Properties

Label 126.4.g.c.109.1
Level $126$
Weight $4$
Character 126.109
Analytic conductor $7.434$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 126.g (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.43424066072\)
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 109.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 126.109
Dual form 126.4.g.c.37.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} +(-10.0000 - 15.5885i) q^{7} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} +(-10.0000 - 15.5885i) q^{7} +8.00000 q^{8} +(7.00000 - 12.1244i) q^{10} +(17.5000 - 30.3109i) q^{11} +66.0000 q^{13} +(-17.0000 + 32.9090i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(29.5000 - 51.0955i) q^{17} +(-68.5000 - 118.645i) q^{19} -28.0000 q^{20} -70.0000 q^{22} +(-3.50000 - 6.06218i) q^{23} +(38.0000 - 65.8179i) q^{25} +(-66.0000 - 114.315i) q^{26} +(74.0000 - 3.46410i) q^{28} -106.000 q^{29} +(-37.5000 + 64.9519i) q^{31} +(-16.0000 + 27.7128i) q^{32} -118.000 q^{34} +(59.5000 - 115.181i) q^{35} +(-5.50000 - 9.52628i) q^{37} +(-137.000 + 237.291i) q^{38} +(28.0000 + 48.4974i) q^{40} +498.000 q^{41} +260.000 q^{43} +(70.0000 + 121.244i) q^{44} +(-7.00000 + 12.1244i) q^{46} +(-85.5000 - 148.090i) q^{47} +(-143.000 + 311.769i) q^{49} -152.000 q^{50} +(-132.000 + 228.631i) q^{52} +(-208.500 + 361.133i) q^{53} +245.000 q^{55} +(-80.0000 - 124.708i) q^{56} +(106.000 + 183.597i) q^{58} +(-8.50000 + 14.7224i) q^{59} +(-25.5000 - 44.1673i) q^{61} +150.000 q^{62} +64.0000 q^{64} +(231.000 + 400.104i) q^{65} +(-219.500 + 380.185i) q^{67} +(118.000 + 204.382i) q^{68} +(-259.000 + 12.1244i) q^{70} +784.000 q^{71} +(-147.500 + 255.477i) q^{73} +(-11.0000 + 19.0526i) q^{74} +548.000 q^{76} +(-647.500 + 30.3109i) q^{77} +(247.500 + 428.683i) q^{79} +(56.0000 - 96.9948i) q^{80} +(-498.000 - 862.561i) q^{82} -932.000 q^{83} +413.000 q^{85} +(-260.000 - 450.333i) q^{86} +(140.000 - 242.487i) q^{88} +(-436.500 - 756.040i) q^{89} +(-660.000 - 1028.84i) q^{91} +28.0000 q^{92} +(-171.000 + 296.181i) q^{94} +(479.500 - 830.518i) q^{95} -290.000 q^{97} +(683.000 - 64.0859i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} - 4q^{4} + 7q^{5} - 20q^{7} + 16q^{8} + O(q^{10}) \) \( 2q - 2q^{2} - 4q^{4} + 7q^{5} - 20q^{7} + 16q^{8} + 14q^{10} + 35q^{11} + 132q^{13} - 34q^{14} - 16q^{16} + 59q^{17} - 137q^{19} - 56q^{20} - 140q^{22} - 7q^{23} + 76q^{25} - 132q^{26} + 148q^{28} - 212q^{29} - 75q^{31} - 32q^{32} - 236q^{34} + 119q^{35} - 11q^{37} - 274q^{38} + 56q^{40} + 996q^{41} + 520q^{43} + 140q^{44} - 14q^{46} - 171q^{47} - 286q^{49} - 304q^{50} - 264q^{52} - 417q^{53} + 490q^{55} - 160q^{56} + 212q^{58} - 17q^{59} - 51q^{61} + 300q^{62} + 128q^{64} + 462q^{65} - 439q^{67} + 236q^{68} - 518q^{70} + 1568q^{71} - 295q^{73} - 22q^{74} + 1096q^{76} - 1295q^{77} + 495q^{79} + 112q^{80} - 996q^{82} - 1864q^{83} + 826q^{85} - 520q^{86} + 280q^{88} - 873q^{89} - 1320q^{91} + 56q^{92} - 342q^{94} + 959q^{95} - 580q^{97} + 1366q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 \(-0.0653161\pi\)
−0.665971 + 0.745977i \(0.731983\pi\)
\(6\) 0 0
\(7\) −10.0000 15.5885i −0.539949 0.841698i
\(8\) 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 \(-0.251376\pi\)
0.704043 + 0.710158i \(0.251376\pi\)
\(14\) −17.0000 + 32.9090i −0.324532 + 0.628235i
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 29.5000 51.0955i 0.420871 0.728969i −0.575154 0.818045i \(-0.695058\pi\)
0.996025 + 0.0890757i \(0.0283913\pi\)
\(18\) 0 0
\(19\) −68.5000 118.645i −0.827104 1.43259i −0.900301 0.435269i \(-0.856653\pi\)
0.0731965 0.997318i \(-0.476680\pi\)
\(20\) −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
\(28\) 74.0000 3.46410i 0.499453 0.0233805i
\(29\) −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 \(-0.903047\pi\)
0.736706 + 0.676213i \(0.236380\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −118.000 −0.595201
\(35\) 59.5000 115.181i 0.287352 0.556263i
\(36\) 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 \(-0.102631\pi\)
0.948470 + 0.316867i \(0.102631\pi\)
\(42\) 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 \(-0.252154\pi\)
−0.967655 + 0.252276i \(0.918821\pi\)
\(48\) 0 0
\(49\) −143.000 + 311.769i −0.416910 + 0.908948i
\(50\) −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
\(56\) −80.0000 124.708i −0.190901 0.297585i
\(57\) 0 0
\(58\) 106.000 + 183.597i 0.239974 + 0.415647i
\(59\) −8.50000 + 14.7224i −0.0187560 + 0.0324864i −0.875251 0.483669i \(-0.839304\pi\)
0.856495 + 0.516155i \(0.172637\pi\)
\(60\) 0 0
\(61\) −25.5000 44.1673i −0.0535236 0.0927056i 0.838022 0.545636i \(-0.183712\pi\)
−0.891546 + 0.452930i \(0.850379\pi\)
\(62\) 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
\(70\) −259.000 + 12.1244i −0.442235 + 0.0207020i
\(71\) 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 \(-0.909329\pi\)
0.723217 + 0.690621i \(0.242663\pi\)
\(74\) −11.0000 + 19.0526i −0.0172801 + 0.0299299i
\(75\) 0 0
\(76\) 548.000 0.827104
\(77\) −647.500 + 30.3109i −0.958305 + 0.0448603i
\(78\) 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 \(-0.711356\pi\)
−0.616267 + 0.787537i \(0.711356\pi\)
\(84\) 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 \(-0.992645\pi\)
0.479858 0.877346i \(-0.340688\pi\)
\(90\) 0 0
\(91\) −660.000 1028.84i −0.760294 1.18518i
\(92\) 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 \(-0.548500\pi\)
−0.151779 + 0.988415i \(0.548500\pi\)
\(98\) 683.000 64.0859i 0.704014 0.0660577i
\(99\) 0 0
\(100\) 152.000 + 263.272i 0.152000 + 0.263272i
\(101\) −542.500 + 939.638i −0.534463 + 0.925717i 0.464726 + 0.885454i \(0.346153\pi\)
−0.999189 + 0.0402627i \(0.987181\pi\)
\(102\) 0 0
\(103\) −776.500 1344.94i −0.742823 1.28661i −0.951205 0.308560i \(-0.900153\pi\)
0.208381 0.978048i \(-0.433181\pi\)
\(104\) 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
\(112\) −136.000 + 263.272i −0.114739 + 0.222115i
\(113\) 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
\(119\) −1091.50 + 51.0955i −0.840821 + 0.0393606i
\(120\) 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 \(-0.247680\pi\)
−0.964014 + 0.265851i \(0.914347\pi\)
\(132\) 0 0
\(133\) −1164.50 + 2254.26i −0.759210 + 1.46970i
\(134\) 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 \(-0.497281\pi\)
0.00854291 + 0.999964i \(0.497281\pi\)
\(140\) 280.000 + 436.477i 0.169031 + 0.263493i
\(141\) 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
\(154\) 700.000 + 1091.19i 0.366283 + 0.570979i
\(155\) −525.000 −0.272058
\(156\) 0 0
\(157\) −779.500 + 1350.13i −0.396248 + 0.686321i −0.993260 0.115911i \(-0.963021\pi\)
0.597012 + 0.802232i \(0.296354\pi\)
\(158\) 495.000 857.365i 0.249241 0.431698i
\(159\) 0 0
\(160\) −224.000 −0.110680
\(161\) −59.5000 + 115.181i −0.0291258 + 0.0563824i
\(162\) 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 \(-0.723532\pi\)
−0.645934 + 0.763393i \(0.723532\pi\)
\(168\) 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 \(-0.0538797\pi\)
−0.638746 + 0.769418i \(0.720546\pi\)
\(174\) 0 0
\(175\) −1406.00 + 65.8179i −0.607335 + 0.0284307i
\(176\) −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 \(-0.577225\pi\)
−0.240236 + 0.970715i \(0.577225\pi\)
\(182\) −1122.00 + 2171.99i −0.456968 + 0.884608i
\(183\) 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
\(196\) −794.000 1118.90i −0.289359 0.407764i
\(197\) 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 \(-0.964151\pi\)
0.594162 + 0.804345i \(0.297484\pi\)
\(200\) 304.000 526.543i 0.107480 0.186161i
\(201\) 0 0
\(202\) 2170.00 0.755845
\(203\) 1060.00 + 1652.38i 0.366490 + 0.571301i
\(204\) 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
\(217\) 1387.50 64.9519i 0.434054 0.0203190i
\(218\) −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 \(-0.401713\pi\)
0.303895 + 0.952706i \(0.401713\pi\)
\(224\) 592.000 27.7128i 0.176583 0.00826625i
\(225\) 0 0
\(226\) −50.0000 86.6025i −0.0147166 0.0254899i
\(227\) 1285.50 2226.55i 0.375866 0.651019i −0.614590 0.788847i \(-0.710679\pi\)
0.990456 + 0.137827i \(0.0440119\pi\)
\(228\) 0 0
\(229\) −447.500 775.093i −0.129134 0.223666i 0.794207 0.607647i \(-0.207886\pi\)
−0.923341 + 0.383980i \(0.874553\pi\)
\(230\) −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
\(238\) 1180.00 + 1839.44i 0.321378 + 0.500979i
\(239\) 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 \(-0.644816\pi\)
0.997645 0.0685917i \(-0.0218506\pi\)
\(242\) 106.000 183.597i 0.0281568 0.0487690i
\(243\) 0 0
\(244\) 204.000 0.0535236
\(245\) −2390.50 + 224.301i −0.623361 + 0.0584900i
\(246\) 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 \(-0.299741\pi\)
0.588444 + 0.808538i \(0.299741\pi\)
\(252\) 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 \(-0.234748\pi\)
−0.952420 + 0.304788i \(0.901414\pi\)
\(258\) 0 0
\(259\) −93.5000 + 180.999i −0.0224317 + 0.0434237i
\(260\) −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
\(266\) 5069.00 237.291i 1.16842 0.0546964i
\(267\) 0 0
\(268\) −878.000 1520.74i −0.200121 0.346619i
\(269\) 987.500 1710.40i 0.223825 0.387676i −0.732141 0.681153i \(-0.761479\pi\)
0.955966 + 0.293476i \(0.0948122\pi\)
\(270\) 0 0
\(271\) 4219.50 + 7308.39i 0.945817 + 1.63820i 0.754107 + 0.656751i \(0.228070\pi\)
0.191710 + 0.981452i \(0.438597\pi\)
\(272\) −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
\(280\) 476.000 921.451i 0.101594 0.196669i
\(281\) 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 \(-0.518894\pi\)
0.894161 0.447745i \(-0.147773\pi\)
\(284\) −1568.00 + 2715.86i −0.327619 + 0.567452i
\(285\) 0 0
\(286\) −4620.00 −0.955197
\(287\) −4980.00 7763.05i −1.02425 1.59665i
\(288\) 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 \(-0.510093\pi\)
−0.0317027 + 0.999497i \(0.510093\pi\)
\(294\) 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
\(301\) −2600.00 4053.00i −0.497879 0.776116i
\(302\) −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 \(-0.772797\pi\)
−0.755892 + 0.654696i \(0.772797\pi\)
\(308\) 1190.00 2303.63i 0.220151 0.426173i
\(309\) 0 0
\(310\) 525.000 + 909.327i 0.0961871 + 0.166601i
\(311\) −464.500 + 804.538i −0.0846925 + 0.146692i −0.905260 0.424858i \(-0.860324\pi\)
0.820568 + 0.571549i \(0.193657\pi\)
\(312\) 0 0
\(313\) 104.500 + 180.999i 0.0188712 + 0.0326859i 0.875307 0.483568i \(-0.160659\pi\)
−0.856436 + 0.516254i \(0.827326\pi\)
\(314\) 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
\(322\) 259.000 12.1244i 0.0448246 0.00209834i
\(323\) −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
\(329\) −1453.50 + 2813.72i −0.243569 + 0.471505i
\(330\) 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
\(343\) 6290.00 888.542i 0.990169 0.139874i
\(344\) 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 \(-0.133236\pi\)
0.913670 + 0.406456i \(0.133236\pi\)
\(350\) 1520.00 + 2369.45i 0.232135 + 0.361863i
\(351\) 0 0
\(352\) 560.000 + 969.948i 0.0847957 + 0.146871i
\(353\) 4561.50 7900.75i 0.687774 1.19126i −0.284783 0.958592i \(-0.591921\pi\)
0.972556 0.232667i \(-0.0747452\pi\)
\(354\) 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
\(364\) 4884.00 228.631i 0.703272 0.0329217i
\(365\) −2065.00 −0.296129
\(366\) 0 0
\(367\) −4835.50 + 8375.33i −0.687769 + 1.19125i 0.284790 + 0.958590i \(0.408076\pi\)
−0.972558 + 0.232660i \(0.925257\pi\)
\(368\) −56.0000 + 96.9948i −0.00793261 + 0.0137397i
\(369\) 0 0
\(370\) −154.000 −0.0216381
\(371\) 7714.50 361.133i 1.07956 0.0505366i
\(372\) 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 \(0.0308616\pi\)
−0.413818 + 0.910360i \(0.635805\pi\)
\(384\) 0 0
\(385\) −2450.00 3819.17i −0.324321 0.505566i
\(386\) 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
\(392\) −1144.00 + 2494.15i −0.147400 + 0.321362i
\(393\) 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 \(-0.186780\pi\)
−0.895870 + 0.444316i \(0.853447\pi\)
\(398\) 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
\(406\) 1802.00 3488.35i 0.220275 0.426414i
\(407\) −385.000 −0.0468888
\(408\) 0 0
\(409\) 66.5000 115.181i 0.00803964 0.0139251i −0.861978 0.506946i \(-0.830774\pi\)
0.870017 + 0.493021i \(0.164108\pi\)
\(410\) 3486.00 6037.93i 0.419906 0.727298i
\(411\) 0 0
\(412\) 6212.00 0.742823
\(413\) 314.500 14.7224i 0.0374710 0.00175410i
\(414\) 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 \(-0.377894\pi\)
0.374269 + 0.927320i \(0.377894\pi\)
\(420\) 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
\(427\) −433.500 + 839.179i −0.0491301 + 0.0951070i
\(428\) −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 \(-0.524365\pi\)
−0.0764693 + 0.997072i \(0.524365\pi\)
\(434\) −1500.00 2338.27i −0.165904 0.258619i
\(435\) 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 \(-0.118677\pi\)
−0.781104 + 0.624401i \(0.785343\pi\)
\(440\) 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
\(448\) −640.000 997.661i −0.0674937 0.105212i
\(449\) −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
\(455\) 3927.00 7601.97i 0.404617 0.783266i
\(456\) 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 \(-0.340786\pi\)
0.479587 + 0.877494i \(0.340786\pi\)
\(462\) 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 \(-0.187293\pi\)
−0.896585 + 0.442872i \(0.853960\pi\)
\(468\) 0 0
\(469\) 8121.50 380.185i 0.799608 0.0374314i
\(470\) −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
\(476\) 2006.00 3883.26i 0.193161 0.373926i
\(477\) 0 0
\(478\) −5100.00 8833.46i −0.488010 0.845257i
\(479\) 9143.50 15837.0i 0.872186 1.51067i 0.0124559 0.999922i \(-0.496035\pi\)
0.859730 0.510748i \(-0.170632\pi\)
\(480\) 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
\(490\) 2779.00 + 3916.17i 0.256209 + 0.361050i
\(491\) −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
\(497\) −7840.00 12221.4i −0.707590 1.10302i
\(498\) 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 \(-0.621432\pi\)
−0.372304 + 0.928111i \(0.621432\pi\)
\(504\) 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 \(-0.199781\pi\)
−0.913265 + 0.407365i \(0.866448\pi\)
\(510\) 0 0
\(511\) 5457.50 255.477i 0.472457 0.0221167i
\(512\) 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
\(518\) 407.000 19.0526i 0.0345223 0.00161606i
\(519\) 0 0
\(520\) 1848.00 + 3200.83i 0.155846 + 0.269934i
\(521\) −4576.50 + 7926.73i −0.384837 + 0.666557i −0.991747 0.128214i \(-0.959076\pi\)
0.606910 + 0.794771i \(0.292409\pi\)
\(522\) 0 0
\(523\) 6903.50 + 11957.2i 0.577187 + 0.999718i 0.995800 + 0.0915530i \(0.0291831\pi\)
−0.418613 + 0.908165i \(0.637484\pi\)
\(524\) 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
\(532\) −5480.00 8542.47i −0.446594 0.696172i
\(533\) 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
\(539\) 6947.50 + 9790.42i 0.555195 + 0.782381i
\(540\) 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
\(553\) 4207.50 8144.97i 0.323546 0.626328i
\(554\) 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
\(560\) −2072.00 + 96.9948i −0.156354 + 0.00731925i
\(561\) 0 0
\(562\) −202.000 349.874i −0.0151617 0.0262608i
\(563\) −9876.50 + 17106.6i −0.739334 + 1.28056i 0.213462 + 0.976951i \(0.431526\pi\)
−0.952796 + 0.303612i \(0.901807\pi\)
\(564\) 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
\(574\) −8466.00 + 16388.7i −0.615617 + 1.19172i
\(575\) −532.000 −0.0385842
\(576\) 0 0
\(577\) −63.5000 + 109.985i −0.00458152 + 0.00793543i −0.868307 0.496027i \(-0.834792\pi\)
0.863726 + 0.503962i \(0.168125\pi\)
\(578\) 1432.00 2480.30i 0.103051 0.178489i
\(579\) 0 0
\(580\) 2968.00 0.212482
\(581\) 9320.00 + 14528.4i 0.665506 + 1.03742i
\(582\) 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 \(-0.602998\pi\)
−0.317961 + 0.948104i \(0.602998\pi\)
\(588\) 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 \(-0.287487\pi\)
−0.989646 + 0.143532i \(0.954154\pi\)
\(594\) 0 0
\(595\) −4130.00 6438.03i −0.284560 0.443586i
\(596\) −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 \(-0.515150\pi\)
−0.0475780 + 0.998868i \(0.515150\pi\)
\(602\) −4420.00 + 8556.33i −0.299245 + 0.579286i
\(603\) 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 \(-0.236671\pi\)
−0.954244 + 0.299028i \(0.903338\pi\)
\(608\) 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
\(616\) −5180.00 + 242.487i −0.338812 + 0.0158605i
\(617\) −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 \(-0.868698\pi\)
0.805250 + 0.592936i \(0.202031\pi\)
\(620\) 1050.00 1818.65i 0.0680145 0.117805i
\(621\) 0 0
\(622\) 1858.00 0.119773
\(623\) −7420.50 + 14364.8i −0.477201 + 0.923775i
\(624\) 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
\(637\) −9438.00 + 20576.8i −0.587044 + 1.27988i
\(638\) 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 \(-0.432534\pi\)
0.210367 + 0.977622i \(0.432534\pi\)
\(644\) −280.000 436.477i −0.0171328 0.0267074i
\(645\) 0 0
\(646\) 8083.00 + 14000.2i 0.492293 + 0.852677i
\(647\) 7231.50 12525.3i 0.439412 0.761084i −0.558232 0.829685i \(-0.688520\pi\)
0.997644 + 0.0686008i \(0.0218535\pi\)
\(648\) 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
\(658\) 6327.00 296.181i 0.374851 0.0175476i
\(659\) 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 \(-0.962319\pi\)
0.598780 + 0.800914i \(0.295652\pi\)
\(662\) 6571.00 11381.3i 0.385784 0.668198i
\(663\) 0 0
\(664\) −7456.00 −0.435766
\(665\) −17741.5 + 830.518i −1.03457 + 0.0484303i
\(666\) 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 \(-0.902421\pi\)
0.215344 0.976538i \(-0.430913\pi\)
\(678\) 0 0
\(679\) 2900.00 + 4520.65i 0.163905 + 0.255503i
\(680\) 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
\(686\) −7829.00 10006.1i −0.435733 0.556899i
\(687\) 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 \(-0.876954\pi\)
0.136610 0.990625i \(-0.456379\pi\)
\(692\) −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
\(700\) 2584.00 5002.16i 0.139523 0.270091i
\(701\) 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
\(707\) 20072.5 939.638i 1.06776 0.0499840i
\(708\) 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 0.996511 0.0834645i \(-0.0265985\pi\)
−0.570538 + 0.821271i \(0.693265\pi\)
\(720\) 0 0
\(721\) −13200.5 + 25553.8i −0.681848 + 1.31994i
\(722\) 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 \(-0.549171\pi\)
−0.153861 + 0.988092i \(0.549171\pi\)
\(728\) −5280.00 8230.71i −0.268805 0.419025i
\(729\) 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 \(-0.292137\pi\)
−0.991636 + 0.129062i \(0.958803\pi\)
\(734\) 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
\(742\) −8340.00 13000.8i −0.412629 0.643226i
\(743\) −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
\(749\) 1096.50 2122.63i 0.0534916 0.103550i
\(750\) 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 \(-0.984258\pi\)
0.456576 0.889684i \(-0.349076\pi\)
\(762\) 0 0
\(763\) −17852.5 + 835.715i −0.847056 + 0.0396526i
\(764\) 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 \(-0.471857\pi\)
0.0883000 + 0.996094i \(0.471857\pi\)
\(770\) −4165.00 + 8062.70i −0.194930 + 0.377350i
\(771\) 0 0
\(772\) −70.0000 121.244i −0.00326341 0.00565240i
\(773\) −13430.5 + 23262.3i −0.624918 + 1.08239i 0.363639 + 0.931540i \(0.381534\pi\)
−0.988557 + 0.150849i \(0.951799\pi\)
\(774\) 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
\(784\) 5464.00 512.687i 0.248907 0.0233549i
\(785\) −10913.0 −0.496180
\(786\) 0 0
\(787\) 1048.50 1816.06i 0.0474905 0.0822559i −0.841303 0.540564i \(-0.818211\pi\)
0.888793 + 0.458308i \(0.151544\pi\)
\(788\) −5468.00 + 9470.85i −0.247195 + 0.428154i
\(789\) 0 0
\(790\) 6930.00 0.312099
\(791\) −500.000 779.423i −0.0224753 0.0350355i
\(792\) 0 0
\(793\) −1683.00 2915.04i −0.0753658 0.130537i
\(794\) −999.000 + 1730.32i −0.0446514 + 0.0773384i
\(795\) 0 0
\(796\) −4486.00 7769.98i −0.199751 0.345979i
\(797\) 35334.0 1.57038 0.785191 0.619254i \(-0.212565\pi\)
0.785191 + 0.619254i \(0.212565\pi\)
\(798\) 0 0
\(799\) −10089.0 −0.446712
\(800\) 1216.00