Properties

Label 225.2.e.a.76.1
Level $225$
Weight $2$
Character 225.76
Analytic conductor $1.797$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) 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: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 76.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 225.76
Dual form 225.2.e.a.151.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.73205i q^{6} +(-1.50000 - 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.73205i q^{6} +(-1.50000 - 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.00000 + 1.73205i) q^{11} +(1.50000 - 0.866025i) q^{12} +(-1.00000 + 1.73205i) q^{13} +(1.50000 - 2.59808i) q^{14} +(0.500000 + 0.866025i) q^{16} -4.00000 q^{17} +(-1.50000 + 2.59808i) q^{18} -8.00000 q^{19} -5.19615i q^{21} +(-1.00000 + 1.73205i) q^{22} +(1.50000 - 2.59808i) q^{23} +(4.50000 + 2.59808i) q^{24} -2.00000 q^{26} +5.19615i q^{27} -3.00000 q^{28} +(0.500000 + 0.866025i) q^{29} +(2.50000 - 4.33013i) q^{32} +3.46410i q^{33} +(-2.00000 - 3.46410i) q^{34} +3.00000 q^{36} +4.00000 q^{37} +(-4.00000 - 6.92820i) q^{38} +(-3.00000 + 1.73205i) q^{39} +(-2.50000 + 4.33013i) q^{41} +(4.50000 - 2.59808i) q^{42} +(-4.00000 - 6.92820i) q^{43} +2.00000 q^{44} +3.00000 q^{46} +(3.50000 + 6.06218i) q^{47} +1.73205i q^{48} +(-1.00000 + 1.73205i) q^{49} +(-6.00000 - 3.46410i) q^{51} +(1.00000 + 1.73205i) q^{52} +2.00000 q^{53} +(-4.50000 + 2.59808i) q^{54} +(-4.50000 - 7.79423i) q^{56} +(-12.0000 - 6.92820i) q^{57} +(-0.500000 + 0.866025i) q^{58} +(7.00000 - 12.1244i) q^{59} +(-3.50000 - 6.06218i) q^{61} +(4.50000 - 7.79423i) q^{63} +7.00000 q^{64} +(-3.00000 + 1.73205i) q^{66} +(-1.50000 + 2.59808i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(4.50000 - 2.59808i) q^{69} +2.00000 q^{71} +(4.50000 + 7.79423i) q^{72} -4.00000 q^{73} +(2.00000 + 3.46410i) q^{74} +(-4.00000 + 6.92820i) q^{76} +(3.00000 - 5.19615i) q^{77} +(-3.00000 - 1.73205i) q^{78} +(3.00000 + 5.19615i) q^{79} +(-4.50000 + 7.79423i) q^{81} -5.00000 q^{82} +(4.50000 + 7.79423i) q^{83} +(-4.50000 - 2.59808i) q^{84} +(4.00000 - 6.92820i) q^{86} +1.73205i q^{87} +(3.00000 + 5.19615i) q^{88} -15.0000 q^{89} +6.00000 q^{91} +(-1.50000 - 2.59808i) q^{92} +(-3.50000 + 6.06218i) q^{94} +(7.50000 - 4.33013i) q^{96} +(1.00000 + 1.73205i) q^{97} -2.00000 q^{98} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + 3 q^{3} + q^{4} - 3 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + 3 q^{3} + q^{4} - 3 q^{7} + 6 q^{8} + 3 q^{9} + 2 q^{11} + 3 q^{12} - 2 q^{13} + 3 q^{14} + q^{16} - 8 q^{17} - 3 q^{18} - 16 q^{19} - 2 q^{22} + 3 q^{23} + 9 q^{24} - 4 q^{26} - 6 q^{28} + q^{29} + 5 q^{32} - 4 q^{34} + 6 q^{36} + 8 q^{37} - 8 q^{38} - 6 q^{39} - 5 q^{41} + 9 q^{42} - 8 q^{43} + 4 q^{44} + 6 q^{46} + 7 q^{47} - 2 q^{49} - 12 q^{51} + 2 q^{52} + 4 q^{53} - 9 q^{54} - 9 q^{56} - 24 q^{57} - q^{58} + 14 q^{59} - 7 q^{61} + 9 q^{63} + 14 q^{64} - 6 q^{66} - 3 q^{67} - 4 q^{68} + 9 q^{69} + 4 q^{71} + 9 q^{72} - 8 q^{73} + 4 q^{74} - 8 q^{76} + 6 q^{77} - 6 q^{78} + 6 q^{79} - 9 q^{81} - 10 q^{82} + 9 q^{83} - 9 q^{84} + 8 q^{86} + 6 q^{88} - 30 q^{89} + 12 q^{91} - 3 q^{92} - 7 q^{94} + 15 q^{96} + 2 q^{97} - 4 q^{98} - 6 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i 0.986869 0.161521i \(-0.0516399\pi\)
−0.633316 + 0.773893i \(0.718307\pi\)
\(3\) 1.50000 + 0.866025i 0.866025 + 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 1.73205i 0.707107i
\(7\) −1.50000 2.59808i −0.566947 0.981981i −0.996866 0.0791130i \(-0.974791\pi\)
0.429919 0.902867i \(-0.358542\pi\)
\(8\) 3.00000 1.06066
\(9\) 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 \(0.735842\pi\)
\(12\) 1.50000 0.866025i 0.433013 0.250000i
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 1.50000 2.59808i 0.400892 0.694365i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −4.00000 −0.970143 −0.485071 0.874475i \(-0.661206\pi\)
−0.485071 + 0.874475i \(0.661206\pi\)
\(18\) −1.50000 + 2.59808i −0.353553 + 0.612372i
\(19\) −8.00000 −1.83533 −0.917663 0.397360i \(-0.869927\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 0 0
\(21\) 5.19615i 1.13389i
\(22\) −1.00000 + 1.73205i −0.213201 + 0.369274i
\(23\) 1.50000 2.59808i 0.312772 0.541736i −0.666190 0.745782i \(-0.732076\pi\)
0.978961 + 0.204046i \(0.0654092\pi\)
\(24\) 4.50000 + 2.59808i 0.918559 + 0.530330i
\(25\) 0 0
\(26\) −2.00000 −0.392232
\(27\) 5.19615i 1.00000i
\(28\) −3.00000 −0.566947
\(29\) 0.500000 + 0.866025i 0.0928477 + 0.160817i 0.908708 0.417432i \(-0.137070\pi\)
−0.815861 + 0.578249i \(0.803736\pi\)
\(30\) 0 0
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) 2.50000 4.33013i 0.441942 0.765466i
\(33\) 3.46410i 0.603023i
\(34\) −2.00000 3.46410i −0.342997 0.594089i
\(35\) 0 0
\(36\) 3.00000 0.500000
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) −4.00000 6.92820i −0.648886 1.12390i
\(39\) −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 \(0.294342\pi\)
\(42\) 4.50000 2.59808i 0.694365 0.400892i
\(43\) −4.00000 6.92820i −0.609994 1.05654i −0.991241 0.132068i \(-0.957838\pi\)
0.381246 0.924473i \(-0.375495\pi\)
\(44\) 2.00000 0.301511
\(45\) 0 0
\(46\) 3.00000 0.442326
\(47\) 3.50000 + 6.06218i 0.510527 + 0.884260i 0.999926 + 0.0121990i \(0.00388317\pi\)
−0.489398 + 0.872060i \(0.662783\pi\)
\(48\) 1.73205i 0.250000i
\(49\) −1.00000 + 1.73205i −0.142857 + 0.247436i
\(50\) 0 0
\(51\) −6.00000 3.46410i −0.840168 0.485071i
\(52\) 1.00000 + 1.73205i 0.138675 + 0.240192i
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) −4.50000 + 2.59808i −0.612372 + 0.353553i
\(55\) 0 0
\(56\) −4.50000 7.79423i −0.601338 1.04155i
\(57\) −12.0000 6.92820i −1.58944 0.917663i
\(58\) −0.500000 + 0.866025i −0.0656532 + 0.113715i
\(59\) 7.00000 12.1244i 0.911322 1.57846i 0.0991242 0.995075i \(-0.468396\pi\)
0.812198 0.583382i \(-0.198271\pi\)
\(60\) 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
\(63\) 4.50000 7.79423i 0.566947 0.981981i
\(64\) 7.00000 0.875000
\(65\) 0 0
\(66\) −3.00000 + 1.73205i −0.369274 + 0.213201i
\(67\) −1.50000 + 2.59808i −0.183254 + 0.317406i −0.942987 0.332830i \(-0.891996\pi\)
0.759733 + 0.650236i \(0.225330\pi\)
\(68\) −2.00000 + 3.46410i −0.242536 + 0.420084i
\(69\) 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 \(0.462134\pi\)
\(72\) 4.50000 + 7.79423i 0.530330 + 0.918559i
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) 2.00000 + 3.46410i 0.232495 + 0.402694i
\(75\) 0 0
\(76\) −4.00000 + 6.92820i −0.458831 + 0.794719i
\(77\) 3.00000 5.19615i 0.341882 0.592157i
\(78\) −3.00000 1.73205i −0.339683 0.196116i
\(79\) 3.00000 + 5.19615i 0.337526 + 0.584613i 0.983967 0.178352i \(-0.0570765\pi\)
−0.646440 + 0.762964i \(0.723743\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) −5.00000 −0.552158
\(83\) 4.50000 + 7.79423i 0.493939 + 0.855528i 0.999976 0.00698436i \(-0.00222321\pi\)
−0.506036 + 0.862512i \(0.668890\pi\)
\(84\) −4.50000 2.59808i −0.490990 0.283473i
\(85\) 0 0
\(86\) 4.00000 6.92820i 0.431331 0.747087i
\(87\) 1.73205i 0.185695i
\(88\) 3.00000 + 5.19615i 0.319801 + 0.553912i
\(89\) −15.0000 −1.59000 −0.794998 0.606612i \(-0.792528\pi\)
−0.794998 + 0.606612i \(0.792528\pi\)
\(90\) 0 0
\(91\) 6.00000 0.628971
\(92\) −1.50000 2.59808i −0.156386 0.270868i
\(93\) 0 0
\(94\) −3.50000 + 6.06218i −0.360997 + 0.625266i
\(95\) 0 0
\(96\) 7.50000 4.33013i 0.765466 0.441942i
\(97\) 1.00000 + 1.73205i 0.101535 + 0.175863i 0.912317 0.409484i \(-0.134291\pi\)
−0.810782 + 0.585348i \(0.800958\pi\)
\(98\) −2.00000 −0.202031
\(99\) −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 \(0.480128\pi\)
\(102\) 6.92820i 0.685994i
\(103\) 4.00000 6.92820i 0.394132 0.682656i −0.598858 0.800855i \(-0.704379\pi\)
0.992990 + 0.118199i \(0.0377120\pi\)
\(104\) −3.00000 + 5.19615i −0.294174 + 0.509525i
\(105\) 0 0
\(106\) 1.00000 + 1.73205i 0.0971286 + 0.168232i
\(107\) −3.00000 −0.290021 −0.145010 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) 4.50000 + 2.59808i 0.433013 + 0.250000i
\(109\) 5.00000 0.478913 0.239457 0.970907i \(-0.423031\pi\)
0.239457 + 0.970907i \(0.423031\pi\)
\(110\) 0 0
\(111\) 6.00000 + 3.46410i 0.569495 + 0.328798i
\(112\) 1.50000 2.59808i 0.141737 0.245495i
\(113\) −4.00000 + 6.92820i −0.376288 + 0.651751i −0.990519 0.137376i \(-0.956133\pi\)
0.614231 + 0.789127i \(0.289466\pi\)
\(114\) 13.8564i 1.29777i
\(115\) 0 0
\(116\) 1.00000 0.0928477
\(117\) −6.00000 −0.554700
\(118\) 14.0000 1.28880
\(119\) 6.00000 + 10.3923i 0.550019 + 0.952661i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 3.50000 6.06218i 0.316875 0.548844i
\(123\) −7.50000 + 4.33013i −0.676252 + 0.390434i
\(124\) 0 0
\(125\) 0 0
\(126\) 9.00000 0.801784
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) −1.50000 2.59808i −0.132583 0.229640i
\(129\) 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 \(0.0822479\pi\)
\(132\) 3.00000 + 1.73205i 0.261116 + 0.150756i
\(133\) 12.0000 + 20.7846i 1.04053 + 1.80225i
\(134\) −3.00000 −0.259161
\(135\) 0 0
\(136\) −12.0000 −1.02899
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) 4.50000 + 2.59808i 0.383065 + 0.221163i
\(139\) 8.00000 13.8564i 0.678551 1.17529i −0.296866 0.954919i \(-0.595942\pi\)
0.975417 0.220366i \(-0.0707252\pi\)
\(140\) 0 0
\(141\) 12.1244i 1.02105i
\(142\) 1.00000 + 1.73205i 0.0839181 + 0.145350i
\(143\) −4.00000 −0.334497
\(144\) −1.50000 + 2.59808i −0.125000 + 0.216506i
\(145\) 0 0
\(146\) −2.00000 3.46410i −0.165521 0.286691i
\(147\) −3.00000 + 1.73205i −0.247436 + 0.142857i
\(148\) 2.00000 3.46410i 0.164399 0.284747i
\(149\) −8.50000 + 14.7224i −0.696347 + 1.20611i 0.273377 + 0.961907i \(0.411859\pi\)
−0.969724 + 0.244202i \(0.921474\pi\)
\(150\) 0 0
\(151\) 1.00000 + 1.73205i 0.0813788 + 0.140952i 0.903842 0.427865i \(-0.140734\pi\)
−0.822464 + 0.568818i \(0.807401\pi\)
\(152\) −24.0000 −1.94666
\(153\) −6.00000 10.3923i −0.485071 0.840168i
\(154\) 6.00000 0.483494
\(155\) 0 0
\(156\) 3.46410i 0.277350i
\(157\) 7.00000 12.1244i 0.558661 0.967629i −0.438948 0.898513i \(-0.644649\pi\)
0.997609 0.0691164i \(-0.0220180\pi\)
\(158\) −3.00000 + 5.19615i −0.238667 + 0.413384i
\(159\) 3.00000 + 1.73205i 0.237915 + 0.137361i
\(160\) 0 0
\(161\) −9.00000 −0.709299
\(162\) −9.00000 −0.707107
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) 2.50000 + 4.33013i 0.195217 + 0.338126i
\(165\) 0 0
\(166\) −4.50000 + 7.79423i −0.349268 + 0.604949i
\(167\) −4.50000 + 7.79423i −0.348220 + 0.603136i −0.985933 0.167139i \(-0.946547\pi\)
0.637713 + 0.770274i \(0.279881\pi\)
\(168\) 15.5885i 1.20268i
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 0 0
\(171\) −12.0000 20.7846i −0.917663 1.58944i
\(172\) −8.00000 −0.609994
\(173\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(174\) −1.50000 + 0.866025i −0.113715 + 0.0656532i
\(175\) 0 0
\(176\) −1.00000 + 1.73205i −0.0753778 + 0.130558i
\(177\) 21.0000 12.1244i 1.57846 0.911322i
\(178\) −7.50000 12.9904i −0.562149 0.973670i
\(179\) −2.00000 −0.149487 −0.0747435 0.997203i \(-0.523814\pi\)
−0.0747435 + 0.997203i \(0.523814\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 3.00000 + 5.19615i 0.222375 + 0.385164i
\(183\) 12.1244i 0.896258i
\(184\) 4.50000 7.79423i 0.331744 0.574598i
\(185\) 0 0
\(186\) 0 0
\(187\) −4.00000 6.92820i −0.292509 0.506640i
\(188\) 7.00000 0.510527
\(189\) 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 \(0.926799\pi\)
\(192\) 10.5000 + 6.06218i 0.757772 + 0.437500i
\(193\) −5.00000 + 8.66025i −0.359908 + 0.623379i −0.987945 0.154805i \(-0.950525\pi\)
0.628037 + 0.778183i \(0.283859\pi\)
\(194\) −1.00000 + 1.73205i −0.0717958 + 0.124354i
\(195\) 0 0
\(196\) 1.00000 + 1.73205i 0.0714286 + 0.123718i
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) −6.00000 −0.426401
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) 0 0
\(201\) −4.50000 + 2.59808i −0.317406 + 0.183254i
\(202\) −9.00000 + 15.5885i −0.633238 + 1.09680i
\(203\) 1.50000 2.59808i 0.105279 0.182349i
\(204\) −6.00000 + 3.46410i −0.420084 + 0.242536i
\(205\) 0 0
\(206\) 8.00000 0.557386
\(207\) 9.00000 0.625543
\(208\) −2.00000 −0.138675
\(209\) −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 \(-0.106801\pi\)
\(212\) 1.00000 1.73205i 0.0686803 0.118958i
\(213\) 3.00000 + 1.73205i 0.205557 + 0.118678i
\(214\) −1.50000 2.59808i −0.102538 0.177601i
\(215\) 0 0
\(216\) 15.5885i 1.06066i
\(217\) 0 0
\(218\) 2.50000 + 4.33013i 0.169321 + 0.293273i
\(219\) −6.00000 3.46410i −0.405442 0.234082i
\(220\) 0 0
\(221\) 4.00000 6.92820i 0.269069 0.466041i
\(222\) 6.92820i 0.464991i
\(223\) −9.50000 16.4545i −0.636167 1.10187i −0.986267 0.165161i \(-0.947186\pi\)
0.350100 0.936713i \(-0.386148\pi\)
\(224\) −15.0000 −1.00223
\(225\) 0 0
\(226\) −8.00000 −0.532152
\(227\) −2.00000 3.46410i −0.132745 0.229920i 0.791989 0.610535i \(-0.209046\pi\)
−0.924734 + 0.380615i \(0.875712\pi\)
\(228\) −12.0000 + 6.92820i −0.794719 + 0.458831i
\(229\) −7.50000 + 12.9904i −0.495614 + 0.858429i −0.999987 0.00505719i \(-0.998390\pi\)
0.504373 + 0.863486i \(0.331724\pi\)
\(230\) 0 0
\(231\) 9.00000 5.19615i 0.592157 0.341882i
\(232\) 1.50000 + 2.59808i 0.0984798 + 0.170572i
\(233\) −24.0000 −1.57229 −0.786146 0.618041i \(-0.787927\pi\)
−0.786146 + 0.618041i \(0.787927\pi\)
\(234\) −3.00000 5.19615i −0.196116 0.339683i
\(235\) 0 0
\(236\) −7.00000 12.1244i −0.455661 0.789228i
\(237\) 10.3923i 0.675053i
\(238\) −6.00000 + 10.3923i −0.388922 + 0.673633i
\(239\) 4.00000 6.92820i 0.258738 0.448148i −0.707166 0.707048i \(-0.750027\pi\)
0.965904 + 0.258900i \(0.0833599\pi\)
\(240\) 0 0
\(241\) 5.50000 + 9.52628i 0.354286 + 0.613642i 0.986996 0.160748i \(-0.0513906\pi\)
−0.632709 + 0.774389i \(0.718057\pi\)
\(242\) 7.00000 0.449977
\(243\) −13.5000 + 7.79423i −0.866025 + 0.500000i
\(244\) −7.00000 −0.448129
\(245\) 0 0
\(246\) −7.50000 4.33013i −0.478183 0.276079i
\(247\) 8.00000 13.8564i 0.509028 0.881662i
\(248\) 0 0
\(249\) 15.5885i 0.987878i
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) −4.50000 7.79423i −0.283473 0.490990i
\(253\) 6.00000 0.377217
\(254\) 2.50000 + 4.33013i 0.156864 + 0.271696i
\(255\) 0 0
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) −3.00000 + 5.19615i −0.187135 + 0.324127i −0.944294 0.329104i \(-0.893253\pi\)
0.757159 + 0.653231i \(0.226587\pi\)
\(258\) 12.0000 6.92820i 0.747087 0.431331i
\(259\) −6.00000 10.3923i −0.372822 0.645746i
\(260\) 0 0
\(261\) −1.50000 + 2.59808i −0.0928477 + 0.160817i
\(262\) 6.00000 0.370681
\(263\) −8.00000 13.8564i −0.493301 0.854423i 0.506669 0.862141i \(-0.330877\pi\)
−0.999970 + 0.00771799i \(0.997543\pi\)
\(264\) 10.3923i 0.639602i
\(265\) 0 0
\(266\) −12.0000 + 20.7846i −0.735767 + 1.27439i
\(267\) −22.5000 12.9904i −1.37698 0.794998i
\(268\) 1.50000 + 2.59808i 0.0916271 + 0.158703i
\(269\) 25.0000 1.52428 0.762138 0.647414i \(-0.224150\pi\)
0.762138 + 0.647414i \(0.224150\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) −2.00000 3.46410i −0.121268 0.210042i
\(273\) 9.00000 + 5.19615i 0.544705 + 0.314485i
\(274\) −6.00000 + 10.3923i −0.362473 + 0.627822i
\(275\) 0 0
\(276\) 5.19615i 0.312772i
\(277\) 6.00000 + 10.3923i 0.360505 + 0.624413i 0.988044 0.154172i \(-0.0492710\pi\)
−0.627539 + 0.778585i \(0.715938\pi\)
\(278\) 16.0000 0.959616
\(279\) 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 \(0.685679\pi\)
\(282\) −10.5000 + 6.06218i −0.625266 + 0.360997i
\(283\) 10.5000 18.1865i 0.624160 1.08108i −0.364542 0.931187i \(-0.618775\pi\)
0.988703 0.149890i \(-0.0478921\pi\)
\(284\) 1.00000 1.73205i 0.0593391 0.102778i
\(285\) 0 0
\(286\) −2.00000 3.46410i −0.118262 0.204837i
\(287\) 15.0000 0.885422
\(288\) 15.0000 0.883883
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) 3.46410i 0.203069i
\(292\) −2.00000 + 3.46410i −0.117041 + 0.202721i
\(293\) 6.00000 10.3923i 0.350524 0.607125i −0.635818 0.771839i \(-0.719337\pi\)
0.986341 + 0.164714i \(0.0526703\pi\)
\(294\) −3.00000 1.73205i −0.174964 0.101015i
\(295\) 0 0
\(296\) 12.0000 0.697486
\(297\) −9.00000 + 5.19615i −0.522233 + 0.301511i
\(298\) −17.0000 −0.984784
\(299\) 3.00000 + 5.19615i 0.173494 + 0.300501i
\(300\) 0 0
\(301\) −12.0000 + 20.7846i −0.691669 + 1.19800i
\(302\) −1.00000 + 1.73205i −0.0575435 + 0.0996683i
\(303\) 31.1769i 1.79107i
\(304\) −4.00000 6.92820i −0.229416 0.397360i
\(305\) 0 0
\(306\) 6.00000 10.3923i 0.342997 0.594089i
\(307\) −7.00000 −0.399511 −0.199756 0.979846i \(-0.564015\pi\)
−0.199756 + 0.979846i \(0.564015\pi\)
\(308\) −3.00000 5.19615i −0.170941 0.296078i
\(309\) 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 \(0.166667\pi\)
\(312\) −9.00000 + 5.19615i −0.509525 + 0.294174i
\(313\) 7.00000 + 12.1244i 0.395663 + 0.685309i 0.993186 0.116543i \(-0.0371814\pi\)
−0.597522 + 0.801852i \(0.703848\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) 6.00000 0.337526
\(317\) −17.0000 29.4449i −0.954815 1.65379i −0.734791 0.678294i \(-0.762720\pi\)
−0.220024 0.975494i \(-0.570614\pi\)
\(318\) 3.46410i 0.194257i
\(319\) −1.00000 + 1.73205i −0.0559893 + 0.0969762i
\(320\) 0 0
\(321\) −4.50000 2.59808i −0.251166 0.145010i
\(322\) −4.50000 7.79423i −0.250775 0.434355i
\(323\) 32.0000 1.78053
\(324\) 4.50000 + 7.79423i 0.250000 + 0.433013i
\(325\) 0 0
\(326\) 2.00000 + 3.46410i 0.110770 + 0.191859i
\(327\) 7.50000 + 4.33013i 0.414751 + 0.239457i
\(328\) −7.50000 + 12.9904i −0.414118 + 0.717274i
\(329\) 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 \(0.780605\pi\)
\(332\) 9.00000 0.493939
\(333\) 6.00000 + 10.3923i 0.328798 + 0.569495i
\(334\) −9.00000 −0.492458
\(335\) 0 0
\(336\) 4.50000 2.59808i 0.245495 0.141737i
\(337\) −4.00000 + 6.92820i −0.217894 + 0.377403i −0.954164 0.299285i \(-0.903252\pi\)
0.736270 + 0.676688i \(0.236585\pi\)
\(338\) −4.50000 + 7.79423i −0.244768 + 0.423950i
\(339\) −12.0000 + 6.92820i −0.651751 + 0.376288i
\(340\) 0 0
\(341\) 0 0
\(342\) 12.0000 20.7846i 0.648886 1.12390i
\(343\) −15.0000 −0.809924
\(344\) −12.0000 20.7846i −0.646997 1.12063i
\(345\) 0 0
\(346\) 0 0
\(347\) 2.00000 3.46410i 0.107366 0.185963i −0.807337 0.590091i \(-0.799092\pi\)
0.914702 + 0.404128i \(0.132425\pi\)
\(348\) 1.50000 + 0.866025i 0.0804084 + 0.0464238i
\(349\) 2.50000 + 4.33013i 0.133822 + 0.231786i 0.925147 0.379610i \(-0.123942\pi\)
−0.791325 + 0.611396i \(0.790608\pi\)
\(350\) 0 0
\(351\) −9.00000 5.19615i −0.480384 0.277350i
\(352\) 10.0000 0.533002
\(353\) 12.0000 + 20.7846i 0.638696 + 1.10625i 0.985719 + 0.168397i \(0.0538590\pi\)
−0.347024 + 0.937856i \(0.612808\pi\)
\(354\) 21.0000 + 12.1244i 1.11614 + 0.644402i
\(355\) 0 0
\(356\) −7.50000 + 12.9904i −0.397499 + 0.688489i
\(357\) 20.7846i 1.10004i
\(358\) −1.00000 1.73205i −0.0528516 0.0915417i
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 0 0
\(361\) 45.0000 2.36842
\(362\) −3.50000 6.06218i −0.183956 0.318621i
\(363\) 10.5000 6.06218i 0.551107 0.318182i
\(364\) 3.00000 5.19615i 0.157243 0.272352i
\(365\) 0 0
\(366\) 10.5000 6.06218i 0.548844 0.316875i
\(367\) 12.0000 + 20.7846i 0.626395 + 1.08495i 0.988269 + 0.152721i \(0.0488036\pi\)
−0.361874 + 0.932227i \(0.617863\pi\)
\(368\) 3.00000 0.156386
\(369\) −15.0000 −0.780869
\(370\) 0 0
\(371\) −3.00000 5.19615i −0.155752 0.269771i
\(372\) 0 0
\(373\) 5.00000 8.66025i 0.258890 0.448411i −0.707055 0.707159i \(-0.749977\pi\)
0.965945 + 0.258748i \(0.0833099\pi\)
\(374\) 4.00000 6.92820i 0.206835 0.358249i
\(375\) 0 0
\(376\) 10.5000 + 18.1865i 0.541496 + 0.937899i
\(377\) −2.00000 −0.103005
\(378\) 13.5000 + 7.79423i 0.694365 + 0.400892i
\(379\) −26.0000 −1.33553 −0.667765 0.744372i \(-0.732749\pi\)
−0.667765 + 0.744372i \(0.732749\pi\)
\(380\) 0 0
\(381\) 7.50000 + 4.33013i 0.384237 + 0.221839i
\(382\) 4.00000 6.92820i 0.204658 0.354478i
\(383\) 18.0000 31.1769i 0.919757 1.59307i 0.119974 0.992777i \(-0.461719\pi\)
0.799783 0.600289i \(-0.204948\pi\)
\(384\) 5.19615i 0.265165i
\(385\) 0 0
\(386\) −10.0000 −0.508987
\(387\) 12.0000 20.7846i 0.609994 1.05654i
\(388\) 2.00000 0.101535
\(389\) −16.5000 28.5788i −0.836583 1.44900i −0.892735 0.450582i \(-0.851216\pi\)
0.0561516 0.998422i \(-0.482117\pi\)
\(390\) 0 0
\(391\) −6.00000 + 10.3923i −0.303433 + 0.525561i
\(392\) −3.00000 + 5.19615i −0.151523 + 0.262445i
\(393\) 9.00000 5.19615i 0.453990 0.262111i
\(394\) 6.00000 + 10.3923i 0.302276 + 0.523557i
\(395\) 0 0
\(396\) 3.00000 + 5.19615i 0.150756 + 0.261116i
\(397\) −34.0000 −1.70641 −0.853206 0.521575i \(-0.825345\pi\)
−0.853206 + 0.521575i \(0.825345\pi\)
\(398\) 2.00000 + 3.46410i 0.100251 + 0.173640i
\(399\) 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 \(0.0182907\pi\)
\(402\) −4.50000 2.59808i −0.224440 0.129580i
\(403\) 0 0
\(404\) 18.0000 0.895533
\(405\) 0 0
\(406\) 3.00000 0.148888
\(407\) 4.00000 + 6.92820i 0.198273 + 0.343418i
\(408\) −18.0000 10.3923i −0.891133 0.514496i
\(409\) −7.00000 + 12.1244i −0.346128 + 0.599511i −0.985558 0.169338i \(-0.945837\pi\)
0.639430 + 0.768849i \(0.279170\pi\)
\(410\) 0 0
\(411\) 20.7846i 1.02523i
\(412\) −4.00000 6.92820i −0.197066 0.341328i
\(413\) −42.0000 −2.06668
\(414\) 4.50000 + 7.79423i 0.221163 + 0.383065i
\(415\) 0 0
\(416\) 5.00000 + 8.66025i 0.245145 + 0.424604i
\(417\) 24.0000 13.8564i 1.17529 0.678551i
\(418\) 8.00000 13.8564i 0.391293 0.677739i
\(419\) −13.0000 + 22.5167i −0.635092 + 1.10001i 0.351404 + 0.936224i \(0.385704\pi\)
−0.986496 + 0.163787i \(0.947629\pi\)
\(420\) 0 0
\(421\) −17.0000 29.4449i −0.828529 1.43505i −0.899192 0.437555i \(-0.855845\pi\)
0.0706626 0.997500i \(-0.477489\pi\)
\(422\) 22.0000 1.07094
\(423\) −10.5000 + 18.1865i −0.510527 + 0.884260i
\(424\) 6.00000 0.291386
\(425\) 0 0
\(426\) 3.46410i 0.167836i
\(427\) −10.5000 + 18.1865i −0.508131 + 0.880108i
\(428\) −1.50000 + 2.59808i −0.0725052 + 0.125583i
\(429\) −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 \(0.757018\pi\)
\(432\) −4.50000 + 2.59808i −0.216506 + 0.125000i
\(433\) −28.0000 −1.34559 −0.672797 0.739827i \(-0.734907\pi\)
−0.672797 + 0.739827i \(0.734907\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2.50000 4.33013i 0.119728 0.207375i
\(437\) −12.0000 + 20.7846i −0.574038 + 0.994263i
\(438\) 6.92820i 0.331042i
\(439\) −14.0000 24.2487i −0.668184 1.15733i −0.978412 0.206666i \(-0.933739\pi\)
0.310228 0.950662i \(-0.399595\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) 8.00000 0.380521
\(443\) 7.50000 + 12.9904i 0.356336 + 0.617192i 0.987346 0.158583i \(-0.0506926\pi\)
−0.631010 + 0.775775i \(0.717359\pi\)
\(444\) 6.00000 3.46410i 0.284747 0.164399i
\(445\) 0 0
\(446\) 9.50000 16.4545i 0.449838 0.779142i
\(447\) −25.5000 + 14.7224i −1.20611 + 0.696347i
\(448\) −10.5000 18.1865i −0.496078 0.859233i
\(449\) −26.0000 −1.22702 −0.613508 0.789689i \(-0.710242\pi\)
−0.613508 + 0.789689i \(0.710242\pi\)
\(450\) 0 0
\(451\) −10.0000 −0.470882
\(452\) 4.00000 + 6.92820i 0.188144 + 0.325875i
\(453\) 3.46410i 0.162758i
\(454\) 2.00000 3.46410i 0.0938647 0.162578i
\(455\) 0 0
\(456\) −36.0000 20.7846i −1.68585 0.973329i
\(457\) −10.0000 17.3205i −0.467780 0.810219i 0.531542 0.847032i \(-0.321613\pi\)
−0.999322 + 0.0368128i \(0.988279\pi\)
\(458\) −15.0000 −0.700904
\(459\) 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 \(0.900545\pi\)
\(462\) 9.00000 + 5.19615i 0.418718 + 0.241747i
\(463\) −18.0000 + 31.1769i −0.836531 + 1.44891i 0.0562469 + 0.998417i \(0.482087\pi\)
−0.892778 + 0.450497i \(0.851247\pi\)
\(464\) −0.500000 + 0.866025i −0.0232119 + 0.0402042i
\(465\) 0 0
\(466\) −12.0000 20.7846i −0.555889 0.962828i
\(467\) −20.0000 −0.925490 −0.462745 0.886492i \(-0.653135\pi\)
−0.462745 + 0.886492i \(0.653135\pi\)
\(468\) −3.00000 + 5.19615i −0.138675 + 0.240192i
\(469\) 9.00000 0.415581
\(470\) 0 0
\(471\) 21.0000 12.1244i 0.967629 0.558661i
\(472\) 21.0000 36.3731i 0.966603 1.67421i
\(473\) 8.00000 13.8564i 0.367840 0.637118i
\(474\) −9.00000 + 5.19615i −0.413384 + 0.238667i
\(475\) 0 0
\(476\) 12.0000 0.550019
\(477\) 3.00000 + 5.19615i 0.137361 + 0.237915i
\(478\) 8.00000 0.365911
\(479\) 9.00000 + 15.5885i 0.411220 + 0.712255i 0.995023 0.0996406i \(-0.0317693\pi\)
−0.583803 + 0.811895i \(0.698436\pi\)
\(480\) 0 0
\(481\) −4.00000 + 6.92820i −0.182384 + 0.315899i
\(482\) −5.50000 + 9.52628i −0.250518 + 0.433910i
\(483\) −13.5000 7.79423i −0.614271 0.354650i
\(484\) −3.50000 6.06218i −0.159091 0.275554i
\(485\) 0 0
\(486\) −13.5000 7.79423i −0.612372 0.353553i
\(487\) 16.0000 0.725029 0.362515 0.931978i \(-0.381918\pi\)
0.362515 + 0.931978i \(0.381918\pi\)
\(488\) −10.5000 18.1865i −0.475313 0.823266i
\(489\) 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 \(0.315704\pi\)
\(492\) 8.66025i 0.390434i
\(493\) −2.00000 3.46410i −0.0900755 0.156015i
\(494\) 16.0000 0.719874
\(495\) 0 0
\(496\) 0 0
\(497\) −3.00000 5.19615i −0.134568 0.233079i
\(498\) −13.5000 + 7.79423i −0.604949 + 0.349268i
\(499\) 16.0000 27.7128i 0.716258 1.24060i −0.246214 0.969216i \(-0.579187\pi\)
0.962472 0.271380i \(-0.0874801\pi\)
\(500\) 0 0
\(501\) −13.5000 + 7.79423i −0.603136 + 0.348220i
\(502\) 0 0
\(503\) 7.00000 0.312115 0.156057 0.987748i \(-0.450122\pi\)
0.156057 + 0.987748i \(0.450122\pi\)
\(504\) 13.5000 23.3827i 0.601338 1.04155i
\(505\) 0 0
\(506\) 3.00000 + 5.19615i 0.133366 + 0.230997i
\(507\) 15.5885i 0.692308i
\(508\) 2.50000 4.33013i 0.110920 0.192118i
\(509\) −21.5000 + 37.2391i −0.952971 + 1.65059i −0.214026 + 0.976828i \(0.568658\pi\)
−0.738945 + 0.673766i \(0.764676\pi\)
\(510\) 0 0
\(511\) 6.00000 + 10.3923i 0.265424 + 0.459728i
\(512\) 11.0000 0.486136
\(513\) 41.5692i 1.83533i
\(514\) −6.00000 −0.264649
\(515\) 0 0
\(516\) −12.0000 6.92820i −0.528271 0.304997i
\(517\) −7.00000 + 12.1244i −0.307860 + 0.533229i
\(518\) 6.00000 10.3923i 0.263625 0.456612i
\(519\) 0 0
\(520\) 0 0
\(521\) 11.0000 0.481919 0.240959 0.970535i \(-0.422538\pi\)
0.240959 + 0.970535i \(0.422538\pi\)
\(522\) −3.00000 −0.131306
\(523\) 29.0000 1.26808 0.634041 0.773300i \(-0.281395\pi\)
0.634041 + 0.773300i \(0.281395\pi\)
\(524\) −3.00000 5.19615i −0.131056 0.226995i
\(525\) 0 0
\(526\) 8.00000 13.8564i 0.348817 0.604168i
\(527\) 0 0
\(528\) −3.00000 + 1.73205i −0.130558 + 0.0753778i
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) 0 0
\(531\) 42.0000 1.82264
\(532\) 24.0000 1.04053
\(533\) −5.00000 8.66025i −0.216574 0.375117i
\(534\) 25.9808i 1.12430i
\(535\) 0 0
\(536\) −4.50000 + 7.79423i −0.194370 + 0.336659i
\(537\) −3.00000 1.73205i −0.129460 0.0747435i
\(538\) 12.5000 + 21.6506i 0.538913 + 0.933425i
\(539\) −4.00000 −0.172292
\(540\) 0 0
\(541\) −39.0000 −1.67674 −0.838370 0.545101i \(-0.816491\pi\)
−0.838370 + 0.545101i \(0.816491\pi\)
\(542\) −4.00000 6.92820i −0.171815 0.297592i
\(543\) −10.5000 6.06218i −0.450598 0.260153i
\(544\) −10.0000 + 17.3205i −0.428746 + 0.742611i
\(545\) 0 0
\(546\) 10.3923i 0.444750i
\(547\) −14.5000 25.1147i −0.619975 1.07383i −0.989490 0.144604i \(-0.953809\pi\)
0.369514 0.929225i \(-0.379524\pi\)
\(548\) 12.0000 0.512615
\(549\) 10.5000 18.1865i 0.448129 0.776182i
\(550\) 0 0
\(551\) −4.00000 6.92820i −0.170406 0.295151i
\(552\) 13.5000 7.79423i 0.574598 0.331744i
\(553\) 9.00000 15.5885i 0.382719 0.662889i
\(554\) −6.00000 + 10.3923i −0.254916 + 0.441527i
\(555\) 0 0
\(556\) −8.00000 13.8564i −0.339276 0.587643i
\(557\) 30.0000 1.27114 0.635570 0.772043i \(-0.280765\pi\)
0.635570 + 0.772043i \(0.280765\pi\)
\(558\) 0 0
\(559\) 16.0000 0.676728
\(560\) 0 0
\(561\) 13.8564i 0.585018i
\(562\) −7.50000 + 12.9904i −0.316368 + 0.547966i
\(563\) −10.5000 + 18.1865i −0.442522 + 0.766471i −0.997876 0.0651433i \(-0.979250\pi\)
0.555354 + 0.831614i \(0.312583\pi\)
\(564\) 10.5000 + 6.06218i 0.442130 + 0.255264i
\(565\) 0 0
\(566\) 21.0000 0.882696
\(567\) 27.0000 1.13389
\(568\) 6.00000 0.251754
\(569\) 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i \(-0.126528\pi\)
−0.796266 + 0.604947i \(0.793194\pi\)
\(570\) 0 0
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) −2.00000 + 3.46410i −0.0836242 + 0.144841i
\(573\) 13.8564i 0.578860i
\(574\) 7.50000 + 12.9904i 0.313044 + 0.542208i
\(575\) 0 0
\(576\) 10.5000 + 18.1865i 0.437500 + 0.757772i
\(577\) 10.0000 0.416305 0.208153 0.978096i \(-0.433255\pi\)
0.208153 + 0.978096i \(0.433255\pi\)
\(578\) −0.500000 0.866025i −0.0207973 0.0360219i
\(579\) −15.0000 + 8.66025i −0.623379 + 0.359908i
\(580\) 0 0
\(581\) 13.5000 23.3827i 0.560074 0.970077i
\(582\) −3.00000 + 1.73205i −0.124354 + 0.0717958i
\(583\) 2.00000 + 3.46410i 0.0828315 + 0.143468i
\(584\) −12.0000 −0.496564
\(585\) 0 0
\(586\) 12.0000 0.495715
\(587\) −16.5000 28.5788i −0.681028 1.17957i −0.974668 0.223659i \(-0.928200\pi\)
0.293640 0.955916i \(-0.405133\pi\)
\(588\) 3.46410i 0.142857i
\(589\) 0 0
\(590\) 0 0
\(591\) 18.0000 + 10.3923i 0.740421 + 0.427482i
\(592\) 2.00000 + 3.46410i 0.0821995 + 0.142374i
\(593\) −20.0000 −0.821302 −0.410651 0.911793i \(-0.634698\pi\)
−0.410651 + 0.911793i \(0.634698\pi\)
\(594\) −9.00000 5.19615i −0.369274 0.213201i
\(595\) 0 0
\(596\) 8.50000 + 14.7224i 0.348174 + 0.603054i
\(597\) 6.00000 + 3.46410i 0.245564 + 0.141776i
\(598\) −3.00000 + 5.19615i −0.122679 + 0.212486i
\(599\) 5.00000 8.66025i 0.204294 0.353848i −0.745613 0.666379i \(-0.767843\pi\)
0.949908 + 0.312531i \(0.101177\pi\)
\(600\) 0 0
\(601\) −1.00000 1.73205i −0.0407909 0.0706518i 0.844909 0.534910i \(-0.179654\pi\)
−0.885700 + 0.464258i \(0.846321\pi\)
\(602\) −24.0000 −0.978167
\(603\) −9.00000 −0.366508
\(604\) 2.00000 0.0813788
\(605\) 0 0
\(606\) −27.0000 + 15.5885i −1.09680 + 0.633238i
\(607\) −20.5000 + 35.5070i −0.832069 + 1.44119i 0.0643251 + 0.997929i \(0.479511\pi\)
−0.896394 + 0.443257i \(0.853823\pi\)
\(608\) −20.0000 + 34.6410i −0.811107 + 1.40488i
\(609\) 4.50000 2.59808i 0.182349 0.105279i
\(610\) 0 0
\(611\) −14.0000 −0.566379
\(612\) −12.0000 −0.485071
\(613\) 44.0000 1.77714 0.888572 0.458738i \(-0.151698\pi\)
0.888572 + 0.458738i \(0.151698\pi\)
\(614\) −3.50000 6.06218i −0.141249 0.244650i
\(615\) 0 0
\(616\) 9.00000 15.5885i 0.362620 0.628077i
\(617\) −18.0000 + 31.1769i −0.724653 + 1.25514i 0.234464 + 0.972125i \(0.424666\pi\)
−0.959117 + 0.283011i \(0.908667\pi\)
\(618\) 12.0000 + 6.92820i 0.482711 + 0.278693i
\(619\) 2.00000 + 3.46410i 0.0803868 + 0.139234i 0.903416 0.428765i \(-0.141051\pi\)
−0.823029 + 0.567999i \(0.807718\pi\)
\(620\) 0 0
\(621\) 13.5000 + 7.79423i 0.541736 + 0.312772i
\(622\) 0 0
\(623\) 22.5000 + 38.9711i 0.901443 + 1.56135i
\(624\) −3.00000 1.73205i −0.120096 0.0693375i
\(625\) 0 0
\(626\) −7.00000 + 12.1244i −0.279776 + 0.484587i
\(627\) 27.7128i 1.10674i
\(628\) −7.00000 12.1244i −0.279330 0.483814i
\(629\) −16.0000 −0.637962
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) 9.00000 + 15.5885i 0.358001 + 0.620076i
\(633\) 33.0000 19.0526i 1.31163 0.757271i
\(634\) 17.0000 29.4449i 0.675156 1.16940i
\(635\) 0 0
\(636\) 3.00000 1.73205i 0.118958 0.0686803i
\(637\) −2.00000 3.46410i −0.0792429 0.137253i
\(638\) −2.00000 −0.0791808
\(639\) 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 \(-0.392615\pi\)
\(642\) 5.19615i 0.205076i
\(643\) −4.50000 + 7.79423i −0.177463 + 0.307374i −0.941011 0.338377i \(-0.890122\pi\)
0.763548 + 0.645751i \(0.223456\pi\)
\(644\) −4.50000 + 7.79423i −0.177325 + 0.307136i
\(645\) 0 0
\(646\) 16.0000 + 27.7128i 0.629512 + 1.09035i
\(647\) 17.0000 0.668339 0.334169 0.942513i \(-0.391544\pi\)
0.334169 + 0.942513i \(0.391544\pi\)
\(648\) −13.5000 + 23.3827i −0.530330 + 0.918559i
\(649\) 28.0000 1.09910
\(650\) 0 0
\(651\) 0 0
\(652\) 2.00000 3.46410i 0.0783260 0.135665i
\(653\) −2.00000 + 3.46410i −0.0782660 + 0.135561i −0.902502 0.430686i \(-0.858272\pi\)
0.824236 + 0.566247i \(0.191605\pi\)
\(654\) 8.66025i 0.338643i
\(655\) 0 0
\(656\) −5.00000 −0.195217
\(657\) −6.00000 10.3923i −0.234082 0.405442i
\(658\) 21.0000 0.818665
\(659\) 4.00000 + 6.92820i 0.155818 + 0.269884i 0.933357 0.358951i \(-0.116865\pi\)
−0.777539 + 0.628835i \(0.783532\pi\)
\(660\) 0 0
\(661\) 7.00000 12.1244i 0.272268 0.471583i −0.697174 0.716902i \(-0.745559\pi\)
0.969442 + 0.245319i \(0.0788928\pi\)
\(662\) −3.00000 + 5.19615i −0.116598 + 0.201954i
\(663\) 12.0000 6.92820i 0.466041 0.269069i
\(664\) 13.5000 + 23.3827i 0.523902 + 0.907424i
\(665\) 0 0
\(666\) −6.00000 + 10.3923i −0.232495 + 0.402694i
\(667\) 3.00000 0.116160
\(668\) 4.50000 + 7.79423i 0.174110 + 0.301568i
\(669\) 32.9090i 1.27233i
\(670\) 0 0
\(671\) 7.00000 12.1244i 0.270232 0.468056i
\(672\) −22.5000 12.9904i −0.867956 0.501115i
\(673\) 3.00000 + 5.19615i 0.115642 + 0.200297i 0.918036 0.396497i \(-0.129774\pi\)
−0.802395 + 0.596794i \(0.796441\pi\)
\(674\) −8.00000 −0.308148
\(675\) 0 0
\(676\) 9.00000 0.346154
\(677\) −21.0000 36.3731i −0.807096 1.39793i −0.914867 0.403755i \(-0.867705\pi\)
0.107772 0.994176i \(-0.465628\pi\)
\(678\) −12.0000 6.92820i −0.460857 0.266076i
\(679\) 3.00000 5.19615i 0.115129 0.199410i
\(680\) 0 0
\(681\) 6.92820i 0.265489i
\(682\) 0 0
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) −24.0000 −0.917663
\(685\) 0 0
\(686\) −7.50000 12.9904i −0.286351 0.495975i
\(687\) −22.5000 + 12.9904i −0.858429 + 0.495614i
\(688\) 4.00000 6.92820i 0.152499 0.264135i
\(689\) −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
\(693\) 18.0000 0.683763
\(694\) 4.00000 0.151838
\(695\) 0 0
\(696\) 5.19615i 0.196960i
\(697\) 10.0000 17.3205i 0.378777 0.656061i
\(698\) −2.50000 + 4.33013i −0.0946264 + 0.163898i
\(699\) −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 \(0.356978\pi\)
\(702\) 10.3923i 0.392232i
\(703\) −32.0000 −1.20690
\(704\) 7.00000 + 12.1244i 0.263822 + 0.456954i
\(705\) 0 0
\(706\) −12.0000 + 20.7846i −0.451626 + 0.782239i
\(707\) 27.0000 46.7654i 1.01544 1.75879i
\(708\) 24.2487i 0.911322i
\(709\) 20.5000 + 35.5070i 0.769894 + 1.33349i 0.937620 + 0.347661i \(0.113024\pi\)
−0.167727 + 0.985834i \(0.553643\pi\)
\(710\) 0 0
\(711\) −9.00000 + 15.5885i −0.337526 + 0.584613i
\(712\) −45.0000 −1.68645
\(713\) 0 0
\(714\) −18.0000 + 10.3923i −0.673633 + 0.388922i
\(715\) 0 0
\(716\) −1.00000 + 1.73205i −0.0373718 + 0.0647298i
\(717\) 12.0000 6.92820i 0.448148 0.258738i
\(718\) 12.0000 + 20.7846i 0.447836 + 0.775675i
\(719\) 6.00000 0.223762 0.111881 0.993722i \(-0.464312\pi\)
0.111881 + 0.993722i \(0.464312\pi\)
\(720\) 0 0
\(721\) −24.0000 −0.893807
\(722\) 22.5000 + 38.9711i 0.837363 + 1.45036i
\(723\) 19.0526i 0.708572i
\(724\) −3.50000 + 6.06218i −0.130076 + 0.225299i
\(725\) 0 0
\(726\) 10.5000 + 6.06218i 0.389692 + 0.224989i
\(727\) 11.5000 + 19.9186i 0.426511 + 0.738739i 0.996560 0.0828714i \(-0.0264091\pi\)
−0.570049 + 0.821611i \(0.693076\pi\)
\(728\) 18.0000 0.667124
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 16.0000 + 27.7128i 0.591781 + 1.02500i
\(732\) −10.5000 6.06218i −0.388091 0.224065i
\(733\) −17.0000 + 29.4449i −0.627909 + 1.08757i 0.360061 + 0.932929i \(0.382756\pi\)
−0.987971 + 0.154642i \(0.950578\pi\)
\(734\) −12.0000 + 20.7846i −0.442928 + 0.767174i
\(735\) 0 0
\(736\) −7.50000 12.9904i −0.276454 0.478832i
\(737\) −6.00000 −0.221013
\(738\) −7.50000 12.9904i −0.276079 0.478183i
\(739\) −2.00000 −0.0735712 −0.0367856 0.999323i \(-0.511712\pi\)
−0.0367856 + 0.999323i \(0.511712\pi\)
\(740\) 0 0
\(741\) 24.0000 13.8564i 0.881662 0.509028i
\(742\) 3.00000 5.19615i 0.110133 0.190757i
\(743\) −14.5000 + 25.1147i −0.531953 + 0.921370i 0.467351 + 0.884072i \(0.345209\pi\)
−0.999304 + 0.0372984i \(0.988125\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 10.0000 0.366126
\(747\) −13.5000 + 23.3827i −0.493939 + 0.855528i
\(748\) −8.00000 −0.292509
\(749\) 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 \(0.225070\pi\)
\(752\) −3.50000 + 6.06218i −0.127632 + 0.221065i
\(753\) 0 0
\(754\) −1.00000 1.73205i −0.0364179 0.0630776i
\(755\) 0 0
\(756\) 15.5885i 0.566947i
\(757\) 26.0000 0.944986 0.472493 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) −13.0000 22.5167i −0.472181 0.817842i
\(759\) 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 \(0.254310\pi\)
\(762\) 8.66025i 0.313728i
\(763\) −7.50000 12.9904i −0.271518 0.470283i
\(764\) −8.00000 −0.289430
\(765\) 0 0
\(766\) 36.0000 1.30073
\(767\) 14.0000 + 24.2487i 0.505511 + 0.875570i
\(768\) 25.5000 14.7224i 0.920152 0.531250i
\(769\) −2.50000 + 4.33013i −0.0901523 + 0.156148i −0.907575 0.419890i \(-0.862069\pi\)
0.817423 + 0.576038i \(0.195402\pi\)
\(770\) 0 0
\(771\) −9.00000 + 5.19615i −0.324127 + 0.187135i
\(772\) 5.00000 + 8.66025i 0.179954 + 0.311689i
\(773\) 24.0000 0.863220 0.431610 0.902060i \(-0.357946\pi\)
0.431610 + 0.902060i \(0.357946\pi\)
\(774\) 24.0000 0.862662
\(775\) 0 0
\(776\) 3.00000 + 5.19615i 0.107694 + 0.186531i
\(777\) 20.7846i 0.745644i
\(778\) 16.5000 28.5788i 0.591554 1.02460i
\(779\) 20.0000 34.6410i 0.716574 1.24114i
\(780\) 0 0
\(781\) 2.00000 + 3.46410i 0.0715656 + 0.123955i
\(782\) −12.0000 −0.429119
\(783\) −4.50000 + 2.59808i −0.160817 + 0.0928477i
\(784\) −2.00000