Properties

Label 585.2.i.b.391.1
Level $585$
Weight $2$
Character 585.391
Analytic conductor $4.671$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 391.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 585.391
Dual form 585.2.i.b.196.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} -1.73205i q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.50000 - 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} +3.00000 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} -1.73205i q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.50000 - 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} +3.00000 q^{8} -3.00000 q^{9} +1.00000 q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.50000 - 0.866025i) q^{12} +(0.500000 - 0.866025i) q^{13} +(1.00000 - 1.73205i) q^{14} +(-1.50000 - 0.866025i) q^{15} +(0.500000 + 0.866025i) q^{16} +2.00000 q^{17} +(-1.50000 - 2.59808i) q^{18} -3.00000 q^{19} +(-0.500000 - 0.866025i) q^{20} +(-3.00000 + 1.73205i) q^{21} +(-0.500000 + 0.866025i) q^{22} -5.19615i q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{26} +5.19615i q^{27} -2.00000 q^{28} +(-2.50000 - 4.33013i) q^{29} -1.73205i q^{30} +(0.500000 - 0.866025i) q^{31} +(2.50000 - 4.33013i) q^{32} +(1.50000 - 0.866025i) q^{33} +(1.00000 + 1.73205i) q^{34} -2.00000 q^{35} +(-1.50000 + 2.59808i) q^{36} -5.00000 q^{37} +(-1.50000 - 2.59808i) q^{38} +(-1.50000 - 0.866025i) q^{39} +(1.50000 - 2.59808i) q^{40} +(-3.00000 - 1.73205i) q^{42} +(4.00000 + 6.92820i) q^{43} +1.00000 q^{44} +(-1.50000 + 2.59808i) q^{45} +(1.00000 + 1.73205i) q^{47} +(1.50000 - 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +(0.500000 - 0.866025i) q^{50} -3.46410i q^{51} +(-0.500000 - 0.866025i) q^{52} +14.0000 q^{53} +(-4.50000 + 2.59808i) q^{54} +1.00000 q^{55} +(-3.00000 - 5.19615i) q^{56} +5.19615i q^{57} +(2.50000 - 4.33013i) q^{58} +(4.50000 - 7.79423i) q^{59} +(-1.50000 + 0.866025i) q^{60} +(0.500000 + 0.866025i) q^{61} +1.00000 q^{62} +(3.00000 + 5.19615i) q^{63} +7.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +(1.50000 + 0.866025i) q^{66} +(-7.00000 + 12.1244i) q^{67} +(1.00000 - 1.73205i) q^{68} +(-1.00000 - 1.73205i) q^{70} -9.00000 q^{72} +6.00000 q^{73} +(-2.50000 - 4.33013i) q^{74} +(-1.50000 + 0.866025i) q^{75} +(-1.50000 + 2.59808i) q^{76} +(1.00000 - 1.73205i) q^{77} -1.73205i q^{78} +(6.00000 + 10.3923i) q^{79} +1.00000 q^{80} +9.00000 q^{81} +(5.00000 + 8.66025i) q^{83} +3.46410i q^{84} +(1.00000 - 1.73205i) q^{85} +(-4.00000 + 6.92820i) q^{86} +(-7.50000 + 4.33013i) q^{87} +(1.50000 + 2.59808i) q^{88} +2.00000 q^{89} -3.00000 q^{90} -2.00000 q^{91} +(-1.50000 - 0.866025i) q^{93} +(-1.00000 + 1.73205i) q^{94} +(-1.50000 + 2.59808i) q^{95} +(-7.50000 - 4.33013i) q^{96} +(-0.500000 - 0.866025i) q^{97} +3.00000 q^{98} +(-1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + q^{4} + q^{5} + 3 q^{6} - 2 q^{7} + 6 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + q^{4} + q^{5} + 3 q^{6} - 2 q^{7} + 6 q^{8} - 6 q^{9} + 2 q^{10} + q^{11} - 3 q^{12} + q^{13} + 2 q^{14} - 3 q^{15} + q^{16} + 4 q^{17} - 3 q^{18} - 6 q^{19} - q^{20} - 6 q^{21} - q^{22} - q^{25} + 2 q^{26} - 4 q^{28} - 5 q^{29} + q^{31} + 5 q^{32} + 3 q^{33} + 2 q^{34} - 4 q^{35} - 3 q^{36} - 10 q^{37} - 3 q^{38} - 3 q^{39} + 3 q^{40} - 6 q^{42} + 8 q^{43} + 2 q^{44} - 3 q^{45} + 2 q^{47} + 3 q^{48} + 3 q^{49} + q^{50} - q^{52} + 28 q^{53} - 9 q^{54} + 2 q^{55} - 6 q^{56} + 5 q^{58} + 9 q^{59} - 3 q^{60} + q^{61} + 2 q^{62} + 6 q^{63} + 14 q^{64} - q^{65} + 3 q^{66} - 14 q^{67} + 2 q^{68} - 2 q^{70} - 18 q^{72} + 12 q^{73} - 5 q^{74} - 3 q^{75} - 3 q^{76} + 2 q^{77} + 12 q^{79} + 2 q^{80} + 18 q^{81} + 10 q^{83} + 2 q^{85} - 8 q^{86} - 15 q^{87} + 3 q^{88} + 4 q^{89} - 6 q^{90} - 4 q^{91} - 3 q^{93} - 2 q^{94} - 3 q^{95} - 15 q^{96} - q^{97} + 6 q^{98} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i 0.986869 0.161521i \(-0.0516399\pi\)
−0.633316 + 0.773893i \(0.718307\pi\)
\(3\) 1.73205i 1.00000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 1.50000 0.866025i 0.612372 0.353553i
\(7\) −1.00000 1.73205i −0.377964 0.654654i 0.612801 0.790237i \(-0.290043\pi\)
−0.990766 + 0.135583i \(0.956709\pi\)
\(8\) 3.00000 1.06066
\(9\) −3.00000 −1.00000
\(10\) 1.00000 0.316228
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i 0.931505 0.363727i \(-0.118496\pi\)
−0.780750 + 0.624844i \(0.785163\pi\)
\(12\) −1.50000 0.866025i −0.433013 0.250000i
\(13\) 0.500000 0.866025i 0.138675 0.240192i
\(14\) 1.00000 1.73205i 0.267261 0.462910i
\(15\) −1.50000 0.866025i −0.387298 0.223607i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) −1.50000 2.59808i −0.353553 0.612372i
\(19\) −3.00000 −0.688247 −0.344124 0.938924i \(-0.611824\pi\)
−0.344124 + 0.938924i \(0.611824\pi\)
\(20\) −0.500000 0.866025i −0.111803 0.193649i
\(21\) −3.00000 + 1.73205i −0.654654 + 0.377964i
\(22\) −0.500000 + 0.866025i −0.106600 + 0.184637i
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 5.19615i 1.06066i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 1.00000 0.196116
\(27\) 5.19615i 1.00000i
\(28\) −2.00000 −0.377964
\(29\) −2.50000 4.33013i −0.464238 0.804084i 0.534928 0.844897i \(-0.320339\pi\)
−0.999167 + 0.0408130i \(0.987005\pi\)
\(30\) 1.73205i 0.316228i
\(31\) 0.500000 0.866025i 0.0898027 0.155543i −0.817625 0.575751i \(-0.804710\pi\)
0.907428 + 0.420208i \(0.138043\pi\)
\(32\) 2.50000 4.33013i 0.441942 0.765466i
\(33\) 1.50000 0.866025i 0.261116 0.150756i
\(34\) 1.00000 + 1.73205i 0.171499 + 0.297044i
\(35\) −2.00000 −0.338062
\(36\) −1.50000 + 2.59808i −0.250000 + 0.433013i
\(37\) −5.00000 −0.821995 −0.410997 0.911636i \(-0.634819\pi\)
−0.410997 + 0.911636i \(0.634819\pi\)
\(38\) −1.50000 2.59808i −0.243332 0.421464i
\(39\) −1.50000 0.866025i −0.240192 0.138675i
\(40\) 1.50000 2.59808i 0.237171 0.410792i
\(41\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(42\) −3.00000 1.73205i −0.462910 0.267261i
\(43\) 4.00000 + 6.92820i 0.609994 + 1.05654i 0.991241 + 0.132068i \(0.0421616\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) 1.00000 0.150756
\(45\) −1.50000 + 2.59808i −0.223607 + 0.387298i
\(46\) 0 0
\(47\) 1.00000 + 1.73205i 0.145865 + 0.252646i 0.929695 0.368329i \(-0.120070\pi\)
−0.783830 + 0.620975i \(0.786737\pi\)
\(48\) 1.50000 0.866025i 0.216506 0.125000i
\(49\) 1.50000 2.59808i 0.214286 0.371154i
\(50\) 0.500000 0.866025i 0.0707107 0.122474i
\(51\) 3.46410i 0.485071i
\(52\) −0.500000 0.866025i −0.0693375 0.120096i
\(53\) 14.0000 1.92305 0.961524 0.274721i \(-0.0885855\pi\)
0.961524 + 0.274721i \(0.0885855\pi\)
\(54\) −4.50000 + 2.59808i −0.612372 + 0.353553i
\(55\) 1.00000 0.134840
\(56\) −3.00000 5.19615i −0.400892 0.694365i
\(57\) 5.19615i 0.688247i
\(58\) 2.50000 4.33013i 0.328266 0.568574i
\(59\) 4.50000 7.79423i 0.585850 1.01472i −0.408919 0.912571i \(-0.634094\pi\)
0.994769 0.102151i \(-0.0325726\pi\)
\(60\) −1.50000 + 0.866025i −0.193649 + 0.111803i
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) 1.00000 0.127000
\(63\) 3.00000 + 5.19615i 0.377964 + 0.654654i
\(64\) 7.00000 0.875000
\(65\) −0.500000 0.866025i −0.0620174 0.107417i
\(66\) 1.50000 + 0.866025i 0.184637 + 0.106600i
\(67\) −7.00000 + 12.1244i −0.855186 + 1.48123i 0.0212861 + 0.999773i \(0.493224\pi\)
−0.876472 + 0.481452i \(0.840109\pi\)
\(68\) 1.00000 1.73205i 0.121268 0.210042i
\(69\) 0 0
\(70\) −1.00000 1.73205i −0.119523 0.207020i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) −9.00000 −1.06066
\(73\) 6.00000 0.702247 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) −2.50000 4.33013i −0.290619 0.503367i
\(75\) −1.50000 + 0.866025i −0.173205 + 0.100000i
\(76\) −1.50000 + 2.59808i −0.172062 + 0.298020i
\(77\) 1.00000 1.73205i 0.113961 0.197386i
\(78\) 1.73205i 0.196116i
\(79\) 6.00000 + 10.3923i 0.675053 + 1.16923i 0.976453 + 0.215728i \(0.0692125\pi\)
−0.301401 + 0.953498i \(0.597454\pi\)
\(80\) 1.00000 0.111803
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 5.00000 + 8.66025i 0.548821 + 0.950586i 0.998356 + 0.0573233i \(0.0182566\pi\)
−0.449534 + 0.893263i \(0.648410\pi\)
\(84\) 3.46410i 0.377964i
\(85\) 1.00000 1.73205i 0.108465 0.187867i
\(86\) −4.00000 + 6.92820i −0.431331 + 0.747087i
\(87\) −7.50000 + 4.33013i −0.804084 + 0.464238i
\(88\) 1.50000 + 2.59808i 0.159901 + 0.276956i
\(89\) 2.00000 0.212000 0.106000 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) −3.00000 −0.316228
\(91\) −2.00000 −0.209657
\(92\) 0 0
\(93\) −1.50000 0.866025i −0.155543 0.0898027i
\(94\) −1.00000 + 1.73205i −0.103142 + 0.178647i
\(95\) −1.50000 + 2.59808i −0.153897 + 0.266557i
\(96\) −7.50000 4.33013i −0.765466 0.441942i
\(97\) −0.500000 0.866025i −0.0507673 0.0879316i 0.839525 0.543321i \(-0.182833\pi\)
−0.890292 + 0.455389i \(0.849500\pi\)
\(98\) 3.00000 0.303046
\(99\) −1.50000 2.59808i −0.150756 0.261116i
\(100\) −1.00000 −0.100000
\(101\) −1.50000 2.59808i −0.149256 0.258518i 0.781697 0.623658i \(-0.214354\pi\)
−0.930953 + 0.365140i \(0.881021\pi\)
\(102\) 3.00000 1.73205i 0.297044 0.171499i
\(103\) 0.500000 0.866025i 0.0492665 0.0853320i −0.840341 0.542059i \(-0.817645\pi\)
0.889607 + 0.456727i \(0.150978\pi\)
\(104\) 1.50000 2.59808i 0.147087 0.254762i
\(105\) 3.46410i 0.338062i
\(106\) 7.00000 + 12.1244i 0.679900 + 1.17762i
\(107\) 19.0000 1.83680 0.918400 0.395654i \(-0.129482\pi\)
0.918400 + 0.395654i \(0.129482\pi\)
\(108\) 4.50000 + 2.59808i 0.433013 + 0.250000i
\(109\) −14.0000 −1.34096 −0.670478 0.741929i \(-0.733911\pi\)
−0.670478 + 0.741929i \(0.733911\pi\)
\(110\) 0.500000 + 0.866025i 0.0476731 + 0.0825723i
\(111\) 8.66025i 0.821995i
\(112\) 1.00000 1.73205i 0.0944911 0.163663i
\(113\) −5.00000 + 8.66025i −0.470360 + 0.814688i −0.999425 0.0338931i \(-0.989209\pi\)
0.529065 + 0.848581i \(0.322543\pi\)
\(114\) −4.50000 + 2.59808i −0.421464 + 0.243332i
\(115\) 0 0
\(116\) −5.00000 −0.464238
\(117\) −1.50000 + 2.59808i −0.138675 + 0.240192i
\(118\) 9.00000 0.828517
\(119\) −2.00000 3.46410i −0.183340 0.317554i
\(120\) −4.50000 2.59808i −0.410792 0.237171i
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) −0.500000 + 0.866025i −0.0452679 + 0.0784063i
\(123\) 0 0
\(124\) −0.500000 0.866025i −0.0449013 0.0777714i
\(125\) −1.00000 −0.0894427
\(126\) −3.00000 + 5.19615i −0.267261 + 0.462910i
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) −1.50000 2.59808i −0.132583 0.229640i
\(129\) 12.0000 6.92820i 1.05654 0.609994i
\(130\) 0.500000 0.866025i 0.0438529 0.0759555i
\(131\) 2.00000 3.46410i 0.174741 0.302660i −0.765331 0.643637i \(-0.777425\pi\)
0.940072 + 0.340977i \(0.110758\pi\)
\(132\) 1.73205i 0.150756i
\(133\) 3.00000 + 5.19615i 0.260133 + 0.450564i
\(134\) −14.0000 −1.20942
\(135\) 4.50000 + 2.59808i 0.387298 + 0.223607i
\(136\) 6.00000 0.514496
\(137\) 2.50000 + 4.33013i 0.213589 + 0.369948i 0.952835 0.303488i \(-0.0981512\pi\)
−0.739246 + 0.673436i \(0.764818\pi\)
\(138\) 0 0
\(139\) −6.00000 + 10.3923i −0.508913 + 0.881464i 0.491033 + 0.871141i \(0.336619\pi\)
−0.999947 + 0.0103230i \(0.996714\pi\)
\(140\) −1.00000 + 1.73205i −0.0845154 + 0.146385i
\(141\) 3.00000 1.73205i 0.252646 0.145865i
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) −1.50000 2.59808i −0.125000 0.216506i
\(145\) −5.00000 −0.415227
\(146\) 3.00000 + 5.19615i 0.248282 + 0.430037i
\(147\) −4.50000 2.59808i −0.371154 0.214286i
\(148\) −2.50000 + 4.33013i −0.205499 + 0.355934i
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) −1.50000 0.866025i −0.122474 0.0707107i
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) −9.00000 −0.729996
\(153\) −6.00000 −0.485071
\(154\) 2.00000 0.161165
\(155\) −0.500000 0.866025i −0.0401610 0.0695608i
\(156\) −1.50000 + 0.866025i −0.120096 + 0.0693375i
\(157\) 3.00000 5.19615i 0.239426 0.414698i −0.721124 0.692806i \(-0.756374\pi\)
0.960550 + 0.278108i \(0.0897074\pi\)
\(158\) −6.00000 + 10.3923i −0.477334 + 0.826767i
\(159\) 24.2487i 1.92305i
\(160\) −2.50000 4.33013i −0.197642 0.342327i
\(161\) 0 0
\(162\) 4.50000 + 7.79423i 0.353553 + 0.612372i
\(163\) −12.0000 −0.939913 −0.469956 0.882690i \(-0.655730\pi\)
−0.469956 + 0.882690i \(0.655730\pi\)
\(164\) 0 0
\(165\) 1.73205i 0.134840i
\(166\) −5.00000 + 8.66025i −0.388075 + 0.672166i
\(167\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(168\) −9.00000 + 5.19615i −0.694365 + 0.400892i
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) 2.00000 0.153393
\(171\) 9.00000 0.688247
\(172\) 8.00000 0.609994
\(173\) −6.00000 10.3923i −0.456172 0.790112i 0.542583 0.840002i \(-0.317446\pi\)
−0.998755 + 0.0498898i \(0.984113\pi\)
\(174\) −7.50000 4.33013i −0.568574 0.328266i
\(175\) −1.00000 + 1.73205i −0.0755929 + 0.130931i
\(176\) −0.500000 + 0.866025i −0.0376889 + 0.0652791i
\(177\) −13.5000 7.79423i −1.01472 0.585850i
\(178\) 1.00000 + 1.73205i 0.0749532 + 0.129823i
\(179\) −18.0000 −1.34538 −0.672692 0.739923i \(-0.734862\pi\)
−0.672692 + 0.739923i \(0.734862\pi\)
\(180\) 1.50000 + 2.59808i 0.111803 + 0.193649i
\(181\) 17.0000 1.26360 0.631800 0.775131i \(-0.282316\pi\)
0.631800 + 0.775131i \(0.282316\pi\)
\(182\) −1.00000 1.73205i −0.0741249 0.128388i
\(183\) 1.50000 0.866025i 0.110883 0.0640184i
\(184\) 0 0
\(185\) −2.50000 + 4.33013i −0.183804 + 0.318357i
\(186\) 1.73205i 0.127000i
\(187\) 1.00000 + 1.73205i 0.0731272 + 0.126660i
\(188\) 2.00000 0.145865
\(189\) 9.00000 5.19615i 0.654654 0.377964i
\(190\) −3.00000 −0.217643
\(191\) −9.00000 15.5885i −0.651217 1.12794i −0.982828 0.184525i \(-0.940925\pi\)
0.331611 0.943416i \(-0.392408\pi\)
\(192\) 12.1244i 0.875000i
\(193\) −6.50000 + 11.2583i −0.467880 + 0.810392i −0.999326 0.0366998i \(-0.988315\pi\)
0.531446 + 0.847092i \(0.321649\pi\)
\(194\) 0.500000 0.866025i 0.0358979 0.0621770i
\(195\) −1.50000 + 0.866025i −0.107417 + 0.0620174i
\(196\) −1.50000 2.59808i −0.107143 0.185577i
\(197\) 15.0000 1.06871 0.534353 0.845262i \(-0.320555\pi\)
0.534353 + 0.845262i \(0.320555\pi\)
\(198\) 1.50000 2.59808i 0.106600 0.184637i
\(199\) −22.0000 −1.55954 −0.779769 0.626067i \(-0.784664\pi\)
−0.779769 + 0.626067i \(0.784664\pi\)
\(200\) −1.50000 2.59808i −0.106066 0.183712i
\(201\) 21.0000 + 12.1244i 1.48123 + 0.855186i
\(202\) 1.50000 2.59808i 0.105540 0.182800i
\(203\) −5.00000 + 8.66025i −0.350931 + 0.607831i
\(204\) −3.00000 1.73205i −0.210042 0.121268i
\(205\) 0 0
\(206\) 1.00000 0.0696733
\(207\) 0 0
\(208\) 1.00000 0.0693375
\(209\) −1.50000 2.59808i −0.103757 0.179713i
\(210\) −3.00000 + 1.73205i −0.207020 + 0.119523i
\(211\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(212\) 7.00000 12.1244i 0.480762 0.832704i
\(213\) 0 0
\(214\) 9.50000 + 16.4545i 0.649407 + 1.12481i
\(215\) 8.00000 0.545595
\(216\) 15.5885i 1.06066i
\(217\) −2.00000 −0.135769
\(218\) −7.00000 12.1244i −0.474100 0.821165i
\(219\) 10.3923i 0.702247i
\(220\) 0.500000 0.866025i 0.0337100 0.0583874i
\(221\) 1.00000 1.73205i 0.0672673 0.116510i
\(222\) −7.50000 + 4.33013i −0.503367 + 0.290619i
\(223\) 13.0000 + 22.5167i 0.870544 + 1.50783i 0.861435 + 0.507869i \(0.169566\pi\)
0.00910984 + 0.999959i \(0.497100\pi\)
\(224\) −10.0000 −0.668153
\(225\) 1.50000 + 2.59808i 0.100000 + 0.173205i
\(226\) −10.0000 −0.665190
\(227\) 13.0000 + 22.5167i 0.862840 + 1.49448i 0.869176 + 0.494503i \(0.164650\pi\)
−0.00633544 + 0.999980i \(0.502017\pi\)
\(228\) 4.50000 + 2.59808i 0.298020 + 0.172062i
\(229\) 8.00000 13.8564i 0.528655 0.915657i −0.470787 0.882247i \(-0.656030\pi\)
0.999442 0.0334101i \(-0.0106368\pi\)
\(230\) 0 0
\(231\) −3.00000 1.73205i −0.197386 0.113961i
\(232\) −7.50000 12.9904i −0.492399 0.852860i
\(233\) −14.0000 −0.917170 −0.458585 0.888650i \(-0.651644\pi\)
−0.458585 + 0.888650i \(0.651644\pi\)
\(234\) −3.00000 −0.196116
\(235\) 2.00000 0.130466
\(236\) −4.50000 7.79423i −0.292925 0.507361i
\(237\) 18.0000 10.3923i 1.16923 0.675053i
\(238\) 2.00000 3.46410i 0.129641 0.224544i
\(239\) −7.50000 + 12.9904i −0.485135 + 0.840278i −0.999854 0.0170808i \(-0.994563\pi\)
0.514719 + 0.857359i \(0.327896\pi\)
\(240\) 1.73205i 0.111803i
\(241\) −5.00000 8.66025i −0.322078 0.557856i 0.658838 0.752285i \(-0.271048\pi\)
−0.980917 + 0.194429i \(0.937715\pi\)
\(242\) 10.0000 0.642824
\(243\) 15.5885i 1.00000i
\(244\) 1.00000 0.0640184
\(245\) −1.50000 2.59808i −0.0958315 0.165985i
\(246\) 0 0
\(247\) −1.50000 + 2.59808i −0.0954427 + 0.165312i
\(248\) 1.50000 2.59808i 0.0952501 0.164978i
\(249\) 15.0000 8.66025i 0.950586 0.548821i
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 6.00000 0.377964
\(253\) 0 0
\(254\) −4.00000 6.92820i −0.250982 0.434714i
\(255\) −3.00000 1.73205i −0.187867 0.108465i
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) 14.0000 24.2487i 0.873296 1.51259i 0.0147291 0.999892i \(-0.495311\pi\)
0.858567 0.512702i \(-0.171355\pi\)
\(258\) 12.0000 + 6.92820i 0.747087 + 0.431331i
\(259\) 5.00000 + 8.66025i 0.310685 + 0.538122i
\(260\) −1.00000 −0.0620174
\(261\) 7.50000 + 12.9904i 0.464238 + 0.804084i
\(262\) 4.00000 0.247121
\(263\) 8.00000 + 13.8564i 0.493301 + 0.854423i 0.999970 0.00771799i \(-0.00245674\pi\)
−0.506669 + 0.862141i \(0.669123\pi\)
\(264\) 4.50000 2.59808i 0.276956 0.159901i
\(265\) 7.00000 12.1244i 0.430007 0.744793i
\(266\) −3.00000 + 5.19615i −0.183942 + 0.318597i
\(267\) 3.46410i 0.212000i
\(268\) 7.00000 + 12.1244i 0.427593 + 0.740613i
\(269\) 3.00000 0.182913 0.0914566 0.995809i \(-0.470848\pi\)
0.0914566 + 0.995809i \(0.470848\pi\)
\(270\) 5.19615i 0.316228i
\(271\) −7.00000 −0.425220 −0.212610 0.977137i \(-0.568196\pi\)
−0.212610 + 0.977137i \(0.568196\pi\)
\(272\) 1.00000 + 1.73205i 0.0606339 + 0.105021i
\(273\) 3.46410i 0.209657i
\(274\) −2.50000 + 4.33013i −0.151031 + 0.261593i
\(275\) 0.500000 0.866025i 0.0301511 0.0522233i
\(276\) 0 0
\(277\) −5.00000 8.66025i −0.300421 0.520344i 0.675810 0.737075i \(-0.263794\pi\)
−0.976231 + 0.216731i \(0.930460\pi\)
\(278\) −12.0000 −0.719712
\(279\) −1.50000 + 2.59808i −0.0898027 + 0.155543i
\(280\) −6.00000 −0.358569
\(281\) 6.00000 + 10.3923i 0.357930 + 0.619953i 0.987615 0.156898i \(-0.0501493\pi\)
−0.629685 + 0.776851i \(0.716816\pi\)
\(282\) 3.00000 + 1.73205i 0.178647 + 0.103142i
\(283\) 12.5000 21.6506i 0.743048 1.28700i −0.208053 0.978117i \(-0.566713\pi\)
0.951101 0.308879i \(-0.0999539\pi\)
\(284\) 0 0
\(285\) 4.50000 + 2.59808i 0.266557 + 0.153897i
\(286\) 0.500000 + 0.866025i 0.0295656 + 0.0512092i
\(287\) 0 0
\(288\) −7.50000 + 12.9904i −0.441942 + 0.765466i
\(289\) −13.0000 −0.764706
\(290\) −2.50000 4.33013i −0.146805 0.254274i
\(291\) −1.50000 + 0.866025i −0.0879316 + 0.0507673i
\(292\) 3.00000 5.19615i 0.175562 0.304082i
\(293\) −0.500000 + 0.866025i −0.0292103 + 0.0505937i −0.880261 0.474490i \(-0.842633\pi\)
0.851051 + 0.525084i \(0.175966\pi\)
\(294\) 5.19615i 0.303046i
\(295\) −4.50000 7.79423i −0.262000 0.453798i
\(296\) −15.0000 −0.871857
\(297\) −4.50000 + 2.59808i −0.261116 + 0.150756i
\(298\) −6.00000 −0.347571
\(299\) 0 0
\(300\) 1.73205i 0.100000i
\(301\) 8.00000 13.8564i 0.461112 0.798670i
\(302\) −4.00000 + 6.92820i −0.230174 + 0.398673i
\(303\) −4.50000 + 2.59808i −0.258518 + 0.149256i
\(304\) −1.50000 2.59808i −0.0860309 0.149010i
\(305\) 1.00000 0.0572598
\(306\) −3.00000 5.19615i −0.171499 0.297044i
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) −1.00000 1.73205i −0.0569803 0.0986928i
\(309\) −1.50000 0.866025i −0.0853320 0.0492665i
\(310\) 0.500000 0.866025i 0.0283981 0.0491869i
\(311\) 2.00000 3.46410i 0.113410 0.196431i −0.803733 0.594990i \(-0.797156\pi\)
0.917143 + 0.398559i \(0.130489\pi\)
\(312\) −4.50000 2.59808i −0.254762 0.147087i
\(313\) 14.0000 + 24.2487i 0.791327 + 1.37062i 0.925146 + 0.379612i \(0.123943\pi\)
−0.133819 + 0.991006i \(0.542724\pi\)
\(314\) 6.00000 0.338600
\(315\) 6.00000 0.338062
\(316\) 12.0000 0.675053
\(317\) 13.5000 + 23.3827i 0.758236 + 1.31330i 0.943750 + 0.330661i \(0.107272\pi\)
−0.185514 + 0.982642i \(0.559395\pi\)
\(318\) 21.0000 12.1244i 1.17762 0.679900i
\(319\) 2.50000 4.33013i 0.139973 0.242441i
\(320\) 3.50000 6.06218i 0.195656 0.338886i
\(321\) 32.9090i 1.83680i
\(322\) 0 0
\(323\) −6.00000 −0.333849
\(324\) 4.50000 7.79423i 0.250000 0.433013i
\(325\) −1.00000 −0.0554700
\(326\) −6.00000 10.3923i −0.332309 0.575577i
\(327\) 24.2487i 1.34096i
\(328\) 0 0
\(329\) 2.00000 3.46410i 0.110264 0.190982i
\(330\) 1.50000 0.866025i 0.0825723 0.0476731i
\(331\) −13.5000 23.3827i −0.742027 1.28523i −0.951571 0.307429i \(-0.900531\pi\)
0.209544 0.977799i \(-0.432802\pi\)
\(332\) 10.0000 0.548821
\(333\) 15.0000 0.821995
\(334\) 0 0
\(335\) 7.00000 + 12.1244i 0.382451 + 0.662424i
\(336\) −3.00000 1.73205i −0.163663 0.0944911i
\(337\) 11.0000 19.0526i 0.599208 1.03786i −0.393730 0.919226i \(-0.628816\pi\)
0.992938 0.118633i \(-0.0378512\pi\)
\(338\) 0.500000 0.866025i 0.0271964 0.0471056i
\(339\) 15.0000 + 8.66025i 0.814688 + 0.470360i
\(340\) −1.00000 1.73205i −0.0542326 0.0939336i
\(341\) 1.00000 0.0541530
\(342\) 4.50000 + 7.79423i 0.243332 + 0.421464i
\(343\) −20.0000 −1.07990
\(344\) 12.0000 + 20.7846i 0.646997 + 1.12063i
\(345\) 0 0
\(346\) 6.00000 10.3923i 0.322562 0.558694i
\(347\) −8.50000 + 14.7224i −0.456304 + 0.790342i −0.998762 0.0497412i \(-0.984160\pi\)
0.542458 + 0.840083i \(0.317494\pi\)
\(348\) 8.66025i 0.464238i
\(349\) −6.00000 10.3923i −0.321173 0.556287i 0.659558 0.751654i \(-0.270744\pi\)
−0.980730 + 0.195367i \(0.937410\pi\)
\(350\) −2.00000 −0.106904
\(351\) 4.50000 + 2.59808i 0.240192 + 0.138675i
\(352\) 5.00000 0.266501
\(353\) 1.50000 + 2.59808i 0.0798369 + 0.138282i 0.903179 0.429263i \(-0.141227\pi\)
−0.823343 + 0.567545i \(0.807893\pi\)
\(354\) 15.5885i 0.828517i
\(355\) 0 0
\(356\) 1.00000 1.73205i 0.0529999 0.0917985i
\(357\) −6.00000 + 3.46410i −0.317554 + 0.183340i
\(358\) −9.00000 15.5885i −0.475665 0.823876i
\(359\) −31.0000 −1.63612 −0.818059 0.575135i \(-0.804950\pi\)
−0.818059 + 0.575135i \(0.804950\pi\)
\(360\) −4.50000 + 7.79423i −0.237171 + 0.410792i
\(361\) −10.0000 −0.526316
\(362\) 8.50000 + 14.7224i 0.446750 + 0.773794i
\(363\) −15.0000 8.66025i −0.787296 0.454545i
\(364\) −1.00000 + 1.73205i −0.0524142 + 0.0907841i
\(365\) 3.00000 5.19615i 0.157027 0.271979i
\(366\) 1.50000 + 0.866025i 0.0784063 + 0.0452679i
\(367\) −12.5000 21.6506i −0.652495 1.13015i −0.982516 0.186180i \(-0.940389\pi\)
0.330021 0.943974i \(-0.392944\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −5.00000 −0.259938
\(371\) −14.0000 24.2487i −0.726844 1.25893i
\(372\) −1.50000 + 0.866025i −0.0777714 + 0.0449013i
\(373\) 10.0000 17.3205i 0.517780 0.896822i −0.482006 0.876168i \(-0.660092\pi\)
0.999787 0.0206542i \(-0.00657489\pi\)
\(374\) −1.00000 + 1.73205i −0.0517088 + 0.0895622i
\(375\) 1.73205i 0.0894427i
\(376\) 3.00000 + 5.19615i 0.154713 + 0.267971i
\(377\) −5.00000 −0.257513
\(378\) 9.00000 + 5.19615i 0.462910 + 0.267261i
\(379\) −23.0000 −1.18143 −0.590715 0.806880i \(-0.701154\pi\)
−0.590715 + 0.806880i \(0.701154\pi\)
\(380\) 1.50000 + 2.59808i 0.0769484 + 0.133278i
\(381\) 13.8564i 0.709885i
\(382\) 9.00000 15.5885i 0.460480 0.797575i
\(383\) 6.00000 10.3923i 0.306586 0.531022i −0.671027 0.741433i \(-0.734147\pi\)
0.977613 + 0.210411i \(0.0674801\pi\)
\(384\) −4.50000 + 2.59808i −0.229640 + 0.132583i
\(385\) −1.00000 1.73205i −0.0509647 0.0882735i
\(386\) −13.0000 −0.661683
\(387\) −12.0000 20.7846i −0.609994 1.05654i
\(388\) −1.00000 −0.0507673
\(389\) 11.0000 + 19.0526i 0.557722 + 0.966003i 0.997686 + 0.0679877i \(0.0216579\pi\)
−0.439964 + 0.898015i \(0.645009\pi\)
\(390\) −1.50000 0.866025i −0.0759555 0.0438529i
\(391\) 0 0
\(392\) 4.50000 7.79423i 0.227284 0.393668i
\(393\) −6.00000 3.46410i −0.302660 0.174741i
\(394\) 7.50000 + 12.9904i 0.377845 + 0.654446i
\(395\) 12.0000 0.603786
\(396\) −3.00000 −0.150756
\(397\) −30.0000 −1.50566 −0.752828 0.658217i \(-0.771311\pi\)
−0.752828 + 0.658217i \(0.771311\pi\)
\(398\) −11.0000 19.0526i −0.551380 0.955018i
\(399\) 9.00000 5.19615i 0.450564 0.260133i
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) −14.0000 + 24.2487i −0.699127 + 1.21092i 0.269643 + 0.962960i \(0.413094\pi\)
−0.968770 + 0.247962i \(0.920239\pi\)
\(402\) 24.2487i 1.20942i
\(403\) −0.500000 0.866025i −0.0249068 0.0431398i
\(404\) −3.00000 −0.149256
\(405\) 4.50000 7.79423i 0.223607 0.387298i
\(406\) −10.0000 −0.496292
\(407\) −2.50000 4.33013i −0.123920 0.214636i
\(408\) 10.3923i 0.514496i
\(409\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(410\) 0 0
\(411\) 7.50000 4.33013i 0.369948 0.213589i
\(412\) −0.500000 0.866025i −0.0246332 0.0426660i
\(413\) −18.0000 −0.885722
\(414\) 0 0
\(415\) 10.0000 0.490881
\(416\) −2.50000 4.33013i −0.122573 0.212302i
\(417\) 18.0000 + 10.3923i 0.881464 + 0.508913i
\(418\) 1.50000 2.59808i 0.0733674 0.127076i
\(419\) −10.0000 + 17.3205i −0.488532 + 0.846162i −0.999913 0.0131919i \(-0.995801\pi\)
0.511381 + 0.859354i \(0.329134\pi\)
\(420\) 3.00000 + 1.73205i 0.146385 + 0.0845154i
\(421\) −5.00000 8.66025i −0.243685 0.422075i 0.718076 0.695965i \(-0.245023\pi\)
−0.961761 + 0.273890i \(0.911690\pi\)
\(422\) 0 0
\(423\) −3.00000 5.19615i −0.145865 0.252646i
\(424\) 42.0000 2.03970
\(425\) −1.00000 1.73205i −0.0485071 0.0840168i
\(426\) 0 0
\(427\) 1.00000 1.73205i 0.0483934 0.0838198i
\(428\) 9.50000 16.4545i 0.459200 0.795357i
\(429\) 1.73205i 0.0836242i
\(430\) 4.00000 + 6.92820i 0.192897 + 0.334108i
\(431\) 17.0000 0.818861 0.409431 0.912341i \(-0.365727\pi\)
0.409431 + 0.912341i \(0.365727\pi\)
\(432\) −4.50000 + 2.59808i −0.216506 + 0.125000i
\(433\) −38.0000 −1.82616 −0.913082 0.407777i \(-0.866304\pi\)
−0.913082 + 0.407777i \(0.866304\pi\)
\(434\) −1.00000 1.73205i −0.0480015 0.0831411i
\(435\) 8.66025i 0.415227i
\(436\) −7.00000 + 12.1244i −0.335239 + 0.580651i
\(437\) 0 0
\(438\) 9.00000 5.19615i 0.430037 0.248282i
\(439\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 3.00000 0.143019
\(441\) −4.50000 + 7.79423i −0.214286 + 0.371154i
\(442\) 2.00000 0.0951303
\(443\) 3.50000 + 6.06218i 0.166290 + 0.288023i 0.937113 0.349027i \(-0.113488\pi\)
−0.770823 + 0.637050i \(0.780155\pi\)
\(444\) 7.50000 + 4.33013i 0.355934 + 0.205499i
\(445\) 1.00000 1.73205i 0.0474045 0.0821071i
\(446\) −13.0000 + 22.5167i −0.615568 + 1.06619i
\(447\) 9.00000 + 5.19615i 0.425685 + 0.245770i
\(448\) −7.00000 12.1244i −0.330719 0.572822i
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) −1.50000 + 2.59808i −0.0707107 + 0.122474i
\(451\) 0 0
\(452\) 5.00000 + 8.66025i 0.235180 + 0.407344i
\(453\) 12.0000 6.92820i 0.563809 0.325515i
\(454\) −13.0000 + 22.5167i −0.610120 + 1.05676i
\(455\) −1.00000 + 1.73205i −0.0468807 + 0.0811998i
\(456\) 15.5885i 0.729996i
\(457\) −13.0000 22.5167i −0.608114 1.05328i −0.991551 0.129718i \(-0.958593\pi\)
0.383437 0.923567i \(-0.374740\pi\)
\(458\) 16.0000 0.747631
\(459\) 10.3923i 0.485071i
\(460\) 0 0
\(461\) 13.0000 + 22.5167i 0.605470 + 1.04871i 0.991977 + 0.126419i \(0.0403483\pi\)
−0.386507 + 0.922287i \(0.626318\pi\)
\(462\) 3.46410i 0.161165i
\(463\) 3.00000 5.19615i 0.139422 0.241486i −0.787856 0.615859i \(-0.788809\pi\)
0.927278 + 0.374374i \(0.122142\pi\)
\(464\) 2.50000 4.33013i 0.116060 0.201021i
\(465\) −1.50000 + 0.866025i −0.0695608 + 0.0401610i
\(466\) −7.00000 12.1244i −0.324269 0.561650i
\(467\) −28.0000 −1.29569 −0.647843 0.761774i \(-0.724329\pi\)
−0.647843 + 0.761774i \(0.724329\pi\)
\(468\) 1.50000 + 2.59808i 0.0693375 + 0.120096i
\(469\) 28.0000 1.29292
\(470\) 1.00000 + 1.73205i 0.0461266 + 0.0798935i
\(471\) −9.00000 5.19615i −0.414698 0.239426i
\(472\) 13.5000 23.3827i 0.621388 1.07628i
\(473\) −4.00000 + 6.92820i −0.183920 + 0.318559i
\(474\) 18.0000 + 10.3923i 0.826767 + 0.477334i
\(475\) 1.50000 + 2.59808i 0.0688247 + 0.119208i
\(476\) −4.00000 −0.183340
\(477\) −42.0000 −1.92305
\(478\) −15.0000 −0.686084
\(479\) −7.50000 12.9904i −0.342684 0.593546i 0.642246 0.766498i \(-0.278003\pi\)
−0.984930 + 0.172953i \(0.944669\pi\)
\(480\) −7.50000 + 4.33013i −0.342327 + 0.197642i
\(481\) −2.50000 + 4.33013i −0.113990 + 0.197437i
\(482\) 5.00000 8.66025i 0.227744 0.394464i
\(483\) 0 0
\(484\) −5.00000 8.66025i −0.227273 0.393648i
\(485\) −1.00000 −0.0454077
\(486\) 13.5000 7.79423i 0.612372 0.353553i
\(487\) −34.0000 −1.54069 −0.770344 0.637629i \(-0.779915\pi\)
−0.770344 + 0.637629i \(0.779915\pi\)
\(488\) 1.50000 + 2.59808i 0.0679018 + 0.117609i
\(489\) 20.7846i 0.939913i
\(490\) 1.50000 2.59808i 0.0677631 0.117369i
\(491\) 3.00000 5.19615i 0.135388 0.234499i −0.790358 0.612646i \(-0.790105\pi\)
0.925746 + 0.378147i \(0.123439\pi\)
\(492\) 0 0
\(493\) −5.00000 8.66025i −0.225189 0.390038i
\(494\) −3.00000 −0.134976
\(495\) −3.00000 −0.134840
\(496\) 1.00000 0.0449013
\(497\) 0 0
\(498\) 15.0000 + 8.66025i 0.672166 + 0.388075i
\(499\) −14.0000 + 24.2487i −0.626726 + 1.08552i 0.361478 + 0.932381i \(0.382272\pi\)
−0.988204 + 0.153141i \(0.951061\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) 0 0
\(502\) 6.00000 + 10.3923i 0.267793 + 0.463831i
\(503\) −9.00000 −0.401290 −0.200645 0.979664i \(-0.564304\pi\)
−0.200645 + 0.979664i \(0.564304\pi\)
\(504\) 9.00000 + 15.5885i 0.400892 + 0.694365i
\(505\) −3.00000 −0.133498
\(506\) 0 0
\(507\) −1.50000 + 0.866025i −0.0666173 + 0.0384615i
\(508\) −4.00000 + 6.92820i −0.177471 + 0.307389i
\(509\) 12.0000 20.7846i 0.531891 0.921262i −0.467416 0.884037i \(-0.654815\pi\)
0.999307 0.0372243i \(-0.0118516\pi\)
\(510\) 3.46410i 0.153393i
\(511\) −6.00000 10.3923i −0.265424 0.459728i
\(512\) 11.0000 0.486136
\(513\) 15.5885i 0.688247i
\(514\) 28.0000 1.23503
\(515\) −0.500000 0.866025i −0.0220326 0.0381616i
\(516\) 13.8564i 0.609994i
\(517\) −1.00000 + 1.73205i −0.0439799 + 0.0761755i
\(518\) −5.00000 + 8.66025i −0.219687 + 0.380510i
\(519\) −18.0000 + 10.3923i −0.790112 + 0.456172i
\(520\) −1.50000 2.59808i −0.0657794 0.113933i
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) −7.50000 + 12.9904i −0.328266 + 0.568574i
\(523\) −15.0000 −0.655904 −0.327952 0.944694i \(-0.606358\pi\)
−0.327952 + 0.944694i \(0.606358\pi\)
\(524\) −2.00000 3.46410i −0.0873704 0.151330i
\(525\) 3.00000 + 1.73205i 0.130931 + 0.0755929i
\(526\) −8.00000 + 13.8564i −0.348817 + 0.604168i
\(527\) 1.00000 1.73205i 0.0435607 0.0754493i
\(528\) 1.50000 + 0.866025i 0.0652791 + 0.0376889i
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 14.0000 0.608121
\(531\) −13.5000 + 23.3827i −0.585850 + 1.01472i
\(532\) 6.00000 0.260133
\(533\) 0 0
\(534\) 3.00000 1.73205i 0.129823 0.0749532i
\(535\) 9.50000 16.4545i 0.410721 0.711389i
\(536\) −21.0000 + 36.3731i −0.907062 + 1.57108i
\(537\) 31.1769i 1.34538i
\(538\) 1.50000 + 2.59808i 0.0646696 + 0.112011i
\(539\) 3.00000 0.129219
\(540\) 4.50000 2.59808i 0.193649 0.111803i
\(541\) 32.0000 1.37579 0.687894 0.725811i \(-0.258536\pi\)
0.687894 + 0.725811i \(0.258536\pi\)
\(542\) −3.50000 6.06218i −0.150338 0.260393i
\(543\) 29.4449i 1.26360i
\(544\) 5.00000 8.66025i 0.214373 0.371305i
\(545\) −7.00000 + 12.1244i −0.299847 + 0.519350i
\(546\) −3.00000 + 1.73205i −0.128388 + 0.0741249i
\(547\) 7.50000 + 12.9904i 0.320677 + 0.555429i 0.980628 0.195880i \(-0.0627563\pi\)
−0.659951 + 0.751309i \(0.729423\pi\)
\(548\) 5.00000 0.213589
\(549\) −1.50000 2.59808i −0.0640184 0.110883i
\(550\) 1.00000 0.0426401
\(551\) 7.50000 + 12.9904i 0.319511 + 0.553409i
\(552\) 0 0
\(553\) 12.0000 20.7846i 0.510292 0.883852i
\(554\) 5.00000 8.66025i 0.212430 0.367939i
\(555\) 7.50000 + 4.33013i 0.318357 + 0.183804i
\(556\) 6.00000 + 10.3923i 0.254457 + 0.440732i
\(557\) −5.00000 −0.211857 −0.105928 0.994374i \(-0.533781\pi\)
−0.105928 + 0.994374i \(0.533781\pi\)
\(558\) −3.00000 −0.127000
\(559\) 8.00000 0.338364
\(560\) −1.00000 1.73205i −0.0422577 0.0731925i
\(561\) 3.00000 1.73205i 0.126660 0.0731272i
\(562\) −6.00000 + 10.3923i −0.253095 + 0.438373i
\(563\) 9.50000 16.4545i 0.400377 0.693474i −0.593394 0.804912i \(-0.702212\pi\)
0.993771 + 0.111438i \(0.0355457\pi\)
\(564\) 3.46410i 0.145865i
\(565\) 5.00000 + 8.66025i 0.210352 + 0.364340i
\(566\) 25.0000 1.05083
\(567\) −9.00000 15.5885i −0.377964 0.654654i
\(568\) 0 0
\(569\) 5.50000 + 9.52628i 0.230572 + 0.399362i 0.957977 0.286846i \(-0.0926069\pi\)
−0.727405 + 0.686209i \(0.759274\pi\)
\(570\) 5.19615i 0.217643i
\(571\) −6.00000 + 10.3923i −0.251092 + 0.434904i −0.963827 0.266529i \(-0.914123\pi\)
0.712735 + 0.701434i \(0.247456\pi\)
\(572\) 0.500000 0.866025i 0.0209061 0.0362103i
\(573\) −27.0000 + 15.5885i −1.12794 + 0.651217i
\(574\) 0 0
\(575\) 0 0
\(576\) −21.0000 −0.875000
\(577\) 11.0000 0.457936 0.228968 0.973434i \(-0.426465\pi\)
0.228968 + 0.973434i \(0.426465\pi\)
\(578\) −6.50000 11.2583i −0.270364 0.468285i
\(579\) 19.5000 + 11.2583i 0.810392 + 0.467880i
\(580\) −2.50000 + 4.33013i −0.103807 + 0.179799i
\(581\) 10.0000 17.3205i 0.414870 0.718576i
\(582\) −1.50000 0.866025i −0.0621770 0.0358979i
\(583\) 7.00000 + 12.1244i 0.289910 + 0.502140i
\(584\) 18.0000 0.744845
\(585\) 1.50000 + 2.59808i 0.0620174 + 0.107417i
\(586\) −1.00000 −0.0413096
\(587\) 7.00000 + 12.1244i 0.288921 + 0.500426i 0.973552 0.228464i \(-0.0733702\pi\)
−0.684632 + 0.728889i \(0.740037\pi\)
\(588\) −4.50000 + 2.59808i −0.185577 + 0.107143i
\(589\) −1.50000 + 2.59808i −0.0618064 + 0.107052i
\(590\) 4.50000 7.79423i 0.185262 0.320883i
\(591\) 25.9808i 1.06871i
\(592\) −2.50000 4.33013i −0.102749 0.177967i
\(593\) −31.0000 −1.27302 −0.636509 0.771270i \(-0.719622\pi\)
−0.636509 + 0.771270i \(0.719622\pi\)
\(594\) −4.50000 2.59808i −0.184637 0.106600i
\(595\) −4.00000 −0.163984
\(596\) 3.00000 + 5.19615i 0.122885 + 0.212843i
\(597\) 38.1051i 1.55954i
\(598\) 0 0
\(599\) −7.00000 + 12.1244i −0.286012 + 0.495388i −0.972854 0.231419i \(-0.925663\pi\)
0.686842 + 0.726807i \(0.258996\pi\)
\(600\) −4.50000 + 2.59808i −0.183712 + 0.106066i
\(601\) 8.50000 + 14.7224i 0.346722 + 0.600541i 0.985665 0.168714i \(-0.0539613\pi\)
−0.638943 + 0.769254i \(0.720628\pi\)
\(602\) 16.0000 0.652111
\(603\) 21.0000 36.3731i 0.855186 1.48123i
\(604\) 8.00000 0.325515
\(605\) −5.00000 8.66025i −0.203279 0.352089i
\(606\) −4.50000 2.59808i −0.182800 0.105540i
\(607\) 4.00000 6.92820i 0.162355 0.281207i −0.773358 0.633970i \(-0.781424\pi\)
0.935713 + 0.352763i \(0.114758\pi\)
\(608\) −7.50000 + 12.9904i −0.304165 + 0.526830i
\(609\) 15.0000 + 8.66025i 0.607831 + 0.350931i
\(610\) 0.500000 + 0.866025i 0.0202444 + 0.0350643i
\(611\) 2.00000 0.0809113
\(612\) −3.00000 + 5.19615i −0.121268 + 0.210042i
\(613\) 30.0000 1.21169 0.605844 0.795583i \(-0.292835\pi\)
0.605844 + 0.795583i \(0.292835\pi\)
\(614\) 1.00000 + 1.73205i 0.0403567 + 0.0698999i
\(615\) 0 0
\(616\) 3.00000 5.19615i 0.120873 0.209359i
\(617\) −4.50000 + 7.79423i −0.181163 + 0.313784i −0.942277 0.334835i \(-0.891320\pi\)
0.761114 + 0.648618i \(0.224653\pi\)
\(618\) 1.73205i 0.0696733i
\(619\) 5.50000 + 9.52628i 0.221064 + 0.382893i 0.955131 0.296183i \(-0.0957138\pi\)
−0.734068 + 0.679076i \(0.762380\pi\)
\(620\) −1.00000 −0.0401610
\(621\) 0 0
\(622\) 4.00000 0.160385
\(623\) −2.00000 3.46410i −0.0801283 0.138786i
\(624\) 1.73205i 0.0693375i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −14.0000 + 24.2487i −0.559553 + 0.969173i
\(627\) −4.50000 + 2.59808i −0.179713 + 0.103757i
\(628\) −3.00000 5.19615i −0.119713 0.207349i
\(629\) −10.0000 −0.398726
\(630\) 3.00000 + 5.19615i 0.119523 + 0.207020i
\(631\) −5.00000 −0.199047 −0.0995234 0.995035i \(-0.531732\pi\)
−0.0995234 + 0.995035i \(0.531732\pi\)
\(632\) 18.0000 + 31.1769i 0.716002 + 1.24015i
\(633\) 0 0
\(634\) −13.5000 + 23.3827i −0.536153 + 0.928645i
\(635\) −4.00000 + 6.92820i −0.158735 + 0.274937i
\(636\) −21.0000 12.1244i −0.832704 0.480762i
\(637\) −1.50000 2.59808i −0.0594322 0.102940i
\(638\) 5.00000 0.197952
\(639\) 0 0
\(640\) −3.00000 −0.118585
\(641\) −8.50000 14.7224i −0.335730 0.581501i 0.647895 0.761730i \(-0.275650\pi\)
−0.983625 + 0.180229i \(0.942316\pi\)
\(642\) 28.5000 16.4545i 1.12481 0.649407i
\(643\) −16.0000 + 27.7128i −0.630978 + 1.09289i 0.356374 + 0.934344i \(0.384013\pi\)
−0.987352 + 0.158543i \(0.949320\pi\)
\(644\) 0 0
\(645\) 13.8564i 0.545595i
\(646\) −3.00000 5.19615i −0.118033 0.204440i
\(647\) 41.0000 1.61188 0.805938 0.592000i \(-0.201661\pi\)
0.805938 + 0.592000i \(0.201661\pi\)
\(648\) 27.0000 1.06066
\(649\) 9.00000 0.353281
\(650\) −0.500000 0.866025i −0.0196116 0.0339683i
\(651\) 3.46410i 0.135769i
\(652\) −6.00000 + 10.3923i −0.234978 + 0.406994i
\(653\) −24.0000 + 41.5692i −0.939193 + 1.62673i −0.172211 + 0.985060i \(0.555091\pi\)
−0.766982 + 0.641669i \(0.778242\pi\)
\(654\) −21.0000 + 12.1244i −0.821165 + 0.474100i
\(655\) −2.00000 3.46410i −0.0781465 0.135354i
\(656\) 0 0
\(657\) −18.0000 −0.702247
\(658\) 4.00000 0.155936
\(659\) 18.0000 + 31.1769i 0.701180 + 1.21448i 0.968052 + 0.250748i \(0.0806766\pi\)
−0.266872 + 0.963732i \(0.585990\pi\)
\(660\) −1.50000 0.866025i −0.0583874 0.0337100i
\(661\) −19.0000 + 32.9090i −0.739014 + 1.28001i 0.213925 + 0.976850i \(0.431375\pi\)
−0.952940 + 0.303160i \(0.901958\pi\)
\(662\) 13.5000 23.3827i 0.524692 0.908794i
\(663\) −3.00000 1.73205i −0.116510 0.0672673i
\(664\) 15.0000 + 25.9808i 0.582113 + 1.00825i
\(665\) 6.00000 0.232670
\(666\) 7.50000 + 12.9904i 0.290619 + 0.503367i
\(667\) 0 0
\(668\) 0 0
\(669\) 39.0000 22.5167i 1.50783 0.870544i
\(670\) −7.00000 + 12.1244i −0.270434 + 0.468405i
\(671\) −0.500000 + 0.866025i −0.0193023 + 0.0334325i
\(672\) 17.3205i 0.668153i
\(673\) −12.0000 20.7846i −0.462566 0.801188i 0.536522 0.843886i \(-0.319738\pi\)
−0.999088 + 0.0426985i \(0.986405\pi\)
\(674\) 22.0000 0.847408
\(675\) 4.50000 2.59808i 0.173205 0.100000i
\(676\) −1.00000 −0.0384615
\(677\) −3.00000 5.19615i −0.115299 0.199704i 0.802600 0.596518i \(-0.203449\pi\)
−0.917899 + 0.396813i \(0.870116\pi\)
\(678\) 17.3205i 0.665190i
\(679\) −1.00000 + 1.73205i −0.0383765 + 0.0664700i
\(680\) 3.00000 5.19615i 0.115045 0.199263i
\(681\) 39.0000 22.5167i 1.49448 0.862840i
\(682\) 0.500000 + 0.866025i 0.0191460 + 0.0331618i
\(683\) −20.0000 −0.765279 −0.382639 0.923898i \(-0.624985\pi\)
−0.382639 + 0.923898i \(0.624985\pi\)
\(684\) 4.50000 7.79423i 0.172062 0.298020i
\(685\) 5.00000 0.191040
\(686\) −10.0000 17.3205i −0.381802 0.661300i
\(687\) −24.0000 13.8564i −0.915657 0.528655i
\(688\) −4.00000 + 6.92820i −0.152499 + 0.264135i
\(689\) 7.00000 12.1244i 0.266679 0.461901i
\(690\) 0 0
\(691\) −0.500000 0.866025i −0.0190209 0.0329452i 0.856358 0.516382i \(-0.172722\pi\)
−0.875379 + 0.483437i \(0.839388\pi\)
\(692\) −12.0000 −0.456172
\(693\) −3.00000 + 5.19615i −0.113961 + 0.197386i
\(694\) −17.0000 −0.645311
\(695\) 6.00000 + 10.3923i 0.227593 + 0.394203i
\(696\) −22.5000 + 12.9904i −0.852860 + 0.492399i
\(697\) 0 0
\(698\) 6.00000 10.3923i 0.227103 0.393355i
\(699\) 24.2487i 0.917170i
\(700\) 1.00000 + 1.73205i 0.0377964 + 0.0654654i
\(701\) −5.00000 −0.188847 −0.0944237 0.995532i \(-0.530101\pi\)
−0.0944237 + 0.995532i \(0.530101\pi\)
\(702\) 5.19615i 0.196116i
\(703\) 15.0000 0.565736
\(704\) 3.50000 + 6.06218i 0.131911 + 0.228477i
\(705\) 3.46410i 0.130466i
\(706\) −1.50000 + 2.59808i −0.0564532 + 0.0977799i
\(707\) −3.00000 + 5.19615i −0.112827 + 0.195421i
\(708\) −13.5000 + 7.79423i −0.507361 + 0.292925i
\(709\) −2.00000 3.46410i −0.0751116 0.130097i 0.826023 0.563636i \(-0.190598\pi\)
−0.901135 + 0.433539i \(0.857265\pi\)
\(710\) 0 0
\(711\) −18.0000 31.1769i −0.675053 1.16923i
\(712\) 6.00000 0.224860
\(713\) 0 0
\(714\) −6.00000 3.46410i −0.224544 0.129641i
\(715\) 0.500000 0.866025i 0.0186989 0.0323875i
\(716\) −9.00000 + 15.5885i −0.336346 + 0.582568i
\(717\) 22.5000 + 12.9904i 0.840278 + 0.485135i
\(718\) −15.5000 26.8468i −0.578455 1.00191i
\(719\) −2.00000 −0.0745874 −0.0372937 0.999304i \(-0.511874\pi\)
−0.0372937 + 0.999304i \(0.511874\pi\)
\(720\) −3.00000 −0.111803
\(721\) −2.00000 −0.0744839
\(722\) −5.00000 8.66025i −0.186081 0.322301i
\(723\) −15.0000 + 8.66025i −0.557856 + 0.322078i
\(724\) 8.50000 14.7224i 0.315900 0.547155i
\(725\) −2.50000 + 4.33013i −0.0928477 + 0.160817i
\(726\) 17.3205i 0.642824i
\(727\) −24.0000 41.5692i −0.890111 1.54172i −0.839742 0.542986i \(-0.817294\pi\)
−0.0503692 0.998731i \(-0.516040\pi\)
\(728\) −6.00000 −0.222375
\(729\) −27.0000 −1.00000
\(730\) 6.00000 0.222070
\(731\) 8.00000 + 13.8564i 0.295891 + 0.512498i
\(732\) 1.73205i 0.0640184i
\(733\) −6.50000 + 11.2583i −0.240083 + 0.415836i −0.960738 0.277458i \(-0.910508\pi\)
0.720655 + 0.693294i \(0.243841\pi\)
\(734\) 12.5000 21.6506i 0.461383 0.799140i
\(735\) −4.50000 + 2.59808i −0.165985 + 0.0958315i
\(736\) 0 0
\(737\) −14.0000 −0.515697
\(738\) 0 0
\(739\) 9.00000 0.331070 0.165535 0.986204i \(-0.447065\pi\)
0.165535 + 0.986204i \(0.447065\pi\)
\(740\) 2.50000 + 4.33013i 0.0919018 + 0.159179i
\(741\) 4.50000 + 2.59808i 0.165312 + 0.0954427i
\(742\) 14.0000 24.2487i 0.513956 0.890198i
\(743\) 24.0000 41.5692i 0.880475 1.52503i 0.0296605 0.999560i \(-0.490557\pi\)
0.850814 0.525467i \(-0.176109\pi\)
\(744\) −4.50000 2.59808i −0.164978 0.0952501i
\(745\) 3.00000 + 5.19615i 0.109911 + 0.190372i
\(746\) 20.0000 0.732252
\(747\) −15.0000 25.9808i −0.548821 0.950586i
\(748\) 2.00000 0.0731272
\(749\) −19.0000 32.9090i −0.694245 1.20247i
\(750\) −1.50000 + 0.866025i −0.0547723 + 0.0316228i
\(751\) −1.00000 + 1.73205i −0.0364905 + 0.0632034i −0.883694 0.468065i \(-0.844951\pi\)
0.847203 + 0.531269i \(0.178285\pi\)
\(752\) −1.00000 + 1.73205i −0.0364662 + 0.0631614i
\(753\) 20.7846i 0.757433i
\(754\) −2.50000 4.33013i −0.0910446 0.157694i
\(755\) 8.00000 0.291150
\(756\) 10.3923i 0.377964i
\(757\) −16.0000 −0.581530 −0.290765 0.956795i \(-0.593910\pi\)
−0.290765 + 0.956795i \(0.593910\pi\)
\(758\) −11.5000 19.9186i −0.417699 0.723476i
\(759\) 0 0
\(760\) −4.50000 + 7.79423i −0.163232 + 0.282726i
\(761\) 18.0000 31.1769i 0.652499 1.13016i −0.330015 0.943976i \(-0.607054\pi\)
0.982514 0.186187i \(-0.0596129\pi\)
\(762\) −12.0000 + 6.92820i −0.434714 + 0.250982i
\(763\) 14.0000 + 24.2487i 0.506834 + 0.877862i
\(764\) −18.0000 −0.651217
\(765\) −3.00000 + 5.19615i −0.108465 + 0.187867i
\(766\) 12.0000 0.433578
\(767\) −4.50000 7.79423i −0.162486 0.281433i
\(768\) −25.5000 14.7224i −0.920152 0.531250i
\(769\) 20.0000 34.6410i 0.721218 1.24919i −0.239293 0.970947i \(-0.576916\pi\)
0.960512 0.278240i \(-0.0897509\pi\)
\(770\) 1.00000 1.73205i 0.0360375 0.0624188i
\(771\) −42.0000 24.2487i −1.51259 0.873296i
\(772\) 6.50000 + 11.2583i 0.233940 + 0.405196i
\(773\) 31.0000 1.11499 0.557496 0.830179i \(-0.311762\pi\)
0.557496 + 0.830179i \(0.311762\pi\)
\(774\) 12.0000 20.7846i 0.431331 0.747087i
\(775\) −1.00000 −0.0359211
\(776\) −1.50000 2.59808i −0.0538469 0.0932655i
\(777\) 15.0000 8.66025i 0.538122 0.310685i