Properties

Label 1050.2.i.f.151.1
Level $1050$
Weight $2$
Character 1050.151
Analytic conductor $8.384$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
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 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 151.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1050.151
Dual form 1050.2.i.f.751.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.50000 - 4.33013i) q^{11} +(0.500000 + 0.866025i) q^{12} -1.00000 q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-3.50000 - 6.06218i) q^{19} +(0.500000 + 2.59808i) q^{21} -5.00000 q^{22} +(1.50000 + 2.59808i) q^{23} +(0.500000 - 0.866025i) q^{24} +(0.500000 + 0.866025i) q^{26} -1.00000 q^{27} +(-0.500000 - 2.59808i) q^{28} +(3.00000 - 5.19615i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.50000 - 4.33013i) q^{33} +2.00000 q^{34} +1.00000 q^{36} +(-2.50000 - 4.33013i) q^{37} +(-3.50000 + 6.06218i) q^{38} +(-0.500000 + 0.866025i) q^{39} -9.00000 q^{41} +(2.00000 - 1.73205i) q^{42} -10.0000 q^{43} +(2.50000 + 4.33013i) q^{44} +(1.50000 - 2.59808i) q^{46} +(-6.50000 - 11.2583i) q^{47} -1.00000 q^{48} +(1.00000 - 6.92820i) q^{49} +(1.00000 + 1.73205i) q^{51} +(0.500000 - 0.866025i) q^{52} +(-0.500000 + 0.866025i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.00000 + 1.73205i) q^{56} -7.00000 q^{57} +(-2.00000 + 3.46410i) q^{59} +(1.00000 + 1.73205i) q^{61} -6.00000 q^{62} +(2.50000 + 0.866025i) q^{63} +1.00000 q^{64} +(-2.50000 + 4.33013i) q^{66} +(3.00000 - 5.19615i) q^{67} +(-1.00000 - 1.73205i) q^{68} +3.00000 q^{69} -2.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(2.00000 - 3.46410i) q^{73} +(-2.50000 + 4.33013i) q^{74} +7.00000 q^{76} +(2.50000 + 12.9904i) q^{77} +1.00000 q^{78} +(7.00000 + 12.1244i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.50000 + 7.79423i) q^{82} +10.0000 q^{83} +(-2.50000 - 0.866025i) q^{84} +(5.00000 + 8.66025i) q^{86} +(2.50000 - 4.33013i) q^{88} +(-5.00000 - 8.66025i) q^{89} +(2.00000 - 1.73205i) q^{91} -3.00000 q^{92} +(-3.00000 - 5.19615i) q^{93} +(-6.50000 + 11.2583i) q^{94} +(0.500000 + 0.866025i) q^{96} -8.00000 q^{97} +(-6.50000 + 2.59808i) q^{98} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + q^{3} - q^{4} - 2q^{6} - 4q^{7} + 2q^{8} - q^{9} + O(q^{10}) \) \( 2q - q^{2} + q^{3} - q^{4} - 2q^{6} - 4q^{7} + 2q^{8} - q^{9} + 5q^{11} + q^{12} - 2q^{13} + 5q^{14} - q^{16} - 2q^{17} - q^{18} - 7q^{19} + q^{21} - 10q^{22} + 3q^{23} + q^{24} + q^{26} - 2q^{27} - q^{28} + 6q^{31} - q^{32} - 5q^{33} + 4q^{34} + 2q^{36} - 5q^{37} - 7q^{38} - q^{39} - 18q^{41} + 4q^{42} - 20q^{43} + 5q^{44} + 3q^{46} - 13q^{47} - 2q^{48} + 2q^{49} + 2q^{51} + q^{52} - q^{53} + q^{54} - 4q^{56} - 14q^{57} - 4q^{59} + 2q^{61} - 12q^{62} + 5q^{63} + 2q^{64} - 5q^{66} + 6q^{67} - 2q^{68} + 6q^{69} - 4q^{71} - q^{72} + 4q^{73} - 5q^{74} + 14q^{76} + 5q^{77} + 2q^{78} + 14q^{79} - q^{81} + 9q^{82} + 20q^{83} - 5q^{84} + 10q^{86} + 5q^{88} - 10q^{89} + 4q^{91} - 6q^{92} - 6q^{93} - 13q^{94} + q^{96} - 16q^{97} - 13q^{98} - 10q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) −1.00000 −0.408248
\(7\) −2.00000 + 1.73205i −0.755929 + 0.654654i
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 2.50000 4.33013i 0.753778 1.30558i −0.192201 0.981356i \(-0.561563\pi\)
0.945979 0.324227i \(-0.105104\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 2.50000 + 0.866025i 0.668153 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) −0.500000 + 0.866025i −0.117851 + 0.204124i
\(19\) −3.50000 6.06218i −0.802955 1.39076i −0.917663 0.397360i \(-0.869927\pi\)
0.114708 0.993399i \(-0.463407\pi\)
\(20\) 0 0
\(21\) 0.500000 + 2.59808i 0.109109 + 0.566947i
\(22\) −5.00000 −1.06600
\(23\) 1.50000 + 2.59808i 0.312772 + 0.541736i 0.978961 0.204046i \(-0.0654092\pi\)
−0.666190 + 0.745782i \(0.732076\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 0 0
\(26\) 0.500000 + 0.866025i 0.0980581 + 0.169842i
\(27\) −1.00000 −0.192450
\(28\) −0.500000 2.59808i −0.0944911 0.490990i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 3.00000 5.19615i 0.538816 0.933257i −0.460152 0.887840i \(-0.652205\pi\)
0.998968 0.0454165i \(-0.0144615\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −2.50000 4.33013i −0.435194 0.753778i
\(34\) 2.00000 0.342997
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −2.50000 4.33013i −0.410997 0.711868i 0.584002 0.811752i \(-0.301486\pi\)
−0.994999 + 0.0998840i \(0.968153\pi\)
\(38\) −3.50000 + 6.06218i −0.567775 + 0.983415i
\(39\) −0.500000 + 0.866025i −0.0800641 + 0.138675i
\(40\) 0 0
\(41\) −9.00000 −1.40556 −0.702782 0.711405i \(-0.748059\pi\)
−0.702782 + 0.711405i \(0.748059\pi\)
\(42\) 2.00000 1.73205i 0.308607 0.267261i
\(43\) −10.0000 −1.52499 −0.762493 0.646997i \(-0.776025\pi\)
−0.762493 + 0.646997i \(0.776025\pi\)
\(44\) 2.50000 + 4.33013i 0.376889 + 0.652791i
\(45\) 0 0
\(46\) 1.50000 2.59808i 0.221163 0.383065i
\(47\) −6.50000 11.2583i −0.948122 1.64220i −0.749375 0.662145i \(-0.769646\pi\)
−0.198747 0.980051i \(-0.563687\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 0 0
\(51\) 1.00000 + 1.73205i 0.140028 + 0.242536i
\(52\) 0.500000 0.866025i 0.0693375 0.120096i
\(53\) −0.500000 + 0.866025i −0.0686803 + 0.118958i −0.898321 0.439340i \(-0.855212\pi\)
0.829640 + 0.558298i \(0.188546\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −2.00000 + 1.73205i −0.267261 + 0.231455i
\(57\) −7.00000 −0.927173
\(58\) 0 0
\(59\) −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i \(-0.917180\pi\)
0.705965 + 0.708247i \(0.250514\pi\)
\(60\) 0 0
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) −6.00000 −0.762001
\(63\) 2.50000 + 0.866025i 0.314970 + 0.109109i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −2.50000 + 4.33013i −0.307729 + 0.533002i
\(67\) 3.00000 5.19615i 0.366508 0.634811i −0.622509 0.782613i \(-0.713886\pi\)
0.989017 + 0.147802i \(0.0472198\pi\)
\(68\) −1.00000 1.73205i −0.121268 0.210042i
\(69\) 3.00000 0.361158
\(70\) 0 0
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 2.00000 3.46410i 0.234082 0.405442i −0.724923 0.688830i \(-0.758125\pi\)
0.959006 + 0.283387i \(0.0914581\pi\)
\(74\) −2.50000 + 4.33013i −0.290619 + 0.503367i
\(75\) 0 0
\(76\) 7.00000 0.802955
\(77\) 2.50000 + 12.9904i 0.284901 + 1.48039i
\(78\) 1.00000 0.113228
\(79\) 7.00000 + 12.1244i 0.787562 + 1.36410i 0.927457 + 0.373930i \(0.121990\pi\)
−0.139895 + 0.990166i \(0.544677\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 4.50000 + 7.79423i 0.496942 + 0.860729i
\(83\) 10.0000 1.09764 0.548821 0.835940i \(-0.315077\pi\)
0.548821 + 0.835940i \(0.315077\pi\)
\(84\) −2.50000 0.866025i −0.272772 0.0944911i
\(85\) 0 0
\(86\) 5.00000 + 8.66025i 0.539164 + 0.933859i
\(87\) 0 0
\(88\) 2.50000 4.33013i 0.266501 0.461593i
\(89\) −5.00000 8.66025i −0.529999 0.917985i −0.999388 0.0349934i \(-0.988859\pi\)
0.469389 0.882992i \(-0.344474\pi\)
\(90\) 0 0
\(91\) 2.00000 1.73205i 0.209657 0.181568i
\(92\) −3.00000 −0.312772
\(93\) −3.00000 5.19615i −0.311086 0.538816i
\(94\) −6.50000 + 11.2583i −0.670424 + 1.16121i
\(95\) 0 0
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) −8.00000 −0.812277 −0.406138 0.913812i \(-0.633125\pi\)
−0.406138 + 0.913812i \(0.633125\pi\)
\(98\) −6.50000 + 2.59808i −0.656599 + 0.262445i
\(99\) −5.00000 −0.502519
\(100\) 0 0
\(101\) −4.00000 + 6.92820i −0.398015 + 0.689382i −0.993481 0.113998i \(-0.963634\pi\)
0.595466 + 0.803380i \(0.296967\pi\)
\(102\) 1.00000 1.73205i 0.0990148 0.171499i
\(103\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) 1.00000 0.0971286
\(107\) 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i \(0.0302972\pi\)
−0.415432 + 0.909624i \(0.636370\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 9.00000 15.5885i 0.862044 1.49310i −0.00790932 0.999969i \(-0.502518\pi\)
0.869953 0.493135i \(-0.164149\pi\)
\(110\) 0 0
\(111\) −5.00000 −0.474579
\(112\) 2.50000 + 0.866025i 0.236228 + 0.0818317i
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 3.50000 + 6.06218i 0.327805 + 0.567775i
\(115\) 0 0
\(116\) 0 0
\(117\) 0.500000 + 0.866025i 0.0462250 + 0.0800641i
\(118\) 4.00000 0.368230
\(119\) −1.00000 5.19615i −0.0916698 0.476331i
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 1.00000 1.73205i 0.0905357 0.156813i
\(123\) −4.50000 + 7.79423i −0.405751 + 0.702782i
\(124\) 3.00000 + 5.19615i 0.269408 + 0.466628i
\(125\) 0 0
\(126\) −0.500000 2.59808i −0.0445435 0.231455i
\(127\) −9.00000 −0.798621 −0.399310 0.916816i \(-0.630750\pi\)
−0.399310 + 0.916816i \(0.630750\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −5.00000 + 8.66025i −0.440225 + 0.762493i
\(130\) 0 0
\(131\) 8.50000 + 14.7224i 0.742648 + 1.28630i 0.951285 + 0.308312i \(0.0997640\pi\)
−0.208637 + 0.977993i \(0.566903\pi\)
\(132\) 5.00000 0.435194
\(133\) 17.5000 + 6.06218i 1.51744 + 0.525657i
\(134\) −6.00000 −0.518321
\(135\) 0 0
\(136\) −1.00000 + 1.73205i −0.0857493 + 0.148522i
\(137\) −2.00000 + 3.46410i −0.170872 + 0.295958i −0.938725 0.344668i \(-0.887992\pi\)
0.767853 + 0.640626i \(0.221325\pi\)
\(138\) −1.50000 2.59808i −0.127688 0.221163i
\(139\) −8.00000 −0.678551 −0.339276 0.940687i \(-0.610182\pi\)
−0.339276 + 0.940687i \(0.610182\pi\)
\(140\) 0 0
\(141\) −13.0000 −1.09480
\(142\) 1.00000 + 1.73205i 0.0839181 + 0.145350i
\(143\) −2.50000 + 4.33013i −0.209061 + 0.362103i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 0 0
\(146\) −4.00000 −0.331042
\(147\) −5.50000 4.33013i −0.453632 0.357143i
\(148\) 5.00000 0.410997
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 0 0
\(151\) 11.0000 19.0526i 0.895167 1.55048i 0.0615699 0.998103i \(-0.480389\pi\)
0.833597 0.552372i \(-0.186277\pi\)
\(152\) −3.50000 6.06218i −0.283887 0.491708i
\(153\) 2.00000 0.161690
\(154\) 10.0000 8.66025i 0.805823 0.697863i
\(155\) 0 0
\(156\) −0.500000 0.866025i −0.0400320 0.0693375i
\(157\) 6.50000 11.2583i 0.518756 0.898513i −0.481006 0.876717i \(-0.659728\pi\)
0.999762 0.0217953i \(-0.00693820\pi\)
\(158\) 7.00000 12.1244i 0.556890 0.964562i
\(159\) 0.500000 + 0.866025i 0.0396526 + 0.0686803i
\(160\) 0 0
\(161\) −7.50000 2.59808i −0.591083 0.204757i
\(162\) 1.00000 0.0785674
\(163\) −6.00000 10.3923i −0.469956 0.813988i 0.529454 0.848339i \(-0.322397\pi\)
−0.999410 + 0.0343508i \(0.989064\pi\)
\(164\) 4.50000 7.79423i 0.351391 0.608627i
\(165\) 0 0
\(166\) −5.00000 8.66025i −0.388075 0.672166i
\(167\) 19.0000 1.47026 0.735132 0.677924i \(-0.237120\pi\)
0.735132 + 0.677924i \(0.237120\pi\)
\(168\) 0.500000 + 2.59808i 0.0385758 + 0.200446i
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) −3.50000 + 6.06218i −0.267652 + 0.463586i
\(172\) 5.00000 8.66025i 0.381246 0.660338i
\(173\) 3.50000 + 6.06218i 0.266100 + 0.460899i 0.967851 0.251523i \(-0.0809315\pi\)
−0.701751 + 0.712422i \(0.747598\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −5.00000 −0.376889
\(177\) 2.00000 + 3.46410i 0.150329 + 0.260378i
\(178\) −5.00000 + 8.66025i −0.374766 + 0.649113i
\(179\) 5.50000 9.52628i 0.411089 0.712028i −0.583920 0.811811i \(-0.698482\pi\)
0.995009 + 0.0997838i \(0.0318151\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) −2.50000 0.866025i −0.185312 0.0641941i
\(183\) 2.00000 0.147844
\(184\) 1.50000 + 2.59808i 0.110581 + 0.191533i
\(185\) 0 0
\(186\) −3.00000 + 5.19615i −0.219971 + 0.381000i
\(187\) 5.00000 + 8.66025i 0.365636 + 0.633300i
\(188\) 13.0000 0.948122
\(189\) 2.00000 1.73205i 0.145479 0.125988i
\(190\) 0 0
\(191\) 8.00000 + 13.8564i 0.578860 + 1.00261i 0.995610 + 0.0935936i \(0.0298354\pi\)
−0.416751 + 0.909021i \(0.636831\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −9.00000 + 15.5885i −0.647834 + 1.12208i 0.335805 + 0.941932i \(0.390992\pi\)
−0.983639 + 0.180150i \(0.942342\pi\)
\(194\) 4.00000 + 6.92820i 0.287183 + 0.497416i
\(195\) 0 0
\(196\) 5.50000 + 4.33013i 0.392857 + 0.309295i
\(197\) 27.0000 1.92367 0.961835 0.273629i \(-0.0882242\pi\)
0.961835 + 0.273629i \(0.0882242\pi\)
\(198\) 2.50000 + 4.33013i 0.177667 + 0.307729i
\(199\) 7.00000 12.1244i 0.496217 0.859473i −0.503774 0.863836i \(-0.668055\pi\)
0.999990 + 0.00436292i \(0.00138876\pi\)
\(200\) 0 0
\(201\) −3.00000 5.19615i −0.211604 0.366508i
\(202\) 8.00000 0.562878
\(203\) 0 0
\(204\) −2.00000 −0.140028
\(205\) 0 0
\(206\) 0 0
\(207\) 1.50000 2.59808i 0.104257 0.180579i
\(208\) 0.500000 + 0.866025i 0.0346688 + 0.0600481i
\(209\) −35.0000 −2.42100
\(210\) 0 0
\(211\) 19.0000 1.30801 0.654007 0.756489i \(-0.273087\pi\)
0.654007 + 0.756489i \(0.273087\pi\)
\(212\) −0.500000 0.866025i −0.0343401 0.0594789i
\(213\) −1.00000 + 1.73205i −0.0685189 + 0.118678i
\(214\) 6.00000 10.3923i 0.410152 0.710403i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 3.00000 + 15.5885i 0.203653 + 1.05821i
\(218\) −18.0000 −1.21911
\(219\) −2.00000 3.46410i −0.135147 0.234082i
\(220\) 0 0
\(221\) 1.00000 1.73205i 0.0672673 0.116510i
\(222\) 2.50000 + 4.33013i 0.167789 + 0.290619i
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) −0.500000 2.59808i −0.0334077 0.173591i
\(225\) 0 0
\(226\) 3.00000 + 5.19615i 0.199557 + 0.345643i
\(227\) 7.00000 12.1244i 0.464606 0.804722i −0.534577 0.845120i \(-0.679529\pi\)
0.999184 + 0.0403978i \(0.0128625\pi\)
\(228\) 3.50000 6.06218i 0.231793 0.401478i
\(229\) 2.00000 + 3.46410i 0.132164 + 0.228914i 0.924510 0.381157i \(-0.124474\pi\)
−0.792347 + 0.610071i \(0.791141\pi\)
\(230\) 0 0
\(231\) 12.5000 + 4.33013i 0.822440 + 0.284901i
\(232\) 0 0
\(233\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(234\) 0.500000 0.866025i 0.0326860 0.0566139i
\(235\) 0 0
\(236\) −2.00000 3.46410i −0.130189 0.225494i
\(237\) 14.0000 0.909398
\(238\) −4.00000 + 3.46410i −0.259281 + 0.224544i
\(239\) 20.0000 1.29369 0.646846 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 0 0
\(241\) 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i \(-0.823079\pi\)
0.881680 + 0.471848i \(0.156413\pi\)
\(242\) −7.00000 + 12.1244i −0.449977 + 0.779383i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −2.00000 −0.128037
\(245\) 0 0
\(246\) 9.00000 0.573819
\(247\) 3.50000 + 6.06218i 0.222700 + 0.385727i
\(248\) 3.00000 5.19615i 0.190500 0.329956i
\(249\) 5.00000 8.66025i 0.316862 0.548821i
\(250\) 0 0
\(251\) −3.00000 −0.189358 −0.0946792 0.995508i \(-0.530183\pi\)
−0.0946792 + 0.995508i \(0.530183\pi\)
\(252\) −2.00000 + 1.73205i −0.125988 + 0.109109i
\(253\) 15.0000 0.943042
\(254\) 4.50000 + 7.79423i 0.282355 + 0.489053i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −5.00000 8.66025i −0.311891 0.540212i 0.666880 0.745165i \(-0.267629\pi\)
−0.978772 + 0.204953i \(0.934296\pi\)
\(258\) 10.0000 0.622573
\(259\) 12.5000 + 4.33013i 0.776712 + 0.269061i
\(260\) 0 0
\(261\) 0 0
\(262\) 8.50000 14.7224i 0.525132 0.909555i
\(263\) 12.0000 20.7846i 0.739952 1.28163i −0.212565 0.977147i \(-0.568182\pi\)
0.952517 0.304487i \(-0.0984850\pi\)
\(264\) −2.50000 4.33013i −0.153864 0.266501i
\(265\) 0 0
\(266\) −3.50000 18.1865i −0.214599 1.11509i
\(267\) −10.0000 −0.611990
\(268\) 3.00000 + 5.19615i 0.183254 + 0.317406i
\(269\) −7.00000 + 12.1244i −0.426798 + 0.739235i −0.996586 0.0825561i \(-0.973692\pi\)
0.569789 + 0.821791i \(0.307025\pi\)
\(270\) 0 0
\(271\) −4.00000 6.92820i −0.242983 0.420858i 0.718580 0.695444i \(-0.244792\pi\)
−0.961563 + 0.274586i \(0.911459\pi\)
\(272\) 2.00000 0.121268
\(273\) −0.500000 2.59808i −0.0302614 0.157243i
\(274\) 4.00000 0.241649
\(275\) 0 0
\(276\) −1.50000 + 2.59808i −0.0902894 + 0.156386i
\(277\) 1.00000 1.73205i 0.0600842 0.104069i −0.834419 0.551131i \(-0.814196\pi\)
0.894503 + 0.447062i \(0.147530\pi\)
\(278\) 4.00000 + 6.92820i 0.239904 + 0.415526i
\(279\) −6.00000 −0.359211
\(280\) 0 0
\(281\) −11.0000 −0.656205 −0.328102 0.944642i \(-0.606409\pi\)
−0.328102 + 0.944642i \(0.606409\pi\)
\(282\) 6.50000 + 11.2583i 0.387069 + 0.670424i
\(283\) 13.0000 22.5167i 0.772770 1.33848i −0.163270 0.986581i \(-0.552204\pi\)
0.936039 0.351895i \(-0.114463\pi\)
\(284\) 1.00000 1.73205i 0.0593391 0.102778i
\(285\) 0 0
\(286\) 5.00000 0.295656
\(287\) 18.0000 15.5885i 1.06251 0.920158i
\(288\) 1.00000 0.0589256
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 0 0
\(291\) −4.00000 + 6.92820i −0.234484 + 0.406138i
\(292\) 2.00000 + 3.46410i 0.117041 + 0.202721i
\(293\) −1.00000 −0.0584206 −0.0292103 0.999573i \(-0.509299\pi\)
−0.0292103 + 0.999573i \(0.509299\pi\)
\(294\) −1.00000 + 6.92820i −0.0583212 + 0.404061i
\(295\) 0 0
\(296\) −2.50000 4.33013i −0.145310 0.251684i
\(297\) −2.50000 + 4.33013i −0.145065 + 0.251259i
\(298\) 3.00000 5.19615i 0.173785 0.301005i
\(299\) −1.50000 2.59808i −0.0867472 0.150251i
\(300\) 0 0
\(301\) 20.0000 17.3205i 1.15278 0.998337i
\(302\) −22.0000 −1.26596
\(303\) 4.00000 + 6.92820i 0.229794 + 0.398015i
\(304\) −3.50000 + 6.06218i −0.200739 + 0.347690i
\(305\) 0 0
\(306\) −1.00000 1.73205i −0.0571662 0.0990148i
\(307\) −2.00000 −0.114146 −0.0570730 0.998370i \(-0.518177\pi\)
−0.0570730 + 0.998370i \(0.518177\pi\)
\(308\) −12.5000 4.33013i −0.712254 0.246732i
\(309\) 0 0
\(310\) 0 0
\(311\) 13.0000 22.5167i 0.737162 1.27680i −0.216606 0.976259i \(-0.569499\pi\)
0.953768 0.300544i \(-0.0971681\pi\)
\(312\) −0.500000 + 0.866025i −0.0283069 + 0.0490290i
\(313\) −5.00000 8.66025i −0.282617 0.489506i 0.689412 0.724370i \(-0.257869\pi\)
−0.972028 + 0.234863i \(0.924536\pi\)
\(314\) −13.0000 −0.733632
\(315\) 0 0
\(316\) −14.0000 −0.787562
\(317\) 1.00000 + 1.73205i 0.0561656 + 0.0972817i 0.892741 0.450570i \(-0.148779\pi\)
−0.836576 + 0.547852i \(0.815446\pi\)
\(318\) 0.500000 0.866025i 0.0280386 0.0485643i
\(319\) 0 0
\(320\) 0 0
\(321\) 12.0000 0.669775
\(322\) 1.50000 + 7.79423i 0.0835917 + 0.434355i
\(323\) 14.0000 0.778981
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 0 0
\(326\) −6.00000 + 10.3923i −0.332309 + 0.575577i
\(327\) −9.00000 15.5885i −0.497701 0.862044i
\(328\) −9.00000 −0.496942
\(329\) 32.5000 + 11.2583i 1.79178 + 0.620692i
\(330\) 0 0
\(331\) 7.50000 + 12.9904i 0.412237 + 0.714016i 0.995134 0.0985303i \(-0.0314141\pi\)
−0.582897 + 0.812546i \(0.698081\pi\)
\(332\) −5.00000 + 8.66025i −0.274411 + 0.475293i
\(333\) −2.50000 + 4.33013i −0.136999 + 0.237289i
\(334\) −9.50000 16.4545i −0.519817 0.900349i
\(335\) 0 0
\(336\) 2.00000 1.73205i 0.109109 0.0944911i
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 6.00000 + 10.3923i 0.326357 + 0.565267i
\(339\) −3.00000 + 5.19615i −0.162938 + 0.282216i
\(340\) 0 0
\(341\) −15.0000 25.9808i −0.812296 1.40694i
\(342\) 7.00000 0.378517
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) −10.0000 −0.539164
\(345\) 0 0
\(346\) 3.50000 6.06218i 0.188161 0.325905i
\(347\) −8.00000 + 13.8564i −0.429463 + 0.743851i −0.996826 0.0796169i \(-0.974630\pi\)
0.567363 + 0.823468i \(0.307964\pi\)
\(348\) 0 0
\(349\) −24.0000 −1.28469 −0.642345 0.766415i \(-0.722038\pi\)
−0.642345 + 0.766415i \(0.722038\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) 2.50000 + 4.33013i 0.133250 + 0.230797i
\(353\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(354\) 2.00000 3.46410i 0.106299 0.184115i
\(355\) 0 0
\(356\) 10.0000 0.529999
\(357\) −5.00000 1.73205i −0.264628 0.0916698i
\(358\) −11.0000 −0.581368
\(359\) 14.0000 + 24.2487i 0.738892 + 1.27980i 0.952995 + 0.302987i \(0.0979839\pi\)
−0.214103 + 0.976811i \(0.568683\pi\)
\(360\) 0 0
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) 1.00000 + 1.73205i 0.0525588 + 0.0910346i
\(363\) −14.0000 −0.734809
\(364\) 0.500000 + 2.59808i 0.0262071 + 0.136176i
\(365\) 0 0
\(366\) −1.00000 1.73205i −0.0522708 0.0905357i
\(367\) −18.5000 + 32.0429i −0.965692 + 1.67263i −0.257948 + 0.966159i \(0.583046\pi\)
−0.707744 + 0.706469i \(0.750287\pi\)
\(368\) 1.50000 2.59808i 0.0781929 0.135434i
\(369\) 4.50000 + 7.79423i 0.234261 + 0.405751i
\(370\) 0 0
\(371\) −0.500000 2.59808i −0.0259587 0.134885i
\(372\) 6.00000 0.311086
\(373\) 3.00000 + 5.19615i 0.155334 + 0.269047i 0.933181 0.359408i \(-0.117021\pi\)
−0.777847 + 0.628454i \(0.783688\pi\)
\(374\) 5.00000 8.66025i 0.258544 0.447811i
\(375\) 0 0
\(376\) −6.50000 11.2583i −0.335212 0.580604i
\(377\) 0 0
\(378\) −2.50000 0.866025i −0.128586 0.0445435i
\(379\) −1.00000 −0.0513665 −0.0256833 0.999670i \(-0.508176\pi\)
−0.0256833 + 0.999670i \(0.508176\pi\)
\(380\) 0 0
\(381\) −4.50000 + 7.79423i −0.230542 + 0.399310i
\(382\) 8.00000 13.8564i 0.409316 0.708955i
\(383\) −4.50000 7.79423i −0.229939 0.398266i 0.727851 0.685736i \(-0.240519\pi\)
−0.957790 + 0.287469i \(0.907186\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 18.0000 0.916176
\(387\) 5.00000 + 8.66025i 0.254164 + 0.440225i
\(388\) 4.00000 6.92820i 0.203069 0.351726i
\(389\) −3.00000 + 5.19615i −0.152106 + 0.263455i −0.932002 0.362454i \(-0.881939\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(390\) 0 0
\(391\) −6.00000 −0.303433
\(392\) 1.00000 6.92820i 0.0505076 0.349927i
\(393\) 17.0000 0.857537
\(394\) −13.5000 23.3827i −0.680120 1.17800i
\(395\) 0 0
\(396\) 2.50000 4.33013i 0.125630 0.217597i
\(397\) −1.00000 1.73205i −0.0501886 0.0869291i 0.839840 0.542834i \(-0.182649\pi\)
−0.890028 + 0.455905i \(0.849316\pi\)
\(398\) −14.0000 −0.701757
\(399\) 14.0000 12.1244i 0.700877 0.606977i
\(400\) 0 0
\(401\) 13.5000 + 23.3827i 0.674158 + 1.16768i 0.976714 + 0.214544i \(0.0688266\pi\)
−0.302556 + 0.953131i \(0.597840\pi\)
\(402\) −3.00000 + 5.19615i −0.149626 + 0.259161i
\(403\) −3.00000 + 5.19615i −0.149441 + 0.258839i
\(404\) −4.00000 6.92820i −0.199007 0.344691i
\(405\) 0 0
\(406\) 0 0
\(407\) −25.0000 −1.23920
\(408\) 1.00000 + 1.73205i 0.0495074 + 0.0857493i
\(409\) −5.00000 + 8.66025i −0.247234 + 0.428222i −0.962757 0.270367i \(-0.912855\pi\)
0.715523 + 0.698589i \(0.246188\pi\)
\(410\) 0 0
\(411\) 2.00000 + 3.46410i 0.0986527 + 0.170872i
\(412\) 0 0
\(413\) −2.00000 10.3923i −0.0984136 0.511372i
\(414\) −3.00000 −0.147442
\(415\) 0 0
\(416\) 0.500000 0.866025i 0.0245145 0.0424604i
\(417\) −4.00000 + 6.92820i −0.195881 + 0.339276i
\(418\) 17.5000 + 30.3109i 0.855953 + 1.48255i
\(419\) 3.00000 0.146560 0.0732798 0.997311i \(-0.476653\pi\)
0.0732798 + 0.997311i \(0.476653\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) −9.50000 16.4545i −0.462453 0.800992i
\(423\) −6.50000 + 11.2583i −0.316041 + 0.547399i
\(424\) −0.500000 + 0.866025i −0.0242821 + 0.0420579i
\(425\) 0 0
\(426\) 2.00000 0.0969003
\(427\) −5.00000 1.73205i −0.241967 0.0838198i
\(428\) −12.0000 −0.580042
\(429\) 2.50000 + 4.33013i 0.120701 + 0.209061i
\(430\) 0 0
\(431\) −9.00000 + 15.5885i −0.433515 + 0.750870i −0.997173 0.0751385i \(-0.976060\pi\)
0.563658 + 0.826008i \(0.309393\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −4.00000 −0.192228 −0.0961139 0.995370i \(-0.530641\pi\)
−0.0961139 + 0.995370i \(0.530641\pi\)
\(434\) 12.0000 10.3923i 0.576018 0.498847i
\(435\) 0 0
\(436\) 9.00000 + 15.5885i 0.431022 + 0.746552i
\(437\) 10.5000 18.1865i 0.502283 0.869980i
\(438\) −2.00000 + 3.46410i −0.0955637 + 0.165521i
\(439\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 0 0
\(441\) −6.50000 + 2.59808i −0.309524 + 0.123718i
\(442\) −2.00000 −0.0951303
\(443\) −3.00000 5.19615i −0.142534 0.246877i 0.785916 0.618333i \(-0.212192\pi\)
−0.928450 + 0.371457i \(0.878858\pi\)
\(444\) 2.50000 4.33013i 0.118645 0.205499i
\(445\) 0 0
\(446\) 8.00000 + 13.8564i 0.378811 + 0.656120i
\(447\) 6.00000 0.283790
\(448\) −2.00000 + 1.73205i −0.0944911 + 0.0818317i
\(449\) 9.00000 0.424736 0.212368 0.977190i \(-0.431882\pi\)
0.212368 + 0.977190i \(0.431882\pi\)
\(450\) 0 0
\(451\) −22.5000 + 38.9711i −1.05948 + 1.83508i
\(452\) 3.00000 5.19615i 0.141108 0.244406i
\(453\) −11.0000 19.0526i −0.516825 0.895167i
\(454\) −14.0000 −0.657053
\(455\) 0 0
\(456\) −7.00000 −0.327805
\(457\) −19.0000 32.9090i −0.888783 1.53942i −0.841316 0.540544i \(-0.818219\pi\)
−0.0474665 0.998873i \(-0.515115\pi\)
\(458\) 2.00000 3.46410i 0.0934539 0.161867i
\(459\) 1.00000 1.73205i 0.0466760 0.0808452i
\(460\) 0 0
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) −2.50000 12.9904i −0.116311 0.604367i
\(463\) 15.0000 0.697109 0.348555 0.937288i \(-0.386673\pi\)
0.348555 + 0.937288i \(0.386673\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.00000 + 1.73205i 0.0462745 + 0.0801498i 0.888235 0.459390i \(-0.151932\pi\)
−0.841960 + 0.539539i \(0.818598\pi\)
\(468\) −1.00000 −0.0462250
\(469\) 3.00000 + 15.5885i 0.138527 + 0.719808i
\(470\) 0 0
\(471\) −6.50000 11.2583i −0.299504 0.518756i
\(472\) −2.00000 + 3.46410i −0.0920575 + 0.159448i
\(473\) −25.0000 + 43.3013i −1.14950 + 1.99099i
\(474\) −7.00000 12.1244i −0.321521 0.556890i
\(475\) 0 0
\(476\) 5.00000 + 1.73205i 0.229175 + 0.0793884i
\(477\) 1.00000 0.0457869
\(478\) −10.0000 17.3205i −0.457389 0.792222i
\(479\) −4.00000 + 6.92820i −0.182765 + 0.316558i −0.942821 0.333300i \(-0.891838\pi\)
0.760056 + 0.649857i \(0.225171\pi\)
\(480\) 0 0
\(481\) 2.50000 + 4.33013i 0.113990 + 0.197437i
\(482\) −1.00000 −0.0455488
\(483\) −6.00000 + 5.19615i −0.273009 + 0.236433i
\(484\) 14.0000 0.636364
\(485\) 0 0
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) 12.0000 20.7846i 0.543772 0.941841i −0.454911 0.890537i \(-0.650329\pi\)
0.998683 0.0513038i \(-0.0163377\pi\)
\(488\) 1.00000 + 1.73205i 0.0452679 + 0.0784063i
\(489\) −12.0000 −0.542659
\(490\) 0 0
\(491\) 24.0000 1.08310 0.541552 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) −4.50000 7.79423i −0.202876 0.351391i
\(493\) 0 0
\(494\) 3.50000 6.06218i 0.157472 0.272750i
\(495\) 0 0
\(496\) −6.00000 −0.269408
\(497\) 4.00000 3.46410i 0.179425 0.155386i
\(498\) −10.0000 −0.448111
\(499\) 14.0000 + 24.2487i 0.626726 + 1.08552i 0.988204 + 0.153141i \(0.0489388\pi\)
−0.361478 + 0.932381i \(0.617728\pi\)
\(500\) 0 0
\(501\) 9.50000 16.4545i 0.424429 0.735132i
\(502\) 1.50000 + 2.59808i 0.0669483 + 0.115958i
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 2.50000 + 0.866025i 0.111359 + 0.0385758i
\(505\) 0 0
\(506\) −7.50000 12.9904i −0.333416 0.577493i
\(507\) −6.00000 + 10.3923i −0.266469 + 0.461538i
\(508\) 4.50000 7.79423i 0.199655 0.345813i
\(509\) −7.00000 12.1244i −0.310270 0.537403i 0.668151 0.744026i \(-0.267086\pi\)
−0.978421 + 0.206623i \(0.933753\pi\)
\(510\) 0 0
\(511\) 2.00000 + 10.3923i 0.0884748 + 0.459728i
\(512\) 1.00000 0.0441942
\(513\) 3.50000 + 6.06218i 0.154529 + 0.267652i
\(514\) −5.00000 + 8.66025i −0.220541 + 0.381987i
\(515\) 0 0
\(516\) −5.00000 8.66025i −0.220113 0.381246i
\(517\) −65.0000 −2.85870
\(518\) −2.50000 12.9904i −0.109844 0.570765i
\(519\) 7.00000 0.307266
\(520\) 0 0
\(521\) 7.50000 12.9904i 0.328581 0.569119i −0.653650 0.756797i \(-0.726763\pi\)
0.982231 + 0.187678i \(0.0600963\pi\)
\(522\) 0 0
\(523\) 6.00000 + 10.3923i 0.262362 + 0.454424i 0.966869 0.255273i \(-0.0821653\pi\)
−0.704507 + 0.709697i \(0.748832\pi\)
\(524\) −17.0000 −0.742648
\(525\) 0 0
\(526\) −24.0000 −1.04645
\(527\) 6.00000 + 10.3923i 0.261364 + 0.452696i
\(528\) −2.50000 + 4.33013i −0.108799 + 0.188445i
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 0 0
\(531\) 4.00000 0.173585
\(532\) −14.0000 + 12.1244i −0.606977 + 0.525657i
\(533\) 9.00000 0.389833
\(534\) 5.00000 + 8.66025i 0.216371 + 0.374766i
\(535\) 0 0
\(536\) 3.00000 5.19615i 0.129580 0.224440i
\(537\) −5.50000 9.52628i −0.237343 0.411089i
\(538\) 14.0000 0.603583
\(539\) −27.5000 21.6506i −1.18451 0.932559i
\(540\) 0 0
\(541\) −2.00000 3.46410i −0.0859867 0.148933i 0.819825 0.572615i \(-0.194071\pi\)
−0.905811 + 0.423681i \(0.860738\pi\)
\(542\) −4.00000 + 6.92820i −0.171815 + 0.297592i
\(543\) −1.00000 + 1.73205i −0.0429141 + 0.0743294i
\(544\) −1.00000 1.73205i −0.0428746 0.0742611i
\(545\) 0 0
\(546\) −2.00000 + 1.73205i −0.0855921 + 0.0741249i
\(547\) 14.0000 0.598597 0.299298 0.954160i \(-0.403247\pi\)
0.299298 + 0.954160i \(0.403247\pi\)
\(548\) −2.00000 3.46410i −0.0854358 0.147979i
\(549\) 1.00000 1.73205i 0.0426790 0.0739221i
\(550\) 0 0
\(551\) 0 0
\(552\) 3.00000 0.127688
\(553\) −35.0000 12.1244i −1.48835 0.515580i
\(554\) −2.00000 −0.0849719
\(555\) 0 0
\(556\) 4.00000 6.92820i 0.169638 0.293821i
\(557\) −19.5000 + 33.7750i −0.826242 + 1.43109i 0.0747252 + 0.997204i \(0.476192\pi\)
−0.900967 + 0.433888i \(0.857141\pi\)
\(558\) 3.00000 + 5.19615i 0.127000 + 0.219971i
\(559\) 10.0000 0.422955
\(560\) 0 0
\(561\) 10.0000 0.422200
\(562\) 5.50000 + 9.52628i 0.232003 + 0.401842i
\(563\) 15.0000 25.9808i 0.632175 1.09496i −0.354932 0.934892i \(-0.615496\pi\)
0.987106 0.160066i \(-0.0511708\pi\)
\(564\) 6.50000 11.2583i 0.273699 0.474061i
\(565\) 0 0
\(566\) −26.0000 −1.09286
\(567\) −0.500000 2.59808i −0.0209980 0.109109i
\(568\) −2.00000 −0.0839181
\(569\) 1.50000 + 2.59808i 0.0628833 + 0.108917i 0.895753 0.444552i \(-0.146637\pi\)
−0.832870 + 0.553469i \(0.813304\pi\)
\(570\) 0 0
\(571\) 4.00000 6.92820i 0.167395 0.289936i −0.770108 0.637913i \(-0.779798\pi\)
0.937503 + 0.347977i \(0.113131\pi\)
\(572\) −2.50000 4.33013i −0.104530 0.181052i
\(573\) 16.0000 0.668410
\(574\) −22.5000 7.79423i −0.939132 0.325325i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 12.0000 20.7846i 0.499567 0.865275i −0.500433 0.865775i \(-0.666826\pi\)
1.00000 0.000500448i \(0.000159298\pi\)
\(578\) 6.50000 11.2583i 0.270364 0.468285i
\(579\) 9.00000 + 15.5885i 0.374027 + 0.647834i
\(580\) 0 0
\(581\) −20.0000 + 17.3205i −0.829740 + 0.718576i
\(582\) 8.00000 0.331611
\(583\) 2.50000 + 4.33013i 0.103539 + 0.179336i
\(584\) 2.00000 3.46410i 0.0827606 0.143346i
\(585\) 0 0
\(586\) 0.500000 + 0.866025i 0.0206548 + 0.0357752i
\(587\) −2.00000 −0.0825488 −0.0412744 0.999148i \(-0.513142\pi\)
−0.0412744 + 0.999148i \(0.513142\pi\)
\(588\) 6.50000 2.59808i 0.268055 0.107143i
\(589\) −42.0000 −1.73058
\(590\) 0 0
\(591\) 13.5000 23.3827i 0.555316 0.961835i
\(592\) −2.50000 + 4.33013i −0.102749 + 0.177967i
\(593\) −17.0000 29.4449i −0.698106 1.20916i −0.969122 0.246581i \(-0.920693\pi\)
0.271016 0.962575i \(-0.412640\pi\)
\(594\) 5.00000 0.205152
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) −7.00000 12.1244i −0.286491 0.496217i
\(598\) −1.50000 + 2.59808i −0.0613396 + 0.106243i
\(599\) 14.0000 24.2487i 0.572024 0.990775i −0.424333 0.905506i \(-0.639492\pi\)
0.996358 0.0852695i \(-0.0271751\pi\)
\(600\) 0 0
\(601\) −30.0000 −1.22373 −0.611863 0.790964i \(-0.709580\pi\)
−0.611863 + 0.790964i \(0.709580\pi\)
\(602\) −25.0000 8.66025i −1.01892 0.352966i
\(603\) −6.00000 −0.244339
\(604\) 11.0000 + 19.0526i 0.447584 + 0.775238i
\(605\) 0 0
\(606\) 4.00000 6.92820i 0.162489 0.281439i
\(607\) 6.50000 + 11.2583i 0.263827 + 0.456962i 0.967256 0.253804i \(-0.0816819\pi\)
−0.703429 + 0.710766i \(0.748349\pi\)
\(608\) 7.00000 0.283887
\(609\) 0 0
\(610\) 0 0
\(611\) 6.50000 + 11.2583i 0.262962 + 0.455463i
\(612\) −1.00000 + 1.73205i −0.0404226 + 0.0700140i
\(613\) 9.50000 16.4545i 0.383701 0.664590i −0.607887 0.794024i \(-0.707983\pi\)
0.991588 + 0.129433i \(0.0413159\pi\)
\(614\) 1.00000 + 1.73205i 0.0403567 + 0.0698999i
\(615\) 0 0
\(616\) 2.50000 + 12.9904i 0.100728 + 0.523397i
\(617\) −30.0000 −1.20775 −0.603877 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) 0 0
\(619\) −7.50000 + 12.9904i −0.301450 + 0.522127i −0.976465 0.215677i \(-0.930804\pi\)
0.675014 + 0.737805i \(0.264137\pi\)
\(620\) 0 0
\(621\) −1.50000 2.59808i −0.0601929 0.104257i
\(622\) −26.0000 −1.04251
\(623\) 25.0000 + 8.66025i 1.00160 + 0.346966i
\(624\) 1.00000 0.0400320
\(625\) 0 0
\(626\) −5.00000 + 8.66025i −0.199840 + 0.346133i
\(627\) −17.5000 + 30.3109i −0.698883 + 1.21050i
\(628\) 6.50000 + 11.2583i 0.259378 + 0.449256i
\(629\) 10.0000 0.398726
\(630\) 0 0
\(631\) 18.0000 0.716569 0.358284 0.933613i \(-0.383362\pi\)
0.358284 + 0.933613i \(0.383362\pi\)
\(632\) 7.00000 + 12.1244i 0.278445 + 0.482281i
\(633\) 9.50000 16.4545i 0.377591 0.654007i
\(634\) 1.00000 1.73205i 0.0397151 0.0687885i
\(635\) 0 0
\(636\) −1.00000 −0.0396526
\(637\) −1.00000 + 6.92820i −0.0396214 + 0.274505i
\(638\) 0 0
\(639\) 1.00000 + 1.73205i 0.0395594 + 0.0685189i
\(640\) 0 0
\(641\) 16.5000 28.5788i 0.651711 1.12880i −0.330997 0.943632i \(-0.607385\pi\)
0.982708 0.185164i \(-0.0592817\pi\)
\(642\) −6.00000 10.3923i −0.236801 0.410152i
\(643\) −38.0000 −1.49857 −0.749287 0.662246i \(-0.769604\pi\)
−0.749287 + 0.662246i \(0.769604\pi\)
\(644\) 6.00000 5.19615i 0.236433 0.204757i
\(645\) 0 0
\(646\) −7.00000 12.1244i −0.275411 0.477026i
\(647\) −0.500000 + 0.866025i −0.0196570 + 0.0340470i −0.875687 0.482880i \(-0.839591\pi\)
0.856030 + 0.516927i \(0.172924\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 10.0000 + 17.3205i 0.392534 + 0.679889i
\(650\) 0 0
\(651\) 15.0000 + 5.19615i 0.587896 + 0.203653i
\(652\) 12.0000 0.469956
\(653\) 2.50000 + 4.33013i 0.0978326 + 0.169451i 0.910787 0.412876i \(-0.135476\pi\)
−0.812955 + 0.582327i \(0.802142\pi\)
\(654\) −9.00000 + 15.5885i −0.351928 + 0.609557i
\(655\) 0 0
\(656\) 4.50000 + 7.79423i 0.175695 + 0.304314i
\(657\) −4.00000 −0.156055
\(658\) −6.50000 33.7750i −0.253396 1.31669i
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) −20.0000 + 34.6410i −0.777910 + 1.34738i 0.155235 + 0.987878i \(0.450387\pi\)
−0.933144 + 0.359502i \(0.882947\pi\)
\(662\) 7.50000 12.9904i 0.291496 0.504885i
\(663\) −1.00000 1.73205i −0.0388368 0.0672673i
\(664\) 10.0000 0.388075
\(665\) 0 0
\(666\) 5.00000 0.193746
\(667\) 0 0
\(668\) −9.50000 + 16.4545i −0.367566 + 0.636643i
\(669\) −8.00000 + 13.8564i −0.309298 + 0.535720i
\(670\) 0 0
\(671\) 10.0000 0.386046
\(672\) −2.50000 0.866025i −0.0964396 0.0334077i
\(673\) −36.0000 −1.38770 −0.693849 0.720121i \(-0.744086\pi\)
−0.693849 + 0.720121i \(0.744086\pi\)
\(674\) −7.00000 12.1244i −0.269630 0.467013i
\(675\) 0 0
\(676\) 6.00000 10.3923i 0.230769 0.399704i
\(677\) 16.5000 + 28.5788i 0.634147 + 1.09837i 0.986695 + 0.162581i \(0.0519817\pi\)
−0.352549 + 0.935793i \(0.614685\pi\)
\(678\) 6.00000 0.230429
\(679\) 16.0000 13.8564i 0.614024 0.531760i
\(680\) 0 0
\(681\) −7.00000 12.1244i −0.268241 0.464606i
\(682\) −15.0000 + 25.9808i −0.574380 + 0.994855i
\(683\) −2.00000 + 3.46410i −0.0765279 + 0.132550i −0.901750 0.432259i \(-0.857717\pi\)
0.825222 + 0.564809i \(0.191050\pi\)
\(684\) −3.50000 6.06218i −0.133826 0.231793i
\(685\) 0 0
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) 4.00000 0.152610
\(688\) 5.00000 + 8.66025i 0.190623 + 0.330169i
\(689\) 0.500000 0.866025i 0.0190485 0.0329929i
\(690\) 0 0
\(691\) 10.0000 + 17.3205i 0.380418 + 0.658903i 0.991122 0.132956i \(-0.0424468\pi\)
−0.610704 + 0.791859i \(0.709113\pi\)
\(692\) −7.00000 −0.266100
\(693\) 10.0000 8.66025i 0.379869 0.328976i
\(694\) 16.0000 0.607352
\(695\) 0 0
\(696\) 0 0
\(697\) 9.00000 15.5885i 0.340899 0.590455i
\(698\) 12.0000 + 20.7846i 0.454207 + 0.786709i
\(699\) 0 0
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) −0.500000 0.866025i −0.0188713 0.0326860i
\(703\) −17.5000 + 30.3109i −0.660025 + 1.14320i
\(704\) 2.50000 4.33013i 0.0942223 0.163198i
\(705\) 0 0
\(706\) 0 0
\(707\) −4.00000 20.7846i −0.150435 0.781686i
\(708\) −4.00000 −0.150329
\(709\) −8.00000 13.8564i −0.300446 0.520388i 0.675791 0.737093i \(-0.263802\pi\)
−0.976237 + 0.216705i \(0.930469\pi\)
\(710\) 0 0
\(711\) 7.00000 12.1244i 0.262521 0.454699i
\(712\) −5.00000 8.66025i −0.187383 0.324557i
\(713\) 18.0000 0.674105
\(714\) 1.00000 + 5.19615i 0.0374241 + 0.194461i
\(715\) 0 0
\(716\) 5.50000 + 9.52628i 0.205545 + 0.356014i
\(717\) 10.0000 17.3205i 0.373457 0.646846i
\(718\) 14.0000 24.2487i 0.522475 0.904954i
\(719\) 1.00000 + 1.73205i 0.0372937 + 0.0645946i 0.884070 0.467355i \(-0.154793\pi\)
−0.846776 + 0.531949i \(0.821460\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 30.0000 1.11648
\(723\) −0.500000 0.866025i −0.0185952 0.0322078i
\(724\) 1.00000 1.73205i 0.0371647 0.0643712i
\(725\) 0 0
\(726\) 7.00000 + 12.1244i 0.259794 + 0.449977i
\(727\) −53.0000 −1.96566 −0.982831 0.184510i \(-0.940930\pi\)
−0.982831 + 0.184510i \(0.940930\pi\)
\(728\) 2.00000 1.73205i 0.0741249 0.0641941i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 10.0000 17.3205i 0.369863 0.640622i
\(732\) −1.00000 + 1.73205i −0.0369611 + 0.0640184i
\(733\) −10.5000 18.1865i −0.387826 0.671735i 0.604331 0.796734i \(-0.293441\pi\)
−0.992157 + 0.124999i \(0.960107\pi\)
\(734\) 37.0000 1.36569
\(735\) 0 0
\(736\) −3.00000 −0.110581
\(737\) −15.0000 25.9808i −0.552532 0.957014i
\(738\) 4.50000 7.79423i 0.165647 0.286910i
\(739\) −23.5000 + 40.7032i −0.864461 + 1.49729i 0.00311943 + 0.999995i \(0.499007\pi\)
−0.867581 + 0.497296i \(0.834326\pi\)
\(740\) 0 0
\(741\) 7.00000 0.257151
\(742\) −2.00000 + 1.73205i −0.0734223 + 0.0635856i
\(743\) 31.0000 1.13728 0.568640 0.822587i \(-0.307470\pi\)
0.568640 + 0.822587i \(0.307470\pi\)
\(744\) −3.00000 5.19615i −0.109985 0.190500i
\(745\) 0 0
\(746\) 3.00000 5.19615i 0.109838 0.190245i
\(747\) −5.00000 8.66025i −0.182940 0.316862i
\(748\) −10.0000 −0.365636
\(749\) −30.0000 10.3923i −1.09618 0.379727i
\(750\) 0 0
\(751\) −2.00000 3.46410i −0.0729810 0.126407i 0.827225 0.561870i \(-0.189918\pi\)
−0.900207 + 0.435463i \(0.856585\pi\)
\(752\) −6.50000 + 11.2583i −0.237031 + 0.410549i
\(753\) −1.50000 + 2.59808i −0.0546630 + 0.0946792i
\(754\) 0 0
\(755\) 0 0
\(756\) 0.500000 + 2.59808i 0.0181848 + 0.0944911i
\(757\) 26.0000 0.944986 0.472493 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) 0.500000 + 0.866025i 0.0181608 + 0.0314555i
\(759\) 7.50000 12.9904i 0.272233 0.471521i
\(760\) 0 0
\(761\) 1.50000 + 2.59808i 0.0543750 + 0.0941802i 0.891932 0.452170i \(-0.149350\pi\)
−0.837557 + 0.546350i \(0.816017\pi\)
\(762\) 9.00000 0.326036
\(763\) 9.00000 + 46.7654i 0.325822 + 1.69302i
\(764\) −16.0000 −0.578860
\(765\) 0 0
\(766\) −4.50000 + 7.79423i −0.162592 + 0.281617i
\(767\) 2.00000 3.46410i 0.0722158 0.125081i
\(768\) 0.500000 + 0.866025i 0.0180422 + 0.0312500i
\(769\) 51.0000 1.83911 0.919554 0.392965i \(-0.128551\pi\)
0.919554 + 0.392965i \(0.128551\pi\)
\(770\) 0 0
\(771\) −10.0000 −0.360141
\(772\) −9.00000 15.5885i −0.323917 0.561041i
\(773\) −18.5000 + 32.0429i −0.665399 + 1.15250i 0.313778 + 0.949496i \(0.398405\pi\)
−0.979177 + 0.203008i \(0.934928\pi\)
\(774\) 5.00000 8.66025i 0.179721 0.311286i
\(775\) 0 0
\(776\) −8.00000 −0.287183
\(777\) 10.0000 8.66025i 0.358748 0.310685i
\(778\) 6.00000 0.215110
\(779\) 31.5000 + 54.5596i 1.12860 + 1.95480i
\(780\) 0 0
\(781\) −5.00000 + 8.66025i −0.178914 + 0.309888i
\(782\) 3.00000 + 5.19615i 0.107280 + 0.185814i
\(783\) 0 0
\(784\) −6.50000 + 2.59808i −0.232143 + 0.0927884i
\(785\) 0 0
\(786\) −8.50000 14.7224i −0.303185 0.525132i
\(787\) 19.0000 32.9090i 0.677277 1.17308i −0.298521 0.954403i \(-0.596493\pi\)
0.975798 0.218675i \(-0.0701734\pi\)
\(788\) −13.5000 + 23.3827i −0.480918 + 0.832974i
\(789\) −12.0000 20.7846i −0.427211 0.739952i
\(790\) 0 0
\(791\) 12.0000 10.3923i 0.426671 0.369508i
\(792\) −5.00000 −0.177667
\(793\) −1.00000 1.73205i −0.0355110 0.0615069i
\(794\) −1.00000 + 1.73205i −0.0354887 + 0.0614682i
\(795\) 0 0
\(796\) 7.00000 + 12.1244i 0.248108 + 0.429736i
\(797\) 30.0000 1.06265 0.531327 0.847167i \(-0.321693\pi\)
0.531327 + 0.847167i \(0.321693\pi\)
\(798\) −17.5000 6.06218i −0.619493 0.214599i