Properties

Label 21.3.b.a.8.3
Level 21
Weight 3
Character 21.8
Analytic conductor 0.572
Analytic rank 0
Dimension 4
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 21.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(0.572208555157\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.65856.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 8.3
Root \(1.30710i\)
Character \(\chi\) = 21.8
Dual form 21.3.b.a.8.2

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.30710i q^{2}\) \(+(-1.82288 + 2.38267i) q^{3}\) \(+2.29150 q^{4}\) \(-7.37953i q^{5}\) \(+(-3.11438 - 2.38267i) q^{6}\) \(-2.64575 q^{7}\) \(+8.22359i q^{8}\) \(+(-2.35425 - 8.68663i) q^{9}\) \(+O(q^{10})\) \(q\)\(+1.30710i q^{2}\) \(+(-1.82288 + 2.38267i) q^{3}\) \(+2.29150 q^{4}\) \(-7.37953i q^{5}\) \(+(-3.11438 - 2.38267i) q^{6}\) \(-2.64575 q^{7}\) \(+8.22359i q^{8}\) \(+(-2.35425 - 8.68663i) q^{9}\) \(+9.64575 q^{10}\) \(+2.61419i q^{11}\) \(+(-4.17712 + 5.45990i) q^{12}\) \(-6.35425 q^{13}\) \(-3.45825i q^{14}\) \(+(17.5830 + 13.4520i) q^{15}\) \(-1.58301 q^{16}\) \(+12.1449i q^{17}\) \(+(11.3542 - 3.07723i) q^{18}\) \(-10.2288 q^{19}\) \(-16.9102i q^{20}\) \(+(4.82288 - 6.30396i) q^{21}\) \(-3.41699 q^{22}\) \(-4.30231i q^{23}\) \(+(-19.5941 - 14.9906i) q^{24}\) \(-29.4575 q^{25}\) \(-8.30561i q^{26}\) \(+(24.9889 + 10.2252i) q^{27}\) \(-6.06275 q^{28}\) \(-17.3733i q^{29}\) \(+(-17.5830 + 22.9827i) q^{30}\) \(+39.2915 q^{31}\) \(+30.8252i q^{32}\) \(+(-6.22876 - 4.76534i) q^{33}\) \(-15.8745 q^{34}\) \(+19.5244i q^{35}\) \(+(-5.39477 - 19.9054i) q^{36}\) \(+41.0405 q^{37}\) \(-13.3700i q^{38}\) \(+(11.5830 - 15.1401i) q^{39}\) \(+60.6863 q^{40}\) \(+30.2802i q^{41}\) \(+(8.23987 + 6.30396i) q^{42}\) \(-55.8745 q^{43}\) \(+5.99042i q^{44}\) \(+(-64.1033 + 17.3733i) q^{45}\) \(+5.62352 q^{46}\) \(+39.9749i q^{47}\) \(+(2.88562 - 3.77178i) q^{48}\) \(+7.00000 q^{49}\) \(-38.5038i q^{50}\) \(+(-28.9373 - 22.1386i) q^{51}\) \(-14.5608 q^{52}\) \(-105.002i q^{53}\) \(+(-13.3654 + 32.6628i) q^{54}\) \(+19.2915 q^{55}\) \(-21.7576i q^{56}\) \(+(18.6458 - 24.3718i) q^{57}\) \(+22.7085 q^{58}\) \(-41.3640i q^{59}\) \(+(40.2915 + 30.8252i) q^{60}\) \(-20.4797 q^{61}\) \(+51.3577i q^{62}\) \(+(6.22876 + 22.9827i) q^{63}\) \(-46.6235 q^{64}\) \(+46.8914i q^{65}\) \(+(6.22876 - 8.14158i) q^{66}\) \(-27.1660 q^{67}\) \(+27.8300i q^{68}\) \(+(10.2510 + 7.84257i) q^{69}\) \(-25.5203 q^{70}\) \(+67.8049i q^{71}\) \(+(71.4353 - 19.3604i) q^{72}\) \(+60.7895 q^{73}\) \(+53.6439i q^{74}\) \(+(53.6974 - 70.1876i) q^{75}\) \(-23.4392 q^{76}\) \(-6.91650i q^{77}\) \(+(19.7895 + 15.1401i) q^{78}\) \(-63.2470 q^{79}\) \(+11.6818i q^{80}\) \(+(-69.9150 + 40.9010i) q^{81}\) \(-39.5791 q^{82}\) \(-89.9435i q^{83}\) \(+(11.0516 - 14.4455i) q^{84}\) \(+89.6235 q^{85}\) \(-73.0333i q^{86}\) \(+(41.3948 + 31.6693i) q^{87}\) \(-21.4980 q^{88}\) \(-63.1745i q^{89}\) \(+(-22.7085 - 83.7891i) q^{90}\) \(+16.8118 q^{91}\) \(-9.85875i q^{92}\) \(+(-71.6235 + 93.6188i) q^{93}\) \(-52.2510 q^{94}\) \(+75.4835i q^{95}\) \(+(-73.4464 - 56.1906i) q^{96}\) \(+19.1660 q^{97}\) \(+9.14967i q^{98}\) \(+(22.7085 - 6.15445i) q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(4q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 20q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 20q^{9} \) \(\mathstrut +\mathstrut 28q^{10} \) \(\mathstrut -\mathstrut 22q^{12} \) \(\mathstrut -\mathstrut 36q^{13} \) \(\mathstrut +\mathstrut 28q^{15} \) \(\mathstrut +\mathstrut 36q^{16} \) \(\mathstrut +\mathstrut 56q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 14q^{21} \) \(\mathstrut -\mathstrut 56q^{22} \) \(\mathstrut -\mathstrut 126q^{24} \) \(\mathstrut -\mathstrut 12q^{25} \) \(\mathstrut +\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 56q^{28} \) \(\mathstrut -\mathstrut 28q^{30} \) \(\mathstrut +\mathstrut 136q^{31} \) \(\mathstrut +\mathstrut 28q^{33} \) \(\mathstrut +\mathstrut 116q^{36} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 84q^{40} \) \(\mathstrut +\mathstrut 70q^{42} \) \(\mathstrut -\mathstrut 160q^{43} \) \(\mathstrut -\mathstrut 140q^{45} \) \(\mathstrut -\mathstrut 168q^{46} \) \(\mathstrut +\mathstrut 38q^{48} \) \(\mathstrut +\mathstrut 28q^{49} \) \(\mathstrut -\mathstrut 84q^{51} \) \(\mathstrut +\mathstrut 164q^{52} \) \(\mathstrut -\mathstrut 154q^{54} \) \(\mathstrut +\mathstrut 56q^{55} \) \(\mathstrut +\mathstrut 64q^{57} \) \(\mathstrut +\mathstrut 112q^{58} \) \(\mathstrut +\mathstrut 140q^{60} \) \(\mathstrut -\mathstrut 156q^{61} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 4q^{64} \) \(\mathstrut -\mathstrut 28q^{66} \) \(\mathstrut -\mathstrut 24q^{67} \) \(\mathstrut +\mathstrut 168q^{69} \) \(\mathstrut -\mathstrut 28q^{70} \) \(\mathstrut -\mathstrut 32q^{73} \) \(\mathstrut +\mathstrut 146q^{75} \) \(\mathstrut -\mathstrut 316q^{76} \) \(\mathstrut -\mathstrut 196q^{78} \) \(\mathstrut +\mathstrut 128q^{79} \) \(\mathstrut -\mathstrut 68q^{81} \) \(\mathstrut +\mathstrut 392q^{82} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut +\mathstrut 168q^{85} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut +\mathstrut 168q^{88} \) \(\mathstrut -\mathstrut 112q^{90} \) \(\mathstrut -\mathstrut 28q^{91} \) \(\mathstrut -\mathstrut 96q^{93} \) \(\mathstrut -\mathstrut 336q^{94} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 112q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.30710i 0.653548i 0.945103 + 0.326774i \(0.105962\pi\)
−0.945103 + 0.326774i \(0.894038\pi\)
\(3\) −1.82288 + 2.38267i −0.607625 + 0.794224i
\(4\) 2.29150 0.572876
\(5\) 7.37953i 1.47591i −0.674852 0.737953i \(-0.735792\pi\)
0.674852 0.737953i \(-0.264208\pi\)
\(6\) −3.11438 2.38267i −0.519063 0.397112i
\(7\) −2.64575 −0.377964
\(8\) 8.22359i 1.02795i
\(9\) −2.35425 8.68663i −0.261583 0.965181i
\(10\) 9.64575 0.964575
\(11\) 2.61419i 0.237654i 0.992915 + 0.118827i \(0.0379133\pi\)
−0.992915 + 0.118827i \(0.962087\pi\)
\(12\) −4.17712 + 5.45990i −0.348094 + 0.454992i
\(13\) −6.35425 −0.488788 −0.244394 0.969676i \(-0.578589\pi\)
−0.244394 + 0.969676i \(0.578589\pi\)
\(14\) 3.45825i 0.247018i
\(15\) 17.5830 + 13.4520i 1.17220 + 0.896798i
\(16\) −1.58301 −0.0989378
\(17\) 12.1449i 0.714405i 0.934027 + 0.357202i \(0.116269\pi\)
−0.934027 + 0.357202i \(0.883731\pi\)
\(18\) 11.3542 3.07723i 0.630792 0.170957i
\(19\) −10.2288 −0.538356 −0.269178 0.963090i \(-0.586752\pi\)
−0.269178 + 0.963090i \(0.586752\pi\)
\(20\) 16.9102i 0.845511i
\(21\) 4.82288 6.30396i 0.229661 0.300188i
\(22\) −3.41699 −0.155318
\(23\) 4.30231i 0.187057i −0.995617 0.0935284i \(-0.970185\pi\)
0.995617 0.0935284i \(-0.0298146\pi\)
\(24\) −19.5941 14.9906i −0.816422 0.624608i
\(25\) −29.4575 −1.17830
\(26\) 8.30561i 0.319446i
\(27\) 24.9889 + 10.2252i 0.925514 + 0.378713i
\(28\) −6.06275 −0.216527
\(29\) 17.3733i 0.599078i −0.954084 0.299539i \(-0.903167\pi\)
0.954084 0.299539i \(-0.0968328\pi\)
\(30\) −17.5830 + 22.9827i −0.586100 + 0.766089i
\(31\) 39.2915 1.26747 0.633734 0.773551i \(-0.281521\pi\)
0.633734 + 0.773551i \(0.281521\pi\)
\(32\) 30.8252i 0.963288i
\(33\) −6.22876 4.76534i −0.188750 0.144404i
\(34\) −15.8745 −0.466897
\(35\) 19.5244i 0.557840i
\(36\) −5.39477 19.9054i −0.149855 0.552929i
\(37\) 41.0405 1.10920 0.554602 0.832116i \(-0.312871\pi\)
0.554602 + 0.832116i \(0.312871\pi\)
\(38\) 13.3700i 0.351841i
\(39\) 11.5830 15.1401i 0.297000 0.388207i
\(40\) 60.6863 1.51716
\(41\) 30.2802i 0.738541i 0.929322 + 0.369270i \(0.120392\pi\)
−0.929322 + 0.369270i \(0.879608\pi\)
\(42\) 8.23987 + 6.30396i 0.196187 + 0.150094i
\(43\) −55.8745 −1.29941 −0.649704 0.760188i \(-0.725107\pi\)
−0.649704 + 0.760188i \(0.725107\pi\)
\(44\) 5.99042i 0.136146i
\(45\) −64.1033 + 17.3733i −1.42452 + 0.386072i
\(46\) 5.62352 0.122251
\(47\) 39.9749i 0.850530i 0.905069 + 0.425265i \(0.139819\pi\)
−0.905069 + 0.425265i \(0.860181\pi\)
\(48\) 2.88562 3.77178i 0.0601171 0.0785788i
\(49\) 7.00000 0.142857
\(50\) 38.5038i 0.770075i
\(51\) −28.9373 22.1386i −0.567397 0.434090i
\(52\) −14.5608 −0.280015
\(53\) 105.002i 1.98116i −0.136928 0.990581i \(-0.543723\pi\)
0.136928 0.990581i \(-0.456277\pi\)
\(54\) −13.3654 + 32.6628i −0.247507 + 0.604868i
\(55\) 19.2915 0.350755
\(56\) 21.7576i 0.388528i
\(57\) 18.6458 24.3718i 0.327118 0.427575i
\(58\) 22.7085 0.391526
\(59\) 41.3640i 0.701085i −0.936547 0.350542i \(-0.885997\pi\)
0.936547 0.350542i \(-0.114003\pi\)
\(60\) 40.2915 + 30.8252i 0.671525 + 0.513754i
\(61\) −20.4797 −0.335733 −0.167867 0.985810i \(-0.553688\pi\)
−0.167867 + 0.985810i \(0.553688\pi\)
\(62\) 51.3577i 0.828350i
\(63\) 6.22876 + 22.9827i 0.0988692 + 0.364804i
\(64\) −46.6235 −0.728493
\(65\) 46.8914i 0.721406i
\(66\) 6.22876 8.14158i 0.0943751 0.123357i
\(67\) −27.1660 −0.405463 −0.202731 0.979234i \(-0.564982\pi\)
−0.202731 + 0.979234i \(0.564982\pi\)
\(68\) 27.8300i 0.409265i
\(69\) 10.2510 + 7.84257i 0.148565 + 0.113660i
\(70\) −25.5203 −0.364575
\(71\) 67.8049i 0.954999i 0.878632 + 0.477499i \(0.158457\pi\)
−0.878632 + 0.477499i \(0.841543\pi\)
\(72\) 71.4353 19.3604i 0.992157 0.268894i
\(73\) 60.7895 0.832733 0.416367 0.909197i \(-0.363303\pi\)
0.416367 + 0.909197i \(0.363303\pi\)
\(74\) 53.6439i 0.724917i
\(75\) 53.6974 70.1876i 0.715965 0.935834i
\(76\) −23.4392 −0.308411
\(77\) 6.91650i 0.0898246i
\(78\) 19.7895 + 15.1401i 0.253712 + 0.194104i
\(79\) −63.2470 −0.800596 −0.400298 0.916385i \(-0.631093\pi\)
−0.400298 + 0.916385i \(0.631093\pi\)
\(80\) 11.6818i 0.146023i
\(81\) −69.9150 + 40.9010i −0.863148 + 0.504950i
\(82\) −39.5791 −0.482672
\(83\) 89.9435i 1.08366i −0.840489 0.541828i \(-0.817732\pi\)
0.840489 0.541828i \(-0.182268\pi\)
\(84\) 11.0516 14.4455i 0.131567 0.171971i
\(85\) 89.6235 1.05439
\(86\) 73.0333i 0.849224i
\(87\) 41.3948 + 31.6693i 0.475802 + 0.364015i
\(88\) −21.4980 −0.244296
\(89\) 63.1745i 0.709826i −0.934899 0.354913i \(-0.884510\pi\)
0.934899 0.354913i \(-0.115490\pi\)
\(90\) −22.7085 83.7891i −0.252317 0.930990i
\(91\) 16.8118 0.184745
\(92\) 9.85875i 0.107160i
\(93\) −71.6235 + 93.6188i −0.770145 + 1.00665i
\(94\) −52.2510 −0.555862
\(95\) 75.4835i 0.794563i
\(96\) −73.4464 56.1906i −0.765067 0.585318i
\(97\) 19.1660 0.197588 0.0987939 0.995108i \(-0.468502\pi\)
0.0987939 + 0.995108i \(0.468502\pi\)
\(98\) 9.14967i 0.0933639i
\(99\) 22.7085 6.15445i 0.229379 0.0621662i
\(100\) −67.5020 −0.675020
\(101\) 98.7122i 0.977348i 0.872466 + 0.488674i \(0.162519\pi\)
−0.872466 + 0.488674i \(0.837481\pi\)
\(102\) 28.9373 37.8237i 0.283699 0.370821i
\(103\) −56.2510 −0.546126 −0.273063 0.961996i \(-0.588037\pi\)
−0.273063 + 0.961996i \(0.588037\pi\)
\(104\) 52.2547i 0.502449i
\(105\) −46.5203 35.5906i −0.443050 0.338958i
\(106\) 137.247 1.29478
\(107\) 123.137i 1.15081i −0.817868 0.575406i \(-0.804844\pi\)
0.817868 0.575406i \(-0.195156\pi\)
\(108\) 57.2621 + 23.4312i 0.530205 + 0.216955i
\(109\) 164.539 1.50953 0.754764 0.655996i \(-0.227751\pi\)
0.754764 + 0.655996i \(0.227751\pi\)
\(110\) 25.2158i 0.229235i
\(111\) −74.8118 + 97.7861i −0.673980 + 0.880956i
\(112\) 4.18824 0.0373950
\(113\) 144.050i 1.27478i 0.770540 + 0.637391i \(0.219986\pi\)
−0.770540 + 0.637391i \(0.780014\pi\)
\(114\) 31.8562 + 24.3718i 0.279441 + 0.213787i
\(115\) −31.7490 −0.276078
\(116\) 39.8109i 0.343197i
\(117\) 14.9595 + 55.1970i 0.127859 + 0.471769i
\(118\) 54.0667 0.458192
\(119\) 32.1323i 0.270020i
\(120\) −110.624 + 144.595i −0.921863 + 1.20496i
\(121\) 114.166 0.943521
\(122\) 26.7690i 0.219418i
\(123\) −72.1477 55.1970i −0.586567 0.448756i
\(124\) 90.0366 0.726101
\(125\) 32.8944i 0.263155i
\(126\) −30.0405 + 8.14158i −0.238417 + 0.0646157i
\(127\) −36.5830 −0.288055 −0.144028 0.989574i \(-0.546005\pi\)
−0.144028 + 0.989574i \(0.546005\pi\)
\(128\) 62.3595i 0.487184i
\(129\) 101.852 133.131i 0.789553 1.03202i
\(130\) −61.2915 −0.471473
\(131\) 33.6855i 0.257141i −0.991700 0.128570i \(-0.958961\pi\)
0.991700 0.128570i \(-0.0410389\pi\)
\(132\) −14.2732 10.9198i −0.108130 0.0827257i
\(133\) 27.0627 0.203479
\(134\) 35.5086i 0.264989i
\(135\) 75.4575 184.406i 0.558945 1.36597i
\(136\) −99.8745 −0.734371
\(137\) 39.9749i 0.291788i −0.989300 0.145894i \(-0.953394\pi\)
0.989300 0.145894i \(-0.0466058\pi\)
\(138\) −10.2510 + 13.3990i −0.0742825 + 0.0970943i
\(139\) −194.642 −1.40030 −0.700150 0.713995i \(-0.746884\pi\)
−0.700150 + 0.713995i \(0.746884\pi\)
\(140\) 44.7402i 0.319573i
\(141\) −95.2470 72.8693i −0.675511 0.516803i
\(142\) −88.6275 −0.624137
\(143\) 16.6112i 0.116162i
\(144\) 3.72679 + 13.7510i 0.0258805 + 0.0954929i
\(145\) −128.207 −0.884183
\(146\) 79.4577i 0.544231i
\(147\) −12.7601 + 16.6787i −0.0868036 + 0.113461i
\(148\) 94.0445 0.635436
\(149\) 203.685i 1.36701i 0.729945 + 0.683506i \(0.239546\pi\)
−0.729945 + 0.683506i \(0.760454\pi\)
\(150\) 91.7418 + 70.1876i 0.611612 + 0.467917i
\(151\) 165.749 1.09768 0.548838 0.835929i \(-0.315070\pi\)
0.548838 + 0.835929i \(0.315070\pi\)
\(152\) 84.1171i 0.553402i
\(153\) 105.498 28.5921i 0.689530 0.186876i
\(154\) 9.04052 0.0587047
\(155\) 289.953i 1.87066i
\(156\) 26.5425 34.6936i 0.170144 0.222395i
\(157\) −302.723 −1.92817 −0.964086 0.265592i \(-0.914433\pi\)
−0.964086 + 0.265592i \(0.914433\pi\)
\(158\) 82.6699i 0.523227i
\(159\) 250.184 + 191.405i 1.57349 + 1.20380i
\(160\) 227.476 1.42172
\(161\) 11.3828i 0.0707008i
\(162\) −53.4615 91.3856i −0.330009 0.564109i
\(163\) −145.041 −0.889819 −0.444910 0.895576i \(-0.646764\pi\)
−0.444910 + 0.895576i \(0.646764\pi\)
\(164\) 69.3871i 0.423092i
\(165\) −35.1660 + 45.9653i −0.213127 + 0.278578i
\(166\) 117.565 0.708221
\(167\) 19.6594i 0.117721i −0.998266 0.0588604i \(-0.981253\pi\)
0.998266 0.0588604i \(-0.0187467\pi\)
\(168\) 51.8412 + 39.6614i 0.308578 + 0.236080i
\(169\) −128.624 −0.761086
\(170\) 117.146i 0.689097i
\(171\) 24.0810 + 88.8534i 0.140825 + 0.519611i
\(172\) −128.037 −0.744399
\(173\) 19.6884i 0.113806i −0.998380 0.0569030i \(-0.981877\pi\)
0.998380 0.0569030i \(-0.0181226\pi\)
\(174\) −41.3948 + 54.1069i −0.237901 + 0.310959i
\(175\) 77.9373 0.445356
\(176\) 4.13828i 0.0235129i
\(177\) 98.5568 + 75.4014i 0.556818 + 0.425997i
\(178\) 82.5751 0.463905
\(179\) 341.745i 1.90919i 0.297910 + 0.954594i \(0.403711\pi\)
−0.297910 + 0.954594i \(0.596289\pi\)
\(180\) −146.893 + 39.8109i −0.816071 + 0.221171i
\(181\) 215.889 1.19276 0.596378 0.802704i \(-0.296606\pi\)
0.596378 + 0.802704i \(0.296606\pi\)
\(182\) 21.9746i 0.120739i
\(183\) 37.3320 48.7965i 0.204000 0.266648i
\(184\) 35.3804 0.192285
\(185\) 302.860i 1.63708i
\(186\) −122.369 93.6188i −0.657896 0.503327i
\(187\) −31.7490 −0.169781
\(188\) 91.6026i 0.487248i
\(189\) −66.1144 27.0534i −0.349812 0.143140i
\(190\) −98.6640 −0.519284
\(191\) 44.7112i 0.234090i −0.993127 0.117045i \(-0.962658\pi\)
0.993127 0.117045i \(-0.0373422\pi\)
\(192\) 84.9889 111.089i 0.442650 0.578586i
\(193\) −145.122 −0.751925 −0.375963 0.926635i \(-0.622688\pi\)
−0.375963 + 0.926635i \(0.622688\pi\)
\(194\) 25.0518i 0.129133i
\(195\) −111.727 85.4772i −0.572958 0.438344i
\(196\) 16.0405 0.0818394
\(197\) 87.4643i 0.443981i −0.975049 0.221991i \(-0.928745\pi\)
0.975049 0.221991i \(-0.0712554\pi\)
\(198\) 8.04446 + 29.6822i 0.0406286 + 0.149910i
\(199\) 65.4170 0.328729 0.164364 0.986400i \(-0.447443\pi\)
0.164364 + 0.986400i \(0.447443\pi\)
\(200\) 242.247i 1.21123i
\(201\) 49.5203 64.7277i 0.246369 0.322028i
\(202\) −129.026 −0.638743
\(203\) 45.9653i 0.226430i
\(204\) −66.3098 50.7307i −0.325048 0.248680i
\(205\) 223.454 1.09002
\(206\) 73.5254i 0.356919i
\(207\) −37.3725 + 10.1287i −0.180544 + 0.0489309i
\(208\) 10.0588 0.0483597
\(209\) 26.7399i 0.127942i
\(210\) 46.5203 60.8064i 0.221525 0.289554i
\(211\) 40.5830 0.192337 0.0961683 0.995365i \(-0.469341\pi\)
0.0961683 + 0.995365i \(0.469341\pi\)
\(212\) 240.611i 1.13496i
\(213\) −161.557 123.600i −0.758483 0.580281i
\(214\) 160.952 0.752110
\(215\) 412.328i 1.91780i
\(216\) −84.0882 + 205.498i −0.389297 + 0.951381i
\(217\) −103.956 −0.479058
\(218\) 215.068i 0.986548i
\(219\) −110.812 + 144.842i −0.505990 + 0.661377i
\(220\) 44.2065 0.200939
\(221\) 77.1716i 0.349193i
\(222\) −127.816 97.7861i −0.575746 0.440478i
\(223\) 100.959 0.452733 0.226367 0.974042i \(-0.427315\pi\)
0.226367 + 0.974042i \(0.427315\pi\)
\(224\) 81.5559i 0.364089i
\(225\) 69.3503 + 255.886i 0.308224 + 1.13727i
\(226\) −188.288 −0.833131
\(227\) 391.279i 1.72370i 0.507166 + 0.861849i \(0.330693\pi\)
−0.507166 + 0.861849i \(0.669307\pi\)
\(228\) 42.7268 55.8480i 0.187398 0.244947i
\(229\) −6.81176 −0.0297457 −0.0148728 0.999889i \(-0.504734\pi\)
−0.0148728 + 0.999889i \(0.504734\pi\)
\(230\) 41.4990i 0.180430i
\(231\) 16.4797 + 12.6079i 0.0713409 + 0.0545797i
\(232\) 142.871 0.615821
\(233\) 116.877i 0.501616i −0.968037 0.250808i \(-0.919304\pi\)
0.968037 0.250808i \(-0.0806963\pi\)
\(234\) −72.1477 + 19.5535i −0.308324 + 0.0835618i
\(235\) 294.996 1.25530
\(236\) 94.7857i 0.401634i
\(237\) 115.292 150.697i 0.486462 0.635852i
\(238\) 42.0000 0.176471
\(239\) 59.9623i 0.250888i 0.992101 + 0.125444i \(0.0400356\pi\)
−0.992101 + 0.125444i \(0.959964\pi\)
\(240\) −27.8340 21.2945i −0.115975 0.0887273i
\(241\) 134.753 0.559141 0.279570 0.960125i \(-0.409808\pi\)
0.279570 + 0.960125i \(0.409808\pi\)
\(242\) 149.226i 0.616636i
\(243\) 29.9928 241.142i 0.123427 0.992354i
\(244\) −46.9294 −0.192334
\(245\) 51.6567i 0.210844i
\(246\) 72.1477 94.3039i 0.293283 0.383349i
\(247\) 64.9961 0.263142
\(248\) 323.117i 1.30289i
\(249\) 214.306 + 163.956i 0.860666 + 0.658457i
\(250\) −42.9961 −0.171984
\(251\) 268.248i 1.06872i −0.845257 0.534359i \(-0.820553\pi\)
0.845257 0.534359i \(-0.179447\pi\)
\(252\) 14.2732 + 52.6648i 0.0566397 + 0.208987i
\(253\) 11.2470 0.0444547
\(254\) 47.8175i 0.188258i
\(255\) −163.373 + 213.543i −0.640677 + 0.837425i
\(256\) −268.004 −1.04689
\(257\) 234.129i 0.911007i −0.890234 0.455504i \(-0.849459\pi\)
0.890234 0.455504i \(-0.150541\pi\)
\(258\) 174.014 + 133.131i 0.674474 + 0.516010i
\(259\) −108.583 −0.419239
\(260\) 107.452i 0.413276i
\(261\) −150.915 + 40.9010i −0.578218 + 0.156709i
\(262\) 44.0301 0.168054
\(263\) 250.142i 0.951111i −0.879686 0.475555i \(-0.842247\pi\)
0.879686 0.475555i \(-0.157753\pi\)
\(264\) 39.1882 51.2228i 0.148440 0.194026i
\(265\) −774.863 −2.92401
\(266\) 35.3736i 0.132983i
\(267\) 150.524 + 115.159i 0.563761 + 0.431308i
\(268\) −62.2510 −0.232280
\(269\) 340.684i 1.26648i −0.773955 0.633241i \(-0.781724\pi\)
0.773955 0.633241i \(-0.218276\pi\)
\(270\) 241.037 + 98.6301i 0.892728 + 0.365297i
\(271\) −21.2994 −0.0785955 −0.0392977 0.999228i \(-0.512512\pi\)
−0.0392977 + 0.999228i \(0.512512\pi\)
\(272\) 19.2254i 0.0706816i
\(273\) −30.6458 + 40.0569i −0.112255 + 0.146729i
\(274\) 52.2510 0.190697
\(275\) 77.0075i 0.280027i
\(276\) 23.4902 + 17.9713i 0.0851093 + 0.0651133i
\(277\) −226.915 −0.819188 −0.409594 0.912268i \(-0.634330\pi\)
−0.409594 + 0.912268i \(0.634330\pi\)
\(278\) 254.415i 0.915163i
\(279\) −92.5020 341.311i −0.331548 1.22334i
\(280\) −160.561 −0.573431
\(281\) 235.489i 0.838039i 0.907977 + 0.419019i \(0.137626\pi\)
−0.907977 + 0.419019i \(0.862374\pi\)
\(282\) 95.2470 124.497i 0.337755 0.441479i
\(283\) 368.634 1.30259 0.651297 0.758823i \(-0.274225\pi\)
0.651297 + 0.758823i \(0.274225\pi\)
\(284\) 155.375i 0.547096i
\(285\) −179.852 137.597i −0.631061 0.482796i
\(286\) 21.7124 0.0759176
\(287\) 80.1138i 0.279142i
\(288\) 267.767 72.5703i 0.929748 0.251980i
\(289\) 141.502 0.489626
\(290\) 167.578i 0.577856i
\(291\) −34.9373 + 45.6663i −0.120059 + 0.156929i
\(292\) 139.299 0.477053
\(293\) 531.625i 1.81442i 0.420677 + 0.907211i \(0.361793\pi\)
−0.420677 + 0.907211i \(0.638207\pi\)
\(294\) −21.8006 16.6787i −0.0741519 0.0567303i
\(295\) −305.247 −1.03474
\(296\) 337.500i 1.14020i
\(297\) −26.7307 + 65.3257i −0.0900024 + 0.219952i
\(298\) −266.235 −0.893407
\(299\) 27.3379i 0.0914312i
\(300\) 123.048 160.835i 0.410159 0.536117i
\(301\) 147.830 0.491130
\(302\) 216.650i 0.717383i
\(303\) −235.199 179.940i −0.776233 0.593861i
\(304\) 16.1922 0.0532637
\(305\) 151.131i 0.495511i
\(306\) 37.3725 + 137.896i 0.122132 + 0.450640i
\(307\) 567.763 1.84939 0.924696 0.380706i \(-0.124319\pi\)
0.924696 + 0.380706i \(0.124319\pi\)
\(308\) 15.8492i 0.0514583i
\(309\) 102.539 134.028i 0.331840 0.433746i
\(310\) 378.996 1.22257
\(311\) 42.7531i 0.137470i −0.997635 0.0687349i \(-0.978104\pi\)
0.997635 0.0687349i \(-0.0218963\pi\)
\(312\) 124.506 + 95.2539i 0.399057 + 0.305301i
\(313\) −158.118 −0.505168 −0.252584 0.967575i \(-0.581280\pi\)
−0.252584 + 0.967575i \(0.581280\pi\)
\(314\) 395.688i 1.26015i
\(315\) 169.601 45.9653i 0.538417 0.145922i
\(316\) −144.931 −0.458642
\(317\) 140.944i 0.444619i 0.974976 + 0.222309i \(0.0713595\pi\)
−0.974976 + 0.222309i \(0.928641\pi\)
\(318\) −250.184 + 327.015i −0.786743 + 1.02835i
\(319\) 45.4170 0.142373
\(320\) 344.060i 1.07519i
\(321\) 293.395 + 224.463i 0.914002 + 0.699262i
\(322\) −14.8784 −0.0462064
\(323\) 124.227i 0.384604i
\(324\) −160.210 + 93.7247i −0.494477 + 0.289274i
\(325\) 187.180 0.575940
\(326\) 189.582i 0.581539i
\(327\) −299.933 + 392.041i −0.917227 + 1.19890i
\(328\) −249.012 −0.759182
\(329\) 105.764i 0.321470i
\(330\) −60.0810 45.9653i −0.182064 0.139289i
\(331\) −258.369 −0.780570 −0.390285 0.920694i \(-0.627623\pi\)
−0.390285 + 0.920694i \(0.627623\pi\)
\(332\) 206.106i 0.620801i
\(333\) −96.6196 356.504i −0.290149 1.07058i
\(334\) 25.6967 0.0769362
\(335\) 200.472i 0.598425i
\(336\) −7.63464 + 9.97920i −0.0227221 + 0.0297000i
\(337\) 328.959 0.976141 0.488070 0.872804i \(-0.337701\pi\)
0.488070 + 0.872804i \(0.337701\pi\)
\(338\) 168.123i 0.497406i
\(339\) −343.225 262.586i −1.01246 0.774590i
\(340\) 205.373 0.604037
\(341\) 102.715i 0.301218i
\(342\) −116.140 + 31.4762i −0.339590 + 0.0920357i
\(343\) −18.5203 −0.0539949
\(344\) 459.489i 1.33572i
\(345\) 57.8745 75.6475i 0.167752 0.219268i
\(346\) 25.7347 0.0743776
\(347\) 128.635i 0.370707i −0.982672 0.185353i \(-0.940657\pi\)
0.982672 0.185353i \(-0.0593430\pi\)
\(348\) 94.8562 + 72.5703i 0.272575 + 0.208535i
\(349\) −73.4837 −0.210555 −0.105277 0.994443i \(-0.533573\pi\)
−0.105277 + 0.994443i \(0.533573\pi\)
\(350\) 101.871i 0.291061i
\(351\) −158.786 64.9737i −0.452381 0.185110i
\(352\) −80.5830 −0.228929
\(353\) 239.685i 0.678995i 0.940607 + 0.339498i \(0.110257\pi\)
−0.940607 + 0.339498i \(0.889743\pi\)
\(354\) −98.5568 + 128.823i −0.278409 + 0.363907i
\(355\) 500.369 1.40949
\(356\) 144.765i 0.406642i
\(357\) 76.5608 + 58.5732i 0.214456 + 0.164071i
\(358\) −446.693 −1.24775
\(359\) 180.215i 0.501992i −0.967988 0.250996i \(-0.919242\pi\)
0.967988 0.250996i \(-0.0807581\pi\)
\(360\) −142.871 527.159i −0.396863 1.46433i
\(361\) −256.373 −0.710173
\(362\) 282.187i 0.779523i
\(363\) −208.110 + 272.020i −0.573307 + 0.749367i
\(364\) 38.5242 0.105836
\(365\) 448.598i 1.22904i
\(366\) 63.7817 + 48.7965i 0.174267 + 0.133324i
\(367\) 229.786 0.626119 0.313059 0.949734i \(-0.398646\pi\)
0.313059 + 0.949734i \(0.398646\pi\)
\(368\) 6.81057i 0.0185070i
\(369\) 263.033 71.2871i 0.712826 0.193190i
\(370\) 395.867 1.06991
\(371\) 277.808i 0.748809i
\(372\) −164.125 + 214.528i −0.441198 + 0.576687i
\(373\) 441.749 1.18431 0.592157 0.805823i \(-0.298277\pi\)
0.592157 + 0.805823i \(0.298277\pi\)
\(374\) 41.4990i 0.110960i
\(375\) −78.3765 59.9623i −0.209004 0.159900i
\(376\) −328.737 −0.874301
\(377\) 110.394i 0.292822i
\(378\) 35.3614 86.4178i 0.0935487 0.228618i
\(379\) −421.203 −1.11135 −0.555676 0.831399i \(-0.687541\pi\)
−0.555676 + 0.831399i \(0.687541\pi\)
\(380\) 172.971i 0.455186i
\(381\) 66.6863 87.1653i 0.175030 0.228780i
\(382\) 58.4418 0.152989
\(383\) 595.591i 1.55507i −0.628841 0.777534i \(-0.716470\pi\)
0.628841 0.777534i \(-0.283530\pi\)
\(384\) −148.582 113.674i −0.386933 0.296025i
\(385\) −51.0405 −0.132573
\(386\) 189.688i 0.491419i
\(387\) 131.542 + 485.361i 0.339903 + 1.25416i
\(388\) 43.9190 0.113193
\(389\) 367.347i 0.944336i 0.881509 + 0.472168i \(0.156528\pi\)
−0.881509 + 0.472168i \(0.843472\pi\)
\(390\) 111.727 146.038i 0.286479 0.374455i
\(391\) 52.2510 0.133634
\(392\) 57.5651i 0.146850i
\(393\) 80.2614 + 61.4044i 0.204227 + 0.156245i
\(394\) 114.324 0.290163
\(395\) 466.734i 1.18160i
\(396\) 52.0366 14.1029i 0.131406 0.0356135i
\(397\) 408.346 1.02858 0.514290 0.857616i \(-0.328055\pi\)
0.514290 + 0.857616i \(0.328055\pi\)
\(398\) 85.5062i 0.214840i
\(399\) −49.3320 + 64.4816i −0.123639 + 0.161608i
\(400\) 46.6314 0.116578
\(401\) 238.817i 0.595555i 0.954635 + 0.297777i \(0.0962453\pi\)
−0.954635 + 0.297777i \(0.903755\pi\)
\(402\) 84.6052 + 64.7277i 0.210461 + 0.161014i
\(403\) −249.668 −0.619524
\(404\) 226.199i 0.559899i
\(405\) 301.830 + 515.940i 0.745259 + 1.27393i
\(406\) −60.0810 −0.147983
\(407\) 107.288i 0.263606i
\(408\) 182.059 237.968i 0.446223 0.583255i
\(409\) −649.365 −1.58769 −0.793844 0.608121i \(-0.791924\pi\)
−0.793844 + 0.608121i \(0.791924\pi\)
\(410\) 292.075i 0.712378i
\(411\) 95.2470 + 72.8693i 0.231745 + 0.177297i
\(412\) −128.899 −0.312862
\(413\) 109.439i 0.264985i
\(414\) −13.2392 48.8495i −0.0319787 0.117994i
\(415\) −663.741 −1.59938
\(416\) 195.871i 0.470844i
\(417\) 354.808 463.768i 0.850858 1.11215i
\(418\) 34.9516 0.0836163
\(419\) 11.5178i 0.0274888i 0.999906 + 0.0137444i \(0.00437512\pi\)
−0.999906 + 0.0137444i \(0.995625\pi\)
\(420\) −106.601 81.5559i −0.253813 0.194181i
\(421\) −83.9921 −0.199506 −0.0997531 0.995012i \(-0.531805\pi\)
−0.0997531 + 0.995012i \(0.531805\pi\)
\(422\) 53.0458i 0.125701i
\(423\) 347.247 94.1108i 0.820915 0.222484i
\(424\) 863.490 2.03653
\(425\) 357.758i 0.841783i
\(426\) 161.557 211.170i 0.379241 0.495705i
\(427\) 54.1843 0.126895
\(428\) 282.168i 0.659272i
\(429\) 39.5791 + 30.2802i 0.0922589 + 0.0705832i
\(430\) −538.952 −1.25338
\(431\) 694.004i 1.61022i −0.593127 0.805109i \(-0.702107\pi\)
0.593127 0.805109i \(-0.297893\pi\)
\(432\) −39.5575 16.1866i −0.0915684 0.0374690i
\(433\) 116.834 0.269824 0.134912 0.990858i \(-0.456925\pi\)
0.134912 + 0.990858i \(0.456925\pi\)
\(434\) 135.880i 0.313087i
\(435\) 233.705 305.474i 0.537252 0.702239i
\(436\) 377.041 0.864772
\(437\) 44.0072i 0.100703i
\(438\) −189.322 144.842i −0.432241 0.330688i
\(439\) −528.073 −1.20290 −0.601450 0.798910i \(-0.705410\pi\)
−0.601450 + 0.798910i \(0.705410\pi\)
\(440\) 158.645i 0.360558i
\(441\) −16.4797 60.8064i −0.0373690 0.137883i
\(442\) 100.871 0.228214
\(443\) 272.252i 0.614564i −0.951619 0.307282i \(-0.900581\pi\)
0.951619 0.307282i \(-0.0994194\pi\)
\(444\) −171.431 + 224.077i −0.386107 + 0.504678i
\(445\) −466.199 −1.04764
\(446\) 131.964i 0.295883i
\(447\) −485.314 371.292i −1.08571 0.830631i
\(448\) 123.354 0.275344
\(449\) 525.770i 1.17098i 0.810680 + 0.585490i \(0.199098\pi\)
−0.810680 + 0.585490i \(0.800902\pi\)
\(450\) −334.468 + 90.6474i −0.743262 + 0.201439i
\(451\) −79.1581 −0.175517
\(452\) 330.092i 0.730292i
\(453\) −302.140 + 394.925i −0.666975 + 0.871800i
\(454\) −511.439 −1.12652
\(455\) 124.063i 0.272666i
\(456\) 200.423 + 153.335i 0.439525 + 0.336261i
\(457\) −513.786 −1.12426 −0.562129 0.827050i \(-0.690017\pi\)
−0.562129 + 0.827050i \(0.690017\pi\)
\(458\) 8.90362i 0.0194402i
\(459\) −124.184 + 303.487i −0.270554 + 0.661192i
\(460\) −72.7530 −0.158159
\(461\) 687.879i 1.49214i −0.665865 0.746072i \(-0.731937\pi\)
0.665865 0.746072i \(-0.268063\pi\)
\(462\) −16.4797 + 21.5406i −0.0356704 + 0.0466246i
\(463\) 781.061 1.68696 0.843479 0.537162i \(-0.180504\pi\)
0.843479 + 0.537162i \(0.180504\pi\)
\(464\) 27.5020i 0.0592715i
\(465\) 690.863 + 528.548i 1.48573 + 1.13666i
\(466\) 152.769 0.327830
\(467\) 163.353i 0.349792i −0.984587 0.174896i \(-0.944041\pi\)
0.984587 0.174896i \(-0.0559589\pi\)
\(468\) 34.2797 + 126.484i 0.0732472 + 0.270265i
\(469\) 71.8745 0.153251
\(470\) 385.588i 0.820400i
\(471\) 551.826 721.289i 1.17161 1.53140i
\(472\) 340.161 0.720679
\(473\) 146.067i 0.308809i
\(474\) 196.975 + 150.697i 0.415560 + 0.317926i
\(475\) 301.314 0.634345
\(476\) 73.6313i 0.154688i
\(477\) −912.110 + 247.200i −1.91218 + 0.518239i
\(478\) −78.3765 −0.163968
\(479\) 700.159i 1.46171i −0.682533 0.730855i \(-0.739122\pi\)
0.682533 0.730855i \(-0.260878\pi\)
\(480\) −414.660 + 542.000i −0.863875 + 1.12917i
\(481\) −260.782 −0.542166
\(482\) 176.135i 0.365425i
\(483\) −27.1216 20.7495i −0.0561523 0.0429596i
\(484\) 261.612 0.540520
\(485\) 141.436i 0.291621i
\(486\) 315.195 + 39.2035i 0.648550 + 0.0806656i
\(487\) 86.5909 0.177805 0.0889023 0.996040i \(-0.471664\pi\)
0.0889023 + 0.996040i \(0.471664\pi\)
\(488\) 168.417i 0.345117i
\(489\) 264.391 345.584i 0.540677 0.706716i
\(490\) 67.5203 0.137796
\(491\) 741.494i 1.51017i 0.655627 + 0.755085i \(0.272404\pi\)
−0.655627 + 0.755085i \(0.727596\pi\)
\(492\) −165.327 126.484i −0.336030 0.257081i
\(493\) 210.996 0.427984
\(494\) 84.9560i 0.171976i
\(495\) −45.4170 167.578i −0.0917515 0.338542i
\(496\) −62.1987 −0.125401
\(497\) 179.395i 0.360956i
\(498\) −214.306 + 280.118i −0.430333 + 0.562486i
\(499\) 379.814 0.761151 0.380575 0.924750i \(-0.375726\pi\)
0.380575 + 0.924750i \(0.375726\pi\)
\(500\) 75.3775i 0.150755i
\(501\) 46.8419 + 35.8366i 0.0934967 + 0.0715302i
\(502\) 350.626 0.698458
\(503\) 465.808i 0.926059i 0.886343 + 0.463029i \(0.153238\pi\)
−0.886343 + 0.463029i \(0.846762\pi\)
\(504\) −189.000 + 51.2228i −0.375000 + 0.101632i
\(505\) 728.450 1.44247
\(506\) 14.7010i 0.0290533i
\(507\) 234.465 306.468i 0.462455 0.604473i
\(508\) −83.8301 −0.165020
\(509\) 750.503i 1.47447i 0.675639 + 0.737233i \(0.263868\pi\)
−0.675639 + 0.737233i \(0.736132\pi\)
\(510\) −279.122 213.543i −0.547297 0.418713i
\(511\) −160.834 −0.314744
\(512\) 100.868i 0.197009i
\(513\) −255.605 104.592i −0.498256 0.203882i
\(514\) 306.029 0.595387
\(515\) 415.106i 0.806031i
\(516\) 233.395 305.069i 0.452315 0.591219i
\(517\) −104.502 −0.202131
\(518\) 141.928i 0.273993i
\(519\) 46.9111 + 35.8896i 0.0903875 + 0.0691514i
\(520\) −385.616 −0.741569
\(521\) 726.946i 1.39529i 0.716443 + 0.697645i \(0.245769\pi\)
−0.716443 + 0.697645i \(0.754231\pi\)
\(522\) −53.4615 197.260i −0.102417 0.377893i
\(523\) −624.707 −1.19447 −0.597234 0.802067i \(-0.703734\pi\)
−0.597234 + 0.802067i \(0.703734\pi\)
\(524\) 77.1903i 0.147310i
\(525\) −142.070 + 185.699i −0.270609 + 0.353712i
\(526\) 326.959 0.621596
\(527\) 477.190i 0.905485i
\(528\) 9.86015 + 7.54356i 0.0186745 + 0.0142871i
\(529\) 510.490 0.965010
\(530\) 1012.82i 1.91098i
\(531\) −359.314 + 97.3812i −0.676674 + 0.183392i
\(532\) 62.0144 0.116568
\(533\) 192.408i 0.360990i
\(534\) −150.524 + 196.749i −0.281881 + 0.368445i
\(535\) −908.693 −1.69849
\(536\) 223.402i 0.416795i
\(537\) −814.265 622.958i −1.51632 1.16007i
\(538\) 445.306 0.827706
\(539\) 18.2993i 0.0339505i
\(540\) 172.911 422.568i 0.320206 0.782533i
\(541\) −291.757 −0.539292 −0.269646 0.962960i \(-0.586907\pi\)
−0.269646 + 0.962960i \(0.586907\pi\)
\(542\) 27.8403i 0.0513659i
\(543\) −393.539 + 514.392i −0.724749 + 0.947315i
\(544\) −374.369 −0.688178
\(545\) 1214.22i 2.22792i
\(546\) −52.3582 40.0569i −0.0958941 0.0733643i
\(547\) 204.952 0.374683 0.187342 0.982295i \(-0.440013\pi\)
0.187342 + 0.982295i \(0.440013\pi\)
\(548\) 91.6026i 0.167158i
\(549\) 48.2144 + 177.900i 0.0878222 + 0.324044i
\(550\) 100.656 0.183011
\(551\) 177.707i 0.322517i
\(552\) −64.4941 + 84.2999i −0.116837 + 0.152717i
\(553\) 167.336 0.302597
\(554\) 296.599i 0.535378i
\(555\) 721.616 + 552.076i 1.30021 + 0.994731i
\(556\) −446.022 −0.802198
\(557\) 503.883i 0.904637i −0.891857 0.452318i \(-0.850597\pi\)
0.891857 0.452318i \(-0.149403\pi\)
\(558\) 446.125 120.909i 0.799508 0.216683i
\(559\) 355.041 0.635135
\(560\) 30.9072i 0.0551915i
\(561\) 57.8745 75.6475i 0.103163 0.134844i
\(562\) −307.806 −0.547698
\(563\) 108.735i 0.193135i 0.995326 + 0.0965674i \(0.0307863\pi\)
−0.995326 + 0.0965674i \(0.969214\pi\)
\(564\) −218.259 166.980i −0.386984 0.296064i
\(565\) 1063.02 1.88146
\(566\) 481.840i 0.851307i
\(567\) 184.978 108.214i 0.326239 0.190853i
\(568\) −557.600 −0.981690
\(569\) 434.871i 0.764273i −0.924106 0.382136i \(-0.875188\pi\)
0.924106 0.382136i \(-0.124812\pi\)
\(570\) 179.852 235.084i 0.315530 0.412428i
\(571\) 119.122 0.208619 0.104310 0.994545i \(-0.466737\pi\)
0.104310 + 0.994545i \(0.466737\pi\)
\(572\) 38.0646i 0.0665466i
\(573\) 106.532 + 81.5029i 0.185920 + 0.142239i
\(574\) 104.716 0.182433
\(575\) 126.735i 0.220409i
\(576\) 109.763 + 405.001i 0.190561 + 0.703127i
\(577\) −655.417 −1.13590 −0.567952 0.823061i \(-0.692264\pi\)
−0.567952 + 0.823061i \(0.692264\pi\)
\(578\) 184.957i 0.319994i
\(579\) 264.539 345.777i 0.456889 0.597197i
\(580\) −293.786 −0.506527
\(581\) 237.968i 0.409584i
\(582\) −59.6902 45.6663i −0.102560 0.0784645i
\(583\) 274.494 0.470830
\(584\) 499.908i 0.856007i
\(585\) 407.328 110.394i 0.696287 0.188708i
\(586\) −694.885 −1.18581
\(587\) 736.236i 1.25424i 0.778925 + 0.627118i \(0.215765\pi\)
−0.778925 + 0.627118i \(0.784235\pi\)
\(588\) −29.2399 + 38.2193i −0.0497277 + 0.0649988i
\(589\) −401.903 −0.682348
\(590\) 398.987i 0.676249i
\(591\) 208.399 + 159.437i 0.352620 + 0.269774i
\(592\) −64.9674 −0.109742
\(593\) 832.884i 1.40453i 0.711917 + 0.702263i \(0.247827\pi\)
−0.711917 + 0.702263i \(0.752173\pi\)
\(594\) −85.3869 34.9396i −0.143749 0.0588209i
\(595\) −237.122 −0.398524
\(596\) 466.744i 0.783127i
\(597\) −119.247 + 155.867i −0.199744 + 0.261084i
\(598\) −35.7333 −0.0597546
\(599\) 69.3290i 0.115741i 0.998324 + 0.0578706i \(0.0184311\pi\)
−0.998324 + 0.0578706i \(0.981569\pi\)
\(600\) 577.194 + 441.585i 0.961990 + 0.735976i
\(601\) −161.720 −0.269085 −0.134543 0.990908i \(-0.542957\pi\)
−0.134543 + 0.990908i \(0.542957\pi\)
\(602\) 193.228i 0.320977i
\(603\) 63.9555 + 235.981i 0.106062 + 0.391345i
\(604\) 379.814 0.628832
\(605\) 842.492i 1.39255i
\(606\) 235.199 307.427i 0.388117 0.507305i
\(607\) 929.608 1.53148 0.765740 0.643151i \(-0.222373\pi\)
0.765740 + 0.643151i \(0.222373\pi\)
\(608\) 315.304i 0.518592i
\(609\) −109.520 83.7891i −0.179836 0.137585i
\(610\) −197.542 −0.323840
\(611\) 254.010i 0.415729i
\(612\) 241.749 65.5188i 0.395015 0.107057i
\(613\) 297.940 0.486036 0.243018 0.970022i \(-0.421863\pi\)
0.243018 + 0.970022i \(0.421863\pi\)
\(614\) 742.121i 1.20867i
\(615\) −407.328 + 532.417i −0.662322 + 0.865718i
\(616\) 56.8784 0.0923351
\(617\) 975.575i 1.58116i −0.612360 0.790579i \(-0.709780\pi\)
0.612360 0.790579i \(-0.290220\pi\)
\(618\) 175.187 + 134.028i 0.283474 + 0.216873i
\(619\) 357.034 0.576792 0.288396 0.957511i \(-0.406878\pi\)
0.288396 + 0.957511i \(0.406878\pi\)
\(620\) 664.428i 1.07166i
\(621\) 43.9921 107.510i 0.0708408 0.173124i
\(622\) 55.8824 0.0898431
\(623\) 167.144i 0.268289i
\(624\) −18.3360 + 23.9668i −0.0293845 + 0.0384084i
\(625\) −493.693 −0.789908
\(626\) 206.675i 0.330151i
\(627\) 63.7124 + 48.7435i 0.101615 + 0.0777409i
\(628\) −693.690 −1.10460
\(629\) 498.432i 0.792420i
\(630\) 60.0810 + 221.685i 0.0953667 + 0.351881i
\(631\) −813.223 −1.28879 −0.644393 0.764695i \(-0.722890\pi\)
−0.644393 + 0.764695i \(0.722890\pi\)
\(632\) 520.118i 0.822971i
\(633\) −73.9778 + 96.6960i −0.116869 + 0.152758i
\(634\) −184.227 −0.290579
\(635\) 269.966i 0.425143i
\(636\) 573.298 + 438.605i 0.901412 + 0.689630i
\(637\) −44.4797 −0.0698269
\(638\) 59.3643i 0.0930475i
\(639\) 588.996 159.630i 0.921747 0.249812i
\(640\) 460.184 0.719038
\(641\) 646.727i 1.00893i 0.863431 + 0.504467i \(0.168311\pi\)
−0.863431 + 0.504467i \(0.831689\pi\)
\(642\) −293.395 + 383.495i −0.457001 + 0.597344i
\(643\) 144.561 0.224822 0.112411 0.993662i \(-0.464143\pi\)
0.112411 + 0.993662i \(0.464143\pi\)
\(644\) 26.0838i 0.0405028i
\(645\) −982.442 751.622i −1.52317 1.16531i
\(646\) 162.376 0.251357
\(647\) 716.654i 1.10766i −0.832631 0.553828i \(-0.813166\pi\)
0.832631 0.553828i \(-0.186834\pi\)
\(648\) −336.353 574.953i −0.519063 0.887273i
\(649\) 108.133 0.166615
\(650\) 244.663i 0.376404i
\(651\) 189.498 247.692i 0.291088 0.380479i
\(652\) −332.361 −0.509756
\(653\) 378.999i 0.580397i 0.956966 + 0.290199i \(0.0937214\pi\)
−0.956966 + 0.290199i \(0.906279\pi\)
\(654\) −512.435 392.041i −0.783540 0.599452i
\(655\) −248.583 −0.379516
\(656\) 47.9337i 0.0730696i
\(657\) −143.114 528.056i −0.217829 0.803738i
\(658\) 138.243 0.210096
\(659\) 710.721i 1.07848i −0.842151 0.539242i \(-0.818711\pi\)
0.842151 0.539242i \(-0.181289\pi\)
\(660\) −80.5830 + 105.330i −0.122095 + 0.159590i
\(661\) 91.5045 0.138433 0.0692167 0.997602i \(-0.477950\pi\)
0.0692167 + 0.997602i \(0.477950\pi\)
\(662\) 337.712i 0.510139i
\(663\) 183.875 + 140.674i 0.277337 + 0.212178i
\(664\) 739.659 1.11394
\(665\) 199.710i 0.300316i
\(666\) 465.984 126.291i 0.699676 0.189626i
\(667\) −74.7451 −0.112062
\(668\) 45.0495i 0.0674394i
\(669\) −184.037 + 240.553i −0.275092 + 0.359571i
\(670\) −262.037 −0.391099
\(671\) 53.5379i 0.0797883i
\(672\) 194.321 + 148.666i 0.289168 + 0.221230i
\(673\) 645.806 0.959594 0.479797 0.877380i \(-0.340710\pi\)
0.479797 + 0.877380i \(0.340710\pi\)
\(674\) 429.981i 0.637954i
\(675\) −736.110 301.210i −1.09053 0.446237i
\(676\) −294.741 −0.436008
\(677\) 335.571i 0.495674i −0.968802 0.247837i \(-0.920280\pi\)
0.968802 0.247837i \(-0.0797198\pi\)
\(678\) 343.225 448.627i 0.506231 0.661692i
\(679\) −50.7085 −0.0746811
\(680\) 737.027i 1.08386i
\(681\) −932.290 713.254i −1.36900 1.04736i
\(682\) −134.259 −0.196860
\(683\) 113.336i 0.165939i −0.996552 0.0829694i \(-0.973560\pi\)
0.996552 0.0829694i \(-0.0264404\pi\)
\(684\) 55.1818 + 203.608i 0.0806751 + 0.297672i
\(685\) −294.996 −0.430651
\(686\) 24.2077i 0.0352882i
\(687\) 12.4170 16.2302i 0.0180742 0.0236247i
\(688\) 88.4496 0.128561
\(689\) 667.206i 0.968369i
\(690\) 98.8784 + 75.6475i 0.143302 + 0.109634i
\(691\) 565.667 0.818620 0.409310 0.912395i \(-0.365769\pi\)
0.409310 + 0.912395i \(0.365769\pi\)
\(692\) 45.1161i 0.0651967i
\(693\) −60.0810 + 16.2832i −0.0866970 + 0.0234966i
\(694\) 168.138 0.242274
\(695\) 1436.37i 2.06671i
\(696\) −260.435 + 340.414i −0.374189 + 0.489100i
\(697\) −367.749 −0.527617
\(698\) 96.0501i 0.137608i
\(699\) 278.478 + 213.051i 0.398395 + 0.304794i
\(700\) 178.593 0.255133
\(701\) 872.955i 1.24530i −0.782501 0.622650i \(-0.786056\pi\)
0.782501 0.622650i \(-0.213944\pi\)
\(702\) 84.9268 207.548i 0.120978 0.295652i
\(703\) −419.793 −0.597146
\(704\) 121.883i 0.173129i
\(705\) −537.741 + 702.879i −0.762753 + 0.996991i
\(706\) −313.292 −0.443756
\(707\) 261.168i 0.369403i
\(708\) 225.843 + 172.783i 0.318988 + 0.244043i
\(709\) 1092.04 1.54025 0.770125 0.637894i \(-0.220194\pi\)
0.770125 + 0.637894i \(0.220194\pi\)
\(710\) 654.029i 0.921168i
\(711\) 148.899 + 549.404i 0.209422 + 0.772720i
\(712\) 519.522 0.729665
\(713\) 169.044i 0.237088i
\(714\) −76.5608 + 100.072i −0.107228 + 0.140157i
\(715\) −122.583 −0.171445
\(716\) 783.109i 1.09373i
\(717\) −142.871 109.304i −0.199262 0.152446i
\(718\) 235.558 0.328076
\(719\) 901.769i 1.25420i −0.778939 0.627099i \(-0.784242\pi\)
0.778939 0.627099i \(-0.215758\pi\)
\(720\) 101.476 27.5020i 0.140939 0.0381972i
\(721\) 148.826 0.206416
\(722\) 335.103i 0.464132i
\(723\) −245.638 + 321.072i −0.339748 + 0.444083i
\(724\) 494.710 0.683301
\(725\) 511.773i 0.705894i
\(726\) −355.556 272.020i −0.489747 0.374683i
\(727\) 297.506 0.409224 0.204612 0.978843i \(-0.434407\pi\)
0.204612 + 0.978843i \(0.434407\pi\)
\(728\) 138.253i 0.189908i
\(729\) 519.889 + 511.035i 0.713153 + 0.701008i
\(730\) 586.361 0.803234
\(731\) 678.589i 0.928302i
\(732\) 85.5464 111.817i 0.116867 0.152756i
\(733\) 456.966 0.623419 0.311709 0.950177i \(-0.399098\pi\)
0.311709 + 0.950177i \(0.399098\pi\)
\(734\) 300.352i 0.409198i
\(735\) 123.081 + 94.1638i 0.167457 + 0.128114i
\(736\) 132.620 0.180190
\(737\) 71.0171i 0.0963597i
\(738\) 93.1790 + 343.809i 0.126259 + 0.465865i
\(739\) −332.199 −0.449525 −0.224762 0.974414i \(-0.572161\pi\)
−0.224762 + 0.974414i \(0.572161\pi\)
\(740\) 694.004i 0.937844i
\(741\) −118.480 + 154.864i −0.159892 + 0.208994i
\(742\) −363.122 −0.489382
\(743\) 64.5346i 0.0868568i 0.999057 + 0.0434284i \(0.0138280\pi\)
−0.999057 + 0.0434284i \(0.986172\pi\)
\(744\) −769.882 589.003i −1.03479 0.791670i
\(745\) 1503.10 2.01758
\(746\) 577.408i 0.774005i
\(747\) −781.306 + 211.749i −1.04592 + 0.283466i
\(748\) −72.7530 −0.0972633
\(749\) 325.790i 0.434966i
\(750\) 78.3765 102.446i 0.104502 0.136594i
\(751\) −611.668 −0.814471 −0.407236 0.913323i \(-0.633507\pi\)
−0.407236 + 0.913323i \(0.633507\pi\)
\(752\) 63.2805i 0.0841496i
\(753\) 639.148 + 488.983i 0.848802 + 0.649380i
\(754\) −144.295 −0.191373
\(755\) 1223.15i 1.62007i
\(756\) −151.501 61.9930i −0.200399 0.0820014i
\(757\) −207.357 −0.273919 −0.136960 0.990577i \(-0.543733\pi\)
−0.136960 + 0.990577i \(0.543733\pi\)
\(758\) 550.552i 0.726322i
\(759\) −20.5020 + 26.7980i −0.0270118 + 0.0353070i
\(760\) −620.745 −0.816770
\(761\) 337.770i 0.443851i −0.975064 0.221925i \(-0.928766\pi\)
0.975064 0.221925i \(-0.0712341\pi\)
\(762\) 113.933 + 87.1653i 0.149519 + 0.114390i
\(763\) −435.328 −0.570548
\(764\) 102.456i 0.134104i
\(765\) −210.996 778.526i −0.275812 1.01768i
\(766\) 778.494 1.01631
\(767\) 262.837i 0.342682i
\(768\) 488.538 638.565i 0.636117 0.831465i
\(769\) −1042.22 −1.35529 −0.677646 0.735388i \(-0.737000\pi\)
−0.677646 + 0.735388i \(0.737000\pi\)
\(770\) 66.7148i 0.0866426i
\(771\) 557.852 + 426.788i 0.723544 + 0.553551i
\(772\) −332.546 −0.430760
\(773\) 291.448i 0.377035i −0.982070 0.188517i \(-0.939632\pi\)
0.982070 0.188517i \(-0.0603682\pi\)
\(774\) −634.413 + 171.939i −0.819655 + 0.222143i
\(775\) −1157.43 −1.49346
\(776\) 157.613i 0.203110i
\(777\) 197.933 258.718i 0.254740 0.332970i
\(778\) −480.157 −0.617168
\(779\) 309.729i 0.397598i
\(780\) −256.022 195.871i −0.328234 0.251117i
\(781\) −177.255 −0.226959
\(782\) 68.2970i 0.0873363i
\(783\) 177.646 434.138i 0.226878 0.554455i
\(784\) −11.0810 −0.0141340
\(785\) 2233.95i 2.84580i
\(786\) −80.2614 + 104.909i −0.102114 + 0.133472i
\(787\) 293.889 0.373429 0.186715 0.982414i \(-0.440216\pi\)
0.186715 + 0.982414i \(0.440216\pi\)
\(788\) 200.425i 0.254346i