Properties

Label 570.2.i.j.391.2
Level $570$
Weight $2$
Character 570.391
Analytic conductor $4.551$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.29654208.1
Defining polynomial: \(x^{6} + 14 x^{4} + 49 x^{2} + 12\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 391.2
Root \(-2.86514i\) of defining polynomial
Character \(\chi\) \(=\) 570.391
Dual form 570.2.i.j.121.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +1.75353 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(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} +1.75353 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} -2.20905 q^{11} +1.00000 q^{12} +(1.60452 + 2.77912i) q^{13} +(-0.876763 + 1.51860i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.58581 + 6.21081i) q^{17} +1.00000 q^{18} +(0.727762 + 4.29772i) q^{19} +1.00000 q^{20} +(-0.876763 + 1.51860i) q^{21} +(1.10452 - 1.91309i) q^{22} +(-1.10452 - 1.91309i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -3.20905 q^{26} +1.00000 q^{27} +(-0.876763 - 1.51860i) q^{28} +(-3.83229 - 6.63772i) q^{29} +1.00000 q^{30} -3.20905 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.10452 - 1.91309i) q^{33} +(-3.58581 - 6.21081i) q^{34} +(-0.876763 + 1.51860i) q^{35} +(-0.500000 + 0.866025i) q^{36} -1.00000 q^{37} +(-4.08581 - 1.51860i) q^{38} -3.20905 q^{39} +(-0.500000 + 0.866025i) q^{40} +(-5.23481 + 9.06696i) q^{41} +(-0.876763 - 1.51860i) q^{42} +(1.35805 - 2.35221i) q^{43} +(1.10452 + 1.91309i) q^{44} +1.00000 q^{45} +2.20905 q^{46} +(4.96257 + 8.59543i) q^{47} +(-0.500000 - 0.866025i) q^{48} -3.92515 q^{49} +1.00000 q^{50} +(-3.58581 - 6.21081i) q^{51} +(1.60452 - 2.77912i) q^{52} +(-5.48129 - 9.49387i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.10452 - 1.91309i) q^{55} +1.75353 q^{56} +(-4.08581 - 1.51860i) q^{57} +7.66457 q^{58} +(-3.00000 + 5.19615i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(2.98129 + 5.16374i) q^{61} +(1.60452 - 2.77912i) q^{62} +(-0.876763 - 1.51860i) q^{63} +1.00000 q^{64} -3.20905 q^{65} +(1.10452 + 1.91309i) q^{66} +(-0.0187126 - 0.0324111i) q^{67} +7.17162 q^{68} +2.20905 q^{69} +(-0.876763 - 1.51860i) q^{70} +(-3.58581 + 6.21081i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(5.98129 - 10.3599i) q^{73} +(0.500000 - 0.866025i) q^{74} +1.00000 q^{75} +(3.35805 - 2.77912i) q^{76} -3.87362 q^{77} +(1.60452 - 2.77912i) q^{78} +(-0.604525 + 1.04707i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.23481 - 9.06696i) q^{82} +14.8362 q^{83} +1.75353 q^{84} +(-3.58581 - 6.21081i) q^{85} +(1.35805 + 2.35221i) q^{86} +7.66457 q^{87} -2.20905 q^{88} +(5.48129 + 9.49387i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(2.81357 + 4.87325i) q^{91} +(-1.10452 + 1.91309i) q^{92} +(1.60452 - 2.77912i) q^{93} -9.92515 q^{94} +(-4.08581 - 1.51860i) q^{95} +1.00000 q^{96} +(-5.62324 + 9.73973i) q^{97} +(1.96257 - 3.39928i) q^{98} +(1.10452 + 1.91309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{2} - 3q^{3} - 3q^{4} - 3q^{5} - 3q^{6} + 2q^{7} + 6q^{8} - 3q^{9} + O(q^{10}) \) \( 6q - 3q^{2} - 3q^{3} - 3q^{4} - 3q^{5} - 3q^{6} + 2q^{7} + 6q^{8} - 3q^{9} - 3q^{10} + 8q^{11} + 6q^{12} - q^{13} - q^{14} - 3q^{15} - 3q^{16} + 4q^{17} + 6q^{18} - 2q^{19} + 6q^{20} - q^{21} - 4q^{22} + 4q^{23} - 3q^{24} - 3q^{25} + 2q^{26} + 6q^{27} - q^{28} - 6q^{29} + 6q^{30} + 2q^{31} - 3q^{32} - 4q^{33} + 4q^{34} - q^{35} - 3q^{36} - 6q^{37} + q^{38} + 2q^{39} - 3q^{40} - 8q^{41} - q^{42} - 11q^{43} - 4q^{44} + 6q^{45} - 8q^{46} - 3q^{48} + 36q^{49} + 6q^{50} + 4q^{51} - q^{52} - 18q^{53} - 3q^{54} - 4q^{55} + 2q^{56} + q^{57} + 12q^{58} - 18q^{59} - 3q^{60} + 3q^{61} - q^{62} - q^{63} + 6q^{64} + 2q^{65} - 4q^{66} - 15q^{67} - 8q^{68} - 8q^{69} - q^{70} + 4q^{71} - 3q^{72} + 21q^{73} + 3q^{74} + 6q^{75} + q^{76} + 32q^{77} - q^{78} + 7q^{79} - 3q^{80} - 3q^{81} - 8q^{82} + 4q^{83} + 2q^{84} + 4q^{85} - 11q^{86} + 12q^{87} + 8q^{88} + 18q^{89} - 3q^{90} - 15q^{91} + 4q^{92} - q^{93} + q^{95} + 6q^{96} - 38q^{97} - 18q^{98} - 4q^{99} + O(q^{100}) \)

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
\(7\) 1.75353 0.662770 0.331385 0.943496i \(-0.392484\pi\)
0.331385 + 0.943496i \(0.392484\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) −2.20905 −0.666054 −0.333027 0.942917i \(-0.608070\pi\)
−0.333027 + 0.942917i \(0.608070\pi\)
\(12\) 1.00000 0.288675
\(13\) 1.60452 + 2.77912i 0.445015 + 0.770789i 0.998053 0.0623671i \(-0.0198650\pi\)
−0.553038 + 0.833156i \(0.686532\pi\)
\(14\) −0.876763 + 1.51860i −0.234325 + 0.405862i
\(15\) −0.500000 0.866025i −0.129099 0.223607i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.58581 + 6.21081i −0.869687 + 1.50634i −0.00737071 + 0.999973i \(0.502346\pi\)
−0.862317 + 0.506370i \(0.830987\pi\)
\(18\) 1.00000 0.235702
\(19\) 0.727762 + 4.29772i 0.166960 + 0.985964i
\(20\) 1.00000 0.223607
\(21\) −0.876763 + 1.51860i −0.191325 + 0.331385i
\(22\) 1.10452 1.91309i 0.235485 0.407873i
\(23\) −1.10452 1.91309i −0.230309 0.398908i 0.727590 0.686012i \(-0.240640\pi\)
−0.957899 + 0.287105i \(0.907307\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −3.20905 −0.629346
\(27\) 1.00000 0.192450
\(28\) −0.876763 1.51860i −0.165693 0.286988i
\(29\) −3.83229 6.63772i −0.711638 1.23259i −0.964242 0.265023i \(-0.914620\pi\)
0.252604 0.967570i \(-0.418713\pi\)
\(30\) 1.00000 0.182574
\(31\) −3.20905 −0.576362 −0.288181 0.957576i \(-0.593051\pi\)
−0.288181 + 0.957576i \(0.593051\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 1.10452 1.91309i 0.192273 0.333027i
\(34\) −3.58581 6.21081i −0.614962 1.06514i
\(35\) −0.876763 + 1.51860i −0.148200 + 0.256690i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) −4.08581 1.51860i −0.662806 0.246349i
\(39\) −3.20905 −0.513859
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) −5.23481 + 9.06696i −0.817540 + 1.41602i 0.0899490 + 0.995946i \(0.471330\pi\)
−0.907489 + 0.420075i \(0.862004\pi\)
\(42\) −0.876763 1.51860i −0.135287 0.234325i
\(43\) 1.35805 2.35221i 0.207101 0.358709i −0.743699 0.668514i \(-0.766931\pi\)
0.950800 + 0.309805i \(0.100264\pi\)
\(44\) 1.10452 + 1.91309i 0.166513 + 0.288410i
\(45\) 1.00000 0.149071
\(46\) 2.20905 0.325707
\(47\) 4.96257 + 8.59543i 0.723866 + 1.25377i 0.959439 + 0.281916i \(0.0909699\pi\)
−0.235573 + 0.971857i \(0.575697\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) −3.92515 −0.560736
\(50\) 1.00000 0.141421
\(51\) −3.58581 6.21081i −0.502114 0.869687i
\(52\) 1.60452 2.77912i 0.222508 0.385394i
\(53\) −5.48129 9.49387i −0.752913 1.30408i −0.946405 0.322981i \(-0.895315\pi\)
0.193493 0.981102i \(-0.438018\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 1.10452 1.91309i 0.148934 0.257961i
\(56\) 1.75353 0.234325
\(57\) −4.08581 1.51860i −0.541179 0.201143i
\(58\) 7.66457 1.00641
\(59\) −3.00000 + 5.19615i −0.390567 + 0.676481i −0.992524 0.122047i \(-0.961054\pi\)
0.601958 + 0.798528i \(0.294388\pi\)
\(60\) −0.500000 + 0.866025i −0.0645497 + 0.111803i
\(61\) 2.98129 + 5.16374i 0.381715 + 0.661149i 0.991307 0.131565i \(-0.0420003\pi\)
−0.609593 + 0.792715i \(0.708667\pi\)
\(62\) 1.60452 2.77912i 0.203775 0.352948i
\(63\) −0.876763 1.51860i −0.110462 0.191325i
\(64\) 1.00000 0.125000
\(65\) −3.20905 −0.398034
\(66\) 1.10452 + 1.91309i 0.135958 + 0.235485i
\(67\) −0.0187126 0.0324111i −0.00228610 0.00395965i 0.864880 0.501979i \(-0.167394\pi\)
−0.867166 + 0.498019i \(0.834061\pi\)
\(68\) 7.17162 0.869687
\(69\) 2.20905 0.265938
\(70\) −0.876763 1.51860i −0.104793 0.181507i
\(71\) −3.58581 + 6.21081i −0.425558 + 0.737087i −0.996472 0.0839219i \(-0.973255\pi\)
0.570915 + 0.821009i \(0.306589\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 5.98129 10.3599i 0.700057 1.21253i −0.268389 0.963311i \(-0.586491\pi\)
0.968446 0.249223i \(-0.0801753\pi\)
\(74\) 0.500000 0.866025i 0.0581238 0.100673i
\(75\) 1.00000 0.115470
\(76\) 3.35805 2.77912i 0.385195 0.318787i
\(77\) −3.87362 −0.441440
\(78\) 1.60452 2.77912i 0.181677 0.314673i
\(79\) −0.604525 + 1.04707i −0.0680144 + 0.117804i −0.898027 0.439940i \(-0.855000\pi\)
0.830013 + 0.557744i \(0.188333\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −5.23481 9.06696i −0.578088 1.00128i
\(83\) 14.8362 1.62848 0.814242 0.580525i \(-0.197153\pi\)
0.814242 + 0.580525i \(0.197153\pi\)
\(84\) 1.75353 0.191325
\(85\) −3.58581 6.21081i −0.388936 0.673657i
\(86\) 1.35805 + 2.35221i 0.146442 + 0.253645i
\(87\) 7.66457 0.821729
\(88\) −2.20905 −0.235485
\(89\) 5.48129 + 9.49387i 0.581015 + 1.00635i 0.995359 + 0.0962277i \(0.0306777\pi\)
−0.414344 + 0.910120i \(0.635989\pi\)
\(90\) −0.500000 + 0.866025i −0.0527046 + 0.0912871i
\(91\) 2.81357 + 4.87325i 0.294943 + 0.510856i
\(92\) −1.10452 + 1.91309i −0.115155 + 0.199454i
\(93\) 1.60452 2.77912i 0.166381 0.288181i
\(94\) −9.92515 −1.02370
\(95\) −4.08581 1.51860i −0.419195 0.155805i
\(96\) 1.00000 0.102062
\(97\) −5.62324 + 9.73973i −0.570953 + 0.988920i 0.425515 + 0.904951i \(0.360093\pi\)
−0.996468 + 0.0839687i \(0.973240\pi\)
\(98\) 1.96257 3.39928i 0.198250 0.343379i
\(99\) 1.10452 + 1.91309i 0.111009 + 0.192273i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) −0.246475 0.426907i −0.0245252 0.0424788i 0.853502 0.521089i \(-0.174474\pi\)
−0.878027 + 0.478610i \(0.841141\pi\)
\(102\) 7.17162 0.710097
\(103\) 11.6787 1.15073 0.575367 0.817895i \(-0.304859\pi\)
0.575367 + 0.817895i \(0.304859\pi\)
\(104\) 1.60452 + 2.77912i 0.157337 + 0.272515i
\(105\) −0.876763 1.51860i −0.0855633 0.148200i
\(106\) 10.9626 1.06478
\(107\) 8.26058 0.798580 0.399290 0.916825i \(-0.369257\pi\)
0.399290 + 0.916825i \(0.369257\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 2.58581 4.47876i 0.247676 0.428987i −0.715205 0.698915i \(-0.753667\pi\)
0.962881 + 0.269928i \(0.0869999\pi\)
\(110\) 1.10452 + 1.91309i 0.105312 + 0.182406i
\(111\) 0.500000 0.866025i 0.0474579 0.0821995i
\(112\) −0.876763 + 1.51860i −0.0828463 + 0.143494i
\(113\) −2.26058 −0.212657 −0.106329 0.994331i \(-0.533910\pi\)
−0.106329 + 0.994331i \(0.533910\pi\)
\(114\) 3.35805 2.77912i 0.314510 0.260288i
\(115\) 2.20905 0.205995
\(116\) −3.83229 + 6.63772i −0.355819 + 0.616296i
\(117\) 1.60452 2.77912i 0.148338 0.256930i
\(118\) −3.00000 5.19615i −0.276172 0.478345i
\(119\) −6.28781 + 10.8908i −0.576403 + 0.998359i
\(120\) −0.500000 0.866025i −0.0456435 0.0790569i
\(121\) −6.12010 −0.556373
\(122\) −5.96257 −0.539826
\(123\) −5.23481 9.06696i −0.472007 0.817540i
\(124\) 1.60452 + 2.77912i 0.144091 + 0.249572i
\(125\) 1.00000 0.0894427
\(126\) 1.75353 0.156216
\(127\) 6.44386 + 11.1611i 0.571800 + 0.990387i 0.996381 + 0.0849972i \(0.0270881\pi\)
−0.424581 + 0.905390i \(0.639579\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 1.35805 + 2.35221i 0.119570 + 0.207101i
\(130\) 1.60452 2.77912i 0.140726 0.243745i
\(131\) 6.61158 11.4516i 0.577656 1.00053i −0.418091 0.908405i \(-0.637301\pi\)
0.995747 0.0921246i \(-0.0293658\pi\)
\(132\) −2.20905 −0.192273
\(133\) 1.27615 + 7.53615i 0.110656 + 0.653467i
\(134\) 0.0374251 0.00323304
\(135\) −0.500000 + 0.866025i −0.0430331 + 0.0745356i
\(136\) −3.58581 + 6.21081i −0.307481 + 0.532572i
\(137\) 10.7161 + 18.5608i 0.915538 + 1.58576i 0.806111 + 0.591764i \(0.201568\pi\)
0.109427 + 0.993995i \(0.465098\pi\)
\(138\) −1.10452 + 1.91309i −0.0940234 + 0.162853i
\(139\) −3.60452 6.24322i −0.305732 0.529543i 0.671692 0.740830i \(-0.265568\pi\)
−0.977424 + 0.211287i \(0.932234\pi\)
\(140\) 1.75353 0.148200
\(141\) −9.92515 −0.835848
\(142\) −3.58581 6.21081i −0.300915 0.521200i
\(143\) −3.54448 6.13921i −0.296404 0.513387i
\(144\) 1.00000 0.0833333
\(145\) 7.66457 0.636508
\(146\) 5.98129 + 10.3599i 0.495015 + 0.857391i
\(147\) 1.96257 3.39928i 0.161870 0.280368i
\(148\) 0.500000 + 0.866025i 0.0410997 + 0.0711868i
\(149\) 4.37676 7.58078i 0.358558 0.621041i −0.629162 0.777274i \(-0.716602\pi\)
0.987720 + 0.156233i \(0.0499351\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) 8.67867 0.706261 0.353130 0.935574i \(-0.385117\pi\)
0.353130 + 0.935574i \(0.385117\pi\)
\(152\) 0.727762 + 4.29772i 0.0590293 + 0.348591i
\(153\) 7.17162 0.579791
\(154\) 1.93681 3.35466i 0.156073 0.270326i
\(155\) 1.60452 2.77912i 0.128879 0.223224i
\(156\) 1.60452 + 2.77912i 0.128465 + 0.222508i
\(157\) −2.25353 + 3.90322i −0.179851 + 0.311511i −0.941829 0.336092i \(-0.890895\pi\)
0.761978 + 0.647602i \(0.224228\pi\)
\(158\) −0.604525 1.04707i −0.0480934 0.0833002i
\(159\) 10.9626 0.869389
\(160\) 1.00000 0.0790569
\(161\) −1.93681 3.35466i −0.152642 0.264384i
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) 23.6271 1.85062 0.925311 0.379210i \(-0.123804\pi\)
0.925311 + 0.379210i \(0.123804\pi\)
\(164\) 10.4696 0.817540
\(165\) 1.10452 + 1.91309i 0.0859871 + 0.148934i
\(166\) −7.41810 + 12.8485i −0.575756 + 0.997239i
\(167\) −4.89548 8.47921i −0.378823 0.656141i 0.612068 0.790805i \(-0.290338\pi\)
−0.990891 + 0.134664i \(0.957005\pi\)
\(168\) −0.876763 + 1.51860i −0.0676437 + 0.117162i
\(169\) 1.35100 2.34000i 0.103923 0.180000i
\(170\) 7.17162 0.550039
\(171\) 3.35805 2.77912i 0.256797 0.212525i
\(172\) −2.71610 −0.207101
\(173\) −5.72776 + 9.92078i −0.435474 + 0.754263i −0.997334 0.0729694i \(-0.976752\pi\)
0.561860 + 0.827232i \(0.310086\pi\)
\(174\) −3.83229 + 6.63772i −0.290525 + 0.503204i
\(175\) −0.876763 1.51860i −0.0662770 0.114795i
\(176\) 1.10452 1.91309i 0.0832567 0.144205i
\(177\) −3.00000 5.19615i −0.225494 0.390567i
\(178\) −10.9626 −0.821680
\(179\) 6.62715 0.495336 0.247668 0.968845i \(-0.420336\pi\)
0.247668 + 0.968845i \(0.420336\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) −5.13029 8.88592i −0.381331 0.660485i 0.609922 0.792462i \(-0.291201\pi\)
−0.991253 + 0.131977i \(0.957868\pi\)
\(182\) −5.62715 −0.417112
\(183\) −5.96257 −0.440766
\(184\) −1.10452 1.91309i −0.0814267 0.141035i
\(185\) 0.500000 0.866025i 0.0367607 0.0636715i
\(186\) 1.60452 + 2.77912i 0.117649 + 0.203775i
\(187\) 7.92124 13.7200i 0.579258 1.00330i
\(188\) 4.96257 8.59543i 0.361933 0.626886i
\(189\) 1.75353 0.127550
\(190\) 3.35805 2.77912i 0.243619 0.201618i
\(191\) 25.2543 1.82734 0.913668 0.406460i \(-0.133237\pi\)
0.913668 + 0.406460i \(0.133237\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −1.43681 + 2.48863i −0.103424 + 0.179136i −0.913093 0.407751i \(-0.866313\pi\)
0.809669 + 0.586886i \(0.199647\pi\)
\(194\) −5.62324 9.73973i −0.403725 0.699272i
\(195\) 1.60452 2.77912i 0.114902 0.199017i
\(196\) 1.96257 + 3.39928i 0.140184 + 0.242806i
\(197\) −14.8877 −1.06071 −0.530353 0.847777i \(-0.677941\pi\)
−0.530353 + 0.847777i \(0.677941\pi\)
\(198\) −2.20905 −0.156990
\(199\) 0.772238 + 1.33755i 0.0547425 + 0.0948168i 0.892098 0.451842i \(-0.149233\pi\)
−0.837356 + 0.546659i \(0.815900\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) 0.0374251 0.00263977
\(202\) 0.492950 0.0346838
\(203\) −6.72001 11.6394i −0.471652 0.816926i
\(204\) −3.58581 + 6.21081i −0.251057 + 0.434844i
\(205\) −5.23481 9.06696i −0.365615 0.633264i
\(206\) −5.83934 + 10.1140i −0.406846 + 0.704678i
\(207\) −1.10452 + 1.91309i −0.0767698 + 0.132969i
\(208\) −3.20905 −0.222508
\(209\) −1.60766 9.49387i −0.111204 0.656705i
\(210\) 1.75353 0.121005
\(211\) −6.38381 + 11.0571i −0.439480 + 0.761201i −0.997649 0.0685256i \(-0.978171\pi\)
0.558170 + 0.829727i \(0.311504\pi\)
\(212\) −5.48129 + 9.49387i −0.376456 + 0.652042i
\(213\) −3.58581 6.21081i −0.245696 0.425558i
\(214\) −4.13029 + 7.15387i −0.282341 + 0.489028i
\(215\) 1.35805 + 2.35221i 0.0926182 + 0.160419i
\(216\) 1.00000 0.0680414
\(217\) −5.62715 −0.381996
\(218\) 2.58581 + 4.47876i 0.175133 + 0.303340i
\(219\) 5.98129 + 10.3599i 0.404178 + 0.700057i
\(220\) −2.20905 −0.148934
\(221\) −23.0141 −1.54810
\(222\) 0.500000 + 0.866025i 0.0335578 + 0.0581238i
\(223\) −3.57876 + 6.19860i −0.239652 + 0.415089i −0.960614 0.277885i \(-0.910367\pi\)
0.720963 + 0.692974i \(0.243700\pi\)
\(224\) −0.876763 1.51860i −0.0585812 0.101466i
\(225\) −0.500000 + 0.866025i −0.0333333 + 0.0577350i
\(226\) 1.13029 1.95772i 0.0751856 0.130225i
\(227\) −14.2606 −0.946508 −0.473254 0.880926i \(-0.656921\pi\)
−0.473254 + 0.880926i \(0.656921\pi\)
\(228\) 0.727762 + 4.29772i 0.0481972 + 0.284623i
\(229\) −21.2090 −1.40153 −0.700767 0.713390i \(-0.747159\pi\)
−0.700767 + 0.713390i \(0.747159\pi\)
\(230\) −1.10452 + 1.91309i −0.0728302 + 0.126146i
\(231\) 1.93681 3.35466i 0.127433 0.220720i
\(232\) −3.83229 6.63772i −0.251602 0.435787i
\(233\) 2.70200 4.68000i 0.177014 0.306597i −0.763842 0.645403i \(-0.776690\pi\)
0.940856 + 0.338806i \(0.110023\pi\)
\(234\) 1.60452 + 2.77912i 0.104891 + 0.181677i
\(235\) −9.92515 −0.647445
\(236\) 6.00000 0.390567
\(237\) −0.604525 1.04707i −0.0392681 0.0680144i
\(238\) −6.28781 10.8908i −0.407578 0.705946i
\(239\) 21.4322 1.38633 0.693167 0.720777i \(-0.256215\pi\)
0.693167 + 0.720777i \(0.256215\pi\)
\(240\) 1.00000 0.0645497
\(241\) 3.18643 + 5.51905i 0.205256 + 0.355513i 0.950214 0.311598i \(-0.100864\pi\)
−0.744958 + 0.667111i \(0.767531\pi\)
\(242\) 3.06005 5.30016i 0.196707 0.340707i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 2.98129 5.16374i 0.190857 0.330575i
\(245\) 1.96257 3.39928i 0.125384 0.217172i
\(246\) 10.4696 0.667519
\(247\) −10.7761 + 8.91833i −0.685670 + 0.567460i
\(248\) −3.20905 −0.203775
\(249\) −7.41810 + 12.8485i −0.470103 + 0.814242i
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) −9.13420 15.8209i −0.576546 0.998606i −0.995872 0.0907706i \(-0.971067\pi\)
0.419326 0.907836i \(-0.362266\pi\)
\(252\) −0.876763 + 1.51860i −0.0552308 + 0.0956626i
\(253\) 2.43995 + 4.22612i 0.153398 + 0.265694i
\(254\) −12.8877 −0.808648
\(255\) 7.17162 0.449105
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −3.00000 5.19615i −0.187135 0.324127i 0.757159 0.653231i \(-0.226587\pi\)
−0.944294 + 0.329104i \(0.893253\pi\)
\(258\) −2.71610 −0.169097
\(259\) −1.75353 −0.108959
\(260\) 1.60452 + 2.77912i 0.0995084 + 0.172354i
\(261\) −3.83229 + 6.63772i −0.237213 + 0.410864i
\(262\) 6.61158 + 11.4516i 0.408464 + 0.707481i
\(263\) 15.3136 26.5239i 0.944275 1.63553i 0.187080 0.982345i \(-0.440098\pi\)
0.757195 0.653188i \(-0.226569\pi\)
\(264\) 1.10452 1.91309i 0.0679788 0.117743i
\(265\) 10.9626 0.673426
\(266\) −7.16457 2.66290i −0.439288 0.163273i
\(267\) −10.9626 −0.670899
\(268\) −0.0187126 + 0.0324111i −0.00114305 + 0.00197982i
\(269\) 8.79486 15.2331i 0.536232 0.928781i −0.462870 0.886426i \(-0.653180\pi\)
0.999103 0.0423555i \(-0.0134862\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) −9.45552 + 16.3774i −0.574382 + 0.994859i 0.421726 + 0.906723i \(0.361424\pi\)
−0.996108 + 0.0881360i \(0.971909\pi\)
\(272\) −3.58581 6.21081i −0.217422 0.376586i
\(273\) −5.62715 −0.340571
\(274\) −21.4322 −1.29477
\(275\) 1.10452 + 1.91309i 0.0666054 + 0.115364i
\(276\) −1.10452 1.91309i −0.0664846 0.115155i
\(277\) 24.9110 1.49676 0.748380 0.663270i \(-0.230832\pi\)
0.748380 + 0.663270i \(0.230832\pi\)
\(278\) 7.20905 0.432370
\(279\) 1.60452 + 2.77912i 0.0960604 + 0.166381i
\(280\) −0.876763 + 1.51860i −0.0523966 + 0.0907535i
\(281\) −13.4439 23.2855i −0.801994 1.38909i −0.918302 0.395880i \(-0.870439\pi\)
0.116308 0.993213i \(-0.462894\pi\)
\(282\) 4.96257 8.59543i 0.295517 0.511851i
\(283\) −12.8877 + 22.3222i −0.766096 + 1.32692i 0.173570 + 0.984822i \(0.444470\pi\)
−0.939665 + 0.342095i \(0.888864\pi\)
\(284\) 7.17162 0.425558
\(285\) 3.35805 2.77912i 0.198914 0.164621i
\(286\) 7.08895 0.419178
\(287\) −9.17938 + 15.8991i −0.541841 + 0.938497i
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) −17.2161 29.8192i −1.01271 1.75407i
\(290\) −3.83229 + 6.63772i −0.225040 + 0.389780i
\(291\) −5.62324 9.73973i −0.329640 0.570953i
\(292\) −11.9626 −0.700057
\(293\) 1.53037 0.0894055 0.0447027 0.999000i \(-0.485766\pi\)
0.0447027 + 0.999000i \(0.485766\pi\)
\(294\) 1.96257 + 3.39928i 0.114460 + 0.198250i
\(295\) −3.00000 5.19615i −0.174667 0.302532i
\(296\) −1.00000 −0.0581238
\(297\) −2.20905 −0.128182
\(298\) 4.37676 + 7.58078i 0.253539 + 0.439143i
\(299\) 3.54448 6.13921i 0.204982 0.355040i
\(300\) −0.500000 0.866025i −0.0288675 0.0500000i
\(301\) 2.38137 4.12466i 0.137260 0.237742i
\(302\) −4.33934 + 7.51595i −0.249701 + 0.432494i
\(303\) 0.492950 0.0283192
\(304\) −4.08581 1.51860i −0.234337 0.0870975i
\(305\) −5.96257 −0.341416
\(306\) −3.58581 + 6.21081i −0.204987 + 0.355048i
\(307\) 8.88381 15.3872i 0.507026 0.878195i −0.492941 0.870063i \(-0.664078\pi\)
0.999967 0.00813199i \(-0.00258852\pi\)
\(308\) 1.93681 + 3.35466i 0.110360 + 0.191149i
\(309\) −5.83934 + 10.1140i −0.332188 + 0.575367i
\(310\) 1.60452 + 2.77912i 0.0911309 + 0.157843i
\(311\) 11.4040 0.646661 0.323331 0.946286i \(-0.395197\pi\)
0.323331 + 0.946286i \(0.395197\pi\)
\(312\) −3.20905 −0.181677
\(313\) 5.13420 + 8.89269i 0.290202 + 0.502645i 0.973857 0.227160i \(-0.0729441\pi\)
−0.683655 + 0.729805i \(0.739611\pi\)
\(314\) −2.25353 3.90322i −0.127174 0.220271i
\(315\) 1.75353 0.0987999
\(316\) 1.20905 0.0680144
\(317\) 12.4064 + 21.4886i 0.696815 + 1.20692i 0.969565 + 0.244834i \(0.0787334\pi\)
−0.272750 + 0.962085i \(0.587933\pi\)
\(318\) −5.48129 + 9.49387i −0.307375 + 0.532390i
\(319\) 8.46571 + 14.6630i 0.473989 + 0.820973i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) −4.13029 + 7.15387i −0.230530 + 0.399290i
\(322\) 3.87362 0.215869
\(323\) −29.3019 10.8908i −1.63040 0.605981i
\(324\) 1.00000 0.0555556
\(325\) 1.60452 2.77912i 0.0890030 0.154158i
\(326\) −11.8136 + 20.4617i −0.654293 + 1.13327i
\(327\) 2.58581 + 4.47876i 0.142996 + 0.247676i
\(328\) −5.23481 + 9.06696i −0.289044 + 0.500639i
\(329\) 8.70200 + 15.0723i 0.479757 + 0.830963i
\(330\) −2.20905 −0.121604
\(331\) −9.75353 −0.536102 −0.268051 0.963405i \(-0.586380\pi\)
−0.268051 + 0.963405i \(0.586380\pi\)
\(332\) −7.41810 12.8485i −0.407121 0.705154i
\(333\) 0.500000 + 0.866025i 0.0273998 + 0.0474579i
\(334\) 9.79095 0.535737
\(335\) 0.0374251 0.00204475
\(336\) −0.876763 1.51860i −0.0478313 0.0828463i
\(337\) −11.3206 + 19.6079i −0.616674 + 1.06811i 0.373415 + 0.927665i \(0.378187\pi\)
−0.990088 + 0.140446i \(0.955146\pi\)
\(338\) 1.35100 + 2.34000i 0.0734847 + 0.127279i
\(339\) 1.13029 1.95772i 0.0613888 0.106329i
\(340\) −3.58581 + 6.21081i −0.194468 + 0.336828i
\(341\) 7.08895 0.383888
\(342\) 0.727762 + 4.29772i 0.0393529 + 0.232394i
\(343\) −19.1575 −1.03441
\(344\) 1.35805 2.35221i 0.0732211 0.126823i
\(345\) −1.10452 + 1.91309i −0.0594656 + 0.102997i
\(346\) −5.72776 9.92078i −0.307926 0.533344i
\(347\) 12.6271 21.8709i 0.677861 1.17409i −0.297763 0.954640i \(-0.596240\pi\)
0.975624 0.219450i \(-0.0704262\pi\)
\(348\) −3.83229 6.63772i −0.205432 0.355819i
\(349\) 29.2169 1.56394 0.781972 0.623314i \(-0.214214\pi\)
0.781972 + 0.623314i \(0.214214\pi\)
\(350\) 1.75353 0.0937299
\(351\) 1.60452 + 2.77912i 0.0856432 + 0.148338i
\(352\) 1.10452 + 1.91309i 0.0588714 + 0.101968i
\(353\) −32.9189 −1.75209 −0.876047 0.482225i \(-0.839829\pi\)
−0.876047 + 0.482225i \(0.839829\pi\)
\(354\) 6.00000 0.318896
\(355\) −3.58581 6.21081i −0.190315 0.329636i
\(356\) 5.48129 9.49387i 0.290508 0.503174i
\(357\) −6.28781 10.8908i −0.332786 0.576403i
\(358\) −3.31357 + 5.73928i −0.175128 + 0.303330i
\(359\) 1.62324 2.81153i 0.0856712 0.148387i −0.820006 0.572355i \(-0.806030\pi\)
0.905677 + 0.423968i \(0.139363\pi\)
\(360\) 1.00000 0.0527046
\(361\) −17.9407 + 6.25543i −0.944249 + 0.329233i
\(362\) 10.2606 0.539284
\(363\) 3.06005 5.30016i 0.160611 0.278186i
\(364\) 2.81357 4.87325i 0.147471 0.255428i
\(365\) 5.98129 + 10.3599i 0.313075 + 0.542262i
\(366\) 2.98129 5.16374i 0.155834 0.269913i
\(367\) 6.02262 + 10.4315i 0.314378 + 0.544519i 0.979305 0.202389i \(-0.0648706\pi\)
−0.664927 + 0.746909i \(0.731537\pi\)
\(368\) 2.20905 0.115155
\(369\) 10.4696 0.545027
\(370\) 0.500000 + 0.866025i 0.0259938 + 0.0450225i
\(371\) −9.61158 16.6477i −0.499008 0.864307i
\(372\) −3.20905 −0.166381
\(373\) −3.86580 −0.200164 −0.100082 0.994979i \(-0.531910\pi\)
−0.100082 + 0.994979i \(0.531910\pi\)
\(374\) 7.92124 + 13.7200i 0.409597 + 0.709444i
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) 4.96257 + 8.59543i 0.255925 + 0.443276i
\(377\) 12.2980 21.3008i 0.633379 1.09705i
\(378\) −0.876763 + 1.51860i −0.0450958 + 0.0781082i
\(379\) −23.0593 −1.18448 −0.592240 0.805762i \(-0.701756\pi\)
−0.592240 + 0.805762i \(0.701756\pi\)
\(380\) 0.727762 + 4.29772i 0.0373334 + 0.220468i
\(381\) −12.8877 −0.660258
\(382\) −12.6271 + 21.8709i −0.646061 + 1.11901i
\(383\) −1.03743 + 1.79687i −0.0530099 + 0.0918159i −0.891313 0.453389i \(-0.850215\pi\)
0.838303 + 0.545205i \(0.183548\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 1.93681 3.35466i 0.0987091 0.170969i
\(386\) −1.43681 2.48863i −0.0731318 0.126668i
\(387\) −2.71610 −0.138067
\(388\) 11.2465 0.570953
\(389\) 9.83229 + 17.0300i 0.498517 + 0.863456i 0.999999 0.00171186i \(-0.000544903\pi\)
−0.501482 + 0.865168i \(0.667212\pi\)
\(390\) 1.60452 + 2.77912i 0.0812483 + 0.140726i
\(391\) 15.8425 0.801188
\(392\) −3.92515 −0.198250
\(393\) 6.61158 + 11.4516i 0.333510 + 0.577656i
\(394\) 7.44386 12.8931i 0.375016 0.649547i
\(395\) −0.604525 1.04707i −0.0304169 0.0526837i
\(396\) 1.10452 1.91309i 0.0555045 0.0961366i
\(397\) 4.42515 7.66458i 0.222092 0.384674i −0.733351 0.679850i \(-0.762045\pi\)
0.955443 + 0.295176i \(0.0953782\pi\)
\(398\) −1.54448 −0.0774176
\(399\) −7.16457 2.66290i −0.358677 0.133312i
\(400\) 1.00000 0.0500000
\(401\) 0.925150 1.60241i 0.0461998 0.0800204i −0.842001 0.539476i \(-0.818622\pi\)
0.888201 + 0.459456i \(0.151956\pi\)
\(402\) −0.0187126 + 0.0324111i −0.000933298 + 0.00161652i
\(403\) −5.14900 8.91833i −0.256490 0.444254i
\(404\) −0.246475 + 0.426907i −0.0122626 + 0.0212394i
\(405\) −0.500000 0.866025i −0.0248452 0.0430331i
\(406\) 13.4400 0.667017
\(407\) 2.20905 0.109499
\(408\) −3.58581 6.21081i −0.177524 0.307481i
\(409\) −9.02967 15.6399i −0.446489 0.773341i 0.551666 0.834065i \(-0.313992\pi\)
−0.998155 + 0.0607241i \(0.980659\pi\)
\(410\) 10.4696 0.517058
\(411\) −21.4322 −1.05717
\(412\) −5.83934 10.1140i −0.287684 0.498282i
\(413\) −5.26058 + 9.11158i −0.258856 + 0.448352i
\(414\) −1.10452 1.91309i −0.0542844 0.0940234i
\(415\) −7.41810 + 12.8485i −0.364140 + 0.630709i
\(416\) 1.60452 2.77912i 0.0786683 0.136258i
\(417\) 7.20905 0.353029
\(418\) 9.02576 + 3.35466i 0.441464 + 0.164082i
\(419\) −1.44770 −0.0707248 −0.0353624 0.999375i \(-0.511259\pi\)
−0.0353624 + 0.999375i \(0.511259\pi\)
\(420\) −0.876763 + 1.51860i −0.0427816 + 0.0741000i
\(421\) 8.58581 14.8711i 0.418447 0.724771i −0.577337 0.816506i \(-0.695908\pi\)
0.995783 + 0.0917350i \(0.0292413\pi\)
\(422\) −6.38381 11.0571i −0.310759 0.538251i
\(423\) 4.96257 8.59543i 0.241289 0.417924i
\(424\) −5.48129 9.49387i −0.266195 0.461063i
\(425\) 7.17162 0.347875
\(426\) 7.17162 0.347466
\(427\) 5.22776 + 9.05475i 0.252989 + 0.438190i
\(428\) −4.13029 7.15387i −0.199645 0.345795i
\(429\) 7.08895 0.342258
\(430\) −2.71610 −0.130982
\(431\) 9.53429 + 16.5139i 0.459250 + 0.795445i 0.998922 0.0464309i \(-0.0147847\pi\)
−0.539671 + 0.841876i \(0.681451\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 7.94386 + 13.7592i 0.381758 + 0.661224i 0.991314 0.131519i \(-0.0419856\pi\)
−0.609556 + 0.792743i \(0.708652\pi\)
\(434\) 2.81357 4.87325i 0.135056 0.233924i
\(435\) −3.83229 + 6.63772i −0.183744 + 0.318254i
\(436\) −5.17162 −0.247676
\(437\) 7.41810 6.13921i 0.354856 0.293678i
\(438\) −11.9626 −0.571594
\(439\) −1.68329 + 2.91554i −0.0803389 + 0.139151i −0.903396 0.428808i \(-0.858934\pi\)
0.823057 + 0.567959i \(0.192267\pi\)
\(440\) 1.10452 1.91309i 0.0526562 0.0912031i
\(441\) 1.96257 + 3.39928i 0.0934559 + 0.161870i
\(442\) 11.5071 19.9308i 0.547335 0.948011i
\(443\) 11.7949 + 20.4293i 0.560391 + 0.970625i 0.997462 + 0.0711985i \(0.0226824\pi\)
−0.437071 + 0.899427i \(0.643984\pi\)
\(444\) −1.00000 −0.0474579
\(445\) −10.9626 −0.519676
\(446\) −3.57876 6.19860i −0.169459 0.293512i
\(447\) 4.37676 + 7.58078i 0.207014 + 0.358558i
\(448\) 1.75353 0.0828463
\(449\) −10.9626 −0.517356 −0.258678 0.965964i \(-0.583287\pi\)
−0.258678 + 0.965964i \(0.583287\pi\)
\(450\) −0.500000 0.866025i −0.0235702 0.0408248i
\(451\) 11.5640 20.0294i 0.544526 0.943146i
\(452\) 1.13029 + 1.95772i 0.0531643 + 0.0920832i
\(453\) −4.33934 + 7.51595i −0.203880 + 0.353130i
\(454\) 7.13029 12.3500i 0.334641 0.579615i
\(455\) −5.62715 −0.263805
\(456\) −4.08581 1.51860i −0.191336 0.0711148i
\(457\) 26.6491 1.24659 0.623296 0.781986i \(-0.285793\pi\)
0.623296 + 0.781986i \(0.285793\pi\)
\(458\) 10.6045 18.3676i 0.495517 0.858260i
\(459\) −3.58581 + 6.21081i −0.167371 + 0.289896i
\(460\) −1.10452 1.91309i −0.0514987 0.0891984i
\(461\) −2.20905 + 3.82619i −0.102886 + 0.178203i −0.912872 0.408245i \(-0.866141\pi\)
0.809987 + 0.586448i \(0.199474\pi\)
\(462\) 1.93681 + 3.35466i 0.0901087 + 0.156073i
\(463\) −7.67867 −0.356858 −0.178429 0.983953i \(-0.557102\pi\)
−0.178429 + 0.983953i \(0.557102\pi\)
\(464\) 7.66457 0.355819
\(465\) 1.60452 + 2.77912i 0.0744081 + 0.128879i
\(466\) 2.70200 + 4.68000i 0.125168 + 0.216797i
\(467\) 24.0827 1.11441 0.557207 0.830374i \(-0.311873\pi\)
0.557207 + 0.830374i \(0.311873\pi\)
\(468\) −3.20905 −0.148338
\(469\) −0.0328130 0.0568337i −0.00151516 0.00262434i
\(470\) 4.96257 8.59543i 0.228907 0.396478i
\(471\) −2.25353 3.90322i −0.103837 0.179851i
\(472\) −3.00000 + 5.19615i −0.138086 + 0.239172i
\(473\) −3.00000 + 5.19615i −0.137940 + 0.238919i
\(474\) 1.20905 0.0555335
\(475\) 3.35805 2.77912i 0.154078 0.127515i
\(476\) 12.5756 0.576403
\(477\) −5.48129 + 9.49387i −0.250971 + 0.434694i
\(478\) −10.7161 + 18.5608i −0.490143 + 0.848953i
\(479\) −0.451613 0.782216i −0.0206347 0.0357404i 0.855524 0.517764i \(-0.173235\pi\)
−0.876158 + 0.482023i \(0.839902\pi\)
\(480\) −0.500000 + 0.866025i −0.0228218 + 0.0395285i
\(481\) −1.60452 2.77912i −0.0731600 0.126717i
\(482\) −6.37285 −0.290275
\(483\) 3.87362 0.176256
\(484\) 3.06005 + 5.30016i 0.139093 + 0.240916i
\(485\) −5.62324 9.73973i −0.255338 0.442258i
\(486\) 1.00000 0.0453609
\(487\) 12.5727 0.569722 0.284861 0.958569i \(-0.408052\pi\)
0.284861 + 0.958569i \(0.408052\pi\)
\(488\) 2.98129 + 5.16374i 0.134957 + 0.233752i
\(489\) −11.8136 + 20.4617i −0.534228 + 0.925311i
\(490\) 1.96257 + 3.39928i 0.0886601 + 0.153564i
\(491\) 14.5226 25.1539i 0.655397 1.13518i −0.326397 0.945233i \(-0.605835\pi\)
0.981794 0.189948i \(-0.0608319\pi\)
\(492\) −5.23481 + 9.06696i −0.236004 + 0.408770i
\(493\) 54.9675 2.47561
\(494\) −2.33543 13.7916i −0.105076 0.620513i
\(495\) −2.20905 −0.0992894
\(496\) 1.60452 2.77912i 0.0720453 0.124786i
\(497\) −6.28781 + 10.8908i −0.282047 + 0.488520i
\(498\) −7.41810 12.8485i −0.332413 0.575756i
\(499\) −9.63029 + 16.6801i −0.431111 + 0.746706i −0.996969 0.0777965i \(-0.975212\pi\)
0.565858 + 0.824502i \(0.308545\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) 9.79095 0.437427
\(502\) 18.2684 0.815359
\(503\) −8.52262 14.7616i −0.380005 0.658188i 0.611057 0.791586i \(-0.290744\pi\)
−0.991063 + 0.133398i \(0.957411\pi\)
\(504\) −0.876763 1.51860i −0.0390541 0.0676437i
\(505\) 0.492950 0.0219360
\(506\) −4.87990 −0.216938
\(507\) 1.35100 + 2.34000i 0.0600000 + 0.103923i
\(508\) 6.44386 11.1611i 0.285900 0.495194i
\(509\) 9.38067 + 16.2478i 0.415791 + 0.720171i 0.995511 0.0946444i \(-0.0301714\pi\)
−0.579720 + 0.814816i \(0.696838\pi\)
\(510\) −3.58581 + 6.21081i −0.158782 + 0.275019i
\(511\) 10.4883 18.1663i 0.463977 0.803631i
\(512\) 1.00000 0.0441942
\(513\) 0.727762 + 4.29772i 0.0321315 + 0.189749i
\(514\) 6.00000 0.264649
\(515\) −5.83934 + 10.1140i −0.257312 + 0.445677i
\(516\) 1.35805 2.35221i 0.0597848 0.103550i
\(517\) −10.9626 18.9877i −0.482133 0.835080i
\(518\) 0.876763 1.51860i 0.0385227 0.0667233i
\(519\) −5.72776 9.92078i −0.251421 0.435474i
\(520\) −3.20905 −0.140726
\(521\) 1.08895 0.0477078 0.0238539 0.999715i \(-0.492406\pi\)
0.0238539 + 0.999715i \(0.492406\pi\)
\(522\) −3.83229 6.63772i −0.167735 0.290525i
\(523\) 15.6600 + 27.1239i 0.684762 + 1.18604i 0.973511 + 0.228638i \(0.0734273\pi\)
−0.288749 + 0.957405i \(0.593239\pi\)
\(524\) −13.2232 −0.577656
\(525\) 1.75353 0.0765301
\(526\) 15.3136 + 26.5239i 0.667704 + 1.15650i
\(527\) 11.5071 19.9308i 0.501255 0.868199i
\(528\) 1.10452 + 1.91309i 0.0480683 + 0.0832567i
\(529\) 9.06005 15.6925i 0.393915 0.682281i
\(530\) −5.48129 + 9.49387i −0.238092 + 0.412387i
\(531\) 6.00000 0.260378
\(532\) 5.88842 4.87325i 0.255296 0.211282i
\(533\) −33.5975 −1.45527
\(534\) 5.48129 9.49387i 0.237199 0.410840i
\(535\) −4.13029 + 7.15387i −0.178568 + 0.309289i
\(536\) −0.0187126 0.0324111i −0.000808260 0.00139995i
\(537\) −3.31357 + 5.73928i −0.142991 + 0.247668i
\(538\) 8.79486 + 15.2331i 0.379173 + 0.656748i
\(539\) 8.67085 0.373480
\(540\) 1.00000 0.0430331
\(541\) 11.7246 + 20.3076i 0.504081 + 0.873094i 0.999989 + 0.00471871i \(0.00150202\pi\)
−0.495908 + 0.868375i \(0.665165\pi\)
\(542\) −9.45552 16.3774i −0.406150 0.703472i
\(543\) 10.2606 0.440323
\(544\) 7.17162 0.307481
\(545\) 2.58581 + 4.47876i 0.110764 + 0.191849i
\(546\) 2.81357 4.87325i 0.120410 0.208556i
\(547\) 4.60452 + 7.97527i 0.196875 + 0.340998i 0.947514 0.319715i \(-0.103587\pi\)
−0.750638 + 0.660713i \(0.770254\pi\)
\(548\) 10.7161 18.5608i 0.457769 0.792879i
\(549\) 2.98129 5.16374i 0.127238 0.220383i
\(550\) −2.20905 −0.0941942
\(551\) 25.7380 21.3008i 1.09648 0.907443i
\(552\) 2.20905 0.0940234
\(553\) −1.06005 + 1.83606i −0.0450779 + 0.0780772i
\(554\) −12.4555 + 21.5736i −0.529185 + 0.916575i
\(555\) 0.500000 + 0.866025i 0.0212238 + 0.0367607i
\(556\) −3.60452 + 6.24322i −0.152866 + 0.264772i
\(557\) 1.55614 + 2.69531i 0.0659357 + 0.114204i 0.897109 0.441810i \(-0.145663\pi\)
−0.831173 + 0.556014i \(0.812330\pi\)
\(558\) −3.20905 −0.135850
\(559\) 8.71610 0.368652
\(560\) −0.876763 1.51860i −0.0370500 0.0641724i
\(561\) 7.92124 + 13.7200i 0.334435 + 0.579258i
\(562\) 26.8877 1.13419
\(563\) −30.2684 −1.27566 −0.637830 0.770177i \(-0.720168\pi\)
−0.637830 + 0.770177i \(0.720168\pi\)
\(564\) 4.96257 + 8.59543i 0.208962 + 0.361933i
\(565\) 1.13029 1.95772i 0.0475516 0.0823617i
\(566\) −12.8877 22.3222i −0.541711 0.938272i
\(567\) −0.876763 + 1.51860i −0.0368206 + 0.0637751i
\(568\) −3.58581 + 6.21081i −0.150457 + 0.260600i
\(569\) −4.36657 −0.183056 −0.0915282 0.995802i \(-0.529175\pi\)
−0.0915282 + 0.995802i \(0.529175\pi\)
\(570\) 0.727762 + 4.29772i 0.0304826 + 0.180012i
\(571\) −43.4026 −1.81634 −0.908171 0.418599i \(-0.862521\pi\)
−0.908171 + 0.418599i \(0.862521\pi\)
\(572\) −3.54448 + 6.13921i −0.148202 + 0.256693i
\(573\) −12.6271 + 21.8709i −0.527507 + 0.913668i
\(574\) −9.17938 15.8991i −0.383140 0.663617i
\(575\) −1.10452 + 1.91309i −0.0460619 + 0.0797815i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −20.3354 −0.846575 −0.423287 0.905995i \(-0.639124\pi\)
−0.423287 + 0.905995i \(0.639124\pi\)
\(578\) 34.4322 1.43219
\(579\) −1.43681 2.48863i −0.0597119 0.103424i
\(580\) −3.83229 6.63772i −0.159127 0.275616i
\(581\) 26.0156 1.07931
\(582\) 11.2465 0.466181
\(583\) 12.1084 + 20.9724i 0.501480 + 0.868589i
\(584\) 5.98129 10.3599i 0.247507 0.428695i
\(585\) 1.60452 + 2.77912i 0.0663389 + 0.114902i
\(586\) −0.765187 + 1.32534i −0.0316096 + 0.0547494i
\(587\) 6.38067 11.0517i 0.263359 0.456151i −0.703774 0.710424i \(-0.748503\pi\)
0.967132 + 0.254274i \(0.0818364\pi\)
\(588\) −3.92515 −0.161870
\(589\) −2.33543 13.7916i −0.0962295 0.568272i
\(590\) 6.00000 0.247016
\(591\) 7.44386 12.8931i 0.306200 0.530353i
\(592\) 0.500000 0.866025i 0.0205499 0.0355934i
\(593\) 18.4735 + 31.9971i 0.758617 + 1.31396i 0.943556 + 0.331214i \(0.107458\pi\)
−0.184939 + 0.982750i \(0.559209\pi\)
\(594\) 1.10452 1.91309i 0.0453192 0.0784952i
\(595\) −6.28781 10.8908i −0.257775 0.446480i
\(596\) −8.75353 −0.358558
\(597\) −1.54448 −0.0632112
\(598\) 3.54448 + 6.13921i 0.144944 + 0.251051i
\(599\) 10.8090 + 18.7217i 0.441642 + 0.764947i 0.997812 0.0661222i \(-0.0210627\pi\)
−0.556169 + 0.831069i \(0.687729\pi\)
\(600\) 1.00000 0.0408248
\(601\) −36.0141 −1.46905 −0.734523 0.678584i \(-0.762594\pi\)
−0.734523 + 0.678584i \(0.762594\pi\)
\(602\) 2.38137 + 4.12466i 0.0970576 + 0.168109i
\(603\) −0.0187126 + 0.0324111i −0.000762035 + 0.00131988i
\(604\) −4.33934 7.51595i −0.176565 0.305820i
\(605\) 3.06005 5.30016i 0.124409 0.215482i
\(606\) −0.246475 + 0.426907i −0.0100124 + 0.0173419i
\(607\) 1.65047 0.0669907 0.0334953 0.999439i \(-0.489336\pi\)
0.0334953 + 0.999439i \(0.489336\pi\)
\(608\) 3.35805 2.77912i 0.136187 0.112708i
\(609\) 13.4400 0.544617
\(610\) 2.98129 5.16374i 0.120709 0.209074i
\(611\) −15.9251 + 27.5832i −0.644263 + 1.11590i
\(612\) −3.58581 6.21081i −0.144948 0.251057i
\(613\) −12.7691 + 22.1167i −0.515739 + 0.893286i 0.484094 + 0.875016i \(0.339149\pi\)
−0.999833 + 0.0182703i \(0.994184\pi\)
\(614\) 8.88381 + 15.3872i 0.358522 + 0.620977i
\(615\) 10.4696 0.422176
\(616\) −3.87362 −0.156073
\(617\) 6.00000 + 10.3923i 0.241551 + 0.418378i 0.961156 0.276005i \(-0.0890106\pi\)
−0.719605 + 0.694383i \(0.755677\pi\)
\(618\) −5.83934 10.1140i −0.234893 0.406846i
\(619\) 14.7394 0.592427 0.296214 0.955122i \(-0.404276\pi\)
0.296214 + 0.955122i \(0.404276\pi\)
\(620\) −3.20905 −0.128879
\(621\) −1.10452 1.91309i −0.0443231 0.0767698i
\(622\) −5.70200 + 9.87615i −0.228629 + 0.395998i
\(623\) 9.61158 + 16.6477i 0.385080 + 0.666977i
\(624\) 1.60452 2.77912i 0.0642324 0.111254i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −10.2684 −0.410408
\(627\) 9.02576 + 3.35466i 0.360454 + 0.133972i
\(628\) 4.50705 0.179851
\(629\) 3.58581 6.21081i 0.142976 0.247641i
\(630\) −0.876763 + 1.51860i −0.0349311 + 0.0605024i
\(631\) 10.6459 + 18.4392i 0.423805 + 0.734052i 0.996308 0.0858508i \(-0.0273608\pi\)
−0.572503 + 0.819903i \(0.694027\pi\)
\(632\) −0.604525 + 1.04707i −0.0240467 + 0.0416501i
\(633\) −6.38381 11.0571i −0.253734 0.439480i
\(634\) −24.8129 −0.985445
\(635\) −12.8877 −0.511434
\(636\) −5.48129 9.49387i −0.217347 0.376456i
\(637\) −6.29800 10.9085i −0.249536 0.432209i
\(638\) −16.9314 −0.670322
\(639\) 7.17162 0.283705
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) 19.3058 33.4387i 0.762534 1.32075i −0.179006 0.983848i \(-0.557288\pi\)
0.941540 0.336900i \(-0.109378\pi\)
\(642\) −4.13029 7.15387i −0.163009 0.282341i
\(643\) 6.27929 10.8760i 0.247631 0.428909i −0.715237 0.698882i \(-0.753681\pi\)
0.962868 + 0.269973i \(0.0870146\pi\)
\(644\) −1.93681 + 3.35466i −0.0763211 + 0.132192i
\(645\) −2.71610 −0.106946
\(646\) 24.0827 19.9308i 0.947520 0.784167i
\(647\) −24.2373 −0.952865 −0.476432 0.879211i \(-0.658070\pi\)
−0.476432 + 0.879211i \(0.658070\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 6.62715 11.4786i 0.260138 0.450573i
\(650\) 1.60452 + 2.77912i 0.0629346 + 0.109006i
\(651\) 2.81357 4.87325i 0.110273 0.190998i
\(652\) −11.8136 20.4617i −0.462655 0.801342i
\(653\) −5.35247 −0.209458 −0.104729 0.994501i \(-0.533398\pi\)
−0.104729 + 0.994501i \(0.533398\pi\)
\(654\) −5.17162 −0.202227
\(655\) 6.61158 + 11.4516i 0.258336 + 0.447450i
\(656\) −5.23481 9.06696i −0.204385 0.354005i
\(657\) −11.9626 −0.466704
\(658\) −17.4040 −0.678479
\(659\) −1.59747 2.76691i −0.0622288 0.107783i 0.833233 0.552923i \(-0.186488\pi\)
−0.895461 + 0.445139i \(0.853154\pi\)
\(660\) 1.10452 1.91309i 0.0429936 0.0744671i
\(661\) −18.6412 32.2876i −0.725061 1.25584i −0.958949 0.283578i \(-0.908478\pi\)
0.233888 0.972263i \(-0.424855\pi\)
\(662\) 4.87676 8.44680i 0.189541 0.328294i
\(663\) 11.5071 19.9308i 0.446897 0.774048i
\(664\) 14.8362 0.575756
\(665\) −7.16457 2.66290i −0.277830 0.103263i
\(666\) −1.00000 −0.0387492
\(667\) −8.46571 + 14.6630i −0.327794 + 0.567755i
\(668\) −4.89548 + 8.47921i −0.189412 + 0.328071i
\(669\) −3.57876 6.19860i −0.138363 0.239652i
\(670\) −0.0187126 + 0.0324111i −0.000722930 + 0.00125215i
\(671\) −6.58581 11.4070i −0.254242 0.440361i
\(672\) 1.75353 0.0676437
\(673\) 0.940651 0.0362594 0.0181297 0.999836i \(-0.494229\pi\)
0.0181297 + 0.999836i \(0.494229\pi\)
\(674\) −11.3206 19.6079i −0.436054 0.755268i
\(675\) −0.500000 0.866025i −0.0192450 0.0333333i
\(676\) −2.70200 −0.103923
\(677\) 30.8129 1.18423 0.592117 0.805852i \(-0.298292\pi\)
0.592117 + 0.805852i \(0.298292\pi\)
\(678\) 1.13029 + 1.95772i 0.0434084 + 0.0751856i
\(679\) −9.86049 + 17.0789i −0.378411 + 0.655427i
\(680\) −3.58581 6.21081i −0.137510 0.238174i
\(681\) 7.13029 12.3500i 0.273233 0.473254i
\(682\) −3.54448 + 6.13921i −0.135725 + 0.235083i
\(683\) −8.26058 −0.316082 −0.158041 0.987433i \(-0.550518\pi\)
−0.158041 + 0.987433i \(0.550518\pi\)
\(684\) −4.08581 1.51860i −0.156225 0.0580650i
\(685\) −21.4322 −0.818882
\(686\) 9.57876 16.5909i 0.365719 0.633444i
\(687\) 10.6045 18.3676i 0.404588 0.700767i
\(688\) 1.35805 + 2.35221i 0.0517752 + 0.0896772i
\(689\) 17.5897 30.4663i 0.670115 1.16067i
\(690\) −1.10452 1.91309i −0.0420485 0.0728302i
\(691\) 5.97668 0.227363 0.113682 0.993517i \(-0.463736\pi\)
0.113682 + 0.993517i \(0.463736\pi\)
\(692\) 11.4555 0.435474
\(693\) 1.93681 + 3.35466i 0.0735734 + 0.127433i
\(694\) 12.6271 + 21.8709i 0.479320 + 0.830207i
\(695\) 7.20905 0.273455
\(696\) 7.66457 0.290525
\(697\) −37.5421 65.0248i −1.42201 2.46299i
\(698\) −14.6084 + 25.3026i −0.552937 + 0.957716i
\(699\) 2.70200 + 4.68000i 0.102199 + 0.177014i
\(700\) −0.876763 + 1.51860i −0.0331385 + 0.0573976i
\(701\) −22.0593 + 38.2079i −0.833170 + 1.44309i 0.0623415 + 0.998055i \(0.480143\pi\)
−0.895512 + 0.445038i \(0.853190\pi\)
\(702\) −3.20905 −0.121118
\(703\) −0.727762 4.29772i −0.0274481 0.162091i
\(704\) −2.20905 −0.0832567
\(705\) 4.96257 8.59543i 0.186901 0.323723i
\(706\) 16.4594 28.5086i 0.619459 1.07293i
\(707\) −0.432200 0.748592i −0.0162546 0.0281537i
\(708\) −3.00000 + 5.19615i −0.112747 + 0.195283i
\(709\) −14.4135 24.9649i −0.541310 0.937576i −0.998829 0.0483765i \(-0.984595\pi\)
0.457519 0.889200i \(-0.348738\pi\)
\(710\) 7.17162 0.269146
\(711\) 1.20905 0.0453429
\(712\) 5.48129 + 9.49387i 0.205420 + 0.355798i
\(713\) 3.54448 + 6.13921i 0.132742 + 0.229915i
\(714\) 12.5756 0.470631
\(715\) 7.08895 0.265112
\(716\) −3.31357 5.73928i −0.123834 0.214487i
\(717\) −10.7161 + 18.5608i −0.400200 + 0.693167i
\(718\) 1.62324 + 2.81153i 0.0605787 + 0.104925i
\(719\) −22.7988 + 39.4886i −0.850251 + 1.47268i 0.0307311 + 0.999528i \(0.490216\pi\)
−0.880982 + 0.473150i \(0.843117\pi\)
\(720\) −0.500000 + 0.866025i −0.0186339 + 0.0322749i
\(721\) 20.4788 0.762672
\(722\) 3.55300 18.6648i 0.132229 0.694633i
\(723\) −6.37285 −0.237009
\(724\) −5.13029 + 8.88592i −0.190666 + 0.330243i
\(725\) −3.83229 + 6.63772i −0.142328 + 0.246519i
\(726\) 3.06005 + 5.30016i 0.113569 + 0.196707i
\(727\) −2.56710 + 4.44635i −0.0952085 + 0.164906i −0.909696 0.415276i \(-0.863685\pi\)
0.814487 + 0.580182i \(0.197018\pi\)
\(728\) 2.81357 + 4.87325i 0.104278 + 0.180615i
\(729\) 1.00000 0.0370370
\(730\) −11.9626 −0.442755
\(731\) 9.73942 + 16.8692i 0.360226 + 0.623929i
\(732\) 2.98129 + 5.16374i 0.110192 + 0.190857i
\(733\) 17.7910 0.657124 0.328562 0.944482i \(-0.393436\pi\)
0.328562 + 0.944482i \(0.393436\pi\)
\(734\) −12.0452 −0.444598
\(735\) 1.96257 + 3.39928i 0.0723907 + 0.125384i
\(736\) −1.10452 + 1.91309i −0.0407133 + 0.0705176i
\(737\) 0.0413370 + 0.0715978i 0.00152267 + 0.00263734i
\(738\) −5.23481 + 9.06696i −0.192696 + 0.333759i
\(739\) 5.36971 9.30061i 0.197528 0.342129i −0.750198 0.661213i \(-0.770042\pi\)
0.947726 + 0.319084i \(0.103375\pi\)
\(740\) −1.00000 −0.0367607
\(741\) −2.33543 13.7916i −0.0857940 0.506647i
\(742\) 19.2232 0.705704
\(743\) −16.5367 + 28.6424i −0.606674 + 1.05079i 0.385111 + 0.922870i \(0.374163\pi\)
−0.991785 + 0.127919i \(0.959170\pi\)
\(744\) 1.60452 2.77912i 0.0588247 0.101887i
\(745\) 4.37676 + 7.58078i 0.160352 + 0.277738i
\(746\) 1.93290 3.34788i 0.0707685 0.122575i
\(747\) −7.41810 12.8485i −0.271414 0.470103i
\(748\) −15.8425 −0.579258
\(749\) 14.4851 0.529275
\(750\) −0.500000 0.866025i −0.0182574 0.0316228i
\(751\) −12.0600 20.8886i −0.440077 0.762237i 0.557617 0.830098i \(-0.311716\pi\)
−0.997695 + 0.0678616i \(0.978382\pi\)
\(752\) −9.92515 −0.361933
\(753\) 18.2684 0.665737
\(754\) 12.2980 + 21.3008i 0.447867 + 0.775728i
\(755\) −4.33934 + 7.51595i −0.157925 + 0.273534i
\(756\) −0.876763 1.51860i −0.0318875 0.0552308i
\(757\) 15.5827 26.9900i 0.566362 0.980968i −0.430560 0.902562i \(-0.641684\pi\)
0.996922 0.0784055i \(-0.0249829\pi\)
\(758\) 11.5297 19.9700i 0.418777 0.725342i
\(759\) −4.87990 −0.177129
\(760\) −4.08581 1.51860i −0.148208 0.0550853i
\(761\) 11.5586 0.418998 0.209499 0.977809i \(-0.432817\pi\)
0.209499 + 0.977809i \(0.432817\pi\)
\(762\) 6.44386 11.1611i 0.233437 0.404324i
\(763\) 4.53429 7.85362i 0.164152 0.284320i
\(764\) −12.6271 21.8709i −0.456834 0.791260i
\(765\) −3.58581 + 6.21081i −0.129645 + 0.224552i
\(766\) −1.03743 1.79687i −0.0374837 0.0649237i
\(767\) −19.2543 −0.695232
\(768\) 1.00000 0.0360844
\(769\) 7.22385 + 12.5121i 0.260499 + 0.451197i 0.966375 0.257139i \(-0.0827797\pi\)
−0.705876 + 0.708336i \(0.749446\pi\)
\(770\) 1.93681 + 3.35466i 0.0697979 + 0.120893i
\(771\) 6.00000 0.216085
\(772\) 2.87362 0.103424
\(773\) 18.9509 + 32.8239i 0.681617 + 1.18060i 0.974487 + 0.224443i \(0.0720563\pi\)
−0.292870 + 0.956152i \(0.594610\pi\)
\(774\) 1.35805 2.35221i 0.0488141 0.0845485i
\(775\) 1.60452 + 2.77912i 0.0576362 + 0.0998289i
\(776\) −5.62324 + 9.73973i −0.201862 + 0.349636i
\(777\) 0.876763 1.51860i 0.0314537 0.0544794i