Properties

Label 1323.2.g.h.361.9
Level $1323$
Weight $2$
Character 1323.361
Analytic conductor $10.564$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.9
Character \(\chi\) \(=\) 1323.361
Dual form 1323.2.g.h.667.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.649936 - 1.12572i) q^{2} +(0.155166 + 0.268756i) q^{4} +3.52584 q^{5} +3.00314 q^{8} +O(q^{10})\) \(q+(0.649936 - 1.12572i) q^{2} +(0.155166 + 0.268756i) q^{4} +3.52584 q^{5} +3.00314 q^{8} +(2.29157 - 3.96912i) q^{10} -1.17853 q^{11} +(-1.61030 + 2.78913i) q^{13} +(1.64151 - 2.84319i) q^{16} +(2.45159 - 4.24627i) q^{17} +(-3.43318 - 5.94645i) q^{19} +(0.547092 + 0.947591i) q^{20} +(-0.765972 + 1.32670i) q^{22} +4.29987 q^{23} +7.43156 q^{25} +(2.09319 + 3.62551i) q^{26} +(-1.36140 - 2.35802i) q^{29} +(-0.960401 - 1.66346i) q^{31} +(0.869378 + 1.50581i) q^{32} +(-3.18675 - 5.51961i) q^{34} +(4.88229 + 8.45637i) q^{37} -8.92540 q^{38} +10.5886 q^{40} +(-3.32673 + 5.76206i) q^{41} +(4.83441 + 8.37344i) q^{43} +(-0.182869 - 0.316738i) q^{44} +(2.79464 - 4.84046i) q^{46} +(-0.316609 + 0.548383i) q^{47} +(4.83004 - 8.36587i) q^{50} -0.999459 q^{52} +(-1.11378 + 1.92912i) q^{53} -4.15533 q^{55} -3.53930 q^{58} +(-4.10652 - 7.11270i) q^{59} +(-4.82958 + 8.36508i) q^{61} -2.49680 q^{62} +8.82622 q^{64} +(-5.67767 + 9.83402i) q^{65} +(-2.66651 - 4.61852i) q^{67} +1.52161 q^{68} +3.27719 q^{71} +(0.519036 - 0.898997i) q^{73} +12.6927 q^{74} +(1.06543 - 1.84538i) q^{76} +(-0.502039 + 0.869557i) q^{79} +(5.78772 - 10.0246i) q^{80} +(4.32432 + 7.48994i) q^{82} +(-3.65598 - 6.33234i) q^{83} +(8.64391 - 14.9717i) q^{85} +12.5682 q^{86} -3.53930 q^{88} +(-6.02144 - 10.4294i) q^{89} +(0.667195 + 1.15562i) q^{92} +(0.411551 + 0.712828i) q^{94} +(-12.1049 - 20.9662i) q^{95} +(5.46454 + 9.46487i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 4q^{2} - 12q^{4} + 24q^{8} + O(q^{10}) \) \( 24q - 4q^{2} - 12q^{4} + 24q^{8} + 40q^{11} - 12q^{16} + 64q^{23} + 24q^{25} - 16q^{29} - 48q^{32} - 12q^{37} - 56q^{44} + 24q^{46} + 4q^{50} - 32q^{53} + 96q^{64} - 60q^{65} - 12q^{67} + 112q^{71} + 136q^{74} + 12q^{79} + 12q^{85} + 152q^{86} - 16q^{92} - 64q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.649936 1.12572i 0.459574 0.796006i −0.539364 0.842073i \(-0.681335\pi\)
0.998938 + 0.0460668i \(0.0146687\pi\)
\(3\) 0 0
\(4\) 0.155166 + 0.268756i 0.0775831 + 0.134378i
\(5\) 3.52584 1.57680 0.788402 0.615160i \(-0.210909\pi\)
0.788402 + 0.615160i \(0.210909\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 3.00314 1.06177
\(9\) 0 0
\(10\) 2.29157 3.96912i 0.724659 1.25515i
\(11\) −1.17853 −0.355342 −0.177671 0.984090i \(-0.556856\pi\)
−0.177671 + 0.984090i \(0.556856\pi\)
\(12\) 0 0
\(13\) −1.61030 + 2.78913i −0.446618 + 0.773564i −0.998163 0.0605803i \(-0.980705\pi\)
0.551546 + 0.834145i \(0.314038\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.64151 2.84319i 0.410379 0.710797i
\(17\) 2.45159 4.24627i 0.594597 1.02987i −0.399006 0.916948i \(-0.630645\pi\)
0.993604 0.112924i \(-0.0360218\pi\)
\(18\) 0 0
\(19\) −3.43318 5.94645i −0.787627 1.36421i −0.927417 0.374028i \(-0.877976\pi\)
0.139791 0.990181i \(-0.455357\pi\)
\(20\) 0.547092 + 0.947591i 0.122333 + 0.211888i
\(21\) 0 0
\(22\) −0.765972 + 1.32670i −0.163306 + 0.282854i
\(23\) 4.29987 0.896585 0.448293 0.893887i \(-0.352032\pi\)
0.448293 + 0.893887i \(0.352032\pi\)
\(24\) 0 0
\(25\) 7.43156 1.48631
\(26\) 2.09319 + 3.62551i 0.410508 + 0.711020i
\(27\) 0 0
\(28\) 0 0
\(29\) −1.36140 2.35802i −0.252806 0.437873i 0.711491 0.702695i \(-0.248020\pi\)
−0.964297 + 0.264822i \(0.914687\pi\)
\(30\) 0 0
\(31\) −0.960401 1.66346i −0.172493 0.298767i 0.766798 0.641889i \(-0.221849\pi\)
−0.939291 + 0.343122i \(0.888516\pi\)
\(32\) 0.869378 + 1.50581i 0.153686 + 0.266192i
\(33\) 0 0
\(34\) −3.18675 5.51961i −0.546523 0.946606i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.88229 + 8.45637i 0.802643 + 1.39022i 0.917871 + 0.396879i \(0.129907\pi\)
−0.115228 + 0.993339i \(0.536760\pi\)
\(38\) −8.92540 −1.44789
\(39\) 0 0
\(40\) 10.5886 1.67420
\(41\) −3.32673 + 5.76206i −0.519547 + 0.899883i 0.480194 + 0.877162i \(0.340566\pi\)
−0.999742 + 0.0227205i \(0.992767\pi\)
\(42\) 0 0
\(43\) 4.83441 + 8.37344i 0.737240 + 1.27694i 0.953734 + 0.300653i \(0.0972047\pi\)
−0.216493 + 0.976284i \(0.569462\pi\)
\(44\) −0.182869 0.316738i −0.0275685 0.0477501i
\(45\) 0 0
\(46\) 2.79464 4.84046i 0.412047 0.713687i
\(47\) −0.316609 + 0.548383i −0.0461822 + 0.0799899i −0.888192 0.459472i \(-0.848039\pi\)
0.842010 + 0.539461i \(0.181372\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 4.83004 8.36587i 0.683071 1.18311i
\(51\) 0 0
\(52\) −0.999459 −0.138600
\(53\) −1.11378 + 1.92912i −0.152989 + 0.264985i −0.932325 0.361621i \(-0.882223\pi\)
0.779336 + 0.626606i \(0.215557\pi\)
\(54\) 0 0
\(55\) −4.15533 −0.560304
\(56\) 0 0
\(57\) 0 0
\(58\) −3.53930 −0.464733
\(59\) −4.10652 7.11270i −0.534623 0.925995i −0.999181 0.0404521i \(-0.987120\pi\)
0.464558 0.885543i \(-0.346213\pi\)
\(60\) 0 0
\(61\) −4.82958 + 8.36508i −0.618364 + 1.07104i 0.371420 + 0.928465i \(0.378871\pi\)
−0.989784 + 0.142573i \(0.954462\pi\)
\(62\) −2.49680 −0.317093
\(63\) 0 0
\(64\) 8.82622 1.10328
\(65\) −5.67767 + 9.83402i −0.704229 + 1.21976i
\(66\) 0 0
\(67\) −2.66651 4.61852i −0.325766 0.564242i 0.655901 0.754847i \(-0.272289\pi\)
−0.981667 + 0.190604i \(0.938955\pi\)
\(68\) 1.52161 0.184523
\(69\) 0 0
\(70\) 0 0
\(71\) 3.27719 0.388931 0.194466 0.980909i \(-0.437703\pi\)
0.194466 + 0.980909i \(0.437703\pi\)
\(72\) 0 0
\(73\) 0.519036 0.898997i 0.0607486 0.105220i −0.834052 0.551686i \(-0.813985\pi\)
0.894800 + 0.446467i \(0.147318\pi\)
\(74\) 12.6927 1.47550
\(75\) 0 0
\(76\) 1.06543 1.84538i 0.122213 0.211679i
\(77\) 0 0
\(78\) 0 0
\(79\) −0.502039 + 0.869557i −0.0564838 + 0.0978328i −0.892885 0.450285i \(-0.851322\pi\)
0.836401 + 0.548118i \(0.184656\pi\)
\(80\) 5.78772 10.0246i 0.647087 1.12079i
\(81\) 0 0
\(82\) 4.32432 + 7.48994i 0.477541 + 0.827126i
\(83\) −3.65598 6.33234i −0.401296 0.695064i 0.592587 0.805506i \(-0.298107\pi\)
−0.993883 + 0.110442i \(0.964773\pi\)
\(84\) 0 0
\(85\) 8.64391 14.9717i 0.937563 1.62391i
\(86\) 12.5682 1.35527
\(87\) 0 0
\(88\) −3.53930 −0.377291
\(89\) −6.02144 10.4294i −0.638271 1.10552i −0.985812 0.167853i \(-0.946317\pi\)
0.347541 0.937665i \(-0.387017\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.667195 + 1.15562i 0.0695599 + 0.120481i
\(93\) 0 0
\(94\) 0.411551 + 0.712828i 0.0424483 + 0.0735226i
\(95\) −12.1049 20.9662i −1.24193 2.15109i
\(96\) 0 0
\(97\) 5.46454 + 9.46487i 0.554840 + 0.961012i 0.997916 + 0.0645275i \(0.0205540\pi\)
−0.443076 + 0.896484i \(0.646113\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.15313 + 1.99728i 0.115313 + 0.199728i
\(101\) −1.59509 −0.158718 −0.0793588 0.996846i \(-0.525287\pi\)
−0.0793588 + 0.996846i \(0.525287\pi\)
\(102\) 0 0
\(103\) −2.33556 −0.230129 −0.115065 0.993358i \(-0.536708\pi\)
−0.115065 + 0.993358i \(0.536708\pi\)
\(104\) −4.83596 + 8.37613i −0.474205 + 0.821347i
\(105\) 0 0
\(106\) 1.44777 + 2.50761i 0.140620 + 0.243561i
\(107\) −1.11181 1.92571i −0.107483 0.186166i 0.807267 0.590186i \(-0.200946\pi\)
−0.914750 + 0.404021i \(0.867612\pi\)
\(108\) 0 0
\(109\) 0.459782 0.796366i 0.0440391 0.0762780i −0.843166 0.537654i \(-0.819311\pi\)
0.887205 + 0.461376i \(0.152644\pi\)
\(110\) −2.70070 + 4.67774i −0.257501 + 0.446005i
\(111\) 0 0
\(112\) 0 0
\(113\) −1.19327 + 2.06681i −0.112254 + 0.194429i −0.916679 0.399625i \(-0.869140\pi\)
0.804425 + 0.594054i \(0.202474\pi\)
\(114\) 0 0
\(115\) 15.1607 1.41374
\(116\) 0.422488 0.731770i 0.0392270 0.0679432i
\(117\) 0 0
\(118\) −10.6759 −0.982796
\(119\) 0 0
\(120\) 0 0
\(121\) −9.61106 −0.873732
\(122\) 6.27783 + 10.8735i 0.568368 + 0.984443i
\(123\) 0 0
\(124\) 0.298044 0.516227i 0.0267651 0.0463585i
\(125\) 8.57330 0.766819
\(126\) 0 0
\(127\) −3.04170 −0.269907 −0.134954 0.990852i \(-0.543089\pi\)
−0.134954 + 0.990852i \(0.543089\pi\)
\(128\) 3.99772 6.92426i 0.353352 0.612024i
\(129\) 0 0
\(130\) 7.38025 + 12.7830i 0.647291 + 1.12114i
\(131\) −3.26176 −0.284981 −0.142490 0.989796i \(-0.545511\pi\)
−0.142490 + 0.989796i \(0.545511\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −6.93223 −0.598854
\(135\) 0 0
\(136\) 7.36245 12.7521i 0.631325 1.09349i
\(137\) −20.9338 −1.78849 −0.894246 0.447575i \(-0.852288\pi\)
−0.894246 + 0.447575i \(0.852288\pi\)
\(138\) 0 0
\(139\) 8.31195 14.3967i 0.705010 1.22111i −0.261677 0.965155i \(-0.584276\pi\)
0.966688 0.255958i \(-0.0823910\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 2.12997 3.68921i 0.178743 0.309592i
\(143\) 1.89780 3.28708i 0.158702 0.274880i
\(144\) 0 0
\(145\) −4.80009 8.31401i −0.398626 0.690441i
\(146\) −0.674681 1.16858i −0.0558370 0.0967124i
\(147\) 0 0
\(148\) −1.51513 + 2.62429i −0.124543 + 0.215715i
\(149\) −1.12844 −0.0924456 −0.0462228 0.998931i \(-0.514718\pi\)
−0.0462228 + 0.998931i \(0.514718\pi\)
\(150\) 0 0
\(151\) −19.6295 −1.59743 −0.798714 0.601711i \(-0.794486\pi\)
−0.798714 + 0.601711i \(0.794486\pi\)
\(152\) −10.3103 17.8580i −0.836278 1.44848i
\(153\) 0 0
\(154\) 0 0
\(155\) −3.38622 5.86511i −0.271988 0.471097i
\(156\) 0 0
\(157\) 4.66619 + 8.08207i 0.372402 + 0.645020i 0.989935 0.141526i \(-0.0452009\pi\)
−0.617532 + 0.786545i \(0.711868\pi\)
\(158\) 0.652586 + 1.13031i 0.0519170 + 0.0899228i
\(159\) 0 0
\(160\) 3.06529 + 5.30924i 0.242332 + 0.419732i
\(161\) 0 0
\(162\) 0 0
\(163\) −8.45056 14.6368i −0.661899 1.14644i −0.980116 0.198425i \(-0.936417\pi\)
0.318217 0.948018i \(-0.396916\pi\)
\(164\) −2.06478 −0.161232
\(165\) 0 0
\(166\) −9.50460 −0.737700
\(167\) 2.57319 4.45689i 0.199119 0.344885i −0.749124 0.662430i \(-0.769525\pi\)
0.948243 + 0.317545i \(0.102859\pi\)
\(168\) 0 0
\(169\) 1.31385 + 2.27566i 0.101066 + 0.175051i
\(170\) −11.2360 19.4613i −0.861760 1.49261i
\(171\) 0 0
\(172\) −1.50027 + 2.59855i −0.114395 + 0.198138i
\(173\) −4.86834 + 8.43222i −0.370133 + 0.641090i −0.989586 0.143945i \(-0.954021\pi\)
0.619453 + 0.785034i \(0.287355\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.93458 + 3.35079i −0.145825 + 0.252576i
\(177\) 0 0
\(178\) −15.6542 −1.17333
\(179\) 0.687990 1.19163i 0.0514228 0.0890668i −0.839168 0.543872i \(-0.816958\pi\)
0.890591 + 0.454805i \(0.150291\pi\)
\(180\) 0 0
\(181\) 5.66560 0.421120 0.210560 0.977581i \(-0.432471\pi\)
0.210560 + 0.977581i \(0.432471\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 12.9131 0.951967
\(185\) 17.2142 + 29.8158i 1.26561 + 2.19210i
\(186\) 0 0
\(187\) −2.88928 + 5.00438i −0.211285 + 0.365956i
\(188\) −0.196508 −0.0143318
\(189\) 0 0
\(190\) −31.4696 −2.28304
\(191\) −12.5065 + 21.6618i −0.904936 + 1.56740i −0.0839339 + 0.996471i \(0.526748\pi\)
−0.821003 + 0.570925i \(0.806585\pi\)
\(192\) 0 0
\(193\) −8.76688 15.1847i −0.631054 1.09302i −0.987337 0.158640i \(-0.949289\pi\)
0.356282 0.934378i \(-0.384044\pi\)
\(194\) 14.2064 1.01996
\(195\) 0 0
\(196\) 0 0
\(197\) 19.7540 1.40741 0.703707 0.710490i \(-0.251527\pi\)
0.703707 + 0.710490i \(0.251527\pi\)
\(198\) 0 0
\(199\) −9.51110 + 16.4737i −0.674224 + 1.16779i 0.302471 + 0.953158i \(0.402188\pi\)
−0.976695 + 0.214631i \(0.931145\pi\)
\(200\) 22.3180 1.57812
\(201\) 0 0
\(202\) −1.03671 + 1.79563i −0.0729425 + 0.126340i
\(203\) 0 0
\(204\) 0 0
\(205\) −11.7295 + 20.3161i −0.819225 + 1.41894i
\(206\) −1.51796 + 2.62919i −0.105761 + 0.183184i
\(207\) 0 0
\(208\) 5.28667 + 9.15678i 0.366565 + 0.634908i
\(209\) 4.04613 + 7.00810i 0.279876 + 0.484760i
\(210\) 0 0
\(211\) 3.71809 6.43993i 0.255964 0.443343i −0.709193 0.705015i \(-0.750940\pi\)
0.965157 + 0.261672i \(0.0842738\pi\)
\(212\) −0.691283 −0.0474775
\(213\) 0 0
\(214\) −2.89043 −0.197585
\(215\) 17.0454 + 29.5234i 1.16248 + 2.01348i
\(216\) 0 0
\(217\) 0 0
\(218\) −0.597658 1.03517i −0.0404785 0.0701108i
\(219\) 0 0
\(220\) −0.644767 1.11677i −0.0434702 0.0752925i
\(221\) 7.89559 + 13.6756i 0.531115 + 0.919918i
\(222\) 0 0
\(223\) −1.64565 2.85034i −0.110201 0.190873i 0.805650 0.592391i \(-0.201816\pi\)
−0.915851 + 0.401518i \(0.868483\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1.55110 + 2.68659i 0.103178 + 0.178709i
\(227\) −18.0169 −1.19583 −0.597913 0.801561i \(-0.704003\pi\)
−0.597913 + 0.801561i \(0.704003\pi\)
\(228\) 0 0
\(229\) −4.25491 −0.281173 −0.140586 0.990068i \(-0.544899\pi\)
−0.140586 + 0.990068i \(0.544899\pi\)
\(230\) 9.85347 17.0667i 0.649718 1.12535i
\(231\) 0 0
\(232\) −4.08848 7.08146i −0.268422 0.464920i
\(233\) −7.35275 12.7353i −0.481695 0.834320i 0.518084 0.855330i \(-0.326645\pi\)
−0.999779 + 0.0210095i \(0.993312\pi\)
\(234\) 0 0
\(235\) −1.11631 + 1.93351i −0.0728203 + 0.126128i
\(236\) 1.27439 2.20730i 0.0829555 0.143683i
\(237\) 0 0
\(238\) 0 0
\(239\) −7.08187 + 12.2662i −0.458088 + 0.793432i −0.998860 0.0477377i \(-0.984799\pi\)
0.540772 + 0.841169i \(0.318132\pi\)
\(240\) 0 0
\(241\) −7.93503 −0.511140 −0.255570 0.966791i \(-0.582263\pi\)
−0.255570 + 0.966791i \(0.582263\pi\)
\(242\) −6.24657 + 10.8194i −0.401545 + 0.695496i
\(243\) 0 0
\(244\) −2.99755 −0.191899
\(245\) 0 0
\(246\) 0 0
\(247\) 22.1139 1.40707
\(248\) −2.88422 4.99561i −0.183148 0.317221i
\(249\) 0 0
\(250\) 5.57210 9.65115i 0.352410 0.610392i
\(251\) 8.05097 0.508173 0.254087 0.967181i \(-0.418225\pi\)
0.254087 + 0.967181i \(0.418225\pi\)
\(252\) 0 0
\(253\) −5.06755 −0.318594
\(254\) −1.97691 + 3.42411i −0.124042 + 0.214848i
\(255\) 0 0
\(256\) 3.62969 + 6.28681i 0.226856 + 0.392926i
\(257\) −17.5537 −1.09497 −0.547486 0.836815i \(-0.684415\pi\)
−0.547486 + 0.836815i \(0.684415\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −3.52393 −0.218545
\(261\) 0 0
\(262\) −2.11993 + 3.67183i −0.130970 + 0.226846i
\(263\) 23.3486 1.43973 0.719867 0.694112i \(-0.244203\pi\)
0.719867 + 0.694112i \(0.244203\pi\)
\(264\) 0 0
\(265\) −3.92701 + 6.80177i −0.241234 + 0.417830i
\(266\) 0 0
\(267\) 0 0
\(268\) 0.827504 1.43328i 0.0505478 0.0875514i
\(269\) −0.269244 + 0.466344i −0.0164161 + 0.0284335i −0.874117 0.485716i \(-0.838559\pi\)
0.857701 + 0.514149i \(0.171892\pi\)
\(270\) 0 0
\(271\) −7.20749 12.4837i −0.437824 0.758334i 0.559697 0.828697i \(-0.310917\pi\)
−0.997521 + 0.0703635i \(0.977584\pi\)
\(272\) −8.04863 13.9406i −0.488020 0.845275i
\(273\) 0 0
\(274\) −13.6056 + 23.5656i −0.821945 + 1.42365i
\(275\) −8.75835 −0.528148
\(276\) 0 0
\(277\) 21.9066 1.31624 0.658121 0.752912i \(-0.271351\pi\)
0.658121 + 0.752912i \(0.271351\pi\)
\(278\) −10.8045 18.7139i −0.648009 1.12238i
\(279\) 0 0
\(280\) 0 0
\(281\) 0.776622 + 1.34515i 0.0463294 + 0.0802449i 0.888260 0.459341i \(-0.151914\pi\)
−0.841931 + 0.539586i \(0.818581\pi\)
\(282\) 0 0
\(283\) −1.32571 2.29619i −0.0788051 0.136495i 0.823930 0.566692i \(-0.191777\pi\)
−0.902735 + 0.430198i \(0.858444\pi\)
\(284\) 0.508510 + 0.880765i 0.0301745 + 0.0522638i
\(285\) 0 0
\(286\) −2.46689 4.27279i −0.145870 0.252655i
\(287\) 0 0
\(288\) 0 0
\(289\) −3.52056 6.09778i −0.207091 0.358693i
\(290\) −12.4790 −0.732793
\(291\) 0 0
\(292\) 0.322148 0.0188523
\(293\) −5.19314 + 8.99478i −0.303386 + 0.525481i −0.976901 0.213694i \(-0.931451\pi\)
0.673514 + 0.739174i \(0.264784\pi\)
\(294\) 0 0
\(295\) −14.4789 25.0783i −0.842996 1.46011i
\(296\) 14.6622 + 25.3956i 0.852221 + 1.47609i
\(297\) 0 0
\(298\) −0.733415 + 1.27031i −0.0424856 + 0.0735872i
\(299\) −6.92409 + 11.9929i −0.400431 + 0.693566i
\(300\) 0 0
\(301\) 0 0
\(302\) −12.7579 + 22.0974i −0.734137 + 1.27156i
\(303\) 0 0
\(304\) −22.5425 −1.29290
\(305\) −17.0283 + 29.4939i −0.975039 + 1.68882i
\(306\) 0 0
\(307\) 10.6425 0.607400 0.303700 0.952768i \(-0.401778\pi\)
0.303700 + 0.952768i \(0.401778\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −8.80331 −0.499994
\(311\) 6.85479 + 11.8728i 0.388699 + 0.673247i 0.992275 0.124059i \(-0.0395912\pi\)
−0.603576 + 0.797306i \(0.706258\pi\)
\(312\) 0 0
\(313\) 10.6090 18.3752i 0.599653 1.03863i −0.393219 0.919445i \(-0.628638\pi\)
0.992872 0.119185i \(-0.0380282\pi\)
\(314\) 12.1309 0.684586
\(315\) 0 0
\(316\) −0.311598 −0.0175288
\(317\) 1.78521 3.09208i 0.100268 0.173669i −0.811527 0.584315i \(-0.801363\pi\)
0.911795 + 0.410646i \(0.134697\pi\)
\(318\) 0 0
\(319\) 1.60446 + 2.77901i 0.0898326 + 0.155595i
\(320\) 31.1198 1.73965
\(321\) 0 0
\(322\) 0 0
\(323\) −33.6670 −1.87328
\(324\) 0 0
\(325\) −11.9671 + 20.7276i −0.663813 + 1.14976i
\(326\) −21.9693 −1.21677
\(327\) 0 0
\(328\) −9.99062 + 17.3043i −0.551639 + 0.955468i
\(329\) 0 0
\(330\) 0 0
\(331\) 11.9728 20.7375i 0.658085 1.13984i −0.323026 0.946390i \(-0.604700\pi\)
0.981111 0.193446i \(-0.0619666\pi\)
\(332\) 1.13457 1.96513i 0.0622675 0.107851i
\(333\) 0 0
\(334\) −3.34482 5.79339i −0.183020 0.317000i
\(335\) −9.40168 16.2842i −0.513669 0.889700i
\(336\) 0 0
\(337\) −13.7468 + 23.8102i −0.748838 + 1.29703i 0.199542 + 0.979889i \(0.436055\pi\)
−0.948380 + 0.317137i \(0.897279\pi\)
\(338\) 3.41568 0.185788
\(339\) 0 0
\(340\) 5.36497 0.290956
\(341\) 1.13187 + 1.96045i 0.0612940 + 0.106164i
\(342\) 0 0
\(343\) 0 0
\(344\) 14.5184 + 25.1466i 0.782779 + 1.35581i
\(345\) 0 0
\(346\) 6.32822 + 10.9608i 0.340207 + 0.589256i
\(347\) −2.56412 4.44119i −0.137649 0.238416i 0.788957 0.614448i \(-0.210621\pi\)
−0.926606 + 0.376033i \(0.877288\pi\)
\(348\) 0 0
\(349\) 7.56980 + 13.1113i 0.405202 + 0.701830i 0.994345 0.106198i \(-0.0338679\pi\)
−0.589143 + 0.808029i \(0.700535\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.02459 1.77465i −0.0546110 0.0945889i
\(353\) 32.9757 1.75512 0.877559 0.479468i \(-0.159171\pi\)
0.877559 + 0.479468i \(0.159171\pi\)
\(354\) 0 0
\(355\) 11.5549 0.613269
\(356\) 1.86865 3.23659i 0.0990381 0.171539i
\(357\) 0 0
\(358\) −0.894299 1.54897i −0.0472651 0.0818656i
\(359\) −12.0178 20.8154i −0.634274 1.09859i −0.986669 0.162743i \(-0.947966\pi\)
0.352395 0.935851i \(-0.385367\pi\)
\(360\) 0 0
\(361\) −14.0735 + 24.3760i −0.740711 + 1.28295i
\(362\) 3.68227 6.37789i 0.193536 0.335214i
\(363\) 0 0
\(364\) 0 0
\(365\) 1.83004 3.16972i 0.0957886 0.165911i
\(366\) 0 0
\(367\) 2.65501 0.138590 0.0692952 0.997596i \(-0.477925\pi\)
0.0692952 + 0.997596i \(0.477925\pi\)
\(368\) 7.05830 12.2253i 0.367939 0.637290i
\(369\) 0 0
\(370\) 44.7524 2.32657
\(371\) 0 0
\(372\) 0 0
\(373\) −31.9183 −1.65267 −0.826334 0.563181i \(-0.809577\pi\)
−0.826334 + 0.563181i \(0.809577\pi\)
\(374\) 3.75569 + 6.50505i 0.194202 + 0.336368i
\(375\) 0 0
\(376\) −0.950821 + 1.64687i −0.0490348 + 0.0849308i
\(377\) 8.76909 0.451631
\(378\) 0 0
\(379\) 30.2681 1.55477 0.777384 0.629027i \(-0.216546\pi\)
0.777384 + 0.629027i \(0.216546\pi\)
\(380\) 3.75653 6.50651i 0.192706 0.333777i
\(381\) 0 0
\(382\) 16.2568 + 28.1576i 0.831771 + 1.44067i
\(383\) 1.73305 0.0885548 0.0442774 0.999019i \(-0.485901\pi\)
0.0442774 + 0.999019i \(0.485901\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −22.7917 −1.16006
\(387\) 0 0
\(388\) −1.69583 + 2.93726i −0.0860925 + 0.149117i
\(389\) 11.0835 0.561956 0.280978 0.959714i \(-0.409341\pi\)
0.280978 + 0.959714i \(0.409341\pi\)
\(390\) 0 0
\(391\) 10.5415 18.2584i 0.533107 0.923368i
\(392\) 0 0
\(393\) 0 0
\(394\) 12.8388 22.2375i 0.646811 1.12031i
\(395\) −1.77011 + 3.06592i −0.0890639 + 0.154263i
\(396\) 0 0
\(397\) 12.6696 + 21.9443i 0.635867 + 1.10135i 0.986331 + 0.164777i \(0.0526905\pi\)
−0.350464 + 0.936576i \(0.613976\pi\)
\(398\) 12.3632 + 21.4137i 0.619712 + 1.07337i
\(399\) 0 0
\(400\) 12.1990 21.1293i 0.609951 1.05647i
\(401\) 34.8244 1.73905 0.869524 0.493890i \(-0.164425\pi\)
0.869524 + 0.493890i \(0.164425\pi\)
\(402\) 0 0
\(403\) 6.18614 0.308154
\(404\) −0.247505 0.428690i −0.0123138 0.0213281i
\(405\) 0 0
\(406\) 0 0
\(407\) −5.75394 9.96612i −0.285212 0.494002i
\(408\) 0 0
\(409\) −9.12308 15.8016i −0.451107 0.781341i 0.547348 0.836905i \(-0.315638\pi\)
−0.998455 + 0.0555643i \(0.982304\pi\)
\(410\) 15.2469 + 26.4083i 0.752989 + 1.30422i
\(411\) 0 0
\(412\) −0.362400 0.627695i −0.0178541 0.0309243i
\(413\) 0 0
\(414\) 0 0
\(415\) −12.8904 22.3268i −0.632765 1.09598i
\(416\) −5.59985 −0.274555
\(417\) 0 0
\(418\) 10.5189 0.514496
\(419\) −4.20719 + 7.28708i −0.205535 + 0.355997i −0.950303 0.311326i \(-0.899227\pi\)
0.744768 + 0.667323i \(0.232560\pi\)
\(420\) 0 0
\(421\) 0.144291 + 0.249919i 0.00703230 + 0.0121803i 0.869520 0.493897i \(-0.164428\pi\)
−0.862488 + 0.506078i \(0.831095\pi\)
\(422\) −4.83304 8.37108i −0.235269 0.407498i
\(423\) 0 0
\(424\) −3.34483 + 5.79341i −0.162439 + 0.281353i
\(425\) 18.2191 31.5564i 0.883757 1.53071i
\(426\) 0 0
\(427\) 0 0
\(428\) 0.345031 0.597612i 0.0166777 0.0288866i
\(429\) 0 0
\(430\) 44.3136 2.13699
\(431\) −6.74795 + 11.6878i −0.325037 + 0.562981i −0.981520 0.191360i \(-0.938710\pi\)
0.656482 + 0.754341i \(0.272044\pi\)
\(432\) 0 0
\(433\) 4.85211 0.233177 0.116589 0.993180i \(-0.462804\pi\)
0.116589 + 0.993180i \(0.462804\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0.285371 0.0136668
\(437\) −14.7623 25.5690i −0.706174 1.22313i
\(438\) 0 0
\(439\) 1.27397 2.20657i 0.0608031 0.105314i −0.834022 0.551732i \(-0.813967\pi\)
0.894825 + 0.446418i \(0.147301\pi\)
\(440\) −12.4790 −0.594914
\(441\) 0 0
\(442\) 20.5265 0.976347
\(443\) −0.322753 + 0.559025i −0.0153345 + 0.0265601i −0.873591 0.486661i \(-0.838215\pi\)
0.858256 + 0.513221i \(0.171548\pi\)
\(444\) 0 0
\(445\) −21.2306 36.7725i −1.00643 1.74319i
\(446\) −4.27826 −0.202581
\(447\) 0 0
\(448\) 0 0
\(449\) 5.22658 0.246658 0.123329 0.992366i \(-0.460643\pi\)
0.123329 + 0.992366i \(0.460643\pi\)
\(450\) 0 0
\(451\) 3.92066 6.79079i 0.184617 0.319766i
\(452\) −0.740624 −0.0348360
\(453\) 0 0
\(454\) −11.7099 + 20.2821i −0.549571 + 0.951885i
\(455\) 0 0
\(456\) 0 0
\(457\) 1.43037 2.47748i 0.0669101 0.115892i −0.830630 0.556825i \(-0.812019\pi\)
0.897540 + 0.440934i \(0.145353\pi\)
\(458\) −2.76542 + 4.78985i −0.129220 + 0.223815i
\(459\) 0 0
\(460\) 2.35242 + 4.07452i 0.109682 + 0.189975i
\(461\) 1.82624 + 3.16314i 0.0850566 + 0.147322i 0.905415 0.424527i \(-0.139560\pi\)
−0.820359 + 0.571849i \(0.806226\pi\)
\(462\) 0 0
\(463\) −15.4052 + 26.6825i −0.715939 + 1.24004i 0.246657 + 0.969103i \(0.420668\pi\)
−0.962596 + 0.270940i \(0.912666\pi\)
\(464\) −8.93905 −0.414985
\(465\) 0 0
\(466\) −19.1153 −0.885498
\(467\) −10.2885 17.8202i −0.476096 0.824622i 0.523529 0.852008i \(-0.324615\pi\)
−0.999625 + 0.0273858i \(0.991282\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 1.45107 + 2.51332i 0.0669327 + 0.115931i
\(471\) 0 0
\(472\) −12.3324 21.3604i −0.567647 0.983193i
\(473\) −5.69752 9.86839i −0.261972 0.453749i
\(474\) 0 0
\(475\) −25.5139 44.1914i −1.17066 2.02764i
\(476\) 0 0
\(477\) 0 0
\(478\) 9.20552 + 15.9444i 0.421051 + 0.729281i
\(479\) 25.1832 1.15065 0.575325 0.817925i \(-0.304876\pi\)
0.575325 + 0.817925i \(0.304876\pi\)
\(480\) 0 0
\(481\) −31.4478 −1.43390
\(482\) −5.15726 + 8.93264i −0.234907 + 0.406871i
\(483\) 0 0
\(484\) −1.49131 2.58303i −0.0677869 0.117410i
\(485\) 19.2671 + 33.3716i 0.874875 + 1.51533i
\(486\) 0 0
\(487\) 16.3807 28.3723i 0.742282 1.28567i −0.209173 0.977879i \(-0.567077\pi\)
0.951454 0.307791i \(-0.0995896\pi\)
\(488\) −14.5039 + 25.1215i −0.656560 + 1.13720i
\(489\) 0 0
\(490\) 0 0
\(491\) −1.76000 + 3.04841i −0.0794278 + 0.137573i −0.903003 0.429634i \(-0.858643\pi\)
0.823575 + 0.567207i \(0.191976\pi\)
\(492\) 0 0
\(493\) −13.3504 −0.601272
\(494\) 14.3726 24.8941i 0.646654 1.12004i
\(495\) 0 0
\(496\) −6.30605 −0.283150
\(497\) 0 0
\(498\) 0 0
\(499\) 15.6416 0.700216 0.350108 0.936709i \(-0.386145\pi\)
0.350108 + 0.936709i \(0.386145\pi\)
\(500\) 1.33029 + 2.30412i 0.0594922 + 0.103044i
\(501\) 0 0
\(502\) 5.23262 9.06316i 0.233543 0.404509i
\(503\) −36.5427 −1.62936 −0.814678 0.579913i \(-0.803086\pi\)
−0.814678 + 0.579913i \(0.803086\pi\)
\(504\) 0 0
\(505\) −5.62404 −0.250267
\(506\) −3.29358 + 5.70465i −0.146418 + 0.253603i
\(507\) 0 0
\(508\) −0.471969 0.817474i −0.0209402 0.0362696i
\(509\) −37.6458 −1.66862 −0.834311 0.551294i \(-0.814134\pi\)
−0.834311 + 0.551294i \(0.814134\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 25.4272 1.12373
\(513\) 0 0
\(514\) −11.4088 + 19.7606i −0.503221 + 0.871604i
\(515\) −8.23480 −0.362869
\(516\) 0 0
\(517\) 0.373135 0.646289i 0.0164105 0.0284237i
\(518\) 0 0
\(519\) 0 0
\(520\) −17.0508 + 29.5329i −0.747728 + 1.29510i
\(521\) 7.17115 12.4208i 0.314174 0.544165i −0.665088 0.746765i \(-0.731606\pi\)
0.979262 + 0.202600i \(0.0649392\pi\)
\(522\) 0 0
\(523\) 5.24222 + 9.07980i 0.229226 + 0.397032i 0.957579 0.288171i \(-0.0930471\pi\)
−0.728353 + 0.685202i \(0.759714\pi\)
\(524\) −0.506114 0.876616i −0.0221097 0.0382951i
\(525\) 0 0
\(526\) 15.1751 26.2840i 0.661665 1.14604i
\(527\) −9.41802 −0.410256
\(528\) 0 0
\(529\) −4.51110 −0.196135
\(530\) 5.10461 + 8.84144i 0.221730 + 0.384047i
\(531\) 0 0
\(532\) 0 0
\(533\) −10.7141 18.5573i −0.464078 0.803807i
\(534\) 0 0
\(535\) −3.92007 6.78976i −0.169479 0.293547i
\(536\) −8.00788 13.8701i −0.345888 0.599095i
\(537\) 0 0
\(538\) 0.349983 + 0.606188i 0.0150888 + 0.0261346i
\(539\) 0 0
\(540\) 0 0
\(541\) 23.0461 + 39.9170i 0.990830 + 1.71617i 0.612430 + 0.790524i \(0.290192\pi\)
0.378399 + 0.925643i \(0.376475\pi\)
\(542\) −18.7376 −0.804851
\(543\) 0 0
\(544\) 8.52542 0.365525
\(545\) 1.62112 2.80786i 0.0694411 0.120275i
\(546\) 0 0
\(547\) −12.1793 21.0951i −0.520747 0.901961i −0.999709 0.0241250i \(-0.992320\pi\)
0.478962 0.877836i \(-0.341013\pi\)
\(548\) −3.24822 5.62607i −0.138757 0.240334i
\(549\) 0 0
\(550\) −5.69237 + 9.85947i −0.242723 + 0.420409i
\(551\) −9.34790 + 16.1910i −0.398234 + 0.689761i
\(552\) 0 0
\(553\) 0 0
\(554\) 14.2379 24.6608i 0.604911 1.04774i
\(555\) 0 0
\(556\) 5.15894 0.218788
\(557\) 15.2888 26.4809i 0.647806 1.12203i −0.335840 0.941919i \(-0.609020\pi\)
0.983646 0.180114i \(-0.0576466\pi\)
\(558\) 0 0
\(559\) −31.1394 −1.31706
\(560\) 0 0
\(561\) 0 0
\(562\) 2.01902 0.0851672
\(563\) −4.41357 7.64452i −0.186010 0.322178i 0.757907 0.652363i \(-0.226222\pi\)
−0.943916 + 0.330185i \(0.892889\pi\)
\(564\) 0 0
\(565\) −4.20730 + 7.28725i −0.177002 + 0.306577i
\(566\) −3.44650 −0.144867
\(567\) 0 0
\(568\) 9.84186 0.412955
\(569\) 3.56027 6.16658i 0.149254 0.258516i −0.781698 0.623658i \(-0.785646\pi\)
0.930952 + 0.365141i \(0.118979\pi\)
\(570\) 0 0
\(571\) −3.33181 5.77086i −0.139432 0.241503i 0.787850 0.615867i \(-0.211194\pi\)
−0.927282 + 0.374364i \(0.877861\pi\)
\(572\) 1.17790 0.0492503
\(573\) 0 0
\(574\) 0 0
\(575\) 31.9548 1.33261
\(576\) 0 0
\(577\) 3.95629 6.85250i 0.164703 0.285273i −0.771847 0.635808i \(-0.780667\pi\)
0.936550 + 0.350535i \(0.114000\pi\)
\(578\) −9.15254 −0.380696
\(579\) 0 0
\(580\) 1.48963 2.58011i 0.0618533 0.107133i
\(581\) 0 0
\(582\) 0 0
\(583\) 1.31263 2.27354i 0.0543634 0.0941602i
\(584\) 1.55874 2.69981i 0.0645010 0.111719i
\(585\) 0 0
\(586\) 6.75042 + 11.6921i 0.278857 + 0.482995i
\(587\) −9.13891 15.8291i −0.377203 0.653335i 0.613451 0.789733i \(-0.289781\pi\)
−0.990654 + 0.136398i \(0.956447\pi\)
\(588\) 0 0
\(589\) −6.59447 + 11.4220i −0.271720 + 0.470633i
\(590\) −37.6415 −1.54968
\(591\) 0 0
\(592\) 32.0574 1.31755
\(593\) 14.1908 + 24.5792i 0.582745 + 1.00934i 0.995152 + 0.0983450i \(0.0313549\pi\)
−0.412407 + 0.911000i \(0.635312\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.175096 0.303275i −0.00717222 0.0124226i
\(597\) 0 0
\(598\) 9.00044 + 15.5892i 0.368055 + 0.637490i
\(599\) 4.69451 + 8.13113i 0.191813 + 0.332229i 0.945851 0.324601i \(-0.105230\pi\)
−0.754038 + 0.656830i \(0.771897\pi\)
\(600\) 0 0
\(601\) 6.31432 + 10.9367i 0.257566 + 0.446118i 0.965589 0.260071i \(-0.0837460\pi\)
−0.708023 + 0.706189i \(0.750413\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −3.04584 5.27555i −0.123934 0.214659i
\(605\) −33.8871 −1.37771
\(606\) 0 0
\(607\) −24.0265 −0.975207 −0.487604 0.873065i \(-0.662129\pi\)
−0.487604 + 0.873065i \(0.662129\pi\)
\(608\) 5.96947 10.3394i 0.242094 0.419319i
\(609\) 0 0
\(610\) 22.1347 + 38.3383i 0.896206 + 1.55227i
\(611\) −1.01967 1.76613i −0.0412516 0.0714498i
\(612\) 0 0
\(613\) 14.2708 24.7177i 0.576390 0.998337i −0.419499 0.907756i \(-0.637794\pi\)
0.995889 0.0905814i \(-0.0288725\pi\)
\(614\) 6.91695 11.9805i 0.279145 0.483494i
\(615\) 0 0
\(616\) 0 0
\(617\) 6.05549 10.4884i 0.243785 0.422248i −0.718004 0.696039i \(-0.754944\pi\)
0.961789 + 0.273791i \(0.0882776\pi\)
\(618\) 0 0
\(619\) 26.5739 1.06810 0.534048 0.845454i \(-0.320670\pi\)
0.534048 + 0.845454i \(0.320670\pi\)
\(620\) 1.05085 1.82013i 0.0422033 0.0730983i
\(621\) 0 0
\(622\) 17.8207 0.714545
\(623\) 0 0
\(624\) 0 0
\(625\) −6.92971 −0.277188
\(626\) −13.7903 23.8855i −0.551170 0.954655i
\(627\) 0 0
\(628\) −1.44807 + 2.50813i −0.0577843 + 0.100085i
\(629\) 47.8774 1.90900
\(630\) 0 0
\(631\) 3.30962 0.131754 0.0658770 0.997828i \(-0.479015\pi\)
0.0658770 + 0.997828i \(0.479015\pi\)
\(632\) −1.50769 + 2.61140i −0.0599727 + 0.103876i
\(633\) 0 0
\(634\) −2.32055 4.01931i −0.0921608 0.159627i
\(635\) −10.7245 −0.425591
\(636\) 0 0
\(637\) 0 0
\(638\) 4.17119 0.165139
\(639\) 0 0
\(640\) 14.0953 24.4138i 0.557167 0.965041i
\(641\) −32.5844 −1.28701 −0.643503 0.765443i \(-0.722520\pi\)
−0.643503 + 0.765443i \(0.722520\pi\)
\(642\) 0 0
\(643\) −21.5327 + 37.2957i −0.849166 + 1.47080i 0.0327873 + 0.999462i \(0.489562\pi\)
−0.881953 + 0.471337i \(0.843772\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −21.8814 + 37.8997i −0.860912 + 1.49114i
\(647\) −23.0988 + 40.0082i −0.908106 + 1.57289i −0.0914143 + 0.995813i \(0.529139\pi\)
−0.816692 + 0.577074i \(0.804195\pi\)
\(648\) 0 0
\(649\) 4.83968 + 8.38256i 0.189974 + 0.329044i
\(650\) 15.5556 + 26.9432i 0.610143 + 1.05680i
\(651\) 0 0
\(652\) 2.62248 4.54228i 0.102704 0.177889i
\(653\) −32.0005 −1.25228 −0.626138 0.779713i \(-0.715365\pi\)
−0.626138 + 0.779713i \(0.715365\pi\)
\(654\) 0 0
\(655\) −11.5004 −0.449359
\(656\) 10.9217 + 18.9170i 0.426422 + 0.738585i
\(657\) 0 0
\(658\) 0 0
\(659\) −19.2070 33.2674i −0.748197 1.29591i −0.948686 0.316219i \(-0.897587\pi\)
0.200490 0.979696i \(-0.435747\pi\)
\(660\) 0 0
\(661\) 14.0130 + 24.2712i 0.545043 + 0.944042i 0.998604 + 0.0528170i \(0.0168200\pi\)
−0.453561 + 0.891225i \(0.649847\pi\)
\(662\) −15.5631 26.9561i −0.604878 1.04768i
\(663\) 0 0
\(664\) −10.9794 19.0169i −0.426083 0.737998i
\(665\) 0 0
\(666\) 0 0
\(667\) −5.85386 10.1392i −0.226662 0.392591i
\(668\) 1.59709 0.0617932
\(669\) 0 0
\(670\) −24.4420 −0.944275
\(671\) 5.69183 9.85853i 0.219730 0.380584i
\(672\) 0 0
\(673\) 0.796281 + 1.37920i 0.0306944 + 0.0531642i 0.880965 0.473182i \(-0.156895\pi\)
−0.850270 + 0.526347i \(0.823561\pi\)
\(674\) 17.8691 + 30.9503i 0.688293 + 1.19216i
\(675\) 0 0
\(676\) −0.407731 + 0.706211i −0.0156820 + 0.0271619i
\(677\) 21.0167 36.4020i 0.807737 1.39904i −0.106691 0.994292i \(-0.534025\pi\)
0.914428 0.404749i \(-0.132641\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 25.9588 44.9620i 0.995476 1.72421i
\(681\) 0 0
\(682\) 2.94256 0.112676
\(683\) 17.8645 30.9422i 0.683565 1.18397i −0.290321 0.956929i \(-0.593762\pi\)
0.973886 0.227039i \(-0.0729046\pi\)
\(684\) 0 0
\(685\) −73.8092 −2.82010
\(686\) 0 0
\(687\) 0 0
\(688\) 31.7430 1.21019
\(689\) −3.58704 6.21294i −0.136655 0.236694i
\(690\) 0 0
\(691\) −25.5675 + 44.2841i −0.972632 + 1.68465i −0.285094 + 0.958499i \(0.592025\pi\)
−0.687538 + 0.726149i \(0.741308\pi\)
\(692\) −3.02161 −0.114864
\(693\) 0 0
\(694\) −6.66606 −0.253040
\(695\) 29.3066 50.7606i 1.11166 1.92546i
\(696\) 0 0
\(697\) 16.3115 + 28.2524i 0.617843 + 1.07014i
\(698\) 19.6795 0.744881
\(699\) 0 0
\(700\) 0 0
\(701\) 24.5761 0.928226 0.464113 0.885776i \(-0.346373\pi\)
0.464113 + 0.885776i \(0.346373\pi\)
\(702\) 0 0
\(703\) 33.5236 58.0645i 1.26437 2.18995i
\(704\) −10.4020 −0.392040
\(705\) 0 0
\(706\) 21.4321 37.1215i 0.806607 1.39708i
\(707\) 0 0
\(708\) 0 0
\(709\) −15.4488 + 26.7581i −0.580192 + 1.00492i 0.415265 + 0.909701i \(0.363689\pi\)
−0.995456 + 0.0952206i \(0.969644\pi\)
\(710\) 7.50992 13.0076i 0.281842 0.488165i
\(711\) 0 0
\(712\) −18.0832 31.3210i −0.677697 1.17380i
\(713\) −4.12960 7.15268i −0.154655 0.267870i
\(714\) 0 0
\(715\) 6.69133 11.5897i 0.250242 0.433431i
\(716\) 0.427011 0.0159582
\(717\) 0 0
\(718\) −31.2431 −1.16598
\(719\) 3.05690 + 5.29471i 0.114003 + 0.197459i 0.917381 0.398011i \(-0.130299\pi\)
−0.803378 + 0.595470i \(0.796966\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 18.2938 + 31.6857i 0.680823 + 1.17922i
\(723\) 0 0
\(724\) 0.879109 + 1.52266i 0.0326718 + 0.0565893i
\(725\) −10.1174 17.5238i −0.375749 0.650816i
\(726\) 0 0
\(727\) 22.2492 + 38.5367i 0.825176 + 1.42925i 0.901785 + 0.432186i \(0.142257\pi\)
−0.0766087 + 0.997061i \(0.524409\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −2.37882 4.12023i −0.0880440 0.152497i
\(731\) 47.4079 1.75344
\(732\) 0 0
\(733\) 9.83708 0.363341 0.181670 0.983359i \(-0.441850\pi\)
0.181670 + 0.983359i \(0.441850\pi\)
\(734\) 1.72559 2.98881i 0.0636926 0.110319i
\(735\) 0 0
\(736\) 3.73821 + 6.47478i 0.137792 + 0.238663i
\(737\) 3.14257 + 5.44309i 0.115758 + 0.200499i
\(738\) 0 0
\(739\) −7.42464 + 12.8598i −0.273120 + 0.473057i −0.969659 0.244461i \(-0.921389\pi\)
0.696539 + 0.717519i \(0.254722\pi\)
\(740\) −5.34212 + 9.25282i −0.196380 + 0.340140i
\(741\) 0 0
\(742\) 0 0
\(743\) 3.04201 5.26892i 0.111601 0.193298i −0.804815 0.593525i \(-0.797736\pi\)
0.916416 + 0.400228i \(0.131069\pi\)
\(744\) 0 0
\(745\) −3.97871 −0.145769
\(746\) −20.7449 + 35.9311i −0.759523 + 1.31553i
\(747\) 0 0
\(748\) −1.79328 −0.0655686
\(749\) 0 0
\(750\) 0 0
\(751\) 22.2010 0.810127 0.405063 0.914289i \(-0.367249\pi\)
0.405063 + 0.914289i \(0.367249\pi\)
\(752\) 1.03944 + 1.80036i 0.0379044 + 0.0656523i
\(753\) 0 0
\(754\) 5.69934 9.87156i 0.207558 0.359501i
\(755\) −69.2106 −2.51883
\(756\) 0 0
\(757\) 25.0464 0.910329 0.455164 0.890407i \(-0.349581\pi\)
0.455164 + 0.890407i \(0.349581\pi\)
\(758\) 19.6723 34.0735i 0.714531 1.23760i
\(759\) 0 0
\(760\) −36.3526 62.9645i −1.31865 2.28396i
\(761\) −6.75264 −0.244783 −0.122392 0.992482i \(-0.539056\pi\)
−0.122392 + 0.992482i \(0.539056\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −7.76233 −0.280831
\(765\) 0 0
\(766\) 1.12637 1.95094i 0.0406975 0.0704902i
\(767\) 26.4510 0.955089
\(768\) 0 0
\(769\) 21.0805 36.5125i 0.760182 1.31667i −0.182575 0.983192i \(-0.558443\pi\)
0.942757 0.333482i \(-0.108224\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 2.72065 4.71230i 0.0979183 0.169600i
\(773\) 1.64926 2.85660i 0.0593197 0.102745i −0.834841 0.550492i \(-0.814440\pi\)
0.894160 + 0.447747i \(0.147774\pi\)
\(774\) 0 0
\(775\) −7.13728 12.3621i −0.256379 0.444061i
\(776\) 16.4108 + 28.4243i 0.589112 + 1.02037i
\(777\) 0 0
\(778\) 7.20356 12.4769i 0.258260 0.447320i
\(779\) 45.6851 1.63684
\(780\) 0 0
\(781\) −3.86229 −0.138203
\(782\) −13.7026 23.7336i −0.490004 0.848713i
\(783\) 0 0
\(784\) 0 0
\(785\) 16.4522 + 28.4961i 0.587205 + 1.01707i
\(786\) 0 0
\(787\) −3.36455 5.82757i −0.119933 0.207731i 0.799808 0.600256i \(-0.204935\pi\)
−0.919741 + 0.392526i \(0.871601\pi\)
\(788\) 3.06515 + 5.30900i 0.109192 + 0.189125i
\(789\) 0 0
\(790\) 2.30092 + 3.98530i 0.0818629 + 0.141791i
\(791\) 0 0
\(792\) 0 0
\(793\) −15.5542 26.9406i −0.552345 0.956689i
\(794\) 32.9376 1.16891
\(795\) 0 0
\(796\) −5.90321 −0.209234
\(797\) −8.86302