Properties

Label 1950.2.bc.f.901.2
Level $1950$
Weight $2$
Character 1950.901
Analytic conductor $15.571$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.bc (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 901.2
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1950.901
Dual form 1950.2.bc.f.751.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(2.53906 - 1.46593i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(2.53906 - 1.46593i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.992694 - 0.573132i) q^{11} +1.00000 q^{12} +(1.86250 - 3.08725i) q^{13} -2.93185 q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.276457 + 0.478838i) q^{17} +1.00000i q^{18} +(0.723543 - 0.417738i) q^{19} -2.93185i q^{21} +(0.573132 + 0.992694i) q^{22} +(0.496476 - 0.859921i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-3.15660 + 1.74238i) q^{26} -1.00000 q^{27} +(2.53906 + 1.46593i) q^{28} +(1.03786 - 1.79762i) q^{29} -4.36673i q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.992694 + 0.573132i) q^{33} -0.552914i q^{34} +(0.500000 - 0.866025i) q^{36} +(7.00449 + 4.04404i) q^{37} -0.835475 q^{38} +(-1.74238 - 3.15660i) q^{39} +(-9.67739 - 5.58725i) q^{41} +(-1.46593 + 2.53906i) q^{42} +(-3.94036 - 6.82490i) q^{43} -1.14626i q^{44} +(-0.859921 + 0.496476i) q^{46} +10.9489i q^{47} +(0.500000 + 0.866025i) q^{48} +(0.797877 - 1.38196i) q^{49} +0.552914 q^{51} +(3.60488 + 0.0693504i) q^{52} +3.56753 q^{53} +(0.866025 + 0.500000i) q^{54} +(-1.46593 - 2.53906i) q^{56} -0.835475i q^{57} +(-1.79762 + 1.03786i) q^{58} +(-4.75442 + 2.74496i) q^{59} +(-1.43368 - 2.48320i) q^{61} +(-2.18336 + 3.78170i) q^{62} +(-2.53906 - 1.46593i) q^{63} -1.00000 q^{64} +1.14626 q^{66} +(8.88828 + 5.13165i) q^{67} +(-0.276457 + 0.478838i) q^{68} +(-0.496476 - 0.859921i) q^{69} +(9.85992 - 5.69263i) q^{71} +(-0.866025 + 0.500000i) q^{72} -8.19151i q^{73} +(-4.04404 - 7.00449i) q^{74} +(0.723543 + 0.417738i) q^{76} -3.36068 q^{77} +(-0.0693504 + 3.60488i) q^{78} +1.68973 q^{79} +(-0.500000 + 0.866025i) q^{81} +(5.58725 + 9.67739i) q^{82} -8.77729i q^{83} +(2.53906 - 1.46593i) q^{84} +7.88072i q^{86} +(-1.03786 - 1.79762i) q^{87} +(-0.573132 + 0.992694i) q^{88} +(-3.93073 - 2.26941i) q^{89} +(0.203325 - 10.5690i) q^{91} +0.992952 q^{92} +(-3.78170 - 2.18336i) q^{93} +(5.47443 - 9.48200i) q^{94} -1.00000i q^{96} +(9.19453 - 5.30847i) q^{97} +(-1.38196 + 0.797877i) q^{98} +1.14626i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9} + O(q^{10}) \) \( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9} - 12 q^{11} + 8 q^{12} - 8 q^{14} - 4 q^{16} - 4 q^{17} + 12 q^{19} - 8 q^{22} - 4 q^{23} - 8 q^{27} + 4 q^{29} - 12 q^{33} + 4 q^{36} + 24 q^{37} - 4 q^{42} + 4 q^{43} + 12 q^{46} + 4 q^{48} - 16 q^{49} - 8 q^{51} + 8 q^{53} - 4 q^{56} - 12 q^{58} - 12 q^{59} - 16 q^{61} - 4 q^{62} - 8 q^{64} - 16 q^{66} - 24 q^{67} + 4 q^{68} + 4 q^{69} + 60 q^{71} + 16 q^{74} + 12 q^{76} + 8 q^{77} - 8 q^{79} - 4 q^{81} + 20 q^{82} - 4 q^{87} + 8 q^{88} + 24 q^{89} + 8 q^{91} - 8 q^{92} + 24 q^{93} + 16 q^{94} - 12 q^{97} - 12 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) −0.866025 + 0.500000i −0.353553 + 0.204124i
\(7\) 2.53906 1.46593i 0.959674 0.554068i 0.0636011 0.997975i \(-0.479741\pi\)
0.896073 + 0.443908i \(0.146408\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −0.992694 0.573132i −0.299309 0.172806i 0.342824 0.939400i \(-0.388617\pi\)
−0.642132 + 0.766594i \(0.721950\pi\)
\(12\) 1.00000 0.288675
\(13\) 1.86250 3.08725i 0.516565 0.856248i
\(14\) −2.93185 −0.783570
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.276457 + 0.478838i 0.0670507 + 0.116135i 0.897602 0.440807i \(-0.145308\pi\)
−0.830551 + 0.556942i \(0.811974\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 0.723543 0.417738i 0.165992 0.0958356i −0.414703 0.909957i \(-0.636114\pi\)
0.580695 + 0.814121i \(0.302781\pi\)
\(20\) 0 0
\(21\) 2.93185i 0.639782i
\(22\) 0.573132 + 0.992694i 0.122192 + 0.211643i
\(23\) 0.496476 0.859921i 0.103522 0.179306i −0.809611 0.586967i \(-0.800322\pi\)
0.913134 + 0.407661i \(0.133655\pi\)
\(24\) −0.866025 0.500000i −0.176777 0.102062i
\(25\) 0 0
\(26\) −3.15660 + 1.74238i −0.619060 + 0.341709i
\(27\) −1.00000 −0.192450
\(28\) 2.53906 + 1.46593i 0.479837 + 0.277034i
\(29\) 1.03786 1.79762i 0.192725 0.333810i −0.753427 0.657531i \(-0.771601\pi\)
0.946152 + 0.323722i \(0.104934\pi\)
\(30\) 0 0
\(31\) 4.36673i 0.784288i −0.919904 0.392144i \(-0.871734\pi\)
0.919904 0.392144i \(-0.128266\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) −0.992694 + 0.573132i −0.172806 + 0.0997695i
\(34\) 0.552914i 0.0948240i
\(35\) 0 0
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) 7.00449 + 4.04404i 1.15153 + 0.664836i 0.949260 0.314493i \(-0.101835\pi\)
0.202271 + 0.979330i \(0.435168\pi\)
\(38\) −0.835475 −0.135532
\(39\) −1.74238 3.15660i −0.279005 0.505460i
\(40\) 0 0
\(41\) −9.67739 5.58725i −1.51136 0.872581i −0.999912 0.0132641i \(-0.995778\pi\)
−0.511443 0.859317i \(-0.670889\pi\)
\(42\) −1.46593 + 2.53906i −0.226197 + 0.391785i
\(43\) −3.94036 6.82490i −0.600899 1.04079i −0.992685 0.120732i \(-0.961476\pi\)
0.391786 0.920056i \(-0.371857\pi\)
\(44\) 1.14626i 0.172806i
\(45\) 0 0
\(46\) −0.859921 + 0.496476i −0.126789 + 0.0732014i
\(47\) 10.9489i 1.59706i 0.601957 + 0.798528i \(0.294388\pi\)
−0.601957 + 0.798528i \(0.705612\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) 0.797877 1.38196i 0.113982 0.197423i
\(50\) 0 0
\(51\) 0.552914 0.0774235
\(52\) 3.60488 + 0.0693504i 0.499908 + 0.00961716i
\(53\) 3.56753 0.490037 0.245019 0.969518i \(-0.421206\pi\)
0.245019 + 0.969518i \(0.421206\pi\)
\(54\) 0.866025 + 0.500000i 0.117851 + 0.0680414i
\(55\) 0 0
\(56\) −1.46593 2.53906i −0.195893 0.339296i
\(57\) 0.835475i 0.110661i
\(58\) −1.79762 + 1.03786i −0.236039 + 0.136277i
\(59\) −4.75442 + 2.74496i −0.618972 + 0.357364i −0.776469 0.630156i \(-0.782991\pi\)
0.157497 + 0.987520i \(0.449658\pi\)
\(60\) 0 0
\(61\) −1.43368 2.48320i −0.183563 0.317941i 0.759528 0.650474i \(-0.225430\pi\)
−0.943091 + 0.332533i \(0.892097\pi\)
\(62\) −2.18336 + 3.78170i −0.277288 + 0.480276i
\(63\) −2.53906 1.46593i −0.319891 0.184689i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 1.14626 0.141095
\(67\) 8.88828 + 5.13165i 1.08588 + 0.626931i 0.932476 0.361233i \(-0.117644\pi\)
0.153401 + 0.988164i \(0.450977\pi\)
\(68\) −0.276457 + 0.478838i −0.0335254 + 0.0580676i
\(69\) −0.496476 0.859921i −0.0597687 0.103522i
\(70\) 0 0
\(71\) 9.85992 5.69263i 1.17016 0.675591i 0.216440 0.976296i \(-0.430555\pi\)
0.953717 + 0.300705i \(0.0972220\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 8.19151i 0.958744i −0.877612 0.479372i \(-0.840865\pi\)
0.877612 0.479372i \(-0.159135\pi\)
\(74\) −4.04404 7.00449i −0.470110 0.814255i
\(75\) 0 0
\(76\) 0.723543 + 0.417738i 0.0829961 + 0.0479178i
\(77\) −3.36068 −0.382985
\(78\) −0.0693504 + 3.60488i −0.00785238 + 0.408173i
\(79\) 1.68973 0.190109 0.0950545 0.995472i \(-0.469697\pi\)
0.0950545 + 0.995472i \(0.469697\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 5.58725 + 9.67739i 0.617008 + 1.06869i
\(83\) 8.77729i 0.963433i −0.876327 0.481717i \(-0.840013\pi\)
0.876327 0.481717i \(-0.159987\pi\)
\(84\) 2.53906 1.46593i 0.277034 0.159946i
\(85\) 0 0
\(86\) 7.88072i 0.849800i
\(87\) −1.03786 1.79762i −0.111270 0.192725i
\(88\) −0.573132 + 0.992694i −0.0610961 + 0.105822i
\(89\) −3.93073 2.26941i −0.416657 0.240557i 0.276989 0.960873i \(-0.410663\pi\)
−0.693646 + 0.720316i \(0.743997\pi\)
\(90\) 0 0
\(91\) 0.203325 10.5690i 0.0213142 1.10793i
\(92\) 0.992952 0.103522
\(93\) −3.78170 2.18336i −0.392144 0.226404i
\(94\) 5.47443 9.48200i 0.564645 0.977993i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) 9.19453 5.30847i 0.933564 0.538993i 0.0456267 0.998959i \(-0.485472\pi\)
0.887937 + 0.459965i \(0.152138\pi\)
\(98\) −1.38196 + 0.797877i −0.139599 + 0.0805978i
\(99\) 1.14626i 0.115204i
\(100\) 0 0
\(101\) −7.07313 + 12.2510i −0.703803 + 1.21902i 0.263319 + 0.964709i \(0.415183\pi\)
−0.967122 + 0.254314i \(0.918150\pi\)
\(102\) −0.478838 0.276457i −0.0474120 0.0273733i
\(103\) −6.72500 −0.662634 −0.331317 0.943519i \(-0.607493\pi\)
−0.331317 + 0.943519i \(0.607493\pi\)
\(104\) −3.08725 1.86250i −0.302729 0.182633i
\(105\) 0 0
\(106\) −3.08957 1.78376i −0.300085 0.173254i
\(107\) 0.123385 0.213709i 0.0119281 0.0206600i −0.860000 0.510294i \(-0.829536\pi\)
0.871928 + 0.489634i \(0.162870\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 4.13797i 0.396346i −0.980167 0.198173i \(-0.936499\pi\)
0.980167 0.198173i \(-0.0635008\pi\)
\(110\) 0 0
\(111\) 7.00449 4.04404i 0.664836 0.383843i
\(112\) 2.93185i 0.277034i
\(113\) −0.828427 1.43488i −0.0779319 0.134982i 0.824426 0.565970i \(-0.191498\pi\)
−0.902357 + 0.430988i \(0.858165\pi\)
\(114\) −0.417738 + 0.723543i −0.0391247 + 0.0677660i
\(115\) 0 0
\(116\) 2.07571 0.192725
\(117\) −3.60488 0.0693504i −0.333272 0.00641144i
\(118\) 5.48993 0.505389
\(119\) 1.40388 + 0.810531i 0.128694 + 0.0743013i
\(120\) 0 0
\(121\) −4.84304 8.38839i −0.440276 0.762581i
\(122\) 2.86735i 0.259598i
\(123\) −9.67739 + 5.58725i −0.872581 + 0.503785i
\(124\) 3.78170 2.18336i 0.339607 0.196072i
\(125\) 0 0
\(126\) 1.46593 + 2.53906i 0.130595 + 0.226197i
\(127\) 3.80260 6.58630i 0.337426 0.584440i −0.646521 0.762896i \(-0.723777\pi\)
0.983948 + 0.178456i \(0.0571102\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −7.88072 −0.693859
\(130\) 0 0
\(131\) 5.45340 0.476466 0.238233 0.971208i \(-0.423432\pi\)
0.238233 + 0.971208i \(0.423432\pi\)
\(132\) −0.992694 0.573132i −0.0864029 0.0498848i
\(133\) 1.22474 2.12132i 0.106199 0.183942i
\(134\) −5.13165 8.88828i −0.443307 0.767831i
\(135\) 0 0
\(136\) 0.478838 0.276457i 0.0410600 0.0237060i
\(137\) 0.276333 0.159541i 0.0236087 0.0136305i −0.488149 0.872760i \(-0.662328\pi\)
0.511758 + 0.859130i \(0.328994\pi\)
\(138\) 0.992952i 0.0845257i
\(139\) −5.84046 10.1160i −0.495381 0.858026i 0.504605 0.863351i \(-0.331638\pi\)
−0.999986 + 0.00532505i \(0.998305\pi\)
\(140\) 0 0
\(141\) 9.48200 + 5.47443i 0.798528 + 0.461030i
\(142\) −11.3853 −0.955430
\(143\) −3.61829 + 1.99723i −0.302577 + 0.167017i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −4.09575 + 7.09405i −0.338967 + 0.587108i
\(147\) −0.797877 1.38196i −0.0658078 0.113982i
\(148\) 8.08808i 0.664836i
\(149\) 4.33221 2.50120i 0.354908 0.204906i −0.311937 0.950103i \(-0.600978\pi\)
0.666845 + 0.745196i \(0.267644\pi\)
\(150\) 0 0
\(151\) 12.9005i 1.04983i 0.851156 + 0.524914i \(0.175902\pi\)
−0.851156 + 0.524914i \(0.824098\pi\)
\(152\) −0.417738 0.723543i −0.0338830 0.0586871i
\(153\) 0.276457 0.478838i 0.0223502 0.0387117i
\(154\) 2.91043 + 1.68034i 0.234529 + 0.135406i
\(155\) 0 0
\(156\) 1.86250 3.08725i 0.149119 0.247178i
\(157\) 8.66531 0.691567 0.345784 0.938314i \(-0.387613\pi\)
0.345784 + 0.938314i \(0.387613\pi\)
\(158\) −1.46335 0.844863i −0.116418 0.0672137i
\(159\) 1.78376 3.08957i 0.141462 0.245019i
\(160\) 0 0
\(161\) 2.91119i 0.229434i
\(162\) 0.866025 0.500000i 0.0680414 0.0392837i
\(163\) 1.59928 0.923344i 0.125265 0.0723219i −0.436058 0.899919i \(-0.643626\pi\)
0.561323 + 0.827597i \(0.310292\pi\)
\(164\) 11.1745i 0.872581i
\(165\) 0 0
\(166\) −4.38865 + 7.60136i −0.340625 + 0.589980i
\(167\) −18.8898 10.9060i −1.46174 0.843935i −0.462647 0.886543i \(-0.653100\pi\)
−0.999092 + 0.0426077i \(0.986433\pi\)
\(168\) −2.93185 −0.226197
\(169\) −6.06218 11.5000i −0.466321 0.884615i
\(170\) 0 0
\(171\) −0.723543 0.417738i −0.0553307 0.0319452i
\(172\) 3.94036 6.82490i 0.300450 0.520394i
\(173\) −5.93942 10.2874i −0.451565 0.782134i 0.546918 0.837186i \(-0.315801\pi\)
−0.998483 + 0.0550519i \(0.982468\pi\)
\(174\) 2.07571i 0.157359i
\(175\) 0 0
\(176\) 0.992694 0.573132i 0.0748271 0.0432015i
\(177\) 5.48993i 0.412648i
\(178\) 2.26941 + 3.93073i 0.170099 + 0.294621i
\(179\) −4.47746 + 7.75519i −0.334661 + 0.579650i −0.983420 0.181344i \(-0.941955\pi\)
0.648759 + 0.760994i \(0.275288\pi\)
\(180\) 0 0
\(181\) −21.2297 −1.57799 −0.788996 0.614399i \(-0.789399\pi\)
−0.788996 + 0.614399i \(0.789399\pi\)
\(182\) −5.46058 + 9.05135i −0.404765 + 0.670931i
\(183\) −2.86735 −0.211961
\(184\) −0.859921 0.496476i −0.0633943 0.0366007i
\(185\) 0 0
\(186\) 2.18336 + 3.78170i 0.160092 + 0.277288i
\(187\) 0.633786i 0.0463470i
\(188\) −9.48200 + 5.47443i −0.691546 + 0.399264i
\(189\) −2.53906 + 1.46593i −0.184689 + 0.106630i
\(190\) 0 0
\(191\) −2.25347 3.90313i −0.163055 0.282420i 0.772908 0.634519i \(-0.218802\pi\)
−0.935963 + 0.352098i \(0.885468\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −2.30090 1.32843i −0.165623 0.0956223i 0.414898 0.909868i \(-0.363817\pi\)
−0.580520 + 0.814246i \(0.697151\pi\)
\(194\) −10.6169 −0.762251
\(195\) 0 0
\(196\) 1.59575 0.113982
\(197\) −1.68375 0.972112i −0.119962 0.0692601i 0.438818 0.898576i \(-0.355397\pi\)
−0.558780 + 0.829316i \(0.688731\pi\)
\(198\) 0.573132 0.992694i 0.0407307 0.0705477i
\(199\) 7.50877 + 13.0056i 0.532282 + 0.921940i 0.999290 + 0.0376865i \(0.0119988\pi\)
−0.467007 + 0.884253i \(0.654668\pi\)
\(200\) 0 0
\(201\) 8.88828 5.13165i 0.626931 0.361959i
\(202\) 12.2510 7.07313i 0.861979 0.497664i
\(203\) 6.08568i 0.427131i
\(204\) 0.276457 + 0.478838i 0.0193559 + 0.0335254i
\(205\) 0 0
\(206\) 5.82402 + 3.36250i 0.405779 + 0.234277i
\(207\) −0.992952 −0.0690149
\(208\) 1.74238 + 3.15660i 0.120813 + 0.218871i
\(209\) −0.957676 −0.0662438
\(210\) 0 0
\(211\) −0.379882 + 0.657974i −0.0261521 + 0.0452968i −0.878805 0.477181i \(-0.841659\pi\)
0.852653 + 0.522477i \(0.174992\pi\)
\(212\) 1.78376 + 3.08957i 0.122509 + 0.212192i
\(213\) 11.3853i 0.780105i
\(214\) −0.213709 + 0.123385i −0.0146088 + 0.00843441i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −6.40130 11.0874i −0.434549 0.752660i
\(218\) −2.06899 + 3.58359i −0.140129 + 0.242711i
\(219\) −7.09405 4.09575i −0.479372 0.276765i
\(220\) 0 0
\(221\) 1.99319 + 0.0383448i 0.134077 + 0.00257935i
\(222\) −8.08808 −0.542837
\(223\) 18.5939 + 10.7352i 1.24514 + 0.718883i 0.970136 0.242560i \(-0.0779871\pi\)
0.275005 + 0.961443i \(0.411320\pi\)
\(224\) 1.46593 2.53906i 0.0979463 0.169648i
\(225\) 0 0
\(226\) 1.65685i 0.110212i
\(227\) −19.1406 + 11.0508i −1.27041 + 0.733471i −0.975065 0.221920i \(-0.928767\pi\)
−0.295344 + 0.955391i \(0.595434\pi\)
\(228\) 0.723543 0.417738i 0.0479178 0.0276654i
\(229\) 21.6368i 1.42980i 0.699226 + 0.714901i \(0.253528\pi\)
−0.699226 + 0.714901i \(0.746472\pi\)
\(230\) 0 0
\(231\) −1.68034 + 2.91043i −0.110558 + 0.191492i
\(232\) −1.79762 1.03786i −0.118019 0.0681386i
\(233\) 5.95668 0.390235 0.195118 0.980780i \(-0.437491\pi\)
0.195118 + 0.980780i \(0.437491\pi\)
\(234\) 3.08725 + 1.86250i 0.201820 + 0.121756i
\(235\) 0 0
\(236\) −4.75442 2.74496i −0.309486 0.178682i
\(237\) 0.844863 1.46335i 0.0548798 0.0950545i
\(238\) −0.810531 1.40388i −0.0525389 0.0910001i
\(239\) 28.8408i 1.86556i 0.360451 + 0.932778i \(0.382623\pi\)
−0.360451 + 0.932778i \(0.617377\pi\)
\(240\) 0 0
\(241\) 4.95886 2.86300i 0.319428 0.184422i −0.331709 0.943382i \(-0.607625\pi\)
0.651138 + 0.758960i \(0.274292\pi\)
\(242\) 9.68608i 0.622645i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 1.43368 2.48320i 0.0917817 0.158971i
\(245\) 0 0
\(246\) 11.1745 0.712460
\(247\) 0.0579405 3.01179i 0.00368667 0.191636i
\(248\) −4.36673 −0.277288
\(249\) −7.60136 4.38865i −0.481717 0.278119i
\(250\) 0 0
\(251\) 3.33171 + 5.77069i 0.210296 + 0.364243i 0.951807 0.306697i \(-0.0992240\pi\)
−0.741511 + 0.670940i \(0.765891\pi\)
\(252\) 2.93185i 0.184689i
\(253\) −0.985697 + 0.569093i −0.0619703 + 0.0357785i
\(254\) −6.58630 + 3.80260i −0.413261 + 0.238597i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 5.01607 8.68809i 0.312894 0.541948i −0.666094 0.745868i \(-0.732035\pi\)
0.978988 + 0.203920i \(0.0653682\pi\)
\(258\) 6.82490 + 3.94036i 0.424900 + 0.245316i
\(259\) 23.7131 1.47346
\(260\) 0 0
\(261\) −2.07571 −0.128483
\(262\) −4.72279 2.72670i −0.291775 0.168456i
\(263\) 12.5202 21.6856i 0.772027 1.33719i −0.164423 0.986390i \(-0.552576\pi\)
0.936450 0.350800i \(-0.114090\pi\)
\(264\) 0.573132 + 0.992694i 0.0352738 + 0.0610961i
\(265\) 0 0
\(266\) −2.12132 + 1.22474i −0.130066 + 0.0750939i
\(267\) −3.93073 + 2.26941i −0.240557 + 0.138886i
\(268\) 10.2633i 0.626931i
\(269\) −11.6268 20.1382i −0.708899 1.22785i −0.965266 0.261269i \(-0.915859\pi\)
0.256367 0.966579i \(-0.417474\pi\)
\(270\) 0 0
\(271\) −5.32698 3.07554i −0.323591 0.186826i 0.329401 0.944190i \(-0.393153\pi\)
−0.652992 + 0.757365i \(0.726487\pi\)
\(272\) −0.552914 −0.0335254
\(273\) −9.05135 5.46058i −0.547812 0.330489i
\(274\) −0.319082 −0.0192764
\(275\) 0 0
\(276\) 0.496476 0.859921i 0.0298843 0.0517612i
\(277\) 3.44464 + 5.96629i 0.206968 + 0.358480i 0.950758 0.309934i \(-0.100307\pi\)
−0.743790 + 0.668414i \(0.766974\pi\)
\(278\) 11.6809i 0.700575i
\(279\) −3.78170 + 2.18336i −0.226404 + 0.130715i
\(280\) 0 0
\(281\) 0.545617i 0.0325488i 0.999868 + 0.0162744i \(0.00518053\pi\)
−0.999868 + 0.0162744i \(0.994819\pi\)
\(282\) −5.47443 9.48200i −0.325998 0.564645i
\(283\) 4.21329 7.29764i 0.250454 0.433799i −0.713197 0.700964i \(-0.752753\pi\)
0.963651 + 0.267164i \(0.0860867\pi\)
\(284\) 9.85992 + 5.69263i 0.585079 + 0.337795i
\(285\) 0 0
\(286\) 4.13215 + 0.0794938i 0.244339 + 0.00470057i
\(287\) −32.7620 −1.93388
\(288\) −0.866025 0.500000i −0.0510310 0.0294628i
\(289\) 8.34714 14.4577i 0.491008 0.850452i
\(290\) 0 0
\(291\) 10.6169i 0.622376i
\(292\) 7.09405 4.09575i 0.415148 0.239686i
\(293\) −5.87017 + 3.38915i −0.342939 + 0.197996i −0.661571 0.749883i \(-0.730110\pi\)
0.318632 + 0.947879i \(0.396777\pi\)
\(294\) 1.59575i 0.0930663i
\(295\) 0 0
\(296\) 4.04404 7.00449i 0.235055 0.407127i
\(297\) 0.992694 + 0.573132i 0.0576020 + 0.0332565i
\(298\) −5.00240 −0.289781
\(299\) −1.73010 3.13435i −0.100054 0.181264i
\(300\) 0 0
\(301\) −20.0096 11.5525i −1.15333 0.665878i
\(302\) 6.45025 11.1722i 0.371170 0.642885i
\(303\) 7.07313 + 12.2510i 0.406341 + 0.703803i
\(304\) 0.835475i 0.0479178i
\(305\) 0 0
\(306\) −0.478838 + 0.276457i −0.0273733 + 0.0158040i
\(307\) 34.6432i 1.97719i 0.150601 + 0.988595i \(0.451879\pi\)
−0.150601 + 0.988595i \(0.548121\pi\)
\(308\) −1.68034 2.91043i −0.0957462 0.165837i
\(309\) −3.36250 + 5.82402i −0.191286 + 0.331317i
\(310\) 0 0
\(311\) 20.2203 1.14659 0.573293 0.819351i \(-0.305666\pi\)
0.573293 + 0.819351i \(0.305666\pi\)
\(312\) −3.15660 + 1.74238i −0.178707 + 0.0986430i
\(313\) 22.3326 1.26231 0.631157 0.775655i \(-0.282580\pi\)
0.631157 + 0.775655i \(0.282580\pi\)
\(314\) −7.50438 4.33266i −0.423497 0.244506i
\(315\) 0 0
\(316\) 0.844863 + 1.46335i 0.0475273 + 0.0823196i
\(317\) 11.4292i 0.641930i −0.947091 0.320965i \(-0.895993\pi\)
0.947091 0.320965i \(-0.104007\pi\)
\(318\) −3.08957 + 1.78376i −0.173254 + 0.100028i
\(319\) −2.06055 + 1.18966i −0.115368 + 0.0666080i
\(320\) 0 0
\(321\) −0.123385 0.213709i −0.00688666 0.0119281i
\(322\) −1.45559 + 2.52116i −0.0811171 + 0.140499i
\(323\) 0.400057 + 0.230973i 0.0222598 + 0.0128517i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −1.84669 −0.102279
\(327\) −3.58359 2.06899i −0.198173 0.114415i
\(328\) −5.58725 + 9.67739i −0.308504 + 0.534345i
\(329\) 16.0502 + 27.7998i 0.884878 + 1.53265i
\(330\) 0 0
\(331\) 1.53602 0.886823i 0.0844274 0.0487442i −0.457192 0.889368i \(-0.651145\pi\)
0.541619 + 0.840624i \(0.317811\pi\)
\(332\) 7.60136 4.38865i 0.417179 0.240858i
\(333\) 8.08808i 0.443224i
\(334\) 10.9060 + 18.8898i 0.596752 + 1.03361i
\(335\) 0 0
\(336\) 2.53906 + 1.46593i 0.138517 + 0.0799728i
\(337\) 12.0024 0.653815 0.326907 0.945056i \(-0.393994\pi\)
0.326907 + 0.945056i \(0.393994\pi\)
\(338\) −0.500000 + 12.9904i −0.0271964 + 0.706584i
\(339\) −1.65685 −0.0899880
\(340\) 0 0
\(341\) −2.50271 + 4.33483i −0.135530 + 0.234744i
\(342\) 0.417738 + 0.723543i 0.0225887 + 0.0391247i
\(343\) 15.8444i 0.855520i
\(344\) −6.82490 + 3.94036i −0.367974 + 0.212450i
\(345\) 0 0
\(346\) 11.8788i 0.638610i
\(347\) −13.7793 23.8664i −0.739709 1.28121i −0.952626 0.304143i \(-0.901630\pi\)
0.212917 0.977070i \(-0.431704\pi\)
\(348\) 1.03786 1.79762i 0.0556349 0.0963625i
\(349\) 12.2674 + 7.08260i 0.656660 + 0.379123i 0.791003 0.611812i \(-0.209559\pi\)
−0.134343 + 0.990935i \(0.542892\pi\)
\(350\) 0 0
\(351\) −1.86250 + 3.08725i −0.0994130 + 0.164785i
\(352\) −1.14626 −0.0610961
\(353\) 27.3612 + 15.7970i 1.45629 + 0.840790i 0.998826 0.0484373i \(-0.0154241\pi\)
0.457465 + 0.889228i \(0.348757\pi\)
\(354\) 2.74496 4.75442i 0.145893 0.252694i
\(355\) 0 0
\(356\) 4.53882i 0.240557i
\(357\) 1.40388 0.810531i 0.0743013 0.0428979i
\(358\) 7.75519 4.47746i 0.409874 0.236641i
\(359\) 12.1714i 0.642380i 0.947015 + 0.321190i \(0.104083\pi\)
−0.947015 + 0.321190i \(0.895917\pi\)
\(360\) 0 0
\(361\) −9.15099 + 15.8500i −0.481631 + 0.834209i
\(362\) 18.3855 + 10.6149i 0.966318 + 0.557904i
\(363\) −9.68608 −0.508387
\(364\) 9.25467 5.10841i 0.485077 0.267753i
\(365\) 0 0
\(366\) 2.48320 + 1.43368i 0.129799 + 0.0749394i
\(367\) 14.9977 25.9768i 0.782873 1.35598i −0.147389 0.989079i \(-0.547087\pi\)
0.930262 0.366897i \(-0.119580\pi\)
\(368\) 0.496476 + 0.859921i 0.0258806 + 0.0448265i
\(369\) 11.1745i 0.581721i
\(370\) 0 0
\(371\) 9.05816 5.22973i 0.470276 0.271514i
\(372\) 4.36673i 0.226404i
\(373\) −18.3785 31.8325i −0.951604 1.64823i −0.741954 0.670450i \(-0.766101\pi\)
−0.209650 0.977777i \(-0.567232\pi\)
\(374\) −0.316893 + 0.548875i −0.0163861 + 0.0283816i
\(375\) 0 0
\(376\) 10.9489 0.564645
\(377\) −3.61669 6.55219i −0.186269 0.337455i
\(378\) 2.93185 0.150798
\(379\) 4.47699 + 2.58479i 0.229967 + 0.132772i 0.610557 0.791972i \(-0.290946\pi\)
−0.380590 + 0.924744i \(0.624279\pi\)
\(380\) 0 0
\(381\) −3.80260 6.58630i −0.194813 0.337426i
\(382\) 4.50694i 0.230595i
\(383\) −2.42657 + 1.40098i −0.123992 + 0.0715867i −0.560713 0.828010i \(-0.689473\pi\)
0.436721 + 0.899597i \(0.356140\pi\)
\(384\) 0.866025 0.500000i 0.0441942 0.0255155i
\(385\) 0 0
\(386\) 1.32843 + 2.30090i 0.0676152 + 0.117113i
\(387\) −3.94036 + 6.82490i −0.200300 + 0.346929i
\(388\) 9.19453 + 5.30847i 0.466782 + 0.269497i
\(389\) 11.8936 0.603030 0.301515 0.953461i \(-0.402508\pi\)
0.301515 + 0.953461i \(0.402508\pi\)
\(390\) 0 0
\(391\) 0.549017 0.0277650
\(392\) −1.38196 0.797877i −0.0697997 0.0402989i
\(393\) 2.72670 4.72279i 0.137544 0.238233i
\(394\) 0.972112 + 1.68375i 0.0489743 + 0.0848259i
\(395\) 0 0
\(396\) −0.992694 + 0.573132i −0.0498848 + 0.0288010i
\(397\) 33.7790 19.5023i 1.69532 0.978792i 0.745231 0.666806i \(-0.232339\pi\)
0.950087 0.311986i \(-0.100994\pi\)
\(398\) 15.0175i 0.752761i
\(399\) −1.22474 2.12132i −0.0613139 0.106199i
\(400\) 0 0
\(401\) 23.4558 + 13.5422i 1.17133 + 0.676266i 0.953992 0.299831i \(-0.0969303\pi\)
0.217335 + 0.976097i \(0.430264\pi\)
\(402\) −10.2633 −0.511887
\(403\) −13.4812 8.13304i −0.671545 0.405136i
\(404\) −14.1463 −0.703803
\(405\) 0 0
\(406\) −3.04284 + 5.27035i −0.151014 + 0.261563i
\(407\) −4.63554 8.02899i −0.229775 0.397982i
\(408\) 0.552914i 0.0273733i
\(409\) −13.8087 + 7.97248i −0.682798 + 0.394214i −0.800908 0.598787i \(-0.795650\pi\)
0.118110 + 0.993000i \(0.462316\pi\)
\(410\) 0 0
\(411\) 0.319082i 0.0157391i
\(412\) −3.36250 5.82402i −0.165659 0.286929i
\(413\) −8.04782 + 13.9392i −0.396008 + 0.685905i
\(414\) 0.859921 + 0.496476i 0.0422628 + 0.0244005i
\(415\) 0 0
\(416\) 0.0693504 3.60488i 0.00340018 0.176744i
\(417\) −11.6809 −0.572017
\(418\) 0.829371 + 0.478838i 0.0405659 + 0.0234207i
\(419\) −9.71670 + 16.8298i −0.474692 + 0.822190i −0.999580 0.0289808i \(-0.990774\pi\)
0.524888 + 0.851171i \(0.324107\pi\)
\(420\) 0 0
\(421\) 21.5769i 1.05160i 0.850610 + 0.525798i \(0.176233\pi\)
−0.850610 + 0.525798i \(0.823767\pi\)
\(422\) 0.657974 0.379882i 0.0320297 0.0184924i
\(423\) 9.48200 5.47443i 0.461030 0.266176i
\(424\) 3.56753i 0.173254i
\(425\) 0 0
\(426\) −5.69263 + 9.85992i −0.275809 + 0.477715i
\(427\) −7.28037 4.20332i −0.352322 0.203413i
\(428\) 0.246769 0.0119281
\(429\) −0.0794938 + 4.13215i −0.00383800 + 0.199502i
\(430\) 0 0
\(431\) 0.550541 + 0.317855i 0.0265186 + 0.0153105i 0.513201 0.858269i \(-0.328460\pi\)
−0.486682 + 0.873579i \(0.661793\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) 5.30090 + 9.18143i 0.254745 + 0.441232i 0.964826 0.262888i \(-0.0846751\pi\)
−0.710081 + 0.704120i \(0.751342\pi\)
\(434\) 12.8026i 0.614545i
\(435\) 0 0
\(436\) 3.58359 2.06899i 0.171623 0.0990865i
\(437\) 0.829587i 0.0396845i
\(438\) 4.09575 + 7.09405i 0.195703 + 0.338967i
\(439\) −7.65685 + 13.2621i −0.365442 + 0.632964i −0.988847 0.148935i \(-0.952415\pi\)
0.623405 + 0.781899i \(0.285749\pi\)
\(440\) 0 0
\(441\) −1.59575 −0.0759883
\(442\) −1.70698 1.02980i −0.0811929 0.0489828i
\(443\) 18.4800 0.878009 0.439005 0.898485i \(-0.355331\pi\)
0.439005 + 0.898485i \(0.355331\pi\)
\(444\) 7.00449 + 4.04404i 0.332418 + 0.191922i
\(445\) 0 0
\(446\) −10.7352 18.5939i −0.508327 0.880448i
\(447\) 5.00240i 0.236606i
\(448\) −2.53906 + 1.46593i −0.119959 + 0.0692585i
\(449\) 22.5084 12.9952i 1.06224 0.613283i 0.136187 0.990683i \(-0.456515\pi\)
0.926050 + 0.377400i \(0.123182\pi\)
\(450\) 0 0
\(451\) 6.40446 + 11.0929i 0.301574 + 0.522342i
\(452\) 0.828427 1.43488i 0.0389659 0.0674910i
\(453\) 11.1722 + 6.45025i 0.524914 + 0.303059i
\(454\) 22.1017 1.03728
\(455\) 0 0
\(456\) −0.835475 −0.0391247
\(457\) 35.9475 + 20.7543i 1.68155 + 0.970846i 0.960630 + 0.277832i \(0.0896157\pi\)
0.720924 + 0.693014i \(0.243718\pi\)
\(458\) 10.8184 18.7380i 0.505511 0.875571i
\(459\) −0.276457 0.478838i −0.0129039 0.0223502i
\(460\) 0 0
\(461\) 13.8532 7.99818i 0.645210 0.372512i −0.141409 0.989951i \(-0.545163\pi\)
0.786619 + 0.617439i \(0.211830\pi\)
\(462\) 2.91043 1.68034i 0.135406 0.0781764i
\(463\) 18.8328i 0.875232i 0.899162 + 0.437616i \(0.144177\pi\)
−0.899162 + 0.437616i \(0.855823\pi\)
\(464\) 1.03786 + 1.79762i 0.0481813 + 0.0834524i
\(465\) 0 0
\(466\) −5.15864 2.97834i −0.238969 0.137969i
\(467\) 3.43738 0.159063 0.0795316 0.996832i \(-0.474658\pi\)
0.0795316 + 0.996832i \(0.474658\pi\)
\(468\) −1.74238 3.15660i −0.0805417 0.145914i
\(469\) 30.0905 1.38945
\(470\) 0 0
\(471\) 4.33266 7.50438i 0.199638 0.345784i
\(472\) 2.74496 + 4.75442i 0.126347 + 0.218840i
\(473\) 9.03339i 0.415356i
\(474\) −1.46335 + 0.844863i −0.0672137 + 0.0388059i
\(475\) 0 0
\(476\) 1.62106i 0.0743013i
\(477\) −1.78376 3.08957i −0.0816729 0.141462i
\(478\) 14.4204 24.9769i 0.659574 1.14242i
\(479\) 22.4648 + 12.9700i 1.02644 + 0.592617i 0.915963 0.401262i \(-0.131428\pi\)
0.110479 + 0.993878i \(0.464762\pi\)
\(480\) 0 0
\(481\) 25.5308 14.0925i 1.16411 0.642564i
\(482\) −5.72600 −0.260812
\(483\) −2.52116 1.45559i −0.114717 0.0662318i
\(484\) 4.84304 8.38839i 0.220138 0.381290i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) −15.6047 + 9.00939i −0.707117 + 0.408254i −0.809993 0.586440i \(-0.800529\pi\)
0.102875 + 0.994694i \(0.467196\pi\)
\(488\) −2.48320 + 1.43368i −0.112409 + 0.0648995i
\(489\) 1.84669i 0.0835101i
\(490\) 0 0
\(491\) −15.7564 + 27.2908i −0.711075 + 1.23162i 0.253379 + 0.967367i \(0.418458\pi\)
−0.964454 + 0.264251i \(0.914875\pi\)
\(492\) −9.67739 5.58725i −0.436291 0.251893i
\(493\) 1.14769 0.0516894
\(494\) −1.55607 + 2.57932i −0.0700111 + 0.116049i
\(495\) 0 0
\(496\) 3.78170 + 2.18336i 0.169803 + 0.0980360i
\(497\) 16.6899 28.9078i 0.748646 1.29669i
\(498\) 4.38865 + 7.60136i 0.196660 + 0.340625i
\(499\) 5.57925i 0.249762i −0.992172 0.124881i \(-0.960145\pi\)
0.992172 0.124881i \(-0.0398549\pi\)
\(500\) 0 0
\(501\) −18.8898 + 10.9060i −0.843935 + 0.487246i
\(502\) 6.66342i 0.297403i
\(503\) 18.8126 + 32.5844i 0.838812 + 1.45286i 0.890889 + 0.454222i \(0.150083\pi\)
−0.0520768 + 0.998643i \(0.516584\pi\)
\(504\) −1.46593 + 2.53906i −0.0652975 + 0.113099i
\(505\) 0 0
\(506\) 1.13819 0.0505985
\(507\) −12.9904 0.500000i −0.576923 0.0222058i
\(508\) 7.60521 0.337426
\(509\) 25.5466 + 14.7493i 1.13233 + 0.653753i 0.944521 0.328452i \(-0.106527\pi\)
0.187813 + 0.982205i \(0.439860\pi\)
\(510\) 0 0
\(511\) −12.0081 20.7987i −0.531209 0.920081i
\(512\) 1.00000i 0.0441942i
\(513\) −0.723543 + 0.417738i −0.0319452 + 0.0184436i
\(514\) −8.68809 + 5.01607i −0.383215 + 0.221249i
\(515\) 0 0
\(516\) −3.94036 6.82490i −0.173465 0.300450i
\(517\) 6.27515 10.8689i 0.275981 0.478013i
\(518\) −20.5361 11.8565i −0.902305 0.520946i
\(519\) −11.8788 −0.521423
\(520\) 0 0
\(521\) −3.16676 −0.138738 −0.0693692 0.997591i \(-0.522099\pi\)
−0.0693692 + 0.997591i \(0.522099\pi\)
\(522\) 1.79762 + 1.03786i 0.0786797 + 0.0454257i
\(523\) −15.7956 + 27.3587i −0.690691 + 1.19631i 0.280920 + 0.959731i \(0.409360\pi\)
−0.971612 + 0.236581i \(0.923973\pi\)
\(524\) 2.72670 + 4.72279i 0.119117 + 0.206316i
\(525\) 0 0
\(526\) −21.6856 + 12.5202i −0.945536 + 0.545906i
\(527\) 2.09096 1.20721i 0.0910834 0.0525870i
\(528\) 1.14626i 0.0498848i
\(529\) 11.0070 + 19.0647i 0.478566 + 0.828901i
\(530\) 0 0
\(531\) 4.75442 + 2.74496i 0.206324 + 0.119121i
\(532\) 2.44949 0.106199
\(533\) −35.2734 + 19.4702i −1.52786 + 0.843350i
\(534\) 4.53882 0.196414
\(535\) 0 0
\(536\) 5.13165 8.88828i 0.221654 0.383915i
\(537\) 4.47746 + 7.75519i 0.193217 + 0.334661i
\(538\) 23.2536i 1.00253i
\(539\) −1.58410 + 0.914578i −0.0682318 + 0.0393937i
\(540\) 0 0
\(541\) 10.1369i 0.435821i 0.975969 + 0.217911i \(0.0699241\pi\)
−0.975969 + 0.217911i \(0.930076\pi\)
\(542\) 3.07554 + 5.32698i 0.132106 + 0.228814i
\(543\) −10.6149 + 18.3855i −0.455527 + 0.788996i
\(544\) 0.478838 + 0.276457i 0.0205300 + 0.0118530i
\(545\) 0 0
\(546\) 5.10841 + 9.25467i 0.218620 + 0.396063i
\(547\) −32.1457 −1.37445 −0.687225 0.726445i \(-0.741171\pi\)
−0.687225 + 0.726445i \(0.741171\pi\)
\(548\) 0.276333 + 0.159541i 0.0118044 + 0.00681525i
\(549\) −1.43368 + 2.48320i −0.0611878 + 0.105980i
\(550\) 0 0
\(551\) 1.73421i 0.0738797i
\(552\) −0.859921 + 0.496476i −0.0366007 + 0.0211314i
\(553\) 4.29031 2.47701i 0.182443 0.105333i
\(554\) 6.88928i 0.292697i
\(555\) 0 0
\(556\) 5.84046 10.1160i 0.247691 0.429013i
\(557\) −4.50313 2.59988i −0.190804 0.110161i 0.401555 0.915835i \(-0.368470\pi\)
−0.592359 + 0.805674i \(0.701803\pi\)
\(558\) 4.36673 0.184858
\(559\) −28.4091 0.546531i −1.20158 0.0231158i
\(560\) 0 0
\(561\) −0.548875 0.316893i −0.0231735 0.0133792i
\(562\) 0.272809 0.472519i 0.0115077 0.0199320i
\(563\) 8.18180 + 14.1713i 0.344822 + 0.597249i 0.985321 0.170710i \(-0.0546060\pi\)
−0.640500 + 0.767958i \(0.721273\pi\)
\(564\) 10.9489i 0.461030i
\(565\) 0 0
\(566\) −7.29764 + 4.21329i −0.306743 + 0.177098i
\(567\) 2.93185i 0.123126i
\(568\) −5.69263 9.85992i −0.238857 0.413713i
\(569\) 7.90761 13.6964i 0.331504 0.574182i −0.651303 0.758818i \(-0.725777\pi\)
0.982807 + 0.184636i \(0.0591105\pi\)
\(570\) 0 0
\(571\) −18.8170 −0.787467 −0.393734 0.919225i \(-0.628817\pi\)
−0.393734 + 0.919225i \(0.628817\pi\)
\(572\) −3.53880 2.13492i −0.147965 0.0892654i
\(573\) −4.50694 −0.188280
\(574\) 28.3727 + 16.3810i 1.18425 + 0.683729i
\(575\) 0 0
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 22.3581i 0.930778i 0.885106 + 0.465389i \(0.154086\pi\)
−0.885106 + 0.465389i \(0.845914\pi\)
\(578\) −14.4577 + 8.34714i −0.601360 + 0.347195i
\(579\) −2.30090 + 1.32843i −0.0956223 + 0.0552075i
\(580\) 0 0
\(581\) −12.8669 22.2861i −0.533807 0.924582i
\(582\) −5.30847 + 9.19453i −0.220043 + 0.381126i
\(583\) −3.54146 2.04466i −0.146672 0.0846813i
\(584\) −8.19151 −0.338967
\(585\) 0 0
\(586\) 6.77829 0.280009
\(587\) 37.1967 + 21.4755i 1.53527 + 0.886389i 0.999106 + 0.0422761i \(0.0134609\pi\)
0.536165 + 0.844113i \(0.319872\pi\)
\(588\) 0.797877 1.38196i 0.0329039 0.0569912i
\(589\) −1.82415 3.15952i −0.0751627 0.130186i
\(590\) 0 0
\(591\) −1.68375 + 0.972112i −0.0692601 + 0.0399873i
\(592\) −7.00449 + 4.04404i −0.287883 + 0.166209i
\(593\) 30.8372i 1.26633i 0.774016 + 0.633166i \(0.218245\pi\)
−0.774016 + 0.633166i \(0.781755\pi\)
\(594\) −0.573132 0.992694i −0.0235159 0.0407307i
\(595\) 0 0
\(596\) 4.33221 + 2.50120i 0.177454 + 0.102453i
\(597\) 15.0175 0.614627
\(598\) −0.0688616 + 3.57948i −0.00281596 + 0.146376i
\(599\) 9.63447 0.393654 0.196827 0.980438i \(-0.436936\pi\)
0.196827 + 0.980438i \(0.436936\pi\)
\(600\) 0 0
\(601\) −17.1757 + 29.7491i −0.700609 + 1.21349i 0.267643 + 0.963518i \(0.413755\pi\)
−0.968253 + 0.249973i \(0.919578\pi\)
\(602\) 11.5525 + 20.0096i 0.470847 + 0.815531i
\(603\) 10.2633i 0.417954i
\(604\) −11.1722 + 6.45025i −0.454588 + 0.262457i
\(605\) 0 0
\(606\) 14.1463i 0.574653i
\(607\) 14.7047 + 25.4692i 0.596844 + 1.03376i 0.993284 + 0.115704i \(0.0369124\pi\)
−0.396439 + 0.918061i \(0.629754\pi\)
\(608\) 0.417738 0.723543i 0.0169415 0.0293435i
\(609\) −5.27035 3.04284i −0.213565 0.123302i
\(610\) 0 0
\(611\) 33.8018 + 20.3923i 1.36748 + 0.824983i
\(612\) 0.552914 0.0223502
\(613\) 33.2034 + 19.1700i 1.34107 + 0.774268i 0.986965 0.160938i \(-0.0514518\pi\)
0.354106 + 0.935205i \(0.384785\pi\)
\(614\) 17.3216 30.0019i 0.699042 1.21078i
\(615\) 0 0
\(616\) 3.36068i 0.135406i
\(617\) 0.526095 0.303741i 0.0211798 0.0122281i −0.489373 0.872075i \(-0.662774\pi\)
0.510553 + 0.859847i \(0.329441\pi\)
\(618\) 5.82402 3.36250i 0.234277 0.135260i
\(619\) 28.6848i 1.15294i 0.817118 + 0.576470i \(0.195570\pi\)
−0.817118 + 0.576470i \(0.804430\pi\)
\(620\) 0 0
\(621\) −0.496476 + 0.859921i −0.0199229 + 0.0345075i
\(622\) −17.5113 10.1101i −0.702137 0.405379i
\(623\) −13.3071 −0.533139
\(624\) 3.60488 + 0.0693504i 0.144311 + 0.00277624i
\(625\) 0 0
\(626\) −19.3406 11.1663i −0.773006 0.446295i
\(627\) −0.478838 + 0.829371i −0.0191229 + 0.0331219i
\(628\) 4.33266 + 7.50438i 0.172892 + 0.299457i
\(629\) 4.47202i 0.178311i
\(630\) 0 0
\(631\) 3.94547 2.27792i 0.157067 0.0906824i −0.419407 0.907798i \(-0.637762\pi\)
0.576473 + 0.817116i \(0.304429\pi\)
\(632\) 1.68973i 0.0672137i
\(633\) 0.379882 + 0.657974i 0.0150989 + 0.0261521i
\(634\) −5.71462 + 9.89801i −0.226957 + 0.393100i
\(635\) 0 0
\(636\) 3.56753 0.141462
\(637\) −2.78041 5.03715i −0.110164 0.199579i
\(638\) 2.37931 0.0941980
\(639\) −9.85992 5.69263i −0.390052 0.225197i
\(640\) 0 0
\(641\) −11.8057 20.4481i −0.466297 0.807650i 0.532962 0.846139i \(-0.321079\pi\)
−0.999259 + 0.0384890i \(0.987746\pi\)
\(642\) 0.246769i 0.00973921i
\(643\) 9.66855 5.58214i 0.381290 0.220138i −0.297089 0.954850i \(-0.596016\pi\)
0.678379 + 0.734712i \(0.262683\pi\)
\(644\) 2.52116 1.45559i 0.0993477 0.0573584i
\(645\) 0 0
\(646\) −0.230973 0.400057i −0.00908752 0.0157400i
\(647\) −5.68594 + 9.84834i −0.223538 + 0.387178i −0.955880 0.293758i \(-0.905094\pi\)
0.732342 + 0.680937i \(0.238427\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) 6.29291 0.247018
\(650\) 0 0
\(651\) −12.8026 −0.501774
\(652\) 1.59928 + 0.923344i 0.0626326 + 0.0361609i
\(653\) 4.51599 7.82192i 0.176724 0.306096i −0.764032 0.645178i \(-0.776783\pi\)
0.940757 + 0.339082i \(0.110117\pi\)
\(654\) 2.06899 + 3.58359i 0.0809037 + 0.140129i
\(655\) 0 0
\(656\) 9.67739 5.58725i 0.377839 0.218145i
\(657\) −7.09405 + 4.09575i −0.276765 + 0.159791i
\(658\) 32.1005i 1.25141i
\(659\) −9.57118 16.5778i −0.372840 0.645778i 0.617161 0.786837i \(-0.288283\pi\)
−0.990001 + 0.141059i \(0.954949\pi\)
\(660\) 0 0
\(661\) 15.6116 + 9.01337i 0.607221 + 0.350579i 0.771877 0.635772i \(-0.219318\pi\)
−0.164656 + 0.986351i \(0.552651\pi\)
\(662\) −1.77365 −0.0689347
\(663\) 1.02980 1.70698i 0.0399943 0.0662937i
\(664\) −8.77729 −0.340625
\(665\) 0 0
\(666\) −4.04404 + 7.00449i −0.156703 + 0.271418i
\(667\) −1.03054 1.78495i −0.0399027 0.0691135i
\(668\) 21.8121i 0.843935i
\(669\) 18.5939 10.7352i 0.718883 0.415047i
\(670\) 0 0
\(671\) 3.28674i 0.126883i
\(672\) −1.46593 2.53906i −0.0565493 0.0979463i
\(673\) −3.91832 + 6.78672i −0.151040 + 0.261609i −0.931610 0.363459i \(-0.881596\pi\)
0.780570 + 0.625068i \(0.214929\pi\)
\(674\) −10.3944 6.00122i −0.400378 0.231158i
\(675\) 0 0
\(676\) 6.92820 11.0000i 0.266469 0.423077i
\(677\) −23.4860 −0.902641 −0.451321 0.892362i \(-0.649047\pi\)
−0.451321 + 0.892362i \(0.649047\pi\)
\(678\) 1.43488 + 0.828427i 0.0551062 + 0.0318156i
\(679\) 15.5636 26.9570i 0.597278 1.03452i
\(680\) 0 0
\(681\) 22.1017i 0.846939i
\(682\) 4.33483 2.50271i 0.165989 0.0958338i
\(683\) −15.4729 + 8.93327i −0.592053 + 0.341822i −0.765909 0.642949i \(-0.777711\pi\)
0.173856 + 0.984771i \(0.444377\pi\)
\(684\) 0.835475i 0.0319452i
\(685\) 0 0
\(686\) 7.92222 13.7217i 0.302472 0.523897i
\(687\) 18.7380 + 10.8184i 0.714901 + 0.412748i
\(688\) 7.88072 0.300450
\(689\) 6.64452 11.0138i 0.253136 0.419594i
\(690\) 0 0
\(691\) −18.7634 10.8331i −0.713795 0.412109i 0.0986699 0.995120i \(-0.468541\pi\)
−0.812464 + 0.583011i \(0.801875\pi\)
\(692\) 5.93942 10.2874i 0.225783 0.391067i
\(693\) 1.68034 + 2.91043i 0.0638308 + 0.110558i
\(694\) 27.5585i 1.04611i
\(695\) 0 0
\(696\) −1.79762 + 1.03786i −0.0681386 + 0.0393398i
\(697\) 6.17854i 0.234029i
\(698\) −7.08260 12.2674i −0.268080 0.464329i
\(699\) 2.97834 5.15864i 0.112651 0.195118i
\(700\) 0 0
\(701\) 42.8171 1.61718 0.808590 0.588372i \(-0.200231\pi\)
0.808590 + 0.588372i \(0.200231\pi\)
\(702\) 3.15660 1.74238i 0.119138 0.0657620i
\(703\) 6.75739 0.254860
\(704\) 0.992694 + 0.573132i 0.0374136 + 0.0216007i
\(705\) 0 0
\(706\) −15.7970 27.3612i −0.594528 1.02975i
\(707\) 41.4747i 1.55982i
\(708\) −4.75442 + 2.74496i −0.178682 + 0.103162i
\(709\) 10.7389 6.20012i 0.403309 0.232851i −0.284602 0.958646i \(-0.591861\pi\)
0.687911 + 0.725795i \(0.258528\pi\)
\(710\) 0 0
\(711\) −0.844863 1.46335i −0.0316848 0.0548798i
\(712\) −2.26941 + 3.93073i −0.0850497 + 0.147310i
\(713\) −3.75504 2.16798i −0.140628 0.0811913i
\(714\) −1.62106 −0.0606667
\(715\) 0 0
\(716\) −8.95492 −0.334661
\(717\) 24.9769 + 14.4204i 0.932778 + 0.538540i
\(718\) 6.08568 10.5407i 0.227116 0.393376i
\(719\) 0.822357 + 1.42436i 0.0306687 + 0.0531198i 0.880952 0.473205i \(-0.156903\pi\)
−0.850284 + 0.526325i \(0.823570\pi\)
\(720\) 0 0
\(721\) −17.0752 + 9.85835i −0.635913 + 0.367144i
\(722\) 15.8500 9.15099i 0.589875 0.340565i
\(723\) 5.72600i 0.212952i
\(724\) −10.6149 18.3855i −0.394498 0.683290i
\(725\) 0 0
\(726\) 8.38839 + 4.84304i 0.311322 + 0.179742i
\(727\) −48.0577 −1.78236 −0.891180 0.453650i \(-0.850122\pi\)
−0.891180 + 0.453650i \(0.850122\pi\)
\(728\) −10.5690 0.203325i −0.391713 0.00753572i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 2.17868 3.77359i 0.0805814 0.139571i
\(732\) −1.43368 2.48320i −0.0529902 0.0917817i
\(733\) 5.56731i 0.205633i −0.994700 0.102817i \(-0.967214\pi\)
0.994700 0.102817i \(-0.0327855\pi\)
\(734\) −25.9768 + 14.9977i −0.958820 + 0.553575i
\(735\) 0 0
\(736\) 0.992952i 0.0366007i
\(737\) −5.88223 10.1883i −0.216675 0.375292i
\(738\) 5.58725 9.67739i 0.205669 0.356230i
\(739\) −44.1546 25.4927i −1.62425 0.937763i −0.985765 0.168132i \(-0.946227\pi\)
−0.638489 0.769631i \(-0.720440\pi\)
\(740\) 0 0
\(741\) −2.57932 1.55607i −0.0947536 0.0571638i
\(742\) −10.4595 −0.383979
\(743\) −35.1316 20.2832i −1.28885 0.744120i −0.310404 0.950605i \(-0.600464\pi\)
−0.978450 + 0.206485i \(0.933798\pi\)
\(744\) −2.18336 + 3.78170i −0.0800460 + 0.138644i
\(745\) 0 0
\(746\) 36.7571i 1.34577i
\(747\) −7.60136 + 4.38865i −0.278119 + 0.160572i
\(748\) 0.548875 0.316893i 0.0200688 0.0115868i
\(749\) 0.723491i 0.0264358i
\(750\) 0 0
\(751\) 12.1132 20.9807i 0.442018 0.765597i −0.555822 0.831302i \(-0.687596\pi\)
0.997839 + 0.0657048i \(0.0209296\pi\)
\(752\) −9.48200 5.47443i −0.345773 0.199632i
\(753\) 6.66342 0.242829
\(754\) −0.143951 + 7.48270i −0.00524240 + 0.272504i
\(755\) 0 0
\(756\) −2.53906 1.46593i −0.0923446 0.0533152i
\(757\) 21.0629 36.4820i 0.765544 1.32596i −0.174415 0.984672i \(-0.555803\pi\)
0.939959 0.341288i \(-0.110863\pi\)
\(758\) −2.58479 4.47699i −0.0938838 0.162612i
\(759\) 1.13819i 0.0413135i
\(760\) 0 0
\(761\) −7.41955 + 4.28368i −0.268959 + 0.155283i −0.628414 0.777879i \(-0.716296\pi\)
0.359456 + 0.933162i \(0.382962\pi\)
\(762\) 7.60521i 0.275508i
\(763\) −6.06596 10.5066i −0.219602 0.380363i
\(764\) 2.25347 3.90313i 0.0815277 0.141210i
\(765\) 0 0
\(766\) 2.80196 0.101239
\(767\) −0.380728 + 19.7905i −0.0137473 + 0.714595i
\(768\) −1.00000 −0.0360844
\(769\) −42.1226 24.3195i −1.51898 0.876983i −0.999750 0.0223481i \(-0.992886\pi\)
−0.519229 0.854635i \(-0.673781\pi\)
\(770\) 0 0
\(771\) −5.01607 8.68809i −0.180649 0.312894i
\(772\) 2.65685i 0.0956223i
\(773\) 42.1294 24.3234i 1.51529 0.874853i 0.515450 0.856919i \(-0.327625\pi\)
0.999839 0.0179335i \(-0.00570872\pi\)
\(774\) 6.82490 3.94036i 0.245316 0.141633i
\(775\) 0 0
\(776\) −5.30847 9.19453i −0.190563 0.330065i
\(777\) 11.8565 20.5361i 0.425351 0.736729i
\(778\) −10.3002 5.94680i −0.369279 0.213203i
\(779\) −9.33601 −0.334497
\(780\) 0 0
\(781\) −13.0505 −0.466984
\(782\) −0.475463 0.274509i −0.0170025 0.00981641i
\(783\) −1.03786 + 1.79762i −0.0370899 + 0.0642417i
\(784\)