Properties

Label 576.2.bd.a.181.3
Level $576$
Weight $2$
Character 576.181
Analytic conductor $4.599$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bd (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(7\) over \(\Q(\zeta_{16})\)
Twist minimal: no (minimal twist has level 64)
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 181.3
Character \(\chi\) \(=\) 576.181
Dual form 576.2.bd.a.541.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.325482 + 1.37625i) q^{2} +(-1.78812 - 0.895889i) q^{4} +(0.967135 + 1.44742i) q^{5} +(4.53283 + 1.87756i) q^{7} +(1.81497 - 2.16931i) q^{8} +O(q^{10})\) \(q+(-0.325482 + 1.37625i) q^{2} +(-1.78812 - 0.895889i) q^{4} +(0.967135 + 1.44742i) q^{5} +(4.53283 + 1.87756i) q^{7} +(1.81497 - 2.16931i) q^{8} +(-2.30680 + 0.859909i) q^{10} +(0.540778 - 2.71867i) q^{11} +(1.42546 - 2.13334i) q^{13} +(-4.05935 + 5.62719i) q^{14} +(2.39477 + 3.20392i) q^{16} +(2.43954 - 2.43954i) q^{17} +(-1.88371 - 1.25865i) q^{19} +(-0.432628 - 3.45461i) q^{20} +(3.56556 + 1.62913i) q^{22} +(0.690956 + 1.66811i) q^{23} +(0.753743 - 1.81970i) q^{25} +(2.47205 + 2.65615i) q^{26} +(-6.42318 - 7.41822i) q^{28} +(1.50522 + 7.56726i) q^{29} +3.63299i q^{31} +(-5.18884 + 2.25298i) q^{32} +(2.56339 + 4.15144i) q^{34} +(1.66624 + 8.37677i) q^{35} +(-5.55115 + 3.70916i) q^{37} +(2.34533 - 2.18278i) q^{38} +(4.89522 + 0.529009i) q^{40} +(0.926510 + 2.23679i) q^{41} +(-6.41133 - 1.27529i) q^{43} +(-3.40261 + 4.37685i) q^{44} +(-2.52064 + 0.407986i) q^{46} +(-3.58669 + 3.58669i) q^{47} +(12.0716 + 12.0716i) q^{49} +(2.25903 + 1.62962i) q^{50} +(-4.46013 + 2.53763i) q^{52} +(0.513941 - 2.58375i) q^{53} +(4.45807 - 1.84659i) q^{55} +(12.3000 - 6.42539i) q^{56} +(-10.9044 - 0.391449i) q^{58} +(-5.40361 - 8.08707i) q^{59} +(13.1016 - 2.60608i) q^{61} +(-4.99991 - 1.18248i) q^{62} +(-1.41178 - 7.87444i) q^{64} +4.46645 q^{65} +(-2.72425 + 0.541887i) q^{67} +(-6.54775 + 2.17664i) q^{68} +(-12.0708 - 0.433324i) q^{70} +(-4.17620 - 1.72984i) q^{71} +(-5.46867 + 2.26520i) q^{73} +(-3.29793 - 8.84703i) q^{74} +(2.24069 + 3.93822i) q^{76} +(7.55573 - 11.3080i) q^{77} +(-5.71185 - 5.71185i) q^{79} +(-2.32135 + 6.56485i) q^{80} +(-3.37995 + 0.547072i) q^{82} +(-10.3786 - 6.93477i) q^{83} +(5.89040 + 1.17167i) q^{85} +(3.84189 - 8.40850i) q^{86} +(-4.91614 - 6.10742i) q^{88} +(-3.49372 + 8.43458i) q^{89} +(10.4668 - 6.99371i) q^{91} +(0.258932 - 3.60181i) q^{92} +(-3.76877 - 6.10358i) q^{94} -3.94381i q^{95} -9.58124i q^{97} +(-20.5426 + 12.6844i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 8q^{2} - 8q^{4} + 8q^{5} - 8q^{7} + 8q^{8} + O(q^{10}) \) \( 56q + 8q^{2} - 8q^{4} + 8q^{5} - 8q^{7} + 8q^{8} - 8q^{10} + 8q^{11} - 8q^{13} + 8q^{14} - 8q^{16} + 8q^{17} - 8q^{19} + 8q^{20} + 8q^{23} - 8q^{25} - 32q^{26} + 32q^{28} + 8q^{29} - 32q^{32} + 32q^{34} + 8q^{35} - 8q^{37} - 32q^{38} + 32q^{40} + 8q^{41} - 8q^{43} - 8q^{46} + 8q^{47} - 8q^{49} + 32q^{50} - 56q^{52} + 8q^{53} + 56q^{55} + 64q^{56} - 80q^{58} - 56q^{59} - 8q^{61} + 40q^{62} - 104q^{64} + 16q^{65} + 72q^{67} + 56q^{68} - 104q^{70} - 56q^{71} - 8q^{73} + 64q^{74} - 72q^{76} + 8q^{77} + 24q^{79} - 32q^{80} + 72q^{82} + 8q^{83} - 8q^{85} - 96q^{86} + 72q^{88} + 8q^{89} - 8q^{91} - 144q^{92} + 88q^{94} - 128q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{16}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.325482 + 1.37625i −0.230151 + 0.973155i
\(3\) 0 0
\(4\) −1.78812 0.895889i −0.894061 0.447945i
\(5\) 0.967135 + 1.44742i 0.432516 + 0.647306i 0.982150 0.188100i \(-0.0602328\pi\)
−0.549634 + 0.835406i \(0.685233\pi\)
\(6\) 0 0
\(7\) 4.53283 + 1.87756i 1.71325 + 0.709651i 0.999961 + 0.00878062i \(0.00279499\pi\)
0.713288 + 0.700871i \(0.247205\pi\)
\(8\) 1.81497 2.16931i 0.641688 0.766966i
\(9\) 0 0
\(10\) −2.30680 + 0.859909i −0.729473 + 0.271927i
\(11\) 0.540778 2.71867i 0.163051 0.819711i −0.809518 0.587095i \(-0.800271\pi\)
0.972569 0.232616i \(-0.0747286\pi\)
\(12\) 0 0
\(13\) 1.42546 2.13334i 0.395350 0.591683i −0.579383 0.815055i \(-0.696706\pi\)
0.974733 + 0.223372i \(0.0717065\pi\)
\(14\) −4.05935 + 5.62719i −1.08491 + 1.50393i
\(15\) 0 0
\(16\) 2.39477 + 3.20392i 0.598691 + 0.800980i
\(17\) 2.43954 2.43954i 0.591675 0.591675i −0.346409 0.938084i \(-0.612599\pi\)
0.938084 + 0.346409i \(0.112599\pi\)
\(18\) 0 0
\(19\) −1.88371 1.25865i −0.432152 0.288755i 0.320406 0.947280i \(-0.396181\pi\)
−0.752559 + 0.658525i \(0.771181\pi\)
\(20\) −0.432628 3.45461i −0.0967387 0.772474i
\(21\) 0 0
\(22\) 3.56556 + 1.62913i 0.760180 + 0.347331i
\(23\) 0.690956 + 1.66811i 0.144074 + 0.347826i 0.979400 0.201929i \(-0.0647211\pi\)
−0.835326 + 0.549755i \(0.814721\pi\)
\(24\) 0 0
\(25\) 0.753743 1.81970i 0.150749 0.363939i
\(26\) 2.47205 + 2.65615i 0.484809 + 0.520913i
\(27\) 0 0
\(28\) −6.42318 7.41822i −1.21387 1.40191i
\(29\) 1.50522 + 7.56726i 0.279513 + 1.40521i 0.824073 + 0.566483i \(0.191697\pi\)
−0.544560 + 0.838722i \(0.683303\pi\)
\(30\) 0 0
\(31\) 3.63299i 0.652505i 0.945283 + 0.326253i \(0.105786\pi\)
−0.945283 + 0.326253i \(0.894214\pi\)
\(32\) −5.18884 + 2.25298i −0.917267 + 0.398273i
\(33\) 0 0
\(34\) 2.56339 + 4.15144i 0.439617 + 0.711966i
\(35\) 1.66624 + 8.37677i 0.281646 + 1.41593i
\(36\) 0 0
\(37\) −5.55115 + 3.70916i −0.912603 + 0.609782i −0.920737 0.390185i \(-0.872411\pi\)
0.00813317 + 0.999967i \(0.497411\pi\)
\(38\) 2.34533 2.18278i 0.380464 0.354094i
\(39\) 0 0
\(40\) 4.89522 + 0.529009i 0.774002 + 0.0836437i
\(41\) 0.926510 + 2.23679i 0.144697 + 0.349328i 0.979567 0.201118i \(-0.0644575\pi\)
−0.834870 + 0.550446i \(0.814458\pi\)
\(42\) 0 0
\(43\) −6.41133 1.27529i −0.977718 0.194480i −0.319730 0.947509i \(-0.603592\pi\)
−0.657988 + 0.753028i \(0.728592\pi\)
\(44\) −3.40261 + 4.37685i −0.512962 + 0.659834i
\(45\) 0 0
\(46\) −2.52064 + 0.407986i −0.371647 + 0.0601542i
\(47\) −3.58669 + 3.58669i −0.523172 + 0.523172i −0.918528 0.395356i \(-0.870621\pi\)
0.395356 + 0.918528i \(0.370621\pi\)
\(48\) 0 0
\(49\) 12.0716 + 12.0716i 1.72451 + 1.72451i
\(50\) 2.25903 + 1.62962i 0.319475 + 0.230463i
\(51\) 0 0
\(52\) −4.46013 + 2.53763i −0.618509 + 0.351906i
\(53\) 0.513941 2.58375i 0.0705952 0.354906i −0.929301 0.369324i \(-0.879589\pi\)
0.999896 + 0.0144176i \(0.00458942\pi\)
\(54\) 0 0
\(55\) 4.45807 1.84659i 0.601126 0.248994i
\(56\) 12.3000 6.42539i 1.64365 0.858629i
\(57\) 0 0
\(58\) −10.9044 0.391449i −1.43181 0.0513997i
\(59\) −5.40361 8.08707i −0.703490 1.05285i −0.995344 0.0963843i \(-0.969272\pi\)
0.291854 0.956463i \(-0.405728\pi\)
\(60\) 0 0
\(61\) 13.1016 2.60608i 1.67749 0.333674i 0.737624 0.675211i \(-0.235948\pi\)
0.939868 + 0.341537i \(0.110948\pi\)
\(62\) −4.99991 1.18248i −0.634989 0.150174i
\(63\) 0 0
\(64\) −1.41178 7.87444i −0.176472 0.984306i
\(65\) 4.46645 0.553995
\(66\) 0 0
\(67\) −2.72425 + 0.541887i −0.332820 + 0.0662021i −0.358672 0.933464i \(-0.616770\pi\)
0.0258515 + 0.999666i \(0.491770\pi\)
\(68\) −6.54775 + 2.17664i −0.794031 + 0.263956i
\(69\) 0 0
\(70\) −12.0708 0.433324i −1.44274 0.0517921i
\(71\) −4.17620 1.72984i −0.495623 0.205294i 0.120848 0.992671i \(-0.461439\pi\)
−0.616472 + 0.787377i \(0.711439\pi\)
\(72\) 0 0
\(73\) −5.46867 + 2.26520i −0.640059 + 0.265121i −0.679020 0.734119i \(-0.737595\pi\)
0.0389610 + 0.999241i \(0.487595\pi\)
\(74\) −3.29793 8.84703i −0.383376 1.02845i
\(75\) 0 0
\(76\) 2.24069 + 3.93822i 0.257025 + 0.451745i
\(77\) 7.55573 11.3080i 0.861056 1.28866i
\(78\) 0 0
\(79\) −5.71185 5.71185i −0.642633 0.642633i 0.308569 0.951202i \(-0.400150\pi\)
−0.951202 + 0.308569i \(0.900150\pi\)
\(80\) −2.32135 + 6.56485i −0.259535 + 0.733973i
\(81\) 0 0
\(82\) −3.37995 + 0.547072i −0.373253 + 0.0604140i
\(83\) −10.3786 6.93477i −1.13920 0.761189i −0.164871 0.986315i \(-0.552721\pi\)
−0.974330 + 0.225126i \(0.927721\pi\)
\(84\) 0 0
\(85\) 5.89040 + 1.17167i 0.638903 + 0.127086i
\(86\) 3.84189 8.40850i 0.414282 0.906712i
\(87\) 0 0
\(88\) −4.91614 6.10742i −0.524063 0.651053i
\(89\) −3.49372 + 8.43458i −0.370333 + 0.894064i 0.623360 + 0.781935i \(0.285767\pi\)
−0.993694 + 0.112129i \(0.964233\pi\)
\(90\) 0 0
\(91\) 10.4668 6.99371i 1.09722 0.733141i
\(92\) 0.258932 3.60181i 0.0269955 0.375515i
\(93\) 0 0
\(94\) −3.76877 6.10358i −0.388719 0.629536i
\(95\) 3.94381i 0.404626i
\(96\) 0 0
\(97\) 9.58124i 0.972828i −0.873728 0.486414i \(-0.838305\pi\)
0.873728 0.486414i \(-0.161695\pi\)
\(98\) −20.5426 + 12.6844i −2.07512 + 1.28132i
\(99\) 0 0
\(100\) −2.97803 + 2.57857i −0.297803 + 0.257857i
\(101\) 3.78774 2.53089i 0.376894 0.251833i −0.352666 0.935749i \(-0.614725\pi\)
0.729560 + 0.683917i \(0.239725\pi\)
\(102\) 0 0
\(103\) −0.503843 + 1.21638i −0.0496451 + 0.119854i −0.946756 0.321951i \(-0.895662\pi\)
0.897111 + 0.441804i \(0.145662\pi\)
\(104\) −2.04072 6.96420i −0.200109 0.682896i
\(105\) 0 0
\(106\) 3.38861 + 1.54828i 0.329131 + 0.150382i
\(107\) 3.54726 + 0.705594i 0.342927 + 0.0682124i 0.363549 0.931575i \(-0.381565\pi\)
−0.0206225 + 0.999787i \(0.506565\pi\)
\(108\) 0 0
\(109\) −7.61993 5.09147i −0.729857 0.487675i 0.134272 0.990944i \(-0.457130\pi\)
−0.864129 + 0.503270i \(0.832130\pi\)
\(110\) 1.09035 + 6.73645i 0.103961 + 0.642295i
\(111\) 0 0
\(112\) 4.83952 + 19.0191i 0.457292 + 1.79714i
\(113\) 9.25522 + 9.25522i 0.870658 + 0.870658i 0.992544 0.121886i \(-0.0388944\pi\)
−0.121886 + 0.992544i \(0.538894\pi\)
\(114\) 0 0
\(115\) −1.74621 + 2.61340i −0.162835 + 0.243700i
\(116\) 4.08791 14.8797i 0.379552 1.38155i
\(117\) 0 0
\(118\) 12.8886 4.80451i 1.18649 0.442291i
\(119\) 15.6384 6.47764i 1.43357 0.593804i
\(120\) 0 0
\(121\) 3.06392 + 1.26912i 0.278539 + 0.115374i
\(122\) −0.677738 + 18.8793i −0.0613595 + 1.70926i
\(123\) 0 0
\(124\) 3.25476 6.49624i 0.292286 0.583380i
\(125\) 11.8996 2.36697i 1.06433 0.211709i
\(126\) 0 0
\(127\) 8.28837 0.735474 0.367737 0.929930i \(-0.380133\pi\)
0.367737 + 0.929930i \(0.380133\pi\)
\(128\) 11.2967 + 0.620033i 0.998497 + 0.0548037i
\(129\) 0 0
\(130\) −1.45375 + 6.14695i −0.127502 + 0.539123i
\(131\) −12.8274 + 2.55153i −1.12074 + 0.222928i −0.720480 0.693475i \(-0.756079\pi\)
−0.400256 + 0.916404i \(0.631079\pi\)
\(132\) 0 0
\(133\) −6.17534 9.24205i −0.535470 0.801387i
\(134\) 0.140923 3.92562i 0.0121739 0.339122i
\(135\) 0 0
\(136\) −0.864420 9.71979i −0.0741234 0.833465i
\(137\) 3.42304 1.41787i 0.292450 0.121137i −0.231635 0.972803i \(-0.574407\pi\)
0.524085 + 0.851666i \(0.324407\pi\)
\(138\) 0 0
\(139\) −3.82451 + 19.2271i −0.324391 + 1.63082i 0.382822 + 0.923822i \(0.374952\pi\)
−0.707213 + 0.707001i \(0.750048\pi\)
\(140\) 4.52521 16.4715i 0.382450 1.39209i
\(141\) 0 0
\(142\) 3.73996 5.18446i 0.313851 0.435070i
\(143\) −5.02901 5.02901i −0.420547 0.420547i
\(144\) 0 0
\(145\) −9.49725 + 9.49725i −0.788704 + 0.788704i
\(146\) −1.33752 8.26353i −0.110694 0.683895i
\(147\) 0 0
\(148\) 13.2491 1.65922i 1.08907 0.136387i
\(149\) −9.20724 1.83143i −0.754287 0.150037i −0.197053 0.980393i \(-0.563137\pi\)
−0.557234 + 0.830356i \(0.688137\pi\)
\(150\) 0 0
\(151\) −6.60900 15.9555i −0.537833 1.29844i −0.926233 0.376952i \(-0.876972\pi\)
0.388400 0.921491i \(-0.373028\pi\)
\(152\) −6.14928 + 1.80192i −0.498772 + 0.146155i
\(153\) 0 0
\(154\) 13.1033 + 14.0791i 1.05589 + 1.13453i
\(155\) −5.25847 + 3.51360i −0.422370 + 0.282219i
\(156\) 0 0
\(157\) −0.838120 4.21351i −0.0668893 0.336275i 0.932821 0.360340i \(-0.117339\pi\)
−0.999710 + 0.0240647i \(0.992339\pi\)
\(158\) 9.72003 6.00182i 0.773284 0.477479i
\(159\) 0 0
\(160\) −8.27931 5.33150i −0.654537 0.421492i
\(161\) 8.85860i 0.698155i
\(162\) 0 0
\(163\) 1.20061 + 6.03588i 0.0940391 + 0.472766i 0.998893 + 0.0470438i \(0.0149800\pi\)
−0.904854 + 0.425723i \(0.860020\pi\)
\(164\) 0.347205 4.82971i 0.0271121 0.377137i
\(165\) 0 0
\(166\) 12.9220 12.0264i 1.00294 0.933430i
\(167\) 2.59281 6.25960i 0.200638 0.484382i −0.791251 0.611492i \(-0.790570\pi\)
0.991889 + 0.127109i \(0.0405698\pi\)
\(168\) 0 0
\(169\) 2.45565 + 5.92846i 0.188896 + 0.456035i
\(170\) −3.52973 + 7.72530i −0.270718 + 0.592503i
\(171\) 0 0
\(172\) 10.3217 + 8.02422i 0.787024 + 0.611841i
\(173\) −13.9780 9.33980i −1.06273 0.710092i −0.104046 0.994572i \(-0.533179\pi\)
−0.958682 + 0.284480i \(0.908179\pi\)
\(174\) 0 0
\(175\) 6.83318 6.83318i 0.516540 0.516540i
\(176\) 10.0055 4.77798i 0.754189 0.360154i
\(177\) 0 0
\(178\) −10.4709 7.55353i −0.784830 0.566161i
\(179\) 10.0942 15.1070i 0.754476 1.12915i −0.233167 0.972437i \(-0.574909\pi\)
0.987644 0.156717i \(-0.0500911\pi\)
\(180\) 0 0
\(181\) 1.33053 6.68904i 0.0988977 0.497192i −0.899308 0.437316i \(-0.855929\pi\)
0.998206 0.0598766i \(-0.0190707\pi\)
\(182\) 6.21833 + 16.6813i 0.460933 + 1.23650i
\(183\) 0 0
\(184\) 4.87271 + 1.52868i 0.359221 + 0.112696i
\(185\) −10.7374 4.44759i −0.789431 0.326993i
\(186\) 0 0
\(187\) −5.31306 7.95156i −0.388530 0.581476i
\(188\) 9.62672 3.20016i 0.702100 0.233396i
\(189\) 0 0
\(190\) 5.42766 + 1.28364i 0.393764 + 0.0931249i
\(191\) −4.13034 −0.298861 −0.149430 0.988772i \(-0.547744\pi\)
−0.149430 + 0.988772i \(0.547744\pi\)
\(192\) 0 0
\(193\) 2.74997 0.197947 0.0989737 0.995090i \(-0.468444\pi\)
0.0989737 + 0.995090i \(0.468444\pi\)
\(194\) 13.1862 + 3.11852i 0.946712 + 0.223897i
\(195\) 0 0
\(196\) −10.7707 32.4003i −0.769334 2.31431i
\(197\) 1.52669 + 2.28486i 0.108772 + 0.162789i 0.881862 0.471507i \(-0.156290\pi\)
−0.773090 + 0.634296i \(0.781290\pi\)
\(198\) 0 0
\(199\) 0.831551 + 0.344440i 0.0589471 + 0.0244167i 0.411962 0.911201i \(-0.364844\pi\)
−0.353015 + 0.935618i \(0.614844\pi\)
\(200\) −2.57946 4.93779i −0.182395 0.349155i
\(201\) 0 0
\(202\) 2.25029 + 6.03663i 0.158330 + 0.424736i
\(203\) −7.38507 + 37.1273i −0.518331 + 2.60582i
\(204\) 0 0
\(205\) −2.34152 + 3.50433i −0.163539 + 0.244753i
\(206\) −1.51006 1.08932i −0.105211 0.0758968i
\(207\) 0 0
\(208\) 10.2487 0.541817i 0.710619 0.0375682i
\(209\) −4.44054 + 4.44054i −0.307158 + 0.307158i
\(210\) 0 0
\(211\) −11.5419 7.71208i −0.794581 0.530922i 0.0907556 0.995873i \(-0.471072\pi\)
−0.885336 + 0.464951i \(0.846072\pi\)
\(212\) −3.23375 + 4.15964i −0.222095 + 0.285685i
\(213\) 0 0
\(214\) −2.12564 + 4.65226i −0.145306 + 0.318022i
\(215\) −4.35474 10.5133i −0.296991 0.716999i
\(216\) 0 0
\(217\) −6.82117 + 16.4678i −0.463051 + 1.11790i
\(218\) 9.48729 8.82974i 0.642560 0.598025i
\(219\) 0 0
\(220\) −9.62592 0.692001i −0.648979 0.0466547i
\(221\) −1.72692 8.68183i −0.116165 0.584003i
\(222\) 0 0
\(223\) 6.30327i 0.422098i 0.977475 + 0.211049i \(0.0676880\pi\)
−0.977475 + 0.211049i \(0.932312\pi\)
\(224\) −27.7503 + 0.469989i −1.85414 + 0.0314025i
\(225\) 0 0
\(226\) −15.7499 + 9.72508i −1.04767 + 0.646902i
\(227\) −3.46768 17.4332i −0.230158 1.15708i −0.907057 0.421007i \(-0.861677\pi\)
0.676899 0.736076i \(-0.263323\pi\)
\(228\) 0 0
\(229\) 7.65290 5.11350i 0.505718 0.337910i −0.276398 0.961043i \(-0.589141\pi\)
0.782115 + 0.623134i \(0.214141\pi\)
\(230\) −3.02832 3.25384i −0.199682 0.214552i
\(231\) 0 0
\(232\) 19.1476 + 10.4691i 1.25710 + 0.687327i
\(233\) −5.24399 12.6601i −0.343545 0.829391i −0.997352 0.0727295i \(-0.976829\pi\)
0.653807 0.756662i \(-0.273171\pi\)
\(234\) 0 0
\(235\) −8.66026 1.72263i −0.564933 0.112372i
\(236\) 2.41720 + 19.3017i 0.157346 + 1.25643i
\(237\) 0 0
\(238\) 3.82482 + 23.6307i 0.247926 + 1.53175i
\(239\) −8.39091 + 8.39091i −0.542763 + 0.542763i −0.924338 0.381575i \(-0.875382\pi\)
0.381575 + 0.924338i \(0.375382\pi\)
\(240\) 0 0
\(241\) 3.97755 + 3.97755i 0.256217 + 0.256217i 0.823513 0.567297i \(-0.192011\pi\)
−0.567297 + 0.823513i \(0.692011\pi\)
\(242\) −2.74388 + 3.80365i −0.176383 + 0.244508i
\(243\) 0 0
\(244\) −25.7621 7.07763i −1.64925 0.453099i
\(245\) −5.79780 + 29.1475i −0.370408 + 1.86217i
\(246\) 0 0
\(247\) −5.37028 + 2.22444i −0.341703 + 0.141538i
\(248\) 7.88108 + 6.59377i 0.500449 + 0.418705i
\(249\) 0 0
\(250\) −0.615556 + 17.1472i −0.0389312 + 1.08448i
\(251\) 10.0908 + 15.1019i 0.636924 + 0.953224i 0.999772 + 0.0213753i \(0.00680450\pi\)
−0.362848 + 0.931848i \(0.618196\pi\)
\(252\) 0 0
\(253\) 4.90871 0.976404i 0.308608 0.0613860i
\(254\) −2.69772 + 11.4069i −0.169270 + 0.715730i
\(255\) 0 0
\(256\) −4.53020 + 15.3453i −0.283137 + 0.959079i
\(257\) 15.1836 0.947128 0.473564 0.880760i \(-0.342967\pi\)
0.473564 + 0.880760i \(0.342967\pi\)
\(258\) 0 0
\(259\) −32.1266 + 6.39038i −1.99625 + 0.397079i
\(260\) −7.98656 4.00145i −0.495306 0.248159i
\(261\) 0 0
\(262\) 0.663552 18.4842i 0.0409944 1.14196i
\(263\) 19.1921 + 7.94964i 1.18344 + 0.490196i 0.885613 0.464425i \(-0.153739\pi\)
0.297825 + 0.954620i \(0.403739\pi\)
\(264\) 0 0
\(265\) 4.23683 1.75495i 0.260266 0.107806i
\(266\) 14.7293 5.49068i 0.903112 0.336655i
\(267\) 0 0
\(268\) 5.35677 + 1.47167i 0.327217 + 0.0898963i
\(269\) 3.71107 5.55401i 0.226268 0.338634i −0.700914 0.713246i \(-0.747224\pi\)
0.927182 + 0.374612i \(0.122224\pi\)
\(270\) 0 0
\(271\) 2.68097 + 2.68097i 0.162858 + 0.162858i 0.783831 0.620974i \(-0.213263\pi\)
−0.620974 + 0.783831i \(0.713263\pi\)
\(272\) 13.6582 + 1.97396i 0.828150 + 0.119689i
\(273\) 0 0
\(274\) 0.837203 + 5.17245i 0.0505773 + 0.312479i
\(275\) −4.53956 3.03323i −0.273746 0.182911i
\(276\) 0 0
\(277\) −7.35826 1.46365i −0.442115 0.0879421i −0.0309870 0.999520i \(-0.509865\pi\)
−0.411128 + 0.911578i \(0.634865\pi\)
\(278\) −25.2165 11.5216i −1.51238 0.691018i
\(279\) 0 0
\(280\) 21.1959 + 11.5890i 1.26670 + 0.692574i
\(281\) 8.64142 20.8622i 0.515504 1.24454i −0.425136 0.905130i \(-0.639774\pi\)
0.940640 0.339407i \(-0.110226\pi\)
\(282\) 0 0
\(283\) −26.0256 + 17.3898i −1.54706 + 1.03371i −0.569776 + 0.821800i \(0.692970\pi\)
−0.977288 + 0.211915i \(0.932030\pi\)
\(284\) 5.91781 + 6.83457i 0.351157 + 0.405557i
\(285\) 0 0
\(286\) 8.55803 5.28432i 0.506047 0.312468i
\(287\) 11.8786i 0.701171i
\(288\) 0 0
\(289\) 5.09731i 0.299842i
\(290\) −9.97940 16.1618i −0.586010 0.949052i
\(291\) 0 0
\(292\) 11.8080 + 0.848871i 0.691012 + 0.0496764i
\(293\) −16.4610 + 10.9989i −0.961661 + 0.642561i −0.934082 0.357058i \(-0.883780\pi\)
−0.0275790 + 0.999620i \(0.508780\pi\)
\(294\) 0 0
\(295\) 6.47937 15.6426i 0.377243 0.910746i
\(296\) −2.02886 + 18.7742i −0.117925 + 1.09123i
\(297\) 0 0
\(298\) 5.51730 12.0754i 0.319609 0.699507i
\(299\) 4.54359 + 0.903776i 0.262763 + 0.0522667i
\(300\) 0 0
\(301\) −26.6670 17.8183i −1.53706 1.02703i
\(302\) 24.1099 3.90238i 1.38737 0.224557i
\(303\) 0 0
\(304\) −0.478415 9.04943i −0.0274390 0.519020i
\(305\) 16.4431 + 16.4431i 0.941531 + 0.941531i
\(306\) 0 0
\(307\) 14.1044 21.1087i 0.804981 1.20474i −0.170652 0.985331i \(-0.554587\pi\)
0.975633 0.219408i \(-0.0704126\pi\)
\(308\) −23.6413 + 13.4509i −1.34709 + 0.766437i
\(309\) 0 0
\(310\) −3.12405 8.38057i −0.177434 0.475985i
\(311\) −13.9327 + 5.77111i −0.790051 + 0.327250i −0.740964 0.671545i \(-0.765631\pi\)
−0.0490867 + 0.998795i \(0.515631\pi\)
\(312\) 0 0
\(313\) 5.08075 + 2.10452i 0.287181 + 0.118954i 0.521624 0.853176i \(-0.325327\pi\)
−0.234443 + 0.972130i \(0.575327\pi\)
\(314\) 6.07164 + 0.217962i 0.342642 + 0.0123003i
\(315\) 0 0
\(316\) 5.09630 + 15.3307i 0.286689 + 0.862417i
\(317\) 4.93180 0.980996i 0.276997 0.0550982i −0.0546367 0.998506i \(-0.517400\pi\)
0.331634 + 0.943408i \(0.392400\pi\)
\(318\) 0 0
\(319\) 21.3869 1.19744
\(320\) 10.0322 9.65909i 0.560820 0.539959i
\(321\) 0 0
\(322\) −12.1916 2.88332i −0.679413 0.160681i
\(323\) −7.66591 + 1.52484i −0.426543 + 0.0848446i
\(324\) 0 0
\(325\) −2.80761 4.20189i −0.155738 0.233079i
\(326\) −8.69765 0.312231i −0.481718 0.0172929i
\(327\) 0 0
\(328\) 6.53387 + 2.04982i 0.360773 + 0.113183i
\(329\) −22.9921 + 9.52364i −1.26760 + 0.525055i
\(330\) 0 0
\(331\) −1.36801 + 6.87743i −0.0751924 + 0.378018i −0.999997 0.00242459i \(-0.999228\pi\)
0.924805 + 0.380442i \(0.124228\pi\)
\(332\) 12.3454 + 21.6983i 0.677544 + 1.19085i
\(333\) 0 0
\(334\) 7.77085 + 5.60574i 0.425202 + 0.306733i
\(335\) −3.41906 3.41906i −0.186803 0.186803i
\(336\) 0 0
\(337\) −11.6065 + 11.6065i −0.632248 + 0.632248i −0.948631 0.316383i \(-0.897531\pi\)
0.316383 + 0.948631i \(0.397531\pi\)
\(338\) −8.95831 + 1.44998i −0.487268 + 0.0788683i
\(339\) 0 0
\(340\) −9.48307 7.37224i −0.514291 0.399816i
\(341\) 9.87693 + 1.96464i 0.534866 + 0.106391i
\(342\) 0 0
\(343\) 18.9104 + 45.6538i 1.02107 + 2.46507i
\(344\) −14.4029 + 11.5935i −0.776550 + 0.625081i
\(345\) 0 0
\(346\) 17.4035 16.1973i 0.935617 0.870771i
\(347\) −14.1994 + 9.48772i −0.762262 + 0.509327i −0.874897 0.484309i \(-0.839071\pi\)
0.112635 + 0.993636i \(0.464071\pi\)
\(348\) 0 0
\(349\) −2.26631 11.3935i −0.121313 0.609881i −0.992832 0.119519i \(-0.961865\pi\)
0.871519 0.490362i \(-0.163135\pi\)
\(350\) 7.18008 + 11.6282i 0.383792 + 0.621556i
\(351\) 0 0
\(352\) 3.31909 + 15.3251i 0.176908 + 0.816833i
\(353\) 11.5221i 0.613261i −0.951829 0.306631i \(-0.900798\pi\)
0.951829 0.306631i \(-0.0992016\pi\)
\(354\) 0 0
\(355\) −1.53515 7.71770i −0.0814770 0.409613i
\(356\) 13.8036 11.9521i 0.731592 0.633459i
\(357\) 0 0
\(358\) 17.5056 + 18.8092i 0.925198 + 0.994098i
\(359\) 1.31387 3.17197i 0.0693435 0.167410i −0.885408 0.464815i \(-0.846121\pi\)
0.954752 + 0.297405i \(0.0961210\pi\)
\(360\) 0 0
\(361\) −5.30684 12.8118i −0.279307 0.674307i
\(362\) 8.77271 + 4.00831i 0.461084 + 0.210672i
\(363\) 0 0
\(364\) −24.9816 + 3.12850i −1.30939 + 0.163978i
\(365\) −8.56763 5.72471i −0.448450 0.299645i
\(366\) 0 0
\(367\) −22.5749 + 22.5749i −1.17840 + 1.17840i −0.198245 + 0.980152i \(0.563524\pi\)
−0.980152 + 0.198245i \(0.936476\pi\)
\(368\) −3.68983 + 6.20851i −0.192346 + 0.323641i
\(369\) 0 0
\(370\) 9.61582 13.3298i 0.499903 0.692981i
\(371\) 7.18076 10.7468i 0.372807 0.557945i
\(372\) 0 0
\(373\) −6.61395 + 33.2506i −0.342457 + 1.72165i 0.298793 + 0.954318i \(0.403416\pi\)
−0.641250 + 0.767332i \(0.721584\pi\)
\(374\) 12.6726 4.72400i 0.655286 0.244272i
\(375\) 0 0
\(376\) 1.27090 + 14.2904i 0.0655416 + 0.736969i
\(377\) 18.2892 + 7.57563i 0.941942 + 0.390165i
\(378\) 0 0
\(379\) −11.6484 17.4330i −0.598337 0.895474i 0.401455 0.915879i \(-0.368505\pi\)
−0.999792 + 0.0204046i \(0.993505\pi\)
\(380\) −3.53321 + 7.05201i −0.181250 + 0.361760i
\(381\) 0 0
\(382\) 1.34435 5.68437i 0.0687830 0.290838i
\(383\) −0.0590227 −0.00301592 −0.00150796 0.999999i \(-0.500480\pi\)
−0.00150796 + 0.999999i \(0.500480\pi\)
\(384\) 0 0
\(385\) 23.6748 1.20658
\(386\) −0.895067 + 3.78465i −0.0455577 + 0.192633i
\(387\) 0 0
\(388\) −8.58373 + 17.1324i −0.435773 + 0.869768i
\(389\) 1.79208 + 2.68204i 0.0908621 + 0.135985i 0.874116 0.485717i \(-0.161442\pi\)
−0.783254 + 0.621702i \(0.786442\pi\)
\(390\) 0 0
\(391\) 5.75504 + 2.38382i 0.291045 + 0.120555i
\(392\) 48.0965 4.27742i 2.42924 0.216042i
\(393\) 0 0
\(394\) −3.64144 + 1.35743i −0.183453 + 0.0683863i
\(395\) 2.74331 13.7916i 0.138031 0.693929i
\(396\) 0 0
\(397\) 3.22276 4.82320i 0.161746 0.242069i −0.741740 0.670687i \(-0.765999\pi\)
0.903486 + 0.428618i \(0.140999\pi\)
\(398\) −0.744690 + 1.03231i −0.0373279 + 0.0517451i
\(399\) 0 0
\(400\) 7.63520 1.94282i 0.381760 0.0971408i
\(401\) −18.2413 + 18.2413i −0.910926 + 0.910926i −0.996345 0.0854187i \(-0.972777\pi\)
0.0854187 + 0.996345i \(0.472777\pi\)
\(402\) 0 0
\(403\) 7.75043 + 5.17867i 0.386076 + 0.257968i
\(404\) −9.04034 + 1.13214i −0.449774 + 0.0563261i
\(405\) 0 0
\(406\) −48.6927 22.2480i −2.41658 1.10415i
\(407\) 7.08206 + 17.0976i 0.351045 + 0.847497i
\(408\) 0 0
\(409\) 3.91775 9.45829i 0.193720 0.467682i −0.796936 0.604064i \(-0.793547\pi\)
0.990656 + 0.136381i \(0.0435473\pi\)
\(410\) −4.06071 4.36311i −0.200544 0.215479i
\(411\) 0 0
\(412\) 1.99068 1.72366i 0.0980737 0.0849185i
\(413\) −9.30969 46.8030i −0.458100 2.30302i
\(414\) 0 0
\(415\) 21.7291i 1.06664i
\(416\) −2.59009 + 14.2811i −0.126990 + 0.700189i
\(417\) 0 0
\(418\) −4.66597 7.55660i −0.228220 0.369606i
\(419\) −6.22515 31.2959i −0.304119 1.52891i −0.766511 0.642232i \(-0.778009\pi\)
0.462392 0.886676i \(-0.346991\pi\)
\(420\) 0 0
\(421\) 9.43550 6.30460i 0.459858 0.307268i −0.303976 0.952680i \(-0.598314\pi\)
0.763835 + 0.645412i \(0.223314\pi\)
\(422\) 14.3704 13.3745i 0.699542 0.651058i
\(423\) 0 0
\(424\) −4.67217 5.80433i −0.226901 0.281883i
\(425\) −2.60044 6.27801i −0.126140 0.304528i
\(426\) 0 0
\(427\) 64.2806 + 12.7862i 3.11076 + 0.618768i
\(428\) −5.71081 4.43964i −0.276042 0.214598i
\(429\) 0 0
\(430\) 15.8863 2.57132i 0.766103 0.124000i
\(431\) 19.4613 19.4613i 0.937417 0.937417i −0.0607373 0.998154i \(-0.519345\pi\)
0.998154 + 0.0607373i \(0.0193452\pi\)
\(432\) 0 0
\(433\) −25.2269 25.2269i −1.21233 1.21233i −0.970259 0.242069i \(-0.922174\pi\)
−0.242069 0.970259i \(-0.577826\pi\)
\(434\) −20.4436 14.7476i −0.981323 0.707907i
\(435\) 0 0
\(436\) 9.06397 + 15.9308i 0.434086 + 0.762947i
\(437\) 0.798020 4.01192i 0.0381745 0.191916i
\(438\) 0 0
\(439\) 26.5392 10.9929i 1.26665 0.524662i 0.354704 0.934979i \(-0.384582\pi\)
0.911943 + 0.410316i \(0.134582\pi\)
\(440\) 4.08543 13.0224i 0.194765 0.620820i
\(441\) 0 0
\(442\) 12.5104 + 0.449104i 0.595061 + 0.0213617i
\(443\) −0.00461809 0.00691146i −0.000219412 0.000328373i 0.831360 0.555734i \(-0.187563\pi\)
−0.831579 + 0.555406i \(0.812563\pi\)
\(444\) 0 0
\(445\) −15.5873 + 3.10050i −0.738908 + 0.146978i
\(446\) −8.67487 2.05160i −0.410767 0.0971462i
\(447\) 0 0
\(448\) 8.38539 38.3442i 0.396173 1.81160i
\(449\) −13.9393 −0.657838 −0.328919 0.944358i \(-0.606684\pi\)
−0.328919 + 0.944358i \(0.606684\pi\)
\(450\) 0 0
\(451\) 6.58215 1.30927i 0.309941 0.0616511i
\(452\) −8.25782 24.8411i −0.388415 1.16843i
\(453\) 0 0
\(454\) 25.1211 + 0.901807i 1.17899 + 0.0423239i
\(455\) 20.2457 + 8.38604i 0.949132 + 0.393143i
\(456\) 0 0
\(457\) −13.6237 + 5.64312i −0.637290 + 0.263974i −0.677847 0.735203i \(-0.737087\pi\)
0.0405569 + 0.999177i \(0.487087\pi\)
\(458\) 4.54657 + 12.1966i 0.212447 + 0.569912i
\(459\) 0 0
\(460\) 5.46376 3.10866i 0.254749 0.144942i
\(461\) −16.5649 + 24.7911i −0.771504 + 1.15464i 0.212616 + 0.977136i \(0.431802\pi\)
−0.984120 + 0.177502i \(0.943198\pi\)
\(462\) 0 0
\(463\) −7.31500 7.31500i −0.339957 0.339957i 0.516394 0.856351i \(-0.327274\pi\)
−0.856351 + 0.516394i \(0.827274\pi\)
\(464\) −20.6402 + 22.9444i −0.958199 + 1.06517i
\(465\) 0 0
\(466\) 19.1303 3.09639i 0.886193 0.143438i
\(467\) 26.6310 + 17.7943i 1.23233 + 0.823420i 0.989200 0.146573i \(-0.0468242\pi\)
0.243135 + 0.969992i \(0.421824\pi\)
\(468\) 0 0
\(469\) −13.3660 2.65866i −0.617185 0.122766i
\(470\) 5.18953 11.3580i 0.239375 0.523905i
\(471\) 0 0
\(472\) −27.3507 2.95570i −1.25892 0.136047i
\(473\) −6.93421 + 16.7407i −0.318835 + 0.769737i
\(474\) 0 0
\(475\) −3.71020 + 2.47908i −0.170236 + 0.113748i
\(476\) −33.7666 2.42746i −1.54769 0.111262i
\(477\) 0 0
\(478\) −8.81689 14.2791i −0.403275 0.653110i
\(479\) 24.2263i 1.10693i 0.832873 + 0.553465i \(0.186695\pi\)
−0.832873 + 0.553465i \(0.813305\pi\)
\(480\) 0 0
\(481\) 17.1298i 0.781050i
\(482\) −6.76873 + 4.17948i −0.308307 + 0.190370i
\(483\) 0 0
\(484\) −4.34168 5.01428i −0.197349 0.227922i
\(485\) 13.8681 9.26636i 0.629717 0.420764i
\(486\) 0 0
\(487\) 12.2953 29.6835i 0.557153 1.34509i −0.354857 0.934921i \(-0.615470\pi\)
0.912011 0.410167i \(-0.134530\pi\)
\(488\) 18.1257 33.1514i 0.820511 1.50069i
\(489\) 0 0
\(490\) −38.2272 17.4662i −1.72693 0.789043i
\(491\) 17.7528 + 3.53125i 0.801173 + 0.159363i 0.578663 0.815567i \(-0.303575\pi\)
0.222510 + 0.974930i \(0.428575\pi\)
\(492\) 0 0
\(493\) 22.1327 + 14.7886i 0.996805 + 0.666044i
\(494\) −1.31346 8.11487i −0.0590953 0.365105i
\(495\) 0 0
\(496\) −11.6398 + 8.70017i −0.522643 + 0.390649i
\(497\) −15.6821 15.6821i −0.703440 0.703440i
\(498\) 0 0
\(499\) 15.7545 23.5782i 0.705267 1.05551i −0.289875 0.957064i \(-0.593614\pi\)
0.995143 0.0984427i \(-0.0313861\pi\)
\(500\) −23.3984 6.42826i −1.04641 0.287481i
\(501\) 0 0
\(502\) −24.0683 + 8.97201i −1.07422 + 0.400440i
\(503\) 29.1486 12.0738i 1.29967 0.538342i 0.377819 0.925880i \(-0.376674\pi\)
0.921854 + 0.387538i \(0.126674\pi\)
\(504\) 0 0
\(505\) 7.32651 + 3.03474i 0.326025 + 0.135044i
\(506\) −0.253924 + 7.07342i −0.0112883 + 0.314452i
\(507\) 0 0
\(508\) −14.8206 7.42546i −0.657559 0.329452i
\(509\) −5.86884 + 1.16739i −0.260132 + 0.0517435i −0.323433 0.946251i \(-0.604837\pi\)
0.0633013 + 0.997994i \(0.479837\pi\)
\(510\) 0 0
\(511\) −29.0416 −1.28473
\(512\) −19.6444 11.2293i −0.868169 0.496269i
\(513\) 0 0
\(514\) −4.94199 + 20.8964i −0.217982 + 0.921702i
\(515\) −2.24790 + 0.447136i −0.0990544 + 0.0197031i
\(516\) 0 0
\(517\) 7.81144 + 11.6906i 0.343547 + 0.514154i
\(518\) 1.66188 46.2942i 0.0730190 2.03405i
\(519\) 0 0
\(520\) 8.10647 9.68910i 0.355492 0.424895i
\(521\) −26.1756 + 10.8423i −1.14678 + 0.475010i −0.873451 0.486912i \(-0.838123\pi\)
−0.273325 + 0.961922i \(0.588123\pi\)
\(522\) 0 0
\(523\) −1.00914 + 5.07326i −0.0441264 + 0.221838i −0.996556 0.0829195i \(-0.973576\pi\)
0.952430 + 0.304758i \(0.0985756\pi\)
\(524\) 25.2229 + 6.92949i 1.10187 + 0.302716i
\(525\) 0 0
\(526\) −17.1874 + 23.8257i −0.749406 + 1.03885i
\(527\) 8.86283 + 8.86283i 0.386071 + 0.386071i
\(528\) 0 0
\(529\) 13.9583 13.9583i 0.606881 0.606881i
\(530\) 1.03624 + 6.40213i 0.0450113 + 0.278091i
\(531\) 0 0
\(532\) 2.76241 + 22.0583i 0.119766 + 0.956350i
\(533\) 6.09255 + 1.21188i 0.263898 + 0.0524925i
\(534\) 0 0
\(535\) 2.40939 + 5.81678i 0.104167 + 0.251481i
\(536\) −3.76891 + 6.89324i −0.162792 + 0.297743i
\(537\) 0 0
\(538\) 6.43581 + 6.91508i 0.277467 + 0.298130i
\(539\) 39.3468 26.2907i 1.69479 1.13242i
\(540\) 0 0
\(541\) 0.217556 + 1.09373i 0.00935346 + 0.0470230i 0.985180 0.171523i \(-0.0548687\pi\)
−0.975827 + 0.218546i \(0.929869\pi\)
\(542\) −4.56230 + 2.81708i −0.195967 + 0.121004i
\(543\) 0 0
\(544\) −7.16216 + 18.1546i −0.307075 + 0.778372i
\(545\) 15.9534i 0.683368i
\(546\) 0 0
\(547\) −1.95857 9.84642i −0.0837426 0.421002i −0.999801 0.0199572i \(-0.993647\pi\)
0.916058 0.401045i \(-0.131353\pi\)
\(548\) −7.39107 0.531339i −0.315731 0.0226977i
\(549\) 0 0
\(550\) 5.65203 5.26030i 0.241003 0.224300i
\(551\) 6.68916 16.1491i 0.284968 0.687973i
\(552\) 0 0
\(553\) −15.1665 36.6152i −0.644946 1.55704i
\(554\) 4.40933 9.65040i 0.187334 0.410006i
\(555\) 0 0
\(556\) 24.0641 30.9541i 1.02054 1.31275i
\(557\) 20.7214 + 13.8456i 0.877994 + 0.586657i 0.910820 0.412804i \(-0.135451\pi\)
−0.0328255 + 0.999461i \(0.510451\pi\)
\(558\) 0 0
\(559\) −11.8597 + 11.8597i −0.501612 + 0.501612i
\(560\) −22.8482 + 25.3989i −0.965514 + 1.07330i
\(561\) 0 0
\(562\) 25.8990 + 18.6830i 1.09248 + 0.788096i
\(563\) −22.4818 + 33.6463i −0.947493 + 1.41802i −0.0394146 + 0.999223i \(0.512549\pi\)
−0.908078 + 0.418800i \(0.862451\pi\)
\(564\) 0 0
\(565\) −4.44514 + 22.3472i −0.187008 + 0.940155i
\(566\) −15.4618 41.4778i −0.649907 1.74344i
\(567\) 0 0
\(568\) −11.3322 + 5.91985i −0.475489 + 0.248391i
\(569\) −21.2575 8.80516i −0.891163 0.369132i −0.110347 0.993893i \(-0.535196\pi\)
−0.780816 + 0.624762i \(0.785196\pi\)
\(570\) 0 0
\(571\) 21.4891 + 32.1606i 0.899289 + 1.34588i 0.938002 + 0.346631i \(0.112674\pi\)
−0.0387126 + 0.999250i \(0.512326\pi\)
\(572\) 4.48706 + 13.4979i 0.187613 + 0.564377i
\(573\) 0 0
\(574\) −16.3479 3.86627i −0.682348 0.161375i
\(575\) 3.55627 0.148307
\(576\) 0 0
\(577\) 12.9731 0.540076 0.270038 0.962850i \(-0.412964\pi\)
0.270038 + 0.962850i \(0.412964\pi\)
\(578\) −7.01517 1.65908i −0.291792 0.0690088i
\(579\) 0 0
\(580\) 25.4907 8.47377i 1.05845 0.351854i
\(581\) −34.0241 50.9206i −1.41156 2.11254i
\(582\) 0 0
\(583\) −6.74646 2.79448i −0.279410 0.115735i
\(584\) −5.01156 + 15.9745i −0.207380 + 0.661029i
\(585\) 0 0
\(586\) −9.77944 26.2344i −0.403985 1.08373i
\(587\) −0.438329 + 2.20363i −0.0180918 + 0.0909534i −0.988776 0.149404i \(-0.952265\pi\)
0.970685 + 0.240357i \(0.0772646\pi\)
\(588\) 0 0
\(589\) 4.57268 6.84350i 0.188414 0.281982i
\(590\) 19.4192 + 14.0086i 0.799474 + 0.576725i
\(591\) 0 0
\(592\) −25.1775 8.90287i −1.03479 0.365906i
\(593\) 25.5913 25.5913i 1.05091 1.05091i 0.0522765 0.998633i \(-0.483352\pi\)
0.998633 0.0522765i \(-0.0166477\pi\)
\(594\) 0 0
\(595\) 24.5003 + 16.3706i 1.00441 + 0.671128i
\(596\) 14.8229 + 11.5235i 0.607170 + 0.472021i
\(597\) 0 0
\(598\) −2.72268 + 5.95895i −0.111339 + 0.243679i
\(599\) −4.71217 11.3762i −0.192534 0.464819i 0.797903 0.602786i \(-0.205943\pi\)
−0.990437 + 0.137968i \(0.955943\pi\)
\(600\) 0 0
\(601\) −8.85882 + 21.3871i −0.361359 + 0.872397i 0.633743 + 0.773543i \(0.281518\pi\)
−0.995102 + 0.0988537i \(0.968482\pi\)
\(602\) 33.2021 30.9009i 1.35322 1.25943i
\(603\) 0 0
\(604\) −2.47669 + 34.4514i −0.100775 + 1.40181i
\(605\) 1.12628 + 5.66219i 0.0457898 + 0.230201i
\(606\) 0 0
\(607\) 11.3561i 0.460929i 0.973081 + 0.230465i \(0.0740246\pi\)
−0.973081 + 0.230465i \(0.925975\pi\)
\(608\) 12.6100 + 2.28701i 0.511402 + 0.0927505i
\(609\) 0 0
\(610\) −27.9818 + 17.2779i −1.13295 + 0.699562i
\(611\) 2.53898 + 12.7643i 0.102716 + 0.516389i
\(612\) 0 0
\(613\) 20.5529 13.7330i 0.830122 0.554670i −0.0663364 0.997797i \(-0.521131\pi\)
0.896459 + 0.443127i \(0.146131\pi\)
\(614\) 24.4601 + 26.2817i 0.987131 + 1.06064i
\(615\) 0 0
\(616\) −10.8170 36.9143i −0.435829 1.48732i
\(617\) 1.48976 + 3.59660i 0.0599754 + 0.144793i 0.951026 0.309110i \(-0.100031\pi\)
−0.891051 + 0.453903i \(0.850031\pi\)
\(618\) 0 0
\(619\) −0.987852 0.196496i −0.0397051 0.00789784i 0.175198 0.984533i \(-0.443944\pi\)
−0.214903 + 0.976635i \(0.568944\pi\)
\(620\) 12.5506 1.57174i 0.504043 0.0631225i
\(621\) 0 0
\(622\) −3.40764 21.0532i −0.136634 0.844158i
\(623\) −31.6729 + 31.6729i −1.26895 + 1.26895i
\(624\) 0 0
\(625\) 7.97082 + 7.97082i 0.318833 + 0.318833i
\(626\) −4.55003 + 6.30739i −0.181856 + 0.252094i
\(627\) 0 0
\(628\) −2.27618 + 8.28514i −0.0908295 + 0.330613i
\(629\) −4.49360 + 22.5909i −0.179172 + 0.900757i
\(630\) 0 0
\(631\) −24.1540 + 10.0049i −0.961554 + 0.398289i −0.807561 0.589783i \(-0.799213\pi\)
−0.153992 + 0.988072i \(0.549213\pi\)
\(632\) −22.7576 + 2.02392i −0.905248 + 0.0805073i
\(633\) 0 0
\(634\) −0.255118 + 7.10668i −0.0101320 + 0.282242i
\(635\) 8.01597 + 11.9968i 0.318104 + 0.476077i
\(636\) 0 0
\(637\) 42.9604 8.54535i 1.70215 0.338579i
\(638\) −6.96106 + 29.4337i −0.275591 + 1.16529i
\(639\) 0 0
\(640\) 10.0280 + 16.9507i 0.396391 + 0.670036i
\(641\) 6.97029 0.275310 0.137655 0.990480i \(-0.456044\pi\)
0.137655 + 0.990480i \(0.456044\pi\)
\(642\) 0 0
\(643\) −10.2606 + 2.04096i −0.404638 + 0.0804875i −0.393214 0.919447i \(-0.628637\pi\)
−0.0114247 + 0.999935i \(0.503637\pi\)
\(644\) 7.93632 15.8403i 0.312735 0.624194i
\(645\) 0 0
\(646\) 0.396552 11.0465i 0.0156021 0.434619i
\(647\) −2.38405 0.987505i −0.0937266 0.0388228i 0.335328 0.942102i \(-0.391153\pi\)
−0.429054 + 0.903279i \(0.641153\pi\)
\(648\) 0 0
\(649\) −24.9083 + 10.3173i −0.977735 + 0.404991i
\(650\) 6.69668 2.49633i 0.262665 0.0979143i
\(651\) 0 0
\(652\) 3.26064 11.8685i 0.127696 0.464806i
\(653\) 4.66186 6.97696i 0.182433 0.273030i −0.728970 0.684546i \(-0.760001\pi\)
0.911403 + 0.411516i \(0.135001\pi\)
\(654\) 0 0
\(655\) −16.0990 16.0990i −0.629039 0.629039i
\(656\) −4.94773 + 8.32506i −0.193176 + 0.325039i
\(657\) 0 0
\(658\) −5.62338 34.7426i −0.219222 1.35441i
\(659\) 1.71040 + 1.14285i 0.0666278 + 0.0445192i 0.588438 0.808542i \(-0.299743\pi\)
−0.521810 + 0.853062i \(0.674743\pi\)
\(660\) 0 0
\(661\) −2.70170 0.537402i −0.105084 0.0209025i 0.142268 0.989828i \(-0.454560\pi\)
−0.247352 + 0.968926i \(0.579560\pi\)
\(662\) −9.01979 4.12120i −0.350564 0.160175i
\(663\) 0 0
\(664\) −33.8805 + 9.92800i −1.31482 + 0.385281i
\(665\) 7.40473 17.8766i 0.287143 0.693225i
\(666\) 0 0
\(667\) −11.5830 + 7.73953i −0.448496 + 0.299676i
\(668\) −10.2442 + 8.87006i −0.396359 + 0.343193i
\(669\) 0 0
\(670\) 5.81832 3.59263i 0.224781 0.138795i
\(671\) 37.0284i 1.42947i
\(672\) 0 0
\(673\) 6.84519i 0.263863i −0.991259 0.131931i \(-0.957882\pi\)
0.991259 0.131931i \(-0.0421178\pi\)
\(674\) −12.1958 19.7512i −0.469763 0.760788i
\(675\) 0 0
\(676\) 0.920242 12.8008i 0.0353939 0.492339i
\(677\) −15.3133 + 10.2320i −0.588539 + 0.393249i −0.813882 0.581030i \(-0.802650\pi\)
0.225343 + 0.974280i \(0.427650\pi\)
\(678\) 0 0
\(679\) 17.9894 43.4302i 0.690369 1.66670i
\(680\) 13.2326 10.6515i 0.507447 0.408467i
\(681\) 0 0
\(682\) −5.91860 + 12.9537i −0.226635 + 0.496021i
\(683\) −16.5246 3.28694i −0.632296 0.125771i −0.131471 0.991320i \(-0.541970\pi\)
−0.500825 + 0.865549i \(0.666970\pi\)
\(684\) 0 0
\(685\) 5.36279 + 3.58330i 0.204902 + 0.136911i
\(686\) −68.9860 + 11.1660i −2.63390 + 0.426318i
\(687\) 0 0
\(688\) −11.2677 23.5954i −0.429577 0.899566i
\(689\) −4.77944 4.77944i −0.182082 0.182082i
\(690\) 0 0
\(691\) −6.27571 + 9.39227i −0.238739 + 0.357299i −0.931420 0.363945i \(-0.881429\pi\)
0.692681 + 0.721244i \(0.256429\pi\)
\(692\) 16.6270 + 29.2235i 0.632062 + 1.11091i
\(693\) 0 0
\(694\) −8.43582 22.6300i −0.320219 0.859021i
\(695\) −31.5285 + 13.0595i −1.19595 + 0.495377i
\(696\) 0 0
\(697\) 7.71700 + 3.19648i 0.292302 + 0.121075i
\(698\) 16.4180 + 0.589378i 0.621429 + 0.0223083i
\(699\) 0 0
\(700\) −18.3403 + 6.09680i −0.693200 + 0.230437i
\(701\) 28.6261 5.69409i 1.08119 0.215063i 0.377817 0.925880i \(-0.376675\pi\)
0.703377 + 0.710817i \(0.251675\pi\)
\(702\) 0 0
\(703\) 15.1253 0.570461
\(704\) −22.1715 0.420160i −0.835620 0.0158354i
\(705\) 0 0
\(706\) 15.8573 + 3.75025i 0.596798 + 0.141143i
\(707\) 21.9211 4.36037i 0.824427 0.163989i
\(708\) 0 0
\(709\) −26.7046 39.9663i −1.00291 1.50097i −0.859390 0.511320i \(-0.829157\pi\)
−0.143524 0.989647i \(-0.545843\pi\)
\(710\) 11.1211 + 0.399231i 0.417369 + 0.0149829i
\(711\) 0 0
\(712\) 11.9562 + 22.8874i 0.448078 + 0.857743i
\(713\) −6.06025 + 2.51024i −0.226958 + 0.0940092i
\(714\) 0 0
\(715\) 2.41536 12.1428i 0.0903293 0.454116i
\(716\) −31.5839 + 17.9700i −1.18035 + 0.671569i
\(717\) 0 0
\(718\) 3.93778 + 2.84063i 0.146956 + 0.106012i
\(719\) −17.7608 17.7608i −0.662368 0.662368i 0.293570 0.955938i \(-0.405157\pi\)
−0.955938 + 0.293570i \(0.905157\pi\)
\(720\) 0 0
\(721\) −4.56767 + 4.56767i −0.170109 + 0.170109i
\(722\) 19.3596 3.13350i 0.720488 0.116617i
\(723\) 0 0
\(724\) −8.37179 + 10.7688i −0.311135 + 0.400220i
\(725\) 14.9047 + 2.96472i 0.553546 + 0.110107i
\(726\) 0 0
\(727\) 19.6348 + 47.4026i 0.728214 + 1.75806i 0.648459 + 0.761250i \(0.275414\pi\)
0.0797551 + 0.996814i \(0.474586\pi\)
\(728\) 3.82547 35.3991i 0.141781 1.31198i
\(729\) 0 0
\(730\) 10.6672 9.92790i 0.394812 0.367448i
\(731\) −18.7518 + 12.5296i −0.693560 + 0.463422i
\(732\) 0 0
\(733\) −0.665236 3.34437i −0.0245710 0.123527i 0.966553 0.256467i \(-0.0825584\pi\)
−0.991124 + 0.132940i \(0.957558\pi\)
\(734\) −23.7209 38.4163i −0.875555 1.41797i
\(735\) 0 0
\(736\) −7.34348 7.09888i −0.270684 0.261668i
\(737\) 7.69939i 0.283611i
\(738\) 0 0
\(739\) 4.70308 + 23.6440i 0.173006 + 0.869758i 0.965605 + 0.260015i \(0.0837274\pi\)
−0.792599 + 0.609743i \(0.791273\pi\)
\(740\) 15.2153 + 17.5724i 0.559325 + 0.645973i
\(741\) 0 0
\(742\) 12.4530 + 13.3804i 0.457165 + 0.491210i
\(743\) 16.2703 39.2800i 0.596899 1.44104i −0.279826 0.960051i \(-0.590277\pi\)
0.876725 0.480992i \(-0.159723\pi\)
\(744\) 0 0
\(745\) −6.25379 15.0980i −0.229121 0.553148i
\(746\) −43.6084 19.9249i −1.59662 0.729503i
\(747\) 0 0
\(748\) 2.37669 + 18.9783i 0.0869004 + 0.693914i
\(749\) 14.7544 + 9.85854i 0.539112 + 0.360223i
\(750\) 0 0
\(751\) 1.57525 1.57525i 0.0574817 0.0574817i −0.677782 0.735263i \(-0.737059\pi\)
0.735263 + 0.677782i \(0.237059\pi\)
\(752\) −20.0807 2.90218i −0.732269 0.105832i
\(753\) 0 0
\(754\) −16.3788 + 22.7048i −0.596480 + 0.826859i
\(755\) 16.7026 24.9971i 0.607868 0.909739i
\(756\) 0 0
\(757\) −3.61478 + 18.1727i −0.131382 + 0.660500i 0.857821 + 0.513948i \(0.171817\pi\)
−0.989203 + 0.146552i \(0.953183\pi\)
\(758\) 27.7835 10.3569i 1.00914 0.376180i
\(759\) 0 0
\(760\) −8.55532 7.15788i −0.310334 0.259644i
\(761\) 25.7162 + 10.6520i 0.932211 + 0.386135i 0.796517 0.604616i \(-0.206673\pi\)
0.135694 + 0.990751i \(0.456673\pi\)
\(762\) 0 0
\(763\) −24.9803 37.3857i −0.904348 1.35345i
\(764\) 7.38555 + 3.70032i 0.267200 + 0.133873i
\(765\) 0 0
\(766\) 0.0192108 0.0812300i 0.000694116 0.00293496i
\(767\) −24.9551 −0.901077
\(768\) 0 0
\(769\) 9.14052 0.329615 0.164808 0.986326i \(-0.447300\pi\)
0.164808 + 0.986326i \(0.447300\pi\)
\(770\) −7.70572 + 32.5824i −0.277695 + 1.17419i
\(771\) 0 0
\(772\) −4.91729 2.46367i −0.176977 0.0886694i
\(773\) 21.6826 + 32.4503i 0.779869 + 1.16716i 0.982200 + 0.187839i \(0.0601482\pi\)
−0.202331 + 0.979317i \(0.564852\pi\)
\(774\) 0 0
\(775\) 6.61095 + 2.73835i 0.237472 + 0.0983643i
\(776\) −20.7847 17.3897i −0.746126 0.624252i
\(777\) 0 0
\(778\) −4.27444 + 1.59339i −0.153246 + 0.0571259i
\(779\) 1.07007 5.37962i 0.0383393 0.192745i
\(780\) 0 0
\(781\) −6.96126 + 10.4183i −0.249093 + 0.372795i
\(782\) −5.15389 + 7.14448i −0.184303 + 0.255486i
\(783\) 0 0
\(784\) −9.76777 + 67.5850i −0.348849 + 2.41375i
\(785\) 5.28815 5.28815i 0.188742 0.188742i
\(786\) 0 0
\(787\) −5.88104 3.92959i −0.209637 0.140075i 0.446320 0.894874i \(-0.352734\pi\)
−0.655956 + 0.754799i \(0.727734\pi\)
\(788\) −0.682935 5.45335i −0.0243286