Properties

Label 570.2.i.c.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.c.391.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(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} +3.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +1.00000 q^{11} -1.00000 q^{12} +(-1.00000 + 1.73205i) q^{13} +(-1.50000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +1.00000 q^{18} +(0.500000 + 4.33013i) q^{19} -1.00000 q^{20} +(1.50000 + 2.59808i) q^{21} +(-0.500000 - 0.866025i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +2.00000 q^{26} -1.00000 q^{27} +(-1.50000 + 2.59808i) q^{28} +1.00000 q^{30} +4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} +(-1.00000 + 1.73205i) q^{34} +(1.50000 + 2.59808i) q^{35} +(-0.500000 - 0.866025i) q^{36} +9.00000 q^{37} +(3.50000 - 2.59808i) q^{38} -2.00000 q^{39} +(0.500000 + 0.866025i) q^{40} +(-0.500000 - 0.866025i) q^{41} +(1.50000 - 2.59808i) q^{42} +(5.00000 + 8.66025i) q^{43} +(-0.500000 + 0.866025i) q^{44} -1.00000 q^{45} +1.00000 q^{46} +(0.500000 - 0.866025i) q^{48} +2.00000 q^{49} +1.00000 q^{50} +(1.00000 - 1.73205i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(0.500000 + 0.866025i) q^{54} +(0.500000 + 0.866025i) q^{55} +3.00000 q^{56} +(-3.50000 + 2.59808i) q^{57} +(-6.00000 - 10.3923i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(1.00000 - 1.73205i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-1.50000 + 2.59808i) q^{63} +1.00000 q^{64} -2.00000 q^{65} +(0.500000 - 0.866025i) q^{66} +(1.00000 - 1.73205i) q^{67} +2.00000 q^{68} -1.00000 q^{69} +(1.50000 - 2.59808i) q^{70} +(-4.00000 - 6.92820i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(6.00000 + 10.3923i) q^{73} +(-4.50000 - 7.79423i) 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} +(-0.500000 + 0.866025i) q^{82} +6.00000 q^{83} -3.00000 q^{84} +(1.00000 - 1.73205i) q^{85} +(5.00000 - 8.66025i) q^{86} +1.00000 q^{88} +(2.50000 - 4.33013i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-3.00000 + 5.19615i) q^{91} +(-0.500000 - 0.866025i) q^{92} +(2.00000 + 3.46410i) q^{93} +(-3.50000 + 2.59808i) q^{95} -1.00000 q^{96} +(-4.00000 - 6.92820i) q^{97} +(-1.00000 - 1.73205i) q^{98} +(-0.500000 + 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + q^{3} - q^{4} + q^{5} + q^{6} + 6q^{7} + 2q^{8} - q^{9} + O(q^{10}) \) \( 2q - q^{2} + q^{3} - q^{4} + q^{5} + q^{6} + 6q^{7} + 2q^{8} - q^{9} + q^{10} + 2q^{11} - 2q^{12} - 2q^{13} - 3q^{14} - q^{15} - q^{16} - 2q^{17} + 2q^{18} + q^{19} - 2q^{20} + 3q^{21} - q^{22} - q^{23} + q^{24} - q^{25} + 4q^{26} - 2q^{27} - 3q^{28} + 2q^{30} + 8q^{31} - q^{32} + q^{33} - 2q^{34} + 3q^{35} - q^{36} + 18q^{37} + 7q^{38} - 4q^{39} + q^{40} - q^{41} + 3q^{42} + 10q^{43} - q^{44} - 2q^{45} + 2q^{46} + q^{48} + 4q^{49} + 2q^{50} + 2q^{51} - 2q^{52} - 3q^{53} + q^{54} + q^{55} + 6q^{56} - 7q^{57} - 12q^{59} - q^{60} + 2q^{61} - 4q^{62} - 3q^{63} + 2q^{64} - 4q^{65} + q^{66} + 2q^{67} + 4q^{68} - 2q^{69} + 3q^{70} - 8q^{71} - q^{72} + 12q^{73} - 9q^{74} - 2q^{75} - 8q^{76} + 6q^{77} + 2q^{78} - 14q^{79} + q^{80} - q^{81} - q^{82} + 12q^{83} - 6q^{84} + 2q^{85} + 10q^{86} + 2q^{88} + 5q^{89} + q^{90} - 6q^{91} - q^{92} + 4q^{93} - 7q^{95} - 2q^{96} - 8q^{97} - 2q^{98} - q^{99} + O(q^{100}) \)

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
\(7\) 3.00000 1.13389 0.566947 0.823754i \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) 1.00000 0.301511 0.150756 0.988571i \(-0.451829\pi\)
0.150756 + 0.988571i \(0.451829\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) −1.50000 2.59808i −0.400892 0.694365i
\(15\) −0.500000 + 0.866025i −0.129099 + 0.223607i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.00000 1.73205i −0.242536 0.420084i 0.718900 0.695113i \(-0.244646\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) 1.00000 0.235702
\(19\) 0.500000 + 4.33013i 0.114708 + 0.993399i
\(20\) −1.00000 −0.223607
\(21\) 1.50000 + 2.59808i 0.327327 + 0.566947i
\(22\) −0.500000 0.866025i −0.106600 0.184637i
\(23\) −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
\(26\) 2.00000 0.392232
\(27\) −1.00000 −0.192450
\(28\) −1.50000 + 2.59808i −0.283473 + 0.490990i
\(29\) 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 \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0.500000 + 0.866025i 0.0870388 + 0.150756i
\(34\) −1.00000 + 1.73205i −0.171499 + 0.297044i
\(35\) 1.50000 + 2.59808i 0.253546 + 0.439155i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 9.00000 1.47959 0.739795 0.672832i \(-0.234922\pi\)
0.739795 + 0.672832i \(0.234922\pi\)
\(38\) 3.50000 2.59808i 0.567775 0.421464i
\(39\) −2.00000 −0.320256
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) −0.500000 0.866025i −0.0780869 0.135250i 0.824338 0.566099i \(-0.191548\pi\)
−0.902424 + 0.430848i \(0.858214\pi\)
\(42\) 1.50000 2.59808i 0.231455 0.400892i
\(43\) 5.00000 + 8.66025i 0.762493 + 1.32068i 0.941562 + 0.336840i \(0.109358\pi\)
−0.179069 + 0.983836i \(0.557309\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) −1.00000 −0.149071
\(46\) 1.00000 0.147442
\(47\) 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
\(49\) 2.00000 0.285714
\(50\) 1.00000 0.141421
\(51\) 1.00000 1.73205i 0.140028 0.242536i
\(52\) −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
\(55\) 0.500000 + 0.866025i 0.0674200 + 0.116775i
\(56\) 3.00000 0.400892
\(57\) −3.50000 + 2.59808i −0.463586 + 0.344124i
\(58\) 0 0
\(59\) −6.00000 10.3923i −0.781133 1.35296i −0.931282 0.364299i \(-0.881308\pi\)
0.150148 0.988663i \(-0.452025\pi\)
\(60\) −0.500000 0.866025i −0.0645497 0.111803i
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) −2.00000 3.46410i −0.254000 0.439941i
\(63\) −1.50000 + 2.59808i −0.188982 + 0.327327i
\(64\) 1.00000 0.125000
\(65\) −2.00000 −0.248069
\(66\) 0.500000 0.866025i 0.0615457 0.106600i
\(67\) 1.00000 1.73205i 0.122169 0.211604i −0.798454 0.602056i \(-0.794348\pi\)
0.920623 + 0.390453i \(0.127682\pi\)
\(68\) 2.00000 0.242536
\(69\) −1.00000 −0.120386
\(70\) 1.50000 2.59808i 0.179284 0.310530i
\(71\) −4.00000 6.92820i −0.474713 0.822226i 0.524868 0.851184i \(-0.324115\pi\)
−0.999581 + 0.0289572i \(0.990781\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) 6.00000 + 10.3923i 0.702247 + 1.21633i 0.967676 + 0.252197i \(0.0811531\pi\)
−0.265429 + 0.964130i \(0.585514\pi\)
\(74\) −4.50000 7.79423i −0.523114 0.906061i
\(75\) −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
\(82\) −0.500000 + 0.866025i −0.0552158 + 0.0956365i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) −3.00000 −0.327327
\(85\) 1.00000 1.73205i 0.108465 0.187867i
\(86\) 5.00000 8.66025i 0.539164 0.933859i
\(87\) 0 0
\(88\) 1.00000 0.106600
\(89\) 2.50000 4.33013i 0.264999 0.458993i −0.702564 0.711621i \(-0.747962\pi\)
0.967563 + 0.252628i \(0.0812949\pi\)
\(90\) 0.500000 + 0.866025i 0.0527046 + 0.0912871i
\(91\) −3.00000 + 5.19615i −0.314485 + 0.544705i
\(92\) −0.500000 0.866025i −0.0521286 0.0902894i
\(93\) 2.00000 + 3.46410i 0.207390 + 0.359211i
\(94\) 0 0
\(95\) −3.50000 + 2.59808i −0.359092 + 0.266557i
\(96\) −1.00000 −0.102062
\(97\) −4.00000 6.92820i −0.406138 0.703452i 0.588315 0.808632i \(-0.299792\pi\)
−0.994453 + 0.105180i \(0.966458\pi\)
\(98\) −1.00000 1.73205i −0.101015 0.174964i
\(99\) −0.500000 + 0.866025i −0.0502519 + 0.0870388i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 1.00000 1.73205i 0.0995037 0.172345i −0.811976 0.583691i \(-0.801608\pi\)
0.911479 + 0.411346i \(0.134941\pi\)
\(102\) −2.00000 −0.198030
\(103\) −13.0000 −1.28093 −0.640464 0.767988i \(-0.721258\pi\)
−0.640464 + 0.767988i \(0.721258\pi\)
\(104\) −1.00000 + 1.73205i −0.0980581 + 0.169842i
\(105\) −1.50000 + 2.59808i −0.146385 + 0.253546i
\(106\) 3.00000 0.291386
\(107\) −10.0000 −0.966736 −0.483368 0.875417i \(-0.660587\pi\)
−0.483368 + 0.875417i \(0.660587\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 3.00000 + 5.19615i 0.287348 + 0.497701i 0.973176 0.230063i \(-0.0738931\pi\)
−0.685828 + 0.727764i \(0.740560\pi\)
\(110\) 0.500000 0.866025i 0.0476731 0.0825723i
\(111\) 4.50000 + 7.79423i 0.427121 + 0.739795i
\(112\) −1.50000 2.59808i −0.141737 0.245495i
\(113\) 10.0000 0.940721 0.470360 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) 4.00000 + 1.73205i 0.374634 + 0.162221i
\(115\) −1.00000 −0.0932505
\(116\) 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
\(121\) −10.0000 −0.909091
\(122\) −2.00000 −0.181071
\(123\) 0.500000 0.866025i 0.0450835 0.0780869i
\(124\) −2.00000 + 3.46410i −0.179605 + 0.311086i
\(125\) −1.00000 −0.0894427
\(126\) 3.00000 0.267261
\(127\) 0.500000 0.866025i 0.0443678 0.0768473i −0.842989 0.537931i \(-0.819206\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) −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
\(131\) −10.5000 18.1865i −0.917389 1.58896i −0.803365 0.595487i \(-0.796959\pi\)
−0.114024 0.993478i \(-0.536374\pi\)
\(132\) −1.00000 −0.0870388
\(133\) 1.50000 + 12.9904i 0.130066 + 1.12641i
\(134\) −2.00000 −0.172774
\(135\) −0.500000 0.866025i −0.0430331 0.0745356i
\(136\) −1.00000 1.73205i −0.0857493 0.148522i
\(137\) −2.00000 + 3.46410i −0.170872 + 0.295958i −0.938725 0.344668i \(-0.887992\pi\)
0.767853 + 0.640626i \(0.221325\pi\)
\(138\) 0.500000 + 0.866025i 0.0425628 + 0.0737210i
\(139\) 10.0000 17.3205i 0.848189 1.46911i −0.0346338 0.999400i \(-0.511026\pi\)
0.882823 0.469706i \(-0.155640\pi\)
\(140\) −3.00000 −0.253546
\(141\) 0 0
\(142\) −4.00000 + 6.92820i −0.335673 + 0.581402i
\(143\) −1.00000 + 1.73205i −0.0836242 + 0.144841i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 6.00000 10.3923i 0.496564 0.860073i
\(147\) 1.00000 + 1.73205i 0.0824786 + 0.142857i
\(148\) −4.50000 + 7.79423i −0.369898 + 0.640682i
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 0.500000 + 0.866025i 0.0408248 + 0.0707107i
\(151\) −18.0000 −1.46482 −0.732410 0.680864i \(-0.761604\pi\)
−0.732410 + 0.680864i \(0.761604\pi\)
\(152\) 0.500000 + 4.33013i 0.0405554 + 0.351220i
\(153\) 2.00000 0.161690
\(154\) −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
\(157\) −3.50000 6.06218i −0.279330 0.483814i 0.691888 0.722005i \(-0.256779\pi\)
−0.971219 + 0.238190i \(0.923446\pi\)
\(158\) −7.00000 + 12.1244i −0.556890 + 0.964562i
\(159\) −3.00000 −0.237915
\(160\) −1.00000 −0.0790569
\(161\) −1.50000 + 2.59808i −0.118217 + 0.204757i
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) 2.00000 0.156652 0.0783260 0.996928i \(-0.475042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) 1.00000 0.0780869
\(165\) −0.500000 + 0.866025i −0.0389249 + 0.0674200i
\(166\) −3.00000 5.19615i −0.232845 0.403300i
\(167\) −1.50000 + 2.59808i −0.116073 + 0.201045i −0.918208 0.396098i \(-0.870364\pi\)
0.802135 + 0.597143i \(0.203697\pi\)
\(168\) 1.50000 + 2.59808i 0.115728 + 0.200446i
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) −2.00000 −0.153393
\(171\) −4.00000 1.73205i −0.305888 0.132453i
\(172\) −10.0000 −0.762493
\(173\) −5.50000 9.52628i −0.418157 0.724270i 0.577597 0.816322i \(-0.303991\pi\)
−0.995754 + 0.0920525i \(0.970657\pi\)
\(174\) 0 0
\(175\) −1.50000 + 2.59808i −0.113389 + 0.196396i
\(176\) −0.500000 0.866025i −0.0376889 0.0652791i
\(177\) 6.00000 10.3923i 0.450988 0.781133i
\(178\) −5.00000 −0.374766
\(179\) −13.0000 −0.971666 −0.485833 0.874052i \(-0.661484\pi\)
−0.485833 + 0.874052i \(0.661484\pi\)
\(180\) 0.500000 0.866025i 0.0372678 0.0645497i
\(181\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(182\) 6.00000 0.444750
\(183\) 2.00000 0.147844
\(184\) −0.500000 + 0.866025i −0.0368605 + 0.0638442i
\(185\) 4.50000 + 7.79423i 0.330847 + 0.573043i
\(186\) 2.00000 3.46410i 0.146647 0.254000i
\(187\) −1.00000 1.73205i −0.0731272 0.126660i
\(188\) 0 0
\(189\) −3.00000 −0.218218
\(190\) 4.00000 + 1.73205i 0.290191 + 0.125656i
\(191\) −10.0000 −0.723575 −0.361787 0.932261i \(-0.617833\pi\)
−0.361787 + 0.932261i \(0.617833\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i \(-0.998575\pi\)
0.496119 0.868255i \(-0.334758\pi\)
\(194\) −4.00000 + 6.92820i −0.287183 + 0.497416i
\(195\) −1.00000 1.73205i −0.0716115 0.124035i
\(196\) −1.00000 + 1.73205i −0.0714286 + 0.123718i
\(197\) 5.00000 0.356235 0.178118 0.984009i \(-0.442999\pi\)
0.178118 + 0.984009i \(0.442999\pi\)
\(198\) 1.00000 0.0710669
\(199\) 9.00000 15.5885i 0.637993 1.10504i −0.347879 0.937539i \(-0.613098\pi\)
0.985873 0.167497i \(-0.0535685\pi\)
\(200\) −0.500000 + 0.866025i −0.0353553 + 0.0612372i
\(201\) 2.00000 0.141069
\(202\) −2.00000 −0.140720
\(203\) 0 0
\(204\) 1.00000 + 1.73205i 0.0700140 + 0.121268i
\(205\) 0.500000 0.866025i 0.0349215 0.0604858i
\(206\) 6.50000 + 11.2583i 0.452876 + 0.784405i
\(207\) −0.500000 0.866025i −0.0347524 0.0601929i
\(208\) 2.00000 0.138675
\(209\) 0.500000 + 4.33013i 0.0345857 + 0.299521i
\(210\) 3.00000 0.207020
\(211\) −11.5000 19.9186i −0.791693 1.37125i −0.924918 0.380166i \(-0.875867\pi\)
0.133226 0.991086i \(-0.457467\pi\)
\(212\) −1.50000 2.59808i −0.103020 0.178437i
\(213\) 4.00000 6.92820i 0.274075 0.474713i
\(214\) 5.00000 + 8.66025i 0.341793 + 0.592003i
\(215\) −5.00000 + 8.66025i −0.340997 + 0.590624i
\(216\) −1.00000 −0.0680414
\(217\) 12.0000 0.814613
\(218\) 3.00000 5.19615i 0.203186 0.351928i
\(219\) −6.00000 + 10.3923i −0.405442 + 0.702247i
\(220\) −1.00000 −0.0674200
\(221\) 4.00000 0.269069
\(222\) 4.50000 7.79423i 0.302020 0.523114i
\(223\) −1.50000 2.59808i −0.100447 0.173980i 0.811422 0.584461i \(-0.198694\pi\)
−0.911869 + 0.410481i \(0.865361\pi\)
\(224\) −1.50000 + 2.59808i −0.100223 + 0.173591i
\(225\) −0.500000 0.866025i −0.0333333 0.0577350i
\(226\) −5.00000 8.66025i −0.332595 0.576072i
\(227\) 28.0000 1.85843 0.929213 0.369546i \(-0.120487\pi\)
0.929213 + 0.369546i \(0.120487\pi\)
\(228\) −0.500000 4.33013i −0.0331133 0.286770i
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0.500000 + 0.866025i 0.0329690 + 0.0571040i
\(231\) 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 \(0.0622852\pi\)
\(242\) 5.00000 + 8.66025i 0.321412 + 0.556702i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 1.00000 + 1.73205i 0.0640184 + 0.110883i
\(245\) 1.00000 + 1.73205i 0.0638877 + 0.110657i
\(246\) −1.00000 −0.0637577
\(247\) −8.00000 3.46410i −0.509028 0.220416i
\(248\) 4.00000 0.254000
\(249\) 3.00000 + 5.19615i 0.190117 + 0.329293i
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) −14.0000 + 24.2487i −0.883672 + 1.53057i −0.0364441 + 0.999336i \(0.511603\pi\)
−0.847228 + 0.531229i \(0.821730\pi\)
\(252\) −1.50000 2.59808i −0.0944911 0.163663i
\(253\) −0.500000 + 0.866025i −0.0314347 + 0.0544466i
\(254\) −1.00000 −0.0627456
\(255\) 2.00000 0.125245
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −1.00000 + 1.73205i −0.0623783 + 0.108042i −0.895528 0.445005i \(-0.853202\pi\)
0.833150 + 0.553047i \(0.186535\pi\)
\(258\) 10.0000 0.622573
\(259\) 27.0000 1.67770
\(260\) 1.00000 1.73205i 0.0620174 0.107417i
\(261\) 0 0
\(262\) −10.5000 + 18.1865i −0.648692 + 1.12357i
\(263\) 12.5000 + 21.6506i 0.770783 + 1.33504i 0.937134 + 0.348969i \(0.113468\pi\)
−0.166351 + 0.986067i \(0.553199\pi\)
\(264\) 0.500000 + 0.866025i 0.0307729 + 0.0533002i
\(265\) −3.00000 −0.184289
\(266\) 10.5000 7.79423i 0.643796 0.477895i
\(267\) 5.00000 0.305995
\(268\) 1.00000 + 1.73205i 0.0610847 + 0.105802i
\(269\) 7.00000 + 12.1244i 0.426798 + 0.739235i 0.996586 0.0825561i \(-0.0263084\pi\)
−0.569789 + 0.821791i \(0.692975\pi\)
\(270\) −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 \(0.852681\pi\)
\(272\) −1.00000 + 1.73205i −0.0606339 + 0.105021i
\(273\) −6.00000 −0.363137
\(274\) 4.00000 0.241649
\(275\) −0.500000 + 0.866025i −0.0301511 + 0.0522233i
\(276\) 0.500000 0.866025i 0.0300965 0.0521286i
\(277\) 22.0000 1.32185 0.660926 0.750451i \(-0.270164\pi\)
0.660926 + 0.750451i \(0.270164\pi\)
\(278\) −20.0000 −1.19952
\(279\) −2.00000 + 3.46410i −0.119737 + 0.207390i
\(280\) 1.50000 + 2.59808i 0.0896421 + 0.155265i
\(281\) 10.5000 18.1865i 0.626377 1.08492i −0.361895 0.932219i \(-0.617870\pi\)
0.988273 0.152699i \(-0.0487965\pi\)
\(282\) 0 0
\(283\) −1.00000 1.73205i −0.0594438 0.102960i 0.834772 0.550596i \(-0.185599\pi\)
−0.894216 + 0.447636i \(0.852266\pi\)
\(284\) 8.00000 0.474713
\(285\) −4.00000 1.73205i −0.236940 0.102598i
\(286\) 2.00000 0.118262
\(287\) −1.50000 2.59808i −0.0885422 0.153360i
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) 0 0
\(291\) 4.00000 6.92820i 0.234484 0.406138i
\(292\) −12.0000 −0.702247
\(293\) 1.00000 0.0584206 0.0292103 0.999573i \(-0.490701\pi\)
0.0292103 + 0.999573i \(0.490701\pi\)
\(294\) 1.00000 1.73205i 0.0583212 0.101015i
\(295\) 6.00000 10.3923i 0.349334 0.605063i
\(296\) 9.00000 0.523114
\(297\) −1.00000 −0.0580259
\(298\) 3.00000 5.19615i 0.173785 0.301005i
\(299\) −1.00000 1.73205i −0.0578315 0.100167i
\(300\) 0.500000 0.866025i 0.0288675 0.0500000i
\(301\) 15.0000 + 25.9808i 0.864586 + 1.49751i
\(302\) 9.00000 + 15.5885i 0.517892 + 0.897015i
\(303\) 2.00000 0.114897
\(304\) 3.50000 2.59808i 0.200739 0.149010i
\(305\) 2.00000 0.114520
\(306\) −1.00000 1.73205i −0.0571662 0.0990148i
\(307\) −8.00000 13.8564i −0.456584 0.790827i 0.542194 0.840254i \(-0.317594\pi\)
−0.998778 + 0.0494267i \(0.984261\pi\)
\(308\) −1.50000 + 2.59808i −0.0854704 + 0.148039i
\(309\) −6.50000 11.2583i −0.369772 0.640464i
\(310\) 2.00000 3.46410i 0.113592 0.196748i
\(311\) −16.0000 −0.907277 −0.453638 0.891186i \(-0.649874\pi\)
−0.453638 + 0.891186i \(0.649874\pi\)
\(312\) −2.00000 −0.113228
\(313\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(314\) −3.50000 + 6.06218i −0.197516 + 0.342108i
\(315\) −3.00000 −0.169031
\(316\) 14.0000 0.787562
\(317\) −3.50000 + 6.06218i −0.196580 + 0.340486i −0.947417 0.320001i \(-0.896317\pi\)
0.750838 + 0.660487i \(0.229650\pi\)
\(318\) 1.50000 + 2.59808i 0.0841158 + 0.145693i
\(319\) 0 0
\(320\) 0.500000 + 0.866025i 0.0279508 + 0.0484123i
\(321\) −5.00000 8.66025i −0.279073 0.483368i
\(322\) 3.00000 0.167183
\(323\) 7.00000 5.19615i 0.389490 0.289122i
\(324\) 1.00000 0.0555556
\(325\) −1.00000 1.73205i −0.0554700 0.0960769i
\(326\) −1.00000 1.73205i −0.0553849 0.0959294i
\(327\) −3.00000 + 5.19615i −0.165900 + 0.287348i
\(328\) −0.500000 0.866025i −0.0276079 0.0478183i
\(329\) 0 0
\(330\) 1.00000 0.0550482
\(331\) 13.0000 0.714545 0.357272 0.934000i \(-0.383707\pi\)
0.357272 + 0.934000i \(0.383707\pi\)
\(332\) −3.00000 + 5.19615i −0.164646 + 0.285176i
\(333\) −4.50000 + 7.79423i −0.246598 + 0.427121i
\(334\) 3.00000 0.164153
\(335\) 2.00000 0.109272
\(336\) 1.50000 2.59808i 0.0818317 0.141737i
\(337\) −1.00000 1.73205i −0.0544735 0.0943508i 0.837503 0.546433i \(-0.184015\pi\)
−0.891976 + 0.452082i \(0.850681\pi\)
\(338\) 4.50000 7.79423i 0.244768 0.423950i
\(339\) 5.00000 + 8.66025i 0.271563 + 0.470360i
\(340\) 1.00000 + 1.73205i 0.0542326 + 0.0939336i
\(341\) 4.00000 0.216612
\(342\) 0.500000 + 4.33013i 0.0270369 + 0.234146i
\(343\) −15.0000 −0.809924
\(344\) 5.00000 + 8.66025i 0.269582 + 0.466930i
\(345\) −0.500000 0.866025i −0.0269191 0.0466252i
\(346\) −5.50000 + 9.52628i −0.295682 + 0.512136i
\(347\) −9.00000 15.5885i −0.483145 0.836832i 0.516667 0.856186i \(-0.327172\pi\)
−0.999813 + 0.0193540i \(0.993839\pi\)
\(348\) 0 0
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 3.00000 0.160357
\(351\) 1.00000 1.73205i 0.0533761 0.0924500i
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) 26.0000 1.38384 0.691920 0.721974i \(-0.256765\pi\)
0.691920 + 0.721974i \(0.256765\pi\)
\(354\) −12.0000 −0.637793
\(355\) 4.00000 6.92820i 0.212298 0.367711i
\(356\) 2.50000 + 4.33013i 0.132500 + 0.229496i
\(357\) 3.00000 5.19615i 0.158777 0.275010i
\(358\) 6.50000 + 11.2583i 0.343536 + 0.595021i
\(359\) −6.00000 10.3923i −0.316668 0.548485i 0.663123 0.748511i \(-0.269231\pi\)
−0.979791 + 0.200026i \(0.935897\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −18.5000 + 4.33013i −0.973684 + 0.227901i
\(362\) 0 0
\(363\) −5.00000 8.66025i −0.262432 0.454545i
\(364\) −3.00000 5.19615i −0.157243 0.272352i
\(365\) −6.00000 + 10.3923i −0.314054 + 0.543958i
\(366\) −1.00000 1.73205i −0.0522708 0.0905357i
\(367\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(368\) 1.00000 0.0521286
\(369\) 1.00000 0.0520579
\(370\) 4.50000 7.79423i 0.233944 0.405203i
\(371\) −4.50000 + 7.79423i −0.233628 + 0.404656i
\(372\) −4.00000 −0.207390
\(373\) −37.0000 −1.91579 −0.957894 0.287123i \(-0.907301\pi\)
−0.957894 + 0.287123i \(0.907301\pi\)
\(374\) −1.00000 + 1.73205i −0.0517088 + 0.0895622i
\(375\) −0.500000 0.866025i −0.0258199 0.0447214i
\(376\) 0 0
\(377\) 0 0
\(378\) 1.50000 + 2.59808i 0.0771517 + 0.133631i
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) −0.500000 4.33013i −0.0256495 0.222131i
\(381\) 1.00000 0.0512316
\(382\) 5.00000 + 8.66025i 0.255822 + 0.443097i
\(383\) 12.0000 + 20.7846i 0.613171 + 1.06204i 0.990702 + 0.136047i \(0.0434398\pi\)
−0.377531 + 0.925997i \(0.623227\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) 1.50000 + 2.59808i 0.0764471 + 0.132410i
\(386\) −7.00000 + 12.1244i −0.356291 + 0.617113i
\(387\) −10.0000 −0.508329
\(388\) 8.00000 0.406138
\(389\) −4.00000 + 6.92820i −0.202808 + 0.351274i −0.949432 0.313972i \(-0.898340\pi\)
0.746624 + 0.665246i \(0.231673\pi\)
\(390\) −1.00000 + 1.73205i −0.0506370 + 0.0877058i
\(391\) 2.00000 0.101144
\(392\) 2.00000 0.101015
\(393\) 10.5000 18.1865i 0.529655 0.917389i
\(394\) −2.50000 4.33013i −0.125948 0.218149i
\(395\) 7.00000 12.1244i 0.352208 0.610043i
\(396\) −0.500000 0.866025i −0.0251259 0.0435194i
\(397\) 7.50000 + 12.9904i 0.376414 + 0.651969i 0.990538 0.137241i \(-0.0438236\pi\)
−0.614123 + 0.789210i \(0.710490\pi\)
\(398\) −18.0000 −0.902258
\(399\) −10.5000 + 7.79423i −0.525657 + 0.390199i
\(400\) 1.00000 0.0500000
\(401\) 1.00000 + 1.73205i 0.0499376 + 0.0864945i 0.889914 0.456129i \(-0.150764\pi\)
−0.839976 + 0.542623i \(0.817431\pi\)
\(402\) −1.00000 1.73205i −0.0498755 0.0863868i
\(403\) −4.00000 + 6.92820i −0.199254 + 0.345118i
\(404\) 1.00000 + 1.73205i 0.0497519 + 0.0861727i
\(405\) 0.500000 0.866025i 0.0248452 0.0430331i
\(406\) 0 0
\(407\) 9.00000 0.446113
\(408\) 1.00000 1.73205i 0.0495074 0.0857493i
\(409\) −10.5000 + 18.1865i −0.519192 + 0.899266i 0.480560 + 0.876962i \(0.340434\pi\)
−0.999751 + 0.0223042i \(0.992900\pi\)
\(410\) −1.00000 −0.0493865
\(411\) −4.00000 −0.197305
\(412\) 6.50000 11.2583i 0.320232 0.554658i
\(413\) −18.0000 31.1769i −0.885722 1.53412i
\(414\) −0.500000 + 0.866025i −0.0245737 + 0.0425628i
\(415\) 3.00000 + 5.19615i 0.147264 + 0.255069i
\(416\) −1.00000 1.73205i −0.0490290 0.0849208i
\(417\) 20.0000 0.979404
\(418\) 3.50000 2.59808i 0.171191 0.127076i
\(419\) −15.0000 −0.732798 −0.366399 0.930458i \(-0.619409\pi\)
−0.366399 + 0.930458i \(0.619409\pi\)
\(420\) −1.50000 2.59808i −0.0731925 0.126773i
\(421\) 11.0000 + 19.0526i 0.536107 + 0.928565i 0.999109 + 0.0422075i \(0.0134391\pi\)
−0.463002 + 0.886357i \(0.653228\pi\)
\(422\) −11.5000 + 19.9186i −0.559811 + 0.969622i
\(423\) 0 0
\(424\) −1.50000 + 2.59808i −0.0728464 + 0.126174i
\(425\) 2.00000 0.0970143
\(426\) −8.00000 −0.387601
\(427\) 3.00000 5.19615i 0.145180 0.251459i
\(428\) 5.00000 8.66025i 0.241684 0.418609i
\(429\) −2.00000 −0.0965609
\(430\) 10.0000 0.482243
\(431\) −19.0000 + 32.9090i −0.915198 + 1.58517i −0.108586 + 0.994087i \(0.534632\pi\)
−0.806611 + 0.591082i \(0.798701\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −8.00000 + 13.8564i −0.384455 + 0.665896i −0.991693 0.128624i \(-0.958944\pi\)
0.607238 + 0.794520i \(0.292277\pi\)
\(434\) −6.00000 10.3923i −0.288009 0.498847i
\(435\) 0 0
\(436\) −6.00000 −0.287348
\(437\) −4.00000 1.73205i −0.191346 0.0828552i
\(438\) 12.0000 0.573382
\(439\) −15.0000 25.9808i −0.715911 1.23999i −0.962607 0.270901i \(-0.912678\pi\)
0.246696 0.969093i \(-0.420655\pi\)
\(440\) 0.500000 + 0.866025i 0.0238366 + 0.0412861i
\(441\) −1.00000 + 1.73205i −0.0476190 + 0.0824786i
\(442\) −2.00000 3.46410i −0.0951303 0.164771i
\(443\) −11.0000 + 19.0526i −0.522626 + 0.905214i 0.477028 + 0.878888i \(0.341714\pi\)
−0.999653 + 0.0263261i \(0.991619\pi\)
\(444\) −9.00000 −0.427121
\(445\) 5.00000 0.237023
\(446\) −1.50000 + 2.59808i −0.0710271 + 0.123022i
\(447\) −3.00000 + 5.19615i −0.141895 + 0.245770i
\(448\) 3.00000 0.141737
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) −0.500000 + 0.866025i −0.0235702 + 0.0408248i
\(451\) −0.500000 0.866025i −0.0235441 0.0407795i
\(452\) −5.00000 + 8.66025i −0.235180 + 0.407344i
\(453\) −9.00000 15.5885i −0.422857 0.732410i
\(454\) −14.0000 24.2487i −0.657053 1.13805i
\(455\) −6.00000 −0.281284
\(456\) −3.50000 + 2.59808i −0.163903 + 0.121666i
\(457\) −18.0000 −0.842004 −0.421002 0.907060i \(-0.638322\pi\)
−0.421002 + 0.907060i \(0.638322\pi\)
\(458\) −7.00000 12.1244i −0.327089 0.566534i
\(459\) 1.00000 + 1.73205i 0.0466760 + 0.0808452i
\(460\) 0.500000 0.866025i 0.0233126 0.0403786i
\(461\) −11.0000 19.0526i −0.512321 0.887366i −0.999898 0.0142861i \(-0.995452\pi\)
0.487577 0.873080i \(-0.337881\pi\)
\(462\) 1.50000 2.59808i 0.0697863 0.120873i
\(463\) −25.0000 −1.16185 −0.580924 0.813958i \(-0.697309\pi\)
−0.580924 + 0.813958i \(0.697309\pi\)
\(464\) 0 0
\(465\) −2.00000 + 3.46410i −0.0927478 + 0.160644i
\(466\) −3.00000 + 5.19615i −0.138972 + 0.240707i
\(467\) 32.0000 1.48078 0.740392 0.672176i \(-0.234640\pi\)
0.740392 + 0.672176i \(0.234640\pi\)
\(468\) 2.00000 0.0924500
\(469\) 3.00000 5.19615i 0.138527 0.239936i
\(470\) 0 0
\(471\) 3.50000 6.06218i 0.161271 0.279330i
\(472\) −6.00000 10.3923i −0.276172 0.478345i
\(473\) 5.00000 + 8.66025i 0.229900 + 0.398199i
\(474\) −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
\(479\) −10.0000 + 17.3205i −0.456912 + 0.791394i −0.998796 0.0490589i \(-0.984378\pi\)
0.541884 + 0.840453i \(0.317711\pi\)
\(480\) −0.500000 0.866025i −0.0228218 0.0395285i
\(481\) −9.00000 + 15.5885i −0.410365 + 0.710772i
\(482\) −10.0000 −0.455488
\(483\) −3.00000 −0.136505
\(484\) 5.00000 8.66025i 0.227273 0.393648i
\(485\) 4.00000 6.92820i 0.181631 0.314594i
\(486\) −1.00000 −0.0453609
\(487\) −41.0000 −1.85789 −0.928944 0.370221i \(-0.879282\pi\)
−0.928944 + 0.370221i \(0.879282\pi\)
\(488\) 1.00000 1.73205i 0.0452679 0.0784063i
\(489\) 1.00000 + 1.73205i 0.0452216 + 0.0783260i
\(490\) 1.00000 1.73205i 0.0451754 0.0782461i
\(491\) 16.5000 + 28.5788i 0.744635 + 1.28974i 0.950365 + 0.311136i \(0.100710\pi\)
−0.205731 + 0.978609i \(0.565957\pi\)
\(492\) 0.500000 + 0.866025i 0.0225417 + 0.0390434i
\(493\) 0 0
\(494\) 1.00000 + 8.66025i 0.0449921 + 0.389643i
\(495\) −1.00000 −0.0449467
\(496\) −2.00000 3.46410i −0.0898027 0.155543i
\(497\) −12.0000 20.7846i −0.538274 0.932317i
\(498\) 3.00000 5.19615i 0.134433 0.232845i
\(499\) −7.50000 12.9904i −0.335746 0.581529i 0.647882 0.761741i \(-0.275655\pi\)
−0.983628 + 0.180212i \(0.942322\pi\)
\(500\) 0.500000 0.866025i 0.0223607 0.0387298i
\(501\) −3.00000 −0.134030
\(502\) 28.0000 1.24970
\(503\) 4.50000 7.79423i 0.200645 0.347527i −0.748091 0.663596i \(-0.769030\pi\)
0.948736 + 0.316068i \(0.102363\pi\)
\(504\) −1.50000 + 2.59808i −0.0668153 + 0.115728i
\(505\) 2.00000 0.0889988
\(506\) 1.00000 0.0444554
\(507\) −4.50000 + 7.79423i −0.199852 + 0.346154i
\(508\) 0.500000 + 0.866025i 0.0221839 + 0.0384237i
\(509\) −15.0000 + 25.9808i −0.664863 + 1.15158i 0.314459 + 0.949271i \(0.398177\pi\)
−0.979322 + 0.202306i \(0.935156\pi\)
\(510\) −1.00000 1.73205i −0.0442807 0.0766965i
\(511\) 18.0000 + 31.1769i 0.796273 + 1.37919i
\(512\) 1.00000 0.0441942
\(513\) −0.500000 4.33013i −0.0220755 0.191180i
\(514\) 2.00000 0.0882162
\(515\) −6.50000 11.2583i −0.286424 0.496101i
\(516\) −5.00000 8.66025i −0.220113 0.381246i
\(517\) 0 0
\(518\) −13.5000 23.3827i −0.593156 1.02738i
\(519\) 5.50000 9.52628i 0.241423 0.418157i
\(520\) −2.00000 −0.0877058
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 0 0
\(523\) 16.0000 27.7128i 0.699631 1.21180i −0.268963 0.963150i \(-0.586681\pi\)
0.968594 0.248646i \(-0.0799857\pi\)
\(524\) 21.0000 0.917389
\(525\) −3.00000 −0.130931
\(526\) 12.5000 21.6506i 0.545026 0.944013i
\(527\) −4.00000 6.92820i −0.174243 0.301797i
\(528\) 0.500000 0.866025i 0.0217597 0.0376889i
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) 1.50000 + 2.59808i 0.0651558 + 0.112853i
\(531\) 12.0000 0.520756
\(532\) −12.0000 5.19615i −0.520266 0.225282i
\(533\) 2.00000 0.0866296
\(534\) −2.50000 4.33013i −0.108186 0.187383i
\(535\) −5.00000 8.66025i −0.216169 0.374415i
\(536\) 1.00000 1.73205i 0.0431934 0.0748132i
\(537\) −6.50000 11.2583i −0.280496 0.485833i
\(538\) 7.00000 12.1244i 0.301791 0.522718i
\(539\) 2.00000 0.0861461
\(540\) 1.00000 0.0430331
\(541\) −10.0000 + 17.3205i −0.429934 + 0.744667i −0.996867 0.0790969i \(-0.974796\pi\)
0.566933 + 0.823764i \(0.308130\pi\)
\(542\) −1.00000 + 1.73205i −0.0429537 + 0.0743980i
\(543\) 0 0
\(544\) 2.00000 0.0857493
\(545\) −3.00000 + 5.19615i −0.128506 + 0.222579i
\(546\) 3.00000 + 5.19615i 0.128388 + 0.222375i
\(547\) −1.00000 + 1.73205i −0.0427569 + 0.0740571i −0.886612 0.462514i \(-0.846947\pi\)
0.843855 + 0.536571i \(0.180281\pi\)
\(548\) −2.00000 3.46410i −0.0854358 0.147979i
\(549\) 1.00000 + 1.73205i 0.0426790 + 0.0739221i
\(550\) 1.00000 0.0426401
\(551\) 0 0
\(552\) −1.00000 −0.0425628
\(553\) −21.0000 36.3731i −0.893011 1.54674i
\(554\) −11.0000 19.0526i −0.467345 0.809466i
\(555\) −4.50000 + 7.79423i −0.191014 + 0.330847i
\(556\) 10.0000 + 17.3205i 0.424094 + 0.734553i
\(557\) −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
\(560\) 1.50000 2.59808i 0.0633866 0.109789i
\(561\) 1.00000 1.73205i 0.0422200 0.0731272i
\(562\) −21.0000 −0.885832
\(563\) 28.0000 1.18006 0.590030 0.807382i \(-0.299116\pi\)
0.590030 + 0.807382i \(0.299116\pi\)
\(564\) 0 0
\(565\) 5.00000 + 8.66025i 0.210352 + 0.364340i
\(566\) −1.00000 + 1.73205i −0.0420331 + 0.0728035i
\(567\) −1.50000 2.59808i −0.0629941 0.109109i
\(568\) −4.00000 6.92820i −0.167836 0.290701i
\(569\) 31.0000 1.29959 0.649794 0.760111i \(-0.274855\pi\)
0.649794 + 0.760111i \(0.274855\pi\)
\(570\) 0.500000 + 4.33013i 0.0209427 + 0.181369i
\(571\) −20.0000 −0.836974 −0.418487 0.908223i \(-0.637439\pi\)
−0.418487 + 0.908223i \(0.637439\pi\)
\(572\) −1.00000 1.73205i −0.0418121 0.0724207i
\(573\) −5.00000 8.66025i −0.208878 0.361787i
\(574\) −1.50000 + 2.59808i −0.0626088 + 0.108442i
\(575\) −0.500000 0.866025i −0.0208514 0.0361158i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 42.0000 1.74848 0.874241 0.485491i \(-0.161359\pi\)
0.874241 + 0.485491i \(0.161359\pi\)
\(578\) −13.0000 −0.540729
\(579\) 7.00000 12.1244i 0.290910 0.503871i
\(580\) 0 0
\(581\) 18.0000 0.746766
\(582\) −8.00000 −0.331611
\(583\) −1.50000 + 2.59808i −0.0621237 + 0.107601i
\(584\) 6.00000 + 10.3923i 0.248282 + 0.430037i
\(585\) 1.00000 1.73205i 0.0413449 0.0716115i
\(586\) −0.500000 0.866025i −0.0206548 0.0357752i
\(587\) 14.0000 + 24.2487i 0.577842 + 1.00085i 0.995726 + 0.0923513i \(0.0294383\pi\)
−0.417885 + 0.908500i \(0.637228\pi\)
\(588\) −2.00000 −0.0824786
\(589\) 2.00000 + 17.3205i 0.0824086 + 0.713679i
\(590\) −12.0000 −0.494032
\(591\) 2.50000 + 4.33013i 0.102836 + 0.178118i
\(592\) −4.50000 7.79423i −0.184949 0.320341i
\(593\) 22.0000 38.1051i 0.903432 1.56479i 0.0804231 0.996761i \(-0.474373\pi\)
0.823009 0.568029i \(-0.192294\pi\)
\(594\) 0.500000 + 0.866025i 0.0205152 + 0.0355335i
\(595\) 3.00000 5.19615i 0.122988 0.213021i
\(596\) −6.00000 −0.245770
\(597\) 18.0000 0.736691
\(598\) −1.00000 + 1.73205i −0.0408930 + 0.0708288i
\(599\) −17.0000 + 29.4449i −0.694601 + 1.20308i 0.275714 + 0.961240i \(0.411086\pi\)
−0.970315 + 0.241845i \(0.922248\pi\)
\(600\) −1.00000 −0.0408248
\(601\) 25.0000 1.01977 0.509886 0.860242i \(-0.329688\pi\)
0.509886 + 0.860242i \(0.329688\pi\)
\(602\) 15.0000 25.9808i 0.611354 1.05890i
\(603\) 1.00000 + 1.73205i 0.0407231 + 0.0705346i
\(604\) 9.00000 15.5885i 0.366205 0.634285i
\(605\) −5.00000 8.66025i −0.203279 0.352089i
\(606\) −1.00000 1.73205i −0.0406222 0.0703598i
\(607\) −5.00000 −0.202944 −0.101472 0.994838i \(-0.532355\pi\)
−0.101472 + 0.994838i \(0.532355\pi\)
\(608\) −4.00000 1.73205i −0.162221 0.0702439i
\(609\) 0 0
\(610\) −1.00000 1.73205i −0.0404888 0.0701287i
\(611\) 0 0
\(612\) −1.00000 + 1.73205i −0.0404226 + 0.0700140i
\(613\) 5.50000 + 9.52628i 0.222143 + 0.384763i 0.955458 0.295126i \(-0.0953615\pi\)
−0.733316 + 0.679888i \(0.762028\pi\)
\(614\) −8.00000 + 13.8564i −0.322854 + 0.559199i
\(615\) 1.00000 0.0403239
\(616\) 3.00000 0.120873
\(617\) −8.00000 + 13.8564i −0.322068 + 0.557838i −0.980915 0.194439i \(-0.937711\pi\)
0.658847 + 0.752277i \(0.271045\pi\)
\(618\) −6.50000 + 11.2583i −0.261468 + 0.452876i
\(619\) 13.0000 0.522514 0.261257 0.965269i \(-0.415863\pi\)
0.261257 + 0.965269i \(0.415863\pi\)
\(620\) −4.00000 −0.160644
\(621\) 0.500000 0.866025i 0.0200643 0.0347524i
\(622\) 8.00000 + 13.8564i 0.320771 + 0.555591i
\(623\) 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
\(626\) 0 0
\(627\) −3.50000 + 2.59808i −0.139777 + 0.103757i
\(628\) 7.00000 0.279330
\(629\) −9.00000 15.5885i −0.358854 0.621552i
\(630\) 1.50000 + 2.59808i 0.0597614 + 0.103510i
\(631\) 4.00000 6.92820i 0.159237 0.275807i −0.775356 0.631524i \(-0.782430\pi\)
0.934594 + 0.355716i \(0.115763\pi\)
\(632\) −7.00000 12.1244i −0.278445 0.482281i
\(633\) 11.5000 19.9186i 0.457084 0.791693i
\(634\) 7.00000 0.278006
\(635\) 1.00000 0.0396838
\(636\) 1.50000 2.59808i 0.0594789 0.103020i
\(637\) −2.00000 + 3.46410i −0.0792429 + 0.137253i
\(638\) 0 0
\(639\) 8.00000 0.316475
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) −21.0000 36.3731i −0.829450 1.43665i −0.898470 0.439034i \(-0.855321\pi\)
0.0690201 0.997615i \(-0.478013\pi\)
\(642\) −5.00000 + 8.66025i −0.197334 + 0.341793i
\(643\) −7.00000 12.1244i −0.276053 0.478138i 0.694347 0.719640i \(-0.255693\pi\)
−0.970400 + 0.241502i \(0.922360\pi\)
\(644\) −1.50000 2.59808i −0.0591083 0.102379i
\(645\) −10.0000 −0.393750
\(646\) −8.00000 3.46410i −0.314756 0.136293i
\(647\) −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
\(649\) −6.00000 10.3923i −0.235521 0.407934i
\(650\) −1.00000 + 1.73205i −0.0392232 + 0.0679366i
\(651\) 6.00000 + 10.3923i 0.235159 + 0.407307i
\(652\) −1.00000 + 1.73205i −0.0391630 + 0.0678323i
\(653\) 9.00000 0.352197 0.176099 0.984373i \(-0.443652\pi\)
0.176099 + 0.984373i \(0.443652\pi\)
\(654\) 6.00000 0.234619
\(655\) 10.5000 18.1865i 0.410269 0.710607i
\(656\) −0.500000 + 0.866025i −0.0195217 + 0.0338126i
\(657\) −12.0000 −0.468165
\(658\) 0 0
\(659\) 7.50000 12.9904i 0.292159 0.506033i −0.682161 0.731202i \(-0.738960\pi\)
0.974320 + 0.225168i \(0.0722932\pi\)
\(660\) −0.500000 0.866025i −0.0194625 0.0337100i
\(661\) −2.00000 + 3.46410i −0.0777910 + 0.134738i −0.902297 0.431116i \(-0.858120\pi\)
0.824506 + 0.565854i \(0.191453\pi\)
\(662\) −6.50000 11.2583i −0.252630 0.437567i
\(663\) 2.00000 + 3.46410i 0.0776736 + 0.134535i
\(664\) 6.00000 0.232845
\(665\) −10.5000 + 7.79423i −0.407173 + 0.302247i
\(666\) 9.00000 0.348743
\(667\) 0 0
\(668\) −1.50000 2.59808i −0.0580367 0.100523i
\(669\) 1.50000 2.59808i 0.0579934 0.100447i
\(670\) −1.00000 1.73205i −0.0386334 0.0669150i
\(671\) 1.00000 1.73205i 0.0386046 0.0668651i
\(672\) −3.00000 −0.115728
\(673\) 16.0000 0.616755 0.308377 0.951264i \(-0.400214\pi\)
0.308377 + 0.951264i \(0.400214\pi\)
\(674\) −1.00000 + 1.73205i −0.0385186 + 0.0667161i
\(675\) 0.500000 0.866025i 0.0192450 0.0333333i
\(676\) −9.00000 −0.346154
\(677\) −39.0000 −1.49889 −0.749446 0.662066i \(-0.769680\pi\)
−0.749446 + 0.662066i \(0.769680\pi\)
\(678\) 5.00000 8.66025i 0.192024 0.332595i
\(679\) −12.0000 20.7846i −0.460518 0.797640i
\(680\) 1.00000 1.73205i 0.0383482 0.0664211i
\(681\) 14.0000 + 24.2487i 0.536481 + 0.929213i
\(682\) −2.00000 3.46410i −0.0765840 0.132647i
\(683\) 6.00000 0.229584 0.114792 0.993390i \(-0.463380\pi\)
0.114792 + 0.993390i \(0.463380\pi\)
\(684\) 3.50000 2.59808i 0.133826 0.0993399i
\(685\) −4.00000 −0.152832
\(686\) 7.50000 + 12.9904i 0.286351 + 0.495975i
\(687\) 7.00000 + 12.1244i 0.267067 + 0.462573i
\(688\) 5.00000 8.66025i 0.190623 0.330169i
\(689\) −3.00000 5.19615i −0.114291 0.197958i
\(690\) −0.500000 + 0.866025i −0.0190347 + 0.0329690i
\(691\) 23.0000 0.874961 0.437481 0.899228i \(-0.355871\pi\)
0.437481 + 0.899228i \(0.355871\pi\)
\(692\) 11.0000 0.418157
\(693\) −1.50000 + 2.59808i −0.0569803 + 0.0986928i
\(694\) −9.00000 + 15.5885i −0.341635 + 0.591730i
\(695\) 20.0000 0.758643
\(696\) 0 0
\(697\) −1.00000 + 1.73205i −0.0378777 + 0.0656061i
\(698\) −13.0000 22.5167i −0.492057 0.852268i
\(699\) 3.00000 5.19615i 0.113470 0.196537i
\(700\) −1.50000 2.59808i −0.0566947 0.0981981i
\(701\) 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
\(703\) 4.50000 + 38.9711i 0.169721 + 1.46982i
\(704\) 1.00000 0.0376889
\(705\) 0 0
\(706\) −13.0000 22.5167i −0.489261 0.847426i
\(707\) 3.00000 5.19615i 0.112827 0.195421i
\(708\) 6.00000 + 10.3923i 0.225494 + 0.390567i
\(709\) −19.0000 + 32.9090i −0.713560 + 1.23592i 0.249952 + 0.968258i \(0.419585\pi\)
−0.963512 + 0.267664i \(0.913748\pi\)
\(710\) −8.00000 −0.300235
\(711\) 14.0000 0.525041
\(712\) 2.50000 4.33013i 0.0936915 0.162278i
\(713\) −2.00000 + 3.46410i −0.0749006 + 0.129732i
\(714\) −6.00000 −0.224544
\(715\) −2.00000 −0.0747958
\(716\) 6.50000 11.2583i 0.242916 0.420744i
\(717\) 6.00000 + 10.3923i 0.224074 + 0.388108i
\(718\) −6.00000 + 10.3923i −0.223918 + 0.387837i
\(719\) −14.0000 24.2487i −0.522112 0.904324i −0.999669 0.0257237i \(-0.991811\pi\)
0.477557 0.878601i \(-0.341522\pi\)
\(720\) 0.500000 + 0.866025i 0.0186339 + 0.0322749i
\(721\) −39.0000 −1.45244
\(722\) 13.0000 + 13.8564i 0.483810 + 0.515682i
\(723\) 10.0000 0.371904
\(724\) 0 0
\(725\) 0 0
\(726\) −5.00000 + 8.66025i −0.185567 + 0.321412i
\(727\) 16.0000 + 27.7128i 0.593407 + 1.02781i 0.993770 + 0.111454i \(0.0355509\pi\)
−0.400362 + 0.916357i \(0.631116\pi\)
\(728\) −3.00000 + 5.19615i −0.111187 + 0.192582i
\(729\) 1.00000 0.0370370
\(730\) 12.0000 0.444140
\(731\) 10.0000 17.3205i 0.369863 0.640622i
\(732\) −1.00000 + 1.73205i −0.0369611 + 0.0640184i
\(733\) −35.0000 −1.29275 −0.646377 0.763018i \(-0.723717\pi\)
−0.646377 + 0.763018i \(0.723717\pi\)
\(734\) 0 0
\(735\) −1.00000 + 1.73205i −0.0368856 + 0.0638877i
\(736\) −0.500000 0.866025i −0.0184302 0.0319221i
\(737\) 1.00000 1.73205i 0.0368355 0.0638009i
\(738\) −0.500000 0.866025i −0.0184053 0.0318788i
\(739\) −3.50000 6.06218i −0.128750 0.223001i 0.794443 0.607339i \(-0.207763\pi\)
−0.923192 + 0.384338i \(0.874430\pi\)
\(740\) −9.00000 −0.330847
\(741\) −1.00000 8.66025i −0.0367359 0.318142i
\(742\) 9.00000 0.330400
\(743\) 11.5000 + 19.9186i 0.421894 + 0.730742i 0.996125 0.0879516i \(-0.0280321\pi\)
−0.574231 + 0.818694i \(0.694699\pi\)
\(744\) 2.00000 + 3.46410i 0.0733236 + 0.127000i
\(745\) −3.00000 + 5.19615i −0.109911 + 0.190372i
\(746\) 18.5000 + 32.0429i 0.677333 + 1.17318i
\(747\) −3.00000 + 5.19615i −0.109764 + 0.190117i
\(748\) 2.00000 0.0731272
\(749\) −30.0000 −1.09618
\(750\) −0.500000 + 0.866025i −0.0182574 + 0.0316228i
\(751\) −16.0000 + 27.7128i −0.583848 + 1.01125i 0.411170 + 0.911559i \(0.365120\pi\)
−0.995018 + 0.0996961i \(0.968213\pi\)
\(752\) 0 0
\(753\) −28.0000 −1.02038
\(754\) 0 0
\(755\) −9.00000 15.5885i −0.327544 0.567322i
\(756\) 1.50000 2.59808i 0.0545545 0.0944911i
\(757\) 9.50000 + 16.4545i 0.345283 + 0.598048i 0.985405 0.170225i \(-0.0544495\pi\)
−0.640122 + 0.768273i \(0.721116\pi\)
\(758\) −8.00000 13.8564i −0.290573 0.503287i
\(759\) −1.00000 −0.0362977
\(760\) −3.50000 + 2.59808i −0.126958 + 0.0942421i
\(761\) −45.0000 −1.63125 −0.815624 0.578582i \(-0.803606\pi\)
−0.815624 + 0.578582i \(0.803606\pi\)
\(762\) −0.500000 0.866025i −0.0181131 0.0313728i
\(763\) 9.00000 + 15.5885i 0.325822 + 0.564340i
\(764\) 5.00000 8.66025i 0.180894 0.313317i
\(765\) 1.00000 + 1.73205i 0.0361551 + 0.0626224i
\(766\) 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
\(771\) −2.00000 −0.0720282
\(772\) 14.0000 0.503871
\(773\) 22.5000 38.9711i 0.809269 1.40169i −0.104102 0.994567i \(-0.533197\pi\)
0.913371 0.407128i \(-0.133470\pi\)
\(774\) 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
\(777\) 13.5000 + 23.3827i 0.484310 + 0.838849i
\(778\) 8.00000 0.286814
\(779\) 3.50000 2.59808i 0.125401 0.0930857i
\(780\) 2.00000