Properties

Label 1950.2.bc.f.751.1
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: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
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 751.1
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1950.751
Dual form 1950.2.bc.f.901.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-0.807007 - 0.465926i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(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} +(-0.807007 - 0.465926i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.45680 - 0.841081i) q^{11} +1.00000 q^{12} +(-1.86250 - 3.08725i) q^{13} +0.931852 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.27646 + 2.21089i) q^{17} -1.00000i q^{18} +(2.27646 + 1.31431i) q^{19} -0.931852i q^{21} +(-0.841081 + 1.45680i) q^{22} +(-3.22853 - 5.59197i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(3.15660 + 1.74238i) q^{26} -1.00000 q^{27} +(-0.807007 + 0.465926i) q^{28} +(1.69419 + 2.93443i) q^{29} -9.29493i q^{31} +(0.866025 + 0.500000i) q^{32} +(1.45680 + 0.841081i) q^{33} -2.55291i q^{34} +(0.500000 + 0.866025i) q^{36} +(-7.93269 + 4.57994i) q^{37} -2.62863 q^{38} +(1.74238 - 3.15660i) q^{39} +(1.01714 - 0.587246i) q^{41} +(0.465926 + 0.807007i) q^{42} +(1.47626 - 2.55695i) q^{43} -1.68216i q^{44} +(5.59197 + 3.22853i) q^{46} -3.97934i q^{47} +(0.500000 - 0.866025i) q^{48} +(-3.06583 - 5.31017i) q^{49} -2.55291 q^{51} +(-3.60488 + 0.0693504i) q^{52} +5.36068 q^{53} +(0.866025 - 0.500000i) q^{54} +(0.465926 - 0.807007i) q^{56} +2.62863i q^{57} +(-2.93443 - 1.69419i) q^{58} +(-3.44174 - 1.98709i) q^{59} +(4.36188 - 7.55500i) q^{61} +(4.64747 + 8.04965i) q^{62} +(0.807007 - 0.465926i) q^{63} -1.00000 q^{64} -1.68216 q^{66} +(-4.49598 + 2.59575i) q^{67} +(1.27646 + 2.21089i) q^{68} +(3.22853 - 5.59197i) q^{69} +(3.40803 + 1.96763i) q^{71} +(-0.866025 - 0.500000i) q^{72} -7.26330i q^{73} +(4.57994 - 7.93269i) q^{74} +(2.27646 - 1.31431i) q^{76} -1.56753 q^{77} +(0.0693504 + 3.60488i) q^{78} -3.68973 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-0.587246 + 1.01714i) q^{82} -3.84909i q^{83} +(-0.807007 - 0.465926i) q^{84} +2.95252i q^{86} +(-1.69419 + 2.93443i) q^{87} +(0.841081 + 1.45680i) q^{88} +(11.6628 - 6.73351i) q^{89} +(0.0646242 + 3.35922i) q^{91} -6.45705 q^{92} +(8.04965 - 4.64747i) q^{93} +(1.98967 + 3.44621i) q^{94} +1.00000i q^{96} +(-12.1945 - 7.04052i) q^{97} +(5.31017 + 3.06583i) q^{98} +1.68216i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9} - 12 q^{11} + 8 q^{12} - 8 q^{14} - 4 q^{16} - 4 q^{17} + 12 q^{19} - 8 q^{22} - 4 q^{23} - 8 q^{27} + 4 q^{29} - 12 q^{33} + 4 q^{36} + 24 q^{37} - 4 q^{42} + 4 q^{43} + 12 q^{46} + 4 q^{48} - 16 q^{49} - 8 q^{51} + 8 q^{53} - 4 q^{56} - 12 q^{58} - 12 q^{59} - 16 q^{61} - 4 q^{62} - 8 q^{64} - 16 q^{66} - 24 q^{67} + 4 q^{68} + 4 q^{69} + 60 q^{71} + 16 q^{74} + 12 q^{76} + 8 q^{77} - 8 q^{79} - 4 q^{81} + 20 q^{82} - 4 q^{87} + 8 q^{88} + 24 q^{89} + 8 q^{91} - 8 q^{92} + 24 q^{93} + 16 q^{94} - 12 q^{97} - 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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
\(7\) −0.807007 0.465926i −0.305020 0.176103i 0.339676 0.940543i \(-0.389683\pi\)
−0.644696 + 0.764439i \(0.723016\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 1.45680 0.841081i 0.439240 0.253596i −0.264035 0.964513i \(-0.585053\pi\)
0.703275 + 0.710918i \(0.251720\pi\)
\(12\) 1.00000 0.288675
\(13\) −1.86250 3.08725i −0.516565 0.856248i
\(14\) 0.931852 0.249048
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.27646 + 2.21089i −0.309586 + 0.536219i −0.978272 0.207326i \(-0.933524\pi\)
0.668686 + 0.743545i \(0.266857\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 2.27646 + 1.31431i 0.522255 + 0.301524i 0.737857 0.674957i \(-0.235838\pi\)
−0.215602 + 0.976481i \(0.569171\pi\)
\(20\) 0 0
\(21\) 0.931852i 0.203347i
\(22\) −0.841081 + 1.45680i −0.179319 + 0.310590i
\(23\) −3.22853 5.59197i −0.673194 1.16601i −0.976993 0.213271i \(-0.931588\pi\)
0.303799 0.952736i \(-0.401745\pi\)
\(24\) −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
\(28\) −0.807007 + 0.465926i −0.152510 + 0.0880517i
\(29\) 1.69419 + 2.93443i 0.314604 + 0.544910i 0.979353 0.202156i \(-0.0647949\pi\)
−0.664749 + 0.747067i \(0.731462\pi\)
\(30\) 0 0
\(31\) 9.29493i 1.66942i −0.550690 0.834710i \(-0.685635\pi\)
0.550690 0.834710i \(-0.314365\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 1.45680 + 0.841081i 0.253596 + 0.146413i
\(34\) 2.55291i 0.437821i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) −7.93269 + 4.57994i −1.30413 + 0.752938i −0.981109 0.193456i \(-0.938030\pi\)
−0.323017 + 0.946393i \(0.604697\pi\)
\(38\) −2.62863 −0.426419
\(39\) 1.74238 3.15660i 0.279005 0.505460i
\(40\) 0 0
\(41\) 1.01714 0.587246i 0.158851 0.0917124i −0.418467 0.908232i \(-0.637433\pi\)
0.577318 + 0.816519i \(0.304099\pi\)
\(42\) 0.465926 + 0.807007i 0.0718939 + 0.124524i
\(43\) 1.47626 2.55695i 0.225127 0.389932i −0.731230 0.682131i \(-0.761054\pi\)
0.956358 + 0.292199i \(0.0943869\pi\)
\(44\) 1.68216i 0.253596i
\(45\) 0 0
\(46\) 5.59197 + 3.22853i 0.824491 + 0.476020i
\(47\) 3.97934i 0.580446i −0.956959 0.290223i \(-0.906271\pi\)
0.956959 0.290223i \(-0.0937294\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) −3.06583 5.31017i −0.437975 0.758595i
\(50\) 0 0
\(51\) −2.55291 −0.357480
\(52\) −3.60488 + 0.0693504i −0.499908 + 0.00961716i
\(53\) 5.36068 0.736346 0.368173 0.929757i \(-0.379983\pi\)
0.368173 + 0.929757i \(0.379983\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 0 0
\(56\) 0.465926 0.807007i 0.0622620 0.107841i
\(57\) 2.62863i 0.348170i
\(58\) −2.93443 1.69419i −0.385310 0.222459i
\(59\) −3.44174 1.98709i −0.448076 0.258697i 0.258941 0.965893i \(-0.416626\pi\)
−0.707017 + 0.707196i \(0.749960\pi\)
\(60\) 0 0
\(61\) 4.36188 7.55500i 0.558481 0.967318i −0.439142 0.898418i \(-0.644718\pi\)
0.997624 0.0689005i \(-0.0219491\pi\)
\(62\) 4.64747 + 8.04965i 0.590229 + 1.02231i
\(63\) 0.807007 0.465926i 0.101673 0.0587011i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −1.68216 −0.207060
\(67\) −4.49598 + 2.59575i −0.549271 + 0.317122i −0.748828 0.662764i \(-0.769383\pi\)
0.199557 + 0.979886i \(0.436050\pi\)
\(68\) 1.27646 + 2.21089i 0.154793 + 0.268110i
\(69\) 3.22853 5.59197i 0.388669 0.673194i
\(70\) 0 0
\(71\) 3.40803 + 1.96763i 0.404458 + 0.233514i 0.688406 0.725326i \(-0.258311\pi\)
−0.283947 + 0.958840i \(0.591644\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 7.26330i 0.850106i −0.905169 0.425053i \(-0.860256\pi\)
0.905169 0.425053i \(-0.139744\pi\)
\(74\) 4.57994 7.93269i 0.532407 0.922156i
\(75\) 0 0
\(76\) 2.27646 1.31431i 0.261128 0.150762i
\(77\) −1.56753 −0.178636
\(78\) 0.0693504 + 3.60488i 0.00785238 + 0.408173i
\(79\) −3.68973 −0.415127 −0.207563 0.978222i \(-0.566553\pi\)
−0.207563 + 0.978222i \(0.566553\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −0.587246 + 1.01714i −0.0648505 + 0.112324i
\(83\) 3.84909i 0.422493i −0.977433 0.211246i \(-0.932248\pi\)
0.977433 0.211246i \(-0.0677522\pi\)
\(84\) −0.807007 0.465926i −0.0880517 0.0508367i
\(85\) 0 0
\(86\) 2.95252i 0.318378i
\(87\) −1.69419 + 2.93443i −0.181637 + 0.314604i
\(88\) 0.841081 + 1.45680i 0.0896596 + 0.155295i
\(89\) 11.6628 6.73351i 1.23625 0.713751i 0.267926 0.963439i \(-0.413662\pi\)
0.968326 + 0.249689i \(0.0803283\pi\)
\(90\) 0 0
\(91\) 0.0646242 + 3.35922i 0.00677446 + 0.352142i
\(92\) −6.45705 −0.673194
\(93\) 8.04965 4.64747i 0.834710 0.481920i
\(94\) 1.98967 + 3.44621i 0.205219 + 0.355449i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −12.1945 7.04052i −1.23817 0.714856i −0.269448 0.963015i \(-0.586841\pi\)
−0.968719 + 0.248159i \(0.920175\pi\)
\(98\) 5.31017 + 3.06583i 0.536408 + 0.309695i
\(99\) 1.68216i 0.169064i
\(100\) 0 0
\(101\) −5.65892 9.80153i −0.563083 0.975289i −0.997225 0.0744445i \(-0.976282\pi\)
0.434142 0.900845i \(-0.357052\pi\)
\(102\) 2.21089 1.27646i 0.218911 0.126388i
\(103\) 0.725003 0.0714366 0.0357183 0.999362i \(-0.488628\pi\)
0.0357183 + 0.999362i \(0.488628\pi\)
\(104\) 3.08725 1.86250i 0.302729 0.182633i
\(105\) 0 0
\(106\) −4.64248 + 2.68034i −0.450918 + 0.260337i
\(107\) 8.60867 + 14.9106i 0.832231 + 1.44147i 0.896265 + 0.443519i \(0.146270\pi\)
−0.0640338 + 0.997948i \(0.520397\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 10.2816i 0.984795i −0.870370 0.492398i \(-0.836121\pi\)
0.870370 0.492398i \(-0.163879\pi\)
\(110\) 0 0
\(111\) −7.93269 4.57994i −0.752938 0.434709i
\(112\) 0.931852i 0.0880517i
\(113\) 4.82843 8.36308i 0.454220 0.786732i −0.544423 0.838811i \(-0.683251\pi\)
0.998643 + 0.0520785i \(0.0165846\pi\)
\(114\) −1.31431 2.27646i −0.123097 0.213210i
\(115\) 0 0
\(116\) 3.38839 0.314604
\(117\) 3.60488 0.0693504i 0.333272 0.00641144i
\(118\) 3.97418 0.365853
\(119\) 2.06022 1.18947i 0.188860 0.109038i
\(120\) 0 0
\(121\) −4.08516 + 7.07571i −0.371379 + 0.643247i
\(122\) 8.72376i 0.789812i
\(123\) 1.01714 + 0.587246i 0.0917124 + 0.0529502i
\(124\) −8.04965 4.64747i −0.722880 0.417355i
\(125\) 0 0
\(126\) −0.465926 + 0.807007i −0.0415080 + 0.0718939i
\(127\) −0.338502 0.586302i −0.0300372 0.0520259i 0.850616 0.525787i \(-0.176229\pi\)
−0.880653 + 0.473761i \(0.842896\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 2.95252 0.259955
\(130\) 0 0
\(131\) 1.86710 0.163130 0.0815648 0.996668i \(-0.474008\pi\)
0.0815648 + 0.996668i \(0.474008\pi\)
\(132\) 1.45680 0.841081i 0.126798 0.0732067i
\(133\) −1.22474 2.12132i −0.106199 0.183942i
\(134\) 2.59575 4.49598i 0.224239 0.388393i
\(135\) 0 0
\(136\) −2.21089 1.27646i −0.189582 0.109455i
\(137\) 6.31212 + 3.64431i 0.539281 + 0.311354i 0.744788 0.667302i \(-0.232551\pi\)
−0.205506 + 0.978656i \(0.565884\pi\)
\(138\) 6.45705i 0.549661i
\(139\) −2.35569 + 4.08018i −0.199807 + 0.346076i −0.948466 0.316879i \(-0.897365\pi\)
0.748659 + 0.662956i \(0.230698\pi\)
\(140\) 0 0
\(141\) 3.44621 1.98967i 0.290223 0.167560i
\(142\) −3.93525 −0.330239
\(143\) −5.30991 2.93097i −0.444037 0.245100i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 3.63165 + 6.29021i 0.300558 + 0.520581i
\(147\) 3.06583 5.31017i 0.252865 0.437975i
\(148\) 9.15988i 0.752938i
\(149\) −2.60016 1.50120i −0.213013 0.122983i 0.389698 0.920943i \(-0.372579\pi\)
−0.602711 + 0.797960i \(0.705913\pi\)
\(150\) 0 0
\(151\) 12.4200i 1.01073i −0.862907 0.505363i \(-0.831358\pi\)
0.862907 0.505363i \(-0.168642\pi\)
\(152\) −1.31431 + 2.27646i −0.106605 + 0.184645i
\(153\) −1.27646 2.21089i −0.103195 0.178740i
\(154\) 1.35752 0.783763i 0.109392 0.0631574i
\(155\) 0 0
\(156\) −1.86250 3.08725i −0.149119 0.247178i
\(157\) −22.5217 −1.79743 −0.898714 0.438535i \(-0.855498\pi\)
−0.898714 + 0.438535i \(0.855498\pi\)
\(158\) 3.19540 1.84486i 0.254212 0.146769i
\(159\) 2.68034 + 4.64248i 0.212565 + 0.368173i
\(160\) 0 0
\(161\) 6.01702i 0.474207i
\(162\) 0.866025 + 0.500000i 0.0680414 + 0.0392837i
\(163\) −2.40313 1.38745i −0.188227 0.108673i 0.402925 0.915233i \(-0.367994\pi\)
−0.591152 + 0.806560i \(0.701327\pi\)
\(164\) 1.17449i 0.0917124i
\(165\) 0 0
\(166\) 1.92455 + 3.33341i 0.149374 + 0.258723i
\(167\) 19.2296 11.1022i 1.48803 0.859114i 0.488122 0.872775i \(-0.337682\pi\)
0.999907 + 0.0136615i \(0.00434872\pi\)
\(168\) 0.931852 0.0718939
\(169\) −6.06218 + 11.5000i −0.466321 + 0.884615i
\(170\) 0 0
\(171\) −2.27646 + 1.31431i −0.174085 + 0.100508i
\(172\) −1.47626 2.55695i −0.112564 0.194966i
\(173\) 0.475314 0.823267i 0.0361374 0.0625919i −0.847391 0.530969i \(-0.821828\pi\)
0.883528 + 0.468377i \(0.155161\pi\)
\(174\) 3.38839i 0.256873i
\(175\) 0 0
\(176\) −1.45680 0.841081i −0.109810 0.0633989i
\(177\) 3.97418i 0.298717i
\(178\) −6.73351 + 11.6628i −0.504698 + 0.874162i
\(179\) 4.94156 + 8.55904i 0.369350 + 0.639732i 0.989464 0.144779i \(-0.0462471\pi\)
−0.620114 + 0.784511i \(0.712914\pi\)
\(180\) 0 0
\(181\) 14.3015 1.06302 0.531511 0.847051i \(-0.321624\pi\)
0.531511 + 0.847051i \(0.321624\pi\)
\(182\) −1.73557 2.87686i −0.128649 0.213247i
\(183\) 8.72376 0.644879
\(184\) 5.59197 3.22853i 0.412246 0.238010i
\(185\) 0 0
\(186\) −4.64747 + 8.04965i −0.340769 + 0.590229i
\(187\) 4.29442i 0.314039i
\(188\) −3.44621 1.98967i −0.251340 0.145111i
\(189\) 0.807007 + 0.465926i 0.0587011 + 0.0338911i
\(190\) 0 0
\(191\) 0.0573183 0.0992782i 0.00414741 0.00718352i −0.863944 0.503587i \(-0.832013\pi\)
0.868092 + 0.496404i \(0.165347\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 7.49706 4.32843i 0.539650 0.311567i −0.205287 0.978702i \(-0.565813\pi\)
0.744937 + 0.667135i \(0.232479\pi\)
\(194\) 14.0810 1.01096
\(195\) 0 0
\(196\) −6.13165 −0.437975
\(197\) 17.7363 10.2401i 1.26366 0.729574i 0.289879 0.957063i \(-0.406385\pi\)
0.973781 + 0.227489i \(0.0730516\pi\)
\(198\) −0.841081 1.45680i −0.0597731 0.103530i
\(199\) 0.955336 1.65469i 0.0677220 0.117298i −0.830176 0.557501i \(-0.811760\pi\)
0.897898 + 0.440203i \(0.145094\pi\)
\(200\) 0 0
\(201\) −4.49598 2.59575i −0.317122 0.183090i
\(202\) 9.80153 + 5.65892i 0.689634 + 0.398160i
\(203\) 3.15748i 0.221611i
\(204\) −1.27646 + 2.21089i −0.0893699 + 0.154793i
\(205\) 0 0
\(206\) −0.627871 + 0.362501i −0.0437458 + 0.0252567i
\(207\) 6.45705 0.448796
\(208\) −1.74238 + 3.15660i −0.120813 + 0.218871i
\(209\) 4.42178 0.305861
\(210\) 0 0
\(211\) −0.620118 1.07408i −0.0426907 0.0739425i 0.843891 0.536515i \(-0.180260\pi\)
−0.886581 + 0.462573i \(0.846926\pi\)
\(212\) 2.68034 4.64248i 0.184086 0.318847i
\(213\) 3.93525i 0.269639i
\(214\) −14.9106 8.60867i −1.01927 0.588476i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −4.33075 + 7.50108i −0.293990 + 0.509206i
\(218\) 5.14078 + 8.90410i 0.348178 + 0.603062i
\(219\) 6.29021 3.63165i 0.425053 0.245404i
\(220\) 0 0
\(221\) 9.20296 0.177046i 0.619058 0.0119094i
\(222\) 9.15988 0.614771
\(223\) 12.7984 7.38915i 0.857043 0.494814i −0.00597823 0.999982i \(-0.501903\pi\)
0.863021 + 0.505168i \(0.168570\pi\)
\(224\) −0.465926 0.807007i −0.0311310 0.0539204i
\(225\) 0 0
\(226\) 9.65685i 0.642364i
\(227\) 8.28423 + 4.78290i 0.549843 + 0.317452i 0.749059 0.662503i \(-0.230506\pi\)
−0.199215 + 0.979956i \(0.563839\pi\)
\(228\) 2.27646 + 1.31431i 0.150762 + 0.0870425i
\(229\) 15.1478i 1.00099i −0.865739 0.500497i \(-0.833151\pi\)
0.865739 0.500497i \(-0.166849\pi\)
\(230\) 0 0
\(231\) −0.783763 1.35752i −0.0515678 0.0893181i
\(232\) −2.93443 + 1.69419i −0.192655 + 0.111229i
\(233\) −18.7413 −1.22778 −0.613891 0.789391i \(-0.710397\pi\)
−0.613891 + 0.789391i \(0.710397\pi\)
\(234\) −3.08725 + 1.86250i −0.201820 + 0.121756i
\(235\) 0 0
\(236\) −3.44174 + 1.98709i −0.224038 + 0.129348i
\(237\) −1.84486 3.19540i −0.119837 0.207563i
\(238\) −1.18947 + 2.06022i −0.0771018 + 0.133544i
\(239\) 4.62330i 0.299057i −0.988757 0.149528i \(-0.952224\pi\)
0.988757 0.149528i \(-0.0477755\pi\)
\(240\) 0 0
\(241\) 15.2373 + 8.79725i 0.981520 + 0.566681i 0.902729 0.430210i \(-0.141561\pi\)
0.0787915 + 0.996891i \(0.474894\pi\)
\(242\) 8.17033i 0.525209i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −4.36188 7.55500i −0.279241 0.483659i
\(245\) 0 0
\(246\) −1.17449 −0.0748829
\(247\) −0.182296 9.47589i −0.0115992 0.602937i
\(248\) 9.29493 0.590229
\(249\) 3.33341 1.92455i 0.211246 0.121963i
\(250\) 0 0
\(251\) −13.2599 + 22.9668i −0.836958 + 1.44965i 0.0554676 + 0.998460i \(0.482335\pi\)
−0.892426 + 0.451194i \(0.850998\pi\)
\(252\) 0.931852i 0.0587011i
\(253\) −9.40661 5.43091i −0.591388 0.341438i
\(254\) 0.586302 + 0.338502i 0.0367879 + 0.0212395i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0.912132 + 1.57986i 0.0568972 + 0.0985489i 0.893071 0.449916i \(-0.148546\pi\)
−0.836174 + 0.548464i \(0.815213\pi\)
\(258\) −2.55695 + 1.47626i −0.159189 + 0.0919078i
\(259\) 8.53565 0.530379
\(260\) 0 0
\(261\) −3.38839 −0.209736
\(262\) −1.61696 + 0.933552i −0.0998960 + 0.0576750i
\(263\) 6.06828 + 10.5106i 0.374186 + 0.648110i 0.990205 0.139622i \(-0.0445887\pi\)
−0.616019 + 0.787732i \(0.711255\pi\)
\(264\) −0.841081 + 1.45680i −0.0517650 + 0.0896596i
\(265\) 0 0
\(266\) 2.12132 + 1.22474i 0.130066 + 0.0750939i
\(267\) 11.6628 + 6.73351i 0.713751 + 0.412084i
\(268\) 5.19151i 0.317122i
\(269\) −11.7655 + 20.3784i −0.717355 + 1.24250i 0.244689 + 0.969602i \(0.421314\pi\)
−0.962044 + 0.272894i \(0.912019\pi\)
\(270\) 0 0
\(271\) 10.9872 6.34349i 0.667427 0.385339i −0.127674 0.991816i \(-0.540751\pi\)
0.795101 + 0.606477i \(0.207418\pi\)
\(272\) 2.55291 0.154793
\(273\) −2.87686 + 1.73557i −0.174115 + 0.105042i
\(274\) −7.28861 −0.440321
\(275\) 0 0
\(276\) −3.22853 5.59197i −0.194334 0.336597i
\(277\) 6.41177 11.1055i 0.385246 0.667265i −0.606558 0.795040i \(-0.707450\pi\)
0.991803 + 0.127774i \(0.0407833\pi\)
\(278\) 4.71139i 0.282570i
\(279\) 8.04965 + 4.64747i 0.481920 + 0.278237i
\(280\) 0 0
\(281\) 5.16720i 0.308249i −0.988051 0.154125i \(-0.950744\pi\)
0.988051 0.154125i \(-0.0492557\pi\)
\(282\) −1.98967 + 3.44621i −0.118483 + 0.205219i
\(283\) −6.48124 11.2258i −0.385270 0.667307i 0.606537 0.795055i \(-0.292558\pi\)
−0.991807 + 0.127749i \(0.959225\pi\)
\(284\) 3.40803 1.96763i 0.202229 0.116757i
\(285\) 0 0
\(286\) 6.06400 0.116659i 0.358572 0.00689817i
\(287\) −1.09445 −0.0646035
\(288\) −0.866025 + 0.500000i −0.0510310 + 0.0294628i
\(289\) 5.24131 + 9.07822i 0.308313 + 0.534013i
\(290\) 0 0
\(291\) 14.0810i 0.825445i
\(292\) −6.29021 3.63165i −0.368107 0.212526i
\(293\) −11.6657 6.73521i −0.681519 0.393475i 0.118908 0.992905i \(-0.462061\pi\)
−0.800427 + 0.599430i \(0.795394\pi\)
\(294\) 6.13165i 0.357605i
\(295\) 0 0
\(296\) −4.57994 7.93269i −0.266204 0.461078i
\(297\) −1.45680 + 0.841081i −0.0845319 + 0.0488045i
\(298\) 3.00240 0.173925
\(299\) −11.2507 + 20.3823i −0.650642 + 1.17874i
\(300\) 0 0
\(301\) −2.38270 + 1.37565i −0.137337 + 0.0792913i
\(302\) 6.21001 + 10.7561i 0.357346 + 0.618941i
\(303\) 5.65892 9.80153i 0.325096 0.563083i
\(304\) 2.62863i 0.150762i
\(305\) 0 0
\(306\) 2.21089 + 1.27646i 0.126388 + 0.0729702i
\(307\) 21.4620i 1.22490i −0.790510 0.612450i \(-0.790184\pi\)
0.790510 0.612450i \(-0.209816\pi\)
\(308\) −0.783763 + 1.35752i −0.0446590 + 0.0773517i
\(309\) 0.362501 + 0.627871i 0.0206220 + 0.0357183i
\(310\) 0 0
\(311\) −14.7562 −0.836745 −0.418372 0.908276i \(-0.637399\pi\)
−0.418372 + 0.908276i \(0.637399\pi\)
\(312\) 3.15660 + 1.74238i 0.178707 + 0.0986430i
\(313\) −1.40441 −0.0793819 −0.0396910 0.999212i \(-0.512637\pi\)
−0.0396910 + 0.999212i \(0.512637\pi\)
\(314\) 19.5044 11.2609i 1.10070 0.635487i
\(315\) 0 0
\(316\) −1.84486 + 3.19540i −0.103782 + 0.179755i
\(317\) 33.1421i 1.86144i −0.365729 0.930722i \(-0.619180\pi\)
0.365729 0.930722i \(-0.380820\pi\)
\(318\) −4.64248 2.68034i −0.260337 0.150306i
\(319\) 4.93619 + 2.84991i 0.276374 + 0.159564i
\(320\) 0 0
\(321\) −8.60867 + 14.9106i −0.480489 + 0.832231i
\(322\) −3.00851 5.21089i −0.167658 0.290391i
\(323\) −5.81160 + 3.35533i −0.323366 + 0.186695i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) 2.77489 0.153687
\(327\) 8.90410 5.14078i 0.492398 0.284286i
\(328\) 0.587246 + 1.01714i 0.0324252 + 0.0561622i
\(329\) −1.85408 + 3.21135i −0.102218 + 0.177048i
\(330\) 0 0
\(331\) −6.05268 3.49452i −0.332686 0.192076i 0.324347 0.945938i \(-0.394855\pi\)
−0.657033 + 0.753862i \(0.728189\pi\)
\(332\) −3.33341 1.92455i −0.182945 0.105623i
\(333\) 9.15988i 0.501958i
\(334\) −11.1022 + 19.2296i −0.607485 + 1.05220i
\(335\) 0 0
\(336\) −0.807007 + 0.465926i −0.0440259 + 0.0254183i
\(337\) −35.3229 −1.92416 −0.962082 0.272761i \(-0.912063\pi\)
−0.962082 + 0.272761i \(0.912063\pi\)
\(338\) −0.500000 12.9904i −0.0271964 0.706584i
\(339\) 9.65685 0.524488
\(340\) 0 0
\(341\) −7.81779 13.5408i −0.423357 0.733276i
\(342\) 1.31431 2.27646i 0.0710699 0.123097i
\(343\) 12.2368i 0.660723i
\(344\) 2.55695 + 1.47626i 0.137862 + 0.0795945i
\(345\) 0 0
\(346\) 0.950627i 0.0511060i
\(347\) −1.80920 + 3.13363i −0.0971232 + 0.168222i −0.910493 0.413525i \(-0.864297\pi\)
0.813370 + 0.581747i \(0.197631\pi\)
\(348\) 1.69419 + 2.93443i 0.0908184 + 0.157302i
\(349\) −25.1956 + 14.5467i −1.34869 + 0.778667i −0.988064 0.154043i \(-0.950771\pi\)
−0.360627 + 0.932710i \(0.617437\pi\)
\(350\) 0 0
\(351\) 1.86250 + 3.08725i 0.0994130 + 0.164785i
\(352\) 1.68216 0.0896596
\(353\) −8.30867 + 4.79701i −0.442226 + 0.255319i −0.704541 0.709663i \(-0.748847\pi\)
0.262315 + 0.964982i \(0.415514\pi\)
\(354\) 1.98709 + 3.44174i 0.105613 + 0.182926i
\(355\) 0 0
\(356\) 13.4670i 0.713751i
\(357\) 2.06022 + 1.18947i 0.109038 + 0.0629534i
\(358\) −8.55904 4.94156i −0.452359 0.261170i
\(359\) 6.31495i 0.333290i 0.986017 + 0.166645i \(0.0532935\pi\)
−0.986017 + 0.166645i \(0.946707\pi\)
\(360\) 0 0
\(361\) −6.04516 10.4705i −0.318166 0.551080i
\(362\) −12.3855 + 7.15075i −0.650965 + 0.375835i
\(363\) −8.17033 −0.428831
\(364\) 2.94148 + 1.62364i 0.154175 + 0.0851020i
\(365\) 0 0
\(366\) −7.55500 + 4.36188i −0.394906 + 0.227999i
\(367\) 17.4472 + 30.2194i 0.910735 + 1.57744i 0.813028 + 0.582224i \(0.197818\pi\)
0.0977071 + 0.995215i \(0.468849\pi\)
\(368\) −3.22853 + 5.59197i −0.168299 + 0.291502i
\(369\) 1.17449i 0.0611416i
\(370\) 0 0
\(371\) −4.32611 2.49768i −0.224600 0.129673i
\(372\) 9.29493i 0.481920i
\(373\) −2.40608 + 4.16745i −0.124582 + 0.215782i −0.921569 0.388213i \(-0.873092\pi\)
0.796987 + 0.603996i \(0.206426\pi\)
\(374\) −2.14721 3.71907i −0.111030 0.192309i
\(375\) 0 0
\(376\) 3.97934 0.205219
\(377\) 5.90387 10.6958i 0.304065 0.550861i
\(378\) −0.931852 −0.0479293
\(379\) −24.0847 + 13.9053i −1.23715 + 0.714267i −0.968510 0.248974i \(-0.919907\pi\)
−0.268637 + 0.963241i \(0.586573\pi\)
\(380\) 0 0
\(381\) 0.338502 0.586302i 0.0173420 0.0300372i
\(382\) 0.114637i 0.00586532i
\(383\) −0.697788 0.402868i −0.0356553 0.0205856i 0.482066 0.876135i \(-0.339886\pi\)
−0.517722 + 0.855549i \(0.673220\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) −4.32843 + 7.49706i −0.220311 + 0.381590i
\(387\) 1.47626 + 2.55695i 0.0750424 + 0.129977i
\(388\) −12.1945 + 7.04052i −0.619084 + 0.357428i
\(389\) −27.5013 −1.39437 −0.697186 0.716891i \(-0.745565\pi\)
−0.697186 + 0.716891i \(0.745565\pi\)
\(390\) 0 0
\(391\) 16.4843 0.833647
\(392\) 5.31017 3.06583i 0.268204 0.154848i
\(393\) 0.933552 + 1.61696i 0.0470914 + 0.0815648i
\(394\) −10.2401 + 17.7363i −0.515887 + 0.893542i
\(395\) 0 0
\(396\) 1.45680 + 0.841081i 0.0732067 + 0.0422659i
\(397\) −0.994360 0.574094i −0.0499055 0.0288130i 0.474840 0.880072i \(-0.342506\pi\)
−0.524745 + 0.851259i \(0.675839\pi\)
\(398\) 1.91067i 0.0957733i
\(399\) 1.22474 2.12132i 0.0613139 0.106199i
\(400\) 0 0
\(401\) 11.8647 6.85009i 0.592495 0.342077i −0.173589 0.984818i \(-0.555536\pi\)
0.766083 + 0.642741i \(0.222203\pi\)
\(402\) 5.19151 0.258929
\(403\) −28.6957 + 17.3118i −1.42944 + 0.862363i
\(404\) −11.3178 −0.563083
\(405\) 0 0
\(406\) 1.57874 + 2.73445i 0.0783515 + 0.135709i
\(407\) −7.70420 + 13.3441i −0.381883 + 0.661441i
\(408\) 2.55291i 0.126388i
\(409\) −6.63613 3.83137i −0.328136 0.189449i 0.326878 0.945067i \(-0.394004\pi\)
−0.655013 + 0.755618i \(0.727337\pi\)
\(410\) 0 0
\(411\) 7.28861i 0.359521i
\(412\) 0.362501 0.627871i 0.0178592 0.0309330i
\(413\) 1.85167 + 3.20719i 0.0911148 + 0.157815i
\(414\) −5.59197 + 3.22853i −0.274830 + 0.158673i
\(415\) 0 0
\(416\) −0.0693504 3.60488i −0.00340018 0.176744i
\(417\) −4.71139 −0.230718
\(418\) −3.82937 + 2.21089i −0.187301 + 0.108138i
\(419\) 19.5013 + 33.7773i 0.952701 + 1.65013i 0.739543 + 0.673110i \(0.235042\pi\)
0.213159 + 0.977018i \(0.431625\pi\)
\(420\) 0 0
\(421\) 32.7923i 1.59820i 0.601198 + 0.799100i \(0.294690\pi\)
−0.601198 + 0.799100i \(0.705310\pi\)
\(422\) 1.07408 + 0.620118i 0.0522852 + 0.0301869i
\(423\) 3.44621 + 1.98967i 0.167560 + 0.0967410i
\(424\) 5.36068i 0.260337i
\(425\) 0 0
\(426\) −1.96763 3.40803i −0.0953318 0.165119i
\(427\) −7.04014 + 4.06462i −0.340696 + 0.196701i
\(428\) 17.2173 0.832231
\(429\) −0.116659 6.06400i −0.00563233 0.292773i
\(430\) 0 0
\(431\) −28.6031 + 16.5140i −1.37776 + 0.795452i −0.991890 0.127100i \(-0.959433\pi\)
−0.385873 + 0.922552i \(0.626100\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −4.49706 + 7.78913i −0.216115 + 0.374322i −0.953617 0.301023i \(-0.902672\pi\)
0.737502 + 0.675345i \(0.236005\pi\)
\(434\) 8.66150i 0.415765i
\(435\) 0 0
\(436\) −8.90410 5.14078i −0.426429 0.246199i
\(437\) 16.9732i 0.811937i
\(438\) −3.63165 + 6.29021i −0.173527 + 0.300558i
\(439\) 3.65685 + 6.33386i 0.174532 + 0.302299i 0.939999 0.341176i \(-0.110825\pi\)
−0.765467 + 0.643475i \(0.777492\pi\)
\(440\) 0 0
\(441\) 6.13165 0.291983
\(442\) −7.88147 + 4.75481i −0.374884 + 0.226163i
\(443\) 27.5200 1.30752 0.653758 0.756703i \(-0.273191\pi\)
0.653758 + 0.756703i \(0.273191\pi\)
\(444\) −7.93269 + 4.57994i −0.376469 + 0.217354i
\(445\) 0 0
\(446\) −7.38915 + 12.7984i −0.349886 + 0.606021i
\(447\) 3.00240i 0.142009i
\(448\) 0.807007 + 0.465926i 0.0381275 + 0.0220129i
\(449\) 8.88390 + 5.12912i 0.419257 + 0.242058i 0.694760 0.719242i \(-0.255511\pi\)
−0.275502 + 0.961300i \(0.588844\pi\)
\(450\) 0 0
\(451\) 0.987844 1.71100i 0.0465157 0.0805676i
\(452\) −4.82843 8.36308i −0.227110 0.393366i
\(453\) 10.7561 6.21001i 0.505363 0.291772i
\(454\) −9.56580 −0.448945
\(455\) 0 0
\(456\) −2.62863 −0.123097
\(457\) 12.7653 7.37005i 0.597135 0.344756i −0.170778 0.985309i \(-0.554628\pi\)
0.767914 + 0.640553i \(0.221295\pi\)
\(458\) 7.57389 + 13.1184i 0.353905 + 0.612981i
\(459\) 1.27646 2.21089i 0.0595799 0.103195i
\(460\) 0 0
\(461\) 17.1993 + 9.93003i 0.801052 + 0.462487i 0.843839 0.536597i \(-0.180290\pi\)
−0.0427870 + 0.999084i \(0.513624\pi\)
\(462\) 1.35752 + 0.783763i 0.0631574 + 0.0364640i
\(463\) 32.1533i 1.49429i 0.664662 + 0.747144i \(0.268576\pi\)
−0.664662 + 0.747144i \(0.731424\pi\)
\(464\) 1.69419 2.93443i 0.0786510 0.136228i
\(465\) 0 0
\(466\) 16.2304 9.37064i 0.751860 0.434087i
\(467\) 22.2754 1.03078 0.515392 0.856955i \(-0.327646\pi\)
0.515392 + 0.856955i \(0.327646\pi\)
\(468\) 1.74238 3.15660i 0.0805417 0.145914i
\(469\) 4.83772 0.223385
\(470\) 0 0
\(471\) −11.2609 19.5044i −0.518873 0.898714i
\(472\) 1.98709 3.44174i 0.0914631 0.158419i
\(473\) 4.96661i 0.228365i
\(474\) 3.19540 + 1.84486i 0.146769 + 0.0847374i
\(475\) 0 0
\(476\) 2.37894i 0.109038i
\(477\) −2.68034 + 4.64248i −0.122724 + 0.212565i
\(478\) 2.31165 + 4.00390i 0.105732 + 0.183134i
\(479\) −19.0007 + 10.9700i −0.868163 + 0.501234i −0.866737 0.498765i \(-0.833787\pi\)
−0.00142578 + 0.999999i \(0.500454\pi\)
\(480\) 0 0
\(481\) 28.9140 + 15.9600i 1.31837 + 0.727714i
\(482\) −17.5945 −0.801408
\(483\) −5.21089 + 3.00851i −0.237104 + 0.136892i
\(484\) 4.08516 + 7.07571i 0.185689 + 0.321623i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) −7.84015 4.52651i −0.355271 0.205116i 0.311733 0.950170i \(-0.399090\pi\)
−0.667004 + 0.745054i \(0.732424\pi\)
\(488\) 7.55500 + 4.36188i 0.341999 + 0.197453i
\(489\) 2.77489i 0.125485i
\(490\) 0 0
\(491\) −15.1000 26.1540i −0.681455 1.18031i −0.974537 0.224227i \(-0.928014\pi\)
0.293082 0.956087i \(-0.405319\pi\)
\(492\) 1.01714 0.587246i 0.0458562 0.0264751i
\(493\) −8.65027 −0.389588
\(494\) 4.89582 + 8.11522i 0.220273 + 0.365121i
\(495\) 0 0
\(496\) −8.04965 + 4.64747i −0.361440 + 0.208677i
\(497\) −1.83354 3.17578i −0.0822453 0.142453i
\(498\) −1.92455 + 3.33341i −0.0862410 + 0.149374i
\(499\) 9.04336i 0.404836i −0.979299 0.202418i \(-0.935120\pi\)
0.979299 0.202418i \(-0.0648800\pi\)
\(500\) 0 0
\(501\) 19.2296 + 11.1022i 0.859114 + 0.496010i
\(502\) 26.5198i 1.18364i
\(503\) −15.5446 + 26.9241i −0.693101 + 1.20049i 0.277715 + 0.960663i \(0.410423\pi\)
−0.970817 + 0.239823i \(0.922911\pi\)
\(504\) 0.465926 + 0.807007i 0.0207540 + 0.0359470i
\(505\) 0 0
\(506\) 10.8618 0.482867
\(507\) −12.9904 + 0.500000i −0.576923 + 0.0222058i
\(508\) −0.677003 −0.0300372
\(509\) −22.5466 + 13.0173i −0.999361 + 0.576981i −0.908059 0.418842i \(-0.862436\pi\)
−0.0913018 + 0.995823i \(0.529103\pi\)
\(510\) 0 0
\(511\) −3.38416 + 5.86154i −0.149706 + 0.259299i
\(512\) 1.00000i 0.0441942i
\(513\) −2.27646 1.31431i −0.100508 0.0580283i
\(514\) −1.57986 0.912132i −0.0696846 0.0402324i
\(515\) 0 0
\(516\) 1.47626 2.55695i 0.0649886 0.112564i
\(517\) −3.34695 5.79708i −0.147198 0.254955i
\(518\) −7.39209 + 4.26782i −0.324790 + 0.187517i
\(519\) 0.950627 0.0417279
\(520\) 0 0
\(521\) −24.8332 −1.08796 −0.543982 0.839097i \(-0.683084\pi\)
−0.543982 + 0.839097i \(0.683084\pi\)
\(522\) 2.93443 1.69419i 0.128437 0.0741529i
\(523\) −4.20445 7.28231i −0.183848 0.318433i 0.759340 0.650694i \(-0.225522\pi\)
−0.943188 + 0.332261i \(0.892189\pi\)
\(524\) 0.933552 1.61696i 0.0407824 0.0706372i
\(525\) 0 0
\(526\) −10.5106 6.06828i −0.458283 0.264590i
\(527\) 20.5501 + 11.8646i 0.895175 + 0.516829i
\(528\) 1.68216i 0.0732067i
\(529\) −9.34677 + 16.1891i −0.406381 + 0.703873i
\(530\) 0 0
\(531\) 3.44174 1.98709i 0.149359 0.0862323i
\(532\) −2.44949 −0.106199
\(533\) −3.70740 2.04642i −0.160585 0.0886401i
\(534\) −13.4670 −0.582775
\(535\) 0 0
\(536\) −2.59575 4.49598i −0.112120 0.194197i
\(537\) −4.94156 + 8.55904i −0.213244 + 0.369350i
\(538\) 23.5310i 1.01449i
\(539\) −8.93256 5.15722i −0.384753 0.222137i
\(540\) 0 0
\(541\) 15.7195i 0.675833i −0.941176 0.337916i \(-0.890278\pi\)
0.941176 0.337916i \(-0.109722\pi\)
\(542\) −6.34349 + 10.9872i −0.272476 + 0.471942i
\(543\) 7.15075 + 12.3855i 0.306868 + 0.531511i
\(544\) −2.21089 + 1.27646i −0.0947911 + 0.0547276i
\(545\) 0 0
\(546\) 1.62364 2.94148i 0.0694855 0.125884i
\(547\) −23.0313 −0.984745 −0.492373 0.870385i \(-0.663870\pi\)
−0.492373 + 0.870385i \(0.663870\pi\)
\(548\) 6.31212 3.64431i 0.269641 0.155677i
\(549\) 4.36188 + 7.55500i 0.186160 + 0.322439i
\(550\) 0 0
\(551\) 8.90681i 0.379443i
\(552\) 5.59197 + 3.22853i 0.238010 + 0.137415i
\(553\) 2.97764 + 1.71914i 0.126622 + 0.0731052i
\(554\) 12.8235i 0.544820i
\(555\) 0 0
\(556\) 2.35569 + 4.08018i 0.0999036 + 0.173038i
\(557\) −35.2097 + 20.3283i −1.49188 + 0.861339i −0.999957 0.00929877i \(-0.997040\pi\)
−0.491925 + 0.870637i \(0.663707\pi\)
\(558\) −9.29493 −0.393486
\(559\) −10.6435 + 0.204758i −0.450171 + 0.00866034i
\(560\) 0 0
\(561\) −3.71907 + 2.14721i −0.157019 + 0.0906552i
\(562\) 2.58360 + 4.47492i 0.108982 + 0.188763i
\(563\) −1.71770 + 2.97514i −0.0723923 + 0.125387i −0.899949 0.435995i \(-0.856397\pi\)
0.827557 + 0.561382i \(0.189730\pi\)
\(564\) 3.97934i 0.167560i
\(565\) 0 0
\(566\) 11.2258 + 6.48124i 0.471857 + 0.272427i
\(567\) 0.931852i 0.0391341i
\(568\) −1.96763 + 3.40803i −0.0825597 + 0.142998i
\(569\) −11.0320 19.1079i −0.462484 0.801046i 0.536600 0.843837i \(-0.319708\pi\)
−0.999084 + 0.0427908i \(0.986375\pi\)
\(570\) 0 0
\(571\) 4.56829 0.191177 0.0955885 0.995421i \(-0.469527\pi\)
0.0955885 + 0.995421i \(0.469527\pi\)
\(572\) −5.19325 + 3.13303i −0.217141 + 0.130999i
\(573\) 0.114637 0.00478901
\(574\) 0.947824 0.547226i 0.0395614 0.0228408i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 4.42655i 0.184280i −0.995746 0.0921398i \(-0.970629\pi\)
0.995746 0.0921398i \(-0.0293707\pi\)
\(578\) −9.07822 5.24131i −0.377604 0.218010i
\(579\) 7.49706 + 4.32843i 0.311567 + 0.179883i
\(580\) 0 0
\(581\) −1.79339 + 3.10624i −0.0744024 + 0.128869i
\(582\) 7.04052 + 12.1945i 0.291839 + 0.505480i
\(583\) 7.80941 4.50877i 0.323433 0.186734i
\(584\) 7.26330 0.300558
\(585\) 0 0
\(586\) 13.4704 0.556458
\(587\) 37.3725 21.5770i 1.54253 0.890580i 0.543852 0.839181i \(-0.316965\pi\)
0.998678 0.0513987i \(-0.0163679\pi\)
\(588\) −3.06583 5.31017i −0.126433 0.218988i
\(589\) 12.2165 21.1595i 0.503370 0.871863i
\(590\) 0 0
\(591\) 17.7363 + 10.2401i 0.729574 + 0.421220i
\(592\) 7.93269 + 4.57994i 0.326032 + 0.188234i
\(593\) 28.8372i 1.18420i 0.805864 + 0.592101i \(0.201701\pi\)
−0.805864 + 0.592101i \(0.798299\pi\)
\(594\) 0.841081 1.45680i 0.0345100 0.0597731i
\(595\) 0 0
\(596\) −2.60016 + 1.50120i −0.106507 + 0.0614916i
\(597\) 1.91067 0.0781986
\(598\) −0.447799 23.2769i −0.0183119 0.951864i
\(599\) −28.1704 −1.15101 −0.575505 0.817798i \(-0.695194\pi\)
−0.575505 + 0.817798i \(0.695194\pi\)
\(600\) 0 0
\(601\) 7.31925 + 12.6773i 0.298558 + 0.517118i 0.975806 0.218637i \(-0.0701610\pi\)
−0.677248 + 0.735755i \(0.736828\pi\)
\(602\) 1.37565 2.38270i 0.0560674 0.0971117i
\(603\) 5.19151i 0.211415i
\(604\) −10.7561 6.21001i −0.437657 0.252682i
\(605\) 0 0
\(606\) 11.3178i 0.459756i
\(607\) −6.50853 + 11.2731i −0.264173 + 0.457561i −0.967347 0.253457i \(-0.918432\pi\)
0.703174 + 0.711018i \(0.251766\pi\)
\(608\) 1.31431 + 2.27646i 0.0533024 + 0.0923225i
\(609\) 2.73445 1.57874i 0.110806 0.0639737i
\(610\) 0 0
\(611\) −12.2852 + 7.41152i −0.497006 + 0.299838i
\(612\) −2.55291 −0.103195
\(613\) 23.5813 13.6146i 0.952438 0.549890i 0.0586006 0.998282i \(-0.481336\pi\)
0.893837 + 0.448391i \(0.148003\pi\)
\(614\) 10.7310 + 18.5866i 0.433067 + 0.750094i
\(615\) 0 0
\(616\) 1.56753i 0.0631574i
\(617\) −20.3825 11.7678i −0.820569 0.473755i 0.0300439 0.999549i \(-0.490435\pi\)
−0.850613 + 0.525793i \(0.823769\pi\)
\(618\) −0.627871 0.362501i −0.0252567 0.0145819i
\(619\) 23.0280i 0.925573i −0.886470 0.462786i \(-0.846850\pi\)
0.886470 0.462786i \(-0.153150\pi\)
\(620\) 0 0
\(621\) 3.22853 + 5.59197i 0.129556 + 0.224398i
\(622\) 12.7792 7.37808i 0.512399 0.295834i
\(623\) −12.5493 −0.502776
\(624\) −3.60488 + 0.0693504i −0.144311 + 0.00277624i
\(625\) 0 0
\(626\) 1.21625 0.702205i 0.0486113 0.0280658i
\(627\) 2.21089 + 3.82937i 0.0882944 + 0.152930i
\(628\) −11.2609 + 19.5044i −0.449357 + 0.778309i
\(629\) 23.3844i 0.932397i
\(630\) 0 0
\(631\) −14.3378 8.27792i −0.570778 0.329539i 0.186682 0.982420i \(-0.440227\pi\)
−0.757460 + 0.652882i \(0.773560\pi\)
\(632\) 3.68973i 0.146769i
\(633\) 0.620118 1.07408i 0.0246475 0.0426907i
\(634\) 16.5710 + 28.7019i 0.658119 + 1.13990i
\(635\) 0 0
\(636\) 5.36068 0.212565
\(637\) −10.6837 + 19.3552i −0.423303 + 0.766879i
\(638\) −5.69982 −0.225658
\(639\) −3.40803 + 1.96763i −0.134819 + 0.0778381i
\(640\) 0 0
\(641\) −0.390454 + 0.676286i −0.0154220 + 0.0267117i −0.873633 0.486585i \(-0.838243\pi\)
0.858211 + 0.513296i \(0.171576\pi\)
\(642\) 17.2173i 0.679514i
\(643\) 21.2597 + 12.2743i 0.838399 + 0.484050i 0.856720 0.515782i \(-0.172499\pi\)
−0.0183207 + 0.999832i \(0.505832\pi\)
\(644\) 5.21089 + 3.00851i 0.205338 + 0.118552i
\(645\) 0 0
\(646\) 3.35533 5.81160i 0.132014 0.228654i
\(647\) −1.58200 2.74011i −0.0621950 0.107725i 0.833251 0.552894i \(-0.186477\pi\)
−0.895446 + 0.445170i \(0.853143\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) −6.68521 −0.262417
\(650\) 0 0
\(651\) −8.66150 −0.339471
\(652\) −2.40313 + 1.38745i −0.0941137 + 0.0543366i
\(653\) 16.1443 + 27.9627i 0.631774 + 1.09426i 0.987189 + 0.159556i \(0.0510062\pi\)
−0.355415 + 0.934709i \(0.615660\pi\)
\(654\) −5.14078 + 8.90410i −0.201021 + 0.348178i
\(655\) 0 0
\(656\) −1.01714 0.587246i −0.0397127 0.0229281i
\(657\) 6.29021 + 3.63165i 0.245404 + 0.141684i
\(658\) 3.70815i 0.144559i
\(659\) −17.6775 + 30.6184i −0.688619 + 1.19272i 0.283666 + 0.958923i \(0.408449\pi\)
−0.972285 + 0.233799i \(0.924884\pi\)
\(660\) 0 0
\(661\) 16.9243 9.77124i 0.658279 0.380057i −0.133342 0.991070i \(-0.542571\pi\)
0.791621 + 0.611013i \(0.209238\pi\)
\(662\) 6.98904 0.271637
\(663\) 4.75481 + 7.88147i 0.184661 + 0.306091i
\(664\) 3.84909 0.149374
\(665\) 0 0
\(666\) 4.57994 + 7.93269i 0.177469 + 0.307385i
\(667\) 10.9395 18.9478i 0.423579 0.733661i
\(668\) 22.2044i 0.859114i
\(669\) 12.7984 + 7.38915i 0.494814 + 0.285681i
\(670\) 0 0
\(671\) 14.6748i 0.566514i
\(672\) 0.465926 0.807007i 0.0179735 0.0311310i
\(673\) 1.25806 + 2.17903i 0.0484948 + 0.0839954i 0.889254 0.457414i \(-0.151224\pi\)
−0.840759 + 0.541409i \(0.817891\pi\)
\(674\) 30.5906 17.6615i 1.17830 0.680295i
\(675\) 0 0
\(676\) 6.92820 + 11.0000i 0.266469 + 0.423077i
\(677\) −41.0114 −1.57620 −0.788098 0.615550i \(-0.788934\pi\)
−0.788098 + 0.615550i \(0.788934\pi\)
\(678\) −8.36308 + 4.82843i −0.321182 + 0.185435i
\(679\) 6.56072 + 11.3635i 0.251777 + 0.436091i
\(680\) 0 0
\(681\) 9.56580i 0.366562i
\(682\) 13.5408 + 7.81779i 0.518505 + 0.299359i
\(683\) 20.9177 + 12.0769i 0.800395 + 0.462108i 0.843609 0.536958i \(-0.180426\pi\)
−0.0432142 + 0.999066i \(0.513760\pi\)
\(684\) 2.62863i 0.100508i
\(685\) 0 0
\(686\) −6.11838 10.5973i −0.233601 0.404608i
\(687\) 13.1184 7.57389i 0.500497 0.288962i
\(688\) −2.95252 −0.112564
\(689\) −9.98427 16.5497i −0.380370 0.630494i
\(690\) 0 0
\(691\) −35.7340 + 20.6310i −1.35939 + 0.784841i −0.989541 0.144252i \(-0.953922\pi\)
−0.369844 + 0.929094i \(0.620589\pi\)
\(692\) −0.475314 0.823267i −0.0180687 0.0312959i
\(693\) 0.783763 1.35752i 0.0297727 0.0515678i
\(694\) 3.61841i 0.137353i
\(695\) 0 0
\(696\) −2.93443 1.69419i −0.111229 0.0642183i
\(697\) 2.99838i 0.113572i
\(698\) 14.5467 25.1956i 0.550601 0.953669i
\(699\) −9.37064 16.2304i −0.354430 0.613891i
\(700\) 0 0
\(701\) 27.2880 1.03065 0.515327 0.856994i \(-0.327671\pi\)
0.515327 + 0.856994i \(0.327671\pi\)
\(702\) −3.15660 1.74238i −0.119138 0.0657620i
\(703\) −24.0779 −0.908115
\(704\) −1.45680 + 0.841081i −0.0549051 + 0.0316994i
\(705\) 0 0
\(706\) 4.79701 8.30867i 0.180538 0.312701i
\(707\) 10.5465i 0.396644i
\(708\) −3.44174 1.98709i −0.129348 0.0746793i
\(709\) 2.18928 + 1.26398i 0.0822200 + 0.0474697i 0.540546 0.841314i \(-0.318218\pi\)
−0.458326 + 0.888784i \(0.651551\pi\)
\(710\) 0 0
\(711\) 1.84486 3.19540i 0.0691878 0.119837i
\(712\) 6.73351 + 11.6628i 0.252349 + 0.437081i
\(713\) −51.9770 + 30.0089i −1.94655 + 1.12384i
\(714\) −2.37894 −0.0890295
\(715\) 0 0
\(716\) 9.88312 0.369350
\(717\) 4.00390 2.31165i 0.149528 0.0863302i
\(718\) −3.15748 5.46891i −0.117836 0.204098i
\(719\) 26.6943 46.2359i 0.995530 1.72431i 0.415968 0.909379i \(-0.363443\pi\)
0.579562 0.814928i \(-0.303224\pi\)
\(720\) 0 0
\(721\) −0.585082 0.337797i −0.0217896 0.0125802i
\(722\) 10.4705 + 6.04516i 0.389673 + 0.224978i
\(723\) 17.5945i 0.654347i
\(724\) 7.15075 12.3855i 0.265756 0.460302i
\(725\) 0 0
\(726\) 7.07571 4.08516i 0.262604 0.151615i
\(727\) 2.09614 0.0777417 0.0388709 0.999244i \(-0.487624\pi\)
0.0388709 + 0.999244i \(0.487624\pi\)
\(728\) −3.35922 + 0.0646242i −0.124501 + 0.00239513i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 3.76876 + 6.52768i 0.139393 + 0.241435i
\(732\) 4.36188 7.55500i 0.161220 0.279241i
\(733\) 16.7827i 0.619883i −0.950756 0.309942i \(-0.899690\pi\)
0.950756 0.309942i \(-0.100310\pi\)
\(734\) −30.2194 17.4472i −1.11542 0.643987i
\(735\) 0 0
\(736\) 6.45705i 0.238010i
\(737\) −4.36648 + 7.56297i −0.160841 + 0.278585i
\(738\) −0.587246 1.01714i −0.0216168 0.0374414i
\(739\) 8.24563 4.76062i 0.303321 0.175122i −0.340613 0.940204i \(-0.610635\pi\)
0.643934 + 0.765081i \(0.277301\pi\)
\(740\) 0 0
\(741\) 8.11522 4.89582i 0.298120 0.179852i
\(742\) 4.99536 0.183385
\(743\) 28.2034 16.2832i 1.03468 0.597374i 0.116360 0.993207i \(-0.462877\pi\)
0.918323 + 0.395833i \(0.129544\pi\)
\(744\) 4.64747 + 8.04965i 0.170384 + 0.295114i
\(745\) 0 0
\(746\) 4.81216i 0.176186i
\(747\) 3.33341 + 1.92455i 0.121963 + 0.0704154i
\(748\) 3.71907 + 2.14721i 0.135983 + 0.0785097i
\(749\) 16.0440i 0.586235i
\(750\) 0 0
\(751\) −7.38117 12.7846i −0.269343 0.466515i 0.699350 0.714780i \(-0.253473\pi\)
−0.968692 + 0.248265i \(0.920140\pi\)
\(752\) −3.44621 + 1.98967i −0.125670 + 0.0725557i
\(753\) −26.5198 −0.966436
\(754\) 0.234986 + 12.2148i 0.00855769 + 0.444835i
\(755\) 0 0
\(756\) 0.807007 0.465926i 0.0293506 0.0169456i
\(757\) 17.5781 + 30.4462i 0.638888 + 1.10659i 0.985677 + 0.168643i \(0.0539385\pi\)
−0.346789 + 0.937943i \(0.612728\pi\)
\(758\) 13.9053 24.0847i 0.505063 0.874795i
\(759\) 10.8618i 0.394259i
\(760\) 0 0
\(761\) −36.2215 20.9125i −1.31303 0.758076i −0.330431 0.943830i \(-0.607194\pi\)
−0.982596 + 0.185754i \(0.940527\pi\)
\(762\) 0.677003i 0.0245252i
\(763\) −4.79045 + 8.29730i −0.173426 + 0.300382i
\(764\) −0.0573183 0.0992782i −0.00207370 0.00359176i
\(765\) 0 0
\(766\) 0.805736 0.0291124
\(767\) 0.275611 + 14.3264i 0.00995172 + 0.517298i
\(768\) −1.00000 −0.0360844
\(769\) 39.4957 22.8028i 1.42425 0.822291i 0.427591 0.903972i \(-0.359362\pi\)
0.996659 + 0.0816812i \(0.0260289\pi\)
\(770\) 0 0
\(771\) −0.912132 + 1.57986i −0.0328496 + 0.0568972i
\(772\) 8.65685i 0.311567i
\(773\) 10.9424 + 6.31759i 0.393570 + 0.227228i 0.683706 0.729758i \(-0.260367\pi\)
−0.290136 + 0.956986i \(0.593700\pi\)
\(774\) −2.55695 1.47626i −0.0919078 0.0530630i
\(775\) 0 0
\(776\) 7.04052 12.1945i 0.252740 0.437758i
\(777\) 4.26782 + 7.39209i 0.153107 + 0.265190i
\(778\) 23.8168 13.7507i 0.853875 0.492985i
\(779\) 3.08730 0.110614
\(780\) 0 0
\(781\) 6.61973 0.236873
\(782\) −14.2758 + 8.24215i −0.510502 + 0.294739i