Properties

Label 114.2.h.d.65.1
Level $114$
Weight $2$
Character 114.65
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.h (of order \(6\), degree \(2\), 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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 65.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 114.65
Dual form 114.2.h.d.107.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} -1.73205i q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.00000 + 1.73205i) q^{5} +(-1.50000 - 0.866025i) q^{6} -2.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} -1.73205i q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.00000 + 1.73205i) q^{5} +(-1.50000 - 0.866025i) q^{6} -2.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +(3.00000 - 1.73205i) q^{10} -1.73205i q^{11} +(-1.50000 + 0.866025i) q^{12} +(-3.00000 + 1.73205i) q^{13} +(-1.00000 + 1.73205i) q^{14} +(3.00000 - 5.19615i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.00000 + 3.46410i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(0.500000 + 4.33013i) q^{19} -3.46410i q^{20} +3.46410i q^{21} +(-1.50000 - 0.866025i) q^{22} +1.73205i q^{24} +(3.50000 + 6.06218i) q^{25} +3.46410i q^{26} +5.19615i q^{27} +(1.00000 + 1.73205i) q^{28} +(-3.00000 - 5.19615i) q^{29} +(-3.00000 - 5.19615i) q^{30} -6.92820i q^{31} +(0.500000 + 0.866025i) q^{32} -3.00000 q^{33} +(6.00000 - 3.46410i) q^{34} +(-6.00000 - 3.46410i) q^{35} +(1.50000 + 2.59808i) q^{36} -6.92820i q^{37} +(4.00000 + 1.73205i) q^{38} +(3.00000 + 5.19615i) q^{39} +(-3.00000 - 1.73205i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(3.00000 + 1.73205i) q^{42} +(-4.00000 + 6.92820i) q^{43} +(-1.50000 + 0.866025i) q^{44} +(-9.00000 - 5.19615i) q^{45} +(-3.00000 + 1.73205i) q^{47} +(1.50000 + 0.866025i) q^{48} -3.00000 q^{49} +7.00000 q^{50} +(6.00000 - 10.3923i) q^{51} +(3.00000 + 1.73205i) q^{52} +(3.00000 + 5.19615i) q^{53} +(4.50000 + 2.59808i) q^{54} +(3.00000 - 5.19615i) q^{55} +2.00000 q^{56} +(7.50000 - 0.866025i) q^{57} -6.00000 q^{58} +(1.50000 - 2.59808i) q^{59} -6.00000 q^{60} +(-5.00000 - 8.66025i) q^{61} +(-6.00000 - 3.46410i) q^{62} +6.00000 q^{63} +1.00000 q^{64} -12.0000 q^{65} +(-1.50000 + 2.59808i) q^{66} +(4.50000 - 2.59808i) q^{67} -6.92820i q^{68} +(-6.00000 + 3.46410i) q^{70} +(3.00000 - 5.19615i) q^{71} +3.00000 q^{72} +(-2.50000 + 4.33013i) q^{73} +(-6.00000 - 3.46410i) q^{74} +(10.5000 - 6.06218i) q^{75} +(3.50000 - 2.59808i) q^{76} +3.46410i q^{77} +6.00000 q^{78} +(-12.0000 - 6.92820i) q^{79} +(-3.00000 + 1.73205i) q^{80} +9.00000 q^{81} +(1.50000 + 2.59808i) q^{82} -5.19615i q^{83} +(3.00000 - 1.73205i) q^{84} +(12.0000 + 20.7846i) q^{85} +(4.00000 + 6.92820i) q^{86} +(-9.00000 + 5.19615i) q^{87} +1.73205i q^{88} +(-3.00000 - 5.19615i) q^{89} +(-9.00000 + 5.19615i) q^{90} +(6.00000 - 3.46410i) q^{91} -12.0000 q^{93} +3.46410i q^{94} +(-6.00000 + 13.8564i) q^{95} +(1.50000 - 0.866025i) q^{96} +(7.50000 + 4.33013i) q^{97} +(-1.50000 + 2.59808i) q^{98} +5.19615i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{4} + 6q^{5} - 3q^{6} - 4q^{7} - 2q^{8} - 6q^{9} + O(q^{10}) \) \( 2q + q^{2} - q^{4} + 6q^{5} - 3q^{6} - 4q^{7} - 2q^{8} - 6q^{9} + 6q^{10} - 3q^{12} - 6q^{13} - 2q^{14} + 6q^{15} - q^{16} + 12q^{17} - 3q^{18} + q^{19} - 3q^{22} + 7q^{25} + 2q^{28} - 6q^{29} - 6q^{30} + q^{32} - 6q^{33} + 12q^{34} - 12q^{35} + 3q^{36} + 8q^{38} + 6q^{39} - 6q^{40} - 3q^{41} + 6q^{42} - 8q^{43} - 3q^{44} - 18q^{45} - 6q^{47} + 3q^{48} - 6q^{49} + 14q^{50} + 12q^{51} + 6q^{52} + 6q^{53} + 9q^{54} + 6q^{55} + 4q^{56} + 15q^{57} - 12q^{58} + 3q^{59} - 12q^{60} - 10q^{61} - 12q^{62} + 12q^{63} + 2q^{64} - 24q^{65} - 3q^{66} + 9q^{67} - 12q^{70} + 6q^{71} + 6q^{72} - 5q^{73} - 12q^{74} + 21q^{75} + 7q^{76} + 12q^{78} - 24q^{79} - 6q^{80} + 18q^{81} + 3q^{82} + 6q^{84} + 24q^{85} + 8q^{86} - 18q^{87} - 6q^{89} - 18q^{90} + 12q^{91} - 24q^{93} - 12q^{95} + 3q^{96} + 15q^{97} - 3q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(77\) \(97\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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
\(3\) 1.73205i 1.00000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 3.00000 + 1.73205i 1.34164 + 0.774597i 0.987048 0.160424i \(-0.0512862\pi\)
0.354593 + 0.935021i \(0.384620\pi\)
\(6\) −1.50000 0.866025i −0.612372 0.353553i
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) −1.00000 −0.353553
\(9\) −3.00000 −1.00000
\(10\) 3.00000 1.73205i 0.948683 0.547723i
\(11\) 1.73205i 0.522233i −0.965307 0.261116i \(-0.915909\pi\)
0.965307 0.261116i \(-0.0840907\pi\)
\(12\) −1.50000 + 0.866025i −0.433013 + 0.250000i
\(13\) −3.00000 + 1.73205i −0.832050 + 0.480384i −0.854554 0.519362i \(-0.826170\pi\)
0.0225039 + 0.999747i \(0.492836\pi\)
\(14\) −1.00000 + 1.73205i −0.267261 + 0.462910i
\(15\) 3.00000 5.19615i 0.774597 1.34164i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 6.00000 + 3.46410i 1.45521 + 0.840168i 0.998770 0.0495842i \(-0.0157896\pi\)
0.456444 + 0.889752i \(0.349123\pi\)
\(18\) −1.50000 + 2.59808i −0.353553 + 0.612372i
\(19\) 0.500000 + 4.33013i 0.114708 + 0.993399i
\(20\) 3.46410i 0.774597i
\(21\) 3.46410i 0.755929i
\(22\) −1.50000 0.866025i −0.319801 0.184637i
\(23\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) 1.73205i 0.353553i
\(25\) 3.50000 + 6.06218i 0.700000 + 1.21244i
\(26\) 3.46410i 0.679366i
\(27\) 5.19615i 1.00000i
\(28\) 1.00000 + 1.73205i 0.188982 + 0.327327i
\(29\) −3.00000 5.19615i −0.557086 0.964901i −0.997738 0.0672232i \(-0.978586\pi\)
0.440652 0.897678i \(-0.354747\pi\)
\(30\) −3.00000 5.19615i −0.547723 0.948683i
\(31\) 6.92820i 1.24434i −0.782881 0.622171i \(-0.786251\pi\)
0.782881 0.622171i \(-0.213749\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −3.00000 −0.522233
\(34\) 6.00000 3.46410i 1.02899 0.594089i
\(35\) −6.00000 3.46410i −1.01419 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
\(39\) 3.00000 + 5.19615i 0.480384 + 0.832050i
\(40\) −3.00000 1.73205i −0.474342 0.273861i
\(41\) −1.50000 + 2.59808i −0.234261 + 0.405751i −0.959058 0.283211i \(-0.908600\pi\)
0.724797 + 0.688963i \(0.241934\pi\)
\(42\) 3.00000 + 1.73205i 0.462910 + 0.267261i
\(43\) −4.00000 + 6.92820i −0.609994 + 1.05654i 0.381246 + 0.924473i \(0.375495\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(44\) −1.50000 + 0.866025i −0.226134 + 0.130558i
\(45\) −9.00000 5.19615i −1.34164 0.774597i
\(46\) 0 0
\(47\) −3.00000 + 1.73205i −0.437595 + 0.252646i −0.702577 0.711608i \(-0.747967\pi\)
0.264982 + 0.964253i \(0.414634\pi\)
\(48\) 1.50000 + 0.866025i 0.216506 + 0.125000i
\(49\) −3.00000 −0.428571
\(50\) 7.00000 0.989949
\(51\) 6.00000 10.3923i 0.840168 1.45521i
\(52\) 3.00000 + 1.73205i 0.416025 + 0.240192i
\(53\) 3.00000 + 5.19615i 0.412082 + 0.713746i 0.995117 0.0987002i \(-0.0314685\pi\)
−0.583036 + 0.812447i \(0.698135\pi\)
\(54\) 4.50000 + 2.59808i 0.612372 + 0.353553i
\(55\) 3.00000 5.19615i 0.404520 0.700649i
\(56\) 2.00000 0.267261
\(57\) 7.50000 0.866025i 0.993399 0.114708i
\(58\) −6.00000 −0.787839
\(59\) 1.50000 2.59808i 0.195283 0.338241i −0.751710 0.659494i \(-0.770771\pi\)
0.946993 + 0.321253i \(0.104104\pi\)
\(60\) −6.00000 −0.774597
\(61\) −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i \(-0.945525\pi\)
0.345207 0.938527i \(-0.387809\pi\)
\(62\) −6.00000 3.46410i −0.762001 0.439941i
\(63\) 6.00000 0.755929
\(64\) 1.00000 0.125000
\(65\) −12.0000 −1.48842
\(66\) −1.50000 + 2.59808i −0.184637 + 0.319801i
\(67\) 4.50000 2.59808i 0.549762 0.317406i −0.199264 0.979946i \(-0.563855\pi\)
0.749026 + 0.662540i \(0.230522\pi\)
\(68\) 6.92820i 0.840168i
\(69\) 0 0
\(70\) −6.00000 + 3.46410i −0.717137 + 0.414039i
\(71\) 3.00000 5.19615i 0.356034 0.616670i −0.631260 0.775571i \(-0.717462\pi\)
0.987294 + 0.158901i \(0.0507952\pi\)
\(72\) 3.00000 0.353553
\(73\) −2.50000 + 4.33013i −0.292603 + 0.506803i −0.974424 0.224716i \(-0.927855\pi\)
0.681822 + 0.731519i \(0.261188\pi\)
\(74\) −6.00000 3.46410i −0.697486 0.402694i
\(75\) 10.5000 6.06218i 1.21244 0.700000i
\(76\) 3.50000 2.59808i 0.401478 0.298020i
\(77\) 3.46410i 0.394771i
\(78\) 6.00000 0.679366
\(79\) −12.0000 6.92820i −1.35011 0.779484i −0.361842 0.932240i \(-0.617852\pi\)
−0.988264 + 0.152756i \(0.951185\pi\)
\(80\) −3.00000 + 1.73205i −0.335410 + 0.193649i
\(81\) 9.00000 1.00000
\(82\) 1.50000 + 2.59808i 0.165647 + 0.286910i
\(83\) 5.19615i 0.570352i −0.958475 0.285176i \(-0.907948\pi\)
0.958475 0.285176i \(-0.0920520\pi\)
\(84\) 3.00000 1.73205i 0.327327 0.188982i
\(85\) 12.0000 + 20.7846i 1.30158 + 2.25441i
\(86\) 4.00000 + 6.92820i 0.431331 + 0.747087i
\(87\) −9.00000 + 5.19615i −0.964901 + 0.557086i
\(88\) 1.73205i 0.184637i
\(89\) −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) −9.00000 + 5.19615i −0.948683 + 0.547723i
\(91\) 6.00000 3.46410i 0.628971 0.363137i
\(92\) 0 0
\(93\) −12.0000 −1.24434
\(94\) 3.46410i 0.357295i
\(95\) −6.00000 + 13.8564i −0.615587 + 1.42164i
\(96\) 1.50000 0.866025i 0.153093 0.0883883i
\(97\) 7.50000 + 4.33013i 0.761510 + 0.439658i 0.829837 0.558005i \(-0.188433\pi\)
−0.0683279 + 0.997663i \(0.521766\pi\)
\(98\) −1.50000 + 2.59808i −0.151523 + 0.262445i
\(99\) 5.19615i 0.522233i
\(100\) 3.50000 6.06218i 0.350000 0.606218i
\(101\) 9.00000 5.19615i 0.895533 0.517036i 0.0197851 0.999804i \(-0.493702\pi\)
0.875748 + 0.482768i \(0.160368\pi\)
\(102\) −6.00000 10.3923i −0.594089 1.02899i
\(103\) 10.3923i 1.02398i 0.858990 + 0.511992i \(0.171092\pi\)
−0.858990 + 0.511992i \(0.828908\pi\)
\(104\) 3.00000 1.73205i 0.294174 0.169842i
\(105\) −6.00000 + 10.3923i −0.585540 + 1.01419i
\(106\) 6.00000 0.582772
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 4.50000 2.59808i 0.433013 0.250000i
\(109\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(110\) −3.00000 5.19615i −0.286039 0.495434i
\(111\) −12.0000 −1.13899
\(112\) 1.00000 1.73205i 0.0944911 0.163663i
\(113\) −15.0000 −1.41108 −0.705541 0.708669i \(-0.749296\pi\)
−0.705541 + 0.708669i \(0.749296\pi\)
\(114\) 3.00000 6.92820i 0.280976 0.648886i
\(115\) 0 0
\(116\) −3.00000 + 5.19615i −0.278543 + 0.482451i
\(117\) 9.00000 5.19615i 0.832050 0.480384i
\(118\) −1.50000 2.59808i −0.138086 0.239172i
\(119\) −12.0000 6.92820i −1.10004 0.635107i
\(120\) −3.00000 + 5.19615i −0.273861 + 0.474342i
\(121\) 8.00000 0.727273
\(122\) −10.0000 −0.905357
\(123\) 4.50000 + 2.59808i 0.405751 + 0.234261i
\(124\) −6.00000 + 3.46410i −0.538816 + 0.311086i
\(125\) 6.92820i 0.619677i
\(126\) 3.00000 5.19615i 0.267261 0.462910i
\(127\) −9.00000 + 5.19615i −0.798621 + 0.461084i −0.842989 0.537931i \(-0.819206\pi\)
0.0443678 + 0.999015i \(0.485873\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 12.0000 + 6.92820i 1.05654 + 0.609994i
\(130\) −6.00000 + 10.3923i −0.526235 + 0.911465i
\(131\) 16.5000 + 9.52628i 1.44161 + 0.832315i 0.997957 0.0638831i \(-0.0203485\pi\)
0.443654 + 0.896198i \(0.353682\pi\)
\(132\) 1.50000 + 2.59808i 0.130558 + 0.226134i
\(133\) −1.00000 8.66025i −0.0867110 0.750939i
\(134\) 5.19615i 0.448879i
\(135\) −9.00000 + 15.5885i −0.774597 + 1.34164i
\(136\) −6.00000 3.46410i −0.514496 0.297044i
\(137\) 1.50000 0.866025i 0.128154 0.0739895i −0.434553 0.900646i \(-0.643094\pi\)
0.562706 + 0.826657i \(0.309760\pi\)
\(138\) 0 0
\(139\) −0.500000 0.866025i −0.0424094 0.0734553i 0.844042 0.536278i \(-0.180170\pi\)
−0.886451 + 0.462822i \(0.846837\pi\)
\(140\) 6.92820i 0.585540i
\(141\) 3.00000 + 5.19615i 0.252646 + 0.437595i
\(142\) −3.00000 5.19615i −0.251754 0.436051i
\(143\) 3.00000 + 5.19615i 0.250873 + 0.434524i
\(144\) 1.50000 2.59808i 0.125000 0.216506i
\(145\) 20.7846i 1.72607i
\(146\) 2.50000 + 4.33013i 0.206901 + 0.358364i
\(147\) 5.19615i 0.428571i
\(148\) −6.00000 + 3.46410i −0.493197 + 0.284747i
\(149\) 6.00000 + 3.46410i 0.491539 + 0.283790i 0.725213 0.688525i \(-0.241741\pi\)
−0.233674 + 0.972315i \(0.575075\pi\)
\(150\) 12.1244i 0.989949i
\(151\) 6.92820i 0.563809i 0.959442 + 0.281905i \(0.0909662\pi\)
−0.959442 + 0.281905i \(0.909034\pi\)
\(152\) −0.500000 4.33013i −0.0405554 0.351220i
\(153\) −18.0000 10.3923i −1.45521 0.840168i
\(154\) 3.00000 + 1.73205i 0.241747 + 0.139573i
\(155\) 12.0000 20.7846i 0.963863 1.66946i
\(156\) 3.00000 5.19615i 0.240192 0.416025i
\(157\) 10.0000 17.3205i 0.798087 1.38233i −0.122774 0.992435i \(-0.539179\pi\)
0.920860 0.389892i \(-0.127488\pi\)
\(158\) −12.0000 + 6.92820i −0.954669 + 0.551178i
\(159\) 9.00000 5.19615i 0.713746 0.412082i
\(160\) 3.46410i 0.273861i
\(161\) 0 0
\(162\) 4.50000 7.79423i 0.353553 0.612372i
\(163\) −17.0000 −1.33154 −0.665771 0.746156i \(-0.731897\pi\)
−0.665771 + 0.746156i \(0.731897\pi\)
\(164\) 3.00000 0.234261
\(165\) −9.00000 5.19615i −0.700649 0.404520i
\(166\) −4.50000 2.59808i −0.349268 0.201650i
\(167\) 6.00000 + 10.3923i 0.464294 + 0.804181i 0.999169 0.0407502i \(-0.0129748\pi\)
−0.534875 + 0.844931i \(0.679641\pi\)
\(168\) 3.46410i 0.267261i
\(169\) −0.500000 + 0.866025i −0.0384615 + 0.0666173i
\(170\) 24.0000 1.84072
\(171\) −1.50000 12.9904i −0.114708 0.993399i
\(172\) 8.00000 0.609994
\(173\) 9.00000 15.5885i 0.684257 1.18517i −0.289412 0.957205i \(-0.593460\pi\)
0.973670 0.227964i \(-0.0732068\pi\)
\(174\) 10.3923i 0.787839i
\(175\) −7.00000 12.1244i −0.529150 0.916515i
\(176\) 1.50000 + 0.866025i 0.113067 + 0.0652791i
\(177\) −4.50000 2.59808i −0.338241 0.195283i
\(178\) −6.00000 −0.449719
\(179\) −3.00000 −0.224231 −0.112115 0.993695i \(-0.535763\pi\)
−0.112115 + 0.993695i \(0.535763\pi\)
\(180\) 10.3923i 0.774597i
\(181\) 6.00000 3.46410i 0.445976 0.257485i −0.260153 0.965567i \(-0.583773\pi\)
0.706129 + 0.708083i \(0.250440\pi\)
\(182\) 6.92820i 0.513553i
\(183\) −15.0000 + 8.66025i −1.10883 + 0.640184i
\(184\) 0 0
\(185\) 12.0000 20.7846i 0.882258 1.52811i
\(186\) −6.00000 + 10.3923i −0.439941 + 0.762001i
\(187\) 6.00000 10.3923i 0.438763 0.759961i
\(188\) 3.00000 + 1.73205i 0.218797 + 0.126323i
\(189\) 10.3923i 0.755929i
\(190\) 9.00000 + 12.1244i 0.652929 + 0.879593i
\(191\) 6.92820i 0.501307i 0.968077 + 0.250654i \(0.0806455\pi\)
−0.968077 + 0.250654i \(0.919354\pi\)
\(192\) 1.73205i 0.125000i
\(193\) 18.0000 + 10.3923i 1.29567 + 0.748054i 0.979653 0.200700i \(-0.0643215\pi\)
0.316016 + 0.948754i \(0.397655\pi\)
\(194\) 7.50000 4.33013i 0.538469 0.310885i
\(195\) 20.7846i 1.48842i
\(196\) 1.50000 + 2.59808i 0.107143 + 0.185577i
\(197\) 20.7846i 1.48084i 0.672143 + 0.740421i \(0.265374\pi\)
−0.672143 + 0.740421i \(0.734626\pi\)
\(198\) 4.50000 + 2.59808i 0.319801 + 0.184637i
\(199\) −7.00000 12.1244i −0.496217 0.859473i 0.503774 0.863836i \(-0.331945\pi\)
−0.999990 + 0.00436292i \(0.998611\pi\)
\(200\) −3.50000 6.06218i −0.247487 0.428661i
\(201\) −4.50000 7.79423i −0.317406 0.549762i
\(202\) 10.3923i 0.731200i
\(203\) 6.00000 + 10.3923i 0.421117 + 0.729397i
\(204\) −12.0000 −0.840168
\(205\) −9.00000 + 5.19615i −0.628587 + 0.362915i
\(206\) 9.00000 + 5.19615i 0.627060 + 0.362033i
\(207\) 0 0
\(208\) 3.46410i 0.240192i
\(209\) 7.50000 0.866025i 0.518786 0.0599042i
\(210\) 6.00000 + 10.3923i 0.414039 + 0.717137i
\(211\) 9.00000 + 5.19615i 0.619586 + 0.357718i 0.776708 0.629861i \(-0.216888\pi\)
−0.157122 + 0.987579i \(0.550222\pi\)
\(212\) 3.00000 5.19615i 0.206041 0.356873i
\(213\) −9.00000 5.19615i −0.616670 0.356034i
\(214\) 6.00000 10.3923i 0.410152 0.710403i
\(215\) −24.0000 + 13.8564i −1.63679 + 0.944999i
\(216\) 5.19615i 0.353553i
\(217\) 13.8564i 0.940634i
\(218\) 0 0
\(219\) 7.50000 + 4.33013i 0.506803 + 0.292603i
\(220\) −6.00000 −0.404520
\(221\) −24.0000 −1.61441
\(222\) −6.00000 + 10.3923i −0.402694 + 0.697486i
\(223\) 12.0000 + 6.92820i 0.803579 + 0.463947i 0.844721 0.535207i \(-0.179766\pi\)
−0.0411418 + 0.999153i \(0.513100\pi\)
\(224\) −1.00000 1.73205i −0.0668153 0.115728i
\(225\) −10.5000 18.1865i −0.700000 1.21244i
\(226\) −7.50000 + 12.9904i −0.498893 + 0.864107i
\(227\) −21.0000 −1.39382 −0.696909 0.717159i \(-0.745442\pi\)
−0.696909 + 0.717159i \(0.745442\pi\)
\(228\) −4.50000 6.06218i −0.298020 0.401478i
\(229\) 4.00000 0.264327 0.132164 0.991228i \(-0.457808\pi\)
0.132164 + 0.991228i \(0.457808\pi\)
\(230\) 0 0
\(231\) 6.00000 0.394771
\(232\) 3.00000 + 5.19615i 0.196960 + 0.341144i
\(233\) 1.50000 + 0.866025i 0.0982683 + 0.0567352i 0.548329 0.836263i \(-0.315264\pi\)
−0.450060 + 0.892998i \(0.648598\pi\)
\(234\) 10.3923i 0.679366i
\(235\) −12.0000 −0.782794
\(236\) −3.00000 −0.195283
\(237\) −12.0000 + 20.7846i −0.779484 + 1.35011i
\(238\) −12.0000 + 6.92820i −0.777844 + 0.449089i
\(239\) 6.92820i 0.448148i 0.974572 + 0.224074i \(0.0719358\pi\)
−0.974572 + 0.224074i \(0.928064\pi\)
\(240\) 3.00000 + 5.19615i 0.193649 + 0.335410i
\(241\) 4.50000 2.59808i 0.289870 0.167357i −0.348013 0.937490i \(-0.613143\pi\)
0.637883 + 0.770133i \(0.279810\pi\)
\(242\) 4.00000 6.92820i 0.257130 0.445362i
\(243\) 15.5885i 1.00000i
\(244\) −5.00000 + 8.66025i −0.320092 + 0.554416i
\(245\) −9.00000 5.19615i −0.574989 0.331970i
\(246\) 4.50000 2.59808i 0.286910 0.165647i
\(247\) −9.00000 12.1244i −0.572656 0.771454i
\(248\) 6.92820i 0.439941i
\(249\) −9.00000 −0.570352
\(250\) 6.00000 + 3.46410i 0.379473 + 0.219089i
\(251\) 7.50000 4.33013i 0.473396 0.273315i −0.244264 0.969709i \(-0.578546\pi\)
0.717660 + 0.696393i \(0.245213\pi\)
\(252\) −3.00000 5.19615i −0.188982 0.327327i
\(253\) 0 0
\(254\) 10.3923i 0.652071i
\(255\) 36.0000 20.7846i 2.25441 1.30158i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −7.50000 12.9904i −0.467837 0.810318i 0.531487 0.847066i \(-0.321633\pi\)
−0.999325 + 0.0367485i \(0.988300\pi\)
\(258\) 12.0000 6.92820i 0.747087 0.431331i
\(259\) 13.8564i 0.860995i
\(260\) 6.00000 + 10.3923i 0.372104 + 0.644503i
\(261\) 9.00000 + 15.5885i 0.557086 + 0.964901i
\(262\) 16.5000 9.52628i 1.01937 0.588536i
\(263\) −3.00000 1.73205i −0.184988 0.106803i 0.404646 0.914473i \(-0.367395\pi\)
−0.589634 + 0.807671i \(0.700728\pi\)
\(264\) 3.00000 0.184637
\(265\) 20.7846i 1.27679i
\(266\) −8.00000 3.46410i −0.490511 0.212398i
\(267\) −9.00000 + 5.19615i −0.550791 + 0.317999i
\(268\) −4.50000 2.59808i −0.274881 0.158703i
\(269\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) 9.00000 + 15.5885i 0.547723 + 0.948683i
\(271\) −13.0000 + 22.5167i −0.789694 + 1.36779i 0.136461 + 0.990645i \(0.456427\pi\)
−0.926155 + 0.377144i \(0.876906\pi\)
\(272\) −6.00000 + 3.46410i −0.363803 + 0.210042i
\(273\) −6.00000 10.3923i −0.363137 0.628971i
\(274\) 1.73205i 0.104637i
\(275\) 10.5000 6.06218i 0.633174 0.365563i
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) −1.00000 −0.0599760
\(279\) 20.7846i 1.24434i
\(280\) 6.00000 + 3.46410i 0.358569 + 0.207020i
\(281\) 7.50000 + 12.9904i 0.447412 + 0.774941i 0.998217 0.0596933i \(-0.0190123\pi\)
−0.550804 + 0.834634i \(0.685679\pi\)
\(282\) 6.00000 0.357295
\(283\) 0.500000 0.866025i 0.0297219 0.0514799i −0.850782 0.525519i \(-0.823871\pi\)
0.880504 + 0.474039i \(0.157204\pi\)
\(284\) −6.00000 −0.356034
\(285\) 24.0000 + 10.3923i 1.42164 + 0.615587i
\(286\) 6.00000 0.354787
\(287\) 3.00000 5.19615i 0.177084 0.306719i
\(288\) −1.50000 2.59808i −0.0883883 0.153093i
\(289\) 15.5000 + 26.8468i 0.911765 + 1.57922i
\(290\) −18.0000 10.3923i −1.05700 0.610257i
\(291\) 7.50000 12.9904i 0.439658 0.761510i
\(292\) 5.00000 0.292603
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 4.50000 + 2.59808i 0.262445 + 0.151523i
\(295\) 9.00000 5.19615i 0.524000 0.302532i
\(296\) 6.92820i 0.402694i
\(297\) 9.00000 0.522233
\(298\) 6.00000 3.46410i 0.347571 0.200670i
\(299\) 0 0
\(300\) −10.5000 6.06218i −0.606218 0.350000i
\(301\) 8.00000 13.8564i 0.461112 0.798670i
\(302\) 6.00000 + 3.46410i 0.345261 + 0.199337i
\(303\) −9.00000 15.5885i −0.517036 0.895533i
\(304\) −4.00000 1.73205i −0.229416 0.0993399i
\(305\) 34.6410i 1.98354i
\(306\) −18.0000 + 10.3923i −1.02899 + 0.594089i
\(307\) −4.50000 2.59808i −0.256829 0.148280i 0.366058 0.930592i \(-0.380707\pi\)
−0.622887 + 0.782312i \(0.714040\pi\)
\(308\) 3.00000 1.73205i 0.170941 0.0986928i
\(309\) 18.0000 1.02398
\(310\) −12.0000 20.7846i −0.681554 1.18049i
\(311\) 13.8564i 0.785725i −0.919597 0.392862i \(-0.871485\pi\)
0.919597 0.392862i \(-0.128515\pi\)
\(312\) −3.00000 5.19615i −0.169842 0.294174i
\(313\) −15.5000 26.8468i −0.876112 1.51747i −0.855574 0.517681i \(-0.826795\pi\)
−0.0205381 0.999789i \(-0.506538\pi\)
\(314\) −10.0000 17.3205i −0.564333 0.977453i
\(315\) 18.0000 + 10.3923i 1.01419 + 0.585540i
\(316\) 13.8564i 0.779484i
\(317\) −3.00000 5.19615i −0.168497 0.291845i 0.769395 0.638774i \(-0.220558\pi\)
−0.937892 + 0.346929i \(0.887225\pi\)
\(318\) 10.3923i 0.582772i
\(319\) −9.00000 + 5.19615i −0.503903 + 0.290929i
\(320\) 3.00000 + 1.73205i 0.167705 + 0.0968246i
\(321\) 20.7846i 1.16008i
\(322\) 0 0
\(323\) −12.0000 + 27.7128i −0.667698 + 1.54198i
\(324\) −4.50000 7.79423i −0.250000 0.433013i
\(325\) −21.0000 12.1244i −1.16487 0.672538i
\(326\) −8.50000 + 14.7224i −0.470771 + 0.815400i
\(327\) 0 0
\(328\) 1.50000 2.59808i 0.0828236 0.143455i
\(329\) 6.00000 3.46410i 0.330791 0.190982i
\(330\) −9.00000 + 5.19615i −0.495434 + 0.286039i
\(331\) 8.66025i 0.476011i −0.971264 0.238005i \(-0.923506\pi\)
0.971264 0.238005i \(-0.0764936\pi\)
\(332\) −4.50000 + 2.59808i −0.246970 + 0.142588i
\(333\) 20.7846i 1.13899i
\(334\) 12.0000 0.656611
\(335\) 18.0000 0.983445
\(336\) −3.00000 1.73205i −0.163663 0.0944911i
\(337\) −22.5000 12.9904i −1.22565 0.707631i −0.259536 0.965734i \(-0.583569\pi\)
−0.966118 + 0.258102i \(0.916903\pi\)
\(338\) 0.500000 + 0.866025i 0.0271964 + 0.0471056i
\(339\) 25.9808i 1.41108i
\(340\) 12.0000 20.7846i 0.650791 1.12720i
\(341\) −12.0000 −0.649836
\(342\) −12.0000 5.19615i −0.648886 0.280976i
\(343\) 20.0000 1.07990
\(344\) 4.00000 6.92820i 0.215666 0.373544i
\(345\) 0 0
\(346\) −9.00000 15.5885i −0.483843 0.838041i
\(347\) 7.50000 + 4.33013i 0.402621 + 0.232453i 0.687614 0.726076i \(-0.258658\pi\)
−0.284993 + 0.958530i \(0.591991\pi\)
\(348\) 9.00000 + 5.19615i 0.482451 + 0.278543i
\(349\) 8.00000 0.428230 0.214115 0.976808i \(-0.431313\pi\)
0.214115 + 0.976808i \(0.431313\pi\)
\(350\) −14.0000 −0.748331
\(351\) −9.00000 15.5885i −0.480384 0.832050i
\(352\) 1.50000 0.866025i 0.0799503 0.0461593i
\(353\) 25.9808i 1.38282i 0.722464 + 0.691408i \(0.243009\pi\)
−0.722464 + 0.691408i \(0.756991\pi\)
\(354\) −4.50000 + 2.59808i −0.239172 + 0.138086i
\(355\) 18.0000 10.3923i 0.955341 0.551566i
\(356\) −3.00000 + 5.19615i −0.159000 + 0.275396i
\(357\) −12.0000 + 20.7846i −0.635107 + 1.10004i
\(358\) −1.50000 + 2.59808i −0.0792775 + 0.137313i
\(359\) −6.00000 3.46410i −0.316668 0.182828i 0.333238 0.942843i \(-0.391859\pi\)
−0.649906 + 0.760014i \(0.725192\pi\)
\(360\) 9.00000 + 5.19615i 0.474342 + 0.273861i
\(361\) −18.5000 + 4.33013i −0.973684 + 0.227901i
\(362\) 6.92820i 0.364138i
\(363\) 13.8564i 0.727273i
\(364\) −6.00000 3.46410i −0.314485 0.181568i
\(365\) −15.0000 + 8.66025i −0.785136 + 0.453298i
\(366\) 17.3205i 0.905357i
\(367\) 2.00000 + 3.46410i 0.104399 + 0.180825i 0.913493 0.406855i \(-0.133375\pi\)
−0.809093 + 0.587680i \(0.800041\pi\)
\(368\) 0 0
\(369\) 4.50000 7.79423i 0.234261 0.405751i
\(370\) −12.0000 20.7846i −0.623850 1.08054i
\(371\) −6.00000 10.3923i −0.311504 0.539542i
\(372\) 6.00000 + 10.3923i 0.311086 + 0.538816i
\(373\) 6.92820i 0.358729i 0.983783 + 0.179364i \(0.0574041\pi\)
−0.983783 + 0.179364i \(0.942596\pi\)
\(374\) −6.00000 10.3923i −0.310253 0.537373i
\(375\) 12.0000 0.619677
\(376\) 3.00000 1.73205i 0.154713 0.0893237i
\(377\) 18.0000 + 10.3923i 0.927047 + 0.535231i
\(378\) −9.00000 5.19615i −0.462910 0.267261i
\(379\) 10.3923i 0.533817i 0.963722 + 0.266908i \(0.0860021\pi\)
−0.963722 + 0.266908i \(0.913998\pi\)
\(380\) 15.0000 1.73205i 0.769484 0.0888523i
\(381\) 9.00000 + 15.5885i 0.461084 + 0.798621i
\(382\) 6.00000 + 3.46410i 0.306987 + 0.177239i
\(383\) −9.00000 + 15.5885i −0.459879 + 0.796533i −0.998954 0.0457244i \(-0.985440\pi\)
0.539076 + 0.842257i \(0.318774\pi\)
\(384\) −1.50000 0.866025i −0.0765466 0.0441942i
\(385\) −6.00000 + 10.3923i −0.305788 + 0.529641i
\(386\) 18.0000 10.3923i 0.916176 0.528954i
\(387\) 12.0000 20.7846i 0.609994 1.05654i
\(388\) 8.66025i 0.439658i
\(389\) 30.0000 17.3205i 1.52106 0.878185i 0.521369 0.853331i \(-0.325421\pi\)
0.999691 0.0248535i \(-0.00791191\pi\)
\(390\) 18.0000 + 10.3923i 0.911465 + 0.526235i
\(391\) 0 0
\(392\) 3.00000 0.151523
\(393\) 16.5000 28.5788i 0.832315 1.44161i
\(394\) 18.0000 + 10.3923i 0.906827 + 0.523557i
\(395\) −24.0000 41.5692i −1.20757 2.09157i
\(396\) 4.50000 2.59808i 0.226134 0.130558i
\(397\) −10.0000 + 17.3205i −0.501886 + 0.869291i 0.498112 + 0.867113i \(0.334027\pi\)
−0.999998 + 0.00217869i \(0.999307\pi\)
\(398\) −14.0000 −0.701757
\(399\) −15.0000 + 1.73205i −0.750939 + 0.0867110i
\(400\) −7.00000 −0.350000
\(401\) −1.50000 + 2.59808i −0.0749064 + 0.129742i −0.901046 0.433724i \(-0.857199\pi\)
0.826139 + 0.563466i \(0.190532\pi\)
\(402\) −9.00000 −0.448879
\(403\) 12.0000 + 20.7846i 0.597763 + 1.03536i
\(404\) −9.00000 5.19615i −0.447767 0.258518i
\(405\) 27.0000 + 15.5885i 1.34164 + 0.774597i
\(406\) 12.0000 0.595550
\(407\) −12.0000 −0.594818
\(408\) −6.00000 + 10.3923i −0.297044 + 0.514496i
\(409\) −16.5000 + 9.52628i −0.815872 + 0.471044i −0.848991 0.528407i \(-0.822789\pi\)
0.0331186 + 0.999451i \(0.489456\pi\)
\(410\) 10.3923i 0.513239i
\(411\) −1.50000 2.59808i −0.0739895 0.128154i
\(412\) 9.00000 5.19615i 0.443398 0.255996i
\(413\) −3.00000 + 5.19615i −0.147620 + 0.255686i
\(414\) 0 0
\(415\) 9.00000 15.5885i 0.441793 0.765207i
\(416\) −3.00000 1.73205i −0.147087 0.0849208i
\(417\) −1.50000 + 0.866025i −0.0734553 + 0.0424094i
\(418\) 3.00000 6.92820i 0.146735 0.338869i
\(419\) 10.3923i 0.507697i 0.967244 + 0.253849i \(0.0816965\pi\)
−0.967244 + 0.253849i \(0.918303\pi\)
\(420\) 12.0000 0.585540
\(421\) −12.0000 6.92820i −0.584844 0.337660i 0.178212 0.983992i \(-0.442969\pi\)
−0.763056 + 0.646332i \(0.776302\pi\)
\(422\) 9.00000 5.19615i 0.438113 0.252945i
\(423\) 9.00000 5.19615i 0.437595 0.252646i
\(424\) −3.00000 5.19615i −0.145693 0.252347i
\(425\) 48.4974i 2.35247i
\(426\) −9.00000 + 5.19615i −0.436051 + 0.251754i
\(427\) 10.0000 + 17.3205i 0.483934 + 0.838198i
\(428\) −6.00000 10.3923i −0.290021 0.502331i
\(429\) 9.00000 5.19615i 0.434524 0.250873i
\(430\) 27.7128i 1.33643i
\(431\) −3.00000 5.19615i −0.144505 0.250290i 0.784683 0.619897i \(-0.212826\pi\)
−0.929188 + 0.369607i \(0.879492\pi\)
\(432\) −4.50000 2.59808i −0.216506 0.125000i
\(433\) −12.0000 + 6.92820i −0.576683 + 0.332948i −0.759814 0.650140i \(-0.774710\pi\)
0.183131 + 0.983089i \(0.441377\pi\)
\(434\) 12.0000 + 6.92820i 0.576018 + 0.332564i
\(435\) −36.0000 −1.72607
\(436\) 0 0
\(437\) 0 0
\(438\) 7.50000 4.33013i 0.358364 0.206901i
\(439\) −12.0000 6.92820i −0.572729 0.330665i 0.185510 0.982642i \(-0.440606\pi\)
−0.758238 + 0.651977i \(0.773940\pi\)
\(440\) −3.00000 + 5.19615i −0.143019 + 0.247717i
\(441\) 9.00000 0.428571
\(442\) −12.0000 + 20.7846i −0.570782 + 0.988623i
\(443\) 10.5000 6.06218i 0.498870 0.288023i −0.229377 0.973338i \(-0.573669\pi\)
0.728247 + 0.685315i \(0.240335\pi\)
\(444\) 6.00000 + 10.3923i 0.284747 + 0.493197i
\(445\) 20.7846i 0.985285i
\(446\) 12.0000 6.92820i 0.568216 0.328060i
\(447\) 6.00000 10.3923i 0.283790 0.491539i
\(448\) −2.00000 −0.0944911
\(449\) −3.00000 −0.141579 −0.0707894 0.997491i \(-0.522552\pi\)
−0.0707894 + 0.997491i \(0.522552\pi\)
\(450\) −21.0000 −0.989949
\(451\) 4.50000 + 2.59808i 0.211897 + 0.122339i
\(452\) 7.50000 + 12.9904i 0.352770 + 0.611016i
\(453\) 12.0000 0.563809
\(454\) −10.5000 + 18.1865i −0.492789 + 0.853536i
\(455\) 24.0000 1.12514
\(456\) −7.50000 + 0.866025i −0.351220 + 0.0405554i
\(457\) 17.0000 0.795226 0.397613 0.917553i \(-0.369839\pi\)
0.397613 + 0.917553i \(0.369839\pi\)
\(458\) 2.00000 3.46410i 0.0934539 0.161867i
\(459\) −18.0000 + 31.1769i −0.840168 + 1.45521i
\(460\) 0 0
\(461\) −21.0000 12.1244i −0.978068 0.564688i −0.0763814 0.997079i \(-0.524337\pi\)
−0.901686 + 0.432391i \(0.857670\pi\)
\(462\) 3.00000 5.19615i 0.139573 0.241747i
\(463\) 14.0000 0.650635 0.325318 0.945605i \(-0.394529\pi\)
0.325318 + 0.945605i \(0.394529\pi\)
\(464\) 6.00000 0.278543
\(465\) −36.0000 20.7846i −1.66946 0.963863i
\(466\) 1.50000 0.866025i 0.0694862 0.0401179i
\(467\) 12.1244i 0.561048i −0.959847 0.280524i \(-0.909492\pi\)
0.959847 0.280524i \(-0.0905083\pi\)
\(468\) −9.00000 5.19615i −0.416025 0.240192i
\(469\) −9.00000 + 5.19615i −0.415581 + 0.239936i
\(470\) −6.00000 + 10.3923i −0.276759 + 0.479361i
\(471\) −30.0000 17.3205i −1.38233 0.798087i
\(472\) −1.50000 + 2.59808i −0.0690431 + 0.119586i
\(473\) 12.0000 + 6.92820i 0.551761 + 0.318559i
\(474\) 12.0000 + 20.7846i 0.551178 + 0.954669i
\(475\) −24.5000 + 18.1865i −1.12414 + 0.834455i
\(476\) 13.8564i 0.635107i
\(477\) −9.00000 15.5885i −0.412082 0.713746i
\(478\) 6.00000 + 3.46410i 0.274434 + 0.158444i
\(479\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(480\) 6.00000 0.273861
\(481\) 12.0000 + 20.7846i 0.547153 + 0.947697i
\(482\) 5.19615i 0.236678i
\(483\) 0 0
\(484\) −4.00000 6.92820i −0.181818 0.314918i
\(485\) 15.0000 + 25.9808i 0.681115 + 1.17973i
\(486\) −13.5000 7.79423i −0.612372 0.353553i
\(487\) 6.92820i 0.313947i 0.987603 + 0.156973i \(0.0501737\pi\)
−0.987603 + 0.156973i \(0.949826\pi\)
\(488\) 5.00000 + 8.66025i 0.226339 + 0.392031i
\(489\) 29.4449i 1.33154i
\(490\) −9.00000 + 5.19615i −0.406579 + 0.234738i
\(491\) −27.0000 15.5885i −1.21849 0.703497i −0.253897 0.967231i \(-0.581713\pi\)
−0.964595 + 0.263734i \(0.915046\pi\)
\(492\) 5.19615i 0.234261i
\(493\) 41.5692i 1.87218i
\(494\) −15.0000 + 1.73205i −0.674882 + 0.0779287i
\(495\) −9.00000 + 15.5885i −0.404520 + 0.700649i
\(496\) 6.00000 + 3.46410i 0.269408 + 0.155543i
\(497\) −6.00000 + 10.3923i −0.269137 + 0.466159i
\(498\) −4.50000 + 7.79423i −0.201650 + 0.349268i
\(499\) 20.5000 35.5070i 0.917706 1.58951i 0.114816 0.993387i \(-0.463372\pi\)
0.802890 0.596127i \(-0.203294\pi\)
\(500\) 6.00000 3.46410i 0.268328 0.154919i
\(501\) 18.0000 10.3923i 0.804181 0.464294i
\(502\) 8.66025i 0.386526i
\(503\) 18.0000 10.3923i 0.802580 0.463370i −0.0417923 0.999126i \(-0.513307\pi\)
0.844373 + 0.535756i \(0.179973\pi\)
\(504\) −6.00000 −0.267261
\(505\) 36.0000 1.60198
\(506\) 0 0
\(507\) 1.50000 + 0.866025i 0.0666173 + 0.0384615i
\(508\) 9.00000 + 5.19615i 0.399310 + 0.230542i
\(509\) −12.0000 20.7846i −0.531891 0.921262i −0.999307 0.0372243i \(-0.988148\pi\)
0.467416 0.884037i \(-0.345185\pi\)
\(510\) 41.5692i 1.84072i
\(511\) 5.00000 8.66025i 0.221187 0.383107i
\(512\) −1.00000 −0.0441942
\(513\) −22.5000 + 2.59808i −0.993399 + 0.114708i
\(514\) −15.0000 −0.661622
\(515\) −18.0000 + 31.1769i −0.793175 + 1.37382i
\(516\) 13.8564i 0.609994i
\(517\) 3.00000 + 5.19615i 0.131940 + 0.228527i
\(518\) 12.0000 + 6.92820i 0.527250 + 0.304408i
\(519\) −27.0000 15.5885i −1.18517 0.684257i
\(520\) 12.0000 0.526235
\(521\) 21.0000 0.920027 0.460013 0.887912i \(-0.347845\pi\)
0.460013 + 0.887912i \(0.347845\pi\)
\(522\) 18.0000 0.787839
\(523\) 15.0000 8.66025i 0.655904 0.378686i −0.134810 0.990871i \(-0.543043\pi\)
0.790715 + 0.612185i \(0.209709\pi\)
\(524\) 19.0526i 0.832315i
\(525\) −21.0000 + 12.1244i −0.916515 + 0.529150i
\(526\) −3.00000 + 1.73205i −0.130806 + 0.0755210i
\(527\) 24.0000 41.5692i 1.04546 1.81078i
\(528\) 1.50000 2.59808i 0.0652791 0.113067i
\(529\) −11.5000 + 19.9186i −0.500000 + 0.866025i
\(530\) 18.0000 + 10.3923i 0.781870 + 0.451413i
\(531\) −4.50000 + 7.79423i −0.195283 + 0.338241i
\(532\) −7.00000 + 5.19615i −0.303488 + 0.225282i
\(533\) 10.3923i 0.450141i
\(534\) 10.3923i 0.449719i
\(535\) 36.0000 + 20.7846i 1.55642 + 0.898597i
\(536\) −4.50000 + 2.59808i −0.194370 + 0.112220i
\(537\) 5.19615i 0.224231i
\(538\) 0 0
\(539\) 5.19615i 0.223814i
\(540\) 18.0000 0.774597
\(541\) −10.0000 17.3205i −0.429934 0.744667i 0.566933 0.823764i \(-0.308130\pi\)
−0.996867 + 0.0790969i \(0.974796\pi\)
\(542\) 13.0000 + 22.5167i 0.558398 + 0.967173i
\(543\) −6.00000 10.3923i −0.257485 0.445976i
\(544\) 6.92820i 0.297044i
\(545\) 0 0
\(546\) −12.0000 −0.513553
\(547\) −21.0000 + 12.1244i −0.897895 + 0.518400i −0.876517 0.481371i \(-0.840139\pi\)
−0.0213785 + 0.999771i \(0.506805\pi\)
\(548\) −1.50000 0.866025i −0.0640768 0.0369948i
\(549\) 15.0000 + 25.9808i 0.640184 + 1.10883i
\(550\) 12.1244i 0.516984i
\(551\) 21.0000 15.5885i 0.894630 0.664091i
\(552\) 0 0
\(553\) 24.0000 + 13.8564i 1.02058 + 0.589234i
\(554\) −1.00000 + 1.73205i −0.0424859 + 0.0735878i
\(555\) −36.0000 20.7846i −1.52811 0.882258i
\(556\) −0.500000 + 0.866025i −0.0212047 + 0.0367277i
\(557\) −12.0000 + 6.92820i −0.508456 + 0.293557i −0.732199 0.681091i \(-0.761506\pi\)
0.223743 + 0.974648i \(0.428173\pi\)
\(558\) 18.0000 + 10.3923i 0.762001 + 0.439941i
\(559\) 27.7128i 1.17213i
\(560\) 6.00000 3.46410i 0.253546 0.146385i
\(561\) −18.0000 10.3923i −0.759961 0.438763i
\(562\) 15.0000 0.632737
\(563\) 21.0000 0.885044 0.442522 0.896758i \(-0.354084\pi\)
0.442522 + 0.896758i \(0.354084\pi\)
\(564\) 3.00000 5.19615i 0.126323 0.218797i
\(565\) −45.0000 25.9808i −1.89316 1.09302i
\(566\) −0.500000 0.866025i −0.0210166 0.0364018i
\(567\) −18.0000 −0.755929
\(568\) −3.00000 + 5.19615i −0.125877 + 0.218026i
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 21.0000 15.5885i 0.879593 0.652929i
\(571\) −43.0000 −1.79949 −0.899747 0.436412i \(-0.856249\pi\)
−0.899747 + 0.436412i \(0.856249\pi\)
\(572\) 3.00000 5.19615i 0.125436 0.217262i
\(573\) 12.0000 0.501307
\(574\) −3.00000 5.19615i −0.125218 0.216883i
\(575\) 0 0
\(576\) −3.00000 −0.125000
\(577\) −29.0000 −1.20729 −0.603643 0.797255i \(-0.706285\pi\)
−0.603643 + 0.797255i \(0.706285\pi\)
\(578\) 31.0000 1.28943
\(579\) 18.0000 31.1769i 0.748054 1.29567i
\(580\) −18.0000 + 10.3923i −0.747409 + 0.431517i
\(581\) 10.3923i 0.431145i
\(582\) −7.50000 12.9904i −0.310885 0.538469i
\(583\) 9.00000 5.19615i 0.372742 0.215203i
\(584\) 2.50000 4.33013i 0.103451 0.179182i
\(585\) 36.0000 1.48842
\(586\) 3.00000 5.19615i 0.123929 0.214651i
\(587\) 33.0000 + 19.0526i 1.36206 + 0.786383i 0.989897 0.141786i \(-0.0452845\pi\)
0.372158 + 0.928169i \(0.378618\pi\)
\(588\) 4.50000 2.59808i 0.185577 0.107143i
\(589\) 30.0000 3.46410i 1.23613 0.142736i
\(590\) 10.3923i 0.427844i
\(591\) 36.0000 1.48084
\(592\) 6.00000 + 3.46410i 0.246598 + 0.142374i
\(593\) −22.5000 + 12.9904i −0.923964 + 0.533451i −0.884898 0.465786i \(-0.845772\pi\)
−0.0390666 + 0.999237i \(0.512438\pi\)
\(594\) 4.50000 7.79423i 0.184637 0.319801i
\(595\) −24.0000 41.5692i −0.983904 1.70417i
\(596\) 6.92820i 0.283790i
\(597\) −21.0000 + 12.1244i −0.859473 + 0.496217i
\(598\) 0 0
\(599\) −18.0000 31.1769i −0.735460 1.27385i −0.954521 0.298143i \(-0.903633\pi\)
0.219061 0.975711i \(-0.429701\pi\)
\(600\) −10.5000 + 6.06218i −0.428661 + 0.247487i
\(601\) 8.66025i 0.353259i −0.984277 0.176630i \(-0.943481\pi\)
0.984277 0.176630i \(-0.0565195\pi\)
\(602\) −8.00000 13.8564i −0.326056 0.564745i
\(603\) −13.5000 + 7.79423i −0.549762 + 0.317406i
\(604\) 6.00000 3.46410i 0.244137 0.140952i
\(605\) 24.0000 + 13.8564i 0.975739 + 0.563343i
\(606\) −18.0000 −0.731200
\(607\) 31.1769i 1.26543i 0.774384 + 0.632716i \(0.218060\pi\)
−0.774384 + 0.632716i \(0.781940\pi\)
\(608\) −3.50000 + 2.59808i −0.141944 + 0.105366i
\(609\) 18.0000 10.3923i 0.729397 0.421117i
\(610\) −30.0000 17.3205i −1.21466 0.701287i
\(611\) 6.00000 10.3923i 0.242734 0.420428i
\(612\) 20.7846i 0.840168i
\(613\) −17.0000 + 29.4449i −0.686624 + 1.18927i 0.286300 + 0.958140i \(0.407575\pi\)
−0.972924 + 0.231127i \(0.925759\pi\)
\(614\) −4.50000 + 2.59808i −0.181605 + 0.104850i
\(615\) 9.00000 + 15.5885i 0.362915 + 0.628587i
\(616\) 3.46410i 0.139573i
\(617\) 1.50000 0.866025i 0.0603877 0.0348649i −0.469502 0.882931i \(-0.655567\pi\)
0.529890 + 0.848066i \(0.322233\pi\)
\(618\) 9.00000 15.5885i 0.362033 0.627060i
\(619\) 40.0000 1.60774 0.803868 0.594808i \(-0.202772\pi\)
0.803868 + 0.594808i \(0.202772\pi\)
\(620\) −24.0000 −0.963863
\(621\) 0 0
\(622\) −12.0000 6.92820i −0.481156 0.277796i
\(623\) 6.00000 + 10.3923i 0.240385 + 0.416359i
\(624\) −6.00000 −0.240192
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) −31.0000 −1.23901
\(627\) −1.50000 12.9904i −0.0599042 0.518786i
\(628\) −20.0000 −0.798087
\(629\) 24.0000 41.5692i 0.956943 1.65747i
\(630\) 18.0000 10.3923i 0.717137 0.414039i
\(631\) 1.00000 + 1.73205i 0.0398094 + 0.0689519i 0.885244 0.465128i \(-0.153992\pi\)
−0.845434 + 0.534080i \(0.820658\pi\)
\(632\) 12.0000 + 6.92820i 0.477334 + 0.275589i
\(633\) 9.00000 15.5885i 0.357718 0.619586i
\(634\) −6.00000 −0.238290
\(635\) −36.0000 −1.42862
\(636\) −9.00000 5.19615i −0.356873 0.206041i
\(637\) 9.00000 5.19615i 0.356593 0.205879i
\(638\) 10.3923i 0.411435i
\(639\) −9.00000 + 15.5885i −0.356034 + 0.616670i
\(640\) 3.00000 1.73205i 0.118585 0.0684653i
\(641\) −22.5000 + 38.9711i −0.888697 + 1.53927i −0.0472793 + 0.998882i \(0.515055\pi\)
−0.841417 + 0.540386i \(0.818278\pi\)
\(642\) −18.0000 10.3923i −0.710403 0.410152i
\(643\) 24.5000 42.4352i 0.966186 1.67348i 0.259791 0.965665i \(-0.416346\pi\)
0.706395 0.707818i \(-0.250320\pi\)
\(644\) 0 0
\(645\) 24.0000 + 41.5692i 0.944999 + 1.63679i
\(646\) 18.0000 + 24.2487i 0.708201 + 0.954053i
\(647\) 24.2487i 0.953315i 0.879089 + 0.476658i \(0.158152\pi\)
−0.879089 + 0.476658i \(0.841848\pi\)
\(648\) −9.00000 −0.353553
\(649\) −4.50000 2.59808i −0.176640 0.101983i
\(650\) −21.0000 + 12.1244i −0.823688 + 0.475556i
\(651\) 24.0000 0.940634
\(652\) 8.50000 + 14.7224i 0.332886 + 0.576575i
\(653\) 6.92820i 0.271122i 0.990769 + 0.135561i \(0.0432836\pi\)
−0.990769 + 0.135561i \(0.956716\pi\)
\(654\) 0 0
\(655\) 33.0000 + 57.1577i 1.28942 + 2.23334i
\(656\) −1.50000 2.59808i −0.0585652 0.101438i
\(657\) 7.50000 12.9904i 0.292603 0.506803i
\(658\) 6.92820i 0.270089i
\(659\) 18.0000 + 31.1769i 0.701180 + 1.21448i 0.968052 + 0.250748i \(0.0806766\pi\)
−0.266872 + 0.963732i \(0.585990\pi\)
\(660\) 10.3923i 0.404520i
\(661\) −33.0000 + 19.0526i −1.28355 + 0.741059i −0.977496 0.210955i \(-0.932343\pi\)
−0.306055 + 0.952014i \(0.599009\pi\)
\(662\) −7.50000 4.33013i −0.291496 0.168295i
\(663\) 41.5692i 1.61441i
\(664\) 5.19615i 0.201650i
\(665\) 12.0000 27.7128i 0.465340 1.07466i
\(666\) 18.0000 + 10.3923i 0.697486 + 0.402694i
\(667\) 0 0
\(668\) 6.00000 10.3923i 0.232147 0.402090i
\(669\) 12.0000 20.7846i 0.463947 0.803579i
\(670\) 9.00000 15.5885i 0.347700 0.602235i
\(671\) −15.0000 + 8.66025i −0.579069 + 0.334325i
\(672\) −3.00000 + 1.73205i −0.115728 + 0.0668153i
\(673\) 20.7846i 0.801188i −0.916256 0.400594i \(-0.868804\pi\)
0.916256 0.400594i \(-0.131196\pi\)
\(674\) −22.5000 + 12.9904i −0.866668 + 0.500371i
\(675\) −31.5000 + 18.1865i −1.21244 + 0.700000i
\(676\) 1.00000 0.0384615
\(677\) −42.0000 −1.61419 −0.807096 0.590421i \(-0.798962\pi\)
−0.807096 + 0.590421i \(0.798962\pi\)
\(678\) 22.5000 + 12.9904i 0.864107 + 0.498893i
\(679\) −15.0000 8.66025i −0.575647 0.332350i
\(680\) −12.0000 20.7846i −0.460179 0.797053i
\(681\) 36.3731i 1.39382i
\(682\) −6.00000 + 10.3923i −0.229752 + 0.397942i
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) −10.5000 + 7.79423i −0.401478 + 0.298020i
\(685\) 6.00000 0.229248
\(686\) 10.0000 17.3205i 0.381802 0.661300i
\(687\) 6.92820i 0.264327i
\(688\) −4.00000 6.92820i −0.152499 0.264135i
\(689\) −18.0000 10.3923i −0.685745 0.395915i
\(690\) 0 0
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) −18.0000 −0.684257
\(693\) 10.3923i 0.394771i
\(694\) 7.50000 4.33013i 0.284696 0.164369i
\(695\) 3.46410i 0.131401i
\(696\) 9.00000 5.19615i 0.341144 0.196960i
\(697\) −18.0000 + 10.3923i −0.681799 + 0.393637i
\(698\) 4.00000 6.92820i 0.151402 0.262236i
\(699\) 1.50000 2.59808i 0.0567352 0.0982683i
\(700\) −7.00000 + 12.1244i −0.264575 + 0.458258i
\(701\) −9.00000 5.19615i −0.339925 0.196256i 0.320314 0.947312i \(-0.396212\pi\)
−0.660239 + 0.751056i \(0.729545\pi\)
\(702\) −18.0000 −0.679366
\(703\) 30.0000 3.46410i 1.13147 0.130651i
\(704\) 1.73205i 0.0652791i
\(705\) 20.7846i 0.782794i
\(706\) 22.5000 + 12.9904i 0.846799 + 0.488899i
\(707\) −18.0000 + 10.3923i −0.676960 + 0.390843i
\(708\) 5.19615i 0.195283i
\(709\) −4.00000 6.92820i −0.150223 0.260194i 0.781086 0.624423i \(-0.214666\pi\)
−0.931309 + 0.364229i \(0.881333\pi\)
\(710\) 20.7846i 0.780033i
\(711\) 36.0000 + 20.7846i 1.35011 + 0.779484i
\(712\) 3.00000 + 5.19615i 0.112430 + 0.194734i
\(713\) 0 0
\(714\) 12.0000 + 20.7846i 0.449089 + 0.777844i
\(715\) 20.7846i 0.777300i
\(716\) 1.50000 + 2.59808i 0.0560576 + 0.0970947i
\(717\) 12.0000 0.448148
\(718\) −6.00000 + 3.46410i −0.223918 + 0.129279i
\(719\) −3.00000 1.73205i −0.111881 0.0645946i 0.443015 0.896514i \(-0.353909\pi\)
−0.554896 + 0.831919i \(0.687242\pi\)
\(720\) 9.00000 5.19615i 0.335410 0.193649i
\(721\) 20.7846i 0.774059i
\(722\) −5.50000 + 18.1865i −0.204689 + 0.676833i
\(723\) −4.50000 7.79423i −0.167357 0.289870i
\(724\) −6.00000 3.46410i −0.222988 0.128742i
\(725\) 21.0000 36.3731i 0.779920 1.35086i
\(726\) −12.0000 6.92820i −0.445362 0.257130i
\(727\) −4.00000 + 6.92820i −0.148352 + 0.256953i −0.930618 0.365991i \(-0.880730\pi\)
0.782267 + 0.622944i \(0.214063\pi\)
\(728\) −6.00000 + 3.46410i −0.222375 + 0.128388i
\(729\) −27.0000 −1.00000
\(730\) 17.3205i 0.641061i
\(731\) −48.0000 + 27.7128i −1.77534 + 1.02500i
\(732\) 15.0000 + 8.66025i 0.554416 + 0.320092i
\(733\) −4.00000 −0.147743 −0.0738717 0.997268i \(-0.523536\pi\)
−0.0738717 + 0.997268i \(0.523536\pi\)
\(734\) 4.00000 0.147643
\(735\) −9.00000 + 15.5885i −0.331970 + 0.574989i
\(736\) 0 0
\(737\) −4.50000 7.79423i −0.165760 0.287104i
\(738\) −4.50000 7.79423i −0.165647 0.286910i
\(739\) 5.50000 9.52628i 0.202321 0.350430i −0.746955 0.664875i \(-0.768485\pi\)
0.949276 + 0.314445i \(0.101818\pi\)
\(740\) −24.0000 −0.882258
\(741\) −21.0000 + 15.5885i −0.771454 + 0.572656i
\(742\) −12.0000 −0.440534
\(743\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(744\) 12.0000 0.439941
\(745\) 12.0000 + 20.7846i 0.439646 + 0.761489i
\(746\) 6.00000 + 3.46410i 0.219676 + 0.126830i
\(747\) 15.5885i 0.570352i
\(748\) −12.0000 −0.438763
\(749\) −24.0000 −0.876941
\(750\) 6.00000 10.3923i 0.219089 0.379473i
\(751\) −33.0000 + 19.0526i −1.20419 + 0.695238i −0.961483 0.274863i \(-0.911368\pi\)
−0.242704 + 0.970100i \(0.578034\pi\)
\(752\) 3.46410i 0.126323i
\(753\) −7.50000 12.9904i −0.273315 0.473396i
\(754\) 18.0000 10.3923i 0.655521 0.378465i
\(755\) −12.0000 + 20.7846i −0.436725 + 0.756429i
\(756\) −9.00000 + 5.19615i −0.327327 + 0.188982i
\(757\) 19.0000 32.9090i 0.690567 1.19610i −0.281086 0.959683i \(-0.590695\pi\)
0.971652 0.236414i \(-0.0759722\pi\)
\(758\) 9.00000 + 5.19615i 0.326895 + 0.188733i
\(759\) 0 0
\(760\) 6.00000 13.8564i 0.217643 0.502625i
\(761\) 8.66025i 0.313934i 0.987604 + 0.156967i \(0.0501716\pi\)
−0.987604 + 0.156967i \(0.949828\pi\)
\(762\) 18.0000 0.652071
\(763\) 0 0
\(764\) 6.00000 3.46410i 0.217072 0.125327i
\(765\) −36.0000 62.3538i −1.30158 2.25441i
\(766\) 9.00000 + 15.5885i 0.325183 + 0.563234i
\(767\) 10.3923i 0.375244i
\(768\) −1.50000 + 0.866025i −0.0541266 + 0.0312500i
\(769\) 7.00000 + 12.1244i 0.252426 + 0.437215i 0.964193 0.265200i \(-0.0854381\pi\)
−0.711767 + 0.702416i \(0.752105\pi\)
\(770\) 6.00000 + 10.3923i 0.216225 + 0.374513i
\(771\) −22.5000 + 12.9904i −0.810318 + 0.467837i
\(772\) 20.7846i 0.748054i
\(773\) 3.00000 + 5.19615i 0.107903 + 0.186893i 0.914920 0.403634i \(-0.132253\pi\)
−0.807018 + 0.590527i \(0.798920\pi\)
\(774\) −12.0000 20.7846i −0.431331 0.747087i
\(775\) 42.0000 24.2487i 1.50868 0.871039i
\(776\) −7.50000 4.33013i −0.269234 0.155443i
\(777\) 24.0000