Properties

Label 1050.2.i.o.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.o.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 \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 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 −0.718900 0.695113i \(-0.755354\pi\)
0.961436 + 0.275029i \(0.0886875\pi\)
\(18\) 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 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) 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 0.994999 0.0998840i \(-0.0318472\pi\)
−0.584002 + 0.811752i \(0.698514\pi\)
\(38\) 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 \(-0.223975\pi\)
0.762493 + 0.646997i \(0.223975\pi\)
\(44\) 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 \(0.230354\pi\)
0.198747 + 0.980051i \(0.436313\pi\)
\(48\) 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 −0.829640 0.558298i \(-0.811454\pi\)
0.898321 + 0.439340i \(0.144788\pi\)
\(54\) 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 −0.989017 0.147802i \(-0.952780\pi\)
0.622509 + 0.782613i \(0.286114\pi\)
\(68\) 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 −0.959006 0.283387i \(-0.908542\pi\)
0.724923 + 0.688830i \(0.241875\pi\)
\(74\) −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 \(-0.684923\pi\)
−0.548821 + 0.835940i \(0.684923\pi\)
\(84\) −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 \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) 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 \(-0.969703\pi\)
0.415432 0.909624i \(-0.363630\pi\)
\(108\) −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 \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 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 \(-0.369250\pi\)
0.399310 + 0.916816i \(0.369250\pi\)
\(128\) 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 −0.767853 0.640626i \(-0.778675\pi\)
0.938725 + 0.344668i \(0.112008\pi\)
\(138\) 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 \(0.340272\pi\)
−0.999762 + 0.0217953i \(0.993062\pi\)
\(158\) −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 0.999410 0.0343508i \(-0.0109363\pi\)
−0.529454 + 0.848339i \(0.677603\pi\)
\(164\) 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 \(-0.762880\pi\)
−0.735132 + 0.677924i \(0.762880\pi\)
\(168\) −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 0.701751 0.712422i \(-0.252402\pi\)
−0.967851 + 0.251523i \(0.919068\pi\)
\(174\) 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 \(-0.609008\pi\)
0.983639 0.180150i \(-0.0576584\pi\)
\(194\) 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 \(-0.911776\pi\)
−0.961835 + 0.273629i \(0.911776\pi\)
\(198\) −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 \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) −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 −0.999184 0.0403978i \(-0.987137\pi\)
0.534577 + 0.845120i \(0.320471\pi\)
\(228\) −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 0.978772 0.204953i \(-0.0657041\pi\)
−0.666880 + 0.745165i \(0.732371\pi\)
\(258\) −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 \(0.431818\pi\)
−0.952517 + 0.304487i \(0.901515\pi\)
\(264\) −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 −0.894503 0.447062i \(-0.852470\pi\)
0.834419 + 0.551131i \(0.185804\pi\)
\(278\) −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 \(0.447796\pi\)
−0.936039 + 0.351895i \(0.885537\pi\)
\(284\) 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 \(-0.490701\pi\)
0.0292103 + 0.999573i \(0.490701\pi\)
\(294\) −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 \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) 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 0.972028 0.234863i \(-0.0754642\pi\)
−0.689412 + 0.724370i \(0.742131\pi\)
\(314\) −13.0000 −0.733632
\(315\) 0 0
\(316\) −14.0000 −0.787562
\(317\) −1.00000 1.73205i −0.0561656 0.0972817i 0.836576 0.547852i \(-0.184554\pi\)
−0.892741 + 0.450570i \(0.851221\pi\)
\(318\) −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 \(-0.624528\pi\)
−0.381314 + 0.924445i \(0.624528\pi\)
\(338\) −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 −0.567363 0.823468i \(-0.692036\pi\)
0.996826 + 0.0796169i \(0.0253697\pi\)
\(348\) 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 \(-0.416954\pi\)
0.707744 0.706469i \(-0.249713\pi\)
\(368\) −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 0.777847 0.628454i \(-0.216312\pi\)
−0.933181 + 0.359408i \(0.882979\pi\)
\(374\) 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 0.957790 0.287469i \(-0.0928139\pi\)
−0.727851 + 0.685736i \(0.759481\pi\)
\(384\) −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 0.890028 0.455905i \(-0.150684\pi\)
−0.839840 + 0.542834i \(0.817351\pi\)
\(398\) 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 \(-0.469359\pi\)
0.0961139 + 0.995370i \(0.469359\pi\)
\(434\) 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 0.928450 0.371457i \(-0.121142\pi\)
−0.785916 + 0.618333i \(0.787808\pi\)
\(444\) 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 \(0.181781\pi\)
0.0474665 + 0.998873i \(0.484885\pi\)
\(458\) −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 \(-0.613327\pi\)
−0.348555 + 0.937288i \(0.613327\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1.00000 1.73205i −0.0462745 0.0801498i 0.841960 0.539539i \(-0.181402\pi\)
−0.888235 + 0.459390i \(0.848068\pi\)
\(468\) 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 \(0.349671\pi\)
−0.998683 + 0.0513038i \(0.983662\pi\)
\(488\) −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 \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 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 0.704507 0.709697i \(-0.251168\pi\)
−0.966869 + 0.255273i \(0.917835\pi\)
\(524\) −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 \(-0.596753\pi\)
−0.299298 + 0.954160i \(0.596753\pi\)
\(548\) 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 \(-0.523808\pi\)
0.900967 0.433888i \(-0.142859\pi\)
\(558\) −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 \(0.384504\pi\)
−0.987106 + 0.160066i \(0.948829\pi\)
\(564\) 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 −1.00000 0.000500448i \(-0.999841\pi\)
0.500433 + 0.865775i \(0.333174\pi\)
\(578\) −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 \(-0.486858\pi\)
0.0412744 + 0.999148i \(0.486858\pi\)
\(588\) −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 \(0.0793071\pi\)
−0.271016 + 0.962575i \(0.587360\pi\)
\(594\) 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 0.703429 0.710766i \(-0.251651\pi\)
−0.967256 + 0.253804i \(0.918318\pi\)
\(608\) −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 −0.991588 0.129433i \(-0.958684\pi\)
0.607887 + 0.794024i \(0.292017\pi\)
\(614\) 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 \(-0.293622\pi\)
0.603877 + 0.797077i \(0.293622\pi\)
\(618\) 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 \(-0.230396\pi\)
0.749287 + 0.662246i \(0.230396\pi\)
\(644\) 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 −0.856030 0.516927i \(-0.827076\pi\)
0.875687 + 0.482880i \(0.160409\pi\)
\(648\) 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 0.812955 0.582327i \(-0.197858\pi\)
−0.910787 + 0.412876i \(0.864524\pi\)
\(654\) −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 \(-0.255914\pi\)
0.693849 + 0.720121i \(0.255914\pi\)
\(674\) −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 \(-0.948018\pi\)
0.352549 0.935793i \(-0.385315\pi\)
\(678\) −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 −0.825222 0.564809i \(-0.808950\pi\)
0.901750 + 0.432259i \(0.142283\pi\)
\(684\) −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 \(-0.0590699\pi\)
0.982831 + 0.184510i \(0.0590699\pi\)
\(728\) −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 0.992157 0.124999i \(-0.0398927\pi\)
−0.604331 + 0.796734i \(0.706559\pi\)
\(734\) 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 \(-0.692530\pi\)
−0.568640 + 0.822587i \(0.692530\pi\)
\(744\) −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 \(-0.656646\pi\)
−0.472493 + 0.881334i \(0.656646\pi\)
\(758\) −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 \(-0.601595\pi\)
0.979177 0.203008i \(-0.0650718\pi\)
\(774\) 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 \(0.403507\pi\)
−0.975798 + 0.218675i \(0.929827\pi\)
\(788\) 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 \(-0.678307\pi\)
−0.531327 + 0.847167i \(0.678307\pi\)
\(798\) 17.5000 + 6.06218i 0.619493 + 0.214599i
\(799\) 26.0000 0.919814
\(800\) 0