Properties

Label 63.4.p.a.17.7
Level $63$
Weight $4$
Character 63.17
Analytic conductor $3.717$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.71712033036\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} - 1762200 x^{2} + 810000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.7
Root \(3.91663 - 2.26127i\) of defining polynomial
Character \(\chi\) \(=\) 63.17
Dual form 63.4.p.a.26.7

$q$-expansion

\(f(q)\) \(=\) \(q+(3.91663 - 2.26127i) q^{2} +(6.22668 - 10.7849i) q^{4} +(0.632851 + 1.09613i) q^{5} +(13.4032 - 12.7810i) q^{7} -20.1405i q^{8} +O(q^{10})\) \(q+(3.91663 - 2.26127i) q^{2} +(6.22668 - 10.7849i) q^{4} +(0.632851 + 1.09613i) q^{5} +(13.4032 - 12.7810i) q^{7} -20.1405i q^{8} +(4.95730 + 2.86210i) q^{10} +(-36.0248 - 20.7989i) q^{11} +85.7355i q^{13} +(23.5942 - 80.3668i) q^{14} +(4.27028 + 7.39634i) q^{16} +(-38.8929 + 67.3645i) q^{17} +(42.1638 - 24.3433i) q^{19} +15.7623 q^{20} -188.128 q^{22} +(-78.7639 + 45.4743i) q^{23} +(61.6990 - 106.866i) q^{25} +(193.871 + 335.795i) q^{26} +(-54.3848 - 224.136i) q^{28} -151.196i q^{29} +(76.3661 + 44.0900i) q^{31} +(172.988 + 99.8747i) q^{32} +351.790i q^{34} +(22.4919 + 6.60319i) q^{35} +(-45.2914 - 78.4470i) q^{37} +(110.093 - 190.687i) q^{38} +(22.0767 - 12.7460i) q^{40} -383.530 q^{41} -227.894 q^{43} +(-448.630 + 259.017i) q^{44} +(-205.660 + 356.213i) q^{46} +(-69.5529 - 120.469i) q^{47} +(16.2918 - 342.613i) q^{49} -558.072i q^{50} +(924.652 + 533.848i) q^{52} +(289.749 + 167.287i) q^{53} -52.6505i q^{55} +(-257.416 - 269.948i) q^{56} +(-341.895 - 592.179i) q^{58} +(440.050 - 762.189i) q^{59} +(11.3944 - 6.57854i) q^{61} +398.797 q^{62} +835.050 q^{64} +(-93.9774 + 54.2579i) q^{65} +(221.212 - 383.151i) q^{67} +(484.348 + 838.915i) q^{68} +(103.024 - 24.9980i) q^{70} +341.552i q^{71} +(-798.218 - 460.851i) q^{73} +(-354.780 - 204.832i) q^{74} -606.311i q^{76} +(-748.678 + 181.661i) q^{77} +(206.564 + 357.780i) q^{79} +(-5.40490 + 9.36157i) q^{80} +(-1502.15 + 867.265i) q^{82} +954.307 q^{83} -98.4538 q^{85} +(-892.579 + 515.331i) q^{86} +(-418.901 + 725.558i) q^{88} +(14.8490 + 25.7193i) q^{89} +(1095.79 + 1149.13i) q^{91} +1132.62i q^{92} +(-544.826 - 314.556i) q^{94} +(53.3668 + 30.8113i) q^{95} +1199.63i q^{97} +(-710.931 - 1378.73i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 32q^{4} + 56q^{7} + O(q^{10}) \) \( 16q + 32q^{4} + 56q^{7} - 72q^{10} - 188q^{16} - 612q^{19} + 528q^{22} - 20q^{25} + 1036q^{28} + 1128q^{31} - 1196q^{37} - 3204q^{40} + 328q^{43} - 1392q^{46} + 784q^{49} + 4452q^{52} - 3372q^{58} - 1632q^{61} + 5432q^{64} + 308q^{67} + 3612q^{70} + 4068q^{73} - 2176q^{79} - 10188q^{82} - 4608q^{85} + 708q^{88} + 924q^{91} - 2916q^{94} + O(q^{100}) \)

Character values

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

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.91663 2.26127i 1.38474 0.799480i 0.392023 0.919955i \(-0.371775\pi\)
0.992716 + 0.120476i \(0.0384420\pi\)
\(3\) 0 0
\(4\) 6.22668 10.7849i 0.778336 1.34812i
\(5\) 0.632851 + 1.09613i 0.0566040 + 0.0980409i 0.892939 0.450178i \(-0.148639\pi\)
−0.836335 + 0.548219i \(0.815306\pi\)
\(6\) 0 0
\(7\) 13.4032 12.7810i 0.723705 0.690109i
\(8\) 20.1405i 0.890094i
\(9\) 0 0
\(10\) 4.95730 + 2.86210i 0.156763 + 0.0905074i
\(11\) −36.0248 20.7989i −0.987443 0.570101i −0.0829344 0.996555i \(-0.526429\pi\)
−0.904509 + 0.426454i \(0.859763\pi\)
\(12\) 0 0
\(13\) 85.7355i 1.82914i 0.404433 + 0.914568i \(0.367469\pi\)
−0.404433 + 0.914568i \(0.632531\pi\)
\(14\) 23.5942 80.3668i 0.450415 1.53421i
\(15\) 0 0
\(16\) 4.27028 + 7.39634i 0.0667231 + 0.115568i
\(17\) −38.8929 + 67.3645i −0.554878 + 0.961076i 0.443035 + 0.896504i \(0.353902\pi\)
−0.997913 + 0.0645722i \(0.979432\pi\)
\(18\) 0 0
\(19\) 42.1638 24.3433i 0.509107 0.293933i −0.223360 0.974736i \(-0.571702\pi\)
0.732466 + 0.680803i \(0.238369\pi\)
\(20\) 15.7623 0.176227
\(21\) 0 0
\(22\) −188.128 −1.82314
\(23\) −78.7639 + 45.4743i −0.714061 + 0.412263i −0.812563 0.582874i \(-0.801928\pi\)
0.0985019 + 0.995137i \(0.468595\pi\)
\(24\) 0 0
\(25\) 61.6990 106.866i 0.493592 0.854926i
\(26\) 193.871 + 335.795i 1.46236 + 2.53288i
\(27\) 0 0
\(28\) −54.3848 224.136i −0.367063 1.51278i
\(29\) 151.196i 0.968151i −0.875026 0.484075i \(-0.839156\pi\)
0.875026 0.484075i \(-0.160844\pi\)
\(30\) 0 0
\(31\) 76.3661 + 44.0900i 0.442444 + 0.255445i 0.704634 0.709571i \(-0.251111\pi\)
−0.262190 + 0.965016i \(0.584445\pi\)
\(32\) 172.988 + 99.8747i 0.955633 + 0.551735i
\(33\) 0 0
\(34\) 351.790i 1.77445i
\(35\) 22.4919 + 6.60319i 0.108624 + 0.0318898i
\(36\) 0 0
\(37\) −45.2914 78.4470i −0.201239 0.348557i 0.747689 0.664050i \(-0.231164\pi\)
−0.948928 + 0.315493i \(0.897830\pi\)
\(38\) 110.093 190.687i 0.469987 0.814041i
\(39\) 0 0
\(40\) 22.0767 12.7460i 0.0872657 0.0503829i
\(41\) −383.530 −1.46091 −0.730455 0.682961i \(-0.760692\pi\)
−0.730455 + 0.682961i \(0.760692\pi\)
\(42\) 0 0
\(43\) −227.894 −0.808222 −0.404111 0.914710i \(-0.632419\pi\)
−0.404111 + 0.914710i \(0.632419\pi\)
\(44\) −448.630 + 259.017i −1.53712 + 0.887459i
\(45\) 0 0
\(46\) −205.660 + 356.213i −0.659192 + 1.14175i
\(47\) −69.5529 120.469i −0.215858 0.373877i 0.737680 0.675151i \(-0.235922\pi\)
−0.953538 + 0.301274i \(0.902588\pi\)
\(48\) 0 0
\(49\) 16.2918 342.613i 0.0474981 0.998871i
\(50\) 558.072i 1.57847i
\(51\) 0 0
\(52\) 924.652 + 533.848i 2.46589 + 1.42368i
\(53\) 289.749 + 167.287i 0.750945 + 0.433558i 0.826035 0.563619i \(-0.190591\pi\)
−0.0750904 + 0.997177i \(0.523925\pi\)
\(54\) 0 0
\(55\) 52.6505i 0.129080i
\(56\) −257.416 269.948i −0.614263 0.644166i
\(57\) 0 0
\(58\) −341.895 592.179i −0.774017 1.34064i
\(59\) 440.050 762.189i 0.971010 1.68184i 0.278493 0.960438i \(-0.410165\pi\)
0.692518 0.721401i \(-0.256501\pi\)
\(60\) 0 0
\(61\) 11.3944 6.57854i 0.0239164 0.0138081i −0.487994 0.872847i \(-0.662271\pi\)
0.511911 + 0.859039i \(0.328938\pi\)
\(62\) 398.797 0.816892
\(63\) 0 0
\(64\) 835.050 1.63096
\(65\) −93.9774 + 54.2579i −0.179330 + 0.103536i
\(66\) 0 0
\(67\) 221.212 383.151i 0.403364 0.698647i −0.590766 0.806843i \(-0.701174\pi\)
0.994130 + 0.108197i \(0.0345076\pi\)
\(68\) 484.348 + 838.915i 0.863762 + 1.49608i
\(69\) 0 0
\(70\) 103.024 24.9980i 0.175911 0.0426833i
\(71\) 341.552i 0.570912i 0.958392 + 0.285456i \(0.0921450\pi\)
−0.958392 + 0.285456i \(0.907855\pi\)
\(72\) 0 0
\(73\) −798.218 460.851i −1.27979 0.738885i −0.302977 0.952998i \(-0.597981\pi\)
−0.976809 + 0.214113i \(0.931314\pi\)
\(74\) −354.780 204.832i −0.557328 0.321774i
\(75\) 0 0
\(76\) 606.311i 0.915114i
\(77\) −748.678 + 181.661i −1.10805 + 0.268859i
\(78\) 0 0
\(79\) 206.564 + 357.780i 0.294181 + 0.509537i 0.974794 0.223107i \(-0.0716198\pi\)
−0.680613 + 0.732643i \(0.738286\pi\)
\(80\) −5.40490 + 9.36157i −0.00755358 + 0.0130832i
\(81\) 0 0
\(82\) −1502.15 + 867.265i −2.02298 + 1.16797i
\(83\) 954.307 1.26203 0.631017 0.775769i \(-0.282638\pi\)
0.631017 + 0.775769i \(0.282638\pi\)
\(84\) 0 0
\(85\) −98.4538 −0.125633
\(86\) −892.579 + 515.331i −1.11918 + 0.646157i
\(87\) 0 0
\(88\) −418.901 + 725.558i −0.507444 + 0.878918i
\(89\) 14.8490 + 25.7193i 0.0176853 + 0.0306319i 0.874733 0.484606i \(-0.161037\pi\)
−0.857047 + 0.515238i \(0.827704\pi\)
\(90\) 0 0
\(91\) 1095.79 + 1149.13i 1.26230 + 1.32375i
\(92\) 1132.62i 1.28352i
\(93\) 0 0
\(94\) −544.826 314.556i −0.597814 0.345148i
\(95\) 53.3668 + 30.8113i 0.0576349 + 0.0332755i
\(96\) 0 0
\(97\) 1199.63i 1.25572i 0.778328 + 0.627858i \(0.216068\pi\)
−0.778328 + 0.627858i \(0.783932\pi\)
\(98\) −710.931 1378.73i −0.732805 1.42115i
\(99\) 0 0
\(100\) −768.360 1330.84i −0.768360 1.33084i
\(101\) −327.422 + 567.111i −0.322571 + 0.558710i −0.981018 0.193918i \(-0.937881\pi\)
0.658447 + 0.752628i \(0.271214\pi\)
\(102\) 0 0
\(103\) −1186.01 + 684.744i −1.13457 + 0.655047i −0.945081 0.326836i \(-0.894018\pi\)
−0.189493 + 0.981882i \(0.560684\pi\)
\(104\) 1726.76 1.62810
\(105\) 0 0
\(106\) 1513.12 1.38648
\(107\) 371.311 214.377i 0.335477 0.193688i −0.322793 0.946470i \(-0.604622\pi\)
0.658270 + 0.752782i \(0.271289\pi\)
\(108\) 0 0
\(109\) 334.261 578.957i 0.293728 0.508752i −0.680960 0.732321i \(-0.738437\pi\)
0.974688 + 0.223568i \(0.0717706\pi\)
\(110\) −119.057 206.213i −0.103197 0.178742i
\(111\) 0 0
\(112\) 151.768 + 44.5562i 0.128042 + 0.0375908i
\(113\) 914.837i 0.761598i 0.924658 + 0.380799i \(0.124351\pi\)
−0.924658 + 0.380799i \(0.875649\pi\)
\(114\) 0 0
\(115\) −99.6917 57.5570i −0.0808374 0.0466715i
\(116\) −1630.64 941.449i −1.30518 0.753546i
\(117\) 0 0
\(118\) 3980.29i 3.10521i
\(119\) 339.696 + 1399.99i 0.261680 + 1.07846i
\(120\) 0 0
\(121\) 199.690 + 345.873i 0.150030 + 0.259859i
\(122\) 29.7517 51.5314i 0.0220786 0.0382413i
\(123\) 0 0
\(124\) 951.015 549.069i 0.688739 0.397644i
\(125\) 314.398 0.224965
\(126\) 0 0
\(127\) 1260.95 0.881034 0.440517 0.897744i \(-0.354795\pi\)
0.440517 + 0.897744i \(0.354795\pi\)
\(128\) 1886.68 1089.28i 1.30282 0.752182i
\(129\) 0 0
\(130\) −245.383 + 425.016i −0.165550 + 0.286742i
\(131\) −683.600 1184.03i −0.455926 0.789688i 0.542814 0.839853i \(-0.317359\pi\)
−0.998741 + 0.0501648i \(0.984025\pi\)
\(132\) 0 0
\(133\) 253.998 865.173i 0.165597 0.564060i
\(134\) 2000.88i 1.28992i
\(135\) 0 0
\(136\) 1356.76 + 783.325i 0.855449 + 0.493894i
\(137\) 953.631 + 550.579i 0.594702 + 0.343351i 0.766955 0.641701i \(-0.221771\pi\)
−0.172252 + 0.985053i \(0.555104\pi\)
\(138\) 0 0
\(139\) 2306.56i 1.40748i 0.710458 + 0.703739i \(0.248488\pi\)
−0.710458 + 0.703739i \(0.751512\pi\)
\(140\) 211.265 201.458i 0.127537 0.121616i
\(141\) 0 0
\(142\) 772.341 + 1337.73i 0.456432 + 0.790564i
\(143\) 1783.21 3088.60i 1.04279 1.80617i
\(144\) 0 0
\(145\) 165.730 95.6845i 0.0949184 0.0548012i
\(146\) −4168.44 −2.36289
\(147\) 0 0
\(148\) −1128.06 −0.626527
\(149\) −1520.57 + 877.901i −0.836040 + 0.482688i −0.855916 0.517115i \(-0.827006\pi\)
0.0198764 + 0.999802i \(0.493673\pi\)
\(150\) 0 0
\(151\) 262.491 454.647i 0.141465 0.245024i −0.786584 0.617484i \(-0.788152\pi\)
0.928048 + 0.372460i \(0.121485\pi\)
\(152\) −490.286 849.201i −0.261628 0.453153i
\(153\) 0 0
\(154\) −2521.52 + 2404.46i −1.31941 + 1.25816i
\(155\) 111.610i 0.0578368i
\(156\) 0 0
\(157\) −1141.44 659.009i −0.580233 0.334998i 0.180993 0.983484i \(-0.442069\pi\)
−0.761226 + 0.648487i \(0.775402\pi\)
\(158\) 1618.07 + 934.195i 0.814728 + 0.470384i
\(159\) 0 0
\(160\) 252.823i 0.124921i
\(161\) −474.481 + 1616.18i −0.232263 + 0.791137i
\(162\) 0 0
\(163\) 223.916 + 387.834i 0.107598 + 0.186365i 0.914797 0.403915i \(-0.132351\pi\)
−0.807199 + 0.590280i \(0.799017\pi\)
\(164\) −2388.12 + 4136.35i −1.13708 + 1.96948i
\(165\) 0 0
\(166\) 3737.67 2157.95i 1.74759 1.00897i
\(167\) −811.124 −0.375848 −0.187924 0.982184i \(-0.560176\pi\)
−0.187924 + 0.982184i \(0.560176\pi\)
\(168\) 0 0
\(169\) −5153.58 −2.34574
\(170\) −385.608 + 222.631i −0.173969 + 0.100441i
\(171\) 0 0
\(172\) −1419.03 + 2457.82i −0.629068 + 1.08958i
\(173\) −1121.24 1942.04i −0.492751 0.853470i 0.507214 0.861820i \(-0.330675\pi\)
−0.999965 + 0.00834994i \(0.997342\pi\)
\(174\) 0 0
\(175\) −538.888 2220.92i −0.232778 0.959347i
\(176\) 355.269i 0.152156i
\(177\) 0 0
\(178\) 116.317 + 67.1554i 0.0489792 + 0.0282781i
\(179\) 2531.77 + 1461.72i 1.05717 + 0.610357i 0.924648 0.380824i \(-0.124359\pi\)
0.132521 + 0.991180i \(0.457693\pi\)
\(180\) 0 0
\(181\) 282.859i 0.116159i −0.998312 0.0580794i \(-0.981502\pi\)
0.998312 0.0580794i \(-0.0184977\pi\)
\(182\) 6890.29 + 2022.86i 2.80628 + 0.823869i
\(183\) 0 0
\(184\) 915.878 + 1586.35i 0.366953 + 0.635582i
\(185\) 57.3255 99.2906i 0.0227819 0.0394594i
\(186\) 0 0
\(187\) 2802.22 1617.86i 1.09582 0.632672i
\(188\) −1732.34 −0.672040
\(189\) 0 0
\(190\) 278.691 0.106412
\(191\) 3998.63 2308.61i 1.51482 0.874582i 0.514971 0.857208i \(-0.327803\pi\)
0.999849 0.0173741i \(-0.00553064\pi\)
\(192\) 0 0
\(193\) 2077.73 3598.73i 0.774912 1.34219i −0.159933 0.987128i \(-0.551128\pi\)
0.934844 0.355058i \(-0.115539\pi\)
\(194\) 2712.70 + 4698.53i 1.00392 + 1.73884i
\(195\) 0 0
\(196\) −3593.61 2309.05i −1.30963 0.841490i
\(197\) 1626.36i 0.588190i 0.955776 + 0.294095i \(0.0950183\pi\)
−0.955776 + 0.294095i \(0.904982\pi\)
\(198\) 0 0
\(199\) 150.861 + 87.0995i 0.0537399 + 0.0310267i 0.526629 0.850095i \(-0.323456\pi\)
−0.472889 + 0.881122i \(0.656789\pi\)
\(200\) −2152.33 1242.65i −0.760965 0.439344i
\(201\) 0 0
\(202\) 2961.56i 1.03156i
\(203\) −1932.44 2026.51i −0.668130 0.700656i
\(204\) 0 0
\(205\) −242.718 420.399i −0.0826933 0.143229i
\(206\) −3096.78 + 5363.78i −1.04739 + 1.81414i
\(207\) 0 0
\(208\) −634.129 + 366.115i −0.211389 + 0.122046i
\(209\) −2025.25 −0.670286
\(210\) 0 0
\(211\) −2942.35 −0.959999 −0.479999 0.877269i \(-0.659363\pi\)
−0.479999 + 0.877269i \(0.659363\pi\)
\(212\) 3608.35 2083.28i 1.16897 0.674907i
\(213\) 0 0
\(214\) 969.527 1679.27i 0.309699 0.536414i
\(215\) −144.223 249.802i −0.0457486 0.0792389i
\(216\) 0 0
\(217\) 1587.06 385.088i 0.496484 0.120468i
\(218\) 3023.42i 0.939319i
\(219\) 0 0
\(220\) −567.832 327.838i −0.174015 0.100467i
\(221\) −5775.53 3334.51i −1.75794 1.01495i
\(222\) 0 0
\(223\) 3374.75i 1.01341i 0.862120 + 0.506704i \(0.169136\pi\)
−0.862120 + 0.506704i \(0.830864\pi\)
\(224\) 3595.09 872.320i 1.07235 0.260198i
\(225\) 0 0
\(226\) 2068.69 + 3583.08i 0.608882 + 1.05461i
\(227\) −1515.43 + 2624.79i −0.443094 + 0.767461i −0.997917 0.0645069i \(-0.979453\pi\)
0.554823 + 0.831968i \(0.312786\pi\)
\(228\) 0 0
\(229\) 960.030 554.274i 0.277033 0.159945i −0.355046 0.934849i \(-0.615535\pi\)
0.632080 + 0.774904i \(0.282202\pi\)
\(230\) −520.608 −0.149252
\(231\) 0 0
\(232\) −3045.17 −0.861746
\(233\) −2684.57 + 1549.94i −0.754815 + 0.435793i −0.827431 0.561567i \(-0.810199\pi\)
0.0726160 + 0.997360i \(0.476865\pi\)
\(234\) 0 0
\(235\) 88.0333 152.478i 0.0244368 0.0423259i
\(236\) −5480.10 9491.82i −1.51154 2.61807i
\(237\) 0 0
\(238\) 4496.23 + 4715.11i 1.22457 + 1.28418i
\(239\) 1735.25i 0.469640i −0.972039 0.234820i \(-0.924550\pi\)
0.972039 0.234820i \(-0.0754501\pi\)
\(240\) 0 0
\(241\) −1039.26 600.019i −0.277779 0.160376i 0.354638 0.935004i \(-0.384604\pi\)
−0.632418 + 0.774628i \(0.717937\pi\)
\(242\) 1564.22 + 903.104i 0.415504 + 0.239892i
\(243\) 0 0
\(244\) 163.850i 0.0429894i
\(245\) 385.859 198.965i 0.100619 0.0518833i
\(246\) 0 0
\(247\) 2087.08 + 3614.93i 0.537643 + 0.931225i
\(248\) 887.996 1538.05i 0.227370 0.393817i
\(249\) 0 0
\(250\) 1231.38 710.939i 0.311518 0.179855i
\(251\) 3712.56 0.933603 0.466802 0.884362i \(-0.345406\pi\)
0.466802 + 0.884362i \(0.345406\pi\)
\(252\) 0 0
\(253\) 3783.27 0.940126
\(254\) 4938.69 2851.35i 1.22000 0.704369i
\(255\) 0 0
\(256\) 1586.09 2747.20i 0.387230 0.670702i
\(257\) 389.574 + 674.762i 0.0945563 + 0.163776i 0.909423 0.415872i \(-0.136523\pi\)
−0.814867 + 0.579648i \(0.803190\pi\)
\(258\) 0 0
\(259\) −1609.68 472.572i −0.386180 0.113375i
\(260\) 1351.39i 0.322344i
\(261\) 0 0
\(262\) −5354.82 3091.61i −1.26268 0.729008i
\(263\) −1702.07 982.690i −0.399065 0.230400i 0.287015 0.957926i \(-0.407337\pi\)
−0.686080 + 0.727526i \(0.740670\pi\)
\(264\) 0 0
\(265\) 423.470i 0.0981644i
\(266\) −961.571 3962.92i −0.221646 0.913468i
\(267\) 0 0
\(268\) −2754.84 4771.52i −0.627905 1.08756i
\(269\) 1236.41 2141.53i 0.280243 0.485395i −0.691201 0.722662i \(-0.742918\pi\)
0.971444 + 0.237267i \(0.0762516\pi\)
\(270\) 0 0
\(271\) 4095.79 2364.71i 0.918088 0.530058i 0.0350633 0.999385i \(-0.488837\pi\)
0.883025 + 0.469327i \(0.155503\pi\)
\(272\) −664.334 −0.148093
\(273\) 0 0
\(274\) 4980.03 1.09801
\(275\) −4445.39 + 2566.54i −0.974788 + 0.562794i
\(276\) 0 0
\(277\) −586.579 + 1015.98i −0.127235 + 0.220378i −0.922604 0.385747i \(-0.873944\pi\)
0.795369 + 0.606125i \(0.207277\pi\)
\(278\) 5215.74 + 9033.93i 1.12525 + 1.94899i
\(279\) 0 0
\(280\) 132.992 452.999i 0.0283849 0.0966852i
\(281\) 8195.18i 1.73980i 0.493229 + 0.869899i \(0.335816\pi\)
−0.493229 + 0.869899i \(0.664184\pi\)
\(282\) 0 0
\(283\) 2242.44 + 1294.67i 0.471021 + 0.271944i 0.716667 0.697415i \(-0.245667\pi\)
−0.245646 + 0.969360i \(0.579000\pi\)
\(284\) 3683.61 + 2126.74i 0.769656 + 0.444361i
\(285\) 0 0
\(286\) 16129.2i 3.33476i
\(287\) −5140.53 + 4901.90i −1.05727 + 1.00819i
\(288\) 0 0
\(289\) −568.820 985.225i −0.115779 0.200534i
\(290\) 432.737 749.523i 0.0876248 0.151771i
\(291\) 0 0
\(292\) −9940.50 + 5739.15i −1.99221 + 1.15020i
\(293\) 8871.16 1.76880 0.884400 0.466729i \(-0.154568\pi\)
0.884400 + 0.466729i \(0.154568\pi\)
\(294\) 0 0
\(295\) 1113.94 0.219852
\(296\) −1579.96 + 912.193i −0.310249 + 0.179122i
\(297\) 0 0
\(298\) −3970.34 + 6876.84i −0.771798 + 1.33679i
\(299\) −3898.77 6752.86i −0.754085 1.30611i
\(300\) 0 0
\(301\) −3054.51 + 2912.72i −0.584915 + 0.557762i
\(302\) 2374.25i 0.452393i
\(303\) 0 0
\(304\) 360.102 + 207.905i 0.0679383 + 0.0392242i
\(305\) 14.4219 + 8.32647i 0.00270752 + 0.00156319i
\(306\) 0 0
\(307\) 2707.52i 0.503344i −0.967813 0.251672i \(-0.919020\pi\)
0.967813 0.251672i \(-0.0809804\pi\)
\(308\) −2702.59 + 9205.59i −0.499981 + 1.70304i
\(309\) 0 0
\(310\) 252.379 + 437.134i 0.0462393 + 0.0800889i
\(311\) 1080.55 1871.56i 0.197017 0.341243i −0.750543 0.660822i \(-0.770208\pi\)
0.947560 + 0.319579i \(0.103541\pi\)
\(312\) 0 0
\(313\) −7300.25 + 4214.80i −1.31832 + 0.761133i −0.983459 0.181133i \(-0.942023\pi\)
−0.334863 + 0.942267i \(0.608690\pi\)
\(314\) −5960.79 −1.07130
\(315\) 0 0
\(316\) 5144.84 0.915886
\(317\) 8310.07 4797.82i 1.47237 0.850071i 0.472848 0.881144i \(-0.343226\pi\)
0.999517 + 0.0310734i \(0.00989256\pi\)
\(318\) 0 0
\(319\) −3144.71 + 5446.80i −0.551943 + 0.955994i
\(320\) 528.463 + 915.324i 0.0923186 + 0.159901i
\(321\) 0 0
\(322\) 1796.26 + 7402.93i 0.310875 + 1.28121i
\(323\) 3787.12i 0.652387i
\(324\) 0 0
\(325\) 9162.20 + 5289.80i 1.56378 + 0.902847i
\(326\) 1753.99 + 1012.67i 0.297990 + 0.172045i
\(327\) 0 0
\(328\) 7724.50i 1.30035i
\(329\) −2471.95 725.717i −0.414234 0.121611i
\(330\) 0 0
\(331\) −4271.96 7399.25i −0.709390 1.22870i −0.965084 0.261941i \(-0.915637\pi\)
0.255694 0.966758i \(-0.417696\pi\)
\(332\) 5942.17 10292.1i 0.982286 1.70137i
\(333\) 0 0
\(334\) −3176.88 + 1834.17i −0.520452 + 0.300483i
\(335\) 559.978 0.0913280
\(336\) 0 0
\(337\) 598.875 0.0968036 0.0484018 0.998828i \(-0.484587\pi\)
0.0484018 + 0.998828i \(0.484587\pi\)
\(338\) −20184.7 + 11653.6i −3.24823 + 1.87537i
\(339\) 0 0
\(340\) −613.041 + 1061.82i −0.0977847 + 0.169368i
\(341\) −1834.05 3176.66i −0.291259 0.504475i
\(342\) 0 0
\(343\) −4160.57 4800.34i −0.654956 0.755667i
\(344\) 4589.91i 0.719394i
\(345\) 0 0
\(346\) −8782.94 5070.83i −1.36466 0.787889i
\(347\) 6149.62 + 3550.49i 0.951381 + 0.549280i 0.893510 0.449044i \(-0.148235\pi\)
0.0578712 + 0.998324i \(0.481569\pi\)
\(348\) 0 0
\(349\) 3620.71i 0.555336i −0.960677 0.277668i \(-0.910438\pi\)
0.960677 0.277668i \(-0.0895616\pi\)
\(350\) −7132.73 7479.96i −1.08931 1.14234i
\(351\) 0 0
\(352\) −4154.57 7195.92i −0.629089 1.08961i
\(353\) −1164.89 + 2017.64i −0.175639 + 0.304216i −0.940382 0.340119i \(-0.889533\pi\)
0.764743 + 0.644335i \(0.222866\pi\)
\(354\) 0 0
\(355\) −374.386 + 216.152i −0.0559727 + 0.0323159i
\(356\) 369.841 0.0550605
\(357\) 0 0
\(358\) 13221.3 1.95187
\(359\) 1522.43 878.975i 0.223818 0.129222i −0.383899 0.923375i \(-0.625419\pi\)
0.607717 + 0.794154i \(0.292086\pi\)
\(360\) 0 0
\(361\) −2244.31 + 3887.26i −0.327207 + 0.566739i
\(362\) −639.621 1107.86i −0.0928667 0.160850i
\(363\) 0 0
\(364\) 19216.4 4662.71i 2.76707 0.671407i
\(365\) 1166.60i 0.167295i
\(366\) 0 0
\(367\) 1458.89 + 842.290i 0.207503 + 0.119802i 0.600150 0.799887i \(-0.295107\pi\)
−0.392648 + 0.919689i \(0.628441\pi\)
\(368\) −672.687 388.376i −0.0952887 0.0550150i
\(369\) 0 0
\(370\) 518.513i 0.0728547i
\(371\) 6021.65 1461.11i 0.842665 0.204466i
\(372\) 0 0
\(373\) 148.646 + 257.462i 0.0206343 + 0.0357397i 0.876158 0.482024i \(-0.160098\pi\)
−0.855524 + 0.517763i \(0.826765\pi\)
\(374\) 7316.84 12673.1i 1.01162 1.75217i
\(375\) 0 0
\(376\) −2426.31 + 1400.83i −0.332786 + 0.192134i
\(377\) 12962.9 1.77088
\(378\) 0 0
\(379\) −7402.78 −1.00331 −0.501656 0.865067i \(-0.667276\pi\)
−0.501656 + 0.865067i \(0.667276\pi\)
\(380\) 664.596 383.705i 0.0897186 0.0517991i
\(381\) 0 0
\(382\) 10440.8 18084.0i 1.39842 2.42214i
\(383\) 6263.77 + 10849.2i 0.835676 + 1.44743i 0.893479 + 0.449105i \(0.148257\pi\)
−0.0578031 + 0.998328i \(0.518410\pi\)
\(384\) 0 0
\(385\) −672.926 705.685i −0.0890792 0.0934157i
\(386\) 18793.2i 2.47810i
\(387\) 0 0
\(388\) 12938.0 + 7469.75i 1.69285 + 0.977368i
\(389\) −6904.14 3986.11i −0.899881 0.519547i −0.0227196 0.999742i \(-0.507233\pi\)
−0.877162 + 0.480195i \(0.840566\pi\)
\(390\) 0 0
\(391\) 7074.52i 0.915023i
\(392\) −6900.41 328.126i −0.889090 0.0422778i
\(393\) 0 0
\(394\) 3677.64 + 6369.87i 0.470246 + 0.814491i
\(395\) −261.449 + 452.843i −0.0333036 + 0.0576836i
\(396\) 0 0
\(397\) 10832.5 6254.16i 1.36944 0.790648i 0.378586 0.925566i \(-0.376410\pi\)
0.990857 + 0.134918i \(0.0430770\pi\)
\(398\) 787.822 0.0992210
\(399\) 0 0
\(400\) 1053.89 0.131736
\(401\) 6943.55 4008.86i 0.864699 0.499234i −0.000883860 1.00000i \(-0.500281\pi\)
0.865583 + 0.500765i \(0.166948\pi\)
\(402\) 0 0
\(403\) −3780.08 + 6547.29i −0.467243 + 0.809289i
\(404\) 4077.51 + 7062.45i 0.502137 + 0.869728i
\(405\) 0 0
\(406\) −12151.1 3567.34i −1.48535 0.436069i
\(407\) 3768.05i 0.458907i
\(408\) 0 0
\(409\) −7566.04 4368.26i −0.914711 0.528109i −0.0327670 0.999463i \(-0.510432\pi\)
−0.881944 + 0.471354i \(0.843765\pi\)
\(410\) −1901.27 1097.70i −0.229017 0.132223i
\(411\) 0 0
\(412\) 17054.7i 2.03938i
\(413\) −3843.46 15840.1i −0.457928 1.88726i
\(414\) 0 0
\(415\) 603.935 + 1046.05i 0.0714361 + 0.123731i
\(416\) −8562.81 + 14831.2i −1.00920 + 1.74798i
\(417\) 0 0
\(418\) −7932.18 + 4579.64i −0.928171 + 0.535880i
\(419\) −3926.67 −0.457829 −0.228914 0.973447i \(-0.573518\pi\)
−0.228914 + 0.973447i \(0.573518\pi\)
\(420\) 0 0
\(421\) 1443.44 0.167100 0.0835499 0.996504i \(-0.473374\pi\)
0.0835499 + 0.996504i \(0.473374\pi\)
\(422\) −11524.1 + 6653.45i −1.32935 + 0.767500i
\(423\) 0 0
\(424\) 3369.24 5835.70i 0.385908 0.668412i
\(425\) 4799.31 + 8312.65i 0.547766 + 0.948759i
\(426\) 0 0
\(427\) 68.6406 233.805i 0.00777928 0.0264979i
\(428\) 5339.42i 0.603016i
\(429\) 0 0
\(430\) −1129.74 652.255i −0.126700 0.0731501i
\(431\) −12820.5 7401.92i −1.43281 0.827234i −0.435477 0.900200i \(-0.643420\pi\)
−0.997334 + 0.0729655i \(0.976754\pi\)
\(432\) 0 0
\(433\) 15872.1i 1.76158i 0.473508 + 0.880790i \(0.342988\pi\)
−0.473508 + 0.880790i \(0.657012\pi\)
\(434\) 5345.16 5097.03i 0.591189 0.563745i
\(435\) 0 0
\(436\) −4162.67 7209.96i −0.457238 0.791960i
\(437\) −2213.99 + 3834.74i −0.242356 + 0.419772i
\(438\) 0 0
\(439\) −2626.58 + 1516.45i −0.285557 + 0.164867i −0.635937 0.771741i \(-0.719386\pi\)
0.350379 + 0.936608i \(0.386053\pi\)
\(440\) −1060.41 −0.114893
\(441\) 0 0
\(442\) −30160.9 −3.24572
\(443\) −11126.8 + 6424.08i −1.19334 + 0.688978i −0.959064 0.283191i \(-0.908607\pi\)
−0.234281 + 0.972169i \(0.575274\pi\)
\(444\) 0 0
\(445\) −18.7945 + 32.5530i −0.00200212 + 0.00346777i
\(446\) 7631.22 + 13217.7i 0.810199 + 1.40331i
\(447\) 0 0
\(448\) 11192.3 10672.8i 1.18033 1.12554i
\(449\) 107.668i 0.0113166i 0.999984 + 0.00565831i \(0.00180111\pi\)
−0.999984 + 0.00565831i \(0.998199\pi\)
\(450\) 0 0
\(451\) 13816.6 + 7977.01i 1.44257 + 0.832866i
\(452\) 9866.45 + 5696.40i 1.02672 + 0.592779i
\(453\) 0 0
\(454\) 13707.1i 1.41698i
\(455\) −566.128 + 1928.35i −0.0583308 + 0.198687i
\(456\) 0 0
\(457\) 4888.53 + 8467.18i 0.500385 + 0.866691i 1.00000 0.000444115i \(0.000141366\pi\)
−0.499615 + 0.866247i \(0.666525\pi\)
\(458\) 2506.72 4341.77i 0.255746 0.442965i
\(459\) 0 0
\(460\) −1241.50 + 716.779i −0.125837 + 0.0726521i
\(461\) 638.874 0.0645452 0.0322726 0.999479i \(-0.489726\pi\)
0.0322726 + 0.999479i \(0.489726\pi\)
\(462\) 0 0
\(463\) −5602.26 −0.562331 −0.281165 0.959659i \(-0.590721\pi\)
−0.281165 + 0.959659i \(0.590721\pi\)
\(464\) 1118.30 645.648i 0.111887 0.0645980i
\(465\) 0 0
\(466\) −7009.65 + 12141.1i −0.696815 + 1.20692i
\(467\) −2759.44 4779.49i −0.273430 0.473594i 0.696308 0.717743i \(-0.254825\pi\)
−0.969738 + 0.244149i \(0.921491\pi\)
\(468\) 0 0
\(469\) −1932.10 7962.76i −0.190226 0.783979i
\(470\) 796.268i 0.0781470i
\(471\) 0 0
\(472\) −15350.9 8862.84i −1.49700 0.864291i
\(473\) 8209.84 + 4739.95i 0.798074 + 0.460768i
\(474\) 0 0
\(475\) 6007.82i 0.580332i
\(476\) 17214.0 + 5053.70i 1.65757 + 0.486630i
\(477\) 0 0
\(478\) −3923.87 6796.34i −0.375468 0.650329i
\(479\) −2734.40 + 4736.11i −0.260830 + 0.451771i −0.966463 0.256807i \(-0.917330\pi\)
0.705632 + 0.708578i \(0.250663\pi\)
\(480\) 0 0
\(481\) 6725.70 3883.08i 0.637558 0.368094i
\(482\) −5427.22 −0.512869
\(483\) 0 0
\(484\) 4973.62 0.467094
\(485\) −1314.96 + 759.190i −0.123112 + 0.0710785i
\(486\) 0 0
\(487\) 5866.72 10161.5i 0.545886 0.945502i −0.452665 0.891681i \(-0.649527\pi\)
0.998551 0.0538213i \(-0.0171401\pi\)
\(488\) −132.495 229.489i −0.0122905 0.0212878i
\(489\) 0 0
\(490\) 1061.35 1651.80i 0.0978512 0.152288i
\(491\) 3514.92i 0.323068i 0.986867 + 0.161534i \(0.0516441\pi\)
−0.986867 + 0.161534i \(0.948356\pi\)
\(492\) 0 0
\(493\) 10185.2 + 5880.45i 0.930467 + 0.537205i
\(494\) 16348.7 + 9438.91i 1.48899 + 0.859670i
\(495\) 0 0
\(496\) 753.106i 0.0681763i
\(497\) 4365.38 + 4577.89i 0.393992 + 0.413172i
\(498\) 0 0
\(499\) −4944.49 8564.11i −0.443579 0.768301i 0.554373 0.832268i \(-0.312958\pi\)
−0.997952 + 0.0639672i \(0.979625\pi\)
\(500\) 1957.66 3390.76i 0.175098 0.303279i
\(501\) 0 0
\(502\) 14540.7 8395.09i 1.29280 0.746397i
\(503\) −10172.2 −0.901698 −0.450849 0.892600i \(-0.648879\pi\)
−0.450849 + 0.892600i \(0.648879\pi\)
\(504\) 0 0
\(505\) −828.838 −0.0730353
\(506\) 14817.7 8554.99i 1.30183 0.751612i
\(507\) 0 0
\(508\) 7851.55 13599.3i 0.685740 1.18774i
\(509\) −2149.56 3723.15i −0.187186 0.324216i 0.757125 0.653270i \(-0.226603\pi\)
−0.944311 + 0.329054i \(0.893270\pi\)
\(510\) 0 0
\(511\) −16588.8 + 4025.14i −1.43610 + 0.348458i
\(512\) 3082.06i 0.266033i
\(513\) 0 0
\(514\) 3051.64 + 1761.86i 0.261872 + 0.151192i
\(515\) −1501.14 866.682i −0.128443 0.0741565i
\(516\) 0 0
\(517\) 5786.50i 0.492243i
\(518\) −7373.15 + 1789.03i −0.625400 + 0.151748i
\(519\) 0 0
\(520\) 1092.78 + 1892.76i 0.0921571 + 0.159621i
\(521\) −5496.48 + 9520.18i −0.462198 + 0.800550i −0.999070 0.0431133i \(-0.986272\pi\)
0.536872 + 0.843664i \(0.319606\pi\)
\(522\) 0 0
\(523\) 7386.80 4264.77i 0.617595 0.356569i −0.158337 0.987385i \(-0.550613\pi\)
0.775932 + 0.630817i \(0.217280\pi\)
\(524\) −17026.2 −1.41946
\(525\) 0 0
\(526\) −8888.51 −0.736801
\(527\) −5940.20 + 3429.58i −0.491004 + 0.283481i
\(528\) 0 0
\(529\) −1947.67 + 3373.46i −0.160078 + 0.277263i
\(530\) 957.581 + 1658.58i 0.0784805 + 0.135932i
\(531\) 0 0
\(532\) −7749.26 8126.51i −0.631529 0.662272i
\(533\) 32882.2i 2.67220i
\(534\) 0 0
\(535\) 469.970 + 271.337i 0.0379786 + 0.0219270i
\(536\) −7716.86 4455.33i −0.621862 0.359032i
\(537\) 0 0
\(538\) 11183.4i 0.896195i
\(539\) −7712.89 + 12003.7i −0.616359 + 0.959250i
\(540\) 0 0
\(541\) 4352.93 + 7539.49i 0.345928 + 0.599165i 0.985522 0.169548i \(-0.0542308\pi\)
−0.639594 + 0.768713i \(0.720897\pi\)
\(542\) 10694.5 18523.4i 0.847542 1.46799i
\(543\) 0 0
\(544\) −13456.0 + 7768.84i −1.06052 + 0.612291i
\(545\) 846.150 0.0665047
\(546\) 0 0
\(547\) 17183.8 1.34319 0.671596 0.740917i \(-0.265609\pi\)
0.671596 + 0.740917i \(0.265609\pi\)
\(548\) 11875.9 6856.56i 0.925756 0.534485i
\(549\) 0 0
\(550\) −11607.3 + 20104.4i −0.899885 + 1.55865i
\(551\) −3680.60 6374.99i −0.284571 0.492892i
\(552\) 0 0
\(553\) 7341.41 + 2155.30i 0.564536 + 0.165737i
\(554\) 5305.66i 0.406888i
\(555\) 0 0
\(556\) 24876.0 + 14362.2i 1.89744 + 1.09549i
\(557\) −8989.79 5190.26i −0.683859 0.394826i 0.117448 0.993079i \(-0.462529\pi\)
−0.801307 + 0.598253i \(0.795862\pi\)
\(558\) 0 0
\(559\) 19538.6i 1.47835i
\(560\) 47.2072 + 194.555i 0.00356226 + 0.0146812i
\(561\) 0 0
\(562\) 18531.5 + 32097.5i 1.39093 + 2.40917i
\(563\) 9248.22 16018.4i 0.692302 1.19910i −0.278780 0.960355i \(-0.589930\pi\)
0.971082 0.238747i \(-0.0767366\pi\)
\(564\) 0 0
\(565\) −1002.78 + 578.956i −0.0746678 + 0.0431095i
\(566\) 11710.4 0.869656
\(567\) 0 0
\(568\) 6879.04 0.508166
\(569\) −3493.45 + 2016.94i −0.257386 + 0.148602i −0.623142 0.782109i \(-0.714144\pi\)
0.365755 + 0.930711i \(0.380811\pi\)
\(570\) 0 0
\(571\) −6430.01 + 11137.1i −0.471257 + 0.816241i −0.999459 0.0328777i \(-0.989533\pi\)
0.528203 + 0.849118i \(0.322866\pi\)
\(572\) −22206.9 38463.5i −1.62328 2.81161i
\(573\) 0 0
\(574\) −9049.07 + 30823.1i −0.658015 + 2.24134i
\(575\) 11222.9i 0.813959i
\(576\) 0 0
\(577\) −17669.2 10201.3i −1.27483 0.736026i −0.298940 0.954272i \(-0.596633\pi\)
−0.975894 + 0.218246i \(0.929967\pi\)
\(578\) −4455.72 2572.51i −0.320646 0.185125i
\(579\) 0 0
\(580\) 2383.19i 0.170615i
\(581\) 12790.8 12197.0i 0.913340 0.870941i
\(582\) 0 0
\(583\) −6958.76 12052.9i −0.494344 0.856228i
\(584\) −9281.80 + 16076.5i −0.657677 + 1.13913i
\(585\) 0 0
\(586\) 34745.1 20060.1i 2.44933 1.41412i
\(587\) −16279.7 −1.14470 −0.572348 0.820011i \(-0.693967\pi\)
−0.572348 + 0.820011i \(0.693967\pi\)
\(588\) 0 0
\(589\) 4293.17 0.300335
\(590\) 4362.91 2518.93i 0.304438 0.175767i
\(591\) 0 0
\(592\) 386.814 669.981i 0.0268546 0.0465136i
\(593\) 1342.16 + 2324.68i 0.0929440 + 0.160984i 0.908749 0.417344i \(-0.137039\pi\)
−0.815805 + 0.578328i \(0.803706\pi\)
\(594\) 0 0
\(595\) −1319.60 + 1258.34i −0.0909213 + 0.0867006i
\(596\) 21865.7i 1.50277i
\(597\) 0 0
\(598\) −30540.1 17632.3i −2.08842 1.20575i
\(599\) 12224.6 + 7057.90i 0.833865 + 0.481432i 0.855174 0.518341i \(-0.173450\pi\)
−0.0213091 + 0.999773i \(0.506783\pi\)
\(600\) 0 0
\(601\) 11096.1i 0.753109i −0.926394 0.376555i \(-0.877109\pi\)
0.926394 0.376555i \(-0.122891\pi\)
\(602\) −5376.97 + 18315.1i −0.364035 + 1.23998i
\(603\) 0 0
\(604\) −3268.89 5661.89i −0.220214 0.381422i
\(605\) −252.748 + 437.772i −0.0169846 + 0.0294181i
\(606\) 0 0
\(607\) −9592.70 + 5538.35i −0.641442 + 0.370337i −0.785170 0.619280i \(-0.787424\pi\)
0.143728 + 0.989617i \(0.454091\pi\)
\(608\) 9725.10 0.648692
\(609\) 0 0
\(610\) 75.3136 0.00499895
\(611\) 10328.5 5963.15i 0.683872 0.394834i
\(612\) 0 0
\(613\) 3801.34 6584.11i 0.250464 0.433817i −0.713189 0.700971i \(-0.752750\pi\)
0.963654 + 0.267154i \(0.0860834\pi\)
\(614\) −6122.44 10604.4i −0.402413 0.697000i
\(615\) 0 0
\(616\) 3658.74 + 15078.8i 0.239310 + 0.986269i
\(617\) 11325.9i 0.738998i 0.929231 + 0.369499i \(0.120471\pi\)
−0.929231 + 0.369499i \(0.879529\pi\)
\(618\) 0 0
\(619\) −16595.2 9581.22i −1.07757 0.622136i −0.147330 0.989087i \(-0.547068\pi\)
−0.930240 + 0.366952i \(0.880401\pi\)
\(620\) 1203.70 + 694.958i 0.0779707 + 0.0450164i
\(621\) 0 0
\(622\) 9773.64i 0.630044i
\(623\) 527.743 + 154.935i 0.0339383 + 0.00996365i
\(624\) 0 0
\(625\) −7513.41 13013.6i −0.480858 0.832871i
\(626\) −19061.6 + 33015.7i −1.21702 + 2.10794i
\(627\) 0 0
\(628\) −14214.7 + 8206.88i −0.903232 + 0.521481i
\(629\) 7046.06 0.446653
\(630\) 0 0
\(631\) 10140.7 0.639768 0.319884 0.947457i \(-0.396356\pi\)
0.319884 + 0.947457i \(0.396356\pi\)
\(632\) 7205.88 4160.32i 0.453536 0.261849i
\(633\) 0 0
\(634\) 21698.3 37582.6i 1.35923 2.35425i
\(635\) 797.995 + 1382.17i 0.0498700 + 0.0863774i
\(636\) 0 0
\(637\) 29374.1 + 1396.79i 1.82707 + 0.0868804i
\(638\) 28444.2i 1.76507i
\(639\) 0 0
\(640\) 2387.98 + 1378.70i 0.147489 + 0.0851530i
\(641\) −2950.66 1703.56i −0.181816 0.104972i 0.406330 0.913727i \(-0.366808\pi\)
−0.588146 + 0.808755i \(0.700142\pi\)
\(642\) 0 0
\(643\) 659.110i 0.0404242i −0.999796 0.0202121i \(-0.993566\pi\)
0.999796 0.0202121i \(-0.00643415\pi\)
\(644\) 14476.0 + 15180.7i 0.885767 + 0.928888i
\(645\) 0 0
\(646\) 8563.71 + 14832.8i 0.521570 + 0.903386i
\(647\) 3303.47 5721.78i 0.200731 0.347676i −0.748033 0.663661i \(-0.769002\pi\)
0.948764 + 0.315985i \(0.102335\pi\)
\(648\) 0 0
\(649\) −31705.4 + 18305.1i −1.91764 + 1.10715i
\(650\) 47846.6 2.88723
\(651\) 0 0
\(652\) 5577.01 0.334989
\(653\) 22417.1 12942.5i 1.34342 0.775622i 0.356109 0.934444i \(-0.384103\pi\)
0.987307 + 0.158823i \(0.0507698\pi\)
\(654\) 0 0
\(655\) 865.234 1498.63i 0.0516145 0.0893989i
\(656\) −1637.78 2836.72i −0.0974764 0.168834i
\(657\) 0 0
\(658\) −11322.8 + 2747.37i −0.670831 + 0.162772i
\(659\) 7468.86i 0.441495i −0.975331 0.220748i \(-0.929150\pi\)
0.975331 0.220748i \(-0.0708497\pi\)
\(660\) 0 0
\(661\) −5501.96 3176.56i −0.323754 0.186919i 0.329311 0.944222i \(-0.393184\pi\)
−0.653065 + 0.757302i \(0.726517\pi\)
\(662\) −33463.4 19320.1i −1.96464 1.13429i
\(663\) 0 0
\(664\) 19220.3i 1.12333i
\(665\) 1109.09 269.111i 0.0646744 0.0156927i
\(666\) 0 0
\(667\) 6875.53 + 11908.8i 0.399133 + 0.691319i
\(668\) −5050.61 + 8747.92i −0.292536 + 0.506687i
\(669\) 0 0
\(670\) 2193.23 1266.26i 0.126465 0.0730148i
\(671\) −547.306 −0.0314881
\(672\) 0 0
\(673\) −20238.2 −1.15918 −0.579589 0.814909i \(-0.696787\pi\)
−0.579589 + 0.814909i \(0.696787\pi\)
\(674\) 2345.58 1354.22i 0.134048 0.0773925i
\(675\) 0 0
\(676\) −32089.7 + 55581.1i −1.82577 + 3.16233i
\(677\) 5658.37 + 9800.59i 0.321224 + 0.556377i 0.980741 0.195313i \(-0.0625723\pi\)
−0.659516 + 0.751690i \(0.729239\pi\)
\(678\) 0 0
\(679\) 15332.5 + 16078.9i 0.866581 + 0.908768i
\(680\) 1982.91i 0.111825i
\(681\) 0 0
\(682\) −14366.6 8294.55i −0.806635 0.465711i
\(683\) 14869.4 + 8584.87i 0.833035 + 0.480953i 0.854891 0.518808i \(-0.173624\pi\)
−0.0218557 + 0.999761i \(0.506957\pi\)
\(684\) 0 0
\(685\) 1393.74i 0.0777402i
\(686\) −27150.3 9392.98i −1.51108 0.522778i
\(687\) 0 0
\(688\) −973.172 1685.58i −0.0539271 0.0934044i
\(689\) −14342.4 + 24841.8i −0.793037 + 1.37358i
\(690\) 0 0
\(691\) −7238.59 + 4179.20i −0.398508 + 0.230079i −0.685840 0.727752i \(-0.740565\pi\)
0.287332 + 0.957831i \(0.407232\pi\)
\(692\) −27926.3 −1.53410
\(693\) 0 0
\(694\) 32114.4 1.75655
\(695\) −2528.29 + 1459.71i −0.137990 + 0.0796688i
\(696\) 0 0
\(697\) 14916.6 25836.3i 0.810627 1.40405i
\(698\) −8187.41 14181.0i −0.443980 0.768996i
\(699\) 0 0
\(700\) −27308.0 8017.09i −1.47449 0.432882i
\(701\) 19235.8i 1.03641i 0.855256 + 0.518206i \(0.173400\pi\)
−0.855256 + 0.518206i \(0.826600\pi\)
\(702\) 0 0
\(703\) −3819.31 2205.08i −0.204905 0.118302i
\(704\) −30082.5 17368.1i −1.61048 0.929810i
\(705\) 0 0
\(706\) 10536.5i 0.561680i
\(707\) 2859.75 + 11785.9i 0.152124 + 0.626951i
\(708\) 0 0
\(709\) 5160.17 + 8937.67i 0.273334 + 0.473429i 0.969714 0.244245i \(-0.0785401\pi\)
−0.696379 + 0.717674i \(0.745207\pi\)
\(710\) −977.554 + 1693.17i −0.0516718 + 0.0894981i
\(711\) 0 0
\(712\) 518.001 299.068i 0.0272653 0.0157416i
\(713\) −8019.85 −0.421242
\(714\) 0 0
\(715\) 4514.02 0.236105
\(716\) 31529.0 18203.3i 1.64566 0.950124i
\(717\) 0 0
\(718\) 3975.20 6885.25i 0.206620 0.357876i
\(719\) −11679.8 20229.9i −0.605815 1.04930i −0.991922 0.126849i \(-0.959514\pi\)
0.386107 0.922454i \(-0.373820\pi\)
\(720\) 0 0
\(721\) −7144.63 + 24336.2i −0.369043 + 1.25704i
\(722\) 20300.0i 1.04638i
\(723\) 0 0
\(724\) −3050.62 1761.28i −0.156596 0.0904106i
\(725\) −16157.7 9328.63i −0.827698 0.477871i
\(726\) 0 0
\(727\) 22260.4i 1.13561i 0.823162 + 0.567807i \(0.192208\pi\)
−0.823162 + 0.567807i \(0.807792\pi\)
\(728\) 23144.1 22069.7i 1.17827 1.12357i
\(729\) 0 0
\(730\) −2638.00 4569.15i −0.133749 0.231660i
\(731\) 8863.48 15352.0i 0.448464 0.776763i
\(732\) 0 0
\(733\) 9047.84 5223.77i 0.455920 0.263226i −0.254407 0.967097i \(-0.581880\pi\)
0.710327 + 0.703872i \(0.248547\pi\)
\(734\) 7618.58 0.383116
\(735\) 0 0
\(736\) −18166.9 −0.909840
\(737\) −15938.2 + 9201.95i −0.796598 + 0.459916i
\(738\) 0 0
\(739\) −6595.44 + 11423.6i −0.328304 + 0.568640i −0.982176 0.187966i \(-0.939811\pi\)
0.653871 + 0.756606i \(0.273144\pi\)
\(740\) −713.895 1236.50i −0.0354639 0.0614253i
\(741\) 0 0
\(742\) 20280.7 19339.2i 1.00341 0.956825i
\(743\) 35382.2i 1.74703i −0.486795 0.873517i \(-0.661834\pi\)
0.486795 0.873517i \(-0.338166\pi\)
\(744\) 0 0
\(745\) −1924.59 1111.16i −0.0946463 0.0546441i
\(746\) 1164.38 + 672.258i 0.0571463 + 0.0329934i
\(747\) 0 0
\(748\) 40295.6i 1.96973i
\(749\) 2236.81 7619.07i 0.109121 0.371688i
\(750\) 0 0
\(751\) 14692.3 + 25447.8i 0.713888 + 1.23649i 0.963387 + 0.268116i \(0.0864010\pi\)
−0.249498 + 0.968375i \(0.580266\pi\)
\(752\) 594.020 1028.87i 0.0288054 0.0498925i
\(753\) 0 0
\(754\) 50770.8 29312.5i 2.45221 1.41578i
\(755\) 664.470 0.0320299
\(756\) 0 0
\(757\) 11329.1 0.543939 0.271969 0.962306i \(-0.412325\pi\)
0.271969 + 0.962306i \(0.412325\pi\)
\(758\) −28994.0 + 16739.7i −1.38932 + 0.802127i
\(759\) 0 0
\(760\) 620.557 1074.84i 0.0296184 0.0513005i
\(761\) 12696.5 + 21990.9i 0.604792 + 1.04753i 0.992084 + 0.125574i \(0.0400772\pi\)
−0.387292 + 0.921957i \(0.626589\pi\)
\(762\) 0 0
\(763\) −2919.48 12032.1i −0.138522 0.570891i
\(764\) 57499.9i 2.72287i
\(765\) 0 0
\(766\) 49065.8 + 28328.2i 2.31439 + 1.33621i
\(767\) 65346.7 + 37727.9i 3.07631 + 1.77611i
\(768\) 0 0
\(769\) 18120.8i 0.849744i 0.905253 + 0.424872i \(0.139681\pi\)
−0.905253 + 0.424872i \(0.860319\pi\)
\(770\) −4231.35 1242.24i −0.198035 0.0581394i
\(771\) 0 0
\(772\) −25874.7 44816.3i −1.20628 2.08934i
\(773\) 8673.05 15022.2i 0.403555 0.698978i −0.590597 0.806967i \(-0.701108\pi\)
0.994152 + 0.107989i \(0.0344410\pi\)
\(774\) 0 0
\(775\) 9423.42 5440.61i 0.436773 0.252171i
\(776\) 24161.3 1.11771
\(777\) 0 0
\(778\) −36054.7 −1.66147
\(779\) −16171.1 + 9336.37i −0.743759 + 0.429410i
\(780\) 0 0
\(781\) 7103.91 12304.3i 0.325477 0.563743i
\(782\) −15997.4 27708.3i −0.731542 1.26707i
\(783\) 0 0
\(784\) 2603.65 1342.55i 0.118607 0.0611585i
\(785\) 1668.22i 0.0758488i
\(786\) 0 0