Properties

Label 61.2.f.a.14.1
Level 61
Weight 2
Character 61.14
Analytic conductor 0.487
Analytic rank 1
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 61.f (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.487087452330\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
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 14.1
Root \(0.500000 - 0.866025i\)
Character \(\chi\) = 61.14
Dual form 61.2.f.a.48.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 + 0.866025i) q^{2} -2.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(3.00000 - 1.73205i) q^{6} +(-3.00000 + 1.73205i) q^{7} -1.73205i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-1.50000 + 0.866025i) q^{2} -2.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(3.00000 - 1.73205i) q^{6} +(-3.00000 + 1.73205i) q^{7} -1.73205i q^{8} +1.00000 q^{9} +(4.50000 + 2.59808i) q^{10} +3.46410i q^{11} +(-1.00000 + 1.73205i) q^{12} +(1.00000 + 1.73205i) q^{13} +(3.00000 - 5.19615i) q^{14} +(3.00000 + 5.19615i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-6.00000 - 3.46410i) q^{17} +(-1.50000 + 0.866025i) q^{18} +(1.00000 - 1.73205i) q^{19} -3.00000 q^{20} +(6.00000 - 3.46410i) q^{21} +(-3.00000 - 5.19615i) q^{22} +3.46410i q^{24} +(-2.00000 + 3.46410i) q^{25} +(-3.00000 - 1.73205i) q^{26} +4.00000 q^{27} +3.46410i q^{28} +(-1.50000 - 0.866025i) q^{29} +(-9.00000 - 5.19615i) q^{30} +(-9.00000 - 5.19615i) q^{31} +(-4.50000 - 2.59808i) q^{32} -6.92820i q^{33} +12.0000 q^{34} +(9.00000 + 5.19615i) q^{35} +(0.500000 - 0.866025i) q^{36} +1.73205i q^{37} +3.46410i q^{38} +(-2.00000 - 3.46410i) q^{39} +(-4.50000 + 2.59808i) q^{40} +3.00000 q^{41} +(-6.00000 + 10.3923i) q^{42} +(3.00000 - 1.73205i) q^{43} +(3.00000 + 1.73205i) q^{44} +(-1.50000 - 2.59808i) q^{45} +(-6.00000 + 10.3923i) q^{47} +(-5.00000 - 8.66025i) q^{48} +(2.50000 - 4.33013i) q^{49} -6.92820i q^{50} +(12.0000 + 6.92820i) q^{51} +2.00000 q^{52} +5.19615i q^{53} +(-6.00000 + 3.46410i) q^{54} +(9.00000 - 5.19615i) q^{55} +(3.00000 + 5.19615i) q^{56} +(-2.00000 + 3.46410i) q^{57} +3.00000 q^{58} +(-3.00000 + 1.73205i) q^{59} +6.00000 q^{60} +(-0.500000 - 7.79423i) q^{61} +18.0000 q^{62} +(-3.00000 + 1.73205i) q^{63} -1.00000 q^{64} +(3.00000 - 5.19615i) q^{65} +(6.00000 + 10.3923i) q^{66} +(-3.00000 + 1.73205i) q^{67} +(-6.00000 + 3.46410i) q^{68} -18.0000 q^{70} +(-9.00000 - 5.19615i) q^{71} -1.73205i q^{72} +(3.50000 - 6.06218i) q^{73} +(-1.50000 - 2.59808i) q^{74} +(4.00000 - 6.92820i) q^{75} +(-1.00000 - 1.73205i) q^{76} +(-6.00000 - 10.3923i) q^{77} +(6.00000 + 3.46410i) q^{78} +(-9.00000 + 5.19615i) q^{79} +(7.50000 - 12.9904i) q^{80} -11.0000 q^{81} +(-4.50000 + 2.59808i) q^{82} +(-3.00000 - 5.19615i) q^{83} -6.92820i q^{84} +20.7846i q^{85} +(-3.00000 + 5.19615i) q^{86} +(3.00000 + 1.73205i) q^{87} +6.00000 q^{88} +15.5885i q^{89} +(4.50000 + 2.59808i) q^{90} +(-6.00000 - 3.46410i) q^{91} +(18.0000 + 10.3923i) q^{93} -20.7846i q^{94} -6.00000 q^{95} +(9.00000 + 5.19615i) q^{96} +(-0.500000 + 0.866025i) q^{97} +8.66025i q^{98} +3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 3q^{2} - 4q^{3} + q^{4} - 3q^{5} + 6q^{6} - 6q^{7} + 2q^{9} + O(q^{10}) \) \( 2q - 3q^{2} - 4q^{3} + q^{4} - 3q^{5} + 6q^{6} - 6q^{7} + 2q^{9} + 9q^{10} - 2q^{12} + 2q^{13} + 6q^{14} + 6q^{15} + 5q^{16} - 12q^{17} - 3q^{18} + 2q^{19} - 6q^{20} + 12q^{21} - 6q^{22} - 4q^{25} - 6q^{26} + 8q^{27} - 3q^{29} - 18q^{30} - 18q^{31} - 9q^{32} + 24q^{34} + 18q^{35} + q^{36} - 4q^{39} - 9q^{40} + 6q^{41} - 12q^{42} + 6q^{43} + 6q^{44} - 3q^{45} - 12q^{47} - 10q^{48} + 5q^{49} + 24q^{51} + 4q^{52} - 12q^{54} + 18q^{55} + 6q^{56} - 4q^{57} + 6q^{58} - 6q^{59} + 12q^{60} - q^{61} + 36q^{62} - 6q^{63} - 2q^{64} + 6q^{65} + 12q^{66} - 6q^{67} - 12q^{68} - 36q^{70} - 18q^{71} + 7q^{73} - 3q^{74} + 8q^{75} - 2q^{76} - 12q^{77} + 12q^{78} - 18q^{79} + 15q^{80} - 22q^{81} - 9q^{82} - 6q^{83} - 6q^{86} + 6q^{87} + 12q^{88} + 9q^{90} - 12q^{91} + 36q^{93} - 12q^{95} + 18q^{96} - q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/61\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.50000 + 0.866025i −1.06066 + 0.612372i −0.925615 0.378467i \(-0.876451\pi\)
−0.135045 + 0.990839i \(0.543118\pi\)
\(3\) −2.00000 −1.15470 −0.577350 0.816497i \(-0.695913\pi\)
−0.577350 + 0.816497i \(0.695913\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i \(-0.932609\pi\)
0.306851 0.951757i \(-0.400725\pi\)
\(6\) 3.00000 1.73205i 1.22474 0.707107i
\(7\) −3.00000 + 1.73205i −1.13389 + 0.654654i −0.944911 0.327327i \(-0.893852\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 1.73205i 0.612372i
\(9\) 1.00000 0.333333
\(10\) 4.50000 + 2.59808i 1.42302 + 0.821584i
\(11\) 3.46410i 1.04447i 0.852803 + 0.522233i \(0.174901\pi\)
−0.852803 + 0.522233i \(0.825099\pi\)
\(12\) −1.00000 + 1.73205i −0.288675 + 0.500000i
\(13\) 1.00000 + 1.73205i 0.277350 + 0.480384i 0.970725 0.240192i \(-0.0772105\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 3.00000 5.19615i 0.801784 1.38873i
\(15\) 3.00000 + 5.19615i 0.774597 + 1.34164i
\(16\) 2.50000 + 4.33013i 0.625000 + 1.08253i
\(17\) −6.00000 3.46410i −1.45521 0.840168i −0.456444 0.889752i \(-0.650877\pi\)
−0.998770 + 0.0495842i \(0.984210\pi\)
\(18\) −1.50000 + 0.866025i −0.353553 + 0.204124i
\(19\) 1.00000 1.73205i 0.229416 0.397360i −0.728219 0.685344i \(-0.759652\pi\)
0.957635 + 0.287984i \(0.0929851\pi\)
\(20\) −3.00000 −0.670820
\(21\) 6.00000 3.46410i 1.30931 0.755929i
\(22\) −3.00000 5.19615i −0.639602 1.10782i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 3.46410i 0.707107i
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) −3.00000 1.73205i −0.588348 0.339683i
\(27\) 4.00000 0.769800
\(28\) 3.46410i 0.654654i
\(29\) −1.50000 0.866025i −0.278543 0.160817i 0.354221 0.935162i \(-0.384746\pi\)
−0.632764 + 0.774345i \(0.718080\pi\)
\(30\) −9.00000 5.19615i −1.64317 0.948683i
\(31\) −9.00000 5.19615i −1.61645 0.933257i −0.987829 0.155543i \(-0.950287\pi\)
−0.628619 0.777714i \(-0.716379\pi\)
\(32\) −4.50000 2.59808i −0.795495 0.459279i
\(33\) 6.92820i 1.20605i
\(34\) 12.0000 2.05798
\(35\) 9.00000 + 5.19615i 1.52128 + 0.878310i
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) 1.73205i 0.284747i 0.989813 + 0.142374i \(0.0454735\pi\)
−0.989813 + 0.142374i \(0.954527\pi\)
\(38\) 3.46410i 0.561951i
\(39\) −2.00000 3.46410i −0.320256 0.554700i
\(40\) −4.50000 + 2.59808i −0.711512 + 0.410792i
\(41\) 3.00000 0.468521 0.234261 0.972174i \(-0.424733\pi\)
0.234261 + 0.972174i \(0.424733\pi\)
\(42\) −6.00000 + 10.3923i −0.925820 + 1.60357i
\(43\) 3.00000 1.73205i 0.457496 0.264135i −0.253495 0.967337i \(-0.581580\pi\)
0.710991 + 0.703201i \(0.248247\pi\)
\(44\) 3.00000 + 1.73205i 0.452267 + 0.261116i
\(45\) −1.50000 2.59808i −0.223607 0.387298i
\(46\) 0 0
\(47\) −6.00000 + 10.3923i −0.875190 + 1.51587i −0.0186297 + 0.999826i \(0.505930\pi\)
−0.856560 + 0.516047i \(0.827403\pi\)
\(48\) −5.00000 8.66025i −0.721688 1.25000i
\(49\) 2.50000 4.33013i 0.357143 0.618590i
\(50\) 6.92820i 0.979796i
\(51\) 12.0000 + 6.92820i 1.68034 + 0.970143i
\(52\) 2.00000 0.277350
\(53\) 5.19615i 0.713746i 0.934153 + 0.356873i \(0.116157\pi\)
−0.934153 + 0.356873i \(0.883843\pi\)
\(54\) −6.00000 + 3.46410i −0.816497 + 0.471405i
\(55\) 9.00000 5.19615i 1.21356 0.700649i
\(56\) 3.00000 + 5.19615i 0.400892 + 0.694365i
\(57\) −2.00000 + 3.46410i −0.264906 + 0.458831i
\(58\) 3.00000 0.393919
\(59\) −3.00000 + 1.73205i −0.390567 + 0.225494i −0.682406 0.730974i \(-0.739066\pi\)
0.291839 + 0.956467i \(0.405733\pi\)
\(60\) 6.00000 0.774597
\(61\) −0.500000 7.79423i −0.0640184 0.997949i
\(62\) 18.0000 2.28600
\(63\) −3.00000 + 1.73205i −0.377964 + 0.218218i
\(64\) −1.00000 −0.125000
\(65\) 3.00000 5.19615i 0.372104 0.644503i
\(66\) 6.00000 + 10.3923i 0.738549 + 1.27920i
\(67\) −3.00000 + 1.73205i −0.366508 + 0.211604i −0.671932 0.740613i \(-0.734535\pi\)
0.305424 + 0.952217i \(0.401202\pi\)
\(68\) −6.00000 + 3.46410i −0.727607 + 0.420084i
\(69\) 0 0
\(70\) −18.0000 −2.15141
\(71\) −9.00000 5.19615i −1.06810 0.616670i −0.140441 0.990089i \(-0.544852\pi\)
−0.927663 + 0.373419i \(0.878185\pi\)
\(72\) 1.73205i 0.204124i
\(73\) 3.50000 6.06218i 0.409644 0.709524i −0.585206 0.810885i \(-0.698986\pi\)
0.994850 + 0.101361i \(0.0323196\pi\)
\(74\) −1.50000 2.59808i −0.174371 0.302020i
\(75\) 4.00000 6.92820i 0.461880 0.800000i
\(76\) −1.00000 1.73205i −0.114708 0.198680i
\(77\) −6.00000 10.3923i −0.683763 1.18431i
\(78\) 6.00000 + 3.46410i 0.679366 + 0.392232i
\(79\) −9.00000 + 5.19615i −1.01258 + 0.584613i −0.911946 0.410311i \(-0.865420\pi\)
−0.100633 + 0.994924i \(0.532087\pi\)
\(80\) 7.50000 12.9904i 0.838525 1.45237i
\(81\) −11.0000 −1.22222
\(82\) −4.50000 + 2.59808i −0.496942 + 0.286910i
\(83\) −3.00000 5.19615i −0.329293 0.570352i 0.653079 0.757290i \(-0.273477\pi\)
−0.982372 + 0.186938i \(0.940144\pi\)
\(84\) 6.92820i 0.755929i
\(85\) 20.7846i 2.25441i
\(86\) −3.00000 + 5.19615i −0.323498 + 0.560316i
\(87\) 3.00000 + 1.73205i 0.321634 + 0.185695i
\(88\) 6.00000 0.639602
\(89\) 15.5885i 1.65237i 0.563397 + 0.826187i \(0.309494\pi\)
−0.563397 + 0.826187i \(0.690506\pi\)
\(90\) 4.50000 + 2.59808i 0.474342 + 0.273861i
\(91\) −6.00000 3.46410i −0.628971 0.363137i
\(92\) 0 0
\(93\) 18.0000 + 10.3923i 1.86651 + 1.07763i
\(94\) 20.7846i 2.14377i
\(95\) −6.00000 −0.615587
\(96\) 9.00000 + 5.19615i 0.918559 + 0.530330i
\(97\) −0.500000 + 0.866025i −0.0507673 + 0.0879316i −0.890292 0.455389i \(-0.849500\pi\)
0.839525 + 0.543321i \(0.182833\pi\)
\(98\) 8.66025i 0.874818i
\(99\) 3.46410i 0.348155i
\(100\) 2.00000 + 3.46410i 0.200000 + 0.346410i
\(101\) 13.5000 7.79423i 1.34330 0.775555i 0.356010 0.934482i \(-0.384137\pi\)
0.987290 + 0.158927i \(0.0508036\pi\)
\(102\) −24.0000 −2.37635
\(103\) 4.00000 6.92820i 0.394132 0.682656i −0.598858 0.800855i \(-0.704379\pi\)
0.992990 + 0.118199i \(0.0377120\pi\)
\(104\) 3.00000 1.73205i 0.294174 0.169842i
\(105\) −18.0000 10.3923i −1.75662 1.01419i
\(106\) −4.50000 7.79423i −0.437079 0.757042i
\(107\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(108\) 2.00000 3.46410i 0.192450 0.333333i
\(109\) 3.50000 + 6.06218i 0.335239 + 0.580651i 0.983531 0.180741i \(-0.0578495\pi\)
−0.648292 + 0.761392i \(0.724516\pi\)
\(110\) −9.00000 + 15.5885i −0.858116 + 1.48630i
\(111\) 3.46410i 0.328798i
\(112\) −15.0000 8.66025i −1.41737 0.818317i
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 6.92820i 0.648886i
\(115\) 0 0
\(116\) −1.50000 + 0.866025i −0.139272 + 0.0804084i
\(117\) 1.00000 + 1.73205i 0.0924500 + 0.160128i
\(118\) 3.00000 5.19615i 0.276172 0.478345i
\(119\) 24.0000 2.20008
\(120\) 9.00000 5.19615i 0.821584 0.474342i
\(121\) −1.00000 −0.0909091
\(122\) 7.50000 + 11.2583i 0.679018 + 1.01928i
\(123\) −6.00000 −0.541002
\(124\) −9.00000 + 5.19615i −0.808224 + 0.466628i
\(125\) −3.00000 −0.268328
\(126\) 3.00000 5.19615i 0.267261 0.462910i
\(127\) 1.00000 + 1.73205i 0.0887357 + 0.153695i 0.906977 0.421180i \(-0.138384\pi\)
−0.818241 + 0.574875i \(0.805051\pi\)
\(128\) 10.5000 6.06218i 0.928078 0.535826i
\(129\) −6.00000 + 3.46410i −0.528271 + 0.304997i
\(130\) 10.3923i 0.911465i
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) −6.00000 3.46410i −0.522233 0.301511i
\(133\) 6.92820i 0.600751i
\(134\) 3.00000 5.19615i 0.259161 0.448879i
\(135\) −6.00000 10.3923i −0.516398 0.894427i
\(136\) −6.00000 + 10.3923i −0.514496 + 0.891133i
\(137\) 1.50000 + 2.59808i 0.128154 + 0.221969i 0.922961 0.384893i \(-0.125762\pi\)
−0.794808 + 0.606861i \(0.792428\pi\)
\(138\) 0 0
\(139\) 6.00000 + 3.46410i 0.508913 + 0.293821i 0.732387 0.680889i \(-0.238406\pi\)
−0.223474 + 0.974710i \(0.571740\pi\)
\(140\) 9.00000 5.19615i 0.760639 0.439155i
\(141\) 12.0000 20.7846i 1.01058 1.75038i
\(142\) 18.0000 1.51053
\(143\) −6.00000 + 3.46410i −0.501745 + 0.289683i
\(144\) 2.50000 + 4.33013i 0.208333 + 0.360844i
\(145\) 5.19615i 0.431517i
\(146\) 12.1244i 1.00342i
\(147\) −5.00000 + 8.66025i −0.412393 + 0.714286i
\(148\) 1.50000 + 0.866025i 0.123299 + 0.0711868i
\(149\) −15.0000 −1.22885 −0.614424 0.788976i \(-0.710612\pi\)
−0.614424 + 0.788976i \(0.710612\pi\)
\(150\) 13.8564i 1.13137i
\(151\) −3.00000 1.73205i −0.244137 0.140952i 0.372940 0.927855i \(-0.378350\pi\)
−0.617076 + 0.786903i \(0.711683\pi\)
\(152\) −3.00000 1.73205i −0.243332 0.140488i
\(153\) −6.00000 3.46410i −0.485071 0.280056i
\(154\) 18.0000 + 10.3923i 1.45048 + 0.837436i
\(155\) 31.1769i 2.50419i
\(156\) −4.00000 −0.320256
\(157\) 12.0000 + 6.92820i 0.957704 + 0.552931i 0.895466 0.445130i \(-0.146843\pi\)
0.0622385 + 0.998061i \(0.480176\pi\)
\(158\) 9.00000 15.5885i 0.716002 1.24015i
\(159\) 10.3923i 0.824163i
\(160\) 15.5885i 1.23238i
\(161\) 0 0
\(162\) 16.5000 9.52628i 1.29636 0.748455i
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) 1.50000 2.59808i 0.117130 0.202876i
\(165\) −18.0000 + 10.3923i −1.40130 + 0.809040i
\(166\) 9.00000 + 5.19615i 0.698535 + 0.403300i
\(167\) −9.00000 15.5885i −0.696441 1.20627i −0.969693 0.244328i \(-0.921432\pi\)
0.273252 0.961943i \(-0.411901\pi\)
\(168\) −6.00000 10.3923i −0.462910 0.801784i
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) −18.0000 31.1769i −1.38054 2.39116i
\(171\) 1.00000 1.73205i 0.0764719 0.132453i
\(172\) 3.46410i 0.264135i
\(173\) −7.50000 4.33013i −0.570214 0.329213i 0.187021 0.982356i \(-0.440117\pi\)
−0.757235 + 0.653143i \(0.773450\pi\)
\(174\) −6.00000 −0.454859
\(175\) 13.8564i 1.04745i
\(176\) −15.0000 + 8.66025i −1.13067 + 0.652791i
\(177\) 6.00000 3.46410i 0.450988 0.260378i
\(178\) −13.5000 23.3827i −1.01187 1.75261i
\(179\) −3.00000 + 5.19615i −0.224231 + 0.388379i −0.956088 0.293079i \(-0.905320\pi\)
0.731858 + 0.681457i \(0.238654\pi\)
\(180\) −3.00000 −0.223607
\(181\) −19.5000 + 11.2583i −1.44942 + 0.836825i −0.998447 0.0557107i \(-0.982258\pi\)
−0.450977 + 0.892536i \(0.648924\pi\)
\(182\) 12.0000 0.889499
\(183\) 1.00000 + 15.5885i 0.0739221 + 1.15233i
\(184\) 0 0
\(185\) 4.50000 2.59808i 0.330847 0.191014i
\(186\) −36.0000 −2.63965
\(187\) 12.0000 20.7846i 0.877527 1.51992i
\(188\) 6.00000 + 10.3923i 0.437595 + 0.757937i
\(189\) −12.0000 + 6.92820i −0.872872 + 0.503953i
\(190\) 9.00000 5.19615i 0.652929 0.376969i
\(191\) 13.8564i 1.00261i −0.865269 0.501307i \(-0.832853\pi\)
0.865269 0.501307i \(-0.167147\pi\)
\(192\) 2.00000 0.144338
\(193\) −10.5000 6.06218i −0.755807 0.436365i 0.0719816 0.997406i \(-0.477068\pi\)
−0.827788 + 0.561041i \(0.810401\pi\)
\(194\) 1.73205i 0.124354i
\(195\) −6.00000 + 10.3923i −0.429669 + 0.744208i
\(196\) −2.50000 4.33013i −0.178571 0.309295i
\(197\) −1.50000 + 2.59808i −0.106871 + 0.185105i −0.914501 0.404584i \(-0.867416\pi\)
0.807630 + 0.589689i \(0.200750\pi\)
\(198\) −3.00000 5.19615i −0.213201 0.369274i
\(199\) 2.00000 + 3.46410i 0.141776 + 0.245564i 0.928166 0.372168i \(-0.121385\pi\)
−0.786389 + 0.617731i \(0.788052\pi\)
\(200\) 6.00000 + 3.46410i 0.424264 + 0.244949i
\(201\) 6.00000 3.46410i 0.423207 0.244339i
\(202\) −13.5000 + 23.3827i −0.949857 + 1.64520i
\(203\) 6.00000 0.421117
\(204\) 12.0000 6.92820i 0.840168 0.485071i
\(205\) −4.50000 7.79423i −0.314294 0.544373i
\(206\) 13.8564i 0.965422i
\(207\) 0 0
\(208\) −5.00000 + 8.66025i −0.346688 + 0.600481i
\(209\) 6.00000 + 3.46410i 0.415029 + 0.239617i
\(210\) 36.0000 2.48424
\(211\) 3.46410i 0.238479i −0.992866 0.119239i \(-0.961954\pi\)
0.992866 0.119239i \(-0.0380456\pi\)
\(212\) 4.50000 + 2.59808i 0.309061 + 0.178437i
\(213\) 18.0000 + 10.3923i 1.23334 + 0.712069i
\(214\) 0 0
\(215\) −9.00000 5.19615i −0.613795 0.354375i
\(216\) 6.92820i 0.471405i
\(217\) 36.0000 2.44384
\(218\) −10.5000 6.06218i −0.711150 0.410582i
\(219\) −7.00000 + 12.1244i −0.473016 + 0.819288i
\(220\) 10.3923i 0.700649i
\(221\) 13.8564i 0.932083i
\(222\) 3.00000 + 5.19615i 0.201347 + 0.348743i
\(223\) −12.0000 + 6.92820i −0.803579 + 0.463947i −0.844721 0.535207i \(-0.820234\pi\)
0.0411418 + 0.999153i \(0.486900\pi\)
\(224\) 18.0000 1.20268
\(225\) −2.00000 + 3.46410i −0.133333 + 0.230940i
\(226\) −9.00000 + 5.19615i −0.598671 + 0.345643i
\(227\) 6.00000 + 3.46410i 0.398234 + 0.229920i 0.685722 0.727864i \(-0.259487\pi\)
−0.287488 + 0.957784i \(0.592820\pi\)
\(228\) 2.00000 + 3.46410i 0.132453 + 0.229416i
\(229\) −9.50000 16.4545i −0.627778 1.08734i −0.987997 0.154475i \(-0.950631\pi\)
0.360219 0.932868i \(-0.382702\pi\)
\(230\) 0 0
\(231\) 12.0000 + 20.7846i 0.789542 + 1.36753i
\(232\) −1.50000 + 2.59808i −0.0984798 + 0.170572i
\(233\) 12.1244i 0.794293i 0.917755 + 0.397146i \(0.130000\pi\)
−0.917755 + 0.397146i \(0.870000\pi\)
\(234\) −3.00000 1.73205i −0.196116 0.113228i
\(235\) 36.0000 2.34838
\(236\) 3.46410i 0.225494i
\(237\) 18.0000 10.3923i 1.16923 0.675053i
\(238\) −36.0000 + 20.7846i −2.33353 + 1.34727i
\(239\) −3.00000 5.19615i −0.194054 0.336111i 0.752536 0.658551i \(-0.228830\pi\)
−0.946590 + 0.322440i \(0.895497\pi\)
\(240\) −15.0000 + 25.9808i −0.968246 + 1.67705i
\(241\) −11.0000 −0.708572 −0.354286 0.935137i \(-0.615276\pi\)
−0.354286 + 0.935137i \(0.615276\pi\)
\(242\) 1.50000 0.866025i 0.0964237 0.0556702i
\(243\) 10.0000 0.641500
\(244\) −7.00000 3.46410i −0.448129 0.221766i
\(245\) −15.0000 −0.958315
\(246\) 9.00000 5.19615i 0.573819 0.331295i
\(247\) 4.00000 0.254514
\(248\) −9.00000 + 15.5885i −0.571501 + 0.989868i
\(249\) 6.00000 + 10.3923i 0.380235 + 0.658586i
\(250\) 4.50000 2.59808i 0.284605 0.164317i
\(251\) 12.0000 6.92820i 0.757433 0.437304i −0.0709402 0.997481i \(-0.522600\pi\)
0.828373 + 0.560176i \(0.189267\pi\)
\(252\) 3.46410i 0.218218i
\(253\) 0 0
\(254\) −3.00000 1.73205i −0.188237 0.108679i
\(255\) 41.5692i 2.60317i
\(256\) −9.50000 + 16.4545i −0.593750 + 1.02841i
\(257\) 7.50000 + 12.9904i 0.467837 + 0.810318i 0.999325 0.0367485i \(-0.0117000\pi\)
−0.531487 + 0.847066i \(0.678367\pi\)
\(258\) 6.00000 10.3923i 0.373544 0.646997i
\(259\) −3.00000 5.19615i −0.186411 0.322873i
\(260\) −3.00000 5.19615i −0.186052 0.322252i
\(261\) −1.50000 0.866025i −0.0928477 0.0536056i
\(262\) 0 0
\(263\) 3.00000 5.19615i 0.184988 0.320408i −0.758585 0.651575i \(-0.774109\pi\)
0.943572 + 0.331166i \(0.107442\pi\)
\(264\) −12.0000 −0.738549
\(265\) 13.5000 7.79423i 0.829298 0.478796i
\(266\) −6.00000 10.3923i −0.367884 0.637193i
\(267\) 31.1769i 1.90800i
\(268\) 3.46410i 0.211604i
\(269\) −4.50000 + 7.79423i −0.274370 + 0.475223i −0.969976 0.243201i \(-0.921803\pi\)
0.695606 + 0.718423i \(0.255136\pi\)
\(270\) 18.0000 + 10.3923i 1.09545 + 0.632456i
\(271\) −10.0000 −0.607457 −0.303728 0.952759i \(-0.598232\pi\)
−0.303728 + 0.952759i \(0.598232\pi\)
\(272\) 34.6410i 2.10042i
\(273\) 12.0000 + 6.92820i 0.726273 + 0.419314i
\(274\) −4.50000 2.59808i −0.271855 0.156956i
\(275\) −12.0000 6.92820i −0.723627 0.417786i
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) −12.0000 −0.719712
\(279\) −9.00000 5.19615i −0.538816 0.311086i
\(280\) 9.00000 15.5885i 0.537853 0.931589i
\(281\) 19.0526i 1.13658i 0.822828 + 0.568290i \(0.192395\pi\)
−0.822828 + 0.568290i \(0.807605\pi\)
\(282\) 41.5692i 2.47541i
\(283\) −13.0000 22.5167i −0.772770 1.33848i −0.936039 0.351895i \(-0.885537\pi\)
0.163270 0.986581i \(-0.447796\pi\)
\(284\) −9.00000 + 5.19615i −0.534052 + 0.308335i
\(285\) 12.0000 0.710819
\(286\) 6.00000 10.3923i 0.354787 0.614510i
\(287\) −9.00000 + 5.19615i −0.531253 + 0.306719i
\(288\) −4.50000 2.59808i −0.265165 0.153093i
\(289\) 15.5000 + 26.8468i 0.911765 + 1.57922i
\(290\) −4.50000 7.79423i −0.264249 0.457693i
\(291\) 1.00000 1.73205i 0.0586210 0.101535i
\(292\) −3.50000 6.06218i −0.204822 0.354762i
\(293\) −3.00000 + 5.19615i −0.175262 + 0.303562i −0.940252 0.340480i \(-0.889411\pi\)
0.764990 + 0.644042i \(0.222744\pi\)
\(294\) 17.3205i 1.01015i
\(295\) 9.00000 + 5.19615i 0.524000 + 0.302532i
\(296\) 3.00000 0.174371
\(297\) 13.8564i 0.804030i
\(298\) 22.5000 12.9904i 1.30339 0.752513i
\(299\) 0 0
\(300\) −4.00000 6.92820i −0.230940 0.400000i
\(301\) −6.00000 + 10.3923i −0.345834 + 0.599002i
\(302\) 6.00000 0.345261
\(303\) −27.0000 + 15.5885i −1.55111 + 0.895533i
\(304\) 10.0000 0.573539
\(305\) −19.5000 + 12.9904i −1.11657 + 0.743827i
\(306\) 12.0000 0.685994
\(307\) −3.00000 + 1.73205i −0.171219 + 0.0988534i −0.583161 0.812357i \(-0.698184\pi\)
0.411941 + 0.911210i \(0.364851\pi\)
\(308\) −12.0000 −0.683763
\(309\) −8.00000 + 13.8564i −0.455104 + 0.788263i
\(310\) −27.0000 46.7654i −1.53350 2.65609i
\(311\) 12.0000 6.92820i 0.680458 0.392862i −0.119570 0.992826i \(-0.538152\pi\)
0.800027 + 0.599963i \(0.204818\pi\)
\(312\) −6.00000 + 3.46410i −0.339683 + 0.196116i
\(313\) 20.7846i 1.17482i 0.809291 + 0.587408i \(0.199852\pi\)
−0.809291 + 0.587408i \(0.800148\pi\)
\(314\) −24.0000 −1.35440
\(315\) 9.00000 + 5.19615i 0.507093 + 0.292770i
\(316\) 10.3923i 0.584613i
\(317\) 3.00000 5.19615i 0.168497 0.291845i −0.769395 0.638774i \(-0.779442\pi\)
0.937892 + 0.346929i \(0.112775\pi\)
\(318\) 9.00000 + 15.5885i 0.504695 + 0.874157i
\(319\) 3.00000 5.19615i 0.167968 0.290929i
\(320\) 1.50000 + 2.59808i 0.0838525 + 0.145237i
\(321\) 0 0
\(322\) 0 0
\(323\) −12.0000 + 6.92820i −0.667698 + 0.385496i
\(324\) −5.50000 + 9.52628i −0.305556 + 0.529238i
\(325\) −8.00000 −0.443760
\(326\) −6.00000 + 3.46410i −0.332309 + 0.191859i
\(327\) −7.00000 12.1244i −0.387101 0.670478i
\(328\) 5.19615i 0.286910i
\(329\) 41.5692i 2.29179i
\(330\) 18.0000 31.1769i 0.990867 1.71623i
\(331\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(332\) −6.00000 −0.329293
\(333\) 1.73205i 0.0949158i
\(334\) 27.0000 + 15.5885i 1.47737 + 0.852962i
\(335\) 9.00000 + 5.19615i 0.491723 + 0.283896i
\(336\) 30.0000 + 17.3205i 1.63663 + 0.944911i
\(337\) −24.0000 13.8564i −1.30736 0.754807i −0.325708 0.945470i \(-0.605603\pi\)
−0.981655 + 0.190664i \(0.938936\pi\)
\(338\) 15.5885i 0.847900i
\(339\) −12.0000 −0.651751
\(340\) 18.0000 + 10.3923i 0.976187 + 0.563602i
\(341\) 18.0000 31.1769i 0.974755 1.68832i
\(342\) 3.46410i 0.187317i
\(343\) 6.92820i 0.374088i
\(344\) −3.00000 5.19615i −0.161749 0.280158i
\(345\) 0 0
\(346\) 15.0000 0.806405
\(347\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(348\) 3.00000 1.73205i 0.160817 0.0928477i
\(349\) 4.50000 + 2.59808i 0.240879 + 0.139072i 0.615581 0.788074i \(-0.288921\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 12.0000 + 20.7846i 0.641427 + 1.11098i
\(351\) 4.00000 + 6.92820i 0.213504 + 0.369800i
\(352\) 9.00000 15.5885i 0.479702 0.830868i
\(353\) 3.00000 + 5.19615i 0.159674 + 0.276563i 0.934751 0.355303i \(-0.115622\pi\)
−0.775077 + 0.631867i \(0.782289\pi\)
\(354\) −6.00000 + 10.3923i −0.318896 + 0.552345i
\(355\) 31.1769i 1.65470i
\(356\) 13.5000 + 7.79423i 0.715499 + 0.413093i
\(357\) −48.0000 −2.54043
\(358\) 10.3923i 0.549250i
\(359\) −15.0000 + 8.66025i −0.791670 + 0.457071i −0.840550 0.541734i \(-0.817768\pi\)
0.0488803 + 0.998805i \(0.484435\pi\)
\(360\) −4.50000 + 2.59808i −0.237171 + 0.136931i
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 19.5000 33.7750i 1.02490 1.77517i
\(363\) 2.00000 0.104973
\(364\) −6.00000 + 3.46410i −0.314485 + 0.181568i
\(365\) −21.0000 −1.09919
\(366\) −15.0000 22.5167i −0.784063 1.17696i
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 0 0
\(369\) 3.00000 0.156174
\(370\) −4.50000 + 7.79423i −0.233944 + 0.405203i
\(371\) −9.00000 15.5885i −0.467257 0.809312i
\(372\) 18.0000 10.3923i 0.933257 0.538816i
\(373\) 25.5000 14.7224i 1.32034 0.762299i 0.336557 0.941663i \(-0.390737\pi\)
0.983783 + 0.179364i \(0.0574041\pi\)
\(374\) 41.5692i 2.14949i
\(375\) 6.00000 0.309839
\(376\) 18.0000 + 10.3923i 0.928279 + 0.535942i
\(377\) 3.46410i 0.178410i
\(378\) 12.0000 20.7846i 0.617213 1.06904i
\(379\) 8.00000 + 13.8564i 0.410932 + 0.711756i 0.994992 0.0999550i \(-0.0318699\pi\)
−0.584060 + 0.811711i \(0.698537\pi\)
\(380\) −3.00000 + 5.19615i −0.153897 + 0.266557i
\(381\) −2.00000 3.46410i −0.102463 0.177471i
\(382\) 12.0000 + 20.7846i 0.613973 + 1.06343i
\(383\) 18.0000 + 10.3923i 0.919757 + 0.531022i 0.883558 0.468323i \(-0.155141\pi\)
0.0361995 + 0.999345i \(0.488475\pi\)
\(384\) −21.0000 + 12.1244i −1.07165 + 0.618718i
\(385\) −18.0000 + 31.1769i −0.917365 + 1.58892i
\(386\) 21.0000 1.06887
\(387\) 3.00000 1.73205i 0.152499 0.0880451i
\(388\) 0.500000 + 0.866025i 0.0253837 + 0.0439658i
\(389\) 29.4449i 1.49291i −0.665434 0.746457i \(-0.731753\pi\)
0.665434 0.746457i \(-0.268247\pi\)
\(390\) 20.7846i 1.05247i
\(391\) 0 0
\(392\) −7.50000 4.33013i −0.378807 0.218704i
\(393\) 0 0
\(394\) 5.19615i 0.261778i
\(395\) 27.0000 + 15.5885i 1.35852 + 0.784340i
\(396\) 3.00000 + 1.73205i 0.150756 + 0.0870388i
\(397\) −28.5000 16.4545i −1.43037 0.825827i −0.433225 0.901286i \(-0.642624\pi\)
−0.997149 + 0.0754589i \(0.975958\pi\)
\(398\) −6.00000 3.46410i −0.300753 0.173640i
\(399\) 13.8564i 0.693688i
\(400\) −20.0000 −1.00000
\(401\) −1.50000 0.866025i −0.0749064 0.0432472i 0.462079 0.886839i \(-0.347104\pi\)
−0.536985 + 0.843592i \(0.680437\pi\)
\(402\) −6.00000 + 10.3923i −0.299253 + 0.518321i
\(403\) 20.7846i 1.03536i
\(404\) 15.5885i 0.775555i
\(405\) 16.5000 + 28.5788i 0.819892 + 1.42009i
\(406\) −9.00000 + 5.19615i −0.446663 + 0.257881i
\(407\) −6.00000 −0.297409
\(408\) 12.0000 20.7846i 0.594089 1.02899i
\(409\) 31.5000 18.1865i 1.55757 0.899266i 0.560087 0.828434i \(-0.310768\pi\)
0.997488 0.0708321i \(-0.0225654\pi\)
\(410\) 13.5000 + 7.79423i 0.666717 + 0.384930i
\(411\) −3.00000 5.19615i −0.147979 0.256307i
\(412\) −4.00000 6.92820i −0.197066 0.341328i
\(413\) 6.00000 10.3923i 0.295241 0.511372i
\(414\) 0 0
\(415\) −9.00000 + 15.5885i −0.441793 + 0.765207i
\(416\) 10.3923i 0.509525i
\(417\) −12.0000 6.92820i −0.587643 0.339276i
\(418\) −12.0000 −0.586939
\(419\) 27.7128i 1.35386i 0.736048 + 0.676930i \(0.236690\pi\)
−0.736048 + 0.676930i \(0.763310\pi\)
\(420\) −18.0000 + 10.3923i −0.878310 + 0.507093i
\(421\) −18.0000 + 10.3923i −0.877266 + 0.506490i −0.869756 0.493482i \(-0.835724\pi\)
−0.00751023 + 0.999972i \(0.502391\pi\)
\(422\) 3.00000 + 5.19615i 0.146038 + 0.252945i
\(423\) −6.00000 + 10.3923i −0.291730 + 0.505291i
\(424\) 9.00000 0.437079
\(425\) 24.0000 13.8564i 1.16417 0.672134i
\(426\) −36.0000 −1.74421
\(427\) 15.0000 + 22.5167i 0.725901 + 1.08966i
\(428\) 0 0
\(429\) 12.0000 6.92820i 0.579365 0.334497i
\(430\) 18.0000 0.868037
\(431\) −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i \(-0.926659\pi\)
0.684564 + 0.728953i \(0.259993\pi\)
\(432\) 10.0000 + 17.3205i 0.481125 + 0.833333i
\(433\) −34.5000 + 19.9186i −1.65796 + 0.957226i −0.684312 + 0.729190i \(0.739897\pi\)
−0.973653 + 0.228036i \(0.926769\pi\)
\(434\) −54.0000 + 31.1769i −2.59208 + 1.49654i
\(435\) 10.3923i 0.498273i
\(436\) 7.00000 0.335239
\(437\) 0 0
\(438\) 24.2487i 1.15865i
\(439\) −10.0000 + 17.3205i −0.477274 + 0.826663i −0.999661 0.0260459i \(-0.991708\pi\)
0.522387 + 0.852709i \(0.325042\pi\)
\(440\) −9.00000 15.5885i −0.429058 0.743151i
\(441\) 2.50000 4.33013i 0.119048 0.206197i
\(442\) 12.0000 + 20.7846i 0.570782 + 0.988623i
\(443\) 3.00000 + 5.19615i 0.142534 + 0.246877i 0.928450 0.371457i \(-0.121142\pi\)
−0.785916 + 0.618333i \(0.787808\pi\)
\(444\) −3.00000 1.73205i −0.142374 0.0821995i
\(445\) 40.5000 23.3827i 1.91988 1.10845i
\(446\) 12.0000 20.7846i 0.568216 0.984180i
\(447\) 30.0000 1.41895
\(448\) 3.00000 1.73205i 0.141737 0.0818317i
\(449\) −15.0000 25.9808i −0.707894 1.22611i −0.965637 0.259895i \(-0.916312\pi\)
0.257743 0.966213i \(-0.417021\pi\)
\(450\) 6.92820i 0.326599i
\(451\) 10.3923i 0.489355i
\(452\) 3.00000 5.19615i 0.141108 0.244406i
\(453\) 6.00000 + 3.46410i 0.281905 + 0.162758i
\(454\) −12.0000 −0.563188
\(455\) 20.7846i 0.974398i
\(456\) 6.00000 + 3.46410i 0.280976 + 0.162221i
\(457\) −19.5000 11.2583i −0.912172 0.526642i −0.0310423 0.999518i \(-0.509883\pi\)
−0.881129 + 0.472876i \(0.843216\pi\)
\(458\) 28.5000 + 16.4545i 1.33172 + 0.768867i
\(459\) −24.0000 13.8564i −1.12022 0.646762i
\(460\) 0 0
\(461\) 27.0000 1.25752 0.628758 0.777601i \(-0.283564\pi\)
0.628758 + 0.777601i \(0.283564\pi\)
\(462\) −36.0000 20.7846i −1.67487 0.966988i
\(463\) −20.0000 + 34.6410i −0.929479 + 1.60990i −0.145284 + 0.989390i \(0.546410\pi\)
−0.784195 + 0.620515i \(0.786924\pi\)
\(464\) 8.66025i 0.402042i
\(465\) 62.3538i 2.89159i
\(466\) −10.5000 18.1865i −0.486403 0.842475i
\(467\) 18.0000 10.3923i 0.832941 0.480899i −0.0219178 0.999760i \(-0.506977\pi\)
0.854858 + 0.518861i \(0.173644\pi\)
\(468\) 2.00000 0.0924500
\(469\) 6.00000 10.3923i 0.277054 0.479872i
\(470\) −54.0000 + 31.1769i −2.49083 + 1.43808i
\(471\) −24.0000 13.8564i −1.10586 0.638470i
\(472\) 3.00000 + 5.19615i 0.138086 + 0.239172i
\(473\) 6.00000 + 10.3923i 0.275880 + 0.477839i
\(474\) −18.0000 + 31.1769i −0.826767 + 1.43200i
\(475\) 4.00000 + 6.92820i 0.183533 + 0.317888i
\(476\) 12.0000 20.7846i 0.550019 0.952661i
\(477\) 5.19615i 0.237915i
\(478\) 9.00000 + 5.19615i 0.411650 + 0.237666i
\(479\) −6.00000 −0.274147 −0.137073 0.990561i \(-0.543770\pi\)
−0.137073 + 0.990561i \(0.543770\pi\)
\(480\) 31.1769i 1.42302i
\(481\) −3.00000 + 1.73205i −0.136788 + 0.0789747i
\(482\) 16.5000 9.52628i 0.751554 0.433910i
\(483\) 0 0
\(484\) −0.500000 + 0.866025i −0.0227273 + 0.0393648i
\(485\) 3.00000 0.136223
\(486\) −15.0000 + 8.66025i −0.680414 + 0.392837i
\(487\) 2.00000 0.0906287 0.0453143 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) −13.5000 + 0.866025i −0.611116 + 0.0392031i
\(489\) −8.00000 −0.361773
\(490\) 22.5000 12.9904i 1.01645 0.586846i
\(491\) 30.0000 1.35388 0.676941 0.736038i \(-0.263305\pi\)
0.676941 + 0.736038i \(0.263305\pi\)
\(492\) −3.00000 + 5.19615i −0.135250 + 0.234261i
\(493\) 6.00000 + 10.3923i 0.270226 + 0.468046i
\(494\) −6.00000 + 3.46410i −0.269953 + 0.155857i
\(495\) 9.00000 5.19615i 0.404520 0.233550i
\(496\) 51.9615i 2.33314i
\(497\) 36.0000 1.61482
\(498\) −18.0000 10.3923i −0.806599 0.465690i
\(499\) 34.6410i 1.55074i −0.631504 0.775372i \(-0.717562\pi\)
0.631504 0.775372i \(-0.282438\pi\)
\(500\) −1.50000 + 2.59808i −0.0670820 + 0.116190i
\(501\) 18.0000 + 31.1769i 0.804181 + 1.39288i
\(502\) −12.0000 + 20.7846i −0.535586 + 0.927663i
\(503\) −18.0000 31.1769i −0.802580 1.39011i −0.917912 0.396783i \(-0.870127\pi\)
0.115332 0.993327i \(-0.463207\pi\)
\(504\) 3.00000 + 5.19615i 0.133631 + 0.231455i
\(505\) −40.5000 23.3827i −1.80223 1.04052i
\(506\) 0 0
\(507\) −9.00000 + 15.5885i −0.399704 + 0.692308i
\(508\) 2.00000 0.0887357
\(509\) −13.5000 + 7.79423i −0.598377 + 0.345473i −0.768403 0.639966i \(-0.778948\pi\)
0.170026 + 0.985440i \(0.445615\pi\)
\(510\) 36.0000 + 62.3538i 1.59411 + 2.76107i
\(511\) 24.2487i 1.07270i
\(512\) 8.66025i 0.382733i
\(513\) 4.00000 6.92820i 0.176604 0.305888i
\(514\) −22.5000 12.9904i −0.992432 0.572981i
\(515\) −24.0000 −1.05757
\(516\) 6.92820i 0.304997i
\(517\) −36.0000 20.7846i −1.58328 0.914106i
\(518\) 9.00000 + 5.19615i 0.395437 + 0.228306i
\(519\) 15.0000 + 8.66025i 0.658427 + 0.380143i
\(520\) −9.00000 5.19615i −0.394676 0.227866i
\(521\) 25.9808i 1.13824i −0.822255 0.569119i \(-0.807284\pi\)
0.822255 0.569119i \(-0.192716\pi\)
\(522\) 3.00000 0.131306
\(523\) −18.0000 10.3923i −0.787085 0.454424i 0.0518503 0.998655i \(-0.483488\pi\)
−0.838935 + 0.544231i \(0.816821\pi\)
\(524\) 0 0
\(525\) 27.7128i 1.20949i
\(526\) 10.3923i 0.453126i
\(527\) 36.0000 + 62.3538i 1.56818 + 2.71618i
\(528\) 30.0000 17.3205i 1.30558 0.753778i
\(529\) 23.0000 1.00000
\(530\) −13.5000 + 23.3827i −0.586403 + 1.01568i
\(531\) −3.00000 + 1.73205i −0.130189 + 0.0751646i
\(532\) 6.00000 + 3.46410i 0.260133 + 0.150188i
\(533\) 3.00000 + 5.19615i 0.129944 + 0.225070i
\(534\) 27.0000 + 46.7654i 1.16840 + 2.02374i
\(535\) 0 0
\(536\) 3.00000 + 5.19615i 0.129580 + 0.224440i
\(537\) 6.00000 10.3923i 0.258919 0.448461i
\(538\) 15.5885i 0.672066i
\(539\) 15.0000 + 8.66025i 0.646096 + 0.373024i
\(540\) −12.0000 −0.516398
\(541\) 13.8564i 0.595733i 0.954607 + 0.297867i \(0.0962751\pi\)
−0.954607 + 0.297867i \(0.903725\pi\)
\(542\) 15.0000 8.66025i 0.644305 0.371990i
\(543\) 39.0000 22.5167i 1.67365 0.966282i
\(544\) 18.0000 + 31.1769i 0.771744 + 1.33670i
\(545\) 10.5000 18.1865i 0.449771 0.779026i
\(546\) −24.0000 −1.02711
\(547\) 33.0000 19.0526i 1.41098 0.814629i 0.415498 0.909594i \(-0.363607\pi\)
0.995481 + 0.0949657i \(0.0302741\pi\)
\(548\) 3.00000 0.128154
\(549\) −0.500000 7.79423i −0.0213395 0.332650i
\(550\) 24.0000 1.02336
\(551\) −3.00000 + 1.73205i −0.127804 + 0.0737878i
\(552\) 0 0
\(553\) 18.0000 31.1769i 0.765438 1.32578i
\(554\) 0 0
\(555\) −9.00000 + 5.19615i −0.382029 + 0.220564i
\(556\) 6.00000 3.46410i 0.254457 0.146911i
\(557\) 1.73205i 0.0733893i −0.999327 0.0366947i \(-0.988317\pi\)
0.999327 0.0366947i \(-0.0116829\pi\)
\(558\) 18.0000 0.762001
\(559\) 6.00000 + 3.46410i 0.253773 + 0.146516i
\(560\) 51.9615i 2.19578i
\(561\) −24.0000 + 41.5692i −1.01328 + 1.75505i
\(562\) −16.5000 28.5788i −0.696010 1.20553i
\(563\) −21.0000 + 36.3731i −0.885044 + 1.53294i −0.0393818 + 0.999224i \(0.512539\pi\)
−0.845663 + 0.533718i \(0.820794\pi\)
\(564\) −12.0000 20.7846i −0.505291 0.875190i
\(565\) −9.00000 15.5885i −0.378633 0.655811i
\(566\) 39.0000 + 22.5167i 1.63929 + 0.946446i
\(567\) 33.0000 19.0526i 1.38587 0.800132i
\(568\) −9.00000 + 15.5885i −0.377632 + 0.654077i
\(569\) 6.00000 0.251533 0.125767 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) −18.0000 + 10.3923i −0.753937 + 0.435286i
\(571\) 10.0000 + 17.3205i 0.418487 + 0.724841i 0.995788 0.0916910i \(-0.0292272\pi\)
−0.577301 + 0.816532i \(0.695894\pi\)
\(572\) 6.92820i 0.289683i
\(573\) 27.7128i 1.15772i
\(574\) 9.00000 15.5885i 0.375653 0.650650i
\(575\) 0 0
\(576\) −1.00000 −0.0416667
\(577\) 22.5167i 0.937381i −0.883362 0.468690i \(-0.844726\pi\)
0.883362 0.468690i \(-0.155274\pi\)
\(578\) −46.5000 26.8468i −1.93415 1.11668i
\(579\) 21.0000 + 12.1244i 0.872730 + 0.503871i
\(580\) 4.50000 + 2.59808i 0.186852 + 0.107879i
\(581\) 18.0000 + 10.3923i 0.746766 + 0.431145i
\(582\) 3.46410i 0.143592i
\(583\) −18.0000 −0.745484
\(584\) −10.5000 6.06218i −0.434493 0.250855i
\(585\) 3.00000 5.19615i 0.124035 0.214834i
\(586\) 10.3923i 0.429302i
\(587\) 6.92820i 0.285958i 0.989726 + 0.142979i \(0.0456681\pi\)
−0.989726 + 0.142979i \(0.954332\pi\)
\(588\) 5.00000 + 8.66025i 0.206197 + 0.357143i
\(589\) −18.0000 + 10.3923i −0.741677 + 0.428207i
\(590\) −18.0000 −0.741048
\(591\) 3.00000 5.19615i 0.123404 0.213741i
\(592\) −7.50000 + 4.33013i −0.308248 + 0.177967i
\(593\) −1.50000 0.866025i −0.0615976 0.0355634i 0.468885 0.883259i \(-0.344656\pi\)
−0.530483 + 0.847696i \(0.677989\pi\)
\(594\) −12.0000 20.7846i −0.492366 0.852803i
\(595\) −36.0000 62.3538i −1.47586 2.55626i
\(596\) −7.50000 + 12.9904i −0.307212 + 0.532107i
\(597\) −4.00000 6.92820i −0.163709 0.283552i
\(598\) 0 0
\(599\) 17.3205i 0.707697i −0.935303 0.353848i \(-0.884873\pi\)
0.935303 0.353848i \(-0.115127\pi\)
\(600\) −12.0000 6.92820i −0.489898 0.282843i
\(601\) −5.00000 −0.203954 −0.101977 0.994787i \(-0.532517\pi\)
−0.101977 + 0.994787i \(0.532517\pi\)
\(602\) 20.7846i 0.847117i
\(603\) −3.00000 + 1.73205i −0.122169 + 0.0705346i
\(604\) −3.00000 + 1.73205i −0.122068 + 0.0704761i
\(605\) 1.50000 + 2.59808i 0.0609837 + 0.105627i
\(606\) 27.0000 46.7654i 1.09680 1.89971i
\(607\) −22.0000 −0.892952 −0.446476 0.894795i \(-0.647321\pi\)
−0.446476 + 0.894795i \(0.647321\pi\)
\(608\) −9.00000 + 5.19615i −0.364998 + 0.210732i
\(609\) −12.0000 −0.486265
\(610\) 18.0000 36.3731i 0.728799 1.47270i
\(611\) −24.0000 −0.970936
\(612\) −6.00000 + 3.46410i −0.242536 + 0.140028i
\(613\) −5.00000 −0.201948 −0.100974 0.994889i \(-0.532196\pi\)
−0.100974 + 0.994889i \(0.532196\pi\)
\(614\) 3.00000 5.19615i 0.121070 0.209700i
\(615\) 9.00000 + 15.5885i 0.362915 + 0.628587i
\(616\) −18.0000 + 10.3923i −0.725241 + 0.418718i
\(617\) −18.0000 + 10.3923i −0.724653 + 0.418378i −0.816463 0.577398i \(-0.804068\pi\)
0.0918100 + 0.995777i \(0.470735\pi\)
\(618\) 27.7128i 1.11477i
\(619\) −32.0000 −1.28619 −0.643094 0.765787i \(-0.722350\pi\)
−0.643094 + 0.765787i \(0.722350\pi\)
\(620\) 27.0000 + 15.5885i 1.08435 + 0.626048i
\(621\) 0 0
\(622\) −12.0000 + 20.7846i −0.481156 + 0.833387i
\(623\) −27.0000 46.7654i −1.08173 1.87362i
\(624\) 10.0000 17.3205i 0.400320 0.693375i
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) −18.0000 31.1769i −0.719425 1.24608i
\(627\) −12.0000 6.92820i −0.479234 0.276686i
\(628\) 12.0000 6.92820i 0.478852 0.276465i
\(629\) 6.00000 10.3923i 0.239236 0.414368i
\(630\) −18.0000 −0.717137
\(631\) 15.0000 8.66025i 0.597141 0.344759i −0.170775 0.985310i \(-0.554627\pi\)
0.767916 + 0.640551i \(0.221294\pi\)
\(632\) 9.00000 + 15.5885i 0.358001 + 0.620076i
\(633\) 6.92820i 0.275371i
\(634\) 10.3923i 0.412731i
\(635\) 3.00000 5.19615i 0.119051 0.206203i
\(636\) −9.00000 5.19615i −0.356873 0.206041i
\(637\) 10.0000 0.396214
\(638\) 10.3923i 0.411435i
\(639\) −9.00000 5.19615i −0.356034 0.205557i
\(640\) −31.5000 18.1865i −1.24515 0.718886i
\(641\) 28.5000 + 16.4545i 1.12568 + 0.649913i 0.942845 0.333230i \(-0.108139\pi\)
0.182837 + 0.983143i \(0.441472\pi\)
\(642\) 0 0
\(643\) 24.2487i 0.956276i 0.878285 + 0.478138i \(0.158688\pi\)
−0.878285 + 0.478138i \(0.841312\pi\)
\(644\) 0 0
\(645\) 18.0000 + 10.3923i 0.708749 + 0.409197i
\(646\) 12.0000 20.7846i 0.472134 0.817760i
\(647\) 13.8564i 0.544752i 0.962191 + 0.272376i \(0.0878094\pi\)
−0.962191 + 0.272376i \(0.912191\pi\)
\(648\) 19.0526i 0.748455i
\(649\) −6.00000 10.3923i −0.235521 0.407934i
\(650\) 12.0000 6.92820i 0.470679 0.271746i
\(651\) −72.0000 −2.82190
\(652\) 2.00000 3.46410i 0.0783260 0.135665i
\(653\) 31.5000 18.1865i 1.23269 0.711694i 0.265100 0.964221i \(-0.414595\pi\)
0.967590 + 0.252527i \(0.0812616\pi\)
\(654\) 21.0000 + 12.1244i 0.821165 + 0.474100i
\(655\) 0 0
\(656\) 7.50000 + 12.9904i 0.292826 + 0.507189i
\(657\) 3.50000 6.06218i 0.136548 0.236508i
\(658\) 36.0000 + 62.3538i 1.40343 + 2.43081i
\(659\) 9.00000 15.5885i 0.350590 0.607240i −0.635763 0.771885i \(-0.719314\pi\)
0.986353 + 0.164644i \(0.0526477\pi\)
\(660\) 20.7846i 0.809040i
\(661\) −1.50000 0.866025i −0.0583432 0.0336845i 0.470545 0.882376i \(-0.344057\pi\)
−0.528888 + 0.848692i \(0.677391\pi\)
\(662\) 0 0
\(663\) 27.7128i 1.07628i
\(664\) −9.00000 + 5.19615i −0.349268 + 0.201650i
\(665\) 18.0000 10.3923i 0.698010 0.402996i
\(666\) −1.50000 2.59808i −0.0581238 0.100673i
\(667\) 0 0
\(668\) −18.0000 −0.696441
\(669\) 24.0000 13.8564i 0.927894 0.535720i
\(670\) −18.0000 −0.695401
\(671\) 27.0000 1.73205i 1.04232 0.0668651i
\(672\) −36.0000 −1.38873
\(673\) −25.5000 + 14.7224i −0.982953 + 0.567508i −0.903160 0.429303i \(-0.858759\pi\)
−0.0797925 + 0.996811i \(0.525426\pi\)
\(674\) 48.0000 1.84889
\(675\) −8.00000 + 13.8564i −0.307920 + 0.533333i
\(676\) −4.50000 7.79423i −0.173077 0.299778i
\(677\) −13.5000 + 7.79423i −0.518847 + 0.299557i −0.736463 0.676478i \(-0.763505\pi\)
0.217616 + 0.976035i \(0.430172\pi\)
\(678\) 18.0000 10.3923i 0.691286 0.399114i
\(679\) 3.46410i 0.132940i
\(680\) 36.0000 1.38054
\(681\) −12.0000 6.92820i −0.459841 0.265489i
\(682\) 62.3538i 2.38765i
\(683\) 18.0000 31.1769i 0.688751 1.19295i −0.283491 0.958975i \(-0.591493\pi\)
0.972242 0.233977i \(-0.0751739\pi\)
\(684\) −1.00000 1.73205i −0.0382360 0.0662266i
\(685\) 4.50000 7.79423i 0.171936 0.297802i
\(686\) 6.00000 + 10.3923i 0.229081 + 0.396780i
\(687\) 19.0000 + 32.9090i 0.724895 + 1.25556i
\(688\) 15.0000 + 8.66025i 0.571870 + 0.330169i
\(689\) −9.00000 + 5.19615i −0.342873 + 0.197958i
\(690\) 0 0
\(691\) −8.00000 −0.304334 −0.152167 0.988355i \(-0.548625\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(692\) −7.50000 + 4.33013i −0.285107 + 0.164607i
\(693\) −6.00000 10.3923i −0.227921 0.394771i
\(694\) 0 0
\(695\) 20.7846i 0.788405i
\(696\) 3.00000 5.19615i 0.113715 0.196960i
\(697\) −18.0000 10.3923i −0.681799 0.393637i
\(698\) −9.00000 −0.340655
\(699\) 24.2487i 0.917170i
\(700\) −12.0000 6.92820i −0.453557 0.261861i
\(701\) −10.5000 6.06218i −0.396580 0.228965i 0.288428 0.957502i \(-0.406868\pi\)
−0.685007 + 0.728536i \(0.740201\pi\)
\(702\) −12.0000 6.92820i −0.452911 0.261488i
\(703\) 3.00000 + 1.73205i 0.113147 + 0.0653255i
\(704\) 3.46410i 0.130558i
\(705\) −72.0000 −2.71168
\(706\) −9.00000 5.19615i −0.338719 0.195560i
\(707\) −27.0000 + 46.7654i −1.01544 + 1.75879i
\(708\) 6.92820i 0.260378i
\(709\) 39.8372i 1.49612i 0.663633 + 0.748058i \(0.269014\pi\)
−0.663633 + 0.748058i \(0.730986\pi\)
\(710\) −27.0000 46.7654i −1.01329 1.75507i
\(711\) −9.00000 + 5.19615i −0.337526 + 0.194871i
\(712\) 27.0000 1.01187
\(713\) 0 0
\(714\) 72.0000 41.5692i 2.69453 1.55569i
\(715\) 18.0000 + 10.3923i 0.673162 + 0.388650i
\(716\) 3.00000 + 5.19615i 0.112115 + 0.194189i
\(717\) 6.00000 + 10.3923i 0.224074 + 0.388108i
\(718\) 15.0000 25.9808i 0.559795 0.969593i
\(719\) 15.0000 + 25.9808i 0.559406 + 0.968919i 0.997546 + 0.0700124i \(0.0223039\pi\)
−0.438141 + 0.898906i \(0.644363\pi\)
\(720\) 7.50000 12.9904i 0.279508 0.484123i
\(721\) 27.7128i 1.03208i
\(722\) −22.5000 12.9904i −0.837363 0.483452i
\(723\) 22.0000 0.818189
\(724\) 22.5167i 0.836825i
\(725\) 6.00000 3.46410i 0.222834 0.128654i
\(726\) −3.00000 + 1.73205i −0.111340 + 0.0642824i
\(727\) −5.00000 8.66025i −0.185440 0.321191i 0.758285 0.651923i \(-0.226038\pi\)
−0.943725 + 0.330732i \(0.892704\pi\)
\(728\) −6.00000 + 10.3923i −0.222375 + 0.385164i
\(729\) 13.0000 0.481481
\(730\) 31.5000 18.1865i 1.16587 0.673114i
\(731\) −24.0000 −0.887672
\(732\) 14.0000 + 6.92820i 0.517455 + 0.256074i
\(733\) 41.0000 1.51437 0.757185 0.653201i \(-0.226574\pi\)
0.757185 + 0.653201i \(0.226574\pi\)
\(734\) 12.0000 6.92820i 0.442928 0.255725i
\(735\) 30.0000 1.10657
\(736\) 0 0
\(737\) −6.00000 10.3923i −0.221013 0.382805i
\(738\) −4.50000 + 2.59808i −0.165647 + 0.0956365i
\(739\) 45.0000 25.9808i 1.65535 0.955718i 0.680534 0.732717i \(-0.261748\pi\)
0.974818 0.223001i \(-0.0715853\pi\)
\(740\) 5.19615i 0.191014i
\(741\) −8.00000 −0.293887
\(742\) 27.0000 + 15.5885i 0.991201 + 0.572270i
\(743\) 27.7128i 1.01668i 0.861155 + 0.508342i \(0.169742\pi\)
−0.861155 + 0.508342i \(0.830258\pi\)
\(744\) 18.0000 31.1769i 0.659912 1.14300i
\(745\) 22.5000 + 38.9711i 0.824336 + 1.42779i
\(746\) −25.5000 + 44.1673i −0.933621 + 1.61708i
\(747\) −3.00000 5.19615i −0.109764 0.190117i
\(748\) −12.0000 20.7846i −0.438763 0.759961i
\(749\) 0 0
\(750\) −9.00000 + 5.19615i −0.328634 + 0.189737i
\(751\) 20.0000 34.6410i 0.729810 1.26407i −0.227153 0.973859i \(-0.572942\pi\)
0.956963 0.290209i \(-0.0937250\pi\)
\(752\) −60.0000 −2.18797
\(753\) −24.0000 + 13.8564i −0.874609 + 0.504956i
\(754\) 3.00000 + 5.19615i 0.109254 + 0.189233i
\(755\) 10.3923i 0.378215i
\(756\) 13.8564i 0.503953i
\(757\) −11.5000 + 19.9186i −0.417975 + 0.723953i −0.995736 0.0922527i \(-0.970593\pi\)
0.577761 + 0.816206i \(0.303927\pi\)
\(758\) −24.0000 13.8564i −0.871719 0.503287i
\(759\) 0 0
\(760\) 10.3923i 0.376969i
\(761\) −30.0000 17.3205i −1.08750 0.627868i −0.154590 0.987979i \(-0.549406\pi\)
−0.932910 + 0.360111i \(0.882739\pi\)
\(762\) 6.00000 + 3.46410i 0.217357 + 0.125491i
\(763\) −21.0000 12.1244i −0.760251 0.438931i
\(764\) −12.0000 6.92820i −0.434145 0.250654i
\(765\) 20.7846i 0.751469i
\(766\) −36.0000 −1.30073
\(767\) −6.00000 3.46410i −0.216647 0.125081i
\(768\) 19.0000 32.9090i 0.685603 1.18750i
\(769\) 43.3013i 1.56148i 0.624854 + 0.780742i \(0.285159\pi\)
−0.624854 + 0.780742i \(0.714841\pi\)
\(770\) 62.3538i 2.24708i
\(771\) −15.0000 25.9808i −0.540212 0.935674i
\(772\) −10.5000 + 6.06218i −0.377903 + 0.218183i
\(773\) −39.0000 −1.40273 −0.701366 0.712801i \(-0.747426\pi\)
−0.701366 + 0.712801i \(0.747426\pi\)
\(774\) −3.00000 + 5.19615i −0.107833 + 0.186772i
\(775\) 36.0000 20.7846i 1.29316 0.746605i
\(776\) 1.50000 + 0.866025i 0.0538469 + 0.0310885i
\(777\) 6.00000 + 10.3923i 0.215249 + 0.372822i
\(778\) 25.5000 + 44.1673i 0.914219 + 1.58347i
\(779\) 3.00000 5.19615i 0.107486 0.186171i
\(780\) 6.00000 + 10.3923i 0.214834 + 0.372104i
\(781\) 18.0000 31.1769i 0.644091 1.11560i
\(782\) 0 0
\(783\) −6.00000 3.46410i −0.214423 0.123797i
\(784\) 25.0000 0.892857
\(785\) 41.5692i 1.48367i
\(786\) 0 0
\(787\) −9.00000 + 5.19615i −0.320815 + 0.185223i −0.651756 0.758429i \(-0.725967\pi\)
0.330941 + 0.943652i \(0.392634\pi\)
\(788\)