Properties

Label 1950.2.y.j.49.4
Level $1950$
Weight $2$
Character 1950.49
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.y (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: 8.0.17284886784.1
Defining polynomial: \(x^{8} - 2 x^{7} + 2 x^{6} + 30 x^{5} + 185 x^{4} + 36 x^{3} + 8 x^{2} + 208 x + 2704\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.4
Root \(-1.70006 + 1.70006i\) of defining polynomial
Character \(\chi\) \(=\) 1950.49
Dual form 1950.2.y.j.199.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(2.32233 - 4.02239i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(2.32233 - 4.02239i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(3.81062 - 2.20006i) q^{11} +1.00000i q^{12} +(-1.32233 - 3.35432i) q^{13} -4.64466 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.46410 - 2.00000i) q^{17} -1.00000 q^{18} +(6.96699 + 4.02239i) q^{19} -4.64466i q^{21} +(-3.81062 - 2.20006i) q^{22} +(0.845746 - 0.488292i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-2.24376 + 2.82233i) q^{26} -1.00000i q^{27} +(2.32233 + 4.02239i) q^{28} +(-2.15637 - 3.73494i) q^{29} +6.44069i q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.20006 - 3.81062i) q^{33} +4.00000i q^{34} +(0.500000 + 0.866025i) q^{36} +(-1.89801 - 3.28745i) q^{37} -8.04479i q^{38} +(-2.82233 - 2.24376i) q^{39} +(-6.31274 + 3.64466i) q^{41} +(-4.02239 + 2.32233i) q^{42} +(0.620469 + 0.358228i) q^{43} +4.40013i q^{44} +(-0.845746 - 0.488292i) q^{46} +9.75342 q^{47} +(-0.866025 - 0.500000i) q^{48} +(-7.28643 - 12.6205i) q^{49} -4.00000 q^{51} +(3.56609 + 0.531987i) q^{52} +13.5089i q^{53} +(-0.866025 + 0.500000i) q^{54} +(2.32233 - 4.02239i) q^{56} +8.04479 q^{57} +(-2.15637 + 3.73494i) q^{58} +(1.88842 + 1.09028i) q^{59} +(-3.73205 + 6.46410i) q^{61} +(5.57780 - 3.22034i) q^{62} +(-2.32233 - 4.02239i) q^{63} +1.00000 q^{64} -4.40013 q^{66} +(0.912609 + 1.58068i) q^{67} +(3.46410 - 2.00000i) q^{68} +(0.488292 - 0.845746i) q^{69} +(-6.88764 - 3.97658i) q^{71} +(0.500000 - 0.866025i) q^{72} +4.36112 q^{73} +(-1.89801 + 3.28745i) q^{74} +(-6.96699 + 4.02239i) q^{76} -20.4371i q^{77} +(-0.531987 + 3.56609i) q^{78} +14.9340 q^{79} +(-0.500000 - 0.866025i) q^{81} +(6.31274 + 3.64466i) q^{82} -3.51093 q^{83} +(4.02239 + 2.32233i) q^{84} -0.716456i q^{86} +(-3.73494 - 2.15637i) q^{87} +(3.81062 - 2.20006i) q^{88} +(-7.07780 + 4.08637i) q^{89} +(-16.5633 - 2.47090i) q^{91} +0.976584i q^{92} +(3.22034 + 5.57780i) q^{93} +(-4.87671 - 8.44671i) q^{94} +1.00000i q^{96} +(6.91261 - 11.9730i) q^{97} +(-7.28643 + 12.6205i) q^{98} -4.40013i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{2} - 4q^{4} + 2q^{7} + 8q^{8} + 4q^{9} + O(q^{10}) \) \( 8q - 4q^{2} - 4q^{4} + 2q^{7} + 8q^{8} + 4q^{9} + 6q^{11} + 6q^{13} - 4q^{14} - 4q^{16} - 8q^{18} + 6q^{19} - 6q^{22} + 6q^{23} - 12q^{26} + 2q^{28} + 8q^{29} - 4q^{32} + 2q^{33} + 4q^{36} - 10q^{37} - 6q^{39} - 48q^{43} - 6q^{46} - 16q^{47} - 14q^{49} - 32q^{51} + 6q^{52} + 2q^{56} + 8q^{58} - 24q^{59} - 16q^{61} + 30q^{62} - 2q^{63} + 8q^{64} - 4q^{66} - 12q^{67} - 4q^{69} - 12q^{71} + 4q^{72} + 24q^{73} - 10q^{74} - 6q^{76} - 6q^{78} + 20q^{79} - 4q^{81} - 32q^{83} + 6q^{87} + 6q^{88} - 42q^{89} - 10q^{91} + 4q^{93} + 8q^{94} + 36q^{97} - 14q^{98} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0.866025 0.500000i 0.500000 0.288675i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) −0.866025 0.500000i −0.353553 0.204124i
\(7\) 2.32233 4.02239i 0.877758 1.52032i 0.0239629 0.999713i \(-0.492372\pi\)
0.853795 0.520609i \(-0.174295\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0 0
\(11\) 3.81062 2.20006i 1.14895 0.663344i 0.200316 0.979731i \(-0.435803\pi\)
0.948630 + 0.316387i \(0.102470\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −1.32233 3.35432i −0.366748 0.930320i
\(14\) −4.64466 −1.24134
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.46410 2.00000i −0.840168 0.485071i 0.0171533 0.999853i \(-0.494540\pi\)
−0.857321 + 0.514782i \(0.827873\pi\)
\(18\) −1.00000 −0.235702
\(19\) 6.96699 + 4.02239i 1.59834 + 0.922800i 0.991808 + 0.127739i \(0.0407720\pi\)
0.606529 + 0.795061i \(0.292561\pi\)
\(20\) 0 0
\(21\) 4.64466i 1.01355i
\(22\) −3.81062 2.20006i −0.812427 0.469055i
\(23\) 0.845746 0.488292i 0.176350 0.101816i −0.409226 0.912433i \(-0.634201\pi\)
0.585577 + 0.810617i \(0.300868\pi\)
\(24\) 0.866025 0.500000i 0.176777 0.102062i
\(25\) 0 0
\(26\) −2.24376 + 2.82233i −0.440037 + 0.553504i
\(27\) 1.00000i 0.192450i
\(28\) 2.32233 + 4.02239i 0.438879 + 0.760161i
\(29\) −2.15637 3.73494i −0.400427 0.693561i 0.593350 0.804945i \(-0.297805\pi\)
−0.993777 + 0.111384i \(0.964472\pi\)
\(30\) 0 0
\(31\) 6.44069i 1.15678i 0.815760 + 0.578391i \(0.196319\pi\)
−0.815760 + 0.578391i \(0.803681\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 2.20006 3.81062i 0.382982 0.663344i
\(34\) 4.00000i 0.685994i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) −1.89801 3.28745i −0.312031 0.540454i 0.666771 0.745263i \(-0.267676\pi\)
−0.978802 + 0.204809i \(0.934343\pi\)
\(38\) 8.04479i 1.30504i
\(39\) −2.82233 2.24376i −0.451934 0.359289i
\(40\) 0 0
\(41\) −6.31274 + 3.64466i −0.985884 + 0.569200i −0.904041 0.427445i \(-0.859414\pi\)
−0.0818424 + 0.996645i \(0.526080\pi\)
\(42\) −4.02239 + 2.32233i −0.620669 + 0.358343i
\(43\) 0.620469 + 0.358228i 0.0946207 + 0.0546293i 0.546564 0.837418i \(-0.315936\pi\)
−0.451943 + 0.892047i \(0.649269\pi\)
\(44\) 4.40013i 0.663344i
\(45\) 0 0
\(46\) −0.845746 0.488292i −0.124698 0.0719947i
\(47\) 9.75342 1.42268 0.711341 0.702847i \(-0.248088\pi\)
0.711341 + 0.702847i \(0.248088\pi\)
\(48\) −0.866025 0.500000i −0.125000 0.0721688i
\(49\) −7.28643 12.6205i −1.04092 1.80292i
\(50\) 0 0
\(51\) −4.00000 −0.560112
\(52\) 3.56609 + 0.531987i 0.494528 + 0.0737734i
\(53\) 13.5089i 1.85559i 0.373092 + 0.927794i \(0.378297\pi\)
−0.373092 + 0.927794i \(0.621703\pi\)
\(54\) −0.866025 + 0.500000i −0.117851 + 0.0680414i
\(55\) 0 0
\(56\) 2.32233 4.02239i 0.310334 0.537515i
\(57\) 8.04479 1.06556
\(58\) −2.15637 + 3.73494i −0.283145 + 0.490421i
\(59\) 1.88842 + 1.09028i 0.245851 + 0.141942i 0.617863 0.786286i \(-0.287999\pi\)
−0.372012 + 0.928228i \(0.621332\pi\)
\(60\) 0 0
\(61\) −3.73205 + 6.46410i −0.477840 + 0.827643i −0.999677 0.0254017i \(-0.991914\pi\)
0.521837 + 0.853045i \(0.325247\pi\)
\(62\) 5.57780 3.22034i 0.708381 0.408984i
\(63\) −2.32233 4.02239i −0.292586 0.506774i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −4.40013 −0.541618
\(67\) 0.912609 + 1.58068i 0.111493 + 0.193111i 0.916372 0.400327i \(-0.131103\pi\)
−0.804879 + 0.593438i \(0.797770\pi\)
\(68\) 3.46410 2.00000i 0.420084 0.242536i
\(69\) 0.488292 0.845746i 0.0587834 0.101816i
\(70\) 0 0
\(71\) −6.88764 3.97658i −0.817413 0.471934i 0.0321105 0.999484i \(-0.489777\pi\)
−0.849524 + 0.527551i \(0.823110\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 4.36112 0.510430 0.255215 0.966884i \(-0.417854\pi\)
0.255215 + 0.966884i \(0.417854\pi\)
\(74\) −1.89801 + 3.28745i −0.220640 + 0.382159i
\(75\) 0 0
\(76\) −6.96699 + 4.02239i −0.799168 + 0.461400i
\(77\) 20.4371i 2.32902i
\(78\) −0.531987 + 3.56609i −0.0602357 + 0.403780i
\(79\) 14.9340 1.68020 0.840102 0.542429i \(-0.182495\pi\)
0.840102 + 0.542429i \(0.182495\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 6.31274 + 3.64466i 0.697125 + 0.402485i
\(83\) −3.51093 −0.385375 −0.192688 0.981260i \(-0.561720\pi\)
−0.192688 + 0.981260i \(0.561720\pi\)
\(84\) 4.02239 + 2.32233i 0.438879 + 0.253387i
\(85\) 0 0
\(86\) 0.716456i 0.0772575i
\(87\) −3.73494 2.15637i −0.400427 0.231187i
\(88\) 3.81062 2.20006i 0.406214 0.234528i
\(89\) −7.07780 + 4.08637i −0.750245 + 0.433154i −0.825782 0.563989i \(-0.809266\pi\)
0.0755374 + 0.997143i \(0.475933\pi\)
\(90\) 0 0
\(91\) −16.5633 2.47090i −1.73630 0.259021i
\(92\) 0.976584i 0.101816i
\(93\) 3.22034 + 5.57780i 0.333934 + 0.578391i
\(94\) −4.87671 8.44671i −0.502994 0.871212i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) 6.91261 11.9730i 0.701869 1.21567i −0.265941 0.963989i \(-0.585682\pi\)
0.967810 0.251683i \(-0.0809842\pi\)
\(98\) −7.28643 + 12.6205i −0.736041 + 1.27486i
\(99\) 4.40013i 0.442229i
\(100\) 0 0
\(101\) −3.40013 5.88919i −0.338325 0.585997i 0.645793 0.763513i \(-0.276527\pi\)
−0.984118 + 0.177516i \(0.943194\pi\)
\(102\) 2.00000 + 3.46410i 0.198030 + 0.342997i
\(103\) 5.29137i 0.521374i −0.965423 0.260687i \(-0.916051\pi\)
0.965423 0.260687i \(-0.0839490\pi\)
\(104\) −1.32233 3.35432i −0.129665 0.328918i
\(105\) 0 0
\(106\) 11.6990 6.75444i 1.13631 0.656050i
\(107\) −14.6603 + 8.46410i −1.41726 + 0.818256i −0.996057 0.0887109i \(-0.971725\pi\)
−0.421203 + 0.906966i \(0.638392\pi\)
\(108\) 0.866025 + 0.500000i 0.0833333 + 0.0481125i
\(109\) 12.8003i 1.22604i −0.790067 0.613021i \(-0.789954\pi\)
0.790067 0.613021i \(-0.210046\pi\)
\(110\) 0 0
\(111\) −3.28745 1.89801i −0.312031 0.180151i
\(112\) −4.64466 −0.438879
\(113\) −11.3156 6.53308i −1.06448 0.614580i −0.137815 0.990458i \(-0.544008\pi\)
−0.926669 + 0.375878i \(0.877341\pi\)
\(114\) −4.02239 6.96699i −0.376732 0.652518i
\(115\) 0 0
\(116\) 4.31274 0.400427
\(117\) −3.56609 0.531987i −0.329685 0.0491823i
\(118\) 2.18056i 0.200737i
\(119\) −16.0896 + 9.28932i −1.47493 + 0.851550i
\(120\) 0 0
\(121\) 4.18056 7.24094i 0.380051 0.658267i
\(122\) 7.46410 0.675768
\(123\) −3.64466 + 6.31274i −0.328628 + 0.569200i
\(124\) −5.57780 3.22034i −0.500901 0.289195i
\(125\) 0 0
\(126\) −2.32233 + 4.02239i −0.206890 + 0.358343i
\(127\) 10.5825 6.10978i 0.939041 0.542156i 0.0493816 0.998780i \(-0.484275\pi\)
0.889660 + 0.456624i \(0.150942\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0.716456 0.0630805
\(130\) 0 0
\(131\) −0.378757 −0.0330921 −0.0165461 0.999863i \(-0.505267\pi\)
−0.0165461 + 0.999863i \(0.505267\pi\)
\(132\) 2.20006 + 3.81062i 0.191491 + 0.331672i
\(133\) 32.3593 18.6826i 2.80591 1.61999i
\(134\) 0.912609 1.58068i 0.0788374 0.136550i
\(135\) 0 0
\(136\) −3.46410 2.00000i −0.297044 0.171499i
\(137\) −0.626177 + 1.08457i −0.0534979 + 0.0926612i −0.891534 0.452953i \(-0.850370\pi\)
0.838036 + 0.545615i \(0.183704\pi\)
\(138\) −0.976584 −0.0831323
\(139\) 1.67767 2.90581i 0.142298 0.246468i −0.786064 0.618146i \(-0.787884\pi\)
0.928362 + 0.371678i \(0.121217\pi\)
\(140\) 0 0
\(141\) 8.44671 4.87671i 0.711341 0.410693i
\(142\) 7.95317i 0.667415i
\(143\) −12.4186 9.87282i −1.03850 0.825607i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) −2.18056 3.77684i −0.180464 0.312573i
\(147\) −12.6205 7.28643i −1.04092 0.600975i
\(148\) 3.79603 0.312031
\(149\) 4.00077 + 2.30985i 0.327756 + 0.189230i 0.654844 0.755764i \(-0.272734\pi\)
−0.327088 + 0.944994i \(0.606067\pi\)
\(150\) 0 0
\(151\) 11.2425i 0.914901i 0.889235 + 0.457450i \(0.151237\pi\)
−0.889235 + 0.457450i \(0.848763\pi\)
\(152\) 6.96699 + 4.02239i 0.565097 + 0.326259i
\(153\) −3.46410 + 2.00000i −0.280056 + 0.161690i
\(154\) −17.6990 + 10.2185i −1.42623 + 0.823434i
\(155\) 0 0
\(156\) 3.35432 1.32233i 0.268560 0.105871i
\(157\) 1.50311i 0.119961i 0.998200 + 0.0599807i \(0.0191039\pi\)
−0.998200 + 0.0599807i \(0.980896\pi\)
\(158\) −7.46699 12.9332i −0.594042 1.02891i
\(159\) 6.75444 + 11.6990i 0.535662 + 0.927794i
\(160\) 0 0
\(161\) 4.53590i 0.357479i
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) 0.0881650 0.152706i 0.00690561 0.0119609i −0.862552 0.505969i \(-0.831135\pi\)
0.869458 + 0.494008i \(0.164469\pi\)
\(164\) 7.28932i 0.569200i
\(165\) 0 0
\(166\) 1.75547 + 3.04056i 0.136251 + 0.235993i
\(167\) −4.34081 7.51851i −0.335902 0.581800i 0.647756 0.761848i \(-0.275708\pi\)
−0.983658 + 0.180049i \(0.942374\pi\)
\(168\) 4.64466i 0.358343i
\(169\) −9.50289 + 8.87103i −0.730991 + 0.682387i
\(170\) 0 0
\(171\) 6.96699 4.02239i 0.532779 0.307600i
\(172\) −0.620469 + 0.358228i −0.0473103 + 0.0273146i
\(173\) 1.54190 + 0.890216i 0.117228 + 0.0676818i 0.557468 0.830199i \(-0.311773\pi\)
−0.440239 + 0.897880i \(0.645106\pi\)
\(174\) 4.31274i 0.326948i
\(175\) 0 0
\(176\) −3.81062 2.20006i −0.287236 0.165836i
\(177\) 2.18056 0.163901
\(178\) 7.07780 + 4.08637i 0.530503 + 0.306286i
\(179\) 8.70786 + 15.0825i 0.650856 + 1.12732i 0.982916 + 0.184057i \(0.0589232\pi\)
−0.332059 + 0.943258i \(0.607743\pi\)
\(180\) 0 0
\(181\) −10.3611 −0.770136 −0.385068 0.922888i \(-0.625822\pi\)
−0.385068 + 0.922888i \(0.625822\pi\)
\(182\) 6.14177 + 15.5797i 0.455258 + 1.15484i
\(183\) 7.46410i 0.551762i
\(184\) 0.845746 0.488292i 0.0623492 0.0359973i
\(185\) 0 0
\(186\) 3.22034 5.57780i 0.236127 0.408984i
\(187\) −17.6005 −1.28708
\(188\) −4.87671 + 8.44671i −0.355671 + 0.616040i
\(189\) −4.02239 2.32233i −0.292586 0.168925i
\(190\) 0 0
\(191\) 0.448507 0.776837i 0.0324528 0.0562100i −0.849343 0.527842i \(-0.823001\pi\)
0.881796 + 0.471632i \(0.156335\pi\)
\(192\) 0.866025 0.500000i 0.0625000 0.0360844i
\(193\) 10.1322 + 17.5494i 0.729330 + 1.26324i 0.957167 + 0.289537i \(0.0935015\pi\)
−0.227837 + 0.973699i \(0.573165\pi\)
\(194\) −13.8252 −0.992593
\(195\) 0 0
\(196\) 14.5729 1.04092
\(197\) −4.59028 7.95060i −0.327044 0.566457i 0.654880 0.755733i \(-0.272719\pi\)
−0.981924 + 0.189276i \(0.939386\pi\)
\(198\) −3.81062 + 2.20006i −0.270809 + 0.156352i
\(199\) 8.10876 14.0448i 0.574815 0.995609i −0.421247 0.906946i \(-0.638407\pi\)
0.996062 0.0886625i \(-0.0282593\pi\)
\(200\) 0 0
\(201\) 1.58068 + 0.912609i 0.111493 + 0.0643705i
\(202\) −3.40013 + 5.88919i −0.239232 + 0.414362i
\(203\) −20.0312 −1.40591
\(204\) 2.00000 3.46410i 0.140028 0.242536i
\(205\) 0 0
\(206\) −4.58246 + 2.64568i −0.319275 + 0.184333i
\(207\) 0.976584i 0.0678773i
\(208\) −2.24376 + 2.82233i −0.155577 + 0.195693i
\(209\) 35.3981 2.44854
\(210\) 0 0
\(211\) 0.809848 + 1.40270i 0.0557522 + 0.0965657i 0.892555 0.450939i \(-0.148911\pi\)
−0.836802 + 0.547505i \(0.815578\pi\)
\(212\) −11.6990 6.75444i −0.803493 0.463897i
\(213\) −7.95317 −0.544942
\(214\) 14.6603 + 8.46410i 1.00215 + 0.578594i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 25.9070 + 14.9574i 1.75868 + 1.01537i
\(218\) −11.0853 + 6.40013i −0.750794 + 0.433471i
\(219\) 3.77684 2.18056i 0.255215 0.147348i
\(220\) 0 0
\(221\) −2.12795 + 14.2644i −0.143141 + 0.959524i
\(222\) 3.79603i 0.254773i
\(223\) 1.11836 + 1.93705i 0.0748906 + 0.129714i 0.901039 0.433739i \(-0.142806\pi\)
−0.826148 + 0.563453i \(0.809473\pi\)
\(224\) 2.32233 + 4.02239i 0.155167 + 0.268757i
\(225\) 0 0
\(226\) 13.0662i 0.869148i
\(227\) −7.66025 + 13.2679i −0.508429 + 0.880625i 0.491523 + 0.870864i \(0.336440\pi\)
−0.999952 + 0.00976038i \(0.996893\pi\)
\(228\) −4.02239 + 6.96699i −0.266389 + 0.461400i
\(229\) 10.1279i 0.669274i 0.942347 + 0.334637i \(0.108614\pi\)
−0.942347 + 0.334637i \(0.891386\pi\)
\(230\) 0 0
\(231\) −10.2185 17.6990i −0.672331 1.16451i
\(232\) −2.15637 3.73494i −0.141572 0.245211i
\(233\) 20.7519i 1.35950i 0.733444 + 0.679750i \(0.237912\pi\)
−0.733444 + 0.679750i \(0.762088\pi\)
\(234\) 1.32233 + 3.35432i 0.0864434 + 0.219279i
\(235\) 0 0
\(236\) −1.88842 + 1.09028i −0.122926 + 0.0709711i
\(237\) 12.9332 7.46699i 0.840102 0.485033i
\(238\) 16.0896 + 9.28932i 1.04293 + 0.602137i
\(239\) 24.3539i 1.57532i 0.616107 + 0.787662i \(0.288709\pi\)
−0.616107 + 0.787662i \(0.711291\pi\)
\(240\) 0 0
\(241\) −17.2066 9.93423i −1.10837 0.639920i −0.169966 0.985450i \(-0.554366\pi\)
−0.938408 + 0.345530i \(0.887699\pi\)
\(242\) −8.36112 −0.537473
\(243\) −0.866025 0.500000i −0.0555556 0.0320750i
\(244\) −3.73205 6.46410i −0.238920 0.413822i
\(245\) 0 0
\(246\) 7.28932 0.464750
\(247\) 4.27973 28.6884i 0.272312 1.82540i
\(248\) 6.44069i 0.408984i
\(249\) −3.04056 + 1.75547i −0.192688 + 0.111248i
\(250\) 0 0
\(251\) 6.78566 11.7531i 0.428307 0.741849i −0.568416 0.822741i \(-0.692444\pi\)
0.996723 + 0.0808920i \(0.0257769\pi\)
\(252\) 4.64466 0.292586
\(253\) 2.14855 3.72139i 0.135078 0.233962i
\(254\) −10.5825 6.10978i −0.664002 0.383362i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0.573569 0.331150i 0.0357783 0.0206566i −0.482004 0.876169i \(-0.660091\pi\)
0.517782 + 0.855512i \(0.326758\pi\)
\(258\) −0.358228 0.620469i −0.0223023 0.0386287i
\(259\) −17.6312 −1.09555
\(260\) 0 0
\(261\) −4.31274 −0.266952
\(262\) 0.189378 + 0.328013i 0.0116998 + 0.0202647i
\(263\) 26.6301 15.3749i 1.64208 0.948058i 0.661993 0.749510i \(-0.269711\pi\)
0.980091 0.198548i \(-0.0636225\pi\)
\(264\) 2.20006 3.81062i 0.135405 0.234528i
\(265\) 0 0
\(266\) −32.3593 18.6826i −1.98408 1.14551i
\(267\) −4.08637 + 7.07780i −0.250082 + 0.433154i
\(268\) −1.82522 −0.111493
\(269\) −1.87205 + 3.24249i −0.114141 + 0.197698i −0.917436 0.397883i \(-0.869745\pi\)
0.803295 + 0.595581i \(0.203078\pi\)
\(270\) 0 0
\(271\) 24.0419 13.8806i 1.46044 0.843186i 0.461410 0.887187i \(-0.347344\pi\)
0.999031 + 0.0440009i \(0.0140104\pi\)
\(272\) 4.00000i 0.242536i
\(273\) −15.5797 + 6.14177i −0.942924 + 0.371717i
\(274\) 1.25235 0.0756575
\(275\) 0 0
\(276\) 0.488292 + 0.845746i 0.0293917 + 0.0509079i
\(277\) −10.3855 5.99609i −0.624006 0.360270i 0.154421 0.988005i \(-0.450649\pi\)
−0.778427 + 0.627735i \(0.783982\pi\)
\(278\) −3.35534 −0.201240
\(279\) 5.57780 + 3.22034i 0.333934 + 0.192797i
\(280\) 0 0
\(281\) 3.63888i 0.217078i 0.994092 + 0.108539i \(0.0346172\pi\)
−0.994092 + 0.108539i \(0.965383\pi\)
\(282\) −8.44671 4.87671i −0.502994 0.290404i
\(283\) −4.19538 + 2.42220i −0.249389 + 0.143985i −0.619485 0.785009i \(-0.712658\pi\)
0.370095 + 0.928994i \(0.379325\pi\)
\(284\) 6.88764 3.97658i 0.408707 0.235967i
\(285\) 0 0
\(286\) −2.34081 + 15.6912i −0.138415 + 0.927843i
\(287\) 33.8564i 1.99848i
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) −0.500000 0.866025i −0.0294118 0.0509427i
\(290\) 0 0
\(291\) 13.8252i 0.810449i
\(292\) −2.18056 + 3.77684i −0.127608 + 0.221023i
\(293\) −1.85041 + 3.20500i −0.108102 + 0.187238i −0.915001 0.403451i \(-0.867811\pi\)
0.806899 + 0.590689i \(0.201144\pi\)
\(294\) 14.5729i 0.849907i
\(295\) 0 0
\(296\) −1.89801 3.28745i −0.110320 0.191079i
\(297\) −2.20006 3.81062i −0.127661 0.221115i
\(298\) 4.61970i 0.267612i
\(299\) −2.75624 2.19122i −0.159398 0.126721i
\(300\) 0 0
\(301\) 2.88187 1.66385i 0.166108 0.0959026i
\(302\) 9.73628 5.62124i 0.560260 0.323466i
\(303\) −5.88919 3.40013i −0.338325 0.195332i
\(304\) 8.04479i 0.461400i
\(305\) 0 0
\(306\) 3.46410 + 2.00000i 0.198030 + 0.114332i
\(307\) −7.11454 −0.406048 −0.203024 0.979174i \(-0.565077\pi\)
−0.203024 + 0.979174i \(0.565077\pi\)
\(308\) 17.6990 + 10.2185i 1.00850 + 0.582256i
\(309\) −2.64568 4.58246i −0.150508 0.260687i
\(310\) 0 0
\(311\) −19.9148 −1.12926 −0.564632 0.825343i \(-0.690982\pi\)
−0.564632 + 0.825343i \(0.690982\pi\)
\(312\) −2.82233 2.24376i −0.159783 0.127028i
\(313\) 6.13950i 0.347025i 0.984832 + 0.173513i \(0.0555117\pi\)
−0.984832 + 0.173513i \(0.944488\pi\)
\(314\) 1.30173 0.751556i 0.0734611 0.0424128i
\(315\) 0 0
\(316\) −7.46699 + 12.9332i −0.420051 + 0.727550i
\(317\) 7.85286 0.441061 0.220530 0.975380i \(-0.429221\pi\)
0.220530 + 0.975380i \(0.429221\pi\)
\(318\) 6.75444 11.6990i 0.378770 0.656050i
\(319\) −16.4342 9.48829i −0.920139 0.531242i
\(320\) 0 0
\(321\) −8.46410 + 14.6603i −0.472420 + 0.818256i
\(322\) −3.92820 + 2.26795i −0.218910 + 0.126388i
\(323\) −16.0896 27.8680i −0.895248 1.55061i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −0.176330 −0.00976601
\(327\) −6.40013 11.0853i −0.353928 0.613021i
\(328\) −6.31274 + 3.64466i −0.348563 + 0.201243i
\(329\) 22.6507 39.2321i 1.24877 2.16294i
\(330\) 0 0
\(331\) 27.7093 + 15.9980i 1.52304 + 0.879327i 0.999629 + 0.0272463i \(0.00867385\pi\)
0.523410 + 0.852081i \(0.324659\pi\)
\(332\) 1.75547 3.04056i 0.0963438 0.166872i
\(333\) −3.79603 −0.208021
\(334\) −4.34081 + 7.51851i −0.237519 + 0.411394i
\(335\) 0 0
\(336\) −4.02239 + 2.32233i −0.219440 + 0.126693i
\(337\) 35.6432i 1.94161i 0.239867 + 0.970806i \(0.422896\pi\)
−0.239867 + 0.970806i \(0.577104\pi\)
\(338\) 12.4340 + 3.79423i 0.676319 + 0.206379i
\(339\) −13.0662 −0.709656
\(340\) 0 0
\(341\) 14.1699 + 24.5430i 0.767344 + 1.32908i
\(342\) −6.96699 4.02239i −0.376732 0.217506i
\(343\) −35.1734 −1.89918
\(344\) 0.620469 + 0.358228i 0.0334535 + 0.0193144i
\(345\) 0 0
\(346\) 1.78043i 0.0957166i
\(347\) −5.97299 3.44851i −0.320647 0.185126i 0.331034 0.943619i \(-0.392603\pi\)
−0.651681 + 0.758493i \(0.725936\pi\)
\(348\) 3.73494 2.15637i 0.200214 0.115593i
\(349\) −16.7321 + 9.66025i −0.895646 + 0.517102i −0.875785 0.482701i \(-0.839656\pi\)
−0.0198610 + 0.999803i \(0.506322\pi\)
\(350\) 0 0
\(351\) −3.35432 + 1.32233i −0.179040 + 0.0705807i
\(352\) 4.40013i 0.234528i
\(353\) −13.7086 23.7441i −0.729637 1.26377i −0.957037 0.289967i \(-0.906356\pi\)
0.227400 0.973802i \(-0.426978\pi\)
\(354\) −1.09028 1.88842i −0.0579477 0.100368i
\(355\) 0 0
\(356\) 8.17274i 0.433154i
\(357\) −9.28932 + 16.0896i −0.491643 + 0.851550i
\(358\) 8.70786 15.0825i 0.460225 0.797133i
\(359\) 14.3611i 0.757951i −0.925407 0.378975i \(-0.876277\pi\)
0.925407 0.378975i \(-0.123723\pi\)
\(360\) 0 0
\(361\) 22.8593 + 39.5935i 1.20312 + 2.08387i
\(362\) 5.18056 + 8.97299i 0.272284 + 0.471610i
\(363\) 8.36112i 0.438845i
\(364\) 10.4215 13.1088i 0.546235 0.687086i
\(365\) 0 0
\(366\) 6.46410 3.73205i 0.337884 0.195077i
\(367\) 11.9298 6.88764i 0.622728 0.359532i −0.155202 0.987883i \(-0.549603\pi\)
0.777930 + 0.628351i \(0.216270\pi\)
\(368\) −0.845746 0.488292i −0.0440876 0.0254540i
\(369\) 7.28932i 0.379467i
\(370\) 0 0
\(371\) 54.3381 + 31.3721i 2.82109 + 1.62876i
\(372\) −6.44069 −0.333934
\(373\) 28.9795 + 16.7313i 1.50050 + 0.866316i 1.00000 0.000581860i \(0.000185212\pi\)
0.500504 + 0.865734i \(0.333148\pi\)
\(374\) 8.80025 + 15.2425i 0.455050 + 0.788170i
\(375\) 0 0
\(376\) 9.75342 0.502994
\(377\) −9.67674 + 12.1720i −0.498377 + 0.626888i
\(378\) 4.64466i 0.238896i
\(379\) 28.9052 16.6884i 1.48476 0.857227i 0.484910 0.874564i \(-0.338852\pi\)
0.999850 + 0.0173371i \(0.00551884\pi\)
\(380\) 0 0
\(381\) 6.10978 10.5825i 0.313014 0.542156i
\(382\) −0.897014 −0.0458952
\(383\) −3.66519 + 6.34829i −0.187282 + 0.324383i −0.944343 0.328962i \(-0.893301\pi\)
0.757061 + 0.653344i \(0.226635\pi\)
\(384\) −0.866025 0.500000i −0.0441942 0.0255155i
\(385\) 0 0
\(386\) 10.1322 17.5494i 0.515714 0.893243i
\(387\) 0.620469 0.358228i 0.0315402 0.0182098i
\(388\) 6.91261 + 11.9730i 0.350935 + 0.607836i
\(389\) 32.6198 1.65389 0.826946 0.562282i \(-0.190076\pi\)
0.826946 + 0.562282i \(0.190076\pi\)
\(390\) 0 0
\(391\) −3.90633 −0.197552
\(392\) −7.28643 12.6205i −0.368020 0.637430i
\(393\) −0.328013 + 0.189378i −0.0165461 + 0.00955288i
\(394\) −4.59028 + 7.95060i −0.231255 + 0.400545i
\(395\) 0 0
\(396\) 3.81062 + 2.20006i 0.191491 + 0.110557i
\(397\) 7.23416 12.5299i 0.363072 0.628860i −0.625392 0.780310i \(-0.715061\pi\)
0.988465 + 0.151451i \(0.0483945\pi\)
\(398\) −16.2175 −0.812911
\(399\) 18.6826 32.3593i 0.935302 1.61999i
\(400\) 0 0
\(401\) −6.31096 + 3.64364i −0.315154 + 0.181955i −0.649231 0.760592i \(-0.724909\pi\)
0.334076 + 0.942546i \(0.391576\pi\)
\(402\) 1.82522i 0.0910336i
\(403\) 21.6041 8.51671i 1.07618 0.424248i
\(404\) 6.80025 0.338325
\(405\) 0 0
\(406\) 10.0156 + 17.3475i 0.497066 + 0.860943i
\(407\) −14.4652 8.35150i −0.717014 0.413968i
\(408\) −4.00000 −0.198030
\(409\) 21.2840 + 12.2883i 1.05242 + 0.607617i 0.923327 0.384015i \(-0.125459\pi\)
0.129097 + 0.991632i \(0.458792\pi\)
\(410\) 0 0
\(411\) 1.25235i 0.0617741i
\(412\) 4.58246 + 2.64568i 0.225761 + 0.130343i
\(413\) 8.77106 5.06397i 0.431596 0.249182i
\(414\) −0.845746 + 0.488292i −0.0415662 + 0.0239982i
\(415\) 0 0
\(416\) 3.56609 + 0.531987i 0.174842 + 0.0260828i
\(417\) 3.35534i 0.164312i
\(418\) −17.6990 30.6556i −0.865688 1.49942i
\(419\) 7.77684 + 13.4699i 0.379923 + 0.658047i 0.991051 0.133486i \(-0.0426170\pi\)
−0.611127 + 0.791532i \(0.709284\pi\)
\(420\) 0 0
\(421\) 22.3143i 1.08753i −0.839237 0.543766i \(-0.816998\pi\)
0.839237 0.543766i \(-0.183002\pi\)
\(422\) 0.809848 1.40270i 0.0394228 0.0682822i
\(423\) 4.87671 8.44671i 0.237114 0.410693i
\(424\) 13.5089i 0.656050i
\(425\) 0 0
\(426\) 3.97658 + 6.88764i 0.192666 + 0.333707i
\(427\) 17.3341 + 30.0236i 0.838856 + 1.45294i
\(428\) 16.9282i 0.818256i
\(429\) −15.6912 2.34081i −0.757580 0.113015i
\(430\) 0 0
\(431\) 21.0135 12.1322i 1.01219 0.584386i 0.100356 0.994952i \(-0.468002\pi\)
0.911831 + 0.410565i \(0.134669\pi\)
\(432\) −0.866025 + 0.500000i −0.0416667 + 0.0240563i
\(433\) −20.0042 11.5494i −0.961342 0.555031i −0.0647561 0.997901i \(-0.520627\pi\)
−0.896586 + 0.442870i \(0.853960\pi\)
\(434\) 29.9148i 1.43596i
\(435\) 0 0
\(436\) 11.0853 + 6.40013i 0.530892 + 0.306510i
\(437\) 7.85641 0.375823
\(438\) −3.77684 2.18056i −0.180464 0.104191i
\(439\) 19.9980 + 34.6375i 0.954450 + 1.65316i 0.735621 + 0.677393i \(0.236890\pi\)
0.218829 + 0.975763i \(0.429776\pi\)
\(440\) 0 0
\(441\) −14.5729 −0.693946
\(442\) 13.4173 5.28932i 0.638194 0.251587i
\(443\) 15.6036i 0.741350i −0.928763 0.370675i \(-0.879126\pi\)
0.928763 0.370675i \(-0.120874\pi\)
\(444\) 3.28745 1.89801i 0.156016 0.0900757i
\(445\) 0 0
\(446\) 1.11836 1.93705i 0.0529557 0.0917219i
\(447\) 4.61970 0.218504
\(448\) 2.32233 4.02239i 0.109720 0.190040i
\(449\) −23.3863 13.5021i −1.10367 0.637203i −0.166486 0.986044i \(-0.553242\pi\)
−0.937182 + 0.348841i \(0.886575\pi\)
\(450\) 0 0
\(451\) −16.0370 + 27.7768i −0.755151 + 1.30796i
\(452\) 11.3156 6.53308i 0.532242 0.307290i
\(453\) 5.62124 + 9.73628i 0.264109 + 0.457450i
\(454\) 15.3205 0.719027
\(455\) 0 0
\(456\) 8.04479 0.376732
\(457\) −8.89342 15.4039i −0.416017 0.720562i 0.579518 0.814959i \(-0.303241\pi\)
−0.995535 + 0.0943975i \(0.969908\pi\)
\(458\) 8.77106 5.06397i 0.409845 0.236624i
\(459\) −2.00000 + 3.46410i −0.0933520 + 0.161690i
\(460\) 0 0
\(461\) 21.6205 + 12.4826i 1.00697 + 0.581372i 0.910302 0.413945i \(-0.135849\pi\)
0.0966638 + 0.995317i \(0.469183\pi\)
\(462\) −10.2185 + 17.6990i −0.475410 + 0.823434i
\(463\) −15.6389 −0.726801 −0.363400 0.931633i \(-0.618384\pi\)
−0.363400 + 0.931633i \(0.618384\pi\)
\(464\) −2.15637 + 3.73494i −0.100107 + 0.173390i
\(465\) 0 0
\(466\) 17.9716 10.3759i 0.832521 0.480656i
\(467\) 2.43914i 0.112870i 0.998406 + 0.0564349i \(0.0179733\pi\)
−0.998406 + 0.0564349i \(0.982027\pi\)
\(468\) 2.24376 2.82233i 0.103718 0.130462i
\(469\) 8.47751 0.391455
\(470\) 0 0
\(471\) 0.751556 + 1.30173i 0.0346299 + 0.0599807i
\(472\) 1.88842 + 1.09028i 0.0869215 + 0.0501842i
\(473\) 3.15250 0.144952
\(474\) −12.9332 7.46699i −0.594042 0.342970i
\(475\) 0 0
\(476\) 18.5786i 0.851550i
\(477\) 11.6990 + 6.75444i 0.535662 + 0.309265i
\(478\) 21.0911 12.1770i 0.964685 0.556961i
\(479\) −12.2857 + 7.09317i −0.561349 + 0.324095i −0.753687 0.657234i \(-0.771726\pi\)
0.192338 + 0.981329i \(0.438393\pi\)
\(480\) 0 0
\(481\) −8.51737 + 10.7136i −0.388358 + 0.488500i
\(482\) 19.8685i 0.904983i
\(483\) −2.26795 3.92820i −0.103195 0.178739i
\(484\) 4.18056 + 7.24094i 0.190025 + 0.329134i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 2.88164 4.99115i 0.130580 0.226171i −0.793320 0.608804i \(-0.791649\pi\)
0.923900 + 0.382633i \(0.124983\pi\)
\(488\) −3.73205 + 6.46410i −0.168942 + 0.292616i
\(489\) 0.176330i 0.00797392i
\(490\) 0 0
\(491\) −0.537671 0.931273i −0.0242647 0.0420278i 0.853638 0.520867i \(-0.174391\pi\)
−0.877903 + 0.478839i \(0.841058\pi\)
\(492\) −3.64466 6.31274i −0.164314 0.284600i
\(493\) 17.2509i 0.776943i
\(494\) −26.9848 + 10.6379i −1.21410 + 0.478620i
\(495\) 0 0
\(496\) 5.57780 3.22034i 0.250450 0.144598i
\(497\) −31.9908 + 18.4699i −1.43498 + 0.828487i
\(498\) 3.04056 + 1.75547i 0.136251 + 0.0786644i
\(499\) 14.7534i 0.660454i −0.943902 0.330227i \(-0.892875\pi\)
0.943902 0.330227i \(-0.107125\pi\)
\(500\) 0 0
\(501\) −7.51851 4.34081i −0.335902 0.193933i
\(502\) −13.5713 −0.605717
\(503\) 23.0898 + 13.3309i 1.02952 + 0.594395i 0.916848 0.399236i \(-0.130725\pi\)
0.112675 + 0.993632i \(0.464058\pi\)
\(504\) −2.32233 4.02239i −0.103445 0.179172i
\(505\) 0 0
\(506\) −4.29709 −0.191029
\(507\) −3.79423 + 12.4340i −0.168508 + 0.552212i
\(508\) 12.2196i 0.542156i
\(509\) −12.2807 + 7.09028i −0.544333 + 0.314271i −0.746833 0.665011i \(-0.768427\pi\)
0.202500 + 0.979282i \(0.435093\pi\)
\(510\) 0 0
\(511\) 10.1279 17.5421i 0.448034 0.776018i
\(512\) 1.00000 0.0441942
\(513\) 4.02239 6.96699i 0.177593 0.307600i
\(514\) −0.573569 0.331150i −0.0252990 0.0146064i
\(515\) 0 0
\(516\) −0.358228 + 0.620469i −0.0157701 + 0.0273146i
\(517\) 37.1666 21.4581i 1.63459 0.943728i
\(518\) 8.81562 + 15.2691i 0.387336 + 0.670886i
\(519\) 1.78043 0.0781523
\(520\) 0 0
\(521\) 23.7476 1.04040 0.520202 0.854043i \(-0.325857\pi\)
0.520202 + 0.854043i \(0.325857\pi\)
\(522\) 2.15637 + 3.73494i 0.0943817 + 0.163474i
\(523\) 11.9950 6.92532i 0.524505 0.302823i −0.214271 0.976774i \(-0.568738\pi\)
0.738776 + 0.673951i \(0.235404\pi\)
\(524\) 0.189378 0.328013i 0.00827303 0.0143293i
\(525\) 0 0
\(526\) −26.6301 15.3749i −1.16113 0.670378i
\(527\) 12.8814 22.3112i 0.561121 0.971891i
\(528\) −4.40013 −0.191491
\(529\) −11.0231 + 19.0926i −0.479267 + 0.830115i
\(530\) 0 0
\(531\) 1.88842 1.09028i 0.0819504 0.0473141i
\(532\) 37.3653i 1.61999i
\(533\) 20.5729 + 16.3555i 0.891110 + 0.708434i
\(534\) 8.17274 0.353669
\(535\) 0 0
\(536\) 0.912609 + 1.58068i 0.0394187 + 0.0682752i
\(537\) 15.0825 + 8.70786i 0.650856 + 0.375772i
\(538\) 3.74410 0.161420
\(539\) −55.5317 32.0612i −2.39192 1.38097i
\(540\) 0 0
\(541\) 14.8898i 0.640164i 0.947390 + 0.320082i \(0.103710\pi\)
−0.947390 + 0.320082i \(0.896290\pi\)
\(542\) −24.0419 13.8806i −1.03269 0.596223i
\(543\) −8.97299 + 5.18056i −0.385068 + 0.222319i
\(544\) 3.46410 2.00000i 0.148522 0.0857493i
\(545\) 0 0
\(546\) 13.1088 + 10.4215i 0.561003 + 0.445999i
\(547\) 22.2019i 0.949284i 0.880179 + 0.474642i \(0.157422\pi\)
−0.880179 + 0.474642i \(0.842578\pi\)
\(548\) −0.626177 1.08457i −0.0267490 0.0463306i
\(549\) 3.73205 + 6.46410i 0.159280 + 0.275881i
\(550\) 0 0
\(551\) 34.6950i 1.47806i
\(552\) 0.488292 0.845746i 0.0207831 0.0359973i
\(553\) 34.6816 60.0703i 1.47481 2.55445i
\(554\) 11.9922i 0.509499i
\(555\) 0 0
\(556\) 1.67767 + 2.90581i 0.0711491 + 0.123234i
\(557\) −0.949847 1.64518i −0.0402463 0.0697087i 0.845201 0.534449i \(-0.179481\pi\)
−0.885447 + 0.464741i \(0.846148\pi\)
\(558\) 6.44069i 0.272656i
\(559\) 0.381146 2.55495i 0.0161207 0.108063i
\(560\) 0 0
\(561\) −15.2425 + 8.80025i −0.643538 + 0.371547i
\(562\) 3.15137 1.81944i 0.132932 0.0767485i
\(563\) −1.48956 0.860000i −0.0627777 0.0362447i 0.468283 0.883579i \(-0.344873\pi\)
−0.531060 + 0.847334i \(0.678206\pi\)
\(564\) 9.75342i 0.410693i
\(565\) 0 0
\(566\) 4.19538 + 2.42220i 0.176345 + 0.101813i
\(567\) −4.64466 −0.195057
\(568\) −6.88764 3.97658i −0.288999 0.166854i
\(569\) 0.300960 + 0.521278i 0.0126169 + 0.0218531i 0.872265 0.489034i \(-0.162650\pi\)
−0.859648 + 0.510887i \(0.829317\pi\)
\(570\) 0 0
\(571\) 11.9808 0.501381 0.250691 0.968067i \(-0.419342\pi\)
0.250691 + 0.968067i \(0.419342\pi\)
\(572\) 14.7594 5.81842i 0.617122 0.243280i
\(573\) 0.897014i 0.0374733i
\(574\) 29.3205 16.9282i 1.22381 0.706570i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) −43.0293 −1.79133 −0.895667 0.444725i \(-0.853301\pi\)
−0.895667 + 0.444725i \(0.853301\pi\)
\(578\) −0.500000 + 0.866025i −0.0207973 + 0.0360219i
\(579\) 17.5494 + 10.1322i 0.729330 + 0.421079i
\(580\) 0 0
\(581\) −8.15355 + 14.1224i −0.338266 + 0.585894i
\(582\) −11.9730 + 6.91261i −0.496296 + 0.286537i
\(583\) 29.7204 + 51.4773i 1.23089 + 2.13197i
\(584\) 4.36112 0.180464
\(585\) 0 0
\(586\) 3.70081 0.152879
\(587\) 8.95740 + 15.5147i 0.369711 + 0.640359i 0.989520 0.144394i \(-0.0461233\pi\)
−0.619809 + 0.784753i \(0.712790\pi\)
\(588\) 12.6205 7.28643i 0.520459 0.300487i
\(589\) −25.9070 + 44.8722i −1.06748 + 1.84893i
\(590\) 0 0
\(591\) −7.95060 4.59028i −0.327044 0.188819i
\(592\) −1.89801 + 3.28745i −0.0780078 + 0.135114i
\(593\) −0.669624 −0.0274981 −0.0137491 0.999905i \(-0.504377\pi\)
−0.0137491 + 0.999905i \(0.504377\pi\)
\(594\) −2.20006 + 3.81062i −0.0902697 + 0.156352i
\(595\) 0 0
\(596\) −4.00077 + 2.30985i −0.163878 + 0.0946151i
\(597\) 16.2175i 0.663739i
\(598\) −0.519530 + 3.48258i −0.0212452 + 0.142413i
\(599\) −1.29241 −0.0528066 −0.0264033 0.999651i \(-0.508405\pi\)
−0.0264033 + 0.999651i \(0.508405\pi\)
\(600\) 0 0
\(601\) 5.73671 + 9.93627i 0.234005 + 0.405309i 0.958983 0.283463i \(-0.0914834\pi\)
−0.724978 + 0.688772i \(0.758150\pi\)
\(602\) −2.88187 1.66385i −0.117456 0.0678134i
\(603\) 1.82522 0.0743286
\(604\) −9.73628 5.62124i −0.396164 0.228725i
\(605\) 0 0
\(606\) 6.80025i 0.276241i
\(607\) −20.9010 12.0672i −0.848344 0.489792i 0.0117477 0.999931i \(-0.496261\pi\)
−0.860092 + 0.510139i \(0.829594\pi\)
\(608\) −6.96699 + 4.02239i −0.282549 + 0.163130i
\(609\) −17.3475 + 10.0156i −0.702957 + 0.405852i
\(610\) 0 0
\(611\) −12.8972 32.7161i −0.521766 1.32355i
\(612\) 4.00000i 0.161690i
\(613\) 14.4751 + 25.0716i 0.584644 + 1.01263i 0.994920 + 0.100671i \(0.0320991\pi\)
−0.410276 + 0.911961i \(0.634568\pi\)
\(614\) 3.55727 + 6.16137i 0.143560 + 0.248653i
\(615\) 0 0
\(616\) 20.4371i 0.823434i
\(617\) −0.420655 + 0.728597i −0.0169349 + 0.0293322i −0.874369 0.485262i \(-0.838724\pi\)
0.857434 + 0.514594i \(0.172057\pi\)
\(618\) −2.64568 + 4.58246i −0.106425 + 0.184333i
\(619\) 6.25076i 0.251239i 0.992078 + 0.125620i \(0.0400919\pi\)
−0.992078 + 0.125620i \(0.959908\pi\)
\(620\) 0 0
\(621\) −0.488292 0.845746i −0.0195945 0.0339386i
\(622\) 9.95740 + 17.2467i 0.399255 + 0.691530i
\(623\) 37.9596i 1.52082i
\(624\) −0.531987 + 3.56609i −0.0212965 + 0.142758i
\(625\) 0 0
\(626\) 5.31696 3.06975i 0.212509 0.122692i
\(627\) 30.6556 17.6990i 1.22427 0.706832i
\(628\) −1.30173 0.751556i −0.0519448 0.0299904i
\(629\) 15.1841i 0.605430i
\(630\) 0 0
\(631\) 2.61970 + 1.51248i 0.104288 + 0.0602110i 0.551237 0.834349i \(-0.314156\pi\)
−0.446949 + 0.894560i \(0.647489\pi\)
\(632\) 14.9340 0.594042
\(633\) 1.40270 + 0.809848i 0.0557522 + 0.0321886i
\(634\) −3.92643 6.80078i −0.155938 0.270093i
\(635\) 0 0
\(636\) −13.5089 −0.535662
\(637\) −32.6980 + 41.1294i −1.29554 + 1.62961i
\(638\) 18.9766i 0.751290i
\(639\) −6.88764 + 3.97658i −0.272471 + 0.157311i
\(640\) 0 0
\(641\) 0.386305 0.669099i 0.0152581 0.0264278i −0.858296 0.513156i \(-0.828476\pi\)
0.873554 + 0.486728i \(0.161810\pi\)
\(642\) 16.9282 0.668103
\(643\) −9.68726 + 16.7788i −0.382028 + 0.661693i −0.991352 0.131229i \(-0.958108\pi\)
0.609324 + 0.792922i \(0.291441\pi\)
\(644\) 3.92820 + 2.26795i 0.154793 + 0.0893697i
\(645\) 0 0
\(646\) −16.0896 + 27.8680i −0.633036 + 1.09645i
\(647\) −23.5477 + 13.5953i −0.925755 + 0.534485i −0.885466 0.464703i \(-0.846161\pi\)
−0.0402882 + 0.999188i \(0.512828\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 9.59473 0.376626
\(650\) 0 0
\(651\) 29.9148 1.17245
\(652\) 0.0881650 + 0.152706i 0.00345281 + 0.00598044i
\(653\) 13.6797 7.89799i 0.535329 0.309072i −0.207855 0.978160i \(-0.566648\pi\)
0.743184 + 0.669088i \(0.233315\pi\)
\(654\) −6.40013 + 11.0853i −0.250265 + 0.433471i
\(655\) 0 0
\(656\) 6.31274 + 3.64466i 0.246471 + 0.142300i
\(657\) 2.18056 3.77684i 0.0850717 0.147348i
\(658\) −45.3013 −1.76603
\(659\) 15.2381 26.3932i 0.593593 1.02813i −0.400151 0.916449i \(-0.631042\pi\)
0.993744 0.111684i \(-0.0356243\pi\)
\(660\) 0 0
\(661\) −24.1514 + 13.9438i −0.939379 + 0.542351i −0.889766 0.456418i \(-0.849132\pi\)
−0.0496136 + 0.998768i \(0.515799\pi\)
\(662\) 31.9959i 1.24356i
\(663\) 5.28932 + 13.4173i 0.205420 + 0.521084i
\(664\) −3.51093 −0.136251
\(665\) 0 0
\(666\) 1.89801 + 3.28745i 0.0735465 + 0.127386i
\(667\) −3.64748 2.10587i −0.141231 0.0815397i
\(668\) 8.68162 0.335902
\(669\) 1.93705 + 1.11836i 0.0748906 + 0.0432381i
\(670\) 0 0
\(671\) 32.8430i 1.26789i
\(672\) 4.02239 + 2.32233i 0.155167 + 0.0895858i
\(673\) 0.847086 0.489066i 0.0326528 0.0188521i −0.483585 0.875298i \(-0.660666\pi\)
0.516238 + 0.856445i \(0.327332\pi\)
\(674\) 30.8680 17.8216i 1.18899 0.686463i
\(675\) 0 0
\(676\) −2.93109 12.6653i −0.112734 0.487125i
\(677\) 19.1926i 0.737630i 0.929503 + 0.368815i \(0.120236\pi\)
−0.929503 + 0.368815i \(0.879764\pi\)
\(678\) 6.53308 + 11.3156i 0.250901 + 0.434574i
\(679\) −32.1067 55.6105i −1.23214 2.13413i
\(680\) 0 0
\(681\) 15.3205i 0.587083i
\(682\) 14.1699 24.5430i 0.542594 0.939801i
\(683\) 0.755467 1.30851i 0.0289071 0.0500687i −0.851210 0.524825i \(-0.824131\pi\)
0.880117 + 0.474757i \(0.157464\pi\)
\(684\) 8.04479i 0.307600i
\(685\) 0 0
\(686\) 17.5867 + 30.4610i 0.671463 + 1.16301i
\(687\) 5.06397 + 8.77106i 0.193203 + 0.334637i
\(688\) 0.716456i 0.0273146i
\(689\) 45.3131 17.8632i 1.72629 0.680534i
\(690\) 0 0
\(691\) 28.6798 16.5583i 1.09103 0.629907i 0.157180 0.987570i \(-0.449760\pi\)
0.933851 + 0.357663i \(0.116426\pi\)
\(692\) −1.54190 + 0.890216i −0.0586142 + 0.0338409i
\(693\) −17.6990 10.2185i −0.672331 0.388170i
\(694\) 6.89701i 0.261807i
\(695\) 0 0
\(696\) −3.73494 2.15637i −0.141572 0.0817369i
\(697\) 29.1573 1.10441
\(698\) 16.7321 + 9.66025i 0.633317 + 0.365646i
\(699\) 10.3759 + 17.9716i 0.392454 + 0.679750i
\(700\) 0 0
\(701\) 27.8695 1.05262 0.526308 0.850294i \(-0.323576\pi\)
0.526308 + 0.850294i \(0.323576\pi\)
\(702\) 2.82233 + 2.24376i 0.106522 + 0.0846852i
\(703\) 30.5382i 1.15177i
\(704\) 3.81062 2.20006i 0.143618 0.0829180i
\(705\) 0 0
\(706\) −13.7086 + 23.7441i −0.515931 + 0.893619i
\(707\) −31.5849 −1.18787
\(708\) −1.09028 + 1.88842i −0.0409752 + 0.0709711i
\(709\) 9.57491 + 5.52808i 0.359593 + 0.207611i 0.668902 0.743350i \(-0.266764\pi\)
−0.309309 + 0.950962i \(0.600098\pi\)
\(710\) 0 0
\(711\) 7.46699 12.9332i 0.280034 0.485033i
\(712\) −7.07780 + 4.08637i −0.265252 + 0.153143i
\(713\) 3.14493 + 5.44719i 0.117779 + 0.203999i
\(714\) 18.5786 0.695288
\(715\) 0 0
\(716\) −17.4157 −0.650856
\(717\) 12.1770 + 21.0911i 0.454757 + 0.787662i
\(718\) −12.4371 + 7.18056i −0.464148 + 0.267976i
\(719\) −5.85641 + 10.1436i −0.218407 + 0.378292i −0.954321 0.298783i \(-0.903419\pi\)
0.735914 + 0.677075i \(0.236753\pi\)
\(720\) 0 0
\(721\) −21.2840 12.2883i −0.792656 0.457640i
\(722\) 22.8593 39.5935i 0.850735 1.47352i
\(723\) −19.8685 −0.738916
\(724\) 5.18056 8.97299i 0.192534 0.333479i
\(725\) 0 0
\(726\) −7.24094 + 4.18056i −0.268736 + 0.155155i
\(727\) 19.4152i 0.720071i 0.932939 + 0.360035i \(0.117235\pi\)
−0.932939 + 0.360035i \(0.882765\pi\)
\(728\) −16.5633 2.47090i −0.613876 0.0915777i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −1.43291 2.48188i −0.0529982 0.0917956i
\(732\) −6.46410 3.73205i −0.238920 0.137941i
\(733\) −11.9340 −0.440792 −0.220396 0.975411i \(-0.570735\pi\)
−0.220396 + 0.975411i \(0.570735\pi\)
\(734\) −11.9298 6.88764i −0.440335 0.254228i
\(735\) 0 0
\(736\) 0.976584i 0.0359973i
\(737\) 6.95521 + 4.01559i 0.256199 + 0.147916i
\(738\) 6.31274 3.64466i 0.232375 0.134162i
\(739\) −17.2017 + 9.93141i −0.632775 + 0.365333i −0.781826 0.623497i \(-0.785711\pi\)
0.149051 + 0.988830i \(0.452378\pi\)
\(740\) 0 0
\(741\) −10.6379 26.9848i −0.390792 0.991310i
\(742\) 62.7442i 2.30341i
\(743\) 8.24383 + 14.2787i 0.302437 + 0.523836i 0.976687 0.214667i \(-0.0688666\pi\)
−0.674251 + 0.738503i \(0.735533\pi\)
\(744\) 3.22034 + 5.57780i 0.118063 + 0.204492i
\(745\) 0 0
\(746\) 33.4627i 1.22516i
\(747\) −1.75547 + 3.04056i −0.0642292 + 0.111248i
\(748\) 8.80025 15.2425i 0.321769 0.557320i
\(749\) 78.6257i 2.87292i
\(750\) 0 0
\(751\) −23.3312 40.4109i −0.851368 1.47461i −0.879974 0.475022i \(-0.842440\pi\)
0.0286056 0.999591i \(-0.490893\pi\)
\(752\) −4.87671 8.44671i −0.177835 0.308020i
\(753\) 13.5713i 0.494566i
\(754\) 15.3796 + 2.29432i 0.560092 + 0.0835542i
\(755\) 0 0
\(756\) 4.02239 2.32233i 0.146293 0.0844623i
\(757\) −2.28282 + 1.31799i −0.0829705 + 0.0479030i −0.540911 0.841080i \(-0.681921\pi\)
0.457941 + 0.888983i \(0.348587\pi\)
\(758\) −28.9052 16.6884i −1.04988 0.606151i
\(759\) 4.29709i 0.155975i
\(760\) 0 0
\(761\) 0.0693410 + 0.0400340i 0.00251361 + 0.00145123i 0.501256 0.865299i \(-0.332871\pi\)
−0.498743 + 0.866750i \(0.666205\pi\)
\(762\) −12.2196 −0.442668
\(763\) −51.4877 29.7264i −1.86398 1.07617i
\(764\) 0.448507 + 0.776837i 0.0162264 + 0.0281050i
\(765\) 0 0
\(766\) 7.33038 0.264857
\(767\) 1.16003 7.77606i 0.0418862 0.280777i
\(768\) 1.00000i 0.0360844i
\(769\) −4.92177 + 2.84159i −0.177484 + 0.102470i −0.586110 0.810232i \(-0.699341\pi\)
0.408626 + 0.912702i \(0.366008\pi\)
\(770\) 0 0
\(771\) 0.331150 0.573569i 0.0119261 0.0206566i
\(772\) −20.2644 −0.729330
\(773\) 3.79425 6.57184i 0.136470 0.236373i −0.789688 0.613508i \(-0.789758\pi\)
0.926158 + 0.377136i \(0.123091\pi\)
\(774\) −0.620469 0.358228i −0.0223023 0.0128762i
\(775\) 0 0
\(776\) 6.91261 11.9730i 0.248148 0.429805i
\(777\) −15.2691 + 8.81562i −0.547776 + 0.316259i
\(778\) −16.3099 28.2496i −0.584739 1.01280i
\(779\) −58.6410 −2.10103
\(780\) 0 0
\(781\) −34.9949 −1.25222
\(782\) 1.95317 + 3.38298i 0.0698451 + 0.120975i
\(783\) −3.73494 + 2.15637i −0.133476 + 0.0770623i
\(784\) −7.28643 + 12.6205i −0.260230 + 0.450731i
\(785\)