Properties

Label 570.2.i.a.121.1
Level $570$
Weight $2$
Character 570.121
Analytic conductor $4.551$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
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 \(\chi\) \(=\) 570.121
Dual form 570.2.i.a.391.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} -1.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(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} +(-0.500000 + 0.866025i) q^{6} -1.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} -3.00000 q^{11} +1.00000 q^{12} +(-1.00000 + 1.73205i) q^{13} +(0.500000 + 0.866025i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +1.00000 q^{18} +(-3.50000 - 2.59808i) q^{19} -1.00000 q^{20} +(0.500000 + 0.866025i) q^{21} +(1.50000 + 2.59808i) q^{22} +(-4.50000 + 7.79423i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +2.00000 q^{26} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} -1.00000 q^{30} -4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{33} +(3.00000 - 5.19615i) q^{34} +(-0.500000 - 0.866025i) q^{35} +(-0.500000 - 0.866025i) q^{36} +5.00000 q^{37} +(-0.500000 + 4.33013i) q^{38} +2.00000 q^{39} +(0.500000 + 0.866025i) q^{40} +(1.50000 + 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{42} +(5.00000 + 8.66025i) q^{43} +(1.50000 - 2.59808i) q^{44} -1.00000 q^{45} +9.00000 q^{46} +(-0.500000 + 0.866025i) q^{48} -6.00000 q^{49} +1.00000 q^{50} +(3.00000 - 5.19615i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-1.50000 - 2.59808i) q^{55} -1.00000 q^{56} +(-0.500000 + 4.33013i) q^{57} +(6.00000 + 10.3923i) q^{59} +(0.500000 + 0.866025i) q^{60} +(5.00000 - 8.66025i) q^{61} +(2.00000 + 3.46410i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} -2.00000 q^{65} +(1.50000 - 2.59808i) q^{66} +(5.00000 - 8.66025i) q^{67} -6.00000 q^{68} +9.00000 q^{69} +(-0.500000 + 0.866025i) q^{70} +(-0.500000 + 0.866025i) q^{72} +(2.00000 + 3.46410i) q^{73} +(-2.50000 - 4.33013i) q^{74} +1.00000 q^{75} +(4.00000 - 1.73205i) q^{76} +3.00000 q^{77} +(-1.00000 - 1.73205i) q^{78} +(-7.00000 - 12.1244i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.50000 - 2.59808i) q^{82} -18.0000 q^{83} -1.00000 q^{84} +(-3.00000 + 5.19615i) q^{85} +(5.00000 - 8.66025i) q^{86} -3.00000 q^{88} +(-7.50000 + 12.9904i) q^{89} +(0.500000 + 0.866025i) q^{90} +(1.00000 - 1.73205i) q^{91} +(-4.50000 - 7.79423i) q^{92} +(2.00000 + 3.46410i) q^{93} +(0.500000 - 4.33013i) q^{95} +1.00000 q^{96} +(-4.00000 - 6.92820i) q^{97} +(3.00000 + 5.19615i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - 2q^{7} + 2q^{8} - q^{9} + O(q^{10}) \) \( 2q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - 2q^{7} + 2q^{8} - q^{9} + q^{10} - 6q^{11} + 2q^{12} - 2q^{13} + q^{14} + q^{15} - q^{16} + 6q^{17} + 2q^{18} - 7q^{19} - 2q^{20} + q^{21} + 3q^{22} - 9q^{23} - q^{24} - q^{25} + 4q^{26} + 2q^{27} + q^{28} - 2q^{30} - 8q^{31} - q^{32} + 3q^{33} + 6q^{34} - q^{35} - q^{36} + 10q^{37} - q^{38} + 4q^{39} + q^{40} + 3q^{41} + q^{42} + 10q^{43} + 3q^{44} - 2q^{45} + 18q^{46} - q^{48} - 12q^{49} + 2q^{50} + 6q^{51} - 2q^{52} - 3q^{53} - q^{54} - 3q^{55} - 2q^{56} - q^{57} + 12q^{59} + q^{60} + 10q^{61} + 4q^{62} + q^{63} + 2q^{64} - 4q^{65} + 3q^{66} + 10q^{67} - 12q^{68} + 18q^{69} - q^{70} - q^{72} + 4q^{73} - 5q^{74} + 2q^{75} + 8q^{76} + 6q^{77} - 2q^{78} - 14q^{79} + q^{80} - q^{81} + 3q^{82} - 36q^{83} - 2q^{84} - 6q^{85} + 10q^{86} - 6q^{88} - 15q^{89} + q^{90} + 2q^{91} - 9q^{92} + 4q^{93} + q^{95} + 2q^{96} - 8q^{97} + 6q^{98} + 3q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 1.00000 0.288675
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 0.500000 + 0.866025i 0.133631 + 0.231455i
\(15\) 0.500000 0.866025i 0.129099 0.223607i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.00000 + 5.19615i 0.727607 + 1.26025i 0.957892 + 0.287129i \(0.0927008\pi\)
−0.230285 + 0.973123i \(0.573966\pi\)
\(18\) 1.00000 0.235702
\(19\) −3.50000 2.59808i −0.802955 0.596040i
\(20\) −1.00000 −0.223607
\(21\) 0.500000 + 0.866025i 0.109109 + 0.188982i
\(22\) 1.50000 + 2.59808i 0.319801 + 0.553912i
\(23\) −4.50000 + 7.79423i −0.938315 + 1.62521i −0.169701 + 0.985496i \(0.554280\pi\)
−0.768613 + 0.639713i \(0.779053\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 2.00000 0.392232
\(27\) 1.00000 0.192450
\(28\) 0.500000 0.866025i 0.0944911 0.163663i
\(29\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(30\) −1.00000 −0.182574
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 1.50000 + 2.59808i 0.261116 + 0.452267i
\(34\) 3.00000 5.19615i 0.514496 0.891133i
\(35\) −0.500000 0.866025i −0.0845154 0.146385i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 5.00000 0.821995 0.410997 0.911636i \(-0.365181\pi\)
0.410997 + 0.911636i \(0.365181\pi\)
\(38\) −0.500000 + 4.33013i −0.0811107 + 0.702439i
\(39\) 2.00000 0.320256
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) 1.50000 + 2.59808i 0.234261 + 0.405751i 0.959058 0.283211i \(-0.0913998\pi\)
−0.724797 + 0.688963i \(0.758066\pi\)
\(42\) 0.500000 0.866025i 0.0771517 0.133631i
\(43\) 5.00000 + 8.66025i 0.762493 + 1.32068i 0.941562 + 0.336840i \(0.109358\pi\)
−0.179069 + 0.983836i \(0.557309\pi\)
\(44\) 1.50000 2.59808i 0.226134 0.391675i
\(45\) −1.00000 −0.149071
\(46\) 9.00000 1.32698
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) −6.00000 −0.857143
\(50\) 1.00000 0.141421
\(51\) 3.00000 5.19615i 0.420084 0.727607i
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) −1.50000 + 2.59808i −0.206041 + 0.356873i −0.950464 0.310835i \(-0.899391\pi\)
0.744423 + 0.667708i \(0.232725\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) −1.50000 2.59808i −0.202260 0.350325i
\(56\) −1.00000 −0.133631
\(57\) −0.500000 + 4.33013i −0.0662266 + 0.573539i
\(58\) 0 0
\(59\) 6.00000 + 10.3923i 0.781133 + 1.35296i 0.931282 + 0.364299i \(0.118692\pi\)
−0.150148 + 0.988663i \(0.547975\pi\)
\(60\) 0.500000 + 0.866025i 0.0645497 + 0.111803i
\(61\) 5.00000 8.66025i 0.640184 1.10883i −0.345207 0.938527i \(-0.612191\pi\)
0.985391 0.170305i \(-0.0544754\pi\)
\(62\) 2.00000 + 3.46410i 0.254000 + 0.439941i
\(63\) 0.500000 0.866025i 0.0629941 0.109109i
\(64\) 1.00000 0.125000
\(65\) −2.00000 −0.248069
\(66\) 1.50000 2.59808i 0.184637 0.319801i
\(67\) 5.00000 8.66025i 0.610847 1.05802i −0.380251 0.924883i \(-0.624162\pi\)
0.991098 0.133135i \(-0.0425044\pi\)
\(68\) −6.00000 −0.727607
\(69\) 9.00000 1.08347
\(70\) −0.500000 + 0.866025i −0.0597614 + 0.103510i
\(71\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) 2.00000 + 3.46410i 0.234082 + 0.405442i 0.959006 0.283387i \(-0.0914581\pi\)
−0.724923 + 0.688830i \(0.758125\pi\)
\(74\) −2.50000 4.33013i −0.290619 0.503367i
\(75\) 1.00000 0.115470
\(76\) 4.00000 1.73205i 0.458831 0.198680i
\(77\) 3.00000 0.341882
\(78\) −1.00000 1.73205i −0.113228 0.196116i
\(79\) −7.00000 12.1244i −0.787562 1.36410i −0.927457 0.373930i \(-0.878010\pi\)
0.139895 0.990166i \(-0.455323\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.50000 2.59808i 0.165647 0.286910i
\(83\) −18.0000 −1.97576 −0.987878 0.155230i \(-0.950388\pi\)
−0.987878 + 0.155230i \(0.950388\pi\)
\(84\) −1.00000 −0.109109
\(85\) −3.00000 + 5.19615i −0.325396 + 0.563602i
\(86\) 5.00000 8.66025i 0.539164 0.933859i
\(87\) 0 0
\(88\) −3.00000 −0.319801
\(89\) −7.50000 + 12.9904i −0.794998 + 1.37698i 0.127842 + 0.991795i \(0.459195\pi\)
−0.922840 + 0.385183i \(0.874138\pi\)
\(90\) 0.500000 + 0.866025i 0.0527046 + 0.0912871i
\(91\) 1.00000 1.73205i 0.104828 0.181568i
\(92\) −4.50000 7.79423i −0.469157 0.812605i
\(93\) 2.00000 + 3.46410i 0.207390 + 0.359211i
\(94\) 0 0
\(95\) 0.500000 4.33013i 0.0512989 0.444262i
\(96\) 1.00000 0.102062
\(97\) −4.00000 6.92820i −0.406138 0.703452i 0.588315 0.808632i \(-0.299792\pi\)
−0.994453 + 0.105180i \(0.966458\pi\)
\(98\) 3.00000 + 5.19615i 0.303046 + 0.524891i
\(99\) 1.50000 2.59808i 0.150756 0.261116i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) −6.00000 −0.594089
\(103\) −1.00000 −0.0985329 −0.0492665 0.998786i \(-0.515688\pi\)
−0.0492665 + 0.998786i \(0.515688\pi\)
\(104\) −1.00000 + 1.73205i −0.0980581 + 0.169842i
\(105\) −0.500000 + 0.866025i −0.0487950 + 0.0845154i
\(106\) 3.00000 0.291386
\(107\) 6.00000 0.580042 0.290021 0.957020i \(-0.406338\pi\)
0.290021 + 0.957020i \(0.406338\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −1.00000 1.73205i −0.0957826 0.165900i 0.814152 0.580651i \(-0.197202\pi\)
−0.909935 + 0.414751i \(0.863869\pi\)
\(110\) −1.50000 + 2.59808i −0.143019 + 0.247717i
\(111\) −2.50000 4.33013i −0.237289 0.410997i
\(112\) 0.500000 + 0.866025i 0.0472456 + 0.0818317i
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 4.00000 1.73205i 0.374634 0.162221i
\(115\) −9.00000 −0.839254
\(116\) 0 0
\(117\) −1.00000 1.73205i −0.0924500 0.160128i
\(118\) 6.00000 10.3923i 0.552345 0.956689i
\(119\) −3.00000 5.19615i −0.275010 0.476331i
\(120\) 0.500000 0.866025i 0.0456435 0.0790569i
\(121\) −2.00000 −0.181818
\(122\) −10.0000 −0.905357
\(123\) 1.50000 2.59808i 0.135250 0.234261i
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) −1.00000 −0.0894427
\(126\) −1.00000 −0.0890871
\(127\) −5.50000 + 9.52628i −0.488046 + 0.845321i −0.999905 0.0137486i \(-0.995624\pi\)
0.511859 + 0.859069i \(0.328957\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 5.00000 8.66025i 0.440225 0.762493i
\(130\) 1.00000 + 1.73205i 0.0877058 + 0.151911i
\(131\) −4.50000 7.79423i −0.393167 0.680985i 0.599699 0.800226i \(-0.295287\pi\)
−0.992865 + 0.119241i \(0.961954\pi\)
\(132\) −3.00000 −0.261116
\(133\) 3.50000 + 2.59808i 0.303488 + 0.225282i
\(134\) −10.0000 −0.863868
\(135\) 0.500000 + 0.866025i 0.0430331 + 0.0745356i
\(136\) 3.00000 + 5.19615i 0.257248 + 0.445566i
\(137\) 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i \(-0.662010\pi\)
0.999893 0.0146279i \(-0.00465636\pi\)
\(138\) −4.50000 7.79423i −0.383065 0.663489i
\(139\) 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i \(-0.779074\pi\)
0.938293 + 0.345843i \(0.112407\pi\)
\(140\) 1.00000 0.0845154
\(141\) 0 0
\(142\) 0 0
\(143\) 3.00000 5.19615i 0.250873 0.434524i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 2.00000 3.46410i 0.165521 0.286691i
\(147\) 3.00000 + 5.19615i 0.247436 + 0.428571i
\(148\) −2.50000 + 4.33013i −0.205499 + 0.355934i
\(149\) −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i \(-0.902763\pi\)
0.216394 0.976306i \(-0.430570\pi\)
\(150\) −0.500000 0.866025i −0.0408248 0.0707107i
\(151\) −10.0000 −0.813788 −0.406894 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) −3.50000 2.59808i −0.283887 0.210732i
\(153\) −6.00000 −0.485071
\(154\) −1.50000 2.59808i −0.120873 0.209359i
\(155\) −2.00000 3.46410i −0.160644 0.278243i
\(156\) −1.00000 + 1.73205i −0.0800641 + 0.138675i
\(157\) 6.50000 + 11.2583i 0.518756 + 0.898513i 0.999762 + 0.0217953i \(0.00693820\pi\)
−0.481006 + 0.876717i \(0.659728\pi\)
\(158\) −7.00000 + 12.1244i −0.556890 + 0.964562i
\(159\) 3.00000 0.237915
\(160\) −1.00000 −0.0790569
\(161\) 4.50000 7.79423i 0.354650 0.614271i
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) −22.0000 −1.72317 −0.861586 0.507611i \(-0.830529\pi\)
−0.861586 + 0.507611i \(0.830529\pi\)
\(164\) −3.00000 −0.234261
\(165\) −1.50000 + 2.59808i −0.116775 + 0.202260i
\(166\) 9.00000 + 15.5885i 0.698535 + 1.20990i
\(167\) 10.5000 18.1865i 0.812514 1.40732i −0.0985846 0.995129i \(-0.531432\pi\)
0.911099 0.412188i \(-0.135235\pi\)
\(168\) 0.500000 + 0.866025i 0.0385758 + 0.0668153i
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 6.00000 0.460179
\(171\) 4.00000 1.73205i 0.305888 0.132453i
\(172\) −10.0000 −0.762493
\(173\) 10.5000 + 18.1865i 0.798300 + 1.38270i 0.920722 + 0.390218i \(0.127601\pi\)
−0.122422 + 0.992478i \(0.539066\pi\)
\(174\) 0 0
\(175\) 0.500000 0.866025i 0.0377964 0.0654654i
\(176\) 1.50000 + 2.59808i 0.113067 + 0.195837i
\(177\) 6.00000 10.3923i 0.450988 0.781133i
\(178\) 15.0000 1.12430
\(179\) 15.0000 1.12115 0.560576 0.828103i \(-0.310580\pi\)
0.560576 + 0.828103i \(0.310580\pi\)
\(180\) 0.500000 0.866025i 0.0372678 0.0645497i
\(181\) 8.00000 13.8564i 0.594635 1.02994i −0.398963 0.916967i \(-0.630630\pi\)
0.993598 0.112972i \(-0.0360369\pi\)
\(182\) −2.00000 −0.148250
\(183\) −10.0000 −0.739221
\(184\) −4.50000 + 7.79423i −0.331744 + 0.574598i
\(185\) 2.50000 + 4.33013i 0.183804 + 0.318357i
\(186\) 2.00000 3.46410i 0.146647 0.254000i
\(187\) −9.00000 15.5885i −0.658145 1.13994i
\(188\) 0 0
\(189\) −1.00000 −0.0727393
\(190\) −4.00000 + 1.73205i −0.290191 + 0.125656i
\(191\) 6.00000 0.434145 0.217072 0.976156i \(-0.430349\pi\)
0.217072 + 0.976156i \(0.430349\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 5.00000 + 8.66025i 0.359908 + 0.623379i 0.987945 0.154805i \(-0.0494748\pi\)
−0.628037 + 0.778183i \(0.716141\pi\)
\(194\) −4.00000 + 6.92820i −0.287183 + 0.497416i
\(195\) 1.00000 + 1.73205i 0.0716115 + 0.124035i
\(196\) 3.00000 5.19615i 0.214286 0.371154i
\(197\) −3.00000 −0.213741 −0.106871 0.994273i \(-0.534083\pi\)
−0.106871 + 0.994273i \(0.534083\pi\)
\(198\) −3.00000 −0.213201
\(199\) 5.00000 8.66025i 0.354441 0.613909i −0.632581 0.774494i \(-0.718005\pi\)
0.987022 + 0.160585i \(0.0513380\pi\)
\(200\) −0.500000 + 0.866025i −0.0353553 + 0.0612372i
\(201\) −10.0000 −0.705346
\(202\) 6.00000 0.422159
\(203\) 0 0
\(204\) 3.00000 + 5.19615i 0.210042 + 0.363803i
\(205\) −1.50000 + 2.59808i −0.104765 + 0.181458i
\(206\) 0.500000 + 0.866025i 0.0348367 + 0.0603388i
\(207\) −4.50000 7.79423i −0.312772 0.541736i
\(208\) 2.00000 0.138675
\(209\) 10.5000 + 7.79423i 0.726300 + 0.539138i
\(210\) 1.00000 0.0690066
\(211\) 12.5000 + 21.6506i 0.860535 + 1.49049i 0.871413 + 0.490550i \(0.163204\pi\)
−0.0108774 + 0.999941i \(0.503462\pi\)
\(212\) −1.50000 2.59808i −0.103020 0.178437i
\(213\) 0 0
\(214\) −3.00000 5.19615i −0.205076 0.355202i
\(215\) −5.00000 + 8.66025i −0.340997 + 0.590624i
\(216\) 1.00000 0.0680414
\(217\) 4.00000 0.271538
\(218\) −1.00000 + 1.73205i −0.0677285 + 0.117309i
\(219\) 2.00000 3.46410i 0.135147 0.234082i
\(220\) 3.00000 0.202260
\(221\) −12.0000 −0.807207
\(222\) −2.50000 + 4.33013i −0.167789 + 0.290619i
\(223\) 0.500000 + 0.866025i 0.0334825 + 0.0579934i 0.882281 0.470723i \(-0.156007\pi\)
−0.848799 + 0.528716i \(0.822674\pi\)
\(224\) 0.500000 0.866025i 0.0334077 0.0578638i
\(225\) −0.500000 0.866025i −0.0333333 0.0577350i
\(226\) 3.00000 + 5.19615i 0.199557 + 0.345643i
\(227\) 12.0000 0.796468 0.398234 0.917284i \(-0.369623\pi\)
0.398234 + 0.917284i \(0.369623\pi\)
\(228\) −3.50000 2.59808i −0.231793 0.172062i
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 4.50000 + 7.79423i 0.296721 + 0.513936i
\(231\) −1.50000 2.59808i −0.0986928 0.170941i
\(232\) 0 0
\(233\) −3.00000 5.19615i −0.196537 0.340411i 0.750867 0.660454i \(-0.229636\pi\)
−0.947403 + 0.320043i \(0.896303\pi\)
\(234\) −1.00000 + 1.73205i −0.0653720 + 0.113228i
\(235\) 0 0
\(236\) −12.0000 −0.781133
\(237\) −7.00000 + 12.1244i −0.454699 + 0.787562i
\(238\) −3.00000 + 5.19615i −0.194461 + 0.336817i
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) 1.00000 + 1.73205i 0.0642824 + 0.111340i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 5.00000 + 8.66025i 0.320092 + 0.554416i
\(245\) −3.00000 5.19615i −0.191663 0.331970i
\(246\) −3.00000 −0.191273
\(247\) 8.00000 3.46410i 0.509028 0.220416i
\(248\) −4.00000 −0.254000
\(249\) 9.00000 + 15.5885i 0.570352 + 0.987878i
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 6.00000 10.3923i 0.378717 0.655956i −0.612159 0.790735i \(-0.709699\pi\)
0.990876 + 0.134778i \(0.0430322\pi\)
\(252\) 0.500000 + 0.866025i 0.0314970 + 0.0545545i
\(253\) 13.5000 23.3827i 0.848738 1.47006i
\(254\) 11.0000 0.690201
\(255\) 6.00000 0.375735
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 3.00000 5.19615i 0.187135 0.324127i −0.757159 0.653231i \(-0.773413\pi\)
0.944294 + 0.329104i \(0.106747\pi\)
\(258\) −10.0000 −0.622573
\(259\) −5.00000 −0.310685
\(260\) 1.00000 1.73205i 0.0620174 0.107417i
\(261\) 0 0
\(262\) −4.50000 + 7.79423i −0.278011 + 0.481529i
\(263\) −7.50000 12.9904i −0.462470 0.801021i 0.536614 0.843828i \(-0.319703\pi\)
−0.999083 + 0.0428069i \(0.986370\pi\)
\(264\) 1.50000 + 2.59808i 0.0923186 + 0.159901i
\(265\) −3.00000 −0.184289
\(266\) 0.500000 4.33013i 0.0306570 0.265497i
\(267\) 15.0000 0.917985
\(268\) 5.00000 + 8.66025i 0.305424 + 0.529009i
\(269\) 15.0000 + 25.9808i 0.914566 + 1.58408i 0.807535 + 0.589819i \(0.200801\pi\)
0.107031 + 0.994256i \(0.465866\pi\)
\(270\) 0.500000 0.866025i 0.0304290 0.0527046i
\(271\) −1.00000 1.73205i −0.0607457 0.105215i 0.834053 0.551684i \(-0.186015\pi\)
−0.894799 + 0.446469i \(0.852681\pi\)
\(272\) 3.00000 5.19615i 0.181902 0.315063i
\(273\) −2.00000 −0.121046
\(274\) −12.0000 −0.724947
\(275\) 1.50000 2.59808i 0.0904534 0.156670i
\(276\) −4.50000 + 7.79423i −0.270868 + 0.469157i
\(277\) −10.0000 −0.600842 −0.300421 0.953807i \(-0.597127\pi\)
−0.300421 + 0.953807i \(0.597127\pi\)
\(278\) −4.00000 −0.239904
\(279\) 2.00000 3.46410i 0.119737 0.207390i
\(280\) −0.500000 0.866025i −0.0298807 0.0517549i
\(281\) −7.50000 + 12.9904i −0.447412 + 0.774941i −0.998217 0.0596933i \(-0.980988\pi\)
0.550804 + 0.834634i \(0.314321\pi\)
\(282\) 0 0
\(283\) 11.0000 + 19.0526i 0.653882 + 1.13256i 0.982173 + 0.187980i \(0.0601941\pi\)
−0.328291 + 0.944577i \(0.606473\pi\)
\(284\) 0 0
\(285\) −4.00000 + 1.73205i −0.236940 + 0.102598i
\(286\) −6.00000 −0.354787
\(287\) −1.50000 2.59808i −0.0885422 0.153360i
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 0 0
\(291\) −4.00000 + 6.92820i −0.234484 + 0.406138i
\(292\) −4.00000 −0.234082
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) 3.00000 5.19615i 0.174964 0.303046i
\(295\) −6.00000 + 10.3923i −0.349334 + 0.605063i
\(296\) 5.00000 0.290619
\(297\) −3.00000 −0.174078
\(298\) −9.00000 + 15.5885i −0.521356 + 0.903015i
\(299\) −9.00000 15.5885i −0.520483 0.901504i
\(300\) −0.500000 + 0.866025i −0.0288675 + 0.0500000i
\(301\) −5.00000 8.66025i −0.288195 0.499169i
\(302\) 5.00000 + 8.66025i 0.287718 + 0.498342i
\(303\) 6.00000 0.344691
\(304\) −0.500000 + 4.33013i −0.0286770 + 0.248350i
\(305\) 10.0000 0.572598
\(306\) 3.00000 + 5.19615i 0.171499 + 0.297044i
\(307\) 8.00000 + 13.8564i 0.456584 + 0.790827i 0.998778 0.0494267i \(-0.0157394\pi\)
−0.542194 + 0.840254i \(0.682406\pi\)
\(308\) −1.50000 + 2.59808i −0.0854704 + 0.148039i
\(309\) 0.500000 + 0.866025i 0.0284440 + 0.0492665i
\(310\) −2.00000 + 3.46410i −0.113592 + 0.196748i
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 2.00000 0.113228
\(313\) −4.00000 + 6.92820i −0.226093 + 0.391605i −0.956647 0.291250i \(-0.905929\pi\)
0.730554 + 0.682855i \(0.239262\pi\)
\(314\) 6.50000 11.2583i 0.366816 0.635344i
\(315\) 1.00000 0.0563436
\(316\) 14.0000 0.787562
\(317\) −7.50000 + 12.9904i −0.421242 + 0.729612i −0.996061 0.0886679i \(-0.971739\pi\)
0.574819 + 0.818280i \(0.305072\pi\)
\(318\) −1.50000 2.59808i −0.0841158 0.145693i
\(319\) 0 0
\(320\) 0.500000 + 0.866025i 0.0279508 + 0.0484123i
\(321\) −3.00000 5.19615i −0.167444 0.290021i
\(322\) −9.00000 −0.501550
\(323\) 3.00000 25.9808i 0.166924 1.44561i
\(324\) 1.00000 0.0555556
\(325\) −1.00000 1.73205i −0.0554700 0.0960769i
\(326\) 11.0000 + 19.0526i 0.609234 + 1.05522i
\(327\) −1.00000 + 1.73205i −0.0553001 + 0.0957826i
\(328\) 1.50000 + 2.59808i 0.0828236 + 0.143455i
\(329\) 0 0
\(330\) 3.00000 0.165145
\(331\) 5.00000 0.274825 0.137412 0.990514i \(-0.456121\pi\)
0.137412 + 0.990514i \(0.456121\pi\)
\(332\) 9.00000 15.5885i 0.493939 0.855528i
\(333\) −2.50000 + 4.33013i −0.136999 + 0.237289i
\(334\) −21.0000 −1.14907
\(335\) 10.0000 0.546358
\(336\) 0.500000 0.866025i 0.0272772 0.0472456i
\(337\) 11.0000 + 19.0526i 0.599208 + 1.03786i 0.992938 + 0.118633i \(0.0378512\pi\)
−0.393730 + 0.919226i \(0.628816\pi\)
\(338\) 4.50000 7.79423i 0.244768 0.423950i
\(339\) 3.00000 + 5.19615i 0.162938 + 0.282216i
\(340\) −3.00000 5.19615i −0.162698 0.281801i
\(341\) 12.0000 0.649836
\(342\) −3.50000 2.59808i −0.189258 0.140488i
\(343\) 13.0000 0.701934
\(344\) 5.00000 + 8.66025i 0.269582 + 0.466930i
\(345\) 4.50000 + 7.79423i 0.242272 + 0.419627i
\(346\) 10.5000 18.1865i 0.564483 0.977714i
\(347\) 15.0000 + 25.9808i 0.805242 + 1.39472i 0.916127 + 0.400887i \(0.131298\pi\)
−0.110885 + 0.993833i \(0.535369\pi\)
\(348\) 0 0
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) −1.00000 −0.0534522
\(351\) −1.00000 + 1.73205i −0.0533761 + 0.0924500i
\(352\) 1.50000 2.59808i 0.0799503 0.138478i
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) −12.0000 −0.637793
\(355\) 0 0
\(356\) −7.50000 12.9904i −0.397499 0.688489i
\(357\) −3.00000 + 5.19615i −0.158777 + 0.275010i
\(358\) −7.50000 12.9904i −0.396387 0.686563i
\(359\) 6.00000 + 10.3923i 0.316668 + 0.548485i 0.979791 0.200026i \(-0.0641026\pi\)
−0.663123 + 0.748511i \(0.730769\pi\)
\(360\) −1.00000 −0.0527046
\(361\) 5.50000 + 18.1865i 0.289474 + 0.957186i
\(362\) −16.0000 −0.840941
\(363\) 1.00000 + 1.73205i 0.0524864 + 0.0909091i
\(364\) 1.00000 + 1.73205i 0.0524142 + 0.0907841i
\(365\) −2.00000 + 3.46410i −0.104685 + 0.181319i
\(366\) 5.00000 + 8.66025i 0.261354 + 0.452679i
\(367\) −4.00000 + 6.92820i −0.208798 + 0.361649i −0.951336 0.308155i \(-0.900289\pi\)
0.742538 + 0.669804i \(0.233622\pi\)
\(368\) 9.00000 0.469157
\(369\) −3.00000 −0.156174
\(370\) 2.50000 4.33013i 0.129969 0.225113i
\(371\) 1.50000 2.59808i 0.0778761 0.134885i
\(372\) −4.00000 −0.207390
\(373\) 23.0000 1.19089 0.595447 0.803394i \(-0.296975\pi\)
0.595447 + 0.803394i \(0.296975\pi\)
\(374\) −9.00000 + 15.5885i −0.465379 + 0.806060i
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) 0 0
\(377\) 0 0
\(378\) 0.500000 + 0.866025i 0.0257172 + 0.0445435i
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 3.50000 + 2.59808i 0.179546 + 0.133278i
\(381\) 11.0000 0.563547
\(382\) −3.00000 5.19615i −0.153493 0.265858i
\(383\) −12.0000 20.7846i −0.613171 1.06204i −0.990702 0.136047i \(-0.956560\pi\)
0.377531 0.925997i \(-0.376773\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) 1.50000 + 2.59808i 0.0764471 + 0.132410i
\(386\) 5.00000 8.66025i 0.254493 0.440795i
\(387\) −10.0000 −0.508329
\(388\) 8.00000 0.406138
\(389\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(390\) 1.00000 1.73205i 0.0506370 0.0877058i
\(391\) −54.0000 −2.73090
\(392\) −6.00000 −0.303046
\(393\) −4.50000 + 7.79423i −0.226995 + 0.393167i
\(394\) 1.50000 + 2.59808i 0.0755689 + 0.130889i
\(395\) 7.00000 12.1244i 0.352208 0.610043i
\(396\) 1.50000 + 2.59808i 0.0753778 + 0.130558i
\(397\) −14.5000 25.1147i −0.727734 1.26047i −0.957839 0.287307i \(-0.907240\pi\)
0.230105 0.973166i \(-0.426093\pi\)
\(398\) −10.0000 −0.501255
\(399\) 0.500000 4.33013i 0.0250313 0.216777i
\(400\) 1.00000 0.0500000
\(401\) 9.00000 + 15.5885i 0.449439 + 0.778450i 0.998350 0.0574304i \(-0.0182907\pi\)
−0.548911 + 0.835881i \(0.684957\pi\)
\(402\) 5.00000 + 8.66025i 0.249377 + 0.431934i
\(403\) 4.00000 6.92820i 0.199254 0.345118i
\(404\) −3.00000 5.19615i −0.149256 0.258518i
\(405\) 0.500000 0.866025i 0.0248452 0.0430331i
\(406\) 0 0
\(407\) −15.0000 −0.743522
\(408\) 3.00000 5.19615i 0.148522 0.257248i
\(409\) −2.50000 + 4.33013i −0.123617 + 0.214111i −0.921192 0.389109i \(-0.872783\pi\)
0.797574 + 0.603220i \(0.206116\pi\)
\(410\) 3.00000 0.148159
\(411\) −12.0000 −0.591916
\(412\) 0.500000 0.866025i 0.0246332 0.0426660i
\(413\) −6.00000 10.3923i −0.295241 0.511372i
\(414\) −4.50000 + 7.79423i −0.221163 + 0.383065i
\(415\) −9.00000 15.5885i −0.441793 0.765207i
\(416\) −1.00000 1.73205i −0.0490290 0.0849208i
\(417\) −4.00000 −0.195881
\(418\) 1.50000 12.9904i 0.0733674 0.635380i
\(419\) 21.0000 1.02592 0.512959 0.858413i \(-0.328549\pi\)
0.512959 + 0.858413i \(0.328549\pi\)
\(420\) −0.500000 0.866025i −0.0243975 0.0422577i
\(421\) −13.0000 22.5167i −0.633581 1.09739i −0.986814 0.161859i \(-0.948251\pi\)
0.353233 0.935536i \(-0.385082\pi\)
\(422\) 12.5000 21.6506i 0.608490 1.05394i
\(423\) 0 0
\(424\) −1.50000 + 2.59808i −0.0728464 + 0.126174i
\(425\) −6.00000 −0.291043
\(426\) 0 0
\(427\) −5.00000 + 8.66025i −0.241967 + 0.419099i
\(428\) −3.00000 + 5.19615i −0.145010 + 0.251166i
\(429\) −6.00000 −0.289683
\(430\) 10.0000 0.482243
\(431\) −15.0000 + 25.9808i −0.722525 + 1.25145i 0.237460 + 0.971397i \(0.423685\pi\)
−0.959985 + 0.280052i \(0.909648\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 8.00000 13.8564i 0.384455 0.665896i −0.607238 0.794520i \(-0.707723\pi\)
0.991693 + 0.128624i \(0.0410559\pi\)
\(434\) −2.00000 3.46410i −0.0960031 0.166282i
\(435\) 0 0
\(436\) 2.00000 0.0957826
\(437\) 36.0000 15.5885i 1.72211 0.745697i
\(438\) −4.00000 −0.191127
\(439\) −7.00000 12.1244i −0.334092 0.578664i 0.649218 0.760602i \(-0.275096\pi\)
−0.983310 + 0.181938i \(0.941763\pi\)
\(440\) −1.50000 2.59808i −0.0715097 0.123858i
\(441\) 3.00000 5.19615i 0.142857 0.247436i
\(442\) 6.00000 + 10.3923i 0.285391 + 0.494312i
\(443\) 9.00000 15.5885i 0.427603 0.740630i −0.569057 0.822298i \(-0.692691\pi\)
0.996660 + 0.0816684i \(0.0260248\pi\)
\(444\) 5.00000 0.237289
\(445\) −15.0000 −0.711068
\(446\) 0.500000 0.866025i 0.0236757 0.0410075i
\(447\) −9.00000 + 15.5885i −0.425685 + 0.737309i
\(448\) −1.00000 −0.0472456
\(449\) 3.00000 0.141579 0.0707894 0.997491i \(-0.477448\pi\)
0.0707894 + 0.997491i \(0.477448\pi\)
\(450\) −0.500000 + 0.866025i −0.0235702 + 0.0408248i
\(451\) −4.50000 7.79423i −0.211897 0.367016i
\(452\) 3.00000 5.19615i 0.141108 0.244406i
\(453\) 5.00000 + 8.66025i 0.234920 + 0.406894i
\(454\) −6.00000 10.3923i −0.281594 0.487735i
\(455\) 2.00000 0.0937614
\(456\) −0.500000 + 4.33013i −0.0234146 + 0.202777i
\(457\) 38.0000 1.77757 0.888783 0.458329i \(-0.151552\pi\)
0.888783 + 0.458329i \(0.151552\pi\)
\(458\) 5.00000 + 8.66025i 0.233635 + 0.404667i
\(459\) 3.00000 + 5.19615i 0.140028 + 0.242536i
\(460\) 4.50000 7.79423i 0.209814 0.363408i
\(461\) −15.0000 25.9808i −0.698620 1.21004i −0.968945 0.247276i \(-0.920465\pi\)
0.270326 0.962769i \(-0.412869\pi\)
\(462\) −1.50000 + 2.59808i −0.0697863 + 0.120873i
\(463\) 11.0000 0.511213 0.255607 0.966781i \(-0.417725\pi\)
0.255607 + 0.966781i \(0.417725\pi\)
\(464\) 0 0
\(465\) −2.00000 + 3.46410i −0.0927478 + 0.160644i
\(466\) −3.00000 + 5.19615i −0.138972 + 0.240707i
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 2.00000 0.0924500
\(469\) −5.00000 + 8.66025i −0.230879 + 0.399893i
\(470\) 0 0
\(471\) 6.50000 11.2583i 0.299504 0.518756i
\(472\) 6.00000 + 10.3923i 0.276172 + 0.478345i
\(473\) −15.0000 25.9808i −0.689701 1.19460i
\(474\) 14.0000 0.643041
\(475\) 4.00000 1.73205i 0.183533 0.0794719i
\(476\) 6.00000 0.275010
\(477\) −1.50000 2.59808i −0.0686803 0.118958i
\(478\) −6.00000 10.3923i −0.274434 0.475333i
\(479\) −6.00000 + 10.3923i −0.274147 + 0.474837i −0.969920 0.243426i \(-0.921729\pi\)
0.695773 + 0.718262i \(0.255062\pi\)
\(480\) 0.500000 + 0.866025i 0.0228218 + 0.0395285i
\(481\) −5.00000 + 8.66025i −0.227980 + 0.394874i
\(482\) −10.0000 −0.455488
\(483\) −9.00000 −0.409514
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) 4.00000 6.92820i 0.181631 0.314594i
\(486\) 1.00000 0.0453609
\(487\) 11.0000 0.498458 0.249229 0.968445i \(-0.419823\pi\)
0.249229 + 0.968445i \(0.419823\pi\)
\(488\) 5.00000 8.66025i 0.226339 0.392031i
\(489\) 11.0000 + 19.0526i 0.497437 + 0.861586i
\(490\) −3.00000 + 5.19615i −0.135526 + 0.234738i
\(491\) −1.50000 2.59808i −0.0676941 0.117250i 0.830192 0.557478i \(-0.188231\pi\)
−0.897886 + 0.440228i \(0.854898\pi\)
\(492\) 1.50000 + 2.59808i 0.0676252 + 0.117130i
\(493\) 0 0
\(494\) −7.00000 5.19615i −0.314945 0.233786i
\(495\) 3.00000 0.134840
\(496\) 2.00000 + 3.46410i 0.0898027 + 0.155543i
\(497\) 0 0
\(498\) 9.00000 15.5885i 0.403300 0.698535i
\(499\) 12.5000 + 21.6506i 0.559577 + 0.969216i 0.997532 + 0.0702185i \(0.0223697\pi\)
−0.437955 + 0.898997i \(0.644297\pi\)
\(500\) 0.500000 0.866025i 0.0223607 0.0387298i
\(501\) −21.0000 −0.938211
\(502\) −12.0000 −0.535586
\(503\) −19.5000 + 33.7750i −0.869462 + 1.50595i −0.00691465 + 0.999976i \(0.502201\pi\)
−0.862547 + 0.505976i \(0.831132\pi\)
\(504\) 0.500000 0.866025i 0.0222718 0.0385758i
\(505\) −6.00000 −0.266996
\(506\) −27.0000 −1.20030
\(507\) 4.50000 7.79423i 0.199852 0.346154i
\(508\) −5.50000 9.52628i −0.244023 0.422660i
\(509\) 9.00000 15.5885i 0.398918 0.690946i −0.594675 0.803966i \(-0.702719\pi\)
0.993593 + 0.113020i \(0.0360525\pi\)
\(510\) −3.00000 5.19615i −0.132842 0.230089i
\(511\) −2.00000 3.46410i −0.0884748 0.153243i
\(512\) 1.00000 0.0441942
\(513\) −3.50000 2.59808i −0.154529 0.114708i
\(514\) −6.00000 −0.264649
\(515\) −0.500000 0.866025i −0.0220326 0.0381616i
\(516\) 5.00000 + 8.66025i 0.220113 + 0.381246i
\(517\) 0 0
\(518\) 2.50000 + 4.33013i 0.109844 + 0.190255i
\(519\) 10.5000 18.1865i 0.460899 0.798300i
\(520\) −2.00000 −0.0877058
\(521\) −42.0000 −1.84005 −0.920027 0.391856i \(-0.871833\pi\)
−0.920027 + 0.391856i \(0.871833\pi\)
\(522\) 0 0
\(523\) 8.00000 13.8564i 0.349816 0.605898i −0.636401 0.771358i \(-0.719578\pi\)
0.986216 + 0.165460i \(0.0529109\pi\)
\(524\) 9.00000 0.393167
\(525\) −1.00000 −0.0436436
\(526\) −7.50000 + 12.9904i −0.327016 + 0.566408i
\(527\) −12.0000 20.7846i −0.522728 0.905392i
\(528\) 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
\(532\) −4.00000 + 1.73205i −0.173422 + 0.0750939i
\(533\) −6.00000 −0.259889
\(534\) −7.50000 12.9904i −0.324557 0.562149i
\(535\) 3.00000 + 5.19615i 0.129701 + 0.224649i
\(536\) 5.00000 8.66025i 0.215967 0.374066i
\(537\) −7.50000 12.9904i −0.323649 0.560576i
\(538\) 15.0000 25.9808i 0.646696 1.12011i
\(539\) 18.0000 0.775315
\(540\) −1.00000 −0.0430331
\(541\) 2.00000 3.46410i 0.0859867 0.148933i −0.819825 0.572615i \(-0.805929\pi\)
0.905811 + 0.423681i \(0.139262\pi\)
\(542\) −1.00000 + 1.73205i −0.0429537 + 0.0743980i
\(543\) −16.0000 −0.686626
\(544\) −6.00000 −0.257248
\(545\) 1.00000 1.73205i 0.0428353 0.0741929i
\(546\) 1.00000 + 1.73205i 0.0427960 + 0.0741249i
\(547\) −13.0000 + 22.5167i −0.555840 + 0.962743i 0.441998 + 0.897016i \(0.354270\pi\)
−0.997838 + 0.0657267i \(0.979063\pi\)
\(548\) 6.00000 + 10.3923i 0.256307 + 0.443937i
\(549\) 5.00000 + 8.66025i 0.213395 + 0.369611i
\(550\) −3.00000 −0.127920
\(551\) 0 0
\(552\) 9.00000 0.383065
\(553\) 7.00000 + 12.1244i 0.297670 + 0.515580i
\(554\) 5.00000 + 8.66025i 0.212430 + 0.367939i
\(555\) 2.50000 4.33013i 0.106119 0.183804i
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) −16.5000 + 28.5788i −0.699127 + 1.21092i 0.269642 + 0.962961i \(0.413095\pi\)
−0.968769 + 0.247964i \(0.920239\pi\)
\(558\) −4.00000 −0.169334
\(559\) −20.0000 −0.845910
\(560\) −0.500000 + 0.866025i −0.0211289 + 0.0365963i
\(561\) −9.00000 + 15.5885i −0.379980 + 0.658145i
\(562\) 15.0000 0.632737
\(563\) 12.0000 0.505740 0.252870 0.967500i \(-0.418626\pi\)
0.252870 + 0.967500i \(0.418626\pi\)
\(564\) 0 0
\(565\) −3.00000 5.19615i −0.126211 0.218604i
\(566\) 11.0000 19.0526i 0.462364 0.800839i
\(567\) 0.500000 + 0.866025i 0.0209980 + 0.0363696i
\(568\) 0 0
\(569\) −45.0000 −1.88650 −0.943249 0.332086i \(-0.892248\pi\)
−0.943249 + 0.332086i \(0.892248\pi\)
\(570\) 3.50000 + 2.59808i 0.146599 + 0.108821i
\(571\) 44.0000 1.84134 0.920671 0.390339i \(-0.127642\pi\)
0.920671 + 0.390339i \(0.127642\pi\)
\(572\) 3.00000 + 5.19615i 0.125436 + 0.217262i
\(573\) −3.00000 5.19615i −0.125327 0.217072i
\(574\) −1.50000 + 2.59808i −0.0626088 + 0.108442i
\(575\) −4.50000 7.79423i −0.187663 0.325042i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 19.0000 0.790296
\(579\) 5.00000 8.66025i 0.207793 0.359908i
\(580\) 0 0
\(581\) 18.0000 0.746766
\(582\) 8.00000 0.331611
\(583\) 4.50000 7.79423i 0.186371 0.322804i
\(584\) 2.00000 + 3.46410i 0.0827606 + 0.143346i
\(585\) 1.00000 1.73205i 0.0413449 0.0716115i
\(586\) −4.50000 7.79423i −0.185893 0.321977i
\(587\) 6.00000 + 10.3923i 0.247647 + 0.428936i 0.962872 0.269957i \(-0.0870095\pi\)
−0.715226 + 0.698893i \(0.753676\pi\)
\(588\) −6.00000 −0.247436
\(589\) 14.0000 + 10.3923i 0.576860 + 0.428207i
\(590\) 12.0000 0.494032
\(591\) 1.50000 + 2.59808i 0.0617018 + 0.106871i
\(592\) −2.50000 4.33013i −0.102749 0.177967i
\(593\) 6.00000 10.3923i 0.246390 0.426761i −0.716131 0.697966i \(-0.754089\pi\)
0.962522 + 0.271205i \(0.0874221\pi\)
\(594\) 1.50000 + 2.59808i 0.0615457 + 0.106600i
\(595\) 3.00000 5.19615i 0.122988 0.213021i
\(596\) 18.0000 0.737309
\(597\) −10.0000 −0.409273
\(598\) −9.00000 + 15.5885i −0.368037 + 0.637459i
\(599\) 15.0000 25.9808i 0.612883 1.06155i −0.377869 0.925859i \(-0.623343\pi\)
0.990752 0.135686i \(-0.0433238\pi\)
\(600\) 1.00000 0.0408248
\(601\) 17.0000 0.693444 0.346722 0.937968i \(-0.387295\pi\)
0.346722 + 0.937968i \(0.387295\pi\)
\(602\) −5.00000 + 8.66025i −0.203785 + 0.352966i
\(603\) 5.00000 + 8.66025i 0.203616 + 0.352673i
\(604\) 5.00000 8.66025i 0.203447 0.352381i
\(605\) −1.00000 1.73205i −0.0406558 0.0704179i
\(606\) −3.00000 5.19615i −0.121867 0.211079i
\(607\) −49.0000 −1.98885 −0.994424 0.105453i \(-0.966371\pi\)
−0.994424 + 0.105453i \(0.966371\pi\)
\(608\) 4.00000 1.73205i 0.162221 0.0702439i
\(609\) 0 0
\(610\) −5.00000 8.66025i −0.202444 0.350643i
\(611\) 0 0
\(612\) 3.00000 5.19615i 0.121268 0.210042i
\(613\) 3.50000 + 6.06218i 0.141364 + 0.244849i 0.928010 0.372554i \(-0.121518\pi\)
−0.786647 + 0.617403i \(0.788185\pi\)
\(614\) 8.00000 13.8564i 0.322854 0.559199i
\(615\) 3.00000 0.120972
\(616\) 3.00000 0.120873
\(617\) −12.0000 + 20.7846i −0.483102 + 0.836757i −0.999812 0.0194037i \(-0.993823\pi\)
0.516710 + 0.856161i \(0.327157\pi\)
\(618\) 0.500000 0.866025i 0.0201129 0.0348367i
\(619\) −19.0000 −0.763674 −0.381837 0.924230i \(-0.624709\pi\)
−0.381837 + 0.924230i \(0.624709\pi\)
\(620\) 4.00000 0.160644
\(621\) −4.50000 + 7.79423i −0.180579 + 0.312772i
\(622\) 0 0
\(623\) 7.50000 12.9904i 0.300481 0.520449i
\(624\) −1.00000 1.73205i −0.0400320 0.0693375i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 8.00000 0.319744
\(627\) 1.50000 12.9904i 0.0599042 0.518786i
\(628\) −13.0000 −0.518756
\(629\) 15.0000 + 25.9808i 0.598089 + 1.03592i
\(630\) −0.500000 0.866025i −0.0199205 0.0345033i
\(631\) −16.0000 + 27.7128i −0.636950 + 1.10323i 0.349148 + 0.937067i \(0.386471\pi\)
−0.986098 + 0.166162i \(0.946862\pi\)
\(632\) −7.00000 12.1244i −0.278445 0.482281i
\(633\) 12.5000 21.6506i 0.496830 0.860535i
\(634\) 15.0000 0.595726
\(635\) −11.0000 −0.436522
\(636\) −1.50000 + 2.59808i −0.0594789 + 0.103020i
\(637\) 6.00000 10.3923i 0.237729 0.411758i
\(638\) 0 0
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) 3.00000 + 5.19615i 0.118493 + 0.205236i 0.919171 0.393860i \(-0.128860\pi\)
−0.800678 + 0.599095i \(0.795527\pi\)
\(642\) −3.00000 + 5.19615i −0.118401 + 0.205076i
\(643\) 17.0000 + 29.4449i 0.670415 + 1.16119i 0.977787 + 0.209603i \(0.0672170\pi\)
−0.307372 + 0.951589i \(0.599450\pi\)
\(644\) 4.50000 + 7.79423i 0.177325 + 0.307136i
\(645\) 10.0000 0.393750
\(646\) −24.0000 + 10.3923i −0.944267 + 0.408880i
\(647\) −39.0000 −1.53325 −0.766624 0.642096i \(-0.778065\pi\)
−0.766624 + 0.642096i \(0.778065\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) −18.0000 31.1769i −0.706562 1.22380i
\(650\) −1.00000 + 1.73205i −0.0392232 + 0.0679366i
\(651\) −2.00000 3.46410i −0.0783862 0.135769i
\(652\) 11.0000 19.0526i 0.430793 0.746156i
\(653\) −15.0000 −0.586995 −0.293498 0.955960i \(-0.594819\pi\)
−0.293498 + 0.955960i \(0.594819\pi\)
\(654\) 2.00000 0.0782062
\(655\) 4.50000 7.79423i 0.175830 0.304546i
\(656\) 1.50000 2.59808i 0.0585652 0.101438i
\(657\) −4.00000 −0.156055
\(658\) 0 0
\(659\) 13.5000 23.3827i 0.525885 0.910860i −0.473660 0.880708i \(-0.657067\pi\)
0.999545 0.0301523i \(-0.00959924\pi\)
\(660\) −1.50000 2.59808i −0.0583874 0.101130i
\(661\) 2.00000 3.46410i 0.0777910 0.134738i −0.824506 0.565854i \(-0.808547\pi\)
0.902297 + 0.431116i \(0.141880\pi\)
\(662\) −2.50000 4.33013i −0.0971653 0.168295i
\(663\) 6.00000 + 10.3923i 0.233021 + 0.403604i
\(664\) −18.0000 −0.698535
\(665\) −0.500000 + 4.33013i −0.0193892 + 0.167915i
\(666\) 5.00000 0.193746
\(667\) 0 0
\(668\) 10.5000 + 18.1865i 0.406257 + 0.703658i
\(669\) 0.500000 0.866025i 0.0193311 0.0334825i
\(670\) −5.00000 8.66025i −0.193167 0.334575i
\(671\) −15.0000 + 25.9808i −0.579069 + 1.00298i
\(672\) −1.00000 −0.0385758
\(673\) 32.0000 1.23351 0.616755 0.787155i \(-0.288447\pi\)
0.616755 + 0.787155i \(0.288447\pi\)
\(674\) 11.0000 19.0526i 0.423704 0.733877i
\(675\) −0.500000 + 0.866025i −0.0192450 + 0.0333333i
\(676\) −9.00000 −0.346154
\(677\) 33.0000 1.26829 0.634147 0.773213i \(-0.281352\pi\)
0.634147 + 0.773213i \(0.281352\pi\)
\(678\) 3.00000 5.19615i 0.115214 0.199557i
\(679\) 4.00000 + 6.92820i 0.153506 + 0.265880i
\(680\) −3.00000 + 5.19615i −0.115045 + 0.199263i
\(681\) −6.00000 10.3923i −0.229920 0.398234i
\(682\) −6.00000 10.3923i −0.229752 0.397942i
\(683\) 30.0000 1.14792 0.573959 0.818884i \(-0.305407\pi\)
0.573959 + 0.818884i \(0.305407\pi\)
\(684\) −0.500000 + 4.33013i −0.0191180 + 0.165567i
\(685\) 12.0000 0.458496
\(686\) −6.50000 11.2583i −0.248171 0.429845i
\(687\) 5.00000 + 8.66025i 0.190762 + 0.330409i
\(688\) 5.00000 8.66025i 0.190623 0.330169i
\(689\) −3.00000 5.19615i −0.114291 0.197958i
\(690\) 4.50000 7.79423i 0.171312 0.296721i
\(691\) −1.00000 −0.0380418 −0.0190209 0.999819i \(-0.506055\pi\)
−0.0190209 + 0.999819i \(0.506055\pi\)
\(692\) −21.0000 −0.798300
\(693\) −1.50000 + 2.59808i −0.0569803 + 0.0986928i
\(694\) 15.0000 25.9808i 0.569392 0.986216i
\(695\) 4.00000 0.151729
\(696\) 0 0
\(697\) −9.00000 + 15.5885i −0.340899 + 0.590455i
\(698\) −1.00000 1.73205i −0.0378506 0.0655591i
\(699\) −3.00000 + 5.19615i −0.113470 + 0.196537i
\(700\) 0.500000 + 0.866025i 0.0188982 + 0.0327327i
\(701\) 21.0000 + 36.3731i 0.793159 + 1.37379i 0.924002 + 0.382389i \(0.124898\pi\)
−0.130843 + 0.991403i \(0.541768\pi\)
\(702\) 2.00000 0.0754851
\(703\) −17.5000 12.9904i −0.660025 0.489942i
\(704\) −3.00000 −0.113067
\(705\) 0 0
\(706\) 3.00000 + 5.19615i 0.112906 + 0.195560i
\(707\) 3.00000 5.19615i 0.112827 0.195421i
\(708\) 6.00000 + 10.3923i 0.225494 + 0.390567i
\(709\) −7.00000 + 12.1244i −0.262891 + 0.455340i −0.967009 0.254743i \(-0.918009\pi\)
0.704118 + 0.710083i \(0.251342\pi\)
\(710\) 0 0
\(711\) 14.0000 0.525041
\(712\) −7.50000 + 12.9904i −0.281074 + 0.486835i
\(713\) 18.0000 31.1769i 0.674105 1.16758i
\(714\) 6.00000 0.224544
\(715\) 6.00000 0.224387
\(716\) −7.50000 + 12.9904i −0.280288 + 0.485473i
\(717\) −6.00000 10.3923i −0.224074 0.388108i
\(718\) 6.00000 10.3923i 0.223918 0.387837i
\(719\) −18.0000 31.1769i −0.671287 1.16270i −0.977539 0.210752i \(-0.932409\pi\)
0.306253 0.951950i \(-0.400925\pi\)
\(720\) 0.500000 + 0.866025i 0.0186339 + 0.0322749i
\(721\) 1.00000 0.0372419
\(722\) 13.0000 13.8564i 0.483810 0.515682i
\(723\) −10.0000 −0.371904
\(724\) 8.00000 + 13.8564i 0.297318 + 0.514969i
\(725\) 0 0
\(726\) 1.00000 1.73205i 0.0371135 0.0642824i
\(727\) 20.0000 + 34.6410i 0.741759 + 1.28476i 0.951694 + 0.307049i \(0.0993415\pi\)
−0.209935 + 0.977715i \(0.567325\pi\)
\(728\) 1.00000 1.73205i 0.0370625 0.0641941i
\(729\) 1.00000 0.0370370
\(730\) 4.00000 0.148047
\(731\) −30.0000 + 51.9615i −1.10959 + 1.92187i
\(732\) 5.00000 8.66025i 0.184805 0.320092i
\(733\) 41.0000 1.51437 0.757185 0.653201i \(-0.226574\pi\)
0.757185 + 0.653201i \(0.226574\pi\)
\(734\) 8.00000 0.295285
\(735\) −3.00000 + 5.19615i −0.110657 + 0.191663i
\(736\) −4.50000 7.79423i −0.165872 0.287299i
\(737\) −15.0000 + 25.9808i −0.552532 + 0.957014i
\(738\) 1.50000 + 2.59808i 0.0552158 + 0.0956365i
\(739\) 24.5000 + 42.4352i 0.901247 + 1.56101i 0.825877 + 0.563850i \(0.190680\pi\)
0.0753699 + 0.997156i \(0.475986\pi\)
\(740\) −5.00000 −0.183804
\(741\) −7.00000 5.19615i −0.257151 0.190885i
\(742\) −3.00000 −0.110133
\(743\) 19.5000 + 33.7750i 0.715386 + 1.23908i 0.962811 + 0.270177i \(0.0870823\pi\)
−0.247425 + 0.968907i \(0.579584\pi\)
\(744\) 2.00000 + 3.46410i 0.0733236 + 0.127000i
\(745\) 9.00000 15.5885i 0.329734 0.571117i
\(746\) −11.5000 19.9186i −0.421045 0.729271i
\(747\) 9.00000 15.5885i 0.329293 0.570352i
\(748\) 18.0000 0.658145
\(749\) −6.00000 −0.219235
\(750\) 0.500000 0.866025i 0.0182574 0.0316228i
\(751\) −4.00000 + 6.92820i −0.145962 + 0.252814i −0.929731 0.368238i \(-0.879961\pi\)
0.783769 + 0.621052i \(0.213294\pi\)
\(752\) 0 0
\(753\) −12.0000 −0.437304
\(754\) 0 0
\(755\) −5.00000 8.66025i −0.181969 0.315179i
\(756\) 0.500000 0.866025i 0.0181848 0.0314970i
\(757\) 3.50000 + 6.06218i 0.127210 + 0.220334i 0.922595 0.385771i \(-0.126065\pi\)
−0.795385 + 0.606105i \(0.792731\pi\)
\(758\) 8.00000 + 13.8564i 0.290573 + 0.503287i
\(759\) −27.0000 −0.980038
\(760\) 0.500000 4.33013i 0.0181369 0.157070i
\(761\) 15.0000 0.543750 0.271875 0.962333i \(-0.412356\pi\)
0.271875 + 0.962333i \(0.412356\pi\)
\(762\) −5.50000 9.52628i −0.199244 0.345101i
\(763\) 1.00000 + 1.73205i 0.0362024 + 0.0627044i
\(764\) −3.00000 + 5.19615i −0.108536 + 0.187990i
\(765\) −3.00000 5.19615i −0.108465 0.187867i
\(766\) −12.0000 + 20.7846i −0.433578 + 0.750978i
\(767\) −24.0000 −0.866590
\(768\) 1.00000 0.0360844
\(769\) −1.00000 + 1.73205i −0.0360609 + 0.0624593i −0.883493 0.468445i \(-0.844814\pi\)
0.847432 + 0.530904i \(0.178148\pi\)
\(770\) 1.50000 2.59808i 0.0540562 0.0936282i
\(771\) −6.00000 −0.216085
\(772\) −10.0000 −0.359908
\(773\) 10.5000 18.1865i 0.377659 0.654124i −0.613062 0.790034i \(-0.710063\pi\)
0.990721 + 0.135910i \(0.0433959\pi\)
\(774\) 5.00000 + 8.66025i 0.179721 + 0.311286i
\(775\) 2.00000 3.46410i 0.0718421 0.124434i
\(776\) −4.00000 6.92820i −0.143592 0.248708i
\(777\) 2.50000 + 4.33013i 0.0896870 + 0.155342i
\(778\) 0 0
\(779\) 1.50000 12.9904i 0.0537431 0.465429i
\(780\) −2.00000 −0.0716115