Properties

Label 210.2.i.b.121.1
Level $210$
Weight $2$
Character 210.121
Analytic conductor $1.677$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.67685844245\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
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 121.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 210.121
Dual form 210.2.i.b.151.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(2.50000 + 4.33013i) q^{11} +(0.500000 - 0.866025i) q^{12} -5.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(3.50000 - 6.06218i) q^{19} +1.00000 q^{20} +(-2.50000 - 0.866025i) q^{21} -5.00000 q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.50000 - 4.33013i) q^{26} -1.00000 q^{27} +(2.50000 + 0.866025i) q^{28} +(0.500000 - 0.866025i) q^{30} +(1.00000 + 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.50000 + 4.33013i) q^{33} -4.00000 q^{34} +(-0.500000 - 2.59808i) q^{35} +1.00000 q^{36} +(-0.500000 + 0.866025i) q^{37} +(3.50000 + 6.06218i) q^{38} +(-2.50000 - 4.33013i) q^{39} +(-0.500000 + 0.866025i) q^{40} +5.00000 q^{41} +(2.00000 - 1.73205i) q^{42} +12.0000 q^{43} +(2.50000 - 4.33013i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(5.50000 - 9.52628i) q^{47} -1.00000 q^{48} +(1.00000 - 6.92820i) q^{49} +1.00000 q^{50} +(-2.00000 + 3.46410i) q^{51} +(2.50000 + 4.33013i) q^{52} +(4.50000 + 7.79423i) q^{53} +(0.500000 - 0.866025i) q^{54} -5.00000 q^{55} +(-2.00000 + 1.73205i) q^{56} +7.00000 q^{57} +(-2.00000 - 3.46410i) q^{59} +(0.500000 + 0.866025i) q^{60} +(-2.00000 + 3.46410i) q^{61} -2.00000 q^{62} +(-0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(2.50000 - 4.33013i) q^{65} +(-2.50000 - 4.33013i) q^{66} +(6.00000 + 10.3923i) q^{67} +(2.00000 - 3.46410i) q^{68} -1.00000 q^{69} +(2.50000 + 0.866025i) q^{70} +2.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-5.00000 - 8.66025i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(0.500000 - 0.866025i) q^{75} -7.00000 q^{76} +(-12.5000 - 4.33013i) q^{77} +5.00000 q^{78} +(6.00000 - 10.3923i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.50000 + 4.33013i) q^{82} -12.0000 q^{83} +(0.500000 + 2.59808i) q^{84} -4.00000 q^{85} +(-6.00000 + 10.3923i) q^{86} +(2.50000 + 4.33013i) q^{88} +(-7.00000 + 12.1244i) q^{89} +1.00000 q^{90} +(10.0000 - 8.66025i) q^{91} +1.00000 q^{92} +(-1.00000 + 1.73205i) q^{93} +(5.50000 + 9.52628i) q^{94} +(3.50000 + 6.06218i) q^{95} +(0.500000 - 0.866025i) q^{96} -8.00000 q^{97} +(5.50000 + 4.33013i) q^{98} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + q^{3} - q^{4} - q^{5} - 2q^{6} - 4q^{7} + 2q^{8} - q^{9} + O(q^{10}) \) \( 2q - q^{2} + q^{3} - q^{4} - q^{5} - 2q^{6} - 4q^{7} + 2q^{8} - q^{9} - q^{10} + 5q^{11} + q^{12} - 10q^{13} - q^{14} - 2q^{15} - q^{16} + 4q^{17} - q^{18} + 7q^{19} + 2q^{20} - 5q^{21} - 10q^{22} - q^{23} + q^{24} - q^{25} + 5q^{26} - 2q^{27} + 5q^{28} + q^{30} + 2q^{31} - q^{32} - 5q^{33} - 8q^{34} - q^{35} + 2q^{36} - q^{37} + 7q^{38} - 5q^{39} - q^{40} + 10q^{41} + 4q^{42} + 24q^{43} + 5q^{44} - q^{45} - q^{46} + 11q^{47} - 2q^{48} + 2q^{49} + 2q^{50} - 4q^{51} + 5q^{52} + 9q^{53} + q^{54} - 10q^{55} - 4q^{56} + 14q^{57} - 4q^{59} + q^{60} - 4q^{61} - 4q^{62} - q^{63} + 2q^{64} + 5q^{65} - 5q^{66} + 12q^{67} + 4q^{68} - 2q^{69} + 5q^{70} + 4q^{71} - q^{72} - 10q^{73} - q^{74} + q^{75} - 14q^{76} - 25q^{77} + 10q^{78} + 12q^{79} - q^{80} - q^{81} - 5q^{82} - 24q^{83} + q^{84} - 8q^{85} - 12q^{86} + 5q^{88} - 14q^{89} + 2q^{90} + 20q^{91} + 2q^{92} - 2q^{93} + 11q^{94} + 7q^{95} + q^{96} - 16q^{97} + 11q^{98} - 10q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) −1.00000 −0.408248
\(7\) −2.00000 + 1.73205i −0.755929 + 0.654654i
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) 2.50000 + 4.33013i 0.753778 + 1.30558i 0.945979 + 0.324227i \(0.105104\pi\)
−0.192201 + 0.981356i \(0.561563\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) −5.00000 −1.38675 −0.693375 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) −0.500000 2.59808i −0.133631 0.694365i
\(15\) −1.00000 −0.258199
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.00000 + 3.46410i 0.485071 + 0.840168i 0.999853 0.0171533i \(-0.00546033\pi\)
−0.514782 + 0.857321i \(0.672127\pi\)
\(18\) −0.500000 0.866025i −0.117851 0.204124i
\(19\) 3.50000 6.06218i 0.802955 1.39076i −0.114708 0.993399i \(-0.536593\pi\)
0.917663 0.397360i \(-0.130073\pi\)
\(20\) 1.00000 0.223607
\(21\) −2.50000 0.866025i −0.545545 0.188982i
\(22\) −5.00000 −1.06600
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i −0.913434 0.406986i \(-0.866580\pi\)
0.809177 + 0.587565i \(0.199913\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 2.50000 4.33013i 0.490290 0.849208i
\(27\) −1.00000 −0.192450
\(28\) 2.50000 + 0.866025i 0.472456 + 0.163663i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0.500000 0.866025i 0.0912871 0.158114i
\(31\) 1.00000 + 1.73205i 0.179605 + 0.311086i 0.941745 0.336327i \(-0.109185\pi\)
−0.762140 + 0.647412i \(0.775851\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −2.50000 + 4.33013i −0.435194 + 0.753778i
\(34\) −4.00000 −0.685994
\(35\) −0.500000 2.59808i −0.0845154 0.439155i
\(36\) 1.00000 0.166667
\(37\) −0.500000 + 0.866025i −0.0821995 + 0.142374i −0.904194 0.427121i \(-0.859528\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) 3.50000 + 6.06218i 0.567775 + 0.983415i
\(39\) −2.50000 4.33013i −0.400320 0.693375i
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) 5.00000 0.780869 0.390434 0.920631i \(-0.372325\pi\)
0.390434 + 0.920631i \(0.372325\pi\)
\(42\) 2.00000 1.73205i 0.308607 0.267261i
\(43\) 12.0000 1.82998 0.914991 0.403473i \(-0.132197\pi\)
0.914991 + 0.403473i \(0.132197\pi\)
\(44\) 2.50000 4.33013i 0.376889 0.652791i
\(45\) −0.500000 0.866025i −0.0745356 0.129099i
\(46\) −0.500000 0.866025i −0.0737210 0.127688i
\(47\) 5.50000 9.52628i 0.802257 1.38955i −0.115870 0.993264i \(-0.536965\pi\)
0.918127 0.396286i \(-0.129701\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 1.00000 0.141421
\(51\) −2.00000 + 3.46410i −0.280056 + 0.485071i
\(52\) 2.50000 + 4.33013i 0.346688 + 0.600481i
\(53\) 4.50000 + 7.79423i 0.618123 + 1.07062i 0.989828 + 0.142269i \(0.0454398\pi\)
−0.371706 + 0.928351i \(0.621227\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) −5.00000 −0.674200
\(56\) −2.00000 + 1.73205i −0.267261 + 0.231455i
\(57\) 7.00000 0.927173
\(58\) 0 0
\(59\) −2.00000 3.46410i −0.260378 0.450988i 0.705965 0.708247i \(-0.250514\pi\)
−0.966342 + 0.257260i \(0.917180\pi\)
\(60\) 0.500000 + 0.866025i 0.0645497 + 0.111803i
\(61\) −2.00000 + 3.46410i −0.256074 + 0.443533i −0.965187 0.261562i \(-0.915762\pi\)
0.709113 + 0.705095i \(0.249096\pi\)
\(62\) −2.00000 −0.254000
\(63\) −0.500000 2.59808i −0.0629941 0.327327i
\(64\) 1.00000 0.125000
\(65\) 2.50000 4.33013i 0.310087 0.537086i
\(66\) −2.50000 4.33013i −0.307729 0.533002i
\(67\) 6.00000 + 10.3923i 0.733017 + 1.26962i 0.955588 + 0.294706i \(0.0952216\pi\)
−0.222571 + 0.974916i \(0.571445\pi\)
\(68\) 2.00000 3.46410i 0.242536 0.420084i
\(69\) −1.00000 −0.120386
\(70\) 2.50000 + 0.866025i 0.298807 + 0.103510i
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) −5.00000 8.66025i −0.585206 1.01361i −0.994850 0.101361i \(-0.967680\pi\)
0.409644 0.912245i \(-0.365653\pi\)
\(74\) −0.500000 0.866025i −0.0581238 0.100673i
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) −7.00000 −0.802955
\(77\) −12.5000 4.33013i −1.42451 0.493464i
\(78\) 5.00000 0.566139
\(79\) 6.00000 10.3923i 0.675053 1.16923i −0.301401 0.953498i \(-0.597454\pi\)
0.976453 0.215728i \(-0.0692125\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.50000 + 4.33013i −0.276079 + 0.478183i
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0.500000 + 2.59808i 0.0545545 + 0.283473i
\(85\) −4.00000 −0.433861
\(86\) −6.00000 + 10.3923i −0.646997 + 1.12063i
\(87\) 0 0
\(88\) 2.50000 + 4.33013i 0.266501 + 0.461593i
\(89\) −7.00000 + 12.1244i −0.741999 + 1.28518i 0.209585 + 0.977790i \(0.432789\pi\)
−0.951584 + 0.307389i \(0.900545\pi\)
\(90\) 1.00000 0.105409
\(91\) 10.0000 8.66025i 1.04828 0.907841i
\(92\) 1.00000 0.104257
\(93\) −1.00000 + 1.73205i −0.103695 + 0.179605i
\(94\) 5.50000 + 9.52628i 0.567282 + 0.982561i
\(95\) 3.50000 + 6.06218i 0.359092 + 0.621966i
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) −8.00000 −0.812277 −0.406138 0.913812i \(-0.633125\pi\)
−0.406138 + 0.913812i \(0.633125\pi\)
\(98\) 5.50000 + 4.33013i 0.555584 + 0.437409i
\(99\) −5.00000 −0.502519
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) −2.00000 3.46410i −0.198030 0.342997i
\(103\) −4.00000 + 6.92820i −0.394132 + 0.682656i −0.992990 0.118199i \(-0.962288\pi\)
0.598858 + 0.800855i \(0.295621\pi\)
\(104\) −5.00000 −0.490290
\(105\) 2.00000 1.73205i 0.195180 0.169031i
\(106\) −9.00000 −0.874157
\(107\) 1.00000 1.73205i 0.0966736 0.167444i −0.813632 0.581380i \(-0.802513\pi\)
0.910306 + 0.413936i \(0.135846\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i \(-0.136131\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) 2.50000 4.33013i 0.238366 0.412861i
\(111\) −1.00000 −0.0949158
\(112\) −0.500000 2.59808i −0.0472456 0.245495i
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) −3.50000 + 6.06218i −0.327805 + 0.567775i
\(115\) −0.500000 0.866025i −0.0466252 0.0807573i
\(116\) 0 0
\(117\) 2.50000 4.33013i 0.231125 0.400320i
\(118\) 4.00000 0.368230
\(119\) −10.0000 3.46410i −0.916698 0.317554i
\(120\) −1.00000 −0.0912871
\(121\) −7.00000 + 12.1244i −0.636364 + 1.10221i
\(122\) −2.00000 3.46410i −0.181071 0.313625i
\(123\) 2.50000 + 4.33013i 0.225417 + 0.390434i
\(124\) 1.00000 1.73205i 0.0898027 0.155543i
\(125\) 1.00000 0.0894427
\(126\) 2.50000 + 0.866025i 0.222718 + 0.0771517i
\(127\) 9.00000 0.798621 0.399310 0.916816i \(-0.369250\pi\)
0.399310 + 0.916816i \(0.369250\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 6.00000 + 10.3923i 0.528271 + 0.914991i
\(130\) 2.50000 + 4.33013i 0.219265 + 0.379777i
\(131\) 4.50000 7.79423i 0.393167 0.680985i −0.599699 0.800226i \(-0.704713\pi\)
0.992865 + 0.119241i \(0.0380462\pi\)
\(132\) 5.00000 0.435194
\(133\) 3.50000 + 18.1865i 0.303488 + 1.57697i
\(134\) −12.0000 −1.03664
\(135\) 0.500000 0.866025i 0.0430331 0.0745356i
\(136\) 2.00000 + 3.46410i 0.171499 + 0.297044i
\(137\) 1.00000 + 1.73205i 0.0854358 + 0.147979i 0.905577 0.424182i \(-0.139438\pi\)
−0.820141 + 0.572161i \(0.806105\pi\)
\(138\) 0.500000 0.866025i 0.0425628 0.0737210i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) −2.00000 + 1.73205i −0.169031 + 0.146385i
\(141\) 11.0000 0.926367
\(142\) −1.00000 + 1.73205i −0.0839181 + 0.145350i
\(143\) −12.5000 21.6506i −1.04530 1.81052i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 0 0
\(146\) 10.0000 0.827606
\(147\) 6.50000 2.59808i 0.536111 0.214286i
\(148\) 1.00000 0.0821995
\(149\) −6.00000 + 10.3923i −0.491539 + 0.851371i −0.999953 0.00974235i \(-0.996899\pi\)
0.508413 + 0.861113i \(0.330232\pi\)
\(150\) 0.500000 + 0.866025i 0.0408248 + 0.0707107i
\(151\) −7.00000 12.1244i −0.569652 0.986666i −0.996600 0.0823900i \(-0.973745\pi\)
0.426948 0.904276i \(-0.359589\pi\)
\(152\) 3.50000 6.06218i 0.283887 0.491708i
\(153\) −4.00000 −0.323381
\(154\) 10.0000 8.66025i 0.805823 0.697863i
\(155\) −2.00000 −0.160644
\(156\) −2.50000 + 4.33013i −0.200160 + 0.346688i
\(157\) −5.50000 9.52628i −0.438948 0.760280i 0.558661 0.829396i \(-0.311315\pi\)
−0.997609 + 0.0691164i \(0.977982\pi\)
\(158\) 6.00000 + 10.3923i 0.477334 + 0.826767i
\(159\) −4.50000 + 7.79423i −0.356873 + 0.618123i
\(160\) 1.00000 0.0790569
\(161\) −0.500000 2.59808i −0.0394055 0.204757i
\(162\) 1.00000 0.0785674
\(163\) 12.0000 20.7846i 0.939913 1.62798i 0.174282 0.984696i \(-0.444240\pi\)
0.765631 0.643280i \(-0.222427\pi\)
\(164\) −2.50000 4.33013i −0.195217 0.338126i
\(165\) −2.50000 4.33013i −0.194625 0.337100i
\(166\) 6.00000 10.3923i 0.465690 0.806599i
\(167\) 11.0000 0.851206 0.425603 0.904910i \(-0.360062\pi\)
0.425603 + 0.904910i \(0.360062\pi\)
\(168\) −2.50000 0.866025i −0.192879 0.0668153i
\(169\) 12.0000 0.923077
\(170\) 2.00000 3.46410i 0.153393 0.265684i
\(171\) 3.50000 + 6.06218i 0.267652 + 0.463586i
\(172\) −6.00000 10.3923i −0.457496 0.792406i
\(173\) 6.50000 11.2583i 0.494186 0.855955i −0.505792 0.862656i \(-0.668800\pi\)
0.999978 + 0.00670064i \(0.00213290\pi\)
\(174\) 0 0
\(175\) 2.50000 + 0.866025i 0.188982 + 0.0654654i
\(176\) −5.00000 −0.376889
\(177\) 2.00000 3.46410i 0.150329 0.260378i
\(178\) −7.00000 12.1244i −0.524672 0.908759i
\(179\) 11.5000 + 19.9186i 0.859550 + 1.48878i 0.872358 + 0.488867i \(0.162590\pi\)
−0.0128080 + 0.999918i \(0.504077\pi\)
\(180\) −0.500000 + 0.866025i −0.0372678 + 0.0645497i
\(181\) 20.0000 1.48659 0.743294 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) 2.50000 + 12.9904i 0.185312 + 0.962911i
\(183\) −4.00000 −0.295689
\(184\) −0.500000 + 0.866025i −0.0368605 + 0.0638442i
\(185\) −0.500000 0.866025i −0.0367607 0.0636715i
\(186\) −1.00000 1.73205i −0.0733236 0.127000i
\(187\) −10.0000 + 17.3205i −0.731272 + 1.26660i
\(188\) −11.0000 −0.802257
\(189\) 2.00000 1.73205i 0.145479 0.125988i
\(190\) −7.00000 −0.507833
\(191\) −7.00000 + 12.1244i −0.506502 + 0.877288i 0.493469 + 0.869763i \(0.335728\pi\)
−0.999972 + 0.00752447i \(0.997605\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −5.00000 8.66025i −0.359908 0.623379i 0.628037 0.778183i \(-0.283859\pi\)
−0.987945 + 0.154805i \(0.950525\pi\)
\(194\) 4.00000 6.92820i 0.287183 0.497416i
\(195\) 5.00000 0.358057
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) −3.00000 −0.213741 −0.106871 0.994273i \(-0.534083\pi\)
−0.106871 + 0.994273i \(0.534083\pi\)
\(198\) 2.50000 4.33013i 0.177667 0.307729i
\(199\) 2.00000 + 3.46410i 0.141776 + 0.245564i 0.928166 0.372168i \(-0.121385\pi\)
−0.786389 + 0.617731i \(0.788052\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) −6.00000 + 10.3923i −0.423207 + 0.733017i
\(202\) 0 0
\(203\) 0 0
\(204\) 4.00000 0.280056
\(205\) −2.50000 + 4.33013i −0.174608 + 0.302429i
\(206\) −4.00000 6.92820i −0.278693 0.482711i
\(207\) −0.500000 0.866025i −0.0347524 0.0601929i
\(208\) 2.50000 4.33013i 0.173344 0.300240i
\(209\) 35.0000 2.42100
\(210\) 0.500000 + 2.59808i 0.0345033 + 0.179284i
\(211\) 17.0000 1.17033 0.585164 0.810915i \(-0.301030\pi\)
0.585164 + 0.810915i \(0.301030\pi\)
\(212\) 4.50000 7.79423i 0.309061 0.535310i
\(213\) 1.00000 + 1.73205i 0.0685189 + 0.118678i
\(214\) 1.00000 + 1.73205i 0.0683586 + 0.118401i
\(215\) −6.00000 + 10.3923i −0.409197 + 0.708749i
\(216\) −1.00000 −0.0680414
\(217\) −5.00000 1.73205i −0.339422 0.117579i
\(218\) −2.00000 −0.135457
\(219\) 5.00000 8.66025i 0.337869 0.585206i
\(220\) 2.50000 + 4.33013i 0.168550 + 0.291937i
\(221\) −10.0000 17.3205i −0.672673 1.16510i
\(222\) 0.500000 0.866025i 0.0335578 0.0581238i
\(223\) −12.0000 −0.803579 −0.401790 0.915732i \(-0.631612\pi\)
−0.401790 + 0.915732i \(0.631612\pi\)
\(224\) 2.50000 + 0.866025i 0.167038 + 0.0578638i
\(225\) 1.00000 0.0666667
\(226\) 7.00000 12.1244i 0.465633 0.806500i
\(227\) 6.00000 + 10.3923i 0.398234 + 0.689761i 0.993508 0.113761i \(-0.0362899\pi\)
−0.595274 + 0.803523i \(0.702957\pi\)
\(228\) −3.50000 6.06218i −0.231793 0.401478i
\(229\) −5.00000 + 8.66025i −0.330409 + 0.572286i −0.982592 0.185776i \(-0.940520\pi\)
0.652183 + 0.758062i \(0.273853\pi\)
\(230\) 1.00000 0.0659380
\(231\) −2.50000 12.9904i −0.164488 0.854704i
\(232\) 0 0
\(233\) 7.00000 12.1244i 0.458585 0.794293i −0.540301 0.841472i \(-0.681690\pi\)
0.998886 + 0.0471787i \(0.0150230\pi\)
\(234\) 2.50000 + 4.33013i 0.163430 + 0.283069i
\(235\) 5.50000 + 9.52628i 0.358780 + 0.621426i
\(236\) −2.00000 + 3.46410i −0.130189 + 0.225494i
\(237\) 12.0000 0.779484
\(238\) 8.00000 6.92820i 0.518563 0.449089i
\(239\) −22.0000 −1.42306 −0.711531 0.702655i \(-0.751998\pi\)
−0.711531 + 0.702655i \(0.751998\pi\)
\(240\) 0.500000 0.866025i 0.0322749 0.0559017i
\(241\) −7.50000 12.9904i −0.483117 0.836784i 0.516695 0.856170i \(-0.327162\pi\)
−0.999812 + 0.0193858i \(0.993829\pi\)
\(242\) −7.00000 12.1244i −0.449977 0.779383i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 4.00000 0.256074
\(245\) 5.50000 + 4.33013i 0.351382 + 0.276642i
\(246\) −5.00000 −0.318788
\(247\) −17.5000 + 30.3109i −1.11350 + 1.92864i
\(248\) 1.00000 + 1.73205i 0.0635001 + 0.109985i
\(249\) −6.00000 10.3923i −0.380235 0.658586i
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) 1.00000 0.0631194 0.0315597 0.999502i \(-0.489953\pi\)
0.0315597 + 0.999502i \(0.489953\pi\)
\(252\) −2.00000 + 1.73205i −0.125988 + 0.109109i
\(253\) −5.00000 −0.314347
\(254\) −4.50000 + 7.79423i −0.282355 + 0.489053i
\(255\) −2.00000 3.46410i −0.125245 0.216930i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 8.00000 13.8564i 0.499026 0.864339i −0.500973 0.865463i \(-0.667024\pi\)
0.999999 + 0.00112398i \(0.000357774\pi\)
\(258\) −12.0000 −0.747087
\(259\) −0.500000 2.59808i −0.0310685 0.161437i
\(260\) −5.00000 −0.310087
\(261\) 0 0
\(262\) 4.50000 + 7.79423i 0.278011 + 0.481529i
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) −2.50000 + 4.33013i −0.153864 + 0.266501i
\(265\) −9.00000 −0.552866
\(266\) −17.5000 6.06218i −1.07299 0.371696i
\(267\) −14.0000 −0.856786
\(268\) 6.00000 10.3923i 0.366508 0.634811i
\(269\) 12.0000 + 20.7846i 0.731653 + 1.26726i 0.956176 + 0.292791i \(0.0945841\pi\)
−0.224523 + 0.974469i \(0.572083\pi\)
\(270\) 0.500000 + 0.866025i 0.0304290 + 0.0527046i
\(271\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(272\) −4.00000 −0.242536
\(273\) 12.5000 + 4.33013i 0.756534 + 0.262071i
\(274\) −2.00000 −0.120824
\(275\) 2.50000 4.33013i 0.150756 0.261116i
\(276\) 0.500000 + 0.866025i 0.0300965 + 0.0521286i
\(277\) −7.00000 12.1244i −0.420589 0.728482i 0.575408 0.817867i \(-0.304843\pi\)
−0.995997 + 0.0893846i \(0.971510\pi\)
\(278\) 2.00000 3.46410i 0.119952 0.207763i
\(279\) −2.00000 −0.119737
\(280\) −0.500000 2.59808i −0.0298807 0.155265i
\(281\) 7.00000 0.417585 0.208792 0.977960i \(-0.433047\pi\)
0.208792 + 0.977960i \(0.433047\pi\)
\(282\) −5.50000 + 9.52628i −0.327520 + 0.567282i
\(283\) 5.00000 + 8.66025i 0.297219 + 0.514799i 0.975499 0.220005i \(-0.0706075\pi\)
−0.678280 + 0.734804i \(0.737274\pi\)
\(284\) −1.00000 1.73205i −0.0593391 0.102778i
\(285\) −3.50000 + 6.06218i −0.207322 + 0.359092i
\(286\) 25.0000 1.47828
\(287\) −10.0000 + 8.66025i −0.590281 + 0.511199i
\(288\) 1.00000 0.0589256
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 0 0
\(291\) −4.00000 6.92820i −0.234484 0.406138i
\(292\) −5.00000 + 8.66025i −0.292603 + 0.506803i
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) −1.00000 + 6.92820i −0.0583212 + 0.404061i
\(295\) 4.00000 0.232889
\(296\) −0.500000 + 0.866025i −0.0290619 + 0.0503367i
\(297\) −2.50000 4.33013i −0.145065 0.251259i
\(298\) −6.00000 10.3923i −0.347571 0.602010i
\(299\) 2.50000 4.33013i 0.144579 0.250418i
\(300\) −1.00000 −0.0577350
\(301\) −24.0000 + 20.7846i −1.38334 + 1.19800i
\(302\) 14.0000 0.805609
\(303\) 0 0
\(304\) 3.50000 + 6.06218i 0.200739 + 0.347690i
\(305\) −2.00000 3.46410i −0.114520 0.198354i
\(306\) 2.00000 3.46410i 0.114332 0.198030i
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) 2.50000 + 12.9904i 0.142451 + 0.740196i
\(309\) −8.00000 −0.455104
\(310\) 1.00000 1.73205i 0.0567962 0.0983739i
\(311\) −4.00000 6.92820i −0.226819 0.392862i 0.730044 0.683400i \(-0.239499\pi\)
−0.956864 + 0.290537i \(0.906166\pi\)
\(312\) −2.50000 4.33013i −0.141535 0.245145i
\(313\) −8.00000 + 13.8564i −0.452187 + 0.783210i −0.998522 0.0543564i \(-0.982689\pi\)
0.546335 + 0.837567i \(0.316023\pi\)
\(314\) 11.0000 0.620766
\(315\) 2.50000 + 0.866025i 0.140859 + 0.0487950i
\(316\) −12.0000 −0.675053
\(317\) 11.0000 19.0526i 0.617822 1.07010i −0.372061 0.928208i \(-0.621349\pi\)
0.989882 0.141890i \(-0.0453179\pi\)
\(318\) −4.50000 7.79423i −0.252347 0.437079i
\(319\) 0 0
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) 2.00000 0.111629
\(322\) 2.50000 + 0.866025i 0.139320 + 0.0482617i
\(323\) 28.0000 1.55796
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 2.50000 + 4.33013i 0.138675 + 0.240192i
\(326\) 12.0000 + 20.7846i 0.664619 + 1.15115i
\(327\) −1.00000 + 1.73205i −0.0553001 + 0.0957826i
\(328\) 5.00000 0.276079
\(329\) 5.50000 + 28.5788i 0.303225 + 1.57560i
\(330\) 5.00000 0.275241
\(331\) −15.5000 + 26.8468i −0.851957 + 1.47563i 0.0274825 + 0.999622i \(0.491251\pi\)
−0.879440 + 0.476011i \(0.842082\pi\)
\(332\) 6.00000 + 10.3923i 0.329293 + 0.570352i
\(333\) −0.500000 0.866025i −0.0273998 0.0474579i
\(334\) −5.50000 + 9.52628i −0.300947 + 0.521255i
\(335\) −12.0000 −0.655630
\(336\) 2.00000 1.73205i 0.109109 0.0944911i
\(337\) −16.0000 −0.871576 −0.435788 0.900049i \(-0.643530\pi\)
−0.435788 + 0.900049i \(0.643530\pi\)
\(338\) −6.00000 + 10.3923i −0.326357 + 0.565267i
\(339\) −7.00000 12.1244i −0.380188 0.658505i
\(340\) 2.00000 + 3.46410i 0.108465 + 0.187867i
\(341\) −5.00000 + 8.66025i −0.270765 + 0.468979i
\(342\) −7.00000 −0.378517
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 12.0000 0.646997
\(345\) 0.500000 0.866025i 0.0269191 0.0466252i
\(346\) 6.50000 + 11.2583i 0.349442 + 0.605252i
\(347\) 9.00000 + 15.5885i 0.483145 + 0.836832i 0.999813 0.0193540i \(-0.00616095\pi\)
−0.516667 + 0.856186i \(0.672828\pi\)
\(348\) 0 0
\(349\) −4.00000 −0.214115 −0.107058 0.994253i \(-0.534143\pi\)
−0.107058 + 0.994253i \(0.534143\pi\)
\(350\) −2.00000 + 1.73205i −0.106904 + 0.0925820i
\(351\) 5.00000 0.266880
\(352\) 2.50000 4.33013i 0.133250 0.230797i
\(353\) −12.0000 20.7846i −0.638696 1.10625i −0.985719 0.168397i \(-0.946141\pi\)
0.347024 0.937856i \(-0.387192\pi\)
\(354\) 2.00000 + 3.46410i 0.106299 + 0.184115i
\(355\) −1.00000 + 1.73205i −0.0530745 + 0.0919277i
\(356\) 14.0000 0.741999
\(357\) −2.00000 10.3923i −0.105851 0.550019i
\(358\) −23.0000 −1.21559
\(359\) 10.0000 17.3205i 0.527780 0.914141i −0.471696 0.881761i \(-0.656358\pi\)
0.999476 0.0323801i \(-0.0103087\pi\)
\(360\) −0.500000 0.866025i −0.0263523 0.0456435i
\(361\) −15.0000 25.9808i −0.789474 1.36741i
\(362\) −10.0000 + 17.3205i −0.525588 + 0.910346i
\(363\) −14.0000 −0.734809
\(364\) −12.5000 4.33013i −0.655178 0.226960i
\(365\) 10.0000 0.523424
\(366\) 2.00000 3.46410i 0.104542 0.181071i
\(367\) −3.50000 6.06218i −0.182699 0.316443i 0.760100 0.649806i \(-0.225150\pi\)
−0.942799 + 0.333363i \(0.891817\pi\)
\(368\) −0.500000 0.866025i −0.0260643 0.0451447i
\(369\) −2.50000 + 4.33013i −0.130145 + 0.225417i
\(370\) 1.00000 0.0519875
\(371\) −22.5000 7.79423i −1.16814 0.404656i
\(372\) 2.00000 0.103695
\(373\) 11.0000 19.0526i 0.569558 0.986504i −0.427051 0.904227i \(-0.640448\pi\)
0.996610 0.0822766i \(-0.0262191\pi\)
\(374\) −10.0000 17.3205i −0.517088 0.895622i
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) 5.50000 9.52628i 0.283641 0.491280i
\(377\) 0 0
\(378\) 0.500000 + 2.59808i 0.0257172 + 0.133631i
\(379\) 1.00000 0.0513665 0.0256833 0.999670i \(-0.491824\pi\)
0.0256833 + 0.999670i \(0.491824\pi\)
\(380\) 3.50000 6.06218i 0.179546 0.310983i
\(381\) 4.50000 + 7.79423i 0.230542 + 0.399310i
\(382\) −7.00000 12.1244i −0.358151 0.620336i
\(383\) −10.5000 + 18.1865i −0.536525 + 0.929288i 0.462563 + 0.886586i \(0.346930\pi\)
−0.999088 + 0.0427020i \(0.986403\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 10.0000 8.66025i 0.509647 0.441367i
\(386\) 10.0000 0.508987
\(387\) −6.00000 + 10.3923i −0.304997 + 0.528271i
\(388\) 4.00000 + 6.92820i 0.203069 + 0.351726i
\(389\) −9.00000 15.5885i −0.456318 0.790366i 0.542445 0.840091i \(-0.317499\pi\)
−0.998763 + 0.0497253i \(0.984165\pi\)
\(390\) −2.50000 + 4.33013i −0.126592 + 0.219265i
\(391\) −4.00000 −0.202289
\(392\) 1.00000 6.92820i 0.0505076 0.349927i
\(393\) 9.00000 0.453990
\(394\) 1.50000 2.59808i 0.0755689 0.130889i
\(395\) 6.00000 + 10.3923i 0.301893 + 0.522894i
\(396\) 2.50000 + 4.33013i 0.125630 + 0.217597i
\(397\) 7.00000 12.1244i 0.351320 0.608504i −0.635161 0.772380i \(-0.719066\pi\)
0.986481 + 0.163876i \(0.0523996\pi\)
\(398\) −4.00000 −0.200502
\(399\) −14.0000 + 12.1244i −0.700877 + 0.606977i
\(400\) 1.00000 0.0500000
\(401\) 10.5000 18.1865i 0.524345 0.908192i −0.475253 0.879849i \(-0.657644\pi\)
0.999598 0.0283431i \(-0.00902310\pi\)
\(402\) −6.00000 10.3923i −0.299253 0.518321i
\(403\) −5.00000 8.66025i −0.249068 0.431398i
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) −5.00000 −0.247841
\(408\) −2.00000 + 3.46410i −0.0990148 + 0.171499i
\(409\) −5.00000 8.66025i −0.247234 0.428222i 0.715523 0.698589i \(-0.246188\pi\)
−0.962757 + 0.270367i \(0.912855\pi\)
\(410\) −2.50000 4.33013i −0.123466 0.213850i
\(411\) −1.00000 + 1.73205i −0.0493264 + 0.0854358i
\(412\) 8.00000 0.394132
\(413\) 10.0000 + 3.46410i 0.492068 + 0.170457i
\(414\) 1.00000 0.0491473
\(415\) 6.00000 10.3923i 0.294528 0.510138i
\(416\) 2.50000 + 4.33013i 0.122573 + 0.212302i
\(417\) −2.00000 3.46410i −0.0979404 0.169638i
\(418\) −17.5000 + 30.3109i −0.855953 + 1.48255i
\(419\) 15.0000 0.732798 0.366399 0.930458i \(-0.380591\pi\)
0.366399 + 0.930458i \(0.380591\pi\)
\(420\) −2.50000 0.866025i −0.121988 0.0422577i
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) −8.50000 + 14.7224i −0.413774 + 0.716677i
\(423\) 5.50000 + 9.52628i 0.267419 + 0.463184i
\(424\) 4.50000 + 7.79423i 0.218539 + 0.378521i
\(425\) 2.00000 3.46410i 0.0970143 0.168034i
\(426\) −2.00000 −0.0969003
\(427\) −2.00000 10.3923i −0.0967868 0.502919i
\(428\) −2.00000 −0.0966736
\(429\) 12.5000 21.6506i 0.603506 1.04530i
\(430\) −6.00000 10.3923i −0.289346 0.501161i
\(431\) −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) 24.0000 1.15337 0.576683 0.816968i \(-0.304347\pi\)
0.576683 + 0.816968i \(0.304347\pi\)
\(434\) 4.00000 3.46410i 0.192006 0.166282i
\(435\) 0 0
\(436\) 1.00000 1.73205i 0.0478913 0.0829502i
\(437\) 3.50000 + 6.06218i 0.167428 + 0.289993i
\(438\) 5.00000 + 8.66025i 0.238909 + 0.413803i
\(439\) 20.0000 34.6410i 0.954548 1.65333i 0.219149 0.975691i \(-0.429672\pi\)
0.735399 0.677634i \(-0.236995\pi\)
\(440\) −5.00000 −0.238366
\(441\) 5.50000 + 4.33013i 0.261905 + 0.206197i
\(442\) 20.0000 0.951303
\(443\) 14.0000 24.2487i 0.665160 1.15209i −0.314082 0.949396i \(-0.601697\pi\)
0.979242 0.202695i \(-0.0649700\pi\)
\(444\) 0.500000 + 0.866025i 0.0237289 + 0.0410997i
\(445\) −7.00000 12.1244i −0.331832 0.574750i
\(446\) 6.00000 10.3923i 0.284108 0.492090i
\(447\) −12.0000 −0.567581
\(448\) −2.00000 + 1.73205i −0.0944911 + 0.0818317i
\(449\) −29.0000 −1.36859 −0.684297 0.729203i \(-0.739891\pi\)
−0.684297 + 0.729203i \(0.739891\pi\)
\(450\) −0.500000 + 0.866025i −0.0235702 + 0.0408248i
\(451\) 12.5000 + 21.6506i 0.588602 + 1.01949i
\(452\) 7.00000 + 12.1244i 0.329252 + 0.570282i
\(453\) 7.00000 12.1244i 0.328889 0.569652i
\(454\) −12.0000 −0.563188
\(455\) 2.50000 + 12.9904i 0.117202 + 0.608998i
\(456\) 7.00000 0.327805
\(457\) 7.00000 12.1244i 0.327446 0.567153i −0.654558 0.756012i \(-0.727145\pi\)
0.982004 + 0.188858i \(0.0604787\pi\)
\(458\) −5.00000 8.66025i −0.233635 0.404667i
\(459\) −2.00000 3.46410i −0.0933520 0.161690i
\(460\) −0.500000 + 0.866025i −0.0233126 + 0.0403786i
\(461\) −4.00000 −0.186299 −0.0931493 0.995652i \(-0.529693\pi\)
−0.0931493 + 0.995652i \(0.529693\pi\)
\(462\) 12.5000 + 4.33013i 0.581553 + 0.201456i
\(463\) −19.0000 −0.883005 −0.441502 0.897260i \(-0.645554\pi\)
−0.441502 + 0.897260i \(0.645554\pi\)
\(464\) 0 0
\(465\) −1.00000 1.73205i −0.0463739 0.0803219i
\(466\) 7.00000 + 12.1244i 0.324269 + 0.561650i
\(467\) 10.0000 17.3205i 0.462745 0.801498i −0.536352 0.843995i \(-0.680198\pi\)
0.999097 + 0.0424970i \(0.0135313\pi\)
\(468\) −5.00000 −0.231125
\(469\) −30.0000 10.3923i −1.38527 0.479872i
\(470\) −11.0000 −0.507392
\(471\) 5.50000 9.52628i 0.253427 0.438948i
\(472\) −2.00000 3.46410i −0.0920575 0.159448i
\(473\) 30.0000 + 51.9615i 1.37940 + 2.38919i
\(474\) −6.00000 + 10.3923i −0.275589 + 0.477334i
\(475\) −7.00000 −0.321182
\(476\) 2.00000 + 10.3923i 0.0916698 + 0.476331i
\(477\) −9.00000 −0.412082
\(478\) 11.0000 19.0526i 0.503128 0.871444i
\(479\) −9.00000 15.5885i −0.411220 0.712255i 0.583803 0.811895i \(-0.301564\pi\)
−0.995023 + 0.0996406i \(0.968231\pi\)
\(480\) 0.500000 + 0.866025i 0.0228218 + 0.0395285i
\(481\) 2.50000 4.33013i 0.113990 0.197437i
\(482\) 15.0000 0.683231
\(483\) 2.00000 1.73205i 0.0910032 0.0788110i
\(484\) 14.0000 0.636364
\(485\) 4.00000 6.92820i 0.181631 0.314594i
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(488\) −2.00000 + 3.46410i −0.0905357 + 0.156813i
\(489\) 24.0000 1.08532
\(490\) −6.50000 + 2.59808i −0.293640 + 0.117369i
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) 2.50000 4.33013i 0.112709 0.195217i
\(493\) 0 0
\(494\) −17.5000 30.3109i −0.787362 1.36375i
\(495\) 2.50000 4.33013i 0.112367 0.194625i
\(496\) −2.00000 −0.0898027
\(497\) −4.00000 + 3.46410i −0.179425 + 0.155386i
\(498\) 12.0000 0.537733
\(499\) −20.0000 + 34.6410i −0.895323 + 1.55074i −0.0619186 + 0.998081i \(0.519722\pi\)
−0.833404 + 0.552664i \(0.813611\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) 5.50000 + 9.52628i 0.245722 + 0.425603i
\(502\) −0.500000 + 0.866025i −0.0223161 + 0.0386526i
\(503\) −20.0000 −0.891756 −0.445878 0.895094i \(-0.647108\pi\)
−0.445878 + 0.895094i \(0.647108\pi\)
\(504\) −0.500000 2.59808i −0.0222718 0.115728i
\(505\) 0 0
\(506\) 2.50000 4.33013i 0.111139 0.192498i
\(507\) 6.00000 + 10.3923i 0.266469 + 0.461538i
\(508\) −4.50000 7.79423i −0.199655 0.345813i
\(509\) 5.00000 8.66025i 0.221621 0.383859i −0.733679 0.679496i \(-0.762199\pi\)
0.955300 + 0.295637i \(0.0955319\pi\)
\(510\) 4.00000 0.177123
\(511\) 25.0000 + 8.66025i 1.10593 + 0.383107i
\(512\) 1.00000 0.0441942
\(513\) −3.50000 + 6.06218i −0.154529 + 0.267652i
\(514\) 8.00000 + 13.8564i 0.352865 + 0.611180i
\(515\) −4.00000 6.92820i −0.176261 0.305293i
\(516\) 6.00000 10.3923i 0.264135 0.457496i
\(517\) 55.0000 2.41890
\(518\) 2.50000 + 0.866025i 0.109844 + 0.0380510i
\(519\) 13.0000 0.570637
\(520\) 2.50000 4.33013i 0.109632 0.189889i
\(521\) 16.5000 + 28.5788i 0.722878 + 1.25206i 0.959841 + 0.280543i \(0.0905145\pi\)
−0.236963 + 0.971519i \(0.576152\pi\)
\(522\) 0 0
\(523\) 11.0000 19.0526i 0.480996 0.833110i −0.518766 0.854916i \(-0.673608\pi\)
0.999762 + 0.0218062i \(0.00694167\pi\)
\(524\) −9.00000 −0.393167
\(525\) 0.500000 + 2.59808i 0.0218218 + 0.113389i
\(526\) 0 0
\(527\) −4.00000 + 6.92820i −0.174243 + 0.301797i
\(528\) −2.50000 4.33013i −0.108799 0.188445i
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) 4.50000 7.79423i 0.195468 0.338560i
\(531\) 4.00000 0.173585
\(532\) 14.0000 12.1244i 0.606977 0.525657i
\(533\) −25.0000 −1.08287
\(534\) 7.00000 12.1244i 0.302920 0.524672i
\(535\) 1.00000 + 1.73205i 0.0432338 + 0.0748831i
\(536\) 6.00000 + 10.3923i 0.259161 + 0.448879i
\(537\) −11.5000 + 19.9186i −0.496262 + 0.859550i
\(538\) −24.0000 −1.03471
\(539\) 32.5000 12.9904i 1.39987 0.559535i
\(540\) −1.00000 −0.0430331
\(541\) −1.00000 + 1.73205i −0.0429934 + 0.0744667i −0.886721 0.462304i \(-0.847023\pi\)
0.843728 + 0.536771i \(0.180356\pi\)
\(542\) 0 0
\(543\) 10.0000 + 17.3205i 0.429141 + 0.743294i
\(544\) 2.00000 3.46410i 0.0857493 0.148522i
\(545\) −2.00000 −0.0856706
\(546\) −10.0000 + 8.66025i −0.427960 + 0.370625i
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) 1.00000 1.73205i 0.0427179 0.0739895i
\(549\) −2.00000 3.46410i −0.0853579 0.147844i
\(550\) 2.50000 + 4.33013i 0.106600 + 0.184637i
\(551\) 0 0
\(552\) −1.00000 −0.0425628
\(553\) 6.00000 + 31.1769i 0.255146 + 1.32578i
\(554\) 14.0000 0.594803
\(555\) 0.500000 0.866025i 0.0212238 0.0367607i
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) −18.5000 32.0429i −0.783870 1.35770i −0.929672 0.368389i \(-0.879909\pi\)
0.145802 0.989314i \(-0.453424\pi\)
\(558\) 1.00000 1.73205i 0.0423334 0.0733236i
\(559\) −60.0000 −2.53773
\(560\) 2.50000 + 0.866025i 0.105644 + 0.0365963i
\(561\) −20.0000 −0.844401
\(562\) −3.50000 + 6.06218i −0.147639 + 0.255718i
\(563\) 9.00000 + 15.5885i 0.379305 + 0.656975i 0.990961 0.134148i \(-0.0428299\pi\)
−0.611656 + 0.791123i \(0.709497\pi\)
\(564\) −5.50000 9.52628i −0.231592 0.401129i
\(565\) 7.00000 12.1244i 0.294492 0.510075i
\(566\) −10.0000 −0.420331
\(567\) 2.50000 + 0.866025i 0.104990 + 0.0363696i
\(568\) 2.00000 0.0839181
\(569\) −19.5000 + 33.7750i −0.817483 + 1.41592i 0.0900490 + 0.995937i \(0.471298\pi\)
−0.907532 + 0.419984i \(0.862036\pi\)
\(570\) −3.50000 6.06218i −0.146599 0.253917i
\(571\) −20.0000 34.6410i −0.836974 1.44968i −0.892413 0.451219i \(-0.850989\pi\)
0.0554391 0.998462i \(-0.482344\pi\)
\(572\) −12.5000 + 21.6506i −0.522651 + 0.905259i
\(573\) −14.0000 −0.584858
\(574\) −2.50000 12.9904i −0.104348 0.542208i
\(575\) 1.00000 0.0417029
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −13.0000 22.5167i −0.541197 0.937381i −0.998836 0.0482425i \(-0.984638\pi\)
0.457639 0.889138i \(-0.348695\pi\)
\(578\) 0.500000 + 0.866025i 0.0207973 + 0.0360219i
\(579\) 5.00000 8.66025i 0.207793 0.359908i
\(580\) 0 0
\(581\) 24.0000 20.7846i 0.995688 0.862291i
\(582\) 8.00000 0.331611
\(583\) −22.5000 + 38.9711i −0.931855 + 1.61402i
\(584\) −5.00000 8.66025i −0.206901 0.358364i
\(585\) 2.50000 + 4.33013i 0.103362 + 0.179029i
\(586\) −4.50000 + 7.79423i −0.185893 + 0.321977i
\(587\) −30.0000 −1.23823 −0.619116 0.785299i \(-0.712509\pi\)
−0.619116 + 0.785299i \(0.712509\pi\)
\(588\) −5.50000 4.33013i −0.226816 0.178571i
\(589\) 14.0000 0.576860
\(590\) −2.00000 + 3.46410i −0.0823387 + 0.142615i
\(591\) −1.50000 2.59808i −0.0617018 0.106871i
\(592\) −0.500000 0.866025i −0.0205499 0.0355934i
\(593\) −18.0000 + 31.1769i −0.739171 + 1.28028i 0.213697 + 0.976900i \(0.431449\pi\)
−0.952869 + 0.303383i \(0.901884\pi\)
\(594\) 5.00000 0.205152
\(595\) 8.00000 6.92820i 0.327968 0.284029i
\(596\) 12.0000 0.491539
\(597\) −2.00000 + 3.46410i −0.0818546 + 0.141776i
\(598\) 2.50000 + 4.33013i 0.102233 + 0.177072i
\(599\) 5.00000 + 8.66025i 0.204294 + 0.353848i 0.949908 0.312531i \(-0.101177\pi\)
−0.745613 + 0.666379i \(0.767843\pi\)
\(600\) 0.500000 0.866025i 0.0204124 0.0353553i
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) −6.00000 31.1769i −0.244542 1.27068i
\(603\) −12.0000 −0.488678
\(604\) −7.00000 + 12.1244i −0.284826 + 0.493333i
\(605\) −7.00000 12.1244i −0.284590 0.492925i
\(606\) 0 0
\(607\) 13.5000 23.3827i 0.547948 0.949074i −0.450467 0.892793i \(-0.648742\pi\)
0.998415 0.0562808i \(-0.0179242\pi\)
\(608\) −7.00000 −0.283887
\(609\) 0 0
\(610\) 4.00000 0.161955
\(611\) −27.5000 + 47.6314i −1.11253 + 1.92696i
\(612\) 2.00000 + 3.46410i 0.0808452 + 0.140028i
\(613\) 21.5000 + 37.2391i 0.868377 + 1.50407i 0.863655 + 0.504084i \(0.168170\pi\)
0.00472215 + 0.999989i \(0.498497\pi\)
\(614\) −4.00000 + 6.92820i −0.161427 + 0.279600i
\(615\) −5.00000 −0.201619
\(616\) −12.5000 4.33013i −0.503639 0.174466i
\(617\) −8.00000 −0.322068 −0.161034 0.986949i \(-0.551483\pi\)
−0.161034 + 0.986949i \(0.551483\pi\)
\(618\) 4.00000 6.92820i 0.160904 0.278693i
\(619\) −12.5000 21.6506i −0.502417 0.870212i −0.999996 0.00279365i \(-0.999111\pi\)
0.497579 0.867419i \(-0.334223\pi\)
\(620\) 1.00000 + 1.73205i 0.0401610 + 0.0695608i
\(621\) 0.500000 0.866025i 0.0200643 0.0347524i
\(622\) 8.00000 0.320771
\(623\) −7.00000 36.3731i −0.280449 1.45726i
\(624\) 5.00000 0.200160
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −8.00000 13.8564i −0.319744 0.553813i
\(627\) 17.5000 + 30.3109i 0.698883 + 1.21050i
\(628\) −5.50000 + 9.52628i −0.219474 + 0.380140i
\(629\) −4.00000 −0.159490
\(630\) −2.00000 + 1.73205i −0.0796819 + 0.0690066i
\(631\) 6.00000 0.238856 0.119428 0.992843i \(-0.461894\pi\)
0.119428 + 0.992843i \(0.461894\pi\)
\(632\) 6.00000 10.3923i 0.238667 0.413384i
\(633\) 8.50000 + 14.7224i 0.337845 + 0.585164i
\(634\) 11.0000 + 19.0526i 0.436866 + 0.756674i
\(635\) −4.50000 + 7.79423i −0.178577 + 0.309305i
\(636\) 9.00000 0.356873
\(637\) −5.00000 + 34.6410i −0.198107 + 1.37253i
\(638\) 0 0
\(639\) −1.00000 + 1.73205i −0.0395594 + 0.0685189i
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) −10.5000 18.1865i −0.414725 0.718325i 0.580674 0.814136i \(-0.302789\pi\)
−0.995400 + 0.0958109i \(0.969456\pi\)
\(642\) −1.00000 + 1.73205i −0.0394669 + 0.0683586i
\(643\) 34.0000 1.34083 0.670415 0.741987i \(-0.266116\pi\)
0.670415 + 0.741987i \(0.266116\pi\)
\(644\) −2.00000 + 1.73205i −0.0788110 + 0.0682524i
\(645\) −12.0000 −0.472500
\(646\) −14.0000 + 24.2487i −0.550823 + 0.954053i
\(647\) 11.5000 + 19.9186i 0.452112 + 0.783080i 0.998517 0.0544405i \(-0.0173375\pi\)
−0.546405 + 0.837521i \(0.684004\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 10.0000 17.3205i 0.392534 0.679889i
\(650\) −5.00000 −0.196116
\(651\) −1.00000 5.19615i −0.0391931 0.203653i
\(652\) −24.0000 −0.939913
\(653\) 9.50000 16.4545i 0.371764 0.643914i −0.618073 0.786121i \(-0.712086\pi\)
0.989837 + 0.142207i \(0.0454198\pi\)
\(654\) −1.00000 1.73205i −0.0391031 0.0677285i
\(655\) 4.50000 + 7.79423i 0.175830 + 0.304546i
\(656\) −2.50000 + 4.33013i −0.0976086 + 0.169063i
\(657\) 10.0000 0.390137
\(658\) −27.5000 9.52628i −1.07206 0.371373i
\(659\) −20.0000 −0.779089 −0.389545 0.921008i \(-0.627368\pi\)
−0.389545 + 0.921008i \(0.627368\pi\)
\(660\) −2.50000 + 4.33013i −0.0973124 + 0.168550i
\(661\) 20.0000 + 34.6410i 0.777910 + 1.34738i 0.933144 + 0.359502i \(0.117053\pi\)
−0.155235 + 0.987878i \(0.549613\pi\)
\(662\) −15.5000 26.8468i −0.602425 1.04343i
\(663\) 10.0000 17.3205i 0.388368 0.672673i
\(664\) −12.0000 −0.465690
\(665\) −17.5000 6.06218i −0.678621 0.235081i
\(666\) 1.00000 0.0387492
\(667\) 0 0
\(668\) −5.50000 9.52628i −0.212801 0.368583i
\(669\) −6.00000 10.3923i −0.231973 0.401790i
\(670\) 6.00000 10.3923i 0.231800 0.401490i
\(671\) −20.0000 −0.772091
\(672\) 0.500000 + 2.59808i 0.0192879 + 0.100223i
\(673\) −4.00000 −0.154189 −0.0770943 0.997024i \(-0.524564\pi\)
−0.0770943 + 0.997024i \(0.524564\pi\)
\(674\) 8.00000 13.8564i 0.308148 0.533729i
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) −6.00000 10.3923i −0.230769 0.399704i
\(677\) −16.5000 + 28.5788i −0.634147 + 1.09837i 0.352549 + 0.935793i \(0.385315\pi\)
−0.986695 + 0.162581i \(0.948018\pi\)
\(678\) 14.0000 0.537667
\(679\) 16.0000 13.8564i 0.614024 0.531760i
\(680\) −4.00000 −0.153393
\(681\) −6.00000 + 10.3923i −0.229920 + 0.398234i
\(682\) −5.00000 8.66025i −0.191460 0.331618i
\(683\) 2.00000 + 3.46410i 0.0765279 + 0.132550i 0.901750 0.432259i \(-0.142283\pi\)
−0.825222 + 0.564809i \(0.808950\pi\)
\(684\) 3.50000 6.06218i 0.133826 0.231793i
\(685\) −2.00000 −0.0764161
\(686\) −18.5000 + 0.866025i −0.706333 + 0.0330650i
\(687\) −10.0000 −0.381524
\(688\) −6.00000 + 10.3923i −0.228748 + 0.396203i
\(689\) −22.5000 38.9711i −0.857182 1.48468i
\(690\) 0.500000 + 0.866025i 0.0190347 + 0.0329690i
\(691\) −14.0000 + 24.2487i −0.532585 + 0.922464i 0.466691 + 0.884420i \(0.345446\pi\)
−0.999276 + 0.0380440i \(0.987887\pi\)
\(692\) −13.0000 −0.494186
\(693\) 10.0000 8.66025i 0.379869 0.328976i
\(694\) −18.0000 −0.683271
\(695\) 2.00000 3.46410i 0.0758643 0.131401i
\(696\) 0 0
\(697\) 10.0000 + 17.3205i 0.378777 + 0.656061i
\(698\) 2.00000 3.46410i 0.0757011 0.131118i
\(699\) 14.0000 0.529529
\(700\) −0.500000 2.59808i −0.0188982 0.0981981i
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) −2.50000 + 4.33013i −0.0943564 + 0.163430i
\(703\) 3.50000 + 6.06218i 0.132005 + 0.228639i
\(704\) 2.50000 + 4.33013i 0.0942223 + 0.163198i
\(705\) −5.50000 + 9.52628i −0.207142 + 0.358780i
\(706\) 24.0000 0.903252
\(707\) 0 0
\(708\) −4.00000 −0.150329
\(709\) −14.0000 + 24.2487i −0.525781 + 0.910679i 0.473768 + 0.880650i \(0.342894\pi\)
−0.999549 + 0.0300298i \(0.990440\pi\)
\(710\) −1.00000 1.73205i −0.0375293 0.0650027i
\(711\) 6.00000 + 10.3923i 0.225018 + 0.389742i
\(712\) −7.00000 + 12.1244i −0.262336 + 0.454379i
\(713\) −2.00000 −0.0749006
\(714\) 10.0000 + 3.46410i 0.374241 + 0.129641i
\(715\) 25.0000 0.934947
\(716\) 11.5000 19.9186i 0.429775 0.744392i
\(717\) −11.0000 19.0526i −0.410803 0.711531i
\(718\) 10.0000 + 17.3205i 0.373197 + 0.646396i
\(719\) 3.00000 5.19615i 0.111881 0.193784i −0.804648 0.593753i \(-0.797646\pi\)
0.916529 + 0.399969i \(0.130979\pi\)
\(720\) 1.00000 0.0372678
\(721\) −4.00000 20.7846i −0.148968 0.774059i
\(722\) 30.0000 1.11648
\(723\) 7.50000 12.9904i 0.278928 0.483117i
\(724\) −10.0000 17.3205i −0.371647 0.643712i
\(725\) 0 0
\(726\) 7.00000 12.1244i 0.259794 0.449977i
\(727\) −3.00000 −0.111264 −0.0556319 0.998451i \(-0.517717\pi\)
−0.0556319 + 0.998451i \(0.517717\pi\)
\(728\) 10.0000 8.66025i 0.370625 0.320970i
\(729\) 1.00000 0.0370370
\(730\) −5.00000 + 8.66025i −0.185058 + 0.320530i
\(731\) 24.0000 + 41.5692i 0.887672 + 1.53749i
\(732\) 2.00000 + 3.46410i 0.0739221 + 0.128037i
\(733\) −4.50000 + 7.79423i −0.166211 + 0.287886i −0.937085 0.349102i \(-0.886487\pi\)
0.770873 + 0.636988i \(0.219820\pi\)
\(734\) 7.00000 0.258375
\(735\) −1.00000 + 6.92820i −0.0368856 + 0.255551i
\(736\) 1.00000 0.0368605
\(737\) −30.0000 + 51.9615i −1.10506 + 1.91403i
\(738\) −2.50000 4.33013i −0.0920263 0.159394i
\(739\) 7.50000 + 12.9904i 0.275892 + 0.477859i 0.970360 0.241665i \(-0.0776935\pi\)
−0.694468 + 0.719524i \(0.744360\pi\)
\(740\) −0.500000 + 0.866025i −0.0183804 + 0.0318357i
\(741\) −35.0000 −1.28576
\(742\) 18.0000 15.5885i 0.660801 0.572270i
\(743\) 15.0000 0.550297 0.275148 0.961402i \(-0.411273\pi\)
0.275148 + 0.961402i \(0.411273\pi\)
\(744\) −1.00000 + 1.73205i −0.0366618 + 0.0635001i
\(745\) −6.00000 10.3923i −0.219823 0.380745i
\(746\) 11.0000 + 19.0526i 0.402739 + 0.697564i
\(747\) 6.00000 10.3923i 0.219529 0.380235i
\(748\) 20.0000 0.731272
\(749\) 1.00000 + 5.19615i 0.0365392 + 0.189863i
\(750\) −1.00000 −0.0365148
\(751\) 25.0000 43.3013i 0.912263 1.58009i 0.101403 0.994845i \(-0.467667\pi\)
0.810860 0.585240i \(-0.199000\pi\)
\(752\) 5.50000 + 9.52628i 0.200564 + 0.347388i
\(753\) 0.500000 + 0.866025i 0.0182210 + 0.0315597i
\(754\) 0 0
\(755\) 14.0000 0.509512
\(756\) −2.50000 0.866025i −0.0909241 0.0314970i
\(757\) −34.0000 −1.23575 −0.617876 0.786276i \(-0.712006\pi\)
−0.617876 + 0.786276i \(0.712006\pi\)
\(758\) −0.500000 + 0.866025i −0.0181608 + 0.0314555i
\(759\) −2.50000 4.33013i −0.0907443 0.157174i
\(760\) 3.50000 + 6.06218i 0.126958 + 0.219898i
\(761\) 18.5000 32.0429i 0.670624 1.16156i −0.307103 0.951676i \(-0.599360\pi\)
0.977727 0.209879i \(-0.0673071\pi\)
\(762\) −9.00000 −0.326036
\(763\) −5.00000 1.73205i −0.181012 0.0627044i
\(764\) 14.0000 0.506502
\(765\) 2.00000 3.46410i 0.0723102 0.125245i
\(766\) −10.5000 18.1865i −0.379380 0.657106i
\(767\) 10.0000 + 17.3205i 0.361079 + 0.625407i
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) −5.00000 −0.180305 −0.0901523 0.995928i \(-0.528735\pi\)
−0.0901523 + 0.995928i \(0.528735\pi\)
\(770\) 2.50000 + 12.9904i 0.0900937 + 0.468141i
\(771\) 16.0000 0.576226
\(772\) −5.00000 + 8.66025i −0.179954 + 0.311689i
\(773\) 2.50000 + 4.33013i 0.0899188 + 0.155744i 0.907477 0.420103i \(-0.138006\pi\)
−0.817558 + 0.575846i \(0.804673\pi\)
\(774\) −6.00000 10.3923i −0.215666 0.373544i
\(775\) 1.00000 1.73205i 0.0359211 0.0622171i
\(776\) −8.00000 −0.287183
\(777\) 2.00000 1.73205i 0.0717496 0.0621370i
\(778\) 18.0000 0.645331
\(779\) 17.5000 30.3109i 0.627003 1.08600i
\(780\) −2.50000 4.33013i −0.0895144 0.155043i
\(781\) 5.00000 + 8.66025i 0.178914 + 0.309888i
\(782\) 2.00000 3.46410i 0.0715199 0.123876i
\(783\) 0 0
\(784\) 5.50000 + 4.33013i 0.196429 + 0.154647i
\(785\) 11.0000 0.392607
\(786\) −4.50000 + 7.79423i −0.160510 + 0.278011i
\(787\) −1.00000 1.73205i −0.0356462 0.0617409i 0.847652 0.530553i \(-0.178016\pi\)
−0.883298 + 0.468812i \(0.844682\pi\)
\(788\) 1.50000 + 2.59808i 0.0534353 + 0.0925526i
\(789\) 0 0
\(790\) −12.0000 −0.426941
\(791\) 28.0000 24.2487i 0.995565 0.862185i