Properties

Label 1323.2.g.h.667.10
Level $1323$
Weight $2$
Character 1323.667
Analytic conductor $10.564$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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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 667.10
Character \(\chi\) \(=\) 1323.667
Dual form 1323.2.g.h.361.10

$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.649936 + 1.12572i 0.459574 + 0.796006i 0.998938 0.0460668i \(-0.0146687\pi\)
−0.539364 + 0.842073i \(0.681335\pi\)
\(3\) 0 0
\(4\) 0.155166 0.268756i 0.0775831 0.134378i
\(5\) −3.52584 −1.57680 −0.788402 0.615160i \(-0.789091\pi\)
−0.788402 + 0.615160i \(0.789091\pi\)
\(6\) 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 \(-0.0192951\pi\)
−0.551546 + 0.834145i \(0.685962\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.64151 + 2.84319i 0.410379 + 0.710797i
\(17\) −2.45159 4.24627i −0.594597 1.02987i −0.993604 0.112924i \(-0.963978\pi\)
0.399006 0.916948i \(-0.369355\pi\)
\(18\) 0 0
\(19\) 3.43318 5.94645i 0.787627 1.36421i −0.139791 0.990181i \(-0.544643\pi\)
0.927417 0.374028i \(-0.122024\pi\)
\(20\) −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 −0.964297 0.264822i \(-0.914687\pi\)
0.711491 + 0.702695i \(0.248020\pi\)
\(30\) 0 0
\(31\) 0.960401 1.66346i 0.172493 0.298767i −0.766798 0.641889i \(-0.778151\pi\)
0.939291 + 0.343122i \(0.111484\pi\)
\(32\) 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 −0.115228 0.993339i \(-0.536760\pi\)
0.917871 0.396879i \(-0.129907\pi\)
\(38\) 8.92540 1.44789
\(39\) 0 0
\(40\) −10.5886 −1.67420
\(41\) 3.32673 + 5.76206i 0.519547 + 0.899883i 0.999742 + 0.0227205i \(0.00723278\pi\)
−0.480194 + 0.877162i \(0.659434\pi\)
\(42\) 0 0
\(43\) 4.83441 8.37344i 0.737240 1.27694i −0.216493 0.976284i \(-0.569462\pi\)
0.953734 0.300653i \(-0.0972047\pi\)
\(44\) −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 \(-0.151961\pi\)
−0.842010 + 0.539461i \(0.818628\pi\)
\(48\) 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 0.779336 0.626606i \(-0.215557\pi\)
−0.932325 + 0.361621i \(0.882223\pi\)
\(54\) 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 −0.464558 0.885543i \(-0.653787\pi\)
0.999181 0.0404521i \(-0.0128798\pi\)
\(60\) 0 0
\(61\) 4.82958 + 8.36508i 0.618364 + 1.07104i 0.989784 + 0.142573i \(0.0455376\pi\)
−0.371420 + 0.928465i \(0.621129\pi\)
\(62\) 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 −0.981667 0.190604i \(-0.938955\pi\)
0.655901 + 0.754847i \(0.272289\pi\)
\(68\) −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 \(-0.186015\pi\)
−0.894800 + 0.446467i \(0.852682\pi\)
\(74\) 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 0.836401 0.548118i \(-0.184656\pi\)
−0.892885 + 0.450285i \(0.851322\pi\)
\(80\) −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 \(-0.701893\pi\)
0.993883 + 0.110442i \(0.0352267\pi\)
\(84\) 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 −0.347541 0.937665i \(-0.612983\pi\)
0.985812 0.167853i \(-0.0536834\pi\)
\(90\) 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 0.443076 + 0.896484i \(0.353887\pi\)
−0.997916 + 0.0645275i \(0.979446\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.15313 1.99728i 0.115313 0.199728i
\(101\) 1.59509 0.158718 0.0793588 0.996846i \(-0.474713\pi\)
0.0793588 + 0.996846i \(0.474713\pi\)
\(102\) 0 0
\(103\) 2.33556 0.230129 0.115065 0.993358i \(-0.463292\pi\)
0.115065 + 0.993358i \(0.463292\pi\)
\(104\) 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 −0.914750 0.404021i \(-0.867612\pi\)
0.807267 + 0.590186i \(0.200946\pi\)
\(108\) 0 0
\(109\) 0.459782 + 0.796366i 0.0440391 + 0.0762780i 0.887205 0.461376i \(-0.152644\pi\)
−0.843166 + 0.537654i \(0.819311\pi\)
\(110\) 2.70070 + 4.67774i 0.257501 + 0.446005i
\(111\) 0 0
\(112\) 0 0
\(113\) −1.19327 2.06681i −0.112254 0.194429i 0.804425 0.594054i \(-0.202474\pi\)
−0.916679 + 0.399625i \(0.869140\pi\)
\(114\) 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 \(-0.454489\pi\)
0.142490 + 0.989796i \(0.454489\pi\)
\(132\) 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 −0.966688 0.255958i \(-0.917609\pi\)
0.261677 0.965155i \(-0.415724\pi\)
\(140\) 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 \(-0.954799\pi\)
0.617532 + 0.786545i \(0.288132\pi\)
\(158\) 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 0.318217 + 0.948018i \(0.396916\pi\)
−0.980116 + 0.198425i \(0.936417\pi\)
\(164\) 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 \(-0.230475\pi\)
−0.948243 + 0.317545i \(0.897141\pi\)
\(168\) 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 \(-0.0459787\pi\)
−0.619453 + 0.785034i \(0.712645\pi\)
\(174\) 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 0.890591 0.454805i \(-0.150291\pi\)
−0.839168 + 0.543872i \(0.816958\pi\)
\(180\) 0 0
\(181\) −5.66560 −0.421120 −0.210560 0.977581i \(-0.567529\pi\)
−0.210560 + 0.977581i \(0.567529\pi\)
\(182\) 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 −0.821003 0.570925i \(-0.806585\pi\)
−0.0839339 0.996471i \(-0.526748\pi\)
\(192\) 0 0
\(193\) −8.76688 + 15.1847i −0.631054 + 1.09302i 0.356282 + 0.934378i \(0.384044\pi\)
−0.987337 + 0.158640i \(0.949289\pi\)
\(194\) −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 0.976695 + 0.214631i \(0.0688550\pi\)
−0.302471 + 0.953158i \(0.597812\pi\)
\(200\) 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 0.965157 0.261672i \(-0.0842738\pi\)
−0.709193 + 0.705015i \(0.750940\pi\)
\(212\) −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 \(-0.798184\pi\)
0.915851 + 0.401518i \(0.131517\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1.55110 2.68659i 0.103178 0.178709i
\(227\) 18.0169 1.19583 0.597913 0.801561i \(-0.295997\pi\)
0.597913 + 0.801561i \(0.295997\pi\)
\(228\) 0 0
\(229\) 4.25491 0.281173 0.140586 0.990068i \(-0.455101\pi\)
0.140586 + 0.990068i \(0.455101\pi\)
\(230\) −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 −0.999779 0.0210095i \(-0.993312\pi\)
0.518084 + 0.855330i \(0.326645\pi\)
\(234\) 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 0.540772 0.841169i \(-0.318132\pi\)
−0.998860 + 0.0477377i \(0.984799\pi\)
\(240\) 0 0
\(241\) 7.93503 0.511140 0.255570 0.966791i \(-0.417737\pi\)
0.255570 + 0.966791i \(0.417737\pi\)
\(242\) −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 \(-0.581775\pi\)
−0.254087 + 0.967181i \(0.581775\pi\)
\(252\) 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 \(-0.315585\pi\)
0.547486 + 0.836815i \(0.315585\pi\)
\(258\) 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 \(-0.161441\pi\)
−0.857701 + 0.514149i \(0.828108\pi\)
\(270\) 0 0
\(271\) 7.20749 12.4837i 0.437824 0.758334i −0.559697 0.828697i \(-0.689083\pi\)
0.997521 + 0.0703635i \(0.0224159\pi\)
\(272\) 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 −0.841931 0.539586i \(-0.818581\pi\)
0.888260 + 0.459341i \(0.151914\pi\)
\(282\) 0 0
\(283\) 1.32571 2.29619i 0.0788051 0.136495i −0.823930 0.566692i \(-0.808223\pi\)
0.902735 + 0.430198i \(0.141556\pi\)
\(284\) 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 \(-0.0685494\pi\)
−0.673514 + 0.739174i \(0.735216\pi\)
\(294\) 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 \(-0.598222\pi\)
−0.303700 + 0.952768i \(0.598222\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −8.80331 −0.499994
\(311\) −6.85479 + 11.8728i −0.388699 + 0.673247i −0.992275 0.124059i \(-0.960409\pi\)
0.603576 + 0.797306i \(0.293742\pi\)
\(312\) 0 0
\(313\) −10.6090 18.3752i −0.599653 1.03863i −0.992872 0.119185i \(-0.961972\pi\)
0.393219 0.919445i \(-0.371362\pi\)
\(314\) −12.1309 −0.684586
\(315\) 0 0
\(316\) −0.311598 −0.0175288
\(317\) 1.78521 + 3.09208i 0.100268 + 0.173669i 0.911795 0.410646i \(-0.134697\pi\)
−0.811527 + 0.584315i \(0.801363\pi\)
\(318\) 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 0.981111 + 0.193446i \(0.0619666\pi\)
−0.323026 + 0.946390i \(0.604700\pi\)
\(332\) −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 −0.948380 0.317137i \(-0.897279\pi\)
0.199542 0.979889i \(-0.436055\pi\)
\(338\) 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 −0.926606 0.376033i \(-0.877288\pi\)
0.788957 + 0.614448i \(0.210621\pi\)
\(348\) 0 0
\(349\) −7.56980 + 13.1113i −0.405202 + 0.701830i −0.994345 0.106198i \(-0.966132\pi\)
0.589143 + 0.808029i \(0.299465\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.02459 + 1.77465i −0.0546110 + 0.0945889i
\(353\) −32.9757 −1.75512 −0.877559 0.479468i \(-0.840829\pi\)
−0.877559 + 0.479468i \(0.840829\pi\)
\(354\) 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 0.352395 + 0.935851i \(0.385367\pi\)
−0.986669 + 0.162743i \(0.947966\pi\)
\(360\) 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 \(-0.522075\pi\)
−0.0692952 + 0.997596i \(0.522075\pi\)
\(368\) 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 \(-0.514099\pi\)
−0.0442774 + 0.999019i \(0.514099\pi\)
\(384\) 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 0.350464 + 0.936576i \(0.386024\pi\)
−0.986331 + 0.164777i \(0.947310\pi\)
\(398\) −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 \(-0.684362\pi\)
0.998455 + 0.0555643i \(0.0176958\pi\)
\(410\) 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 \(-0.100773\pi\)
−0.744768 + 0.667323i \(0.767440\pi\)
\(420\) 0 0
\(421\) 0.144291 0.249919i 0.00703230 0.0121803i −0.862488 0.506078i \(-0.831095\pi\)
0.869520 + 0.493897i \(0.164428\pi\)
\(422\) −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 0.656482 0.754341i \(-0.272044\pi\)
−0.981520 + 0.191360i \(0.938710\pi\)
\(432\) 0 0
\(433\) −4.85211 −0.233177 −0.116589 0.993180i \(-0.537196\pi\)
−0.116589 + 0.993180i \(0.537196\pi\)
\(434\) 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 \(-0.186033\pi\)
−0.894825 + 0.446418i \(0.852699\pi\)
\(440\) 12.4790 0.594914
\(441\) 0 0
\(442\) 20.5265 0.976347
\(443\) −0.322753 0.559025i −0.0153345 0.0265601i 0.858256 0.513221i \(-0.171548\pi\)
−0.873591 + 0.486661i \(0.838215\pi\)
\(444\) 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 0.897540 0.440934i \(-0.145353\pi\)
−0.830630 + 0.556825i \(0.812019\pi\)
\(458\) 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 \(-0.860440\pi\)
0.820359 + 0.571849i \(0.193774\pi\)
\(462\) 0 0
\(463\) −15.4052 26.6825i −0.715939 1.24004i −0.962596 0.270940i \(-0.912666\pi\)
0.246657 0.969103i \(-0.420668\pi\)
\(464\) −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 \(-0.675385\pi\)
0.999625 + 0.0273858i \(0.00871825\pi\)
\(468\) 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 \(-0.695124\pi\)
−0.575325 + 0.817925i \(0.695124\pi\)
\(480\) 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 0.951454 + 0.307791i \(0.0995896\pi\)
−0.209173 + 0.977879i \(0.567077\pi\)
\(488\) 14.5039 + 25.1215i 0.656560 + 1.13720i
\(489\) 0 0
\(490\) 0 0
\(491\) −1.76000 3.04841i −0.0794278 0.137573i 0.823575 0.567207i \(-0.191976\pi\)
−0.903003 + 0.429634i \(0.858643\pi\)
\(492\) 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 \(-0.196914\pi\)
0.814678 + 0.579913i \(0.196914\pi\)
\(504\) 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 \(-0.185866\pi\)
0.834311 + 0.551294i \(0.185866\pi\)
\(510\) 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 \(-0.268394\pi\)
−0.979262 + 0.202600i \(0.935061\pi\)
\(522\) 0 0
\(523\) −5.24222 + 9.07980i −0.229226 + 0.397032i −0.957579 0.288171i \(-0.906953\pi\)
0.728353 + 0.685202i \(0.240286\pi\)
\(524\) 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 0.378399 0.925643i \(-0.376475\pi\)
0.612430 0.790524i \(-0.290192\pi\)
\(542\) 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 0.478962 + 0.877836i \(0.341013\pi\)
−0.999709 + 0.0241250i \(0.992320\pi\)
\(548\) −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 0.983646 + 0.180114i \(0.0576466\pi\)
−0.335840 + 0.941919i \(0.609020\pi\)
\(558\) 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 \(-0.773778\pi\)
0.943916 + 0.330185i \(0.107111\pi\)
\(564\) 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 0.930952 0.365141i \(-0.118979\pi\)
−0.781698 + 0.623658i \(0.785646\pi\)
\(570\) 0 0
\(571\) −3.33181 + 5.77086i −0.139432 + 0.241503i −0.927282 0.374364i \(-0.877861\pi\)
0.787850 + 0.615867i \(0.211194\pi\)
\(572\) −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 \(-0.219333\pi\)
−0.936550 + 0.350535i \(0.886000\pi\)
\(578\) −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 \(-0.710219\pi\)
0.990654 + 0.136398i \(0.0435525\pi\)
\(588\) 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 0.412407 + 0.911000i \(0.364688\pi\)
−0.995152 + 0.0983450i \(0.968645\pi\)
\(594\) 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 −0.754038 0.656830i \(-0.771897\pi\)
0.945851 + 0.324601i \(0.105230\pi\)
\(600\) 0 0
\(601\) −6.31432 + 10.9367i −0.257566 + 0.446118i −0.965589 0.260071i \(-0.916254\pi\)
0.708023 + 0.706189i \(0.249587\pi\)
\(602\) 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 \(-0.337871\pi\)
0.487604 + 0.873065i \(0.337871\pi\)
\(608\) −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 0.995889 + 0.0905814i \(0.0288725\pi\)
−0.419499 + 0.907756i \(0.637794\pi\)
\(614\) −6.91695 11.9805i −0.279145 0.483494i
\(615\) 0 0
\(616\) 0 0
\(617\) 6.05549 + 10.4884i 0.243785 + 0.422248i 0.961789 0.273791i \(-0.0882776\pi\)
−0.718004 + 0.696039i \(0.754944\pi\)
\(618\) 0 0
\(619\) −26.5739 −1.06810 −0.534048 0.845454i \(-0.679330\pi\)
−0.534048 + 0.845454i \(0.679330\pi\)
\(620\) 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 0.881953 + 0.471337i \(0.156228\pi\)
−0.0327873 + 0.999462i \(0.510438\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −21.8814 37.8997i −0.860912 1.49114i
\(647\) 23.0988 + 40.0082i 0.908106 + 1.57289i 0.816692 + 0.577074i \(0.195805\pi\)
0.0914143 + 0.995813i \(0.470861\pi\)
\(648\) 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 0.200490 + 0.979696i \(0.435747\pi\)
−0.948686 + 0.316219i \(0.897587\pi\)
\(660\) 0 0
\(661\) −14.0130 + 24.2712i −0.545043 + 0.944042i 0.453561 + 0.891225i \(0.350153\pi\)
−0.998604 + 0.0528170i \(0.983180\pi\)
\(662\) −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 −0.850270 0.526347i \(-0.823561\pi\)
0.880965 + 0.473182i \(0.156895\pi\)
\(674\) 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 −0.914428 0.404749i \(-0.867359\pi\)
0.106691 0.994292i \(-0.465975\pi\)
\(678\) 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 0.973886 + 0.227039i \(0.0729046\pi\)
−0.290321 + 0.956929i \(0.593762\pi\)
\(684\) 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 0.687538 + 0.726149i \(0.258692\pi\)
0.285094 + 0.958499i \(0.407975\pi\)
\(692\) 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 −0.995456 0.0952206i \(-0.969644\pi\)
0.415265 0.909701i \(-0.363689\pi\)
\(710\) −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 \(-0.869701\pi\)
0.803378 + 0.595470i \(0.203034\pi\)
\(720\) 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 0.0766087 + 0.997061i \(0.475591\pi\)
−0.901785 + 0.432186i \(0.857743\pi\)
\(728\) 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 \(-0.558150\pi\)
−0.181670 + 0.983359i \(0.558150\pi\)
\(734\) −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 0.696539 0.717519i \(-0.254722\pi\)
−0.969659 + 0.244461i \(0.921389\pi\)
\(740\) 5.34212 + 9.25282i 0.196380 + 0.340140i
\(741\) 0 0
\(742\) 0 0
\(743\) 3.04201 + 5.26892i 0.111601 + 0.193298i 0.916416 0.400228i \(-0.131069\pi\)
−0.804815 + 0.593525i \(0.797736\pi\)
\(744\) 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 \(-0.460944\pi\)
0.122392 + 0.992482i \(0.460944\pi\)
\(762\) 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 −0.942757 0.333482i \(-0.891776\pi\)
0.182575 0.983192i \(-0.441557\pi\)
\(770\) 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 \(-0.185560\pi\)
−0.894160 + 0.447747i \(0.852226\pi\)
\(774\) 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 \(-0.795065\pi\)
0.919741 + 0.392526i \(0.128399\pi\)
\(788\) 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