Properties

Label 63.4.e.c.37.1
Level $63$
Weight $4$
Character 63.37
Analytic conductor $3.717$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.71712033036\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.9924270768.1
Defining polynomial: \(x^{6} - x^{5} + 25 x^{4} + 12 x^{3} + 582 x^{2} - 144 x + 36\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.1
Root \(-2.27818 + 3.94593i\) of defining polynomial
Character \(\chi\) \(=\) 63.37
Dual form 63.4.e.c.46.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.27818 + 3.94593i) q^{2} +(-6.38024 - 11.0509i) q^{4} +(8.93660 - 15.4786i) q^{5} +(2.26047 - 18.3818i) q^{7} +21.6905 q^{8} +O(q^{10})\) \(q+(-2.27818 + 3.94593i) q^{2} +(-6.38024 - 11.0509i) q^{4} +(8.93660 - 15.4786i) q^{5} +(2.26047 - 18.3818i) q^{7} +21.6905 q^{8} +(40.7184 + 70.5264i) q^{10} +(-5.69708 - 9.86762i) q^{11} -13.0987 q^{13} +(67.3835 + 50.7968i) q^{14} +(1.62706 - 2.81815i) q^{16} +(26.6337 + 46.1309i) q^{17} +(21.2111 - 36.7388i) q^{19} -228.071 q^{20} +51.9159 q^{22} +(76.0427 - 131.710i) q^{23} +(-97.2257 - 168.400i) q^{25} +(29.8412 - 51.6864i) q^{26} +(-217.558 + 92.2999i) q^{28} -186.493 q^{29} +(78.9369 + 136.723i) q^{31} +(94.1753 + 163.116i) q^{32} -242.706 q^{34} +(-264.324 - 199.260i) q^{35} +(-1.87294 + 3.24403i) q^{37} +(96.6457 + 167.395i) q^{38} +(193.839 - 335.739i) q^{40} +39.3230 q^{41} +429.439 q^{43} +(-72.6974 + 125.916i) q^{44} +(346.478 + 600.118i) q^{46} +(10.5934 - 18.3484i) q^{47} +(-332.781 - 83.1031i) q^{49} +885.992 q^{50} +(83.5726 + 144.752i) q^{52} +(182.952 + 316.882i) q^{53} -203.650 q^{55} +(49.0307 - 398.709i) q^{56} +(424.866 - 735.889i) q^{58} +(-113.289 - 196.222i) q^{59} +(-325.987 + 564.626i) q^{61} -719.331 q^{62} -832.161 q^{64} +(-117.058 + 202.750i) q^{65} +(-72.7166 - 125.949i) q^{67} +(339.858 - 588.652i) q^{68} +(1388.44 - 589.055i) q^{70} +368.962 q^{71} +(-304.453 - 527.328i) q^{73} +(-8.53380 - 14.7810i) q^{74} -541.328 q^{76} +(-194.263 + 82.4170i) q^{77} +(-455.119 + 788.289i) q^{79} +(-29.0808 - 50.3694i) q^{80} +(-89.5850 + 155.166i) q^{82} +327.929 q^{83} +952.058 q^{85} +(-978.340 + 1694.53i) q^{86} +(-123.572 - 214.033i) q^{88} +(-18.8059 + 32.5728i) q^{89} +(-29.6092 + 240.777i) q^{91} -1940.68 q^{92} +(48.2676 + 83.6019i) q^{94} +(-379.111 - 656.640i) q^{95} +722.013 q^{97} +(1086.05 - 1123.80i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + q^{2} - 25q^{4} + 11q^{5} - 13q^{7} - 78q^{8} + O(q^{10}) \) \( 6q + q^{2} - 25q^{4} + 11q^{5} - 13q^{7} - 78q^{8} + 55q^{10} + 35q^{11} + 124q^{13} + 326q^{14} - 241q^{16} + 48q^{17} + 202q^{19} - 878q^{20} - 14q^{22} + 216q^{23} - 130q^{25} + 274q^{26} - 201q^{28} - 106q^{29} + 95q^{31} + 683q^{32} - 48q^{34} - 56q^{35} - 262q^{37} - 398q^{38} - 21q^{40} - 488q^{41} + 720q^{43} - 905q^{44} + 1056q^{46} - 210q^{47} - 303q^{49} + 2756q^{50} - 324q^{52} + 393q^{53} - 2062q^{55} - 1299q^{56} + 1249q^{58} + 1143q^{59} + 70q^{61} - 2118q^{62} - 798q^{64} - 472q^{65} + 628q^{67} + 1944q^{68} + 3251q^{70} - 636q^{71} - 988q^{73} + 1002q^{74} - 4680q^{76} - 1073q^{77} - 861q^{79} + 175q^{80} - 124q^{82} - 1038q^{83} + 3600q^{85} - 3208q^{86} + 891q^{88} + 1766q^{89} - 654q^{91} + 1344q^{92} + 3294q^{94} - 736q^{95} + 38q^{97} + 4267q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.27818 + 3.94593i −0.805459 + 1.39510i 0.110521 + 0.993874i \(0.464748\pi\)
−0.915981 + 0.401223i \(0.868585\pi\)
\(3\) 0 0
\(4\) −6.38024 11.0509i −0.797530 1.38136i
\(5\) 8.93660 15.4786i 0.799314 1.38445i −0.120749 0.992683i \(-0.538530\pi\)
0.920063 0.391769i \(-0.128137\pi\)
\(6\) 0 0
\(7\) 2.26047 18.3818i 0.122054 0.992523i
\(8\) 21.6905 0.958592
\(9\) 0 0
\(10\) 40.7184 + 70.5264i 1.28763 + 2.23024i
\(11\) −5.69708 9.86762i −0.156158 0.270473i 0.777322 0.629102i \(-0.216577\pi\)
−0.933480 + 0.358630i \(0.883244\pi\)
\(12\) 0 0
\(13\) −13.0987 −0.279455 −0.139728 0.990190i \(-0.544623\pi\)
−0.139728 + 0.990190i \(0.544623\pi\)
\(14\) 67.3835 + 50.7968i 1.28636 + 0.969714i
\(15\) 0 0
\(16\) 1.62706 2.81815i 0.0254228 0.0440336i
\(17\) 26.6337 + 46.1309i 0.379977 + 0.658140i 0.991059 0.133428i \(-0.0425984\pi\)
−0.611081 + 0.791568i \(0.709265\pi\)
\(18\) 0 0
\(19\) 21.2111 36.7388i 0.256114 0.443603i −0.709083 0.705125i \(-0.750891\pi\)
0.965198 + 0.261522i \(0.0842244\pi\)
\(20\) −228.071 −2.54991
\(21\) 0 0
\(22\) 51.9159 0.503114
\(23\) 76.0427 131.710i 0.689391 1.19406i −0.282644 0.959225i \(-0.591211\pi\)
0.972035 0.234836i \(-0.0754553\pi\)
\(24\) 0 0
\(25\) −97.2257 168.400i −0.777806 1.34720i
\(26\) 29.8412 51.6864i 0.225090 0.389867i
\(27\) 0 0
\(28\) −217.558 + 92.2999i −1.46838 + 0.622966i
\(29\) −186.493 −1.19417 −0.597085 0.802178i \(-0.703675\pi\)
−0.597085 + 0.802178i \(0.703675\pi\)
\(30\) 0 0
\(31\) 78.9369 + 136.723i 0.457338 + 0.792133i 0.998819 0.0485801i \(-0.0154696\pi\)
−0.541481 + 0.840713i \(0.682136\pi\)
\(32\) 94.1753 + 163.116i 0.520250 + 0.901099i
\(33\) 0 0
\(34\) −242.706 −1.22423
\(35\) −264.324 199.260i −1.27654 0.962316i
\(36\) 0 0
\(37\) −1.87294 + 3.24403i −0.00832188 + 0.0144139i −0.870156 0.492776i \(-0.835982\pi\)
0.861834 + 0.507190i \(0.169316\pi\)
\(38\) 96.6457 + 167.395i 0.412579 + 0.714608i
\(39\) 0 0
\(40\) 193.839 335.739i 0.766216 1.32712i
\(41\) 39.3230 0.149786 0.0748930 0.997192i \(-0.476138\pi\)
0.0748930 + 0.997192i \(0.476138\pi\)
\(42\) 0 0
\(43\) 429.439 1.52300 0.761498 0.648168i \(-0.224464\pi\)
0.761498 + 0.648168i \(0.224464\pi\)
\(44\) −72.6974 + 125.916i −0.249080 + 0.431420i
\(45\) 0 0
\(46\) 346.478 + 600.118i 1.11055 + 1.92354i
\(47\) 10.5934 18.3484i 0.0328768 0.0569444i −0.849119 0.528202i \(-0.822866\pi\)
0.881996 + 0.471258i \(0.156200\pi\)
\(48\) 0 0
\(49\) −332.781 83.1031i −0.970206 0.242283i
\(50\) 885.992 2.50596
\(51\) 0 0
\(52\) 83.5726 + 144.752i 0.222874 + 0.386029i
\(53\) 182.952 + 316.882i 0.474158 + 0.821266i 0.999562 0.0295866i \(-0.00941909\pi\)
−0.525404 + 0.850853i \(0.676086\pi\)
\(54\) 0 0
\(55\) −203.650 −0.499276
\(56\) 49.0307 398.709i 0.117000 0.951425i
\(57\) 0 0
\(58\) 424.866 735.889i 0.961856 1.66598i
\(59\) −113.289 196.222i −0.249982 0.432982i 0.713538 0.700616i \(-0.247091\pi\)
−0.963521 + 0.267634i \(0.913758\pi\)
\(60\) 0 0
\(61\) −325.987 + 564.626i −0.684235 + 1.18513i 0.289442 + 0.957196i \(0.406530\pi\)
−0.973677 + 0.227934i \(0.926803\pi\)
\(62\) −719.331 −1.47347
\(63\) 0 0
\(64\) −832.161 −1.62532
\(65\) −117.058 + 202.750i −0.223372 + 0.386892i
\(66\) 0 0
\(67\) −72.7166 125.949i −0.132593 0.229658i 0.792082 0.610414i \(-0.208997\pi\)
−0.924675 + 0.380756i \(0.875664\pi\)
\(68\) 339.858 588.652i 0.606086 1.04977i
\(69\) 0 0
\(70\) 1388.44 589.055i 2.37073 1.00579i
\(71\) 368.962 0.616728 0.308364 0.951268i \(-0.400218\pi\)
0.308364 + 0.951268i \(0.400218\pi\)
\(72\) 0 0
\(73\) −304.453 527.328i −0.488130 0.845466i 0.511777 0.859119i \(-0.328988\pi\)
−0.999907 + 0.0136522i \(0.995654\pi\)
\(74\) −8.53380 14.7810i −0.0134059 0.0232197i
\(75\) 0 0
\(76\) −541.328 −0.817034
\(77\) −194.263 + 82.4170i −0.287510 + 0.121978i
\(78\) 0 0
\(79\) −455.119 + 788.289i −0.648163 + 1.12265i 0.335399 + 0.942076i \(0.391129\pi\)
−0.983561 + 0.180574i \(0.942204\pi\)
\(80\) −29.0808 50.3694i −0.0406416 0.0703933i
\(81\) 0 0
\(82\) −89.5850 + 155.166i −0.120646 + 0.208966i
\(83\) 327.929 0.433674 0.216837 0.976208i \(-0.430426\pi\)
0.216837 + 0.976208i \(0.430426\pi\)
\(84\) 0 0
\(85\) 952.058 1.21489
\(86\) −978.340 + 1694.53i −1.22671 + 2.12473i
\(87\) 0 0
\(88\) −123.572 214.033i −0.149691 0.259273i
\(89\) −18.8059 + 32.5728i −0.0223980 + 0.0387945i −0.877007 0.480477i \(-0.840463\pi\)
0.854609 + 0.519272i \(0.173797\pi\)
\(90\) 0 0
\(91\) −29.6092 + 240.777i −0.0341086 + 0.277366i
\(92\) −1940.68 −2.19924
\(93\) 0 0
\(94\) 48.2676 + 83.6019i 0.0529619 + 0.0917327i
\(95\) −379.111 656.640i −0.409431 0.709156i
\(96\) 0 0
\(97\) 722.013 0.755766 0.377883 0.925853i \(-0.376652\pi\)
0.377883 + 0.925853i \(0.376652\pi\)
\(98\) 1086.05 1123.80i 1.11947 1.15838i
\(99\) 0 0
\(100\) −1240.65 + 2148.86i −1.24065 + 2.14886i
\(101\) 759.336 + 1315.21i 0.748087 + 1.29572i 0.948739 + 0.316062i \(0.102361\pi\)
−0.200652 + 0.979663i \(0.564306\pi\)
\(102\) 0 0
\(103\) 525.942 910.957i 0.503132 0.871450i −0.496862 0.867830i \(-0.665514\pi\)
0.999993 0.00361990i \(-0.00115225\pi\)
\(104\) −284.116 −0.267883
\(105\) 0 0
\(106\) −1667.19 −1.52766
\(107\) 383.260 663.826i 0.346273 0.599762i −0.639312 0.768948i \(-0.720781\pi\)
0.985584 + 0.169186i \(0.0541139\pi\)
\(108\) 0 0
\(109\) 713.524 + 1235.86i 0.627002 + 1.08600i 0.988150 + 0.153491i \(0.0490516\pi\)
−0.361148 + 0.932509i \(0.617615\pi\)
\(110\) 463.952 803.588i 0.402146 0.696538i
\(111\) 0 0
\(112\) −48.1247 36.2786i −0.0406014 0.0306072i
\(113\) −362.564 −0.301833 −0.150917 0.988546i \(-0.548222\pi\)
−0.150917 + 0.988546i \(0.548222\pi\)
\(114\) 0 0
\(115\) −1359.13 2354.08i −1.10208 1.90886i
\(116\) 1189.87 + 2060.92i 0.952386 + 1.64958i
\(117\) 0 0
\(118\) 1032.37 0.805402
\(119\) 908.173 385.297i 0.699597 0.296808i
\(120\) 0 0
\(121\) 600.587 1040.25i 0.451230 0.781553i
\(122\) −1485.31 2572.64i −1.10225 1.90915i
\(123\) 0 0
\(124\) 1007.27 1744.65i 0.729481 1.26350i
\(125\) −1241.32 −0.888216
\(126\) 0 0
\(127\) 974.777 0.681082 0.340541 0.940230i \(-0.389390\pi\)
0.340541 + 0.940230i \(0.389390\pi\)
\(128\) 1142.41 1978.72i 0.788875 1.36637i
\(129\) 0 0
\(130\) −533.357 923.802i −0.359835 0.623252i
\(131\) −896.351 + 1552.53i −0.597821 + 1.03546i 0.395321 + 0.918543i \(0.370633\pi\)
−0.993142 + 0.116914i \(0.962700\pi\)
\(132\) 0 0
\(133\) −627.377 472.946i −0.409026 0.308343i
\(134\) 662.647 0.427194
\(135\) 0 0
\(136\) 577.697 + 1000.60i 0.364243 + 0.630888i
\(137\) 842.208 + 1458.75i 0.525217 + 0.909702i 0.999569 + 0.0293665i \(0.00934900\pi\)
−0.474352 + 0.880335i \(0.657318\pi\)
\(138\) 0 0
\(139\) 315.089 0.192270 0.0961350 0.995368i \(-0.469352\pi\)
0.0961350 + 0.995368i \(0.469352\pi\)
\(140\) −515.547 + 4192.35i −0.311226 + 2.53084i
\(141\) 0 0
\(142\) −840.563 + 1455.90i −0.496750 + 0.860396i
\(143\) 74.6241 + 129.253i 0.0436390 + 0.0755850i
\(144\) 0 0
\(145\) −1666.62 + 2886.67i −0.954517 + 1.65327i
\(146\) 2774.40 1.57268
\(147\) 0 0
\(148\) 47.7992 0.0265478
\(149\) 946.887 1640.06i 0.520617 0.901736i −0.479095 0.877763i \(-0.659035\pi\)
0.999713 0.0239729i \(-0.00763155\pi\)
\(150\) 0 0
\(151\) 1005.92 + 1742.31i 0.542124 + 0.938986i 0.998782 + 0.0493434i \(0.0157129\pi\)
−0.456658 + 0.889642i \(0.650954\pi\)
\(152\) 460.079 796.881i 0.245509 0.425234i
\(153\) 0 0
\(154\) 117.355 954.308i 0.0614071 0.499353i
\(155\) 2821.71 1.46223
\(156\) 0 0
\(157\) 1914.25 + 3315.58i 0.973082 + 1.68543i 0.686125 + 0.727483i \(0.259310\pi\)
0.286956 + 0.957944i \(0.407357\pi\)
\(158\) −2073.69 3591.73i −1.04414 1.80850i
\(159\) 0 0
\(160\) 3366.43 1.66337
\(161\) −2249.17 1695.53i −1.10099 0.829977i
\(162\) 0 0
\(163\) 1754.63 3039.11i 0.843148 1.46038i −0.0440718 0.999028i \(-0.514033\pi\)
0.887220 0.461347i \(-0.152634\pi\)
\(164\) −250.890 434.554i −0.119459 0.206909i
\(165\) 0 0
\(166\) −747.083 + 1293.99i −0.349307 + 0.605017i
\(167\) 343.008 0.158939 0.0794694 0.996837i \(-0.474677\pi\)
0.0794694 + 0.996837i \(0.474677\pi\)
\(168\) 0 0
\(169\) −2025.42 −0.921905
\(170\) −2168.96 + 3756.75i −0.978541 + 1.69488i
\(171\) 0 0
\(172\) −2739.92 4745.68i −1.21463 2.10381i
\(173\) −2093.61 + 3626.23i −0.920081 + 1.59363i −0.120793 + 0.992678i \(0.538544\pi\)
−0.799288 + 0.600949i \(0.794790\pi\)
\(174\) 0 0
\(175\) −3315.27 + 1406.52i −1.43206 + 0.607559i
\(176\) −37.0779 −0.0158798
\(177\) 0 0
\(178\) −85.6866 148.413i −0.0360813 0.0624947i
\(179\) −985.143 1706.32i −0.411358 0.712493i 0.583681 0.811983i \(-0.301612\pi\)
−0.995039 + 0.0994906i \(0.968279\pi\)
\(180\) 0 0
\(181\) −3613.10 −1.48376 −0.741878 0.670535i \(-0.766065\pi\)
−0.741878 + 0.670535i \(0.766065\pi\)
\(182\) −882.634 665.370i −0.359479 0.270992i
\(183\) 0 0
\(184\) 1649.40 2856.85i 0.660845 1.14462i
\(185\) 33.4755 + 57.9812i 0.0133036 + 0.0230425i
\(186\) 0 0
\(187\) 303.468 525.622i 0.118673 0.205547i
\(188\) −270.355 −0.104881
\(189\) 0 0
\(190\) 3454.74 1.31912
\(191\) 953.884 1652.18i 0.361365 0.625902i −0.626821 0.779163i \(-0.715644\pi\)
0.988186 + 0.153261i \(0.0489776\pi\)
\(192\) 0 0
\(193\) −1199.96 2078.40i −0.447540 0.775162i 0.550685 0.834713i \(-0.314366\pi\)
−0.998225 + 0.0595509i \(0.981033\pi\)
\(194\) −1644.88 + 2849.01i −0.608738 + 1.05437i
\(195\) 0 0
\(196\) 1204.86 + 4207.74i 0.439087 + 1.53343i
\(197\) −1514.32 −0.547668 −0.273834 0.961777i \(-0.588292\pi\)
−0.273834 + 0.961777i \(0.588292\pi\)
\(198\) 0 0
\(199\) −683.889 1184.53i −0.243616 0.421955i 0.718126 0.695914i \(-0.245000\pi\)
−0.961742 + 0.273958i \(0.911667\pi\)
\(200\) −2108.87 3652.67i −0.745598 1.29141i
\(201\) 0 0
\(202\) −6919.63 −2.41021
\(203\) −421.563 + 3428.08i −0.145753 + 1.18524i
\(204\) 0 0
\(205\) 351.414 608.667i 0.119726 0.207371i
\(206\) 2396.38 + 4150.66i 0.810504 + 1.40383i
\(207\) 0 0
\(208\) −21.3123 + 36.9140i −0.00710453 + 0.0123054i
\(209\) −483.366 −0.159977
\(210\) 0 0
\(211\) 4302.52 1.40378 0.701891 0.712285i \(-0.252339\pi\)
0.701891 + 0.712285i \(0.252339\pi\)
\(212\) 2334.55 4043.57i 0.756311 1.30997i
\(213\) 0 0
\(214\) 1746.27 + 3024.64i 0.557817 + 0.966167i
\(215\) 3837.72 6647.13i 1.21735 2.10851i
\(216\) 0 0
\(217\) 2691.64 1141.94i 0.842030 0.357236i
\(218\) −6502.16 −2.02010
\(219\) 0 0
\(220\) 1299.34 + 2250.51i 0.398187 + 0.689680i
\(221\) −348.866 604.253i −0.106187 0.183921i
\(222\) 0 0
\(223\) −1497.19 −0.449592 −0.224796 0.974406i \(-0.572172\pi\)
−0.224796 + 0.974406i \(0.572172\pi\)
\(224\) 3211.25 1362.39i 0.957861 0.406377i
\(225\) 0 0
\(226\) 825.987 1430.65i 0.243114 0.421086i
\(227\) 801.662 + 1388.52i 0.234397 + 0.405988i 0.959097 0.283076i \(-0.0913550\pi\)
−0.724700 + 0.689065i \(0.758022\pi\)
\(228\) 0 0
\(229\) −505.261 + 875.137i −0.145802 + 0.252536i −0.929672 0.368389i \(-0.879909\pi\)
0.783870 + 0.620925i \(0.213243\pi\)
\(230\) 12385.4 3.55072
\(231\) 0 0
\(232\) −4045.13 −1.14472
\(233\) 99.1084 171.661i 0.0278661 0.0482656i −0.851756 0.523939i \(-0.824462\pi\)
0.879622 + 0.475673i \(0.157795\pi\)
\(234\) 0 0
\(235\) −189.339 327.944i −0.0525578 0.0910329i
\(236\) −1445.62 + 2503.88i −0.398736 + 0.690631i
\(237\) 0 0
\(238\) −548.629 + 4461.36i −0.149422 + 1.21507i
\(239\) 1201.19 0.325098 0.162549 0.986700i \(-0.448028\pi\)
0.162549 + 0.986700i \(0.448028\pi\)
\(240\) 0 0
\(241\) 1366.35 + 2366.58i 0.365204 + 0.632551i 0.988809 0.149188i \(-0.0476660\pi\)
−0.623605 + 0.781739i \(0.714333\pi\)
\(242\) 2736.49 + 4739.74i 0.726894 + 1.25902i
\(243\) 0 0
\(244\) 8319.49 2.18279
\(245\) −4260.25 + 4408.33i −1.11093 + 1.14954i
\(246\) 0 0
\(247\) −277.838 + 481.229i −0.0715724 + 0.123967i
\(248\) 1712.18 + 2965.58i 0.438401 + 0.759332i
\(249\) 0 0
\(250\) 2827.95 4898.16i 0.715422 1.23915i
\(251\) −7565.82 −1.90259 −0.951295 0.308281i \(-0.900246\pi\)
−0.951295 + 0.308281i \(0.900246\pi\)
\(252\) 0 0
\(253\) −1732.88 −0.430615
\(254\) −2220.72 + 3846.40i −0.548584 + 0.950175i
\(255\) 0 0
\(256\) 1876.61 + 3250.38i 0.458156 + 0.793550i
\(257\) 2504.34 4337.64i 0.607846 1.05282i −0.383749 0.923437i \(-0.625367\pi\)
0.991595 0.129382i \(-0.0412994\pi\)
\(258\) 0 0
\(259\) 55.3973 + 41.7610i 0.0132904 + 0.0100189i
\(260\) 2987.42 0.712584
\(261\) 0 0
\(262\) −4084.10 7073.88i −0.963041 1.66804i
\(263\) −3124.40 5411.63i −0.732544 1.26880i −0.955793 0.294042i \(-0.905000\pi\)
0.223249 0.974761i \(-0.428334\pi\)
\(264\) 0 0
\(265\) 6539.88 1.51601
\(266\) 3295.49 1398.13i 0.759622 0.322274i
\(267\) 0 0
\(268\) −927.898 + 1607.17i −0.211494 + 0.366318i
\(269\) −1794.22 3107.69i −0.406676 0.704383i 0.587839 0.808978i \(-0.299979\pi\)
−0.994515 + 0.104595i \(0.966645\pi\)
\(270\) 0 0
\(271\) 991.571 1717.45i 0.222264 0.384973i −0.733231 0.679980i \(-0.761988\pi\)
0.955495 + 0.295007i \(0.0953218\pi\)
\(272\) 173.338 0.0386404
\(273\) 0 0
\(274\) −7674.81 −1.69216
\(275\) −1107.80 + 1918.77i −0.242920 + 0.420751i
\(276\) 0 0
\(277\) −3681.96 6377.33i −0.798654 1.38331i −0.920493 0.390760i \(-0.872212\pi\)
0.121838 0.992550i \(-0.461121\pi\)
\(278\) −717.831 + 1243.32i −0.154866 + 0.268235i
\(279\) 0 0
\(280\) −5733.32 4322.04i −1.22368 0.922468i
\(281\) 5312.05 1.12772 0.563861 0.825869i \(-0.309315\pi\)
0.563861 + 0.825869i \(0.309315\pi\)
\(282\) 0 0
\(283\) 545.882 + 945.495i 0.114662 + 0.198600i 0.917645 0.397402i \(-0.130088\pi\)
−0.802983 + 0.596002i \(0.796755\pi\)
\(284\) −2354.06 4077.36i −0.491859 0.851925i
\(285\) 0 0
\(286\) −680.030 −0.140598
\(287\) 88.8886 722.827i 0.0182820 0.148666i
\(288\) 0 0
\(289\) 1037.79 1797.51i 0.211234 0.365869i
\(290\) −7593.72 13152.7i −1.53765 2.66329i
\(291\) 0 0
\(292\) −3884.96 + 6728.95i −0.778597 + 1.34857i
\(293\) 7191.86 1.43397 0.716985 0.697089i \(-0.245522\pi\)
0.716985 + 0.697089i \(0.245522\pi\)
\(294\) 0 0
\(295\) −4049.67 −0.799257
\(296\) −40.6249 + 70.3645i −0.00797729 + 0.0138171i
\(297\) 0 0
\(298\) 4314.36 + 7472.70i 0.838672 + 1.45262i
\(299\) −996.058 + 1725.22i −0.192654 + 0.333687i
\(300\) 0 0
\(301\) 970.735 7893.85i 0.185888 1.51161i
\(302\) −9166.69 −1.74663
\(303\) 0 0
\(304\) −69.0236 119.552i −0.0130223 0.0225552i
\(305\) 5826.43 + 10091.7i 1.09384 + 1.89458i
\(306\) 0 0
\(307\) 541.355 0.100641 0.0503204 0.998733i \(-0.483976\pi\)
0.0503204 + 0.998733i \(0.483976\pi\)
\(308\) 2150.22 + 1620.94i 0.397793 + 0.299875i
\(309\) 0 0
\(310\) −6428.37 + 11134.3i −1.17776 + 2.03995i
\(311\) 27.0084 + 46.7799i 0.00492446 + 0.00852941i 0.868477 0.495729i \(-0.165099\pi\)
−0.863553 + 0.504259i \(0.831766\pi\)
\(312\) 0 0
\(313\) −1886.47 + 3267.46i −0.340670 + 0.590058i −0.984557 0.175063i \(-0.943987\pi\)
0.643887 + 0.765120i \(0.277321\pi\)
\(314\) −17444.1 −3.13511
\(315\) 0 0
\(316\) 11615.1 2.06772
\(317\) 859.618 1488.90i 0.152306 0.263802i −0.779769 0.626068i \(-0.784663\pi\)
0.932075 + 0.362266i \(0.117997\pi\)
\(318\) 0 0
\(319\) 1062.47 + 1840.25i 0.186479 + 0.322991i
\(320\) −7436.70 + 12880.7i −1.29914 + 2.25017i
\(321\) 0 0
\(322\) 11814.5 5012.34i 2.04470 0.867475i
\(323\) 2259.72 0.389270
\(324\) 0 0
\(325\) 1273.53 + 2205.81i 0.217362 + 0.376482i
\(326\) 7994.73 + 13847.3i 1.35824 + 2.35255i
\(327\) 0 0
\(328\) 852.934 0.143584
\(329\) −313.330 236.202i −0.0525059 0.0395813i
\(330\) 0 0
\(331\) −4204.11 + 7281.73i −0.698123 + 1.20918i 0.270994 + 0.962581i \(0.412648\pi\)
−0.969117 + 0.246603i \(0.920686\pi\)
\(332\) −2092.27 3623.91i −0.345868 0.599060i
\(333\) 0 0
\(334\) −781.436 + 1353.49i −0.128019 + 0.221735i
\(335\) −2599.36 −0.423935
\(336\) 0 0
\(337\) 2789.46 0.450894 0.225447 0.974255i \(-0.427616\pi\)
0.225447 + 0.974255i \(0.427616\pi\)
\(338\) 4614.29 7992.18i 0.742557 1.28615i
\(339\) 0 0
\(340\) −6074.36 10521.1i −0.968907 1.67820i
\(341\) 899.419 1557.84i 0.142834 0.247395i
\(342\) 0 0
\(343\) −2279.82 + 5929.25i −0.358889 + 0.933380i
\(344\) 9314.72 1.45993
\(345\) 0 0
\(346\) −9539.24 16522.4i −1.48217 2.56720i
\(347\) −1735.98 3006.81i −0.268566 0.465170i 0.699926 0.714216i \(-0.253216\pi\)
−0.968492 + 0.249046i \(0.919883\pi\)
\(348\) 0 0
\(349\) −6626.12 −1.01630 −0.508149 0.861269i \(-0.669670\pi\)
−0.508149 + 0.861269i \(0.669670\pi\)
\(350\) 2002.76 16286.1i 0.305863 2.48723i
\(351\) 0 0
\(352\) 1073.05 1858.57i 0.162482 0.281427i
\(353\) 4734.20 + 8199.87i 0.713813 + 1.23636i 0.963416 + 0.268012i \(0.0863666\pi\)
−0.249603 + 0.968348i \(0.580300\pi\)
\(354\) 0 0
\(355\) 3297.27 5711.03i 0.492960 0.853831i
\(356\) 479.944 0.0714522
\(357\) 0 0
\(358\) 8977.35 1.32533
\(359\) −3139.78 + 5438.25i −0.461591 + 0.799499i −0.999040 0.0437971i \(-0.986054\pi\)
0.537450 + 0.843296i \(0.319388\pi\)
\(360\) 0 0
\(361\) 2529.68 + 4381.53i 0.368811 + 0.638800i
\(362\) 8231.31 14257.0i 1.19510 2.06998i
\(363\) 0 0
\(364\) 2849.71 1209.01i 0.410345 0.174091i
\(365\) −10883.1 −1.56068
\(366\) 0 0
\(367\) 5413.91 + 9377.17i 0.770038 + 1.33374i 0.937542 + 0.347873i \(0.113096\pi\)
−0.167504 + 0.985871i \(0.553571\pi\)
\(368\) −247.452 428.599i −0.0350525 0.0607127i
\(369\) 0 0
\(370\) −305.053 −0.0428620
\(371\) 6238.42 2646.68i 0.872999 0.370374i
\(372\) 0 0
\(373\) −2619.61 + 4537.30i −0.363642 + 0.629846i −0.988557 0.150846i \(-0.951800\pi\)
0.624915 + 0.780693i \(0.285134\pi\)
\(374\) 1382.71 + 2394.93i 0.191172 + 0.331120i
\(375\) 0 0
\(376\) 229.777 397.985i 0.0315155 0.0545864i
\(377\) 2442.81 0.333717
\(378\) 0 0
\(379\) −11050.4 −1.49768 −0.748839 0.662751i \(-0.769389\pi\)
−0.748839 + 0.662751i \(0.769389\pi\)
\(380\) −4837.64 + 8379.03i −0.653067 + 1.13115i
\(381\) 0 0
\(382\) 4346.25 + 7527.92i 0.582129 + 1.00828i
\(383\) −5234.02 + 9065.59i −0.698292 + 1.20948i 0.270766 + 0.962645i \(0.412723\pi\)
−0.969058 + 0.246832i \(0.920610\pi\)
\(384\) 0 0
\(385\) −460.345 + 3743.45i −0.0609386 + 0.495543i
\(386\) 10934.9 1.44190
\(387\) 0 0
\(388\) −4606.61 7978.88i −0.602745 1.04399i
\(389\) −5807.02 10058.1i −0.756884 1.31096i −0.944432 0.328705i \(-0.893388\pi\)
0.187549 0.982255i \(-0.439946\pi\)
\(390\) 0 0
\(391\) 8101.19 1.04781
\(392\) −7218.16 1802.54i −0.930031 0.232251i
\(393\) 0 0
\(394\) 3449.89 5975.38i 0.441124 0.764049i
\(395\) 8134.43 + 14089.2i 1.03617 + 1.79470i
\(396\) 0 0
\(397\) 3353.65 5808.69i 0.423967 0.734332i −0.572356 0.820005i \(-0.693971\pi\)
0.996323 + 0.0856726i \(0.0273039\pi\)
\(398\) 6232.10 0.784892
\(399\) 0 0
\(400\) −632.768 −0.0790960
\(401\) 2763.19 4785.98i 0.344107 0.596011i −0.641084 0.767471i \(-0.721515\pi\)
0.985191 + 0.171459i \(0.0548482\pi\)
\(402\) 0 0
\(403\) −1033.97 1790.89i −0.127805 0.221366i
\(404\) 9689.49 16782.7i 1.19324 2.06676i
\(405\) 0 0
\(406\) −12566.6 9473.26i −1.53613 1.15800i
\(407\) 42.6811 0.00519810
\(408\) 0 0
\(409\) 659.453 + 1142.21i 0.0797258 + 0.138089i 0.903132 0.429364i \(-0.141262\pi\)
−0.823406 + 0.567453i \(0.807929\pi\)
\(410\) 1601.17 + 2773.31i 0.192869 + 0.334059i
\(411\) 0 0
\(412\) −13422.5 −1.60505
\(413\) −3863.00 + 1638.90i −0.460256 + 0.195266i
\(414\) 0 0
\(415\) 2930.57 5075.90i 0.346641 0.600401i
\(416\) −1233.57 2136.61i −0.145387 0.251817i
\(417\) 0 0
\(418\) 1101.20 1907.33i 0.128855 0.223183i
\(419\) −3656.13 −0.426286 −0.213143 0.977021i \(-0.568370\pi\)
−0.213143 + 0.977021i \(0.568370\pi\)
\(420\) 0 0
\(421\) −135.389 −0.0156733 −0.00783663 0.999969i \(-0.502495\pi\)
−0.00783663 + 0.999969i \(0.502495\pi\)
\(422\) −9801.93 + 16977.4i −1.13069 + 1.95841i
\(423\) 0 0
\(424\) 3968.31 + 6873.32i 0.454524 + 0.787259i
\(425\) 5178.96 8970.22i 0.591097 1.02381i
\(426\) 0 0
\(427\) 9641.94 + 7268.54i 1.09276 + 0.823769i
\(428\) −9781.16 −1.10465
\(429\) 0 0
\(430\) 17486.1 + 30286.8i 1.96105 + 3.39665i
\(431\) 4194.58 + 7265.23i 0.468784 + 0.811958i 0.999363 0.0356776i \(-0.0113589\pi\)
−0.530579 + 0.847635i \(0.678026\pi\)
\(432\) 0 0
\(433\) −8243.02 −0.914859 −0.457430 0.889246i \(-0.651230\pi\)
−0.457430 + 0.889246i \(0.651230\pi\)
\(434\) −1626.03 + 13222.6i −0.179843 + 1.46245i
\(435\) 0 0
\(436\) 9104.91 15770.2i 1.00011 1.73223i
\(437\) −3225.91 5587.43i −0.353126 0.611632i
\(438\) 0 0
\(439\) 9141.59 15833.7i 0.993859 1.72142i 0.401104 0.916032i \(-0.368626\pi\)
0.592755 0.805383i \(-0.298040\pi\)
\(440\) −4417.26 −0.478602
\(441\) 0 0
\(442\) 3179.12 0.342116
\(443\) 605.218 1048.27i 0.0649092 0.112426i −0.831745 0.555159i \(-0.812658\pi\)
0.896654 + 0.442733i \(0.145991\pi\)
\(444\) 0 0
\(445\) 336.122 + 582.180i 0.0358061 + 0.0620179i
\(446\) 3410.86 5907.79i 0.362128 0.627224i
\(447\) 0 0
\(448\) −1881.08 + 15296.6i −0.198376 + 1.61316i
\(449\) 8301.16 0.872508 0.436254 0.899824i \(-0.356305\pi\)
0.436254 + 0.899824i \(0.356305\pi\)
\(450\) 0 0
\(451\) −224.026 388.025i −0.0233902 0.0405130i
\(452\) 2313.24 + 4006.66i 0.240721 + 0.416941i
\(453\) 0 0
\(454\) −7305.34 −0.755190
\(455\) 3462.30 + 2610.04i 0.356736 + 0.268924i
\(456\) 0 0
\(457\) 6146.88 10646.7i 0.629188 1.08979i −0.358527 0.933519i \(-0.616721\pi\)
0.987715 0.156266i \(-0.0499458\pi\)
\(458\) −2302.15 3987.45i −0.234875 0.406815i
\(459\) 0 0
\(460\) −17343.1 + 30039.1i −1.75788 + 3.04474i
\(461\) −19434.2 −1.96343 −0.981717 0.190346i \(-0.939039\pi\)
−0.981717 + 0.190346i \(0.939039\pi\)
\(462\) 0 0
\(463\) −12491.1 −1.25380 −0.626902 0.779098i \(-0.715678\pi\)
−0.626902 + 0.779098i \(0.715678\pi\)
\(464\) −303.436 + 525.566i −0.0303592 + 0.0525836i
\(465\) 0 0
\(466\) 451.574 + 782.150i 0.0448901 + 0.0777519i
\(467\) 1692.59 2931.65i 0.167716 0.290493i −0.769900 0.638164i \(-0.779694\pi\)
0.937617 + 0.347671i \(0.113027\pi\)
\(468\) 0 0
\(469\) −2479.54 + 1051.96i −0.244125 + 0.103571i
\(470\) 1725.39 0.169333
\(471\) 0 0
\(472\) −2457.29 4256.14i −0.239631 0.415053i
\(473\) −2446.54 4237.54i −0.237827 0.411929i
\(474\) 0 0
\(475\) −8249.07 −0.796828
\(476\) −10052.2 7577.84i −0.967948 0.729684i
\(477\) 0 0
\(478\) −2736.53 + 4739.80i −0.261853 + 0.453543i
\(479\) 2989.71 + 5178.32i 0.285184 + 0.493953i 0.972654 0.232260i \(-0.0746120\pi\)
−0.687470 + 0.726213i \(0.741279\pi\)
\(480\) 0 0
\(481\) 24.5330 42.4925i 0.00232559 0.00402804i
\(482\) −12451.1 −1.17663
\(483\) 0 0
\(484\) −15327.5 −1.43948
\(485\) 6452.34 11175.8i 0.604094 1.04632i
\(486\) 0 0
\(487\) 557.481 + 965.586i 0.0518725 + 0.0898457i 0.890796 0.454404i \(-0.150148\pi\)
−0.838923 + 0.544250i \(0.816814\pi\)
\(488\) −7070.80 + 12247.0i −0.655902 + 1.13606i
\(489\) 0 0
\(490\) −7689.34 26853.6i −0.708916 2.47576i
\(491\) −1086.23 −0.0998387 −0.0499194 0.998753i \(-0.515896\pi\)
−0.0499194 + 0.998753i \(0.515896\pi\)
\(492\) 0 0
\(493\) −4967.00 8603.10i −0.453758 0.785932i
\(494\) −1265.93 2192.66i −0.115297 0.199701i
\(495\) 0 0
\(496\) 513.740 0.0465073
\(497\) 834.028 6782.18i 0.0752742 0.612117i
\(498\) 0 0
\(499\) 1106.75 1916.95i 0.0992884 0.171973i −0.812102 0.583516i \(-0.801677\pi\)
0.911390 + 0.411543i \(0.135010\pi\)
\(500\) 7919.92 + 13717.7i 0.708379 + 1.22695i
\(501\) 0 0
\(502\) 17236.3 29854.2i 1.53246 2.65430i
\(503\) 2643.32 0.234314 0.117157 0.993113i \(-0.462622\pi\)
0.117157 + 0.993113i \(0.462622\pi\)
\(504\) 0 0
\(505\) 27143.5 2.39183
\(506\) 3947.83 6837.84i 0.346843 0.600749i
\(507\) 0 0
\(508\) −6219.31 10772.2i −0.543183 0.940821i
\(509\) −332.584 + 576.053i −0.0289618 + 0.0501633i −0.880143 0.474709i \(-0.842553\pi\)
0.851181 + 0.524872i \(0.175887\pi\)
\(510\) 0 0
\(511\) −10381.4 + 4404.38i −0.898724 + 0.381288i
\(512\) 1177.58 0.101645
\(513\) 0 0
\(514\) 11410.7 + 19763.9i 0.979190 + 1.69601i
\(515\) −9400.26 16281.7i −0.804320 1.39312i
\(516\) 0 0
\(517\) −241.406 −0.0205359
\(518\) −290.991 + 123.455i −0.0246823 + 0.0104716i
\(519\) 0 0
\(520\) −2539.03 + 4397.73i −0.214123 + 0.370872i
\(521\) −5880.99 10186.2i −0.494531 0.856554i 0.505449 0.862857i \(-0.331327\pi\)
−0.999980 + 0.00630307i \(0.997994\pi\)
\(522\) 0 0
\(523\) −5061.30 + 8766.43i −0.423165 + 0.732943i −0.996247 0.0865547i \(-0.972414\pi\)
0.573082 + 0.819498i \(0.305748\pi\)
\(524\) 22875.7 1.90712
\(525\) 0 0
\(526\) 28471.9 2.36014
\(527\) −4204.76 + 7282.85i −0.347556 + 0.601985i
\(528\) 0 0
\(529\) −5481.49 9494.22i −0.450521 0.780325i
\(530\) −14899.0 + 25805.9i −1.22108 + 2.11497i
\(531\) 0 0
\(532\) −1223.66 + 9950.58i −0.0997224 + 0.810926i
\(533\) −515.079 −0.0418585
\(534\) 0 0
\(535\) −6850.09 11864.7i −0.553561 0.958796i
\(536\) −1577.26 2731.89i −0.127103 0.220148i
\(537\) 0 0
\(538\) 16350.3 1.31024
\(539\) 1075.85 + 3757.20i 0.0859740 + 0.300249i
\(540\) 0 0
\(541\) −8058.98 + 13958.6i −0.640449 + 1.10929i 0.344884 + 0.938645i \(0.387918\pi\)
−0.985333 + 0.170644i \(0.945415\pi\)
\(542\) 4517.96 + 7825.34i 0.358050 + 0.620161i
\(543\) 0 0
\(544\) −5016.47 + 8688.78i −0.395366 + 0.684795i
\(545\) 25505.9 2.00469
\(546\) 0 0
\(547\) −626.100 −0.0489399 −0.0244699 0.999701i \(-0.507790\pi\)
−0.0244699 + 0.999701i \(0.507790\pi\)
\(548\) 10747.0 18614.3i 0.837751 1.45103i
\(549\) 0 0
\(550\) −5047.56 8742.64i −0.391325 0.677795i
\(551\) −3955.74 + 6851.54i −0.305844 + 0.529737i
\(552\) 0 0
\(553\) 13461.4 + 10147.8i 1.03515 + 0.780341i
\(554\) 33552.7 2.57313
\(555\) 0 0
\(556\) −2010.34 3482.02i −0.153341 0.265594i
\(557\) 10385.6 + 17988.4i 0.790039 + 1.36839i 0.925942 + 0.377665i \(0.123273\pi\)
−0.135903 + 0.990722i \(0.543394\pi\)
\(558\) 0 0
\(559\) −5625.08 −0.425609
\(560\) −991.615 + 420.698i −0.0748275 + 0.0317460i
\(561\) 0 0
\(562\) −12101.8 + 20961.0i −0.908335 + 1.57328i
\(563\) −2760.86 4781.95i −0.206672 0.357966i 0.743992 0.668188i \(-0.232930\pi\)
−0.950664 + 0.310222i \(0.899597\pi\)
\(564\) 0 0
\(565\) −3240.09 + 5612.00i −0.241260 + 0.417874i
\(566\) −4974.48 −0.369422
\(567\) 0 0
\(568\) 8002.95 0.591191
\(569\) 3787.40 6559.97i 0.279044 0.483319i −0.692103 0.721799i \(-0.743316\pi\)
0.971147 + 0.238480i \(0.0766491\pi\)
\(570\) 0 0
\(571\) 165.624 + 286.869i 0.0121386 + 0.0210247i 0.872031 0.489451i \(-0.162803\pi\)
−0.859892 + 0.510476i \(0.829469\pi\)
\(572\) 952.239 1649.33i 0.0696068 0.120563i
\(573\) 0 0
\(574\) 2649.72 + 1997.48i 0.192678 + 0.145250i
\(575\) −29573.2 −2.14485
\(576\) 0 0
\(577\) −1019.06 1765.06i −0.0735248 0.127349i 0.826919 0.562321i \(-0.190091\pi\)
−0.900444 + 0.434972i \(0.856758\pi\)
\(578\) 4728.57 + 8190.13i 0.340281 + 0.589385i
\(579\) 0 0
\(580\) 42533.6 3.04502
\(581\) 741.275 6027.93i 0.0529316 0.430431i
\(582\) 0 0
\(583\) 2084.58 3610.60i 0.148087 0.256494i
\(584\) −6603.72 11438.0i −0.467918 0.810457i
\(585\) 0 0
\(586\) −16384.4 + 28378.6i −1.15500 + 2.00053i
\(587\) −5232.90 −0.367947 −0.183973 0.982931i \(-0.558896\pi\)
−0.183973 + 0.982931i \(0.558896\pi\)
\(588\) 0 0
\(589\) 6697.36 0.468523
\(590\) 9225.88 15979.7i 0.643769 1.11504i
\(591\) 0 0
\(592\) 6.09477 + 10.5565i 0.000423131 + 0.000732884i
\(593\) −2860.12 + 4953.87i −0.198062 + 0.343054i −0.947900 0.318568i \(-0.896798\pi\)
0.749838 + 0.661622i \(0.230132\pi\)
\(594\) 0 0
\(595\) 2152.10 17500.5i 0.148282 1.20580i
\(596\) −24165.5 −1.66083
\(597\) 0 0
\(598\) −4538.41 7860.75i −0.310350 0.537542i
\(599\) 9044.21 + 15665.0i 0.616922 + 1.06854i 0.990044 + 0.140758i \(0.0449540\pi\)
−0.373122 + 0.927782i \(0.621713\pi\)
\(600\) 0 0
\(601\) −1821.43 −0.123623 −0.0618117 0.998088i \(-0.519688\pi\)
−0.0618117 + 0.998088i \(0.519688\pi\)
\(602\) 28937.1 + 21814.1i 1.95911 + 1.47687i
\(603\) 0 0
\(604\) 12836.0 22232.6i 0.864719 1.49774i
\(605\) −10734.4 18592.5i −0.721348 1.24941i
\(606\) 0 0
\(607\) −1186.10 + 2054.39i −0.0793120 + 0.137372i −0.902953 0.429739i \(-0.858606\pi\)
0.823641 + 0.567111i \(0.191939\pi\)
\(608\) 7990.26 0.532974
\(609\) 0 0
\(610\) −53094.7 −3.52416
\(611\) −138.760 + 240.339i −0.00918760 + 0.0159134i
\(612\) 0 0
\(613\) −4862.54 8422.16i −0.320385 0.554923i 0.660182 0.751105i \(-0.270479\pi\)
−0.980567 + 0.196182i \(0.937146\pi\)
\(614\) −1233.30 + 2136.15i −0.0810621 + 0.140404i
\(615\) 0 0
\(616\) −4213.65 + 1787.66i −0.275605 + 0.116927i
\(617\) 5329.51 0.347744 0.173872 0.984768i \(-0.444372\pi\)
0.173872 + 0.984768i \(0.444372\pi\)
\(618\) 0 0
\(619\) 7988.29 + 13836.1i 0.518702 + 0.898418i 0.999764 + 0.0217314i \(0.00691786\pi\)
−0.481062 + 0.876687i \(0.659749\pi\)
\(620\) −18003.2 31182.4i −1.16617 2.01986i
\(621\) 0 0
\(622\) −246.120 −0.0158658
\(623\) 556.236 + 419.316i 0.0357706 + 0.0269656i
\(624\) 0 0
\(625\) 1060.03 1836.03i 0.0678420 0.117506i
\(626\) −8595.45 14887.8i −0.548791 0.950535i
\(627\) 0 0
\(628\) 24426.7 42308.4i 1.55212 2.68836i
\(629\) −199.533 −0.0126485
\(630\) 0 0
\(631\) −4199.98 −0.264974 −0.132487 0.991185i \(-0.542296\pi\)
−0.132487 + 0.991185i \(0.542296\pi\)
\(632\) −9871.73 + 17098.3i −0.621324 + 1.07616i
\(633\) 0 0
\(634\) 3916.74 + 6783.99i 0.245352 + 0.424963i
\(635\) 8711.19 15088.2i 0.544399 0.942926i
\(636\) 0 0
\(637\) 4358.98 + 1088.54i 0.271129 + 0.0677072i
\(638\) −9681.97 −0.600804
\(639\) 0 0
\(640\) −20418.6 35366.0i −1.26112 2.18432i
\(641\) 1324.25 + 2293.67i 0.0815988 + 0.141333i 0.903937 0.427666i \(-0.140664\pi\)
−0.822338 + 0.568999i \(0.807331\pi\)
\(642\) 0 0
\(643\) 13.4305 0.000823715 0.000411857 1.00000i \(-0.499869\pi\)
0.000411857 1.00000i \(0.499869\pi\)
\(644\) −4386.86 + 35673.2i −0.268426 + 2.18280i
\(645\) 0 0
\(646\) −5148.06 + 8916.70i −0.313541 + 0.543070i
\(647\) 5812.07 + 10066.8i 0.353162 + 0.611695i 0.986802 0.161934i \(-0.0517730\pi\)
−0.633639 + 0.773628i \(0.718440\pi\)
\(648\) 0 0
\(649\) −1290.83 + 2235.78i −0.0780732 + 0.135227i
\(650\) −11605.3 −0.700305
\(651\) 0 0
\(652\) −44779.8 −2.68974
\(653\) −14258.3 + 24696.1i −0.854471 + 1.47999i 0.0226638 + 0.999743i \(0.492785\pi\)
−0.877135 + 0.480244i \(0.840548\pi\)
\(654\) 0 0
\(655\) 16020.7 + 27748.6i 0.955694 + 1.65531i
\(656\) 63.9809 110.818i 0.00380798 0.00659561i
\(657\) 0 0
\(658\) 1645.86 698.265i 0.0975111 0.0413696i
\(659\) −18048.6 −1.06688 −0.533440 0.845838i \(-0.679101\pi\)
−0.533440 + 0.845838i \(0.679101\pi\)
\(660\) 0 0
\(661\) −8920.72 15451.1i −0.524926 0.909198i −0.999579 0.0290250i \(-0.990760\pi\)
0.474653 0.880173i \(-0.342574\pi\)
\(662\) −19155.5 33178.2i −1.12462 1.94790i
\(663\) 0 0
\(664\) 7112.94 0.415716
\(665\) −12927.2 + 5484.42i −0.753826 + 0.319815i
\(666\) 0 0
\(667\) −14181.5 + 24563.0i −0.823251 + 1.42591i
\(668\) −2188.47 3790.55i −0.126758 0.219552i
\(669\) 0 0
\(670\) 5921.81 10256.9i 0.341462 0.591430i
\(671\) 7428.68 0.427394
\(672\) 0 0
\(673\) −6826.13 −0.390978 −0.195489 0.980706i \(-0.562629\pi\)
−0.195489 + 0.980706i \(0.562629\pi\)
\(674\) −6354.89 + 11007.0i −0.363177 + 0.629041i
\(675\) 0 0
\(676\) 12922.7 + 22382.8i 0.735246 + 1.27348i
\(677\) −10643.4 + 18435.0i −0.604225 + 1.04655i 0.387949 + 0.921681i \(0.373184\pi\)
−0.992173 + 0.124867i \(0.960150\pi\)
\(678\) 0 0
\(679\) 1632.09 13271.9i 0.0922443 0.750115i
\(680\) 20650.6 1.16458
\(681\) 0 0
\(682\) 4098.08 + 7098.08i 0.230093 + 0.398533i
\(683\) −10348.4 17924.0i −0.579753 1.00416i −0.995507 0.0946842i \(-0.969816\pi\)
0.415755 0.909477i \(-0.363517\pi\)
\(684\) 0 0
\(685\) 30105.9 1.67925
\(686\) −18202.5 22503.9i −1.01308 1.25248i
\(687\) 0 0
\(688\) 698.722 1210.22i 0.0387188 0.0670629i
\(689\) −2396.43 4150.74i −0.132506 0.229507i
\(690\) 0 0
\(691\) −15671.0 + 27142.9i −0.862738 + 1.49431i 0.00653825 + 0.999979i \(0.497919\pi\)
−0.869276 + 0.494327i \(0.835415\pi\)
\(692\) 53430.8 2.93517
\(693\) 0 0
\(694\) 15819.5 0.865276
\(695\) 2815.83 4877.16i 0.153684 0.266189i
\(696\) 0 0
\(697\) 1047.32 + 1814.01i 0.0569153 + 0.0985801i
\(698\) 15095.5 26146.2i 0.818587 1.41783i
\(699\) 0 0
\(700\) 36695.5 + 27662.7i 1.98137 + 1.49365i
\(701\) 9213.32 0.496408 0.248204 0.968708i \(-0.420160\pi\)
0.248204 + 0.968708i \(0.420160\pi\)
\(702\) 0 0
\(703\) 79.4544 + 137.619i 0.00426270 + 0.00738322i
\(704\) 4740.89 + 8211.46i 0.253805 + 0.439604i
\(705\) 0 0
\(706\) −43141.5 −2.29979
\(707\) 25892.4 10985.0i 1.37734 0.584345i
\(708\) 0 0
\(709\) −7258.27 + 12571.7i −0.384471 + 0.665923i −0.991696 0.128607i \(-0.958949\pi\)
0.607225 + 0.794530i \(0.292283\pi\)
\(710\) 15023.5 + 26021.6i 0.794118 + 1.37545i
\(711\) 0 0
\(712\) −407.908 + 706.518i −0.0214705 + 0.0371880i
\(713\) 24010.3 1.26114
\(714\) 0 0
\(715\) 2667.54 0.139525
\(716\) −12570.9 + 21773.4i −0.656140 + 1.13647i
\(717\) 0 0
\(718\) −14306.0 24778.7i −0.743585 1.28793i
\(719\) 12941.2 22414.8i 0.671246 1.16263i −0.306306 0.951933i \(-0.599093\pi\)
0.977551 0.210698i \(-0.0675737\pi\)
\(720\) 0 0
\(721\) −15556.2 11726.9i −0.803525 0.605734i
\(722\) −23052.3 −1.18825
\(723\) 0 0
\(724\) 23052.4 + 39928.0i 1.18334 + 2.04960i
\(725\) 18132.0 + 31405.5i 0.928833 + 1.60879i
\(726\) 0 0
\(727\) 32181.2 1.64172 0.820862 0.571127i \(-0.193494\pi\)
0.820862 + 0.571127i \(0.193494\pi\)
\(728\) −642.237 + 5222.56i −0.0326963 + 0.265881i
\(729\) 0 0
\(730\) 24793.7 42943.9i 1.25706 2.17730i
\(731\) 11437.5 + 19810.4i 0.578704 + 1.00234i
\(732\) 0 0
\(733\) −10418.1 + 18044.6i −0.524966 + 0.909268i 0.474611 + 0.880195i \(0.342589\pi\)
−0.999577 + 0.0290722i \(0.990745\pi\)
\(734\) −49335.5 −2.48094
\(735\) 0 0
\(736\) 28645.4 1.43462
\(737\) −828.544 + 1435.08i −0.0414109 + 0.0717257i
\(738\) 0 0
\(739\) −13217.4 22893.3i −0.657931 1.13957i −0.981150 0.193246i \(-0.938098\pi\)
0.323219 0.946324i \(-0.395235\pi\)
\(740\) 427.163 739.867i 0.0212200 0.0367541i
\(741\) 0 0
\(742\) −3768.64 + 30646.0i −0.186457 + 1.51624i
\(743\) −9954.69 −0.491524 −0.245762 0.969330i \(-0.579038\pi\)
−0.245762 + 0.969330i \(0.579038\pi\)
\(744\) 0 0
\(745\) −16923.9 29313.1i −0.832274 1.44154i
\(746\) −11935.9 20673.6i −0.585798 1.01463i
\(747\) 0 0
\(748\) −7744.79 −0.378580
\(749\) −11336.0 8545.57i −0.553014 0.416887i
\(750\) 0 0
\(751\) 16602.3 28756.0i 0.806692 1.39723i −0.108451 0.994102i \(-0.534589\pi\)
0.915143 0.403129i \(-0.132077\pi\)
\(752\) −34.4723 59.7078i −0.00167164 0.00289537i
\(753\) 0 0
\(754\) −5565.18 + 9639.17i −0.268796 + 0.465568i
\(755\) 35958.1 1.73331
\(756\) 0 0
\(757\) 1964.06 0.0942998 0.0471499 0.998888i \(-0.484986\pi\)
0.0471499 + 0.998888i \(0.484986\pi\)
\(758\) 25174.8 43604.0i 1.20632 2.08941i
\(759\) 0 0
\(760\) −8223.09 14242.8i −0.392477 0.679791i
\(761\) −19276.9 + 33388.6i −0.918248 + 1.59045i −0.116174 + 0.993229i \(0.537063\pi\)
−0.802075 + 0.597224i \(0.796270\pi\)
\(762\) 0 0
\(763\) 24330.2 10322.2i 1.15441 0.489764i
\(764\) −24344.0 −1.15280
\(765\) 0 0
\(766\) −23848.1 41306.1i −1.12489 1.94837i
\(767\) 1483.93 + 2570.25i 0.0698588 + 0.120999i
\(768\) 0 0
\(769\) −19715.0 −0.924501 −0.462251 0.886749i \(-0.652958\pi\)
−0.462251 + 0.886749i \(0.652958\pi\)
\(770\) −13722.6 10344.8i −0.642246 0.484155i
\(771\) 0 0
\(772\) −15312.1 + 26521.3i −0.713853 + 1.23643i
\(773\) −7350.34 12731.2i −0.342010 0.592378i 0.642796 0.766037i \(-0.277774\pi\)
−0.984806 + 0.173659i \(0.944441\pi\)
\(774\) 0 0
\(775\) 15349.4 26585.9i 0.711440 1.23225i
\(776\) 15660.8 0.724471
\(777\) 0 0
\(778\) 52917.8 2.43856
\(779\) 834.086 1444.68i 0.0383623 0.0664454i
\(780\) 0 0
\(781\) −2102.00 3640.78i −0.0963068 0.166808i
\(782\) −18456.0 + 31966.7i −0.843970 + 1.46180i
\(783\) 0 0
\(784\) −775.650 + 802.612i −0.0353339 + 0.0365621i
\(785\) 68427.6 3.11119
\(7