Properties

Label 441.2.f.h.295.3
Level $441$
Weight $2$
Character 441.295
Analytic conductor $3.521$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 295.3
Character \(\chi\) \(=\) 441.295
Dual form 441.2.f.h.148.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.649936 + 1.12572i) q^{2} +(-0.0514049 + 1.73129i) q^{3} +(0.155166 + 0.268756i) q^{4} +(1.76292 + 3.05347i) q^{5} +(-1.91554 - 1.18309i) q^{6} -3.00314 q^{8} +(-2.99472 - 0.177994i) q^{9} +O(q^{10})\) \(q+(-0.649936 + 1.12572i) q^{2} +(-0.0514049 + 1.73129i) q^{3} +(0.155166 + 0.268756i) q^{4} +(1.76292 + 3.05347i) q^{5} +(-1.91554 - 1.18309i) q^{6} -3.00314 q^{8} +(-2.99472 - 0.177994i) q^{9} -4.58314 q^{10} +(-0.589267 + 1.02064i) q^{11} +(-0.473270 + 0.254822i) q^{12} +(-1.61030 - 2.78913i) q^{13} +(-5.37706 + 2.89516i) q^{15} +(1.64151 - 2.84319i) q^{16} +4.90317 q^{17} +(2.14674 - 3.25553i) q^{18} +6.86637 q^{19} +(-0.547092 + 0.947591i) q^{20} +(-0.765972 - 1.32670i) q^{22} +(2.14994 + 3.72380i) q^{23} +(0.154376 - 5.19929i) q^{24} +(-3.71578 + 6.43592i) q^{25} +4.18637 q^{26} +(0.462101 - 5.17556i) q^{27} +(1.36140 - 2.35802i) q^{29} +(0.235596 - 7.93474i) q^{30} +(-0.960401 - 1.66346i) q^{31} +(-0.869378 - 1.50581i) q^{32} +(-1.73673 - 1.07266i) q^{33} +(-3.18675 + 5.51961i) q^{34} +(-0.416842 - 0.832466i) q^{36} -9.76457 q^{37} +(-4.46270 + 7.72962i) q^{38} +(4.91156 - 2.64452i) q^{39} +(-5.29429 - 9.16998i) q^{40} +(3.32673 + 5.76206i) q^{41} +(4.83441 - 8.37344i) q^{43} -0.365738 q^{44} +(-4.73595 - 9.45806i) q^{45} -5.58928 q^{46} +(0.316609 - 0.548383i) q^{47} +(4.83799 + 2.98809i) q^{48} +(-4.83004 - 8.36587i) q^{50} +(-0.252047 + 8.48880i) q^{51} +(0.499729 - 0.865557i) q^{52} -2.22756 q^{53} +(5.52591 + 3.88398i) q^{54} -4.15533 q^{55} +(-0.352965 + 11.8877i) q^{57} +(1.76965 + 3.06512i) q^{58} +(4.10652 + 7.11270i) q^{59} +(-1.61243 - 0.995884i) q^{60} +(-4.82958 + 8.36508i) q^{61} +2.49680 q^{62} +8.82622 q^{64} +(5.67767 - 9.83402i) q^{65} +(2.33628 - 1.25792i) q^{66} +(-2.66651 - 4.61852i) q^{67} +(0.760807 + 1.31776i) q^{68} +(-6.55748 + 3.53074i) q^{69} -3.27719 q^{71} +(8.99354 + 0.534539i) q^{72} -1.03807 q^{73} +(6.34635 - 10.9922i) q^{74} +(-10.9514 - 6.76392i) q^{75} +(1.06543 + 1.84538i) q^{76} +(-0.215200 + 7.24782i) q^{78} +(-0.502039 + 0.869557i) q^{79} +11.5754 q^{80} +(8.93664 + 1.06608i) q^{81} -8.64864 q^{82} +(3.65598 - 6.33234i) q^{83} +(8.64391 + 14.9717i) q^{85} +(6.28411 + 10.8844i) q^{86} +(4.01243 + 2.47820i) q^{87} +(1.76965 - 3.06512i) q^{88} -12.0429 q^{89} +(13.7252 + 0.815770i) q^{90} +(-0.667195 + 1.15562i) q^{92} +(2.92930 - 1.57722i) q^{93} +(0.411551 + 0.712828i) q^{94} +(12.1049 + 20.9662i) q^{95} +(2.65168 - 1.42774i) q^{96} +(5.46454 - 9.46487i) q^{97} +(1.94636 - 2.95164i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} + 8q^{9} + O(q^{10}) \) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} + 8q^{9} + 20q^{11} + 4q^{15} - 12q^{16} + 4q^{18} + 32q^{23} - 12q^{25} + 16q^{29} + 48q^{32} - 4q^{36} + 24q^{37} + 32q^{39} - 112q^{44} - 48q^{46} - 4q^{50} - 56q^{51} - 64q^{53} - 12q^{57} - 88q^{60} + 96q^{64} + 60q^{65} - 12q^{67} - 112q^{71} + 168q^{72} + 68q^{74} - 60q^{78} + 12q^{79} + 80q^{81} + 12q^{85} + 76q^{86} + 16q^{92} - 80q^{93} + 64q^{95} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 −0.998938 0.0460668i \(-0.985331\pi\)
0.539364 + 0.842073i \(0.318665\pi\)
\(3\) −0.0514049 + 1.73129i −0.0296787 + 0.999559i
\(4\) 0.155166 + 0.268756i 0.0775831 + 0.134378i
\(5\) 1.76292 + 3.05347i 0.788402 + 1.36555i 0.926945 + 0.375196i \(0.122425\pi\)
−0.138543 + 0.990356i \(0.544242\pi\)
\(6\) −1.91554 1.18309i −0.782016 0.482996i
\(7\) 0 0
\(8\) −3.00314 −1.06177
\(9\) −2.99472 0.177994i −0.998238 0.0593312i
\(10\) −4.58314 −1.44932
\(11\) −0.589267 + 1.02064i −0.177671 + 0.307735i −0.941082 0.338178i \(-0.890190\pi\)
0.763412 + 0.645912i \(0.223523\pi\)
\(12\) −0.473270 + 0.254822i −0.136621 + 0.0735608i
\(13\) −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
\(15\) −5.37706 + 2.89516i −1.38835 + 0.747527i
\(16\) 1.64151 2.84319i 0.410379 0.710797i
\(17\) 4.90317 1.18919 0.594597 0.804024i \(-0.297312\pi\)
0.594597 + 0.804024i \(0.297312\pi\)
\(18\) 2.14674 3.25553i 0.505993 0.767336i
\(19\) 6.86637 1.57525 0.787627 0.616153i \(-0.211310\pi\)
0.787627 + 0.616153i \(0.211310\pi\)
\(20\) −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 \(-0.0186989\pi\)
−0.549982 + 0.835176i \(0.685366\pi\)
\(24\) 0.154376 5.19929i 0.0315119 1.06130i
\(25\) −3.71578 + 6.43592i −0.743156 + 1.28718i
\(26\) 4.18637 0.821016
\(27\) 0.462101 5.17556i 0.0889314 0.996038i
\(28\) 0 0
\(29\) 1.36140 2.35802i 0.252806 0.437873i −0.711491 0.702695i \(-0.751980\pi\)
0.964297 + 0.264822i \(0.0853131\pi\)
\(30\) 0.235596 7.93474i 0.0430138 1.44868i
\(31\) −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
\(33\) −1.73673 1.07266i −0.302326 0.186726i
\(34\) −3.18675 + 5.51961i −0.546523 + 0.946606i
\(35\) 0 0
\(36\) −0.416842 0.832466i −0.0694737 0.138744i
\(37\) −9.76457 −1.60529 −0.802643 0.596460i \(-0.796573\pi\)
−0.802643 + 0.596460i \(0.796573\pi\)
\(38\) −4.46270 + 7.72962i −0.723946 + 1.25391i
\(39\) 4.91156 2.64452i 0.786479 0.423462i
\(40\) −5.29429 9.16998i −0.837101 1.44990i
\(41\) 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 \(-0.0972047\pi\)
\(44\) −0.365738 −0.0551370
\(45\) −4.73595 9.45806i −0.705993 1.40992i
\(46\) −5.58928 −0.824095
\(47\) 0.316609 0.548383i 0.0461822 0.0799899i −0.842010 0.539461i \(-0.818628\pi\)
0.888192 + 0.459472i \(0.151961\pi\)
\(48\) 4.83799 + 2.98809i 0.698304 + 0.431293i
\(49\) 0 0
\(50\) −4.83004 8.36587i −0.683071 1.18311i
\(51\) −0.252047 + 8.48880i −0.0352937 + 1.18867i
\(52\) 0.499729 0.865557i 0.0693000 0.120031i
\(53\) −2.22756 −0.305978 −0.152989 0.988228i \(-0.548890\pi\)
−0.152989 + 0.988228i \(0.548890\pi\)
\(54\) 5.52591 + 3.88398i 0.751981 + 0.528543i
\(55\) −4.15533 −0.560304
\(56\) 0 0
\(57\) −0.352965 + 11.8877i −0.0467514 + 1.57456i
\(58\) 1.76965 + 3.06512i 0.232366 + 0.402471i
\(59\) 4.10652 + 7.11270i 0.534623 + 0.925995i 0.999181 + 0.0404521i \(0.0128798\pi\)
−0.464558 + 0.885543i \(0.653787\pi\)
\(60\) −1.61243 0.995884i −0.208164 0.128568i
\(61\) −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
\(66\) 2.33628 1.25792i 0.287576 0.154839i
\(67\) −2.66651 4.61852i −0.325766 0.564242i 0.655901 0.754847i \(-0.272289\pi\)
−0.981667 + 0.190604i \(0.938955\pi\)
\(68\) 0.760807 + 1.31776i 0.0922614 + 0.159801i
\(69\) −6.55748 + 3.53074i −0.789428 + 0.425051i
\(70\) 0 0
\(71\) −3.27719 −0.388931 −0.194466 0.980909i \(-0.562297\pi\)
−0.194466 + 0.980909i \(0.562297\pi\)
\(72\) 8.99354 + 0.534539i 1.05990 + 0.0629960i
\(73\) −1.03807 −0.121497 −0.0607486 0.998153i \(-0.519349\pi\)
−0.0607486 + 0.998153i \(0.519349\pi\)
\(74\) 6.34635 10.9922i 0.737748 1.27782i
\(75\) −10.9514 6.76392i −1.26456 0.781031i
\(76\) 1.06543 + 1.84538i 0.122213 + 0.211679i
\(77\) 0 0
\(78\) −0.215200 + 7.24782i −0.0243666 + 0.820654i
\(79\) −0.502039 + 0.869557i −0.0564838 + 0.0978328i −0.892885 0.450285i \(-0.851322\pi\)
0.836401 + 0.548118i \(0.184656\pi\)
\(80\) 11.5754 1.29417
\(81\) 8.93664 + 1.06608i 0.992960 + 0.118453i
\(82\) −8.64864 −0.955082
\(83\) 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
\(86\) 6.28411 + 10.8844i 0.677633 + 1.17369i
\(87\) 4.01243 + 2.47820i 0.430177 + 0.265690i
\(88\) 1.76965 3.06512i 0.188645 0.326743i
\(89\) −12.0429 −1.27654 −0.638271 0.769812i \(-0.720350\pi\)
−0.638271 + 0.769812i \(0.720350\pi\)
\(90\) 13.7252 + 0.815770i 1.44676 + 0.0859897i
\(91\) 0 0
\(92\) −0.667195 + 1.15562i −0.0695599 + 0.120481i
\(93\) 2.92930 1.57722i 0.303755 0.163550i
\(94\) 0.411551 + 0.712828i 0.0424483 + 0.0735226i
\(95\) 12.1049 + 20.9662i 1.24193 + 2.15109i
\(96\) 2.65168 1.42774i 0.270636 0.145718i
\(97\) 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
\(99\) 1.94636 2.95164i 0.195616 0.296651i
\(100\) −2.30626 −0.230626
\(101\) −0.797546 + 1.38139i −0.0793588 + 0.137453i −0.902973 0.429696i \(-0.858621\pi\)
0.823615 + 0.567150i \(0.191954\pi\)
\(102\) −9.39222 5.80092i −0.929969 0.574376i
\(103\) 1.16778 + 2.02265i 0.115065 + 0.199298i 0.917806 0.397030i \(-0.129959\pi\)
−0.802741 + 0.596328i \(0.796626\pi\)
\(104\) 4.83596 + 8.37613i 0.474205 + 0.821347i
\(105\) 0 0
\(106\) 1.44777 2.50761i 0.140620 0.243561i
\(107\) −2.22362 −0.214966 −0.107483 0.994207i \(-0.534279\pi\)
−0.107483 + 0.994207i \(0.534279\pi\)
\(108\) 1.46267 0.678881i 0.140745 0.0653253i
\(109\) −0.919564 −0.0880782 −0.0440391 0.999030i \(-0.514023\pi\)
−0.0440391 + 0.999030i \(0.514023\pi\)
\(110\) 2.70070 4.67774i 0.257501 0.446005i
\(111\) 0.501947 16.9053i 0.0476427 1.60458i
\(112\) 0 0
\(113\) 1.19327 + 2.06681i 0.112254 + 0.194429i 0.916679 0.399625i \(-0.130860\pi\)
−0.804425 + 0.594054i \(0.797526\pi\)
\(114\) −13.1528 8.12356i −1.23187 0.760841i
\(115\) −7.58033 + 13.1295i −0.706870 + 1.22433i
\(116\) 0.844976 0.0784540
\(117\) 4.32595 + 8.63926i 0.399934 + 0.798700i
\(118\) −10.6759 −0.982796
\(119\) 0 0
\(120\) 16.1480 8.69456i 1.47411 0.793701i
\(121\) 4.80553 + 8.32342i 0.436866 + 0.756674i
\(122\) −6.27783 10.8735i −0.568368 0.984443i
\(123\) −10.1468 + 5.46332i −0.914906 + 0.492611i
\(124\) 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
\(129\) 14.2483 + 8.80019i 1.25449 + 0.774813i
\(130\) 7.38025 + 12.7830i 0.647291 + 1.12114i
\(131\) −1.63088 2.82476i −0.142490 0.246801i 0.785943 0.618298i \(-0.212178\pi\)
−0.928434 + 0.371498i \(0.878844\pi\)
\(132\) 0.0188007 0.633197i 0.00163639 0.0551127i
\(133\) 0 0
\(134\) 6.93223 0.598854
\(135\) 16.6181 7.71310i 1.43026 0.663838i
\(136\) −14.7249 −1.26265
\(137\) −10.4669 + 18.1292i −0.894246 + 1.54888i −0.0595120 + 0.998228i \(0.518954\pi\)
−0.834734 + 0.550653i \(0.814379\pi\)
\(138\) 0.287317 9.67666i 0.0244580 0.823732i
\(139\) 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
\(141\) 0.933134 + 0.576331i 0.0785840 + 0.0485358i
\(142\) 2.12997 3.68921i 0.178743 0.309592i
\(143\) 3.79559 0.317404
\(144\) −5.42194 + 8.22235i −0.451828 + 0.685196i
\(145\) 9.60019 0.797252
\(146\) 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 \(-0.181385\pi\)
−0.888211 + 0.459435i \(0.848052\pi\)
\(150\) 14.7320 7.93214i 1.20286 0.647657i
\(151\) 9.81476 16.9997i 0.798714 1.38341i −0.121740 0.992562i \(-0.538847\pi\)
0.920454 0.390851i \(-0.127819\pi\)
\(152\) −20.6206 −1.67256
\(153\) −14.6836 0.872733i −1.18710 0.0705563i
\(154\) 0 0
\(155\) 3.38622 5.86511i 0.271988 0.471097i
\(156\) 1.47284 + 0.909669i 0.117921 + 0.0728318i
\(157\) 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
\(159\) 0.114507 3.85654i 0.00908103 0.305844i
\(160\) 3.06529 5.30924i 0.242332 0.419732i
\(161\) 0 0
\(162\) −7.00835 + 9.36729i −0.550628 + 0.735964i
\(163\) 16.9011 1.32380 0.661899 0.749593i \(-0.269751\pi\)
0.661899 + 0.749593i \(0.269751\pi\)
\(164\) −1.03239 + 1.78815i −0.0806162 + 0.139631i
\(165\) 0.213604 7.19407i 0.0166291 0.560057i
\(166\) 4.75230 + 8.23123i 0.368850 + 0.638867i
\(167\) −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
\(170\) −22.4719 −1.72352
\(171\) −20.5628 1.22217i −1.57248 0.0934616i
\(172\) 3.00055 0.228790
\(173\) 4.86834 8.43222i 0.370133 0.641090i −0.619453 0.785034i \(-0.712645\pi\)
0.989586 + 0.143945i \(0.0459787\pi\)
\(174\) −5.39758 + 2.90621i −0.409190 + 0.220319i
\(175\) 0 0
\(176\) 1.93458 + 3.35079i 0.145825 + 0.252576i
\(177\) −12.5252 + 6.74394i −0.941454 + 0.506905i
\(178\) 7.82710 13.5569i 0.586666 1.01613i
\(179\) 1.37598 0.102846 0.0514228 0.998677i \(-0.483624\pi\)
0.0514228 + 0.998677i \(0.483624\pi\)
\(180\) 1.80705 2.74039i 0.134689 0.204256i
\(181\) 5.66560 0.421120 0.210560 0.977581i \(-0.432471\pi\)
0.210560 + 0.977581i \(0.432471\pi\)
\(182\) 0 0
\(183\) −14.2341 8.79140i −1.05221 0.649879i
\(184\) −6.45655 11.1831i −0.475983 0.824427i
\(185\) −17.2142 29.8158i −1.26561 2.19210i
\(186\) −0.128348 + 4.32267i −0.00941091 + 0.316954i
\(187\) −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 \(-0.473252\pi\)
0.821003 0.570925i \(-0.193415\pi\)
\(192\) −0.453711 + 15.2807i −0.0327438 + 1.10279i
\(193\) −8.76688 15.1847i −0.631054 1.09302i −0.987337 0.158640i \(-0.949289\pi\)
0.356282 0.934378i \(-0.384044\pi\)
\(194\) 7.10321 + 12.3031i 0.509981 + 0.883312i
\(195\) 16.7337 + 10.3352i 1.19832 + 0.740119i
\(196\) 0 0
\(197\) −19.7540 −1.40741 −0.703707 0.710490i \(-0.748473\pi\)
−0.703707 + 0.710490i \(0.748473\pi\)
\(198\) 2.05772 + 4.10943i 0.146236 + 0.292045i
\(199\) 19.0222 1.34845 0.674224 0.738527i \(-0.264478\pi\)
0.674224 + 0.738527i \(0.264478\pi\)
\(200\) 11.1590 19.3279i 0.789060 1.36669i
\(201\) 8.13307 4.37907i 0.573662 0.308876i
\(202\) −1.03671 1.79563i −0.0729425 0.126340i
\(203\) 0 0
\(204\) −2.32053 + 1.24944i −0.162469 + 0.0874781i
\(205\) −11.7295 + 20.3161i −0.819225 + 1.41894i
\(206\) −3.03593 −0.211523
\(207\) −5.77563 11.5344i −0.401434 0.801696i
\(208\) −10.5733 −0.733129
\(209\) −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
\(213\) 0.168464 5.67376i 0.0115430 0.388760i
\(214\) 1.44521 2.50318i 0.0987927 0.171114i
\(215\) 34.0907 2.32497
\(216\) −1.38775 + 15.5429i −0.0944246 + 1.05756i
\(217\) 0 0
\(218\) 0.597658 1.03517i 0.0404785 0.0701108i
\(219\) 0.0533620 1.79720i 0.00360587 0.121444i
\(220\) −0.644767 1.11677i −0.0434702 0.0752925i
\(221\) −7.89559 13.6756i −0.531115 0.919918i
\(222\) 18.7044 + 11.5524i 1.25536 + 0.775347i
\(223\) −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
\(225\) 12.2733 18.6124i 0.818217 1.24082i
\(226\) −3.10221 −0.206356
\(227\) −9.00847 + 15.6031i −0.597913 + 1.03562i 0.395215 + 0.918589i \(0.370670\pi\)
−0.993129 + 0.117028i \(0.962663\pi\)
\(228\) −3.24965 + 1.74970i −0.215213 + 0.115877i
\(229\) 2.12746 + 3.68486i 0.140586 + 0.243503i 0.927718 0.373283i \(-0.121768\pi\)
−0.787131 + 0.616785i \(0.788435\pi\)
\(230\) −9.85347 17.0667i −0.649718 1.12535i
\(231\) 0 0
\(232\) −4.08848 + 7.08146i −0.268422 + 0.464920i
\(233\) −14.7055 −0.963390 −0.481695 0.876339i \(-0.659979\pi\)
−0.481695 + 0.876339i \(0.659979\pi\)
\(234\) −12.5370 0.745148i −0.819569 0.0487118i
\(235\) 2.23263 0.145641
\(236\) −1.27439 + 2.20730i −0.0829555 + 0.143683i
\(237\) −1.47965 0.913873i −0.0961133 0.0593624i
\(238\) 0 0
\(239\) 7.08187 + 12.2662i 0.458088 + 0.793432i 0.998860 0.0477377i \(-0.0152011\pi\)
−0.540772 + 0.841169i \(0.681868\pi\)
\(240\) −0.595035 + 20.0404i −0.0384093 + 1.29360i
\(241\) 3.96752 6.87194i 0.255570 0.442661i −0.709480 0.704726i \(-0.751070\pi\)
0.965050 + 0.262065i \(0.0844035\pi\)
\(242\) −12.4931 −0.803090
\(243\) −2.30508 + 15.4171i −0.147871 + 0.989007i
\(244\) −2.99755 −0.191899
\(245\) 0 0
\(246\) 0.444583 14.9733i 0.0283456 0.954662i
\(247\) −11.0569 19.1512i −0.703536 1.21856i
\(248\) 2.88422 + 4.99561i 0.183148 + 0.317221i
\(249\) 10.7752 + 6.65506i 0.682848 + 0.421747i
\(250\) 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
\(255\) −26.3646 + 14.1955i −1.65102 + 0.888955i
\(256\) 3.62969 + 6.28681i 0.226856 + 0.392926i
\(257\) −8.77687 15.2020i −0.547486 0.948273i −0.998446 0.0557293i \(-0.982252\pi\)
0.450960 0.892544i \(-0.351082\pi\)
\(258\) −19.1671 + 10.3201i −1.19329 + 0.642501i
\(259\) 0 0
\(260\) 3.52393 0.218545
\(261\) −4.49673 + 6.81928i −0.278340 + 0.422103i
\(262\) 4.23986 0.261940
\(263\) 11.6743 20.2205i 0.719867 1.24685i −0.241185 0.970479i \(-0.577536\pi\)
0.961052 0.276367i \(-0.0891306\pi\)
\(264\) 5.21564 + 3.22134i 0.321001 + 0.198260i
\(265\) −3.92701 6.80177i −0.241234 0.417830i
\(266\) 0 0
\(267\) 0.619063 20.8497i 0.0378861 1.27598i
\(268\) 0.827504 1.43328i 0.0505478 0.0875514i
\(269\) −0.538488 −0.0328322 −0.0164161 0.999865i \(-0.505226\pi\)
−0.0164161 + 0.999865i \(0.505226\pi\)
\(270\) −2.11788 + 23.7204i −0.128890 + 1.44357i
\(271\) 14.4150 0.875648 0.437824 0.899061i \(-0.355749\pi\)
0.437824 + 0.899061i \(0.355749\pi\)
\(272\) 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
\(276\) −1.96641 1.21451i −0.118364 0.0731050i
\(277\) −10.9533 + 18.9717i −0.658121 + 1.13990i 0.322980 + 0.946406i \(0.395315\pi\)
−0.981101 + 0.193494i \(0.938018\pi\)
\(278\) −21.6089 −1.29602
\(279\) 2.58004 + 5.15254i 0.154463 + 0.308475i
\(280\) 0 0
\(281\) −0.776622 + 1.34515i −0.0463294 + 0.0802449i −0.888260 0.459341i \(-0.848086\pi\)
0.841931 + 0.539586i \(0.181419\pi\)
\(282\) −1.25527 + 0.675871i −0.0747500 + 0.0402475i
\(283\) −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
\(285\) −36.9208 + 19.8792i −2.18700 + 1.17754i
\(286\) −2.46689 + 4.27279i −0.145870 + 0.252655i
\(287\) 0 0
\(288\) 2.33552 + 4.66421i 0.137622 + 0.274841i
\(289\) 7.04111 0.414183
\(290\) −6.23951 + 10.8071i −0.366396 + 0.634617i
\(291\) 16.1055 + 9.94724i 0.944121 + 0.583118i
\(292\) −0.161074 0.278988i −0.00942613 0.0163265i
\(293\) 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
\(296\) 29.3243 1.70444
\(297\) 5.01009 + 3.52143i 0.290715 + 0.204334i
\(298\) 1.46683 0.0849712
\(299\) 6.92409 11.9929i 0.400431 0.693566i
\(300\) 0.118553 3.99279i 0.00684466 0.230524i
\(301\) 0 0
\(302\) 12.7579 + 22.0974i 0.734137 + 1.27156i
\(303\) −2.35059 1.45179i −0.135038 0.0834033i
\(304\) 11.2712 19.5224i 0.646450 1.11968i
\(305\) −34.0567 −1.95008
\(306\) 10.5259 15.9624i 0.601723 0.912512i
\(307\) 10.6425 0.607400 0.303700 0.952768i \(-0.401778\pi\)
0.303700 + 0.952768i \(0.401778\pi\)
\(308\) 0 0
\(309\) −3.56182 + 1.91779i −0.202625 + 0.109099i
\(310\) 4.40165 + 7.62389i 0.249997 + 0.433008i
\(311\) −6.85479 11.8728i −0.388699 0.673247i 0.603576 0.797306i \(-0.293742\pi\)
−0.992275 + 0.124059i \(0.960409\pi\)
\(312\) −14.7501 + 7.94186i −0.835059 + 0.449619i
\(313\) 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 −0.911795 0.410646i \(-0.865303\pi\)
0.811527 + 0.584315i \(0.198637\pi\)
\(318\) 4.26697 + 2.63541i 0.239280 + 0.147786i
\(319\) 1.60446 + 2.77901i 0.0898326 + 0.155595i
\(320\) 15.5599 + 26.9506i 0.869826 + 1.50658i
\(321\) 0.114305 3.84973i 0.00637989 0.214871i
\(322\) 0 0
\(323\) 33.6670 1.87328
\(324\) 1.10015 + 2.56719i 0.0611194 + 0.142622i
\(325\) 23.9341 1.32763
\(326\) −10.9846 + 19.0260i −0.608383 + 1.05375i
\(327\) 0.0472701 1.59203i 0.00261404 0.0880394i
\(328\) −9.99062 17.3043i −0.551639 0.955468i
\(329\) 0 0
\(330\) 7.95969 + 4.91614i 0.438167 + 0.270625i
\(331\) 11.9728 20.7375i 0.658085 1.13984i −0.323026 0.946390i \(-0.604700\pi\)
0.981111 0.193446i \(-0.0619666\pi\)
\(332\) 2.26914 0.124535
\(333\) 29.2421 + 1.73803i 1.60246 + 0.0952435i
\(334\) 6.68963 0.366040
\(335\) 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
\(339\) −3.63959 + 1.95966i −0.197675 + 0.106434i
\(340\) −2.68249 + 4.64620i −0.145478 + 0.251976i
\(341\) 2.26373 0.122588
\(342\) 14.7403 22.3537i 0.797066 1.20875i
\(343\) 0 0
\(344\) −14.5184 + 25.1466i −0.782779 + 1.35581i
\(345\) −22.3413 13.7987i −1.20282 0.742895i
\(346\) 6.32822 + 10.9608i 0.340207 + 0.589256i
\(347\) 2.56412 + 4.44119i 0.137649 + 0.238416i 0.926606 0.376033i \(-0.122712\pi\)
−0.788957 + 0.614448i \(0.789379\pi\)
\(348\) −0.0434359 + 1.46290i −0.00232841 + 0.0784195i
\(349\) 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
\(351\) −15.1794 + 7.04537i −0.810218 + 0.376054i
\(352\) 2.04918 0.109222
\(353\) 16.4878 28.5578i 0.877559 1.51998i 0.0235477 0.999723i \(-0.492504\pi\)
0.854011 0.520254i \(-0.174163\pi\)
\(354\) 0.548794 18.4831i 0.0291681 0.982363i
\(355\) −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
\(359\) −24.0355 −1.26855 −0.634274 0.773109i \(-0.718701\pi\)
−0.634274 + 0.773109i \(0.718701\pi\)
\(360\) 14.2227 + 28.4038i 0.749602 + 1.49701i
\(361\) 28.1470 1.48142
\(362\) −3.68227 + 6.37789i −0.193536 + 0.335214i
\(363\) −14.6573 + 7.89189i −0.769307 + 0.414217i
\(364\) 0 0
\(365\) −1.83004 3.16972i −0.0957886 0.165911i
\(366\) 19.1479 10.3098i 1.00088 0.538901i
\(367\) −1.32751 + 2.29931i −0.0692952 + 0.120023i −0.898591 0.438787i \(-0.855408\pi\)
0.829296 + 0.558810i \(0.188742\pi\)
\(368\) 14.1166 0.735879
\(369\) −8.93699 17.8479i −0.465241 0.929123i
\(370\) 44.7524 2.32657
\(371\) 0 0
\(372\) 0.878416 + 0.542536i 0.0455438 + 0.0281292i
\(373\) 15.9592 + 27.6421i 0.826334 + 1.43125i 0.900896 + 0.434036i \(0.142911\pi\)
−0.0745621 + 0.997216i \(0.523756\pi\)
\(374\) −3.75569 6.50505i −0.194202 0.336368i
\(375\) 0.440710 14.8428i 0.0227582 0.766481i
\(376\) −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
\(381\) 0.156358 5.26606i 0.00801048 0.269788i
\(382\) 16.2568 + 28.1576i 0.831771 + 1.44067i
\(383\) 0.866526 + 1.50087i 0.0442774 + 0.0766907i 0.887315 0.461164i \(-0.152568\pi\)
−0.843037 + 0.537855i \(0.819235\pi\)
\(384\) −11.7824 7.27715i −0.601267 0.371360i
\(385\) 0 0
\(386\) 22.7917 1.16006
\(387\) −15.9681 + 24.2156i −0.811704 + 1.23095i
\(388\) 3.39165 0.172185
\(389\) 5.54175 9.59859i 0.280978 0.486668i −0.690648 0.723191i \(-0.742675\pi\)
0.971626 + 0.236523i \(0.0760079\pi\)
\(390\) −22.5104 + 12.1202i −1.13986 + 0.613731i
\(391\) 10.5415 + 18.2584i 0.533107 + 0.923368i
\(392\) 0 0
\(393\) 4.97431 2.67831i 0.250921 0.135103i
\(394\) 12.8388 22.2375i 0.646811 1.12031i
\(395\) −3.54022 −0.178128
\(396\) 1.09528 + 0.0650989i 0.0550399 + 0.00327134i
\(397\) −25.3391 −1.27173 −0.635867 0.771799i \(-0.719357\pi\)
−0.635867 + 0.771799i \(0.719357\pi\)
\(398\) −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 0.862483 + 0.506085i \(0.168908\pi\)
0.00704089 + 0.999975i \(0.497759\pi\)
\(402\) −0.356351 + 12.0017i −0.0177732 + 0.598590i
\(403\) −3.09307 + 5.35736i −0.154077 + 0.266869i
\(404\) −0.495009 −0.0246276
\(405\) 12.4993 + 29.1672i 0.621097 + 1.44933i
\(406\) 0 0
\(407\) 5.75394 9.96612i 0.285212 0.494002i
\(408\) 0.756933 25.4930i 0.0374738 1.26209i
\(409\) −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
\(411\) −30.8488 19.0531i −1.52166 0.939821i
\(412\) −0.362400 + 0.627695i −0.0178541 + 0.0309243i
\(413\) 0 0
\(414\) 16.7383 + 0.994856i 0.822643 + 0.0488945i
\(415\) 25.7808 1.26553
\(416\) −2.79992 + 4.84961i −0.137278 + 0.237772i
\(417\) −25.3521 + 13.6503i −1.24150 + 0.668459i
\(418\) −5.25945 9.10963i −0.257248 0.445567i
\(419\) 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 \(0.164428\pi\)
\(422\) −9.66609 −0.470538
\(423\) −1.04576 + 1.58590i −0.0508467 + 0.0771090i
\(424\) 6.68966 0.324878
\(425\) −18.2191 + 31.5564i −0.883757 + 1.53071i
\(426\) 6.27759 + 3.87723i 0.304150 + 0.187852i
\(427\) 0 0
\(428\) −0.345031 0.597612i −0.0166777 0.0288866i
\(429\) −0.195112 + 6.57127i −0.00942011 + 0.317264i
\(430\) −22.1568 + 38.3767i −1.06849 + 1.85069i
\(431\) −13.4959 −0.650075 −0.325037 0.945701i \(-0.605377\pi\)
−0.325037 + 0.945701i \(0.605377\pi\)
\(432\) −13.9565 9.80960i −0.671485 0.471965i
\(433\) 4.85211 0.233177 0.116589 0.993180i \(-0.462804\pi\)
0.116589 + 0.993180i \(0.462804\pi\)
\(434\) 0 0
\(435\) −0.493497 + 16.6207i −0.0236614 + 0.796901i
\(436\) −0.142685 0.247138i −0.00683339 0.0118358i
\(437\) 14.7623 + 25.5690i 0.706174 + 1.22313i
\(438\) 1.98847 + 1.22814i 0.0950127 + 0.0586827i
\(439\) 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 −0.858256 0.513221i \(-0.828452\pi\)
0.873591 + 0.486661i \(0.161785\pi\)
\(444\) 4.62128 2.48823i 0.219316 0.118086i
\(445\) −21.2306 36.7725i −1.00643 1.74319i
\(446\) −2.13913 3.70508i −0.101291 0.175441i
\(447\) 1.72092 0.926593i 0.0813968 0.0438264i
\(448\) 0 0
\(449\) −5.22658 −0.246658 −0.123329 0.992366i \(-0.539357\pi\)
−0.123329 + 0.992366i \(0.539357\pi\)
\(450\) 12.9755 + 25.9131i 0.611672 + 1.22156i
\(451\) −7.84133 −0.369234
\(452\) −0.370312 + 0.641399i −0.0174180 + 0.0301689i
\(453\) 28.9268 + 17.8660i 1.35910 + 0.839420i
\(454\) −11.7099 20.2821i −0.549571 0.951885i
\(455\) 0 0
\(456\) 1.06000 35.7003i 0.0496392 1.67182i
\(457\) 1.43037 2.47748i 0.0669101 0.115892i −0.830630 0.556825i \(-0.812019\pi\)
0.897540 + 0.440934i \(0.145353\pi\)
\(458\) −5.53084 −0.258439
\(459\) 2.26576 25.3767i 0.105757 1.18448i
\(460\) −4.70485 −0.219365
\(461\) −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 \(-0.420668\pi\)
\(464\) −4.46953 7.74145i −0.207493 0.359388i
\(465\) 9.98012 + 6.16402i 0.462817 + 0.285850i
\(466\) 9.55764 16.5543i 0.442749 0.766864i
\(467\) −20.5770 −0.952191 −0.476096 0.879393i \(-0.657948\pi\)
−0.476096 + 0.879393i \(0.657948\pi\)
\(468\) −1.65061 + 2.50315i −0.0762995 + 0.115708i
\(469\) 0 0
\(470\) −1.45107 + 2.51332i −0.0669327 + 0.115931i
\(471\) −14.2323 + 7.66305i −0.655788 + 0.353095i
\(472\) −12.3324 21.3604i −0.567647 0.983193i
\(473\) 5.69752 + 9.86839i 0.261972 + 0.453749i
\(474\) 1.99044 1.07171i 0.0914240 0.0492253i
\(475\) −25.5139 + 44.1914i −1.17066 + 2.02764i
\(476\) 0 0
\(477\) 6.67090 + 0.396491i 0.305439 + 0.0181541i
\(478\) −18.4110 −0.842102
\(479\) 12.5916 21.8093i 0.575325 0.996492i −0.420682 0.907208i \(-0.638209\pi\)
0.996006 0.0892833i \(-0.0284577\pi\)
\(480\) 9.03425 + 5.57982i 0.412355 + 0.254683i
\(481\) 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
\(485\) 38.5342 1.74975
\(486\) −15.8572 12.6150i −0.719297 0.572228i
\(487\) −32.7615 −1.48456 −0.742282 0.670088i \(-0.766256\pi\)
−0.742282 + 0.670088i \(0.766256\pi\)
\(488\) 14.5039 25.1215i 0.656560 1.13720i
\(489\) −0.868801 + 29.2607i −0.0392886 + 1.32321i
\(490\) 0 0
\(491\) 1.76000 + 3.04841i 0.0794278 + 0.137573i 0.903003 0.429634i \(-0.141357\pi\)
−0.823575 + 0.567207i \(0.808024\pi\)
\(492\) −3.04274 1.87929i −0.137177 0.0847248i
\(493\) 6.67520 11.5618i 0.300636 0.520716i
\(494\) 28.7452 1.29331
\(495\) 12.4440 + 0.739621i 0.559317 + 0.0332435i
\(496\) −6.30605 −0.283150
\(497\) 0 0
\(498\) −14.4949 + 7.80448i −0.649533 + 0.349727i
\(499\) −7.82082 13.5461i −0.350108 0.606405i 0.636160 0.771557i \(-0.280522\pi\)
−0.986268 + 0.165152i \(0.947188\pi\)
\(500\) −1.33029 2.30412i −0.0594922 0.103044i
\(501\) 7.84844 4.22582i 0.350642 0.188796i
\(502\) 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
\(507\) 3.87228 + 2.39164i 0.171974 + 0.106216i
\(508\) −0.471969 0.817474i −0.0209402 0.0362696i
\(509\) −18.8229 32.6023i −0.834311 1.44507i −0.894590 0.446888i \(-0.852532\pi\)
0.0602789 0.998182i \(-0.480801\pi\)
\(510\) 1.15517 38.9054i 0.0511518 1.72276i
\(511\) 0 0
\(512\) −25.4272 −1.12373
\(513\) 3.17296 35.5373i 0.140089 1.56901i
\(514\) 22.8176 1.00644
\(515\) −4.11740 + 7.13155i −0.181434 + 0.314254i
\(516\) −0.154243 + 5.19481i −0.00679017 + 0.228689i
\(517\) 0.373135 + 0.646289i 0.0164105 + 0.0284237i
\(518\) 0 0
\(519\) 14.3483 + 8.86196i 0.629822 + 0.388997i
\(520\) −17.0508 + 29.5329i −0.747728 + 1.29510i
\(521\) 14.3423 0.628347 0.314174 0.949366i \(-0.398273\pi\)
0.314174 + 0.949366i \(0.398273\pi\)
\(522\) −4.75403 9.49416i −0.208078 0.415548i
\(523\) −10.4844 −0.458453 −0.229226 0.973373i \(-0.573620\pi\)
−0.229226 + 0.973373i \(0.573620\pi\)
\(524\) 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
\(528\) −5.90063 + 3.17707i −0.256792 + 0.138264i
\(529\) 2.25555 3.90673i 0.0980674 0.169858i
\(530\) 10.2092 0.443460
\(531\) −11.0318 22.0314i −0.478741 0.956083i
\(532\) 0 0
\(533\) 10.7141 18.5573i 0.464078 0.803807i
\(534\) 23.0686 + 14.2479i 0.998276 + 0.616565i
\(535\) −3.92007 6.78976i −0.169479 0.293547i
\(536\) 8.00788 + 13.8701i 0.345888 + 0.599095i
\(537\) −0.0707321 + 2.38222i −0.00305232 + 0.102800i
\(538\) 0.349983 0.606188i 0.0150888 0.0261346i
\(539\) 0 0
\(540\) 4.65150 + 3.26939i 0.200169 + 0.140692i
\(541\) −46.0922 −1.98166 −0.990830 0.135118i \(-0.956859\pi\)
−0.990830 + 0.135118i \(0.956859\pi\)
\(542\) −9.36882 + 16.2273i −0.402425 + 0.697021i
\(543\) −0.291240 + 9.80878i −0.0124983 + 0.420935i
\(544\) −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 \(0.992320\pi\)
\(548\) −6.49643 −0.277514
\(549\) 15.9521 24.1914i 0.680821 1.03246i
\(550\) 11.3847 0.485447
\(551\) 9.34790 16.1910i 0.398234 0.689761i
\(552\) 19.6930 10.6033i 0.838191 0.451306i
\(553\) 0 0
\(554\) −14.2379 24.6608i −0.604911 1.04774i
\(555\) 52.5046 28.2700i 2.22870 1.19999i
\(556\) −2.57947 + 4.46777i −0.109394 + 0.189476i
\(557\) 30.5775 1.29561 0.647806 0.761805i \(-0.275687\pi\)
0.647806 + 0.761805i \(0.275687\pi\)
\(558\) −7.47719 0.444414i −0.316535 0.0188135i
\(559\) −31.1394 −1.31706
\(560\) 0 0
\(561\) −8.51550 5.25943i −0.359525 0.222053i
\(562\) −1.00951 1.74852i −0.0425836 0.0737570i
\(563\) 4.41357 + 7.64452i 0.186010 + 0.322178i 0.943916 0.330185i \(-0.107111\pi\)
−0.757907 + 0.652363i \(0.773778\pi\)
\(564\) −0.0101015 + 0.340212i −0.000425350 + 0.0143255i
\(565\) −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 \(-0.881021\pi\)
0.781698 + 0.623658i \(0.214354\pi\)
\(570\) 1.61769 54.4829i 0.0677576 2.28204i
\(571\) −3.33181 5.77086i −0.139432 0.241503i 0.787850 0.615867i \(-0.211194\pi\)
−0.927282 + 0.374364i \(0.877861\pi\)
\(572\) 0.588948 + 1.02009i 0.0246252 + 0.0426520i
\(573\) 36.8600 + 22.7658i 1.53985 + 0.951056i
\(574\) 0 0
\(575\) −31.9548 −1.33261
\(576\) −26.4320 1.57101i −1.10133 0.0654587i
\(577\) −7.91259 −0.329405 −0.164703 0.986343i \(-0.552666\pi\)
−0.164703 + 0.986343i \(0.552666\pi\)
\(578\) −4.57627 + 7.92633i −0.190348 + 0.329692i
\(579\) 26.7397 14.3974i 1.11127 0.598337i
\(580\) 1.48963 + 2.58011i 0.0618533 + 0.107133i
\(581\) 0 0
\(582\) −21.6654 + 11.6653i −0.898059 + 0.483540i
\(583\) 1.31263 2.27354i 0.0543634 0.0941602i
\(584\) 3.11747 0.129002
\(585\) −18.7534 + 28.4395i −0.775358 + 1.17583i
\(586\) −13.5008 −0.557714
\(587\) 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
\(590\) −18.8208 32.5985i −0.774839 1.34206i
\(591\) 1.01545 34.1999i 0.0417702 1.40679i
\(592\) −16.0287 + 27.7625i −0.658775 + 1.14103i
\(593\) 28.3816 1.16549 0.582745 0.812655i \(-0.301978\pi\)
0.582745 + 0.812655i \(0.301978\pi\)
\(594\) −7.22039 + 3.35127i −0.296256 + 0.137504i
\(595\) 0 0
\(596\) 0.175096 0.303275i 0.00717222 0.0124226i
\(597\) −0.977835 + 32.9329i −0.0400201 + 1.34785i
\(598\) 9.00044 + 15.5892i 0.368055 + 0.637490i
\(599\) −4.69451 8.13113i −0.191813 0.332229i 0.754038 0.656830i \(-0.228103\pi\)
−0.945851 + 0.324601i \(0.894770\pi\)
\(600\) 32.8886 + 20.3130i 1.34267 + 0.829274i
\(601\) 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
\(603\) 7.16336 + 14.3058i 0.291714 + 0.582577i
\(604\) 6.09168 0.247867
\(605\) −16.9435 + 29.3471i −0.688853 + 1.19313i
\(606\) 3.16205 1.70254i 0.128449 0.0691608i
\(607\) 12.0133 + 20.8076i 0.487604 + 0.844554i 0.999898 0.0142555i \(-0.00453781\pi\)
−0.512295 + 0.858810i \(0.671204\pi\)
\(608\) −5.96947 10.3394i −0.242094 0.419319i
\(609\) 0 0
\(610\) 22.1347 38.3383i 0.896206 1.55227i
\(611\) −2.03935 −0.0825031
\(612\) −2.04385 4.08172i −0.0826177 0.164994i
\(613\) −28.5415 −1.15278 −0.576390 0.817175i \(-0.695539\pi\)
−0.576390 + 0.817175i \(0.695539\pi\)
\(614\) −6.91695 + 11.9805i −0.279145 + 0.483494i
\(615\) −34.5701 21.3515i −1.39400 0.860976i
\(616\) 0 0
\(617\) −6.05549 10.4884i −0.243785 0.422248i 0.718004 0.696039i \(-0.245056\pi\)
−0.961789 + 0.273791i \(0.911722\pi\)
\(618\) 0.156062 5.25606i 0.00627772 0.211430i
\(619\) −13.2870 + 23.0137i −0.534048 + 0.924998i 0.465161 + 0.885226i \(0.345997\pi\)
−0.999209 + 0.0397721i \(0.987337\pi\)
\(620\) 2.10171 0.0844067
\(621\) 20.2662 9.40636i 0.813256 0.377464i
\(622\) 17.8207 0.714545
\(623\) 0 0
\(624\) 0.543522 18.3055i 0.0217583 0.732806i
\(625\) 3.46486 + 6.00131i 0.138594 + 0.240052i
\(626\) 13.7903 + 23.8855i 0.551170 + 0.954655i
\(627\) −11.9250 7.36526i −0.476240 0.294140i
\(628\) −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
\(633\) −11.3405 + 6.10604i −0.450744 + 0.242693i
\(634\) −2.32055 4.01931i −0.0921608 0.159627i
\(635\) −5.36227 9.28773i −0.212795 0.368572i
\(636\) 1.05424 0.567631i 0.0418032 0.0225080i
\(637\) 0 0
\(638\) −4.17119 −0.165139
\(639\) 9.81426 + 0.583319i 0.388246 + 0.0230757i
\(640\) −28.1907 −1.11433
\(641\) −16.2922 + 28.2189i −0.643503 + 1.11458i 0.341142 + 0.940012i \(0.389186\pi\)
−0.984645 + 0.174568i \(0.944147\pi\)
\(642\) 4.25944 + 2.63075i 0.168107 + 0.103828i
\(643\) −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
\(645\) −1.75243 + 59.0208i −0.0690019 + 2.32394i
\(646\) −21.8814 + 37.8997i −0.860912 + 1.49114i
\(647\) −46.1975 −1.81621 −0.908106 0.418739i \(-0.862472\pi\)
−0.908106 + 0.418739i \(0.862472\pi\)
\(648\) −26.8379 3.20158i −1.05429 0.125770i
\(649\) −9.67935 −0.379948
\(650\) −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 −0.988320 0.152395i \(-0.951301\pi\)
0.362182 0.932107i \(-0.382032\pi\)
\(654\) 1.76146 + 1.08793i 0.0688786 + 0.0425414i
\(655\) 5.75022 9.95967i 0.224680 0.389156i
\(656\) 21.8435 0.852845
\(657\) 3.10873 + 0.184770i 0.121283 + 0.00720857i
\(658\) 0 0
\(659\) 19.2070 33.2674i 0.748197 1.29591i −0.200490 0.979696i \(-0.564253\pi\)
0.948686 0.316219i \(-0.102413\pi\)
\(660\) 1.96659 1.05887i 0.0765495 0.0412164i
\(661\) 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
\(663\) 24.0822 12.9666i 0.935276 0.503579i
\(664\) −10.9794 + 19.0169i −0.426083 + 0.737998i
\(665\) 0 0
\(666\) −20.9620 + 31.7889i −0.812263 + 1.23179i
\(667\) 11.7077 0.453325
\(668\) 0.798544 1.38312i 0.0308966 0.0535145i
\(669\) −4.85017 2.99561i −0.187518 0.115817i
\(670\) 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 \(0.156895\pi\)
\(674\) 35.7383 1.37659
\(675\) 31.5925 + 22.2053i 1.21599 + 0.854683i
\(676\) 0.815462 0.0313639
\(677\) −21.0167 + 36.4020i −0.807737 + 1.39904i 0.106691 + 0.994292i \(0.465975\pi\)
−0.914428 + 0.404749i \(0.867359\pi\)
\(678\) 0.159469 5.37082i 0.00612437 0.206265i
\(679\) 0 0
\(680\) −25.9588 44.9620i −0.995476 1.72421i
\(681\) −26.5504 16.3983i −1.01741 0.628386i
\(682\) −1.47128 + 2.54833i −0.0563382 + 0.0975807i
\(683\) 35.7289 1.36713 0.683565 0.729890i \(-0.260429\pi\)
0.683565 + 0.729890i \(0.260429\pi\)
\(684\) −2.86219 5.71602i −0.109439 0.218557i
\(685\) −73.8092 −2.82010
\(686\) 0 0
\(687\) −6.48892 + 3.49382i −0.247568 + 0.133298i
\(688\) −15.8715 27.4902i −0.605095 1.04806i
\(689\) 3.58704 + 6.21294i 0.136655 + 0.236694i
\(690\) 30.0539 16.1819i 1.14413 0.616033i
\(691\) −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
\(696\) −12.0499 7.44236i −0.456749 0.282102i
\(697\) 16.3115 + 28.2524i 0.617843 + 1.07014i
\(698\) 9.83977 + 17.0430i 0.372441 + 0.645086i
\(699\) 0.755936 25.4595i 0.0285921 0.962965i
\(700\) 0 0
\(701\) −24.5761 −0.928226 −0.464113 0.885776i \(-0.653627\pi\)
−0.464113 + 0.885776i \(0.653627\pi\)
\(702\) 1.93453 21.6668i 0.0730141 0.817763i
\(703\) −67.0472 −2.52873
\(704\) −5.20100 + 9.00840i −0.196020 + 0.339517i
\(705\) −0.114768 + 3.86532i −0.00432242 + 0.145576i
\(706\) 21.4321 + 37.1215i 0.806607 + 1.39708i
\(707\) 0 0
\(708\) −3.75597 2.31980i −0.141158 0.0871833i
\(709\) −15.4488 + 26.7581i −0.580192 + 1.00492i 0.415265 + 0.909701i \(0.363689\pi\)
−0.995456 + 0.0952206i \(0.969644\pi\)
\(710\) 15.0198 0.563685
\(711\) 1.65824 2.51471i 0.0621888 0.0943092i
\(712\) 36.1664 1.35539
\(713\) 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
\(717\) −21.6003 + 11.6302i −0.806677 + 0.434338i
\(718\) 15.6216 27.0573i 0.582992 1.00977i
\(719\) 6.11380 0.228006 0.114003 0.993480i \(-0.463633\pi\)
0.114003 + 0.993480i \(0.463633\pi\)
\(720\) −34.6651 2.06035i −1.29189 0.0767848i
\(721\) 0 0
\(722\) −18.2938 + 31.6857i −0.680823 + 1.17922i
\(723\) 11.6934 + 7.22216i 0.434881 + 0.268595i
\(724\) 0.879109 + 1.52266i 0.0326718 + 0.0565893i
\(725\) 10.1174 + 17.5238i 0.375749 + 0.650816i
\(726\) 0.642209 21.6292i 0.0238346 0.802736i
\(727\) 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
\(729\) −26.5729 4.78327i −0.984182 0.177158i
\(730\) 4.75763 0.176088
\(731\) 23.7039 41.0564i 0.876722 1.51853i
\(732\) 0.154089 5.18962i 0.00569529 0.191814i
\(733\) −4.91854 8.51916i −0.181670 0.314662i 0.760779 0.649011i \(-0.224817\pi\)
−0.942449 + 0.334349i \(0.891484\pi\)
\(734\) −1.72559 2.98881i −0.0636926 0.110319i
\(735\) 0 0
\(736\) 3.73821 6.47478i 0.137792 0.238663i
\(737\) 6.28514 0.231516
\(738\) 25.9002 + 1.53940i 0.953400 + 0.0566662i
\(739\) 14.8493 0.546239 0.273120 0.961980i \(-0.411944\pi\)
0.273120 + 0.961980i \(0.411944\pi\)
\(740\) 5.34212 9.25282i 0.196380 0.340140i
\(741\) 33.7246 18.1583i 1.23890 0.667061i
\(742\) 0 0
\(743\) −3.04201 5.26892i −0.111601 0.193298i 0.804815 0.593525i \(-0.202264\pi\)
−0.916416 + 0.400228i \(0.868931\pi\)
\(744\) −8.79710 + 4.73661i −0.322517 + 0.173652i
\(745\) 1.98935 3.44566i 0.0728843 0.126239i
\(746\) −41.4897 −1.51905
\(747\) −12.0757 + 18.3128i −0.441828 + 0.670031i
\(748\) −1.79328 −0.0655686
\(749\) 0 0
\(750\) 16.4225 + 10.1430i 0.599665 + 0.370371i
\(751\) −11.1005 19.2266i −0.405063 0.701590i 0.589266 0.807939i \(-0.299417\pi\)
−0.994329 + 0.106349i \(0.966084\pi\)
\(752\) −1.03944 1.80036i −0.0379044 0.0656523i
\(753\) 0.413860 13.9386i 0.0150819 0.507949i
\(754\) 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
\(759\) 0.260497 8.77338i 0.00945544 0.318454i
\(760\) −36.3526 62.9645i −1.31865 2.28396i
\(761\) −3.37632 5.84796i −0.122392 0.211988i 0.798319 0.602235i \(-0.205723\pi\)
−0.920710 + 0.390247i \(0.872390\pi\)
\(762\) 5.82649 + 3.59862i 0.211072 + 0.130364i
\(763\) 0 0
\(764\) 7.76233 0.280831
\(765\) −23.2212 46.3745i −0.839563 1.67667i
\(766\) −2.25275 −0.0813950
\(767\) 13.2255 22.9072i 0.477544 0.827131i
\(768\) −11.0709 + 5.96087i −0.399485 + 0.215094i
\(769\) 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
\(771\) 26.7702 14.4138i 0.964104 0.519101i
\(772\) 2.72065 4.71230i 0.0979183 0.169600i
\(773\) 3.29852 0.118639 0.0593197 0.998239i \(-0.481107\pi\)
0.0593197 + 0.998239i \(0.481107\pi\)
\(774\) −16.8818 33.7142i −0.606803 1.21183i
\(775\) 14.2746 0.512757
\(776\) −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
\(780\) −0.181148 + 6.10094i −0.00648612 + 0.218449i
\(781\) 1.93114 3.34484i 0.0691017 0.119688i
\(782\) −27.4052 −0.980009
\(783\) −11.5750 8.13567i −0.413656 0.290745i