Properties

Label 63.4.e.c.46.2
Level $63$
Weight $4$
Character 63.46
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 46.2
Root \(0.124036 + 0.214837i\) of defining polynomial
Character \(\chi\) \(=\) 63.46
Dual form 63.4.e.c.37.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.124036 + 0.214837i) q^{2} +(3.96923 - 6.87491i) q^{4} +(-6.21730 - 10.7687i) q^{5} +(-18.4385 + 1.73873i) q^{7} +3.95388 q^{8} +O(q^{10})\) \(q+(0.124036 + 0.214837i) q^{2} +(3.96923 - 6.87491i) q^{4} +(-6.21730 - 10.7687i) q^{5} +(-18.4385 + 1.73873i) q^{7} +3.95388 q^{8} +(1.54234 - 2.67141i) q^{10} +(30.1558 - 52.2313i) q^{11} +36.4269 q^{13} +(-2.66058 - 3.74559i) q^{14} +(-31.2634 - 54.1498i) q^{16} +(-24.3731 + 42.2154i) q^{17} +(25.2750 + 43.7776i) q^{19} -98.7116 q^{20} +14.9616 q^{22} +(69.3962 + 120.198i) q^{23} +(-14.8097 + 25.6511i) q^{25} +(4.51824 + 7.82583i) q^{26} +(-61.2329 + 133.664i) q^{28} +61.1345 q^{29} +(0.584676 - 1.01269i) q^{31} +(23.5711 - 40.8264i) q^{32} -12.0925 q^{34} +(133.361 + 187.748i) q^{35} +(-34.7634 - 60.2120i) q^{37} +(-6.27001 + 10.8600i) q^{38} +(-24.5825 - 42.5781i) q^{40} -308.115 q^{41} +174.443 q^{43} +(-239.390 - 414.636i) q^{44} +(-17.2153 + 29.8177i) q^{46} +(194.681 + 337.197i) q^{47} +(336.954 - 64.1190i) q^{49} -7.34774 q^{50} +(144.587 - 250.432i) q^{52} +(157.467 - 272.742i) q^{53} -749.950 q^{55} +(-72.9035 + 6.87474i) q^{56} +(7.58287 + 13.1339i) q^{58} +(422.263 - 731.381i) q^{59} +(169.269 + 293.182i) q^{61} +0.290084 q^{62} -488.520 q^{64} +(-226.477 - 392.270i) q^{65} +(485.775 - 841.387i) q^{67} +(193.485 + 335.125i) q^{68} +(-23.7935 + 51.9384i) q^{70} +98.4698 q^{71} +(-355.117 + 615.082i) q^{73} +(8.62383 - 14.9369i) q^{74} +401.289 q^{76} +(-465.210 + 1015.50i) q^{77} +(243.442 + 421.654i) q^{79} +(-388.748 + 673.332i) q^{80} +(-38.2174 - 66.1944i) q^{82} -605.688 q^{83} +606.139 q^{85} +(21.6372 + 37.4767i) q^{86} +(119.232 - 206.517i) q^{88} +(109.034 + 188.853i) q^{89} +(-671.656 + 63.3365i) q^{91} +1101.80 q^{92} +(-48.2949 + 83.6491i) q^{94} +(314.284 - 544.357i) q^{95} -782.288 q^{97} +(55.5695 + 64.4369i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + q^{2} - 25q^{4} + 11q^{5} - 13q^{7} - 78q^{8} + O(q^{10}) \) \( 6q + q^{2} - 25q^{4} + 11q^{5} - 13q^{7} - 78q^{8} + 55q^{10} + 35q^{11} + 124q^{13} + 326q^{14} - 241q^{16} + 48q^{17} + 202q^{19} - 878q^{20} - 14q^{22} + 216q^{23} - 130q^{25} + 274q^{26} - 201q^{28} - 106q^{29} + 95q^{31} + 683q^{32} - 48q^{34} - 56q^{35} - 262q^{37} - 398q^{38} - 21q^{40} - 488q^{41} + 720q^{43} - 905q^{44} + 1056q^{46} - 210q^{47} - 303q^{49} + 2756q^{50} - 324q^{52} + 393q^{53} - 2062q^{55} - 1299q^{56} + 1249q^{58} + 1143q^{59} + 70q^{61} - 2118q^{62} - 798q^{64} - 472q^{65} + 628q^{67} + 1944q^{68} + 3251q^{70} - 636q^{71} - 988q^{73} + 1002q^{74} - 4680q^{76} - 1073q^{77} - 861q^{79} + 175q^{80} - 124q^{82} - 1038q^{83} + 3600q^{85} - 3208q^{86} + 891q^{88} + 1766q^{89} - 654q^{91} + 1344q^{92} + 3294q^{94} - 736q^{95} + 38q^{97} + 4267q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.124036 + 0.214837i 0.0438533 + 0.0759562i 0.887119 0.461541i \(-0.152703\pi\)
−0.843266 + 0.537497i \(0.819370\pi\)
\(3\) 0 0
\(4\) 3.96923 6.87491i 0.496154 0.859364i
\(5\) −6.21730 10.7687i −0.556092 0.963180i −0.997818 0.0660299i \(-0.978967\pi\)
0.441725 0.897150i \(-0.354367\pi\)
\(6\) 0 0
\(7\) −18.4385 + 1.73873i −0.995583 + 0.0938826i
\(8\) 3.95388 0.174739
\(9\) 0 0
\(10\) 1.54234 2.67141i 0.0487730 0.0844773i
\(11\) 30.1558 52.2313i 0.826573 1.43167i −0.0741379 0.997248i \(-0.523621\pi\)
0.900711 0.434419i \(-0.143046\pi\)
\(12\) 0 0
\(13\) 36.4269 0.777154 0.388577 0.921416i \(-0.372967\pi\)
0.388577 + 0.921416i \(0.372967\pi\)
\(14\) −2.66058 3.74559i −0.0507906 0.0715037i
\(15\) 0 0
\(16\) −31.2634 54.1498i −0.488491 0.846091i
\(17\) −24.3731 + 42.2154i −0.347726 + 0.602279i −0.985845 0.167659i \(-0.946379\pi\)
0.638119 + 0.769937i \(0.279713\pi\)
\(18\) 0 0
\(19\) 25.2750 + 43.7776i 0.305183 + 0.528593i 0.977302 0.211851i \(-0.0679490\pi\)
−0.672119 + 0.740443i \(0.734616\pi\)
\(20\) −98.7116 −1.10363
\(21\) 0 0
\(22\) 14.9616 0.144992
\(23\) 69.3962 + 120.198i 0.629135 + 1.08969i 0.987726 + 0.156199i \(0.0499241\pi\)
−0.358590 + 0.933495i \(0.616743\pi\)
\(24\) 0 0
\(25\) −14.8097 + 25.6511i −0.118478 + 0.205209i
\(26\) 4.51824 + 7.82583i 0.0340808 + 0.0590297i
\(27\) 0 0
\(28\) −61.2329 + 133.664i −0.413283 + 0.902148i
\(29\) 61.1345 0.391462 0.195731 0.980658i \(-0.437292\pi\)
0.195731 + 0.980658i \(0.437292\pi\)
\(30\) 0 0
\(31\) 0.584676 1.01269i 0.00338745 0.00586724i −0.864327 0.502931i \(-0.832255\pi\)
0.867714 + 0.497064i \(0.165588\pi\)
\(32\) 23.5711 40.8264i 0.130213 0.225536i
\(33\) 0 0
\(34\) −12.0925 −0.0609957
\(35\) 133.361 + 187.748i 0.644062 + 0.906719i
\(36\) 0 0
\(37\) −34.7634 60.2120i −0.154461 0.267535i 0.778401 0.627767i \(-0.216031\pi\)
−0.932863 + 0.360232i \(0.882698\pi\)
\(38\) −6.27001 + 10.8600i −0.0267666 + 0.0463611i
\(39\) 0 0
\(40\) −24.5825 42.5781i −0.0971708 0.168305i
\(41\) −308.115 −1.17365 −0.586823 0.809715i \(-0.699622\pi\)
−0.586823 + 0.809715i \(0.699622\pi\)
\(42\) 0 0
\(43\) 174.443 0.618657 0.309329 0.950955i \(-0.399896\pi\)
0.309329 + 0.950955i \(0.399896\pi\)
\(44\) −239.390 414.636i −0.820215 1.42065i
\(45\) 0 0
\(46\) −17.2153 + 29.8177i −0.0551794 + 0.0955734i
\(47\) 194.681 + 337.197i 0.604194 + 1.04649i 0.992178 + 0.124829i \(0.0398382\pi\)
−0.387984 + 0.921666i \(0.626828\pi\)
\(48\) 0 0
\(49\) 336.954 64.1190i 0.982372 0.186936i
\(50\) −7.34774 −0.0207825
\(51\) 0 0
\(52\) 144.587 250.432i 0.385588 0.667858i
\(53\) 157.467 272.742i 0.408110 0.706867i −0.586568 0.809900i \(-0.699521\pi\)
0.994678 + 0.103033i \(0.0328547\pi\)
\(54\) 0 0
\(55\) −749.950 −1.83860
\(56\) −72.9035 + 6.87474i −0.173967 + 0.0164049i
\(57\) 0 0
\(58\) 7.58287 + 13.1339i 0.0171669 + 0.0297339i
\(59\) 422.263 731.381i 0.931762 1.61386i 0.151455 0.988464i \(-0.451604\pi\)
0.780308 0.625396i \(-0.215062\pi\)
\(60\) 0 0
\(61\) 169.269 + 293.182i 0.355290 + 0.615380i 0.987167 0.159688i \(-0.0510489\pi\)
−0.631878 + 0.775068i \(0.717716\pi\)
\(62\) 0.290084 0.000594204
\(63\) 0 0
\(64\) −488.520 −0.954141
\(65\) −226.477 392.270i −0.432169 0.748539i
\(66\) 0 0
\(67\) 485.775 841.387i 0.885774 1.53421i 0.0409498 0.999161i \(-0.486962\pi\)
0.844824 0.535044i \(-0.179705\pi\)
\(68\) 193.485 + 335.125i 0.345051 + 0.597646i
\(69\) 0 0
\(70\) −23.7935 + 51.9384i −0.0406266 + 0.0886832i
\(71\) 98.4698 0.164595 0.0822973 0.996608i \(-0.473774\pi\)
0.0822973 + 0.996608i \(0.473774\pi\)
\(72\) 0 0
\(73\) −355.117 + 615.082i −0.569361 + 0.986162i 0.427268 + 0.904125i \(0.359476\pi\)
−0.996629 + 0.0820374i \(0.973857\pi\)
\(74\) 8.62383 14.9369i 0.0135473 0.0234646i
\(75\) 0 0
\(76\) 401.289 0.605671
\(77\) −465.210 + 1015.50i −0.688514 + 1.50294i
\(78\) 0 0
\(79\) 243.442 + 421.654i 0.346701 + 0.600504i 0.985661 0.168736i \(-0.0539686\pi\)
−0.638960 + 0.769240i \(0.720635\pi\)
\(80\) −388.748 + 673.332i −0.543292 + 0.941010i
\(81\) 0 0
\(82\) −38.2174 66.1944i −0.0514683 0.0891458i
\(83\) −605.688 −0.800999 −0.400499 0.916297i \(-0.631163\pi\)
−0.400499 + 0.916297i \(0.631163\pi\)
\(84\) 0 0
\(85\) 606.139 0.773470
\(86\) 21.6372 + 37.4767i 0.0271302 + 0.0469908i
\(87\) 0 0
\(88\) 119.232 206.517i 0.144434 0.250168i
\(89\) 109.034 + 188.853i 0.129861 + 0.224925i 0.923622 0.383303i \(-0.125214\pi\)
−0.793762 + 0.608229i \(0.791880\pi\)
\(90\) 0 0
\(91\) −671.656 + 63.3365i −0.773722 + 0.0729612i
\(92\) 1101.80 1.24859
\(93\) 0 0
\(94\) −48.2949 + 83.6491i −0.0529919 + 0.0917846i
\(95\) 314.284 544.357i 0.339420 0.587893i
\(96\) 0 0
\(97\) −782.288 −0.818859 −0.409429 0.912342i \(-0.634272\pi\)
−0.409429 + 0.912342i \(0.634272\pi\)
\(98\) 55.5695 + 64.4369i 0.0572792 + 0.0664195i
\(99\) 0 0
\(100\) 117.566 + 203.631i 0.117566 + 0.203631i
\(101\) −155.823 + 269.893i −0.153514 + 0.265895i −0.932517 0.361126i \(-0.882392\pi\)
0.779003 + 0.627021i \(0.215726\pi\)
\(102\) 0 0
\(103\) 74.6289 + 129.261i 0.0713922 + 0.123655i 0.899512 0.436897i \(-0.143922\pi\)
−0.828119 + 0.560552i \(0.810589\pi\)
\(104\) 144.028 0.135799
\(105\) 0 0
\(106\) 78.1265 0.0715879
\(107\) 425.760 + 737.437i 0.384670 + 0.666269i 0.991723 0.128393i \(-0.0409818\pi\)
−0.607053 + 0.794661i \(0.707648\pi\)
\(108\) 0 0
\(109\) −680.939 + 1179.42i −0.598369 + 1.03640i 0.394694 + 0.918813i \(0.370851\pi\)
−0.993062 + 0.117592i \(0.962483\pi\)
\(110\) −93.0208 161.117i −0.0806289 0.139653i
\(111\) 0 0
\(112\) 670.601 + 944.081i 0.565767 + 0.796493i
\(113\) −1048.55 −0.872917 −0.436459 0.899724i \(-0.643767\pi\)
−0.436459 + 0.899724i \(0.643767\pi\)
\(114\) 0 0
\(115\) 862.914 1494.61i 0.699715 1.21194i
\(116\) 242.657 420.294i 0.194225 0.336408i
\(117\) 0 0
\(118\) 209.503 0.163444
\(119\) 376.001 820.765i 0.289646 0.632264i
\(120\) 0 0
\(121\) −1153.24 1997.47i −0.866446 1.50073i
\(122\) −41.9909 + 72.7303i −0.0311613 + 0.0539729i
\(123\) 0 0
\(124\) −4.64143 8.03919i −0.00336139 0.00582210i
\(125\) −1186.02 −0.848647
\(126\) 0 0
\(127\) 488.408 0.341254 0.170627 0.985336i \(-0.445421\pi\)
0.170627 + 0.985336i \(0.445421\pi\)
\(128\) −249.163 431.563i −0.172056 0.298009i
\(129\) 0 0
\(130\) 56.1826 97.3111i 0.0379041 0.0656519i
\(131\) −927.114 1605.81i −0.618338 1.07099i −0.989789 0.142541i \(-0.954473\pi\)
0.371451 0.928453i \(-0.378861\pi\)
\(132\) 0 0
\(133\) −542.149 763.244i −0.353461 0.497607i
\(134\) 241.014 0.155377
\(135\) 0 0
\(136\) −96.3683 + 166.915i −0.0607611 + 0.105241i
\(137\) −255.558 + 442.639i −0.159370 + 0.276038i −0.934642 0.355591i \(-0.884280\pi\)
0.775271 + 0.631628i \(0.217613\pi\)
\(138\) 0 0
\(139\) 2266.10 1.38279 0.691397 0.722475i \(-0.256995\pi\)
0.691397 + 0.722475i \(0.256995\pi\)
\(140\) 1820.09 171.633i 1.09875 0.103612i
\(141\) 0 0
\(142\) 12.2138 + 21.1549i 0.00721802 + 0.0125020i
\(143\) 1098.48 1902.62i 0.642375 1.11263i
\(144\) 0 0
\(145\) −380.091 658.338i −0.217689 0.377048i
\(146\) −176.189 −0.0998735
\(147\) 0 0
\(148\) −551.936 −0.306546
\(149\) 753.950 + 1305.88i 0.414537 + 0.717999i 0.995380 0.0960168i \(-0.0306102\pi\)
−0.580843 + 0.814016i \(0.697277\pi\)
\(150\) 0 0
\(151\) −795.913 + 1378.56i −0.428943 + 0.742952i −0.996780 0.0801897i \(-0.974447\pi\)
0.567836 + 0.823142i \(0.307781\pi\)
\(152\) 99.9344 + 173.091i 0.0533273 + 0.0923656i
\(153\) 0 0
\(154\) −275.869 + 26.0142i −0.144352 + 0.0136122i
\(155\) −14.5404 −0.00753494
\(156\) 0 0
\(157\) −582.080 + 1008.19i −0.295892 + 0.512500i −0.975192 0.221361i \(-0.928950\pi\)
0.679300 + 0.733861i \(0.262283\pi\)
\(158\) −60.3911 + 104.601i −0.0304080 + 0.0526682i
\(159\) 0 0
\(160\) −586.195 −0.289642
\(161\) −1488.55 2095.60i −0.728660 1.02582i
\(162\) 0 0
\(163\) 577.940 + 1001.02i 0.277716 + 0.481019i 0.970817 0.239822i \(-0.0770892\pi\)
−0.693101 + 0.720841i \(0.743756\pi\)
\(164\) −1222.98 + 2118.26i −0.582309 + 1.00859i
\(165\) 0 0
\(166\) −75.1271 130.124i −0.0351265 0.0608408i
\(167\) 2890.61 1.33941 0.669707 0.742626i \(-0.266420\pi\)
0.669707 + 0.742626i \(0.266420\pi\)
\(168\) 0 0
\(169\) −870.082 −0.396032
\(170\) 75.1830 + 130.221i 0.0339193 + 0.0587499i
\(171\) 0 0
\(172\) 692.403 1199.28i 0.306949 0.531651i
\(173\) 947.468 + 1641.06i 0.416385 + 0.721200i 0.995573 0.0939940i \(-0.0299635\pi\)
−0.579188 + 0.815194i \(0.696630\pi\)
\(174\) 0 0
\(175\) 228.467 498.718i 0.0986887 0.215426i
\(176\) −3771.09 −1.61509
\(177\) 0 0
\(178\) −27.0483 + 46.8491i −0.0113897 + 0.0197275i
\(179\) −2144.25 + 3713.94i −0.895355 + 1.55080i −0.0619893 + 0.998077i \(0.519744\pi\)
−0.833365 + 0.552723i \(0.813589\pi\)
\(180\) 0 0
\(181\) 383.732 0.157583 0.0787917 0.996891i \(-0.474894\pi\)
0.0787917 + 0.996891i \(0.474894\pi\)
\(182\) −96.9165 136.440i −0.0394721 0.0555694i
\(183\) 0 0
\(184\) 274.385 + 475.248i 0.109934 + 0.190412i
\(185\) −432.269 + 748.712i −0.171790 + 0.297548i
\(186\) 0 0
\(187\) 1469.98 + 2546.07i 0.574841 + 0.995655i
\(188\) 3090.93 1.19909
\(189\) 0 0
\(190\) 155.930 0.0595388
\(191\) 192.655 + 333.689i 0.0729845 + 0.126413i 0.900208 0.435460i \(-0.143414\pi\)
−0.827224 + 0.561873i \(0.810081\pi\)
\(192\) 0 0
\(193\) −315.112 + 545.790i −0.117525 + 0.203559i −0.918786 0.394756i \(-0.870829\pi\)
0.801262 + 0.598314i \(0.204163\pi\)
\(194\) −97.0318 168.064i −0.0359097 0.0621974i
\(195\) 0 0
\(196\) 896.634 2571.03i 0.326762 0.936964i
\(197\) 1250.23 0.452158 0.226079 0.974109i \(-0.427409\pi\)
0.226079 + 0.974109i \(0.427409\pi\)
\(198\) 0 0
\(199\) 546.122 945.912i 0.194541 0.336954i −0.752209 0.658924i \(-0.771012\pi\)
0.946750 + 0.321970i \(0.104345\pi\)
\(200\) −58.5558 + 101.422i −0.0207026 + 0.0358580i
\(201\) 0 0
\(202\) −77.3105 −0.0269285
\(203\) −1127.23 + 106.296i −0.389733 + 0.0367514i
\(204\) 0 0
\(205\) 1915.65 + 3318.00i 0.652656 + 1.13043i
\(206\) −18.5133 + 32.0660i −0.00626158 + 0.0108454i
\(207\) 0 0
\(208\) −1138.83 1972.51i −0.379633 0.657543i
\(209\) 3048.75 1.00902
\(210\) 0 0
\(211\) −3620.05 −1.18111 −0.590556 0.806997i \(-0.701091\pi\)
−0.590556 + 0.806997i \(0.701091\pi\)
\(212\) −1250.05 2165.15i −0.404970 0.701429i
\(213\) 0 0
\(214\) −105.619 + 182.937i −0.0337382 + 0.0584362i
\(215\) −1084.56 1878.52i −0.344030 0.595878i
\(216\) 0 0
\(217\) −9.01974 + 19.6890i −0.00282166 + 0.00615935i
\(218\) −337.844 −0.104962
\(219\) 0 0
\(220\) −2976.72 + 5155.84i −0.912230 + 1.58003i
\(221\) −887.835 + 1537.78i −0.270236 + 0.468063i
\(222\) 0 0
\(223\) −183.844 −0.0552069 −0.0276034 0.999619i \(-0.508788\pi\)
−0.0276034 + 0.999619i \(0.508788\pi\)
\(224\) −363.629 + 793.759i −0.108464 + 0.236765i
\(225\) 0 0
\(226\) −130.058 225.268i −0.0382803 0.0663035i
\(227\) 1139.76 1974.12i 0.333253 0.577211i −0.649895 0.760024i \(-0.725187\pi\)
0.983148 + 0.182813i \(0.0585203\pi\)
\(228\) 0 0
\(229\) −2706.34 4687.51i −0.780960 1.35266i −0.931383 0.364040i \(-0.881397\pi\)
0.150424 0.988622i \(-0.451936\pi\)
\(230\) 428.130 0.122739
\(231\) 0 0
\(232\) 241.719 0.0684035
\(233\) 569.184 + 985.856i 0.160036 + 0.277191i 0.934882 0.354960i \(-0.115506\pi\)
−0.774845 + 0.632151i \(0.782172\pi\)
\(234\) 0 0
\(235\) 2420.78 4192.91i 0.671975 1.16390i
\(236\) −3352.12 5806.04i −0.924595 1.60145i
\(237\) 0 0
\(238\) 222.968 21.0257i 0.0607263 0.00572644i
\(239\) 6226.36 1.68515 0.842573 0.538583i \(-0.181040\pi\)
0.842573 + 0.538583i \(0.181040\pi\)
\(240\) 0 0
\(241\) 1598.10 2767.99i 0.427147 0.739841i −0.569471 0.822012i \(-0.692852\pi\)
0.996618 + 0.0821704i \(0.0261852\pi\)
\(242\) 286.086 495.516i 0.0759931 0.131624i
\(243\) 0 0
\(244\) 2687.47 0.705113
\(245\) −2785.42 3229.90i −0.726343 0.842248i
\(246\) 0 0
\(247\) 920.689 + 1594.68i 0.237174 + 0.410798i
\(248\) 2.31174 4.00406i 0.000591919 0.00102523i
\(249\) 0 0
\(250\) −147.109 254.801i −0.0372160 0.0644600i
\(251\) −239.608 −0.0602546 −0.0301273 0.999546i \(-0.509591\pi\)
−0.0301273 + 0.999546i \(0.509591\pi\)
\(252\) 0 0
\(253\) 8370.78 2.08010
\(254\) 60.5802 + 104.928i 0.0149651 + 0.0259203i
\(255\) 0 0
\(256\) −1892.27 + 3277.51i −0.461980 + 0.800173i
\(257\) 349.559 + 605.453i 0.0848439 + 0.146954i 0.905325 0.424720i \(-0.139628\pi\)
−0.820481 + 0.571674i \(0.806294\pi\)
\(258\) 0 0
\(259\) 745.676 + 1049.77i 0.178896 + 0.251852i
\(260\) −3595.76 −0.857690
\(261\) 0 0
\(262\) 229.991 398.356i 0.0542324 0.0939333i
\(263\) −459.520 + 795.912i −0.107738 + 0.186609i −0.914854 0.403785i \(-0.867694\pi\)
0.807115 + 0.590394i \(0.201028\pi\)
\(264\) 0 0
\(265\) −3916.09 −0.907787
\(266\) 96.7268 211.143i 0.0222959 0.0486693i
\(267\) 0 0
\(268\) −3856.30 6679.32i −0.878960 1.52240i
\(269\) −1389.59 + 2406.84i −0.314961 + 0.545529i −0.979429 0.201788i \(-0.935325\pi\)
0.664468 + 0.747317i \(0.268658\pi\)
\(270\) 0 0
\(271\) −1113.49 1928.62i −0.249593 0.432308i 0.713820 0.700329i \(-0.246964\pi\)
−0.963413 + 0.268021i \(0.913630\pi\)
\(272\) 3047.94 0.679443
\(273\) 0 0
\(274\) −126.793 −0.0279557
\(275\) 893.195 + 1547.06i 0.195861 + 0.339241i
\(276\) 0 0
\(277\) −3653.85 + 6328.65i −0.792557 + 1.37275i 0.131821 + 0.991273i \(0.457917\pi\)
−0.924379 + 0.381476i \(0.875416\pi\)
\(278\) 281.078 + 486.842i 0.0606402 + 0.105032i
\(279\) 0 0
\(280\) 527.295 + 742.333i 0.112543 + 0.158439i
\(281\) −2730.61 −0.579696 −0.289848 0.957073i \(-0.593605\pi\)
−0.289848 + 0.957073i \(0.593605\pi\)
\(282\) 0 0
\(283\) 884.926 1532.74i 0.185878 0.321950i −0.757994 0.652261i \(-0.773821\pi\)
0.943872 + 0.330312i \(0.107154\pi\)
\(284\) 390.849 676.971i 0.0816642 0.141447i
\(285\) 0 0
\(286\) 545.004 0.112681
\(287\) 5681.17 535.729i 1.16846 0.110185i
\(288\) 0 0
\(289\) 1268.41 + 2196.95i 0.258174 + 0.447170i
\(290\) 94.2900 163.315i 0.0190928 0.0330696i
\(291\) 0 0
\(292\) 2819.09 + 4882.80i 0.564981 + 0.978576i
\(293\) −8228.81 −1.64072 −0.820362 0.571844i \(-0.806228\pi\)
−0.820362 + 0.571844i \(0.806228\pi\)
\(294\) 0 0
\(295\) −10501.4 −2.07258
\(296\) −137.451 238.071i −0.0269904 0.0467487i
\(297\) 0 0
\(298\) −187.034 + 323.952i −0.0363577 + 0.0629733i
\(299\) 2527.89 + 4378.43i 0.488935 + 0.846860i
\(300\) 0 0
\(301\) −3216.45 + 303.309i −0.615925 + 0.0580811i
\(302\) −394.887 −0.0752424
\(303\) 0 0
\(304\) 1580.36 2737.27i 0.298158 0.516425i
\(305\) 2104.79 3645.61i 0.395148 0.684416i
\(306\) 0 0
\(307\) 6019.62 1.11908 0.559541 0.828803i \(-0.310977\pi\)
0.559541 + 0.828803i \(0.310977\pi\)
\(308\) 5134.93 + 7229.02i 0.949967 + 1.33738i
\(309\) 0 0
\(310\) −1.80354 3.12382i −0.000330432 0.000572326i
\(311\) 596.857 1033.79i 0.108825 0.188491i −0.806469 0.591276i \(-0.798624\pi\)
0.915295 + 0.402785i \(0.131958\pi\)
\(312\) 0 0
\(313\) 4423.02 + 7660.89i 0.798734 + 1.38345i 0.920441 + 0.390882i \(0.127830\pi\)
−0.121707 + 0.992566i \(0.538837\pi\)
\(314\) −288.795 −0.0519034
\(315\) 0 0
\(316\) 3865.11 0.688068
\(317\) 3040.72 + 5266.68i 0.538750 + 0.933142i 0.998972 + 0.0453380i \(0.0144365\pi\)
−0.460222 + 0.887804i \(0.652230\pi\)
\(318\) 0 0
\(319\) 1843.56 3193.13i 0.323572 0.560442i
\(320\) 3037.28 + 5260.72i 0.530590 + 0.919009i
\(321\) 0 0
\(322\) 265.578 579.725i 0.0459630 0.100332i
\(323\) −2464.12 −0.424480
\(324\) 0 0
\(325\) −539.471 + 934.391i −0.0920753 + 0.159479i
\(326\) −143.371 + 248.325i −0.0243576 + 0.0421885i
\(327\) 0 0
\(328\) −1218.25 −0.205082
\(329\) −4175.91 5878.90i −0.699773 0.985149i
\(330\) 0 0
\(331\) −1526.65 2644.23i −0.253511 0.439094i 0.710979 0.703213i \(-0.248252\pi\)
−0.964490 + 0.264119i \(0.914919\pi\)
\(332\) −2404.12 + 4164.05i −0.397419 + 0.688349i
\(333\) 0 0
\(334\) 358.539 + 621.009i 0.0587377 + 0.101737i
\(335\) −12080.8 −1.97029
\(336\) 0 0
\(337\) 3865.80 0.624877 0.312438 0.949938i \(-0.398854\pi\)
0.312438 + 0.949938i \(0.398854\pi\)
\(338\) −107.921 186.925i −0.0173673 0.0300811i
\(339\) 0 0
\(340\) 2405.90 4167.15i 0.383760 0.664692i
\(341\) −35.2627 61.0768i −0.00559995 0.00969940i
\(342\) 0 0
\(343\) −6101.42 + 1768.13i −0.960483 + 0.278338i
\(344\) 689.726 0.108103
\(345\) 0 0
\(346\) −235.040 + 407.101i −0.0365198 + 0.0632541i
\(347\) −49.7965 + 86.2501i −0.00770380 + 0.0133434i −0.869852 0.493313i \(-0.835786\pi\)
0.862148 + 0.506657i \(0.169119\pi\)
\(348\) 0 0
\(349\) −3607.34 −0.553285 −0.276643 0.960973i \(-0.589222\pi\)
−0.276643 + 0.960973i \(0.589222\pi\)
\(350\) 135.481 12.7757i 0.0206907 0.00195112i
\(351\) 0 0
\(352\) −1421.61 2462.30i −0.215262 0.372844i
\(353\) 3565.37 6175.40i 0.537579 0.931114i −0.461455 0.887164i \(-0.652672\pi\)
0.999034 0.0439501i \(-0.0139942\pi\)
\(354\) 0 0
\(355\) −612.216 1060.39i −0.0915298 0.158534i
\(356\) 1731.13 0.257724
\(357\) 0 0
\(358\) −1063.85 −0.157057
\(359\) −3250.14 5629.41i −0.477816 0.827602i 0.521860 0.853031i \(-0.325238\pi\)
−0.999677 + 0.0254289i \(0.991905\pi\)
\(360\) 0 0
\(361\) 2151.85 3727.11i 0.313727 0.543390i
\(362\) 47.5966 + 82.4398i 0.00691056 + 0.0119694i
\(363\) 0 0
\(364\) −2230.52 + 4868.97i −0.321185 + 0.701108i
\(365\) 8831.49 1.26647
\(366\) 0 0
\(367\) −412.443 + 714.372i −0.0586631 + 0.101607i −0.893866 0.448335i \(-0.852017\pi\)
0.835202 + 0.549943i \(0.185350\pi\)
\(368\) 4339.12 7515.58i 0.614654 1.06461i
\(369\) 0 0
\(370\) −214.468 −0.0301342
\(371\) −2429.23 + 5302.73i −0.339945 + 0.742059i
\(372\) 0 0
\(373\) −666.925 1155.15i −0.0925793 0.160352i 0.816016 0.578029i \(-0.196178\pi\)
−0.908596 + 0.417677i \(0.862845\pi\)
\(374\) −364.660 + 631.610i −0.0504174 + 0.0873255i
\(375\) 0 0
\(376\) 769.746 + 1333.24i 0.105576 + 0.182863i
\(377\) 2226.94 0.304226
\(378\) 0 0
\(379\) −1338.29 −0.181380 −0.0906902 0.995879i \(-0.528907\pi\)
−0.0906902 + 0.995879i \(0.528907\pi\)
\(380\) −2494.93 4321.35i −0.336809 0.583370i
\(381\) 0 0
\(382\) −47.7924 + 82.7788i −0.00640123 + 0.0110873i
\(383\) 176.688 + 306.032i 0.0235727 + 0.0408290i 0.877571 0.479447i \(-0.159163\pi\)
−0.853998 + 0.520276i \(0.825829\pi\)
\(384\) 0 0
\(385\) 13827.9 1303.96i 1.83048 0.172613i
\(386\) −156.341 −0.0206154
\(387\) 0 0
\(388\) −3105.08 + 5378.16i −0.406280 + 0.703697i
\(389\) 5868.59 10164.7i 0.764908 1.32486i −0.175387 0.984500i \(-0.556118\pi\)
0.940295 0.340360i \(-0.110549\pi\)
\(390\) 0 0
\(391\) −6765.59 −0.875066
\(392\) 1332.28 253.519i 0.171658 0.0326649i
\(393\) 0 0
\(394\) 155.073 + 268.595i 0.0198286 + 0.0343442i
\(395\) 3027.11 5243.10i 0.385595 0.667871i
\(396\) 0 0
\(397\) −6640.71 11502.1i −0.839516 1.45408i −0.890300 0.455374i \(-0.849505\pi\)
0.0507841 0.998710i \(-0.483828\pi\)
\(398\) 270.955 0.0341250
\(399\) 0 0
\(400\) 1852.01 0.231501
\(401\) −3741.18 6479.91i −0.465899 0.806961i 0.533343 0.845899i \(-0.320936\pi\)
−0.999242 + 0.0389385i \(0.987602\pi\)
\(402\) 0 0
\(403\) 21.2979 36.8891i 0.00263257 0.00455975i
\(404\) 1236.99 + 2142.54i 0.152333 + 0.263849i
\(405\) 0 0
\(406\) −162.653 228.985i −0.0198826 0.0279909i
\(407\) −4193.27 −0.510694
\(408\) 0 0
\(409\) 6898.30 11948.2i 0.833983 1.44450i −0.0608735 0.998145i \(-0.519389\pi\)
0.894856 0.446355i \(-0.147278\pi\)
\(410\) −475.218 + 823.102i −0.0572423 + 0.0991466i
\(411\) 0 0
\(412\) 1184.88 0.141686
\(413\) −6514.21 + 14219.7i −0.776134 + 1.69421i
\(414\) 0 0
\(415\) 3765.75 + 6522.46i 0.445429 + 0.771506i
\(416\) 858.622 1487.18i 0.101196 0.175276i
\(417\) 0 0
\(418\) 378.154 + 654.982i 0.0442491 + 0.0766417i
\(419\) −9497.56 −1.10737 −0.553683 0.832728i \(-0.686778\pi\)
−0.553683 + 0.832728i \(0.686778\pi\)
\(420\) 0 0
\(421\) 624.367 0.0722797 0.0361399 0.999347i \(-0.488494\pi\)
0.0361399 + 0.999347i \(0.488494\pi\)
\(422\) −449.016 777.719i −0.0517957 0.0897127i
\(423\) 0 0
\(424\) 622.608 1078.39i 0.0713126 0.123517i
\(425\) −721.915 1250.39i −0.0823954 0.142713i
\(426\) 0 0
\(427\) −3630.82 5111.52i −0.411494 0.579306i
\(428\) 6759.75 0.763423
\(429\) 0 0
\(430\) 269.050 466.007i 0.0301738 0.0522625i
\(431\) −6698.64 + 11602.4i −0.748636 + 1.29668i 0.199840 + 0.979829i \(0.435958\pi\)
−0.948476 + 0.316848i \(0.897376\pi\)
\(432\) 0 0
\(433\) −14057.3 −1.56016 −0.780079 0.625681i \(-0.784821\pi\)
−0.780079 + 0.625681i \(0.784821\pi\)
\(434\) −5.34870 + 0.504377i −0.000591580 + 5.57854e-5i
\(435\) 0 0
\(436\) 5405.61 + 9362.79i 0.593766 + 1.02843i
\(437\) −3507.98 + 6075.99i −0.384003 + 0.665112i
\(438\) 0 0
\(439\) 8184.42 + 14175.8i 0.889798 + 1.54117i 0.840114 + 0.542409i \(0.182488\pi\)
0.0496832 + 0.998765i \(0.484179\pi\)
\(440\) −2965.22 −0.321275
\(441\) 0 0
\(442\) −440.494 −0.0474031
\(443\) −589.354 1020.79i −0.0632078 0.109479i 0.832690 0.553740i \(-0.186800\pi\)
−0.895898 + 0.444261i \(0.853466\pi\)
\(444\) 0 0
\(445\) 1355.80 2348.31i 0.144429 0.250159i
\(446\) −22.8033 39.4965i −0.00242101 0.00419331i
\(447\) 0 0
\(448\) 9007.56 849.404i 0.949926 0.0895772i
\(449\) 12400.9 1.30342 0.651709 0.758469i \(-0.274052\pi\)
0.651709 + 0.758469i \(0.274052\pi\)
\(450\) 0 0
\(451\) −9291.45 + 16093.3i −0.970105 + 1.68027i
\(452\) −4161.95 + 7208.71i −0.433101 + 0.750153i
\(453\) 0 0
\(454\) 565.484 0.0584570
\(455\) 4857.94 + 6839.07i 0.500535 + 0.704660i
\(456\) 0 0
\(457\) −4962.79 8595.81i −0.507986 0.879858i −0.999957 0.00924618i \(-0.997057\pi\)
0.491971 0.870611i \(-0.336277\pi\)
\(458\) 671.366 1162.84i 0.0684954 0.118637i
\(459\) 0 0
\(460\) −6850.21 11864.9i −0.694332 1.20262i
\(461\) 16010.3 1.61751 0.808755 0.588146i \(-0.200142\pi\)
0.808755 + 0.588146i \(0.200142\pi\)
\(462\) 0 0
\(463\) 17372.4 1.74377 0.871883 0.489714i \(-0.162899\pi\)
0.871883 + 0.489714i \(0.162899\pi\)
\(464\) −1911.27 3310.42i −0.191225 0.331212i
\(465\) 0 0
\(466\) −141.199 + 244.563i −0.0140363 + 0.0243115i
\(467\) 1054.03 + 1825.64i 0.104443 + 0.180900i 0.913510 0.406815i \(-0.133361\pi\)
−0.809068 + 0.587716i \(0.800027\pi\)
\(468\) 0 0
\(469\) −7494.00 + 16358.5i −0.737826 + 1.61059i
\(470\) 1201.05 0.117873
\(471\) 0 0
\(472\) 1669.58 2891.80i 0.162815 0.282004i
\(473\) 5260.45 9111.37i 0.511365 0.885711i
\(474\) 0 0
\(475\) −1497.26 −0.144629
\(476\) −4150.25 5842.77i −0.399635 0.562612i
\(477\) 0 0
\(478\) 772.293 + 1337.65i 0.0738992 + 0.127997i
\(479\) −1225.02 + 2121.80i −0.116853 + 0.202395i −0.918519 0.395377i \(-0.870614\pi\)
0.801666 + 0.597772i \(0.203947\pi\)
\(480\) 0 0
\(481\) −1266.32 2193.34i −0.120040 0.207916i
\(482\) 792.887 0.0749274
\(483\) 0 0
\(484\) −18309.9 −1.71956
\(485\) 4863.72 + 8424.21i 0.455361 + 0.788709i
\(486\) 0 0
\(487\) −322.618 + 558.791i −0.0300189 + 0.0519943i −0.880645 0.473778i \(-0.842890\pi\)
0.850626 + 0.525772i \(0.176223\pi\)
\(488\) 669.270 + 1159.21i 0.0620828 + 0.107531i
\(489\) 0 0
\(490\) 348.408 999.034i 0.0321214 0.0921056i
\(491\) −11766.1 −1.08146 −0.540731 0.841196i \(-0.681852\pi\)
−0.540731 + 0.841196i \(0.681852\pi\)
\(492\) 0 0
\(493\) −1490.03 + 2580.81i −0.136121 + 0.235769i
\(494\) −228.397 + 395.595i −0.0208018 + 0.0360297i
\(495\) 0 0
\(496\) −73.1159 −0.00661896
\(497\) −1815.63 + 171.212i −0.163868 + 0.0154526i
\(498\) 0 0
\(499\) 22.0104 + 38.1232i 0.00197459 + 0.00342010i 0.867011 0.498289i \(-0.166038\pi\)
−0.865036 + 0.501709i \(0.832705\pi\)
\(500\) −4707.59 + 8153.78i −0.421059 + 0.729296i
\(501\) 0 0
\(502\) −29.7200 51.4765i −0.00264236 0.00457671i
\(503\) −8290.27 −0.734880 −0.367440 0.930047i \(-0.619766\pi\)
−0.367440 + 0.930047i \(0.619766\pi\)
\(504\) 0 0
\(505\) 3875.19 0.341473
\(506\) 1038.28 + 1798.35i 0.0912195 + 0.157997i
\(507\) 0 0
\(508\) 1938.60 3357.76i 0.169314 0.293261i
\(509\) 3457.52 + 5988.60i 0.301084 + 0.521493i 0.976382 0.216052i \(-0.0693181\pi\)
−0.675298 + 0.737545i \(0.735985\pi\)
\(510\) 0 0
\(511\) 5478.36 11958.6i 0.474263 1.03526i
\(512\) −4925.45 −0.425148
\(513\) 0 0
\(514\) −86.7157 + 150.196i −0.00744137 + 0.0128888i
\(515\) 927.980 1607.31i 0.0794014 0.137527i
\(516\) 0 0
\(517\) 23483.0 1.99764
\(518\) −133.039 + 290.408i −0.0112845 + 0.0246328i
\(519\) 0 0
\(520\) −895.464 1550.99i −0.0755167 0.130799i
\(521\) 6699.64 11604.1i 0.563371 0.975788i −0.433828 0.900996i \(-0.642837\pi\)
0.997199 0.0747919i \(-0.0238293\pi\)
\(522\) 0 0
\(523\) 4968.50 + 8605.69i 0.415406 + 0.719504i 0.995471 0.0950662i \(-0.0303063\pi\)
−0.580065 + 0.814570i \(0.696973\pi\)
\(524\) −14719.7 −1.22716
\(525\) 0 0
\(526\) −227.988 −0.0188988
\(527\) 28.5007 + 49.3647i 0.00235581 + 0.00408038i
\(528\) 0 0
\(529\) −3548.17 + 6145.60i −0.291622 + 0.505104i
\(530\) −485.736 841.320i −0.0398095 0.0689521i
\(531\) 0 0
\(532\) −7399.15 + 697.733i −0.602996 + 0.0568620i
\(533\) −11223.7 −0.912104
\(534\) 0 0
\(535\) 5294.15 9169.74i 0.427825 0.741014i
\(536\) 1920.70 3326.75i 0.154779 0.268085i
\(537\) 0 0
\(538\) −689.435 −0.0552484
\(539\) 6812.07 19533.1i 0.544373 1.56095i
\(540\) 0 0
\(541\) −4643.08 8042.06i −0.368987 0.639103i 0.620421 0.784269i \(-0.286962\pi\)
−0.989407 + 0.145166i \(0.953628\pi\)
\(542\) 276.226 478.437i 0.0218910 0.0379163i
\(543\) 0 0
\(544\) 1149.00 + 1990.13i 0.0905570 + 0.156849i
\(545\) 16934.4 1.33099
\(546\) 0 0
\(547\) −16821.6 −1.31488 −0.657438 0.753508i \(-0.728360\pi\)
−0.657438 + 0.753508i \(0.728360\pi\)
\(548\) 2028.73 + 3513.87i 0.158144 + 0.273914i
\(549\) 0 0
\(550\) −221.577 + 383.782i −0.0171783 + 0.0297537i
\(551\) 1545.17 + 2676.32i 0.119467 + 0.206924i
\(552\) 0 0
\(553\) −5221.84 7351.37i −0.401546 0.565302i
\(554\) −1812.83 −0.139025
\(555\) 0 0
\(556\) 8994.69 15579.3i 0.686079 1.18832i
\(557\) 902.972 1563.99i 0.0686897 0.118974i −0.829635 0.558306i \(-0.811451\pi\)
0.898325 + 0.439332i \(0.144785\pi\)
\(558\) 0 0
\(559\) 6354.40 0.480792
\(560\) 5997.18 13091.1i 0.452548 0.987859i
\(561\) 0 0
\(562\) −338.694 586.635i −0.0254216 0.0440315i
\(563\) 6107.45 10578.4i 0.457190 0.791877i −0.541621 0.840623i \(-0.682189\pi\)
0.998811 + 0.0487460i \(0.0155225\pi\)
\(564\) 0 0
\(565\) 6519.17 + 11291.5i 0.485423 + 0.840776i
\(566\) 439.050 0.0326054
\(567\) 0 0
\(568\) 389.338 0.0287610
\(569\) 2141.89 + 3709.86i 0.157808 + 0.273331i 0.934078 0.357070i \(-0.116224\pi\)
−0.776270 + 0.630400i \(0.782891\pi\)
\(570\) 0 0
\(571\) −3179.97 + 5507.87i −0.233060 + 0.403673i −0.958707 0.284395i \(-0.908207\pi\)
0.725647 + 0.688067i \(0.241541\pi\)
\(572\) −8720.25 15103.9i −0.637433 1.10407i
\(573\) 0 0
\(574\) 819.764 + 1154.07i 0.0596103 + 0.0839201i
\(575\) −4110.95 −0.298153
\(576\) 0 0
\(577\) −7234.36 + 12530.3i −0.521959 + 0.904059i 0.477715 + 0.878515i \(0.341465\pi\)
−0.999674 + 0.0255444i \(0.991868\pi\)
\(578\) −314.656 + 545.001i −0.0226436 + 0.0392198i
\(579\) 0 0
\(580\) −6034.68 −0.432028
\(581\) 11168.0 1053.13i 0.797461 0.0751998i
\(582\) 0 0
\(583\) −9497.10 16449.5i −0.674665 1.16855i
\(584\) −1404.09 + 2431.96i −0.0994894 + 0.172321i
\(585\) 0 0
\(586\) −1020.67 1767.85i −0.0719513 0.124623i
\(587\) 11132.6 0.782777 0.391388 0.920226i \(-0.371995\pi\)
0.391388 + 0.920226i \(0.371995\pi\)
\(588\) 0 0
\(589\) 59.1108 0.00413517
\(590\) −1302.55 2256.07i −0.0908897 0.157426i
\(591\) 0 0
\(592\) −2173.65 + 3764.87i −0.150906 + 0.261377i
\(593\) −9887.81 17126.2i −0.684728 1.18598i −0.973522 0.228592i \(-0.926588\pi\)
0.288794 0.957391i \(-0.406746\pi\)
\(594\) 0 0
\(595\) −11176.3 + 1053.91i −0.770054 + 0.0726154i
\(596\) 11970.4 0.822696
\(597\) 0 0
\(598\) −627.098 + 1086.17i −0.0428829 + 0.0742753i
\(599\) −11945.5 + 20690.2i −0.814825 + 1.41132i 0.0946282 + 0.995513i \(0.469834\pi\)
−0.909453 + 0.415806i \(0.863500\pi\)
\(600\) 0 0
\(601\) 19395.5 1.31641 0.658204 0.752840i \(-0.271317\pi\)
0.658204 + 0.752840i \(0.271317\pi\)
\(602\) −464.118 653.391i −0.0314220 0.0442362i
\(603\) 0 0
\(604\) 6318.32 + 10943.7i 0.425644 + 0.737237i
\(605\) −14340.1 + 24837.8i −0.963648 + 1.66909i
\(606\) 0 0
\(607\) −7298.36 12641.1i −0.488025 0.845285i 0.511880 0.859057i \(-0.328949\pi\)
−0.999905 + 0.0137724i \(0.995616\pi\)
\(608\) 2383.04 0.158956
\(609\) 0 0
\(610\) 1044.28 0.0693142
\(611\) 7091.62 + 12283.0i 0.469552 + 0.813288i
\(612\) 0 0
\(613\) −989.898 + 1714.55i −0.0652229 + 0.112969i −0.896793 0.442451i \(-0.854109\pi\)
0.831570 + 0.555420i \(0.187442\pi\)
\(614\) 746.650 + 1293.24i 0.0490755 + 0.0850012i
\(615\) 0 0
\(616\) −1839.39 + 4015.16i −0.120310 + 0.262622i
\(617\) −16262.4 −1.06110 −0.530551 0.847653i \(-0.678015\pi\)
−0.530551 + 0.847653i \(0.678015\pi\)
\(618\) 0 0
\(619\) 6010.49 10410.5i 0.390278 0.675981i −0.602208 0.798339i \(-0.705712\pi\)
0.992486 + 0.122358i \(0.0390457\pi\)
\(620\) −57.7143 + 99.9642i −0.00373849 + 0.00647526i
\(621\) 0 0
\(622\) 296.127 0.0190894
\(623\) −2338.79 3292.58i −0.150404 0.211740i
\(624\) 0 0
\(625\) 9225.06 + 15978.3i 0.590404 + 1.02261i
\(626\) −1097.23 + 1900.45i −0.0700543 + 0.121338i
\(627\) 0 0
\(628\) 4620.82 + 8003.49i 0.293616 + 0.508557i
\(629\) 3389.16 0.214841
\(630\) 0 0
\(631\) 25347.6 1.59916 0.799582 0.600557i \(-0.205055\pi\)
0.799582 + 0.600557i \(0.205055\pi\)
\(632\) 962.542 + 1667.17i 0.0605821 + 0.104931i
\(633\) 0 0
\(634\) −754.317 + 1306.51i −0.0472519 + 0.0818428i
\(635\) −3036.58 5259.51i −0.189769 0.328689i
\(636\) 0 0
\(637\) 12274.2 2335.66i 0.763454 0.145278i
\(638\) 914.669 0.0567588
\(639\) 0 0
\(640\) −3098.24 + 5366.31i −0.191358 + 0.331441i
\(641\) −2555.80 + 4426.78i −0.157485 + 0.272772i −0.933961 0.357374i \(-0.883672\pi\)
0.776476 + 0.630147i \(0.217005\pi\)
\(642\) 0 0
\(643\) −10931.3 −0.670435 −0.335217 0.942141i \(-0.608810\pi\)
−0.335217 + 0.942141i \(0.608810\pi\)
\(644\) −20315.5 + 1915.73i −1.24308 + 0.117221i
\(645\) 0 0
\(646\) −305.639 529.382i −0.0186149 0.0322419i
\(647\) −9203.06 + 15940.2i −0.559211 + 0.968582i 0.438352 + 0.898804i \(0.355563\pi\)
−0.997563 + 0.0697783i \(0.977771\pi\)
\(648\) 0 0
\(649\) −25467.3 44110.7i −1.54034 2.66795i
\(650\) −267.655 −0.0161512
\(651\) 0 0
\(652\) 9175.91 0.551160
\(653\) 9960.71 + 17252.5i 0.596926 + 1.03391i 0.993272 + 0.115805i \(0.0369447\pi\)
−0.396346 + 0.918101i \(0.629722\pi\)
\(654\) 0 0
\(655\) −11528.3 + 19967.6i −0.687707 + 1.19114i
\(656\) 9632.74 + 16684.4i 0.573316 + 0.993012i
\(657\) 0 0
\(658\) 745.040 1626.33i 0.0441408 0.0963542i
\(659\) 18858.8 1.11477 0.557385 0.830254i \(-0.311805\pi\)
0.557385 + 0.830254i \(0.311805\pi\)
\(660\) 0 0
\(661\) −12916.0 + 22371.2i −0.760023 + 1.31640i 0.182815 + 0.983147i \(0.441479\pi\)
−0.942838 + 0.333251i \(0.891854\pi\)
\(662\) 378.718 655.960i 0.0222346 0.0385115i
\(663\) 0 0
\(664\) −2394.82 −0.139965
\(665\) −4848.43 + 10583.6i −0.282728 + 0.617162i
\(666\) 0 0
\(667\) 4242.50 + 7348.22i 0.246282 + 0.426573i
\(668\) 11473.5 19872.7i 0.664555 1.15104i
\(669\) 0 0
\(670\) −1498.46 2595.41i −0.0864037 0.149656i
\(671\) 20417.7 1.17469
\(672\) 0 0
\(673\) −16275.0 −0.932178 −0.466089 0.884738i \(-0.654337\pi\)
−0.466089 + 0.884738i \(0.654337\pi\)
\(674\) 479.498 + 830.515i 0.0274029 + 0.0474633i
\(675\) 0 0
\(676\) −3453.55 + 5981.73i −0.196493 + 0.340335i
\(677\) −13135.9 22752.0i −0.745720 1.29163i −0.949857 0.312683i \(-0.898772\pi\)
0.204137 0.978942i \(-0.434561\pi\)
\(678\) 0 0
\(679\) 14424.2 1360.19i 0.815242 0.0768766i
\(680\) 2396.60 0.135155
\(681\) 0 0
\(682\) 8.74769 15.1514i 0.000491153 0.000850702i
\(683\) −4036.14 + 6990.81i −0.226118 + 0.391648i −0.956654 0.291226i \(-0.905937\pi\)
0.730536 + 0.682874i \(0.239270\pi\)
\(684\) 0 0
\(685\) 6355.51 0.354499
\(686\) −1136.65 1091.50i −0.0632619 0.0607486i
\(687\) 0 0
\(688\) −5453.67 9446.04i −0.302208 0.523440i
\(689\) 5736.05 9935.13i 0.317164 0.549344i
\(690\) 0 0
\(691\) 12242.6 + 21204.9i 0.673997 + 1.16740i 0.976761 + 0.214332i \(0.0687575\pi\)
−0.302763 + 0.953066i \(0.597909\pi\)
\(692\) 15042.9 0.826364
\(693\) 0 0
\(694\) −24.7062 −0.00135135
\(695\) −14089.1 24403.0i −0.768962 1.33188i
\(696\) 0 0
\(697\) 7509.71 13007.2i 0.408107 0.706862i
\(698\) −447.440 774.989i −0.0242634 0.0420254i
\(699\) 0 0
\(700\) −2521.80 3550.22i −0.136164 0.191694i
\(701\) −778.448 −0.0419423 −0.0209712 0.999780i \(-0.506676\pi\)
−0.0209712 + 0.999780i \(0.506676\pi\)
\(702\) 0 0
\(703\) 1757.29 3043.72i 0.0942780 0.163294i
\(704\) −14731.7 + 25516.0i −0.788667 + 1.36601i
\(705\) 0 0
\(706\) 1768.93 0.0942985
\(707\) 2403.86 5247.35i 0.127873 0.279133i
\(708\) 0 0
\(709\) 12086.0 + 20933.6i 0.640197 + 1.10885i 0.985389 + 0.170322i \(0.0544806\pi\)
−0.345192 + 0.938532i \(0.612186\pi\)
\(710\) 151.874 263.053i 0.00802777 0.0139045i
\(711\) 0 0
\(712\) 431.109 + 746.703i 0.0226917 + 0.0393032i
\(713\) 162.297 0.00852466
\(714\) 0 0
\(715\) −27318.3 −1.42888
\(716\) 17022.0 + 29483.0i 0.888467 + 1.53887i
\(717\) 0 0
\(718\) 806.269 1396.50i 0.0419077 0.0725862i
\(719\) −40.9418 70.9132i −0.00212360 0.00367819i 0.864962 0.501838i \(-0.167343\pi\)
−0.867085 + 0.498160i \(0.834009\pi\)
\(720\) 0 0
\(721\) −1600.79 2253.61i −0.0826860 0.116406i
\(722\) 1067.63 0.0550318
\(723\) 0 0
\(724\) 1523.12 2638.13i 0.0781856 0.135421i
\(725\) −905.382 + 1568.17i −0.0463794 + 0.0803315i
\(726\) 0 0
\(727\) −32542.9 −1.66018 −0.830088 0.557632i \(-0.811710\pi\)
−0.830088 + 0.557632i \(0.811710\pi\)
\(728\) −2655.65 + 250.425i −0.135199 + 0.0127491i
\(729\) 0 0
\(730\) 1095.42 + 1897.33i 0.0555389 + 0.0961962i
\(731\) −4251.70 + 7364.16i −0.215123 + 0.372604i
\(732\) 0 0
\(733\) 2534.47 + 4389.83i 0.127712 + 0.221203i 0.922790 0.385304i \(-0.125903\pi\)
−0.795078 + 0.606507i \(0.792570\pi\)
\(734\) −204.631 −0.0102903
\(735\) 0 0
\(736\) 6542.98 0.327687
\(737\) −29297.8 50745.3i −1.46431 2.53627i
\(738\) 0 0
\(739\) 19214.2 33280.0i 0.956437 1.65660i 0.225392 0.974268i \(-0.427634\pi\)
0.731045 0.682329i \(-0.239033\pi\)
\(740\) 3431.55 + 5943.62i 0.170468 + 0.295259i
\(741\) 0 0
\(742\) −1440.53 + 135.841i −0.0712717 + 0.00672086i
\(743\) −21592.9 −1.06617 −0.533086 0.846061i \(-0.678968\pi\)
−0.533086 + 0.846061i \(0.678968\pi\)
\(744\) 0 0
\(745\) 9375.07 16238.1i 0.461042 0.798548i
\(746\) 165.445 286.560i 0.00811982 0.0140639i
\(747\) 0 0
\(748\) 23338.7 1.14084
\(749\) −9132.55 12856.9i −0.445522 0.627212i
\(750\) 0 0
\(751\) −4056.30 7025.72i −0.197093 0.341374i 0.750492 0.660880i \(-0.229817\pi\)
−0.947585 + 0.319505i \(0.896483\pi\)
\(752\) 12172.8 21083.9i 0.590287 1.02241i
\(753\) 0 0
\(754\) 276.220 + 478.428i 0.0133413 + 0.0231078i
\(755\) 19793.7 0.954129
\(756\) 0 0
\(757\) 3108.01 0.149224 0.0746120 0.997213i \(-0.476228\pi\)
0.0746120 + 0.997213i \(0.476228\pi\)
\(758\) −165.996 287.513i −0.00795414 0.0137770i
\(759\) 0 0
\(760\) 1242.64 2152.32i 0.0593098 0.102728i
\(761\) −3605.96 6245.71i −0.171769 0.297512i 0.767269 0.641325i \(-0.221615\pi\)
−0.939038 + 0.343812i \(0.888282\pi\)
\(762\) 0 0
\(763\) 10504.8 22930.7i 0.498425 1.08800i
\(764\) 3058.77 0.144846
\(765\) 0 0
\(766\) −43.8313 + 75.9181i −0.00206748 + 0.00358098i
\(767\) 15381.7 26641.9i 0.724123 1.25422i
\(768\) 0 0
\(769\) −7533.07 −0.353250 −0.176625 0.984278i \(-0.556518\pi\)
−0.176625 + 0.984278i \(0.556518\pi\)
\(770\) 1995.30 + 2809.01i 0.0933838 + 0.131467i
\(771\) 0 0
\(772\) 2501.50 + 4332.73i 0.116621 + 0.201993i
\(773\) −12416.3 + 21505.7i −0.577728 + 1.00065i 0.418012 + 0.908442i \(0.362727\pi\)
−0.995739 + 0.0922122i \(0.970606\pi\)
\(774\) 0 0
\(775\) 17.3178 + 29.9952i 0.000802674 + 0.00139027i
\(776\) −3093.08 −0.143086
\(777\) 0 0
\(778\) 2911.66 0.134175
\(779\) −7787.61 13488.5i −0.358177 0.620381i
\(780\) 0 0
\(781\) 2969.43 5143.20i 0.136049 0.235644i
\(782\) −839.177 1453.50i −0.0383746 0.0664667i
\(783\) 0 0
\(784\) −14006.4 16241.4i −0.638045 0.739860i
\(785\) 14475.9 0.658173