Properties

Label 170.2.d.a.169.2
Level 170
Weight 2
Character 170.169
Analytic conductor 1.357
Analytic rank 0
Dimension 2
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 170 = 2 \cdot 5 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 170.d (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(1.35745683436\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 169.2
Root \(1.00000i\)
Character \(\chi\) = 170.169
Dual form 170.2.d.a.169.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000i q^{2}\) \(-1.00000 q^{3}\) \(-1.00000 q^{4}\) \(+(-2.00000 + 1.00000i) q^{5}\) \(-1.00000i q^{6}\) \(-2.00000 q^{7}\) \(-1.00000i q^{8}\) \(-2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000i q^{2}\) \(-1.00000 q^{3}\) \(-1.00000 q^{4}\) \(+(-2.00000 + 1.00000i) q^{5}\) \(-1.00000i q^{6}\) \(-2.00000 q^{7}\) \(-1.00000i q^{8}\) \(-2.00000 q^{9}\) \(+(-1.00000 - 2.00000i) q^{10}\) \(+1.00000 q^{12}\) \(+1.00000i q^{13}\) \(-2.00000i q^{14}\) \(+(2.00000 - 1.00000i) q^{15}\) \(+1.00000 q^{16}\) \(+(-1.00000 + 4.00000i) q^{17}\) \(-2.00000i q^{18}\) \(-5.00000 q^{19}\) \(+(2.00000 - 1.00000i) q^{20}\) \(+2.00000 q^{21}\) \(+4.00000 q^{23}\) \(+1.00000i q^{24}\) \(+(3.00000 - 4.00000i) q^{25}\) \(-1.00000 q^{26}\) \(+5.00000 q^{27}\) \(+2.00000 q^{28}\) \(+9.00000i q^{29}\) \(+(1.00000 + 2.00000i) q^{30}\) \(-5.00000i q^{31}\) \(+1.00000i q^{32}\) \(+(-4.00000 - 1.00000i) q^{34}\) \(+(4.00000 - 2.00000i) q^{35}\) \(+2.00000 q^{36}\) \(-2.00000 q^{37}\) \(-5.00000i q^{38}\) \(-1.00000i q^{39}\) \(+(1.00000 + 2.00000i) q^{40}\) \(+10.0000i q^{41}\) \(+2.00000i q^{42}\) \(+6.00000i q^{43}\) \(+(4.00000 - 2.00000i) q^{45}\) \(+4.00000i q^{46}\) \(-7.00000i q^{47}\) \(-1.00000 q^{48}\) \(-3.00000 q^{49}\) \(+(4.00000 + 3.00000i) q^{50}\) \(+(1.00000 - 4.00000i) q^{51}\) \(-1.00000i q^{52}\) \(+1.00000i q^{53}\) \(+5.00000i q^{54}\) \(+2.00000i q^{56}\) \(+5.00000 q^{57}\) \(-9.00000 q^{58}\) \(-5.00000 q^{59}\) \(+(-2.00000 + 1.00000i) q^{60}\) \(-5.00000i q^{61}\) \(+5.00000 q^{62}\) \(+4.00000 q^{63}\) \(-1.00000 q^{64}\) \(+(-1.00000 - 2.00000i) q^{65}\) \(-2.00000i q^{67}\) \(+(1.00000 - 4.00000i) q^{68}\) \(-4.00000 q^{69}\) \(+(2.00000 + 4.00000i) q^{70}\) \(-5.00000i q^{71}\) \(+2.00000i q^{72}\) \(-11.0000 q^{73}\) \(-2.00000i q^{74}\) \(+(-3.00000 + 4.00000i) q^{75}\) \(+5.00000 q^{76}\) \(+1.00000 q^{78}\) \(-16.0000i q^{79}\) \(+(-2.00000 + 1.00000i) q^{80}\) \(+1.00000 q^{81}\) \(-10.0000 q^{82}\) \(+6.00000i q^{83}\) \(-2.00000 q^{84}\) \(+(-2.00000 - 9.00000i) q^{85}\) \(-6.00000 q^{86}\) \(-9.00000i q^{87}\) \(+5.00000 q^{89}\) \(+(2.00000 + 4.00000i) q^{90}\) \(-2.00000i q^{91}\) \(-4.00000 q^{92}\) \(+5.00000i q^{93}\) \(+7.00000 q^{94}\) \(+(10.0000 - 5.00000i) q^{95}\) \(-1.00000i q^{96}\) \(-7.00000 q^{97}\) \(-3.00000i q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 6q^{25} \) \(\mathstrut -\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 10q^{27} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 4q^{36} \) \(\mathstrut -\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 8q^{45} \) \(\mathstrut -\mathstrut 2q^{48} \) \(\mathstrut -\mathstrut 6q^{49} \) \(\mathstrut +\mathstrut 8q^{50} \) \(\mathstrut +\mathstrut 2q^{51} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 10q^{59} \) \(\mathstrut -\mathstrut 4q^{60} \) \(\mathstrut +\mathstrut 10q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut -\mathstrut 2q^{64} \) \(\mathstrut -\mathstrut 2q^{65} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut +\mathstrut 4q^{70} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 6q^{75} \) \(\mathstrut +\mathstrut 10q^{76} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut -\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 4q^{84} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 12q^{86} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 4q^{90} \) \(\mathstrut -\mathstrut 8q^{92} \) \(\mathstrut +\mathstrut 14q^{94} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 14q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).

\(n\) \(71\) \(137\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.00000 −0.577350 −0.288675 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) −1.00000 −0.500000
\(5\) −2.00000 + 1.00000i −0.894427 + 0.447214i
\(6\) 1.00000i 0.408248i
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −2.00000 −0.666667
\(10\) −1.00000 2.00000i −0.316228 0.632456i
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 1.00000 0.288675
\(13\) 1.00000i 0.277350i 0.990338 + 0.138675i \(0.0442844\pi\)
−0.990338 + 0.138675i \(0.955716\pi\)
\(14\) 2.00000i 0.534522i
\(15\) 2.00000 1.00000i 0.516398 0.258199i
\(16\) 1.00000 0.250000
\(17\) −1.00000 + 4.00000i −0.242536 + 0.970143i
\(18\) 2.00000i 0.471405i
\(19\) −5.00000 −1.14708 −0.573539 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) 2.00000 1.00000i 0.447214 0.223607i
\(21\) 2.00000 0.436436
\(22\) 0 0
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 1.00000i 0.204124i
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) −1.00000 −0.196116
\(27\) 5.00000 0.962250
\(28\) 2.00000 0.377964
\(29\) 9.00000i 1.67126i 0.549294 + 0.835629i \(0.314897\pi\)
−0.549294 + 0.835629i \(0.685103\pi\)
\(30\) 1.00000 + 2.00000i 0.182574 + 0.365148i
\(31\) 5.00000i 0.898027i −0.893525 0.449013i \(-0.851776\pi\)
0.893525 0.449013i \(-0.148224\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) −4.00000 1.00000i −0.685994 0.171499i
\(35\) 4.00000 2.00000i 0.676123 0.338062i
\(36\) 2.00000 0.333333
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 5.00000i 0.811107i
\(39\) 1.00000i 0.160128i
\(40\) 1.00000 + 2.00000i 0.158114 + 0.316228i
\(41\) 10.0000i 1.56174i 0.624695 + 0.780869i \(0.285223\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 2.00000i 0.308607i
\(43\) 6.00000i 0.914991i 0.889212 + 0.457496i \(0.151253\pi\)
−0.889212 + 0.457496i \(0.848747\pi\)
\(44\) 0 0
\(45\) 4.00000 2.00000i 0.596285 0.298142i
\(46\) 4.00000i 0.589768i
\(47\) 7.00000i 1.02105i −0.859861 0.510527i \(-0.829450\pi\)
0.859861 0.510527i \(-0.170550\pi\)
\(48\) −1.00000 −0.144338
\(49\) −3.00000 −0.428571
\(50\) 4.00000 + 3.00000i 0.565685 + 0.424264i
\(51\) 1.00000 4.00000i 0.140028 0.560112i
\(52\) 1.00000i 0.138675i
\(53\) 1.00000i 0.137361i 0.997639 + 0.0686803i \(0.0218788\pi\)
−0.997639 + 0.0686803i \(0.978121\pi\)
\(54\) 5.00000i 0.680414i
\(55\) 0 0
\(56\) 2.00000i 0.267261i
\(57\) 5.00000 0.662266
\(58\) −9.00000 −1.18176
\(59\) −5.00000 −0.650945 −0.325472 0.945552i \(-0.605523\pi\)
−0.325472 + 0.945552i \(0.605523\pi\)
\(60\) −2.00000 + 1.00000i −0.258199 + 0.129099i
\(61\) 5.00000i 0.640184i −0.947386 0.320092i \(-0.896286\pi\)
0.947386 0.320092i \(-0.103714\pi\)
\(62\) 5.00000 0.635001
\(63\) 4.00000 0.503953
\(64\) −1.00000 −0.125000
\(65\) −1.00000 2.00000i −0.124035 0.248069i
\(66\) 0 0
\(67\) 2.00000i 0.244339i −0.992509 0.122169i \(-0.961015\pi\)
0.992509 0.122169i \(-0.0389851\pi\)
\(68\) 1.00000 4.00000i 0.121268 0.485071i
\(69\) −4.00000 −0.481543
\(70\) 2.00000 + 4.00000i 0.239046 + 0.478091i
\(71\) 5.00000i 0.593391i −0.954972 0.296695i \(-0.904115\pi\)
0.954972 0.296695i \(-0.0958846\pi\)
\(72\) 2.00000i 0.235702i
\(73\) −11.0000 −1.28745 −0.643726 0.765256i \(-0.722612\pi\)
−0.643726 + 0.765256i \(0.722612\pi\)
\(74\) 2.00000i 0.232495i
\(75\) −3.00000 + 4.00000i −0.346410 + 0.461880i
\(76\) 5.00000 0.573539
\(77\) 0 0
\(78\) 1.00000 0.113228
\(79\) 16.0000i 1.80014i −0.435745 0.900070i \(-0.643515\pi\)
0.435745 0.900070i \(-0.356485\pi\)
\(80\) −2.00000 + 1.00000i −0.223607 + 0.111803i
\(81\) 1.00000 0.111111
\(82\) −10.0000 −1.10432
\(83\) 6.00000i 0.658586i 0.944228 + 0.329293i \(0.106810\pi\)
−0.944228 + 0.329293i \(0.893190\pi\)
\(84\) −2.00000 −0.218218
\(85\) −2.00000 9.00000i −0.216930 0.976187i
\(86\) −6.00000 −0.646997
\(87\) 9.00000i 0.964901i
\(88\) 0 0
\(89\) 5.00000 0.529999 0.264999 0.964249i \(-0.414628\pi\)
0.264999 + 0.964249i \(0.414628\pi\)
\(90\) 2.00000 + 4.00000i 0.210819 + 0.421637i
\(91\) 2.00000i 0.209657i
\(92\) −4.00000 −0.417029
\(93\) 5.00000i 0.518476i
\(94\) 7.00000 0.721995
\(95\) 10.0000 5.00000i 1.02598 0.512989i
\(96\) 1.00000i 0.102062i
\(97\) −7.00000 −0.710742 −0.355371 0.934725i \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) 3.00000i 0.303046i
\(99\) 0 0
\(100\) −3.00000 + 4.00000i −0.300000 + 0.400000i
\(101\) −8.00000 −0.796030 −0.398015 0.917379i \(-0.630301\pi\)
−0.398015 + 0.917379i \(0.630301\pi\)
\(102\) 4.00000 + 1.00000i 0.396059 + 0.0990148i
\(103\) 16.0000i 1.57653i 0.615338 + 0.788263i \(0.289020\pi\)
−0.615338 + 0.788263i \(0.710980\pi\)
\(104\) 1.00000 0.0980581
\(105\) −4.00000 + 2.00000i −0.390360 + 0.195180i
\(106\) −1.00000 −0.0971286
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) −5.00000 −0.481125
\(109\) 9.00000i 0.862044i 0.902342 + 0.431022i \(0.141847\pi\)
−0.902342 + 0.431022i \(0.858153\pi\)
\(110\) 0 0
\(111\) 2.00000 0.189832
\(112\) −2.00000 −0.188982
\(113\) 9.00000 0.846649 0.423324 0.905978i \(-0.360863\pi\)
0.423324 + 0.905978i \(0.360863\pi\)
\(114\) 5.00000i 0.468293i
\(115\) −8.00000 + 4.00000i −0.746004 + 0.373002i
\(116\) 9.00000i 0.835629i
\(117\) 2.00000i 0.184900i
\(118\) 5.00000i 0.460287i
\(119\) 2.00000 8.00000i 0.183340 0.733359i
\(120\) −1.00000 2.00000i −0.0912871 0.182574i
\(121\) 11.0000 1.00000
\(122\) 5.00000 0.452679
\(123\) 10.0000i 0.901670i
\(124\) 5.00000i 0.449013i
\(125\) −2.00000 + 11.0000i −0.178885 + 0.983870i
\(126\) 4.00000i 0.356348i
\(127\) 7.00000i 0.621150i −0.950549 0.310575i \(-0.899478\pi\)
0.950549 0.310575i \(-0.100522\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 6.00000i 0.528271i
\(130\) 2.00000 1.00000i 0.175412 0.0877058i
\(131\) 20.0000i 1.74741i 0.486458 + 0.873704i \(0.338289\pi\)
−0.486458 + 0.873704i \(0.661711\pi\)
\(132\) 0 0
\(133\) 10.0000 0.867110
\(134\) 2.00000 0.172774
\(135\) −10.0000 + 5.00000i −0.860663 + 0.430331i
\(136\) 4.00000 + 1.00000i 0.342997 + 0.0857493i
\(137\) 2.00000i 0.170872i −0.996344 0.0854358i \(-0.972772\pi\)
0.996344 0.0854358i \(-0.0272282\pi\)
\(138\) 4.00000i 0.340503i
\(139\) 14.0000i 1.18746i 0.804663 + 0.593732i \(0.202346\pi\)
−0.804663 + 0.593732i \(0.797654\pi\)
\(140\) −4.00000 + 2.00000i −0.338062 + 0.169031i
\(141\) 7.00000i 0.589506i
\(142\) 5.00000 0.419591
\(143\) 0 0
\(144\) −2.00000 −0.166667
\(145\) −9.00000 18.0000i −0.747409 1.49482i
\(146\) 11.0000i 0.910366i
\(147\) 3.00000 0.247436
\(148\) 2.00000 0.164399
\(149\) 20.0000 1.63846 0.819232 0.573462i \(-0.194400\pi\)
0.819232 + 0.573462i \(0.194400\pi\)
\(150\) −4.00000 3.00000i −0.326599 0.244949i
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 5.00000i 0.405554i
\(153\) 2.00000 8.00000i 0.161690 0.646762i
\(154\) 0 0
\(155\) 5.00000 + 10.0000i 0.401610 + 0.803219i
\(156\) 1.00000i 0.0800641i
\(157\) 18.0000i 1.43656i 0.695756 + 0.718278i \(0.255069\pi\)
−0.695756 + 0.718278i \(0.744931\pi\)
\(158\) 16.0000 1.27289
\(159\) 1.00000i 0.0793052i
\(160\) −1.00000 2.00000i −0.0790569 0.158114i
\(161\) −8.00000 −0.630488
\(162\) 1.00000i 0.0785674i
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) 10.0000i 0.780869i
\(165\) 0 0
\(166\) −6.00000 −0.465690
\(167\) 18.0000 1.39288 0.696441 0.717614i \(-0.254766\pi\)
0.696441 + 0.717614i \(0.254766\pi\)
\(168\) 2.00000i 0.154303i
\(169\) 12.0000 0.923077
\(170\) 9.00000 2.00000i 0.690268 0.153393i
\(171\) 10.0000 0.764719
\(172\) 6.00000i 0.457496i
\(173\) −16.0000 −1.21646 −0.608229 0.793762i \(-0.708120\pi\)
−0.608229 + 0.793762i \(0.708120\pi\)
\(174\) 9.00000 0.682288
\(175\) −6.00000 + 8.00000i −0.453557 + 0.604743i
\(176\) 0 0
\(177\) 5.00000 0.375823
\(178\) 5.00000i 0.374766i
\(179\) 20.0000 1.49487 0.747435 0.664335i \(-0.231285\pi\)
0.747435 + 0.664335i \(0.231285\pi\)
\(180\) −4.00000 + 2.00000i −0.298142 + 0.149071i
\(181\) 10.0000i 0.743294i −0.928374 0.371647i \(-0.878793\pi\)
0.928374 0.371647i \(-0.121207\pi\)
\(182\) 2.00000 0.148250
\(183\) 5.00000i 0.369611i
\(184\) 4.00000i 0.294884i
\(185\) 4.00000 2.00000i 0.294086 0.147043i
\(186\) −5.00000 −0.366618
\(187\) 0 0
\(188\) 7.00000i 0.510527i
\(189\) −10.0000 −0.727393
\(190\) 5.00000 + 10.0000i 0.362738 + 0.725476i
\(191\) −18.0000 −1.30243 −0.651217 0.758891i \(-0.725741\pi\)
−0.651217 + 0.758891i \(0.725741\pi\)
\(192\) 1.00000 0.0721688
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 7.00000i 0.502571i
\(195\) 1.00000 + 2.00000i 0.0716115 + 0.143223i
\(196\) 3.00000 0.214286
\(197\) 8.00000 0.569976 0.284988 0.958531i \(-0.408010\pi\)
0.284988 + 0.958531i \(0.408010\pi\)
\(198\) 0 0
\(199\) 1.00000i 0.0708881i −0.999372 0.0354441i \(-0.988715\pi\)
0.999372 0.0354441i \(-0.0112846\pi\)
\(200\) −4.00000 3.00000i −0.282843 0.212132i
\(201\) 2.00000i 0.141069i
\(202\) 8.00000i 0.562878i
\(203\) 18.0000i 1.26335i
\(204\) −1.00000 + 4.00000i −0.0700140 + 0.280056i
\(205\) −10.0000 20.0000i −0.698430 1.39686i
\(206\) −16.0000 −1.11477
\(207\) −8.00000 −0.556038
\(208\) 1.00000i 0.0693375i
\(209\) 0 0
\(210\) −2.00000 4.00000i −0.138013 0.276026i
\(211\) 20.0000i 1.37686i 0.725304 + 0.688428i \(0.241699\pi\)
−0.725304 + 0.688428i \(0.758301\pi\)
\(212\) 1.00000i 0.0686803i
\(213\) 5.00000i 0.342594i
\(214\) 12.0000i 0.820303i
\(215\) −6.00000 12.0000i −0.409197 0.818393i
\(216\) 5.00000i 0.340207i
\(217\) 10.0000i 0.678844i
\(218\) −9.00000 −0.609557
\(219\) 11.0000 0.743311
\(220\) 0 0
\(221\) −4.00000 1.00000i −0.269069 0.0672673i
\(222\) 2.00000i 0.134231i
\(223\) 9.00000i 0.602685i −0.953516 0.301342i \(-0.902565\pi\)
0.953516 0.301342i \(-0.0974347\pi\)
\(224\) 2.00000i 0.133631i
\(225\) −6.00000 + 8.00000i −0.400000 + 0.533333i
\(226\) 9.00000i 0.598671i
\(227\) −27.0000 −1.79205 −0.896026 0.444001i \(-0.853559\pi\)
−0.896026 + 0.444001i \(0.853559\pi\)
\(228\) −5.00000 −0.331133
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) −4.00000 8.00000i −0.263752 0.527504i
\(231\) 0 0
\(232\) 9.00000 0.590879
\(233\) −21.0000 −1.37576 −0.687878 0.725826i \(-0.741458\pi\)
−0.687878 + 0.725826i \(0.741458\pi\)
\(234\) 2.00000 0.130744
\(235\) 7.00000 + 14.0000i 0.456630 + 0.913259i
\(236\) 5.00000 0.325472
\(237\) 16.0000i 1.03931i
\(238\) 8.00000 + 2.00000i 0.518563 + 0.129641i
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 2.00000 1.00000i 0.129099 0.0645497i
\(241\) 10.0000i 0.644157i −0.946713 0.322078i \(-0.895619\pi\)
0.946713 0.322078i \(-0.104381\pi\)
\(242\) 11.0000i 0.707107i
\(243\) −16.0000 −1.02640
\(244\) 5.00000i 0.320092i
\(245\) 6.00000 3.00000i 0.383326 0.191663i
\(246\) 10.0000 0.637577
\(247\) 5.00000i 0.318142i
\(248\) −5.00000 −0.317500
\(249\) 6.00000i 0.380235i
\(250\) −11.0000 2.00000i −0.695701 0.126491i
\(251\) −8.00000 −0.504956 −0.252478 0.967603i \(-0.581245\pi\)
−0.252478 + 0.967603i \(0.581245\pi\)
\(252\) −4.00000 −0.251976
\(253\) 0 0
\(254\) 7.00000 0.439219
\(255\) 2.00000 + 9.00000i 0.125245 + 0.563602i
\(256\) 1.00000 0.0625000
\(257\) 18.0000i 1.12281i 0.827541 + 0.561405i \(0.189739\pi\)
−0.827541 + 0.561405i \(0.810261\pi\)
\(258\) 6.00000 0.373544
\(259\) 4.00000 0.248548
\(260\) 1.00000 + 2.00000i 0.0620174 + 0.124035i
\(261\) 18.0000i 1.11417i
\(262\) −20.0000 −1.23560
\(263\) 21.0000i 1.29492i 0.762101 + 0.647458i \(0.224168\pi\)
−0.762101 + 0.647458i \(0.775832\pi\)
\(264\) 0 0
\(265\) −1.00000 2.00000i −0.0614295 0.122859i
\(266\) 10.0000i 0.613139i
\(267\) −5.00000 −0.305995
\(268\) 2.00000i 0.122169i
\(269\) 1.00000i 0.0609711i −0.999535 0.0304855i \(-0.990295\pi\)
0.999535 0.0304855i \(-0.00970535\pi\)
\(270\) −5.00000 10.0000i −0.304290 0.608581i
\(271\) 22.0000 1.33640 0.668202 0.743980i \(-0.267064\pi\)
0.668202 + 0.743980i \(0.267064\pi\)
\(272\) −1.00000 + 4.00000i −0.0606339 + 0.242536i
\(273\) 2.00000i 0.121046i
\(274\) 2.00000 0.120824
\(275\) 0 0
\(276\) 4.00000 0.240772
\(277\) 18.0000 1.08152 0.540758 0.841178i \(-0.318138\pi\)
0.540758 + 0.841178i \(0.318138\pi\)
\(278\) −14.0000 −0.839664
\(279\) 10.0000i 0.598684i
\(280\) −2.00000 4.00000i −0.119523 0.239046i
\(281\) −23.0000 −1.37206 −0.686032 0.727571i \(-0.740649\pi\)
−0.686032 + 0.727571i \(0.740649\pi\)
\(282\) −7.00000 −0.416844
\(283\) −21.0000 −1.24832 −0.624160 0.781296i \(-0.714559\pi\)
−0.624160 + 0.781296i \(0.714559\pi\)
\(284\) 5.00000i 0.296695i
\(285\) −10.0000 + 5.00000i −0.592349 + 0.296174i
\(286\) 0 0
\(287\) 20.0000i 1.18056i
\(288\) 2.00000i 0.117851i
\(289\) −15.0000 8.00000i −0.882353 0.470588i
\(290\) 18.0000 9.00000i 1.05700 0.528498i
\(291\) 7.00000 0.410347
\(292\) 11.0000 0.643726
\(293\) 29.0000i 1.69420i −0.531435 0.847099i \(-0.678347\pi\)
0.531435 0.847099i \(-0.321653\pi\)
\(294\) 3.00000i 0.174964i
\(295\) 10.0000 5.00000i 0.582223 0.291111i
\(296\) 2.00000i 0.116248i
\(297\) 0 0
\(298\) 20.0000i 1.15857i
\(299\) 4.00000i 0.231326i
\(300\) 3.00000 4.00000i 0.173205 0.230940i
\(301\) 12.0000i 0.691669i
\(302\) 8.00000i 0.460348i
\(303\) 8.00000 0.459588
\(304\) −5.00000 −0.286770
\(305\) 5.00000 + 10.0000i 0.286299 + 0.572598i
\(306\) 8.00000 + 2.00000i 0.457330 + 0.114332i
\(307\) 2.00000i 0.114146i −0.998370 0.0570730i \(-0.981823\pi\)
0.998370 0.0570730i \(-0.0181768\pi\)
\(308\) 0 0
\(309\) 16.0000i 0.910208i
\(310\) −10.0000 + 5.00000i −0.567962 + 0.283981i
\(311\) 20.0000i 1.13410i −0.823685 0.567048i \(-0.808085\pi\)
0.823685 0.567048i \(-0.191915\pi\)
\(312\) −1.00000 −0.0566139
\(313\) 14.0000 0.791327 0.395663 0.918396i \(-0.370515\pi\)
0.395663 + 0.918396i \(0.370515\pi\)
\(314\) −18.0000 −1.01580
\(315\) −8.00000 + 4.00000i −0.450749 + 0.225374i
\(316\) 16.0000i 0.900070i
\(317\) −12.0000 −0.673987 −0.336994 0.941507i \(-0.609410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(318\) 1.00000 0.0560772
\(319\) 0 0
\(320\) 2.00000 1.00000i 0.111803 0.0559017i
\(321\) 12.0000 0.669775
\(322\) 8.00000i 0.445823i
\(323\) 5.00000 20.0000i 0.278207 1.11283i
\(324\) −1.00000 −0.0555556
\(325\) 4.00000 + 3.00000i 0.221880 + 0.166410i
\(326\) 4.00000i 0.221540i
\(327\) 9.00000i 0.497701i
\(328\) 10.0000 0.552158
\(329\) 14.0000i 0.771845i
\(330\) 0 0
\(331\) 7.00000 0.384755 0.192377 0.981321i \(-0.438380\pi\)
0.192377 + 0.981321i \(0.438380\pi\)
\(332\) 6.00000i 0.329293i
\(333\) 4.00000 0.219199
\(334\) 18.0000i 0.984916i
\(335\) 2.00000 + 4.00000i 0.109272 + 0.218543i
\(336\) 2.00000 0.109109
\(337\) 23.0000 1.25289 0.626445 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(338\) 12.0000i 0.652714i
\(339\) −9.00000 −0.488813
\(340\) 2.00000 + 9.00000i 0.108465 + 0.488094i
\(341\) 0 0
\(342\) 10.0000i 0.540738i
\(343\) 20.0000 1.07990
\(344\) 6.00000 0.323498
\(345\) 8.00000 4.00000i 0.430706 0.215353i
\(346\) 16.0000i 0.860165i
\(347\) 23.0000 1.23470 0.617352 0.786687i \(-0.288205\pi\)
0.617352 + 0.786687i \(0.288205\pi\)
\(348\) 9.00000i 0.482451i
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) −8.00000 6.00000i −0.427618 0.320713i
\(351\) 5.00000i 0.266880i
\(352\) 0 0
\(353\) 4.00000i 0.212899i −0.994318 0.106449i \(-0.966052\pi\)
0.994318 0.106449i \(-0.0339482\pi\)
\(354\) 5.00000i 0.265747i
\(355\) 5.00000 + 10.0000i 0.265372 + 0.530745i
\(356\) −5.00000 −0.264999
\(357\) −2.00000 + 8.00000i −0.105851 + 0.423405i
\(358\) 20.0000i 1.05703i
\(359\) −30.0000 −1.58334 −0.791670 0.610949i \(-0.790788\pi\)
−0.791670 + 0.610949i \(0.790788\pi\)
\(360\) −2.00000 4.00000i −0.105409 0.210819i
\(361\) 6.00000 0.315789
\(362\) 10.0000 0.525588
\(363\) −11.0000 −0.577350
\(364\) 2.00000i 0.104828i
\(365\) 22.0000 11.0000i 1.15153 0.575766i
\(366\) −5.00000 −0.261354
\(367\) −2.00000 −0.104399 −0.0521996 0.998637i \(-0.516623\pi\)
−0.0521996 + 0.998637i \(0.516623\pi\)
\(368\) 4.00000 0.208514
\(369\) 20.0000i 1.04116i
\(370\) 2.00000 + 4.00000i 0.103975 + 0.207950i
\(371\) 2.00000i 0.103835i
\(372\) 5.00000i 0.259238i
\(373\) 34.0000i 1.76045i −0.474554 0.880227i \(-0.657390\pi\)
0.474554 0.880227i \(-0.342610\pi\)
\(374\) 0 0
\(375\) 2.00000 11.0000i 0.103280 0.568038i
\(376\) −7.00000 −0.360997
\(377\) −9.00000 −0.463524
\(378\) 10.0000i 0.514344i
\(379\) 4.00000i 0.205466i 0.994709 + 0.102733i \(0.0327588\pi\)
−0.994709 + 0.102733i \(0.967241\pi\)
\(380\) −10.0000 + 5.00000i −0.512989 + 0.256495i
\(381\) 7.00000i 0.358621i
\(382\) 18.0000i 0.920960i
\(383\) 31.0000i 1.58403i 0.610504 + 0.792013i \(0.290967\pi\)
−0.610504 + 0.792013i \(0.709033\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 0 0
\(386\) 14.0000i 0.712581i
\(387\) 12.0000i 0.609994i
\(388\) 7.00000 0.355371
\(389\) −10.0000 −0.507020 −0.253510 0.967333i \(-0.581585\pi\)
−0.253510 + 0.967333i \(0.581585\pi\)
\(390\) −2.00000 + 1.00000i −0.101274 + 0.0506370i
\(391\) −4.00000 + 16.0000i −0.202289 + 0.809155i
\(392\) 3.00000i 0.151523i
\(393\) 20.0000i 1.00887i
\(394\) 8.00000i 0.403034i
\(395\) 16.0000 + 32.0000i 0.805047 + 1.61009i
\(396\) 0 0
\(397\) 18.0000 0.903394 0.451697 0.892171i \(-0.350819\pi\)
0.451697 + 0.892171i \(0.350819\pi\)
\(398\) 1.00000 0.0501255
\(399\) −10.0000 −0.500626
\(400\) 3.00000 4.00000i 0.150000 0.200000i
\(401\) 10.0000i 0.499376i 0.968326 + 0.249688i \(0.0803281\pi\)
−0.968326 + 0.249688i \(0.919672\pi\)
\(402\) −2.00000 −0.0997509
\(403\) 5.00000 0.249068
\(404\) 8.00000 0.398015
\(405\) −2.00000 + 1.00000i −0.0993808 + 0.0496904i
\(406\) 18.0000 0.893325
\(407\) 0 0
\(408\) −4.00000 1.00000i −0.198030 0.0495074i
\(409\) −25.0000 −1.23617 −0.618085 0.786111i \(-0.712091\pi\)
−0.618085 + 0.786111i \(0.712091\pi\)
\(410\) 20.0000 10.0000i 0.987730 0.493865i
\(411\) 2.00000i 0.0986527i
\(412\) 16.0000i 0.788263i
\(413\) 10.0000 0.492068
\(414\) 8.00000i 0.393179i
\(415\) −6.00000 12.0000i −0.294528 0.589057i
\(416\) −1.00000 −0.0490290
\(417\) 14.0000i 0.685583i
\(418\) 0 0
\(419\) 24.0000i 1.17248i 0.810139 + 0.586238i \(0.199392\pi\)
−0.810139 + 0.586238i \(0.800608\pi\)
\(420\) 4.00000 2.00000i 0.195180 0.0975900i
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) −20.0000 −0.973585
\(423\) 14.0000i 0.680703i
\(424\) 1.00000 0.0485643
\(425\) 13.0000 + 16.0000i 0.630593 + 0.776114i
\(426\) −5.00000 −0.242251
\(427\) 10.0000i 0.483934i
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) 12.0000 6.00000i 0.578691 0.289346i
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 5.00000 0.240563
\(433\) 6.00000i 0.288342i 0.989553 + 0.144171i \(0.0460515\pi\)
−0.989553 + 0.144171i \(0.953949\pi\)
\(434\) −10.0000 −0.480015
\(435\) 9.00000 + 18.0000i 0.431517 + 0.863034i
\(436\) 9.00000i 0.431022i
\(437\) −20.0000 −0.956730
\(438\) 11.0000i 0.525600i
\(439\) 24.0000i 1.14546i 0.819745 + 0.572729i \(0.194115\pi\)
−0.819745 + 0.572729i \(0.805885\pi\)
\(440\) 0 0
\(441\) 6.00000 0.285714
\(442\) 1.00000 4.00000i 0.0475651 0.190261i
\(443\) 26.0000i 1.23530i 0.786454 + 0.617649i \(0.211915\pi\)
−0.786454 + 0.617649i \(0.788085\pi\)
\(444\) −2.00000 −0.0949158
\(445\) −10.0000 + 5.00000i −0.474045 + 0.237023i
\(446\) 9.00000 0.426162
\(447\) −20.0000 −0.945968
\(448\) 2.00000 0.0944911
\(449\) 16.0000i 0.755087i −0.925992 0.377543i \(-0.876769\pi\)
0.925992 0.377543i \(-0.123231\pi\)
\(450\) −8.00000 6.00000i −0.377124 0.282843i
\(451\) 0 0
\(452\) −9.00000 −0.423324
\(453\) 8.00000 0.375873
\(454\) 27.0000i 1.26717i
\(455\) 2.00000 + 4.00000i 0.0937614 + 0.187523i
\(456\) 5.00000i 0.234146i
\(457\) 18.0000i 0.842004i 0.907060 + 0.421002i \(0.138322\pi\)
−0.907060 + 0.421002i \(0.861678\pi\)
\(458\) 0 0
\(459\) −5.00000 + 20.0000i −0.233380 + 0.933520i
\(460\) 8.00000 4.00000i 0.373002 0.186501i
\(461\) 32.0000 1.49039 0.745194 0.666847i \(-0.232357\pi\)
0.745194 + 0.666847i \(0.232357\pi\)
\(462\) 0 0
\(463\) 29.0000i 1.34774i −0.738848 0.673872i \(-0.764630\pi\)
0.738848 0.673872i \(-0.235370\pi\)
\(464\) 9.00000i 0.417815i
\(465\) −5.00000 10.0000i −0.231869 0.463739i
\(466\) 21.0000i 0.972806i
\(467\) 12.0000i 0.555294i −0.960683 0.277647i \(-0.910445\pi\)
0.960683 0.277647i \(-0.0895545\pi\)
\(468\) 2.00000i 0.0924500i
\(469\) 4.00000i 0.184703i
\(470\) −14.0000 + 7.00000i −0.645772 + 0.322886i
\(471\) 18.0000i 0.829396i
\(472\) 5.00000i 0.230144i
\(473\) 0 0
\(474\) −16.0000 −0.734904
\(475\) −15.0000 + 20.0000i −0.688247 + 0.917663i
\(476\) −2.00000 + 8.00000i −0.0916698 + 0.366679i
\(477\) 2.00000i 0.0915737i
\(478\) 0 0
\(479\) 21.0000i 0.959514i −0.877401 0.479757i \(-0.840725\pi\)
0.877401 0.479757i \(-0.159275\pi\)
\(480\) 1.00000 + 2.00000i 0.0456435 + 0.0912871i
\(481\) 2.00000i 0.0911922i
\(482\) 10.0000 0.455488
\(483\) 8.00000 0.364013
\(484\) −11.0000 −0.500000
\(485\) 14.0000 7.00000i 0.635707 0.317854i
\(486\) 16.0000i 0.725775i
\(487\) −32.0000 −1.45006 −0.725029 0.688718i \(-0.758174\pi\)
−0.725029 + 0.688718i \(0.758174\pi\)
\(488\) −5.00000 −0.226339
\(489\) −4.00000 −0.180886
\(490\) 3.00000 + 6.00000i 0.135526 + 0.271052i
\(491\) −33.0000 −1.48927 −0.744635 0.667472i \(-0.767376\pi\)
−0.744635 + 0.667472i \(0.767376\pi\)
\(492\) 10.0000i 0.450835i
\(493\) −36.0000 9.00000i −1.62136 0.405340i
\(494\) 5.00000 0.224961
\(495\) 0 0
\(496\) 5.00000i 0.224507i
\(497\) 10.0000i 0.448561i
\(498\) 6.00000 0.268866
\(499\) 6.00000i 0.268597i −0.990941 0.134298i \(-0.957122\pi\)
0.990941 0.134298i \(-0.0428781\pi\)
\(500\) 2.00000 11.0000i 0.0894427 0.491935i
\(501\) −18.0000 −0.804181
\(502\) 8.00000i 0.357057i
\(503\) −6.00000 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(504\) 4.00000i 0.178174i
\(505\) 16.0000 8.00000i 0.711991 0.355995i
\(506\) 0 0
\(507\) −12.0000 −0.532939
\(508\) 7.00000i 0.310575i
\(509\) −20.0000 −0.886484 −0.443242 0.896402i \(-0.646172\pi\)
−0.443242 + 0.896402i \(0.646172\pi\)
\(510\) −9.00000 + 2.00000i −0.398527 + 0.0885615i
\(511\) 22.0000 0.973223
\(512\) 1.00000i 0.0441942i
\(513\) −25.0000 −1.10378
\(514\) −18.0000 −0.793946
\(515\) −16.0000 32.0000i −0.705044 1.41009i
\(516\) 6.00000i 0.264135i
\(517\) 0 0
\(518\) 4.00000i 0.175750i
\(519\) 16.0000 0.702322
\(520\) −2.00000 + 1.00000i −0.0877058 + 0.0438529i
\(521\) 40.0000i 1.75243i 0.481919 + 0.876216i \(0.339940\pi\)
−0.481919 + 0.876216i \(0.660060\pi\)
\(522\) 18.0000 0.787839
\(523\) 34.0000i 1.48672i −0.668894 0.743358i \(-0.733232\pi\)
0.668894 0.743358i \(-0.266768\pi\)
\(524\) 20.0000i 0.873704i
\(525\) 6.00000 8.00000i 0.261861 0.349149i
\(526\) −21.0000 −0.915644
\(527\) 20.0000 + 5.00000i 0.871214 + 0.217803i
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 2.00000 1.00000i 0.0868744 0.0434372i
\(531\) 10.0000 0.433963
\(532\) −10.0000 −0.433555
\(533\) −10.0000 −0.433148
\(534\) 5.00000i 0.216371i
\(535\) 24.0000 12.0000i 1.03761 0.518805i
\(536\) −2.00000 −0.0863868
\(537\) −20.0000 −0.863064
\(538\) 1.00000 0.0431131
\(539\) 0 0
\(540\) 10.0000 5.00000i 0.430331 0.215166i
\(541\) 10.0000i 0.429934i 0.976621 + 0.214967i \(0.0689643\pi\)
−0.976621 + 0.214967i \(0.931036\pi\)
\(542\) 22.0000i 0.944981i
\(543\) 10.0000i 0.429141i
\(544\) −4.00000 1.00000i −0.171499 0.0428746i
\(545\) −9.00000 18.0000i −0.385518 0.771035i
\(546\) −2.00000 −0.0855921
\(547\) 13.0000 0.555840 0.277920 0.960604i \(-0.410355\pi\)
0.277920 + 0.960604i \(0.410355\pi\)
\(548\) 2.00000i 0.0854358i
\(549\) 10.0000i 0.426790i
\(550\) 0 0
\(551\) 45.0000i 1.91706i
\(552\) 4.00000i 0.170251i
\(553\) 32.0000i 1.36078i
\(554\) 18.0000i 0.764747i
\(555\) −4.00000 + 2.00000i −0.169791 + 0.0848953i
\(556\) 14.0000i 0.593732i
\(557\) 3.00000i 0.127114i 0.997978 + 0.0635570i \(0.0202445\pi\)
−0.997978 + 0.0635570i \(0.979756\pi\)
\(558\) −10.0000 −0.423334
\(559\) −6.00000 −0.253773
\(560\) 4.00000 2.00000i 0.169031 0.0845154i
\(561\) 0 0
\(562\) 23.0000i 0.970196i
\(563\) 24.0000i 1.01148i −0.862686 0.505740i \(-0.831220\pi\)
0.862686 0.505740i \(-0.168780\pi\)
\(564\) 7.00000i 0.294753i
\(565\) −18.0000 + 9.00000i −0.757266 + 0.378633i
\(566\) 21.0000i 0.882696i
\(567\) −2.00000 −0.0839921
\(568\) −5.00000 −0.209795
\(569\) 15.0000 0.628833 0.314416 0.949285i \(-0.398191\pi\)
0.314416 + 0.949285i \(0.398191\pi\)
\(570\) −5.00000 10.0000i −0.209427 0.418854i
\(571\) 20.0000i 0.836974i 0.908223 + 0.418487i \(0.137439\pi\)
−0.908223 + 0.418487i \(0.862561\pi\)
\(572\) 0 0
\(573\) 18.0000 0.751961
\(574\) 20.0000 0.834784
\(575\) 12.0000 16.0000i 0.500435 0.667246i
\(576\) 2.00000 0.0833333
\(577\) 28.0000i 1.16566i 0.812596 + 0.582828i \(0.198054\pi\)
−0.812596 + 0.582828i \(0.801946\pi\)
\(578\) 8.00000 15.0000i 0.332756 0.623918i
\(579\) −14.0000 −0.581820
\(580\) 9.00000 + 18.0000i 0.373705 + 0.747409i
\(581\) 12.0000i 0.497844i
\(582\) 7.00000i 0.290159i
\(583\) 0 0
\(584\) 11.0000i 0.455183i
\(585\) 2.00000 + 4.00000i 0.0826898 + 0.165380i
\(586\) 29.0000 1.19798
\(587\) 12.0000i 0.495293i −0.968850 0.247647i \(-0.920343\pi\)
0.968850 0.247647i \(-0.0796572\pi\)
\(588\) −3.00000 −0.123718
\(589\) 25.0000i 1.03011i
\(590\) 5.00000 + 10.0000i 0.205847 + 0.411693i
\(591\) −8.00000 −0.329076
\(592\) −2.00000 −0.0821995
\(593\) 6.00000i 0.246390i 0.992382 + 0.123195i \(0.0393141\pi\)
−0.992382 + 0.123195i \(0.960686\pi\)
\(594\) 0 0
\(595\) 4.00000 + 18.0000i 0.163984 + 0.737928i
\(596\) −20.0000 −0.819232
\(597\) 1.00000i 0.0409273i
\(598\) −4.00000 −0.163572
\(599\) 20.0000 0.817178 0.408589 0.912719i \(-0.366021\pi\)
0.408589 + 0.912719i \(0.366021\pi\)
\(600\) 4.00000 + 3.00000i 0.163299 + 0.122474i
\(601\) 30.0000i 1.22373i 0.790964 + 0.611863i \(0.209580\pi\)
−0.790964 + 0.611863i \(0.790420\pi\)
\(602\) 12.0000 0.489083
\(603\) 4.00000i 0.162893i
\(604\) 8.00000 0.325515
\(605\) −22.0000 + 11.0000i −0.894427 + 0.447214i
\(606\) 8.00000i 0.324978i
\(607\) 38.0000 1.54237 0.771186 0.636610i \(-0.219664\pi\)
0.771186 + 0.636610i \(0.219664\pi\)
\(608\) 5.00000i 0.202777i
\(609\) 18.0000i 0.729397i
\(610\) −10.0000 + 5.00000i −0.404888 + 0.202444i
\(611\) 7.00000 0.283190
\(612\) −2.00000 + 8.00000i −0.0808452 + 0.323381i
\(613\) 41.0000i 1.65597i 0.560747 + 0.827987i \(0.310514\pi\)
−0.560747 + 0.827987i \(0.689486\pi\)
\(614\) 2.00000 0.0807134
\(615\) 10.0000 + 20.0000i 0.403239 + 0.806478i
\(616\) 0 0
\(617\) 33.0000 1.32853 0.664265 0.747497i \(-0.268745\pi\)
0.664265 + 0.747497i \(0.268745\pi\)
\(618\) 16.0000 0.643614
\(619\) 26.0000i 1.04503i −0.852631 0.522514i \(-0.824994\pi\)
0.852631 0.522514i \(-0.175006\pi\)
\(620\) −5.00000 10.0000i −0.200805 0.401610i
\(621\) 20.0000 0.802572
\(622\) 20.0000 0.801927
\(623\) −10.0000 −0.400642
\(624\) 1.00000i 0.0400320i
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 14.0000i 0.559553i
\(627\) 0 0
\(628\) 18.0000i 0.718278i
\(629\) 2.00000 8.00000i 0.0797452 0.318981i
\(630\) −4.00000 8.00000i −0.159364 0.318728i
\(631\) 2.00000 0.0796187 0.0398094 0.999207i \(-0.487325\pi\)
0.0398094 + 0.999207i \(0.487325\pi\)
\(632\) −16.0000 −0.636446
\(633\) 20.0000i 0.794929i
\(634\) 12.0000i 0.476581i
\(635\) 7.00000 + 14.0000i 0.277787 + 0.555573i
\(636\) 1.00000i 0.0396526i
\(637\) 3.00000i 0.118864i
\(638\) 0 0
\(639\) 10.0000i 0.395594i
\(640\) 1.00000 + 2.00000i 0.0395285 + 0.0790569i
\(641\) 10.0000i 0.394976i 0.980305 + 0.197488i \(0.0632784\pi\)
−0.980305 + 0.197488i \(0.936722\pi\)
\(642\) 12.0000i 0.473602i
\(643\) −36.0000 −1.41970 −0.709851 0.704352i \(-0.751238\pi\)
−0.709851 + 0.704352i \(0.751238\pi\)
\(644\) 8.00000 0.315244
\(645\) 6.00000 + 12.0000i 0.236250 + 0.472500i
\(646\) 20.0000 + 5.00000i 0.786889 + 0.196722i
\(647\) 37.0000i 1.45462i −0.686309 0.727310i \(-0.740770\pi\)
0.686309 0.727310i \(-0.259230\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 0 0
\(650\) −3.00000 + 4.00000i −0.117670 + 0.156893i
\(651\) 10.0000i 0.391931i
\(652\) −4.00000 −0.156652
\(653\) 24.0000 0.939193 0.469596 0.882881i \(-0.344399\pi\)
0.469596 + 0.882881i \(0.344399\pi\)
\(654\) 9.00000 0.351928
\(655\) −20.0000 40.0000i −0.781465 1.56293i
\(656\) 10.0000i 0.390434i
\(657\) 22.0000 0.858302
\(658\) −14.0000 −0.545777
\(659\) −5.00000 −0.194772 −0.0973862 0.995247i \(-0.531048\pi\)
−0.0973862 + 0.995247i \(0.531048\pi\)
\(660\) 0 0
\(661\) −8.00000 −0.311164 −0.155582 0.987823i \(-0.549725\pi\)
−0.155582 + 0.987823i \(0.549725\pi\)
\(662\) 7.00000i 0.272063i
\(663\) 4.00000 + 1.00000i 0.155347 + 0.0388368i
\(664\) 6.00000 0.232845
\(665\) −20.0000 + 10.0000i −0.775567 + 0.387783i
\(666\) 4.00000i 0.154997i
\(667\) 36.0000i 1.39393i
\(668\) −18.0000 −0.696441
\(669\) 9.00000i 0.347960i
\(670\) −4.00000 + 2.00000i −0.154533 + 0.0772667i
\(671\) 0 0
\(672\) 2.00000i 0.0771517i
\(673\) −1.00000 −0.0385472 −0.0192736 0.999814i \(-0.506135\pi\)
−0.0192736 + 0.999814i \(0.506135\pi\)
\(674\) 23.0000i 0.885927i
\(675\) 15.0000 20.0000i 0.577350 0.769800i
\(676\) −12.0000 −0.461538
\(677\) −2.00000 −0.0768662 −0.0384331 0.999261i \(-0.512237\pi\)
−0.0384331 + 0.999261i \(0.512237\pi\)
\(678\) 9.00000i 0.345643i
\(679\) 14.0000 0.537271
\(680\) −9.00000 + 2.00000i −0.345134 + 0.0766965i
\(681\) 27.0000 1.03464
\(682\) 0 0
\(683\) 39.0000 1.49229 0.746147 0.665782i \(-0.231902\pi\)
0.746147 + 0.665782i \(0.231902\pi\)
\(684\) −10.0000 −0.382360
\(685\) 2.00000 + 4.00000i 0.0764161 + 0.152832i
\(686\) 20.0000i 0.763604i
\(687\) 0 0
\(688\) 6.00000i 0.228748i
\(689\) −1.00000 −0.0380970
\(690\) 4.00000 + 8.00000i 0.152277 + 0.304555i
\(691\) 30.0000i 1.14125i −0.821209 0.570627i \(-0.806700\pi\)
0.821209 0.570627i \(-0.193300\pi\)
\(692\) 16.0000 0.608229
\(693\) 0 0
\(694\) 23.0000i 0.873068i
\(695\) −14.0000 28.0000i −0.531050 1.06210i
\(696\) −9.00000 −0.341144
\(697\) −40.0000 10.0000i −1.51511 0.378777i
\(698\) 10.0000i 0.378506i
\(699\) 21.0000 0.794293
\(700\) 6.00000 8.00000i 0.226779 0.302372i
\(701\) −48.0000 −1.81293 −0.906467 0.422276i \(-0.861231\pi\)
−0.906467 + 0.422276i \(0.861231\pi\)
\(702\) −5.00000 −0.188713
\(703\) 10.0000 0.377157
\(704\) 0 0
\(705\) −7.00000 14.0000i −0.263635 0.527271i
\(706\) 4.00000 0.150542
\(707\) 16.0000 0.601742
\(708\) −5.00000 −0.187912
\(709\) 31.0000i 1.16423i −0.813107 0.582115i \(-0.802225\pi\)
0.813107 0.582115i \(-0.197775\pi\)
\(710\) −10.0000 + 5.00000i −0.375293 + 0.187647i
\(711\) 32.0000i 1.20009i
\(712\) 5.00000i 0.187383i
\(713\) 20.0000i 0.749006i
\(714\) −8.00000 2.00000i −0.299392 0.0748481i
\(715\) 0 0
\(716\) −20.0000 −0.747435
\(717\) 0 0
\(718\) 30.0000i 1.11959i
\(719\) 51.0000i 1.90198i −0.309223 0.950990i \(-0.600069\pi\)
0.309223 0.950990i \(-0.399931\pi\)
\(720\) 4.00000 2.00000i 0.149071 0.0745356i
\(721\) 32.0000i 1.19174i
\(722\) 6.00000i 0.223297i
\(723\) 10.0000i 0.371904i
\(724\) 10.0000i 0.371647i
\(725\) 36.0000 + 27.0000i 1.33701 + 1.00275i
\(726\) 11.0000i 0.408248i
\(727\) 33.0000i 1.22390i 0.790896 + 0.611951i \(0.209615\pi\)
−0.790896 + 0.611951i \(0.790385\pi\)
\(728\) −2.00000 −0.0741249
\(729\) 13.0000 0.481481
\(730\) 11.0000 + 22.0000i 0.407128 + 0.814257i
\(731\) −24.0000 6.00000i −0.887672 0.221918i
\(732\) 5.00000i 0.184805i
\(733\) 6.00000i 0.221615i 0.993842 + 0.110808i \(0.0353437\pi\)
−0.993842 + 0.110808i \(0.964656\pi\)
\(734\) 2.00000i 0.0738213i
\(735\) −6.00000 + 3.00000i −0.221313 + 0.110657i
\(736\) 4.00000i 0.147442i
\(737\) 0 0
\(738\) 20.0000 0.736210
\(739\) −15.0000 −0.551784 −0.275892 0.961189i \(-0.588973\pi\)
−0.275892 + 0.961189i \(0.588973\pi\)
\(740\) −4.00000 + 2.00000i −0.147043 + 0.0735215i
\(741\) 5.00000i 0.183680i
\(742\) 2.00000 0.0734223
\(743\) 34.0000 1.24734 0.623670 0.781688i \(-0.285641\pi\)
0.623670 + 0.781688i \(0.285641\pi\)
\(744\) 5.00000 0.183309
\(745\) −40.0000 + 20.0000i −1.46549 + 0.732743i
\(746\) 34.0000 1.24483
\(747\) 12.0000i 0.439057i
\(748\) 0 0
\(749\) 24.0000 0.876941
\(750\) 11.0000 + 2.00000i 0.401663 + 0.0730297i
\(751\) 25.0000i 0.912263i 0.889912 + 0.456131i \(0.150765\pi\)
−0.889912 + 0.456131i \(0.849235\pi\)
\(752\) 7.00000i 0.255264i
\(753\) 8.00000 0.291536
\(754\) 9.00000i 0.327761i
\(755\) 16.0000 8.00000i 0.582300 0.291150i
\(756\) 10.0000 0.363696
\(757\) 13.0000i 0.472493i 0.971693 + 0.236247i \(0.0759173\pi\)
−0.971693 + 0.236247i \(0.924083\pi\)
\(758\) −4.00000 −0.145287
\(759\) 0 0
\(760\) −5.00000 10.0000i −0.181369 0.362738i
\(761\) 22.0000 0.797499 0.398750 0.917060i \(-0.369444\pi\)
0.398750 + 0.917060i \(0.369444\pi\)
\(762\) −7.00000 −0.253583
\(763\) 18.0000i 0.651644i
\(764\) 18.0000 0.651217
\(765\) 4.00000 + 18.0000i 0.144620 + 0.650791i
\(766\) −31.0000 −1.12008
\(767\) 5.00000i 0.180540i
\(768\) −1.00000 −0.0360844
\(769\) 35.0000 1.26213 0.631066 0.775729i \(-0.282618\pi\)
0.631066 + 0.775729i \(0.282618\pi\)
\(770\) 0 0
\(771\) 18.0000i 0.648254i
\(772\) −14.0000 −0.503871
\(773\) 26.0000i 0.935155i 0.883952 + 0.467578i \(0.154873\pi\)
−0.883952 + 0.467578i \(0.845127\pi\)
\(774\) 12.0000 0.431331
\(775\) −20.0000 15.0000i −0.718421 0.538816i
\(776\) 7.00000i 0.251285i
\(777\) −4.00000 −0.143499
\(778\) 10.0000i 0.358517i
\(779\) 50.0000i 1.79144i
\(780\) −1.00000 2.00000i −0.0358057 0.0716115i
\(781\) 0 0
\(782\) −16.0000 4.00000i −0.572159 0.143040i
\(783\) 45.0000i 1.60817i
\(784\) −3.00000 −0.107143
\(785\) −18.0000 36.0000i −0.642448 1.28490i
\(786\) 20.0000 0.713376
\(787\) −7.00000 −0.249523 −0.124762 0.992187i \(-0.539817\pi\)
−0.124762 + 0.992187i \(0.539817\pi\)
\(788\) −8.00000 −0.284988
\(789\) 21.0000i 0.747620i
\(790\) −32.0000 + 16.0000i −1.13851 + 0.569254i
\(791\) −18.0000 −0.640006
\(792\) 0 0
\(793\) 5.00000 0.177555
\(794\) 18.0000i 0.638796i
\(795\) 1.00000 + 2.00000i 0.0354663 + 0.0709327i
\(796\) 1.00000i 0.0354441i
\(797\) 2.00000i 0.0708436i −0.999372 0.0354218i \(-0.988723\pi\)
0.999372 0.0354218i \(-0.0112775\pi\)
\(798\) 10.0000i 0.353996i
\(799\) 28.0000 + 7.00000i 0.990569 + 0.247642i
\(800\) 4.00000 + 3.00000i