Properties

Label 225.4.h.a.91.6
Level $225$
Weight $4$
Character 225.91
Analytic conductor $13.275$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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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: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 91.6
Character \(\chi\) \(=\) 225.91
Dual form 225.4.h.a.136.6

$q$-expansion

\(f(q)\) \(=\) \(q+(3.16070 + 2.29638i) q^{2} +(2.24451 + 6.90789i) q^{4} +(11.0852 + 1.45535i) q^{5} +22.0918 q^{7} +(0.889297 - 2.73697i) q^{8} +O(q^{10})\) \(q+(3.16070 + 2.29638i) q^{2} +(2.24451 + 6.90789i) q^{4} +(11.0852 + 1.45535i) q^{5} +22.0918 q^{7} +(0.889297 - 2.73697i) q^{8} +(31.6950 + 30.0558i) q^{10} +(-31.5999 - 22.9587i) q^{11} +(55.3321 - 40.2012i) q^{13} +(69.8255 + 50.7312i) q^{14} +(56.1056 - 40.7631i) q^{16} +(-31.1744 + 95.9450i) q^{17} +(-29.0621 + 89.4438i) q^{19} +(14.8275 + 79.8420i) q^{20} +(-47.1559 - 145.131i) q^{22} +(-130.565 - 94.8612i) q^{23} +(120.764 + 32.2658i) q^{25} +267.205 q^{26} +(49.5852 + 152.608i) q^{28} +(15.8462 + 48.7695i) q^{29} +(-80.4233 + 247.517i) q^{31} +247.918 q^{32} +(-318.859 + 231.665i) q^{34} +(244.892 + 32.1513i) q^{35} +(70.1129 - 50.9400i) q^{37} +(-297.254 + 215.967i) q^{38} +(13.8413 - 29.0457i) q^{40} +(-42.4765 + 30.8610i) q^{41} -53.3748 q^{43} +(87.6698 - 269.820i) q^{44} +(-194.840 - 599.656i) q^{46} +(-74.7809 - 230.152i) q^{47} +145.047 q^{49} +(307.604 + 379.302i) q^{50} +(401.899 + 291.997i) q^{52} +(-18.2798 - 56.2594i) q^{53} +(-316.879 - 300.491i) q^{55} +(19.6461 - 60.4646i) q^{56} +(-61.9084 + 190.534i) q^{58} +(-524.396 + 380.996i) q^{59} +(-530.204 - 385.216i) q^{61} +(-822.588 + 597.645i) q^{62} +(334.749 + 243.209i) q^{64} +(671.875 - 365.111i) q^{65} +(240.635 - 740.598i) q^{67} -732.749 q^{68} +(700.198 + 663.986i) q^{70} +(-69.2398 - 213.098i) q^{71} +(-281.749 - 204.703i) q^{73} +338.583 q^{74} -683.098 q^{76} +(-698.099 - 507.198i) q^{77} +(49.9257 + 153.655i) q^{79} +(681.267 - 370.214i) q^{80} -205.124 q^{82} +(12.3245 - 37.9308i) q^{83} +(-485.209 + 1018.20i) q^{85} +(-168.702 - 122.569i) q^{86} +(-90.9391 + 66.0711i) q^{88} +(-375.213 - 272.608i) q^{89} +(1222.39 - 888.115i) q^{91} +(362.236 - 1114.85i) q^{92} +(292.157 - 899.167i) q^{94} +(-452.331 + 949.208i) q^{95} +(177.512 + 546.326i) q^{97} +(458.449 + 333.082i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.16070 + 2.29638i 1.11748 + 0.811894i 0.983825 0.179135i \(-0.0573298\pi\)
0.133651 + 0.991028i \(0.457330\pi\)
\(3\) 0 0
\(4\) 2.24451 + 6.90789i 0.280564 + 0.863487i
\(5\) 11.0852 + 1.45535i 0.991492 + 0.130171i
\(6\) 0 0
\(7\) 22.0918 1.19284 0.596422 0.802671i \(-0.296589\pi\)
0.596422 + 0.802671i \(0.296589\pi\)
\(8\) 0.889297 2.73697i 0.0393017 0.120958i
\(9\) 0 0
\(10\) 31.6950 + 30.0558i 1.00228 + 0.950448i
\(11\) −31.5999 22.9587i −0.866158 0.629301i 0.0633953 0.997988i \(-0.479807\pi\)
−0.929553 + 0.368688i \(0.879807\pi\)
\(12\) 0 0
\(13\) 55.3321 40.2012i 1.18049 0.857676i 0.188264 0.982119i \(-0.439714\pi\)
0.992227 + 0.124442i \(0.0397141\pi\)
\(14\) 69.8255 + 50.7312i 1.33297 + 0.968462i
\(15\) 0 0
\(16\) 56.1056 40.7631i 0.876650 0.636923i
\(17\) −31.1744 + 95.9450i −0.444759 + 1.36883i 0.437988 + 0.898981i \(0.355691\pi\)
−0.882747 + 0.469848i \(0.844309\pi\)
\(18\) 0 0
\(19\) −29.0621 + 89.4438i −0.350910 + 1.07999i 0.607433 + 0.794371i \(0.292199\pi\)
−0.958343 + 0.285619i \(0.907801\pi\)
\(20\) 14.8275 + 79.8420i 0.165776 + 0.892661i
\(21\) 0 0
\(22\) −47.1559 145.131i −0.456985 1.40646i
\(23\) −130.565 94.8612i −1.18368 0.859997i −0.191102 0.981570i \(-0.561206\pi\)
−0.992582 + 0.121573i \(0.961206\pi\)
\(24\) 0 0
\(25\) 120.764 + 32.2658i 0.966111 + 0.258126i
\(26\) 267.205 2.01551
\(27\) 0 0
\(28\) 49.5852 + 152.608i 0.334669 + 1.03000i
\(29\) 15.8462 + 48.7695i 0.101468 + 0.312285i 0.988885 0.148681i \(-0.0475029\pi\)
−0.887418 + 0.460966i \(0.847503\pi\)
\(30\) 0 0
\(31\) −80.4233 + 247.517i −0.465950 + 1.43405i 0.391834 + 0.920036i \(0.371841\pi\)
−0.857784 + 0.514011i \(0.828159\pi\)
\(32\) 247.918 1.36957
\(33\) 0 0
\(34\) −318.859 + 231.665i −1.60835 + 1.16854i
\(35\) 244.892 + 32.1513i 1.18269 + 0.155273i
\(36\) 0 0
\(37\) 70.1129 50.9400i 0.311527 0.226337i −0.421025 0.907049i \(-0.638329\pi\)
0.732551 + 0.680712i \(0.238329\pi\)
\(38\) −297.254 + 215.967i −1.26897 + 0.921961i
\(39\) 0 0
\(40\) 13.8413 29.0457i 0.0547126 0.114813i
\(41\) −42.4765 + 30.8610i −0.161798 + 0.117553i −0.665738 0.746185i \(-0.731883\pi\)
0.503940 + 0.863739i \(0.331883\pi\)
\(42\) 0 0
\(43\) −53.3748 −0.189293 −0.0946463 0.995511i \(-0.530172\pi\)
−0.0946463 + 0.995511i \(0.530172\pi\)
\(44\) 87.6698 269.820i 0.300380 0.924475i
\(45\) 0 0
\(46\) −194.840 599.656i −0.624512 1.92205i
\(47\) −74.7809 230.152i −0.232083 0.714279i −0.997495 0.0707380i \(-0.977465\pi\)
0.765412 0.643541i \(-0.222535\pi\)
\(48\) 0 0
\(49\) 145.047 0.422876
\(50\) 307.604 + 379.302i 0.870035 + 1.07283i
\(51\) 0 0
\(52\) 401.899 + 291.997i 1.07179 + 0.778705i
\(53\) −18.2798 56.2594i −0.0473759 0.145808i 0.924570 0.381012i \(-0.124424\pi\)
−0.971946 + 0.235204i \(0.924424\pi\)
\(54\) 0 0
\(55\) −316.879 300.491i −0.776872 0.736695i
\(56\) 19.6461 60.4646i 0.0468808 0.144284i
\(57\) 0 0
\(58\) −61.9084 + 190.534i −0.140155 + 0.431352i
\(59\) −524.396 + 380.996i −1.15713 + 0.840703i −0.989412 0.145132i \(-0.953639\pi\)
−0.167716 + 0.985835i \(0.553639\pi\)
\(60\) 0 0
\(61\) −530.204 385.216i −1.11288 0.808555i −0.129765 0.991545i \(-0.541422\pi\)
−0.983115 + 0.182990i \(0.941422\pi\)
\(62\) −822.588 + 597.645i −1.68498 + 1.22421i
\(63\) 0 0
\(64\) 334.749 + 243.209i 0.653807 + 0.475018i
\(65\) 671.875 365.111i 1.28209 0.696714i
\(66\) 0 0
\(67\) 240.635 740.598i 0.438779 1.35042i −0.450384 0.892835i \(-0.648713\pi\)
0.889164 0.457589i \(-0.151287\pi\)
\(68\) −732.749 −1.30675
\(69\) 0 0
\(70\) 700.198 + 663.986i 1.19557 + 1.13374i
\(71\) −69.2398 213.098i −0.115736 0.356199i 0.876364 0.481650i \(-0.159962\pi\)
−0.992100 + 0.125451i \(0.959962\pi\)
\(72\) 0 0
\(73\) −281.749 204.703i −0.451729 0.328200i 0.338549 0.940949i \(-0.390064\pi\)
−0.790278 + 0.612748i \(0.790064\pi\)
\(74\) 338.583 0.531886
\(75\) 0 0
\(76\) −683.098 −1.03101
\(77\) −698.099 507.198i −1.03319 0.750657i
\(78\) 0 0
\(79\) 49.9257 + 153.655i 0.0711022 + 0.218830i 0.980293 0.197550i \(-0.0632985\pi\)
−0.909191 + 0.416380i \(0.863299\pi\)
\(80\) 681.267 370.214i 0.952099 0.517390i
\(81\) 0 0
\(82\) −205.124 −0.276246
\(83\) 12.3245 37.9308i 0.0162986 0.0501620i −0.942576 0.333991i \(-0.891605\pi\)
0.958875 + 0.283829i \(0.0916047\pi\)
\(84\) 0 0
\(85\) −485.209 + 1018.20i −0.619156 + 1.29929i
\(86\) −168.702 122.569i −0.211530 0.153685i
\(87\) 0 0
\(88\) −90.9391 + 66.0711i −0.110161 + 0.0800364i
\(89\) −375.213 272.608i −0.446882 0.324679i 0.341481 0.939889i \(-0.389071\pi\)
−0.788364 + 0.615210i \(0.789071\pi\)
\(90\) 0 0
\(91\) 1222.39 888.115i 1.40814 1.02307i
\(92\) 362.236 1114.85i 0.410497 1.26338i
\(93\) 0 0
\(94\) 292.157 899.167i 0.320571 0.986617i
\(95\) −452.331 + 949.208i −0.488508 + 1.02512i
\(96\) 0 0
\(97\) 177.512 + 546.326i 0.185810 + 0.571866i 0.999961 0.00878766i \(-0.00279724\pi\)
−0.814151 + 0.580653i \(0.802797\pi\)
\(98\) 458.449 + 333.082i 0.472554 + 0.343331i
\(99\) 0 0
\(100\) 48.1674 + 906.645i 0.0481674 + 0.906645i
\(101\) 1074.69 1.05877 0.529383 0.848383i \(-0.322423\pi\)
0.529383 + 0.848383i \(0.322423\pi\)
\(102\) 0 0
\(103\) 288.232 + 887.086i 0.275731 + 0.848613i 0.989025 + 0.147748i \(0.0472025\pi\)
−0.713294 + 0.700865i \(0.752797\pi\)
\(104\) −60.8228 187.193i −0.0573478 0.176498i
\(105\) 0 0
\(106\) 71.4162 219.797i 0.0654392 0.201401i
\(107\) 1102.95 0.996511 0.498255 0.867030i \(-0.333974\pi\)
0.498255 + 0.867030i \(0.333974\pi\)
\(108\) 0 0
\(109\) 1186.41 861.976i 1.04254 0.757453i 0.0717636 0.997422i \(-0.477137\pi\)
0.970781 + 0.239969i \(0.0771373\pi\)
\(110\) −311.517 1677.44i −0.270018 1.45398i
\(111\) 0 0
\(112\) 1239.47 900.529i 1.04571 0.759750i
\(113\) −1253.89 + 911.005i −1.04386 + 0.758408i −0.971035 0.238936i \(-0.923201\pi\)
−0.0728243 + 0.997345i \(0.523201\pi\)
\(114\) 0 0
\(115\) −1309.29 1241.58i −1.06167 1.00676i
\(116\) −301.327 + 218.927i −0.241186 + 0.175232i
\(117\) 0 0
\(118\) −2532.37 −1.97563
\(119\) −688.699 + 2119.60i −0.530528 + 1.63280i
\(120\) 0 0
\(121\) 60.1524 + 185.130i 0.0451934 + 0.139091i
\(122\) −791.213 2435.10i −0.587156 1.80708i
\(123\) 0 0
\(124\) −1890.33 −1.36901
\(125\) 1291.74 + 533.427i 0.924291 + 0.381689i
\(126\) 0 0
\(127\) −786.360 571.324i −0.549434 0.399187i 0.278143 0.960540i \(-0.410281\pi\)
−0.827577 + 0.561352i \(0.810281\pi\)
\(128\) −113.347 348.848i −0.0782703 0.240891i
\(129\) 0 0
\(130\) 2962.03 + 388.878i 1.99836 + 0.262360i
\(131\) 360.986 1111.00i 0.240760 0.740982i −0.755545 0.655096i \(-0.772628\pi\)
0.996305 0.0858855i \(-0.0273719\pi\)
\(132\) 0 0
\(133\) −642.032 + 1975.97i −0.418581 + 1.28826i
\(134\) 2461.27 1788.22i 1.58673 1.15282i
\(135\) 0 0
\(136\) 234.876 + 170.647i 0.148091 + 0.107595i
\(137\) 867.865 630.541i 0.541217 0.393217i −0.283320 0.959025i \(-0.591436\pi\)
0.824537 + 0.565808i \(0.191436\pi\)
\(138\) 0 0
\(139\) 276.953 + 201.218i 0.168999 + 0.122785i 0.669070 0.743200i \(-0.266693\pi\)
−0.500071 + 0.865984i \(0.666693\pi\)
\(140\) 327.565 + 1763.85i 0.197745 + 1.06480i
\(141\) 0 0
\(142\) 270.509 832.540i 0.159863 0.492009i
\(143\) −2671.46 −1.56223
\(144\) 0 0
\(145\) 104.681 + 563.682i 0.0599539 + 0.322836i
\(146\) −420.448 1294.01i −0.238333 0.733512i
\(147\) 0 0
\(148\) 509.257 + 369.997i 0.282842 + 0.205497i
\(149\) −1268.97 −0.697704 −0.348852 0.937178i \(-0.613428\pi\)
−0.348852 + 0.937178i \(0.613428\pi\)
\(150\) 0 0
\(151\) −1863.93 −1.00453 −0.502266 0.864713i \(-0.667500\pi\)
−0.502266 + 0.864713i \(0.667500\pi\)
\(152\) 218.961 + 159.084i 0.116842 + 0.0848910i
\(153\) 0 0
\(154\) −1041.76 3206.20i −0.545112 1.67768i
\(155\) −1251.73 + 2626.74i −0.648656 + 1.36119i
\(156\) 0 0
\(157\) −1891.87 −0.961705 −0.480852 0.876802i \(-0.659673\pi\)
−0.480852 + 0.876802i \(0.659673\pi\)
\(158\) −195.051 + 600.307i −0.0982118 + 0.302265i
\(159\) 0 0
\(160\) 2748.22 + 360.808i 1.35791 + 0.178277i
\(161\) −2884.42 2095.65i −1.41195 1.02584i
\(162\) 0 0
\(163\) −2559.85 + 1859.84i −1.23008 + 0.893705i −0.996896 0.0787280i \(-0.974914\pi\)
−0.233183 + 0.972433i \(0.574914\pi\)
\(164\) −308.524 224.155i −0.146900 0.106729i
\(165\) 0 0
\(166\) 126.057 91.5861i 0.0589395 0.0428220i
\(167\) −1089.41 + 3352.87i −0.504798 + 1.55361i 0.296312 + 0.955091i \(0.404243\pi\)
−0.801110 + 0.598517i \(0.795757\pi\)
\(168\) 0 0
\(169\) 766.603 2359.36i 0.348932 1.07390i
\(170\) −3871.78 + 2104.00i −1.74678 + 0.949233i
\(171\) 0 0
\(172\) −119.800 368.707i −0.0531086 0.163452i
\(173\) 3140.81 + 2281.93i 1.38030 + 1.00285i 0.996852 + 0.0792825i \(0.0252629\pi\)
0.383446 + 0.923563i \(0.374737\pi\)
\(174\) 0 0
\(175\) 2667.89 + 712.808i 1.15242 + 0.307904i
\(176\) −2708.80 −1.16013
\(177\) 0 0
\(178\) −559.923 1723.27i −0.235775 0.725641i
\(179\) −154.209 474.606i −0.0643917 0.198177i 0.913685 0.406424i \(-0.133224\pi\)
−0.978076 + 0.208247i \(0.933224\pi\)
\(180\) 0 0
\(181\) −1375.55 + 4233.49i −0.564881 + 1.73853i 0.103422 + 0.994638i \(0.467021\pi\)
−0.668304 + 0.743888i \(0.732979\pi\)
\(182\) 5903.04 2.40419
\(183\) 0 0
\(184\) −375.744 + 272.994i −0.150545 + 0.109377i
\(185\) 851.352 462.642i 0.338339 0.183860i
\(186\) 0 0
\(187\) 3187.88 2316.13i 1.24664 0.905734i
\(188\) 1422.02 1033.16i 0.551656 0.400802i
\(189\) 0 0
\(190\) −3609.43 + 1961.44i −1.37819 + 0.748934i
\(191\) 3212.06 2333.70i 1.21684 0.884088i 0.221008 0.975272i \(-0.429065\pi\)
0.995834 + 0.0911844i \(0.0290653\pi\)
\(192\) 0 0
\(193\) 3115.35 1.16190 0.580952 0.813938i \(-0.302680\pi\)
0.580952 + 0.813938i \(0.302680\pi\)
\(194\) −693.510 + 2134.41i −0.256655 + 0.789904i
\(195\) 0 0
\(196\) 325.559 + 1001.97i 0.118644 + 0.365148i
\(197\) 445.849 + 1372.18i 0.161246 + 0.496263i 0.998740 0.0501827i \(-0.0159804\pi\)
−0.837494 + 0.546446i \(0.815980\pi\)
\(198\) 0 0
\(199\) −2015.36 −0.717916 −0.358958 0.933354i \(-0.616868\pi\)
−0.358958 + 0.933354i \(0.616868\pi\)
\(200\) 195.706 301.834i 0.0691924 0.106714i
\(201\) 0 0
\(202\) 3396.76 + 2467.89i 1.18315 + 0.859606i
\(203\) 350.070 + 1077.40i 0.121035 + 0.372507i
\(204\) 0 0
\(205\) −515.775 + 280.283i −0.175723 + 0.0954916i
\(206\) −1126.07 + 3465.70i −0.380861 + 1.17217i
\(207\) 0 0
\(208\) 1465.72 4511.02i 0.488602 1.50376i
\(209\) 2971.87 2159.19i 0.983582 0.714614i
\(210\) 0 0
\(211\) 192.025 + 139.514i 0.0626517 + 0.0455192i 0.618670 0.785651i \(-0.287672\pi\)
−0.556019 + 0.831170i \(0.687672\pi\)
\(212\) 347.605 252.550i 0.112611 0.0818169i
\(213\) 0 0
\(214\) 3486.11 + 2532.80i 1.11358 + 0.809061i
\(215\) −591.671 77.6791i −0.187682 0.0246403i
\(216\) 0 0
\(217\) −1776.69 + 5468.10i −0.555806 + 1.71059i
\(218\) 5729.31 1.77999
\(219\) 0 0
\(220\) 1364.52 2863.42i 0.418164 0.877508i
\(221\) 2132.15 + 6562.09i 0.648978 + 1.99735i
\(222\) 0 0
\(223\) 236.890 + 172.111i 0.0711361 + 0.0516834i 0.622785 0.782393i \(-0.286001\pi\)
−0.551649 + 0.834076i \(0.686001\pi\)
\(224\) 5476.95 1.63368
\(225\) 0 0
\(226\) −6055.19 −1.78223
\(227\) 172.374 + 125.237i 0.0504003 + 0.0366180i 0.612700 0.790315i \(-0.290083\pi\)
−0.562300 + 0.826933i \(0.690083\pi\)
\(228\) 0 0
\(229\) −1001.94 3083.67i −0.289128 0.889845i −0.985131 0.171806i \(-0.945040\pi\)
0.696003 0.718039i \(-0.254960\pi\)
\(230\) −1287.13 6930.87i −0.369004 1.98699i
\(231\) 0 0
\(232\) 147.573 0.0417613
\(233\) 1229.34 3783.53i 0.345652 1.06381i −0.615582 0.788073i \(-0.711079\pi\)
0.961234 0.275735i \(-0.0889211\pi\)
\(234\) 0 0
\(235\) −494.010 2660.12i −0.137131 0.738412i
\(236\) −3808.89 2767.32i −1.05058 0.763294i
\(237\) 0 0
\(238\) −7044.17 + 5117.89i −1.91851 + 1.39388i
\(239\) −3905.56 2837.55i −1.05703 0.767975i −0.0834914 0.996508i \(-0.526607\pi\)
−0.973536 + 0.228533i \(0.926607\pi\)
\(240\) 0 0
\(241\) 1630.46 1184.60i 0.435798 0.316625i −0.348165 0.937433i \(-0.613195\pi\)
0.783963 + 0.620808i \(0.213195\pi\)
\(242\) −235.006 + 723.273i −0.0624245 + 0.192123i
\(243\) 0 0
\(244\) 1470.98 4527.21i 0.385942 1.18781i
\(245\) 1607.87 + 211.094i 0.419278 + 0.0550461i
\(246\) 0 0
\(247\) 1987.68 + 6117.45i 0.512036 + 1.57589i
\(248\) 605.929 + 440.233i 0.155147 + 0.112721i
\(249\) 0 0
\(250\) 2857.84 + 4652.32i 0.722981 + 1.17695i
\(251\) 278.293 0.0699830 0.0349915 0.999388i \(-0.488860\pi\)
0.0349915 + 0.999388i \(0.488860\pi\)
\(252\) 0 0
\(253\) 1947.96 + 5995.22i 0.484061 + 1.48979i
\(254\) −1173.47 3611.57i −0.289882 0.892165i
\(255\) 0 0
\(256\) 1465.73 4511.06i 0.357845 1.10133i
\(257\) 2149.20 0.521647 0.260823 0.965387i \(-0.416006\pi\)
0.260823 + 0.965387i \(0.416006\pi\)
\(258\) 0 0
\(259\) 1548.92 1125.36i 0.371603 0.269985i
\(260\) 4030.18 + 3821.75i 0.961311 + 0.911595i
\(261\) 0 0
\(262\) 3692.25 2682.58i 0.870641 0.632558i
\(263\) −5778.91 + 4198.62i −1.35492 + 0.984404i −0.356165 + 0.934423i \(0.615916\pi\)
−0.998750 + 0.0499805i \(0.984084\pi\)
\(264\) 0 0
\(265\) −120.758 650.251i −0.0279929 0.150734i
\(266\) −6566.86 + 4771.10i −1.51368 + 1.09976i
\(267\) 0 0
\(268\) 5656.08 1.28918
\(269\) −273.812 + 842.706i −0.0620617 + 0.191006i −0.977280 0.211952i \(-0.932018\pi\)
0.915218 + 0.402958i \(0.132018\pi\)
\(270\) 0 0
\(271\) −238.067 732.696i −0.0533637 0.164237i 0.920823 0.389981i \(-0.127519\pi\)
−0.974187 + 0.225745i \(0.927519\pi\)
\(272\) 2161.96 + 6653.82i 0.481941 + 1.48326i
\(273\) 0 0
\(274\) 4191.02 0.924047
\(275\) −3075.35 3792.18i −0.674366 0.831552i
\(276\) 0 0
\(277\) 6061.62 + 4404.02i 1.31483 + 0.955278i 0.999981 + 0.00613595i \(0.00195315\pi\)
0.314847 + 0.949142i \(0.398047\pi\)
\(278\) 413.291 + 1271.98i 0.0891639 + 0.274418i
\(279\) 0 0
\(280\) 305.779 641.671i 0.0652635 0.136954i
\(281\) −678.424 + 2087.98i −0.144026 + 0.443267i −0.996884 0.0788752i \(-0.974867\pi\)
0.852858 + 0.522143i \(0.174867\pi\)
\(282\) 0 0
\(283\) 1728.33 5319.25i 0.363033 1.11730i −0.588170 0.808737i \(-0.700151\pi\)
0.951203 0.308564i \(-0.0998485\pi\)
\(284\) 1316.65 956.602i 0.275101 0.199873i
\(285\) 0 0
\(286\) −8443.67 6134.69i −1.74575 1.26836i
\(287\) −938.382 + 681.775i −0.193000 + 0.140223i
\(288\) 0 0
\(289\) −4258.90 3094.27i −0.866864 0.629814i
\(290\) −963.562 + 2022.02i −0.195111 + 0.409437i
\(291\) 0 0
\(292\) 781.675 2405.75i 0.156658 0.482143i
\(293\) 2905.73 0.579367 0.289684 0.957122i \(-0.406450\pi\)
0.289684 + 0.957122i \(0.406450\pi\)
\(294\) 0 0
\(295\) −6367.53 + 3460.24i −1.25672 + 0.682926i
\(296\) −77.0703 237.198i −0.0151339 0.0465772i
\(297\) 0 0
\(298\) −4010.83 2914.04i −0.779667 0.566461i
\(299\) −11038.0 −2.13493
\(300\) 0 0
\(301\) −1179.14 −0.225796
\(302\) −5891.32 4280.29i −1.12254 0.815573i
\(303\) 0 0
\(304\) 2015.46 + 6202.96i 0.380246 + 1.17028i
\(305\) −5316.80 5041.83i −0.998161 0.946540i
\(306\) 0 0
\(307\) −1896.85 −0.352635 −0.176317 0.984333i \(-0.556419\pi\)
−0.176317 + 0.984333i \(0.556419\pi\)
\(308\) 1936.78 5960.80i 0.358306 1.10275i
\(309\) 0 0
\(310\) −9988.35 + 5427.87i −1.83000 + 0.994459i
\(311\) 7137.00 + 5185.33i 1.30129 + 0.945444i 0.999967 0.00807744i \(-0.00257116\pi\)
0.301325 + 0.953522i \(0.402571\pi\)
\(312\) 0 0
\(313\) 6034.71 4384.47i 1.08978 0.791774i 0.110420 0.993885i \(-0.464780\pi\)
0.979363 + 0.202111i \(0.0647803\pi\)
\(314\) −5979.63 4344.46i −1.07468 0.780802i
\(315\) 0 0
\(316\) −949.376 + 689.762i −0.169008 + 0.122792i
\(317\) 1742.87 5364.01i 0.308799 0.950387i −0.669433 0.742873i \(-0.733463\pi\)
0.978232 0.207514i \(-0.0665372\pi\)
\(318\) 0 0
\(319\) 618.946 1904.92i 0.108634 0.334342i
\(320\) 3356.81 + 3183.21i 0.586410 + 0.556083i
\(321\) 0 0
\(322\) −4304.36 13247.5i −0.744946 2.29271i
\(323\) −7675.70 5576.72i −1.32225 0.960672i
\(324\) 0 0
\(325\) 7979.25 3069.51i 1.36187 0.523895i
\(326\) −12361.8 −2.10018
\(327\) 0 0
\(328\) 46.6915 + 143.702i 0.00786009 + 0.0241909i
\(329\) −1652.04 5084.47i −0.276839 0.852023i
\(330\) 0 0
\(331\) 1361.95 4191.66i 0.226162 0.696055i −0.772010 0.635611i \(-0.780748\pi\)
0.998172 0.0604442i \(-0.0192517\pi\)
\(332\) 289.684 0.0478870
\(333\) 0 0
\(334\) −11142.8 + 8095.69i −1.82546 + 1.32628i
\(335\) 3745.32 7859.48i 0.610832 1.28182i
\(336\) 0 0
\(337\) −3620.77 + 2630.64i −0.585269 + 0.425223i −0.840620 0.541626i \(-0.817809\pi\)
0.255351 + 0.966848i \(0.417809\pi\)
\(338\) 7841.00 5696.82i 1.26182 0.916763i
\(339\) 0 0
\(340\) −8122.68 1066.41i −1.29563 0.170100i
\(341\) 8224.05 5975.12i 1.30603 0.948888i
\(342\) 0 0
\(343\) −4373.14 −0.688418
\(344\) −47.4660 + 146.085i −0.00743952 + 0.0228965i
\(345\) 0 0
\(346\) 4686.97 + 14425.0i 0.728246 + 2.24131i
\(347\) 216.151 + 665.244i 0.0334397 + 0.102917i 0.966383 0.257106i \(-0.0827689\pi\)
−0.932944 + 0.360023i \(0.882769\pi\)
\(348\) 0 0
\(349\) −7119.97 −1.09204 −0.546022 0.837771i \(-0.683858\pi\)
−0.546022 + 0.837771i \(0.683858\pi\)
\(350\) 6795.51 + 8379.46i 1.03782 + 1.27972i
\(351\) 0 0
\(352\) −7834.19 5691.87i −1.18626 0.861868i
\(353\) 1094.30 + 3367.90i 0.164996 + 0.507806i 0.999036 0.0438984i \(-0.0139778\pi\)
−0.834040 + 0.551704i \(0.813978\pi\)
\(354\) 0 0
\(355\) −457.405 2463.01i −0.0683846 0.368233i
\(356\) 1040.98 3203.80i 0.154977 0.476970i
\(357\) 0 0
\(358\) 602.470 1854.21i 0.0889428 0.273738i
\(359\) 9430.47 6851.64i 1.38641 1.00729i 0.390161 0.920747i \(-0.372419\pi\)
0.996248 0.0865388i \(-0.0275807\pi\)
\(360\) 0 0
\(361\) −1606.55 1167.22i −0.234224 0.170174i
\(362\) −14069.4 + 10222.0i −2.04274 + 1.48414i
\(363\) 0 0
\(364\) 8878.66 + 6450.72i 1.27848 + 0.928873i
\(365\) −2825.33 2679.22i −0.405164 0.384210i
\(366\) 0 0
\(367\) 22.7126 69.9022i 0.00323048 0.00994241i −0.949428 0.313984i \(-0.898336\pi\)
0.952659 + 0.304042i \(0.0983362\pi\)
\(368\) −11192.3 −1.58543
\(369\) 0 0
\(370\) 3753.27 + 492.758i 0.527360 + 0.0692359i
\(371\) −403.833 1242.87i −0.0565121 0.173926i
\(372\) 0 0
\(373\) −2082.90 1513.32i −0.289139 0.210071i 0.433755 0.901031i \(-0.357188\pi\)
−0.722894 + 0.690959i \(0.757188\pi\)
\(374\) 15394.7 2.12845
\(375\) 0 0
\(376\) −696.422 −0.0955193
\(377\) 2837.39 + 2061.48i 0.387621 + 0.281623i
\(378\) 0 0
\(379\) 18.7531 + 57.7162i 0.00254164 + 0.00782238i 0.952319 0.305103i \(-0.0986910\pi\)
−0.949778 + 0.312926i \(0.898691\pi\)
\(380\) −7572.29 994.148i −1.02224 0.134207i
\(381\) 0 0
\(382\) 15511.4 2.07758
\(383\) −1174.60 + 3615.05i −0.156708 + 0.482299i −0.998330 0.0577690i \(-0.981601\pi\)
0.841622 + 0.540068i \(0.181601\pi\)
\(384\) 0 0
\(385\) −7000.42 6638.38i −0.926687 0.878762i
\(386\) 9846.67 + 7154.02i 1.29840 + 0.943343i
\(387\) 0 0
\(388\) −3375.53 + 2452.47i −0.441667 + 0.320890i
\(389\) 7911.32 + 5747.91i 1.03116 + 0.749179i 0.968540 0.248858i \(-0.0800554\pi\)
0.0626169 + 0.998038i \(0.480055\pi\)
\(390\) 0 0
\(391\) 13171.8 9569.84i 1.70364 1.23777i
\(392\) 128.989 396.989i 0.0166198 0.0511504i
\(393\) 0 0
\(394\) −1741.86 + 5360.89i −0.222725 + 0.685477i
\(395\) 329.814 + 1775.96i 0.0420120 + 0.226224i
\(396\) 0 0
\(397\) −4430.53 13635.8i −0.560106 1.72383i −0.682063 0.731294i \(-0.738917\pi\)
0.121957 0.992535i \(-0.461083\pi\)
\(398\) −6369.95 4628.04i −0.802253 0.582871i
\(399\) 0 0
\(400\) 8090.78 3112.42i 1.01135 0.389052i
\(401\) −2086.59 −0.259849 −0.129924 0.991524i \(-0.541473\pi\)
−0.129924 + 0.991524i \(0.541473\pi\)
\(402\) 0 0
\(403\) 5500.49 + 16928.8i 0.679899 + 2.09251i
\(404\) 2412.15 + 7423.83i 0.297052 + 0.914231i
\(405\) 0 0
\(406\) −1367.67 + 4209.24i −0.167183 + 0.514535i
\(407\) −3385.08 −0.412266
\(408\) 0 0
\(409\) 338.014 245.582i 0.0408649 0.0296901i −0.567165 0.823604i \(-0.691960\pi\)
0.608030 + 0.793914i \(0.291960\pi\)
\(410\) −2273.85 298.528i −0.273896 0.0359591i
\(411\) 0 0
\(412\) −5480.95 + 3982.15i −0.655406 + 0.476180i
\(413\) −11584.8 + 8416.88i −1.38027 + 1.00283i
\(414\) 0 0
\(415\) 191.822 402.534i 0.0226896 0.0476136i
\(416\) 13717.8 9966.58i 1.61676 1.17464i
\(417\) 0 0
\(418\) 14351.5 1.67932
\(419\) 385.525 1186.52i 0.0449502 0.138342i −0.926063 0.377370i \(-0.876829\pi\)
0.971013 + 0.239027i \(0.0768286\pi\)
\(420\) 0 0
\(421\) 3257.63 + 10026.0i 0.377119 + 1.16065i 0.942038 + 0.335507i \(0.108908\pi\)
−0.564919 + 0.825147i \(0.691092\pi\)
\(422\) 286.554 + 881.924i 0.0330551 + 0.101733i
\(423\) 0 0
\(424\) −170.237 −0.0194987
\(425\) −6860.49 + 10580.8i −0.783018 + 1.20764i
\(426\) 0 0
\(427\) −11713.2 8510.10i −1.32749 0.964480i
\(428\) 2475.59 + 7619.09i 0.279585 + 0.860473i
\(429\) 0 0
\(430\) −1691.71 1604.22i −0.189725 0.179913i
\(431\) 2759.44 8492.68i 0.308393 0.949137i −0.669996 0.742365i \(-0.733704\pi\)
0.978389 0.206772i \(-0.0662958\pi\)
\(432\) 0 0
\(433\) 750.382 2309.44i 0.0832819 0.256315i −0.900741 0.434356i \(-0.856976\pi\)
0.984023 + 0.178041i \(0.0569759\pi\)
\(434\) −18172.4 + 13203.1i −2.00992 + 1.46029i
\(435\) 0 0
\(436\) 8617.34 + 6260.87i 0.946550 + 0.687709i
\(437\) 12279.2 8921.39i 1.34416 0.976586i
\(438\) 0 0
\(439\) 7139.64 + 5187.25i 0.776211 + 0.563950i 0.903839 0.427872i \(-0.140737\pi\)
−0.127629 + 0.991822i \(0.540737\pi\)
\(440\) −1104.24 + 600.064i −0.119642 + 0.0650157i
\(441\) 0 0
\(442\) −8329.98 + 25637.0i −0.896418 + 2.75889i
\(443\) 11494.3 1.23275 0.616377 0.787451i \(-0.288600\pi\)
0.616377 + 0.787451i \(0.288600\pi\)
\(444\) 0 0
\(445\) −3762.58 3567.99i −0.400816 0.380087i
\(446\) 353.506 + 1087.98i 0.0375314 + 0.115510i
\(447\) 0 0
\(448\) 7395.20 + 5372.93i 0.779889 + 0.566623i
\(449\) −1582.63 −0.166345 −0.0831727 0.996535i \(-0.526505\pi\)
−0.0831727 + 0.996535i \(0.526505\pi\)
\(450\) 0 0
\(451\) 2050.78 0.214119
\(452\) −9107.50 6616.98i −0.947745 0.688577i
\(453\) 0 0
\(454\) 257.230 + 791.673i 0.0265912 + 0.0818394i
\(455\) 14842.9 8065.94i 1.52933 0.831071i
\(456\) 0 0
\(457\) 6765.77 0.692537 0.346269 0.938135i \(-0.387449\pi\)
0.346269 + 0.938135i \(0.387449\pi\)
\(458\) 3914.43 12047.4i 0.399366 1.22912i
\(459\) 0 0
\(460\) 5637.96 11831.1i 0.571459 1.19920i
\(461\) 9394.53 + 6825.53i 0.949126 + 0.689580i 0.950600 0.310419i \(-0.100469\pi\)
−0.00147406 + 0.999999i \(0.500469\pi\)
\(462\) 0 0
\(463\) 3221.48 2340.54i 0.323358 0.234934i −0.414249 0.910164i \(-0.635956\pi\)
0.737607 + 0.675230i \(0.235956\pi\)
\(464\) 2877.05 + 2090.30i 0.287853 + 0.209137i
\(465\) 0 0
\(466\) 12574.0 9135.55i 1.24996 0.908147i
\(467\) −3420.76 + 10528.0i −0.338959 + 1.04321i 0.625780 + 0.779999i \(0.284781\pi\)
−0.964739 + 0.263208i \(0.915219\pi\)
\(468\) 0 0
\(469\) 5316.05 16361.1i 0.523395 1.61085i
\(470\) 4547.23 9542.26i 0.446272 0.936493i
\(471\) 0 0
\(472\) 576.433 + 1774.08i 0.0562129 + 0.173005i
\(473\) 1686.64 + 1225.42i 0.163957 + 0.119122i
\(474\) 0 0
\(475\) −6395.62 + 9863.87i −0.617792 + 0.952812i
\(476\) −16187.7 −1.55875
\(477\) 0 0
\(478\) −5828.19 17937.3i −0.557688 1.71639i
\(479\) 305.633 + 940.643i 0.0291540 + 0.0897267i 0.964575 0.263810i \(-0.0849791\pi\)
−0.935421 + 0.353536i \(0.884979\pi\)
\(480\) 0 0
\(481\) 1831.65 5637.24i 0.173630 0.534378i
\(482\) 7873.69 0.744059
\(483\) 0 0
\(484\) −1143.85 + 831.052i −0.107424 + 0.0780477i
\(485\) 1172.66 + 6314.48i 0.109789 + 0.591187i
\(486\) 0 0
\(487\) −9577.72 + 6958.62i −0.891187 + 0.647485i −0.936187 0.351502i \(-0.885671\pi\)
0.0450004 + 0.998987i \(0.485671\pi\)
\(488\) −1525.83 + 1108.58i −0.141540 + 0.102835i
\(489\) 0 0
\(490\) 4597.25 + 4359.49i 0.423842 + 0.401922i
\(491\) 10575.2 7683.33i 0.971999 0.706199i 0.0160929 0.999871i \(-0.494877\pi\)
0.955906 + 0.293672i \(0.0948772\pi\)
\(492\) 0 0
\(493\) −5173.18 −0.472593
\(494\) −7765.54 + 23899.9i −0.707264 + 2.17673i
\(495\) 0 0
\(496\) 5577.38 + 17165.4i 0.504903 + 1.55393i
\(497\) −1529.63 4707.72i −0.138055 0.424889i
\(498\) 0 0
\(499\) 107.268 0.00962323 0.00481162 0.999988i \(-0.498468\pi\)
0.00481162 + 0.999988i \(0.498468\pi\)
\(500\) −785.542 + 10120.5i −0.0702610 + 0.905201i
\(501\) 0 0
\(502\) 879.602 + 639.068i 0.0782043 + 0.0568187i
\(503\) 1599.76 + 4923.56i 0.141809 + 0.436443i 0.996587 0.0825511i \(-0.0263068\pi\)
−0.854778 + 0.518994i \(0.826307\pi\)
\(504\) 0 0
\(505\) 11913.1 + 1564.05i 1.04976 + 0.137820i
\(506\) −7610.38 + 23422.3i −0.668622 + 2.05781i
\(507\) 0 0
\(508\) 2181.65 6714.43i 0.190542 0.586427i
\(509\) −4039.84 + 2935.11i −0.351793 + 0.255593i −0.749621 0.661868i \(-0.769764\pi\)
0.397828 + 0.917460i \(0.369764\pi\)
\(510\) 0 0
\(511\) −6224.34 4522.24i −0.538842 0.391492i
\(512\) 12617.9 9167.42i 1.08913 0.791302i
\(513\) 0 0
\(514\) 6792.96 + 4935.38i 0.582928 + 0.423522i
\(515\) 1904.09 + 10253.0i 0.162921 + 0.877285i
\(516\) 0 0
\(517\) −2920.92 + 8989.66i −0.248475 + 0.764729i
\(518\) 7479.91 0.634456
\(519\) 0 0
\(520\) −401.802 2163.60i −0.0338849 0.182462i
\(521\) −4258.29 13105.7i −0.358079 1.10205i −0.954203 0.299161i \(-0.903293\pi\)
0.596124 0.802893i \(-0.296707\pi\)
\(522\) 0 0
\(523\) −17345.4 12602.2i −1.45021 1.05364i −0.985781 0.168034i \(-0.946258\pi\)
−0.464433 0.885608i \(-0.653742\pi\)
\(524\) 8484.91 0.707376
\(525\) 0 0
\(526\) −27907.0 −2.31332
\(527\) −21240.9 15432.4i −1.75573 1.27561i
\(528\) 0 0
\(529\) 4288.83 + 13199.7i 0.352497 + 1.08487i
\(530\) 1111.55 2332.56i 0.0910990 0.191169i
\(531\) 0 0
\(532\) −15090.9 −1.22983
\(533\) −1109.67 + 3415.21i −0.0901785 + 0.277541i
\(534\) 0 0
\(535\) 12226.5 + 1605.19i 0.988032 + 0.129716i
\(536\) −1813.00 1317.22i −0.146100 0.106148i
\(537\) 0 0
\(538\) −2800.61 + 2034.76i −0.224429 + 0.163057i
\(539\) −4583.46 3330.08i −0.366278 0.266116i
\(540\) 0 0
\(541\) 19412.5 14104.0i 1.54272 1.12085i 0.594113 0.804382i \(-0.297503\pi\)
0.948603 0.316467i \(-0.102497\pi\)
\(542\) 930.091 2862.53i 0.0737100 0.226856i
\(543\) 0 0
\(544\) −7728.70 + 23786.5i −0.609127 + 1.87470i
\(545\) 14406.1 7828.55i 1.13227 0.615299i
\(546\) 0 0
\(547\) −6911.76 21272.2i −0.540266 1.66277i −0.731987 0.681319i \(-0.761407\pi\)
0.191721 0.981450i \(-0.438593\pi\)
\(548\) 6303.64 + 4579.86i 0.491383 + 0.357011i
\(549\) 0 0
\(550\) −1011.97 19048.1i −0.0784555 1.47675i
\(551\) −4822.65 −0.372871
\(552\) 0 0
\(553\) 1102.95 + 3394.52i 0.0848138 + 0.261030i
\(554\) 9045.63 + 27839.6i 0.693704 + 2.13500i
\(555\) 0 0
\(556\) −768.369 + 2364.80i −0.0586081 + 0.180377i
\(557\) −5920.24 −0.450357 −0.225178 0.974318i \(-0.572297\pi\)
−0.225178 + 0.974318i \(0.572297\pi\)
\(558\) 0 0
\(559\) −2953.34 + 2145.73i −0.223458 + 0.162352i
\(560\) 15050.4 8178.69i 1.13571 0.617165i
\(561\) 0 0
\(562\) −6939.08 + 5041.54i −0.520832 + 0.378407i
\(563\) −2602.59 + 1890.89i −0.194824 + 0.141548i −0.680921 0.732357i \(-0.738420\pi\)
0.486097 + 0.873905i \(0.338420\pi\)
\(564\) 0 0
\(565\) −15225.5 + 8273.83i −1.13370 + 0.616076i
\(566\) 17677.7 12843.6i 1.31281 0.953813i
\(567\) 0 0
\(568\) −644.819 −0.0476338
\(569\) −1869.17 + 5752.70i −0.137714 + 0.423841i −0.996002 0.0893271i \(-0.971528\pi\)
0.858288 + 0.513168i \(0.171528\pi\)
\(570\) 0 0
\(571\) 1450.75 + 4464.95i 0.106326 + 0.327237i 0.990039 0.140791i \(-0.0449646\pi\)
−0.883714 + 0.468028i \(0.844965\pi\)
\(572\) −5996.11 18454.1i −0.438304 1.34896i
\(573\) 0 0
\(574\) −4531.56 −0.329518
\(575\) −12706.8 15668.6i −0.921583 1.13639i
\(576\) 0 0
\(577\) 15913.7 + 11562.0i 1.14817 + 0.834197i 0.988237 0.152930i \(-0.0488709\pi\)
0.159937 + 0.987127i \(0.448871\pi\)
\(578\) −6355.47 19560.1i −0.457358 1.40760i
\(579\) 0 0
\(580\) −3658.89 + 1988.32i −0.261944 + 0.142345i
\(581\) 272.269 837.958i 0.0194417 0.0598354i
\(582\) 0 0
\(583\) −714.003 + 2197.47i −0.0507221 + 0.156107i
\(584\) −810.824 + 589.098i −0.0574523 + 0.0417415i
\(585\) 0 0
\(586\) 9184.14 + 6672.67i 0.647429 + 0.470384i
\(587\) −8058.17 + 5854.60i −0.566603 + 0.411661i −0.833870 0.551961i \(-0.813880\pi\)
0.267266 + 0.963623i \(0.413880\pi\)
\(588\) 0 0
\(589\) −19801.6 14386.7i −1.38525 1.00644i
\(590\) −28071.9 3685.49i −1.95882 0.257168i
\(591\) 0 0
\(592\) 1857.25 5716.04i 0.128940 0.396837i
\(593\) 24115.5 1.66999 0.834995 0.550257i \(-0.185470\pi\)
0.834995 + 0.550257i \(0.185470\pi\)
\(594\) 0 0
\(595\) −10719.1 + 22493.9i −0.738557 + 1.54985i
\(596\) −2848.21 8765.89i −0.195750 0.602458i
\(597\) 0 0
\(598\) −34887.8 25347.4i −2.38573 1.73333i
\(599\) −13381.7 −0.912790 −0.456395 0.889777i \(-0.650860\pi\)
−0.456395 + 0.889777i \(0.650860\pi\)
\(600\) 0 0
\(601\) 23840.2 1.61807 0.809037 0.587758i \(-0.199989\pi\)
0.809037 + 0.587758i \(0.199989\pi\)
\(602\) −3726.92 2707.76i −0.252322 0.183323i
\(603\) 0 0
\(604\) −4183.61 12875.8i −0.281835 0.867400i
\(605\) 397.373 + 2139.75i 0.0267033 + 0.143790i
\(606\) 0 0
\(607\) −17213.0 −1.15100 −0.575499 0.817803i \(-0.695192\pi\)
−0.575499 + 0.817803i \(0.695192\pi\)
\(608\) −7205.00 + 22174.7i −0.480594 + 1.47912i
\(609\) 0 0
\(610\) −5226.83 28145.1i −0.346932 1.86814i
\(611\) −13390.2 9728.52i −0.886593 0.644147i
\(612\) 0 0
\(613\) −6213.79 + 4514.58i −0.409417 + 0.297459i −0.773366 0.633960i \(-0.781428\pi\)
0.363949 + 0.931419i \(0.381428\pi\)
\(614\) −5995.37 4355.89i −0.394061 0.286302i
\(615\) 0 0
\(616\) −2009.01 + 1459.63i −0.131404 + 0.0954709i
\(617\) −5822.57 + 17920.0i −0.379915 + 1.16926i 0.560187 + 0.828366i \(0.310729\pi\)
−0.940102 + 0.340893i \(0.889271\pi\)
\(618\) 0 0
\(619\) −8736.42 + 26887.9i −0.567280 + 1.74591i 0.0937989 + 0.995591i \(0.470099\pi\)
−0.661079 + 0.750317i \(0.729901\pi\)
\(620\) −20954.8 2751.10i −1.35736 0.178205i
\(621\) 0 0
\(622\) 10650.4 + 32778.5i 0.686562 + 2.11302i
\(623\) −8289.12 6022.40i −0.533060 0.387291i
\(624\) 0 0
\(625\) 13542.8 + 7793.08i 0.866742 + 0.498757i
\(626\) 29142.3 1.86064
\(627\) 0 0
\(628\) −4246.32 13068.8i −0.269820 0.830419i
\(629\) 2701.71 + 8315.01i 0.171263 + 0.527092i
\(630\) 0 0
\(631\) −2799.20 + 8615.05i −0.176600 + 0.543518i −0.999703 0.0243738i \(-0.992241\pi\)
0.823103 + 0.567892i \(0.192241\pi\)
\(632\) 464.950 0.0292638
\(633\) 0 0
\(634\) 17826.5 12951.7i 1.11669 0.811322i
\(635\) −7885.49 7477.68i −0.492797 0.467311i
\(636\) 0 0
\(637\) 8025.74 5831.04i 0.499201 0.362691i
\(638\) 6330.72 4599.54i 0.392846 0.285419i
\(639\) 0 0
\(640\) −748.785 4032.01i −0.0462474 0.249030i
\(641\) −6259.41 + 4547.73i −0.385697 + 0.280225i −0.763690 0.645583i \(-0.776614\pi\)
0.377993 + 0.925809i \(0.376614\pi\)
\(642\) 0 0
\(643\) 20694.2 1.26921 0.634604 0.772837i \(-0.281163\pi\)
0.634604 + 0.772837i \(0.281163\pi\)
\(644\) 8002.44 24629.0i 0.489659 1.50701i
\(645\) 0 0
\(646\) −11454.3 35252.7i −0.697620 2.14705i
\(647\) −2688.19 8273.39i −0.163344 0.502721i 0.835566 0.549389i \(-0.185140\pi\)
−0.998910 + 0.0466682i \(0.985140\pi\)
\(648\) 0 0
\(649\) 25318.1 1.53131
\(650\) 32268.8 + 8621.59i 1.94721 + 0.520256i
\(651\) 0 0
\(652\) −18593.2 13508.7i −1.11682 0.811416i
\(653\) −3741.70 11515.8i −0.224233 0.690118i −0.998369 0.0570980i \(-0.981815\pi\)
0.774136 0.633020i \(-0.218185\pi\)
\(654\) 0 0
\(655\) 5618.51 11790.3i 0.335165 0.703337i
\(656\) −1125.18 + 3462.95i −0.0669679 + 0.206106i
\(657\) 0 0
\(658\) 6454.27 19864.2i 0.382391 1.17688i
\(659\) −1436.42 + 1043.62i −0.0849091 + 0.0616901i −0.629430 0.777057i \(-0.716712\pi\)
0.544521 + 0.838747i \(0.316712\pi\)
\(660\) 0 0
\(661\) 9947.42 + 7227.23i 0.585340 + 0.425275i 0.840645 0.541586i \(-0.182176\pi\)
−0.255305 + 0.966861i \(0.582176\pi\)
\(662\) 13930.4 10121.0i 0.817853 0.594205i
\(663\) 0 0
\(664\) −92.8555 67.4634i −0.00542694 0.00394291i
\(665\) −9992.80 + 20969.7i −0.582713 + 1.22281i
\(666\) 0 0
\(667\) 2557.37 7870.78i 0.148459 0.456908i
\(668\) −25606.4 −1.48315
\(669\) 0 0
\(670\) 29886.2 16240.8i 1.72329 0.936470i
\(671\) 7910.36 + 24345.6i 0.455106 + 1.40067i
\(672\) 0 0
\(673\) 23862.6 + 17337.2i 1.36677 + 0.993016i 0.997982 + 0.0635025i \(0.0202271\pi\)
0.368788 + 0.929514i \(0.379773\pi\)
\(674\) −17485.1 −0.999260
\(675\) 0 0
\(676\) 18018.9 1.02520
\(677\) 27342.4 + 19865.4i 1.55222 + 1.12776i 0.942043 + 0.335491i \(0.108902\pi\)
0.610178 + 0.792264i \(0.291098\pi\)
\(678\) 0 0
\(679\) 3921.55 + 12069.3i 0.221643 + 0.682146i
\(680\) 2355.30 + 2233.49i 0.132826 + 0.125956i
\(681\) 0 0
\(682\) 39714.9 2.22986
\(683\) 659.833 2030.76i 0.0369661 0.113770i −0.930871 0.365349i \(-0.880950\pi\)
0.967837 + 0.251579i \(0.0809498\pi\)
\(684\) 0 0
\(685\) 10538.1 5726.63i 0.587797 0.319421i
\(686\) −13822.2 10042.4i −0.769291 0.558923i
\(687\) 0 0
\(688\) −2994.62 + 2175.72i −0.165943 + 0.120565i
\(689\) −3273.16 2378.09i −0.180983 0.131492i
\(690\) 0 0
\(691\) −17933.3 + 13029.3i −0.987285 + 0.717305i −0.959325 0.282304i \(-0.908901\pi\)
−0.0279602 + 0.999609i \(0.508901\pi\)
\(692\) −8713.77 + 26818.2i −0.478682 + 1.47323i
\(693\) 0 0
\(694\) −844.467 + 2599.00i −0.0461895 + 0.142157i
\(695\) 2777.24 + 2633.61i 0.151578 + 0.143739i
\(696\) 0 0
\(697\) −1636.78 5037.49i −0.0889489 0.273757i
\(698\) −22504.1 16350.2i −1.22033 0.886623i
\(699\) 0 0
\(700\) 1064.10 + 20029.4i 0.0574561 + 1.08149i
\(701\) −12304.2 −0.662941 −0.331471 0.943466i \(-0.607545\pi\)
−0.331471 + 0.943466i \(0.607545\pi\)
\(702\) 0 0
\(703\) 2518.64 + 7751.59i 0.135124 + 0.415870i
\(704\) −4994.28 15370.8i −0.267371 0.822882i
\(705\) 0 0
\(706\) −4275.25 + 13157.9i −0.227905 + 0.701420i
\(707\) 23741.8 1.26294
\(708\) 0 0
\(709\) −9554.64 + 6941.85i −0.506110 + 0.367711i −0.811346 0.584566i \(-0.801265\pi\)
0.305236 + 0.952277i \(0.401265\pi\)
\(710\) 4210.28 8835.20i 0.222548 0.467013i
\(711\) 0 0
\(712\) −1079.80 + 784.519i −0.0568358 + 0.0412937i
\(713\) 33980.3 24688.1i 1.78481 1.29674i
\(714\) 0 0
\(715\) −29613.7 3887.91i −1.54894 0.203356i
\(716\) 2932.41 2130.52i 0.153058 0.111203i
\(717\) 0 0
\(718\) 45540.8 2.36709
\(719\) 9386.90 28889.9i 0.486888 1.49849i −0.342340 0.939576i \(-0.611219\pi\)
0.829228 0.558911i \(-0.188781\pi\)
\(720\) 0 0
\(721\) 6367.55 + 19597.3i 0.328904 + 1.01226i
\(722\) −2397.42 7378.48i −0.123577 0.380331i
\(723\) 0 0
\(724\) −32332.0 −1.65968
\(725\) 340.060 + 6400.88i 0.0174200 + 0.327893i
\(726\) 0 0
\(727\) −24645.5 17906.0i −1.25729 0.913475i −0.258668 0.965966i \(-0.583284\pi\)
−0.998621 + 0.0524916i \(0.983284\pi\)
\(728\) −1343.68 4135.43i −0.0684069 0.210535i
\(729\) 0 0
\(730\) −2777.52 14956.2i −0.140823 0.758295i
\(731\) 1663.93 5121.05i 0.0841896 0.259109i
\(732\) 0 0
\(733\) −7869.55 + 24220.0i −0.396546 + 1.22044i 0.531205 + 0.847244i \(0.321740\pi\)
−0.927751 + 0.373200i \(0.878260\pi\)
\(734\) 232.310 168.783i 0.0116822 0.00848759i
\(735\) 0 0
\(736\) −32369.5 23517.8i −1.62113 1.17782i
\(737\) −24607.2 + 17878.2i −1.22988 + 0.893557i
\(738\) 0 0
\(739\) −19811.5 14393.9i −0.986167 0.716492i −0.0270884 0.999633i \(-0.508624\pi\)
−0.959078 + 0.283141i \(0.908624\pi\)
\(740\) 5106.75 + 4842.64i 0.253686 + 0.240566i
\(741\) 0 0
\(742\) 1577.71 4855.70i 0.0780588 0.240240i
\(743\) −11738.9 −0.579622 −0.289811 0.957084i \(-0.593592\pi\)
−0.289811 + 0.957084i \(0.593592\pi\)
\(744\) 0 0
\(745\) −14066.8 1846.79i −0.691768 0.0908206i
\(746\) −3108.27 9566.29i −0.152550 0.469499i
\(747\) 0 0
\(748\) 23154.8 + 16823.0i 1.13185 + 0.822338i
\(749\) 24366.2 1.18868
\(750\) 0 0
\(751\) −12224.7 −0.593989 −0.296995 0.954879i \(-0.595984\pi\)
−0.296995 + 0.954879i \(0.595984\pi\)
\(752\) −13577.3 9864.51i −0.658397 0.478353i
\(753\) 0 0
\(754\) 4234.18 + 13031.5i 0.204509 + 0.629414i
\(755\) −20662.0 2712.67i −0.995985 0.130761i
\(756\) 0 0
\(757\) −22653.2 −1.08764 −0.543822 0.839201i \(-0.683023\pi\)
−0.543822 + 0.839201i \(0.683023\pi\)
\(758\) −73.2654 + 225.488i −0.00351071 + 0.0108049i
\(759\) 0 0
\(760\) 2195.70 + 2082.15i 0.104798 + 0.0993782i
\(761\) 6237.17 + 4531.57i 0.297106 + 0.215860i 0.726344 0.687331i \(-0.241218\pi\)
−0.429238 + 0.903191i \(0.641218\pi\)
\(762\) 0 0
\(763\) 26209.9 19042.6i 1.24359 0.903523i
\(764\) 23330.5 + 16950.6i 1.10480 + 0.802684i
\(765\) 0 0
\(766\) −12014.1 + 8728.75i −0.566693 + 0.411727i
\(767\) −13699.5 + 42162.7i −0.644928 + 1.98488i
\(768\) 0 0
\(769\) 8640.68 26593.3i 0.405190 1.24705i −0.515547 0.856861i \(-0.672411\pi\)
0.920737 0.390184i \(-0.127589\pi\)
\(770\) −6881.96 37057.6i −0.322089 1.73437i
\(771\) 0 0
\(772\) 6992.42 + 21520.5i 0.325988 + 1.00329i
\(773\) 31856.0 + 23144.7i 1.48225 + 1.07692i 0.976823 + 0.214049i \(0.0686653\pi\)
0.505428 + 0.862869i \(0.331335\pi\)
\(774\) 0 0
\(775\) −17698.6 + 27296.3i −0.820324 + 1.26517i
\(776\) 1653.14 0.0764746
\(777\) 0 0
\(778\) 11805.9 + 36334.8i 0.544039 + 1.67438i
\(779\) −1525.87 4696.15i −0.0701797 0.215991i
\(780\) 0 0
\(781\) −2704.48 + 8323.54i −0.123910 + 0.381357i
\(782\) 63608.0 2.90872
\(783\) 0 0
\(784\) 8137.92 5912.55i 0.370714 0.269340i
\(785\) −20971.8