Properties

Label 882.4.g.d.667.1
Level $882$
Weight $4$
Character 882.667
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 667.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.667
Dual form 882.4.g.d.361.1

$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −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 −0.979021 0.203760i \(-0.934684\pi\)
0.665971 + 0.745977i \(0.268017\pi\)
\(6\) 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 0.999728 0.0233099i \(-0.00742046\pi\)
−0.520051 + 0.854135i \(0.674087\pi\)
\(12\) 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 0.575154 0.818045i \(-0.304942\pi\)
−0.996025 + 0.0890757i \(0.971609\pi\)
\(18\) 0 0
\(19\) 68.5000 118.645i 0.827104 1.43259i −0.0731965 0.997318i \(-0.523320\pi\)
0.900301 0.435269i \(-0.143347\pi\)
\(20\) 28.0000 0.313050
\(21\) 0 0
\(22\) −70.0000 −0.678366
\(23\) −3.50000 + 6.06218i −0.0317305 + 0.0549588i −0.881455 0.472269i \(-0.843435\pi\)
0.849724 + 0.527228i \(0.176768\pi\)
\(24\) 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 0.953971 0.299900i \(-0.0969533\pi\)
−0.736706 + 0.676213i \(0.763620\pi\)
\(32\) −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 −0.877986 0.478687i \(-0.841113\pi\)
0.853548 + 0.521014i \(0.174446\pi\)
\(38\) 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 −0.702305 0.711876i \(-0.747846\pi\)
0.967655 + 0.252276i \(0.0811791\pi\)
\(48\) 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 −0.998883 0.0472619i \(-0.984950\pi\)
0.458511 0.888689i \(-0.348383\pi\)
\(54\) 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 0.875251 0.483669i \(-0.160696\pi\)
−0.856495 + 0.516155i \(0.827363\pi\)
\(60\) 0 0
\(61\) 25.5000 44.1673i 0.0535236 0.0927056i −0.838022 0.545636i \(-0.816288\pi\)
0.891546 + 0.452930i \(0.149621\pi\)
\(62\) −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 0.593513 0.804824i \(-0.297740\pi\)
−0.993755 + 0.111585i \(0.964407\pi\)
\(68\) −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 0.959704 0.281013i \(-0.0906705\pi\)
−0.723217 + 0.690621i \(0.757337\pi\)
\(74\) −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 −0.634203 0.773166i \(-0.718672\pi\)
0.986683 + 0.162653i \(0.0520051\pi\)
\(80\) −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 −0.479858 0.877346i \(-0.659312\pi\)
0.999733 0.0231042i \(-0.00735495\pi\)
\(90\) 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 0.999189 + 0.0402627i \(0.0128195\pi\)
−0.464726 + 0.885454i \(0.653847\pi\)
\(102\) 0 0
\(103\) 776.500 1344.94i 0.742823 1.28661i −0.208381 0.978048i \(-0.566819\pi\)
0.951205 0.308560i \(-0.0998472\pi\)
\(104\) −528.000 −0.497833
\(105\) 0 0
\(106\) 834.000 0.764200
\(107\) 64.5000 111.717i 0.0582752 0.100936i −0.835416 0.549618i \(-0.814773\pi\)
0.893691 + 0.448682i \(0.148107\pi\)
\(108\) 0 0
\(109\) 482.500 + 835.715i 0.423992 + 0.734376i 0.996326 0.0856452i \(-0.0272952\pi\)
−0.572334 + 0.820021i \(0.693962\pi\)
\(110\) 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 −0.712241 0.701935i \(-0.752320\pi\)
0.964014 + 0.265851i \(0.0856529\pi\)
\(132\) 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 −0.954752 0.297403i \(-0.903879\pi\)
0.219817 0.975541i \(-0.429454\pi\)
\(138\) 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 −0.356446 0.934316i \(-0.616012\pi\)
0.987364 0.158467i \(-0.0506551\pi\)
\(150\) 0 0
\(151\) 554.500 + 960.422i 0.298838 + 0.517603i 0.975870 0.218350i \(-0.0700676\pi\)
−0.677032 + 0.735953i \(0.736734\pi\)
\(152\) 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 0.993260 0.115911i \(-0.0369789\pi\)
−0.597012 + 0.802232i \(0.703646\pi\)
\(158\) 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 −0.458022 0.888941i \(-0.651442\pi\)
0.998856 0.0478115i \(-0.0152247\pi\)
\(164\) 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 −0.985708 0.168461i \(-0.946120\pi\)
0.638746 + 0.769418i \(0.279454\pi\)
\(174\) 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 0.999908 + 0.0135883i \(0.00432541\pi\)
−0.488186 + 0.872740i \(0.662341\pi\)
\(180\) 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 −0.961144 0.276048i \(-0.910975\pi\)
0.719637 + 0.694351i \(0.244308\pi\)
\(192\) 0 0
\(193\) −17.5000 30.3109i −0.00652683 0.0113048i 0.862744 0.505642i \(-0.168744\pi\)
−0.869270 + 0.494337i \(0.835411\pi\)
\(194\) −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 0.993665 0.112387i \(-0.0358495\pi\)
−0.594162 + 0.804345i \(0.702516\pi\)
\(200\) 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 0.614590 0.788847i \(-0.289321\pi\)
−0.990456 + 0.137827i \(0.955988\pi\)
\(228\) 0 0
\(229\) 447.500 775.093i 0.129134 0.223666i −0.794207 0.607647i \(-0.792114\pi\)
0.923341 + 0.383980i \(0.125447\pi\)
\(230\) 98.0000 0.0280953
\(231\) 0 0
\(232\) −848.000 −0.239974
\(233\) 893.500 1547.59i 0.251224 0.435132i −0.712639 0.701531i \(-0.752500\pi\)
0.963863 + 0.266398i \(0.0858337\pi\)
\(234\) 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 −0.997645 0.0685917i \(-0.978149\pi\)
0.439420 0.898282i \(-0.355184\pi\)
\(242\) 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 −0.740164 0.672426i \(-0.765252\pi\)
0.952420 + 0.304788i \(0.0985856\pi\)
\(258\) 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 −0.999598 0.0283689i \(-0.990969\pi\)
0.475231 0.879861i \(-0.342365\pi\)
\(264\) 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 0.732141 0.681153i \(-0.238521\pi\)
−0.955966 + 0.293476i \(0.905188\pi\)
\(270\) 0 0
\(271\) −4219.50 + 7308.39i −0.945817 + 1.63820i −0.191710 + 0.981452i \(0.561403\pi\)
−0.754107 + 0.656751i \(0.771930\pi\)
\(272\) 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 0.836032 0.548681i \(-0.184870\pi\)
−0.893188 + 0.449684i \(0.851537\pi\)
\(278\) 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 −0.894161 0.447745i \(-0.852227\pi\)
0.0593220 0.998239i \(-0.481106\pi\)
\(284\) −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 0.905260 0.424858i \(-0.139676\pi\)
−0.820568 + 0.571549i \(0.806343\pi\)
\(312\) 0 0
\(313\) −104.500 + 180.999i −0.0188712 + 0.0326859i −0.875307 0.483568i \(-0.839341\pi\)
0.856436 + 0.516254i \(0.172674\pi\)
\(314\) −3118.00 −0.560379
\(315\) 0 0
\(316\) −1980.00 −0.352480
\(317\) 3565.50 6175.63i 0.631730 1.09419i −0.355468 0.934689i \(-0.615678\pi\)
0.987198 0.159500i \(-0.0509882\pi\)
\(318\) 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 −0.452989 0.891516i \(-0.649642\pi\)
0.998570 0.0534583i \(-0.0170244\pi\)
\(332\) −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 −0.944737 0.327831i \(-0.893682\pi\)
0.188459 0.982081i \(-0.439651\pi\)
\(348\) 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 −0.972556 0.232667i \(-0.925255\pi\)
0.284783 0.958592i \(-0.408079\pi\)
\(354\) 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 −0.393960 0.919128i \(-0.628895\pi\)
0.992968 0.118385i \(-0.0377716\pi\)
\(360\) 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 0.972558 + 0.232660i \(0.0747429\pi\)
−0.284790 + 0.958590i \(0.591924\pi\)
\(368\) −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 −0.687461 0.726221i \(-0.741275\pi\)
0.972657 + 0.232248i \(0.0746081\pi\)
\(374\) 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 0.413818 + 0.910360i \(0.364195\pi\)
−0.995304 + 0.0968028i \(0.969138\pi\)
\(384\) 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 0.871288 0.490772i \(-0.163285\pi\)
−0.860665 + 0.509171i \(0.829952\pi\)
\(390\) 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 −0.832724 0.553689i \(-0.813220\pi\)
0.895870 + 0.444316i \(0.146553\pi\)
\(398\) −4486.00 −0.564982
\(399\) 0 0
\(400\) −1216.00 −0.152000
\(401\) −7378.50 + 12779.9i −0.918865 + 1.59152i −0.117722 + 0.993047i \(0.537559\pi\)
−0.801143 + 0.598474i \(0.795774\pi\)
\(402\) 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 0.861978 0.506946i \(-0.169226\pi\)
−0.870017 + 0.493021i \(0.835892\pi\)
\(410\) 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 −0.881119 0.472894i \(-0.843209\pi\)
0.0310213 0.999519i \(-0.490124\pi\)
\(432\) 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 −0.931299 0.364256i \(-0.881323\pi\)
0.781104 + 0.624401i \(0.214657\pi\)
\(440\) −1960.00 −0.212362
\(441\) 0 0
\(442\) −7788.00 −0.838094
\(443\) 2924.50 5065.38i 0.313651 0.543259i −0.665499 0.746399i \(-0.731781\pi\)
0.979150 + 0.203140i \(0.0651146\pi\)
\(444\) 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 0.402901 + 0.915244i \(0.368002\pi\)
−0.994075 + 0.108700i \(0.965331\pi\)
\(458\) 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 −0.831831 0.555030i \(-0.812707\pi\)
0.896585 + 0.442872i \(0.146040\pi\)
\(468\) 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 −0.859730 0.510748i \(-0.829368\pi\)
−0.0124559 0.999922i \(-0.503965\pi\)
\(480\) 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 0.969953 + 0.243291i \(0.0782269\pi\)
−0.274281 + 0.961650i \(0.588440\pi\)
\(488\) 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 −0.714900 0.699226i \(-0.753528\pi\)
0.962998 + 0.269509i \(0.0868612\pi\)
\(500\) 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 −0.809421 0.587228i \(-0.800219\pi\)
0.913265 + 0.407365i \(0.133552\pi\)
\(510\) 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 0.991747 0.128214i \(-0.0409243\pi\)
−0.606910 + 0.794771i \(0.707591\pi\)
\(522\) 0 0
\(523\) −6903.50 + 11957.2i −0.577187 + 0.999718i 0.418613 + 0.908165i \(0.362516\pi\)
−0.995800 + 0.0915530i \(0.970817\pi\)
\(524\) −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 −0.981479 0.191571i \(-0.938642\pi\)
0.656645 + 0.754200i \(0.271975\pi\)
\(542\) −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 0.967919 0.251261i \(-0.0808452\pi\)
−0.701558 + 0.712612i \(0.747512\pi\)
\(558\) 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 0.952796 + 0.303612i \(0.0981927\pi\)
−0.213462 + 0.976951i \(0.568474\pi\)
\(564\) 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 −0.964644 0.263557i \(-0.915104\pi\)
0.710569 + 0.703628i \(0.248438\pi\)
\(570\) 0 0
\(571\) −12457.5 21577.0i −0.913013 1.58138i −0.809785 0.586726i \(-0.800416\pi\)
−0.103227 0.994658i \(-0.532917\pi\)
\(572\) −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 0.868307 0.496027i \(-0.165208\pi\)
−0.863726 + 0.503962i \(0.831875\pi\)
\(578\) 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 −0.619125 0.785292i \(-0.712513\pi\)
0.989646 + 0.143532i \(0.0458460\pi\)
\(594\) 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 0.965091 + 0.261913i \(0.0843533\pi\)
−0.255722 + 0.966750i \(0.582313\pi\)
\(600\) 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 −0.736088 0.676886i \(-0.763329\pi\)
0.954244 + 0.299028i \(0.0966625\pi\)
\(608\) −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 0.504145 0.863619i \(-0.331808\pi\)
−0.999989 + 0.00479285i \(0.998474\pi\)
\(614\) −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 0.916122 0.400899i \(-0.131302\pi\)
−0.805250 + 0.592936i \(0.797969\pi\)
\(620\) 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 0.652660 0.757651i \(-0.273653\pi\)
−0.982475 + 0.186395i \(0.940320\pi\)
\(642\) 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 0.558232 0.829685i \(-0.311480\pi\)
−0.997644 + 0.0686008i \(0.978147\pi\)
\(648\) 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 −0.762436 0.647063i \(-0.775997\pi\)
0.941591 + 0.336758i \(0.109330\pi\)
\(654\) 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 0.993001 0.118102i \(-0.0376810\pi\)
−0.598780 + 0.800914i \(0.704348\pi\)
\(662\) 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 −0.215344 0.976538i \(-0.569087\pi\)
0.953379 0.301776i \(-0.0975795\pi\)
\(678\) 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 0.715949 0.698152i \(-0.245994\pi\)
−0.962592 + 0.270954i \(0.912661\pi\)
\(684\) 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 −0.136610 0.990625i \(-0.543621\pi\)
0.926211 0.377004i \(-0.123046\pi\)
\(692\) 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 −0.882216 0.470845i \(-0.843949\pi\)
0.848871 + 0.528599i \(0.177283\pi\)
\(710\) −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 −0.996511 0.0834645i \(-0.973401\pi\)
0.570538 + 0.821271i \(0.306735\pi\)
\(720\) 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 −0.607589 0.794251i \(-0.707863\pi\)
0.991636 + 0.129062i \(0.0411967\pi\)
\(734\) −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 0.963583 0.267411i \(-0.0861681\pi\)
−0.713376 + 0.700782i \(0.752835\pi\)
\(740\) −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 −0.971767 0.235943i \(-0.924182\pi\)
0.690216 + 0.723603i \(0.257515\pi\)
\(752\) 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 −0.456576 0.889684i \(-0.650924\pi\)
0.998777 0.0494360i \(-0.0157424\pi\)
\(762\) 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 0.988557 + 0.150849i \(0.0482009\pi\)
−0.363639 + 0.931540i \(0.618466\pi\)
\(774\) 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 0.841303 0.540564i \(-0.181789\pi\)
−0.888793 + 0.458308i \(0.848456\pi\)
\(788\) −5468.00 9470.85i −0.247195 0.428154i
\(789\) 0 0
\(790\) −6930.00 −0.312099
\(791\)