Properties

Label 930.2.d.b.559.2
Level $930$
Weight $2$
Character 930.559
Analytic conductor $7.426$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 559.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 930.559
Dual form 930.2.d.b.559.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} +1.00000 q^{6} +1.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} +1.00000 q^{6} +1.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(2.00000 - 1.00000i) q^{10} -5.00000 q^{11} +1.00000i q^{12} +4.00000i q^{13} -1.00000 q^{14} +(-2.00000 + 1.00000i) q^{15} +1.00000 q^{16} -1.00000i q^{18} +5.00000 q^{19} +(1.00000 + 2.00000i) q^{20} +1.00000 q^{21} -5.00000i q^{22} +9.00000i q^{23} -1.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} -4.00000 q^{26} +1.00000i q^{27} -1.00000i q^{28} +2.00000 q^{29} +(-1.00000 - 2.00000i) q^{30} +1.00000 q^{31} +1.00000i q^{32} +5.00000i q^{33} +(2.00000 - 1.00000i) q^{35} +1.00000 q^{36} +8.00000i q^{37} +5.00000i q^{38} +4.00000 q^{39} +(-2.00000 + 1.00000i) q^{40} +6.00000 q^{41} +1.00000i q^{42} -1.00000i q^{43} +5.00000 q^{44} +(1.00000 + 2.00000i) q^{45} -9.00000 q^{46} -12.0000i q^{47} -1.00000i q^{48} +6.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} -4.00000i q^{52} +13.0000i q^{53} -1.00000 q^{54} +(5.00000 + 10.0000i) q^{55} +1.00000 q^{56} -5.00000i q^{57} +2.00000i q^{58} -10.0000 q^{59} +(2.00000 - 1.00000i) q^{60} -14.0000 q^{61} +1.00000i q^{62} -1.00000i q^{63} -1.00000 q^{64} +(8.00000 - 4.00000i) q^{65} -5.00000 q^{66} +14.0000i q^{67} +9.00000 q^{69} +(1.00000 + 2.00000i) q^{70} -9.00000 q^{71} +1.00000i q^{72} +9.00000i q^{73} -8.00000 q^{74} +(4.00000 + 3.00000i) q^{75} -5.00000 q^{76} -5.00000i q^{77} +4.00000i q^{78} -5.00000 q^{79} +(-1.00000 - 2.00000i) q^{80} +1.00000 q^{81} +6.00000i q^{82} -6.00000i q^{83} -1.00000 q^{84} +1.00000 q^{86} -2.00000i q^{87} +5.00000i q^{88} -3.00000 q^{89} +(-2.00000 + 1.00000i) q^{90} -4.00000 q^{91} -9.00000i q^{92} -1.00000i q^{93} +12.0000 q^{94} +(-5.00000 - 10.0000i) q^{95} +1.00000 q^{96} -18.0000i q^{97} +6.00000i q^{98} +5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{9} + 4 q^{10} - 10 q^{11} - 2 q^{14} - 4 q^{15} + 2 q^{16} + 10 q^{19} + 2 q^{20} + 2 q^{21} - 2 q^{24} - 6 q^{25} - 8 q^{26} + 4 q^{29} - 2 q^{30} + 2 q^{31} + 4 q^{35} + 2 q^{36} + 8 q^{39} - 4 q^{40} + 12 q^{41} + 10 q^{44} + 2 q^{45} - 18 q^{46} + 12 q^{49} - 8 q^{50} - 2 q^{54} + 10 q^{55} + 2 q^{56} - 20 q^{59} + 4 q^{60} - 28 q^{61} - 2 q^{64} + 16 q^{65} - 10 q^{66} + 18 q^{69} + 2 q^{70} - 18 q^{71} - 16 q^{74} + 8 q^{75} - 10 q^{76} - 10 q^{79} - 2 q^{80} + 2 q^{81} - 2 q^{84} + 2 q^{86} - 6 q^{89} - 4 q^{90} - 8 q^{91} + 24 q^{94} - 10 q^{95} + 2 q^{96} + 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) −1.00000 2.00000i −0.447214 0.894427i
\(6\) 1.00000 0.408248
\(7\) 1.00000i 0.377964i 0.981981 + 0.188982i \(0.0605189\pi\)
−0.981981 + 0.188982i \(0.939481\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) 2.00000 1.00000i 0.632456 0.316228i
\(11\) −5.00000 −1.50756 −0.753778 0.657129i \(-0.771771\pi\)
−0.753778 + 0.657129i \(0.771771\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 4.00000i 1.10940i 0.832050 + 0.554700i \(0.187167\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) −1.00000 −0.267261
\(15\) −2.00000 + 1.00000i −0.516398 + 0.258199i
\(16\) 1.00000 0.250000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 5.00000 1.14708 0.573539 0.819178i \(-0.305570\pi\)
0.573539 + 0.819178i \(0.305570\pi\)
\(20\) 1.00000 + 2.00000i 0.223607 + 0.447214i
\(21\) 1.00000 0.218218
\(22\) 5.00000i 1.06600i
\(23\) 9.00000i 1.87663i 0.345782 + 0.938315i \(0.387614\pi\)
−0.345782 + 0.938315i \(0.612386\pi\)
\(24\) −1.00000 −0.204124
\(25\) −3.00000 + 4.00000i −0.600000 + 0.800000i
\(26\) −4.00000 −0.784465
\(27\) 1.00000i 0.192450i
\(28\) 1.00000i 0.188982i
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) −1.00000 2.00000i −0.182574 0.365148i
\(31\) 1.00000 0.179605
\(32\) 1.00000i 0.176777i
\(33\) 5.00000i 0.870388i
\(34\) 0 0
\(35\) 2.00000 1.00000i 0.338062 0.169031i
\(36\) 1.00000 0.166667
\(37\) 8.00000i 1.31519i 0.753371 + 0.657596i \(0.228427\pi\)
−0.753371 + 0.657596i \(0.771573\pi\)
\(38\) 5.00000i 0.811107i
\(39\) 4.00000 0.640513
\(40\) −2.00000 + 1.00000i −0.316228 + 0.158114i
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 1.00000i 0.154303i
\(43\) 1.00000i 0.152499i −0.997089 0.0762493i \(-0.975706\pi\)
0.997089 0.0762493i \(-0.0242945\pi\)
\(44\) 5.00000 0.753778
\(45\) 1.00000 + 2.00000i 0.149071 + 0.298142i
\(46\) −9.00000 −1.32698
\(47\) 12.0000i 1.75038i −0.483779 0.875190i \(-0.660736\pi\)
0.483779 0.875190i \(-0.339264\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 6.00000 0.857143
\(50\) −4.00000 3.00000i −0.565685 0.424264i
\(51\) 0 0
\(52\) 4.00000i 0.554700i
\(53\) 13.0000i 1.78569i 0.450367 + 0.892844i \(0.351293\pi\)
−0.450367 + 0.892844i \(0.648707\pi\)
\(54\) −1.00000 −0.136083
\(55\) 5.00000 + 10.0000i 0.674200 + 1.34840i
\(56\) 1.00000 0.133631
\(57\) 5.00000i 0.662266i
\(58\) 2.00000i 0.262613i
\(59\) −10.0000 −1.30189 −0.650945 0.759125i \(-0.725627\pi\)
−0.650945 + 0.759125i \(0.725627\pi\)
\(60\) 2.00000 1.00000i 0.258199 0.129099i
\(61\) −14.0000 −1.79252 −0.896258 0.443533i \(-0.853725\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 1.00000i 0.127000i
\(63\) 1.00000i 0.125988i
\(64\) −1.00000 −0.125000
\(65\) 8.00000 4.00000i 0.992278 0.496139i
\(66\) −5.00000 −0.615457
\(67\) 14.0000i 1.71037i 0.518321 + 0.855186i \(0.326557\pi\)
−0.518321 + 0.855186i \(0.673443\pi\)
\(68\) 0 0
\(69\) 9.00000 1.08347
\(70\) 1.00000 + 2.00000i 0.119523 + 0.239046i
\(71\) −9.00000 −1.06810 −0.534052 0.845452i \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 9.00000i 1.05337i 0.850060 + 0.526685i \(0.176565\pi\)
−0.850060 + 0.526685i \(0.823435\pi\)
\(74\) −8.00000 −0.929981
\(75\) 4.00000 + 3.00000i 0.461880 + 0.346410i
\(76\) −5.00000 −0.573539
\(77\) 5.00000i 0.569803i
\(78\) 4.00000i 0.452911i
\(79\) −5.00000 −0.562544 −0.281272 0.959628i \(-0.590756\pi\)
−0.281272 + 0.959628i \(0.590756\pi\)
\(80\) −1.00000 2.00000i −0.111803 0.223607i
\(81\) 1.00000 0.111111
\(82\) 6.00000i 0.662589i
\(83\) 6.00000i 0.658586i −0.944228 0.329293i \(-0.893190\pi\)
0.944228 0.329293i \(-0.106810\pi\)
\(84\) −1.00000 −0.109109
\(85\) 0 0
\(86\) 1.00000 0.107833
\(87\) 2.00000i 0.214423i
\(88\) 5.00000i 0.533002i
\(89\) −3.00000 −0.317999 −0.159000 0.987279i \(-0.550827\pi\)
−0.159000 + 0.987279i \(0.550827\pi\)
\(90\) −2.00000 + 1.00000i −0.210819 + 0.105409i
\(91\) −4.00000 −0.419314
\(92\) 9.00000i 0.938315i
\(93\) 1.00000i 0.103695i
\(94\) 12.0000 1.23771
\(95\) −5.00000 10.0000i −0.512989 1.02598i
\(96\) 1.00000 0.102062
\(97\) 18.0000i 1.82762i −0.406138 0.913812i \(-0.633125\pi\)
0.406138 0.913812i \(-0.366875\pi\)
\(98\) 6.00000i 0.606092i
\(99\) 5.00000 0.502519
\(100\) 3.00000 4.00000i 0.300000 0.400000i
\(101\) −7.00000 −0.696526 −0.348263 0.937397i \(-0.613228\pi\)
−0.348263 + 0.937397i \(0.613228\pi\)
\(102\) 0 0
\(103\) 8.00000i 0.788263i −0.919054 0.394132i \(-0.871045\pi\)
0.919054 0.394132i \(-0.128955\pi\)
\(104\) 4.00000 0.392232
\(105\) −1.00000 2.00000i −0.0975900 0.195180i
\(106\) −13.0000 −1.26267
\(107\) 11.0000i 1.06341i 0.846930 + 0.531705i \(0.178449\pi\)
−0.846930 + 0.531705i \(0.821551\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) −10.0000 + 5.00000i −0.953463 + 0.476731i
\(111\) 8.00000 0.759326
\(112\) 1.00000i 0.0944911i
\(113\) 13.0000i 1.22294i −0.791269 0.611469i \(-0.790579\pi\)
0.791269 0.611469i \(-0.209421\pi\)
\(114\) 5.00000 0.468293
\(115\) 18.0000 9.00000i 1.67851 0.839254i
\(116\) −2.00000 −0.185695
\(117\) 4.00000i 0.369800i
\(118\) 10.0000i 0.920575i
\(119\) 0 0
\(120\) 1.00000 + 2.00000i 0.0912871 + 0.182574i
\(121\) 14.0000 1.27273
\(122\) 14.0000i 1.26750i
\(123\) 6.00000i 0.541002i
\(124\) −1.00000 −0.0898027
\(125\) 11.0000 + 2.00000i 0.983870 + 0.178885i
\(126\) 1.00000 0.0890871
\(127\) 20.0000i 1.77471i 0.461084 + 0.887357i \(0.347461\pi\)
−0.461084 + 0.887357i \(0.652539\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −1.00000 −0.0880451
\(130\) 4.00000 + 8.00000i 0.350823 + 0.701646i
\(131\) −6.00000 −0.524222 −0.262111 0.965038i \(-0.584419\pi\)
−0.262111 + 0.965038i \(0.584419\pi\)
\(132\) 5.00000i 0.435194i
\(133\) 5.00000i 0.433555i
\(134\) −14.0000 −1.20942
\(135\) 2.00000 1.00000i 0.172133 0.0860663i
\(136\) 0 0
\(137\) 2.00000i 0.170872i 0.996344 + 0.0854358i \(0.0272282\pi\)
−0.996344 + 0.0854358i \(0.972772\pi\)
\(138\) 9.00000i 0.766131i
\(139\) −16.0000 −1.35710 −0.678551 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) −2.00000 + 1.00000i −0.169031 + 0.0845154i
\(141\) −12.0000 −1.01058
\(142\) 9.00000i 0.755263i
\(143\) 20.0000i 1.67248i
\(144\) −1.00000 −0.0833333
\(145\) −2.00000 4.00000i −0.166091 0.332182i
\(146\) −9.00000 −0.744845
\(147\) 6.00000i 0.494872i
\(148\) 8.00000i 0.657596i
\(149\) −7.00000 −0.573462 −0.286731 0.958011i \(-0.592569\pi\)
−0.286731 + 0.958011i \(0.592569\pi\)
\(150\) −3.00000 + 4.00000i −0.244949 + 0.326599i
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 5.00000i 0.405554i
\(153\) 0 0
\(154\) 5.00000 0.402911
\(155\) −1.00000 2.00000i −0.0803219 0.160644i
\(156\) −4.00000 −0.320256
\(157\) 13.0000i 1.03751i 0.854922 + 0.518756i \(0.173605\pi\)
−0.854922 + 0.518756i \(0.826395\pi\)
\(158\) 5.00000i 0.397779i
\(159\) 13.0000 1.03097
\(160\) 2.00000 1.00000i 0.158114 0.0790569i
\(161\) −9.00000 −0.709299
\(162\) 1.00000i 0.0785674i
\(163\) 4.00000i 0.313304i −0.987654 0.156652i \(-0.949930\pi\)
0.987654 0.156652i \(-0.0500701\pi\)
\(164\) −6.00000 −0.468521
\(165\) 10.0000 5.00000i 0.778499 0.389249i
\(166\) 6.00000 0.465690
\(167\) 9.00000i 0.696441i −0.937413 0.348220i \(-0.886786\pi\)
0.937413 0.348220i \(-0.113214\pi\)
\(168\) 1.00000i 0.0771517i
\(169\) −3.00000 −0.230769
\(170\) 0 0
\(171\) −5.00000 −0.382360
\(172\) 1.00000i 0.0762493i
\(173\) 6.00000i 0.456172i 0.973641 + 0.228086i \(0.0732467\pi\)
−0.973641 + 0.228086i \(0.926753\pi\)
\(174\) 2.00000 0.151620
\(175\) −4.00000 3.00000i −0.302372 0.226779i
\(176\) −5.00000 −0.376889
\(177\) 10.0000i 0.751646i
\(178\) 3.00000i 0.224860i
\(179\) 16.0000 1.19590 0.597948 0.801535i \(-0.295983\pi\)
0.597948 + 0.801535i \(0.295983\pi\)
\(180\) −1.00000 2.00000i −0.0745356 0.149071i
\(181\) 17.0000 1.26360 0.631800 0.775131i \(-0.282316\pi\)
0.631800 + 0.775131i \(0.282316\pi\)
\(182\) 4.00000i 0.296500i
\(183\) 14.0000i 1.03491i
\(184\) 9.00000 0.663489
\(185\) 16.0000 8.00000i 1.17634 0.588172i
\(186\) 1.00000 0.0733236
\(187\) 0 0
\(188\) 12.0000i 0.875190i
\(189\) −1.00000 −0.0727393
\(190\) 10.0000 5.00000i 0.725476 0.362738i
\(191\) 8.00000 0.578860 0.289430 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 22.0000i 1.58359i 0.610784 + 0.791797i \(0.290854\pi\)
−0.610784 + 0.791797i \(0.709146\pi\)
\(194\) 18.0000 1.29232
\(195\) −4.00000 8.00000i −0.286446 0.572892i
\(196\) −6.00000 −0.428571
\(197\) 10.0000i 0.712470i −0.934396 0.356235i \(-0.884060\pi\)
0.934396 0.356235i \(-0.115940\pi\)
\(198\) 5.00000i 0.355335i
\(199\) 11.0000 0.779769 0.389885 0.920864i \(-0.372515\pi\)
0.389885 + 0.920864i \(0.372515\pi\)
\(200\) 4.00000 + 3.00000i 0.282843 + 0.212132i
\(201\) 14.0000 0.987484
\(202\) 7.00000i 0.492518i
\(203\) 2.00000i 0.140372i
\(204\) 0 0
\(205\) −6.00000 12.0000i −0.419058 0.838116i
\(206\) 8.00000 0.557386
\(207\) 9.00000i 0.625543i
\(208\) 4.00000i 0.277350i
\(209\) −25.0000 −1.72929
\(210\) 2.00000 1.00000i 0.138013 0.0690066i
\(211\) −13.0000 −0.894957 −0.447478 0.894295i \(-0.647678\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) 13.0000i 0.892844i
\(213\) 9.00000i 0.616670i
\(214\) −11.0000 −0.751945
\(215\) −2.00000 + 1.00000i −0.136399 + 0.0681994i
\(216\) 1.00000 0.0680414
\(217\) 1.00000i 0.0678844i
\(218\) 2.00000i 0.135457i
\(219\) 9.00000 0.608164
\(220\) −5.00000 10.0000i −0.337100 0.674200i
\(221\) 0 0
\(222\) 8.00000i 0.536925i
\(223\) 16.0000i 1.07144i −0.844396 0.535720i \(-0.820040\pi\)
0.844396 0.535720i \(-0.179960\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 3.00000 4.00000i 0.200000 0.266667i
\(226\) 13.0000 0.864747
\(227\) 15.0000i 0.995585i 0.867296 + 0.497792i \(0.165856\pi\)
−0.867296 + 0.497792i \(0.834144\pi\)
\(228\) 5.00000i 0.331133i
\(229\) 19.0000 1.25556 0.627778 0.778393i \(-0.283965\pi\)
0.627778 + 0.778393i \(0.283965\pi\)
\(230\) 9.00000 + 18.0000i 0.593442 + 1.18688i
\(231\) −5.00000 −0.328976
\(232\) 2.00000i 0.131306i
\(233\) 1.00000i 0.0655122i 0.999463 + 0.0327561i \(0.0104285\pi\)
−0.999463 + 0.0327561i \(0.989572\pi\)
\(234\) 4.00000 0.261488
\(235\) −24.0000 + 12.0000i −1.56559 + 0.782794i
\(236\) 10.0000 0.650945
\(237\) 5.00000i 0.324785i
\(238\) 0 0
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) −2.00000 + 1.00000i −0.129099 + 0.0645497i
\(241\) 24.0000 1.54598 0.772988 0.634421i \(-0.218761\pi\)
0.772988 + 0.634421i \(0.218761\pi\)
\(242\) 14.0000i 0.899954i
\(243\) 1.00000i 0.0641500i
\(244\) 14.0000 0.896258
\(245\) −6.00000 12.0000i −0.383326 0.766652i
\(246\) 6.00000 0.382546
\(247\) 20.0000i 1.27257i
\(248\) 1.00000i 0.0635001i
\(249\) −6.00000 −0.380235
\(250\) −2.00000 + 11.0000i −0.126491 + 0.695701i
\(251\) −28.0000 −1.76734 −0.883672 0.468106i \(-0.844936\pi\)
−0.883672 + 0.468106i \(0.844936\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) 45.0000i 2.82913i
\(254\) −20.0000 −1.25491
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 7.00000i 0.436648i −0.975876 0.218324i \(-0.929941\pi\)
0.975876 0.218324i \(-0.0700590\pi\)
\(258\) 1.00000i 0.0622573i
\(259\) −8.00000 −0.497096
\(260\) −8.00000 + 4.00000i −0.496139 + 0.248069i
\(261\) −2.00000 −0.123797
\(262\) 6.00000i 0.370681i
\(263\) 8.00000i 0.493301i 0.969104 + 0.246651i \(0.0793300\pi\)
−0.969104 + 0.246651i \(0.920670\pi\)
\(264\) 5.00000 0.307729
\(265\) 26.0000 13.0000i 1.59717 0.798584i
\(266\) −5.00000 −0.306570
\(267\) 3.00000i 0.183597i
\(268\) 14.0000i 0.855186i
\(269\) 22.0000 1.34136 0.670682 0.741745i \(-0.266002\pi\)
0.670682 + 0.741745i \(0.266002\pi\)
\(270\) 1.00000 + 2.00000i 0.0608581 + 0.121716i
\(271\) −25.0000 −1.51864 −0.759321 0.650716i \(-0.774469\pi\)
−0.759321 + 0.650716i \(0.774469\pi\)
\(272\) 0 0
\(273\) 4.00000i 0.242091i
\(274\) −2.00000 −0.120824
\(275\) 15.0000 20.0000i 0.904534 1.20605i
\(276\) −9.00000 −0.541736
\(277\) 2.00000i 0.120168i −0.998193 0.0600842i \(-0.980863\pi\)
0.998193 0.0600842i \(-0.0191369\pi\)
\(278\) 16.0000i 0.959616i
\(279\) −1.00000 −0.0598684
\(280\) −1.00000 2.00000i −0.0597614 0.119523i
\(281\) 12.0000 0.715860 0.357930 0.933748i \(-0.383483\pi\)
0.357930 + 0.933748i \(0.383483\pi\)
\(282\) 12.0000i 0.714590i
\(283\) 26.0000i 1.54554i −0.634686 0.772770i \(-0.718871\pi\)
0.634686 0.772770i \(-0.281129\pi\)
\(284\) 9.00000 0.534052
\(285\) −10.0000 + 5.00000i −0.592349 + 0.296174i
\(286\) 20.0000 1.18262
\(287\) 6.00000i 0.354169i
\(288\) 1.00000i 0.0589256i
\(289\) 17.0000 1.00000
\(290\) 4.00000 2.00000i 0.234888 0.117444i
\(291\) −18.0000 −1.05518
\(292\) 9.00000i 0.526685i
\(293\) 14.0000i 0.817889i 0.912559 + 0.408944i \(0.134103\pi\)
−0.912559 + 0.408944i \(0.865897\pi\)
\(294\) 6.00000 0.349927
\(295\) 10.0000 + 20.0000i 0.582223 + 1.16445i
\(296\) 8.00000 0.464991
\(297\) 5.00000i 0.290129i
\(298\) 7.00000i 0.405499i
\(299\) −36.0000 −2.08193
\(300\) −4.00000 3.00000i −0.230940 0.173205i
\(301\) 1.00000 0.0576390
\(302\) 0 0
\(303\) 7.00000i 0.402139i
\(304\) 5.00000 0.286770
\(305\) 14.0000 + 28.0000i 0.801638 + 1.60328i
\(306\) 0 0
\(307\) 8.00000i 0.456584i −0.973593 0.228292i \(-0.926686\pi\)
0.973593 0.228292i \(-0.0733141\pi\)
\(308\) 5.00000i 0.284901i
\(309\) −8.00000 −0.455104
\(310\) 2.00000 1.00000i 0.113592 0.0567962i
\(311\) −8.00000 −0.453638 −0.226819 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) 4.00000i 0.226455i
\(313\) 6.00000i 0.339140i −0.985518 0.169570i \(-0.945762\pi\)
0.985518 0.169570i \(-0.0542379\pi\)
\(314\) −13.0000 −0.733632
\(315\) −2.00000 + 1.00000i −0.112687 + 0.0563436i
\(316\) 5.00000 0.281272
\(317\) 34.0000i 1.90963i 0.297200 + 0.954815i \(0.403947\pi\)
−0.297200 + 0.954815i \(0.596053\pi\)
\(318\) 13.0000i 0.729004i
\(319\) −10.0000 −0.559893
\(320\) 1.00000 + 2.00000i 0.0559017 + 0.111803i
\(321\) 11.0000 0.613960
\(322\) 9.00000i 0.501550i
\(323\) 0 0
\(324\) −1.00000 −0.0555556
\(325\) −16.0000 12.0000i −0.887520 0.665640i
\(326\) 4.00000 0.221540
\(327\) 2.00000i 0.110600i
\(328\) 6.00000i 0.331295i
\(329\) 12.0000 0.661581
\(330\) 5.00000 + 10.0000i 0.275241 + 0.550482i
\(331\) −24.0000 −1.31916 −0.659580 0.751635i \(-0.729266\pi\)
−0.659580 + 0.751635i \(0.729266\pi\)
\(332\) 6.00000i 0.329293i
\(333\) 8.00000i 0.438397i
\(334\) 9.00000 0.492458
\(335\) 28.0000 14.0000i 1.52980 0.764902i
\(336\) 1.00000 0.0545545
\(337\) 2.00000i 0.108947i 0.998515 + 0.0544735i \(0.0173480\pi\)
−0.998515 + 0.0544735i \(0.982652\pi\)
\(338\) 3.00000i 0.163178i
\(339\) −13.0000 −0.706063
\(340\) 0 0
\(341\) −5.00000 −0.270765
\(342\) 5.00000i 0.270369i
\(343\) 13.0000i 0.701934i
\(344\) −1.00000 −0.0539164
\(345\) −9.00000 18.0000i −0.484544 0.969087i
\(346\) −6.00000 −0.322562
\(347\) 18.0000i 0.966291i −0.875540 0.483145i \(-0.839494\pi\)
0.875540 0.483145i \(-0.160506\pi\)
\(348\) 2.00000i 0.107211i
\(349\) −4.00000 −0.214115 −0.107058 0.994253i \(-0.534143\pi\)
−0.107058 + 0.994253i \(0.534143\pi\)
\(350\) 3.00000 4.00000i 0.160357 0.213809i
\(351\) −4.00000 −0.213504
\(352\) 5.00000i 0.266501i
\(353\) 4.00000i 0.212899i 0.994318 + 0.106449i \(0.0339482\pi\)
−0.994318 + 0.106449i \(0.966052\pi\)
\(354\) −10.0000 −0.531494
\(355\) 9.00000 + 18.0000i 0.477670 + 0.955341i
\(356\) 3.00000 0.159000
\(357\) 0 0
\(358\) 16.0000i 0.845626i
\(359\) 9.00000 0.475002 0.237501 0.971387i \(-0.423672\pi\)
0.237501 + 0.971387i \(0.423672\pi\)
\(360\) 2.00000 1.00000i 0.105409 0.0527046i
\(361\) 6.00000 0.315789
\(362\) 17.0000i 0.893500i
\(363\) 14.0000i 0.734809i
\(364\) 4.00000 0.209657
\(365\) 18.0000 9.00000i 0.942163 0.471082i
\(366\) −14.0000 −0.731792
\(367\) 18.0000i 0.939592i 0.882775 + 0.469796i \(0.155673\pi\)
−0.882775 + 0.469796i \(0.844327\pi\)
\(368\) 9.00000i 0.469157i
\(369\) −6.00000 −0.312348
\(370\) 8.00000 + 16.0000i 0.415900 + 0.831800i
\(371\) −13.0000 −0.674926
\(372\) 1.00000i 0.0518476i
\(373\) 1.00000i 0.0517780i −0.999665 0.0258890i \(-0.991758\pi\)
0.999665 0.0258890i \(-0.00824165\pi\)
\(374\) 0 0
\(375\) 2.00000 11.0000i 0.103280 0.568038i
\(376\) −12.0000 −0.618853
\(377\) 8.00000i 0.412021i
\(378\) 1.00000i 0.0514344i
\(379\) 11.0000 0.565032 0.282516 0.959263i \(-0.408831\pi\)
0.282516 + 0.959263i \(0.408831\pi\)
\(380\) 5.00000 + 10.0000i 0.256495 + 0.512989i
\(381\) 20.0000 1.02463
\(382\) 8.00000i 0.409316i
\(383\) 12.0000i 0.613171i −0.951843 0.306586i \(-0.900813\pi\)
0.951843 0.306586i \(-0.0991866\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −10.0000 + 5.00000i −0.509647 + 0.254824i
\(386\) −22.0000 −1.11977
\(387\) 1.00000i 0.0508329i
\(388\) 18.0000i 0.913812i
\(389\) 16.0000 0.811232 0.405616 0.914044i \(-0.367057\pi\)
0.405616 + 0.914044i \(0.367057\pi\)
\(390\) 8.00000 4.00000i 0.405096 0.202548i
\(391\) 0 0
\(392\) 6.00000i 0.303046i
\(393\) 6.00000i 0.302660i
\(394\) 10.0000 0.503793
\(395\) 5.00000 + 10.0000i 0.251577 + 0.503155i
\(396\) −5.00000 −0.251259
\(397\) 3.00000i 0.150566i −0.997162 0.0752828i \(-0.976014\pi\)
0.997162 0.0752828i \(-0.0239860\pi\)
\(398\) 11.0000i 0.551380i
\(399\) 5.00000 0.250313
\(400\) −3.00000 + 4.00000i −0.150000 + 0.200000i
\(401\) −25.0000 −1.24844 −0.624220 0.781248i \(-0.714583\pi\)
−0.624220 + 0.781248i \(0.714583\pi\)
\(402\) 14.0000i 0.698257i
\(403\) 4.00000i 0.199254i
\(404\) 7.00000 0.348263
\(405\) −1.00000 2.00000i −0.0496904 0.0993808i
\(406\) −2.00000 −0.0992583
\(407\) 40.0000i 1.98273i
\(408\) 0 0
\(409\) 28.0000 1.38451 0.692255 0.721653i \(-0.256617\pi\)
0.692255 + 0.721653i \(0.256617\pi\)
\(410\) 12.0000 6.00000i 0.592638 0.296319i
\(411\) 2.00000 0.0986527
\(412\) 8.00000i 0.394132i
\(413\) 10.0000i 0.492068i
\(414\) 9.00000 0.442326
\(415\) −12.0000 + 6.00000i −0.589057 + 0.294528i
\(416\) −4.00000 −0.196116
\(417\) 16.0000i 0.783523i
\(418\) 25.0000i 1.22279i
\(419\) −30.0000 −1.46560 −0.732798 0.680446i \(-0.761786\pi\)
−0.732798 + 0.680446i \(0.761786\pi\)
\(420\) 1.00000 + 2.00000i 0.0487950 + 0.0975900i
\(421\) −26.0000 −1.26716 −0.633581 0.773676i \(-0.718416\pi\)
−0.633581 + 0.773676i \(0.718416\pi\)
\(422\) 13.0000i 0.632830i
\(423\) 12.0000i 0.583460i
\(424\) 13.0000 0.631336
\(425\) 0 0
\(426\) −9.00000 −0.436051
\(427\) 14.0000i 0.677507i
\(428\) 11.0000i 0.531705i
\(429\) −20.0000 −0.965609
\(430\) −1.00000 2.00000i −0.0482243 0.0964486i
\(431\) −32.0000 −1.54139 −0.770693 0.637207i \(-0.780090\pi\)
−0.770693 + 0.637207i \(0.780090\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 11.0000i 0.528626i 0.964437 + 0.264313i \(0.0851452\pi\)
−0.964437 + 0.264313i \(0.914855\pi\)
\(434\) −1.00000 −0.0480015
\(435\) −4.00000 + 2.00000i −0.191785 + 0.0958927i
\(436\) −2.00000 −0.0957826
\(437\) 45.0000i 2.15264i
\(438\) 9.00000i 0.430037i
\(439\) −20.0000 −0.954548 −0.477274 0.878755i \(-0.658375\pi\)
−0.477274 + 0.878755i \(0.658375\pi\)
\(440\) 10.0000 5.00000i 0.476731 0.238366i
\(441\) −6.00000 −0.285714
\(442\) 0 0
\(443\) 13.0000i 0.617649i −0.951119 0.308824i \(-0.900064\pi\)
0.951119 0.308824i \(-0.0999355\pi\)
\(444\) −8.00000 −0.379663
\(445\) 3.00000 + 6.00000i 0.142214 + 0.284427i
\(446\) 16.0000 0.757622
\(447\) 7.00000i 0.331089i
\(448\) 1.00000i 0.0472456i
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 4.00000 + 3.00000i 0.188562 + 0.141421i
\(451\) −30.0000 −1.41264
\(452\) 13.0000i 0.611469i
\(453\) 0 0
\(454\) −15.0000 −0.703985
\(455\) 4.00000 + 8.00000i 0.187523 + 0.375046i
\(456\) −5.00000 −0.234146
\(457\) 22.0000i 1.02912i −0.857455 0.514558i \(-0.827956\pi\)
0.857455 0.514558i \(-0.172044\pi\)
\(458\) 19.0000i 0.887812i
\(459\) 0 0
\(460\) −18.0000 + 9.00000i −0.839254 + 0.419627i
\(461\) 36.0000 1.67669 0.838344 0.545142i \(-0.183524\pi\)
0.838344 + 0.545142i \(0.183524\pi\)
\(462\) 5.00000i 0.232621i
\(463\) 30.0000i 1.39422i −0.716965 0.697109i \(-0.754469\pi\)
0.716965 0.697109i \(-0.245531\pi\)
\(464\) 2.00000 0.0928477
\(465\) −2.00000 + 1.00000i −0.0927478 + 0.0463739i
\(466\) −1.00000 −0.0463241
\(467\) 20.0000i 0.925490i 0.886492 + 0.462745i \(0.153135\pi\)
−0.886492 + 0.462745i \(0.846865\pi\)
\(468\) 4.00000i 0.184900i
\(469\) −14.0000 −0.646460
\(470\) −12.0000 24.0000i −0.553519 1.10704i
\(471\) 13.0000 0.599008
\(472\) 10.0000i 0.460287i
\(473\) 5.00000i 0.229900i
\(474\) −5.00000 −0.229658
\(475\) −15.0000 + 20.0000i −0.688247 + 0.917663i
\(476\) 0 0
\(477\) 13.0000i 0.595229i
\(478\) 6.00000i 0.274434i
\(479\) 21.0000 0.959514 0.479757 0.877401i \(-0.340725\pi\)
0.479757 + 0.877401i \(0.340725\pi\)
\(480\) −1.00000 2.00000i −0.0456435 0.0912871i
\(481\) −32.0000 −1.45907
\(482\) 24.0000i 1.09317i
\(483\) 9.00000i 0.409514i
\(484\) −14.0000 −0.636364
\(485\) −36.0000 + 18.0000i −1.63468 + 0.817338i
\(486\) 1.00000 0.0453609
\(487\) 24.0000i 1.08754i 0.839233 + 0.543772i \(0.183004\pi\)
−0.839233 + 0.543772i \(0.816996\pi\)
\(488\) 14.0000i 0.633750i
\(489\) −4.00000 −0.180886
\(490\) 12.0000 6.00000i 0.542105 0.271052i
\(491\) 15.0000 0.676941 0.338470 0.940977i \(-0.390091\pi\)
0.338470 + 0.940977i \(0.390091\pi\)
\(492\) 6.00000i 0.270501i
\(493\) 0 0
\(494\) −20.0000 −0.899843
\(495\) −5.00000 10.0000i −0.224733 0.449467i
\(496\) 1.00000 0.0449013
\(497\) 9.00000i 0.403705i
\(498\) 6.00000i 0.268866i
\(499\) −6.00000 −0.268597 −0.134298 0.990941i \(-0.542878\pi\)
−0.134298 + 0.990941i \(0.542878\pi\)
\(500\) −11.0000 2.00000i −0.491935 0.0894427i
\(501\) −9.00000 −0.402090
\(502\) 28.0000i 1.24970i
\(503\) 22.0000i 0.980932i −0.871460 0.490466i \(-0.836827\pi\)
0.871460 0.490466i \(-0.163173\pi\)
\(504\) −1.00000 −0.0445435
\(505\) 7.00000 + 14.0000i 0.311496 + 0.622992i
\(506\) 45.0000 2.00049
\(507\) 3.00000i 0.133235i
\(508\) 20.0000i 0.887357i
\(509\) 20.0000 0.886484 0.443242 0.896402i \(-0.353828\pi\)
0.443242 + 0.896402i \(0.353828\pi\)
\(510\) 0 0
\(511\) −9.00000 −0.398137
\(512\) 1.00000i 0.0441942i
\(513\) 5.00000i 0.220755i
\(514\) 7.00000 0.308757
\(515\) −16.0000 + 8.00000i −0.705044 + 0.352522i
\(516\) 1.00000 0.0440225
\(517\) 60.0000i 2.63880i
\(518\) 8.00000i 0.351500i
\(519\) 6.00000 0.263371
\(520\) −4.00000 8.00000i −0.175412 0.350823i
\(521\) −36.0000 −1.57719 −0.788594 0.614914i \(-0.789191\pi\)
−0.788594 + 0.614914i \(0.789191\pi\)
\(522\) 2.00000i 0.0875376i
\(523\) 17.0000i 0.743358i −0.928361 0.371679i \(-0.878782\pi\)
0.928361 0.371679i \(-0.121218\pi\)
\(524\) 6.00000 0.262111
\(525\) −3.00000 + 4.00000i −0.130931 + 0.174574i
\(526\) −8.00000 −0.348817
\(527\) 0 0
\(528\) 5.00000i 0.217597i
\(529\) −58.0000 −2.52174
\(530\) 13.0000 + 26.0000i 0.564684 + 1.12937i
\(531\) 10.0000 0.433963
\(532\) 5.00000i 0.216777i
\(533\) 24.0000i 1.03956i
\(534\) −3.00000 −0.129823
\(535\) 22.0000 11.0000i 0.951143 0.475571i
\(536\) 14.0000 0.604708
\(537\) 16.0000i 0.690451i
\(538\) 22.0000i 0.948487i
\(539\) −30.0000 −1.29219
\(540\) −2.00000 + 1.00000i −0.0860663 + 0.0430331i
\(541\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) 25.0000i 1.07384i
\(543\) 17.0000i 0.729540i
\(544\) 0 0
\(545\) −2.00000 4.00000i −0.0856706 0.171341i
\(546\) −4.00000 −0.171184
\(547\) 16.0000i 0.684111i 0.939680 + 0.342055i \(0.111123\pi\)
−0.939680 + 0.342055i \(0.888877\pi\)
\(548\) 2.00000i 0.0854358i
\(549\) 14.0000 0.597505
\(550\) 20.0000 + 15.0000i 0.852803 + 0.639602i
\(551\) 10.0000 0.426014
\(552\) 9.00000i 0.383065i
\(553\) 5.00000i 0.212622i
\(554\) 2.00000 0.0849719
\(555\) −8.00000 16.0000i −0.339581 0.679162i
\(556\) 16.0000 0.678551
\(557\) 7.00000i 0.296600i 0.988942 + 0.148300i \(0.0473800\pi\)
−0.988942 + 0.148300i \(0.952620\pi\)
\(558\) 1.00000i 0.0423334i
\(559\) 4.00000 0.169182
\(560\) 2.00000 1.00000i 0.0845154 0.0422577i
\(561\) 0 0
\(562\) 12.0000i 0.506189i
\(563\) 44.0000i 1.85438i 0.374593 + 0.927189i \(0.377783\pi\)
−0.374593 + 0.927189i \(0.622217\pi\)
\(564\) 12.0000 0.505291
\(565\) −26.0000 + 13.0000i −1.09383 + 0.546914i
\(566\) 26.0000 1.09286
\(567\) 1.00000i 0.0419961i
\(568\) 9.00000i 0.377632i
\(569\) 21.0000 0.880366 0.440183 0.897908i \(-0.354914\pi\)
0.440183 + 0.897908i \(0.354914\pi\)
\(570\) −5.00000 10.0000i −0.209427 0.418854i
\(571\) −10.0000 −0.418487 −0.209243 0.977864i \(-0.567100\pi\)
−0.209243 + 0.977864i \(0.567100\pi\)
\(572\) 20.0000i 0.836242i
\(573\) 8.00000i 0.334205i
\(574\) −6.00000 −0.250435
\(575\) −36.0000 27.0000i −1.50130 1.12598i
\(576\) 1.00000 0.0416667
\(577\) 2.00000i 0.0832611i −0.999133 0.0416305i \(-0.986745\pi\)
0.999133 0.0416305i \(-0.0132552\pi\)
\(578\) 17.0000i 0.707107i
\(579\) 22.0000 0.914289
\(580\) 2.00000 + 4.00000i 0.0830455 + 0.166091i
\(581\) 6.00000 0.248922
\(582\) 18.0000i 0.746124i
\(583\) 65.0000i 2.69202i
\(584\) 9.00000 0.372423
\(585\) −8.00000 + 4.00000i −0.330759 + 0.165380i
\(586\) −14.0000 −0.578335
\(587\) 6.00000i 0.247647i −0.992304 0.123823i \(-0.960484\pi\)
0.992304 0.123823i \(-0.0395156\pi\)
\(588\) 6.00000i 0.247436i
\(589\) 5.00000 0.206021
\(590\) −20.0000 + 10.0000i −0.823387 + 0.411693i
\(591\) −10.0000 −0.411345
\(592\) 8.00000i 0.328798i
\(593\) 10.0000i 0.410651i 0.978694 + 0.205325i \(0.0658253\pi\)
−0.978694 + 0.205325i \(0.934175\pi\)
\(594\) 5.00000 0.205152
\(595\) 0 0
\(596\) 7.00000 0.286731
\(597\) 11.0000i 0.450200i
\(598\) 36.0000i 1.47215i
\(599\) 39.0000 1.59350 0.796748 0.604311i \(-0.206552\pi\)
0.796748 + 0.604311i \(0.206552\pi\)
\(600\) 3.00000 4.00000i 0.122474 0.163299i
\(601\) −12.0000 −0.489490 −0.244745 0.969587i \(-0.578704\pi\)
−0.244745 + 0.969587i \(0.578704\pi\)
\(602\) 1.00000i 0.0407570i
\(603\) 14.0000i 0.570124i
\(604\) 0 0
\(605\) −14.0000 28.0000i −0.569181 1.13836i
\(606\) −7.00000 −0.284356
\(607\) 13.0000i 0.527654i 0.964570 + 0.263827i \(0.0849848\pi\)
−0.964570 + 0.263827i \(0.915015\pi\)
\(608\) 5.00000i 0.202777i
\(609\) 2.00000 0.0810441
\(610\) −28.0000 + 14.0000i −1.13369 + 0.566843i
\(611\) 48.0000 1.94187
\(612\) 0 0
\(613\) 4.00000i 0.161558i −0.996732 0.0807792i \(-0.974259\pi\)
0.996732 0.0807792i \(-0.0257409\pi\)
\(614\) 8.00000 0.322854
\(615\) −12.0000 + 6.00000i −0.483887 + 0.241943i
\(616\) −5.00000 −0.201456
\(617\) 9.00000i 0.362326i 0.983453 + 0.181163i \(0.0579862\pi\)
−0.983453 + 0.181163i \(0.942014\pi\)
\(618\) 8.00000i 0.321807i
\(619\) −16.0000 −0.643094 −0.321547 0.946894i \(-0.604203\pi\)
−0.321547 + 0.946894i \(0.604203\pi\)
\(620\) 1.00000 + 2.00000i 0.0401610 + 0.0803219i
\(621\) −9.00000 −0.361158
\(622\) 8.00000i 0.320771i
\(623\) 3.00000i 0.120192i
\(624\) 4.00000 0.160128
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 6.00000 0.239808
\(627\) 25.0000i 0.998404i
\(628\) 13.0000i 0.518756i
\(629\) 0 0
\(630\) −1.00000 2.00000i −0.0398410 0.0796819i
\(631\) 31.0000 1.23409 0.617045 0.786928i \(-0.288330\pi\)
0.617045 + 0.786928i \(0.288330\pi\)
\(632\) 5.00000i 0.198889i
\(633\) 13.0000i 0.516704i
\(634\) −34.0000 −1.35031
\(635\) 40.0000 20.0000i 1.58735 0.793676i
\(636\) −13.0000 −0.515484
\(637\) 24.0000i 0.950915i
\(638\) 10.0000i 0.395904i
\(639\) 9.00000 0.356034
\(640\) −2.00000 + 1.00000i −0.0790569 + 0.0395285i
\(641\) −2.00000 −0.0789953 −0.0394976 0.999220i \(-0.512576\pi\)
−0.0394976 + 0.999220i \(0.512576\pi\)
\(642\) 11.0000i 0.434135i
\(643\) 5.00000i 0.197181i 0.995128 + 0.0985904i \(0.0314334\pi\)
−0.995128 + 0.0985904i \(0.968567\pi\)
\(644\) 9.00000 0.354650
\(645\) 1.00000 + 2.00000i 0.0393750 + 0.0787499i
\(646\) 0 0
\(647\) 5.00000i 0.196570i 0.995158 + 0.0982851i \(0.0313357\pi\)
−0.995158 + 0.0982851i \(0.968664\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 50.0000 1.96267
\(650\) 12.0000 16.0000i 0.470679 0.627572i
\(651\) 1.00000 0.0391931
\(652\) 4.00000i 0.156652i
\(653\) 18.0000i 0.704394i −0.935926 0.352197i \(-0.885435\pi\)
0.935926 0.352197i \(-0.114565\pi\)
\(654\) 2.00000 0.0782062
\(655\) 6.00000 + 12.0000i 0.234439 + 0.468879i
\(656\) 6.00000 0.234261
\(657\) 9.00000i 0.351123i
\(658\) 12.0000i 0.467809i
\(659\) −30.0000 −1.16863 −0.584317 0.811525i \(-0.698638\pi\)
−0.584317 + 0.811525i \(0.698638\pi\)
\(660\) −10.0000 + 5.00000i −0.389249 + 0.194625i
\(661\) 28.0000 1.08907 0.544537 0.838737i \(-0.316705\pi\)
0.544537 + 0.838737i \(0.316705\pi\)
\(662\) 24.0000i 0.932786i
\(663\) 0 0
\(664\) −6.00000 −0.232845
\(665\) 10.0000 5.00000i 0.387783 0.193892i
\(666\) 8.00000 0.309994
\(667\) 18.0000i 0.696963i
\(668\) 9.00000i 0.348220i
\(669\) −16.0000 −0.618596
\(670\) 14.0000 + 28.0000i 0.540867 + 1.08173i
\(671\) 70.0000 2.70232
\(672\) 1.00000i 0.0385758i
\(673\) 38.0000i 1.46479i −0.680879 0.732396i \(-0.738402\pi\)
0.680879 0.732396i \(-0.261598\pi\)
\(674\) −2.00000 −0.0770371
\(675\) −4.00000 3.00000i −0.153960 0.115470i
\(676\) 3.00000 0.115385
\(677\) 51.0000i 1.96009i 0.198778 + 0.980045i \(0.436303\pi\)
−0.198778 + 0.980045i \(0.563697\pi\)
\(678\) 13.0000i 0.499262i
\(679\) 18.0000 0.690777
\(680\) 0 0
\(681\) 15.0000 0.574801
\(682\) 5.00000i 0.191460i
\(683\) 3.00000i 0.114792i −0.998351 0.0573959i \(-0.981720\pi\)
0.998351 0.0573959i \(-0.0182797\pi\)
\(684\) 5.00000 0.191180
\(685\) 4.00000 2.00000i 0.152832 0.0764161i
\(686\) −13.0000 −0.496342
\(687\) 19.0000i 0.724895i
\(688\) 1.00000i 0.0381246i
\(689\) −52.0000 −1.98104
\(690\) 18.0000 9.00000i 0.685248 0.342624i
\(691\) 27.0000 1.02713 0.513564 0.858051i \(-0.328325\pi\)
0.513564 + 0.858051i \(0.328325\pi\)
\(692\) 6.00000i 0.228086i
\(693\) 5.00000i 0.189934i
\(694\) 18.0000 0.683271
\(695\) 16.0000 + 32.0000i 0.606915 + 1.21383i
\(696\) −2.00000 −0.0758098
\(697\) 0 0
\(698\) 4.00000i 0.151402i
\(699\) 1.00000 0.0378235
\(700\) 4.00000 + 3.00000i 0.151186 + 0.113389i
\(701\) 29.0000 1.09531 0.547657 0.836703i \(-0.315520\pi\)
0.547657 + 0.836703i \(0.315520\pi\)
\(702\) 4.00000i 0.150970i
\(703\) 40.0000i 1.50863i
\(704\) 5.00000 0.188445
\(705\) 12.0000 + 24.0000i 0.451946 + 0.903892i
\(706\) −4.00000 −0.150542
\(707\) 7.00000i 0.263262i
\(708\) 10.0000i 0.375823i
\(709\) 17.0000 0.638448 0.319224 0.947679i \(-0.396578\pi\)
0.319224 + 0.947679i \(0.396578\pi\)
\(710\) −18.0000 + 9.00000i −0.675528 + 0.337764i
\(711\) 5.00000 0.187515
\(712\) 3.00000i 0.112430i
\(713\) 9.00000i 0.337053i
\(714\) 0 0
\(715\) −40.0000 + 20.0000i −1.49592 + 0.747958i
\(716\) −16.0000 −0.597948
\(717\) 6.00000i 0.224074i
\(718\) 9.00000i 0.335877i
\(719\) 30.0000 1.11881 0.559406 0.828894i \(-0.311029\pi\)
0.559406 + 0.828894i \(0.311029\pi\)
\(720\) 1.00000 + 2.00000i 0.0372678 + 0.0745356i
\(721\) 8.00000 0.297936
\(722\) 6.00000i 0.223297i
\(723\) 24.0000i 0.892570i
\(724\) −17.0000 −0.631800
\(725\) −6.00000 + 8.00000i −0.222834 + 0.297113i
\(726\) 14.0000 0.519589
\(727\) 1.00000i 0.0370879i 0.999828 + 0.0185440i \(0.00590307\pi\)
−0.999828 + 0.0185440i \(0.994097\pi\)
\(728\) 4.00000i 0.148250i
\(729\) −1.00000 −0.0370370
\(730\) 9.00000 + 18.0000i 0.333105 + 0.666210i
\(731\) 0 0
\(732\) 14.0000i 0.517455i
\(733\) 14.0000i 0.517102i 0.965998 + 0.258551i \(0.0832450\pi\)
−0.965998 + 0.258551i \(0.916755\pi\)
\(734\) −18.0000 −0.664392
\(735\) −12.0000 + 6.00000i −0.442627 + 0.221313i
\(736\) −9.00000 −0.331744
\(737\) 70.0000i 2.57848i
\(738\) 6.00000i 0.220863i
\(739\) −10.0000 −0.367856 −0.183928 0.982940i \(-0.558881\pi\)
−0.183928 + 0.982940i \(0.558881\pi\)
\(740\) −16.0000 + 8.00000i −0.588172 + 0.294086i
\(741\) 20.0000 0.734718
\(742\) 13.0000i 0.477245i
\(743\) 43.0000i 1.57752i 0.614703 + 0.788759i \(0.289276\pi\)
−0.614703 + 0.788759i \(0.710724\pi\)
\(744\) −1.00000 −0.0366618
\(745\) 7.00000 + 14.0000i 0.256460 + 0.512920i
\(746\) 1.00000 0.0366126
\(747\) 6.00000i 0.219529i
\(748\) 0 0
\(749\) −11.0000 −0.401931
\(750\) 11.0000 + 2.00000i 0.401663 + 0.0730297i
\(751\) 18.0000 0.656829 0.328415 0.944534i \(-0.393486\pi\)
0.328415 + 0.944534i \(0.393486\pi\)
\(752\) 12.0000i 0.437595i
\(753\) 28.0000i 1.02038i
\(754\) −8.00000 −0.291343
\(755\) 0 0
\(756\) 1.00000 0.0363696
\(757\) 20.0000i 0.726912i −0.931611 0.363456i \(-0.881597\pi\)
0.931611 0.363456i \(-0.118403\pi\)
\(758\) 11.0000i 0.399538i
\(759\) −45.0000 −1.63340
\(760\) −10.0000 + 5.00000i −0.362738 + 0.181369i
\(761\) 15.0000 0.543750 0.271875 0.962333i \(-0.412356\pi\)
0.271875 + 0.962333i \(0.412356\pi\)
\(762\) 20.0000i 0.724524i
\(763\) 2.00000i 0.0724049i
\(764\) −8.00000 −0.289430
\(765\) 0 0
\(766\) 12.0000 0.433578
\(767\) 40.0000i 1.44432i
\(768\) 1.00000i 0.0360844i
\(769\) 35.0000 1.26213 0.631066 0.775729i \(-0.282618\pi\)
0.631066 + 0.775729i \(0.282618\pi\)
\(770\) −5.00000 10.0000i −0.180187 0.360375i
\(771\) −7.00000 −0.252099
\(772\) 22.0000i 0.791797i
\(773\) 27.0000i 0.971123i 0.874203 + 0.485561i \(0.161385\pi\)
−0.874203 + 0.485561i \(0.838615\pi\)
\(774\) −1.00000 −0.0359443
\(775\) −3.00000 + 4.00000i −0.107763 + 0.143684i
\(776\) −18.0000 −0.646162
\(777\) 8.00000i 0.286998i
\(778\) 16.0000i 0.573628i
\(779\) 30.0000 1.07486
\(780\) 4.00000 + 8.00000i 0.143223 + 0.286446i
\(781\) 45.0000 1.61023
\(782\) 0 0
\(783\) 2.00000i 0.0714742i
\(784\) 6.00000 0.214286
\(785\) 26.0000 13.0000i 0.927980 0.463990i
\(786\) −6.00000 −0.214013
\(787\) 23.0000i 0.819861i −0.912117 0.409931i \(-0.865553\pi\)