \(-0.0243982\pi\)
−0.759177 + 0.650885i \(0.774398\pi\)
\(44\) −12.6872 + 1.92615i −1.91267 + 0.290378i
\(45\) 0 0
\(46\) −9.15633 1.11350i −1.35003 0.164177i
\(47\) 6.58283i 0.960204i 0.877213 + 0.480102i \(0.159400\pi\)
−0.877213 + 0.480102i \(0.840600\pi\)
\(48\) 0 0
\(49\) 6.97838i 0.996912i
\(50\) −0.614329 + 5.05163i −0.0868793 + 0.714408i
\(51\) 0 0
\(52\) 7.47341 10.1488i 1.03637 1.40738i
\(53\) 3.68433 + 8.89477i 0.506082 + 1.22179i 0.946121 + 0.323812i \(0.104965\pi\)
−0.440039 + 0.897979i \(0.645035\pi\)
\(54\) 0 0
\(55\) 13.3039 + 13.3039i 1.79389 + 1.79389i
\(56\) 0.388734 + 0.147675i 0.0519468 + 0.0197339i
\(57\) 0 0
\(58\) 0.232777 + 0.835612i 0.0305652 + 0.109721i
\(59\) 4.19204 1.73640i 0.545757 0.226060i −0.0927318 0.995691i \(-0.529560\pi\)
0.638489 + 0.769631i \(0.279560\pi\)
\(60\) 0 0
\(61\) 2.57150 6.20815i 0.329247 0.794872i −0.669402 0.742901i \(-0.733449\pi\)
0.998649 0.0519716i \(-0.0165505\pi\)
\(62\) 9.85814 7.72041i 1.25198 0.980493i
\(63\) 0 0
\(64\) −5.31164 + 5.98218i −0.663955 + 0.747772i
\(65\) −18.4787 −2.29199
\(66\) 0 0
\(67\) −2.81795 + 6.80313i −0.344267 + 0.831135i 0.653007 + 0.757352i \(0.273507\pi\)
−0.997274 + 0.0737829i \(0.976493\pi\)
\(68\) 4.29691 + 1.06078i 0.521076 + 0.128639i
\(69\) 0 0
\(70\) −0.163610 0.587319i −0.0195551 0.0701980i
\(71\) 2.74210 2.74210i 0.325427 0.325427i −0.525418 0.850844i \(-0.676091\pi\)
0.850844 + 0.525418i \(0.176091\pi\)
\(72\) 0 0
\(73\) 4.87325 + 4.87325i 0.570371 + 0.570371i 0.932232 0.361861i \(-0.117859\pi\)
−0.361861 + 0.932232i \(0.617859\pi\)
\(74\) 3.40642 6.03712i 0.395989 0.701801i
\(75\) 0 0
\(76\) −0.175748 + 0.238663i −0.0201597 + 0.0273765i
\(77\) −0.871527 0.360998i −0.0993197 0.0411396i
\(78\) 0 0
\(79\) 10.4247i 1.17287i 0.809995 + 0.586437i \(0.199470\pi\)
−0.809995 + 0.586437i \(0.800530\pi\)
\(80\) 11.6803 + 1.07014i 1.30589 + 0.119646i
\(81\) 0 0
\(82\) −7.28437 0.885853i −0.804424 0.0978261i
\(83\) −6.12008 2.53502i −0.671766 0.278255i 0.0206141 0.999788i \(-0.493438\pi\)
−0.692380 + 0.721533i \(0.743438\pi\)
\(84\) 0 0
\(85\) −2.48325 5.99509i −0.269346 0.650258i
\(86\) −5.02067 2.83289i −0.541392 0.305479i
\(87\) 0 0
\(88\) 12.4465 13.2074i 1.32680 1.40792i
\(89\) −7.98297 + 7.98297i −0.846193 + 0.846193i −0.989656 0.143463i \(-0.954176\pi\)
0.143463 + 0.989656i \(0.454176\pi\)
\(90\) 0 0
\(91\) 0.855969 0.354554i 0.0897299 0.0371674i
\(92\) 11.1657 6.74423i 1.16410 0.703134i
\(93\) 0 0
\(94\) −5.74000 7.32937i −0.592036 0.755967i
\(95\) 0.434552 0.0445841
\(96\) 0 0
\(97\) −16.1885 −1.64369 −0.821845 0.569711i \(-0.807055\pi\)
−0.821845 + 0.569711i \(0.807055\pi\)
\(98\) −6.08491 7.76978i −0.614669 0.784867i
\(99\) 0 0
\(100\) −3.72085 6.16019i −0.372085 0.616019i
\(101\) 3.11963 1.29219i 0.310414 0.128578i −0.222037 0.975038i \(-0.571271\pi\)
0.532452 + 0.846460i \(0.321271\pi\)
\(102\) 0 0
\(103\) 8.49008 8.49008i 0.836552 0.836552i −0.151851 0.988403i \(-0.548523\pi\)
0.988403 + 0.151851i \(0.0485235\pi\)
\(104\) 0.528429 + 17.8163i 0.0518167 + 1.74703i
\(105\) 0 0
\(106\) −11.8581 6.69089i −1.15176 0.649877i
\(107\) 1.34331 + 3.24305i 0.129863 + 0.313517i 0.975415 0.220376i \(-0.0707284\pi\)
−0.845552 + 0.533893i \(0.820728\pi\)
\(108\) 0 0
\(109\) 15.7340 + 6.51722i 1.50704 + 0.624236i 0.974945 0.222448i \(-0.0714047\pi\)
0.532096 + 0.846684i \(0.321405\pi\)
\(110\) −26.4131 3.21211i −2.51839 0.306262i
\(111\) 0 0
\(112\) −0.561587 + 0.174541i −0.0530650 + 0.0164925i
\(113\) 15.0322i 1.41411i 0.707159 + 0.707055i \(0.249976\pi\)
−0.707159 + 0.707055i \(0.750024\pi\)
\(114\) 0 0
\(115\) −17.6692 7.31883i −1.64766 0.682485i
\(116\) −0.987801 0.727403i −0.0917151 0.0675377i
\(117\) 0 0
\(118\) −3.15337 + 5.58863i −0.290291 + 0.514475i
\(119\) 0.230058 + 0.230058i 0.0210894 + 0.0210894i
\(120\) 0 0
\(121\) −21.3327 + 21.3327i −1.93934 + 1.93934i
\(122\) 2.55017 + 9.15446i 0.230881 + 0.828806i
\(123\) 0 0
\(124\) −4.24419 + 17.1919i −0.381140 + 1.54388i
\(125\) 1.57284 3.79718i 0.140679 0.339630i
\(126\) 0 0
\(127\) 9.20956 0.817216 0.408608 0.912710i \(-0.366014\pi\)
0.408608 + 0.912710i \(0.366014\pi\)
\(128\) 0.697765 11.2922i 0.0616743 0.998096i
\(129\) 0 0
\(130\) 20.5743 16.1127i 1.80448 1.41318i
\(131\) 5.53164 13.3546i 0.483301 1.16679i −0.474731 0.880131i \(-0.657455\pi\)
0.958032 0.286661i \(-0.0925455\pi\)
\(132\) 0 0
\(133\) −0.0201293 + 0.00833784i −0.00174543 + 0.000722983i
\(134\) −2.79457 10.0318i −0.241414 0.866616i
\(135\) 0 0
\(136\) −5.70917 + 2.56567i −0.489558 + 0.220005i
\(137\) −4.49306 4.49306i −0.383868 0.383868i 0.488626 0.872494i \(-0.337498\pi\)
−0.872494 + 0.488626i \(0.837498\pi\)
\(138\) 0 0
\(139\) −6.81127 16.4439i −0.577725 1.39475i −0.894850 0.446367i \(-0.852718\pi\)
0.317125 0.948384i \(-0.397282\pi\)
\(140\) 0.694286 + 0.511262i 0.0586779 + 0.0432096i
\(141\) 0 0
\(142\) −0.662056 + 5.44408i −0.0555585 + 0.456857i
\(143\) 40.4341i 3.38127i
\(144\) 0 0
\(145\) 1.79857i 0.149363i
\(146\) −9.67522 1.17660i −0.800727 0.0973765i
\(147\) 0 0
\(148\) 1.47143 + 9.69206i 0.120951 + 0.796683i
\(149\) 3.92523 + 9.47635i 0.321567 + 0.776332i 0.999163 + 0.0408980i \(0.0130219\pi\)
−0.677596 + 0.735434i \(0.736978\pi\)
\(150\) 0 0
\(151\) 8.02344 + 8.02344i 0.652938 + 0.652938i 0.953699 0.300761i \(-0.0972408\pi\)
−0.300761 + 0.953699i \(0.597241\pi\)
\(152\) −0.0124268 0.418975i −0.00100794 0.0339833i
\(153\) 0 0
\(154\) 1.28514 0.358003i 0.103560 0.0288487i
\(155\) 23.9863 9.93547i 1.92663 0.798036i
\(156\) 0 0
\(157\) 0.580046 1.40036i 0.0462927 0.111761i −0.899042 0.437863i \(-0.855735\pi\)
0.945334 + 0.326103i \(0.105735\pi\)
\(158\) −9.09000 11.6070i −0.723162 0.923401i
\(159\) 0 0
\(160\) −13.9380 + 8.99328i −1.10190 + 0.710981i
\(161\) 0.958903 0.0755721
\(162\) 0 0
\(163\) 0.468891 1.13200i 0.0367264 0.0886654i −0.904452 0.426575i \(-0.859720\pi\)
0.941178 + 0.337910i \(0.109720\pi\)
\(164\) 8.88290 5.36540i 0.693638 0.418967i
\(165\) 0 0
\(166\) 9.02459 2.51399i 0.700444 0.195123i
\(167\) 0.0351278 0.0351278i 0.00271827 0.00271827i −0.705746 0.708465i \(-0.749388\pi\)
0.708465 + 0.705746i \(0.249388\pi\)
\(168\) 0 0
\(169\) 18.8884 + 18.8884i 1.45296 + 1.45296i
\(170\) 7.99237 + 4.50967i 0.612987 + 0.345876i
\(171\) 0 0
\(172\) 8.06023 1.22369i 0.614587 0.0933052i
\(173\) −12.1569 5.03557i −0.924275 0.382847i −0.130771 0.991413i \(-0.541745\pi\)
−0.793504 + 0.608565i \(0.791745\pi\)
\(174\) 0 0
\(175\) 0.529035i 0.0399913i
\(176\) −2.34164 + 25.5582i −0.176507 + 1.92652i
\(177\) 0 0
\(178\) 1.92742 15.8492i 0.144466 1.18795i
\(179\) −0.169903 0.0703763i −0.0126992 0.00526017i 0.376325 0.926488i \(-0.377188\pi\)
−0.389024 + 0.921228i \(0.627188\pi\)
\(180\) 0 0
\(181\) 1.78537 + 4.31025i 0.132705 + 0.320379i 0.976239 0.216698i \(-0.0695287\pi\)
−0.843534 + 0.537076i \(0.819529\pi\)
\(182\) −0.643883 + 1.14114i −0.0477278 + 0.0845868i
\(183\) 0 0
\(184\) −6.55120 + 17.2451i −0.482961 + 1.27133i
\(185\) 10.1631 10.1631i 0.747208 0.747208i
\(186\) 0 0
\(187\) 13.1182 5.43372i 0.959295 0.397353i
\(188\) 12.7819 + 3.15549i 0.932217 + 0.230138i
\(189\) 0 0
\(190\) −0.483833 + 0.378914i −0.0351009 + 0.0274893i
\(191\) 20.4471 1.47950 0.739751 0.672881i \(-0.234943\pi\)
0.739751 + 0.672881i \(0.234943\pi\)
\(192\) 0 0
\(193\) −5.47189 −0.393876 −0.196938 0.980416i \(-0.563100\pi\)
−0.196938 + 0.980416i \(0.563100\pi\)
\(194\) 18.0244 14.1158i 1.29407 1.01346i
\(195\) 0 0
\(196\) 13.5500 + 3.34510i 0.967855 + 0.238936i
\(197\) 3.99952 1.65666i 0.284954 0.118032i −0.235628 0.971843i \(-0.575715\pi\)
0.520583 + 0.853811i \(0.325715\pi\)
\(198\) 0 0
\(199\) −6.23859 + 6.23859i −0.442242 + 0.442242i −0.892765 0.450523i \(-0.851237\pi\)
0.450523 + 0.892765i \(0.351237\pi\)
\(200\) 9.51429 + 3.61435i 0.672762 + 0.255573i
\(201\) 0 0
\(202\) −2.34667 + 4.15894i −0.165111 + 0.292622i
\(203\) −0.0345095 0.0833133i −0.00242209 0.00584745i
\(204\) 0 0
\(205\) −14.0568 5.82253i −0.981772 0.406663i
\(206\) −2.04986 + 16.8560i −0.142820 + 1.17441i
\(207\) 0 0
\(208\) −16.1235 19.3760i −1.11797 1.34348i
\(209\) 0.950865i 0.0657727i
\(210\) 0 0
\(211\) 6.05933 + 2.50986i 0.417142 + 0.172786i 0.581375 0.813636i \(-0.302515\pi\)
−0.164233 + 0.986422i \(0.552515\pi\)
\(212\) 19.0371 2.89017i 1.30747 0.198498i
\(213\) 0 0
\(214\) −4.32348 2.43951i −0.295547 0.166761i
\(215\) −8.45198 8.45198i −0.576420 0.576420i
\(216\) 0 0
\(217\) −0.920462 + 0.920462i −0.0624851 + 0.0624851i
\(218\) −23.2011 + 6.46315i −1.57138 + 0.437740i
\(219\) 0 0
\(220\) 32.2094 19.4550i 2.17156 1.31165i
\(221\) −5.33672 + 12.8840i −0.358987 + 0.866671i
\(222\) 0 0
\(223\) 17.2782 1.15703 0.578517 0.815670i \(-0.303632\pi\)
0.578517 + 0.815670i \(0.303632\pi\)
\(224\) 0.473081 0.684019i 0.0316091 0.0457029i
\(225\) 0 0
\(226\) −13.1076 16.7369i −0.871901 1.11333i
\(227\) −1.80066 + 4.34717i −0.119514 + 0.288532i −0.972303 0.233723i \(-0.924909\pi\)
0.852789 + 0.522255i \(0.174909\pi\)
\(228\) 0 0
\(229\) 8.11150 3.35989i 0.536023 0.222028i −0.0982160 0.995165i \(-0.531314\pi\)
0.634239 + 0.773137i \(0.281314\pi\)
\(230\) 26.0548 7.25812i 1.71800 0.478586i
\(231\) 0 0
\(232\) 1.73410 0.0514332i 0.113849 0.00337675i
\(233\) −2.65249 2.65249i −0.173771 0.173771i 0.614863 0.788634i \(-0.289211\pi\)
−0.788634 + 0.614863i \(0.789211\pi\)
\(234\) 0 0
\(235\) −7.38686 17.8335i −0.481866 1.16333i
\(236\) −1.36212 8.97205i −0.0886662 0.584031i
\(237\) 0 0
\(238\) −0.456751 0.0555456i −0.0296068 0.00360049i
\(239\) 6.07668i 0.393068i −0.980497 0.196534i \(-0.937031\pi\)
0.980497 0.196534i \(-0.0629685\pi\)
\(240\) 0 0
\(241\) 22.9953i 1.48126i −0.671913 0.740630i \(-0.734527\pi\)
0.671913 0.740630i \(-0.265473\pi\)
\(242\) 5.15060 42.3534i 0.331093 2.72258i
\(243\) 0 0
\(244\) −10.8217 7.96898i −0.692792 0.510162i
\(245\) −7.83073 18.9051i −0.500287 1.20780i
\(246\) 0 0
\(247\) −0.660361 0.660361i −0.0420178 0.0420178i
\(248\) −10.2652 22.8424i −0.651844 1.45049i
\(249\) 0 0
\(250\) 1.55979 + 5.59927i 0.0986500 + 0.354129i
\(251\) −3.05607 + 1.26587i −0.192898 + 0.0799008i −0.477041 0.878881i \(-0.658291\pi\)
0.284144 + 0.958782i \(0.408291\pi\)
\(252\) 0 0
\(253\) 16.0147 38.6629i 1.00684 2.43072i
\(254\) −10.2540 + 8.03042i −0.643393 + 0.503873i
\(255\) 0 0
\(256\) 9.06949 + 13.1812i 0.566843 + 0.823826i
\(257\) 4.05144 0.252722 0.126361 0.991984i \(-0.459670\pi\)
0.126361 + 0.991984i \(0.459670\pi\)
\(258\) 0 0
\(259\) −0.275775 + 0.665779i −0.0171358 + 0.0413695i
\(260\) −8.85777 + 35.8801i −0.549336 + 2.22519i
\(261\) 0 0
\(262\) 5.48575 + 19.6925i 0.338911 + 1.21660i
\(263\) −7.96691 + 7.96691i −0.491261 + 0.491261i −0.908703 0.417442i \(-0.862927\pi\)
0.417442 + 0.908703i \(0.362927\pi\)
\(264\) 0 0
\(265\) −19.9624 19.9624i −1.22628 1.22628i
\(266\) 0.0151418 0.0268355i 0.000928405 0.00164539i
\(267\) 0 0
\(268\) 11.8589 + 8.73272i 0.724397 + 0.533436i
\(269\) −13.3531 5.53105i −0.814155 0.337234i −0.0635444 0.997979i \(-0.520240\pi\)
−0.750610 + 0.660745i \(0.770240\pi\)
\(270\) 0 0
\(271\) 16.2842i 0.989195i −0.869122 0.494598i \(-0.835315\pi\)
0.869122 0.494598i \(-0.164685\pi\)
\(272\) 4.11946 7.83484i 0.249779 0.475057i
\(273\) 0 0
\(274\) 8.92040 + 1.08481i 0.538901 + 0.0655359i
\(275\) −21.3307 8.83546i −1.28629 0.532798i
\(276\) 0 0
\(277\) 2.21965 + 5.35871i 0.133366 + 0.321974i 0.976428 0.215842i \(-0.0692496\pi\)
−0.843062 + 0.537816i \(0.819250\pi\)
\(278\) 21.9222 + 12.3695i 1.31481 + 0.741875i
\(279\) 0 0
\(280\) −1.21883 + 0.0361503i −0.0728388 + 0.00216039i
\(281\) 18.2054 18.2054i 1.08605 1.08605i 0.0901138 0.995931i \(-0.471277\pi\)
0.995931 0.0901138i \(-0.0287231\pi\)
\(282\) 0 0
\(283\) −17.9055 + 7.41670i −1.06437 + 0.440877i −0.845001 0.534765i \(-0.820400\pi\)
−0.219370 + 0.975642i \(0.570400\pi\)
\(284\) −4.00992 6.63877i −0.237945 0.393939i
\(285\) 0 0
\(286\) 35.2571 + 45.0196i 2.08480 + 2.66207i
\(287\) 0.762860 0.0450302
\(288\) 0 0
\(289\) 12.1028 0.711931
\(290\) −1.56829 2.00254i −0.0920931 0.117593i
\(291\) 0 0
\(292\) 11.7984 7.12642i 0.690450 0.417042i
\(293\) −11.8974 + 4.92807i −0.695054 + 0.287901i −0.702104 0.712074i \(-0.747756\pi\)
0.00705007 + 0.999975i \(0.497756\pi\)
\(294\) 0 0
\(295\) −9.40811 + 9.40811i −0.547762 + 0.547762i
\(296\) −10.0894 9.50818i −0.586437 0.552652i
\(297\) 0 0
\(298\) −12.6334 7.12837i −0.731835 0.412935i
\(299\) 15.7288 + 37.9728i 0.909622 + 2.19602i
\(300\) 0 0
\(301\) 0.553683 + 0.229343i 0.0319138 + 0.0132191i
\(302\) −15.9295 1.93719i −0.916641 0.111473i
\(303\) 0 0
\(304\) 0.379168 + 0.455654i 0.0217468 + 0.0261335i
\(305\) 19.7040i 1.12825i
\(306\) 0 0
\(307\) 15.3702 + 6.36654i 0.877223 + 0.363358i 0.775419 0.631447i \(-0.217539\pi\)
0.101804 + 0.994804i \(0.467539\pi\)
\(308\) −1.11872 + 1.51920i −0.0637450 + 0.0865646i
\(309\) 0 0
\(310\) −18.0432 + 31.9775i −1.02478 + 1.81620i
\(311\) 7.70248 + 7.70248i 0.436767 + 0.436767i 0.890923 0.454155i \(-0.150059\pi\)
−0.454155 + 0.890923i \(0.650059\pi\)
\(312\) 0 0
\(313\) −10.5231 + 10.5231i −0.594802 + 0.594802i −0.938925 0.344123i \(-0.888176\pi\)
0.344123 + 0.938925i \(0.388176\pi\)
\(314\) 0.575234 + 2.06495i 0.0324624 + 0.116532i
\(315\) 0 0
\(316\) 20.2418 + 4.99711i 1.13869 + 0.281109i
\(317\) −6.57566 + 15.8750i −0.369326 + 0.891631i 0.624535 + 0.780997i \(0.285288\pi\)
−0.993861 + 0.110635i \(0.964712\pi\)
\(318\) 0 0
\(319\) −3.93554 −0.220348
\(320\) 7.67685 22.1667i 0.429149 1.23915i
\(321\) 0 0
\(322\) −1.06765 + 0.836130i −0.0594978 + 0.0465957i
\(323\) 0.125501 0.302985i 0.00698304 0.0168586i
\(324\) 0 0
\(325\) 20.9499 8.67773i 1.16209 0.481354i
\(326\) 0.465002 + 1.66924i 0.0257541 + 0.0924506i
\(327\) 0 0
\(328\) −5.21184 + 13.7195i −0.287776 + 0.757531i
\(329\) 0.684349 + 0.684349i 0.0377294 + 0.0377294i
\(330\) 0 0
\(331\) −10.3554 25.0003i −0.569187 1.37414i −0.902242 0.431231i \(-0.858079\pi\)
0.333055 0.942907i \(-0.391921\pi\)
\(332\) −7.85593 + 10.6682i −0.431150 + 0.585495i
\(333\) 0 0
\(334\) −0.00848130 + 0.0697417i −0.000464076 + 0.00381610i
\(335\) 21.5924i 1.17972i
\(336\) 0 0
\(337\) 2.65115i 0.144417i −0.997390 0.0722087i \(-0.976995\pi\)
0.997390 0.0722087i \(-0.0230048\pi\)
\(338\) −37.5006 4.56046i −2.03976 0.248056i
\(339\) 0 0
\(340\) −12.8310 + 1.94798i −0.695861 + 0.105644i
\(341\) 21.7403 + 52.4857i 1.17730 + 2.84226i
\(342\) 0 0
\(343\) 1.45319 + 1.45319i 0.0784648 + 0.0784648i
\(344\) −7.90731 + 8.39071i −0.426334 + 0.452397i
\(345\) 0 0
\(346\) 17.9265 4.99379i 0.963733 0.268468i
\(347\) 22.3756 9.26828i 1.20119 0.497547i 0.309804 0.950801i \(-0.399737\pi\)
0.891382 + 0.453253i \(0.149737\pi\)
\(348\) 0 0
\(349\) −7.56347 + 18.2598i −0.404863 + 0.977426i 0.581605 + 0.813472i \(0.302425\pi\)
−0.986468 + 0.163955i \(0.947575\pi\)
\(350\) 0.461300 + 0.589031i 0.0246575 + 0.0314850i
\(351\) 0 0
\(352\) −19.6787 30.4985i −1.04888 1.62558i
\(353\) 13.5186 0.719521 0.359761 0.933045i \(-0.382858\pi\)
0.359761 + 0.933045i \(0.382858\pi\)
\(354\) 0 0
\(355\) −4.35156 + 10.5056i −0.230957 + 0.557579i
\(356\) 11.6739 + 19.3272i 0.618717 + 1.02434i
\(357\) 0 0
\(358\) 0.250537 0.0697925i 0.0132413 0.00368865i
\(359\) −14.2729 + 14.2729i −0.753297 + 0.753297i −0.975093 0.221796i \(-0.928808\pi\)
0.221796 + 0.975093i \(0.428808\pi\)
\(360\) 0 0
\(361\) −13.4195 13.4195i −0.706289 0.706289i
\(362\) −5.74623 3.24229i −0.302015 0.170411i
\(363\) 0 0
\(364\) −0.278129 1.83200i −0.0145779 0.0960227i
\(365\) −18.6705 7.73359i −0.977260 0.404794i
\(366\) 0 0
\(367\) 19.2022i 1.00234i 0.865348 + 0.501172i \(0.167098\pi\)
−0.865348 + 0.501172i \(0.832902\pi\)
\(368\) −7.74302 24.9133i −0.403633 1.29870i
\(369\) 0 0
\(370\) −2.45380 + 20.1776i −0.127567 + 1.04898i
\(371\) 1.30772 + 0.541676i 0.0678935 + 0.0281224i
\(372\) 0 0
\(373\) −8.73051 21.0773i −0.452048 1.09134i −0.971542 0.236867i \(-0.923879\pi\)
0.519494 0.854474i \(-0.326121\pi\)
\(374\) −9.86784 + 17.4885i −0.510254 + 0.904310i
\(375\) 0 0
\(376\) −16.9830 + 7.63205i −0.875829 + 0.393593i
\(377\) 2.73317 2.73317i 0.140765 0.140765i
\(378\) 0 0
\(379\) −17.7998 + 7.37290i −0.914312 + 0.378721i −0.789706 0.613486i \(-0.789767\pi\)
−0.124606 + 0.992206i \(0.539767\pi\)
\(380\) 0.208303 0.843772i 0.0106857 0.0432846i
\(381\) 0 0
\(382\) −22.7660 + 17.8292i −1.16481 + 0.912221i
\(383\) −9.29759 −0.475084 −0.237542 0.971377i \(-0.576342\pi\)
−0.237542 + 0.971377i \(0.576342\pi\)
\(384\) 0 0
\(385\) 2.76613 0.140975
\(386\) 6.09245 4.77130i 0.310097 0.242853i
\(387\) 0 0
\(388\) −7.75997 + 31.4333i −0.393953 + 1.59578i
\(389\) −20.7514 + 8.59553i −1.05214 + 0.435811i −0.840655 0.541571i \(-0.817830\pi\)
−0.211485 + 0.977381i \(0.567830\pi\)
\(390\) 0 0
\(391\) −10.2059 + 10.2059i −0.516135 + 0.516135i
\(392\) −18.0034 + 8.09065i −0.909312 + 0.408640i
\(393\) 0 0
\(394\) −3.00855 + 5.33198i −0.151569 + 0.268621i
\(395\) −11.6980 28.2415i −0.588591 1.42098i
\(396\) 0 0
\(397\) −14.4613 5.99007i −0.725792 0.300633i −0.0109706 0.999940i \(-0.503492\pi\)
−0.714822 + 0.699307i \(0.753492\pi\)
\(398\) 1.50625 12.3859i 0.0755017 0.620850i
\(399\) 0 0
\(400\) −13.7449 + 4.27189i −0.687244 + 0.213595i
\(401\) 0.299530i 0.0149578i 0.999972 + 0.00747890i \(0.00238063\pi\)
−0.999972 + 0.00747890i \(0.997619\pi\)
\(402\) 0 0
\(403\) −51.5488 21.3522i −2.56783 1.06363i
\(404\) −1.01366 6.67681i −0.0504314 0.332184i
\(405\) 0 0
\(406\) 0.111070 + 0.0626706i 0.00551229 + 0.00311029i
\(407\) 22.2385 + 22.2385i 1.10232 + 1.10232i
\(408\) 0 0
\(409\) 3.25402 3.25402i 0.160901 0.160901i −0.622065 0.782966i \(-0.713706\pi\)
0.782966 + 0.622065i \(0.213706\pi\)
\(410\) 20.7280 5.77423i 1.02368 0.285169i
\(411\) 0 0
\(412\) −12.4155 20.5550i −0.611668 1.01267i
\(413\) 0.255288 0.616319i 0.0125619 0.0303271i
\(414\) 0 0
\(415\) 19.4245 0.953510
\(416\) 34.8472 + 7.51420i 1.70853 + 0.368414i
\(417\) 0 0
\(418\) −0.829122 1.05870i −0.0405537 0.0517827i
\(419\) −3.29846 + 7.96319i −0.161140 + 0.389027i −0.983741 0.179592i \(-0.942522\pi\)
0.822601 + 0.568619i \(0.192522\pi\)
\(420\) 0 0
\(421\) 18.5634 7.68923i 0.904727 0.374750i 0.118691 0.992931i \(-0.462130\pi\)
0.786036 + 0.618181i \(0.212130\pi\)
\(422\) −8.93501 + 2.48904i −0.434950 + 0.121164i
\(423\) 0 0
\(424\) −18.6759 + 19.8177i −0.906984 + 0.962430i
\(425\) 5.63069 + 5.63069i 0.273129 + 0.273129i
\(426\) 0 0
\(427\) −0.378065 0.912730i −0.0182959 0.0441701i
\(428\) 6.94097 1.05376i 0.335504 0.0509355i
\(429\) 0 0
\(430\) 16.7803 + 2.04066i 0.809219 + 0.0984093i
\(431\) 15.9187i 0.766778i 0.923587 + 0.383389i \(0.125243\pi\)
−0.923587 + 0.383389i \(0.874757\pi\)
\(432\) 0 0
\(433\) 41.1903i 1.97948i 0.142877 + 0.989740i \(0.454365\pi\)
−0.142877 + 0.989740i \(0.545635\pi\)
\(434\) 0.222238 1.82746i 0.0106678 0.0877209i
\(435\) 0 0
\(436\) 20.1966 27.4267i 0.967243 1.31350i
\(437\) −0.369886 0.892984i −0.0176941 0.0427172i
\(438\) 0 0
\(439\) −5.58206 5.58206i −0.266417 0.266417i 0.561238 0.827655i \(-0.310325\pi\)
−0.827655 + 0.561238i \(0.810325\pi\)
\(440\) −18.8981 + 49.7468i −0.900934 + 2.37159i
\(441\) 0 0
\(442\) −5.29245 18.9986i −0.251736 0.903670i
\(443\) −12.9536 + 5.36555i −0.615443 + 0.254925i −0.668554 0.743664i \(-0.733086\pi\)
0.0531107 + 0.998589i \(0.483086\pi\)
\(444\) 0 0
\(445\) 12.6685 30.5846i 0.600547 1.44985i
\(446\) −19.2377 + 15.0660i −0.910930 + 0.713396i
\(447\) 0 0
\(448\) 0.0697089 + 1.17410i 0.00329344 + 0.0554711i
\(449\) −27.5435 −1.29986 −0.649929 0.759995i \(-0.725201\pi\)
−0.649929 + 0.759995i \(0.725201\pi\)
\(450\) 0 0
\(451\) 12.7406 30.7585i 0.599931 1.44836i
\(452\) 29.1881 + 7.20570i 1.37289 + 0.338928i
\(453\) 0 0
\(454\) −1.78572 6.41028i −0.0838079 0.300849i
\(455\) −1.92104 + 1.92104i −0.0900595 + 0.0900595i
\(456\) 0 0
\(457\) 5.65142 + 5.65142i 0.264362 + 0.264362i 0.826824 0.562461i \(-0.190145\pi\)
−0.562461 + 0.826824i \(0.690145\pi\)
\(458\) −6.10169 + 10.8139i −0.285113 + 0.505299i
\(459\) 0 0
\(460\) −22.6808 + 30.8001i −1.05750 + 1.43606i
\(461\) −30.4680 12.6202i −1.41903 0.587783i −0.464416 0.885617i \(-0.653736\pi\)
−0.954618 + 0.297834i \(0.903736\pi\)
\(462\) 0 0
\(463\) 2.21705i 0.103035i −0.998672 0.0515176i \(-0.983594\pi\)
0.998672 0.0515176i \(-0.0164058\pi\)
\(464\) −1.88591 + 1.56934i −0.0875510 + 0.0728547i
\(465\) 0 0
\(466\) 5.26619 + 0.640422i 0.243952 + 0.0296670i
\(467\) −18.1070 7.50016i −0.837892 0.347066i −0.0778697 0.996964i \(-0.524812\pi\)
−0.760022 + 0.649897i \(0.774812\pi\)
\(468\) 0 0
\(469\) 0.414298 + 1.00020i 0.0191305 + 0.0461852i
\(470\) 23.7748 + 13.4148i 1.09665 + 0.618779i
\(471\) 0 0
\(472\) 9.33991 + 8.80183i 0.429904 + 0.405137i
\(473\) 18.4942 18.4942i 0.850365 0.850365i
\(474\) 0 0
\(475\) −0.492667 + 0.204069i −0.0226051 + 0.00936334i
\(476\) 0.556984 0.336426i 0.0255293 0.0154201i
\(477\) 0 0
\(478\) 5.29865 + 6.76582i 0.242355 + 0.309461i
\(479\) −32.8286 −1.49997 −0.749987 0.661452i \(-0.769941\pi\)
−0.749987 + 0.661452i \(0.769941\pi\)
\(480\) 0 0
\(481\) −30.8885 −1.40839
\(482\) 20.0512 + 25.6032i 0.913305 + 1.16619i
\(483\) 0 0
\(484\) 31.1960 + 51.6477i 1.41800 + 2.34762i
\(485\) 43.8560 18.1658i 1.99140 0.824864i
\(486\) 0 0
\(487\) 8.00548 8.00548i 0.362763 0.362763i −0.502066 0.864829i \(-0.667427\pi\)
0.864829 + 0.502066i \(0.167427\pi\)
\(488\) 18.9977 0.563470i 0.859985 0.0255071i
\(489\) 0 0
\(490\) 25.2034 + 14.2209i 1.13857 + 0.642435i
\(491\) 9.65556 + 23.3106i 0.435749 + 1.05199i 0.977402 + 0.211390i \(0.0677989\pi\)
−0.541652 + 0.840603i \(0.682201\pi\)
\(492\) 0 0
\(493\) 1.25403 + 0.519435i 0.0564785 + 0.0233942i
\(494\) 1.31106 + 0.159439i 0.0589875 + 0.00717348i
\(495\) 0 0
\(496\) 31.3472 + 16.4819i 1.40753 + 0.740061i
\(497\) 0.570135i 0.0255741i
\(498\) 0 0
\(499\) −10.0010 4.14254i −0.447705 0.185446i 0.147428 0.989073i \(-0.452901\pi\)
−0.595133 + 0.803627i \(0.702901\pi\)
\(500\) −6.61906 4.87418i −0.296013 0.217980i
\(501\) 0 0
\(502\) 2.29886 4.07422i 0.102603 0.181841i
\(503\) −0.259100 0.259100i −0.0115527 0.0115527i 0.701307 0.712860i \(-0.252600\pi\)
−0.712860 + 0.701307i \(0.752600\pi\)
\(504\) 0 0
\(505\) −7.00132 + 7.00132i −0.311555 + 0.311555i
\(506\) 15.8819 + 57.0119i 0.706035 + 2.53449i
\(507\) 0 0
\(508\) 4.41462 17.8823i 0.195867 0.793397i
\(509\) 17.2463 41.6364i 0.764431 1.84550i 0.336538 0.941670i \(-0.390744\pi\)
0.427893 0.903829i \(-0.359256\pi\)
\(510\) 0 0
\(511\) 1.01324 0.0448232
\(512\) −21.5916 6.76778i −0.954223 0.299096i
\(513\) 0 0
\(514\) −4.51090 + 3.53272i −0.198967 + 0.155821i
\(515\) −13.4733 + 32.5274i −0.593704 + 1.43333i
\(516\) 0 0
\(517\) 39.0223 16.1636i 1.71620 0.710873i
\(518\) −0.273487 0.981749i −0.0120163 0.0431356i
\(519\) 0 0
\(520\) −21.4239 47.6728i −0.939501 2.09059i
\(521\) 29.6467 + 29.6467i 1.29885 + 1.29885i 0.929154 + 0.369693i \(0.120537\pi\)
0.369693 + 0.929154i \(0.379463\pi\)
\(522\) 0 0
\(523\) 2.55510 + 6.16856i 0.111727 + 0.269732i 0.969846 0.243718i \(-0.0783671\pi\)
−0.858119 + 0.513450i \(0.828367\pi\)
\(524\) −23.2790 17.1423i −1.01695 0.748866i
\(525\) 0 0
\(526\) 1.92354 15.8173i 0.0838705 0.689667i
\(527\) 19.5936i 0.853509i
\(528\) 0 0
\(529\) 19.5392i 0.849529i
\(530\) 39.6328 + 4.81975i 1.72154 + 0.209356i
\(531\) 0 0
\(532\) 0.00654061 + 0.0430820i 0.000283571 + 0.00186784i
\(533\) 12.5132 + 30.2094i 0.542005 + 1.30852i
\(534\) 0 0
\(535\) −7.27831 7.27831i −0.314669 0.314669i
\(536\) −20.8184 + 0.617472i −0.899218 + 0.0266707i
\(537\) 0 0
\(538\) 19.6904 5.48516i 0.848912 0.236482i
\(539\) 41.3671 17.1348i 1.78181 0.738049i
\(540\) 0 0
\(541\) −6.21660 + 15.0082i −0.267272 + 0.645252i −0.999353 0.0359654i \(-0.988549\pi\)
0.732081 + 0.681218i \(0.238549\pi\)
\(542\) 14.1993 + 18.1310i 0.609911 + 0.778791i
\(543\) 0 0
\(544\) 2.24508 + 12.3154i 0.0962569 + 0.528018i
\(545\) −49.9379 −2.13911
\(546\) 0 0
\(547\) 14.4297 34.8365i 0.616971 1.48950i −0.238233 0.971208i \(-0.576568\pi\)
0.855204 0.518291i \(-0.173432\pi\)
\(548\) −10.8780 + 6.57045i −0.464683 + 0.280676i
\(549\) 0 0
\(550\) 31.4539 8.76216i 1.34120 0.373620i
\(551\) −0.0642744 + 0.0642744i −0.00273818 + 0.00273818i
\(552\) 0 0
\(553\) 1.08375 + 1.08375i 0.0460858 + 0.0460858i
\(554\) −7.14399 4.03097i −0.303519 0.171260i
\(555\) 0 0
\(556\) −35.1941 + 5.34309i −1.49256 + 0.226598i
\(557\) 9.72338 + 4.02756i 0.411993 + 0.170653i 0.579046 0.815295i \(-0.303425\pi\)
−0.167053 + 0.985948i \(0.553425\pi\)
\(558\) 0 0
\(559\) 25.6879i 1.08648i
\(560\) 1.32553 1.10302i 0.0560138 0.0466113i
\(561\) 0 0
\(562\) −4.39555 + 36.1446i −0.185415 + 1.52467i
\(563\) −24.6470 10.2091i −1.03875 0.430263i −0.202884 0.979203i \(-0.565032\pi\)
−0.835862 + 0.548940i \(0.815032\pi\)
\(564\) 0 0
\(565\) −16.8682 40.7235i −0.709652 1.71325i
\(566\) 13.4690 23.8708i 0.566144 1.00336i
\(567\) 0 0
\(568\) 10.2534 + 3.89515i 0.430225 + 0.163437i
\(569\) 11.6321 11.6321i 0.487641 0.487641i −0.419920 0.907561i \(-0.637942\pi\)
0.907561 + 0.419920i \(0.137942\pi\)
\(570\) 0 0
\(571\) −12.6477 + 5.23886i −0.529291 + 0.219239i −0.631293 0.775545i \(-0.717475\pi\)
0.102002 + 0.994784i \(0.467475\pi\)
\(572\) −78.5111 19.3821i −3.28271 0.810408i
\(573\) 0 0
\(574\) −0.849374 + 0.665188i −0.0354522 + 0.0277644i
\(575\) 23.4692 0.978734
\(576\) 0 0
\(577\) −6.58449 −0.274116 −0.137058 0.990563i \(-0.543765\pi\)
−0.137058 + 0.990563i \(0.543765\pi\)
\(578\) −13.4754 + 10.5533i −0.560502 + 0.438958i
\(579\) 0 0
\(580\) 3.49229 + 0.862146i 0.145009 + 0.0357987i
\(581\) −0.899782 + 0.372702i −0.0373292 + 0.0154623i
\(582\) 0 0
\(583\) 43.6807 43.6807i 1.80907 1.80907i
\(584\) −6.92245 + 18.2224i −0.286453 + 0.754049i
\(585\) 0 0
\(586\) 8.94955 15.8611i 0.369703 0.655215i
\(587\) 8.31848 + 20.0826i 0.343341 + 0.828897i 0.997373 + 0.0724312i \(0.0230758\pi\)
−0.654033 + 0.756466i \(0.726924\pi\)
\(588\) 0 0
\(589\) 1.21224 + 0.502128i 0.0499496 + 0.0206898i
\(590\) 2.27151 18.6786i 0.0935166 0.768986i
\(591\) 0 0
\(592\) 19.5245 + 1.78883i 0.802451 + 0.0735204i
\(593\) 27.2466i 1.11888i −0.828870 0.559441i \(-0.811016\pi\)
0.828870 0.559441i \(-0.188984\pi\)
\(594\) 0 0
\(595\) −0.881405 0.365090i −0.0361341 0.0149672i
\(596\) 20.2818 3.07914i 0.830777 0.126127i
\(597\) 0 0
\(598\) −50.6236 28.5642i −2.07015 1.16808i
\(599\) −0.762457 0.762457i −0.0311532 0.0311532i 0.691359 0.722512i \(-0.257012\pi\)
−0.722512 + 0.691359i \(0.757012\pi\)
\(600\) 0 0
\(601\) 23.5435 23.5435i 0.960358 0.960358i −0.0388853 0.999244i \(-0.512381\pi\)
0.999244 + 0.0388853i \(0.0123807\pi\)
\(602\) −0.816454 + 0.227440i −0.0332762 + 0.00926978i
\(603\) 0 0
\(604\) 19.4252 11.7331i 0.790400 0.477413i
\(605\) 33.8539 81.7305i 1.37636 3.32282i
\(606\) 0 0
\(607\) 19.4844 0.790847 0.395423 0.918499i \(-0.370598\pi\)
0.395423 + 0.918499i \(0.370598\pi\)
\(608\) −0.819483 0.176707i −0.0332344 0.00716642i
\(609\) 0 0
\(610\) −17.1812 21.9386i −0.695647 0.888267i
\(611\) −15.8750 + 38.3257i −0.642235 + 1.55049i
\(612\) 0 0
\(613\) −31.3025 + 12.9659i −1.26430 + 0.523688i −0.911225 0.411909i \(-0.864862\pi\)
−0.353070 + 0.935597i \(0.614862\pi\)
\(614\) −22.6647 + 6.31373i −0.914672 + 0.254801i
\(615\) 0 0
\(616\) −0.0791024 2.66698i −0.00318712 0.107456i
\(617\) −10.4435 10.4435i −0.420440 0.420440i 0.464915 0.885355i \(-0.346085\pi\)
−0.885355 + 0.464915i \(0.846085\pi\)
\(618\) 0 0
\(619\) 0.884297 + 2.13488i 0.0355429 + 0.0858082i 0.940654 0.339366i \(-0.110213\pi\)
−0.905111 + 0.425175i \(0.860213\pi\)
\(620\) −7.79386 51.3370i −0.313009 2.06174i
\(621\) 0 0
\(622\) −15.2923 1.85970i −0.613165 0.0745671i
\(623\) 1.65981i 0.0664991i
\(624\) 0 0
\(625\) 30.0436i 1.20174i
\(626\) 2.54072 20.8923i 0.101548 0.835025i
\(627\) 0 0
\(628\) −2.44103 1.79754i −0.0974078 0.0717297i
\(629\) −4.15094 10.0213i −0.165509 0.399574i
\(630\) 0 0
\(631\) 5.30466 + 5.30466i 0.211175 + 0.211175i 0.804767 0.593591i \(-0.202290\pi\)
−0.593591 + 0.804767i \(0.702290\pi\)
\(632\) −26.8946 + 12.0863i −1.06981 + 0.480767i
\(633\) 0 0
\(634\) −6.52111 23.4091i −0.258986 0.929696i
\(635\) −24.9495 + 10.3344i −0.990091 + 0.410109i
\(636\) 0 0
\(637\) −16.8290 + 40.6287i −0.666787 + 1.60977i
\(638\) 4.38186 3.43165i 0.173479 0.135861i
\(639\) 0 0
\(640\) 10.7811 + 31.3745i 0.426160 + 1.24018i
\(641\) −44.4168 −1.75436 −0.877179 0.480163i \(-0.840578\pi\)
−0.877179 + 0.480163i \(0.840578\pi\)
\(642\) 0 0
\(643\) 7.60023 18.3486i 0.299724 0.723598i −0.700229 0.713918i \(-0.746919\pi\)
0.999953 0.00967946i \(-0.00308112\pi\)
\(644\) 0.459652 1.86191i 0.0181128 0.0733694i
\(645\) 0 0
\(646\) 0.124460 + 0.446778i 0.00489679 + 0.0175783i
\(647\) −34.4364 + 34.4364i −1.35384 + 1.35384i −0.472511 + 0.881325i \(0.656652\pi\)
−0.881325 + 0.472511i \(0.843348\pi\)
\(648\) 0 0
\(649\) −20.5864 20.5864i −0.808086 0.808086i
\(650\) −15.7591 + 27.9294i −0.618122 + 1.09548i
\(651\) 0 0
\(652\) −1.97326 1.45308i −0.0772786 0.0569069i
\(653\) 39.6908 + 16.4405i 1.55322 + 0.643365i 0.983895 0.178747i \(-0.0572043\pi\)
0.569326 + 0.822112i \(0.307204\pi\)
\(654\) 0 0
\(655\) 42.3859i 1.65616i
\(656\) −6.16000 19.8199i −0.240508 0.773837i
\(657\) 0 0
\(658\) −1.35869 0.165230i −0.0529672 0.00644135i
\(659\) 22.7805 + 9.43601i 0.887404 + 0.367575i 0.779364 0.626572i \(-0.215543\pi\)
0.108040 + 0.994147i \(0.465543\pi\)
\(660\) 0 0
\(661\) 10.0305 + 24.2157i 0.390140 + 0.941881i 0.989909 + 0.141707i \(0.0452592\pi\)
−0.599769 + 0.800173i \(0.704741\pi\)
\(662\) 33.3292 + 18.8059i 1.29538 + 0.730911i
\(663\) 0 0
\(664\) −0.555477 18.7282i −0.0215567 0.726795i
\(665\) 0.0451759 0.0451759i 0.00175185 0.00175185i
\(666\) 0 0
\(667\) 3.69597 1.53092i 0.143109 0.0592776i
\(668\) −0.0513692 0.0850463i −0.00198754 0.00329054i
\(669\) 0 0
\(670\) 18.8278 + 24.0412i 0.727383 + 0.928791i
\(671\) −43.1154 −1.66445
\(672\) 0 0
\(673\) 24.0093 0.925491 0.462745 0.886491i \(-0.346864\pi\)
0.462745 + 0.886491i \(0.346864\pi\)
\(674\) 2.31171 + 2.95181i 0.0890439 + 0.113700i
\(675\) 0 0
\(676\) 45.7300 27.6216i 1.75885 1.06237i
\(677\) 26.8088 11.1046i 1.03034 0.426783i 0.197508 0.980301i \(-0.436715\pi\)
0.832837 + 0.553518i \(0.186715\pi\)
\(678\) 0 0
\(679\) −1.68295 + 1.68295i −0.0645857 + 0.0645857i
\(680\) 12.5876 13.3571i 0.482713 0.512222i
\(681\) 0 0
\(682\) −69.9716 39.4812i −2.67935 1.51181i
\(683\) −11.2367 27.1277i −0.429959 1.03801i −0.979300 0.202415i \(-0.935121\pi\)
0.549341 0.835598i \(-0.314879\pi\)
\(684\) 0 0
\(685\) 17.2139 + 7.13025i 0.657711 + 0.272433i
\(686\) −2.88512 0.350860i −0.110154 0.0133959i
\(687\) 0 0
\(688\) 1.48765 16.2372i 0.0567160 0.619037i
\(689\) 60.6711i 2.31139i
\(690\) 0 0
\(691\) 11.4155 + 4.72846i 0.434266 + 0.179879i 0.589098 0.808062i \(-0.299483\pi\)
−0.154831 + 0.987941i \(0.549483\pi\)
\(692\) −15.6050 + 21.1914i −0.593215 + 0.805576i
\(693\) 0 0
\(694\) −16.8315 + 29.8301i −0.638916 + 1.13234i
\(695\) 36.9047 + 36.9047i 1.39987 + 1.39987i
\(696\) 0 0
\(697\) −8.11936 + 8.11936i −0.307543 + 0.307543i
\(698\) −7.50072 26.9257i −0.283907 1.01915i
\(699\) 0 0
\(700\) −1.02723 0.253594i −0.0388256 0.00958494i
\(701\) −1.29537 + 3.12731i −0.0489255 + 0.118117i −0.946453 0.322842i \(-0.895362\pi\)
0.897527 + 0.440959i \(0.145362\pi\)
\(702\) 0 0
\(703\) 0.726387 0.0273962
\(704\) 48.5040 + 16.7981i 1.82806 + 0.633103i
\(705\) 0 0
\(706\) −15.0517 + 11.7877i −0.566478 + 0.443637i
\(707\) 0.189980 0.458651i 0.00714492 0.0172494i
\(708\) 0 0
\(709\) −8.62991 + 3.57463i −0.324103 + 0.134248i −0.538802 0.842432i \(-0.681123\pi\)
0.214699 + 0.976680i \(0.431123\pi\)
\(710\) −4.31546 15.4914i −0.161956 0.581382i
\(711\) 0 0
\(712\) −29.8505 11.3398i −1.11870 0.424977i
\(713\) −40.8339 40.8339i −1.52924 1.52924i
\(714\) 0 0
\(715\) 45.3727 + 109.539i 1.69684 + 4.09654i
\(716\) −0.218094 + 0.296167i −0.00815054 + 0.0110683i
\(717\) 0 0
\(718\) 3.44608 28.3371i 0.128607 1.05753i
\(719\) 27.2259i 1.01535i −0.861547 0.507677i \(-0.830504\pi\)
0.861547 0.507677i \(-0.169496\pi\)
\(720\) 0 0
\(721\) 1.76525i 0.0657414i
\(722\) 26.6427 + 3.24003i 0.991539 + 0.120581i
\(723\) 0 0
\(724\) 9.22506 1.40053i 0.342847 0.0520502i
\(725\) −0.844623 2.03910i −0.0313685 0.0757303i
\(726\) 0 0
\(727\) 14.7795 + 14.7795i 0.548142 + 0.548142i 0.925903 0.377761i \(-0.123306\pi\)
−0.377761 + 0.925903i \(0.623306\pi\)
\(728\) 1.90711 + 1.79724i 0.0706822 + 0.0666101i
\(729\) 0 0
\(730\) 27.5313 7.66943i 1.01898 0.283858i
\(731\) −8.33400 + 3.45206i −0.308244 + 0.127679i
\(732\) 0 0
\(733\) 9.31269 22.4828i 0.343972 0.830422i −0.653334 0.757070i \(-0.726630\pi\)
0.997306 0.0733521i \(-0.0233697\pi\)
\(734\) −16.7436 21.3798i −0.618018 0.789143i
\(735\) 0 0
\(736\) 30.3447 + 20.9870i 1.11852 + 0.773591i
\(737\) 47.2475 1.74038
\(738\) 0 0
\(739\) −0.759150 + 1.83275i −0.0279258 + 0.0674188i −0.937227 0.348719i \(-0.886617\pi\)
0.909301 + 0.416138i \(0.136617\pi\)
\(740\) −14.8621 24.6055i −0.546341 0.904516i
\(741\) 0 0
\(742\) −1.92835 + 0.537182i −0.0707919 + 0.0197206i
\(743\) −3.29885 + 3.29885i −0.121023 + 0.121023i −0.765024 0.644001i \(-0.777273\pi\)
0.644001 + 0.765024i \(0.277273\pi\)
\(744\) 0 0
\(745\) −21.2676 21.2676i −0.779184 0.779184i
\(746\) 28.0993 + 15.8549i 1.02879 + 0.580490i
\(747\) 0 0
\(748\) −4.26248 28.0763i −0.155852 1.02657i
\(749\) 0.476797 + 0.197496i 0.0174218 + 0.00721634i
\(750\) 0 0
\(751\) 53.4430i 1.95016i −0.221850 0.975081i \(-0.571209\pi\)
0.221850 0.975081i \(-0.428791\pi\)
\(752\) 12.2541 23.3061i 0.446860 0.849887i
\(753\) 0 0
\(754\) −0.659901 + 5.42636i −0.0240322 + 0.197616i
\(755\) −30.7396 12.7328i −1.11873 0.463393i
\(756\) 0 0
\(757\) −0.204624 0.494007i −0.00743720 0.0179550i 0.920117 0.391643i \(-0.128093\pi\)
−0.927555 + 0.373688i \(0.878093\pi\)
\(758\) 13.3895 23.7298i 0.486327 0.861906i
\(759\) 0 0
\(760\) 0.503814 + 1.12109i 0.0182753 + 0.0406664i
\(761\) 27.0608 27.0608i 0.980952 0.980952i −0.0188700 0.999822i \(-0.506007\pi\)
0.999822 + 0.0188700i \(0.00600687\pi\)
\(762\) 0 0
\(763\) 2.31323 0.958170i 0.0837444 0.0346881i
\(764\) 9.80136 39.7023i 0.354601 1.43638i
\(765\) 0 0
\(766\) 10.3520 8.10718i 0.374033 0.292924i
\(767\) 28.5938 1.03246
\(768\) 0 0
\(769\) −42.1236 −1.51901 −0.759507 0.650499i \(-0.774560\pi\)
−0.759507 + 0.650499i \(0.774560\pi\)
\(770\) −3.07983 + 2.41197i −0.110989 + 0.0869215i
\(771\) 0 0
\(772\) −2.62296 + 10.6248i −0.0944024 + 0.382395i
\(773\) −2.05352 + 0.850597i −0.0738601 + 0.0305939i −0.419308 0.907844i \(-0.637727\pi\)
0.345448 + 0.938438i \(0.387727\pi\)
\(774\) 0 0
\(775\) −22.5284 + 22.5284i −0.809243 + 0.809243i
\(776\) −18.7687 41.7645i −0.673758 1.49926i
\(777\) 0 0
\(778\) 15.6098 27.6649i 0.559639 0.991834i
\(779\) −0.294265 0.710418i −0.0105431 0.0254534i
\(780\) 0 0
\(781\) −22.9878 9.52187i −0.822569 0.340719i
\(782\) 2.46413 20.2625i 0.0881172 0.724587i
\(783\) 0 0
\(784\) 12.9904 24.7066i 0.463943 0.882378i
\(785\) 4.44458i 0.158634i
\(786\) 0 0
\(787\) 32.6127 + 13.5086i 1.16252 + 0.481530i 0.878712 0.477352i \(-0.158403\pi\)
0.283804 + 0.958882i \(0.408403\pi\)
\(788\) −1.29956 8.56002i −0.0462950 0.304938i