Properties

Label 756.2.ba.a.71.11
Level $756$
Weight $2$
Character 756.71
Analytic conductor $6.037$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.ba (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 71.11
Character \(\chi\) \(=\) 756.71
Dual form 756.2.ba.a.575.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.802493 + 1.16448i) q^{2} +(-0.712009 - 1.86897i) q^{4} +(2.73233 + 1.57751i) q^{5} +(0.866025 - 0.500000i) q^{7} +(2.74775 + 0.670717i) q^{8} +O(q^{10})\) \(q+(-0.802493 + 1.16448i) q^{2} +(-0.712009 - 1.86897i) q^{4} +(2.73233 + 1.57751i) q^{5} +(0.866025 - 0.500000i) q^{7} +(2.74775 + 0.670717i) q^{8} +(-4.02965 + 1.91579i) q^{10} +(2.55685 + 4.42859i) q^{11} +(2.38370 - 4.12868i) q^{13} +(-0.112741 + 1.40971i) q^{14} +(-2.98609 + 2.66145i) q^{16} -7.22631i q^{17} +0.531576i q^{19} +(1.00287 - 6.22984i) q^{20} +(-7.20884 - 0.576526i) q^{22} +(-1.59577 + 2.76396i) q^{23} +(2.47708 + 4.29042i) q^{25} +(2.89485 + 6.08899i) q^{26} +(-1.55110 - 1.26257i) q^{28} +(1.50966 - 0.871600i) q^{29} +(-1.47432 - 0.851200i) q^{31} +(-0.702876 - 5.61302i) q^{32} +(8.41487 + 5.79907i) q^{34} +3.15502 q^{35} +3.11392 q^{37} +(-0.619007 - 0.426586i) q^{38} +(6.44969 + 6.16722i) q^{40} +(2.32723 + 1.34363i) q^{41} +(4.39025 - 2.53471i) q^{43} +(6.45640 - 7.93187i) q^{44} +(-1.93797 - 4.07630i) q^{46} +(-1.47750 - 2.55911i) q^{47} +(0.500000 - 0.866025i) q^{49} +(-6.98393 - 0.558538i) q^{50} +(-9.41359 - 1.51539i) q^{52} +13.6811i q^{53} +16.1338i q^{55} +(2.71498 - 0.793018i) q^{56} +(-0.196531 + 2.45741i) q^{58} +(-3.71140 + 6.42833i) q^{59} +(3.23838 + 5.60903i) q^{61} +(2.17433 - 1.03373i) q^{62} +(7.10028 + 3.68593i) q^{64} +(13.0261 - 7.52061i) q^{65} +(-1.72700 - 0.997087i) q^{67} +(-13.5057 + 5.14520i) q^{68} +(-2.53188 + 3.67395i) q^{70} -13.0667 q^{71} -6.59684 q^{73} +(-2.49890 + 3.62609i) q^{74} +(0.993498 - 0.378487i) q^{76} +(4.42859 + 2.55685i) q^{77} +(1.73014 - 0.998899i) q^{79} +(-12.3574 + 2.56136i) q^{80} +(-3.43221 + 1.63175i) q^{82} +(3.28016 + 5.68140i) q^{83} +(11.3996 - 19.7446i) q^{85} +(-0.571535 + 7.14643i) q^{86} +(4.05525 + 13.8836i) q^{88} +9.77920i q^{89} -4.76739i q^{91} +(6.30196 + 1.01448i) q^{92} +(4.16571 + 0.333152i) q^{94} +(-0.838566 + 1.45244i) q^{95} +(-6.15806 - 10.6661i) q^{97} +(0.607219 + 1.27722i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + O(q^{10}) \) \( 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.802493 + 1.16448i −0.567448 + 0.823409i
\(3\) 0 0
\(4\) −0.712009 1.86897i −0.356005 0.934484i
\(5\) 2.73233 + 1.57751i 1.22193 + 0.705484i 0.965330 0.261033i \(-0.0840630\pi\)
0.256604 + 0.966517i \(0.417396\pi\)
\(6\) 0 0
\(7\) 0.866025 0.500000i 0.327327 0.188982i
\(8\) 2.74775 + 0.670717i 0.971477 + 0.237134i
\(9\) 0 0
\(10\) −4.02965 + 1.91579i −1.27429 + 0.605826i
\(11\) 2.55685 + 4.42859i 0.770919 + 1.33527i 0.937060 + 0.349169i \(0.113536\pi\)
−0.166141 + 0.986102i \(0.553131\pi\)
\(12\) 0 0
\(13\) 2.38370 4.12868i 0.661118 1.14509i −0.319204 0.947686i \(-0.603416\pi\)
0.980322 0.197404i \(-0.0632511\pi\)
\(14\) −0.112741 + 1.40971i −0.0301314 + 0.376762i
\(15\) 0 0
\(16\) −2.98609 + 2.66145i −0.746521 + 0.665361i
\(17\) 7.22631i 1.75264i −0.481731 0.876319i \(-0.659992\pi\)
0.481731 0.876319i \(-0.340008\pi\)
\(18\) 0 0
\(19\) 0.531576i 0.121952i 0.998139 + 0.0609759i \(0.0194213\pi\)
−0.998139 + 0.0609759i \(0.980579\pi\)
\(20\) 1.00287 6.22984i 0.224249 1.39303i
\(21\) 0 0
\(22\) −7.20884 0.576526i −1.53693 0.122916i
\(23\) −1.59577 + 2.76396i −0.332742 + 0.576325i −0.983048 0.183346i \(-0.941307\pi\)
0.650307 + 0.759672i \(0.274640\pi\)
\(24\) 0 0
\(25\) 2.47708 + 4.29042i 0.495415 + 0.858084i
\(26\) 2.89485 + 6.08899i 0.567727 + 1.19415i
\(27\) 0 0
\(28\) −1.55110 1.26257i −0.293131 0.238603i
\(29\) 1.50966 0.871600i 0.280336 0.161852i −0.353240 0.935533i \(-0.614920\pi\)
0.633575 + 0.773681i \(0.281587\pi\)
\(30\) 0 0
\(31\) −1.47432 0.851200i −0.264796 0.152880i 0.361724 0.932285i \(-0.382188\pi\)
−0.626520 + 0.779405i \(0.715521\pi\)
\(32\) −0.702876 5.61302i −0.124252 0.992251i
\(33\) 0 0
\(34\) 8.41487 + 5.79907i 1.44314 + 0.994532i
\(35\) 3.15502 0.533296
\(36\) 0 0
\(37\) 3.11392 0.511926 0.255963 0.966687i \(-0.417608\pi\)
0.255963 + 0.966687i \(0.417608\pi\)
\(38\) −0.619007 0.426586i −0.100416 0.0692014i
\(39\) 0 0
\(40\) 6.44969 + 6.16722i 1.01979 + 0.975124i
\(41\) 2.32723 + 1.34363i 0.363452 + 0.209839i 0.670594 0.741825i \(-0.266039\pi\)
−0.307142 + 0.951664i \(0.599373\pi\)
\(42\) 0 0
\(43\) 4.39025 2.53471i 0.669507 0.386540i −0.126383 0.991982i \(-0.540337\pi\)
0.795890 + 0.605441i \(0.207003\pi\)
\(44\) 6.45640 7.93187i 0.973339 1.19577i
\(45\) 0 0
\(46\) −1.93797 4.07630i −0.285738 0.601017i
\(47\) −1.47750 2.55911i −0.215516 0.373285i 0.737916 0.674892i \(-0.235810\pi\)
−0.953432 + 0.301608i \(0.902477\pi\)
\(48\) 0 0
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) −6.98393 0.558538i −0.987677 0.0789893i
\(51\) 0 0
\(52\) −9.41359 1.51539i −1.30543 0.210147i
\(53\) 13.6811i 1.87925i 0.342209 + 0.939624i \(0.388825\pi\)
−0.342209 + 0.939624i \(0.611175\pi\)
\(54\) 0 0
\(55\) 16.1338i 2.17548i
\(56\) 2.71498 0.793018i 0.362805 0.105971i
\(57\) 0 0
\(58\) −0.196531 + 2.45741i −0.0258058 + 0.322674i
\(59\) −3.71140 + 6.42833i −0.483183 + 0.836898i −0.999814 0.0193107i \(-0.993853\pi\)
0.516630 + 0.856209i \(0.327186\pi\)
\(60\) 0 0
\(61\) 3.23838 + 5.60903i 0.414632 + 0.718163i 0.995390 0.0959130i \(-0.0305771\pi\)
−0.580758 + 0.814076i \(0.697244\pi\)
\(62\) 2.17433 1.03373i 0.276141 0.131284i
\(63\) 0 0
\(64\) 7.10028 + 3.68593i 0.887535 + 0.460741i
\(65\) 13.0261 7.52061i 1.61569 0.932816i
\(66\) 0 0
\(67\) −1.72700 0.997087i −0.210987 0.121814i 0.390783 0.920483i \(-0.372204\pi\)
−0.601770 + 0.798669i \(0.705538\pi\)
\(68\) −13.5057 + 5.14520i −1.63781 + 0.623947i
\(69\) 0 0
\(70\) −2.53188 + 3.67395i −0.302618 + 0.439120i
\(71\) −13.0667 −1.55074 −0.775368 0.631509i \(-0.782436\pi\)
−0.775368 + 0.631509i \(0.782436\pi\)
\(72\) 0 0
\(73\) −6.59684 −0.772101 −0.386051 0.922478i \(-0.626161\pi\)
−0.386051 + 0.922478i \(0.626161\pi\)
\(74\) −2.49890 + 3.62609i −0.290491 + 0.421524i
\(75\) 0 0
\(76\) 0.993498 0.378487i 0.113962 0.0434154i
\(77\) 4.42859 + 2.55685i 0.504685 + 0.291380i
\(78\) 0 0
\(79\) 1.73014 0.998899i 0.194656 0.112385i −0.399504 0.916731i \(-0.630818\pi\)
0.594161 + 0.804346i \(0.297484\pi\)
\(80\) −12.3574 + 2.56136i −1.38160 + 0.286369i
\(81\) 0 0
\(82\) −3.43221 + 1.63175i −0.379024 + 0.180197i
\(83\) 3.28016 + 5.68140i 0.360044 + 0.623615i 0.987968 0.154660i \(-0.0494282\pi\)
−0.627923 + 0.778275i \(0.716095\pi\)
\(84\) 0 0
\(85\) 11.3996 19.7446i 1.23646 2.14161i
\(86\) −0.571535 + 7.14643i −0.0616302 + 0.770620i
\(87\) 0 0
\(88\) 4.05525 + 13.8836i 0.432292 + 1.48000i
\(89\) 9.77920i 1.03659i 0.855201 + 0.518297i \(0.173434\pi\)
−0.855201 + 0.518297i \(0.826566\pi\)
\(90\) 0 0
\(91\) 4.76739i 0.499758i
\(92\) 6.30196 + 1.01448i 0.657025 + 0.105767i
\(93\) 0 0
\(94\) 4.16571 + 0.333152i 0.429660 + 0.0343620i
\(95\) −0.838566 + 1.45244i −0.0860350 + 0.149017i
\(96\) 0 0
\(97\) −6.15806 10.6661i −0.625257 1.08298i −0.988491 0.151279i \(-0.951661\pi\)
0.363234 0.931698i \(-0.381672\pi\)
\(98\) 0.607219 + 1.27722i 0.0613384 + 0.129018i
\(99\) 0 0
\(100\) 6.25496 7.68439i 0.625496 0.768439i
\(101\) 3.16824 1.82918i 0.315251 0.182010i −0.334023 0.942565i \(-0.608406\pi\)
0.649274 + 0.760555i \(0.275073\pi\)
\(102\) 0 0
\(103\) 2.62116 + 1.51333i 0.258270 + 0.149112i 0.623545 0.781787i \(-0.285692\pi\)
−0.365275 + 0.930900i \(0.619025\pi\)
\(104\) 9.31898 9.74581i 0.913801 0.955655i
\(105\) 0 0
\(106\) −15.9314 10.9790i −1.54739 1.06638i
\(107\) 4.00810 0.387478 0.193739 0.981053i \(-0.437939\pi\)
0.193739 + 0.981053i \(0.437939\pi\)
\(108\) 0 0
\(109\) −1.58898 −0.152197 −0.0760984 0.997100i \(-0.524246\pi\)
−0.0760984 + 0.997100i \(0.524246\pi\)
\(110\) −18.7874 12.9473i −1.79131 1.23447i
\(111\) 0 0
\(112\) −1.25530 + 3.79792i −0.118615 + 0.358870i
\(113\) −5.56042 3.21031i −0.523080 0.302001i 0.215114 0.976589i \(-0.430988\pi\)
−0.738194 + 0.674588i \(0.764321\pi\)
\(114\) 0 0
\(115\) −8.72035 + 5.03470i −0.813177 + 0.469488i
\(116\) −2.70388 2.20091i −0.251049 0.204349i
\(117\) 0 0
\(118\) −4.50727 9.48053i −0.414928 0.872754i
\(119\) −3.61316 6.25817i −0.331217 0.573685i
\(120\) 0 0
\(121\) −7.57496 + 13.1202i −0.688632 + 1.19275i
\(122\) −9.13036 0.730199i −0.826624 0.0661091i
\(123\) 0 0
\(124\) −0.541135 + 3.36152i −0.0485954 + 0.301874i
\(125\) 0.144654i 0.0129383i
\(126\) 0 0
\(127\) 5.15607i 0.457527i 0.973482 + 0.228764i \(0.0734683\pi\)
−0.973482 + 0.228764i \(0.926532\pi\)
\(128\) −9.99010 + 5.31017i −0.883008 + 0.469357i
\(129\) 0 0
\(130\) −1.69577 + 21.2038i −0.148729 + 1.85969i
\(131\) 7.48154 12.9584i 0.653666 1.13218i −0.328561 0.944483i \(-0.606564\pi\)
0.982227 0.187699i \(-0.0601030\pi\)
\(132\) 0 0
\(133\) 0.265788 + 0.460358i 0.0230467 + 0.0399181i
\(134\) 2.54699 1.21090i 0.220027 0.104606i
\(135\) 0 0
\(136\) 4.84681 19.8561i 0.415610 1.70265i
\(137\) −0.472178 + 0.272612i −0.0403409 + 0.0232908i −0.520035 0.854145i \(-0.674081\pi\)
0.479694 + 0.877436i \(0.340748\pi\)
\(138\) 0 0
\(139\) −8.99978 5.19603i −0.763351 0.440721i 0.0671463 0.997743i \(-0.478611\pi\)
−0.830498 + 0.557022i \(0.811944\pi\)
\(140\) −2.24640 5.89663i −0.189856 0.498356i
\(141\) 0 0
\(142\) 10.4860 15.2159i 0.879963 1.27689i
\(143\) 24.3790 2.03867
\(144\) 0 0
\(145\) 5.49983 0.456736
\(146\) 5.29392 7.68186i 0.438128 0.635755i
\(147\) 0 0
\(148\) −2.21714 5.81982i −0.182248 0.478387i
\(149\) −11.1828 6.45637i −0.916127 0.528926i −0.0337298 0.999431i \(-0.510739\pi\)
−0.882398 + 0.470505i \(0.844072\pi\)
\(150\) 0 0
\(151\) 2.78931 1.61041i 0.226991 0.131053i −0.382192 0.924083i \(-0.624831\pi\)
0.609183 + 0.793030i \(0.291497\pi\)
\(152\) −0.356537 + 1.46064i −0.0289189 + 0.118473i
\(153\) 0 0
\(154\) −6.53131 + 3.10514i −0.526308 + 0.250219i
\(155\) −2.68555 4.65151i −0.215709 0.373618i
\(156\) 0 0
\(157\) 3.13601 5.43172i 0.250281 0.433499i −0.713322 0.700836i \(-0.752810\pi\)
0.963603 + 0.267337i \(0.0861438\pi\)
\(158\) −0.225235 + 2.81632i −0.0179187 + 0.224054i
\(159\) 0 0
\(160\) 6.93410 16.4454i 0.548189 1.30012i
\(161\) 3.19155i 0.251529i
\(162\) 0 0
\(163\) 17.5965i 1.37826i 0.724636 + 0.689132i \(0.242008\pi\)
−0.724636 + 0.689132i \(0.757992\pi\)
\(164\) 0.854187 5.30619i 0.0667008 0.414344i
\(165\) 0 0
\(166\) −9.24816 0.739620i −0.717797 0.0574057i
\(167\) −1.40973 + 2.44173i −0.109088 + 0.188946i −0.915401 0.402543i \(-0.868126\pi\)
0.806313 + 0.591489i \(0.201460\pi\)
\(168\) 0 0
\(169\) −4.86401 8.42471i −0.374154 0.648054i
\(170\) 13.8441 + 29.1195i 1.06179 + 2.23336i
\(171\) 0 0
\(172\) −7.86320 6.40050i −0.599563 0.488034i
\(173\) −3.41022 + 1.96889i −0.259274 + 0.149692i −0.624003 0.781422i \(-0.714495\pi\)
0.364729 + 0.931114i \(0.381162\pi\)
\(174\) 0 0
\(175\) 4.29042 + 2.47708i 0.324325 + 0.187249i
\(176\) −19.4214 6.41924i −1.46395 0.483869i
\(177\) 0 0
\(178\) −11.3876 7.84774i −0.853540 0.588213i
\(179\) −1.19273 −0.0891491 −0.0445746 0.999006i \(-0.514193\pi\)
−0.0445746 + 0.999006i \(0.514193\pi\)
\(180\) 0 0
\(181\) −0.516134 −0.0383639 −0.0191820 0.999816i \(-0.506106\pi\)
−0.0191820 + 0.999816i \(0.506106\pi\)
\(182\) 5.55151 + 3.82580i 0.411505 + 0.283587i
\(183\) 0 0
\(184\) −6.23862 + 6.52436i −0.459917 + 0.480982i
\(185\) 8.50826 + 4.91224i 0.625540 + 0.361155i
\(186\) 0 0
\(187\) 32.0024 18.4766i 2.34025 1.35114i
\(188\) −3.73090 + 4.58352i −0.272104 + 0.334287i
\(189\) 0 0
\(190\) −1.01839 2.14206i −0.0738815 0.155402i
\(191\) −13.1346 22.7498i −0.950385 1.64611i −0.744593 0.667518i \(-0.767357\pi\)
−0.205791 0.978596i \(-0.565977\pi\)
\(192\) 0 0
\(193\) 8.21149 14.2227i 0.591076 1.02377i −0.403012 0.915195i \(-0.632037\pi\)
0.994088 0.108579i \(-0.0346300\pi\)
\(194\) 17.3622 + 1.38854i 1.24653 + 0.0996913i
\(195\) 0 0
\(196\) −1.97458 0.317866i −0.141041 0.0227047i
\(197\) 5.79981i 0.413219i −0.978423 0.206610i \(-0.933757\pi\)
0.978423 0.206610i \(-0.0662430\pi\)
\(198\) 0 0
\(199\) 25.1918i 1.78580i −0.450253 0.892901i \(-0.648666\pi\)
0.450253 0.892901i \(-0.351334\pi\)
\(200\) 3.92873 + 13.4504i 0.277803 + 0.951089i
\(201\) 0 0
\(202\) −0.412450 + 5.15724i −0.0290198 + 0.362862i
\(203\) 0.871600 1.50966i 0.0611743 0.105957i
\(204\) 0 0
\(205\) 4.23917 + 7.34245i 0.296076 + 0.512819i
\(206\) −3.86569 + 1.83784i −0.269335 + 0.128048i
\(207\) 0 0
\(208\) 3.87034 + 18.6727i 0.268360 + 1.29472i
\(209\) −2.35413 + 1.35916i −0.162839 + 0.0940150i
\(210\) 0 0
\(211\) −12.6040 7.27691i −0.867694 0.500963i −0.00111255 0.999999i \(-0.500354\pi\)
−0.866581 + 0.499036i \(0.833687\pi\)
\(212\) 25.5696 9.74109i 1.75613 0.669021i
\(213\) 0 0
\(214\) −3.21647 + 4.66734i −0.219874 + 0.319053i
\(215\) 15.9941 1.09079
\(216\) 0 0
\(217\) −1.70240 −0.115566
\(218\) 1.27515 1.85033i 0.0863638 0.125320i
\(219\) 0 0
\(220\) 30.1536 11.4874i 2.03296 0.774482i
\(221\) −29.8351 17.2253i −2.00693 1.15870i
\(222\) 0 0
\(223\) 13.1948 7.61804i 0.883591 0.510141i 0.0117502 0.999931i \(-0.496260\pi\)
0.871841 + 0.489789i \(0.162926\pi\)
\(224\) −3.41522 4.50958i −0.228189 0.301309i
\(225\) 0 0
\(226\) 8.20053 3.89872i 0.545491 0.259339i
\(227\) −2.90472 5.03112i −0.192793 0.333927i 0.753382 0.657583i \(-0.228421\pi\)
−0.946175 + 0.323656i \(0.895088\pi\)
\(228\) 0 0
\(229\) −7.47034 + 12.9390i −0.493654 + 0.855034i −0.999973 0.00731207i \(-0.997672\pi\)
0.506319 + 0.862346i \(0.331006\pi\)
\(230\) 1.13524 14.1949i 0.0748554 0.935987i
\(231\) 0 0
\(232\) 4.73275 1.38239i 0.310721 0.0907583i
\(233\) 0.536725i 0.0351620i −0.999845 0.0175810i \(-0.994404\pi\)
0.999845 0.0175810i \(-0.00559649\pi\)
\(234\) 0 0
\(235\) 9.32310i 0.608172i
\(236\) 14.6569 + 2.35946i 0.954083 + 0.153588i
\(237\) 0 0
\(238\) 10.1870 + 0.814705i 0.660327 + 0.0528095i
\(239\) −10.0017 + 17.3234i −0.646956 + 1.12056i 0.336890 + 0.941544i \(0.390625\pi\)
−0.983846 + 0.179017i \(0.942708\pi\)
\(240\) 0 0
\(241\) 8.07407 + 13.9847i 0.520096 + 0.900833i 0.999727 + 0.0233628i \(0.00743728\pi\)
−0.479631 + 0.877470i \(0.659229\pi\)
\(242\) −9.19932 19.3497i −0.591355 1.24385i
\(243\) 0 0
\(244\) 8.17735 10.0461i 0.523501 0.643136i
\(245\) 2.73233 1.57751i 0.174562 0.100783i
\(246\) 0 0
\(247\) 2.19471 + 1.26711i 0.139646 + 0.0806246i
\(248\) −3.48015 3.32774i −0.220990 0.211312i
\(249\) 0 0
\(250\) 0.168446 + 0.116084i 0.0106535 + 0.00734180i
\(251\) −25.4053 −1.60357 −0.801785 0.597613i \(-0.796116\pi\)
−0.801785 + 0.597613i \(0.796116\pi\)
\(252\) 0 0
\(253\) −16.3206 −1.02607
\(254\) −6.00412 4.13771i −0.376732 0.259623i
\(255\) 0 0
\(256\) 1.83342 15.8946i 0.114589 0.993413i
\(257\) 5.65981 + 3.26769i 0.353049 + 0.203833i 0.666027 0.745927i \(-0.267993\pi\)
−0.312978 + 0.949760i \(0.601327\pi\)
\(258\) 0 0
\(259\) 2.69674 1.55696i 0.167567 0.0967449i
\(260\) −23.3305 18.9906i −1.44689 1.17775i
\(261\) 0 0
\(262\) 9.08588 + 19.1111i 0.561327 + 1.18069i
\(263\) 2.54968 + 4.41617i 0.157220 + 0.272313i 0.933865 0.357625i \(-0.116414\pi\)
−0.776645 + 0.629938i \(0.783080\pi\)
\(264\) 0 0
\(265\) −21.5821 + 37.3813i −1.32578 + 2.29632i
\(266\) −0.749369 0.0599306i −0.0459468 0.00367458i
\(267\) 0 0
\(268\) −0.633880 + 3.93765i −0.0387204 + 0.240530i
\(269\) 23.1813i 1.41339i −0.707519 0.706694i \(-0.750186\pi\)
0.707519 0.706694i \(-0.249814\pi\)
\(270\) 0 0
\(271\) 3.33548i 0.202616i 0.994855 + 0.101308i \(0.0323027\pi\)
−0.994855 + 0.101308i \(0.967697\pi\)
\(272\) 19.2324 + 21.5784i 1.16614 + 1.30838i
\(273\) 0 0
\(274\) 0.0614694 0.768609i 0.00371350 0.0464334i
\(275\) −12.6670 + 21.9399i −0.763850 + 1.32303i
\(276\) 0 0
\(277\) −6.01165 10.4125i −0.361205 0.625625i 0.626954 0.779056i \(-0.284301\pi\)
−0.988159 + 0.153430i \(0.950968\pi\)
\(278\) 13.2729 6.31025i 0.796056 0.378464i
\(279\) 0 0
\(280\) 8.66921 + 2.11613i 0.518084 + 0.126463i
\(281\) −16.0334 + 9.25689i −0.956472 + 0.552220i −0.895086 0.445894i \(-0.852886\pi\)
−0.0613869 + 0.998114i \(0.519552\pi\)
\(282\) 0 0
\(283\) −18.7908 10.8489i −1.11700 0.644899i −0.176365 0.984325i \(-0.556434\pi\)
−0.940633 + 0.339426i \(0.889767\pi\)
\(284\) 9.30364 + 24.4213i 0.552069 + 1.44914i
\(285\) 0 0
\(286\) −19.5640 + 28.3888i −1.15684 + 1.67866i
\(287\) 2.68725 0.158624
\(288\) 0 0
\(289\) −35.2196 −2.07174
\(290\) −4.41358 + 6.40442i −0.259174 + 0.376081i
\(291\) 0 0
\(292\) 4.69701 + 12.3293i 0.274872 + 0.721517i
\(293\) 11.5943 + 6.69399i 0.677348 + 0.391067i 0.798855 0.601524i \(-0.205439\pi\)
−0.121507 + 0.992591i \(0.538773\pi\)
\(294\) 0 0
\(295\) −20.2815 + 11.7095i −1.18084 + 0.681756i
\(296\) 8.55629 + 2.08856i 0.497324 + 0.121395i
\(297\) 0 0
\(298\) 16.4924 7.84086i 0.955378 0.454209i
\(299\) 7.60767 + 13.1769i 0.439963 + 0.762038i
\(300\) 0 0
\(301\) 2.53471 4.39025i 0.146098 0.253050i
\(302\) −0.363120 + 4.54043i −0.0208952 + 0.261272i
\(303\) 0 0
\(304\) −1.41476 1.58733i −0.0811420 0.0910396i
\(305\) 20.4343i 1.17006i
\(306\) 0 0
\(307\) 14.9315i 0.852187i 0.904679 + 0.426093i \(0.140111\pi\)
−0.904679 + 0.426093i \(0.859889\pi\)
\(308\) 1.62547 10.0974i 0.0926198 0.575353i
\(309\) 0 0
\(310\) 7.57171 + 0.605546i 0.430044 + 0.0343927i
\(311\) 3.83776 6.64720i 0.217619 0.376928i −0.736460 0.676481i \(-0.763504\pi\)
0.954080 + 0.299553i \(0.0968375\pi\)
\(312\) 0 0
\(313\) 11.6398 + 20.1608i 0.657923 + 1.13956i 0.981152 + 0.193236i \(0.0618982\pi\)
−0.323229 + 0.946321i \(0.604768\pi\)
\(314\) 3.80849 + 8.01072i 0.214925 + 0.452071i
\(315\) 0 0
\(316\) −3.09879 2.52236i −0.174320 0.141894i
\(317\) −23.4749 + 13.5533i −1.31848 + 0.761226i −0.983485 0.180992i \(-0.942069\pi\)
−0.334998 + 0.942219i \(0.608736\pi\)
\(318\) 0 0
\(319\) 7.71992 + 4.45710i 0.432233 + 0.249550i
\(320\) 13.5857 + 21.2719i 0.759464 + 1.18914i
\(321\) 0 0
\(322\) −3.71648 2.56119i −0.207111 0.142730i
\(323\) 3.84133 0.213737
\(324\) 0 0
\(325\) 23.6184 1.31011
\(326\) −20.4907 14.1211i −1.13488 0.782094i
\(327\) 0 0
\(328\) 5.49345 + 5.25286i 0.303325 + 0.290041i
\(329\) −2.55911 1.47750i −0.141088 0.0814574i
\(330\) 0 0
\(331\) −15.5271 + 8.96456i −0.853445 + 0.492737i −0.861812 0.507228i \(-0.830670\pi\)
0.00836643 + 0.999965i \(0.497337\pi\)
\(332\) 8.28286 10.1757i 0.454581 0.558466i
\(333\) 0 0
\(334\) −1.71203 3.60107i −0.0936782 0.197042i
\(335\) −3.14583 5.44873i −0.171875 0.297696i
\(336\) 0 0
\(337\) −3.33464 + 5.77577i −0.181650 + 0.314626i −0.942442 0.334368i \(-0.891477\pi\)
0.760793 + 0.648995i \(0.224810\pi\)
\(338\) 13.7137 + 1.09675i 0.745927 + 0.0596554i
\(339\) 0 0
\(340\) −45.0187 7.24708i −2.44148 0.393028i
\(341\) 8.70556i 0.471432i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 13.7634 4.02015i 0.742073 0.216752i
\(345\) 0 0
\(346\) 0.443951 5.55114i 0.0238670 0.298431i
\(347\) 15.7139 27.2173i 0.843568 1.46110i −0.0432902 0.999063i \(-0.513784\pi\)
0.886859 0.462041i \(-0.152883\pi\)
\(348\) 0 0
\(349\) −3.17117 5.49263i −0.169749 0.294014i 0.768583 0.639751i \(-0.220962\pi\)
−0.938332 + 0.345737i \(0.887629\pi\)
\(350\) −6.32753 + 3.00826i −0.338221 + 0.160798i
\(351\) 0 0
\(352\) 23.0606 17.4644i 1.22914 0.930855i
\(353\) −22.5568 + 13.0232i −1.20058 + 0.693155i −0.960684 0.277644i \(-0.910447\pi\)
−0.239896 + 0.970799i \(0.577113\pi\)
\(354\) 0 0
\(355\) −35.7026 20.6129i −1.89490 1.09402i
\(356\) 18.2770 6.96288i 0.968680 0.369032i
\(357\) 0 0
\(358\) 0.957161 1.38891i 0.0505875 0.0734062i
\(359\) −31.2925 −1.65156 −0.825778 0.563996i \(-0.809263\pi\)
−0.825778 + 0.563996i \(0.809263\pi\)
\(360\) 0 0
\(361\) 18.7174 0.985128
\(362\) 0.414194 0.601025i 0.0217695 0.0315892i
\(363\) 0 0
\(364\) −8.91010 + 3.39443i −0.467016 + 0.177916i
\(365\) −18.0247 10.4066i −0.943457 0.544705i
\(366\) 0 0
\(367\) 19.3046 11.1455i 1.00769 0.581792i 0.0971776 0.995267i \(-0.469019\pi\)
0.910515 + 0.413475i \(0.135685\pi\)
\(368\) −2.59101 12.5005i −0.135066 0.651633i
\(369\) 0 0
\(370\) −12.5480 + 5.96562i −0.652340 + 0.310138i
\(371\) 6.84057 + 11.8482i 0.355144 + 0.615128i
\(372\) 0 0
\(373\) 9.29840 16.1053i 0.481453 0.833901i −0.518321 0.855186i \(-0.673443\pi\)
0.999773 + 0.0212856i \(0.00677594\pi\)
\(374\) −4.16616 + 52.0934i −0.215427 + 2.69368i
\(375\) 0 0
\(376\) −2.34337 8.02279i −0.120850 0.413744i
\(377\) 8.31051i 0.428013i
\(378\) 0 0
\(379\) 21.2022i 1.08908i 0.838733 + 0.544542i \(0.183297\pi\)
−0.838733 + 0.544542i \(0.816703\pi\)
\(380\) 3.31163 + 0.533103i 0.169883 + 0.0273476i
\(381\) 0 0
\(382\) 37.0320 + 2.96162i 1.89472 + 0.151530i
\(383\) 5.85031 10.1330i 0.298937 0.517774i −0.676956 0.736023i \(-0.736701\pi\)
0.975893 + 0.218250i \(0.0700347\pi\)
\(384\) 0 0
\(385\) 8.06691 + 13.9723i 0.411128 + 0.712094i
\(386\) 9.97235 + 20.9757i 0.507579 + 1.06764i
\(387\) 0 0
\(388\) −15.5500 + 19.1036i −0.789430 + 0.969837i
\(389\) 20.6139 11.9014i 1.04517 0.603427i 0.123874 0.992298i \(-0.460468\pi\)
0.921292 + 0.388871i \(0.127135\pi\)
\(390\) 0 0
\(391\) 19.9732 + 11.5316i 1.01009 + 0.583176i
\(392\) 1.95473 2.04426i 0.0987290 0.103251i
\(393\) 0 0
\(394\) 6.75374 + 4.65431i 0.340249 + 0.234481i
\(395\) 6.30309 0.317143
\(396\) 0 0
\(397\) −9.08225 −0.455825 −0.227912 0.973682i \(-0.573190\pi\)
−0.227912 + 0.973682i \(0.573190\pi\)
\(398\) 29.3353 + 20.2163i 1.47045 + 1.01335i
\(399\) 0 0
\(400\) −18.8155 6.21896i −0.940774 0.310948i
\(401\) 22.6865 + 13.0981i 1.13291 + 0.654087i 0.944666 0.328035i \(-0.106386\pi\)
0.188246 + 0.982122i \(0.439720\pi\)
\(402\) 0 0
\(403\) −7.02866 + 4.05800i −0.350123 + 0.202143i
\(404\) −5.67450 4.61894i −0.282317 0.229801i
\(405\) 0 0
\(406\) 1.05850 + 2.22645i 0.0525327 + 0.110497i
\(407\) 7.96183 + 13.7903i 0.394653 + 0.683560i
\(408\) 0 0
\(409\) −4.62676 + 8.01379i −0.228779 + 0.396256i −0.957446 0.288611i \(-0.906807\pi\)
0.728668 + 0.684867i \(0.240140\pi\)
\(410\) −11.9520 0.955860i −0.590268 0.0472066i
\(411\) 0 0
\(412\) 0.962070 5.97636i 0.0473978 0.294434i
\(413\) 7.42280i 0.365252i
\(414\) 0 0
\(415\) 20.6979i 1.01602i
\(416\) −24.8498 10.4778i −1.21836 0.513715i
\(417\) 0 0
\(418\) 0.306467 3.83205i 0.0149898 0.187432i
\(419\) 14.3147 24.7937i 0.699317 1.21125i −0.269387 0.963032i \(-0.586821\pi\)
0.968704 0.248220i \(-0.0798457\pi\)
\(420\) 0 0
\(421\) −6.82164 11.8154i −0.332466 0.575849i 0.650528 0.759482i \(-0.274547\pi\)
−0.982995 + 0.183633i \(0.941214\pi\)
\(422\) 18.5884 8.83736i 0.904869 0.430196i
\(423\) 0 0
\(424\) −9.17617 + 37.5924i −0.445634 + 1.82565i
\(425\) 31.0039 17.9001i 1.50391 0.868283i
\(426\) 0 0
\(427\) 5.60903 + 3.23838i 0.271440 + 0.156716i
\(428\) −2.85380 7.49101i −0.137944 0.362092i
\(429\) 0 0
\(430\) −12.8352 + 18.6248i −0.618968 + 0.898167i
\(431\) −11.9995 −0.577994 −0.288997 0.957330i \(-0.593322\pi\)
−0.288997 + 0.957330i \(0.593322\pi\)
\(432\) 0 0
\(433\) 18.6726 0.897349 0.448674 0.893695i \(-0.351896\pi\)
0.448674 + 0.893695i \(0.351896\pi\)
\(434\) 1.36616 1.98240i 0.0655780 0.0951584i
\(435\) 0 0
\(436\) 1.13137 + 2.96975i 0.0541827 + 0.142225i
\(437\) −1.46925 0.848274i −0.0702839 0.0405784i
\(438\) 0 0
\(439\) −22.6620 + 13.0839i −1.08160 + 0.624461i −0.931327 0.364184i \(-0.881348\pi\)
−0.150271 + 0.988645i \(0.548015\pi\)
\(440\) −10.8212 + 44.3317i −0.515882 + 2.11343i
\(441\) 0 0
\(442\) 44.0010 20.9191i 2.09291 0.995020i
\(443\) 17.3363 + 30.0273i 0.823671 + 1.42664i 0.902931 + 0.429786i \(0.141411\pi\)
−0.0792601 + 0.996854i \(0.525256\pi\)
\(444\) 0 0
\(445\) −15.4268 + 26.7200i −0.731300 + 1.26665i
\(446\) −1.71774 + 21.4785i −0.0813372 + 1.01704i
\(447\) 0 0
\(448\) 7.99198 0.358033i 0.377586 0.0169155i
\(449\) 14.5939i 0.688731i −0.938836 0.344365i \(-0.888094\pi\)
0.938836 0.344365i \(-0.111906\pi\)
\(450\) 0 0
\(451\) 13.7418i 0.647076i
\(452\) −2.04090 + 12.6780i −0.0959958 + 0.596324i
\(453\) 0 0
\(454\) 8.18963 + 0.654964i 0.384358 + 0.0307390i
\(455\) 7.52061 13.0261i 0.352571 0.610672i
\(456\) 0 0
\(457\) 0.0109808 + 0.0190193i 0.000513661 + 0.000889687i 0.866282 0.499555i \(-0.166503\pi\)
−0.865768 + 0.500445i \(0.833170\pi\)
\(458\) −9.07227 19.0825i −0.423919 0.891667i
\(459\) 0 0
\(460\) 15.6187 + 12.7133i 0.728224 + 0.592761i
\(461\) −7.01426 + 4.04969i −0.326687 + 0.188613i −0.654369 0.756175i \(-0.727066\pi\)
0.327682 + 0.944788i \(0.393732\pi\)
\(462\) 0 0
\(463\) −27.8853 16.0996i −1.29594 0.748211i −0.316239 0.948680i \(-0.602420\pi\)
−0.979700 + 0.200469i \(0.935753\pi\)
\(464\) −2.18824 + 6.62054i −0.101587 + 0.307351i
\(465\) 0 0
\(466\) 0.625003 + 0.430718i 0.0289527 + 0.0199526i
\(467\) 11.6187 0.537648 0.268824 0.963189i \(-0.413365\pi\)
0.268824 + 0.963189i \(0.413365\pi\)
\(468\) 0 0
\(469\) −1.99417 −0.0920824
\(470\) 10.8565 + 7.48173i 0.500774 + 0.345106i
\(471\) 0 0
\(472\) −14.5096 + 15.1742i −0.667858 + 0.698448i
\(473\) 22.4504 + 12.9618i 1.03227 + 0.595982i
\(474\) 0 0
\(475\) −2.28068 + 1.31675i −0.104645 + 0.0604168i
\(476\) −9.12372 + 11.2087i −0.418185 + 0.513752i
\(477\) 0 0
\(478\) −12.1464 25.5487i −0.555566 1.16857i
\(479\) −3.05275 5.28752i −0.139484 0.241593i 0.787818 0.615909i \(-0.211211\pi\)
−0.927301 + 0.374316i \(0.877878\pi\)
\(480\) 0 0
\(481\) 7.42264 12.8564i 0.338443 0.586201i
\(482\) −22.7642 1.82056i −1.03688 0.0829244i
\(483\) 0 0
\(484\) 29.9147 + 4.81564i 1.35976 + 0.218893i
\(485\) 38.8576i 1.76443i
\(486\) 0 0
\(487\) 18.6740i 0.846201i −0.906083 0.423100i \(-0.860942\pi\)
0.906083 0.423100i \(-0.139058\pi\)
\(488\) 5.13618 + 17.5843i 0.232504 + 0.796002i
\(489\) 0 0
\(490\) −0.355702 + 4.44767i −0.0160690 + 0.200925i
\(491\) −1.67975 + 2.90941i −0.0758060 + 0.131300i −0.901437 0.432911i \(-0.857486\pi\)
0.825630 + 0.564211i \(0.190820\pi\)
\(492\) 0 0
\(493\) −6.29845 10.9092i −0.283668 0.491327i
\(494\) −3.23676 + 1.53883i −0.145629 + 0.0692353i
\(495\) 0 0
\(496\) 6.66787 1.38207i 0.299396 0.0620568i
\(497\) −11.3161 + 6.53337i −0.507598 + 0.293062i
\(498\) 0 0
\(499\) 37.5927 + 21.7041i 1.68288 + 0.971610i 0.959733 + 0.280915i \(0.0906378\pi\)
0.723146 + 0.690696i \(0.242696\pi\)
\(500\) −0.270354 + 0.102995i −0.0120906 + 0.00460608i
\(501\) 0 0
\(502\) 20.3876 29.5839i 0.909943 1.32039i
\(503\) 7.34385 0.327446 0.163723 0.986506i \(-0.447650\pi\)
0.163723 + 0.986506i \(0.447650\pi\)
\(504\) 0 0
\(505\) 11.5422 0.513622
\(506\) 13.0972 19.0050i 0.582240 0.844873i
\(507\) 0 0
\(508\) 9.63653 3.67117i 0.427552 0.162882i
\(509\) −7.79196 4.49869i −0.345372 0.199401i 0.317273 0.948334i \(-0.397233\pi\)
−0.662645 + 0.748933i \(0.730566\pi\)
\(510\) 0 0
\(511\) −5.71303 + 3.29842i −0.252730 + 0.145913i
\(512\) 17.0376 + 14.8903i 0.752962 + 0.658064i
\(513\) 0 0
\(514\) −8.34710 + 3.96841i −0.368175 + 0.175039i
\(515\) 4.77457 + 8.26980i 0.210393 + 0.364411i
\(516\) 0 0
\(517\) 7.55551 13.0865i 0.332291 0.575544i
\(518\) −0.351068 + 4.38974i −0.0154251 + 0.192874i
\(519\) 0 0
\(520\) 40.8366 11.9280i 1.79080 0.523075i
\(521\) 9.29655i 0.407289i 0.979045 + 0.203645i \(0.0652787\pi\)
−0.979045 + 0.203645i \(0.934721\pi\)
\(522\) 0 0
\(523\) 9.26367i 0.405072i −0.979275 0.202536i \(-0.935082\pi\)
0.979275 0.202536i \(-0.0649183\pi\)
\(524\) −29.5458 4.75626i −1.29071 0.207778i
\(525\) 0 0
\(526\) −7.18863 0.574909i −0.313439 0.0250672i
\(527\) −6.15103 + 10.6539i −0.267943 + 0.464091i
\(528\) 0 0
\(529\) 6.40702 + 11.0973i 0.278566 + 0.482490i
\(530\) −26.2102 55.1301i −1.13850 2.39470i
\(531\) 0 0
\(532\) 0.671151 0.824528i 0.0290981 0.0357478i
\(533\) 11.0948 6.40559i 0.480570 0.277457i
\(534\) 0 0
\(535\) 10.9514 + 6.32282i 0.473472 + 0.273359i
\(536\) −4.07662 3.89808i −0.176083 0.168371i
\(537\) 0 0
\(538\) 26.9940 + 18.6028i 1.16380 + 0.802025i
\(539\) 5.11370 0.220263
\(540\) 0 0
\(541\) −39.0275 −1.67792 −0.838962 0.544189i \(-0.816837\pi\)
−0.838962 + 0.544189i \(0.816837\pi\)
\(542\) −3.88409 2.67670i −0.166836 0.114974i
\(543\) 0 0
\(544\) −40.5614 + 5.07920i −1.73906 + 0.217769i
\(545\) −4.34162 2.50663i −0.185974 0.107372i
\(546\) 0 0
\(547\) 15.6709 9.04762i 0.670041 0.386848i −0.126051 0.992024i \(-0.540230\pi\)
0.796092 + 0.605175i \(0.206897\pi\)
\(548\) 0.845698 + 0.688383i 0.0361264 + 0.0294063i
\(549\) 0 0
\(550\) −15.3833 32.3571i −0.655947 1.37971i
\(551\) 0.463321 + 0.802496i 0.0197381 + 0.0341875i
\(552\) 0 0
\(553\) 0.998899 1.73014i 0.0424775 0.0735732i
\(554\) 16.9494 + 1.35552i 0.720111 + 0.0575907i
\(555\) 0 0
\(556\) −3.30328 + 20.5199i −0.140090 + 0.870239i
\(557\) 11.4867i 0.486705i −0.969938 0.243353i \(-0.921753\pi\)
0.969938 0.243353i \(-0.0782472\pi\)
\(558\) 0 0
\(559\) 24.1679i 1.02219i
\(560\) −9.42116 + 8.39691i −0.398117 + 0.354834i
\(561\) 0 0
\(562\) 2.08727 26.0991i 0.0880462 1.10092i
\(563\) 1.41954 2.45871i 0.0598263 0.103622i −0.834561 0.550915i \(-0.814279\pi\)
0.894387 + 0.447293i \(0.147612\pi\)
\(564\) 0 0
\(565\) −10.1286 17.5432i −0.426113 0.738050i
\(566\) 27.7128 13.1753i 1.16485 0.553799i
\(567\) 0 0
\(568\) −35.9041 8.76408i −1.50650 0.367733i
\(569\) −5.82245 + 3.36159i −0.244090 + 0.140925i −0.617055 0.786920i \(-0.711674\pi\)
0.372965 + 0.927845i \(0.378341\pi\)
\(570\) 0 0
\(571\) −14.0370 8.10429i −0.587432 0.339154i 0.176650 0.984274i \(-0.443474\pi\)
−0.764081 + 0.645120i \(0.776807\pi\)
\(572\) −17.3581 45.5636i −0.725777 1.90511i
\(573\) 0 0
\(574\) −2.15650 + 3.12924i −0.0900107 + 0.130612i
\(575\) −15.8114 −0.659381
\(576\) 0 0
\(577\) −5.47679 −0.228002 −0.114001 0.993481i \(-0.536367\pi\)
−0.114001 + 0.993481i \(0.536367\pi\)
\(578\) 28.2635 41.0124i 1.17561 1.70589i
\(579\) 0 0
\(580\) −3.91593 10.2790i −0.162600 0.426813i
\(581\) 5.68140 + 3.28016i 0.235704 + 0.136084i
\(582\) 0 0
\(583\) −60.5882 + 34.9806i −2.50931 + 1.44875i
\(584\) −18.1265 4.42461i −0.750079 0.183092i
\(585\) 0 0
\(586\) −17.0994 + 8.12944i −0.706368 + 0.335824i
\(587\) −18.7598 32.4930i −0.774301 1.34113i −0.935187 0.354155i \(-0.884769\pi\)
0.160886 0.986973i \(-0.448565\pi\)
\(588\) 0 0
\(589\) 0.452477 0.783713i 0.0186440 0.0322923i
\(590\) 2.64030 33.0142i 0.108700 1.35917i
\(591\) 0 0
\(592\) −9.29844 + 8.28754i −0.382164 + 0.340616i
\(593\) 47.4039i 1.94665i 0.229438 + 0.973323i \(0.426311\pi\)
−0.229438 + 0.973323i \(0.573689\pi\)
\(594\) 0 0
\(595\) 22.7992i 0.934674i
\(596\) −4.10452 + 25.4972i −0.168128 + 1.04441i
\(597\) 0 0
\(598\) −21.4493 1.71540i −0.877126 0.0701479i
\(599\) 15.9337 27.5979i 0.651032 1.12762i −0.331841 0.943335i \(-0.607670\pi\)
0.982873 0.184285i \(-0.0589970\pi\)
\(600\) 0 0
\(601\) 12.7566 + 22.0950i 0.520351 + 0.901274i 0.999720 + 0.0236606i \(0.00753212\pi\)
−0.479369 + 0.877613i \(0.659135\pi\)
\(602\) 3.07825 + 6.47476i 0.125460 + 0.263892i
\(603\) 0 0
\(604\) −4.99582 4.06650i −0.203277 0.165464i
\(605\) −41.3945 + 23.8991i −1.68293 + 0.971638i
\(606\) 0 0
\(607\) 13.9168 + 8.03488i 0.564866 + 0.326126i 0.755096 0.655614i \(-0.227590\pi\)
−0.190230 + 0.981740i \(0.560923\pi\)
\(608\) 2.98374 0.373632i 0.121007 0.0151528i
\(609\) 0 0
\(610\) −23.7952 16.3984i −0.963441 0.663951i
\(611\) −14.0877 −0.569926
\(612\) 0 0
\(613\) 10.1572 0.410246 0.205123 0.978736i \(-0.434240\pi\)
0.205123 + 0.978736i \(0.434240\pi\)
\(614\) −17.3874 11.9824i −0.701698 0.483572i
\(615\) 0 0
\(616\) 10.4538 + 9.99592i 0.421194 + 0.402747i
\(617\) 3.85193 + 2.22391i 0.155073 + 0.0895312i 0.575528 0.817782i \(-0.304796\pi\)
−0.420456 + 0.907313i \(0.638130\pi\)
\(618\) 0 0
\(619\) 32.5736 18.8064i 1.30924 0.755892i 0.327273 0.944930i \(-0.393870\pi\)
0.981970 + 0.189038i \(0.0605369\pi\)
\(620\) −6.78139 + 8.33113i −0.272347 + 0.334586i
\(621\) 0 0
\(622\) 4.66072 + 9.80331i 0.186878 + 0.393077i
\(623\) 4.88960 + 8.46904i 0.195898 + 0.339305i
\(624\) 0 0
\(625\) 12.6136 21.8473i 0.504543 0.873894i
\(626\) −32.8177 2.62459i −1.31166 0.104900i
\(627\) 0 0
\(628\) −12.3846 1.99366i −0.494199 0.0795557i
\(629\) 22.5022i 0.897221i
\(630\) 0 0
\(631\) 21.9573i 0.874106i −0.899436 0.437053i \(-0.856022\pi\)
0.899436 0.437053i \(-0.143978\pi\)
\(632\) 5.42398 1.58429i 0.215754 0.0630196i
\(633\) 0 0
\(634\) 3.05603 38.2124i 0.121370 1.51761i
\(635\) −8.13375 + 14.0881i −0.322778 + 0.559068i
\(636\) 0 0
\(637\) −2.38370 4.12868i −0.0944454 0.163584i
\(638\) −11.3854 + 5.41287i −0.450751 + 0.214298i
\(639\) 0 0
\(640\) −35.6731 1.25035i −1.41010 0.0494244i
\(641\) 23.3369 13.4735i 0.921750 0.532173i 0.0375573 0.999294i \(-0.488042\pi\)
0.884193 + 0.467122i \(0.154709\pi\)
\(642\) 0 0
\(643\) −22.9917 13.2743i −0.906704 0.523486i −0.0273346 0.999626i \(-0.508702\pi\)
−0.879369 + 0.476141i \(0.842035\pi\)
\(644\) 5.96490 2.27241i 0.235050 0.0895455i
\(645\) 0 0
\(646\) −3.08264 + 4.47314i −0.121285 + 0.175993i
\(647\) 23.8568 0.937906 0.468953 0.883223i \(-0.344631\pi\)
0.468953 + 0.883223i \(0.344631\pi\)
\(648\) 0 0
\(649\) −37.9580 −1.48998
\(650\) −18.9536 + 27.5030i −0.743421 + 1.07876i
\(651\) 0 0
\(652\) 32.8873 12.5289i 1.28797 0.490668i
\(653\) −23.4749 13.5532i −0.918642 0.530378i −0.0354406 0.999372i \(-0.511283\pi\)
−0.883202 + 0.468993i \(0.844617\pi\)
\(654\) 0 0
\(655\) 40.8841 23.6044i 1.59747 0.922301i
\(656\) −10.5253 + 2.18161i −0.410944 + 0.0851775i
\(657\) 0 0
\(658\) 3.77419 1.79434i 0.147133 0.0699505i
\(659\) 14.6668 + 25.4036i 0.571338 + 0.989586i 0.996429 + 0.0844352i \(0.0269086\pi\)
−0.425091 + 0.905150i \(0.639758\pi\)
\(660\) 0 0
\(661\) 9.65945 16.7307i 0.375709 0.650747i −0.614724 0.788742i \(-0.710733\pi\)
0.990433 + 0.137995i \(0.0440659\pi\)
\(662\) 2.02136 25.2749i 0.0785622 0.982337i
\(663\) 0 0
\(664\) 5.20245 + 17.8111i 0.201894 + 0.691206i
\(665\) 1.67713i 0.0650364i
\(666\) 0 0
\(667\) 5.56350i 0.215420i
\(668\) 5.56725 + 0.896212i 0.215403 + 0.0346755i
\(669\) 0 0
\(670\) 8.86943 + 0.709331i 0.342656 + 0.0274038i
\(671\) −16.5601 + 28.6829i −0.639295 + 1.10729i
\(672\) 0 0
\(673\) 24.8176 + 42.9853i 0.956648 + 1.65696i 0.730552 + 0.682857i \(0.239263\pi\)
0.226096 + 0.974105i \(0.427404\pi\)
\(674\) −4.04972 8.51813i −0.155989 0.328106i
\(675\) 0 0
\(676\) −12.2823 + 15.0891i −0.472396 + 0.580352i
\(677\) −27.9037 + 16.1102i −1.07243 + 0.619166i −0.928844 0.370472i \(-0.879196\pi\)
−0.143584 + 0.989638i \(0.545863\pi\)
\(678\) 0 0
\(679\) −10.6661 6.15806i −0.409327 0.236325i
\(680\) 44.5663 46.6075i 1.70904 1.78732i
\(681\) 0 0
\(682\) 10.1374 + 6.98615i 0.388182 + 0.267513i
\(683\) −48.7831 −1.86663 −0.933316 0.359055i \(-0.883099\pi\)
−0.933316 + 0.359055i \(0.883099\pi\)
\(684\) 0 0
\(685\) −1.72019 −0.0657252
\(686\) 1.16448 + 0.802493i 0.0444599 + 0.0306393i
\(687\) 0 0
\(688\) −6.36367 + 19.2533i −0.242613 + 0.734025i
\(689\) 56.4850 + 32.6116i 2.15191 + 1.24240i
\(690\) 0 0
\(691\) 33.1524 19.1405i 1.26118 0.728140i 0.287874 0.957668i \(-0.407052\pi\)
0.973302 + 0.229528i \(0.0737182\pi\)
\(692\) 6.10790 + 4.97172i 0.232188 + 0.188997i
\(693\) 0 0
\(694\) 19.0836 + 40.1402i 0.724404 + 1.52370i
\(695\) −16.3936 28.3945i −0.621843 1.07706i
\(696\) 0 0
\(697\) 9.70946 16.8173i 0.367772 0.637000i
\(698\) 8.94088 + 0.715045i 0.338417 + 0.0270649i
\(699\) 0 0
\(700\) 1.57476 9.78236i 0.0595202 0.369739i
\(701\) 16.4250i 0.620365i 0.950677 + 0.310183i \(0.100390\pi\)
−0.950677 + 0.310183i \(0.899610\pi\)
\(702\) 0 0
\(703\) 1.65529i 0.0624303i
\(704\) 1.83087 + 40.8686i 0.0690036 + 1.54029i
\(705\) 0 0
\(706\) 2.93651 36.7179i 0.110517 1.38190i
\(707\) 1.82918 3.16824i 0.0687935 0.119154i
\(708\) 0 0
\(709\) 2.30143 + 3.98619i 0.0864320 + 0.149705i 0.906001 0.423277i \(-0.139120\pi\)
−0.819569 + 0.572981i \(0.805787\pi\)
\(710\) 52.6543 25.0331i 1.97608 0.939476i
\(711\) 0 0
\(712\) −6.55907 + 26.8708i −0.245812 + 1.00703i
\(713\) 4.70536 2.71664i 0.176217 0.101739i
\(714\) 0 0
\(715\) 66.6114 + 38.4581i 2.49113 + 1.43825i
\(716\) 0.849237 + 2.22918i 0.0317375 + 0.0833084i
\(717\) 0 0
\(718\) 25.1120 36.4394i 0.937173 1.35991i
\(719\) 27.4630 1.02420 0.512099 0.858927i \(-0.328868\pi\)
0.512099 + 0.858927i \(0.328868\pi\)
\(720\) 0 0
\(721\) 3.02665 0.112718
\(722\) −15.0206 + 21.7960i −0.559009 + 0.811163i
\(723\) 0 0
\(724\) 0.367492 + 0.964637i 0.0136577 + 0.0358505i
\(725\) 7.47906 + 4.31804i 0.277765 + 0.160368i
\(726\) 0 0
\(727\) 12.1777 7.03079i 0.451645 0.260758i −0.256879 0.966443i \(-0.582694\pi\)
0.708525 + 0.705686i \(0.249361\pi\)
\(728\) 3.19757 13.0996i 0.118510 0.485504i
\(729\) 0 0
\(730\) 26.5829 12.6381i 0.983878 0.467759i
\(731\) −18.3166 31.7253i −0.677465 1.17340i
\(732\) 0 0
\(733\) 18.2356 31.5851i 0.673549 1.16662i −0.303342 0.952882i \(-0.598102\pi\)
0.976891 0.213739i \(-0.0685642\pi\)
\(734\) −2.51313 + 31.4240i −0.0927612 + 1.15988i
\(735\) 0 0
\(736\) 16.6358 + 7.01438i 0.613203 + 0.258554i
\(737\) 10.1976i 0.375633i
\(738\) 0 0
\(739\) 0.413262i 0.0152021i 0.999971 + 0.00760104i \(0.00241951\pi\)
−0.999971 + 0.00760104i \(0.997580\pi\)
\(740\) 3.12287 19.3992i 0.114799 0.713130i
\(741\) 0 0
\(742\) −19.2865 1.54243i −0.708028 0.0566244i
\(743\) 8.68868 15.0492i 0.318757 0.552103i −0.661472 0.749970i \(-0.730068\pi\)
0.980229 + 0.197867i \(0.0634013\pi\)
\(744\) 0 0
\(745\) −20.3700 35.2818i −0.746298 1.29263i
\(746\) 11.2923 + 23.7522i 0.413442 + 0.869628i
\(747\) 0 0
\(748\) −57.3182 46.6560i −2.09576 1.70591i
\(749\) 3.47112 2.00405i 0.126832 0.0732264i
\(750\) 0 0
\(751\) 3.19940 + 1.84717i 0.116748 + 0.0674044i 0.557237 0.830354i \(-0.311862\pi\)
−0.440489 + 0.897758i \(0.645195\pi\)
\(752\) 11.2229 + 3.70943i 0.409256 + 0.135269i
\(753\) 0 0
\(754\) 9.67739 + 6.66913i 0.352430 + 0.242875i
\(755\) 10.1617 0.369824
\(756\) 0 0
\(757\) −2.01887 −0.0733772 −0.0366886 0.999327i \(-0.511681\pi\)
−0.0366886 + 0.999327i \(0.511681\pi\)
\(758\) −24.6895 17.0146i −0.896762 0.617999i
\(759\) 0 0
\(760\) −3.27835 + 3.42850i −0.118918 + 0.124365i
\(761\) 16.4382 + 9.49062i 0.595886 + 0.344035i 0.767421 0.641143i \(-0.221540\pi\)
−0.171536 + 0.985178i \(0.554873\pi\)
\(762\) 0 0
\(763\) −1.37610 + 0.794490i −0.0498181 + 0.0287625i
\(764\) −33.1666 + 40.7461i −1.19993 + 1.47414i
\(765\) 0 0
\(766\) 7.10484 + 14.9442i 0.256708 + 0.539957i
\(767\) 17.6937 + 30.6464i 0.638882 + 1.10658i
\(768\) 0 0
\(769\) −11.1454 + 19.3043i −0.401912 + 0.696131i −0.993957 0.109774i \(-0.964987\pi\)
0.592045 + 0.805905i \(0.298321\pi\)
\(770\) −22.7440 1.81895i −0.819639 0.0655504i
\(771\) 0 0
\(772\) −32.4285 5.22031i −1.16713 0.187883i
\(773\) 38.1241i 1.37123i 0.727965 + 0.685614i \(0.240466\pi\)
−0.727965 + 0.685614i \(0.759534\pi\)
\(774\) 0 0
\(775\) 8.43394i 0.302956i
\(776\) −9.76691 33.4381i −0.350612 1.20036i
\(777\) 0 0
\(778\) −2.68357 + 33.5552i −0.0962107 + 1.20301i
\(779\) −0.714239 + 1.23710i −0.0255903 + 0.0443236i
\(780\) 0 0
\(781\) −33.4097 57.8673i −1.19549 2.07065i
\(782\) −29.4566 + 14.0044i −1.05337 + 0.500795i
\(783\) 0 0
\(784\) 0.811836 + 3.91675i 0.0289942 + 0.139884i
\(785\) 17.1372 9.89416i 0.611653 0.353138i
\(786\) 0 0
\(787\) 14.7144 + 8.49538i 0.524513 + 0.302828i 0.738779 0.673948i \(-0.235403\pi\)
−0.214266 + 0.976775i \(0.568736\pi\)
\(788\) −10.8397 + 4.12952i −0.386147 + 0.147108i
\(789\) 0 0
\(790\) −5.05819 + <