Properties

Label 225.4.h.d.46.5
Level $225$
Weight $4$
Character 225.46
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
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.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 46.5
Character \(\chi\) \(=\) 225.46
Dual form 225.4.h.d.181.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.856692 + 2.63663i) q^{2} +(0.254251 + 0.184724i) q^{4} +(-7.75979 - 8.04895i) q^{5} -7.15708 q^{7} +(-18.6477 + 13.5483i) q^{8} +O(q^{10})\) \(q+(-0.856692 + 2.63663i) q^{2} +(0.254251 + 0.184724i) q^{4} +(-7.75979 - 8.04895i) q^{5} -7.15708 q^{7} +(-18.6477 + 13.5483i) q^{8} +(27.8698 - 13.5642i) q^{10} +(15.3917 - 47.3707i) q^{11} +(16.6242 + 51.1641i) q^{13} +(6.13142 - 18.8706i) q^{14} +(-18.9696 - 58.3826i) q^{16} +(-10.7434 + 7.80553i) q^{17} +(124.404 - 90.3850i) q^{19} +(-0.486099 - 3.47988i) q^{20} +(111.713 + 81.1643i) q^{22} +(66.4882 - 204.630i) q^{23} +(-4.57128 + 124.916i) q^{25} -149.143 q^{26} +(-1.81970 - 1.32209i) q^{28} +(-56.2588 - 40.8744i) q^{29} +(122.680 - 89.1322i) q^{31} -14.2140 q^{32} +(-11.3765 - 35.0133i) q^{34} +(55.5375 + 57.6070i) q^{35} +(-92.0967 - 283.445i) q^{37} +(131.735 + 405.440i) q^{38} +(253.752 + 44.9620i) q^{40} +(110.882 + 341.260i) q^{41} +451.178 q^{43} +(12.6639 - 9.20084i) q^{44} +(482.572 + 350.609i) q^{46} +(124.804 + 90.6754i) q^{47} -291.776 q^{49} +(-325.442 - 119.068i) q^{50} +(-5.22453 + 16.0794i) q^{52} +(39.5720 + 28.7507i) q^{53} +(-500.721 + 243.700i) q^{55} +(133.463 - 96.9665i) q^{56} +(155.967 - 113.317i) q^{58} +(-9.36171 - 28.8124i) q^{59} +(175.261 - 539.399i) q^{61} +(129.909 + 399.820i) q^{62} +(163.934 - 504.537i) q^{64} +(282.817 - 530.831i) q^{65} +(-557.154 + 404.796i) q^{67} -4.17339 q^{68} +(-199.467 + 97.0802i) q^{70} +(-684.549 - 497.354i) q^{71} +(-110.215 + 339.207i) q^{73} +826.236 q^{74} +48.3262 q^{76} +(-110.160 + 339.036i) q^{77} +(-158.437 - 115.111i) q^{79} +(-322.718 + 605.722i) q^{80} -994.767 q^{82} +(580.078 - 421.451i) q^{83} +(146.193 + 25.9038i) q^{85} +(-386.521 + 1189.59i) q^{86} +(354.775 + 1091.88i) q^{88} +(371.049 - 1141.97i) q^{89} +(-118.981 - 366.186i) q^{91} +(54.7048 - 39.7453i) q^{92} +(-345.996 + 251.381i) q^{94} +(-1692.85 - 299.955i) q^{95} +(-1001.28 - 727.475i) q^{97} +(249.962 - 769.305i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 72 q^{4} + 20 q^{7} + O(q^{10}) \) \( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.856692 + 2.63663i −0.302886 + 0.932189i 0.677571 + 0.735457i \(0.263033\pi\)
−0.980457 + 0.196731i \(0.936967\pi\)
\(3\) 0 0
\(4\) 0.254251 + 0.184724i 0.0317814 + 0.0230905i
\(5\) −7.75979 8.04895i −0.694057 0.719920i
\(6\) 0 0
\(7\) −7.15708 −0.386446 −0.193223 0.981155i \(-0.561894\pi\)
−0.193223 + 0.981155i \(0.561894\pi\)
\(8\) −18.6477 + 13.5483i −0.824118 + 0.598757i
\(9\) 0 0
\(10\) 27.8698 13.5642i 0.881322 0.428938i
\(11\) 15.3917 47.3707i 0.421888 1.29844i −0.484055 0.875037i \(-0.660837\pi\)
0.905943 0.423400i \(-0.139163\pi\)
\(12\) 0 0
\(13\) 16.6242 + 51.1641i 0.354672 + 1.09157i 0.956200 + 0.292716i \(0.0945589\pi\)
−0.601528 + 0.798852i \(0.705441\pi\)
\(14\) 6.13142 18.8706i 0.117049 0.360241i
\(15\) 0 0
\(16\) −18.9696 58.3826i −0.296401 0.912228i
\(17\) −10.7434 + 7.80553i −0.153274 + 0.111360i −0.661779 0.749699i \(-0.730198\pi\)
0.508505 + 0.861059i \(0.330198\pi\)
\(18\) 0 0
\(19\) 124.404 90.3850i 1.50212 1.09135i 0.532593 0.846372i \(-0.321218\pi\)
0.969527 0.244983i \(-0.0787822\pi\)
\(20\) −0.486099 3.47988i −0.00543475 0.0389062i
\(21\) 0 0
\(22\) 111.713 + 81.1643i 1.08260 + 0.786558i
\(23\) 66.4882 204.630i 0.602772 1.85514i 0.0913347 0.995820i \(-0.470887\pi\)
0.511437 0.859321i \(-0.329113\pi\)
\(24\) 0 0
\(25\) −4.57128 + 124.916i −0.0365702 + 0.999331i
\(26\) −149.143 −1.12497
\(27\) 0 0
\(28\) −1.81970 1.32209i −0.0122818 0.00892325i
\(29\) −56.2588 40.8744i −0.360241 0.261730i 0.392912 0.919576i \(-0.371468\pi\)
−0.753153 + 0.657846i \(0.771468\pi\)
\(30\) 0 0
\(31\) 122.680 89.1322i 0.710773 0.516407i −0.172650 0.984983i \(-0.555233\pi\)
0.883423 + 0.468576i \(0.155233\pi\)
\(32\) −14.2140 −0.0785218
\(33\) 0 0
\(34\) −11.3765 35.0133i −0.0573839 0.176610i
\(35\) 55.5375 + 57.6070i 0.268216 + 0.278210i
\(36\) 0 0
\(37\) −92.0967 283.445i −0.409206 1.25941i −0.917332 0.398123i \(-0.869662\pi\)
0.508127 0.861282i \(-0.330338\pi\)
\(38\) 131.735 + 405.440i 0.562376 + 1.73082i
\(39\) 0 0
\(40\) 253.752 + 44.9620i 1.00304 + 0.177728i
\(41\) 110.882 + 341.260i 0.422363 + 1.29990i 0.905497 + 0.424352i \(0.139498\pi\)
−0.483135 + 0.875546i \(0.660502\pi\)
\(42\) 0 0
\(43\) 451.178 1.60009 0.800047 0.599937i \(-0.204808\pi\)
0.800047 + 0.599937i \(0.204808\pi\)
\(44\) 12.6639 9.20084i 0.0433898 0.0315245i
\(45\) 0 0
\(46\) 482.572 + 350.609i 1.54677 + 1.12379i
\(47\) 124.804 + 90.6754i 0.387330 + 0.281412i 0.764361 0.644789i \(-0.223055\pi\)
−0.377030 + 0.926201i \(0.623055\pi\)
\(48\) 0 0
\(49\) −291.776 −0.850659
\(50\) −325.442 119.068i −0.920489 0.336774i
\(51\) 0 0
\(52\) −5.22453 + 16.0794i −0.0139329 + 0.0428811i
\(53\) 39.5720 + 28.7507i 0.102559 + 0.0745135i 0.637883 0.770133i \(-0.279810\pi\)
−0.535324 + 0.844647i \(0.679810\pi\)
\(54\) 0 0
\(55\) −500.721 + 243.700i −1.22759 + 0.597464i
\(56\) 133.463 96.9665i 0.318477 0.231387i
\(57\) 0 0
\(58\) 155.967 113.317i 0.353094 0.256538i
\(59\) −9.36171 28.8124i −0.0206575 0.0635772i 0.940196 0.340633i \(-0.110641\pi\)
−0.960854 + 0.277056i \(0.910641\pi\)
\(60\) 0 0
\(61\) 175.261 539.399i 0.367868 1.13218i −0.580298 0.814404i \(-0.697064\pi\)
0.948166 0.317776i \(-0.102936\pi\)
\(62\) 129.909 + 399.820i 0.266105 + 0.818987i
\(63\) 0 0
\(64\) 163.934 504.537i 0.320184 0.985425i
\(65\) 282.817 530.831i 0.539679 1.01295i
\(66\) 0 0
\(67\) −557.154 + 404.796i −1.01593 + 0.738115i −0.965444 0.260610i \(-0.916076\pi\)
−0.0504840 + 0.998725i \(0.516076\pi\)
\(68\) −4.17339 −0.00744262
\(69\) 0 0
\(70\) −199.467 + 97.0802i −0.340584 + 0.165761i
\(71\) −684.549 497.354i −1.14424 0.831339i −0.156536 0.987672i \(-0.550033\pi\)
−0.987704 + 0.156333i \(0.950033\pi\)
\(72\) 0 0
\(73\) −110.215 + 339.207i −0.176708 + 0.543851i −0.999707 0.0241912i \(-0.992299\pi\)
0.822999 + 0.568042i \(0.192299\pi\)
\(74\) 826.236 1.29795
\(75\) 0 0
\(76\) 48.3262 0.0729394
\(77\) −110.160 + 339.036i −0.163037 + 0.501776i
\(78\) 0 0
\(79\) −158.437 115.111i −0.225640 0.163937i 0.469222 0.883080i \(-0.344535\pi\)
−0.694862 + 0.719143i \(0.744535\pi\)
\(80\) −322.718 + 605.722i −0.451012 + 0.846523i
\(81\) 0 0
\(82\) −994.767 −1.33968
\(83\) 580.078 421.451i 0.767130 0.557353i −0.133959 0.990987i \(-0.542769\pi\)
0.901089 + 0.433634i \(0.142769\pi\)
\(84\) 0 0
\(85\) 146.193 + 25.9038i 0.186551 + 0.0330548i
\(86\) −386.521 + 1189.59i −0.484647 + 1.49159i
\(87\) 0 0
\(88\) 354.775 + 1091.88i 0.429763 + 1.32267i
\(89\) 371.049 1141.97i 0.441922 1.36010i −0.443902 0.896076i \(-0.646406\pi\)
0.885824 0.464022i \(-0.153594\pi\)
\(90\) 0 0
\(91\) −118.981 366.186i −0.137062 0.421832i
\(92\) 54.7048 39.7453i 0.0619931 0.0450406i
\(93\) 0 0
\(94\) −345.996 + 251.381i −0.379646 + 0.275829i
\(95\) −1692.85 299.955i −1.82824 0.323945i
\(96\) 0 0
\(97\) −1001.28 727.475i −1.04809 0.761483i −0.0762433 0.997089i \(-0.524293\pi\)
−0.971849 + 0.235606i \(0.924293\pi\)
\(98\) 249.962 769.305i 0.257653 0.792975i
\(99\) 0 0
\(100\) −24.2373 + 30.9157i −0.0242373 + 0.0309157i
\(101\) −365.423 −0.360010 −0.180005 0.983666i \(-0.557611\pi\)
−0.180005 + 0.983666i \(0.557611\pi\)
\(102\) 0 0
\(103\) −157.043 114.098i −0.150232 0.109150i 0.510130 0.860097i \(-0.329597\pi\)
−0.660362 + 0.750947i \(0.729597\pi\)
\(104\) −1003.19 728.861i −0.945875 0.687218i
\(105\) 0 0
\(106\) −109.706 + 79.7060i −0.100524 + 0.0730352i
\(107\) −286.289 −0.258660 −0.129330 0.991602i \(-0.541283\pi\)
−0.129330 + 0.991602i \(0.541283\pi\)
\(108\) 0 0
\(109\) −437.785 1347.36i −0.384699 1.18398i −0.936699 0.350137i \(-0.886135\pi\)
0.552000 0.833844i \(-0.313865\pi\)
\(110\) −213.582 1528.99i −0.185130 1.32530i
\(111\) 0 0
\(112\) 135.767 + 417.849i 0.114543 + 0.352527i
\(113\) 348.438 + 1072.38i 0.290074 + 0.892755i 0.984832 + 0.173512i \(0.0555114\pi\)
−0.694758 + 0.719244i \(0.744489\pi\)
\(114\) 0 0
\(115\) −2162.99 + 1052.72i −1.75391 + 0.853626i
\(116\) −6.75336 20.7847i −0.00540547 0.0166363i
\(117\) 0 0
\(118\) 83.9877 0.0655228
\(119\) 76.8914 55.8648i 0.0592321 0.0430346i
\(120\) 0 0
\(121\) −930.279 675.887i −0.698933 0.507804i
\(122\) 1272.05 + 924.198i 0.943983 + 0.685844i
\(123\) 0 0
\(124\) 47.6564 0.0345135
\(125\) 1040.92 932.531i 0.744820 0.667265i
\(126\) 0 0
\(127\) −294.997 + 907.909i −0.206116 + 0.634361i 0.793549 + 0.608506i \(0.208231\pi\)
−0.999666 + 0.0258551i \(0.991769\pi\)
\(128\) 1097.84 + 797.629i 0.758097 + 0.550790i
\(129\) 0 0
\(130\) 1157.32 + 1200.44i 0.780795 + 0.809890i
\(131\) −1193.22 + 866.926i −0.795818 + 0.578196i −0.909684 0.415300i \(-0.863677\pi\)
0.113866 + 0.993496i \(0.463677\pi\)
\(132\) 0 0
\(133\) −890.371 + 646.893i −0.580489 + 0.421750i
\(134\) −589.987 1815.79i −0.380352 1.17060i
\(135\) 0 0
\(136\) 94.5873 291.110i 0.0596382 0.183547i
\(137\) 286.735 + 882.480i 0.178813 + 0.550331i 0.999787 0.0206352i \(-0.00656884\pi\)
−0.820974 + 0.570966i \(0.806569\pi\)
\(138\) 0 0
\(139\) 285.429 878.460i 0.174171 0.536043i −0.825424 0.564514i \(-0.809064\pi\)
0.999595 + 0.0284706i \(0.00906369\pi\)
\(140\) 3.47905 + 24.9058i 0.00210024 + 0.0150352i
\(141\) 0 0
\(142\) 1897.79 1378.82i 1.12154 0.814846i
\(143\) 2679.56 1.56696
\(144\) 0 0
\(145\) 107.560 + 770.001i 0.0616027 + 0.441001i
\(146\) −799.941 581.191i −0.453449 0.329450i
\(147\) 0 0
\(148\) 28.9434 89.0786i 0.0160752 0.0494744i
\(149\) 1993.74 1.09620 0.548098 0.836414i \(-0.315352\pi\)
0.548098 + 0.836414i \(0.315352\pi\)
\(150\) 0 0
\(151\) 1706.75 0.919825 0.459913 0.887964i \(-0.347881\pi\)
0.459913 + 0.887964i \(0.347881\pi\)
\(152\) −1095.28 + 3370.94i −0.584469 + 1.79881i
\(153\) 0 0
\(154\) −799.539 580.899i −0.418368 0.303962i
\(155\) −1669.39 295.798i −0.865088 0.153284i
\(156\) 0 0
\(157\) 489.227 0.248692 0.124346 0.992239i \(-0.460317\pi\)
0.124346 + 0.992239i \(0.460317\pi\)
\(158\) 439.238 319.125i 0.221164 0.160685i
\(159\) 0 0
\(160\) 110.297 + 114.408i 0.0544986 + 0.0565295i
\(161\) −475.862 + 1464.55i −0.232939 + 0.716912i
\(162\) 0 0
\(163\) −1064.87 3277.32i −0.511698 1.57485i −0.789210 0.614123i \(-0.789510\pi\)
0.277512 0.960722i \(-0.410490\pi\)
\(164\) −34.8471 + 107.248i −0.0165921 + 0.0510652i
\(165\) 0 0
\(166\) 614.262 + 1890.50i 0.287205 + 0.883925i
\(167\) −748.980 + 544.166i −0.347053 + 0.252148i −0.747632 0.664114i \(-0.768809\pi\)
0.400579 + 0.916262i \(0.368809\pi\)
\(168\) 0 0
\(169\) −563.993 + 409.765i −0.256710 + 0.186511i
\(170\) −193.541 + 363.265i −0.0873171 + 0.163889i
\(171\) 0 0
\(172\) 114.713 + 83.3436i 0.0508532 + 0.0369470i
\(173\) 200.254 616.317i 0.0880058 0.270854i −0.897362 0.441295i \(-0.854519\pi\)
0.985368 + 0.170441i \(0.0545193\pi\)
\(174\) 0 0
\(175\) 32.7170 894.037i 0.0141324 0.386188i
\(176\) −3057.60 −1.30952
\(177\) 0 0
\(178\) 2693.08 + 1956.64i 1.13401 + 0.823910i
\(179\) 1657.52 + 1204.26i 0.692115 + 0.502851i 0.877355 0.479842i \(-0.159306\pi\)
−0.185240 + 0.982693i \(0.559306\pi\)
\(180\) 0 0
\(181\) 729.361 529.912i 0.299519 0.217614i −0.427867 0.903842i \(-0.640735\pi\)
0.727386 + 0.686228i \(0.240735\pi\)
\(182\) 1067.43 0.434741
\(183\) 0 0
\(184\) 1532.54 + 4716.67i 0.614023 + 1.88977i
\(185\) −1566.78 + 2940.75i −0.622659 + 1.16869i
\(186\) 0 0
\(187\) 204.395 + 629.062i 0.0799295 + 0.245998i
\(188\) 14.9816 + 46.1086i 0.00581195 + 0.0178873i
\(189\) 0 0
\(190\) 2241.13 4206.46i 0.855728 1.60615i
\(191\) 899.058 + 2767.02i 0.340594 + 1.04824i 0.963900 + 0.266264i \(0.0857892\pi\)
−0.623306 + 0.781978i \(0.714211\pi\)
\(192\) 0 0
\(193\) 184.846 0.0689406 0.0344703 0.999406i \(-0.489026\pi\)
0.0344703 + 0.999406i \(0.489026\pi\)
\(194\) 2775.87 2016.79i 1.02730 0.746377i
\(195\) 0 0
\(196\) −74.1844 53.8981i −0.0270351 0.0196422i
\(197\) 2578.89 + 1873.67i 0.932682 + 0.677633i 0.946648 0.322269i \(-0.104446\pi\)
−0.0139660 + 0.999902i \(0.504446\pi\)
\(198\) 0 0
\(199\) 2048.58 0.729749 0.364874 0.931057i \(-0.381112\pi\)
0.364874 + 0.931057i \(0.381112\pi\)
\(200\) −1607.16 2391.33i −0.568218 0.845463i
\(201\) 0 0
\(202\) 313.055 963.485i 0.109042 0.335597i
\(203\) 402.649 + 292.541i 0.139214 + 0.101145i
\(204\) 0 0
\(205\) 1886.36 3540.59i 0.642679 1.20627i
\(206\) 435.373 316.317i 0.147252 0.106985i
\(207\) 0 0
\(208\) 2671.74 1941.13i 0.890633 0.647083i
\(209\) −2366.81 7284.29i −0.783329 2.41084i
\(210\) 0 0
\(211\) −921.101 + 2834.86i −0.300527 + 0.924927i 0.680782 + 0.732487i \(0.261640\pi\)
−0.981309 + 0.192441i \(0.938360\pi\)
\(212\) 4.75026 + 14.6198i 0.00153891 + 0.00473628i
\(213\) 0 0
\(214\) 245.261 754.837i 0.0783445 0.241120i
\(215\) −3501.05 3631.51i −1.11056 1.15194i
\(216\) 0 0
\(217\) −878.030 + 637.926i −0.274676 + 0.199563i
\(218\) 3927.54 1.22021
\(219\) 0 0
\(220\) −172.326 30.5343i −0.0528101 0.00935737i
\(221\) −577.964 419.915i −0.175919 0.127812i
\(222\) 0 0
\(223\) −575.194 + 1770.27i −0.172726 + 0.531595i −0.999522 0.0309059i \(-0.990161\pi\)
0.826797 + 0.562501i \(0.190161\pi\)
\(224\) 101.731 0.0303445
\(225\) 0 0
\(226\) −3125.98 −0.920076
\(227\) −405.456 + 1247.86i −0.118551 + 0.364862i −0.992671 0.120848i \(-0.961439\pi\)
0.874120 + 0.485710i \(0.161439\pi\)
\(228\) 0 0
\(229\) 3473.56 + 2523.69i 1.00236 + 0.728255i 0.962592 0.270955i \(-0.0873393\pi\)
0.0397643 + 0.999209i \(0.487339\pi\)
\(230\) −922.623 6604.86i −0.264504 1.89353i
\(231\) 0 0
\(232\) 1602.87 0.453594
\(233\) 355.013 257.932i 0.0998184 0.0725223i −0.536756 0.843737i \(-0.680351\pi\)
0.636575 + 0.771215i \(0.280351\pi\)
\(234\) 0 0
\(235\) −238.611 1708.16i −0.0662351 0.474163i
\(236\) 2.94212 9.05492i 0.000811508 0.00249756i
\(237\) 0 0
\(238\) 81.4226 + 250.593i 0.0221758 + 0.0682501i
\(239\) −1047.42 + 3223.62i −0.283480 + 0.872462i 0.703370 + 0.710824i \(0.251678\pi\)
−0.986850 + 0.161638i \(0.948322\pi\)
\(240\) 0 0
\(241\) −850.354 2617.12i −0.227287 0.699517i −0.998051 0.0623969i \(-0.980126\pi\)
0.770765 0.637120i \(-0.219874\pi\)
\(242\) 2579.03 1873.77i 0.685067 0.497730i
\(243\) 0 0
\(244\) 144.201 104.768i 0.0378340 0.0274880i
\(245\) 2264.12 + 2348.49i 0.590406 + 0.612407i
\(246\) 0 0
\(247\) 6692.59 + 4862.45i 1.72405 + 1.25259i
\(248\) −1080.10 + 3324.21i −0.276559 + 0.851160i
\(249\) 0 0
\(250\) 1566.99 + 3543.41i 0.396421 + 0.896419i
\(251\) −3369.50 −0.847334 −0.423667 0.905818i \(-0.639257\pi\)
−0.423667 + 0.905818i \(0.639257\pi\)
\(252\) 0 0
\(253\) −8670.09 6299.19i −2.15448 1.56532i
\(254\) −2141.10 1555.60i −0.528914 0.384279i
\(255\) 0 0
\(256\) 389.919 283.293i 0.0951951 0.0691633i
\(257\) −4556.70 −1.10599 −0.552994 0.833185i \(-0.686515\pi\)
−0.552994 + 0.833185i \(0.686515\pi\)
\(258\) 0 0
\(259\) 659.144 + 2028.64i 0.158136 + 0.486692i
\(260\) 169.964 82.7211i 0.0405412 0.0197313i
\(261\) 0 0
\(262\) −1263.54 3888.77i −0.297945 0.916981i
\(263\) −1302.86 4009.78i −0.305466 0.940129i −0.979503 0.201431i \(-0.935441\pi\)
0.674036 0.738698i \(-0.264559\pi\)
\(264\) 0 0
\(265\) −75.6570 541.612i −0.0175380 0.125551i
\(266\) −942.841 2901.77i −0.217328 0.668867i
\(267\) 0 0
\(268\) −216.433 −0.0493311
\(269\) −525.519 + 381.812i −0.119113 + 0.0865408i −0.645747 0.763551i \(-0.723454\pi\)
0.526634 + 0.850092i \(0.323454\pi\)
\(270\) 0 0
\(271\) −1185.38 861.228i −0.265707 0.193047i 0.446952 0.894558i \(-0.352509\pi\)
−0.712659 + 0.701510i \(0.752509\pi\)
\(272\) 659.505 + 479.159i 0.147016 + 0.106813i
\(273\) 0 0
\(274\) −2572.41 −0.567172
\(275\) 5847.02 + 2139.22i 1.28214 + 0.469090i
\(276\) 0 0
\(277\) 711.145 2188.68i 0.154255 0.474747i −0.843830 0.536611i \(-0.819704\pi\)
0.998085 + 0.0618637i \(0.0197044\pi\)
\(278\) 2071.65 + 1505.14i 0.446939 + 0.324721i
\(279\) 0 0
\(280\) −1816.12 321.797i −0.387622 0.0686823i
\(281\) −6769.19 + 4918.10i −1.43707 + 1.04409i −0.448423 + 0.893822i \(0.648014\pi\)
−0.988645 + 0.150269i \(0.951986\pi\)
\(282\) 0 0
\(283\) −470.418 + 341.779i −0.0988108 + 0.0717903i −0.636094 0.771612i \(-0.719451\pi\)
0.537283 + 0.843402i \(0.319451\pi\)
\(284\) −82.1740 252.906i −0.0171695 0.0528422i
\(285\) 0 0
\(286\) −2295.56 + 7064.99i −0.474612 + 1.46071i
\(287\) −793.592 2442.43i −0.163220 0.502341i
\(288\) 0 0
\(289\) −1463.71 + 4504.82i −0.297925 + 0.916919i
\(290\) −2122.35 376.057i −0.429754 0.0761478i
\(291\) 0 0
\(292\) −90.6819 + 65.8843i −0.0181738 + 0.0132041i
\(293\) 2079.50 0.414627 0.207313 0.978275i \(-0.433528\pi\)
0.207313 + 0.978275i \(0.433528\pi\)
\(294\) 0 0
\(295\) −159.265 + 298.930i −0.0314330 + 0.0589979i
\(296\) 5557.58 + 4037.82i 1.09131 + 0.792884i
\(297\) 0 0
\(298\) −1708.02 + 5256.74i −0.332023 + 1.02186i
\(299\) 11575.0 2.23880
\(300\) 0 0
\(301\) −3229.12 −0.618350
\(302\) −1462.16 + 4500.07i −0.278603 + 0.857451i
\(303\) 0 0
\(304\) −7636.81 5548.47i −1.44079 1.04680i
\(305\) −5701.59 + 2774.95i −1.07040 + 0.520962i
\(306\) 0 0
\(307\) 5017.05 0.932698 0.466349 0.884601i \(-0.345569\pi\)
0.466349 + 0.884601i \(0.345569\pi\)
\(308\) −90.6364 + 65.8512i −0.0167678 + 0.0121825i
\(309\) 0 0
\(310\) 2210.06 4148.16i 0.404913 0.759998i
\(311\) 926.375 2851.09i 0.168906 0.519841i −0.830396 0.557173i \(-0.811886\pi\)
0.999303 + 0.0373323i \(0.0118860\pi\)
\(312\) 0 0
\(313\) −1432.91 4410.05i −0.258763 0.796392i −0.993065 0.117568i \(-0.962490\pi\)
0.734302 0.678823i \(-0.237510\pi\)
\(314\) −419.117 + 1289.91i −0.0753253 + 0.231827i
\(315\) 0 0
\(316\) −19.0190 58.5344i −0.00338576 0.0104203i
\(317\) 1121.63 814.913i 0.198729 0.144385i −0.483971 0.875084i \(-0.660806\pi\)
0.682699 + 0.730699i \(0.260806\pi\)
\(318\) 0 0
\(319\) −2802.17 + 2035.89i −0.491822 + 0.357329i
\(320\) −5333.09 + 2595.61i −0.931653 + 0.453434i
\(321\) 0 0
\(322\) −3453.81 2509.34i −0.597743 0.434286i
\(323\) −631.021 + 1942.08i −0.108703 + 0.334552i
\(324\) 0 0
\(325\) −6467.23 + 1842.75i −1.10381 + 0.314516i
\(326\) 9553.34 1.62304
\(327\) 0 0
\(328\) −6691.19 4861.43i −1.12640 0.818377i
\(329\) −893.232 648.971i −0.149682 0.108751i
\(330\) 0 0
\(331\) −6494.76 + 4718.72i −1.07850 + 0.783578i −0.977421 0.211300i \(-0.932230\pi\)
−0.101081 + 0.994878i \(0.532230\pi\)
\(332\) 225.338 0.0372500
\(333\) 0 0
\(334\) −793.117 2440.96i −0.129932 0.399891i
\(335\) 7581.58 + 1343.37i 1.23650 + 0.219093i
\(336\) 0 0
\(337\) 2266.96 + 6976.97i 0.366436 + 1.12777i 0.949077 + 0.315045i \(0.102019\pi\)
−0.582641 + 0.812730i \(0.697981\pi\)
\(338\) −597.229 1838.08i −0.0961094 0.295794i
\(339\) 0 0
\(340\) 32.3846 + 33.5914i 0.00516560 + 0.00535809i
\(341\) −2334.00 7183.33i −0.370655 1.14076i
\(342\) 0 0
\(343\) 4543.15 0.715180
\(344\) −8413.42 + 6112.71i −1.31867 + 0.958067i
\(345\) 0 0
\(346\) 1453.44 + 1055.99i 0.225831 + 0.164076i
\(347\) 5317.34 + 3863.27i 0.822621 + 0.597669i 0.917462 0.397823i \(-0.130234\pi\)
−0.0948410 + 0.995492i \(0.530234\pi\)
\(348\) 0 0
\(349\) 11655.8 1.78774 0.893868 0.448331i \(-0.147981\pi\)
0.893868 + 0.448331i \(0.147981\pi\)
\(350\) 2329.21 + 852.177i 0.355719 + 0.130145i
\(351\) 0 0
\(352\) −218.777 + 673.326i −0.0331274 + 0.101956i
\(353\) −569.531 413.788i −0.0858727 0.0623902i 0.544021 0.839072i \(-0.316901\pi\)
−0.629893 + 0.776682i \(0.716901\pi\)
\(354\) 0 0
\(355\) 1308.78 + 9369.27i 0.195670 + 1.40076i
\(356\) 305.289 221.806i 0.0454503 0.0330216i
\(357\) 0 0
\(358\) −4595.16 + 3338.58i −0.678384 + 0.492875i
\(359\) −1732.60 5332.39i −0.254716 0.783935i −0.993885 0.110416i \(-0.964782\pi\)
0.739170 0.673519i \(-0.235218\pi\)
\(360\) 0 0
\(361\) 5187.42 15965.2i 0.756294 2.32763i
\(362\) 772.342 + 2377.03i 0.112137 + 0.345121i
\(363\) 0 0
\(364\) 37.3924 115.082i 0.00538432 0.0165712i
\(365\) 3585.50 1745.06i 0.514175 0.250248i
\(366\) 0 0
\(367\) −1908.15 + 1386.35i −0.271402 + 0.197185i −0.715159 0.698962i \(-0.753646\pi\)
0.443756 + 0.896147i \(0.353646\pi\)
\(368\) −13208.1 −1.87097
\(369\) 0 0
\(370\) −6411.42 6650.34i −0.900848 0.934418i
\(371\) −283.220 205.771i −0.0396335 0.0287954i
\(372\) 0 0
\(373\) −1665.42 + 5125.62i −0.231185 + 0.711514i 0.766420 + 0.642340i \(0.222036\pi\)
−0.997605 + 0.0691739i \(0.977964\pi\)
\(374\) −1833.71 −0.253526
\(375\) 0 0
\(376\) −3555.80 −0.487703
\(377\) 1156.04 3557.94i 0.157929 0.486056i
\(378\) 0 0
\(379\) 2275.81 + 1653.47i 0.308445 + 0.224098i 0.731229 0.682132i \(-0.238947\pi\)
−0.422784 + 0.906230i \(0.638947\pi\)
\(380\) −375.001 388.975i −0.0506241 0.0525106i
\(381\) 0 0
\(382\) −8065.81 −1.08032
\(383\) 7657.03 5563.16i 1.02156 0.742204i 0.0549545 0.998489i \(-0.482499\pi\)
0.966601 + 0.256285i \(0.0824986\pi\)
\(384\) 0 0
\(385\) 3583.70 1744.18i 0.474396 0.230888i
\(386\) −158.357 + 487.371i −0.0208812 + 0.0642657i
\(387\) 0 0
\(388\) −120.195 369.923i −0.0157268 0.0484020i
\(389\) −4368.83 + 13445.9i −0.569431 + 1.75253i 0.0849726 + 0.996383i \(0.472920\pi\)
−0.654404 + 0.756145i \(0.727080\pi\)
\(390\) 0 0
\(391\) 882.934 + 2717.39i 0.114199 + 0.351469i
\(392\) 5440.94 3953.08i 0.701044 0.509338i
\(393\) 0 0
\(394\) −7149.50 + 5194.41i −0.914179 + 0.664190i
\(395\) 302.914 + 2168.49i 0.0385854 + 0.276225i
\(396\) 0 0
\(397\) −11467.9 8331.93i −1.44977 1.05332i −0.985885 0.167423i \(-0.946455\pi\)
−0.463884 0.885896i \(-0.653545\pi\)
\(398\) −1755.00 + 5401.34i −0.221031 + 0.680264i
\(399\) 0 0
\(400\) 7379.65 2102.74i 0.922457 0.262842i
\(401\) 5740.98 0.714940 0.357470 0.933925i \(-0.383639\pi\)
0.357470 + 0.933925i \(0.383639\pi\)
\(402\) 0 0
\(403\) 6599.83 + 4795.06i 0.815784 + 0.592702i
\(404\) −92.9092 67.5025i −0.0114416 0.00831281i
\(405\) 0 0
\(406\) −1116.27 + 811.017i −0.136452 + 0.0991382i
\(407\) −14844.5 −1.80790
\(408\) 0 0
\(409\) 312.072 + 960.459i 0.0377285 + 0.116117i 0.968147 0.250382i \(-0.0805563\pi\)
−0.930418 + 0.366499i \(0.880556\pi\)
\(410\) 7719.18 + 8006.83i 0.929813 + 0.964462i
\(411\) 0 0
\(412\) −18.8516 58.0193i −0.00225425 0.00693788i
\(413\) 67.0026 + 206.213i 0.00798300 + 0.0245692i
\(414\) 0 0
\(415\) −7893.52 1398.65i −0.933681 0.165438i
\(416\) −236.296 727.246i −0.0278495 0.0857119i
\(417\) 0 0
\(418\) 21233.6 2.48462
\(419\) −1306.11 + 948.947i −0.152286 + 0.110642i −0.661319 0.750105i \(-0.730003\pi\)
0.509033 + 0.860747i \(0.330003\pi\)
\(420\) 0 0
\(421\) 7924.08 + 5757.18i 0.917330 + 0.666480i 0.942858 0.333195i \(-0.108127\pi\)
−0.0255276 + 0.999674i \(0.508127\pi\)
\(422\) −6685.36 4857.20i −0.771181 0.560296i
\(423\) 0 0
\(424\) −1127.45 −0.129136
\(425\) −925.928 1377.71i −0.105680 0.157244i
\(426\) 0 0
\(427\) −1254.36 + 3860.53i −0.142161 + 0.437527i
\(428\) −72.7893 52.8845i −0.00822057 0.00597259i
\(429\) 0 0
\(430\) 12574.3 6119.88i 1.41020 0.686341i
\(431\) 2915.55 2118.27i 0.325840 0.236736i −0.412824 0.910811i \(-0.635457\pi\)
0.738663 + 0.674075i \(0.235457\pi\)
\(432\) 0 0
\(433\) 8305.22 6034.09i 0.921763 0.669700i −0.0221993 0.999754i \(-0.507067\pi\)
0.943962 + 0.330054i \(0.107067\pi\)
\(434\) −929.773 2861.55i −0.102835 0.316494i
\(435\) 0 0
\(436\) 137.583 423.438i 0.0151125 0.0465115i
\(437\) −10224.0 31466.3i −1.11918 3.44448i
\(438\) 0 0
\(439\) 4195.10 12911.2i 0.456084 1.40368i −0.413773 0.910380i \(-0.635789\pi\)
0.869858 0.493303i \(-0.164211\pi\)
\(440\) 6035.55 11328.4i 0.653940 1.22741i
\(441\) 0 0
\(442\) 1602.30 1164.14i 0.172429 0.125277i
\(443\) −16740.4 −1.79540 −0.897699 0.440609i \(-0.854762\pi\)
−0.897699 + 0.440609i \(0.854762\pi\)
\(444\) 0 0
\(445\) −12070.9 + 5874.90i −1.28588 + 0.625836i
\(446\) −4174.77 3033.15i −0.443231 0.322026i
\(447\) 0 0
\(448\) −1173.29 + 3611.02i −0.123734 + 0.380814i
\(449\) 18160.7 1.90882 0.954408 0.298505i \(-0.0964880\pi\)
0.954408 + 0.298505i \(0.0964880\pi\)
\(450\) 0 0
\(451\) 17872.4 1.86603
\(452\) −109.504 + 337.020i −0.0113952 + 0.0350710i
\(453\) 0 0
\(454\) −2942.80 2138.07i −0.304213 0.221024i
\(455\) −2024.15 + 3799.20i −0.208557 + 0.391449i
\(456\) 0 0
\(457\) 2032.75 0.208070 0.104035 0.994574i \(-0.466825\pi\)
0.104035 + 0.994574i \(0.466825\pi\)
\(458\) −9629.81 + 6996.47i −0.982471 + 0.713807i
\(459\) 0 0
\(460\) −744.406 131.901i −0.0754524 0.0133693i
\(461\) 1858.95 5721.26i 0.187809 0.578017i −0.812176 0.583412i \(-0.801717\pi\)
0.999985 + 0.00539516i \(0.00171734\pi\)
\(462\) 0 0
\(463\) 1811.95 + 5576.62i 0.181876 + 0.559757i 0.999881 0.0154550i \(-0.00491968\pi\)
−0.818005 + 0.575212i \(0.804920\pi\)
\(464\) −1319.14 + 4059.90i −0.131982 + 0.406199i
\(465\) 0 0
\(466\) 375.934 + 1157.01i 0.0373709 + 0.115016i
\(467\) 7272.50 5283.78i 0.720624 0.523564i −0.165960 0.986133i \(-0.553072\pi\)
0.886583 + 0.462569i \(0.153072\pi\)
\(468\) 0 0
\(469\) 3987.60 2897.16i 0.392602 0.285242i
\(470\) 4708.21 + 834.242i 0.462071 + 0.0818739i
\(471\) 0 0
\(472\) 564.933 + 410.448i 0.0550915 + 0.0400263i
\(473\) 6944.39 21372.6i 0.675060 2.07762i
\(474\) 0 0
\(475\) 10721.9 + 15953.3i 1.03569 + 1.54103i
\(476\) 29.8693 0.00287617
\(477\) 0 0
\(478\) −7602.16 5523.30i −0.727437 0.528514i
\(479\) −5375.66 3905.65i −0.512777 0.372554i 0.301099 0.953593i \(-0.402647\pi\)
−0.813876 + 0.581039i \(0.802647\pi\)
\(480\) 0 0
\(481\) 12971.2 9424.10i 1.22959 0.893351i
\(482\) 7628.87 0.720924
\(483\) 0 0
\(484\) −111.672 343.690i −0.0104876 0.0322774i
\(485\) 1914.34 + 13704.3i 0.179228 + 1.28306i
\(486\) 0 0
\(487\) 2239.85 + 6893.56i 0.208414 + 0.641431i 0.999556 + 0.0297992i \(0.00948677\pi\)
−0.791142 + 0.611632i \(0.790513\pi\)
\(488\) 4039.74 + 12433.0i 0.374734 + 1.15331i
\(489\) 0 0
\(490\) −8131.76 + 3957.71i −0.749705 + 0.364880i
\(491\) 4273.47 + 13152.4i 0.392788 + 1.20888i 0.930671 + 0.365858i \(0.119224\pi\)
−0.537883 + 0.843020i \(0.680776\pi\)
\(492\) 0 0
\(493\) 923.456 0.0843618
\(494\) −18554.0 + 13480.2i −1.68984 + 1.22774i
\(495\) 0 0
\(496\) −7530.96 5471.56i −0.681754 0.495323i
\(497\) 4899.38 + 3559.61i 0.442187 + 0.321268i
\(498\) 0 0
\(499\) 9216.11 0.826793 0.413397 0.910551i \(-0.364342\pi\)
0.413397 + 0.910551i \(0.364342\pi\)
\(500\) 436.916 44.8142i 0.0390789 0.00400831i
\(501\) 0 0
\(502\) 2886.62 8884.12i 0.256646 0.789876i
\(503\) −10276.2 7466.09i −0.910919 0.661822i 0.0303278 0.999540i \(-0.490345\pi\)
−0.941247 + 0.337718i \(0.890345\pi\)
\(504\) 0 0
\(505\) 2835.61 + 2941.27i 0.249867 + 0.259178i
\(506\) 24036.2 17463.3i 2.11174 1.53427i
\(507\) 0 0
\(508\) −242.716 + 176.344i −0.0211984 + 0.0154015i
\(509\) 2793.42 + 8597.26i 0.243254 + 0.748658i 0.995919 + 0.0902544i \(0.0287680\pi\)
−0.752665 + 0.658404i \(0.771232\pi\)
\(510\) 0 0
\(511\) 788.817 2427.73i 0.0682881 0.210169i
\(512\) 3767.60 + 11595.5i 0.325207 + 1.00088i
\(513\) 0 0
\(514\) 3903.69 12014.3i 0.334989 1.03099i
\(515\) 300.248 + 2149.41i 0.0256903 + 0.183911i
\(516\) 0 0
\(517\) 6216.30 4516.41i 0.528806 0.384200i
\(518\) −5913.44 −0.501586
\(519\) 0 0
\(520\) 1917.99 + 13730.4i 0.161749 + 1.15792i
\(521\) 10554.5 + 7668.29i 0.887526 + 0.644825i 0.935232 0.354036i \(-0.115191\pi\)
−0.0477059 + 0.998861i \(0.515191\pi\)
\(522\) 0 0
\(523\) −3201.49 + 9853.17i −0.267670 + 0.823803i 0.723396 + 0.690433i \(0.242580\pi\)
−0.991066 + 0.133370i \(0.957420\pi\)
\(524\) −463.520 −0.0386431
\(525\) 0 0
\(526\) 11688.5 0.968899
\(527\) −622.274 + 1915.16i −0.0514359 + 0.158303i
\(528\) 0 0
\(529\) −27609.3 20059.3i −2.26920 1.64867i
\(530\) 1492.84 + 264.516i 0.122349 + 0.0216789i
\(531\) 0 0
\(532\) −345.875 −0.0281872
\(533\) −15616.9 + 11346.4i −1.26913 + 0.922074i
\(534\) 0 0
\(535\) 2221.54 + 2304.33i 0.179525 + 0.186214i
\(536\) 4905.31 15097.0i 0.395293 1.21659i
\(537\) 0 0
\(538\) −556.487 1712.69i −0.0445946 0.137248i
\(539\) −4490.92 + 13821.6i −0.358883 + 1.10453i
\(540\) 0 0
\(541\) −1162.41 3577.53i −0.0923770 0.284307i 0.894184 0.447699i \(-0.147756\pi\)
−0.986561 + 0.163392i \(0.947756\pi\)
\(542\) 3286.24 2387.59i 0.260436 0.189218i
\(543\) 0 0
\(544\) 152.706 110.948i 0.0120353 0.00874419i
\(545\) −7447.74 + 13979.0i −0.585369 + 1.09870i
\(546\) 0 0
\(547\) 7890.38 + 5732.70i 0.616761 + 0.448103i 0.851789 0.523886i \(-0.175518\pi\)
−0.235028 + 0.971989i \(0.575518\pi\)
\(548\) −90.1127 + 277.338i −0.00702449 + 0.0216192i
\(549\) 0 0
\(550\) −10649.4 + 13583.8i −0.825623 + 1.05312i
\(551\) −10693.3 −0.826766
\(552\) 0 0
\(553\) 1133.95 + 823.861i 0.0871978 + 0.0633529i
\(554\) 5161.50 + 3750.05i 0.395832 + 0.287589i
\(555\) 0 0
\(556\) 234.844 170.624i 0.0179129 0.0130145i
\(557\) −16009.1 −1.21783 −0.608913 0.793237i \(-0.708394\pi\)
−0.608913 + 0.793237i \(0.708394\pi\)
\(558\) 0 0
\(559\) 7500.49 + 23084.1i 0.567508 + 1.74661i
\(560\) 2309.72 4335.21i 0.174292 0.327135i
\(561\) 0 0
\(562\) −7168.10 22061.1i −0.538021 1.65586i
\(563\) 850.464 + 2617.46i 0.0636639 + 0.195937i 0.977829 0.209404i \(-0.0671525\pi\)
−0.914165 + 0.405342i \(0.867153\pi\)
\(564\) 0 0
\(565\) 5927.75 11126.0i 0.441385 0.828453i
\(566\) −498.140 1533.12i −0.0369936 0.113855i
\(567\) 0 0
\(568\) 19503.6 1.44076
\(569\) −4062.83 + 2951.82i −0.299337 + 0.217481i −0.727308 0.686312i \(-0.759229\pi\)
0.427971 + 0.903793i \(0.359229\pi\)
\(570\) 0 0
\(571\) 10.2190 + 7.42452i 0.000748950 + 0.000544144i 0.588160 0.808745i \(-0.299853\pi\)
−0.587411 + 0.809289i \(0.699853\pi\)
\(572\) 681.280 + 494.979i 0.0498003 + 0.0361820i
\(573\) 0 0
\(574\) 7119.63 0.517714
\(575\) 25257.7 + 9240.89i 1.83186 + 0.670212i
\(576\) 0 0
\(577\) −5786.32 + 17808.5i −0.417483 + 1.28488i 0.492528 + 0.870296i \(0.336073\pi\)
−0.910011 + 0.414584i \(0.863927\pi\)
\(578\) −10623.6 7718.50i −0.764504 0.555445i
\(579\) 0 0
\(580\) −114.891 + 215.643i −0.00822512 + 0.0154381i
\(581\) −4151.66 + 3016.36i −0.296455 + 0.215387i
\(582\) 0 0
\(583\) 1971.02 1432.03i 0.140019 0.101730i
\(584\) −2540.43 7818.64i −0.180006 0.554002i
\(585\) 0 0
\(586\) −1781.49 + 5482.86i −0.125585 + 0.386510i
\(587\) −5487.34 16888.3i −0.385838 1.18749i −0.935871 0.352344i \(-0.885385\pi\)
0.550033 0.835143i \(-0.314615\pi\)
\(588\) 0 0
\(589\) 7205.69 22176.8i 0.504084 1.55141i
\(590\) −651.727 676.013i −0.0454765 0.0471712i
\(591\) 0 0
\(592\) −14801.2 + 10753.7i −1.02758 + 0.746577i
\(593\) 22731.1 1.57413 0.787063 0.616873i \(-0.211601\pi\)
0.787063 + 0.616873i \(0.211601\pi\)
\(594\) 0 0
\(595\) −1046.31 185.395i −0.0720919 0.0127739i
\(596\) 506.909 + 368.291i 0.0348386 + 0.0253117i
\(597\) 0 0
\(598\) −9916.23 + 30519.0i −0.678102 + 2.08698i
\(599\) 13575.9 0.926036 0.463018 0.886349i \(-0.346767\pi\)
0.463018 + 0.886349i \(0.346767\pi\)
\(600\) 0 0
\(601\) −28512.0 −1.93516 −0.967578 0.252573i \(-0.918723\pi\)
−0.967578 + 0.252573i \(0.918723\pi\)
\(602\) 2766.36 8513.99i 0.187290 0.576419i
\(603\) 0 0
\(604\) 433.944 + 315.279i 0.0292333 + 0.0212393i
\(605\) 1778.59 + 12732.5i 0.119520 + 0.855621i
\(606\) 0 0
\(607\) −23489.6 −1.57070 −0.785349 0.619053i \(-0.787517\pi\)
−0.785349 + 0.619053i \(0.787517\pi\)
\(608\) −1768.28 + 1284.73i −0.117949 + 0.0856951i
\(609\) 0 0
\(610\) −2432.01 17410.3i −0.161425 1.15561i
\(611\) −2564.56 + 7892.89i −0.169805 + 0.522606i
\(612\) 0 0
\(613\) −6495.01 19989.6i −0.427946 1.31708i −0.900145 0.435590i \(-0.856540\pi\)
0.472199 0.881492i \(-0.343460\pi\)
\(614\) −4298.07 + 13228.1i −0.282502 + 0.869451i
\(615\) 0 0
\(616\) −2539.15 7814.71i −0.166080 0.511142i
\(617\) 3053.20 2218.28i 0.199217 0.144740i −0.483704 0.875231i \(-0.660709\pi\)
0.682922 + 0.730492i \(0.260709\pi\)
\(618\) 0 0
\(619\) −13979.6 + 10156.8i −0.907736 + 0.659509i −0.940441 0.339956i \(-0.889588\pi\)
0.0327052 + 0.999465i \(0.489588\pi\)
\(620\) −369.804 383.584i −0.0239543 0.0248469i
\(621\) 0 0
\(622\) 6723.64 + 4885.01i 0.433430 + 0.314905i
\(623\) −2655.63 + 8173.18i −0.170779 + 0.525604i
\(624\) 0 0
\(625\) −15583.2 1142.05i −0.997325 0.0730915i
\(626\) 12855.2 0.820763
\(627\) 0 0
\(628\) 124.387 + 90.3721i 0.00790376 + 0.00574242i
\(629\) 3201.87 + 2326.29i 0.202968 + 0.147465i
\(630\) 0 0
\(631\) 7560.47 5493.00i 0.476985 0.346550i −0.323172 0.946340i \(-0.604749\pi\)
0.800157 + 0.599790i \(0.204749\pi\)
\(632\) 4514.05 0.284113
\(633\) 0 0
\(634\) 1187.73 + 3655.45i 0.0744018 + 0.228985i
\(635\) 9596.83 4670.76i 0.599746 0.291895i
\(636\) 0 0
\(637\) −4850.55 14928.5i −0.301705 0.928552i
\(638\) −2967.30 9132.40i −0.184132 0.566701i
\(639\) 0 0
\(640\) −2098.95 15025.9i −0.129638 0.928049i
\(641\) −1411.17 4343.13i −0.0869544 0.267618i 0.898119 0.439752i \(-0.144934\pi\)
−0.985074 + 0.172134i \(0.944934\pi\)
\(642\) 0 0
\(643\) −752.275 −0.0461381 −0.0230691 0.999734i \(-0.507344\pi\)
−0.0230691 + 0.999734i \(0.507344\pi\)
\(644\) −391.527 + 284.461i −0.0239570 + 0.0174058i
\(645\) 0 0
\(646\) −4579.96 3327.53i −0.278941 0.202663i
\(647\) −20747.7 15074.1i −1.26070 0.915956i −0.261913 0.965092i \(-0.584353\pi\)
−0.998792 + 0.0491360i \(0.984353\pi\)
\(648\) 0 0
\(649\) −1508.96 −0.0912661
\(650\) 681.772 18630.4i 0.0411405 1.12422i
\(651\) 0 0
\(652\) 334.657 1029.97i 0.0201015 0.0618661i
\(653\) −8512.09 6184.40i −0.510113 0.370619i 0.302753 0.953069i \(-0.402094\pi\)
−0.812866 + 0.582450i \(0.802094\pi\)
\(654\) 0 0
\(655\) 16237.0 + 2877.02i 0.968598 + 0.171625i
\(656\) 17820.2 12947.2i 1.06061 0.770582i
\(657\) 0 0
\(658\) 2476.32 1799.15i 0.146713 0.106593i
\(659\) −2193.75 6751.65i −0.129676 0.399100i 0.865048 0.501688i \(-0.167288\pi\)
−0.994724 + 0.102588i \(0.967288\pi\)
\(660\) 0 0
\(661\) −6944.82 + 21373.9i −0.408657 + 1.25772i 0.509146 + 0.860680i \(0.329961\pi\)
−0.917803 + 0.397036i \(0.870039\pi\)
\(662\) −6877.50 21166.8i −0.403779 1.24270i
\(663\) 0 0
\(664\) −5107.14 + 15718.2i −0.298487 + 0.918649i
\(665\) 12115.9 + 2146.81i 0.706518 + 0.125187i
\(666\) 0 0
\(667\) −12104.7 + 8794.55i −0.702690 + 0.510534i
\(668\) −290.950 −0.0168521
\(669\) 0 0
\(670\) −10037.1 + 18839.0i −0.578754 + 1.08629i
\(671\) −22854.2 16604.5i −1.31487 0.955306i
\(672\) 0 0
\(673\) −9009.19 + 27727.4i −0.516016 + 1.58813i 0.265409 + 0.964136i \(0.414493\pi\)
−0.781426 + 0.623999i \(0.785507\pi\)
\(674\) −20337.8 −1.16229
\(675\) 0 0
\(676\) −219.089 −0.0124653
\(677\) −4869.04 + 14985.4i −0.276414 + 0.850716i 0.712428 + 0.701746i \(0.247596\pi\)
−0.988842 + 0.148970i \(0.952404\pi\)
\(678\) 0 0
\(679\) 7166.27 + 5206.60i 0.405031 + 0.294272i
\(680\) −3077.11 + 1497.62i −0.173532 + 0.0844576i
\(681\) 0 0
\(682\) 20939.3 1.17567
\(683\) 9068.24 6588.47i 0.508033 0.369108i −0.304044 0.952658i \(-0.598337\pi\)
0.812077 + 0.583550i \(0.198337\pi\)
\(684\) 0 0
\(685\) 4878.03 9155.77i 0.272088 0.510692i
\(686\) −3892.08 + 11978.6i −0.216618 + 0.666683i
\(687\) 0 0
\(688\) −8558.69 26340.9i −0.474269 1.45965i
\(689\) −813.152 + 2502.62i −0.0449617 + 0.138378i
\(690\) 0 0
\(691\) 570.544 + 1755.95i 0.0314103 + 0.0966709i 0.965533 0.260282i \(-0.0838156\pi\)
−0.934122 + 0.356953i \(0.883816\pi\)
\(692\) 164.763 119.708i 0.00905111 0.00657601i
\(693\) 0 0
\(694\) −14741.3 + 10710.2i −0.806301 + 0.585812i
\(695\) −9285.55 + 4519.26i −0.506793 + 0.246655i
\(696\) 0 0
\(697\) −3854.96 2800.79i −0.209494 0.152206i
\(698\) −9985.42 + 30732.0i −0.541481 + 1.66651i
\(699\) 0 0
\(700\) 173.469 221.266i 0.00936643 0.0119473i
\(701\) 8002.88 0.431191 0.215595 0.976483i \(-0.430831\pi\)
0.215595 + 0.976483i \(0.430831\pi\)
\(702\) 0 0
\(703\) −37076.3 26937.5i −1.98913 1.44519i
\(704\) −21377.1 15531.4i −1.14443 0.831477i
\(705\) 0 0
\(706\) 1578.92 1147.15i 0.0841691 0.0611524i
\(707\) 2615.36 0.139124
\(708\) 0 0
\(709\) −2060.93 6342.89i −0.109168 0.335983i 0.881518 0.472150i \(-0.156522\pi\)
−0.990686 + 0.136166i \(0.956522\pi\)
\(710\) −25824.5 4575.82i −1.36504 0.241869i
\(711\) 0 0
\(712\) 8552.59 + 26322.2i 0.450171 + 1.38548i
\(713\) −10082.3 31030.2i −0.529573 1.62986i
\(714\) 0 0
\(715\) −20792.8 21567.6i −1.08756 1.12809i
\(716\) 198.970 + 612.367i 0.0103853 + 0.0319626i
\(717\) 0 0
\(718\) 15543.8 0.807926
\(719\) 6078.70 4416.43i 0.315295 0.229075i −0.418870 0.908046i \(-0.637574\pi\)
0.734165 + 0.678971i \(0.237574\pi\)
\(720\) 0 0
\(721\) 1123.97 + 816.612i 0.0580566 + 0.0421806i
\(722\) 37650.4 + 27354.6i 1.94072 + 1.41002i
\(723\) 0 0
\(724\) 283.329 0.0145440
\(725\) 5363.06 6840.79i 0.274729 0.350429i
\(726\) 0 0
\(727\) 10212.2 31429.8i 0.520974 1.60339i −0.251169 0.967943i \(-0.580815\pi\)
0.772142 0.635449i \(-0.219185\pi\)
\(728\) 7179.92 + 5216.52i 0.365530 + 0.265573i
\(729\) 0 0
\(730\) 1529.40 + 10948.6i 0.0775417 + 0.555105i
\(731\) −4847.19 + 3521.69i −0.245253 + 0.178186i
\(732\) 0 0
\(733\) 12580.8 9140.51i 0.633948 0.460590i −0.223818 0.974631i \(-0.571852\pi\)
0.857766 + 0.514041i \(0.171852\pi\)
\(734\) −2020.60 6218.76i −0.101610 0.312723i
\(735\) 0 0
\(736\) −945.062 + 2908.60i −0.0473308 + 0.145669i
\(737\) 10599.9 + 32623.3i 0.529788 + 1.63052i
\(738\) 0 0
\(739\) −2576.39 + 7929.33i −0.128247 + 0.394702i −0.994479 0.104940i \(-0.966535\pi\)
0.866232 + 0.499642i \(0.166535\pi\)
\(740\) −941.584 + 458.267i −0.0467747 + 0.0227652i
\(741\) 0 0
\(742\) 785.174 570.463i 0.0388472 0.0282242i
\(743\) 9492.12 0.468684 0.234342 0.972154i \(-0.424706\pi\)
0.234342 + 0.972154i \(0.424706\pi\)
\(744\) 0 0
\(745\) −15471.0 16047.5i −0.760822 0.789173i
\(746\) −12087.6 8782.17i −0.593243 0.431016i
\(747\) 0 0
\(748\) −64.2355 + 197.696i −0.00313995 + 0.00966377i
\(749\) 2048.99 0.0999581
\(750\) 0 0
\(751\) 8136.39 0.395341 0.197671 0.980269i \(-0.436662\pi\)
0.197671 + 0.980269i \(0.436662\pi\)
\(752\) 2926.37 9006.45i 0.141907 0.436744i
\(753\) 0 0
\(754\) 8390.58 + 6096.11i 0.405261 + 0.294439i
\(755\) −13244.0 13737.6i −0.638411 0.662201i
\(756\) 0 0
\(757\) 6875.91 0.330131 0.165066 0.986283i \(-0.447216\pi\)
0.165066 + 0.986283i \(0.447216\pi\)
\(758\) −6309.27 + 4583.95i −0.302326 + 0.219653i
\(759\) 0 0
\(760\) 35631.7 17341.9i 1.70065 0.827705i
\(761\) −5507.46 + 16950.2i −0.262346 + 0.807417i 0.729947 + 0.683504i \(0.239545\pi\)
−0.992293 + 0.123914i \(0.960455\pi\)
\(762\) 0 0
\(763\) 3133.26 + 9643.19i 0.148665 + 0.457545i
\(764\) −282.548 + 869.595i −0.0133799 + 0.0411791i
\(765\) 0 0
\(766\) 8108.26 + 24954.6i 0.382458 + 1.17709i
\(767\) 1318.53 957.968i 0.0620722 0.0450981i
\(768\) 0 0
\(769\) −18966.1 + 13779.6i −0.889380 + 0.646173i −0.935716 0.352753i \(-0.885245\pi\)
0.0463361 + 0.998926i \(0.485245\pi\)
\(770\) 1528.63 + 10943.1i 0.0715427 + 0.512159i
\(771\) 0 0
\(772\) 46.9974 + 34.1456i 0.00219103 + 0.00159188i
\(773\) 4531.20 13945.6i 0.210836 0.648886i −0.788587 0.614923i \(-0.789187\pi\)
0.999423 0.0339629i \(-0.0108128\pi\)
\(774\) 0 0
\(775\) 10573.3 + 15732.2i 0.490068 + 0.729183i
\(776\) 28527.7 1.31969
\(777\) 0 0
\(778\) −31709.1 23038.0i −1.46121 1.06163i
\(779\) 44638.9 + 32432.1i 2.05309 + 1.49166i
\(780\) 0 0
\(781\) −34096.4 + 24772.5i −1.56218 + 1.13499i
\(782\) −7921.16 −0.362225
\(783\) 0 0
\(784\) 5534.89 + 17034.6i 0.252136 + 0.775995i
\(785\) −3796.30 3937.77i −0.172606 0.179038i
\(786\) 0 0
\(787\) 2673.75 + 8228.97i 0.121104 + 0.372720i 0.993171 0.116666i \(-0.0372207\pi\)
−0.872067 + 0.489387i \(0.837221\pi\)
\(788\)