Properties

Label 114.2.b.c.113.1
Level $114$
Weight $2$
Character 114.113
Analytic conductor $0.910$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 114.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.910294583043\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 113.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 114.113
Dual form 114.2.b.c.113.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} -3.46410i q^{5} +(-1.50000 - 0.866025i) q^{6} +1.00000 q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} -3.46410i q^{5} +(-1.50000 - 0.866025i) q^{6} +1.00000 q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} -3.46410i q^{10} +3.46410i q^{11} +(-1.50000 - 0.866025i) q^{12} +1.73205i q^{13} +1.00000 q^{14} +(-3.00000 + 5.19615i) q^{15} +1.00000 q^{16} -1.73205i q^{17} +(1.50000 + 2.59808i) q^{18} +(-4.00000 - 1.73205i) q^{19} -3.46410i q^{20} +(-1.50000 - 0.866025i) q^{21} +3.46410i q^{22} +5.19615i q^{23} +(-1.50000 - 0.866025i) q^{24} -7.00000 q^{25} +1.73205i q^{26} -5.19615i q^{27} +1.00000 q^{28} +9.00000 q^{29} +(-3.00000 + 5.19615i) q^{30} +10.3923i q^{31} +1.00000 q^{32} +(3.00000 - 5.19615i) q^{33} -1.73205i q^{34} -3.46410i q^{35} +(1.50000 + 2.59808i) q^{36} -6.92820i q^{37} +(-4.00000 - 1.73205i) q^{38} +(1.50000 - 2.59808i) q^{39} -3.46410i q^{40} +(-1.50000 - 0.866025i) q^{42} +2.00000 q^{43} +3.46410i q^{44} +(9.00000 - 5.19615i) q^{45} +5.19615i q^{46} -3.46410i q^{47} +(-1.50000 - 0.866025i) q^{48} -6.00000 q^{49} -7.00000 q^{50} +(-1.50000 + 2.59808i) q^{51} +1.73205i q^{52} -9.00000 q^{53} -5.19615i q^{54} +12.0000 q^{55} +1.00000 q^{56} +(4.50000 + 6.06218i) q^{57} +9.00000 q^{58} -3.00000 q^{59} +(-3.00000 + 5.19615i) q^{60} -8.00000 q^{61} +10.3923i q^{62} +(1.50000 + 2.59808i) q^{63} +1.00000 q^{64} +6.00000 q^{65} +(3.00000 - 5.19615i) q^{66} -8.66025i q^{67} -1.73205i q^{68} +(4.50000 - 7.79423i) q^{69} -3.46410i q^{70} -12.0000 q^{71} +(1.50000 + 2.59808i) q^{72} +11.0000 q^{73} -6.92820i q^{74} +(10.5000 + 6.06218i) q^{75} +(-4.00000 - 1.73205i) q^{76} +3.46410i q^{77} +(1.50000 - 2.59808i) q^{78} -6.92820i q^{79} -3.46410i q^{80} +(-4.50000 + 7.79423i) q^{81} -10.3923i q^{83} +(-1.50000 - 0.866025i) q^{84} -6.00000 q^{85} +2.00000 q^{86} +(-13.5000 - 7.79423i) q^{87} +3.46410i q^{88} +6.00000 q^{89} +(9.00000 - 5.19615i) q^{90} +1.73205i q^{91} +5.19615i q^{92} +(9.00000 - 15.5885i) q^{93} -3.46410i q^{94} +(-6.00000 + 13.8564i) q^{95} +(-1.50000 - 0.866025i) q^{96} +13.8564i q^{97} -6.00000 q^{98} +(-9.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - 3q^{3} + 2q^{4} - 3q^{6} + 2q^{7} + 2q^{8} + 3q^{9} + O(q^{10}) \) \( 2q + 2q^{2} - 3q^{3} + 2q^{4} - 3q^{6} + 2q^{7} + 2q^{8} + 3q^{9} - 3q^{12} + 2q^{14} - 6q^{15} + 2q^{16} + 3q^{18} - 8q^{19} - 3q^{21} - 3q^{24} - 14q^{25} + 2q^{28} + 18q^{29} - 6q^{30} + 2q^{32} + 6q^{33} + 3q^{36} - 8q^{38} + 3q^{39} - 3q^{42} + 4q^{43} + 18q^{45} - 3q^{48} - 12q^{49} - 14q^{50} - 3q^{51} - 18q^{53} + 24q^{55} + 2q^{56} + 9q^{57} + 18q^{58} - 6q^{59} - 6q^{60} - 16q^{61} + 3q^{63} + 2q^{64} + 12q^{65} + 6q^{66} + 9q^{69} - 24q^{71} + 3q^{72} + 22q^{73} + 21q^{75} - 8q^{76} + 3q^{78} - 9q^{81} - 3q^{84} - 12q^{85} + 4q^{86} - 27q^{87} + 12q^{89} + 18q^{90} + 18q^{93} - 12q^{95} - 3q^{96} - 12q^{98} - 18q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(97\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.50000 0.866025i −0.866025 0.500000i
\(4\) 1.00000 0.500000
\(5\) 3.46410i 1.54919i −0.632456 0.774597i \(-0.717953\pi\)
0.632456 0.774597i \(-0.282047\pi\)
\(6\) −1.50000 0.866025i −0.612372 0.353553i
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 3.46410i 1.09545i
\(11\) 3.46410i 1.04447i 0.852803 + 0.522233i \(0.174901\pi\)
−0.852803 + 0.522233i \(0.825099\pi\)
\(12\) −1.50000 0.866025i −0.433013 0.250000i
\(13\) 1.73205i 0.480384i 0.970725 + 0.240192i \(0.0772105\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 1.00000 0.267261
\(15\) −3.00000 + 5.19615i −0.774597 + 1.34164i
\(16\) 1.00000 0.250000
\(17\) 1.73205i 0.420084i −0.977692 0.210042i \(-0.932640\pi\)
0.977692 0.210042i \(-0.0673601\pi\)
\(18\) 1.50000 + 2.59808i 0.353553 + 0.612372i
\(19\) −4.00000 1.73205i −0.917663 0.397360i
\(20\) 3.46410i 0.774597i
\(21\) −1.50000 0.866025i −0.327327 0.188982i
\(22\) 3.46410i 0.738549i
\(23\) 5.19615i 1.08347i 0.840548 + 0.541736i \(0.182233\pi\)
−0.840548 + 0.541736i \(0.817767\pi\)
\(24\) −1.50000 0.866025i −0.306186 0.176777i
\(25\) −7.00000 −1.40000
\(26\) 1.73205i 0.339683i
\(27\) 5.19615i 1.00000i
\(28\) 1.00000 0.188982
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) −3.00000 + 5.19615i −0.547723 + 0.948683i
\(31\) 10.3923i 1.86651i 0.359211 + 0.933257i \(0.383046\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.00000 5.19615i 0.522233 0.904534i
\(34\) 1.73205i 0.297044i
\(35\) 3.46410i 0.585540i
\(36\) 1.50000 + 2.59808i 0.250000 + 0.433013i
\(37\) 6.92820i 1.13899i −0.821995 0.569495i \(-0.807139\pi\)
0.821995 0.569495i \(-0.192861\pi\)
\(38\) −4.00000 1.73205i −0.648886 0.280976i
\(39\) 1.50000 2.59808i 0.240192 0.416025i
\(40\) 3.46410i 0.547723i
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) −1.50000 0.866025i −0.231455 0.133631i
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 3.46410i 0.522233i
\(45\) 9.00000 5.19615i 1.34164 0.774597i
\(46\) 5.19615i 0.766131i
\(47\) 3.46410i 0.505291i −0.967559 0.252646i \(-0.918699\pi\)
0.967559 0.252646i \(-0.0813007\pi\)
\(48\) −1.50000 0.866025i −0.216506 0.125000i
\(49\) −6.00000 −0.857143
\(50\) −7.00000 −0.989949
\(51\) −1.50000 + 2.59808i −0.210042 + 0.363803i
\(52\) 1.73205i 0.240192i
\(53\) −9.00000 −1.23625 −0.618123 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) 5.19615i 0.707107i
\(55\) 12.0000 1.61808
\(56\) 1.00000 0.133631
\(57\) 4.50000 + 6.06218i 0.596040 + 0.802955i
\(58\) 9.00000 1.18176
\(59\) −3.00000 −0.390567 −0.195283 0.980747i \(-0.562563\pi\)
−0.195283 + 0.980747i \(0.562563\pi\)
\(60\) −3.00000 + 5.19615i −0.387298 + 0.670820i
\(61\) −8.00000 −1.02430 −0.512148 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) 10.3923i 1.31982i
\(63\) 1.50000 + 2.59808i 0.188982 + 0.327327i
\(64\) 1.00000 0.125000
\(65\) 6.00000 0.744208
\(66\) 3.00000 5.19615i 0.369274 0.639602i
\(67\) 8.66025i 1.05802i −0.848616 0.529009i \(-0.822564\pi\)
0.848616 0.529009i \(-0.177436\pi\)
\(68\) 1.73205i 0.210042i
\(69\) 4.50000 7.79423i 0.541736 0.938315i
\(70\) 3.46410i 0.414039i
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 1.50000 + 2.59808i 0.176777 + 0.306186i
\(73\) 11.0000 1.28745 0.643726 0.765256i \(-0.277388\pi\)
0.643726 + 0.765256i \(0.277388\pi\)
\(74\) 6.92820i 0.805387i
\(75\) 10.5000 + 6.06218i 1.21244 + 0.700000i
\(76\) −4.00000 1.73205i −0.458831 0.198680i
\(77\) 3.46410i 0.394771i
\(78\) 1.50000 2.59808i 0.169842 0.294174i
\(79\) 6.92820i 0.779484i −0.920924 0.389742i \(-0.872564\pi\)
0.920924 0.389742i \(-0.127436\pi\)
\(80\) 3.46410i 0.387298i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) 10.3923i 1.14070i −0.821401 0.570352i \(-0.806807\pi\)
0.821401 0.570352i \(-0.193193\pi\)
\(84\) −1.50000 0.866025i −0.163663 0.0944911i
\(85\) −6.00000 −0.650791
\(86\) 2.00000 0.215666
\(87\) −13.5000 7.79423i −1.44735 0.835629i
\(88\) 3.46410i 0.369274i
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 9.00000 5.19615i 0.948683 0.547723i
\(91\) 1.73205i 0.181568i
\(92\) 5.19615i 0.541736i
\(93\) 9.00000 15.5885i 0.933257 1.61645i
\(94\) 3.46410i 0.357295i
\(95\) −6.00000 + 13.8564i −0.615587 + 1.42164i
\(96\) −1.50000 0.866025i −0.153093 0.0883883i
\(97\) 13.8564i 1.40690i 0.710742 + 0.703452i \(0.248359\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) −6.00000 −0.606092
\(99\) −9.00000 + 5.19615i −0.904534 + 0.522233i
\(100\) −7.00000 −0.700000
\(101\) 10.3923i 1.03407i 0.855963 + 0.517036i \(0.172965\pi\)
−0.855963 + 0.517036i \(0.827035\pi\)
\(102\) −1.50000 + 2.59808i −0.148522 + 0.257248i
\(103\) 3.46410i 0.341328i −0.985329 0.170664i \(-0.945409\pi\)
0.985329 0.170664i \(-0.0545913\pi\)
\(104\) 1.73205i 0.169842i
\(105\) −3.00000 + 5.19615i −0.292770 + 0.507093i
\(106\) −9.00000 −0.874157
\(107\) 3.00000 0.290021 0.145010 0.989430i \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) 5.19615i 0.500000i
\(109\) 15.5885i 1.49310i 0.665327 + 0.746552i \(0.268292\pi\)
−0.665327 + 0.746552i \(0.731708\pi\)
\(110\) 12.0000 1.14416
\(111\) −6.00000 + 10.3923i −0.569495 + 0.986394i
\(112\) 1.00000 0.0944911
\(113\) −12.0000 −1.12887 −0.564433 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) 4.50000 + 6.06218i 0.421464 + 0.567775i
\(115\) 18.0000 1.67851
\(116\) 9.00000 0.835629
\(117\) −4.50000 + 2.59808i −0.416025 + 0.240192i
\(118\) −3.00000 −0.276172
\(119\) 1.73205i 0.158777i
\(120\) −3.00000 + 5.19615i −0.273861 + 0.474342i
\(121\) −1.00000 −0.0909091
\(122\) −8.00000 −0.724286
\(123\) 0 0
\(124\) 10.3923i 0.933257i
\(125\) 6.92820i 0.619677i
\(126\) 1.50000 + 2.59808i 0.133631 + 0.231455i
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.00000 1.73205i −0.264135 0.152499i
\(130\) 6.00000 0.526235
\(131\) 3.46410i 0.302660i −0.988483 0.151330i \(-0.951644\pi\)
0.988483 0.151330i \(-0.0483556\pi\)
\(132\) 3.00000 5.19615i 0.261116 0.452267i
\(133\) −4.00000 1.73205i −0.346844 0.150188i
\(134\) 8.66025i 0.748132i
\(135\) −18.0000 −1.54919
\(136\) 1.73205i 0.148522i
\(137\) 8.66025i 0.739895i −0.929053 0.369948i \(-0.879376\pi\)
0.929053 0.369948i \(-0.120624\pi\)
\(138\) 4.50000 7.79423i 0.383065 0.663489i
\(139\) −14.0000 −1.18746 −0.593732 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) 3.46410i 0.292770i
\(141\) −3.00000 + 5.19615i −0.252646 + 0.437595i
\(142\) −12.0000 −1.00702
\(143\) −6.00000 −0.501745
\(144\) 1.50000 + 2.59808i 0.125000 + 0.216506i
\(145\) 31.1769i 2.58910i
\(146\) 11.0000 0.910366
\(147\) 9.00000 + 5.19615i 0.742307 + 0.428571i
\(148\) 6.92820i 0.569495i
\(149\) 6.92820i 0.567581i −0.958886 0.283790i \(-0.908408\pi\)
0.958886 0.283790i \(-0.0915919\pi\)
\(150\) 10.5000 + 6.06218i 0.857321 + 0.494975i
\(151\) 3.46410i 0.281905i 0.990016 + 0.140952i \(0.0450164\pi\)
−0.990016 + 0.140952i \(0.954984\pi\)
\(152\) −4.00000 1.73205i −0.324443 0.140488i
\(153\) 4.50000 2.59808i 0.363803 0.210042i
\(154\) 3.46410i 0.279145i
\(155\) 36.0000 2.89159
\(156\) 1.50000 2.59808i 0.120096 0.208013i
\(157\) 4.00000 0.319235 0.159617 0.987179i \(-0.448974\pi\)
0.159617 + 0.987179i \(0.448974\pi\)
\(158\) 6.92820i 0.551178i
\(159\) 13.5000 + 7.79423i 1.07062 + 0.618123i
\(160\) 3.46410i 0.273861i
\(161\) 5.19615i 0.409514i
\(162\) −4.50000 + 7.79423i −0.353553 + 0.612372i
\(163\) 10.0000 0.783260 0.391630 0.920123i \(-0.371911\pi\)
0.391630 + 0.920123i \(0.371911\pi\)
\(164\) 0 0
\(165\) −18.0000 10.3923i −1.40130 0.809040i
\(166\) 10.3923i 0.806599i
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) −1.50000 0.866025i −0.115728 0.0668153i
\(169\) 10.0000 0.769231
\(170\) −6.00000 −0.460179
\(171\) −1.50000 12.9904i −0.114708 0.993399i
\(172\) 2.00000 0.152499
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) −13.5000 7.79423i −1.02343 0.590879i
\(175\) −7.00000 −0.529150
\(176\) 3.46410i 0.261116i
\(177\) 4.50000 + 2.59808i 0.338241 + 0.195283i
\(178\) 6.00000 0.449719
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 9.00000 5.19615i 0.670820 0.387298i
\(181\) 13.8564i 1.02994i 0.857209 + 0.514969i \(0.172197\pi\)
−0.857209 + 0.514969i \(0.827803\pi\)
\(182\) 1.73205i 0.128388i
\(183\) 12.0000 + 6.92820i 0.887066 + 0.512148i
\(184\) 5.19615i 0.383065i
\(185\) −24.0000 −1.76452
\(186\) 9.00000 15.5885i 0.659912 1.14300i
\(187\) 6.00000 0.438763
\(188\) 3.46410i 0.252646i
\(189\) 5.19615i 0.377964i
\(190\) −6.00000 + 13.8564i −0.435286 + 1.00525i
\(191\) 19.0526i 1.37859i −0.724479 0.689297i \(-0.757919\pi\)
0.724479 0.689297i \(-0.242081\pi\)
\(192\) −1.50000 0.866025i −0.108253 0.0625000i
\(193\) 3.46410i 0.249351i 0.992198 + 0.124676i \(0.0397891\pi\)
−0.992198 + 0.124676i \(0.960211\pi\)
\(194\) 13.8564i 0.994832i
\(195\) −9.00000 5.19615i −0.644503 0.372104i
\(196\) −6.00000 −0.428571
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −9.00000 + 5.19615i −0.639602 + 0.369274i
\(199\) 11.0000 0.779769 0.389885 0.920864i \(-0.372515\pi\)
0.389885 + 0.920864i \(0.372515\pi\)
\(200\) −7.00000 −0.494975
\(201\) −7.50000 + 12.9904i −0.529009 + 0.916271i
\(202\) 10.3923i 0.731200i
\(203\) 9.00000 0.631676
\(204\) −1.50000 + 2.59808i −0.105021 + 0.181902i
\(205\) 0 0
\(206\) 3.46410i 0.241355i
\(207\) −13.5000 + 7.79423i −0.938315 + 0.541736i
\(208\) 1.73205i 0.120096i
\(209\) 6.00000 13.8564i 0.415029 0.958468i
\(210\) −3.00000 + 5.19615i −0.207020 + 0.358569i
\(211\) 12.1244i 0.834675i −0.908752 0.417338i \(-0.862963\pi\)
0.908752 0.417338i \(-0.137037\pi\)
\(212\) −9.00000 −0.618123
\(213\) 18.0000 + 10.3923i 1.23334 + 0.712069i
\(214\) 3.00000 0.205076
\(215\) 6.92820i 0.472500i
\(216\) 5.19615i 0.353553i
\(217\) 10.3923i 0.705476i
\(218\) 15.5885i 1.05578i
\(219\) −16.5000 9.52628i −1.11497 0.643726i
\(220\) 12.0000 0.809040
\(221\) 3.00000 0.201802
\(222\) −6.00000 + 10.3923i −0.402694 + 0.697486i
\(223\) 10.3923i 0.695920i −0.937509 0.347960i \(-0.886874\pi\)
0.937509 0.347960i \(-0.113126\pi\)
\(224\) 1.00000 0.0668153
\(225\) −10.5000 18.1865i −0.700000 1.21244i
\(226\) −12.0000 −0.798228
\(227\) −3.00000 −0.199117 −0.0995585 0.995032i \(-0.531743\pi\)
−0.0995585 + 0.995032i \(0.531743\pi\)
\(228\) 4.50000 + 6.06218i 0.298020 + 0.401478i
\(229\) −8.00000 −0.528655 −0.264327 0.964433i \(-0.585150\pi\)
−0.264327 + 0.964433i \(0.585150\pi\)
\(230\) 18.0000 1.18688
\(231\) 3.00000 5.19615i 0.197386 0.341882i
\(232\) 9.00000 0.590879
\(233\) 6.92820i 0.453882i −0.973909 0.226941i \(-0.927128\pi\)
0.973909 0.226941i \(-0.0728724\pi\)
\(234\) −4.50000 + 2.59808i −0.294174 + 0.169842i
\(235\) −12.0000 −0.782794
\(236\) −3.00000 −0.195283
\(237\) −6.00000 + 10.3923i −0.389742 + 0.675053i
\(238\) 1.73205i 0.112272i
\(239\) 12.1244i 0.784259i 0.919910 + 0.392130i \(0.128262\pi\)
−0.919910 + 0.392130i \(0.871738\pi\)
\(240\) −3.00000 + 5.19615i −0.193649 + 0.335410i
\(241\) 13.8564i 0.892570i −0.894891 0.446285i \(-0.852747\pi\)
0.894891 0.446285i \(-0.147253\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 13.5000 7.79423i 0.866025 0.500000i
\(244\) −8.00000 −0.512148
\(245\) 20.7846i 1.32788i
\(246\) 0 0
\(247\) 3.00000 6.92820i 0.190885 0.440831i
\(248\) 10.3923i 0.659912i
\(249\) −9.00000 + 15.5885i −0.570352 + 0.987878i
\(250\) 6.92820i 0.438178i
\(251\) 13.8564i 0.874609i 0.899314 + 0.437304i \(0.144067\pi\)
−0.899314 + 0.437304i \(0.855933\pi\)
\(252\) 1.50000 + 2.59808i 0.0944911 + 0.163663i
\(253\) −18.0000 −1.13165
\(254\) 0 0
\(255\) 9.00000 + 5.19615i 0.563602 + 0.325396i
\(256\) 1.00000 0.0625000
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) −3.00000 1.73205i −0.186772 0.107833i
\(259\) 6.92820i 0.430498i
\(260\) 6.00000 0.372104
\(261\) 13.5000 + 23.3827i 0.835629 + 1.44735i
\(262\) 3.46410i 0.214013i
\(263\) 3.46410i 0.213606i 0.994280 + 0.106803i \(0.0340614\pi\)
−0.994280 + 0.106803i \(0.965939\pi\)
\(264\) 3.00000 5.19615i 0.184637 0.319801i
\(265\) 31.1769i 1.91518i
\(266\) −4.00000 1.73205i −0.245256 0.106199i
\(267\) −9.00000 5.19615i −0.550791 0.317999i
\(268\) 8.66025i 0.529009i
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) −18.0000 −1.09545
\(271\) −1.00000 −0.0607457 −0.0303728 0.999539i \(-0.509669\pi\)
−0.0303728 + 0.999539i \(0.509669\pi\)
\(272\) 1.73205i 0.105021i
\(273\) 1.50000 2.59808i 0.0907841 0.157243i
\(274\) 8.66025i 0.523185i
\(275\) 24.2487i 1.46225i
\(276\) 4.50000 7.79423i 0.270868 0.469157i
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) −14.0000 −0.839664
\(279\) −27.0000 + 15.5885i −1.61645 + 0.933257i
\(280\) 3.46410i 0.207020i
\(281\) −12.0000 −0.715860 −0.357930 0.933748i \(-0.616517\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) −3.00000 + 5.19615i −0.178647 + 0.309426i
\(283\) −10.0000 −0.594438 −0.297219 0.954809i \(-0.596059\pi\)
−0.297219 + 0.954809i \(0.596059\pi\)
\(284\) −12.0000 −0.712069
\(285\) 21.0000 15.5885i 1.24393 0.923381i
\(286\) −6.00000 −0.354787
\(287\) 0 0
\(288\) 1.50000 + 2.59808i 0.0883883 + 0.153093i
\(289\) 14.0000 0.823529
\(290\) 31.1769i 1.83077i
\(291\) 12.0000 20.7846i 0.703452 1.21842i
\(292\) 11.0000 0.643726
\(293\) −21.0000 −1.22683 −0.613417 0.789760i \(-0.710205\pi\)
−0.613417 + 0.789760i \(0.710205\pi\)
\(294\) 9.00000 + 5.19615i 0.524891 + 0.303046i
\(295\) 10.3923i 0.605063i
\(296\) 6.92820i 0.402694i
\(297\) 18.0000 1.04447
\(298\) 6.92820i 0.401340i
\(299\) −9.00000 −0.520483
\(300\) 10.5000 + 6.06218i 0.606218 + 0.350000i
\(301\) 2.00000 0.115278
\(302\) 3.46410i 0.199337i
\(303\) 9.00000 15.5885i 0.517036 0.895533i
\(304\) −4.00000 1.73205i −0.229416 0.0993399i
\(305\) 27.7128i 1.58683i
\(306\) 4.50000 2.59808i 0.257248 0.148522i
\(307\) 10.3923i 0.593120i −0.955014 0.296560i \(-0.904160\pi\)
0.955014 0.296560i \(-0.0958395\pi\)
\(308\) 3.46410i 0.197386i
\(309\) −3.00000 + 5.19615i −0.170664 + 0.295599i
\(310\) 36.0000 2.04466
\(311\) 22.5167i 1.27680i 0.769704 + 0.638401i \(0.220404\pi\)
−0.769704 + 0.638401i \(0.779596\pi\)
\(312\) 1.50000 2.59808i 0.0849208 0.147087i
\(313\) 13.0000 0.734803 0.367402 0.930062i \(-0.380247\pi\)
0.367402 + 0.930062i \(0.380247\pi\)
\(314\) 4.00000 0.225733
\(315\) 9.00000 5.19615i 0.507093 0.292770i
\(316\) 6.92820i 0.389742i
\(317\) 3.00000 0.168497 0.0842484 0.996445i \(-0.473151\pi\)
0.0842484 + 0.996445i \(0.473151\pi\)
\(318\) 13.5000 + 7.79423i 0.757042 + 0.437079i
\(319\) 31.1769i 1.74557i
\(320\) 3.46410i 0.193649i
\(321\) −4.50000 2.59808i −0.251166 0.145010i
\(322\) 5.19615i 0.289570i
\(323\) −3.00000 + 6.92820i −0.166924 + 0.385496i
\(324\) −4.50000 + 7.79423i −0.250000 + 0.433013i
\(325\) 12.1244i 0.672538i
\(326\) 10.0000 0.553849
\(327\) 13.5000 23.3827i 0.746552 1.29307i
\(328\) 0 0
\(329\) 3.46410i 0.190982i
\(330\) −18.0000 10.3923i −0.990867 0.572078i
\(331\) 19.0526i 1.04722i −0.851957 0.523612i \(-0.824584\pi\)
0.851957 0.523612i \(-0.175416\pi\)
\(332\) 10.3923i 0.570352i
\(333\) 18.0000 10.3923i 0.986394 0.569495i
\(334\) 0 0
\(335\) −30.0000 −1.63908
\(336\) −1.50000 0.866025i −0.0818317 0.0472456i
\(337\) 24.2487i 1.32091i −0.750865 0.660456i \(-0.770363\pi\)
0.750865 0.660456i \(-0.229637\pi\)
\(338\) 10.0000 0.543928
\(339\) 18.0000 + 10.3923i 0.977626 + 0.564433i
\(340\) −6.00000 −0.325396
\(341\) −36.0000 −1.94951
\(342\) −1.50000 12.9904i −0.0811107 0.702439i
\(343\) −13.0000 −0.701934
\(344\) 2.00000 0.107833
\(345\) −27.0000 15.5885i −1.45363 0.839254i
\(346\) 6.00000 0.322562
\(347\) 27.7128i 1.48770i 0.668346 + 0.743851i \(0.267003\pi\)
−0.668346 + 0.743851i \(0.732997\pi\)
\(348\) −13.5000 7.79423i −0.723676 0.417815i
\(349\) −28.0000 −1.49881 −0.749403 0.662114i \(-0.769659\pi\)
−0.749403 + 0.662114i \(0.769659\pi\)
\(350\) −7.00000 −0.374166
\(351\) 9.00000 0.480384
\(352\) 3.46410i 0.184637i
\(353\) 25.9808i 1.38282i −0.722464 0.691408i \(-0.756991\pi\)
0.722464 0.691408i \(-0.243009\pi\)
\(354\) 4.50000 + 2.59808i 0.239172 + 0.138086i
\(355\) 41.5692i 2.20627i
\(356\) 6.00000 0.317999
\(357\) −1.50000 + 2.59808i −0.0793884 + 0.137505i
\(358\) 12.0000 0.634220
\(359\) 19.0526i 1.00556i −0.864416 0.502778i \(-0.832311\pi\)
0.864416 0.502778i \(-0.167689\pi\)
\(360\) 9.00000 5.19615i 0.474342 0.273861i
\(361\) 13.0000 + 13.8564i 0.684211 + 0.729285i
\(362\) 13.8564i 0.728277i
\(363\) 1.50000 + 0.866025i 0.0787296 + 0.0454545i
\(364\) 1.73205i 0.0907841i
\(365\) 38.1051i 1.99451i
\(366\) 12.0000 + 6.92820i 0.627250 + 0.362143i
\(367\) 32.0000 1.67039 0.835193 0.549957i \(-0.185356\pi\)
0.835193 + 0.549957i \(0.185356\pi\)
\(368\) 5.19615i 0.270868i
\(369\) 0 0
\(370\) −24.0000 −1.24770
\(371\) −9.00000 −0.467257
\(372\) 9.00000 15.5885i 0.466628 0.808224i
\(373\) 29.4449i 1.52460i 0.647225 + 0.762299i \(0.275929\pi\)
−0.647225 + 0.762299i \(0.724071\pi\)
\(374\) 6.00000 0.310253
\(375\) 6.00000 10.3923i 0.309839 0.536656i
\(376\) 3.46410i 0.178647i
\(377\) 15.5885i 0.802846i
\(378\) 5.19615i 0.267261i
\(379\) 12.1244i 0.622786i −0.950281 0.311393i \(-0.899204\pi\)
0.950281 0.311393i \(-0.100796\pi\)
\(380\) −6.00000 + 13.8564i −0.307794 + 0.710819i
\(381\) 0 0
\(382\) 19.0526i 0.974814i
\(383\) 6.00000 0.306586 0.153293 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) −1.50000 0.866025i −0.0765466 0.0441942i
\(385\) 12.0000 0.611577
\(386\) 3.46410i 0.176318i
\(387\) 3.00000 + 5.19615i 0.152499 + 0.264135i
\(388\) 13.8564i 0.703452i
\(389\) 3.46410i 0.175637i 0.996136 + 0.0878185i \(0.0279895\pi\)
−0.996136 + 0.0878185i \(0.972010\pi\)
\(390\) −9.00000 5.19615i −0.455733 0.263117i
\(391\) 9.00000 0.455150
\(392\) −6.00000 −0.303046
\(393\) −3.00000 + 5.19615i −0.151330 + 0.262111i
\(394\) 0 0
\(395\) −24.0000 −1.20757
\(396\) −9.00000 + 5.19615i −0.452267 + 0.261116i
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) 11.0000 0.551380
\(399\) 4.50000 + 6.06218i 0.225282 + 0.303488i
\(400\) −7.00000 −0.350000
\(401\) 24.0000 1.19850 0.599251 0.800561i \(-0.295465\pi\)
0.599251 + 0.800561i \(0.295465\pi\)
\(402\) −7.50000 + 12.9904i −0.374066 + 0.647901i
\(403\) −18.0000 −0.896644
\(404\) 10.3923i 0.517036i
\(405\) 27.0000 + 15.5885i 1.34164 + 0.774597i
\(406\) 9.00000 0.446663
\(407\) 24.0000 1.18964
\(408\) −1.50000 + 2.59808i −0.0742611 + 0.128624i
\(409\) 38.1051i 1.88418i −0.335365 0.942088i \(-0.608860\pi\)
0.335365 0.942088i \(-0.391140\pi\)
\(410\) 0 0
\(411\) −7.50000 + 12.9904i −0.369948 + 0.640768i
\(412\) 3.46410i 0.170664i
\(413\) −3.00000 −0.147620
\(414\) −13.5000 + 7.79423i −0.663489 + 0.383065i
\(415\) −36.0000 −1.76717
\(416\) 1.73205i 0.0849208i
\(417\) 21.0000 + 12.1244i 1.02837 + 0.593732i
\(418\) 6.00000 13.8564i 0.293470 0.677739i
\(419\) 10.3923i 0.507697i −0.967244 0.253849i \(-0.918303\pi\)
0.967244 0.253849i \(-0.0816965\pi\)
\(420\) −3.00000 + 5.19615i −0.146385 + 0.253546i
\(421\) 12.1244i 0.590905i 0.955357 + 0.295452i \(0.0954704\pi\)
−0.955357 + 0.295452i \(0.904530\pi\)
\(422\) 12.1244i 0.590204i
\(423\) 9.00000 5.19615i 0.437595 0.252646i
\(424\) −9.00000 −0.437079
\(425\) 12.1244i 0.588118i
\(426\) 18.0000 + 10.3923i 0.872103 + 0.503509i
\(427\) −8.00000 −0.387147
\(428\) 3.00000 0.145010
\(429\) 9.00000 + 5.19615i 0.434524 + 0.250873i
\(430\) 6.92820i 0.334108i
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 5.19615i 0.250000i
\(433\) 10.3923i 0.499422i −0.968320 0.249711i \(-0.919664\pi\)
0.968320 0.249711i \(-0.0803357\pi\)
\(434\) 10.3923i 0.498847i
\(435\) −27.0000 + 46.7654i −1.29455 + 2.24223i
\(436\) 15.5885i 0.746552i
\(437\) 9.00000 20.7846i 0.430528 0.994263i
\(438\) −16.5000 9.52628i −0.788400 0.455183i
\(439\) 20.7846i 0.991995i 0.868324 + 0.495998i \(0.165198\pi\)
−0.868324 + 0.495998i \(0.834802\pi\)
\(440\) 12.0000 0.572078
\(441\) −9.00000 15.5885i −0.428571 0.742307i
\(442\) 3.00000 0.142695
\(443\) 17.3205i 0.822922i 0.911427 + 0.411461i \(0.134981\pi\)
−0.911427 + 0.411461i \(0.865019\pi\)
\(444\) −6.00000 + 10.3923i −0.284747 + 0.493197i
\(445\) 20.7846i 0.985285i
\(446\) 10.3923i 0.492090i
\(447\) −6.00000 + 10.3923i −0.283790 + 0.491539i
\(448\) 1.00000 0.0472456
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) −10.5000 18.1865i −0.494975 0.857321i
\(451\) 0 0
\(452\) −12.0000 −0.564433
\(453\) 3.00000 5.19615i 0.140952 0.244137i
\(454\) −3.00000 −0.140797
\(455\) 6.00000 0.281284
\(456\) 4.50000 + 6.06218i 0.210732 + 0.283887i
\(457\) −25.0000 −1.16945 −0.584725 0.811231i \(-0.698798\pi\)
−0.584725 + 0.811231i \(0.698798\pi\)
\(458\) −8.00000 −0.373815
\(459\) −9.00000 −0.420084
\(460\) 18.0000 0.839254
\(461\) 13.8564i 0.645357i 0.946509 + 0.322679i \(0.104583\pi\)
−0.946509 + 0.322679i \(0.895417\pi\)
\(462\) 3.00000 5.19615i 0.139573 0.241747i
\(463\) −40.0000 −1.85896 −0.929479 0.368875i \(-0.879743\pi\)
−0.929479 + 0.368875i \(0.879743\pi\)
\(464\) 9.00000 0.417815
\(465\) −54.0000 31.1769i −2.50419 1.44579i
\(466\) 6.92820i 0.320943i
\(467\) 27.7128i 1.28240i −0.767375 0.641198i \(-0.778438\pi\)
0.767375 0.641198i \(-0.221562\pi\)
\(468\) −4.50000 + 2.59808i −0.208013 + 0.120096i
\(469\) 8.66025i 0.399893i
\(470\) −12.0000 −0.553519
\(471\) −6.00000 3.46410i −0.276465 0.159617i
\(472\) −3.00000 −0.138086
\(473\) 6.92820i 0.318559i
\(474\) −6.00000 + 10.3923i −0.275589 + 0.477334i
\(475\) 28.0000 + 12.1244i 1.28473 + 0.556304i
\(476\) 1.73205i 0.0793884i
\(477\) −13.5000 23.3827i −0.618123 1.07062i
\(478\) 12.1244i 0.554555i
\(479\) 10.3923i 0.474837i 0.971408 + 0.237418i \(0.0763012\pi\)
−0.971408 + 0.237418i \(0.923699\pi\)
\(480\) −3.00000 + 5.19615i −0.136931 + 0.237171i
\(481\) 12.0000 0.547153
\(482\) 13.8564i 0.631142i
\(483\) 4.50000 7.79423i 0.204757 0.354650i
\(484\) −1.00000 −0.0454545
\(485\) 48.0000 2.17957
\(486\) 13.5000 7.79423i 0.612372 0.353553i
\(487\) 3.46410i 0.156973i 0.996915 + 0.0784867i \(0.0250088\pi\)
−0.996915 + 0.0784867i \(0.974991\pi\)
\(488\) −8.00000 −0.362143
\(489\) −15.0000 8.66025i −0.678323 0.391630i
\(490\) 20.7846i 0.938953i
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 15.5885i 0.702069i
\(494\) 3.00000 6.92820i 0.134976 0.311715i
\(495\) 18.0000 + 31.1769i 0.809040 + 1.40130i
\(496\) 10.3923i 0.466628i
\(497\) −12.0000 −0.538274
\(498\) −9.00000 + 15.5885i −0.403300 + 0.698535i
\(499\) 10.0000 0.447661 0.223831 0.974628i \(-0.428144\pi\)
0.223831 + 0.974628i \(0.428144\pi\)
\(500\) 6.92820i 0.309839i
\(501\) 0 0
\(502\) 13.8564i 0.618442i
\(503\) 25.9808i 1.15842i 0.815177 + 0.579212i \(0.196640\pi\)
−0.815177 + 0.579212i \(0.803360\pi\)
\(504\) 1.50000 + 2.59808i 0.0668153 + 0.115728i
\(505\) 36.0000 1.60198
\(506\) −18.0000 −0.800198
\(507\) −15.0000 8.66025i −0.666173 0.384615i
\(508\) 0 0
\(509\) 6.00000 0.265945 0.132973 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) 9.00000 + 5.19615i 0.398527 + 0.230089i
\(511\) 11.0000 0.486611
\(512\) 1.00000 0.0441942
\(513\) −9.00000 + 20.7846i −0.397360 + 0.917663i
\(514\) 6.00000 0.264649
\(515\) −12.0000 −0.528783
\(516\) −3.00000 1.73205i −0.132068 0.0762493i
\(517\) 12.0000 0.527759
\(518\) 6.92820i 0.304408i
\(519\) −9.00000 5.19615i −0.395056 0.228086i
\(520\) 6.00000 0.263117
\(521\) −24.0000 −1.05146 −0.525730 0.850652i \(-0.676208\pi\)
−0.525730 + 0.850652i \(0.676208\pi\)
\(522\) 13.5000 + 23.3827i 0.590879 + 1.02343i
\(523\) 32.9090i 1.43901i 0.694488 + 0.719504i \(0.255631\pi\)
−0.694488 + 0.719504i \(0.744369\pi\)
\(524\) 3.46410i 0.151330i
\(525\) 10.5000 + 6.06218i 0.458258 + 0.264575i
\(526\) 3.46410i 0.151042i
\(527\) 18.0000 0.784092
\(528\) 3.00000 5.19615i 0.130558 0.226134i
\(529\) −4.00000 −0.173913
\(530\) 31.1769i 1.35424i
\(531\) −4.50000 7.79423i −0.195283 0.338241i
\(532\) −4.00000 1.73205i −0.173422 0.0750939i
\(533\) 0 0
\(534\) −9.00000 5.19615i −0.389468 0.224860i
\(535\) 10.3923i 0.449299i
\(536\) 8.66025i 0.374066i
\(537\) −18.0000 10.3923i −0.776757 0.448461i
\(538\) 18.0000 0.776035
\(539\) 20.7846i 0.895257i
\(540\) −18.0000 −0.774597
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) −1.00000 −0.0429537
\(543\) 12.0000 20.7846i 0.514969 0.891953i
\(544\) 1.73205i 0.0742611i
\(545\) 54.0000 2.31311
\(546\) 1.50000 2.59808i 0.0641941 0.111187i
\(547\) 24.2487i 1.03680i −0.855138 0.518400i \(-0.826528\pi\)
0.855138 0.518400i \(-0.173472\pi\)
\(548\) 8.66025i 0.369948i
\(549\) −12.0000 20.7846i −0.512148 0.887066i
\(550\) 24.2487i 1.03397i
\(551\) −36.0000 15.5885i −1.53365 0.664091i
\(552\) 4.50000 7.79423i 0.191533 0.331744i
\(553\) 6.92820i 0.294617i
\(554\) −2.00000 −0.0849719
\(555\) 36.0000 + 20.7846i 1.52811 + 0.882258i
\(556\) −14.0000 −0.593732
\(557\) 45.0333i 1.90812i −0.299611 0.954062i \(-0.596857\pi\)
0.299611 0.954062i \(-0.403143\pi\)
\(558\) −27.0000 + 15.5885i −1.14300 + 0.659912i
\(559\) 3.46410i 0.146516i
\(560\) 3.46410i 0.146385i
\(561\) −9.00000 5.19615i −0.379980 0.219382i
\(562\) −12.0000 −0.506189
\(563\) −24.0000 −1.01148 −0.505740 0.862686i \(-0.668780\pi\)
−0.505740 + 0.862686i \(0.668780\pi\)
\(564\) −3.00000 + 5.19615i −0.126323 + 0.218797i
\(565\) 41.5692i 1.74883i
\(566\) −10.0000 −0.420331
\(567\) −4.50000 + 7.79423i −0.188982 + 0.327327i
\(568\) −12.0000 −0.503509
\(569\) 24.0000 1.00613 0.503066 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) 21.0000 15.5885i 0.879593 0.652929i
\(571\) −16.0000 −0.669579 −0.334790 0.942293i \(-0.608665\pi\)
−0.334790 + 0.942293i \(0.608665\pi\)
\(572\) −6.00000 −0.250873
\(573\) −16.5000 + 28.5788i −0.689297 + 1.19390i
\(574\) 0 0
\(575\) 36.3731i 1.51686i
\(576\) 1.50000 + 2.59808i 0.0625000 + 0.108253i
\(577\) 25.0000 1.04076 0.520382 0.853934i \(-0.325790\pi\)
0.520382 + 0.853934i \(0.325790\pi\)
\(578\) 14.0000 0.582323
\(579\) 3.00000 5.19615i 0.124676 0.215945i
\(580\) 31.1769i 1.29455i
\(581\) 10.3923i 0.431145i
\(582\) 12.0000 20.7846i 0.497416 0.861550i
\(583\) 31.1769i 1.29122i
\(584\) 11.0000 0.455183
\(585\) 9.00000 + 15.5885i 0.372104 + 0.644503i
\(586\) −21.0000 −0.867502
\(587\) 13.8564i 0.571915i 0.958242 + 0.285958i \(0.0923116\pi\)
−0.958242 + 0.285958i \(0.907688\pi\)
\(588\) 9.00000 + 5.19615i 0.371154 + 0.214286i
\(589\) 18.0000 41.5692i 0.741677 1.71283i
\(590\) 10.3923i 0.427844i
\(591\) 0 0
\(592\) 6.92820i 0.284747i
\(593\) 20.7846i 0.853522i 0.904365 + 0.426761i \(0.140345\pi\)
−0.904365 + 0.426761i \(0.859655\pi\)
\(594\) 18.0000 0.738549
\(595\) −6.00000 −0.245976
\(596\) 6.92820i 0.283790i
\(597\) −16.5000 9.52628i −0.675300 0.389885i
\(598\) −9.00000 −0.368037
\(599\) 12.0000 0.490307 0.245153 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) 10.5000 + 6.06218i 0.428661 + 0.247487i
\(601\) 10.3923i 0.423911i −0.977279 0.211955i \(-0.932017\pi\)
0.977279 0.211955i \(-0.0679832\pi\)
\(602\) 2.00000 0.0815139
\(603\) 22.5000 12.9904i 0.916271 0.529009i
\(604\) 3.46410i 0.140952i
\(605\) 3.46410i 0.140836i
\(606\) 9.00000 15.5885i 0.365600 0.633238i
\(607\) 27.7128i 1.12483i −0.826856 0.562414i \(-0.809873\pi\)
0.826856 0.562414i \(-0.190127\pi\)
\(608\) −4.00000 1.73205i −0.162221 0.0702439i
\(609\) −13.5000 7.79423i −0.547048 0.315838i
\(610\) 27.7128i 1.12206i
\(611\) 6.00000 0.242734
\(612\) 4.50000 2.59808i 0.181902 0.105021i
\(613\) −2.00000 −0.0807792 −0.0403896 0.999184i \(-0.512860\pi\)
−0.0403896 + 0.999184i \(0.512860\pi\)
\(614\) 10.3923i 0.419399i
\(615\) 0 0
\(616\) 3.46410i 0.139573i
\(617\) 48.4974i 1.95243i 0.216799 + 0.976216i \(0.430439\pi\)
−0.216799 + 0.976216i \(0.569561\pi\)
\(618\) −3.00000 + 5.19615i −0.120678 + 0.209020i
\(619\) 4.00000 0.160774 0.0803868 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) 36.0000 1.44579
\(621\) 27.0000 1.08347
\(622\) 22.5167i 0.902836i
\(623\) 6.00000 0.240385
\(624\) 1.50000 2.59808i 0.0600481 0.104006i
\(625\) −11.0000 −0.440000
\(626\) 13.0000 0.519584
\(627\) −21.0000 + 15.5885i −0.838659 + 0.622543i
\(628\) 4.00000 0.159617
\(629\) −12.0000 −0.478471
\(630\) 9.00000 5.19615i 0.358569 0.207020i
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) 6.92820i 0.275589i
\(633\) −10.5000 + 18.1865i −0.417338 + 0.722850i
\(634\) 3.00000 0.119145
\(635\) 0 0
\(636\) 13.5000 + 7.79423i 0.535310 + 0.309061i
\(637\) 10.3923i 0.411758i
\(638\) 31.1769i 1.23431i
\(639\) −18.0000 31.1769i −0.712069 1.23334i
\(640\) 3.46410i 0.136931i
\(641\) −30.0000 −1.18493 −0.592464 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) −4.50000 2.59808i −0.177601 0.102538i
\(643\) −28.0000 −1.10421 −0.552106 0.833774i \(-0.686176\pi\)
−0.552106 + 0.833774i \(0.686176\pi\)
\(644\) 5.19615i 0.204757i
\(645\) −6.00000 + 10.3923i −0.236250 + 0.409197i
\(646\) −3.00000 + 6.92820i −0.118033 + 0.272587i
\(647\) 1.73205i 0.0680939i −0.999420 0.0340470i \(-0.989160\pi\)
0.999420 0.0340470i \(-0.0108396\pi\)
\(648\) −4.50000 + 7.79423i −0.176777 + 0.306186i
\(649\) 10.3923i 0.407934i
\(650\) 12.1244i 0.475556i
\(651\) 9.00000 15.5885i 0.352738 0.610960i
\(652\) 10.0000 0.391630
\(653\) 17.3205i 0.677804i 0.940822 + 0.338902i \(0.110055\pi\)
−0.940822 + 0.338902i \(0.889945\pi\)
\(654\) 13.5000 23.3827i 0.527892 0.914335i
\(655\) −12.0000 −0.468879
\(656\) 0 0
\(657\) 16.5000 + 28.5788i 0.643726 + 1.11497i
\(658\) 3.46410i 0.135045i
\(659\) −33.0000 −1.28550 −0.642749 0.766077i \(-0.722206\pi\)
−0.642749 + 0.766077i \(0.722206\pi\)
\(660\) −18.0000 10.3923i −0.700649 0.404520i
\(661\) 22.5167i 0.875797i 0.899025 + 0.437898i \(0.144277\pi\)
−0.899025 + 0.437898i \(0.855723\pi\)
\(662\) 19.0526i 0.740499i
\(663\) −4.50000 2.59808i −0.174766 0.100901i
\(664\) 10.3923i 0.403300i
\(665\) −6.00000 + 13.8564i −0.232670 + 0.537328i
\(666\) 18.0000 10.3923i 0.697486 0.402694i
\(667\) 46.7654i 1.81076i
\(668\) 0 0
\(669\) −9.00000 + 15.5885i −0.347960 + 0.602685i
\(670\) −30.0000 −1.15900
\(671\) 27.7128i 1.06984i
\(672\) −1.50000 0.866025i −0.0578638 0.0334077i
\(673\) 48.4974i 1.86944i 0.355387 + 0.934719i \(0.384349\pi\)
−0.355387 + 0.934719i \(0.615651\pi\)
\(674\) 24.2487i 0.934025i
\(675\) 36.3731i 1.40000i
\(676\) 10.0000 0.384615
\(677\) −15.0000 −0.576497 −0.288248 0.957556i \(-0.593073\pi\)
−0.288248 + 0.957556i \(0.593073\pi\)
\(678\) 18.0000 + 10.3923i 0.691286 + 0.399114i
\(679\) 13.8564i 0.531760i
\(680\) −6.00000 −0.230089
\(681\) 4.50000 + 2.59808i 0.172440 + 0.0995585i
\(682\) −36.0000 −1.37851
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) −1.50000 12.9904i −0.0573539 0.496700i
\(685\) −30.0000 −1.14624
\(686\) −13.0000 −0.496342
\(687\) 12.0000 + 6.92820i 0.457829 + 0.264327i
\(688\) 2.00000 0.0762493
\(689\) 15.5885i 0.593873i
\(690\) −27.0000 15.5885i −1.02787 0.593442i
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) 6.00000 0.228086
\(693\) −9.00000 + 5.19615i −0.341882 + 0.197386i
\(694\) 27.7128i 1.05196i
\(695\) 48.4974i 1.83961i
\(696\) −13.5000 7.79423i −0.511716 0.295439i
\(697\) 0 0
\(698\) −28.0000 −1.05982
\(699\) −6.00000 + 10.3923i −0.226941 + 0.393073i
\(700\) −7.00000 −0.264575
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 9.00000 0.339683
\(703\) −12.0000 + 27.7128i −0.452589 + 1.04521i
\(704\) 3.46410i 0.130558i
\(705\) 18.0000 + 10.3923i 0.677919 + 0.391397i
\(706\) 25.9808i 0.977799i
\(707\) 10.3923i 0.390843i
\(708\) 4.50000 + 2.59808i 0.169120 + 0.0976417i
\(709\) −4.00000 −0.150223 −0.0751116 0.997175i \(-0.523931\pi\)
−0.0751116 + 0.997175i \(0.523931\pi\)
\(710\) 41.5692i 1.56007i
\(711\) 18.0000 10.3923i 0.675053 0.389742i
\(712\) 6.00000 0.224860
\(713\) −54.0000 −2.02232
\(714\) −1.50000 + 2.59808i −0.0561361 + 0.0972306i
\(715\) 20.7846i 0.777300i
\(716\) 12.0000 0.448461
\(717\) 10.5000 18.1865i 0.392130 0.679189i
\(718\) 19.0526i 0.711035i
\(719\) 8.66025i 0.322973i 0.986875 + 0.161486i \(0.0516288\pi\)
−0.986875 + 0.161486i \(0.948371\pi\)
\(720\) 9.00000 5.19615i 0.335410 0.193649i
\(721\) 3.46410i 0.129010i
\(722\) 13.0000 + 13.8564i 0.483810 + 0.515682i
\(723\) −12.0000 + 20.7846i −0.446285 + 0.772988i
\(724\) 13.8564i 0.514969i
\(725\) −63.0000 −2.33976
\(726\) 1.50000 + 0.866025i 0.0556702 + 0.0321412i
\(727\) −7.00000 −0.259616 −0.129808 0.991539i \(-0.541436\pi\)
−0.129808 + 0.991539i \(0.541436\pi\)
\(728\) 1.73205i 0.0641941i
\(729\) −27.0000 −1.00000
\(730\) 38.1051i 1.41033i
\(731\) 3.46410i 0.128124i
\(732\) 12.0000 + 6.92820i 0.443533 + 0.256074i
\(733\) −22.0000 −0.812589 −0.406294 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) 32.0000 1.18114
\(735\) 18.0000 31.1769i 0.663940 1.14998i
\(736\) 5.19615i 0.191533i
\(737\) 30.0000 1.10506
\(738\) 0 0
\(739\) 40.0000 1.47142 0.735712 0.677295i \(-0.236848\pi\)
0.735712 + 0.677295i \(0.236848\pi\)
\(740\) −24.0000 −0.882258
\(741\) −10.5000 + 7.79423i −0.385727 + 0.286328i
\(742\) −9.00000 −0.330400
\(743\) 30.0000 1.10059 0.550297 0.834969i \(-0.314515\pi\)
0.550297 + 0.834969i \(0.314515\pi\)
\(744\) 9.00000 15.5885i 0.329956 0.571501i
\(745\) −24.0000 −0.879292
\(746\) 29.4449i 1.07805i
\(747\) 27.0000 15.5885i 0.987878 0.570352i
\(748\) 6.00000 0.219382
\(749\) 3.00000 0.109618
\(750\) 6.00000 10.3923i 0.219089 0.379473i
\(751\) 6.92820i 0.252814i −0.991978 0.126407i \(-0.959656\pi\)
0.991978 0.126407i \(-0.0403445\pi\)
\(752\) 3.46410i 0.126323i
\(753\) 12.0000 20.7846i 0.437304 0.757433i
\(754\) 15.5885i 0.567698i
\(755\) 12.0000 0.436725
\(756\) 5.19615i 0.188982i
\(757\) 16.0000 0.581530 0.290765 0.956795i \(-0.406090\pi\)
0.290765 + 0.956795i \(0.406090\pi\)
\(758\) 12.1244i 0.440376i
\(759\) 27.0000 + 15.5885i 0.980038 + 0.565825i
\(760\) −6.00000 + 13.8564i −0.217643 + 0.502625i
\(761\) 8.66025i 0.313934i 0.987604 + 0.156967i \(0.0501716\pi\)
−0.987604 + 0.156967i \(0.949828\pi\)
\(762\) 0 0
\(763\) 15.5885i 0.564340i
\(764\) 19.0526i 0.689297i
\(765\) −9.00000 15.5885i −0.325396 0.563602i
\(766\) 6.00000 0.216789
\(767\) 5.19615i 0.187622i
\(768\) −1.50000 0.866025i −0.0541266 0.0312500i
\(769\) 49.0000 1.76699 0.883493 0.468445i \(-0.155186\pi\)
0.883493 + 0.468445i \(0.155186\pi\)
\(770\) 12.0000 0.432450
\(771\) −9.00000 5.19615i −0.324127 0.187135i
\(772\) 3.46410i 0.124676i
\(773\) −3.00000 −0.107903 −0.0539513 0.998544i \(-0.517182\pi\)
−0.0539513 + 0.998544i \(0.517182\pi\)
\(774\) 3.00000 + 5.19615i 0.107833 + 0.186772i
\(775\) 72.7461i 2.61312i
\(776\) 13.8564i 0.497416i
\(777\) −6.00000 + 10.3923i −0.215249 + 0.372822i
\(778\) 3.46410i 0.124194i
\(779\) 0 0
\(780\) −9.00000 5.19615i −0.322252 0.186052i
\(781\) 41.5692i 1.48746i
\(782\) 9.00000 0.321839
\(783\) 46.7654i 1.67126i
\(784\) −6.00000 −0.214286
\(785\) 13.8564i 0.494556i