Properties

Label 432.2.be.b.95.5
Level $432$
Weight $2$
Character 432.95
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.be (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 95.5
Character \(\chi\) \(=\) 432.95
Dual form 432.2.be.b.191.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.63553 + 0.570126i) q^{3} +(2.34697 - 2.79701i) q^{5} +(0.550750 - 1.51317i) q^{7} +(2.34991 + 1.86492i) q^{9} +O(q^{10})\) \(q+(1.63553 + 0.570126i) q^{3} +(2.34697 - 2.79701i) q^{5} +(0.550750 - 1.51317i) q^{7} +(2.34991 + 1.86492i) q^{9} +(-2.21396 + 1.85773i) q^{11} +(0.121792 - 0.690719i) q^{13} +(5.43318 - 3.23652i) q^{15} +(-5.56131 - 3.21082i) q^{17} +(-1.62624 + 0.938910i) q^{19} +(1.76347 - 2.16084i) q^{21} +(-2.18387 + 0.794864i) q^{23} +(-1.44675 - 8.20494i) q^{25} +(2.78011 + 4.38987i) q^{27} +(5.54988 - 0.978594i) q^{29} +(3.63921 + 9.99865i) q^{31} +(-4.68013 + 1.77614i) q^{33} +(-2.93977 - 5.09183i) q^{35} +(-4.10464 + 7.10944i) q^{37} +(0.592992 - 1.06025i) q^{39} +(6.18442 + 1.09048i) q^{41} +(5.65989 + 6.74520i) q^{43} +(10.7314 - 2.19583i) q^{45} +(-1.67459 - 0.609501i) q^{47} +(3.37594 + 2.83275i) q^{49} +(-7.26511 - 8.42204i) q^{51} -0.849889i q^{53} +10.5525i q^{55} +(-3.19506 + 0.608453i) q^{57} +(-4.54459 - 3.81337i) q^{59} +(-9.95979 - 3.62507i) q^{61} +(4.11616 - 2.52872i) q^{63} +(-1.64610 - 1.96175i) q^{65} +(-14.5520 - 2.56590i) q^{67} +(-4.02496 + 0.0549417i) q^{69} +(5.80783 - 10.0595i) q^{71} +(3.12044 + 5.40475i) q^{73} +(2.31165 - 14.2443i) q^{75} +(1.59173 + 4.37325i) q^{77} +(4.47831 - 0.789647i) q^{79} +(2.04418 + 8.76478i) q^{81} +(-1.28300 - 7.27624i) q^{83} +(-22.0329 + 8.01933i) q^{85} +(9.63492 + 1.56361i) q^{87} +(-6.02277 + 3.47725i) q^{89} +(-0.978101 - 0.564707i) q^{91} +(0.251545 + 18.4279i) q^{93} +(-1.19060 + 6.75220i) q^{95} +(1.35281 - 1.13514i) q^{97} +(-8.66711 + 0.236660i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{17}{18}\right)\)

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 0
\(3\) 1.63553 + 0.570126i 0.944273 + 0.329162i
\(4\) 0 0
\(5\) 2.34697 2.79701i 1.04960 1.25086i 0.0824620 0.996594i \(-0.473722\pi\)
0.967134 0.254266i \(-0.0818339\pi\)
\(6\) 0 0
\(7\) 0.550750 1.51317i 0.208164 0.571926i −0.791042 0.611762i \(-0.790461\pi\)
0.999206 + 0.0398355i \(0.0126834\pi\)
\(8\) 0 0
\(9\) 2.34991 + 1.86492i 0.783304 + 0.621639i
\(10\) 0 0
\(11\) −2.21396 + 1.85773i −0.667533 + 0.560127i −0.912334 0.409447i \(-0.865722\pi\)
0.244801 + 0.969573i \(0.421277\pi\)
\(12\) 0 0
\(13\) 0.121792 0.690719i 0.0337791 0.191571i −0.963249 0.268610i \(-0.913436\pi\)
0.997028 + 0.0770394i \(0.0245467\pi\)
\(14\) 0 0
\(15\) 5.43318 3.23652i 1.40284 0.835666i
\(16\) 0 0
\(17\) −5.56131 3.21082i −1.34882 0.778739i −0.360734 0.932669i \(-0.617474\pi\)
−0.988082 + 0.153930i \(0.950807\pi\)
\(18\) 0 0
\(19\) −1.62624 + 0.938910i −0.373085 + 0.215401i −0.674805 0.737996i \(-0.735772\pi\)
0.301720 + 0.953396i \(0.402439\pi\)
\(20\) 0 0
\(21\) 1.76347 2.16084i 0.384820 0.471535i
\(22\) 0 0
\(23\) −2.18387 + 0.794864i −0.455369 + 0.165741i −0.559513 0.828822i \(-0.689012\pi\)
0.104144 + 0.994562i \(0.466790\pi\)
\(24\) 0 0
\(25\) −1.44675 8.20494i −0.289351 1.64099i
\(26\) 0 0
\(27\) 2.78011 + 4.38987i 0.535033 + 0.844831i
\(28\) 0 0
\(29\) 5.54988 0.978594i 1.03059 0.181720i 0.367313 0.930097i \(-0.380278\pi\)
0.663274 + 0.748377i \(0.269167\pi\)
\(30\) 0 0
\(31\) 3.63921 + 9.99865i 0.653622 + 1.79581i 0.603917 + 0.797047i \(0.293606\pi\)
0.0497045 + 0.998764i \(0.484172\pi\)
\(32\) 0 0
\(33\) −4.68013 + 1.77614i −0.814706 + 0.309186i
\(34\) 0 0
\(35\) −2.93977 5.09183i −0.496911 0.860676i
\(36\) 0 0
\(37\) −4.10464 + 7.10944i −0.674798 + 1.16878i 0.301730 + 0.953393i \(0.402436\pi\)
−0.976528 + 0.215391i \(0.930897\pi\)
\(38\) 0 0
\(39\) 0.592992 1.06025i 0.0949547 0.169777i
\(40\) 0 0
\(41\) 6.18442 + 1.09048i 0.965843 + 0.170304i 0.634258 0.773121i \(-0.281306\pi\)
0.331585 + 0.943425i \(0.392417\pi\)
\(42\) 0 0
\(43\) 5.65989 + 6.74520i 0.863125 + 1.02863i 0.999280 + 0.0379452i \(0.0120812\pi\)
−0.136154 + 0.990688i \(0.543474\pi\)
\(44\) 0 0
\(45\) 10.7314 2.19583i 1.59974 0.327334i
\(46\) 0 0
\(47\) −1.67459 0.609501i −0.244264 0.0889049i 0.216987 0.976174i \(-0.430377\pi\)
−0.461251 + 0.887270i \(0.652599\pi\)
\(48\) 0 0
\(49\) 3.37594 + 2.83275i 0.482277 + 0.404679i
\(50\) 0 0
\(51\) −7.26511 8.42204i −1.01732 1.17932i
\(52\) 0 0
\(53\) 0.849889i 0.116741i −0.998295 0.0583706i \(-0.981409\pi\)
0.998295 0.0583706i \(-0.0185905\pi\)
\(54\) 0 0
\(55\) 10.5525i 1.42290i
\(56\) 0 0
\(57\) −3.19506 + 0.608453i −0.423196 + 0.0805916i
\(58\) 0 0
\(59\) −4.54459 3.81337i −0.591656 0.496458i 0.297096 0.954848i \(-0.403982\pi\)
−0.888751 + 0.458390i \(0.848426\pi\)
\(60\) 0 0
\(61\) −9.95979 3.62507i −1.27522 0.464142i −0.386372 0.922343i \(-0.626272\pi\)
−0.888849 + 0.458201i \(0.848494\pi\)
\(62\) 0 0
\(63\) 4.11616 2.52872i 0.518587 0.318589i
\(64\) 0 0
\(65\) −1.64610 1.96175i −0.204174 0.243325i
\(66\) 0 0
\(67\) −14.5520 2.56590i −1.77781 0.313475i −0.814156 0.580646i \(-0.802800\pi\)
−0.963649 + 0.267171i \(0.913911\pi\)
\(68\) 0 0
\(69\) −4.02496 + 0.0549417i −0.484548 + 0.00661420i
\(70\) 0 0
\(71\) 5.80783 10.0595i 0.689263 1.19384i −0.282814 0.959175i \(-0.591268\pi\)
0.972077 0.234663i \(-0.0753988\pi\)
\(72\) 0 0
\(73\) 3.12044 + 5.40475i 0.365219 + 0.632579i 0.988811 0.149171i \(-0.0476606\pi\)
−0.623592 + 0.781750i \(0.714327\pi\)
\(74\) 0 0
\(75\) 2.31165 14.2443i 0.266926 1.64479i
\(76\) 0 0
\(77\) 1.59173 + 4.37325i 0.181395 + 0.498378i
\(78\) 0 0
\(79\) 4.47831 0.789647i 0.503849 0.0888422i 0.0840543 0.996461i \(-0.473213\pi\)
0.419795 + 0.907619i \(0.362102\pi\)
\(80\) 0 0
\(81\) 2.04418 + 8.76478i 0.227131 + 0.973864i
\(82\) 0 0
\(83\) −1.28300 7.27624i −0.140827 0.798671i −0.970623 0.240604i \(-0.922654\pi\)
0.829796 0.558067i \(-0.188457\pi\)
\(84\) 0 0
\(85\) −22.0329 + 8.01933i −2.38981 + 0.869818i
\(86\) 0 0
\(87\) 9.63492 + 1.56361i 1.03297 + 0.167637i
\(88\) 0 0
\(89\) −6.02277 + 3.47725i −0.638412 + 0.368588i −0.784003 0.620757i \(-0.786825\pi\)
0.145590 + 0.989345i \(0.453492\pi\)
\(90\) 0 0
\(91\) −0.978101 0.564707i −0.102533 0.0591974i
\(92\) 0 0
\(93\) 0.251545 + 18.4279i 0.0260840 + 1.91088i
\(94\) 0 0
\(95\) −1.19060 + 6.75220i −0.122152 + 0.692761i
\(96\) 0 0
\(97\) 1.35281 1.13514i 0.137357 0.115256i −0.571521 0.820588i \(-0.693646\pi\)
0.708878 + 0.705331i \(0.249202\pi\)
\(98\) 0 0
\(99\) −8.66711 + 0.236660i −0.871078 + 0.0237853i
\(100\) 0 0
\(101\) 3.88953 10.6864i 0.387023 1.06334i −0.581312 0.813681i \(-0.697460\pi\)
0.968335 0.249656i \(-0.0803175\pi\)
\(102\) 0 0
\(103\) 10.6329 12.6718i 1.04769 1.24859i 0.0799054 0.996802i \(-0.474538\pi\)
0.967783 0.251784i \(-0.0810174\pi\)
\(104\) 0 0
\(105\) −1.90509 10.0039i −0.185918 0.976278i
\(106\) 0 0
\(107\) −16.6875 −1.61324 −0.806619 0.591071i \(-0.798705\pi\)
−0.806619 + 0.591071i \(0.798705\pi\)
\(108\) 0 0
\(109\) 10.2128 0.978212 0.489106 0.872224i \(-0.337323\pi\)
0.489106 + 0.872224i \(0.337323\pi\)
\(110\) 0 0
\(111\) −10.7665 + 9.28753i −1.02191 + 0.881534i
\(112\) 0 0
\(113\) −9.06215 + 10.7998i −0.852495 + 1.01596i 0.147144 + 0.989115i \(0.452992\pi\)
−0.999639 + 0.0268492i \(0.991453\pi\)
\(114\) 0 0
\(115\) −2.90224 + 7.97383i −0.270635 + 0.743564i
\(116\) 0 0
\(117\) 1.57433 1.39600i 0.145547 0.129060i
\(118\) 0 0
\(119\) −7.92143 + 6.64687i −0.726156 + 0.609317i
\(120\) 0 0
\(121\) −0.459688 + 2.60702i −0.0417898 + 0.237002i
\(122\) 0 0
\(123\) 9.49308 + 5.30941i 0.855962 + 0.478733i
\(124\) 0 0
\(125\) −10.5345 6.08208i −0.942232 0.543998i
\(126\) 0 0
\(127\) −6.11030 + 3.52779i −0.542202 + 0.313040i −0.745971 0.665979i \(-0.768014\pi\)
0.203769 + 0.979019i \(0.434681\pi\)
\(128\) 0 0
\(129\) 5.41131 + 14.2588i 0.476439 + 1.25542i
\(130\) 0 0
\(131\) −13.6909 + 4.98310i −1.19618 + 0.435375i −0.861891 0.507094i \(-0.830720\pi\)
−0.334293 + 0.942469i \(0.608497\pi\)
\(132\) 0 0
\(133\) 0.525082 + 2.97789i 0.0455304 + 0.258216i
\(134\) 0 0
\(135\) 18.8033 + 2.52689i 1.61833 + 0.217480i
\(136\) 0 0
\(137\) 14.3046 2.52229i 1.22212 0.215493i 0.474884 0.880048i \(-0.342490\pi\)
0.747240 + 0.664555i \(0.231379\pi\)
\(138\) 0 0
\(139\) −3.14344 8.63654i −0.266624 0.732542i −0.998683 0.0513016i \(-0.983663\pi\)
0.732060 0.681240i \(-0.238559\pi\)
\(140\) 0 0
\(141\) −2.39135 1.95158i −0.201388 0.164353i
\(142\) 0 0
\(143\) 1.01353 + 1.75548i 0.0847553 + 0.146801i
\(144\) 0 0
\(145\) 10.2883 17.8198i 0.854394 1.47985i
\(146\) 0 0
\(147\) 3.90642 + 6.55776i 0.322196 + 0.540875i
\(148\) 0 0
\(149\) −1.24126 0.218868i −0.101688 0.0179304i 0.122573 0.992460i \(-0.460886\pi\)
−0.224261 + 0.974529i \(0.571997\pi\)
\(150\) 0 0
\(151\) −7.74987 9.23593i −0.630675 0.751609i 0.352191 0.935928i \(-0.385437\pi\)
−0.982867 + 0.184319i \(0.940992\pi\)
\(152\) 0 0
\(153\) −7.08067 17.9165i −0.572439 1.44847i
\(154\) 0 0
\(155\) 36.5074 + 13.2876i 2.93235 + 1.06729i
\(156\) 0 0
\(157\) −2.80380 2.35267i −0.223767 0.187763i 0.524011 0.851711i \(-0.324435\pi\)
−0.747779 + 0.663948i \(0.768879\pi\)
\(158\) 0 0
\(159\) 0.484544 1.39002i 0.0384268 0.110236i
\(160\) 0 0
\(161\) 3.74235i 0.294939i
\(162\) 0 0
\(163\) 2.44194i 0.191267i 0.995417 + 0.0956336i \(0.0304877\pi\)
−0.995417 + 0.0956336i \(0.969512\pi\)
\(164\) 0 0
\(165\) −6.01625 + 17.2589i −0.468364 + 1.34360i
\(166\) 0 0
\(167\) −4.06934 3.41458i −0.314895 0.264229i 0.471617 0.881804i \(-0.343671\pi\)
−0.786512 + 0.617575i \(0.788115\pi\)
\(168\) 0 0
\(169\) 11.7537 + 4.27801i 0.904134 + 0.329078i
\(170\) 0 0
\(171\) −5.57251 0.826444i −0.426141 0.0631998i
\(172\) 0 0
\(173\) −16.8612 20.0945i −1.28194 1.52775i −0.698560 0.715551i \(-0.746176\pi\)
−0.583377 0.812202i \(-0.698269\pi\)
\(174\) 0 0
\(175\) −13.2123 2.32969i −0.998757 0.176108i
\(176\) 0 0
\(177\) −5.25872 8.82786i −0.395269 0.663543i
\(178\) 0 0
\(179\) −5.42787 + 9.40134i −0.405698 + 0.702689i −0.994402 0.105659i \(-0.966305\pi\)
0.588705 + 0.808348i \(0.299638\pi\)
\(180\) 0 0
\(181\) 2.12621 + 3.68270i 0.158040 + 0.273733i 0.934162 0.356850i \(-0.116149\pi\)
−0.776122 + 0.630583i \(0.782816\pi\)
\(182\) 0 0
\(183\) −14.2228 11.6072i −1.05138 0.858032i
\(184\) 0 0
\(185\) 10.2517 + 28.1663i 0.753720 + 2.07083i
\(186\) 0 0
\(187\) 18.2773 3.22279i 1.33657 0.235674i
\(188\) 0 0
\(189\) 8.17379 1.78907i 0.594556 0.130136i
\(190\) 0 0
\(191\) −1.25388 7.11111i −0.0907276 0.514542i −0.995973 0.0896529i \(-0.971424\pi\)
0.905245 0.424889i \(-0.139687\pi\)
\(192\) 0 0
\(193\) −15.5914 + 5.67481i −1.12229 + 0.408482i −0.835489 0.549507i \(-0.814815\pi\)
−0.286805 + 0.957989i \(0.592593\pi\)
\(194\) 0 0
\(195\) −1.57381 4.14699i −0.112703 0.296972i
\(196\) 0 0
\(197\) 4.35620 2.51505i 0.310367 0.179190i −0.336724 0.941603i \(-0.609319\pi\)
0.647091 + 0.762413i \(0.275986\pi\)
\(198\) 0 0
\(199\) 12.8199 + 7.40159i 0.908781 + 0.524685i 0.880039 0.474902i \(-0.157517\pi\)
0.0287420 + 0.999587i \(0.490850\pi\)
\(200\) 0 0
\(201\) −22.3373 12.4931i −1.57555 0.881193i
\(202\) 0 0
\(203\) 1.57582 8.93690i 0.110601 0.627247i
\(204\) 0 0
\(205\) 17.5647 14.7385i 1.22677 1.02938i
\(206\) 0 0
\(207\) −6.61426 2.20488i −0.459723 0.153249i
\(208\) 0 0
\(209\) 1.85618 5.09982i 0.128395 0.352762i
\(210\) 0 0
\(211\) 7.82727 9.32818i 0.538851 0.642178i −0.426078 0.904686i \(-0.640105\pi\)
0.964930 + 0.262508i \(0.0845497\pi\)
\(212\) 0 0
\(213\) 15.2340 13.1413i 1.04382 0.900430i
\(214\) 0 0
\(215\) 32.1500 2.19261
\(216\) 0 0
\(217\) 17.1340 1.16313
\(218\) 0 0
\(219\) 2.02217 + 10.6187i 0.136646 + 0.717544i
\(220\) 0 0
\(221\) −2.89510 + 3.45025i −0.194746 + 0.232089i
\(222\) 0 0
\(223\) 3.42628 9.41364i 0.229441 0.630384i −0.770535 0.637398i \(-0.780011\pi\)
0.999975 + 0.00701461i \(0.00223284\pi\)
\(224\) 0 0
\(225\) 11.9018 21.9790i 0.793453 1.46526i
\(226\) 0 0
\(227\) 7.69615 6.45783i 0.510811 0.428622i −0.350603 0.936524i \(-0.614023\pi\)
0.861415 + 0.507903i \(0.169579\pi\)
\(228\) 0 0
\(229\) −2.02551 + 11.4872i −0.133849 + 0.759096i 0.841805 + 0.539782i \(0.181493\pi\)
−0.975654 + 0.219315i \(0.929618\pi\)
\(230\) 0 0
\(231\) 0.110022 + 8.06006i 0.00723890 + 0.530313i
\(232\) 0 0
\(233\) 11.1464 + 6.43535i 0.730222 + 0.421594i 0.818503 0.574502i \(-0.194804\pi\)
−0.0882815 + 0.996096i \(0.528137\pi\)
\(234\) 0 0
\(235\) −5.63499 + 3.25336i −0.367586 + 0.212226i
\(236\) 0 0
\(237\) 7.77461 + 1.26171i 0.505015 + 0.0819569i
\(238\) 0 0
\(239\) 3.79461 1.38112i 0.245453 0.0893375i −0.216364 0.976313i \(-0.569420\pi\)
0.461817 + 0.886975i \(0.347198\pi\)
\(240\) 0 0
\(241\) −3.73127 21.1611i −0.240352 1.36311i −0.831043 0.556208i \(-0.812256\pi\)
0.590691 0.806898i \(-0.298855\pi\)
\(242\) 0 0
\(243\) −1.65372 + 15.5005i −0.106086 + 0.994357i
\(244\) 0 0
\(245\) 15.8465 2.79416i 1.01239 0.178512i
\(246\) 0 0
\(247\) 0.450459 + 1.23763i 0.0286620 + 0.0787483i
\(248\) 0 0
\(249\) 2.04999 12.6320i 0.129913 0.800519i
\(250\) 0 0
\(251\) −2.12275 3.67671i −0.133987 0.232072i 0.791223 0.611528i \(-0.209445\pi\)
−0.925210 + 0.379455i \(0.876111\pi\)
\(252\) 0 0
\(253\) 3.35835 5.81684i 0.211138 0.365702i
\(254\) 0 0
\(255\) −40.6075 + 0.554302i −2.54294 + 0.0347117i
\(256\) 0 0
\(257\) 5.12260 + 0.903252i 0.319539 + 0.0563433i 0.331117 0.943590i \(-0.392574\pi\)
−0.0115784 + 0.999933i \(0.503686\pi\)
\(258\) 0 0
\(259\) 8.49719 + 10.1266i 0.527990 + 0.629233i
\(260\) 0 0
\(261\) 14.8667 + 8.05045i 0.920228 + 0.498310i
\(262\) 0 0
\(263\) 22.9602 + 8.35683i 1.41579 + 0.515304i 0.932823 0.360336i \(-0.117338\pi\)
0.482964 + 0.875640i \(0.339560\pi\)
\(264\) 0 0
\(265\) −2.37715 1.99466i −0.146027 0.122531i
\(266\) 0 0
\(267\) −11.8329 + 2.25340i −0.724161 + 0.137906i
\(268\) 0 0
\(269\) 0.485873i 0.0296242i −0.999890 0.0148121i \(-0.995285\pi\)
0.999890 0.0148121i \(-0.00471501\pi\)
\(270\) 0 0
\(271\) 15.4958i 0.941306i −0.882318 0.470653i \(-0.844018\pi\)
0.882318 0.470653i \(-0.155982\pi\)
\(272\) 0 0
\(273\) −1.27776 1.48124i −0.0773335 0.0896485i
\(274\) 0 0
\(275\) 18.4456 + 15.4777i 1.11231 + 0.933341i
\(276\) 0 0
\(277\) −13.7884 5.01856i −0.828463 0.301536i −0.107235 0.994234i \(-0.534200\pi\)
−0.721228 + 0.692698i \(0.756422\pi\)
\(278\) 0 0
\(279\) −10.0948 + 30.2828i −0.604361 + 1.81298i
\(280\) 0 0
\(281\) 0.732164 + 0.872559i 0.0436772 + 0.0520525i 0.787441 0.616390i \(-0.211406\pi\)
−0.743764 + 0.668443i \(0.766961\pi\)
\(282\) 0 0
\(283\) 4.21444 + 0.743119i 0.250522 + 0.0441739i 0.297499 0.954722i \(-0.403848\pi\)
−0.0469766 + 0.998896i \(0.514959\pi\)
\(284\) 0 0
\(285\) −5.79686 + 10.3646i −0.343376 + 0.613948i
\(286\) 0 0
\(287\) 5.05615 8.75752i 0.298455 0.516940i
\(288\) 0 0
\(289\) 12.1188 + 20.9903i 0.712869 + 1.23472i
\(290\) 0 0
\(291\) 2.85974 1.08529i 0.167641 0.0636207i
\(292\) 0 0
\(293\) −2.29569 6.30736i −0.134116 0.368480i 0.854396 0.519622i \(-0.173927\pi\)
−0.988512 + 0.151142i \(0.951705\pi\)
\(294\) 0 0
\(295\) −21.3320 + 3.76141i −1.24200 + 0.218998i
\(296\) 0 0
\(297\) −14.3102 4.55428i −0.830365 0.264266i
\(298\) 0 0
\(299\) 0.283049 + 1.60525i 0.0163691 + 0.0928340i
\(300\) 0 0
\(301\) 13.3238 4.84948i 0.767974 0.279520i
\(302\) 0 0
\(303\) 12.4540 15.2604i 0.715466 0.876687i
\(304\) 0 0
\(305\) −33.5147 + 19.3497i −1.91904 + 1.10796i
\(306\) 0 0
\(307\) −9.47236 5.46887i −0.540616 0.312125i 0.204713 0.978822i \(-0.434374\pi\)
−0.745329 + 0.666697i \(0.767707\pi\)
\(308\) 0 0
\(309\) 24.6149 14.6630i 1.40029 0.834147i
\(310\) 0 0
\(311\) −1.99845 + 11.3338i −0.113322 + 0.642678i 0.874246 + 0.485483i \(0.161356\pi\)
−0.987568 + 0.157195i \(0.949755\pi\)
\(312\) 0 0
\(313\) −5.50981 + 4.62328i −0.311433 + 0.261323i −0.785084 0.619389i \(-0.787380\pi\)
0.473651 + 0.880713i \(0.342936\pi\)
\(314\) 0 0
\(315\) 2.58763 17.4478i 0.145797 0.983070i
\(316\) 0 0
\(317\) −5.58824 + 15.3536i −0.313867 + 0.862342i 0.678000 + 0.735062i \(0.262847\pi\)
−0.991867 + 0.127280i \(0.959375\pi\)
\(318\) 0 0
\(319\) −10.4692 + 12.4767i −0.586164 + 0.698564i
\(320\) 0 0
\(321\) −27.2928 9.51396i −1.52334 0.531018i
\(322\) 0 0
\(323\) 12.0587 0.670964
\(324\) 0 0
\(325\) −5.84351 −0.324140
\(326\) 0 0
\(327\) 16.7034 + 5.82260i 0.923700 + 0.321991i
\(328\) 0 0
\(329\) −1.84456 + 2.19826i −0.101694 + 0.121194i
\(330\) 0 0
\(331\) 8.42268 23.1411i 0.462952 1.27195i −0.460302 0.887762i \(-0.652259\pi\)
0.923255 0.384189i \(-0.125519\pi\)
\(332\) 0 0
\(333\) −22.9040 + 9.05175i −1.25513 + 0.496033i
\(334\) 0 0
\(335\) −41.3299 + 34.6799i −2.25809 + 1.89476i
\(336\) 0 0
\(337\) 0.871464 4.94232i 0.0474717 0.269225i −0.951829 0.306631i \(-0.900798\pi\)
0.999300 + 0.0374058i \(0.0119094\pi\)
\(338\) 0 0
\(339\) −20.9787 + 12.4969i −1.13941 + 0.678738i
\(340\) 0 0
\(341\) −26.6319 15.3759i −1.44220 0.832652i
\(342\) 0 0
\(343\) 15.9076 9.18425i 0.858929 0.495903i
\(344\) 0 0
\(345\) −9.29278 + 11.3868i −0.500307 + 0.613044i
\(346\) 0 0
\(347\) 14.1651 5.15569i 0.760424 0.276772i 0.0674388 0.997723i \(-0.478517\pi\)
0.692985 + 0.720952i \(0.256295\pi\)
\(348\) 0 0
\(349\) −0.0306727 0.173953i −0.00164187 0.00931151i 0.983976 0.178302i \(-0.0570604\pi\)
−0.985618 + 0.168990i \(0.945949\pi\)
\(350\) 0 0
\(351\) 3.37076 1.38562i 0.179918 0.0739591i
\(352\) 0 0
\(353\) 4.03523 0.711520i 0.214774 0.0378704i −0.0652259 0.997871i \(-0.520777\pi\)
0.280000 + 0.960000i \(0.409666\pi\)
\(354\) 0 0
\(355\) −14.5056 39.8538i −0.769877 2.11522i
\(356\) 0 0
\(357\) −16.7453 + 6.35493i −0.886254 + 0.336339i
\(358\) 0 0
\(359\) 0.130804 + 0.226558i 0.00690355 + 0.0119573i 0.869457 0.494009i \(-0.164469\pi\)
−0.862553 + 0.505967i \(0.831136\pi\)
\(360\) 0 0
\(361\) −7.73689 + 13.4007i −0.407205 + 0.705300i
\(362\) 0 0
\(363\) −2.23816 + 4.00178i −0.117473 + 0.210039i
\(364\) 0 0
\(365\) 22.4407 + 3.95690i 1.17460 + 0.207114i
\(366\) 0 0
\(367\) −9.25704 11.0321i −0.483214 0.575872i 0.468264 0.883588i \(-0.344880\pi\)
−0.951478 + 0.307717i \(0.900435\pi\)
\(368\) 0 0
\(369\) 12.4992 + 14.0959i 0.650681 + 0.733806i
\(370\) 0 0
\(371\) −1.28603 0.468077i −0.0667674 0.0243013i
\(372\) 0 0
\(373\) 0.506826 + 0.425278i 0.0262425 + 0.0220200i 0.655815 0.754922i \(-0.272325\pi\)
−0.629572 + 0.776942i \(0.716770\pi\)
\(374\) 0 0
\(375\) −13.7619 15.9534i −0.710661 0.823830i
\(376\) 0 0
\(377\) 3.95259i 0.203569i
\(378\) 0 0
\(379\) 1.73288i 0.0890121i 0.999009 + 0.0445061i \(0.0141714\pi\)
−0.999009 + 0.0445061i \(0.985829\pi\)
\(380\) 0 0
\(381\) −12.0049 + 2.28615i −0.615028 + 0.117123i
\(382\) 0 0
\(383\) −17.1332 14.3765i −0.875466 0.734603i 0.0897757 0.995962i \(-0.471385\pi\)
−0.965242 + 0.261359i \(0.915829\pi\)
\(384\) 0 0
\(385\) 15.9678 + 5.81179i 0.813792 + 0.296196i
\(386\) 0 0
\(387\) 0.721026 + 26.4058i 0.0366518 + 1.34228i
\(388\) 0 0
\(389\) 2.05959 + 2.45453i 0.104426 + 0.124450i 0.815726 0.578439i \(-0.196338\pi\)
−0.711300 + 0.702888i \(0.751893\pi\)
\(390\) 0 0
\(391\) 14.6974 + 2.59154i 0.743277 + 0.131060i
\(392\) 0 0
\(393\) −25.2329 + 0.344435i −1.27283 + 0.0173745i
\(394\) 0 0
\(395\) 8.30181 14.3791i 0.417709 0.723494i
\(396\) 0 0
\(397\) 6.32972 + 10.9634i 0.317680 + 0.550237i 0.980003 0.198981i \(-0.0637630\pi\)
−0.662324 + 0.749218i \(0.730430\pi\)
\(398\) 0 0
\(399\) −0.838985 + 5.16979i −0.0420018 + 0.258813i
\(400\) 0 0
\(401\) −4.72777 12.9894i −0.236094 0.648662i −0.999994 0.00332813i \(-0.998941\pi\)
0.763901 0.645334i \(-0.223282\pi\)
\(402\) 0 0
\(403\) 7.34949 1.29591i 0.366104 0.0645540i
\(404\) 0 0
\(405\) 29.3128 + 14.8531i 1.45656 + 0.738055i
\(406\) 0 0
\(407\) −4.11993 23.3653i −0.204217 1.15817i
\(408\) 0 0
\(409\) 35.2902 12.8446i 1.74499 0.635124i 0.745482 0.666526i \(-0.232219\pi\)
0.999507 + 0.0314018i \(0.00999714\pi\)
\(410\) 0 0
\(411\) 24.8336 + 4.03015i 1.22495 + 0.198793i
\(412\) 0 0
\(413\) −8.27323 + 4.77655i −0.407099 + 0.235039i
\(414\) 0 0
\(415\) −23.3629 13.4885i −1.14684 0.662127i
\(416\) 0 0
\(417\) −0.217277 15.9175i −0.0106401 0.779482i
\(418\) 0 0
\(419\) −6.05967 + 34.3661i −0.296034 + 1.67889i 0.366934 + 0.930247i \(0.380407\pi\)
−0.662969 + 0.748647i \(0.730704\pi\)
\(420\) 0 0
\(421\) −3.66182 + 3.07264i −0.178466 + 0.149751i −0.727645 0.685954i \(-0.759385\pi\)
0.549179 + 0.835705i \(0.314941\pi\)
\(422\) 0 0
\(423\) −2.79847 4.55524i −0.136066 0.221484i
\(424\) 0 0
\(425\) −18.2988 + 50.2755i −0.887621 + 2.43872i
\(426\) 0 0
\(427\) −10.9707 + 13.0744i −0.530910 + 0.632714i
\(428\) 0 0
\(429\) 0.656808 + 3.44897i 0.0317110 + 0.166518i
\(430\) 0 0
\(431\) −27.7539 −1.33686 −0.668430 0.743775i \(-0.733033\pi\)
−0.668430 + 0.743775i \(0.733033\pi\)
\(432\) 0 0
\(433\) 2.25395 0.108318 0.0541589 0.998532i \(-0.482752\pi\)
0.0541589 + 0.998532i \(0.482752\pi\)
\(434\) 0 0
\(435\) 26.9863 23.2792i 1.29389 1.11615i
\(436\) 0 0
\(437\) 2.80519 3.34310i 0.134191 0.159922i
\(438\) 0 0
\(439\) 5.90435 16.2221i 0.281799 0.774237i −0.715349 0.698767i \(-0.753732\pi\)
0.997148 0.0754693i \(-0.0240455\pi\)
\(440\) 0 0
\(441\) 2.65032 + 12.9526i 0.126206 + 0.616789i
\(442\) 0 0
\(443\) −5.44673 + 4.57035i −0.258782 + 0.217144i −0.762943 0.646466i \(-0.776246\pi\)
0.504161 + 0.863610i \(0.331802\pi\)
\(444\) 0 0
\(445\) −4.40936 + 25.0067i −0.209024 + 1.18543i
\(446\) 0 0
\(447\) −1.90534 1.06564i −0.0901194 0.0504031i
\(448\) 0 0
\(449\) 15.7138 + 9.07236i 0.741579 + 0.428151i 0.822643 0.568558i \(-0.192499\pi\)
−0.0810641 + 0.996709i \(0.525832\pi\)
\(450\) 0 0
\(451\) −15.7178 + 9.07470i −0.740124 + 0.427311i
\(452\) 0 0
\(453\) −7.40949 19.5240i −0.348128 0.917319i
\(454\) 0 0
\(455\) −3.87506 + 1.41041i −0.181666 + 0.0661209i
\(456\) 0 0
\(457\) −4.70335 26.6740i −0.220014 1.24776i −0.871991 0.489521i \(-0.837172\pi\)
0.651978 0.758238i \(-0.273939\pi\)
\(458\) 0 0
\(459\) −1.36597 33.3399i −0.0637581 1.55617i
\(460\) 0 0
\(461\) 12.6352 2.22793i 0.588482 0.103765i 0.128525 0.991706i \(-0.458976\pi\)
0.459957 + 0.887941i \(0.347865\pi\)
\(462\) 0 0
\(463\) 0.136338 + 0.374586i 0.00633617 + 0.0174085i 0.942820 0.333301i \(-0.108163\pi\)
−0.936484 + 0.350710i \(0.885940\pi\)
\(464\) 0 0
\(465\) 52.1334 + 42.5461i 2.41763 + 1.97303i
\(466\) 0 0
\(467\) −4.12333 7.14182i −0.190805 0.330484i 0.754712 0.656056i \(-0.227777\pi\)
−0.945517 + 0.325572i \(0.894443\pi\)
\(468\) 0 0
\(469\) −11.8972 + 20.6065i −0.549360 + 0.951519i
\(470\) 0 0
\(471\) −3.24438 5.44637i −0.149493 0.250956i
\(472\) 0 0
\(473\) −25.0615 4.41902i −1.15233 0.203187i
\(474\) 0 0
\(475\) 10.0565 + 11.9848i 0.461423 + 0.549902i
\(476\) 0 0
\(477\) 1.58497 1.99717i 0.0725709 0.0914439i
\(478\) 0 0
\(479\) 23.0690 + 8.39642i 1.05405 + 0.383642i 0.810189 0.586169i \(-0.199364\pi\)
0.243859 + 0.969811i \(0.421587\pi\)
\(480\) 0 0
\(481\) 4.41071 + 3.70102i 0.201111 + 0.168752i
\(482\) 0 0
\(483\) −2.13361 + 6.12073i −0.0970827 + 0.278503i
\(484\) 0 0
\(485\) 6.44797i 0.292787i
\(486\) 0 0
\(487\) 5.60176i 0.253840i −0.991913 0.126920i \(-0.959491\pi\)
0.991913 0.126920i \(-0.0405092\pi\)
\(488\) 0 0
\(489\) −1.39221 + 3.99386i −0.0629580 + 0.180609i
\(490\) 0 0
\(491\) 27.3869 + 22.9803i 1.23595 + 1.03709i 0.997829 + 0.0658512i \(0.0209763\pi\)
0.238122 + 0.971235i \(0.423468\pi\)
\(492\) 0 0
\(493\) −34.0067 12.3774i −1.53158 0.557451i
\(494\) 0 0
\(495\) −19.6795 + 24.7974i −0.884528 + 1.11456i
\(496\) 0 0
\(497\) −12.0231 14.3285i −0.539308 0.642722i
\(498\) 0 0
\(499\) 40.9591 + 7.22219i 1.83358 + 0.323310i 0.980205 0.197987i \(-0.0634404\pi\)
0.853376 + 0.521297i \(0.174551\pi\)
\(500\) 0 0
\(501\) −4.70879 7.90469i −0.210373 0.353156i
\(502\) 0 0
\(503\) −10.1863 + 17.6431i −0.454183 + 0.786668i −0.998641 0.0521202i \(-0.983402\pi\)
0.544458 + 0.838788i \(0.316735\pi\)
\(504\) 0 0
\(505\) −20.7614 35.9597i −0.923868 1.60019i
\(506\) 0 0
\(507\) 16.7846 + 13.6979i 0.745430 + 0.608347i
\(508\) 0 0
\(509\) 2.66835 + 7.33124i 0.118273 + 0.324952i 0.984676 0.174393i \(-0.0557963\pi\)
−0.866403 + 0.499345i \(0.833574\pi\)
\(510\) 0 0
\(511\) 9.89692 1.74509i 0.437814 0.0771984i
\(512\) 0 0
\(513\) −8.64283 4.52871i −0.381590 0.199947i
\(514\) 0 0
\(515\) −10.4880 59.4805i −0.462157 2.62102i
\(516\) 0 0
\(517\) 4.83976 1.76153i 0.212852 0.0774719i
\(518\) 0 0
\(519\) −16.1207 42.4781i −0.707620 1.86458i
\(520\) 0 0
\(521\) 10.5688 6.10193i 0.463030 0.267330i −0.250288 0.968172i \(-0.580525\pi\)
0.713317 + 0.700841i \(0.247192\pi\)
\(522\) 0 0
\(523\) −1.11506 0.643783i −0.0487584 0.0281507i 0.475423 0.879758i \(-0.342295\pi\)
−0.524181 + 0.851607i \(0.675628\pi\)
\(524\) 0 0
\(525\) −20.2809 11.3430i −0.885131 0.495047i
\(526\) 0 0
\(527\) 11.8651 67.2905i 0.516853 2.93122i
\(528\) 0 0
\(529\) −13.4815 + 11.3124i −0.586154 + 0.491841i
\(530\) 0 0
\(531\) −3.56779 17.4364i −0.154829 0.756674i
\(532\) 0 0
\(533\) 1.50643 4.13888i 0.0652507 0.179275i
\(534\) 0 0
\(535\) −39.1650 + 46.6750i −1.69325 + 2.01794i
\(536\) 0 0
\(537\) −14.2374 + 12.2816i −0.614389 + 0.529990i
\(538\) 0 0
\(539\) −12.7367 −0.548607
\(540\) 0 0
\(541\) −33.3756 −1.43493 −0.717465 0.696594i \(-0.754698\pi\)
−0.717465 + 0.696594i \(0.754698\pi\)
\(542\) 0 0
\(543\) 1.37787 + 7.23537i 0.0591302 + 0.310500i
\(544\) 0 0
\(545\) 23.9692 28.5654i 1.02673 1.22361i
\(546\) 0 0
\(547\) −15.6515 + 43.0020i −0.669208 + 1.83863i −0.139980 + 0.990154i \(0.544704\pi\)
−0.529228 + 0.848480i \(0.677518\pi\)
\(548\) 0 0
\(549\) −16.6442 27.0928i −0.710357 1.15629i
\(550\) 0 0
\(551\) −8.10663 + 6.80227i −0.345354 + 0.289786i
\(552\) 0 0
\(553\) 1.27156 7.21136i 0.0540721 0.306658i
\(554\) 0 0
\(555\) 0.708606 + 51.9116i 0.0300786 + 2.20353i
\(556\) 0 0
\(557\) 18.3056 + 10.5687i 0.775631 + 0.447811i 0.834880 0.550432i \(-0.185537\pi\)
−0.0592484 + 0.998243i \(0.518870\pi\)
\(558\) 0 0
\(559\) 5.34837 3.08788i 0.226212 0.130603i
\(560\) 0 0
\(561\) 31.7305 + 5.14942i 1.33966 + 0.217409i
\(562\) 0 0
\(563\) −14.9675 + 5.44771i −0.630803 + 0.229594i −0.637581 0.770383i \(-0.720065\pi\)
0.00677752 + 0.999977i \(0.497843\pi\)
\(564\) 0 0
\(565\) 8.93869 + 50.6938i 0.376053 + 2.13270i
\(566\) 0 0
\(567\) 14.3885 + 1.73401i 0.604259 + 0.0728215i
\(568\) 0 0
\(569\) 5.38391 0.949329i 0.225705 0.0397979i −0.0596516 0.998219i \(-0.518999\pi\)
0.285357 + 0.958421i \(0.407888\pi\)
\(570\) 0 0
\(571\) 5.95709 + 16.3670i 0.249297 + 0.684937i 0.999713 + 0.0239711i \(0.00763096\pi\)
−0.750416 + 0.660966i \(0.770147\pi\)
\(572\) 0 0
\(573\) 2.00347 12.3453i 0.0836962 0.515732i
\(574\) 0 0
\(575\) 9.68134 + 16.7686i 0.403740 + 0.699298i
\(576\) 0 0
\(577\) −6.89556 + 11.9435i −0.287066 + 0.497213i −0.973108 0.230349i \(-0.926013\pi\)
0.686042 + 0.727562i \(0.259347\pi\)
\(578\) 0 0
\(579\) −28.7356 + 0.392247i −1.19421 + 0.0163012i
\(580\) 0 0
\(581\) −11.7168 2.06599i −0.486096 0.0857118i
\(582\) 0 0
\(583\) 1.57886 + 1.88162i 0.0653899 + 0.0779286i
\(584\) 0 0
\(585\) −0.209701 7.67979i −0.00867006 0.317520i
\(586\) 0 0
\(587\) 21.4195 + 7.79604i 0.884075 + 0.321777i 0.743853 0.668343i \(-0.232996\pi\)
0.140222 + 0.990120i \(0.455218\pi\)
\(588\) 0 0
\(589\) −15.3061 12.8433i −0.630676 0.529200i
\(590\) 0 0
\(591\) 8.55859 1.62986i 0.352054 0.0670435i
\(592\) 0 0
\(593\) 34.0284i 1.39738i −0.715426 0.698689i \(-0.753767\pi\)
0.715426 0.698689i \(-0.246233\pi\)
\(594\) 0 0
\(595\) 37.7563i 1.54786i
\(596\) 0 0
\(597\) 16.7475 + 19.4145i 0.685431 + 0.794582i
\(598\) 0 0
\(599\) −25.6710 21.5405i −1.04889 0.880122i −0.0559128 0.998436i \(-0.517807\pi\)
−0.992976 + 0.118313i \(0.962251\pi\)
\(600\) 0 0
\(601\) 33.9607 + 12.3607i 1.38529 + 0.504203i 0.923777 0.382931i \(-0.125085\pi\)
0.461510 + 0.887135i \(0.347308\pi\)
\(602\) 0 0
\(603\) −29.4107 33.1678i −1.19769 1.35070i
\(604\) 0 0
\(605\) 6.21298 + 7.40434i 0.252594 + 0.301029i
\(606\) 0 0
\(607\) 20.9011 + 3.68542i 0.848348 + 0.149587i 0.580889 0.813983i \(-0.302705\pi\)
0.267459 + 0.963569i \(0.413816\pi\)
\(608\) 0 0
\(609\) 7.67245 13.7181i 0.310904 0.555887i
\(610\) 0 0
\(611\) −0.624946 + 1.08244i −0.0252826 + 0.0437908i
\(612\) 0 0
\(613\) −17.4558 30.2343i −0.705032 1.22115i −0.966680 0.255987i \(-0.917599\pi\)
0.261648 0.965163i \(-0.415734\pi\)
\(614\) 0 0
\(615\) 37.1304 14.0912i 1.49724 0.568213i
\(616\) 0 0
\(617\) −4.96269 13.6349i −0.199790 0.548920i 0.798823 0.601566i \(-0.205456\pi\)
−0.998613 + 0.0526468i \(0.983234\pi\)
\(618\) 0 0
\(619\) 2.94818 0.519843i 0.118497 0.0208943i −0.114085 0.993471i \(-0.536394\pi\)
0.232582 + 0.972577i \(0.425283\pi\)
\(620\) 0 0
\(621\) −9.56076 7.37710i −0.383660 0.296033i
\(622\) 0 0
\(623\) 1.94464 + 11.0286i 0.0779103 + 0.441851i
\(624\) 0 0
\(625\) −2.59037 + 0.942816i −0.103615 + 0.0377126i
\(626\) 0 0
\(627\) 5.94338 7.28265i 0.237356 0.290841i
\(628\) 0 0
\(629\) 45.6543 26.3585i 1.82036 1.05098i
\(630\) 0 0
\(631\) 42.0709 + 24.2896i 1.67481 + 0.966955i 0.964882 + 0.262685i \(0.0846080\pi\)
0.709933 + 0.704269i \(0.248725\pi\)
\(632\) 0 0
\(633\) 18.1200 10.7940i 0.720204 0.429022i
\(634\) 0 0
\(635\) −4.47345 + 25.3702i −0.177523 + 1.00678i
\(636\) 0 0
\(637\) 2.36780 1.98682i 0.0938156 0.0787206i
\(638\) 0 0
\(639\) 32.4079 12.8077i 1.28204 0.506666i
\(640\) 0 0
\(641\) 5.70164 15.6651i 0.225201 0.618735i −0.774707 0.632321i \(-0.782102\pi\)
0.999908 + 0.0135858i \(0.00432462\pi\)
\(642\) 0 0
\(643\) 24.0202 28.6262i 0.947265 1.12891i −0.0442639 0.999020i \(-0.514094\pi\)
0.991529 0.129887i \(-0.0414613\pi\)
\(644\) 0 0
\(645\) 52.5822 + 18.3295i 2.07042 + 0.721725i
\(646\) 0 0
\(647\) 30.1624 1.18580 0.592902 0.805274i \(-0.297982\pi\)
0.592902 + 0.805274i \(0.297982\pi\)
\(648\) 0 0
\(649\) 17.1457 0.673029
\(650\) 0 0
\(651\) 28.0232 + 9.76854i 1.09831 + 0.382859i
\(652\) 0 0
\(653\) −1.61055 + 1.91938i −0.0630256 + 0.0751110i −0.796636 0.604459i \(-0.793389\pi\)
0.733611 + 0.679570i \(0.237834\pi\)
\(654\) 0 0
\(655\) −18.1945 + 49.9888i −0.710916 + 1.95323i
\(656\) 0 0
\(657\) −2.74666 + 18.5200i −0.107157 + 0.722536i
\(658\) 0 0
\(659\) −26.7567 + 22.4515i −1.04229 + 0.874587i −0.992262 0.124161i \(-0.960376\pi\)
−0.0500301 + 0.998748i \(0.515932\pi\)
\(660\) 0 0
\(661\) 5.01298 28.4300i 0.194982 1.10580i −0.717461 0.696598i \(-0.754696\pi\)
0.912444 0.409202i \(-0.134193\pi\)
\(662\) 0 0
\(663\) −6.70210 + 3.99241i −0.260288 + 0.155052i
\(664\) 0 0
\(665\) 9.56154 + 5.52036i 0.370781 + 0.214070i
\(666\) 0 0
\(667\) −11.3424 + 6.54853i −0.439179 + 0.253560i
\(668\) 0 0
\(669\) 10.9707 13.4429i 0.424154 0.519731i
\(670\) 0 0
\(671\) 28.7849 10.4769i 1.11123 0.404455i
\(672\) 0 0
\(673\) 5.70280 + 32.3422i 0.219827 + 1.24670i 0.872331 + 0.488915i \(0.162607\pi\)
−0.652504 + 0.757785i \(0.726282\pi\)
\(674\) 0 0
\(675\) 31.9965 29.1617i 1.23155 1.12244i
\(676\) 0 0
\(677\) −4.92975 + 0.869249i −0.189466 + 0.0334079i −0.267576 0.963537i \(-0.586223\pi\)
0.0781100 + 0.996945i \(0.475111\pi\)
\(678\) 0 0
\(679\) −0.972608 2.67222i −0.0373253 0.102550i
\(680\) 0 0
\(681\) 16.2691 6.17420i 0.623431 0.236596i
\(682\) 0 0
\(683\) −15.9017 27.5426i −0.608463 1.05389i −0.991494 0.130153i \(-0.958453\pi\)
0.383031 0.923735i \(-0.374880\pi\)
\(684\) 0 0
\(685\) 26.5176 45.9298i 1.01318 1.75489i
\(686\) 0 0
\(687\) −9.86193 + 17.6329i −0.376256 + 0.672736i
\(688\) 0 0
\(689\) −0.587035 0.103510i −0.0223642 0.00394342i
\(690\) 0 0
\(691\) −17.8704 21.2971i −0.679822 0.810180i 0.310263 0.950651i \(-0.399583\pi\)
−0.990085 + 0.140471i \(0.955138\pi\)
\(692\) 0 0
\(693\) −4.41531 + 13.2452i −0.167724 + 0.503143i
\(694\) 0 0
\(695\) −31.5341 11.4775i −1.19615 0.435365i
\(696\) 0 0
\(697\) −30.8921 25.9216i −1.17012 0.981849i
\(698\) 0 0
\(699\) 14.5612 + 16.8800i 0.550756 + 0.638461i
\(700\) 0 0
\(701\) 50.2148i 1.89659i 0.317393 + 0.948294i \(0.397193\pi\)
−0.317393 + 0.948294i \(0.602807\pi\)
\(702\) 0 0
\(703\) 15.4155i 0.581408i
\(704\) 0 0
\(705\) −11.0710 + 2.10832i −0.416959 + 0.0794038i
\(706\) 0 0
\(707\) −14.0282 11.7711i −0.527586 0.442697i
\(708\) 0 0
\(709\) 1.61463 + 0.587679i 0.0606388 + 0.0220707i 0.372161 0.928168i \(-0.378617\pi\)
−0.311523 + 0.950239i \(0.600839\pi\)
\(710\) 0 0
\(711\) 11.9963 + 6.49607i 0.449895 + 0.243622i
\(712\) 0 0
\(713\) −15.8951 18.9431i −0.595278 0.709425i
\(714\) 0 0
\(715\) 7.28880 + 1.28521i 0.272586 + 0.0480642i
\(716\) 0 0
\(717\) 6.99361 0.0954644i 0.261181 0.00356518i
\(718\) 0 0
\(719\) −24.3767 + 42.2217i −0.909099 + 1.57461i −0.0937803 + 0.995593i \(0.529895\pi\)
−0.815319 + 0.579013i \(0.803438\pi\)
\(720\) 0 0
\(721\) −13.3185 23.0684i −0.496008 0.859112i
\(722\) 0 0
\(723\) 5.96189 36.7369i 0.221725 1.36626i
\(724\) 0 0
\(725\) −16.0586 44.1207i −0.596402 1.63860i
\(726\) 0 0
\(727\) −39.8914 + 7.03393i −1.47949 + 0.260874i −0.854374 0.519659i \(-0.826059\pi\)
−0.625115 + 0.780532i \(0.714948\pi\)
\(728\) 0 0
\(729\) −11.5419 + 24.4087i −0.427479 + 0.904025i
\(730\) 0 0
\(731\) −9.81877 55.6850i −0.363160 2.05959i
\(732\) 0 0
\(733\) 16.7735 6.10505i 0.619543 0.225495i −0.0131304 0.999914i \(-0.504180\pi\)
0.632674 + 0.774418i \(0.281957\pi\)
\(734\) 0 0
\(735\) 27.5104 + 4.46455i 1.01473 + 0.164677i
\(736\) 0 0
\(737\) 36.9842 21.3528i 1.36233 0.786541i
\(738\) 0 0
\(739\) −1.22996 0.710118i −0.0452448 0.0261221i 0.477207 0.878791i \(-0.341649\pi\)
−0.522452 + 0.852669i \(0.674983\pi\)
\(740\) 0 0
\(741\) 0.0311361 + 2.28099i 0.00114381 + 0.0837944i
\(742\) 0 0
\(743\) 1.09307 6.19911i 0.0401009 0.227423i −0.958170 0.286198i \(-0.907608\pi\)
0.998271 + 0.0587751i \(0.0187195\pi\)
\(744\) 0 0
\(745\) −3.52538 + 2.95814i −0.129160 + 0.108378i
\(746\) 0 0
\(747\) 10.5546 19.4912i 0.386174 0.713146i
\(748\) 0 0
\(749\) −9.19063 + 25.2511i −0.335818 + 0.922653i
\(750\) 0 0
\(751\) −11.8427 + 14.1136i −0.432146 + 0.515012i −0.937540 0.347877i \(-0.886903\pi\)
0.505394 + 0.862889i \(0.331347\pi\)
\(752\) 0 0
\(753\) −1.37563 7.22361i −0.0501308 0.263243i
\(754\) 0 0
\(755\) −44.0217 −1.60211
\(756\) 0 0
\(757\) 10.3039 0.374500 0.187250 0.982312i \(-0.440043\pi\)
0.187250 + 0.982312i \(0.440043\pi\)
\(758\) 0 0
\(759\) 8.80902 7.59893i 0.319747 0.275824i
\(760\) 0 0
\(761\) −12.5156 + 14.9156i −0.453692 + 0.540689i −0.943601 0.331085i \(-0.892585\pi\)
0.489909 + 0.871773i \(0.337030\pi\)
\(762\) 0 0
\(763\) 5.62472 15.4538i 0.203629 0.559465i
\(764\) 0 0
\(765\) −66.7308 22.2448i −2.41266 0.804263i
\(766\) 0 0
\(767\) −3.18746 + 2.67460i −0.115093 + 0.0965741i
\(768\) 0 0
\(769\) −4.85410 + 27.5290i −0.175043 + 0.992721i 0.763050 + 0.646339i \(0.223701\pi\)
−0.938094 + 0.346382i \(0.887410\pi\)
\(770\) 0 0
\(771\) 7.86319 + 4.39782i 0.283186 + 0.158384i
\(772\) 0 0
\(773\) 15.1159 + 8.72717i 0.543681 + 0.313894i 0.746569 0.665307i \(-0.231700\pi\)
−0.202888 + 0.979202i \(0.565033\pi\)
\(774\) 0 0
\(775\) 76.7733 44.3251i 2.75778 1.59220i
\(776\) 0 0
\(777\) 8.12399 + 21.4067i 0.291446 + 0.767963i
\(778\) 0 0
\(779\) −11.0812 + 4.03323i −0.397025 + 0.144505i
\(780\) 0 0
\(781\) 5.82947 + 33.0606i 0.208595 + 1.18300i
\(782\) 0 0
\(783\) 19.7252 + 21.6427i 0.704921 + 0.773446i
\(784\) 0 0
\(785\) −13.1609 + 2.32061i −0.469731 + 0.0828263i
\(786\) 0 0
\(787\) −0.407887 1.12066i −0.0145396 0.0399472i 0.932211 0.361916i \(-0.117877\pi\)
−0.946750 + 0.321969i \(0.895655\pi\)
\(788\) 0 0
\(789\) 32.7876 + 26.7581i 1.16727 + 0.952612i
\(790\) 0 0
\(791\) 11.3511 + 19.6606i 0.403598 + 0.699052i
\(792\) 0 0
\(793\) −3.71693 + 6.43791i −0.131992 + 0.228617i
\(794\) 0 0
\(795\)