Properties

Label 966.2.i.e.277.1
Level $966$
Weight $2$
Character 966.277
Analytic conductor $7.714$
Analytic rank $0$
Dimension $2$
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: \(2\)
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 277.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 966.277
Dual form 966.2.i.e.415.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -1.00000 q^{6} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -1.00000 q^{6} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{10} +(2.50000 - 4.33013i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-2.00000 + 1.73205i) q^{14} +3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(0.500000 - 0.866025i) q^{18} +3.00000 q^{20} +(-2.50000 - 0.866025i) q^{21} +5.00000 q^{22} +(-0.500000 - 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +1.00000 q^{27} +(-2.50000 - 0.866025i) q^{28} -3.00000 q^{29} +(1.50000 + 2.59808i) q^{30} +(4.50000 - 7.79423i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.50000 + 4.33013i) q^{33} +4.00000 q^{34} +(6.00000 - 5.19615i) q^{35} +1.00000 q^{36} +(6.00000 + 10.3923i) q^{37} +(1.50000 + 2.59808i) q^{40} +12.0000 q^{41} +(-0.500000 - 2.59808i) q^{42} +6.00000 q^{43} +(2.50000 + 4.33013i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-1.00000 - 1.73205i) q^{47} +1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} -4.00000 q^{50} +(2.00000 + 3.46410i) q^{51} +(-2.50000 + 4.33013i) q^{53} +(0.500000 + 0.866025i) q^{54} -15.0000 q^{55} +(-0.500000 - 2.59808i) q^{56} +(-1.50000 - 2.59808i) q^{58} +(4.50000 - 7.79423i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(1.00000 + 1.73205i) q^{61} +9.00000 q^{62} +(2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-2.50000 + 4.33013i) q^{66} +(1.00000 - 1.73205i) q^{67} +(2.00000 + 3.46410i) q^{68} +1.00000 q^{69} +(7.50000 + 2.59808i) q^{70} +6.00000 q^{71} +(0.500000 + 0.866025i) q^{72} +(7.00000 - 12.1244i) q^{73} +(-6.00000 + 10.3923i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(12.5000 + 4.33013i) q^{77} +(-5.50000 - 9.52628i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.00000 + 10.3923i) q^{82} -17.0000 q^{83} +(2.00000 - 1.73205i) q^{84} -12.0000 q^{85} +(3.00000 + 5.19615i) q^{86} +(1.50000 - 2.59808i) q^{87} +(-2.50000 + 4.33013i) q^{88} +(-5.00000 - 8.66025i) q^{89} -3.00000 q^{90} +1.00000 q^{92} +(4.50000 + 7.79423i) q^{93} +(1.00000 - 1.73205i) q^{94} +(0.500000 + 0.866025i) q^{96} -13.0000 q^{97} +(-5.50000 - 4.33013i) q^{98} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{3} - q^{4} - 3 q^{5} - 2 q^{6} + q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{3} - q^{4} - 3 q^{5} - 2 q^{6} + q^{7} - 2 q^{8} - q^{9} + 3 q^{10} + 5 q^{11} - q^{12} - 4 q^{14} + 6 q^{15} - q^{16} + 4 q^{17} + q^{18} + 6 q^{20} - 5 q^{21} + 10 q^{22} - q^{23} + q^{24} - 4 q^{25} + 2 q^{27} - 5 q^{28} - 6 q^{29} + 3 q^{30} + 9 q^{31} + q^{32} + 5 q^{33} + 8 q^{34} + 12 q^{35} + 2 q^{36} + 12 q^{37} + 3 q^{40} + 24 q^{41} - q^{42} + 12 q^{43} + 5 q^{44} - 3 q^{45} + q^{46} - 2 q^{47} + 2 q^{48} - 13 q^{49} - 8 q^{50} + 4 q^{51} - 5 q^{53} + q^{54} - 30 q^{55} - q^{56} - 3 q^{58} + 9 q^{59} - 3 q^{60} + 2 q^{61} + 18 q^{62} + 4 q^{63} + 2 q^{64} - 5 q^{66} + 2 q^{67} + 4 q^{68} + 2 q^{69} + 15 q^{70} + 12 q^{71} + q^{72} + 14 q^{73} - 12 q^{74} - 4 q^{75} + 25 q^{77} - 11 q^{79} - 3 q^{80} - q^{81} + 12 q^{82} - 34 q^{83} + 4 q^{84} - 24 q^{85} + 6 q^{86} + 3 q^{87} - 5 q^{88} - 10 q^{89} - 6 q^{90} + 2 q^{92} + 9 q^{93} + 2 q^{94} + q^{96} - 26 q^{97} - 11 q^{98} - 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(5\) −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i \(-0.932609\pi\)
0.306851 0.951757i \(-0.400725\pi\)
\(6\) −1.00000 −0.408248
\(7\) 0.500000 + 2.59808i 0.188982 + 0.981981i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.50000 2.59808i 0.474342 0.821584i
\(11\) 2.50000 4.33013i 0.753778 1.30558i −0.192201 0.981356i \(-0.561563\pi\)
0.945979 0.324227i \(-0.105104\pi\)
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −2.00000 + 1.73205i −0.534522 + 0.462910i
\(15\) 3.00000 0.774597
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.00000 3.46410i 0.485071 0.840168i −0.514782 0.857321i \(-0.672127\pi\)
0.999853 + 0.0171533i \(0.00546033\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(20\) 3.00000 0.670820
\(21\) −2.50000 0.866025i −0.545545 0.188982i
\(22\) 5.00000 1.06600
\(23\) −0.500000 0.866025i −0.104257 0.180579i
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −2.50000 0.866025i −0.472456 0.163663i
\(29\) −3.00000 −0.557086 −0.278543 0.960424i \(-0.589851\pi\)
−0.278543 + 0.960424i \(0.589851\pi\)
\(30\) 1.50000 + 2.59808i 0.273861 + 0.474342i
\(31\) 4.50000 7.79423i 0.808224 1.39988i −0.105869 0.994380i \(-0.533762\pi\)
0.914093 0.405505i \(-0.132904\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 2.50000 + 4.33013i 0.435194 + 0.753778i
\(34\) 4.00000 0.685994
\(35\) 6.00000 5.19615i 1.01419 0.878310i
\(36\) 1.00000 0.166667
\(37\) 6.00000 + 10.3923i 0.986394 + 1.70848i 0.635571 + 0.772043i \(0.280765\pi\)
0.350823 + 0.936442i \(0.385902\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 1.50000 + 2.59808i 0.237171 + 0.410792i
\(41\) 12.0000 1.87409 0.937043 0.349215i \(-0.113552\pi\)
0.937043 + 0.349215i \(0.113552\pi\)
\(42\) −0.500000 2.59808i −0.0771517 0.400892i
\(43\) 6.00000 0.914991 0.457496 0.889212i \(-0.348747\pi\)
0.457496 + 0.889212i \(0.348747\pi\)
\(44\) 2.50000 + 4.33013i 0.376889 + 0.652791i
\(45\) −1.50000 + 2.59808i −0.223607 + 0.387298i
\(46\) 0.500000 0.866025i 0.0737210 0.127688i
\(47\) −1.00000 1.73205i −0.145865 0.252646i 0.783830 0.620975i \(-0.213263\pi\)
−0.929695 + 0.368329i \(0.879930\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) −4.00000 −0.565685
\(51\) 2.00000 + 3.46410i 0.280056 + 0.485071i
\(52\) 0 0
\(53\) −2.50000 + 4.33013i −0.343401 + 0.594789i −0.985062 0.172200i \(-0.944912\pi\)
0.641661 + 0.766989i \(0.278246\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) −15.0000 −2.02260
\(56\) −0.500000 2.59808i −0.0668153 0.347183i
\(57\) 0 0
\(58\) −1.50000 2.59808i −0.196960 0.341144i
\(59\) 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 + 2.59808i −0.193649 + 0.335410i
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) 9.00000 1.14300
\(63\) 2.00000 1.73205i 0.251976 0.218218i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −2.50000 + 4.33013i −0.307729 + 0.533002i
\(67\) 1.00000 1.73205i 0.122169 0.211604i −0.798454 0.602056i \(-0.794348\pi\)
0.920623 + 0.390453i \(0.127682\pi\)
\(68\) 2.00000 + 3.46410i 0.242536 + 0.420084i
\(69\) 1.00000 0.120386
\(70\) 7.50000 + 2.59808i 0.896421 + 0.310530i
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) 7.00000 12.1244i 0.819288 1.41905i −0.0869195 0.996215i \(-0.527702\pi\)
0.906208 0.422833i \(-0.138964\pi\)
\(74\) −6.00000 + 10.3923i −0.697486 + 1.20808i
\(75\) −2.00000 3.46410i −0.230940 0.400000i
\(76\) 0 0
\(77\) 12.5000 + 4.33013i 1.42451 + 0.493464i
\(78\) 0 0
\(79\) −5.50000 9.52628i −0.618798 1.07179i −0.989705 0.143120i \(-0.954286\pi\)
0.370907 0.928670i \(-0.379047\pi\)
\(80\) −1.50000 + 2.59808i −0.167705 + 0.290474i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 6.00000 + 10.3923i 0.662589 + 1.14764i
\(83\) −17.0000 −1.86599 −0.932996 0.359886i \(-0.882816\pi\)
−0.932996 + 0.359886i \(0.882816\pi\)
\(84\) 2.00000 1.73205i 0.218218 0.188982i
\(85\) −12.0000 −1.30158
\(86\) 3.00000 + 5.19615i 0.323498 + 0.560316i
\(87\) 1.50000 2.59808i 0.160817 0.278543i
\(88\) −2.50000 + 4.33013i −0.266501 + 0.461593i
\(89\) −5.00000 8.66025i −0.529999 0.917985i −0.999388 0.0349934i \(-0.988859\pi\)
0.469389 0.882992i \(-0.344474\pi\)
\(90\) −3.00000 −0.316228
\(91\) 0 0
\(92\) 1.00000 0.104257
\(93\) 4.50000 + 7.79423i 0.466628 + 0.808224i
\(94\) 1.00000 1.73205i 0.103142 0.178647i
\(95\) 0 0
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) −13.0000 −1.31995 −0.659975 0.751288i \(-0.729433\pi\)
−0.659975 + 0.751288i \(0.729433\pi\)
\(98\) −5.50000 4.33013i −0.555584 0.437409i
\(99\) −5.00000 −0.502519
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) 1.00000 1.73205i 0.0995037 0.172345i −0.811976 0.583691i \(-0.801608\pi\)
0.911479 + 0.411346i \(0.134941\pi\)
\(102\) −2.00000 + 3.46410i −0.198030 + 0.342997i
\(103\) −4.00000 6.92820i −0.394132 0.682656i 0.598858 0.800855i \(-0.295621\pi\)
−0.992990 + 0.118199i \(0.962288\pi\)
\(104\) 0 0
\(105\) 1.50000 + 7.79423i 0.146385 + 0.760639i
\(106\) −5.00000 −0.485643
\(107\) 9.50000 + 16.4545i 0.918400 + 1.59071i 0.801846 + 0.597530i \(0.203851\pi\)
0.116553 + 0.993184i \(0.462815\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −3.00000 + 5.19615i −0.287348 + 0.497701i −0.973176 0.230063i \(-0.926107\pi\)
0.685828 + 0.727764i \(0.259440\pi\)
\(110\) −7.50000 12.9904i −0.715097 1.23858i
\(111\) −12.0000 −1.13899
\(112\) 2.00000 1.73205i 0.188982 0.163663i
\(113\) 12.0000 1.12887 0.564433 0.825479i \(-0.309095\pi\)
0.564433 + 0.825479i \(0.309095\pi\)
\(114\) 0 0
\(115\) −1.50000 + 2.59808i −0.139876 + 0.242272i
\(116\) 1.50000 2.59808i 0.139272 0.241225i
\(117\) 0 0
\(118\) 9.00000 0.828517
\(119\) 10.0000 + 3.46410i 0.916698 + 0.317554i
\(120\) −3.00000 −0.273861
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) −1.00000 + 1.73205i −0.0905357 + 0.156813i
\(123\) −6.00000 + 10.3923i −0.541002 + 0.937043i
\(124\) 4.50000 + 7.79423i 0.404112 + 0.699942i
\(125\) −3.00000 −0.268328
\(126\) 2.50000 + 0.866025i 0.222718 + 0.0771517i
\(127\) −11.0000 −0.976092 −0.488046 0.872818i \(-0.662290\pi\)
−0.488046 + 0.872818i \(0.662290\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −3.00000 + 5.19615i −0.264135 + 0.457496i
\(130\) 0 0
\(131\) −1.50000 2.59808i −0.131056 0.226995i 0.793028 0.609185i \(-0.208503\pi\)
−0.924084 + 0.382190i \(0.875170\pi\)
\(132\) −5.00000 −0.435194
\(133\) 0 0
\(134\) 2.00000 0.172774
\(135\) −1.50000 2.59808i −0.129099 0.223607i
\(136\) −2.00000 + 3.46410i −0.171499 + 0.297044i
\(137\) 3.00000 5.19615i 0.256307 0.443937i −0.708942 0.705266i \(-0.750827\pi\)
0.965250 + 0.261329i \(0.0841608\pi\)
\(138\) 0.500000 + 0.866025i 0.0425628 + 0.0737210i
\(139\) −6.00000 −0.508913 −0.254457 0.967084i \(-0.581897\pi\)
−0.254457 + 0.967084i \(0.581897\pi\)
\(140\) 1.50000 + 7.79423i 0.126773 + 0.658733i
\(141\) 2.00000 0.168430
\(142\) 3.00000 + 5.19615i 0.251754 + 0.436051i
\(143\) 0 0
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 4.50000 + 7.79423i 0.373705 + 0.647275i
\(146\) 14.0000 1.15865
\(147\) 1.00000 6.92820i 0.0824786 0.571429i
\(148\) −12.0000 −0.986394
\(149\) 7.00000 + 12.1244i 0.573462 + 0.993266i 0.996207 + 0.0870170i \(0.0277334\pi\)
−0.422744 + 0.906249i \(0.638933\pi\)
\(150\) 2.00000 3.46410i 0.163299 0.282843i
\(151\) 4.50000 7.79423i 0.366205 0.634285i −0.622764 0.782410i \(-0.713990\pi\)
0.988969 + 0.148124i \(0.0473236\pi\)
\(152\) 0 0
\(153\) −4.00000 −0.323381
\(154\) 2.50000 + 12.9904i 0.201456 + 1.04679i
\(155\) −27.0000 −2.16869
\(156\) 0 0
\(157\) 4.00000 6.92820i 0.319235 0.552931i −0.661094 0.750303i \(-0.729907\pi\)
0.980329 + 0.197372i \(0.0632408\pi\)
\(158\) 5.50000 9.52628i 0.437557 0.757870i
\(159\) −2.50000 4.33013i −0.198263 0.343401i
\(160\) −3.00000 −0.237171
\(161\) 2.00000 1.73205i 0.157622 0.136505i
\(162\) −1.00000 −0.0785674
\(163\) 10.0000 + 17.3205i 0.783260 + 1.35665i 0.930033 + 0.367477i \(0.119778\pi\)
−0.146772 + 0.989170i \(0.546888\pi\)
\(164\) −6.00000 + 10.3923i −0.468521 + 0.811503i
\(165\) 7.50000 12.9904i 0.583874 1.01130i
\(166\) −8.50000 14.7224i −0.659728 1.14268i
\(167\) −2.00000 −0.154765 −0.0773823 0.997001i \(-0.524656\pi\)
−0.0773823 + 0.997001i \(0.524656\pi\)
\(168\) 2.50000 + 0.866025i 0.192879 + 0.0668153i
\(169\) −13.0000 −1.00000
\(170\) −6.00000 10.3923i −0.460179 0.797053i
\(171\) 0 0
\(172\) −3.00000 + 5.19615i −0.228748 + 0.396203i
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 3.00000 0.227429
\(175\) −10.0000 3.46410i −0.755929 0.261861i
\(176\) −5.00000 −0.376889
\(177\) 4.50000 + 7.79423i 0.338241 + 0.585850i
\(178\) 5.00000 8.66025i 0.374766 0.649113i
\(179\) 10.0000 17.3205i 0.747435 1.29460i −0.201613 0.979465i \(-0.564618\pi\)
0.949048 0.315130i \(-0.102048\pi\)
\(180\) −1.50000 2.59808i −0.111803 0.193649i
\(181\) −8.00000 −0.594635 −0.297318 0.954779i \(-0.596092\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(182\) 0 0
\(183\) −2.00000 −0.147844
\(184\) 0.500000 + 0.866025i 0.0368605 + 0.0638442i
\(185\) 18.0000 31.1769i 1.32339 2.29217i
\(186\) −4.50000 + 7.79423i −0.329956 + 0.571501i
\(187\) −10.0000 17.3205i −0.731272 1.26660i
\(188\) 2.00000 0.145865
\(189\) 0.500000 + 2.59808i 0.0363696 + 0.188982i
\(190\) 0 0
\(191\) −6.00000 10.3923i −0.434145 0.751961i 0.563081 0.826402i \(-0.309616\pi\)
−0.997225 + 0.0744412i \(0.976283\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −6.50000 + 11.2583i −0.467880 + 0.810392i −0.999326 0.0366998i \(-0.988315\pi\)
0.531446 + 0.847092i \(0.321649\pi\)
\(194\) −6.50000 11.2583i −0.466673 0.808301i
\(195\) 0 0
\(196\) 1.00000 6.92820i 0.0714286 0.494872i
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) −2.50000 4.33013i −0.177667 0.307729i
\(199\) 10.0000 17.3205i 0.708881 1.22782i −0.256391 0.966573i \(-0.582534\pi\)
0.965272 0.261245i \(-0.0841331\pi\)
\(200\) 2.00000 3.46410i 0.141421 0.244949i
\(201\) 1.00000 + 1.73205i 0.0705346 + 0.122169i
\(202\) 2.00000 0.140720
\(203\) −1.50000 7.79423i −0.105279 0.547048i
\(204\) −4.00000 −0.280056
\(205\) −18.0000 31.1769i −1.25717 2.17749i
\(206\) 4.00000 6.92820i 0.278693 0.482711i
\(207\) −0.500000 + 0.866025i −0.0347524 + 0.0601929i
\(208\) 0 0
\(209\) 0 0
\(210\) −6.00000 + 5.19615i −0.414039 + 0.358569i
\(211\) 6.00000 0.413057 0.206529 0.978441i \(-0.433783\pi\)
0.206529 + 0.978441i \(0.433783\pi\)
\(212\) −2.50000 4.33013i −0.171701 0.297394i
\(213\) −3.00000 + 5.19615i −0.205557 + 0.356034i
\(214\) −9.50000 + 16.4545i −0.649407 + 1.12481i
\(215\) −9.00000 15.5885i −0.613795 1.06312i
\(216\) −1.00000 −0.0680414
\(217\) 22.5000 + 7.79423i 1.52740 + 0.529107i
\(218\) −6.00000 −0.406371
\(219\) 7.00000 + 12.1244i 0.473016 + 0.819288i
\(220\) 7.50000 12.9904i 0.505650 0.875811i
\(221\) 0 0
\(222\) −6.00000 10.3923i −0.402694 0.697486i
\(223\) 13.0000 0.870544 0.435272 0.900299i \(-0.356652\pi\)
0.435272 + 0.900299i \(0.356652\pi\)
\(224\) 2.50000 + 0.866025i 0.167038 + 0.0578638i
\(225\) 4.00000 0.266667
\(226\) 6.00000 + 10.3923i 0.399114 + 0.691286i
\(227\) −2.50000 + 4.33013i −0.165931 + 0.287401i −0.936985 0.349368i \(-0.886396\pi\)
0.771055 + 0.636769i \(0.219730\pi\)
\(228\) 0 0
\(229\) 12.0000 + 20.7846i 0.792982 + 1.37349i 0.924113 + 0.382121i \(0.124806\pi\)
−0.131130 + 0.991365i \(0.541861\pi\)
\(230\) −3.00000 −0.197814
\(231\) −10.0000 + 8.66025i −0.657952 + 0.569803i
\(232\) 3.00000 0.196960
\(233\) −10.0000 17.3205i −0.655122 1.13470i −0.981863 0.189590i \(-0.939284\pi\)
0.326741 0.945114i \(-0.394049\pi\)
\(234\) 0 0
\(235\) −3.00000 + 5.19615i −0.195698 + 0.338960i
\(236\) 4.50000 + 7.79423i 0.292925 + 0.507361i
\(237\) 11.0000 0.714527
\(238\) 2.00000 + 10.3923i 0.129641 + 0.673633i
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) −1.50000 2.59808i −0.0968246 0.167705i
\(241\) −9.50000 + 16.4545i −0.611949 + 1.05993i 0.378963 + 0.925412i \(0.376281\pi\)
−0.990912 + 0.134515i \(0.957053\pi\)
\(242\) 7.00000 12.1244i 0.449977 0.779383i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −2.00000 −0.128037
\(245\) 16.5000 + 12.9904i 1.05415 + 0.829925i
\(246\) −12.0000 −0.765092
\(247\) 0 0
\(248\) −4.50000 + 7.79423i −0.285750 + 0.494934i
\(249\) 8.50000 14.7224i 0.538666 0.932996i
\(250\) −1.50000 2.59808i −0.0948683 0.164317i
\(251\) −5.00000 −0.315597 −0.157799 0.987471i \(-0.550440\pi\)
−0.157799 + 0.987471i \(0.550440\pi\)
\(252\) 0.500000 + 2.59808i 0.0314970 + 0.163663i
\(253\) −5.00000 −0.314347
\(254\) −5.50000 9.52628i −0.345101 0.597732i
\(255\) 6.00000 10.3923i 0.375735 0.650791i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −5.00000 8.66025i −0.311891 0.540212i 0.666880 0.745165i \(-0.267629\pi\)
−0.978772 + 0.204953i \(0.934296\pi\)
\(258\) −6.00000 −0.373544
\(259\) −24.0000 + 20.7846i −1.49129 + 1.29149i
\(260\) 0 0
\(261\) 1.50000 + 2.59808i 0.0928477 + 0.160817i
\(262\) 1.50000 2.59808i 0.0926703 0.160510i
\(263\) −9.00000 + 15.5885i −0.554964 + 0.961225i 0.442943 + 0.896550i \(0.353935\pi\)
−0.997906 + 0.0646755i \(0.979399\pi\)
\(264\) −2.50000 4.33013i −0.153864 0.266501i
\(265\) 15.0000 0.921443
\(266\) 0 0
\(267\) 10.0000 0.611990
\(268\) 1.00000 + 1.73205i 0.0610847 + 0.105802i
\(269\) −4.50000 + 7.79423i −0.274370 + 0.475223i −0.969976 0.243201i \(-0.921803\pi\)
0.695606 + 0.718423i \(0.255136\pi\)
\(270\) 1.50000 2.59808i 0.0912871 0.158114i
\(271\) 6.50000 + 11.2583i 0.394847 + 0.683895i 0.993082 0.117426i \(-0.0374643\pi\)
−0.598235 + 0.801321i \(0.704131\pi\)
\(272\) −4.00000 −0.242536
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) 10.0000 + 17.3205i 0.603023 + 1.04447i
\(276\) −0.500000 + 0.866025i −0.0300965 + 0.0521286i
\(277\) −4.00000 + 6.92820i −0.240337 + 0.416275i −0.960810 0.277207i \(-0.910591\pi\)
0.720473 + 0.693482i \(0.243925\pi\)
\(278\) −3.00000 5.19615i −0.179928 0.311645i
\(279\) −9.00000 −0.538816
\(280\) −6.00000 + 5.19615i −0.358569 + 0.310530i
\(281\) 2.00000 0.119310 0.0596550 0.998219i \(-0.481000\pi\)
0.0596550 + 0.998219i \(0.481000\pi\)
\(282\) 1.00000 + 1.73205i 0.0595491 + 0.103142i
\(283\) −3.00000 + 5.19615i −0.178331 + 0.308879i −0.941309 0.337546i \(-0.890403\pi\)
0.762978 + 0.646425i \(0.223737\pi\)
\(284\) −3.00000 + 5.19615i −0.178017 + 0.308335i
\(285\) 0 0
\(286\) 0 0
\(287\) 6.00000 + 31.1769i 0.354169 + 1.84032i
\(288\) −1.00000 −0.0589256
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) −4.50000 + 7.79423i −0.264249 + 0.457693i
\(291\) 6.50000 11.2583i 0.381037 0.659975i
\(292\) 7.00000 + 12.1244i 0.409644 + 0.709524i
\(293\) 33.0000 1.92788 0.963940 0.266119i \(-0.0857413\pi\)
0.963940 + 0.266119i \(0.0857413\pi\)
\(294\) 6.50000 2.59808i 0.379088 0.151523i
\(295\) −27.0000 −1.57200
\(296\) −6.00000 10.3923i −0.348743 0.604040i
\(297\) 2.50000 4.33013i 0.145065 0.251259i
\(298\) −7.00000 + 12.1244i −0.405499 + 0.702345i
\(299\) 0 0
\(300\) 4.00000 0.230940
\(301\) 3.00000 + 15.5885i 0.172917 + 0.898504i
\(302\) 9.00000 0.517892
\(303\) 1.00000 + 1.73205i 0.0574485 + 0.0995037i
\(304\) 0 0
\(305\) 3.00000 5.19615i 0.171780 0.297531i
\(306\) −2.00000 3.46410i −0.114332 0.198030i
\(307\) 12.0000 0.684876 0.342438 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) −10.0000 + 8.66025i −0.569803 + 0.493464i
\(309\) 8.00000 0.455104
\(310\) −13.5000 23.3827i −0.766748 1.32805i
\(311\) −10.0000 + 17.3205i −0.567048 + 0.982156i 0.429808 + 0.902920i \(0.358581\pi\)
−0.996856 + 0.0792356i \(0.974752\pi\)
\(312\) 0 0
\(313\) 5.50000 + 9.52628i 0.310878 + 0.538457i 0.978553 0.205996i \(-0.0660435\pi\)
−0.667674 + 0.744453i \(0.732710\pi\)
\(314\) 8.00000 0.451466
\(315\) −7.50000 2.59808i −0.422577 0.146385i
\(316\) 11.0000 0.618798
\(317\) −2.50000 4.33013i −0.140414 0.243204i 0.787239 0.616649i \(-0.211510\pi\)
−0.927653 + 0.373444i \(0.878177\pi\)
\(318\) 2.50000 4.33013i 0.140193 0.242821i
\(319\) −7.50000 + 12.9904i −0.419919 + 0.727322i
\(320\) −1.50000 2.59808i −0.0838525 0.145237i
\(321\) −19.0000 −1.06048
\(322\) 2.50000 + 0.866025i 0.139320 + 0.0482617i
\(323\) 0 0
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 0 0
\(326\) −10.0000 + 17.3205i −0.553849 + 0.959294i
\(327\) −3.00000 5.19615i −0.165900 0.287348i
\(328\) −12.0000 −0.662589
\(329\) 4.00000 3.46410i 0.220527 0.190982i
\(330\) 15.0000 0.825723
\(331\) 8.00000 + 13.8564i 0.439720 + 0.761617i 0.997668 0.0682590i \(-0.0217444\pi\)
−0.557948 + 0.829876i \(0.688411\pi\)
\(332\) 8.50000 14.7224i 0.466498 0.807998i
\(333\) 6.00000 10.3923i 0.328798 0.569495i
\(334\) −1.00000 1.73205i −0.0547176 0.0947736i
\(335\) −6.00000 −0.327815
\(336\) 0.500000 + 2.59808i 0.0272772 + 0.141737i
\(337\) 21.0000 1.14394 0.571971 0.820274i \(-0.306179\pi\)
0.571971 + 0.820274i \(0.306179\pi\)
\(338\) −6.50000 11.2583i −0.353553 0.612372i
\(339\) −6.00000 + 10.3923i −0.325875 + 0.564433i
\(340\) 6.00000 10.3923i 0.325396 0.563602i
\(341\) −22.5000 38.9711i −1.21844 2.11041i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) −6.00000 −0.323498
\(345\) −1.50000 2.59808i −0.0807573 0.139876i
\(346\) −3.00000 + 5.19615i −0.161281 + 0.279347i
\(347\) 2.00000 3.46410i 0.107366 0.185963i −0.807337 0.590091i \(-0.799092\pi\)
0.914702 + 0.404128i \(0.132425\pi\)
\(348\) 1.50000 + 2.59808i 0.0804084 + 0.139272i
\(349\) 22.0000 1.17763 0.588817 0.808267i \(-0.299594\pi\)
0.588817 + 0.808267i \(0.299594\pi\)
\(350\) −2.00000 10.3923i −0.106904 0.555492i
\(351\) 0 0
\(352\) −2.50000 4.33013i −0.133250 0.230797i
\(353\) −2.00000 + 3.46410i −0.106449 + 0.184376i −0.914329 0.404971i \(-0.867282\pi\)
0.807880 + 0.589347i \(0.200615\pi\)
\(354\) −4.50000 + 7.79423i −0.239172 + 0.414259i
\(355\) −9.00000 15.5885i −0.477670 0.827349i
\(356\) 10.0000 0.529999
\(357\) −8.00000 + 6.92820i −0.423405 + 0.366679i
\(358\) 20.0000 1.05703
\(359\) 5.00000 + 8.66025i 0.263890 + 0.457071i 0.967272 0.253741i \(-0.0816611\pi\)
−0.703382 + 0.710812i \(0.748328\pi\)
\(360\) 1.50000 2.59808i 0.0790569 0.136931i
\(361\) 9.50000 16.4545i 0.500000 0.866025i
\(362\) −4.00000 6.92820i −0.210235 0.364138i
\(363\) 14.0000 0.734809
\(364\) 0 0
\(365\) −42.0000 −2.19838
\(366\) −1.00000 1.73205i −0.0522708 0.0905357i
\(367\) −12.5000 + 21.6506i −0.652495 + 1.13015i 0.330021 + 0.943974i \(0.392944\pi\)
−0.982516 + 0.186180i \(0.940389\pi\)
\(368\) −0.500000 + 0.866025i −0.0260643 + 0.0451447i
\(369\) −6.00000 10.3923i −0.312348 0.541002i
\(370\) 36.0000 1.87155
\(371\) −12.5000 4.33013i −0.648968 0.224809i
\(372\) −9.00000 −0.466628
\(373\) 4.00000 + 6.92820i 0.207112 + 0.358729i 0.950804 0.309794i \(-0.100260\pi\)
−0.743691 + 0.668523i \(0.766927\pi\)
\(374\) 10.0000 17.3205i 0.517088 0.895622i
\(375\) 1.50000 2.59808i 0.0774597 0.134164i
\(376\) 1.00000 + 1.73205i 0.0515711 + 0.0893237i
\(377\) 0 0
\(378\) −2.00000 + 1.73205i −0.102869 + 0.0890871i
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 0 0
\(381\) 5.50000 9.52628i 0.281774 0.488046i
\(382\) 6.00000 10.3923i 0.306987 0.531717i
\(383\) 9.00000 + 15.5885i 0.459879 + 0.796533i 0.998954 0.0457244i \(-0.0145596\pi\)
−0.539076 + 0.842257i \(0.681226\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −7.50000 38.9711i −0.382235 1.98615i
\(386\) −13.0000 −0.661683
\(387\) −3.00000 5.19615i −0.152499 0.264135i
\(388\) 6.50000 11.2583i 0.329988 0.571555i
\(389\) −9.00000 + 15.5885i −0.456318 + 0.790366i −0.998763 0.0497253i \(-0.984165\pi\)
0.542445 + 0.840091i \(0.317499\pi\)
\(390\) 0 0
\(391\) −4.00000 −0.202289
\(392\) 6.50000 2.59808i 0.328300 0.131223i
\(393\) 3.00000 0.151330
\(394\) −1.00000 1.73205i −0.0503793 0.0872595i
\(395\) −16.5000 + 28.5788i −0.830205 + 1.43796i
\(396\) 2.50000 4.33013i 0.125630 0.217597i
\(397\) 4.00000 + 6.92820i 0.200754 + 0.347717i 0.948772 0.315963i \(-0.102327\pi\)
−0.748017 + 0.663679i \(0.768994\pi\)
\(398\) 20.0000 1.00251
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) −16.0000 27.7128i −0.799002 1.38391i −0.920267 0.391292i \(-0.872028\pi\)
0.121265 0.992620i \(-0.461305\pi\)
\(402\) −1.00000 + 1.73205i −0.0498755 + 0.0863868i
\(403\) 0 0
\(404\) 1.00000 + 1.73205i 0.0497519 + 0.0861727i
\(405\) 3.00000 0.149071
\(406\) 6.00000 5.19615i 0.297775 0.257881i
\(407\) 60.0000 2.97409
\(408\) −2.00000 3.46410i −0.0990148 0.171499i
\(409\) −3.50000 + 6.06218i −0.173064 + 0.299755i −0.939490 0.342578i \(-0.888700\pi\)
0.766426 + 0.642333i \(0.222033\pi\)
\(410\) 18.0000 31.1769i 0.888957 1.53972i
\(411\) 3.00000 + 5.19615i 0.147979 + 0.256307i
\(412\) 8.00000 0.394132
\(413\) 22.5000 + 7.79423i 1.10715 + 0.383529i
\(414\) −1.00000 −0.0491473
\(415\) 25.5000 + 44.1673i 1.25175 + 2.16809i
\(416\) 0 0
\(417\) 3.00000 5.19615i 0.146911 0.254457i
\(418\) 0 0
\(419\) −16.0000 −0.781651 −0.390826 0.920465i \(-0.627810\pi\)
−0.390826 + 0.920465i \(0.627810\pi\)
\(420\) −7.50000 2.59808i −0.365963 0.126773i
\(421\) −6.00000 −0.292422 −0.146211 0.989253i \(-0.546708\pi\)
−0.146211 + 0.989253i \(0.546708\pi\)
\(422\) 3.00000 + 5.19615i 0.146038 + 0.252945i
\(423\) −1.00000 + 1.73205i −0.0486217 + 0.0842152i
\(424\) 2.50000 4.33013i 0.121411 0.210290i
\(425\) 8.00000 + 13.8564i 0.388057 + 0.672134i
\(426\) −6.00000 −0.290701
\(427\) −4.00000 + 3.46410i −0.193574 + 0.167640i
\(428\) −19.0000 −0.918400
\(429\) 0 0
\(430\) 9.00000 15.5885i 0.434019 0.751742i
\(431\) 6.00000 10.3923i 0.289010 0.500580i −0.684564 0.728953i \(-0.740007\pi\)
0.973574 + 0.228373i \(0.0733406\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 4.50000 + 23.3827i 0.216007 + 1.12240i
\(435\) −9.00000 −0.431517
\(436\) −3.00000 5.19615i −0.143674 0.248851i
\(437\) 0 0
\(438\) −7.00000 + 12.1244i −0.334473 + 0.579324i
\(439\) 6.50000 + 11.2583i 0.310228 + 0.537331i 0.978412 0.206666i \(-0.0662612\pi\)
−0.668184 + 0.743996i \(0.732928\pi\)
\(440\) 15.0000 0.715097
\(441\) 5.50000 + 4.33013i 0.261905 + 0.206197i
\(442\) 0 0
\(443\) 14.5000 + 25.1147i 0.688916 + 1.19324i 0.972189 + 0.234198i \(0.0752464\pi\)
−0.283273 + 0.959039i \(0.591420\pi\)
\(444\) 6.00000 10.3923i 0.284747 0.493197i
\(445\) −15.0000 + 25.9808i −0.711068 + 1.23161i
\(446\) 6.50000 + 11.2583i 0.307784 + 0.533097i
\(447\) −14.0000 −0.662177
\(448\) 0.500000 + 2.59808i 0.0236228 + 0.122748i
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 2.00000 + 3.46410i 0.0942809 + 0.163299i
\(451\) 30.0000 51.9615i 1.41264 2.44677i
\(452\) −6.00000 + 10.3923i −0.282216 + 0.488813i
\(453\) 4.50000 + 7.79423i 0.211428 + 0.366205i
\(454\) −5.00000 −0.234662
\(455\) 0 0
\(456\) 0 0
\(457\) 10.5000 + 18.1865i 0.491169 + 0.850730i 0.999948 0.0101670i \(-0.00323631\pi\)
−0.508779 + 0.860897i \(0.669903\pi\)
\(458\) −12.0000 + 20.7846i −0.560723 + 0.971201i
\(459\) 2.00000 3.46410i 0.0933520 0.161690i
\(460\) −1.50000 2.59808i −0.0699379 0.121136i
\(461\) 14.0000 0.652045 0.326023 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) −12.5000 4.33013i −0.581553 0.201456i
\(463\) −32.0000 −1.48717 −0.743583 0.668644i \(-0.766875\pi\)
−0.743583 + 0.668644i \(0.766875\pi\)
\(464\) 1.50000 + 2.59808i 0.0696358 + 0.120613i
\(465\) 13.5000 23.3827i 0.626048 1.08435i
\(466\) 10.0000 17.3205i 0.463241 0.802357i
\(467\) −14.0000 24.2487i −0.647843 1.12210i −0.983637 0.180161i \(-0.942338\pi\)
0.335794 0.941935i \(-0.390995\pi\)
\(468\) 0 0
\(469\) 5.00000 + 1.73205i 0.230879 + 0.0799787i
\(470\) −6.00000 −0.276759
\(471\) 4.00000 + 6.92820i 0.184310 + 0.319235i
\(472\) −4.50000 + 7.79423i −0.207129 + 0.358758i
\(473\) 15.0000 25.9808i 0.689701 1.19460i
\(474\) 5.50000 + 9.52628i 0.252623 + 0.437557i
\(475\) 0 0
\(476\) −8.00000 + 6.92820i −0.366679 + 0.317554i
\(477\) 5.00000 0.228934
\(478\) −12.0000 20.7846i −0.548867 0.950666i
\(479\) −9.00000 + 15.5885i −0.411220 + 0.712255i −0.995023 0.0996406i \(-0.968231\pi\)
0.583803 + 0.811895i \(0.301564\pi\)
\(480\) 1.50000 2.59808i 0.0684653 0.118585i
\(481\) 0 0
\(482\) −19.0000 −0.865426
\(483\) 0.500000 + 2.59808i 0.0227508 + 0.118217i
\(484\) 14.0000 0.636364
\(485\) 19.5000 + 33.7750i 0.885449 + 1.53364i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) 11.5000 19.9186i 0.521115 0.902597i −0.478584 0.878042i \(-0.658850\pi\)
0.999698 0.0245553i \(-0.00781698\pi\)
\(488\) −1.00000 1.73205i −0.0452679 0.0784063i
\(489\) −20.0000 −0.904431
\(490\) −3.00000 + 20.7846i −0.135526 + 0.938953i
\(491\) 27.0000 1.21849 0.609246 0.792981i \(-0.291472\pi\)
0.609246 + 0.792981i \(0.291472\pi\)
\(492\) −6.00000 10.3923i −0.270501 0.468521i
\(493\) −6.00000 + 10.3923i −0.270226 + 0.468046i
\(494\) 0 0
\(495\) 7.50000 + 12.9904i 0.337100 + 0.583874i
\(496\) −9.00000 −0.404112
\(497\) 3.00000 + 15.5885i 0.134568 + 0.699238i
\(498\) 17.0000 0.761788
\(499\) −5.00000 8.66025i −0.223831 0.387686i 0.732137 0.681157i \(-0.238523\pi\)
−0.955968 + 0.293471i \(0.905190\pi\)
\(500\) 1.50000 2.59808i 0.0670820 0.116190i
\(501\) 1.00000 1.73205i 0.0446767 0.0773823i
\(502\) −2.50000 4.33013i −0.111580 0.193263i
\(503\) 12.0000 0.535054 0.267527 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) −2.00000 + 1.73205i −0.0890871 + 0.0771517i
\(505\) −6.00000 −0.266996
\(506\) −2.50000 4.33013i −0.111139 0.192498i
\(507\) 6.50000 11.2583i 0.288675 0.500000i
\(508\) 5.50000 9.52628i 0.244023 0.422660i
\(509\) 15.5000 + 26.8468i 0.687025 + 1.18996i 0.972796 + 0.231665i \(0.0744172\pi\)
−0.285770 + 0.958298i \(0.592249\pi\)
\(510\) 12.0000 0.531369
\(511\) 35.0000 + 12.1244i 1.54831 + 0.536350i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 5.00000 8.66025i 0.220541 0.381987i
\(515\) −12.0000 + 20.7846i −0.528783 + 0.915879i
\(516\) −3.00000 5.19615i −0.132068 0.228748i
\(517\) −10.0000 −0.439799
\(518\) −30.0000 10.3923i −1.31812 0.456612i
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) −15.0000 + 25.9808i −0.657162 + 1.13824i 0.324185 + 0.945994i \(0.394910\pi\)
−0.981347 + 0.192244i \(0.938423\pi\)
\(522\) −1.50000 + 2.59808i −0.0656532 + 0.113715i
\(523\) −18.0000 31.1769i −0.787085 1.36327i −0.927746 0.373213i \(-0.878256\pi\)
0.140660 0.990058i \(-0.455077\pi\)
\(524\) 3.00000 0.131056
\(525\) 8.00000 6.92820i 0.349149 0.302372i
\(526\) −18.0000 −0.784837
\(527\) −18.0000 31.1769i −0.784092 1.35809i
\(528\) 2.50000 4.33013i 0.108799 0.188445i
\(529\) −0.500000 + 0.866025i −0.0217391 + 0.0376533i
\(530\) 7.50000 + 12.9904i 0.325779 + 0.564266i
\(531\) −9.00000 −0.390567
\(532\) 0 0
\(533\) 0 0
\(534\) 5.00000 + 8.66025i 0.216371 + 0.374766i
\(535\) 28.5000 49.3634i 1.23216 2.13417i
\(536\) −1.00000 + 1.73205i −0.0431934 + 0.0748132i
\(537\) 10.0000 + 17.3205i 0.431532 + 0.747435i
\(538\) −9.00000 −0.388018
\(539\) −5.00000 + 34.6410i −0.215365 + 1.49209i
\(540\) 3.00000 0.129099
\(541\) 17.0000 + 29.4449i 0.730887 + 1.26593i 0.956504 + 0.291718i \(0.0942267\pi\)
−0.225617 + 0.974216i \(0.572440\pi\)
\(542\) −6.50000 + 11.2583i −0.279199 + 0.483587i
\(543\) 4.00000 6.92820i 0.171656 0.297318i
\(544\) −2.00000 3.46410i −0.0857493 0.148522i
\(545\) 18.0000 0.771035
\(546\) 0 0
\(547\) −44.0000 −1.88130 −0.940652 0.339372i \(-0.889785\pi\)
−0.940652 + 0.339372i \(0.889785\pi\)
\(548\) 3.00000 + 5.19615i 0.128154 + 0.221969i
\(549\) 1.00000 1.73205i 0.0426790 0.0739221i
\(550\) −10.0000 + 17.3205i −0.426401 + 0.738549i
\(551\) 0 0
\(552\) −1.00000 −0.0425628
\(553\) 22.0000 19.0526i 0.935535 0.810197i
\(554\) −8.00000 −0.339887
\(555\) 18.0000 + 31.1769i 0.764057 + 1.32339i
\(556\) 3.00000 5.19615i 0.127228 0.220366i
\(557\) −1.50000 + 2.59808i −0.0635570 + 0.110084i −0.896053 0.443947i \(-0.853578\pi\)
0.832496 + 0.554031i \(0.186911\pi\)
\(558\) −4.50000 7.79423i −0.190500 0.329956i
\(559\) 0 0
\(560\) −7.50000 2.59808i −0.316933 0.109789i
\(561\) 20.0000 0.844401
\(562\) 1.00000 + 1.73205i 0.0421825 + 0.0730622i
\(563\) −19.5000 + 33.7750i −0.821827 + 1.42345i 0.0824933 + 0.996592i \(0.473712\pi\)
−0.904320 + 0.426855i \(0.859622\pi\)
\(564\) −1.00000 + 1.73205i −0.0421076 + 0.0729325i
\(565\) −18.0000 31.1769i −0.757266 1.31162i
\(566\) −6.00000 −0.252199
\(567\) −2.50000 0.866025i −0.104990 0.0363696i
\(568\) −6.00000 −0.251754
\(569\) −10.0000 17.3205i −0.419222 0.726113i 0.576640 0.816999i \(-0.304364\pi\)
−0.995861 + 0.0908852i \(0.971030\pi\)
\(570\) 0 0
\(571\) −5.00000 + 8.66025i −0.209243 + 0.362420i −0.951476 0.307722i \(-0.900433\pi\)
0.742233 + 0.670142i \(0.233767\pi\)
\(572\) 0 0
\(573\) 12.0000 0.501307
\(574\) −24.0000 + 20.7846i −1.00174 + 0.867533i
\(575\) 4.00000 0.166812
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −19.5000 + 33.7750i −0.811796 + 1.40607i 0.0998105 + 0.995006i \(0.468176\pi\)
−0.911606 + 0.411065i \(0.865157\pi\)
\(578\) −0.500000 + 0.866025i −0.0207973 + 0.0360219i
\(579\) −6.50000 11.2583i −0.270131 0.467880i
\(580\) −9.00000 −0.373705
\(581\) −8.50000 44.1673i −0.352639 1.83237i
\(582\) 13.0000 0.538867
\(583\) 12.5000 + 21.6506i 0.517697 + 0.896678i
\(584\) −7.00000 + 12.1244i −0.289662 + 0.501709i
\(585\) 0 0
\(586\) 16.5000 + 28.5788i 0.681609 + 1.18058i
\(587\) −15.0000 −0.619116 −0.309558 0.950881i \(-0.600181\pi\)
−0.309558 + 0.950881i \(0.600181\pi\)
\(588\) 5.50000 + 4.33013i 0.226816 + 0.178571i
\(589\) 0 0
\(590\) −13.5000 23.3827i −0.555786 0.962650i
\(591\) 1.00000 1.73205i 0.0411345 0.0712470i
\(592\) 6.00000 10.3923i 0.246598 0.427121i
\(593\) −4.00000 6.92820i −0.164260 0.284507i 0.772132 0.635462i \(-0.219190\pi\)
−0.936392 + 0.350955i \(0.885857\pi\)
\(594\) 5.00000 0.205152
\(595\) −6.00000 31.1769i −0.245976 1.27813i
\(596\) −14.0000 −0.573462
\(597\) 10.0000 + 17.3205i 0.409273 + 0.708881i
\(598\) 0 0
\(599\) 11.0000 19.0526i 0.449448 0.778466i −0.548902 0.835887i \(-0.684954\pi\)
0.998350 + 0.0574201i \(0.0182874\pi\)
\(600\) 2.00000 + 3.46410i 0.0816497 + 0.141421i
\(601\) 11.0000 0.448699 0.224350 0.974509i \(-0.427974\pi\)
0.224350 + 0.974509i \(0.427974\pi\)
\(602\) −12.0000 + 10.3923i −0.489083 + 0.423559i
\(603\) −2.00000 −0.0814463
\(604\) 4.50000 + 7.79423i 0.183102 + 0.317143i
\(605\) −21.0000 + 36.3731i −0.853771 + 1.47878i
\(606\) −1.00000 + 1.73205i −0.0406222 + 0.0703598i
\(607\) 7.50000 + 12.9904i 0.304416 + 0.527263i 0.977131 0.212638i \(-0.0682055\pi\)
−0.672715 + 0.739901i \(0.734872\pi\)
\(608\) 0 0
\(609\) 7.50000 + 2.59808i 0.303915 + 0.105279i
\(610\) 6.00000 0.242933
\(611\) 0 0
\(612\) 2.00000 3.46410i 0.0808452 0.140028i
\(613\) −8.00000 + 13.8564i −0.323117 + 0.559655i −0.981129 0.193352i \(-0.938064\pi\)
0.658012 + 0.753007i \(0.271397\pi\)
\(614\) 6.00000 + 10.3923i 0.242140 + 0.419399i
\(615\) 36.0000 1.45166
\(616\) −12.5000 4.33013i −0.503639 0.174466i
\(617\) 42.0000 1.69086 0.845428 0.534089i \(-0.179345\pi\)
0.845428 + 0.534089i \(0.179345\pi\)
\(618\) 4.00000 + 6.92820i 0.160904 + 0.278693i
\(619\) 23.0000 39.8372i 0.924448 1.60119i 0.132002 0.991250i \(-0.457860\pi\)
0.792446 0.609941i \(-0.208807\pi\)
\(620\) 13.5000 23.3827i 0.542173 0.939071i
\(621\) −0.500000 0.866025i −0.0200643 0.0347524i
\(622\) −20.0000 −0.801927
\(623\) 20.0000 17.3205i 0.801283 0.693932i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) −5.50000 + 9.52628i −0.219824 + 0.380747i
\(627\) 0 0
\(628\) 4.00000 + 6.92820i 0.159617 + 0.276465i
\(629\) 48.0000 1.91389
\(630\) −1.50000 7.79423i −0.0597614 0.310530i
\(631\) 37.0000 1.47295 0.736473 0.676467i \(-0.236490\pi\)
0.736473 + 0.676467i \(0.236490\pi\)
\(632\) 5.50000 + 9.52628i 0.218778 + 0.378935i
\(633\) −3.00000 + 5.19615i −0.119239 + 0.206529i
\(634\) 2.50000 4.33013i 0.0992877 0.171971i
\(635\) 16.5000 + 28.5788i 0.654783 + 1.13412i
\(636\) 5.00000 0.198263
\(637\) 0 0
\(638\) −15.0000 −0.593856
\(639\) −3.00000 5.19615i −0.118678 0.205557i
\(640\) 1.50000 2.59808i 0.0592927 0.102698i
\(641\) −15.0000 + 25.9808i −0.592464 + 1.02618i 0.401435 + 0.915888i \(0.368512\pi\)
−0.993899 + 0.110291i \(0.964822\pi\)
\(642\) −9.50000 16.4545i −0.374935 0.649407i
\(643\) −14.0000 −0.552106 −0.276053 0.961142i \(-0.589027\pi\)
−0.276053 + 0.961142i \(0.589027\pi\)
\(644\) 0.500000 + 2.59808i 0.0197028 + 0.102379i
\(645\) 18.0000 0.708749
\(646\) 0 0
\(647\) 9.00000 15.5885i 0.353827 0.612845i −0.633090 0.774078i \(-0.718214\pi\)
0.986916 + 0.161233i \(0.0515470\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) −22.5000 38.9711i −0.883202 1.52975i
\(650\) 0 0
\(651\) −18.0000 + 15.5885i −0.705476 + 0.610960i
\(652\) −20.0000 −0.783260
\(653\) 8.50000 + 14.7224i 0.332631 + 0.576133i 0.983027 0.183462i \(-0.0587304\pi\)
−0.650396 + 0.759595i \(0.725397\pi\)
\(654\) 3.00000 5.19615i 0.117309 0.203186i
\(655\) −4.50000 + 7.79423i −0.175830 + 0.304546i
\(656\) −6.00000 10.3923i −0.234261 0.405751i
\(657\) −14.0000 −0.546192
\(658\) 5.00000 + 1.73205i 0.194920 + 0.0675224i
\(659\) −24.0000 −0.934907 −0.467454 0.884018i \(-0.654829\pi\)
−0.467454 + 0.884018i \(0.654829\pi\)
\(660\) 7.50000 + 12.9904i 0.291937 + 0.505650i
\(661\) −11.0000 + 19.0526i −0.427850 + 0.741059i −0.996682 0.0813955i \(-0.974062\pi\)
0.568831 + 0.822454i \(0.307396\pi\)
\(662\) −8.00000 + 13.8564i −0.310929 + 0.538545i
\(663\) 0 0
\(664\) 17.0000 0.659728
\(665\) 0 0
\(666\) 12.0000 0.464991
\(667\) 1.50000 + 2.59808i 0.0580802 + 0.100598i
\(668\) 1.00000 1.73205i 0.0386912 0.0670151i
\(669\) −6.50000 + 11.2583i −0.251305 + 0.435272i
\(670\) −3.00000 5.19615i −0.115900 0.200745i
\(671\) 10.0000 0.386046
\(672\) −2.00000 + 1.73205i −0.0771517 + 0.0668153i
\(673\) 13.0000 0.501113 0.250557 0.968102i \(-0.419386\pi\)
0.250557 + 0.968102i \(0.419386\pi\)
\(674\) 10.5000 + 18.1865i 0.404445 + 0.700519i
\(675\) −2.00000 + 3.46410i −0.0769800 + 0.133333i
\(676\) 6.50000 11.2583i 0.250000 0.433013i
\(677\) −15.5000 26.8468i −0.595713 1.03181i −0.993446 0.114304i \(-0.963536\pi\)
0.397732 0.917501i \(-0.369797\pi\)
\(678\) −12.0000 −0.460857
\(679\) −6.50000 33.7750i −0.249447 1.29617i
\(680\) 12.0000 0.460179
\(681\) −2.50000 4.33013i −0.0958002 0.165931i
\(682\) 22.5000 38.9711i 0.861570 1.49228i
\(683\) 21.5000 37.2391i 0.822675 1.42491i −0.0810089 0.996713i \(-0.525814\pi\)
0.903684 0.428201i \(-0.140852\pi\)
\(684\) 0 0
\(685\) −18.0000 −0.687745
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) −24.0000 −0.915657
\(688\) −3.00000 5.19615i −0.114374 0.198101i
\(689\) 0 0
\(690\) 1.50000 2.59808i 0.0571040 0.0989071i
\(691\) −14.0000 24.2487i −0.532585 0.922464i −0.999276 0.0380440i \(-0.987887\pi\)
0.466691 0.884420i \(-0.345446\pi\)
\(692\) −6.00000 −0.228086
\(693\) −2.50000 12.9904i −0.0949671 0.493464i
\(694\) 4.00000 0.151838
\(695\) 9.00000 + 15.5885i 0.341389 + 0.591304i
\(696\) −1.50000 + 2.59808i −0.0568574 + 0.0984798i
\(697\) 24.0000 41.5692i 0.909065 1.57455i
\(698\) 11.0000 + 19.0526i 0.416356 + 0.721150i
\(699\) 20.0000 0.756469
\(700\) 8.00000 6.92820i 0.302372 0.261861i
\(701\) 9.00000 0.339925 0.169963 0.985451i \(-0.445635\pi\)
0.169963 + 0.985451i \(0.445635\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 2.50000 4.33013i 0.0942223 0.163198i
\(705\) −3.00000 5.19615i −0.112987 0.195698i
\(706\) −4.00000 −0.150542
\(707\) 5.00000 + 1.73205i 0.188044 + 0.0651405i
\(708\) −9.00000 −0.338241
\(709\) 11.0000 + 19.0526i 0.413114 + 0.715534i 0.995228 0.0975728i \(-0.0311079\pi\)
−0.582115 + 0.813107i \(0.697775\pi\)
\(710\) 9.00000 15.5885i 0.337764 0.585024i
\(711\) −5.50000 + 9.52628i −0.206266 + 0.357263i
\(712\) 5.00000 + 8.66025i 0.187383 + 0.324557i
\(713\) −9.00000 −0.337053
\(714\) −10.0000 3.46410i −0.374241 0.129641i
\(715\) 0 0
\(716\) 10.0000 + 17.3205i 0.373718 + 0.647298i
\(717\) 12.0000 20.7846i 0.448148 0.776215i
\(718\) −5.00000 + 8.66025i −0.186598 + 0.323198i
\(719\) −7.00000 12.1244i −0.261056 0.452162i 0.705467 0.708743i \(-0.250737\pi\)
−0.966523 + 0.256581i \(0.917404\pi\)
\(720\) 3.00000 0.111803
\(721\) 16.0000 13.8564i 0.595871 0.516040i
\(722\) 19.0000 0.707107
\(723\) −9.50000 16.4545i −0.353309 0.611949i
\(724\) 4.00000 6.92820i 0.148659 0.257485i
\(725\) 6.00000 10.3923i 0.222834 0.385961i
\(726\) 7.00000 + 12.1244i 0.259794 + 0.449977i
\(727\) 7.00000 0.259616 0.129808 0.991539i \(-0.458564\pi\)
0.129808 + 0.991539i \(0.458564\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −21.0000 36.3731i −0.777245 1.34623i
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) 1.00000 1.73205i 0.0369611 0.0640184i
\(733\) 23.0000 + 39.8372i 0.849524 + 1.47142i 0.881633 + 0.471935i \(0.156444\pi\)
−0.0321090 + 0.999484i \(0.510222\pi\)
\(734\) −25.0000 −0.922767
\(735\) −19.5000 + 7.79423i −0.719268 + 0.287494i
\(736\) −1.00000 −0.0368605
\(737\) −5.00000 8.66025i −0.184177 0.319005i
\(738\) 6.00000 10.3923i 0.220863 0.382546i
\(739\) −1.00000 + 1.73205i −0.0367856 + 0.0637145i −0.883832 0.467804i \(-0.845045\pi\)
0.847046 + 0.531519i \(0.178379\pi\)
\(740\) 18.0000 + 31.1769i 0.661693 + 1.14609i
\(741\) 0 0
\(742\) −2.50000 12.9904i −0.0917779 0.476892i
\(743\) −26.0000 −0.953847 −0.476924 0.878945i \(-0.658248\pi\)
−0.476924 + 0.878945i \(0.658248\pi\)
\(744\) −4.50000 7.79423i −0.164978 0.285750i
\(745\) 21.0000 36.3731i 0.769380 1.33261i
\(746\) −4.00000 + 6.92820i −0.146450 + 0.253660i
\(747\) 8.50000 + 14.7224i 0.310999 + 0.538666i
\(748\) 20.0000 0.731272
\(749\) −38.0000 + 32.9090i −1.38849 + 1.20247i
\(750\) 3.00000 0.109545
\(751\) −2.50000 4.33013i −0.0912263 0.158009i 0.816801 0.576919i \(-0.195745\pi\)
−0.908027 + 0.418911i \(0.862412\pi\)
\(752\) −1.00000 + 1.73205i −0.0364662 + 0.0631614i
\(753\) 2.50000 4.33013i 0.0911051 0.157799i
\(754\) 0 0
\(755\) −27.0000 −0.982631
\(756\) −2.50000 0.866025i −0.0909241 0.0314970i
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) −8.00000 13.8564i −0.290573 0.503287i
\(759\) 2.50000 4.33013i 0.0907443 0.157174i
\(760\) 0 0
\(761\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(762\) 11.0000 0.398488
\(763\) −15.0000 5.19615i −0.543036 0.188113i
\(764\) 12.0000 0.434145
\(765\) 6.00000 + 10.3923i 0.216930 + 0.375735i
\(766\) −9.00000 + 15.5885i −0.325183 + 0.563234i
\(767\) 0 0
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) −31.0000 −1.11789 −0.558944 0.829205i \(-0.688793\pi\)
−0.558944 + 0.829205i \(0.688793\pi\)
\(770\) 30.0000 25.9808i 1.08112 0.936282i
\(771\) 10.0000 0.360141
\(772\) −6.50000 11.2583i −0.233940 0.405196i
\(773\) −23.0000 + 39.8372i −0.827253 + 1.43284i 0.0729331 + 0.997337i \(0.476764\pi\)
−0.900186 + 0.435507i \(0.856569\pi\)
\(774\) 3.00000 5.19615i 0.107833 0.186772i
\(775\) 18.0000 + 31.1769i 0.646579 + 1.11991i
\(776\) 13.0000 0.466673
\(777\) −6.00000 31.1769i −0.215249 1.11847i
\(778\) −18.0000 −0.645331