Properties

Label 950.2.e.a.201.1
Level $950$
Weight $2$
Character 950.201
Analytic conductor $7.586$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
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: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 950.201
Dual form 950.2.e.a.501.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -2.00000 q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -2.00000 q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} -3.00000 q^{11} +1.00000 q^{12} +(3.00000 + 5.19615i) q^{13} +(1.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} -2.00000 q^{18} +(3.50000 + 2.59808i) q^{19} +(1.00000 - 1.73205i) q^{21} +(1.50000 - 2.59808i) q^{22} +(-4.00000 - 6.92820i) q^{23} +(-0.500000 + 0.866025i) q^{24} -6.00000 q^{26} -5.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(1.00000 + 1.73205i) q^{29} -8.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +(1.00000 + 1.73205i) q^{34} +(1.00000 - 1.73205i) q^{36} -8.00000 q^{37} +(-4.00000 + 1.73205i) q^{38} -6.00000 q^{39} +(-2.50000 + 4.33013i) q^{41} +(1.00000 + 1.73205i) q^{42} +(1.50000 + 2.59808i) q^{44} +8.00000 q^{46} +(-3.00000 - 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{48} -3.00000 q^{49} +(1.00000 + 1.73205i) q^{51} +(3.00000 - 5.19615i) q^{52} +(3.00000 + 5.19615i) q^{53} +(2.50000 - 4.33013i) q^{54} -2.00000 q^{56} +(-4.00000 + 1.73205i) q^{57} -2.00000 q^{58} +(-2.50000 + 4.33013i) q^{59} +(-7.00000 - 12.1244i) q^{61} +(4.00000 - 6.92820i) q^{62} +(-2.00000 - 3.46410i) q^{63} +1.00000 q^{64} +(1.50000 + 2.59808i) q^{66} +(-2.50000 - 4.33013i) q^{67} -2.00000 q^{68} +8.00000 q^{69} +(3.00000 - 5.19615i) q^{71} +(1.00000 + 1.73205i) q^{72} +(-4.50000 + 7.79423i) q^{73} +(4.00000 - 6.92820i) q^{74} +(0.500000 - 4.33013i) q^{76} +6.00000 q^{77} +(3.00000 - 5.19615i) q^{78} +(-4.00000 + 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-2.50000 - 4.33013i) q^{82} +11.0000 q^{83} -2.00000 q^{84} -2.00000 q^{87} -3.00000 q^{88} +(-7.00000 - 12.1244i) q^{89} +(-6.00000 - 10.3923i) q^{91} +(-4.00000 + 6.92820i) q^{92} +(4.00000 - 6.92820i) q^{93} +6.00000 q^{94} +1.00000 q^{96} +(-7.50000 + 12.9904i) q^{97} +(1.50000 - 2.59808i) q^{98} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{3} - q^{4} - q^{6} - 4q^{7} + 2q^{8} + 2q^{9} + O(q^{10}) \) \( 2q - q^{2} - q^{3} - q^{4} - q^{6} - 4q^{7} + 2q^{8} + 2q^{9} - 6q^{11} + 2q^{12} + 6q^{13} + 2q^{14} - q^{16} + 2q^{17} - 4q^{18} + 7q^{19} + 2q^{21} + 3q^{22} - 8q^{23} - q^{24} - 12q^{26} - 10q^{27} + 2q^{28} + 2q^{29} - 16q^{31} - q^{32} + 3q^{33} + 2q^{34} + 2q^{36} - 16q^{37} - 8q^{38} - 12q^{39} - 5q^{41} + 2q^{42} + 3q^{44} + 16q^{46} - 6q^{47} - q^{48} - 6q^{49} + 2q^{51} + 6q^{52} + 6q^{53} + 5q^{54} - 4q^{56} - 8q^{57} - 4q^{58} - 5q^{59} - 14q^{61} + 8q^{62} - 4q^{63} + 2q^{64} + 3q^{66} - 5q^{67} - 4q^{68} + 16q^{69} + 6q^{71} + 2q^{72} - 9q^{73} + 8q^{74} + q^{76} + 12q^{77} + 6q^{78} - 8q^{79} - q^{81} - 5q^{82} + 22q^{83} - 4q^{84} - 4q^{87} - 6q^{88} - 14q^{89} - 12q^{91} - 8q^{92} + 8q^{93} + 12q^{94} + 2q^{96} - 15q^{97} + 3q^{98} - 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i −0.973494 0.228714i \(-0.926548\pi\)
0.684819 + 0.728714i \(0.259881\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) −0.500000 0.866025i −0.204124 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
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 0 0
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 1.00000 0.288675
\(13\) 3.00000 + 5.19615i 0.832050 + 1.44115i 0.896410 + 0.443227i \(0.146166\pi\)
−0.0643593 + 0.997927i \(0.520500\pi\)
\(14\) 1.00000 1.73205i 0.267261 0.462910i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.00000 1.73205i 0.242536 0.420084i −0.718900 0.695113i \(-0.755354\pi\)
0.961436 + 0.275029i \(0.0886875\pi\)
\(18\) −2.00000 −0.471405
\(19\) 3.50000 + 2.59808i 0.802955 + 0.596040i
\(20\) 0 0
\(21\) 1.00000 1.73205i 0.218218 0.377964i
\(22\) 1.50000 2.59808i 0.319801 0.553912i
\(23\) −4.00000 6.92820i −0.834058 1.44463i −0.894795 0.446476i \(-0.852679\pi\)
0.0607377 0.998154i \(-0.480655\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 0 0
\(26\) −6.00000 −1.17670
\(27\) −5.00000 −0.962250
\(28\) 1.00000 + 1.73205i 0.188982 + 0.327327i
\(29\) 1.00000 + 1.73205i 0.185695 + 0.321634i 0.943811 0.330487i \(-0.107213\pi\)
−0.758115 + 0.652121i \(0.773880\pi\)
\(30\) 0 0
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 1.50000 2.59808i 0.261116 0.452267i
\(34\) 1.00000 + 1.73205i 0.171499 + 0.297044i
\(35\) 0 0
\(36\) 1.00000 1.73205i 0.166667 0.288675i
\(37\) −8.00000 −1.31519 −0.657596 0.753371i \(-0.728427\pi\)
−0.657596 + 0.753371i \(0.728427\pi\)
\(38\) −4.00000 + 1.73205i −0.648886 + 0.280976i
\(39\) −6.00000 −0.960769
\(40\) 0 0
\(41\) −2.50000 + 4.33013i −0.390434 + 0.676252i −0.992507 0.122189i \(-0.961009\pi\)
0.602072 + 0.798441i \(0.294342\pi\)
\(42\) 1.00000 + 1.73205i 0.154303 + 0.267261i
\(43\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(44\) 1.50000 + 2.59808i 0.226134 + 0.391675i
\(45\) 0 0
\(46\) 8.00000 1.17954
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) −3.00000 −0.428571
\(50\) 0 0
\(51\) 1.00000 + 1.73205i 0.140028 + 0.242536i
\(52\) 3.00000 5.19615i 0.416025 0.720577i
\(53\) 3.00000 + 5.19615i 0.412082 + 0.713746i 0.995117 0.0987002i \(-0.0314685\pi\)
−0.583036 + 0.812447i \(0.698135\pi\)
\(54\) 2.50000 4.33013i 0.340207 0.589256i
\(55\) 0 0
\(56\) −2.00000 −0.267261
\(57\) −4.00000 + 1.73205i −0.529813 + 0.229416i
\(58\) −2.00000 −0.262613
\(59\) −2.50000 + 4.33013i −0.325472 + 0.563735i −0.981608 0.190909i \(-0.938857\pi\)
0.656136 + 0.754643i \(0.272190\pi\)
\(60\) 0 0
\(61\) −7.00000 12.1244i −0.896258 1.55236i −0.832240 0.554416i \(-0.812942\pi\)
−0.0640184 0.997949i \(-0.520392\pi\)
\(62\) 4.00000 6.92820i 0.508001 0.879883i
\(63\) −2.00000 3.46410i −0.251976 0.436436i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.50000 + 2.59808i 0.184637 + 0.319801i
\(67\) −2.50000 4.33013i −0.305424 0.529009i 0.671932 0.740613i \(-0.265465\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) −2.00000 −0.242536
\(69\) 8.00000 0.963087
\(70\) 0 0
\(71\) 3.00000 5.19615i 0.356034 0.616670i −0.631260 0.775571i \(-0.717462\pi\)
0.987294 + 0.158901i \(0.0507952\pi\)
\(72\) 1.00000 + 1.73205i 0.117851 + 0.204124i
\(73\) −4.50000 + 7.79423i −0.526685 + 0.912245i 0.472831 + 0.881153i \(0.343232\pi\)
−0.999517 + 0.0310925i \(0.990101\pi\)
\(74\) 4.00000 6.92820i 0.464991 0.805387i
\(75\) 0 0
\(76\) 0.500000 4.33013i 0.0573539 0.496700i
\(77\) 6.00000 0.683763
\(78\) 3.00000 5.19615i 0.339683 0.588348i
\(79\) −4.00000 + 6.92820i −0.450035 + 0.779484i −0.998388 0.0567635i \(-0.981922\pi\)
0.548352 + 0.836247i \(0.315255\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −2.50000 4.33013i −0.276079 0.478183i
\(83\) 11.0000 1.20741 0.603703 0.797209i \(-0.293691\pi\)
0.603703 + 0.797209i \(0.293691\pi\)
\(84\) −2.00000 −0.218218
\(85\) 0 0
\(86\) 0 0
\(87\) −2.00000 −0.214423
\(88\) −3.00000 −0.319801
\(89\) −7.00000 12.1244i −0.741999 1.28518i −0.951584 0.307389i \(-0.900545\pi\)
0.209585 0.977790i \(-0.432789\pi\)
\(90\) 0 0
\(91\) −6.00000 10.3923i −0.628971 1.08941i
\(92\) −4.00000 + 6.92820i −0.417029 + 0.722315i
\(93\) 4.00000 6.92820i 0.414781 0.718421i
\(94\) 6.00000 0.618853
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) −7.50000 + 12.9904i −0.761510 + 1.31897i 0.180563 + 0.983563i \(0.442208\pi\)
−0.942072 + 0.335410i \(0.891125\pi\)
\(98\) 1.50000 2.59808i 0.151523 0.262445i
\(99\) −3.00000 5.19615i −0.301511 0.522233i
\(100\) 0 0
\(101\) 5.00000 + 8.66025i 0.497519 + 0.861727i 0.999996 0.00286291i \(-0.000911295\pi\)
−0.502477 + 0.864590i \(0.667578\pi\)
\(102\) −2.00000 −0.198030
\(103\) −6.00000 −0.591198 −0.295599 0.955312i \(-0.595519\pi\)
−0.295599 + 0.955312i \(0.595519\pi\)
\(104\) 3.00000 + 5.19615i 0.294174 + 0.509525i
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 2.50000 + 4.33013i 0.240563 + 0.416667i
\(109\) 4.00000 6.92820i 0.383131 0.663602i −0.608377 0.793648i \(-0.708179\pi\)
0.991508 + 0.130046i \(0.0415126\pi\)
\(110\) 0 0
\(111\) 4.00000 6.92820i 0.379663 0.657596i
\(112\) 1.00000 1.73205i 0.0944911 0.163663i
\(113\) 13.0000 1.22294 0.611469 0.791269i \(-0.290579\pi\)
0.611469 + 0.791269i \(0.290579\pi\)
\(114\) 0.500000 4.33013i 0.0468293 0.405554i
\(115\) 0 0
\(116\) 1.00000 1.73205i 0.0928477 0.160817i
\(117\) −6.00000 + 10.3923i −0.554700 + 0.960769i
\(118\) −2.50000 4.33013i −0.230144 0.398621i
\(119\) −2.00000 + 3.46410i −0.183340 + 0.317554i
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 14.0000 1.26750
\(123\) −2.50000 4.33013i −0.225417 0.390434i
\(124\) 4.00000 + 6.92820i 0.359211 + 0.622171i
\(125\) 0 0
\(126\) 4.00000 0.356348
\(127\) 3.00000 + 5.19615i 0.266207 + 0.461084i 0.967879 0.251416i \(-0.0808962\pi\)
−0.701672 + 0.712500i \(0.747563\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) −3.50000 + 6.06218i −0.305796 + 0.529655i −0.977438 0.211221i \(-0.932256\pi\)
0.671642 + 0.740876i \(0.265589\pi\)
\(132\) −3.00000 −0.261116
\(133\) −7.00000 5.19615i −0.606977 0.450564i
\(134\) 5.00000 0.431934
\(135\) 0 0
\(136\) 1.00000 1.73205i 0.0857493 0.148522i
\(137\) −1.50000 2.59808i −0.128154 0.221969i 0.794808 0.606861i \(-0.207572\pi\)
−0.922961 + 0.384893i \(0.874238\pi\)
\(138\) −4.00000 + 6.92820i −0.340503 + 0.589768i
\(139\) −4.50000 7.79423i −0.381685 0.661098i 0.609618 0.792695i \(-0.291323\pi\)
−0.991303 + 0.131597i \(0.957989\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 3.00000 + 5.19615i 0.251754 + 0.436051i
\(143\) −9.00000 15.5885i −0.752618 1.30357i
\(144\) −2.00000 −0.166667
\(145\) 0 0
\(146\) −4.50000 7.79423i −0.372423 0.645055i
\(147\) 1.50000 2.59808i 0.123718 0.214286i
\(148\) 4.00000 + 6.92820i 0.328798 + 0.569495i
\(149\) −2.00000 + 3.46410i −0.163846 + 0.283790i −0.936245 0.351348i \(-0.885723\pi\)
0.772399 + 0.635138i \(0.219057\pi\)
\(150\) 0 0
\(151\) 12.0000 0.976546 0.488273 0.872691i \(-0.337627\pi\)
0.488273 + 0.872691i \(0.337627\pi\)
\(152\) 3.50000 + 2.59808i 0.283887 + 0.210732i
\(153\) 4.00000 0.323381
\(154\) −3.00000 + 5.19615i −0.241747 + 0.418718i
\(155\) 0 0
\(156\) 3.00000 + 5.19615i 0.240192 + 0.416025i
\(157\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(158\) −4.00000 6.92820i −0.318223 0.551178i
\(159\) −6.00000 −0.475831
\(160\) 0 0
\(161\) 8.00000 + 13.8564i 0.630488 + 1.09204i
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) −3.00000 −0.234978 −0.117489 0.993074i \(-0.537485\pi\)
−0.117489 + 0.993074i \(0.537485\pi\)
\(164\) 5.00000 0.390434
\(165\) 0 0
\(166\) −5.50000 + 9.52628i −0.426883 + 0.739383i
\(167\) 4.00000 + 6.92820i 0.309529 + 0.536120i 0.978259 0.207385i \(-0.0664952\pi\)
−0.668730 + 0.743505i \(0.733162\pi\)
\(168\) 1.00000 1.73205i 0.0771517 0.133631i
\(169\) −11.5000 + 19.9186i −0.884615 + 1.53220i
\(170\) 0 0
\(171\) −1.00000 + 8.66025i −0.0764719 + 0.662266i
\(172\) 0 0
\(173\) −9.00000 + 15.5885i −0.684257 + 1.18517i 0.289412 + 0.957205i \(0.406540\pi\)
−0.973670 + 0.227964i \(0.926793\pi\)
\(174\) 1.00000 1.73205i 0.0758098 0.131306i
\(175\) 0 0
\(176\) 1.50000 2.59808i 0.113067 0.195837i
\(177\) −2.50000 4.33013i −0.187912 0.325472i
\(178\) 14.0000 1.04934
\(179\) 3.00000 0.224231 0.112115 0.993695i \(-0.464237\pi\)
0.112115 + 0.993695i \(0.464237\pi\)
\(180\) 0 0
\(181\) 8.00000 + 13.8564i 0.594635 + 1.02994i 0.993598 + 0.112972i \(0.0360369\pi\)
−0.398963 + 0.916967i \(0.630630\pi\)
\(182\) 12.0000 0.889499
\(183\) 14.0000 1.03491
\(184\) −4.00000 6.92820i −0.294884 0.510754i
\(185\) 0 0
\(186\) 4.00000 + 6.92820i 0.293294 + 0.508001i
\(187\) −3.00000 + 5.19615i −0.219382 + 0.379980i
\(188\) −3.00000 + 5.19615i −0.218797 + 0.378968i
\(189\) 10.0000 0.727393
\(190\) 0 0
\(191\) −4.00000 −0.289430 −0.144715 0.989473i \(-0.546227\pi\)
−0.144715 + 0.989473i \(0.546227\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) 5.00000 8.66025i 0.359908 0.623379i −0.628037 0.778183i \(-0.716141\pi\)
0.987945 + 0.154805i \(0.0494748\pi\)
\(194\) −7.50000 12.9904i −0.538469 0.932655i
\(195\) 0 0
\(196\) 1.50000 + 2.59808i 0.107143 + 0.185577i
\(197\) −8.00000 −0.569976 −0.284988 0.958531i \(-0.591990\pi\)
−0.284988 + 0.958531i \(0.591990\pi\)
\(198\) 6.00000 0.426401
\(199\) 11.0000 + 19.0526i 0.779769 + 1.35060i 0.932075 + 0.362267i \(0.117997\pi\)
−0.152305 + 0.988334i \(0.548670\pi\)
\(200\) 0 0
\(201\) 5.00000 0.352673
\(202\) −10.0000 −0.703598
\(203\) −2.00000 3.46410i −0.140372 0.243132i
\(204\) 1.00000 1.73205i 0.0700140 0.121268i
\(205\) 0 0
\(206\) 3.00000 5.19615i 0.209020 0.362033i
\(207\) 8.00000 13.8564i 0.556038 0.963087i
\(208\) −6.00000 −0.416025
\(209\) −10.5000 7.79423i −0.726300 0.539138i
\(210\) 0 0
\(211\) 2.00000 3.46410i 0.137686 0.238479i −0.788935 0.614477i \(-0.789367\pi\)
0.926620 + 0.375999i \(0.122700\pi\)
\(212\) 3.00000 5.19615i 0.206041 0.356873i
\(213\) 3.00000 + 5.19615i 0.205557 + 0.356034i
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) 0 0
\(216\) −5.00000 −0.340207
\(217\) 16.0000 1.08615
\(218\) 4.00000 + 6.92820i 0.270914 + 0.469237i
\(219\) −4.50000 7.79423i −0.304082 0.526685i
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) 4.00000 + 6.92820i 0.268462 + 0.464991i
\(223\) −8.00000 + 13.8564i −0.535720 + 0.927894i 0.463409 + 0.886145i \(0.346626\pi\)
−0.999128 + 0.0417488i \(0.986707\pi\)
\(224\) 1.00000 + 1.73205i 0.0668153 + 0.115728i
\(225\) 0 0
\(226\) −6.50000 + 11.2583i −0.432374 + 0.748893i
\(227\) 7.00000 0.464606 0.232303 0.972643i \(-0.425374\pi\)
0.232303 + 0.972643i \(0.425374\pi\)
\(228\) 3.50000 + 2.59808i 0.231793 + 0.172062i
\(229\) −24.0000 −1.58596 −0.792982 0.609245i \(-0.791473\pi\)
−0.792982 + 0.609245i \(0.791473\pi\)
\(230\) 0 0
\(231\) −3.00000 + 5.19615i −0.197386 + 0.341882i
\(232\) 1.00000 + 1.73205i 0.0656532 + 0.113715i
\(233\) 5.50000 9.52628i 0.360317 0.624087i −0.627696 0.778459i \(-0.716002\pi\)
0.988013 + 0.154371i \(0.0493352\pi\)
\(234\) −6.00000 10.3923i −0.392232 0.679366i
\(235\) 0 0
\(236\) 5.00000 0.325472
\(237\) −4.00000 6.92820i −0.259828 0.450035i
\(238\) −2.00000 3.46410i −0.129641 0.224544i
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) 9.50000 + 16.4545i 0.611949 + 1.05993i 0.990912 + 0.134515i \(0.0429475\pi\)
−0.378963 + 0.925412i \(0.623719\pi\)
\(242\) 1.00000 1.73205i 0.0642824 0.111340i
\(243\) −8.00000 13.8564i −0.513200 0.888889i
\(244\) −7.00000 + 12.1244i −0.448129 + 0.776182i
\(245\) 0 0
\(246\) 5.00000 0.318788
\(247\) −3.00000 + 25.9808i −0.190885 + 1.65312i
\(248\) −8.00000 −0.508001
\(249\) −5.50000 + 9.52628i −0.348548 + 0.603703i
\(250\) 0 0
\(251\) 8.50000 + 14.7224i 0.536515 + 0.929272i 0.999088 + 0.0426905i \(0.0135929\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(252\) −2.00000 + 3.46410i −0.125988 + 0.218218i
\(253\) 12.0000 + 20.7846i 0.754434 + 1.30672i
\(254\) −6.00000 −0.376473
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 1.50000 + 2.59808i 0.0935674 + 0.162064i 0.909010 0.416775i \(-0.136840\pi\)
−0.815442 + 0.578838i \(0.803506\pi\)
\(258\) 0 0
\(259\) 16.0000 0.994192
\(260\) 0 0
\(261\) −2.00000 + 3.46410i −0.123797 + 0.214423i
\(262\) −3.50000 6.06218i −0.216231 0.374523i
\(263\) −13.0000 + 22.5167i −0.801614 + 1.38844i 0.116939 + 0.993139i \(0.462692\pi\)
−0.918553 + 0.395298i \(0.870641\pi\)
\(264\) 1.50000 2.59808i 0.0923186 0.159901i
\(265\) 0 0
\(266\) 8.00000 3.46410i 0.490511 0.212398i
\(267\) 14.0000 0.856786
\(268\) −2.50000 + 4.33013i −0.152712 + 0.264505i
\(269\) 14.0000 24.2487i 0.853595 1.47847i −0.0243472 0.999704i \(-0.507751\pi\)
0.877942 0.478766i \(-0.158916\pi\)
\(270\) 0 0
\(271\) 11.0000 19.0526i 0.668202 1.15736i −0.310204 0.950670i \(-0.600397\pi\)
0.978406 0.206691i \(-0.0662693\pi\)
\(272\) 1.00000 + 1.73205i 0.0606339 + 0.105021i
\(273\) 12.0000 0.726273
\(274\) 3.00000 0.181237
\(275\) 0 0
\(276\) −4.00000 6.92820i −0.240772 0.417029i
\(277\) 14.0000 0.841178 0.420589 0.907251i \(-0.361823\pi\)
0.420589 + 0.907251i \(0.361823\pi\)
\(278\) 9.00000 0.539784
\(279\) −8.00000 13.8564i −0.478947 0.829561i
\(280\) 0 0
\(281\) −3.50000 6.06218i −0.208792 0.361639i 0.742542 0.669800i \(-0.233620\pi\)
−0.951334 + 0.308160i \(0.900287\pi\)
\(282\) −3.00000 + 5.19615i −0.178647 + 0.309426i
\(283\) −14.5000 + 25.1147i −0.861936 + 1.49292i 0.00812260 + 0.999967i \(0.497414\pi\)
−0.870058 + 0.492949i \(0.835919\pi\)
\(284\) −6.00000 −0.356034
\(285\) 0 0
\(286\) 18.0000 1.06436
\(287\) 5.00000 8.66025i 0.295141 0.511199i
\(288\) 1.00000 1.73205i 0.0589256 0.102062i
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 0 0
\(291\) −7.50000 12.9904i −0.439658 0.761510i
\(292\) 9.00000 0.526685
\(293\) −22.0000 −1.28525 −0.642627 0.766179i \(-0.722155\pi\)
−0.642627 + 0.766179i \(0.722155\pi\)
\(294\) 1.50000 + 2.59808i 0.0874818 + 0.151523i
\(295\) 0 0
\(296\) −8.00000 −0.464991
\(297\) 15.0000 0.870388
\(298\) −2.00000 3.46410i −0.115857 0.200670i
\(299\) 24.0000 41.5692i 1.38796 2.40401i
\(300\) 0 0
\(301\) 0 0
\(302\) −6.00000 + 10.3923i −0.345261 + 0.598010i
\(303\) −10.0000 −0.574485
\(304\) −4.00000 + 1.73205i −0.229416 + 0.0993399i
\(305\) 0 0
\(306\) −2.00000 + 3.46410i −0.114332 + 0.198030i
\(307\) −2.50000 + 4.33013i −0.142683 + 0.247133i −0.928506 0.371318i \(-0.878906\pi\)
0.785823 + 0.618451i \(0.212239\pi\)
\(308\) −3.00000 5.19615i −0.170941 0.296078i
\(309\) 3.00000 5.19615i 0.170664 0.295599i
\(310\) 0 0
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) −6.00000 −0.339683
\(313\) 6.50000 + 11.2583i 0.367402 + 0.636358i 0.989158 0.146852i \(-0.0469141\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) −15.0000 25.9808i −0.842484 1.45922i −0.887788 0.460252i \(-0.847759\pi\)
0.0453045 0.998973i \(-0.485574\pi\)
\(318\) 3.00000 5.19615i 0.168232 0.291386i
\(319\) −3.00000 5.19615i −0.167968 0.290929i
\(320\) 0 0
\(321\) −6.00000 + 10.3923i −0.334887 + 0.580042i
\(322\) −16.0000 −0.891645
\(323\) 8.00000 3.46410i 0.445132 0.192748i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 1.50000 2.59808i 0.0830773 0.143894i
\(327\) 4.00000 + 6.92820i 0.221201 + 0.383131i
\(328\) −2.50000 + 4.33013i −0.138039 + 0.239091i
\(329\) 6.00000 + 10.3923i 0.330791 + 0.572946i
\(330\) 0 0
\(331\) −17.0000 −0.934405 −0.467202 0.884150i \(-0.654738\pi\)
−0.467202 + 0.884150i \(0.654738\pi\)
\(332\) −5.50000 9.52628i −0.301852 0.522823i
\(333\) −8.00000 13.8564i −0.438397 0.759326i
\(334\) −8.00000 −0.437741
\(335\) 0 0
\(336\) 1.00000 + 1.73205i 0.0545545 + 0.0944911i
\(337\) 9.50000 16.4545i 0.517498 0.896333i −0.482295 0.876009i \(-0.660197\pi\)
0.999793 0.0203242i \(-0.00646983\pi\)
\(338\) −11.5000 19.9186i −0.625518 1.08343i
\(339\) −6.50000 + 11.2583i −0.353032 + 0.611469i
\(340\) 0 0
\(341\) 24.0000 1.29967
\(342\) −7.00000 5.19615i −0.378517 0.280976i
\(343\) 20.0000 1.07990
\(344\) 0 0
\(345\) 0 0
\(346\) −9.00000 15.5885i −0.483843 0.838041i
\(347\) −13.5000 + 23.3827i −0.724718 + 1.25525i 0.234372 + 0.972147i \(0.424697\pi\)
−0.959090 + 0.283101i \(0.908637\pi\)
\(348\) 1.00000 + 1.73205i 0.0536056 + 0.0928477i
\(349\) 16.0000 0.856460 0.428230 0.903670i \(-0.359137\pi\)
0.428230 + 0.903670i \(0.359137\pi\)
\(350\) 0 0
\(351\) −15.0000 25.9808i −0.800641 1.38675i
\(352\) 1.50000 + 2.59808i 0.0799503 + 0.138478i
\(353\) 21.0000 1.11772 0.558859 0.829263i \(-0.311239\pi\)
0.558859 + 0.829263i \(0.311239\pi\)
\(354\) 5.00000 0.265747
\(355\) 0 0
\(356\) −7.00000 + 12.1244i −0.370999 + 0.642590i
\(357\) −2.00000 3.46410i −0.105851 0.183340i
\(358\) −1.50000 + 2.59808i −0.0792775 + 0.137313i
\(359\) −12.0000 + 20.7846i −0.633336 + 1.09697i 0.353529 + 0.935423i \(0.384981\pi\)
−0.986865 + 0.161546i \(0.948352\pi\)
\(360\) 0 0
\(361\) 5.50000 + 18.1865i 0.289474 + 0.957186i
\(362\) −16.0000 −0.840941
\(363\) 1.00000 1.73205i 0.0524864 0.0909091i
\(364\) −6.00000 + 10.3923i −0.314485 + 0.544705i
\(365\) 0 0
\(366\) −7.00000 + 12.1244i −0.365896 + 0.633750i
\(367\) −14.0000 24.2487i −0.730794 1.26577i −0.956544 0.291587i \(-0.905817\pi\)
0.225750 0.974185i \(-0.427517\pi\)
\(368\) 8.00000 0.417029
\(369\) −10.0000 −0.520579
\(370\) 0 0
\(371\) −6.00000 10.3923i −0.311504 0.539542i
\(372\) −8.00000 −0.414781
\(373\) 24.0000 1.24267 0.621336 0.783544i \(-0.286590\pi\)
0.621336 + 0.783544i \(0.286590\pi\)
\(374\) −3.00000 5.19615i −0.155126 0.268687i
\(375\) 0 0
\(376\) −3.00000 5.19615i −0.154713 0.267971i
\(377\) −6.00000 + 10.3923i −0.309016 + 0.535231i
\(378\) −5.00000 + 8.66025i −0.257172 + 0.445435i
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) 0 0
\(381\) −6.00000 −0.307389
\(382\) 2.00000 3.46410i 0.102329 0.177239i
\(383\) 3.00000 5.19615i 0.153293 0.265511i −0.779143 0.626846i \(-0.784346\pi\)
0.932436 + 0.361335i \(0.117679\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 0 0
\(386\) 5.00000 + 8.66025i 0.254493 + 0.440795i
\(387\) 0 0
\(388\) 15.0000 0.761510
\(389\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(390\) 0 0
\(391\) −16.0000 −0.809155
\(392\) −3.00000 −0.151523
\(393\) −3.50000 6.06218i −0.176552 0.305796i
\(394\) 4.00000 6.92820i 0.201517 0.349038i
\(395\) 0 0
\(396\) −3.00000 + 5.19615i −0.150756 + 0.261116i
\(397\) 8.00000 13.8564i 0.401508 0.695433i −0.592400 0.805644i \(-0.701819\pi\)
0.993908 + 0.110211i \(0.0351527\pi\)
\(398\) −22.0000 −1.10276
\(399\) 8.00000 3.46410i 0.400501 0.173422i
\(400\) 0 0
\(401\) 1.50000 2.59808i 0.0749064 0.129742i −0.826139 0.563466i \(-0.809468\pi\)
0.901046 + 0.433724i \(0.142801\pi\)
\(402\) −2.50000 + 4.33013i −0.124689 + 0.215967i
\(403\) −24.0000 41.5692i −1.19553 2.07071i
\(404\) 5.00000 8.66025i 0.248759 0.430864i
\(405\) 0 0
\(406\) 4.00000 0.198517
\(407\) 24.0000 1.18964
\(408\) 1.00000 + 1.73205i 0.0495074 + 0.0857493i
\(409\) 9.50000 + 16.4545i 0.469745 + 0.813622i 0.999402 0.0345902i \(-0.0110126\pi\)
−0.529657 + 0.848212i \(0.677679\pi\)
\(410\) 0 0
\(411\) 3.00000 0.147979
\(412\) 3.00000 + 5.19615i 0.147799 + 0.255996i
\(413\) 5.00000 8.66025i 0.246034 0.426143i
\(414\) 8.00000 + 13.8564i 0.393179 + 0.681005i
\(415\) 0 0
\(416\) 3.00000 5.19615i 0.147087 0.254762i
\(417\) 9.00000 0.440732
\(418\) 12.0000 5.19615i 0.586939 0.254152i
\(419\) 28.0000 1.36789 0.683945 0.729534i \(-0.260263\pi\)
0.683945 + 0.729534i \(0.260263\pi\)
\(420\) 0 0
\(421\) 4.00000 6.92820i 0.194948 0.337660i −0.751935 0.659237i \(-0.770879\pi\)
0.946883 + 0.321577i \(0.104213\pi\)
\(422\) 2.00000 + 3.46410i 0.0973585 + 0.168630i
\(423\) 6.00000 10.3923i 0.291730 0.505291i
\(424\) 3.00000 + 5.19615i 0.145693 + 0.252347i
\(425\) 0 0
\(426\) −6.00000 −0.290701
\(427\) 14.0000 + 24.2487i 0.677507 + 1.17348i
\(428\) −6.00000 10.3923i −0.290021 0.502331i
\(429\) 18.0000 0.869048
\(430\) 0 0
\(431\) 3.00000 + 5.19615i 0.144505 + 0.250290i 0.929188 0.369607i \(-0.120508\pi\)
−0.784683 + 0.619897i \(0.787174\pi\)
\(432\) 2.50000 4.33013i 0.120281 0.208333i
\(433\) 15.0000 + 25.9808i 0.720854 + 1.24856i 0.960658 + 0.277734i \(0.0895835\pi\)
−0.239804 + 0.970821i \(0.577083\pi\)
\(434\) −8.00000 + 13.8564i −0.384012 + 0.665129i
\(435\) 0 0
\(436\) −8.00000 −0.383131
\(437\) 4.00000 34.6410i 0.191346 1.65710i
\(438\) 9.00000 0.430037
\(439\) 4.00000 6.92820i 0.190910 0.330665i −0.754642 0.656136i \(-0.772190\pi\)
0.945552 + 0.325471i \(0.105523\pi\)
\(440\) 0 0
\(441\) −3.00000 5.19615i −0.142857 0.247436i
\(442\) −6.00000 + 10.3923i −0.285391 + 0.494312i
\(443\) −4.50000 7.79423i −0.213801 0.370315i 0.739100 0.673596i \(-0.235251\pi\)
−0.952901 + 0.303281i \(0.901918\pi\)
\(444\) −8.00000 −0.379663
\(445\) 0 0
\(446\) −8.00000 13.8564i −0.378811 0.656120i
\(447\) −2.00000 3.46410i −0.0945968 0.163846i
\(448\) −2.00000 −0.0944911
\(449\) 29.0000 1.36859 0.684297 0.729203i \(-0.260109\pi\)
0.684297 + 0.729203i \(0.260109\pi\)
\(450\) 0 0
\(451\) 7.50000 12.9904i 0.353161 0.611693i
\(452\) −6.50000 11.2583i −0.305734 0.529547i
\(453\) −6.00000 + 10.3923i −0.281905 + 0.488273i
\(454\) −3.50000 + 6.06218i −0.164263 + 0.284512i
\(455\) 0 0
\(456\) −4.00000 + 1.73205i −0.187317 + 0.0811107i
\(457\) −13.0000 −0.608114 −0.304057 0.952654i \(-0.598341\pi\)
−0.304057 + 0.952654i \(0.598341\pi\)
\(458\) 12.0000 20.7846i 0.560723 0.971201i
\(459\) −5.00000 + 8.66025i −0.233380 + 0.404226i
\(460\) 0 0
\(461\) 11.0000 19.0526i 0.512321 0.887366i −0.487577 0.873080i \(-0.662119\pi\)
0.999898 0.0142861i \(-0.00454755\pi\)
\(462\) −3.00000 5.19615i −0.139573 0.241747i
\(463\) −34.0000 −1.58011 −0.790057 0.613033i \(-0.789949\pi\)
−0.790057 + 0.613033i \(0.789949\pi\)
\(464\) −2.00000 −0.0928477
\(465\) 0 0
\(466\) 5.50000 + 9.52628i 0.254783 + 0.441296i
\(467\) −7.00000 −0.323921 −0.161961 0.986797i \(-0.551782\pi\)
−0.161961 + 0.986797i \(0.551782\pi\)
\(468\) 12.0000 0.554700
\(469\) 5.00000 + 8.66025i 0.230879 + 0.399893i
\(470\) 0 0
\(471\) 0 0
\(472\) −2.50000 + 4.33013i −0.115072 + 0.199310i
\(473\) 0 0
\(474\) 8.00000 0.367452
\(475\) 0 0
\(476\) 4.00000 0.183340
\(477\) −6.00000 + 10.3923i −0.274721 + 0.475831i
\(478\) −6.00000 + 10.3923i −0.274434 + 0.475333i
\(479\) −6.00000 10.3923i −0.274147 0.474837i 0.695773 0.718262i \(-0.255062\pi\)
−0.969920 + 0.243426i \(0.921729\pi\)
\(480\) 0 0
\(481\) −24.0000 41.5692i −1.09431 1.89539i
\(482\) −19.0000 −0.865426
\(483\) −16.0000 −0.728025
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) 0 0
\(486\) 16.0000 0.725775
\(487\) −4.00000 −0.181257 −0.0906287 0.995885i \(-0.528888\pi\)
−0.0906287 + 0.995885i \(0.528888\pi\)
\(488\) −7.00000 12.1244i −0.316875 0.548844i
\(489\) 1.50000 2.59808i 0.0678323 0.117489i
\(490\) 0 0
\(491\) −10.0000 + 17.3205i −0.451294 + 0.781664i −0.998467 0.0553560i \(-0.982371\pi\)
0.547173 + 0.837020i \(0.315704\pi\)
\(492\) −2.50000 + 4.33013i −0.112709 + 0.195217i
\(493\) 4.00000 0.180151
\(494\) −21.0000 15.5885i −0.944835 0.701358i
\(495\) 0 0
\(496\) 4.00000 6.92820i 0.179605 0.311086i
\(497\) −6.00000 + 10.3923i −0.269137 + 0.466159i
\(498\) −5.50000 9.52628i −0.246461 0.426883i
\(499\) −16.5000 + 28.5788i −0.738641 + 1.27936i 0.214466 + 0.976732i \(0.431199\pi\)
−0.953107 + 0.302633i \(0.902134\pi\)
\(500\) 0 0
\(501\) −8.00000 −0.357414
\(502\) −17.0000 −0.758747
\(503\) 2.00000 + 3.46410i 0.0891756 + 0.154457i 0.907163 0.420780i \(-0.138243\pi\)
−0.817987 + 0.575236i \(0.804910\pi\)
\(504\) −2.00000 3.46410i −0.0890871 0.154303i
\(505\) 0 0
\(506\) −24.0000 −1.06693
\(507\) −11.5000 19.9186i −0.510733 0.884615i
\(508\) 3.00000 5.19615i 0.133103 0.230542i
\(509\) −6.00000 10.3923i −0.265945 0.460631i 0.701866 0.712309i \(-0.252351\pi\)
−0.967811 + 0.251679i \(0.919017\pi\)
\(510\) 0 0
\(511\) 9.00000 15.5885i 0.398137 0.689593i
\(512\) 1.00000 0.0441942
\(513\) −17.5000 12.9904i −0.772644 0.573539i
\(514\) −3.00000 −0.132324
\(515\) 0 0
\(516\) 0 0
\(517\) 9.00000 + 15.5885i 0.395820 + 0.685580i
\(518\) −8.00000 + 13.8564i −0.351500 + 0.608816i
\(519\) −9.00000 15.5885i −0.395056 0.684257i
\(520\) 0 0
\(521\) 21.0000 0.920027 0.460013 0.887912i \(-0.347845\pi\)
0.460013 + 0.887912i \(0.347845\pi\)
\(522\) −2.00000 3.46410i −0.0875376 0.151620i
\(523\) 4.00000 + 6.92820i 0.174908 + 0.302949i 0.940129 0.340818i \(-0.110704\pi\)
−0.765222 + 0.643767i \(0.777371\pi\)
\(524\) 7.00000 0.305796
\(525\) 0 0
\(526\) −13.0000 22.5167i −0.566827 0.981773i
\(527\) −8.00000 + 13.8564i −0.348485 + 0.603595i
\(528\) 1.50000 + 2.59808i 0.0652791 + 0.113067i
\(529\) −20.5000 + 35.5070i −0.891304 + 1.54378i
\(530\) 0 0
\(531\) −10.0000 −0.433963
\(532\) −1.00000 + 8.66025i −0.0433555 + 0.375470i
\(533\) −30.0000 −1.29944
\(534\) −7.00000 + 12.1244i −0.302920 + 0.524672i
\(535\) 0 0
\(536\) −2.50000 4.33013i −0.107984 0.187033i
\(537\) −1.50000 + 2.59808i −0.0647298 + 0.112115i
\(538\) 14.0000 + 24.2487i 0.603583 + 1.04544i
\(539\) 9.00000 0.387657
\(540\) 0 0
\(541\) −4.00000 6.92820i −0.171973 0.297867i 0.767136 0.641484i \(-0.221681\pi\)
−0.939110 + 0.343617i \(0.888348\pi\)
\(542\) 11.0000 + 19.0526i 0.472490 + 0.818377i
\(543\) −16.0000 −0.686626
\(544\) −2.00000 −0.0857493
\(545\) 0 0
\(546\) −6.00000 + 10.3923i −0.256776 + 0.444750i
\(547\) −4.00000 6.92820i −0.171028 0.296229i 0.767752 0.640747i \(-0.221375\pi\)
−0.938779 + 0.344519i \(0.888042\pi\)
\(548\) −1.50000 + 2.59808i −0.0640768 + 0.110984i
\(549\) 14.0000 24.2487i 0.597505 1.03491i
\(550\) 0 0
\(551\) −1.00000 + 8.66025i −0.0426014 + 0.368939i
\(552\) 8.00000 0.340503
\(553\) 8.00000 13.8564i 0.340195 0.589234i
\(554\) −7.00000 + 12.1244i −0.297402 + 0.515115i
\(555\) 0 0
\(556\) −4.50000 + 7.79423i −0.190843 + 0.330549i
\(557\) −20.0000 34.6410i −0.847427 1.46779i −0.883497 0.468438i \(-0.844817\pi\)
0.0360693 0.999349i \(-0.488516\pi\)
\(558\) 16.0000 0.677334
\(559\) 0 0
\(560\) 0 0
\(561\) −3.00000 5.19615i −0.126660 0.219382i
\(562\) 7.00000 0.295277
\(563\) 23.0000 0.969334 0.484667 0.874699i \(-0.338941\pi\)
0.484667 + 0.874699i \(0.338941\pi\)
\(564\) −3.00000 5.19615i −0.126323 0.218797i
\(565\) 0 0
\(566\) −14.5000 25.1147i −0.609480 1.05565i
\(567\) 1.00000 1.73205i 0.0419961 0.0727393i
\(568\) 3.00000 5.19615i 0.125877 0.218026i
\(569\) 34.0000 1.42535 0.712677 0.701492i \(-0.247483\pi\)
0.712677 + 0.701492i \(0.247483\pi\)
\(570\) 0 0
\(571\) −29.0000 −1.21361 −0.606806 0.794850i \(-0.707550\pi\)
−0.606806 + 0.794850i \(0.707550\pi\)
\(572\) −9.00000 + 15.5885i −0.376309 + 0.651786i
\(573\) 2.00000 3.46410i 0.0835512 0.144715i
\(574\) 5.00000 + 8.66025i 0.208696 + 0.361472i
\(575\) 0 0
\(576\) 1.00000 + 1.73205i 0.0416667 + 0.0721688i
\(577\) −7.00000 −0.291414 −0.145707 0.989328i \(-0.546546\pi\)
−0.145707 + 0.989328i \(0.546546\pi\)
\(578\) −13.0000 −0.540729
\(579\) 5.00000 + 8.66025i 0.207793 + 0.359908i
\(580\) 0 0
\(581\) −22.0000 −0.912714
\(582\) 15.0000 0.621770
\(583\) −9.00000 15.5885i −0.372742 0.645608i
\(584\) −4.50000 + 7.79423i −0.186211 + 0.322527i
\(585\) 0 0
\(586\) 11.0000 19.0526i 0.454406 0.787054i
\(587\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(588\) −3.00000 −0.123718
\(589\) −28.0000 20.7846i −1.15372 0.856415i
\(590\) 0 0
\(591\) 4.00000 6.92820i 0.164538 0.284988i
\(592\) 4.00000 6.92820i 0.164399 0.284747i
\(593\) −6.50000 11.2583i −0.266923 0.462324i 0.701143 0.713021i \(-0.252674\pi\)
−0.968066 + 0.250697i \(0.919340\pi\)
\(594\) −7.50000 + 12.9904i −0.307729 + 0.533002i
\(595\) 0 0
\(596\) 4.00000 0.163846
\(597\) −22.0000 −0.900400
\(598\) 24.0000 + 41.5692i 0.981433 + 1.69989i
\(599\) −24.0000 41.5692i −0.980613 1.69847i −0.660006 0.751260i \(-0.729446\pi\)
−0.320607 0.947212i \(-0.603887\pi\)
\(600\) 0 0
\(601\) −37.0000 −1.50926 −0.754631 0.656150i \(-0.772184\pi\)
−0.754631 + 0.656150i \(0.772184\pi\)
\(602\) 0 0
\(603\) 5.00000 8.66025i 0.203616 0.352673i
\(604\) −6.00000 10.3923i −0.244137 0.422857i
\(605\) 0 0
\(606\) 5.00000 8.66025i 0.203111 0.351799i
\(607\) 14.0000 0.568242 0.284121 0.958788i \(-0.408298\pi\)
0.284121 + 0.958788i \(0.408298\pi\)
\(608\) 0.500000 4.33013i 0.0202777 0.175610i
\(609\) 4.00000 0.162088
\(610\) 0 0
\(611\) 18.0000 31.1769i 0.728202 1.26128i
\(612\) −2.00000 3.46410i −0.0808452 0.140028i
\(613\) −17.0000 + 29.4449i −0.686624 + 1.18927i 0.286300 + 0.958140i \(0.407575\pi\)
−0.972924 + 0.231127i \(0.925759\pi\)
\(614\) −2.50000 4.33013i −0.100892 0.174750i
\(615\) 0 0
\(616\) 6.00000 0.241747
\(617\) 9.50000 + 16.4545i 0.382456 + 0.662433i 0.991413 0.130771i \(-0.0417452\pi\)
−0.608957 + 0.793203i \(0.708412\pi\)
\(618\) 3.00000 + 5.19615i 0.120678 + 0.209020i
\(619\) 40.0000 1.60774 0.803868 0.594808i \(-0.202772\pi\)
0.803868 + 0.594808i \(0.202772\pi\)
\(620\) 0 0
\(621\) 20.0000 + 34.6410i 0.802572 + 1.39010i
\(622\) 12.0000 20.7846i 0.481156 0.833387i
\(623\) 14.0000 + 24.2487i 0.560898 + 0.971504i
\(624\) 3.00000 5.19615i 0.120096 0.208013i
\(625\) 0 0
\(626\) −13.0000 −0.519584
\(627\) 12.0000 5.19615i 0.479234 0.207514i
\(628\) 0 0
\(629\) −8.00000 + 13.8564i −0.318981 + 0.552491i
\(630\) 0 0
\(631\) 15.0000 + 25.9808i 0.597141 + 1.03428i 0.993241 + 0.116071i \(0.0370299\pi\)
−0.396100 + 0.918207i \(0.629637\pi\)
\(632\) −4.00000 + 6.92820i −0.159111 + 0.275589i
\(633\) 2.00000 + 3.46410i 0.0794929 + 0.137686i
\(634\) 30.0000 1.19145
\(635\) 0 0
\(636\) 3.00000 + 5.19615i 0.118958 + 0.206041i
\(637\) −9.00000 15.5885i −0.356593 0.617637i
\(638\) 6.00000 0.237542
\(639\) 12.0000 0.474713
\(640\) 0 0
\(641\) −10.5000 + 18.1865i −0.414725 + 0.718325i −0.995400 0.0958109i \(-0.969456\pi\)
0.580674 + 0.814136i \(0.302789\pi\)
\(642\) −6.00000 10.3923i −0.236801 0.410152i
\(643\) −2.50000 + 4.33013i −0.0985904 + 0.170764i −0.911101 0.412182i \(-0.864767\pi\)
0.812511 + 0.582946i \(0.198100\pi\)
\(644\) 8.00000 13.8564i 0.315244 0.546019i
\(645\) 0 0
\(646\) −1.00000 + 8.66025i −0.0393445 + 0.340733i
\(647\) −6.00000 −0.235884 −0.117942 0.993020i \(-0.537630\pi\)
−0.117942 + 0.993020i \(0.537630\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 7.50000 12.9904i 0.294401 0.509917i
\(650\) 0 0
\(651\) −8.00000 + 13.8564i −0.313545 + 0.543075i
\(652\) 1.50000 + 2.59808i 0.0587445 + 0.101749i
\(653\) 36.0000 1.40879 0.704394 0.709809i \(-0.251219\pi\)
0.704394 + 0.709809i \(0.251219\pi\)
\(654\) −8.00000 −0.312825
\(655\) 0 0
\(656\) −2.50000 4.33013i −0.0976086 0.169063i
\(657\) −18.0000 −0.702247
\(658\) −12.0000 −0.467809
\(659\) 6.00000 + 10.3923i 0.233727 + 0.404827i 0.958902 0.283738i \(-0.0915745\pi\)
−0.725175 + 0.688565i \(0.758241\pi\)
\(660\) 0 0
\(661\) 11.0000 + 19.0526i 0.427850 + 0.741059i 0.996682 0.0813955i \(-0.0259377\pi\)
−0.568831 + 0.822454i \(0.692604\pi\)
\(662\) 8.50000 14.7224i 0.330362 0.572204i
\(663\) −6.00000 + 10.3923i −0.233021 + 0.403604i
\(664\) 11.0000 0.426883
\(665\) 0 0
\(666\) 16.0000 0.619987
\(667\) 8.00000 13.8564i 0.309761 0.536522i
\(668\) 4.00000 6.92820i 0.154765 0.268060i
\(669\) −8.00000 13.8564i −0.309298 0.535720i
\(670\) 0 0
\(671\) 21.0000 + 36.3731i 0.810696 + 1.40417i
\(672\) −2.00000 −0.0771517
\(673\) −26.0000 −1.00223 −0.501113 0.865382i \(-0.667076\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(674\) 9.50000 + 16.4545i 0.365926 + 0.633803i
\(675\) 0 0
\(676\) 23.0000 0.884615
\(677\) 2.00000 0.0768662 0.0384331 0.999261i \(-0.487763\pi\)
0.0384331 + 0.999261i \(0.487763\pi\)
\(678\) −6.50000 11.2583i −0.249631 0.432374i
\(679\) 15.0000 25.9808i 0.575647 0.997050i
\(680\) 0 0
\(681\) −3.50000 + 6.06218i −0.134120 + 0.232303i
\(682\) −12.0000 + 20.7846i −0.459504 + 0.795884i
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 8.00000 3.46410i 0.305888 0.132453i
\(685\) 0 0
\(686\) −10.0000 + 17.3205i −0.381802 + 0.661300i
\(687\) 12.0000 20.7846i 0.457829 0.792982i
\(688\) 0 0
\(689\) −18.0000 + 31.1769i −0.685745 + 1.18775i
\(690\) 0 0
\(691\) 28.0000 1.06517 0.532585 0.846376i \(-0.321221\pi\)
0.532585 + 0.846376i \(0.321221\pi\)
\(692\) 18.0000 0.684257
\(693\) 6.00000 + 10.3923i 0.227921 + 0.394771i
\(694\) −13.5000 23.3827i −0.512453 0.887595i
\(695\) 0 0
\(696\) −2.00000 −0.0758098
\(697\) 5.00000 + 8.66025i 0.189389 + 0.328031i
\(698\) −8.00000 + 13.8564i −0.302804 + 0.524473i
\(699\) 5.50000 + 9.52628i 0.208029 + 0.360317i
\(700\) 0 0
\(701\) 21.0000 36.3731i 0.793159 1.37379i −0.130843 0.991403i \(-0.541768\pi\)
0.924002 0.382389i \(-0.124898\pi\)
\(702\) 30.0000 1.13228
\(703\) −28.0000 20.7846i −1.05604 0.783906i
\(704\) −3.00000 −0.113067
\(705\) 0 0
\(706\) −10.5000 + 18.1865i −0.395173 + 0.684459i
\(707\) −10.0000 17.3205i −0.376089 0.651405i
\(708\) −2.50000 + 4.33013i −0.0939558 + 0.162736i
\(709\) −10.0000 17.3205i −0.375558 0.650485i 0.614852 0.788642i \(-0.289216\pi\)
−0.990410 + 0.138157i \(0.955882\pi\)
\(710\) 0 0
\(711\) −16.0000 −0.600047
\(712\) −7.00000 12.1244i −0.262336 0.454379i
\(713\) 32.0000 + 55.4256i 1.19841 + 2.07571i
\(714\) 4.00000 0.149696
\(715\) 0 0
\(716\) −1.50000 2.59808i −0.0560576 0.0970947i
\(717\) −6.00000 + 10.3923i −0.224074 + 0.388108i
\(718\) −12.0000 20.7846i −0.447836 0.775675i
\(719\) −25.0000 + 43.3013i −0.932343 + 1.61486i −0.153037 + 0.988220i \(0.548906\pi\)
−0.779305 + 0.626644i \(0.784428\pi\)
\(720\) 0 0
\(721\) 12.0000 0.446903
\(722\) −18.5000 4.33013i −0.688499 0.161151i
\(723\) −19.0000 −0.706618
\(724\) 8.00000 13.8564i 0.297318 0.514969i
\(725\) 0 0
\(726\) 1.00000 + 1.73205i 0.0371135 + 0.0642824i
\(727\) 4.00000 6.92820i 0.148352 0.256953i −0.782267 0.622944i \(-0.785937\pi\)
0.930618 + 0.365991i \(0.119270\pi\)
\(728\) −6.00000 10.3923i −0.222375 0.385164i
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 0 0
\(732\) −7.00000 12.1244i −0.258727 0.448129i
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 28.0000 1.03350
\(735\) 0 0
\(736\) −4.00000 + 6.92820i −0.147442 + 0.255377i
\(737\) 7.50000 + 12.9904i 0.276266 + 0.478507i
\(738\) 5.00000 8.66025i 0.184053 0.318788i
\(739\) −2.50000 + 4.33013i −0.0919640 + 0.159286i −0.908337 0.418238i \(-0.862648\pi\)
0.816373 + 0.577524i \(0.195981\pi\)
\(740\) 0 0
\(741\) −21.0000 15.5885i −0.771454 0.572656i
\(742\) 12.0000 0.440534
\(743\) 2.00000 3.46410i 0.0733729 0.127086i −0.827005 0.562195i \(-0.809957\pi\)
0.900378 + 0.435110i \(0.143290\pi\)
\(744\) 4.00000 6.92820i 0.146647 0.254000i
\(745\) 0 0
\(746\) −12.0000 + 20.7846i −0.439351 + 0.760979i
\(747\) 11.0000 + 19.0526i 0.402469 + 0.697097i
\(748\) 6.00000 0.219382
\(749\) −24.0000 −0.876941
\(750\) 0 0
\(751\) 19.0000 + 32.9090i 0.693320 + 1.20087i 0.970744 + 0.240118i \(0.0771860\pi\)
−0.277424 + 0.960748i \(0.589481\pi\)
\(752\) 6.00000 0.218797
\(753\) −17.0000 −0.619514
\(754\) −6.00000 10.3923i −0.218507 0.378465i
\(755\) 0 0
\(756\) −5.00000 8.66025i −0.181848 0.314970i
\(757\) 17.0000 29.4449i 0.617876 1.07019i −0.371997 0.928234i \(-0.621327\pi\)
0.989873 0.141958i \(-0.0453398\pi\)
\(758\) 14.0000 24.2487i 0.508503 0.880753i
\(759\) −24.0000 −0.871145
\(760\) 0 0
\(761\) −3.00000 −0.108750 −0.0543750 0.998521i \(-0.517317\pi\)
−0.0543750 + 0.998521i \(0.517317\pi\)
\(762\) 3.00000 5.19615i 0.108679 0.188237i
\(763\) −8.00000 + 13.8564i −0.289619 + 0.501636i
\(764\) 2.00000 + 3.46410i 0.0723575 + 0.125327i
\(765\) 0 0
\(766\) 3.00000 + 5.19615i 0.108394 + 0.187745i
\(767\) −30.0000 −1.08324
\(768\) 1.00000 0.0360844
\(769\) 25.0000 + 43.3013i 0.901523 + 1.56148i 0.825518 + 0.564376i \(0.190883\pi\)
0.0760054 + 0.997107i \(0.475783\pi\)
\(770\) 0 0
\(771\) −3.00000 −0.108042
\(772\) −10.0000 −0.359908
\(773\) 15.0000 + 25.9808i 0.539513 + 0.934463i 0.998930 + 0.0462427i \(0.0147248\pi\)
−0.459418 + 0.888220i \(0.651942\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −7.50000 + 12.9904i −0.269234 + 0.466328i
\(777\) −8.00000 + 13.8564i −0.286998 + 0.497096i
\(778\) 0 0
\(779\) −20.0000 + 8.66025i −0.716574 + 0.310286i
\(780\) 0 0
\(781\) −9.00000 + 15.5885i −0.322045 + 0.557799i
\(782\) 8.00000 13.8564i 0.286079 0.495504i
\(783\) −5.00000 8.66025i −0.178685 0.309492i
\(784\) 1.50000 2.59808i 0.0535714 0.0927884i
\(785\) 0 0
\(786\) 7.00000