Properties

Label 441.2.g.h.67.4
Level $441$
Weight $2$
Character 441.67
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.g (of order \(3\), degree \(2\), not 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 67.4
Character \(\chi\) \(=\) 441.67
Dual form 441.2.g.h.79.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.649936 + 1.12572i) q^{2} +(1.52504 + 0.821126i) q^{3} +(0.155166 + 0.268756i) q^{4} -3.52584 q^{5} +(-1.91554 + 1.18309i) q^{6} -3.00314 q^{8} +(1.65150 + 2.50450i) q^{9} +O(q^{10})\) \(q+(-0.649936 + 1.12572i) q^{2} +(1.52504 + 0.821126i) q^{3} +(0.155166 + 0.268756i) q^{4} -3.52584 q^{5} +(-1.91554 + 1.18309i) q^{6} -3.00314 q^{8} +(1.65150 + 2.50450i) q^{9} +(2.29157 - 3.96912i) q^{10} +1.17853 q^{11} +(0.0159526 + 0.537275i) q^{12} +(-1.61030 + 2.78913i) q^{13} +(-5.37706 - 2.89516i) q^{15} +(1.64151 - 2.84319i) q^{16} +(-2.45159 + 4.24627i) q^{17} +(-3.89275 + 0.231369i) q^{18} +(-3.43318 - 5.94645i) q^{19} +(-0.547092 - 0.947591i) q^{20} +(-0.765972 + 1.32670i) q^{22} -4.29987 q^{23} +(-4.57991 - 2.46595i) q^{24} +7.43156 q^{25} +(-2.09319 - 3.62551i) q^{26} +(0.462101 + 5.17556i) q^{27} +(1.36140 + 2.35802i) q^{29} +(6.75389 - 4.17140i) q^{30} +(-0.960401 - 1.66346i) q^{31} +(-0.869378 - 1.50581i) q^{32} +(1.79731 + 0.967725i) q^{33} +(-3.18675 - 5.51961i) q^{34} +(-0.416842 + 0.832466i) q^{36} +(4.88229 + 8.45637i) q^{37} +8.92540 q^{38} +(-4.74600 + 2.93127i) q^{39} +10.5886 q^{40} +(3.32673 - 5.76206i) q^{41} +(4.83441 + 8.37344i) q^{43} +(0.182869 + 0.316738i) q^{44} +(-5.82294 - 8.83048i) q^{45} +(2.79464 - 4.84046i) q^{46} +(0.316609 - 0.548383i) q^{47} +(4.83799 - 2.98809i) q^{48} +(-4.83004 + 8.36587i) q^{50} +(-7.22550 + 4.46268i) q^{51} -0.999459 q^{52} +(1.11378 - 1.92912i) q^{53} +(-6.12658 - 2.84359i) q^{54} -4.15533 q^{55} +(-0.352965 - 11.8877i) q^{57} -3.53930 q^{58} +(4.10652 + 7.11270i) q^{59} +(-0.0562464 - 1.89435i) q^{60} +(-4.82958 + 8.36508i) q^{61} +2.49680 q^{62} +8.82622 q^{64} +(5.67767 - 9.83402i) q^{65} +(-2.25753 + 1.39432i) q^{66} +(-2.66651 - 4.61852i) q^{67} -1.52161 q^{68} +(-6.55748 - 3.53074i) q^{69} -3.27719 q^{71} +(-4.95969 - 7.52136i) q^{72} +(0.519036 - 0.898997i) q^{73} -12.6927 q^{74} +(11.3334 + 6.10225i) q^{75} +(1.06543 - 1.84538i) q^{76} +(-0.215200 - 7.24782i) q^{78} +(-0.502039 + 0.869557i) q^{79} +(-5.78772 + 10.0246i) q^{80} +(-3.54507 + 8.27239i) q^{81} +(4.32432 + 7.48994i) q^{82} +(3.65598 + 6.33234i) q^{83} +(8.64391 - 14.9717i) q^{85} -12.5682 q^{86} +(0.139966 + 4.71396i) q^{87} -3.53930 q^{88} +(6.02144 + 10.4294i) q^{89} +(13.7252 - 0.815770i) q^{90} +(-0.667195 - 1.15562i) q^{92} +(-0.0987387 - 3.32546i) q^{93} +(0.411551 + 0.712828i) q^{94} +(12.1049 + 20.9662i) q^{95} +(-0.0893807 - 3.01029i) q^{96} +(5.46454 + 9.46487i) q^{97} +(1.94636 + 2.95164i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} - 4q^{9} + O(q^{10}) \) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} - 4q^{9} - 40q^{11} + 4q^{15} - 12q^{16} + 28q^{18} - 64q^{23} + 24q^{25} + 16q^{29} + 84q^{30} + 48q^{32} - 4q^{36} - 12q^{37} - 40q^{39} + 56q^{44} + 24q^{46} - 4q^{50} - 8q^{51} + 32q^{53} - 12q^{57} + 56q^{60} + 96q^{64} + 60q^{65} - 12q^{67} - 112q^{71} - 168q^{72} - 136q^{74} - 60q^{78} + 12q^{79} - 40q^{81} + 12q^{85} - 152q^{86} + 16q^{92} + 112q^{93} + 64q^{95} + 20q^{99} + O(q^{100}) \)

Character values

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

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

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 \(-0.985331\pi\)
0.539364 + 0.842073i \(0.318665\pi\)
\(3\) 1.52504 + 0.821126i 0.880483 + 0.474077i
\(4\) 0.155166 + 0.268756i 0.0775831 + 0.134378i
\(5\) −3.52584 −1.57680 −0.788402 0.615160i \(-0.789091\pi\)
−0.788402 + 0.615160i \(0.789091\pi\)
\(6\) −1.91554 + 1.18309i −0.782016 + 0.482996i
\(7\) 0 0
\(8\) −3.00314 −1.06177
\(9\) 1.65150 + 2.50450i 0.550501 + 0.834834i
\(10\) 2.29157 3.96912i 0.724659 1.25515i
\(11\) 1.17853 0.355342 0.177671 0.984090i \(-0.443144\pi\)
0.177671 + 0.984090i \(0.443144\pi\)
\(12\) 0.0159526 + 0.537275i 0.00460513 + 0.155098i
\(13\) −1.61030 + 2.78913i −0.446618 + 0.773564i −0.998163 0.0605803i \(-0.980705\pi\)
0.551546 + 0.834145i \(0.314038\pi\)
\(14\) 0 0
\(15\) −5.37706 2.89516i −1.38835 0.747527i
\(16\) 1.64151 2.84319i 0.410379 0.710797i
\(17\) −2.45159 + 4.24627i −0.594597 + 1.02987i 0.399006 + 0.916948i \(0.369355\pi\)
−0.993604 + 0.112924i \(0.963978\pi\)
\(18\) −3.89275 + 0.231369i −0.917529 + 0.0545342i
\(19\) −3.43318 5.94645i −0.787627 1.36421i −0.927417 0.374028i \(-0.877976\pi\)
0.139791 0.990181i \(-0.455357\pi\)
\(20\) −0.547092 0.947591i −0.122333 0.211888i
\(21\) 0 0
\(22\) −0.765972 + 1.32670i −0.163306 + 0.282854i
\(23\) −4.29987 −0.896585 −0.448293 0.893887i \(-0.647968\pi\)
−0.448293 + 0.893887i \(0.647968\pi\)
\(24\) −4.57991 2.46595i −0.934870 0.503361i
\(25\) 7.43156 1.48631
\(26\) −2.09319 3.62551i −0.410508 0.711020i
\(27\) 0.462101 + 5.17556i 0.0889314 + 0.996038i
\(28\) 0 0
\(29\) 1.36140 + 2.35802i 0.252806 + 0.437873i 0.964297 0.264822i \(-0.0853131\pi\)
−0.711491 + 0.702695i \(0.751980\pi\)
\(30\) 6.75389 4.17140i 1.23309 0.761590i
\(31\) −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
\(33\) 1.79731 + 0.967725i 0.312872 + 0.168459i
\(34\) −3.18675 5.51961i −0.546523 0.946606i
\(35\) 0 0
\(36\) −0.416842 + 0.832466i −0.0694737 + 0.138744i
\(37\) 4.88229 + 8.45637i 0.802643 + 1.39022i 0.917871 + 0.396879i \(0.129907\pi\)
−0.115228 + 0.993339i \(0.536760\pi\)
\(38\) 8.92540 1.44789
\(39\) −4.74600 + 2.93127i −0.759969 + 0.469379i
\(40\) 10.5886 1.67420
\(41\) 3.32673 5.76206i 0.519547 0.899883i −0.480194 0.877162i \(-0.659434\pi\)
0.999742 0.0227205i \(-0.00723278\pi\)
\(42\) 0 0
\(43\) 4.83441 + 8.37344i 0.737240 + 1.27694i 0.953734 + 0.300653i \(0.0972047\pi\)
−0.216493 + 0.976284i \(0.569462\pi\)
\(44\) 0.182869 + 0.316738i 0.0275685 + 0.0477501i
\(45\) −5.82294 8.83048i −0.868033 1.31637i
\(46\) 2.79464 4.84046i 0.412047 0.713687i
\(47\) 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
\(51\) −7.22550 + 4.46268i −1.01177 + 0.624900i
\(52\) −0.999459 −0.138600
\(53\) 1.11378 1.92912i 0.152989 0.264985i −0.779336 0.626606i \(-0.784443\pi\)
0.932325 + 0.361621i \(0.117777\pi\)
\(54\) −6.12658 2.84359i −0.833722 0.386963i
\(55\) −4.15533 −0.560304
\(56\) 0 0
\(57\) −0.352965 11.8877i −0.0467514 1.57456i
\(58\) −3.53930 −0.464733
\(59\) 4.10652 + 7.11270i 0.534623 + 0.925995i 0.999181 + 0.0404521i \(0.0128798\pi\)
−0.464558 + 0.885543i \(0.653787\pi\)
\(60\) −0.0562464 1.89435i −0.00726138 0.244559i
\(61\) −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
\(66\) −2.25753 + 1.39432i −0.277883 + 0.171629i
\(67\) −2.66651 4.61852i −0.325766 0.564242i 0.655901 0.754847i \(-0.272289\pi\)
−0.981667 + 0.190604i \(0.938955\pi\)
\(68\) −1.52161 −0.184523
\(69\) −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 \(0.562297\pi\)
\(72\) −4.95969 7.52136i −0.584506 0.886401i
\(73\) 0.519036 0.898997i 0.0607486 0.105220i −0.834052 0.551686i \(-0.813985\pi\)
0.894800 + 0.446467i \(0.147318\pi\)
\(74\) −12.6927 −1.47550
\(75\) 11.3334 + 6.10225i 1.30867 + 0.704627i
\(76\) 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 \(0.184656\pi\)
\(80\) −5.78772 + 10.0246i −0.647087 + 1.12079i
\(81\) −3.54507 + 8.27239i −0.393896 + 0.919155i
\(82\) 4.32432 + 7.48994i 0.477541 + 0.827126i
\(83\) 3.65598 + 6.33234i 0.401296 + 0.695064i 0.993883 0.110442i \(-0.0352267\pi\)
−0.592587 + 0.805506i \(0.701893\pi\)
\(84\) 0 0
\(85\) 8.64391 14.9717i 0.937563 1.62391i
\(86\) −12.5682 −1.35527
\(87\) 0.139966 + 4.71396i 0.0150059 + 0.505390i
\(88\) −3.53930 −0.377291
\(89\) 6.02144 + 10.4294i 0.638271 + 1.10552i 0.985812 + 0.167853i \(0.0536834\pi\)
−0.347541 + 0.937665i \(0.612983\pi\)
\(90\) 13.7252 0.815770i 1.44676 0.0859897i
\(91\) 0 0
\(92\) −0.667195 1.15562i −0.0695599 0.120481i
\(93\) −0.0987387 3.32546i −0.0102387 0.344834i
\(94\) 0.411551 + 0.712828i 0.0424483 + 0.0735226i
\(95\) 12.1049 + 20.9662i 1.24193 + 2.15109i
\(96\) −0.0893807 3.01029i −0.00912238 0.307236i
\(97\) 5.46454 + 9.46487i 0.554840 + 0.961012i 0.997916 + 0.0645275i \(0.0205540\pi\)
−0.443076 + 0.896484i \(0.646113\pi\)
\(98\) 0 0
\(99\) 1.94636 + 2.95164i 0.195616 + 0.296651i
\(100\) 1.15313 + 1.99728i 0.115313 + 0.199728i
\(101\) 1.59509 0.158718 0.0793588 0.996846i \(-0.474713\pi\)
0.0793588 + 0.996846i \(0.474713\pi\)
\(102\) −0.327629 11.0344i −0.0324401 1.09256i
\(103\) −2.33556 −0.230129 −0.115065 0.993358i \(-0.536708\pi\)
−0.115065 + 0.993358i \(0.536708\pi\)
\(104\) 4.83596 8.37613i 0.474205 0.821347i
\(105\) 0 0
\(106\) 1.44777 + 2.50761i 0.140620 + 0.243561i
\(107\) 1.11181 + 1.92571i 0.107483 + 0.186166i 0.914750 0.404021i \(-0.132388\pi\)
−0.807267 + 0.590186i \(0.799054\pi\)
\(108\) −1.31926 + 0.927265i −0.126946 + 0.0892262i
\(109\) 0.459782 0.796366i 0.0440391 0.0762780i −0.843166 0.537654i \(-0.819311\pi\)
0.887205 + 0.461376i \(0.152644\pi\)
\(110\) 2.70070 4.67774i 0.257501 0.446005i
\(111\) 0.501947 + 16.9053i 0.0476427 + 1.60458i
\(112\) 0 0
\(113\) 1.19327 2.06681i 0.112254 0.194429i −0.804425 0.594054i \(-0.797526\pi\)
0.916679 + 0.399625i \(0.130860\pi\)
\(114\) 13.6116 + 7.32888i 1.27484 + 0.686412i
\(115\) 15.1607 1.41374
\(116\) −0.422488 + 0.731770i −0.0392270 + 0.0679432i
\(117\) −9.64479 + 0.573247i −0.891662 + 0.0529967i
\(118\) −10.6759 −0.982796
\(119\) 0 0
\(120\) 16.1480 + 8.69456i 1.47411 + 0.793701i
\(121\) −9.61106 −0.873732
\(122\) −6.27783 10.8735i −0.568368 0.984443i
\(123\) 9.80477 6.05572i 0.884067 0.546026i
\(124\) 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
\(129\) 0.497025 + 16.7395i 0.0437606 + 1.47383i
\(130\) 7.38025 + 12.7830i 0.647291 + 1.12114i
\(131\) 3.26176 0.284981 0.142490 0.989796i \(-0.454489\pi\)
0.142490 + 0.989796i \(0.454489\pi\)
\(132\) 0.0188007 + 0.633197i 0.00163639 + 0.0551127i
\(133\) 0 0
\(134\) 6.93223 0.598854
\(135\) −1.62930 18.2482i −0.140227 1.57056i
\(136\) 7.36245 12.7521i 0.631325 1.09349i
\(137\) 20.9338 1.78849 0.894246 0.447575i \(-0.147712\pi\)
0.894246 + 0.447575i \(0.147712\pi\)
\(138\) 8.23657 5.08715i 0.701144 0.433047i
\(139\) 8.31195 14.3967i 0.705010 1.22111i −0.261677 0.965155i \(-0.584276\pi\)
0.966688 0.255958i \(-0.0823910\pi\)
\(140\) 0 0
\(141\) 0.933134 0.576331i 0.0785840 0.0485358i
\(142\) 2.12997 3.68921i 0.178743 0.309592i
\(143\) −1.89780 + 3.28708i −0.158702 + 0.274880i
\(144\) 9.83174 0.584358i 0.819311 0.0486965i
\(145\) −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 \(-0.485282\pi\)
0.0462228 + 0.998931i \(0.485282\pi\)
\(150\) −14.2354 + 8.79224i −1.16232 + 0.717883i
\(151\) −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
\(153\) −14.6836 + 0.872733i −1.18710 + 0.0705563i
\(154\) 0 0
\(155\) 3.38622 + 5.86511i 0.271988 + 0.471097i
\(156\) −1.52422 0.820681i −0.122035 0.0657071i
\(157\) 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
\(159\) 3.28261 2.02744i 0.260328 0.160786i
\(160\) 3.06529 + 5.30924i 0.242332 + 0.419732i
\(161\) 0 0
\(162\) −7.00835 9.36729i −0.550628 0.735964i
\(163\) −8.45056 14.6368i −0.661899 1.14644i −0.980116 0.198425i \(-0.936417\pi\)
0.318217 0.948018i \(-0.396916\pi\)
\(164\) 2.06478 0.161232
\(165\) −6.33705 3.41205i −0.493338 0.265627i
\(166\) −9.50460 −0.737700
\(167\) −2.57319 + 4.45689i −0.199119 + 0.344885i −0.948243 0.317545i \(-0.897141\pi\)
0.749124 + 0.662430i \(0.230475\pi\)
\(168\) 0 0
\(169\) 1.31385 + 2.27566i 0.101066 + 0.175051i
\(170\) 11.2360 + 19.4613i 0.861760 + 1.49261i
\(171\) 9.22298 18.4190i 0.705299 1.40854i
\(172\) −1.50027 + 2.59855i −0.114395 + 0.198138i
\(173\) 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
\(177\) 0.422191 + 14.2191i 0.0317338 + 1.06878i
\(178\) −15.6542 −1.17333
\(179\) −0.687990 + 1.19163i −0.0514228 + 0.0890668i −0.890591 0.454805i \(-0.849709\pi\)
0.839168 + 0.543872i \(0.183042\pi\)
\(180\) 1.46972 2.93514i 0.109546 0.218773i
\(181\) 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
\(184\) 12.9131 0.951967
\(185\) −17.2142 29.8158i −1.26561 2.19210i
\(186\) 3.80772 + 2.05018i 0.279196 + 0.150327i
\(187\) −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 \(-0.193415\pi\)
\(192\) 13.4604 + 7.24744i 0.971417 + 0.523039i
\(193\) −8.76688 15.1847i −0.631054 1.09302i −0.987337 0.158640i \(-0.949289\pi\)
0.356282 0.934378i \(-0.384044\pi\)
\(194\) −14.2064 −1.01996
\(195\) 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 \(0.748473\pi\)
\(198\) −4.58774 + 0.272676i −0.326036 + 0.0193783i
\(199\) −9.51110 + 16.4737i −0.674224 + 1.16779i 0.302471 + 0.953158i \(0.402188\pi\)
−0.976695 + 0.214631i \(0.931145\pi\)
\(200\) −22.3180 −1.57812
\(201\) −0.274143 9.23298i −0.0193366 0.651244i
\(202\) −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
\(206\) 1.51796 2.62919i 0.105761 0.183184i
\(207\) −7.10126 10.7690i −0.493572 0.748500i
\(208\) 5.28667 + 9.15678i 0.366565 + 0.634908i
\(209\) −4.04613 7.00810i −0.279876 0.484760i
\(210\) 0 0
\(211\) 3.71809 6.43993i 0.255964 0.443343i −0.709193 0.705015i \(-0.750940\pi\)
0.965157 + 0.261672i \(0.0842738\pi\)
\(212\) 0.691283 0.0474775
\(213\) −4.99786 2.69099i −0.342447 0.184383i
\(214\) −2.89043 −0.197585
\(215\) −17.0454 29.5234i −1.16248 2.01348i
\(216\) −1.38775 15.5429i −0.0944246 1.05756i
\(217\) 0 0
\(218\) 0.597658 + 1.03517i 0.0404785 + 0.0701108i
\(219\) 1.52974 0.944814i 0.103370 0.0638446i
\(220\) −0.644767 1.11677i −0.0434702 0.0752925i
\(221\) −7.89559 13.6756i −0.531115 0.919918i
\(222\) −19.3569 10.4223i −1.29915 0.699499i
\(223\) −1.64565 2.85034i −0.110201 0.190873i 0.805650 0.592391i \(-0.201816\pi\)
−0.915851 + 0.401518i \(0.868483\pi\)
\(224\) 0 0
\(225\) 12.2733 + 18.6124i 0.818217 + 1.24082i
\(226\) 1.55110 + 2.68659i 0.103178 + 0.178709i
\(227\) 18.0169 1.19583 0.597913 0.801561i \(-0.295997\pi\)
0.597913 + 0.801561i \(0.295997\pi\)
\(228\) 3.14011 1.93943i 0.207959 0.128442i
\(229\) −4.25491 −0.281173 −0.140586 0.990068i \(-0.544899\pi\)
−0.140586 + 0.990068i \(0.544899\pi\)
\(230\) −9.85347 + 17.0667i −0.649718 + 1.12535i
\(231\) 0 0
\(232\) −4.08848 7.08146i −0.268422 0.464920i
\(233\) 7.35275 + 12.7353i 0.481695 + 0.834320i 0.999779 0.0210095i \(-0.00668801\pi\)
−0.518084 + 0.855330i \(0.673355\pi\)
\(234\) 5.62318 11.2299i 0.367599 0.734124i
\(235\) −1.11631 + 1.93351i −0.0728203 + 0.126128i
\(236\) −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 −0.540772 0.841169i \(-0.681868\pi\)
0.998860 + 0.0477377i \(0.0152011\pi\)
\(240\) −17.0580 + 10.5355i −1.10109 + 0.680065i
\(241\) −7.93503 −0.511140 −0.255570 0.966791i \(-0.582263\pi\)
−0.255570 + 0.966791i \(0.582263\pi\)
\(242\) 6.24657 10.8194i 0.401545 0.695496i
\(243\) −12.1991 + 9.70480i −0.782569 + 0.622563i
\(244\) −2.99755 −0.191899
\(245\) 0 0
\(246\) 0.444583 + 14.9733i 0.0283456 + 0.954662i
\(247\) 22.1139 1.40707
\(248\) 2.88422 + 4.99561i 0.183148 + 0.317221i
\(249\) 0.375871 + 12.6591i 0.0238198 + 0.802238i
\(250\) 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
\(255\) 25.4760 15.7347i 1.59537 0.985346i
\(256\) 3.62969 + 6.28681i 0.226856 + 0.392926i
\(257\) 17.5537 1.09497 0.547486 0.836815i \(-0.315585\pi\)
0.547486 + 0.836815i \(0.315585\pi\)
\(258\) −19.1671 10.3201i −1.19329 0.642501i
\(259\) 0 0
\(260\) 3.52393 0.218545
\(261\) −3.65730 + 7.30392i −0.226381 + 0.452101i
\(262\) −2.11993 + 3.67183i −0.130970 + 0.226846i
\(263\) −23.3486 −1.43973 −0.719867 0.694112i \(-0.755797\pi\)
−0.719867 + 0.694112i \(0.755797\pi\)
\(264\) −5.39758 2.90621i −0.332198 0.178865i
\(265\) −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
\(269\) 0.269244 0.466344i 0.0164161 0.0284335i −0.857701 0.514149i \(-0.828108\pi\)
0.874117 + 0.485716i \(0.161441\pi\)
\(270\) 21.6014 + 10.0260i 1.31462 + 0.610165i
\(271\) −7.20749 12.4837i −0.437824 0.758334i 0.559697 0.828697i \(-0.310917\pi\)
−0.997521 + 0.0703635i \(0.977584\pi\)
\(272\) 8.04863 + 13.9406i 0.488020 + 0.845275i
\(273\) 0 0
\(274\) −13.6056 + 23.5656i −0.821945 + 1.42365i
\(275\) 8.75835 0.528148
\(276\) −0.0685943 2.31021i −0.00412889 0.139059i
\(277\) 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
\(279\) 2.58004 5.15254i 0.154463 0.308475i
\(280\) 0 0
\(281\) −0.776622 1.34515i −0.0463294 0.0802449i 0.841931 0.539586i \(-0.181419\pi\)
−0.888260 + 0.459341i \(0.848086\pi\)
\(282\) 0.0423116 + 1.42503i 0.00251962 + 0.0848592i
\(283\) −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
\(285\) 1.24450 + 41.9140i 0.0737178 + 2.48277i
\(286\) −2.46689 4.27279i −0.145870 0.252655i
\(287\) 0 0
\(288\) 2.33552 4.66421i 0.137622 0.274841i
\(289\) −3.52056 6.09778i −0.207091 0.358693i
\(290\) 12.4790 0.732793
\(291\) 0.561809 + 18.9214i 0.0329338 + 1.10919i
\(292\) 0.322148 0.0188523
\(293\) 5.19314 8.99478i 0.303386 0.525481i −0.673514 0.739174i \(-0.735216\pi\)
0.976901 + 0.213694i \(0.0685494\pi\)
\(294\) 0 0
\(295\) −14.4789 25.0783i −0.842996 1.46011i
\(296\) −14.6622 25.3956i −0.852221 1.47609i
\(297\) 0.544602 + 6.09958i 0.0316010 + 0.353934i
\(298\) −0.733415 + 1.27031i −0.0424856 + 0.0735872i
\(299\) 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
\(303\) 2.43258 + 1.30977i 0.139748 + 0.0752444i
\(304\) −22.5425 −1.29290
\(305\) 17.0283 29.4939i 0.975039 1.68882i
\(306\) 8.56095 17.0969i 0.489397 0.977364i
\(307\) 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
\(310\) −8.80331 −0.499994
\(311\) −6.85479 11.8728i −0.388699 0.673247i 0.603576 0.797306i \(-0.293742\pi\)
−0.992275 + 0.124059i \(0.960409\pi\)
\(312\) 14.2529 8.80301i 0.806911 0.498372i
\(313\) 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 \(0.198637\pi\)
\(318\) 0.148845 + 5.01301i 0.00834681 + 0.281116i
\(319\) 1.60446 + 2.77901i 0.0898326 + 0.155595i
\(320\) −31.1198 −1.73965
\(321\) 0.114305 + 3.84973i 0.00637989 + 0.214871i
\(322\) 0 0
\(323\) 33.6670 1.87328
\(324\) −2.77333 + 0.330839i −0.154074 + 0.0183800i
\(325\) −11.9671 + 20.7276i −0.663813 + 1.14976i
\(326\) 21.9693 1.21677
\(327\) 1.35510 0.836952i 0.0749374 0.0462835i
\(328\) −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 \(-0.0619666\pi\)
\(332\) −1.13457 + 1.96513i −0.0622675 + 0.107851i
\(333\) −13.1159 + 26.1934i −0.718746 + 1.43539i
\(334\) −3.34482 5.79339i −0.183020 0.317000i
\(335\) 9.40168 + 16.2842i 0.513669 + 0.889700i
\(336\) 0 0
\(337\) −13.7468 + 23.8102i −0.748838 + 1.29703i 0.199542 + 0.979889i \(0.436055\pi\)
−0.948380 + 0.317137i \(0.897279\pi\)
\(338\) −3.41568 −0.185788
\(339\) 3.51691 2.17215i 0.191012 0.117975i
\(340\) 5.36497 0.290956
\(341\) −1.13187 1.96045i −0.0612940 0.106164i
\(342\) 14.7403 + 22.3537i 0.797066 + 1.20875i
\(343\) 0 0
\(344\) −14.5184 25.1466i −0.782779 1.35581i
\(345\) 23.1207 + 12.4488i 1.24477 + 0.670222i
\(346\) 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 \(0.789379\pi\)
\(348\) −1.24519 + 0.769065i −0.0667490 + 0.0412262i
\(349\) 7.56980 + 13.1113i 0.405202 + 0.701830i 0.994345 0.106198i \(-0.0338679\pi\)
−0.589143 + 0.808029i \(0.700535\pi\)
\(350\) 0 0
\(351\) −15.1794 7.04537i −0.810218 0.376054i
\(352\) −1.02459 1.77465i −0.0546110 0.0945889i
\(353\) −32.9757 −1.75512 −0.877559 0.479468i \(-0.840829\pi\)
−0.877559 + 0.479468i \(0.840829\pi\)
\(354\) −16.2812 8.76626i −0.865336 0.465921i
\(355\) 11.5549 0.613269
\(356\) −1.86865 + 3.23659i −0.0990381 + 0.171539i
\(357\) 0 0
\(358\) −0.894299 1.54897i −0.0472651 0.0818656i
\(359\) 12.0178 + 20.8154i 0.634274 + 1.09859i 0.986669 + 0.162743i \(0.0520341\pi\)
−0.352395 + 0.935851i \(0.614633\pi\)
\(360\) 17.4871 + 26.5191i 0.921651 + 1.39768i
\(361\) −14.0735 + 24.3760i −0.740711 + 1.28295i
\(362\) −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
\(366\) −0.645424 21.7375i −0.0337368 1.13624i
\(367\) 2.65501 0.138590 0.0692952 0.997596i \(-0.477925\pi\)
0.0692952 + 0.997596i \(0.477925\pi\)
\(368\) −7.05830 + 12.2253i −0.367939 + 0.637290i
\(369\) 19.9252 1.18427i 1.03726 0.0616507i
\(370\) 44.7524 2.32657
\(371\) 0 0
\(372\) 0.878416 0.542536i 0.0455438 0.0281292i
\(373\) −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
\(375\) −13.0746 7.03976i −0.675171 0.363531i
\(376\) −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
\(381\) −4.63872 2.49762i −0.237649 0.127957i
\(382\) 16.2568 + 28.1576i 0.831771 + 1.44067i
\(383\) −1.73305 −0.0885548 −0.0442774 0.999019i \(-0.514099\pi\)
−0.0442774 + 0.999019i \(0.514099\pi\)
\(384\) −11.7824 + 7.27715i −0.601267 + 0.371360i
\(385\) 0 0
\(386\) 22.7917 1.16006
\(387\) −12.9873 + 25.9366i −0.660179 + 1.31843i
\(388\) −1.69583 + 2.93726i −0.0860925 + 0.149117i
\(389\) −11.0835 −0.561956 −0.280978 0.959714i \(-0.590659\pi\)
−0.280978 + 0.959714i \(0.590659\pi\)
\(390\) 0.758762 + 25.5547i 0.0384214 + 1.29401i
\(391\) 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
\(395\) 1.77011 3.06592i 0.0890639 0.154263i
\(396\) −0.491263 + 0.981090i −0.0246869 + 0.0493016i
\(397\) 12.6696 + 21.9443i 0.635867 + 1.10135i 0.986331 + 0.164777i \(0.0526905\pi\)
−0.350464 + 0.936576i \(0.613976\pi\)
\(398\) −12.3632 21.4137i −0.619712 1.07337i
\(399\) 0 0
\(400\) 12.1990 21.1293i 0.609951 1.05647i
\(401\) −34.8244 −1.73905 −0.869524 0.493890i \(-0.835575\pi\)
−0.869524 + 0.493890i \(0.835575\pi\)
\(402\) 10.5719 + 5.69224i 0.527281 + 0.283903i
\(403\) 6.18614 0.308154
\(404\) 0.247505 + 0.428690i 0.0123138 + 0.0213281i
\(405\) 12.4993 29.1672i 0.621097 1.44933i
\(406\) 0 0
\(407\) 5.75394 + 9.96612i 0.285212 + 0.494002i
\(408\) 21.6992 13.4020i 1.07427 0.663500i
\(409\) −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
\(411\) 31.9249 + 17.1893i 1.57474 + 0.847884i
\(412\) −0.362400 0.627695i −0.0178541 0.0309243i
\(413\) 0 0
\(414\) 16.7383 0.994856i 0.822643 0.0488945i
\(415\) −12.8904 22.3268i −0.632765 1.09598i
\(416\) 5.59985 0.274555
\(417\) 24.4976 15.1304i 1.19965 0.740941i
\(418\) 10.5189 0.514496
\(419\) 4.20719 7.28708i 0.205535 0.355997i −0.744768 0.667323i \(-0.767440\pi\)
0.950303 + 0.311326i \(0.100773\pi\)
\(420\) 0 0
\(421\) 0.144291 + 0.249919i 0.00703230 + 0.0121803i 0.869520 0.493897i \(-0.164428\pi\)
−0.862488 + 0.506078i \(0.831095\pi\)
\(422\) 4.83304 + 8.37108i 0.235269 + 0.407498i
\(423\) 1.89631 0.112709i 0.0922017 0.00548009i
\(424\) −3.34483 + 5.79341i −0.162439 + 0.281353i
\(425\) −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
\(429\) −5.59333 + 3.45461i −0.270048 + 0.166790i
\(430\) 44.3136 2.13699
\(431\) 6.74795 11.6878i 0.325037 0.562981i −0.656482 0.754341i \(-0.727956\pi\)
0.981520 + 0.191360i \(0.0612898\pi\)
\(432\) 15.4736 + 7.18192i 0.744476 + 0.345540i
\(433\) 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
\(436\) 0.285371 0.0136668
\(437\) 14.7623 + 25.5690i 0.706174 + 1.22313i
\(438\) 0.0693638 + 2.33613i 0.00331433 + 0.111625i
\(439\) 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 \(0.161785\pi\)
\(444\) −4.46551 + 2.75803i −0.211924 + 0.130890i
\(445\) −21.2306 36.7725i −1.00643 1.74319i
\(446\) 4.27826 0.202581
\(447\) 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 \(0.539357\pi\)
\(450\) −28.9292 + 1.71943i −1.36373 + 0.0810548i
\(451\) 3.92066 6.79079i 0.184617 0.319766i
\(452\) 0.740624 0.0348360
\(453\) −29.9358 16.1183i −1.40651 0.757304i
\(454\) −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 \(0.145353\pi\)
\(458\) 2.76542 4.78985i 0.129220 0.223815i
\(459\) −23.1097 10.7261i −1.07867 0.500653i
\(460\) 2.35242 + 4.07452i 0.109682 + 0.189975i
\(461\) −1.82624 3.16314i −0.0850566 0.147322i 0.820359 0.571849i \(-0.193774\pi\)
−0.905415 + 0.424527i \(0.860440\pi\)
\(462\) 0 0
\(463\) −15.4052 + 26.6825i −0.715939 + 1.24004i 0.246657 + 0.969103i \(0.420668\pi\)
−0.962596 + 0.270940i \(0.912666\pi\)
\(464\) 8.93905 0.414985
\(465\) 0.348137 + 11.7250i 0.0161445 + 0.543736i
\(466\) −19.1153 −0.885498
\(467\) 10.2885 + 17.8202i 0.476096 + 0.824622i 0.999625 0.0273858i \(-0.00871825\pi\)
−0.523529 + 0.852008i \(0.675385\pi\)
\(468\) −1.65061 2.50315i −0.0762995 0.115708i
\(469\) 0 0
\(470\) −1.45107 2.51332i −0.0669327 0.115931i
\(471\) 0.479730 + 16.1570i 0.0221048 + 0.744476i
\(472\) −12.3324 21.3604i −0.567647 0.983193i
\(473\) 5.69752 + 9.86839i 0.261972 + 0.453749i
\(474\) −0.0670923 2.25963i −0.00308165 0.103788i
\(475\) −25.5139 44.1914i −1.17066 2.02764i
\(476\) 0 0
\(477\) 6.67090 0.396491i 0.305439 0.0181541i
\(478\) 9.20552 + 15.9444i 0.421051 + 0.729281i
\(479\) −25.1832 −1.15065 −0.575325 0.817925i \(-0.695124\pi\)
−0.575325 + 0.817925i \(0.695124\pi\)
\(480\) 0.315142 + 10.6138i 0.0143842 + 0.484451i
\(481\) −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
\(486\) −2.99631 20.0402i −0.135915 0.909044i
\(487\) 16.3807 28.3723i 0.742282 1.28567i −0.209173 0.977879i \(-0.567077\pi\)
0.951454 0.307791i \(-0.0995896\pi\)
\(488\) 14.5039 25.1215i 0.656560 1.13720i
\(489\) −0.868801 29.2607i −0.0392886 1.32321i
\(490\) 0 0
\(491\) 1.76000 3.04841i 0.0794278 0.137573i −0.823575 0.567207i \(-0.808024\pi\)
0.903003 + 0.429634i \(0.141357\pi\)
\(492\) 3.14888 + 1.69545i 0.141962 + 0.0764367i
\(493\) −13.3504 −0.601272
\(494\) −14.3726 + 24.8941i −0.646654 + 1.12004i
\(495\) −6.86254 10.4070i −0.308448 0.467761i
\(496\) −6.30605 −0.283150
\(497\) 0 0
\(498\) −14.4949 7.80448i −0.649533 0.349727i
\(499\) 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
\(501\) −7.58389 + 4.68404i −0.338823 + 0.209267i
\(502\) 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
\(507\) 0.135077 + 4.54931i 0.00599898 + 0.202042i
\(508\) −0.471969 0.817474i −0.0209402 0.0362696i
\(509\) 37.6458 1.66862 0.834311 0.551294i \(-0.185866\pi\)
0.834311 + 0.551294i \(0.185866\pi\)
\(510\) 1.15517 + 38.9054i 0.0511518 + 1.72276i
\(511\) 0 0
\(512\) −25.4272 −1.12373
\(513\) 29.1898 20.5165i 1.28876 0.905827i
\(514\) −11.4088 + 19.7606i −0.503221 + 0.871604i
\(515\) 8.23480 0.362869
\(516\) −4.42172 + 2.73098i −0.194655 + 0.120225i
\(517\) 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
\(521\) −7.17115 + 12.4208i −0.314174 + 0.544165i −0.979262 0.202600i \(-0.935061\pi\)
0.665088 + 0.746765i \(0.268394\pi\)
\(522\) −5.84517 8.86419i −0.255836 0.387975i
\(523\) 5.24222 + 9.07980i 0.229226 + 0.397032i 0.957579 0.288171i \(-0.0930471\pi\)
−0.728353 + 0.685202i \(0.759714\pi\)
\(524\) 0.506114 + 0.876616i 0.0221097 + 0.0382951i
\(525\) 0 0
\(526\) 15.1751 26.2840i 0.661665 1.14604i
\(527\) 9.41802 0.410256
\(528\) 5.70174 3.52156i 0.248136 0.153256i
\(529\) −4.51110 −0.196135
\(530\) −5.10461 8.84144i −0.221730 0.384047i
\(531\) −11.0318 + 22.0314i −0.478741 + 0.956083i
\(532\) 0 0
\(533\) 10.7141 + 18.5573i 0.464078 + 0.803807i
\(534\) −23.8733 12.8541i −1.03310 0.556250i
\(535\) −3.92007 6.78976i −0.169479 0.293547i
\(536\) 8.00788 + 13.8701i 0.345888 + 0.599095i
\(537\) −2.02769 + 1.25236i −0.0875014 + 0.0540435i
\(538\) 0.349983 + 0.606188i 0.0150888 + 0.0261346i
\(539\) 0 0
\(540\) 4.65150 3.26939i 0.200169 0.140692i
\(541\) 23.0461 + 39.9170i 0.990830 + 1.71617i 0.612430 + 0.790524i \(0.290192\pi\)
0.378399 + 0.925643i \(0.376475\pi\)
\(542\) 18.7376 0.804851
\(543\) 8.64027 + 4.65217i 0.370789 + 0.199644i
\(544\) 8.52542 0.365525
\(545\) −1.62112 + 2.80786i −0.0694411 + 0.120275i
\(546\) 0 0
\(547\) −12.1793 21.0951i −0.520747 0.901961i −0.999709 0.0241250i \(-0.992320\pi\)
0.478962 0.877836i \(-0.341013\pi\)
\(548\) 3.24822 + 5.62607i 0.138757 + 0.240334i
\(549\) −28.9264 + 1.71927i −1.23455 + 0.0733765i
\(550\) −5.69237 + 9.85947i −0.242723 + 0.420409i
\(551\) 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
\(555\) −1.76979 59.6054i −0.0751233 2.53011i
\(556\) 5.15894 0.218788
\(557\) −15.2888 + 26.4809i −0.647806 + 1.12203i 0.335840 + 0.941919i \(0.390980\pi\)
−0.983646 + 0.180114i \(0.942353\pi\)
\(558\) 4.12347 + 6.25323i 0.174560 + 0.264720i
\(559\) −31.1394 −1.31706
\(560\) 0 0
\(561\) −8.51550 + 5.25943i −0.359525 + 0.222053i
\(562\) 2.01902 0.0851672
\(563\) 4.41357 + 7.64452i 0.186010 + 0.322178i 0.943916 0.330185i \(-0.107111\pi\)
−0.757907 + 0.652363i \(0.773778\pi\)
\(564\) 0.299683 + 0.161358i 0.0126189 + 0.00679440i
\(565\) −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 \(0.214354\pi\)
\(570\) −47.9924 25.8405i −2.01018 1.08234i
\(571\) −3.33181 5.77086i −0.139432 0.241503i 0.787850 0.615867i \(-0.211194\pi\)
−0.927282 + 0.374364i \(0.877861\pi\)
\(572\) −1.17790 −0.0492503
\(573\) 36.8600 22.7658i 1.53985 0.951056i
\(574\) 0 0
\(575\) −31.9548 −1.33261
\(576\) 14.5765 + 22.1053i 0.607356 + 0.921054i
\(577\) 3.95629 6.85250i 0.164703 0.285273i −0.771847 0.635808i \(-0.780667\pi\)
0.936550 + 0.350535i \(0.114000\pi\)
\(578\) 9.15254 0.380696
\(579\) −0.901323 30.3560i −0.0374577 1.26155i
\(580\) 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
\(584\) −1.55874 + 2.69981i −0.0645010 + 0.111719i
\(585\) 34.0060 2.02118i 1.40598 0.0835654i
\(586\) 6.75042 + 11.6921i 0.278857 + 0.482995i
\(587\) 9.13891 + 15.8291i 0.377203 + 0.653335i 0.990654 0.136398i \(-0.0435525\pi\)
−0.613451 + 0.789733i \(0.710219\pi\)
\(588\) 0 0
\(589\) −6.59447 + 11.4220i −0.271720 + 0.470633i
\(590\) 37.6415 1.54968
\(591\) −30.1257 16.2205i −1.23920 0.667223i
\(592\) 32.0574 1.31755
\(593\) −14.1908 24.5792i −0.582745 1.00934i −0.995152 0.0983450i \(-0.968645\pi\)
0.412407 0.911000i \(-0.364688\pi\)
\(594\) −7.22039 3.35127i −0.296256 0.137504i
\(595\) 0 0
\(596\) 0.175096 + 0.303275i 0.00717222 + 0.0124226i
\(597\) −28.0318 + 17.3133i −1.14727 + 0.708585i
\(598\) 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 \(0.894770\pi\)
\(600\) −34.0359 18.3259i −1.38951 0.748151i
\(601\) 6.31432 + 10.9367i 0.257566 + 0.446118i 0.965589 0.260071i \(-0.0837460\pi\)
−0.708023 + 0.706189i \(0.750413\pi\)
\(602\) 0 0
\(603\) 7.16336 14.3058i 0.291714 0.582577i
\(604\) −3.04584 5.27555i −0.123934 0.214659i
\(605\) 33.8871 1.37771
\(606\) −3.05546 + 1.88714i −0.124120 + 0.0766600i
\(607\) −24.0265 −0.975207 −0.487604 0.873065i \(-0.662129\pi\)
−0.487604 + 0.873065i \(0.662129\pi\)
\(608\) −5.96947 + 10.3394i −0.242094 + 0.419319i
\(609\) 0 0
\(610\) 22.1347 + 38.3383i 0.896206 + 1.55227i
\(611\) 1.01967 + 1.76613i 0.0412516 + 0.0714498i
\(612\) −2.51295 3.81089i −0.101580 0.154046i
\(613\) 14.2708 24.7177i 0.576390 0.998337i −0.419499 0.907756i \(-0.637794\pi\)
0.995889 0.0905814i \(-0.0288725\pi\)
\(614\) −6.91695 + 11.9805i −0.279145 + 0.483494i
\(615\) −34.5701 + 21.3515i −1.39400 + 0.860976i
\(616\) 0 0
\(617\) −6.05549 + 10.4884i −0.243785 + 0.422248i −0.961789 0.273791i \(-0.911722\pi\)
0.718004 + 0.696039i \(0.245056\pi\)
\(618\) 4.47385 2.76318i 0.179965 0.111152i
\(619\) 26.5739 1.06810 0.534048 0.845454i \(-0.320670\pi\)
0.534048 + 0.845454i \(0.320670\pi\)
\(620\) −1.05085 + 1.82013i −0.0422033 + 0.0730983i
\(621\) −1.98698 22.2543i −0.0797346 0.893033i
\(622\) 17.8207 0.714545
\(623\) 0 0
\(624\) 0.543522 + 18.3055i 0.0217583 + 0.732806i
\(625\) −6.92971 −0.277188
\(626\) 13.7903 + 23.8855i 0.551170 + 0.954655i
\(627\) −0.415982 14.0100i −0.0166127 0.559506i
\(628\) −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
\(633\) 10.9582 6.76813i 0.435551 0.269009i
\(634\) −2.32055 4.01931i −0.0921608 0.159627i
\(635\) 10.7245 0.425591
\(636\) 1.05424 + 0.567631i 0.0418032 + 0.0225080i
\(637\) 0 0
\(638\) −4.17119 −0.165139
\(639\) −5.41230 8.20774i −0.214107 0.324693i
\(640\) 14.0953 24.4138i 0.557167 0.965041i
\(641\) 32.5844 1.28701 0.643503 0.765443i \(-0.277480\pi\)
0.643503 + 0.765443i \(0.277480\pi\)
\(642\) −4.40802 2.37340i −0.173971 0.0936707i
\(643\) −21.5327 + 37.2957i −0.849166 + 1.47080i 0.0327873 + 0.999462i \(0.489562\pi\)
−0.881953 + 0.471337i \(0.843772\pi\)
\(644\) 0 0
\(645\) −1.75243 59.0208i −0.0690019 2.32394i
\(646\) −21.8814 + 37.8997i −0.860912 + 1.49114i
\(647\) 23.0988 40.0082i 0.908106 1.57289i 0.0914143 0.995813i \(-0.470861\pi\)
0.816692 0.577074i \(-0.195805\pi\)
\(648\) 10.6463 24.8431i 0.418227 0.975930i
\(649\) 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 \(-0.284635\pi\)
0.626138 + 0.779713i \(0.284635\pi\)
\(654\) 0.0614451 + 2.06943i 0.00240269 + 0.0809213i
\(655\) −11.5004 −0.449359
\(656\) −10.9217 18.9170i −0.426422 0.738585i
\(657\) 3.10873 0.184770i 0.121283 0.00720857i
\(658\) 0 0
\(659\) 19.2070 + 33.2674i 0.748197 + 1.29591i 0.948686 + 0.316219i \(0.102413\pi\)
−0.200490 + 0.979696i \(0.564253\pi\)
\(660\) −0.0662884 2.23255i −0.00258027 0.0869020i
\(661\) 14.0130 + 24.2712i 0.545043 + 0.944042i 0.998604 + 0.0528170i \(0.0168200\pi\)
−0.453561 + 0.891225i \(0.649847\pi\)
\(662\) 15.5631 + 26.9561i 0.604878 + 1.04768i
\(663\) −0.811745 27.3391i −0.0315256 1.06176i
\(664\) −10.9794 19.0169i −0.426083 0.737998i
\(665\) 0 0
\(666\) −20.9620 31.7889i −0.812263 1.23179i
\(667\) −5.85386 10.1392i −0.226662 0.392591i
\(668\) −1.59709 −0.0617932
\(669\) −0.169189 5.69817i −0.00654121 0.220304i
\(670\) −24.4420 −0.944275
\(671\) −5.69183 + 9.85853i −0.219730 + 0.380584i
\(672\) 0 0
\(673\) 0.796281 + 1.37920i 0.0306944 + 0.0531642i 0.880965 0.473182i \(-0.156895\pi\)
−0.850270 + 0.526347i \(0.823561\pi\)
\(674\) −17.8691 30.9503i −0.688293 1.19216i
\(675\) 3.43413 + 38.4625i 0.132180 + 1.48042i
\(676\) −0.407731 + 0.706211i −0.0156820 + 0.0271619i
\(677\) −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
\(681\) 27.4766 + 14.7942i 1.05291 + 0.566914i
\(682\) 2.94256 0.112676
\(683\) −17.8645 + 30.9422i −0.683565 + 1.18397i 0.290321 + 0.956929i \(0.406238\pi\)
−0.973886 + 0.227039i \(0.927095\pi\)
\(684\) 6.38131 0.379279i 0.243996 0.0145021i
\(685\) −73.8092 −2.82010
\(686\) 0 0
\(687\) −6.48892 3.49382i −0.247568 0.133298i
\(688\) 31.7430 1.21019
\(689\) 3.58704 + 6.21294i 0.136655 + 0.236694i
\(690\) −29.0409 + 17.9365i −1.10557 + 0.682831i
\(691\) −25.5675 + 44.2841i −0.972632 + 1.68465i −0.285094 + 0.958499i \(0.592025\pi\)
−0.687538 + 0.726149i \(0.741308\pi\)
\(692\) 3.02161 0.114864
\(693\) 0 0
\(694\) −6.66606 −0.253040
\(695\) −29.3066 + 50.7606i −1.11166 + 1.92546i
\(696\) −0.420336 14.1567i −0.0159328 0.536607i
\(697\) 16.3115 + 28.2524i 0.617843 + 1.07014i
\(698\) −19.6795 −0.744881
\(699\) 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 \(0.653627\pi\)
\(702\) 17.7968 12.5088i 0.671696 0.472113i
\(703\) 33.5236 58.0645i 1.26437 2.18995i
\(704\) 10.4020 0.392040
\(705\) −3.29008 + 2.03205i −0.123912 + 0.0765315i
\(706\) 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 \(0.969644\pi\)
\(710\) −7.50992 + 13.0076i −0.281842 + 0.488165i
\(711\) −3.00693 + 0.178719i −0.112769 + 0.00670250i
\(712\) −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
\(717\) 20.8722 12.8913i 0.779487 0.481434i
\(718\) −31.2431 −1.16598
\(719\) −3.05690 5.29471i −0.114003 0.197459i 0.803378 0.595470i \(-0.203034\pi\)
−0.917381 + 0.398011i \(0.869701\pi\)
\(720\) −34.6651 + 2.06035i −1.29189 + 0.0767848i
\(721\) 0 0
\(722\) −18.2938 31.6857i −0.680823 1.17922i
\(723\) −12.1013 6.51566i −0.450051 0.242320i
\(724\) 0.879109 + 1.52266i 0.0326718 + 0.0565893i
\(725\) 10.1174 + 17.5238i 0.375749 + 0.650816i
\(726\) 18.4104 11.3708i 0.683272 0.422009i
\(727\) 22.2492 + 38.5367i 0.825176 + 1.42925i 0.901785 + 0.432186i \(0.142257\pi\)
−0.0766087 + 0.997061i \(0.524409\pi\)
\(728\) 0 0
\(729\) −26.5729 + 4.78327i −0.984182 + 0.177158i
\(730\) −2.37882 4.12023i −0.0880440 0.152497i
\(731\) −47.4079 −1.75344
\(732\) −4.57139 2.46137i −0.168963 0.0909747i
\(733\) 9.83708 0.363341 0.181670 0.983359i \(-0.441850\pi\)
0.181670 + 0.983359i \(0.441850\pi\)
\(734\) −1.72559 + 2.98881i −0.0636926 + 0.110319i
\(735\) 0 0
\(736\) 3.73821 + 6.47478i 0.137792 + 0.238663i
\(737\) −3.14257 5.44309i −0.115758 0.200499i
\(738\) −11.6169 + 23.1999i −0.427626 + 0.854002i
\(739\) −7.42464 + 12.8598i −0.273120 + 0.473057i −0.969659 0.244461i \(-0.921389\pi\)
0.696539 + 0.717519i \(0.254722\pi\)
\(740\) 5.34212 9.25282i 0.196380 0.340140i
\(741\) 33.7246 + 18.1583i 1.23890 + 0.667061i
\(742\) 0 0
\(743\) −3.04201 + 5.26892i −0.111601 + 0.193298i −0.916416 0.400228i \(-0.868931\pi\)
0.804815 + 0.593525i \(0.202264\pi\)
\(744\) 0.296526 + 9.98681i 0.0108712 + 0.366134i
\(745\) −3.97871 −0.145769
\(746\) 20.7449 35.9311i 0.759523 1.31553i
\(747\) −9.82149 + 19.6143i −0.359350 + 0.717649i
\(748\) −1.79328 −0.0655686
\(749\) 0 0
\(750\) 16.4225 10.1430i 0.599665 0.370371i
\(751\) 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
\(753\) −12.2781 6.61086i −0.447438 0.240913i
\(754\) 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
\(759\) −7.72822 4.16110i −0.280517 0.151038i
\(760\) −36.3526 62.9645i −1.31865 2.28396i
\(761\) 6.75264 0.244783 0.122392 0.992482i \(-0.460944\pi\)
0.122392 + 0.992482i \(0.460944\pi\)
\(762\) 5.82649 3.59862i 0.211072 0.130364i
\(763\) 0 0
\(764\) 7.76233 0.280831
\(765\) 51.7721 3.07712i 1.87182 0.111253i
\(766\) 1.12637 1.95094i 0.0406975 0.0704902i
\(767\) −26.4510 −0.955089
\(768\) 0.373168 + 12.5681i 0.0134656 + 0.453512i
\(769\) 21.0805 36.5125i 0.760182 1.31667i −0.182575 0.983192i \(-0.558443\pi\)
0.942757 0.333482i \(-0.108224\pi\)
\(770\) 0 0
\(771\) 26.7702 + 14.4138i 0.964104 + 0.519101i
\(772\) 2.72065 4.71230i 0.0979183 0.169600i
\(773\) −1.64926 + 2.85660i −0.0593197 + 0.102745i −0.894160 0.447747i \(-0.852226\pi\)
0.834841 + 0.550492i \(0.185560\pi\)
\(774\) −20.7565 31.4771i −0.746076 1.13142i
\(775\) −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
\(780\) 5.37414 + 2.89359i 0.192425 + 0.103607i
\(781\) −3.86229 −0.138203
\(782\) 13.7026 + 23.7336i 0.490004 + 0.848713i
\(783\) −11.5750 + 8.13567i</