Properties

Label 210.2.i.c.151.1
Level $210$
Weight $2$
Character 210.151
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 151.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 210.151
Dual form 210.2.i.c.121.1

$q$-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} +(-1.50000 + 2.59808i) q^{11} +(-0.500000 - 0.866025i) q^{12} +5.00000 q^{13} +(-2.50000 - 0.866025i) q^{14} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.500000 - 0.866025i) q^{18} +(-2.50000 - 4.33013i) q^{19} -1.00000 q^{20} +(-0.500000 - 2.59808i) q^{21} -3.00000 q^{22} +(4.50000 + 7.79423i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.50000 + 4.33013i) q^{26} +1.00000 q^{27} +(-0.500000 - 2.59808i) q^{28} +(-0.500000 - 0.866025i) q^{30} +(5.00000 - 8.66025i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} +(-2.50000 - 0.866025i) q^{35} +1.00000 q^{36} +(0.500000 + 0.866025i) q^{37} +(2.50000 - 4.33013i) q^{38} +(-2.50000 + 4.33013i) q^{39} +(-0.500000 - 0.866025i) q^{40} +9.00000 q^{41} +(2.00000 - 1.73205i) q^{42} +8.00000 q^{43} +(-1.50000 - 2.59808i) q^{44} +(0.500000 - 0.866025i) q^{45} +(-4.50000 + 7.79423i) q^{46} +(-1.50000 - 2.59808i) q^{47} +1.00000 q^{48} +(1.00000 - 6.92820i) q^{49} -1.00000 q^{50} +(-2.50000 + 4.33013i) q^{52} +(1.50000 - 2.59808i) q^{53} +(0.500000 + 0.866025i) q^{54} -3.00000 q^{55} +(2.00000 - 1.73205i) q^{56} +5.00000 q^{57} +(-6.00000 + 10.3923i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-4.00000 - 6.92820i) q^{61} +10.0000 q^{62} +(2.50000 + 0.866025i) q^{63} +1.00000 q^{64} +(2.50000 + 4.33013i) q^{65} +(1.50000 - 2.59808i) q^{66} +(-4.00000 + 6.92820i) q^{67} -9.00000 q^{69} +(-0.500000 - 2.59808i) q^{70} -6.00000 q^{71} +(0.500000 + 0.866025i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(-0.500000 + 0.866025i) q^{74} +(-0.500000 - 0.866025i) q^{75} +5.00000 q^{76} +(-1.50000 - 7.79423i) q^{77} -5.00000 q^{78} +(-4.00000 - 6.92820i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.50000 + 7.79423i) q^{82} +(2.50000 + 0.866025i) q^{84} +(4.00000 + 6.92820i) q^{86} +(1.50000 - 2.59808i) q^{88} +(-3.00000 - 5.19615i) q^{89} +1.00000 q^{90} +(-10.0000 + 8.66025i) q^{91} -9.00000 q^{92} +(5.00000 + 8.66025i) q^{93} +(1.50000 - 2.59808i) q^{94} +(2.50000 - 4.33013i) q^{95} +(0.500000 + 0.866025i) q^{96} +8.00000 q^{97} +(6.50000 - 2.59808i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{3} - q^{4} + q^{5} - 2q^{6} - 4q^{7} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} - q^{3} - q^{4} + q^{5} - 2q^{6} - 4q^{7} - 2q^{8} - q^{9} - q^{10} - 3q^{11} - q^{12} + 10q^{13} - 5q^{14} - 2q^{15} - q^{16} + q^{18} - 5q^{19} - 2q^{20} - q^{21} - 6q^{22} + 9q^{23} + q^{24} - q^{25} + 5q^{26} + 2q^{27} - q^{28} - q^{30} + 10q^{31} + q^{32} - 3q^{33} - 5q^{35} + 2q^{36} + q^{37} + 5q^{38} - 5q^{39} - q^{40} + 18q^{41} + 4q^{42} + 16q^{43} - 3q^{44} + q^{45} - 9q^{46} - 3q^{47} + 2q^{48} + 2q^{49} - 2q^{50} - 5q^{52} + 3q^{53} + q^{54} - 6q^{55} + 4q^{56} + 10q^{57} - 12q^{59} + q^{60} - 8q^{61} + 20q^{62} + 5q^{63} + 2q^{64} + 5q^{65} + 3q^{66} - 8q^{67} - 18q^{69} - q^{70} - 12q^{71} + q^{72} - 2q^{73} - q^{74} - q^{75} + 10q^{76} - 3q^{77} - 10q^{78} - 8q^{79} + q^{80} - q^{81} + 9q^{82} + 5q^{84} + 8q^{86} + 3q^{88} - 6q^{89} + 2q^{90} - 20q^{91} - 18q^{92} + 10q^{93} + 3q^{94} + 5q^{95} + q^{96} + 16q^{97} + 13q^{98} + 6q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) 5.00000 1.38675 0.693375 0.720577i \(-0.256123\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) −2.50000 0.866025i −0.668153 0.231455i
\(15\) −1.00000 −0.258199
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) −2.50000 4.33013i −0.573539 0.993399i −0.996199 0.0871106i \(-0.972237\pi\)
0.422659 0.906289i \(-0.361097\pi\)
\(20\) −1.00000 −0.223607
\(21\) −0.500000 2.59808i −0.109109 0.566947i
\(22\) −3.00000 −0.639602
\(23\) 4.50000 + 7.79423i 0.938315 + 1.62521i 0.768613 + 0.639713i \(0.220947\pi\)
0.169701 + 0.985496i \(0.445720\pi\)
\(24\) 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
\(28\) −0.500000 2.59808i −0.0944911 0.490990i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) −0.500000 0.866025i −0.0912871 0.158114i
\(31\) 5.00000 8.66025i 0.898027 1.55543i 0.0680129 0.997684i \(-0.478334\pi\)
0.830014 0.557743i \(-0.188333\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −1.50000 2.59808i −0.261116 0.452267i
\(34\) 0 0
\(35\) −2.50000 0.866025i −0.422577 0.146385i
\(36\) 1.00000 0.166667
\(37\) 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 2.50000 4.33013i 0.405554 0.702439i
\(39\) −2.50000 + 4.33013i −0.400320 + 0.693375i
\(40\) −0.500000 0.866025i −0.0790569 0.136931i
\(41\) 9.00000 1.40556 0.702782 0.711405i \(-0.251941\pi\)
0.702782 + 0.711405i \(0.251941\pi\)
\(42\) 2.00000 1.73205i 0.308607 0.267261i
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) −1.50000 2.59808i −0.226134 0.391675i
\(45\) 0.500000 0.866025i 0.0745356 0.129099i
\(46\) −4.50000 + 7.79423i −0.663489 + 1.14920i
\(47\) −1.50000 2.59808i −0.218797 0.378968i 0.735643 0.677369i \(-0.236880\pi\)
−0.954441 + 0.298401i \(0.903547\pi\)
\(48\) 1.00000 0.144338
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) −2.50000 + 4.33013i −0.346688 + 0.600481i
\(53\) 1.50000 2.59808i 0.206041 0.356873i −0.744423 0.667708i \(-0.767275\pi\)
0.950464 + 0.310835i \(0.100609\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) −3.00000 −0.404520
\(56\) 2.00000 1.73205i 0.267261 0.231455i
\(57\) 5.00000 0.662266
\(58\) 0 0
\(59\) −6.00000 + 10.3923i −0.781133 + 1.35296i 0.150148 + 0.988663i \(0.452025\pi\)
−0.931282 + 0.364299i \(0.881308\pi\)
\(60\) 0.500000 0.866025i 0.0645497 0.111803i
\(61\) −4.00000 6.92820i −0.512148 0.887066i −0.999901 0.0140840i \(-0.995517\pi\)
0.487753 0.872982i \(-0.337817\pi\)
\(62\) 10.0000 1.27000
\(63\) 2.50000 + 0.866025i 0.314970 + 0.109109i
\(64\) 1.00000 0.125000
\(65\) 2.50000 + 4.33013i 0.310087 + 0.537086i
\(66\) 1.50000 2.59808i 0.184637 0.319801i
\(67\) −4.00000 + 6.92820i −0.488678 + 0.846415i −0.999915 0.0130248i \(-0.995854\pi\)
0.511237 + 0.859440i \(0.329187\pi\)
\(68\) 0 0
\(69\) −9.00000 −1.08347
\(70\) −0.500000 2.59808i −0.0597614 0.310530i
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) −1.00000 + 1.73205i −0.117041 + 0.202721i −0.918594 0.395203i \(-0.870674\pi\)
0.801553 + 0.597924i \(0.204008\pi\)
\(74\) −0.500000 + 0.866025i −0.0581238 + 0.100673i
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) 5.00000 0.573539
\(77\) −1.50000 7.79423i −0.170941 0.888235i
\(78\) −5.00000 −0.566139
\(79\) −4.00000 6.92820i −0.450035 0.779484i 0.548352 0.836247i \(-0.315255\pi\)
−0.998388 + 0.0567635i \(0.981922\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 4.50000 + 7.79423i 0.496942 + 0.860729i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 2.50000 + 0.866025i 0.272772 + 0.0944911i
\(85\) 0 0
\(86\) 4.00000 + 6.92820i 0.431331 + 0.747087i
\(87\) 0 0
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 1.00000 0.105409
\(91\) −10.0000 + 8.66025i −1.04828 + 0.907841i
\(92\) −9.00000 −0.938315
\(93\) 5.00000 + 8.66025i 0.518476 + 0.898027i
\(94\) 1.50000 2.59808i 0.154713 0.267971i
\(95\) 2.50000 4.33013i 0.256495 0.444262i
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 8.00000 0.812277 0.406138 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) 6.50000 2.59808i 0.656599 0.262445i
\(99\) 3.00000 0.301511
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) −4.00000 6.92820i −0.394132 0.682656i 0.598858 0.800855i \(-0.295621\pi\)
−0.992990 + 0.118199i \(0.962288\pi\)
\(104\) −5.00000 −0.490290
\(105\) 2.00000 1.73205i 0.195180 0.169031i
\(106\) 3.00000 0.291386
\(107\) −3.00000 5.19615i −0.290021 0.502331i 0.683793 0.729676i \(-0.260329\pi\)
−0.973814 + 0.227345i \(0.926996\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −7.00000 + 12.1244i −0.670478 + 1.16130i 0.307290 + 0.951616i \(0.400578\pi\)
−0.977769 + 0.209687i \(0.932756\pi\)
\(110\) −1.50000 2.59808i −0.143019 0.247717i
\(111\) −1.00000 −0.0949158
\(112\) 2.50000 + 0.866025i 0.236228 + 0.0818317i
\(113\) −18.0000 −1.69330 −0.846649 0.532152i \(-0.821383\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) 2.50000 + 4.33013i 0.234146 + 0.405554i
\(115\) −4.50000 + 7.79423i −0.419627 + 0.726816i
\(116\) 0 0
\(117\) −2.50000 4.33013i −0.231125 0.400320i
\(118\) −12.0000 −1.10469
\(119\) 0 0
\(120\) 1.00000 0.0912871
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 4.00000 6.92820i 0.362143 0.627250i
\(123\) −4.50000 + 7.79423i −0.405751 + 0.702782i
\(124\) 5.00000 + 8.66025i 0.449013 + 0.777714i
\(125\) −1.00000 −0.0894427
\(126\) 0.500000 + 2.59808i 0.0445435 + 0.231455i
\(127\) −13.0000 −1.15356 −0.576782 0.816898i \(-0.695692\pi\)
−0.576782 + 0.816898i \(0.695692\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −4.00000 + 6.92820i −0.352180 + 0.609994i
\(130\) −2.50000 + 4.33013i −0.219265 + 0.379777i
\(131\) 4.50000 + 7.79423i 0.393167 + 0.680985i 0.992865 0.119241i \(-0.0380462\pi\)
−0.599699 + 0.800226i \(0.704713\pi\)
\(132\) 3.00000 0.261116
\(133\) 12.5000 + 4.33013i 1.08389 + 0.375470i
\(134\) −8.00000 −0.691095
\(135\) 0.500000 + 0.866025i 0.0430331 + 0.0745356i
\(136\) 0 0
\(137\) 9.00000 15.5885i 0.768922 1.33181i −0.169226 0.985577i \(-0.554127\pi\)
0.938148 0.346235i \(-0.112540\pi\)
\(138\) −4.50000 7.79423i −0.383065 0.663489i
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 2.00000 1.73205i 0.169031 0.146385i
\(141\) 3.00000 0.252646
\(142\) −3.00000 5.19615i −0.251754 0.436051i
\(143\) −7.50000 + 12.9904i −0.627182 + 1.08631i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) 5.50000 + 4.33013i 0.453632 + 0.357143i
\(148\) −1.00000 −0.0821995
\(149\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(150\) 0.500000 0.866025i 0.0408248 0.0707107i
\(151\) 5.00000 8.66025i 0.406894 0.704761i −0.587646 0.809118i \(-0.699945\pi\)
0.994540 + 0.104357i \(0.0332784\pi\)
\(152\) 2.50000 + 4.33013i 0.202777 + 0.351220i
\(153\) 0 0
\(154\) 6.00000 5.19615i 0.483494 0.418718i
\(155\) 10.0000 0.803219
\(156\) −2.50000 4.33013i −0.200160 0.346688i
\(157\) −2.50000 + 4.33013i −0.199522 + 0.345582i −0.948373 0.317156i \(-0.897272\pi\)
0.748852 + 0.662738i \(0.230606\pi\)
\(158\) 4.00000 6.92820i 0.318223 0.551178i
\(159\) 1.50000 + 2.59808i 0.118958 + 0.206041i
\(160\) 1.00000 0.0790569
\(161\) −22.5000 7.79423i −1.77325 0.614271i
\(162\) −1.00000 −0.0785674
\(163\) 8.00000 + 13.8564i 0.626608 + 1.08532i 0.988227 + 0.152992i \(0.0488907\pi\)
−0.361619 + 0.932326i \(0.617776\pi\)
\(164\) −4.50000 + 7.79423i −0.351391 + 0.608627i
\(165\) 1.50000 2.59808i 0.116775 0.202260i
\(166\) 0 0
\(167\) −3.00000 −0.232147 −0.116073 0.993241i \(-0.537031\pi\)
−0.116073 + 0.993241i \(0.537031\pi\)
\(168\) 0.500000 + 2.59808i 0.0385758 + 0.200446i
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) −2.50000 + 4.33013i −0.191180 + 0.331133i
\(172\) −4.00000 + 6.92820i −0.304997 + 0.528271i
\(173\) −4.50000 7.79423i −0.342129 0.592584i 0.642699 0.766119i \(-0.277815\pi\)
−0.984828 + 0.173534i \(0.944481\pi\)
\(174\) 0 0
\(175\) −0.500000 2.59808i −0.0377964 0.196396i
\(176\) 3.00000 0.226134
\(177\) −6.00000 10.3923i −0.450988 0.781133i
\(178\) 3.00000 5.19615i 0.224860 0.389468i
\(179\) 7.50000 12.9904i 0.560576 0.970947i −0.436870 0.899525i \(-0.643913\pi\)
0.997446 0.0714220i \(-0.0227537\pi\)
\(180\) 0.500000 + 0.866025i 0.0372678 + 0.0645497i
\(181\) 8.00000 0.594635 0.297318 0.954779i \(-0.403908\pi\)
0.297318 + 0.954779i \(0.403908\pi\)
\(182\) −12.5000 4.33013i −0.926562 0.320970i
\(183\) 8.00000 0.591377
\(184\) −4.50000 7.79423i −0.331744 0.574598i
\(185\) −0.500000 + 0.866025i −0.0367607 + 0.0636715i
\(186\) −5.00000 + 8.66025i −0.366618 + 0.635001i
\(187\) 0 0
\(188\) 3.00000 0.218797
\(189\) −2.00000 + 1.73205i −0.145479 + 0.125988i
\(190\) 5.00000 0.362738
\(191\) −9.00000 15.5885i −0.651217 1.12794i −0.982828 0.184525i \(-0.940925\pi\)
0.331611 0.943416i \(-0.392408\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) 5.00000 8.66025i 0.359908 0.623379i −0.628037 0.778183i \(-0.716141\pi\)
0.987945 + 0.154805i \(0.0494748\pi\)
\(194\) 4.00000 + 6.92820i 0.287183 + 0.497416i
\(195\) −5.00000 −0.358057
\(196\) 5.50000 + 4.33013i 0.392857 + 0.309295i
\(197\) 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
\(199\) 8.00000 13.8564i 0.567105 0.982255i −0.429745 0.902950i \(-0.641397\pi\)
0.996850 0.0793045i \(-0.0252700\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) −4.00000 6.92820i −0.282138 0.488678i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 4.50000 + 7.79423i 0.314294 + 0.544373i
\(206\) 4.00000 6.92820i 0.278693 0.482711i
\(207\) 4.50000 7.79423i 0.312772 0.541736i
\(208\) −2.50000 4.33013i −0.173344 0.300240i
\(209\) 15.0000 1.03757
\(210\) 2.50000 + 0.866025i 0.172516 + 0.0597614i
\(211\) 5.00000 0.344214 0.172107 0.985078i \(-0.444942\pi\)
0.172107 + 0.985078i \(0.444942\pi\)
\(212\) 1.50000 + 2.59808i 0.103020 + 0.178437i
\(213\) 3.00000 5.19615i 0.205557 0.356034i
\(214\) 3.00000 5.19615i 0.205076 0.355202i
\(215\) 4.00000 + 6.92820i 0.272798 + 0.472500i
\(216\) −1.00000 −0.0680414
\(217\) 5.00000 + 25.9808i 0.339422 + 1.76369i
\(218\) −14.0000 −0.948200
\(219\) −1.00000 1.73205i −0.0675737 0.117041i
\(220\) 1.50000 2.59808i 0.101130 0.175162i
\(221\) 0 0
\(222\) −0.500000 0.866025i −0.0335578 0.0581238i
\(223\) −28.0000 −1.87502 −0.937509 0.347960i \(-0.886874\pi\)
−0.937509 + 0.347960i \(0.886874\pi\)
\(224\) 0.500000 + 2.59808i 0.0334077 + 0.173591i
\(225\) 1.00000 0.0666667
\(226\) −9.00000 15.5885i −0.598671 1.03693i
\(227\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(228\) −2.50000 + 4.33013i −0.165567 + 0.286770i
\(229\) −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i \(-0.319740\pi\)
−0.999088 + 0.0426906i \(0.986407\pi\)
\(230\) −9.00000 −0.593442
\(231\) 7.50000 + 2.59808i 0.493464 + 0.170941i
\(232\) 0 0
\(233\) 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i \(-0.103697\pi\)
−0.750867 + 0.660454i \(0.770364\pi\)
\(234\) 2.50000 4.33013i 0.163430 0.283069i
\(235\) 1.50000 2.59808i 0.0978492 0.169480i
\(236\) −6.00000 10.3923i −0.390567 0.676481i
\(237\) 8.00000 0.519656
\(238\) 0 0
\(239\) 30.0000 1.94054 0.970269 0.242028i \(-0.0778125\pi\)
0.970269 + 0.242028i \(0.0778125\pi\)
\(240\) 0.500000 + 0.866025i 0.0322749 + 0.0559017i
\(241\) 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i \(-0.823079\pi\)
0.881680 + 0.471848i \(0.156413\pi\)
\(242\) −1.00000 + 1.73205i −0.0642824 + 0.111340i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 8.00000 0.512148
\(245\) 6.50000 2.59808i 0.415270 0.165985i
\(246\) −9.00000 −0.573819
\(247\) −12.5000 21.6506i −0.795356 1.37760i
\(248\) −5.00000 + 8.66025i −0.317500 + 0.549927i
\(249\) 0 0
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) 9.00000 0.568075 0.284037 0.958813i \(-0.408326\pi\)
0.284037 + 0.958813i \(0.408326\pi\)
\(252\) −2.00000 + 1.73205i −0.125988 + 0.109109i
\(253\) −27.0000 −1.69748
\(254\) −6.50000 11.2583i −0.407846 0.706410i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 6.00000 + 10.3923i 0.374270 + 0.648254i 0.990217 0.139533i \(-0.0445601\pi\)
−0.615948 + 0.787787i \(0.711227\pi\)
\(258\) −8.00000 −0.498058
\(259\) −2.50000 0.866025i −0.155342 0.0538122i
\(260\) −5.00000 −0.310087
\(261\) 0 0
\(262\) −4.50000 + 7.79423i −0.278011 + 0.481529i
\(263\) 12.0000 20.7846i 0.739952 1.28163i −0.212565 0.977147i \(-0.568182\pi\)
0.952517 0.304487i \(-0.0984850\pi\)
\(264\) 1.50000 + 2.59808i 0.0923186 + 0.159901i
\(265\) 3.00000 0.184289
\(266\) 2.50000 + 12.9904i 0.153285 + 0.796491i
\(267\) 6.00000 0.367194
\(268\) −4.00000 6.92820i −0.244339 0.423207i
\(269\) −6.00000 + 10.3923i −0.365826 + 0.633630i −0.988908 0.148527i \(-0.952547\pi\)
0.623082 + 0.782157i \(0.285880\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) 0 0
\(273\) −2.50000 12.9904i −0.151307 0.786214i
\(274\) 18.0000 1.08742
\(275\) −1.50000 2.59808i −0.0904534 0.156670i
\(276\) 4.50000 7.79423i 0.270868 0.469157i
\(277\) −13.0000 + 22.5167i −0.781094 + 1.35290i 0.150210 + 0.988654i \(0.452005\pi\)
−0.931305 + 0.364241i \(0.881328\pi\)
\(278\) 10.0000 + 17.3205i 0.599760 + 1.03882i
\(279\) −10.0000 −0.598684
\(280\) 2.50000 + 0.866025i 0.149404 + 0.0517549i
\(281\) −21.0000 −1.25275 −0.626377 0.779520i \(-0.715463\pi\)
−0.626377 + 0.779520i \(0.715463\pi\)
\(282\) 1.50000 + 2.59808i 0.0893237 + 0.154713i
\(283\) 11.0000 19.0526i 0.653882 1.13256i −0.328291 0.944577i \(-0.606473\pi\)
0.982173 0.187980i \(-0.0601941\pi\)
\(284\) 3.00000 5.19615i 0.178017 0.308335i
\(285\) 2.50000 + 4.33013i 0.148087 + 0.256495i
\(286\) −15.0000 −0.886969
\(287\) −18.0000 + 15.5885i −1.06251 + 0.920158i
\(288\) −1.00000 −0.0589256
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) 0 0
\(291\) −4.00000 + 6.92820i −0.234484 + 0.406138i
\(292\) −1.00000 1.73205i −0.0585206 0.101361i
\(293\) −21.0000 −1.22683 −0.613417 0.789760i \(-0.710205\pi\)
−0.613417 + 0.789760i \(0.710205\pi\)
\(294\) −1.00000 + 6.92820i −0.0583212 + 0.404061i
\(295\) −12.0000 −0.698667
\(296\) −0.500000 0.866025i −0.0290619 0.0503367i
\(297\) −1.50000 + 2.59808i −0.0870388 + 0.150756i
\(298\) 0 0
\(299\) 22.5000 + 38.9711i 1.30121 + 2.25376i
\(300\) 1.00000 0.0577350
\(301\) −16.0000 + 13.8564i −0.922225 + 0.798670i
\(302\) 10.0000 0.575435
\(303\) 0 0
\(304\) −2.50000 + 4.33013i −0.143385 + 0.248350i
\(305\) 4.00000 6.92820i 0.229039 0.396708i
\(306\) 0 0
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 7.50000 + 2.59808i 0.427352 + 0.148039i
\(309\) 8.00000 0.455104
\(310\) 5.00000 + 8.66025i 0.283981 + 0.491869i
\(311\) 6.00000 10.3923i 0.340229 0.589294i −0.644246 0.764818i \(-0.722829\pi\)
0.984475 + 0.175525i \(0.0561621\pi\)
\(312\) 2.50000 4.33013i 0.141535 0.245145i
\(313\) 2.00000 + 3.46410i 0.113047 + 0.195803i 0.916997 0.398894i \(-0.130606\pi\)
−0.803951 + 0.594696i \(0.797272\pi\)
\(314\) −5.00000 −0.282166
\(315\) 0.500000 + 2.59808i 0.0281718 + 0.146385i
\(316\) 8.00000 0.450035
\(317\) 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i \(0.00202172\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(318\) −1.50000 + 2.59808i −0.0841158 + 0.145693i
\(319\) 0 0
\(320\) 0.500000 + 0.866025i 0.0279508 + 0.0484123i
\(321\) 6.00000 0.334887
\(322\) −4.50000 23.3827i −0.250775 1.30307i
\(323\) 0 0
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) −2.50000 + 4.33013i −0.138675 + 0.240192i
\(326\) −8.00000 + 13.8564i −0.443079 + 0.767435i
\(327\) −7.00000 12.1244i −0.387101 0.670478i
\(328\) −9.00000 −0.496942
\(329\) 7.50000 + 2.59808i 0.413488 + 0.143237i
\(330\) 3.00000 0.165145
\(331\) −5.50000 9.52628i −0.302307 0.523612i 0.674351 0.738411i \(-0.264424\pi\)
−0.976658 + 0.214799i \(0.931090\pi\)
\(332\) 0 0
\(333\) 0.500000 0.866025i 0.0273998 0.0474579i
\(334\) −1.50000 2.59808i −0.0820763 0.142160i
\(335\) −8.00000 −0.437087
\(336\) −2.00000 + 1.73205i −0.109109 + 0.0944911i
\(337\) 20.0000 1.08947 0.544735 0.838608i \(-0.316630\pi\)
0.544735 + 0.838608i \(0.316630\pi\)
\(338\) 6.00000 + 10.3923i 0.326357 + 0.565267i
\(339\) 9.00000 15.5885i 0.488813 0.846649i
\(340\) 0 0
\(341\) 15.0000 + 25.9808i 0.812296 + 1.40694i
\(342\) −5.00000 −0.270369
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) −8.00000 −0.431331
\(345\) −4.50000 7.79423i −0.242272 0.419627i
\(346\) 4.50000 7.79423i 0.241921 0.419020i
\(347\) −15.0000 + 25.9808i −0.805242 + 1.39472i 0.110885 + 0.993833i \(0.464631\pi\)
−0.916127 + 0.400887i \(0.868702\pi\)
\(348\) 0 0
\(349\) −28.0000 −1.49881 −0.749403 0.662114i \(-0.769659\pi\)
−0.749403 + 0.662114i \(0.769659\pi\)
\(350\) 2.00000 1.73205i 0.106904 0.0925820i
\(351\) 5.00000 0.266880
\(352\) 1.50000 + 2.59808i 0.0799503 + 0.138478i
\(353\) −12.0000 + 20.7846i −0.638696 + 1.10625i 0.347024 + 0.937856i \(0.387192\pi\)
−0.985719 + 0.168397i \(0.946141\pi\)
\(354\) 6.00000 10.3923i 0.318896 0.552345i
\(355\) −3.00000 5.19615i −0.159223 0.275783i
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) 15.0000 0.792775
\(359\) −6.00000 10.3923i −0.316668 0.548485i 0.663123 0.748511i \(-0.269231\pi\)
−0.979791 + 0.200026i \(0.935897\pi\)
\(360\) −0.500000 + 0.866025i −0.0263523 + 0.0456435i
\(361\) −3.00000 + 5.19615i −0.157895 + 0.273482i
\(362\) 4.00000 + 6.92820i 0.210235 + 0.364138i
\(363\) −2.00000 −0.104973
\(364\) −2.50000 12.9904i −0.131036 0.680881i
\(365\) −2.00000 −0.104685
\(366\) 4.00000 + 6.92820i 0.209083 + 0.362143i
\(367\) 9.50000 16.4545i 0.495896 0.858917i −0.504093 0.863649i \(-0.668173\pi\)
0.999989 + 0.00473247i \(0.00150640\pi\)
\(368\) 4.50000 7.79423i 0.234579 0.406302i
\(369\) −4.50000 7.79423i −0.234261 0.405751i
\(370\) −1.00000 −0.0519875
\(371\) 1.50000 + 7.79423i 0.0778761 + 0.404656i
\(372\) −10.0000 −0.518476
\(373\) 5.00000 + 8.66025i 0.258890 + 0.448411i 0.965945 0.258748i \(-0.0833099\pi\)
−0.707055 + 0.707159i \(0.749977\pi\)
\(374\) 0 0
\(375\) 0.500000 0.866025i 0.0258199 0.0447214i
\(376\) 1.50000 + 2.59808i 0.0773566 + 0.133986i
\(377\) 0 0
\(378\) −2.50000 0.866025i −0.128586 0.0445435i
\(379\) −19.0000 −0.975964 −0.487982 0.872854i \(-0.662267\pi\)
−0.487982 + 0.872854i \(0.662267\pi\)
\(380\) 2.50000 + 4.33013i 0.128247 + 0.222131i
\(381\) 6.50000 11.2583i 0.333005 0.576782i
\(382\) 9.00000 15.5885i 0.460480 0.797575i
\(383\) −13.5000 23.3827i −0.689818 1.19480i −0.971897 0.235408i \(-0.924357\pi\)
0.282079 0.959391i \(-0.408976\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 6.00000 5.19615i 0.305788 0.264820i
\(386\) 10.0000 0.508987
\(387\) −4.00000 6.92820i −0.203331 0.352180i
\(388\) −4.00000 + 6.92820i −0.203069 + 0.351726i
\(389\) 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i \(-0.784728\pi\)
0.932002 + 0.362454i \(0.118061\pi\)
\(390\) −2.50000 4.33013i −0.126592 0.219265i
\(391\) 0 0
\(392\) −1.00000 + 6.92820i −0.0505076 + 0.349927i
\(393\) −9.00000 −0.453990
\(394\) 7.50000 + 12.9904i 0.377845 + 0.654446i
\(395\) 4.00000 6.92820i 0.201262 0.348596i
\(396\) −1.50000 + 2.59808i −0.0753778 + 0.130558i
\(397\) −7.00000 12.1244i −0.351320 0.608504i 0.635161 0.772380i \(-0.280934\pi\)
−0.986481 + 0.163876i \(0.947600\pi\)
\(398\) 16.0000 0.802008
\(399\) −10.0000 + 8.66025i −0.500626 + 0.433555i
\(400\) 1.00000 0.0500000
\(401\) −7.50000 12.9904i −0.374532 0.648709i 0.615725 0.787961i \(-0.288863\pi\)
−0.990257 + 0.139253i \(0.955530\pi\)
\(402\) 4.00000 6.92820i 0.199502 0.345547i
\(403\) 25.0000 43.3013i 1.24534 2.15699i
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −3.00000 −0.148704
\(408\) 0 0
\(409\) −1.00000 + 1.73205i −0.0494468 + 0.0856444i −0.889689 0.456566i \(-0.849079\pi\)
0.840243 + 0.542211i \(0.182412\pi\)
\(410\) −4.50000 + 7.79423i −0.222239 + 0.384930i
\(411\) 9.00000 + 15.5885i 0.443937 + 0.768922i
\(412\) 8.00000 0.394132
\(413\) −6.00000 31.1769i −0.295241 1.53412i
\(414\) 9.00000 0.442326
\(415\) 0 0
\(416\) 2.50000 4.33013i 0.122573 0.212302i
\(417\) −10.0000 + 17.3205i −0.489702 + 0.848189i
\(418\) 7.50000 + 12.9904i 0.366837 + 0.635380i
\(419\) −9.00000 −0.439679 −0.219839 0.975536i \(-0.570553\pi\)
−0.219839 + 0.975536i \(0.570553\pi\)
\(420\) 0.500000 + 2.59808i 0.0243975 + 0.126773i
\(421\) 14.0000 0.682318 0.341159 0.940006i \(-0.389181\pi\)
0.341159 + 0.940006i \(0.389181\pi\)
\(422\) 2.50000 + 4.33013i 0.121698 + 0.210787i
\(423\) −1.50000 + 2.59808i −0.0729325 + 0.126323i
\(424\) −1.50000 + 2.59808i −0.0728464 + 0.126174i
\(425\) 0 0
\(426\) 6.00000 0.290701
\(427\) 20.0000 + 6.92820i 0.967868 + 0.335279i
\(428\) 6.00000 0.290021
\(429\) −7.50000 12.9904i −0.362103 0.627182i
\(430\) −4.00000 + 6.92820i −0.192897 + 0.334108i
\(431\) 12.0000 20.7846i 0.578020 1.00116i −0.417687 0.908591i \(-0.637159\pi\)
0.995706 0.0925683i \(-0.0295076\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −16.0000 −0.768911 −0.384455 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) −20.0000 + 17.3205i −0.960031 + 0.831411i
\(435\) 0 0
\(436\) −7.00000 12.1244i −0.335239 0.580651i
\(437\) 22.5000 38.9711i 1.07632 1.86424i
\(438\) 1.00000 1.73205i 0.0477818 0.0827606i
\(439\) −4.00000 6.92820i −0.190910 0.330665i 0.754642 0.656136i \(-0.227810\pi\)
−0.945552 + 0.325471i \(0.894477\pi\)
\(440\) 3.00000 0.143019
\(441\) −6.50000 + 2.59808i −0.309524 + 0.123718i
\(442\) 0 0
\(443\) 12.0000 + 20.7846i 0.570137 + 0.987507i 0.996551 + 0.0829786i \(0.0264433\pi\)
−0.426414 + 0.904528i \(0.640223\pi\)
\(444\) 0.500000 0.866025i 0.0237289 0.0410997i
\(445\) 3.00000 5.19615i 0.142214 0.246321i
\(446\) −14.0000 24.2487i −0.662919 1.14821i
\(447\) 0 0
\(448\) −2.00000 + 1.73205i −0.0944911 + 0.0818317i
\(449\) −33.0000 −1.55737 −0.778683 0.627417i \(-0.784112\pi\)
−0.778683 + 0.627417i \(0.784112\pi\)
\(450\) 0.500000 + 0.866025i 0.0235702 + 0.0408248i
\(451\) −13.5000 + 23.3827i −0.635690 + 1.10105i
\(452\) 9.00000 15.5885i 0.423324 0.733219i
\(453\) 5.00000 + 8.66025i 0.234920 + 0.406894i
\(454\) 0 0
\(455\) −12.5000 4.33013i −0.586009 0.202999i
\(456\) −5.00000 −0.234146
\(457\) 5.00000 + 8.66025i 0.233890 + 0.405110i 0.958950 0.283577i \(-0.0915211\pi\)
−0.725059 + 0.688686i \(0.758188\pi\)
\(458\) 7.00000 12.1244i 0.327089 0.566534i
\(459\) 0 0
\(460\) −4.50000 7.79423i −0.209814 0.363408i
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 1.50000 + 7.79423i 0.0697863 + 0.362620i
\(463\) −1.00000 −0.0464739 −0.0232370 0.999730i \(-0.507397\pi\)
−0.0232370 + 0.999730i \(0.507397\pi\)
\(464\) 0 0
\(465\) −5.00000 + 8.66025i −0.231869 + 0.401610i
\(466\) −3.00000 + 5.19615i −0.138972 + 0.240707i
\(467\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(468\) 5.00000 0.231125
\(469\) −4.00000 20.7846i −0.184703 0.959744i
\(470\) 3.00000 0.138380
\(471\) −2.50000 4.33013i −0.115194 0.199522i
\(472\) 6.00000 10.3923i 0.276172 0.478345i
\(473\) −12.0000 + 20.7846i −0.551761 + 0.955677i
\(474\) 4.00000 + 6.92820i 0.183726 + 0.318223i
\(475\) 5.00000 0.229416
\(476\) 0 0
\(477\) −3.00000 −0.137361
\(478\) 15.0000 + 25.9808i 0.686084 + 1.18833i
\(479\) 9.00000 15.5885i 0.411220 0.712255i −0.583803 0.811895i \(-0.698436\pi\)
0.995023 + 0.0996406i \(0.0317693\pi\)
\(480\) −0.500000 + 0.866025i −0.0228218 + 0.0395285i
\(481\) 2.50000 + 4.33013i 0.113990 + 0.197437i
\(482\) 1.00000 0.0455488
\(483\) 18.0000 15.5885i 0.819028 0.709299i
\(484\) −2.00000 −0.0909091
\(485\) 4.00000 + 6.92820i 0.181631 + 0.314594i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) 20.0000 34.6410i 0.906287 1.56973i 0.0871056 0.996199i \(-0.472238\pi\)
0.819181 0.573535i \(-0.194428\pi\)
\(488\) 4.00000 + 6.92820i 0.181071 + 0.313625i
\(489\) −16.0000 −0.723545
\(490\) 5.50000 + 4.33013i 0.248465 + 0.195615i
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) −4.50000 7.79423i −0.202876 0.351391i
\(493\) 0 0
\(494\) 12.5000 21.6506i 0.562402 0.974108i
\(495\) 1.50000 + 2.59808i 0.0674200 + 0.116775i
\(496\) −10.0000 −0.449013
\(497\) 12.0000 10.3923i 0.538274 0.466159i
\(498\) 0 0
\(499\) 8.00000 + 13.8564i 0.358129 + 0.620298i 0.987648 0.156687i \(-0.0500814\pi\)
−0.629519 + 0.776985i \(0.716748\pi\)
\(500\) 0.500000 0.866025i 0.0223607 0.0387298i
\(501\) 1.50000 2.59808i 0.0670151 0.116073i
\(502\) 4.50000 + 7.79423i 0.200845 + 0.347873i
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) −2.50000 0.866025i −0.111359 0.0385758i
\(505\) 0 0
\(506\) −13.5000 23.3827i −0.600148 1.03949i
\(507\) −6.00000 + 10.3923i −0.266469 + 0.461538i
\(508\) 6.50000 11.2583i 0.288391 0.499508i
\(509\) −3.00000 5.19615i −0.132973 0.230315i 0.791849 0.610718i \(-0.209119\pi\)
−0.924821 + 0.380402i \(0.875786\pi\)
\(510\) 0 0
\(511\) −1.00000 5.19615i −0.0442374 0.229864i
\(512\) −1.00000 −0.0441942
\(513\) −2.50000 4.33013i −0.110378 0.191180i
\(514\) −6.00000 + 10.3923i −0.264649 + 0.458385i
\(515\) 4.00000 6.92820i 0.176261 0.305293i
\(516\) −4.00000 6.92820i −0.176090 0.304997i
\(517\) 9.00000 0.395820
\(518\) −0.500000 2.59808i −0.0219687 0.114153i
\(519\) 9.00000 0.395056
\(520\) −2.50000 4.33013i −0.109632 0.189889i
\(521\) −13.5000 + 23.3827i −0.591446 + 1.02441i 0.402592 + 0.915379i \(0.368109\pi\)
−0.994038 + 0.109035i \(0.965224\pi\)
\(522\) 0 0
\(523\) 11.0000 + 19.0526i 0.480996 + 0.833110i 0.999762 0.0218062i \(-0.00694167\pi\)
−0.518766 + 0.854916i \(0.673608\pi\)
\(524\) −9.00000 −0.393167
\(525\) 2.50000 + 0.866025i 0.109109 + 0.0377964i
\(526\) 24.0000 1.04645
\(527\) 0 0
\(528\) −1.50000 + 2.59808i −0.0652791 + 0.113067i
\(529\) −29.0000 + 50.2295i −1.26087 + 2.18389i
\(530\) 1.50000 + 2.59808i 0.0651558 + 0.112853i
\(531\) 12.0000 0.520756
\(532\) −10.0000 + 8.66025i −0.433555 + 0.375470i
\(533\) 45.0000 1.94917
\(534\) 3.00000 + 5.19615i 0.129823 + 0.224860i
\(535\) 3.00000 5.19615i 0.129701 0.224649i
\(536\) 4.00000 6.92820i 0.172774 0.299253i
\(537\) 7.50000 + 12.9904i 0.323649 + 0.560576i
\(538\) −12.0000 −0.517357
\(539\) 16.5000 + 12.9904i 0.710705 + 0.559535i
\(540\) −1.00000 −0.0430331
\(541\) 5.00000 + 8.66025i 0.214967 + 0.372333i 0.953262 0.302144i \(-0.0977023\pi\)
−0.738296 + 0.674477i \(0.764369\pi\)
\(542\) −8.00000 + 13.8564i −0.343629 + 0.595184i
\(543\) −4.00000 + 6.92820i −0.171656 + 0.297318i
\(544\) 0 0
\(545\) −14.0000 −0.599694
\(546\) 10.0000 8.66025i 0.427960 0.370625i
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 9.00000 + 15.5885i 0.384461 + 0.665906i
\(549\) −4.00000 + 6.92820i −0.170716 + 0.295689i
\(550\) 1.50000 2.59808i 0.0639602 0.110782i
\(551\) 0 0
\(552\) 9.00000 0.383065
\(553\) 20.0000 + 6.92820i 0.850487 + 0.294617i
\(554\) −26.0000 −1.10463
\(555\) −0.500000 0.866025i −0.0212238 0.0367607i
\(556\) −10.0000 + 17.3205i −0.424094 + 0.734553i
\(557\) −19.5000 + 33.7750i −0.826242 + 1.43109i 0.0747252 + 0.997204i \(0.476192\pi\)
−0.900967 + 0.433888i \(0.857141\pi\)
\(558\) −5.00000 8.66025i −0.211667 0.366618i
\(559\) 40.0000 1.69182
\(560\) 0.500000 + 2.59808i 0.0211289 + 0.109789i
\(561\) 0 0
\(562\) −10.5000 18.1865i −0.442916 0.767153i
\(563\) 3.00000 5.19615i 0.126435 0.218992i −0.795858 0.605483i \(-0.792980\pi\)
0.922293 + 0.386492i \(0.126313\pi\)
\(564\) −1.50000 + 2.59808i −0.0631614 + 0.109399i
\(565\) −9.00000 15.5885i −0.378633 0.655811i
\(566\) 22.0000 0.924729
\(567\) −0.500000 2.59808i −0.0209980 0.109109i
\(568\) 6.00000 0.251754
\(569\) −13.5000 23.3827i −0.565949 0.980253i −0.996961 0.0779066i \(-0.975176\pi\)
0.431011 0.902347i \(-0.358157\pi\)
\(570\) −2.50000 + 4.33013i −0.104713 + 0.181369i
\(571\) 8.00000 13.8564i 0.334790 0.579873i −0.648655 0.761083i \(-0.724668\pi\)
0.983444 + 0.181210i \(0.0580014\pi\)
\(572\) −7.50000 12.9904i −0.313591 0.543155i
\(573\) 18.0000 0.751961
\(574\) −22.5000 7.79423i −0.939132 0.325325i
\(575\) −9.00000 −0.375326
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 11.0000 19.0526i 0.457936 0.793168i −0.540916 0.841077i \(-0.681922\pi\)
0.998852 + 0.0479084i \(0.0152556\pi\)
\(578\) −8.50000 + 14.7224i −0.353553 + 0.612372i
\(579\) 5.00000 + 8.66025i 0.207793 + 0.359908i
\(580\) 0 0
\(581\) 0 0
\(582\) −8.00000 −0.331611
\(583\) 4.50000 + 7.79423i 0.186371 + 0.322804i
\(584\) 1.00000 1.73205i 0.0413803 0.0716728i
\(585\) 2.50000 4.33013i 0.103362 0.179029i
\(586\) −10.5000 18.1865i −0.433751 0.751279i
\(587\) −42.0000 −1.73353 −0.866763 0.498721i \(-0.833803\pi\)
−0.866763 + 0.498721i \(0.833803\pi\)
\(588\) −6.50000 + 2.59808i −0.268055 + 0.107143i
\(589\) −50.0000 −2.06021
\(590\) −6.00000 10.3923i −0.247016 0.427844i
\(591\) −7.50000 + 12.9904i −0.308509 + 0.534353i
\(592\) 0.500000 0.866025i 0.0205499 0.0355934i
\(593\) −12.0000 20.7846i −0.492781 0.853522i 0.507184 0.861838i \(-0.330686\pi\)
−0.999965 + 0.00831589i \(0.997353\pi\)
\(594\) −3.00000 −0.123091
\(595\) 0 0
\(596\) 0 0
\(597\) 8.00000 + 13.8564i 0.327418 + 0.567105i
\(598\) −22.5000 + 38.9711i −0.920093 + 1.59365i
\(599\) −9.00000 + 15.5885i −0.367730 + 0.636927i −0.989210 0.146503i \(-0.953198\pi\)
0.621480 + 0.783430i \(0.286532\pi\)
\(600\) 0.500000 + 0.866025i 0.0204124 + 0.0353553i
\(601\) 38.0000 1.55005 0.775026 0.631929i \(-0.217737\pi\)
0.775026 + 0.631929i \(0.217737\pi\)
\(602\) −20.0000 6.92820i −0.815139 0.282372i
\(603\) 8.00000 0.325785
\(604\) 5.00000 + 8.66025i 0.203447 + 0.352381i
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) 0 0
\(607\) 12.5000 + 21.6506i 0.507359 + 0.878772i 0.999964 + 0.00851879i \(0.00271165\pi\)
−0.492604 + 0.870253i \(0.663955\pi\)
\(608\) −5.00000 −0.202777
\(609\) 0 0
\(610\) 8.00000 0.323911
\(611\) −7.50000 12.9904i −0.303418 0.525535i
\(612\) 0 0
\(613\) −5.50000 + 9.52628i −0.222143 + 0.384763i −0.955458 0.295126i \(-0.904638\pi\)
0.733316 + 0.679888i \(0.237972\pi\)
\(614\) −14.0000 24.2487i −0.564994 0.978598i
\(615\) −9.00000 −0.362915
\(616\) 1.50000 + 7.79423i 0.0604367 + 0.314038i
\(617\) 12.0000 0.483102 0.241551 0.970388i \(-0.422344\pi\)
0.241551 + 0.970388i \(0.422344\pi\)
\(618\) 4.00000 + 6.92820i 0.160904 + 0.278693i
\(619\) −14.5000 + 25.1147i −0.582804 + 1.00945i 0.412341 + 0.911030i \(0.364711\pi\)
−0.995145 + 0.0984169i \(0.968622\pi\)
\(620\) −5.00000 + 8.66025i −0.200805 + 0.347804i
\(621\) 4.50000 + 7.79423i 0.180579 + 0.312772i
\(622\) 12.0000 0.481156
\(623\) 15.0000 + 5.19615i 0.600962 + 0.208179i
\(624\) 5.00000 0.200160
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −2.00000 + 3.46410i −0.0799361 + 0.138453i
\(627\) −7.50000 + 12.9904i −0.299521 + 0.518786i
\(628\) −2.50000 4.33013i −0.0997609 0.172791i
\(629\) 0 0
\(630\) −2.00000 + 1.73205i −0.0796819 + 0.0690066i
\(631\) −34.0000 −1.35352 −0.676759 0.736204i \(-0.736616\pi\)
−0.676759 + 0.736204i \(0.736616\pi\)
\(632\) 4.00000 + 6.92820i 0.159111 + 0.275589i
\(633\) −2.50000 + 4.33013i −0.0993661 + 0.172107i
\(634\) −9.00000 + 15.5885i −0.357436 + 0.619097i
\(635\) −6.50000 11.2583i −0.257945 0.446773i
\(636\) −3.00000 −0.118958
\(637\) 5.00000 34.6410i 0.198107 1.37253i
\(638\) 0 0
\(639\) 3.00000 + 5.19615i 0.118678 + 0.205557i
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) −16.5000 + 28.5788i −0.651711 + 1.12880i 0.330997 + 0.943632i \(0.392615\pi\)
−0.982708 + 0.185164i \(0.940718\pi\)
\(642\) 3.00000 + 5.19615i 0.118401 + 0.205076i
\(643\) −34.0000 −1.34083 −0.670415 0.741987i \(-0.733884\pi\)
−0.670415 + 0.741987i \(0.733884\pi\)
\(644\) 18.0000 15.5885i 0.709299 0.614271i
\(645\) −8.00000 −0.315000
\(646\) 0 0
\(647\) 4.50000 7.79423i 0.176913 0.306423i −0.763908 0.645325i \(-0.776722\pi\)
0.940822 + 0.338902i \(0.110055\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) −18.0000 31.1769i −0.706562 1.22380i
\(650\) −5.00000 −0.196116
\(651\) −25.0000 8.66025i −0.979827 0.339422i
\(652\) −16.0000 −0.626608
\(653\) −19.5000 33.7750i −0.763094 1.32172i −0.941248 0.337715i \(-0.890346\pi\)
0.178154 0.984003i \(-0.442987\pi\)
\(654\) 7.00000 12.1244i 0.273722 0.474100i
\(655\) −4.50000 + 7.79423i −0.175830 + 0.304546i
\(656\) −4.50000 7.79423i −0.175695 0.304314i
\(657\) 2.00000 0.0780274
\(658\) 1.50000 + 7.79423i 0.0584761 + 0.303851i
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 1.50000 + 2.59808i 0.0583874 + 0.101130i
\(661\) 20.0000 34.6410i 0.777910 1.34738i −0.155235 0.987878i \(-0.549613\pi\)
0.933144 0.359502i \(-0.117053\pi\)
\(662\) 5.50000 9.52628i 0.213764 0.370249i
\(663\) 0 0
\(664\) 0 0
\(665\) 2.50000 + 12.9904i 0.0969458 + 0.503745i
\(666\) 1.00000 0.0387492
\(667\) 0 0
\(668\) 1.50000 2.59808i 0.0580367 0.100523i
\(669\) 14.0000 24.2487i 0.541271 0.937509i
\(670\) −4.00000 6.92820i −0.154533 0.267660i
\(671\) 24.0000 0.926510
\(672\) −2.50000 0.866025i −0.0964396 0.0334077i
\(673\) 20.0000 0.770943 0.385472 0.922720i \(-0.374039\pi\)
0.385472 + 0.922720i \(0.374039\pi\)
\(674\) 10.0000 + 17.3205i 0.385186 + 0.667161i
\(675\) −0.500000 + 0.866025i −0.0192450 + 0.0333333i
\(676\) −6.00000 + 10.3923i −0.230769 + 0.399704i
\(677\) −1.50000 2.59808i −0.0576497 0.0998522i 0.835760 0.549095i \(-0.185027\pi\)
−0.893410 + 0.449242i \(0.851694\pi\)
\(678\) 18.0000 0.691286
\(679\) −16.0000 + 13.8564i −0.614024 + 0.531760i
\(680\) 0 0
\(681\) 0 0
\(682\) −15.0000 + 25.9808i −0.574380 + 0.994855i
\(683\) 6.00000 10.3923i 0.229584 0.397650i −0.728101 0.685470i \(-0.759597\pi\)
0.957685 + 0.287819i \(0.0929302\pi\)
\(684\) −2.50000 4.33013i −0.0955899 0.165567i
\(685\) 18.0000 0.687745
\(686\) −8.50000 + 16.4545i −0.324532 + 0.628235i
\(687\) 14.0000 0.534133
\(688\) −4.00000 6.92820i −0.152499 0.264135i
\(689\) 7.50000 12.9904i 0.285727 0.494894i
\(690\) 4.50000 7.79423i 0.171312 0.296721i
\(691\) 14.0000 + 24.2487i 0.532585 + 0.922464i 0.999276 + 0.0380440i \(0.0121127\pi\)
−0.466691 + 0.884420i \(0.654554\pi\)
\(692\) 9.00000 0.342129
\(693\) −6.00000 + 5.19615i −0.227921 + 0.197386i
\(694\) −30.0000 −1.13878
\(695\) 10.0000 + 17.3205i 0.379322 + 0.657004i
\(696\) 0 0
\(697\) 0 0
\(698\) −14.0000 24.2487i −0.529908 0.917827i
\(699\) −6.00000 −0.226941
\(700\) 2.50000 + 0.866025i 0.0944911 + 0.0327327i
\(701\) −42.0000 −1.58632 −0.793159 0.609015i \(-0.791565\pi\)
−0.793159 + 0.609015i \(0.791565\pi\)
\(702\) 2.50000 + 4.33013i 0.0943564 + 0.163430i
\(703\) 2.50000 4.33013i 0.0942893 0.163314i
\(704\) −1.50000 + 2.59808i −0.0565334 + 0.0979187i
\(705\) 1.50000 + 2.59808i 0.0564933 + 0.0978492i
\(706\) −24.0000 −0.903252
\(707\) 0 0
\(708\) 12.0000 0.450988
\(709\) 14.0000 + 24.2487i 0.525781 + 0.910679i 0.999549 + 0.0300298i \(0.00956021\pi\)
−0.473768 + 0.880650i \(0.657106\pi\)
\(710\) 3.00000 5.19615i 0.112588 0.195008i
\(711\) −4.00000 + 6.92820i −0.150012 + 0.259828i
\(712\) 3.00000 + 5.19615i 0.112430 + 0.194734i
\(713\) 90.0000 3.37053
\(714\) 0 0
\(715\) −15.0000 −0.560968
\(716\) 7.50000 + 12.9904i 0.280288 + 0.485473i
\(717\) −15.0000 + 25.9808i −0.560185 + 0.970269i
\(718\) 6.00000 10.3923i 0.223918 0.387837i
\(719\) −9.00000 15.5885i −0.335643 0.581351i 0.647965 0.761670i \(-0.275620\pi\)
−0.983608 + 0.180319i \(0.942287\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 20.0000 + 6.92820i 0.744839 + 0.258020i
\(722\) −6.00000 −0.223297
\(723\) 0.500000 + 0.866025i 0.0185952 + 0.0322078i
\(724\) −4.00000 + 6.92820i −0.148659 + 0.257485i
\(725\) 0 0
\(726\) −1.00000 1.73205i −0.0371135 0.0642824i
\(727\) 23.0000 0.853023 0.426511 0.904482i \(-0.359742\pi\)
0.426511 + 0.904482i \(0.359742\pi\)
\(728\) 10.0000 8.66025i 0.370625 0.320970i
\(729\) 1.00000 0.0370370
\(730\) −1.00000 1.73205i −0.0370117 0.0641061i
\(731\) 0 0
\(732\) −4.00000 + 6.92820i −0.147844 + 0.256074i
\(733\) 0.500000 + 0.866025i 0.0184679 + 0.0319874i 0.875112 0.483921i \(-0.160788\pi\)
−0.856644 + 0.515908i \(0.827454\pi\)
\(734\) 19.0000 0.701303
\(735\) −1.00000 + 6.92820i −0.0368856 + 0.255551i
\(736\) 9.00000 0.331744
\(737\) −12.0000 20.7846i −0.442026 0.765611i
\(738\) 4.50000 7.79423i 0.165647 0.286910i
\(739\) −2.50000 + 4.33013i −0.0919640 + 0.159286i −0.908337 0.418238i \(-0.862648\pi\)
0.816373 + 0.577524i \(0.195981\pi\)
\(740\) −0.500000 0.866025i −0.0183804 0.0318357i
\(741\) 25.0000 0.918398
\(742\) −6.00000 + 5.19615i −0.220267 + 0.190757i
\(743\) −39.0000 −1.43077 −0.715386 0.698730i \(-0.753749\pi\)
−0.715386 + 0.698730i \(0.753749\pi\)
\(744\) −5.00000 8.66025i −0.183309 0.317500i
\(745\) 0 0
\(746\) −5.00000 + 8.66025i −0.183063 + 0.317074i
\(747\) 0 0
\(748\) 0 0
\(749\) 15.0000 + 5.19615i 0.548088 + 0.189863i
\(750\) 1.00000 0.0365148
\(751\) −1.00000 1.73205i −0.0364905 0.0632034i 0.847203 0.531269i \(-0.178285\pi\)
−0.883694 + 0.468065i \(0.844951\pi\)
\(752\) −1.50000 + 2.59808i −0.0546994 + 0.0947421i
\(753\) −4.50000 + 7.79423i −0.163989 + 0.284037i
\(754\) 0 0
\(755\) 10.0000 0.363937
\(756\) −0.500000 2.59808i −0.0181848 0.0944911i
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −9.50000 16.4545i −0.345056 0.597654i
\(759\) 13.5000 23.3827i 0.490019 0.848738i
\(760\) −2.50000 + 4.33013i −0.0906845 + 0.157070i
\(761\) 16.5000 + 28.5788i 0.598125 + 1.03598i 0.993098 + 0.117289i \(0.0374205\pi\)
−0.394973 + 0.918693i \(0.629246\pi\)
\(762\) 13.0000 0.470940
\(763\) −7.00000 36.3731i −0.253417 1.31679i
\(764\) 18.0000 0.651217
\(765\) 0 0
\(766\) 13.5000 23.3827i 0.487775 0.844851i
\(767\) −30.0000 + 51.9615i −1.08324 + 1.87622i
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) 35.0000 1.26213 0.631066 0.775729i \(-0.282618\pi\)
0.631066 + 0.775729i \(0.282618\pi\)
\(770\) 7.50000 + 2.59808i 0.270281 + 0.0936282i
\(771\) −12.0000 −0.432169
\(772\) 5.00000 + 8.66025i 0.179954 + 0.311689i
\(773\) −16.5000 + 28.5788i −0.593464 + 1.02791i 0.400298 + 0.916385i \(0.368907\pi\)
−0.993762 + 0.111524i \(0.964427\pi\)
\(774\) 4.00000 6.92820i 0.143777 0.249029i
\(775\) 5.00000 + 8.66025i 0.179605 + 0.311086i
\(776\) −8.00000 −0.287183
\(777\) 2.00000 1.73205i 0.0717496 0.0621370i
\(778\) 6.00000 0.215110
\(779\) −22.5000 38.9711i −0.806146 1.39629i
\(780\) 2.50000 4.33013i 0.0895144 0.155043i