Properties

Label 1950.2.z.m.1699.4
Level $1950$
Weight $2$
Character 1950.1699
Analytic conductor $15.571$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.z (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.1731891456.1
Defining polynomial: \(x^{8} - 9 x^{6} + 65 x^{4} - 144 x^{2} + 256\)
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 1699.4
Root \(2.21837 - 1.28078i\) of defining polynomial
Character \(\chi\) \(=\) 1950.1699
Dual form 1950.2.z.m.1849.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(3.08440 - 1.78078i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(3.08440 - 1.78078i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.280776 - 0.486319i) q^{11} -1.00000i q^{12} +(-2.21837 + 2.84233i) q^{13} +3.56155 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.70469 - 1.56155i) q^{17} +1.00000i q^{18} +(-1.21922 - 2.11176i) q^{19} -3.56155 q^{21} +(0.486319 - 0.280776i) q^{22} +(6.65511 + 3.84233i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-3.34233 + 1.35234i) q^{26} -1.00000i q^{27} +(3.08440 + 1.78078i) q^{28} +(0.561553 - 0.972638i) q^{29} +4.00000 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.486319 + 0.280776i) q^{33} +3.12311 q^{34} +(-0.500000 + 0.866025i) q^{36} +(0.486319 + 0.280776i) q^{37} -2.43845i q^{38} +(3.34233 - 1.35234i) q^{39} +(1.56155 - 2.70469i) q^{41} +(-3.08440 - 1.78078i) q^{42} +(0.379706 - 0.219224i) q^{43} +0.561553 q^{44} +(3.84233 + 6.65511i) q^{46} -4.00000i q^{47} +(0.866025 - 0.500000i) q^{48} +(2.84233 - 4.92306i) q^{49} -3.12311 q^{51} +(-3.57071 - 0.500000i) q^{52} +4.24621i q^{53} +(0.500000 - 0.866025i) q^{54} +(1.78078 + 3.08440i) q^{56} +2.43845i q^{57} +(0.972638 - 0.561553i) q^{58} +(-5.12311 - 8.87348i) q^{59} +(0.842329 + 1.45896i) q^{61} +(3.46410 + 2.00000i) q^{62} +(3.08440 + 1.78078i) q^{63} -1.00000 q^{64} -0.561553 q^{66} +(10.2258 + 5.90388i) q^{67} +(2.70469 + 1.56155i) q^{68} +(-3.84233 - 6.65511i) q^{69} +(-6.28078 - 10.8786i) q^{71} +(-0.866025 + 0.500000i) q^{72} +9.00000i q^{73} +(0.280776 + 0.486319i) q^{74} +(1.21922 - 2.11176i) q^{76} -2.00000i q^{77} +(3.57071 + 0.500000i) q^{78} +15.8078 q^{79} +(-0.500000 + 0.866025i) q^{81} +(2.70469 - 1.56155i) q^{82} +6.56155i q^{83} +(-1.78078 - 3.08440i) q^{84} +0.438447 q^{86} +(-0.972638 + 0.561553i) q^{87} +(0.486319 + 0.280776i) q^{88} +(5.12311 - 8.87348i) q^{89} +(-1.78078 + 12.7173i) q^{91} +7.68466i q^{92} +(-3.46410 - 2.00000i) q^{93} +(2.00000 - 3.46410i) q^{94} +1.00000 q^{96} +(2.43160 - 1.40388i) q^{97} +(4.92306 - 2.84233i) q^{98} +0.561553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} - 4q^{6} + 4q^{9} + O(q^{10}) \) \( 8q + 4q^{4} - 4q^{6} + 4q^{9} - 6q^{11} + 12q^{14} - 4q^{16} - 18q^{19} - 12q^{21} + 4q^{24} - 2q^{26} - 12q^{29} + 32q^{31} - 8q^{34} - 4q^{36} + 2q^{39} - 4q^{41} - 12q^{44} + 6q^{46} - 2q^{49} + 8q^{51} + 4q^{54} + 6q^{56} - 8q^{59} - 18q^{61} - 8q^{64} + 12q^{66} - 6q^{69} - 42q^{71} - 6q^{74} + 18q^{76} + 44q^{79} - 4q^{81} - 6q^{84} + 20q^{86} + 8q^{89} - 6q^{91} + 16q^{94} + 8q^{96} - 12q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\)

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
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) 3.08440 1.78078i 1.16579 0.673070i 0.213107 0.977029i \(-0.431642\pi\)
0.952685 + 0.303959i \(0.0983085\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 0.280776 0.486319i 0.0846573 0.146631i −0.820588 0.571520i \(-0.806354\pi\)
0.905245 + 0.424890i \(0.139687\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −2.21837 + 2.84233i −0.615265 + 0.788320i
\(14\) 3.56155 0.951865
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.70469 1.56155i 0.655983 0.378732i −0.134761 0.990878i \(-0.543027\pi\)
0.790745 + 0.612146i \(0.209693\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −1.21922 2.11176i −0.279709 0.484470i 0.691603 0.722278i \(-0.256905\pi\)
−0.971312 + 0.237807i \(0.923571\pi\)
\(20\) 0 0
\(21\) −3.56155 −0.777195
\(22\) 0.486319 0.280776i 0.103684 0.0598617i
\(23\) 6.65511 + 3.84233i 1.38769 + 0.801181i 0.993054 0.117658i \(-0.0375387\pi\)
0.394632 + 0.918839i \(0.370872\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 0 0
\(26\) −3.34233 + 1.35234i −0.655485 + 0.265217i
\(27\) 1.00000i 0.192450i
\(28\) 3.08440 + 1.78078i 0.582896 + 0.336535i
\(29\) 0.561553 0.972638i 0.104278 0.180614i −0.809165 0.587581i \(-0.800080\pi\)
0.913443 + 0.406967i \(0.133414\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) −0.486319 + 0.280776i −0.0846573 + 0.0488769i
\(34\) 3.12311 0.535608
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 0.486319 + 0.280776i 0.0799504 + 0.0461594i 0.539442 0.842023i \(-0.318635\pi\)
−0.459492 + 0.888182i \(0.651968\pi\)
\(38\) 2.43845i 0.395568i
\(39\) 3.34233 1.35234i 0.535201 0.216548i
\(40\) 0 0
\(41\) 1.56155 2.70469i 0.243874 0.422401i −0.717941 0.696104i \(-0.754915\pi\)
0.961814 + 0.273703i \(0.0882485\pi\)
\(42\) −3.08440 1.78078i −0.475933 0.274780i
\(43\) 0.379706 0.219224i 0.0579047 0.0334313i −0.470768 0.882257i \(-0.656023\pi\)
0.528673 + 0.848826i \(0.322690\pi\)
\(44\) 0.561553 0.0846573
\(45\) 0 0
\(46\) 3.84233 + 6.65511i 0.566521 + 0.981242i
\(47\) 4.00000i 0.583460i −0.956501 0.291730i \(-0.905769\pi\)
0.956501 0.291730i \(-0.0942309\pi\)
\(48\) 0.866025 0.500000i 0.125000 0.0721688i
\(49\) 2.84233 4.92306i 0.406047 0.703294i
\(50\) 0 0
\(51\) −3.12311 −0.437322
\(52\) −3.57071 0.500000i −0.495169 0.0693375i
\(53\) 4.24621i 0.583262i 0.956531 + 0.291631i \(0.0941979\pi\)
−0.956531 + 0.291631i \(0.905802\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) 1.78078 + 3.08440i 0.237966 + 0.412170i
\(57\) 2.43845i 0.322980i
\(58\) 0.972638 0.561553i 0.127714 0.0737355i
\(59\) −5.12311 8.87348i −0.666972 1.15523i −0.978747 0.205073i \(-0.934257\pi\)
0.311775 0.950156i \(-0.399076\pi\)
\(60\) 0 0
\(61\) 0.842329 + 1.45896i 0.107849 + 0.186800i 0.914899 0.403683i \(-0.132270\pi\)
−0.807050 + 0.590484i \(0.798937\pi\)
\(62\) 3.46410 + 2.00000i 0.439941 + 0.254000i
\(63\) 3.08440 + 1.78078i 0.388597 + 0.224357i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −0.561553 −0.0691224
\(67\) 10.2258 + 5.90388i 1.24928 + 0.721274i 0.970967 0.239215i \(-0.0768902\pi\)
0.278317 + 0.960489i \(0.410224\pi\)
\(68\) 2.70469 + 1.56155i 0.327992 + 0.189366i
\(69\) −3.84233 6.65511i −0.462562 0.801181i
\(70\) 0 0
\(71\) −6.28078 10.8786i −0.745391 1.29106i −0.950012 0.312214i \(-0.898929\pi\)
0.204621 0.978841i \(-0.434404\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 9.00000i 1.05337i 0.850060 + 0.526685i \(0.176565\pi\)
−0.850060 + 0.526685i \(0.823435\pi\)
\(74\) 0.280776 + 0.486319i 0.0326396 + 0.0565334i
\(75\) 0 0
\(76\) 1.21922 2.11176i 0.139855 0.242235i
\(77\) 2.00000i 0.227921i
\(78\) 3.57071 + 0.500000i 0.404304 + 0.0566139i
\(79\) 15.8078 1.77851 0.889256 0.457409i \(-0.151223\pi\)
0.889256 + 0.457409i \(0.151223\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 2.70469 1.56155i 0.298683 0.172445i
\(83\) 6.56155i 0.720224i 0.932909 + 0.360112i \(0.117262\pi\)
−0.932909 + 0.360112i \(0.882738\pi\)
\(84\) −1.78078 3.08440i −0.194299 0.336535i
\(85\) 0 0
\(86\) 0.438447 0.0472790
\(87\) −0.972638 + 0.561553i −0.104278 + 0.0602048i
\(88\) 0.486319 + 0.280776i 0.0518418 + 0.0299309i
\(89\) 5.12311 8.87348i 0.543048 0.940587i −0.455679 0.890144i \(-0.650603\pi\)
0.998727 0.0504427i \(-0.0160632\pi\)
\(90\) 0 0
\(91\) −1.78078 + 12.7173i −0.186676 + 1.33313i
\(92\) 7.68466i 0.801181i
\(93\) −3.46410 2.00000i −0.359211 0.207390i
\(94\) 2.00000 3.46410i 0.206284 0.357295i
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 2.43160 1.40388i 0.246891 0.142543i −0.371449 0.928453i \(-0.621139\pi\)
0.618340 + 0.785911i \(0.287806\pi\)
\(98\) 4.92306 2.84233i 0.497304 0.287119i
\(99\) 0.561553 0.0564382
\(100\) 0 0
\(101\) 3.12311 5.40938i 0.310761 0.538253i −0.667767 0.744371i \(-0.732750\pi\)
0.978527 + 0.206118i \(0.0660829\pi\)
\(102\) −2.70469 1.56155i −0.267804 0.154617i
\(103\) 4.43845i 0.437333i −0.975800 0.218667i \(-0.929829\pi\)
0.975800 0.218667i \(-0.0701707\pi\)
\(104\) −2.84233 2.21837i −0.278713 0.217529i
\(105\) 0 0
\(106\) −2.12311 + 3.67733i −0.206214 + 0.357174i
\(107\) 4.64996 + 2.68466i 0.449529 + 0.259536i 0.707631 0.706582i \(-0.249764\pi\)
−0.258102 + 0.966118i \(0.583097\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) 2.80776 0.268935 0.134468 0.990918i \(-0.457068\pi\)
0.134468 + 0.990918i \(0.457068\pi\)
\(110\) 0 0
\(111\) −0.280776 0.486319i −0.0266501 0.0461594i
\(112\) 3.56155i 0.336535i
\(113\) 3.46410 2.00000i 0.325875 0.188144i −0.328133 0.944632i \(-0.606419\pi\)
0.654008 + 0.756487i \(0.273086\pi\)
\(114\) −1.21922 + 2.11176i −0.114191 + 0.197784i
\(115\) 0 0
\(116\) 1.12311 0.104278
\(117\) −3.57071 0.500000i −0.330113 0.0462250i
\(118\) 10.2462i 0.943240i
\(119\) 5.56155 9.63289i 0.509827 0.883046i
\(120\) 0 0
\(121\) 5.34233 + 9.25319i 0.485666 + 0.841199i
\(122\) 1.68466i 0.152522i
\(123\) −2.70469 + 1.56155i −0.243874 + 0.140800i
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) 0 0
\(126\) 1.78078 + 3.08440i 0.158644 + 0.274780i
\(127\) 18.8861 + 10.9039i 1.67587 + 0.967563i 0.964249 + 0.264998i \(0.0853713\pi\)
0.711619 + 0.702565i \(0.247962\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −0.438447 −0.0386031
\(130\) 0 0
\(131\) 0.876894 0.0766146 0.0383073 0.999266i \(-0.487803\pi\)
0.0383073 + 0.999266i \(0.487803\pi\)
\(132\) −0.486319 0.280776i −0.0423286 0.0244384i
\(133\) −7.52113 4.34233i −0.652165 0.376528i
\(134\) 5.90388 + 10.2258i 0.510018 + 0.883377i
\(135\) 0 0
\(136\) 1.56155 + 2.70469i 0.133902 + 0.231925i
\(137\) −14.2829 + 8.24621i −1.22027 + 0.704521i −0.964975 0.262343i \(-0.915505\pi\)
−0.255292 + 0.966864i \(0.582172\pi\)
\(138\) 7.68466i 0.654162i
\(139\) 10.7808 + 18.6729i 0.914414 + 1.58381i 0.807758 + 0.589515i \(0.200681\pi\)
0.106656 + 0.994296i \(0.465986\pi\)
\(140\) 0 0
\(141\) −2.00000 + 3.46410i −0.168430 + 0.291730i
\(142\) 12.5616i 1.05414i
\(143\) 0.759413 + 1.87689i 0.0635053 + 0.156954i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) −4.50000 + 7.79423i −0.372423 + 0.645055i
\(147\) −4.92306 + 2.84233i −0.406047 + 0.234431i
\(148\) 0.561553i 0.0461594i
\(149\) −5.12311 8.87348i −0.419701 0.726944i 0.576208 0.817303i \(-0.304532\pi\)
−0.995909 + 0.0903593i \(0.971198\pi\)
\(150\) 0 0
\(151\) −16.6847 −1.35778 −0.678889 0.734241i \(-0.737538\pi\)
−0.678889 + 0.734241i \(0.737538\pi\)
\(152\) 2.11176 1.21922i 0.171286 0.0988921i
\(153\) 2.70469 + 1.56155i 0.218661 + 0.126244i
\(154\) 1.00000 1.73205i 0.0805823 0.139573i
\(155\) 0 0
\(156\) 2.84233 + 2.21837i 0.227568 + 0.177612i
\(157\) 17.2462i 1.37640i −0.725522 0.688199i \(-0.758402\pi\)
0.725522 0.688199i \(-0.241598\pi\)
\(158\) 13.6899 + 7.90388i 1.08911 + 0.628799i
\(159\) 2.12311 3.67733i 0.168373 0.291631i
\(160\) 0 0
\(161\) 27.3693 2.15700
\(162\) −0.866025 + 0.500000i −0.0680414 + 0.0392837i
\(163\) −14.2829 + 8.24621i −1.11872 + 0.645893i −0.941074 0.338201i \(-0.890182\pi\)
−0.177646 + 0.984094i \(0.556848\pi\)
\(164\) 3.12311 0.243874
\(165\) 0 0
\(166\) −3.28078 + 5.68247i −0.254638 + 0.441045i
\(167\) 20.5115 + 11.8423i 1.58723 + 0.916387i 0.993761 + 0.111529i \(0.0355748\pi\)
0.593468 + 0.804858i \(0.297759\pi\)
\(168\) 3.56155i 0.274780i
\(169\) −3.15767 12.6107i −0.242898 0.970052i
\(170\) 0 0
\(171\) 1.21922 2.11176i 0.0932364 0.161490i
\(172\) 0.379706 + 0.219224i 0.0289523 + 0.0167156i
\(173\) −7.68762 + 4.43845i −0.584479 + 0.337449i −0.762911 0.646503i \(-0.776231\pi\)
0.178433 + 0.983952i \(0.442897\pi\)
\(174\) −1.12311 −0.0851424
\(175\) 0 0
\(176\) 0.280776 + 0.486319i 0.0211643 + 0.0366577i
\(177\) 10.2462i 0.770152i
\(178\) 8.87348 5.12311i 0.665095 0.383993i
\(179\) −7.84233 + 13.5833i −0.586163 + 1.01526i 0.408566 + 0.912729i \(0.366029\pi\)
−0.994729 + 0.102536i \(0.967304\pi\)
\(180\) 0 0
\(181\) −15.4924 −1.15154 −0.575771 0.817611i \(-0.695298\pi\)
−0.575771 + 0.817611i \(0.695298\pi\)
\(182\) −7.90084 + 10.1231i −0.585649 + 0.750375i
\(183\) 1.68466i 0.124534i
\(184\) −3.84233 + 6.65511i −0.283260 + 0.490621i
\(185\) 0 0
\(186\) −2.00000 3.46410i −0.146647 0.254000i
\(187\) 1.75379i 0.128250i
\(188\) 3.46410 2.00000i 0.252646 0.145865i
\(189\) −1.78078 3.08440i −0.129532 0.224357i
\(190\) 0 0
\(191\) −7.96543 13.7965i −0.576359 0.998282i −0.995893 0.0905428i \(-0.971140\pi\)
0.419534 0.907740i \(-0.362194\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) −2.59808 1.50000i −0.187014 0.107972i 0.403570 0.914949i \(-0.367769\pi\)
−0.590584 + 0.806976i \(0.701102\pi\)
\(194\) 2.80776 0.201586
\(195\) 0 0
\(196\) 5.68466 0.406047
\(197\) 4.43674 + 2.56155i 0.316105 + 0.182503i 0.649655 0.760229i \(-0.274913\pi\)
−0.333550 + 0.942732i \(0.608247\pi\)
\(198\) 0.486319 + 0.280776i 0.0345612 + 0.0199539i
\(199\) −2.21922 3.84381i −0.157317 0.272480i 0.776584 0.630014i \(-0.216951\pi\)
−0.933900 + 0.357534i \(0.883618\pi\)
\(200\) 0 0
\(201\) −5.90388 10.2258i −0.416428 0.721274i
\(202\) 5.40938 3.12311i 0.380602 0.219741i
\(203\) 4.00000i 0.280745i
\(204\) −1.56155 2.70469i −0.109331 0.189366i
\(205\) 0 0
\(206\) 2.21922 3.84381i 0.154621 0.267811i
\(207\) 7.68466i 0.534121i
\(208\) −1.35234 3.34233i −0.0937682 0.231749i
\(209\) −1.36932 −0.0947176
\(210\) 0 0
\(211\) −0.561553 + 0.972638i −0.0386589 + 0.0669592i −0.884707 0.466147i \(-0.845642\pi\)
0.846049 + 0.533106i \(0.178975\pi\)
\(212\) −3.67733 + 2.12311i −0.252560 + 0.145815i
\(213\) 12.5616i 0.860703i
\(214\) 2.68466 + 4.64996i 0.183519 + 0.317865i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 12.3376 7.12311i 0.837530 0.483548i
\(218\) 2.43160 + 1.40388i 0.164688 + 0.0950829i
\(219\) 4.50000 7.79423i 0.304082 0.526685i
\(220\) 0 0
\(221\) −1.56155 + 11.1517i −0.105041 + 0.750146i
\(222\) 0.561553i 0.0376890i
\(223\) 0.379706 + 0.219224i 0.0254270 + 0.0146803i 0.512660 0.858592i \(-0.328660\pi\)
−0.487233 + 0.873272i \(0.661994\pi\)
\(224\) −1.78078 + 3.08440i −0.118983 + 0.206085i
\(225\) 0 0
\(226\) 4.00000 0.266076
\(227\) −25.7077 + 14.8423i −1.70628 + 0.985120i −0.767205 + 0.641402i \(0.778353\pi\)
−0.939073 + 0.343718i \(0.888314\pi\)
\(228\) −2.11176 + 1.21922i −0.139855 + 0.0807451i
\(229\) −9.49242 −0.627277 −0.313638 0.949542i \(-0.601548\pi\)
−0.313638 + 0.949542i \(0.601548\pi\)
\(230\) 0 0
\(231\) −1.00000 + 1.73205i −0.0657952 + 0.113961i
\(232\) 0.972638 + 0.561553i 0.0638568 + 0.0368677i
\(233\) 25.3693i 1.66200i −0.556273 0.831000i \(-0.687769\pi\)
0.556273 0.831000i \(-0.312231\pi\)
\(234\) −2.84233 2.21837i −0.185809 0.145019i
\(235\) 0 0
\(236\) 5.12311 8.87348i 0.333486 0.577614i
\(237\) −13.6899 7.90388i −0.889256 0.513412i
\(238\) 9.63289 5.56155i 0.624408 0.360502i
\(239\) −27.0540 −1.74998 −0.874988 0.484144i \(-0.839131\pi\)
−0.874988 + 0.484144i \(0.839131\pi\)
\(240\) 0 0
\(241\) −7.78078 13.4767i −0.501204 0.868111i −0.999999 0.00139067i \(-0.999557\pi\)
0.498795 0.866720i \(-0.333776\pi\)
\(242\) 10.6847i 0.686836i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) −0.842329 + 1.45896i −0.0539246 + 0.0934002i
\(245\) 0 0
\(246\) −3.12311 −0.199122
\(247\) 8.70700 + 1.21922i 0.554013 + 0.0775773i
\(248\) 4.00000i 0.254000i
\(249\) 3.28078 5.68247i 0.207911 0.360112i
\(250\) 0 0
\(251\) −11.9654 20.7247i −0.755252 1.30813i −0.945249 0.326350i \(-0.894181\pi\)
0.189998 0.981785i \(-0.439152\pi\)
\(252\) 3.56155i 0.224357i
\(253\) 3.73720 2.15767i 0.234955 0.135652i
\(254\) 10.9039 + 18.8861i 0.684170 + 1.18502i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −11.7914 6.80776i −0.735527 0.424657i 0.0849138 0.996388i \(-0.472939\pi\)
−0.820441 + 0.571732i \(0.806272\pi\)
\(258\) −0.379706 0.219224i −0.0236395 0.0136483i
\(259\) 2.00000 0.124274
\(260\) 0 0
\(261\) 1.12311 0.0695185
\(262\) 0.759413 + 0.438447i 0.0469167 + 0.0270874i
\(263\) −5.46925 3.15767i −0.337248 0.194710i 0.321806 0.946806i \(-0.395710\pi\)
−0.659054 + 0.752095i \(0.729043\pi\)
\(264\) −0.280776 0.486319i −0.0172806 0.0299309i
\(265\) 0 0
\(266\) −4.34233 7.52113i −0.266245 0.461150i
\(267\) −8.87348 + 5.12311i −0.543048 + 0.313529i
\(268\) 11.8078i 0.721274i
\(269\) −1.68466 2.91791i −0.102715 0.177908i 0.810087 0.586310i \(-0.199420\pi\)
−0.912803 + 0.408401i \(0.866086\pi\)
\(270\) 0 0
\(271\) −4.46543 + 7.73436i −0.271256 + 0.469829i −0.969184 0.246339i \(-0.920772\pi\)
0.697928 + 0.716168i \(0.254106\pi\)
\(272\) 3.12311i 0.189366i
\(273\) 7.90084 10.1231i 0.478181 0.612678i
\(274\) −16.4924 −0.996344
\(275\) 0 0
\(276\) 3.84233 6.65511i 0.231281 0.400591i
\(277\) −4.33013 + 2.50000i −0.260172 + 0.150210i −0.624413 0.781094i \(-0.714662\pi\)
0.364241 + 0.931305i \(0.381328\pi\)
\(278\) 21.5616i 1.29318i
\(279\) 2.00000 + 3.46410i 0.119737 + 0.207390i
\(280\) 0 0
\(281\) −1.75379 −0.104622 −0.0523111 0.998631i \(-0.516659\pi\)
−0.0523111 + 0.998631i \(0.516659\pi\)
\(282\) −3.46410 + 2.00000i −0.206284 + 0.119098i
\(283\) −25.6478 14.8078i −1.52460 0.880230i −0.999575 0.0291454i \(-0.990721\pi\)
−0.525028 0.851085i \(-0.675945\pi\)
\(284\) 6.28078 10.8786i 0.372696 0.645528i
\(285\) 0 0
\(286\) −0.280776 + 2.00514i −0.0166027 + 0.118567i
\(287\) 11.1231i 0.656576i
\(288\) −0.866025 0.500000i −0.0510310 0.0294628i
\(289\) −3.62311 + 6.27540i −0.213124 + 0.369141i
\(290\) 0 0
\(291\) −2.80776 −0.164594
\(292\) −7.79423 + 4.50000i −0.456123 + 0.263343i
\(293\) 17.5337 10.1231i 1.02433 0.591398i 0.108976 0.994044i \(-0.465243\pi\)
0.915356 + 0.402646i \(0.131910\pi\)
\(294\) −5.68466 −0.331536
\(295\) 0 0
\(296\) −0.280776 + 0.486319i −0.0163198 + 0.0282667i
\(297\) −0.486319 0.280776i −0.0282191 0.0162923i
\(298\) 10.2462i 0.593547i
\(299\) −25.6847 + 10.3923i −1.48538 + 0.601003i
\(300\) 0 0
\(301\) 0.780776 1.35234i 0.0450032 0.0779478i
\(302\) −14.4493 8.34233i −0.831466 0.480047i
\(303\) −5.40938 + 3.12311i −0.310761 + 0.179418i
\(304\) 2.43845 0.139855
\(305\) 0 0
\(306\) 1.56155 + 2.70469i 0.0892680 + 0.154617i
\(307\) 22.2462i 1.26966i −0.772653 0.634829i \(-0.781070\pi\)
0.772653 0.634829i \(-0.218930\pi\)
\(308\) 1.73205 1.00000i 0.0986928 0.0569803i
\(309\) −2.21922 + 3.84381i −0.126247 + 0.218667i
\(310\) 0 0
\(311\) −10.3153 −0.584929 −0.292465 0.956276i \(-0.594475\pi\)
−0.292465 + 0.956276i \(0.594475\pi\)
\(312\) 1.35234 + 3.34233i 0.0765614 + 0.189222i
\(313\) 31.0000i 1.75222i 0.482108 + 0.876112i \(0.339871\pi\)
−0.482108 + 0.876112i \(0.660129\pi\)
\(314\) 8.62311 14.9357i 0.486630 0.842868i
\(315\) 0 0
\(316\) 7.90388 + 13.6899i 0.444628 + 0.770118i
\(317\) 16.2462i 0.912478i −0.889857 0.456239i \(-0.849196\pi\)
0.889857 0.456239i \(-0.150804\pi\)
\(318\) 3.67733 2.12311i 0.206214 0.119058i
\(319\) −0.315342 0.546188i −0.0176557 0.0305806i
\(320\) 0 0
\(321\) −2.68466 4.64996i −0.149843 0.259536i
\(322\) 23.7025 + 13.6847i 1.32089 + 0.762616i
\(323\) −6.59524 3.80776i −0.366969 0.211870i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −16.4924 −0.913431
\(327\) −2.43160 1.40388i −0.134468 0.0776349i
\(328\) 2.70469 + 1.56155i 0.149341 + 0.0862223i
\(329\) −7.12311 12.3376i −0.392710 0.680193i
\(330\) 0 0
\(331\) 8.34233 + 14.4493i 0.458536 + 0.794207i 0.998884 0.0472342i \(-0.0150407\pi\)
−0.540348 + 0.841442i \(0.681707\pi\)
\(332\) −5.68247 + 3.28078i −0.311866 + 0.180056i
\(333\) 0.561553i 0.0307729i
\(334\) 11.8423 + 20.5115i 0.647983 + 1.12234i
\(335\) 0 0
\(336\) 1.78078 3.08440i 0.0971493 0.168268i
\(337\) 8.05398i 0.438728i −0.975643 0.219364i \(-0.929602\pi\)
0.975643 0.219364i \(-0.0703982\pi\)
\(338\) 3.57071 12.5000i 0.194221 0.679910i
\(339\) −4.00000 −0.217250
\(340\) 0 0
\(341\) 1.12311 1.94528i 0.0608196 0.105343i
\(342\) 2.11176 1.21922i 0.114191 0.0659281i
\(343\) 4.68466i 0.252948i
\(344\) 0.219224 + 0.379706i 0.0118197 + 0.0204724i
\(345\) 0 0
\(346\) −8.87689 −0.477225
\(347\) 21.4842 12.4039i 1.15333 0.665875i 0.203633 0.979047i \(-0.434725\pi\)
0.949696 + 0.313172i \(0.101392\pi\)
\(348\) −0.972638 0.561553i −0.0521389 0.0301024i
\(349\) −9.62311 + 16.6677i −0.515113 + 0.892202i 0.484733 + 0.874662i \(0.338917\pi\)
−0.999846 + 0.0175398i \(0.994417\pi\)
\(350\) 0 0
\(351\) 2.84233 + 2.21837i 0.151712 + 0.118408i
\(352\) 0.561553i 0.0299309i
\(353\) −1.94528 1.12311i −0.103537 0.0597769i 0.447338 0.894365i \(-0.352372\pi\)
−0.550874 + 0.834588i \(0.685706\pi\)
\(354\) −5.12311 + 8.87348i −0.272290 + 0.471620i
\(355\) 0 0
\(356\) 10.2462 0.543048
\(357\) −9.63289 + 5.56155i −0.509827 + 0.294349i
\(358\) −13.5833 + 7.84233i −0.717900 + 0.414480i
\(359\) 4.87689 0.257393 0.128696 0.991684i \(-0.458921\pi\)
0.128696 + 0.991684i \(0.458921\pi\)
\(360\) 0 0
\(361\) 6.52699 11.3051i 0.343526 0.595004i
\(362\) −13.4168 7.74621i −0.705173 0.407132i
\(363\) 10.6847i 0.560799i
\(364\) −11.9039 + 4.81645i −0.623933 + 0.252450i
\(365\) 0 0
\(366\) 0.842329 1.45896i 0.0440293 0.0762609i
\(367\) −8.82674 5.09612i −0.460752 0.266015i 0.251609 0.967829i \(-0.419040\pi\)
−0.712360 + 0.701814i \(0.752374\pi\)
\(368\) −6.65511 + 3.84233i −0.346922 + 0.200295i
\(369\) 3.12311 0.162582
\(370\) 0 0
\(371\) 7.56155 + 13.0970i 0.392576 + 0.679962i
\(372\) 4.00000i 0.207390i
\(373\) −8.22068 + 4.74621i −0.425651 + 0.245750i −0.697492 0.716593i \(-0.745701\pi\)
0.271841 + 0.962342i \(0.412367\pi\)
\(374\) 0.876894 1.51883i 0.0453431 0.0785366i
\(375\) 0 0
\(376\) 4.00000 0.206284
\(377\) 1.51883 + 3.75379i 0.0782235 + 0.193330i
\(378\) 3.56155i 0.183187i
\(379\) −12.0270 + 20.8314i −0.617785 + 1.07003i 0.372104 + 0.928191i \(0.378636\pi\)
−0.989889 + 0.141844i \(0.954697\pi\)
\(380\) 0 0
\(381\) −10.9039 18.8861i −0.558623 0.967563i
\(382\) 15.9309i 0.815094i
\(383\) −4.70983 + 2.71922i −0.240661 + 0.138946i −0.615481 0.788152i \(-0.711038\pi\)
0.374819 + 0.927098i \(0.377705\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) 0 0
\(386\) −1.50000 2.59808i −0.0763480 0.132239i
\(387\) 0.379706 + 0.219224i 0.0193016 + 0.0111438i
\(388\) 2.43160 + 1.40388i 0.123446 + 0.0712713i
\(389\) −11.3693 −0.576447 −0.288224 0.957563i \(-0.593065\pi\)
−0.288224 + 0.957563i \(0.593065\pi\)
\(390\) 0 0
\(391\) 24.0000 1.21373
\(392\) 4.92306 + 2.84233i 0.248652 + 0.143559i
\(393\) −0.759413 0.438447i −0.0383073 0.0221167i
\(394\) 2.56155 + 4.43674i 0.129049 + 0.223520i
\(395\) 0 0
\(396\) 0.280776 + 0.486319i 0.0141095 + 0.0244384i
\(397\) 8.49377 4.90388i 0.426290 0.246119i −0.271475 0.962446i \(-0.587511\pi\)
0.697765 + 0.716327i \(0.254178\pi\)
\(398\) 4.43845i 0.222479i
\(399\) 4.34233 + 7.52113i 0.217388 + 0.376528i
\(400\) 0 0
\(401\) 6.31534 10.9385i 0.315373 0.546242i −0.664144 0.747605i \(-0.731204\pi\)
0.979517 + 0.201363i \(0.0645370\pi\)
\(402\) 11.8078i 0.588918i
\(403\) −8.87348 + 11.3693i −0.442019 + 0.566346i
\(404\) 6.24621 0.310761
\(405\) 0 0
\(406\) 2.00000 3.46410i 0.0992583 0.171920i
\(407\) 0.273094 0.157671i 0.0135368 0.00781545i
\(408\) 3.12311i 0.154617i
\(409\) 8.12311 + 14.0696i 0.401662 + 0.695699i 0.993927 0.110045i \(-0.0350994\pi\)
−0.592265 + 0.805743i \(0.701766\pi\)
\(410\) 0 0
\(411\) 16.4924 0.813511
\(412\) 3.84381 2.21922i 0.189371 0.109333i
\(413\) −31.6034 18.2462i −1.55510 0.897837i
\(414\) −3.84233 + 6.65511i −0.188840 + 0.327081i
\(415\) 0 0
\(416\) 0.500000 3.57071i 0.0245145 0.175069i
\(417\) 21.5616i 1.05587i
\(418\) −1.18586 0.684658i −0.0580025 0.0334877i
\(419\) −5.96543 + 10.3324i −0.291431 + 0.504773i −0.974148 0.225910i \(-0.927465\pi\)
0.682718 + 0.730682i \(0.260798\pi\)
\(420\) 0 0
\(421\) 31.2462 1.52285 0.761424 0.648255i \(-0.224501\pi\)
0.761424 + 0.648255i \(0.224501\pi\)
\(422\) −0.972638 + 0.561553i −0.0473473 + 0.0273360i
\(423\) 3.46410 2.00000i 0.168430 0.0972433i
\(424\) −4.24621 −0.206214
\(425\) 0 0
\(426\) −6.28078 + 10.8786i −0.304305 + 0.527071i
\(427\) 5.19615 + 3.00000i 0.251459 + 0.145180i
\(428\) 5.36932i 0.259536i
\(429\) 0.280776 2.00514i 0.0135560 0.0968093i
\(430\) 0 0
\(431\) −9.15767 + 15.8616i −0.441109 + 0.764024i −0.997772 0.0667146i \(-0.978748\pi\)
0.556663 + 0.830739i \(0.312082\pi\)
\(432\) 0.866025 + 0.500000i 0.0416667 + 0.0240563i
\(433\) −11.8513 + 6.84233i −0.569535 + 0.328821i −0.756964 0.653457i \(-0.773318\pi\)
0.187428 + 0.982278i \(0.439985\pi\)
\(434\) 14.2462 0.683840
\(435\) 0 0
\(436\) 1.40388 + 2.43160i 0.0672338 + 0.116452i
\(437\) 18.7386i 0.896390i
\(438\) 7.79423 4.50000i 0.372423 0.215018i
\(439\) −3.46543 + 6.00231i −0.165396 + 0.286475i −0.936796 0.349876i \(-0.886224\pi\)
0.771400 + 0.636351i \(0.219557\pi\)
\(440\) 0 0
\(441\) 5.68466 0.270698
\(442\) −6.92820 + 8.87689i −0.329541 + 0.422231i
\(443\) 2.80776i 0.133401i −0.997773 0.0667004i \(-0.978753\pi\)
0.997773 0.0667004i \(-0.0212472\pi\)
\(444\) 0.280776 0.486319i 0.0133251 0.0230797i
\(445\) 0 0
\(446\) 0.219224 + 0.379706i 0.0103805 + 0.0179796i
\(447\) 10.2462i 0.484629i
\(448\) −3.08440 + 1.78078i −0.145724 + 0.0841338i
\(449\) −1.56155 2.70469i −0.0736942 0.127642i 0.826823 0.562462i \(-0.190146\pi\)
−0.900518 + 0.434819i \(0.856812\pi\)
\(450\) 0 0
\(451\) −0.876894 1.51883i −0.0412913 0.0715187i
\(452\) 3.46410 + 2.00000i 0.162938 + 0.0940721i
\(453\) 14.4493 + 8.34233i 0.678889 + 0.391957i
\(454\) −29.6847 −1.39317
\(455\) 0 0
\(456\) −2.43845 −0.114191
\(457\) 3.90368 + 2.25379i 0.182606 + 0.105428i 0.588517 0.808485i \(-0.299712\pi\)
−0.405910 + 0.913913i \(0.633045\pi\)
\(458\) −8.22068 4.74621i −0.384127 0.221776i
\(459\) −1.56155 2.70469i −0.0728870 0.126244i
\(460\) 0 0
\(461\) −5.31534 9.20644i −0.247560 0.428787i 0.715288 0.698830i \(-0.246295\pi\)
−0.962848 + 0.270043i \(0.912962\pi\)
\(462\) −1.73205 + 1.00000i −0.0805823 + 0.0465242i
\(463\) 27.8078i 1.29234i 0.763195 + 0.646168i \(0.223630\pi\)
−0.763195 + 0.646168i \(0.776370\pi\)
\(464\) 0.561553 + 0.972638i 0.0260694 + 0.0451536i
\(465\) 0 0
\(466\) 12.6847 21.9705i 0.587605 1.01776i
\(467\) 3.43845i 0.159112i 0.996830 + 0.0795562i \(0.0253503\pi\)
−0.996830 + 0.0795562i \(0.974650\pi\)
\(468\) −1.35234 3.34233i −0.0625121 0.154499i
\(469\) 42.0540 1.94187
\(470\) 0 0
\(471\) −8.62311 + 14.9357i −0.397332 + 0.688199i
\(472\) 8.87348 5.12311i 0.408435 0.235810i
\(473\) 0.246211i 0.0113208i
\(474\) −7.90388 13.6899i −0.363037 0.628799i
\(475\) 0 0
\(476\) 11.1231 0.509827
\(477\) −3.67733 + 2.12311i −0.168373 + 0.0972103i
\(478\) −23.4294 13.5270i −1.07164 0.618710i
\(479\) −5.80776 + 10.0593i −0.265364 + 0.459623i −0.967659 0.252263i \(-0.918825\pi\)
0.702295 + 0.711886i \(0.252159\pi\)
\(480\) 0 0
\(481\) −1.87689 + 0.759413i −0.0855790 + 0.0346262i
\(482\) 15.5616i 0.708809i
\(483\) −23.7025 13.6847i −1.07850 0.622674i
\(484\) −5.34233 + 9.25319i −0.242833 + 0.420599i
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) −36.9660 + 21.3423i −1.67509 + 0.967113i −0.710372 + 0.703827i \(0.751473\pi\)
−0.964718 + 0.263286i \(0.915194\pi\)
\(488\) −1.45896 + 0.842329i −0.0660439 + 0.0381305i
\(489\) 16.4924 0.745813
\(490\) 0 0
\(491\) −15.6501 + 27.1068i −0.706279 + 1.22331i 0.259949 + 0.965622i \(0.416294\pi\)
−0.966228 + 0.257689i \(0.917039\pi\)
\(492\) −2.70469 1.56155i −0.121937 0.0704002i
\(493\) 3.50758i 0.157973i
\(494\) 6.93087 + 5.40938i 0.311835 + 0.243379i
\(495\) 0 0
\(496\) −2.00000 + 3.46410i −0.0898027 + 0.155543i
\(497\) −38.7448 22.3693i −1.73794 1.00340i
\(498\) 5.68247 3.28078i 0.254638 0.147015i
\(499\) −6.05398 −0.271013 −0.135507 0.990776i \(-0.543266\pi\)
−0.135507 + 0.990776i \(0.543266\pi\)
\(500\) 0 0
\(501\) −11.8423 20.5115i −0.529076 0.916387i
\(502\) 23.9309i 1.06809i
\(503\) −21.0577 + 12.1577i −0.938917 + 0.542084i −0.889621 0.456700i \(-0.849031\pi\)
−0.0492961 + 0.998784i \(0.515698\pi\)
\(504\) −1.78078 + 3.08440i −0.0793221 + 0.137390i
\(505\) 0 0
\(506\) 4.31534 0.191840
\(507\) −3.57071 + 12.5000i −0.158581 + 0.555144i
\(508\) 21.8078i 0.967563i
\(509\) −8.12311 + 14.0696i −0.360050 + 0.623625i −0.987969 0.154654i \(-0.950574\pi\)
0.627918 + 0.778279i \(0.283907\pi\)
\(510\) 0 0
\(511\) 16.0270 + 27.7596i 0.708992 + 1.22801i
\(512\) 1.00000i 0.0441942i
\(513\) −2.11176 + 1.21922i −0.0932364 + 0.0538300i
\(514\) −6.80776 11.7914i −0.300278 0.520096i
\(515\) 0 0
\(516\) −0.219224 0.379706i −0.00965078 0.0167156i
\(517\) −1.94528 1.12311i −0.0855531 0.0493941i
\(518\) 1.73205 + 1.00000i 0.0761019 + 0.0439375i
\(519\) 8.87689 0.389652
\(520\) 0 0
\(521\) 34.7386 1.52193 0.760964 0.648795i \(-0.224727\pi\)
0.760964 + 0.648795i \(0.224727\pi\)
\(522\) 0.972638 + 0.561553i 0.0425712 + 0.0245785i
\(523\) −21.5908 12.4654i −0.944098 0.545075i −0.0528556 0.998602i \(-0.516832\pi\)
−0.891243 + 0.453527i \(0.850166\pi\)
\(524\) 0.438447 + 0.759413i 0.0191537 + 0.0331751i
\(525\) 0 0
\(526\) −3.15767 5.46925i −0.137681 0.238470i
\(527\) 10.8188 6.24621i 0.471272 0.272089i
\(528\) 0.561553i 0.0244384i
\(529\) 18.0270 + 31.2237i 0.783782 + 1.35755i
\(530\) 0 0
\(531\) 5.12311 8.87348i 0.222324 0.385076i
\(532\) 8.68466i 0.376528i
\(533\) 4.22351 + 10.4384i 0.182941 + 0.452139i
\(534\) −10.2462 −0.443397
\(535\) 0 0
\(536\) −5.90388 + 10.2258i −0.255009 + 0.441688i
\(537\) 13.5833 7.84233i 0.586163 0.338421i
\(538\) 3.36932i 0.145262i
\(539\) −1.59612 2.76456i −0.0687497 0.119078i
\(540\) 0 0
\(541\) −22.3153 −0.959411 −0.479706 0.877429i \(-0.659257\pi\)
−0.479706 + 0.877429i \(0.659257\pi\)
\(542\) −7.73436 + 4.46543i −0.332219 + 0.191807i
\(543\) 13.4168 + 7.74621i 0.575771 + 0.332422i
\(544\) −1.56155 + 2.70469i −0.0669510 + 0.115963i
\(545\) 0 0
\(546\) 11.9039 4.81645i 0.509439 0.206125i
\(547\) 30.9309i 1.32251i 0.750162 + 0.661254i \(0.229976\pi\)
−0.750162 + 0.661254i \(0.770024\pi\)
\(548\) −14.2829 8.24621i −0.610133 0.352261i
\(549\) −0.842329 + 1.45896i −0.0359497 + 0.0622668i
\(550\) 0 0
\(551\) −2.73863 −0.116670
\(552\) 6.65511 3.84233i 0.283260 0.163540i
\(553\) 48.7574 28.1501i 2.07338 1.19706i
\(554\) −5.00000 −0.212430
\(555\) 0 0
\(556\) −10.7808 + 18.6729i −0.457207 + 0.791905i
\(557\) −27.3799 15.8078i −1.16012 0.669796i −0.208788 0.977961i \(-0.566952\pi\)
−0.951333 + 0.308164i \(0.900285\pi\)
\(558\) 4.00000i 0.169334i
\(559\) −0.219224 + 1.56557i −0.00927217 + 0.0662165i
\(560\) 0 0
\(561\) −0.876894 + 1.51883i −0.0370225 + 0.0641249i
\(562\) −1.51883 0.876894i −0.0640678 0.0369896i
\(563\) 18.0201 10.4039i 0.759455 0.438471i −0.0696453 0.997572i \(-0.522187\pi\)
0.829100 + 0.559100i \(0.188853\pi\)
\(564\) −4.00000 −0.168430
\(565\) 0 0
\(566\) −14.8078 25.6478i −0.622417 1.07806i
\(567\) 3.56155i 0.149571i
\(568\) 10.8786 6.28078i 0.456457 0.263536i
\(569\) −5.75379 + 9.96585i −0.241211 + 0.417790i −0.961060 0.276341i \(-0.910878\pi\)
0.719848 + 0.694131i \(0.244211\pi\)
\(570\) 0 0
\(571\) 21.4233 0.896537 0.448268 0.893899i \(-0.352041\pi\)
0.448268 + 0.893899i \(0.352041\pi\)
\(572\) −1.24573 + 1.59612i −0.0520867 + 0.0667370i
\(573\) 15.9309i 0.665522i
\(574\) 5.56155 9.63289i 0.232135 0.402069i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 23.0000i 0.957503i −0.877951 0.478751i \(-0.841090\pi\)
0.877951 0.478751i \(-0.158910\pi\)
\(578\) −6.27540 + 3.62311i −0.261022 + 0.150701i
\(579\) 1.50000 + 2.59808i 0.0623379 + 0.107972i
\(580\) 0 0
\(581\) 11.6847 + 20.2384i 0.484761 + 0.839631i
\(582\) −2.43160 1.40388i −0.100793 0.0581928i
\(583\) 2.06501 + 1.19224i 0.0855241 + 0.0493774i
\(584\) −9.00000 −0.372423
\(585\) 0 0
\(586\) 20.2462 0.836363
\(587\) −15.5286 8.96543i −0.640933 0.370043i 0.144041 0.989572i \(-0.453990\pi\)
−0.784974 + 0.619529i \(0.787324\pi\)
\(588\) −4.92306 2.84233i −0.203024 0.117216i
\(589\) −4.87689 8.44703i −0.200949 0.348054i
\(590\) 0 0
\(591\) −2.56155 4.43674i −0.105368 0.182503i
\(592\) −0.486319 + 0.280776i −0.0199876 + 0.0115398i
\(593\) 38.9848i 1.60092i −0.599389 0.800458i \(-0.704590\pi\)
0.599389 0.800458i \(-0.295410\pi\)
\(594\) −0.280776 0.486319i −0.0115204 0.0199539i
\(595\) 0 0
\(596\) 5.12311 8.87348i 0.209851 0.363472i
\(597\) 4.43845i 0.181654i
\(598\) −27.4397 3.84233i −1.12209 0.157125i
\(599\) 18.3153 0.748345 0.374172 0.927359i \(-0.377927\pi\)
0.374172 + 0.927359i \(0.377927\pi\)
\(600\) 0 0
\(601\) 2.90388 5.02967i 0.118452 0.205165i −0.800703 0.599062i \(-0.795540\pi\)
0.919154 + 0.393898i \(0.128874\pi\)
\(602\) 1.35234 0.780776i 0.0551174 0.0318221i
\(603\) 11.8078i 0.480849i
\(604\) −8.34233 14.4493i −0.339445 0.587935i
\(605\) 0 0
\(606\) −6.24621 −0.253735
\(607\) 34.0948 19.6847i 1.38387 0.798976i 0.391252 0.920284i \(-0.372042\pi\)
0.992615 + 0.121308i \(0.0387089\pi\)
\(608\) 2.11176 + 1.21922i 0.0856431 + 0.0494460i
\(609\) −2.00000 + 3.46410i −0.0810441 + 0.140372i
\(610\) 0 0
\(611\) 11.3693 + 8.87348i 0.459953 + 0.358983i
\(612\) 3.12311i 0.126244i
\(613\) 31.6501 + 18.2732i 1.27834 + 0.738048i 0.976542 0.215326i \(-0.0690813\pi\)
0.301794 + 0.953373i \(0.402415\pi\)
\(614\) 11.1231 19.2658i 0.448892 0.777504i
\(615\) 0 0
\(616\) 2.00000 0.0805823
\(617\) −41.0230 + 23.6847i −1.65153 + 0.953508i −0.675079 + 0.737745i \(0.735891\pi\)
−0.976446 + 0.215763i \(0.930776\pi\)
\(618\) −3.84381 + 2.21922i −0.154621 + 0.0892703i
\(619\) 12.3002 0.494386 0.247193 0.968966i \(-0.420492\pi\)
0.247193 + 0.968966i \(0.420492\pi\)
\(620\) 0 0
\(621\) 3.84233 6.65511i 0.154187 0.267060i
\(622\) −8.93335 5.15767i −0.358195 0.206804i
\(623\) 36.4924i 1.46204i
\(624\) −0.500000 + 3.57071i −0.0200160 + 0.142943i
\(625\) 0 0
\(626\) −15.5000 + 26.8468i −0.619505 + 1.07301i
\(627\) 1.18586 + 0.684658i 0.0473588 + 0.0273426i
\(628\) 14.9357 8.62311i 0.595998 0.344099i
\(629\) 1.75379 0.0699281
\(630\) 0 0
\(631\) −16.4654 28.5190i −0.655479 1.13532i −0.981774 0.190054i \(-0.939134\pi\)
0.326295 0.945268i \(-0.394200\pi\)
\(632\) 15.8078i 0.628799i
\(633\) 0.972638 0.561553i 0.0386589 0.0223197i
\(634\) 8.12311 14.0696i 0.322610 0.558776i
\(635\) 0 0
\(636\) 4.24621 0.168373
\(637\) 7.68762 + 19.0000i 0.304594 + 0.752807i
\(638\) 0.630683i 0.0249690i
\(639\) 6.28078 10.8786i 0.248464 0.430352i
\(640\) 0 0
\(641\) −19.1231 33.1222i −0.755317 1.30825i −0.945216 0.326444i \(-0.894149\pi\)
0.189899 0.981804i \(-0.439184\pi\)
\(642\) 5.36932i 0.211910i
\(643\) 21.2578 12.2732i 0.838326 0.484008i −0.0183689 0.999831i \(-0.505847\pi\)
0.856695 + 0.515824i \(0.172514\pi\)
\(644\) 13.6847 + 23.7025i 0.539251 + 0.934010i
\(645\) 0 0
\(646\) −3.80776 6.59524i −0.149814 0.259486i
\(647\) 28.0794 + 16.2116i 1.10391 + 0.637346i 0.937247 0.348667i \(-0.113366\pi\)
0.166668 + 0.986013i \(0.446699\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) −5.75379 −0.225856
\(650\) 0 0
\(651\) −14.2462 −0.558353
\(652\) −14.2829 8.24621i −0.559360 0.322947i
\(653\) 32.5760 + 18.8078i 1.27480 + 0.736005i 0.975887 0.218276i \(-0.0700435\pi\)
0.298911 + 0.954281i \(0.403377\pi\)
\(654\) −1.40388 2.43160i −0.0548961 0.0950829i
\(655\) 0 0
\(656\) 1.56155 + 2.70469i 0.0609684 + 0.105600i
\(657\) −7.79423 + 4.50000i −0.304082 + 0.175562i
\(658\) 14.2462i 0.555375i
\(659\) 9.15767 + 15.8616i 0.356732 + 0.617878i 0.987413 0.158164i \(-0.0505575\pi\)
−0.630681 + 0.776042i \(0.717224\pi\)
\(660\) 0 0
\(661\) 24.2732 42.0424i 0.944118 1.63526i 0.186610 0.982434i \(-0.440250\pi\)
0.757508 0.652826i \(-0.226417\pi\)
\(662\) 16.6847i 0.648468i
\(663\) 6.92820 8.87689i 0.269069 0.344750i
\(664\) −6.56155 −0.254638
\(665\) 0 0
\(666\) −0.280776 + 0.486319i −0.0108799 + 0.0188445i
\(667\) 7.47439 4.31534i 0.289410 0.167091i
\(668\) 23.6847i 0.916387i
\(669\) −0.219224 0.379706i −0.00847567 0.0146803i
\(670\) 0 0
\(671\) 0.946025 0.0365209
\(672\) 3.08440 1.78078i 0.118983 0.0686949i
\(673\) −24.9015 14.3769i −0.959883 0.554189i −0.0637458 0.997966i \(-0.520305\pi\)
−0.896137 + 0.443778i \(0.853638\pi\)
\(674\) 4.02699 6.97495i 0.155114 0.268665i
\(675\) 0 0
\(676\) 9.34233 9.03996i 0.359320 0.347691i
\(677\) 11.6155i 0.446421i −0.974770 0.223211i \(-0.928346\pi\)
0.974770 0.223211i \(-0.0716537\pi\)
\(678\) −3.46410 2.00000i −0.133038 0.0768095i
\(679\) 5.00000 8.66025i 0.191882 0.332350i
\(680\) 0 0
\(681\) 29.6847 1.13752
\(682\) 1.94528 1.12311i 0.0744885 0.0430059i
\(683\) 13.3701 7.71922i 0.511592 0.295368i −0.221896 0.975070i \(-0.571224\pi\)
0.733488 + 0.679703i \(0.237891\pi\)
\(684\) 2.43845 0.0932364
\(685\) 0 0
\(686\) −2.34233 + 4.05703i −0.0894305 + 0.154898i
\(687\) 8.22068 + 4.74621i 0.313638 + 0.181079i
\(688\) 0.438447i 0.0167156i
\(689\) −12.0691 9.41967i −0.459797 0.358861i
\(690\) 0 0
\(691\) 2.41146 4.17677i 0.0917362 0.158892i −0.816506 0.577338i \(-0.804092\pi\)
0.908242 + 0.418446i \(0.137425\pi\)
\(692\) −7.68762 4.43845i −0.292239 0.168724i
\(693\) 1.73205 1.00000i 0.0657952 0.0379869i
\(694\) 24.8078 0.941690
\(695\) 0 0
\(696\) −0.561553 0.972638i −0.0212856 0.0368677i
\(697\) 9.75379i 0.369451i
\(698\) −16.6677 + 9.62311i −0.630882 + 0.364240i
\(699\) −12.6847 + 21.9705i −0.479778 + 0.831000i
\(700\) 0 0
\(701\) −0.876894 −0.0331198 −0.0165599 0.999863i \(-0.505271\pi\)
−0.0165599 + 0.999863i \(0.505271\pi\)
\(702\) 1.35234 + 3.34233i 0.0510410 + 0.126148i
\(703\) 1.36932i 0.0516448i
\(704\) −0.280776 + 0.486319i −0.0105822 + 0.0183288i
\(705\) 0 0
\(706\) −1.12311 1.94528i −0.0422686 0.0732114i
\(707\) 22.2462i 0.836655i
\(708\) −8.87348 + 5.12311i −0.333486 + 0.192538i
\(709\) −14.3769 24.9015i −0.539936 0.935196i −0.998907 0.0467448i \(-0.985115\pi\)
0.458971 0.888451i \(-0.348218\pi\)
\(710\) 0 0
\(711\) 7.90388 + 13.6899i 0.296419 + 0.513412i
\(712\) 8.87348 + 5.12311i 0.332548 + 0.191997i
\(713\) 26.6204 + 15.3693i 0.996943 + 0.575585i
\(714\) −11.1231 −0.416272
\(715\) 0 0
\(716\) −15.6847 −0.586163
\(717\) 23.4294 + 13.5270i 0.874988 + 0.505175i
\(718\) 4.22351 + 2.43845i 0.157620 + 0.0910020i
\(719\) −8.71922 15.1021i −0.325172 0.563215i 0.656375 0.754435i \(-0.272089\pi\)
−0.981547 + 0.191220i \(0.938756\pi\)
\(720\) 0 0
\(721\) −7.90388 13.6899i −0.294356 0.509839i
\(722\) 11.3051 6.52699i 0.420731 0.242909i
\(723\) 15.5616i 0.578740i
\(724\) −7.74621 13.4168i −0.287886 0.498633i
\(725\) 0 0
\(726\) 5.34233 9.25319i 0.198272 0.343418i
\(727\) 50.7926i 1.88379i 0.335902 + 0.941897i \(0.390959\pi\)
−0.335902 + 0.941897i \(0.609041\pi\)
\(728\) −12.7173 1.78078i −0.471334 0.0660000i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 0.684658 1.18586i 0.0253230 0.0438607i
\(732\) 1.45896 0.842329i 0.0539246 0.0311334i
\(733\) 47.9848i 1.77236i −0.463340 0.886180i \(-0.653349\pi\)
0.463340 0.886180i \(-0.346651\pi\)
\(734\) −5.09612 8.82674i −0.188101 0.325801i
\(735\) 0 0
\(736\) −7.68466 −0.283260
\(737\) 5.74234 3.31534i 0.211522 0.122122i
\(738\) 2.70469 + 1.56155i 0.0995610 + 0.0574816i
\(739\) −6.56155 + 11.3649i −0.241371 + 0.418066i −0.961105 0.276183i \(-0.910930\pi\)
0.719734 + 0.694250i \(0.244264\pi\)
\(740\) 0 0
\(741\) −6.93087 5.40938i −0.254612 0.198718i
\(742\) 15.1231i 0.555187i
\(743\) −9.63289 5.56155i −0.353397 0.204034i 0.312784 0.949824i \(-0.398739\pi\)
−0.666180 + 0.745791i \(0.732072\pi\)
\(744\) 2.00000 3.46410i 0.0733236 0.127000i
\(745\) 0 0
\(746\) −9.49242 −0.347542
\(747\) −5.68247 + 3.28078i −0.207911 + 0.120037i
\(748\) 1.51883 0.876894i 0.0555338 0.0320624i
\(749\) 19.1231 0.698743
\(750\) 0 0
\(751\) −25.1231 + 43.5145i −0.916755 + 1.58787i −0.112444 + 0.993658i \(0.535868\pi\)
−0.804311 + 0.594208i \(0.797465\pi\)
\(752\) 3.46410 + 2.00000i 0.126323 + 0.0729325i
\(753\) 23.9309i 0.872089i
\(754\) −0.561553 + 4.01029i −0.0204505 + 0.146046i
\(755\) 0 0
\(756\) 1.78078 3.08440i 0.0647662 0.112178i
\(757\) −26.5737 15.3423i −0.965837 0.557626i −0.0678727 0.997694i \(-0.521621\pi\)
−0.897965 + 0.440068i \(0.854954\pi\)
\(758\) −20.8314 + 12.0270i −0.756629 + 0.436840i
\(759\) −4.31534 −0.156637
\(760\) 0 0
\(761\) 11.4924 + 19.9055i 0.416600 + 0.721572i 0.995595 0.0937588i \(-0.0298882\pi\)
−0.578995 + 0.815331i \(0.696555\pi\)
\(762\) 21.8078i 0.790012i
\(763\) 8.66025 5.00000i 0.313522 0.181012i
\(764\) 7.96543 13.7965i 0.288179 0.499141i
\(765\) 0 0
\(766\) −5.43845 −0.196499
\(767\) 36.5863 + 5.12311i 1.32105 + 0.184985i
\(768\) 1.00000i 0.0360844i
\(769\) −4.65767 + 8.06732i −0.167960 + 0.290915i −0.937702 0.347439i \(-0.887051\pi\)
0.769743 + 0.638354i \(0.220385\pi\)
\(770\) 0 0
\(771\) 6.80776 + 11.7914i 0.245176 + 0.424657i
\(772\) 3.00000i 0.107972i
\(773\) −25.6478 + 14.8078i −0.922487 + 0.532598i −0.884428 0.466677i \(-0.845451\pi\)
−0.0380595 + 0.999275i \(0.512118\pi\)
\(774\) 0.219224 + 0.379706i 0.00787983 + 0.0136483i
\(775\) 0 0
\(776\) 1.40388 + 2.43160i 0.0503964 + 0.0872892i
\(777\) −1.73205 1.00000i −0.0621370 0.0358748i
\(778\) −9.84612 5.68466i −0.353000 0.203805i
\(779\) −7.61553 −0.272855
\(780\) 0 0
\(781\) −7.05398 −0.252411
\(782\) 20.7846 + 12.0000i 0.743256 + 0.429119i
\(783\) −0.972638 0.561553i −0.0347592 0.0200683i
\(784\) 2.84233 + 4.92306i 0.101512 + 0.175824i