Properties

Label 882.4.g.d.361.1
Level $882$
Weight $4$
Character 882.361
Analytic conductor $52.040$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(52.0396846251\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.4.g.d.667.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-3.50000 - 6.06218i) q^{5} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-3.50000 - 6.06218i) q^{5} +8.00000 q^{8} +(-7.00000 + 12.1244i) q^{10} +(17.5000 - 30.3109i) q^{11} -66.0000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-29.5000 + 51.0955i) q^{17} +(68.5000 + 118.645i) q^{19} +28.0000 q^{20} -70.0000 q^{22} +(-3.50000 - 6.06218i) q^{23} +(38.0000 - 65.8179i) q^{25} +(66.0000 + 114.315i) q^{26} -106.000 q^{29} +(37.5000 - 64.9519i) q^{31} +(-16.0000 + 27.7128i) q^{32} +118.000 q^{34} +(-5.50000 - 9.52628i) q^{37} +(137.000 - 237.291i) q^{38} +(-28.0000 - 48.4974i) q^{40} -498.000 q^{41} +260.000 q^{43} +(70.0000 + 121.244i) q^{44} +(-7.00000 + 12.1244i) q^{46} +(85.5000 + 148.090i) q^{47} -152.000 q^{50} +(132.000 - 228.631i) q^{52} +(-208.500 + 361.133i) q^{53} -245.000 q^{55} +(106.000 + 183.597i) q^{58} +(8.50000 - 14.7224i) q^{59} +(25.5000 + 44.1673i) q^{61} -150.000 q^{62} +64.0000 q^{64} +(231.000 + 400.104i) q^{65} +(-219.500 + 380.185i) q^{67} +(-118.000 - 204.382i) q^{68} +784.000 q^{71} +(147.500 - 255.477i) q^{73} +(-11.0000 + 19.0526i) q^{74} -548.000 q^{76} +(247.500 + 428.683i) q^{79} +(-56.0000 + 96.9948i) q^{80} +(498.000 + 862.561i) q^{82} +932.000 q^{83} +413.000 q^{85} +(-260.000 - 450.333i) q^{86} +(140.000 - 242.487i) q^{88} +(436.500 + 756.040i) q^{89} +28.0000 q^{92} +(171.000 - 296.181i) q^{94} +(479.500 - 830.518i) q^{95} +290.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} - 4q^{4} - 7q^{5} + 16q^{8} + O(q^{10}) \) \( 2q - 2q^{2} - 4q^{4} - 7q^{5} + 16q^{8} - 14q^{10} + 35q^{11} - 132q^{13} - 16q^{16} - 59q^{17} + 137q^{19} + 56q^{20} - 140q^{22} - 7q^{23} + 76q^{25} + 132q^{26} - 212q^{29} + 75q^{31} - 32q^{32} + 236q^{34} - 11q^{37} + 274q^{38} - 56q^{40} - 996q^{41} + 520q^{43} + 140q^{44} - 14q^{46} + 171q^{47} - 304q^{50} + 264q^{52} - 417q^{53} - 490q^{55} + 212q^{58} + 17q^{59} + 51q^{61} - 300q^{62} + 128q^{64} + 462q^{65} - 439q^{67} - 236q^{68} + 1568q^{71} + 295q^{73} - 22q^{74} - 1096q^{76} + 495q^{79} - 112q^{80} + 996q^{82} + 1864q^{83} + 826q^{85} - 520q^{86} + 280q^{88} + 873q^{89} + 56q^{92} + 342q^{94} + 959q^{95} + 580q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.73205i −0.353553 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) −3.50000 6.06218i −0.313050 0.542218i 0.665971 0.745977i \(-0.268017\pi\)
−0.979021 + 0.203760i \(0.934684\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) −7.00000 + 12.1244i −0.221359 + 0.383406i
\(11\) 17.5000 30.3109i 0.479677 0.830825i −0.520051 0.854135i \(-0.674087\pi\)
0.999728 + 0.0233099i \(0.00742046\pi\)
\(12\) 0 0
\(13\) −66.0000 −1.40809 −0.704043 0.710158i \(-0.748624\pi\)
−0.704043 + 0.710158i \(0.748624\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −29.5000 + 51.0955i −0.420871 + 0.728969i −0.996025 0.0890757i \(-0.971609\pi\)
0.575154 + 0.818045i \(0.304942\pi\)
\(18\) 0 0
\(19\) 68.5000 + 118.645i 0.827104 + 1.43259i 0.900301 + 0.435269i \(0.143347\pi\)
−0.0731965 + 0.997318i \(0.523320\pi\)
\(20\) 28.0000 0.313050
\(21\) 0 0
\(22\) −70.0000 −0.678366
\(23\) −3.50000 6.06218i −0.0317305 0.0549588i 0.849724 0.527228i \(-0.176768\pi\)
−0.881455 + 0.472269i \(0.843435\pi\)
\(24\) 0 0
\(25\) 38.0000 65.8179i 0.304000 0.526543i
\(26\) 66.0000 + 114.315i 0.497833 + 0.862273i
\(27\) 0 0
\(28\) 0 0
\(29\) −106.000 −0.678748 −0.339374 0.940651i \(-0.610215\pi\)
−0.339374 + 0.940651i \(0.610215\pi\)
\(30\) 0 0
\(31\) 37.5000 64.9519i 0.217264 0.376313i −0.736706 0.676213i \(-0.763620\pi\)
0.953971 + 0.299900i \(0.0969533\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 118.000 0.595201
\(35\) 0 0
\(36\) 0 0
\(37\) −5.50000 9.52628i −0.0244377 0.0423273i 0.853548 0.521014i \(-0.174446\pi\)
−0.877986 + 0.478687i \(0.841113\pi\)
\(38\) 137.000 237.291i 0.584851 1.01299i
\(39\) 0 0
\(40\) −28.0000 48.4974i −0.110680 0.191703i
\(41\) −498.000 −1.89694 −0.948470 0.316867i \(-0.897369\pi\)
−0.948470 + 0.316867i \(0.897369\pi\)
\(42\) 0 0
\(43\) 260.000 0.922084 0.461042 0.887378i \(-0.347476\pi\)
0.461042 + 0.887378i \(0.347476\pi\)
\(44\) 70.0000 + 121.244i 0.239839 + 0.415413i
\(45\) 0 0
\(46\) −7.00000 + 12.1244i −0.0224368 + 0.0388617i
\(47\) 85.5000 + 148.090i 0.265350 + 0.459600i 0.967655 0.252276i \(-0.0811791\pi\)
−0.702305 + 0.711876i \(0.747846\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −152.000 −0.429921
\(51\) 0 0
\(52\) 132.000 228.631i 0.352021 0.609719i
\(53\) −208.500 + 361.133i −0.540371 + 0.935951i 0.458511 + 0.888689i \(0.348383\pi\)
−0.998883 + 0.0472619i \(0.984950\pi\)
\(54\) 0 0
\(55\) −245.000 −0.600651
\(56\) 0 0
\(57\) 0 0
\(58\) 106.000 + 183.597i 0.239974 + 0.415647i
\(59\) 8.50000 14.7224i 0.0187560 0.0324864i −0.856495 0.516155i \(-0.827363\pi\)
0.875251 + 0.483669i \(0.160696\pi\)
\(60\) 0 0
\(61\) 25.5000 + 44.1673i 0.0535236 + 0.0927056i 0.891546 0.452930i \(-0.149621\pi\)
−0.838022 + 0.545636i \(0.816288\pi\)
\(62\) −150.000 −0.307258
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 231.000 + 400.104i 0.440800 + 0.763489i
\(66\) 0 0
\(67\) −219.500 + 380.185i −0.400242 + 0.693239i −0.993755 0.111585i \(-0.964407\pi\)
0.593513 + 0.804824i \(0.297740\pi\)
\(68\) −118.000 204.382i −0.210435 0.364485i
\(69\) 0 0
\(70\) 0 0
\(71\) 784.000 1.31047 0.655237 0.755423i \(-0.272569\pi\)
0.655237 + 0.755423i \(0.272569\pi\)
\(72\) 0 0
\(73\) 147.500 255.477i 0.236487 0.409608i −0.723217 0.690621i \(-0.757337\pi\)
0.959704 + 0.281013i \(0.0906705\pi\)
\(74\) −11.0000 + 19.0526i −0.0172801 + 0.0299299i
\(75\) 0 0
\(76\) −548.000 −0.827104
\(77\) 0 0
\(78\) 0 0
\(79\) 247.500 + 428.683i 0.352480 + 0.610513i 0.986683 0.162653i \(-0.0520051\pi\)
−0.634203 + 0.773166i \(0.718672\pi\)
\(80\) −56.0000 + 96.9948i −0.0782624 + 0.135554i
\(81\) 0 0
\(82\) 498.000 + 862.561i 0.670670 + 1.16163i
\(83\) 932.000 1.23253 0.616267 0.787537i \(-0.288644\pi\)
0.616267 + 0.787537i \(0.288644\pi\)
\(84\) 0 0
\(85\) 413.000 0.527013
\(86\) −260.000 450.333i −0.326006 0.564659i
\(87\) 0 0
\(88\) 140.000 242.487i 0.169591 0.293741i
\(89\) 436.500 + 756.040i 0.519875 + 0.900451i 0.999733 + 0.0231042i \(0.00735495\pi\)
−0.479858 + 0.877346i \(0.659312\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 28.0000 0.0317305
\(93\) 0 0
\(94\) 171.000 296.181i 0.187631 0.324986i
\(95\) 479.500 830.518i 0.517849 0.896941i
\(96\) 0 0
\(97\) 290.000 0.303557 0.151779 0.988415i \(-0.451500\pi\)
0.151779 + 0.988415i \(0.451500\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 152.000 + 263.272i 0.152000 + 0.263272i
\(101\) 542.500 939.638i 0.534463 0.925717i −0.464726 0.885454i \(-0.653847\pi\)
0.999189 0.0402627i \(-0.0128195\pi\)
\(102\) 0 0
\(103\) 776.500 + 1344.94i 0.742823 + 1.28661i 0.951205 + 0.308560i \(0.0998472\pi\)
−0.208381 + 0.978048i \(0.566819\pi\)
\(104\) −528.000 −0.497833
\(105\) 0 0
\(106\) 834.000 0.764200
\(107\) 64.5000 + 111.717i 0.0582752 + 0.100936i 0.893691 0.448682i \(-0.148107\pi\)
−0.835416 + 0.549618i \(0.814773\pi\)
\(108\) 0 0
\(109\) 482.500 835.715i 0.423992 0.734376i −0.572334 0.820021i \(-0.693962\pi\)
0.996326 + 0.0856452i \(0.0272952\pi\)
\(110\) 245.000 + 424.352i 0.212362 + 0.367822i
\(111\) 0 0
\(112\) 0 0
\(113\) 50.0000 0.0416248 0.0208124 0.999783i \(-0.493375\pi\)
0.0208124 + 0.999783i \(0.493375\pi\)
\(114\) 0 0
\(115\) −24.5000 + 42.4352i −0.0198664 + 0.0344096i
\(116\) 212.000 367.195i 0.169687 0.293907i
\(117\) 0 0
\(118\) −34.0000 −0.0265250
\(119\) 0 0
\(120\) 0 0
\(121\) 53.0000 + 91.7987i 0.0398197 + 0.0689697i
\(122\) 51.0000 88.3346i 0.0378469 0.0655528i
\(123\) 0 0
\(124\) 150.000 + 259.808i 0.108632 + 0.188157i
\(125\) −1407.00 −1.00677
\(126\) 0 0
\(127\) 936.000 0.653989 0.326994 0.945026i \(-0.393964\pi\)
0.326994 + 0.945026i \(0.393964\pi\)
\(128\) −64.0000 110.851i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 462.000 800.207i 0.311693 0.539868i
\(131\) 377.500 + 653.849i 0.251773 + 0.436084i 0.964014 0.265851i \(-0.0856529\pi\)
−0.712241 + 0.701935i \(0.752320\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 878.000 0.566027
\(135\) 0 0
\(136\) −236.000 + 408.764i −0.148800 + 0.257730i
\(137\) −1178.50 + 2041.22i −0.734935 + 1.27294i 0.219817 + 0.975541i \(0.429454\pi\)
−0.954752 + 0.297403i \(0.903879\pi\)
\(138\) 0 0
\(139\) −28.0000 −0.0170858 −0.00854291 0.999964i \(-0.502719\pi\)
−0.00854291 + 0.999964i \(0.502719\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −784.000 1357.93i −0.463323 0.802498i
\(143\) −1155.00 + 2000.52i −0.675426 + 1.16987i
\(144\) 0 0
\(145\) 371.000 + 642.591i 0.212482 + 0.368029i
\(146\) −590.000 −0.334443
\(147\) 0 0
\(148\) 44.0000 0.0244377
\(149\) 1147.50 + 1987.53i 0.630919 + 1.09278i 0.987364 + 0.158467i \(0.0506551\pi\)
−0.356446 + 0.934316i \(0.616012\pi\)
\(150\) 0 0
\(151\) 554.500 960.422i 0.298838 0.517603i −0.677032 0.735953i \(-0.736734\pi\)
0.975870 + 0.218350i \(0.0700676\pi\)
\(152\) 548.000 + 949.164i 0.292425 + 0.506496i
\(153\) 0 0
\(154\) 0 0
\(155\) −525.000 −0.272058
\(156\) 0 0
\(157\) 779.500 1350.13i 0.396248 0.686321i −0.597012 0.802232i \(-0.703646\pi\)
0.993260 + 0.115911i \(0.0369789\pi\)
\(158\) 495.000 857.365i 0.249241 0.431698i
\(159\) 0 0
\(160\) 224.000 0.110680
\(161\) 0 0
\(162\) 0 0
\(163\) 1125.50 + 1949.42i 0.540834 + 0.936752i 0.998856 + 0.0478115i \(0.0152247\pi\)
−0.458022 + 0.888941i \(0.651442\pi\)
\(164\) 996.000 1725.12i 0.474235 0.821399i
\(165\) 0 0
\(166\) −932.000 1614.27i −0.435766 0.754770i
\(167\) 2788.00 1.29187 0.645934 0.763393i \(-0.276468\pi\)
0.645934 + 0.763393i \(0.276468\pi\)
\(168\) 0 0
\(169\) 2159.00 0.982704
\(170\) −413.000 715.337i −0.186327 0.322728i
\(171\) 0 0
\(172\) −520.000 + 900.666i −0.230521 + 0.399274i
\(173\) −789.500 1367.45i −0.346963 0.600957i 0.638746 0.769418i \(-0.279454\pi\)
−0.985708 + 0.168461i \(0.946120\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −560.000 −0.239839
\(177\) 0 0
\(178\) 873.000 1512.08i 0.367607 0.636715i
\(179\) 1225.50 2122.63i 0.511722 0.886328i −0.488186 0.872740i \(-0.662341\pi\)
0.999908 0.0135883i \(-0.00432541\pi\)
\(180\) 0 0
\(181\) 1170.00 0.480472 0.240236 0.970715i \(-0.422775\pi\)
0.240236 + 0.970715i \(0.422775\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −28.0000 48.4974i −0.0112184 0.0194309i
\(185\) −38.5000 + 66.6840i −0.0153004 + 0.0265011i
\(186\) 0 0
\(187\) 1032.50 + 1788.34i 0.403764 + 0.699340i
\(188\) −684.000 −0.265350
\(189\) 0 0
\(190\) −1918.00 −0.732349
\(191\) −637.500 1104.18i −0.241507 0.418303i 0.719637 0.694351i \(-0.244308\pi\)
−0.961144 + 0.276048i \(0.910975\pi\)
\(192\) 0 0
\(193\) −17.5000 + 30.3109i −0.00652683 + 0.0113048i −0.869270 0.494337i \(-0.835411\pi\)
0.862744 + 0.505642i \(0.168744\pi\)
\(194\) −290.000 502.295i −0.107324 0.185890i
\(195\) 0 0
\(196\) 0 0
\(197\) 2734.00 0.988779 0.494389 0.869241i \(-0.335392\pi\)
0.494389 + 0.869241i \(0.335392\pi\)
\(198\) 0 0
\(199\) 1121.50 1942.49i 0.399503 0.691959i −0.594162 0.804345i \(-0.702516\pi\)
0.993665 + 0.112387i \(0.0358495\pi\)
\(200\) 304.000 526.543i 0.107480 0.186161i
\(201\) 0 0
\(202\) −2170.00 −0.755845
\(203\) 0 0
\(204\) 0 0
\(205\) 1743.00 + 3018.96i 0.593836 + 1.02855i
\(206\) 1553.00 2689.87i 0.525256 0.909769i
\(207\) 0 0
\(208\) 528.000 + 914.523i 0.176011 + 0.304859i
\(209\) 4795.00 1.58697
\(210\) 0 0
\(211\) 1172.00 0.382388 0.191194 0.981552i \(-0.438764\pi\)
0.191194 + 0.981552i \(0.438764\pi\)
\(212\) −834.000 1444.53i −0.270186 0.467975i
\(213\) 0 0
\(214\) 129.000 223.435i 0.0412068 0.0713723i
\(215\) −910.000 1576.17i −0.288658 0.499970i
\(216\) 0 0
\(217\) 0 0
\(218\) −1930.00 −0.599615
\(219\) 0 0
\(220\) 490.000 848.705i 0.150163 0.260089i
\(221\) 1947.00 3372.30i 0.592622 1.02645i
\(222\) 0 0
\(223\) −2024.00 −0.607790 −0.303895 0.952706i \(-0.598287\pi\)
−0.303895 + 0.952706i \(0.598287\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −50.0000 86.6025i −0.0147166 0.0254899i
\(227\) −1285.50 + 2226.55i −0.375866 + 0.651019i −0.990456 0.137827i \(-0.955988\pi\)
0.614590 + 0.788847i \(0.289321\pi\)
\(228\) 0 0
\(229\) 447.500 + 775.093i 0.129134 + 0.223666i 0.923341 0.383980i \(-0.125447\pi\)
−0.794207 + 0.607647i \(0.792114\pi\)
\(230\) 98.0000 0.0280953
\(231\) 0 0
\(232\) −848.000 −0.239974
\(233\) 893.500 + 1547.59i 0.251224 + 0.435132i 0.963863 0.266398i \(-0.0858337\pi\)
−0.712639 + 0.701531i \(0.752500\pi\)
\(234\) 0 0
\(235\) 598.500 1036.63i 0.166135 0.287755i
\(236\) 34.0000 + 58.8897i 0.00937801 + 0.0162432i
\(237\) 0 0
\(238\) 0 0
\(239\) 5100.00 1.38030 0.690150 0.723667i \(-0.257545\pi\)
0.690150 + 0.723667i \(0.257545\pi\)
\(240\) 0 0
\(241\) −2088.50 + 3617.39i −0.558225 + 0.966873i 0.439420 + 0.898282i \(0.355184\pi\)
−0.997645 + 0.0685917i \(0.978149\pi\)
\(242\) 106.000 183.597i 0.0281568 0.0487690i
\(243\) 0 0
\(244\) −204.000 −0.0535236
\(245\) 0 0
\(246\) 0 0
\(247\) −4521.00 7830.60i −1.16463 2.01720i
\(248\) 300.000 519.615i 0.0768146 0.133047i
\(249\) 0 0
\(250\) 1407.00 + 2437.00i 0.355946 + 0.616517i
\(251\) −4680.00 −1.17689 −0.588444 0.808538i \(-0.700259\pi\)
−0.588444 + 0.808538i \(0.700259\pi\)
\(252\) 0 0
\(253\) −245.000 −0.0608815
\(254\) −936.000 1621.20i −0.231220 0.400485i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 874.500 + 1514.68i 0.212256 + 0.367638i 0.952420 0.304788i \(-0.0985856\pi\)
−0.740164 + 0.672426i \(0.765252\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −1848.00 −0.440800
\(261\) 0 0
\(262\) 755.000 1307.70i 0.178031 0.308358i
\(263\) −2236.50 + 3873.73i −0.524367 + 0.908230i 0.475231 + 0.879861i \(0.342365\pi\)
−0.999598 + 0.0283689i \(0.990969\pi\)
\(264\) 0 0
\(265\) 2919.00 0.676652
\(266\) 0 0
\(267\) 0 0
\(268\) −878.000 1520.74i −0.200121 0.346619i
\(269\) −987.500 + 1710.40i −0.223825 + 0.387676i −0.955966 0.293476i \(-0.905188\pi\)
0.732141 + 0.681153i \(0.238521\pi\)
\(270\) 0 0
\(271\) −4219.50 7308.39i −0.945817 1.63820i −0.754107 0.656751i \(-0.771930\pi\)
−0.191710 0.981452i \(-0.561403\pi\)
\(272\) 944.000 0.210435
\(273\) 0 0
\(274\) 4714.00 1.03935
\(275\) −1330.00 2303.63i −0.291644 0.505142i
\(276\) 0 0
\(277\) −263.500 + 456.395i −0.0571559 + 0.0989969i −0.893188 0.449684i \(-0.851537\pi\)
0.836032 + 0.548681i \(0.184870\pi\)
\(278\) 28.0000 + 48.4974i 0.00604075 + 0.0104629i
\(279\) 0 0
\(280\) 0 0
\(281\) 202.000 0.0428837 0.0214418 0.999770i \(-0.493174\pi\)
0.0214418 + 0.999770i \(0.493174\pi\)
\(282\) 0 0
\(283\) −3974.50 + 6884.04i −0.834839 + 1.44598i 0.0593220 + 0.998239i \(0.481106\pi\)
−0.894161 + 0.447745i \(0.852227\pi\)
\(284\) −1568.00 + 2715.86i −0.327619 + 0.567452i
\(285\) 0 0
\(286\) 4620.00 0.955197
\(287\) 0 0
\(288\) 0 0
\(289\) 716.000 + 1240.15i 0.145736 + 0.252422i
\(290\) 742.000 1285.18i 0.150247 0.260236i
\(291\) 0 0
\(292\) 590.000 + 1021.91i 0.118244 + 0.204804i
\(293\) 318.000 0.0634053 0.0317027 0.999497i \(-0.489907\pi\)
0.0317027 + 0.999497i \(0.489907\pi\)
\(294\) 0 0
\(295\) −119.000 −0.0234863
\(296\) −44.0000 76.2102i −0.00864003 0.0149650i
\(297\) 0 0
\(298\) 2295.00 3975.06i 0.446127 0.772714i
\(299\) 231.000 + 400.104i 0.0446792 + 0.0773866i
\(300\) 0 0
\(301\) 0 0
\(302\) −2218.00 −0.422621
\(303\) 0 0
\(304\) 1096.00 1898.33i 0.206776 0.358147i
\(305\) 178.500 309.171i 0.0335111 0.0580429i
\(306\) 0 0
\(307\) 8132.00 1.51178 0.755892 0.654696i \(-0.227203\pi\)
0.755892 + 0.654696i \(0.227203\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 525.000 + 909.327i 0.0961871 + 0.166601i
\(311\) 464.500 804.538i 0.0846925 0.146692i −0.820568 0.571549i \(-0.806343\pi\)
0.905260 + 0.424858i \(0.139676\pi\)
\(312\) 0 0
\(313\) −104.500 180.999i −0.0188712 0.0326859i 0.856436 0.516254i \(-0.172674\pi\)
−0.875307 + 0.483568i \(0.839341\pi\)
\(314\) −3118.00 −0.560379
\(315\) 0 0
\(316\) −1980.00 −0.352480
\(317\) 3565.50 + 6175.63i 0.631730 + 1.09419i 0.987198 + 0.159500i \(0.0509882\pi\)
−0.355468 + 0.934689i \(0.615678\pi\)
\(318\) 0 0
\(319\) −1855.00 + 3212.95i −0.325580 + 0.563921i
\(320\) −224.000 387.979i −0.0391312 0.0677772i
\(321\) 0 0
\(322\) 0 0
\(323\) −8083.00 −1.39242
\(324\) 0 0
\(325\) −2508.00 + 4343.98i −0.428058 + 0.741418i
\(326\) 2251.00 3898.85i 0.382427 0.662384i
\(327\) 0 0
\(328\) −3984.00 −0.670670
\(329\) 0 0
\(330\) 0 0
\(331\) 3285.50 + 5690.65i 0.545581 + 0.944975i 0.998570 + 0.0534583i \(0.0170244\pi\)
−0.452989 + 0.891516i \(0.649642\pi\)
\(332\) −1864.00 + 3228.54i −0.308133 + 0.533703i
\(333\) 0 0
\(334\) −2788.00 4828.96i −0.456744 0.791104i
\(335\) 3073.00 0.501182
\(336\) 0 0
\(337\) −11466.0 −1.85339 −0.926696 0.375813i \(-0.877364\pi\)
−0.926696 + 0.375813i \(0.877364\pi\)
\(338\) −2159.00 3739.50i −0.347438 0.601781i
\(339\) 0 0
\(340\) −826.000 + 1430.67i −0.131753 + 0.228203i
\(341\) −1312.50 2273.32i −0.208434 0.361018i
\(342\) 0 0
\(343\) 0 0
\(344\) 2080.00 0.326006
\(345\) 0 0
\(346\) −1579.00 + 2734.91i −0.245340 + 0.424941i
\(347\) −4888.50 + 8467.13i −0.756278 + 1.30991i 0.188459 + 0.982081i \(0.439651\pi\)
−0.944737 + 0.327831i \(0.893682\pi\)
\(348\) 0 0
\(349\) −11914.0 −1.82734 −0.913670 0.406456i \(-0.866764\pi\)
−0.913670 + 0.406456i \(0.866764\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 560.000 + 969.948i 0.0847957 + 0.146871i
\(353\) −4561.50 + 7900.75i −0.687774 + 1.19126i 0.284783 + 0.958592i \(0.408079\pi\)
−0.972556 + 0.232667i \(0.925255\pi\)
\(354\) 0 0
\(355\) −2744.00 4752.75i −0.410243 0.710562i
\(356\) −3492.00 −0.519875
\(357\) 0 0
\(358\) −4902.00 −0.723684
\(359\) 4074.50 + 7057.24i 0.599008 + 1.03751i 0.992968 + 0.118385i \(0.0377716\pi\)
−0.393960 + 0.919128i \(0.628895\pi\)
\(360\) 0 0
\(361\) −5955.00 + 10314.4i −0.868202 + 1.50377i
\(362\) −1170.00 2026.50i −0.169872 0.294228i
\(363\) 0 0
\(364\) 0 0
\(365\) −2065.00 −0.296129
\(366\) 0 0
\(367\) 4835.50 8375.33i 0.687769 1.19125i −0.284790 0.958590i \(-0.591924\pi\)
0.972558 0.232660i \(-0.0747429\pi\)
\(368\) −56.0000 + 96.9948i −0.00793261 + 0.0137397i
\(369\) 0 0
\(370\) 154.000 0.0216381
\(371\) 0 0
\(372\) 0 0
\(373\) 2054.50 + 3558.50i 0.285196 + 0.493973i 0.972657 0.232248i \(-0.0746081\pi\)
−0.687461 + 0.726221i \(0.741275\pi\)
\(374\) 2065.00 3576.68i 0.285504 0.494508i
\(375\) 0 0
\(376\) 684.000 + 1184.72i 0.0938154 + 0.162493i
\(377\) 6996.00 0.955736
\(378\) 0 0
\(379\) −3488.00 −0.472735 −0.236367 0.971664i \(-0.575957\pi\)
−0.236367 + 0.971664i \(0.575957\pi\)
\(380\) 1918.00 + 3322.07i 0.258925 + 0.448470i
\(381\) 0 0
\(382\) −1275.00 + 2208.36i −0.170771 + 0.295785i
\(383\) −4358.50 7549.14i −0.581485 1.00716i −0.995304 0.0968028i \(-0.969138\pi\)
0.413818 0.910360i \(-0.364195\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 70.0000 0.00923033
\(387\) 0 0
\(388\) −580.000 + 1004.59i −0.0758893 + 0.131444i
\(389\) 81.5000 141.162i 0.0106227 0.0183990i −0.860665 0.509171i \(-0.829952\pi\)
0.871288 + 0.490772i \(0.163285\pi\)
\(390\) 0 0
\(391\) 413.000 0.0534177
\(392\) 0 0
\(393\) 0 0
\(394\) −2734.00 4735.43i −0.349586 0.605501i
\(395\) 1732.50 3000.78i 0.220687 0.382242i
\(396\) 0 0
\(397\) 499.500 + 865.159i 0.0631466 + 0.109373i 0.895870 0.444316i \(-0.146553\pi\)
−0.832724 + 0.553689i \(0.813220\pi\)
\(398\) −4486.00 −0.564982
\(399\) 0 0
\(400\) −1216.00 −0.152000
\(401\) −7378.50 12779.9i −0.918865 1.59152i −0.801143 0.598474i \(-0.795774\pi\)
−0.117722 0.993047i \(-0.537559\pi\)
\(402\) 0 0
\(403\) −2475.00 + 4286.83i −0.305927 + 0.529881i
\(404\) 2170.00 + 3758.55i 0.267232 + 0.462859i
\(405\) 0 0
\(406\) 0 0
\(407\) −385.000 −0.0468888
\(408\) 0 0
\(409\) −66.5000 + 115.181i −0.00803964 + 0.0139251i −0.870017 0.493021i \(-0.835892\pi\)
0.861978 + 0.506946i \(0.169226\pi\)
\(410\) 3486.00 6037.93i 0.419906 0.727298i
\(411\) 0 0
\(412\) −6212.00 −0.742823
\(413\) 0 0
\(414\) 0 0
\(415\) −3262.00 5649.95i −0.385844 0.668302i
\(416\) 1056.00 1829.05i 0.124458 0.215568i
\(417\) 0 0
\(418\) −4795.00 8305.18i −0.561079 0.971818i
\(419\) −6420.00 −0.748538 −0.374269 0.927320i \(-0.622106\pi\)
−0.374269 + 0.927320i \(0.622106\pi\)
\(420\) 0 0
\(421\) 10266.0 1.18844 0.594221 0.804302i \(-0.297460\pi\)
0.594221 + 0.804302i \(0.297460\pi\)
\(422\) −1172.00 2029.96i −0.135194 0.234164i
\(423\) 0 0
\(424\) −1668.00 + 2889.06i −0.191050 + 0.330908i
\(425\) 2242.00 + 3883.26i 0.255889 + 0.443213i
\(426\) 0 0
\(427\) 0 0
\(428\) −516.000 −0.0582752
\(429\) 0 0
\(430\) −1820.00 + 3152.33i −0.204112 + 0.353532i
\(431\) −7606.50 + 13174.8i −0.850098 + 1.47241i 0.0310213 + 0.999519i \(0.490124\pi\)
−0.881119 + 0.472894i \(0.843209\pi\)
\(432\) 0 0
\(433\) 1378.00 0.152939 0.0764693 0.997072i \(-0.475635\pi\)
0.0764693 + 0.997072i \(0.475635\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1930.00 + 3342.86i 0.211996 + 0.367188i
\(437\) 479.500 830.518i 0.0524888 0.0909132i
\(438\) 0 0
\(439\) −1381.50 2392.83i −0.150195 0.260145i 0.781104 0.624401i \(-0.214657\pi\)
−0.931299 + 0.364256i \(0.881323\pi\)
\(440\) −1960.00 −0.212362
\(441\) 0 0
\(442\) −7788.00 −0.838094
\(443\) 2924.50 + 5065.38i 0.313651 + 0.543259i 0.979150 0.203140i \(-0.0651146\pi\)
−0.665499 + 0.746399i \(0.731781\pi\)
\(444\) 0 0
\(445\) 3055.50 5292.28i 0.325493 0.563771i
\(446\) 2024.00 + 3505.67i 0.214886 + 0.372194i
\(447\) 0 0
\(448\) 0 0
\(449\) −4582.00 −0.481599 −0.240799 0.970575i \(-0.577410\pi\)
−0.240799 + 0.970575i \(0.577410\pi\)
\(450\) 0 0
\(451\) −8715.00 + 15094.8i −0.909919 + 1.57603i
\(452\) −100.000 + 173.205i −0.0104062 + 0.0180241i
\(453\) 0 0
\(454\) 5142.00 0.531555
\(455\) 0 0
\(456\) 0 0
\(457\) −5775.50 10003.5i −0.591174 1.02394i −0.994075 0.108700i \(-0.965331\pi\)
0.402901 0.915244i \(-0.368002\pi\)
\(458\) 895.000 1550.19i 0.0913114 0.158156i
\(459\) 0 0
\(460\) −98.0000 169.741i −0.00993320 0.0172048i
\(461\) −9494.00 −0.959175 −0.479587 0.877494i \(-0.659214\pi\)
−0.479587 + 0.877494i \(0.659214\pi\)
\(462\) 0 0
\(463\) −10160.0 −1.01982 −0.509908 0.860229i \(-0.670321\pi\)
−0.509908 + 0.860229i \(0.670321\pi\)
\(464\) 848.000 + 1468.78i 0.0848436 + 0.146953i
\(465\) 0 0
\(466\) 1787.00 3095.17i 0.177642 0.307685i
\(467\) 653.500 + 1131.90i 0.0647545 + 0.112158i 0.896585 0.442872i \(-0.146040\pi\)
−0.831831 + 0.555030i \(0.812707\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −2394.00 −0.234951
\(471\) 0 0
\(472\) 68.0000 117.779i 0.00663126 0.0114857i
\(473\) 4550.00 7880.83i 0.442303 0.766091i
\(474\) 0 0
\(475\) 10412.0 1.00576
\(476\) 0 0
\(477\) 0 0
\(478\) −5100.00 8833.46i −0.488010 0.845257i
\(479\) −9143.50 + 15837.0i −0.872186 + 1.51067i −0.0124559 + 0.999922i \(0.503965\pi\)
−0.859730 + 0.510748i \(0.829368\pi\)
\(480\) 0 0
\(481\) 363.000 + 628.734i 0.0344103 + 0.0596005i
\(482\) 8354.00 0.789449
\(483\) 0 0
\(484\) −424.000 −0.0398197
\(485\) −1015.00 1758.03i −0.0950284 0.164594i
\(486\) 0 0
\(487\) 7476.50 12949.7i 0.695673 1.20494i −0.274281 0.961650i \(-0.588440\pi\)
0.969953 0.243291i \(-0.0782269\pi\)
\(488\) 204.000 + 353.338i 0.0189235 + 0.0327764i
\(489\) 0 0
\(490\) 0 0
\(491\) −14352.0 −1.31914 −0.659569 0.751644i \(-0.729261\pi\)
−0.659569 + 0.751644i \(0.729261\pi\)
\(492\) 0 0
\(493\) 3127.00 5416.12i 0.285665 0.494787i
\(494\) −9042.00 + 15661.2i −0.823520 + 1.42638i
\(495\) 0 0
\(496\) −1200.00 −0.108632
\(497\) 0 0
\(498\) 0 0
\(499\) 2765.50 + 4789.99i 0.248098 + 0.429718i 0.962998 0.269509i \(-0.0868612\pi\)
−0.714900 + 0.699226i \(0.753528\pi\)
\(500\) 2814.00 4873.99i 0.251692 0.435943i
\(501\) 0 0
\(502\) 4680.00 + 8106.00i 0.416093 + 0.720694i
\(503\) 8400.00 0.744607 0.372304 0.928111i \(-0.378568\pi\)
0.372304 + 0.928111i \(0.378568\pi\)
\(504\) 0 0
\(505\) −7595.00 −0.669254
\(506\) 245.000 + 424.352i 0.0215249 + 0.0372821i
\(507\) 0 0
\(508\) −1872.00 + 3242.40i −0.163497 + 0.283185i
\(509\) 1192.50 + 2065.47i 0.103844 + 0.179863i 0.913265 0.407365i \(-0.133552\pi\)
−0.809421 + 0.587228i \(0.800219\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) 1749.00 3029.36i 0.150088 0.259960i
\(515\) 5435.50 9414.56i 0.465081 0.805544i
\(516\) 0 0
\(517\) 5985.00 0.509130
\(518\) 0 0
\(519\) 0 0
\(520\) 1848.00 + 3200.83i 0.155846 + 0.269934i
\(521\) 4576.50 7926.73i 0.384837 0.666557i −0.606910 0.794771i \(-0.707591\pi\)
0.991747 + 0.128214i \(0.0409243\pi\)
\(522\) 0 0
\(523\) −6903.50 11957.2i −0.577187 0.999718i −0.995800 0.0915530i \(-0.970817\pi\)
0.418613 0.908165i \(-0.362516\pi\)
\(524\) −3020.00 −0.251773
\(525\) 0 0
\(526\) 8946.00 0.741567
\(527\) 2212.50 + 3832.16i 0.182880 + 0.316758i
\(528\) 0 0
\(529\) 6059.00 10494.5i 0.497986 0.862538i
\(530\) −2919.00 5055.86i −0.239233 0.414363i
\(531\) 0 0
\(532\) 0 0
\(533\) 32868.0 2.67105
\(534\) 0 0
\(535\) 451.500 782.021i 0.0364861 0.0631957i
\(536\) −1756.00 + 3041.48i −0.141507 + 0.245097i
\(537\) 0 0
\(538\) 3950.00 0.316536
\(539\) 0 0
\(540\) 0 0
\(541\) −4087.50 7079.76i −0.324834 0.562629i 0.656645 0.754200i \(-0.271975\pi\)
−0.981479 + 0.191571i \(0.938642\pi\)
\(542\) −8439.00 + 14616.8i −0.668794 + 1.15838i
\(543\) 0 0
\(544\) −944.000 1635.06i −0.0744001 0.128865i
\(545\) −6755.00 −0.530922
\(546\) 0 0
\(547\) 4656.00 0.363942 0.181971 0.983304i \(-0.441752\pi\)
0.181971 + 0.983304i \(0.441752\pi\)
\(548\) −4714.00 8164.89i −0.367467 0.636472i
\(549\) 0 0
\(550\) −2660.00 + 4607.26i −0.206223 + 0.357189i
\(551\) −7261.00 12576.4i −0.561396 0.972366i
\(552\) 0 0
\(553\) 0 0
\(554\) 1054.00 0.0808306
\(555\) 0 0
\(556\) 56.0000 96.9948i 0.00427146 0.00739838i
\(557\) 3501.50 6064.78i 0.266361 0.461352i −0.701558 0.712612i \(-0.747512\pi\)
0.967919 + 0.251261i \(0.0808452\pi\)
\(558\) 0 0
\(559\) −17160.0 −1.29837
\(560\) 0 0
\(561\) 0 0
\(562\) −202.000 349.874i −0.0151617 0.0262608i
\(563\) 9876.50 17106.6i 0.739334 1.28056i −0.213462 0.976951i \(-0.568474\pi\)
0.952796 0.303612i \(-0.0981927\pi\)
\(564\) 0 0
\(565\) −175.000 303.109i −0.0130306 0.0225697i
\(566\) 15898.0 1.18064
\(567\) 0 0
\(568\) 6272.00 0.463323
\(569\) −3448.50 5972.98i −0.254075 0.440071i 0.710569 0.703628i \(-0.248438\pi\)
−0.964644 + 0.263557i \(0.915104\pi\)
\(570\) 0 0
\(571\) −12457.5 + 21577.0i −0.913013 + 1.58138i −0.103227 + 0.994658i \(0.532917\pi\)
−0.809785 + 0.586726i \(0.800416\pi\)
\(572\) −4620.00 8002.07i −0.337713 0.584936i
\(573\) 0 0
\(574\) 0 0
\(575\) −532.000 −0.0385842
\(576\) 0 0
\(577\) 63.5000 109.985i 0.00458152 0.00793543i −0.863726 0.503962i \(-0.831875\pi\)
0.868307 + 0.496027i \(0.165208\pi\)
\(578\) 1432.00 2480.30i 0.103051 0.178489i
\(579\) 0 0
\(580\) −2968.00 −0.212482
\(581\) 0 0
\(582\) 0 0
\(583\) 7297.50 + 12639.6i 0.518407 + 0.897908i
\(584\) 1180.00 2043.82i 0.0836109 0.144818i
\(585\) 0 0
\(586\) −318.000 550.792i −0.0224172 0.0388277i
\(587\) 9044.00 0.635921 0.317961 0.948104i \(-0.397002\pi\)
0.317961 + 0.948104i \(0.397002\pi\)
\(588\) 0 0
\(589\) 10275.0 0.718801
\(590\) 119.000 + 206.114i 0.00830365 + 0.0143823i
\(591\) 0 0
\(592\) −88.0000 + 152.420i −0.00610942 + 0.0105818i
\(593\) 5350.50 + 9267.34i 0.370521 + 0.641760i 0.989646 0.143532i \(-0.0458460\pi\)
−0.619125 + 0.785292i \(0.712513\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −9180.00 −0.630919
\(597\) 0 0
\(598\) 462.000 800.207i 0.0315930 0.0547206i
\(599\) 10399.5 18012.5i 0.709369 1.22866i −0.255722 0.966750i \(-0.582313\pi\)
0.965091 0.261913i \(-0.0843533\pi\)
\(600\) 0 0
\(601\) 1402.00 0.0951560 0.0475780 0.998868i \(-0.484850\pi\)
0.0475780 + 0.998868i \(0.484850\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 2218.00 + 3841.69i 0.149419 + 0.258801i
\(605\) 371.000 642.591i 0.0249311 0.0431819i
\(606\) 0 0
\(607\) 3262.50 + 5650.82i 0.218156 + 0.377858i 0.954244 0.299028i \(-0.0966625\pi\)
−0.736088 + 0.676886i \(0.763329\pi\)
\(608\) −4384.00 −0.292425
\(609\) 0 0
\(610\) −714.000 −0.0473918
\(611\) −5643.00 9773.96i −0.373636 0.647156i
\(612\) 0 0
\(613\) −7525.50 + 13034.5i −0.495844 + 0.858826i −0.999989 0.00479285i \(-0.998474\pi\)
0.504145 + 0.863619i \(0.331808\pi\)
\(614\) −8132.00 14085.0i −0.534496 0.925775i
\(615\) 0 0
\(616\) 0 0
\(617\) −11150.0 −0.727524 −0.363762 0.931492i \(-0.618508\pi\)
−0.363762 + 0.931492i \(0.618508\pi\)
\(618\) 0 0
\(619\) 1707.50 2957.48i 0.110873 0.192037i −0.805250 0.592936i \(-0.797969\pi\)
0.916122 + 0.400899i \(0.131302\pi\)
\(620\) 1050.00 1818.65i 0.0680145 0.117805i
\(621\) 0 0
\(622\) −1858.00 −0.119773
\(623\) 0 0
\(624\) 0 0
\(625\) 174.500 + 302.243i 0.0111680 + 0.0193435i
\(626\) −209.000 + 361.999i −0.0133440 + 0.0231124i
\(627\) 0 0
\(628\) 3118.00 + 5400.53i 0.198124 + 0.343160i
\(629\) 649.000 0.0411404
\(630\) 0 0
\(631\) −21184.0 −1.33648 −0.668242 0.743944i \(-0.732953\pi\)
−0.668242 + 0.743944i \(0.732953\pi\)
\(632\) 1980.00 + 3429.46i 0.124621 + 0.215849i
\(633\) 0 0
\(634\) 7131.00 12351.3i 0.446701 0.773708i
\(635\) −3276.00 5674.20i −0.204731 0.354604i
\(636\) 0 0
\(637\) 0 0
\(638\) 7420.00 0.460440
\(639\) 0 0
\(640\) −448.000 + 775.959i −0.0276699 + 0.0479257i
\(641\) −5352.50 + 9270.80i −0.329814 + 0.571255i −0.982475 0.186395i \(-0.940320\pi\)
0.652660 + 0.757651i \(0.273653\pi\)
\(642\) 0 0
\(643\) −6860.00 −0.420734 −0.210367 0.977622i \(-0.567466\pi\)
−0.210367 + 0.977622i \(0.567466\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 8083.00 + 14000.2i 0.492293 + 0.852677i
\(647\) −7231.50 + 12525.3i −0.439412 + 0.761084i −0.997644 0.0686008i \(-0.978147\pi\)
0.558232 + 0.829685i \(0.311480\pi\)
\(648\) 0 0
\(649\) −297.500 515.285i −0.0179937 0.0311660i
\(650\) 10032.0 0.605365
\(651\) 0 0
\(652\) −9004.00 −0.540834
\(653\) 2989.50 + 5177.97i 0.179155 + 0.310305i 0.941591 0.336758i \(-0.109330\pi\)
−0.762436 + 0.647063i \(0.775997\pi\)
\(654\) 0 0
\(655\) 2642.50 4576.94i 0.157635 0.273032i
\(656\) 3984.00 + 6900.49i 0.237117 + 0.410700i
\(657\) 0 0
\(658\) 0 0
\(659\) 6940.00 0.410234 0.205117 0.978737i \(-0.434243\pi\)
0.205117 + 0.978737i \(0.434243\pi\)
\(660\) 0 0
\(661\) 6699.50 11603.9i 0.394221 0.682812i −0.598780 0.800914i \(-0.704348\pi\)
0.993001 + 0.118102i \(0.0376810\pi\)
\(662\) 6571.00 11381.3i 0.385784 0.668198i
\(663\) 0 0
\(664\) 7456.00 0.435766
\(665\) 0 0
\(666\) 0 0
\(667\) 371.000 + 642.591i 0.0215370 + 0.0373032i
\(668\) −5576.00 + 9657.92i −0.322967 + 0.559395i
\(669\) 0 0
\(670\) −3073.00 5322.59i −0.177195 0.306910i
\(671\) 1785.00 0.102696
\(672\) 0 0
\(673\) 29510.0 1.69023 0.845117 0.534582i \(-0.179531\pi\)
0.845117 + 0.534582i \(0.179531\pi\)
\(674\) 11466.0 + 19859.7i 0.655273 + 1.13497i
\(675\) 0 0
\(676\) −4318.00 + 7479.00i −0.245676 + 0.425523i
\(677\) 13000.5 + 22517.5i 0.738035 + 1.27831i 0.953379 + 0.301776i \(0.0975795\pi\)
−0.215344 + 0.976538i \(0.569087\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 3304.00 0.186327
\(681\) 0 0
\(682\) −2625.00 + 4546.63i −0.147385 + 0.255278i
\(683\) −4402.50 + 7625.35i −0.246643 + 0.427198i −0.962592 0.270954i \(-0.912661\pi\)
0.715949 + 0.698152i \(0.245994\pi\)
\(684\) 0 0
\(685\) 16499.0 0.920284
\(686\) 0 0
\(687\) 0 0
\(688\) −2080.00 3602.67i −0.115261 0.199637i
\(689\) 13761.0 23834.8i 0.760889 1.31790i
\(690\) 0 0
\(691\) 14342.5 + 24841.9i 0.789601 + 1.36763i 0.926211 + 0.377004i \(0.123046\pi\)
−0.136610 + 0.990625i \(0.543621\pi\)
\(692\) 6316.00 0.346963
\(693\) 0 0
\(694\) 19554.0 1.06954
\(695\) 98.0000 + 169.741i 0.00534871 + 0.00926423i
\(696\) 0 0
\(697\) 14691.0 25445.6i 0.798366 1.38281i
\(698\) 11914.0 + 20635.7i 0.646062 + 1.11901i
\(699\) 0 0
\(700\) 0 0
\(701\) 3146.00 0.169505 0.0847523 0.996402i \(-0.472990\pi\)
0.0847523 + 0.996402i \(0.472990\pi\)
\(702\) 0 0
\(703\) 753.500 1305.10i 0.0404250 0.0700182i
\(704\) 1120.00 1939.90i 0.0599596 0.103853i
\(705\) 0 0
\(706\) 18246.0 0.972659
\(707\) 0 0
\(708\) 0 0
\(709\) −629.500 1090.33i −0.0333447 0.0577547i 0.848871 0.528599i \(-0.177283\pi\)
−0.882216 + 0.470845i \(0.843949\pi\)
\(710\) −5488.00 + 9505.49i −0.290086 + 0.502443i
\(711\) 0 0
\(712\) 3492.00 + 6048.32i 0.183804 + 0.318357i
\(713\) −525.000 −0.0275756
\(714\) 0 0
\(715\) 16170.0 0.845767
\(716\) 4902.00 + 8490.51i 0.255861 + 0.443164i
\(717\) 0 0
\(718\) 8149.00 14114.5i 0.423563 0.733632i
\(719\) −8212.50 14224.5i −0.425973 0.737807i 0.570538 0.821271i \(-0.306735\pi\)
−0.996511 + 0.0834645i \(0.973401\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 23820.0 1.22782
\(723\) 0 0
\(724\) −2340.00 + 4053.00i −0.120118 + 0.208050i
\(725\) −4028.00 + 6976.70i −0.206340 + 0.357391i
\(726\) 0 0
\(727\) 6032.00 0.307723 0.153861 0.988092i \(-0.450829\pi\)
0.153861 + 0.988092i \(0.450829\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 2065.00 + 3576.68i 0.104697 + 0.181341i
\(731\) −7670.00 + 13284.8i −0.388078 + 0.672171i
\(732\) 0 0
\(733\) 7621.50 + 13200.8i 0.384047 + 0.665189i 0.991636 0.129062i \(-0.0411967\pi\)
−0.607589 + 0.794251i \(0.707863\pi\)
\(734\) −19342.0 −0.972652
\(735\) 0 0
\(736\) 224.000 0.0112184
\(737\) 7682.50 + 13306.5i 0.383974 + 0.665062i
\(738\) 0 0
\(739\) 5026.50 8706.15i 0.250207 0.433371i −0.713376 0.700782i \(-0.752835\pi\)
0.963583 + 0.267411i \(0.0861681\pi\)
\(740\) −154.000 266.736i −0.00765021 0.0132505i
\(741\) 0 0
\(742\) 0 0
\(743\) −24384.0 −1.20399 −0.601993 0.798501i \(-0.705627\pi\)
−0.601993 + 0.798501i \(0.705627\pi\)
\(744\) 0 0
\(745\) 8032.50 13912.7i 0.395017 0.684190i
\(746\) 4109.00 7117.00i 0.201664 0.349292i
\(747\) 0 0
\(748\) −8260.00 −0.403764
\(749\) 0 0
\(750\) 0 0
\(751\) −5794.50 10036.4i −0.281550 0.487660i 0.690216 0.723603i \(-0.257515\pi\)
−0.971767 + 0.235943i \(0.924182\pi\)
\(752\) 1368.00 2369.45i 0.0663375 0.114900i
\(753\) 0 0
\(754\) −6996.00 12117.4i −0.337904 0.585266i
\(755\) −7763.00 −0.374205
\(756\) 0 0
\(757\) 14562.0 0.699161 0.349581 0.936906i \(-0.386324\pi\)
0.349581 + 0.936906i \(0.386324\pi\)
\(758\) 3488.00 + 6041.39i 0.167137 + 0.289490i
\(759\) 0 0
\(760\) 3836.00 6644.15i 0.183087 0.317116i
\(761\) 11382.5 + 19715.1i 0.542201 + 0.939120i 0.998777 + 0.0494360i \(0.0157424\pi\)
−0.456576 + 0.889684i \(0.650924\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 5100.00 0.241507
\(765\) 0 0
\(766\) −8717.00 + 15098.3i −0.411172 + 0.712171i
\(767\) −561.000 + 971.681i −0.0264101 + 0.0457436i
\(768\) 0 0
\(769\) −3766.00 −0.176600 −0.0883000 0.996094i \(-0.528143\pi\)
−0.0883000 + 0.996094i \(0.528143\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −70.0000 121.244i −0.00326341 0.00565240i
\(773\) 13430.5 23262.3i 0.624918 1.08239i −0.363639 0.931540i \(-0.618466\pi\)
0.988557 0.150849i \(-0.0482009\pi\)
\(774\) 0 0
\(775\) −2850.00 4936.34i −0.132097 0.228798i
\(776\) 2320.00 0.107324
\(777\) 0 0
\(778\) −326.000 −0.0150227
\(779\) −34113.0 59085.4i −1.56897 2.71753i
\(780\) 0 0
\(781\) 13720.0 23763.7i 0.628605 1.08878i
\(782\) −413.000 715.337i −0.0188860 0.0327115i
\(783\) 0 0
\(784\) 0 0
\(785\) −10913.0 −0.496180
\(786\) 0 0
\(787\) −1048.50 + 1816.06i −0.0474905 + 0.0822559i −0.888793 0.458308i \(-0.848456\pi\)
0.841303 + 0.540564i \(0.181789\pi\)
\(788\) −5468.00 + 9470.85i −0.247195 + 0.428154i
\(789\) 0 0
\(790\) −6930.00 −0.312099
\(791\)