Properties

Label 585.2.bs.a.289.2
Level $585$
Weight $2$
Character 585.289
Analytic conductor $4.671$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.bs (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 8x^{10} + 54x^{8} - 78x^{6} + 92x^{4} - 10x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 289.2
Root \(-1.02826 - 0.593667i\) of defining polynomial
Character \(\chi\) \(=\) 585.289
Dual form 585.2.bs.a.334.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.02826 + 0.593667i) q^{2} +(-0.295120 + 0.511162i) q^{4} +(-1.44045 + 1.71029i) q^{5} +(-1.75765 - 1.01478i) q^{7} -3.07548i q^{8} +O(q^{10})\) \(q+(-1.02826 + 0.593667i) q^{2} +(-0.295120 + 0.511162i) q^{4} +(-1.44045 + 1.71029i) q^{5} +(-1.75765 - 1.01478i) q^{7} -3.07548i q^{8} +(0.465813 - 2.61378i) q^{10} +(1.94045 + 3.36096i) q^{11} +(-2.96232 + 2.05540i) q^{13} +2.40976 q^{14} +(1.23557 + 2.14007i) q^{16} +(-4.71996 - 2.72507i) q^{17} +(2.94045 - 5.09301i) q^{19} +(-0.449133 - 1.24105i) q^{20} +(-3.99058 - 2.30396i) q^{22} +(-0.298874 + 0.172555i) q^{23} +(-0.850210 - 4.92718i) q^{25} +(1.82581 - 3.87212i) q^{26} +(1.03743 - 0.598962i) q^{28} +(-1.50000 - 2.59808i) q^{29} +1.18048 q^{31} +(2.78591 + 1.60845i) q^{32} +6.47114 q^{34} +(4.26737 - 1.54436i) q^{35} +(4.71996 - 2.72507i) q^{37} +6.98259i q^{38} +(5.25997 + 4.43007i) q^{40} +(0.0902394 + 0.156299i) q^{41} +(-1.15990 - 0.669668i) q^{43} -2.29066 q^{44} +(0.204880 - 0.354863i) q^{46} -12.2807i q^{47} +(-1.44045 - 2.49493i) q^{49} +(3.79934 + 4.56169i) q^{50} +(-0.176407 - 2.12081i) q^{52} +2.42636i q^{53} +(-8.54334 - 1.52255i) q^{55} +(-3.12093 + 5.40561i) q^{56} +(3.08478 + 1.78100i) q^{58} +(3.53069 - 6.11533i) q^{59} +(-3.38090 + 5.85589i) q^{61} +(-1.21384 + 0.700811i) q^{62} -8.76180 q^{64} +(0.751722 - 8.02714i) q^{65} +(-3.81417 + 2.20211i) q^{67} +(2.78591 - 1.60845i) q^{68} +(-3.47114 + 4.12140i) q^{70} +(-0.940450 + 1.62891i) q^{71} -8.86014i q^{73} +(-3.23557 + 5.60417i) q^{74} +(1.73557 + 3.00609i) q^{76} -7.87651i q^{77} -11.1805 q^{79} +(-5.43992 - 0.969475i) q^{80} +(-0.185579 - 0.107144i) q^{82} +7.83540i q^{83} +(11.4595 - 4.14720i) q^{85} +1.59024 q^{86} +(10.3365 - 5.96781i) q^{88} +(-6.12093 - 10.6018i) q^{89} +(7.29249 - 0.606582i) q^{91} -0.203698i q^{92} +(7.29066 + 12.6278i) q^{94} +(4.47497 + 12.3653i) q^{95} +(5.02801 + 2.90292i) q^{97} +(2.96232 + 1.71029i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} + 6 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{4} + 6 q^{5} + 7 q^{10} + 44 q^{14} - 16 q^{16} + 12 q^{19} + q^{20} - 2 q^{25} - 24 q^{26} - 18 q^{29} - 16 q^{31} + 16 q^{34} - 10 q^{35} + 70 q^{40} - 14 q^{41} + 4 q^{44} + 10 q^{46} + 6 q^{49} + 31 q^{50} - 26 q^{55} + 16 q^{56} + 4 q^{59} + 6 q^{61} - 12 q^{64} - 23 q^{65} + 20 q^{70} + 12 q^{71} - 8 q^{74} - 10 q^{76} - 104 q^{79} - 33 q^{80} + 21 q^{85} + 4 q^{86} - 20 q^{89} - 44 q^{91} + 56 q^{94} - 20 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.02826 + 0.593667i −0.727090 + 0.419786i −0.817357 0.576132i \(-0.804561\pi\)
0.0902665 + 0.995918i \(0.471228\pi\)
\(3\) 0 0
\(4\) −0.295120 + 0.511162i −0.147560 + 0.255581i
\(5\) −1.44045 + 1.71029i −0.644189 + 0.764867i
\(6\) 0 0
\(7\) −1.75765 1.01478i −0.664328 0.383550i 0.129596 0.991567i \(-0.458632\pi\)
−0.793924 + 0.608017i \(0.791965\pi\)
\(8\) 3.07548i 1.08735i
\(9\) 0 0
\(10\) 0.465813 2.61378i 0.147303 0.826548i
\(11\) 1.94045 + 3.36096i 0.585068 + 1.01337i 0.994867 + 0.101191i \(0.0322653\pi\)
−0.409799 + 0.912176i \(0.634401\pi\)
\(12\) 0 0
\(13\) −2.96232 + 2.05540i −0.821599 + 0.570066i
\(14\) 2.40976 0.644036
\(15\) 0 0
\(16\) 1.23557 + 2.14007i 0.308892 + 0.535017i
\(17\) −4.71996 2.72507i −1.14476 0.660927i −0.197155 0.980372i \(-0.563170\pi\)
−0.947605 + 0.319445i \(0.896503\pi\)
\(18\) 0 0
\(19\) 2.94045 5.09301i 0.674585 1.16842i −0.302005 0.953306i \(-0.597656\pi\)
0.976590 0.215110i \(-0.0690109\pi\)
\(20\) −0.449133 1.24105i −0.100429 0.277506i
\(21\) 0 0
\(22\) −3.99058 2.30396i −0.850794 0.491206i
\(23\) −0.298874 + 0.172555i −0.0623195 + 0.0359802i −0.530836 0.847475i \(-0.678122\pi\)
0.468516 + 0.883455i \(0.344789\pi\)
\(24\) 0 0
\(25\) −0.850210 4.92718i −0.170042 0.985437i
\(26\) 1.82581 3.87212i 0.358071 0.759385i
\(27\) 0 0
\(28\) 1.03743 0.598962i 0.196056 0.113193i
\(29\) −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) 0 0
\(31\) 1.18048 0.212020 0.106010 0.994365i \(-0.466192\pi\)
0.106010 + 0.994365i \(0.466192\pi\)
\(32\) 2.78591 + 1.60845i 0.492484 + 0.284336i
\(33\) 0 0
\(34\) 6.47114 1.10979
\(35\) 4.26737 1.54436i 0.721318 0.261044i
\(36\) 0 0
\(37\) 4.71996 2.72507i 0.775957 0.447999i −0.0590384 0.998256i \(-0.518803\pi\)
0.834996 + 0.550257i \(0.185470\pi\)
\(38\) 6.98259i 1.13273i
\(39\) 0 0
\(40\) 5.25997 + 4.43007i 0.831674 + 0.700456i
\(41\) 0.0902394 + 0.156299i 0.0140930 + 0.0244098i 0.872986 0.487745i \(-0.162181\pi\)
−0.858893 + 0.512155i \(0.828847\pi\)
\(42\) 0 0
\(43\) −1.15990 0.669668i −0.176883 0.102123i 0.408944 0.912559i \(-0.365897\pi\)
−0.585827 + 0.810436i \(0.699230\pi\)
\(44\) −2.29066 −0.345330
\(45\) 0 0
\(46\) 0.204880 0.354863i 0.0302079 0.0523217i
\(47\) 12.2807i 1.79133i −0.444731 0.895664i \(-0.646701\pi\)
0.444731 0.895664i \(-0.353299\pi\)
\(48\) 0 0
\(49\) −1.44045 2.49493i −0.205779 0.356419i
\(50\) 3.79934 + 4.56169i 0.537308 + 0.645120i
\(51\) 0 0
\(52\) −0.176407 2.12081i −0.0244633 0.294104i
\(53\) 2.42636i 0.333286i 0.986017 + 0.166643i \(0.0532928\pi\)
−0.986017 + 0.166643i \(0.946707\pi\)
\(54\) 0 0
\(55\) −8.54334 1.52255i −1.15198 0.205301i
\(56\) −3.12093 + 5.40561i −0.417052 + 0.722355i
\(57\) 0 0
\(58\) 3.08478 + 1.78100i 0.405052 + 0.233857i
\(59\) 3.53069 6.11533i 0.459657 0.796149i −0.539286 0.842123i \(-0.681306\pi\)
0.998943 + 0.0459741i \(0.0146392\pi\)
\(60\) 0 0
\(61\) −3.38090 + 5.85589i −0.432880 + 0.749770i −0.997120 0.0758409i \(-0.975836\pi\)
0.564240 + 0.825611i \(0.309169\pi\)
\(62\) −1.21384 + 0.700811i −0.154158 + 0.0890031i
\(63\) 0 0
\(64\) −8.76180 −1.09522
\(65\) 0.751722 8.02714i 0.0932396 0.995644i
\(66\) 0 0
\(67\) −3.81417 + 2.20211i −0.465975 + 0.269031i −0.714553 0.699581i \(-0.753370\pi\)
0.248578 + 0.968612i \(0.420037\pi\)
\(68\) 2.78591 1.60845i 0.337841 0.195053i
\(69\) 0 0
\(70\) −3.47114 + 4.12140i −0.414880 + 0.492601i
\(71\) −0.940450 + 1.62891i −0.111611 + 0.193316i −0.916420 0.400218i \(-0.868934\pi\)
0.804809 + 0.593534i \(0.202268\pi\)
\(72\) 0 0
\(73\) 8.86014i 1.03700i −0.855077 0.518501i \(-0.826490\pi\)
0.855077 0.518501i \(-0.173510\pi\)
\(74\) −3.23557 + 5.60417i −0.376127 + 0.651472i
\(75\) 0 0
\(76\) 1.73557 + 3.00609i 0.199083 + 0.344823i
\(77\) 7.87651i 0.897611i
\(78\) 0 0
\(79\) −11.1805 −1.25790 −0.628951 0.777445i \(-0.716515\pi\)
−0.628951 + 0.777445i \(0.716515\pi\)
\(80\) −5.43992 0.969475i −0.608202 0.108391i
\(81\) 0 0
\(82\) −0.185579 0.107144i −0.0204938 0.0118321i
\(83\) 7.83540i 0.860047i 0.902818 + 0.430024i \(0.141495\pi\)
−0.902818 + 0.430024i \(0.858505\pi\)
\(84\) 0 0
\(85\) 11.4595 4.14720i 1.24296 0.449827i
\(86\) 1.59024 0.171480
\(87\) 0 0
\(88\) 10.3365 5.96781i 1.10188 0.636171i
\(89\) −6.12093 10.6018i −0.648817 1.12378i −0.983406 0.181420i \(-0.941931\pi\)
0.334589 0.942364i \(-0.391403\pi\)
\(90\) 0 0
\(91\) 7.29249 0.606582i 0.764460 0.0635870i
\(92\) 0.203698i 0.0212369i
\(93\) 0 0
\(94\) 7.29066 + 12.6278i 0.751974 + 1.30246i
\(95\) 4.47497 + 12.3653i 0.459122 + 1.26865i
\(96\) 0 0
\(97\) 5.02801 + 2.90292i 0.510517 + 0.294747i 0.733046 0.680179i \(-0.238098\pi\)
−0.222529 + 0.974926i \(0.571431\pi\)
\(98\) 2.96232 + 1.71029i 0.299239 + 0.172766i
\(99\) 0 0
\(100\) 2.76950 + 1.01951i 0.276950 + 0.101951i
\(101\) −2.97114 5.14616i −0.295639 0.512062i 0.679494 0.733681i \(-0.262199\pi\)
−0.975133 + 0.221619i \(0.928866\pi\)
\(102\) 0 0
\(103\) 6.43378i 0.633939i 0.948436 + 0.316970i \(0.102665\pi\)
−0.948436 + 0.316970i \(0.897335\pi\)
\(104\) 6.32135 + 9.11054i 0.619859 + 0.893362i
\(105\) 0 0
\(106\) −1.44045 2.49493i −0.139909 0.242329i
\(107\) −15.3106 + 8.83959i −1.48013 + 0.854555i −0.999747 0.0225015i \(-0.992837\pi\)
−0.480387 + 0.877057i \(0.659504\pi\)
\(108\) 0 0
\(109\) −5.76180 −0.551880 −0.275940 0.961175i \(-0.588989\pi\)
−0.275940 + 0.961175i \(0.588989\pi\)
\(110\) 9.68867 3.50632i 0.923779 0.334314i
\(111\) 0 0
\(112\) 5.01532i 0.473903i
\(113\) 4.12222 + 2.37996i 0.387785 + 0.223888i 0.681200 0.732097i \(-0.261458\pi\)
−0.293415 + 0.955985i \(0.594792\pi\)
\(114\) 0 0
\(115\) 0.135393 0.759719i 0.0126255 0.0708442i
\(116\) 1.77072 0.164407
\(117\) 0 0
\(118\) 8.38421i 0.771829i
\(119\) 5.53069 + 9.57943i 0.506997 + 0.878145i
\(120\) 0 0
\(121\) −2.03069 + 3.51726i −0.184608 + 0.319751i
\(122\) 8.02851i 0.726867i
\(123\) 0 0
\(124\) −0.348383 + 0.603416i −0.0312857 + 0.0541884i
\(125\) 9.65162 + 5.64325i 0.863267 + 0.504748i
\(126\) 0 0
\(127\) −14.4679 + 8.35307i −1.28382 + 0.741215i −0.977545 0.210728i \(-0.932417\pi\)
−0.306277 + 0.951942i \(0.599083\pi\)
\(128\) 3.43760 1.98470i 0.303844 0.175424i
\(129\) 0 0
\(130\) 3.99248 + 8.70026i 0.350163 + 0.763063i
\(131\) −10.0000 −0.873704 −0.436852 0.899533i \(-0.643907\pi\)
−0.436852 + 0.899533i \(0.643907\pi\)
\(132\) 0 0
\(133\) −10.3365 + 5.96781i −0.896292 + 0.517475i
\(134\) 2.61464 4.52869i 0.225871 0.391219i
\(135\) 0 0
\(136\) −8.38090 + 14.5161i −0.718656 + 1.24475i
\(137\) 1.71288 + 0.988931i 0.146341 + 0.0844901i 0.571383 0.820684i \(-0.306407\pi\)
−0.425042 + 0.905174i \(0.639741\pi\)
\(138\) 0 0
\(139\) 4.35021 7.53478i 0.368980 0.639092i −0.620426 0.784265i \(-0.713040\pi\)
0.989406 + 0.145173i \(0.0463737\pi\)
\(140\) −0.469969 + 2.63709i −0.0397196 + 0.222875i
\(141\) 0 0
\(142\) 2.23325i 0.187411i
\(143\) −12.6563 5.96781i −1.05838 0.499053i
\(144\) 0 0
\(145\) 6.60415 + 1.17696i 0.548445 + 0.0977410i
\(146\) 5.25997 + 9.11054i 0.435318 + 0.753993i
\(147\) 0 0
\(148\) 3.21689i 0.264427i
\(149\) −11.1516 + 19.3152i −0.913576 + 1.58236i −0.104603 + 0.994514i \(0.533357\pi\)
−0.808973 + 0.587846i \(0.799976\pi\)
\(150\) 0 0
\(151\) −19.1626 −1.55943 −0.779717 0.626132i \(-0.784637\pi\)
−0.779717 + 0.626132i \(0.784637\pi\)
\(152\) −15.6634 9.04329i −1.27047 0.733507i
\(153\) 0 0
\(154\) 4.67602 + 8.09910i 0.376804 + 0.652644i
\(155\) −1.70042 + 2.01897i −0.136581 + 0.162167i
\(156\) 0 0
\(157\) 6.20265i 0.495025i −0.968885 0.247513i \(-0.920387\pi\)
0.968885 0.247513i \(-0.0796132\pi\)
\(158\) 11.4964 6.63748i 0.914608 0.528049i
\(159\) 0 0
\(160\) −6.76387 + 2.44784i −0.534731 + 0.193519i
\(161\) 0.700420 0.0552008
\(162\) 0 0
\(163\) 10.3365 + 5.96781i 0.809621 + 0.467435i 0.846824 0.531873i \(-0.178512\pi\)
−0.0372032 + 0.999308i \(0.511845\pi\)
\(164\) −0.106526 −0.00831826
\(165\) 0 0
\(166\) −4.65162 8.05684i −0.361036 0.625332i
\(167\) 1.75765 1.01478i 0.136011 0.0785259i −0.430451 0.902614i \(-0.641645\pi\)
0.566461 + 0.824088i \(0.308312\pi\)
\(168\) 0 0
\(169\) 4.55063 12.1775i 0.350048 0.936732i
\(170\) −9.32135 + 11.0675i −0.714915 + 0.848842i
\(171\) 0 0
\(172\) 0.684619 0.395265i 0.0522017 0.0301387i
\(173\) −1.15990 0.669668i −0.0881855 0.0509139i 0.455259 0.890359i \(-0.349547\pi\)
−0.543444 + 0.839445i \(0.682880\pi\)
\(174\) 0 0
\(175\) −3.50563 + 9.52303i −0.265001 + 0.719873i
\(176\) −4.79512 + 8.30539i −0.361446 + 0.626042i
\(177\) 0 0
\(178\) 12.5878 + 7.26758i 0.943497 + 0.544728i
\(179\) −10.1120 17.5145i −0.755807 1.30910i −0.944972 0.327151i \(-0.893911\pi\)
0.189165 0.981945i \(-0.439422\pi\)
\(180\) 0 0
\(181\) 19.8232 1.47345 0.736723 0.676195i \(-0.236372\pi\)
0.736723 + 0.676195i \(0.236372\pi\)
\(182\) −7.13847 + 4.95303i −0.529139 + 0.367143i
\(183\) 0 0
\(184\) 0.530689 + 0.919180i 0.0391229 + 0.0677629i
\(185\) −2.13820 + 11.9979i −0.157203 + 0.882100i
\(186\) 0 0
\(187\) 21.1515i 1.54675i
\(188\) 6.27745 + 3.62429i 0.457830 + 0.264328i
\(189\) 0 0
\(190\) −11.9423 10.0581i −0.866384 0.729689i
\(191\) 0.768891 1.33176i 0.0556350 0.0963626i −0.836867 0.547407i \(-0.815615\pi\)
0.892502 + 0.451044i \(0.148948\pi\)
\(192\) 0 0
\(193\) −18.3625 + 10.6016i −1.32176 + 0.763118i −0.984009 0.178117i \(-0.942999\pi\)
−0.337750 + 0.941236i \(0.609666\pi\)
\(194\) −6.89347 −0.494923
\(195\) 0 0
\(196\) 1.70042 0.121459
\(197\) 8.01675 4.62847i 0.571170 0.329765i −0.186447 0.982465i \(-0.559697\pi\)
0.757616 + 0.652700i \(0.226364\pi\)
\(198\) 0 0
\(199\) −8.70225 + 15.0727i −0.616886 + 1.06848i 0.373164 + 0.927765i \(0.378273\pi\)
−0.990050 + 0.140713i \(0.955061\pi\)
\(200\) −15.1534 + 2.61480i −1.07151 + 0.184894i
\(201\) 0 0
\(202\) 6.11021 + 3.52773i 0.429913 + 0.248210i
\(203\) 6.08867i 0.427341i
\(204\) 0 0
\(205\) −0.397303 0.0708053i −0.0277488 0.00494526i
\(206\) −3.81952 6.61560i −0.266119 0.460931i
\(207\) 0 0
\(208\) −8.05885 3.79997i −0.558781 0.263480i
\(209\) 22.8232 1.57871
\(210\) 0 0
\(211\) 3.64087 + 6.30617i 0.250648 + 0.434135i 0.963704 0.266972i \(-0.0860231\pi\)
−0.713057 + 0.701107i \(0.752690\pi\)
\(212\) −1.24026 0.716067i −0.0851817 0.0491797i
\(213\) 0 0
\(214\) 10.4955 18.1788i 0.717460 1.24268i
\(215\) 2.81611 1.01915i 0.192057 0.0695052i
\(216\) 0 0
\(217\) −2.07487 1.19792i −0.140851 0.0813204i
\(218\) 5.92463 3.42059i 0.401267 0.231671i
\(219\) 0 0
\(220\) 3.29958 3.91770i 0.222458 0.264131i
\(221\) 19.5831 1.62891i 1.31731 0.109572i
\(222\) 0 0
\(223\) 16.8589 9.73351i 1.12896 0.651804i 0.185285 0.982685i \(-0.440679\pi\)
0.943672 + 0.330881i \(0.107346\pi\)
\(224\) −3.26443 5.65416i −0.218114 0.377784i
\(225\) 0 0
\(226\) −5.65162 −0.375940
\(227\) 4.16698 + 2.40581i 0.276572 + 0.159679i 0.631871 0.775074i \(-0.282287\pi\)
−0.355298 + 0.934753i \(0.615621\pi\)
\(228\) 0 0
\(229\) −1.52360 −0.100682 −0.0503410 0.998732i \(-0.516031\pi\)
−0.0503410 + 0.998732i \(0.516031\pi\)
\(230\) 0.311800 + 0.861568i 0.0205595 + 0.0568101i
\(231\) 0 0
\(232\) −7.99033 + 4.61322i −0.524591 + 0.302873i
\(233\) 13.9652i 0.914889i −0.889238 0.457445i \(-0.848765\pi\)
0.889238 0.457445i \(-0.151235\pi\)
\(234\) 0 0
\(235\) 21.0037 + 17.6898i 1.37013 + 1.15395i
\(236\) 2.08395 + 3.60951i 0.135654 + 0.234959i
\(237\) 0 0
\(238\) −11.3740 6.56677i −0.737266 0.425661i
\(239\) 4.00000 0.258738 0.129369 0.991596i \(-0.458705\pi\)
0.129369 + 0.991596i \(0.458705\pi\)
\(240\) 0 0
\(241\) 8.73294 15.1259i 0.562538 0.974344i −0.434736 0.900558i \(-0.643158\pi\)
0.997274 0.0737864i \(-0.0235083\pi\)
\(242\) 4.82221i 0.309983i
\(243\) 0 0
\(244\) −1.99554 3.45638i −0.127751 0.221272i
\(245\) 6.34196 + 1.13023i 0.405173 + 0.0722078i
\(246\) 0 0
\(247\) 1.75765 + 21.1309i 0.111836 + 1.34453i
\(248\) 3.63054i 0.230539i
\(249\) 0 0
\(250\) −13.2746 0.0728904i −0.839559 0.00460999i
\(251\) 4.64979 8.05367i 0.293492 0.508343i −0.681141 0.732152i \(-0.738516\pi\)
0.974633 + 0.223809i \(0.0718492\pi\)
\(252\) 0 0
\(253\) −1.15990 0.669668i −0.0729223 0.0421017i
\(254\) 9.91788 17.1783i 0.622303 1.07786i
\(255\) 0 0
\(256\) 6.40530 11.0943i 0.400331 0.693394i
\(257\) −9.43076 + 5.44485i −0.588274 + 0.339640i −0.764415 0.644725i \(-0.776972\pi\)
0.176141 + 0.984365i \(0.443639\pi\)
\(258\) 0 0
\(259\) −11.0614 −0.687321
\(260\) 3.88132 + 2.75322i 0.240709 + 0.170747i
\(261\) 0 0
\(262\) 10.2826 5.93667i 0.635262 0.366769i
\(263\) −11.6399 + 6.72031i −0.717749 + 0.414392i −0.813923 0.580972i \(-0.802673\pi\)
0.0961749 + 0.995364i \(0.469339\pi\)
\(264\) 0 0
\(265\) −4.14979 3.49505i −0.254920 0.214699i
\(266\) 7.08578 12.2729i 0.434457 0.752502i
\(267\) 0 0
\(268\) 2.59955i 0.158793i
\(269\) −1.83027 + 3.17012i −0.111593 + 0.193286i −0.916413 0.400234i \(-0.868929\pi\)
0.804819 + 0.593520i \(0.202262\pi\)
\(270\) 0 0
\(271\) −11.0018 19.0557i −0.668313 1.15755i −0.978376 0.206837i \(-0.933683\pi\)
0.310062 0.950716i \(-0.399650\pi\)
\(272\) 13.4681i 0.816621i
\(273\) 0 0
\(274\) −2.34838 −0.141871
\(275\) 14.9103 12.4185i 0.899123 0.748862i
\(276\) 0 0
\(277\) −8.56973 4.94774i −0.514905 0.297281i 0.219943 0.975513i \(-0.429413\pi\)
−0.734848 + 0.678232i \(0.762746\pi\)
\(278\) 10.3303i 0.619570i
\(279\) 0 0
\(280\) −4.74964 13.1242i −0.283845 0.784321i
\(281\) −4.06138 −0.242281 −0.121141 0.992635i \(-0.538655\pi\)
−0.121141 + 0.992635i \(0.538655\pi\)
\(282\) 0 0
\(283\) 5.27294 3.04434i 0.313444 0.180967i −0.335023 0.942210i \(-0.608744\pi\)
0.648467 + 0.761243i \(0.275411\pi\)
\(284\) −0.555090 0.961445i −0.0329386 0.0570513i
\(285\) 0 0
\(286\) 16.5569 1.37719i 0.979031 0.0814348i
\(287\) 0.366292i 0.0216215i
\(288\) 0 0
\(289\) 6.35204 + 11.0021i 0.373649 + 0.647180i
\(290\) −7.48951 + 2.71044i −0.439799 + 0.159163i
\(291\) 0 0
\(292\) 4.52897 + 2.61480i 0.265038 + 0.153020i
\(293\) 8.48019 + 4.89604i 0.495418 + 0.286030i 0.726819 0.686829i \(-0.240998\pi\)
−0.231401 + 0.972858i \(0.574331\pi\)
\(294\) 0 0
\(295\) 5.37324 + 14.8473i 0.312842 + 0.864446i
\(296\) −8.38090 14.5161i −0.487130 0.843734i
\(297\) 0 0
\(298\) 26.4814i 1.53402i
\(299\) 0.530689 1.12547i 0.0306905 0.0650876i
\(300\) 0 0
\(301\) 1.35913 + 2.35408i 0.0783390 + 0.135687i
\(302\) 19.7042 11.3762i 1.13385 0.654628i
\(303\) 0 0
\(304\) 14.5325 0.833497
\(305\) −5.14528 14.2174i −0.294618 0.814088i
\(306\) 0 0
\(307\) 22.1046i 1.26158i −0.775955 0.630788i \(-0.782732\pi\)
0.775955 0.630788i \(-0.217268\pi\)
\(308\) 4.02617 + 2.32451i 0.229412 + 0.132451i
\(309\) 0 0
\(310\) 0.549883 3.08551i 0.0312313 0.175245i
\(311\) −7.63904 −0.433170 −0.216585 0.976264i \(-0.569492\pi\)
−0.216585 + 0.976264i \(0.569492\pi\)
\(312\) 0 0
\(313\) 26.1425i 1.47766i −0.673891 0.738831i \(-0.735378\pi\)
0.673891 0.738831i \(-0.264622\pi\)
\(314\) 3.68231 + 6.37794i 0.207805 + 0.359928i
\(315\) 0 0
\(316\) 3.29958 5.71504i 0.185616 0.321496i
\(317\) 11.8428i 0.665159i −0.943075 0.332580i \(-0.892081\pi\)
0.943075 0.332580i \(-0.107919\pi\)
\(318\) 0 0
\(319\) 5.82135 10.0829i 0.325933 0.564532i
\(320\) 12.6209 14.9852i 0.705531 0.837701i
\(321\) 0 0
\(322\) −0.720215 + 0.415816i −0.0401360 + 0.0231725i
\(323\) −27.7576 + 16.0259i −1.54448 + 0.891704i
\(324\) 0 0
\(325\) 12.6459 + 12.8484i 0.701471 + 0.712698i
\(326\) −14.1716 −0.784890
\(327\) 0 0
\(328\) 0.480695 0.277529i 0.0265419 0.0153240i
\(329\) −12.4622 + 21.5852i −0.687064 + 1.19003i
\(330\) 0 0
\(331\) 6.35021 10.9989i 0.349039 0.604553i −0.637040 0.770831i \(-0.719841\pi\)
0.986079 + 0.166277i \(0.0531747\pi\)
\(332\) −4.00516 2.31238i −0.219812 0.126908i
\(333\) 0 0
\(334\) −1.20488 + 2.08691i −0.0659281 + 0.114191i
\(335\) 1.72786 9.69538i 0.0944031 0.529715i
\(336\) 0 0
\(337\) 15.2939i 0.833113i −0.909110 0.416556i \(-0.863237\pi\)
0.909110 0.416556i \(-0.136763\pi\)
\(338\) 2.55015 + 15.2232i 0.138710 + 0.828034i
\(339\) 0 0
\(340\) −1.26205 + 7.08161i −0.0684441 + 0.384054i
\(341\) 2.29066 + 3.96754i 0.124046 + 0.214854i
\(342\) 0 0
\(343\) 20.0538i 1.08281i
\(344\) −2.05955 + 3.56725i −0.111044 + 0.192333i
\(345\) 0 0
\(346\) 1.59024 0.0854918
\(347\) 10.5998 + 6.11981i 0.569029 + 0.328529i 0.756761 0.653691i \(-0.226781\pi\)
−0.187733 + 0.982220i \(0.560114\pi\)
\(348\) 0 0
\(349\) 9.35021 + 16.1950i 0.500505 + 0.866901i 1.00000 0.000583538i \(0.000185746\pi\)
−0.499495 + 0.866317i \(0.666481\pi\)
\(350\) −2.04880 11.8733i −0.109513 0.634656i
\(351\) 0 0
\(352\) 12.4844i 0.665422i
\(353\) 1.13348 0.654413i 0.0603288 0.0348309i −0.469532 0.882915i \(-0.655577\pi\)
0.529861 + 0.848084i \(0.322244\pi\)
\(354\) 0 0
\(355\) −1.43124 3.95480i −0.0759623 0.209899i
\(356\) 7.22563 0.382957
\(357\) 0 0
\(358\) 20.7956 + 12.0063i 1.09908 + 0.634554i
\(359\) −29.4082 −1.55210 −0.776051 0.630670i \(-0.782780\pi\)
−0.776051 + 0.630670i \(0.782780\pi\)
\(360\) 0 0
\(361\) −7.79249 13.4970i −0.410131 0.710368i
\(362\) −20.3834 + 11.7684i −1.07133 + 0.618531i
\(363\) 0 0
\(364\) −1.84210 + 3.90666i −0.0965520 + 0.204765i
\(365\) 15.1534 + 12.7626i 0.793168 + 0.668024i
\(366\) 0 0
\(367\) −28.9531 + 16.7161i −1.51134 + 0.872573i −0.511429 + 0.859326i \(0.670884\pi\)
−0.999912 + 0.0132473i \(0.995783\pi\)
\(368\) −0.738559 0.426407i −0.0385001 0.0222280i
\(369\) 0 0
\(370\) −4.92410 13.6063i −0.255992 0.707358i
\(371\) 2.46222 4.26469i 0.127832 0.221412i
\(372\) 0 0
\(373\) −29.8589 17.2391i −1.54604 0.892604i −0.998438 0.0558628i \(-0.982209\pi\)
−0.547598 0.836742i \(-0.684458\pi\)
\(374\) 12.5569 + 21.7492i 0.649303 + 1.12463i
\(375\) 0 0
\(376\) −37.7691 −1.94779
\(377\) 9.78357 + 4.61322i 0.503879 + 0.237593i
\(378\) 0 0
\(379\) −8.70225 15.0727i −0.447004 0.774234i 0.551185 0.834383i \(-0.314176\pi\)
−0.998189 + 0.0601487i \(0.980843\pi\)
\(380\) −7.64130 1.36179i −0.391991 0.0698585i
\(381\) 0 0
\(382\) 1.82586i 0.0934191i
\(383\) −1.51271 0.873366i −0.0772961 0.0446269i 0.460854 0.887476i \(-0.347543\pi\)
−0.538150 + 0.842849i \(0.680877\pi\)
\(384\) 0 0
\(385\) 13.4711 + 11.3457i 0.686553 + 0.578231i
\(386\) 12.5876 21.8024i 0.640692 1.10971i
\(387\) 0 0
\(388\) −2.96773 + 1.71342i −0.150664 + 0.0869857i
\(389\) 22.0435 1.11765 0.558826 0.829285i \(-0.311252\pi\)
0.558826 + 0.829285i \(0.311252\pi\)
\(390\) 0 0
\(391\) 1.88090 0.0951212
\(392\) −7.67311 + 4.43007i −0.387550 + 0.223752i
\(393\) 0 0
\(394\) −5.49554 + 9.51855i −0.276861 + 0.479538i
\(395\) 16.1049 19.1219i 0.810326 0.962127i
\(396\) 0 0
\(397\) 19.5132 + 11.2660i 0.979339 + 0.565422i 0.902071 0.431588i \(-0.142047\pi\)
0.0772687 + 0.997010i \(0.475380\pi\)
\(398\) 20.6649i 1.03584i
\(399\) 0 0
\(400\) 9.49402 7.90739i 0.474701 0.395369i
\(401\) −1.85204 3.20782i −0.0924863 0.160191i 0.816070 0.577953i \(-0.196148\pi\)
−0.908557 + 0.417761i \(0.862815\pi\)
\(402\) 0 0
\(403\) −3.49695 + 2.42636i −0.174196 + 0.120866i
\(404\) 3.50737 0.174498
\(405\) 0 0
\(406\) −3.61464 6.26074i −0.179392 0.310715i
\(407\) 18.3177 + 10.5757i 0.907975 + 0.524220i
\(408\) 0 0
\(409\) −6.74186 + 11.6772i −0.333363 + 0.577402i −0.983169 0.182698i \(-0.941517\pi\)
0.649806 + 0.760100i \(0.274850\pi\)
\(410\) 0.450566 0.163059i 0.0222519 0.00805292i
\(411\) 0 0
\(412\) −3.28871 1.89874i −0.162023 0.0935440i
\(413\) −12.4114 + 7.16573i −0.610726 + 0.352603i
\(414\) 0 0
\(415\) −13.4008 11.2865i −0.657821 0.554033i
\(416\) −11.5587 + 0.961445i −0.566714 + 0.0471387i
\(417\) 0 0
\(418\) −23.4682 + 13.5494i −1.14787 + 0.662721i
\(419\) −8.41159 14.5693i −0.410933 0.711757i 0.584059 0.811711i \(-0.301464\pi\)
−0.994992 + 0.0999544i \(0.968130\pi\)
\(420\) 0 0
\(421\) 17.1013 0.833464 0.416732 0.909029i \(-0.363175\pi\)
0.416732 + 0.909029i \(0.363175\pi\)
\(422\) −7.48753 4.32293i −0.364487 0.210437i
\(423\) 0 0
\(424\) 7.46222 0.362397
\(425\) −9.41397 + 25.5730i −0.456645 + 1.24047i
\(426\) 0 0
\(427\) 11.8849 6.86173i 0.575149 0.332062i
\(428\) 10.4349i 0.504392i
\(429\) 0 0
\(430\) −2.29066 + 2.71978i −0.110465 + 0.131159i
\(431\) 4.83027 + 8.36627i 0.232666 + 0.402989i 0.958592 0.284784i \(-0.0919218\pi\)
−0.725926 + 0.687773i \(0.758588\pi\)
\(432\) 0 0
\(433\) 21.4538 + 12.3863i 1.03100 + 0.595249i 0.917272 0.398262i \(-0.130387\pi\)
0.113730 + 0.993512i \(0.463720\pi\)
\(434\) 2.84467 0.136549
\(435\) 0 0
\(436\) 1.70042 2.94521i 0.0814354 0.141050i
\(437\) 2.02956i 0.0970869i
\(438\) 0 0
\(439\) 3.53069 + 6.11533i 0.168511 + 0.291869i 0.937896 0.346915i \(-0.112771\pi\)
−0.769386 + 0.638784i \(0.779438\pi\)
\(440\) −4.68257 + 26.2749i −0.223233 + 1.25261i
\(441\) 0 0
\(442\) −19.1696 + 13.3008i −0.911803 + 0.632655i
\(443\) 38.2438i 1.81702i −0.417865 0.908509i \(-0.637222\pi\)
0.417865 0.908509i \(-0.362778\pi\)
\(444\) 0 0
\(445\) 26.9490 + 4.80271i 1.27751 + 0.227670i
\(446\) −11.5569 + 20.0172i −0.547236 + 0.947840i
\(447\) 0 0
\(448\) 15.4002 + 8.89128i 0.727589 + 0.420074i
\(449\) 6.24003 10.8080i 0.294485 0.510063i −0.680380 0.732860i \(-0.738185\pi\)
0.974865 + 0.222796i \(0.0715185\pi\)
\(450\) 0 0
\(451\) −0.350210 + 0.606582i −0.0164908 + 0.0285628i
\(452\) −2.43309 + 1.40475i −0.114443 + 0.0660738i
\(453\) 0 0
\(454\) −5.71300 −0.268124
\(455\) −9.46703 + 13.3460i −0.443821 + 0.625672i
\(456\) 0 0
\(457\) 7.12930 4.11610i 0.333495 0.192543i −0.323897 0.946092i \(-0.604993\pi\)
0.657392 + 0.753549i \(0.271660\pi\)
\(458\) 1.56665 0.904508i 0.0732050 0.0422649i
\(459\) 0 0
\(460\) 0.348383 + 0.293416i 0.0162434 + 0.0136806i
\(461\) −2.27072 + 3.93300i −0.105758 + 0.183178i −0.914048 0.405607i \(-0.867060\pi\)
0.808290 + 0.588785i \(0.200394\pi\)
\(462\) 0 0
\(463\) 1.98845i 0.0924113i 0.998932 + 0.0462056i \(0.0147130\pi\)
−0.998932 + 0.0462056i \(0.985287\pi\)
\(464\) 3.70671 6.42021i 0.172080 0.298051i
\(465\) 0 0
\(466\) 8.29066 + 14.3598i 0.384057 + 0.665207i
\(467\) 32.8043i 1.51800i 0.651091 + 0.759000i \(0.274312\pi\)
−0.651091 + 0.759000i \(0.725688\pi\)
\(468\) 0 0
\(469\) 8.93862 0.412747
\(470\) −32.0991 5.72053i −1.48062 0.263868i
\(471\) 0 0
\(472\) −18.8076 10.8586i −0.865689 0.499806i
\(473\) 5.19783i 0.238997i
\(474\) 0 0
\(475\) −27.5942 10.1580i −1.26611 0.466081i
\(476\) −6.52886 −0.299250
\(477\) 0 0
\(478\) −4.11304 + 2.37467i −0.188126 + 0.108615i
\(479\) 15.4027 + 26.6782i 0.703766 + 1.21896i 0.967135 + 0.254263i \(0.0818329\pi\)
−0.263369 + 0.964695i \(0.584834\pi\)
\(480\) 0 0
\(481\) −8.38090 + 17.7740i −0.382136 + 0.810423i
\(482\) 20.7378i 0.944582i
\(483\) 0 0
\(484\) −1.19859 2.07602i −0.0544815 0.0943647i
\(485\) −12.2074 + 4.41786i −0.554312 + 0.200605i
\(486\) 0 0
\(487\) 19.3341 + 11.1626i 0.876113 + 0.505824i 0.869375 0.494153i \(-0.164522\pi\)
0.00673807 + 0.999977i \(0.497855\pi\)
\(488\) 18.0097 + 10.3979i 0.815259 + 0.470690i
\(489\) 0 0
\(490\) −7.19217 + 2.60284i −0.324909 + 0.117584i
\(491\) 5.34129 + 9.25139i 0.241049 + 0.417509i 0.961013 0.276502i \(-0.0891752\pi\)
−0.719964 + 0.694011i \(0.755842\pi\)
\(492\) 0 0
\(493\) 16.3504i 0.736386i
\(494\) −14.3520 20.6846i −0.645729 0.930646i
\(495\) 0 0
\(496\) 1.45856 + 2.52631i 0.0654914 + 0.113434i
\(497\) 3.30596 1.90870i 0.148292 0.0856167i
\(498\) 0 0
\(499\) −18.8195 −0.842477 −0.421239 0.906950i \(-0.638405\pi\)
−0.421239 + 0.906950i \(0.638405\pi\)
\(500\) −5.73300 + 3.26811i −0.256388 + 0.146154i
\(501\) 0 0
\(502\) 11.0417i 0.492815i
\(503\) 4.92013 + 2.84064i 0.219378 + 0.126658i 0.605662 0.795722i \(-0.292908\pi\)
−0.386284 + 0.922380i \(0.626242\pi\)
\(504\) 0 0
\(505\) 13.0812 + 2.33127i 0.582107 + 0.103740i
\(506\) 1.59024 0.0706948
\(507\) 0 0
\(508\) 9.86062i 0.437494i
\(509\) −13.9622 24.1833i −0.618864 1.07190i −0.989693 0.143203i \(-0.954260\pi\)
0.370829 0.928701i \(-0.379074\pi\)
\(510\) 0 0
\(511\) −8.99108 + 15.5730i −0.397742 + 0.688909i
\(512\) 23.1492i 1.02306i
\(513\) 0 0
\(514\) 6.46485 11.1975i 0.285152 0.493898i
\(515\) −11.0037 9.26754i −0.484879 0.408376i
\(516\) 0 0
\(517\) 41.2750 23.8301i 1.81527 1.04805i
\(518\) 11.3740 6.56677i 0.499744 0.288527i
\(519\) 0 0
\(520\) −24.6873 2.31190i −1.08261 0.101384i
\(521\) −6.29958 −0.275990 −0.137995 0.990433i \(-0.544066\pi\)
−0.137995 + 0.990433i \(0.544066\pi\)
\(522\) 0 0
\(523\) −19.7948 + 11.4285i −0.865567 + 0.499735i −0.865873 0.500265i \(-0.833236\pi\)
0.000305526 1.00000i \(0.499903\pi\)
\(524\) 2.95120 5.11162i 0.128924 0.223302i
\(525\) 0 0
\(526\) 7.97925 13.8205i 0.347912 0.602601i
\(527\) −5.57182 3.21689i −0.242712 0.140130i
\(528\) 0 0
\(529\) −11.4404 + 19.8154i −0.497411 + 0.861541i
\(530\) 6.34196 + 1.13023i 0.275477 + 0.0490941i
\(531\) 0 0
\(532\) 7.04487i 0.305434i
\(533\) −0.588576 0.277529i −0.0254940 0.0120211i
\(534\) 0 0
\(535\) 6.93588 38.9186i 0.299864 1.68260i
\(536\) 6.77255 + 11.7304i 0.292529 + 0.506676i
\(537\) 0 0
\(538\) 4.34628i 0.187381i
\(539\) 5.59024 9.68258i 0.240789 0.417058i
\(540\) 0 0
\(541\) −9.48006 −0.407580 −0.203790 0.979015i \(-0.565326\pi\)
−0.203790 + 0.979015i \(0.565326\pi\)
\(542\) 22.6255 + 13.0628i 0.971848 + 0.561097i
\(543\) 0 0
\(544\) −8.76626 15.1836i −0.375850 0.650992i
\(545\) 8.29958 9.85437i 0.355515 0.422115i
\(546\) 0 0
\(547\) 33.3911i 1.42770i 0.700299 + 0.713850i \(0.253050\pi\)
−0.700299 + 0.713850i \(0.746950\pi\)
\(548\) −1.01101 + 0.583706i −0.0431882 + 0.0249347i
\(549\) 0 0
\(550\) −7.95921 + 21.6212i −0.339382 + 0.921929i
\(551\) −17.6427 −0.751604
\(552\) 0 0
\(553\) 19.6513 + 11.3457i 0.835660 + 0.482469i
\(554\) 11.7492 0.499177
\(555\) 0 0
\(556\) 2.56767 + 4.44733i 0.108893 + 0.188609i
\(557\) 32.7053 18.8824i 1.38577 0.800073i 0.392932 0.919567i \(-0.371461\pi\)
0.992835 + 0.119495i \(0.0381274\pi\)
\(558\) 0 0
\(559\) 4.81243 0.400293i 0.203544 0.0169306i
\(560\) 8.57766 + 7.22431i 0.362472 + 0.305283i
\(561\) 0 0
\(562\) 4.17616 2.41110i 0.176161 0.101706i
\(563\) −22.4307 12.9504i −0.945343 0.545794i −0.0537120 0.998556i \(-0.517105\pi\)
−0.891631 + 0.452762i \(0.850439\pi\)
\(564\) 0 0
\(565\) −10.0083 + 3.62198i −0.421051 + 0.152378i
\(566\) −3.61464 + 6.26074i −0.151935 + 0.263159i
\(567\) 0 0
\(568\) 5.00967 + 2.89233i 0.210201 + 0.121360i
\(569\) 10.7725 + 18.6586i 0.451609 + 0.782209i 0.998486 0.0550035i \(-0.0175170\pi\)
−0.546878 + 0.837213i \(0.684184\pi\)
\(570\) 0 0
\(571\) −2.22036 −0.0929192 −0.0464596 0.998920i \(-0.514794\pi\)
−0.0464596 + 0.998920i \(0.514794\pi\)
\(572\) 6.78566 4.70823i 0.283723 0.196861i
\(573\) 0 0
\(574\) 0.217455 + 0.376644i 0.00907641 + 0.0157208i
\(575\) 1.10432 + 1.32590i 0.0460532 + 0.0552938i
\(576\) 0 0
\(577\) 6.20265i 0.258220i 0.991630 + 0.129110i \(0.0412120\pi\)
−0.991630 + 0.129110i \(0.958788\pi\)
\(578\) −13.0631 7.54199i −0.543353 0.313705i
\(579\) 0 0
\(580\) −2.55063 + 3.02845i −0.105909 + 0.125749i
\(581\) 7.95120 13.7719i 0.329871 0.571354i
\(582\) 0 0
\(583\) −8.15489 + 4.70823i −0.337741 + 0.194995i
\(584\) −27.2492 −1.12758
\(585\) 0 0
\(586\) −11.6265 −0.480285
\(587\) −1.58391 + 0.914469i −0.0653748 + 0.0377442i −0.532331 0.846536i \(-0.678684\pi\)
0.466956 + 0.884280i \(0.345351\pi\)
\(588\) 0 0
\(589\) 3.47114 6.01219i 0.143026 0.247728i
\(590\) −14.3395 12.0770i −0.590346 0.497204i
\(591\) 0 0
\(592\) 11.6637 + 6.73403i 0.479374 + 0.276767i
\(593\) 0.0728761i 0.00299266i 0.999999 + 0.00149633i \(0.000476297\pi\)
−0.999999 + 0.00149633i \(0.999524\pi\)
\(594\) 0 0
\(595\) −24.3503 4.33959i −0.998266 0.177906i
\(596\) −6.58212 11.4006i −0.269614 0.466986i
\(597\) 0 0
\(598\) 0.122467 + 1.47233i 0.00500804 + 0.0602080i
\(599\) −14.5813 −0.595777 −0.297888 0.954601i \(-0.596282\pi\)
−0.297888 + 0.954601i \(0.596282\pi\)
\(600\) 0 0
\(601\) 22.2041 + 38.4586i 0.905723 + 1.56876i 0.819944 + 0.572444i \(0.194005\pi\)
0.0857795 + 0.996314i \(0.472662\pi\)
\(602\) −2.79508 1.61374i −0.113919 0.0657712i
\(603\) 0 0
\(604\) 5.65527 9.79522i 0.230110 0.398562i
\(605\) −3.09044 8.53951i −0.125644 0.347180i
\(606\) 0 0
\(607\) 31.3808 + 18.1177i 1.27371 + 0.735375i 0.975684 0.219183i \(-0.0703392\pi\)
0.298024 + 0.954558i \(0.403672\pi\)
\(608\) 16.3836 9.45910i 0.664445 0.383617i
\(609\) 0 0
\(610\) 13.7311 + 11.5647i 0.555956 + 0.468239i
\(611\) 25.2419 + 36.3794i 1.02118 + 1.47175i
\(612\) 0 0
\(613\) 2.90838 1.67915i 0.117468 0.0678203i −0.440115 0.897942i \(-0.645062\pi\)
0.557583 + 0.830121i \(0.311729\pi\)
\(614\) 13.1228 + 22.7293i 0.529591 + 0.917279i
\(615\) 0 0
\(616\) −24.2240 −0.976013
\(617\) 18.3441 + 10.5910i 0.738507 + 0.426377i 0.821526 0.570171i \(-0.193123\pi\)
−0.0830194 + 0.996548i \(0.526456\pi\)
\(618\) 0 0
\(619\) −25.4082 −1.02124 −0.510620 0.859807i \(-0.670584\pi\)
−0.510620 + 0.859807i \(0.670584\pi\)
\(620\) −0.530192 1.46503i −0.0212930 0.0588369i
\(621\) 0 0
\(622\) 7.85493 4.53504i 0.314954 0.181839i
\(623\) 24.8455i 0.995416i
\(624\) 0 0
\(625\) −23.5543 + 8.37828i −0.942171 + 0.335131i
\(626\) 15.5199 + 26.8813i 0.620302 + 1.07439i
\(627\) 0 0
\(628\) 3.17056 + 1.83052i 0.126519 + 0.0730459i
\(629\) −29.7041 −1.18438
\(630\) 0 0
\(631\) −21.7725 + 37.7112i −0.866751 + 1.50126i −0.00145375 + 0.999999i \(0.500463\pi\)
−0.865298 + 0.501258i \(0.832871\pi\)
\(632\) 34.3853i 1.36777i
\(633\) 0 0
\(634\) 7.03069 + 12.1775i 0.279224 + 0.483631i
\(635\) 6.55413 36.7766i 0.260093 1.45943i
\(636\) 0 0
\(637\) 9.39516 + 4.43007i 0.372250 + 0.175526i
\(638\) 13.8238i 0.547288i
\(639\) 0 0
\(640\) −1.55727 + 8.73816i −0.0615565 + 0.345406i
\(641\) 24.1427 41.8164i 0.953579 1.65165i 0.215993 0.976395i \(-0.430701\pi\)
0.737586 0.675253i \(-0.235965\pi\)
\(642\) 0 0
\(643\) −36.6710 21.1720i −1.44616 0.834943i −0.447913 0.894077i \(-0.647833\pi\)
−0.998250 + 0.0591344i \(0.981166\pi\)
\(644\) −0.206708 + 0.358028i −0.00814543 + 0.0141083i
\(645\) 0 0
\(646\) 19.0281 32.9576i 0.748649 1.29670i
\(647\) 29.7958 17.2026i 1.17139 0.676305i 0.217386 0.976086i \(-0.430247\pi\)
0.954008 + 0.299781i \(0.0969136\pi\)
\(648\) 0 0
\(649\) 27.4045 1.07572
\(650\) −20.6310 5.70398i −0.809213 0.223729i
\(651\) 0 0
\(652\) −6.10104 + 3.52244i −0.238935 + 0.137949i
\(653\) −12.4114 + 7.16573i −0.485696 + 0.280417i −0.722787 0.691071i \(-0.757139\pi\)
0.237091 + 0.971487i \(0.423806\pi\)
\(654\) 0 0
\(655\) 14.4045 17.1029i 0.562830 0.668267i
\(656\) −0.222994 + 0.386237i −0.00870646 + 0.0150800i
\(657\) 0 0
\(658\) 29.5936i 1.15368i
\(659\) −11.4116 + 19.7655i −0.444532 + 0.769953i −0.998020 0.0629051i \(-0.979963\pi\)
0.553487 + 0.832858i \(0.313297\pi\)
\(660\) 0 0
\(661\) −7.20934 12.4869i −0.280411 0.485686i 0.691075 0.722783i \(-0.257137\pi\)
−0.971486 + 0.237097i \(0.923804\pi\)
\(662\) 15.0796i 0.586087i
\(663\) 0 0
\(664\) 24.0976 0.935168
\(665\) 4.68257 26.2749i 0.181582 1.01890i
\(666\) 0 0
\(667\) 0.896622 + 0.517665i 0.0347173 + 0.0200441i
\(668\) 1.19792i 0.0463491i
\(669\) 0 0
\(670\) 3.97913 + 10.9952i 0.153727 + 0.424780i
\(671\) −26.2419 −1.01306
\(672\) 0 0
\(673\) 29.5956 17.0871i 1.14083 0.658657i 0.194193 0.980963i \(-0.437791\pi\)
0.946636 + 0.322306i \(0.104458\pi\)
\(674\) 9.07949 + 15.7261i 0.349729 + 0.605748i
\(675\) 0 0
\(676\) 4.88170 + 5.91993i 0.187758 + 0.227690i
\(677\) 5.84695i 0.224716i −0.993668 0.112358i \(-0.964160\pi\)
0.993668 0.112358i \(-0.0358404\pi\)
\(678\) 0 0
\(679\) −5.89165 10.2046i −0.226101 0.391618i
\(680\) −12.7546 35.2436i −0.489117 1.35153i
\(681\) 0 0
\(682\) −4.71079 2.71978i −0.180386 0.104146i
\(683\) 9.82834 + 5.67439i 0.376071 + 0.217125i 0.676107 0.736803i \(-0.263666\pi\)
−0.300036 + 0.953928i \(0.596999\pi\)
\(684\) 0 0
\(685\) −4.15868 + 1.50502i −0.158895 + 0.0575039i
\(686\) −11.9053 20.6206i −0.454546 0.787298i
\(687\) 0 0
\(688\) 3.30969i 0.126181i
\(689\) −4.98715 7.18765i −0.189995 0.273828i
\(690\) 0 0
\(691\) 9.41159 + 16.3013i 0.358034 + 0.620133i 0.987632 0.156788i \(-0.0501140\pi\)
−0.629599 + 0.776921i \(0.716781\pi\)
\(692\) 0.684619 0.395265i 0.0260253 0.0150257i
\(693\) 0 0
\(694\) −14.5325 −0.551647
\(695\) 6.62044 + 18.2936i 0.251128 + 0.693916i
\(696\) 0 0
\(697\) 0.983636i 0.0372579i
\(698\) −19.2289 11.1018i −0.727825 0.420210i
\(699\) 0 0
\(700\) −3.83323 4.60238i −0.144883 0.173954i
\(701\) −19.1626 −0.723763 −0.361881 0.932224i \(-0.617865\pi\)
−0.361881 + 0.932224i \(0.617865\pi\)
\(702\) 0 0
\(703\) 32.0518i 1.20885i
\(704\) −17.0018 29.4480i −0.640780 1.10986i
\(705\) 0 0
\(706\) −0.777006 + 1.34581i −0.0292430 + 0.0506504i
\(707\) 12.0602i 0.453570i
\(708\) 0 0
\(709\) 11.7419 20.3375i 0.440975 0.763791i −0.556787 0.830655i \(-0.687966\pi\)
0.997762 + 0.0668645i \(0.0212995\pi\)
\(710\) 3.81952 + 3.21689i 0.143344 + 0.120728i
\(711\) 0 0
\(712\) −32.6055 + 18.8248i −1.22194 + 0.705488i
\(713\) −0.352814 + 0.203698i −0.0132130 + 0.00762853i
\(714\) 0 0
\(715\) 28.4375 13.0497i 1.06350 0.488033i
\(716\) 11.9370 0.446107
\(717\) 0 0
\(718\) 30.2393 17.4586i 1.12852 0.651551i
\(719\) 7.05429 12.2184i 0.263080 0.455669i −0.703978 0.710221i \(-0.748595\pi\)
0.967059 + 0.254553i \(0.0819282\pi\)
\(720\) 0 0
\(721\) 6.52886 11.3083i 0.243148 0.421144i
\(722\) 16.0254 + 9.25228i 0.596404 + 0.344334i
\(723\) 0 0
\(724\) −5.85021 + 10.1329i −0.217421 + 0.376585i
\(725\) −11.5259 + 9.59969i −0.428061 + 0.356523i
\(726\) 0 0
\(727\) 25.3762i 0.941153i 0.882359 + 0.470576i \(0.155954\pi\)
−0.882359 + 0.470576i \(0.844046\pi\)
\(728\) −1.86553 22.4279i −0.0691411 0.831233i
\(729\) 0 0
\(730\) −23.1584 4.12717i −0.857131 0.152754i
\(731\) 3.64979 + 6.32162i 0.134992 + 0.233814i
\(732\) 0 0
\(733\) 10.6692i 0.394074i 0.980396 + 0.197037i \(0.0631320\pi\)
−0.980396 + 0.197037i \(0.936868\pi\)
\(734\) 19.8476 34.3770i 0.732587 1.26888i
\(735\) 0 0
\(736\) −1.11018 −0.0409218
\(737\) −14.8024 8.54617i −0.545254 0.314802i
\(738\) 0 0
\(739\) −0.707513 1.22545i −0.0260263 0.0450788i 0.852719 0.522370i \(-0.174952\pi\)
−0.878745 + 0.477291i \(0.841619\pi\)
\(740\) −5.50183 4.63377i −0.202251 0.170341i
\(741\) 0 0
\(742\) 5.84695i 0.214648i
\(743\) −25.8748 + 14.9389i −0.949256 + 0.548053i −0.892850 0.450355i \(-0.851298\pi\)
−0.0564064 + 0.998408i \(0.517964\pi\)
\(744\) 0 0
\(745\) −16.9713 46.8951i −0.621779 1.71810i
\(746\) 40.9370 1.49881
\(747\) 0 0
\(748\) 10.8118 + 6.24221i 0.395320 + 0.228238i
\(749\) 35.8809 1.31106
\(750\) 0 0
\(751\) 9.99291 + 17.3082i 0.364646 + 0.631586i 0.988719 0.149780i \(-0.0478565\pi\)
−0.624073 + 0.781366i \(0.714523\pi\)
\(752\) 26.2816 15.1737i 0.958391 0.553328i
\(753\) 0 0
\(754\) −12.7988 + 1.06459i −0.466104 + 0.0387701i
\(755\) 27.6028 32.7737i 1.00457 1.19276i
\(756\) 0 0
\(757\) −14.8024 + 8.54617i −0.538003 + 0.310616i −0.744269 0.667880i \(-0.767202\pi\)
0.206266 + 0.978496i \(0.433869\pi\)
\(758\) 17.8964 + 10.3325i 0.650025 + 0.375292i
\(759\) 0 0
\(760\) 38.0291 13.7627i 1.37946 0.499225i
\(761\) −21.1120 + 36.5671i −0.765310 + 1.32556i 0.174773 + 0.984609i \(0.444081\pi\)
−0.940083 + 0.340947i \(0.889252\pi\)
\(762\) 0 0
\(763\) 10.1272 + 5.84695i 0.366630 + 0.211674i
\(764\) 0.453830 + 0.786056i 0.0164190 + 0.0284385i
\(765\) 0 0
\(766\) 2.07395 0.0749350
\(767\) 2.11046 + 25.3725i 0.0762044 + 0.916149i
\(768\) 0 0
\(769\) −11.8827 20.5815i −0.428502 0.742187i 0.568238 0.822864i \(-0.307625\pi\)
−0.996740 + 0.0806767i \(0.974292\pi\)
\(770\) −20.5874 3.66898i −0.741919 0.132221i
\(771\) 0 0
\(772\) 12.5149i 0.450422i
\(773\) 0.246026 + 0.142043i 0.00884894 + 0.00510894i 0.504418 0.863460i \(-0.331707\pi\)
−0.495569 + 0.868569i \(0.665040\pi\)
\(774\) 0 0
\(775\) −1.00366 5.81644i −0.0360524 0.208933i
\(776\) 8.92787 15.4635i 0.320492 0.555108i
\(777\) 0 0
\(778\) −22.6665 + 13.0865i −0.812634 + 0.469174i
\(779\) 1.06138 0.0380278
\(780\) 0 0
\(781\) −7.29958 −0.261199
\(782\) −1.93405 + 1.11663i −0.0691617 + 0.0399305i
\(783\) 0 0
\(784\) 3.55955 6.16532i 0.127127 0.220190i
\(785\) 10.6084 + 8.93460i 0.378628 + 0.318890i
\(786\) 0