Properties

Label 225.2.k.a.124.1
Level $225$
Weight $2$
Character 225.124
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 124.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 225.124
Dual form 225.2.k.a.49.1

$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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 0.161521 0.986869i \(-0.448360\pi\)
−0.773893 + 0.633316i \(0.781693\pi\)
\(3\) 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 0.902867 0.429919i \(-0.141458\pi\)
0.0791130 + 0.996866i \(0.474791\pi\)
\(8\) 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 −0.674967 0.737848i \(-0.735842\pi\)
0.976478 + 0.215615i \(0.0691756\pi\)
\(12\) 0.866025 1.50000i 0.250000 0.433013i
\(13\) 1.73205 1.00000i 0.480384 0.277350i −0.240192 0.970725i \(-0.577210\pi\)
0.720577 + 0.693375i \(0.243877\pi\)
\(14\) −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 \(0.161206\pi\)
−0.874475 + 0.485071i \(0.838794\pi\)
\(18\) 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 −0.745782 0.666190i \(-0.767924\pi\)
0.204046 + 0.978961i \(0.434591\pi\)
\(24\) −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 −0.908708 0.417432i \(-0.862930\pi\)
0.815861 + 0.578249i \(0.196264\pi\)
\(30\) 0 0
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) 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 \(-0.893356\pi\)
0.944400 0.328798i \(-0.106644\pi\)
\(38\) −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 0.602072 0.798441i \(-0.294342\pi\)
−0.992507 + 0.122189i \(0.961009\pi\)
\(42\) 2.59808 4.50000i 0.400892 0.694365i
\(43\) −6.92820 4.00000i −1.05654 0.609994i −0.132068 0.991241i \(-0.542162\pi\)
−0.924473 + 0.381246i \(0.875495\pi\)
\(44\) −2.00000 −0.301511
\(45\) 0 0
\(46\) 3.00000 0.442326
\(47\) −6.06218 3.50000i −0.884260 0.510527i −0.0121990 0.999926i \(-0.503883\pi\)
−0.872060 + 0.489398i \(0.837217\pi\)
\(48\) 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 \(0.0438619\pi\)
−0.990521 + 0.137361i \(0.956138\pi\)
\(54\) 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 −0.812198 0.583382i \(-0.801729\pi\)
−0.0991242 0.995075i \(-0.531604\pi\)
\(60\) 0 0
\(61\) −3.50000 + 6.06218i −0.448129 + 0.776182i −0.998264 0.0588933i \(-0.981243\pi\)
0.550135 + 0.835076i \(0.314576\pi\)
\(62\) 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 −0.650236 0.759733i \(-0.725330\pi\)
0.332830 + 0.942987i \(0.391996\pi\)
\(68\) 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 \(-0.924791\pi\)
0.972217 0.234082i \(-0.0752085\pi\)
\(74\) −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 −0.983967 0.178352i \(-0.942924\pi\)
0.646440 + 0.762964i \(0.276257\pi\)
\(80\) 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 0.862512 0.506036i \(-0.168890\pi\)
−0.00698436 + 0.999976i \(0.502223\pi\)
\(84\) 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 0.409484 0.912317i \(-0.365709\pi\)
−0.585348 + 0.810782i \(0.699042\pi\)
\(98\) 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 0.0623905 0.998052i \(-0.480128\pi\)
0.833143 0.553058i \(-0.186539\pi\)
\(102\) 6.92820 0.685994
\(103\) −6.92820 + 4.00000i −0.682656 + 0.394132i −0.800855 0.598858i \(-0.795621\pi\)
0.118199 + 0.992990i \(0.462288\pi\)
\(104\) 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 \(0.0463216\pi\)
−0.989430 + 0.145010i \(0.953678\pi\)
\(108\) 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 −0.137376 0.990519i \(-0.543867\pi\)
0.789127 + 0.614231i \(0.210534\pi\)
\(114\) 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 \(-0.928794\pi\)
0.975083 0.221839i \(-0.0712060\pi\)
\(128\) −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 0.966803 0.255524i \(-0.0822479\pi\)
−0.704692 + 0.709514i \(0.748915\pi\)
\(132\) −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 −0.0146279 0.999893i \(-0.504656\pi\)
−0.873247 + 0.487278i \(0.837990\pi\)
\(138\) 2.59808 + 4.50000i 0.221163 + 0.383065i
\(139\) −8.00000 13.8564i −0.678551 1.17529i −0.975417 0.220366i \(-0.929275\pi\)
0.296866 0.954919i \(-0.404058\pi\)
\(140\) 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 0.969724 + 0.244202i \(0.0785259\pi\)
−0.273377 + 0.961907i \(0.588141\pi\)
\(150\) 0 0
\(151\) 1.00000 1.73205i 0.0813788 0.140952i −0.822464 0.568818i \(-0.807401\pi\)
0.903842 + 0.427865i \(0.140734\pi\)
\(152\) 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 0.0691164 0.997609i \(-0.477982\pi\)
0.898513 + 0.438948i \(0.144649\pi\)
\(158\) 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 \(0.0500701\pi\)
−0.987654 + 0.156652i \(0.949930\pi\)
\(164\) −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 −0.770274 0.637713i \(-0.779881\pi\)
0.167139 + 0.985933i \(0.446547\pi\)
\(168\) −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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(174\) 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 −0.973674 0.227946i \(-0.926799\pi\)
0.684244 + 0.729253i \(0.260132\pi\)
\(192\) −6.06218 10.5000i −0.437500 0.757772i
\(193\) 8.66025 5.00000i 0.623379 0.359908i −0.154805 0.987945i \(-0.549475\pi\)
0.778183 + 0.628037i \(0.216141\pi\)
\(194\) 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 \(-0.859401\pi\)
0.904024 0.427482i \(-0.140599\pi\)
\(198\) 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 0.944237 + 0.329266i \(0.106801\pi\)
−0.186966 + 0.982366i \(0.559865\pi\)
\(212\) 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 −0.165161 0.986267i \(-0.552814\pi\)
−0.936713 + 0.350100i \(0.886148\pi\)
\(224\) 15.0000 1.00223
\(225\) 0 0
\(226\) −8.00000 −0.532152
\(227\) 3.46410 + 2.00000i 0.229920 + 0.132745i 0.610535 0.791989i \(-0.290954\pi\)
−0.380615 + 0.924734i \(0.624288\pi\)
\(228\) 6.92820 12.0000i 0.458831 0.794719i
\(229\) 7.50000 + 12.9904i 0.495614 + 0.858429i 0.999987 0.00505719i \(-0.00160976\pi\)
−0.504373 + 0.863486i \(0.668276\pi\)
\(230\) 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 \(-0.712073\pi\)
0.618041 0.786146i \(-0.287927\pi\)
\(234\) 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 0.707166 0.707048i \(-0.249973\pi\)
−0.965904 + 0.258900i \(0.916640\pi\)
\(240\) 0 0
\(241\) 5.50000 9.52628i 0.354286 0.613642i −0.632709 0.774389i \(-0.718057\pi\)
0.986996 + 0.160748i \(0.0513906\pi\)
\(242\) 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 −0.653231 0.757159i \(-0.726587\pi\)
0.329104 + 0.944294i \(0.393253\pi\)
\(258\) −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 0.00771799 0.999970i \(-0.497543\pi\)
−0.862141 + 0.506669i \(0.830877\pi\)
\(264\) 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 0.154172 0.988044i \(-0.450729\pi\)
−0.778585 + 0.627539i \(0.784062\pi\)
\(278\) 16.0000i 0.959616i
\(279\) 0 0
\(280\) 0 0
\(281\) 7.50000 12.9904i 0.447412 0.774941i −0.550804 0.834634i \(-0.685679\pi\)
0.998217 + 0.0596933i \(0.0190123\pi\)
\(282\) −6.06218 + 10.5000i −0.360997 + 0.625266i
\(283\) −18.1865 + 10.5000i −1.08108 + 0.624160i −0.931187 0.364542i \(-0.881225\pi\)
−0.149890 + 0.988703i \(0.547892\pi\)
\(284\) −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 −0.771839 0.635818i \(-0.780663\pi\)
0.164714 + 0.986341i \(0.447330\pi\)
\(294\) 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 \(0.0640148\pi\)
−0.979846 + 0.199756i \(0.935985\pi\)
\(308\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(312\) −5.19615 + 9.00000i −0.294174 + 0.509525i
\(313\) 12.1244 + 7.00000i 0.685309 + 0.395663i 0.801852 0.597522i \(-0.203848\pi\)
−0.116543 + 0.993186i \(0.537181\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) 6.00000 0.337526
\(317\) 29.4449 + 17.0000i 1.65379 + 0.954815i 0.975494 + 0.220024i \(0.0706137\pi\)
0.678294 + 0.734791i \(0.262720\pi\)
\(318\) 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 −0.771723 0.635959i \(-0.780605\pi\)
0.936618 + 0.350352i \(0.113938\pi\)
\(332\) 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 −0.676688 0.736270i \(-0.736585\pi\)
0.299285 + 0.954164i \(0.403252\pi\)
\(338\) 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 −0.404128 0.914702i \(-0.632425\pi\)
0.590091 + 0.807337i \(0.299092\pi\)
\(348\) 0.866025 + 1.50000i 0.0464238 + 0.0804084i
\(349\) −2.50000 + 4.33013i −0.133822 + 0.231786i −0.925147 0.379610i \(-0.876058\pi\)
0.791325 + 0.611396i \(0.209392\pi\)
\(350\) 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 0.937856 0.347024i \(-0.112808\pi\)
0.168397 + 0.985719i \(0.446141\pi\)
\(354\) −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 −0.152721 0.988269i \(-0.548804\pi\)
−0.932227 + 0.361874i \(0.882137\pi\)
\(368\) 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 −0.707159 0.707055i \(-0.750023\pi\)
0.258748 + 0.965945i \(0.416690\pi\)
\(374\) −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 −0.600289 + 0.799783i \(0.704948\pi\)
−0.992777 + 0.119974i \(0.961719\pi\)
\(384\) 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 −0.0561516 0.998422i \(-0.517883\pi\)
0.892735 0.450582i \(-0.148784\pi\)
\(390\) 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 \(0.325345\pi\)
−0.521575 + 0.853206i \(0.674655\pi\)
\(398\) 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 0.998350 0.0574304i \(-0.0182907\pi\)
−0.548911 + 0.835881i \(0.684957\pi\)
\(402\) 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 0.985558 0.169338i \(-0.0541630\pi\)
−0.639430 + 0.768849i \(0.720830\pi\)
\(410\) 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 0.986496 + 0.163787i \(0.0523710\pi\)
−0.351404 + 0.936224i \(0.614296\pi\)
\(420\) 0 0
\(421\) −17.0000 + 29.4449i −0.828529 + 1.43505i 0.0706626 + 0.997500i \(0.477489\pi\)
−0.899192 + 0.437555i \(0.855845\pi\)
\(422\) 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 \(-0.765093\pi\)
0.739827 0.672797i \(-0.234907\pi\)
\(434\) 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 −0.310228 0.950662i \(-0.600405\pi\)
0.978412 0.206666i \(-0.0662612\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) 8.00000i 0.380521i
\(443\) 12.9904 + 7.50000i 0.617192 + 0.356336i 0.775775 0.631010i \(-0.217359\pi\)
−0.158583 + 0.987346i \(0.550693\pi\)
\(444\) −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 0.847032 0.531542i \(-0.178387\pi\)
−0.0368128 + 0.999322i \(0.511721\pi\)
\(458\) 15.0000i 0.700904i
\(459\) 20.7846i 0.970143i
\(460\) 0 0
\(461\) −4.50000 + 7.79423i −0.209586 + 0.363013i −0.951584 0.307388i \(-0.900545\pi\)
0.741998 + 0.670402i \(0.233878\pi\)
\(462\) −5.19615 9.00000i −0.241747 0.418718i
\(463\) 31.1769 18.0000i 1.44891 0.836531i 0.450497 0.892778i \(-0.351247\pi\)
0.998417 + 0.0562469i \(0.0179134\pi\)
\(464\) 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 \(0.153135\pi\)
−0.886492 + 0.462745i \(0.846865\pi\)
\(468\) 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 −0.995023 0.0996406i \(-0.968231\pi\)
0.583803 + 0.811895i \(0.301564\pi\)
\(480\) 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 \(-0.881918\pi\)
0.931978 0.362515i \(-0.118082\pi\)
\(488\) −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 0.547173 0.837020i \(-0.315704\pi\)
−0.998467 + 0.0553560i \(0.982371\pi\)
\(492\) −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 −0.962472 0.271380i \(-0.912520\pi\)
0.246214 0.969216i \(-0.420813\pi\)
\(500\) 0 0
\(501\) −13.5000 7.79423i −0.603136 0.348220i
\(502\) 0 0
\(503\) 7.00000i 0.312115i 0.987748 + 0.156057i \(0.0498784\pi\)
−0.987748 + 0.156057i \(0.950122\pi\)
\(504\) −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 0.738945 + 0.673766i \(0.235324\pi\)
0.214026 + 0.976828i \(0.431342\pi\)
\(510\) 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 \(0.218605\pi\)
−0.773300 + 0.634041i \(0.781395\pi\)
\(524\) 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 0.929225 0.369514i \(-0.120476\pi\)
0.144604 + 0.989490i \(0.453809\pi\)
\(548\) 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 \(-0.780765\pi\)
0.772043 0.635570i \(-0.219235\pi\)
\(558\) 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 −0.0651433 0.997876i \(-0.520750\pi\)
0.831614 + 0.555354i \(0.187417\pi\)
\(564\) −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 −0.922032 0.387113i \(-0.873472\pi\)
0.796266 + 0.604947i \(0.206806\pi\)
\(570\) 0 0
\(571\) −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i \(-0.933141\pi\)
0.308443 0.951243i \(-0.400192\pi\)
\(572\) −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 \(-0.933255\pi\)
0.978096 0.208153i \(-0.0667451\pi\)
\(578\) −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 0.955916 0.293640i \(-0.0948666\pi\)
0.223659 + 0.974668i \(0.428200\pi\)
\(588\) 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 \(-0.865302\pi\)
0.911793 0.410651i \(-0.134698\pi\)
\(594\) 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 0.745613 0.666379i \(-0.232157\pi\)
−0.949908 + 0.312531i \(0.898823\pi\)
\(600\) 0 0
\(601\) −1.00000 + 1.73205i −0.0407909 + 0.0706518i −0.885700 0.464258i \(-0.846321\pi\)
0.844909 + 0.534910i \(0.179654\pi\)
\(602\) 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 −0.997929 0.0643251i \(-0.979511\pi\)
−0.443257 + 0.896394i \(0.646177\pi\)
\(608\) 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 \(0.348302\pi\)
−0.458738 + 0.888572i \(0.651698\pi\)
\(614\) 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 −0.972125 0.234464i \(-0.924666\pi\)
−0.283011 + 0.959117i \(0.591333\pi\)
\(618\) 6.92820 + 12.0000i 0.278693 + 0.482711i
\(619\) −2.00000 + 3.46410i −0.0803868 + 0.139234i −0.903416 0.428765i \(-0.858949\pi\)
0.823029 + 0.567999i \(0.192282\pi\)
\(620\) 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 0.330997 + 0.943632i \(0.392615\pi\)
−0.982708 + 0.185164i \(0.940718\pi\)
\(642\) 5.19615 0.205076
\(643\) 7.79423 4.50000i 0.307374 0.177463i −0.338377 0.941011i \(-0.609878\pi\)
0.645751 + 0.763548i \(0.276544\pi\)
\(644\) 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 \(-0.891544\pi\)
0.942513 0.334169i \(-0.108456\pi\)
\(648\) 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 −0.430686 0.902502i \(-0.641728\pi\)
0.566247 + 0.824236i \(0.308395\pi\)
\(654\) 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 −0.933357 0.358951i \(-0.883135\pi\)
0.777539 + 0.628835i \(0.216468\pi\)
\(660\) 0 0
\(661\) 7.00000 + 12.1244i 0.272268 + 0.471583i 0.969442 0.245319i \(-0.0788928\pi\)
−0.697174 + 0.716902i \(0.745559\pi\)
\(662\) −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 0.596794 0.802395i \(-0.296441\pi\)
−0.396497 + 0.918036i \(0.629774\pi\)
\(674\) 8.00000 0.308148
\(675\) 0 0
\(676\) 9.00000 0.346154
\(677\) 36.3731 + 21.0000i 1.39793 + 0.807096i 0.994176 0.107772i \(-0.0343715\pi\)
0.403755 + 0.914867i \(0.367705\pi\)
\(678\) −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 \(-0.926264\pi\)
0.973289 0.229584i \(-0.0737364\pi\)
\(684\) 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 −0.701609 0.712562i \(-0.747535\pi\)
0.967901 + 0.251330i \(0.0808679\pi\)
\(692\) 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 0.167727 + 0.985834i \(0.446357\pi\)
−0.937620 + 0.347661i \(0.886976\pi\)
\(710\) 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 0.0828714 0.996560i \(-0.473591\pi\)
−0.821611 + 0.570049i \(0.806924\pi\)
\(728\) 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 0.154642 0.987971i \(-0.450578\pi\)
0.932929 + 0.360061i \(0.117244\pi\)
\(734\) 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 0.0372984 0.999304i \(-0.488125\pi\)
0.884072 + 0.467351i \(0.154791\pi\)
\(744\) 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 0.760263 0.649616i \(-0.225070\pi\)
−0.942715 + 0.333599i \(0.891737\pi\)
\(752\) −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 \(-0.843354\pi\)
0.881334 0.472493i \(-0.156646\pi\)
\(758\) −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 0.697467 0.716617i \(-0.254310\pi\)
−0.969342 + 0.245716i \(0.920977\pi\)
\(762\) −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 0.907575 0.419890i \(-0.137931\pi\)
−0.817423 + 0.576038i \(0.804598\pi\)
\(770\) 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 \(0.142054\pi\)
−0.902060 + 0.431610i \(0.857946\pi\)
\(774\) −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