Properties

Label 225.4.k.a.124.3
Level $225$
Weight $4$
Character 225.124
Analytic conductor $13.275$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.303595776.1
Defining polynomial: \(x^{8} + 5 x^{6} + 16 x^{4} + 45 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 124.3
Root \(1.26217 + 1.18614i\) of defining polynomial
Character \(\chi\) \(=\) 225.124
Dual form 225.4.k.a.49.3

$q$-expansion

\(f(q)\) \(=\) \(q+(2.05446 + 1.18614i) q^{2} +(-4.97494 - 1.50000i) q^{3} +(-1.18614 - 2.05446i) q^{4} +(-8.44158 - 8.98266i) q^{6} +(6.38458 + 3.68614i) q^{7} -24.6060i q^{8} +(22.5000 + 14.9248i) q^{9} +O(q^{10})\) \(q+(2.05446 + 1.18614i) q^{2} +(-4.97494 - 1.50000i) q^{3} +(-1.18614 - 2.05446i) q^{4} +(-8.44158 - 8.98266i) q^{6} +(6.38458 + 3.68614i) q^{7} -24.6060i q^{8} +(22.5000 + 14.9248i) q^{9} +(2.06930 - 3.58413i) q^{11} +(2.81929 + 12.0000i) q^{12} +(-68.3972 + 39.4891i) q^{13} +(8.74456 + 15.1460i) q^{14} +(19.6970 - 34.1162i) q^{16} +33.3070i q^{17} +(28.5223 + 57.3505i) q^{18} -89.3070 q^{19} +(-26.2337 - 27.9152i) q^{21} +(8.50256 - 4.90895i) q^{22} +(-172.826 + 99.7812i) q^{23} +(-36.9090 + 122.413i) q^{24} -187.359 q^{26} +(-89.5489 - 108.000i) q^{27} -17.4891i q^{28} +(25.2405 - 43.7179i) q^{29} +(3.00000 + 5.19615i) q^{31} +(-89.5419 + 51.6970i) q^{32} +(-15.6708 + 14.7269i) q^{33} +(-39.5068 + 68.4278i) q^{34} +(3.97420 - 63.9282i) q^{36} +290.277i q^{37} +(-183.477 - 105.931i) q^{38} +(399.505 - 93.8602i) q^{39} +(26.6684 + 46.1911i) q^{41} +(-20.7846 - 88.4674i) q^{42} +(258.412 + 149.194i) q^{43} -9.81791 q^{44} -473.418 q^{46} +(-362.782 - 209.452i) q^{47} +(-149.166 + 140.181i) q^{48} +(-144.325 - 249.978i) q^{49} +(49.9605 - 165.700i) q^{51} +(162.257 + 93.6793i) q^{52} +399.228i q^{53} +(-55.8710 - 328.099i) q^{54} +(90.7011 - 157.099i) q^{56} +(444.297 + 133.961i) q^{57} +(103.711 - 59.8776i) q^{58} +(49.1209 + 85.0799i) q^{59} +(341.797 - 592.011i) q^{61} +14.2337i q^{62} +(88.6382 + 178.227i) q^{63} -560.432 q^{64} +(-49.6631 + 11.6679i) q^{66} +(-195.289 + 112.750i) q^{67} +(68.4278 - 39.5068i) q^{68} +(1009.47 - 237.166i) q^{69} +512.951 q^{71} +(367.239 - 553.634i) q^{72} -994.318i q^{73} +(-344.310 + 596.362i) q^{74} +(105.931 + 183.477i) q^{76} +(26.4232 - 15.2554i) q^{77} +(932.097 + 281.038i) q^{78} +(-100.853 + 174.683i) q^{79} +(283.500 + 671.617i) q^{81} +126.530i q^{82} +(-959.247 - 553.822i) q^{83} +(-26.2337 + 87.0073i) q^{84} +(353.931 + 613.026i) q^{86} +(-191.147 + 179.633i) q^{87} +(-88.1909 - 50.9171i) q^{88} -372.269 q^{89} -582.250 q^{91} +(409.992 + 236.709i) q^{92} +(-7.13058 - 30.3505i) q^{93} +(-496.880 - 860.622i) q^{94} +(523.011 - 122.877i) q^{96} +(-120.578 - 69.6156i) q^{97} -684.758i q^{98} +(100.052 - 49.7590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{4} - 102 q^{6} + 180 q^{9} + O(q^{10}) \) \( 8 q + 2 q^{4} - 102 q^{6} + 180 q^{9} + 74 q^{11} + 24 q^{14} + 238 q^{16} - 140 q^{19} - 72 q^{21} - 54 q^{24} - 304 q^{26} + 650 q^{29} + 24 q^{31} - 902 q^{34} + 342 q^{36} + 1128 q^{39} - 476 q^{41} + 404 q^{44} - 984 q^{46} - 1258 q^{49} - 462 q^{51} - 1998 q^{54} + 312 q^{56} - 170 q^{59} + 494 q^{61} - 2852 q^{64} - 1776 q^{66} + 3078 q^{69} + 1576 q^{71} + 968 q^{74} + 790 q^{76} - 1680 q^{79} + 2268 q^{81} - 72 q^{84} + 2774 q^{86} + 4260 q^{89} - 2544 q^{91} + 1264 q^{94} + 48 q^{96} + 180 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.05446 + 1.18614i 0.726360 + 0.419364i 0.817089 0.576512i \(-0.195586\pi\)
−0.0907292 + 0.995876i \(0.528920\pi\)
\(3\) −4.97494 1.50000i −0.957427 0.288675i
\(4\) −1.18614 2.05446i −0.148268 0.256807i
\(5\) 0 0
\(6\) −8.44158 8.98266i −0.574377 0.611193i
\(7\) 6.38458 + 3.68614i 0.344735 + 0.199033i 0.662364 0.749182i \(-0.269553\pi\)
−0.317629 + 0.948215i \(0.602887\pi\)
\(8\) 24.6060i 1.08744i
\(9\) 22.5000 + 14.9248i 0.833333 + 0.552771i
\(10\) 0 0
\(11\) 2.06930 3.58413i 0.0567197 0.0982414i −0.836271 0.548316i \(-0.815269\pi\)
0.892991 + 0.450074i \(0.148603\pi\)
\(12\) 2.81929 + 12.0000i 0.0678216 + 0.288675i
\(13\) −68.3972 + 39.4891i −1.45923 + 0.842486i −0.998973 0.0453014i \(-0.985575\pi\)
−0.460254 + 0.887787i \(0.652242\pi\)
\(14\) 8.74456 + 15.1460i 0.166934 + 0.289139i
\(15\) 0 0
\(16\) 19.6970 34.1162i 0.307766 0.533066i
\(17\) 33.3070i 0.475185i 0.971365 + 0.237592i \(0.0763583\pi\)
−0.971365 + 0.237592i \(0.923642\pi\)
\(18\) 28.5223 + 57.3505i 0.373488 + 0.750981i
\(19\) −89.3070 −1.07834 −0.539169 0.842197i \(-0.681262\pi\)
−0.539169 + 0.842197i \(0.681262\pi\)
\(20\) 0 0
\(21\) −26.2337 27.9152i −0.272603 0.290076i
\(22\) 8.50256 4.90895i 0.0823978 0.0475724i
\(23\) −172.826 + 99.7812i −1.56682 + 0.904601i −0.570278 + 0.821452i \(0.693165\pi\)
−0.996537 + 0.0831494i \(0.973502\pi\)
\(24\) −36.9090 + 122.413i −0.313917 + 1.04114i
\(25\) 0 0
\(26\) −187.359 −1.41323
\(27\) −89.5489 108.000i −0.638285 0.769800i
\(28\) 17.4891i 0.118041i
\(29\) 25.2405 43.7179i 0.161622 0.279938i −0.773828 0.633395i \(-0.781661\pi\)
0.935451 + 0.353457i \(0.114994\pi\)
\(30\) 0 0
\(31\) 3.00000 + 5.19615i 0.0173812 + 0.0301050i 0.874585 0.484872i \(-0.161134\pi\)
−0.857204 + 0.514977i \(0.827800\pi\)
\(32\) −89.5419 + 51.6970i −0.494654 + 0.285588i
\(33\) −15.6708 + 14.7269i −0.0826648 + 0.0776854i
\(34\) −39.5068 + 68.4278i −0.199275 + 0.345155i
\(35\) 0 0
\(36\) 3.97420 63.9282i 0.0183991 0.295964i
\(37\) 290.277i 1.28976i 0.764282 + 0.644882i \(0.223094\pi\)
−0.764282 + 0.644882i \(0.776906\pi\)
\(38\) −183.477 105.931i −0.783262 0.452217i
\(39\) 399.505 93.8602i 1.64031 0.385376i
\(40\) 0 0
\(41\) 26.6684 + 46.1911i 0.101583 + 0.175947i 0.912337 0.409440i \(-0.134276\pi\)
−0.810754 + 0.585387i \(0.800943\pi\)
\(42\) −20.7846 88.4674i −0.0763604 0.325019i
\(43\) 258.412 + 149.194i 0.916453 + 0.529114i 0.882502 0.470309i \(-0.155858\pi\)
0.0339510 + 0.999424i \(0.489191\pi\)
\(44\) −9.81791 −0.0336388
\(45\) 0 0
\(46\) −473.418 −1.51743
\(47\) −362.782 209.452i −1.12590 0.650038i −0.182998 0.983113i \(-0.558580\pi\)
−0.942900 + 0.333075i \(0.891914\pi\)
\(48\) −149.166 + 140.181i −0.448546 + 0.421528i
\(49\) −144.325 249.978i −0.420772 0.728798i
\(50\) 0 0
\(51\) 49.9605 165.700i 0.137174 0.454955i
\(52\) 162.257 + 93.6793i 0.432712 + 0.249827i
\(53\) 399.228i 1.03468i 0.855779 + 0.517342i \(0.173078\pi\)
−0.855779 + 0.517342i \(0.826922\pi\)
\(54\) −55.8710 328.099i −0.140798 0.826826i
\(55\) 0 0
\(56\) 90.7011 157.099i 0.216436 0.374879i
\(57\) 444.297 + 133.961i 1.03243 + 0.311290i
\(58\) 103.711 59.8776i 0.234792 0.135557i
\(59\) 49.1209 + 85.0799i 0.108390 + 0.187737i 0.915118 0.403186i \(-0.132097\pi\)
−0.806728 + 0.590923i \(0.798764\pi\)
\(60\) 0 0
\(61\) 341.797 592.011i 0.717421 1.24261i −0.244597 0.969625i \(-0.578656\pi\)
0.962018 0.272985i \(-0.0880109\pi\)
\(62\) 14.2337i 0.0291561i
\(63\) 88.6382 + 178.227i 0.177260 + 0.356420i
\(64\) −560.432 −1.09459
\(65\) 0 0
\(66\) −49.6631 + 11.6679i −0.0926228 + 0.0217609i
\(67\) −195.289 + 112.750i −0.356094 + 0.205591i −0.667366 0.744730i \(-0.732578\pi\)
0.311272 + 0.950321i \(0.399245\pi\)
\(68\) 68.4278 39.5068i 0.122031 0.0704545i
\(69\) 1009.47 237.166i 1.76125 0.413789i
\(70\) 0 0
\(71\) 512.951 0.857410 0.428705 0.903445i \(-0.358970\pi\)
0.428705 + 0.903445i \(0.358970\pi\)
\(72\) 367.239 553.634i 0.601105 0.906200i
\(73\) 994.318i 1.59419i −0.603852 0.797096i \(-0.706368\pi\)
0.603852 0.797096i \(-0.293632\pi\)
\(74\) −344.310 + 596.362i −0.540881 + 0.936833i
\(75\) 0 0
\(76\) 105.931 + 183.477i 0.159883 + 0.276925i
\(77\) 26.4232 15.2554i 0.0391065 0.0225782i
\(78\) 932.097 + 281.038i 1.35307 + 0.407965i
\(79\) −100.853 + 174.683i −0.143631 + 0.248777i −0.928862 0.370427i \(-0.879211\pi\)
0.785230 + 0.619204i \(0.212545\pi\)
\(80\) 0 0
\(81\) 283.500 + 671.617i 0.388889 + 0.921285i
\(82\) 126.530i 0.170401i
\(83\) −959.247 553.822i −1.26857 0.732408i −0.293850 0.955851i \(-0.594937\pi\)
−0.974717 + 0.223444i \(0.928270\pi\)
\(84\) −26.2337 + 87.0073i −0.0340754 + 0.113015i
\(85\) 0 0
\(86\) 353.931 + 613.026i 0.443783 + 0.768655i
\(87\) −191.147 + 179.633i −0.235553 + 0.221364i
\(88\) −88.1909 50.9171i −0.106832 0.0616793i
\(89\) −372.269 −0.443375 −0.221688 0.975118i \(-0.571157\pi\)
−0.221688 + 0.975118i \(0.571157\pi\)
\(90\) 0 0
\(91\) −582.250 −0.670729
\(92\) 409.992 + 236.709i 0.464616 + 0.268246i
\(93\) −7.13058 30.3505i −0.00795061 0.0338409i
\(94\) −496.880 860.622i −0.545205 0.944323i
\(95\) 0 0
\(96\) 523.011 122.877i 0.556037 0.130636i
\(97\) −120.578 69.6156i −0.126215 0.0728700i 0.435563 0.900158i \(-0.356549\pi\)
−0.561778 + 0.827288i \(0.689882\pi\)
\(98\) 684.758i 0.705826i
\(99\) 100.052 49.7590i 0.101571 0.0505148i
\(100\) 0 0
\(101\) −985.872 + 1707.58i −0.971267 + 1.68228i −0.279525 + 0.960139i \(0.590177\pi\)
−0.691742 + 0.722145i \(0.743156\pi\)
\(102\) 299.186 281.164i 0.290429 0.272935i
\(103\) 1569.85 906.353i 1.50177 0.867045i 0.501768 0.865002i \(-0.332683\pi\)
0.999998 0.00204255i \(-0.000650165\pi\)
\(104\) 971.668 + 1682.98i 0.916153 + 1.58682i
\(105\) 0 0
\(106\) −473.541 + 820.197i −0.433909 + 0.751552i
\(107\) 259.217i 0.234201i 0.993120 + 0.117100i \(0.0373600\pi\)
−0.993120 + 0.117100i \(0.962640\pi\)
\(108\) −115.664 + 312.077i −0.103053 + 0.278052i
\(109\) −775.556 −0.681512 −0.340756 0.940152i \(-0.610683\pi\)
−0.340756 + 0.940152i \(0.610683\pi\)
\(110\) 0 0
\(111\) 435.416 1444.11i 0.372323 1.23486i
\(112\) 251.514 145.212i 0.212195 0.122511i
\(113\) −186.417 + 107.628i −0.155191 + 0.0895997i −0.575585 0.817742i \(-0.695225\pi\)
0.420393 + 0.907342i \(0.361892\pi\)
\(114\) 753.892 + 802.215i 0.619373 + 0.659073i
\(115\) 0 0
\(116\) −119.755 −0.0958534
\(117\) −2128.30 132.310i −1.68172 0.104547i
\(118\) 233.057i 0.181819i
\(119\) −122.774 + 212.652i −0.0945774 + 0.163813i
\(120\) 0 0
\(121\) 656.936 + 1137.85i 0.493566 + 0.854881i
\(122\) 1404.42 810.840i 1.04221 0.601721i
\(123\) −63.3872 269.800i −0.0464669 0.197781i
\(124\) 7.11684 12.3267i 0.00515412 0.00892721i
\(125\) 0 0
\(126\) −29.2989 + 471.297i −0.0207155 + 0.333226i
\(127\) 2424.76i 1.69420i −0.531436 0.847098i \(-0.678348\pi\)
0.531436 0.847098i \(-0.321652\pi\)
\(128\) −435.048 251.175i −0.300415 0.173445i
\(129\) −1061.79 1129.85i −0.724694 0.771145i
\(130\) 0 0
\(131\) −130.247 225.595i −0.0868684 0.150461i 0.819317 0.573340i \(-0.194353\pi\)
−0.906186 + 0.422880i \(0.861019\pi\)
\(132\) 48.8435 + 14.7269i 0.0322067 + 0.00971067i
\(133\) −570.188 329.198i −0.371741 0.214625i
\(134\) −534.949 −0.344870
\(135\) 0 0
\(136\) 819.552 0.516735
\(137\) −350.427 202.319i −0.218533 0.126170i 0.386738 0.922190i \(-0.373602\pi\)
−0.605271 + 0.796020i \(0.706935\pi\)
\(138\) 2355.23 + 710.127i 1.45283 + 0.438044i
\(139\) −883.841 1530.86i −0.539327 0.934141i −0.998940 0.0460221i \(-0.985346\pi\)
0.459614 0.888119i \(-0.347988\pi\)
\(140\) 0 0
\(141\) 1490.64 + 1586.19i 0.890316 + 0.947383i
\(142\) 1053.84 + 608.432i 0.622788 + 0.359567i
\(143\) 326.859i 0.191142i
\(144\) 952.361 473.641i 0.551135 0.274098i
\(145\) 0 0
\(146\) 1179.40 2042.78i 0.668547 1.15796i
\(147\) 343.040 + 1460.11i 0.192472 + 0.819237i
\(148\) 596.362 344.310i 0.331220 0.191230i
\(149\) 960.344 + 1663.36i 0.528016 + 0.914551i 0.999467 + 0.0326584i \(0.0103973\pi\)
−0.471450 + 0.881893i \(0.656269\pi\)
\(150\) 0 0
\(151\) 1262.28 2186.33i 0.680284 1.17829i −0.294611 0.955617i \(-0.595190\pi\)
0.974894 0.222668i \(-0.0714767\pi\)
\(152\) 2197.49i 1.17263i
\(153\) −497.101 + 749.408i −0.262668 + 0.395987i
\(154\) 72.3804 0.0378739
\(155\) 0 0
\(156\) −666.701 709.435i −0.342172 0.364104i
\(157\) −1682.43 + 971.350i −0.855238 + 0.493772i −0.862415 0.506202i \(-0.831049\pi\)
0.00717683 + 0.999974i \(0.497716\pi\)
\(158\) −414.397 + 239.252i −0.208656 + 0.120468i
\(159\) 598.842 1986.13i 0.298687 0.990634i
\(160\) 0 0
\(161\) −1471.23 −0.720181
\(162\) −214.193 + 1716.08i −0.103880 + 0.832270i
\(163\) 1051.21i 0.505134i −0.967579 0.252567i \(-0.918725\pi\)
0.967579 0.252567i \(-0.0812748\pi\)
\(164\) 63.2650 109.578i 0.0301230 0.0521745i
\(165\) 0 0
\(166\) −1313.82 2275.60i −0.614291 1.06398i
\(167\) 2439.11 1408.22i 1.13020 0.652524i 0.186218 0.982508i \(-0.440377\pi\)
0.943986 + 0.329985i \(0.107044\pi\)
\(168\) −686.880 + 645.505i −0.315440 + 0.296439i
\(169\) 2020.28 3499.23i 0.919564 1.59273i
\(170\) 0 0
\(171\) −2009.41 1332.89i −0.898616 0.596074i
\(172\) 707.861i 0.313802i
\(173\) 1249.20 + 721.225i 0.548987 + 0.316958i 0.748713 0.662894i \(-0.230672\pi\)
−0.199726 + 0.979852i \(0.564005\pi\)
\(174\) −605.772 + 142.321i −0.263928 + 0.0620075i
\(175\) 0 0
\(176\) −81.5179 141.193i −0.0349128 0.0604707i
\(177\) −116.754 496.948i −0.0495804 0.211033i
\(178\) −764.809 441.563i −0.322050 0.185936i
\(179\) −1534.89 −0.640912 −0.320456 0.947263i \(-0.603836\pi\)
−0.320456 + 0.947263i \(0.603836\pi\)
\(180\) 0 0
\(181\) −3650.43 −1.49908 −0.749542 0.661956i \(-0.769726\pi\)
−0.749542 + 0.661956i \(0.769726\pi\)
\(182\) −1196.21 690.630i −0.487191 0.281280i
\(183\) −2588.44 + 2432.52i −1.04559 + 0.982606i
\(184\) 2455.21 + 4252.56i 0.983700 + 1.70382i
\(185\) 0 0
\(186\) 21.3505 70.8117i 0.00841665 0.0279149i
\(187\) 119.377 + 68.9221i 0.0466828 + 0.0269523i
\(188\) 993.760i 0.385518i
\(189\) −173.629 1019.62i −0.0668235 0.392417i
\(190\) 0 0
\(191\) −678.644 + 1175.45i −0.257094 + 0.445300i −0.965462 0.260543i \(-0.916098\pi\)
0.708368 + 0.705843i \(0.249432\pi\)
\(192\) 2788.11 + 840.648i 1.04799 + 0.315982i
\(193\) −1561.48 + 901.520i −0.582371 + 0.336232i −0.762075 0.647488i \(-0.775819\pi\)
0.179704 + 0.983721i \(0.442486\pi\)
\(194\) −165.148 286.044i −0.0611181 0.105860i
\(195\) 0 0
\(196\) −342.379 + 593.018i −0.124774 + 0.216114i
\(197\) 263.403i 0.0952624i 0.998865 + 0.0476312i \(0.0151672\pi\)
−0.998865 + 0.0476312i \(0.984833\pi\)
\(198\) 264.573 + 16.4476i 0.0949614 + 0.00590344i
\(199\) −492.853 −0.175565 −0.0877824 0.996140i \(-0.527978\pi\)
−0.0877824 + 0.996140i \(0.527978\pi\)
\(200\) 0 0
\(201\) 1140.67 267.991i 0.400283 0.0940429i
\(202\) −4050.86 + 2338.77i −1.41098 + 0.814629i
\(203\) 322.300 186.080i 0.111434 0.0643363i
\(204\) −399.684 + 93.9022i −0.137174 + 0.0322278i
\(205\) 0 0
\(206\) 4300.25 1.45443
\(207\) −5377.80 334.320i −1.80572 0.112255i
\(208\) 3111.27i 1.03715i
\(209\) −184.803 + 320.088i −0.0611630 + 0.105937i
\(210\) 0 0
\(211\) 500.772 + 867.362i 0.163387 + 0.282994i 0.936081 0.351784i \(-0.114425\pi\)
−0.772695 + 0.634778i \(0.781092\pi\)
\(212\) 820.197 473.541i 0.265714 0.153410i
\(213\) −2551.90 769.426i −0.820907 0.247513i
\(214\) −307.468 + 532.551i −0.0982155 + 0.170114i
\(215\) 0 0
\(216\) −2657.44 + 2203.44i −0.837112 + 0.694097i
\(217\) 44.2337i 0.0138377i
\(218\) −1593.35 919.919i −0.495023 0.285802i
\(219\) −1491.48 + 4946.67i −0.460204 + 1.52632i
\(220\) 0 0
\(221\) −1315.27 2278.11i −0.400336 0.693403i
\(222\) 2607.46 2450.40i 0.788294 0.740810i
\(223\) −485.969 280.574i −0.145932 0.0842540i 0.425256 0.905073i \(-0.360184\pi\)
−0.571188 + 0.820819i \(0.693517\pi\)
\(224\) −762.250 −0.227366
\(225\) 0 0
\(226\) −510.646 −0.150300
\(227\) −3383.09 1953.23i −0.989180 0.571103i −0.0841506 0.996453i \(-0.526818\pi\)
−0.905029 + 0.425350i \(0.860151\pi\)
\(228\) −251.783 1071.68i −0.0731347 0.311290i
\(229\) 1498.45 + 2595.40i 0.432405 + 0.748947i 0.997080 0.0763664i \(-0.0243319\pi\)
−0.564675 + 0.825313i \(0.690999\pi\)
\(230\) 0 0
\(231\) −154.337 + 36.2601i −0.0439594 + 0.0103279i
\(232\) −1075.72 621.067i −0.304416 0.175755i
\(233\) 4194.30i 1.17930i 0.807658 + 0.589651i \(0.200735\pi\)
−0.807658 + 0.589651i \(0.799265\pi\)
\(234\) −4215.57 2796.29i −1.17769 0.781194i
\(235\) 0 0
\(236\) 116.529 201.833i 0.0321414 0.0556705i
\(237\) 763.763 717.757i 0.209332 0.196723i
\(238\) −504.469 + 291.255i −0.137394 + 0.0793247i
\(239\) −83.2362 144.169i −0.0225276 0.0390190i 0.854542 0.519383i \(-0.173838\pi\)
−0.877069 + 0.480364i \(0.840505\pi\)
\(240\) 0 0
\(241\) −307.272 + 532.210i −0.0821291 + 0.142252i −0.904164 0.427185i \(-0.859505\pi\)
0.822035 + 0.569437i \(0.192839\pi\)
\(242\) 3116.87i 0.827935i
\(243\) −402.970 3766.50i −0.106381 0.994325i
\(244\) −1621.68 −0.425481
\(245\) 0 0
\(246\) 189.795 629.479i 0.0491906 0.163147i
\(247\) 6108.35 3526.66i 1.57354 0.908485i
\(248\) 127.856 73.8179i 0.0327374 0.0189010i
\(249\) 3941.46 + 4194.10i 1.00313 + 1.06743i
\(250\) 0 0
\(251\) −6136.16 −1.54307 −0.771536 0.636185i \(-0.780511\pi\)
−0.771536 + 0.636185i \(0.780511\pi\)
\(252\) 261.022 393.505i 0.0652493 0.0983671i
\(253\) 825.908i 0.205235i
\(254\) 2876.11 4981.57i 0.710485 1.23060i
\(255\) 0 0
\(256\) 1645.87 + 2850.73i 0.401824 + 0.695979i
\(257\) −4720.19 + 2725.20i −1.14567 + 0.661453i −0.947828 0.318781i \(-0.896727\pi\)
−0.197842 + 0.980234i \(0.563393\pi\)
\(258\) −841.244 3580.66i −0.202998 0.864040i
\(259\) −1070.00 + 1853.30i −0.256705 + 0.444627i
\(260\) 0 0
\(261\) 1220.39 606.942i 0.289427 0.143942i
\(262\) 617.967i 0.145718i
\(263\) 678.305 + 391.620i 0.159035 + 0.0918186i 0.577405 0.816458i \(-0.304065\pi\)
−0.418371 + 0.908276i \(0.637399\pi\)
\(264\) 362.369 + 385.596i 0.0844782 + 0.0898930i
\(265\) 0 0
\(266\) −780.951 1352.65i −0.180012 0.311790i
\(267\) 1852.01 + 558.403i 0.424499 + 0.127991i
\(268\) 463.279 + 267.474i 0.105594 + 0.0609649i
\(269\) −141.019 −0.0319632 −0.0159816 0.999872i \(-0.505087\pi\)
−0.0159816 + 0.999872i \(0.505087\pi\)
\(270\) 0 0
\(271\) 6375.83 1.42917 0.714583 0.699551i \(-0.246616\pi\)
0.714583 + 0.699551i \(0.246616\pi\)
\(272\) 1136.31 + 656.049i 0.253305 + 0.146246i
\(273\) 2896.66 + 873.375i 0.642174 + 0.193623i
\(274\) −479.958 831.312i −0.105822 0.183290i
\(275\) 0 0
\(276\) −1684.62 1792.60i −0.367400 0.390949i
\(277\) 5909.04 + 3411.59i 1.28173 + 0.740008i 0.977165 0.212482i \(-0.0681548\pi\)
0.304567 + 0.952491i \(0.401488\pi\)
\(278\) 4193.44i 0.904697i
\(279\) −10.0516 + 161.688i −0.00215689 + 0.0346953i
\(280\) 0 0
\(281\) −294.846 + 510.689i −0.0625945 + 0.108417i −0.895624 0.444811i \(-0.853271\pi\)
0.833030 + 0.553228i \(0.186604\pi\)
\(282\) 1181.02 + 5026.86i 0.249392 + 1.06151i
\(283\) −5175.39 + 2988.01i −1.08709 + 0.627629i −0.932799 0.360397i \(-0.882641\pi\)
−0.154286 + 0.988026i \(0.549308\pi\)
\(284\) −608.432 1053.84i −0.127126 0.220189i
\(285\) 0 0
\(286\) −387.701 + 671.517i −0.0801581 + 0.138838i
\(287\) 393.214i 0.0808736i
\(288\) −2786.26 173.212i −0.570076 0.0354397i
\(289\) 3803.64 0.774199
\(290\) 0 0
\(291\) 495.443 + 527.200i 0.0998055 + 0.106203i
\(292\) −2042.78 + 1179.40i −0.409400 + 0.236367i
\(293\) 6977.99 4028.74i 1.39133 0.803282i 0.397864 0.917445i \(-0.369752\pi\)
0.993462 + 0.114162i \(0.0364184\pi\)
\(294\) −1027.14 + 3406.63i −0.203755 + 0.675777i
\(295\) 0 0
\(296\) 7142.55 1.40254
\(297\) −572.389 + 97.4705i −0.111830 + 0.0190431i
\(298\) 4556.41i 0.885724i
\(299\) 7880.55 13649.5i 1.52423 2.64004i
\(300\) 0 0
\(301\) 1099.90 + 1905.09i 0.210622 + 0.364808i
\(302\) 5186.59 2994.48i 0.988261 0.570573i
\(303\) 7466.02 7016.30i 1.41555 1.33028i
\(304\) −1759.08 + 3046.82i −0.331876 + 0.574826i
\(305\) 0 0
\(306\) −1910.18 + 949.994i −0.356855 + 0.177476i
\(307\) 4546.58i 0.845235i 0.906308 + 0.422618i \(0.138889\pi\)
−0.906308 + 0.422618i \(0.861111\pi\)
\(308\) −62.6832 36.1902i −0.0115965 0.00669522i
\(309\) −9169.43 + 2154.28i −1.68813 + 0.396610i
\(310\) 0 0
\(311\) 2101.40 + 3639.73i 0.383149 + 0.663633i 0.991510 0.130027i \(-0.0415063\pi\)
−0.608362 + 0.793660i \(0.708173\pi\)
\(312\) −2309.52 9830.22i −0.419073 1.78374i
\(313\) 6039.04 + 3486.64i 1.09056 + 0.629637i 0.933727 0.357987i \(-0.116537\pi\)
0.156838 + 0.987624i \(0.449870\pi\)
\(314\) −4608.63 −0.828281
\(315\) 0 0
\(316\) 478.505 0.0851835
\(317\) −6373.97 3680.02i −1.12933 0.652020i −0.185565 0.982632i \(-0.559411\pi\)
−0.943767 + 0.330612i \(0.892745\pi\)
\(318\) 3586.13 3370.12i 0.632391 0.594298i
\(319\) −104.460 180.930i −0.0183343 0.0317560i
\(320\) 0 0
\(321\) 388.826 1289.59i 0.0676080 0.224230i
\(322\) −3022.58 1745.09i −0.523111 0.302018i
\(323\) 2974.55i 0.512410i
\(324\) 1043.54 1379.07i 0.178933 0.236466i
\(325\) 0 0
\(326\) 1246.88 2159.66i 0.211835 0.366909i
\(327\) 3858.34 + 1163.33i 0.652498 + 0.196736i
\(328\) 1136.58 656.203i 0.191332 0.110466i
\(329\) −1544.14 2674.53i −0.258758 0.448182i
\(330\) 0 0
\(331\) 3417.06 5918.52i 0.567428 0.982814i −0.429391 0.903119i \(-0.641272\pi\)
0.996819 0.0796957i \(-0.0253949\pi\)
\(332\) 2627.64i 0.434369i
\(333\) −4332.33 + 6531.24i −0.712944 + 1.07480i
\(334\) 6681.39 1.09458
\(335\) 0 0
\(336\) −1469.09 + 345.149i −0.238528 + 0.0560399i
\(337\) 6000.24 3464.24i 0.969893 0.559968i 0.0706891 0.997498i \(-0.477480\pi\)
0.899204 + 0.437531i \(0.144147\pi\)
\(338\) 8301.16 4792.68i 1.33587 0.771264i
\(339\) 1088.85 255.816i 0.174449 0.0409853i
\(340\) 0 0
\(341\) 24.8316 0.00394341
\(342\) −2547.24 5121.81i −0.402746 0.809812i
\(343\) 4656.70i 0.733055i
\(344\) 3671.07 6358.48i 0.575380 0.996588i
\(345\) 0 0
\(346\) 1710.95 + 2963.45i 0.265842 + 0.460451i
\(347\) 6530.35 3770.30i 1.01028 0.583286i 0.0990071 0.995087i \(-0.468433\pi\)
0.911274 + 0.411801i \(0.135100\pi\)
\(348\) 595.775 + 179.633i 0.0917726 + 0.0276705i
\(349\) −922.084 + 1597.10i −0.141427 + 0.244959i −0.928034 0.372495i \(-0.878502\pi\)
0.786607 + 0.617454i \(0.211836\pi\)
\(350\) 0 0
\(351\) 10389.7 + 3850.69i 1.57995 + 0.585568i
\(352\) 427.906i 0.0647939i
\(353\) 6146.61 + 3548.74i 0.926773 + 0.535073i 0.885789 0.464087i \(-0.153618\pi\)
0.0409833 + 0.999160i \(0.486951\pi\)
\(354\) 349.586 1159.44i 0.0524866 0.174079i
\(355\) 0 0
\(356\) 441.563 + 764.809i 0.0657382 + 0.113862i
\(357\) 929.772 873.766i 0.137840 0.129537i
\(358\) −3153.37 1820.60i −0.465532 0.268775i
\(359\) −7709.65 −1.13342 −0.566712 0.823916i \(-0.691785\pi\)
−0.566712 + 0.823916i \(0.691785\pi\)
\(360\) 0 0
\(361\) 1116.75 0.162815
\(362\) −7499.65 4329.92i −1.08888 0.628662i
\(363\) −1561.45 6646.12i −0.225770 0.960966i
\(364\) 690.630 + 1196.21i 0.0994474 + 0.172248i
\(365\) 0 0
\(366\) −8203.14 + 1927.25i −1.17154 + 0.275244i
\(367\) −4552.17 2628.19i −0.647469 0.373816i 0.140017 0.990149i \(-0.455284\pi\)
−0.787486 + 0.616333i \(0.788618\pi\)
\(368\) 7861.57i 1.11362i
\(369\) −89.3535 + 1437.32i −0.0126058 + 0.202775i
\(370\) 0 0
\(371\) −1471.61 + 2548.91i −0.205936 + 0.356692i
\(372\) −53.8960 + 50.6495i −0.00751176 + 0.00705928i
\(373\) 862.955 498.227i 0.119791 0.0691615i −0.438907 0.898532i \(-0.644634\pi\)
0.558698 + 0.829371i \(0.311301\pi\)
\(374\) 163.503 + 283.195i 0.0226057 + 0.0391542i
\(375\) 0 0
\(376\) −5153.78 + 8926.61i −0.706878 + 1.22435i
\(377\) 3986.90i 0.544658i
\(378\) 852.705 2300.72i 0.116028 0.313059i
\(379\) 2735.20 0.370707 0.185354 0.982672i \(-0.440657\pi\)
0.185354 + 0.982672i \(0.440657\pi\)
\(380\) 0 0
\(381\) −3637.14 + 12063.0i −0.489072 + 1.62207i
\(382\) −2788.49 + 1609.93i −0.373485 + 0.215632i
\(383\) −7741.80 + 4469.73i −1.03287 + 0.596325i −0.917804 0.397033i \(-0.870040\pi\)
−0.115062 + 0.993358i \(0.536707\pi\)
\(384\) 1787.57 + 1902.15i 0.237557 + 0.252783i
\(385\) 0 0
\(386\) −4277.32 −0.564015
\(387\) 3587.57 + 7213.62i 0.471232 + 0.947517i
\(388\) 330.295i 0.0432170i
\(389\) −5566.93 + 9642.21i −0.725590 + 1.25676i 0.233140 + 0.972443i \(0.425100\pi\)
−0.958731 + 0.284316i \(0.908233\pi\)
\(390\) 0 0
\(391\) −3323.42 5756.33i −0.429853 0.744527i
\(392\) −6150.95 + 3551.25i −0.792525 + 0.457564i
\(393\) 309.580 + 1317.69i 0.0397360 + 0.169132i
\(394\) −312.433 + 541.150i −0.0399496 + 0.0691948i
\(395\) 0 0
\(396\) −220.903 146.530i −0.0280323 0.0185945i
\(397\) 9479.40i 1.19838i 0.800606 + 0.599191i \(0.204511\pi\)
−0.800606 + 0.599191i \(0.795489\pi\)
\(398\) −1012.54 584.593i −0.127523 0.0736256i
\(399\) 2342.85 + 2493.02i 0.293958 + 0.312800i
\(400\) 0 0
\(401\) −4713.80 8164.54i −0.587022 1.01675i −0.994620 0.103591i \(-0.966967\pi\)
0.407598 0.913162i \(-0.366367\pi\)
\(402\) 2661.34 + 802.423i 0.330188 + 0.0995553i
\(403\) −410.383 236.935i −0.0507261 0.0292868i
\(404\) 4677.53 0.576029
\(405\) 0 0
\(406\) 882.869 0.107921
\(407\) 1040.39 + 600.670i 0.126708 + 0.0731550i
\(408\) −4077.22 1229.33i −0.494736 0.149169i
\(409\) 204.093 + 353.500i 0.0246742 + 0.0427370i 0.878099 0.478479i \(-0.158812\pi\)
−0.853425 + 0.521216i \(0.825478\pi\)
\(410\) 0 0
\(411\) 1439.87 + 1532.17i 0.172807 + 0.183884i
\(412\) −3724.12 2150.12i −0.445326 0.257109i
\(413\) 724.266i 0.0862925i
\(414\) −10651.9 7065.68i −1.26452 0.838790i
\(415\) 0 0
\(416\) 4082.94 7071.86i 0.481208 0.833477i
\(417\) 2100.77 + 8941.68i 0.246703 + 1.05006i
\(418\) −759.338 + 438.404i −0.0888527 + 0.0512992i
\(419\) 4406.94 + 7633.05i 0.513826 + 0.889973i 0.999871 + 0.0160393i \(0.00510569\pi\)
−0.486045 + 0.873934i \(0.661561\pi\)
\(420\) 0 0
\(421\) 1174.68 2034.61i 0.135987 0.235537i −0.789987 0.613124i \(-0.789913\pi\)
0.925974 + 0.377587i \(0.123246\pi\)
\(422\) 2375.94i 0.274074i
\(423\) −5036.56 10127.1i −0.578927 1.16406i
\(424\) 9823.40 1.12516
\(425\) 0 0
\(426\) −4330.12 4607.66i −0.492476 0.524042i
\(427\) 4364.47 2519.83i 0.494640 0.285581i
\(428\) 532.551 307.468i 0.0601444 0.0347244i
\(429\) 490.288 1626.10i 0.0551780 0.183005i
\(430\) 0 0
\(431\) 4481.16 0.500812 0.250406 0.968141i \(-0.419436\pi\)
0.250406 + 0.968141i \(0.419436\pi\)
\(432\) −5448.40 + 927.792i −0.606797 + 0.103330i
\(433\) 3422.69i 0.379871i 0.981797 + 0.189935i \(0.0608279\pi\)
−0.981797 + 0.189935i \(0.939172\pi\)
\(434\) −52.4674 + 90.8762i −0.00580303 + 0.0100511i
\(435\) 0 0
\(436\) 919.919 + 1593.35i 0.101046 + 0.175017i
\(437\) 15434.6 8911.17i 1.68956 0.975467i
\(438\) −8931.62 + 8393.61i −0.974359 + 0.915667i
\(439\) −4064.59 + 7040.07i −0.441896 + 0.765386i −0.997830 0.0658402i \(-0.979027\pi\)
0.555934 + 0.831226i \(0.312361\pi\)
\(440\) 0 0
\(441\) 483.565 7778.52i 0.0522152 0.839922i
\(442\) 6240.36i 0.671547i
\(443\) −2035.83 1175.39i −0.218342 0.126060i 0.386840 0.922147i \(-0.373566\pi\)
−0.605182 + 0.796087i \(0.706900\pi\)
\(444\) −3483.33 + 818.376i −0.372323 + 0.0874739i
\(445\) 0 0
\(446\) −665.601 1152.86i −0.0706662 0.122397i
\(447\) −2282.60 9715.65i −0.241529 1.02804i
\(448\) −3578.12 2065.83i −0.377345 0.217860i
\(449\) −4760.99 −0.500412 −0.250206 0.968193i \(-0.580498\pi\)
−0.250206 + 0.968193i \(0.580498\pi\)
\(450\) 0 0
\(451\) 220.740 0.0230471
\(452\) 442.233 + 255.323i 0.0460196 + 0.0265695i
\(453\) −9559.26 + 8983.44i −0.991464 + 0.931742i
\(454\) −4633.61 8025.65i −0.479000 0.829653i
\(455\) 0 0
\(456\) 3296.23 10932.4i 0.338509 1.12271i
\(457\) 1930.44 + 1114.54i 0.197598 + 0.114083i 0.595535 0.803330i \(-0.296940\pi\)
−0.397937 + 0.917413i \(0.630274\pi\)
\(458\) 7109.51i 0.725340i
\(459\) 3597.16 2982.61i 0.365797 0.303303i
\(460\) 0 0
\(461\) −2868.31 + 4968.06i −0.289784 + 0.501921i −0.973758 0.227585i \(-0.926917\pi\)
0.683974 + 0.729507i \(0.260250\pi\)
\(462\) −360.088 108.571i −0.0362615 0.0109332i
\(463\) −3121.13 + 1801.99i −0.313286 + 0.180876i −0.648396 0.761303i \(-0.724560\pi\)
0.335110 + 0.942179i \(0.391227\pi\)
\(464\) −994.326 1722.22i −0.0994836 0.172311i
\(465\) 0 0
\(466\) −4975.03 + 8617.00i −0.494557 + 0.856598i
\(467\) 3780.37i 0.374593i 0.982303 + 0.187296i \(0.0599725\pi\)
−0.982303 + 0.187296i \(0.940028\pi\)
\(468\) 2252.64 + 4529.44i 0.222497 + 0.447380i
\(469\) −1662.45 −0.163677
\(470\) 0 0
\(471\) 9827.00 2308.76i 0.961368 0.225865i
\(472\) 2093.47 1208.67i 0.204152 0.117867i
\(473\) 1069.46 617.454i 0.103962 0.0600224i
\(474\) 2420.48 568.670i 0.234549 0.0551052i
\(475\) 0 0
\(476\) 582.511 0.0560911
\(477\) −5958.40 + 8982.63i −0.571943 + 0.862236i
\(478\) 394.920i 0.0377891i
\(479\) −7230.58 + 12523.7i −0.689715 + 1.19462i 0.282215 + 0.959351i \(0.408931\pi\)
−0.971930 + 0.235271i \(0.924402\pi\)
\(480\) 0 0
\(481\) −11462.8 19854.1i −1.08661 1.88206i
\(482\) −1262.55 + 728.935i −0.119311 + 0.0688840i
\(483\) 7319.28 + 2206.85i 0.689521 + 0.207898i
\(484\) 1558.44 2699.29i 0.146360 0.253502i
\(485\) 0 0
\(486\) 3639.71 8216.09i 0.339714 0.766850i
\(487\) 3581.74i 0.333273i −0.986018 0.166636i \(-0.946709\pi\)
0.986018 0.166636i \(-0.0532906\pi\)
\(488\) −14567.0 8410.26i −1.35126 0.780153i
\(489\) −1576.81 + 5229.69i −0.145820 + 0.483629i
\(490\) 0 0
\(491\) 3507.69 + 6075.50i 0.322403 + 0.558419i 0.980983 0.194092i \(-0.0621760\pi\)
−0.658580 + 0.752511i \(0.728843\pi\)
\(492\) −479.107 + 450.247i −0.0439021 + 0.0412576i
\(493\) 1456.11 + 840.687i 0.133022 + 0.0768005i
\(494\) 16732.4 1.52394
\(495\) 0 0
\(496\) 236.364 0.0213973
\(497\) 3274.98 + 1890.81i 0.295579 + 0.170653i
\(498\) 3122.77 + 13291.7i 0.280993 + 1.19602i
\(499\) 1259.90 + 2182.21i 0.113028 + 0.195769i 0.916990 0.398911i \(-0.130612\pi\)
−0.803962 + 0.594681i \(0.797279\pi\)
\(500\) 0 0
\(501\) −14246.8 + 3347.15i −1.27046 + 0.298482i
\(502\) −12606.5 7278.35i −1.12083 0.647109i
\(503\) 4989.32i 0.442272i −0.975243 0.221136i \(-0.929024\pi\)
0.975243 0.221136i \(-0.0709764\pi\)
\(504\) 4385.44 2181.03i 0.387586 0.192759i
\(505\) 0 0
\(506\) −979.643 + 1696.79i −0.0860681 + 0.149074i
\(507\) −15299.6 + 14378.0i −1.34020 + 1.25947i
\(508\) −4981.57 + 2876.11i −0.435081 + 0.251194i
\(509\) 2359.76 + 4087.22i 0.205490 + 0.355919i 0.950289 0.311370i \(-0.100788\pi\)
−0.744799 + 0.667289i \(0.767454\pi\)
\(510\) 0 0
\(511\) 3665.19 6348.30i 0.317297 0.549574i
\(512\) 11827.7i 1.02093i
\(513\) 7997.34 + 9645.16i 0.688287 + 0.830106i
\(514\) −12929.9 −1.10956
\(515\) 0 0
\(516\) −1061.79 + 3521.57i −0.0905868 + 0.300442i
\(517\) −1501.41 + 866.839i −0.127721 + 0.0737399i
\(518\) −4396.55 + 2538.35i −0.372921 + 0.215306i
\(519\) −5132.85 5461.85i −0.434117 0.461943i
\(520\) 0 0
\(521\) −10711.0 −0.900682 −0.450341 0.892857i \(-0.648698\pi\)
−0.450341 + 0.892857i \(0.648698\pi\)
\(522\) 3227.16 + 200.622i 0.270592 + 0.0168218i
\(523\) 10566.4i 0.883433i −0.897155 0.441717i \(-0.854370\pi\)
0.897155 0.441717i \(-0.145630\pi\)
\(524\) −308.983 + 535.175i −0.0257595 + 0.0446168i
\(525\) 0 0
\(526\) 929.032 + 1609.13i 0.0770109 + 0.133387i
\(527\) −173.068 + 99.9211i −0.0143055 + 0.00825926i
\(528\) 193.757 + 824.704i 0.0159700 + 0.0679747i
\(529\) 13829.1 23952.7i 1.13661 1.96866i
\(530\) 0 0
\(531\) −164.581 + 2647.42i −0.0134505 + 0.216362i
\(532\) 1561.90i 0.127288i
\(533\) −3648.09 2106.23i −0.296466 0.171165i
\(534\) 3142.53 + 3343.96i 0.254664 + 0.270988i
\(535\) 0 0
\(536\) 2774.32 + 4805.26i 0.223568 + 0.387231i
\(537\) 7635.99 + 2302.34i 0.613626 + 0.185015i
\(538\) −289.718 167.269i −0.0232168 0.0134042i
\(539\) −1194.60 −0.0954642
\(540\) 0 0
\(541\) −6595.81 −0.524170 −0.262085 0.965045i \(-0.584410\pi\)
−0.262085 + 0.965045i \(0.584410\pi\)
\(542\) 13098.9 + 7562.63i 1.03809 + 0.599341i
\(543\) 18160.7 + 5475.65i 1.43526 + 0.432749i
\(544\) −1721.87 2982.37i −0.135707 0.235052i
\(545\) 0 0
\(546\) 4915.11 + 5230.15i 0.385251 + 0.409945i
\(547\) −5532.85 3194.39i −0.432482 0.249693i 0.267922 0.963441i \(-0.413663\pi\)
−0.700403 + 0.713747i \(0.746997\pi\)
\(548\) 959.916i 0.0748277i
\(549\) 16526.1 8218.97i 1.28473 0.638939i
\(550\) 0 0
\(551\) −2254.16 + 3904.31i −0.174284 + 0.301868i
\(552\) −5835.70 24839.0i −0.449971 1.91525i
\(553\) −1287.81 + 743.519i −0.0990296 + 0.0571748i
\(554\) 8093.24 + 14017.9i 0.620666 + 1.07502i
\(555\) 0 0
\(556\) −2096.72 + 3631.62i −0.159929 + 0.277006i
\(557\) 15992.4i 1.21655i −0.793726 0.608276i \(-0.791862\pi\)
0.793726 0.608276i \(-0.208138\pi\)
\(558\) −212.435 + 320.258i −0.0161167 + 0.0242968i
\(559\) −23566.2 −1.78308
\(560\) 0 0
\(561\) −490.508 521.948i −0.0369149 0.0392811i
\(562\) −1211.50 + 699.459i −0.0909323 + 0.0524998i
\(563\) −5500.23 + 3175.56i −0.411736 + 0.237716i −0.691535 0.722343i \(-0.743065\pi\)
0.279800 + 0.960058i \(0.409732\pi\)
\(564\) 1490.64 4943.89i 0.111290 0.369106i
\(565\) 0 0
\(566\) −14176.8 −1.05282
\(567\) −665.644 + 5333.01i −0.0493023 + 0.395001i
\(568\) 12621.7i 0.932382i
\(569\) 4810.21 8331.53i 0.354402 0.613842i −0.632614 0.774468i \(-0.718018\pi\)
0.987015 + 0.160626i \(0.0513512\pi\)
\(570\) 0 0
\(571\) 2532.30 + 4386.08i 0.185593 + 0.321456i 0.943776 0.330585i \(-0.107246\pi\)
−0.758183 + 0.652042i \(0.773913\pi\)
\(572\) 671.517 387.701i 0.0490866 0.0283402i
\(573\) 5139.38 4829.80i 0.374696 0.352125i
\(574\) −466.408 + 807.842i −0.0339155 + 0.0587433i
\(575\) 0 0
\(576\) −12609.7 8364.34i −0.912161 0.605059i
\(577\) 11355.1i 0.819273i −0.912249 0.409637i \(-0.865655\pi\)
0.912249 0.409637i \(-0.134345\pi\)
\(578\) 7814.41 + 4511.65i 0.562347 + 0.324671i
\(579\) 9120.54 2142.79i 0.654640 0.153802i
\(580\) 0 0
\(581\) −4082.93 7071.84i −0.291546 0.504973i
\(582\) 392.533 + 1670.77i 0.0279571 + 0.118996i
\(583\) 1430.88 + 826.121i 0.101649 + 0.0586869i
\(584\) −24466.2 −1.73359
\(585\) 0 0
\(586\) 19114.6 1.34747
\(587\) −8687.96 5016.00i −0.610887 0.352696i 0.162426 0.986721i \(-0.448068\pi\)
−0.773312 + 0.634025i \(0.781402\pi\)
\(588\) 2592.84 2436.66i 0.181848 0.170895i
\(589\) −267.921 464.053i −0.0187428 0.0324634i
\(590\) 0 0
\(591\) 395.105 1310.41i 0.0274999 0.0912068i
\(592\) 9903.16 + 5717.59i 0.687530 + 0.396945i
\(593\) 1325.12i 0.0917643i −0.998947 0.0458821i \(-0.985390\pi\)
0.998947 0.0458821i \(-0.0146099\pi\)
\(594\) −1291.56 478.685i −0.0892145 0.0330651i
\(595\) 0 0
\(596\) 2278.21 3945.97i 0.156575 0.271197i
\(597\) 2451.91 + 739.279i 0.168091 + 0.0506812i
\(598\) 32380.5 18694.9i 2.21427 1.27841i
\(599\) 8285.78 + 14351.4i 0.565188 + 0.978935i 0.997032 + 0.0769865i \(0.0245298\pi\)
−0.431844 + 0.901948i \(0.642137\pi\)
\(600\) 0 0
\(601\) −8604.49 + 14903.4i −0.584001 + 1.01152i 0.410998 + 0.911636i \(0.365180\pi\)
−0.994999 + 0.0998833i \(0.968153\pi\)
\(602\) 5218.55i 0.353310i
\(603\) −6076.76 377.772i −0.410390 0.0255126i
\(604\) −5988.96 −0.403456
\(605\) 0 0
\(606\) 23660.9 5558.92i 1.58607 0.372633i
\(607\) −3618.24 + 2088.99i −0.241944 + 0.139686i −0.616070 0.787692i \(-0.711276\pi\)
0.374126 + 0.927378i \(0.377943\pi\)
\(608\) 7996.72 4616.91i 0.533404 0.307961i
\(609\) −1882.54 + 442.287i −0.125262 + 0.0294292i
\(610\) 0 0
\(611\) 33084.4 2.19059
\(612\) 2129.26 + 132.369i 0.140638 + 0.00874297i
\(613\) 14944.2i 0.984649i 0.870412 + 0.492324i \(0.163853\pi\)
−0.870412 + 0.492324i \(0.836147\pi\)
\(614\) −5392.89 + 9340.75i −0.354461 + 0.613945i
\(615\) 0 0
\(616\) −375.375 650.168i −0.0245524 0.0425260i
\(617\) −17756.0 + 10251.4i −1.15856 + 0.668893i −0.950958 0.309320i \(-0.899898\pi\)
−0.207600 + 0.978214i \(0.566565\pi\)
\(618\) −21393.5 6450.37i −1.39251 0.419858i
\(619\) 1364.26 2362.97i 0.0885854 0.153434i −0.818328 0.574751i \(-0.805099\pi\)
0.906913 + 0.421317i \(0.138432\pi\)
\(620\) 0 0
\(621\) 26252.8 + 9729.93i 1.69644 + 0.628742i
\(622\) 9970.21i 0.642715i
\(623\) −2376.78 1372.23i −0.152847 0.0882463i
\(624\) 4666.91 15478.4i 0.299400 0.992999i
\(625\) 0 0
\(626\) 8271.29 + 14326.3i 0.528095 + 0.914687i
\(627\) 1399.51 1315.21i 0.0891407 0.0837712i
\(628\) 3991.19 + 2304.32i 0.253608 + 0.146421i
\(629\) −9668.27 −0.612876
\(630\) 0 0
\(631\) −3393.08 −0.214067 −0.107034 0.994255i \(-0.534135\pi\)
−0.107034 + 0.994255i \(0.534135\pi\)
\(632\) 4298.25 + 2481.59i 0.270530 + 0.156191i
\(633\) −1190.27 5066.23i −0.0747374 0.318112i
\(634\) −8730.03 15120.9i −0.546867 0.947202i
\(635\) 0 0
\(636\) −4790.74 + 1125.54i −0.298687 + 0.0701739i
\(637\) 19742.8 + 11398.5i 1.22800 + 0.708988i
\(638\) 495.618i 0.0307550i
\(639\) 11541.4 + 7655.70i 0.714508 + 0.473951i
\(640\) 0 0
\(641\) −6780.88 + 11744.8i −0.417830 + 0.723702i −0.995721 0.0924116i \(-0.970542\pi\)
0.577891 + 0.816114i \(0.303876\pi\)
\(642\) 2328.46 2188.20i 0.143142 0.134520i
\(643\) 11229.7 6483.44i 0.688731 0.397639i −0.114405 0.993434i \(-0.536496\pi\)
0.803137 + 0.595795i \(0.203163\pi\)
\(644\) 1745.09 + 3022.58i 0.106780 + 0.184948i
\(645\) 0 0
\(646\) 3528.24 6111.09i 0.214886 0.372194i
\(647\) 25837.9i 1.57000i −0.619495 0.785001i \(-0.712663\pi\)
0.619495 0.785001i \(-0.287337\pi\)
\(648\) 16525.8 6975.79i 1.00184 0.422894i
\(649\) 406.583 0.0245913
\(650\) 0 0
\(651\) 66.3505 220.060i 0.00399460 0.0132486i
\(652\) −2159.66 + 1246.88i −0.129722 + 0.0748950i
\(653\) −24479.8 + 14133.4i −1.46703 + 0.846989i −0.999319 0.0368938i \(-0.988254\pi\)
−0.467709 + 0.883883i \(0.654920\pi\)
\(654\) 6546.92 + 6966.56i 0.391445 + 0.416535i
\(655\) 0 0
\(656\) 2101.15 0.125055
\(657\) 14840.0 22372.1i 0.881223 1.32849i
\(658\) 7326.28i 0.434055i
\(659\) −7978.92 + 13819.9i −0.471646 + 0.816914i −0.999474 0.0324369i \(-0.989673\pi\)
0.527828 + 0.849351i \(0.323007\pi\)
\(660\) 0 0
\(661\) −12028.9 20834.6i −0.707821 1.22598i −0.965664 0.259795i \(-0.916345\pi\)
0.257843 0.966187i \(-0.416988\pi\)
\(662\) 14040.4 8106.23i 0.824314 0.475918i
\(663\) 3126.20 + 13306.3i 0.183125 + 0.779450i
\(664\) −13627.3 + 23603.2i −0.796450 + 1.37949i
\(665\) 0 0
\(666\) −16647.6 + 8279.38i −0.968588 + 0.481711i
\(667\) 10074.1i 0.584815i
\(668\) −5786.26 3340.70i −0.335145 0.193496i
\(669\) 1996.80 + 2124.79i 0.115397 + 0.122794i
\(670\) 0 0
\(671\) −1414.56 2450.09i −0.0813838 0.140961i
\(672\) 3792.15 + 1143.37i 0.217686 + 0.0656349i
\(673\) −1085.16 626.519i −0.0621545 0.0358849i 0.468601 0.883410i \(-0.344758\pi\)
−0.530755 + 0.847525i \(0.678092\pi\)
\(674\) 16436.3 0.939321
\(675\) 0 0
\(676\) −9585.35 −0.545366
\(677\) 762.733 + 440.364i 0.0433002 + 0.0249994i 0.521494 0.853255i \(-0.325375\pi\)
−0.478194 + 0.878254i \(0.658708\pi\)
\(678\) 2540.43 + 765.970i 0.143901 + 0.0433877i
\(679\) −513.226 888.933i −0.0290071 0.0502417i
\(680\) 0 0
\(681\) 13900.8 + 14791.8i 0.782204 + 0.832341i
\(682\) 51.0153 + 29.4537i 0.00286434 + 0.00165373i
\(683\) 26686.4i 1.49506i −0.664227 0.747531i \(-0.731239\pi\)
0.664227 0.747531i \(-0.268761\pi\)
\(684\) −354.924 + 5709.24i −0.0198404 + 0.319149i
\(685\) 0 0
\(686\) 5523.50 9566.98i 0.307417 0.532462i
\(687\) −3561.62 15159.6i −0.197794 0.841886i
\(688\) 10179.9 5877.36i 0.564106 0.325687i
\(689\) −15765.2 27306.1i −0.871706 1.50984i
\(690\) 0 0
\(691\) 85.7060 148.447i 0.00471839 0.00817249i −0.863657 0.504081i \(-0.831831\pi\)
0.868375 + 0.495908i \(0.165165\pi\)
\(692\) 3421.90i 0.187978i
\(693\) 822.206 + 51.1138i 0.0450693 + 0.00280181i
\(694\) 17888.4 0.978437
\(695\) 0 0
\(696\) 4420.04 + 4703.35i 0.240720 + 0.256150i
\(697\) −1538.49 + 888.247i −0.0836075 + 0.0482708i
\(698\) −3788.76 + 2187.44i −0.205454 + 0.118619i
\(699\) 6291.44 20866.4i 0.340435 1.12910i
\(700\) 0 0
\(701\) −14229.6 −0.766684 −0.383342 0.923607i \(-0.625227\pi\)
−0.383342 + 0.923607i \(0.625227\pi\)
\(702\) 16777.8 + 20234.7i 0.902045 + 1.08791i
\(703\) 25923.8i 1.39080i
\(704\) −1159.70 + 2008.66i −0.0620850 + 0.107534i
\(705\) 0 0
\(706\) 8418.62 + 14581.5i 0.448780 + 0.777310i
\(707\) −12588.8 + 7268.13i −0.669659 + 0.386628i
\(708\) −882.472 + 829.316i −0.0468437 + 0.0440220i
\(709\) −3887.04 + 6732.55i −0.205897 + 0.356624i −0.950418 0.310975i \(-0.899344\pi\)
0.744521 + 0.667599i \(0.232678\pi\)
\(710\) 0 0
\(711\) −4876.31 + 2425.15i −0.257210 + 0.127919i
\(712\) 9160.03i 0.482144i
\(713\) −1036.96 598.687i −0.0544661 0.0314460i
\(714\) 2946.59 692.274i 0.154444 0.0362853i
\(715\) 0 0
\(716\) 1820.60 + 3153.37i 0.0950264 + 0.164591i
\(717\) 197.841 + 842.088i 0.0103047 + 0.0438610i
\(718\) −15839.1 9144.72i −0.823274 0.475318i
\(719\) 22091.8 1.14588 0.572939 0.819598i \(-0.305803\pi\)
0.572939 + 0.819598i \(0.305803\pi\)
\(720\) 0 0
\(721\) 13363.8 0.690282
\(722\) 2294.31 + 1324.62i 0.118262 + 0.0682786i
\(723\) 2326.97 2186.81i 0.119697 0.112487i
\(724\) 4329.92 + 7499.65i 0.222266 + 0.384975i
\(725\) 0 0
\(726\) 4675.31 15506.3i 0.239004 0.792687i
\(727\) 5753.42 + 3321.74i 0.293511 + 0.169459i 0.639524 0.768771i \(-0.279131\pi\)
−0.346013 + 0.938230i \(0.612465\pi\)
\(728\) 14326.8i 0.729378i
\(729\) −3645.00 + 19342.6i −0.185185 + 0.982704i
\(730\) 0 0
\(731\) −4969.22 + 8606.94i −0.251427 + 0.435484i
\(732\) 8067.75 + 2432.52i 0.407367 + 0.122826i
\(733\) −2704.43 + 1561.40i −0.136276 + 0.0786791i −0.566588 0.824001i \(-0.691737\pi\)
0.430312 + 0.902680i \(0.358404\pi\)
\(734\) −6234.82 10799.0i −0.313530 0.543050i
\(735\) 0 0
\(736\) 10316.8 17869.2i 0.516687 0.894928i
\(737\) 933.252i 0.0466442i
\(738\) −1888.44 + 2846.93i −0.0941929 + 0.142001i
\(739\) −19549.5 −0.973127 −0.486563 0.873645i \(-0.661750\pi\)
−0.486563 + 0.873645i \(0.661750\pi\)
\(740\) 0 0
\(741\) −35678.6 + 8382.37i −1.76881 + 0.415566i
\(742\) −6046.72 + 3491.08i −0.299167 + 0.172724i
\(743\) 8133.58 4695.92i 0.401604 0.231866i −0.285572 0.958357i \(-0.592183\pi\)
0.687176 + 0.726491i \(0.258850\pi\)
\(744\) −746.804 + 175.455i −0.0368000 + 0.00864582i
\(745\) 0 0
\(746\) 2363.87 0.116015
\(747\) −13317.4 26777.6i −0.652286 1.31157i
\(748\) 327.005i 0.0159846i
\(749\) −955.512 + 1655.00i −0.0466137 + 0.0807373i
\(750\) 0 0
\(751\) 9136.01 + 15824.0i 0.443912 + 0.768878i 0.997976 0.0635962i \(-0.0202570\pi\)
−0.554064 + 0.832474i \(0.686924\pi\)
\(752\) −14291.5 + 8251.18i −0.693026 + 0.400119i
\(753\) 30527.0 + 9204.25i 1.47738 + 0.445447i
\(754\) −4729.03 + 8190.92i −0.228410 + 0.395618i
\(755\) 0 0
\(756\) −1888.83 + 1566.13i −0.0908676 + 0.0753434i
\(757\) 2016.30i 0.0968082i −0.998828 0.0484041i \(-0.984586\pi\)
0.998828 0.0484041i \(-0.0154135\pi\)
\(758\) 5619.36 + 3244.34i 0.269267 + 0.155461i
\(759\) 1238.86 4108.84i 0.0592462 0.196497i
\(760\) 0 0
\(761\) 8846.39 + 15322.4i 0.421395 + 0.729877i 0.996076 0.0885001i \(-0.0282074\pi\)
−0.574681 + 0.818377i \(0.694874\pi\)
\(762\) −21780.8 + 20468.8i −1.03548 + 0.973107i
\(763\) −4951.60 2858.81i −0.234941 0.135643i
\(764\) 3219.87 0.152475
\(765\) 0 0
\(766\) −21206.9 −1.00031
\(767\) −6719.46 3879.48i −0.316331 0.182634i
\(768\) −3912.00 16651.0i −0.183805 0.782346i
\(769\) −4879.86 8452.16i −0.228833 0.396350i 0.728630 0.684908i \(-0.240157\pi\)
−0.957462 + 0.288558i \(0.906824\pi\)
\(770\) 0 0
\(771\) 27570.4 6477.43i 1.28784 0.302567i
\(772\) 3704.27 + 2138.66i 0.172694 + 0.0997047i
\(773\) 10338.3i 0.481038i −0.970644 0.240519i \(-0.922682\pi\)
0.970644 0.240519i \(-0.0773177\pi\)
\(774\) −1185.86 + 19075.4i −0.0550707 + 0.885856i
\(775\) 0 0
\(776\) −1712.96 + 2966.93i −0.0792418 + 0.137251i
\(777\) 8103.14 7615.04i 0.374130 0.351593i
\(778\) −22874.0 +