Properties

Label 432.2.be.b.191.5
Level $432$
Weight $2$
Character 432.191
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 191.5
Character \(\chi\) \(=\) 432.191
Dual form 432.2.be.b.95.5

$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

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

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 0.967134 + 0.254266i \(0.0818339\pi\)
0.0824620 + 0.996594i \(0.473722\pi\)
\(6\) 0 0
\(7\) 0.550750 + 1.51317i 0.208164 + 0.571926i 0.999206 0.0398355i \(-0.0126834\pi\)
−0.791042 + 0.611762i \(0.790461\pi\)
\(8\) 0 0
\(9\) 2.34991 1.86492i 0.783304 0.621639i
\(10\) 0 0
\(11\) −2.21396 1.85773i −0.667533 0.560127i 0.244801 0.969573i \(-0.421277\pi\)
−0.912334 + 0.409447i \(0.865722\pi\)
\(12\) 0 0
\(13\) 0.121792 + 0.690719i 0.0337791 + 0.191571i 0.997028 0.0770394i \(-0.0245467\pi\)
−0.963249 + 0.268610i \(0.913436\pi\)
\(14\) 0 0
\(15\) 5.43318 + 3.23652i 1.40284 + 0.835666i
\(16\) 0 0
\(17\) −5.56131 + 3.21082i −1.34882 + 0.778739i −0.988082 0.153930i \(-0.950807\pi\)
−0.360734 + 0.932669i \(0.617474\pi\)
\(18\) 0 0
\(19\) −1.62624 0.938910i −0.373085 0.215401i 0.301720 0.953396i \(-0.402439\pi\)
−0.674805 + 0.737996i \(0.735772\pi\)
\(20\) 0 0
\(21\) 1.76347 + 2.16084i 0.384820 + 0.471535i
\(22\) 0 0
\(23\) −2.18387 0.794864i −0.455369 0.165741i 0.104144 0.994562i \(-0.466790\pi\)
−0.559513 + 0.828822i \(0.689012\pi\)
\(24\) 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 0.663274 0.748377i \(-0.269167\pi\)
0.367313 + 0.930097i \(0.380278\pi\)
\(30\) 0 0
\(31\) 3.63921 9.99865i 0.653622 1.79581i 0.0497045 0.998764i \(-0.484172\pi\)
0.603917 0.797047i \(-0.293606\pi\)
\(32\) 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 −0.976528 0.215391i \(-0.930897\pi\)
0.301730 0.953393i \(-0.402436\pi\)
\(38\) 0 0
\(39\) 0.592992 + 1.06025i 0.0949547 + 0.169777i
\(40\) 0 0
\(41\) 6.18442 1.09048i 0.965843 0.170304i 0.331585 0.943425i \(-0.392417\pi\)
0.634258 + 0.773121i \(0.281306\pi\)
\(42\) 0 0
\(43\) 5.65989 6.74520i 0.863125 1.02863i −0.136154 0.990688i \(-0.543474\pi\)
0.999280 0.0379452i \(-0.0120812\pi\)
\(44\) 0 0
\(45\) 10.7314 + 2.19583i 1.59974 + 0.327334i
\(46\) 0 0
\(47\) −1.67459 + 0.609501i −0.244264 + 0.0889049i −0.461251 0.887270i \(-0.652599\pi\)
0.216987 + 0.976174i \(0.430377\pi\)
\(48\) 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 \(0.0185905\pi\)
−0.998295 + 0.0583706i \(0.981409\pi\)
\(54\) 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 −0.888751 0.458390i \(-0.848426\pi\)
0.297096 + 0.954848i \(0.403982\pi\)
\(60\) 0 0
\(61\) −9.95979 + 3.62507i −1.27522 + 0.464142i −0.888849 0.458201i \(-0.848494\pi\)
−0.386372 + 0.922343i \(0.626272\pi\)
\(62\) 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 −0.963649 0.267171i \(-0.913911\pi\)
−0.814156 + 0.580646i \(0.802800\pi\)
\(68\) 0 0
\(69\) −4.02496 0.0549417i −0.484548 0.00661420i
\(70\) 0 0
\(71\) 5.80783 + 10.0595i 0.689263 + 1.19384i 0.972077 + 0.234663i \(0.0753988\pi\)
−0.282814 + 0.959175i \(0.591268\pi\)
\(72\) 0 0
\(73\) 3.12044 5.40475i 0.365219 0.632579i −0.623592 0.781750i \(-0.714327\pi\)
0.988811 + 0.149171i \(0.0476606\pi\)
\(74\) 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 0.419795 0.907619i \(-0.362102\pi\)
0.0840543 + 0.996461i \(0.473213\pi\)
\(80\) 0 0
\(81\) 2.04418 8.76478i 0.227131 0.973864i
\(82\) 0 0
\(83\) −1.28300 + 7.27624i −0.140827 + 0.798671i 0.829796 + 0.558067i \(0.188457\pi\)
−0.970623 + 0.240604i \(0.922654\pi\)
\(84\) 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 0.145590 0.989345i \(-0.453492\pi\)
−0.784003 + 0.620757i \(0.786825\pi\)
\(90\) 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 0.708878 0.705331i \(-0.249202\pi\)
−0.571521 + 0.820588i \(0.693646\pi\)
\(98\) 0 0
\(99\) −8.66711 0.236660i −0.871078 0.0237853i
\(100\) 0 0
\(101\) 3.88953 + 10.6864i 0.387023 + 1.06334i 0.968335 + 0.249656i \(0.0803175\pi\)
−0.581312 + 0.813681i \(0.697460\pi\)
\(102\) 0 0
\(103\) 10.6329 + 12.6718i 1.04769 + 1.24859i 0.967783 + 0.251784i \(0.0810174\pi\)
0.0799054 + 0.996802i \(0.474538\pi\)
\(104\) 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 −0.999639 0.0268492i \(-0.991453\pi\)
0.147144 0.989115i \(-0.452992\pi\)
\(114\) 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 0.203769 0.979019i \(-0.434681\pi\)
−0.745971 + 0.665979i \(0.768014\pi\)
\(128\) 0 0
\(129\) 5.41131 14.2588i 0.476439 1.25542i
\(130\) 0 0
\(131\) −13.6909 4.98310i −1.19618 0.435375i −0.334293 0.942469i \(-0.608497\pi\)
−0.861891 + 0.507094i \(0.830720\pi\)
\(132\) 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 0.747240 0.664555i \(-0.231379\pi\)
0.474884 + 0.880048i \(0.342490\pi\)
\(138\) 0 0
\(139\) −3.14344 + 8.63654i −0.266624 + 0.732542i 0.732060 + 0.681240i \(0.238559\pi\)
−0.998683 + 0.0513016i \(0.983663\pi\)
\(140\) 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 −0.224261 0.974529i \(-0.571997\pi\)
0.122573 + 0.992460i \(0.460886\pi\)
\(150\) 0 0
\(151\) −7.74987 + 9.23593i −0.630675 + 0.751609i −0.982867 0.184319i \(-0.940992\pi\)
0.352191 + 0.935928i \(0.385437\pi\)
\(152\) 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 −0.747779 0.663948i \(-0.768879\pi\)
0.524011 + 0.851711i \(0.324435\pi\)
\(158\) 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 \(-0.969512\pi\)
0.995417 0.0956336i \(-0.0304877\pi\)
\(164\) 0 0
\(165\) −6.01625 17.2589i −0.468364 1.34360i
\(166\) 0 0
\(167\) −4.06934 + 3.41458i −0.314895 + 0.264229i −0.786512 0.617575i \(-0.788115\pi\)
0.471617 + 0.881804i \(0.343671\pi\)
\(168\) 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 −0.583377 + 0.812202i \(0.698269\pi\)
−0.698560 + 0.715551i \(0.746176\pi\)
\(174\) 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 0.588705 0.808348i \(-0.299638\pi\)
−0.994402 + 0.105659i \(0.966305\pi\)
\(180\) 0 0
\(181\) 2.12621 3.68270i 0.158040 0.273733i −0.776122 0.630583i \(-0.782816\pi\)
0.934162 + 0.356850i \(0.116149\pi\)
\(182\) 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 0.905245 + 0.424889i \(0.139687\pi\)
−0.995973 + 0.0896529i \(0.971424\pi\)
\(192\) 0 0
\(193\) −15.5914 5.67481i −1.12229 0.408482i −0.286805 0.957989i \(-0.592593\pi\)
−0.835489 + 0.549507i \(0.814815\pi\)
\(194\) 0 0
\(195\) −1.57381 + 4.14699i −0.112703 + 0.296972i
\(196\) 0 0
\(197\) 4.35620 + 2.51505i 0.310367 + 0.179190i 0.647091 0.762413i \(-0.275986\pi\)
−0.336724 + 0.941603i \(0.609319\pi\)
\(198\) 0 0
\(199\) 12.8199 7.40159i 0.908781 0.524685i 0.0287420 0.999587i \(-0.490850\pi\)
0.880039 + 0.474902i \(0.157517\pi\)
\(200\) 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 0.964930 0.262508i \(-0.0845497\pi\)
−0.426078 + 0.904686i \(0.640105\pi\)
\(212\) 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 0.999975 0.00701461i \(-0.00223284\pi\)
−0.770535 + 0.637398i \(0.780011\pi\)
\(224\) 0 0
\(225\) 11.9018 + 21.9790i 0.793453 + 1.46526i
\(226\) 0 0
\(227\) 7.69615 + 6.45783i 0.510811 + 0.428622i 0.861415 0.507903i \(-0.169579\pi\)
−0.350603 + 0.936524i \(0.614023\pi\)
\(228\) 0 0
\(229\) −2.02551 11.4872i −0.133849 0.759096i −0.975654 0.219315i \(-0.929618\pi\)
0.841805 0.539782i \(-0.181493\pi\)
\(230\) 0 0
\(231\) 0.110022 8.06006i 0.00723890 0.530313i
\(232\) 0 0
\(233\) 11.1464 6.43535i 0.730222 0.421594i −0.0882815 0.996096i \(-0.528137\pi\)
0.818503 + 0.574502i \(0.194804\pi\)
\(234\) 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 0.461817 0.886975i \(-0.347198\pi\)
−0.216364 + 0.976313i \(0.569420\pi\)
\(240\) 0 0
\(241\) −3.73127 + 21.1611i −0.240352 + 1.36311i 0.590691 + 0.806898i \(0.298855\pi\)
−0.831043 + 0.556208i \(0.812256\pi\)
\(242\) 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 −0.925210 0.379455i \(-0.876111\pi\)
0.791223 + 0.611528i \(0.209445\pi\)
\(252\) 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 −0.0115784 0.999933i \(-0.503686\pi\)
0.331117 + 0.943590i \(0.392574\pi\)
\(258\) 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 0.482964 0.875640i \(-0.339560\pi\)
0.932823 + 0.360336i \(0.117338\pi\)
\(264\) 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 \(0.00471501\pi\)
−0.999890 + 0.0148121i \(0.995285\pi\)
\(270\) 0 0
\(271\) 15.4958i 0.941306i 0.882318 + 0.470653i \(0.155982\pi\)
−0.882318 + 0.470653i \(0.844018\pi\)
\(272\) 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 −0.721228 0.692698i \(-0.756422\pi\)
−0.107235 + 0.994234i \(0.534200\pi\)
\(278\) 0 0
\(279\) −10.0948 30.2828i −0.604361 1.81298i
\(280\) 0 0
\(281\) 0.732164 0.872559i 0.0436772 0.0520525i −0.743764 0.668443i \(-0.766961\pi\)
0.787441 + 0.616390i \(0.211406\pi\)
\(282\) 0 0
\(283\) 4.21444 0.743119i 0.250522 0.0441739i −0.0469766 0.998896i \(-0.514959\pi\)
0.297499 + 0.954722i \(0.403848\pi\)
\(284\) 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 −0.988512 0.151142i \(-0.951705\pi\)
0.854396 + 0.519622i \(0.173927\pi\)
\(294\) 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 −0.745329 0.666697i \(-0.767707\pi\)
0.204713 + 0.978822i \(0.434374\pi\)
\(308\) 0 0
\(309\) 24.6149 + 14.6630i 1.40029 + 0.834147i
\(310\) 0 0
\(311\) −1.99845 11.3338i −0.113322 0.642678i −0.987568 0.157195i \(-0.949755\pi\)
0.874246 0.485483i \(-0.161356\pi\)
\(312\) 0 0
\(313\) −5.50981 4.62328i −0.311433 0.261323i 0.473651 0.880713i \(-0.342936\pi\)
−0.785084 + 0.619389i \(0.787380\pi\)
\(314\) 0 0
\(315\) 2.58763 + 17.4478i 0.145797 + 0.983070i
\(316\) 0 0
\(317\) −5.58824 15.3536i −0.313867 0.862342i −0.991867 0.127280i \(-0.959375\pi\)
0.678000 0.735062i \(-0.262847\pi\)
\(318\) 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 0.923255 + 0.384189i \(0.125519\pi\)
−0.460302 + 0.887762i \(0.652259\pi\)
\(332\) 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 0.999300 0.0374058i \(-0.0119094\pi\)
−0.951829 + 0.306631i \(0.900798\pi\)
\(338\) 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 0.692985 0.720952i \(-0.256295\pi\)
0.0674388 + 0.997723i \(0.478517\pi\)
\(348\) 0 0
\(349\) −0.0306727 + 0.173953i −0.00164187 + 0.00931151i −0.985618 0.168990i \(-0.945949\pi\)
0.983976 + 0.178302i \(0.0570604\pi\)
\(350\) 0 0
\(351\) 3.37076 + 1.38562i 0.179918 + 0.0739591i
\(352\) 0 0
\(353\) 4.03523 + 0.711520i 0.214774 + 0.0378704i 0.280000 0.960000i \(-0.409666\pi\)
−0.0652259 + 0.997871i \(0.520777\pi\)
\(354\) 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 −0.862553 0.505967i \(-0.831136\pi\)
0.869457 + 0.494009i \(0.164469\pi\)
\(360\) 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 −0.951478 0.307717i \(-0.900435\pi\)
0.468264 + 0.883588i \(0.344880\pi\)
\(368\) 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 −0.629572 0.776942i \(-0.716770\pi\)
0.655815 + 0.754922i \(0.272325\pi\)
\(374\) 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 \(-0.985829\pi\)
0.999009 0.0445061i \(-0.0141714\pi\)
\(380\) 0 0
\(381\) −12.0049 2.28615i −0.615028 0.117123i
\(382\) 0 0
\(383\) −17.1332 + 14.3765i −0.875466 + 0.734603i −0.965242 0.261359i \(-0.915829\pi\)
0.0897757 + 0.995962i \(0.471385\pi\)
\(384\) 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 −0.711300 0.702888i \(-0.751893\pi\)
0.815726 + 0.578439i \(0.196338\pi\)
\(390\) 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 −0.662324 0.749218i \(-0.730430\pi\)
0.980003 + 0.198981i \(0.0637630\pi\)
\(398\) 0 0
\(399\) −0.838985 5.16979i −0.0420018 0.258813i
\(400\) 0 0
\(401\) −4.72777 + 12.9894i −0.236094 + 0.648662i 0.763901 + 0.645334i \(0.223282\pi\)
−0.999994 + 0.00332813i \(0.998941\pi\)
\(402\) 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 0.999507 0.0314018i \(-0.00999714\pi\)
0.745482 + 0.666526i \(0.232219\pi\)
\(410\) 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 −0.662969 0.748647i \(-0.730704\pi\)
0.366934 0.930247i \(-0.380407\pi\)
\(420\) 0 0
\(421\) −3.66182 3.07264i −0.178466 0.149751i 0.549179 0.835705i \(-0.314941\pi\)
−0.727645 + 0.685954i \(0.759385\pi\)
\(422\) 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 0.997148 + 0.0754693i \(0.0240455\pi\)
−0.715349 + 0.698767i \(0.753732\pi\)
\(440\) 0 0
\(441\) 2.65032 12.9526i 0.126206 0.616789i
\(442\) 0 0
\(443\) −5.44673 4.57035i −0.258782 0.217144i 0.504161 0.863610i \(-0.331802\pi\)
−0.762943 + 0.646466i \(0.776246\pi\)
\(444\) 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 −0.0810641 0.996709i \(-0.525832\pi\)
0.822643 + 0.568558i \(0.192499\pi\)
\(450\) 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 0.651978 + 0.758238i \(0.273939\pi\)
−0.871991 + 0.489521i \(0.837172\pi\)
\(458\) 0 0
\(459\) −1.36597 + 33.3399i −0.0637581 + 1.55617i
\(460\) 0 0
\(461\) 12.6352 + 2.22793i 0.588482 + 0.103765i 0.459957 0.887941i \(-0.347865\pi\)
0.128525 + 0.991706i \(0.458976\pi\)
\(462\) 0 0
\(463\) 0.136338 0.374586i 0.00633617 0.0174085i −0.936484 0.350710i \(-0.885940\pi\)
0.942820 + 0.333301i \(0.108163\pi\)
\(464\) 0 0
\(465\) 52.1334 42.5461i 2.41763 1.97303i
\(466\) 0 0
\(467\) −4.12333 + 7.14182i −0.190805 + 0.330484i −0.945517 0.325572i \(-0.894443\pi\)
0.754712 + 0.656056i \(0.227777\pi\)
\(468\) 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 0.243859 0.969811i \(-0.421587\pi\)
0.810189 + 0.586169i \(0.199364\pi\)
\(480\) 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 \(0.0405092\pi\)
−0.991913 + 0.126920i \(0.959491\pi\)
\(488\) 0 0
\(489\) −1.39221 3.99386i −0.0629580 0.180609i
\(490\) 0 0
\(491\) 27.3869 22.9803i 1.23595 1.03709i 0.238122 0.971235i \(-0.423468\pi\)
0.997829 0.0658512i \(-0.0209763\pi\)
\(492\) 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 0.853376 0.521297i \(-0.174551\pi\)
0.980205 + 0.197987i \(0.0634404\pi\)
\(500\) 0 0
\(501\) −4.70879 + 7.90469i −0.210373 + 0.353156i
\(502\) 0 0
\(503\) −10.1863 17.6431i −0.454183 0.786668i 0.544458 0.838788i \(-0.316735\pi\)
−0.998641 + 0.0521202i \(0.983402\pi\)
\(504\) 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 −0.866403 0.499345i \(-0.833574\pi\)
0.984676 + 0.174393i \(0.0557963\pi\)
\(510\) 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 0.713317 0.700841i \(-0.247192\pi\)
−0.250288 + 0.968172i \(0.580525\pi\)
\(522\) 0 0
\(523\) −1.11506 + 0.643783i −0.0487584 + 0.0281507i −0.524181 0.851607i \(-0.675628\pi\)
0.475423 + 0.879758i \(0.342295\pi\)
\(524\) 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 −0.529228 0.848480i \(-0.677518\pi\)
−0.139980 0.990154i \(-0.544704\pi\)
\(548\) 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 −0.0592484 0.998243i \(-0.518870\pi\)
0.834880 + 0.550432i \(0.185537\pi\)
\(558\) 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 0.00677752 0.999977i \(-0.497843\pi\)
−0.637581 + 0.770383i \(0.720065\pi\)
\(564\) 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 0.285357 0.958421i \(-0.407888\pi\)
−0.0596516 + 0.998219i \(0.518999\pi\)
\(570\) 0 0
\(571\) 5.95709 16.3670i 0.249297 0.684937i −0.750416 0.660966i \(-0.770147\pi\)
0.999713 0.0239711i \(-0.00763096\pi\)
\(572\) 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 0.686042 0.727562i \(-0.259347\pi\)
−0.973108 + 0.230349i \(0.926013\pi\)
\(578\) 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 0.140222 0.990120i \(-0.455218\pi\)
0.743853 + 0.668343i \(0.232996\pi\)
\(588\) 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 \(0.246233\pi\)
−0.715426 + 0.698689i \(0.753767\pi\)
\(594\) 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 −0.992976 0.118313i \(-0.962251\pi\)
−0.0559128 + 0.998436i \(0.517807\pi\)
\(600\) 0 0
\(601\) 33.9607 12.3607i 1.38529 0.504203i 0.461510 0.887135i \(-0.347308\pi\)
0.923777 + 0.382931i \(0.125085\pi\)
\(602\) 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 0.267459 0.963569i \(-0.413816\pi\)
0.580889 + 0.813983i \(0.302705\pi\)
\(608\) 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 0.261648 + 0.965163i \(0.415734\pi\)
−0.966680 + 0.255987i \(0.917599\pi\)
\(614\) 0 0
\(615\) 37.1304 + 14.0912i 1.49724 + 0.568213i
\(616\) 0 0
\(617\) −4.96269 + 13.6349i −0.199790 + 0.548920i −0.998613 0.0526468i \(-0.983234\pi\)
0.798823 + 0.601566i \(0.205456\pi\)
\(618\) 0 0
\(619\) 2.94818 + 0.519843i 0.118497 + 0.0208943i 0.232582 0.972577i \(-0.425283\pi\)
−0.114085 + 0.993471i \(0.536394\pi\)
\(620\) 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 0.709933 0.704269i \(-0.248725\pi\)
0.964882 0.262685i \(-0.0846080\pi\)
\(632\) 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 0.999908 0.0135858i \(-0.00432462\pi\)
−0.774707 + 0.632321i \(0.782102\pi\)
\(642\) 0 0
\(643\) 24.0202 + 28.6262i 0.947265 + 1.12891i 0.991529 + 0.129887i \(0.0414613\pi\)
−0.0442639 + 0.999020i \(0.514094\pi\)
\(644\) 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 0.733611 0.679570i \(-0.237834\pi\)
−0.796636 + 0.604459i \(0.793389\pi\)
\(654\) 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 −0.0500301 0.998748i \(-0.515932\pi\)
−0.992262 + 0.124161i \(0.960376\pi\)
\(660\) 0 0
\(661\) 5.01298 + 28.4300i 0.194982 + 1.10580i 0.912444 + 0.409202i \(0.134193\pi\)
−0.717461 + 0.696598i \(0.754696\pi\)
\(662\) 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 −0.652504 0.757785i \(-0.726282\pi\)
0.872331 0.488915i \(-0.162607\pi\)
\(674\) 0 0
\(675\) 31.9965 + 29.1617i 1.23155 + 1.12244i
\(676\) 0 0
\(677\) −4.92975 0.869249i −0.189466 0.0334079i 0.0781100 0.996945i \(-0.475111\pi\)
−0.267576 + 0.963537i \(0.586223\pi\)
\(678\) 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 0.383031 + 0.923735i \(0.374880\pi\)
−0.991494 + 0.130153i \(0.958453\pi\)
\(684\) 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 −0.990085 0.140471i \(-0.955138\pi\)
0.310263 + 0.950651i \(0.399583\pi\)
\(692\) 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 \(-0.602807\pi\)
0.317393 0.948294i \(-0.397193\pi\)
\(702\) 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 −0.311523 0.950239i \(-0.600839\pi\)
0.372161 + 0.928168i \(0.378617\pi\)
\(710\) 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 −0.815319 0.579013i \(-0.803438\pi\)
−0.0937803 0.995593i \(-0.529895\pi\)
\(720\) 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 −0.625115 0.780532i \(-0.714948\pi\)
−0.854374 + 0.519659i \(0.826059\pi\)
\(728\) 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 0.632674 0.774418i \(-0.281957\pi\)
−0.0131304 + 0.999914i \(0.504180\pi\)
\(734\) 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 −0.522452 0.852669i \(-0.674983\pi\)
0.477207 + 0.878791i \(0.341649\pi\)
\(740\) 0 0
\(741\) 0.0311361 2.28099i 0.00114381 0.0837944i
\(742\) 0 0
\(743\) 1.09307 + 6.19911i 0.0401009 + 0.227423i 0.998271 0.0587751i \(-0.0187195\pi\)
−0.958170 + 0.286198i \(0.907608\pi\)
\(744\) 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 0.505394 0.862889i \(-0.331347\pi\)
−0.937540 + 0.347877i \(0.886903\pi\)
\(752\) 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 0.489909 0.871773i \(-0.337030\pi\)
−0.943601 + 0.331085i \(0.892585\pi\)
\(762\) 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 −0.938094 0.346382i \(-0.887410\pi\)
0.763050 0.646339i \(-0.223701\pi\)
\(770\) 0 0
\(771\) 7.86319 4.39782i 0.283186 0.158384i
\(772\) 0 0
\(773\) 15.1159 8.72717i 0.543681 0.313894i −0.202888 0.979202i \(-0.565033\pi\)
0.746569 + 0.665307i \(0.231700\pi\)
\(774\) 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 −0.946750 0.321969i \(-0.895655\pi\)
0.932211 + 0.361916i \(0.117877\pi\)
\(788\) 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