Properties

Label 1950.2.bc.g.751.1
Level $1950$
Weight $2$
Character 1950.751
Analytic conductor $15.571$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.bc (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 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 751.1
Root \(1.33404 - 1.33404i\) of defining polynomial
Character \(\chi\) \(=\) 1950.751
Dual form 1950.2.bc.g.901.1

$q$-expansion

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

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) −0.866025 0.500000i −0.353553 0.204124i
\(7\) −4.02239 2.32233i −1.52032 0.877758i −0.999713 0.0239629i \(-0.992372\pi\)
−0.520609 0.853795i \(-0.674295\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −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 \(0.102470\pi\)
\(12\) 1.00000 0.288675
\(13\) 3.35432 1.32233i 0.930320 0.366748i
\(14\) 4.64466 1.24134
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i \(-0.994540\pi\)
0.514782 + 0.857321i \(0.327873\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −6.96699 4.02239i −1.59834 0.922800i −0.991808 0.127739i \(-0.959228\pi\)
−0.606529 0.795061i \(-0.707439\pi\)
\(20\) 0 0
\(21\) 4.64466i 1.01355i
\(22\) −2.20006 + 3.81062i −0.469055 + 0.812427i
\(23\) 0.488292 + 0.845746i 0.101816 + 0.176350i 0.912433 0.409226i \(-0.134201\pi\)
−0.810617 + 0.585577i \(0.800868\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) 0 0
\(26\) −2.24376 + 2.82233i −0.440037 + 0.553504i
\(27\) −1.00000 −0.192450
\(28\) −4.02239 + 2.32233i −0.760161 + 0.438879i
\(29\) 2.15637 + 3.73494i 0.400427 + 0.693561i 0.993777 0.111384i \(-0.0355283\pi\)
−0.593350 + 0.804945i \(0.702195\pi\)
\(30\) 0 0
\(31\) 6.44069i 1.15678i 0.815760 + 0.578391i \(0.196319\pi\)
−0.815760 + 0.578391i \(0.803681\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 3.81062 + 2.20006i 0.663344 + 0.382982i
\(34\) 4.00000i 0.685994i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) −3.28745 + 1.89801i −0.540454 + 0.312031i −0.745263 0.666771i \(-0.767676\pi\)
0.204809 + 0.978802i \(0.434343\pi\)
\(38\) 8.04479 1.30504
\(39\) 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 \(0.526080\pi\)
\(42\) 2.32233 + 4.02239i 0.358343 + 0.620669i
\(43\) −0.358228 + 0.620469i −0.0546293 + 0.0946207i −0.892047 0.451943i \(-0.850731\pi\)
0.837418 + 0.546564i \(0.184064\pi\)
\(44\) 4.40013i 0.663344i
\(45\) 0 0
\(46\) −0.845746 0.488292i −0.124698 0.0719947i
\(47\) 9.75342i 1.42268i −0.702847 0.711341i \(-0.748088\pi\)
0.702847 0.711341i \(-0.251912\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) 7.28643 + 12.6205i 1.04092 + 1.80292i
\(50\) 0 0
\(51\) −4.00000 −0.560112
\(52\) 0.531987 3.56609i 0.0737734 0.494528i
\(53\) −13.5089 −1.85559 −0.927794 0.373092i \(-0.878297\pi\)
−0.927794 + 0.373092i \(0.878297\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 0 0
\(56\) 2.32233 4.02239i 0.310334 0.537515i
\(57\) 8.04479i 1.06556i
\(58\) −3.73494 2.15637i −0.490421 0.283145i
\(59\) −1.88842 1.09028i −0.245851 0.141942i 0.372012 0.928228i \(-0.378668\pi\)
−0.617863 + 0.786286i \(0.712001\pi\)
\(60\) 0 0
\(61\) −3.73205 + 6.46410i −0.477840 + 0.827643i −0.999677 0.0254017i \(-0.991914\pi\)
0.521837 + 0.853045i \(0.325247\pi\)
\(62\) −3.22034 5.57780i −0.408984 0.708381i
\(63\) 4.02239 2.32233i 0.506774 0.292586i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −4.40013 −0.541618
\(67\) 1.58068 0.912609i 0.193111 0.111493i −0.400327 0.916372i \(-0.631103\pi\)
0.593438 + 0.804879i \(0.297770\pi\)
\(68\) 2.00000 + 3.46410i 0.242536 + 0.420084i
\(69\) −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 \(0.823110\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 4.36112i 0.510430i 0.966884 + 0.255215i \(0.0821463\pi\)
−0.966884 + 0.255215i \(0.917854\pi\)
\(74\) 1.89801 3.28745i 0.220640 0.382159i
\(75\) 0 0
\(76\) −6.96699 + 4.02239i −0.799168 + 0.461400i
\(77\) −20.4371 −2.32902
\(78\) −3.56609 0.531987i −0.403780 0.0602357i
\(79\) −14.9340 −1.68020 −0.840102 0.542429i \(-0.817505\pi\)
−0.840102 + 0.542429i \(0.817505\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 3.64466 6.31274i 0.402485 0.697125i
\(83\) 3.51093i 0.385375i −0.981260 0.192688i \(-0.938280\pi\)
0.981260 0.192688i \(-0.0617204\pi\)
\(84\) −4.02239 2.32233i −0.438879 0.253387i
\(85\) 0 0
\(86\) 0.716456i 0.0772575i
\(87\) −2.15637 + 3.73494i −0.231187 + 0.400427i
\(88\) 2.20006 + 3.81062i 0.234528 + 0.406214i
\(89\) 7.07780 4.08637i 0.750245 0.433154i −0.0755374 0.997143i \(-0.524067\pi\)
0.825782 + 0.563989i \(0.190734\pi\)
\(90\) 0 0
\(91\) −16.5633 2.47090i −1.73630 0.259021i
\(92\) 0.976584 0.101816
\(93\) −5.57780 + 3.22034i −0.578391 + 0.333934i
\(94\) 4.87671 + 8.44671i 0.502994 + 0.871212i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −11.9730 6.91261i −1.21567 0.701869i −0.251683 0.967810i \(-0.580984\pi\)
−0.963989 + 0.265941i \(0.914318\pi\)
\(98\) −12.6205 7.28643i −1.27486 0.736041i
\(99\) 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 \(0.943194\pi\)
\(102\) 3.46410 2.00000i 0.342997 0.198030i
\(103\) 5.29137 0.521374 0.260687 0.965423i \(-0.416051\pi\)
0.260687 + 0.965423i \(0.416051\pi\)
\(104\) 1.32233 + 3.35432i 0.129665 + 0.328918i
\(105\) 0 0
\(106\) 11.6990 6.75444i 1.13631 0.656050i
\(107\) 8.46410 + 14.6603i 0.818256 + 1.41726i 0.906966 + 0.421203i \(0.138392\pi\)
−0.0887109 + 0.996057i \(0.528275\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 12.8003i 1.22604i 0.790067 + 0.613021i \(0.210046\pi\)
−0.790067 + 0.613021i \(0.789954\pi\)
\(110\) 0 0
\(111\) −3.28745 1.89801i −0.312031 0.180151i
\(112\) 4.64466i 0.438879i
\(113\) 6.53308 11.3156i 0.614580 1.06448i −0.375878 0.926669i \(-0.622659\pi\)
0.990458 0.137815i \(-0.0440079\pi\)
\(114\) 4.02239 + 6.96699i 0.376732 + 0.652518i
\(115\) 0 0
\(116\) 4.31274 0.400427
\(117\) −0.531987 + 3.56609i −0.0491823 + 0.329685i
\(118\) 2.18056 0.200737
\(119\) 16.0896 9.28932i 1.47493 0.851550i
\(120\) 0 0
\(121\) 4.18056 7.24094i 0.380051 0.658267i
\(122\) 7.46410i 0.675768i
\(123\) −6.31274 3.64466i −0.569200 0.328628i
\(124\) 5.57780 + 3.22034i 0.500901 + 0.289195i
\(125\) 0 0
\(126\) −2.32233 + 4.02239i −0.206890 + 0.358343i
\(127\) −6.10978 10.5825i −0.542156 0.939041i −0.998780 0.0493816i \(-0.984275\pi\)
0.456624 0.889660i \(-0.349058\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −0.716456 −0.0630805
\(130\) 0 0
\(131\) −0.378757 −0.0330921 −0.0165461 0.999863i \(-0.505267\pi\)
−0.0165461 + 0.999863i \(0.505267\pi\)
\(132\) 3.81062 2.20006i 0.331672 0.191491i
\(133\) 18.6826 + 32.3593i 1.61999 + 2.80591i
\(134\) −0.912609 + 1.58068i −0.0788374 + 0.136550i
\(135\) 0 0
\(136\) −3.46410 2.00000i −0.297044 0.171499i
\(137\) 1.08457 + 0.626177i 0.0926612 + 0.0534979i 0.545615 0.838036i \(-0.316296\pi\)
−0.452953 + 0.891534i \(0.649630\pi\)
\(138\) 0.976584i 0.0831323i
\(139\) −1.67767 + 2.90581i −0.142298 + 0.246468i −0.928362 0.371678i \(-0.878783\pi\)
0.786064 + 0.618146i \(0.212116\pi\)
\(140\) 0 0
\(141\) 8.44671 4.87671i 0.711341 0.410693i
\(142\) 7.95317 0.667415
\(143\) 9.87282 12.4186i 0.825607 1.03850i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −2.18056 3.77684i −0.180464 0.312573i
\(147\) −7.28643 + 12.6205i −0.600975 + 1.04092i
\(148\) 3.79603i 0.312031i
\(149\) −4.00077 2.30985i −0.327756 0.189230i 0.327088 0.944994i \(-0.393933\pi\)
−0.654844 + 0.755764i \(0.727266\pi\)
\(150\) 0 0
\(151\) 11.2425i 0.914901i 0.889235 + 0.457450i \(0.151237\pi\)
−0.889235 + 0.457450i \(0.848763\pi\)
\(152\) 4.02239 6.96699i 0.326259 0.565097i
\(153\) −2.00000 3.46410i −0.161690 0.280056i
\(154\) 17.6990 10.2185i 1.42623 0.823434i
\(155\) 0 0
\(156\) 3.35432 1.32233i 0.268560 0.105871i
\(157\) 1.50311 0.119961 0.0599807 0.998200i \(-0.480896\pi\)
0.0599807 + 0.998200i \(0.480896\pi\)
\(158\) 12.9332 7.46699i 1.02891 0.594042i
\(159\) −6.75444 11.6990i −0.535662 0.927794i
\(160\) 0 0
\(161\) 4.53590i 0.357479i
\(162\) 0.866025 + 0.500000i 0.0680414 + 0.0392837i
\(163\) 0.152706 + 0.0881650i 0.0119609 + 0.00690561i 0.505969 0.862552i \(-0.331135\pi\)
−0.494008 + 0.869458i \(0.664469\pi\)
\(164\) 7.28932i 0.569200i
\(165\) 0 0
\(166\) 1.75547 + 3.04056i 0.136251 + 0.235993i
\(167\) −7.51851 + 4.34081i −0.581800 + 0.335902i −0.761848 0.647756i \(-0.775708\pi\)
0.180049 + 0.983658i \(0.442374\pi\)
\(168\) 4.64466 0.358343
\(169\) 9.50289 8.87103i 0.730991 0.682387i
\(170\) 0 0
\(171\) 6.96699 4.02239i 0.532779 0.307600i
\(172\) 0.358228 + 0.620469i 0.0273146 + 0.0473103i
\(173\) −0.890216 + 1.54190i −0.0676818 + 0.117228i −0.897880 0.440239i \(-0.854894\pi\)
0.830199 + 0.557468i \(0.188227\pi\)
\(174\) 4.31274i 0.326948i
\(175\) 0 0
\(176\) −3.81062 2.20006i −0.287236 0.165836i
\(177\) 2.18056i 0.163901i
\(178\) −4.08637 + 7.07780i −0.306286 + 0.530503i
\(179\) −8.70786 15.0825i −0.650856 1.12732i −0.982916 0.184057i \(-0.941077\pi\)
0.332059 0.943258i \(-0.392257\pi\)
\(180\) 0 0
\(181\) −10.3611 −0.770136 −0.385068 0.922888i \(-0.625822\pi\)
−0.385068 + 0.922888i \(0.625822\pi\)
\(182\) 15.5797 6.14177i 1.15484 0.455258i
\(183\) −7.46410 −0.551762
\(184\) −0.845746 + 0.488292i −0.0623492 + 0.0359973i
\(185\) 0 0
\(186\) 3.22034 5.57780i 0.236127 0.408984i
\(187\) 17.6005i 1.28708i
\(188\) −8.44671 4.87671i −0.616040 0.355671i
\(189\) 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 \(0.156335\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −17.5494 + 10.1322i −1.26324 + 0.729330i −0.973699 0.227837i \(-0.926835\pi\)
−0.289537 + 0.957167i \(0.593501\pi\)
\(194\) 13.8252 0.992593
\(195\) 0 0
\(196\) 14.5729 1.04092
\(197\) −7.95060 + 4.59028i −0.566457 + 0.327044i −0.755733 0.654880i \(-0.772719\pi\)
0.189276 + 0.981924i \(0.439386\pi\)
\(198\) −2.20006 3.81062i −0.156352 0.270809i
\(199\) −8.10876 + 14.0448i −0.574815 + 0.995609i 0.421247 + 0.906946i \(0.361593\pi\)
−0.996062 + 0.0886625i \(0.971741\pi\)
\(200\) 0 0
\(201\) 1.58068 + 0.912609i 0.111493 + 0.0643705i
\(202\) 5.88919 + 3.40013i 0.414362 + 0.239232i
\(203\) 20.0312i 1.40591i
\(204\) −2.00000 + 3.46410i −0.140028 + 0.242536i
\(205\) 0 0
\(206\) −4.58246 + 2.64568i −0.319275 + 0.184333i
\(207\) −0.976584 −0.0678773
\(208\) −2.82233 2.24376i −0.195693 0.155577i
\(209\) −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 \(0.815578\pi\)
\(212\) −6.75444 + 11.6990i −0.463897 + 0.803493i
\(213\) 7.95317i 0.544942i
\(214\) −14.6603 8.46410i −1.00215 0.578594i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 14.9574 25.9070i 1.01537 1.75868i
\(218\) −6.40013 11.0853i −0.433471 0.750794i
\(219\) −3.77684 + 2.18056i −0.255215 + 0.147348i
\(220\) 0 0
\(221\) −2.12795 + 14.2644i −0.143141 + 0.959524i
\(222\) 3.79603 0.254773
\(223\) −1.93705 + 1.11836i −0.129714 + 0.0748906i −0.563453 0.826148i \(-0.690527\pi\)
0.433739 + 0.901039i \(0.357194\pi\)
\(224\) −2.32233 4.02239i −0.155167 0.268757i
\(225\) 0 0
\(226\) 13.0662i 0.869148i
\(227\) 13.2679 + 7.66025i 0.880625 + 0.508429i 0.870864 0.491523i \(-0.163560\pi\)
0.00976038 + 0.999952i \(0.496893\pi\)
\(228\) −6.96699 4.02239i −0.461400 0.266389i
\(229\) 10.1279i 0.669274i −0.942347 0.334637i \(-0.891386\pi\)
0.942347 0.334637i \(-0.108614\pi\)
\(230\) 0 0
\(231\) −10.2185 17.6990i −0.672331 1.16451i
\(232\) −3.73494 + 2.15637i −0.245211 + 0.141572i
\(233\) −20.7519 −1.35950 −0.679750 0.733444i \(-0.737912\pi\)
−0.679750 + 0.733444i \(0.737912\pi\)
\(234\) −1.32233 3.35432i −0.0864434 0.219279i
\(235\) 0 0
\(236\) −1.88842 + 1.09028i −0.122926 + 0.0709711i
\(237\) −7.46699 12.9332i −0.485033 0.840102i
\(238\) −9.28932 + 16.0896i −0.602137 + 1.04293i
\(239\) 24.3539i 1.57532i −0.616107 0.787662i \(-0.711291\pi\)
0.616107 0.787662i \(-0.288709\pi\)
\(240\) 0 0
\(241\) −17.2066 9.93423i −1.10837 0.639920i −0.169966 0.985450i \(-0.554366\pi\)
−0.938408 + 0.345530i \(0.887699\pi\)
\(242\) 8.36112i 0.537473i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 3.73205 + 6.46410i 0.238920 + 0.413822i
\(245\) 0 0
\(246\) 7.28932 0.464750
\(247\) −28.6884 4.27973i −1.82540 0.272312i
\(248\) −6.44069 −0.408984
\(249\) 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 \(0.0257769\pi\)
\(252\) 4.64466i 0.292586i
\(253\) 3.72139 + 2.14855i 0.233962 + 0.135078i
\(254\) 10.5825 + 6.10978i 0.664002 + 0.383362i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −0.331150 0.573569i −0.0206566 0.0357783i 0.855512 0.517782i \(-0.173242\pi\)
−0.876169 + 0.482004i \(0.839909\pi\)
\(258\) 0.620469 0.358228i 0.0386287 0.0223023i
\(259\) 17.6312 1.09555
\(260\) 0 0
\(261\) −4.31274 −0.266952
\(262\) 0.328013 0.189378i 0.0202647 0.0116998i
\(263\) 15.3749 + 26.6301i 0.948058 + 1.64208i 0.749510 + 0.661993i \(0.230289\pi\)
0.198548 + 0.980091i \(0.436377\pi\)
\(264\) −2.20006 + 3.81062i −0.135405 + 0.234528i
\(265\) 0 0
\(266\) −32.3593 18.6826i −1.98408 1.14551i
\(267\) 7.07780 + 4.08637i 0.433154 + 0.250082i
\(268\) 1.82522i 0.111493i
\(269\) 1.87205 3.24249i 0.114141 0.197698i −0.803295 0.595581i \(-0.796922\pi\)
0.917436 + 0.397883i \(0.130255\pi\)
\(270\) 0 0
\(271\) 24.0419 13.8806i 1.46044 0.843186i 0.461410 0.887187i \(-0.347344\pi\)
0.999031 + 0.0440009i \(0.0140104\pi\)
\(272\) 4.00000 0.242536
\(273\) −6.14177 15.5797i −0.371717 0.942924i
\(274\) −1.25235 −0.0756575
\(275\) 0 0
\(276\) 0.488292 + 0.845746i 0.0293917 + 0.0509079i
\(277\) −5.99609 + 10.3855i −0.360270 + 0.624006i −0.988005 0.154421i \(-0.950649\pi\)
0.627735 + 0.778427i \(0.283982\pi\)
\(278\) 3.35534i 0.201240i
\(279\) −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 \(0.965383\pi\)
\(282\) −4.87671 + 8.44671i −0.290404 + 0.502994i
\(283\) −2.42220 4.19538i −0.143985 0.249389i 0.785009 0.619485i \(-0.212658\pi\)
−0.928994 + 0.370095i \(0.879325\pi\)
\(284\) −6.88764 + 3.97658i −0.408707 + 0.235967i
\(285\) 0 0
\(286\) −2.34081 + 15.6912i −0.138415 + 0.927843i
\(287\) 33.8564 1.99848
\(288\) −0.866025 + 0.500000i −0.0510310 + 0.0294628i
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) 13.8252i 0.810449i
\(292\) 3.77684 + 2.18056i 0.221023 + 0.127608i
\(293\) −3.20500 1.85041i −0.187238 0.108102i 0.403451 0.915001i \(-0.367811\pi\)
−0.590689 + 0.806899i \(0.701144\pi\)
\(294\) 14.5729i 0.849907i
\(295\) 0 0
\(296\) −1.89801 3.28745i −0.110320 0.191079i
\(297\) −3.81062 + 2.20006i −0.221115 + 0.127661i
\(298\) 4.61970 0.267612
\(299\) 2.75624 + 2.19122i 0.159398 + 0.126721i
\(300\) 0 0
\(301\) 2.88187 1.66385i 0.166108 0.0959026i
\(302\) −5.62124 9.73628i −0.323466 0.560260i
\(303\) 3.40013 5.88919i 0.195332 0.338325i
\(304\) 8.04479i 0.461400i
\(305\) 0 0
\(306\) 3.46410 + 2.00000i 0.198030 + 0.114332i
\(307\) 7.11454i 0.406048i 0.979174 + 0.203024i \(0.0650770\pi\)
−0.979174 + 0.203024i \(0.934923\pi\)
\(308\) −10.2185 + 17.6990i −0.582256 + 1.00850i
\(309\) 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 \(0.690982\pi\)
\(312\) −2.24376 + 2.82233i −0.127028 + 0.159783i
\(313\) −6.13950 −0.347025 −0.173513 0.984832i \(-0.555512\pi\)
−0.173513 + 0.984832i \(0.555512\pi\)
\(314\) −1.30173 + 0.751556i −0.0734611 + 0.0424128i
\(315\) 0 0
\(316\) −7.46699 + 12.9332i −0.420051 + 0.727550i
\(317\) 7.85286i 0.441061i −0.975380 0.220530i \(-0.929221\pi\)
0.975380 0.220530i \(-0.0707788\pi\)
\(318\) 11.6990 + 6.75444i 0.656050 + 0.378770i
\(319\) 16.4342 + 9.48829i 0.920139 + 0.531242i
\(320\) 0 0
\(321\) −8.46410 + 14.6603i −0.472420 + 0.818256i
\(322\) 2.26795 + 3.92820i 0.126388 + 0.218910i
\(323\) 27.8680 16.0896i 1.55061 0.895248i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −0.176330 −0.00976601
\(327\) −11.0853 + 6.40013i −0.613021 + 0.353928i
\(328\) −3.64466 6.31274i −0.201243 0.348563i
\(329\) −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 \(0.324659\pi\)
\(332\) −3.04056 1.75547i −0.166872 0.0963438i
\(333\) 3.79603i 0.208021i
\(334\) 4.34081 7.51851i 0.237519 0.411394i
\(335\) 0 0
\(336\) −4.02239 + 2.32233i −0.219440 + 0.126693i
\(337\) 35.6432 1.94161 0.970806 0.239867i \(-0.0771039\pi\)
0.970806 + 0.239867i \(0.0771039\pi\)
\(338\) −3.79423 + 12.4340i −0.206379 + 0.676319i
\(339\) 13.0662 0.709656
\(340\) 0 0
\(341\) 14.1699 + 24.5430i 0.767344 + 1.32908i
\(342\) −4.02239 + 6.96699i −0.217506 + 0.376732i
\(343\) 35.1734i 1.89918i
\(344\) −0.620469 0.358228i −0.0334535 0.0193144i
\(345\) 0 0
\(346\) 1.78043i 0.0957166i
\(347\) −3.44851 + 5.97299i −0.185126 + 0.320647i −0.943619 0.331034i \(-0.892603\pi\)
0.758493 + 0.651681i \(0.225936\pi\)
\(348\) 2.15637 + 3.73494i 0.115593 + 0.200214i
\(349\) 16.7321 9.66025i 0.895646 0.517102i 0.0198610 0.999803i \(-0.493678\pi\)
0.875785 + 0.482701i \(0.160344\pi\)
\(350\) 0 0
\(351\) −3.35432 + 1.32233i −0.179040 + 0.0705807i
\(352\) 4.40013 0.234528
\(353\) 23.7441 13.7086i 1.26377 0.729637i 0.289967 0.957037i \(-0.406356\pi\)
0.973802 + 0.227400i \(0.0730224\pi\)
\(354\) 1.09028 + 1.88842i 0.0579477 + 0.100368i
\(355\) 0 0
\(356\) 8.17274i 0.433154i
\(357\) 16.0896 + 9.28932i 0.851550 + 0.491643i
\(358\) 15.0825 + 8.70786i 0.797133 + 0.460225i
\(359\) 14.3611i 0.757951i 0.925407 + 0.378975i \(0.123723\pi\)
−0.925407 + 0.378975i \(0.876277\pi\)
\(360\) 0 0
\(361\) 22.8593 + 39.5935i 1.20312 + 2.08387i
\(362\) 8.97299 5.18056i 0.471610 0.272284i
\(363\) 8.36112 0.438845
\(364\) −10.4215 + 13.1088i −0.546235 + 0.687086i
\(365\) 0 0
\(366\) 6.46410 3.73205i 0.337884 0.195077i
\(367\) −6.88764 11.9298i −0.359532 0.622728i 0.628351 0.777930i \(-0.283730\pi\)
−0.987883 + 0.155202i \(0.950397\pi\)
\(368\) 0.488292 0.845746i 0.0254540 0.0440876i
\(369\) 7.28932i 0.379467i
\(370\) 0 0
\(371\) 54.3381 + 31.3721i 2.82109 + 1.62876i
\(372\) 6.44069i 0.333934i
\(373\) −16.7313 + 28.9795i −0.866316 + 1.50050i −0.000581860 1.00000i \(0.500185\pi\)
−0.865734 + 0.500504i \(0.833148\pi\)
\(374\) −8.80025 15.2425i −0.455050 0.788170i
\(375\) 0 0
\(376\) 9.75342 0.502994
\(377\) 12.1720 + 9.67674i 0.626888 + 0.498377i
\(378\) −4.64466 −0.238896
\(379\) −28.9052 + 16.6884i −1.48476 + 0.857227i −0.999850 0.0173371i \(-0.994481\pi\)
−0.484910 + 0.874564i \(0.661148\pi\)
\(380\) 0 0
\(381\) 6.10978 10.5825i 0.313014 0.542156i
\(382\) 0.897014i 0.0458952i
\(383\) −6.34829 3.66519i −0.324383 0.187282i 0.328962 0.944343i \(-0.393301\pi\)
−0.653344 + 0.757061i \(0.726635\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) 10.1322 17.5494i 0.515714 0.893243i
\(387\) −0.358228 0.620469i −0.0182098 0.0315402i
\(388\) −11.9730 + 6.91261i −0.607836 + 0.350935i
\(389\) −32.6198 −1.65389 −0.826946 0.562282i \(-0.809924\pi\)
−0.826946 + 0.562282i \(0.809924\pi\)
\(390\) 0 0
\(391\) −3.90633 −0.197552
\(392\) −12.6205 + 7.28643i −0.637430 + 0.368020i
\(393\) −0.189378 0.328013i −0.00955288 0.0165461i
\(394\) 4.59028 7.95060i 0.231255 0.400545i
\(395\) 0 0
\(396\) 3.81062 + 2.20006i 0.191491 + 0.110557i
\(397\) −12.5299 7.23416i −0.628860 0.363072i 0.151451 0.988465i \(-0.451606\pi\)
−0.780310 + 0.625392i \(0.784939\pi\)
\(398\) 16.2175i 0.812911i
\(399\) −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 \(0.391576\pi\)
\(402\) −1.82522 −0.0910336
\(403\) 8.51671 + 21.6041i 0.424248 + 1.07618i
\(404\) −6.80025 −0.338325
\(405\) 0 0
\(406\) 10.0156 + 17.3475i 0.497066 + 0.860943i
\(407\) −8.35150 + 14.4652i −0.413968 + 0.717014i
\(408\) 4.00000i 0.198030i
\(409\) −21.2840 12.2883i −1.05242 0.607617i −0.129097 0.991632i \(-0.541208\pi\)
−0.923327 + 0.384015i \(0.874541\pi\)
\(410\) 0 0
\(411\) 1.25235i 0.0617741i
\(412\) 2.64568 4.58246i 0.130343 0.225761i
\(413\) 5.06397 + 8.77106i 0.249182 + 0.431596i
\(414\) 0.845746 0.488292i 0.0415662 0.0239982i
\(415\) 0 0
\(416\) 3.56609 + 0.531987i 0.174842 + 0.0260828i
\(417\) −3.35534 −0.164312
\(418\) 30.6556 17.6990i 1.49942 0.865688i
\(419\) −7.77684 13.4699i −0.379923 0.658047i 0.611127 0.791532i \(-0.290716\pi\)
−0.991051 + 0.133486i \(0.957383\pi\)
\(420\) 0 0
\(421\) 22.3143i 1.08753i −0.839237 0.543766i \(-0.816998\pi\)
0.839237 0.543766i \(-0.183002\pi\)
\(422\) −1.40270 0.809848i −0.0682822 0.0394228i
\(423\) 8.44671 + 4.87671i 0.410693 + 0.237114i
\(424\) 13.5089i 0.656050i
\(425\) 0 0
\(426\) 3.97658 + 6.88764i 0.192666 + 0.333707i
\(427\) 30.0236 17.3341i 1.45294 0.838856i
\(428\) 16.9282 0.818256
\(429\) 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 \(0.134669\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) 11.5494 20.0042i 0.555031 0.961342i −0.442870 0.896586i \(-0.646040\pi\)
0.997901 0.0647561i \(-0.0206269\pi\)
\(434\) 29.9148i 1.43596i
\(435\) 0 0
\(436\) 11.0853 + 6.40013i 0.530892 + 0.306510i
\(437\) 7.85641i 0.375823i
\(438\) 2.18056 3.77684i 0.104191 0.180464i
\(439\) −19.9980 34.6375i −0.954450 1.65316i −0.735621 0.677393i \(-0.763110\pi\)
−0.218829 0.975763i \(-0.570224\pi\)
\(440\) 0 0
\(441\) −14.5729 −0.693946
\(442\) −5.28932 13.4173i −0.251587 0.638194i
\(443\) 15.6036 0.741350 0.370675 0.928763i \(-0.379126\pi\)
0.370675 + 0.928763i \(0.379126\pi\)
\(444\) −3.28745 + 1.89801i −0.156016 + 0.0900757i
\(445\) 0 0
\(446\) 1.11836 1.93705i 0.0529557 0.0917219i
\(447\) 4.61970i 0.218504i
\(448\) 4.02239 + 2.32233i 0.190040 + 0.109720i
\(449\) 23.3863 + 13.5021i 1.10367 + 0.637203i 0.937182 0.348841i \(-0.113425\pi\)
0.166486 + 0.986044i \(0.446758\pi\)
\(450\) 0 0
\(451\) −16.0370 + 27.7768i −0.755151 + 1.30796i
\(452\) −6.53308 11.3156i −0.307290 0.532242i
\(453\) −9.73628 + 5.62124i −0.457450 + 0.264109i
\(454\) −15.3205 −0.719027
\(455\) 0 0
\(456\) 8.04479 0.376732
\(457\) −15.4039 + 8.89342i −0.720562 + 0.416017i −0.814959 0.579518i \(-0.803241\pi\)
0.0943975 + 0.995535i \(0.469908\pi\)
\(458\) 5.06397 + 8.77106i 0.236624 + 0.409845i
\(459\) 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 \(0.469183\pi\)
\(462\) 17.6990 + 10.2185i 0.823434 + 0.475410i
\(463\) 15.6389i 0.726801i −0.931633 0.363400i \(-0.881616\pi\)
0.931633 0.363400i \(-0.118384\pi\)
\(464\) 2.15637 3.73494i 0.100107 0.173390i
\(465\) 0 0
\(466\) 17.9716 10.3759i 0.832521 0.480656i
\(467\) 2.43914 0.112870 0.0564349 0.998406i \(-0.482027\pi\)
0.0564349 + 0.998406i \(0.482027\pi\)
\(468\) 2.82233 + 2.24376i 0.130462 + 0.103718i
\(469\) −8.47751 −0.391455
\(470\) 0 0
\(471\) 0.751556 + 1.30173i 0.0346299 + 0.0599807i
\(472\) 1.09028 1.88842i 0.0501842 0.0869215i
\(473\) 3.15250i 0.144952i
\(474\) 12.9332 + 7.46699i 0.594042 + 0.342970i
\(475\) 0 0
\(476\) 18.5786i 0.851550i
\(477\) 6.75444 11.6990i 0.309265 0.535662i
\(478\) 12.1770 + 21.0911i 0.556961 + 0.964685i
\(479\) 12.2857 7.09317i 0.561349 0.324095i −0.192338 0.981329i \(-0.561607\pi\)
0.753687 + 0.657234i \(0.228274\pi\)
\(480\) 0 0
\(481\) −8.51737 + 10.7136i −0.388358 + 0.488500i
\(482\) 19.8685 0.904983
\(483\) 3.92820 2.26795i 0.178739 0.103195i
\(484\) −4.18056 7.24094i −0.190025 0.329134i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) −4.99115 2.88164i −0.226171 0.130580i 0.382633 0.923900i \(-0.375017\pi\)
−0.608804 + 0.793320i \(0.708351\pi\)
\(488\) −6.46410 3.73205i −0.292616 0.168942i
\(489\) 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 \(0.841058\pi\)
\(492\) −6.31274 + 3.64466i −0.284600 + 0.164314i
\(493\) −17.2509 −0.776943
\(494\) 26.9848 10.6379i 1.21410 0.478620i
\(495\) 0 0
\(496\) 5.57780 3.22034i 0.250450 0.144598i
\(497\) 18.4699 + 31.9908i 0.828487 + 1.43498i
\(498\) −1.75547 + 3.04056i −0.0786644 + 0.136251i
\(499\) 14.7534i 0.660454i 0.943902 + 0.330227i \(0.107125\pi\)
−0.943902 + 0.330227i \(0.892875\pi\)
\(500\) 0 0
\(501\) −7.51851 4.34081i −0.335902 0.193933i
\(502\) 13.5713i 0.605717i
\(503\) −13.3309 + 23.0898i −0.594395 + 1.02952i 0.399236 + 0.916848i \(0.369275\pi\)
−0.993632 + 0.112675i \(0.964058\pi\)
\(504\) 2.32233 + 4.02239i 0.103445 + 0.179172i
\(505\) 0 0
\(506\) −4.29709 −0.191029
\(507\) 12.4340 + 3.79423i 0.552212 + 0.168508i
\(508\) −12.2196 −0.542156
\(509\) 12.2807 7.09028i 0.544333 0.314271i −0.202500 0.979282i \(-0.564907\pi\)
0.746833 + 0.665011i \(0.231573\pi\)
\(510\) 0 0
\(511\) 10.1279 17.5421i 0.448034 0.776018i
\(512\) 1.00000i 0.0441942i
\(513\) 6.96699 + 4.02239i 0.307600 + 0.177593i
\(514\) 0.573569 + 0.331150i 0.0252990 + 0.0146064i
\(515\) 0 0
\(516\) −0.358228 + 0.620469i −0.0157701 + 0.0273146i
\(517\) −21.4581 37.1666i −0.943728 1.63459i
\(518\) −15.2691 + 8.81562i −0.670886 + 0.387336i
\(519\) −1.78043 −0.0781523
\(520\) 0 0
\(521\) 23.7476 1.04040 0.520202 0.854043i \(-0.325857\pi\)
0.520202 + 0.854043i \(0.325857\pi\)
\(522\) 3.73494 2.15637i 0.163474 0.0943817i
\(523\) 6.92532 + 11.9950i 0.302823 + 0.524505i 0.976774 0.214271i \(-0.0687376\pi\)
−0.673951 + 0.738776i \(0.735404\pi\)
\(524\) −0.189378 + 0.328013i −0.00827303 + 0.0143293i
\(525\) 0 0
\(526\) −26.6301 15.3749i −1.16113 0.670378i
\(527\) −22.3112 12.8814i −0.971891 0.561121i
\(528\) 4.40013i 0.191491i
\(529\) 11.0231 19.0926i 0.479267 0.830115i
\(530\) 0 0
\(531\) 1.88842 1.09028i 0.0819504 0.0473141i
\(532\) 37.3653 1.61999
\(533\) −16.3555 + 20.5729i −0.708434 + 0.891110i
\(534\) −8.17274 −0.353669
\(535\) 0 0
\(536\) 0.912609 + 1.58068i 0.0394187 + 0.0682752i
\(537\) 8.70786 15.0825i 0.375772 0.650856i
\(538\) 3.74410i 0.161420i
\(539\) 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 \(0.896290\pi\)
\(542\) −13.8806 + 24.0419i −0.596223 + 1.03269i
\(543\) −5.18056 8.97299i −0.222319 0.385068i
\(544\) −3.46410 + 2.00000i −0.148522 + 0.0857493i
\(545\) 0 0
\(546\) 13.1088 + 10.4215i 0.561003 + 0.445999i
\(547\) 22.2019 0.949284 0.474642 0.880179i \(-0.342578\pi\)
0.474642 + 0.880179i \(0.342578\pi\)
\(548\) 1.08457 0.626177i 0.0463306 0.0267490i
\(549\) −3.73205 6.46410i −0.159280 0.275881i
\(550\) 0 0
\(551\) 34.6950i 1.47806i
\(552\) −0.845746 0.488292i −0.0359973 0.0207831i
\(553\) 60.0703 + 34.6816i 2.55445 + 1.47481i
\(554\) 11.9922i 0.509499i
\(555\) 0 0
\(556\) 1.67767 + 2.90581i 0.0711491 + 0.123234i
\(557\) −1.64518 + 0.949847i −0.0697087 + 0.0402463i −0.534449 0.845201i \(-0.679481\pi\)
0.464741 + 0.885447i \(0.346148\pi\)
\(558\) 6.44069 0.272656
\(559\) −0.381146 + 2.55495i −0.0161207 + 0.108063i
\(560\) 0 0
\(561\) −15.2425 + 8.80025i −0.643538 + 0.371547i
\(562\) −1.81944 3.15137i −0.0767485 0.132932i
\(563\) 0.860000 1.48956i 0.0362447 0.0627777i −0.847334 0.531060i \(-0.821794\pi\)
0.883579 + 0.468283i \(0.155127\pi\)
\(564\) 9.75342i 0.410693i
\(565\) 0 0
\(566\) 4.19538 + 2.42220i 0.176345 + 0.101813i
\(567\) 4.64466i 0.195057i
\(568\) 3.97658 6.88764i 0.166854 0.288999i
\(569\) −0.300960 0.521278i −0.0126169 0.0218531i 0.859648 0.510887i \(-0.170683\pi\)
−0.872265 + 0.489034i \(0.837350\pi\)
\(570\) 0 0
\(571\) 11.9808 0.501381 0.250691 0.968067i \(-0.419342\pi\)
0.250691 + 0.968067i \(0.419342\pi\)
\(572\) −5.81842 14.7594i −0.243280 0.617122i
\(573\) 0.897014 0.0374733
\(574\) −29.3205 + 16.9282i −1.22381 + 0.706570i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 43.0293i 1.79133i 0.444725 + 0.895667i \(0.353301\pi\)
−0.444725 + 0.895667i \(0.646699\pi\)
\(578\) −0.866025 0.500000i −0.0360219 0.0207973i
\(579\) −17.5494 10.1322i −0.729330 0.421079i
\(580\) 0 0
\(581\) −8.15355 + 14.1224i −0.338266 + 0.585894i
\(582\) 6.91261 + 11.9730i 0.286537 + 0.496296i
\(583\) −51.4773 + 29.7204i −2.13197 + 1.23089i
\(584\) −4.36112 −0.180464
\(585\) 0 0
\(586\) 3.70081 0.152879
\(587\) 15.5147 8.95740i 0.640359 0.369711i −0.144394 0.989520i \(-0.546123\pi\)
0.784753 + 0.619809i \(0.212790\pi\)
\(588\) 7.28643 + 12.6205i 0.300487 + 0.520459i
\(589\) 25.9070 44.8722i 1.06748 1.84893i
\(590\) 0 0
\(591\) −7.95060 4.59028i −0.327044 0.188819i
\(592\) 3.28745 + 1.89801i 0.135114 + 0.0780078i
\(593\) 0.669624i 0.0274981i −0.999905 0.0137491i \(-0.995623\pi\)
0.999905 0.0137491i \(-0.00437660\pi\)
\(594\) 2.20006 3.81062i 0.0902697 0.156352i
\(595\) 0 0
\(596\) −4.00077 + 2.30985i −0.163878 + 0.0946151i
\(597\) −16.2175 −0.663739
\(598\) −3.48258 0.519530i −0.142413 0.0212452i
\(599\) 1.29241 0.0528066 0.0264033 0.999651i \(-0.491595\pi\)
0.0264033 + 0.999651i \(0.491595\pi\)
\(600\) 0 0
\(601\) 5.73671 + 9.93627i 0.234005 + 0.405309i 0.958983 0.283463i \(-0.0914834\pi\)
−0.724978 + 0.688772i \(0.758150\pi\)
\(602\) −1.66385 + 2.88187i −0.0678134 + 0.117456i
\(603\) 1.82522i 0.0743286i
\(604\) 9.73628 + 5.62124i 0.396164 + 0.228725i
\(605\) 0 0
\(606\) 6.80025i 0.276241i
\(607\) −12.0672 + 20.9010i −0.489792 + 0.848344i −0.999931 0.0117477i \(-0.996261\pi\)
0.510139 + 0.860092i \(0.329594\pi\)
\(608\) −4.02239 6.96699i −0.163130 0.282549i
\(609\) 17.3475 10.0156i 0.702957 0.405852i
\(610\) 0 0
\(611\) −12.8972 32.7161i −0.521766 1.32355i
\(612\) −4.00000 −0.161690
\(613\) −25.0716 + 14.4751i −1.01263 + 0.584644i −0.911961 0.410276i \(-0.865432\pi\)
−0.100671 + 0.994920i \(0.532099\pi\)
\(614\) −3.55727 6.16137i −0.143560 0.248653i
\(615\) 0 0
\(616\) 20.4371i 0.823434i
\(617\) 0.728597 + 0.420655i 0.0293322 + 0.0169349i 0.514594 0.857434i \(-0.327943\pi\)
−0.485262 + 0.874369i \(0.661276\pi\)
\(618\) −4.58246 2.64568i −0.184333 0.106425i
\(619\) 6.25076i 0.251239i −0.992078 0.125620i \(-0.959908\pi\)
0.992078 0.125620i \(-0.0400919\pi\)
\(620\) 0 0
\(621\) −0.488292 0.845746i −0.0195945 0.0339386i
\(622\) 17.2467 9.95740i 0.691530 0.399255i
\(623\) −37.9596 −1.52082
\(624\) 0.531987 3.56609i 0.0212965 0.142758i
\(625\) 0 0
\(626\) 5.31696 3.06975i 0.212509 0.122692i
\(627\) −17.6990 30.6556i −0.706832 1.22427i
\(628\) 0.751556 1.30173i 0.0299904 0.0519448i
\(629\) 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 \(0.647489\pi\)
\(632\) 14.9340i 0.594042i
\(633\) −0.809848 + 1.40270i −0.0321886 + 0.0557522i
\(634\) 3.92643 + 6.80078i 0.155938 + 0.270093i
\(635\) 0 0
\(636\) −13.5089 −0.535662
\(637\) 41.1294 + 32.6980i 1.62961 + 1.29554i
\(638\) −18.9766 −0.751290
\(639\) 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 \(0.161810\pi\)
\(642\) 16.9282i 0.668103i
\(643\) −16.7788 9.68726i −0.661693 0.382028i 0.131229 0.991352i \(-0.458108\pi\)
−0.792922 + 0.609324i \(0.791441\pi\)
\(644\) −3.92820 2.26795i −0.154793 0.0893697i
\(645\) 0 0
\(646\) −16.0896 + 27.8680i −0.633036 + 1.09645i
\(647\) 13.5953 + 23.5477i 0.534485 + 0.925755i 0.999188 + 0.0402882i \(0.0128276\pi\)
−0.464703 + 0.885466i \(0.653839\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) −9.59473 −0.376626
\(650\) 0 0
\(651\) 29.9148 1.17245
\(652\) 0.152706 0.0881650i 0.00598044 0.00345281i
\(653\) 7.89799 + 13.6797i 0.309072 + 0.535329i 0.978160 0.207855i \(-0.0666482\pi\)
−0.669088 + 0.743184i \(0.733315\pi\)
\(654\) 6.40013 11.0853i 0.250265 0.433471i
\(655\) 0 0
\(656\) 6.31274 + 3.64466i 0.246471 + 0.142300i
\(657\) −3.77684 2.18056i −0.147348 0.0850717i
\(658\) 45.3013i 1.76603i
\(659\) −15.2381 + 26.3932i −0.593593 + 1.02813i 0.400151 + 0.916449i \(0.368958\pi\)
−0.993744 + 0.111684i \(0.964376\pi\)
\(660\) 0 0
\(661\) −24.1514 + 13.9438i −0.939379 + 0.542351i −0.889766 0.456418i \(-0.849132\pi\)
−0.0496136 + 0.998768i \(0.515799\pi\)
\(662\) −31.9959 −1.24356
\(663\) −13.4173 + 5.28932i −0.521084 + 0.205420i
\(664\) 3.51093 0.136251
\(665\) 0 0
\(666\) 1.89801 + 3.28745i 0.0735465 + 0.127386i
\(667\) −2.10587 + 3.64748i −0.0815397 + 0.141231i
\(668\) 8.68162i 0.335902i
\(669\) −1.93705 1.11836i −0.0748906 0.0432381i
\(670\) 0 0
\(671\) 32.8430i 1.26789i
\(672\) 2.32233 4.02239i 0.0895858 0.155167i
\(673\) 0.489066 + 0.847086i 0.0188521 + 0.0326528i 0.875298 0.483585i \(-0.160666\pi\)
−0.856445 + 0.516238i \(0.827332\pi\)
\(674\) −30.8680 + 17.8216i −1.18899 + 0.686463i
\(675\) 0 0
\(676\) −2.93109 12.6653i −0.112734 0.487125i
\(677\) 19.1926 0.737630 0.368815 0.929503i \(-0.379764\pi\)
0.368815 + 0.929503i \(0.379764\pi\)
\(678\) −11.3156 + 6.53308i −0.434574 + 0.250901i
\(679\) 32.1067 + 55.6105i 1.23214 + 2.13413i
\(680\) 0 0
\(681\) 15.3205i 0.587083i
\(682\) −24.5430 14.1699i −0.939801 0.542594i
\(683\) 1.30851 + 0.755467i 0.0500687 + 0.0289071i 0.524825 0.851210i \(-0.324131\pi\)
−0.474757 + 0.880117i \(0.657464\pi\)
\(684\) 8.04479i 0.307600i
\(685\) 0 0
\(686\) 17.5867 + 30.4610i 0.671463 + 1.16301i
\(687\) 8.77106 5.06397i 0.334637 0.193203i
\(688\) 0.716456 0.0273146
\(689\) −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 \(0.116426\pi\)
\(692\) 0.890216 + 1.54190i 0.0338409 + 0.0586142i
\(693\) 10.2185 17.6990i 0.388170 0.672331i
\(694\) 6.89701i 0.261807i
\(695\) 0 0
\(696\) −3.73494 2.15637i −0.141572 0.0817369i
\(697\) 29.1573i 1.10441i
\(698\) −9.66025 + 16.7321i −0.365646 + 0.633317i
\(699\) −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 \(0.323576\pi\)
\(702\) 2.24376 2.82233i 0.0846852 0.106522i
\(703\) 30.5382 1.15177
\(704\) −3.81062 + 2.20006i −0.143618 + 0.0829180i
\(705\) 0 0
\(706\) −13.7086 + 23.7441i −0.515931 + 0.893619i
\(707\) 31.5849i 1.18787i
\(708\) −1.88842 1.09028i −0.0709711 0.0409752i
\(709\) −9.57491 5.52808i −0.359593 0.207611i 0.309309 0.950962i \(-0.399902\pi\)
−0.668902 + 0.743350i \(0.733236\pi\)
\(710\) 0 0
\(711\) 7.46699 12.9332i 0.280034 0.485033i
\(712\) 4.08637 + 7.07780i 0.153143 + 0.265252i
\(713\) −5.44719 + 3.14493i −0.203999 + 0.117779i
\(714\) −18.5786 −0.695288
\(715\) 0 0
\(716\) −17.4157 −0.650856
\(717\) 21.0911 12.1770i 0.787662 0.454757i
\(718\) −7.18056 12.4371i −0.267976 0.464148i
\(719\) 5.85641 10.1436i 0.218407 0.378292i −0.735914 0.677075i \(-0.763247\pi\)
0.954321 + 0.298783i \(0.0965806\pi\)
\(720\) 0 0
\(721\) −21.2840 12.2883i −0.792656 0.457640i
\(722\) −39.5935 22.8593i −1.47352 0.850735i
\(723\) 19.8685i 0.738916i
\(724\) −5.18056 + 8.97299i −0.192534 + 0.333479i
\(725\) 0 0
\(726\) −7.24094 + 4.18056i −0.268736 + 0.155155i
\(727\) 19.4152 0.720071 0.360035 0.932939i \(-0.382765\pi\)
0.360035 + 0.932939i \(0.382765\pi\)
\(728\) 2.47090 16.5633i 0.0915777 0.613876i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −1.43291 2.48188i −0.0529982 0.0917956i
\(732\) −3.73205 + 6.46410i −0.137941 + 0.238920i
\(733\) 11.9340i 0.440792i −0.975411 0.220396i \(-0.929265\pi\)
0.975411 0.220396i \(-0.0707349\pi\)
\(734\) 11.9298 + 6.88764i 0.440335 + 0.254228i
\(735\) 0 0
\(736\) 0.976584i 0.0359973i
\(737\) 4.01559 6.95521i 0.147916 0.256199i
\(738\) 3.64466 + 6.31274i 0.134162 + 0.232375i
\(739\) 17.2017 9.93141i 0.632775 0.365333i −0.149051 0.988830i \(-0.547622\pi\)
0.781826 + 0.623497i \(0.214289\pi\)
\(740\) 0 0
\(741\) −10.6379 26.9848i −0.390792 0.991310i
\(742\) −62.7442 −2.30341
\(743\) −14.2787 + 8.24383i −0.523836 + 0.302437i −0.738503 0.674251i \(-0.764467\pi\)
0.214667 + 0.976687i \(0.431133\pi\)
\(744\) −3.22034 5.57780i −0.118063 0.204492i
\(745\) 0 0
\(746\) 33.4627i 1.22516i
\(747\) 3.04056 + 1.75547i 0.111248 + 0.0642292i
\(748\) 15.2425 + 8.80025i 0.557320 + 0.321769i
\(749\) 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 \(-0.490893\pi\)
\(752\) −8.44671 + 4.87671i −0.308020 + 0.177835i
\(753\) 13.5713 0.494566
\(754\) −15.3796 2.29432i −0.560092 0.0835542i
\(755\) 0 0
\(756\) 4.02239 2.32233i 0.146293 0.0844623i
\(757\) 1.31799 + 2.28282i 0.0479030 + 0.0829705i 0.888983 0.457941i \(-0.151413\pi\)
−0.841080 + 0.540911i \(0.818079\pi\)
\(758\) 16.6884 28.9052i 0.606151 1.04988i
\(759\) 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 \(0.666205\pi\)
\(762\) 12.2196i 0.442668i
\(763\) 29.7264 51.4877i 1.07617 1.86398i
\(764\) −0.448507 0.776837i −0.0162264 0.0281050i
\(765\) 0 0
\(766\) 7.33038 0.264857
\(767\) −7.77606 1.16003i −0.280777 0.0418862i
\(768\) −1.00000 −0.0360844
\(769\) 4.92177 2.84159i 0.177484 0.102470i −0.408626 0.912702i \(-0.633992\pi\)
0.586110 + 0.810232i \(0.300659\pi\)
\(770\) 0 0
\(771\) 0.331150 0.573569i 0.0119261 0.0206566i
\(772\) 20.2644i 0.729330i
\(773\) 6.57184 + 3.79425i 0.236373 + 0.136470i 0.613508 0.789688i \(-0.289758\pi\)
−0.377136 + 0.926158i \(0.623091\pi\)
\(774\) 0.620469 + 0.358228i 0.0223023 + 0.0128762i
\(775\) 0 0
\(776\) 6.91261 11.9730i 0.248148 0.429805i
\(777\) 8.81562 + 15.2691i 0.316259 + 0.547776i
\(778\) 28.2496 16.3099i 1.01280 0.584739i
\(779\) 58.6410 2.10103
\(780\) 0 0
\(781\) −34.9949 −1.25222
\(782\) 3.38298 1.95317i 0.120975 0.0698451i
\(783\) −2.15637 3.73494i −0.0770623 0.133476i
\(784\) 7.28643 12.6205i 0.260230 0.450731i