Properties

Label 45.2.e.a.31.1
Level $45$
Weight $2$
Character 45.31
Analytic conductor $0.359$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 45.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.359326809096\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
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 31.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 45.31
Dual form 45.2.e.a.16.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.73205i q^{6} +(1.50000 + 2.59808i) q^{7} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.73205i q^{6} +(1.50000 + 2.59808i) q^{7} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} -1.00000 q^{10} +(1.00000 + 1.73205i) q^{11} +(-1.50000 + 0.866025i) q^{12} +(1.00000 - 1.73205i) q^{13} +(1.50000 - 2.59808i) q^{14} +(-1.50000 + 0.866025i) q^{15} +(0.500000 + 0.866025i) q^{16} +4.00000 q^{17} +(1.50000 - 2.59808i) q^{18} -8.00000 q^{19} +(-0.500000 - 0.866025i) q^{20} -5.19615i q^{21} +(1.00000 - 1.73205i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(4.50000 + 2.59808i) q^{24} +(-0.500000 - 0.866025i) q^{25} -2.00000 q^{26} -5.19615i q^{27} +3.00000 q^{28} +(0.500000 + 0.866025i) q^{29} +(1.50000 + 0.866025i) q^{30} +(-2.50000 + 4.33013i) q^{32} -3.46410i q^{33} +(-2.00000 - 3.46410i) q^{34} +3.00000 q^{35} +3.00000 q^{36} -4.00000 q^{37} +(4.00000 + 6.92820i) q^{38} +(-3.00000 + 1.73205i) q^{39} +(-1.50000 + 2.59808i) q^{40} +(-2.50000 + 4.33013i) q^{41} +(-4.50000 + 2.59808i) q^{42} +(4.00000 + 6.92820i) q^{43} +2.00000 q^{44} +3.00000 q^{45} +3.00000 q^{46} +(-3.50000 - 6.06218i) q^{47} -1.73205i q^{48} +(-1.00000 + 1.73205i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-6.00000 - 3.46410i) q^{51} +(-1.00000 - 1.73205i) q^{52} -2.00000 q^{53} +(-4.50000 + 2.59808i) q^{54} +2.00000 q^{55} +(-4.50000 - 7.79423i) q^{56} +(12.0000 + 6.92820i) q^{57} +(0.500000 - 0.866025i) q^{58} +(7.00000 - 12.1244i) q^{59} +1.73205i q^{60} +(-3.50000 - 6.06218i) q^{61} +(-4.50000 + 7.79423i) q^{63} +7.00000 q^{64} +(-1.00000 - 1.73205i) q^{65} +(-3.00000 + 1.73205i) q^{66} +(1.50000 - 2.59808i) q^{67} +(2.00000 - 3.46410i) q^{68} +(4.50000 - 2.59808i) q^{69} +(-1.50000 - 2.59808i) q^{70} +2.00000 q^{71} +(-4.50000 - 7.79423i) q^{72} +4.00000 q^{73} +(2.00000 + 3.46410i) q^{74} +1.73205i q^{75} +(-4.00000 + 6.92820i) q^{76} +(-3.00000 + 5.19615i) q^{77} +(3.00000 + 1.73205i) q^{78} +(3.00000 + 5.19615i) q^{79} +1.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} +5.00000 q^{82} +(-4.50000 - 7.79423i) q^{83} +(-4.50000 - 2.59808i) q^{84} +(2.00000 - 3.46410i) q^{85} +(4.00000 - 6.92820i) q^{86} -1.73205i q^{87} +(-3.00000 - 5.19615i) q^{88} -15.0000 q^{89} +(-1.50000 - 2.59808i) q^{90} +6.00000 q^{91} +(1.50000 + 2.59808i) q^{92} +(-3.50000 + 6.06218i) q^{94} +(-4.00000 + 6.92820i) q^{95} +(7.50000 - 4.33013i) q^{96} +(-1.00000 - 1.73205i) q^{97} +2.00000 q^{98} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - 3 q^{3} + q^{4} + q^{5} + 3 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - 3 q^{3} + q^{4} + q^{5} + 3 q^{7} - 6 q^{8} + 3 q^{9} - 2 q^{10} + 2 q^{11} - 3 q^{12} + 2 q^{13} + 3 q^{14} - 3 q^{15} + q^{16} + 8 q^{17} + 3 q^{18} - 16 q^{19} - q^{20} + 2 q^{22} - 3 q^{23} + 9 q^{24} - q^{25} - 4 q^{26} + 6 q^{28} + q^{29} + 3 q^{30} - 5 q^{32} - 4 q^{34} + 6 q^{35} + 6 q^{36} - 8 q^{37} + 8 q^{38} - 6 q^{39} - 3 q^{40} - 5 q^{41} - 9 q^{42} + 8 q^{43} + 4 q^{44} + 6 q^{45} + 6 q^{46} - 7 q^{47} - 2 q^{49} - q^{50} - 12 q^{51} - 2 q^{52} - 4 q^{53} - 9 q^{54} + 4 q^{55} - 9 q^{56} + 24 q^{57} + q^{58} + 14 q^{59} - 7 q^{61} - 9 q^{63} + 14 q^{64} - 2 q^{65} - 6 q^{66} + 3 q^{67} + 4 q^{68} + 9 q^{69} - 3 q^{70} + 4 q^{71} - 9 q^{72} + 8 q^{73} + 4 q^{74} - 8 q^{76} - 6 q^{77} + 6 q^{78} + 6 q^{79} + 2 q^{80} - 9 q^{81} + 10 q^{82} - 9 q^{83} - 9 q^{84} + 4 q^{85} + 8 q^{86} - 6 q^{88} - 30 q^{89} - 3 q^{90} + 12 q^{91} + 3 q^{92} - 7 q^{94} - 8 q^{95} + 15 q^{96} - 2 q^{97} + 4 q^{98} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i 0.633316 0.773893i \(-0.281693\pi\)
−0.986869 + 0.161521i \(0.948360\pi\)
\(3\) −1.50000 0.866025i −0.866025 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 1.73205i 0.707107i
\(7\) 1.50000 + 2.59808i 0.566947 + 0.981981i 0.996866 + 0.0791130i \(0.0252088\pi\)
−0.429919 + 0.902867i \(0.641458\pi\)
\(8\) −3.00000 −1.06066
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) −1.00000 −0.316228
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) −1.50000 + 0.866025i −0.433013 + 0.250000i
\(13\) 1.00000 1.73205i 0.277350 0.480384i −0.693375 0.720577i \(-0.743877\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) 1.50000 2.59808i 0.400892 0.694365i
\(15\) −1.50000 + 0.866025i −0.387298 + 0.223607i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) 1.50000 2.59808i 0.353553 0.612372i
\(19\) −8.00000 −1.83533 −0.917663 0.397360i \(-0.869927\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) −0.500000 0.866025i −0.111803 0.193649i
\(21\) 5.19615i 1.13389i
\(22\) 1.00000 1.73205i 0.213201 0.369274i
\(23\) −1.50000 + 2.59808i −0.312772 + 0.541736i −0.978961 0.204046i \(-0.934591\pi\)
0.666190 + 0.745782i \(0.267924\pi\)
\(24\) 4.50000 + 2.59808i 0.918559 + 0.530330i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −2.00000 −0.392232
\(27\) 5.19615i 1.00000i
\(28\) 3.00000 0.566947
\(29\) 0.500000 + 0.866025i 0.0928477 + 0.160817i 0.908708 0.417432i \(-0.137070\pi\)
−0.815861 + 0.578249i \(0.803736\pi\)
\(30\) 1.50000 + 0.866025i 0.273861 + 0.158114i
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) −2.50000 + 4.33013i −0.441942 + 0.765466i
\(33\) 3.46410i 0.603023i
\(34\) −2.00000 3.46410i −0.342997 0.594089i
\(35\) 3.00000 0.507093
\(36\) 3.00000 0.500000
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 4.00000 + 6.92820i 0.648886 + 1.12390i
\(39\) −3.00000 + 1.73205i −0.480384 + 0.277350i
\(40\) −1.50000 + 2.59808i −0.237171 + 0.410792i
\(41\) −2.50000 + 4.33013i −0.390434 + 0.676252i −0.992507 0.122189i \(-0.961009\pi\)
0.602072 + 0.798441i \(0.294342\pi\)
\(42\) −4.50000 + 2.59808i −0.694365 + 0.400892i
\(43\) 4.00000 + 6.92820i 0.609994 + 1.05654i 0.991241 + 0.132068i \(0.0421616\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) 2.00000 0.301511
\(45\) 3.00000 0.447214
\(46\) 3.00000 0.442326
\(47\) −3.50000 6.06218i −0.510527 0.884260i −0.999926 0.0121990i \(-0.996117\pi\)
0.489398 0.872060i \(-0.337217\pi\)
\(48\) 1.73205i 0.250000i
\(49\) −1.00000 + 1.73205i −0.142857 + 0.247436i
\(50\) −0.500000 + 0.866025i −0.0707107 + 0.122474i
\(51\) −6.00000 3.46410i −0.840168 0.485071i
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) −4.50000 + 2.59808i −0.612372 + 0.353553i
\(55\) 2.00000 0.269680
\(56\) −4.50000 7.79423i −0.601338 1.04155i
\(57\) 12.0000 + 6.92820i 1.58944 + 0.917663i
\(58\) 0.500000 0.866025i 0.0656532 0.113715i
\(59\) 7.00000 12.1244i 0.911322 1.57846i 0.0991242 0.995075i \(-0.468396\pi\)
0.812198 0.583382i \(-0.198271\pi\)
\(60\) 1.73205i 0.223607i
\(61\) −3.50000 6.06218i −0.448129 0.776182i 0.550135 0.835076i \(-0.314576\pi\)
−0.998264 + 0.0588933i \(0.981243\pi\)
\(62\) 0 0
\(63\) −4.50000 + 7.79423i −0.566947 + 0.981981i
\(64\) 7.00000 0.875000
\(65\) −1.00000 1.73205i −0.124035 0.214834i
\(66\) −3.00000 + 1.73205i −0.369274 + 0.213201i
\(67\) 1.50000 2.59808i 0.183254 0.317406i −0.759733 0.650236i \(-0.774670\pi\)
0.942987 + 0.332830i \(0.108004\pi\)
\(68\) 2.00000 3.46410i 0.242536 0.420084i
\(69\) 4.50000 2.59808i 0.541736 0.312772i
\(70\) −1.50000 2.59808i −0.179284 0.310530i
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) −4.50000 7.79423i −0.530330 0.918559i
\(73\) 4.00000 0.468165 0.234082 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) 2.00000 + 3.46410i 0.232495 + 0.402694i
\(75\) 1.73205i 0.200000i
\(76\) −4.00000 + 6.92820i −0.458831 + 0.794719i
\(77\) −3.00000 + 5.19615i −0.341882 + 0.592157i
\(78\) 3.00000 + 1.73205i 0.339683 + 0.196116i
\(79\) 3.00000 + 5.19615i 0.337526 + 0.584613i 0.983967 0.178352i \(-0.0570765\pi\)
−0.646440 + 0.762964i \(0.723743\pi\)
\(80\) 1.00000 0.111803
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 5.00000 0.552158
\(83\) −4.50000 7.79423i −0.493939 0.855528i 0.506036 0.862512i \(-0.331110\pi\)
−0.999976 + 0.00698436i \(0.997777\pi\)
\(84\) −4.50000 2.59808i −0.490990 0.283473i
\(85\) 2.00000 3.46410i 0.216930 0.375735i
\(86\) 4.00000 6.92820i 0.431331 0.747087i
\(87\) 1.73205i 0.185695i
\(88\) −3.00000 5.19615i −0.319801 0.553912i
\(89\) −15.0000 −1.59000 −0.794998 0.606612i \(-0.792528\pi\)
−0.794998 + 0.606612i \(0.792528\pi\)
\(90\) −1.50000 2.59808i −0.158114 0.273861i
\(91\) 6.00000 0.628971
\(92\) 1.50000 + 2.59808i 0.156386 + 0.270868i
\(93\) 0 0
\(94\) −3.50000 + 6.06218i −0.360997 + 0.625266i
\(95\) −4.00000 + 6.92820i −0.410391 + 0.710819i
\(96\) 7.50000 4.33013i 0.765466 0.441942i
\(97\) −1.00000 1.73205i −0.101535 0.175863i 0.810782 0.585348i \(-0.199042\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) 2.00000 0.202031
\(99\) −3.00000 + 5.19615i −0.301511 + 0.522233i
\(100\) −1.00000 −0.100000
\(101\) 9.00000 + 15.5885i 0.895533 + 1.55111i 0.833143 + 0.553058i \(0.186539\pi\)
0.0623905 + 0.998052i \(0.480128\pi\)
\(102\) 6.92820i 0.685994i
\(103\) −4.00000 + 6.92820i −0.394132 + 0.682656i −0.992990 0.118199i \(-0.962288\pi\)
0.598858 + 0.800855i \(0.295621\pi\)
\(104\) −3.00000 + 5.19615i −0.294174 + 0.509525i
\(105\) −4.50000 2.59808i −0.439155 0.253546i
\(106\) 1.00000 + 1.73205i 0.0971286 + 0.168232i
\(107\) 3.00000 0.290021 0.145010 0.989430i \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) −4.50000 2.59808i −0.433013 0.250000i
\(109\) 5.00000 0.478913 0.239457 0.970907i \(-0.423031\pi\)
0.239457 + 0.970907i \(0.423031\pi\)
\(110\) −1.00000 1.73205i −0.0953463 0.165145i
\(111\) 6.00000 + 3.46410i 0.569495 + 0.328798i
\(112\) −1.50000 + 2.59808i −0.141737 + 0.245495i
\(113\) 4.00000 6.92820i 0.376288 0.651751i −0.614231 0.789127i \(-0.710534\pi\)
0.990519 + 0.137376i \(0.0438669\pi\)
\(114\) 13.8564i 1.29777i
\(115\) 1.50000 + 2.59808i 0.139876 + 0.242272i
\(116\) 1.00000 0.0928477
\(117\) 6.00000 0.554700
\(118\) −14.0000 −1.28880
\(119\) 6.00000 + 10.3923i 0.550019 + 0.952661i
\(120\) 4.50000 2.59808i 0.410792 0.237171i
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) −3.50000 + 6.06218i −0.316875 + 0.548844i
\(123\) 7.50000 4.33013i 0.676252 0.390434i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 9.00000 0.801784
\(127\) −5.00000 −0.443678 −0.221839 0.975083i \(-0.571206\pi\)
−0.221839 + 0.975083i \(0.571206\pi\)
\(128\) 1.50000 + 2.59808i 0.132583 + 0.229640i
\(129\) 13.8564i 1.21999i
\(130\) −1.00000 + 1.73205i −0.0877058 + 0.151911i
\(131\) 3.00000 5.19615i 0.262111 0.453990i −0.704692 0.709514i \(-0.748915\pi\)
0.966803 + 0.255524i \(0.0822479\pi\)
\(132\) −3.00000 1.73205i −0.261116 0.150756i
\(133\) −12.0000 20.7846i −1.04053 1.80225i
\(134\) −3.00000 −0.259161
\(135\) −4.50000 2.59808i −0.387298 0.223607i
\(136\) −12.0000 −1.02899
\(137\) −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) −4.50000 2.59808i −0.383065 0.221163i
\(139\) 8.00000 13.8564i 0.678551 1.17529i −0.296866 0.954919i \(-0.595942\pi\)
0.975417 0.220366i \(-0.0707252\pi\)
\(140\) 1.50000 2.59808i 0.126773 0.219578i
\(141\) 12.1244i 1.02105i
\(142\) −1.00000 1.73205i −0.0839181 0.145350i
\(143\) 4.00000 0.334497
\(144\) −1.50000 + 2.59808i −0.125000 + 0.216506i
\(145\) 1.00000 0.0830455
\(146\) −2.00000 3.46410i −0.165521 0.286691i
\(147\) 3.00000 1.73205i 0.247436 0.142857i
\(148\) −2.00000 + 3.46410i −0.164399 + 0.284747i
\(149\) −8.50000 + 14.7224i −0.696347 + 1.20611i 0.273377 + 0.961907i \(0.411859\pi\)
−0.969724 + 0.244202i \(0.921474\pi\)
\(150\) 1.50000 0.866025i 0.122474 0.0707107i
\(151\) 1.00000 + 1.73205i 0.0813788 + 0.140952i 0.903842 0.427865i \(-0.140734\pi\)
−0.822464 + 0.568818i \(0.807401\pi\)
\(152\) 24.0000 1.94666
\(153\) 6.00000 + 10.3923i 0.485071 + 0.840168i
\(154\) 6.00000 0.483494
\(155\) 0 0
\(156\) 3.46410i 0.277350i
\(157\) −7.00000 + 12.1244i −0.558661 + 0.967629i 0.438948 + 0.898513i \(0.355351\pi\)
−0.997609 + 0.0691164i \(0.977982\pi\)
\(158\) 3.00000 5.19615i 0.238667 0.413384i
\(159\) 3.00000 + 1.73205i 0.237915 + 0.137361i
\(160\) 2.50000 + 4.33013i 0.197642 + 0.342327i
\(161\) −9.00000 −0.709299
\(162\) 9.00000 0.707107
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 2.50000 + 4.33013i 0.195217 + 0.338126i
\(165\) −3.00000 1.73205i −0.233550 0.134840i
\(166\) −4.50000 + 7.79423i −0.349268 + 0.604949i
\(167\) 4.50000 7.79423i 0.348220 0.603136i −0.637713 0.770274i \(-0.720119\pi\)
0.985933 + 0.167139i \(0.0534527\pi\)
\(168\) 15.5885i 1.20268i
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) −4.00000 −0.306786
\(171\) −12.0000 20.7846i −0.917663 1.58944i
\(172\) 8.00000 0.609994
\(173\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(174\) −1.50000 + 0.866025i −0.113715 + 0.0656532i
\(175\) 1.50000 2.59808i 0.113389 0.196396i
\(176\) −1.00000 + 1.73205i −0.0753778 + 0.130558i
\(177\) −21.0000 + 12.1244i −1.57846 + 0.911322i
\(178\) 7.50000 + 12.9904i 0.562149 + 0.973670i
\(179\) −2.00000 −0.149487 −0.0747435 0.997203i \(-0.523814\pi\)
−0.0747435 + 0.997203i \(0.523814\pi\)
\(180\) 1.50000 2.59808i 0.111803 0.193649i
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) −3.00000 5.19615i −0.222375 0.385164i
\(183\) 12.1244i 0.896258i
\(184\) 4.50000 7.79423i 0.331744 0.574598i
\(185\) −2.00000 + 3.46410i −0.147043 + 0.254686i
\(186\) 0 0
\(187\) 4.00000 + 6.92820i 0.292509 + 0.506640i
\(188\) −7.00000 −0.510527
\(189\) 13.5000 7.79423i 0.981981 0.566947i
\(190\) 8.00000 0.580381
\(191\) −4.00000 6.92820i −0.289430 0.501307i 0.684244 0.729253i \(-0.260132\pi\)
−0.973674 + 0.227946i \(0.926799\pi\)
\(192\) −10.5000 6.06218i −0.757772 0.437500i
\(193\) 5.00000 8.66025i 0.359908 0.623379i −0.628037 0.778183i \(-0.716141\pi\)
0.987945 + 0.154805i \(0.0494748\pi\)
\(194\) −1.00000 + 1.73205i −0.0717958 + 0.124354i
\(195\) 3.46410i 0.248069i
\(196\) 1.00000 + 1.73205i 0.0714286 + 0.123718i
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 6.00000 0.426401
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) 1.50000 + 2.59808i 0.106066 + 0.183712i
\(201\) −4.50000 + 2.59808i −0.317406 + 0.183254i
\(202\) 9.00000 15.5885i 0.633238 1.09680i
\(203\) −1.50000 + 2.59808i −0.105279 + 0.182349i
\(204\) −6.00000 + 3.46410i −0.420084 + 0.242536i
\(205\) 2.50000 + 4.33013i 0.174608 + 0.302429i
\(206\) 8.00000 0.557386
\(207\) −9.00000 −0.625543
\(208\) 2.00000 0.138675
\(209\) −8.00000 13.8564i −0.553372 0.958468i
\(210\) 5.19615i 0.358569i
\(211\) 11.0000 19.0526i 0.757271 1.31163i −0.186966 0.982366i \(-0.559865\pi\)
0.944237 0.329266i \(-0.106801\pi\)
\(212\) −1.00000 + 1.73205i −0.0686803 + 0.118958i
\(213\) −3.00000 1.73205i −0.205557 0.118678i
\(214\) −1.50000 2.59808i −0.102538 0.177601i
\(215\) 8.00000 0.545595
\(216\) 15.5885i 1.06066i
\(217\) 0 0
\(218\) −2.50000 4.33013i −0.169321 0.293273i
\(219\) −6.00000 3.46410i −0.405442 0.234082i
\(220\) 1.00000 1.73205i 0.0674200 0.116775i
\(221\) 4.00000 6.92820i 0.269069 0.466041i
\(222\) 6.92820i 0.464991i
\(223\) 9.50000 + 16.4545i 0.636167 + 1.10187i 0.986267 + 0.165161i \(0.0528144\pi\)
−0.350100 + 0.936713i \(0.613852\pi\)
\(224\) −15.0000 −1.00223
\(225\) 1.50000 2.59808i 0.100000 0.173205i
\(226\) −8.00000 −0.532152
\(227\) 2.00000 + 3.46410i 0.132745 + 0.229920i 0.924734 0.380615i \(-0.124288\pi\)
−0.791989 + 0.610535i \(0.790954\pi\)
\(228\) 12.0000 6.92820i 0.794719 0.458831i
\(229\) −7.50000 + 12.9904i −0.495614 + 0.858429i −0.999987 0.00505719i \(-0.998390\pi\)
0.504373 + 0.863486i \(0.331724\pi\)
\(230\) 1.50000 2.59808i 0.0989071 0.171312i
\(231\) 9.00000 5.19615i 0.592157 0.341882i
\(232\) −1.50000 2.59808i −0.0984798 0.170572i
\(233\) 24.0000 1.57229 0.786146 0.618041i \(-0.212073\pi\)
0.786146 + 0.618041i \(0.212073\pi\)
\(234\) −3.00000 5.19615i −0.196116 0.339683i
\(235\) −7.00000 −0.456630
\(236\) −7.00000 12.1244i −0.455661 0.789228i
\(237\) 10.3923i 0.675053i
\(238\) 6.00000 10.3923i 0.388922 0.673633i
\(239\) 4.00000 6.92820i 0.258738 0.448148i −0.707166 0.707048i \(-0.750027\pi\)
0.965904 + 0.258900i \(0.0833599\pi\)
\(240\) −1.50000 0.866025i −0.0968246 0.0559017i
\(241\) 5.50000 + 9.52628i 0.354286 + 0.613642i 0.986996 0.160748i \(-0.0513906\pi\)
−0.632709 + 0.774389i \(0.718057\pi\)
\(242\) −7.00000 −0.449977
\(243\) 13.5000 7.79423i 0.866025 0.500000i
\(244\) −7.00000 −0.448129
\(245\) 1.00000 + 1.73205i 0.0638877 + 0.110657i
\(246\) −7.50000 4.33013i −0.478183 0.276079i
\(247\) −8.00000 + 13.8564i −0.509028 + 0.881662i
\(248\) 0 0
\(249\) 15.5885i 0.987878i
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 4.50000 + 7.79423i 0.283473 + 0.490990i
\(253\) −6.00000 −0.377217
\(254\) 2.50000 + 4.33013i 0.156864 + 0.271696i
\(255\) −6.00000 + 3.46410i −0.375735 + 0.216930i
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) 3.00000 5.19615i 0.187135 0.324127i −0.757159 0.653231i \(-0.773413\pi\)
0.944294 + 0.329104i \(0.106747\pi\)
\(258\) −12.0000 + 6.92820i −0.747087 + 0.431331i
\(259\) −6.00000 10.3923i −0.372822 0.645746i
\(260\) −2.00000 −0.124035
\(261\) −1.50000 + 2.59808i −0.0928477 + 0.160817i
\(262\) −6.00000 −0.370681
\(263\) 8.00000 + 13.8564i 0.493301 + 0.854423i 0.999970 0.00771799i \(-0.00245674\pi\)
−0.506669 + 0.862141i \(0.669123\pi\)
\(264\) 10.3923i 0.639602i
\(265\) −1.00000 + 1.73205i −0.0614295 + 0.106399i
\(266\) −12.0000 + 20.7846i −0.735767 + 1.27439i
\(267\) 22.5000 + 12.9904i 1.37698 + 0.794998i
\(268\) −1.50000 2.59808i −0.0916271 0.158703i
\(269\) 25.0000 1.52428 0.762138 0.647414i \(-0.224150\pi\)
0.762138 + 0.647414i \(0.224150\pi\)
\(270\) 5.19615i 0.316228i
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 2.00000 + 3.46410i 0.121268 + 0.210042i
\(273\) −9.00000 5.19615i −0.544705 0.314485i
\(274\) −6.00000 + 10.3923i −0.362473 + 0.627822i
\(275\) 1.00000 1.73205i 0.0603023 0.104447i
\(276\) 5.19615i 0.312772i
\(277\) −6.00000 10.3923i −0.360505 0.624413i 0.627539 0.778585i \(-0.284062\pi\)
−0.988044 + 0.154172i \(0.950729\pi\)
\(278\) −16.0000 −0.959616
\(279\) 0 0
\(280\) −9.00000 −0.537853
\(281\) 7.50000 + 12.9904i 0.447412 + 0.774941i 0.998217 0.0596933i \(-0.0190123\pi\)
−0.550804 + 0.834634i \(0.685679\pi\)
\(282\) 10.5000 6.06218i 0.625266 0.360997i
\(283\) −10.5000 + 18.1865i −0.624160 + 1.08108i 0.364542 + 0.931187i \(0.381225\pi\)
−0.988703 + 0.149890i \(0.952108\pi\)
\(284\) 1.00000 1.73205i 0.0593391 0.102778i
\(285\) 12.0000 6.92820i 0.710819 0.410391i
\(286\) −2.00000 3.46410i −0.118262 0.204837i
\(287\) −15.0000 −0.885422
\(288\) −15.0000 −0.883883
\(289\) −1.00000 −0.0588235
\(290\) −0.500000 0.866025i −0.0293610 0.0508548i
\(291\) 3.46410i 0.203069i
\(292\) 2.00000 3.46410i 0.117041 0.202721i
\(293\) −6.00000 + 10.3923i −0.350524 + 0.607125i −0.986341 0.164714i \(-0.947330\pi\)
0.635818 + 0.771839i \(0.280663\pi\)
\(294\) −3.00000 1.73205i −0.174964 0.101015i
\(295\) −7.00000 12.1244i −0.407556 0.705907i
\(296\) 12.0000 0.697486
\(297\) 9.00000 5.19615i 0.522233 0.301511i
\(298\) 17.0000 0.984784
\(299\) 3.00000 + 5.19615i 0.173494 + 0.300501i
\(300\) 1.50000 + 0.866025i 0.0866025 + 0.0500000i
\(301\) −12.0000 + 20.7846i −0.691669 + 1.19800i
\(302\) 1.00000 1.73205i 0.0575435 0.0996683i
\(303\) 31.1769i 1.79107i
\(304\) −4.00000 6.92820i −0.229416 0.397360i
\(305\) −7.00000 −0.400819
\(306\) 6.00000 10.3923i 0.342997 0.594089i
\(307\) 7.00000 0.399511 0.199756 0.979846i \(-0.435985\pi\)
0.199756 + 0.979846i \(0.435985\pi\)
\(308\) 3.00000 + 5.19615i 0.170941 + 0.296078i
\(309\) 12.0000 6.92820i 0.682656 0.394132i
\(310\) 0 0
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 9.00000 5.19615i 0.509525 0.294174i
\(313\) −7.00000 12.1244i −0.395663 0.685309i 0.597522 0.801852i \(-0.296152\pi\)
−0.993186 + 0.116543i \(0.962819\pi\)
\(314\) 14.0000 0.790066
\(315\) 4.50000 + 7.79423i 0.253546 + 0.439155i
\(316\) 6.00000 0.337526
\(317\) 17.0000 + 29.4449i 0.954815 + 1.65379i 0.734791 + 0.678294i \(0.237280\pi\)
0.220024 + 0.975494i \(0.429386\pi\)
\(318\) 3.46410i 0.194257i
\(319\) −1.00000 + 1.73205i −0.0559893 + 0.0969762i
\(320\) 3.50000 6.06218i 0.195656 0.338886i
\(321\) −4.50000 2.59808i −0.251166 0.145010i
\(322\) 4.50000 + 7.79423i 0.250775 + 0.434355i
\(323\) −32.0000 −1.78053
\(324\) 4.50000 + 7.79423i 0.250000 + 0.433013i
\(325\) −2.00000 −0.110940
\(326\) 2.00000 + 3.46410i 0.110770 + 0.191859i
\(327\) −7.50000 4.33013i −0.414751 0.239457i
\(328\) 7.50000 12.9904i 0.414118 0.717274i
\(329\) 10.5000 18.1865i 0.578884 1.00266i
\(330\) 3.46410i 0.190693i
\(331\) 3.00000 + 5.19615i 0.164895 + 0.285606i 0.936618 0.350352i \(-0.113938\pi\)
−0.771723 + 0.635959i \(0.780605\pi\)
\(332\) −9.00000 −0.493939
\(333\) −6.00000 10.3923i −0.328798 0.569495i
\(334\) −9.00000 −0.492458
\(335\) −1.50000 2.59808i −0.0819538 0.141948i
\(336\) 4.50000 2.59808i 0.245495 0.141737i
\(337\) 4.00000 6.92820i 0.217894 0.377403i −0.736270 0.676688i \(-0.763415\pi\)
0.954164 + 0.299285i \(0.0967480\pi\)
\(338\) 4.50000 7.79423i 0.244768 0.423950i
\(339\) −12.0000 + 6.92820i −0.651751 + 0.376288i
\(340\) −2.00000 3.46410i −0.108465 0.187867i
\(341\) 0 0
\(342\) −12.0000 + 20.7846i −0.648886 + 1.12390i
\(343\) 15.0000 0.809924
\(344\) −12.0000 20.7846i −0.646997 1.12063i
\(345\) 5.19615i 0.279751i
\(346\) 0 0
\(347\) −2.00000 + 3.46410i −0.107366 + 0.185963i −0.914702 0.404128i \(-0.867575\pi\)
0.807337 + 0.590091i \(0.200908\pi\)
\(348\) −1.50000 0.866025i −0.0804084 0.0464238i
\(349\) 2.50000 + 4.33013i 0.133822 + 0.231786i 0.925147 0.379610i \(-0.123942\pi\)
−0.791325 + 0.611396i \(0.790608\pi\)
\(350\) −3.00000 −0.160357
\(351\) −9.00000 5.19615i −0.480384 0.277350i
\(352\) −10.0000 −0.533002
\(353\) −12.0000 20.7846i −0.638696 1.10625i −0.985719 0.168397i \(-0.946141\pi\)
0.347024 0.937856i \(-0.387192\pi\)
\(354\) 21.0000 + 12.1244i 1.11614 + 0.644402i
\(355\) 1.00000 1.73205i 0.0530745 0.0919277i
\(356\) −7.50000 + 12.9904i −0.397499 + 0.688489i
\(357\) 20.7846i 1.10004i
\(358\) 1.00000 + 1.73205i 0.0528516 + 0.0915417i
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) −9.00000 −0.474342
\(361\) 45.0000 2.36842
\(362\) 3.50000 + 6.06218i 0.183956 + 0.318621i
\(363\) −10.5000 + 6.06218i −0.551107 + 0.318182i
\(364\) 3.00000 5.19615i 0.157243 0.272352i
\(365\) 2.00000 3.46410i 0.104685 0.181319i
\(366\) 10.5000 6.06218i 0.548844 0.316875i
\(367\) −12.0000 20.7846i −0.626395 1.08495i −0.988269 0.152721i \(-0.951196\pi\)
0.361874 0.932227i \(-0.382137\pi\)
\(368\) −3.00000 −0.156386
\(369\) −15.0000 −0.780869
\(370\) 4.00000 0.207950
\(371\) −3.00000 5.19615i −0.155752 0.269771i
\(372\) 0 0
\(373\) −5.00000 + 8.66025i −0.258890 + 0.448411i −0.965945 0.258748i \(-0.916690\pi\)
0.707055 + 0.707159i \(0.250023\pi\)
\(374\) 4.00000 6.92820i 0.206835 0.358249i
\(375\) 1.50000 + 0.866025i 0.0774597 + 0.0447214i
\(376\) 10.5000 + 18.1865i 0.541496 + 0.937899i
\(377\) 2.00000 0.103005
\(378\) −13.5000 7.79423i −0.694365 0.400892i
\(379\) −26.0000 −1.33553 −0.667765 0.744372i \(-0.732749\pi\)
−0.667765 + 0.744372i \(0.732749\pi\)
\(380\) 4.00000 + 6.92820i 0.205196 + 0.355409i
\(381\) 7.50000 + 4.33013i 0.384237 + 0.221839i
\(382\) −4.00000 + 6.92820i −0.204658 + 0.354478i
\(383\) −18.0000 + 31.1769i −0.919757 + 1.59307i −0.119974 + 0.992777i \(0.538281\pi\)
−0.799783 + 0.600289i \(0.795052\pi\)
\(384\) 5.19615i 0.265165i
\(385\) 3.00000 + 5.19615i 0.152894 + 0.264820i
\(386\) −10.0000 −0.508987
\(387\) −12.0000 + 20.7846i −0.609994 + 1.05654i
\(388\) −2.00000 −0.101535
\(389\) −16.5000 28.5788i −0.836583 1.44900i −0.892735 0.450582i \(-0.851216\pi\)
0.0561516 0.998422i \(-0.482117\pi\)
\(390\) 3.00000 1.73205i 0.151911 0.0877058i
\(391\) −6.00000 + 10.3923i −0.303433 + 0.525561i
\(392\) 3.00000 5.19615i 0.151523 0.262445i
\(393\) −9.00000 + 5.19615i −0.453990 + 0.262111i
\(394\) 6.00000 + 10.3923i 0.302276 + 0.523557i
\(395\) 6.00000 0.301893
\(396\) 3.00000 + 5.19615i 0.150756 + 0.261116i
\(397\) 34.0000 1.70641 0.853206 0.521575i \(-0.174655\pi\)
0.853206 + 0.521575i \(0.174655\pi\)
\(398\) −2.00000 3.46410i −0.100251 0.173640i
\(399\) 41.5692i 2.08106i
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i \(-0.684957\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) 4.50000 + 2.59808i 0.224440 + 0.129580i
\(403\) 0 0
\(404\) 18.0000 0.895533
\(405\) 4.50000 + 7.79423i 0.223607 + 0.387298i
\(406\) 3.00000 0.148888
\(407\) −4.00000 6.92820i −0.198273 0.343418i
\(408\) 18.0000 + 10.3923i 0.891133 + 0.514496i
\(409\) −7.00000 + 12.1244i −0.346128 + 0.599511i −0.985558 0.169338i \(-0.945837\pi\)
0.639430 + 0.768849i \(0.279170\pi\)
\(410\) 2.50000 4.33013i 0.123466 0.213850i
\(411\) 20.7846i 1.02523i
\(412\) 4.00000 + 6.92820i 0.197066 + 0.341328i
\(413\) 42.0000 2.06668
\(414\) 4.50000 + 7.79423i 0.221163 + 0.383065i
\(415\) −9.00000 −0.441793
\(416\) 5.00000 + 8.66025i 0.245145 + 0.424604i
\(417\) −24.0000 + 13.8564i −1.17529 + 0.678551i
\(418\) −8.00000 + 13.8564i −0.391293 + 0.677739i
\(419\) −13.0000 + 22.5167i −0.635092 + 1.10001i 0.351404 + 0.936224i \(0.385704\pi\)
−0.986496 + 0.163787i \(0.947629\pi\)
\(420\) −4.50000 + 2.59808i −0.219578 + 0.126773i
\(421\) −17.0000 29.4449i −0.828529 1.43505i −0.899192 0.437555i \(-0.855845\pi\)
0.0706626 0.997500i \(-0.477489\pi\)
\(422\) −22.0000 −1.07094
\(423\) 10.5000 18.1865i 0.510527 0.884260i
\(424\) 6.00000 0.291386
\(425\) −2.00000 3.46410i −0.0970143 0.168034i
\(426\) 3.46410i 0.167836i
\(427\) 10.5000 18.1865i 0.508131 0.880108i
\(428\) 1.50000 2.59808i 0.0725052 0.125583i
\(429\) −6.00000 3.46410i −0.289683 0.167248i
\(430\) −4.00000 6.92820i −0.192897 0.334108i
\(431\) −30.0000 −1.44505 −0.722525 0.691345i \(-0.757018\pi\)
−0.722525 + 0.691345i \(0.757018\pi\)
\(432\) 4.50000 2.59808i 0.216506 0.125000i
\(433\) 28.0000 1.34559 0.672797 0.739827i \(-0.265093\pi\)
0.672797 + 0.739827i \(0.265093\pi\)
\(434\) 0 0
\(435\) −1.50000 0.866025i −0.0719195 0.0415227i
\(436\) 2.50000 4.33013i 0.119728 0.207375i
\(437\) 12.0000 20.7846i 0.574038 0.994263i
\(438\) 6.92820i 0.331042i
\(439\) −14.0000 24.2487i −0.668184 1.15733i −0.978412 0.206666i \(-0.933739\pi\)
0.310228 0.950662i \(-0.399595\pi\)
\(440\) −6.00000 −0.286039
\(441\) −6.00000 −0.285714
\(442\) −8.00000 −0.380521
\(443\) −7.50000 12.9904i −0.356336 0.617192i 0.631010 0.775775i \(-0.282641\pi\)
−0.987346 + 0.158583i \(0.949307\pi\)
\(444\) 6.00000 3.46410i 0.284747 0.164399i
\(445\) −7.50000 + 12.9904i −0.355534 + 0.615803i
\(446\) 9.50000 16.4545i 0.449838 0.779142i
\(447\) 25.5000 14.7224i 1.20611 0.696347i
\(448\) 10.5000 + 18.1865i 0.496078 + 0.859233i
\(449\) −26.0000 −1.22702 −0.613508 0.789689i \(-0.710242\pi\)
−0.613508 + 0.789689i \(0.710242\pi\)
\(450\) −3.00000 −0.141421
\(451\) −10.0000 −0.470882
\(452\) −4.00000 6.92820i −0.188144 0.325875i
\(453\) 3.46410i 0.162758i
\(454\) 2.00000 3.46410i 0.0938647 0.162578i
\(455\) 3.00000 5.19615i 0.140642 0.243599i
\(456\) −36.0000 20.7846i −1.68585 0.973329i
\(457\) 10.0000 + 17.3205i 0.467780 + 0.810219i 0.999322 0.0368128i \(-0.0117205\pi\)
−0.531542 + 0.847032i \(0.678387\pi\)
\(458\) 15.0000 0.700904
\(459\) 20.7846i 0.970143i
\(460\) 3.00000 0.139876
\(461\) −4.50000 7.79423i −0.209586 0.363013i 0.741998 0.670402i \(-0.233878\pi\)
−0.951584 + 0.307388i \(0.900545\pi\)
\(462\) −9.00000 5.19615i −0.418718 0.241747i
\(463\) 18.0000 31.1769i 0.836531 1.44891i −0.0562469 0.998417i \(-0.517913\pi\)
0.892778 0.450497i \(-0.148753\pi\)
\(464\) −0.500000 + 0.866025i −0.0232119 + 0.0402042i
\(465\) 0 0
\(466\) −12.0000 20.7846i −0.555889 0.962828i
\(467\) 20.0000 0.925490 0.462745 0.886492i \(-0.346865\pi\)
0.462745 + 0.886492i \(0.346865\pi\)
\(468\) 3.00000 5.19615i 0.138675 0.240192i
\(469\) 9.00000 0.415581
\(470\) 3.50000 + 6.06218i 0.161443 + 0.279627i
\(471\) 21.0000 12.1244i 0.967629 0.558661i
\(472\) −21.0000 + 36.3731i −0.966603 + 1.67421i
\(473\) −8.00000 + 13.8564i −0.367840 + 0.637118i
\(474\) −9.00000 + 5.19615i −0.413384 + 0.238667i
\(475\) 4.00000 + 6.92820i 0.183533 + 0.317888i
\(476\) 12.0000 0.550019
\(477\) −3.00000 5.19615i −0.137361 0.237915i
\(478\) −8.00000 −0.365911
\(479\) 9.00000 + 15.5885i 0.411220 + 0.712255i 0.995023 0.0996406i \(-0.0317693\pi\)
−0.583803 + 0.811895i \(0.698436\pi\)
\(480\) 8.66025i 0.395285i
\(481\) −4.00000 + 6.92820i −0.182384 + 0.315899i
\(482\) 5.50000 9.52628i 0.250518 0.433910i
\(483\) 13.5000 + 7.79423i 0.614271 + 0.354650i
\(484\) −3.50000 6.06218i −0.159091 0.275554i
\(485\) −2.00000 −0.0908153
\(486\) −13.5000 7.79423i −0.612372 0.353553i
\(487\) −16.0000 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) 10.5000 + 18.1865i 0.475313 + 0.823266i
\(489\) 6.00000 + 3.46410i 0.271329 + 0.156652i
\(490\) 1.00000 1.73205i 0.0451754 0.0782461i
\(491\) −10.0000 + 17.3205i −0.451294 + 0.781664i −0.998467 0.0553560i \(-0.982371\pi\)
0.547173 + 0.837020i \(0.315704\pi\)
\(492\) 8.66025i 0.390434i
\(493\) 2.00000 + 3.46410i 0.0900755 + 0.156015i
\(494\) 16.0000 0.719874
\(495\) 3.00000 + 5.19615i 0.134840 + 0.233550i
\(496\) 0 0
\(497\) 3.00000 + 5.19615i 0.134568 + 0.233079i
\(498\) 13.5000 7.79423i 0.604949 0.349268i
\(499\) 16.0000 27.7128i 0.716258 1.24060i −0.246214 0.969216i \(-0.579187\pi\)
0.962472 0.271380i \(-0.0874801\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) −13.5000 + 7.79423i −0.603136 + 0.348220i
\(502\) 0 0
\(503\) −7.00000 −0.312115 −0.156057 0.987748i \(-0.549878\pi\)
−0.156057 + 0.987748i \(0.549878\pi\)
\(504\) 13.5000 23.3827i 0.601338 1.04155i
\(505\) 18.0000 0.800989
\(506\) 3.00000 + 5.19615i 0.133366 + 0.230997i
\(507\) 15.5885i 0.692308i
\(508\) −2.50000 + 4.33013i −0.110920 + 0.192118i
\(509\) −21.5000 + 37.2391i −0.952971 + 1.65059i −0.214026 + 0.976828i \(0.568658\pi\)
−0.738945 + 0.673766i \(0.764676\pi\)
\(510\) 6.00000 + 3.46410i 0.265684 + 0.153393i
\(511\) 6.00000 + 10.3923i 0.265424 + 0.459728i
\(512\) −11.0000 −0.486136
\(513\) 41.5692i 1.83533i
\(514\) −6.00000 −0.264649
\(515\) 4.00000 + 6.92820i 0.176261 + 0.305293i
\(516\) −12.0000 6.92820i −0.528271 0.304997i
\(517\) 7.00000 12.1244i 0.307860 0.533229i
\(518\) −6.00000 + 10.3923i −0.263625 + 0.456612i
\(519\) 0 0
\(520\) 3.00000 + 5.19615i 0.131559 + 0.227866i
\(521\) 11.0000 0.481919 0.240959 0.970535i \(-0.422538\pi\)
0.240959 + 0.970535i \(0.422538\pi\)
\(522\) 3.00000 0.131306
\(523\) −29.0000 −1.26808 −0.634041 0.773300i \(-0.718605\pi\)
−0.634041 + 0.773300i \(0.718605\pi\)
\(524\) −3.00000 5.19615i −0.131056 0.226995i
\(525\) −4.50000 + 2.59808i −0.196396 + 0.113389i
\(526\) 8.00000 13.8564i 0.348817 0.604168i
\(527\) 0 0
\(528\) 3.00000 1.73205i 0.130558 0.0753778i
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) 2.00000 0.0868744
\(531\) 42.0000 1.82264
\(532\) −24.0000 −1.04053
\(533\) 5.00000 + 8.66025i 0.216574 + 0.375117i
\(534\) 25.9808i 1.12430i
\(535\) 1.50000 2.59808i 0.0648507 0.112325i
\(536\) −4.50000 + 7.79423i −0.194370 + 0.336659i
\(537\) 3.00000 + 1.73205i 0.129460 + 0.0747435i
\(538\) −12.5000 21.6506i −0.538913 0.933425i
\(539\) −4.00000 −0.172292
\(540\) −4.50000 + 2.59808i −0.193649 + 0.111803i
\(541\) −39.0000 −1.67674 −0.838370 0.545101i \(-0.816491\pi\)
−0.838370 + 0.545101i \(0.816491\pi\)
\(542\) 4.00000 + 6.92820i 0.171815 + 0.297592i
\(543\) 10.5000 + 6.06218i 0.450598 + 0.260153i
\(544\) −10.0000 + 17.3205i −0.428746 + 0.742611i
\(545\) 2.50000 4.33013i 0.107088 0.185482i
\(546\) 10.3923i 0.444750i
\(547\) 14.5000 + 25.1147i 0.619975 + 1.07383i 0.989490 + 0.144604i \(0.0461907\pi\)
−0.369514 + 0.929225i \(0.620476\pi\)
\(548\) −12.0000 −0.512615
\(549\) 10.5000 18.1865i 0.448129 0.776182i
\(550\) −2.00000 −0.0852803
\(551\) −4.00000 6.92820i −0.170406 0.295151i
\(552\) −13.5000 + 7.79423i −0.574598 + 0.331744i
\(553\) −9.00000 + 15.5885i −0.382719 + 0.662889i
\(554\) −6.00000 + 10.3923i −0.254916 + 0.441527i
\(555\) 6.00000 3.46410i 0.254686 0.147043i
\(556\) −8.00000 13.8564i −0.339276 0.587643i
\(557\) −30.0000 −1.27114 −0.635570 0.772043i \(-0.719235\pi\)
−0.635570 + 0.772043i \(0.719235\pi\)
\(558\) 0 0
\(559\) 16.0000 0.676728
\(560\) 1.50000 + 2.59808i 0.0633866 + 0.109789i
\(561\) 13.8564i 0.585018i
\(562\) 7.50000 12.9904i 0.316368 0.547966i
\(563\) 10.5000 18.1865i 0.442522 0.766471i −0.555354 0.831614i \(-0.687417\pi\)
0.997876 + 0.0651433i \(0.0207504\pi\)
\(564\) 10.5000 + 6.06218i 0.442130 + 0.255264i
\(565\) −4.00000 6.92820i −0.168281 0.291472i
\(566\) 21.0000 0.882696
\(567\) −27.0000 −1.13389
\(568\) −6.00000 −0.251754
\(569\) 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i \(-0.126528\pi\)
−0.796266 + 0.604947i \(0.793194\pi\)
\(570\) −12.0000 6.92820i −0.502625 0.290191i
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) 2.00000 3.46410i 0.0836242 0.144841i
\(573\) 13.8564i 0.578860i
\(574\) 7.50000 + 12.9904i 0.313044 + 0.542208i
\(575\) 3.00000 0.125109
\(576\) 10.5000 + 18.1865i 0.437500 + 0.757772i
\(577\) −10.0000 −0.416305 −0.208153 0.978096i \(-0.566745\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(578\) 0.500000 + 0.866025i 0.0207973 + 0.0360219i
\(579\) −15.0000 + 8.66025i −0.623379 + 0.359908i
\(580\) 0.500000 0.866025i 0.0207614 0.0359597i
\(581\) 13.5000 23.3827i 0.560074 0.970077i
\(582\) 3.00000 1.73205i 0.124354 0.0717958i
\(583\) −2.00000 3.46410i −0.0828315 0.143468i
\(584\) −12.0000 −0.496564
\(585\) 3.00000 5.19615i 0.124035 0.214834i
\(586\) 12.0000 0.495715
\(587\) 16.5000 + 28.5788i 0.681028 + 1.17957i 0.974668 + 0.223659i \(0.0718001\pi\)
−0.293640 + 0.955916i \(0.594867\pi\)
\(588\) 3.46410i 0.142857i
\(589\) 0 0
\(590\) −7.00000 + 12.1244i −0.288185 + 0.499152i
\(591\) 18.0000 + 10.3923i 0.740421 + 0.427482i
\(592\) −2.00000 3.46410i −0.0821995 0.142374i
\(593\) 20.0000 0.821302 0.410651 0.911793i \(-0.365302\pi\)
0.410651 + 0.911793i \(0.365302\pi\)
\(594\) −9.00000 5.19615i −0.369274 0.213201i
\(595\) 12.0000 0.491952
\(596\) 8.50000 + 14.7224i 0.348174 + 0.603054i
\(597\) −6.00000 3.46410i −0.245564 0.141776i
\(598\) 3.00000 5.19615i 0.122679 0.212486i
\(599\) 5.00000 8.66025i 0.204294 0.353848i −0.745613 0.666379i \(-0.767843\pi\)
0.949908 + 0.312531i \(0.101177\pi\)
\(600\) 5.19615i 0.212132i
\(601\) −1.00000 1.73205i −0.0407909 0.0706518i 0.844909 0.534910i \(-0.179654\pi\)
−0.885700 + 0.464258i \(0.846321\pi\)
\(602\) 24.0000 0.978167
\(603\) 9.00000 0.366508
\(604\) 2.00000 0.0813788
\(605\) −3.50000 6.06218i −0.142295 0.246463i
\(606\) −27.0000 + 15.5885i −1.09680 + 0.633238i
\(607\) 20.5000 35.5070i 0.832069 1.44119i −0.0643251 0.997929i \(-0.520489\pi\)
0.896394 0.443257i \(-0.146177\pi\)
\(608\) 20.0000 34.6410i 0.811107 1.40488i
\(609\) 4.50000 2.59808i 0.182349 0.105279i
\(610\) 3.50000 + 6.06218i 0.141711 + 0.245450i
\(611\) −14.0000 −0.566379
\(612\) 12.0000 0.485071
\(613\) −44.0000 −1.77714 −0.888572 0.458738i \(-0.848302\pi\)
−0.888572 + 0.458738i \(0.848302\pi\)
\(614\) −3.50000 6.06218i −0.141249 0.244650i
\(615\) 8.66025i 0.349215i
\(616\) 9.00000 15.5885i 0.362620 0.628077i
\(617\) 18.0000 31.1769i 0.724653 1.25514i −0.234464 0.972125i \(-0.575334\pi\)
0.959117 0.283011i \(-0.0913331\pi\)
\(618\) −12.0000 6.92820i −0.482711 0.278693i
\(619\) 2.00000 + 3.46410i 0.0803868 + 0.139234i 0.903416 0.428765i \(-0.141051\pi\)
−0.823029 + 0.567999i \(0.807718\pi\)
\(620\) 0 0
\(621\) 13.5000 + 7.79423i 0.541736 + 0.312772i
\(622\) 0 0
\(623\) −22.5000 38.9711i −0.901443 1.56135i
\(624\) −3.00000 1.73205i −0.120096 0.0693375i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −7.00000 + 12.1244i −0.279776 + 0.484587i
\(627\) 27.7128i 1.10674i
\(628\) 7.00000 + 12.1244i 0.279330 + 0.483814i
\(629\) −16.0000 −0.637962
\(630\) 4.50000 7.79423i 0.179284 0.310530i
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) −9.00000 15.5885i −0.358001 0.620076i
\(633\) −33.0000 + 19.0526i −1.31163 + 0.757271i
\(634\) 17.0000 29.4449i 0.675156 1.16940i
\(635\) −2.50000 + 4.33013i −0.0992095 + 0.171836i
\(636\) 3.00000 1.73205i 0.118958 0.0686803i
\(637\) 2.00000 + 3.46410i 0.0792429 + 0.137253i
\(638\) 2.00000 0.0791808
\(639\) 3.00000 + 5.19615i 0.118678 + 0.205557i
\(640\) 3.00000 0.118585
\(641\) −16.5000 28.5788i −0.651711 1.12880i −0.982708 0.185164i \(-0.940718\pi\)
0.330997 0.943632i \(-0.392615\pi\)
\(642\) 5.19615i 0.205076i
\(643\) 4.50000 7.79423i 0.177463 0.307374i −0.763548 0.645751i \(-0.776544\pi\)
0.941011 + 0.338377i \(0.109878\pi\)
\(644\) −4.50000 + 7.79423i −0.177325 + 0.307136i
\(645\) −12.0000 6.92820i −0.472500 0.272798i
\(646\) 16.0000 + 27.7128i 0.629512 + 1.09035i
\(647\) −17.0000 −0.668339 −0.334169 0.942513i \(-0.608456\pi\)
−0.334169 + 0.942513i \(0.608456\pi\)
\(648\) 13.5000 23.3827i 0.530330 0.918559i
\(649\) 28.0000 1.09910
\(650\) 1.00000 + 1.73205i 0.0392232 + 0.0679366i
\(651\) 0 0
\(652\) −2.00000 + 3.46410i −0.0783260 + 0.135665i
\(653\) 2.00000 3.46410i 0.0782660 0.135561i −0.824236 0.566247i \(-0.808395\pi\)
0.902502 + 0.430686i \(0.141728\pi\)
\(654\) 8.66025i 0.338643i
\(655\) −3.00000 5.19615i −0.117220 0.203030i
\(656\) −5.00000 −0.195217
\(657\) 6.00000 + 10.3923i 0.234082 + 0.405442i
\(658\) −21.0000 −0.818665
\(659\) 4.00000 + 6.92820i 0.155818 + 0.269884i 0.933357 0.358951i \(-0.116865\pi\)
−0.777539 + 0.628835i \(0.783532\pi\)
\(660\) −3.00000 + 1.73205i −0.116775 + 0.0674200i
\(661\) 7.00000 12.1244i 0.272268 0.471583i −0.697174 0.716902i \(-0.745559\pi\)
0.969442 + 0.245319i \(0.0788928\pi\)
\(662\) 3.00000 5.19615i 0.116598 0.201954i
\(663\) −12.0000 + 6.92820i −0.466041 + 0.269069i
\(664\) 13.5000 + 23.3827i 0.523902 + 0.907424i
\(665\) −24.0000 −0.930680
\(666\) −6.00000 + 10.3923i −0.232495 + 0.402694i
\(667\) −3.00000 −0.116160
\(668\) −4.50000 7.79423i −0.174110 0.301568i
\(669\) 32.9090i 1.27233i
\(670\) −1.50000 + 2.59808i −0.0579501 + 0.100372i
\(671\) 7.00000 12.1244i 0.270232 0.468056i
\(672\) 22.5000 + 12.9904i 0.867956 + 0.501115i
\(673\) −3.00000 5.19615i −0.115642 0.200297i 0.802395 0.596794i \(-0.203559\pi\)
−0.918036 + 0.396497i \(0.870226\pi\)
\(674\) −8.00000 −0.308148
\(675\) −4.50000 + 2.59808i −0.173205 + 0.100000i
\(676\) 9.00000 0.346154
\(677\) 21.0000 + 36.3731i 0.807096 + 1.39793i 0.914867 + 0.403755i \(0.132295\pi\)
−0.107772 + 0.994176i \(0.534372\pi\)
\(678\) 12.0000 + 6.92820i 0.460857 + 0.266076i
\(679\) 3.00000 5.19615i 0.115129 0.199410i
\(680\) −6.00000 + 10.3923i −0.230089 + 0.398527i
\(681\) 6.92820i 0.265489i
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) −24.0000 −0.917663
\(685\) −12.0000 −0.458496
\(686\) −7.50000 12.9904i −0.286351 0.495975i
\(687\) 22.5000 12.9904i 0.858429 0.495614i
\(688\) −4.00000 + 6.92820i −0.152499 + 0.264135i
\(689\) −2.00000 + 3.46410i −0.0761939 + 0.131972i
\(690\) −4.50000 + 2.59808i −0.171312 + 0.0989071i
\(691\) 7.00000 + 12.1244i 0.266293 + 0.461232i 0.967901 0.251330i \(-0.0808679\pi\)
−0.701609 + 0.712562i \(0.747535\pi\)
\(692\) 0 0
\(693\) −18.0000 −0.683763
\(694\) 4.00000 0.151838
\(695\) −8.00000 13.8564i −0.303457 0.525603i
\(696\) 5.19615i 0.196960i
\(697\) −10.0000 + 17.3205i −0.378777 + 0.656061i
\(698\) 2.50000 4.33013i 0.0946264 0.163898i
\(699\) −36.0000 20.7846i −1.36165 0.786146i
\(700\) −1.50000 2.59808i −0.0566947 0.0981981i
\(701\) 23.0000 0.868698 0.434349 0.900745i \(-0.356978\pi\)
0.434349 + 0.900745i \(0.356978\pi\)
\(702\) 10.3923i 0.392232i
\(703\) 32.0000 1.20690
\(704\) 7.00000 + 12.1244i 0.263822 + 0.456954i
\(705\) 10.5000 + 6.06218i 0.395453 + 0.228315i
\(706\) −12.0000 + 20.7846i −0.451626 + 0.782239i
\(707\) −27.0000 + 46.7654i −1.01544 + 1.75879i
\(708\) 24.2487i 0.911322i
\(709\) 20.5000 + 35.5070i 0.769894 + 1.33349i 0.937620 + 0.347661i \(0.113024\pi\)
−0.167727 + 0.985834i \(0.553643\pi\)
\(710\) −2.00000 −0.0750587
\(711\) −9.00000 + 15.5885i −0.337526 + 0.584613i
\(712\) 45.0000 1.68645
\(713\) 0 0
\(714\) −18.0000 + 10.3923i −0.673633 + 0.388922i
\(715\) 2.00000 3.46410i 0.0747958 0.129550i
\(716\) −1.00000 + 1.73205i −0.0373718 + 0.0647298i
\(717\) −12.0000 + 6.92820i −0.448148 + 0.258738i
\(718\) −12.0000 20.7846i −0.447836 0.775675i
\(719\) 6.00000 0.223762 0.111881 0.993722i \(-0.464312\pi\)
0.111881 + 0.993722i \(0.464312\pi\)
\(720\) 1.50000 + 2.59808i 0.0559017 + 0.0968246i
\(721\) −24.0000 −0.893807
\(722\) −22.5000 38.9711i −0.837363 1.45036i
\(723\) 19.0526i 0.708572i
\(724\) −3.50000 + 6.06218i −0.130076 + 0.225299i
\(725\) 0.500000 0.866025i 0.0185695 0.0321634i
\(726\) 10.5000 + 6.06218i 0.389692 + 0.224989i
\(727\) −11.5000 19.9186i −0.426511 0.738739i 0.570049 0.821611i \(-0.306924\pi\)
−0.996560 + 0.0828714i \(0.973591\pi\)
\(728\) −18.0000 −0.667124
\(729\) −27.0000 −1.00000
\(730\) −4.00000 −0.148047
\(731\) 16.0000 + 27.7128i 0.591781 + 1.02500i
\(732\) 10.5000 + 6.06218i 0.388091 + 0.224065i
\(733\) 17.0000 29.4449i 0.627909 1.08757i −0.360061 0.932929i \(-0.617244\pi\)
0.987971 0.154642i \(-0.0494225\pi\)
\(734\) −12.0000 + 20.7846i −0.442928 + 0.767174i
\(735\) 3.46410i 0.127775i
\(736\) −7.50000 12.9904i −0.276454 0.478832i
\(737\) 6.00000 0.221013
\(738\) 7.50000 + 12.9904i 0.276079 + 0.478183i
\(739\) −2.00000 −0.0735712 −0.0367856 0.999323i \(-0.511712\pi\)
−0.0367856 + 0.999323i \(0.511712\pi\)
\(740\) 2.00000 + 3.46410i 0.0735215 + 0.127343i
\(741\) 24.0000 13.8564i 0.881662 0.509028i
\(742\) −3.00000 + 5.19615i −0.110133 + 0.190757i
\(743\) 14.5000 25.1147i 0.531953 0.921370i −0.467351 0.884072i \(-0.654791\pi\)
0.999304 0.0372984i \(-0.0118752\pi\)
\(744\) 0 0
\(745\) 8.50000 + 14.7224i 0.311416 + 0.539388i
\(746\) 10.0000 0.366126
\(747\) 13.5000 23.3827i 0.493939 0.855528i
\(748\) 8.00000 0.292509
\(749\) 4.50000 + 7.79423i 0.164426 + 0.284795i
\(750\) 1.73205i 0.0632456i
\(751\) −5.00000 + 8.66025i −0.182453 + 0.316017i −0.942715 0.333599i \(-0.891737\pi\)
0.760263 + 0.649616i \(0.225070\pi\)
\(752\) 3.50000 6.06218i 0.127632 0.221065i
\(753\) 0 0
\(754\) −1.00000 1.73205i −0.0364179 0.0630776i
\(755\) 2.00000 0.0727875
\(756\) 15.5885i 0.566947i
\(757\) −26.0000 −0.944986 −0.472493 0.881334i \(-0.656646\pi\)
−0.472493 + 0.881334i \(0.656646\pi\)
\(758\) 13.0000 + 22.5167i 0.472181 + 0.817842i
\(759\) 9.00000 + 5.19615i 0.326679 + 0.188608i
\(760\) 12.0000 20.7846i 0.435286 0.753937i
\(761\) −7.50000 + 12.9904i −0.271875 + 0.470901i −0.969342 0.245716i \(-0.920977\pi\)
0.697467 + 0.716617i \(0.254310\pi\)
\(762\) 8.66025i 0.313728i
\(763\) 7.50000 + 12.9904i 0.271518 + 0.470283i
\(764\) −8.00000 −0.289430
\(765\) 12.0000 0.433861
\(766\) 36.0000 1.30073
\(767\) −14.0000 24.2487i −0.505511 0.875570i
\(768\) −25.5000 + 14.7224i −0.920152 + 0.531250i
\(769\) −2.50000 + 4.33013i −0.0901523 + 0.156148i −0.907575 0.419890i \(-0.862069\pi\)
0.817423 + 0.576038i \(0.195402\pi\)
\(770\) 3.00000 5.19615i 0.108112 0.187256i
\(771\) −9.00000 + 5.19615i −0.324127 + 0.187135i
\(772\) −5.00000 8.66025i −0.179954 0.311689i
\(773\) −24.0000 −0.863220 −0.431610 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) 24.0000 0.862662
\(775\) 0 0