Properties

Label 225.4.p.b.32.16
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 32.16
Character \(\chi\) \(=\) 225.32
Dual form 225.4.p.b.218.16

$q$-expansion

\(f(q)\) \(=\) \(q+(5.27515 + 1.41347i) q^{2} +(-1.94123 + 4.81992i) q^{3} +(18.9011 + 10.9125i) q^{4} +(-17.0531 + 22.6819i) q^{6} +(-1.13077 + 4.22008i) q^{7} +(53.3880 + 53.3880i) q^{8} +(-19.4633 - 18.7131i) q^{9} +O(q^{10})\) \(q+(5.27515 + 1.41347i) q^{2} +(-1.94123 + 4.81992i) q^{3} +(18.9011 + 10.9125i) q^{4} +(-17.0531 + 22.6819i) q^{6} +(-1.13077 + 4.22008i) q^{7} +(53.3880 + 53.3880i) q^{8} +(-19.4633 - 18.7131i) q^{9} +(-5.91593 + 3.41556i) q^{11} +(-89.2889 + 69.9180i) q^{12} +(6.54783 + 24.4368i) q^{13} +(-11.9299 + 20.6632i) q^{14} +(118.867 + 205.883i) q^{16} +(36.0612 - 36.0612i) q^{17} +(-76.2213 - 126.225i) q^{18} -59.8443i q^{19} +(-18.1454 - 13.6423i) q^{21} +(-36.0352 + 9.65561i) q^{22} +(-50.9044 + 13.6398i) q^{23} +(-360.964 + 153.688i) q^{24} +138.163i q^{26} +(127.978 - 57.4851i) q^{27} +(-67.4245 + 67.4245i) q^{28} +(22.1046 + 38.2863i) q^{29} +(67.9692 - 117.726i) q^{31} +(179.699 + 670.646i) q^{32} +(-4.97859 - 35.1447i) q^{33} +(241.199 - 139.257i) q^{34} +(-163.669 - 566.092i) q^{36} +(-233.330 - 233.330i) q^{37} +(84.5883 - 315.688i) q^{38} +(-130.494 - 15.8774i) q^{39} +(335.678 + 193.804i) q^{41} +(-76.4365 - 97.6133i) q^{42} +(306.315 + 82.0769i) q^{43} -149.090 q^{44} -287.808 q^{46} +(-316.977 - 84.9338i) q^{47} +(-1223.09 + 173.263i) q^{48} +(280.516 + 161.956i) q^{49} +(103.809 + 243.815i) q^{51} +(-142.907 + 533.336i) q^{52} +(43.1181 + 43.1181i) q^{53} +(756.358 - 122.349i) q^{54} +(-285.671 + 164.932i) q^{56} +(288.445 + 116.171i) q^{57} +(62.4884 + 233.210i) q^{58} +(248.925 - 431.152i) q^{59} +(36.3039 + 62.8801i) q^{61} +(524.950 - 524.950i) q^{62} +(100.979 - 60.9764i) q^{63} +1889.88i q^{64} +(23.4132 - 192.431i) q^{66} +(-178.215 + 47.7525i) q^{67} +(1075.11 - 288.076i) q^{68} +(33.0742 - 271.833i) q^{69} -563.835i q^{71} +(-40.0503 - 2038.16i) q^{72} +(-84.7460 + 84.7460i) q^{73} +(-901.044 - 1560.65i) q^{74} +(653.054 - 1131.12i) q^{76} +(-7.72441 - 28.8279i) q^{77} +(-665.935 - 268.206i) q^{78} +(186.138 - 107.467i) q^{79} +(28.6389 + 728.437i) q^{81} +(1496.82 + 1496.82i) q^{82} +(249.226 - 930.125i) q^{83} +(-194.095 - 455.867i) q^{84} +(1499.84 + 865.935i) q^{86} +(-227.447 + 32.2201i) q^{87} +(-498.190 - 133.490i) q^{88} +288.322 q^{89} -110.529 q^{91} +(-1110.99 - 297.690i) q^{92} +(435.487 + 556.139i) q^{93} +(-1552.05 - 896.076i) q^{94} +(-3581.30 - 435.740i) q^{96} +(425.658 - 1588.58i) q^{97} +(1250.84 + 1250.84i) q^{98} +(179.059 + 44.2274i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.27515 + 1.41347i 1.86505 + 0.499738i 0.999998 0.00195086i \(-0.000620979\pi\)
0.865048 + 0.501689i \(0.167288\pi\)
\(3\) −1.94123 + 4.81992i −0.373589 + 0.927594i
\(4\) 18.9011 + 10.9125i 2.36264 + 1.36407i
\(5\) 0 0
\(6\) −17.0531 + 22.6819i −1.16031 + 1.54331i
\(7\) −1.13077 + 4.22008i −0.0610556 + 0.227863i −0.989711 0.143081i \(-0.954299\pi\)
0.928655 + 0.370944i \(0.120966\pi\)
\(8\) 53.3880 + 53.3880i 2.35944 + 2.35944i
\(9\) −19.4633 18.7131i −0.720862 0.693078i
\(10\) 0 0
\(11\) −5.91593 + 3.41556i −0.162156 + 0.0936210i −0.578882 0.815411i \(-0.696511\pi\)
0.416726 + 0.909032i \(0.363178\pi\)
\(12\) −89.2889 + 69.9180i −2.14796 + 1.68197i
\(13\) 6.54783 + 24.4368i 0.139696 + 0.521351i 0.999934 + 0.0114594i \(0.00364774\pi\)
−0.860239 + 0.509891i \(0.829686\pi\)
\(14\) −11.9299 + 20.6632i −0.227743 + 0.394463i
\(15\) 0 0
\(16\) 118.867 + 205.883i 1.85729 + 3.21693i
\(17\) 36.0612 36.0612i 0.514477 0.514477i −0.401418 0.915895i \(-0.631482\pi\)
0.915895 + 0.401418i \(0.131482\pi\)
\(18\) −76.2213 126.225i −0.998085 1.65287i
\(19\) 59.8443i 0.722591i −0.932451 0.361296i \(-0.882335\pi\)
0.932451 0.361296i \(-0.117665\pi\)
\(20\) 0 0
\(21\) −18.1454 13.6423i −0.188554 0.141762i
\(22\) −36.0352 + 9.65561i −0.349215 + 0.0935719i
\(23\) −50.9044 + 13.6398i −0.461491 + 0.123656i −0.482071 0.876132i \(-0.660115\pi\)
0.0205799 + 0.999788i \(0.493449\pi\)
\(24\) −360.964 + 153.688i −3.07006 + 1.30714i
\(25\) 0 0
\(26\) 138.163i 1.04215i
\(27\) 127.978 57.4851i 0.912202 0.409741i
\(28\) −67.4245 + 67.4245i −0.455073 + 0.455073i
\(29\) 22.1046 + 38.2863i 0.141542 + 0.245158i 0.928077 0.372387i \(-0.121461\pi\)
−0.786535 + 0.617545i \(0.788127\pi\)
\(30\) 0 0
\(31\) 67.9692 117.726i 0.393794 0.682072i −0.599152 0.800635i \(-0.704496\pi\)
0.992946 + 0.118563i \(0.0378289\pi\)
\(32\) 179.699 + 670.646i 0.992706 + 3.70483i
\(33\) −4.97859 35.1447i −0.0262625 0.185391i
\(34\) 241.199 139.257i 1.21663 0.702421i
\(35\) 0 0
\(36\) −163.669 566.092i −0.757729 2.62080i
\(37\) −233.330 233.330i −1.03674 1.03674i −0.999299 0.0374360i \(-0.988081\pi\)
−0.0374360 0.999299i \(-0.511919\pi\)
\(38\) 84.5883 315.688i 0.361106 1.34767i
\(39\) −130.494 15.8774i −0.535791 0.0651902i
\(40\) 0 0
\(41\) 335.678 + 193.804i 1.27864 + 0.738221i 0.976598 0.215074i \(-0.0689993\pi\)
0.302039 + 0.953295i \(0.402333\pi\)
\(42\) −76.4365 97.6133i −0.280819 0.358620i
\(43\) 306.315 + 82.0769i 1.08634 + 0.291084i 0.757191 0.653194i \(-0.226571\pi\)
0.329149 + 0.944278i \(0.393238\pi\)
\(44\) −149.090 −0.510822
\(45\) 0 0
\(46\) −287.808 −0.922499
\(47\) −316.977 84.9338i −0.983742 0.263593i −0.269122 0.963106i \(-0.586734\pi\)
−0.714620 + 0.699513i \(0.753400\pi\)
\(48\) −1223.09 + 173.263i −3.67787 + 0.521007i
\(49\) 280.516 + 161.956i 0.817832 + 0.472175i
\(50\) 0 0
\(51\) 103.809 + 243.815i 0.285023 + 0.669430i
\(52\) −142.907 + 533.336i −0.381108 + 1.42232i
\(53\) 43.1181 + 43.1181i 0.111749 + 0.111749i 0.760770 0.649021i \(-0.224821\pi\)
−0.649021 + 0.760770i \(0.724821\pi\)
\(54\) 756.358 122.349i 1.90606 0.308325i
\(55\) 0 0
\(56\) −285.671 + 164.932i −0.681685 + 0.393571i
\(57\) 288.445 + 116.171i 0.670271 + 0.269952i
\(58\) 62.4884 + 233.210i 0.141468 + 0.527965i
\(59\) 248.925 431.152i 0.549277 0.951376i −0.449047 0.893508i \(-0.648237\pi\)
0.998324 0.0578676i \(-0.0184301\pi\)
\(60\) 0 0
\(61\) 36.3039 + 62.8801i 0.0762006 + 0.131983i 0.901608 0.432555i \(-0.142388\pi\)
−0.825407 + 0.564538i \(0.809054\pi\)
\(62\) 524.950 524.950i 1.07530 1.07530i
\(63\) 100.979 60.9764i 0.201939 0.121941i
\(64\) 1889.88i 3.69118i
\(65\) 0 0
\(66\) 23.4132 192.431i 0.0436662 0.358887i
\(67\) −178.215 + 47.7525i −0.324961 + 0.0870730i −0.417612 0.908626i \(-0.637133\pi\)
0.0926506 + 0.995699i \(0.470466\pi\)
\(68\) 1075.11 288.076i 1.91730 0.513740i
\(69\) 33.0742 271.833i 0.0577053 0.474273i
\(70\) 0 0
\(71\) 563.835i 0.942464i −0.882009 0.471232i \(-0.843809\pi\)
0.882009 0.471232i \(-0.156191\pi\)
\(72\) −40.0503 2038.16i −0.0655552 3.33611i
\(73\) −84.7460 + 84.7460i −0.135874 + 0.135874i −0.771772 0.635899i \(-0.780630\pi\)
0.635899 + 0.771772i \(0.280630\pi\)
\(74\) −901.044 1560.65i −1.41546 2.45165i
\(75\) 0 0
\(76\) 653.054 1131.12i 0.985663 1.70722i
\(77\) −7.72441 28.8279i −0.0114322 0.0426655i
\(78\) −665.935 268.206i −0.966697 0.389338i
\(79\) 186.138 107.467i 0.265091 0.153050i −0.361564 0.932347i \(-0.617757\pi\)
0.626655 + 0.779297i \(0.284424\pi\)
\(80\) 0 0
\(81\) 28.6389 + 728.437i 0.0392852 + 0.999228i
\(82\) 1496.82 + 1496.82i 2.01580 + 2.01580i
\(83\) 249.226 930.125i 0.329592 1.23005i −0.580022 0.814601i \(-0.696956\pi\)
0.909614 0.415454i \(-0.136377\pi\)
\(84\) −194.095 455.867i −0.252113 0.592133i
\(85\) 0 0
\(86\) 1499.84 + 865.935i 1.88061 + 1.08577i
\(87\) −227.447 + 32.2201i −0.280286 + 0.0397052i
\(88\) −498.190 133.490i −0.603491 0.161705i
\(89\) 288.322 0.343394 0.171697 0.985150i \(-0.445075\pi\)
0.171697 + 0.985150i \(0.445075\pi\)
\(90\) 0 0
\(91\) −110.529 −0.127326
\(92\) −1110.99 297.690i −1.25901 0.337351i
\(93\) 435.487 + 556.139i 0.485569 + 0.620096i
\(94\) −1552.05 896.076i −1.70300 0.983226i
\(95\) 0 0
\(96\) −3581.30 435.740i −3.80744 0.463255i
\(97\) 425.658 1588.58i 0.445556 1.66284i −0.268907 0.963166i \(-0.586662\pi\)
0.714463 0.699673i \(-0.246671\pi\)
\(98\) 1250.84 + 1250.84i 1.28933 + 1.28933i
\(99\) 179.059 + 44.2274i 0.181779 + 0.0448992i
\(100\) 0 0
\(101\) −1256.46 + 725.417i −1.23785 + 0.714670i −0.968653 0.248416i \(-0.920090\pi\)
−0.269192 + 0.963087i \(0.586757\pi\)
\(102\) 202.983 + 1432.89i 0.197042 + 1.39095i
\(103\) 84.4689 + 315.242i 0.0808055 + 0.301570i 0.994487 0.104861i \(-0.0334397\pi\)
−0.913681 + 0.406431i \(0.866773\pi\)
\(104\) −955.059 + 1654.21i −0.900492 + 1.55970i
\(105\) 0 0
\(106\) 166.508 + 288.400i 0.152573 + 0.264263i
\(107\) −1233.98 + 1233.98i −1.11489 + 1.11489i −0.122409 + 0.992480i \(0.539062\pi\)
−0.992480 + 0.122409i \(0.960938\pi\)
\(108\) 3046.24 + 310.038i 2.71411 + 0.276236i
\(109\) 577.196i 0.507205i 0.967308 + 0.253603i \(0.0816156\pi\)
−0.967308 + 0.253603i \(0.918384\pi\)
\(110\) 0 0
\(111\) 1577.58 671.686i 1.34898 0.574357i
\(112\) −1003.25 + 268.821i −0.846417 + 0.226797i
\(113\) −1833.26 + 491.221i −1.52618 + 0.408940i −0.921772 0.387732i \(-0.873259\pi\)
−0.604412 + 0.796672i \(0.706592\pi\)
\(114\) 1357.38 + 1020.53i 1.11518 + 0.838433i
\(115\) 0 0
\(116\) 964.869i 0.772292i
\(117\) 329.847 598.152i 0.260636 0.472642i
\(118\) 1922.54 1922.54i 1.49987 1.49987i
\(119\) 111.404 + 192.958i 0.0858185 + 0.148642i
\(120\) 0 0
\(121\) −642.168 + 1112.27i −0.482470 + 0.835663i
\(122\) 102.629 + 383.017i 0.0761606 + 0.284235i
\(123\) −1585.75 + 1241.73i −1.16245 + 0.910265i
\(124\) 2569.38 1483.43i 1.86078 1.07432i
\(125\) 0 0
\(126\) 618.869 178.928i 0.437565 0.126510i
\(127\) −1405.14 1405.14i −0.981780 0.981780i 0.0180574 0.999837i \(-0.494252\pi\)
−0.999837 + 0.0180574i \(0.994252\pi\)
\(128\) −1233.71 + 4604.25i −0.851916 + 3.17939i
\(129\) −990.231 + 1317.09i −0.675853 + 0.898937i
\(130\) 0 0
\(131\) −1336.30 771.513i −0.891244 0.514560i −0.0168950 0.999857i \(-0.505378\pi\)
−0.874349 + 0.485297i \(0.838711\pi\)
\(132\) 289.417 718.602i 0.190837 0.473835i
\(133\) 252.548 + 67.6700i 0.164652 + 0.0441183i
\(134\) −1007.61 −0.649581
\(135\) 0 0
\(136\) 3850.47 2.42776
\(137\) −119.427 32.0003i −0.0744767 0.0199560i 0.221388 0.975186i \(-0.428941\pi\)
−0.295865 + 0.955230i \(0.595608\pi\)
\(138\) 558.700 1387.21i 0.344635 0.855704i
\(139\) −308.354 178.028i −0.188160 0.108634i 0.402961 0.915217i \(-0.367981\pi\)
−0.591121 + 0.806583i \(0.701314\pi\)
\(140\) 0 0
\(141\) 1024.70 1362.93i 0.612022 0.814038i
\(142\) 796.965 2974.32i 0.470985 1.75774i
\(143\) −122.202 122.202i −0.0714619 0.0714619i
\(144\) 1539.18 6231.54i 0.890729 3.60621i
\(145\) 0 0
\(146\) −566.834 + 327.262i −0.321312 + 0.185509i
\(147\) −1325.16 + 1037.67i −0.743520 + 0.582217i
\(148\) −1863.96 6956.41i −1.03525 3.86360i
\(149\) −601.701 + 1042.18i −0.330827 + 0.573009i −0.982674 0.185341i \(-0.940661\pi\)
0.651847 + 0.758350i \(0.273994\pi\)
\(150\) 0 0
\(151\) −820.064 1420.39i −0.441959 0.765496i 0.555876 0.831265i \(-0.312383\pi\)
−0.997835 + 0.0657697i \(0.979050\pi\)
\(152\) 3194.97 3194.97i 1.70491 1.70491i
\(153\) −1376.69 + 27.0521i −0.727441 + 0.0142944i
\(154\) 162.990i 0.0852862i
\(155\) 0 0
\(156\) −2293.22 1724.13i −1.17695 0.884876i
\(157\) 3385.35 907.102i 1.72089 0.461112i 0.742842 0.669467i \(-0.233478\pi\)
0.978053 + 0.208355i \(0.0668109\pi\)
\(158\) 1133.81 303.803i 0.570892 0.152970i
\(159\) −291.528 + 124.124i −0.145407 + 0.0619098i
\(160\) 0 0
\(161\) 230.244i 0.112707i
\(162\) −878.551 + 3883.09i −0.426083 + 1.88324i
\(163\) −1206.55 + 1206.55i −0.579781 + 0.579781i −0.934843 0.355062i \(-0.884460\pi\)
0.355062 + 0.934843i \(0.384460\pi\)
\(164\) 4229.79 + 7326.20i 2.01397 + 3.48830i
\(165\) 0 0
\(166\) 2629.41 4554.27i 1.22941 2.12940i
\(167\) −88.3316 329.658i −0.0409299 0.152753i 0.942437 0.334385i \(-0.108529\pi\)
−0.983367 + 0.181632i \(0.941862\pi\)
\(168\) −240.408 1697.08i −0.110404 0.779361i
\(169\) 1348.37 778.483i 0.613734 0.354339i
\(170\) 0 0
\(171\) −1119.87 + 1164.77i −0.500812 + 0.520889i
\(172\) 4894.02 + 4894.02i 2.16957 + 2.16957i
\(173\) −192.001 + 716.558i −0.0843790 + 0.314907i −0.995196 0.0979039i \(-0.968786\pi\)
0.910817 + 0.412811i \(0.135453\pi\)
\(174\) −1245.36 151.524i −0.542588 0.0660172i
\(175\) 0 0
\(176\) −1406.42 811.995i −0.602344 0.347764i
\(177\) 1594.90 + 2036.76i 0.677287 + 0.864930i
\(178\) 1520.94 + 407.535i 0.640445 + 0.171607i
\(179\) −2527.65 −1.05545 −0.527725 0.849416i \(-0.676955\pi\)
−0.527725 + 0.849416i \(0.676955\pi\)
\(180\) 0 0
\(181\) −2223.82 −0.913232 −0.456616 0.889664i \(-0.650939\pi\)
−0.456616 + 0.889664i \(0.650939\pi\)
\(182\) −583.059 156.230i −0.237468 0.0636294i
\(183\) −373.551 + 52.9172i −0.150895 + 0.0213757i
\(184\) −3445.89 1989.48i −1.38062 0.797101i
\(185\) 0 0
\(186\) 1511.17 + 3549.26i 0.595723 + 1.39916i
\(187\) −90.1661 + 336.505i −0.0352599 + 0.131592i
\(188\) −5064.37 5064.37i −1.96466 1.96466i
\(189\) 97.8781 + 605.081i 0.0376698 + 0.232874i
\(190\) 0 0
\(191\) −2292.92 + 1323.82i −0.868639 + 0.501509i −0.866896 0.498490i \(-0.833888\pi\)
−0.00174321 + 0.999998i \(0.500555\pi\)
\(192\) −9109.09 3668.69i −3.42392 1.37898i
\(193\) 265.955 + 992.559i 0.0991911 + 0.370186i 0.997622 0.0689296i \(-0.0219584\pi\)
−0.898430 + 0.439116i \(0.855292\pi\)
\(194\) 4490.81 7778.32i 1.66197 2.87861i
\(195\) 0 0
\(196\) 3534.71 + 6122.29i 1.28816 + 2.23116i
\(197\) −1735.07 + 1735.07i −0.627507 + 0.627507i −0.947440 0.319933i \(-0.896340\pi\)
0.319933 + 0.947440i \(0.396340\pi\)
\(198\) 882.050 + 486.401i 0.316589 + 0.174581i
\(199\) 764.080i 0.272182i −0.990696 0.136091i \(-0.956546\pi\)
0.990696 0.136091i \(-0.0434539\pi\)
\(200\) 0 0
\(201\) 115.792 951.679i 0.0406334 0.333961i
\(202\) −7653.36 + 2050.71i −2.66579 + 0.714295i
\(203\) −186.566 + 49.9902i −0.0645043 + 0.0172839i
\(204\) −698.536 + 5741.19i −0.239742 + 1.97041i
\(205\) 0 0
\(206\) 1782.34i 0.602824i
\(207\) 1246.01 + 687.105i 0.418375 + 0.230710i
\(208\) −4252.82 + 4252.82i −1.41769 + 1.41769i
\(209\) 204.402 + 354.035i 0.0676497 + 0.117173i
\(210\) 0 0
\(211\) 1529.60 2649.34i 0.499061 0.864398i −0.500939 0.865483i \(-0.667012\pi\)
0.999999 + 0.00108439i \(0.000345174\pi\)
\(212\) 344.450 + 1285.51i 0.111589 + 0.416457i
\(213\) 2717.64 + 1094.53i 0.874224 + 0.352094i
\(214\) −8253.61 + 4765.22i −2.63647 + 1.52217i
\(215\) 0 0
\(216\) 9901.53 + 3763.49i 3.11904 + 1.18552i
\(217\) 419.956 + 419.956i 0.131375 + 0.131375i
\(218\) −815.851 + 3044.80i −0.253470 + 0.945962i
\(219\) −243.958 572.980i −0.0752747 0.176796i
\(220\) 0 0
\(221\) 1117.34 + 645.099i 0.340093 + 0.196353i
\(222\) 9271.36 1313.38i 2.80294 0.397064i
\(223\) 4196.27 + 1124.39i 1.26010 + 0.337644i 0.826231 0.563331i \(-0.190480\pi\)
0.433872 + 0.900975i \(0.357147\pi\)
\(224\) −3033.37 −0.904803
\(225\) 0 0
\(226\) −10365.1 −3.05077
\(227\) −2591.73 694.451i −0.757793 0.203050i −0.140821 0.990035i \(-0.544974\pi\)
−0.616972 + 0.786985i \(0.711641\pi\)
\(228\) 4184.20 + 5343.43i 1.21537 + 1.55209i
\(229\) 4176.87 + 2411.52i 1.20531 + 0.695884i 0.961731 0.273997i \(-0.0883459\pi\)
0.243577 + 0.969882i \(0.421679\pi\)
\(230\) 0 0
\(231\) 153.943 + 18.7304i 0.0438472 + 0.00533493i
\(232\) −863.908 + 3224.15i −0.244475 + 0.912395i
\(233\) −1004.66 1004.66i −0.282479 0.282479i 0.551618 0.834097i \(-0.314011\pi\)
−0.834097 + 0.551618i \(0.814011\pi\)
\(234\) 2585.46 2689.11i 0.722295 0.751250i
\(235\) 0 0
\(236\) 9409.92 5432.82i 2.59548 1.49850i
\(237\) 156.646 + 1105.79i 0.0429335 + 0.303075i
\(238\) 314.933 + 1175.35i 0.0857735 + 0.320111i
\(239\) −3310.25 + 5733.51i −0.895908 + 1.55176i −0.0632311 + 0.997999i \(0.520141\pi\)
−0.832677 + 0.553759i \(0.813193\pi\)
\(240\) 0 0
\(241\) −1226.12 2123.69i −0.327722 0.567631i 0.654337 0.756203i \(-0.272948\pi\)
−0.982059 + 0.188571i \(0.939614\pi\)
\(242\) −4959.69 + 4959.69i −1.31744 + 1.31744i
\(243\) −3566.60 1276.02i −0.941555 0.336860i
\(244\) 1584.67i 0.415771i
\(245\) 0 0
\(246\) −10120.2 + 4308.88i −2.62293 + 1.11676i
\(247\) 1462.41 391.851i 0.376723 0.100943i
\(248\) 9913.90 2656.42i 2.53844 0.680173i
\(249\) 3999.33 + 3006.83i 1.01786 + 0.765262i
\(250\) 0 0
\(251\) 6563.11i 1.65044i 0.564814 + 0.825219i \(0.308948\pi\)
−0.564814 + 0.825219i \(0.691052\pi\)
\(252\) 2574.02 50.5801i 0.643446 0.0126438i
\(253\) 254.559 254.559i 0.0632569 0.0632569i
\(254\) −5426.20 9398.45i −1.34043 2.32170i
\(255\) 0 0
\(256\) −5456.43 + 9450.81i −1.33214 + 2.30733i
\(257\) −807.694 3014.35i −0.196041 0.731635i −0.991995 0.126278i \(-0.959697\pi\)
0.795954 0.605357i \(-0.206970\pi\)
\(258\) −7085.28 + 5548.16i −1.70973 + 1.33881i
\(259\) 1248.51 720.829i 0.299532 0.172935i
\(260\) 0 0
\(261\) 286.227 1158.82i 0.0678813 0.274825i
\(262\) −5958.66 5958.66i −1.40507 1.40507i
\(263\) 1215.51 4536.33i 0.284986 1.06358i −0.663863 0.747854i \(-0.731084\pi\)
0.948849 0.315729i \(-0.102249\pi\)
\(264\) 1610.51 2142.10i 0.375454 0.499384i
\(265\) 0 0
\(266\) 1236.58 + 713.938i 0.285035 + 0.164565i
\(267\) −559.698 + 1389.69i −0.128288 + 0.318530i
\(268\) −3889.55 1042.20i −0.886538 0.237547i
\(269\) −4107.03 −0.930893 −0.465446 0.885076i \(-0.654106\pi\)
−0.465446 + 0.885076i \(0.654106\pi\)
\(270\) 0 0
\(271\) −358.244 −0.0803017 −0.0401508 0.999194i \(-0.512784\pi\)
−0.0401508 + 0.999194i \(0.512784\pi\)
\(272\) 11710.9 + 3137.92i 2.61057 + 0.699501i
\(273\) 214.563 532.743i 0.0475675 0.118107i
\(274\) −584.762 337.612i −0.128930 0.0744376i
\(275\) 0 0
\(276\) 3591.53 4777.02i 0.783278 1.04182i
\(277\) −433.653 + 1618.41i −0.0940637 + 0.351051i −0.996876 0.0789846i \(-0.974832\pi\)
0.902812 + 0.430035i \(0.141499\pi\)
\(278\) −1374.97 1374.97i −0.296638 0.296638i
\(279\) −3525.92 + 1019.42i −0.756601 + 0.218750i
\(280\) 0 0
\(281\) 3329.19 1922.11i 0.706771 0.408054i −0.103094 0.994672i \(-0.532874\pi\)
0.809864 + 0.586617i \(0.199541\pi\)
\(282\) 7331.90 5741.27i 1.54826 1.21237i
\(283\) −293.688 1096.06i −0.0616888 0.230226i 0.928198 0.372087i \(-0.121358\pi\)
−0.989886 + 0.141862i \(0.954691\pi\)
\(284\) 6152.88 10657.1i 1.28559 2.22670i
\(285\) 0 0
\(286\) −471.905 817.363i −0.0975676 0.168992i
\(287\) −1197.44 + 1197.44i −0.246281 + 0.246281i
\(288\) 9052.33 16415.7i 1.85213 3.35869i
\(289\) 2312.18i 0.470626i
\(290\) 0 0
\(291\) 6830.51 + 5135.42i 1.37599 + 1.03451i
\(292\) −2526.59 + 676.997i −0.506360 + 0.135679i
\(293\) −434.952 + 116.545i −0.0867241 + 0.0232377i −0.301920 0.953333i \(-0.597628\pi\)
0.215196 + 0.976571i \(0.430961\pi\)
\(294\) −8457.14 + 3600.80i −1.67766 + 0.714296i
\(295\) 0 0
\(296\) 24914.0i 4.89223i
\(297\) −560.767 + 777.196i −0.109559 + 0.151843i
\(298\) −4647.15 + 4647.15i −0.903362 + 0.903362i
\(299\) −666.627 1154.63i −0.128937 0.223325i
\(300\) 0 0
\(301\) −692.742 + 1199.86i −0.132654 + 0.229764i
\(302\) −2318.27 8651.91i −0.441727 1.64855i
\(303\) −1057.38 7464.23i −0.200479 1.41521i
\(304\) 12321.0 7113.51i 2.32452 1.34206i
\(305\) 0 0
\(306\) −7300.46 1803.20i −1.36385 0.336870i
\(307\) −1217.81 1217.81i −0.226398 0.226398i 0.584788 0.811186i \(-0.301178\pi\)
−0.811186 + 0.584788i \(0.801178\pi\)
\(308\) 168.586 629.171i 0.0311886 0.116397i
\(309\) −1683.42 204.823i −0.309923 0.0377086i
\(310\) 0 0
\(311\) −4660.61 2690.81i −0.849772 0.490616i 0.0108020 0.999942i \(-0.496562\pi\)
−0.860574 + 0.509326i \(0.829895\pi\)
\(312\) −6119.18 7814.50i −1.11035 1.41798i
\(313\) 4661.02 + 1248.92i 0.841714 + 0.225537i 0.653817 0.756652i \(-0.273166\pi\)
0.187896 + 0.982189i \(0.439833\pi\)
\(314\) 19140.4 3.43998
\(315\) 0 0
\(316\) 4690.95 0.835084
\(317\) 3721.99 + 997.303i 0.659456 + 0.176701i 0.573001 0.819555i \(-0.305779\pi\)
0.0864556 + 0.996256i \(0.472446\pi\)
\(318\) −1713.30 + 242.705i −0.302129 + 0.0427995i
\(319\) −261.538 150.999i −0.0459039 0.0265026i
\(320\) 0 0
\(321\) −3552.25 8343.11i −0.617654 1.45068i
\(322\) 325.443 1214.57i 0.0563238 0.210203i
\(323\) −2158.06 2158.06i −0.371757 0.371757i
\(324\) −7407.80 + 14080.8i −1.27020 + 2.41440i
\(325\) 0 0
\(326\) −8070.15 + 4659.30i −1.37106 + 0.791579i
\(327\) −2782.04 1120.47i −0.470481 0.189486i
\(328\) 7574.39 + 28268.0i 1.27508 + 4.75865i
\(329\) 716.854 1241.63i 0.120126 0.208064i
\(330\) 0 0
\(331\) 2384.56 + 4130.18i 0.395974 + 0.685847i 0.993225 0.116207i \(-0.0370737\pi\)
−0.597251 + 0.802054i \(0.703740\pi\)
\(332\) 14860.7 14860.7i 2.45658 2.45658i
\(333\) 175.038 + 8907.69i 0.0288049 + 1.46588i
\(334\) 1863.85i 0.305345i
\(335\) 0 0
\(336\) 651.846 5357.45i 0.105837 0.869860i
\(337\) 9743.49 2610.76i 1.57496 0.422009i 0.637599 0.770368i \(-0.279928\pi\)
0.937361 + 0.348359i \(0.113261\pi\)
\(338\) 8213.23 2200.73i 1.32172 0.354153i
\(339\) 1191.13 9789.75i 0.190835 1.56846i
\(340\) 0 0
\(341\) 928.612i 0.147470i
\(342\) −7553.86 + 4561.41i −1.19435 + 0.721207i
\(343\) −2060.30 + 2060.30i −0.324332 + 0.324332i
\(344\) 11971.6 + 20735.5i 1.87636 + 3.24995i
\(345\) 0 0
\(346\) −2025.67 + 3508.56i −0.314742 + 0.545148i
\(347\) 2600.02 + 9703.39i 0.402237 + 1.50117i 0.809095 + 0.587677i \(0.199958\pi\)
−0.406858 + 0.913491i \(0.633376\pi\)
\(348\) −4650.59 1873.03i −0.716373 0.288520i
\(349\) 5945.55 3432.67i 0.911914 0.526494i 0.0308677 0.999523i \(-0.490173\pi\)
0.881047 + 0.473030i \(0.156840\pi\)
\(350\) 0 0
\(351\) 2242.74 + 2750.98i 0.341050 + 0.418338i
\(352\) −3353.72 3353.72i −0.507823 0.507823i
\(353\) −2316.48 + 8645.22i −0.349274 + 1.30351i 0.538265 + 0.842776i \(0.319080\pi\)
−0.887539 + 0.460733i \(0.847587\pi\)
\(354\) 5534.41 + 12998.6i 0.830933 + 1.95160i
\(355\) 0 0
\(356\) 5449.59 + 3146.32i 0.811314 + 0.468412i
\(357\) −1146.30 + 162.385i −0.169940 + 0.0240737i
\(358\) −13333.7 3572.76i −1.96846 0.527448i
\(359\) 2589.44 0.380684 0.190342 0.981718i \(-0.439040\pi\)
0.190342 + 0.981718i \(0.439040\pi\)
\(360\) 0 0
\(361\) 3277.66 0.477862
\(362\) −11731.0 3143.30i −1.70322 0.456376i
\(363\) −4114.45 5254.36i −0.594911 0.759731i
\(364\) −2089.13 1206.16i −0.300824 0.173681i
\(365\) 0 0
\(366\) −2045.34 248.858i −0.292108 0.0355410i
\(367\) 2048.55 7645.28i 0.291371 1.08741i −0.652686 0.757629i \(-0.726358\pi\)
0.944057 0.329783i \(-0.106976\pi\)
\(368\) −8859.06 8859.06i −1.25492 1.25492i
\(369\) −2906.73 10053.6i −0.410076 1.41835i
\(370\) 0 0
\(371\) −230.718 + 133.205i −0.0322865 + 0.0186406i
\(372\) 2162.28 + 15263.9i 0.301369 + 2.12741i
\(373\) −1565.16 5841.25i −0.217268 0.810854i −0.985356 0.170510i \(-0.945458\pi\)
0.768088 0.640344i \(-0.221208\pi\)
\(374\) −951.279 + 1647.66i −0.131523 + 0.227804i
\(375\) 0 0
\(376\) −12388.3 21457.2i −1.69915 2.94301i
\(377\) −790.858 + 790.858i −0.108040 + 0.108040i
\(378\) −338.943 + 3330.24i −0.0461200 + 0.453146i
\(379\) 13501.8i 1.82992i −0.403542 0.914961i \(-0.632221\pi\)
0.403542 0.914961i \(-0.367779\pi\)
\(380\) 0 0
\(381\) 9500.36 4044.97i 1.27748 0.543911i
\(382\) −13966.7 + 3742.36i −1.87067 + 0.501246i
\(383\) 9329.14 2499.74i 1.24464 0.333500i 0.424376 0.905486i \(-0.360494\pi\)
0.820263 + 0.571986i \(0.193827\pi\)
\(384\) −19797.2 14884.3i −2.63092 1.97802i
\(385\) 0 0
\(386\) 5611.82i 0.739984i
\(387\) −4425.98 7329.59i −0.581358 0.962750i
\(388\) 25380.8 25380.8i 3.32091 3.32091i
\(389\) −2925.52 5067.16i −0.381311 0.660450i 0.609939 0.792448i \(-0.291194\pi\)
−0.991250 + 0.131998i \(0.957861\pi\)
\(390\) 0 0
\(391\) −1343.81 + 2327.54i −0.173809 + 0.301045i
\(392\) 6329.69 + 23622.7i 0.815555 + 3.04369i
\(393\) 6312.69 4943.18i 0.810262 0.634479i
\(394\) −11605.2 + 6700.29i −1.48392 + 0.856741i
\(395\) 0 0
\(396\) 2901.78 + 2789.94i 0.368232 + 0.354039i
\(397\) −4637.81 4637.81i −0.586309 0.586309i 0.350321 0.936630i \(-0.386073\pi\)
−0.936630 + 0.350321i \(0.886073\pi\)
\(398\) 1080.01 4030.64i 0.136020 0.507632i
\(399\) −816.416 + 1085.90i −0.102436 + 0.136248i
\(400\) 0 0
\(401\) −5746.08 3317.50i −0.715576 0.413138i 0.0975465 0.995231i \(-0.468901\pi\)
−0.813122 + 0.582093i \(0.802234\pi\)
\(402\) 1955.99 4856.58i 0.242676 0.602548i
\(403\) 3321.90 + 890.102i 0.410610 + 0.110023i
\(404\) −31664.6 −3.89944
\(405\) 0 0
\(406\) −1054.82 −0.128941
\(407\) 2177.32 + 583.410i 0.265173 + 0.0710530i
\(408\) −7474.63 + 18559.0i −0.906983 + 2.25197i
\(409\) 4763.16 + 2750.01i 0.575851 + 0.332468i 0.759483 0.650527i \(-0.225452\pi\)
−0.183632 + 0.982995i \(0.558785\pi\)
\(410\) 0 0
\(411\) 386.073 513.507i 0.0463347 0.0616288i
\(412\) −1843.54 + 6880.19i −0.220448 + 0.822725i
\(413\) 1538.02 + 1538.02i 0.183247 + 0.183247i
\(414\) 5601.68 + 5385.78i 0.664995 + 0.639364i
\(415\) 0 0
\(416\) −15211.8 + 8782.55i −1.79284 + 1.03510i
\(417\) 1456.67 1140.65i 0.171063 0.133952i
\(418\) 577.833 + 2156.50i 0.0676142 + 0.252340i
\(419\) 393.101 680.870i 0.0458335 0.0793859i −0.842199 0.539167i \(-0.818739\pi\)
0.888032 + 0.459782i \(0.152072\pi\)
\(420\) 0 0
\(421\) 7854.61 + 13604.6i 0.909289 + 1.57493i 0.815055 + 0.579384i \(0.196707\pi\)
0.0942338 + 0.995550i \(0.469960\pi\)
\(422\) 11813.6 11813.6i 1.36274 1.36274i
\(423\) 4580.04 + 7584.72i 0.526452 + 0.871824i
\(424\) 4603.98i 0.527332i
\(425\) 0 0
\(426\) 12788.9 + 9615.13i 1.45451 + 1.09356i
\(427\) −306.410 + 82.1024i −0.0347265 + 0.00930495i
\(428\) −36789.3 + 9857.68i −4.15486 + 1.11329i
\(429\) 826.226 351.783i 0.0929851 0.0395903i
\(430\) 0 0
\(431\) 1343.42i 0.150140i −0.997178 0.0750702i \(-0.976082\pi\)
0.997178 0.0750702i \(-0.0239181\pi\)
\(432\) 27047.6 + 19515.5i 3.01234 + 2.17348i
\(433\) 4364.85 4364.85i 0.484437 0.484437i −0.422108 0.906545i \(-0.638710\pi\)
0.906545 + 0.422108i \(0.138710\pi\)
\(434\) 1621.73 + 2808.93i 0.179368 + 0.310675i
\(435\) 0 0
\(436\) −6298.68 + 10909.6i −0.691863 + 1.19834i
\(437\) 816.264 + 3046.34i 0.0893529 + 0.333470i
\(438\) −477.023 3367.38i −0.0520389 0.367351i
\(439\) −6104.30 + 3524.32i −0.663649 + 0.383158i −0.793666 0.608354i \(-0.791830\pi\)
0.130017 + 0.991512i \(0.458497\pi\)
\(440\) 0 0
\(441\) −2429.06 8401.53i −0.262290 0.907195i
\(442\) 4982.32 + 4982.32i 0.536165 + 0.536165i
\(443\) 1521.13 5676.94i 0.163140 0.608848i −0.835130 0.550053i \(-0.814608\pi\)
0.998270 0.0587949i \(-0.0187258\pi\)
\(444\) 37147.7 + 4519.80i 3.97061 + 0.483109i
\(445\) 0 0
\(446\) 20546.7 + 11862.6i 2.18142 + 1.25944i
\(447\) −3855.17 4923.25i −0.407927 0.520943i
\(448\) −7975.46 2137.02i −0.841083 0.225367i
\(449\) 9280.82 0.975477 0.487738 0.872990i \(-0.337822\pi\)
0.487738 + 0.872990i \(0.337822\pi\)
\(450\) 0 0
\(451\) −2647.80 −0.276452
\(452\) −40011.1 10720.9i −4.16364 1.11564i
\(453\) 8438.11 1195.34i 0.875181 0.123978i
\(454\) −12690.2 7326.67i −1.31185 0.757395i
\(455\) 0 0
\(456\) 9197.34 + 21601.7i 0.944529 + 2.21840i
\(457\) −790.554 + 2950.39i −0.0809203 + 0.301999i −0.994510 0.104638i \(-0.966632\pi\)
0.913590 + 0.406636i \(0.133298\pi\)
\(458\) 18625.0 + 18625.0i 1.90019 + 1.90019i
\(459\) 2542.07 6688.03i 0.258504 0.680110i
\(460\) 0 0
\(461\) 6729.62 3885.35i 0.679890 0.392535i −0.119923 0.992783i \(-0.538265\pi\)
0.799814 + 0.600248i \(0.204932\pi\)
\(462\) 785.597 + 316.400i 0.0791110 + 0.0318620i
\(463\) −990.276 3695.76i −0.0993997 0.370965i 0.898250 0.439485i \(-0.144839\pi\)
−0.997650 + 0.0685201i \(0.978172\pi\)
\(464\) −5255.00 + 9101.94i −0.525770 + 0.910661i
\(465\) 0 0
\(466\) −3879.68 6719.80i −0.385671 0.668002i
\(467\) −3050.23 + 3050.23i −0.302243 + 0.302243i −0.841891 0.539648i \(-0.818557\pi\)
0.539648 + 0.841891i \(0.318557\pi\)
\(468\) 12761.8 7706.24i 1.26050 0.761156i
\(469\) 806.077i 0.0793628i
\(470\) 0 0
\(471\) −2199.57 + 18078.0i −0.215182 + 1.76856i
\(472\) 36308.0 9728.69i 3.54070 0.948727i
\(473\) −2092.48 + 560.678i −0.203409 + 0.0545032i
\(474\) −736.671 + 6054.62i −0.0713849 + 0.586704i
\(475\) 0 0
\(476\) 4862.81i 0.468249i
\(477\) −32.3460 1646.09i −0.00310487 0.158007i
\(478\) −25566.2 + 25566.2i −2.44638 + 2.44638i
\(479\) 1094.98 + 1896.57i 0.104449 + 0.180911i 0.913513 0.406810i \(-0.133359\pi\)
−0.809064 + 0.587721i \(0.800025\pi\)
\(480\) 0 0
\(481\) 4174.04 7229.65i 0.395675 0.685330i
\(482\) −3466.16 12935.9i −0.327550 1.22243i
\(483\) 1109.76 + 446.956i 0.104546 + 0.0421060i
\(484\) −24275.3 + 14015.4i −2.27980 + 1.31624i
\(485\) 0 0
\(486\) −17010.7 11772.5i −1.58770 1.09879i
\(487\) 1824.01 + 1824.01i 0.169721 + 0.169721i 0.786857 0.617136i \(-0.211707\pi\)
−0.617136 + 0.786857i \(0.711707\pi\)
\(488\) −1418.85 + 5295.24i −0.131616 + 0.491197i
\(489\) −3473.29 8157.66i −0.321201 0.754401i
\(490\) 0 0
\(491\) −2339.22 1350.55i −0.215005 0.124133i 0.388630 0.921394i \(-0.372948\pi\)
−0.603635 + 0.797260i \(0.706282\pi\)
\(492\) −43522.7 + 6165.42i −3.98812 + 0.564957i
\(493\) 2177.76 + 583.530i 0.198948 + 0.0533081i
\(494\) 8268.28 0.753052
\(495\) 0 0
\(496\) 32317.1 2.92557
\(497\) 2379.43 + 637.566i 0.214753 + 0.0575428i
\(498\) 16847.0 + 21514.4i 1.51592 + 1.93591i
\(499\) 14609.9 + 8435.02i 1.31068 + 0.756720i 0.982208 0.187795i \(-0.0601340\pi\)
0.328469 + 0.944515i \(0.393467\pi\)
\(500\) 0 0
\(501\) 1760.40 + 214.189i 0.156983 + 0.0191003i
\(502\) −9276.77 + 34621.4i −0.824786 + 3.07814i
\(503\) −3851.44 3851.44i −0.341406 0.341406i 0.515490 0.856896i \(-0.327610\pi\)
−0.856896 + 0.515490i \(0.827610\pi\)
\(504\) 8646.49 + 2135.67i 0.764177 + 0.188751i
\(505\) 0 0
\(506\) 1702.65 983.026i 0.149589 0.0863653i
\(507\) 1134.73 + 8010.26i 0.0993989 + 0.701673i
\(508\) −11225.0 41892.3i −0.980373 3.65880i
\(509\) 1119.01 1938.18i 0.0974443 0.168779i −0.813182 0.582010i \(-0.802267\pi\)
0.910626 + 0.413231i \(0.135600\pi\)
\(510\) 0 0
\(511\) −261.807 453.463i −0.0226647 0.0392564i
\(512\) −15177.5 + 15177.5i −1.31007 + 1.31007i
\(513\) −3440.16 7658.78i −0.296075 0.659149i
\(514\) 17042.8i 1.46250i
\(515\) 0 0
\(516\) −33089.2 + 14088.4i −2.82300 + 1.20195i
\(517\) 2165.31 580.193i 0.184198 0.0493557i
\(518\) 7604.96 2037.74i 0.645063 0.172844i
\(519\) −3081.03 2316.43i −0.260583 0.195915i
\(520\) 0 0
\(521\) 11295.2i 0.949810i −0.880037 0.474905i \(-0.842482\pi\)
0.880037 0.474905i \(-0.157518\pi\)
\(522\) 3147.85 5708.38i 0.263942 0.478638i
\(523\) −7883.52 + 7883.52i −0.659125 + 0.659125i −0.955173 0.296048i \(-0.904331\pi\)
0.296048 + 0.955173i \(0.404331\pi\)
\(524\) −16838.3 29164.8i −1.40379 2.43144i
\(525\) 0 0
\(526\) 12824.0 22211.7i 1.06302 1.84121i
\(527\) −1794.29 6696.39i −0.148312 0.553509i
\(528\) 6643.92 5202.55i 0.547613 0.428811i
\(529\) −8131.72 + 4694.85i −0.668342 + 0.385867i
\(530\) 0 0
\(531\) −12913.1 + 3733.46i −1.05533 + 0.305119i
\(532\) 4034.97 + 4034.97i 0.328831 + 0.328831i
\(533\) −2537.99 + 9471.91i −0.206252 + 0.769745i
\(534\) −4916.77 + 6539.69i −0.398445 + 0.529963i
\(535\) 0 0
\(536\) −12063.9 6965.12i −0.972169 0.561282i
\(537\) 4906.74 12183.1i 0.394304 0.979029i
\(538\) −21665.2 5805.17i −1.73616 0.465202i
\(539\) −2212.69 −0.176822
\(540\) 0 0
\(541\) −9200.65 −0.731177 −0.365588 0.930777i \(-0.619132\pi\)
−0.365588 + 0.930777i \(0.619132\pi\)
\(542\) −1889.79 506.367i −0.149766 0.0401298i
\(543\) 4316.93 10718.6i 0.341173 0.847109i
\(544\) 30664.4 + 17704.1i 2.41678 + 1.39533i
\(545\) 0 0
\(546\) 1884.87 2507.02i 0.147738 0.196503i
\(547\) −4617.23 + 17231.7i −0.360911 + 1.34694i 0.511969 + 0.859004i \(0.328916\pi\)
−0.872880 + 0.487934i \(0.837751\pi\)
\(548\) −1908.09 1908.09i −0.148740 0.148740i
\(549\) 470.091 1903.21i 0.0365446 0.147955i
\(550\) 0 0
\(551\) 2291.22 1322.83i 0.177149 0.102277i
\(552\) 16278.4 12746.9i 1.25517 0.982867i
\(553\) 243.040 + 907.038i 0.0186892 + 0.0697490i
\(554\) −4575.16 + 7924.41i −0.350866 + 0.607719i
\(555\) 0 0
\(556\) −3885.48 6729.85i −0.296369 0.513326i
\(557\) 9243.69 9243.69i 0.703174 0.703174i −0.261917 0.965091i \(-0.584355\pi\)
0.965091 + 0.261917i \(0.0843545\pi\)
\(558\) −20040.7 + 393.804i −1.52041 + 0.0298764i
\(559\) 8022.80i 0.607027i
\(560\) 0 0
\(561\) −1446.89 1087.82i −0.108891 0.0818681i
\(562\) 20278.8 5433.68i 1.52208 0.407840i
\(563\) −14763.8 + 3955.94i −1.10518 + 0.296133i −0.764874 0.644180i \(-0.777199\pi\)
−0.340310 + 0.940313i \(0.610532\pi\)
\(564\) 34240.9 14578.8i 2.55639 1.08843i
\(565\) 0 0
\(566\) 6196.99i 0.460210i
\(567\) −3106.45 702.834i −0.230085 0.0520569i
\(568\) 30102.1 30102.1i 2.22369 2.22369i
\(569\) 7749.24 + 13422.1i 0.570941 + 0.988898i 0.996470 + 0.0839534i \(0.0267547\pi\)
−0.425529 + 0.904945i \(0.639912\pi\)
\(570\) 0 0
\(571\) 986.984 1709.51i 0.0723362 0.125290i −0.827589 0.561335i \(-0.810288\pi\)
0.899925 + 0.436045i \(0.143621\pi\)
\(572\) −976.216 3643.29i −0.0713595 0.266317i
\(573\) −1929.63 13621.5i −0.140683 0.993103i
\(574\) −8009.23 + 4624.13i −0.582402 + 0.336250i
\(575\) 0 0
\(576\) 35365.6 36783.4i 2.55828 2.66083i
\(577\) 2600.22 + 2600.22i 0.187606 + 0.187606i 0.794660 0.607055i \(-0.207649\pi\)
−0.607055 + 0.794660i \(0.707649\pi\)
\(578\) −3268.21 + 12197.1i −0.235189 + 0.877739i
\(579\) −5300.34 644.897i −0.380439 0.0462884i
\(580\) 0 0
\(581\) 3643.38 + 2103.51i 0.260160 + 0.150203i
\(582\) 28773.2 + 36744.8i 2.04929 + 2.61705i
\(583\) −402.356 107.811i −0.0285830 0.00765879i
\(584\) −9048.84 −0.641171
\(585\) 0 0
\(586\) −2459.17 −0.173357
\(587\) 20290.6 + 5436.85i 1.42672 + 0.382288i 0.887862 0.460110i \(-0.152190\pi\)
0.538856 + 0.842398i \(0.318857\pi\)
\(588\) −36370.6 + 5152.26i −2.55085 + 0.361353i
\(589\) −7045.24 4067.57i −0.492859 0.284552i
\(590\) 0 0
\(591\) −4994.75 11731.1i −0.347642 0.816502i
\(592\) 20303.6 75774.0i 1.40958 5.26063i
\(593\) −1706.61 1706.61i −0.118182 0.118182i 0.645542 0.763725i \(-0.276631\pi\)
−0.763725 + 0.645542i \(0.776631\pi\)
\(594\) −4056.67 + 3307.20i −0.280214 + 0.228444i
\(595\) 0 0
\(596\) −22745.6 + 13132.2i −1.56325 + 0.902541i
\(597\) 3682.81 + 1483.25i 0.252474 + 0.101684i
\(598\) −1884.52 7033.11i −0.128869 0.480945i
\(599\) −6939.25 + 12019.1i −0.473339 + 0.819847i −0.999534 0.0305164i \(-0.990285\pi\)
0.526195 + 0.850364i \(0.323618\pi\)
\(600\) 0 0
\(601\) 11793.6 + 20427.2i 0.800454 + 1.38643i 0.919318 + 0.393516i \(0.128741\pi\)
−0.118864 + 0.992911i \(0.537925\pi\)
\(602\) −5350.29 + 5350.29i −0.362228 + 0.362228i
\(603\) 4362.24 + 2405.53i 0.294601 + 0.162456i
\(604\) 35795.9i 2.41145i
\(605\) 0 0
\(606\) 4972.63 40869.5i 0.333332 2.73962i
\(607\) −25746.1 + 6898.66i −1.72159 + 0.461298i −0.978218 0.207583i \(-0.933440\pi\)
−0.743370 + 0.668881i \(0.766774\pi\)
\(608\) 40134.3 10754.0i 2.67708 0.717320i
\(609\) 121.218 996.276i 0.00806568 0.0662909i
\(610\) 0 0
\(611\) 8302.05i 0.549697i
\(612\) −26316.0 14511.8i −1.73818 0.958506i
\(613\) −2171.14 + 2171.14i −0.143053 + 0.143053i −0.775006 0.631953i \(-0.782253\pi\)
0.631953 + 0.775006i \(0.282253\pi\)
\(614\) −4702.80 8145.49i −0.309103 0.535383i
\(615\) 0 0
\(616\) 1126.67 1951.45i 0.0736931 0.127640i
\(617\) −250.327 934.234i −0.0163335 0.0609576i 0.957278 0.289169i \(-0.0933789\pi\)
−0.973612 + 0.228211i \(0.926712\pi\)
\(618\) −8590.76 3459.93i −0.559176 0.225209i
\(619\) −5225.86 + 3017.15i −0.339330 + 0.195912i −0.659976 0.751287i \(-0.729433\pi\)
0.320646 + 0.947199i \(0.396100\pi\)
\(620\) 0 0
\(621\) −5730.58 + 4671.84i −0.370306 + 0.301892i
\(622\) −20782.0 20782.0i −1.33968 1.33968i
\(623\) −326.025 + 1216.74i −0.0209661 + 0.0782466i
\(624\) −12242.6 28753.9i −0.785409 1.84468i
\(625\) 0 0
\(626\) 22822.3 + 13176.4i 1.45713 + 0.841272i
\(627\) −2103.21 + 297.941i −0.133962 + 0.0189770i
\(628\) 73885.6 + 19797.6i 4.69484 + 1.25798i
\(629\) −16828.3 −1.06675
\(630\) 0 0
\(631\) −15462.3 −0.975505 −0.487753 0.872982i \(-0.662183\pi\)
−0.487753 + 0.872982i \(0.662183\pi\)
\(632\) 15675.0 + 4200.10i 0.986579 + 0.264353i
\(633\) 9800.31 + 12515.5i 0.615367 + 0.785856i
\(634\) 18224.4 + 10521.8i 1.14161 + 0.659110i
\(635\) 0 0
\(636\) −6864.69 835.234i −0.427992 0.0520742i
\(637\) −2120.92 + 7915.39i −0.131922 + 0.492338i
\(638\) −1166.22 1166.22i −0.0723685 0.0723685i
\(639\) −10551.1 + 10974.1i −0.653201 + 0.679387i
\(640\) 0 0
\(641\) 1917.34 1106.98i 0.118144 0.0682105i −0.439763 0.898114i \(-0.644938\pi\)
0.557908 + 0.829903i \(0.311604\pi\)
\(642\) −6945.88 49032.1i −0.426997 3.01424i
\(643\) −1472.27 5494.59i −0.0902965 0.336991i 0.905968 0.423346i \(-0.139145\pi\)
−0.996264 + 0.0863552i \(0.972478\pi\)
\(644\) 2512.55 4351.86i 0.153740 0.266285i
\(645\) 0 0
\(646\) −8333.71 14434.4i −0.507563 0.879125i
\(647\) −8395.00 + 8395.00i −0.510110 + 0.510110i −0.914560 0.404450i \(-0.867463\pi\)
0.404450 + 0.914560i \(0.367463\pi\)
\(648\) −37360.8 + 40418.8i −2.26493 + 2.45031i
\(649\) 3400.88i 0.205695i
\(650\) 0 0
\(651\) −2839.38 + 1208.93i −0.170944 + 0.0727827i
\(652\) −35971.6 + 9638.56i −2.16067 + 0.578950i
\(653\) −4064.57 + 1089.10i −0.243582 + 0.0652676i −0.378544 0.925583i \(-0.623575\pi\)
0.134962 + 0.990851i \(0.456909\pi\)
\(654\) −13091.9 9842.97i −0.782775 0.588518i
\(655\) 0 0
\(656\) 92147.4i 5.48438i
\(657\) 3235.30 63.5743i 0.192117 0.00377514i
\(658\) 5536.52 5536.52i 0.328018 0.328018i
\(659\) 15566.0 + 26961.1i 0.920129 + 1.59371i 0.799214 + 0.601047i \(0.205249\pi\)
0.120915 + 0.992663i \(0.461417\pi\)
\(660\) 0 0
\(661\) 7194.58 12461.4i 0.423354 0.733270i −0.572911 0.819617i \(-0.694186\pi\)
0.996265 + 0.0863471i \(0.0275194\pi\)
\(662\) 6741.02 + 25157.8i 0.395766 + 1.47702i
\(663\) −5278.34 + 4133.23i −0.309191 + 0.242113i
\(664\) 62963.2 36351.8i 3.67989 2.12459i
\(665\) 0 0
\(666\) −11667.4 + 47236.8i −0.678834 + 2.74833i
\(667\) −1647.44 1647.44i −0.0956357 0.0956357i
\(668\) 1927.84 7194.81i 0.111662 0.416730i
\(669\) −13565.4 + 18043.0i −0.783957 + 1.04272i
\(670\) 0 0
\(671\) −429.542 247.996i −0.0247128 0.0142679i
\(672\) 5888.46 14620.6i 0.338024 0.839290i
\(673\) −18240.0 4887.41i −1.04473 0.279934i −0.304657 0.952462i \(-0.598542\pi\)
−0.740072 + 0.672528i \(0.765208\pi\)
\(674\) 55088.6 3.14827
\(675\) 0 0
\(676\) 33980.9 1.93337
\(677\) 20847.9 + 5586.18i 1.18353 + 0.317126i 0.796326 0.604867i \(-0.206774\pi\)
0.387205 + 0.921994i \(0.373441\pi\)
\(678\) 20120.9 49958.8i 1.13973 2.82987i
\(679\) 6222.59 + 3592.62i 0.351695 + 0.203051i
\(680\) 0 0
\(681\) 8378.33 11143.8i 0.471451 0.627067i
\(682\) −1312.57 + 4898.57i −0.0736962 + 0.275038i
\(683\) 13485.0 + 13485.0i 0.755474 + 0.755474i 0.975495 0.220021i \(-0.0706126\pi\)
−0.220021 + 0.975495i \(0.570613\pi\)
\(684\) −33877.4 + 9794.69i −1.89376 + 0.547528i
\(685\) 0 0
\(686\) −13780.6 + 7956.21i −0.766974 + 0.442813i
\(687\) −19731.6 + 15450.9i −1.09579 + 0.858061i
\(688\) 19512.4 + 72821.4i 1.08126 + 4.03531i
\(689\) −771.339 + 1336.00i −0.0426498 + 0.0738716i
\(690\) 0 0
\(691\) 9014.75 + 15614.0i 0.496291 + 0.859602i 0.999991 0.00427721i \(-0.00136148\pi\)
−0.503700 + 0.863879i \(0.668028\pi\)
\(692\) −11448.5 + 11448.5i −0.628911 + 0.628911i
\(693\) −389.117 + 705.633i −0.0213295 + 0.0386794i
\(694\) 54861.9i 3.00076i
\(695\) 0 0
\(696\) −13863.1 10422.8i −0.754999 0.567635i
\(697\) 19093.7 5116.15i 1.03763 0.278032i
\(698\) 36215.6 9703.95i 1.96387 0.526218i
\(699\) 6792.67 2892.12i 0.367557 0.156495i
\(700\) 0 0
\(701\) 5187.88i 0.279520i 0.990185 + 0.139760i \(0.0446331\pi\)
−0.990185 + 0.139760i \(0.955367\pi\)
\(702\) 7942.33 + 17681.9i 0.427014 + 0.950655i
\(703\) −13963.5 + 13963.5i −0.749135 + 0.749135i
\(704\) −6455.02 11180.4i −0.345572 0.598548i
\(705\) 0 0
\(706\) −24439.5 + 42330.5i −1.30282 + 2.25656i
\(707\) −1640.55 6122.63i −0.0872693 0.325694i
\(708\) 7918.99 + 55901.4i 0.420358 + 2.96738i
\(709\) −3337.90 + 1927.14i −0.176809 + 0.102081i −0.585793 0.810461i \(-0.699217\pi\)
0.408984 + 0.912542i \(0.365883\pi\)
\(710\) 0 0
\(711\) −5633.90 1391.57i −0.297170 0.0734005i
\(712\) 15392.9 + 15392.9i 0.810217 + 0.810217i
\(713\) −1854.17 + 6919.86i −0.0973903 + 0.363465i
\(714\) −6276.44 763.660i −0.328977 0.0400270i
\(715\) 0 0
\(716\) −47775.3 27583.1i −2.49364 1.43970i
\(717\) −21209.2 27085.2i −1.10470 1.41076i
\(718\) 13659.7 + 3660.11i 0.709994 + 0.190242i
\(719\) −9734.47 −0.504916 −0.252458 0.967608i \(-0.581239\pi\)
−0.252458 + 0.967608i \(0.581239\pi\)
\(720\) 0 0
\(721\) −1425.86 −0.0736503
\(722\) 17290.1 + 4632.88i 0.891235 + 0.238806i
\(723\) 12616.2 1787.21i 0.648965 0.0919323i
\(724\) −42032.5 24267.5i −2.15763 1.24571i
\(725\) 0 0
\(726\) −14277.4 33533.2i −0.729870 1.71423i
\(727\) −3115.30 + 11626.5i −0.158927 + 0.593125i 0.839810 + 0.542881i \(0.182666\pi\)
−0.998737 + 0.0502438i \(0.984000\pi\)
\(728\) −5900.95 5900.95i −0.300417 0.300417i
\(729\) 13073.9 14713.7i 0.664224 0.747534i
\(730\) 0 0
\(731\) 14005.9 8086.29i 0.708654 0.409141i
\(732\) −7637.99 3076.20i −0.385667 0.155327i
\(733\) 6750.61 + 25193.6i 0.340163 + 1.26951i 0.898162 + 0.439664i \(0.144903\pi\)
−0.557999 + 0.829842i \(0.688431\pi\)
\(734\) 21612.8 37434.4i 1.08684 1.88246i
\(735\) 0 0
\(736\) −18294.9 31687.8i −0.916250 1.58699i
\(737\) 891.204 891.204i 0.0445426 0.0445426i
\(738\) −1122.87 57143.0i −0.0560074 2.85022i
\(739\) 24108.3i 1.20005i −0.799981 0.600025i \(-0.795157\pi\)
0.799981 0.600025i \(-0.204843\pi\)
\(740\) 0 0
\(741\) −950.172 + 7809.35i −0.0471058 + 0.387158i
\(742\) −1405.35 + 376.563i −0.0695312 + 0.0186308i
\(743\) 1607.80 430.808i 0.0793867 0.0212716i −0.218907 0.975746i \(-0.570249\pi\)
0.298294 + 0.954474i \(0.403582\pi\)
\(744\) −6441.38 + 52940.9i −0.317409 + 2.60875i
\(745\) 0 0
\(746\) 33025.8i 1.62086i
\(747\) −22256.3 + 13439.5i −1.09011 + 0.658267i
\(748\) −5376.36 + 5376.36i −0.262806 + 0.262806i
\(749\) −3812.14 6602.82i −0.185971 0.322112i
\(750\) 0 0
\(751\) −11016.0 + 19080.3i −0.535259 + 0.927096i 0.463892 + 0.885892i \(0.346453\pi\)
−0.999151 + 0.0412042i \(0.986881\pi\)
\(752\) −20191.6 75356.1i −0.979139 3.65420i
\(753\) −31633.7 12740.5i −1.53094 0.616585i
\(754\) −5289.75 + 3054.04i −0.255492 + 0.147509i
\(755\) 0 0
\(756\) −4752.97 + 12504.8i −0.228656 + 0.601580i
\(757\) 25360.2 + 25360.2i 1.21761 + 1.21761i 0.968466 + 0.249145i \(0.0801494\pi\)
0.249145 + 0.968466i \(0.419851\pi\)
\(758\) 19084.4 71224.0i 0.914481 3.41289i
\(759\) 732.799 + 1721.11i 0.0350447 + 0.0823089i
\(760\) 0 0
\(761\) −14614.3 8437.57i −0.696147 0.401921i 0.109763 0.993958i \(-0.464991\pi\)
−0.805911 + 0.592037i \(0.798324\pi\)
\(762\) 55833.2 7909.33i 2.65436 0.376017i
\(763\) −2435.81 652.674i −0.115573 0.0309678i
\(764\) −57784.9 −2.73637
\(765\) 0 0
\(766\) 52745.9 2.48797
\(767\) 12165.9 + 3259.84i 0.572732 + 0.153463i
\(768\) −34960.0 44645.7i −1.64259 2.09767i
\(769\) −4117.86 2377.45i −0.193100 0.111486i 0.400333 0.916370i \(-0.368894\pi\)
−0.593433 + 0.804883i \(0.702228\pi\)
\(770\) 0 0
\(771\) 16096.9 + 1958.52i 0.751900 + 0.0914844i
\(772\) −5804.50 + 21662.7i −0.270607 + 1.00992i
\(773\) 15286.0 + 15286.0i 0.711252 + 0.711252i 0.966797 0.255545i \(-0.0822549\pi\)
−0.255545 + 0.966797i \(0.582255\pi\)
\(774\) −12987.5 44920.7i −0.603137 2.08610i
\(775\) 0 0
\(776\) 107536. 62085.9i 4.97463 2.87210i
\(777\) 1050.69 + 7417.02i 0.0485115 + 0.342451i
\(778\) −8270.29 30865.1i −0.381111 1.42233i
\(779\) 11598.1 20088.4i 0.533432 0.923932i
\(780\) 0