Properties

Label 21.3.d.a.13.2
Level 21
Weight 3
Character 21.13
Analytic conductor 0.572
Analytic rank 0
Dimension 2
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 21.d (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(0.572208555157\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 13.2
Root \(0.500000 + 0.866025i\)
Character \(\chi\) = 21.13
Dual form 21.3.d.a.13.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.73205i q^{3}\) \(-3.00000 q^{4}\) \(-6.92820i q^{5}\) \(+1.73205i q^{6}\) \(+(1.00000 + 6.92820i) q^{7}\) \(-7.00000 q^{8}\) \(-3.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.73205i q^{3}\) \(-3.00000 q^{4}\) \(-6.92820i q^{5}\) \(+1.73205i q^{6}\) \(+(1.00000 + 6.92820i) q^{7}\) \(-7.00000 q^{8}\) \(-3.00000 q^{9}\) \(-6.92820i q^{10}\) \(+10.0000 q^{11}\) \(-5.19615i q^{12}\) \(+6.92820i q^{13}\) \(+(1.00000 + 6.92820i) q^{14}\) \(+12.0000 q^{15}\) \(+5.00000 q^{16}\) \(-3.00000 q^{18}\) \(-20.7846i q^{19}\) \(+20.7846i q^{20}\) \(+(-12.0000 + 1.73205i) q^{21}\) \(+10.0000 q^{22}\) \(-14.0000 q^{23}\) \(-12.1244i q^{24}\) \(-23.0000 q^{25}\) \(+6.92820i q^{26}\) \(-5.19615i q^{27}\) \(+(-3.00000 - 20.7846i) q^{28}\) \(-38.0000 q^{29}\) \(+12.0000 q^{30}\) \(+27.7128i q^{31}\) \(+33.0000 q^{32}\) \(+17.3205i q^{33}\) \(+(48.0000 - 6.92820i) q^{35}\) \(+9.00000 q^{36}\) \(+26.0000 q^{37}\) \(-20.7846i q^{38}\) \(-12.0000 q^{39}\) \(+48.4974i q^{40}\) \(-69.2820i q^{41}\) \(+(-12.0000 + 1.73205i) q^{42}\) \(+26.0000 q^{43}\) \(-30.0000 q^{44}\) \(+20.7846i q^{45}\) \(-14.0000 q^{46}\) \(+27.7128i q^{47}\) \(+8.66025i q^{48}\) \(+(-47.0000 + 13.8564i) q^{49}\) \(-23.0000 q^{50}\) \(-20.7846i q^{52}\) \(+10.0000 q^{53}\) \(-5.19615i q^{54}\) \(-69.2820i q^{55}\) \(+(-7.00000 - 48.4974i) q^{56}\) \(+36.0000 q^{57}\) \(-38.0000 q^{58}\) \(+76.2102i q^{59}\) \(-36.0000 q^{60}\) \(+34.6410i q^{61}\) \(+27.7128i q^{62}\) \(+(-3.00000 - 20.7846i) q^{63}\) \(+13.0000 q^{64}\) \(+48.0000 q^{65}\) \(+17.3205i q^{66}\) \(+74.0000 q^{67}\) \(-24.2487i q^{69}\) \(+(48.0000 - 6.92820i) q^{70}\) \(-62.0000 q^{71}\) \(+21.0000 q^{72}\) \(-41.5692i q^{73}\) \(+26.0000 q^{74}\) \(-39.8372i q^{75}\) \(+62.3538i q^{76}\) \(+(10.0000 + 69.2820i) q^{77}\) \(-12.0000 q^{78}\) \(-46.0000 q^{79}\) \(-34.6410i q^{80}\) \(+9.00000 q^{81}\) \(-69.2820i q^{82}\) \(+90.0666i q^{83}\) \(+(36.0000 - 5.19615i) q^{84}\) \(+26.0000 q^{86}\) \(-65.8179i q^{87}\) \(-70.0000 q^{88}\) \(-41.5692i q^{89}\) \(+20.7846i q^{90}\) \(+(-48.0000 + 6.92820i) q^{91}\) \(+42.0000 q^{92}\) \(-48.0000 q^{93}\) \(+27.7128i q^{94}\) \(-144.000 q^{95}\) \(+57.1577i q^{96}\) \(+55.4256i q^{97}\) \(+(-47.0000 + 13.8564i) q^{98}\) \(-30.0000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 14q^{8} \) \(\mathstrut -\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 14q^{8} \) \(\mathstrut -\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut 20q^{11} \) \(\mathstrut +\mathstrut 2q^{14} \) \(\mathstrut +\mathstrut 24q^{15} \) \(\mathstrut +\mathstrut 10q^{16} \) \(\mathstrut -\mathstrut 6q^{18} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut +\mathstrut 20q^{22} \) \(\mathstrut -\mathstrut 28q^{23} \) \(\mathstrut -\mathstrut 46q^{25} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut -\mathstrut 76q^{29} \) \(\mathstrut +\mathstrut 24q^{30} \) \(\mathstrut +\mathstrut 66q^{32} \) \(\mathstrut +\mathstrut 96q^{35} \) \(\mathstrut +\mathstrut 18q^{36} \) \(\mathstrut +\mathstrut 52q^{37} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 24q^{42} \) \(\mathstrut +\mathstrut 52q^{43} \) \(\mathstrut -\mathstrut 60q^{44} \) \(\mathstrut -\mathstrut 28q^{46} \) \(\mathstrut -\mathstrut 94q^{49} \) \(\mathstrut -\mathstrut 46q^{50} \) \(\mathstrut +\mathstrut 20q^{53} \) \(\mathstrut -\mathstrut 14q^{56} \) \(\mathstrut +\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 76q^{58} \) \(\mathstrut -\mathstrut 72q^{60} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut +\mathstrut 26q^{64} \) \(\mathstrut +\mathstrut 96q^{65} \) \(\mathstrut +\mathstrut 148q^{67} \) \(\mathstrut +\mathstrut 96q^{70} \) \(\mathstrut -\mathstrut 124q^{71} \) \(\mathstrut +\mathstrut 42q^{72} \) \(\mathstrut +\mathstrut 52q^{74} \) \(\mathstrut +\mathstrut 20q^{77} \) \(\mathstrut -\mathstrut 24q^{78} \) \(\mathstrut -\mathstrut 92q^{79} \) \(\mathstrut +\mathstrut 18q^{81} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut +\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 140q^{88} \) \(\mathstrut -\mathstrut 96q^{91} \) \(\mathstrut +\mathstrut 84q^{92} \) \(\mathstrut -\mathstrut 96q^{93} \) \(\mathstrut -\mathstrut 288q^{95} \) \(\mathstrut -\mathstrut 94q^{98} \) \(\mathstrut -\mathstrut 60q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.500000 0.250000 0.968246i \(-0.419569\pi\)
0.250000 + 0.968246i \(0.419569\pi\)
\(3\) 1.73205i 0.577350i
\(4\) −3.00000 −0.750000
\(5\) 6.92820i 1.38564i −0.721110 0.692820i \(-0.756368\pi\)
0.721110 0.692820i \(-0.243632\pi\)
\(6\) 1.73205i 0.288675i
\(7\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(8\) −7.00000 −0.875000
\(9\) −3.00000 −0.333333
\(10\) 6.92820i 0.692820i
\(11\) 10.0000 0.909091 0.454545 0.890724i \(-0.349802\pi\)
0.454545 + 0.890724i \(0.349802\pi\)
\(12\) 5.19615i 0.433013i
\(13\) 6.92820i 0.532939i 0.963843 + 0.266469i \(0.0858571\pi\)
−0.963843 + 0.266469i \(0.914143\pi\)
\(14\) 1.00000 + 6.92820i 0.0714286 + 0.494872i
\(15\) 12.0000 0.800000
\(16\) 5.00000 0.312500
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) −3.00000 −0.166667
\(19\) 20.7846i 1.09393i −0.837157 0.546963i \(-0.815784\pi\)
0.837157 0.546963i \(-0.184216\pi\)
\(20\) 20.7846i 1.03923i
\(21\) −12.0000 + 1.73205i −0.571429 + 0.0824786i
\(22\) 10.0000 0.454545
\(23\) −14.0000 −0.608696 −0.304348 0.952561i \(-0.598439\pi\)
−0.304348 + 0.952561i \(0.598439\pi\)
\(24\) 12.1244i 0.505181i
\(25\) −23.0000 −0.920000
\(26\) 6.92820i 0.266469i
\(27\) 5.19615i 0.192450i
\(28\) −3.00000 20.7846i −0.107143 0.742307i
\(29\) −38.0000 −1.31034 −0.655172 0.755479i \(-0.727404\pi\)
−0.655172 + 0.755479i \(0.727404\pi\)
\(30\) 12.0000 0.400000
\(31\) 27.7128i 0.893962i 0.894544 + 0.446981i \(0.147501\pi\)
−0.894544 + 0.446981i \(0.852499\pi\)
\(32\) 33.0000 1.03125
\(33\) 17.3205i 0.524864i
\(34\) 0 0
\(35\) 48.0000 6.92820i 1.37143 0.197949i
\(36\) 9.00000 0.250000
\(37\) 26.0000 0.702703 0.351351 0.936244i \(-0.385722\pi\)
0.351351 + 0.936244i \(0.385722\pi\)
\(38\) 20.7846i 0.546963i
\(39\) −12.0000 −0.307692
\(40\) 48.4974i 1.21244i
\(41\) 69.2820i 1.68981i −0.534920 0.844903i \(-0.679658\pi\)
0.534920 0.844903i \(-0.320342\pi\)
\(42\) −12.0000 + 1.73205i −0.285714 + 0.0412393i
\(43\) 26.0000 0.604651 0.302326 0.953205i \(-0.402237\pi\)
0.302326 + 0.953205i \(0.402237\pi\)
\(44\) −30.0000 −0.681818
\(45\) 20.7846i 0.461880i
\(46\) −14.0000 −0.304348
\(47\) 27.7128i 0.589634i 0.955554 + 0.294817i \(0.0952587\pi\)
−0.955554 + 0.294817i \(0.904741\pi\)
\(48\) 8.66025i 0.180422i
\(49\) −47.0000 + 13.8564i −0.959184 + 0.282784i
\(50\) −23.0000 −0.460000
\(51\) 0 0
\(52\) 20.7846i 0.399704i
\(53\) 10.0000 0.188679 0.0943396 0.995540i \(-0.469926\pi\)
0.0943396 + 0.995540i \(0.469926\pi\)
\(54\) 5.19615i 0.0962250i
\(55\) 69.2820i 1.25967i
\(56\) −7.00000 48.4974i −0.125000 0.866025i
\(57\) 36.0000 0.631579
\(58\) −38.0000 −0.655172
\(59\) 76.2102i 1.29170i 0.763465 + 0.645849i \(0.223497\pi\)
−0.763465 + 0.645849i \(0.776503\pi\)
\(60\) −36.0000 −0.600000
\(61\) 34.6410i 0.567886i 0.958841 + 0.283943i \(0.0916426\pi\)
−0.958841 + 0.283943i \(0.908357\pi\)
\(62\) 27.7128i 0.446981i
\(63\) −3.00000 20.7846i −0.0476190 0.329914i
\(64\) 13.0000 0.203125
\(65\) 48.0000 0.738462
\(66\) 17.3205i 0.262432i
\(67\) 74.0000 1.10448 0.552239 0.833686i \(-0.313774\pi\)
0.552239 + 0.833686i \(0.313774\pi\)
\(68\) 0 0
\(69\) 24.2487i 0.351431i
\(70\) 48.0000 6.92820i 0.685714 0.0989743i
\(71\) −62.0000 −0.873239 −0.436620 0.899646i \(-0.643824\pi\)
−0.436620 + 0.899646i \(0.643824\pi\)
\(72\) 21.0000 0.291667
\(73\) 41.5692i 0.569441i −0.958611 0.284721i \(-0.908099\pi\)
0.958611 0.284721i \(-0.0919009\pi\)
\(74\) 26.0000 0.351351
\(75\) 39.8372i 0.531162i
\(76\) 62.3538i 0.820445i
\(77\) 10.0000 + 69.2820i 0.129870 + 0.899767i
\(78\) −12.0000 −0.153846
\(79\) −46.0000 −0.582278 −0.291139 0.956681i \(-0.594034\pi\)
−0.291139 + 0.956681i \(0.594034\pi\)
\(80\) 34.6410i 0.433013i
\(81\) 9.00000 0.111111
\(82\) 69.2820i 0.844903i
\(83\) 90.0666i 1.08514i 0.840011 + 0.542570i \(0.182549\pi\)
−0.840011 + 0.542570i \(0.817451\pi\)
\(84\) 36.0000 5.19615i 0.428571 0.0618590i
\(85\) 0 0
\(86\) 26.0000 0.302326
\(87\) 65.8179i 0.756528i
\(88\) −70.0000 −0.795455
\(89\) 41.5692i 0.467070i −0.972348 0.233535i \(-0.924971\pi\)
0.972348 0.233535i \(-0.0750293\pi\)
\(90\) 20.7846i 0.230940i
\(91\) −48.0000 + 6.92820i −0.527473 + 0.0761341i
\(92\) 42.0000 0.456522
\(93\) −48.0000 −0.516129
\(94\) 27.7128i 0.294817i
\(95\) −144.000 −1.51579
\(96\) 57.1577i 0.595392i
\(97\) 55.4256i 0.571398i 0.958319 + 0.285699i \(0.0922258\pi\)
−0.958319 + 0.285699i \(0.907774\pi\)
\(98\) −47.0000 + 13.8564i −0.479592 + 0.141392i
\(99\) −30.0000 −0.303030
\(100\) 69.0000 0.690000
\(101\) 117.779i 1.16613i −0.812424 0.583067i \(-0.801853\pi\)
0.812424 0.583067i \(-0.198147\pi\)
\(102\) 0 0
\(103\) 96.9948i 0.941698i −0.882214 0.470849i \(-0.843948\pi\)
0.882214 0.470849i \(-0.156052\pi\)
\(104\) 48.4974i 0.466321i
\(105\) 12.0000 + 83.1384i 0.114286 + 0.791795i
\(106\) 10.0000 0.0943396
\(107\) 10.0000 0.0934579 0.0467290 0.998908i \(-0.485120\pi\)
0.0467290 + 0.998908i \(0.485120\pi\)
\(108\) 15.5885i 0.144338i
\(109\) 74.0000 0.678899 0.339450 0.940624i \(-0.389759\pi\)
0.339450 + 0.940624i \(0.389759\pi\)
\(110\) 69.2820i 0.629837i
\(111\) 45.0333i 0.405706i
\(112\) 5.00000 + 34.6410i 0.0446429 + 0.309295i
\(113\) 178.000 1.57522 0.787611 0.616173i \(-0.211318\pi\)
0.787611 + 0.616173i \(0.211318\pi\)
\(114\) 36.0000 0.315789
\(115\) 96.9948i 0.843433i
\(116\) 114.000 0.982759
\(117\) 20.7846i 0.177646i
\(118\) 76.2102i 0.645849i
\(119\) 0 0
\(120\) −84.0000 −0.700000
\(121\) −21.0000 −0.173554
\(122\) 34.6410i 0.283943i
\(123\) 120.000 0.975610
\(124\) 83.1384i 0.670471i
\(125\) 13.8564i 0.110851i
\(126\) −3.00000 20.7846i −0.0238095 0.164957i
\(127\) −190.000 −1.49606 −0.748031 0.663663i \(-0.769001\pi\)
−0.748031 + 0.663663i \(0.769001\pi\)
\(128\) −119.000 −0.929688
\(129\) 45.0333i 0.349096i
\(130\) 48.0000 0.369231
\(131\) 48.4974i 0.370209i −0.982719 0.185105i \(-0.940738\pi\)
0.982719 0.185105i \(-0.0592624\pi\)
\(132\) 51.9615i 0.393648i
\(133\) 144.000 20.7846i 1.08271 0.156275i
\(134\) 74.0000 0.552239
\(135\) −36.0000 −0.266667
\(136\) 0 0
\(137\) −206.000 −1.50365 −0.751825 0.659363i \(-0.770826\pi\)
−0.751825 + 0.659363i \(0.770826\pi\)
\(138\) 24.2487i 0.175715i
\(139\) 117.779i 0.847334i −0.905818 0.423667i \(-0.860743\pi\)
0.905818 0.423667i \(-0.139257\pi\)
\(140\) −144.000 + 20.7846i −1.02857 + 0.148461i
\(141\) −48.0000 −0.340426
\(142\) −62.0000 −0.436620
\(143\) 69.2820i 0.484490i
\(144\) −15.0000 −0.104167
\(145\) 263.272i 1.81567i
\(146\) 41.5692i 0.284721i
\(147\) −24.0000 81.4064i −0.163265 0.553785i
\(148\) −78.0000 −0.527027
\(149\) 106.000 0.711409 0.355705 0.934598i \(-0.384241\pi\)
0.355705 + 0.934598i \(0.384241\pi\)
\(150\) 39.8372i 0.265581i
\(151\) −46.0000 −0.304636 −0.152318 0.988332i \(-0.548674\pi\)
−0.152318 + 0.988332i \(0.548674\pi\)
\(152\) 145.492i 0.957186i
\(153\) 0 0
\(154\) 10.0000 + 69.2820i 0.0649351 + 0.449883i
\(155\) 192.000 1.23871
\(156\) 36.0000 0.230769
\(157\) 242.487i 1.54450i −0.635316 0.772252i \(-0.719130\pi\)
0.635316 0.772252i \(-0.280870\pi\)
\(158\) −46.0000 −0.291139
\(159\) 17.3205i 0.108934i
\(160\) 228.631i 1.42894i
\(161\) −14.0000 96.9948i −0.0869565 0.602452i
\(162\) 9.00000 0.0555556
\(163\) 170.000 1.04294 0.521472 0.853268i \(-0.325383\pi\)
0.521472 + 0.853268i \(0.325383\pi\)
\(164\) 207.846i 1.26735i
\(165\) 120.000 0.727273
\(166\) 90.0666i 0.542570i
\(167\) 96.9948i 0.580807i 0.956904 + 0.290404i \(0.0937896\pi\)
−0.956904 + 0.290404i \(0.906210\pi\)
\(168\) 84.0000 12.1244i 0.500000 0.0721688i
\(169\) 121.000 0.715976
\(170\) 0 0
\(171\) 62.3538i 0.364642i
\(172\) −78.0000 −0.453488
\(173\) 173.205i 1.00119i 0.865683 + 0.500593i \(0.166885\pi\)
−0.865683 + 0.500593i \(0.833115\pi\)
\(174\) 65.8179i 0.378264i
\(175\) −23.0000 159.349i −0.131429 0.910564i
\(176\) 50.0000 0.284091
\(177\) −132.000 −0.745763
\(178\) 41.5692i 0.233535i
\(179\) −38.0000 −0.212291 −0.106145 0.994351i \(-0.533851\pi\)
−0.106145 + 0.994351i \(0.533851\pi\)
\(180\) 62.3538i 0.346410i
\(181\) 187.061i 1.03349i 0.856140 + 0.516744i \(0.172856\pi\)
−0.856140 + 0.516744i \(0.827144\pi\)
\(182\) −48.0000 + 6.92820i −0.263736 + 0.0380671i
\(183\) −60.0000 −0.327869
\(184\) 98.0000 0.532609
\(185\) 180.133i 0.973693i
\(186\) −48.0000 −0.258065
\(187\) 0 0
\(188\) 83.1384i 0.442226i
\(189\) 36.0000 5.19615i 0.190476 0.0274929i
\(190\) −144.000 −0.757895
\(191\) 82.0000 0.429319 0.214660 0.976689i \(-0.431136\pi\)
0.214660 + 0.976689i \(0.431136\pi\)
\(192\) 22.5167i 0.117274i
\(193\) 50.0000 0.259067 0.129534 0.991575i \(-0.458652\pi\)
0.129534 + 0.991575i \(0.458652\pi\)
\(194\) 55.4256i 0.285699i
\(195\) 83.1384i 0.426351i
\(196\) 141.000 41.5692i 0.719388 0.212088i
\(197\) −278.000 −1.41117 −0.705584 0.708627i \(-0.749315\pi\)
−0.705584 + 0.708627i \(0.749315\pi\)
\(198\) −30.0000 −0.151515
\(199\) 290.985i 1.46223i 0.682252 + 0.731117i \(0.261001\pi\)
−0.682252 + 0.731117i \(0.738999\pi\)
\(200\) 161.000 0.805000
\(201\) 128.172i 0.637670i
\(202\) 117.779i 0.583067i
\(203\) −38.0000 263.272i −0.187192 1.29691i
\(204\) 0 0
\(205\) −480.000 −2.34146
\(206\) 96.9948i 0.470849i
\(207\) 42.0000 0.202899
\(208\) 34.6410i 0.166543i
\(209\) 207.846i 0.994479i
\(210\) 12.0000 + 83.1384i 0.0571429 + 0.395897i
\(211\) 74.0000 0.350711 0.175355 0.984505i \(-0.443893\pi\)
0.175355 + 0.984505i \(0.443893\pi\)
\(212\) −30.0000 −0.141509
\(213\) 107.387i 0.504165i
\(214\) 10.0000 0.0467290
\(215\) 180.133i 0.837829i
\(216\) 36.3731i 0.168394i
\(217\) −192.000 + 27.7128i −0.884793 + 0.127709i
\(218\) 74.0000 0.339450
\(219\) 72.0000 0.328767
\(220\) 207.846i 0.944755i
\(221\) 0 0
\(222\) 45.0333i 0.202853i
\(223\) 304.841i 1.36700i 0.729951 + 0.683500i \(0.239543\pi\)
−0.729951 + 0.683500i \(0.760457\pi\)
\(224\) 33.0000 + 228.631i 0.147321 + 1.02067i
\(225\) 69.0000 0.306667
\(226\) 178.000 0.787611
\(227\) 6.92820i 0.0305207i 0.999884 + 0.0152604i \(0.00485771\pi\)
−0.999884 + 0.0152604i \(0.995142\pi\)
\(228\) −108.000 −0.473684
\(229\) 284.056i 1.24042i −0.784436 0.620210i \(-0.787047\pi\)
0.784436 0.620210i \(-0.212953\pi\)
\(230\) 96.9948i 0.421717i
\(231\) −120.000 + 17.3205i −0.519481 + 0.0749806i
\(232\) 266.000 1.14655
\(233\) 178.000 0.763948 0.381974 0.924173i \(-0.375244\pi\)
0.381974 + 0.924173i \(0.375244\pi\)
\(234\) 20.7846i 0.0888231i
\(235\) 192.000 0.817021
\(236\) 228.631i 0.968774i
\(237\) 79.6743i 0.336179i
\(238\) 0 0
\(239\) 34.0000 0.142259 0.0711297 0.997467i \(-0.477340\pi\)
0.0711297 + 0.997467i \(0.477340\pi\)
\(240\) 60.0000 0.250000
\(241\) 193.990i 0.804936i −0.915434 0.402468i \(-0.868152\pi\)
0.915434 0.402468i \(-0.131848\pi\)
\(242\) −21.0000 −0.0867769
\(243\) 15.5885i 0.0641500i
\(244\) 103.923i 0.425914i
\(245\) 96.0000 + 325.626i 0.391837 + 1.32908i
\(246\) 120.000 0.487805
\(247\) 144.000 0.582996
\(248\) 193.990i 0.782216i
\(249\) −156.000 −0.626506
\(250\) 13.8564i 0.0554256i
\(251\) 187.061i 0.745265i 0.927979 + 0.372632i \(0.121545\pi\)
−0.927979 + 0.372632i \(0.878455\pi\)
\(252\) 9.00000 + 62.3538i 0.0357143 + 0.247436i
\(253\) −140.000 −0.553360
\(254\) −190.000 −0.748031
\(255\) 0 0
\(256\) −171.000 −0.667969
\(257\) 138.564i 0.539160i 0.962978 + 0.269580i \(0.0868848\pi\)
−0.962978 + 0.269580i \(0.913115\pi\)
\(258\) 45.0333i 0.174548i
\(259\) 26.0000 + 180.133i 0.100386 + 0.695495i
\(260\) −144.000 −0.553846
\(261\) 114.000 0.436782
\(262\) 48.4974i 0.185105i
\(263\) −62.0000 −0.235741 −0.117871 0.993029i \(-0.537607\pi\)
−0.117871 + 0.993029i \(0.537607\pi\)
\(264\) 121.244i 0.459256i
\(265\) 69.2820i 0.261442i
\(266\) 144.000 20.7846i 0.541353 0.0781376i
\(267\) 72.0000 0.269663
\(268\) −222.000 −0.828358
\(269\) 228.631i 0.849928i 0.905210 + 0.424964i \(0.139713\pi\)
−0.905210 + 0.424964i \(0.860287\pi\)
\(270\) −36.0000 −0.133333
\(271\) 332.554i 1.22714i −0.789642 0.613568i \(-0.789734\pi\)
0.789642 0.613568i \(-0.210266\pi\)
\(272\) 0 0
\(273\) −12.0000 83.1384i −0.0439560 0.304536i
\(274\) −206.000 −0.751825
\(275\) −230.000 −0.836364
\(276\) 72.7461i 0.263573i
\(277\) 26.0000 0.0938628 0.0469314 0.998898i \(-0.485056\pi\)
0.0469314 + 0.998898i \(0.485056\pi\)
\(278\) 117.779i 0.423667i
\(279\) 83.1384i 0.297987i
\(280\) −336.000 + 48.4974i −1.20000 + 0.173205i
\(281\) −494.000 −1.75801 −0.879004 0.476815i \(-0.841791\pi\)
−0.879004 + 0.476815i \(0.841791\pi\)
\(282\) −48.0000 −0.170213
\(283\) 200.918i 0.709957i −0.934874 0.354979i \(-0.884488\pi\)
0.934874 0.354979i \(-0.115512\pi\)
\(284\) 186.000 0.654930
\(285\) 249.415i 0.875141i
\(286\) 69.2820i 0.242245i
\(287\) 480.000 69.2820i 1.67247 0.241401i
\(288\) −99.0000 −0.343750
\(289\) 289.000 1.00000
\(290\) 263.272i 0.907834i
\(291\) −96.0000 −0.329897
\(292\) 124.708i 0.427081i
\(293\) 491.902i 1.67885i 0.543477 + 0.839424i \(0.317107\pi\)
−0.543477 + 0.839424i \(0.682893\pi\)
\(294\) −24.0000 81.4064i −0.0816327 0.276892i
\(295\) 528.000 1.78983
\(296\) −182.000 −0.614865
\(297\) 51.9615i 0.174955i
\(298\) 106.000 0.355705
\(299\) 96.9948i 0.324397i
\(300\) 119.512i 0.398372i
\(301\) 26.0000 + 180.133i 0.0863787 + 0.598449i
\(302\) −46.0000 −0.152318
\(303\) 204.000 0.673267
\(304\) 103.923i 0.341852i
\(305\) 240.000 0.786885
\(306\) 0 0
\(307\) 20.7846i 0.0677023i −0.999427 0.0338512i \(-0.989223\pi\)
0.999427 0.0338512i \(-0.0107772\pi\)
\(308\) −30.0000 207.846i −0.0974026 0.674825i
\(309\) 168.000 0.543689
\(310\) 192.000 0.619355
\(311\) 13.8564i 0.0445544i 0.999752 + 0.0222772i \(0.00709163\pi\)
−0.999752 + 0.0222772i \(0.992908\pi\)
\(312\) 84.0000 0.269231
\(313\) 263.272i 0.841124i 0.907264 + 0.420562i \(0.138167\pi\)
−0.907264 + 0.420562i \(0.861833\pi\)
\(314\) 242.487i 0.772252i
\(315\) −144.000 + 20.7846i −0.457143 + 0.0659829i
\(316\) 138.000 0.436709
\(317\) 250.000 0.788644 0.394322 0.918972i \(-0.370980\pi\)
0.394322 + 0.918972i \(0.370980\pi\)
\(318\) 17.3205i 0.0544670i
\(319\) −380.000 −1.19122
\(320\) 90.0666i 0.281458i
\(321\) 17.3205i 0.0539580i
\(322\) −14.0000 96.9948i −0.0434783 0.301226i
\(323\) 0 0
\(324\) −27.0000 −0.0833333
\(325\) 159.349i 0.490304i
\(326\) 170.000 0.521472
\(327\) 128.172i 0.391963i
\(328\) 484.974i 1.47858i
\(329\) −192.000 + 27.7128i −0.583587 + 0.0842335i
\(330\) 120.000 0.363636
\(331\) −646.000 −1.95166 −0.975831 0.218527i \(-0.929875\pi\)
−0.975831 + 0.218527i \(0.929875\pi\)
\(332\) 270.200i 0.813855i
\(333\) −78.0000 −0.234234
\(334\) 96.9948i 0.290404i
\(335\) 512.687i 1.53041i
\(336\) −60.0000 + 8.66025i −0.178571 + 0.0257746i
\(337\) 146.000 0.433234 0.216617 0.976257i \(-0.430498\pi\)
0.216617 + 0.976257i \(0.430498\pi\)
\(338\) 121.000 0.357988
\(339\) 308.305i 0.909454i
\(340\) 0 0
\(341\) 277.128i 0.812692i
\(342\) 62.3538i 0.182321i
\(343\) −143.000 311.769i −0.416910 0.908948i
\(344\) −182.000 −0.529070
\(345\) −168.000 −0.486957
\(346\) 173.205i 0.500593i
\(347\) 106.000 0.305476 0.152738 0.988267i \(-0.451191\pi\)
0.152738 + 0.988267i \(0.451191\pi\)
\(348\) 197.454i 0.567396i
\(349\) 630.466i 1.80649i −0.429121 0.903247i \(-0.641177\pi\)
0.429121 0.903247i \(-0.358823\pi\)
\(350\) −23.0000 159.349i −0.0657143 0.455282i
\(351\) 36.0000 0.102564
\(352\) 330.000 0.937500
\(353\) 304.841i 0.863572i −0.901976 0.431786i \(-0.857884\pi\)
0.901976 0.431786i \(-0.142116\pi\)
\(354\) −132.000 −0.372881
\(355\) 429.549i 1.21000i
\(356\) 124.708i 0.350302i
\(357\) 0 0
\(358\) −38.0000 −0.106145
\(359\) −494.000 −1.37604 −0.688022 0.725690i \(-0.741521\pi\)
−0.688022 + 0.725690i \(0.741521\pi\)
\(360\) 145.492i 0.404145i
\(361\) −71.0000 −0.196676
\(362\) 187.061i 0.516744i
\(363\) 36.3731i 0.100201i
\(364\) 144.000 20.7846i 0.395604 0.0571006i
\(365\) −288.000 −0.789041
\(366\) −60.0000 −0.163934
\(367\) 554.256i 1.51024i 0.655589 + 0.755118i \(0.272420\pi\)
−0.655589 + 0.755118i \(0.727580\pi\)
\(368\) −70.0000 −0.190217
\(369\) 207.846i 0.563269i
\(370\) 180.133i 0.486847i
\(371\) 10.0000 + 69.2820i 0.0269542 + 0.186744i
\(372\) 144.000 0.387097
\(373\) 218.000 0.584450 0.292225 0.956350i \(-0.405604\pi\)
0.292225 + 0.956350i \(0.405604\pi\)
\(374\) 0 0
\(375\) 24.0000 0.0640000
\(376\) 193.990i 0.515930i
\(377\) 263.272i 0.698333i
\(378\) 36.0000 5.19615i 0.0952381 0.0137464i
\(379\) −550.000 −1.45119 −0.725594 0.688123i \(-0.758435\pi\)
−0.725594 + 0.688123i \(0.758435\pi\)
\(380\) 432.000 1.13684
\(381\) 329.090i 0.863752i
\(382\) 82.0000 0.214660
\(383\) 55.4256i 0.144714i 0.997379 + 0.0723572i \(0.0230522\pi\)
−0.997379 + 0.0723572i \(0.976948\pi\)
\(384\) 206.114i 0.536755i
\(385\) 480.000 69.2820i 1.24675 0.179953i
\(386\) 50.0000 0.129534
\(387\) −78.0000 −0.201550
\(388\) 166.277i 0.428549i
\(389\) 394.000 1.01285 0.506427 0.862283i \(-0.330966\pi\)
0.506427 + 0.862283i \(0.330966\pi\)
\(390\) 83.1384i 0.213175i
\(391\) 0 0
\(392\) 329.000 96.9948i 0.839286 0.247436i
\(393\) 84.0000 0.213740
\(394\) −278.000 −0.705584
\(395\) 318.697i 0.806829i
\(396\) 90.0000 0.227273
\(397\) 103.923i 0.261771i −0.991397 0.130885i \(-0.958218\pi\)
0.991397 0.130885i \(-0.0417820\pi\)
\(398\) 290.985i 0.731117i
\(399\) 36.0000 + 249.415i 0.0902256 + 0.625101i
\(400\) −115.000 −0.287500
\(401\) 178.000 0.443890 0.221945 0.975059i \(-0.428759\pi\)
0.221945 + 0.975059i \(0.428759\pi\)
\(402\) 128.172i 0.318835i
\(403\) −192.000 −0.476427
\(404\) 353.338i 0.874600i
\(405\) 62.3538i 0.153960i
\(406\) −38.0000 263.272i −0.0935961 0.648453i
\(407\) 260.000 0.638821
\(408\) 0 0
\(409\) 651.251i 1.59230i 0.605099 + 0.796150i \(0.293134\pi\)
−0.605099 + 0.796150i \(0.706866\pi\)
\(410\) −480.000 −1.17073
\(411\) 356.802i 0.868133i
\(412\) 290.985i 0.706273i
\(413\) −528.000 + 76.2102i −1.27845 + 0.184528i
\(414\) 42.0000 0.101449
\(415\) 624.000 1.50361
\(416\) 228.631i 0.549593i
\(417\) 204.000 0.489209
\(418\) 207.846i 0.497239i
\(419\) 713.605i 1.70311i −0.524262 0.851557i \(-0.675659\pi\)
0.524262 0.851557i \(-0.324341\pi\)
\(420\) −36.0000 249.415i −0.0857143 0.593846i
\(421\) 602.000 1.42993 0.714964 0.699161i \(-0.246443\pi\)
0.714964 + 0.699161i \(0.246443\pi\)
\(422\) 74.0000 0.175355
\(423\) 83.1384i 0.196545i
\(424\) −70.0000 −0.165094
\(425\) 0 0
\(426\) 107.387i 0.252083i
\(427\) −240.000 + 34.6410i −0.562061 + 0.0811265i
\(428\) −30.0000 −0.0700935
\(429\) −120.000 −0.279720
\(430\) 180.133i 0.418915i
\(431\) 34.0000 0.0788863 0.0394432 0.999222i \(-0.487442\pi\)
0.0394432 + 0.999222i \(0.487442\pi\)
\(432\) 25.9808i 0.0601407i
\(433\) 415.692i 0.960028i −0.877261 0.480014i \(-0.840632\pi\)
0.877261 0.480014i \(-0.159368\pi\)
\(434\) −192.000 + 27.7128i −0.442396 + 0.0638544i
\(435\) −456.000 −1.04828
\(436\) −222.000 −0.509174
\(437\) 290.985i 0.665869i
\(438\) 72.0000 0.164384
\(439\) 96.9948i 0.220945i 0.993879 + 0.110472i \(0.0352364\pi\)
−0.993879 + 0.110472i \(0.964764\pi\)
\(440\) 484.974i 1.10221i
\(441\) 141.000 41.5692i 0.319728 0.0942613i
\(442\) 0 0
\(443\) −470.000 −1.06095 −0.530474 0.847701i \(-0.677986\pi\)
−0.530474 + 0.847701i \(0.677986\pi\)
\(444\) 135.100i 0.304279i
\(445\) −288.000 −0.647191
\(446\) 304.841i 0.683500i
\(447\) 183.597i 0.410732i
\(448\) 13.0000 + 90.0666i 0.0290179 + 0.201042i
\(449\) 514.000 1.14477 0.572383 0.819986i \(-0.306019\pi\)
0.572383 + 0.819986i \(0.306019\pi\)
\(450\) 69.0000 0.153333
\(451\) 692.820i 1.53619i
\(452\) −534.000 −1.18142
\(453\) 79.6743i 0.175882i
\(454\) 6.92820i 0.0152604i
\(455\) 48.0000 + 332.554i 0.105495 + 0.730887i
\(456\) −252.000 −0.552632
\(457\) −478.000 −1.04595 −0.522976 0.852347i \(-0.675178\pi\)
−0.522976 + 0.852347i \(0.675178\pi\)
\(458\) 284.056i 0.620210i
\(459\) 0 0
\(460\) 290.985i 0.632575i
\(461\) 672.036i 1.45778i 0.684632 + 0.728889i \(0.259963\pi\)
−0.684632 + 0.728889i \(0.740037\pi\)
\(462\) −120.000 + 17.3205i −0.259740 + 0.0374903i
\(463\) −430.000 −0.928726 −0.464363 0.885645i \(-0.653717\pi\)
−0.464363 + 0.885645i \(0.653717\pi\)
\(464\) −190.000 −0.409483
\(465\) 332.554i 0.715169i
\(466\) 178.000 0.381974
\(467\) 852.169i 1.82477i −0.409330 0.912387i \(-0.634237\pi\)
0.409330 0.912387i \(-0.365763\pi\)
\(468\) 62.3538i 0.133235i
\(469\) 74.0000 + 512.687i 0.157783 + 1.09315i
\(470\) 192.000 0.408511
\(471\) 420.000 0.891720
\(472\) 533.472i 1.13024i
\(473\) 260.000 0.549683
\(474\) 79.6743i 0.168089i
\(475\) 478.046i 1.00641i
\(476\) 0 0
\(477\) −30.0000 −0.0628931
\(478\) 34.0000 0.0711297
\(479\) 387.979i 0.809978i −0.914322 0.404989i \(-0.867275\pi\)
0.914322 0.404989i \(-0.132725\pi\)
\(480\) 396.000 0.825000
\(481\) 180.133i 0.374497i
\(482\) 193.990i 0.402468i
\(483\) 168.000 24.2487i 0.347826 0.0502044i
\(484\) 63.0000 0.130165
\(485\) 384.000 0.791753
\(486\) 15.5885i 0.0320750i
\(487\) 818.000 1.67967 0.839836 0.542841i \(-0.182651\pi\)
0.839836 + 0.542841i \(0.182651\pi\)
\(488\) 242.487i 0.496900i
\(489\) 294.449i 0.602144i
\(490\) 96.0000 + 325.626i 0.195918 + 0.664542i
\(491\) 490.000 0.997963 0.498982 0.866613i \(-0.333707\pi\)
0.498982 + 0.866613i \(0.333707\pi\)
\(492\) −360.000 −0.731707
\(493\) 0 0
\(494\) 144.000 0.291498
\(495\) 207.846i 0.419891i
\(496\) 138.564i 0.279363i
\(497\) −62.0000 429.549i −0.124748 0.864283i
\(498\) −156.000 −0.313253
\(499\) 554.000 1.11022 0.555110 0.831777i \(-0.312676\pi\)
0.555110 + 0.831777i \(0.312676\pi\)
\(500\) 41.5692i 0.0831384i
\(501\) −168.000 −0.335329
\(502\) 187.061i 0.372632i
\(503\) 290.985i 0.578498i 0.957254 + 0.289249i \(0.0934056\pi\)
−0.957254 + 0.289249i \(0.906594\pi\)
\(504\) 21.0000 + 145.492i 0.0416667 + 0.288675i
\(505\) −816.000 −1.61584
\(506\) −140.000 −0.276680
\(507\) 209.578i 0.413369i
\(508\) 570.000 1.12205
\(509\) 963.020i 1.89198i −0.324189 0.945992i \(-0.605091\pi\)
0.324189 0.945992i \(-0.394909\pi\)
\(510\) 0 0
\(511\) 288.000 41.5692i 0.563601 0.0813488i
\(512\) 305.000 0.595703
\(513\) −108.000 −0.210526
\(514\) 138.564i 0.269580i
\(515\) −672.000 −1.30485
\(516\) 135.100i 0.261822i
\(517\) 277.128i 0.536031i
\(518\) 26.0000 + 180.133i 0.0501931 + 0.347748i
\(519\) −300.000 −0.578035
\(520\) −336.000 −0.646154
\(521\) 124.708i 0.239362i −0.992812 0.119681i \(-0.961813\pi\)
0.992812 0.119681i \(-0.0381872\pi\)
\(522\) 114.000 0.218391
\(523\) 62.3538i 0.119223i −0.998222 0.0596117i \(-0.981014\pi\)
0.998222 0.0596117i \(-0.0189862\pi\)
\(524\) 145.492i 0.277657i
\(525\) 276.000 39.8372i 0.525714 0.0758803i
\(526\) −62.0000 −0.117871
\(527\) 0 0
\(528\) 86.6025i 0.164020i
\(529\) −333.000 −0.629490
\(530\) 69.2820i 0.130721i
\(531\) 228.631i 0.430566i
\(532\) −432.000 + 62.3538i −0.812030 + 0.117206i
\(533\) 480.000 0.900563
\(534\) 72.0000 0.134831
\(535\) 69.2820i 0.129499i
\(536\) −518.000 −0.966418
\(537\) 65.8179i 0.122566i
\(538\) 228.631i 0.424964i
\(539\) −470.000 + 138.564i −0.871985 + 0.257076i
\(540\) 108.000 0.200000
\(541\) −118.000 −0.218115 −0.109057 0.994035i \(-0.534783\pi\)
−0.109057 + 0.994035i \(0.534783\pi\)
\(542\) 332.554i 0.613568i
\(543\) −324.000 −0.596685
\(544\) 0 0
\(545\) 512.687i 0.940710i
\(546\) −12.0000 83.1384i −0.0219780 0.152268i
\(547\) −406.000 −0.742230 −0.371115 0.928587i \(-0.621024\pi\)
−0.371115 + 0.928587i \(0.621024\pi\)
\(548\) 618.000 1.12774
\(549\) 103.923i 0.189295i
\(550\) −230.000 −0.418182
\(551\) 789.815i 1.43342i
\(552\) 169.741i 0.307502i
\(553\) −46.0000 318.697i −0.0831826 0.576306i
\(554\) 26.0000 0.0469314
\(555\) 312.000 0.562162
\(556\) 353.338i 0.635501i
\(557\) −998.000 −1.79174 −0.895871 0.444315i \(-0.853447\pi\)
−0.895871 + 0.444315i \(0.853447\pi\)
\(558\) 83.1384i 0.148994i
\(559\) 180.133i 0.322242i
\(560\) 240.000 34.6410i 0.428571 0.0618590i
\(561\) 0 0
\(562\) −494.000 −0.879004
\(563\) 367.195i 0.652211i 0.945333 + 0.326105i \(0.105736\pi\)
−0.945333 + 0.326105i \(0.894264\pi\)
\(564\) 144.000 0.255319
\(565\) 1233.22i 2.18269i
\(566\) 200.918i 0.354979i
\(567\) 9.00000 + 62.3538i 0.0158730 + 0.109971i
\(568\) 434.000 0.764085
\(569\) −62.0000 −0.108963 −0.0544815 0.998515i \(-0.517351\pi\)
−0.0544815 + 0.998515i \(0.517351\pi\)
\(570\) 249.415i 0.437571i
\(571\) 410.000 0.718039 0.359019 0.933330i \(-0.383111\pi\)
0.359019 + 0.933330i \(0.383111\pi\)
\(572\) 207.846i 0.363367i
\(573\) 142.028i 0.247868i
\(574\) 480.000 69.2820i 0.836237 0.120700i
\(575\) 322.000 0.560000
\(576\) −39.0000 −0.0677083
\(577\) 831.384i 1.44087i 0.693520 + 0.720437i \(0.256059\pi\)
−0.693520 + 0.720437i \(0.743941\pi\)
\(578\) 289.000 0.500000
\(579\) 86.6025i 0.149573i
\(580\) 789.815i 1.36175i
\(581\) −624.000 + 90.0666i −1.07401 + 0.155020i
\(582\) −96.0000 −0.164948
\(583\) 100.000 0.171527
\(584\) 290.985i 0.498261i
\(585\) −144.000 −0.246154
\(586\) 491.902i 0.839424i
\(587\) 547.328i 0.932416i 0.884675 + 0.466208i \(0.154380\pi\)
−0.884675 + 0.466208i \(0.845620\pi\)
\(588\) 72.0000 + 244.219i 0.122449 + 0.415339i
\(589\) 576.000 0.977929
\(590\) 528.000 0.894915
\(591\) 481.510i 0.814738i
\(592\) 130.000 0.219595
\(593\) 997.661i 1.68240i 0.540727 + 0.841198i \(0.318149\pi\)
−0.540727 + 0.841198i \(0.681851\pi\)
\(594\) 51.9615i 0.0874773i
\(595\) 0 0
\(596\) −318.000 −0.533557
\(597\) −504.000 −0.844221
\(598\) 96.9948i 0.162199i
\(599\) 1186.00 1.97997 0.989983 0.141184i \(-0.0450911\pi\)
0.989983 + 0.141184i \(0.0450911\pi\)
\(600\) 278.860i 0.464767i
\(601\) 401.836i 0.668612i −0.942465 0.334306i \(-0.891498\pi\)
0.942465 0.334306i \(-0.108502\pi\)
\(602\) 26.0000 + 180.133i 0.0431894 + 0.299225i
\(603\) −222.000 −0.368159
\(604\) 138.000 0.228477
\(605\) 145.492i 0.240483i
\(606\) 204.000 0.336634
\(607\) 138.564i 0.228277i −0.993465 0.114138i \(-0.963589\pi\)
0.993465 0.114138i \(-0.0364107\pi\)
\(608\) 685.892i 1.12811i
\(609\) 456.000 65.8179i 0.748768 0.108075i
\(610\) 240.000 0.393443
\(611\) −192.000 −0.314239
\(612\) 0 0
\(613\) 26.0000 0.0424144 0.0212072 0.999775i \(-0.493249\pi\)
0.0212072 + 0.999775i \(0.493249\pi\)
\(614\) 20.7846i 0.0338512i
\(615\) 831.384i 1.35184i
\(616\) −70.0000 484.974i −0.113636 0.787296i
\(617\) −734.000 −1.18963 −0.594814 0.803864i \(-0.702774\pi\)
−0.594814 + 0.803864i \(0.702774\pi\)
\(618\) 168.000 0.271845
\(619\) 838.313i 1.35430i −0.735844 0.677151i \(-0.763215\pi\)
0.735844 0.677151i \(-0.236785\pi\)
\(620\) −576.000 −0.929032
\(621\) 72.7461i 0.117144i
\(622\) 13.8564i 0.0222772i
\(623\) 288.000 41.5692i 0.462279 0.0667243i
\(624\) −60.0000 −0.0961538
\(625\) −671.000 −1.07360
\(626\) 263.272i 0.420562i
\(627\) 360.000 0.574163
\(628\) 727.461i 1.15838i
\(629\) 0 0
\(630\) −144.000 + 20.7846i −0.228571 + 0.0329914i
\(631\) −286.000 −0.453249 −0.226624 0.973982i \(-0.572769\pi\)
−0.226624 + 0.973982i \(0.572769\pi\)
\(632\) 322.000 0.509494
\(633\) 128.172i 0.202483i
\(634\) 250.000 0.394322
\(635\) 1316.36i 2.07301i
\(636\) 51.9615i 0.0817005i
\(637\) −96.0000 325.626i −0.150706 0.511186i
\(638\) −380.000 −0.595611
\(639\) 186.000 0.291080
\(640\) 824.456i 1.28821i
\(641\) 658.000 1.02652 0.513261 0.858233i \(-0.328437\pi\)
0.513261 + 0.858233i \(0.328437\pi\)
\(642\) 17.3205i 0.0269790i
\(643\) 325.626i 0.506416i −0.967412 0.253208i \(-0.918514\pi\)
0.967412 0.253208i \(-0.0814857\pi\)
\(644\) 42.0000 + 290.985i 0.0652174 + 0.451839i
\(645\) 312.000 0.483721
\(646\) 0 0
\(647\) 457.261i 0.706741i −0.935483 0.353370i \(-0.885036\pi\)
0.935483 0.353370i \(-0.114964\pi\)
\(648\) −63.0000 −0.0972222
\(649\) 762.102i 1.17427i
\(650\) 159.349i 0.245152i
\(651\) −48.0000 332.554i −0.0737327 0.510835i
\(652\) −510.000 −0.782209
\(653\) −614.000 −0.940276 −0.470138 0.882593i \(-0.655796\pi\)
−0.470138 + 0.882593i \(0.655796\pi\)
\(654\) 128.172i 0.195981i
\(655\) −336.000 −0.512977
\(656\) 346.410i 0.528064i
\(657\) 124.708i 0.189814i
\(658\) −192.000 + 27.7128i −0.291793 + 0.0421167i
\(659\) 442.000 0.670713 0.335357 0.942091i \(-0.391143\pi\)
0.335357 + 0.942091i \(0.391143\pi\)
\(660\) −360.000 −0.545455
\(661\) 34.6410i 0.0524070i −0.999657 0.0262035i \(-0.991658\pi\)
0.999657 0.0262035i \(-0.00834179\pi\)
\(662\) −646.000 −0.975831
\(663\) 0 0
\(664\) 630.466i 0.949498i
\(665\) −144.000 997.661i −0.216541 1.50024i
\(666\) −78.0000 −0.117117
\(667\) 532.000 0.797601
\(668\) 290.985i 0.435606i
\(669\) −528.000 −0.789238
\(670\) 512.687i 0.765205i
\(671\) 346.410i 0.516260i
\(672\) −396.000 + 57.1577i −0.589286 + 0.0850561i
\(673\) 386.000 0.573551 0.286776 0.957998i \(-0.407417\pi\)
0.286776 + 0.957998i \(0.407417\pi\)
\(674\) 146.000 0.216617
\(675\) 119.512i 0.177054i
\(676\) −363.000 −0.536982
\(677\) 782.887i 1.15641i −0.815893 0.578203i \(-0.803754\pi\)
0.815893 0.578203i \(-0.196246\pi\)
\(678\) 308.305i 0.454727i
\(679\) −384.000 + 55.4256i −0.565538 + 0.0816283i
\(680\) 0 0
\(681\) −12.0000 −0.0176211
\(682\) 277.128i 0.406346i
\(683\) 298.000 0.436310 0.218155 0.975914i \(-0.429996\pi\)
0.218155 + 0.975914i \(0.429996\pi\)
\(684\) 187.061i 0.273482i
\(685\) 1427.21i 2.08352i
\(686\) −143.000 311.769i −0.208455 0.454474i
\(687\) 492.000 0.716157
\(688\) 130.000 0.188953
\(689\) 69.2820i 0.100554i
\(690\) −168.000 −0.243478
\(691\) 866.025i 1.25329i 0.779304 + 0.626646i \(0.215573\pi\)
−0.779304 + 0.626646i \(0.784427\pi\)
\(692\) 519.615i 0.750889i
\(693\) −30.0000 207.846i −0.0432900 0.299922i
\(694\) 106.000 0.152738
\(695\) −816.000 −1.17410
\(696\) 460.726i 0.661962i
\(697\) 0 0
\(698\) 630.466i 0.903247i
\(699\) 308.305i 0.441066i
\(700\) 69.0000 + 478.046i 0.0985714 + 0.682923i
\(701\) 154.000 0.219686 0.109843 0.993949i \(-0.464965\pi\)
0.109843 + 0.993949i \(0.464965\pi\)
\(702\) 36.0000 0.0512821
\(703\) 540.400i 0.768705i
\(704\) 130.000 0.184659
\(705\) 332.554i 0.471707i
\(706\) 304.841i 0.431786i
\(707\) 816.000 117.779i 1.15417 0.166590i
\(708\) 396.000 0.559322
\(709\) 890.000 1.25529 0.627645 0.778500i \(-0.284019\pi\)
0.627645 + 0.778500i \(0.284019\pi\)
\(710\) 429.549i 0.604998i
\(711\) 138.000 0.194093
\(712\) 290.985i 0.408686i
\(713\) 387.979i 0.544151i
\(714\) 0 0
\(715\) 480.000 0.671329
\(716\) 114.000 0.159218
\(717\) 58.8897i 0.0821335i
\(718\) −494.000 −0.688022
\(719\) 83.1384i 0.115631i 0.998327 + 0.0578153i \(0.0184135\pi\)
−0.998327 + 0.0578153i \(0.981587\pi\)
\(720\) 103.923i 0.144338i
\(721\) 672.000 96.9948i 0.932039 0.134528i
\(722\) −71.0000 −0.0983380
\(723\) 336.000 0.464730
\(724\) 561.184i 0.775117i
\(725\) 874.000 1.20552
\(726\) 36.3731i 0.0501006i
\(727\) 235.559i 0.324015i −0.986790 0.162008i \(-0.948203\pi\)
0.986790 0.162008i \(-0.0517969\pi\)
\(728\) 336.000 48.4974i 0.461538 0.0666173i
\(729\) −27.0000 −0.0370370
\(730\) −288.000 −0.394521
\(731\) 0 0
\(732\) 180.000 0.245902
\(733\) 76.2102i 0.103970i −0.998648 0.0519852i \(-0.983445\pi\)
0.998648 0.0519852i \(-0.0165549\pi\)
\(734\) 554.256i 0.755118i
\(735\) −564.000 + 166.277i −0.767347 + 0.226227i
\(736\) −462.000 −0.627717
\(737\) 740.000 1.00407
\(738\) 207.846i 0.281634i
\(739\) −982.000 −1.32882 −0.664411 0.747367i \(-0.731318\pi\)
−0.664411 + 0.747367i \(0.731318\pi\)
\(740\) 540.400i 0.730270i
\(741\) 249.415i 0.336593i
\(742\) 10.0000 + 69.2820i 0.0134771 + 0.0933720i
\(743\) −686.000 −0.923284 −0.461642 0.887066i \(-0.652740\pi\)
−0.461642 + 0.887066i \(0.652740\pi\)
\(744\) 336.000 0.451613
\(745\) 734.390i 0.985758i
\(746\) 218.000 0.292225
\(747\) 270.200i 0.361713i
\(748\) 0 0
\(749\) 10.0000 + 69.2820i 0.0133511 + 0.0924994i
\(750\) 24.0000 0.0320000
\(751\) 290.000 0.386152 0.193076 0.981184i \(-0.438154\pi\)
0.193076 + 0.981184i \(0.438154\pi\)
\(752\) 138.564i 0.184261i
\(753\) −324.000 −0.430279
\(754\) 263.272i 0.349167i
\(755\) 318.697i 0.422116i
\(756\) −108.000 + 15.5885i −0.142857 + 0.0206197i
\(757\) −358.000 −0.472919 −0.236460 0.971641i \(-0.575987\pi\)
−0.236460 + 0.971641i \(0.575987\pi\)
\(758\) −550.000 −0.725594
\(759\) 242.487i 0.319482i
\(760\) 1008.00 1.32632
\(761\) 651.251i 0.855783i −0.903830 0.427892i \(-0.859256\pi\)
0.903830 0.427892i \(-0.140744\pi\)
\(762\) 329.090i 0.431876i
\(763\) 74.0000 + 512.687i 0.0969856 + 0.671936i
\(764\) −246.000 −0.321990
\(765\) 0 0
\(766\) 55.4256i 0.0723572i
\(767\) −528.000 −0.688396
\(768\) 296.181i 0.385652i
\(769\) 775.959i 1.00905i 0.863397 + 0.504525i \(0.168332\pi\)
−0.863397 + 0.504525i \(0.831668\pi\)
\(770\) 480.000 69.2820i 0.623377 0.0899767i
\(771\) −240.000 −0.311284
\(772\) −150.000 −0.194301
\(773\) 228.631i 0.295771i −0.989005 0.147885i \(-0.952753\pi\)
0.989005 0.147885i \(-0.0472467\pi\)
\(774\) −78.0000 −0.100775
\(775\) 637.395i 0.822445i
\(776\) 387.979i 0.499973i
\(777\) −312.000 + 45.0333i −0.401544 + 0.0579579i
\(778\) 394.000 0.506427
\(779\) −1440.00 −1.84852
\(780\) 249.415i 0.319763i
\(781\) −620.000 −0.793854
\(782\) 0 0
\(783\) 197.454i 0.252176i
\(784\) −235.000 + 69.2820i −0.299745 + 0.0883699i
\(785\) −1680.00 −2.14013
\(786\) 84.0000 0.106870
\(787\) 76.2102i 0.0968364i −0.998827 0.0484182i \(-0.984582\pi\)
0.998827 0.0484182i \(-0.0154180\pi\)
\(788\) 834.000 1.05838
\(789\) 107.387i 0.136105i
\(790\) 318.697i 0.403414i
\(791\) 178.000 + 1233.22i 0.225032 + 1.55906i
\(792\) 210.000 0.265152
\(793\) −240.000 −0.302648
\(794\) 103.923i 0.130885i
\(795\) 120.000 0.150943
\(796\) 872.954i 1.09668i
\(797\) 866.025i 1.08661i 0.839537 + 0.543303i \(0.182827\pi\)
−0.839537 + 0.543303i \(0.817173\pi\)
\(798\) 36.0000 + 249.415i 0.0451128 + 0.312551i
\(799\) 0 0
\(800\) −759.000 −0.948750