Properties

Label 570.2.i.c.391.1
Level $570$
Weight $2$
Character 570.391
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 391.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 570.391
Dual form 570.2.i.c.121.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +3.00000 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 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 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) −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 −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) 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 0.809177 0.587565i \(-0.199913\pi\)
−0.913434 + 0.406986i \(0.866580\pi\)
\(24\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(30\) 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 −0.902424 0.430848i \(-0.858214\pi\)
0.824338 + 0.566099i \(0.191548\pi\)
\(42\) 1.50000 + 2.59808i 0.231455 + 0.400892i
\(43\) 5.00000 8.66025i 0.762493 1.32068i −0.179069 0.983836i \(-0.557309\pi\)
0.941562 0.336840i \(-0.109358\pi\)
\(44\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 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 0.744423 0.667708i \(-0.232725\pi\)
−0.950464 + 0.310835i \(0.899391\pi\)
\(54\) 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 0.150148 + 0.988663i \(0.452025\pi\)
−0.931282 + 0.364299i \(0.881308\pi\)
\(60\) −0.500000 + 0.866025i −0.0645497 + 0.111803i
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) −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 0.920623 0.390453i \(-0.127682\pi\)
−0.798454 + 0.602056i \(0.794348\pi\)
\(68\) 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 −0.999581 0.0289572i \(-0.990781\pi\)
0.524868 + 0.851184i \(0.324115\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 6.00000 10.3923i 0.702247 1.21633i −0.265429 0.964130i \(-0.585514\pi\)
0.967676 0.252197i \(-0.0811531\pi\)
\(74\) −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 0.139895 + 0.990166i \(0.455323\pi\)
−0.927457 + 0.373930i \(0.878010\pi\)
\(80\) 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 0.967563 0.252628i \(-0.0812949\pi\)
−0.702564 + 0.711621i \(0.747962\pi\)
\(90\) 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 −0.994453 0.105180i \(-0.966458\pi\)
0.588315 + 0.808632i \(0.299792\pi\)
\(98\) −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 0.911479 0.411346i \(-0.134941\pi\)
−0.811976 + 0.583691i \(0.801608\pi\)
\(102\) −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 −0.685828 0.727764i \(-0.740560\pi\)
0.973176 + 0.230063i \(0.0738931\pi\)
\(110\) 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 0.887357 0.461084i \(-0.152539\pi\)
−0.842989 + 0.537931i \(0.819206\pi\)
\(128\) −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 −0.114024 + 0.993478i \(0.536374\pi\)
−0.803365 + 0.595487i \(0.796959\pi\)
\(132\) −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 0.767853 0.640626i \(-0.221325\pi\)
−0.938725 + 0.344668i \(0.887992\pi\)
\(138\) 0.500000 0.866025i 0.0425628 0.0737210i
\(139\) 10.0000 + 17.3205i 0.848189 + 1.46911i 0.882823 + 0.469706i \(0.155640\pi\)
−0.0346338 + 0.999400i \(0.511026\pi\)
\(140\) −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 −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 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 −0.971219 0.238190i \(-0.923446\pi\)
0.691888 + 0.722005i \(0.256779\pi\)
\(158\) −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 0.802135 0.597143i \(-0.203697\pi\)
−0.918208 + 0.396098i \(0.870364\pi\)
\(168\) 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 −0.995754 0.0920525i \(-0.970657\pi\)
0.577597 + 0.816322i \(0.303991\pi\)
\(174\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(182\) 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 0.496119 + 0.868255i \(0.334758\pi\)
−0.999990 + 0.00447566i \(0.998575\pi\)
\(194\) −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 0.985873 + 0.167497i \(0.0535685\pi\)
−0.347879 + 0.937539i \(0.613098\pi\)
\(200\) −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 0.133226 + 0.991086i \(0.457467\pi\)
−0.924918 + 0.380166i \(0.875867\pi\)
\(212\) −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 −0.911869 0.410481i \(-0.865361\pi\)
0.811422 + 0.584461i \(0.198694\pi\)
\(224\) −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 −0.947403 0.320043i \(-0.896303\pi\)
0.750867 + 0.660454i \(0.229636\pi\)
\(234\) −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 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) 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 −0.847228 0.531229i \(-0.821730\pi\)
−0.0364441 0.999336i \(-0.511603\pi\)
\(252\) −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 0.833150 0.553047i \(-0.186535\pi\)
−0.895528 + 0.445005i \(0.853202\pi\)
\(258\) 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 −0.166351 0.986067i \(-0.553199\pi\)
0.937134 0.348969i \(-0.113468\pi\)
\(264\) 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 −0.569789 0.821791i \(-0.692975\pi\)
0.996586 + 0.0825561i \(0.0263084\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) −1.00000 + 1.73205i −0.0607457 + 0.105215i −0.894799 0.446469i \(-0.852681\pi\)
0.834053 + 0.551684i \(0.186015\pi\)
\(272\) −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 0.988273 + 0.152699i \(0.0487965\pi\)
−0.361895 + 0.932219i \(0.617870\pi\)
\(282\) 0 0
\(283\) −1.00000 + 1.73205i −0.0594438 + 0.102960i −0.894216 0.447636i \(-0.852266\pi\)
0.834772 + 0.550596i \(0.185599\pi\)
\(284\) 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 −0.998778 0.0494267i \(-0.984261\pi\)
0.542194 + 0.840254i \(0.317594\pi\)
\(308\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(314\) −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 0.750838 0.660487i \(-0.229650\pi\)
−0.947417 + 0.320001i \(0.896317\pi\)
\(318\) 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 −0.891976 0.452082i \(-0.850681\pi\)
0.837503 + 0.546433i \(0.184015\pi\)
\(338\) 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 −0.999813 0.0193540i \(-0.993839\pi\)
0.516667 + 0.856186i \(0.327172\pi\)
\(348\) 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 −0.979791 0.200026i \(-0.935897\pi\)
0.663123 + 0.748511i \(0.269231\pi\)
\(360\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(368\) 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 −0.377531 0.925997i \(-0.623227\pi\)
0.990702 0.136047i \(-0.0434398\pi\)
\(384\) 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 0.746624 0.665246i \(-0.231673\pi\)
−0.949432 + 0.313972i \(0.898340\pi\)
\(390\) −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 −0.614123 0.789210i \(-0.710490\pi\)
0.990538 + 0.137241i \(0.0438236\pi\)
\(398\) −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 −0.839976 0.542623i \(-0.817431\pi\)
0.889914 + 0.456129i \(0.150764\pi\)
\(402\) −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 −0.999751 0.0223042i \(-0.992900\pi\)
0.480560 0.876962i \(-0.340434\pi\)
\(410\) −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 −0.463002 0.886357i \(-0.653228\pi\)
0.999109 0.0422075i \(-0.0134391\pi\)
\(422\) −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 −0.806611 0.591082i \(-0.798701\pi\)
−0.108586 0.994087i \(-0.534632\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −8.00000 13.8564i −0.384455 0.665896i 0.607238 0.794520i \(-0.292277\pi\)
−0.991693 + 0.128624i \(0.958944\pi\)
\(434\) −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 0.246696 + 0.969093i \(0.420655\pi\)
−0.962607 + 0.270901i \(0.912678\pi\)
\(440\) 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 −0.999653 0.0263261i \(-0.991619\pi\)
0.477028 0.878888i \(-0.341714\pi\)
\(444\) −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 0.487577 + 0.873080i \(0.337881\pi\)
−0.999898 + 0.0142861i \(0.995452\pi\)
\(462\) 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 0.541884 0.840453i \(-0.317711\pi\)
−0.998796 + 0.0490589i \(0.984378\pi\)
\(480\) −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 −0.205731 0.978609i \(-0.565957\pi\)
0.950365 0.311136i \(-0.100710\pi\)
\(492\) 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 −0.983628 0.180212i \(-0.942322\pi\)
0.647882 + 0.761741i \(0.275655\pi\)
\(500\) 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 0.948736 0.316068i \(-0.102363\pi\)
−0.748091 + 0.663596i \(0.769030\pi\)
\(504\) −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 −0.979322 0.202306i \(-0.935156\pi\)
0.314459 0.949271i \(-0.398177\pi\)
\(510\) −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 0.968594 + 0.248646i \(0.0799857\pi\)
−0.268963 + 0.963150i \(0.586681\pi\)
\(524\) 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 0.566933 0.823764i \(-0.308130\pi\)
−0.996867 + 0.0790969i \(0.974796\pi\)
\(542\) −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 0.843855 0.536571i \(-0.180281\pi\)
−0.886612 + 0.462514i \(0.846947\pi\)
\(548\) −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 −0.968769 0.247964i \(-0.920239\pi\)
0.269642 0.962961i \(-0.413095\pi\)
\(558\) 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 −0.417885 0.908500i \(-0.637228\pi\)
0.995726 0.0923513i \(-0.0294383\pi\)
\(588\) −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 0.823009 + 0.568029i \(0.192294\pi\)
0.0804231 + 0.996761i \(0.474373\pi\)
\(594\) 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 −0.970315 0.241845i \(-0.922248\pi\)
0.275714 0.961240i \(-0.411086\pi\)
\(600\) −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 −0.733316 0.679888i \(-0.762028\pi\)
0.955458 + 0.295126i \(0.0953615\pi\)
\(614\) −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 0.658847 0.752277i \(-0.271045\pi\)
−0.980915 + 0.194439i \(0.937711\pi\)
\(618\) −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 0.934594 0.355716i \(-0.115763\pi\)
−0.775356 + 0.631524i \(0.782430\pi\)
\(632\) −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 0.0690201 + 0.997615i \(0.478013\pi\)
−0.898470 + 0.439034i \(0.855321\pi\)
\(642\) −5.00000 8.66025i −0.197334 0.341793i
\(643\) −7.00000 + 12.1244i −0.276053 + 0.478138i −0.970400 0.241502i \(-0.922360\pi\)
0.694347 + 0.719640i \(0.255693\pi\)
\(644\) −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 0.974320 0.225168i \(-0.0722932\pi\)
−0.682161 + 0.731202i \(0.738960\pi\)
\(660\) −0.500000 + 0.866025i −0.0194625 + 0.0337100i
\(661\) −2.00000 3.46410i −0.0777910 0.134738i 0.824506 0.565854i \(-0.191453\pi\)
−0.902297 + 0.431116i \(0.858120\pi\)
\(662\) −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 −0.130843 0.991403i \(-0.541768\pi\)
0.924002 0.382389i \(-0.124898\pi\)
\(702\) −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 −0.963512 0.267664i \(-0.913748\pi\)
0.249952 0.968258i \(-0.419585\pi\)
\(710\) −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 0.477557 + 0.878601i \(0.341522\pi\)
−0.999669 + 0.0257237i \(0.991811\pi\)
\(720\) 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 −0.400362 0.916357i \(-0.631116\pi\)
0.993770 0.111454i \(-0.0355509\pi\)
\(728\) −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 −0.923192 0.384338i \(-0.874430\pi\)
0.794443 + 0.607339i \(0.207763\pi\)
\(740\) −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 −0.574231 0.818694i \(-0.694699\pi\)
0.996125 + 0.0879516i \(0.0280321\pi\)
\(744\) 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 −0.995018 0.0996961i \(-0.968213\pi\)
0.411170 0.911559i \(-0.365120\pi\)
\(752\) 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 −0.640122 0.768273i \(-0.721116\pi\)
0.985405 + 0.170225i \(0.0544495\pi\)
\(758\) −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 0.847432 0.530904i \(-0.178148\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) 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 0.913371 + 0.407128i \(0.133470\pi\)
−0.104102 + 0.994567i \(0.533197\pi\)
\(774\) 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