Properties

Label 338.2.e.c.23.1
Level $338$
Weight $2$
Character 338.23
Analytic conductor $2.699$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 338 = 2 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 338.e (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.69894358832\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 26)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 23.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 338.23
Dual form 338.2.e.c.147.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(2.59808 + 1.50000i) q^{7} +1.00000i q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(2.59808 + 1.50000i) q^{7} +1.00000i q^{8} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{10} +1.00000 q^{12} -3.00000 q^{14} +(-2.59808 + 1.50000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +2.00000i q^{18} +(-5.19615 - 3.00000i) q^{19} +(2.59808 + 1.50000i) q^{20} +3.00000i q^{21} +(3.00000 + 5.19615i) q^{23} +(-0.866025 + 0.500000i) q^{24} -4.00000 q^{25} +5.00000 q^{27} +(2.59808 - 1.50000i) q^{28} +(1.50000 - 2.59808i) q^{30} +(0.866025 + 0.500000i) q^{32} -3.00000i q^{34} +(-4.50000 + 7.79423i) q^{35} +(-1.00000 - 1.73205i) q^{36} +(-2.59808 + 1.50000i) q^{37} +6.00000 q^{38} -3.00000 q^{40} +(-1.50000 - 2.59808i) q^{42} +(0.500000 - 0.866025i) q^{43} +(5.19615 + 3.00000i) q^{45} +(-5.19615 - 3.00000i) q^{46} -3.00000i q^{47} +(0.500000 - 0.866025i) q^{48} +(1.00000 + 1.73205i) q^{49} +(3.46410 - 2.00000i) q^{50} -3.00000 q^{51} -6.00000 q^{53} +(-4.33013 + 2.50000i) q^{54} +(-1.50000 + 2.59808i) q^{56} -6.00000i q^{57} +(-5.19615 - 3.00000i) q^{59} +3.00000i q^{60} +(4.00000 - 6.92820i) q^{61} +(5.19615 - 3.00000i) q^{63} -1.00000 q^{64} +(10.3923 - 6.00000i) q^{67} +(1.50000 + 2.59808i) q^{68} +(-3.00000 + 5.19615i) q^{69} -9.00000i q^{70} +(12.9904 + 7.50000i) q^{71} +(1.73205 + 1.00000i) q^{72} -6.00000i q^{73} +(1.50000 - 2.59808i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(-5.19615 + 3.00000i) q^{76} +10.0000 q^{79} +(2.59808 - 1.50000i) q^{80} +(-0.500000 - 0.866025i) q^{81} -6.00000i q^{83} +(2.59808 + 1.50000i) q^{84} +(-7.79423 - 4.50000i) q^{85} +1.00000i q^{86} +(5.19615 - 3.00000i) q^{89} -6.00000 q^{90} +6.00000 q^{92} +(1.50000 + 2.59808i) q^{94} +(9.00000 - 15.5885i) q^{95} +1.00000i q^{96} +(-10.3923 - 6.00000i) q^{97} +(-1.73205 - 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} + 2 q^{4} + 4 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{3} + 2 q^{4} + 4 q^{9} - 6 q^{10} + 4 q^{12} - 12 q^{14} - 2 q^{16} - 6 q^{17} + 12 q^{23} - 16 q^{25} + 20 q^{27} + 6 q^{30} - 18 q^{35} - 4 q^{36} + 24 q^{38} - 12 q^{40} - 6 q^{42} + 2 q^{43} + 2 q^{48} + 4 q^{49} - 12 q^{51} - 24 q^{53} - 6 q^{56} + 16 q^{61} - 4 q^{64} + 6 q^{68} - 12 q^{69} + 6 q^{74} - 8 q^{75} + 40 q^{79} - 2 q^{81} - 24 q^{90} + 24 q^{92} + 6 q^{94} + 36 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/338\mathbb{Z}\right)^\times\).

\(n\) \(171\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i 0.973494 0.228714i \(-0.0734519\pi\)
−0.684819 + 0.728714i \(0.740119\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 3.00000i 1.34164i 0.741620 + 0.670820i \(0.234058\pi\)
−0.741620 + 0.670820i \(0.765942\pi\)
\(6\) −0.866025 0.500000i −0.353553 0.204124i
\(7\) 2.59808 + 1.50000i 0.981981 + 0.566947i 0.902867 0.429919i \(-0.141458\pi\)
0.0791130 + 0.996866i \(0.474791\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000 1.73205i 0.333333 0.577350i
\(10\) −1.50000 2.59808i −0.474342 0.821584i
\(11\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0
\(14\) −3.00000 −0.801784
\(15\) −2.59808 + 1.50000i −0.670820 + 0.387298i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 2.00000i 0.471405i
\(19\) −5.19615 3.00000i −1.19208 0.688247i −0.233301 0.972404i \(-0.574953\pi\)
−0.958778 + 0.284157i \(0.908286\pi\)
\(20\) 2.59808 + 1.50000i 0.580948 + 0.335410i
\(21\) 3.00000i 0.654654i
\(22\) 0 0
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 2.59808 1.50000i 0.490990 0.283473i
\(29\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(30\) 1.50000 2.59808i 0.273861 0.474342i
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 3.00000i 0.514496i
\(35\) −4.50000 + 7.79423i −0.760639 + 1.31747i
\(36\) −1.00000 1.73205i −0.166667 0.288675i
\(37\) −2.59808 + 1.50000i −0.427121 + 0.246598i −0.698119 0.715981i \(-0.745980\pi\)
0.270998 + 0.962580i \(0.412646\pi\)
\(38\) 6.00000 0.973329
\(39\) 0 0
\(40\) −3.00000 −0.474342
\(41\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(42\) −1.50000 2.59808i −0.231455 0.400892i
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) 0 0
\(45\) 5.19615 + 3.00000i 0.774597 + 0.447214i
\(46\) −5.19615 3.00000i −0.766131 0.442326i
\(47\) 3.00000i 0.437595i −0.975770 0.218797i \(-0.929787\pi\)
0.975770 0.218797i \(-0.0702134\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) 1.00000 + 1.73205i 0.142857 + 0.247436i
\(50\) 3.46410 2.00000i 0.489898 0.282843i
\(51\) −3.00000 −0.420084
\(52\) 0 0
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) −4.33013 + 2.50000i −0.589256 + 0.340207i
\(55\) 0 0
\(56\) −1.50000 + 2.59808i −0.200446 + 0.347183i
\(57\) 6.00000i 0.794719i
\(58\) 0 0
\(59\) −5.19615 3.00000i −0.676481 0.390567i 0.122047 0.992524i \(-0.461054\pi\)
−0.798528 + 0.601958i \(0.794388\pi\)
\(60\) 3.00000i 0.387298i
\(61\) 4.00000 6.92820i 0.512148 0.887066i −0.487753 0.872982i \(-0.662183\pi\)
0.999901 0.0140840i \(-0.00448323\pi\)
\(62\) 0 0
\(63\) 5.19615 3.00000i 0.654654 0.377964i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 10.3923 6.00000i 1.26962 0.733017i 0.294706 0.955588i \(-0.404778\pi\)
0.974916 + 0.222571i \(0.0714450\pi\)
\(68\) 1.50000 + 2.59808i 0.181902 + 0.315063i
\(69\) −3.00000 + 5.19615i −0.361158 + 0.625543i
\(70\) 9.00000i 1.07571i
\(71\) 12.9904 + 7.50000i 1.54167 + 0.890086i 0.998733 + 0.0503155i \(0.0160227\pi\)
0.542941 + 0.839771i \(0.317311\pi\)
\(72\) 1.73205 + 1.00000i 0.204124 + 0.117851i
\(73\) 6.00000i 0.702247i −0.936329 0.351123i \(-0.885800\pi\)
0.936329 0.351123i \(-0.114200\pi\)
\(74\) 1.50000 2.59808i 0.174371 0.302020i
\(75\) −2.00000 3.46410i −0.230940 0.400000i
\(76\) −5.19615 + 3.00000i −0.596040 + 0.344124i
\(77\) 0 0
\(78\) 0 0
\(79\) 10.0000 1.12509 0.562544 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) 2.59808 1.50000i 0.290474 0.167705i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 6.00000i 0.658586i −0.944228 0.329293i \(-0.893190\pi\)
0.944228 0.329293i \(-0.106810\pi\)
\(84\) 2.59808 + 1.50000i 0.283473 + 0.163663i
\(85\) −7.79423 4.50000i −0.845403 0.488094i
\(86\) 1.00000i 0.107833i
\(87\) 0 0
\(88\) 0 0
\(89\) 5.19615 3.00000i 0.550791 0.317999i −0.198650 0.980071i \(-0.563656\pi\)
0.749441 + 0.662071i \(0.230322\pi\)
\(90\) −6.00000 −0.632456
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 0 0
\(94\) 1.50000 + 2.59808i 0.154713 + 0.267971i
\(95\) 9.00000 15.5885i 0.923381 1.59934i
\(96\) 1.00000i 0.102062i
\(97\) −10.3923 6.00000i −1.05518 0.609208i −0.131084 0.991371i \(-0.541846\pi\)
−0.924095 + 0.382164i \(0.875179\pi\)
\(98\) −1.73205 1.00000i −0.174964 0.101015i
\(99\) 0 0
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) −6.00000 10.3923i −0.597022 1.03407i −0.993258 0.115924i \(-0.963017\pi\)
0.396236 0.918149i \(-0.370316\pi\)
\(102\) 2.59808 1.50000i 0.257248 0.148522i
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 0 0
\(105\) −9.00000 −0.878310
\(106\) 5.19615 3.00000i 0.504695 0.291386i
\(107\) 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i \(0.0302972\pi\)
−0.415432 + 0.909624i \(0.636370\pi\)
\(108\) 2.50000 4.33013i 0.240563 0.416667i
\(109\) 9.00000i 0.862044i −0.902342 0.431022i \(-0.858153\pi\)
0.902342 0.431022i \(-0.141847\pi\)
\(110\) 0 0
\(111\) −2.59808 1.50000i −0.246598 0.142374i
\(112\) 3.00000i 0.283473i
\(113\) 3.00000 5.19615i 0.282216 0.488813i −0.689714 0.724082i \(-0.742264\pi\)
0.971930 + 0.235269i \(0.0755971\pi\)
\(114\) 3.00000 + 5.19615i 0.280976 + 0.486664i
\(115\) −15.5885 + 9.00000i −1.45363 + 0.839254i
\(116\) 0 0
\(117\) 0 0
\(118\) 6.00000 0.552345
\(119\) −7.79423 + 4.50000i −0.714496 + 0.412514i
\(120\) −1.50000 2.59808i −0.136931 0.237171i
\(121\) −5.50000 + 9.52628i −0.500000 + 0.866025i
\(122\) 8.00000i 0.724286i
\(123\) 0 0
\(124\) 0 0
\(125\) 3.00000i 0.268328i
\(126\) −3.00000 + 5.19615i −0.267261 + 0.462910i
\(127\) 1.00000 + 1.73205i 0.0887357 + 0.153695i 0.906977 0.421180i \(-0.138384\pi\)
−0.818241 + 0.574875i \(0.805051\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 1.00000 0.0880451
\(130\) 0 0
\(131\) −3.00000 −0.262111 −0.131056 0.991375i \(-0.541837\pi\)
−0.131056 + 0.991375i \(0.541837\pi\)
\(132\) 0 0
\(133\) −9.00000 15.5885i −0.780399 1.35169i
\(134\) −6.00000 + 10.3923i −0.518321 + 0.897758i
\(135\) 15.0000i 1.29099i
\(136\) −2.59808 1.50000i −0.222783 0.128624i
\(137\) 15.5885 + 9.00000i 1.33181 + 0.768922i 0.985577 0.169226i \(-0.0541268\pi\)
0.346235 + 0.938148i \(0.387460\pi\)
\(138\) 6.00000i 0.510754i
\(139\) −2.50000 + 4.33013i −0.212047 + 0.367277i −0.952355 0.304991i \(-0.901346\pi\)
0.740308 + 0.672268i \(0.234680\pi\)
\(140\) 4.50000 + 7.79423i 0.380319 + 0.658733i
\(141\) 2.59808 1.50000i 0.218797 0.126323i
\(142\) −15.0000 −1.25877
\(143\) 0 0
\(144\) −2.00000 −0.166667
\(145\) 0 0
\(146\) 3.00000 + 5.19615i 0.248282 + 0.430037i
\(147\) −1.00000 + 1.73205i −0.0824786 + 0.142857i
\(148\) 3.00000i 0.246598i
\(149\) −5.19615 3.00000i −0.425685 0.245770i 0.271821 0.962348i \(-0.412374\pi\)
−0.697507 + 0.716578i \(0.745707\pi\)
\(150\) 3.46410 + 2.00000i 0.282843 + 0.163299i
\(151\) 15.0000i 1.22068i 0.792139 + 0.610341i \(0.208968\pi\)
−0.792139 + 0.610341i \(0.791032\pi\)
\(152\) 3.00000 5.19615i 0.243332 0.421464i
\(153\) 3.00000 + 5.19615i 0.242536 + 0.420084i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −22.0000 −1.75579 −0.877896 0.478852i \(-0.841053\pi\)
−0.877896 + 0.478852i \(0.841053\pi\)
\(158\) −8.66025 + 5.00000i −0.688973 + 0.397779i
\(159\) −3.00000 5.19615i −0.237915 0.412082i
\(160\) −1.50000 + 2.59808i −0.118585 + 0.205396i
\(161\) 18.0000i 1.41860i
\(162\) 0.866025 + 0.500000i 0.0680414 + 0.0392837i
\(163\) 5.19615 + 3.00000i 0.406994 + 0.234978i 0.689497 0.724288i \(-0.257831\pi\)
−0.282503 + 0.959266i \(0.591165\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 3.00000 + 5.19615i 0.232845 + 0.403300i
\(167\) 10.3923 6.00000i 0.804181 0.464294i −0.0407502 0.999169i \(-0.512975\pi\)
0.844931 + 0.534875i \(0.179641\pi\)
\(168\) −3.00000 −0.231455
\(169\) 0 0
\(170\) 9.00000 0.690268
\(171\) −10.3923 + 6.00000i −0.794719 + 0.458831i
\(172\) −0.500000 0.866025i −0.0381246 0.0660338i
\(173\) 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) 0 0
\(175\) −10.3923 6.00000i −0.785584 0.453557i
\(176\) 0 0
\(177\) 6.00000i 0.450988i
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) −7.50000 12.9904i −0.560576 0.970947i −0.997446 0.0714220i \(-0.977246\pi\)
0.436870 0.899525i \(-0.356087\pi\)
\(180\) 5.19615 3.00000i 0.387298 0.223607i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) 8.00000 0.591377
\(184\) −5.19615 + 3.00000i −0.383065 + 0.221163i
\(185\) −4.50000 7.79423i −0.330847 0.573043i
\(186\) 0 0
\(187\) 0 0
\(188\) −2.59808 1.50000i −0.189484 0.109399i
\(189\) 12.9904 + 7.50000i 0.944911 + 0.545545i
\(190\) 18.0000i 1.30586i
\(191\) −6.00000 + 10.3923i −0.434145 + 0.751961i −0.997225 0.0744412i \(-0.976283\pi\)
0.563081 + 0.826402i \(0.309616\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −5.19615 + 3.00000i −0.374027 + 0.215945i −0.675216 0.737620i \(-0.735950\pi\)
0.301189 + 0.953564i \(0.402616\pi\)
\(194\) 12.0000 0.861550
\(195\) 0 0
\(196\) 2.00000 0.142857
\(197\) −2.59808 + 1.50000i −0.185105 + 0.106871i −0.589689 0.807630i \(-0.700750\pi\)
0.404584 + 0.914501i \(0.367416\pi\)
\(198\) 0 0
\(199\) 10.0000 17.3205i 0.708881 1.22782i −0.256391 0.966573i \(-0.582534\pi\)
0.965272 0.261245i \(-0.0841331\pi\)
\(200\) 4.00000i 0.282843i
\(201\) 10.3923 + 6.00000i 0.733017 + 0.423207i
\(202\) 10.3923 + 6.00000i 0.731200 + 0.422159i
\(203\) 0 0
\(204\) −1.50000 + 2.59808i −0.105021 + 0.181902i
\(205\) 0 0
\(206\) −12.1244 + 7.00000i −0.844744 + 0.487713i
\(207\) 12.0000 0.834058
\(208\) 0 0
\(209\) 0 0
\(210\) 7.79423 4.50000i 0.537853 0.310530i
\(211\) 11.5000 + 19.9186i 0.791693 + 1.37125i 0.924918 + 0.380166i \(0.124133\pi\)
−0.133226 + 0.991086i \(0.542533\pi\)
\(212\) −3.00000 + 5.19615i −0.206041 + 0.356873i
\(213\) 15.0000i 1.02778i
\(214\) −10.3923 6.00000i −0.710403 0.410152i
\(215\) 2.59808 + 1.50000i 0.177187 + 0.102299i
\(216\) 5.00000i 0.340207i
\(217\) 0 0
\(218\) 4.50000 + 7.79423i 0.304778 + 0.527892i
\(219\) 5.19615 3.00000i 0.351123 0.202721i
\(220\) 0 0
\(221\) 0 0
\(222\) 3.00000 0.201347
\(223\) 7.79423 4.50000i 0.521940 0.301342i −0.215788 0.976440i \(-0.569232\pi\)
0.737728 + 0.675098i \(0.235899\pi\)
\(224\) 1.50000 + 2.59808i 0.100223 + 0.173591i
\(225\) −4.00000 + 6.92820i −0.266667 + 0.461880i
\(226\) 6.00000i 0.399114i
\(227\) −10.3923 6.00000i −0.689761 0.398234i 0.113761 0.993508i \(-0.463710\pi\)
−0.803523 + 0.595274i \(0.797043\pi\)
\(228\) −5.19615 3.00000i −0.344124 0.198680i
\(229\) 9.00000i 0.594737i −0.954763 0.297368i \(-0.903891\pi\)
0.954763 0.297368i \(-0.0961089\pi\)
\(230\) 9.00000 15.5885i 0.593442 1.02787i
\(231\) 0 0
\(232\) 0 0
\(233\) −21.0000 −1.37576 −0.687878 0.725826i \(-0.741458\pi\)
−0.687878 + 0.725826i \(0.741458\pi\)
\(234\) 0 0
\(235\) 9.00000 0.587095
\(236\) −5.19615 + 3.00000i −0.338241 + 0.195283i
\(237\) 5.00000 + 8.66025i 0.324785 + 0.562544i
\(238\) 4.50000 7.79423i 0.291692 0.505225i
\(239\) 9.00000i 0.582162i −0.956698 0.291081i \(-0.905985\pi\)
0.956698 0.291081i \(-0.0940149\pi\)
\(240\) 2.59808 + 1.50000i 0.167705 + 0.0968246i
\(241\) −25.9808 15.0000i −1.67357 0.966235i −0.965615 0.259975i \(-0.916286\pi\)
−0.707953 0.706260i \(-0.750381\pi\)
\(242\) 11.0000i 0.707107i
\(243\) 8.00000 13.8564i 0.513200 0.888889i
\(244\) −4.00000 6.92820i −0.256074 0.443533i
\(245\) −5.19615 + 3.00000i −0.331970 + 0.191663i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 5.19615 3.00000i 0.329293 0.190117i
\(250\) −1.50000 2.59808i −0.0948683 0.164317i
\(251\) −6.00000 + 10.3923i −0.378717 + 0.655956i −0.990876 0.134778i \(-0.956968\pi\)
0.612159 + 0.790735i \(0.290301\pi\)
\(252\) 6.00000i 0.377964i
\(253\) 0 0
\(254\) −1.73205 1.00000i −0.108679 0.0627456i
\(255\) 9.00000i 0.563602i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −1.50000 2.59808i −0.0935674 0.162064i 0.815442 0.578838i \(-0.196494\pi\)
−0.909010 + 0.416775i \(0.863160\pi\)
\(258\) −0.866025 + 0.500000i −0.0539164 + 0.0311286i
\(259\) −9.00000 −0.559233
\(260\) 0 0
\(261\) 0 0
\(262\) 2.59808 1.50000i 0.160510 0.0926703i
\(263\) −12.0000 20.7846i −0.739952 1.28163i −0.952517 0.304487i \(-0.901515\pi\)
0.212565 0.977147i \(-0.431818\pi\)
\(264\) 0 0
\(265\) 18.0000i 1.10573i
\(266\) 15.5885 + 9.00000i 0.955790 + 0.551825i
\(267\) 5.19615 + 3.00000i 0.317999 + 0.183597i
\(268\) 12.0000i 0.733017i
\(269\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) −7.50000 12.9904i −0.456435 0.790569i
\(271\) −12.9904 + 7.50000i −0.789109 + 0.455593i −0.839649 0.543130i \(-0.817239\pi\)
0.0505395 + 0.998722i \(0.483906\pi\)
\(272\) 3.00000 0.181902
\(273\) 0 0
\(274\) −18.0000 −1.08742
\(275\) 0 0
\(276\) 3.00000 + 5.19615i 0.180579 + 0.312772i
\(277\) −4.00000 + 6.92820i −0.240337 + 0.416275i −0.960810 0.277207i \(-0.910591\pi\)
0.720473 + 0.693482i \(0.243925\pi\)
\(278\) 5.00000i 0.299880i
\(279\) 0 0
\(280\) −7.79423 4.50000i −0.465794 0.268926i
\(281\) 30.0000i 1.78965i 0.446417 + 0.894825i \(0.352700\pi\)
−0.446417 + 0.894825i \(0.647300\pi\)
\(282\) −1.50000 + 2.59808i −0.0893237 + 0.154713i
\(283\) −2.00000 3.46410i −0.118888 0.205919i 0.800439 0.599414i \(-0.204600\pi\)
−0.919327 + 0.393494i \(0.871266\pi\)
\(284\) 12.9904 7.50000i 0.770837 0.445043i
\(285\) 18.0000 1.06623
\(286\) 0 0
\(287\) 0 0
\(288\) 1.73205 1.00000i 0.102062 0.0589256i
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 0 0
\(291\) 12.0000i 0.703452i
\(292\) −5.19615 3.00000i −0.304082 0.175562i
\(293\) −7.79423 4.50000i −0.455344 0.262893i 0.254741 0.967009i \(-0.418010\pi\)
−0.710084 + 0.704117i \(0.751343\pi\)
\(294\) 2.00000i 0.116642i
\(295\) 9.00000 15.5885i 0.524000 0.907595i
\(296\) −1.50000 2.59808i −0.0871857 0.151010i
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) 0 0
\(300\) −4.00000 −0.230940
\(301\) 2.59808 1.50000i 0.149751 0.0864586i
\(302\) −7.50000 12.9904i −0.431577 0.747512i
\(303\) 6.00000 10.3923i 0.344691 0.597022i
\(304\) 6.00000i 0.344124i
\(305\) 20.7846 + 12.0000i 1.19012 + 0.687118i
\(306\) −5.19615 3.00000i −0.297044 0.171499i
\(307\) 18.0000i 1.02731i −0.857996 0.513657i \(-0.828290\pi\)
0.857996 0.513657i \(-0.171710\pi\)
\(308\) 0 0
\(309\) 7.00000 + 12.1244i 0.398216 + 0.689730i
\(310\) 0 0
\(311\) −18.0000 −1.02069 −0.510343 0.859971i \(-0.670482\pi\)
−0.510343 + 0.859971i \(0.670482\pi\)
\(312\) 0 0
\(313\) 19.0000 1.07394 0.536972 0.843600i \(-0.319568\pi\)
0.536972 + 0.843600i \(0.319568\pi\)
\(314\) 19.0526 11.0000i 1.07520 0.620766i
\(315\) 9.00000 + 15.5885i 0.507093 + 0.878310i
\(316\) 5.00000 8.66025i 0.281272 0.487177i
\(317\) 18.0000i 1.01098i −0.862832 0.505490i \(-0.831312\pi\)
0.862832 0.505490i \(-0.168688\pi\)
\(318\) 5.19615 + 3.00000i 0.291386 + 0.168232i
\(319\) 0 0
\(320\) 3.00000i 0.167705i
\(321\) −6.00000 + 10.3923i −0.334887 + 0.580042i
\(322\) −9.00000 15.5885i −0.501550 0.868711i
\(323\) 15.5885 9.00000i 0.867365 0.500773i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −6.00000 −0.332309
\(327\) 7.79423 4.50000i 0.431022 0.248851i
\(328\) 0 0
\(329\) 4.50000 7.79423i 0.248093 0.429710i
\(330\) 0 0
\(331\) 25.9808 + 15.0000i 1.42803 + 0.824475i 0.996965 0.0778456i \(-0.0248041\pi\)
0.431066 + 0.902320i \(0.358137\pi\)
\(332\) −5.19615 3.00000i −0.285176 0.164646i
\(333\) 6.00000i 0.328798i
\(334\) −6.00000 + 10.3923i −0.328305 + 0.568642i
\(335\) 18.0000 + 31.1769i 0.983445 + 1.70338i
\(336\) 2.59808 1.50000i 0.141737 0.0818317i
\(337\) 13.0000 0.708155 0.354078 0.935216i \(-0.384795\pi\)
0.354078 + 0.935216i \(0.384795\pi\)
\(338\) 0 0
\(339\) 6.00000 0.325875
\(340\) −7.79423 + 4.50000i −0.422701 + 0.244047i
\(341\) 0 0
\(342\) 6.00000 10.3923i 0.324443 0.561951i
\(343\) 15.0000i 0.809924i
\(344\) 0.866025 + 0.500000i 0.0466930 + 0.0269582i
\(345\) −15.5885 9.00000i −0.839254 0.484544i
\(346\) 6.00000i 0.322562i
\(347\) −16.5000 + 28.5788i −0.885766 + 1.53419i −0.0409337 + 0.999162i \(0.513033\pi\)
−0.844833 + 0.535031i \(0.820300\pi\)
\(348\) 0 0
\(349\) 18.1865 10.5000i 0.973503 0.562052i 0.0732005 0.997317i \(-0.476679\pi\)
0.900302 + 0.435265i \(0.143345\pi\)
\(350\) 12.0000 0.641427
\(351\) 0 0
\(352\) 0 0
\(353\) −5.19615 + 3.00000i −0.276563 + 0.159674i −0.631867 0.775077i \(-0.717711\pi\)
0.355303 + 0.934751i \(0.384378\pi\)
\(354\) 3.00000 + 5.19615i 0.159448 + 0.276172i
\(355\) −22.5000 + 38.9711i −1.19418 + 2.06837i
\(356\) 6.00000i 0.317999i
\(357\) −7.79423 4.50000i −0.412514 0.238165i
\(358\) 12.9904 + 7.50000i 0.686563 + 0.396387i
\(359\) 24.0000i 1.26667i −0.773877 0.633336i \(-0.781685\pi\)
0.773877 0.633336i \(-0.218315\pi\)
\(360\) −3.00000 + 5.19615i −0.158114 + 0.273861i
\(361\) 8.50000 + 14.7224i 0.447368 + 0.774865i
\(362\) −1.73205 + 1.00000i −0.0910346 + 0.0525588i
\(363\) −11.0000 −0.577350
\(364\) 0 0
\(365\) 18.0000 0.942163
\(366\) −6.92820 + 4.00000i −0.362143 + 0.209083i
\(367\) −4.00000 6.92820i −0.208798 0.361649i 0.742538 0.669804i \(-0.233622\pi\)
−0.951336 + 0.308155i \(0.900289\pi\)
\(368\) 3.00000 5.19615i 0.156386 0.270868i
\(369\) 0 0
\(370\) 7.79423 + 4.50000i 0.405203 + 0.233944i
\(371\) −15.5885 9.00000i −0.809312 0.467257i
\(372\) 0 0
\(373\) −2.00000 + 3.46410i −0.103556 + 0.179364i −0.913147 0.407630i \(-0.866355\pi\)
0.809591 + 0.586994i \(0.199689\pi\)
\(374\) 0 0
\(375\) −2.59808 + 1.50000i −0.134164 + 0.0774597i
\(376\) 3.00000 0.154713
\(377\) 0 0
\(378\) −15.0000 −0.771517
\(379\) 5.19615 3.00000i 0.266908 0.154100i −0.360573 0.932731i \(-0.617419\pi\)
0.627482 + 0.778631i \(0.284086\pi\)
\(380\) −9.00000 15.5885i −0.461690 0.799671i
\(381\) −1.00000 + 1.73205i −0.0512316 + 0.0887357i
\(382\) 12.0000i 0.613973i
\(383\) −7.79423 4.50000i −0.398266 0.229939i 0.287469 0.957790i \(-0.407186\pi\)
−0.685736 + 0.727851i \(0.740519\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) 3.00000 5.19615i 0.152696 0.264477i
\(387\) −1.00000 1.73205i −0.0508329 0.0880451i
\(388\) −10.3923 + 6.00000i −0.527589 + 0.304604i
\(389\) −30.0000 −1.52106 −0.760530 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) 0 0
\(391\) −18.0000 −0.910299
\(392\) −1.73205 + 1.00000i −0.0874818 + 0.0505076i
\(393\) −1.50000 2.59808i −0.0756650 0.131056i
\(394\) 1.50000 2.59808i 0.0755689 0.130889i
\(395\) 30.0000i 1.50946i
\(396\) 0 0
\(397\) 15.5885 + 9.00000i 0.782362 + 0.451697i 0.837267 0.546795i \(-0.184152\pi\)
−0.0549046 + 0.998492i \(0.517485\pi\)
\(398\) 20.0000i 1.00251i
\(399\) 9.00000 15.5885i 0.450564 0.780399i
\(400\) 2.00000 + 3.46410i 0.100000 + 0.173205i
\(401\) −25.9808 + 15.0000i −1.29742 + 0.749064i −0.979957 0.199207i \(-0.936163\pi\)
−0.317460 + 0.948272i \(0.602830\pi\)
\(402\) −12.0000 −0.598506
\(403\) 0 0
\(404\) −12.0000 −0.597022
\(405\) 2.59808 1.50000i 0.129099 0.0745356i
\(406\) 0 0
\(407\) 0 0
\(408\) 3.00000i 0.148522i
\(409\) −5.19615 3.00000i −0.256933 0.148340i 0.366002 0.930614i \(-0.380726\pi\)
−0.622935 + 0.782274i \(0.714060\pi\)
\(410\) 0 0
\(411\) 18.0000i 0.887875i
\(412\) 7.00000 12.1244i 0.344865 0.597324i
\(413\) −9.00000 15.5885i −0.442861 0.767058i
\(414\) −10.3923 + 6.00000i −0.510754 + 0.294884i
\(415\) 18.0000 0.883585
\(416\) 0 0
\(417\) −5.00000 −0.244851
\(418\) 0 0
\(419\) −7.50000 12.9904i −0.366399 0.634622i 0.622601 0.782540i \(-0.286076\pi\)
−0.989000 + 0.147918i \(0.952743\pi\)
\(420\) −4.50000 + 7.79423i −0.219578 + 0.380319i
\(421\) 15.0000i 0.731055i 0.930800 + 0.365528i \(0.119111\pi\)
−0.930800 + 0.365528i \(0.880889\pi\)
\(422\) −19.9186 11.5000i −0.969622 0.559811i
\(423\) −5.19615 3.00000i −0.252646 0.145865i
\(424\) 6.00000i 0.291386i
\(425\) 6.00000 10.3923i 0.291043 0.504101i
\(426\) −7.50000 12.9904i −0.363376 0.629386i
\(427\) 20.7846 12.0000i 1.00584 0.580721i
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) −3.00000 −0.144673
\(431\) 12.9904 7.50000i 0.625725 0.361262i −0.153370 0.988169i \(-0.549013\pi\)
0.779094 + 0.626907i \(0.215679\pi\)
\(432\) −2.50000 4.33013i −0.120281 0.208333i
\(433\) 5.50000 9.52628i 0.264313 0.457804i −0.703070 0.711120i \(-0.748188\pi\)
0.967383 + 0.253317i \(0.0815214\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −7.79423 4.50000i −0.373276 0.215511i
\(437\) 36.0000i 1.72211i
\(438\) −3.00000 + 5.19615i −0.143346 + 0.248282i
\(439\) 5.00000 + 8.66025i 0.238637 + 0.413331i 0.960323 0.278889i \(-0.0899661\pi\)
−0.721686 + 0.692220i \(0.756633\pi\)
\(440\) 0 0
\(441\) 4.00000 0.190476
\(442\) 0 0
\(443\) −21.0000 −0.997740 −0.498870 0.866677i \(-0.666252\pi\)
−0.498870 + 0.866677i \(0.666252\pi\)
\(444\) −2.59808 + 1.50000i −0.123299 + 0.0711868i
\(445\) 9.00000 + 15.5885i 0.426641 + 0.738964i
\(446\) −4.50000 + 7.79423i −0.213081 + 0.369067i
\(447\) 6.00000i 0.283790i
\(448\) −2.59808 1.50000i −0.122748 0.0708683i
\(449\) 20.7846 + 12.0000i 0.980886 + 0.566315i 0.902538 0.430611i \(-0.141702\pi\)
0.0783487 + 0.996926i \(0.475035\pi\)
\(450\) 8.00000i 0.377124i
\(451\) 0 0
\(452\) −3.00000 5.19615i −0.141108 0.244406i
\(453\) −12.9904 + 7.50000i −0.610341 + 0.352381i
\(454\) 12.0000 0.563188
\(455\) 0 0
\(456\) 6.00000 0.280976
\(457\) −15.5885 + 9.00000i −0.729197 + 0.421002i −0.818128 0.575036i \(-0.804988\pi\)
0.0889312 + 0.996038i \(0.471655\pi\)
\(458\) 4.50000 + 7.79423i 0.210271 + 0.364200i
\(459\) −7.50000 + 12.9904i −0.350070 + 0.606339i
\(460\) 18.0000i 0.839254i
\(461\) −12.9904 7.50000i −0.605022 0.349310i 0.165992 0.986127i \(-0.446917\pi\)
−0.771015 + 0.636817i \(0.780251\pi\)
\(462\) 0 0
\(463\) 24.0000i 1.11537i 0.830051 + 0.557687i \(0.188311\pi\)
−0.830051 + 0.557687i \(0.811689\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 18.1865 10.5000i 0.842475 0.486403i
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) 36.0000 1.66233
\(470\) −7.79423 + 4.50000i −0.359521 + 0.207570i
\(471\) −11.0000 19.0526i −0.506853 0.877896i
\(472\) 3.00000 5.19615i 0.138086 0.239172i
\(473\) 0 0
\(474\) −8.66025 5.00000i −0.397779 0.229658i
\(475\) 20.7846 + 12.0000i 0.953663 + 0.550598i
\(476\) 9.00000i 0.412514i
\(477\) −6.00000 + 10.3923i −0.274721 + 0.475831i
\(478\) 4.50000 + 7.79423i 0.205825 + 0.356500i
\(479\) −33.7750 + 19.5000i −1.54322 + 0.890978i −0.544586 + 0.838705i \(0.683313\pi\)
−0.998633 + 0.0522726i \(0.983354\pi\)
\(480\) −3.00000 −0.136931
\(481\) 0 0
\(482\) 30.0000 1.36646
\(483\) −15.5885 + 9.00000i −0.709299 + 0.409514i
\(484\) 5.50000 + 9.52628i 0.250000 + 0.433013i
\(485\) 18.0000 31.1769i 0.817338 1.41567i
\(486\) 16.0000i 0.725775i
\(487\) −10.3923 6.00000i −0.470920 0.271886i 0.245705 0.969345i \(-0.420981\pi\)
−0.716625 + 0.697459i \(0.754314\pi\)
\(488\) 6.92820 + 4.00000i 0.313625 + 0.181071i
\(489\) 6.00000i 0.271329i
\(490\) 3.00000 5.19615i 0.135526 0.234738i
\(491\) −13.5000 23.3827i −0.609246 1.05525i −0.991365 0.131132i \(-0.958139\pi\)
0.382118 0.924113i \(-0.375195\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 22.5000 + 38.9711i 1.00926 + 1.74809i
\(498\) −3.00000 + 5.19615i −0.134433 + 0.232845i
\(499\) 36.0000i 1.61158i 0.592200 + 0.805791i \(0.298259\pi\)
−0.592200 + 0.805791i \(0.701741\pi\)
\(500\) 2.59808 + 1.50000i 0.116190 + 0.0670820i
\(501\) 10.3923 + 6.00000i 0.464294 + 0.268060i
\(502\) 12.0000i 0.535586i
\(503\) 3.00000 5.19615i 0.133763 0.231685i −0.791361 0.611349i \(-0.790627\pi\)
0.925124 + 0.379664i \(0.123960\pi\)
\(504\) 3.00000 + 5.19615i 0.133631 + 0.231455i
\(505\) 31.1769 18.0000i 1.38735 0.800989i
\(506\) 0 0
\(507\) 0 0
\(508\) 2.00000 0.0887357
\(509\) 5.19615 3.00000i 0.230315 0.132973i −0.380402 0.924821i \(-0.624214\pi\)
0.610718 + 0.791849i \(0.290881\pi\)
\(510\) 4.50000 + 7.79423i 0.199263 + 0.345134i
\(511\) 9.00000 15.5885i 0.398137 0.689593i
\(512\) 1.00000i 0.0441942i
\(513\) −25.9808 15.0000i −1.14708 0.662266i
\(514\) 2.59808 + 1.50000i 0.114596 + 0.0661622i
\(515\) 42.0000i 1.85074i
\(516\) 0.500000 0.866025i 0.0220113 0.0381246i
\(517\) 0 0
\(518\) 7.79423 4.50000i 0.342459 0.197719i
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) 27.0000 1.18289 0.591446 0.806345i \(-0.298557\pi\)
0.591446 + 0.806345i \(0.298557\pi\)
\(522\) 0 0
\(523\) 8.00000 + 13.8564i 0.349816 + 0.605898i 0.986216 0.165460i \(-0.0529109\pi\)
−0.636401 + 0.771358i \(0.719578\pi\)
\(524\) −1.50000 + 2.59808i −0.0655278 + 0.113497i
\(525\) 12.0000i 0.523723i
\(526\) 20.7846 + 12.0000i 0.906252 + 0.523225i
\(527\) 0 0
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 9.00000 + 15.5885i 0.390935 + 0.677119i
\(531\) −10.3923 + 6.00000i −0.450988 + 0.260378i
\(532\) −18.0000 −0.780399
\(533\) 0 0
\(534\) −6.00000 −0.259645
\(535\) −31.1769 + 18.0000i −1.34790 + 0.778208i
\(536\) 6.00000 + 10.3923i 0.259161 + 0.448879i
\(537\) 7.50000 12.9904i 0.323649 0.560576i
\(538\) 0 0
\(539\) 0 0
\(540\) 12.9904 + 7.50000i 0.559017 + 0.322749i
\(541\) 15.0000i 0.644900i 0.946586 + 0.322450i \(0.104506\pi\)
−0.946586 + 0.322450i \(0.895494\pi\)
\(542\) 7.50000 12.9904i 0.322153 0.557985i
\(543\) 1.00000 + 1.73205i 0.0429141 + 0.0743294i
\(544\) −2.59808 + 1.50000i −0.111392 + 0.0643120i
\(545\) 27.0000 1.15655
\(546\) 0 0
\(547\) −37.0000 −1.58201 −0.791003 0.611812i \(-0.790441\pi\)
−0.791003 + 0.611812i \(0.790441\pi\)
\(548\) 15.5885 9.00000i 0.665906 0.384461i
\(549\) −8.00000 13.8564i −0.341432 0.591377i
\(550\) 0 0
\(551\) 0 0
\(552\) −5.19615 3.00000i −0.221163 0.127688i
\(553\) 25.9808 + 15.0000i 1.10481 + 0.637865i
\(554\) 8.00000i 0.339887i
\(555\) 4.50000 7.79423i 0.191014 0.330847i
\(556\) 2.50000 + 4.33013i 0.106024 + 0.183638i
\(557\) 23.3827 13.5000i 0.990756 0.572013i 0.0852559 0.996359i \(-0.472829\pi\)
0.905500 + 0.424346i \(0.139496\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 9.00000 0.380319
\(561\) 0 0
\(562\) −15.0000 25.9808i −0.632737 1.09593i
\(563\) −19.5000 + 33.7750i −0.821827 + 1.42345i 0.0824933 + 0.996592i \(0.473712\pi\)
−0.904320 + 0.426855i \(0.859622\pi\)
\(564\) 3.00000i 0.126323i
\(565\) 15.5885 + 9.00000i 0.655811 + 0.378633i
\(566\) 3.46410 + 2.00000i 0.145607 + 0.0840663i
\(567\) 3.00000i 0.125988i
\(568\) −7.50000 + 12.9904i −0.314693 + 0.545064i
\(569\) −22.5000 38.9711i −0.943249 1.63376i −0.759220 0.650835i \(-0.774419\pi\)
−0.184030 0.982921i \(-0.558914\pi\)
\(570\) −15.5885 + 9.00000i −0.652929 + 0.376969i
\(571\) −23.0000 −0.962520 −0.481260 0.876578i \(-0.659821\pi\)
−0.481260 + 0.876578i \(0.659821\pi\)
\(572\) 0 0
\(573\) −12.0000 −0.501307
\(574\) 0 0
\(575\) −12.0000 20.7846i −0.500435 0.866778i
\(576\) −1.00000 + 1.73205i −0.0416667 + 0.0721688i
\(577\) 42.0000i 1.74848i 0.485491 + 0.874241i \(0.338641\pi\)
−0.485491 + 0.874241i \(0.661359\pi\)
\(578\) −6.92820 4.00000i −0.288175 0.166378i
\(579\) −5.19615 3.00000i −0.215945 0.124676i
\(580\) 0 0
\(581\) 9.00000 15.5885i 0.373383 0.646718i
\(582\) 6.00000 + 10.3923i 0.248708 + 0.430775i
\(583\) 0 0
\(584\) 6.00000 0.248282
\(585\) 0 0
\(586\) 9.00000 0.371787
\(587\) −15.5885 + 9.00000i −0.643404 + 0.371470i −0.785925 0.618322i \(-0.787813\pi\)
0.142520 + 0.989792i \(0.454479\pi\)
\(588\) 1.00000 + 1.73205i 0.0412393 + 0.0714286i
\(589\) 0 0
\(590\) 18.0000i 0.741048i
\(591\) −2.59808 1.50000i −0.106871 0.0617018i
\(592\) 2.59808 + 1.50000i 0.106780 + 0.0616496i
\(593\) 36.0000i 1.47834i −0.673517 0.739171i \(-0.735217\pi\)
0.673517 0.739171i \(-0.264783\pi\)
\(594\) 0 0
\(595\) −13.5000 23.3827i −0.553446 0.958597i
\(596\) −5.19615 + 3.00000i −0.212843 + 0.122885i
\(597\) 20.0000 0.818546
\(598\) 0 0
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 3.46410 2.00000i 0.141421 0.0816497i
\(601\) −18.5000 32.0429i −0.754631 1.30706i −0.945558 0.325455i \(-0.894483\pi\)
0.190927 0.981604i \(-0.438851\pi\)
\(602\) −1.50000 + 2.59808i −0.0611354 + 0.105890i
\(603\) 24.0000i 0.977356i
\(604\) 12.9904 + 7.50000i 0.528571 + 0.305171i
\(605\) −28.5788 16.5000i −1.16190 0.670820i
\(606\) 12.0000i 0.487467i
\(607\) 11.0000 19.0526i 0.446476 0.773320i −0.551678 0.834058i \(-0.686012\pi\)
0.998154 + 0.0607380i \(0.0193454\pi\)
\(608\) −3.00000 5.19615i −0.121666 0.210732i
\(609\) 0 0
\(610\) −24.0000 −0.971732
\(611\) 0 0
\(612\) 6.00000 0.242536
\(613\) −5.19615 + 3.00000i −0.209871 + 0.121169i −0.601251 0.799060i \(-0.705331\pi\)
0.391381 + 0.920229i \(0.371998\pi\)
\(614\) 9.00000 + 15.5885i 0.363210 + 0.629099i
\(615\) 0 0
\(616\) 0 0
\(617\) −10.3923 6.00000i −0.418378 0.241551i 0.276005 0.961156i \(-0.410989\pi\)
−0.694383 + 0.719605i \(0.744323\pi\)
\(618\) −12.1244 7.00000i −0.487713 0.281581i
\(619\) 24.0000i 0.964641i −0.875995 0.482321i \(-0.839794\pi\)
0.875995 0.482321i \(-0.160206\pi\)
\(620\) 0 0
\(621\) 15.0000 + 25.9808i 0.601929 + 1.04257i
\(622\) 15.5885 9.00000i 0.625040 0.360867i
\(623\) 18.0000 0.721155
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) −16.4545 + 9.50000i −0.657653 + 0.379696i
\(627\) 0 0
\(628\) −11.0000 + 19.0526i −0.438948 + 0.760280i
\(629\) 9.00000i 0.358854i
\(630\) −15.5885 9.00000i −0.621059 0.358569i
\(631\) −12.9904 7.50000i −0.517139 0.298570i 0.218624 0.975809i \(-0.429843\pi\)
−0.735763 + 0.677239i \(0.763176\pi\)
\(632\) 10.0000i 0.397779i
\(633\) −11.5000 + 19.9186i −0.457084 + 0.791693i
\(634\) 9.00000 + 15.5885i 0.357436 + 0.619097i
\(635\) −5.19615 + 3.00000i −0.206203 + 0.119051i
\(636\) −6.00000 −0.237915
\(637\) 0 0
\(638\) 0 0
\(639\) 25.9808 15.0000i 1.02778 0.593391i
\(640\) 1.50000 + 2.59808i 0.0592927 + 0.102698i
\(641\) 9.00000 15.5885i 0.355479 0.615707i −0.631721 0.775196i \(-0.717651\pi\)
0.987200 + 0.159489i \(0.0509845\pi\)
\(642\) 12.0000i 0.473602i
\(643\) 31.1769 + 18.0000i 1.22950 + 0.709851i 0.966925 0.255062i \(-0.0820957\pi\)
0.262573 + 0.964912i \(0.415429\pi\)
\(644\) 15.5885 + 9.00000i 0.614271 + 0.354650i
\(645\) 3.00000i 0.118125i
\(646\) −9.00000 + 15.5885i −0.354100 + 0.613320i
\(647\) 21.0000 + 36.3731i 0.825595 + 1.42997i 0.901464 + 0.432855i \(0.142494\pi\)
−0.0758684 + 0.997118i \(0.524173\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 5.19615 3.00000i 0.203497 0.117489i
\(653\) 18.0000 + 31.1769i 0.704394 + 1.22005i 0.966910 + 0.255119i \(0.0821147\pi\)
−0.262515 + 0.964928i \(0.584552\pi\)
\(654\) −4.50000 + 7.79423i −0.175964 + 0.304778i
\(655\) 9.00000i 0.351659i
\(656\) 0 0
\(657\) −10.3923 6.00000i −0.405442 0.234082i
\(658\) 9.00000i 0.350857i
\(659\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(660\) 0 0
\(661\) −25.9808 + 15.0000i −1.01053 + 0.583432i −0.911348 0.411636i \(-0.864957\pi\)
−0.0991864 + 0.995069i \(0.531624\pi\)
\(662\) −30.0000 −1.16598
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 46.7654 27.0000i 1.81348 1.04702i
\(666\) −3.00000 5.19615i −0.116248 0.201347i
\(667\) 0 0
\(668\) 12.0000i 0.464294i
\(669\) 7.79423 + 4.50000i 0.301342 + 0.173980i
\(670\) −31.1769 18.0000i −1.20447 0.695401i
\(671\) 0 0
\(672\) −1.50000 + 2.59808i −0.0578638 + 0.100223i
\(673\) 0.500000 + 0.866025i 0.0192736 + 0.0333828i 0.875501 0.483216i \(-0.160531\pi\)
−0.856228 + 0.516599i \(0.827198\pi\)
\(674\) −11.2583 + 6.50000i −0.433655 + 0.250371i
\(675\) −20.0000 −0.769800
\(676\) 0 0
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) −5.19615 + 3.00000i −0.199557 + 0.115214i
\(679\) −18.0000 31.1769i −0.690777 1.19646i
\(680\) 4.50000 7.79423i 0.172567 0.298895i
\(681\) 12.0000i 0.459841i
\(682\) 0 0
\(683\) 5.19615 + 3.00000i 0.198825 + 0.114792i 0.596107 0.802905i \(-0.296713\pi\)
−0.397282 + 0.917697i \(0.630047\pi\)
\(684\) 12.0000i 0.458831i
\(685\) −27.0000 + 46.7654i −1.03162 + 1.78681i
\(686\) 7.50000 + 12.9904i 0.286351 + 0.495975i
\(687\) 7.79423 4.50000i 0.297368 0.171686i
\(688\) −1.00000 −0.0381246
\(689\) 0 0
\(690\) 18.0000 0.685248
\(691\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(692\) −3.00000 5.19615i −0.114043 0.197528i
\(693\) 0 0
\(694\) 33.0000i 1.25266i
\(695\) −12.9904 7.50000i −0.492753 0.284491i
\(696\) 0 0
\(697\) 0 0
\(698\) −10.5000 + 18.1865i −0.397431 + 0.688370i
\(699\) −10.5000 18.1865i −0.397146 0.687878i
\(700\) −10.3923 + 6.00000i −0.392792 + 0.226779i
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) 0 0
\(703\) 18.0000 0.678883
\(704\) 0 0
\(705\) 4.50000 + 7.79423i 0.169480 + 0.293548i
\(706\) 3.00000 5.19615i 0.112906 0.195560i
\(707\) 36.0000i 1.35392i
\(708\) −5.19615 3.00000i −0.195283 0.112747i
\(709\) −5.19615 3.00000i −0.195146 0.112667i 0.399244 0.916845i \(-0.369273\pi\)
−0.594389 + 0.804178i \(0.702606\pi\)
\(710\) 45.0000i 1.68882i
\(711\) 10.0000 17.3205i 0.375029 0.649570i
\(712\) 3.00000 + 5.19615i 0.112430 + 0.194734i
\(713\) 0 0
\(714\) 9.00000 0.336817
\(715\) 0 0
\(716\) −15.0000 −0.560576
\(717\) 7.79423 4.50000i 0.291081 0.168056i
\(718\) 12.0000 + 20.7846i 0.447836 + 0.775675i
\(719\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) 6.00000i 0.223607i
\(721\) 36.3731 + 21.0000i 1.35460 + 0.782081i
\(722\) −14.7224 8.50000i −0.547912 0.316337i
\(723\) 30.0000i 1.11571i
\(724\) 1.00000 1.73205i 0.0371647 0.0643712i
\(725\) 0 0
\(726\) 9.52628 5.50000i 0.353553 0.204124i
\(727\) 28.0000 1.03846 0.519231 0.854634i \(-0.326218\pi\)
0.519231 + 0.854634i \(0.326218\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) −15.5885 + 9.00000i −0.576955 + 0.333105i
\(731\) 1.50000 + 2.59808i 0.0554795 + 0.0960933i
\(732\) 4.00000 6.92820i 0.147844 0.256074i
\(733\) 9.00000i 0.332423i 0.986090 + 0.166211i \(0.0531534\pi\)
−0.986090 + 0.166211i \(0.946847\pi\)
\(734\) 6.92820 + 4.00000i 0.255725 + 0.147643i
\(735\) −5.19615 3.00000i −0.191663 0.110657i
\(736\) 6.00000i 0.221163i
\(737\) 0 0
\(738\) 0 0
\(739\) 31.1769 18.0000i 1.14686 0.662141i 0.198741 0.980052i \(-0.436315\pi\)
0.948120 + 0.317911i \(0.102981\pi\)
\(740\) −9.00000 −0.330847
\(741\) 0 0
\(742\) 18.0000 0.660801
\(743\) 33.7750 19.5000i 1.23908 0.715386i 0.270177 0.962811i \(-0.412918\pi\)
0.968907 + 0.247425i \(0.0795844\pi\)
\(744\) 0 0
\(745\) 9.00000 15.5885i 0.329734 0.571117i
\(746\) 4.00000i 0.146450i
\(747\) −10.3923 6.00000i −0.380235 0.219529i
\(748\) 0 0
\(749\) 36.0000i 1.31541i
\(750\) 1.50000 2.59808i 0.0547723 0.0948683i
\(751\) −16.0000 27.7128i −0.583848 1.01125i −0.995018 0.0996961i \(-0.968213\pi\)
0.411170 0.911559i \(-0.365120\pi\)
\(752\) −2.59808 + 1.50000i −0.0947421 + 0.0546994i
\(753\) −12.0000 −0.437304
\(754\) 0 0
\(755\) −45.0000 −1.63772
\(756\) 12.9904 7.50000i 0.472456 0.272772i
\(757\) 1.00000 + 1.73205i 0.0363456 + 0.0629525i 0.883626 0.468193i \(-0.155095\pi\)
−0.847280 + 0.531146i \(0.821762\pi\)
\(758\) −3.00000 + 5.19615i −0.108965 + 0.188733i
\(759\) 0 0
\(760\) 15.5885 + 9.00000i 0.565453 + 0.326464i
\(761\) −25.9808 15.0000i −0.941802 0.543750i −0.0512772 0.998684i \(-0.516329\pi\)
−0.890525 + 0.454935i \(0.849663\pi\)
\(762\) 2.00000i 0.0724524i
\(763\) 13.5000 23.3827i 0.488733 0.846510i
\(764\) 6.00000 + 10.3923i 0.217072 + 0.375980i
\(765\) −15.5885 + 9.00000i −0.563602 + 0.325396i
\(766\) 9.00000 0.325183
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) −20.7846 + 12.0000i −0.749512 + 0.432731i −0.825518 0.564376i \(-0.809117\pi\)
0.0760054 + 0.997107i \(0.475783\pi\)
\(770\) 0 0
\(771\) 1.50000 2.59808i 0.0540212 0.0935674i
\(772\) 6.00000i 0.215945i
\(773\) 18.1865 + 10.5000i 0.654124 + 0.377659i 0.790034 0.613062i \(-0.210063\pi\)
−0.135910 + 0.990721i \(0.543396\pi\)
\(774\) 1.73205 + 1.00000i 0.0622573 + 0.0359443i
\(775\) 0 0
\(776\) 6.00000 10.3923i 0.215387 0.373062i
\(777\) −4.50000 7.79423i −0.161437 0.279616i
\(778\) 25.9808 15.0000i 0.931455 0.537776i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 15.5885 9.00000i 0.557442 0.321839i
\(783\) 0 0
\(784\) 1.00000 1.73205i 0.0357143 0.0618590i
\(785\) 66.0000i 2.35564i
\(786\) 2.59808 + 1.50000i 0.0926703 + 0.0535032i