Properties

Label 105.3.k.b.62.1
Level 105
Weight 3
Character 105.62
Analytic conductor 2.861
Analytic rank 0
Dimension 4
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 62.1
Root \(-0.707107 + 0.707107i\) of \(x^{4} + 1\)
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.b.83.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.29289 + 2.70711i) q^{3} +3.00000i q^{4} +(-0.707107 + 4.94975i) q^{5} +(-2.82843 - 1.00000i) q^{6} -7.00000i q^{7} +(-4.94975 - 4.94975i) q^{8} +(-5.65685 + 7.00000i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.29289 + 2.70711i) q^{3} +3.00000i q^{4} +(-0.707107 + 4.94975i) q^{5} +(-2.82843 - 1.00000i) q^{6} -7.00000i q^{7} +(-4.94975 - 4.94975i) q^{8} +(-5.65685 + 7.00000i) q^{9} +(-3.00000 - 4.00000i) q^{10} -9.89949i q^{11} +(-8.12132 + 3.87868i) q^{12} +(8.00000 + 8.00000i) q^{13} +(4.94975 + 4.94975i) q^{14} +(-14.3137 + 4.48528i) q^{15} -5.00000 q^{16} +(18.3848 + 18.3848i) q^{17} +(-0.949747 - 8.94975i) q^{18} -10.0000 q^{19} +(-14.8492 - 2.12132i) q^{20} +(18.9497 - 9.05025i) q^{21} +(7.00000 + 7.00000i) q^{22} +(24.0416 + 24.0416i) q^{23} +(7.00000 - 19.7990i) q^{24} +(-24.0000 - 7.00000i) q^{25} -11.3137 q^{26} +(-26.2635 - 6.26346i) q^{27} +21.0000 q^{28} +4.24264 q^{29} +(6.94975 - 13.2929i) q^{30} -14.0000i q^{31} +(23.3345 - 23.3345i) q^{32} +(26.7990 - 12.7990i) q^{33} -26.0000 q^{34} +(34.6482 + 4.94975i) q^{35} +(-21.0000 - 16.9706i) q^{36} +(30.0000 + 30.0000i) q^{37} +(7.07107 - 7.07107i) q^{38} +(-11.3137 + 32.0000i) q^{39} +(28.0000 - 21.0000i) q^{40} +33.9411 q^{41} +(-7.00000 + 19.7990i) q^{42} +(36.0000 - 36.0000i) q^{43} +29.6985 q^{44} +(-30.6482 - 32.9497i) q^{45} -34.0000 q^{46} +(4.24264 + 4.24264i) q^{47} +(-6.46447 - 13.5355i) q^{48} -49.0000 q^{49} +(21.9203 - 12.0208i) q^{50} +(-26.0000 + 73.5391i) q^{51} +(-24.0000 + 24.0000i) q^{52} +(-70.7107 - 70.7107i) q^{53} +(23.0000 - 14.1421i) q^{54} +(49.0000 + 7.00000i) q^{55} +(-34.6482 + 34.6482i) q^{56} +(-12.9289 - 27.0711i) q^{57} +(-3.00000 + 3.00000i) q^{58} +29.6985i q^{59} +(-13.4558 - 42.9411i) q^{60} +14.0000i q^{61} +(9.89949 + 9.89949i) q^{62} +(49.0000 + 39.5980i) q^{63} +13.0000i q^{64} +(-45.2548 + 33.9411i) q^{65} +(-9.89949 + 28.0000i) q^{66} +(32.0000 + 32.0000i) q^{67} +(-55.1543 + 55.1543i) q^{68} +(-34.0000 + 96.1665i) q^{69} +(-28.0000 + 21.0000i) q^{70} -59.3970i q^{71} +(62.6482 - 6.64823i) q^{72} +(39.0000 + 39.0000i) q^{73} -42.4264 q^{74} +(-12.0797 - 74.0208i) q^{75} -30.0000i q^{76} -69.2965 q^{77} +(-14.6274 - 30.6274i) q^{78} -56.0000i q^{79} +(3.53553 - 24.7487i) q^{80} +(-17.0000 - 79.1960i) q^{81} +(-24.0000 + 24.0000i) q^{82} +(36.7696 - 36.7696i) q^{83} +(27.1508 + 56.8492i) q^{84} +(-104.000 + 78.0000i) q^{85} +50.9117i q^{86} +(5.48528 + 11.4853i) q^{87} +(-49.0000 + 49.0000i) q^{88} +19.7990i q^{89} +(44.9706 + 1.62742i) q^{90} +(56.0000 - 56.0000i) q^{91} +(-72.1249 + 72.1249i) q^{92} +(37.8995 - 18.1005i) q^{93} -6.00000 q^{94} +(7.07107 - 49.4975i) q^{95} +(93.3381 + 33.0000i) q^{96} +(113.000 - 113.000i) q^{97} +(34.6482 - 34.6482i) q^{98} +(69.2965 + 56.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 8q^{3} + O(q^{10}) \) \( 4q + 8q^{3} - 12q^{10} - 24q^{12} + 32q^{13} - 12q^{15} - 20q^{16} + 16q^{18} - 40q^{19} + 56q^{21} + 28q^{22} + 28q^{24} - 96q^{25} - 40q^{27} + 84q^{28} + 8q^{30} + 28q^{33} - 104q^{34} - 84q^{36} + 120q^{37} + 112q^{40} - 28q^{42} + 144q^{43} + 16q^{45} - 136q^{46} - 40q^{48} - 196q^{49} - 104q^{51} - 96q^{52} + 92q^{54} + 196q^{55} - 80q^{57} - 12q^{58} + 48q^{60} + 196q^{63} + 128q^{67} - 136q^{69} - 112q^{70} + 112q^{72} + 156q^{73} - 136q^{75} + 32q^{78} - 68q^{81} - 96q^{82} + 168q^{84} - 416q^{85} - 12q^{87} - 196q^{88} + 112q^{90} + 224q^{91} + 112q^{93} - 24q^{94} + 452q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.353553 + 0.353553i −0.861430 0.507877i \(-0.830431\pi\)
0.507877 + 0.861430i \(0.330431\pi\)
\(3\) 1.29289 + 2.70711i 0.430964 + 0.902369i
\(4\) 3.00000i 0.750000i
\(5\) −0.707107 + 4.94975i −0.141421 + 0.989949i
\(6\) −2.82843 1.00000i −0.471405 0.166667i
\(7\) 7.00000i 1.00000i
\(8\) −4.94975 4.94975i −0.618718 0.618718i
\(9\) −5.65685 + 7.00000i −0.628539 + 0.777778i
\(10\) −3.00000 4.00000i −0.300000 0.400000i
\(11\) 9.89949i 0.899954i −0.893040 0.449977i \(-0.851432\pi\)
0.893040 0.449977i \(-0.148568\pi\)
\(12\) −8.12132 + 3.87868i −0.676777 + 0.323223i
\(13\) 8.00000 + 8.00000i 0.615385 + 0.615385i 0.944344 0.328959i \(-0.106698\pi\)
−0.328959 + 0.944344i \(0.606698\pi\)
\(14\) 4.94975 + 4.94975i 0.353553 + 0.353553i
\(15\) −14.3137 + 4.48528i −0.954247 + 0.299019i
\(16\) −5.00000 −0.312500
\(17\) 18.3848 + 18.3848i 1.08146 + 1.08146i 0.996374 + 0.0850836i \(0.0271157\pi\)
0.0850836 + 0.996374i \(0.472884\pi\)
\(18\) −0.949747 8.94975i −0.0527637 0.497208i
\(19\) −10.0000 −0.526316 −0.263158 0.964753i \(-0.584764\pi\)
−0.263158 + 0.964753i \(0.584764\pi\)
\(20\) −14.8492 2.12132i −0.742462 0.106066i
\(21\) 18.9497 9.05025i 0.902369 0.430964i
\(22\) 7.00000 + 7.00000i 0.318182 + 0.318182i
\(23\) 24.0416 + 24.0416i 1.04529 + 1.04529i 0.998925 + 0.0463637i \(0.0147633\pi\)
0.0463637 + 0.998925i \(0.485237\pi\)
\(24\) 7.00000 19.7990i 0.291667 0.824958i
\(25\) −24.0000 7.00000i −0.960000 0.280000i
\(26\) −11.3137 −0.435143
\(27\) −26.2635 6.26346i −0.972721 0.231980i
\(28\) 21.0000 0.750000
\(29\) 4.24264 0.146298 0.0731490 0.997321i \(-0.476695\pi\)
0.0731490 + 0.997321i \(0.476695\pi\)
\(30\) 6.94975 13.2929i 0.231658 0.443096i
\(31\) 14.0000i 0.451613i −0.974172 0.225806i \(-0.927498\pi\)
0.974172 0.225806i \(-0.0725017\pi\)
\(32\) 23.3345 23.3345i 0.729204 0.729204i
\(33\) 26.7990 12.7990i 0.812091 0.387848i
\(34\) −26.0000 −0.764706
\(35\) 34.6482 + 4.94975i 0.989949 + 0.141421i
\(36\) −21.0000 16.9706i −0.583333 0.471405i
\(37\) 30.0000 + 30.0000i 0.810811 + 0.810811i 0.984755 0.173945i \(-0.0556514\pi\)
−0.173945 + 0.984755i \(0.555651\pi\)
\(38\) 7.07107 7.07107i 0.186081 0.186081i
\(39\) −11.3137 + 32.0000i −0.290095 + 0.820513i
\(40\) 28.0000 21.0000i 0.700000 0.525000i
\(41\) 33.9411 0.827832 0.413916 0.910315i \(-0.364161\pi\)
0.413916 + 0.910315i \(0.364161\pi\)
\(42\) −7.00000 + 19.7990i −0.166667 + 0.471405i
\(43\) 36.0000 36.0000i 0.837209 0.837209i −0.151281 0.988491i \(-0.548340\pi\)
0.988491 + 0.151281i \(0.0483400\pi\)
\(44\) 29.6985 0.674966
\(45\) −30.6482 32.9497i −0.681072 0.732217i
\(46\) −34.0000 −0.739130
\(47\) 4.24264 + 4.24264i 0.0902690 + 0.0902690i 0.750799 0.660530i \(-0.229669\pi\)
−0.660530 + 0.750799i \(0.729669\pi\)
\(48\) −6.46447 13.5355i −0.134676 0.281990i
\(49\) −49.0000 −1.00000
\(50\) 21.9203 12.0208i 0.438406 0.240416i
\(51\) −26.0000 + 73.5391i −0.509804 + 1.44194i
\(52\) −24.0000 + 24.0000i −0.461538 + 0.461538i
\(53\) −70.7107 70.7107i −1.33416 1.33416i −0.901606 0.432557i \(-0.857611\pi\)
−0.432557 0.901606i \(-0.642389\pi\)
\(54\) 23.0000 14.1421i 0.425926 0.261891i
\(55\) 49.0000 + 7.00000i 0.890909 + 0.127273i
\(56\) −34.6482 + 34.6482i −0.618718 + 0.618718i
\(57\) −12.9289 27.0711i −0.226823 0.474931i
\(58\) −3.00000 + 3.00000i −0.0517241 + 0.0517241i
\(59\) 29.6985i 0.503364i 0.967810 + 0.251682i \(0.0809837\pi\)
−0.967810 + 0.251682i \(0.919016\pi\)
\(60\) −13.4558 42.9411i −0.224264 0.715685i
\(61\) 14.0000i 0.229508i 0.993394 + 0.114754i \(0.0366080\pi\)
−0.993394 + 0.114754i \(0.963392\pi\)
\(62\) 9.89949 + 9.89949i 0.159669 + 0.159669i
\(63\) 49.0000 + 39.5980i 0.777778 + 0.628539i
\(64\) 13.0000i 0.203125i
\(65\) −45.2548 + 33.9411i −0.696228 + 0.522171i
\(66\) −9.89949 + 28.0000i −0.149992 + 0.424242i
\(67\) 32.0000 + 32.0000i 0.477612 + 0.477612i 0.904367 0.426755i \(-0.140343\pi\)
−0.426755 + 0.904367i \(0.640343\pi\)
\(68\) −55.1543 + 55.1543i −0.811093 + 0.811093i
\(69\) −34.0000 + 96.1665i −0.492754 + 1.39372i
\(70\) −28.0000 + 21.0000i −0.400000 + 0.300000i
\(71\) 59.3970i 0.836577i −0.908314 0.418289i \(-0.862630\pi\)
0.908314 0.418289i \(-0.137370\pi\)
\(72\) 62.6482 6.64823i 0.870114 0.0923366i
\(73\) 39.0000 + 39.0000i 0.534247 + 0.534247i 0.921833 0.387587i \(-0.126691\pi\)
−0.387587 + 0.921833i \(0.626691\pi\)
\(74\) −42.4264 −0.573330
\(75\) −12.0797 74.0208i −0.161063 0.986944i
\(76\) 30.0000i 0.394737i
\(77\) −69.2965 −0.899954
\(78\) −14.6274 30.6274i −0.187531 0.392659i
\(79\) 56.0000i 0.708861i −0.935082 0.354430i \(-0.884675\pi\)
0.935082 0.354430i \(-0.115325\pi\)
\(80\) 3.53553 24.7487i 0.0441942 0.309359i
\(81\) −17.0000 79.1960i −0.209877 0.977728i
\(82\) −24.0000 + 24.0000i −0.292683 + 0.292683i
\(83\) 36.7696 36.7696i 0.443007 0.443007i −0.450015 0.893021i \(-0.648581\pi\)
0.893021 + 0.450015i \(0.148581\pi\)
\(84\) 27.1508 + 56.8492i 0.323223 + 0.676777i
\(85\) −104.000 + 78.0000i −1.22353 + 0.917647i
\(86\) 50.9117i 0.591996i
\(87\) 5.48528 + 11.4853i 0.0630492 + 0.132015i
\(88\) −49.0000 + 49.0000i −0.556818 + 0.556818i
\(89\) 19.7990i 0.222461i 0.993795 + 0.111230i \(0.0354791\pi\)
−0.993795 + 0.111230i \(0.964521\pi\)
\(90\) 44.9706 + 1.62742i 0.499673 + 0.0180824i
\(91\) 56.0000 56.0000i 0.615385 0.615385i
\(92\) −72.1249 + 72.1249i −0.783966 + 0.783966i
\(93\) 37.8995 18.1005i 0.407521 0.194629i
\(94\) −6.00000 −0.0638298
\(95\) 7.07107 49.4975i 0.0744323 0.521026i
\(96\) 93.3381 + 33.0000i 0.972272 + 0.343750i
\(97\) 113.000 113.000i 1.16495 1.16495i 0.181571 0.983378i \(-0.441882\pi\)
0.983378 0.181571i \(-0.0581181\pi\)
\(98\) 34.6482 34.6482i 0.353553 0.353553i
\(99\) 69.2965 + 56.0000i 0.699964 + 0.565657i
\(100\) 21.0000 72.0000i 0.210000 0.720000i
\(101\) −91.9239 −0.910137 −0.455069 0.890456i \(-0.650385\pi\)
−0.455069 + 0.890456i \(0.650385\pi\)
\(102\) −33.6152 70.3848i −0.329561 0.690047i
\(103\) −5.00000 5.00000i −0.0485437 0.0485437i 0.682418 0.730962i \(-0.260928\pi\)
−0.730962 + 0.682418i \(0.760928\pi\)
\(104\) 79.1960i 0.761500i
\(105\) 31.3970 + 100.196i 0.299019 + 0.954247i
\(106\) 100.000 0.943396
\(107\) 4.24264 4.24264i 0.0396508 0.0396508i −0.687003 0.726654i \(-0.741074\pi\)
0.726654 + 0.687003i \(0.241074\pi\)
\(108\) 18.7904 78.7904i 0.173985 0.729540i
\(109\) 70.0000i 0.642202i −0.947045 0.321101i \(-0.895947\pi\)
0.947045 0.321101i \(-0.104053\pi\)
\(110\) −39.5980 + 29.6985i −0.359982 + 0.269986i
\(111\) −42.4264 + 120.000i −0.382220 + 1.08108i
\(112\) 35.0000i 0.312500i
\(113\) −12.7279 12.7279i −0.112636 0.112636i 0.648542 0.761179i \(-0.275379\pi\)
−0.761179 + 0.648542i \(0.775379\pi\)
\(114\) 28.2843 + 10.0000i 0.248108 + 0.0877193i
\(115\) −136.000 + 102.000i −1.18261 + 0.886957i
\(116\) 12.7279i 0.109723i
\(117\) −101.255 + 10.7452i −0.865426 + 0.0918390i
\(118\) −21.0000 21.0000i −0.177966 0.177966i
\(119\) 128.693 128.693i 1.08146 1.08146i
\(120\) 93.0503 + 48.6482i 0.775419 + 0.405402i
\(121\) 23.0000 0.190083
\(122\) −9.89949 9.89949i −0.0811434 0.0811434i
\(123\) 43.8823 + 91.8823i 0.356766 + 0.747010i
\(124\) 42.0000 0.338710
\(125\) 51.6188 113.844i 0.412950 0.910754i
\(126\) −62.6482 + 6.64823i −0.497208 + 0.0527637i
\(127\) −111.000 111.000i −0.874016 0.874016i 0.118892 0.992907i \(-0.462066\pi\)
−0.992907 + 0.118892i \(0.962066\pi\)
\(128\) 84.1457 + 84.1457i 0.657388 + 0.657388i
\(129\) 144.000 + 50.9117i 1.11628 + 0.394664i
\(130\) 8.00000 56.0000i 0.0615385 0.430769i
\(131\) 38.1838 0.291479 0.145740 0.989323i \(-0.453444\pi\)
0.145740 + 0.989323i \(0.453444\pi\)
\(132\) 38.3970 + 80.3970i 0.290886 + 0.609068i
\(133\) 70.0000i 0.526316i
\(134\) −45.2548 −0.337723
\(135\) 49.5736 125.569i 0.367212 0.930137i
\(136\) 182.000i 1.33824i
\(137\) 18.3848 18.3848i 0.134195 0.134195i −0.636818 0.771014i \(-0.719750\pi\)
0.771014 + 0.636818i \(0.219750\pi\)
\(138\) −43.9584 92.0416i −0.318539 0.666968i
\(139\) −138.000 −0.992806 −0.496403 0.868092i \(-0.665346\pi\)
−0.496403 + 0.868092i \(0.665346\pi\)
\(140\) −14.8492 + 103.945i −0.106066 + 0.742462i
\(141\) −6.00000 + 16.9706i −0.0425532 + 0.120359i
\(142\) 42.0000 + 42.0000i 0.295775 + 0.295775i
\(143\) 79.1960 79.1960i 0.553818 0.553818i
\(144\) 28.2843 35.0000i 0.196419 0.243056i
\(145\) −3.00000 + 21.0000i −0.0206897 + 0.144828i
\(146\) −55.1543 −0.377769
\(147\) −63.3518 132.648i −0.430964 0.902369i
\(148\) −90.0000 + 90.0000i −0.608108 + 0.608108i
\(149\) −199.404 −1.33828 −0.669141 0.743135i \(-0.733338\pi\)
−0.669141 + 0.743135i \(0.733338\pi\)
\(150\) 60.8823 + 43.7990i 0.405882 + 0.291993i
\(151\) 78.0000 0.516556 0.258278 0.966071i \(-0.416845\pi\)
0.258278 + 0.966071i \(0.416845\pi\)
\(152\) 49.4975 + 49.4975i 0.325641 + 0.325641i
\(153\) −232.693 + 24.6934i −1.52087 + 0.161395i
\(154\) 49.0000 49.0000i 0.318182 0.318182i
\(155\) 69.2965 + 9.89949i 0.447074 + 0.0638677i
\(156\) −96.0000 33.9411i −0.615385 0.217571i
\(157\) 46.0000 46.0000i 0.292994 0.292994i −0.545268 0.838262i \(-0.683572\pi\)
0.838262 + 0.545268i \(0.183572\pi\)
\(158\) 39.5980 + 39.5980i 0.250620 + 0.250620i
\(159\) 100.000 282.843i 0.628931 1.77888i
\(160\) 99.0000 + 132.000i 0.618750 + 0.825000i
\(161\) 168.291 168.291i 1.04529 1.04529i
\(162\) 68.0208 + 43.9792i 0.419882 + 0.271476i
\(163\) −138.000 + 138.000i −0.846626 + 0.846626i −0.989710 0.143085i \(-0.954298\pi\)
0.143085 + 0.989710i \(0.454298\pi\)
\(164\) 101.823i 0.620874i
\(165\) 44.4020 + 141.698i 0.269103 + 0.858779i
\(166\) 52.0000i 0.313253i
\(167\) −91.9239 91.9239i −0.550442 0.550442i 0.376126 0.926568i \(-0.377256\pi\)
−0.926568 + 0.376126i \(0.877256\pi\)
\(168\) −138.593 49.0000i −0.824958 0.291667i
\(169\) 41.0000i 0.242604i
\(170\) 18.3848 128.693i 0.108146 0.757020i
\(171\) 56.5685 70.0000i 0.330810 0.409357i
\(172\) 108.000 + 108.000i 0.627907 + 0.627907i
\(173\) −223.446 + 223.446i −1.29159 + 1.29159i −0.357793 + 0.933801i \(0.616471\pi\)
−0.933801 + 0.357793i \(0.883529\pi\)
\(174\) −12.0000 4.24264i −0.0689655 0.0243830i
\(175\) −49.0000 + 168.000i −0.280000 + 0.960000i
\(176\) 49.4975i 0.281236i
\(177\) −80.3970 + 38.3970i −0.454220 + 0.216932i
\(178\) −14.0000 14.0000i −0.0786517 0.0786517i
\(179\) −12.7279 −0.0711057 −0.0355529 0.999368i \(-0.511319\pi\)
−0.0355529 + 0.999368i \(0.511319\pi\)
\(180\) 98.8492 91.9447i 0.549162 0.510804i
\(181\) 350.000i 1.93370i 0.255342 + 0.966851i \(0.417812\pi\)
−0.255342 + 0.966851i \(0.582188\pi\)
\(182\) 79.1960i 0.435143i
\(183\) −37.8995 + 18.1005i −0.207101 + 0.0989099i
\(184\) 238.000i 1.29348i
\(185\) −169.706 + 127.279i −0.917328 + 0.687996i
\(186\) −14.0000 + 39.5980i −0.0752688 + 0.212892i
\(187\) 182.000 182.000i 0.973262 0.973262i
\(188\) −12.7279 + 12.7279i −0.0677017 + 0.0677017i
\(189\) −43.8442 + 183.844i −0.231980 + 0.972721i
\(190\) 30.0000 + 40.0000i 0.157895 + 0.210526i
\(191\) 118.794i 0.621958i −0.950417 0.310979i \(-0.899343\pi\)
0.950417 0.310979i \(-0.100657\pi\)
\(192\) −35.1924 + 16.8076i −0.183294 + 0.0875396i
\(193\) 67.0000 67.0000i 0.347150 0.347150i −0.511897 0.859047i \(-0.671057\pi\)
0.859047 + 0.511897i \(0.171057\pi\)
\(194\) 159.806i 0.823743i
\(195\) −150.392 78.6274i −0.771241 0.403218i
\(196\) 147.000i 0.750000i
\(197\) 56.5685 56.5685i 0.287150 0.287150i −0.548802 0.835952i \(-0.684916\pi\)
0.835952 + 0.548802i \(0.184916\pi\)
\(198\) −88.5980 + 9.40202i −0.447465 + 0.0474850i
\(199\) 120.000 0.603015 0.301508 0.953464i \(-0.402510\pi\)
0.301508 + 0.953464i \(0.402510\pi\)
\(200\) 84.1457 + 153.442i 0.420729 + 0.767211i
\(201\) −45.2548 + 128.000i −0.225148 + 0.636816i
\(202\) 65.0000 65.0000i 0.321782 0.321782i
\(203\) 29.6985i 0.146298i
\(204\) −220.617 78.0000i −1.08146 0.382353i
\(205\) −24.0000 + 168.000i −0.117073 + 0.819512i
\(206\) 7.07107 0.0343256
\(207\) −304.291 + 32.2914i −1.47001 + 0.155997i
\(208\) −40.0000 40.0000i −0.192308 0.192308i
\(209\) 98.9949i 0.473660i
\(210\) −93.0503 48.6482i −0.443096 0.231658i
\(211\) 86.0000 0.407583 0.203791 0.979014i \(-0.434674\pi\)
0.203791 + 0.979014i \(0.434674\pi\)
\(212\) 212.132 212.132i 1.00062 1.00062i
\(213\) 160.794 76.7939i 0.754901 0.360535i
\(214\) 6.00000i 0.0280374i
\(215\) 152.735 + 203.647i 0.710396 + 0.947194i
\(216\) 98.9949 + 161.000i 0.458310 + 0.745370i
\(217\) −98.0000 −0.451613
\(218\) 49.4975 + 49.4975i 0.227053 + 0.227053i
\(219\) −55.1543 + 156.000i −0.251846 + 0.712329i
\(220\) −21.0000 + 147.000i −0.0954545 + 0.668182i
\(221\) 294.156i 1.33102i
\(222\) −54.8528 114.853i −0.247085 0.517355i
\(223\) −237.000 237.000i −1.06278 1.06278i −0.997893 0.0648877i \(-0.979331\pi\)
−0.0648877 0.997893i \(-0.520669\pi\)
\(224\) −163.342 163.342i −0.729204 0.729204i
\(225\) 184.765 128.402i 0.821176 0.570676i
\(226\) 18.0000 0.0796460
\(227\) 117.380 + 117.380i 0.517091 + 0.517091i 0.916690 0.399599i \(-0.130851\pi\)
−0.399599 + 0.916690i \(0.630851\pi\)
\(228\) 81.2132 38.7868i 0.356198 0.170118i
\(229\) −374.000 −1.63319 −0.816594 0.577213i \(-0.804140\pi\)
−0.816594 + 0.577213i \(0.804140\pi\)
\(230\) 24.0416 168.291i 0.104529 0.731702i
\(231\) −89.5929 187.593i −0.387848 0.812091i
\(232\) −21.0000 21.0000i −0.0905172 0.0905172i
\(233\) −173.948 173.948i −0.746559 0.746559i 0.227272 0.973831i \(-0.427019\pi\)
−0.973831 + 0.227272i \(0.927019\pi\)
\(234\) 64.0000 79.1960i 0.273504 0.338444i
\(235\) −24.0000 + 18.0000i −0.102128 + 0.0765957i
\(236\) −89.0955 −0.377523
\(237\) 151.598 72.4020i 0.639654 0.305494i
\(238\) 182.000i 0.764706i
\(239\) 291.328 1.21895 0.609473 0.792807i \(-0.291381\pi\)
0.609473 + 0.792807i \(0.291381\pi\)
\(240\) 71.5685 22.4264i 0.298202 0.0934434i
\(241\) 14.0000i 0.0580913i 0.999578 + 0.0290456i \(0.00924682\pi\)
−0.999578 + 0.0290456i \(0.990753\pi\)
\(242\) −16.2635 + 16.2635i −0.0672044 + 0.0672044i
\(243\) 192.413 148.413i 0.791822 0.610752i
\(244\) −42.0000 −0.172131
\(245\) 34.6482 242.538i 0.141421 0.989949i
\(246\) −96.0000 33.9411i −0.390244 0.137972i
\(247\) −80.0000 80.0000i −0.323887 0.323887i
\(248\) −69.2965 + 69.2965i −0.279421 + 0.279421i
\(249\) 147.078 + 52.0000i 0.590676 + 0.208835i
\(250\) 44.0000 + 117.000i 0.176000 + 0.468000i
\(251\) 439.820 1.75227 0.876136 0.482063i \(-0.160113\pi\)
0.876136 + 0.482063i \(0.160113\pi\)
\(252\) −118.794 + 147.000i −0.471405 + 0.583333i
\(253\) 238.000 238.000i 0.940711 0.940711i
\(254\) 156.978 0.618022
\(255\) −345.615 180.693i −1.35535 0.708602i
\(256\) −171.000 −0.667969
\(257\) −35.3553 35.3553i −0.137569 0.137569i 0.634969 0.772538i \(-0.281013\pi\)
−0.772538 + 0.634969i \(0.781013\pi\)
\(258\) −137.823 + 65.8234i −0.534199 + 0.255129i
\(259\) 210.000 210.000i 0.810811 0.810811i
\(260\) −101.823 135.765i −0.391628 0.522171i
\(261\) −24.0000 + 29.6985i −0.0919540 + 0.113787i
\(262\) −27.0000 + 27.0000i −0.103053 + 0.103053i
\(263\) 315.370 + 315.370i 1.19912 + 1.19912i 0.974429 + 0.224695i \(0.0721385\pi\)
0.224695 + 0.974429i \(0.427861\pi\)
\(264\) −196.000 69.2965i −0.742424 0.262487i
\(265\) 400.000 300.000i 1.50943 1.13208i
\(266\) −49.4975 49.4975i −0.186081 0.186081i
\(267\) −53.5980 + 25.5980i −0.200741 + 0.0958726i
\(268\) −96.0000 + 96.0000i −0.358209 + 0.358209i
\(269\) 267.286i 0.993630i −0.867857 0.496815i \(-0.834503\pi\)
0.867857 0.496815i \(-0.165497\pi\)
\(270\) 53.7365 + 123.844i 0.199024 + 0.458682i
\(271\) 112.000i 0.413284i −0.978417 0.206642i \(-0.933746\pi\)
0.978417 0.206642i \(-0.0662536\pi\)
\(272\) −91.9239 91.9239i −0.337955 0.337955i
\(273\) 224.000 + 79.1960i 0.820513 + 0.290095i
\(274\) 26.0000i 0.0948905i
\(275\) −69.2965 + 237.588i −0.251987 + 0.863956i
\(276\) −288.500 102.000i −1.04529 0.369565i
\(277\) 102.000 + 102.000i 0.368231 + 0.368231i 0.866832 0.498601i \(-0.166153\pi\)
−0.498601 + 0.866832i \(0.666153\pi\)
\(278\) 97.5807 97.5807i 0.351010 0.351010i
\(279\) 98.0000 + 79.1960i 0.351254 + 0.283856i
\(280\) −147.000 196.000i −0.525000 0.700000i
\(281\) 296.985i 1.05689i 0.848969 + 0.528443i \(0.177224\pi\)
−0.848969 + 0.528443i \(0.822776\pi\)
\(282\) −7.75736 16.2426i −0.0275084 0.0575980i
\(283\) 102.000 + 102.000i 0.360424 + 0.360424i 0.863969 0.503545i \(-0.167971\pi\)
−0.503545 + 0.863969i \(0.667971\pi\)
\(284\) 178.191 0.627433
\(285\) 143.137 44.8528i 0.502235 0.157378i
\(286\) 112.000i 0.391608i
\(287\) 237.588i 0.827832i
\(288\) 31.3417 + 295.342i 0.108825 + 1.02549i
\(289\) 387.000i 1.33910i
\(290\) −12.7279 16.9706i −0.0438894 0.0585192i
\(291\) 452.000 + 159.806i 1.55326 + 0.549162i
\(292\) −117.000 + 117.000i −0.400685 + 0.400685i
\(293\) 185.262 185.262i 0.632293 0.632293i −0.316349 0.948643i \(-0.602457\pi\)
0.948643 + 0.316349i \(0.102457\pi\)
\(294\) 138.593 + 49.0000i 0.471405 + 0.166667i
\(295\) −147.000 21.0000i −0.498305 0.0711864i
\(296\) 296.985i 1.00333i
\(297\) −62.0051 + 259.995i −0.208771 + 0.875404i
\(298\) 141.000 141.000i 0.473154 0.473154i
\(299\) 384.666i 1.28651i
\(300\) 222.062 36.2391i 0.740208 0.120797i
\(301\) −252.000 252.000i −0.837209 0.837209i
\(302\) −55.1543 + 55.1543i −0.182630 + 0.182630i
\(303\) −118.848 248.848i −0.392237 0.821280i
\(304\) 50.0000 0.164474
\(305\) −69.2965 9.89949i −0.227202 0.0324574i
\(306\) 147.078 182.000i 0.480648 0.594771i
\(307\) −90.0000 + 90.0000i −0.293160 + 0.293160i −0.838327 0.545168i \(-0.816466\pi\)
0.545168 + 0.838327i \(0.316466\pi\)
\(308\) 207.889i 0.674966i
\(309\) 7.07107 20.0000i 0.0228837 0.0647249i
\(310\) −56.0000 + 42.0000i −0.180645 + 0.135484i
\(311\) −299.813 −0.964030 −0.482015 0.876163i \(-0.660095\pi\)
−0.482015 + 0.876163i \(0.660095\pi\)
\(312\) 214.392 102.392i 0.687154 0.328179i
\(313\) 177.000 + 177.000i 0.565495 + 0.565495i 0.930863 0.365368i \(-0.119057\pi\)
−0.365368 + 0.930863i \(0.619057\pi\)
\(314\) 65.0538i 0.207178i
\(315\) −230.648 + 214.538i −0.732217 + 0.681072i
\(316\) 168.000 0.531646
\(317\) −213.546 + 213.546i −0.673647 + 0.673647i −0.958555 0.284908i \(-0.908037\pi\)
0.284908 + 0.958555i \(0.408037\pi\)
\(318\) 129.289 + 270.711i 0.406570 + 0.851291i
\(319\) 42.0000i 0.131661i
\(320\) −64.3467 9.19239i −0.201083 0.0287262i
\(321\) 16.9706 + 6.00000i 0.0528678 + 0.0186916i
\(322\) 238.000i 0.739130i
\(323\) −183.848 183.848i −0.569188 0.569188i
\(324\) 237.588 51.0000i 0.733296 0.157407i
\(325\) −136.000 248.000i −0.418462 0.763077i
\(326\) 195.161i 0.598655i
\(327\) 189.497 90.5025i 0.579503 0.276766i
\(328\) −168.000 168.000i −0.512195 0.512195i
\(329\) 29.6985 29.6985i 0.0902690 0.0902690i
\(330\) −131.593 68.7990i −0.398766 0.208482i
\(331\) 102.000 0.308157 0.154079 0.988059i \(-0.450759\pi\)
0.154079 + 0.988059i \(0.450759\pi\)
\(332\) 110.309 + 110.309i 0.332255 + 0.332255i
\(333\) −379.706 + 40.2944i −1.14026 + 0.121004i
\(334\) 130.000 0.389222
\(335\) −181.019 + 135.765i −0.540356 + 0.405267i
\(336\) −94.7487 + 45.2513i −0.281990 + 0.134676i
\(337\) 253.000 + 253.000i 0.750742 + 0.750742i 0.974618 0.223876i \(-0.0718710\pi\)
−0.223876 + 0.974618i \(0.571871\pi\)
\(338\) 28.9914 + 28.9914i 0.0857733 + 0.0857733i
\(339\) 18.0000 50.9117i 0.0530973 0.150182i
\(340\) −234.000 312.000i −0.688235 0.917647i
\(341\) −138.593 −0.406431
\(342\) 9.49747 + 89.4975i 0.0277704 + 0.261689i
\(343\) 343.000i 1.00000i
\(344\) −356.382 −1.03599
\(345\) −451.958 236.291i −1.31002 0.684903i
\(346\) 316.000i 0.913295i
\(347\) −169.706 + 169.706i −0.489065 + 0.489065i −0.908011 0.418946i \(-0.862400\pi\)
0.418946 + 0.908011i \(0.362400\pi\)
\(348\) −34.4558 + 16.4558i −0.0990110 + 0.0472869i
\(349\) −446.000 −1.27794 −0.638968 0.769233i \(-0.720639\pi\)
−0.638968 + 0.769233i \(0.720639\pi\)
\(350\) −84.1457 153.442i −0.240416 0.438406i
\(351\) −160.000 260.215i −0.455840 0.741354i
\(352\) −231.000 231.000i −0.656250 0.656250i
\(353\) 97.5807 97.5807i 0.276433 0.276433i −0.555250 0.831683i \(-0.687378\pi\)
0.831683 + 0.555250i \(0.187378\pi\)
\(354\) 29.6985 84.0000i 0.0838940 0.237288i
\(355\) 294.000 + 42.0000i 0.828169 + 0.118310i
\(356\) −59.3970 −0.166845
\(357\) 514.774 + 182.000i 1.44194 + 0.509804i
\(358\) 9.00000 9.00000i 0.0251397 0.0251397i
\(359\) −248.902 −0.693319 −0.346660 0.937991i \(-0.612684\pi\)
−0.346660 + 0.937991i \(0.612684\pi\)
\(360\) −11.3919 + 314.794i −0.0316442 + 0.874428i
\(361\) −261.000 −0.722992
\(362\) −247.487 247.487i −0.683667 0.683667i
\(363\) 29.7365 + 62.2635i 0.0819189 + 0.171525i
\(364\) 168.000 + 168.000i 0.461538 + 0.461538i
\(365\) −220.617 + 165.463i −0.604431 + 0.453323i
\(366\) 14.0000 39.5980i 0.0382514 0.108191i
\(367\) −185.000 + 185.000i −0.504087 + 0.504087i −0.912705 0.408618i \(-0.866011\pi\)
0.408618 + 0.912705i \(0.366011\pi\)
\(368\) −120.208 120.208i −0.326653 0.326653i
\(369\) −192.000 + 237.588i −0.520325 + 0.643870i
\(370\) 30.0000 210.000i 0.0810811 0.567568i
\(371\) −494.975 + 494.975i −1.33416 + 1.33416i
\(372\) 54.3015 + 113.698i 0.145972 + 0.305641i
\(373\) 492.000 492.000i 1.31903 1.31903i 0.404494 0.914540i \(-0.367448\pi\)
0.914540 0.404494i \(-0.132552\pi\)
\(374\) 257.387i 0.688200i
\(375\) 374.926 7.45079i 0.999803 0.0198688i
\(376\) 42.0000i 0.111702i
\(377\) 33.9411 + 33.9411i 0.0900295 + 0.0900295i
\(378\) −98.9949 161.000i −0.261891 0.425926i
\(379\) 266.000i 0.701847i 0.936404 + 0.350923i \(0.114132\pi\)
−0.936404 + 0.350923i \(0.885868\pi\)
\(380\) 148.492 + 21.2132i 0.390770 + 0.0558242i
\(381\) 156.978 444.000i 0.412015 1.16535i
\(382\) 84.0000 + 84.0000i 0.219895 + 0.219895i
\(383\) −134.350 + 134.350i −0.350784 + 0.350784i −0.860401 0.509617i \(-0.829787\pi\)
0.509617 + 0.860401i \(0.329787\pi\)
\(384\) −119.000 + 336.583i −0.309896 + 0.876518i
\(385\) 49.0000 343.000i 0.127273 0.890909i
\(386\) 94.7523i 0.245472i
\(387\) 48.3532 + 455.647i 0.124944 + 1.17738i
\(388\) 339.000 + 339.000i 0.873711 + 0.873711i
\(389\) −329.512 −0.847074 −0.423537 0.905879i \(-0.639212\pi\)
−0.423537 + 0.905879i \(0.639212\pi\)
\(390\) 161.941 50.7452i 0.415234 0.130116i
\(391\) 884.000i 2.26087i
\(392\) 242.538 + 242.538i 0.618718 + 0.618718i
\(393\) 49.3675 + 103.368i 0.125617 + 0.263022i
\(394\) 80.0000i 0.203046i
\(395\) 277.186 + 39.5980i 0.701736 + 0.100248i
\(396\) −168.000 + 207.889i −0.424242 + 0.524973i
\(397\) 30.0000 30.0000i 0.0755668 0.0755668i −0.668313 0.743880i \(-0.732983\pi\)
0.743880 + 0.668313i \(0.232983\pi\)
\(398\) −84.8528 + 84.8528i −0.213198 + 0.213198i
\(399\) −189.497 + 90.5025i −0.474931 + 0.226823i
\(400\) 120.000 + 35.0000i 0.300000 + 0.0875000i
\(401\) 79.1960i 0.197496i 0.995112 + 0.0987481i \(0.0314838\pi\)
−0.995112 + 0.0987481i \(0.968516\pi\)
\(402\) −58.5097 122.510i −0.145546 0.304750i
\(403\) 112.000 112.000i 0.277916 0.277916i
\(404\) 275.772i 0.682603i
\(405\) 404.021 28.1457i 0.997582 0.0694956i
\(406\) 21.0000 + 21.0000i 0.0517241 + 0.0517241i
\(407\) 296.985 296.985i 0.729693 0.729693i
\(408\) 492.693 235.307i 1.20758 0.576732i
\(409\) 302.000 0.738386 0.369193 0.929353i \(-0.379634\pi\)
0.369193 + 0.929353i \(0.379634\pi\)
\(410\) −101.823 135.765i −0.248350 0.331133i
\(411\) 73.5391 + 26.0000i 0.178927 + 0.0632603i
\(412\) 15.0000 15.0000i 0.0364078 0.0364078i
\(413\) 207.889 0.503364
\(414\) 192.333 238.000i 0.464573 0.574879i
\(415\) 156.000 + 208.000i 0.375904 + 0.501205i
\(416\) 373.352 0.897482
\(417\) −178.419 373.581i −0.427864 0.895877i
\(418\) −70.0000 70.0000i −0.167464 0.167464i
\(419\) 366.281i 0.874180i −0.899418 0.437090i \(-0.856009\pi\)
0.899418 0.437090i \(-0.143991\pi\)
\(420\) −300.588 + 94.1909i −0.715685 + 0.224264i
\(421\) −614.000 −1.45843 −0.729216 0.684283i \(-0.760115\pi\)
−0.729216 + 0.684283i \(0.760115\pi\)
\(422\) −60.8112 + 60.8112i −0.144102 + 0.144102i
\(423\) −53.6985 + 5.69848i −0.126947 + 0.0134716i
\(424\) 700.000i 1.65094i
\(425\) −312.541 569.928i −0.735391 1.34101i
\(426\) −59.3970 + 168.000i −0.139430 + 0.394366i
\(427\) 98.0000 0.229508
\(428\) 12.7279 + 12.7279i 0.0297381 + 0.0297381i
\(429\) 316.784 + 112.000i 0.738424 + 0.261072i
\(430\) −252.000 36.0000i −0.586047 0.0837209i
\(431\) 554.372i 1.28625i −0.765763 0.643123i \(-0.777639\pi\)
0.765763 0.643123i \(-0.222361\pi\)
\(432\) 131.317 + 31.3173i 0.303975 + 0.0724937i
\(433\) −153.000 153.000i −0.353349 0.353349i 0.508005 0.861354i \(-0.330383\pi\)
−0.861354 + 0.508005i \(0.830383\pi\)
\(434\) 69.2965 69.2965i 0.159669 0.159669i
\(435\) −60.7279 + 19.0294i −0.139604 + 0.0437458i
\(436\) 210.000 0.481651
\(437\) −240.416 240.416i −0.550152 0.550152i
\(438\) −71.3087 149.309i −0.162805 0.340887i
\(439\) −248.000 −0.564920 −0.282460 0.959279i \(-0.591150\pi\)
−0.282460 + 0.959279i \(0.591150\pi\)
\(440\) −207.889 277.186i −0.472476 0.629968i
\(441\) 277.186 343.000i 0.628539 0.777778i
\(442\) −208.000 208.000i −0.470588 0.470588i
\(443\) 14.1421 + 14.1421i 0.0319236 + 0.0319236i 0.722888 0.690965i \(-0.242814\pi\)
−0.690965 + 0.722888i \(0.742814\pi\)
\(444\) −360.000 127.279i −0.810811 0.286665i
\(445\) −98.0000 14.0000i −0.220225 0.0314607i
\(446\) 335.169 0.751499
\(447\) −257.808 539.808i −0.576752 1.20762i
\(448\) 91.0000 0.203125
\(449\) 647.710 1.44256 0.721280 0.692643i \(-0.243554\pi\)
0.721280 + 0.692643i \(0.243554\pi\)
\(450\) −39.8543 + 221.442i −0.0885651 + 0.492094i
\(451\) 336.000i 0.745011i
\(452\) 38.1838 38.1838i 0.0844774 0.0844774i
\(453\) 100.846 + 211.154i 0.222617 + 0.466124i
\(454\) −166.000 −0.365639
\(455\) 237.588 + 316.784i 0.522171 + 0.696228i
\(456\) −70.0000 + 197.990i −0.153509 + 0.434188i
\(457\) −313.000 313.000i −0.684902 0.684902i 0.276199 0.961100i \(-0.410925\pi\)
−0.961100 + 0.276199i \(0.910925\pi\)
\(458\) 264.458 264.458i 0.577419 0.577419i
\(459\) −367.696 598.000i −0.801080 1.30283i
\(460\) −306.000 408.000i −0.665217 0.886957i
\(461\) 142.836 0.309839 0.154919 0.987927i \(-0.450488\pi\)
0.154919 + 0.987927i \(0.450488\pi\)
\(462\) 196.000 + 69.2965i 0.424242 + 0.149992i
\(463\) 29.0000 29.0000i 0.0626350 0.0626350i −0.675095 0.737730i \(-0.735898\pi\)
0.737730 + 0.675095i \(0.235898\pi\)
\(464\) −21.2132 −0.0457181
\(465\) 62.7939 + 200.392i 0.135041 + 0.430950i
\(466\) 246.000 0.527897
\(467\) 350.725 + 350.725i 0.751017 + 0.751017i 0.974669 0.223652i \(-0.0717979\pi\)
−0.223652 + 0.974669i \(0.571798\pi\)
\(468\) −32.2355 303.765i −0.0688793 0.649069i
\(469\) 224.000 224.000i 0.477612 0.477612i
\(470\) 4.24264 29.6985i 0.00902690 0.0631883i
\(471\) 184.000 + 65.0538i 0.390658 + 0.138119i
\(472\) 147.000 147.000i 0.311441 0.311441i
\(473\) −356.382 356.382i −0.753450 0.753450i
\(474\) −56.0000 + 158.392i −0.118143 + 0.334160i
\(475\) 240.000 + 70.0000i 0.505263 + 0.147368i
\(476\) 386.080 + 386.080i 0.811093 + 0.811093i
\(477\) 894.975 94.9747i 1.87626 0.199108i
\(478\) −206.000 + 206.000i −0.430962 + 0.430962i
\(479\) 79.1960i 0.165336i 0.996577 + 0.0826680i \(0.0263441\pi\)
−0.996577 + 0.0826680i \(0.973656\pi\)
\(480\) −229.342 + 438.665i −0.477795 + 0.913886i
\(481\) 480.000i 0.997921i
\(482\) −9.89949 9.89949i −0.0205384 0.0205384i
\(483\) 673.166 + 238.000i 1.39372 + 0.492754i
\(484\) 69.0000i 0.142562i
\(485\) 479.418 + 639.225i 0.988492 + 1.31799i
\(486\) −31.1127 + 241.000i −0.0640179 + 0.495885i
\(487\) −101.000 101.000i −0.207392 0.207392i 0.595766 0.803158i \(-0.296849\pi\)
−0.803158 + 0.595766i \(0.796849\pi\)
\(488\) 69.2965 69.2965i 0.142001 0.142001i
\(489\) −552.000 195.161i −1.12883 0.399103i
\(490\) 147.000 + 196.000i 0.300000 + 0.400000i
\(491\) 346.482i 0.705667i −0.935686 0.352833i \(-0.885218\pi\)
0.935686 0.352833i \(-0.114782\pi\)
\(492\) −275.647 + 131.647i −0.560258 + 0.267575i
\(493\) 78.0000 + 78.0000i 0.158215 + 0.158215i
\(494\) 113.137 0.229022
\(495\) −326.186 + 303.402i −0.658961 + 0.612933i
\(496\) 70.0000i 0.141129i
\(497\) −415.779 −0.836577
\(498\) −140.770 + 67.2304i −0.282670 + 0.135001i
\(499\) 602.000i 1.20641i −0.797585 0.603206i \(-0.793890\pi\)
0.797585 0.603206i \(-0.206110\pi\)
\(500\) 341.533 + 154.856i 0.683065 + 0.309713i
\(501\) 130.000 367.696i 0.259481 0.733923i
\(502\) −311.000 + 311.000i −0.619522 + 0.619522i
\(503\) −626.497 + 626.497i −1.24552 + 1.24552i −0.287842 + 0.957678i \(0.592938\pi\)
−0.957678 + 0.287842i \(0.907062\pi\)
\(504\) −46.5376 438.538i −0.0923366 0.870114i
\(505\) 65.0000 455.000i 0.128713 0.900990i
\(506\) 336.583i 0.665183i
\(507\) 110.991 53.0086i 0.218918 0.104553i
\(508\) 333.000 333.000i 0.655512 0.655512i
\(509\) 386.080i 0.758507i −0.925293 0.379254i \(-0.876181\pi\)
0.925293 0.379254i \(-0.123819\pi\)
\(510\) 372.156 116.617i 0.729718 0.228661i
\(511\) 273.000 273.000i 0.534247 0.534247i
\(512\) −215.668 + 215.668i −0.421226 + 0.421226i
\(513\) 262.635 + 62.6346i 0.511958 + 0.122095i
\(514\) 50.0000 0.0972763
\(515\) 28.2843 21.2132i 0.0549209 0.0411907i
\(516\) −152.735 + 432.000i −0.295998 + 0.837209i
\(517\) 42.0000 42.0000i 0.0812379 0.0812379i
\(518\) 296.985i 0.573330i
\(519\) −893.783 316.000i −1.72213 0.608863i
\(520\) 392.000 + 56.0000i 0.753846 + 0.107692i
\(521\) −379.009 −0.727465 −0.363732 0.931503i \(-0.618498\pi\)
−0.363732 + 0.931503i \(0.618498\pi\)
\(522\) −4.02944 37.9706i −0.00771923 0.0727405i
\(523\) −642.000 642.000i −1.22753 1.22753i −0.964894 0.262639i \(-0.915407\pi\)
−0.262639 0.964894i \(-0.584593\pi\)
\(524\) 114.551i 0.218609i
\(525\) −518.146 + 84.5578i −0.986944 + 0.161063i
\(526\) −446.000 −0.847909
\(527\) 257.387 257.387i 0.488400 0.488400i
\(528\) −133.995 + 63.9949i −0.253778 + 0.121203i
\(529\) 627.000i 1.18526i
\(530\) −70.7107 + 494.975i −0.133416 + 0.933915i
\(531\) −207.889 168.000i −0.391505 0.316384i
\(532\) −210.000 −0.394737
\(533\) 271.529 + 271.529i 0.509435 + 0.509435i
\(534\) 19.7990 56.0000i 0.0370768 0.104869i
\(535\) 18.0000 + 24.0000i 0.0336449 + 0.0448598i
\(536\) 316.784i 0.591015i
\(537\) −16.4558 34.4558i −0.0306440 0.0641636i
\(538\) 189.000 + 189.000i 0.351301 + 0.351301i
\(539\) 485.075i 0.899954i
\(540\) 376.706 + 148.721i 0.697603 + 0.275409i
\(541\) 270.000 0.499076 0.249538 0.968365i \(-0.419721\pi\)
0.249538 + 0.968365i \(0.419721\pi\)
\(542\) 79.1960 + 79.1960i 0.146118 + 0.146118i
\(543\) −947.487 + 452.513i −1.74491 + 0.833357i
\(544\) 858.000 1.57721
\(545\) 346.482 + 49.4975i 0.635747 + 0.0908211i
\(546\) −214.392 + 102.392i −0.392659 + 0.187531i
\(547\) 176.000 + 176.000i 0.321755 + 0.321755i 0.849440 0.527685i \(-0.176940\pi\)
−0.527685 + 0.849440i \(0.676940\pi\)
\(548\) 55.1543 + 55.1543i 0.100647 + 0.100647i
\(549\) −98.0000 79.1960i −0.178506 0.144255i
\(550\) −119.000 217.000i −0.216364 0.394545i
\(551\) −42.4264 −0.0769989
\(552\) 644.291 307.709i 1.16719 0.557443i
\(553\) −392.000 −0.708861
\(554\) −144.250 −0.260379
\(555\) −563.970 294.853i −1.01616 0.531266i
\(556\) 414.000i 0.744604i
\(557\) 364.867 364.867i 0.655058 0.655058i −0.299149 0.954206i \(-0.596703\pi\)
0.954206 + 0.299149i \(0.0967027\pi\)
\(558\) −125.296 + 13.2965i −0.224546 + 0.0238288i
\(559\) 576.000 1.03041
\(560\) −173.241 24.7487i −0.309359 0.0441942i
\(561\) 728.000 + 257.387i 1.29768 + 0.458800i
\(562\) −210.000 210.000i −0.373665 0.373665i
\(563\) −615.183 + 615.183i −1.09269 + 1.09269i −0.0974464 + 0.995241i \(0.531067\pi\)
−0.995241 + 0.0974464i \(0.968933\pi\)
\(564\) −50.9117 18.0000i −0.0902690 0.0319149i
\(565\) 72.0000 54.0000i 0.127434 0.0955752i
\(566\) −144.250 −0.254858
\(567\) −554.372 + 119.000i −0.977728 + 0.209877i
\(568\) −294.000 + 294.000i −0.517606 + 0.517606i
\(569\) 28.2843 0.0497087 0.0248544 0.999691i \(-0.492088\pi\)
0.0248544 + 0.999691i \(0.492088\pi\)
\(570\) −69.4975 + 132.929i −0.121925 + 0.233209i
\(571\) −734.000 −1.28546 −0.642732 0.766091i \(-0.722199\pi\)
−0.642732 + 0.766091i \(0.722199\pi\)
\(572\) 237.588 + 237.588i 0.415363 + 0.415363i
\(573\) 321.588 153.588i 0.561235 0.268042i
\(574\) 168.000 + 168.000i 0.292683 + 0.292683i
\(575\) −408.708 745.291i −0.710796 1.29616i
\(576\) −91.0000 73.5391i −0.157986 0.127672i
\(577\) −647.000 + 647.000i −1.12132 + 1.12132i −0.129773 + 0.991544i \(0.541425\pi\)
−0.991544 + 0.129773i \(0.958575\pi\)
\(578\) −273.650 273.650i −0.473443 0.473443i
\(579\) 268.000 + 94.7523i 0.462867 + 0.163648i
\(580\) −63.0000 9.00000i −0.108621 0.0155172i
\(581\) −257.387 257.387i −0.443007 0.443007i
\(582\) −432.612 + 206.612i −0.743320 + 0.355004i
\(583\) −700.000 + 700.000i −1.20069 + 1.20069i
\(584\) 386.080i 0.661096i
\(585\) 18.4121 508.784i 0.0314737 0.869716i
\(586\) 262.000i 0.447099i
\(587\) 630.739 + 630.739i 1.07451 + 1.07451i 0.996991 + 0.0775226i \(0.0247010\pi\)
0.0775226 + 0.996991i \(0.475299\pi\)
\(588\) 397.945 190.055i 0.676777 0.323223i
\(589\) 140.000i 0.237691i
\(590\) 118.794 89.0955i 0.201346 0.151009i
\(591\) 226.274 + 80.0000i 0.382867 + 0.135364i
\(592\) −150.000 150.000i −0.253378 0.253378i
\(593\) 618.011 618.011i 1.04218 1.04218i 0.0431072 0.999070i \(-0.486274\pi\)
0.999070 0.0431072i \(-0.0137257\pi\)
\(594\) −140.000 227.688i −0.235690 0.383314i
\(595\) 546.000 + 728.000i 0.917647 + 1.22353i
\(596\) 598.212i 1.00371i
\(597\) 155.147 + 324.853i 0.259878 + 0.544142i
\(598\) −272.000 272.000i −0.454849 0.454849i
\(599\) 96.1665 0.160545 0.0802726 0.996773i \(-0.474421\pi\)
0.0802726 + 0.996773i \(0.474421\pi\)
\(600\) −306.593 + 426.176i −0.510988 + 0.710293i
\(601\) 476.000i 0.792013i −0.918248 0.396007i \(-0.870396\pi\)
0.918248 0.396007i \(-0.129604\pi\)
\(602\) 356.382 0.591996
\(603\) −405.019 + 42.9807i −0.671674 + 0.0712780i
\(604\) 234.000i 0.387417i
\(605\) −16.2635 + 113.844i −0.0268817 + 0.188172i
\(606\) 260.000 + 91.9239i 0.429043 + 0.151690i
\(607\) 345.000 345.000i 0.568369 0.568369i −0.363302 0.931671i \(-0.618351\pi\)
0.931671 + 0.363302i \(0.118351\pi\)
\(608\) −233.345 + 233.345i −0.383792 + 0.383792i
\(609\) 80.3970 38.3970i 0.132015 0.0630492i
\(610\) 56.0000 42.0000i 0.0918033 0.0688525i
\(611\) 67.8823i 0.111100i
\(612\) −74.0803 698.080i −0.121046 1.14065i
\(613\) 116.000 116.000i 0.189233 0.189233i −0.606131 0.795365i \(-0.707279\pi\)
0.795365 + 0.606131i \(0.207279\pi\)
\(614\) 127.279i 0.207295i
\(615\) −485.823 + 152.235i −0.789957 + 0.247537i
\(616\) 343.000 + 343.000i 0.556818 + 0.556818i
\(617\) −468.105 + 468.105i −0.758679 + 0.758679i −0.976082 0.217403i \(-0.930241\pi\)
0.217403 + 0.976082i \(0.430241\pi\)
\(618\) 9.14214 + 19.1421i 0.0147931 + 0.0309743i
\(619\) 1058.00 1.70921 0.854604 0.519280i \(-0.173800\pi\)
0.854604 + 0.519280i \(0.173800\pi\)
\(620\) −29.6985 + 207.889i −0.0479008 + 0.335305i
\(621\) −480.833 782.000i −0.774288 1.25926i
\(622\) 212.000 212.000i 0.340836 0.340836i
\(623\) 138.593 0.222461
\(624\) 56.5685 160.000i 0.0906547 0.256410i
\(625\) 527.000 + 336.000i 0.843200 + 0.537600i
\(626\) −250.316 −0.399865
\(627\) −267.990 + 127.990i −0.427416 + 0.204131i
\(628\) 138.000 + 138.000i 0.219745 + 0.219745i
\(629\) 1103.09i 1.75371i
\(630\) 11.3919 314.794i 0.0180824 0.499673i
\(631\) 128.000 0.202853 0.101426 0.994843i \(-0.467659\pi\)
0.101426 + 0.994843i \(0.467659\pi\)
\(632\) −277.186 + 277.186i −0.438585 + 0.438585i
\(633\) 111.189 + 232.811i 0.175654 + 0.367790i
\(634\) 302.000i 0.476341i
\(635\) 627.911 470.933i 0.988836 0.741627i
\(636\) 848.528 + 300.000i 1.33416 + 0.471698i
\(637\) −392.000 392.000i −0.615385 0.615385i
\(638\) 29.6985 + 29.6985i 0.0465493 + 0.0465493i
\(639\) 415.779 + 336.000i 0.650671 + 0.525822i
\(640\) −476.000 + 357.000i −0.743750 + 0.557813i
\(641\) 277.186i 0.432427i −0.976346 0.216214i \(-0.930629\pi\)
0.976346 0.216214i \(-0.0693708\pi\)
\(642\) −16.2426 + 7.75736i −0.0253001 + 0.0120831i
\(643\) −636.000 636.000i −0.989114 0.989114i 0.0108278 0.999941i \(-0.496553\pi\)
−0.999941 + 0.0108278i \(0.996553\pi\)
\(644\) 504.874 + 504.874i 0.783966 + 0.783966i
\(645\) −353.823 + 676.764i −0.548563 + 1.04925i
\(646\) 260.000 0.402477
\(647\) −535.987 535.987i −0.828419 0.828419i 0.158879 0.987298i \(-0.449212\pi\)
−0.987298 + 0.158879i \(0.949212\pi\)
\(648\) −307.854 + 476.146i −0.475084 + 0.734793i
\(649\) 294.000 0.453005
\(650\) 271.529 + 79.1960i 0.417737 + 0.121840i
\(651\) −126.704 265.296i −0.194629 0.407521i
\(652\) −414.000 414.000i −0.634969 0.634969i
\(653\) 380.423 + 380.423i 0.582578 + 0.582578i 0.935611 0.353033i \(-0.114850\pi\)
−0.353033 + 0.935611i \(0.614850\pi\)
\(654\) −70.0000 + 197.990i −0.107034 + 0.302737i
\(655\) −27.0000 + 189.000i −0.0412214 + 0.288550i
\(656\) −169.706 −0.258698
\(657\) −493.617 + 52.3827i −0.751320 + 0.0797301i
\(658\) 42.0000i 0.0638298i
\(659\) −253.144 −0.384134 −0.192067 0.981382i \(-0.561519\pi\)
−0.192067 + 0.981382i \(0.561519\pi\)
\(660\) −425.095 + 133.206i −0.644084 + 0.201827i
\(661\) 1106.00i 1.67322i 0.547797 + 0.836611i \(0.315467\pi\)
−0.547797 + 0.836611i \(0.684533\pi\)
\(662\) −72.1249 + 72.1249i −0.108950 + 0.108950i
\(663\) −796.313 + 380.313i −1.20108 + 0.573624i
\(664\) −364.000 −0.548193
\(665\) −346.482 49.4975i −0.521026 0.0744323i
\(666\) 240.000 296.985i 0.360360 0.445923i
\(667\) 102.000 + 102.000i 0.152924 + 0.152924i
\(668\) 275.772 275.772i 0.412832 0.412832i
\(669\) 335.169 948.000i 0.500999 1.41704i
\(670\) 32.0000 224.000i 0.0477612 0.334328i
\(671\) 138.593 0.206547
\(672\) 231.000 653.367i 0.343750 0.972272i
\(673\) 393.000 393.000i 0.583952 0.583952i −0.352035 0.935987i \(-0.614510\pi\)
0.935987 + 0.352035i \(0.114510\pi\)
\(674\) −357.796 −0.530855
\(675\) 586.479 + 334.167i 0.868857 + 0.495062i
\(676\) 123.000 0.181953
\(677\) −144.250 144.250i −0.213072 0.213072i 0.592499 0.805571i \(-0.298141\pi\)
−0.805571 + 0.592499i \(0.798141\pi\)
\(678\) 23.2721 + 48.7279i 0.0343246 + 0.0718701i
\(679\) −791.000 791.000i −1.16495 1.16495i
\(680\) 900.854 + 128.693i 1.32479 + 0.189255i
\(681\) −166.000 + 469.519i −0.243759 + 0.689455i
\(682\) 98.0000 98.0000i 0.143695 0.143695i
\(683\) 592.555 + 592.555i 0.867578 + 0.867578i 0.992204 0.124626i \(-0.0397732\pi\)
−0.124626 + 0.992204i \(0.539773\pi\)
\(684\) 210.000 + 169.706i 0.307018 + 0.248108i
\(685\) 78.0000 + 104.000i 0.113869 + 0.151825i
\(686\) −242.538 242.538i −0.353553 0.353553i
\(687\) −483.542 1012.46i −0.703846 1.47374i
\(688\) −180.000 + 180.000i −0.261628 + 0.261628i
\(689\) 1131.37i 1.64205i
\(690\) 486.666 152.500i 0.705313 0.221014i
\(691\) 574.000i 0.830680i 0.909666 + 0.415340i \(0.136337\pi\)
−0.909666 + 0.415340i \(0.863663\pi\)
\(692\) −670.337 670.337i −0.968695 0.968695i
\(693\) 392.000 485.075i 0.565657 0.699964i
\(694\) 240.000i 0.345821i
\(695\) 97.5807 683.065i 0.140404 0.982828i
\(696\) 29.6985 84.0000i 0.0426702 0.120690i
\(697\) 624.000 + 624.000i 0.895265 + 0.895265i
\(698\) 315.370 315.370i 0.451819 0.451819i
\(699\) 246.000 695.793i 0.351931 0.995412i
\(700\) −504.000 147.000i −0.720000 0.210000i
\(701\) 1118.64i 1.59578i 0.602802 + 0.797891i \(0.294051\pi\)
−0.602802 + 0.797891i \(0.705949\pi\)
\(702\) 297.137 + 70.8629i 0.423272 + 0.100944i
\(703\) −300.000 300.000i −0.426743 0.426743i
\(704\) 128.693 0.182803
\(705\) −79.7574 41.6985i −0.113131 0.0591468i
\(706\) 138.000i 0.195467i
\(707\) 643.467i 0.910137i
\(708\) −115.191 241.191i −0.162699 0.340665i
\(709\) 546.000i 0.770099i −0.922896 0.385049i \(-0.874184\pi\)
0.922896 0.385049i \(-0.125816\pi\)
\(710\) −237.588 + 178.191i −0.334631 + 0.250973i
\(711\) 392.000 + 316.784i 0.551336 + 0.445547i
\(712\) 98.0000 98.0000i 0.137640 0.137640i
\(713\) 336.583 336.583i 0.472066 0.472066i
\(714\) −492.693 + 235.307i −0.690047 + 0.329561i
\(715\) 336.000 + 448.000i 0.469930 + 0.626573i
\(716\) 38.1838i 0.0533293i
\(717\) 376.656 + 788.656i 0.525322 + 1.09994i
\(718\) 176.000 176.000i 0.245125 0.245125i
\(719\) 277.186i 0.385516i −0.981246 0.192758i \(-0.938257\pi\)
0.981246 0.192758i \(-0.0617432\pi\)
\(720\) 153.241 + 164.749i 0.212835 + 0.228818i
\(721\) −35.0000 + 35.0000i −0.0485437 + 0.0485437i
\(722\) 184.555 184.555i 0.255616 0.255616i
\(723\) −37.8995 + 18.1005i −0.0524198 + 0.0250353i
\(724\) −1050.00 −1.45028
\(725\) −101.823 29.6985i −0.140446 0.0409634i
\(726\) −65.0538 23.0000i −0.0896058 0.0316804i
\(727\) 225.000 225.000i 0.309491 0.309491i −0.535221 0.844712i \(-0.679772\pi\)
0.844712 + 0.535221i \(0.179772\pi\)
\(728\) −554.372 −0.761500
\(729\) 650.538 + 329.000i 0.892371 + 0.451303i
\(730\) 39.0000 273.000i 0.0534247 0.373973i
\(731\) 1323.70 1.81081
\(732\) −54.3015 113.698i −0.0741824 0.155326i
\(733\) −124.000 124.000i −0.169168 0.169168i 0.617446 0.786614i \(-0.288168\pi\)
−0.786614 + 0.617446i \(0.788168\pi\)
\(734\) 261.630i 0.356443i
\(735\) 701.372 219.779i 0.954247 0.299019i
\(736\) 1122.00 1.52446
\(737\) 316.784 316.784i 0.429829 0.429829i
\(738\) −32.2355 303.765i −0.0436795 0.411605i
\(739\) 350.000i 0.473613i 0.971557 + 0.236806i \(0.0761007\pi\)
−0.971557 + 0.236806i \(0.923899\pi\)
\(740\) −381.838 509.117i −0.515997 0.687996i
\(741\) 113.137 320.000i 0.152682 0.431849i
\(742\) 700.000i 0.943396i
\(743\) −666.095 666.095i −0.896493 0.896493i 0.0986307 0.995124i \(-0.468554\pi\)
−0.995124 + 0.0986307i \(0.968554\pi\)
\(744\) −277.186 98.0000i −0.372562 0.131720i
\(745\) 141.000 987.000i 0.189262 1.32483i
\(746\) 695.793i 0.932698i
\(747\) 49.3869 + 465.387i 0.0661136 + 0.623008i
\(748\) 546.000 + 546.000i 0.729947 + 0.729947i
\(749\) −29.6985 29.6985i −0.0396508 0.0396508i
\(750\) −259.844 + 270.381i −0.346459 + 0.360508i
\(751\) −1172.00 −1.56059 −0.780293 0.625414i \(-0.784930\pi\)
−0.780293 + 0.625414i \(0.784930\pi\)
\(752\) −21.2132 21.2132i −0.0282090 0.0282090i
\(753\) 568.641 + 1190.64i 0.755167 + 1.58120i
\(754\) −48.0000 −0.0636605
\(755\) −55.1543 + 386.080i −0.0730521 + 0.511365i
\(756\) −551.533 131.533i −0.729540 0.173985i
\(757\) 302.000 + 302.000i 0.398943 + 0.398943i 0.877860 0.478917i \(-0.158971\pi\)
−0.478917 + 0.877860i \(0.658971\pi\)
\(758\) −188.090 188.090i −0.248140 0.248140i
\(759\) 952.000 + 336.583i 1.25428 + 0.443456i
\(760\) −280.000 + 210.000i −0.368421 + 0.276316i
\(761\) 701.450 0.921748 0.460874 0.887466i \(-0.347536\pi\)
0.460874 + 0.887466i \(0.347536\pi\)
\(762\) 202.955 + 424.955i 0.266346 + 0.557684i
\(763\) −490.000 −0.642202
\(764\) 356.382 0.466468
\(765\) 42.3128 1169.23i 0.0553109 1.52841i
\(766\) 190.000i 0.248042i
\(767\) −237.588 + 237.588i −0.309763 + 0.309763i
\(768\) −221.085 462.915i −0.287871 0.602754i
\(769\) 436.000 0.566970 0.283485 0.958977i \(-0.408509\pi\)
0.283485 + 0.958977i \(0.408509\pi\)
\(770\) 207.889 + 277.186i 0.269986 + 0.359982i
\(771\) 50.0000 141.421i 0.0648508 0.183426i
\(772\) 201.000 + 201.000i 0.260363 + 0.260363i
\(773\) −684.479 + 684.479i −0.885484 + 0.885484i −0.994085 0.108601i \(-0.965363\pi\)
0.108601 + 0.994085i \(0.465363\pi\)
\(774\) −356.382 288.000i −0.460442 0.372093i
\(775\) −98.0000 + 336.000i −0.126452 + 0.433548i
\(776\) −1118.64 −1.44155
\(777\) 840.000 + 296.985i 1.08108 + 0.382220i
\(778\) 233.000 233.000i 0.299486 0.299486i
\(779\) −339.411 −0.435701
\(780\) 235.882 451.176i 0.302413 0.578430i
\(781\) −588.000 −0.752881