Properties

Label 105.3.k.a.62.1
Level 105
Weight 3
Character 105.62
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 62.1
Root \(-0.707107 + 0.707107i\) of \(x^{4} + 1\)
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.a.83.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.29289 - 2.70711i) q^{3} +3.00000i q^{4} +(0.707107 - 4.94975i) q^{5} +(2.82843 + 1.00000i) q^{6} -7.00000 q^{7} +(-4.94975 - 4.94975i) q^{8} +(-5.65685 + 7.00000i) q^{9} +O(q^{10})\) \(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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

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

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
\(7\) −7.00000 −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 \(-0.851432\pi\)
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 0.328959 0.944344i \(-0.393302\pi\)
−0.944344 + 0.328959i \(0.893302\pi\)
\(14\) 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 \(-0.972884\pi\)
−0.0850836 0.996374i \(-0.527116\pi\)
\(18\) −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 0.998925 + 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
\(28\) 21.0000i 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 \(0.0725017\pi\)
−0.974172 + 0.225806i \(0.927498\pi\)
\(32\) 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 0.984755 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 \(-0.635839\pi\)
−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 −0.151281 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 0.660530 0.750799i \(-0.270331\pi\)
−0.750799 + 0.660530i \(0.770331\pi\)
\(48\) 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 \(-0.919016\pi\)
0.967810 0.251682i \(-0.0809837\pi\)
\(60\) −13.4558 42.9411i −0.224264 0.715685i
\(61\) 14.0000i 0.229508i −0.993394 0.114754i \(-0.963392\pi\)
0.993394 0.114754i \(-0.0366080\pi\)
\(62\) −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 0.904367 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
\(70\) −21.0000 28.0000i −0.300000 0.400000i
\(71\) 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 0.387587 0.921833i \(-0.373309\pi\)
−0.921833 + 0.387587i \(0.873309\pi\)
\(74\) −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 \(-0.884675\pi\)
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 −0.893021 0.450015i \(-0.851419\pi\)
0.450015 + 0.893021i \(0.351419\pi\)
\(84\) −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 \(-0.964521\pi\)
0.993795 0.111230i \(-0.0354791\pi\)
\(90\) −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 \(0.558118\pi\)
−0.983378 + 0.181571i \(0.941882\pi\)
\(98\) −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 0.730962 0.682418i \(-0.239072\pi\)
−0.682418 + 0.730962i \(0.739072\pi\)
\(104\) 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 −0.687003 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
\(112\) 35.0000 0.312500
\(113\) −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
\(126\) 6.64823 + 62.6482i 0.0527637 + 0.497208i
\(127\) −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 \(-0.546556\pi\)
−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 −0.636818 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 \(-0.334654\pi\)
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 −0.838262 0.545268i \(-0.816428\pi\)
0.545268 + 0.838262i \(0.316428\pi\)
\(158\) 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 0.926568 0.376126i \(-0.122744\pi\)
−0.376126 + 0.926568i \(0.622744\pi\)
\(168\) 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 0.357793 0.933801i \(-0.383529\pi\)
0.933801 0.357793i \(-0.116471\pi\)
\(174\) 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 \(-0.582188\pi\)
0.255342 0.966851i \(-0.417812\pi\)
\(182\) −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 \(-0.899343\pi\)
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 \(-0.597490\pi\)
−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 0.997893 + 0.0648877i \(0.0206689\pi\)
0.0648877 + 0.997893i \(0.479331\pi\)
\(224\) −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 0.399599 0.916690i \(-0.369149\pi\)
−0.916690 + 0.399599i \(0.869149\pi\)
\(228\) 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 0.227272 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
\(238\) −182.000 −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 \(-0.990753\pi\)
0.999578 0.0290456i \(-0.00924682\pi\)
\(242\) −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 0.772538 0.634969i \(-0.218987\pi\)
−0.634969 + 0.772538i \(0.718987\pi\)
\(258\) 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 \(0.165497\pi\)
−0.867857 + 0.496815i \(0.834503\pi\)
\(270\) 53.7365 + 123.844i 0.199024 + 0.458682i
\(271\) 112.000i 0.413284i 0.978417 + 0.206642i \(0.0662536\pi\)
−0.978417 + 0.206642i \(0.933746\pi\)
\(272\) 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 0.866832 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
\(280\) 196.000 147.000i 0.700000 0.525000i
\(281\) 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 0.503545 0.863969i \(-0.332029\pi\)
−0.863969 + 0.503545i \(0.832029\pi\)
\(284\) 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 −0.948643 0.316349i \(-0.897543\pi\)
0.316349 + 0.948643i \(0.397543\pi\)
\(294\) 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 −0.545168 0.838327i \(-0.683534\pi\)
0.838327 + 0.545168i \(0.183534\pi\)
\(308\) −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 0.365368 0.930863i \(-0.380943\pi\)
−0.930863 + 0.365368i \(0.880943\pi\)
\(314\) 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 −0.958555 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
\(322\) 238.000 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 0.974618 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
\(343\) −343.000 −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 −0.908011 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 \(-0.279361\pi\)
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 −0.831683 0.555250i \(-0.812622\pi\)
0.555250 + 0.831683i \(0.312622\pi\)
\(354\) 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 −0.408618 0.912705i \(-0.633989\pi\)
0.912705 + 0.408618i \(0.133989\pi\)
\(368\) −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
\(378\) 161.000 98.9949i 0.425926 0.261891i
\(379\) 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 −0.509617 0.860401i \(-0.670213\pi\)
0.860401 + 0.509617i \(0.170213\pi\)
\(384\) 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 −0.743880 0.668313i \(-0.767017\pi\)
0.668313 + 0.743880i \(0.267017\pi\)
\(398\) 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 \(0.0314838\pi\)
−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 \(-0.620366\pi\)
−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 \(0.143991\pi\)
−0.899418 + 0.437090i \(0.856009\pi\)
\(420\) 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 \(-0.777639\pi\)
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 0.861354 0.508005i \(-0.169617\pi\)
−0.508005 + 0.861354i \(0.669617\pi\)
\(434\) 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 0.722888 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
\(448\) 91.0000i 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 0.276199 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 \(-0.549512\pi\)
−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 −0.675095 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 0.223652 0.974669i \(-0.428202\pi\)
−0.974669 + 0.223652i \(0.928202\pi\)
\(468\) 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 \(-0.973656\pi\)
0.996577 0.0826680i \(-0.0263441\pi\)
\(480\) −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 0.595766 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
\(497\) 415.779i 0.836577i
\(498\) −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 \(-0.407062\pi\)
0.957678 0.287842i \(-0.0929379\pi\)
\(504\) −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 \(0.123819\pi\)
−0.925293 + 0.379254i \(0.876181\pi\)
\(510\) −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 0.964894 + 0.262639i \(0.0845930\pi\)
0.262639 + 0.964894i \(0.415407\pi\)
\(524\) 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 0.849440 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
\(553\) 392.000i 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 −0.299149 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
\(560\) 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 0.0974464 0.995241i \(-0.468933\pi\)
0.995241 0.0974464i \(-0.0310675\pi\)
\(564\) −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 0.129773 0.991544i \(-0.458575\pi\)
0.991544 0.129773i \(-0.0414250\pi\)
\(578\) −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 \(-0.975299\pi\)
−0.0775226 0.996991i \(-0.524701\pi\)
\(588\) 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 \(0.513726\pi\)
−0.999070 + 0.0431072i \(0.986274\pi\)
\(594\) 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 \(0.129604\pi\)
−0.918248 + 0.396007i \(0.870396\pi\)
\(602\) 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 −0.931671 0.363302i \(-0.881649\pi\)
0.363302 + 0.931671i \(0.381649\pi\)
\(608\) 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 −0.606131 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 \(-0.826200\pi\)
−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 \(-0.930629\pi\)
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 0.999941 0.0108278i \(-0.00344668\pi\)
−0.0108278 + 0.999941i \(0.503447\pi\)
\(644\) 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 0.987298 0.158879i \(-0.0507881\pi\)
−0.158879 + 0.987298i \(0.550788\pi\)
\(648\) −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 0.935611 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
\(658\) −42.0000 −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 \(-0.684533\pi\)
0.547797 0.836611i \(-0.315467\pi\)
\(662\) −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 −0.352035 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 0.805571 0.592499i \(-0.201859\pi\)
−0.592499 + 0.805571i \(0.701859\pi\)
\(678\) −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 \(-0.863663\pi\)
0.909666 0.415340i \(-0.136337\pi\)
\(692\) 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 \(0.294051\pi\)
−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
\(707\) −643.467 −0.910137
\(708\) −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
\(714\) 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 \(0.0617432\pi\)
−0.981246 + 0.192758i \(0.938257\pi\)
\(720\) −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 −0.844712 0.535221i \(-0.820228\pi\)
0.535221 + 0.844712i \(0.320228\pi\)
\(728\) 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 0.786614 0.617446i \(-0.211832\pi\)
−0.617446 + 0.786614i \(0.711832\pi\)
\(734\) 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
\(742\) −700.000 −0.943396
\(743\) −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
\(756\) 131.533 551.533i 0.173985 0.729540i
\(757\) 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 \(-0.652464\pi\)
−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 −0.108601 0.994085i \(-0.534637\pi\)
0.994085 + 0.108601i \(0.0346371\pi\)
\(774\) −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
\(781\)