Properties

Label 30.2.c.a.19.2
Level 30
Weight 2
Character 30.19
Analytic conductor 0.240
Analytic rank 0
Dimension 2
CM No
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 30 = 2 \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 30.c (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(0.239551206064\)
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 19.2
Root \(1.00000i\)
Character \(\chi\) = 30.19
Dual form 30.2.c.a.19.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000i q^{2}\) \(-1.00000i q^{3}\) \(-1.00000 q^{4}\) \(+(-2.00000 + 1.00000i) q^{5}\) \(+1.00000 q^{6}\) \(-2.00000i q^{7}\) \(-1.00000i q^{8}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000i q^{2}\) \(-1.00000i q^{3}\) \(-1.00000 q^{4}\) \(+(-2.00000 + 1.00000i) q^{5}\) \(+1.00000 q^{6}\) \(-2.00000i q^{7}\) \(-1.00000i q^{8}\) \(-1.00000 q^{9}\) \(+(-1.00000 - 2.00000i) q^{10}\) \(+2.00000 q^{11}\) \(+1.00000i q^{12}\) \(+6.00000i q^{13}\) \(+2.00000 q^{14}\) \(+(1.00000 + 2.00000i) q^{15}\) \(+1.00000 q^{16}\) \(-2.00000i q^{17}\) \(-1.00000i q^{18}\) \(+(2.00000 - 1.00000i) q^{20}\) \(-2.00000 q^{21}\) \(+2.00000i q^{22}\) \(-4.00000i q^{23}\) \(-1.00000 q^{24}\) \(+(3.00000 - 4.00000i) q^{25}\) \(-6.00000 q^{26}\) \(+1.00000i q^{27}\) \(+2.00000i q^{28}\) \(+(-2.00000 + 1.00000i) q^{30}\) \(-8.00000 q^{31}\) \(+1.00000i q^{32}\) \(-2.00000i q^{33}\) \(+2.00000 q^{34}\) \(+(2.00000 + 4.00000i) q^{35}\) \(+1.00000 q^{36}\) \(-2.00000i q^{37}\) \(+6.00000 q^{39}\) \(+(1.00000 + 2.00000i) q^{40}\) \(+2.00000 q^{41}\) \(-2.00000i q^{42}\) \(-4.00000i q^{43}\) \(-2.00000 q^{44}\) \(+(2.00000 - 1.00000i) q^{45}\) \(+4.00000 q^{46}\) \(+8.00000i q^{47}\) \(-1.00000i q^{48}\) \(+3.00000 q^{49}\) \(+(4.00000 + 3.00000i) q^{50}\) \(-2.00000 q^{51}\) \(-6.00000i q^{52}\) \(+6.00000i q^{53}\) \(-1.00000 q^{54}\) \(+(-4.00000 + 2.00000i) q^{55}\) \(-2.00000 q^{56}\) \(-10.0000 q^{59}\) \(+(-1.00000 - 2.00000i) q^{60}\) \(+2.00000 q^{61}\) \(-8.00000i q^{62}\) \(+2.00000i q^{63}\) \(-1.00000 q^{64}\) \(+(-6.00000 - 12.0000i) q^{65}\) \(+2.00000 q^{66}\) \(+8.00000i q^{67}\) \(+2.00000i q^{68}\) \(-4.00000 q^{69}\) \(+(-4.00000 + 2.00000i) q^{70}\) \(+12.0000 q^{71}\) \(+1.00000i q^{72}\) \(-4.00000i q^{73}\) \(+2.00000 q^{74}\) \(+(-4.00000 - 3.00000i) q^{75}\) \(-4.00000i q^{77}\) \(+6.00000i q^{78}\) \(+(-2.00000 + 1.00000i) q^{80}\) \(+1.00000 q^{81}\) \(+2.00000i q^{82}\) \(-4.00000i q^{83}\) \(+2.00000 q^{84}\) \(+(2.00000 + 4.00000i) q^{85}\) \(+4.00000 q^{86}\) \(-2.00000i q^{88}\) \(+10.0000 q^{89}\) \(+(1.00000 + 2.00000i) q^{90}\) \(+12.0000 q^{91}\) \(+4.00000i q^{92}\) \(+8.00000i q^{93}\) \(-8.00000 q^{94}\) \(+1.00000 q^{96}\) \(+8.00000i q^{97}\) \(+3.00000i q^{98}\) \(-2.00000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 2q^{16} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 2q^{24} \) \(\mathstrut +\mathstrut 6q^{25} \) \(\mathstrut -\mathstrut 12q^{26} \) \(\mathstrut -\mathstrut 4q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut +\mathstrut 4q^{34} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 2q^{36} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut +\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 4q^{45} \) \(\mathstrut +\mathstrut 8q^{46} \) \(\mathstrut +\mathstrut 6q^{49} \) \(\mathstrut +\mathstrut 8q^{50} \) \(\mathstrut -\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 2q^{54} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 4q^{56} \) \(\mathstrut -\mathstrut 20q^{59} \) \(\mathstrut -\mathstrut 2q^{60} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 2q^{64} \) \(\mathstrut -\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 4q^{66} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 24q^{71} \) \(\mathstrut +\mathstrut 4q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut +\mathstrut 4q^{84} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut -\mathstrut 16q^{94} \) \(\mathstrut +\mathstrut 2q^{96} \) \(\mathstrut -\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/30\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(11\)
\(\chi(n)\) \(-1\) \(1\)

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
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) −2.00000 + 1.00000i −0.894427 + 0.447214i
\(6\) 1.00000 0.408248
\(7\) 2.00000i 0.755929i −0.925820 0.377964i \(-0.876624\pi\)
0.925820 0.377964i \(-0.123376\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) −1.00000 2.00000i −0.316228 0.632456i
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 6.00000i 1.66410i 0.554700 + 0.832050i \(0.312833\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 2.00000 0.534522
\(15\) 1.00000 + 2.00000i 0.258199 + 0.516398i
\(16\) 1.00000 0.250000
\(17\) 2.00000i 0.485071i −0.970143 0.242536i \(-0.922021\pi\)
0.970143 0.242536i \(-0.0779791\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 2.00000 1.00000i 0.447214 0.223607i
\(21\) −2.00000 −0.436436
\(22\) 2.00000i 0.426401i
\(23\) 4.00000i 0.834058i −0.908893 0.417029i \(-0.863071\pi\)
0.908893 0.417029i \(-0.136929\pi\)
\(24\) −1.00000 −0.204124
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) −6.00000 −1.17670
\(27\) 1.00000i 0.192450i
\(28\) 2.00000i 0.377964i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) −2.00000 + 1.00000i −0.365148 + 0.182574i
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.00000i 0.348155i
\(34\) 2.00000 0.342997
\(35\) 2.00000 + 4.00000i 0.338062 + 0.676123i
\(36\) 1.00000 0.166667
\(37\) 2.00000i 0.328798i −0.986394 0.164399i \(-0.947432\pi\)
0.986394 0.164399i \(-0.0525685\pi\)
\(38\) 0 0
\(39\) 6.00000 0.960769
\(40\) 1.00000 + 2.00000i 0.158114 + 0.316228i
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 2.00000i 0.308607i
\(43\) 4.00000i 0.609994i −0.952353 0.304997i \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) −2.00000 −0.301511
\(45\) 2.00000 1.00000i 0.298142 0.149071i
\(46\) 4.00000 0.589768
\(47\) 8.00000i 1.16692i 0.812142 + 0.583460i \(0.198301\pi\)
−0.812142 + 0.583460i \(0.801699\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 3.00000 0.428571
\(50\) 4.00000 + 3.00000i 0.565685 + 0.424264i
\(51\) −2.00000 −0.280056
\(52\) 6.00000i 0.832050i
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) −1.00000 −0.136083
\(55\) −4.00000 + 2.00000i −0.539360 + 0.269680i
\(56\) −2.00000 −0.267261
\(57\) 0 0
\(58\) 0 0
\(59\) −10.0000 −1.30189 −0.650945 0.759125i \(-0.725627\pi\)
−0.650945 + 0.759125i \(0.725627\pi\)
\(60\) −1.00000 2.00000i −0.129099 0.258199i
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 8.00000i 1.01600i
\(63\) 2.00000i 0.251976i
\(64\) −1.00000 −0.125000
\(65\) −6.00000 12.0000i −0.744208 1.48842i
\(66\) 2.00000 0.246183
\(67\) 8.00000i 0.977356i 0.872464 + 0.488678i \(0.162521\pi\)
−0.872464 + 0.488678i \(0.837479\pi\)
\(68\) 2.00000i 0.242536i
\(69\) −4.00000 −0.481543
\(70\) −4.00000 + 2.00000i −0.478091 + 0.239046i
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 4.00000i 0.468165i −0.972217 0.234082i \(-0.924791\pi\)
0.972217 0.234082i \(-0.0752085\pi\)
\(74\) 2.00000 0.232495
\(75\) −4.00000 3.00000i −0.461880 0.346410i
\(76\) 0 0
\(77\) 4.00000i 0.455842i
\(78\) 6.00000i 0.679366i
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) −2.00000 + 1.00000i −0.223607 + 0.111803i
\(81\) 1.00000 0.111111
\(82\) 2.00000i 0.220863i
\(83\) 4.00000i 0.439057i −0.975606 0.219529i \(-0.929548\pi\)
0.975606 0.219529i \(-0.0704519\pi\)
\(84\) 2.00000 0.218218
\(85\) 2.00000 + 4.00000i 0.216930 + 0.433861i
\(86\) 4.00000 0.431331
\(87\) 0 0
\(88\) 2.00000i 0.213201i
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) 1.00000 + 2.00000i 0.105409 + 0.210819i
\(91\) 12.0000 1.25794
\(92\) 4.00000i 0.417029i
\(93\) 8.00000i 0.829561i
\(94\) −8.00000 −0.825137
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 8.00000i 0.812277i 0.913812 + 0.406138i \(0.133125\pi\)
−0.913812 + 0.406138i \(0.866875\pi\)
\(98\) 3.00000i 0.303046i
\(99\) −2.00000 −0.201008
\(100\) −3.00000 + 4.00000i −0.300000 + 0.400000i
\(101\) −8.00000 −0.796030 −0.398015 0.917379i \(-0.630301\pi\)
−0.398015 + 0.917379i \(0.630301\pi\)
\(102\) 2.00000i 0.198030i
\(103\) 14.0000i 1.37946i −0.724066 0.689730i \(-0.757729\pi\)
0.724066 0.689730i \(-0.242271\pi\)
\(104\) 6.00000 0.588348
\(105\) 4.00000 2.00000i 0.390360 0.195180i
\(106\) −6.00000 −0.582772
\(107\) 12.0000i 1.16008i −0.814587 0.580042i \(-0.803036\pi\)
0.814587 0.580042i \(-0.196964\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) −2.00000 4.00000i −0.190693 0.381385i
\(111\) −2.00000 −0.189832
\(112\) 2.00000i 0.188982i
\(113\) 6.00000i 0.564433i 0.959351 + 0.282216i \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) 0 0
\(115\) 4.00000 + 8.00000i 0.373002 + 0.746004i
\(116\) 0 0
\(117\) 6.00000i 0.554700i
\(118\) 10.0000i 0.920575i
\(119\) −4.00000 −0.366679
\(120\) 2.00000 1.00000i 0.182574 0.0912871i
\(121\) −7.00000 −0.636364
\(122\) 2.00000i 0.181071i
\(123\) 2.00000i 0.180334i
\(124\) 8.00000 0.718421
\(125\) −2.00000 + 11.0000i −0.178885 + 0.983870i
\(126\) −2.00000 −0.178174
\(127\) 2.00000i 0.177471i −0.996055 0.0887357i \(-0.971717\pi\)
0.996055 0.0887357i \(-0.0282826\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −4.00000 −0.352180
\(130\) 12.0000 6.00000i 1.05247 0.526235i
\(131\) −18.0000 −1.57267 −0.786334 0.617802i \(-0.788023\pi\)
−0.786334 + 0.617802i \(0.788023\pi\)
\(132\) 2.00000i 0.174078i
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) −1.00000 2.00000i −0.0860663 0.172133i
\(136\) −2.00000 −0.171499
\(137\) 18.0000i 1.53784i 0.639343 + 0.768922i \(0.279207\pi\)
−0.639343 + 0.768922i \(0.720793\pi\)
\(138\) 4.00000i 0.340503i
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) −2.00000 4.00000i −0.169031 0.338062i
\(141\) 8.00000 0.673722
\(142\) 12.0000i 1.00702i
\(143\) 12.0000i 1.00349i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 4.00000 0.331042
\(147\) 3.00000i 0.247436i
\(148\) 2.00000i 0.164399i
\(149\) 20.0000 1.63846 0.819232 0.573462i \(-0.194400\pi\)
0.819232 + 0.573462i \(0.194400\pi\)
\(150\) 3.00000 4.00000i 0.244949 0.326599i
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 0 0
\(153\) 2.00000i 0.161690i
\(154\) 4.00000 0.322329
\(155\) 16.0000 8.00000i 1.28515 0.642575i
\(156\) −6.00000 −0.480384
\(157\) 22.0000i 1.75579i −0.478852 0.877896i \(-0.658947\pi\)
0.478852 0.877896i \(-0.341053\pi\)
\(158\) 0 0
\(159\) 6.00000 0.475831
\(160\) −1.00000 2.00000i −0.0790569 0.158114i
\(161\) −8.00000 −0.630488
\(162\) 1.00000i 0.0785674i
\(163\) 16.0000i 1.25322i 0.779334 + 0.626608i \(0.215557\pi\)
−0.779334 + 0.626608i \(0.784443\pi\)
\(164\) −2.00000 −0.156174
\(165\) 2.00000 + 4.00000i 0.155700 + 0.311400i
\(166\) 4.00000 0.310460
\(167\) 12.0000i 0.928588i −0.885681 0.464294i \(-0.846308\pi\)
0.885681 0.464294i \(-0.153692\pi\)
\(168\) 2.00000i 0.154303i
\(169\) −23.0000 −1.76923
\(170\) −4.00000 + 2.00000i −0.306786 + 0.153393i
\(171\) 0 0
\(172\) 4.00000i 0.304997i
\(173\) 14.0000i 1.06440i −0.846619 0.532200i \(-0.821365\pi\)
0.846619 0.532200i \(-0.178635\pi\)
\(174\) 0 0
\(175\) −8.00000 6.00000i −0.604743 0.453557i
\(176\) 2.00000 0.150756
\(177\) 10.0000i 0.751646i
\(178\) 10.0000i 0.749532i
\(179\) −10.0000 −0.747435 −0.373718 0.927543i \(-0.621917\pi\)
−0.373718 + 0.927543i \(0.621917\pi\)
\(180\) −2.00000 + 1.00000i −0.149071 + 0.0745356i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 12.0000i 0.889499i
\(183\) 2.00000i 0.147844i
\(184\) −4.00000 −0.294884
\(185\) 2.00000 + 4.00000i 0.147043 + 0.294086i
\(186\) −8.00000 −0.586588
\(187\) 4.00000i 0.292509i
\(188\) 8.00000i 0.583460i
\(189\) 2.00000 0.145479
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 4.00000i 0.287926i −0.989583 0.143963i \(-0.954015\pi\)
0.989583 0.143963i \(-0.0459847\pi\)
\(194\) −8.00000 −0.574367
\(195\) −12.0000 + 6.00000i −0.859338 + 0.429669i
\(196\) −3.00000 −0.214286
\(197\) 22.0000i 1.56744i −0.621117 0.783718i \(-0.713321\pi\)
0.621117 0.783718i \(-0.286679\pi\)
\(198\) 2.00000i 0.142134i
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) −4.00000 3.00000i −0.282843 0.212132i
\(201\) 8.00000 0.564276
\(202\) 8.00000i 0.562878i
\(203\) 0 0
\(204\) 2.00000 0.140028
\(205\) −4.00000 + 2.00000i −0.279372 + 0.139686i
\(206\) 14.0000 0.975426
\(207\) 4.00000i 0.278019i
\(208\) 6.00000i 0.416025i
\(209\) 0 0
\(210\) 2.00000 + 4.00000i 0.138013 + 0.276026i
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 12.0000i 0.822226i
\(214\) 12.0000 0.820303
\(215\) 4.00000 + 8.00000i 0.272798 + 0.545595i
\(216\) 1.00000 0.0680414
\(217\) 16.0000i 1.08615i
\(218\) 10.0000i 0.677285i
\(219\) −4.00000 −0.270295
\(220\) 4.00000 2.00000i 0.269680 0.134840i
\(221\) 12.0000 0.807207
\(222\) 2.00000i 0.134231i
\(223\) 26.0000i 1.74109i 0.492090 + 0.870544i \(0.336233\pi\)
−0.492090 + 0.870544i \(0.663767\pi\)
\(224\) 2.00000 0.133631
\(225\) −3.00000 + 4.00000i −0.200000 + 0.266667i
\(226\) −6.00000 −0.399114
\(227\) 28.0000i 1.85843i 0.369546 + 0.929213i \(0.379513\pi\)
−0.369546 + 0.929213i \(0.620487\pi\)
\(228\) 0 0
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) −8.00000 + 4.00000i −0.527504 + 0.263752i
\(231\) −4.00000 −0.263181
\(232\) 0 0
\(233\) 14.0000i 0.917170i −0.888650 0.458585i \(-0.848356\pi\)
0.888650 0.458585i \(-0.151644\pi\)
\(234\) 6.00000 0.392232
\(235\) −8.00000 16.0000i −0.521862 1.04372i
\(236\) 10.0000 0.650945
\(237\) 0 0
\(238\) 4.00000i 0.259281i
\(239\) −20.0000 −1.29369 −0.646846 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 1.00000 + 2.00000i 0.0645497 + 0.129099i
\(241\) 22.0000 1.41714 0.708572 0.705638i \(-0.249340\pi\)
0.708572 + 0.705638i \(0.249340\pi\)
\(242\) 7.00000i 0.449977i
\(243\) 1.00000i 0.0641500i
\(244\) −2.00000 −0.128037
\(245\) −6.00000 + 3.00000i −0.383326 + 0.191663i
\(246\) 2.00000 0.127515
\(247\) 0 0
\(248\) 8.00000i 0.508001i
\(249\) −4.00000 −0.253490
\(250\) −11.0000 2.00000i −0.695701 0.126491i
\(251\) −18.0000 −1.13615 −0.568075 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 2.00000i 0.125988i
\(253\) 8.00000i 0.502956i
\(254\) 2.00000 0.125491
\(255\) 4.00000 2.00000i 0.250490 0.125245i
\(256\) 1.00000 0.0625000
\(257\) 18.0000i 1.12281i 0.827541 + 0.561405i \(0.189739\pi\)
−0.827541 + 0.561405i \(0.810261\pi\)
\(258\) 4.00000i 0.249029i
\(259\) −4.00000 −0.248548
\(260\) 6.00000 + 12.0000i 0.372104 + 0.744208i
\(261\) 0 0
\(262\) 18.0000i 1.11204i
\(263\) 4.00000i 0.246651i −0.992366 0.123325i \(-0.960644\pi\)
0.992366 0.123325i \(-0.0393559\pi\)
\(264\) −2.00000 −0.123091
\(265\) −6.00000 12.0000i −0.368577 0.737154i
\(266\) 0 0
\(267\) 10.0000i 0.611990i
\(268\) 8.00000i 0.488678i
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 2.00000 1.00000i 0.121716 0.0608581i
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 12.0000i 0.726273i
\(274\) −18.0000 −1.08742
\(275\) 6.00000 8.00000i 0.361814 0.482418i
\(276\) 4.00000 0.240772
\(277\) 2.00000i 0.120168i −0.998193 0.0600842i \(-0.980863\pi\)
0.998193 0.0600842i \(-0.0191369\pi\)
\(278\) 20.0000i 1.19952i
\(279\) 8.00000 0.478947
\(280\) 4.00000 2.00000i 0.239046 0.119523i
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 8.00000i 0.476393i
\(283\) 16.0000i 0.951101i 0.879688 + 0.475551i \(0.157751\pi\)
−0.879688 + 0.475551i \(0.842249\pi\)
\(284\) −12.0000 −0.712069
\(285\) 0 0
\(286\) −12.0000 −0.709575
\(287\) 4.00000i 0.236113i
\(288\) 1.00000i 0.0589256i
\(289\) 13.0000 0.764706
\(290\) 0 0
\(291\) 8.00000 0.468968
\(292\) 4.00000i 0.234082i
\(293\) 6.00000i 0.350524i 0.984522 + 0.175262i \(0.0560772\pi\)
−0.984522 + 0.175262i \(0.943923\pi\)
\(294\) 3.00000 0.174964
\(295\) 20.0000 10.0000i 1.16445 0.582223i
\(296\) −2.00000 −0.116248
\(297\) 2.00000i 0.116052i
\(298\) 20.0000i 1.15857i
\(299\) 24.0000 1.38796
\(300\) 4.00000 + 3.00000i 0.230940 + 0.173205i
\(301\) −8.00000 −0.461112
\(302\) 8.00000i 0.460348i
\(303\) 8.00000i 0.459588i
\(304\) 0 0
\(305\) −4.00000 + 2.00000i −0.229039 + 0.114520i
\(306\) −2.00000 −0.114332
\(307\) 12.0000i 0.684876i −0.939540 0.342438i \(-0.888747\pi\)
0.939540 0.342438i \(-0.111253\pi\)
\(308\) 4.00000i 0.227921i
\(309\) −14.0000 −0.796432
\(310\) 8.00000 + 16.0000i 0.454369 + 0.908739i
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 6.00000i 0.339683i
\(313\) 4.00000i 0.226093i −0.993590 0.113047i \(-0.963939\pi\)
0.993590 0.113047i \(-0.0360610\pi\)
\(314\) 22.0000 1.24153
\(315\) −2.00000 4.00000i −0.112687 0.225374i
\(316\) 0 0
\(317\) 2.00000i 0.112331i −0.998421 0.0561656i \(-0.982113\pi\)
0.998421 0.0561656i \(-0.0178875\pi\)
\(318\) 6.00000i 0.336463i
\(319\) 0 0
\(320\) 2.00000 1.00000i 0.111803 0.0559017i
\(321\) −12.0000 −0.669775
\(322\) 8.00000i 0.445823i
\(323\) 0 0
\(324\) −1.00000 −0.0555556
\(325\) 24.0000 + 18.0000i 1.33128 + 0.998460i
\(326\) −16.0000 −0.886158
\(327\) 10.0000i 0.553001i
\(328\) 2.00000i 0.110432i
\(329\) 16.0000 0.882109
\(330\) −4.00000 + 2.00000i −0.220193 + 0.110096i
\(331\) −8.00000 −0.439720 −0.219860 0.975531i \(-0.570560\pi\)
−0.219860 + 0.975531i \(0.570560\pi\)
\(332\) 4.00000i 0.219529i
\(333\) 2.00000i 0.109599i
\(334\) 12.0000 0.656611
\(335\) −8.00000 16.0000i −0.437087 0.874173i
\(336\) −2.00000 −0.109109
\(337\) 28.0000i 1.52526i 0.646837 + 0.762629i \(0.276092\pi\)
−0.646837 + 0.762629i \(0.723908\pi\)
\(338\) 23.0000i 1.25104i
\(339\) 6.00000 0.325875
\(340\) −2.00000 4.00000i −0.108465 0.216930i
\(341\) −16.0000 −0.866449
\(342\) 0 0
\(343\) 20.0000i 1.07990i
\(344\) −4.00000 −0.215666
\(345\) 8.00000 4.00000i 0.430706 0.215353i
\(346\) 14.0000 0.752645
\(347\) 12.0000i 0.644194i −0.946707 0.322097i \(-0.895612\pi\)
0.946707 0.322097i \(-0.104388\pi\)
\(348\) 0 0
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 6.00000 8.00000i 0.320713 0.427618i
\(351\) −6.00000 −0.320256
\(352\) 2.00000i 0.106600i
\(353\) 14.0000i 0.745145i −0.928003 0.372572i \(-0.878476\pi\)
0.928003 0.372572i \(-0.121524\pi\)
\(354\) −10.0000 −0.531494
\(355\) −24.0000 + 12.0000i −1.27379 + 0.636894i
\(356\) −10.0000 −0.529999
\(357\) 4.00000i 0.211702i
\(358\) 10.0000i 0.528516i
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) −1.00000 2.00000i −0.0527046 0.105409i
\(361\) −19.0000 −1.00000
\(362\) 2.00000i 0.105118i
\(363\) 7.00000i 0.367405i
\(364\) −12.0000 −0.628971
\(365\) 4.00000 + 8.00000i 0.209370 + 0.418739i
\(366\) 2.00000 0.104542
\(367\) 2.00000i 0.104399i −0.998637 0.0521996i \(-0.983377\pi\)
0.998637 0.0521996i \(-0.0166232\pi\)
\(368\) 4.00000i 0.208514i
\(369\) −2.00000 −0.104116
\(370\) −4.00000 + 2.00000i −0.207950 + 0.103975i
\(371\) 12.0000 0.623009
\(372\) 8.00000i 0.414781i
\(373\) 6.00000i 0.310668i 0.987862 + 0.155334i \(0.0496454\pi\)
−0.987862 + 0.155334i \(0.950355\pi\)
\(374\) 4.00000 0.206835
\(375\) 11.0000 + 2.00000i 0.568038 + 0.103280i
\(376\) 8.00000 0.412568
\(377\) 0 0
\(378\) 2.00000i 0.102869i
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) −2.00000 −0.102463
\(382\) 12.0000i 0.613973i
\(383\) 16.0000i 0.817562i 0.912633 + 0.408781i \(0.134046\pi\)
−0.912633 + 0.408781i \(0.865954\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 4.00000 + 8.00000i 0.203859 + 0.407718i
\(386\) 4.00000 0.203595
\(387\) 4.00000i 0.203331i
\(388\) 8.00000i 0.406138i
\(389\) −20.0000 −1.01404 −0.507020 0.861934i \(-0.669253\pi\)
−0.507020 + 0.861934i \(0.669253\pi\)
\(390\) −6.00000 12.0000i −0.303822 0.607644i
\(391\) −8.00000 −0.404577
\(392\) 3.00000i 0.151523i
\(393\) 18.0000i 0.907980i
\(394\) 22.0000 1.10834
\(395\) 0 0
\(396\) 2.00000 0.100504
\(397\) 2.00000i 0.100377i −0.998740 0.0501886i \(-0.984018\pi\)
0.998740 0.0501886i \(-0.0159822\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 3.00000 4.00000i 0.150000 0.200000i
\(401\) 22.0000 1.09863 0.549314 0.835616i \(-0.314889\pi\)
0.549314 + 0.835616i \(0.314889\pi\)
\(402\) 8.00000i 0.399004i
\(403\) 48.0000i 2.39105i
\(404\) 8.00000 0.398015
\(405\) −2.00000 + 1.00000i −0.0993808 + 0.0496904i
\(406\) 0 0
\(407\) 4.00000i 0.198273i
\(408\) 2.00000i 0.0990148i
\(409\) 10.0000 0.494468 0.247234 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) −2.00000 4.00000i −0.0987730 0.197546i
\(411\) 18.0000 0.887875
\(412\) 14.0000i 0.689730i
\(413\) 20.0000i 0.984136i
\(414\) −4.00000 −0.196589
\(415\) 4.00000 + 8.00000i 0.196352 + 0.392705i
\(416\) −6.00000 −0.294174
\(417\) 20.0000i 0.979404i
\(418\) 0 0
\(419\) 10.0000 0.488532 0.244266 0.969708i \(-0.421453\pi\)
0.244266 + 0.969708i \(0.421453\pi\)
\(420\) −4.00000 + 2.00000i −0.195180 + 0.0975900i
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) 12.0000i 0.584151i
\(423\) 8.00000i 0.388973i
\(424\) 6.00000 0.291386
\(425\) −8.00000 6.00000i −0.388057 0.291043i
\(426\) 12.0000 0.581402
\(427\) 4.00000i 0.193574i
\(428\) 12.0000i 0.580042i
\(429\) 12.0000 0.579365
\(430\) −8.00000 + 4.00000i −0.385794 + 0.192897i
\(431\) 32.0000 1.54139 0.770693 0.637207i \(-0.219910\pi\)
0.770693 + 0.637207i \(0.219910\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 4.00000i 0.192228i −0.995370 0.0961139i \(-0.969359\pi\)
0.995370 0.0961139i \(-0.0306413\pi\)
\(434\) −16.0000 −0.768025
\(435\) 0 0
\(436\) 10.0000 0.478913
\(437\) 0 0
\(438\) 4.00000i 0.191127i
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 2.00000 + 4.00000i 0.0953463 + 0.190693i
\(441\) −3.00000 −0.142857
\(442\) 12.0000i 0.570782i
\(443\) 36.0000i 1.71041i 0.518289 + 0.855206i \(0.326569\pi\)
−0.518289 + 0.855206i \(0.673431\pi\)
\(444\) 2.00000 0.0949158
\(445\) −20.0000 + 10.0000i −0.948091 + 0.474045i
\(446\) −26.0000 −1.23114
\(447\) 20.0000i 0.945968i
\(448\) 2.00000i 0.0944911i
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) −4.00000 3.00000i −0.188562 0.141421i
\(451\) 4.00000 0.188353
\(452\) 6.00000i 0.282216i
\(453\) 8.00000i 0.375873i
\(454\) −28.0000 −1.31411
\(455\) −24.0000 + 12.0000i −1.12514 + 0.562569i
\(456\) 0 0
\(457\) 32.0000i 1.49690i −0.663193 0.748448i \(-0.730799\pi\)
0.663193 0.748448i \(-0.269201\pi\)
\(458\) 10.0000i 0.467269i
\(459\) 2.00000 0.0933520
\(460\) −4.00000 8.00000i −0.186501 0.373002i
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 4.00000i 0.186097i
\(463\) 6.00000i 0.278844i 0.990233 + 0.139422i \(0.0445244\pi\)
−0.990233 + 0.139422i \(0.955476\pi\)
\(464\) 0 0
\(465\) −8.00000 16.0000i −0.370991 0.741982i
\(466\) 14.0000 0.648537
\(467\) 12.0000i 0.555294i −0.960683 0.277647i \(-0.910445\pi\)
0.960683 0.277647i \(-0.0895545\pi\)
\(468\) 6.00000i 0.277350i
\(469\) 16.0000 0.738811
\(470\) 16.0000 8.00000i 0.738025 0.369012i
\(471\) −22.0000 −1.01371
\(472\) 10.0000i 0.460287i
\(473\) 8.00000i 0.367840i
\(474\) 0 0
\(475\) 0 0
\(476\) 4.00000 0.183340
\(477\) 6.00000i 0.274721i
\(478\) 20.0000i 0.914779i
\(479\) −20.0000 −0.913823 −0.456912 0.889512i \(-0.651044\pi\)
−0.456912 + 0.889512i \(0.651044\pi\)
\(480\) −2.00000 + 1.00000i −0.0912871 + 0.0456435i
\(481\) 12.0000 0.547153
\(482\) 22.0000i 1.00207i
\(483\) 8.00000i 0.364013i
\(484\) 7.00000 0.318182
\(485\) −8.00000 16.0000i −0.363261 0.726523i
\(486\) 1.00000 0.0453609
\(487\) 18.0000i 0.815658i 0.913058 + 0.407829i \(0.133714\pi\)
−0.913058 + 0.407829i \(0.866286\pi\)
\(488\) 2.00000i 0.0905357i
\(489\) 16.0000 0.723545
\(490\) −3.00000 6.00000i −0.135526 0.271052i
\(491\) −18.0000 −0.812329 −0.406164 0.913800i \(-0.633134\pi\)
−0.406164 + 0.913800i \(0.633134\pi\)
\(492\) 2.00000i 0.0901670i
\(493\) 0 0
\(494\) 0 0
\(495\) 4.00000 2.00000i 0.179787 0.0898933i
\(496\) −8.00000 −0.359211
\(497\) 24.0000i 1.07655i
\(498\) 4.00000i 0.179244i
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 2.00000 11.0000i 0.0894427 0.491935i
\(501\) −12.0000 −0.536120
\(502\) 18.0000i 0.803379i
\(503\) 24.0000i 1.07011i −0.844818 0.535054i \(-0.820291\pi\)
0.844818 0.535054i \(-0.179709\pi\)
\(504\) 2.00000 0.0890871
\(505\) 16.0000 8.00000i 0.711991 0.355995i
\(506\) 8.00000 0.355643
\(507\) 23.0000i 1.02147i
\(508\) 2.00000i 0.0887357i
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 2.00000 + 4.00000i 0.0885615 + 0.177123i
\(511\) −8.00000 −0.353899
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −18.0000 −0.793946
\(515\) 14.0000 + 28.0000i 0.616914 + 1.23383i
\(516\) 4.00000 0.176090
\(517\) 16.0000i 0.703679i
\(518\) 4.00000i 0.175750i
\(519\) −14.0000 −0.614532
\(520\) −12.0000 + 6.00000i −0.526235 + 0.263117i
\(521\) 22.0000 0.963837 0.481919 0.876216i \(-0.339940\pi\)
0.481919 + 0.876216i \(0.339940\pi\)
\(522\) 0 0
\(523\) 16.0000i 0.699631i 0.936819 + 0.349816i \(0.113756\pi\)
−0.936819 + 0.349816i \(0.886244\pi\)
\(524\) 18.0000 0.786334
\(525\) −6.00000 + 8.00000i −0.261861 + 0.349149i
\(526\) 4.00000 0.174408
\(527\) 16.0000i 0.696971i
\(528\) 2.00000i 0.0870388i
\(529\) 7.00000 0.304348
\(530\) 12.0000 6.00000i 0.521247 0.260623i
\(531\) 10.0000 0.433963
\(532\) 0 0
\(533\) 12.0000i 0.519778i
\(534\) 10.0000 0.432742
\(535\) 12.0000 + 24.0000i 0.518805 + 1.03761i
\(536\) 8.00000 0.345547
\(537\) 10.0000i 0.431532i
\(538\) 0 0
\(539\) 6.00000 0.258438
\(540\) 1.00000 + 2.00000i 0.0430331 + 0.0860663i
\(541\) −38.0000 −1.63375 −0.816874 0.576816i \(-0.804295\pi\)
−0.816874 + 0.576816i \(0.804295\pi\)
\(542\) 8.00000i 0.343629i
\(543\) 2.00000i 0.0858282i
\(544\) 2.00000 0.0857493
\(545\) 20.0000 10.0000i 0.856706 0.428353i
\(546\) 12.0000 0.513553
\(547\) 28.0000i 1.19719i 0.801050 + 0.598597i \(0.204275\pi\)
−0.801050 + 0.598597i \(0.795725\pi\)
\(548\) 18.0000i 0.768922i
\(549\) −2.00000 −0.0853579
\(550\) 8.00000 + 6.00000i 0.341121 + 0.255841i
\(551\) 0 0
\(552\) 4.00000i 0.170251i
\(553\) 0 0
\(554\) 2.00000 0.0849719
\(555\) 4.00000 2.00000i 0.169791 0.0848953i
\(556\) −20.0000 −0.848189
\(557\) 18.0000i 0.762684i 0.924434 + 0.381342i \(0.124538\pi\)
−0.924434 + 0.381342i \(0.875462\pi\)
\(558\) 8.00000i 0.338667i
\(559\) 24.0000 1.01509
\(560\) 2.00000 + 4.00000i 0.0845154 + 0.169031i
\(561\) −4.00000 −0.168880
\(562\) 18.0000i 0.759284i
\(563\) 44.0000i 1.85438i −0.374593 0.927189i \(-0.622217\pi\)
0.374593 0.927189i \(-0.377783\pi\)
\(564\) −8.00000 −0.336861
\(565\) −6.00000 12.0000i −0.252422 0.504844i
\(566\) −16.0000 −0.672530
\(567\) 2.00000i 0.0839921i
\(568\) 12.0000i 0.503509i
\(569\) 10.0000 0.419222 0.209611 0.977785i \(-0.432780\pi\)
0.209611 + 0.977785i \(0.432780\pi\)
\(570\) 0 0
\(571\) −8.00000 −0.334790 −0.167395 0.985890i \(-0.553535\pi\)
−0.167395 + 0.985890i \(0.553535\pi\)
\(572\) 12.0000i 0.501745i
\(573\) 12.0000i 0.501307i
\(574\) 4.00000 0.166957
\(575\) −16.0000 12.0000i −0.667246 0.500435i
\(576\) 1.00000 0.0416667
\(577\) 32.0000i 1.33218i −0.745873 0.666089i \(-0.767967\pi\)
0.745873 0.666089i \(-0.232033\pi\)
\(578\) 13.0000i 0.540729i
\(579\) −4.00000 −0.166234
\(580\) 0 0
\(581\) −8.00000 −0.331896
\(582\) 8.00000i 0.331611i
\(583\) 12.0000i 0.496989i
\(584\) −4.00000 −0.165521
\(585\) 6.00000 + 12.0000i 0.248069 + 0.496139i
\(586\) −6.00000 −0.247858
\(587\) 12.0000i 0.495293i −0.968850 0.247647i \(-0.920343\pi\)
0.968850 0.247647i \(-0.0796572\pi\)
\(588\) 3.00000i 0.123718i
\(589\) 0 0
\(590\) 10.0000 + 20.0000i 0.411693 + 0.823387i
\(591\) −22.0000 −0.904959
\(592\) 2.00000i 0.0821995i
\(593\) 6.00000i 0.246390i 0.992382 + 0.123195i \(0.0393141\pi\)
−0.992382 + 0.123195i \(0.960686\pi\)
\(594\) −2.00000 −0.0820610
\(595\) 8.00000 4.00000i 0.327968 0.163984i
\(596\) −20.0000 −0.819232
\(597\) 0 0
\(598\) 24.0000i 0.981433i
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) −3.00000 + 4.00000i −0.122474 + 0.163299i
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) 8.00000i 0.326056i
\(603\) 8.00000i 0.325785i
\(604\) 8.00000 0.325515
\(605\) 14.0000 7.00000i 0.569181 0.284590i
\(606\) −8.00000 −0.324978
\(607\) 22.0000i 0.892952i −0.894795 0.446476i \(-0.852679\pi\)
0.894795 0.446476i \(-0.147321\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −2.00000 4.00000i −0.0809776 0.161955i
\(611\) −48.0000 −1.94187
\(612\) 2.00000i 0.0808452i
\(613\) 26.0000i 1.05013i 0.851062 + 0.525065i \(0.175959\pi\)
−0.851062 + 0.525065i \(0.824041\pi\)
\(614\) 12.0000 0.484281
\(615\) 2.00000 + 4.00000i 0.0806478 + 0.161296i
\(616\) −4.00000 −0.161165
\(617\) 2.00000i 0.0805170i −0.999189 0.0402585i \(-0.987182\pi\)
0.999189 0.0402585i \(-0.0128181\pi\)
\(618\) 14.0000i 0.563163i
\(619\) −20.0000 −0.803868 −0.401934 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) −16.0000 + 8.00000i −0.642575 + 0.321288i
\(621\) 4.00000 0.160514
\(622\) 12.0000i 0.481156i
\(623\) 20.0000i 0.801283i
\(624\) 6.00000 0.240192
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 4.00000 0.159872
\(627\) 0 0
\(628\) 22.0000i 0.877896i
\(629\) −4.00000 −0.159490
\(630\) 4.00000 2.00000i 0.159364 0.0796819i
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) 0 0
\(633\) 12.0000i 0.476957i
\(634\) 2.00000 0.0794301
\(635\) 2.00000 + 4.00000i 0.0793676 + 0.158735i
\(636\) −6.00000 −0.237915
\(637\) 18.0000i 0.713186i
\(638\) 0 0
\(639\) −12.0000 −0.474713
\(640\) 1.00000 + 2.00000i 0.0395285 + 0.0790569i
\(641\) 2.00000 0.0789953 0.0394976 0.999220i \(-0.487424\pi\)
0.0394976 + 0.999220i \(0.487424\pi\)
\(642\) 12.0000i 0.473602i
\(643\) 24.0000i 0.946468i −0.880937 0.473234i \(-0.843087\pi\)
0.880937 0.473234i \(-0.156913\pi\)
\(644\) 8.00000 0.315244
\(645\) 8.00000 4.00000i 0.315000 0.157500i
\(646\) 0 0
\(647\) 48.0000i 1.88707i 0.331266 + 0.943537i \(0.392524\pi\)
−0.331266 + 0.943537i \(0.607476\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −20.0000 −0.785069
\(650\) −18.0000 + 24.0000i −0.706018 + 0.941357i
\(651\) 16.0000 0.627089
\(652\) 16.0000i 0.626608i
\(653\) 26.0000i 1.01746i 0.860927 + 0.508729i \(0.169885\pi\)
−0.860927 + 0.508729i \(0.830115\pi\)
\(654\) −10.0000 −0.391031
\(655\) 36.0000 18.0000i 1.40664 0.703318i
\(656\) 2.00000 0.0780869
\(657\) 4.00000i 0.156055i
\(658\) 16.0000i 0.623745i
\(659\) 50.0000 1.94772 0.973862 0.227142i \(-0.0729380\pi\)
0.973862 + 0.227142i \(0.0729380\pi\)
\(660\) −2.00000 4.00000i −0.0778499 0.155700i
\(661\) 2.00000 0.0777910 0.0388955 0.999243i \(-0.487616\pi\)
0.0388955 + 0.999243i \(0.487616\pi\)
\(662\) 8.00000i 0.310929i
\(663\) 12.0000i 0.466041i
\(664\) −4.00000 −0.155230
\(665\) 0 0
\(666\) −2.00000 −0.0774984
\(667\) 0 0
\(668\) 12.0000i 0.464294i
\(669\) 26.0000 1.00522
\(670\) 16.0000 8.00000i 0.618134 0.309067i
\(671\) 4.00000 0.154418
\(672\) 2.00000i 0.0771517i
\(673\) 36.0000i 1.38770i 0.720121 + 0.693849i \(0.244086\pi\)
−0.720121 + 0.693849i \(0.755914\pi\)
\(674\) −28.0000 −1.07852
\(675\) 4.00000 + 3.00000i 0.153960 + 0.115470i
\(676\) 23.0000 0.884615
\(677\) 2.00000i 0.0768662i −0.999261 0.0384331i \(-0.987763\pi\)
0.999261 0.0384331i \(-0.0122367\pi\)
\(678\) 6.00000i 0.230429i
\(679\) 16.0000 0.614024
\(680\) 4.00000 2.00000i 0.153393 0.0766965i
\(681\) 28.0000 1.07296
\(682\) 16.0000i 0.612672i
\(683\) 4.00000i 0.153056i −0.997067 0.0765279i \(-0.975617\pi\)
0.997067 0.0765279i \(-0.0243834\pi\)
\(684\) 0 0
\(685\) −18.0000 36.0000i −0.687745 1.37549i
\(686\) 20.0000 0.763604
\(687\) 10.0000i 0.381524i
\(688\) 4.00000i 0.152499i
\(689\) −36.0000 −1.37149
\(690\) 4.00000 + 8.00000i 0.152277 + 0.304555i
\(691\) −8.00000 −0.304334 −0.152167 0.988355i \(-0.548625\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(692\) 14.0000i 0.532200i
\(693\) 4.00000i 0.151947i
\(694\) 12.0000 0.455514
\(695\) −40.0000 + 20.0000i −1.51729 + 0.758643i
\(696\) 0 0
\(697\) 4.00000i 0.151511i
\(698\) 10.0000i 0.378506i
\(699\) −14.0000 −0.529529
\(700\) 8.00000 + 6.00000i 0.302372 + 0.226779i
\(701\) 32.0000 1.20862 0.604312 0.796748i \(-0.293448\pi\)
0.604312 + 0.796748i \(0.293448\pi\)
\(702\) 6.00000i 0.226455i
\(703\) 0 0
\(704\) −2.00000 −0.0753778
\(705\) −16.0000 + 8.00000i −0.602595 + 0.301297i
\(706\) 14.0000 0.526897
\(707\) 16.0000i 0.601742i
\(708\) 10.0000i 0.375823i
\(709\) −30.0000 −1.12667 −0.563337 0.826227i \(-0.690483\pi\)
−0.563337 + 0.826227i \(0.690483\pi\)
\(710\) −12.0000 24.0000i −0.450352 0.900704i
\(711\) 0 0
\(712\) 10.0000i 0.374766i
\(713\) 32.0000i 1.19841i
\(714\) −4.00000 −0.149696
\(715\) −12.0000 24.0000i −0.448775 0.897549i
\(716\) 10.0000 0.373718
\(717\) 20.0000i 0.746914i
\(718\) 0 0
\(719\) 40.0000 1.49175 0.745874 0.666087i \(-0.232032\pi\)
0.745874 + 0.666087i \(0.232032\pi\)
\(720\) 2.00000 1.00000i 0.0745356 0.0372678i
\(721\) −28.0000 −1.04277
\(722\) 19.0000i 0.707107i
\(723\) 22.0000i 0.818189i
\(724\) −2.00000 −0.0743294
\(725\) 0 0
\(726\) −7.00000 −0.259794
\(727\) 18.0000i 0.667583i 0.942647 + 0.333792i \(0.108328\pi\)
−0.942647 + 0.333792i \(0.891672\pi\)
\(728\) 12.0000i 0.444750i
\(729\) −1.00000 −0.0370370
\(730\) −8.00000 + 4.00000i −0.296093 + 0.148047i
\(731\) −8.00000 −0.295891
\(732\) 2.00000i 0.0739221i
\(733\) 14.0000i 0.517102i −0.965998 0.258551i \(-0.916755\pi\)
0.965998 0.258551i \(-0.0832450\pi\)
\(734\) 2.00000 0.0738213
\(735\) 3.00000 + 6.00000i 0.110657 + 0.221313i
\(736\) 4.00000 0.147442
\(737\) 16.0000i 0.589368i
\(738\) 2.00000i 0.0736210i
\(739\) −40.0000 −1.47142 −0.735712 0.677295i \(-0.763152\pi\)
−0.735712 + 0.677295i \(0.763152\pi\)
\(740\) −2.00000 4.00000i −0.0735215 0.147043i
\(741\) 0 0
\(742\) 12.0000i 0.440534i
\(743\) 24.0000i 0.880475i −0.897881 0.440237i \(-0.854894\pi\)
0.897881 0.440237i \(-0.145106\pi\)
\(744\) 8.00000 0.293294
\(745\) −40.0000 + 20.0000i −1.46549 + 0.732743i
\(746\) −6.00000 −0.219676
\(747\) 4.00000i 0.146352i
\(748\) 4.00000i 0.146254i
\(749\) −24.0000 −0.876941
\(750\) −2.00000 + 11.0000i −0.0730297 + 0.401663i
\(751\) 32.0000 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 18.0000i 0.655956i
\(754\) 0 0
\(755\) 16.0000 8.00000i 0.582300 0.291150i
\(756\) −2.00000 −0.0727393
\(757\) 2.00000i 0.0726912i −0.999339 0.0363456i \(-0.988428\pi\)
0.999339 0.0363456i \(-0.0115717\pi\)
\(758\) 20.0000i 0.726433i
\(759\) −8.00000 −0.290382
\(760\) 0 0
\(761\) −18.0000 −0.652499 −0.326250 0.945284i \(-0.605785\pi\)
−0.326250 + 0.945284i \(0.605785\pi\)
\(762\) 2.00000i 0.0724524i
\(763\) 20.0000i 0.724049i
\(764\) −12.0000 −0.434145
\(765\) −2.00000 4.00000i −0.0723102 0.144620i
\(766\) −16.0000 −0.578103
\(767\) 60.0000i 2.16647i
\(768\) 1.00000i 0.0360844i
\(769\) 30.0000 1.08183 0.540914 0.841078i \(-0.318079\pi\)
0.540914 + 0.841078i \(0.318079\pi\)
\(770\) −8.00000 + 4.00000i −0.288300 + 0.144150i
\(771\) 18.0000 0.648254
\(772\) 4.00000i 0.143963i
\(773\) 54.0000i 1.94225i −0.238581 0.971123i \(-0.576682\pi\)
0.238581 0.971123i \(-0.423318\pi\)
\(774\) −4.00000 −0.143777
\(775\) −24.0000 + 32.0000i −0.862105 + 1.14947i
\(776\) 8.00000 0.287183
\(777\) 4.00000i 0.143499i
\(778\) 20.0000i 0.717035i
\(779\) 0 0
\(780\) 12.0000 6.00000i 0.429669 0.214834i
\(781\) 24.0000 0.858788
\(782\) 8.00000i 0.286079i
\(783\) 0 0
\(784\) 3.00000 0.107143
\(785\) 22.0000 + 44.0000i 0.785214 + 1.57043i
\(786\) −18.0000 −0.642039
\(787\) 32.0000i 1.14068i −0.821410 0.570338i \(-0.806812\pi\)
0.821410 0.570338i \(-0.193188\pi\)
\(788\) 22.0000i 0.783718i
\(789\) −4.00000 −0.142404
\(790\) 0 0
\(791\) 12.0000 0.426671
\(792\) 2.00000i 0.0710669i
\(793\) 12.0000i 0.426132i
\(794\) 2.00000 0.0709773
\(795\) −12.0000 + 6.00000i −0.425596 + 0.212798i
\(796\) 0 0
\(797\) 2.00000i 0.0708436i −0.999372 0.0354218i \(-0.988723\pi\)
0.999372 0.0354218i \(-0.0112775\pi\)
\(798\) 0 0
\(799\) 16.0000 0.566039
\(800\) 4.00000 + 3.00000i 0.141421 + 0.106066i
\(801\) −10.0000 −0.353333