Properties

Label 864.2.w.a.107.13
Level $864$
Weight $2$
Character 864.107
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.w (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 107.13
Character \(\chi\) \(=\) 864.107
Dual form 864.2.w.a.323.13

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.394008 - 1.35822i) q^{2} +(-1.68952 + 1.07030i) q^{4} +(-2.44724 - 1.01368i) q^{5} +(3.38875 - 3.38875i) q^{7} +(2.11938 + 1.87302i) q^{8} +O(q^{10})\) \(q+(-0.394008 - 1.35822i) q^{2} +(-1.68952 + 1.07030i) q^{4} +(-2.44724 - 1.01368i) q^{5} +(3.38875 - 3.38875i) q^{7} +(2.11938 + 1.87302i) q^{8} +(-0.412566 + 3.72328i) q^{10} +(4.19398 + 1.73720i) q^{11} +(2.12813 + 5.13777i) q^{13} +(-5.93786 - 3.26747i) q^{14} +(1.70892 - 3.61657i) q^{16} -3.78123 q^{17} +(6.01757 - 2.49256i) q^{19} +(5.21959 - 0.906648i) q^{20} +(0.707039 - 6.38081i) q^{22} +(0.521933 - 0.521933i) q^{23} +(1.42590 + 1.42590i) q^{25} +(6.13971 - 4.91479i) q^{26} +(-2.09837 + 9.35232i) q^{28} +(-1.96141 - 4.73526i) q^{29} -2.30887i q^{31} +(-5.58542 - 0.896134i) q^{32} +(1.48984 + 5.13574i) q^{34} +(-11.7282 + 4.85798i) q^{35} +(0.301775 - 0.728548i) q^{37} +(-5.75641 - 7.19109i) q^{38} +(-3.28799 - 6.73211i) q^{40} +(5.11319 + 5.11319i) q^{41} +(-1.04025 + 2.51140i) q^{43} +(-8.94511 + 1.55378i) q^{44} +(-0.914544 - 0.503253i) q^{46} -6.05530i q^{47} -15.9673i q^{49} +(1.37487 - 2.49850i) q^{50} +(-9.09446 - 6.40260i) q^{52} +(3.39385 - 8.19348i) q^{53} +(-8.50270 - 8.50270i) q^{55} +(13.5293 - 0.834842i) q^{56} +(-5.65871 + 4.52976i) q^{58} +(3.61257 - 8.72153i) q^{59} +(-0.171884 + 0.0711965i) q^{61} +(-3.13594 + 0.909712i) q^{62} +(0.983556 + 7.93931i) q^{64} -14.7306i q^{65} +(0.155362 + 0.375078i) q^{67} +(6.38845 - 4.04705i) q^{68} +(11.2192 + 14.0154i) q^{70} +(-4.96412 - 4.96412i) q^{71} +(-1.96331 + 1.96331i) q^{73} +(-1.10843 - 0.122822i) q^{74} +(-7.49899 + 10.6518i) q^{76} +(20.0993 - 8.32540i) q^{77} -8.19131 q^{79} +(-7.84819 + 7.11831i) q^{80} +(4.93019 - 8.95946i) q^{82} +(4.85181 + 11.7133i) q^{83} +(9.25358 + 3.83296i) q^{85} +(3.82089 + 0.423382i) q^{86} +(5.63482 + 11.5372i) q^{88} +(-6.59205 + 6.59205i) q^{89} +(24.6223 + 10.1989i) q^{91} +(-0.323190 + 1.44044i) q^{92} +(-8.22442 + 2.38584i) q^{94} -17.2531 q^{95} -6.02797 q^{97} +(-21.6870 + 6.29123i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q+O(q^{10}) \) Copy content Toggle raw display \( 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.394008 1.35822i −0.278606 0.960406i
\(3\) 0 0
\(4\) −1.68952 + 1.07030i −0.844758 + 0.535149i
\(5\) −2.44724 1.01368i −1.09444 0.453331i −0.238886 0.971048i \(-0.576782\pi\)
−0.855552 + 0.517716i \(0.826782\pi\)
\(6\) 0 0
\(7\) 3.38875 3.38875i 1.28083 1.28083i 0.340630 0.940197i \(-0.389360\pi\)
0.940197 0.340630i \(-0.110640\pi\)
\(8\) 2.11938 + 1.87302i 0.749315 + 0.662214i
\(9\) 0 0
\(10\) −0.412566 + 3.72328i −0.130465 + 1.17741i
\(11\) 4.19398 + 1.73720i 1.26453 + 0.523786i 0.911297 0.411749i \(-0.135082\pi\)
0.353234 + 0.935535i \(0.385082\pi\)
\(12\) 0 0
\(13\) 2.12813 + 5.13777i 0.590238 + 1.42496i 0.883273 + 0.468859i \(0.155335\pi\)
−0.293035 + 0.956102i \(0.594665\pi\)
\(14\) −5.93786 3.26747i −1.58696 0.873268i
\(15\) 0 0
\(16\) 1.70892 3.61657i 0.427231 0.904143i
\(17\) −3.78123 −0.917084 −0.458542 0.888673i \(-0.651628\pi\)
−0.458542 + 0.888673i \(0.651628\pi\)
\(18\) 0 0
\(19\) 6.01757 2.49256i 1.38053 0.571832i 0.435903 0.899993i \(-0.356429\pi\)
0.944622 + 0.328161i \(0.106429\pi\)
\(20\) 5.21959 0.906648i 1.16714 0.202733i
\(21\) 0 0
\(22\) 0.707039 6.38081i 0.150741 1.36039i
\(23\) 0.521933 0.521933i 0.108830 0.108830i −0.650595 0.759425i \(-0.725480\pi\)
0.759425 + 0.650595i \(0.225480\pi\)
\(24\) 0 0
\(25\) 1.42590 + 1.42590i 0.285180 + 0.285180i
\(26\) 6.13971 4.91479i 1.20410 0.963871i
\(27\) 0 0
\(28\) −2.09837 + 9.35232i −0.396555 + 1.76742i
\(29\) −1.96141 4.73526i −0.364225 0.879316i −0.994673 0.103085i \(-0.967129\pi\)
0.630448 0.776232i \(-0.282871\pi\)
\(30\) 0 0
\(31\) 2.30887i 0.414684i −0.978268 0.207342i \(-0.933519\pi\)
0.978268 0.207342i \(-0.0664814\pi\)
\(32\) −5.58542 0.896134i −0.987373 0.158416i
\(33\) 0 0
\(34\) 1.48984 + 5.13574i 0.255505 + 0.880773i
\(35\) −11.7282 + 4.85798i −1.98243 + 0.821148i
\(36\) 0 0
\(37\) 0.301775 0.728548i 0.0496114 0.119773i −0.897131 0.441765i \(-0.854353\pi\)
0.946742 + 0.321992i \(0.104353\pi\)
\(38\) −5.75641 7.19109i −0.933813 1.16655i
\(39\) 0 0
\(40\) −3.28799 6.73211i −0.519876 1.06444i
\(41\) 5.11319 + 5.11319i 0.798546 + 0.798546i 0.982866 0.184321i \(-0.0590084\pi\)
−0.184321 + 0.982866i \(0.559008\pi\)
\(42\) 0 0
\(43\) −1.04025 + 2.51140i −0.158637 + 0.382984i −0.983135 0.182881i \(-0.941458\pi\)
0.824498 + 0.565865i \(0.191458\pi\)
\(44\) −8.94511 + 1.55378i −1.34853 + 0.234241i
\(45\) 0 0
\(46\) −0.914544 0.503253i −0.134842 0.0742006i
\(47\) 6.05530i 0.883256i −0.897198 0.441628i \(-0.854401\pi\)
0.897198 0.441628i \(-0.145599\pi\)
\(48\) 0 0
\(49\) 15.9673i 2.28104i
\(50\) 1.37487 2.49850i 0.194436 0.353341i
\(51\) 0 0
\(52\) −9.09446 6.40260i −1.26117 0.887881i
\(53\) 3.39385 8.19348i 0.466181 1.12546i −0.499635 0.866236i \(-0.666533\pi\)
0.965817 0.259226i \(-0.0834673\pi\)
\(54\) 0 0
\(55\) −8.50270 8.50270i −1.14650 1.14650i
\(56\) 13.5293 0.834842i 1.80792 0.111560i
\(57\) 0 0
\(58\) −5.65871 + 4.52976i −0.743025 + 0.594786i
\(59\) 3.61257 8.72153i 0.470317 1.13545i −0.493706 0.869629i \(-0.664358\pi\)
0.964023 0.265817i \(-0.0856418\pi\)
\(60\) 0 0
\(61\) −0.171884 + 0.0711965i −0.0220074 + 0.00911578i −0.393660 0.919256i \(-0.628791\pi\)
0.371653 + 0.928372i \(0.378791\pi\)
\(62\) −3.13594 + 0.909712i −0.398265 + 0.115533i
\(63\) 0 0
\(64\) 0.983556 + 7.93931i 0.122945 + 0.992414i
\(65\) 14.7306i 1.82711i
\(66\) 0 0
\(67\) 0.155362 + 0.375078i 0.0189805 + 0.0458231i 0.933086 0.359654i \(-0.117105\pi\)
−0.914105 + 0.405477i \(0.867105\pi\)
\(68\) 6.38845 4.04705i 0.774714 0.490777i
\(69\) 0 0
\(70\) 11.2192 + 14.0154i 1.34095 + 1.67516i
\(71\) −4.96412 4.96412i −0.589132 0.589132i 0.348264 0.937396i \(-0.386771\pi\)
−0.937396 + 0.348264i \(0.886771\pi\)
\(72\) 0 0
\(73\) −1.96331 + 1.96331i −0.229788 + 0.229788i −0.812604 0.582816i \(-0.801951\pi\)
0.582816 + 0.812604i \(0.301951\pi\)
\(74\) −1.10843 0.122822i −0.128852 0.0142778i
\(75\) 0 0
\(76\) −7.49899 + 10.6518i −0.860194 + 1.22185i
\(77\) 20.0993 8.32540i 2.29053 0.948767i
\(78\) 0 0
\(79\) −8.19131 −0.921594 −0.460797 0.887505i \(-0.652436\pi\)
−0.460797 + 0.887505i \(0.652436\pi\)
\(80\) −7.84819 + 7.11831i −0.877454 + 0.795851i
\(81\) 0 0
\(82\) 4.93019 8.95946i 0.544448 0.989407i
\(83\) 4.85181 + 11.7133i 0.532555 + 1.28570i 0.929826 + 0.368000i \(0.119957\pi\)
−0.397271 + 0.917701i \(0.630043\pi\)
\(84\) 0 0
\(85\) 9.25358 + 3.83296i 1.00369 + 0.415743i
\(86\) 3.82089 + 0.423382i 0.412017 + 0.0456545i
\(87\) 0 0
\(88\) 5.63482 + 11.5372i 0.600673 + 1.22987i
\(89\) −6.59205 + 6.59205i −0.698756 + 0.698756i −0.964142 0.265386i \(-0.914501\pi\)
0.265386 + 0.964142i \(0.414501\pi\)
\(90\) 0 0
\(91\) 24.6223 + 10.1989i 2.58112 + 1.06914i
\(92\) −0.323190 + 1.44044i −0.0336948 + 0.150176i
\(93\) 0 0
\(94\) −8.22442 + 2.38584i −0.848284 + 0.246080i
\(95\) −17.2531 −1.77013
\(96\) 0 0
\(97\) −6.02797 −0.612048 −0.306024 0.952024i \(-0.598999\pi\)
−0.306024 + 0.952024i \(0.598999\pi\)
\(98\) −21.6870 + 6.29123i −2.19072 + 0.635510i
\(99\) 0 0
\(100\) −3.93522 0.882941i −0.393522 0.0882941i
\(101\) 1.74724 + 0.723731i 0.173857 + 0.0720140i 0.467914 0.883774i \(-0.345006\pi\)
−0.294057 + 0.955788i \(0.595006\pi\)
\(102\) 0 0
\(103\) 5.68112 5.68112i 0.559777 0.559777i −0.369467 0.929244i \(-0.620460\pi\)
0.929244 + 0.369467i \(0.120460\pi\)
\(104\) −5.11284 + 14.8749i −0.501356 + 1.45861i
\(105\) 0 0
\(106\) −12.4657 1.38129i −1.21078 0.134163i
\(107\) 11.3023 + 4.68159i 1.09264 + 0.452586i 0.854926 0.518749i \(-0.173602\pi\)
0.237713 + 0.971335i \(0.423602\pi\)
\(108\) 0 0
\(109\) −2.63231 6.35496i −0.252130 0.608695i 0.746246 0.665670i \(-0.231854\pi\)
−0.998376 + 0.0569753i \(0.981854\pi\)
\(110\) −8.19839 + 14.8987i −0.781686 + 1.42053i
\(111\) 0 0
\(112\) −6.46454 18.0468i −0.610842 1.70526i
\(113\) 16.8015 1.58055 0.790276 0.612751i \(-0.209937\pi\)
0.790276 + 0.612751i \(0.209937\pi\)
\(114\) 0 0
\(115\) −1.80637 + 0.748222i −0.168445 + 0.0697720i
\(116\) 8.38198 + 5.90101i 0.778247 + 0.547895i
\(117\) 0 0
\(118\) −13.2691 1.47031i −1.22152 0.135353i
\(119\) −12.8137 + 12.8137i −1.17463 + 1.17463i
\(120\) 0 0
\(121\) 6.79340 + 6.79340i 0.617582 + 0.617582i
\(122\) 0.164424 + 0.205403i 0.0148862 + 0.0185964i
\(123\) 0 0
\(124\) 2.47117 + 3.90086i 0.221918 + 0.350308i
\(125\) 3.02429 + 7.30128i 0.270500 + 0.653046i
\(126\) 0 0
\(127\) 9.50016i 0.843003i 0.906828 + 0.421501i \(0.138497\pi\)
−0.906828 + 0.421501i \(0.861503\pi\)
\(128\) 10.3958 4.46404i 0.918866 0.394569i
\(129\) 0 0
\(130\) −20.0074 + 5.80398i −1.75476 + 0.509042i
\(131\) −19.3884 + 8.03093i −1.69397 + 0.701666i −0.999835 0.0181772i \(-0.994214\pi\)
−0.694137 + 0.719843i \(0.744214\pi\)
\(132\) 0 0
\(133\) 11.9454 28.8387i 1.03580 2.50063i
\(134\) 0.448224 0.358800i 0.0387206 0.0309956i
\(135\) 0 0
\(136\) −8.01388 7.08235i −0.687184 0.607306i
\(137\) −10.5560 10.5560i −0.901864 0.901864i 0.0937337 0.995597i \(-0.470120\pi\)
−0.995597 + 0.0937337i \(0.970120\pi\)
\(138\) 0 0
\(139\) −0.124526 + 0.300633i −0.0105622 + 0.0254994i −0.929073 0.369897i \(-0.879393\pi\)
0.918510 + 0.395397i \(0.129393\pi\)
\(140\) 14.6155 20.7603i 1.23523 1.75456i
\(141\) 0 0
\(142\) −4.78645 + 8.69826i −0.401670 + 0.729942i
\(143\) 25.2447i 2.11107i
\(144\) 0 0
\(145\) 13.5766i 1.12747i
\(146\) 3.44017 + 1.89305i 0.284710 + 0.156670i
\(147\) 0 0
\(148\) 0.269911 + 1.55388i 0.0221866 + 0.127728i
\(149\) −2.37298 + 5.72888i −0.194402 + 0.469328i −0.990782 0.135469i \(-0.956746\pi\)
0.796380 + 0.604797i \(0.206746\pi\)
\(150\) 0 0
\(151\) −9.09870 9.09870i −0.740442 0.740442i 0.232221 0.972663i \(-0.425401\pi\)
−0.972663 + 0.232221i \(0.925401\pi\)
\(152\) 17.4222 + 5.98837i 1.41312 + 0.485721i
\(153\) 0 0
\(154\) −19.2270 24.0190i −1.54936 1.93550i
\(155\) −2.34045 + 5.65035i −0.187989 + 0.453847i
\(156\) 0 0
\(157\) 14.6827 6.08178i 1.17181 0.485379i 0.290018 0.957021i \(-0.406339\pi\)
0.881790 + 0.471642i \(0.156339\pi\)
\(158\) 3.22744 + 11.1256i 0.256762 + 0.885104i
\(159\) 0 0
\(160\) 12.7605 + 7.85488i 1.00880 + 0.620983i
\(161\) 3.53740i 0.278786i
\(162\) 0 0
\(163\) 2.81351 + 6.79241i 0.220371 + 0.532023i 0.994940 0.100466i \(-0.0320334\pi\)
−0.774569 + 0.632489i \(0.782033\pi\)
\(164\) −14.1114 3.16617i −1.10192 0.247237i
\(165\) 0 0
\(166\) 13.9976 11.2049i 1.08642 0.869673i
\(167\) 10.4693 + 10.4693i 0.810140 + 0.810140i 0.984655 0.174515i \(-0.0558356\pi\)
−0.174515 + 0.984655i \(0.555836\pi\)
\(168\) 0 0
\(169\) −12.6753 + 12.6753i −0.975026 + 0.975026i
\(170\) 1.56001 14.0786i 0.119647 1.07978i
\(171\) 0 0
\(172\) −0.930417 5.35642i −0.0709436 0.408423i
\(173\) 14.7918 6.12697i 1.12460 0.465825i 0.258658 0.965969i \(-0.416720\pi\)
0.865942 + 0.500144i \(0.166720\pi\)
\(174\) 0 0
\(175\) 9.66403 0.730532
\(176\) 13.4499 12.1991i 1.01382 0.919539i
\(177\) 0 0
\(178\) 11.5508 + 6.35612i 0.865766 + 0.476412i
\(179\) 2.32212 + 5.60609i 0.173563 + 0.419019i 0.986592 0.163204i \(-0.0521830\pi\)
−0.813029 + 0.582223i \(0.802183\pi\)
\(180\) 0 0
\(181\) 9.25503 + 3.83356i 0.687921 + 0.284946i 0.699134 0.714991i \(-0.253569\pi\)
−0.0112129 + 0.999937i \(0.503569\pi\)
\(182\) 4.15094 37.4610i 0.307688 2.77679i
\(183\) 0 0
\(184\) 2.08377 0.128582i 0.153617 0.00947916i
\(185\) −1.47703 + 1.47703i −0.108593 + 0.108593i
\(186\) 0 0
\(187\) −15.8584 6.56877i −1.15968 0.480356i
\(188\) 6.48098 + 10.2305i 0.472674 + 0.746137i
\(189\) 0 0
\(190\) 6.79786 + 23.4335i 0.493168 + 1.70004i
\(191\) 7.97826 0.577287 0.288643 0.957437i \(-0.406796\pi\)
0.288643 + 0.957437i \(0.406796\pi\)
\(192\) 0 0
\(193\) −11.9488 −0.860091 −0.430045 0.902807i \(-0.641502\pi\)
−0.430045 + 0.902807i \(0.641502\pi\)
\(194\) 2.37507 + 8.18731i 0.170520 + 0.587814i
\(195\) 0 0
\(196\) 17.0897 + 26.9769i 1.22070 + 1.92692i
\(197\) −4.88423 2.02312i −0.347987 0.144141i 0.201842 0.979418i \(-0.435307\pi\)
−0.549829 + 0.835277i \(0.685307\pi\)
\(198\) 0 0
\(199\) 15.8193 15.8193i 1.12140 1.12140i 0.129871 0.991531i \(-0.458544\pi\)
0.991531 0.129871i \(-0.0414563\pi\)
\(200\) 0.351280 + 5.69277i 0.0248392 + 0.402539i
\(201\) 0 0
\(202\) 0.294558 2.65829i 0.0207250 0.187037i
\(203\) −22.6934 9.39990i −1.59276 0.659743i
\(204\) 0 0
\(205\) −7.33006 17.6963i −0.511953 1.23596i
\(206\) −9.95461 5.47779i −0.693570 0.381656i
\(207\) 0 0
\(208\) 22.2179 + 1.08351i 1.54054 + 0.0751279i
\(209\) 29.5676 2.04524
\(210\) 0 0
\(211\) −25.3944 + 10.5187i −1.74823 + 0.724139i −0.750207 + 0.661202i \(0.770046\pi\)
−0.998018 + 0.0629360i \(0.979954\pi\)
\(212\) 3.03551 + 17.4754i 0.208479 + 1.20022i
\(213\) 0 0
\(214\) 1.90540 17.1956i 0.130250 1.17547i
\(215\) 5.09150 5.09150i 0.347237 0.347237i
\(216\) 0 0
\(217\) −7.82417 7.82417i −0.531139 0.531139i
\(218\) −7.59428 + 6.07916i −0.514349 + 0.411733i
\(219\) 0 0
\(220\) 23.4659 + 5.26502i 1.58207 + 0.354967i
\(221\) −8.04697 19.4271i −0.541298 1.30681i
\(222\) 0 0
\(223\) 11.8736i 0.795117i −0.917577 0.397558i \(-0.869858\pi\)
0.917577 0.397558i \(-0.130142\pi\)
\(224\) −21.9644 + 15.8908i −1.46756 + 1.06175i
\(225\) 0 0
\(226\) −6.61992 22.8201i −0.440351 1.51797i
\(227\) 16.0487 6.64758i 1.06519 0.441215i 0.219898 0.975523i \(-0.429428\pi\)
0.845290 + 0.534308i \(0.179428\pi\)
\(228\) 0 0
\(229\) −0.190035 + 0.458786i −0.0125579 + 0.0303174i −0.930034 0.367473i \(-0.880223\pi\)
0.917476 + 0.397791i \(0.130223\pi\)
\(230\) 1.72797 + 2.15864i 0.113939 + 0.142336i
\(231\) 0 0
\(232\) 4.71229 13.7096i 0.309377 0.900079i
\(233\) −4.46281 4.46281i −0.292369 0.292369i 0.545647 0.838015i \(-0.316284\pi\)
−0.838015 + 0.545647i \(0.816284\pi\)
\(234\) 0 0
\(235\) −6.13813 + 14.8188i −0.400408 + 0.966670i
\(236\) 3.23113 + 18.6017i 0.210329 + 1.21087i
\(237\) 0 0
\(238\) 22.4524 + 12.3551i 1.45538 + 0.800860i
\(239\) 8.12218i 0.525380i 0.964880 + 0.262690i \(0.0846096\pi\)
−0.964880 + 0.262690i \(0.915390\pi\)
\(240\) 0 0
\(241\) 3.91627i 0.252269i 0.992013 + 0.126135i \(0.0402571\pi\)
−0.992013 + 0.126135i \(0.959743\pi\)
\(242\) 6.55027 11.9036i 0.421067 0.765191i
\(243\) 0 0
\(244\) 0.214198 0.304254i 0.0137126 0.0194779i
\(245\) −16.1857 + 39.0757i −1.03407 + 2.49646i
\(246\) 0 0
\(247\) 25.6124 + 25.6124i 1.62968 + 1.62968i
\(248\) 4.32456 4.89337i 0.274610 0.310729i
\(249\) 0 0
\(250\) 8.72513 6.98440i 0.551826 0.441733i
\(251\) 3.33165 8.04332i 0.210292 0.507690i −0.783176 0.621800i \(-0.786402\pi\)
0.993468 + 0.114110i \(0.0364017\pi\)
\(252\) 0 0
\(253\) 3.09568 1.28227i 0.194624 0.0806157i
\(254\) 12.9033 3.74314i 0.809625 0.234865i
\(255\) 0 0
\(256\) −10.1592 12.3609i −0.634948 0.772555i
\(257\) 4.79986i 0.299407i 0.988731 + 0.149704i \(0.0478319\pi\)
−0.988731 + 0.149704i \(0.952168\pi\)
\(258\) 0 0
\(259\) −1.44623 3.49151i −0.0898643 0.216952i
\(260\) 15.7661 + 24.8876i 0.977774 + 1.54346i
\(261\) 0 0
\(262\) 18.5469 + 23.1694i 1.14583 + 1.43141i
\(263\) −6.41988 6.41988i −0.395867 0.395867i 0.480906 0.876772i \(-0.340308\pi\)
−0.876772 + 0.480906i \(0.840308\pi\)
\(264\) 0 0
\(265\) −16.6111 + 16.6111i −1.02041 + 1.02041i
\(266\) −43.8758 4.86176i −2.69020 0.298093i
\(267\) 0 0
\(268\) −0.663932 0.467416i −0.0405561 0.0285520i
\(269\) −24.9505 + 10.3349i −1.52126 + 0.630127i −0.977844 0.209335i \(-0.932870\pi\)
−0.543418 + 0.839462i \(0.682870\pi\)
\(270\) 0 0
\(271\) −13.2069 −0.802264 −0.401132 0.916020i \(-0.631383\pi\)
−0.401132 + 0.916020i \(0.631383\pi\)
\(272\) −6.46184 + 13.6751i −0.391807 + 0.829175i
\(273\) 0 0
\(274\) −10.1782 + 18.4966i −0.614890 + 1.11742i
\(275\) 3.50311 + 8.45726i 0.211246 + 0.509992i
\(276\) 0 0
\(277\) 24.2560 + 10.0471i 1.45740 + 0.603675i 0.963946 0.266098i \(-0.0857344\pi\)
0.493453 + 0.869772i \(0.335734\pi\)
\(278\) 0.457390 + 0.0506821i 0.0274324 + 0.00303971i
\(279\) 0 0
\(280\) −33.9556 11.6713i −2.02924 0.697493i
\(281\) 4.07978 4.07978i 0.243379 0.243379i −0.574867 0.818247i \(-0.694946\pi\)
0.818247 + 0.574867i \(0.194946\pi\)
\(282\) 0 0
\(283\) 22.5628 + 9.34580i 1.34122 + 0.555550i 0.933834 0.357707i \(-0.116441\pi\)
0.407383 + 0.913257i \(0.366441\pi\)
\(284\) 13.7000 + 3.07387i 0.812948 + 0.182400i
\(285\) 0 0
\(286\) 34.2878 9.94661i 2.02748 0.588156i
\(287\) 34.6546 2.04560
\(288\) 0 0
\(289\) −2.70227 −0.158957
\(290\) 18.4399 5.34928i 1.08283 0.314120i
\(291\) 0 0
\(292\) 1.21572 5.41837i 0.0711444 0.317086i
\(293\) 18.8574 + 7.81101i 1.10166 + 0.456324i 0.858059 0.513551i \(-0.171670\pi\)
0.243604 + 0.969875i \(0.421670\pi\)
\(294\) 0 0
\(295\) −17.6817 + 17.6817i −1.02947 + 1.02947i
\(296\) 2.00416 0.978841i 0.116490 0.0568940i
\(297\) 0 0
\(298\) 8.71604 + 0.965800i 0.504907 + 0.0559473i
\(299\) 3.79231 + 1.57083i 0.219315 + 0.0908433i
\(300\) 0 0
\(301\) 4.98533 + 12.0357i 0.287350 + 0.693724i
\(302\) −8.77306 + 15.9430i −0.504833 + 0.917416i
\(303\) 0 0
\(304\) 1.26905 26.0226i 0.0727851 1.49250i
\(305\) 0.492811 0.0282182
\(306\) 0 0
\(307\) −8.73142 + 3.61667i −0.498328 + 0.206414i −0.617668 0.786439i \(-0.711922\pi\)
0.119339 + 0.992854i \(0.461922\pi\)
\(308\) −25.0474 + 35.5781i −1.42721 + 2.02725i
\(309\) 0 0
\(310\) 8.59656 + 0.952560i 0.488252 + 0.0541018i
\(311\) −1.57810 + 1.57810i −0.0894860 + 0.0894860i −0.750433 0.660947i \(-0.770155\pi\)
0.660947 + 0.750433i \(0.270155\pi\)
\(312\) 0 0
\(313\) −11.4730 11.4730i −0.648492 0.648492i 0.304137 0.952628i \(-0.401632\pi\)
−0.952628 + 0.304137i \(0.901632\pi\)
\(314\) −14.0455 17.5461i −0.792633 0.990182i
\(315\) 0 0
\(316\) 13.8393 8.76714i 0.778524 0.493190i
\(317\) −9.79160 23.6390i −0.549951 1.32770i −0.917515 0.397701i \(-0.869808\pi\)
0.367564 0.929998i \(-0.380192\pi\)
\(318\) 0 0
\(319\) 23.2670i 1.30270i
\(320\) 5.64092 20.4264i 0.315337 1.14187i
\(321\) 0 0
\(322\) −4.80456 + 1.39376i −0.267748 + 0.0776714i
\(323\) −22.7538 + 9.42495i −1.26606 + 0.524418i
\(324\) 0 0
\(325\) −4.29144 + 10.3604i −0.238046 + 0.574694i
\(326\) 8.11703 6.49762i 0.449561 0.359870i
\(327\) 0 0
\(328\) 1.25967 + 20.4139i 0.0695535 + 1.12717i
\(329\) −20.5199 20.5199i −1.13130 1.13130i
\(330\) 0 0
\(331\) 0.460135 1.11086i 0.0252913 0.0610586i −0.910729 0.413004i \(-0.864480\pi\)
0.936021 + 0.351945i \(0.114480\pi\)
\(332\) −20.7339 14.5969i −1.13792 0.801110i
\(333\) 0 0
\(334\) 10.0946 18.3446i 0.552353 1.00377i
\(335\) 1.07539i 0.0587550i
\(336\) 0 0
\(337\) 28.2686i 1.53989i 0.638110 + 0.769945i \(0.279716\pi\)
−0.638110 + 0.769945i \(0.720284\pi\)
\(338\) 22.2101 + 12.2217i 1.20807 + 0.664773i
\(339\) 0 0
\(340\) −19.7365 + 3.42825i −1.07036 + 0.185923i
\(341\) 4.01097 9.68333i 0.217206 0.524382i
\(342\) 0 0
\(343\) −30.3878 30.3878i −1.64079 1.64079i
\(344\) −6.90860 + 3.37418i −0.372487 + 0.181924i
\(345\) 0 0
\(346\) −14.1498 17.6764i −0.760701 0.950291i
\(347\) −3.19400 + 7.71101i −0.171463 + 0.413949i −0.986129 0.165982i \(-0.946920\pi\)
0.814666 + 0.579931i \(0.196920\pi\)
\(348\) 0 0
\(349\) −15.0741 + 6.24391i −0.806900 + 0.334229i −0.747716 0.664018i \(-0.768850\pi\)
−0.0591837 + 0.998247i \(0.518850\pi\)
\(350\) −3.80771 13.1259i −0.203531 0.701607i
\(351\) 0 0
\(352\) −21.8684 13.4614i −1.16559 0.717494i
\(353\) 25.0652i 1.33409i 0.745019 + 0.667043i \(0.232440\pi\)
−0.745019 + 0.667043i \(0.767560\pi\)
\(354\) 0 0
\(355\) 7.11636 + 17.1804i 0.377697 + 0.911841i
\(356\) 4.08191 18.1928i 0.216341 0.964218i
\(357\) 0 0
\(358\) 6.69936 5.36279i 0.354072 0.283432i
\(359\) −12.3171 12.3171i −0.650069 0.650069i 0.302940 0.953010i \(-0.402032\pi\)
−0.953010 + 0.302940i \(0.902032\pi\)
\(360\) 0 0
\(361\) 16.5633 16.5633i 0.871751 0.871751i
\(362\) 1.56025 14.0808i 0.0820051 0.740070i
\(363\) 0 0
\(364\) −52.5157 + 9.12204i −2.75257 + 0.478125i
\(365\) 6.79486 2.81452i 0.355659 0.147319i
\(366\) 0 0
\(367\) 1.24387 0.0649297 0.0324649 0.999473i \(-0.489664\pi\)
0.0324649 + 0.999473i \(0.489664\pi\)
\(368\) −0.995663 2.77955i −0.0519025 0.144894i
\(369\) 0 0
\(370\) 2.58809 + 1.42417i 0.134548 + 0.0740389i
\(371\) −16.2648 39.2666i −0.844424 2.03862i
\(372\) 0 0
\(373\) −14.2613 5.90724i −0.738424 0.305865i −0.0184154 0.999830i \(-0.505862\pi\)
−0.720009 + 0.693965i \(0.755862\pi\)
\(374\) −2.67348 + 24.1273i −0.138242 + 1.24759i
\(375\) 0 0
\(376\) 11.3417 12.8335i 0.584905 0.661837i
\(377\) 20.1546 20.1546i 1.03801 1.03801i
\(378\) 0 0
\(379\) −6.21100 2.57268i −0.319037 0.132150i 0.217417 0.976079i \(-0.430237\pi\)
−0.536455 + 0.843929i \(0.680237\pi\)
\(380\) 29.1494 18.4659i 1.49533 0.947283i
\(381\) 0 0
\(382\) −3.14350 10.8362i −0.160835 0.554429i
\(383\) 13.6072 0.695296 0.347648 0.937625i \(-0.386980\pi\)
0.347648 + 0.937625i \(0.386980\pi\)
\(384\) 0 0
\(385\) −57.6271 −2.93695
\(386\) 4.70791 + 16.2290i 0.239626 + 0.826036i
\(387\) 0 0
\(388\) 10.1844 6.45173i 0.517032 0.327537i
\(389\) 2.68660 + 1.11283i 0.136216 + 0.0564226i 0.449750 0.893154i \(-0.351513\pi\)
−0.313534 + 0.949577i \(0.601513\pi\)
\(390\) 0 0
\(391\) −1.97355 + 1.97355i −0.0998067 + 0.0998067i
\(392\) 29.9071 33.8407i 1.51054 1.70921i
\(393\) 0 0
\(394\) −0.823406 + 7.43098i −0.0414826 + 0.374367i
\(395\) 20.0461 + 8.30336i 1.00863 + 0.417788i
\(396\) 0 0
\(397\) 2.81875 + 6.80507i 0.141469 + 0.341537i 0.978695 0.205321i \(-0.0658239\pi\)
−0.837226 + 0.546858i \(0.815824\pi\)
\(398\) −27.7190 15.2532i −1.38943 0.764572i
\(399\) 0 0
\(400\) 7.59362 2.72011i 0.379681 0.136006i
\(401\) 33.3220 1.66402 0.832012 0.554758i \(-0.187189\pi\)
0.832012 + 0.554758i \(0.187189\pi\)
\(402\) 0 0
\(403\) 11.8624 4.91358i 0.590909 0.244763i
\(404\) −3.72660 + 0.647315i −0.185405 + 0.0322051i
\(405\) 0 0
\(406\) −3.82575 + 34.5262i −0.189869 + 1.71351i
\(407\) 2.53127 2.53127i 0.125470 0.125470i
\(408\) 0 0
\(409\) 8.50034 + 8.50034i 0.420315 + 0.420315i 0.885312 0.464997i \(-0.153945\pi\)
−0.464997 + 0.885312i \(0.653945\pi\)
\(410\) −21.1474 + 16.9283i −1.04439 + 0.836030i
\(411\) 0 0
\(412\) −3.51785 + 15.6788i −0.173312 + 0.772440i
\(413\) −17.3130 41.7972i −0.851915 2.05671i
\(414\) 0 0
\(415\) 33.5834i 1.64855i
\(416\) −7.28240 30.6037i −0.357049 1.50047i
\(417\) 0 0
\(418\) −11.6499 40.1593i −0.569815 1.96426i
\(419\) −8.90474 + 3.68846i −0.435025 + 0.180193i −0.589439 0.807813i \(-0.700651\pi\)
0.154414 + 0.988006i \(0.450651\pi\)
\(420\) 0 0
\(421\) −9.24819 + 22.3271i −0.450729 + 1.08816i 0.521316 + 0.853363i \(0.325441\pi\)
−0.972045 + 0.234793i \(0.924559\pi\)
\(422\) 24.2923 + 30.3467i 1.18253 + 1.47726i
\(423\) 0 0
\(424\) 22.5395 11.0083i 1.09461 0.534613i
\(425\) −5.39166 5.39166i −0.261534 0.261534i
\(426\) 0 0
\(427\) −0.341203 + 0.823738i −0.0165120 + 0.0398635i
\(428\) −24.1062 + 4.18727i −1.16522 + 0.202399i
\(429\) 0 0
\(430\) −8.92146 4.90928i −0.430231 0.236746i
\(431\) 34.2686i 1.65066i 0.564650 + 0.825331i \(0.309011\pi\)
−0.564650 + 0.825331i \(0.690989\pi\)
\(432\) 0 0
\(433\) 0.323021i 0.0155234i −0.999970 0.00776171i \(-0.997529\pi\)
0.999970 0.00776171i \(-0.00247065\pi\)
\(434\) −7.54415 + 13.7097i −0.362131 + 0.658088i
\(435\) 0 0
\(436\) 11.2490 + 7.91945i 0.538731 + 0.379273i
\(437\) 1.83982 4.44171i 0.0880104 0.212476i
\(438\) 0 0
\(439\) −1.22080 1.22080i −0.0582654 0.0582654i 0.677374 0.735639i \(-0.263118\pi\)
−0.735639 + 0.677374i \(0.763118\pi\)
\(440\) −2.09470 33.9462i −0.0998608 1.61832i
\(441\) 0 0
\(442\) −23.2157 + 18.5840i −1.10426 + 0.883950i
\(443\) −3.37120 + 8.13880i −0.160171 + 0.386686i −0.983508 0.180867i \(-0.942110\pi\)
0.823337 + 0.567553i \(0.192110\pi\)
\(444\) 0 0
\(445\) 22.8145 9.45009i 1.08151 0.447977i
\(446\) −16.1270 + 4.67830i −0.763635 + 0.221524i
\(447\) 0 0
\(448\) 30.2374 + 23.5713i 1.42858 + 1.11364i
\(449\) 4.83707i 0.228276i −0.993465 0.114138i \(-0.963589\pi\)
0.993465 0.114138i \(-0.0364105\pi\)
\(450\) 0 0
\(451\) 12.5620 + 30.3272i 0.591519 + 1.42805i
\(452\) −28.3864 + 17.9826i −1.33518 + 0.845831i
\(453\) 0 0
\(454\) −15.3522 19.1784i −0.720513 0.900087i
\(455\) −49.9183 49.9183i −2.34021 2.34021i
\(456\) 0 0
\(457\) −7.23423 + 7.23423i −0.338403 + 0.338403i −0.855766 0.517363i \(-0.826914\pi\)
0.517363 + 0.855766i \(0.326914\pi\)
\(458\) 0.698006 + 0.0773441i 0.0326157 + 0.00361405i
\(459\) 0 0
\(460\) 2.25106 3.19748i 0.104956 0.149083i
\(461\) −4.04570 + 1.67578i −0.188427 + 0.0780490i −0.474902 0.880039i \(-0.657516\pi\)
0.286475 + 0.958088i \(0.407516\pi\)
\(462\) 0 0
\(463\) −39.1299 −1.81852 −0.909261 0.416227i \(-0.863352\pi\)
−0.909261 + 0.416227i \(0.863352\pi\)
\(464\) −20.4773 0.998625i −0.950635 0.0463600i
\(465\) 0 0
\(466\) −4.30309 + 7.81986i −0.199337 + 0.362248i
\(467\) 2.71550 + 6.55579i 0.125658 + 0.303366i 0.974172 0.225808i \(-0.0725021\pi\)
−0.848514 + 0.529173i \(0.822502\pi\)
\(468\) 0 0
\(469\) 1.79753 + 0.744561i 0.0830022 + 0.0343807i
\(470\) 22.5456 + 2.49821i 1.03995 + 0.115234i
\(471\) 0 0
\(472\) 23.9921 11.7178i 1.10432 0.539356i
\(473\) −8.72560 + 8.72560i −0.401204 + 0.401204i
\(474\) 0 0
\(475\) 12.1346 + 5.02631i 0.556773 + 0.230623i
\(476\) 7.93444 35.3633i 0.363674 1.62087i
\(477\) 0 0
\(478\) 11.0317 3.20020i 0.504578 0.146374i
\(479\) 19.3768 0.885349 0.442674 0.896682i \(-0.354030\pi\)
0.442674 + 0.896682i \(0.354030\pi\)
\(480\) 0 0
\(481\) 4.38533 0.199954
\(482\) 5.31915 1.54304i 0.242281 0.0702837i
\(483\) 0 0
\(484\) −18.7485 4.20659i −0.852206 0.191209i
\(485\) 14.7519 + 6.11044i 0.669849 + 0.277461i
\(486\) 0 0
\(487\) −28.1905 + 28.1905i −1.27743 + 1.27743i −0.335334 + 0.942099i \(0.608849\pi\)
−0.942099 + 0.335334i \(0.891151\pi\)
\(488\) −0.497640 0.171050i −0.0225271 0.00774305i
\(489\) 0 0
\(490\) 59.4507 + 6.58756i 2.68571 + 0.297596i
\(491\) −21.4812 8.89781i −0.969434 0.401553i −0.158933 0.987289i \(-0.550805\pi\)
−0.810501 + 0.585737i \(0.800805\pi\)
\(492\) 0 0
\(493\) 7.41655 + 17.9051i 0.334025 + 0.806407i
\(494\) 24.6957 44.8787i 1.11111 2.01919i
\(495\) 0 0
\(496\) −8.35017 3.94567i −0.374934 0.177166i
\(497\) −33.6443 −1.50915
\(498\) 0 0
\(499\) 24.2391 10.0402i 1.08509 0.449459i 0.232798 0.972525i \(-0.425212\pi\)
0.852292 + 0.523066i \(0.175212\pi\)
\(500\) −12.9241 9.09873i −0.577984 0.406907i
\(501\) 0 0
\(502\) −12.2373 1.35598i −0.546177 0.0605203i
\(503\) 8.27072 8.27072i 0.368773 0.368773i −0.498256 0.867030i \(-0.666026\pi\)
0.867030 + 0.498256i \(0.166026\pi\)
\(504\) 0 0
\(505\) −3.54229 3.54229i −0.157630 0.157630i
\(506\) −2.96133 3.69938i −0.131647 0.164458i
\(507\) 0 0
\(508\) −10.1680 16.0507i −0.451132 0.712133i
\(509\) 14.1181 + 34.0841i 0.625774 + 1.51075i 0.844827 + 0.535039i \(0.179703\pi\)
−0.219054 + 0.975713i \(0.570297\pi\)
\(510\) 0 0
\(511\) 13.3063i 0.588638i
\(512\) −12.7860 + 18.6686i −0.565066 + 0.825046i
\(513\) 0 0
\(514\) 6.51926 1.89118i 0.287552 0.0834166i
\(515\) −19.6619 + 8.14422i −0.866406 + 0.358877i
\(516\) 0 0
\(517\) 10.5193 25.3958i 0.462637 1.11691i
\(518\) −4.17240 + 3.33998i −0.183325 + 0.146750i
\(519\) 0 0
\(520\) 27.5908 31.2198i 1.20994 1.36908i
\(521\) −6.11354 6.11354i −0.267839 0.267839i 0.560390 0.828229i \(-0.310651\pi\)
−0.828229 + 0.560390i \(0.810651\pi\)
\(522\) 0 0
\(523\) −10.2211 + 24.6760i −0.446939 + 1.07901i 0.526524 + 0.850160i \(0.323495\pi\)
−0.973463 + 0.228846i \(0.926505\pi\)
\(524\) 24.1615 34.3197i 1.05550 1.49926i
\(525\) 0 0
\(526\) −6.19012 + 11.2491i −0.269902 + 0.490483i
\(527\) 8.73036i 0.380300i
\(528\) 0 0
\(529\) 22.4552i 0.976312i
\(530\) 29.1065 + 16.0166i 1.26430 + 0.695718i
\(531\) 0 0
\(532\) 10.6841 + 61.5086i 0.463215 + 2.66673i
\(533\) −15.3888 + 37.1519i −0.666564 + 1.60923i
\(534\) 0 0
\(535\) −22.9139 22.9139i −0.990655 0.990655i
\(536\) −0.373258 + 1.08593i −0.0161223 + 0.0469051i
\(537\) 0 0
\(538\) 23.8677 + 29.8163i 1.02901 + 1.28547i
\(539\) 27.7384 66.9664i 1.19478 2.88445i
\(540\) 0 0
\(541\) −26.2040 + 10.8540i −1.12660 + 0.466652i −0.866623 0.498964i \(-0.833714\pi\)
−0.259974 + 0.965616i \(0.583714\pi\)
\(542\) 5.20364 + 17.9379i 0.223515 + 0.770498i
\(543\) 0 0
\(544\) 21.1198 + 3.38849i 0.905504 + 0.145280i
\(545\) 18.2204i 0.780478i
\(546\) 0 0
\(547\) −2.86307 6.91207i −0.122416 0.295539i 0.850777 0.525526i \(-0.176131\pi\)
−0.973194 + 0.229987i \(0.926131\pi\)
\(548\) 29.1327 + 6.53648i 1.24449 + 0.279225i
\(549\) 0 0
\(550\) 10.1066 8.09022i 0.430945 0.344968i
\(551\) −23.6058 23.6058i −1.00564 1.00564i
\(552\) 0 0
\(553\) −27.7583 + 27.7583i −1.18040 + 1.18040i
\(554\) 4.08918 36.9035i 0.173733 1.56788i
\(555\) 0 0
\(556\) −0.111378 0.641205i −0.00472348 0.0271931i
\(557\) −9.83837 + 4.07519i −0.416865 + 0.172671i −0.581250 0.813725i \(-0.697436\pi\)
0.164385 + 0.986396i \(0.447436\pi\)
\(558\) 0 0
\(559\) −15.1168 −0.639371
\(560\) −2.47337 + 50.7177i −0.104519 + 2.14322i
\(561\) 0 0
\(562\) −7.14870 3.93377i −0.301550 0.165936i
\(563\) 1.54232 + 3.72350i 0.0650012 + 0.156927i 0.953042 0.302837i \(-0.0979339\pi\)
−0.888041 + 0.459764i \(0.847934\pi\)
\(564\) 0 0
\(565\) −41.1173 17.0313i −1.72982 0.716513i
\(566\) 3.80373 34.3275i 0.159883 1.44289i
\(567\) 0 0
\(568\) −1.22294 19.8188i −0.0513136 0.831577i
\(569\) −8.57127 + 8.57127i −0.359327 + 0.359327i −0.863565 0.504238i \(-0.831773\pi\)
0.504238 + 0.863565i \(0.331773\pi\)
\(570\) 0 0
\(571\) −26.2074 10.8554i −1.09674 0.454286i −0.240390 0.970676i \(-0.577275\pi\)
−0.856353 + 0.516390i \(0.827275\pi\)
\(572\) −27.0194 42.6513i −1.12974 1.78334i
\(573\) 0 0
\(574\) −13.6542 47.0686i −0.569916 1.96460i
\(575\) 1.48845 0.0620725
\(576\) 0 0
\(577\) 40.8448 1.70039 0.850196 0.526466i \(-0.176483\pi\)
0.850196 + 0.526466i \(0.176483\pi\)
\(578\) 1.06472 + 3.67027i 0.0442863 + 0.152663i
\(579\) 0 0
\(580\) −14.5310 22.9378i −0.603366 0.952441i
\(581\) 56.1350 + 23.2519i 2.32887 + 0.964651i
\(582\) 0 0
\(583\) 28.4675 28.4675i 1.17900 1.17900i
\(584\) −7.83834 + 0.483675i −0.324353 + 0.0200146i
\(585\) 0 0
\(586\) 3.17907 28.6901i 0.131326 1.18518i
\(587\) 30.3985 + 12.5915i 1.25468 + 0.519705i 0.908273 0.418379i \(-0.137402\pi\)
0.346407 + 0.938084i \(0.387402\pi\)
\(588\) 0 0
\(589\) −5.75498 13.8938i −0.237130 0.572482i
\(590\) 30.9823 + 17.0488i 1.27552 + 0.701890i
\(591\) 0 0
\(592\) −2.11914 2.33642i −0.0870960 0.0960264i
\(593\) −5.64301 −0.231731 −0.115865 0.993265i \(-0.536964\pi\)
−0.115865 + 0.993265i \(0.536964\pi\)
\(594\) 0 0
\(595\) 44.3470 18.3691i 1.81805 0.753062i
\(596\) −2.12242 12.2188i −0.0869379 0.500502i
\(597\) 0 0
\(598\) 0.639325 5.76971i 0.0261439 0.235941i
\(599\) 5.75089 5.75089i 0.234975 0.234975i −0.579790 0.814766i \(-0.696866\pi\)
0.814766 + 0.579790i \(0.196866\pi\)
\(600\) 0 0
\(601\) −22.4340 22.4340i −0.915102 0.915102i 0.0815662 0.996668i \(-0.474008\pi\)
−0.996668 + 0.0815662i \(0.974008\pi\)
\(602\) 14.3828 11.5133i 0.586199 0.469248i
\(603\) 0 0
\(604\) 25.1107 + 5.63407i 1.02174 + 0.229247i
\(605\) −9.73875 23.5114i −0.395936 0.955875i
\(606\) 0 0
\(607\) 7.67228i 0.311408i 0.987804 + 0.155704i \(0.0497647\pi\)
−0.987804 + 0.155704i \(0.950235\pi\)
\(608\) −35.8443 + 8.52945i −1.45368 + 0.345915i
\(609\) 0 0
\(610\) −0.194171 0.669344i −0.00786177 0.0271010i
\(611\) 31.1107 12.8865i 1.25861 0.521332i
\(612\) 0 0
\(613\) −3.65989 + 8.83576i −0.147822 + 0.356873i −0.980395 0.197042i \(-0.936867\pi\)
0.832573 + 0.553915i \(0.186867\pi\)
\(614\) 8.35248 + 10.4342i 0.337079 + 0.421089i
\(615\) 0 0
\(616\) 58.1918 + 20.0018i 2.34461 + 0.805895i
\(617\) −7.16767 7.16767i −0.288560 0.288560i 0.547951 0.836511i \(-0.315408\pi\)
−0.836511 + 0.547951i \(0.815408\pi\)
\(618\) 0 0
\(619\) −13.8565 + 33.4525i −0.556939 + 1.34457i 0.355239 + 0.934776i \(0.384400\pi\)
−0.912178 + 0.409794i \(0.865600\pi\)
\(620\) −2.09333 12.0513i −0.0840701 0.483993i
\(621\) 0 0
\(622\) 2.76519 + 1.52162i 0.110874 + 0.0610115i
\(623\) 44.6776i 1.78997i
\(624\) 0 0
\(625\) 31.0163i 1.24065i
\(626\) −11.0624 + 20.1033i −0.442141 + 0.803488i
\(627\) 0 0
\(628\) −18.2973 + 25.9901i −0.730144 + 1.03712i
\(629\) −1.14108 + 2.75481i −0.0454979 + 0.109842i
\(630\) 0 0
\(631\) 4.00538 + 4.00538i 0.159452 + 0.159452i 0.782324 0.622872i \(-0.214034\pi\)
−0.622872 + 0.782324i \(0.714034\pi\)
\(632\) −17.3605 15.3425i −0.690564 0.610293i
\(633\) 0 0
\(634\) −28.2490 + 22.6131i −1.12191 + 0.898081i
\(635\) 9.63012 23.2492i 0.382160 0.922615i
\(636\) 0 0
\(637\) 82.0361 33.9805i 3.25039 1.34636i
\(638\) −31.6016 + 9.16737i −1.25112 + 0.362940i
\(639\) 0 0
\(640\) −29.9661 + 0.386566i −1.18451 + 0.0152804i
\(641\) 0.320061i 0.0126416i −0.999980 0.00632082i \(-0.997988\pi\)
0.999980 0.00632082i \(-0.00201199\pi\)
\(642\) 0 0
\(643\) 15.3875 + 37.1487i 0.606824 + 1.46500i 0.866435 + 0.499289i \(0.166405\pi\)
−0.259612 + 0.965713i \(0.583595\pi\)
\(644\) 3.78607 + 5.97649i 0.149192 + 0.235507i
\(645\) 0 0
\(646\) 21.7663 + 27.1912i 0.856385 + 1.06982i
\(647\) −11.1884 11.1884i −0.439863 0.439863i 0.452103 0.891966i \(-0.350674\pi\)
−0.891966 + 0.452103i \(0.850674\pi\)
\(648\) 0 0
\(649\) 30.3021 30.3021i 1.18946 1.18946i
\(650\) 15.7626 + 1.74661i 0.618260 + 0.0685077i
\(651\) 0 0
\(652\) −12.0234 8.46459i −0.470871 0.331499i
\(653\) −44.2880 + 18.3447i −1.73312 + 0.717884i −0.733870 + 0.679290i \(0.762288\pi\)
−0.999255 + 0.0385936i \(0.987712\pi\)
\(654\) 0 0
\(655\) 55.5888 2.17203
\(656\) 27.2302 9.75415i 1.06316 0.380836i
\(657\) 0 0
\(658\) −19.7855 + 35.9555i −0.771319 + 1.40169i
\(659\) 7.81320 + 18.8627i 0.304359 + 0.734788i 0.999868 + 0.0162701i \(0.00517915\pi\)
−0.695509 + 0.718518i \(0.744821\pi\)
\(660\) 0 0
\(661\) −19.8609 8.22666i −0.772500 0.319980i −0.0386153 0.999254i \(-0.512295\pi\)
−0.733885 + 0.679274i \(0.762295\pi\)
\(662\) −1.69009 0.187274i −0.0656873 0.00727863i
\(663\) 0 0
\(664\) −11.6565 + 33.9125i −0.452359 + 1.31606i
\(665\) −58.4664 + 58.4664i −2.26723 + 2.26723i
\(666\) 0 0
\(667\) −3.49521 1.44776i −0.135335 0.0560577i
\(668\) −28.8934 6.48278i −1.11792 0.250826i
\(669\) 0 0
\(670\) −1.46062 + 0.423714i −0.0564286 + 0.0163695i
\(671\) −0.844558 −0.0326038
\(672\) 0 0
\(673\) 43.3143 1.66964 0.834821 0.550522i \(-0.185571\pi\)
0.834821 + 0.550522i \(0.185571\pi\)
\(674\) 38.3950 11.1381i 1.47892 0.429022i
\(675\) 0 0
\(676\) 7.84879 34.9816i 0.301876 1.34545i
\(677\) −39.7727 16.4744i −1.52859 0.633162i −0.549298 0.835626i \(-0.685105\pi\)
−0.979290 + 0.202465i \(0.935105\pi\)
\(678\) 0 0
\(679\) −20.4273 + 20.4273i −0.783928 + 0.783928i
\(680\) 12.4326 + 25.4557i 0.476770 + 0.976181i
\(681\) 0 0
\(682\) −14.7324 1.63246i −0.564134 0.0625101i
\(683\) 5.40622 + 2.23933i 0.206863 + 0.0856856i 0.483709 0.875229i \(-0.339289\pi\)
−0.276846 + 0.960914i \(0.589289\pi\)
\(684\) 0 0
\(685\) 15.1327 + 36.5336i 0.578191 + 1.39588i
\(686\) −29.3003 + 53.2464i −1.11869 + 2.03296i
\(687\) 0 0
\(688\) 7.30492 + 8.05393i 0.278498 + 0.307053i
\(689\) 49.3188 1.87890
\(690\) 0 0
\(691\) −17.4054 + 7.20955i −0.662132 + 0.274264i −0.688336 0.725392i \(-0.741658\pi\)
0.0262032 + 0.999657i \(0.491658\pi\)
\(692\) −18.4333 + 26.1832i −0.700729 + 0.995338i
\(693\) 0 0
\(694\) 11.7317 + 1.29996i 0.445329 + 0.0493457i
\(695\) 0.609492 0.609492i 0.0231193 0.0231193i
\(696\) 0 0
\(697\) −19.3342 19.3342i −0.732333 0.732333i
\(698\) 14.4199 + 18.0138i 0.545802 + 0.681833i
\(699\) 0 0
\(700\) −16.3275 + 10.3434i −0.617123 + 0.390944i
\(701\) 10.6696 + 25.7586i 0.402984 + 0.972889i 0.986938 + 0.161102i \(0.0515048\pi\)
−0.583954 + 0.811787i \(0.698495\pi\)
\(702\) 0 0
\(703\) 5.13628i 0.193719i
\(704\) −9.66717 + 35.0059i −0.364345 + 1.31934i
\(705\) 0 0
\(706\) 34.0440 9.87589i 1.28126 0.371684i
\(707\) 8.37351 3.46842i 0.314918 0.130443i
\(708\) 0 0
\(709\) −0.671243 + 1.62052i −0.0252091 + 0.0608601i −0.935983 0.352046i \(-0.885486\pi\)
0.910774 + 0.412906i \(0.135486\pi\)
\(710\) 20.5308 16.4348i 0.770509 0.616787i
\(711\) 0 0
\(712\) −26.3181 + 1.62400i −0.986314 + 0.0608618i
\(713\) −1.20507 1.20507i −0.0451303 0.0451303i
\(714\) 0 0
\(715\) 25.5900 61.7798i 0.957013 2.31043i
\(716\) −9.92344 6.98622i −0.370857 0.261087i
\(717\) 0 0
\(718\) −11.8762 + 21.5823i −0.443217 + 0.805443i
\(719\) 22.7818i 0.849618i −0.905283 0.424809i \(-0.860341\pi\)
0.905283 0.424809i \(-0.139659\pi\)
\(720\) 0 0
\(721\) 38.5038i 1.43396i
\(722\) −29.0226 15.9705i −1.08011 0.594359i
\(723\) 0 0
\(724\) −19.7396 + 3.42878i −0.733615 + 0.127430i
\(725\) 3.95523 9.54878i 0.146894 0.354633i
\(726\) 0 0
\(727\) 12.5833 + 12.5833i 0.466688 + 0.466688i 0.900840 0.434152i \(-0.142952\pi\)
−0.434152 + 0.900840i \(0.642952\pi\)
\(728\) 33.0813 + 67.7336i 1.22608 + 2.51038i
\(729\) 0 0
\(730\) −6.49997 8.11996i −0.240575 0.300533i
\(731\) 3.93344 9.49617i 0.145484 0.351229i
\(732\) 0 0
\(733\) 35.2843 14.6152i 1.30326 0.539826i 0.380347 0.924844i \(-0.375805\pi\)
0.922909 + 0.385017i \(0.125805\pi\)
\(734\) −0.490096 1.68945i −0.0180898 0.0623588i
\(735\) 0 0
\(736\) −3.38294 + 2.44749i −0.124697 + 0.0902158i
\(737\) 1.84296i 0.0678865i
\(738\) 0 0
\(739\) 14.2438 + 34.3875i 0.523965 + 1.26496i 0.935421 + 0.353535i \(0.115020\pi\)
−0.411456 + 0.911430i \(0.634980\pi\)
\(740\) 0.914602 4.07632i 0.0336214 0.149849i
\(741\) 0 0
\(742\) −46.9242 + 37.5624i −1.72264 + 1.37896i
\(743\) −5.48927 5.48927i −0.201382 0.201382i 0.599210 0.800592i \(-0.295481\pi\)
−0.800592 + 0.599210i \(0.795481\pi\)
\(744\) 0 0
\(745\) 11.6145 11.6145i 0.425522 0.425522i
\(746\) −2.40424 + 21.6975i −0.0880255 + 0.794402i
\(747\) 0 0
\(748\) 33.8236 5.87519i 1.23671 0.214818i
\(749\) 54.1656 22.4361i 1.97917 0.819798i
\(750\) 0 0
\(751\) 13.1151 0.478576 0.239288 0.970949i \(-0.423086\pi\)
0.239288 + 0.970949i \(0.423086\pi\)
\(752\) −21.8994 10.3480i −0.798590 0.377354i
\(753\) 0 0
\(754\) −35.3153 19.4332i −1.28611 0.707717i
\(755\) 13.0435 + 31.4899i 0.474702 + 1.14603i
\(756\) 0 0
\(757\) 24.2944 + 10.0631i 0.882994 + 0.365748i 0.777657 0.628689i \(-0.216408\pi\)
0.105337 + 0.994437i \(0.466408\pi\)
\(758\) −1.04708 + 9.44955i −0.0380316 + 0.343223i
\(759\) 0 0
\(760\) −36.5659 32.3155i −1.32638 1.17220i
\(761\) −10.1791 + 10.1791i −0.368993 + 0.368993i −0.867110 0.498117i \(-0.834025\pi\)
0.498117 + 0.867110i \(0.334025\pi\)
\(762\) 0 0
\(763\) −30.4556 12.6151i −1.10257 0.456699i
\(764\) −13.4794 + 8.53912i −0.487667 + 0.308934i
\(765\) 0 0
\(766\) −5.36135 18.4816i −0.193713 0.667766i
\(767\) 52.4972 1.89557
\(768\) 0 0
\(769\) 10.7380 0.387221 0.193611 0.981078i \(-0.437980\pi\)
0.193611 + 0.981078i \(0.437980\pi\)
\(770\) 22.7055 + 78.2701i 0.818250 + 2.82066i
\(771\) 0 0
\(772\) 20.1876 12.7887i 0.726568 0.460277i
\(773\) −27.6103 11.4366i −0.993073 0.411344i −0.173820 0.984777i \(-0.555611\pi\)
−0.819252 + 0.573433i \(0.805611\pi\)
\(774\) 0 0
\(775\) 3.29221 3.29221i 0.118260 0.118260i
\(776\) −12.7756 11.2905i −0.458617 0.405307i
\(777\) 0 0
\(778\) 0.452920 4.08746i 0.0162380 0.146543i
\(779\) 43.5139 + 18.0240i 1.55905 + 0.645778i
\(780\) 0 0
\(781\) −12.1957 29.4431i −0.436397 1.05356i
\(782\) 3.45811 + 1.90292i 0.123662 + 0.0680482i
\(783\) 0 0
\(784\) −57.7467 27.2868i −2.06238 0.974530i
\(785\) −42.0971 −1.50251
\(786\) 0 0
\(787\) −6.96385 + 2.88452i −0.248234 + 0.102822i −0.503331 0.864093i \(-0.667893\pi\)
0.255097 + 0.966915i \(0.417893\pi\)
\(788\) 10.4173 1.80950i 0.371102 0.0644608i
\(789\)