Properties

Label 1950.2.bc.e.751.3
Level $1950$
Weight $2$
Character 1950.751
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 751.3
Root \(-0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1950.751
Dual form 1950.2.bc.e.901.3

$q$-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{3} + 4q^{4} - 4q^{9} + O(q^{10}) \) \( 8q - 4q^{3} + 4q^{4} - 4q^{9} - 12q^{11} - 8q^{12} - 8q^{14} - 4q^{16} + 4q^{17} + 12q^{19} + 8q^{22} + 4q^{23} + 8q^{27} + 4q^{29} + 12q^{33} + 4q^{36} - 24q^{37} + 4q^{42} - 4q^{43} + 12q^{46} - 4q^{48} - 16q^{49} - 8q^{51} - 8q^{53} - 4q^{56} + 12q^{58} - 12q^{59} - 16q^{61} + 4q^{62} - 8q^{64} - 16q^{66} + 24q^{67} - 4q^{68} + 4q^{69} + 60q^{71} + 16q^{74} + 12q^{76} - 8q^{77} - 8q^{79} - 4q^{81} - 20q^{82} + 4q^{87} - 8q^{88} + 24q^{89} + 8q^{91} + 8q^{92} - 24q^{93} + 16q^{94} + 12q^{97} + 12q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

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 \(-0.520259\pi\)
−0.896073 + 0.443908i \(0.853592\pi\)
\(8\) 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 −0.642132 0.766594i \(-0.721950\pi\)
0.342824 + 0.939400i \(0.388617\pi\)
\(12\) −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 \(-0.854692\pi\)
0.830551 + 0.556942i \(0.188026\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 0.723543 + 0.417738i 0.165992 + 0.0958356i 0.580695 0.814121i \(-0.302781\pi\)
−0.414703 + 0.909957i \(0.636114\pi\)
\(20\) 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 \(-0.199678\pi\)
−0.913134 + 0.407661i \(0.866345\pi\)
\(24\) −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 0.946152 0.323722i \(-0.104934\pi\)
−0.753427 + 0.657531i \(0.771601\pi\)
\(30\) 0 0
\(31\) 4.36673i 0.784288i 0.919904 + 0.392144i \(0.128266\pi\)
−0.919904 + 0.392144i \(0.871734\pi\)
\(32\) −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 \(-0.898165\pi\)
−0.202271 + 0.979330i \(0.564832\pi\)
\(38\) 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 −0.511443 + 0.859317i \(0.670889\pi\)
−0.999912 + 0.0132641i \(0.995778\pi\)
\(42\) 1.46593 + 2.53906i 0.226197 + 0.391785i
\(43\) 3.94036 6.82490i 0.600899 1.04079i −0.391786 0.920056i \(-0.628143\pi\)
0.992685 0.120732i \(-0.0385240\pi\)
\(44\) 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 \(-0.578794\pi\)
−0.245019 + 0.969518i \(0.578794\pi\)
\(54\) 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 0.157497 0.987520i \(-0.449658\pi\)
−0.776469 + 0.630156i \(0.782991\pi\)
\(60\) 0 0
\(61\) −1.43368 + 2.48320i −0.183563 + 0.317941i −0.943091 0.332533i \(-0.892097\pi\)
0.759528 + 0.650474i \(0.225430\pi\)
\(62\) 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 \(-0.882356\pi\)
−0.153401 + 0.988164i \(0.549023\pi\)
\(68\) 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 0.953717 0.300705i \(-0.0972220\pi\)
0.216440 + 0.976296i \(0.430555\pi\)
\(72\) 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 −0.693646 0.720316i \(-0.743997\pi\)
0.276989 + 0.960873i \(0.410663\pi\)
\(90\) 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 \(-0.514528\pi\)
−0.887937 + 0.459965i \(0.847862\pi\)
\(98\) 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 −0.967122 0.254314i \(-0.918150\pi\)
0.263319 0.964709i \(-0.415183\pi\)
\(102\) 0.478838 0.276457i 0.0474120 0.0273733i
\(103\) 6.72500 0.662634 0.331317 0.943519i \(-0.392507\pi\)
0.331317 + 0.943519i \(0.392507\pi\)
\(104\) −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 \(-0.170464\pi\)
−0.871928 + 0.489634i \(0.837130\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 4.13797i 0.396346i 0.980167 + 0.198173i \(0.0635008\pi\)
−0.980167 + 0.198173i \(0.936499\pi\)
\(110\) 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 \(-0.808502\pi\)
0.902357 + 0.430988i \(0.141835\pi\)
\(114\) −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 \(-0.276223\pi\)
−0.983948 + 0.178456i \(0.942890\pi\)
\(128\) −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 \(-0.337672\pi\)
−0.511758 + 0.859130i \(0.671006\pi\)
\(138\) 0.992952i 0.0845257i
\(139\) −5.84046 + 10.1160i −0.495381 + 0.858026i −0.999986 0.00532505i \(-0.998305\pi\)
0.504605 + 0.863351i \(0.331638\pi\)
\(140\) 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 0.666845 0.745196i \(-0.267644\pi\)
−0.311937 + 0.950103i \(0.600978\pi\)
\(150\) 0 0
\(151\) 12.9005i 1.04983i −0.851156 0.524914i \(-0.824098\pi\)
0.851156 0.524914i \(-0.175902\pi\)
\(152\) 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 \(-0.612387\pi\)
−0.345784 + 0.938314i \(0.612387\pi\)
\(158\) 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 \(-0.356374\pi\)
−0.561323 + 0.827597i \(0.689708\pi\)
\(164\) 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 \(-0.346900\pi\)
0.999092 + 0.0426077i \(0.0135665\pi\)
\(168\) 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 \(-0.684199\pi\)
0.998483 + 0.0550519i \(0.0175324\pi\)
\(174\) 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 0.648759 0.760994i \(-0.275288\pi\)
−0.983420 + 0.181344i \(0.941955\pi\)
\(180\) 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 −0.935963 0.352098i \(-0.885468\pi\)
0.772908 + 0.634519i \(0.218802\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 2.30090 1.32843i 0.165623 0.0956223i −0.414898 0.909868i \(-0.636183\pi\)
0.580520 + 0.814246i \(0.302849\pi\)
\(194\) −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 \(-0.644603\pi\)
0.558780 + 0.829316i \(0.311269\pi\)
\(198\) −0.573132 0.992694i −0.0407307 0.0705477i
\(199\) 7.50877 13.0056i 0.532282 0.921940i −0.467007 0.884253i \(-0.654668\pi\)
0.999290 0.0376865i \(-0.0119988\pi\)
\(200\) 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 0.852653 0.522477i \(-0.174992\pi\)
−0.878805 + 0.477181i \(0.841659\pi\)
\(212\) −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 \(-0.922013\pi\)
−0.275005 + 0.961443i \(0.588680\pi\)
\(224\) 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 \(-0.0712325\pi\)
0.295344 + 0.955391i \(0.404566\pi\)
\(228\) −0.723543 0.417738i −0.0479178 0.0276654i
\(229\) 21.6368i 1.42980i −0.699226 0.714901i \(-0.746472\pi\)
0.699226 0.714901i \(-0.253528\pi\)
\(230\) 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 \(-0.562509\pi\)
−0.195118 + 0.980780i \(0.562509\pi\)
\(234\) 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 \(-0.617377\pi\)
0.360451 0.932778i \(-0.382623\pi\)
\(240\) 0 0
\(241\) 4.95886 + 2.86300i 0.319428 + 0.184422i 0.651138 0.758960i \(-0.274292\pi\)
−0.331709 + 0.943382i \(0.607625\pi\)
\(242\) 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 −0.741511 0.670940i \(-0.765891\pi\)
0.951807 + 0.306697i \(0.0992240\pi\)
\(252\) 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 \(-0.267965\pi\)
−0.978988 + 0.203920i \(0.934632\pi\)
\(258\) −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 −0.936450 0.350800i \(-0.885910\pi\)
0.164423 0.986390i \(-0.447424\pi\)
\(264\) 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 0.256367 + 0.966579i \(0.417474\pi\)
−0.965266 + 0.261269i \(0.915859\pi\)
\(270\) 0 0
\(271\) −5.32698 + 3.07554i −0.323591 + 0.186826i −0.652992 0.757365i \(-0.726487\pi\)
0.329401 + 0.944190i \(0.393153\pi\)
\(272\) 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 \(-0.899693\pi\)
0.743790 + 0.668414i \(0.233026\pi\)
\(278\) 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 \(-0.994819\pi\)
0.999868 0.0162744i \(-0.00518053\pi\)
\(282\) 5.47443 9.48200i 0.325998 0.564645i
\(283\) −4.21329 7.29764i −0.250454 0.433799i 0.713197 0.700964i \(-0.247247\pi\)
−0.963651 + 0.267164i \(0.913913\pi\)
\(284\) 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 \(-0.269890\pi\)
−0.318632 + 0.947879i \(0.603223\pi\)
\(294\) 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 \(-0.717420\pi\)
−0.631157 + 0.775655i \(0.717420\pi\)
\(314\) −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 0.541619 0.840624i \(-0.317811\pi\)
−0.457192 + 0.889368i \(0.651145\pi\)
\(332\) −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 \(-0.606006\pi\)
−0.326907 + 0.945056i \(0.606006\pi\)
\(338\) 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 −0.212917 0.977070i \(-0.568296\pi\)
0.952626 0.304143i \(-0.0983702\pi\)
\(348\) −1.03786 1.79762i −0.0556349 0.0963625i
\(349\) 12.2674 7.08260i 0.656660 0.379123i −0.134343 0.990935i \(-0.542892\pi\)
0.791003 + 0.611812i \(0.209559\pi\)
\(350\) 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 \(-0.984576\pi\)
−0.457465 + 0.889228i \(0.651243\pi\)
\(354\) 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 \(-0.895917\pi\)
0.947015 0.321190i \(-0.104083\pi\)
\(360\) 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 −0.930262 0.366897i \(-0.880420\pi\)
0.147389 0.989079i \(-0.452913\pi\)
\(368\) −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 0.209650 0.977777i \(-0.432768\pi\)
0.741954 0.670450i \(-0.233899\pi\)
\(374\) −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 −0.380590 0.924744i \(-0.624279\pi\)
0.610557 + 0.791972i \(0.290946\pi\)
\(380\) 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 \(-0.310527\pi\)
−0.436721 + 0.899597i \(0.643860\pi\)
\(384\) 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 −0.950087 0.311986i \(-0.899006\pi\)
−0.745231 0.666806i \(-0.767661\pi\)
\(398\) 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 0.217335 0.976097i \(-0.430264\pi\)
0.953992 + 0.299831i \(0.0969303\pi\)
\(402\) 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 0.118110 0.993000i \(-0.462316\pi\)
−0.800908 + 0.598787i \(0.795650\pi\)
\(410\) 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 0.524888 0.851171i \(-0.324107\pi\)
−0.999580 + 0.0289808i \(0.990774\pi\)
\(420\) 0 0
\(421\) 21.5769i 1.05160i −0.850610 0.525798i \(-0.823767\pi\)
0.850610 0.525798i \(-0.176233\pi\)
\(422\) −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 −0.486682 0.873579i \(-0.661793\pi\)
0.513201 + 0.858269i \(0.328460\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −5.30090 + 9.18143i −0.254745 + 0.441232i −0.964826 0.262888i \(-0.915325\pi\)
0.710081 + 0.704120i \(0.248658\pi\)
\(434\) 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 0.623405 0.781899i \(-0.285749\pi\)
−0.988847 + 0.148935i \(0.952415\pi\)
\(440\) 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 \(-0.644669\pi\)
−0.439005 + 0.898485i \(0.644669\pi\)
\(444\) 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 0.926050 0.377400i \(-0.123182\pi\)
0.136187 + 0.990683i \(0.456515\pi\)
\(450\) 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 −0.720924 + 0.693014i \(0.756282\pi\)
−0.960630 + 0.277832i \(0.910384\pi\)
\(458\) −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 0.786619 0.617439i \(-0.211830\pi\)
−0.141409 + 0.989951i \(0.545163\pi\)
\(462\) −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 \(-0.525342\pi\)
−0.0795316 + 0.996832i \(0.525342\pi\)
\(468\) 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 0.110479 0.993878i \(-0.464762\pi\)
0.915963 + 0.401262i \(0.131428\pi\)
\(480\) 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 \(-0.199471\pi\)
−0.102875 + 0.994694i \(0.532804\pi\)
\(488\) 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 −0.964454 0.264251i \(-0.914875\pi\)
0.253379 0.967367i \(-0.418458\pi\)
\(492\) 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 \(0.0398549\pi\)
−0.992172 + 0.124881i \(0.960145\pi\)
\(500\) 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 0.0520768 + 0.998643i \(0.483416\pi\)
−0.890889 + 0.454222i \(0.849917\pi\)
\(504\) −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 0.187813 0.982205i \(-0.439860\pi\)
0.944521 + 0.328452i \(0.106527\pi\)
\(510\) 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 0.971612 + 0.236581i \(0.0760270\pi\)
−0.280920 + 0.959731i \(0.590640\pi\)
\(524\) 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 \(-0.930076\pi\)
0.975969 0.217911i \(-0.0699241\pi\)
\(542\) −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 \(-0.258829\pi\)
0.687225 + 0.726445i \(0.258829\pi\)
\(548\) −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 \(-0.631530\pi\)
0.592359 + 0.805674i \(0.298197\pi\)
\(558\) −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 \(-0.945394\pi\)
0.640500 + 0.767958i \(0.278727\pi\)
\(564\) 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 0.982807 0.184636i \(-0.0591105\pi\)
−0.651303 + 0.758818i \(0.725777\pi\)
\(570\) 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 −0.536165 + 0.844113i \(0.680128\pi\)
−0.999106 + 0.0422761i \(0.986539\pi\)
\(588\) −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 −0.968253 0.249973i \(-0.919578\pi\)
0.267643 0.963518i \(-0.413755\pi\)
\(602\) −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 0.396439 + 0.918061i \(0.370246\pi\)
−0.993284 + 0.115704i \(0.963088\pi\)
\(608\) −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 \(-0.948548\pi\)
−0.354106 + 0.935205i \(0.615215\pi\)
\(614\) 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 \(-0.337226\pi\)
−0.510553 + 0.859847i \(0.670559\pi\)
\(618\) −5.82402 3.36250i −0.234277 0.135260i
\(619\) 28.6848i 1.15294i −0.817118 0.576470i \(-0.804430\pi\)
0.817118 0.576470i \(-0.195570\pi\)
\(620\) 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 0.576473 0.817116i \(-0.304429\pi\)
−0.419407 + 0.907798i \(0.637762\pi\)
\(632\) 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 −0.999259 0.0384890i \(-0.987746\pi\)
0.532962 + 0.846139i \(0.321079\pi\)
\(642\) 0.246769i 0.00973921i
\(643\) −9.66855 5.58214i −0.381290 0.220138i 0.297089 0.954850i \(-0.403984\pi\)
−0.678379 + 0.734712i \(0.737317\pi\)
\(644\) 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 \(-0.0949061\pi\)
−0.732342 + 0.680937i \(0.761573\pi\)
\(648\) −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 \(-0.223217\pi\)
−0.940757 + 0.339082i \(0.889883\pi\)
\(654\) 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 −0.990001 0.141059i \(-0.954949\pi\)
0.617161 + 0.786837i \(0.288283\pi\)
\(660\) 0 0
\(661\) 15.6116 9.01337i 0.607221 0.350579i −0.164656 0.986351i \(-0.552651\pi\)
0.771877 + 0.635772i \(0.219318\pi\)
\(662\) 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 \(-0.118404\pi\)
−0.780570 + 0.625068i \(0.785071\pi\)
\(674\) −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 \(-0.350953\pi\)
0.451321 + 0.892362i \(0.350953\pi\)
\(678\) −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 \(-0.222289\pi\)
−0.173856 + 0.984771i \(0.555623\pi\)
\(684\) 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 −0.812464 0.583011i \(-0.801875\pi\)
0.0986699 + 0.995120i \(0.468541\pi\)
\(692\) −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 0.687911 0.725795i \(-0.258528\pi\)
−0.284602 + 0.958646i \(0.591861\pi\)
\(710\) 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 −0.850284 0.526325i \(-0.823570\pi\)
0.880952 + 0.473205i \(0.156903\pi\)
\(720\) 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 \(-0.149878\pi\)
0.891180 + 0.453650i \(0.149878\pi\)
\(728\) 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 −0.638489 + 0.769631i \(0.720440\pi\)
−0.985765 + 0.168132i \(0.946227\pi\)
\(740\) 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 \(-0.399536\pi\)
0.978450 + 0.206485i \(0.0662024\pi\)
\(744\) −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 0.997839 0.0657048i \(-0.0209296\pi\)
−0.555822 + 0.831302i \(0.687596\pi\)
\(752\) 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 −0.939959 0.341288i \(-0.889137\pi\)
0.174415 0.984672i \(-0.444197\pi\)
\(758\) 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 0.359456 0.933162i \(-0.382962\pi\)
−0.628414 + 0.777879i \(0.716296\pi\)
\(762\) 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 −0.519229 + 0.854635i \(0.673781\pi\)
−0.999750 + 0.0223481i \(0.992886\pi\)
\(770\) 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 −0.999839 0.0179335i \(-0.994291\pi\)
−0.515450 0.856919i \(-0.672375\pi\)
\(774\) 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 +