Properties

Label 441.2.g.h.67.3
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 67.3
Character \(\chi\) \(=\) 441.67
Dual form 441.2.g.h.79.3

$q$-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 \(-0.210909\pi\)
0.788402 + 0.615160i \(0.210909\pi\)
\(6\) 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 −0.551546 0.834145i \(-0.685962\pi\)
0.998163 + 0.0605803i \(0.0192951\pi\)
\(14\) 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 \(-0.630645\pi\)
0.993604 0.112924i \(-0.0360218\pi\)
\(18\) −3.89275 + 0.231369i −0.917529 + 0.0545342i
\(19\) 3.43318 + 5.94645i 0.787627 + 1.36421i 0.927417 + 0.374028i \(0.122024\pi\)
−0.139791 + 0.990181i \(0.544643\pi\)
\(20\) 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 0.939291 0.343122i \(-0.111484\pi\)
−0.766798 + 0.641889i \(0.778151\pi\)
\(32\) −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 \(0.340566\pi\)
−0.999742 + 0.0227205i \(0.992767\pi\)
\(42\) 0 0
\(43\) 4.83441 + 8.37344i 0.737240 + 1.27694i 0.953734 + 0.300653i \(0.0972047\pi\)
−0.216493 + 0.976284i \(0.569462\pi\)
\(44\) 0.182869 + 0.316738i 0.0275685 + 0.0477501i
\(45\) 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 −0.888192 0.459472i \(-0.848039\pi\)
0.842010 + 0.539461i \(0.181372\pi\)
\(48\) −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 \(-0.987120\pi\)
0.464558 0.885543i \(-0.346213\pi\)
\(60\) −0.0562464 1.89435i −0.00726138 0.244559i
\(61\) 4.82958 8.36508i 0.618364 1.07104i −0.371420 0.928465i \(-0.621129\pi\)
0.989784 0.142573i \(-0.0455376\pi\)
\(62\) −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 −0.894800 0.446467i \(-0.852682\pi\)
0.834052 + 0.551686i \(0.186015\pi\)
\(74\) −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 0.592587 0.805506i \(-0.298107\pi\)
−0.993883 + 0.110442i \(0.964773\pi\)
\(84\) 0 0
\(85\) 8.64391 14.9717i 0.937563 1.62391i
\(86\) −12.5682 −1.35527
\(87\) −0.139966 4.71396i −0.0150059 0.505390i
\(88\) −3.53930 −0.377291
\(89\) −6.02144 10.4294i −0.638271 1.10552i −0.985812 0.167853i \(-0.946317\pi\)
0.347541 0.937665i \(-0.387017\pi\)
\(90\) −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 \(-0.979446\pi\)
0.443076 0.896484i \(-0.353887\pi\)
\(98\) 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 \(-0.525287\pi\)
−0.0793588 + 0.996846i \(0.525287\pi\)
\(102\) −0.327629 11.0344i −0.0324401 1.09256i
\(103\) 2.33556 0.230129 0.115065 0.993358i \(-0.463292\pi\)
0.115065 + 0.993358i \(0.463292\pi\)
\(104\) −4.83596 + 8.37613i −0.474205 + 0.821347i
\(105\) 0 0
\(106\) 1.44777 + 2.50761i 0.140620 + 0.243561i
\(107\) 1.11181 + 1.92571i 0.107483 + 0.186166i 0.914750 0.404021i \(-0.132388\pi\)
−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 \(-0.545511\pi\)
−0.142490 + 0.989796i \(0.545511\pi\)
\(132\) −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 \(0.415724\pi\)
−0.966688 + 0.255958i \(0.917609\pi\)
\(140\) 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 0.617532 0.786545i \(-0.288132\pi\)
−0.989935 + 0.141526i \(0.954799\pi\)
\(158\) −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 −0.749124 0.662430i \(-0.769525\pi\)
0.948243 + 0.317545i \(0.102859\pi\)
\(168\) 0 0
\(169\) 1.31385 + 2.27566i 0.101066 + 0.175051i
\(170\) 11.2360 + 19.4613i 0.861760 + 1.49261i
\(171\) −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 −0.989586 0.143945i \(-0.954021\pi\)
0.619453 + 0.785034i \(0.287355\pi\)
\(174\) 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 \(-0.567529\pi\)
−0.210560 + 0.977581i \(0.567529\pi\)
\(182\) 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 \(-0.597812\pi\)
0.976695 0.214631i \(-0.0688550\pi\)
\(200\) −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 0.915851 0.401518i \(-0.131517\pi\)
−0.805650 + 0.592391i \(0.798184\pi\)
\(224\) 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 \(-0.704003\pi\)
−0.597913 + 0.801561i \(0.704003\pi\)
\(228\) 3.14011 1.93943i 0.207959 0.128442i
\(229\) 4.25491 0.281173 0.140586 0.990068i \(-0.455101\pi\)
0.140586 + 0.990068i \(0.455101\pi\)
\(230\) 9.85347 17.0667i 0.649718 1.12535i
\(231\) 0 0
\(232\) −4.08848 7.08146i −0.268422 0.464920i
\(233\) 7.35275 + 12.7353i 0.481695 + 0.834320i 0.999779 0.0210095i \(-0.00668801\pi\)
−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 \(-0.417737\pi\)
0.255570 + 0.966791i \(0.417737\pi\)
\(242\) 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 \(-0.418225\pi\)
0.254087 + 0.967181i \(0.418225\pi\)
\(252\) 0 0
\(253\) −5.06755 −0.318594
\(254\) 1.97691 3.42411i 0.124042 0.214848i
\(255\) −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 \(-0.684415\pi\)
−0.547486 + 0.836815i \(0.684415\pi\)
\(258\) 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 −0.874117 0.485716i \(-0.838559\pi\)
0.857701 + 0.514149i \(0.171892\pi\)
\(270\) 21.6014 + 10.0260i 1.31462 + 0.610165i
\(271\) 7.20749 + 12.4837i 0.437824 + 0.758334i 0.997521 0.0703635i \(-0.0224159\pi\)
−0.559697 + 0.828697i \(0.689083\pi\)
\(272\) −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 0.902735 0.430198i \(-0.141556\pi\)
−0.823930 + 0.566692i \(0.808223\pi\)
\(284\) −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 −0.976901 0.213694i \(-0.931451\pi\)
0.673514 + 0.739174i \(0.264784\pi\)
\(294\) 0 0
\(295\) −14.4789 25.0783i −0.842996 1.46011i
\(296\) −14.6622 25.3956i −0.852221 1.47609i
\(297\) −0.544602 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 \(-0.598222\pi\)
−0.303700 + 0.952768i \(0.598222\pi\)
\(308\) 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 0.992275 0.124059i \(-0.0395912\pi\)
−0.603576 + 0.797306i \(0.706258\pi\)
\(312\) 14.2529 8.80301i 0.806911 0.498372i
\(313\) −10.6090 + 18.3752i −0.599653 + 1.03863i 0.393219 + 0.919445i \(0.371362\pi\)
−0.992872 + 0.119185i \(0.961972\pi\)
\(314\) 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 0.589143 0.808029i \(-0.299465\pi\)
−0.994345 + 0.106198i \(0.966132\pi\)
\(350\) 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 \(-0.159171\pi\)
0.877559 + 0.479468i \(0.159171\pi\)
\(354\) −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 \(-0.522075\pi\)
−0.0692952 + 0.997596i \(0.522075\pi\)
\(368\) −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 \(-0.485901\pi\)
0.0442774 + 0.999019i \(0.485901\pi\)
\(384\) 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 \(-0.947310\pi\)
0.350464 0.936576i \(-0.386024\pi\)
\(398\) 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 0.998455 0.0555643i \(-0.0176958\pi\)
−0.547348 + 0.836905i \(0.684362\pi\)
\(410\) −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 −0.950303 0.311326i \(-0.899227\pi\)
0.744768 + 0.667323i \(0.232560\pi\)
\(420\) 0 0
\(421\) 0.144291 + 0.249919i 0.00703230 + 0.0121803i 0.869520 0.493897i \(-0.164428\pi\)
−0.862488 + 0.506078i \(0.831095\pi\)
\(422\) 4.83304 + 8.37108i 0.235269 + 0.407498i
\(423\) −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 \(-0.537196\pi\)
−0.116589 + 0.993180i \(0.537196\pi\)
\(434\) 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 −0.894825 0.446418i \(-0.852699\pi\)
0.834022 + 0.551732i \(0.186033\pi\)
\(440\) −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 0.905415 0.424527i \(-0.139560\pi\)
−0.820359 + 0.571849i \(0.806226\pi\)
\(462\) 0 0
\(463\) −15.4052 + 26.6825i −0.715939 + 1.24004i 0.246657 + 0.969103i \(0.420668\pi\)
−0.962596 + 0.270940i \(0.912666\pi\)
\(464\) 8.93905 0.414985
\(465\) −0.348137 11.7250i −0.0161445 0.543736i
\(466\) −19.1153 −0.885498
\(467\) −10.2885 17.8202i −0.476096 0.824622i 0.523529 0.852008i \(-0.324615\pi\)
−0.999625 + 0.0273858i \(0.991282\pi\)
\(468\) 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 \(-0.304876\pi\)
0.575325 + 0.817925i \(0.304876\pi\)
\(480\) 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 \(-0.803086\pi\)
−0.814678 + 0.579913i \(0.803086\pi\)
\(504\) 0 0
\(505\) −5.62404 −0.250267
\(506\) 3.29358 5.70465i 0.146418 0.253603i
\(507\) −0.135077 4.54931i −0.00599898 0.202042i
\(508\) −0.471969 0.817474i −0.0209402 0.0362696i
\(509\) −37.6458 −1.66862 −0.834311 0.551294i \(-0.814134\pi\)
−0.834311 + 0.551294i \(0.814134\pi\)
\(510\) −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 −0.665088 0.746765i \(-0.731606\pi\)
0.979262 + 0.202600i \(0.0649392\pi\)
\(522\) −5.84517 8.86419i −0.255836 0.387975i
\(523\) −5.24222 9.07980i −0.229226 0.397032i 0.728353 0.685202i \(-0.240286\pi\)
−0.957579 + 0.288171i \(0.906953\pi\)
\(524\) −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 0.757907 0.652363i \(-0.226222\pi\)
−0.943916 + 0.330185i \(0.892889\pi\)
\(564\) 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 −0.936550 0.350535i \(-0.886000\pi\)
0.771847 + 0.635808i \(0.219333\pi\)
\(578\) 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 0.613451 0.789733i \(-0.289781\pi\)
−0.990654 + 0.136398i \(0.956447\pi\)
\(588\) 0 0
\(589\) −6.59447 + 11.4220i −0.271720 + 0.470633i
\(590\) 37.6415 1.54968
\(591\) 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 \(0.0313549\pi\)
−0.412407 + 0.911000i \(0.635312\pi\)
\(594\) 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 0.708023 0.706189i \(-0.249587\pi\)
−0.965589 + 0.260071i \(0.916254\pi\)
\(602\) 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 \(-0.337871\pi\)
0.487604 + 0.873065i \(0.337871\pi\)
\(608\) 5.96947 10.3394i 0.242094 0.419319i
\(609\) 0 0
\(610\) 22.1347 + 38.3383i 0.896206 + 1.55227i
\(611\) 1.01967 + 1.76613i 0.0412516 + 0.0714498i
\(612\) 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 \(-0.679330\pi\)
−0.534048 + 0.845454i \(0.679330\pi\)
\(620\) −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 \(-0.510438\pi\)
0.881953 0.471337i \(-0.156228\pi\)
\(644\) 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 \(0.529139\pi\)
−0.816692 + 0.577074i \(0.804195\pi\)
\(648\) 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 \(-0.983180\pi\)
0.453561 0.891225i \(-0.350153\pi\)
\(662\) 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 \(-0.534025\pi\)
0.914428 0.404749i \(-0.132641\pi\)
\(678\) −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 \(-0.407975\pi\)
0.687538 0.726149i \(-0.258692\pi\)
\(692\) −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 0.917381 0.398011i \(-0.130299\pi\)
−0.803378 + 0.595470i \(0.796966\pi\)
\(720\) 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 \(-0.857743\pi\)
0.0766087 0.997061i \(-0.475591\pi\)
\(728\) 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 \(-0.558150\pi\)
−0.181670 + 0.983359i \(0.558150\pi\)
\(734\) 1.72559 2.98881i 0.0636926 0.110319i
\(735\) 0 0
\(736\) 3.73821 + 6.47478i 0.137792 + 0.238663i
\(737\) −3.14257 5.44309i −0.115758 0.200499i
\(738\) 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 \(-0.539056\pi\)
−0.122392 + 0.992482i \(0.539056\pi\)
\(762\) −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 \(0.441557\pi\)
−0.942757 + 0.333482i \(0.891776\pi\)
\(770\) 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 −0.834841 0.550492i \(-0.814440\pi\)
0.894160 + 0.447747i \(0.147774\pi\)
\(774\) −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
\(783\)