Properties

Label 225.4.p.b.32.11
Level $225$
Weight $4$
Character 225.32
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.p (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 32.11
Character \(\chi\) \(=\) 225.32
Dual form 225.4.p.b.218.11

$q$-expansion

\(f(q)\) \(=\) \(q+(2.57169 + 0.689083i) q^{2} +(0.974542 + 5.10395i) q^{3} +(-0.789441 - 0.455784i) q^{4} +(-1.01082 + 13.7973i) q^{6} +(0.400135 - 1.49332i) q^{7} +(-16.7770 - 16.7770i) q^{8} +(-25.1005 + 9.94802i) q^{9} +O(q^{10})\) \(q+(2.57169 + 0.689083i) q^{2} +(0.974542 + 5.10395i) q^{3} +(-0.789441 - 0.455784i) q^{4} +(-1.01082 + 13.7973i) q^{6} +(0.400135 - 1.49332i) q^{7} +(-16.7770 - 16.7770i) q^{8} +(-25.1005 + 9.94802i) q^{9} +(-61.6602 + 35.5995i) q^{11} +(1.55695 - 4.47344i) q^{12} +(10.3499 + 38.6262i) q^{13} +(2.05805 - 3.56464i) q^{14} +(-27.9383 - 48.3905i) q^{16} +(-45.8839 + 45.8839i) q^{17} +(-71.4058 + 8.28689i) q^{18} +3.05396i q^{19} +(8.01179 + 0.586960i) q^{21} +(-183.102 + 49.0620i) q^{22} +(140.507 - 37.6487i) q^{23} +(69.2790 - 101.979i) q^{24} +106.467i q^{26} +(-75.2357 - 118.417i) q^{27} +(-0.996515 + 0.996515i) q^{28} +(-91.6343 - 158.715i) q^{29} +(-89.3086 + 154.687i) q^{31} +(10.6229 + 39.6453i) q^{32} +(-241.788 - 280.017i) q^{33} +(-149.617 + 86.3814i) q^{34} +(24.3495 + 3.58705i) q^{36} +(26.4034 + 26.4034i) q^{37} +(-2.10443 + 7.85383i) q^{38} +(-187.060 + 90.4680i) q^{39} +(79.5097 + 45.9049i) q^{41} +(20.1994 + 7.03027i) q^{42} +(48.4988 + 12.9952i) q^{43} +64.9027 q^{44} +387.283 q^{46} +(-143.078 - 38.3375i) q^{47} +(219.755 - 189.754i) q^{48} +(294.977 + 170.305i) q^{49} +(-278.905 - 189.473i) q^{51} +(9.43460 - 35.2104i) q^{52} +(182.516 + 182.516i) q^{53} +(-111.884 - 356.376i) q^{54} +(-31.7665 + 18.3404i) q^{56} +(-15.5872 + 2.97621i) q^{57} +(-126.287 - 471.310i) q^{58} +(128.795 - 223.079i) q^{59} +(152.085 + 263.419i) q^{61} +(-336.266 + 336.266i) q^{62} +(4.81201 + 41.4638i) q^{63} +556.288i q^{64} +(-428.851 - 886.730i) q^{66} +(231.496 - 62.0292i) q^{67} +(57.1357 - 15.3095i) q^{68} +(329.086 + 680.448i) q^{69} +470.304i q^{71} +(588.009 + 254.214i) q^{72} +(-445.386 + 445.386i) q^{73} +(49.7072 + 86.0954i) q^{74} +(1.39194 - 2.41092i) q^{76} +(28.4892 + 106.323i) q^{77} +(-543.400 + 103.756i) q^{78} +(134.691 - 77.7637i) q^{79} +(531.074 - 499.401i) q^{81} +(172.842 + 172.842i) q^{82} +(-216.080 + 806.421i) q^{83} +(-6.05730 - 4.11501i) q^{84} +(115.769 + 66.8393i) q^{86} +(720.773 - 622.371i) q^{87} +(1631.73 + 437.220i) q^{88} -1352.69 q^{89} +61.8228 q^{91} +(-128.081 - 34.3193i) q^{92} +(-876.550 - 305.077i) q^{93} +(-341.534 - 197.184i) q^{94} +(-191.995 + 92.8548i) q^{96} +(77.0607 - 287.595i) q^{97} +(641.235 + 641.235i) q^{98} +(1193.56 - 1506.96i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} + O(q^{10}) \) \( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.57169 + 0.689083i 0.909230 + 0.243628i 0.682976 0.730441i \(-0.260685\pi\)
0.226254 + 0.974068i \(0.427352\pi\)
\(3\) 0.974542 + 5.10395i 0.187551 + 0.982255i
\(4\) −0.789441 0.455784i −0.0986801 0.0569730i
\(5\) 0 0
\(6\) −1.01082 + 13.7973i −0.0687776 + 0.938788i
\(7\) 0.400135 1.49332i 0.0216052 0.0806319i −0.954281 0.298909i \(-0.903377\pi\)
0.975887 + 0.218278i \(0.0700438\pi\)
\(8\) −16.7770 16.7770i −0.741445 0.741445i
\(9\) −25.1005 + 9.94802i −0.929650 + 0.368445i
\(10\) 0 0
\(11\) −61.6602 + 35.5995i −1.69011 + 0.975787i −0.735696 + 0.677312i \(0.763145\pi\)
−0.954417 + 0.298475i \(0.903522\pi\)
\(12\) 1.55695 4.47344i 0.0374545 0.107614i
\(13\) 10.3499 + 38.6262i 0.220810 + 0.824076i 0.984040 + 0.177948i \(0.0569460\pi\)
−0.763229 + 0.646128i \(0.776387\pi\)
\(14\) 2.05805 3.56464i 0.0392883 0.0680493i
\(15\) 0 0
\(16\) −27.9383 48.3905i −0.436535 0.756101i
\(17\) −45.8839 + 45.8839i −0.654616 + 0.654616i −0.954101 0.299485i \(-0.903185\pi\)
0.299485 + 0.954101i \(0.403185\pi\)
\(18\) −71.4058 + 8.28689i −0.935029 + 0.108513i
\(19\) 3.05396i 0.0368750i 0.999830 + 0.0184375i \(0.00586918\pi\)
−0.999830 + 0.0184375i \(0.994131\pi\)
\(20\) 0 0
\(21\) 8.01179 + 0.586960i 0.0832531 + 0.00609930i
\(22\) −183.102 + 49.0620i −1.77443 + 0.475457i
\(23\) 140.507 37.6487i 1.27381 0.341317i 0.442322 0.896856i \(-0.354155\pi\)
0.831490 + 0.555540i \(0.187488\pi\)
\(24\) 69.2790 101.979i 0.589230 0.867347i
\(25\) 0 0
\(26\) 106.467i 0.803070i
\(27\) −75.2357 118.417i −0.536263 0.844051i
\(28\) −0.996515 + 0.996515i −0.00672584 + 0.00672584i
\(29\) −91.6343 158.715i −0.586761 1.01630i −0.994653 0.103269i \(-0.967070\pi\)
0.407893 0.913030i \(-0.366264\pi\)
\(30\) 0 0
\(31\) −89.3086 + 154.687i −0.517429 + 0.896214i 0.482366 + 0.875970i \(0.339778\pi\)
−0.999795 + 0.0202438i \(0.993556\pi\)
\(32\) 10.6229 + 39.6453i 0.0586839 + 0.219011i
\(33\) −241.788 280.017i −1.27545 1.47711i
\(34\) −149.617 + 86.3814i −0.754679 + 0.435714i
\(35\) 0 0
\(36\) 24.3495 + 3.58705i 0.112729 + 0.0166067i
\(37\) 26.4034 + 26.4034i 0.117316 + 0.117316i 0.763328 0.646012i \(-0.223564\pi\)
−0.646012 + 0.763328i \(0.723564\pi\)
\(38\) −2.10443 + 7.85383i −0.00898377 + 0.0335279i
\(39\) −187.060 + 90.4680i −0.768039 + 0.371448i
\(40\) 0 0
\(41\) 79.5097 + 45.9049i 0.302862 + 0.174857i 0.643728 0.765255i \(-0.277387\pi\)
−0.340866 + 0.940112i \(0.610720\pi\)
\(42\) 20.1994 + 7.03027i 0.0742103 + 0.0258284i
\(43\) 48.4988 + 12.9952i 0.172000 + 0.0460872i 0.343791 0.939046i \(-0.388289\pi\)
−0.171791 + 0.985133i \(0.554955\pi\)
\(44\) 64.9027 0.222374
\(45\) 0 0
\(46\) 387.283 1.24134
\(47\) −143.078 38.3375i −0.444043 0.118981i 0.0298680 0.999554i \(-0.490491\pi\)
−0.473911 + 0.880573i \(0.657158\pi\)
\(48\) 219.755 189.754i 0.660812 0.570596i
\(49\) 294.977 + 170.305i 0.859991 + 0.496516i
\(50\) 0 0
\(51\) −278.905 189.473i −0.765774 0.520226i
\(52\) 9.43460 35.2104i 0.0251605 0.0939001i
\(53\) 182.516 + 182.516i 0.473029 + 0.473029i 0.902893 0.429865i \(-0.141439\pi\)
−0.429865 + 0.902893i \(0.641439\pi\)
\(54\) −111.884 356.376i −0.281953 0.898085i
\(55\) 0 0
\(56\) −31.7665 + 18.3404i −0.0758032 + 0.0437650i
\(57\) −15.5872 + 2.97621i −0.0362207 + 0.00691594i
\(58\) −126.287 471.310i −0.285902 1.06700i
\(59\) 128.795 223.079i 0.284197 0.492243i −0.688217 0.725505i \(-0.741606\pi\)
0.972414 + 0.233261i \(0.0749397\pi\)
\(60\) 0 0
\(61\) 152.085 + 263.419i 0.319221 + 0.552906i 0.980326 0.197387i \(-0.0632455\pi\)
−0.661105 + 0.750293i \(0.729912\pi\)
\(62\) −336.266 + 336.266i −0.688805 + 0.688805i
\(63\) 4.81201 + 41.4638i 0.00962311 + 0.0829197i
\(64\) 556.288i 1.08650i
\(65\) 0 0
\(66\) −428.851 886.730i −0.799816 1.65377i
\(67\) 231.496 62.0292i 0.422116 0.113106i −0.0415072 0.999138i \(-0.513216\pi\)
0.463623 + 0.886033i \(0.346549\pi\)
\(68\) 57.1357 15.3095i 0.101893 0.0273021i
\(69\) 329.086 + 680.448i 0.574164 + 1.18719i
\(70\) 0 0
\(71\) 470.304i 0.786124i 0.919512 + 0.393062i \(0.128584\pi\)
−0.919512 + 0.393062i \(0.871416\pi\)
\(72\) 588.009 + 254.214i 0.962466 + 0.416102i
\(73\) −445.386 + 445.386i −0.714089 + 0.714089i −0.967388 0.253299i \(-0.918484\pi\)
0.253299 + 0.967388i \(0.418484\pi\)
\(74\) 49.7072 + 86.0954i 0.0780858 + 0.135249i
\(75\) 0 0
\(76\) 1.39194 2.41092i 0.00210088 0.00363883i
\(77\) 28.4892 + 106.323i 0.0421642 + 0.157359i
\(78\) −543.400 + 103.756i −0.788820 + 0.150616i
\(79\) 134.691 77.7637i 0.191821 0.110748i −0.401014 0.916072i \(-0.631342\pi\)
0.592835 + 0.805324i \(0.298009\pi\)
\(80\) 0 0
\(81\) 531.074 499.401i 0.728496 0.685050i
\(82\) 172.842 + 172.842i 0.232771 + 0.232771i
\(83\) −216.080 + 806.421i −0.285757 + 1.06646i 0.662527 + 0.749038i \(0.269484\pi\)
−0.948284 + 0.317422i \(0.897183\pi\)
\(84\) −6.05730 4.11501i −0.00786793 0.00534506i
\(85\) 0 0
\(86\) 115.769 + 66.8393i 0.145159 + 0.0838078i
\(87\) 720.773 622.371i 0.888218 0.766956i
\(88\) 1631.73 + 437.220i 1.97662 + 0.529634i
\(89\) −1352.69 −1.61107 −0.805535 0.592549i \(-0.798122\pi\)
−0.805535 + 0.592549i \(0.798122\pi\)
\(90\) 0 0
\(91\) 61.8228 0.0712174
\(92\) −128.081 34.3193i −0.145146 0.0388917i
\(93\) −876.550 305.077i −0.977354 0.340162i
\(94\) −341.534 197.184i −0.374750 0.216362i
\(95\) 0 0
\(96\) −191.995 + 92.8548i −0.204119 + 0.0987183i
\(97\) 77.0607 287.595i 0.0806632 0.301039i −0.913794 0.406177i \(-0.866862\pi\)
0.994458 + 0.105138i \(0.0335283\pi\)
\(98\) 641.235 + 641.235i 0.660965 + 0.660965i
\(99\) 1193.56 1506.96i 1.21169 1.52985i
\(100\) 0 0
\(101\) −1036.67 + 598.524i −1.02132 + 0.589657i −0.914485 0.404620i \(-0.867404\pi\)
−0.106831 + 0.994277i \(0.534070\pi\)
\(102\) −586.694 679.455i −0.569523 0.659569i
\(103\) −122.996 459.029i −0.117662 0.439121i 0.881810 0.471604i \(-0.156325\pi\)
−0.999472 + 0.0324837i \(0.989658\pi\)
\(104\) 474.392 821.672i 0.447288 0.774726i
\(105\) 0 0
\(106\) 343.607 + 595.144i 0.314849 + 0.545335i
\(107\) 1085.11 1085.11i 0.980391 0.980391i −0.0194207 0.999811i \(-0.506182\pi\)
0.999811 + 0.0194207i \(0.00618219\pi\)
\(108\) 5.42153 + 127.774i 0.00483044 + 0.113843i
\(109\) 838.547i 0.736865i 0.929655 + 0.368432i \(0.120105\pi\)
−0.929655 + 0.368432i \(0.879895\pi\)
\(110\) 0 0
\(111\) −109.030 + 160.493i −0.0932314 + 0.137237i
\(112\) −83.4417 + 22.3581i −0.0703973 + 0.0188629i
\(113\) 122.646 32.8629i 0.102102 0.0273582i −0.207406 0.978255i \(-0.566502\pi\)
0.309508 + 0.950897i \(0.399836\pi\)
\(114\) −42.1364 3.08700i −0.0346178 0.00253618i
\(115\) 0 0
\(116\) 167.062i 0.133718i
\(117\) −644.042 866.578i −0.508903 0.684745i
\(118\) 484.939 484.939i 0.378324 0.378324i
\(119\) 50.1597 + 86.8792i 0.0386398 + 0.0669261i
\(120\) 0 0
\(121\) 1869.15 3237.47i 1.40432 2.43236i
\(122\) 209.598 + 782.230i 0.155542 + 0.580490i
\(123\) −156.811 + 450.549i −0.114952 + 0.330282i
\(124\) 141.008 81.4108i 0.102120 0.0589589i
\(125\) 0 0
\(126\) −16.1970 + 109.948i −0.0114519 + 0.0777376i
\(127\) 1460.03 + 1460.03i 1.02013 + 1.02013i 0.999793 + 0.0203375i \(0.00647408\pi\)
0.0203375 + 0.999793i \(0.493526\pi\)
\(128\) −298.345 + 1113.44i −0.206017 + 0.768867i
\(129\) −19.0628 + 260.199i −0.0130107 + 0.177591i
\(130\) 0 0
\(131\) −1319.03 761.541i −0.879725 0.507909i −0.00915702 0.999958i \(-0.502915\pi\)
−0.870568 + 0.492049i \(0.836248\pi\)
\(132\) 63.2504 + 331.260i 0.0417064 + 0.218428i
\(133\) 4.56054 + 1.22199i 0.00297330 + 0.000796694i
\(134\) 638.080 0.411356
\(135\) 0 0
\(136\) 1539.59 0.970724
\(137\) −1157.32 310.102i −0.721724 0.193385i −0.120783 0.992679i \(-0.538541\pi\)
−0.600941 + 0.799293i \(0.705207\pi\)
\(138\) 377.423 + 1976.67i 0.232815 + 1.21931i
\(139\) −261.821 151.163i −0.159765 0.0922406i 0.417986 0.908454i \(-0.362736\pi\)
−0.577751 + 0.816213i \(0.696070\pi\)
\(140\) 0 0
\(141\) 56.2375 767.621i 0.0335890 0.458478i
\(142\) −324.078 + 1209.48i −0.191521 + 0.714768i
\(143\) −2013.25 2013.25i −1.17732 1.17732i
\(144\) 1182.65 + 936.697i 0.684407 + 0.542070i
\(145\) 0 0
\(146\) −1452.30 + 838.488i −0.823243 + 0.475299i
\(147\) −581.760 + 1671.52i −0.326413 + 0.937852i
\(148\) −8.80967 32.8781i −0.00489291 0.0182606i
\(149\) −1115.11 + 1931.43i −0.613110 + 1.06194i 0.377603 + 0.925968i \(0.376748\pi\)
−0.990713 + 0.135970i \(0.956585\pi\)
\(150\) 0 0
\(151\) 837.917 + 1451.32i 0.451581 + 0.782161i 0.998484 0.0550344i \(-0.0175268\pi\)
−0.546903 + 0.837196i \(0.684194\pi\)
\(152\) 51.2362 51.2362i 0.0273408 0.0273408i
\(153\) 695.256 1608.16i 0.367374 0.849754i
\(154\) 293.062i 0.153348i
\(155\) 0 0
\(156\) 188.906 + 13.8397i 0.0969527 + 0.00710296i
\(157\) 468.645 125.573i 0.238229 0.0638333i −0.137729 0.990470i \(-0.543980\pi\)
0.375958 + 0.926637i \(0.377314\pi\)
\(158\) 399.969 107.171i 0.201391 0.0539626i
\(159\) −753.683 + 1109.42i −0.375918 + 0.553352i
\(160\) 0 0
\(161\) 224.886i 0.110084i
\(162\) 1709.89 918.352i 0.829268 0.445386i
\(163\) 2513.57 2513.57i 1.20784 1.20784i 0.236117 0.971725i \(-0.424125\pi\)
0.971725 0.236117i \(-0.0758749\pi\)
\(164\) −41.8454 72.4784i −0.0199243 0.0345098i
\(165\) 0 0
\(166\) −1111.38 + 1924.97i −0.519638 + 0.900039i
\(167\) −436.714 1629.84i −0.202359 0.755213i −0.990238 0.139384i \(-0.955488\pi\)
0.787880 0.615829i \(-0.211179\pi\)
\(168\) −124.566 144.261i −0.0572054 0.0662500i
\(169\) 517.792 298.948i 0.235682 0.136071i
\(170\) 0 0
\(171\) −30.3808 76.6559i −0.0135864 0.0342808i
\(172\) −32.3639 32.3639i −0.0143472 0.0143472i
\(173\) −352.691 + 1316.26i −0.154998 + 0.578460i 0.844108 + 0.536174i \(0.180131\pi\)
−0.999106 + 0.0422861i \(0.986536\pi\)
\(174\) 2282.47 1103.87i 0.994446 0.480945i
\(175\) 0 0
\(176\) 3445.36 + 1989.18i 1.47559 + 0.851931i
\(177\) 1264.10 + 439.961i 0.536810 + 0.186833i
\(178\) −3478.71 932.117i −1.46483 0.392501i
\(179\) −2448.92 −1.02257 −0.511287 0.859410i \(-0.670831\pi\)
−0.511287 + 0.859410i \(0.670831\pi\)
\(180\) 0 0
\(181\) −2882.13 −1.18357 −0.591787 0.806095i \(-0.701577\pi\)
−0.591787 + 0.806095i \(0.701577\pi\)
\(182\) 158.989 + 42.6010i 0.0647531 + 0.0173505i
\(183\) −1196.26 + 1032.95i −0.483225 + 0.417254i
\(184\) −2988.91 1725.65i −1.19753 0.691394i
\(185\) 0 0
\(186\) −2043.99 1388.58i −0.805767 0.547396i
\(187\) 1195.76 4462.65i 0.467609 1.74514i
\(188\) 95.4776 + 95.4776i 0.0370395 + 0.0370395i
\(189\) −206.939 + 64.9684i −0.0796435 + 0.0250040i
\(190\) 0 0
\(191\) 1454.82 839.943i 0.551138 0.318200i −0.198443 0.980112i \(-0.563588\pi\)
0.749581 + 0.661913i \(0.230255\pi\)
\(192\) −2839.26 + 542.125i −1.06722 + 0.203774i
\(193\) −50.4130 188.144i −0.0188021 0.0701705i 0.955887 0.293733i \(-0.0948978\pi\)
−0.974689 + 0.223563i \(0.928231\pi\)
\(194\) 396.353 686.503i 0.146683 0.254062i
\(195\) 0 0
\(196\) −155.244 268.891i −0.0565760 0.0979924i
\(197\) −3351.77 + 3351.77i −1.21220 + 1.21220i −0.241900 + 0.970301i \(0.577770\pi\)
−0.970301 + 0.241900i \(0.922230\pi\)
\(198\) 4107.89 3052.99i 1.47442 1.09579i
\(199\) 1702.11i 0.606327i 0.952939 + 0.303163i \(0.0980428\pi\)
−0.952939 + 0.303163i \(0.901957\pi\)
\(200\) 0 0
\(201\) 542.196 + 1121.09i 0.190267 + 0.393412i
\(202\) −3078.44 + 824.865i −1.07227 + 0.287313i
\(203\) −273.679 + 73.3321i −0.0946232 + 0.0253542i
\(204\) 133.820 + 276.698i 0.0459278 + 0.0949644i
\(205\) 0 0
\(206\) 1265.23i 0.427928i
\(207\) −3152.26 + 2342.76i −1.05844 + 0.786635i
\(208\) 1579.98 1579.98i 0.526693 0.526693i
\(209\) −108.719 188.307i −0.0359822 0.0623230i
\(210\) 0 0
\(211\) −629.684 + 1090.65i −0.205447 + 0.355844i −0.950275 0.311412i \(-0.899198\pi\)
0.744828 + 0.667256i \(0.232531\pi\)
\(212\) −60.8978 227.274i −0.0197287 0.0736283i
\(213\) −2400.41 + 458.331i −0.772174 + 0.147438i
\(214\) 3538.31 2042.84i 1.13025 0.652551i
\(215\) 0 0
\(216\) −724.454 + 3248.91i −0.228207 + 1.02343i
\(217\) 195.262 + 195.262i 0.0610842 + 0.0610842i
\(218\) −577.828 + 2156.48i −0.179520 + 0.669980i
\(219\) −2707.27 1839.18i −0.835345 0.567489i
\(220\) 0 0
\(221\) −2247.21 1297.43i −0.684000 0.394907i
\(222\) −390.985 + 337.607i −0.118203 + 0.102066i
\(223\) 291.153 + 78.0142i 0.0874307 + 0.0234270i 0.302269 0.953223i \(-0.402256\pi\)
−0.214839 + 0.976650i \(0.568923\pi\)
\(224\) 63.4538 0.0189272
\(225\) 0 0
\(226\) 338.053 0.0994996
\(227\) −4581.23 1227.54i −1.33950 0.358918i −0.483252 0.875481i \(-0.660545\pi\)
−0.856249 + 0.516563i \(0.827211\pi\)
\(228\) 13.6617 + 4.75486i 0.00396828 + 0.00138113i
\(229\) −832.697 480.758i −0.240289 0.138731i 0.375021 0.927017i \(-0.377636\pi\)
−0.615310 + 0.788286i \(0.710969\pi\)
\(230\) 0 0
\(231\) −514.904 + 249.024i −0.146659 + 0.0709288i
\(232\) −1125.42 + 4200.11i −0.318479 + 1.18858i
\(233\) −3014.81 3014.81i −0.847668 0.847668i 0.142174 0.989842i \(-0.454591\pi\)
−0.989842 + 0.142174i \(0.954591\pi\)
\(234\) −1059.13 2672.37i −0.295887 0.746574i
\(235\) 0 0
\(236\) −203.351 + 117.405i −0.0560891 + 0.0323831i
\(237\) 528.164 + 611.670i 0.144759 + 0.167647i
\(238\) 69.1284 + 257.991i 0.0188274 + 0.0702649i
\(239\) 2780.59 4816.13i 0.752559 1.30347i −0.194020 0.980998i \(-0.562153\pi\)
0.946579 0.322472i \(-0.104514\pi\)
\(240\) 0 0
\(241\) 1313.39 + 2274.85i 0.351049 + 0.608034i 0.986433 0.164161i \(-0.0524918\pi\)
−0.635385 + 0.772196i \(0.719158\pi\)
\(242\) 7037.77 7037.77i 1.86944 1.86944i
\(243\) 3066.47 + 2223.89i 0.809523 + 0.587088i
\(244\) 277.271i 0.0727478i
\(245\) 0 0
\(246\) −713.735 + 1050.62i −0.184984 + 0.272297i
\(247\) −117.963 + 31.6080i −0.0303878 + 0.00814239i
\(248\) 4093.52 1096.85i 1.04814 0.280848i
\(249\) −4326.51 316.969i −1.10113 0.0806710i
\(250\) 0 0
\(251\) 1692.12i 0.425520i −0.977104 0.212760i \(-0.931755\pi\)
0.977104 0.212760i \(-0.0682453\pi\)
\(252\) 15.0997 34.9264i 0.00377457 0.00873078i
\(253\) −7323.39 + 7323.39i −1.81983 + 1.81983i
\(254\) 2748.66 + 4760.82i 0.679002 + 1.17607i
\(255\) 0 0
\(256\) 690.649 1196.24i 0.168615 0.292051i
\(257\) 1728.24 + 6449.89i 0.419474 + 1.56550i 0.775702 + 0.631099i \(0.217396\pi\)
−0.356228 + 0.934399i \(0.615937\pi\)
\(258\) −228.322 + 656.017i −0.0550959 + 0.158302i
\(259\) 49.9937 28.8639i 0.0119940 0.00692476i
\(260\) 0 0
\(261\) 3878.97 + 3072.26i 0.919932 + 0.728613i
\(262\) −2867.37 2867.37i −0.676132 0.676132i
\(263\) 1216.37 4539.56i 0.285189 1.06434i −0.663513 0.748165i \(-0.730935\pi\)
0.948701 0.316174i \(-0.102398\pi\)
\(264\) −641.360 + 8754.33i −0.149519 + 2.04088i
\(265\) 0 0
\(266\) 10.8863 + 6.28518i 0.00250932 + 0.00144876i
\(267\) −1318.26 6904.07i −0.302157 1.58248i
\(268\) −211.024 56.5438i −0.0480983 0.0128879i
\(269\) 143.325 0.0324859 0.0162429 0.999868i \(-0.494829\pi\)
0.0162429 + 0.999868i \(0.494829\pi\)
\(270\) 0 0
\(271\) −7451.06 −1.67018 −0.835091 0.550111i \(-0.814585\pi\)
−0.835091 + 0.550111i \(0.814585\pi\)
\(272\) 3502.26 + 938.427i 0.780719 + 0.209193i
\(273\) 60.2489 + 315.540i 0.0133569 + 0.0699537i
\(274\) −2762.58 1594.97i −0.609100 0.351664i
\(275\) 0 0
\(276\) 50.3432 687.166i 0.0109794 0.149864i
\(277\) 569.759 2126.37i 0.123587 0.461232i −0.876199 0.481950i \(-0.839929\pi\)
0.999785 + 0.0207183i \(0.00659532\pi\)
\(278\) −569.160 569.160i −0.122791 0.122791i
\(279\) 702.865 4771.17i 0.150822 1.02381i
\(280\) 0 0
\(281\) −1756.49 + 1014.11i −0.372894 + 0.215291i −0.674722 0.738072i \(-0.735737\pi\)
0.301828 + 0.953362i \(0.402403\pi\)
\(282\) 673.580 1935.33i 0.142238 0.408679i
\(283\) 1500.74 + 5600.82i 0.315228 + 1.17645i 0.923777 + 0.382930i \(0.125085\pi\)
−0.608549 + 0.793516i \(0.708248\pi\)
\(284\) 214.357 371.277i 0.0447878 0.0775748i
\(285\) 0 0
\(286\) −3790.16 6564.75i −0.783626 1.35728i
\(287\) 100.365 100.365i 0.0206425 0.0206425i
\(288\) −661.033 889.441i −0.135249 0.181982i
\(289\) 702.339i 0.142955i
\(290\) 0 0
\(291\) 1542.97 + 113.041i 0.310826 + 0.0227717i
\(292\) 554.605 148.606i 0.111150 0.0297826i
\(293\) 6467.33 1732.92i 1.28951 0.345522i 0.452034 0.892001i \(-0.350699\pi\)
0.837473 + 0.546478i \(0.184032\pi\)
\(294\) −2647.92 + 3897.74i −0.525271 + 0.773200i
\(295\) 0 0
\(296\) 885.939i 0.173967i
\(297\) 8854.64 + 4623.26i 1.72996 + 0.903262i
\(298\) −4198.63 + 4198.63i −0.816175 + 0.816175i
\(299\) 2908.45 + 5037.58i 0.562542 + 0.974351i
\(300\) 0 0
\(301\) 38.8121 67.2245i 0.00743220 0.0128729i
\(302\) 1154.79 + 4309.73i 0.220035 + 0.821182i
\(303\) −4065.12 4707.84i −0.770742 0.892602i
\(304\) 147.782 85.3222i 0.0278812 0.0160972i
\(305\) 0 0
\(306\) 2896.14 3656.61i 0.541051 0.683120i
\(307\) −934.416 934.416i −0.173713 0.173713i 0.614895 0.788609i \(-0.289198\pi\)
−0.788609 + 0.614895i \(0.789198\pi\)
\(308\) 25.9698 96.9207i 0.00480444 0.0179304i
\(309\) 2222.99 1075.11i 0.409261 0.197932i
\(310\) 0 0
\(311\) 7156.17 + 4131.61i 1.30479 + 0.753320i 0.981221 0.192886i \(-0.0617847\pi\)
0.323566 + 0.946205i \(0.395118\pi\)
\(312\) 4656.08 + 1620.52i 0.844868 + 0.294051i
\(313\) 7870.92 + 2109.01i 1.42138 + 0.380856i 0.885972 0.463740i \(-0.153493\pi\)
0.535404 + 0.844596i \(0.320159\pi\)
\(314\) 1291.74 0.232157
\(315\) 0 0
\(316\) −141.774 −0.0252386
\(317\) 6286.01 + 1684.33i 1.11375 + 0.298427i 0.768350 0.640030i \(-0.221078\pi\)
0.345396 + 0.938457i \(0.387745\pi\)
\(318\) −2702.72 + 2333.74i −0.476608 + 0.411540i
\(319\) 11300.4 + 6524.27i 1.98338 + 1.14511i
\(320\) 0 0
\(321\) 6595.84 + 4480.87i 1.14687 + 0.779121i
\(322\) 154.965 578.338i 0.0268195 0.100092i
\(323\) −140.127 140.127i −0.0241390 0.0241390i
\(324\) −646.870 + 152.193i −0.110917 + 0.0260961i
\(325\) 0 0
\(326\) 8196.19 4732.07i 1.39247 0.803943i
\(327\) −4279.90 + 817.199i −0.723789 + 0.138199i
\(328\) −563.787 2104.08i −0.0949082 0.354202i
\(329\) −114.501 + 198.321i −0.0191873 + 0.0332334i
\(330\) 0 0
\(331\) −4213.66 7298.28i −0.699710 1.21193i −0.968567 0.248753i \(-0.919979\pi\)
0.268857 0.963180i \(-0.413354\pi\)
\(332\) 538.135 538.135i 0.0889579 0.0889579i
\(333\) −925.400 400.078i −0.152287 0.0658382i
\(334\) 4492.37i 0.735963i
\(335\) 0 0
\(336\) −195.432 404.093i −0.0317312 0.0656103i
\(337\) 496.961 133.160i 0.0803299 0.0215243i −0.218430 0.975853i \(-0.570094\pi\)
0.298760 + 0.954328i \(0.403427\pi\)
\(338\) 1537.60 411.999i 0.247439 0.0663012i
\(339\) 287.254 + 593.952i 0.0460221 + 0.0951594i
\(340\) 0 0
\(341\) 12717.4i 2.01960i
\(342\) −25.3078 218.070i −0.00400143 0.0344792i
\(343\) 747.314 747.314i 0.117642 0.117642i
\(344\) −595.643 1031.68i −0.0933573 0.161700i
\(345\) 0 0
\(346\) −1814.03 + 3141.99i −0.281857 + 0.488191i
\(347\) 216.702 + 808.744i 0.0335251 + 0.125117i 0.980660 0.195717i \(-0.0627034\pi\)
−0.947135 + 0.320834i \(0.896037\pi\)
\(348\) −852.674 + 162.809i −0.131345 + 0.0250789i
\(349\) −3705.03 + 2139.10i −0.568269 + 0.328090i −0.756458 0.654043i \(-0.773072\pi\)
0.188189 + 0.982133i \(0.439738\pi\)
\(350\) 0 0
\(351\) 3795.32 4131.67i 0.577149 0.628297i
\(352\) −2066.36 2066.36i −0.312891 0.312891i
\(353\) −967.800 + 3611.88i −0.145923 + 0.544592i 0.853790 + 0.520618i \(0.174298\pi\)
−0.999713 + 0.0239736i \(0.992368\pi\)
\(354\) 2947.70 + 2002.51i 0.442566 + 0.300656i
\(355\) 0 0
\(356\) 1067.87 + 616.535i 0.158980 + 0.0917874i
\(357\) −394.544 + 340.680i −0.0584916 + 0.0505062i
\(358\) −6297.86 1687.51i −0.929755 0.249127i
\(359\) −325.208 −0.0478102 −0.0239051 0.999714i \(-0.507610\pi\)
−0.0239051 + 0.999714i \(0.507610\pi\)
\(360\) 0 0
\(361\) 6849.67 0.998640
\(362\) −7411.94 1986.02i −1.07614 0.288351i
\(363\) 18345.4 + 6385.01i 2.65258 + 0.923212i
\(364\) −48.8054 28.1778i −0.00702774 0.00405747i
\(365\) 0 0
\(366\) −3788.20 + 1832.09i −0.541017 + 0.261653i
\(367\) 814.170 3038.52i 0.115802 0.432179i −0.883544 0.468349i \(-0.844849\pi\)
0.999346 + 0.0361698i \(0.0115157\pi\)
\(368\) −5747.35 5747.35i −0.814134 0.814134i
\(369\) −2452.40 361.275i −0.345980 0.0509680i
\(370\) 0 0
\(371\) 345.587 199.525i 0.0483611 0.0279213i
\(372\) 552.934 + 640.357i 0.0770654 + 0.0892500i
\(373\) −469.631 1752.69i −0.0651918 0.243299i 0.925639 0.378408i \(-0.123528\pi\)
−0.990831 + 0.135109i \(0.956862\pi\)
\(374\) 6150.27 10652.6i 0.850329 1.47281i
\(375\) 0 0
\(376\) 1757.22 + 3043.60i 0.241016 + 0.417451i
\(377\) 5182.17 5182.17i 0.707945 0.707945i
\(378\) −576.953 + 24.4804i −0.0785059 + 0.00333105i
\(379\) 12501.2i 1.69431i −0.531345 0.847155i \(-0.678313\pi\)
0.531345 0.847155i \(-0.321687\pi\)
\(380\) 0 0
\(381\) −6029.05 + 8874.77i −0.810702 + 1.19335i
\(382\) 4320.15 1157.58i 0.578633 0.155044i
\(383\) 1193.34 319.753i 0.159208 0.0426596i −0.178335 0.983970i \(-0.557071\pi\)
0.337543 + 0.941310i \(0.390404\pi\)
\(384\) −5973.68 437.644i −0.793862 0.0581600i
\(385\) 0 0
\(386\) 518.587i 0.0683818i
\(387\) −1346.62 + 156.280i −0.176880 + 0.0205275i
\(388\) −191.916 + 191.916i −0.0251110 + 0.0251110i
\(389\) 1415.73 + 2452.12i 0.184526 + 0.319608i 0.943417 0.331610i \(-0.107592\pi\)
−0.758891 + 0.651218i \(0.774258\pi\)
\(390\) 0 0
\(391\) −4719.53 + 8174.46i −0.610426 + 1.05729i
\(392\) −2091.62 7806.03i −0.269497 1.00578i
\(393\) 2601.42 7474.40i 0.333903 0.959373i
\(394\) −10929.4 + 6310.07i −1.39750 + 0.806844i
\(395\) 0 0
\(396\) −1629.09 + 645.654i −0.206730 + 0.0819326i
\(397\) 3719.83 + 3719.83i 0.470260 + 0.470260i 0.901999 0.431739i \(-0.142100\pi\)
−0.431739 + 0.901999i \(0.642100\pi\)
\(398\) −1172.89 + 4377.29i −0.147718 + 0.551291i
\(399\) −1.79255 + 24.4676i −0.000224912 + 0.00306996i
\(400\) 0 0
\(401\) −3644.58 2104.20i −0.453870 0.262042i 0.255593 0.966784i \(-0.417729\pi\)
−0.709463 + 0.704743i \(0.751062\pi\)
\(402\) 621.835 + 3256.72i 0.0771501 + 0.404056i
\(403\) −6899.31 1848.66i −0.852802 0.228508i
\(404\) 1091.19 0.134378
\(405\) 0 0
\(406\) −754.350 −0.0922113
\(407\) −2567.98 688.089i −0.312752 0.0838018i
\(408\) 1500.39 + 7857.97i 0.182060 + 0.953499i
\(409\) 8758.07 + 5056.47i 1.05882 + 0.611312i 0.925106 0.379708i \(-0.123976\pi\)
0.133716 + 0.991020i \(0.457309\pi\)
\(410\) 0 0
\(411\) 454.891 6209.09i 0.0545939 0.745187i
\(412\) −112.119 + 418.436i −0.0134071 + 0.0500360i
\(413\) −281.593 281.593i −0.0335504 0.0335504i
\(414\) −9721.01 + 3852.70i −1.15401 + 0.457366i
\(415\) 0 0
\(416\) −1421.40 + 820.647i −0.167524 + 0.0967200i
\(417\) 516.370 1483.64i 0.0606397 0.174230i
\(418\) −149.833 559.185i −0.0175325 0.0654322i
\(419\) −6057.57 + 10492.0i −0.706281 + 1.22331i 0.259946 + 0.965623i \(0.416295\pi\)
−0.966227 + 0.257691i \(0.917038\pi\)
\(420\) 0 0
\(421\) 4457.66 + 7720.89i 0.516040 + 0.893808i 0.999827 + 0.0186217i \(0.00592782\pi\)
−0.483786 + 0.875186i \(0.660739\pi\)
\(422\) −2370.90 + 2370.90i −0.273492 + 0.273492i
\(423\) 3972.70 461.046i 0.456642 0.0529948i
\(424\) 6124.15i 0.701450i
\(425\) 0 0
\(426\) −6488.93 475.393i −0.738004 0.0540677i
\(427\) 454.223 121.709i 0.0514787 0.0137937i
\(428\) −1351.21 + 362.055i −0.152601 + 0.0408893i
\(429\) 8313.52 12237.5i 0.935619 1.37723i
\(430\) 0 0
\(431\) 11279.2i 1.26056i 0.776368 + 0.630279i \(0.217060\pi\)
−0.776368 + 0.630279i \(0.782940\pi\)
\(432\) −3628.30 + 6949.05i −0.404090 + 0.773927i
\(433\) −1968.81 + 1968.81i −0.218510 + 0.218510i −0.807870 0.589360i \(-0.799380\pi\)
0.589360 + 0.807870i \(0.299380\pi\)
\(434\) 367.603 + 636.706i 0.0406578 + 0.0704214i
\(435\) 0 0
\(436\) 382.196 661.983i 0.0419814 0.0727138i
\(437\) 114.977 + 429.101i 0.0125861 + 0.0469718i
\(438\) −5694.93 6595.34i −0.621265 0.719492i
\(439\) 4264.82 2462.29i 0.463664 0.267697i −0.249919 0.968267i \(-0.580404\pi\)
0.713584 + 0.700570i \(0.247071\pi\)
\(440\) 0 0
\(441\) −9098.27 1340.31i −0.982429 0.144726i
\(442\) −4885.10 4885.10i −0.525703 0.525703i
\(443\) −2348.37 + 8764.22i −0.251861 + 0.939957i 0.717949 + 0.696095i \(0.245081\pi\)
−0.969810 + 0.243861i \(0.921586\pi\)
\(444\) 159.223 77.0052i 0.0170189 0.00823086i
\(445\) 0 0
\(446\) 694.997 + 401.257i 0.0737872 + 0.0426010i
\(447\) −10944.6 3809.21i −1.15808 0.403063i
\(448\) 830.717 + 222.590i 0.0876065 + 0.0234741i
\(449\) −5958.93 −0.626323 −0.313162 0.949700i \(-0.601388\pi\)
−0.313162 + 0.949700i \(0.601388\pi\)
\(450\) 0 0
\(451\) −6536.77 −0.682494
\(452\) −111.800 29.9567i −0.0116341 0.00311736i
\(453\) −6590.85 + 5691.05i −0.683588 + 0.590263i
\(454\) −10935.6 6313.69i −1.13047 0.652679i
\(455\) 0 0
\(456\) 311.439 + 211.575i 0.0319834 + 0.0217279i
\(457\) −3712.09 + 13853.7i −0.379966 + 1.41805i 0.465986 + 0.884792i \(0.345700\pi\)
−0.845952 + 0.533259i \(0.820967\pi\)
\(458\) −1810.16 1810.16i −0.184679 0.184679i
\(459\) 8885.54 + 1981.33i 0.903576 + 0.201483i
\(460\) 0 0
\(461\) −681.107 + 393.237i −0.0688120 + 0.0397286i −0.534011 0.845477i \(-0.679316\pi\)
0.465199 + 0.885206i \(0.345983\pi\)
\(462\) −1495.77 + 285.601i −0.150627 + 0.0287605i
\(463\) −1096.96 4093.92i −0.110108 0.410930i 0.888766 0.458361i \(-0.151563\pi\)
−0.998875 + 0.0474312i \(0.984897\pi\)
\(464\) −5120.20 + 8868.45i −0.512283 + 0.887301i
\(465\) 0 0
\(466\) −5675.70 9830.60i −0.564210 0.977240i
\(467\) −10534.2 + 10534.2i −1.04383 + 1.04383i −0.0448309 + 0.998995i \(0.514275\pi\)
−0.998995 + 0.0448309i \(0.985725\pi\)
\(468\) 113.460 + 977.656i 0.0112066 + 0.0965644i
\(469\) 370.518i 0.0364796i
\(470\) 0 0
\(471\) 1097.63 + 2269.56i 0.107381 + 0.222030i
\(472\) −5903.37 + 1581.80i −0.575688 + 0.154255i
\(473\) −3453.07 + 925.246i −0.335670 + 0.0899426i
\(474\) 936.783 + 1936.98i 0.0907761 + 0.187697i
\(475\) 0 0
\(476\) 91.4479i 0.00880569i
\(477\) −6396.93 2765.58i −0.614036 0.265466i
\(478\) 10469.5 10469.5i 1.00181 1.00181i
\(479\) −4528.85 7844.19i −0.432001 0.748247i 0.565045 0.825060i \(-0.308859\pi\)
−0.997045 + 0.0768132i \(0.975525\pi\)
\(480\) 0 0
\(481\) −746.591 + 1293.13i −0.0707726 + 0.122582i
\(482\) 1810.07 + 6755.26i 0.171050 + 0.638368i
\(483\) 1147.81 219.161i 0.108131 0.0206463i
\(484\) −2951.17 + 1703.86i −0.277157 + 0.160017i
\(485\) 0 0
\(486\) 6353.58 + 7832.20i 0.593012 + 0.731020i
\(487\) 1647.82 + 1647.82i 0.153326 + 0.153326i 0.779602 0.626276i \(-0.215422\pi\)
−0.626276 + 0.779602i \(0.715422\pi\)
\(488\) 1867.85 6970.90i 0.173265 0.646635i
\(489\) 15278.7 + 10379.6i 1.41294 + 0.959877i
\(490\) 0 0
\(491\) −3966.40 2290.00i −0.364564 0.210481i 0.306517 0.951865i \(-0.400836\pi\)
−0.671081 + 0.741384i \(0.734170\pi\)
\(492\) 329.146 284.210i 0.0301606 0.0260430i
\(493\) 11487.0 + 3077.93i 1.04939 + 0.281183i
\(494\) −325.144 −0.0296132
\(495\) 0 0
\(496\) 9980.51 0.903504
\(497\) 702.316 + 188.185i 0.0633867 + 0.0169844i
\(498\) −10908.0 3796.47i −0.981526 0.341614i
\(499\) −2616.51 1510.64i −0.234731 0.135522i 0.378022 0.925797i \(-0.376605\pi\)
−0.612753 + 0.790275i \(0.709938\pi\)
\(500\) 0 0
\(501\) 7893.01 3817.31i 0.703859 0.340409i
\(502\) 1166.01 4351.61i 0.103668 0.386896i
\(503\) −4876.93 4876.93i −0.432310 0.432310i 0.457104 0.889413i \(-0.348887\pi\)
−0.889413 + 0.457104i \(0.848887\pi\)
\(504\) 614.906 776.368i 0.0543454 0.0686155i
\(505\) 0 0
\(506\) −23879.9 + 13787.1i −2.09801 + 1.21129i
\(507\) 2030.42 + 2351.45i 0.177858 + 0.205979i
\(508\) −487.149 1818.06i −0.0425467 0.158786i
\(509\) 5209.57 9023.23i 0.453654 0.785752i −0.544956 0.838465i \(-0.683453\pi\)
0.998610 + 0.0527129i \(0.0167868\pi\)
\(510\) 0 0
\(511\) 486.891 + 843.320i 0.0421503 + 0.0730064i
\(512\) 9121.19 9121.19i 0.787311 0.787311i
\(513\) 361.640 229.766i 0.0311244 0.0197747i
\(514\) 17778.0i 1.52559i
\(515\) 0 0
\(516\) 133.644 196.723i 0.0114018 0.0167835i
\(517\) 10187.0 2729.59i 0.866582 0.232200i
\(518\) 148.458 39.7792i 0.0125924 0.00337412i
\(519\) −7061.84 517.365i −0.597265 0.0437569i
\(520\) 0 0
\(521\) 523.372i 0.0440102i −0.999758 0.0220051i \(-0.992995\pi\)
0.999758 0.0220051i \(-0.00700501\pi\)
\(522\) 7858.48 + 10573.8i 0.658920 + 0.886598i
\(523\) 14550.3 14550.3i 1.21652 1.21652i 0.247683 0.968841i \(-0.420331\pi\)
0.968841 0.247683i \(-0.0796692\pi\)
\(524\) 694.196 + 1202.38i 0.0578742 + 0.100241i
\(525\) 0 0
\(526\) 6256.26 10836.2i 0.518604 0.898249i
\(527\) −2999.82 11195.5i −0.247958 0.925393i
\(528\) −6795.01 + 19523.4i −0.560066 + 1.60918i
\(529\) 7787.77 4496.27i 0.640074 0.369547i
\(530\) 0 0
\(531\) −1013.62 + 6880.64i −0.0828388 + 0.562325i
\(532\) −3.04331 3.04331i −0.000248016 0.000248016i
\(533\) −950.220 + 3546.27i −0.0772206 + 0.288191i
\(534\) 1367.33 18663.5i 0.110805 1.51245i
\(535\) 0 0
\(536\) −4924.47 2843.14i −0.396837 0.229114i
\(537\) −2386.57 12499.1i −0.191784 1.00443i
\(538\) 368.588 + 98.7630i 0.0295371 + 0.00791445i
\(539\) −24251.1 −1.93798
\(540\) 0 0
\(541\) 19374.8 1.53972 0.769858 0.638216i \(-0.220327\pi\)
0.769858 + 0.638216i \(0.220327\pi\)
\(542\) −19161.8 5134.39i −1.51858 0.406902i
\(543\) −2808.75 14710.2i −0.221980 1.16257i
\(544\) −2306.50 1331.66i −0.181784 0.104953i
\(545\) 0 0
\(546\) −62.4917 + 852.988i −0.00489817 + 0.0668581i
\(547\) −2731.50 + 10194.1i −0.213511 + 0.796832i 0.773175 + 0.634193i \(0.218667\pi\)
−0.986686 + 0.162640i \(0.947999\pi\)
\(548\) 772.293 + 772.293i 0.0602021 + 0.0602021i
\(549\) −6437.90 5099.01i −0.500479 0.396394i
\(550\) 0 0
\(551\) 484.709 279.847i 0.0374761 0.0216368i
\(552\) 5894.80 16937.0i 0.454528 1.30595i
\(553\) −62.2319 232.253i −0.00478548 0.0178597i
\(554\) 2930.49 5075.76i 0.224737 0.389257i
\(555\) 0 0
\(556\) 137.795 + 238.668i 0.0105104 + 0.0182046i
\(557\) −935.942 + 935.942i −0.0711977 + 0.0711977i −0.741809 0.670611i \(-0.766032\pi\)
0.670611 + 0.741809i \(0.266032\pi\)
\(558\) 5095.28 11785.7i 0.386560 0.894133i
\(559\) 2007.82i 0.151917i
\(560\) 0 0
\(561\) 23942.5 + 1754.07i 1.80187 + 0.132009i
\(562\) −5215.95 + 1397.61i −0.391498 + 0.104901i
\(563\) 81.8572 21.9336i 0.00612765 0.00164190i −0.255754 0.966742i \(-0.582324\pi\)
0.261882 + 0.965100i \(0.415657\pi\)
\(564\) −394.266 + 580.359i −0.0294354 + 0.0433290i
\(565\) 0 0
\(566\) 15437.7i 1.14646i
\(567\) −533.266 992.893i −0.0394975 0.0735407i
\(568\) 7890.29 7890.29i 0.582868 0.582868i
\(569\) 4295.92 + 7440.75i 0.316510 + 0.548212i 0.979757 0.200189i \(-0.0641555\pi\)
−0.663247 + 0.748401i \(0.730822\pi\)
\(570\) 0 0
\(571\) 5232.69 9063.28i 0.383505 0.664249i −0.608056 0.793894i \(-0.708050\pi\)
0.991561 + 0.129645i \(0.0413837\pi\)
\(572\) 671.735 + 2506.95i 0.0491025 + 0.183253i
\(573\) 5704.81 + 6606.78i 0.415919 + 0.481679i
\(574\) 327.269 188.949i 0.0237978 0.0137397i
\(575\) 0 0
\(576\) −5533.96 13963.1i −0.400315 1.01006i
\(577\) −1229.42 1229.42i −0.0887029 0.0887029i 0.661363 0.750066i \(-0.269978\pi\)
−0.750066 + 0.661363i \(0.769978\pi\)
\(578\) −483.970 + 1806.20i −0.0348278 + 0.129979i
\(579\) 911.147 440.660i 0.0653990 0.0316290i
\(580\) 0 0
\(581\) 1117.79 + 645.354i 0.0798168 + 0.0460822i
\(582\) 3890.14 + 1353.94i 0.277064 + 0.0964305i
\(583\) −17751.5 4756.49i −1.26105 0.337897i
\(584\) 14944.5 1.05892
\(585\) 0 0
\(586\) 17826.1 1.25664
\(587\) 17141.8 + 4593.13i 1.20531 + 0.322962i 0.804920 0.593383i \(-0.202208\pi\)
0.400390 + 0.916345i \(0.368875\pi\)
\(588\) 1221.11 1054.40i 0.0856427 0.0739506i
\(589\) −472.408 272.745i −0.0330479 0.0190802i
\(590\) 0 0
\(591\) −20373.7 13840.8i −1.41804 0.963341i
\(592\) 540.008 2015.34i 0.0374902 0.139915i
\(593\) 4295.56 + 4295.56i 0.297466 + 0.297466i 0.840021 0.542555i \(-0.182543\pi\)
−0.542555 + 0.840021i \(0.682543\pi\)
\(594\) 19585.6 + 17991.2i 1.35287 + 1.24274i
\(595\) 0 0
\(596\) 1760.63 1016.50i 0.121003 0.0698614i
\(597\) −8687.46 + 1658.77i −0.595568 + 0.113717i
\(598\) 4008.33 + 14959.3i 0.274101 + 1.02296i
\(599\) −189.493 + 328.212i −0.0129257 + 0.0223879i −0.872416 0.488764i \(-0.837448\pi\)
0.859490 + 0.511152i \(0.170781\pi\)
\(600\) 0 0
\(601\) 10568.0 + 18304.3i 0.717267 + 1.24234i 0.962078 + 0.272773i \(0.0879407\pi\)
−0.244811 + 0.969571i \(0.578726\pi\)
\(602\) 146.136 146.136i 0.00989378 0.00989378i
\(603\) −5193.61 + 3859.89i −0.350746 + 0.260675i
\(604\) 1527.64i 0.102912i
\(605\) 0 0
\(606\) −7210.13 14908.3i −0.483320 0.999355i
\(607\) 20941.3 5611.20i 1.40030 0.375209i 0.521846 0.853040i \(-0.325244\pi\)
0.878452 + 0.477831i \(0.158577\pi\)
\(608\) −121.075 + 32.4419i −0.00807605 + 0.00216397i
\(609\) −640.995 1325.38i −0.0426509 0.0881889i
\(610\) 0 0
\(611\) 5923.33i 0.392197i
\(612\) −1281.84 + 952.663i −0.0846654 + 0.0629234i
\(613\) −9303.05 + 9303.05i −0.612964 + 0.612964i −0.943717 0.330754i \(-0.892697\pi\)
0.330754 + 0.943717i \(0.392697\pi\)
\(614\) −1759.14 3046.92i −0.115624 0.200267i
\(615\) 0 0
\(616\) 1305.82 2261.75i 0.0854107 0.147936i
\(617\) 5190.29 + 19370.4i 0.338660 + 1.26390i 0.899846 + 0.436207i \(0.143679\pi\)
−0.561186 + 0.827690i \(0.689655\pi\)
\(618\) 6457.69 1233.02i 0.420334 0.0802581i
\(619\) −11987.0 + 6920.68i −0.778347 + 0.449379i −0.835844 0.548967i \(-0.815021\pi\)
0.0574971 + 0.998346i \(0.481688\pi\)
\(620\) 0 0
\(621\) −15029.4 13805.9i −0.971187 0.892126i
\(622\) 15556.4 + 15556.4i 1.00282 + 1.00282i
\(623\) −541.259 + 2020.01i −0.0348075 + 0.129904i
\(624\) 9603.91 + 6524.39i 0.616129 + 0.418565i
\(625\) 0 0
\(626\) 18788.3 + 10847.4i 1.19957 + 0.692572i
\(627\) 855.160 738.411i 0.0544686 0.0470324i
\(628\) −427.202 114.468i −0.0271452 0.00727354i
\(629\) −2422.98 −0.153594
\(630\) 0 0
\(631\) −27232.2 −1.71806 −0.859032 0.511922i \(-0.828934\pi\)
−0.859032 + 0.511922i \(0.828934\pi\)
\(632\) −3564.35 955.064i −0.224339 0.0601114i
\(633\) −6180.25 2151.00i −0.388061 0.135062i
\(634\) 15005.0 + 8663.16i 0.939946 + 0.542678i
\(635\) 0 0
\(636\) 1100.64 532.306i 0.0686217 0.0331876i
\(637\) −3525.27 + 13156.5i −0.219272 + 0.818334i
\(638\) 24565.3 + 24565.3i 1.52437 + 1.52437i
\(639\) −4678.59 11804.9i −0.289644 0.730820i
\(640\) 0 0
\(641\) 10303.5 5948.74i 0.634891 0.366554i −0.147753 0.989024i \(-0.547204\pi\)
0.782644 + 0.622470i \(0.213871\pi\)
\(642\) 13874.8 + 16068.5i 0.852951 + 0.987808i
\(643\) 2009.49 + 7499.52i 0.123245 + 0.459957i 0.999771 0.0213976i \(-0.00681159\pi\)
−0.876526 + 0.481355i \(0.840145\pi\)
\(644\) −102.500 + 177.534i −0.00627181 + 0.0108631i
\(645\) 0 0
\(646\) −263.805 456.924i −0.0160670 0.0278288i
\(647\) −1793.65 + 1793.65i −0.108989 + 0.108989i −0.759498 0.650509i \(-0.774555\pi\)
0.650509 + 0.759498i \(0.274555\pi\)
\(648\) −17288.3 531.373i −1.04807 0.0322134i
\(649\) 18340.1i 1.10926i
\(650\) 0 0
\(651\) −806.317 + 1186.90i −0.0485439 + 0.0714566i
\(652\) −3129.96 + 838.671i −0.188004 + 0.0503756i
\(653\) −9662.33 + 2589.01i −0.579045 + 0.155155i −0.536441 0.843938i \(-0.680232\pi\)
−0.0426031 + 0.999092i \(0.513565\pi\)
\(654\) −11569.7 847.620i −0.691760 0.0506798i
\(655\) 0 0
\(656\) 5130.01i 0.305325i
\(657\) 6748.72 15610.1i 0.400750 0.926955i
\(658\) −431.120 + 431.120i −0.0255422 + 0.0255422i
\(659\) −2314.59 4008.99i −0.136819 0.236977i 0.789472 0.613787i \(-0.210354\pi\)
−0.926291 + 0.376810i \(0.877021\pi\)
\(660\) 0 0
\(661\) −6085.01 + 10539.6i −0.358063 + 0.620183i −0.987637 0.156757i \(-0.949896\pi\)
0.629574 + 0.776940i \(0.283229\pi\)
\(662\) −5807.13 21672.5i −0.340937 1.27239i
\(663\) 4432.01 12734.1i 0.259615 0.745927i
\(664\) 17154.5 9904.15i 1.00259 0.578848i
\(665\) 0 0
\(666\) −2104.16 1666.55i −0.122424 0.0969634i
\(667\) −18850.6 18850.6i −1.09430 1.09430i
\(668\) −398.094 + 1485.71i −0.0230580 + 0.0860535i
\(669\) −114.440 + 1562.06i −0.00661359 + 0.0902730i
\(670\) 0 0
\(671\) −18755.2 10828.3i −1.07904 0.622983i
\(672\) 61.8384 + 323.865i 0.00354980 + 0.0185913i
\(673\) 7524.51 + 2016.19i 0.430978 + 0.115480i 0.467785 0.883842i \(-0.345052\pi\)
−0.0368070 + 0.999322i \(0.511719\pi\)
\(674\) 1369.79 0.0782823
\(675\) 0 0
\(676\) −545.022 −0.0310094
\(677\) −9036.11 2421.22i −0.512978 0.137452i −0.00696137 0.999976i \(-0.502216\pi\)
−0.506017 + 0.862524i \(0.668883\pi\)
\(678\) 329.446 + 1725.40i 0.0186612 + 0.0977340i
\(679\) −398.637 230.153i −0.0225306 0.0130081i
\(680\) 0 0
\(681\) 1800.68 24578.6i 0.101325 1.38305i
\(682\) 8763.33 32705.2i 0.492031 1.83628i
\(683\) 15632.3 + 15632.3i 0.875775 + 0.875775i 0.993094 0.117320i \(-0.0374302\pi\)
−0.117320 + 0.993094i \(0.537430\pi\)
\(684\) −10.9547 + 74.3624i −0.000612372 + 0.00415690i
\(685\) 0 0
\(686\) 2436.82 1406.90i 0.135624 0.0783028i
\(687\) 1642.27 4718.56i 0.0912028 0.262044i
\(688\) −726.126 2709.94i −0.0402374 0.150168i
\(689\) −5160.89 + 8938.93i −0.285362 + 0.494261i
\(690\) 0 0
\(691\) 5115.78 + 8860.78i 0.281640 + 0.487815i 0.971789 0.235853i \(-0.0757883\pi\)
−0.690149 + 0.723667i \(0.742455\pi\)
\(692\) 878.360 878.360i 0.0482518 0.0482518i
\(693\) −1772.80 2385.36i −0.0971762 0.130754i
\(694\) 2229.17i 0.121928i
\(695\) 0 0
\(696\) −22533.9 1650.88i −1.22722 0.0899088i
\(697\) −5754.51 + 1541.92i −0.312722 + 0.0837937i
\(698\) −11002.2 + 2948.03i −0.596619 + 0.159864i
\(699\) 12449.4 18325.5i 0.673645 0.991606i
\(700\) 0 0
\(701\) 24579.9i 1.32435i 0.749348 + 0.662176i \(0.230367\pi\)
−0.749348 + 0.662176i \(0.769633\pi\)
\(702\) 12607.5 8010.09i 0.677832 0.430657i
\(703\) −80.6347 + 80.6347i −0.00432603 + 0.00432603i
\(704\) −19803.6 34300.8i −1.06019 1.83631i
\(705\) 0 0
\(706\) −4977.76 + 8621.74i −0.265355 + 0.459608i
\(707\) 478.980 + 1787.58i 0.0254794 + 0.0950903i
\(708\) −797.402 923.478i −0.0423280 0.0490204i
\(709\) −29697.0 + 17145.6i −1.57305 + 0.908203i −0.577262 + 0.816559i \(0.695879\pi\)
−0.995792 + 0.0916440i \(0.970788\pi\)
\(710\) 0 0
\(711\) −2607.21 + 3291.82i −0.137522 + 0.173633i
\(712\) 22694.1 + 22694.1i 1.19452 + 1.19452i
\(713\) −6724.70 + 25096.9i −0.353215 + 1.31821i
\(714\) −1249.40 + 604.250i −0.0654870 + 0.0316716i
\(715\) 0 0
\(716\) 1933.28 + 1116.18i 0.100908 + 0.0582591i
\(717\) 27291.1 + 9498.47i 1.42148 + 0.494738i
\(718\) −836.336 224.095i −0.0434704 0.0116479i
\(719\) 24579.6 1.27492 0.637459 0.770485i \(-0.279986\pi\)
0.637459 + 0.770485i \(0.279986\pi\)
\(720\) 0 0
\(721\) −734.693 −0.0379492
\(722\) 17615.2 + 4719.99i 0.907994 + 0.243296i
\(723\) −10330.8 + 8920.40i −0.531405 + 0.458857i
\(724\) 2275.27 + 1313.63i 0.116795 + 0.0674317i
\(725\) 0 0
\(726\) 42779.0 + 29061.8i 2.18688 + 1.48565i
\(727\) 199.464 744.411i 0.0101757 0.0379761i −0.960651 0.277757i \(-0.910409\pi\)
0.970827 + 0.239781i \(0.0770756\pi\)
\(728\) −1037.20 1037.20i −0.0528039 0.0528039i
\(729\) −8362.19 + 17818.4i −0.424843 + 0.905267i
\(730\) 0 0
\(731\) −2821.58 + 1629.04i −0.142763 + 0.0824244i
\(732\) 1415.18 270.212i 0.0714569 0.0136439i
\(733\) −1654.04 6172.97i −0.0833471 0.311056i 0.911649 0.410970i \(-0.134810\pi\)
−0.994996 + 0.0999142i \(0.968143\pi\)
\(734\) 4187.59 7253.12i 0.210581 0.364738i
\(735\) 0 0
\(736\) 2985.18 + 5170.49i 0.149504 + 0.258949i
\(737\) −12065.9 + 12065.9i −0.603056 + 0.603056i
\(738\) −6057.86 2618.99i −0.302159 0.130632i
\(739\) 11521.7i 0.573521i 0.958002 + 0.286760i \(0.0925784\pi\)
−0.958002 + 0.286760i \(0.907422\pi\)
\(740\) 0 0
\(741\) −276.285 571.272i −0.0136972 0.0283215i
\(742\) 1026.23 274.978i 0.0507738 0.0136048i
\(743\) 23350.0 6256.61i 1.15293 0.308927i 0.368792 0.929512i \(-0.379771\pi\)
0.784139 + 0.620585i \(0.213105\pi\)
\(744\) 9587.59 + 19824.2i 0.472443 + 0.976866i
\(745\) 0 0
\(746\) 4830.98i 0.237098i
\(747\) −2598.57 22391.2i −0.127278 1.09672i
\(748\) −2977.99 + 2977.99i −0.145570 + 0.145570i
\(749\) −1186.23 2054.62i −0.0578692 0.100232i
\(750\) 0 0
\(751\) 14058.2 24349.5i 0.683077 1.18312i −0.290961 0.956735i \(-0.593975\pi\)
0.974037 0.226388i \(-0.0726918\pi\)
\(752\) 2142.17 + 7994.67i 0.103879 + 0.387680i
\(753\) 8636.48 1649.04i 0.417969 0.0798066i
\(754\) 16897.9 9755.99i 0.816160 0.471210i
\(755\) 0 0
\(756\) 192.978 + 43.0309i 0.00928378 + 0.00207013i
\(757\) −8806.75 8806.75i −0.422836 0.422836i 0.463343 0.886179i \(-0.346650\pi\)
−0.886179 + 0.463343i \(0.846650\pi\)
\(758\) 8614.36 32149.2i 0.412781 1.54052i
\(759\) −44515.2 30241.3i −2.12885 1.44623i
\(760\) 0 0
\(761\) 9352.07 + 5399.42i 0.445483 + 0.257200i 0.705920 0.708291i \(-0.250534\pi\)
−0.260438 + 0.965491i \(0.583867\pi\)
\(762\) −21620.3 + 18668.7i −1.02785 + 0.887525i
\(763\) 1252.22 + 335.532i 0.0594148 + 0.0159201i
\(764\) −1531.33 −0.0725151
\(765\) 0 0
\(766\) 3289.23 0.155150
\(767\) 9949.69 + 2666.01i 0.468400 + 0.125507i
\(768\) 6778.61 + 2359.25i 0.318492 + 0.110849i
\(769\) 9203.05 + 5313.38i 0.431561 + 0.249162i 0.700011 0.714132i \(-0.253178\pi\)
−0.268450 + 0.963293i \(0.586512\pi\)
\(770\) 0 0
\(771\) −31235.6 + 15106.5i −1.45905 + 0.705641i
\(772\) −45.9549 + 171.506i −0.00214243 + 0.00799564i
\(773\) −25837.0 25837.0i −1.20219 1.20219i −0.973499 0.228691i \(-0.926556\pi\)
−0.228691 0.973499i \(-0.573444\pi\)
\(774\) −3570.78 526.030i −0.165826 0.0244286i
\(775\) 0 0
\(776\) −6117.82 + 3532.13i −0.283012 + 0.163397i
\(777\) 196.041 + 227.036i 0.00905137 + 0.0104825i
\(778\) 1951.12 + 7281.66i 0.0899112 + 0.335553i
\(779\) −140.192 + 242.819i −0.00644786 + 0.0111680i
\(780\) 0