Properties

Label 98.4.c.e.67.1
Level $98$
Weight $4$
Character 98.67
Analytic conductor $5.782$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 98.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.78218718056\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 98.67
Dual form 98.4.c.e.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} -2.00000 q^{6} -8.00000 q^{8} +(13.0000 + 22.5167i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} -2.00000 q^{6} -8.00000 q^{8} +(13.0000 + 22.5167i) q^{9} +(-7.00000 + 12.1244i) q^{10} +(-17.5000 + 30.3109i) q^{11} +(-2.00000 - 3.46410i) q^{12} -66.0000 q^{13} -7.00000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(29.5000 - 51.0955i) q^{17} +(-26.0000 + 45.0333i) q^{18} +(68.5000 + 118.645i) q^{19} -28.0000 q^{20} -70.0000 q^{22} +(3.50000 + 6.06218i) q^{23} +(4.00000 - 6.92820i) q^{24} +(38.0000 - 65.8179i) q^{25} +(-66.0000 - 114.315i) q^{26} -53.0000 q^{27} +106.000 q^{29} +(-7.00000 - 12.1244i) q^{30} +(37.5000 - 64.9519i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-17.5000 - 30.3109i) q^{33} +118.000 q^{34} -104.000 q^{36} +(-5.50000 - 9.52628i) q^{37} +(-137.000 + 237.291i) q^{38} +(33.0000 - 57.1577i) q^{39} +(-28.0000 - 48.4974i) q^{40} +498.000 q^{41} +260.000 q^{43} +(-70.0000 - 121.244i) q^{44} +(-91.0000 + 157.617i) q^{45} +(-7.00000 + 12.1244i) q^{46} +(-85.5000 - 148.090i) q^{47} +16.0000 q^{48} +152.000 q^{50} +(29.5000 + 51.0955i) q^{51} +(132.000 - 228.631i) q^{52} +(208.500 - 361.133i) q^{53} +(-53.0000 - 91.7987i) q^{54} -245.000 q^{55} -137.000 q^{57} +(106.000 + 183.597i) q^{58} +(-8.50000 + 14.7224i) q^{59} +(14.0000 - 24.2487i) q^{60} +(25.5000 + 44.1673i) q^{61} +150.000 q^{62} +64.0000 q^{64} +(-231.000 - 400.104i) q^{65} +(35.0000 - 60.6218i) q^{66} +(-219.500 + 380.185i) q^{67} +(118.000 + 204.382i) q^{68} -7.00000 q^{69} -784.000 q^{71} +(-104.000 - 180.133i) q^{72} +(147.500 - 255.477i) q^{73} +(11.0000 - 19.0526i) q^{74} +(38.0000 + 65.8179i) q^{75} -548.000 q^{76} +132.000 q^{78} +(247.500 + 428.683i) q^{79} +(56.0000 - 96.9948i) q^{80} +(-324.500 + 562.050i) q^{81} +(498.000 + 862.561i) q^{82} -932.000 q^{83} +413.000 q^{85} +(260.000 + 450.333i) q^{86} +(-53.0000 + 91.7987i) q^{87} +(140.000 - 242.487i) q^{88} +(-436.500 - 756.040i) q^{89} -364.000 q^{90} -28.0000 q^{92} +(37.5000 + 64.9519i) q^{93} +(171.000 - 296.181i) q^{94} +(-479.500 + 830.518i) q^{95} +(16.0000 + 27.7128i) q^{96} +290.000 q^{97} -910.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - q^{3} - 4 q^{4} + 7 q^{5} - 4 q^{6} - 16 q^{8} + 26 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} - q^{3} - 4 q^{4} + 7 q^{5} - 4 q^{6} - 16 q^{8} + 26 q^{9} - 14 q^{10} - 35 q^{11} - 4 q^{12} - 132 q^{13} - 14 q^{15} - 16 q^{16} + 59 q^{17} - 52 q^{18} + 137 q^{19} - 56 q^{20} - 140 q^{22} + 7 q^{23} + 8 q^{24} + 76 q^{25} - 132 q^{26} - 106 q^{27} + 212 q^{29} - 14 q^{30} + 75 q^{31} + 32 q^{32} - 35 q^{33} + 236 q^{34} - 208 q^{36} - 11 q^{37} - 274 q^{38} + 66 q^{39} - 56 q^{40} + 996 q^{41} + 520 q^{43} - 140 q^{44} - 182 q^{45} - 14 q^{46} - 171 q^{47} + 32 q^{48} + 304 q^{50} + 59 q^{51} + 264 q^{52} + 417 q^{53} - 106 q^{54} - 490 q^{55} - 274 q^{57} + 212 q^{58} - 17 q^{59} + 28 q^{60} + 51 q^{61} + 300 q^{62} + 128 q^{64} - 462 q^{65} + 70 q^{66} - 439 q^{67} + 236 q^{68} - 14 q^{69} - 1568 q^{71} - 208 q^{72} + 295 q^{73} + 22 q^{74} + 76 q^{75} - 1096 q^{76} + 264 q^{78} + 495 q^{79} + 112 q^{80} - 649 q^{81} + 996 q^{82} - 1864 q^{83} + 826 q^{85} + 520 q^{86} - 106 q^{87} + 280 q^{88} - 873 q^{89} - 728 q^{90} - 56 q^{92} + 75 q^{93} + 342 q^{94} - 959 q^{95} + 32 q^{96} + 580 q^{97} - 1820 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).

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

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
\(3\) −0.500000 + 0.866025i −0.0962250 + 0.166667i −0.910119 0.414346i \(-0.864010\pi\)
0.813894 + 0.581013i \(0.197344\pi\)
\(4\) −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 \(0.731983\pi\)
\(6\) −2.00000 −0.136083
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) 13.0000 + 22.5167i 0.481481 + 0.833950i
\(10\) −7.00000 + 12.1244i −0.221359 + 0.383406i
\(11\) −17.5000 + 30.3109i −0.479677 + 0.830825i −0.999728 0.0233099i \(-0.992580\pi\)
0.520051 + 0.854135i \(0.325913\pi\)
\(12\) −2.00000 3.46410i −0.0481125 0.0833333i
\(13\) −66.0000 −1.40809 −0.704043 0.710158i \(-0.748624\pi\)
−0.704043 + 0.710158i \(0.748624\pi\)
\(14\) 0 0
\(15\) −7.00000 −0.120493
\(16\) −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 \(0.0283913\pi\)
\(18\) −26.0000 + 45.0333i −0.340459 + 0.589692i
\(19\) 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 0.881455 0.472269i \(-0.156565\pi\)
−0.849724 + 0.527228i \(0.823232\pi\)
\(24\) 4.00000 6.92820i 0.0340207 0.0589256i
\(25\) 38.0000 65.8179i 0.304000 0.526543i
\(26\) −66.0000 114.315i −0.497833 0.862273i
\(27\) −53.0000 −0.377772
\(28\) 0 0
\(29\) 106.000 0.678748 0.339374 0.940651i \(-0.389785\pi\)
0.339374 + 0.940651i \(0.389785\pi\)
\(30\) −7.00000 12.1244i −0.0426006 0.0737865i
\(31\) 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
\(33\) −17.5000 30.3109i −0.0923139 0.159892i
\(34\) 118.000 0.595201
\(35\) 0 0
\(36\) −104.000 −0.481481
\(37\) −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
\(39\) 33.0000 57.1577i 0.135493 0.234681i
\(40\) −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
\(45\) −91.0000 + 157.617i −0.301455 + 0.522136i
\(46\) −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 \(0.918821\pi\)
\(48\) 16.0000 0.0481125
\(49\) 0 0
\(50\) 152.000 0.429921
\(51\) 29.5000 + 51.0955i 0.0809966 + 0.140290i
\(52\) 132.000 228.631i 0.352021 0.609719i
\(53\) 208.500 361.133i 0.540371 0.935951i −0.458511 0.888689i \(-0.651617\pi\)
0.998883 0.0472619i \(-0.0150495\pi\)
\(54\) −53.0000 91.7987i −0.133563 0.231337i
\(55\) −245.000 −0.600651
\(56\) 0 0
\(57\) −137.000 −0.318353
\(58\) 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 \(0.172637\pi\)
\(60\) 14.0000 24.2487i 0.0301232 0.0521749i
\(61\) 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
\(66\) 35.0000 60.6218i 0.0652758 0.113061i
\(67\) −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
\(69\) −7.00000 −0.0122131
\(70\) 0 0
\(71\) −784.000 −1.31047 −0.655237 0.755423i \(-0.727431\pi\)
−0.655237 + 0.755423i \(0.727431\pi\)
\(72\) −104.000 180.133i −0.170229 0.294846i
\(73\) 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
\(75\) 38.0000 + 65.8179i 0.0585048 + 0.101333i
\(76\) −548.000 −0.827104
\(77\) 0 0
\(78\) 132.000 0.191616
\(79\) 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
\(81\) −324.500 + 562.050i −0.445130 + 0.770988i
\(82\) 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
\(87\) −53.0000 + 91.7987i −0.0653126 + 0.113125i
\(88\) 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 \(-0.340688\pi\)
\(90\) −364.000 −0.426322
\(91\) 0 0
\(92\) −28.0000 −0.0317305
\(93\) 37.5000 + 64.9519i 0.0418126 + 0.0724215i
\(94\) 171.000 296.181i 0.187631 0.324986i
\(95\) −479.500 + 830.518i −0.517849 + 0.896941i
\(96\) 16.0000 + 27.7128i 0.0170103 + 0.0294628i
\(97\) 290.000 0.303557 0.151779 0.988415i \(-0.451500\pi\)
0.151779 + 0.988415i \(0.451500\pi\)
\(98\) 0 0
\(99\) −910.000 −0.923823
\(100\) 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 \(0.987181\pi\)
\(102\) −59.0000 + 102.191i −0.0572732 + 0.0992002i
\(103\) 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 0.835416 0.549618i \(-0.185227\pi\)
−0.893691 + 0.448682i \(0.851893\pi\)
\(108\) 106.000 183.597i 0.0944431 0.163580i
\(109\) 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
\(111\) 11.0000 0.00940607
\(112\) 0 0
\(113\) −50.0000 −0.0416248 −0.0208124 0.999783i \(-0.506625\pi\)
−0.0208124 + 0.999783i \(0.506625\pi\)
\(114\) −137.000 237.291i −0.112555 0.194950i
\(115\) −24.5000 + 42.4352i −0.0198664 + 0.0344096i
\(116\) −212.000 + 367.195i −0.169687 + 0.293907i
\(117\) −858.000 1486.10i −0.677967 1.17427i
\(118\) −34.0000 −0.0265250
\(119\) 0 0
\(120\) 56.0000 0.0426006
\(121\) 53.0000 + 91.7987i 0.0398197 + 0.0689697i
\(122\) −51.0000 + 88.3346i −0.0378469 + 0.0655528i
\(123\) −249.000 + 431.281i −0.182533 + 0.316157i
\(124\) 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
\(129\) −130.000 + 225.167i −0.0887276 + 0.153681i
\(130\) 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 \(0.914347\pi\)
\(132\) 140.000 0.0923139
\(133\) 0 0
\(134\) −878.000 −0.566027
\(135\) −185.500 321.295i −0.118261 0.204835i
\(136\) −236.000 + 408.764i −0.148800 + 0.257730i
\(137\) 1178.50 2041.22i 0.734935 1.27294i −0.219817 0.975541i \(-0.570546\pi\)
0.954752 0.297403i \(-0.0961205\pi\)
\(138\) −7.00000 12.1244i −0.00431797 0.00747894i
\(139\) −28.0000 −0.0170858 −0.00854291 0.999964i \(-0.502719\pi\)
−0.00854291 + 0.999964i \(0.502719\pi\)
\(140\) 0 0
\(141\) 171.000 0.102133
\(142\) −784.000 1357.93i −0.463323 0.802498i
\(143\) 1155.00 2000.52i 0.675426 1.16987i
\(144\) 208.000 360.267i 0.120370 0.208488i
\(145\) 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 \(-0.949345\pi\)
0.356446 0.934316i \(-0.383988\pi\)
\(150\) −76.0000 + 131.636i −0.0413692 + 0.0716535i
\(151\) 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
\(153\) 1534.00 0.810566
\(154\) 0 0
\(155\) 525.000 0.272058
\(156\) 132.000 + 228.631i 0.0677465 + 0.117340i
\(157\) 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
\(159\) 208.500 + 361.133i 0.103995 + 0.180124i
\(160\) 224.000 0.110680
\(161\) 0 0
\(162\) −1298.00 −0.629509
\(163\) 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
\(165\) 122.500 212.176i 0.0577976 0.100108i
\(166\) −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
\(171\) −1781.00 + 3084.78i −0.796471 + 1.37953i
\(172\) −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 \(0.720546\pi\)
\(174\) −212.000 −0.0923660
\(175\) 0 0
\(176\) 560.000 0.239839
\(177\) −8.50000 14.7224i −0.00360960 0.00625201i
\(178\) 873.000 1512.08i 0.367607 0.636715i
\(179\) −1225.50 + 2122.63i −0.511722 + 0.886328i 0.488186 + 0.872740i \(0.337659\pi\)
−0.999908 + 0.0135883i \(0.995675\pi\)
\(180\) −364.000 630.466i −0.150728 0.261068i
\(181\) 1170.00 0.480472 0.240236 0.970715i \(-0.422775\pi\)
0.240236 + 0.970715i \(0.422775\pi\)
\(182\) 0 0
\(183\) −51.0000 −0.0206012
\(184\) −28.0000 48.4974i −0.0112184 0.0194309i
\(185\) 38.5000 66.6840i 0.0153004 0.0265011i
\(186\) −75.0000 + 129.904i −0.0295660 + 0.0512097i
\(187\) 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 \(-0.0890249\pi\)
−0.719637 + 0.694351i \(0.755692\pi\)
\(192\) −32.0000 + 55.4256i −0.0120281 + 0.0208333i
\(193\) −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
\(195\) 462.000 0.169664
\(196\) 0 0
\(197\) −2734.00 −0.988779 −0.494389 0.869241i \(-0.664608\pi\)
−0.494389 + 0.869241i \(0.664608\pi\)
\(198\) −910.000 1576.17i −0.326621 0.565724i
\(199\) 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
\(201\) −219.500 380.185i −0.0770265 0.133414i
\(202\) −2170.00 −0.755845
\(203\) 0 0
\(204\) −236.000 −0.0809966
\(205\) 1743.00 + 3018.96i 0.593836 + 1.02855i
\(206\) −1553.00 + 2689.87i −0.525256 + 0.909769i
\(207\) −91.0000 + 157.617i −0.0305553 + 0.0529232i
\(208\) 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
\(213\) 392.000 678.964i 0.126100 0.218412i
\(214\) 129.000 223.435i 0.0412068 0.0713723i
\(215\) 910.000 + 1576.17i 0.288658 + 0.499970i
\(216\) 424.000 0.133563
\(217\) 0 0
\(218\) 1930.00 0.599615
\(219\) 147.500 + 255.477i 0.0455120 + 0.0788291i
\(220\) 490.000 848.705i 0.150163 0.260089i
\(221\) −1947.00 + 3372.30i −0.592622 + 1.02645i
\(222\) 11.0000 + 19.0526i 0.00332555 + 0.00576002i
\(223\) −2024.00 −0.607790 −0.303895 0.952706i \(-0.598287\pi\)
−0.303895 + 0.952706i \(0.598287\pi\)
\(224\) 0 0
\(225\) 1976.00 0.585481
\(226\) −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 \(0.0440119\pi\)
\(228\) 274.000 474.582i 0.0795881 0.137851i
\(229\) 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 0.712639 0.701531i \(-0.247500\pi\)
−0.963863 + 0.266398i \(0.914166\pi\)
\(234\) 1716.00 2972.20i 0.479395 0.830336i
\(235\) 598.500 1036.63i 0.166135 0.287755i
\(236\) −34.0000 58.8897i −0.00937801 0.0162432i
\(237\) −495.000 −0.135670
\(238\) 0 0
\(239\) −5100.00 −1.38030 −0.690150 0.723667i \(-0.742455\pi\)
−0.690150 + 0.723667i \(0.742455\pi\)
\(240\) 56.0000 + 96.9948i 0.0150616 + 0.0260875i
\(241\) −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
\(243\) −1040.00 1801.33i −0.274552 0.475537i
\(244\) −204.000 −0.0535236
\(245\) 0 0
\(246\) −996.000 −0.258141
\(247\) −4521.00 7830.60i −1.16463 2.01720i
\(248\) −300.000 + 519.615i −0.0768146 + 0.133047i
\(249\) 466.000 807.136i 0.118601 0.205422i
\(250\) 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
\(255\) −206.500 + 357.668i −0.0507119 + 0.0878356i
\(256\) −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 \(0.901414\pi\)
\(258\) −520.000 −0.125480
\(259\) 0 0
\(260\) 1848.00 0.440800
\(261\) 1378.00 + 2386.77i 0.326805 + 0.566043i
\(262\) 755.000 1307.70i 0.178031 0.308358i
\(263\) 2236.50 3873.73i 0.524367 0.908230i −0.475231 0.879861i \(-0.657635\pi\)
0.999598 0.0283689i \(-0.00903130\pi\)
\(264\) 140.000 + 242.487i 0.0326379 + 0.0565305i
\(265\) 2919.00 0.676652
\(266\) 0 0
\(267\) 873.000 0.200100
\(268\) −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 \(0.0948122\pi\)
\(270\) 371.000 642.591i 0.0836235 0.144840i
\(271\) −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
\(276\) 14.0000 24.2487i 0.00305326 0.00528841i
\(277\) −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
\(279\) 1950.00 0.418435
\(280\) 0 0
\(281\) −202.000 −0.0428837 −0.0214418 0.999770i \(-0.506826\pi\)
−0.0214418 + 0.999770i \(0.506826\pi\)
\(282\) 171.000 + 296.181i 0.0361096 + 0.0625436i
\(283\) −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
\(285\) −479.500 830.518i −0.0996601 0.172616i
\(286\) 4620.00 0.955197
\(287\) 0 0
\(288\) 832.000 0.170229
\(289\) 716.000 + 1240.15i 0.145736 + 0.252422i
\(290\) −742.000 + 1285.18i −0.150247 + 0.260236i
\(291\) −145.000 + 251.147i −0.0292098 + 0.0505929i
\(292\) 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
\(297\) 927.500 1606.48i 0.181209 0.313863i
\(298\) 2295.00 3975.06i 0.446127 0.772714i
\(299\) −231.000 400.104i −0.0446792 0.0773866i
\(300\) −304.000 −0.0585048
\(301\) 0 0
\(302\) 2218.00 0.422621
\(303\) −542.500 939.638i −0.102857 0.178154i
\(304\) 1096.00 1898.33i 0.206776 0.358147i
\(305\) −178.500 + 309.171i −0.0335111 + 0.0580429i
\(306\) 1534.00 + 2656.97i 0.286578 + 0.496368i
\(307\) 8132.00 1.51178 0.755892 0.654696i \(-0.227203\pi\)
0.755892 + 0.654696i \(0.227203\pi\)
\(308\) 0 0
\(309\) −1553.00 −0.285913
\(310\) 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 \(0.193657\pi\)
\(312\) −264.000 + 457.261i −0.0479040 + 0.0829722i
\(313\) −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 \(-0.949012\pi\)
0.355468 0.934689i \(-0.384322\pi\)
\(318\) −417.000 + 722.265i −0.0735352 + 0.127367i
\(319\) −1855.00 + 3212.95i −0.325580 + 0.563921i
\(320\) 224.000 + 387.979i 0.0391312 + 0.0677772i
\(321\) 129.000 0.0224301
\(322\) 0 0
\(323\) 8083.00 1.39242
\(324\) −1298.00 2248.20i −0.222565 0.385494i
\(325\) −2508.00 + 4343.98i −0.428058 + 0.741418i
\(326\) −2251.00 + 3898.85i −0.382427 + 0.662384i
\(327\) 482.500 + 835.715i 0.0815973 + 0.141331i
\(328\) −3984.00 −0.670670
\(329\) 0 0
\(330\) 490.000 0.0817382
\(331\) 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
\(333\) 143.000 247.683i 0.0235326 0.0407596i
\(334\) −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
\(339\) 25.0000 43.3013i 0.00400535 0.00693747i
\(340\) −826.000 + 1430.67i −0.131753 + 0.228203i
\(341\) 1312.50 + 2273.32i 0.208434 + 0.361018i
\(342\) −7124.00 −1.12638
\(343\) 0 0
\(344\) −2080.00 −0.326006
\(345\) −24.5000 42.4352i −0.00382329 0.00662214i
\(346\) −1579.00 + 2734.91i −0.245340 + 0.424941i
\(347\) 4888.50 8467.13i 0.756278 1.30991i −0.188459 0.982081i \(-0.560349\pi\)
0.944737 0.327831i \(-0.106318\pi\)
\(348\) −212.000 367.195i −0.0326563 0.0565624i
\(349\) −11914.0 −1.82734 −0.913670 0.406456i \(-0.866764\pi\)
−0.913670 + 0.406456i \(0.866764\pi\)
\(350\) 0 0
\(351\) 3498.00 0.531936
\(352\) 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 \(-0.0747452\pi\)
\(354\) 17.0000 29.4449i 0.00255237 0.00442084i
\(355\) −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 \(-0.962228\pi\)
0.393960 0.919128i \(-0.371105\pi\)
\(360\) 728.000 1260.93i 0.106580 0.184603i
\(361\) −5955.00 + 10314.4i −0.868202 + 1.50377i
\(362\) 1170.00 + 2026.50i 0.169872 + 0.294228i
\(363\) −106.000 −0.0153266
\(364\) 0 0
\(365\) 2065.00 0.296129
\(366\) −51.0000 88.3346i −0.00728364 0.0126156i
\(367\) 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
\(369\) 6474.00 + 11213.3i 0.913341 + 1.58195i
\(370\) 154.000 0.0216381
\(371\) 0 0
\(372\) −300.000 −0.0418126
\(373\) 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
\(375\) −703.500 + 1218.50i −0.0968762 + 0.167795i
\(376\) 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
\(381\) −468.000 + 810.600i −0.0629301 + 0.108998i
\(382\) −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 \(0.635805\pi\)
\(384\) −128.000 −0.0170103
\(385\) 0 0
\(386\) −70.0000 −0.00923033
\(387\) 3380.00 + 5854.33i 0.443967 + 0.768973i
\(388\) −580.000 + 1004.59i −0.0758893 + 0.131444i
\(389\) −81.5000 + 141.162i −0.0106227 + 0.0183990i −0.871288 0.490772i \(-0.836715\pi\)
0.860665 + 0.509171i \(0.170048\pi\)
\(390\) 462.000 + 800.207i 0.0599853 + 0.103898i
\(391\) 413.000 0.0534177
\(392\) 0 0
\(393\) 755.000 0.0969077
\(394\) −2734.00 4735.43i −0.349586 0.605501i
\(395\) −1732.50 + 3000.78i −0.220687 + 0.382242i
\(396\) 1820.00 3152.33i 0.230956 0.400027i
\(397\) 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 \(0.204226\pi\)
0.117722 + 0.993047i \(0.462441\pi\)
\(402\) 439.000 760.370i 0.0544660 0.0943379i
\(403\) −2475.00 + 4286.83i −0.305927 + 0.529881i
\(404\) −2170.00 3758.55i −0.267232 0.462859i
\(405\) −4543.00 −0.557391
\(406\) 0 0
\(407\) 385.000 0.0468888
\(408\) −236.000 408.764i −0.0286366 0.0496001i
\(409\) −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
\(411\) 1178.50 + 2041.22i 0.141438 + 0.244978i
\(412\) −6212.00 −0.742823
\(413\) 0 0
\(414\) −364.000 −0.0432117
\(415\) −3262.00 5649.95i −0.385844 0.668302i
\(416\) −1056.00 + 1829.05i −0.124458 + 0.215568i
\(417\) 14.0000 24.2487i 0.00164408 0.00284764i
\(418\) −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
\(423\) 2223.00 3850.35i 0.255522 0.442578i
\(424\) −1668.00 + 2889.06i −0.191050 + 0.330908i
\(425\) −2242.00 3883.26i −0.255889 0.443213i
\(426\) 1568.00 0.178333
\(427\) 0 0
\(428\) 516.000 0.0582752
\(429\) 1155.00 + 2000.52i 0.129986 + 0.225142i
\(430\) −1820.00 + 3152.33i −0.204112 + 0.353532i
\(431\) 7606.50 13174.8i 0.850098 1.47241i −0.0310213 0.999519i \(-0.509876\pi\)
0.881119 0.472894i \(-0.156791\pi\)
\(432\) 424.000 + 734.390i 0.0472215 + 0.0817901i
\(433\) 1378.00 0.152939 0.0764693 0.997072i \(-0.475635\pi\)
0.0764693 + 0.997072i \(0.475635\pi\)
\(434\) 0 0
\(435\) −742.000 −0.0817843
\(436\) 1930.00 + 3342.86i 0.211996 + 0.367188i
\(437\) −479.500 + 830.518i −0.0524888 + 0.0909132i
\(438\) −295.000 + 510.955i −0.0321818 + 0.0557406i
\(439\) −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 0.665499 0.746399i \(-0.268219\pi\)
−0.979150 + 0.203140i \(0.934885\pi\)
\(444\) −22.0000 + 38.1051i −0.00235152 + 0.00407295i
\(445\) 3055.50 5292.28i 0.325493 0.563771i
\(446\) −2024.00 3505.67i −0.214886 0.372194i
\(447\) 2295.00 0.242841
\(448\) 0 0
\(449\) 4582.00 0.481599 0.240799 0.970575i \(-0.422590\pi\)
0.240799 + 0.970575i \(0.422590\pi\)
\(450\) 1976.00 + 3422.53i 0.206999 + 0.358533i
\(451\) −8715.00 + 15094.8i −0.909919 + 1.57603i
\(452\) 100.000 173.205i 0.0104062 0.0180241i
\(453\) 554.500 + 960.422i 0.0575114 + 0.0996127i
\(454\) 5142.00 0.531555
\(455\) 0 0
\(456\) 1096.00 0.112555
\(457\) −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
\(459\) −1563.50 + 2708.06i −0.158993 + 0.275384i
\(460\) −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
\(465\) −262.500 + 454.663i −0.0261788 + 0.0453430i
\(466\) 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 \(0.853960\pi\)
\(468\) 6864.00 0.677967
\(469\) 0 0
\(470\) 2394.00 0.234951
\(471\) 779.500 + 1350.13i 0.0762579 + 0.132083i
\(472\) 68.0000 117.779i 0.00663126 0.0114857i
\(473\) −4550.00 + 7880.83i −0.442303 + 0.766091i
\(474\) −495.000 857.365i −0.0479665 0.0830803i
\(475\) 10412.0 1.00576
\(476\) 0 0
\(477\) 10842.0 1.04072
\(478\) −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 \(-0.170632\pi\)
\(480\) −112.000 + 193.990i −0.0106502 + 0.0184466i
\(481\) 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
\(486\) 2080.00 3602.67i 0.194137 0.336256i
\(487\) 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
\(489\) −2251.00 −0.208167
\(490\) 0 0
\(491\) 14352.0 1.31914 0.659569 0.751644i \(-0.270739\pi\)
0.659569 + 0.751644i \(0.270739\pi\)
\(492\) −996.000 1725.12i −0.0912666 0.158078i
\(493\) 3127.00 5416.12i 0.285665 0.494787i
\(494\) 9042.00 15661.2i 0.823520 1.42638i
\(495\) −3185.00 5516.58i −0.289202 0.500913i
\(496\) −1200.00 −0.108632
\(497\) 0 0
\(498\) 1864.00 0.167727
\(499\) 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
\(501\) 1394.00 2414.48i 0.124310 0.215311i
\(502\) 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
\(507\) −1079.50 + 1869.75i −0.0945607 + 0.163784i
\(508\) −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 \(0.866448\pi\)
\(510\) −826.000 −0.0717174
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) −3630.50 6288.21i −0.312457 0.541192i
\(514\) 1749.00 3029.36i 0.150088 0.259960i
\(515\) −5435.50 + 9414.56i −0.465081 + 0.805544i
\(516\) −520.000 900.666i −0.0443638 0.0768404i
\(517\) 5985.00 0.509130
\(518\) 0 0
\(519\) −1579.00 −0.133546
\(520\) 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 \(0.292409\pi\)
\(522\) −2756.00 + 4773.53i −0.231086 + 0.400253i
\(523\) −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
\(528\) −280.000 + 484.974i −0.0230785 + 0.0399731i
\(529\) 6059.00 10494.5i 0.497986 0.862538i
\(530\) 2919.00 + 5055.86i 0.239233 + 0.414363i
\(531\) −442.000 −0.0361227
\(532\) 0 0
\(533\) −32868.0 −2.67105
\(534\) 873.000 + 1512.08i 0.0707461 + 0.122536i
\(535\) 451.500 782.021i 0.0364861 0.0631957i
\(536\) 1756.00 3041.48i 0.141507 0.245097i
\(537\) −1225.50 2122.63i −0.0984809 0.170574i
\(538\) 3950.00 0.316536
\(539\) 0 0
\(540\) 1484.00 0.118261
\(541\) −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
\(543\) −585.000 + 1013.25i −0.0462334 + 0.0800787i
\(544\) −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
\(549\) −663.000 + 1148.35i −0.0515413 + 0.0892721i
\(550\) −2660.00 + 4607.26i −0.206223 + 0.357189i
\(551\) 7261.00 + 12576.4i 0.561396 + 0.972366i
\(552\) 56.0000 0.00431797
\(553\) 0 0
\(554\) −1054.00 −0.0808306
\(555\) 38.5000 + 66.6840i 0.00294457 + 0.00510014i
\(556\) 56.0000 96.9948i 0.00427146 0.00739838i
\(557\) −3501.50 + 6064.78i −0.266361 + 0.461352i −0.967919 0.251261i \(-0.919155\pi\)
0.701558 + 0.712612i \(0.252488\pi\)
\(558\) 1950.00 + 3377.50i 0.147939 + 0.256238i
\(559\) −17160.0 −1.29837
\(560\) 0 0
\(561\) −2065.00 −0.155409
\(562\) −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 \(0.901807\pi\)
\(564\) −342.000 + 592.361i −0.0255333 + 0.0442250i
\(565\) −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 \(-0.0848957\pi\)
−0.710569 + 0.703628i \(0.751562\pi\)
\(570\) 959.000 1661.04i 0.0704703 0.122058i
\(571\) −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
\(573\) −1275.00 −0.0929562
\(574\) 0 0
\(575\) 532.000 0.0385842
\(576\) 832.000 + 1441.07i 0.0601852 + 0.104244i
\(577\) 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
\(579\) −17.5000 30.3109i −0.00125609 0.00217561i
\(580\) −2968.00 −0.212482
\(581\) 0 0
\(582\) −580.000 −0.0413089
\(583\) 7297.50 + 12639.6i 0.518407 + 0.897908i
\(584\) −1180.00 + 2043.82i −0.0836109 + 0.144818i
\(585\) 6006.00 10402.7i 0.424474 0.735211i
\(586\) −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
\(591\) 1367.00 2367.71i 0.0951453 0.164796i
\(592\) −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 \(0.954154\pi\)
\(594\) 3710.00 0.256268
\(595\) 0 0
\(596\) 9180.00 0.630919
\(597\) 1121.50 + 1942.49i 0.0768843 + 0.133168i
\(598\) 462.000 800.207i 0.0315930 0.0547206i
\(599\) −10399.5 + 18012.5i −0.709369 + 1.22866i 0.255722 + 0.966750i \(0.417687\pi\)
−0.965091 + 0.261913i \(0.915647\pi\)
\(600\) −304.000 526.543i −0.0206846 0.0358267i
\(601\) 1402.00 0.0951560 0.0475780 0.998868i \(-0.484850\pi\)
0.0475780 + 0.998868i \(0.484850\pi\)
\(602\) 0 0
\(603\) −11414.0 −0.770836
\(604\) 2218.00 + 3841.69i 0.149419 + 0.258801i
\(605\) −371.000 + 642.591i −0.0249311 + 0.0431819i
\(606\) 1085.00 1879.28i 0.0727312 0.125974i
\(607\) 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
\(612\) −3068.00 + 5313.93i −0.202641 + 0.350985i
\(613\) −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
\(615\) −3486.00 −0.228568
\(616\) 0 0
\(617\) 11150.0 0.727524 0.363762 0.931492i \(-0.381492\pi\)
0.363762 + 0.931492i \(0.381492\pi\)
\(618\) −1553.00 2689.87i −0.101085 0.175085i
\(619\) 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
\(621\) −185.500 321.295i −0.0119869 0.0207619i
\(622\) −1858.00 −0.119773
\(623\) 0 0
\(624\) −1056.00 −0.0677465
\(625\) 174.500 + 302.243i 0.0111680 + 0.0193435i
\(626\) 209.000 361.999i 0.0133440 0.0231124i
\(627\) 2397.50 4152.59i 0.152706 0.264495i
\(628\) 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
\(633\) −586.000 + 1014.98i −0.0367953 + 0.0637313i
\(634\) 7131.00 12351.3i 0.446701 0.773708i
\(635\) 3276.00 + 5674.20i 0.204731 + 0.354604i
\(636\) −1668.00 −0.103995
\(637\) 0 0
\(638\) −7420.00 −0.460440
\(639\) −10192.0 17653.1i −0.630969 1.09287i
\(640\) −448.000 + 775.959i −0.0276699 + 0.0479257i
\(641\) 5352.50 9270.80i 0.329814 0.571255i −0.652660 0.757651i \(-0.726347\pi\)
0.982475 + 0.186395i \(0.0596805\pi\)
\(642\) 129.000 + 223.435i 0.00793026 + 0.0137356i
\(643\) −6860.00 −0.420734 −0.210367 0.977622i \(-0.567466\pi\)
−0.210367 + 0.977622i \(0.567466\pi\)
\(644\) 0 0
\(645\) −1820.00 −0.111105
\(646\) 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 \(0.0218535\pi\)
\(648\) 2596.00 4496.40i 0.157377 0.272586i
\(649\) −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 \(-0.224003\pi\)
−0.941591 + 0.336758i \(0.890670\pi\)
\(654\) −965.000 + 1671.43i −0.0576980 + 0.0999359i
\(655\) 2642.50 4576.94i 0.157635 0.273032i
\(656\) −3984.00 6900.49i −0.237117 0.410700i
\(657\) 7670.00 0.455457
\(658\) 0 0
\(659\) −6940.00 −0.410234 −0.205117 0.978737i \(-0.565757\pi\)
−0.205117 + 0.978737i \(0.565757\pi\)
\(660\) 490.000 + 848.705i 0.0288988 + 0.0500542i
\(661\) 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
\(663\) −1947.00 3372.30i −0.114050 0.197541i
\(664\) 7456.00 0.435766
\(665\) 0 0
\(666\) 572.000 0.0332801
\(667\) 371.000 + 642.591i 0.0215370 + 0.0373032i
\(668\) 5576.00 9657.92i 0.322967 0.559395i
\(669\) 1012.00 1752.84i 0.0584846 0.101298i
\(670\) −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
\(675\) −2014.00 + 3488.35i −0.114843 + 0.198914i
\(676\) −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 \(-0.430913\pi\)
\(678\) 100.000 0.00566442
\(679\) 0 0
\(680\) −3304.00 −0.186327
\(681\) 1285.50 + 2226.55i 0.0723355 + 0.125289i
\(682\) −2625.00 + 4546.63i −0.147385 + 0.255278i
\(683\) 4402.50 7625.35i 0.246643 0.427198i −0.715949 0.698152i \(-0.754006\pi\)
0.962592 + 0.270954i \(0.0873393\pi\)
\(684\) −7124.00 12339.1i −0.398235 0.689764i
\(685\) 16499.0 0.920284
\(686\) 0 0
\(687\) −895.000 −0.0497036
\(688\) −2080.00 3602.67i −0.115261 0.199637i
\(689\) −13761.0 + 23834.8i −0.760889 + 1.31790i
\(690\) 49.0000 84.8705i 0.00270348 0.00468256i
\(691\) 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
\(696\) 424.000 734.390i 0.0230915 0.0399956i
\(697\) 14691.0 25445.6i 0.798366 1.38281i
\(698\) −11914.0 20635.7i −0.646062 1.11901i
\(699\) 1787.00 0.0966961
\(700\) 0 0
\(701\) −3146.00 −0.169505 −0.0847523 0.996402i \(-0.527010\pi\)
−0.0847523 + 0.996402i \(0.527010\pi\)
\(702\) 3498.00 + 6058.71i 0.188068 + 0.325743i
\(703\) 753.500 1305.10i 0.0404250 0.0700182i
\(704\) −1120.00 + 1939.90i −0.0599596 + 0.103853i
\(705\) 598.500 + 1036.63i 0.0319728 + 0.0553785i
\(706\) 18246.0 0.972659
\(707\) 0 0
\(708\) 68.0000 0.00360960
\(709\) −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
\(711\) −6435.00 + 11145.7i −0.339425 + 0.587902i
\(712\) 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
\(717\) 2550.00 4416.73i 0.132819 0.230050i
\(718\) 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 \(0.693265\pi\)
\(720\) 2912.00 0.150728
\(721\) 0 0
\(722\) −23820.0 −1.22782
\(723\) −2088.50 3617.39i −0.107430 0.186075i
\(724\) −2340.00 + 4053.00i −0.120118 + 0.208050i
\(725\) 4028.00 6976.70i 0.206340 0.357391i
\(726\) −106.000 183.597i −0.00541877 0.00938559i
\(727\) 6032.00 0.307723 0.153861 0.988092i \(-0.450829\pi\)
0.153861 + 0.988092i \(0.450829\pi\)
\(728\) 0 0
\(729\) −15443.0 −0.784586
\(730\) 2065.00 + 3576.68i 0.104697 + 0.181341i
\(731\) 7670.00 13284.8i 0.388078 0.672171i
\(732\) 102.000 176.669i 0.00515031 0.00892060i
\(733\) 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
\(738\) −12948.0 + 22426.6i −0.645830 + 1.11861i
\(739\) 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
\(741\) 9042.00 0.448267
\(742\) 0 0
\(743\) 24384.0 1.20399 0.601993 0.798501i \(-0.294373\pi\)
0.601993 + 0.798501i \(0.294373\pi\)
\(744\) −300.000 519.615i −0.0147830 0.0256049i
\(745\) 8032.50 13912.7i 0.395017 0.684190i
\(746\) −4109.00 + 7117.00i −0.201664 + 0.349292i
\(747\) −12116.0 20985.5i −0.593442 1.02787i
\(748\) −8260.00 −0.403764
\(749\) 0 0
\(750\) −2814.00 −0.137004
\(751\) −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
\(753\) −2340.00 + 4053.00i −0.113246 + 0.196148i
\(754\) −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
\(759\) 122.500 212.176i 0.00585832 0.0101469i
\(760\) 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 \(-0.349076\pi\)
\(762\) −1872.00 −0.0889966
\(763\) 0 0
\(764\) −5100.00 −0.241507
\(765\) 5369.00 + 9299.38i 0.253747 + 0.439503i
\(766\) −8717.00 + 15098.3i −0.411172 + 0.712171i
\(767\) 561.000 971.681i 0.0264101 0.0457436i
\(768\) −128.000 221.703i −0.00601407 0.0104167i
\(769\) −3766.00 −0.176600 −0.0883000 0.996094i \(-0.528143\pi\)
−0.0883000 + 0.996094i \(0.528143\pi\)
\(770\) 0 0
\(771\) 1749.00 0.0816974
\(772\) −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 \(0.951799\pi\)
\(774\) −6760.00 + 11708.7i −0.313932 + 0.543746i
\(775\) −2850.00 4936.34i −0.132097 0.228798i
\(776\) −2320.00 −0.107324
\(777\)