Properties

Label 845.2.l.a.654.2
Level $845$
Weight $2$
Character 845.654
Analytic conductor $6.747$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.l (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.74735897080\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 654.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 845.654
Dual form 845.2.l.a.699.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.00000 + 2.00000i) q^{5} +(-1.73205 + 1.00000i) q^{6} -3.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.00000 + 2.00000i) q^{5} +(-1.73205 + 1.00000i) q^{6} -3.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.23205 - 0.133975i) q^{10} +(-1.73205 - 1.00000i) q^{11} +2.00000i q^{12} +(-0.267949 + 4.46410i) q^{15} +(0.500000 - 0.866025i) q^{16} -1.00000 q^{18} +(-5.19615 + 3.00000i) q^{19} +(-1.23205 + 1.86603i) q^{20} +(1.73205 - 1.00000i) q^{22} +(5.19615 + 3.00000i) q^{23} +(-5.19615 - 3.00000i) q^{24} +(-3.00000 + 4.00000i) q^{25} -4.00000i q^{27} +(-3.00000 + 5.19615i) q^{29} +(-3.73205 - 2.46410i) q^{30} +6.00000i q^{31} +(-2.50000 - 4.33013i) q^{32} +(-2.00000 - 3.46410i) q^{33} +(-0.500000 + 0.866025i) q^{36} +(3.00000 - 5.19615i) q^{37} -6.00000i q^{38} +(-3.00000 - 6.00000i) q^{40} +(6.92820 + 4.00000i) q^{41} +(5.19615 - 3.00000i) q^{43} -2.00000i q^{44} +(-1.23205 + 1.86603i) q^{45} +(-5.19615 + 3.00000i) q^{46} +8.00000 q^{47} +(1.73205 - 1.00000i) q^{48} +(3.50000 - 6.06218i) q^{49} +(-1.96410 - 4.59808i) q^{50} +12.0000i q^{53} +(3.46410 + 2.00000i) q^{54} +(0.267949 - 4.46410i) q^{55} -12.0000 q^{57} +(-3.00000 - 5.19615i) q^{58} +(1.73205 - 1.00000i) q^{59} +(-4.00000 + 2.00000i) q^{60} +(-3.00000 - 5.19615i) q^{61} +(-5.19615 - 3.00000i) q^{62} +7.00000 q^{64} +4.00000 q^{66} +(6.00000 - 10.3923i) q^{67} +(6.00000 + 10.3923i) q^{69} +(-1.73205 + 1.00000i) q^{71} +(-1.50000 - 2.59808i) q^{72} +6.00000 q^{73} +(3.00000 + 5.19615i) q^{74} +(-9.19615 + 3.92820i) q^{75} +(-5.19615 - 3.00000i) q^{76} +(2.23205 + 0.133975i) q^{80} +(5.50000 - 9.52628i) q^{81} +(-6.92820 + 4.00000i) q^{82} +4.00000 q^{83} +6.00000i q^{86} +(-10.3923 + 6.00000i) q^{87} +(5.19615 + 3.00000i) q^{88} +(6.92820 + 4.00000i) q^{89} +(-1.00000 - 2.00000i) q^{90} +6.00000i q^{92} +(-6.00000 + 10.3923i) q^{93} +(-4.00000 + 6.92820i) q^{94} +(-11.1962 - 7.39230i) q^{95} -10.0000i q^{96} +(-3.00000 - 5.19615i) q^{97} +(3.50000 + 6.06218i) q^{98} -2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 2 q^{4} + 4 q^{5} - 12 q^{8} + 2 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{2} + 2 q^{4} + 4 q^{5} - 12 q^{8} + 2 q^{9} - 2 q^{10} - 8 q^{15} + 2 q^{16} - 4 q^{18} + 2 q^{20} - 12 q^{25} - 12 q^{29} - 8 q^{30} - 10 q^{32} - 8 q^{33} - 2 q^{36} + 12 q^{37} - 12 q^{40} + 2 q^{45} + 32 q^{47} + 14 q^{49} + 6 q^{50} + 8 q^{55} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 12 q^{61} + 28 q^{64} + 16 q^{66} + 24 q^{67} + 24 q^{69} - 6 q^{72} + 24 q^{73} + 12 q^{74} - 16 q^{75} + 2 q^{80} + 22 q^{81} + 16 q^{83} - 4 q^{90} - 24 q^{93} - 16 q^{94} - 24 q^{95} - 12 q^{97} + 14 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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 −0.986869 0.161521i \(-0.948360\pi\)
0.633316 + 0.773893i \(0.281693\pi\)
\(3\) 1.73205 + 1.00000i 1.00000 + 0.577350i 0.908248 0.418432i \(-0.137420\pi\)
0.0917517 + 0.995782i \(0.470753\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.00000 + 2.00000i 0.447214 + 0.894427i
\(6\) −1.73205 + 1.00000i −0.707107 + 0.408248i
\(7\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(8\) −3.00000 −1.06066
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) −2.23205 0.133975i −0.705836 0.0423665i
\(11\) −1.73205 1.00000i −0.522233 0.301511i 0.215615 0.976478i \(-0.430824\pi\)
−0.737848 + 0.674967i \(0.764158\pi\)
\(12\) 2.00000i 0.577350i
\(13\) 0 0
\(14\) 0 0
\(15\) −0.267949 + 4.46410i −0.0691842 + 1.15263i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(18\) −1.00000 −0.235702
\(19\) −5.19615 + 3.00000i −1.19208 + 0.688247i −0.958778 0.284157i \(-0.908286\pi\)
−0.233301 + 0.972404i \(0.574953\pi\)
\(20\) −1.23205 + 1.86603i −0.275495 + 0.417256i
\(21\) 0 0
\(22\) 1.73205 1.00000i 0.369274 0.213201i
\(23\) 5.19615 + 3.00000i 1.08347 + 0.625543i 0.931831 0.362892i \(-0.118211\pi\)
0.151642 + 0.988436i \(0.451544\pi\)
\(24\) −5.19615 3.00000i −1.06066 0.612372i
\(25\) −3.00000 + 4.00000i −0.600000 + 0.800000i
\(26\) 0 0
\(27\) 4.00000i 0.769800i
\(28\) 0 0
\(29\) −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) −3.73205 2.46410i −0.681376 0.449881i
\(31\) 6.00000i 1.07763i 0.842424 + 0.538816i \(0.181128\pi\)
−0.842424 + 0.538816i \(0.818872\pi\)
\(32\) −2.50000 4.33013i −0.441942 0.765466i
\(33\) −2.00000 3.46410i −0.348155 0.603023i
\(34\) 0 0
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 3.00000 5.19615i 0.493197 0.854242i −0.506772 0.862080i \(-0.669162\pi\)
0.999969 + 0.00783774i \(0.00249486\pi\)
\(38\) 6.00000i 0.973329i
\(39\) 0 0
\(40\) −3.00000 6.00000i −0.474342 0.948683i
\(41\) 6.92820 + 4.00000i 1.08200 + 0.624695i 0.931436 0.363905i \(-0.118557\pi\)
0.150567 + 0.988600i \(0.451890\pi\)
\(42\) 0 0
\(43\) 5.19615 3.00000i 0.792406 0.457496i −0.0484030 0.998828i \(-0.515413\pi\)
0.840809 + 0.541332i \(0.182080\pi\)
\(44\) 2.00000i 0.301511i
\(45\) −1.23205 + 1.86603i −0.183663 + 0.278171i
\(46\) −5.19615 + 3.00000i −0.766131 + 0.442326i
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 1.73205 1.00000i 0.250000 0.144338i
\(49\) 3.50000 6.06218i 0.500000 0.866025i
\(50\) −1.96410 4.59808i −0.277766 0.650266i
\(51\) 0 0
\(52\) 0 0
\(53\) 12.0000i 1.64833i 0.566352 + 0.824163i \(0.308354\pi\)
−0.566352 + 0.824163i \(0.691646\pi\)
\(54\) 3.46410 + 2.00000i 0.471405 + 0.272166i
\(55\) 0.267949 4.46410i 0.0361303 0.601939i
\(56\) 0 0
\(57\) −12.0000 −1.58944
\(58\) −3.00000 5.19615i −0.393919 0.682288i
\(59\) 1.73205 1.00000i 0.225494 0.130189i −0.382998 0.923749i \(-0.625108\pi\)
0.608492 + 0.793560i \(0.291775\pi\)
\(60\) −4.00000 + 2.00000i −0.516398 + 0.258199i
\(61\) −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i \(-0.292159\pi\)
−0.991645 + 0.128994i \(0.958825\pi\)
\(62\) −5.19615 3.00000i −0.659912 0.381000i
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) 0 0
\(66\) 4.00000 0.492366
\(67\) 6.00000 10.3923i 0.733017 1.26962i −0.222571 0.974916i \(-0.571445\pi\)
0.955588 0.294706i \(-0.0952216\pi\)
\(68\) 0 0
\(69\) 6.00000 + 10.3923i 0.722315 + 1.25109i
\(70\) 0 0
\(71\) −1.73205 + 1.00000i −0.205557 + 0.118678i −0.599245 0.800566i \(-0.704532\pi\)
0.393688 + 0.919244i \(0.371199\pi\)
\(72\) −1.50000 2.59808i −0.176777 0.306186i
\(73\) 6.00000 0.702247 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) 3.00000 + 5.19615i 0.348743 + 0.604040i
\(75\) −9.19615 + 3.92820i −1.06188 + 0.453590i
\(76\) −5.19615 3.00000i −0.596040 0.344124i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 2.23205 + 0.133975i 0.249551 + 0.0149788i
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) −6.92820 + 4.00000i −0.765092 + 0.441726i
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 6.00000i 0.646997i
\(87\) −10.3923 + 6.00000i −1.11417 + 0.643268i
\(88\) 5.19615 + 3.00000i 0.553912 + 0.319801i
\(89\) 6.92820 + 4.00000i 0.734388 + 0.423999i 0.820025 0.572327i \(-0.193959\pi\)
−0.0856373 + 0.996326i \(0.527293\pi\)
\(90\) −1.00000 2.00000i −0.105409 0.210819i
\(91\) 0 0
\(92\) 6.00000i 0.625543i
\(93\) −6.00000 + 10.3923i −0.622171 + 1.07763i
\(94\) −4.00000 + 6.92820i −0.412568 + 0.714590i
\(95\) −11.1962 7.39230i −1.14870 0.758434i
\(96\) 10.0000i 1.02062i
\(97\) −3.00000 5.19615i −0.304604 0.527589i 0.672569 0.740034i \(-0.265191\pi\)
−0.977173 + 0.212445i \(0.931857\pi\)
\(98\) 3.50000 + 6.06218i 0.353553 + 0.612372i
\(99\) 2.00000i 0.201008i
\(100\) −4.96410 0.598076i −0.496410 0.0598076i
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) 0 0
\(103\) 6.00000i 0.591198i −0.955312 0.295599i \(-0.904481\pi\)
0.955312 0.295599i \(-0.0955191\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −10.3923 6.00000i −1.00939 0.582772i
\(107\) −5.19615 3.00000i −0.502331 0.290021i 0.227345 0.973814i \(-0.426996\pi\)
−0.729676 + 0.683793i \(0.760329\pi\)
\(108\) 3.46410 2.00000i 0.333333 0.192450i
\(109\) 12.0000i 1.14939i 0.818367 + 0.574696i \(0.194880\pi\)
−0.818367 + 0.574696i \(0.805120\pi\)
\(110\) 3.73205 + 2.46410i 0.355837 + 0.234943i
\(111\) 10.3923 6.00000i 0.986394 0.569495i
\(112\) 0 0
\(113\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(114\) 6.00000 10.3923i 0.561951 0.973329i
\(115\) −0.803848 + 13.3923i −0.0749592 + 1.24884i
\(116\) −6.00000 −0.557086
\(117\) 0 0
\(118\) 2.00000i 0.184115i
\(119\) 0 0
\(120\) 0.803848 13.3923i 0.0733809 1.22254i
\(121\) −3.50000 6.06218i −0.318182 0.551107i
\(122\) 6.00000 0.543214
\(123\) 8.00000 + 13.8564i 0.721336 + 1.24939i
\(124\) −5.19615 + 3.00000i −0.466628 + 0.269408i
\(125\) −11.0000 2.00000i −0.983870 0.178885i
\(126\) 0 0
\(127\) −1.73205 1.00000i −0.153695 0.0887357i 0.421180 0.906977i \(-0.361616\pi\)
−0.574875 + 0.818241i \(0.694949\pi\)
\(128\) 1.50000 2.59808i 0.132583 0.229640i
\(129\) 12.0000 1.05654
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 2.00000 3.46410i 0.174078 0.301511i
\(133\) 0 0
\(134\) 6.00000 + 10.3923i 0.518321 + 0.897758i
\(135\) 8.00000 4.00000i 0.688530 0.344265i
\(136\) 0 0
\(137\) 1.00000 + 1.73205i 0.0854358 + 0.147979i 0.905577 0.424182i \(-0.139438\pi\)
−0.820141 + 0.572161i \(0.806105\pi\)
\(138\) −12.0000 −1.02151
\(139\) 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i \(-0.112407\pi\)
−0.768655 + 0.639664i \(0.779074\pi\)
\(140\) 0 0
\(141\) 13.8564 + 8.00000i 1.16692 + 0.673722i
\(142\) 2.00000i 0.167836i
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −13.3923 0.803848i −1.11217 0.0667559i
\(146\) −3.00000 + 5.19615i −0.248282 + 0.430037i
\(147\) 12.1244 7.00000i 1.00000 0.577350i
\(148\) 6.00000 0.493197
\(149\) 17.3205 10.0000i 1.41895 0.819232i 0.422744 0.906249i \(-0.361067\pi\)
0.996207 + 0.0870170i \(0.0277334\pi\)
\(150\) 1.19615 9.92820i 0.0976654 0.810634i
\(151\) 18.0000i 1.46482i −0.680864 0.732410i \(-0.738396\pi\)
0.680864 0.732410i \(-0.261604\pi\)
\(152\) 15.5885 9.00000i 1.26439 0.729996i
\(153\) 0 0
\(154\) 0 0
\(155\) −12.0000 + 6.00000i −0.963863 + 0.481932i
\(156\) 0 0
\(157\) 12.0000i 0.957704i −0.877896 0.478852i \(-0.841053\pi\)
0.877896 0.478852i \(-0.158947\pi\)
\(158\) 0 0
\(159\) −12.0000 + 20.7846i −0.951662 + 1.64833i
\(160\) 6.16025 9.33013i 0.487011 0.737611i
\(161\) 0 0
\(162\) 5.50000 + 9.52628i 0.432121 + 0.748455i
\(163\) 6.00000 + 10.3923i 0.469956 + 0.813988i 0.999410 0.0343508i \(-0.0109363\pi\)
−0.529454 + 0.848339i \(0.677603\pi\)
\(164\) 8.00000i 0.624695i
\(165\) 4.92820 7.46410i 0.383660 0.581080i
\(166\) −2.00000 + 3.46410i −0.155230 + 0.268866i
\(167\) −8.00000 + 13.8564i −0.619059 + 1.07224i 0.370599 + 0.928793i \(0.379152\pi\)
−0.989658 + 0.143448i \(0.954181\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) −5.19615 3.00000i −0.397360 0.229416i
\(172\) 5.19615 + 3.00000i 0.396203 + 0.228748i
\(173\) −10.3923 + 6.00000i −0.790112 + 0.456172i −0.840002 0.542583i \(-0.817446\pi\)
0.0498898 + 0.998755i \(0.484113\pi\)
\(174\) 12.0000i 0.909718i
\(175\) 0 0
\(176\) −1.73205 + 1.00000i −0.130558 + 0.0753778i
\(177\) 4.00000 0.300658
\(178\) −6.92820 + 4.00000i −0.519291 + 0.299813i
\(179\) 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i \(-0.685306\pi\)
0.998286 + 0.0585225i \(0.0186389\pi\)
\(180\) −2.23205 0.133975i −0.166367 0.00998588i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 12.0000i 0.887066i
\(184\) −15.5885 9.00000i −1.14920 0.663489i
\(185\) 13.3923 + 0.803848i 0.984622 + 0.0591000i
\(186\) −6.00000 10.3923i −0.439941 0.762001i
\(187\) 0 0
\(188\) 4.00000 + 6.92820i 0.291730 + 0.505291i
\(189\) 0 0
\(190\) 12.0000 6.00000i 0.870572 0.435286i
\(191\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) 12.1244 + 7.00000i 0.875000 + 0.505181i
\(193\) −3.00000 + 5.19615i −0.215945 + 0.374027i −0.953564 0.301189i \(-0.902616\pi\)
0.737620 + 0.675216i \(0.235950\pi\)
\(194\) 6.00000 0.430775
\(195\) 0 0
\(196\) 7.00000 0.500000
\(197\) −1.00000 + 1.73205i −0.0712470 + 0.123404i −0.899448 0.437028i \(-0.856031\pi\)
0.828201 + 0.560431i \(0.189365\pi\)
\(198\) 1.73205 + 1.00000i 0.123091 + 0.0710669i
\(199\) 12.0000 + 20.7846i 0.850657 + 1.47338i 0.880616 + 0.473831i \(0.157129\pi\)
−0.0299585 + 0.999551i \(0.509538\pi\)
\(200\) 9.00000 12.0000i 0.636396 0.848528i
\(201\) 20.7846 12.0000i 1.46603 0.846415i
\(202\) −3.00000 5.19615i −0.211079 0.365600i
\(203\) 0 0
\(204\) 0 0
\(205\) −1.07180 + 17.8564i −0.0748575 + 1.24715i
\(206\) 5.19615 + 3.00000i 0.362033 + 0.209020i
\(207\) 6.00000i 0.417029i
\(208\) 0 0
\(209\) 12.0000 0.830057
\(210\) 0 0
\(211\) 6.00000 10.3923i 0.413057 0.715436i −0.582165 0.813070i \(-0.697794\pi\)
0.995222 + 0.0976347i \(0.0311277\pi\)
\(212\) −10.3923 + 6.00000i −0.713746 + 0.412082i
\(213\) −4.00000 −0.274075
\(214\) 5.19615 3.00000i 0.355202 0.205076i
\(215\) 11.1962 + 7.39230i 0.763571 + 0.504151i
\(216\) 12.0000i 0.816497i
\(217\) 0 0
\(218\) −10.3923 6.00000i −0.703856 0.406371i
\(219\) 10.3923 + 6.00000i 0.702247 + 0.405442i
\(220\) 4.00000 2.00000i 0.269680 0.134840i
\(221\) 0 0
\(222\) 12.0000i 0.805387i
\(223\) 12.0000 20.7846i 0.803579 1.39184i −0.113666 0.993519i \(-0.536260\pi\)
0.917246 0.398321i \(-0.130407\pi\)
\(224\) 0 0
\(225\) −4.96410 0.598076i −0.330940 0.0398717i
\(226\) 0 0
\(227\) −2.00000 3.46410i −0.132745 0.229920i 0.791989 0.610535i \(-0.209046\pi\)
−0.924734 + 0.380615i \(0.875712\pi\)
\(228\) −6.00000 10.3923i −0.397360 0.688247i
\(229\) 12.0000i 0.792982i −0.918039 0.396491i \(-0.870228\pi\)
0.918039 0.396491i \(-0.129772\pi\)
\(230\) −11.1962 7.39230i −0.738252 0.487434i
\(231\) 0 0
\(232\) 9.00000 15.5885i 0.590879 1.02343i
\(233\) 24.0000i 1.57229i 0.618041 + 0.786146i \(0.287927\pi\)
−0.618041 + 0.786146i \(0.712073\pi\)
\(234\) 0 0
\(235\) 8.00000 + 16.0000i 0.521862 + 1.04372i
\(236\) 1.73205 + 1.00000i 0.112747 + 0.0650945i
\(237\) 0 0
\(238\) 0 0
\(239\) 10.0000i 0.646846i −0.946254 0.323423i \(-0.895166\pi\)
0.946254 0.323423i \(-0.104834\pi\)
\(240\) 3.73205 + 2.46410i 0.240903 + 0.159057i
\(241\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(242\) 7.00000 0.449977
\(243\) 8.66025 5.00000i 0.555556 0.320750i
\(244\) 3.00000 5.19615i 0.192055 0.332650i
\(245\) 15.6244 + 0.937822i 0.998203 + 0.0599153i
\(246\) −16.0000 −1.02012
\(247\) 0 0
\(248\) 18.0000i 1.14300i
\(249\) 6.92820 + 4.00000i 0.439057 + 0.253490i
\(250\) 7.23205 8.52628i 0.457395 0.539249i
\(251\) −6.00000 10.3923i −0.378717 0.655956i 0.612159 0.790735i \(-0.290301\pi\)
−0.990876 + 0.134778i \(0.956968\pi\)
\(252\) 0 0
\(253\) −6.00000 10.3923i −0.377217 0.653359i
\(254\) 1.73205 1.00000i 0.108679 0.0627456i
\(255\) 0 0
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) −6.00000 + 10.3923i −0.373544 + 0.646997i
\(259\) 0 0
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) 6.00000 10.3923i 0.370681 0.642039i
\(263\) 5.19615 + 3.00000i 0.320408 + 0.184988i 0.651575 0.758585i \(-0.274109\pi\)
−0.331166 + 0.943572i \(0.607442\pi\)
\(264\) 6.00000 + 10.3923i 0.369274 + 0.639602i
\(265\) −24.0000 + 12.0000i −1.47431 + 0.737154i
\(266\) 0 0
\(267\) 8.00000 + 13.8564i 0.489592 + 0.847998i
\(268\) 12.0000 0.733017
\(269\) 9.00000 + 15.5885i 0.548740 + 0.950445i 0.998361 + 0.0572259i \(0.0182255\pi\)
−0.449622 + 0.893219i \(0.648441\pi\)
\(270\) −0.535898 + 8.92820i −0.0326137 + 0.543353i
\(271\) −5.19615 3.00000i −0.315644 0.182237i 0.333805 0.942642i \(-0.391667\pi\)
−0.649449 + 0.760405i \(0.725000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) 9.19615 3.92820i 0.554549 0.236880i
\(276\) −6.00000 + 10.3923i −0.361158 + 0.625543i
\(277\) 10.3923 6.00000i 0.624413 0.360505i −0.154172 0.988044i \(-0.549271\pi\)
0.778585 + 0.627539i \(0.215938\pi\)
\(278\) −4.00000 −0.239904
\(279\) −5.19615 + 3.00000i −0.311086 + 0.179605i
\(280\) 0 0
\(281\) 8.00000i 0.477240i 0.971113 + 0.238620i \(0.0766950\pi\)
−0.971113 + 0.238620i \(0.923305\pi\)
\(282\) −13.8564 + 8.00000i −0.825137 + 0.476393i
\(283\) −19.0526 11.0000i −1.13256 0.653882i −0.187980 0.982173i \(-0.560194\pi\)
−0.944577 + 0.328291i \(0.893527\pi\)
\(284\) −1.73205 1.00000i −0.102778 0.0593391i
\(285\) −12.0000 24.0000i −0.710819 1.42164i
\(286\) 0 0
\(287\) 0 0
\(288\) 2.50000 4.33013i 0.147314 0.255155i
\(289\) −8.50000 + 14.7224i −0.500000 + 0.866025i
\(290\) 7.39230 11.1962i 0.434091 0.657461i
\(291\) 12.0000i 0.703452i
\(292\) 3.00000 + 5.19615i 0.175562 + 0.304082i
\(293\) −13.0000 22.5167i −0.759468 1.31544i −0.943122 0.332446i \(-0.892126\pi\)
0.183654 0.982991i \(-0.441207\pi\)
\(294\) 14.0000i 0.816497i
\(295\) 3.73205 + 2.46410i 0.217288 + 0.143466i
\(296\) −9.00000 + 15.5885i −0.523114 + 0.906061i
\(297\) −4.00000 + 6.92820i −0.232104 + 0.402015i
\(298\) 20.0000i 1.15857i
\(299\) 0 0
\(300\) −8.00000 6.00000i −0.461880 0.346410i
\(301\) 0 0
\(302\) 15.5885 + 9.00000i 0.897015 + 0.517892i
\(303\) −10.3923 + 6.00000i −0.597022 + 0.344691i
\(304\) 6.00000i 0.344124i
\(305\) 7.39230 11.1962i 0.423282 0.641090i
\(306\) 0 0
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) 6.00000 10.3923i 0.341328 0.591198i
\(310\) 0.803848 13.3923i 0.0456555 0.760632i
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) 8.00000i 0.452187i −0.974106 0.226093i \(-0.927405\pi\)
0.974106 0.226093i \(-0.0725954\pi\)
\(314\) 10.3923 + 6.00000i 0.586472 + 0.338600i
\(315\) 0 0
\(316\) 0 0
\(317\) 2.00000 0.112331 0.0561656 0.998421i \(-0.482113\pi\)
0.0561656 + 0.998421i \(0.482113\pi\)
\(318\) −12.0000 20.7846i −0.672927 1.16554i
\(319\) 10.3923 6.00000i 0.581857 0.335936i
\(320\) 7.00000 + 14.0000i 0.391312 + 0.782624i
\(321\) −6.00000 10.3923i −0.334887 0.580042i
\(322\) 0 0
\(323\) 0 0
\(324\) 11.0000 0.611111
\(325\) 0 0
\(326\) −12.0000 −0.664619
\(327\) −12.0000 + 20.7846i −0.663602 + 1.14939i
\(328\) −20.7846 12.0000i −1.14764 0.662589i
\(329\) 0 0
\(330\) 4.00000 + 8.00000i 0.220193 + 0.440386i
\(331\) −25.9808 + 15.0000i −1.42803 + 0.824475i −0.996965 0.0778456i \(-0.975196\pi\)
−0.431066 + 0.902320i \(0.641863\pi\)
\(332\) 2.00000 + 3.46410i 0.109764 + 0.190117i
\(333\) 6.00000 0.328798
\(334\) −8.00000 13.8564i −0.437741 0.758189i
\(335\) 26.7846 + 1.60770i 1.46340 + 0.0878378i
\(336\) 0 0
\(337\) 32.0000i 1.74315i −0.490261 0.871576i \(-0.663099\pi\)
0.490261 0.871576i \(-0.336901\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 6.00000 10.3923i 0.324918 0.562775i
\(342\) 5.19615 3.00000i 0.280976 0.162221i
\(343\) 0 0
\(344\) −15.5885 + 9.00000i −0.840473 + 0.485247i
\(345\) −14.7846 + 22.3923i −0.795977 + 1.20556i
\(346\) 12.0000i 0.645124i
\(347\) 5.19615 3.00000i 0.278944 0.161048i −0.354001 0.935245i \(-0.615179\pi\)
0.632945 + 0.774197i \(0.281846\pi\)
\(348\) −10.3923 6.00000i −0.557086 0.321634i
\(349\) −10.3923 6.00000i −0.556287 0.321173i 0.195367 0.980730i \(-0.437410\pi\)
−0.751654 + 0.659558i \(0.770744\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 10.0000i 0.533002i
\(353\) −7.00000 + 12.1244i −0.372572 + 0.645314i −0.989960 0.141344i \(-0.954858\pi\)
0.617388 + 0.786659i \(0.288191\pi\)
\(354\) −2.00000 + 3.46410i −0.106299 + 0.184115i
\(355\) −3.73205 2.46410i −0.198077 0.130781i
\(356\) 8.00000i 0.423999i
\(357\) 0 0
\(358\) 6.00000 + 10.3923i 0.317110 + 0.549250i
\(359\) 2.00000i 0.105556i −0.998606 0.0527780i \(-0.983192\pi\)
0.998606 0.0527780i \(-0.0168076\pi\)
\(360\) 3.69615 5.59808i 0.194804 0.295045i
\(361\) 8.50000 14.7224i 0.447368 0.774865i
\(362\) 1.00000 1.73205i 0.0525588 0.0910346i
\(363\) 14.0000i 0.734809i
\(364\) 0 0
\(365\) 6.00000 + 12.0000i 0.314054 + 0.628109i
\(366\) 10.3923 + 6.00000i 0.543214 + 0.313625i
\(367\) −15.5885 9.00000i −0.813711 0.469796i 0.0345320 0.999404i \(-0.489006\pi\)
−0.848243 + 0.529607i \(0.822339\pi\)
\(368\) 5.19615 3.00000i 0.270868 0.156386i
\(369\) 8.00000i 0.416463i
\(370\) −7.39230 + 11.1962i −0.384308 + 0.582060i
\(371\) 0 0
\(372\) −12.0000 −0.622171
\(373\) −3.46410 + 2.00000i −0.179364 + 0.103556i −0.586994 0.809591i \(-0.699689\pi\)
0.407630 + 0.913147i \(0.366355\pi\)
\(374\) 0 0
\(375\) −17.0526 14.4641i −0.880590 0.746923i
\(376\) −24.0000 −1.23771
\(377\) 0 0
\(378\) 0 0
\(379\) −15.5885 9.00000i −0.800725 0.462299i 0.0429994 0.999075i \(-0.486309\pi\)
−0.843725 + 0.536776i \(0.819642\pi\)
\(380\) 0.803848 13.3923i 0.0412365 0.687011i
\(381\) −2.00000 3.46410i −0.102463 0.177471i
\(382\) 0 0
\(383\) 4.00000 + 6.92820i 0.204390 + 0.354015i 0.949938 0.312437i \(-0.101145\pi\)
−0.745548 + 0.666452i \(0.767812\pi\)
\(384\) 5.19615 3.00000i 0.265165 0.153093i
\(385\) 0 0
\(386\) −3.00000 5.19615i −0.152696 0.264477i
\(387\) 5.19615 + 3.00000i 0.264135 + 0.152499i
\(388\) 3.00000 5.19615i 0.152302 0.263795i
\(389\) 6.00000 0.304212 0.152106 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −10.5000 + 18.1865i −0.530330 + 0.918559i
\(393\) −20.7846 12.0000i −1.04844 0.605320i
\(394\) −1.00000 1.73205i −0.0503793 0.0872595i
\(395\) 0 0
\(396\) 1.73205 1.00000i 0.0870388 0.0502519i
\(397\) −9.00000 15.5885i −0.451697 0.782362i 0.546795 0.837267i \(-0.315848\pi\)
−0.998492 + 0.0549046i \(0.982515\pi\)
\(398\) −24.0000 −1.20301
\(399\) 0 0
\(400\) 1.96410 + 4.59808i 0.0982051 + 0.229904i
\(401\) −13.8564 8.00000i −0.691956 0.399501i 0.112388 0.993664i \(-0.464150\pi\)
−0.804344 + 0.594163i \(0.797483\pi\)
\(402\) 24.0000i 1.19701i
\(403\) 0 0
\(404\) −6.00000 −0.298511
\(405\) 24.5526 + 1.47372i 1.22003 + 0.0732298i
\(406\) 0 0
\(407\) −10.3923 + 6.00000i −0.515127 + 0.297409i
\(408\) 0 0
\(409\) −20.7846 + 12.0000i −1.02773 + 0.593362i −0.916334 0.400414i \(-0.868866\pi\)
−0.111398 + 0.993776i \(0.535533\pi\)
\(410\) −14.9282 9.85641i −0.737251 0.486773i
\(411\) 4.00000i 0.197305i
\(412\) 5.19615 3.00000i 0.255996 0.147799i
\(413\) 0 0
\(414\) −5.19615 3.00000i −0.255377 0.147442i
\(415\) 4.00000 + 8.00000i 0.196352 + 0.392705i
\(416\) 0 0
\(417\) 8.00000i 0.391762i
\(418\) −6.00000 + 10.3923i −0.293470 + 0.508304i
\(419\) 6.00000 10.3923i 0.293119 0.507697i −0.681426 0.731887i \(-0.738640\pi\)
0.974546 + 0.224189i \(0.0719734\pi\)
\(420\) 0 0
\(421\) 36.0000i 1.75453i 0.480004 + 0.877266i \(0.340635\pi\)
−0.480004 + 0.877266i \(0.659365\pi\)
\(422\) 6.00000 + 10.3923i 0.292075 + 0.505889i
\(423\) 4.00000 + 6.92820i 0.194487 + 0.336861i
\(424\) 36.0000i 1.74831i
\(425\) 0 0
\(426\) 2.00000 3.46410i 0.0969003 0.167836i
\(427\) 0 0
\(428\) 6.00000i 0.290021i
\(429\) 0 0
\(430\) −12.0000 + 6.00000i −0.578691 + 0.289346i
\(431\) 8.66025 + 5.00000i 0.417150 + 0.240842i 0.693857 0.720113i \(-0.255910\pi\)
−0.276707 + 0.960954i \(0.589243\pi\)
\(432\) −3.46410 2.00000i −0.166667 0.0962250i
\(433\) −13.8564 + 8.00000i −0.665896 + 0.384455i −0.794520 0.607238i \(-0.792277\pi\)
0.128624 + 0.991693i \(0.458944\pi\)
\(434\) 0 0
\(435\) −22.3923 14.7846i −1.07363 0.708868i
\(436\) −10.3923 + 6.00000i −0.497701 + 0.287348i
\(437\) −36.0000 −1.72211
\(438\) −10.3923 + 6.00000i −0.496564 + 0.286691i
\(439\) −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i \(-0.894477\pi\)
0.754642 + 0.656136i \(0.227810\pi\)
\(440\) −0.803848 + 13.3923i −0.0383219 + 0.638453i
\(441\) 7.00000 0.333333
\(442\) 0 0
\(443\) 6.00000i 0.285069i 0.989790 + 0.142534i \(0.0455251\pi\)
−0.989790 + 0.142534i \(0.954475\pi\)
\(444\) 10.3923 + 6.00000i 0.493197 + 0.284747i
\(445\) −1.07180 + 17.8564i −0.0508080 + 0.846475i
\(446\) 12.0000 + 20.7846i 0.568216 + 0.984180i
\(447\) 40.0000 1.89194
\(448\) 0 0
\(449\) −13.8564 + 8.00000i −0.653924 + 0.377543i −0.789958 0.613161i \(-0.789898\pi\)
0.136034 + 0.990704i \(0.456564\pi\)
\(450\) 3.00000 4.00000i 0.141421 0.188562i
\(451\) −8.00000 13.8564i −0.376705 0.652473i
\(452\) 0 0
\(453\) 18.0000 31.1769i 0.845714 1.46482i
\(454\) 4.00000 0.187729
\(455\) 0 0
\(456\) 36.0000 1.68585
\(457\) −15.0000 + 25.9808i −0.701670 + 1.21533i 0.266209 + 0.963915i \(0.414229\pi\)
−0.967880 + 0.251414i \(0.919105\pi\)
\(458\) 10.3923 + 6.00000i 0.485601 + 0.280362i
\(459\) 0 0
\(460\) −12.0000 + 6.00000i −0.559503 + 0.279751i
\(461\) −3.46410 + 2.00000i −0.161339 + 0.0931493i −0.578496 0.815685i \(-0.696360\pi\)
0.417156 + 0.908835i \(0.363027\pi\)
\(462\) 0 0
\(463\) 24.0000 1.11537 0.557687 0.830051i \(-0.311689\pi\)
0.557687 + 0.830051i \(0.311689\pi\)
\(464\) 3.00000 + 5.19615i 0.139272 + 0.241225i
\(465\) −26.7846 1.60770i −1.24211 0.0745551i
\(466\) −20.7846 12.0000i −0.962828 0.555889i
\(467\) 18.0000i 0.832941i −0.909149 0.416470i \(-0.863267\pi\)
0.909149 0.416470i \(-0.136733\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −17.8564 1.07180i −0.823655 0.0494383i
\(471\) 12.0000 20.7846i 0.552931 0.957704i
\(472\) −5.19615 + 3.00000i −0.239172 + 0.138086i
\(473\) −12.0000 −0.551761
\(474\) 0 0
\(475\) 3.58846 29.7846i 0.164650 1.36661i
\(476\) 0 0
\(477\) −10.3923 + 6.00000i −0.475831 + 0.274721i
\(478\) 8.66025 + 5.00000i 0.396111 + 0.228695i
\(479\) −19.0526 11.0000i −0.870534 0.502603i −0.00300810 0.999995i \(-0.500958\pi\)
−0.867526 + 0.497393i \(0.834291\pi\)
\(480\) 20.0000 10.0000i 0.912871 0.456435i
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 3.50000 6.06218i 0.159091 0.275554i
\(485\) 7.39230 11.1962i 0.335667 0.508391i
\(486\) 10.0000i 0.453609i
\(487\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(488\) 9.00000 + 15.5885i 0.407411 + 0.705656i
\(489\) 24.0000i 1.08532i
\(490\) −8.62436 + 13.0622i −0.389609 + 0.590089i
\(491\) −6.00000 + 10.3923i −0.270776 + 0.468998i −0.969061 0.246822i \(-0.920614\pi\)
0.698285 + 0.715820i \(0.253947\pi\)
\(492\) −8.00000 + 13.8564i −0.360668 + 0.624695i
\(493\) 0 0
\(494\) 0 0
\(495\) 4.00000 2.00000i 0.179787 0.0898933i
\(496\) 5.19615 + 3.00000i 0.233314 + 0.134704i
\(497\) 0 0
\(498\) −6.92820 + 4.00000i −0.310460 + 0.179244i
\(499\) 6.00000i 0.268597i −0.990941 0.134298i \(-0.957122\pi\)
0.990941 0.134298i \(-0.0428781\pi\)
\(500\) −3.76795 10.5263i −0.168508 0.470750i
\(501\) −27.7128 + 16.0000i −1.23812 + 0.714827i
\(502\) 12.0000 0.535586
\(503\) −5.19615 + 3.00000i −0.231685 + 0.133763i −0.611349 0.791361i \(-0.709373\pi\)
0.379664 + 0.925124i \(0.376040\pi\)
\(504\) 0 0
\(505\) −13.3923 0.803848i −0.595950 0.0357707i
\(506\) 12.0000 0.533465
\(507\) 0 0
\(508\) 2.00000i 0.0887357i
\(509\) 17.3205 + 10.0000i 0.767718 + 0.443242i 0.832060 0.554686i \(-0.187161\pi\)
−0.0643419 + 0.997928i \(0.520495\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −11.0000 −0.486136
\(513\) 12.0000 + 20.7846i 0.529813 + 0.917663i
\(514\) 0 0
\(515\) 12.0000 6.00000i 0.528783 0.264392i
\(516\) 6.00000 + 10.3923i 0.264135 + 0.457496i
\(517\) −13.8564 8.00000i −0.609404 0.351840i
\(518\) 0 0
\(519\) −24.0000 −1.05348
\(520\) 0 0
\(521\) −30.0000 −1.31432 −0.657162 0.753749i \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) 3.00000 5.19615i 0.131306 0.227429i
\(523\) 36.3731 + 21.0000i 1.59048 + 0.918266i 0.993224 + 0.116218i \(0.0370770\pi\)
0.597259 + 0.802048i \(0.296256\pi\)
\(524\) −6.00000 10.3923i −0.262111 0.453990i
\(525\) 0 0
\(526\) −5.19615 + 3.00000i −0.226563 + 0.130806i
\(527\) 0 0
\(528\) −4.00000 −0.174078
\(529\) 6.50000 + 11.2583i 0.282609 + 0.489493i
\(530\) 1.60770 26.7846i 0.0698338 1.16345i
\(531\) 1.73205 + 1.00000i 0.0751646 + 0.0433963i
\(532\) 0 0
\(533\) 0 0
\(534\) −16.0000 −0.692388
\(535\) 0.803848 13.3923i 0.0347534 0.579000i
\(536\) −18.0000 + 31.1769i −0.777482 + 1.34664i
\(537\) 20.7846 12.0000i 0.896922 0.517838i
\(538\) −18.0000 −0.776035
\(539\) −12.1244 + 7.00000i −0.522233 + 0.301511i
\(540\) 7.46410 + 4.92820i 0.321204 + 0.212076i
\(541\) 12.0000i 0.515920i 0.966156 + 0.257960i \(0.0830503\pi\)
−0.966156 + 0.257960i \(0.916950\pi\)
\(542\) 5.19615 3.00000i 0.223194 0.128861i
\(543\) −3.46410 2.00000i −0.148659 0.0858282i
\(544\) 0 0
\(545\) −24.0000 + 12.0000i −1.02805 + 0.514024i
\(546\) 0 0
\(547\) 18.0000i 0.769624i −0.922995 0.384812i \(-0.874266\pi\)
0.922995 0.384812i \(-0.125734\pi\)
\(548\) −1.00000 + 1.73205i −0.0427179 + 0.0739895i
\(549\) 3.00000 5.19615i 0.128037 0.221766i
\(550\) −1.19615 + 9.92820i −0.0510041 + 0.423340i
\(551\) 36.0000i 1.53365i
\(552\) −18.0000 31.1769i −0.766131 1.32698i
\(553\) 0 0
\(554\) 12.0000i 0.509831i
\(555\) 22.3923 + 14.7846i 0.950500 + 0.627572i
\(556\) −2.00000 + 3.46410i −0.0848189 + 0.146911i
\(557\) 7.00000 12.1244i 0.296600 0.513725i −0.678756 0.734364i \(-0.737481\pi\)
0.975356 + 0.220638i \(0.0708140\pi\)
\(558\) 6.00000i 0.254000i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −6.92820 4.00000i −0.292249 0.168730i
\(563\) 25.9808 15.0000i 1.09496 0.632175i 0.160066 0.987106i \(-0.448829\pi\)
0.934892 + 0.354932i \(0.115496\pi\)
\(564\) 16.0000i 0.673722i
\(565\) 0 0
\(566\) 19.0526 11.0000i 0.800839 0.462364i
\(567\) 0 0
\(568\) 5.19615 3.00000i 0.218026 0.125877i
\(569\) −9.00000 + 15.5885i −0.377300 + 0.653502i −0.990668 0.136295i \(-0.956481\pi\)
0.613369 + 0.789797i \(0.289814\pi\)
\(570\) 26.7846 + 1.60770i 1.12188 + 0.0673389i
\(571\) 12.0000 0.502184 0.251092 0.967963i \(-0.419210\pi\)
0.251092 + 0.967963i \(0.419210\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −27.5885 + 11.7846i −1.15052 + 0.491452i
\(576\) 3.50000 + 6.06218i 0.145833 + 0.252591i
\(577\) −18.0000 −0.749350 −0.374675 0.927156i \(-0.622246\pi\)
−0.374675 + 0.927156i \(0.622246\pi\)
\(578\) −8.50000 14.7224i −0.353553 0.612372i
\(579\) −10.3923 + 6.00000i −0.431889 + 0.249351i
\(580\) −6.00000 12.0000i −0.249136 0.498273i
\(581\) 0 0
\(582\) 10.3923 + 6.00000i 0.430775 + 0.248708i
\(583\) 12.0000 20.7846i 0.496989 0.860811i
\(584\) −18.0000 −0.744845
\(585\) 0 0
\(586\) 26.0000 1.07405
\(587\) 10.0000 17.3205i 0.412744 0.714894i −0.582445 0.812870i \(-0.697904\pi\)
0.995189 + 0.0979766i \(0.0312370\pi\)
\(588\) 12.1244 + 7.00000i 0.500000 + 0.288675i
\(589\) −18.0000 31.1769i −0.741677 1.28462i
\(590\) −4.00000 + 2.00000i −0.164677 + 0.0823387i
\(591\) −3.46410 + 2.00000i −0.142494 + 0.0822690i
\(592\) −3.00000 5.19615i −0.123299 0.213561i
\(593\) 22.0000 0.903432 0.451716 0.892162i \(-0.350812\pi\)
0.451716 + 0.892162i \(0.350812\pi\)
\(594\) −4.00000 6.92820i −0.164122 0.284268i
\(595\) 0 0
\(596\) 17.3205 + 10.0000i 0.709476 + 0.409616i
\(597\) 48.0000i 1.96451i
\(598\) 0 0
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 27.5885 11.7846i 1.12629 0.481105i
\(601\) 3.00000 5.19615i 0.122373 0.211955i −0.798330 0.602220i \(-0.794283\pi\)
0.920703 + 0.390264i \(0.127616\pi\)
\(602\) 0 0
\(603\) 12.0000 0.488678
\(604\) 15.5885 9.00000i 0.634285 0.366205i
\(605\) 8.62436 13.0622i 0.350630 0.531053i
\(606\) 12.0000i 0.487467i
\(607\) 15.5885 9.00000i 0.632716 0.365299i −0.149087 0.988824i \(-0.547634\pi\)
0.781803 + 0.623525i \(0.214300\pi\)
\(608\) 25.9808 + 15.0000i 1.05366 + 0.608330i
\(609\) 0 0
\(610\) 6.00000 + 12.0000i 0.242933 + 0.485866i
\(611\) 0 0
\(612\) 0 0
\(613\) 15.0000 25.9808i 0.605844 1.04935i −0.386073 0.922468i \(-0.626169\pi\)
0.991917 0.126885i \(-0.0404979\pi\)
\(614\) 6.00000 10.3923i 0.242140 0.419399i
\(615\) −19.7128 + 29.8564i −0.794897 + 1.20393i
\(616\) 0 0
\(617\) 17.0000 + 29.4449i 0.684394 + 1.18541i 0.973627 + 0.228147i \(0.0732666\pi\)
−0.289233 + 0.957259i \(0.593400\pi\)
\(618\) 6.00000 + 10.3923i 0.241355 + 0.418040i
\(619\) 18.0000i 0.723481i 0.932279 + 0.361741i \(0.117817\pi\)
−0.932279 + 0.361741i \(0.882183\pi\)
\(620\) −11.1962 7.39230i −0.449648 0.296882i
\(621\) 12.0000 20.7846i 0.481543 0.834058i
\(622\) −12.0000 + 20.7846i −0.481156 + 0.833387i
\(623\) 0 0
\(624\) 0 0
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 6.92820 + 4.00000i 0.276907 + 0.159872i
\(627\) 20.7846 + 12.0000i 0.830057 + 0.479234i
\(628\) 10.3923 6.00000i 0.414698 0.239426i
\(629\) 0 0
\(630\) 0 0
\(631\) 25.9808 15.0000i 1.03428 0.597141i 0.116071 0.993241i \(-0.462970\pi\)
0.918207 + 0.396100i \(0.129637\pi\)
\(632\) 0 0
\(633\) 20.7846 12.0000i 0.826114 0.476957i
\(634\) −1.00000 + 1.73205i −0.0397151 + 0.0687885i
\(635\) 0.267949 4.46410i 0.0106332 0.177152i
\(636\) −24.0000 −0.951662
\(637\) 0 0
\(638\) 12.0000i 0.475085i
\(639\) −1.73205 1.00000i −0.0685189 0.0395594i
\(640\) 6.69615 + 0.401924i 0.264689 + 0.0158874i
\(641\) 15.0000 + 25.9808i 0.592464 + 1.02618i 0.993899 + 0.110291i \(0.0351782\pi\)
−0.401435 + 0.915888i \(0.631488\pi\)
\(642\) 12.0000 0.473602
\(643\) −18.0000 31.1769i −0.709851 1.22950i −0.964912 0.262573i \(-0.915429\pi\)
0.255062 0.966925i \(-0.417904\pi\)
\(644\) 0 0
\(645\) 12.0000 + 24.0000i 0.472500 + 0.944999i
\(646\) 0 0
\(647\) 5.19615 + 3.00000i 0.204282 + 0.117942i 0.598651 0.801010i \(-0.295704\pi\)
−0.394369 + 0.918952i \(0.629037\pi\)
\(648\) −16.5000 + 28.5788i −0.648181 + 1.12268i
\(649\) −4.00000 −0.157014
\(650\) 0 0
\(651\) 0 0
\(652\) −6.00000 + 10.3923i −0.234978 + 0.406994i
\(653\) −31.1769 18.0000i −1.22005 0.704394i −0.255119 0.966910i \(-0.582115\pi\)
−0.964928 + 0.262515i \(0.915448\pi\)
\(654\) −12.0000 20.7846i −0.469237 0.812743i
\(655\) −12.0000 24.0000i −0.468879 0.937758i
\(656\) 6.92820 4.00000i 0.270501 0.156174i
\(657\) 3.00000 + 5.19615i 0.117041 + 0.202721i
\(658\) 0 0
\(659\) −18.0000 31.1769i −0.701180 1.21448i −0.968052 0.250748i \(-0.919323\pi\)
0.266872 0.963732i \(-0.414010\pi\)
\(660\) 8.92820 + 0.535898i 0.347530 + 0.0208598i
\(661\) 10.3923 + 6.00000i 0.404214 + 0.233373i 0.688301 0.725426i \(-0.258357\pi\)
−0.284087 + 0.958799i \(0.591690\pi\)
\(662\) 30.0000i 1.16598i
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) −3.00000 + 5.19615i −0.116248 + 0.201347i
\(667\) −31.1769 + 18.0000i −1.20717 + 0.696963i
\(668\) −16.0000 −0.619059
\(669\) 41.5692 24.0000i 1.60716 0.927894i
\(670\) −14.7846 + 22.3923i −0.571179 + 0.865090i
\(671\) 12.0000i 0.463255i
\(672\) 0 0
\(673\) 41.5692 + 24.0000i 1.60238 + 0.925132i 0.991011 + 0.133783i \(0.0427126\pi\)
0.611365 + 0.791349i \(0.290621\pi\)
\(674\) 27.7128 + 16.0000i 1.06746 + 0.616297i
\(675\) 16.0000 + 12.0000i 0.615840 + 0.461880i
\(676\) 0 0
\(677\) 36.0000i 1.38359i −0.722093 0.691796i \(-0.756820\pi\)
0.722093 0.691796i \(-0.243180\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 8.00000i 0.306561i
\(682\) 6.00000 + 10.3923i 0.229752 + 0.397942i
\(683\) −22.0000 38.1051i −0.841807 1.45805i −0.888366 0.459136i \(-0.848159\pi\)
0.0465592 0.998916i \(-0.485174\pi\)
\(684\) 6.00000i 0.229416i
\(685\) −2.46410 + 3.73205i −0.0941485 + 0.142594i
\(686\) 0 0
\(687\) 12.0000 20.7846i 0.457829 0.792982i
\(688\) 6.00000i 0.228748i
\(689\) 0 0
\(690\) −12.0000 24.0000i −0.456832 0.913664i
\(691\) −36.3731 21.0000i −1.38370 0.798878i −0.391102 0.920348i \(-0.627906\pi\)
−0.992595 + 0.121470i \(0.961239\pi\)
\(692\) −10.3923 6.00000i −0.395056 0.228086i
\(693\) 0 0
\(694\) 6.00000i 0.227757i
\(695\) −4.92820 + 7.46410i −0.186937 + 0.283130i
\(696\) 31.1769 18.0000i 1.18176 0.682288i
\(697\) 0 0
\(698\) 10.3923 6.00000i 0.393355 0.227103i
\(699\) −24.0000 + 41.5692i −0.907763 + 1.57229i
\(700\) 0 0
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) 36.0000i 1.35777i
\(704\) −12.1244 7.00000i −0.456954 0.263822i
\(705\) −2.14359 + 35.7128i −0.0807324 + 1.34502i
\(706\) −7.00000 12.1244i −0.263448 0.456306i
\(707\) 0 0
\(708\) 2.00000 + 3.46410i 0.0751646 + 0.130189i
\(709\) −10.3923 + 6.00000i −0.390291 + 0.225335i −0.682286 0.731085i \(-0.739014\pi\)
0.291995 + 0.956420i \(0.405681\pi\)
\(710\) 4.00000 2.00000i 0.150117 0.0750587i
\(711\) 0 0
\(712\) −20.7846 12.0000i −0.778936 0.449719i
\(713\) −18.0000 + 31.1769i −0.674105 + 1.16758i
\(714\) 0 0
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) 10.0000 17.3205i 0.373457 0.646846i
\(718\) 1.73205 + 1.00000i 0.0646396 + 0.0373197i
\(719\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) 1.00000 + 2.00000i 0.0372678 + 0.0745356i
\(721\) 0 0
\(722\) 8.50000 + 14.7224i 0.316337 + 0.547912i
\(723\) 0 0
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) −11.7846 27.5885i −0.437669 1.02461i
\(726\) 12.1244 + 7.00000i 0.449977 + 0.259794i
\(727\) 26.0000i 0.964287i 0.876092 + 0.482143i \(0.160142\pi\)
−0.876092 + 0.482143i \(0.839858\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) −13.3923 0.803848i −0.495671 0.0297517i
\(731\) 0 0
\(732\) 10.3923 6.00000i 0.384111 0.221766i
\(733\) 42.0000 1.55131 0.775653 0.631160i \(-0.217421\pi\)
0.775653 + 0.631160i \(0.217421\pi\)
\(734\) 15.5885 9.00000i 0.575380 0.332196i
\(735\) 26.1244 + 17.2487i 0.963611 + 0.636228i
\(736\) 30.0000i 1.10581i
\(737\) −20.7846 + 12.0000i −0.765611 + 0.442026i
\(738\) −6.92820 4.00000i −0.255031 0.147242i
\(739\) 5.19615 + 3.00000i 0.191144 + 0.110357i 0.592518 0.805557i \(-0.298134\pi\)
−0.401374 + 0.915914i \(0.631467\pi\)
\(740\) 6.00000 + 12.0000i 0.220564 + 0.441129i
\(741\) 0 0
\(742\) 0 0
\(743\) −8.00000 + 13.8564i −0.293492 + 0.508342i −0.974633 0.223810i \(-0.928151\pi\)
0.681141 + 0.732152i \(0.261484\pi\)
\(744\) 18.0000 31.1769i 0.659912 1.14300i
\(745\) 37.3205 + 24.6410i 1.36732 + 0.902777i
\(746\) 4.00000i 0.146450i
\(747\) 2.00000 + 3.46410i 0.0731762 + 0.126745i
\(748\) 0 0
\(749\) 0 0
\(750\) 21.0526 7.53590i 0.768731 0.275172i
\(751\) 16.0000 27.7128i 0.583848 1.01125i −0.411170 0.911559i \(-0.634880\pi\)
0.995018 0.0996961i \(-0.0317870\pi\)
\(752\) 4.00000 6.92820i 0.145865 0.252646i
\(753\) 24.0000i 0.874609i
\(754\) 0 0
\(755\) 36.0000 18.0000i 1.31017 0.655087i
\(756\) 0 0
\(757\) 17.3205 + 10.0000i 0.629525 + 0.363456i 0.780568 0.625071i \(-0.214930\pi\)
−0.151043 + 0.988527i \(0.548263\pi\)
\(758\) 15.5885 9.00000i 0.566198 0.326895i
\(759\) 24.0000i 0.871145i
\(760\) 33.5885 + 22.1769i 1.21838 + 0.804441i
\(761\) −34.6410 + 20.0000i −1.25574 + 0.724999i −0.972243 0.233975i \(-0.924827\pi\)
−0.283493 + 0.958974i \(0.591493\pi\)
\(762\) 4.00000 0.144905
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −8.00000 −0.289052
\(767\) 0 0
\(768\) 34.0000i 1.22687i
\(769\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −6.00000 −0.215945
\(773\) 19.0000 + 32.9090i 0.683383 + 1.18365i 0.973942 + 0.226796i \(0.0728252\pi\)
−0.290560 + 0.956857i \(0.593841\pi\)
\(774\) −5.19615 + 3.00000i −0.186772 + 0.107833i
\(775\) −24.0000 18.0000i −0.862105 0.646579i
\(776\) 9.00000 + 15.5885i 0.323081 + 0.559593i
\(777\) 0 0
\(778\) −3.00000 + 5.19615i −0.107555 + 0.186291i
\(779\) −48.0000 −1.71978
\(780\) 0 0
\(781\) 4.00000 0.143131
\(782\) 0 0
\(783\) 20.7846 + 12.0000i 0.742781 + 0.428845i
\(784\) −3.50000 6.06218i −0.125000 0.216506i
\(785\) 24.0000 12.0000i 0.856597 0.428298i