Properties

Label 105.3.k.b.62.2
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 62.2
Root \(0.707107 - 0.707107i\) of \(x^{4} + 1\)
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.b.83.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(2.70711 + 1.29289i) q^{3} +3.00000i q^{4} +(0.707107 - 4.94975i) q^{5} +(2.82843 - 1.00000i) q^{6} -7.00000i q^{7} +(4.94975 + 4.94975i) q^{8} +(5.65685 + 7.00000i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(2.70711 + 1.29289i) q^{3} +3.00000i q^{4} +(0.707107 - 4.94975i) q^{5} +(2.82843 - 1.00000i) q^{6} -7.00000i q^{7} +(4.94975 + 4.94975i) q^{8} +(5.65685 + 7.00000i) q^{9} +(-3.00000 - 4.00000i) q^{10} +9.89949i q^{11} +(-3.87868 + 8.12132i) q^{12} +(8.00000 + 8.00000i) q^{13} +(-4.94975 - 4.94975i) q^{14} +(8.31371 - 12.4853i) q^{15} -5.00000 q^{16} +(-18.3848 - 18.3848i) q^{17} +(8.94975 + 0.949747i) 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} +(6.26346 + 26.2635i) q^{27} +21.0000 q^{28} -4.24264 q^{29} +(-2.94975 - 14.7071i) q^{30} -14.0000i q^{31} +(-23.3345 + 23.3345i) q^{32} +(-12.7990 + 26.7990i) q^{33} -26.0000 q^{34} +(-34.6482 - 4.94975i) q^{35} +(-21.0000 + 16.9706i) q^{36} +(30.0000 + 30.0000i) q^{37} +(-7.07107 + 7.07107i) q^{38} +(11.3137 + 32.0000i) q^{39} +(28.0000 - 21.0000i) q^{40} -33.9411 q^{41} +(-7.00000 - 19.7990i) q^{42} +(36.0000 - 36.0000i) q^{43} -29.6985 q^{44} +(38.6482 - 23.0503i) q^{45} -34.0000 q^{46} +(-4.24264 - 4.24264i) q^{47} +(-13.5355 - 6.46447i) 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} +(-27.0711 - 12.9289i) q^{57} +(-3.00000 + 3.00000i) q^{58} -29.6985i q^{59} +(37.4558 + 24.9411i) q^{60} +14.0000i q^{61} +(-9.89949 - 9.89949i) q^{62} +(49.0000 - 39.5980i) q^{63} +13.0000i q^{64} +(45.2548 - 33.9411i) q^{65} +(9.89949 + 28.0000i) q^{66} +(32.0000 + 32.0000i) q^{67} +(55.1543 - 55.1543i) q^{68} +(-34.0000 - 96.1665i) q^{69} +(-28.0000 + 21.0000i) q^{70} +59.3970i q^{71} +(-6.64823 + 62.6482i) q^{72} +(39.0000 + 39.0000i) q^{73} +42.4264 q^{74} +(-55.9203 - 49.9792i) q^{75} -30.0000i q^{76} +69.2965 q^{77} +(30.6274 + 14.6274i) 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} +(-11.4853 - 5.48528i) q^{87} +(-49.0000 + 49.0000i) q^{88} -19.7990i q^{89} +(11.0294 - 43.6274i) q^{90} +(56.0000 - 56.0000i) q^{91} +(72.1249 - 72.1249i) q^{92} +(18.1005 - 37.8995i) q^{93} -6.00000 q^{94} +(-7.07107 + 49.4975i) q^{95} +(-93.3381 + 33.0000i) q^{96} +(113.000 - 113.000i) q^{97} +(-34.6482 + 34.6482i) q^{98} +(-69.2965 + 56.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 8q^{3} + O(q^{10}) \) \( 4q + 8q^{3} - 12q^{10} - 24q^{12} + 32q^{13} - 12q^{15} - 20q^{16} + 16q^{18} - 40q^{19} + 56q^{21} + 28q^{22} + 28q^{24} - 96q^{25} - 40q^{27} + 84q^{28} + 8q^{30} + 28q^{33} - 104q^{34} - 84q^{36} + 120q^{37} + 112q^{40} - 28q^{42} + 144q^{43} + 16q^{45} - 136q^{46} - 40q^{48} - 196q^{49} - 104q^{51} - 96q^{52} + 92q^{54} + 196q^{55} - 80q^{57} - 12q^{58} + 48q^{60} + 196q^{63} + 128q^{67} - 136q^{69} - 112q^{70} + 112q^{72} + 156q^{73} - 136q^{75} + 32q^{78} - 68q^{81} - 96q^{82} + 168q^{84} - 416q^{85} - 12q^{87} - 196q^{88} + 112q^{90} + 224q^{91} + 112q^{93} - 24q^{94} + 452q^{97} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.353553 0.353553i −0.507877 0.861430i \(-0.669569\pi\)
0.861430 + 0.507877i \(0.169569\pi\)
\(3\) 2.70711 + 1.29289i 0.902369 + 0.430964i
\(4\) 3.00000i 0.750000i
\(5\) 0.707107 4.94975i 0.141421 0.989949i
\(6\) 2.82843 1.00000i 0.471405 0.166667i
\(7\) 7.00000i 1.00000i
\(8\) 4.94975 + 4.94975i 0.618718 + 0.618718i
\(9\) 5.65685 + 7.00000i 0.628539 + 0.777778i
\(10\) −3.00000 4.00000i −0.300000 0.400000i
\(11\) 9.89949i 0.899954i 0.893040 + 0.449977i \(0.148568\pi\)
−0.893040 + 0.449977i \(0.851432\pi\)
\(12\) −3.87868 + 8.12132i −0.323223 + 0.676777i
\(13\) 8.00000 + 8.00000i 0.615385 + 0.615385i 0.944344 0.328959i \(-0.106698\pi\)
−0.328959 + 0.944344i \(0.606698\pi\)
\(14\) −4.94975 4.94975i −0.353553 0.353553i
\(15\) 8.31371 12.4853i 0.554247 0.832352i
\(16\) −5.00000 −0.312500
\(17\) −18.3848 18.3848i −1.08146 1.08146i −0.996374 0.0850836i \(-0.972884\pi\)
−0.0850836 0.996374i \(-0.527116\pi\)
\(18\) 8.94975 + 0.949747i 0.497208 + 0.0527637i
\(19\) −10.0000 −0.526316 −0.263158 0.964753i \(-0.584764\pi\)
−0.263158 + 0.964753i \(0.584764\pi\)
\(20\) 14.8492 + 2.12132i 0.742462 + 0.106066i
\(21\) 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 \(-0.985237\pi\)
−0.0463637 0.998925i \(-0.514763\pi\)
\(24\) 7.00000 + 19.7990i 0.291667 + 0.824958i
\(25\) −24.0000 7.00000i −0.960000 0.280000i
\(26\) 11.3137 0.435143
\(27\) 6.26346 + 26.2635i 0.231980 + 0.972721i
\(28\) 21.0000 0.750000
\(29\) −4.24264 −0.146298 −0.0731490 0.997321i \(-0.523305\pi\)
−0.0731490 + 0.997321i \(0.523305\pi\)
\(30\) −2.94975 14.7071i −0.0983249 0.490237i
\(31\) 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
\(33\) −12.7990 + 26.7990i −0.387848 + 0.812091i
\(34\) −26.0000 −0.764706
\(35\) −34.6482 4.94975i −0.989949 0.141421i
\(36\) −21.0000 + 16.9706i −0.583333 + 0.471405i
\(37\) 30.0000 + 30.0000i 0.810811 + 0.810811i 0.984755 0.173945i \(-0.0556514\pi\)
−0.173945 + 0.984755i \(0.555651\pi\)
\(38\) −7.07107 + 7.07107i −0.186081 + 0.186081i
\(39\) 11.3137 + 32.0000i 0.290095 + 0.820513i
\(40\) 28.0000 21.0000i 0.700000 0.525000i
\(41\) −33.9411 −0.827832 −0.413916 0.910315i \(-0.635839\pi\)
−0.413916 + 0.910315i \(0.635839\pi\)
\(42\) −7.00000 19.7990i −0.166667 0.471405i
\(43\) 36.0000 36.0000i 0.837209 0.837209i −0.151281 0.988491i \(-0.548340\pi\)
0.988491 + 0.151281i \(0.0483400\pi\)
\(44\) −29.6985 −0.674966
\(45\) 38.6482 23.0503i 0.858850 0.512228i
\(46\) −34.0000 −0.739130
\(47\) −4.24264 4.24264i −0.0902690 0.0902690i 0.660530 0.750799i \(-0.270331\pi\)
−0.750799 + 0.660530i \(0.770331\pi\)
\(48\) −13.5355 6.46447i −0.281990 0.134676i
\(49\) −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 \(0.142389\pi\)
0.432557 + 0.901606i \(0.357611\pi\)
\(54\) 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
\(57\) −27.0711 12.9289i −0.474931 0.226823i
\(58\) −3.00000 + 3.00000i −0.0517241 + 0.0517241i
\(59\) 29.6985i 0.503364i −0.967810 0.251682i \(-0.919016\pi\)
0.967810 0.251682i \(-0.0809837\pi\)
\(60\) 37.4558 + 24.9411i 0.624264 + 0.415685i
\(61\) 14.0000i 0.229508i 0.993394 + 0.114754i \(0.0366080\pi\)
−0.993394 + 0.114754i \(0.963392\pi\)
\(62\) −9.89949 9.89949i −0.159669 0.159669i
\(63\) 49.0000 39.5980i 0.777778 0.628539i
\(64\) 13.0000i 0.203125i
\(65\) 45.2548 33.9411i 0.696228 0.522171i
\(66\) 9.89949 + 28.0000i 0.149992 + 0.424242i
\(67\) 32.0000 + 32.0000i 0.477612 + 0.477612i 0.904367 0.426755i \(-0.140343\pi\)
−0.426755 + 0.904367i \(0.640343\pi\)
\(68\) 55.1543 55.1543i 0.811093 0.811093i
\(69\) −34.0000 96.1665i −0.492754 1.39372i
\(70\) −28.0000 + 21.0000i −0.400000 + 0.300000i
\(71\) 59.3970i 0.836577i 0.908314 + 0.418289i \(0.137370\pi\)
−0.908314 + 0.418289i \(0.862630\pi\)
\(72\) −6.64823 + 62.6482i −0.0923366 + 0.870114i
\(73\) 39.0000 + 39.0000i 0.534247 + 0.534247i 0.921833 0.387587i \(-0.126691\pi\)
−0.387587 + 0.921833i \(0.626691\pi\)
\(74\) 42.4264 0.573330
\(75\) −55.9203 49.9792i −0.745604 0.666389i
\(76\) 30.0000i 0.394737i
\(77\) 69.2965 0.899954
\(78\) 30.6274 + 14.6274i 0.392659 + 0.187531i
\(79\) 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
\(87\) −11.4853 5.48528i −0.132015 0.0630492i
\(88\) −49.0000 + 49.0000i −0.556818 + 0.556818i
\(89\) 19.7990i 0.222461i −0.993795 0.111230i \(-0.964521\pi\)
0.993795 0.111230i \(-0.0354791\pi\)
\(90\) 11.0294 43.6274i 0.122549 0.484749i
\(91\) 56.0000 56.0000i 0.615385 0.615385i
\(92\) 72.1249 72.1249i 0.783966 0.783966i
\(93\) 18.1005 37.8995i 0.194629 0.407521i
\(94\) −6.00000 −0.0638298
\(95\) −7.07107 + 49.4975i −0.0744323 + 0.521026i
\(96\) −93.3381 + 33.0000i −0.972272 + 0.343750i
\(97\) 113.000 113.000i 1.16495 1.16495i 0.181571 0.983378i \(-0.441882\pi\)
0.983378 0.181571i \(-0.0581181\pi\)
\(98\) −34.6482 + 34.6482i −0.353553 + 0.353553i
\(99\) −69.2965 + 56.0000i −0.699964 + 0.565657i
\(100\) 21.0000 72.0000i 0.210000 0.720000i
\(101\) 91.9239 0.910137 0.455069 0.890456i \(-0.349615\pi\)
0.455069 + 0.890456i \(0.349615\pi\)
\(102\) −70.3848 33.6152i −0.690047 0.329561i
\(103\) −5.00000 5.00000i −0.0485437 0.0485437i 0.682418 0.730962i \(-0.260928\pi\)
−0.730962 + 0.682418i \(0.760928\pi\)
\(104\) 79.1960i 0.761500i
\(105\) −87.3970 58.1960i −0.832352 0.554247i
\(106\) 100.000 0.943396
\(107\) −4.24264 + 4.24264i −0.0396508 + 0.0396508i −0.726654 0.687003i \(-0.758926\pi\)
0.687003 + 0.726654i \(0.258926\pi\)
\(108\) −78.7904 + 18.7904i −0.729540 + 0.173985i
\(109\) 70.0000i 0.642202i −0.947045 0.321101i \(-0.895947\pi\)
0.947045 0.321101i \(-0.104053\pi\)
\(110\) 39.5980 29.6985i 0.359982 0.269986i
\(111\) 42.4264 + 120.000i 0.382220 + 1.08108i
\(112\) 35.0000i 0.312500i
\(113\) 12.7279 + 12.7279i 0.112636 + 0.112636i 0.761179 0.648542i \(-0.224621\pi\)
−0.648542 + 0.761179i \(0.724621\pi\)
\(114\) −28.2843 + 10.0000i −0.248108 + 0.0877193i
\(115\) −136.000 + 102.000i −1.18261 + 0.886957i
\(116\) 12.7279i 0.109723i
\(117\) −10.7452 + 101.255i −0.0918390 + 0.865426i
\(118\) −21.0000 21.0000i −0.177966 0.177966i
\(119\) −128.693 + 128.693i −1.08146 + 1.08146i
\(120\) 102.950 20.6482i 0.857915 0.172069i
\(121\) 23.0000 0.190083
\(122\) 9.89949 + 9.89949i 0.0811434 + 0.0811434i
\(123\) −91.8823 43.8823i −0.747010 0.356766i
\(124\) 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 \(0.546556\pi\)
\(132\) −80.3970 38.3970i −0.609068 0.290886i
\(133\) 70.0000i 0.526316i
\(134\) 45.2548 0.337723
\(135\) 134.426 12.4315i 0.995751 0.0920849i
\(136\) 182.000i 1.33824i
\(137\) −18.3848 + 18.3848i −0.134195 + 0.134195i −0.771014 0.636818i \(-0.780250\pi\)
0.636818 + 0.771014i \(0.280250\pi\)
\(138\) −92.0416 43.9584i −0.666968 0.318539i
\(139\) −138.000 −0.992806 −0.496403 0.868092i \(-0.665346\pi\)
−0.496403 + 0.868092i \(0.665346\pi\)
\(140\) 14.8492 103.945i 0.106066 0.742462i
\(141\) −6.00000 16.9706i −0.0425532 0.120359i
\(142\) 42.0000 + 42.0000i 0.295775 + 0.295775i
\(143\) −79.1960 + 79.1960i −0.553818 + 0.553818i
\(144\) −28.2843 35.0000i −0.196419 0.243056i
\(145\) −3.00000 + 21.0000i −0.0206897 + 0.144828i
\(146\) 55.1543 0.377769
\(147\) −132.648 63.3518i −0.902369 0.430964i
\(148\) −90.0000 + 90.0000i −0.608108 + 0.608108i
\(149\) 199.404 1.33828 0.669141 0.743135i \(-0.266662\pi\)
0.669141 + 0.743135i \(0.266662\pi\)
\(150\) −74.8823 + 4.20101i −0.499215 + 0.0280067i
\(151\) 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
\(153\) 24.6934 232.693i 0.161395 1.52087i
\(154\) 49.0000 49.0000i 0.318182 0.318182i
\(155\) −69.2965 9.89949i −0.447074 0.0638677i
\(156\) −96.0000 + 33.9411i −0.615385 + 0.217571i
\(157\) 46.0000 46.0000i 0.292994 0.292994i −0.545268 0.838262i \(-0.683572\pi\)
0.838262 + 0.545268i \(0.183572\pi\)
\(158\) −39.5980 39.5980i −0.250620 0.250620i
\(159\) 100.000 + 282.843i 0.628931 + 1.77888i
\(160\) 99.0000 + 132.000i 0.618750 + 0.825000i
\(161\) −168.291 + 168.291i −1.04529 + 1.04529i
\(162\) 43.9792 + 68.0208i 0.271476 + 0.419882i
\(163\) −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
\(165\) 123.598 + 82.3015i 0.749079 + 0.498797i
\(166\) 52.0000i 0.313253i
\(167\) 91.9239 + 91.9239i 0.550442 + 0.550442i 0.926568 0.376126i \(-0.122744\pi\)
−0.376126 + 0.926568i \(0.622744\pi\)
\(168\) 138.593 49.0000i 0.824958 0.291667i
\(169\) 41.0000i 0.242604i
\(170\) −18.3848 + 128.693i −0.108146 + 0.757020i
\(171\) −56.5685 70.0000i −0.330810 0.409357i
\(172\) 108.000 + 108.000i 0.627907 + 0.627907i
\(173\) 223.446 223.446i 1.29159 1.29159i 0.357793 0.933801i \(-0.383529\pi\)
0.933801 0.357793i \(-0.116471\pi\)
\(174\) −12.0000 + 4.24264i −0.0689655 + 0.0243830i
\(175\) −49.0000 + 168.000i −0.280000 + 0.960000i
\(176\) 49.4975i 0.281236i
\(177\) 38.3970 80.3970i 0.216932 0.454220i
\(178\) −14.0000 14.0000i −0.0786517 0.0786517i
\(179\) 12.7279 0.0711057 0.0355529 0.999368i \(-0.488681\pi\)
0.0355529 + 0.999368i \(0.488681\pi\)
\(180\) 69.1508 + 115.945i 0.384171 + 0.644137i
\(181\) 350.000i 1.93370i 0.255342 + 0.966851i \(0.417812\pi\)
−0.255342 + 0.966851i \(0.582188\pi\)
\(182\) 79.1960i 0.435143i
\(183\) −18.1005 + 37.8995i −0.0989099 + 0.207101i
\(184\) 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 \(0.899343\pi\)
\(192\) −16.8076 + 35.1924i −0.0875396 + 0.183294i
\(193\) 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
\(195\) 166.392 33.3726i 0.853292 0.171141i
\(196\) 147.000i 0.750000i
\(197\) −56.5685 + 56.5685i −0.287150 + 0.287150i −0.835952 0.548802i \(-0.815084\pi\)
0.548802 + 0.835952i \(0.315084\pi\)
\(198\) −9.40202 + 88.5980i −0.0474850 + 0.447465i
\(199\) 120.000 0.603015 0.301508 0.953464i \(-0.402510\pi\)
0.301508 + 0.953464i \(0.402510\pi\)
\(200\) −84.1457 153.442i −0.420729 0.767211i
\(201\) 45.2548 + 128.000i 0.225148 + 0.636816i
\(202\) 65.0000 65.0000i 0.321782 0.321782i
\(203\) 29.6985i 0.146298i
\(204\) 220.617 78.0000i 1.08146 0.382353i
\(205\) −24.0000 + 168.000i −0.117073 + 0.819512i
\(206\) −7.07107 −0.0343256
\(207\) 32.2914 304.291i 0.155997 1.47001i
\(208\) −40.0000 40.0000i −0.192308 0.192308i
\(209\) 98.9949i 0.473660i
\(210\) −102.950 + 20.6482i −0.490237 + 0.0983249i
\(211\) 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
\(213\) −76.7939 + 160.794i −0.360535 + 0.754901i
\(214\) 6.00000i 0.0280374i
\(215\) −152.735 203.647i −0.710396 0.947194i
\(216\) −98.9949 + 161.000i −0.458310 + 0.745370i
\(217\) −98.0000 −0.451613
\(218\) −49.4975 49.4975i −0.227053 0.227053i
\(219\) 55.1543 + 156.000i 0.251846 + 0.712329i
\(220\) −21.0000 + 147.000i −0.0954545 + 0.668182i
\(221\) 294.156i 1.33102i
\(222\) 114.853 + 54.8528i 0.517355 + 0.247085i
\(223\) −237.000 237.000i −1.06278 1.06278i −0.997893 0.0648877i \(-0.979331\pi\)
−0.0648877 0.997893i \(-0.520669\pi\)
\(224\) 163.342 + 163.342i 0.729204 + 0.729204i
\(225\) −86.7645 207.598i −0.385620 0.922658i
\(226\) 18.0000 0.0796460
\(227\) −117.380 117.380i −0.517091 0.517091i 0.399599 0.916690i \(-0.369149\pi\)
−0.916690 + 0.399599i \(0.869149\pi\)
\(228\) 38.7868 81.2132i 0.170118 0.356198i
\(229\) −374.000 −1.63319 −0.816594 0.577213i \(-0.804140\pi\)
−0.816594 + 0.577213i \(0.804140\pi\)
\(230\) −24.0416 + 168.291i −0.104529 + 0.731702i
\(231\) 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 \(-0.0729807\pi\)
−0.227272 + 0.973831i \(0.572981\pi\)
\(234\) 64.0000 + 79.1960i 0.273504 + 0.338444i
\(235\) −24.0000 + 18.0000i −0.102128 + 0.0765957i
\(236\) 89.0955 0.377523
\(237\) 72.4020 151.598i 0.305494 0.639654i
\(238\) 182.000i 0.764706i
\(239\) −291.328 −1.21895 −0.609473 0.792807i \(-0.708619\pi\)
−0.609473 + 0.792807i \(0.708619\pi\)
\(240\) −41.5685 + 62.4264i −0.173202 + 0.260110i
\(241\) 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
\(243\) −148.413 + 192.413i −0.610752 + 0.791822i
\(244\) −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 \(0.839887\pi\)
\(252\) 118.794 + 147.000i 0.471405 + 0.583333i
\(253\) 238.000 238.000i 0.940711 0.940711i
\(254\) −156.978 −0.618022
\(255\) −382.385 + 76.6934i −1.49955 + 0.300759i
\(256\) −171.000 −0.667969
\(257\) 35.3553 + 35.3553i 0.137569 + 0.137569i 0.772538 0.634969i \(-0.218987\pi\)
−0.634969 + 0.772538i \(0.718987\pi\)
\(258\) 65.8234 137.823i 0.255129 0.534199i
\(259\) 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 \(-0.927861\pi\)
−0.224695 0.974429i \(-0.572139\pi\)
\(264\) −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
\(267\) 25.5980 53.5980i 0.0958726 0.200741i
\(268\) −96.0000 + 96.0000i −0.358209 + 0.358209i
\(269\) 267.286i 0.993630i 0.867857 + 0.496815i \(0.165497\pi\)
−0.867857 + 0.496815i \(0.834503\pi\)
\(270\) 86.2635 103.844i 0.319494 0.384608i
\(271\) 112.000i 0.413284i −0.978417 0.206642i \(-0.933746\pi\)
0.978417 0.206642i \(-0.0662536\pi\)
\(272\) 91.9239 + 91.9239i 0.337955 + 0.337955i
\(273\) 224.000 79.1960i 0.820513 0.290095i
\(274\) 26.0000i 0.0948905i
\(275\) 69.2965 237.588i 0.251987 0.863956i
\(276\) 288.500 102.000i 1.04529 0.369565i
\(277\) 102.000 + 102.000i 0.368231 + 0.368231i 0.866832 0.498601i \(-0.166153\pi\)
−0.498601 + 0.866832i \(0.666153\pi\)
\(278\) −97.5807 + 97.5807i −0.351010 + 0.351010i
\(279\) 98.0000 79.1960i 0.351254 0.283856i
\(280\) −147.000 196.000i −0.525000 0.700000i
\(281\) 296.985i 1.05689i −0.848969 0.528443i \(-0.822776\pi\)
0.848969 0.528443i \(-0.177224\pi\)
\(282\) −16.2426 7.75736i −0.0575980 0.0275084i
\(283\) 102.000 + 102.000i 0.360424 + 0.360424i 0.863969 0.503545i \(-0.167971\pi\)
−0.503545 + 0.863969i \(0.667971\pi\)
\(284\) −178.191 −0.627433
\(285\) −83.1371 + 124.853i −0.291709 + 0.438080i
\(286\) 112.000i 0.391608i
\(287\) 237.588i 0.827832i
\(288\) −295.342 31.3417i −1.02549 0.108825i
\(289\) 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
\(297\) −259.995 + 62.0051i −0.875404 + 0.208771i
\(298\) 141.000 141.000i 0.473154 0.473154i
\(299\) 384.666i 1.28651i
\(300\) 149.938 167.761i 0.499792 0.559203i
\(301\) −252.000 252.000i −0.837209 0.837209i
\(302\) 55.1543 55.1543i 0.182630 0.182630i
\(303\) 248.848 + 118.848i 0.821280 + 0.392237i
\(304\) 50.0000 0.164474
\(305\) 69.2965 + 9.89949i 0.227202 + 0.0324574i
\(306\) −147.078 182.000i −0.480648 0.594771i
\(307\) −90.0000 + 90.0000i −0.293160 + 0.293160i −0.838327 0.545168i \(-0.816466\pi\)
0.545168 + 0.838327i \(0.316466\pi\)
\(308\) 207.889i 0.674966i
\(309\) −7.07107 20.0000i −0.0228837 0.0647249i
\(310\) −56.0000 + 42.0000i −0.180645 + 0.135484i
\(311\) 299.813 0.964030 0.482015 0.876163i \(-0.339905\pi\)
0.482015 + 0.876163i \(0.339905\pi\)
\(312\) −102.392 + 214.392i −0.328179 + 0.687154i
\(313\) 177.000 + 177.000i 0.565495 + 0.565495i 0.930863 0.365368i \(-0.119057\pi\)
−0.365368 + 0.930863i \(0.619057\pi\)
\(314\) 65.0538i 0.207178i
\(315\) −161.352 270.538i −0.512228 0.858850i
\(316\) 168.000 0.531646
\(317\) 213.546 213.546i 0.673647 0.673647i −0.284908 0.958555i \(-0.591963\pi\)
0.958555 + 0.284908i \(0.0919629\pi\)
\(318\) 270.711 + 129.289i 0.851291 + 0.406570i
\(319\) 42.0000i 0.131661i
\(320\) 64.3467 + 9.19239i 0.201083 + 0.0287262i
\(321\) −16.9706 + 6.00000i −0.0528678 + 0.0186916i
\(322\) 238.000i 0.739130i
\(323\) 183.848 + 183.848i 0.569188 + 0.569188i
\(324\) −237.588 51.0000i −0.733296 0.157407i
\(325\) −136.000 248.000i −0.418462 0.763077i
\(326\) 195.161i 0.598655i
\(327\) 90.5025 189.497i 0.276766 0.579503i
\(328\) −168.000 168.000i −0.512195 0.512195i
\(329\) −29.6985 + 29.6985i −0.0902690 + 0.0902690i
\(330\) 145.593 29.2010i 0.441191 0.0884879i
\(331\) 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
\(333\) −40.2944 + 379.706i −0.121004 + 1.14026i
\(334\) 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
\(342\) −89.4975 9.49747i −0.261689 0.0277704i
\(343\) 343.000i 1.00000i
\(344\) 356.382 1.03599
\(345\) −500.042 + 100.291i −1.44940 + 0.290700i
\(346\) 316.000i 0.913295i
\(347\) 169.706 169.706i 0.489065 0.489065i −0.418946 0.908011i \(-0.637600\pi\)
0.908011 + 0.418946i \(0.137600\pi\)
\(348\) 16.4558 34.4558i 0.0472869 0.0990110i
\(349\) −446.000 −1.27794 −0.638968 0.769233i \(-0.720639\pi\)
−0.638968 + 0.769233i \(0.720639\pi\)
\(350\) 84.1457 + 153.442i 0.240416 + 0.438406i
\(351\) −160.000 + 260.215i −0.455840 + 0.741354i
\(352\) −231.000 231.000i −0.656250 0.656250i
\(353\) −97.5807 + 97.5807i −0.276433 + 0.276433i −0.831683 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
\(357\) −514.774 + 182.000i −1.44194 + 0.509804i
\(358\) 9.00000 9.00000i 0.0251397 0.0251397i
\(359\) 248.902 0.693319 0.346660 0.937991i \(-0.387316\pi\)
0.346660 + 0.937991i \(0.387316\pi\)
\(360\) 305.392 + 77.2061i 0.848311 + 0.214461i
\(361\) −261.000 −0.722992
\(362\) 247.487 + 247.487i 0.683667 + 0.683667i
\(363\) 62.2635 + 29.7365i 0.171525 + 0.0819189i
\(364\) 168.000 + 168.000i 0.461538 + 0.461538i
\(365\) 220.617 165.463i 0.604431 0.453323i
\(366\) 14.0000 + 39.5980i 0.0382514 + 0.108191i
\(367\) −185.000 + 185.000i −0.504087 + 0.504087i −0.912705 0.408618i \(-0.866011\pi\)
0.408618 + 0.912705i \(0.366011\pi\)
\(368\) 120.208 + 120.208i 0.326653 + 0.326653i
\(369\) −192.000 237.588i −0.520325 0.643870i
\(370\) 30.0000 210.000i 0.0810811 0.567568i
\(371\) 494.975 494.975i 1.33416 1.33416i
\(372\) 113.698 + 54.3015i 0.305641 + 0.145972i
\(373\) 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
\(375\) −286.926 + 241.451i −0.765136 + 0.643869i
\(376\) 42.0000i 0.111702i
\(377\) −33.9411 33.9411i −0.0900295 0.0900295i
\(378\) 98.9949 161.000i 0.261891 0.425926i
\(379\) 266.000i 0.701847i 0.936404 + 0.350923i \(0.114132\pi\)
−0.936404 + 0.350923i \(0.885868\pi\)
\(380\) −148.492 21.2132i −0.390770 0.0558242i
\(381\) −156.978 444.000i −0.412015 1.16535i
\(382\) 84.0000 + 84.0000i 0.219895 + 0.219895i
\(383\) 134.350 134.350i 0.350784 0.350784i −0.509617 0.860401i \(-0.670213\pi\)
0.860401 + 0.509617i \(0.170213\pi\)
\(384\) −119.000 336.583i −0.309896 0.876518i
\(385\) 49.0000 343.000i 0.127273 0.890909i
\(386\) 94.7523i 0.245472i
\(387\) 455.647 + 48.3532i 1.17738 + 0.124944i
\(388\) 339.000 + 339.000i 0.873711 + 0.873711i
\(389\) 329.512 0.847074 0.423537 0.905879i \(-0.360788\pi\)
0.423537 + 0.905879i \(0.360788\pi\)
\(390\) 94.0589 141.255i 0.241177 0.362192i
\(391\) 884.000i 2.26087i
\(392\) −242.538 242.538i −0.618718 0.618718i
\(393\) −103.368 49.3675i −0.263022 0.125617i
\(394\) 80.0000i 0.203046i
\(395\) −277.186 39.5980i −0.701736 0.100248i
\(396\) −168.000 207.889i −0.424242 0.524973i
\(397\) 30.0000 30.0000i 0.0755668 0.0755668i −0.668313 0.743880i \(-0.732983\pi\)
0.743880 + 0.668313i \(0.232983\pi\)
\(398\) 84.8528 84.8528i 0.213198 0.213198i
\(399\) −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 \(-0.0314838\pi\)
\(402\) 122.510 + 58.5097i 0.304750 + 0.145546i
\(403\) 112.000 112.000i 0.277916 0.277916i
\(404\) 275.772i 0.682603i
\(405\) 379.979 + 140.146i 0.938220 + 0.346039i
\(406\) 21.0000 + 21.0000i 0.0517241 + 0.0517241i
\(407\) −296.985 + 296.985i −0.729693 + 0.729693i
\(408\) 235.307 492.693i 0.576732 1.20758i
\(409\) 302.000 0.738386 0.369193 0.929353i \(-0.379634\pi\)
0.369193 + 0.929353i \(0.379634\pi\)
\(410\) 101.823 + 135.765i 0.248350 + 0.331133i
\(411\) −73.5391 + 26.0000i −0.178927 + 0.0632603i
\(412\) 15.0000 15.0000i 0.0364078 0.0364078i
\(413\) −207.889 −0.503364
\(414\) −192.333 238.000i −0.464573 0.574879i
\(415\) 156.000 + 208.000i 0.375904 + 0.501205i
\(416\) −373.352 −0.897482
\(417\) −373.581 178.419i −0.895877 0.427864i
\(418\) −70.0000 70.0000i −0.167464 0.167464i
\(419\) 366.281i 0.874180i 0.899418 + 0.437090i \(0.143991\pi\)
−0.899418 + 0.437090i \(0.856009\pi\)
\(420\) 174.588 262.191i 0.415685 0.624264i
\(421\) −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
\(423\) 5.69848 53.6985i 0.0134716 0.126947i
\(424\) 700.000i 1.65094i
\(425\) 312.541 + 569.928i 0.735391 + 1.34101i
\(426\) 59.3970 + 168.000i 0.139430 + 0.394366i
\(427\) 98.0000 0.229508
\(428\) −12.7279 12.7279i −0.0297381 0.0297381i
\(429\) −316.784 + 112.000i −0.738424 + 0.261072i
\(430\) −252.000 36.0000i −0.586047 0.0837209i
\(431\) 554.372i 1.28625i 0.765763 + 0.643123i \(0.222361\pi\)
−0.765763 + 0.643123i \(0.777639\pi\)
\(432\) −31.3173 131.317i −0.0724937 0.303975i
\(433\) −153.000 153.000i −0.353349 0.353349i 0.508005 0.861354i \(-0.330383\pi\)
−0.861354 + 0.508005i \(0.830383\pi\)
\(434\) −69.2965 + 69.2965i −0.159669 + 0.159669i
\(435\) −35.2721 + 52.9706i −0.0810852 + 0.121771i
\(436\) 210.000 0.481651
\(437\) 240.416 + 240.416i 0.550152 + 0.550152i
\(438\) 149.309 + 71.3087i 0.340887 + 0.162805i
\(439\) −248.000 −0.564920 −0.282460 0.959279i \(-0.591150\pi\)
−0.282460 + 0.959279i \(0.591150\pi\)
\(440\) 207.889 + 277.186i 0.472476 + 0.629968i
\(441\) −277.186 343.000i −0.628539 0.777778i
\(442\) −208.000 208.000i −0.470588 0.470588i
\(443\) −14.1421 14.1421i −0.0319236 0.0319236i 0.690965 0.722888i \(-0.257186\pi\)
−0.722888 + 0.690965i \(0.757186\pi\)
\(444\) −360.000 + 127.279i −0.810811 + 0.286665i
\(445\) −98.0000 14.0000i −0.220225 0.0314607i
\(446\) −335.169 −0.751499
\(447\) 539.808 + 257.808i 1.20762 + 0.576752i
\(448\) 91.0000 0.203125
\(449\) −647.710 −1.44256 −0.721280 0.692643i \(-0.756446\pi\)
−0.721280 + 0.692643i \(0.756446\pi\)
\(450\) −208.146 85.4422i −0.462546 0.189871i
\(451\) 336.000i 0.745011i
\(452\) −38.1838 + 38.1838i −0.0844774 + 0.0844774i
\(453\) 211.154 + 100.846i 0.466124 + 0.222617i
\(454\) −166.000 −0.365639
\(455\) −237.588 316.784i −0.522171 0.696228i
\(456\) −70.0000 197.990i −0.153509 0.434188i
\(457\) −313.000 313.000i −0.684902 0.684902i 0.276199 0.961100i \(-0.410925\pi\)
−0.961100 + 0.276199i \(0.910925\pi\)
\(458\) −264.458 + 264.458i −0.577419 + 0.577419i
\(459\) 367.696 598.000i 0.801080 1.30283i
\(460\) −306.000 408.000i −0.665217 0.886957i
\(461\) −142.836 −0.309839 −0.154919 0.987927i \(-0.549512\pi\)
−0.154919 + 0.987927i \(0.549512\pi\)
\(462\) 196.000 69.2965i 0.424242 0.149992i
\(463\) 29.0000 29.0000i 0.0626350 0.0626350i −0.675095 0.737730i \(-0.735898\pi\)
0.737730 + 0.675095i \(0.235898\pi\)
\(464\) 21.2132 0.0457181
\(465\) −174.794 116.392i −0.375901 0.250305i
\(466\) 246.000 0.527897
\(467\) −350.725 350.725i −0.751017 0.751017i 0.223652 0.974669i \(-0.428202\pi\)
−0.974669 + 0.223652i \(0.928202\pi\)
\(468\) −303.765 32.2355i −0.649069 0.0688793i
\(469\) 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
\(477\) −94.9747 + 894.975i −0.199108 + 1.87626i
\(478\) −206.000 + 206.000i −0.430962 + 0.430962i
\(479\) 79.1960i 0.165336i −0.996577 0.0826680i \(-0.973656\pi\)
0.996577 0.0826680i \(-0.0263441\pi\)
\(480\) 97.3417 + 485.335i 0.202795 + 1.01111i
\(481\) 480.000i 0.997921i
\(482\) 9.89949 + 9.89949i 0.0205384 + 0.0205384i
\(483\) −673.166 + 238.000i −1.39372 + 0.492754i
\(484\) 69.0000i 0.142562i
\(485\) −479.418 639.225i −0.988492 1.31799i
\(486\) 31.1127 + 241.000i 0.0640179 + 0.495885i
\(487\) −101.000 101.000i −0.207392 0.207392i 0.595766 0.803158i \(-0.296849\pi\)
−0.803158 + 0.595766i \(0.796849\pi\)
\(488\) −69.2965 + 69.2965i −0.142001 + 0.142001i
\(489\) −552.000 + 195.161i −1.12883 + 0.399103i
\(490\) 147.000 + 196.000i 0.300000 + 0.400000i
\(491\) 346.482i 0.705667i 0.935686 + 0.352833i \(0.114782\pi\)
−0.935686 + 0.352833i \(0.885218\pi\)
\(492\) 131.647 275.647i 0.267575 0.560258i
\(493\) 78.0000 + 78.0000i 0.158215 + 0.158215i
\(494\) −113.137 −0.229022
\(495\) 228.186 + 382.598i 0.460982 + 0.772925i
\(496\) 70.0000i 0.141129i
\(497\) 415.779 0.836577
\(498\) −67.2304 + 140.770i −0.135001 + 0.282670i
\(499\) 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
\(507\) 53.0086 110.991i 0.104553 0.218918i
\(508\) 333.000 333.000i 0.655512 0.655512i
\(509\) 386.080i 0.758507i 0.925293 + 0.379254i \(0.123819\pi\)
−0.925293 + 0.379254i \(0.876181\pi\)
\(510\) −216.156 + 324.617i −0.423836 + 0.636505i
\(511\) 273.000 273.000i 0.534247 0.534247i
\(512\) 215.668 215.668i 0.421226 0.421226i
\(513\) −62.6346 262.635i −0.122095 0.511958i
\(514\) 50.0000 0.0972763
\(515\) −28.2843 + 21.2132i −0.0549209 + 0.0411907i
\(516\) 152.735 + 432.000i 0.295998 + 0.837209i
\(517\) 42.0000 42.0000i 0.0812379 0.0812379i
\(518\) 296.985i 0.573330i
\(519\) 893.783 316.000i 1.72213 0.608863i
\(520\) 392.000 + 56.0000i 0.753846 + 0.107692i
\(521\) 379.009 0.727465 0.363732 0.931503i \(-0.381502\pi\)
0.363732 + 0.931503i \(0.381502\pi\)
\(522\) −37.9706 4.02944i −0.0727405 0.00771923i
\(523\) −642.000 642.000i −1.22753 1.22753i −0.964894 0.262639i \(-0.915407\pi\)
−0.262639 0.964894i \(-0.584593\pi\)
\(524\) 114.551i 0.218609i
\(525\) −349.854 + 391.442i −0.666389 + 0.745604i
\(526\) −446.000 −0.847909
\(527\) −257.387 + 257.387i −0.488400 + 0.488400i
\(528\) 63.9949 133.995i 0.121203 0.253778i
\(529\) 627.000i 1.18526i
\(530\) 70.7107 494.975i 0.133416 0.933915i
\(531\) 207.889 168.000i 0.391505 0.316384i
\(532\) −210.000 −0.394737
\(533\) −271.529 271.529i −0.509435 0.509435i
\(534\) −19.7990 56.0000i −0.0370768 0.104869i
\(535\) 18.0000 + 24.0000i 0.0336449 + 0.0448598i
\(536\) 316.784i 0.591015i
\(537\) 34.4558 + 16.4558i 0.0641636 + 0.0306440i
\(538\) 189.000 + 189.000i 0.351301 + 0.351301i
\(539\) 485.075i 0.899954i
\(540\) 37.2944 + 403.279i 0.0690637 + 0.746813i
\(541\) 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
\(543\) −452.513 + 947.487i −0.833357 + 1.74491i
\(544\) 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
\(552\) 307.709 644.291i 0.557443 1.16719i
\(553\) −392.000 −0.708861
\(554\) 144.250 0.260379
\(555\) 623.970 125.147i 1.12427 0.225490i
\(556\) 414.000i 0.744604i
\(557\) −364.867 + 364.867i −0.655058 + 0.655058i −0.954206 0.299149i \(-0.903297\pi\)
0.299149 + 0.954206i \(0.403297\pi\)
\(558\) 13.2965 125.296i 0.0238288 0.224546i
\(559\) 576.000 1.03041
\(560\) 173.241 + 24.7487i 0.309359 + 0.0441942i
\(561\) 728.000 257.387i 1.29768 0.458800i
\(562\) −210.000 210.000i −0.373665 0.373665i
\(563\) 615.183 615.183i 1.09269 1.09269i 0.0974464 0.995241i \(-0.468933\pi\)
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
\(567\) 554.372 + 119.000i 0.977728 + 0.209877i
\(568\) −294.000 + 294.000i −0.517606 + 0.517606i
\(569\) −28.2843 −0.0497087 −0.0248544 0.999691i \(-0.507912\pi\)
−0.0248544 + 0.999691i \(0.507912\pi\)
\(570\) 29.4975 + 147.071i 0.0517500 + 0.258019i
\(571\) −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
\(573\) −153.588 + 321.588i −0.268042 + 0.561235i
\(574\) 168.000 + 168.000i 0.292683 + 0.292683i
\(575\) 408.708 + 745.291i 0.710796 + 1.29616i
\(576\) −91.0000 + 73.5391i −0.157986 + 0.127672i
\(577\) −647.000 + 647.000i −1.12132 + 1.12132i −0.129773 + 0.991544i \(0.541425\pi\)
−0.991544 + 0.129773i \(0.958575\pi\)
\(578\) 273.650 + 273.650i 0.473443 + 0.473443i
\(579\) 268.000 94.7523i 0.462867 0.163648i
\(580\) −63.0000 9.00000i −0.108621 0.0155172i
\(581\) 257.387 + 257.387i 0.443007 + 0.443007i
\(582\) 206.612 432.612i 0.355004 0.743320i
\(583\) −700.000 + 700.000i −1.20069 + 1.20069i
\(584\) 386.080i 0.661096i
\(585\) 493.588 + 124.784i 0.843740 + 0.213306i
\(586\) 262.000i 0.447099i
\(587\) −630.739 630.739i −1.07451 1.07451i −0.996991 0.0775226i \(-0.975299\pi\)
−0.0775226 0.996991i \(-0.524701\pi\)
\(588\) 190.055 397.945i 0.323223 0.676777i
\(589\) 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
\(595\) 546.000 + 728.000i 0.917647 + 1.22353i
\(596\) 598.212i 1.00371i
\(597\) 324.853 + 155.147i 0.544142 + 0.259878i
\(598\) −272.000 272.000i −0.454849 0.454849i
\(599\) −96.1665 −0.160545 −0.0802726 0.996773i \(-0.525579\pi\)
−0.0802726 + 0.996773i \(0.525579\pi\)
\(600\) −29.4071 524.176i −0.0490118 0.873626i
\(601\) 476.000i 0.792013i −0.918248 0.396007i \(-0.870396\pi\)
0.918248 0.396007i \(-0.129604\pi\)
\(602\) −356.382 −0.591996
\(603\) −42.9807 + 405.019i −0.0712780 + 0.671674i
\(604\) 234.000i 0.387417i
\(605\) 16.2635 113.844i 0.0268817 0.188172i
\(606\) 260.000 91.9239i 0.429043 0.151690i
\(607\) 345.000 345.000i 0.568369 0.568369i −0.363302 0.931671i \(-0.618351\pi\)
0.931671 + 0.363302i \(0.118351\pi\)
\(608\) 233.345 233.345i 0.383792 0.383792i
\(609\) −38.3970 + 80.3970i −0.0630492 + 0.132015i
\(610\) 56.0000 42.0000i 0.0918033 0.0688525i
\(611\) 67.8823i 0.111100i
\(612\) 698.080 + 74.0803i 1.14065 + 0.121046i
\(613\) 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
\(615\) −282.177 + 423.765i −0.458824 + 0.689048i
\(616\) 343.000 + 343.000i 0.556818 + 0.556818i
\(617\) 468.105 468.105i 0.758679 0.758679i −0.217403 0.976082i \(-0.569759\pi\)
0.976082 + 0.217403i \(0.0697587\pi\)
\(618\) −19.1421 9.14214i −0.0309743 0.0147931i
\(619\) 1058.00 1.70921 0.854604 0.519280i \(-0.173800\pi\)
0.854604 + 0.519280i \(0.173800\pi\)
\(620\) 29.6985 207.889i 0.0479008 0.335305i
\(621\) 480.833 782.000i 0.774288 1.25926i
\(622\) 212.000 212.000i 0.340836 0.340836i
\(623\) −138.593 −0.222461
\(624\) −56.5685 160.000i −0.0906547 0.256410i
\(625\) 527.000 + 336.000i 0.843200 + 0.537600i
\(626\) 250.316 0.399865
\(627\) 127.990 267.990i 0.204131 0.427416i
\(628\) 138.000 + 138.000i 0.219745 + 0.219745i
\(629\) 1103.09i 1.75371i
\(630\) −305.392 77.2061i −0.484749 0.122549i
\(631\) 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
\(633\) 232.811 + 111.189i 0.367790 + 0.175654i
\(634\) 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 \(0.930629\pi\)
\(642\) −7.75736 + 16.2426i −0.0120831 + 0.0253001i
\(643\) −636.000 636.000i −0.989114 0.989114i 0.0108278 0.999941i \(-0.496553\pi\)
−0.999941 + 0.0108278i \(0.996553\pi\)
\(644\) −504.874 504.874i −0.783966 0.783966i
\(645\) −150.177 748.764i −0.232832 1.16087i
\(646\) 260.000 0.402477
\(647\) 535.987 + 535.987i 0.828419 + 0.828419i 0.987298 0.158879i \(-0.0507881\pi\)
−0.158879 + 0.987298i \(0.550788\pi\)
\(648\) −476.146 + 307.854i −0.734793 + 0.475084i
\(649\) 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 \(-0.385150\pi\)
−0.935611 + 0.353033i \(0.885150\pi\)
\(654\) −70.0000 197.990i −0.107034 0.302737i
\(655\) −27.0000 + 189.000i −0.0412214 + 0.288550i
\(656\) 169.706 0.258698
\(657\) −52.3827 + 493.617i −0.0797301 + 0.751320i
\(658\) 42.0000i 0.0638298i
\(659\) 253.144 0.384134 0.192067 0.981382i \(-0.438481\pi\)
0.192067 + 0.981382i \(0.438481\pi\)
\(660\) −246.905 + 370.794i −0.374098 + 0.561809i
\(661\) 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
\(663\) 380.313 796.313i 0.573624 1.20108i
\(664\) −364.000 −0.548193
\(665\) 346.482 + 49.4975i 0.521026 + 0.0744323i
\(666\) 240.000 + 296.985i 0.360360 + 0.445923i
\(667\) 102.000 + 102.000i 0.152924 + 0.152924i
\(668\) −275.772 + 275.772i −0.412832 + 0.412832i
\(669\) −335.169 948.000i −0.500999 1.41704i
\(670\) 32.0000 224.000i 0.0477612 0.334328i
\(671\) −138.593 −0.206547
\(672\) 231.000 + 653.367i 0.343750 + 0.972272i
\(673\) 393.000 393.000i 0.583952 0.583952i −0.352035 0.935987i \(-0.614510\pi\)
0.935987 + 0.352035i \(0.114510\pi\)
\(674\) 357.796 0.530855
\(675\) 33.5212 674.167i 0.0496611 0.998766i
\(676\) 123.000 0.181953
\(677\) 144.250 + 144.250i 0.213072 + 0.213072i 0.805571 0.592499i \(-0.201859\pi\)
−0.592499 + 0.805571i \(0.701859\pi\)
\(678\) 48.7279 + 23.2721i 0.0718701 + 0.0343246i
\(679\) −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 \(-0.460227\pi\)
−0.992204 + 0.124626i \(0.960227\pi\)
\(684\) 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
\(687\) −1012.46 483.542i −1.47374 0.703846i
\(688\) −180.000 + 180.000i −0.261628 + 0.261628i
\(689\) 1131.37i 1.64205i
\(690\) −282.666 + 424.500i −0.409661 + 0.615217i
\(691\) 574.000i 0.830680i 0.909666 + 0.415340i \(0.136337\pi\)
−0.909666 + 0.415340i \(0.863663\pi\)
\(692\) 670.337 + 670.337i 0.968695 + 0.968695i
\(693\) 392.000 + 485.075i 0.565657 + 0.699964i
\(694\) 240.000i 0.345821i
\(695\) −97.5807 + 683.065i −0.140404 + 0.982828i
\(696\) −29.6985 84.0000i −0.0426702 0.120690i
\(697\) 624.000 + 624.000i 0.895265 + 0.895265i
\(698\) −315.370 + 315.370i −0.451819 + 0.451819i
\(699\) 246.000 + 695.793i 0.351931 + 0.995412i
\(700\) −504.000 147.000i −0.720000 0.210000i
\(701\) 1118.64i 1.59578i −0.602802 0.797891i \(-0.705949\pi\)
0.602802 0.797891i \(-0.294051\pi\)
\(702\) 70.8629 + 297.137i 0.100944 + 0.423272i
\(703\) −300.000 300.000i −0.426743 0.426743i
\(704\) −128.693 −0.182803
\(705\) −88.2426 + 17.6985i −0.125167 + 0.0251042i
\(706\) 138.000i 0.195467i
\(707\) 643.467i 0.910137i
\(708\) 241.191 + 115.191i 0.340665 + 0.162699i
\(709\) 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
\(717\) −788.656 376.656i −1.09994 0.525322i
\(718\) 176.000 176.000i 0.245125 0.245125i
\(719\) 277.186i 0.385516i 0.981246 + 0.192758i \(0.0617432\pi\)
−0.981246 + 0.192758i \(0.938257\pi\)
\(720\) −193.241 + 115.251i −0.268391 + 0.160071i
\(721\) −35.0000 + 35.0000i −0.0485437 + 0.0485437i
\(722\) −184.555 + 184.555i −0.255616 + 0.255616i
\(723\) −18.1005 + 37.8995i −0.0250353 + 0.0524198i
\(724\) −1050.00 −1.45028
\(725\) 101.823 + 29.6985i 0.140446 + 0.0409634i
\(726\) 65.0538 23.0000i 0.0896058 0.0316804i
\(727\) 225.000 225.000i 0.309491 0.309491i −0.535221 0.844712i \(-0.679772\pi\)
0.844712 + 0.535221i \(0.179772\pi\)
\(728\) 554.372 0.761500
\(729\) −650.538 + 329.000i −0.892371 + 0.451303i
\(730\) 39.0000 273.000i 0.0534247 0.373973i
\(731\) −1323.70 −1.81081
\(732\) −113.698 54.3015i −0.155326 0.0741824i
\(733\) −124.000 124.000i −0.169168 0.169168i 0.617446 0.786614i \(-0.288168\pi\)
−0.786614 + 0.617446i \(0.788168\pi\)
\(734\) 261.630i 0.356443i
\(735\) −407.372 + 611.779i −0.554247 + 0.832352i
\(736\) 1122.00 1.52446
\(737\) −316.784 + 316.784i −0.429829 + 0.429829i
\(738\) −303.765 32.2355i −0.411605 0.0436795i
\(739\) 350.000i 0.473613i 0.971557 + 0.236806i \(0.0761007\pi\)
−0.971557 + 0.236806i \(0.923899\pi\)
\(740\) 381.838 + 509.117i 0.515997 + 0.687996i
\(741\) −113.137 320.000i −0.152682 0.431849i
\(742\) 700.000i 0.943396i
\(743\) 666.095 + 666.095i 0.896493 + 0.896493i 0.995124 0.0986307i \(-0.0314463\pi\)
−0.0986307 + 0.995124i \(0.531446\pi\)
\(744\) 277.186 98.0000i 0.372562 0.131720i
\(745\) 141.000 987.000i 0.189262 1.32483i
\(746\) 695.793i 0.932698i
\(747\) −465.387 49.3869i −0.623008 0.0661136i
\(748\) 546.000 + 546.000i 0.729947 + 0.729947i
\(749\) 29.6985 + 29.6985i 0.0396508 + 0.0396508i
\(750\) −32.1558 + 373.619i −0.0428744 + 0.498158i
\(751\) −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
\(753\) −1190.64 568.641i −1.58120 0.755167i
\(754\) −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 \(0.652464\pi\)
\(762\) −424.955 202.955i −0.557684 0.266346i
\(763\) −490.000 −0.642202
\(764\) −356.382 −0.466468
\(765\) −1134.31 286.765i −1.48276 0.374857i
\(766\) 190.000i 0.248042i
\(767\) 237.588 237.588i 0.309763 0.309763i
\(768\) −462.915 221.085i −0.602754 0.287871i
\(769\) 436.000 0.566970 0.283485 0.958977i \(-0.408509\pi\)
0.283485 + 0.958977i \(0.408509\pi\)
\(770\) −207.889 277.186i −0.269986 0.359982i
\(771\) 50.0000 + 141.421i 0.0648508 + 0.183426i
\(772\) 201.000 + 201.000i 0.260363 + 0.260363i
\(773\) 684.479 684.479i 0.885484 0.885484i −0.108601 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
\(777\) 840.000 296.985i 1.08108 0.382220i
\(778\) 233.000 233.000i 0.299486 0.299486i
\(779\) 339.411 0.435701
\(780\) 100.118 + 499.176i 0.128356 + 0.639969i
\(781\) −588.000 −0.752881