Properties

Label 105.3.k.a.83.1
Level 105
Weight 3
Character 105.83
Analytic conductor 2.861
Analytic rank 0
Dimension 4
CM no
Inner twists 4

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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 83.1
Root \(-0.707107 - 0.707107i\) of \(x^{4} + 1\)
Character \(\chi\) \(=\) 105.83
Dual form 105.3.k.a.62.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(-1.29289 + 2.70711i) q^{3} -3.00000i q^{4} +(0.707107 + 4.94975i) q^{5} +(2.82843 - 1.00000i) q^{6} -7.00000 q^{7} +(-4.94975 + 4.94975i) q^{8} +(-5.65685 - 7.00000i) q^{9} +O(q^{10})\) \(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} -7.00000 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} +(9.05025 - 18.9497i) 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} +21.0000i 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} +(-4.94975 - 34.6482i) 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} +(-19.7990 + 7.00000i) 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} +(39.5980 + 49.0000i) 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} +(-21.0000 + 28.0000i) 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} -69.2965i 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} +(-56.8492 - 27.1508i) 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 8q^{3} - 28q^{7} + O(q^{10}) \) \( 4q - 8q^{3} - 28q^{7} + 12q^{10} + 24q^{12} - 32q^{13} - 12q^{15} - 20q^{16} + 16q^{18} + 40q^{19} + 56q^{21} + 28q^{22} - 28q^{24} - 96q^{25} + 40q^{27} + 8q^{30} - 28q^{33} + 104q^{34} - 84q^{36} + 120q^{37} - 112q^{40} + 144q^{43} - 16q^{45} - 136q^{46} + 40q^{48} + 196q^{49} - 104q^{51} + 96q^{52} - 92q^{54} - 196q^{55} - 80q^{57} - 12q^{58} + 48q^{60} + 128q^{67} + 136q^{69} - 84q^{70} + 112q^{72} - 156q^{73} + 136q^{75} + 32q^{78} - 68q^{81} + 96q^{82} - 168q^{84} - 416q^{85} + 12q^{87} - 196q^{88} - 112q^{90} + 224q^{91} + 112q^{93} + 24q^{94} - 452q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\)

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 0.507877 0.861430i \(-0.330431\pi\)
−0.861430 + 0.507877i \(0.830431\pi\)
\(3\) −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
\(7\) −7.00000 −1.00000
\(8\) −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 \(0.148568\pi\)
−0.893040 + 0.449977i \(0.851432\pi\)
\(12\) 8.12132 + 3.87868i 0.676777 + 0.323223i
\(13\) −8.00000 + 8.00000i −0.615385 + 0.615385i −0.944344 0.328959i \(-0.893302\pi\)
0.328959 + 0.944344i \(0.393302\pi\)
\(14\) 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 −0.0850836 + 0.996374i \(0.527116\pi\)
−0.996374 + 0.0850836i \(0.972884\pi\)
\(18\) −0.949747 + 8.94975i −0.0527637 + 0.497208i
\(19\) 10.0000 0.526316 0.263158 0.964753i \(-0.415236\pi\)
0.263158 + 0.964753i \(0.415236\pi\)
\(20\) 14.8492 2.12132i 0.742462 0.106066i
\(21\) 9.05025 18.9497i 0.430964 0.902369i
\(22\) 7.00000 7.00000i 0.318182 0.318182i
\(23\) 24.0416 24.0416i 1.04529 1.04529i 0.0463637 0.998925i \(-0.485237\pi\)
0.998925 0.0463637i \(-0.0147633\pi\)
\(24\) −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
\(28\) 21.0000i 0.750000i
\(29\) 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
\(35\) −4.94975 34.6482i −0.141421 0.989949i
\(36\) −21.0000 + 16.9706i −0.583333 + 0.471405i
\(37\) 30.0000 30.0000i 0.810811 0.810811i −0.173945 0.984755i \(-0.555651\pi\)
0.984755 + 0.173945i \(0.0556514\pi\)
\(38\) −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 \(-0.635839\pi\)
−0.413916 + 0.910315i \(0.635839\pi\)
\(42\) −19.7990 + 7.00000i −0.471405 + 0.166667i
\(43\) 36.0000 + 36.0000i 0.837209 + 0.837209i 0.988491 0.151281i \(-0.0483400\pi\)
−0.151281 + 0.988491i \(0.548340\pi\)
\(44\) 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 \(-0.770331\pi\)
0.660530 + 0.750799i \(0.270331\pi\)
\(48\) 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 −0.432557 + 0.901606i \(0.642389\pi\)
−0.901606 + 0.432557i \(0.857611\pi\)
\(54\) −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
\(63\) 39.5980 + 49.0000i 0.628539 + 0.777778i
\(64\) 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 −0.426755 0.904367i \(-0.640343\pi\)
0.904367 + 0.426755i \(0.140343\pi\)
\(68\) 55.1543 + 55.1543i 0.811093 + 0.811093i
\(69\) 34.0000 + 96.1665i 0.492754 + 1.39372i
\(70\) −21.0000 + 28.0000i −0.300000 + 0.400000i
\(71\) 59.3970i 0.836577i 0.908314 + 0.418289i \(0.137370\pi\)
−0.908314 + 0.418289i \(0.862630\pi\)
\(72\) 62.6482 + 6.64823i 0.870114 + 0.0923366i
\(73\) −39.0000 + 39.0000i −0.534247 + 0.534247i −0.921833 0.387587i \(-0.873309\pi\)
0.387587 + 0.921833i \(0.373309\pi\)
\(74\) −42.4264 −0.573330
\(75\) 12.0797 74.0208i 0.161063 0.986944i
\(76\) 30.0000i 0.394737i
\(77\) 69.2965i 0.899954i
\(78\) −14.6274 + 30.6274i −0.187531 + 0.392659i
\(79\) 56.0000i 0.708861i 0.935082 + 0.354430i \(0.115325\pi\)
−0.935082 + 0.354430i \(0.884675\pi\)
\(80\) −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 \(-0.351419\pi\)
−0.893021 + 0.450015i \(0.851419\pi\)
\(84\) −56.8492 27.1508i −0.676777 0.323223i
\(85\) −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 −0.983378 0.181571i \(-0.941882\pi\)
−0.181571 0.983378i \(-0.558118\pi\)
\(98\) −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 \(-0.349615\pi\)
0.455069 + 0.890456i \(0.349615\pi\)
\(102\) −33.6152 + 70.3848i −0.329561 + 0.690047i
\(103\) 5.00000 5.00000i 0.0485437 0.0485437i −0.682418 0.730962i \(-0.739072\pi\)
0.730962 + 0.682418i \(0.239072\pi\)
\(104\) 79.1960i 0.761500i
\(105\) 100.196 + 31.3970i 0.954247 + 0.299019i
\(106\) 100.000 0.943396
\(107\) 4.24264 + 4.24264i 0.0396508 + 0.0396508i 0.726654 0.687003i \(-0.241074\pi\)
−0.687003 + 0.726654i \(0.741074\pi\)
\(108\) −18.7904 78.7904i −0.173985 0.729540i
\(109\) 70.0000i 0.642202i 0.947045 + 0.321101i \(0.104053\pi\)
−0.947045 + 0.321101i \(0.895947\pi\)
\(110\) 39.5980 + 29.6985i 0.359982 + 0.269986i
\(111\) 42.4264 + 120.000i 0.382220 + 1.08108i
\(112\) 35.0000 0.312500
\(113\) −12.7279 + 12.7279i −0.112636 + 0.112636i −0.761179 0.648542i \(-0.775379\pi\)
0.648542 + 0.761179i \(0.275379\pi\)
\(114\) 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
\(126\) 6.64823 62.6482i 0.0527637 0.497208i
\(127\) −111.000 + 111.000i −0.874016 + 0.874016i −0.992907 0.118892i \(-0.962066\pi\)
0.118892 + 0.992907i \(0.462066\pi\)
\(128\) 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 \(-0.546556\pi\)
−0.145740 + 0.989323i \(0.546556\pi\)
\(132\) −38.3970 + 80.3970i −0.290886 + 0.609068i
\(133\) −70.0000 −0.526316
\(134\) −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 0.771014 0.636818i \(-0.219750\pi\)
−0.636818 + 0.771014i \(0.719750\pi\)
\(138\) 43.9584 92.0416i 0.318539 0.666968i
\(139\) 138.000 0.992806 0.496403 0.868092i \(-0.334654\pi\)
0.496403 + 0.868092i \(0.334654\pi\)
\(140\) −103.945 + 14.8492i −0.742462 + 0.106066i
\(141\) −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 \(-0.316428\pi\)
−0.838262 + 0.545268i \(0.816428\pi\)
\(158\) 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 0.143085 0.989710i \(-0.454298\pi\)
−0.989710 + 0.143085i \(0.954298\pi\)
\(164\) 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 \(-0.622744\pi\)
0.926568 + 0.376126i \(0.122744\pi\)
\(168\) 49.0000 + 138.593i 0.291667 + 0.824958i
\(169\) 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 0.933801 + 0.357793i \(0.116471\pi\)
0.357793 + 0.933801i \(0.383529\pi\)
\(174\) 12.0000 4.24264i 0.0689655 0.0243830i
\(175\) 168.000 49.0000i 0.960000 0.280000i
\(176\) 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 \(0.582188\pi\)
\(182\) −79.1960 −0.435143
\(183\) −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
\(189\) −183.844 + 43.8442i −0.972721 + 0.231980i
\(190\) 30.0000 40.0000i 0.157895 0.210526i
\(191\) 118.794i 0.621958i 0.950417 + 0.310979i \(0.100657\pi\)
−0.950417 + 0.310979i \(0.899343\pi\)
\(192\) 35.1924 + 16.8076i 0.183294 + 0.0875396i
\(193\) 67.0000 + 67.0000i 0.347150 + 0.347150i 0.859047 0.511897i \(-0.171057\pi\)
−0.511897 + 0.859047i \(0.671057\pi\)
\(194\) 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 0.835952 0.548802i \(-0.184916\pi\)
−0.548802 + 0.835952i \(0.684916\pi\)
\(198\) −88.5980 9.40202i −0.447465 0.0474850i
\(199\) −120.000 −0.603015 −0.301508 0.953464i \(-0.597490\pi\)
−0.301508 + 0.953464i \(0.597490\pi\)
\(200\) 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
\(203\) −29.6985 −0.146298
\(204\) −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
\(210\) −48.6482 93.0503i −0.231658 0.443096i
\(211\) 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
\(217\) 98.0000i 0.451613i
\(218\) 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 0.0648877 0.997893i \(-0.479331\pi\)
0.997893 0.0648877i \(-0.0206689\pi\)
\(224\) −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 \(-0.869149\pi\)
0.399599 + 0.916690i \(0.369149\pi\)
\(228\) 81.2132 + 38.7868i 0.356198 + 0.170118i
\(229\) 374.000 1.63319 0.816594 0.577213i \(-0.195860\pi\)
0.816594 + 0.577213i \(0.195860\pi\)
\(230\) −24.0416 168.291i −0.104529 0.731702i
\(231\) 187.593 + 89.5929i 0.812091 + 0.387848i
\(232\) −21.0000 + 21.0000i −0.0905172 + 0.0905172i
\(233\) −173.948 + 173.948i −0.746559 + 0.746559i −0.973831 0.227272i \(-0.927019\pi\)
0.227272 + 0.973831i \(0.427019\pi\)
\(234\) −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
\(238\) −182.000 −0.764706
\(239\) 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 \(-0.839887\pi\)
−0.876136 + 0.482063i \(0.839887\pi\)
\(252\) 147.000 118.794i 0.583333 0.471405i
\(253\) 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 \(-0.718987\pi\)
0.772538 + 0.634969i \(0.218987\pi\)
\(258\) 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 0.224695 0.974429i \(-0.427861\pi\)
0.974429 0.224695i \(-0.0721385\pi\)
\(264\) 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
\(273\) 79.1960 + 224.000i 0.290095 + 0.820513i
\(274\) 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 −0.498601 0.866832i \(-0.666153\pi\)
0.866832 + 0.498601i \(0.166153\pi\)
\(278\) −97.5807 97.5807i −0.351010 0.351010i
\(279\) −98.0000 + 79.1960i −0.351254 + 0.283856i
\(280\) 196.000 + 147.000i 0.700000 + 0.525000i
\(281\) 296.985i 1.05689i −0.848969 0.528443i \(-0.822776\pi\)
0.848969 0.528443i \(-0.177224\pi\)
\(282\) −7.75736 + 16.2426i −0.0275084 + 0.0575980i
\(283\) −102.000 + 102.000i −0.360424 + 0.360424i −0.863969 0.503545i \(-0.832029\pi\)
0.503545 + 0.863969i \(0.332029\pi\)
\(284\) 178.191 0.627433
\(285\) −143.137 44.8528i −0.502235 0.157378i
\(286\) 112.000i 0.391608i
\(287\) 237.588 0.827832
\(288\) 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 \(-0.397543\pi\)
−0.948643 + 0.316349i \(0.897543\pi\)
\(294\) 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 \(-0.183534\pi\)
−0.545168 + 0.838327i \(0.683534\pi\)
\(308\) −207.889 −0.674966
\(309\) 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 \(-0.339905\pi\)
0.482015 + 0.876163i \(0.339905\pi\)
\(312\) 214.392 + 102.392i 0.687154 + 0.328179i
\(313\) −177.000 + 177.000i −0.565495 + 0.565495i −0.930863 0.365368i \(-0.880943\pi\)
0.365368 + 0.930863i \(0.380943\pi\)
\(314\) 65.0538i 0.207178i
\(315\) −214.538 + 230.648i −0.681072 + 0.732217i
\(316\) 168.000 0.531646
\(317\) −213.546 213.546i −0.673647 0.673647i 0.284908 0.958555i \(-0.408037\pi\)
−0.958555 + 0.284908i \(0.908037\pi\)
\(318\) −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
\(322\) 238.000 0.739130
\(323\) −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
\(336\) −45.2513 + 94.7487i −0.134676 + 0.281990i
\(337\) 253.000 253.000i 0.750742 0.750742i −0.223876 0.974618i \(-0.571871\pi\)
0.974618 + 0.223876i \(0.0718710\pi\)
\(338\) 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
\(343\) −343.000 −1.00000
\(344\) −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 0.418946 0.908011i \(-0.362400\pi\)
−0.908011 + 0.418946i \(0.862400\pi\)
\(348\) 34.4558 + 16.4558i 0.0990110 + 0.0472869i
\(349\) 446.000 1.27794 0.638968 0.769233i \(-0.279361\pi\)
0.638968 + 0.769233i \(0.279361\pi\)
\(350\) −153.442 84.1457i −0.438406 0.240416i
\(351\) −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 \(-0.312622\pi\)
−0.831683 + 0.555250i \(0.812622\pi\)
\(354\) 29.6985 + 84.0000i 0.0838940 + 0.237288i
\(355\) −294.000 + 42.0000i −0.828169 + 0.118310i
\(356\) 59.3970 0.166845
\(357\) 182.000 + 514.774i 0.509804 + 1.44194i
\(358\) 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 \(-0.133989\pi\)
−0.408618 + 0.912705i \(0.633989\pi\)
\(368\) −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 0.914540 + 0.404494i \(0.132552\pi\)
0.404494 + 0.914540i \(0.367448\pi\)
\(374\) 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
\(378\) 161.000 + 98.9949i 0.425926 + 0.261891i
\(379\) 266.000i 0.701847i −0.936404 0.350923i \(-0.885868\pi\)
0.936404 0.350923i \(-0.114132\pi\)
\(380\) 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 \(-0.170213\pi\)
−0.509617 + 0.860401i \(0.670213\pi\)
\(384\) 119.000 + 336.583i 0.309896 + 0.876518i
\(385\) 343.000 49.0000i 0.890909 0.127273i
\(386\) 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 \(-0.267017\pi\)
−0.743880 + 0.668313i \(0.767017\pi\)
\(398\) 84.8528 + 84.8528i 0.213198 + 0.213198i
\(399\) 90.5025 189.497i 0.226823 0.474931i
\(400\) 120.000 35.0000i 0.300000 0.0875000i
\(401\) 79.1960i 0.197496i −0.995112 0.0987481i \(-0.968516\pi\)
0.995112 0.0987481i \(-0.0314838\pi\)
\(402\) 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 \(-0.620366\pi\)
−0.369193 + 0.929353i \(0.620366\pi\)
\(410\) −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
\(413\) 207.889i 0.503364i
\(414\) 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 \(-0.143991\pi\)
\(420\) 94.1909 300.588i 0.224264 0.715685i
\(421\) −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
\(427\) 98.0000i 0.229508i
\(428\) 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 \(0.222361\pi\)
−0.765763 + 0.643123i \(0.777639\pi\)
\(432\) −131.317 + 31.3173i −0.303975 + 0.0724937i
\(433\) 153.000 153.000i 0.353349 0.353349i −0.508005 0.861354i \(-0.669617\pi\)
0.861354 + 0.508005i \(0.169617\pi\)
\(434\) 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 \(-0.408850\pi\)
0.282460 + 0.959279i \(0.408850\pi\)
\(440\) 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 −0.690965 0.722888i \(-0.742814\pi\)
0.722888 + 0.690965i \(0.242814\pi\)
\(444\) 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
\(448\) 91.0000i 0.203125i
\(449\) 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
\(455\) 316.784 + 237.588i 0.696228 + 0.522171i
\(456\) −70.0000 197.990i −0.153509 0.434188i
\(457\) −313.000 + 313.000i −0.684902 + 0.684902i −0.961100 0.276199i \(-0.910925\pi\)
0.276199 + 0.961100i \(0.410925\pi\)
\(458\) −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 \(-0.549512\pi\)
−0.154919 + 0.987927i \(0.549512\pi\)
\(462\) −69.2965 196.000i −0.149992 0.424242i
\(463\) 29.0000 + 29.0000i 0.0626350 + 0.0626350i 0.737730 0.675095i \(-0.235898\pi\)
−0.675095 + 0.737730i \(0.735898\pi\)
\(464\) −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 \(-0.928202\pi\)
0.223652 + 0.974669i \(0.428202\pi\)
\(468\) 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
\(483\) −238.000 673.166i −0.492754 1.39372i
\(484\) 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 −0.803158 0.595766i \(-0.796849\pi\)
0.595766 + 0.803158i \(0.296849\pi\)
\(488\) −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 \(0.114782\pi\)
−0.935686 + 0.352833i \(0.885218\pi\)
\(492\) −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
\(497\) 415.779i 0.836577i
\(498\) −140.770 67.2304i −0.282670 0.135001i
\(499\) 602.000i 1.20641i 0.797585 + 0.603206i \(0.206110\pi\)
−0.797585 + 0.603206i \(0.793890\pi\)
\(500\) −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 0.957678 + 0.287842i \(0.0929379\pi\)
0.287842 + 0.957678i \(0.407062\pi\)
\(504\) −438.538 46.5376i −0.870114 0.0923366i
\(505\) 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
\(518\) 296.985 0.573330
\(519\) −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 \(-0.381502\pi\)
0.363732 + 0.931503i \(0.381502\pi\)
\(522\) −4.02944 + 37.9706i −0.00771923 + 0.0727405i
\(523\) 642.000 642.000i 1.22753 1.22753i 0.262639 0.964894i \(-0.415407\pi\)
0.964894 0.262639i \(-0.0845930\pi\)
\(524\) 114.551i 0.218609i
\(525\) −84.5578 + 518.146i −0.161063 + 0.986944i
\(526\) −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
\(532\) 210.000i 0.394737i
\(533\) 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
\(546\) 102.392 214.392i 0.187531 0.392659i
\(547\) 176.000 176.000i 0.321755 0.321755i −0.527685 0.849440i \(-0.676940\pi\)
0.849440 + 0.527685i \(0.176940\pi\)
\(548\) 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
\(553\) 392.000i 0.708861i
\(554\) −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 0.954206 0.299149i \(-0.0967027\pi\)
−0.299149 + 0.954206i \(0.596703\pi\)
\(558\) 125.296 + 13.2965i 0.224546 + 0.0238288i
\(559\) −576.000 −1.03041
\(560\) 24.7487 + 173.241i 0.0441942 + 0.309359i
\(561\) 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 0.995241 + 0.0974464i \(0.0310675\pi\)
0.0974464 + 0.995241i \(0.468933\pi\)
\(564\) −50.9117 + 18.0000i −0.0902690 + 0.0319149i
\(565\) −72.0000 54.0000i −0.127434 0.0955752i
\(566\) 144.250 0.254858
\(567\) 119.000 554.372i 0.209877 0.977728i
\(568\) −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 0.991544 + 0.129773i \(0.0414250\pi\)
0.129773 + 0.991544i \(0.458575\pi\)
\(578\) −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 −0.0775226 + 0.996991i \(0.524701\pi\)
−0.996991 + 0.0775226i \(0.975299\pi\)
\(588\) 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 −0.999070 0.0431072i \(-0.986274\pi\)
−0.0431072 0.999070i \(-0.513726\pi\)
\(594\) 140.000 227.688i 0.235690 0.383314i
\(595\) 728.000 + 546.000i 1.22353 + 0.917647i
\(596\) 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 \(-0.129604\pi\)
\(602\) 356.382i 0.591996i
\(603\) −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 \(-0.381649\pi\)
−0.931671 + 0.363302i \(0.881649\pi\)
\(608\) 233.345 + 233.345i 0.383792 + 0.383792i
\(609\) 38.3970 80.3970i 0.0630492 0.132015i
\(610\) 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 0.795365 0.606131i \(-0.207279\pi\)
−0.606131 + 0.795365i \(0.707279\pi\)
\(614\) 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 0.217403 0.976082i \(-0.430241\pi\)
−0.976082 + 0.217403i \(0.930241\pi\)
\(618\) 9.14214 19.1421i 0.0147931 0.0309743i
\(619\) −1058.00 −1.70921 −0.854604 0.519280i \(-0.826200\pi\)
−0.854604 + 0.519280i \(0.826200\pi\)
\(620\) −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
\(623\) 138.593i 0.222461i
\(624\) 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
\(630\) 314.794 11.3919i 0.499673 0.0180824i
\(631\) 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 \(0.0693708\pi\)
−0.976346 + 0.216214i \(0.930629\pi\)
\(642\) 16.2426 + 7.75736i 0.0253001 + 0.0120831i
\(643\) 636.000 636.000i 0.989114 0.989114i −0.0108278 0.999941i \(-0.503447\pi\)
0.999941 + 0.0108278i \(0.00344668\pi\)
\(644\) 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 \(-0.550788\pi\)
0.987298 + 0.158879i \(0.0507881\pi\)
\(648\) −307.854 476.146i −0.475084 0.734793i
\(649\) −294.000 −0.453005
\(650\) −271.529 + 79.1960i −0.417737 + 0.121840i
\(651\) −265.296 126.704i −0.407521 0.194629i
\(652\) −414.000 + 414.000i −0.634969 + 0.634969i
\(653\) 380.423 380.423i 0.582578 0.582578i −0.353033 0.935611i \(-0.614850\pi\)
0.935611 + 0.353033i \(0.114850\pi\)
\(654\) 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
\(658\) −42.0000 −0.0638298
\(659\) −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
\(665\) −49.4975 346.482i −0.0744323 0.521026i
\(666\) 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
\(672\) 653.367 231.000i 0.972272 0.343750i
\(673\) 393.000 + 393.000i 0.583952 + 0.583952i 0.935987 0.352035i \(-0.114510\pi\)
−0.352035 + 0.935987i \(0.614510\pi\)
\(674\) −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 \(-0.701859\pi\)
0.805571 + 0.592499i \(0.201859\pi\)
\(678\) −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 −0.124626 0.992204i \(-0.539773\pi\)
0.992204 + 0.124626i \(0.0397732\pi\)
\(684\) −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
\(693\) −485.075 + 392.000i −0.699964 + 0.565657i
\(694\) 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
\(700\) −147.000 504.000i −0.210000 0.720000i
\(701\) 1118.64i 1.59578i −0.602802 0.797891i \(-0.705949\pi\)
0.602802 0.797891i \(-0.294051\pi\)
\(702\) 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
\(707\) −643.467 −0.910137
\(708\) −115.191 + 241.191i −0.162699 + 0.340665i
\(709\) 546.000i 0.770099i 0.922896 + 0.385049i \(0.125816\pi\)
−0.922896 + 0.385049i \(0.874184\pi\)
\(710\) 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
\(714\) 235.307 492.693i 0.329561 0.690047i
\(715\) 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 \(-0.320228\pi\)
−0.844712 + 0.535221i \(0.820228\pi\)
\(728\) 554.372i 0.761500i
\(729\) 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 \(-0.711832\pi\)
0.786614 + 0.617446i \(0.211832\pi\)
\(734\) 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 \(-0.923899\pi\)
0.971557 0.236806i \(-0.0761007\pi\)
\(740\) 381.838 509.117i 0.515997 0.687996i
\(741\) −113.137 320.000i −0.152682 0.431849i
\(742\) −700.000 −0.943396
\(743\) −666.095 + 666.095i −0.896493 + 0.896493i −0.995124 0.0986307i \(-0.968554\pi\)
0.0986307 + 0.995124i \(0.468554\pi\)
\(744\) −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
\(756\) 131.533 + 551.533i 0.173985 + 0.729540i
\(757\) 302.000 302.000i 0.398943 0.398943i −0.478917 0.877860i \(-0.658971\pi\)
0.877860 + 0.478917i \(0.158971\pi\)
\(758\) −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 \(-0.652464\pi\)
−0.460874 + 0.887466i \(0.652464\pi\)
\(762\) −202.955 + 424.955i −0.266346 + 0.557684i
\(763\) 490.000i 0.642202i
\(764\) 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 \(-0.591491\pi\)
−0.283485 + 0.958977i \(0.591491\pi\)
\(770\) −277.186 207.889i −0.359982 0.269986i
\(771\) 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 \(-0.0346371\pi\)
−0.108601 + 0.994085i \(0.534637\pi\)
\(774\) −356.382 + 288.000i −0.460442 + 0.372093i
\(775\) 98.0000 + 336.000i 0.126452 + 0.433548i
\(776\) 1118.64 1.44155
\(777\) −296.985 840.000i −0.382220 1.08108i
\(778\) 233.000 + 233.000i 0.299486 + 0.299486i
\(779\) −339.411 −0.435701
\(780\) −235.882 451.176i −0.302413 0.578430i