Properties

Label 1323.2.h.h.802.4
Level $1323$
Weight $2$
Character 1323.802
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.h (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 802.4
Character \(\chi\) \(=\) 1323.802
Dual form 1323.2.h.h.226.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.29987 q^{2} -0.310333 q^{4} +(-1.76292 + 3.05347i) q^{5} +3.00314 q^{8} +O(q^{10})\) \(q-1.29987 q^{2} -0.310333 q^{4} +(-1.76292 + 3.05347i) q^{5} +3.00314 q^{8} +(2.29157 - 3.96912i) q^{10} +(0.589267 + 1.02064i) q^{11} +(-1.61030 - 2.78913i) q^{13} -3.28303 q^{16} +(2.45159 - 4.24627i) q^{17} +(-3.43318 - 5.94645i) q^{19} +(0.547092 - 0.947591i) q^{20} +(-0.765972 - 1.32670i) q^{22} +(-2.14994 + 3.72380i) q^{23} +(-3.71578 - 6.43592i) q^{25} +(2.09319 + 3.62551i) q^{26} +(-1.36140 + 2.35802i) q^{29} +1.92080 q^{31} -1.73876 q^{32} +(-3.18675 + 5.51961i) q^{34} +(4.88229 + 8.45637i) q^{37} +(4.46270 + 7.72962i) q^{38} +(-5.29429 + 9.16998i) q^{40} +(-3.32673 - 5.76206i) q^{41} +(4.83441 - 8.37344i) q^{43} +(-0.182869 - 0.316738i) q^{44} +(2.79464 - 4.84046i) q^{46} +0.633218 q^{47} +(4.83004 + 8.36587i) q^{50} +(0.499729 + 0.865557i) q^{52} +(-1.11378 + 1.92912i) q^{53} -4.15533 q^{55} +(1.76965 - 3.06512i) q^{58} +8.21304 q^{59} +9.65916 q^{61} -2.49680 q^{62} +8.82622 q^{64} +11.3553 q^{65} +5.33301 q^{67} +(-0.760807 + 1.31776i) q^{68} +3.27719 q^{71} +(0.519036 - 0.898997i) q^{73} +(-6.34635 - 10.9922i) q^{74} +(1.06543 + 1.84538i) q^{76} +1.00408 q^{79} +(5.78772 - 10.0246i) q^{80} +(4.32432 + 7.48994i) q^{82} +(-3.65598 + 6.33234i) q^{83} +(8.64391 + 14.9717i) q^{85} +(-6.28411 + 10.8844i) q^{86} +(1.76965 + 3.06512i) q^{88} +(-6.02144 - 10.4294i) q^{89} +(0.667195 - 1.15562i) q^{92} -0.823103 q^{94} +24.2097 q^{95} +(5.46454 - 9.46487i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 24q^{4} + 24q^{8} + O(q^{10}) \) \( 24q + 8q^{2} + 24q^{4} + 24q^{8} - 20q^{11} + 24q^{16} - 32q^{23} - 12q^{25} - 16q^{29} + 96q^{32} - 12q^{37} - 56q^{44} + 24q^{46} + 4q^{50} - 32q^{53} + 96q^{64} + 120q^{65} + 24q^{67} + 112q^{71} - 68q^{74} - 24q^{79} + 12q^{85} - 76q^{86} - 16q^{92} + 128q^{95} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.29987 −0.919148 −0.459574 0.888139i \(-0.651998\pi\)
−0.459574 + 0.888139i \(0.651998\pi\)
\(3\) 0 0
\(4\) −0.310333 −0.155166
\(5\) −1.76292 + 3.05347i −0.788402 + 1.36555i 0.138543 + 0.990356i \(0.455758\pi\)
−0.926945 + 0.375196i \(0.877575\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 3.00314 1.06177
\(9\) 0 0
\(10\) 2.29157 3.96912i 0.724659 1.25515i
\(11\) 0.589267 + 1.02064i 0.177671 + 0.307735i 0.941082 0.338178i \(-0.109810\pi\)
−0.763412 + 0.645912i \(0.776477\pi\)
\(12\) 0 0
\(13\) −1.61030 2.78913i −0.446618 0.773564i 0.551546 0.834145i \(-0.314038\pi\)
−0.998163 + 0.0605803i \(0.980705\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −3.28303 −0.820757
\(17\) 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
\(23\) −2.14994 + 3.72380i −0.448293 + 0.776466i −0.998275 0.0587106i \(-0.981301\pi\)
0.549982 + 0.835176i \(0.314634\pi\)
\(24\) 0 0
\(25\) −3.71578 6.43592i −0.743156 1.28718i
\(26\) 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
\(31\) 1.92080 0.344986 0.172493 0.985011i \(-0.444818\pi\)
0.172493 + 0.985011i \(0.444818\pi\)
\(32\) −1.73876 −0.307372
\(33\) 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 \(0.536760\pi\)
\(38\) 4.46270 + 7.72962i 0.723946 + 1.25391i
\(39\) 0 0
\(40\) −5.29429 + 9.16998i −0.837101 + 1.44990i
\(41\) −3.32673 5.76206i −0.519547 0.899883i −0.999742 0.0227205i \(-0.992767\pi\)
0.480194 0.877162i \(-0.340566\pi\)
\(42\) 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
\(47\) 0.633218 0.0923644 0.0461822 0.998933i \(-0.485295\pi\)
0.0461822 + 0.998933i \(0.485295\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 4.83004 + 8.36587i 0.683071 + 1.18311i
\(51\) 0 0
\(52\) 0.499729 + 0.865557i 0.0693000 + 0.120031i
\(53\) −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
\(58\) 1.76965 3.06512i 0.232366 0.402471i
\(59\) 8.21304 1.06925 0.534623 0.845091i \(-0.320454\pi\)
0.534623 + 0.845091i \(0.320454\pi\)
\(60\) 0 0
\(61\) 9.65916 1.23673 0.618364 0.785892i \(-0.287796\pi\)
0.618364 + 0.785892i \(0.287796\pi\)
\(62\) −2.49680 −0.317093
\(63\) 0 0
\(64\) 8.82622 1.10328
\(65\) 11.3553 1.40846
\(66\) 0 0
\(67\) 5.33301 0.651531 0.325766 0.945451i \(-0.394378\pi\)
0.325766 + 0.945451i \(0.394378\pi\)
\(68\) −0.760807 + 1.31776i −0.0922614 + 0.159801i
\(69\) 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 \(0.147318\pi\)
\(74\) −6.34635 10.9922i −0.737748 1.27782i
\(75\) 0 0
\(76\) 1.06543 + 1.84538i 0.122213 + 0.211679i
\(77\) 0 0
\(78\) 0 0
\(79\) 1.00408 0.112968 0.0564838 0.998404i \(-0.482011\pi\)
0.0564838 + 0.998404i \(0.482011\pi\)
\(80\) 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 −0.993883 0.110442i \(-0.964773\pi\)
0.592587 + 0.805506i \(0.298107\pi\)
\(84\) 0 0
\(85\) 8.64391 + 14.9717i 0.937563 + 1.62391i
\(86\) −6.28411 + 10.8844i −0.677633 + 1.17369i
\(87\) 0 0
\(88\) 1.76965 + 3.06512i 0.188645 + 0.326743i
\(89\) −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
\(94\) −0.823103 −0.0848966
\(95\) 24.2097 2.48387
\(96\) 0 0
\(97\) 5.46454 9.46487i 0.554840 0.961012i −0.443076 0.896484i \(-0.646113\pi\)
0.997916 0.0645275i \(-0.0205540\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.15313 + 1.99728i 0.115313 + 0.199728i
\(101\) 0.797546 + 1.38139i 0.0793588 + 0.137453i 0.902973 0.429696i \(-0.141379\pi\)
−0.823615 + 0.567150i \(0.808046\pi\)
\(102\) 0 0
\(103\) 1.16778 2.02265i 0.115065 0.199298i −0.802741 0.596328i \(-0.796626\pi\)
0.917806 + 0.397030i \(0.129959\pi\)
\(104\) −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 \(0.152644\pi\)
\(110\) 5.40139 0.515003
\(111\) 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
\(115\) −7.58033 13.1295i −0.706870 1.22433i
\(116\) 0.422488 0.731770i 0.0392270 0.0679432i
\(117\) 0 0
\(118\) −10.6759 −0.982796
\(119\) 0 0
\(120\) 0 0
\(121\) 4.80553 8.32342i 0.436866 0.756674i
\(122\) −12.5557 −1.13674
\(123\) 0 0
\(124\) −0.596087 −0.0535302
\(125\) 8.57330 0.766819
\(126\) 0 0
\(127\) −3.04170 −0.269907 −0.134954 0.990852i \(-0.543089\pi\)
−0.134954 + 0.990852i \(0.543089\pi\)
\(128\) −7.99544 −0.706704
\(129\) 0 0
\(130\) −14.7605 −1.29458
\(131\) 1.63088 2.82476i 0.142490 0.246801i −0.785943 0.618298i \(-0.787822\pi\)
0.928434 + 0.371498i \(0.121156\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −6.93223 −0.598854
\(135\) 0 0
\(136\) 7.36245 12.7521i 0.631325 1.09349i
\(137\) 10.4669 + 18.1292i 0.894246 + 1.54888i 0.834734 + 0.550653i \(0.185621\pi\)
0.0595120 + 0.998228i \(0.481046\pi\)
\(138\) 0 0
\(139\) 8.31195 + 14.3967i 0.705010 + 1.22111i 0.966688 + 0.255958i \(0.0823910\pi\)
−0.261677 + 0.965155i \(0.584276\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −4.25993 −0.357486
\(143\) 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
\(149\) 0.564221 0.977260i 0.0462228 0.0800602i −0.841988 0.539496i \(-0.818615\pi\)
0.888211 + 0.459435i \(0.151948\pi\)
\(150\) 0 0
\(151\) 9.81476 + 16.9997i 0.798714 + 1.38341i 0.920454 + 0.390851i \(0.127819\pi\)
−0.121740 + 0.992562i \(0.538847\pi\)
\(152\) −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
\(157\) −9.33237 −0.744804 −0.372402 0.928071i \(-0.621466\pi\)
−0.372402 + 0.928071i \(0.621466\pi\)
\(158\) −1.30517 −0.103834
\(159\) 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 \(-0.396916\pi\)
\(164\) 1.03239 + 1.78815i 0.0806162 + 0.139631i
\(165\) 0 0
\(166\) 4.75230 8.23123i 0.368850 0.638867i
\(167\) 2.57319 + 4.45689i 0.199119 + 0.344885i 0.948243 0.317545i \(-0.102859\pi\)
−0.749124 + 0.662430i \(0.769525\pi\)
\(168\) 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
\(173\) 9.73669 0.740266 0.370133 0.928979i \(-0.379312\pi\)
0.370133 + 0.928979i \(0.379312\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.93458 3.35079i −0.145825 0.252576i
\(177\) 0 0
\(178\) 7.82710 + 13.5569i 0.586666 + 1.01613i
\(179\) 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
\(184\) −6.45655 + 11.1831i −0.475983 + 0.824427i
\(185\) −34.4283 −2.53122
\(186\) 0 0
\(187\) 5.77856 0.422570
\(188\) −0.196508 −0.0143318
\(189\) 0 0
\(190\) −31.4696 −2.28304
\(191\) 25.0129 1.80987 0.904936 0.425547i \(-0.139918\pi\)
0.904936 + 0.425547i \(0.139918\pi\)
\(192\) 0 0
\(193\) 17.5338 1.26211 0.631054 0.775739i \(-0.282623\pi\)
0.631054 + 0.775739i \(0.282623\pi\)
\(194\) −7.10321 + 12.3031i −0.509981 + 0.883312i
\(195\) 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 \(0.931145\pi\)
\(200\) −11.1590 19.3279i −0.789060 1.36669i
\(201\) 0 0
\(202\) −1.03671 1.79563i −0.0729425 0.126340i
\(203\) 0 0
\(204\) 0 0
\(205\) 23.4590 1.63845
\(206\) −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 \(0.750940\pi\)
\(212\) 0.345642 0.598669i 0.0237388 0.0411168i
\(213\) 0 0
\(214\) 1.44521 + 2.50318i 0.0987927 + 0.171114i
\(215\) 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
\(220\) 1.28953 0.0869403
\(221\) −15.7912 −1.06223
\(222\) 0 0
\(223\) −1.64565 + 2.85034i −0.110201 + 0.190873i −0.915851 0.401518i \(-0.868483\pi\)
0.805650 + 0.592391i \(0.201816\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1.55110 + 2.68659i 0.103178 + 0.178709i
\(227\) 9.00847 + 15.6031i 0.597913 + 1.03562i 0.993129 + 0.117028i \(0.0373366\pi\)
−0.395215 + 0.918589i \(0.629330\pi\)
\(228\) 0 0
\(229\) 2.12746 3.68486i 0.140586 0.243503i −0.787131 0.616785i \(-0.788435\pi\)
0.927718 + 0.373283i \(0.121768\pi\)
\(230\) 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
\(236\) −2.54877 −0.165911
\(237\) 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
\(241\) 3.96752 + 6.87194i 0.255570 + 0.442661i 0.965050 0.262065i \(-0.0844035\pi\)
−0.709480 + 0.704726i \(0.751070\pi\)
\(242\) −6.24657 + 10.8194i −0.401545 + 0.695496i
\(243\) 0 0
\(244\) −2.99755 −0.191899
\(245\) 0 0
\(246\) 0 0
\(247\) −11.0569 + 19.1512i −0.703536 + 1.21856i
\(248\) 5.76843 0.366296
\(249\) 0 0
\(250\) −11.1442 −0.704821
\(251\) 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
\(254\) 3.95382 0.248085
\(255\) 0 0
\(256\) −7.25938 −0.453712
\(257\) 8.77687 15.2020i 0.547486 0.948273i −0.450960 0.892544i \(-0.648918\pi\)
0.998446 0.0557293i \(-0.0177484\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −3.52393 −0.218545
\(261\) 0 0
\(262\) −2.11993 + 3.67183i −0.130970 + 0.226846i
\(263\) −11.6743 20.2205i −0.719867 1.24685i −0.961052 0.276367i \(-0.910869\pi\)
0.241185 0.970479i \(-0.422464\pi\)
\(264\) 0 0
\(265\) −3.92701 6.80177i −0.241234 0.417830i
\(266\) 0 0
\(267\) 0 0
\(268\) −1.65501 −0.101096
\(269\) −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
\(275\) 4.37918 7.58495i 0.264074 0.457390i
\(276\) 0 0
\(277\) −10.9533 18.9717i −0.658121 1.13990i −0.981101 0.193494i \(-0.938018\pi\)
0.322980 0.946406i \(-0.395315\pi\)
\(278\) −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
\(283\) 2.65142 0.157610 0.0788051 0.996890i \(-0.474890\pi\)
0.0788051 + 0.996890i \(0.474890\pi\)
\(284\) −1.01702 −0.0603490
\(285\) 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
\(290\) 6.23951 + 10.8071i 0.366396 + 0.634617i
\(291\) 0 0
\(292\) −0.161074 + 0.278988i −0.00942613 + 0.0163265i
\(293\) −5.19314 8.99478i −0.303386 0.525481i 0.673514 0.739174i \(-0.264784\pi\)
−0.976901 + 0.213694i \(0.931451\pi\)
\(294\) 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
\(299\) 13.8482 0.800861
\(300\) 0 0
\(301\) 0 0
\(302\) −12.7579 22.0974i −0.734137 1.27156i
\(303\) 0 0
\(304\) 11.2712 + 19.5224i 0.646450 + 1.11968i
\(305\) −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
\(310\) 4.40165 7.62389i 0.249997 0.433008i
\(311\) −13.7096 −0.777399 −0.388699 0.921365i \(-0.627075\pi\)
−0.388699 + 0.921365i \(0.627075\pi\)
\(312\) 0 0
\(313\) −21.2179 −1.19931 −0.599653 0.800260i \(-0.704695\pi\)
−0.599653 + 0.800260i \(0.704695\pi\)
\(314\) 12.1309 0.684586
\(315\) 0 0
\(316\) −0.311598 −0.0175288
\(317\) −3.57043 −0.200535 −0.100268 0.994961i \(-0.531970\pi\)
−0.100268 + 0.994961i \(0.531970\pi\)
\(318\) 0 0
\(319\) −3.20892 −0.179665
\(320\) −15.5599 + 26.9506i −0.869826 + 1.50658i
\(321\) 0 0
\(322\) 0 0
\(323\) −33.6670 −1.87328
\(324\) 0 0
\(325\) −11.9671 + 20.7276i −0.663813 + 1.14976i
\(326\) 10.9846 + 19.0260i 0.608383 + 1.05375i
\(327\) 0 0
\(328\) −9.99062 17.3043i −0.551639 0.955468i
\(329\) 0 0
\(330\) 0 0
\(331\) −23.9456 −1.31617 −0.658085 0.752944i \(-0.728633\pi\)
−0.658085 + 0.752944i \(0.728633\pi\)
\(332\) 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 \(-0.436055\pi\)
\(338\) −1.70784 + 2.95806i −0.0928942 + 0.160897i
\(339\) 0 0
\(340\) −2.68249 4.64620i −0.145478 0.251976i
\(341\) 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
\(346\) −12.6564 −0.680415
\(347\) 5.12824 0.275299 0.137649 0.990481i \(-0.456045\pi\)
0.137649 + 0.990481i \(0.456045\pi\)
\(348\) 0 0
\(349\) 7.56980 13.1113i 0.405202 0.701830i −0.589143 0.808029i \(-0.700535\pi\)
0.994345 + 0.106198i \(0.0338679\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.02459 1.77465i −0.0546110 0.0945889i
\(353\) −16.4878 28.5578i −0.877559 1.51998i −0.854011 0.520254i \(-0.825837\pi\)
−0.0235477 0.999723i \(-0.507496\pi\)
\(354\) 0 0
\(355\) −5.77743 + 10.0068i −0.306634 + 0.531106i
\(356\) 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
\(362\) −7.36455 −0.387072
\(363\) 0 0
\(364\) 0 0
\(365\) 1.83004 + 3.16972i 0.0957886 + 0.165911i
\(366\) 0 0
\(367\) −1.32751 2.29931i −0.0692952 0.120023i 0.829296 0.558810i \(-0.188742\pi\)
−0.898591 + 0.438787i \(0.855408\pi\)
\(368\) 7.05830 12.2253i 0.367939 0.637290i
\(369\) 0 0
\(370\) 44.7524 2.32657
\(371\) 0 0
\(372\) 0 0
\(373\) 15.9592 27.6421i 0.826334 1.43125i −0.0745621 0.997216i \(-0.523756\pi\)
0.900896 0.434036i \(-0.142911\pi\)
\(374\) −7.51139 −0.388405
\(375\) 0 0
\(376\) 1.90164 0.0980697
\(377\) 8.76909 0.451631
\(378\) 0 0
\(379\) 30.2681 1.55477 0.777384 0.629027i \(-0.216546\pi\)
0.777384 + 0.629027i \(0.216546\pi\)
\(380\) −7.51307 −0.385412
\(381\) 0 0
\(382\) −32.5136 −1.66354
\(383\) −0.866526 + 1.50087i −0.0442774 + 0.0766907i −0.887315 0.461164i \(-0.847432\pi\)
0.843037 + 0.537855i \(0.180765\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −22.7917 −1.16006
\(387\) 0 0
\(388\) −1.69583 + 2.93726i −0.0860925 + 0.149117i
\(389\) −5.54175 9.59859i −0.280978 0.486668i 0.690648 0.723191i \(-0.257325\pi\)
−0.971626 + 0.236523i \(0.923992\pi\)
\(390\) 0 0
\(391\) 10.5415 + 18.2584i 0.533107 + 0.923368i
\(392\) 0 0
\(393\) 0 0
\(394\) −25.6777 −1.29362
\(395\) −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
\(401\) −17.4122 + 30.1588i −0.869524 + 1.50606i −0.00704089 + 0.999975i \(0.502241\pi\)
−0.862483 + 0.506085i \(0.831092\pi\)
\(402\) 0 0
\(403\) −3.09307 5.35736i −0.154077 0.266869i
\(404\) −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
\(409\) 18.2462 0.902215 0.451107 0.892470i \(-0.351029\pi\)
0.451107 + 0.892470i \(0.351029\pi\)
\(410\) −30.4937 −1.50598
\(411\) 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
\(416\) 2.79992 + 4.84961i 0.137278 + 0.237772i
\(417\) 0 0
\(418\) −5.25945 + 9.10963i −0.257248 + 0.445567i
\(419\) −4.20719 7.28708i −0.205535 0.355997i 0.744768 0.667323i \(-0.232560\pi\)
−0.950303 + 0.311326i \(0.899227\pi\)
\(420\) 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
\(425\) −36.4382 −1.76751
\(426\) 0 0
\(427\) 0 0
\(428\) 0.345031 + 0.597612i 0.0166777 + 0.0288866i
\(429\) 0 0
\(430\) −22.1568 38.3767i −1.06849 1.85069i
\(431\) −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
\(436\) −0.142685 + 0.247138i −0.00683339 + 0.0118358i
\(437\) 29.5245 1.41235
\(438\) 0 0
\(439\) −2.54793 −0.121606 −0.0608031 0.998150i \(-0.519366\pi\)
−0.0608031 + 0.998150i \(0.519366\pi\)
\(440\) −12.4790 −0.594914
\(441\) 0 0
\(442\) 20.5265 0.976347
\(443\) 0.645506 0.0306689 0.0153345 0.999882i \(-0.495119\pi\)
0.0153345 + 0.999882i \(0.495119\pi\)
\(444\) 0 0
\(445\) 42.4613 2.01286
\(446\) 2.13913 3.70508i 0.101291 0.175441i
\(447\) 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
\(452\) 0.370312 + 0.641399i 0.0174180 + 0.0301689i
\(453\) 0 0
\(454\) −11.7099 20.2821i −0.549571 0.951885i
\(455\) 0 0
\(456\) 0 0
\(457\) −2.86075 −0.133820 −0.0669101 0.997759i \(-0.521314\pi\)
−0.0669101 + 0.997759i \(0.521314\pi\)
\(458\) −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 −0.820359 0.571849i \(-0.806226\pi\)
0.905415 + 0.424527i \(0.139560\pi\)
\(462\) 0 0
\(463\) −15.4052 26.6825i −0.715939 1.24004i −0.962596 0.270940i \(-0.912666\pi\)
0.246657 0.969103i \(-0.420668\pi\)
\(464\) 4.46953 7.74145i 0.207493 0.359388i
\(465\) 0 0
\(466\) 9.55764 + 16.5543i 0.442749 + 0.766864i
\(467\) −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
\(472\) 24.6649 1.13529
\(473\) 11.3950 0.523944
\(474\) 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
\(479\) −12.5916 21.8093i −0.575325 0.996492i −0.996006 0.0892833i \(-0.971542\pi\)
0.420682 0.907208i \(-0.361791\pi\)
\(480\) 0 0
\(481\) 15.7239 27.2346i 0.716949 1.24179i
\(482\) −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 \(-0.0995896\pi\)
\(488\) 29.0078 1.31312
\(489\) 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
\(493\) 6.67520 + 11.5618i 0.300636 + 0.520716i
\(494\) 14.3726 24.8941i 0.646654 1.12004i
\(495\) 0 0
\(496\) −6.30605 −0.283150
\(497\) 0 0
\(498\) 0 0
\(499\) −7.82082 + 13.5461i −0.350108 + 0.606405i −0.986268 0.165152i \(-0.947188\pi\)
0.636160 + 0.771557i \(0.280522\pi\)
\(500\) −2.66057 −0.118984
\(501\) 0 0
\(502\) −10.4652 −0.467086
\(503\) −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
\(506\) 6.58716 0.292835
\(507\) 0 0
\(508\) 0.943938 0.0418805
\(509\) 18.8229 32.6023i 0.834311 1.44507i −0.0602789 0.998182i \(-0.519199\pi\)
0.894590 0.446888i \(-0.147468\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 25.4272 1.12373
\(513\) 0 0
\(514\) −11.4088 + 19.7606i −0.503221 + 0.871604i
\(515\) 4.11740 + 7.13155i 0.181434 + 0.314254i
\(516\) 0 0
\(517\) 0.373135 + 0.646289i 0.0164105 + 0.0284237i
\(518\) 0 0
\(519\) 0 0
\(520\) 34.1017 1.49546
\(521\) 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
\(527\) 4.70901 8.15625i 0.205128 0.355292i
\(528\) 0 0
\(529\) 2.25555 + 3.90673i 0.0980674 + 0.169858i
\(530\) 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
\(535\) 7.84014 0.338959
\(536\) 16.0158 0.691776
\(537\) 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 \(0.376475\pi\)
\(542\) 9.36882 + 16.2273i 0.402425 + 0.697021i
\(543\) 0 0
\(544\) −4.26271 + 7.38323i −0.182762 + 0.316554i
\(545\) 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
\(551\) 18.6958 0.796468
\(552\) 0 0
\(553\) 0 0
\(554\) 14.2379 + 24.6608i 0.604911 + 1.04774i
\(555\) 0 0
\(556\) −2.57947 4.46777i −0.109394 0.189476i
\(557\) 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
\(562\) −1.00951 + 1.74852i −0.0425836 + 0.0737570i
\(563\) 8.82714 0.372019 0.186010 0.982548i \(-0.440444\pi\)
0.186010 + 0.982548i \(0.440444\pi\)
\(564\) 0 0
\(565\) 8.41459 0.354005
\(566\) −3.44650 −0.144867
\(567\) 0 0
\(568\) 9.84186 0.412955
\(569\) −7.12055 −0.298509 −0.149254 0.988799i \(-0.547687\pi\)
−0.149254 + 0.988799i \(0.547687\pi\)
\(570\) 0 0
\(571\) 6.66361 0.278863 0.139432 0.990232i \(-0.455472\pi\)
0.139432 + 0.990232i \(0.455472\pi\)
\(572\) −0.588948 + 1.02009i −0.0246252 + 0.0426520i
\(573\) 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 \(0.114000\pi\)
\(578\) 4.57627 + 7.92633i 0.190348 + 0.329692i
\(579\) 0 0
\(580\) 1.48963 + 2.58011i 0.0618533 + 0.107133i
\(581\) 0 0
\(582\) 0 0
\(583\) −2.62525 −0.108727
\(584\) 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 −0.990654 0.136398i \(-0.956447\pi\)
0.613451 + 0.789733i \(0.289781\pi\)
\(588\) 0 0
\(589\) −6.59447 11.4220i −0.271720 0.470633i
\(590\) 18.8208 32.5985i 0.774839 1.34206i
\(591\) 0 0
\(592\) −16.0287 27.7625i −0.658775 1.14103i
\(593\) 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
\(598\) −18.0009 −0.736111
\(599\) −9.38902 −0.383625 −0.191813 0.981432i \(-0.561437\pi\)
−0.191813 + 0.981432i \(0.561437\pi\)
\(600\) 0 0
\(601\) 6.31432 10.9367i 0.257566 0.446118i −0.708023 0.706189i \(-0.750413\pi\)
0.965589 + 0.260071i \(0.0837460\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −3.04584 5.27555i −0.123934 0.214659i
\(605\) 16.9435 + 29.3471i 0.688853 + 1.19313i
\(606\) 0 0
\(607\) 12.0133 20.8076i 0.487604 0.844554i −0.512295 0.858810i \(-0.671204\pi\)
0.999898 + 0.0142555i \(0.00453781\pi\)
\(608\) 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 \(-0.0288725\pi\)
\(614\) −13.8339 −0.558291
\(615\) 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
\(619\) −13.2870 23.0137i −0.534048 0.924998i −0.999209 0.0397721i \(-0.987337\pi\)
0.465161 0.885226i \(-0.345997\pi\)
\(620\) 1.05085 1.82013i 0.0422033 0.0730983i
\(621\) 0 0
\(622\) 17.8207 0.714545
\(623\) 0 0
\(624\) 0 0
\(625\) 3.46486 6.00131i 0.138594 0.240052i
\(626\) 27.5806 1.10234
\(627\) 0 0
\(628\) 2.89614 0.115569
\(629\) 47.8774 1.90900
\(630\) 0 0
\(631\) 3.30962 0.131754 0.0658770 0.997828i \(-0.479015\pi\)
0.0658770 + 0.997828i \(0.479015\pi\)
\(632\) 3.01538 0.119945
\(633\) 0 0
\(634\) 4.64110 0.184322
\(635\) 5.36227 9.28773i 0.212795 0.368572i
\(636\) 0 0
\(637\) 0 0
\(638\) 4.17119 0.165139
\(639\) 0 0
\(640\) 14.0953 24.4138i 0.557167 0.965041i
\(641\) 16.2922 + 28.2189i 0.643503 + 1.11458i 0.984645 + 0.174568i \(0.0558530\pi\)
−0.341142 + 0.940012i \(0.610814\pi\)
\(642\) 0 0
\(643\) −21.5327 37.2957i −0.849166 1.47080i −0.881953 0.471337i \(-0.843772\pi\)
0.0327873 0.999462i \(-0.489562\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 43.7628 1.72182
\(647\) −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
\(653\) 16.0002 27.7132i 0.626138 1.08450i −0.362182 0.932107i \(-0.617968\pi\)
0.988320 0.152395i \(-0.0486985\pi\)
\(654\) 0 0
\(655\) 5.75022 + 9.95967i 0.224680 + 0.389156i
\(656\) 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
\(661\) −28.0260 −1.09009 −0.545043 0.838408i \(-0.683487\pi\)
−0.545043 + 0.838408i \(0.683487\pi\)
\(662\) 31.1262 1.20976
\(663\) 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
\(668\) −0.798544 1.38312i −0.0308966 0.0535145i
\(669\) 0 0
\(670\) 12.2210 21.1674i 0.472138 0.817766i
\(671\) 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
\(677\) −42.0334 −1.61547 −0.807737 0.589543i \(-0.799308\pi\)
−0.807737 + 0.589543i \(0.799308\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 25.9588 + 44.9620i 0.995476 + 1.72421i
\(681\) 0 0
\(682\) −1.47128 2.54833i −0.0563382 0.0975807i
\(683\) 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
\(688\) −15.8715 + 27.4902i −0.605095 + 1.04806i
\(689\) 7.17408 0.273311
\(690\) 0 0
\(691\) 51.1349 1.94526 0.972632 0.232351i \(-0.0746418\pi\)
0.972632 + 0.232351i \(0.0746418\pi\)
\(692\) −3.02161 −0.114864
\(693\) 0 0
\(694\) −6.66606 −0.253040
\(695\) −58.6132 −2.22333
\(696\) 0 0
\(697\) −32.6230 −1.23569
\(698\) −9.83977 + 17.0430i −0.372441 + 0.645086i
\(699\) 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
\(704\) 5.20100 + 9.00840i 0.196020 + 0.339517i
\(705\) 0 0
\(706\) 21.4321 + 37.1215i 0.806607 + 1.39708i
\(707\) 0 0
\(708\) 0 0
\(709\) 30.8976 1.16038 0.580192 0.814480i \(-0.302978\pi\)
0.580192 + 0.814480i \(0.302978\pi\)
\(710\) 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
\(716\) −0.213506 + 0.369803i −0.00797908 + 0.0138202i
\(717\) 0 0
\(718\) 15.6216 + 27.0573i 0.582992 + 1.00977i
\(719\) 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
\(724\) −1.75822 −0.0653437
\(725\) 20.2347 0.751498
\(726\) 0 0
\(727\) 22.2492 38.5367i 0.825176 1.42925i −0.0766087 0.997061i \(-0.524409\pi\)
0.901785 0.432186i \(-0.142257\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −2.37882 4.12023i −0.0880440 0.152497i
\(731\) −23.7039 41.0564i −0.876722 1.51853i
\(732\) 0 0
\(733\) −4.91854 + 8.51916i −0.181670 + 0.314662i −0.942449 0.334349i \(-0.891484\pi\)
0.760779 + 0.649011i \(0.224817\pi\)
\(734\) 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 \(0.254722\pi\)
\(740\) 10.6842 0.392760
\(741\) 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
\(745\) 1.98935 + 3.44566i 0.0728843 + 0.126239i
\(746\) −20.7449 + 35.9311i −0.759523 + 1.31553i
\(747\) 0 0
\(748\) −1.79328 −0.0655686
\(749\) 0 0
\(750\) 0 0
\(751\) −11.1005 + 19.2266i −0.405063 + 0.701590i −0.994329 0.106349i \(-0.966084\pi\)
0.589266 + 0.807939i \(0.299417\pi\)
\(752\) −2.07887 −0.0758087
\(753\) 0 0
\(754\) −11.3987 −0.415116
\(755\) −69.2106 −2.51883
\(756\) 0 0
\(757\) 25.0464 0.910329 0.455164 0.890407i \(-0.349581\pi\)
0.455164 + 0.890407i \(0.349581\pi\)
\(758\) −39.3446 −1.42906
\(759\) 0 0
\(760\) 72.7051 2.63729
\(761\) 3.37632 5.84796i 0.122392 0.211988i −0.798319 0.602235i \(-0.794277\pi\)
0.920710 + 0.390247i \(0.127610\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −7.76233 −0.280831
\(765\) 0 0
\(766\) 1.12637 1.95094i 0.0406975 0.0704902i
\(767\) −13.2255 22.9072i −0.477544 0.827131i
\(768\) 0 0
\(769\) 21.0805 + 36.5125i 0.760182 + 1.31667i 0.942757 + 0.333482i \(0.108224\pi\)
−0.182575 + 0.983192i \(0.558443\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −5.44130 −0.195837
\(773\) 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
\(779\) −22.8425 + 39.5644i −0.818419 + 1.41754i
\(780\) 0 0
\(781\) 1.93114 + 3.34484i 0.0691017 + 0.119688i
\(782\) −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
\(787\) 6.72910 0.239867 0.119933 0.992782i \(-0.461732\pi\)
0.119933 + 0.992782i \(0.461732\pi\)
\(788\) −6.13031 −0.218383
\(789\) 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
\(794\) −16.4688 28.5248i −0.584456 1.01231i
\(795\) 0 0
\(796\) 2.95160 5.11233i 0.104617