Properties

Label 1950.2.bc.f.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: \( x^{8} - x^{4} + 1 \) 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 751.3
Root \(0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1950.751
Dual form 1950.2.bc.f.901.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-1.31431 - 0.758819i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(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} +(-1.31431 - 0.758819i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.45680 + 2.57313i) q^{11} +1.00000 q^{12} +(-3.08725 + 1.86250i) q^{13} -1.51764 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.39778 - 4.15307i) q^{17} +1.00000i q^{18} +(-1.39778 - 0.807007i) q^{19} -1.51764i q^{21} +(-2.57313 + 4.45680i) q^{22} +(-2.72122 - 4.71329i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-1.74238 + 3.15660i) q^{26} -1.00000 q^{27} +(-1.31431 + 0.758819i) q^{28} +(-4.93684 - 8.55085i) q^{29} -9.88072i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.45680 - 2.57313i) q^{33} -4.79555i q^{34} +(0.500000 + 0.866025i) q^{36} +(7.56873 - 4.36981i) q^{37} -1.61401 q^{38} +(-3.15660 - 1.74238i) q^{39} +(1.10418 - 0.637499i) q^{41} +(-0.758819 - 1.31431i) q^{42} +(-1.18336 + 2.04965i) q^{43} +5.14626i q^{44} +(-4.71329 - 2.72122i) q^{46} +6.84909i q^{47} +(0.500000 - 0.866025i) q^{48} +(-2.34839 - 4.06753i) q^{49} +4.79555 q^{51} +(0.0693504 + 3.60488i) q^{52} +0.881964 q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.758819 + 1.31431i) q^{56} -1.61401i q^{57} +(-8.55085 - 4.93684i) q^{58} +(-8.04354 - 4.64394i) q^{59} +(-6.24056 + 10.8090i) q^{61} +(-4.94036 - 8.55695i) q^{62} +(1.31431 - 0.758819i) q^{63} -1.00000 q^{64} -5.14626 q^{66} +(-9.98930 + 5.76733i) q^{67} +(-2.39778 - 4.15307i) q^{68} +(2.72122 - 4.71329i) q^{69} +(13.7133 + 7.91737i) q^{71} +(0.866025 + 0.500000i) q^{72} +4.39355i q^{73} +(4.36981 - 7.56873i) q^{74} +(-1.39778 + 0.807007i) q^{76} +7.81017 q^{77} +(-3.60488 + 0.0693504i) q^{78} -11.0382 q^{79} +(-0.500000 - 0.866025i) q^{81} +(0.637499 - 1.10418i) q^{82} +0.979336i q^{83} +(-1.31431 - 0.758819i) q^{84} +2.36673i q^{86} +(4.93684 - 8.55085i) q^{87} +(2.57313 + 4.45680i) q^{88} +(-3.54146 + 2.04466i) q^{89} +(5.47091 - 0.105249i) q^{91} -5.44244 q^{92} +(8.55695 - 4.94036i) q^{93} +(3.42455 + 5.93149i) q^{94} -1.00000i q^{96} +(4.95189 + 2.85898i) q^{97} +(-4.06753 - 2.34839i) q^{98} -5.14626i 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
\(7\) −1.31431 0.758819i −0.496764 0.286807i 0.230612 0.973046i \(-0.425927\pi\)
−0.727376 + 0.686239i \(0.759260\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −4.45680 + 2.57313i −1.34377 + 0.775829i −0.987359 0.158499i \(-0.949335\pi\)
−0.356415 + 0.934328i \(0.616001\pi\)
\(12\) 1.00000 0.288675
\(13\) −3.08725 + 1.86250i −0.856248 + 0.516565i
\(14\) −1.51764 −0.405606
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.39778 4.15307i 0.581546 1.00727i −0.413750 0.910391i \(-0.635781\pi\)
0.995296 0.0968774i \(-0.0308855\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −1.39778 0.807007i −0.320672 0.185140i 0.331020 0.943624i \(-0.392607\pi\)
−0.651692 + 0.758484i \(0.725941\pi\)
\(20\) 0 0
\(21\) 1.51764i 0.331176i
\(22\) −2.57313 + 4.45680i −0.548594 + 0.950192i
\(23\) −2.72122 4.71329i −0.567414 0.982789i −0.996821 0.0796783i \(-0.974611\pi\)
0.429407 0.903111i \(-0.358723\pi\)
\(24\) 0.866025 0.500000i 0.176777 0.102062i
\(25\) 0 0
\(26\) −1.74238 + 3.15660i −0.341709 + 0.619060i
\(27\) −1.00000 −0.192450
\(28\) −1.31431 + 0.758819i −0.248382 + 0.143403i
\(29\) −4.93684 8.55085i −0.916747 1.58785i −0.804323 0.594193i \(-0.797472\pi\)
−0.112425 0.993660i \(-0.535862\pi\)
\(30\) 0 0
\(31\) 9.88072i 1.77463i −0.461164 0.887315i \(-0.652568\pi\)
0.461164 0.887315i \(-0.347432\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) −4.45680 2.57313i −0.775829 0.447925i
\(34\) 4.79555i 0.822431i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 7.56873 4.36981i 1.24429 0.718392i 0.274326 0.961637i \(-0.411545\pi\)
0.969965 + 0.243245i \(0.0782118\pi\)
\(38\) −1.61401 −0.261828
\(39\) −3.15660 1.74238i −0.505460 0.279005i
\(40\) 0 0
\(41\) 1.10418 0.637499i 0.172444 0.0995606i −0.411294 0.911503i \(-0.634923\pi\)
0.583738 + 0.811942i \(0.301590\pi\)
\(42\) −0.758819 1.31431i −0.117088 0.202803i
\(43\) −1.18336 + 2.04965i −0.180461 + 0.312568i −0.942038 0.335507i \(-0.891092\pi\)
0.761576 + 0.648075i \(0.224426\pi\)
\(44\) 5.14626i 0.775829i
\(45\) 0 0
\(46\) −4.71329 2.72122i −0.694937 0.401222i
\(47\) 6.84909i 0.999043i 0.866302 + 0.499521i \(0.166491\pi\)
−0.866302 + 0.499521i \(0.833509\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) −2.34839 4.06753i −0.335484 0.581075i
\(50\) 0 0
\(51\) 4.79555 0.671512
\(52\) 0.0693504 + 3.60488i 0.00961716 + 0.499908i
\(53\) 0.881964 0.121147 0.0605735 0.998164i \(-0.480707\pi\)
0.0605735 + 0.998164i \(0.480707\pi\)
\(54\) −0.866025 + 0.500000i −0.117851 + 0.0680414i
\(55\) 0 0
\(56\) −0.758819 + 1.31431i −0.101401 + 0.175632i
\(57\) 1.61401i 0.213781i
\(58\) −8.55085 4.93684i −1.12278 0.648238i
\(59\) −8.04354 4.64394i −1.04718 0.604590i −0.125322 0.992116i \(-0.539996\pi\)
−0.921859 + 0.387526i \(0.873330\pi\)
\(60\) 0 0
\(61\) −6.24056 + 10.8090i −0.799022 + 1.38395i 0.121232 + 0.992624i \(0.461315\pi\)
−0.920254 + 0.391322i \(0.872018\pi\)
\(62\) −4.94036 8.55695i −0.627426 1.08673i
\(63\) 1.31431 0.758819i 0.165588 0.0956022i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −5.14626 −0.633461
\(67\) −9.98930 + 5.76733i −1.22039 + 0.704591i −0.965001 0.262248i \(-0.915536\pi\)
−0.255387 + 0.966839i \(0.582203\pi\)
\(68\) −2.39778 4.15307i −0.290773 0.503634i
\(69\) 2.72122 4.71329i 0.327596 0.567414i
\(70\) 0 0
\(71\) 13.7133 + 7.91737i 1.62747 + 0.939619i 0.984845 + 0.173437i \(0.0554874\pi\)
0.642623 + 0.766182i \(0.277846\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) 4.39355i 0.514226i 0.966381 + 0.257113i \(0.0827713\pi\)
−0.966381 + 0.257113i \(0.917229\pi\)
\(74\) 4.36981 7.56873i 0.507980 0.879847i
\(75\) 0 0
\(76\) −1.39778 + 0.807007i −0.160336 + 0.0925701i
\(77\) 7.81017 0.890051
\(78\) −3.60488 + 0.0693504i −0.408173 + 0.00785238i
\(79\) −11.0382 −1.24189 −0.620947 0.783853i \(-0.713252\pi\)
−0.620947 + 0.783853i \(0.713252\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0.637499 1.10418i 0.0704000 0.121936i
\(83\) 0.979336i 0.107496i 0.998555 + 0.0537480i \(0.0171168\pi\)
−0.998555 + 0.0537480i \(0.982883\pi\)
\(84\) −1.31431 0.758819i −0.143403 0.0827939i
\(85\) 0 0
\(86\) 2.36673i 0.255211i
\(87\) 4.93684 8.55085i 0.529284 0.916747i
\(88\) 2.57313 + 4.45680i 0.274297 + 0.475096i
\(89\) −3.54146 + 2.04466i −0.375394 + 0.216734i −0.675812 0.737074i \(-0.736207\pi\)
0.300418 + 0.953808i \(0.402874\pi\)
\(90\) 0 0
\(91\) 5.47091 0.105249i 0.573507 0.0110331i
\(92\) −5.44244 −0.567414
\(93\) 8.55695 4.94036i 0.887315 0.512291i
\(94\) 3.42455 + 5.93149i 0.353215 + 0.611786i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) 4.95189 + 2.85898i 0.502789 + 0.290285i 0.729864 0.683592i \(-0.239583\pi\)
−0.227076 + 0.973877i \(0.572917\pi\)
\(98\) −4.06753 2.34839i −0.410882 0.237223i
\(99\) 5.14626i 0.517219i
\(100\) 0 0
\(101\) −3.92687 6.80153i −0.390738 0.676778i 0.601809 0.798640i \(-0.294447\pi\)
−0.992547 + 0.121862i \(0.961113\pi\)
\(102\) 4.15307 2.39778i 0.411215 0.237415i
\(103\) 3.17449 0.312792 0.156396 0.987694i \(-0.450012\pi\)
0.156396 + 0.987694i \(0.450012\pi\)
\(104\) 1.86250 + 3.08725i 0.182633 + 0.302729i
\(105\) 0 0
\(106\) 0.763803 0.440982i 0.0741871 0.0428319i
\(107\) 6.87662 + 11.9106i 0.664787 + 1.15145i 0.979343 + 0.202207i \(0.0648112\pi\)
−0.314555 + 0.949239i \(0.601855\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 16.7895i 1.60814i 0.594533 + 0.804071i \(0.297337\pi\)
−0.594533 + 0.804071i \(0.702663\pi\)
\(110\) 0 0
\(111\) 7.56873 + 4.36981i 0.718392 + 0.414764i
\(112\) 1.51764i 0.143403i
\(113\) 4.82843 8.36308i 0.454220 0.786732i −0.544423 0.838811i \(-0.683251\pi\)
0.998643 + 0.0520785i \(0.0165846\pi\)
\(114\) −0.807007 1.39778i −0.0755831 0.130914i
\(115\) 0 0
\(116\) −9.87367 −0.916747
\(117\) −0.0693504 3.60488i −0.00641144 0.333272i
\(118\) −9.28788 −0.855019
\(119\) −6.30286 + 3.63896i −0.577782 + 0.333583i
\(120\) 0 0
\(121\) 7.74202 13.4096i 0.703820 1.21905i
\(122\) 12.4811i 1.12999i
\(123\) 1.10418 + 0.637499i 0.0995606 + 0.0574813i
\(124\) −8.55695 4.94036i −0.768437 0.443657i
\(125\) 0 0
\(126\) 0.758819 1.31431i 0.0676010 0.117088i
\(127\) 5.99536 + 10.3843i 0.532002 + 0.921454i 0.999302 + 0.0373555i \(0.0118934\pi\)
−0.467300 + 0.884099i \(0.654773\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) −2.36673 −0.208379
\(130\) 0 0
\(131\) −20.3524 −1.77820 −0.889098 0.457717i \(-0.848667\pi\)
−0.889098 + 0.457717i \(0.848667\pi\)
\(132\) −4.45680 + 2.57313i −0.387914 + 0.223962i
\(133\) 1.22474 + 2.12132i 0.106199 + 0.183942i
\(134\) −5.76733 + 9.98930i −0.498221 + 0.862944i
\(135\) 0 0
\(136\) −4.15307 2.39778i −0.356123 0.205608i
\(137\) −6.82684 3.94148i −0.583257 0.336743i 0.179170 0.983818i \(-0.442659\pi\)
−0.762427 + 0.647075i \(0.775992\pi\)
\(138\) 5.44244i 0.463291i
\(139\) −2.05852 + 3.56546i −0.174601 + 0.302419i −0.940023 0.341110i \(-0.889197\pi\)
0.765422 + 0.643529i \(0.222530\pi\)
\(140\) 0 0
\(141\) −5.93149 + 3.42455i −0.499521 + 0.288399i
\(142\) 15.8347 1.32882
\(143\) 8.96676 16.2447i 0.749838 1.35845i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 2.19677 + 3.80493i 0.181806 + 0.314898i
\(147\) 2.34839 4.06753i 0.193692 0.335484i
\(148\) 8.73961i 0.718392i
\(149\) −8.00644 4.62252i −0.655913 0.378692i 0.134805 0.990872i \(-0.456959\pi\)
−0.790718 + 0.612180i \(0.790293\pi\)
\(150\) 0 0
\(151\) 17.1479i 1.39548i −0.716351 0.697740i \(-0.754189\pi\)
0.716351 0.697740i \(-0.245811\pi\)
\(152\) −0.807007 + 1.39778i −0.0654569 + 0.113375i
\(153\) 2.39778 + 4.15307i 0.193849 + 0.335756i
\(154\) 6.76380 3.90508i 0.545043 0.314681i
\(155\) 0 0
\(156\) −3.08725 + 1.86250i −0.247178 + 0.149119i
\(157\) 18.2791 1.45883 0.729415 0.684072i \(-0.239793\pi\)
0.729415 + 0.684072i \(0.239793\pi\)
\(158\) −9.55936 + 5.51910i −0.760502 + 0.439076i
\(159\) 0.440982 + 0.763803i 0.0349721 + 0.0605735i
\(160\) 0 0
\(161\) 8.25966i 0.650952i
\(162\) −0.866025 0.500000i −0.0680414 0.0392837i
\(163\) −1.47555 0.851911i −0.115574 0.0667269i 0.441098 0.897459i \(-0.354589\pi\)
−0.556673 + 0.830732i \(0.687922\pi\)
\(164\) 1.27500i 0.0995606i
\(165\) 0 0
\(166\) 0.489668 + 0.848130i 0.0380056 + 0.0658276i
\(167\) 4.61967 2.66717i 0.357481 0.206392i −0.310494 0.950575i \(-0.600495\pi\)
0.667975 + 0.744184i \(0.267161\pi\)
\(168\) −1.51764 −0.117088
\(169\) 6.06218 11.5000i 0.466321 0.884615i
\(170\) 0 0
\(171\) 1.39778 0.807007i 0.106891 0.0617134i
\(172\) 1.18336 + 2.04965i 0.0902307 + 0.156284i
\(173\) 8.83839 15.3085i 0.671971 1.16389i −0.305374 0.952233i \(-0.598781\pi\)
0.977344 0.211655i \(-0.0678853\pi\)
\(174\) 9.87367i 0.748521i
\(175\) 0 0
\(176\) 4.45680 + 2.57313i 0.335944 + 0.193957i
\(177\) 9.28788i 0.698120i
\(178\) −2.04466 + 3.54146i −0.153254 + 0.265444i
\(179\) −10.7700 18.6542i −0.804987 1.39428i −0.916300 0.400493i \(-0.868839\pi\)
0.111313 0.993785i \(-0.464494\pi\)
\(180\) 0 0
\(181\) 4.08328 0.303507 0.151754 0.988418i \(-0.451508\pi\)
0.151754 + 0.988418i \(0.451508\pi\)
\(182\) 4.68532 2.82660i 0.347299 0.209522i
\(183\) −12.4811 −0.922631
\(184\) −4.71329 + 2.72122i −0.347469 + 0.200611i
\(185\) 0 0
\(186\) 4.94036 8.55695i 0.362245 0.627426i
\(187\) 24.6792i 1.80472i
\(188\) 5.93149 + 3.42455i 0.432598 + 0.249761i
\(189\) 1.31431 + 0.758819i 0.0956022 + 0.0551960i
\(190\) 0 0
\(191\) 6.47822 11.2206i 0.468747 0.811894i −0.530615 0.847613i \(-0.678039\pi\)
0.999362 + 0.0357192i \(0.0113722\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −7.49706 + 4.32843i −0.539650 + 0.311567i −0.744937 0.667135i \(-0.767521\pi\)
0.205287 + 0.978702i \(0.434187\pi\)
\(194\) 5.71795 0.410525
\(195\) 0 0
\(196\) −4.69677 −0.335484
\(197\) −3.76574 + 2.17415i −0.268298 + 0.154902i −0.628114 0.778121i \(-0.716173\pi\)
0.359816 + 0.933023i \(0.382840\pi\)
\(198\) −2.57313 4.45680i −0.182865 0.316731i
\(199\) −3.73351 + 6.46663i −0.264662 + 0.458407i −0.967475 0.252967i \(-0.918594\pi\)
0.702813 + 0.711374i \(0.251927\pi\)
\(200\) 0 0
\(201\) −9.98930 5.76733i −0.704591 0.406796i
\(202\) −6.80153 3.92687i −0.478554 0.276293i
\(203\) 14.9847i 1.05172i
\(204\) 2.39778 4.15307i 0.167878 0.290773i
\(205\) 0 0
\(206\) 2.74919 1.58725i 0.191545 0.110589i
\(207\) 5.44244 0.378276
\(208\) 3.15660 + 1.74238i 0.218871 + 0.120813i
\(209\) 8.30614 0.574548
\(210\) 0 0
\(211\) −6.74384 11.6807i −0.464265 0.804131i 0.534903 0.844914i \(-0.320348\pi\)
−0.999168 + 0.0407826i \(0.987015\pi\)
\(212\) 0.440982 0.763803i 0.0302868 0.0524582i
\(213\) 15.8347i 1.08498i
\(214\) 11.9106 + 6.87662i 0.814195 + 0.470076i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −7.49768 + 12.9864i −0.508976 + 0.881571i
\(218\) 8.39475 + 14.5401i 0.568564 + 0.984782i
\(219\) −3.80493 + 2.19677i −0.257113 + 0.148444i
\(220\) 0 0
\(221\) 0.332573 + 17.2874i 0.0223713 + 1.16288i
\(222\) 8.73961 0.586565
\(223\) 6.08030 3.51047i 0.407167 0.235078i −0.282405 0.959295i \(-0.591132\pi\)
0.689572 + 0.724217i \(0.257799\pi\)
\(224\) 0.758819 + 1.31431i 0.0507007 + 0.0878162i
\(225\) 0 0
\(226\) 9.65685i 0.642364i
\(227\) 7.44370 + 4.29762i 0.494055 + 0.285243i 0.726255 0.687425i \(-0.241259\pi\)
−0.232200 + 0.972668i \(0.574592\pi\)
\(228\) −1.39778 0.807007i −0.0925701 0.0534454i
\(229\) 16.4086i 1.08431i 0.840279 + 0.542155i \(0.182391\pi\)
−0.840279 + 0.542155i \(0.817609\pi\)
\(230\) 0 0
\(231\) 3.90508 + 6.76380i 0.256936 + 0.445026i
\(232\) −8.55085 + 4.93684i −0.561391 + 0.324119i
\(233\) 6.94230 0.454805 0.227403 0.973801i \(-0.426977\pi\)
0.227403 + 0.973801i \(0.426977\pi\)
\(234\) −1.86250 3.08725i −0.121756 0.201820i
\(235\) 0 0
\(236\) −8.04354 + 4.64394i −0.523590 + 0.302295i
\(237\) −5.51910 9.55936i −0.358504 0.620947i
\(238\) −3.63896 + 6.30286i −0.235879 + 0.408554i
\(239\) 18.3056i 1.18409i 0.805904 + 0.592046i \(0.201680\pi\)
−0.805904 + 0.592046i \(0.798320\pi\)
\(240\) 0 0
\(241\) 12.4906 + 7.21147i 0.804592 + 0.464532i 0.845074 0.534649i \(-0.179556\pi\)
−0.0404822 + 0.999180i \(0.512889\pi\)
\(242\) 15.4840i 0.995352i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 6.24056 + 10.8090i 0.399511 + 0.691973i
\(245\) 0 0
\(246\) 1.27500 0.0812909
\(247\) 5.81834 0.111932i 0.370212 0.00712209i
\(248\) −9.88072 −0.627426
\(249\) −0.848130 + 0.489668i −0.0537480 + 0.0310314i
\(250\) 0 0
\(251\) −3.88222 + 6.72420i −0.245044 + 0.424428i −0.962144 0.272542i \(-0.912136\pi\)
0.717100 + 0.696970i \(0.245469\pi\)
\(252\) 1.51764i 0.0956022i
\(253\) 24.2558 + 14.0041i 1.52495 + 0.880432i
\(254\) 10.3843 + 5.99536i 0.651566 + 0.376182i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −9.69031 16.7841i −0.604465 1.04696i −0.992136 0.125166i \(-0.960054\pi\)
0.387671 0.921798i \(-0.373280\pi\)
\(258\) −2.04965 + 1.18336i −0.127606 + 0.0736731i
\(259\) −13.2636 −0.824158
\(260\) 0 0
\(261\) 9.87367 0.611165
\(262\) −17.6257 + 10.1762i −1.08892 + 0.628687i
\(263\) −0.946961 1.64019i −0.0583921 0.101138i 0.835352 0.549716i \(-0.185264\pi\)
−0.893744 + 0.448578i \(0.851931\pi\)
\(264\) −2.57313 + 4.45680i −0.158365 + 0.274297i
\(265\) 0 0
\(266\) 2.12132 + 1.22474i 0.130066 + 0.0750939i
\(267\) −3.54146 2.04466i −0.216734 0.125131i
\(268\) 11.5347i 0.704591i
\(269\) 2.30104 3.98551i 0.140297 0.243001i −0.787312 0.616555i \(-0.788528\pi\)
0.927608 + 0.373554i \(0.121861\pi\)
\(270\) 0 0
\(271\) 7.22596 4.17191i 0.438946 0.253426i −0.264204 0.964467i \(-0.585109\pi\)
0.703150 + 0.711041i \(0.251776\pi\)
\(272\) −4.79555 −0.290773
\(273\) 2.82660 + 4.68532i 0.171074 + 0.283569i
\(274\) −7.88296 −0.476227
\(275\) 0 0
\(276\) −2.72122 4.71329i −0.163798 0.283707i
\(277\) −11.1189 + 19.2585i −0.668068 + 1.15713i 0.310375 + 0.950614i \(0.399545\pi\)
−0.978444 + 0.206514i \(0.933788\pi\)
\(278\) 4.11704i 0.246924i
\(279\) 8.55695 + 4.94036i 0.512291 + 0.295772i
\(280\) 0 0
\(281\) 20.0961i 1.19883i −0.800437 0.599417i \(-0.795399\pi\)
0.800437 0.599417i \(-0.204601\pi\)
\(282\) −3.42455 + 5.93149i −0.203929 + 0.353215i
\(283\) 0.359921 + 0.623402i 0.0213951 + 0.0370574i 0.876525 0.481357i \(-0.159856\pi\)
−0.855130 + 0.518414i \(0.826523\pi\)
\(284\) 13.7133 7.91737i 0.813734 0.469810i
\(285\) 0 0
\(286\) −0.356895 18.5517i −0.0211037 1.09698i
\(287\) −1.93498 −0.114219
\(288\) 0.866025 0.500000i 0.0510310 0.0294628i
\(289\) −2.99867 5.19386i −0.176393 0.305521i
\(290\) 0 0
\(291\) 5.71795i 0.335192i
\(292\) 3.80493 + 2.19677i 0.222666 + 0.128557i
\(293\) −11.4556 6.61389i −0.669243 0.386388i 0.126547 0.991961i \(-0.459611\pi\)
−0.795790 + 0.605573i \(0.792944\pi\)
\(294\) 4.69677i 0.273921i
\(295\) 0 0
\(296\) −4.36981 7.56873i −0.253990 0.439923i
\(297\) 4.45680 2.57313i 0.258610 0.149308i
\(298\) −9.24504 −0.535551
\(299\) 17.1796 + 9.48282i 0.993521 + 0.548405i
\(300\) 0 0
\(301\) 3.11062 1.79592i 0.179293 0.103515i
\(302\) −8.57397 14.8506i −0.493377 0.854553i
\(303\) 3.92687 6.80153i 0.225593 0.390738i
\(304\) 1.61401i 0.0925701i
\(305\) 0 0
\(306\) 4.15307 + 2.39778i 0.237415 + 0.137072i
\(307\) 7.85174i 0.448123i 0.974575 + 0.224061i \(0.0719316\pi\)
−0.974575 + 0.224061i \(0.928068\pi\)
\(308\) 3.90508 6.76380i 0.222513 0.385403i
\(309\) 1.58725 + 2.74919i 0.0902953 + 0.156396i
\(310\) 0 0
\(311\) −15.7708 −0.894278 −0.447139 0.894465i \(-0.647557\pi\)
−0.447139 + 0.894465i \(0.647557\pi\)
\(312\) −1.74238 + 3.15660i −0.0986430 + 0.178707i
\(313\) 21.0613 1.19045 0.595227 0.803558i \(-0.297062\pi\)
0.595227 + 0.803558i \(0.297062\pi\)
\(314\) 15.8301 9.13954i 0.893347 0.515774i
\(315\) 0 0
\(316\) −5.51910 + 9.55936i −0.310474 + 0.537756i
\(317\) 26.4141i 1.48357i −0.670640 0.741783i \(-0.733981\pi\)
0.670640 0.741783i \(-0.266019\pi\)
\(318\) 0.763803 + 0.440982i 0.0428319 + 0.0247290i
\(319\) 44.0049 + 25.4063i 2.46380 + 1.42248i
\(320\) 0 0
\(321\) −6.87662 + 11.9106i −0.383815 + 0.664787i
\(322\) 4.12983 + 7.15307i 0.230146 + 0.398625i
\(323\) −6.70312 + 3.87005i −0.372972 + 0.215335i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −1.70382 −0.0943660
\(327\) −14.5401 + 8.39475i −0.804071 + 0.464231i
\(328\) −0.637499 1.10418i −0.0352000 0.0609681i
\(329\) 5.19722 9.00185i 0.286532 0.496288i
\(330\) 0 0
\(331\) 17.6887 + 10.2126i 0.972260 + 0.561335i 0.899925 0.436046i \(-0.143621\pi\)
0.0723356 + 0.997380i \(0.476955\pi\)
\(332\) 0.848130 + 0.489668i 0.0465472 + 0.0268740i
\(333\) 8.73961i 0.478928i
\(334\) 2.66717 4.61967i 0.145941 0.252777i
\(335\) 0 0
\(336\) −1.31431 + 0.758819i −0.0717017 + 0.0413970i
\(337\) −13.1035 −0.713791 −0.356895 0.934144i \(-0.616165\pi\)
−0.356895 + 0.934144i \(0.616165\pi\)
\(338\) −0.500000 12.9904i −0.0271964 0.706584i
\(339\) 9.65685 0.524488
\(340\) 0 0
\(341\) 25.4244 + 44.0363i 1.37681 + 2.38470i
\(342\) 0.807007 1.39778i 0.0436380 0.0755831i
\(343\) 17.7515i 0.958489i
\(344\) 2.04965 + 1.18336i 0.110510 + 0.0638028i
\(345\) 0 0
\(346\) 17.6768i 0.950310i
\(347\) 8.88027 15.3811i 0.476718 0.825700i −0.522926 0.852378i \(-0.675160\pi\)
0.999644 + 0.0266782i \(0.00849295\pi\)
\(348\) −4.93684 8.55085i −0.264642 0.458374i
\(349\) 0.103747 0.0598981i 0.00555343 0.00320627i −0.497221 0.867624i \(-0.665646\pi\)
0.502774 + 0.864418i \(0.332313\pi\)
\(350\) 0 0
\(351\) 3.08725 1.86250i 0.164785 0.0994130i
\(352\) 5.14626 0.274297
\(353\) −6.54057 + 3.77620i −0.348119 + 0.200987i −0.663857 0.747860i \(-0.731082\pi\)
0.315737 + 0.948847i \(0.397748\pi\)
\(354\) −4.64394 8.04354i −0.246823 0.427510i
\(355\) 0 0
\(356\) 4.08933i 0.216734i
\(357\) −6.30286 3.63896i −0.333583 0.192594i
\(358\) −18.6542 10.7700i −0.985903 0.569212i
\(359\) 29.9693i 1.58172i −0.611997 0.790860i \(-0.709634\pi\)
0.611997 0.790860i \(-0.290366\pi\)
\(360\) 0 0
\(361\) −8.19748 14.1984i −0.431446 0.747287i
\(362\) 3.53622 2.04164i 0.185860 0.107306i
\(363\) 15.4840 0.812701
\(364\) 2.64431 4.79057i 0.138599 0.251094i
\(365\) 0 0
\(366\) −10.8090 + 6.24056i −0.564994 + 0.326199i
\(367\) −14.4472 25.0232i −0.754136 1.30620i −0.945802 0.324742i \(-0.894722\pi\)
0.191666 0.981460i \(-0.438611\pi\)
\(368\) −2.72122 + 4.71329i −0.141853 + 0.245697i
\(369\) 1.27500i 0.0663737i
\(370\) 0 0
\(371\) −1.15918 0.669251i −0.0601814 0.0347458i
\(372\) 9.88072i 0.512291i
\(373\) 7.35583 12.7407i 0.380870 0.659687i −0.610317 0.792158i \(-0.708958\pi\)
0.991187 + 0.132471i \(0.0422911\pi\)
\(374\) 12.3396 + 21.3728i 0.638065 + 1.10516i
\(375\) 0 0
\(376\) 6.84909 0.353215
\(377\) 31.1672 + 17.2037i 1.60519 + 0.886036i
\(378\) 1.51764 0.0780589
\(379\) −27.1285 + 15.6627i −1.39350 + 0.804537i −0.993701 0.112067i \(-0.964253\pi\)
−0.399798 + 0.916603i \(0.630920\pi\)
\(380\) 0 0
\(381\) −5.99536 + 10.3843i −0.307151 + 0.532002i
\(382\) 12.9564i 0.662909i
\(383\) −9.39410 5.42368i −0.480016 0.277137i 0.240407 0.970672i \(-0.422719\pi\)
−0.720423 + 0.693535i \(0.756052\pi\)
\(384\) −0.866025 0.500000i −0.0441942 0.0255155i
\(385\) 0 0
\(386\) −4.32843 + 7.49706i −0.220311 + 0.381590i
\(387\) −1.18336 2.04965i −0.0601538 0.104189i
\(388\) 4.95189 2.85898i 0.251394 0.145143i
\(389\) −18.2977 −0.927730 −0.463865 0.885906i \(-0.653538\pi\)
−0.463865 + 0.885906i \(0.653538\pi\)
\(390\) 0 0
\(391\) −26.0995 −1.31991
\(392\) −4.06753 + 2.34839i −0.205441 + 0.118611i
\(393\) −10.1762 17.6257i −0.513321 0.889098i
\(394\) −2.17415 + 3.76574i −0.109532 + 0.189715i
\(395\) 0 0
\(396\) −4.45680 2.57313i −0.223962 0.129305i
\(397\) 0.266438 + 0.153828i 0.0133721 + 0.00772041i 0.506671 0.862139i \(-0.330876\pi\)
−0.493299 + 0.869860i \(0.664209\pi\)
\(398\) 7.46702i 0.374288i
\(399\) −1.22474 + 2.12132i −0.0613139 + 0.106199i
\(400\) 0 0
\(401\) 1.89266 1.09273i 0.0945149 0.0545682i −0.451998 0.892019i \(-0.649288\pi\)
0.546512 + 0.837451i \(0.315955\pi\)
\(402\) −11.5347 −0.575296
\(403\) 18.4029 + 30.5042i 0.916711 + 1.51952i
\(404\) −7.85374 −0.390738
\(405\) 0 0
\(406\) 7.49233 + 12.9771i 0.371838 + 0.644042i
\(407\) −22.4882 + 38.9507i −1.11470 + 1.93071i
\(408\) 4.79555i 0.237415i
\(409\) 32.6067 + 18.8255i 1.61230 + 0.930860i 0.988836 + 0.149006i \(0.0476073\pi\)
0.623461 + 0.781855i \(0.285726\pi\)
\(410\) 0 0
\(411\) 7.88296i 0.388838i
\(412\) 1.58725 2.74919i 0.0781980 0.135443i
\(413\) 7.04782 + 12.2072i 0.346801 + 0.600676i
\(414\) 4.71329 2.72122i 0.231646 0.133741i
\(415\) 0 0
\(416\) 3.60488 0.0693504i 0.176744 0.00340018i
\(417\) −4.11704 −0.201612
\(418\) 7.19333 4.15307i 0.351837 0.203133i
\(419\) −13.5307 23.4359i −0.661020 1.14492i −0.980348 0.197276i \(-0.936790\pi\)
0.319328 0.947644i \(-0.396543\pi\)
\(420\) 0 0
\(421\) 11.9356i 0.581706i −0.956768 0.290853i \(-0.906061\pi\)
0.956768 0.290853i \(-0.0939390\pi\)
\(422\) −11.6807 6.74384i −0.568607 0.328285i
\(423\) −5.93149 3.42455i −0.288399 0.166507i
\(424\) 0.881964i 0.0428319i
\(425\) 0 0
\(426\) 7.91737 + 13.7133i 0.383598 + 0.664411i
\(427\) 16.4041 9.47091i 0.793850 0.458329i
\(428\) 13.7532 0.664787
\(429\) 18.5517 0.356895i 0.895684 0.0172311i
\(430\) 0 0
\(431\) 25.9671 14.9921i 1.25079 0.722144i 0.279523 0.960139i \(-0.409824\pi\)
0.971266 + 0.237995i \(0.0764903\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) 10.4971 18.1814i 0.504456 0.873744i −0.495530 0.868591i \(-0.665026\pi\)
0.999987 0.00515336i \(-0.00164037\pi\)
\(434\) 14.9954i 0.719800i
\(435\) 0 0
\(436\) 14.5401 + 8.39475i 0.696346 + 0.402036i
\(437\) 8.78418i 0.420204i
\(438\) −2.19677 + 3.80493i −0.104966 + 0.181806i
\(439\) 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
\(441\) 4.69677 0.223656
\(442\) 8.93173 + 14.8051i 0.424839 + 0.704205i
\(443\) 12.8231 0.609244 0.304622 0.952473i \(-0.401470\pi\)
0.304622 + 0.952473i \(0.401470\pi\)
\(444\) 7.56873 4.36981i 0.359196 0.207382i
\(445\) 0 0
\(446\) 3.51047 6.08030i 0.166225 0.287911i
\(447\) 9.24504i 0.437276i
\(448\) 1.31431 + 0.758819i 0.0620955 + 0.0358508i
\(449\) −2.73315 1.57798i −0.128985 0.0744696i 0.434119 0.900855i \(-0.357060\pi\)
−0.563104 + 0.826386i \(0.690393\pi\)
\(450\) 0 0
\(451\) −3.28074 + 5.68240i −0.154484 + 0.267574i
\(452\) −4.82843 8.36308i −0.227110 0.393366i
\(453\) 14.8506 8.57397i 0.697740 0.402840i
\(454\) 8.59524 0.403395
\(455\) 0 0
\(456\) −1.61401 −0.0755831
\(457\) −0.250578 + 0.144671i −0.0117215 + 0.00676743i −0.505849 0.862622i \(-0.668821\pi\)
0.494128 + 0.869389i \(0.335487\pi\)
\(458\) 8.20429 + 14.2102i 0.383361 + 0.664001i
\(459\) −2.39778 + 4.15307i −0.111919 + 0.193849i
\(460\) 0 0
\(461\) −3.07799 1.77708i −0.143356 0.0827668i 0.426606 0.904437i \(-0.359709\pi\)
−0.569963 + 0.821671i \(0.693042\pi\)
\(462\) 6.76380 + 3.90508i 0.314681 + 0.181681i
\(463\) 12.1116i 0.562875i 0.959580 + 0.281438i \(0.0908113\pi\)
−0.959580 + 0.281438i \(0.909189\pi\)
\(464\) −4.93684 + 8.55085i −0.229187 + 0.396963i
\(465\) 0 0
\(466\) 6.01221 3.47115i 0.278510 0.160798i
\(467\) −29.9323 −1.38510 −0.692550 0.721369i \(-0.743513\pi\)
−0.692550 + 0.721369i \(0.743513\pi\)
\(468\) −3.15660 1.74238i −0.145914 0.0805417i
\(469\) 17.5054 0.808326
\(470\) 0 0
\(471\) 9.13954 + 15.8301i 0.421128 + 0.729415i
\(472\) −4.64394 + 8.04354i −0.213755 + 0.370234i
\(473\) 12.1798i 0.560029i
\(474\) −9.55936 5.51910i −0.439076 0.253501i
\(475\) 0 0
\(476\) 7.27792i 0.333583i
\(477\) −0.440982 + 0.763803i −0.0201912 + 0.0349721i
\(478\) 9.15281 + 15.8531i 0.418640 + 0.725106i
\(479\) 2.03012 1.17209i 0.0927584 0.0535541i −0.452903 0.891560i \(-0.649612\pi\)
0.545662 + 0.838006i \(0.316278\pi\)
\(480\) 0 0
\(481\) −15.2278 + 27.5874i −0.694326 + 1.25788i
\(482\) 14.4229 0.656947
\(483\) −7.15307 + 4.12983i −0.325476 + 0.187914i
\(484\) −7.74202 13.4096i −0.351910 0.609526i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 3.23354 + 1.86689i 0.146526 + 0.0845968i 0.571471 0.820623i \(-0.306373\pi\)
−0.424945 + 0.905219i \(0.639706\pi\)
\(488\) 10.8090 + 6.24056i 0.489299 + 0.282497i
\(489\) 1.70382i 0.0770495i
\(490\) 0 0
\(491\) −6.14261 10.6393i −0.277212 0.480145i 0.693479 0.720477i \(-0.256077\pi\)
−0.970691 + 0.240332i \(0.922744\pi\)
\(492\) 1.10418 0.637499i 0.0497803 0.0287407i
\(493\) −47.3497 −2.13252
\(494\) 4.98286 3.00610i 0.224189 0.135251i
\(495\) 0 0
\(496\) −8.55695 + 4.94036i −0.384219 + 0.221829i
\(497\) −12.0157 20.8118i −0.538978 0.933537i
\(498\) −0.489668 + 0.848130i −0.0219425 + 0.0380056i
\(499\) 17.8267i 0.798033i 0.916944 + 0.399016i \(0.130648\pi\)
−0.916944 + 0.399016i \(0.869352\pi\)
\(500\) 0 0
\(501\) 4.61967 + 2.66717i 0.206392 + 0.119160i
\(502\) 7.76444i 0.346544i
\(503\) −2.78988 + 4.83222i −0.124395 + 0.215458i −0.921496 0.388387i \(-0.873032\pi\)
0.797101 + 0.603845i \(0.206366\pi\)
\(504\) −0.758819 1.31431i −0.0338005 0.0585442i
\(505\) 0 0
\(506\) 28.0082 1.24512
\(507\) 12.9904 0.500000i 0.576923 0.0222058i
\(508\) 11.9907 0.532002
\(509\) 27.6679 15.9741i 1.22636 0.708039i 0.260093 0.965584i \(-0.416247\pi\)
0.966266 + 0.257545i \(0.0829134\pi\)
\(510\) 0 0
\(511\) 3.33391 5.77450i 0.147483 0.255449i
\(512\) 1.00000i 0.0441942i
\(513\) 1.39778 + 0.807007i 0.0617134 + 0.0356302i
\(514\) −16.7841 9.69031i −0.740315 0.427421i
\(515\) 0 0
\(516\) −1.18336 + 2.04965i −0.0520947 + 0.0902307i
\(517\) −17.6236 30.5250i −0.775086 1.34249i
\(518\) −11.4866 + 6.63179i −0.504692 + 0.291384i
\(519\) 17.6768 0.775925
\(520\) 0 0
\(521\) −0.338338 −0.0148228 −0.00741142 0.999973i \(-0.502359\pi\)
−0.00741142 + 0.999973i \(0.502359\pi\)
\(522\) 8.55085 4.93684i 0.374261 0.216079i
\(523\) −11.5529 20.0102i −0.505174 0.874986i −0.999982 0.00598438i \(-0.998095\pi\)
0.494808 0.869002i \(-0.335238\pi\)
\(524\) −10.1762 + 17.6257i −0.444549 + 0.769981i
\(525\) 0 0
\(526\) −1.64019 0.946961i −0.0715155 0.0412895i
\(527\) −41.0353 23.6918i −1.78753 1.03203i
\(528\) 5.14626i 0.223962i
\(529\) −3.31008 + 5.73324i −0.143917 + 0.249271i
\(530\) 0 0
\(531\) 8.04354 4.64394i 0.349060 0.201530i
\(532\) 2.44949 0.106199
\(533\) −2.22153 + 4.02465i −0.0962253 + 0.174327i
\(534\) −4.08933 −0.176963
\(535\) 0 0
\(536\) 5.76733 + 9.98930i 0.249111 + 0.431472i
\(537\) 10.7700 18.6542i 0.464759 0.804987i
\(538\) 4.60207i 0.198409i
\(539\) 20.9326 + 12.0854i 0.901629 + 0.520556i
\(540\) 0 0
\(541\) 28.8074i 1.23853i 0.785183 + 0.619264i \(0.212569\pi\)
−0.785183 + 0.619264i \(0.787431\pi\)
\(542\) 4.17191 7.22596i 0.179199 0.310382i
\(543\) 2.04164 + 3.53622i 0.0876151 + 0.151754i
\(544\) −4.15307 + 2.39778i −0.178062 + 0.102804i
\(545\) 0 0
\(546\) 4.79057 + 2.64431i 0.205018 + 0.113166i
\(547\) −33.4957 −1.43217 −0.716086 0.698013i \(-0.754068\pi\)
−0.716086 + 0.698013i \(0.754068\pi\)
\(548\) −6.82684 + 3.94148i −0.291628 + 0.168372i
\(549\) −6.24056 10.8090i −0.266341 0.461315i
\(550\) 0 0
\(551\) 15.9362i 0.678907i
\(552\) −4.71329 2.72122i −0.200611 0.115823i
\(553\) 14.5076 + 8.37599i 0.616928 + 0.356183i
\(554\) 22.2377i 0.944791i
\(555\) 0 0
\(556\) 2.05852 + 3.56546i 0.0873007 + 0.151209i
\(557\) 31.6950 18.2991i 1.34296 0.775358i 0.355718 0.934593i \(-0.384236\pi\)
0.987241 + 0.159236i \(0.0509030\pi\)
\(558\) 9.88072 0.418284
\(559\) −0.164134 8.53179i −0.00694211 0.360856i
\(560\) 0 0
\(561\) −21.3728 + 12.3396i −0.902361 + 0.520978i
\(562\) −10.0481 17.4038i −0.423852 0.734133i
\(563\) −5.18180 + 8.97514i −0.218387 + 0.378257i −0.954315 0.298803i \(-0.903413\pi\)
0.735928 + 0.677060i \(0.236746\pi\)
\(564\) 6.84909i 0.288399i
\(565\) 0 0
\(566\) 0.623402 + 0.359921i 0.0262036 + 0.0151286i
\(567\) 1.51764i 0.0637348i
\(568\) 7.91737 13.7133i 0.332206 0.575397i
\(569\) 15.7893 + 27.3479i 0.661923 + 1.14648i 0.980110 + 0.198456i \(0.0635928\pi\)
−0.318187 + 0.948028i \(0.603074\pi\)
\(570\) 0 0
\(571\) 33.7160 1.41097 0.705485 0.708725i \(-0.250729\pi\)
0.705485 + 0.708725i \(0.250729\pi\)
\(572\) −9.58492 15.8878i −0.400766 0.664302i
\(573\) 12.9564 0.541263
\(574\) −1.67575 + 0.967492i −0.0699443 + 0.0403823i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 40.8530i 1.70073i −0.526193 0.850365i \(-0.676381\pi\)
0.526193 0.850365i \(-0.323619\pi\)
\(578\) −5.19386 2.99867i −0.216036 0.124728i
\(579\) −7.49706 4.32843i −0.311567 0.179883i
\(580\) 0 0
\(581\) 0.743139 1.28715i 0.0308306 0.0534001i
\(582\) 2.85898 + 4.95189i 0.118508 + 0.205263i
\(583\) −3.93073 + 2.26941i −0.162794 + 0.0939893i
\(584\) 4.39355 0.181806
\(585\) 0 0
\(586\) −13.2278 −0.546435
\(587\) −21.3431 + 12.3224i −0.880924 + 0.508602i −0.870963 0.491349i \(-0.836504\pi\)
−0.00996119 + 0.999950i \(0.503171\pi\)
\(588\) −2.34839 4.06753i −0.0968459 0.167742i
\(589\) −7.97381 + 13.8110i −0.328555 + 0.569074i
\(590\) 0 0
\(591\) −3.76574 2.17415i −0.154902 0.0894327i
\(592\) −7.56873 4.36981i −0.311073 0.179598i
\(593\) 21.4887i 0.882436i −0.897400 0.441218i \(-0.854547\pi\)
0.897400 0.441218i \(-0.145453\pi\)
\(594\) 2.57313 4.45680i 0.105577 0.182865i
\(595\) 0 0
\(596\) −8.00644 + 4.62252i −0.327957 + 0.189346i
\(597\) −7.46702 −0.305605
\(598\) 19.6194 0.377435i 0.802296 0.0154345i
\(599\) −29.1850 −1.19247 −0.596233 0.802812i \(-0.703337\pi\)
−0.596233 + 0.802812i \(0.703337\pi\)
\(600\) 0 0
\(601\) −3.31925 5.74910i −0.135395 0.234511i 0.790353 0.612651i \(-0.209897\pi\)
−0.925748 + 0.378140i \(0.876564\pi\)
\(602\) 1.79592 3.11062i 0.0731962 0.126780i
\(603\) 11.5347i 0.469727i
\(604\) −14.8506 8.57397i −0.604260 0.348870i
\(605\) 0 0
\(606\) 7.85374i 0.319036i
\(607\) −11.7047 + 20.2731i −0.475078 + 0.822860i −0.999593 0.0285420i \(-0.990914\pi\)
0.524514 + 0.851402i \(0.324247\pi\)
\(608\) 0.807007 + 1.39778i 0.0327285 + 0.0566874i
\(609\) −12.9771 + 7.49233i −0.525858 + 0.303605i
\(610\) 0 0
\(611\) −12.7564 21.1448i −0.516070 0.855428i
\(612\) 4.79555 0.193849
\(613\) −4.55182 + 2.62799i −0.183846 + 0.106144i −0.589099 0.808061i \(-0.700517\pi\)
0.405252 + 0.914205i \(0.367184\pi\)
\(614\) 3.92587 + 6.79981i 0.158435 + 0.274418i
\(615\) 0 0
\(616\) 7.81017i 0.314681i
\(617\) 22.8678 + 13.2027i 0.920622 + 0.531522i 0.883834 0.467802i \(-0.154954\pi\)
0.0367887 + 0.999323i \(0.488287\pi\)
\(618\) 2.74919 + 1.58725i 0.110589 + 0.0638484i
\(619\) 4.68483i 0.188299i −0.995558 0.0941497i \(-0.969987\pi\)
0.995558 0.0941497i \(-0.0300132\pi\)
\(620\) 0 0
\(621\) 2.72122 + 4.71329i 0.109199 + 0.189138i
\(622\) −13.6579 + 7.88538i −0.547631 + 0.316175i
\(623\) 6.20612 0.248643
\(624\) 0.0693504 + 3.60488i 0.00277624 + 0.144311i
\(625\) 0 0
\(626\) 18.2396 10.5306i 0.729001 0.420889i
\(627\) 4.15307 + 7.19333i 0.165858 + 0.287274i
\(628\) 9.13954 15.8301i 0.364707 0.631692i
\(629\) 41.9113i 1.67111i
\(630\) 0 0
\(631\) 5.85249 + 3.37894i 0.232984 + 0.134513i 0.611948 0.790898i \(-0.290386\pi\)
−0.378964 + 0.925411i \(0.623720\pi\)
\(632\) 11.0382i 0.439076i
\(633\) 6.74384 11.6807i 0.268044 0.464265i
\(634\) −13.2071 22.8753i −0.524520 0.908494i
\(635\) 0 0
\(636\) 0.881964 0.0349721
\(637\) 14.8258 + 8.18358i 0.587420 + 0.324245i
\(638\) 50.8125 2.01169
\(639\) −13.7133 + 7.91737i −0.542489 + 0.313206i
\(640\) 0 0
\(641\) 14.6037 25.2943i 0.576810 0.999064i −0.419033 0.907971i \(-0.637631\pi\)
0.995842 0.0910927i \(-0.0290360\pi\)
\(642\) 13.7532i 0.542797i
\(643\) 6.98298 + 4.03163i 0.275382 + 0.158992i 0.631331 0.775514i \(-0.282509\pi\)
−0.355949 + 0.934505i \(0.615842\pi\)
\(644\) 7.15307 + 4.12983i 0.281871 + 0.162738i
\(645\) 0 0
\(646\) −3.87005 + 6.70312i −0.152265 + 0.263731i
\(647\) 0.360179 + 0.623849i 0.0141601 + 0.0245260i 0.873019 0.487687i \(-0.162159\pi\)
−0.858859 + 0.512213i \(0.828826\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) 47.7979 1.87623
\(650\) 0 0
\(651\) −14.9954 −0.587714
\(652\) −1.47555 + 0.851911i −0.0577871 + 0.0333634i
\(653\) −13.3367 23.0998i −0.521904 0.903963i −0.999675 0.0254795i \(-0.991889\pi\)
0.477772 0.878484i \(-0.341445\pi\)
\(654\) −8.39475 + 14.5401i −0.328261 + 0.568564i
\(655\) 0 0
\(656\) −1.10418 0.637499i −0.0431110 0.0248901i
\(657\) −3.80493 2.19677i −0.148444 0.0857043i
\(658\) 10.3944i 0.405218i
\(659\) 9.02067 15.6243i 0.351396 0.608635i −0.635099 0.772431i \(-0.719041\pi\)
0.986494 + 0.163796i \(0.0523739\pi\)
\(660\) 0 0
\(661\) 10.5904 6.11439i 0.411920 0.237822i −0.279694 0.960089i \(-0.590233\pi\)
0.691614 + 0.722267i \(0.256900\pi\)
\(662\) 20.4252 0.793847
\(663\) −14.8051 + 8.93173i −0.574981 + 0.346880i
\(664\) 0.979336 0.0380056
\(665\) 0 0
\(666\) 4.36981 + 7.56873i 0.169327 + 0.293282i
\(667\) −26.8684 + 46.5375i −1.04035 + 1.80194i
\(668\) 5.33434i 0.206392i
\(669\) 6.08030 + 3.51047i 0.235078 + 0.135722i
\(670\) 0 0
\(671\) 64.2311i 2.47962i
\(672\) −0.758819 + 1.31431i −0.0292721 + 0.0507007i
\(673\) −2.32913 4.03417i −0.0897814 0.155506i 0.817637 0.575734i \(-0.195284\pi\)
−0.907419 + 0.420228i \(0.861950\pi\)
\(674\) −11.3479 + 6.55173i −0.437106 + 0.252363i
\(675\) 0 0
\(676\) −6.92820 11.0000i −0.266469 0.423077i
\(677\) 22.1830 0.852561 0.426280 0.904591i \(-0.359824\pi\)
0.426280 + 0.904591i \(0.359824\pi\)
\(678\) 8.36308 4.82843i 0.321182 0.185435i
\(679\) −4.33889 7.51518i −0.166511 0.288406i
\(680\) 0 0
\(681\) 8.59524i 0.329370i
\(682\) 44.0363 + 25.4244i 1.68624 + 0.973550i
\(683\) −10.9766 6.33735i −0.420008 0.242492i 0.275072 0.961423i \(-0.411298\pi\)
−0.695081 + 0.718931i \(0.744631\pi\)
\(684\) 1.61401i 0.0617134i
\(685\) 0 0
\(686\) 8.87574 + 15.3732i 0.338877 + 0.586952i
\(687\) −14.2102 + 8.20429i −0.542155 + 0.313013i
\(688\) 2.36673 0.0902307
\(689\) −2.72284 + 1.64266i −0.103732 + 0.0625803i
\(690\) 0 0
\(691\) 12.7634 7.36897i 0.485544 0.280329i −0.237180 0.971466i \(-0.576223\pi\)
0.722724 + 0.691137i \(0.242890\pi\)
\(692\) −8.83839 15.3085i −0.335985 0.581944i
\(693\) −3.90508 + 6.76380i −0.148342 + 0.256936i
\(694\) 17.7605i 0.674181i
\(695\) 0 0
\(696\) −8.55085 4.93684i −0.324119 0.187130i
\(697\) 6.11432i 0.231596i
\(698\) 0.0598981 0.103747i 0.00226718 0.00392687i
\(699\) 3.47115 + 6.01221i 0.131291 + 0.227403i
\(700\) 0 0
\(701\) 25.9252 0.979182 0.489591 0.871952i \(-0.337146\pi\)
0.489591 + 0.871952i \(0.337146\pi\)
\(702\) 1.74238 3.15660i 0.0657620 0.119138i
\(703\) −14.1059 −0.532013
\(704\) 4.45680 2.57313i 0.167972 0.0969786i
\(705\) 0 0
\(706\) −3.77620 + 6.54057i −0.142119 + 0.246158i
\(707\) 11.9191i 0.448265i
\(708\) −8.04354 4.64394i −0.302295 0.174530i
\(709\) −28.0091 16.1711i −1.05190 0.607317i −0.128722 0.991681i \(-0.541087\pi\)
−0.923182 + 0.384364i \(0.874421\pi\)
\(710\) 0 0
\(711\) 5.51910 9.55936i 0.206982 0.358504i
\(712\) 2.04466 + 3.54146i 0.0766270 + 0.132722i
\(713\) −46.5707 + 26.8876i −1.74409 + 1.00695i
\(714\) −7.27792 −0.272369
\(715\) 0 0
\(716\) −21.5400 −0.804987
\(717\) −15.8531 + 9.15281i −0.592046 + 0.341818i
\(718\) −14.9847 25.9542i −0.559223 0.968602i
\(719\) −6.84506 + 11.8560i −0.255278 + 0.442154i −0.964971 0.262357i \(-0.915500\pi\)
0.709693 + 0.704511i \(0.248834\pi\)
\(720\) 0 0
\(721\) −4.17228 2.40887i −0.155384 0.0897108i
\(722\) −14.1984 8.19748i −0.528412 0.305079i
\(723\) 14.4229i 0.536395i
\(724\) 2.04164 3.53622i 0.0758769 0.131423i
\(725\) 0 0
\(726\) 13.4096 7.74202i 0.497676 0.287333i
\(727\) 49.1587 1.82319 0.911597 0.411084i \(-0.134850\pi\)
0.911597 + 0.411084i \(0.134850\pi\)
\(728\) −0.105249 5.47091i −0.00390078 0.202765i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 5.67489 + 9.82920i 0.209893 + 0.363546i
\(732\) −6.24056 + 10.8090i −0.230658 + 0.399511i
\(733\) 44.9158i 1.65900i 0.558505 + 0.829501i \(0.311375\pi\)
−0.558505 + 0.829501i \(0.688625\pi\)
\(734\) −25.0232 14.4472i −0.923625 0.533255i
\(735\) 0 0
\(736\) 5.44244i 0.200611i
\(737\) 29.6802 51.4076i 1.09328 1.89362i
\(738\) 0.637499 + 1.10418i 0.0234667 + 0.0406454i
\(739\) 14.2102 8.20427i 0.522731 0.301799i −0.215320 0.976543i \(-0.569080\pi\)
0.738051 + 0.674745i \(0.235746\pi\)
\(740\) 0 0
\(741\) 3.00610 + 4.98286i 0.110432 + 0.183050i
\(742\) −1.33850 −0.0491379
\(743\) 5.73773 3.31268i 0.210497 0.121530i −0.391045 0.920371i \(-0.627886\pi\)
0.601542 + 0.798841i \(0.294553\pi\)
\(744\) −4.94036 8.55695i −0.181122 0.313713i
\(745\) 0 0
\(746\) 14.7117i 0.538632i
\(747\) −0.848130 0.489668i −0.0310314 0.0179160i
\(748\) 21.3728 + 12.3396i 0.781467 + 0.451180i
\(749\) 20.8724i 0.762662i
\(750\) 0 0
\(751\) 20.2807 + 35.1271i 0.740052 + 1.28181i 0.952471 + 0.304629i \(0.0985324\pi\)
−0.212419 + 0.977179i \(0.568134\pi\)
\(752\) 5.93149 3.42455i 0.216299 0.124880i
\(753\) −7.76444 −0.282952
\(754\) 35.5934 0.684743i 1.29624 0.0249369i
\(755\) 0 0
\(756\) 1.31431 0.758819i 0.0478011 0.0275980i
\(757\) −12.1639 21.0685i −0.442105 0.765748i 0.555741 0.831356i \(-0.312435\pi\)
−0.997845 + 0.0656076i \(0.979101\pi\)
\(758\) −15.6627 + 27.1285i −0.568893 + 0.985352i
\(759\) 28.0082i 1.01663i
\(760\) 0 0
\(761\) −0.355702 0.205364i −0.0128942 0.00744446i 0.493539 0.869724i \(-0.335703\pi\)
−0.506433 + 0.862279i \(0.669036\pi\)
\(762\) 11.9907i 0.434378i
\(763\) 12.7402 22.0667i 0.461226 0.798867i
\(764\) −6.47822 11.2206i −0.234374 0.405947i
\(765\) 0 0
\(766\) −10.8474 −0.391931
\(767\) 33.4817 0.644118i 1.20896 0.0232578i
\(768\) −1.00000 −0.0360844
\(769\) −36.0692 + 20.8246i −1.30069 + 0.750954i −0.980522 0.196407i \(-0.937073\pi\)
−0.320168 + 0.947361i \(0.603739\pi\)
\(770\) 0 0
\(771\) 9.69031 16.7841i 0.348988 0.604465i
\(772\) 8.65685i 0.311567i
\(773\) 44.8150 + 25.8739i 1.61188 + 0.930621i 0.988934 + 0.148358i \(0.0473989\pi\)
0.622949 + 0.782262i \(0.285934\pi\)
\(774\) −2.04965 1.18336i −0.0736731 0.0425352i
\(775\) 0 0
\(776\) 2.85898 4.95189i 0.102631 0.177763i
\(777\) −6.63179 11.4866i −0.237914 0.412079i
\(778\) −15.8463 + 9.14884i −0.568116 + 0.328002i
\(779\) −2.05786 −0.0737306
\(780\) 0 0
\(781\) −81.4898 −2.91593
\(782\) −22.6029 + 13.0498i −0.808276 + 0.466659i