Properties

Label 225.2.k.a.49.1
Level $225$
Weight $2$
Character 225.49
Analytic conductor $1.797$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 225.49
Dual form 225.2.k.a.124.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205i q^{6} +(2.59808 - 1.50000i) q^{7} -3.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205i q^{6} +(2.59808 - 1.50000i) q^{7} -3.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(1.00000 + 1.73205i) q^{11} +(0.866025 + 1.50000i) q^{12} +(1.73205 + 1.00000i) q^{13} +(-1.50000 + 2.59808i) q^{14} +(0.500000 + 0.866025i) q^{16} -4.00000i q^{17} +(2.59808 + 1.50000i) q^{18} +8.00000 q^{19} -5.19615i q^{21} +(-1.73205 - 1.00000i) q^{22} +(-2.59808 - 1.50000i) q^{23} +(-4.50000 - 2.59808i) q^{24} -2.00000 q^{26} -5.19615 q^{27} +3.00000i q^{28} +(-0.500000 - 0.866025i) q^{29} +(4.33013 + 2.50000i) q^{32} +3.46410 q^{33} +(2.00000 + 3.46410i) q^{34} +3.00000 q^{36} +4.00000i q^{37} +(-6.92820 + 4.00000i) q^{38} +(3.00000 - 1.73205i) q^{39} +(-2.50000 + 4.33013i) q^{41} +(2.59808 + 4.50000i) q^{42} +(-6.92820 + 4.00000i) q^{43} -2.00000 q^{44} +3.00000 q^{46} +(-6.06218 + 3.50000i) q^{47} +1.73205 q^{48} +(1.00000 - 1.73205i) q^{49} +(-6.00000 - 3.46410i) q^{51} +(-1.73205 + 1.00000i) q^{52} -2.00000i q^{53} +(4.50000 - 2.59808i) q^{54} +(-4.50000 - 7.79423i) q^{56} +(6.92820 - 12.0000i) q^{57} +(0.866025 + 0.500000i) q^{58} +(-7.00000 + 12.1244i) q^{59} +(-3.50000 - 6.06218i) q^{61} +(-7.79423 - 4.50000i) q^{63} -7.00000 q^{64} +(-3.00000 + 1.73205i) q^{66} +(-2.59808 - 1.50000i) q^{67} +(3.46410 + 2.00000i) q^{68} +(-4.50000 + 2.59808i) q^{69} +2.00000 q^{71} +(-7.79423 + 4.50000i) q^{72} +4.00000i q^{73} +(-2.00000 - 3.46410i) q^{74} +(-4.00000 + 6.92820i) q^{76} +(5.19615 + 3.00000i) q^{77} +(-1.73205 + 3.00000i) q^{78} +(-3.00000 - 5.19615i) q^{79} +(-4.50000 + 7.79423i) q^{81} -5.00000i q^{82} +(7.79423 - 4.50000i) q^{83} +(4.50000 + 2.59808i) q^{84} +(4.00000 - 6.92820i) q^{86} -1.73205 q^{87} +(5.19615 - 3.00000i) q^{88} +15.0000 q^{89} +6.00000 q^{91} +(2.59808 - 1.50000i) q^{92} +(3.50000 - 6.06218i) q^{94} +(7.50000 - 4.33013i) q^{96} +(-1.73205 + 1.00000i) q^{97} +2.00000i q^{98} +(3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{4} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{4} - 6 q^{9} + 4 q^{11} - 6 q^{14} + 2 q^{16} + 32 q^{19} - 18 q^{24} - 8 q^{26} - 2 q^{29} + 8 q^{34} + 12 q^{36} + 12 q^{39} - 10 q^{41} - 8 q^{44} + 12 q^{46} + 4 q^{49} - 24 q^{51} + 18 q^{54} - 18 q^{56} - 28 q^{59} - 14 q^{61} - 28 q^{64} - 12 q^{66} - 18 q^{69} + 8 q^{71} - 8 q^{74} - 16 q^{76} - 12 q^{79} - 18 q^{81} + 18 q^{84} + 16 q^{86} + 60 q^{89} + 24 q^{91} + 14 q^{94} + 30 q^{96} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i −0.773893 0.633316i \(-0.781693\pi\)
0.161521 + 0.986869i \(0.448360\pi\)
\(3\) 0.866025 1.50000i 0.500000 0.866025i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 1.73205i 0.707107i
\(7\) 2.59808 1.50000i 0.981981 0.566947i 0.0791130 0.996866i \(-0.474791\pi\)
0.902867 + 0.429919i \(0.141458\pi\)
\(8\) 3.00000i 1.06066i
\(9\) −1.50000 2.59808i −0.500000 0.866025i
\(10\) 0 0
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) 0.866025 + 1.50000i 0.250000 + 0.433013i
\(13\) 1.73205 + 1.00000i 0.480384 + 0.277350i 0.720577 0.693375i \(-0.243877\pi\)
−0.240192 + 0.970725i \(0.577210\pi\)
\(14\) −1.50000 + 2.59808i −0.400892 + 0.694365i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 4.00000i 0.970143i −0.874475 0.485071i \(-0.838794\pi\)
0.874475 0.485071i \(-0.161206\pi\)
\(18\) 2.59808 + 1.50000i 0.612372 + 0.353553i
\(19\) 8.00000 1.83533 0.917663 0.397360i \(-0.130073\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 0 0
\(21\) 5.19615i 1.13389i
\(22\) −1.73205 1.00000i −0.369274 0.213201i
\(23\) −2.59808 1.50000i −0.541736 0.312772i 0.204046 0.978961i \(-0.434591\pi\)
−0.745782 + 0.666190i \(0.767924\pi\)
\(24\) −4.50000 2.59808i −0.918559 0.530330i
\(25\) 0 0
\(26\) −2.00000 −0.392232
\(27\) −5.19615 −1.00000
\(28\) 3.00000i 0.566947i
\(29\) −0.500000 0.866025i −0.0928477 0.160817i 0.815861 0.578249i \(-0.196264\pi\)
−0.908708 + 0.417432i \(0.862930\pi\)
\(30\) 0 0
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) 4.33013 + 2.50000i 0.765466 + 0.441942i
\(33\) 3.46410 0.603023
\(34\) 2.00000 + 3.46410i 0.342997 + 0.594089i
\(35\) 0 0
\(36\) 3.00000 0.500000
\(37\) 4.00000i 0.657596i 0.944400 + 0.328798i \(0.106644\pi\)
−0.944400 + 0.328798i \(0.893356\pi\)
\(38\) −6.92820 + 4.00000i −1.12390 + 0.648886i
\(39\) 3.00000 1.73205i 0.480384 0.277350i
\(40\) 0 0
\(41\) −2.50000 + 4.33013i −0.390434 + 0.676252i −0.992507 0.122189i \(-0.961009\pi\)
0.602072 + 0.798441i \(0.294342\pi\)
\(42\) 2.59808 + 4.50000i 0.400892 + 0.694365i
\(43\) −6.92820 + 4.00000i −1.05654 + 0.609994i −0.924473 0.381246i \(-0.875495\pi\)
−0.132068 + 0.991241i \(0.542162\pi\)
\(44\) −2.00000 −0.301511
\(45\) 0 0
\(46\) 3.00000 0.442326
\(47\) −6.06218 + 3.50000i −0.884260 + 0.510527i −0.872060 0.489398i \(-0.837217\pi\)
−0.0121990 + 0.999926i \(0.503883\pi\)
\(48\) 1.73205 0.250000
\(49\) 1.00000 1.73205i 0.142857 0.247436i
\(50\) 0 0
\(51\) −6.00000 3.46410i −0.840168 0.485071i
\(52\) −1.73205 + 1.00000i −0.240192 + 0.138675i
\(53\) 2.00000i 0.274721i −0.990521 0.137361i \(-0.956138\pi\)
0.990521 0.137361i \(-0.0438619\pi\)
\(54\) 4.50000 2.59808i 0.612372 0.353553i
\(55\) 0 0
\(56\) −4.50000 7.79423i −0.601338 1.04155i
\(57\) 6.92820 12.0000i 0.917663 1.58944i
\(58\) 0.866025 + 0.500000i 0.113715 + 0.0656532i
\(59\) −7.00000 + 12.1244i −0.911322 + 1.57846i −0.0991242 + 0.995075i \(0.531604\pi\)
−0.812198 + 0.583382i \(0.801729\pi\)
\(60\) 0 0
\(61\) −3.50000 6.06218i −0.448129 0.776182i 0.550135 0.835076i \(-0.314576\pi\)
−0.998264 + 0.0588933i \(0.981243\pi\)
\(62\) 0 0
\(63\) −7.79423 4.50000i −0.981981 0.566947i
\(64\) −7.00000 −0.875000
\(65\) 0 0
\(66\) −3.00000 + 1.73205i −0.369274 + 0.213201i
\(67\) −2.59808 1.50000i −0.317406 0.183254i 0.332830 0.942987i \(-0.391996\pi\)
−0.650236 + 0.759733i \(0.725330\pi\)
\(68\) 3.46410 + 2.00000i 0.420084 + 0.242536i
\(69\) −4.50000 + 2.59808i −0.541736 + 0.312772i
\(70\) 0 0
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) −7.79423 + 4.50000i −0.918559 + 0.530330i
\(73\) 4.00000i 0.468165i 0.972217 + 0.234082i \(0.0752085\pi\)
−0.972217 + 0.234082i \(0.924791\pi\)
\(74\) −2.00000 3.46410i −0.232495 0.402694i
\(75\) 0 0
\(76\) −4.00000 + 6.92820i −0.458831 + 0.794719i
\(77\) 5.19615 + 3.00000i 0.592157 + 0.341882i
\(78\) −1.73205 + 3.00000i −0.196116 + 0.339683i
\(79\) −3.00000 5.19615i −0.337526 0.584613i 0.646440 0.762964i \(-0.276257\pi\)
−0.983967 + 0.178352i \(0.942924\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 5.00000i 0.552158i
\(83\) 7.79423 4.50000i 0.855528 0.493939i −0.00698436 0.999976i \(-0.502223\pi\)
0.862512 + 0.506036i \(0.168890\pi\)
\(84\) 4.50000 + 2.59808i 0.490990 + 0.283473i
\(85\) 0 0
\(86\) 4.00000 6.92820i 0.431331 0.747087i
\(87\) −1.73205 −0.185695
\(88\) 5.19615 3.00000i 0.553912 0.319801i
\(89\) 15.0000 1.59000 0.794998 0.606612i \(-0.207472\pi\)
0.794998 + 0.606612i \(0.207472\pi\)
\(90\) 0 0
\(91\) 6.00000 0.628971
\(92\) 2.59808 1.50000i 0.270868 0.156386i
\(93\) 0 0
\(94\) 3.50000 6.06218i 0.360997 0.625266i
\(95\) 0 0
\(96\) 7.50000 4.33013i 0.765466 0.441942i
\(97\) −1.73205 + 1.00000i −0.175863 + 0.101535i −0.585348 0.810782i \(-0.699042\pi\)
0.409484 + 0.912317i \(0.365709\pi\)
\(98\) 2.00000i 0.202031i
\(99\) 3.00000 5.19615i 0.301511 0.522233i
\(100\) 0 0
\(101\) 9.00000 + 15.5885i 0.895533 + 1.55111i 0.833143 + 0.553058i \(0.186539\pi\)
0.0623905 + 0.998052i \(0.480128\pi\)
\(102\) 6.92820 0.685994
\(103\) −6.92820 4.00000i −0.682656 0.394132i 0.118199 0.992990i \(-0.462288\pi\)
−0.800855 + 0.598858i \(0.795621\pi\)
\(104\) 3.00000 5.19615i 0.294174 0.509525i
\(105\) 0 0
\(106\) 1.00000 + 1.73205i 0.0971286 + 0.168232i
\(107\) 3.00000i 0.290021i −0.989430 0.145010i \(-0.953678\pi\)
0.989430 0.145010i \(-0.0463216\pi\)
\(108\) 2.59808 4.50000i 0.250000 0.433013i
\(109\) −5.00000 −0.478913 −0.239457 0.970907i \(-0.576969\pi\)
−0.239457 + 0.970907i \(0.576969\pi\)
\(110\) 0 0
\(111\) 6.00000 + 3.46410i 0.569495 + 0.328798i
\(112\) 2.59808 + 1.50000i 0.245495 + 0.141737i
\(113\) 6.92820 + 4.00000i 0.651751 + 0.376288i 0.789127 0.614231i \(-0.210534\pi\)
−0.137376 + 0.990519i \(0.543867\pi\)
\(114\) 13.8564i 1.29777i
\(115\) 0 0
\(116\) 1.00000 0.0928477
\(117\) 6.00000i 0.554700i
\(118\) 14.0000i 1.28880i
\(119\) −6.00000 10.3923i −0.550019 0.952661i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 6.06218 + 3.50000i 0.548844 + 0.316875i
\(123\) 4.33013 + 7.50000i 0.390434 + 0.676252i
\(124\) 0 0
\(125\) 0 0
\(126\) 9.00000 0.801784
\(127\) 5.00000i 0.443678i 0.975083 + 0.221839i \(0.0712060\pi\)
−0.975083 + 0.221839i \(0.928794\pi\)
\(128\) −2.59808 + 1.50000i −0.229640 + 0.132583i
\(129\) 13.8564i 1.21999i
\(130\) 0 0
\(131\) 3.00000 5.19615i 0.262111 0.453990i −0.704692 0.709514i \(-0.748915\pi\)
0.966803 + 0.255524i \(0.0822479\pi\)
\(132\) −1.73205 + 3.00000i −0.150756 + 0.261116i
\(133\) 20.7846 12.0000i 1.80225 1.04053i
\(134\) 3.00000 0.259161
\(135\) 0 0
\(136\) −12.0000 −1.02899
\(137\) −10.3923 + 6.00000i −0.887875 + 0.512615i −0.873247 0.487278i \(-0.837990\pi\)
−0.0146279 + 0.999893i \(0.504656\pi\)
\(138\) 2.59808 4.50000i 0.221163 0.383065i
\(139\) −8.00000 + 13.8564i −0.678551 + 1.17529i 0.296866 + 0.954919i \(0.404058\pi\)
−0.975417 + 0.220366i \(0.929275\pi\)
\(140\) 0 0
\(141\) 12.1244i 1.02105i
\(142\) −1.73205 + 1.00000i −0.145350 + 0.0839181i
\(143\) 4.00000i 0.334497i
\(144\) 1.50000 2.59808i 0.125000 0.216506i
\(145\) 0 0
\(146\) −2.00000 3.46410i −0.165521 0.286691i
\(147\) −1.73205 3.00000i −0.142857 0.247436i
\(148\) −3.46410 2.00000i −0.284747 0.164399i
\(149\) 8.50000 14.7224i 0.696347 1.20611i −0.273377 0.961907i \(-0.588141\pi\)
0.969724 0.244202i \(-0.0785259\pi\)
\(150\) 0 0
\(151\) 1.00000 + 1.73205i 0.0813788 + 0.140952i 0.903842 0.427865i \(-0.140734\pi\)
−0.822464 + 0.568818i \(0.807401\pi\)
\(152\) 24.0000i 1.94666i
\(153\) −10.3923 + 6.00000i −0.840168 + 0.485071i
\(154\) −6.00000 −0.483494
\(155\) 0 0
\(156\) 3.46410i 0.277350i
\(157\) 12.1244 + 7.00000i 0.967629 + 0.558661i 0.898513 0.438948i \(-0.144649\pi\)
0.0691164 + 0.997609i \(0.477982\pi\)
\(158\) 5.19615 + 3.00000i 0.413384 + 0.238667i
\(159\) −3.00000 1.73205i −0.237915 0.137361i
\(160\) 0 0
\(161\) −9.00000 −0.709299
\(162\) 9.00000i 0.707107i
\(163\) 4.00000i 0.313304i −0.987654 0.156652i \(-0.949930\pi\)
0.987654 0.156652i \(-0.0500701\pi\)
\(164\) −2.50000 4.33013i −0.195217 0.338126i
\(165\) 0 0
\(166\) −4.50000 + 7.79423i −0.349268 + 0.604949i
\(167\) −7.79423 4.50000i −0.603136 0.348220i 0.167139 0.985933i \(-0.446547\pi\)
−0.770274 + 0.637713i \(0.779881\pi\)
\(168\) −15.5885 −1.20268
\(169\) −4.50000 7.79423i −0.346154 0.599556i
\(170\) 0 0
\(171\) −12.0000 20.7846i −0.917663 1.58944i
\(172\) 8.00000i 0.609994i
\(173\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(174\) 1.50000 0.866025i 0.113715 0.0656532i
\(175\) 0 0
\(176\) −1.00000 + 1.73205i −0.0753778 + 0.130558i
\(177\) 12.1244 + 21.0000i 0.911322 + 1.57846i
\(178\) −12.9904 + 7.50000i −0.973670 + 0.562149i
\(179\) 2.00000 0.149487 0.0747435 0.997203i \(-0.476186\pi\)
0.0747435 + 0.997203i \(0.476186\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) −5.19615 + 3.00000i −0.385164 + 0.222375i
\(183\) −12.1244 −0.896258
\(184\) −4.50000 + 7.79423i −0.331744 + 0.574598i
\(185\) 0 0
\(186\) 0 0
\(187\) 6.92820 4.00000i 0.506640 0.292509i
\(188\) 7.00000i 0.510527i
\(189\) −13.5000 + 7.79423i −0.981981 + 0.566947i
\(190\) 0 0
\(191\) −4.00000 6.92820i −0.289430 0.501307i 0.684244 0.729253i \(-0.260132\pi\)
−0.973674 + 0.227946i \(0.926799\pi\)
\(192\) −6.06218 + 10.5000i −0.437500 + 0.757772i
\(193\) 8.66025 + 5.00000i 0.623379 + 0.359908i 0.778183 0.628037i \(-0.216141\pi\)
−0.154805 + 0.987945i \(0.549475\pi\)
\(194\) 1.00000 1.73205i 0.0717958 0.124354i
\(195\) 0 0
\(196\) 1.00000 + 1.73205i 0.0714286 + 0.123718i
\(197\) 12.0000i 0.854965i 0.904024 + 0.427482i \(0.140599\pi\)
−0.904024 + 0.427482i \(0.859401\pi\)
\(198\) 6.00000i 0.426401i
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 0 0
\(201\) −4.50000 + 2.59808i −0.317406 + 0.183254i
\(202\) −15.5885 9.00000i −1.09680 0.633238i
\(203\) −2.59808 1.50000i −0.182349 0.105279i
\(204\) 6.00000 3.46410i 0.420084 0.242536i
\(205\) 0 0
\(206\) 8.00000 0.557386
\(207\) 9.00000i 0.625543i
\(208\) 2.00000i 0.138675i
\(209\) 8.00000 + 13.8564i 0.553372 + 0.958468i
\(210\) 0 0
\(211\) 11.0000 19.0526i 0.757271 1.31163i −0.186966 0.982366i \(-0.559865\pi\)
0.944237 0.329266i \(-0.106801\pi\)
\(212\) 1.73205 + 1.00000i 0.118958 + 0.0686803i
\(213\) 1.73205 3.00000i 0.118678 0.205557i
\(214\) 1.50000 + 2.59808i 0.102538 + 0.177601i
\(215\) 0 0
\(216\) 15.5885i 1.06066i
\(217\) 0 0
\(218\) 4.33013 2.50000i 0.293273 0.169321i
\(219\) 6.00000 + 3.46410i 0.405442 + 0.234082i
\(220\) 0 0
\(221\) 4.00000 6.92820i 0.269069 0.466041i
\(222\) −6.92820 −0.464991
\(223\) −16.4545 + 9.50000i −1.10187 + 0.636167i −0.936713 0.350100i \(-0.886148\pi\)
−0.165161 + 0.986267i \(0.552814\pi\)
\(224\) 15.0000 1.00223
\(225\) 0 0
\(226\) −8.00000 −0.532152
\(227\) 3.46410 2.00000i 0.229920 0.132745i −0.380615 0.924734i \(-0.624288\pi\)
0.610535 + 0.791989i \(0.290954\pi\)
\(228\) 6.92820 + 12.0000i 0.458831 + 0.794719i
\(229\) 7.50000 12.9904i 0.495614 0.858429i −0.504373 0.863486i \(-0.668276\pi\)
0.999987 + 0.00505719i \(0.00160976\pi\)
\(230\) 0 0
\(231\) 9.00000 5.19615i 0.592157 0.341882i
\(232\) −2.59808 + 1.50000i −0.170572 + 0.0984798i
\(233\) 24.0000i 1.57229i 0.618041 + 0.786146i \(0.287927\pi\)
−0.618041 + 0.786146i \(0.712073\pi\)
\(234\) 3.00000 + 5.19615i 0.196116 + 0.339683i
\(235\) 0 0
\(236\) −7.00000 12.1244i −0.455661 0.789228i
\(237\) −10.3923 −0.675053
\(238\) 10.3923 + 6.00000i 0.673633 + 0.388922i
\(239\) −4.00000 + 6.92820i −0.258738 + 0.448148i −0.965904 0.258900i \(-0.916640\pi\)
0.707166 + 0.707048i \(0.249973\pi\)
\(240\) 0 0
\(241\) 5.50000 + 9.52628i 0.354286 + 0.613642i 0.986996 0.160748i \(-0.0513906\pi\)
−0.632709 + 0.774389i \(0.718057\pi\)
\(242\) 7.00000i 0.449977i
\(243\) 7.79423 + 13.5000i 0.500000 + 0.866025i
\(244\) 7.00000 0.448129
\(245\) 0 0
\(246\) −7.50000 4.33013i −0.478183 0.276079i
\(247\) 13.8564 + 8.00000i 0.881662 + 0.509028i
\(248\) 0 0
\(249\) 15.5885i 0.987878i
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 7.79423 4.50000i 0.490990 0.283473i
\(253\) 6.00000i 0.377217i
\(254\) −2.50000 4.33013i −0.156864 0.271696i
\(255\) 0 0
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) −5.19615 3.00000i −0.324127 0.187135i 0.329104 0.944294i \(-0.393253\pi\)
−0.653231 + 0.757159i \(0.726587\pi\)
\(258\) −6.92820 12.0000i −0.431331 0.747087i
\(259\) 6.00000 + 10.3923i 0.372822 + 0.645746i
\(260\) 0 0
\(261\) −1.50000 + 2.59808i −0.0928477 + 0.160817i
\(262\) 6.00000i 0.370681i
\(263\) −13.8564 + 8.00000i −0.854423 + 0.493301i −0.862141 0.506669i \(-0.830877\pi\)
0.00771799 + 0.999970i \(0.497543\pi\)
\(264\) 10.3923i 0.639602i
\(265\) 0 0
\(266\) −12.0000 + 20.7846i −0.735767 + 1.27439i
\(267\) 12.9904 22.5000i 0.794998 1.37698i
\(268\) 2.59808 1.50000i 0.158703 0.0916271i
\(269\) −25.0000 −1.52428 −0.762138 0.647414i \(-0.775850\pi\)
−0.762138 + 0.647414i \(0.775850\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 3.46410 2.00000i 0.210042 0.121268i
\(273\) 5.19615 9.00000i 0.314485 0.544705i
\(274\) 6.00000 10.3923i 0.362473 0.627822i
\(275\) 0 0
\(276\) 5.19615i 0.312772i
\(277\) −10.3923 + 6.00000i −0.624413 + 0.360505i −0.778585 0.627539i \(-0.784062\pi\)
0.154172 + 0.988044i \(0.450729\pi\)
\(278\) 16.0000i 0.959616i
\(279\) 0 0
\(280\) 0 0
\(281\) 7.50000 + 12.9904i 0.447412 + 0.774941i 0.998217 0.0596933i \(-0.0190123\pi\)
−0.550804 + 0.834634i \(0.685679\pi\)
\(282\) −6.06218 10.5000i −0.360997 0.625266i
\(283\) −18.1865 10.5000i −1.08108 0.624160i −0.149890 0.988703i \(-0.547892\pi\)
−0.931187 + 0.364542i \(0.881225\pi\)
\(284\) −1.00000 + 1.73205i −0.0593391 + 0.102778i
\(285\) 0 0
\(286\) −2.00000 3.46410i −0.118262 0.204837i
\(287\) 15.0000i 0.885422i
\(288\) 15.0000i 0.883883i
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 3.46410i 0.203069i
\(292\) −3.46410 2.00000i −0.202721 0.117041i
\(293\) −10.3923 6.00000i −0.607125 0.350524i 0.164714 0.986341i \(-0.447330\pi\)
−0.771839 + 0.635818i \(0.780663\pi\)
\(294\) 3.00000 + 1.73205i 0.174964 + 0.101015i
\(295\) 0 0
\(296\) 12.0000 0.697486
\(297\) −5.19615 9.00000i −0.301511 0.522233i
\(298\) 17.0000i 0.984784i
\(299\) −3.00000 5.19615i −0.173494 0.300501i
\(300\) 0 0
\(301\) −12.0000 + 20.7846i −0.691669 + 1.19800i
\(302\) −1.73205 1.00000i −0.0996683 0.0575435i
\(303\) 31.1769 1.79107
\(304\) 4.00000 + 6.92820i 0.229416 + 0.397360i
\(305\) 0 0
\(306\) 6.00000 10.3923i 0.342997 0.594089i
\(307\) 7.00000i 0.399511i −0.979846 0.199756i \(-0.935985\pi\)
0.979846 0.199756i \(-0.0640148\pi\)
\(308\) −5.19615 + 3.00000i −0.296078 + 0.170941i
\(309\) −12.0000 + 6.92820i −0.682656 + 0.394132i
\(310\) 0 0
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) −5.19615 9.00000i −0.294174 0.509525i
\(313\) 12.1244 7.00000i 0.685309 0.395663i −0.116543 0.993186i \(-0.537181\pi\)
0.801852 + 0.597522i \(0.203848\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) 6.00000 0.337526
\(317\) 29.4449 17.0000i 1.65379 0.954815i 0.678294 0.734791i \(-0.262720\pi\)
0.975494 0.220024i \(-0.0706137\pi\)
\(318\) 3.46410 0.194257
\(319\) 1.00000 1.73205i 0.0559893 0.0969762i
\(320\) 0 0
\(321\) −4.50000 2.59808i −0.251166 0.145010i
\(322\) 7.79423 4.50000i 0.434355 0.250775i
\(323\) 32.0000i 1.78053i
\(324\) −4.50000 7.79423i −0.250000 0.433013i
\(325\) 0 0
\(326\) 2.00000 + 3.46410i 0.110770 + 0.191859i
\(327\) −4.33013 + 7.50000i −0.239457 + 0.414751i
\(328\) 12.9904 + 7.50000i 0.717274 + 0.414118i
\(329\) −10.5000 + 18.1865i −0.578884 + 1.00266i
\(330\) 0 0
\(331\) 3.00000 + 5.19615i 0.164895 + 0.285606i 0.936618 0.350352i \(-0.113938\pi\)
−0.771723 + 0.635959i \(0.780605\pi\)
\(332\) 9.00000i 0.493939i
\(333\) 10.3923 6.00000i 0.569495 0.328798i
\(334\) 9.00000 0.492458
\(335\) 0 0
\(336\) 4.50000 2.59808i 0.245495 0.141737i
\(337\) −6.92820 4.00000i −0.377403 0.217894i 0.299285 0.954164i \(-0.403252\pi\)
−0.676688 + 0.736270i \(0.736585\pi\)
\(338\) 7.79423 + 4.50000i 0.423950 + 0.244768i
\(339\) 12.0000 6.92820i 0.651751 0.376288i
\(340\) 0 0
\(341\) 0 0
\(342\) 20.7846 + 12.0000i 1.12390 + 0.648886i
\(343\) 15.0000i 0.809924i
\(344\) 12.0000 + 20.7846i 0.646997 + 1.12063i
\(345\) 0 0
\(346\) 0 0
\(347\) 3.46410 + 2.00000i 0.185963 + 0.107366i 0.590091 0.807337i \(-0.299092\pi\)
−0.404128 + 0.914702i \(0.632425\pi\)
\(348\) 0.866025 1.50000i 0.0464238 0.0804084i
\(349\) −2.50000 4.33013i −0.133822 0.231786i 0.791325 0.611396i \(-0.209392\pi\)
−0.925147 + 0.379610i \(0.876058\pi\)
\(350\) 0 0
\(351\) −9.00000 5.19615i −0.480384 0.277350i
\(352\) 10.0000i 0.533002i
\(353\) 20.7846 12.0000i 1.10625 0.638696i 0.168397 0.985719i \(-0.446141\pi\)
0.937856 + 0.347024i \(0.112808\pi\)
\(354\) −21.0000 12.1244i −1.11614 0.644402i
\(355\) 0 0
\(356\) −7.50000 + 12.9904i −0.397499 + 0.688489i
\(357\) −20.7846 −1.10004
\(358\) −1.73205 + 1.00000i −0.0915417 + 0.0528516i
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) 45.0000 2.36842
\(362\) 6.06218 3.50000i 0.318621 0.183956i
\(363\) −6.06218 10.5000i −0.318182 0.551107i
\(364\) −3.00000 + 5.19615i −0.157243 + 0.272352i
\(365\) 0 0
\(366\) 10.5000 6.06218i 0.548844 0.316875i
\(367\) −20.7846 + 12.0000i −1.08495 + 0.626395i −0.932227 0.361874i \(-0.882137\pi\)
−0.152721 + 0.988269i \(0.548804\pi\)
\(368\) 3.00000i 0.156386i
\(369\) 15.0000 0.780869
\(370\) 0 0
\(371\) −3.00000 5.19615i −0.155752 0.269771i
\(372\) 0 0
\(373\) −8.66025 5.00000i −0.448411 0.258890i 0.258748 0.965945i \(-0.416690\pi\)
−0.707159 + 0.707055i \(0.750023\pi\)
\(374\) −4.00000 + 6.92820i −0.206835 + 0.358249i
\(375\) 0 0
\(376\) 10.5000 + 18.1865i 0.541496 + 0.937899i
\(377\) 2.00000i 0.103005i
\(378\) 7.79423 13.5000i 0.400892 0.694365i
\(379\) 26.0000 1.33553 0.667765 0.744372i \(-0.267251\pi\)
0.667765 + 0.744372i \(0.267251\pi\)
\(380\) 0 0
\(381\) 7.50000 + 4.33013i 0.384237 + 0.221839i
\(382\) 6.92820 + 4.00000i 0.354478 + 0.204658i
\(383\) −31.1769 18.0000i −1.59307 0.919757i −0.992777 0.119974i \(-0.961719\pi\)
−0.600289 0.799783i \(-0.704948\pi\)
\(384\) 5.19615i 0.265165i
\(385\) 0 0
\(386\) −10.0000 −0.508987
\(387\) 20.7846 + 12.0000i 1.05654 + 0.609994i
\(388\) 2.00000i 0.101535i
\(389\) 16.5000 + 28.5788i 0.836583 + 1.44900i 0.892735 + 0.450582i \(0.148784\pi\)
−0.0561516 + 0.998422i \(0.517883\pi\)
\(390\) 0 0
\(391\) −6.00000 + 10.3923i −0.303433 + 0.525561i
\(392\) −5.19615 3.00000i −0.262445 0.151523i
\(393\) −5.19615 9.00000i −0.262111 0.453990i
\(394\) −6.00000 10.3923i −0.302276 0.523557i
\(395\) 0 0
\(396\) 3.00000 + 5.19615i 0.150756 + 0.261116i
\(397\) 34.0000i 1.70641i −0.521575 0.853206i \(-0.674655\pi\)
0.521575 0.853206i \(-0.325345\pi\)
\(398\) 3.46410 2.00000i 0.173640 0.100251i
\(399\) 41.5692i 2.08106i
\(400\) 0 0
\(401\) 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i \(-0.684957\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) 2.59808 4.50000i 0.129580 0.224440i
\(403\) 0 0
\(404\) −18.0000 −0.895533
\(405\) 0 0
\(406\) 3.00000 0.148888
\(407\) −6.92820 + 4.00000i −0.343418 + 0.198273i
\(408\) −10.3923 + 18.0000i −0.514496 + 0.891133i
\(409\) 7.00000 12.1244i 0.346128 0.599511i −0.639430 0.768849i \(-0.720830\pi\)
0.985558 + 0.169338i \(0.0541630\pi\)
\(410\) 0 0
\(411\) 20.7846i 1.02523i
\(412\) 6.92820 4.00000i 0.341328 0.197066i
\(413\) 42.0000i 2.06668i
\(414\) −4.50000 7.79423i −0.221163 0.383065i
\(415\) 0 0
\(416\) 5.00000 + 8.66025i 0.245145 + 0.424604i
\(417\) 13.8564 + 24.0000i 0.678551 + 1.17529i
\(418\) −13.8564 8.00000i −0.677739 0.391293i
\(419\) 13.0000 22.5167i 0.635092 1.10001i −0.351404 0.936224i \(-0.614296\pi\)
0.986496 0.163787i \(-0.0523710\pi\)
\(420\) 0 0
\(421\) −17.0000 29.4449i −0.828529 1.43505i −0.899192 0.437555i \(-0.855845\pi\)
0.0706626 0.997500i \(-0.477489\pi\)
\(422\) 22.0000i 1.07094i
\(423\) 18.1865 + 10.5000i 0.884260 + 0.510527i
\(424\) −6.00000 −0.291386
\(425\) 0 0
\(426\) 3.46410i 0.167836i
\(427\) −18.1865 10.5000i −0.880108 0.508131i
\(428\) 2.59808 + 1.50000i 0.125583 + 0.0725052i
\(429\) 6.00000 + 3.46410i 0.289683 + 0.167248i
\(430\) 0 0
\(431\) −30.0000 −1.44505 −0.722525 0.691345i \(-0.757018\pi\)
−0.722525 + 0.691345i \(0.757018\pi\)
\(432\) −2.59808 4.50000i −0.125000 0.216506i
\(433\) 28.0000i 1.34559i 0.739827 + 0.672797i \(0.234907\pi\)
−0.739827 + 0.672797i \(0.765093\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2.50000 4.33013i 0.119728 0.207375i
\(437\) −20.7846 12.0000i −0.994263 0.574038i
\(438\) −6.92820 −0.331042
\(439\) 14.0000 + 24.2487i 0.668184 + 1.15733i 0.978412 + 0.206666i \(0.0662612\pi\)
−0.310228 + 0.950662i \(0.600405\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) 8.00000i 0.380521i
\(443\) 12.9904 7.50000i 0.617192 0.356336i −0.158583 0.987346i \(-0.550693\pi\)
0.775775 + 0.631010i \(0.217359\pi\)
\(444\) −6.00000 + 3.46410i −0.284747 + 0.164399i
\(445\) 0 0
\(446\) 9.50000 16.4545i 0.449838 0.779142i
\(447\) −14.7224 25.5000i −0.696347 1.20611i
\(448\) −18.1865 + 10.5000i −0.859233 + 0.496078i
\(449\) 26.0000 1.22702 0.613508 0.789689i \(-0.289758\pi\)
0.613508 + 0.789689i \(0.289758\pi\)
\(450\) 0 0
\(451\) −10.0000 −0.470882
\(452\) −6.92820 + 4.00000i −0.325875 + 0.188144i
\(453\) 3.46410 0.162758
\(454\) −2.00000 + 3.46410i −0.0938647 + 0.162578i
\(455\) 0 0
\(456\) −36.0000 20.7846i −1.68585 0.973329i
\(457\) 17.3205 10.0000i 0.810219 0.467780i −0.0368128 0.999322i \(-0.511721\pi\)
0.847032 + 0.531542i \(0.178387\pi\)
\(458\) 15.0000i 0.700904i
\(459\) 20.7846i 0.970143i
\(460\) 0 0
\(461\) −4.50000 7.79423i −0.209586 0.363013i 0.741998 0.670402i \(-0.233878\pi\)
−0.951584 + 0.307388i \(0.900545\pi\)
\(462\) −5.19615 + 9.00000i −0.241747 + 0.418718i
\(463\) 31.1769 + 18.0000i 1.44891 + 0.836531i 0.998417 0.0562469i \(-0.0179134\pi\)
0.450497 + 0.892778i \(0.351247\pi\)
\(464\) 0.500000 0.866025i 0.0232119 0.0402042i
\(465\) 0 0
\(466\) −12.0000 20.7846i −0.555889 0.962828i
\(467\) 20.0000i 0.925490i −0.886492 0.462745i \(-0.846865\pi\)
0.886492 0.462745i \(-0.153135\pi\)
\(468\) 5.19615 + 3.00000i 0.240192 + 0.138675i
\(469\) −9.00000 −0.415581
\(470\) 0 0
\(471\) 21.0000 12.1244i 0.967629 0.558661i
\(472\) 36.3731 + 21.0000i 1.67421 + 0.966603i
\(473\) −13.8564 8.00000i −0.637118 0.367840i
\(474\) 9.00000 5.19615i 0.413384 0.238667i
\(475\) 0 0
\(476\) 12.0000 0.550019
\(477\) −5.19615 + 3.00000i −0.237915 + 0.137361i
\(478\) 8.00000i 0.365911i
\(479\) −9.00000 15.5885i −0.411220 0.712255i 0.583803 0.811895i \(-0.301564\pi\)
−0.995023 + 0.0996406i \(0.968231\pi\)
\(480\) 0 0
\(481\) −4.00000 + 6.92820i −0.182384 + 0.315899i
\(482\) −9.52628 5.50000i −0.433910 0.250518i
\(483\) −7.79423 + 13.5000i −0.354650 + 0.614271i
\(484\) 3.50000 + 6.06218i 0.159091 + 0.275554i
\(485\) 0 0
\(486\) −13.5000 7.79423i −0.612372 0.353553i
\(487\) 16.0000i 0.725029i 0.931978 + 0.362515i \(0.118082\pi\)
−0.931978 + 0.362515i \(0.881918\pi\)
\(488\) −18.1865 + 10.5000i −0.823266 + 0.475313i
\(489\) −6.00000 3.46410i −0.271329 0.156652i
\(490\) 0 0
\(491\) −10.0000 + 17.3205i −0.451294 + 0.781664i −0.998467 0.0553560i \(-0.982371\pi\)
0.547173 + 0.837020i \(0.315704\pi\)
\(492\) −8.66025 −0.390434
\(493\) −3.46410 + 2.00000i −0.156015 + 0.0900755i
\(494\) −16.0000 −0.719874
\(495\) 0 0
\(496\) 0 0
\(497\) 5.19615 3.00000i 0.233079 0.134568i
\(498\) 7.79423 + 13.5000i 0.349268 + 0.604949i
\(499\) −16.0000 + 27.7128i −0.716258 + 1.24060i 0.246214 + 0.969216i \(0.420813\pi\)
−0.962472 + 0.271380i \(0.912520\pi\)
\(500\) 0 0
\(501\) −13.5000 + 7.79423i −0.603136 + 0.348220i
\(502\) 0 0
\(503\) 7.00000i 0.312115i −0.987748 0.156057i \(-0.950122\pi\)
0.987748 0.156057i \(-0.0498784\pi\)
\(504\) −13.5000 + 23.3827i −0.601338 + 1.04155i
\(505\) 0 0
\(506\) 3.00000 + 5.19615i 0.133366 + 0.230997i
\(507\) −15.5885 −0.692308
\(508\) −4.33013 2.50000i −0.192118 0.110920i
\(509\) 21.5000 37.2391i 0.952971 1.65059i 0.214026 0.976828i \(-0.431342\pi\)
0.738945 0.673766i \(-0.235324\pi\)
\(510\) 0 0
\(511\) 6.00000 + 10.3923i 0.265424 + 0.459728i
\(512\) 11.0000i 0.486136i
\(513\) −41.5692 −1.83533
\(514\) 6.00000 0.264649
\(515\) 0 0
\(516\) −12.0000 6.92820i −0.528271 0.304997i
\(517\) −12.1244 7.00000i −0.533229 0.307860i
\(518\) −10.3923 6.00000i −0.456612 0.263625i
\(519\) 0 0
\(520\) 0 0
\(521\) 11.0000 0.481919 0.240959 0.970535i \(-0.422538\pi\)
0.240959 + 0.970535i \(0.422538\pi\)
\(522\) 3.00000i 0.131306i
\(523\) 29.0000i 1.26808i −0.773300 0.634041i \(-0.781395\pi\)
0.773300 0.634041i \(-0.218605\pi\)
\(524\) 3.00000 + 5.19615i 0.131056 + 0.226995i
\(525\) 0 0
\(526\) 8.00000 13.8564i 0.348817 0.604168i
\(527\) 0 0
\(528\) 1.73205 + 3.00000i 0.0753778 + 0.130558i
\(529\) −7.00000 12.1244i −0.304348 0.527146i
\(530\) 0 0
\(531\) 42.0000 1.82264
\(532\) 24.0000i 1.04053i
\(533\) −8.66025 + 5.00000i −0.375117 + 0.216574i
\(534\) 25.9808i 1.12430i
\(535\) 0 0
\(536\) −4.50000 + 7.79423i −0.194370 + 0.336659i
\(537\) 1.73205 3.00000i 0.0747435 0.129460i
\(538\) 21.6506 12.5000i 0.933425 0.538913i
\(539\) 4.00000 0.172292
\(540\) 0 0
\(541\) −39.0000 −1.67674 −0.838370 0.545101i \(-0.816491\pi\)
−0.838370 + 0.545101i \(0.816491\pi\)
\(542\) 6.92820 4.00000i 0.297592 0.171815i
\(543\) −6.06218 + 10.5000i −0.260153 + 0.450598i
\(544\) 10.0000 17.3205i 0.428746 0.742611i
\(545\) 0 0
\(546\) 10.3923i 0.444750i
\(547\) 25.1147 14.5000i 1.07383 0.619975i 0.144604 0.989490i \(-0.453809\pi\)
0.929225 + 0.369514i \(0.120476\pi\)
\(548\) 12.0000i 0.512615i
\(549\) −10.5000 + 18.1865i −0.448129 + 0.776182i
\(550\) 0 0
\(551\) −4.00000 6.92820i −0.170406 0.295151i
\(552\) 7.79423 + 13.5000i 0.331744 + 0.574598i
\(553\) −15.5885 9.00000i −0.662889 0.382719i
\(554\) 6.00000 10.3923i 0.254916 0.441527i
\(555\) 0 0
\(556\) −8.00000 13.8564i −0.339276 0.587643i
\(557\) 30.0000i 1.27114i 0.772043 + 0.635570i \(0.219235\pi\)
−0.772043 + 0.635570i \(0.780765\pi\)
\(558\) 0 0
\(559\) −16.0000 −0.676728
\(560\) 0 0
\(561\) 13.8564i 0.585018i
\(562\) −12.9904 7.50000i −0.547966 0.316368i
\(563\) 18.1865 + 10.5000i 0.766471 + 0.442522i 0.831614 0.555354i \(-0.187417\pi\)
−0.0651433 + 0.997876i \(0.520750\pi\)
\(564\) −10.5000 6.06218i −0.442130 0.255264i
\(565\) 0 0
\(566\) 21.0000 0.882696
\(567\) 27.0000i 1.13389i
\(568\) 6.00000i 0.251754i
\(569\) −3.00000 5.19615i −0.125767 0.217834i 0.796266 0.604947i \(-0.206806\pi\)
−0.922032 + 0.387113i \(0.873472\pi\)
\(570\) 0 0
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) −3.46410 2.00000i −0.144841 0.0836242i
\(573\) −13.8564 −0.578860
\(574\) −7.50000 12.9904i −0.313044 0.542208i
\(575\) 0 0
\(576\) 10.5000 + 18.1865i 0.437500 + 0.757772i
\(577\) 10.0000i 0.416305i 0.978096 + 0.208153i \(0.0667451\pi\)
−0.978096 + 0.208153i \(0.933255\pi\)
\(578\) −0.866025 + 0.500000i −0.0360219 + 0.0207973i
\(579\) 15.0000 8.66025i 0.623379 0.359908i
\(580\) 0 0
\(581\) 13.5000 23.3827i 0.560074 0.970077i
\(582\) −1.73205 3.00000i −0.0717958 0.124354i
\(583\) 3.46410 2.00000i 0.143468 0.0828315i
\(584\) 12.0000 0.496564
\(585\) 0 0
\(586\) 12.0000 0.495715
\(587\) 28.5788 16.5000i 1.17957 0.681028i 0.223659 0.974668i \(-0.428200\pi\)
0.955916 + 0.293640i \(0.0948666\pi\)
\(588\) 3.46410 0.142857
\(589\) 0 0
\(590\) 0 0
\(591\) 18.0000 + 10.3923i 0.740421 + 0.427482i
\(592\) −3.46410 + 2.00000i −0.142374 + 0.0821995i
\(593\) 20.0000i 0.821302i 0.911793 + 0.410651i \(0.134698\pi\)
−0.911793 + 0.410651i \(0.865302\pi\)
\(594\) 9.00000 + 5.19615i 0.369274 + 0.213201i
\(595\) 0 0
\(596\) 8.50000 + 14.7224i 0.348174 + 0.603054i
\(597\) −3.46410 + 6.00000i −0.141776 + 0.245564i
\(598\) 5.19615 + 3.00000i 0.212486 + 0.122679i
\(599\) −5.00000 + 8.66025i −0.204294 + 0.353848i −0.949908 0.312531i \(-0.898823\pi\)
0.745613 + 0.666379i \(0.232157\pi\)
\(600\) 0 0
\(601\) −1.00000 1.73205i −0.0407909 0.0706518i 0.844909 0.534910i \(-0.179654\pi\)
−0.885700 + 0.464258i \(0.846321\pi\)
\(602\) 24.0000i 0.978167i
\(603\) 9.00000i 0.366508i
\(604\) −2.00000 −0.0813788
\(605\) 0 0
\(606\) −27.0000 + 15.5885i −1.09680 + 0.633238i
\(607\) −35.5070 20.5000i −1.44119 0.832069i −0.443257 0.896394i \(-0.646177\pi\)
−0.997929 + 0.0643251i \(0.979511\pi\)
\(608\) 34.6410 + 20.0000i 1.40488 + 0.811107i
\(609\) −4.50000 + 2.59808i −0.182349 + 0.105279i
\(610\) 0 0
\(611\) −14.0000 −0.566379
\(612\) 12.0000i 0.485071i
\(613\) 44.0000i 1.77714i −0.458738 0.888572i \(-0.651698\pi\)
0.458738 0.888572i \(-0.348302\pi\)
\(614\) 3.50000 + 6.06218i 0.141249 + 0.244650i
\(615\) 0 0
\(616\) 9.00000 15.5885i 0.362620 0.628077i
\(617\) −31.1769 18.0000i −1.25514 0.724653i −0.283011 0.959117i \(-0.591333\pi\)
−0.972125 + 0.234464i \(0.924666\pi\)
\(618\) 6.92820 12.0000i 0.278693 0.482711i
\(619\) −2.00000 3.46410i −0.0803868 0.139234i 0.823029 0.567999i \(-0.192282\pi\)
−0.903416 + 0.428765i \(0.858949\pi\)
\(620\) 0 0
\(621\) 13.5000 + 7.79423i 0.541736 + 0.312772i
\(622\) 0 0
\(623\) 38.9711 22.5000i 1.56135 0.901443i
\(624\) 3.00000 + 1.73205i 0.120096 + 0.0693375i
\(625\) 0 0
\(626\) −7.00000 + 12.1244i −0.279776 + 0.484587i
\(627\) 27.7128 1.10674
\(628\) −12.1244 + 7.00000i −0.483814 + 0.279330i
\(629\) 16.0000 0.637962
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) −15.5885 + 9.00000i −0.620076 + 0.358001i
\(633\) −19.0526 33.0000i −0.757271 1.31163i
\(634\) −17.0000 + 29.4449i −0.675156 + 1.16940i
\(635\) 0 0
\(636\) 3.00000 1.73205i 0.118958 0.0686803i
\(637\) 3.46410 2.00000i 0.137253 0.0792429i
\(638\) 2.00000i 0.0791808i
\(639\) −3.00000 5.19615i −0.118678 0.205557i
\(640\) 0 0
\(641\) −16.5000 28.5788i −0.651711 1.12880i −0.982708 0.185164i \(-0.940718\pi\)
0.330997 0.943632i \(-0.392615\pi\)
\(642\) 5.19615 0.205076
\(643\) 7.79423 + 4.50000i 0.307374 + 0.177463i 0.645751 0.763548i \(-0.276544\pi\)
−0.338377 + 0.941011i \(0.609878\pi\)
\(644\) 4.50000 7.79423i 0.177325 0.307136i
\(645\) 0 0
\(646\) 16.0000 + 27.7128i 0.629512 + 1.09035i
\(647\) 17.0000i 0.668339i 0.942513 + 0.334169i \(0.108456\pi\)
−0.942513 + 0.334169i \(0.891544\pi\)
\(648\) 23.3827 + 13.5000i 0.918559 + 0.530330i
\(649\) −28.0000 −1.09910
\(650\) 0 0
\(651\) 0 0
\(652\) 3.46410 + 2.00000i 0.135665 + 0.0783260i
\(653\) 3.46410 + 2.00000i 0.135561 + 0.0782660i 0.566247 0.824236i \(-0.308395\pi\)
−0.430686 + 0.902502i \(0.641728\pi\)
\(654\) 8.66025i 0.338643i
\(655\) 0 0
\(656\) −5.00000 −0.195217
\(657\) 10.3923 6.00000i 0.405442 0.234082i
\(658\) 21.0000i 0.818665i
\(659\) −4.00000 6.92820i −0.155818 0.269884i 0.777539 0.628835i \(-0.216468\pi\)
−0.933357 + 0.358951i \(0.883135\pi\)
\(660\) 0 0
\(661\) 7.00000 12.1244i 0.272268 0.471583i −0.697174 0.716902i \(-0.745559\pi\)
0.969442 + 0.245319i \(0.0788928\pi\)
\(662\) −5.19615 3.00000i −0.201954 0.116598i
\(663\) −6.92820 12.0000i −0.269069 0.466041i
\(664\) −13.5000 23.3827i −0.523902 0.907424i
\(665\) 0 0
\(666\) −6.00000 + 10.3923i −0.232495 + 0.402694i
\(667\) 3.00000i 0.116160i
\(668\) 7.79423 4.50000i 0.301568 0.174110i
\(669\) 32.9090i 1.27233i
\(670\) 0 0
\(671\) 7.00000 12.1244i 0.270232 0.468056i
\(672\) 12.9904 22.5000i 0.501115 0.867956i
\(673\) 5.19615 3.00000i 0.200297 0.115642i −0.396497 0.918036i \(-0.629774\pi\)
0.596794 + 0.802395i \(0.296441\pi\)
\(674\) 8.00000 0.308148
\(675\) 0 0
\(676\) 9.00000 0.346154
\(677\) 36.3731 21.0000i 1.39793 0.807096i 0.403755 0.914867i \(-0.367705\pi\)
0.994176 + 0.107772i \(0.0343715\pi\)
\(678\) −6.92820 + 12.0000i −0.266076 + 0.460857i
\(679\) −3.00000 + 5.19615i −0.115129 + 0.199410i
\(680\) 0 0
\(681\) 6.92820i 0.265489i
\(682\) 0 0
\(683\) 12.0000i 0.459167i 0.973289 + 0.229584i \(0.0737364\pi\)
−0.973289 + 0.229584i \(0.926264\pi\)
\(684\) 24.0000 0.917663
\(685\) 0 0
\(686\) −7.50000 12.9904i −0.286351 0.495975i
\(687\) −12.9904 22.5000i −0.495614 0.858429i
\(688\) −6.92820 4.00000i −0.264135 0.152499i
\(689\) 2.00000 3.46410i 0.0761939 0.131972i
\(690\) 0 0
\(691\) 7.00000 + 12.1244i 0.266293 + 0.461232i 0.967901 0.251330i \(-0.0808679\pi\)
−0.701609 + 0.712562i \(0.747535\pi\)
\(692\) 0 0
\(693\) 18.0000i 0.683763i
\(694\) −4.00000 −0.151838
\(695\) 0 0
\(696\) 5.19615i 0.196960i
\(697\) 17.3205 + 10.0000i 0.656061 + 0.378777i
\(698\) 4.33013 + 2.50000i 0.163898 + 0.0946264i
\(699\) 36.0000 + 20.7846i 1.36165 + 0.786146i
\(700\) 0 0
\(701\) 23.0000 0.868698 0.434349 0.900745i \(-0.356978\pi\)
0.434349 + 0.900745i \(0.356978\pi\)
\(702\) 10.3923 0.392232
\(703\) 32.0000i 1.20690i
\(704\) −7.00000 12.1244i −0.263822 0.456954i
\(705\) 0 0
\(706\) −12.0000 + 20.7846i −0.451626 + 0.782239i
\(707\) 46.7654 + 27.0000i 1.75879 + 1.01544i
\(708\) −24.2487 −0.911322
\(709\) −20.5000 35.5070i −0.769894 1.33349i −0.937620 0.347661i \(-0.886976\pi\)
0.167727 0.985834i \(-0.446357\pi\)
\(710\) 0 0
\(711\) −9.00000 + 15.5885i −0.337526 + 0.584613i
\(712\) 45.0000i 1.68645i
\(713\) 0 0
\(714\) 18.0000 10.3923i 0.673633 0.388922i
\(715\) 0 0
\(716\) −1.00000 + 1.73205i −0.0373718 + 0.0647298i
\(717\) 6.92820 + 12.0000i 0.258738 + 0.448148i
\(718\) 20.7846 12.0000i 0.775675 0.447836i
\(719\) −6.00000 −0.223762 −0.111881 0.993722i \(-0.535688\pi\)
−0.111881 + 0.993722i \(0.535688\pi\)
\(720\) 0 0
\(721\) −24.0000 −0.893807
\(722\) −38.9711 + 22.5000i −1.45036 + 0.837363i
\(723\) 19.0526 0.708572
\(724\) 3.50000 6.06218i 0.130076 0.225299i
\(725\) 0 0
\(726\) 10.5000 + 6.06218i 0.389692 + 0.224989i
\(727\) −19.9186 + 11.5000i −0.738739 + 0.426511i −0.821611 0.570049i \(-0.806924\pi\)
0.0828714 + 0.996560i \(0.473591\pi\)
\(728\) 18.0000i 0.667124i
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) 16.0000 + 27.7128i 0.591781 + 1.02500i
\(732\) 6.06218 10.5000i 0.224065 0.388091i
\(733\) 29.4449 + 17.0000i 1.08757 + 0.627909i 0.932929 0.360061i \(-0.117244\pi\)
0.154642 + 0.987971i \(0.450578\pi\)
\(734\) 12.0000 20.7846i 0.442928 0.767174i
\(735\) 0 0
\(736\) −7.50000 12.9904i −0.276454 0.478832i
\(737\) 6.00000i 0.221013i
\(738\) −12.9904 + 7.50000i −0.478183 + 0.276079i
\(739\) 2.00000 0.0735712 0.0367856 0.999323i \(-0.488288\pi\)
0.0367856 + 0.999323i \(0.488288\pi\)
\(740\) 0 0
\(741\) 24.0000 13.8564i 0.881662 0.509028i
\(742\) 5.19615 + 3.00000i 0.190757 + 0.110133i
\(743\) 25.1147 + 14.5000i 0.921370 + 0.531953i 0.884072 0.467351i \(-0.154791\pi\)
0.0372984 + 0.999304i \(0.488125\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 10.0000 0.366126
\(747\) −23.3827 13.5000i −0.855528 0.493939i
\(748\) 8.00000i 0.292509i
\(749\) −4.50000 7.79423i −0.164426 0.284795i
\(750\) 0 0
\(751\) −5.00000 + 8.66025i −0.182453 + 0.316017i −0.942715 0.333599i \(-0.891737\pi\)
0.760263 + 0.649616i \(0.225070\pi\)
\(752\) −6.06218 3.50000i −0.221065 0.127632i
\(753\) 0 0
\(754\) 1.00000 + 1.73205i 0.0364179 + 0.0630776i
\(755\) 0 0
\(756\) 15.5885i 0.566947i
\(757\) 26.0000i 0.944986i 0.881334 + 0.472493i \(0.156646\pi\)
−0.881334 + 0.472493i \(0.843354\pi\)
\(758\) −22.5167 + 13.0000i −0.817842 + 0.472181i
\(759\) −9.00000 5.19615i −0.326679 0.188608i
\(760\) 0 0
\(761\) −7.50000 + 12.9904i −0.271875 + 0.470901i −0.969342 0.245716i \(-0.920977\pi\)
0.697467 + 0.716617i \(0.254310\pi\)
\(762\) −8.66025 −0.313728
\(763\) −12.9904 + 7.50000i −0.470283 + 0.271518i
\(764\) 8.00000 0.289430
\(765\) 0 0
\(766\) 36.0000 1.30073
\(767\) −24.2487 + 14.0000i −0.875570 + 0.505511i
\(768\) −14.7224 25.5000i −0.531250 0.920152i
\(769\) 2.50000 4.33013i 0.0901523 0.156148i −0.817423 0.576038i \(-0.804598\pi\)
0.907575 + 0.419890i \(0.137931\pi\)
\(770\) 0 0
\(771\) −9.00000 + 5.19615i −0.324127 + 0.187135i
\(772\) −8.66025 + 5.00000i −0.311689 + 0.179954i
\(773\) 24.0000i 0.863220i −0.902060 0.431610i \(-0.857946\pi\)
0.902060 0.431610i \(-0.142054\pi\)
\(774\) −24.0000 −0.862662
\(775\) 0 0
\(776\) 3.00000 + 5.19615i 0.107694 + 0.186531i
\(777\) 20.7846 0.745644
\(778\) −28.5788 16.5000i −1.02460 0.591554i
\(779\) −20.0000 + 34.6410i −0.716574 + 1.24114i
\(780\) 0 0
\(781\) 2.00000 + 3.46410i 0.0715656 + 0.123955i
\(782\) 12.0000i 0.429119i
\(783\) 2.59808 + 4.50000i 0.0928477 + 0.160817i
\(784\) 2.00000 0.0714286