Properties

Label 966.2.i.n.415.2
Level $966$
Weight $2$
Character 966.415
Analytic conductor $7.714$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.71354883526\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.173309020416.2
Defining polynomial: \( x^{8} - 5x^{6} - 28x^{5} - 4x^{4} + 70x^{3} + 51x^{2} + 406x + 841 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 415.2
Root \(-1.61272 - 2.45863i\) of defining polynomial
Character \(\chi\) \(=\) 966.415
Dual form 966.2.i.n.277.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.739514 + 1.28088i) q^{5} +1.00000 q^{6} +(1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.739514 + 1.28088i) q^{5} +1.00000 q^{6} +(1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.739514 + 1.28088i) q^{10} +(-2.85224 - 4.94022i) q^{11} +(0.500000 - 0.866025i) q^{12} +6.35023 q^{13} +2.64575 q^{14} -1.47903 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.06239 + 3.57216i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.69609 + 2.93771i) q^{19} +1.47903 q^{20} +(-1.32288 + 2.29129i) q^{21} -5.70448 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(1.40624 + 2.43567i) q^{25} +(3.17511 - 5.49946i) q^{26} -1.00000 q^{27} +(1.32288 - 2.29129i) q^{28} +2.39217 q^{29} +(-0.739514 + 1.28088i) q^{30} +(3.90624 + 6.76580i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.85224 - 4.94022i) q^{33} +4.12478 q^{34} -3.91314 q^{35} +1.00000 q^{36} +(-4.17511 + 7.23151i) q^{37} +(1.69609 + 2.93771i) q^{38} +(3.17511 + 5.49946i) q^{39} +(0.739514 - 1.28088i) q^{40} +7.39217 q^{41} +(1.32288 + 2.29129i) q^{42} +2.00000 q^{43} +(-2.85224 + 4.94022i) q^{44} +(-0.739514 - 1.28088i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-5.11071 + 8.85202i) q^{47} -1.00000 q^{48} +(-3.50000 + 6.06218i) q^{49} +2.81247 q^{50} +(-2.06239 + 3.57216i) q^{51} +(-3.17511 - 5.49946i) q^{52} +(-0.260486 - 0.451174i) q^{53} +(-0.500000 + 0.866025i) q^{54} +8.43709 q^{55} +(-1.32288 - 2.29129i) q^{56} -3.39217 q^{57} +(1.19609 - 2.07168i) q^{58} +(-3.68918 - 6.38985i) q^{59} +(0.739514 + 1.28088i) q^{60} +(2.52097 - 4.36645i) q^{61} +7.81247 q^{62} -2.64575 q^{63} +1.00000 q^{64} +(-4.69609 + 8.13386i) q^{65} +(-2.85224 - 4.94022i) q^{66} +(-7.70448 - 13.3445i) q^{67} +(2.06239 - 3.57216i) q^{68} -1.00000 q^{69} +(-1.95657 + 3.38888i) q^{70} +9.87120 q^{71} +(0.500000 - 0.866025i) q^{72} +(-4.46496 - 7.73354i) q^{73} +(4.17511 + 7.23151i) q^{74} +(-1.40624 + 2.43567i) q^{75} +3.39217 q^{76} +(7.54631 - 13.0706i) q^{77} +6.35023 q^{78} +(6.71505 - 11.6308i) q^{79} +(-0.739514 - 1.28088i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.69609 - 6.40181i) q^{82} -9.22143 q^{83} +2.64575 q^{84} -6.10067 q^{85} +(1.00000 - 1.73205i) q^{86} +(1.19609 + 2.07168i) q^{87} +(2.85224 + 4.94022i) q^{88} +(3.21706 - 5.57211i) q^{89} -1.47903 q^{90} +(8.40056 + 14.5502i) q^{91} +1.00000 q^{92} +(-3.90624 + 6.76580i) q^{93} +(5.11071 + 8.85202i) q^{94} +(-2.50856 - 4.34495i) q^{95} +(-0.500000 + 0.866025i) q^{96} -10.3640 q^{97} +(3.50000 + 6.06218i) q^{98} +5.70448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} + 8 q^{6} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} + 8 q^{6} - 8 q^{8} - 4 q^{9} + 2 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{13} - 4 q^{15} - 4 q^{16} + 2 q^{17} + 4 q^{18} + 6 q^{19} + 4 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{24} - 6 q^{25} - 2 q^{26} - 8 q^{27} - 20 q^{29} - 2 q^{30} + 14 q^{31} + 4 q^{32} + 6 q^{33} + 4 q^{34} + 8 q^{36} - 6 q^{37} - 6 q^{38} - 2 q^{39} + 2 q^{40} + 20 q^{41} + 16 q^{43} - 6 q^{44} - 2 q^{45} + 4 q^{46} + 10 q^{47} - 8 q^{48} - 28 q^{49} - 12 q^{50} - 2 q^{51} + 2 q^{52} - 6 q^{53} - 4 q^{54} + 44 q^{55} + 12 q^{57} - 10 q^{58} - 24 q^{59} + 2 q^{60} + 28 q^{61} + 28 q^{62} + 8 q^{64} - 18 q^{65} - 6 q^{66} - 28 q^{67} + 2 q^{68} - 8 q^{69} + 32 q^{71} + 4 q^{72} - 6 q^{73} + 6 q^{74} + 6 q^{75} - 12 q^{76} - 14 q^{77} - 4 q^{78} + 4 q^{79} - 2 q^{80} - 4 q^{81} + 10 q^{82} + 28 q^{83} - 52 q^{85} + 8 q^{86} - 10 q^{87} + 6 q^{88} + 14 q^{89} - 4 q^{90} + 14 q^{91} + 8 q^{92} - 14 q^{93} - 10 q^{94} + 34 q^{95} - 4 q^{96} + 28 q^{98} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.739514 + 1.28088i −0.330721 + 0.572825i −0.982653 0.185452i \(-0.940625\pi\)
0.651933 + 0.758277i \(0.273959\pi\)
\(6\) 1.00000 0.408248
\(7\) 1.32288 + 2.29129i 0.500000 + 0.866025i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.739514 + 1.28088i 0.233855 + 0.405049i
\(11\) −2.85224 4.94022i −0.859982 1.48953i −0.871945 0.489605i \(-0.837141\pi\)
0.0119622 0.999928i \(-0.496192\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) 6.35023 1.76124 0.880618 0.473826i \(-0.157128\pi\)
0.880618 + 0.473826i \(0.157128\pi\)
\(14\) 2.64575 0.707107
\(15\) −1.47903 −0.381884
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.06239 + 3.57216i 0.500203 + 0.866377i 1.00000 0.000234490i \(7.46404e-5\pi\)
−0.499797 + 0.866143i \(0.666592\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) −1.69609 + 2.93771i −0.389109 + 0.673956i −0.992330 0.123618i \(-0.960550\pi\)
0.603221 + 0.797574i \(0.293884\pi\)
\(20\) 1.47903 0.330721
\(21\) −1.32288 + 2.29129i −0.288675 + 0.500000i
\(22\) −5.70448 −1.21620
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 1.40624 + 2.43567i 0.281247 + 0.487135i
\(26\) 3.17511 5.49946i 0.622691 1.07853i
\(27\) −1.00000 −0.192450
\(28\) 1.32288 2.29129i 0.250000 0.433013i
\(29\) 2.39217 0.444215 0.222108 0.975022i \(-0.428706\pi\)
0.222108 + 0.975022i \(0.428706\pi\)
\(30\) −0.739514 + 1.28088i −0.135016 + 0.233855i
\(31\) 3.90624 + 6.76580i 0.701581 + 1.21517i 0.967911 + 0.251292i \(0.0808554\pi\)
−0.266330 + 0.963882i \(0.585811\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 2.85224 4.94022i 0.496511 0.859982i
\(34\) 4.12478 0.707394
\(35\) −3.91314 −0.661442
\(36\) 1.00000 0.166667
\(37\) −4.17511 + 7.23151i −0.686385 + 1.18885i 0.286615 + 0.958046i \(0.407470\pi\)
−0.973000 + 0.230807i \(0.925863\pi\)
\(38\) 1.69609 + 2.93771i 0.275141 + 0.476559i
\(39\) 3.17511 + 5.49946i 0.508425 + 0.880618i
\(40\) 0.739514 1.28088i 0.116927 0.202524i
\(41\) 7.39217 1.15446 0.577232 0.816580i \(-0.304133\pi\)
0.577232 + 0.816580i \(0.304133\pi\)
\(42\) 1.32288 + 2.29129i 0.204124 + 0.353553i
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) −2.85224 + 4.94022i −0.429991 + 0.744767i
\(45\) −0.739514 1.28088i −0.110240 0.190942i
\(46\) 0.500000 + 0.866025i 0.0737210 + 0.127688i
\(47\) −5.11071 + 8.85202i −0.745474 + 1.29120i 0.204499 + 0.978867i \(0.434444\pi\)
−0.949973 + 0.312333i \(0.898890\pi\)
\(48\) −1.00000 −0.144338
\(49\) −3.50000 + 6.06218i −0.500000 + 0.866025i
\(50\) 2.81247 0.397744
\(51\) −2.06239 + 3.57216i −0.288792 + 0.500203i
\(52\) −3.17511 5.49946i −0.440309 0.762638i
\(53\) −0.260486 0.451174i −0.0357804 0.0619736i 0.847581 0.530667i \(-0.178058\pi\)
−0.883361 + 0.468693i \(0.844725\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 8.43709 1.13766
\(56\) −1.32288 2.29129i −0.176777 0.306186i
\(57\) −3.39217 −0.449304
\(58\) 1.19609 2.07168i 0.157054 0.272025i
\(59\) −3.68918 6.38985i −0.480290 0.831887i 0.519454 0.854498i \(-0.326135\pi\)
−0.999744 + 0.0226111i \(0.992802\pi\)
\(60\) 0.739514 + 1.28088i 0.0954709 + 0.165360i
\(61\) 2.52097 4.36645i 0.322777 0.559067i −0.658283 0.752771i \(-0.728717\pi\)
0.981060 + 0.193704i \(0.0620502\pi\)
\(62\) 7.81247 0.992185
\(63\) −2.64575 −0.333333
\(64\) 1.00000 0.125000
\(65\) −4.69609 + 8.13386i −0.582478 + 1.00888i
\(66\) −2.85224 4.94022i −0.351086 0.608099i
\(67\) −7.70448 13.3445i −0.941252 1.63030i −0.763088 0.646295i \(-0.776318\pi\)
−0.178164 0.984001i \(-0.557016\pi\)
\(68\) 2.06239 3.57216i 0.250102 0.433189i
\(69\) −1.00000 −0.120386
\(70\) −1.95657 + 3.38888i −0.233855 + 0.405049i
\(71\) 9.87120 1.17150 0.585748 0.810493i \(-0.300801\pi\)
0.585748 + 0.810493i \(0.300801\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −4.46496 7.73354i −0.522584 0.905143i −0.999655 0.0262776i \(-0.991635\pi\)
0.477070 0.878865i \(-0.341699\pi\)
\(74\) 4.17511 + 7.23151i 0.485347 + 0.840646i
\(75\) −1.40624 + 2.43567i −0.162378 + 0.281247i
\(76\) 3.39217 0.389109
\(77\) 7.54631 13.0706i 0.859982 1.48953i
\(78\) 6.35023 0.719022
\(79\) 6.71505 11.6308i 0.755502 1.30857i −0.189623 0.981857i \(-0.560726\pi\)
0.945124 0.326710i \(-0.105940\pi\)
\(80\) −0.739514 1.28088i −0.0826802 0.143206i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 3.69609 6.40181i 0.408164 0.706961i
\(83\) −9.22143 −1.01218 −0.506092 0.862480i \(-0.668910\pi\)
−0.506092 + 0.862480i \(0.668910\pi\)
\(84\) 2.64575 0.288675
\(85\) −6.10067 −0.661710
\(86\) 1.00000 1.73205i 0.107833 0.186772i
\(87\) 1.19609 + 2.07168i 0.128234 + 0.222108i
\(88\) 2.85224 + 4.94022i 0.304050 + 0.526629i
\(89\) 3.21706 5.57211i 0.341007 0.590642i −0.643613 0.765351i \(-0.722565\pi\)
0.984620 + 0.174709i \(0.0558986\pi\)
\(90\) −1.47903 −0.155903
\(91\) 8.40056 + 14.5502i 0.880618 + 1.52528i
\(92\) 1.00000 0.104257
\(93\) −3.90624 + 6.76580i −0.405058 + 0.701581i
\(94\) 5.11071 + 8.85202i 0.527130 + 0.913016i
\(95\) −2.50856 4.34495i −0.257373 0.445783i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) −10.3640 −1.05231 −0.526154 0.850389i \(-0.676367\pi\)
−0.526154 + 0.850389i \(0.676367\pi\)
\(98\) 3.50000 + 6.06218i 0.353553 + 0.612372i
\(99\) 5.70448 0.573322
\(100\) 1.40624 2.43567i 0.140624 0.243567i
\(101\) −1.40624 2.43567i −0.139926 0.242359i 0.787543 0.616260i \(-0.211353\pi\)
−0.927468 + 0.373902i \(0.878020\pi\)
\(102\) 2.06239 + 3.57216i 0.204207 + 0.353697i
\(103\) 6.27945 10.8763i 0.618732 1.07168i −0.370985 0.928639i \(-0.620980\pi\)
0.989717 0.143037i \(-0.0456868\pi\)
\(104\) −6.35023 −0.622691
\(105\) −1.95657 3.38888i −0.190942 0.330721i
\(106\) −0.520971 −0.0506012
\(107\) 2.61071 4.52189i 0.252387 0.437148i −0.711795 0.702387i \(-0.752118\pi\)
0.964183 + 0.265239i \(0.0854510\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 4.23750 + 7.33957i 0.405879 + 0.703004i 0.994423 0.105462i \(-0.0336320\pi\)
−0.588544 + 0.808465i \(0.700299\pi\)
\(110\) 4.21854 7.30673i 0.402222 0.696669i
\(111\) −8.35023 −0.792569
\(112\) −2.64575 −0.250000
\(113\) 0.725281 0.0682287 0.0341144 0.999418i \(-0.489139\pi\)
0.0341144 + 0.999418i \(0.489139\pi\)
\(114\) −1.69609 + 2.93771i −0.158853 + 0.275141i
\(115\) −0.739514 1.28088i −0.0689601 0.119442i
\(116\) −1.19609 2.07168i −0.111054 0.192351i
\(117\) −3.17511 + 5.49946i −0.293539 + 0.508425i
\(118\) −7.37836 −0.679233
\(119\) −5.45657 + 9.45106i −0.500203 + 0.866377i
\(120\) 1.47903 0.135016
\(121\) −10.7705 + 18.6551i −0.979139 + 1.69592i
\(122\) −2.52097 4.36645i −0.228238 0.395320i
\(123\) 3.69609 + 6.40181i 0.333265 + 0.577232i
\(124\) 3.90624 6.76580i 0.350790 0.607587i
\(125\) −11.5549 −1.03350
\(126\) −1.32288 + 2.29129i −0.117851 + 0.204124i
\(127\) 0.0138109 0.00122552 0.000612760 1.00000i \(-0.499805\pi\)
0.000612760 1.00000i \(0.499805\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 1.00000 + 1.73205i 0.0880451 + 0.152499i
\(130\) 4.69609 + 8.13386i 0.411874 + 0.713387i
\(131\) 7.24807 12.5540i 0.633267 1.09685i −0.353612 0.935392i \(-0.615047\pi\)
0.986879 0.161459i \(-0.0516199\pi\)
\(132\) −5.70448 −0.496511
\(133\) −8.97484 −0.778217
\(134\) −15.4090 −1.33113
\(135\) 0.739514 1.28088i 0.0636473 0.110240i
\(136\) −2.06239 3.57216i −0.176848 0.306311i
\(137\) −4.01206 6.94908i −0.342773 0.593700i 0.642174 0.766559i \(-0.278033\pi\)
−0.984947 + 0.172859i \(0.944700\pi\)
\(138\) −0.500000 + 0.866025i −0.0425628 + 0.0737210i
\(139\) 14.2214 1.20625 0.603123 0.797648i \(-0.293923\pi\)
0.603123 + 0.797648i \(0.293923\pi\)
\(140\) 1.95657 + 3.38888i 0.165360 + 0.286413i
\(141\) −10.2214 −0.860800
\(142\) 4.93560 8.54871i 0.414186 0.717392i
\(143\) −18.1124 31.3715i −1.51463 2.62342i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −1.76905 + 3.06408i −0.146911 + 0.254458i
\(146\) −8.92993 −0.739046
\(147\) −7.00000 −0.577350
\(148\) 8.35023 0.686385
\(149\) 11.6417 20.1641i 0.953728 1.65190i 0.216475 0.976288i \(-0.430544\pi\)
0.737253 0.675617i \(-0.236123\pi\)
\(150\) 1.40624 + 2.43567i 0.114819 + 0.198872i
\(151\) 3.00691 + 5.20811i 0.244698 + 0.423830i 0.962047 0.272884i \(-0.0879777\pi\)
−0.717348 + 0.696715i \(0.754644\pi\)
\(152\) 1.69609 2.93771i 0.137571 0.238279i
\(153\) −4.12478 −0.333469
\(154\) −7.54631 13.0706i −0.608099 1.05326i
\(155\) −11.5549 −0.928110
\(156\) 3.17511 5.49946i 0.254213 0.440309i
\(157\) 8.93359 + 15.4734i 0.712978 + 1.23491i 0.963734 + 0.266864i \(0.0859875\pi\)
−0.250756 + 0.968050i \(0.580679\pi\)
\(158\) −6.71505 11.6308i −0.534220 0.925297i
\(159\) 0.260486 0.451174i 0.0206579 0.0357804i
\(160\) −1.47903 −0.116927
\(161\) −2.64575 −0.208514
\(162\) −1.00000 −0.0785674
\(163\) −6.93560 + 12.0128i −0.543238 + 0.940916i 0.455477 + 0.890247i \(0.349469\pi\)
−0.998716 + 0.0506687i \(0.983865\pi\)
\(164\) −3.69609 6.40181i −0.288616 0.499897i
\(165\) 4.21854 + 7.30673i 0.328413 + 0.568828i
\(166\) −4.61071 + 7.98599i −0.357861 + 0.619833i
\(167\) 5.07551 0.392755 0.196377 0.980528i \(-0.437082\pi\)
0.196377 + 0.980528i \(0.437082\pi\)
\(168\) 1.32288 2.29129i 0.102062 0.176777i
\(169\) 27.3254 2.10195
\(170\) −3.05033 + 5.28333i −0.233950 + 0.405213i
\(171\) −1.69609 2.93771i −0.129703 0.224652i
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) −1.46496 + 2.53739i −0.111379 + 0.192914i −0.916327 0.400432i \(-0.868860\pi\)
0.804947 + 0.593346i \(0.202193\pi\)
\(174\) 2.39217 0.181350
\(175\) −3.72055 + 6.44419i −0.281247 + 0.487135i
\(176\) 5.70448 0.429991
\(177\) 3.68918 6.38985i 0.277296 0.480290i
\(178\) −3.21706 5.57211i −0.241129 0.417647i
\(179\) 3.97187 + 6.87948i 0.296871 + 0.514196i 0.975418 0.220361i \(-0.0707234\pi\)
−0.678547 + 0.734557i \(0.737390\pi\)
\(180\) −0.739514 + 1.28088i −0.0551201 + 0.0954709i
\(181\) −7.39950 −0.550000 −0.275000 0.961444i \(-0.588678\pi\)
−0.275000 + 0.961444i \(0.588678\pi\)
\(182\) 16.8011 1.24538
\(183\) 5.04194 0.372711
\(184\) 0.500000 0.866025i 0.0368605 0.0638442i
\(185\) −6.17511 10.6956i −0.454003 0.786357i
\(186\) 3.90624 + 6.76580i 0.286419 + 0.496093i
\(187\) 11.7649 20.3773i 0.860332 1.49014i
\(188\) 10.2214 0.745474
\(189\) −1.32288 2.29129i −0.0962250 0.166667i
\(190\) −5.01712 −0.363980
\(191\) −10.0883 + 17.4734i −0.729961 + 1.26433i 0.226939 + 0.973909i \(0.427128\pi\)
−0.956899 + 0.290420i \(0.906205\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −6.44399 11.1613i −0.463849 0.803409i 0.535300 0.844662i \(-0.320199\pi\)
−0.999149 + 0.0412525i \(0.986865\pi\)
\(194\) −5.18202 + 8.97552i −0.372047 + 0.644405i
\(195\) −9.39217 −0.672587
\(196\) 7.00000 0.500000
\(197\) −9.80410 −0.698513 −0.349257 0.937027i \(-0.613566\pi\)
−0.349257 + 0.937027i \(0.613566\pi\)
\(198\) 2.85224 4.94022i 0.202700 0.351086i
\(199\) −1.65781 2.87141i −0.117519 0.203549i 0.801265 0.598310i \(-0.204161\pi\)
−0.918784 + 0.394761i \(0.870827\pi\)
\(200\) −1.40624 2.43567i −0.0994360 0.172228i
\(201\) 7.70448 13.3445i 0.543432 0.941252i
\(202\) −2.81247 −0.197885
\(203\) 3.16454 + 5.48115i 0.222108 + 0.384702i
\(204\) 4.12478 0.288792
\(205\) −5.46662 + 9.46846i −0.381805 + 0.661306i
\(206\) −6.27945 10.8763i −0.437510 0.757789i
\(207\) −0.500000 0.866025i −0.0347524 0.0601929i
\(208\) −3.17511 + 5.49946i −0.220155 + 0.381319i
\(209\) 19.3506 1.33851
\(210\) −3.91314 −0.270032
\(211\) −17.9638 −1.23668 −0.618340 0.785910i \(-0.712195\pi\)
−0.618340 + 0.785910i \(0.712195\pi\)
\(212\) −0.260486 + 0.451174i −0.0178902 + 0.0309868i
\(213\) 4.93560 + 8.54871i 0.338182 + 0.585748i
\(214\) −2.61071 4.52189i −0.178465 0.309110i
\(215\) −1.47903 + 2.56175i −0.100869 + 0.174710i
\(216\) 1.00000 0.0680414
\(217\) −10.3349 + 17.9006i −0.701581 + 1.21517i
\(218\) 8.47501 0.574000
\(219\) 4.46496 7.73354i 0.301714 0.522584i
\(220\) −4.21854 7.30673i −0.284414 0.492620i
\(221\) 13.0966 + 22.6841i 0.880976 + 1.52590i
\(222\) −4.17511 + 7.23151i −0.280215 + 0.485347i
\(223\) −1.22947 −0.0823313 −0.0411657 0.999152i \(-0.513107\pi\)
−0.0411657 + 0.999152i \(0.513107\pi\)
\(224\) −1.32288 + 2.29129i −0.0883883 + 0.153093i
\(225\) −2.81247 −0.187498
\(226\) 0.362641 0.628112i 0.0241225 0.0417814i
\(227\) −8.20649 14.2141i −0.544684 0.943420i −0.998627 0.0523891i \(-0.983316\pi\)
0.453943 0.891031i \(-0.350017\pi\)
\(228\) 1.69609 + 2.93771i 0.112326 + 0.194554i
\(229\) 12.7081 22.0111i 0.839778 1.45454i −0.0503028 0.998734i \(-0.516019\pi\)
0.890080 0.455803i \(-0.150648\pi\)
\(230\) −1.47903 −0.0975243
\(231\) 15.0926 0.993022
\(232\) −2.39217 −0.157054
\(233\) −0.275783 + 0.477670i −0.0180671 + 0.0312932i −0.874918 0.484272i \(-0.839085\pi\)
0.856850 + 0.515565i \(0.172418\pi\)
\(234\) 3.17511 + 5.49946i 0.207564 + 0.359511i
\(235\) −7.55889 13.0924i −0.493088 0.854053i
\(236\) −3.68918 + 6.38985i −0.240145 + 0.415944i
\(237\) 13.4301 0.872378
\(238\) 5.45657 + 9.45106i 0.353697 + 0.612621i
\(239\) −11.2634 −0.728567 −0.364283 0.931288i \(-0.618686\pi\)
−0.364283 + 0.931288i \(0.618686\pi\)
\(240\) 0.739514 1.28088i 0.0477354 0.0826802i
\(241\) 14.1642 + 24.5331i 0.912396 + 1.58032i 0.810670 + 0.585503i \(0.199103\pi\)
0.101725 + 0.994813i \(0.467564\pi\)
\(242\) 10.7705 + 18.6551i 0.692356 + 1.19920i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −5.04194 −0.322777
\(245\) −5.17660 8.96614i −0.330721 0.572825i
\(246\) 7.39217 0.471308
\(247\) −10.7705 + 18.6551i −0.685313 + 1.18700i
\(248\) −3.90624 6.76580i −0.248046 0.429629i
\(249\) −4.61071 7.98599i −0.292192 0.506092i
\(250\) −5.77744 + 10.0068i −0.365397 + 0.632886i
\(251\) −7.83659 −0.494641 −0.247320 0.968934i \(-0.579550\pi\)
−0.247320 + 0.968934i \(0.579550\pi\)
\(252\) 1.32288 + 2.29129i 0.0833333 + 0.144338i
\(253\) 5.70448 0.358637
\(254\) 0.00690545 0.0119606i 0.000433287 0.000750475i
\(255\) −3.05033 5.28333i −0.191019 0.330855i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −1.86281 + 3.22648i −0.116199 + 0.201262i −0.918258 0.395982i \(-0.870404\pi\)
0.802060 + 0.597244i \(0.203738\pi\)
\(258\) 2.00000 0.124515
\(259\) −22.0926 −1.37277
\(260\) 9.39217 0.582478
\(261\) −1.19609 + 2.07168i −0.0740358 + 0.128234i
\(262\) −7.24807 12.5540i −0.447787 0.775591i
\(263\) −14.4331 24.9988i −0.889981 1.54149i −0.839896 0.542747i \(-0.817384\pi\)
−0.0500850 0.998745i \(-0.515949\pi\)
\(264\) −2.85224 + 4.94022i −0.175543 + 0.304050i
\(265\) 0.770531 0.0473334
\(266\) −4.48742 + 7.77244i −0.275141 + 0.476559i
\(267\) 6.43411 0.393761
\(268\) −7.70448 + 13.3445i −0.470626 + 0.815148i
\(269\) 0.241001 + 0.417426i 0.0146941 + 0.0254509i 0.873279 0.487221i \(-0.161989\pi\)
−0.858585 + 0.512671i \(0.828656\pi\)
\(270\) −0.739514 1.28088i −0.0450054 0.0779517i
\(271\) 2.44801 4.24008i 0.148706 0.257567i −0.782043 0.623224i \(-0.785822\pi\)
0.930750 + 0.365657i \(0.119156\pi\)
\(272\) −4.12478 −0.250102
\(273\) −8.40056 + 14.5502i −0.508425 + 0.880618i
\(274\) −8.02411 −0.484754
\(275\) 8.02185 13.8942i 0.483736 0.837855i
\(276\) 0.500000 + 0.866025i 0.0300965 + 0.0521286i
\(277\) −7.76320 13.4463i −0.466446 0.807908i 0.532820 0.846229i \(-0.321132\pi\)
−0.999265 + 0.0383211i \(0.987799\pi\)
\(278\) 7.11071 12.3161i 0.426472 0.738672i
\(279\) −7.81247 −0.467721
\(280\) 3.91314 0.233855
\(281\) 13.2003 0.787463 0.393732 0.919225i \(-0.371184\pi\)
0.393732 + 0.919225i \(0.371184\pi\)
\(282\) −5.11071 + 8.85202i −0.304339 + 0.527130i
\(283\) 1.37836 + 2.38739i 0.0819350 + 0.141916i 0.904081 0.427361i \(-0.140557\pi\)
−0.822146 + 0.569277i \(0.807223\pi\)
\(284\) −4.93560 8.54871i −0.292874 0.507273i
\(285\) 2.50856 4.34495i 0.148594 0.257373i
\(286\) −36.2247 −2.14201
\(287\) 9.77892 + 16.9376i 0.577232 + 0.999794i
\(288\) −1.00000 −0.0589256
\(289\) −0.00690545 + 0.0119606i −0.000406203 + 0.000703565i
\(290\) 1.76905 + 3.06408i 0.103882 + 0.179929i
\(291\) −5.18202 8.97552i −0.303775 0.526154i
\(292\) −4.46496 + 7.73354i −0.261292 + 0.452571i
\(293\) 0.0976957 0.00570745 0.00285372 0.999996i \(-0.499092\pi\)
0.00285372 + 0.999996i \(0.499092\pi\)
\(294\) −3.50000 + 6.06218i −0.204124 + 0.353553i
\(295\) 10.9128 0.635368
\(296\) 4.17511 7.23151i 0.242674 0.420323i
\(297\) 2.85224 + 4.94022i 0.165504 + 0.286661i
\(298\) −11.6417 20.1641i −0.674387 1.16807i
\(299\) −3.17511 + 5.49946i −0.183622 + 0.318042i
\(300\) 2.81247 0.162378
\(301\) 2.64575 + 4.58258i 0.152499 + 0.264135i
\(302\) 6.01381 0.346056
\(303\) 1.40624 2.43567i 0.0807862 0.139926i
\(304\) −1.69609 2.93771i −0.0972772 0.168489i
\(305\) 3.72859 + 6.45811i 0.213498 + 0.369790i
\(306\) −2.06239 + 3.57216i −0.117899 + 0.204207i
\(307\) −24.9467 −1.42378 −0.711892 0.702289i \(-0.752161\pi\)
−0.711892 + 0.702289i \(0.752161\pi\)
\(308\) −15.0926 −0.859982
\(309\) 12.5589 0.714450
\(310\) −5.77744 + 10.0068i −0.328136 + 0.568349i
\(311\) −13.2439 22.9391i −0.750992 1.30076i −0.947342 0.320222i \(-0.896242\pi\)
0.196351 0.980534i \(-0.437091\pi\)
\(312\) −3.17511 5.49946i −0.179755 0.311346i
\(313\) 9.61911 16.6608i 0.543704 0.941723i −0.454983 0.890500i \(-0.650355\pi\)
0.998687 0.0512230i \(-0.0163119\pi\)
\(314\) 17.8672 1.00830
\(315\) 1.95657 3.38888i 0.110240 0.190942i
\(316\) −13.4301 −0.755502
\(317\) −12.6892 + 21.9783i −0.712695 + 1.23442i 0.251146 + 0.967949i \(0.419192\pi\)
−0.963842 + 0.266475i \(0.914141\pi\)
\(318\) −0.260486 0.451174i −0.0146073 0.0253006i
\(319\) −6.82304 11.8179i −0.382017 0.661673i
\(320\) −0.739514 + 1.28088i −0.0413401 + 0.0716032i
\(321\) 5.22143 0.291432
\(322\) −1.32288 + 2.29129i −0.0737210 + 0.127688i
\(323\) −13.9920 −0.778533
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 8.92993 + 15.4671i 0.495343 + 0.857960i
\(326\) 6.93560 + 12.0128i 0.384127 + 0.665328i
\(327\) −4.23750 + 7.33957i −0.234335 + 0.405879i
\(328\) −7.39217 −0.408164
\(329\) −27.0434 −1.49095
\(330\) 8.43709 0.464446
\(331\) −1.42137 + 2.46188i −0.0781254 + 0.135317i −0.902441 0.430813i \(-0.858227\pi\)
0.824316 + 0.566130i \(0.191560\pi\)
\(332\) 4.61071 + 7.98599i 0.253046 + 0.438288i
\(333\) −4.17511 7.23151i −0.228795 0.396284i
\(334\) 2.53775 4.39552i 0.138860 0.240512i
\(335\) 22.7903 1.24517
\(336\) −1.32288 2.29129i −0.0721688 0.125000i
\(337\) 26.7793 1.45876 0.729380 0.684109i \(-0.239809\pi\)
0.729380 + 0.684109i \(0.239809\pi\)
\(338\) 13.6627 23.6645i 0.743153 1.28718i
\(339\) 0.362641 + 0.628112i 0.0196959 + 0.0341144i
\(340\) 3.05033 + 5.28333i 0.165428 + 0.286529i
\(341\) 22.2830 38.5954i 1.20669 2.09006i
\(342\) −3.39217 −0.183428
\(343\) −18.5203 −1.00000
\(344\) −2.00000 −0.107833
\(345\) 0.739514 1.28088i 0.0398141 0.0689601i
\(346\) 1.46496 + 2.53739i 0.0787569 + 0.136411i
\(347\) 2.81247 + 4.87135i 0.150982 + 0.261508i 0.931589 0.363514i \(-0.118423\pi\)
−0.780607 + 0.625022i \(0.785090\pi\)
\(348\) 1.19609 2.07168i 0.0641169 0.111054i
\(349\) 20.8011 1.11346 0.556729 0.830694i \(-0.312056\pi\)
0.556729 + 0.830694i \(0.312056\pi\)
\(350\) 3.72055 + 6.44419i 0.198872 + 0.344456i
\(351\) −6.35023 −0.338950
\(352\) 2.85224 4.94022i 0.152025 0.263315i
\(353\) 17.3546 + 30.0591i 0.923692 + 1.59988i 0.793651 + 0.608373i \(0.208178\pi\)
0.130041 + 0.991509i \(0.458489\pi\)
\(354\) −3.68918 6.38985i −0.196078 0.339617i
\(355\) −7.29989 + 12.6438i −0.387438 + 0.671063i
\(356\) −6.43411 −0.341007
\(357\) −10.9131 −0.577585
\(358\) 7.94374 0.419840
\(359\) 2.89200 5.00910i 0.152634 0.264370i −0.779561 0.626326i \(-0.784558\pi\)
0.932195 + 0.361956i \(0.117891\pi\)
\(360\) 0.739514 + 1.28088i 0.0389758 + 0.0675081i
\(361\) 3.74659 + 6.48928i 0.197189 + 0.341541i
\(362\) −3.69975 + 6.40815i −0.194455 + 0.336805i
\(363\) −21.5411 −1.13061
\(364\) 8.40056 14.5502i 0.440309 0.762638i
\(365\) 13.2076 0.691318
\(366\) 2.52097 4.36645i 0.131773 0.228238i
\(367\) −0.334931 0.580118i −0.0174833 0.0302819i 0.857151 0.515065i \(-0.172232\pi\)
−0.874635 + 0.484783i \(0.838899\pi\)
\(368\) −0.500000 0.866025i −0.0260643 0.0451447i
\(369\) −3.69609 + 6.40181i −0.192411 + 0.333265i
\(370\) −12.3502 −0.642058
\(371\) 0.689180 1.19369i 0.0357804 0.0619736i
\(372\) 7.81247 0.405058
\(373\) 4.90004 8.48712i 0.253714 0.439446i −0.710831 0.703363i \(-0.751681\pi\)
0.964546 + 0.263916i \(0.0850143\pi\)
\(374\) −11.7649 20.3773i −0.608346 1.05369i
\(375\) −5.77744 10.0068i −0.298346 0.516750i
\(376\) 5.11071 8.85202i 0.263565 0.456508i
\(377\) 15.1908 0.782368
\(378\) −2.64575 −0.136083
\(379\) −0.742065 −0.0381173 −0.0190587 0.999818i \(-0.506067\pi\)
−0.0190587 + 0.999818i \(0.506067\pi\)
\(380\) −2.50856 + 4.34495i −0.128686 + 0.222891i
\(381\) 0.00690545 + 0.0119606i 0.000353777 + 0.000612760i
\(382\) 10.0883 + 17.4734i 0.516160 + 0.894016i
\(383\) −15.2057 + 26.3371i −0.776975 + 1.34576i 0.156702 + 0.987646i \(0.449914\pi\)
−0.933677 + 0.358115i \(0.883420\pi\)
\(384\) 1.00000 0.0510310
\(385\) 11.1612 + 19.3318i 0.568828 + 0.985239i
\(386\) −12.8880 −0.655981
\(387\) −1.00000 + 1.73205i −0.0508329 + 0.0880451i
\(388\) 5.18202 + 8.97552i 0.263077 + 0.455663i
\(389\) 0.337465 + 0.584506i 0.0171102 + 0.0296357i 0.874454 0.485109i \(-0.161220\pi\)
−0.857344 + 0.514745i \(0.827887\pi\)
\(390\) −4.69609 + 8.13386i −0.237796 + 0.411874i
\(391\) −4.12478 −0.208599
\(392\) 3.50000 6.06218i 0.176777 0.306186i
\(393\) 14.4961 0.731234
\(394\) −4.90205 + 8.49060i −0.246962 + 0.427750i
\(395\) 9.93175 + 17.2023i 0.499720 + 0.865541i
\(396\) −2.85224 4.94022i −0.143330 0.248256i
\(397\) −4.21304 + 7.29719i −0.211446 + 0.366236i −0.952167 0.305577i \(-0.901151\pi\)
0.740721 + 0.671813i \(0.234484\pi\)
\(398\) −3.31561 −0.166197
\(399\) −4.48742 7.77244i −0.224652 0.389109i
\(400\) −2.81247 −0.140624
\(401\) −17.5596 + 30.4141i −0.876885 + 1.51881i −0.0221432 + 0.999755i \(0.507049\pi\)
−0.854741 + 0.519054i \(0.826284\pi\)
\(402\) −7.70448 13.3445i −0.384264 0.665565i
\(403\) 24.8055 + 42.9644i 1.23565 + 2.14021i
\(404\) −1.40624 + 2.43567i −0.0699629 + 0.121179i
\(405\) 1.47903 0.0734935
\(406\) 6.32909 0.314107
\(407\) 47.6337 2.36111
\(408\) 2.06239 3.57216i 0.102104 0.176848i
\(409\) −9.86404 17.0850i −0.487745 0.844800i 0.512155 0.858893i \(-0.328847\pi\)
−0.999901 + 0.0140931i \(0.995514\pi\)
\(410\) 5.46662 + 9.46846i 0.269977 + 0.467614i
\(411\) 4.01206 6.94908i 0.197900 0.342773i
\(412\) −12.5589 −0.618732
\(413\) 9.76065 16.9059i 0.480290 0.831887i
\(414\) −1.00000 −0.0491473
\(415\) 6.81938 11.8115i 0.334750 0.579804i
\(416\) 3.17511 + 5.49946i 0.155673 + 0.269633i
\(417\) 7.11071 + 12.3161i 0.348213 + 0.603123i
\(418\) 9.67528 16.7581i 0.473234 0.819664i
\(419\) 7.26739 0.355035 0.177518 0.984118i \(-0.443193\pi\)
0.177518 + 0.984118i \(0.443193\pi\)
\(420\) −1.95657 + 3.38888i −0.0954709 + 0.165360i
\(421\) 3.82277 0.186311 0.0931553 0.995652i \(-0.470305\pi\)
0.0931553 + 0.995652i \(0.470305\pi\)
\(422\) −8.98191 + 15.5571i −0.437233 + 0.757309i
\(423\) −5.11071 8.85202i −0.248491 0.430400i
\(424\) 0.260486 + 0.451174i 0.0126503 + 0.0219110i
\(425\) −5.80042 + 10.0466i −0.281362 + 0.487333i
\(426\) 9.87120 0.478261
\(427\) 13.3397 0.645555
\(428\) −5.22143 −0.252387
\(429\) 18.1124 31.3715i 0.874473 1.51463i
\(430\) 1.47903 + 2.56175i 0.0713251 + 0.123539i
\(431\) 0.986189 + 1.70813i 0.0475031 + 0.0822777i 0.888799 0.458297i \(-0.151540\pi\)
−0.841296 + 0.540574i \(0.818207\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −31.3929 −1.50865 −0.754323 0.656504i \(-0.772035\pi\)
−0.754323 + 0.656504i \(0.772035\pi\)
\(434\) 10.3349 + 17.9006i 0.496093 + 0.859258i
\(435\) −3.53809 −0.169638
\(436\) 4.23750 7.33957i 0.202940 0.351502i
\(437\) −1.69609 2.93771i −0.0811348 0.140530i
\(438\) −4.46496 7.73354i −0.213344 0.369523i
\(439\) 17.8603 30.9349i 0.852424 1.47644i −0.0265896 0.999646i \(-0.508465\pi\)
0.879014 0.476796i \(-0.158202\pi\)
\(440\) −8.43709 −0.402222
\(441\) −3.50000 6.06218i −0.166667 0.288675i
\(442\) 26.1933 1.24589
\(443\) 0.0572397 0.0991421i 0.00271954 0.00471038i −0.864662 0.502353i \(-0.832468\pi\)
0.867382 + 0.497643i \(0.165801\pi\)
\(444\) 4.17511 + 7.23151i 0.198142 + 0.343192i
\(445\) 4.75812 + 8.24130i 0.225557 + 0.390675i
\(446\) −0.614734 + 1.06475i −0.0291085 + 0.0504174i
\(447\) 23.2835 1.10127
\(448\) 1.32288 + 2.29129i 0.0625000 + 0.108253i
\(449\) −9.26006 −0.437009 −0.218505 0.975836i \(-0.570118\pi\)
−0.218505 + 0.975836i \(0.570118\pi\)
\(450\) −1.40624 + 2.43567i −0.0662906 + 0.114819i
\(451\) −21.0842 36.5190i −0.992818 1.71961i
\(452\) −0.362641 0.628112i −0.0170572 0.0295439i
\(453\) −3.00691 + 5.20811i −0.141277 + 0.244698i
\(454\) −16.4130 −0.770299
\(455\) −24.8493 −1.16496
\(456\) 3.39217 0.158853
\(457\) −2.91865 + 5.05525i −0.136529 + 0.236475i −0.926180 0.377081i \(-0.876928\pi\)
0.789652 + 0.613555i \(0.210261\pi\)
\(458\) −12.7081 22.0111i −0.593812 1.02851i
\(459\) −2.06239 3.57216i −0.0962641 0.166734i
\(460\) −0.739514 + 1.28088i −0.0344800 + 0.0597212i
\(461\) 23.1660 1.07895 0.539474 0.842002i \(-0.318623\pi\)
0.539474 + 0.842002i \(0.318623\pi\)
\(462\) 7.54631 13.0706i 0.351086 0.608099i
\(463\) 0.140148 0.00651322 0.00325661 0.999995i \(-0.498963\pi\)
0.00325661 + 0.999995i \(0.498963\pi\)
\(464\) −1.19609 + 2.07168i −0.0555269 + 0.0961754i
\(465\) −5.77744 10.0068i −0.267922 0.464055i
\(466\) 0.275783 + 0.477670i 0.0127754 + 0.0221276i
\(467\) −7.75848 + 13.4381i −0.359019 + 0.621840i −0.987797 0.155745i \(-0.950222\pi\)
0.628778 + 0.777585i \(0.283555\pi\)
\(468\) 6.35023 0.293539
\(469\) 20.3841 35.3064i 0.941252 1.63030i
\(470\) −15.1178 −0.697332
\(471\) −8.93359 + 15.4734i −0.411638 + 0.712978i
\(472\) 3.68918 + 6.38985i 0.169808 + 0.294117i
\(473\) −5.70448 9.88044i −0.262292 0.454303i
\(474\) 6.71505 11.6308i 0.308432 0.534220i
\(475\) −9.54039 −0.437743
\(476\) 10.9131 0.500203
\(477\) 0.520971 0.0238536
\(478\) −5.63169 + 9.75437i −0.257587 + 0.446154i
\(479\) −7.69609 13.3300i −0.351643 0.609064i 0.634894 0.772599i \(-0.281044\pi\)
−0.986538 + 0.163535i \(0.947710\pi\)
\(480\) −0.739514 1.28088i −0.0337541 0.0584637i
\(481\) −26.5129 + 45.9217i −1.20889 + 2.09385i
\(482\) 28.3284 1.29032
\(483\) −1.32288 2.29129i −0.0601929 0.104257i
\(484\) 21.5411 0.979139
\(485\) 7.66436 13.2751i 0.348021 0.602789i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) 0.277269 + 0.480245i 0.0125643 + 0.0217620i 0.872239 0.489080i \(-0.162667\pi\)
−0.859675 + 0.510842i \(0.829334\pi\)
\(488\) −2.52097 + 4.36645i −0.114119 + 0.197660i
\(489\) −13.8712 −0.627277
\(490\) −10.3532 −0.467710
\(491\) 43.1966 1.94944 0.974718 0.223440i \(-0.0717286\pi\)
0.974718 + 0.223440i \(0.0717286\pi\)
\(492\) 3.69609 6.40181i 0.166632 0.288616i
\(493\) 4.93359 + 8.54523i 0.222198 + 0.384858i
\(494\) 10.7705 + 18.6551i 0.484589 + 0.839333i
\(495\) −4.21854 + 7.30673i −0.189609 + 0.328413i
\(496\) −7.81247 −0.350790
\(497\) 13.0584 + 22.6178i 0.585748 + 1.01455i
\(498\) −9.22143 −0.413222
\(499\) 10.4471 18.0950i 0.467678 0.810042i −0.531640 0.846970i \(-0.678424\pi\)
0.999318 + 0.0369286i \(0.0117574\pi\)
\(500\) 5.77744 + 10.0068i 0.258375 + 0.447518i
\(501\) 2.53775 + 4.39552i 0.113379 + 0.196377i
\(502\) −3.91829 + 6.78668i −0.174882 + 0.302904i
\(503\) −10.1657 −0.453265 −0.226633 0.973980i \(-0.572772\pi\)
−0.226633 + 0.973980i \(0.572772\pi\)
\(504\) 2.64575 0.117851
\(505\) 4.15973 0.185106
\(506\) 2.85224 4.94022i 0.126797 0.219620i
\(507\) 13.6627 + 23.6645i 0.606782 + 1.05098i
\(508\) −0.00690545 0.0119606i −0.000306380 0.000530666i
\(509\) 6.86595 11.8922i 0.304328 0.527111i −0.672784 0.739839i \(-0.734902\pi\)
0.977111 + 0.212728i \(0.0682348\pi\)
\(510\) −6.10067 −0.270142
\(511\) 11.8132 20.4610i 0.522584 0.905143i
\(512\) −1.00000 −0.0441942
\(513\) 1.69609 2.93771i 0.0748840 0.129703i
\(514\) 1.86281 + 3.22648i 0.0821649 + 0.142314i
\(515\) 9.28748 + 16.0864i 0.409255 + 0.708851i
\(516\) 1.00000 1.73205i 0.0440225 0.0762493i
\(517\) 58.3079 2.56438
\(518\) −11.0463 + 19.1328i −0.485347 + 0.840646i
\(519\) −2.92993 −0.128609
\(520\) 4.69609 8.13386i 0.205937 0.356693i
\(521\) 1.81247 + 3.13930i 0.0794059 + 0.137535i 0.902994 0.429654i \(-0.141364\pi\)
−0.823588 + 0.567189i \(0.808031\pi\)
\(522\) 1.19609 + 2.07168i 0.0523512 + 0.0906750i
\(523\) 14.4710 25.0645i 0.632772 1.09599i −0.354210 0.935166i \(-0.615250\pi\)
0.986982 0.160828i \(-0.0514164\pi\)
\(524\) −14.4961 −0.633267
\(525\) −7.44111 −0.324757
\(526\) −28.8661 −1.25862
\(527\) −16.1124 + 27.9074i −0.701866 + 1.21567i
\(528\) 2.85224 + 4.94022i 0.124128 + 0.214996i
\(529\) −0.500000 0.866025i −0.0217391 0.0376533i
\(530\) 0.385266 0.667300i 0.0167349 0.0289857i
\(531\) 7.37836 0.320194
\(532\) 4.48742 + 7.77244i 0.194554 + 0.336978i
\(533\) 46.9420 2.03328
\(534\) 3.21706 5.57211i 0.139216 0.241129i
\(535\) 3.86132 + 6.68801i 0.166939 + 0.289148i
\(536\) 7.70448 + 13.3445i 0.332783 + 0.576397i
\(537\) −3.97187 + 6.87948i −0.171399 + 0.296871i
\(538\) 0.482002 0.0207806
\(539\) 39.9313 1.71996
\(540\) −1.47903 −0.0636473
\(541\) 16.5086 28.5937i 0.709758 1.22934i −0.255188 0.966891i \(-0.582137\pi\)
0.964947 0.262446i \(-0.0845292\pi\)
\(542\) −2.44801 4.24008i −0.105151 0.182127i
\(543\) −3.69975 6.40815i −0.158771 0.275000i
\(544\) −2.06239 + 3.57216i −0.0884242 + 0.153155i
\(545\) −12.5348 −0.536931
\(546\) 8.40056 + 14.5502i 0.359511 + 0.622691i
\(547\) 36.6891 1.56871 0.784357 0.620310i \(-0.212993\pi\)
0.784357 + 0.620310i \(0.212993\pi\)
\(548\) −4.01206 + 6.94908i −0.171387 + 0.296850i
\(549\) 2.52097 + 4.36645i 0.107592 + 0.186356i
\(550\) −8.02185 13.8942i −0.342053 0.592453i
\(551\) −4.05733 + 7.02750i −0.172848 + 0.299381i
\(552\) 1.00000 0.0425628
\(553\) 35.5327 1.51100
\(554\) −15.5264 −0.659654
\(555\) 6.17511 10.6956i 0.262119 0.454003i
\(556\) −7.11071 12.3161i −0.301561 0.522320i
\(557\) −15.4681 26.7915i −0.655405 1.13519i −0.981792 0.189958i \(-0.939165\pi\)
0.326388 0.945236i \(-0.394169\pi\)
\(558\) −3.90624 + 6.76580i −0.165364 + 0.286419i
\(559\) 12.7005 0.537172
\(560\) 1.95657 3.38888i 0.0826802 0.143206i
\(561\) 23.5297 0.993425
\(562\) 6.60014 11.4318i 0.278410 0.482221i
\(563\) −0.276561 0.479018i −0.0116557 0.0201882i 0.860139 0.510060i \(-0.170377\pi\)
−0.871794 + 0.489872i \(0.837044\pi\)
\(564\) 5.11071 + 8.85202i 0.215200 + 0.372737i
\(565\) −0.536356 + 0.928996i −0.0225647 + 0.0390831i
\(566\) 2.75672 0.115874
\(567\) 1.32288 2.29129i 0.0555556 0.0962250i
\(568\) −9.87120 −0.414186
\(569\) −1.19083 + 2.06259i −0.0499224 + 0.0864681i −0.889907 0.456143i \(-0.849231\pi\)
0.839984 + 0.542611i \(0.182564\pi\)
\(570\) −2.50856 4.34495i −0.105072 0.181990i
\(571\) −13.2831 23.0070i −0.555881 0.962814i −0.997834 0.0657760i \(-0.979048\pi\)
0.441954 0.897038i \(-0.354286\pi\)
\(572\) −18.1124 + 31.3715i −0.757316 + 1.31171i
\(573\) −20.1765 −0.842886
\(574\) 19.5578 0.816329
\(575\) −2.81247 −0.117288
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 2.86158 + 4.95640i 0.119129 + 0.206337i 0.919423 0.393271i \(-0.128656\pi\)
−0.800294 + 0.599608i \(0.795323\pi\)
\(578\) 0.00690545 + 0.0119606i 0.000287229 + 0.000497495i
\(579\) 6.44399 11.1613i 0.267803 0.463849i
\(580\) 3.53809 0.146911
\(581\) −12.1988 21.1289i −0.506092 0.876576i
\(582\) −10.3640 −0.429603
\(583\) −1.48593 + 2.57371i −0.0615411 + 0.106592i
\(584\) 4.46496 + 7.73354i 0.184761 + 0.320016i
\(585\) −4.69609 8.13386i −0.194159 0.336294i
\(586\) 0.0488479 0.0846070i 0.00201789 0.00349508i
\(587\) 19.2323 0.793801 0.396900 0.917862i \(-0.370086\pi\)
0.396900 + 0.917862i \(0.370086\pi\)
\(588\) 3.50000 + 6.06218i 0.144338 + 0.250000i
\(589\) −26.5012 −1.09196
\(590\) 5.45640 9.45077i 0.224637 0.389082i
\(591\) −4.90205 8.49060i −0.201643 0.349257i
\(592\) −4.17511 7.23151i −0.171596 0.297213i
\(593\) 10.3429 17.9144i 0.424732 0.735657i −0.571663 0.820488i \(-0.693702\pi\)
0.996395 + 0.0848308i \(0.0270350\pi\)
\(594\) 5.70448 0.234058
\(595\) −8.07043 13.9784i −0.330855 0.573058i
\(596\) −23.2835 −0.953728
\(597\) 1.65781 2.87141i 0.0678495 0.117519i
\(598\) 3.17511 + 5.49946i 0.129840 + 0.224890i
\(599\) 9.80977 + 16.9910i 0.400816 + 0.694234i 0.993825 0.110962i \(-0.0353932\pi\)
−0.593008 + 0.805196i \(0.702060\pi\)
\(600\) 1.40624 2.43567i 0.0574094 0.0994360i
\(601\) −8.88798 −0.362548 −0.181274 0.983433i \(-0.558022\pi\)
−0.181274 + 0.983433i \(0.558022\pi\)
\(602\) 5.29150 0.215666
\(603\) 15.4090 0.627501
\(604\) 3.00691 5.20811i 0.122349 0.211915i
\(605\) −15.9299 27.5914i −0.647644 1.12175i
\(606\) −1.40624 2.43567i −0.0571245 0.0989425i
\(607\) 5.88945 10.2008i 0.239046 0.414039i −0.721395 0.692524i \(-0.756499\pi\)
0.960441 + 0.278485i \(0.0898321\pi\)
\(608\) −3.39217 −0.137571
\(609\) −3.16454 + 5.48115i −0.128234 + 0.222108i
\(610\) 7.45718 0.301932
\(611\) −32.4542 + 56.2123i −1.31296 + 2.27411i
\(612\) 2.06239 + 3.57216i 0.0833672 + 0.144396i
\(613\) −12.3593 21.4070i −0.499188 0.864619i 0.500812 0.865556i \(-0.333035\pi\)
−1.00000 0.000937480i \(0.999702\pi\)
\(614\) −12.4734 + 21.6045i −0.503384 + 0.871886i
\(615\) −10.9332 −0.440871
\(616\) −7.54631 + 13.0706i −0.304050 + 0.526629i
\(617\) −19.0580 −0.767247 −0.383623 0.923490i \(-0.625324\pi\)
−0.383623 + 0.923490i \(0.625324\pi\)
\(618\) 6.27945 10.8763i 0.252596 0.437510i
\(619\) 9.75481 + 16.8958i 0.392079 + 0.679101i 0.992724 0.120415i \(-0.0384227\pi\)
−0.600645 + 0.799516i \(0.705089\pi\)
\(620\) 5.77744 + 10.0068i 0.232027 + 0.401883i
\(621\) 0.500000 0.866025i 0.0200643 0.0347524i
\(622\) −26.4878 −1.06206
\(623\) 17.0231 0.682015
\(624\) −6.35023 −0.254213
\(625\) 1.51381 2.62200i 0.0605524 0.104880i
\(626\) −9.61911 16.6608i −0.384457 0.665899i
\(627\) 9.67528 + 16.7581i 0.386394 + 0.669253i
\(628\) 8.93359 15.4734i 0.356489 0.617457i
\(629\) −34.4429 −1.37333
\(630\) −1.95657 3.38888i −0.0779517 0.135016i
\(631\) −46.6443 −1.85688 −0.928441 0.371481i \(-0.878850\pi\)
−0.928441 + 0.371481i \(0.878850\pi\)
\(632\) −6.71505 + 11.6308i −0.267110 + 0.462648i
\(633\) −8.98191 15.5571i −0.356999 0.618340i
\(634\) 12.6892 + 21.9783i 0.503952 + 0.872870i
\(635\) −0.0102134 + 0.0176901i −0.000405305 + 0.000702009i
\(636\) −0.520971 −0.0206579
\(637\) −22.2258 + 38.4962i −0.880618 + 1.52528i
\(638\) −13.6461 −0.540254
\(639\) −4.93560 + 8.54871i −0.195249 + 0.338182i
\(640\) 0.739514 + 1.28088i 0.0292319 + 0.0506311i
\(641\) 13.2670 + 22.9792i 0.524016 + 0.907623i 0.999609 + 0.0279574i \(0.00890028\pi\)
−0.475593 + 0.879666i \(0.657766\pi\)
\(642\) 2.61071 4.52189i 0.103037 0.178465i
\(643\) 1.53826 0.0606632 0.0303316 0.999540i \(-0.490344\pi\)
0.0303316 + 0.999540i \(0.490344\pi\)
\(644\) 1.32288 + 2.29129i 0.0521286 + 0.0902894i
\(645\) −2.95806 −0.116473
\(646\) −6.99598 + 12.1174i −0.275253 + 0.476752i
\(647\) −18.5310 32.0967i −0.728529 1.26185i −0.957505 0.288418i \(-0.906871\pi\)
0.228975 0.973432i \(-0.426463\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −21.0448 + 36.4507i −0.826082 + 1.43082i
\(650\) 17.8599 0.700521
\(651\) −20.6699 −0.810116
\(652\) 13.8712 0.543238
\(653\) −4.09542 + 7.09347i −0.160266 + 0.277589i −0.934964 0.354742i \(-0.884569\pi\)
0.774698 + 0.632331i \(0.217902\pi\)
\(654\) 4.23750 + 7.33957i 0.165700 + 0.287000i
\(655\) 10.7201 + 18.5678i 0.418869 + 0.725503i
\(656\) −3.69609 + 6.40181i −0.144308 + 0.249949i
\(657\) 8.92993 0.348390
\(658\) −13.5217 + 23.4202i −0.527130 + 0.913016i
\(659\) 24.2174 0.943376 0.471688 0.881765i \(-0.343645\pi\)
0.471688 + 0.881765i \(0.343645\pi\)
\(660\) 4.21854 7.30673i 0.164207 0.284414i
\(661\) 18.7964 + 32.5563i 0.731095 + 1.26629i 0.956416 + 0.292009i \(0.0943238\pi\)
−0.225320 + 0.974285i \(0.572343\pi\)
\(662\) 1.42137 + 2.46188i 0.0552430 + 0.0956837i
\(663\) −13.0966 + 22.6841i −0.508632 + 0.880976i
\(664\) 9.22143 0.357861
\(665\) 6.63702 11.4957i 0.257373 0.445783i
\(666\) −8.35023 −0.323565
\(667\) −1.19609 + 2.07168i −0.0463126 + 0.0802158i
\(668\) −2.53775 4.39552i −0.0981887 0.170068i
\(669\) −0.614734 1.06475i −0.0237670 0.0411657i
\(670\) 11.3951 19.7370i 0.440233 0.762506i
\(671\) −28.7616 −1.11033
\(672\) −2.64575 −0.102062
\(673\) 4.15939 0.160333 0.0801664 0.996781i \(-0.474455\pi\)
0.0801664 + 0.996781i \(0.474455\pi\)
\(674\) 13.3896 23.1915i 0.515750 0.893304i
\(675\) −1.40624 2.43567i −0.0541261 0.0937491i
\(676\) −13.6627 23.6645i −0.525489 0.910173i
\(677\) −6.17258 + 10.6912i −0.237232 + 0.410897i −0.959919 0.280278i \(-0.909573\pi\)
0.722687 + 0.691175i \(0.242907\pi\)
\(678\) 0.725281 0.0278543
\(679\) −13.7103 23.7470i −0.526154 0.911326i
\(680\) 6.10067 0.233950
\(681\) 8.20649 14.2141i 0.314473 0.544684i
\(682\) −22.2830 38.5954i −0.853262 1.47789i
\(683\) −20.5731 35.6337i −0.787209 1.36349i −0.927670 0.373401i \(-0.878192\pi\)
0.140461 0.990086i \(-0.455142\pi\)
\(684\) −1.69609 + 2.93771i −0.0648515 + 0.112326i
\(685\) 11.8679 0.453449
\(686\) −9.26013 + 16.0390i −0.353553 + 0.612372i
\(687\) 25.4163 0.969692
\(688\) −1.00000 + 1.73205i −0.0381246 + 0.0660338i
\(689\) −1.65414 2.86506i −0.0630178 0.109150i
\(690\) −0.739514 1.28088i −0.0281528 0.0487621i
\(691\) 3.08118 5.33677i 0.117214 0.203020i −0.801449 0.598063i \(-0.795937\pi\)
0.918663 + 0.395043i \(0.129270\pi\)
\(692\) 2.92993 0.111379
\(693\) 7.54631 + 13.0706i 0.286661 + 0.496511i
\(694\) 5.62495 0.213520
\(695\) −10.5170 + 18.2159i −0.398931 + 0.690968i
\(696\) −1.19609 2.07168i −0.0453375 0.0785269i
\(697\) 15.2455 + 26.4061i 0.577466 + 1.00020i
\(698\) 10.4006 18.0143i 0.393667 0.681851i
\(699\) −0.551566 −0.0208621
\(700\) 7.44111 0.281247
\(701\) −27.6447 −1.04413 −0.522063 0.852907i \(-0.674837\pi\)
−0.522063 + 0.852907i \(0.674837\pi\)
\(702\) −3.17511 + 5.49946i −0.119837 + 0.207564i
\(703\) −14.1627 24.5305i −0.534156 0.925186i
\(704\) −2.85224 4.94022i −0.107498 0.186192i
\(705\) 7.55889 13.0924i 0.284684 0.493088i
\(706\) 34.7092 1.30630
\(707\) 3.72055 6.44419i 0.139926 0.242359i
\(708\) −7.37836 −0.277296
\(709\) −12.6213 + 21.8607i −0.474002 + 0.820996i −0.999557 0.0297638i \(-0.990524\pi\)
0.525555 + 0.850760i \(0.323858\pi\)
\(710\) 7.29989 + 12.6438i 0.273960 + 0.474513i
\(711\) 6.71505 + 11.6308i 0.251834 + 0.436189i
\(712\) −3.21706 + 5.57211i −0.120564 + 0.208823i
\(713\) −7.81247 −0.292579
\(714\) −5.45657 + 9.45106i −0.204207 + 0.353697i
\(715\) 53.5774 2.00368
\(716\) 3.97187 6.87948i 0.148436 0.257098i
\(717\) −5.63169 9.75437i −0.210319 0.364283i
\(718\) −2.89200 5.00910i −0.107929 0.186938i
\(719\) −19.7038 + 34.1279i −0.734826 + 1.27276i 0.219973 + 0.975506i \(0.429403\pi\)
−0.954799 + 0.297251i \(0.903930\pi\)
\(720\) 1.47903 0.0551201
\(721\) 33.2277 1.23746
\(722\) 7.49317 0.278867
\(723\) −14.1642 + 24.5331i −0.526772 + 0.912396i
\(724\) 3.69975 + 6.40815i 0.137500 + 0.238157i
\(725\) 3.36396 + 5.82655i 0.124934 + 0.216393i
\(726\) −10.7705 + 18.6551i −0.399732 + 0.692356i
\(727\) 33.9963 1.26085 0.630427 0.776248i \(-0.282880\pi\)
0.630427 + 0.776248i \(0.282880\pi\)
\(728\) −8.40056 14.5502i −0.311346 0.539266i
\(729\) 1.00000 0.0370370
\(730\) 6.60381 11.4381i 0.244418 0.423344i
\(731\) 4.12478 + 7.14433i 0.152561 + 0.264243i
\(732\) −2.52097 4.36645i −0.0931778 0.161389i
\(733\) 1.24590 2.15796i 0.0460182 0.0797059i −0.842099 0.539323i \(-0.818680\pi\)
0.888117 + 0.459617i \(0.152013\pi\)
\(734\) −0.669863 −0.0247251
\(735\) 5.17660 8.96614i 0.190942 0.330721i
\(736\) −1.00000 −0.0368605
\(737\) −43.9500 + 76.1237i −1.61892 + 2.80405i
\(738\) 3.69609 + 6.40181i 0.136055 + 0.235654i
\(739\) −23.6488 40.9609i −0.869935 1.50677i −0.862062 0.506803i \(-0.830827\pi\)
−0.00787354 0.999969i \(-0.502506\pi\)
\(740\) −6.17511 + 10.6956i −0.227002 + 0.393179i
\(741\) −21.5411 −0.791331
\(742\) −0.689180 1.19369i −0.0253006 0.0438219i
\(743\) 44.5435 1.63414 0.817072 0.576536i \(-0.195596\pi\)
0.817072 + 0.576536i \(0.195596\pi\)
\(744\) 3.90624 6.76580i 0.143210 0.248046i
\(745\) 17.2185 + 29.8232i 0.630835 + 1.09264i
\(746\) −4.90004 8.48712i −0.179403 0.310735i
\(747\) 4.61071 7.98599i 0.168697 0.292192i
\(748\) −23.5297 −0.860332
\(749\) 13.8146 0.504775
\(750\) −11.5549 −0.421924
\(751\) 6.75523 11.7004i 0.246502 0.426954i −0.716051 0.698048i \(-0.754052\pi\)
0.962553 + 0.271094i \(0.0873855\pi\)
\(752\) −5.11071 8.85202i −0.186369 0.322800i
\(753\) −3.91829 6.78668i −0.142791 0.247320i
\(754\) 7.59542 13.1556i 0.276609 0.479100i
\(755\) −8.89460 −0.323708
\(756\) −1.32288 + 2.29129i −0.0481125 + 0.0833333i
\(757\) −24.9895 −0.908259 −0.454129 0.890936i \(-0.650050\pi\)
−0.454129 + 0.890936i \(0.650050\pi\)
\(758\) −0.371032 + 0.642647i −0.0134765 + 0.0233420i
\(759\) 2.85224 + 4.94022i 0.103530 + 0.179319i
\(760\) 2.50856 + 4.34495i 0.0909950 + 0.157608i
\(761\) 1.26930 2.19849i 0.0460121 0.0796953i −0.842102 0.539318i \(-0.818682\pi\)
0.888114 + 0.459623i \(0.152015\pi\)
\(762\) 0.0138109 0.000500316
\(763\) −11.2114 + 19.4187i −0.405879 + 0.703004i
\(764\) 20.1765 0.729961
\(765\) 3.05033 5.28333i 0.110285 0.191019i
\(766\) 15.2057 + 26.3371i 0.549405 + 0.951597i
\(767\) −23.4271 40.5770i −0.845905 1.46515i
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) −7.59435 −0.273859 −0.136930 0.990581i \(-0.543723\pi\)
−0.136930 + 0.990581i \(0.543723\pi\)
\(770\) 22.3224 0.804445
\(771\) −3.72562 −0.134175
\(772\) −6.44399 + 11.1613i −0.231924 + 0.401705i
\(773\) 10.7843 + 18.6790i 0.387886 + 0.671838i 0.992165 0.124935i \(-0.0398721\pi\)
−0.604279 + 0.796773i \(0.706539\pi\)
\(774\) 1.00000 + 1.73205i 0.0359443 + 0.0622573i
\(775\) −10.9862 + 19.0286i −0.394636 + 0.683529i
\(776\) 10.3640 0.372047