Properties

Label 225.4.e.f.151.12
Level $225$
Weight $4$
Character 225.151
Analytic conductor $13.275$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 151.12
Character \(\chi\) \(=\) 225.151
Dual form 225.4.e.f.76.12

$q$-expansion

\(f(q)\) \(=\) \(q+(2.77209 - 4.80141i) q^{2} +(-0.320819 + 5.18624i) q^{3} +(-11.3690 - 19.6917i) q^{4} +(24.0119 + 15.9171i) q^{6} +(-12.8563 + 22.2678i) q^{7} -81.7101 q^{8} +(-26.7942 - 3.32769i) q^{9} +O(q^{10})\) \(q+(2.77209 - 4.80141i) q^{2} +(-0.320819 + 5.18624i) q^{3} +(-11.3690 - 19.6917i) q^{4} +(24.0119 + 15.9171i) q^{6} +(-12.8563 + 22.2678i) q^{7} -81.7101 q^{8} +(-26.7942 - 3.32769i) q^{9} +(-3.12792 + 5.41771i) q^{11} +(105.773 - 52.6449i) q^{12} +(7.62998 + 13.2155i) q^{13} +(71.2779 + 123.457i) q^{14} +(-135.556 + 234.790i) q^{16} -36.0074 q^{17} +(-90.2535 + 119.425i) q^{18} -52.7512 q^{19} +(-111.362 - 73.8199i) q^{21} +(17.3418 + 30.0368i) q^{22} +(41.8670 + 72.5158i) q^{23} +(26.2142 - 423.768i) q^{24} +84.6040 q^{26} +(25.8543 - 137.893i) q^{27} +584.654 q^{28} +(-59.5457 + 103.136i) q^{29} +(-138.331 - 239.596i) q^{31} +(424.708 + 735.615i) q^{32} +(-27.0941 - 17.9602i) q^{33} +(-99.8157 + 172.886i) q^{34} +(239.095 + 565.454i) q^{36} -117.553 q^{37} +(-146.231 + 253.280i) q^{38} +(-70.9867 + 35.3311i) q^{39} +(79.6608 + 137.977i) q^{41} +(-663.144 + 330.057i) q^{42} +(147.482 - 255.446i) q^{43} +142.245 q^{44} +464.237 q^{46} +(-41.6458 + 72.1327i) q^{47} +(-1174.19 - 778.352i) q^{48} +(-159.070 - 275.518i) q^{49} +(11.5519 - 186.743i) q^{51} +(173.490 - 300.494i) q^{52} +149.018 q^{53} +(-590.411 - 506.390i) q^{54} +(1050.49 - 1819.51i) q^{56} +(16.9236 - 273.580i) q^{57} +(330.132 + 571.806i) q^{58} +(-317.731 - 550.325i) q^{59} +(-298.575 + 517.148i) q^{61} -1533.86 q^{62} +(418.575 - 553.865i) q^{63} +2540.42 q^{64} +(-161.342 + 80.3021i) q^{66} +(165.008 + 285.802i) q^{67} +(409.367 + 709.045i) q^{68} +(-389.516 + 193.868i) q^{69} -1149.79 q^{71} +(2189.35 + 271.906i) q^{72} -130.284 q^{73} +(-325.869 + 564.422i) q^{74} +(599.728 + 1038.76i) q^{76} +(-80.4271 - 139.304i) q^{77} +(-27.1426 + 438.777i) q^{78} +(368.918 - 638.984i) q^{79} +(706.853 + 178.325i) q^{81} +883.309 q^{82} +(184.951 - 320.345i) q^{83} +(-187.568 + 3032.16i) q^{84} +(-817.665 - 1416.24i) q^{86} +(-515.785 - 341.906i) q^{87} +(255.583 - 442.682i) q^{88} -225.638 q^{89} -392.374 q^{91} +(951.972 - 1648.86i) q^{92} +(1286.98 - 640.549i) q^{93} +(230.892 + 399.917i) q^{94} +(-3951.33 + 1966.64i) q^{96} +(5.95671 - 10.3173i) q^{97} -1763.83 q^{98} +(101.838 - 134.754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9} - 29 q^{11} + 77 q^{12} - 24 q^{13} + 69 q^{14} - 192 q^{16} - 158 q^{17} - 125 q^{18} - 150 q^{19} - 60 q^{21} + 18 q^{22} + 318 q^{23} + 342 q^{24} - 308 q^{26} + 394 q^{27} + 192 q^{28} - 106 q^{29} - 60 q^{31} + 914 q^{32} + 80 q^{33} + 108 q^{34} + 1303 q^{36} - 168 q^{37} + 640 q^{38} - 410 q^{39} + 353 q^{41} - 1521 q^{42} + 426 q^{43} + 1142 q^{44} + 540 q^{46} + 1210 q^{47} - 2680 q^{48} - 666 q^{49} - 1369 q^{51} + 75 q^{52} - 896 q^{53} - 2128 q^{54} + 570 q^{56} - 1544 q^{57} - 594 q^{58} - 482 q^{59} - 402 q^{61} - 5088 q^{62} + 1038 q^{63} + 1950 q^{64} + 2041 q^{66} + 201 q^{67} + 3437 q^{68} + 2856 q^{69} - 1888 q^{71} + 5493 q^{72} - 906 q^{73} - 10 q^{74} + 462 q^{76} + 2652 q^{77} + 4589 q^{78} - 258 q^{79} + 3071 q^{81} + 1746 q^{82} + 3012 q^{83} - 2703 q^{84} - 1952 q^{86} - 2708 q^{87} + 216 q^{88} - 1476 q^{89} - 1236 q^{91} + 5232 q^{92} - 3024 q^{93} - 63 q^{94} - 10424 q^{96} + 318 q^{97} - 15022 q^{98} - 1697 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.77209 4.80141i 0.980083 1.69755i 0.318058 0.948071i \(-0.396969\pi\)
0.662025 0.749482i \(-0.269697\pi\)
\(3\) −0.320819 + 5.18624i −0.0617417 + 0.998092i
\(4\) −11.3690 19.6917i −1.42112 2.46146i
\(5\) 0 0
\(6\) 24.0119 + 15.9171i 1.63380 + 1.08302i
\(7\) −12.8563 + 22.2678i −0.694177 + 1.20235i 0.276281 + 0.961077i \(0.410898\pi\)
−0.970457 + 0.241272i \(0.922435\pi\)
\(8\) −81.7101 −3.61111
\(9\) −26.7942 3.32769i −0.992376 0.123248i
\(10\) 0 0
\(11\) −3.12792 + 5.41771i −0.0857366 + 0.148500i −0.905705 0.423909i \(-0.860658\pi\)
0.819968 + 0.572409i \(0.193991\pi\)
\(12\) 105.773 52.6449i 2.54451 1.26644i
\(13\) 7.62998 + 13.2155i 0.162783 + 0.281948i 0.935866 0.352357i \(-0.114620\pi\)
−0.773083 + 0.634305i \(0.781286\pi\)
\(14\) 71.2779 + 123.457i 1.36070 + 2.35680i
\(15\) 0 0
\(16\) −135.556 + 234.790i −2.11806 + 3.66859i
\(17\) −36.0074 −0.513710 −0.256855 0.966450i \(-0.582686\pi\)
−0.256855 + 0.966450i \(0.582686\pi\)
\(18\) −90.2535 + 119.425i −1.18183 + 1.56382i
\(19\) −52.7512 −0.636945 −0.318472 0.947932i \(-0.603170\pi\)
−0.318472 + 0.947932i \(0.603170\pi\)
\(20\) 0 0
\(21\) −111.362 73.8199i −1.15720 0.767087i
\(22\) 17.3418 + 30.0368i 0.168058 + 0.291085i
\(23\) 41.8670 + 72.5158i 0.379560 + 0.657417i 0.990998 0.133875i \(-0.0427420\pi\)
−0.611438 + 0.791292i \(0.709409\pi\)
\(24\) 26.2142 423.768i 0.222956 3.60422i
\(25\) 0 0
\(26\) 84.6040 0.638162
\(27\) 25.8543 137.893i 0.184284 0.982873i
\(28\) 584.654 3.94604
\(29\) −59.5457 + 103.136i −0.381288 + 0.660411i −0.991247 0.132023i \(-0.957853\pi\)
0.609958 + 0.792433i \(0.291186\pi\)
\(30\) 0 0
\(31\) −138.331 239.596i −0.801449 1.38815i −0.918663 0.395043i \(-0.870730\pi\)
0.117214 0.993107i \(-0.462604\pi\)
\(32\) 424.708 + 735.615i 2.34620 + 4.06374i
\(33\) −27.0941 17.9602i −0.142923 0.0947417i
\(34\) −99.8157 + 172.886i −0.503478 + 0.872050i
\(35\) 0 0
\(36\) 239.095 + 565.454i 1.10692 + 2.61784i
\(37\) −117.553 −0.522315 −0.261158 0.965296i \(-0.584104\pi\)
−0.261158 + 0.965296i \(0.584104\pi\)
\(38\) −146.231 + 253.280i −0.624258 + 1.08125i
\(39\) −70.9867 + 35.3311i −0.291461 + 0.145064i
\(40\) 0 0
\(41\) 79.6608 + 137.977i 0.303437 + 0.525569i 0.976912 0.213641i \(-0.0685324\pi\)
−0.673475 + 0.739210i \(0.735199\pi\)
\(42\) −663.144 + 330.057i −2.43632 + 1.21259i
\(43\) 147.482 255.446i 0.523040 0.905932i −0.476600 0.879120i \(-0.658131\pi\)
0.999640 0.0268122i \(-0.00853561\pi\)
\(44\) 142.245 0.487370
\(45\) 0 0
\(46\) 464.237 1.48800
\(47\) −41.6458 + 72.1327i −0.129248 + 0.223865i −0.923386 0.383874i \(-0.874590\pi\)
0.794137 + 0.607738i \(0.207923\pi\)
\(48\) −1174.19 778.352i −3.53082 2.34053i
\(49\) −159.070 275.518i −0.463762 0.803260i
\(50\) 0 0
\(51\) 11.5519 186.743i 0.0317173 0.512730i
\(52\) 173.490 300.494i 0.462669 0.801366i
\(53\) 149.018 0.386212 0.193106 0.981178i \(-0.438144\pi\)
0.193106 + 0.981178i \(0.438144\pi\)
\(54\) −590.411 506.390i −1.48787 1.27613i
\(55\) 0 0
\(56\) 1050.49 1819.51i 2.50675 4.34182i
\(57\) 16.9236 273.580i 0.0393260 0.635729i
\(58\) 330.132 + 571.806i 0.747388 + 1.29451i
\(59\) −317.731 550.325i −0.701102 1.21434i −0.968080 0.250641i \(-0.919359\pi\)
0.266978 0.963703i \(-0.413975\pi\)
\(60\) 0 0
\(61\) −298.575 + 517.148i −0.626699 + 1.08548i 0.361510 + 0.932368i \(0.382261\pi\)
−0.988210 + 0.153107i \(0.951072\pi\)
\(62\) −1533.86 −3.14194
\(63\) 418.575 553.865i 0.837071 1.10763i
\(64\) 2540.42 4.96175
\(65\) 0 0
\(66\) −161.342 + 80.3021i −0.300906 + 0.149765i
\(67\) 165.008 + 285.802i 0.300879 + 0.521138i 0.976335 0.216262i \(-0.0693867\pi\)
−0.675456 + 0.737400i \(0.736053\pi\)
\(68\) 409.367 + 709.045i 0.730045 + 1.26448i
\(69\) −389.516 + 193.868i −0.679598 + 0.338246i
\(70\) 0 0
\(71\) −1149.79 −1.92189 −0.960947 0.276732i \(-0.910749\pi\)
−0.960947 + 0.276732i \(0.910749\pi\)
\(72\) 2189.35 + 271.906i 3.58358 + 0.445062i
\(73\) −130.284 −0.208885 −0.104442 0.994531i \(-0.533306\pi\)
−0.104442 + 0.994531i \(0.533306\pi\)
\(74\) −325.869 + 564.422i −0.511912 + 0.886658i
\(75\) 0 0
\(76\) 599.728 + 1038.76i 0.905177 + 1.56781i
\(77\) −80.4271 139.304i −0.119033 0.206171i
\(78\) −27.1426 + 438.777i −0.0394012 + 0.636945i
\(79\) 368.918 638.984i 0.525398 0.910017i −0.474164 0.880437i \(-0.657250\pi\)
0.999562 0.0295801i \(-0.00941703\pi\)
\(80\) 0 0
\(81\) 706.853 + 178.325i 0.969620 + 0.244616i
\(82\) 883.309 1.18957
\(83\) 184.951 320.345i 0.244591 0.423644i −0.717426 0.696635i \(-0.754680\pi\)
0.962016 + 0.272991i \(0.0880130\pi\)
\(84\) −187.568 + 3032.16i −0.243635 + 3.93852i
\(85\) 0 0
\(86\) −817.665 1416.24i −1.02525 1.77578i
\(87\) −515.785 341.906i −0.635609 0.421336i
\(88\) 255.583 442.682i 0.309605 0.536251i
\(89\) −225.638 −0.268737 −0.134369 0.990931i \(-0.542901\pi\)
−0.134369 + 0.990931i \(0.542901\pi\)
\(90\) 0 0
\(91\) −392.374 −0.452000
\(92\) 951.972 1648.86i 1.07880 1.86854i
\(93\) 1286.98 640.549i 1.43498 0.714213i
\(94\) 230.892 + 399.917i 0.253348 + 0.438812i
\(95\) 0 0
\(96\) −3951.33 + 1966.64i −4.20084 + 2.09082i
\(97\) 5.95671 10.3173i 0.00623518 0.0107996i −0.862891 0.505390i \(-0.831349\pi\)
0.869126 + 0.494590i \(0.164682\pi\)
\(98\) −1763.83 −1.81810
\(99\) 101.838 134.754i 0.103385 0.136801i
\(100\) 0 0
\(101\) −383.267 + 663.838i −0.377589 + 0.654003i −0.990711 0.135985i \(-0.956580\pi\)
0.613122 + 0.789988i \(0.289913\pi\)
\(102\) −864.605 573.133i −0.839300 0.556359i
\(103\) 774.737 + 1341.88i 0.741137 + 1.28369i 0.951978 + 0.306166i \(0.0990463\pi\)
−0.210841 + 0.977520i \(0.567620\pi\)
\(104\) −623.447 1079.84i −0.587827 1.01815i
\(105\) 0 0
\(106\) 413.093 715.497i 0.378520 0.655615i
\(107\) −1218.43 −1.10084 −0.550421 0.834887i \(-0.685533\pi\)
−0.550421 + 0.834887i \(0.685533\pi\)
\(108\) −3009.29 + 1058.59i −2.68119 + 0.943178i
\(109\) −1327.27 −1.16633 −0.583163 0.812355i \(-0.698185\pi\)
−0.583163 + 0.812355i \(0.698185\pi\)
\(110\) 0 0
\(111\) 37.7134 609.660i 0.0322486 0.521319i
\(112\) −3485.51 6037.08i −2.94062 5.09330i
\(113\) 216.828 + 375.557i 0.180509 + 0.312650i 0.942054 0.335462i \(-0.108892\pi\)
−0.761545 + 0.648112i \(0.775559\pi\)
\(114\) −1266.66 839.646i −1.04064 0.689825i
\(115\) 0 0
\(116\) 2707.90 2.16743
\(117\) −160.462 379.489i −0.126792 0.299861i
\(118\) −3523.11 −2.74855
\(119\) 462.922 801.805i 0.356605 0.617658i
\(120\) 0 0
\(121\) 645.932 + 1118.79i 0.485298 + 0.840562i
\(122\) 1655.36 + 2867.16i 1.22843 + 2.12771i
\(123\) −741.136 + 368.875i −0.543301 + 0.270409i
\(124\) −3145.36 + 5447.92i −2.27792 + 3.94547i
\(125\) 0 0
\(126\) −1499.00 3545.11i −1.05986 2.50654i
\(127\) 1850.18 1.29273 0.646365 0.763028i \(-0.276288\pi\)
0.646365 + 0.763028i \(0.276288\pi\)
\(128\) 3644.61 6312.65i 2.51673 4.35910i
\(129\) 1277.49 + 846.827i 0.871911 + 0.577976i
\(130\) 0 0
\(131\) 638.716 + 1106.29i 0.425991 + 0.737839i 0.996512 0.0834443i \(-0.0265921\pi\)
−0.570521 + 0.821283i \(0.693259\pi\)
\(132\) −45.6350 + 737.717i −0.0300910 + 0.486440i
\(133\) 678.186 1174.65i 0.442152 0.765830i
\(134\) 1829.67 1.17954
\(135\) 0 0
\(136\) 2942.17 1.85506
\(137\) −766.766 + 1328.08i −0.478170 + 0.828214i −0.999687 0.0250268i \(-0.992033\pi\)
0.521517 + 0.853241i \(0.325366\pi\)
\(138\) −148.936 + 2407.64i −0.0918717 + 1.48516i
\(139\) −766.669 1327.91i −0.467828 0.810301i 0.531497 0.847060i \(-0.321630\pi\)
−0.999324 + 0.0367593i \(0.988297\pi\)
\(140\) 0 0
\(141\) −360.737 239.127i −0.215457 0.142823i
\(142\) −3187.31 + 5520.59i −1.88362 + 3.26252i
\(143\) −95.4638 −0.0558258
\(144\) 4413.42 5839.91i 2.55406 3.37958i
\(145\) 0 0
\(146\) −361.159 + 625.545i −0.204724 + 0.354593i
\(147\) 1479.94 736.586i 0.830361 0.413283i
\(148\) 1336.46 + 2314.82i 0.742275 + 1.28566i
\(149\) 1251.54 + 2167.73i 0.688120 + 1.19186i 0.972445 + 0.233131i \(0.0748971\pi\)
−0.284325 + 0.958728i \(0.591770\pi\)
\(150\) 0 0
\(151\) 760.321 1316.92i 0.409762 0.709729i −0.585101 0.810961i \(-0.698945\pi\)
0.994863 + 0.101232i \(0.0322784\pi\)
\(152\) 4310.30 2.30008
\(153\) 964.786 + 119.821i 0.509793 + 0.0633136i
\(154\) −891.805 −0.466648
\(155\) 0 0
\(156\) 1502.78 + 996.167i 0.771271 + 0.511264i
\(157\) 1296.44 + 2245.50i 0.659026 + 1.14147i 0.980868 + 0.194674i \(0.0623647\pi\)
−0.321842 + 0.946793i \(0.604302\pi\)
\(158\) −2045.35 3542.65i −1.02987 1.78378i
\(159\) −47.8079 + 772.845i −0.0238454 + 0.385475i
\(160\) 0 0
\(161\) −2153.03 −1.05393
\(162\) 2815.67 2899.55i 1.36556 1.40624i
\(163\) 675.580 0.324635 0.162318 0.986739i \(-0.448103\pi\)
0.162318 + 0.986739i \(0.448103\pi\)
\(164\) 1811.33 3137.31i 0.862444 1.49380i
\(165\) 0 0
\(166\) −1025.40 1776.05i −0.479438 0.830412i
\(167\) −1947.97 3373.97i −0.902623 1.56339i −0.824076 0.566479i \(-0.808305\pi\)
−0.0785470 0.996910i \(-0.525028\pi\)
\(168\) 9099.38 + 6031.84i 4.17876 + 2.77004i
\(169\) 982.067 1700.99i 0.447004 0.774233i
\(170\) 0 0
\(171\) 1413.42 + 175.540i 0.632088 + 0.0785020i
\(172\) −6706.87 −2.97322
\(173\) −25.8304 + 44.7396i −0.0113517 + 0.0196618i −0.871645 0.490137i \(-0.836947\pi\)
0.860294 + 0.509799i \(0.170280\pi\)
\(174\) −3071.44 + 1528.70i −1.33819 + 0.666037i
\(175\) 0 0
\(176\) −848.017 1468.81i −0.363191 0.629066i
\(177\) 2956.05 1471.27i 1.25531 0.624788i
\(178\) −625.490 + 1083.38i −0.263385 + 0.456195i
\(179\) 4553.37 1.90131 0.950656 0.310247i \(-0.100412\pi\)
0.950656 + 0.310247i \(0.100412\pi\)
\(180\) 0 0
\(181\) 2441.01 1.00243 0.501213 0.865324i \(-0.332887\pi\)
0.501213 + 0.865324i \(0.332887\pi\)
\(182\) −1087.70 + 1883.95i −0.442997 + 0.767294i
\(183\) −2586.26 1714.39i −1.04471 0.692523i
\(184\) −3420.96 5925.28i −1.37063 2.37401i
\(185\) 0 0
\(186\) 492.092 7954.97i 0.193989 3.13595i
\(187\) 112.628 195.078i 0.0440437 0.0762860i
\(188\) 1893.88 0.734711
\(189\) 2738.19 + 2348.52i 1.05383 + 0.903861i
\(190\) 0 0
\(191\) −663.053 + 1148.44i −0.251188 + 0.435070i −0.963853 0.266434i \(-0.914154\pi\)
0.712665 + 0.701504i \(0.247488\pi\)
\(192\) −815.015 + 13175.2i −0.306347 + 4.95229i
\(193\) −724.098 1254.17i −0.270061 0.467759i 0.698816 0.715301i \(-0.253710\pi\)
−0.968877 + 0.247542i \(0.920377\pi\)
\(194\) −33.0251 57.2012i −0.0122220 0.0211691i
\(195\) 0 0
\(196\) −3616.94 + 6264.73i −1.31813 + 2.28306i
\(197\) −2398.84 −0.867564 −0.433782 0.901018i \(-0.642821\pi\)
−0.433782 + 0.901018i \(0.642821\pi\)
\(198\) −364.704 862.519i −0.130901 0.309578i
\(199\) 3109.15 1.10755 0.553773 0.832667i \(-0.313187\pi\)
0.553773 + 0.832667i \(0.313187\pi\)
\(200\) 0 0
\(201\) −1535.17 + 764.078i −0.538720 + 0.268129i
\(202\) 2124.90 + 3680.44i 0.740137 + 1.28195i
\(203\) −1531.08 2651.91i −0.529363 0.916883i
\(204\) −3808.61 + 1895.60i −1.30714 + 0.650582i
\(205\) 0 0
\(206\) 8590.57 2.90550
\(207\) −880.481 2082.32i −0.295641 0.699185i
\(208\) −4137.16 −1.37914
\(209\) 165.001 285.791i 0.0546095 0.0945864i
\(210\) 0 0
\(211\) 1654.80 + 2866.19i 0.539910 + 0.935151i 0.998908 + 0.0467139i \(0.0148749\pi\)
−0.458999 + 0.888437i \(0.651792\pi\)
\(212\) −1694.19 2934.42i −0.548855 0.950645i
\(213\) 368.873 5963.07i 0.118661 1.91823i
\(214\) −3377.60 + 5850.18i −1.07892 + 1.86874i
\(215\) 0 0
\(216\) −2112.56 + 11267.3i −0.665469 + 3.54926i
\(217\) 7113.69 2.22539
\(218\) −3679.32 + 6372.76i −1.14310 + 1.97990i
\(219\) 41.7976 675.683i 0.0128969 0.208486i
\(220\) 0 0
\(221\) −274.735 475.856i −0.0836231 0.144839i
\(222\) −2822.68 1871.11i −0.853360 0.565679i
\(223\) −1399.42 + 2423.86i −0.420233 + 0.727865i −0.995962 0.0897754i \(-0.971385\pi\)
0.575729 + 0.817641i \(0.304718\pi\)
\(224\) −21840.7 −6.51471
\(225\) 0 0
\(226\) 2404.27 0.707653
\(227\) −1564.59 + 2709.94i −0.457468 + 0.792358i −0.998826 0.0484343i \(-0.984577\pi\)
0.541358 + 0.840792i \(0.317910\pi\)
\(228\) −5579.66 + 2777.08i −1.62071 + 0.806651i
\(229\) −1487.79 2576.93i −0.429327 0.743616i 0.567487 0.823383i \(-0.307916\pi\)
−0.996814 + 0.0797667i \(0.974582\pi\)
\(230\) 0 0
\(231\) 748.265 372.423i 0.213127 0.106076i
\(232\) 4865.49 8427.27i 1.37687 2.38482i
\(233\) −925.895 −0.260332 −0.130166 0.991492i \(-0.541551\pi\)
−0.130166 + 0.991492i \(0.541551\pi\)
\(234\) −2266.89 281.536i −0.633297 0.0786521i
\(235\) 0 0
\(236\) −7224.55 + 12513.3i −1.99271 + 3.45147i
\(237\) 3195.57 + 2118.29i 0.875842 + 0.580582i
\(238\) −2566.53 4445.36i −0.699005 1.21071i
\(239\) −1305.41 2261.04i −0.353305 0.611942i 0.633521 0.773725i \(-0.281609\pi\)
−0.986826 + 0.161783i \(0.948276\pi\)
\(240\) 0 0
\(241\) 334.737 579.781i 0.0894700 0.154967i −0.817817 0.575478i \(-0.804816\pi\)
0.907287 + 0.420511i \(0.138149\pi\)
\(242\) 7162.34 1.90253
\(243\) −1151.61 + 3608.70i −0.304016 + 0.952667i
\(244\) 13578.0 3.56247
\(245\) 0 0
\(246\) −283.382 + 4581.05i −0.0734464 + 1.18731i
\(247\) −402.490 697.134i −0.103684 0.179585i
\(248\) 11303.0 + 19577.4i 2.89412 + 5.01276i
\(249\) 1602.05 + 1061.97i 0.407734 + 0.270281i
\(250\) 0 0
\(251\) −6463.00 −1.62526 −0.812631 0.582778i \(-0.801966\pi\)
−0.812631 + 0.582778i \(0.801966\pi\)
\(252\) −15665.3 1945.55i −3.91596 0.486341i
\(253\) −523.827 −0.130169
\(254\) 5128.87 8883.46i 1.26698 2.19448i
\(255\) 0 0
\(256\) −10044.7 17398.0i −2.45233 4.24755i
\(257\) 1417.66 + 2455.47i 0.344091 + 0.595984i 0.985188 0.171476i \(-0.0548536\pi\)
−0.641097 + 0.767460i \(0.721520\pi\)
\(258\) 7607.27 3786.25i 1.83569 0.913650i
\(259\) 1511.31 2617.66i 0.362579 0.628005i
\(260\) 0 0
\(261\) 1938.68 2565.30i 0.459775 0.608383i
\(262\) 7082.32 1.67003
\(263\) 816.837 1414.80i 0.191515 0.331713i −0.754238 0.656601i \(-0.771993\pi\)
0.945752 + 0.324888i \(0.105327\pi\)
\(264\) 2213.86 + 1467.53i 0.516112 + 0.342123i
\(265\) 0 0
\(266\) −3759.99 6512.49i −0.866691 1.50115i
\(267\) 72.3891 1170.21i 0.0165923 0.268224i
\(268\) 3751.94 6498.55i 0.855173 1.48120i
\(269\) −4870.30 −1.10389 −0.551947 0.833880i \(-0.686115\pi\)
−0.551947 + 0.833880i \(0.686115\pi\)
\(270\) 0 0
\(271\) −3913.17 −0.877153 −0.438576 0.898694i \(-0.644517\pi\)
−0.438576 + 0.898694i \(0.644517\pi\)
\(272\) 4881.02 8454.17i 1.08807 1.88459i
\(273\) 125.881 2034.95i 0.0279072 0.451138i
\(274\) 4251.09 + 7363.11i 0.937291 + 1.62344i
\(275\) 0 0
\(276\) 8245.99 + 5466.14i 1.79837 + 1.19211i
\(277\) −409.072 + 708.534i −0.0887320 + 0.153688i −0.906975 0.421184i \(-0.861615\pi\)
0.818243 + 0.574872i \(0.194948\pi\)
\(278\) −8501.11 −1.83404
\(279\) 2909.15 + 6880.08i 0.624252 + 1.47634i
\(280\) 0 0
\(281\) 2581.48 4471.25i 0.548035 0.949225i −0.450374 0.892840i \(-0.648709\pi\)
0.998409 0.0563851i \(-0.0179574\pi\)
\(282\) −2148.14 + 1069.16i −0.453617 + 0.225772i
\(283\) 3573.29 + 6189.11i 0.750565 + 1.30002i 0.947549 + 0.319610i \(0.103552\pi\)
−0.196984 + 0.980407i \(0.563115\pi\)
\(284\) 13071.9 + 22641.2i 2.73125 + 4.73067i
\(285\) 0 0
\(286\) −264.635 + 458.360i −0.0547139 + 0.0947672i
\(287\) −4096.58 −0.842556
\(288\) −8931.78 21123.5i −1.82747 4.32192i
\(289\) −3616.47 −0.736102
\(290\) 0 0
\(291\) 51.5971 + 34.2029i 0.0103941 + 0.00689007i
\(292\) 1481.20 + 2565.51i 0.296851 + 0.514161i
\(293\) 732.548 + 1268.81i 0.146061 + 0.252985i 0.929768 0.368145i \(-0.120007\pi\)
−0.783707 + 0.621130i \(0.786674\pi\)
\(294\) 565.871 9147.65i 0.112253 1.81463i
\(295\) 0 0
\(296\) 9605.31 1.88614
\(297\) 666.196 + 571.390i 0.130157 + 0.111634i
\(298\) 13877.5 2.69766
\(299\) −638.889 + 1106.59i −0.123572 + 0.214032i
\(300\) 0 0
\(301\) 3792.14 + 6568.19i 0.726165 + 1.25775i
\(302\) −4215.36 7301.22i −0.803202 1.39119i
\(303\) −3319.86 2200.68i −0.629442 0.417248i
\(304\) 7150.74 12385.4i 1.34909 2.33669i
\(305\) 0 0
\(306\) 3249.79 4300.17i 0.607118 0.803348i
\(307\) −790.554 −0.146968 −0.0734842 0.997296i \(-0.523412\pi\)
−0.0734842 + 0.997296i \(0.523412\pi\)
\(308\) −1828.75 + 3167.49i −0.338321 + 0.585988i
\(309\) −7207.88 + 3587.47i −1.32700 + 0.660466i
\(310\) 0 0
\(311\) −1962.65 3399.42i −0.357852 0.619817i 0.629750 0.776798i \(-0.283157\pi\)
−0.987602 + 0.156981i \(0.949824\pi\)
\(312\) 5800.33 2886.91i 1.05250 0.523843i
\(313\) −2871.19 + 4973.04i −0.518495 + 0.898060i 0.481274 + 0.876570i \(0.340174\pi\)
−0.999769 + 0.0214900i \(0.993159\pi\)
\(314\) 14375.4 2.58360
\(315\) 0 0
\(316\) −16776.9 −2.98663
\(317\) −4068.35 + 7046.59i −0.720824 + 1.24850i 0.239846 + 0.970811i \(0.422903\pi\)
−0.960670 + 0.277693i \(0.910430\pi\)
\(318\) 3578.21 + 2371.94i 0.630994 + 0.418276i
\(319\) −372.508 645.203i −0.0653807 0.113243i
\(320\) 0 0
\(321\) 390.896 6319.07i 0.0679679 1.09874i
\(322\) −5968.39 + 10337.5i −1.03294 + 1.78910i
\(323\) 1899.43 0.327205
\(324\) −4524.68 15946.5i −0.775837 2.73431i
\(325\) 0 0
\(326\) 1872.77 3243.73i 0.318169 0.551085i
\(327\) 425.814 6883.54i 0.0720109 1.16410i
\(328\) −6509.10 11274.1i −1.09575 1.89789i
\(329\) −1070.83 1854.72i −0.179442 0.310803i
\(330\) 0 0
\(331\) 3163.47 5479.29i 0.525317 0.909876i −0.474248 0.880391i \(-0.657280\pi\)
0.999565 0.0294849i \(-0.00938671\pi\)
\(332\) −8410.84 −1.39038
\(333\) 3149.74 + 391.181i 0.518333 + 0.0643742i
\(334\) −21599.8 −3.53858
\(335\) 0 0
\(336\) 32427.9 16139.9i 5.26515 2.62054i
\(337\) −2387.01 4134.42i −0.385842 0.668297i 0.606044 0.795431i \(-0.292756\pi\)
−0.991886 + 0.127134i \(0.959422\pi\)
\(338\) −5444.76 9430.60i −0.876201 1.51762i
\(339\) −2017.29 + 1004.04i −0.323198 + 0.160861i
\(340\) 0 0
\(341\) 1730.75 0.274854
\(342\) 4760.97 6299.80i 0.752760 0.996065i
\(343\) −639.195 −0.100622
\(344\) −12050.7 + 20872.5i −1.88876 + 3.27142i
\(345\) 0 0
\(346\) 143.209 + 248.045i 0.0222513 + 0.0385404i
\(347\) 909.717 + 1575.68i 0.140738 + 0.243766i 0.927775 0.373141i \(-0.121719\pi\)
−0.787037 + 0.616906i \(0.788386\pi\)
\(348\) −868.746 + 14043.8i −0.133821 + 2.16330i
\(349\) 1488.69 2578.48i 0.228331 0.395481i −0.728982 0.684532i \(-0.760006\pi\)
0.957314 + 0.289051i \(0.0933397\pi\)
\(350\) 0 0
\(351\) 2019.60 710.445i 0.307117 0.108036i
\(352\) −5313.80 −0.804621
\(353\) −3473.89 + 6016.95i −0.523786 + 0.907223i 0.475831 + 0.879537i \(0.342147\pi\)
−0.999617 + 0.0276865i \(0.991186\pi\)
\(354\) 1130.28 18271.7i 0.169700 2.74331i
\(355\) 0 0
\(356\) 2565.28 + 4443.19i 0.381909 + 0.661485i
\(357\) 4009.84 + 2658.06i 0.594463 + 0.394060i
\(358\) 12622.4 21862.6i 1.86344 3.22758i
\(359\) −3665.56 −0.538887 −0.269444 0.963016i \(-0.586840\pi\)
−0.269444 + 0.963016i \(0.586840\pi\)
\(360\) 0 0
\(361\) −4076.31 −0.594302
\(362\) 6766.71 11720.3i 0.982460 1.70167i
\(363\) −6009.53 + 2991.03i −0.868921 + 0.432475i
\(364\) 4460.90 + 7726.50i 0.642348 + 1.11258i
\(365\) 0 0
\(366\) −15400.9 + 7665.24i −2.19950 + 1.09472i
\(367\) −4831.54 + 8368.48i −0.687206 + 1.19028i 0.285532 + 0.958369i \(0.407830\pi\)
−0.972738 + 0.231906i \(0.925504\pi\)
\(368\) −22701.3 −3.21573
\(369\) −1675.30 3962.05i −0.236349 0.558960i
\(370\) 0 0
\(371\) −1915.83 + 3318.31i −0.268099 + 0.464362i
\(372\) −27245.1 18060.4i −3.79730 2.51717i
\(373\) 3011.86 + 5216.70i 0.418092 + 0.724157i 0.995748 0.0921237i \(-0.0293655\pi\)
−0.577655 + 0.816281i \(0.696032\pi\)
\(374\) −624.431 1081.55i −0.0863330 0.149533i
\(375\) 0 0
\(376\) 3402.89 5893.97i 0.466730 0.808400i
\(377\) −1817.33 −0.248269
\(378\) 18866.7 6636.85i 2.56719 0.903076i
\(379\) −1229.32 −0.166613 −0.0833063 0.996524i \(-0.526548\pi\)
−0.0833063 + 0.996524i \(0.526548\pi\)
\(380\) 0 0
\(381\) −593.573 + 9595.47i −0.0798154 + 1.29026i
\(382\) 3676.09 + 6367.17i 0.492369 + 0.852809i
\(383\) 1066.80 + 1847.75i 0.142326 + 0.246515i 0.928372 0.371652i \(-0.121209\pi\)
−0.786046 + 0.618168i \(0.787875\pi\)
\(384\) 31569.7 + 20927.0i 4.19540 + 2.78106i
\(385\) 0 0
\(386\) −8029.07 −1.05873
\(387\) −4801.69 + 6353.67i −0.630707 + 0.834562i
\(388\) −270.887 −0.0354439
\(389\) −4920.76 + 8523.01i −0.641369 + 1.11088i 0.343759 + 0.939058i \(0.388300\pi\)
−0.985127 + 0.171825i \(0.945033\pi\)
\(390\) 0 0
\(391\) −1507.52 2611.10i −0.194984 0.337722i
\(392\) 12997.7 + 22512.6i 1.67470 + 2.90066i
\(393\) −5942.39 + 2957.61i −0.762732 + 0.379623i
\(394\) −6649.80 + 11517.8i −0.850284 + 1.47274i
\(395\) 0 0
\(396\) −3811.34 473.348i −0.483654 0.0600672i
\(397\) −2548.71 −0.322207 −0.161104 0.986938i \(-0.551505\pi\)
−0.161104 + 0.986938i \(0.551505\pi\)
\(398\) 8618.85 14928.3i 1.08549 1.88012i
\(399\) 5874.46 + 3894.09i 0.737069 + 0.488592i
\(400\) 0 0
\(401\) 6552.50 + 11349.3i 0.816001 + 1.41335i 0.908607 + 0.417652i \(0.137147\pi\)
−0.0926064 + 0.995703i \(0.529520\pi\)
\(402\) −586.992 + 9489.08i −0.0728271 + 1.17729i
\(403\) 2110.92 3656.22i 0.260924 0.451934i
\(404\) 17429.4 2.14640
\(405\) 0 0
\(406\) −16977.2 −2.07528
\(407\) 367.697 636.871i 0.0447815 0.0775639i
\(408\) −943.903 + 15258.8i −0.114535 + 1.85152i
\(409\) −3108.62 5384.29i −0.375823 0.650944i 0.614627 0.788818i \(-0.289306\pi\)
−0.990450 + 0.137874i \(0.955973\pi\)
\(410\) 0 0
\(411\) −6641.73 4402.70i −0.797111 0.528393i
\(412\) 17616.0 30511.7i 2.10649 3.64856i
\(413\) 16339.4 1.94675
\(414\) −12438.8 1544.84i −1.47666 0.183393i
\(415\) 0 0
\(416\) −6481.02 + 11225.5i −0.763842 + 1.32301i
\(417\) 7132.82 3550.11i 0.837640 0.416906i
\(418\) −914.798 1584.48i −0.107044 0.185405i
\(419\) −4214.03 7298.91i −0.491334 0.851015i 0.508617 0.860993i \(-0.330157\pi\)
−0.999950 + 0.00997827i \(0.996824\pi\)
\(420\) 0 0
\(421\) 6389.69 11067.3i 0.739702 1.28120i −0.212928 0.977068i \(-0.568300\pi\)
0.952629 0.304133i \(-0.0983668\pi\)
\(422\) 18349.0 2.11662
\(423\) 1355.90 1794.15i 0.155854 0.206228i
\(424\) −12176.3 −1.39465
\(425\) 0 0
\(426\) −27608.5 18301.3i −3.14000 2.08146i
\(427\) −7677.17 13297.2i −0.870080 1.50702i
\(428\) 13852.3 + 23992.9i 1.56443 + 2.70968i
\(429\) 30.6266 495.098i 0.00344678 0.0557193i
\(430\) 0 0
\(431\) 3149.70 0.352009 0.176005 0.984389i \(-0.443683\pi\)
0.176005 + 0.984389i \(0.443683\pi\)
\(432\) 28871.3 + 24762.6i 3.21544 + 2.75785i
\(433\) −6999.89 −0.776890 −0.388445 0.921472i \(-0.626988\pi\)
−0.388445 + 0.921472i \(0.626988\pi\)
\(434\) 19719.8 34155.7i 2.18106 3.77771i
\(435\) 0 0
\(436\) 15089.7 + 26136.2i 1.65749 + 2.87086i
\(437\) −2208.53 3825.29i −0.241759 0.418738i
\(438\) −3128.36 2073.74i −0.341276 0.226227i
\(439\) 3861.15 6687.71i 0.419778 0.727077i −0.576139 0.817352i \(-0.695441\pi\)
0.995917 + 0.0902746i \(0.0287745\pi\)
\(440\) 0 0
\(441\) 3345.32 + 7911.61i 0.361226 + 0.854293i
\(442\) −3046.37 −0.327830
\(443\) 3324.37 5757.97i 0.356536 0.617538i −0.630844 0.775910i \(-0.717291\pi\)
0.987380 + 0.158372i \(0.0506244\pi\)
\(444\) −12434.0 + 6188.58i −1.32903 + 0.661480i
\(445\) 0 0
\(446\) 7758.64 + 13438.4i 0.823727 + 1.42674i
\(447\) −11643.9 + 5795.32i −1.23207 + 0.613220i
\(448\) −32660.4 + 56569.5i −3.44433 + 5.96576i
\(449\) −11416.8 −1.19998 −0.599989 0.800008i \(-0.704829\pi\)
−0.599989 + 0.800008i \(0.704829\pi\)
\(450\) 0 0
\(451\) −996.690 −0.104063
\(452\) 4930.23 8539.41i 0.513050 0.888629i
\(453\) 6585.91 + 4365.70i 0.683075 + 0.452800i
\(454\) 8674.35 + 15024.4i 0.896713 + 1.55315i
\(455\) 0 0
\(456\) −1382.83 + 22354.3i −0.142011 + 2.29569i
\(457\) 5595.73 9692.09i 0.572773 0.992072i −0.423507 0.905893i \(-0.639201\pi\)
0.996280 0.0861787i \(-0.0274656\pi\)
\(458\) −16497.2 −1.68310
\(459\) −930.944 + 4965.17i −0.0946683 + 0.504912i
\(460\) 0 0
\(461\) 2450.93 4245.14i 0.247617 0.428885i −0.715247 0.698871i \(-0.753686\pi\)
0.962864 + 0.269987i \(0.0870193\pi\)
\(462\) 286.108 4625.12i 0.0288116 0.465757i
\(463\) 1065.82 + 1846.06i 0.106982 + 0.185299i 0.914546 0.404481i \(-0.132548\pi\)
−0.807564 + 0.589780i \(0.799214\pi\)
\(464\) −16143.6 27961.5i −1.61519 2.79758i
\(465\) 0 0
\(466\) −2566.67 + 4445.60i −0.255147 + 0.441928i
\(467\) −17877.0 −1.77141 −0.885707 0.464246i \(-0.846325\pi\)
−0.885707 + 0.464246i \(0.846325\pi\)
\(468\) −5648.48 + 7474.16i −0.557908 + 0.738234i
\(469\) −8485.57 −0.835452
\(470\) 0 0
\(471\) −12061.6 + 6003.24i −1.17998 + 0.587293i
\(472\) 25961.8 + 44967.2i 2.53176 + 4.38513i
\(473\) 922.621 + 1598.03i 0.0896874 + 0.155343i
\(474\) 19029.2 9471.11i 1.84397 0.917769i
\(475\) 0 0
\(476\) −21051.8 −2.02712
\(477\) −3992.82 495.887i −0.383268 0.0475998i
\(478\) −14474.9 −1.38507
\(479\) −10208.9 + 17682.3i −0.973811 + 1.68669i −0.290006 + 0.957025i \(0.593657\pi\)
−0.683805 + 0.729665i \(0.739676\pi\)
\(480\) 0 0
\(481\) −896.930 1553.53i −0.0850239 0.147266i
\(482\) −1855.84 3214.41i −0.175376 0.303760i
\(483\) 690.732 11166.1i 0.0650712 1.05192i
\(484\) 14687.2 25439.0i 1.37934 2.38908i
\(485\) 0 0
\(486\) 14134.5 + 15533.0i 1.31924 + 1.44978i
\(487\) −8337.59 −0.775795 −0.387898 0.921702i \(-0.626799\pi\)
−0.387898 + 0.921702i \(0.626799\pi\)
\(488\) 24396.6 42256.2i 2.26308 3.91977i
\(489\) −216.739 + 3503.72i −0.0200435 + 0.324016i
\(490\) 0 0
\(491\) −8132.34 14085.6i −0.747469 1.29465i −0.949032 0.315179i \(-0.897935\pi\)
0.201563 0.979476i \(-0.435398\pi\)
\(492\) 15689.7 + 10400.5i 1.43770 + 0.953029i
\(493\) 2144.08 3713.66i 0.195871 0.339259i
\(494\) −4462.96 −0.406474
\(495\) 0 0
\(496\) 75006.2 6.79008
\(497\) 14782.0 25603.2i 1.33413 2.31079i
\(498\) 9540.00 4748.20i 0.858429 0.427253i
\(499\) 8055.83 + 13953.1i 0.722702 + 1.25176i 0.959913 + 0.280299i \(0.0904336\pi\)
−0.237210 + 0.971458i \(0.576233\pi\)
\(500\) 0 0
\(501\) 18123.2 9020.18i 1.61614 0.804375i
\(502\) −17916.0 + 31031.5i −1.59289 + 2.75897i
\(503\) −9219.89 −0.817285 −0.408643 0.912695i \(-0.633998\pi\)
−0.408643 + 0.912695i \(0.633998\pi\)
\(504\) −34201.8 + 45256.4i −3.02276 + 3.99976i
\(505\) 0 0
\(506\) −1452.10 + 2515.10i −0.127576 + 0.220968i
\(507\) 8506.67 + 5638.94i 0.745157 + 0.493953i
\(508\) −21034.7 36433.1i −1.83713 3.18200i
\(509\) −4283.42 7419.11i −0.373005 0.646063i 0.617022 0.786946i \(-0.288339\pi\)
−0.990026 + 0.140883i \(0.955006\pi\)
\(510\) 0 0
\(511\) 1674.97 2901.14i 0.145003 0.251152i
\(512\) −53065.9 −4.58048
\(513\) −1363.84 + 7274.03i −0.117378 + 0.626036i
\(514\) 15719.6 1.34895
\(515\) 0 0
\(516\) 2151.69 34783.4i 0.183572 2.96755i
\(517\) −260.530 451.250i −0.0221626 0.0383868i
\(518\) −8378.96 14512.8i −0.710715 1.23099i
\(519\) −223.743 148.316i −0.0189234 0.0125440i
\(520\) 0 0
\(521\) −2450.94 −0.206099 −0.103050 0.994676i \(-0.532860\pi\)
−0.103050 + 0.994676i \(0.532860\pi\)
\(522\) −6942.82 16419.6i −0.582144 1.37676i
\(523\) −20897.8 −1.74722 −0.873609 0.486628i \(-0.838227\pi\)
−0.873609 + 0.486628i \(0.838227\pi\)
\(524\) 14523.1 25154.8i 1.21077 2.09712i
\(525\) 0 0
\(526\) −4528.70 7843.94i −0.375400 0.650213i
\(527\) 4980.92 + 8627.20i 0.411712 + 0.713106i
\(528\) 7889.65 3926.80i 0.650290 0.323659i
\(529\) 2577.80 4464.89i 0.211868 0.366967i
\(530\) 0 0
\(531\) 6682.01 + 15802.8i 0.546091 + 1.29149i
\(532\) −30841.2 −2.51341
\(533\) −1215.62 + 2105.52i −0.0987887 + 0.171107i
\(534\) −5418.00 3591.51i −0.439063 0.291048i
\(535\) 0 0
\(536\) −13482.8 23352.9i −1.08651 1.88189i
\(537\) −1460.81 + 23614.9i −0.117390 + 1.89768i
\(538\) −13500.9 + 23384.3i −1.08191 + 1.87392i
\(539\) 1990.24 0.159046
\(540\) 0 0
\(541\) −9960.84 −0.791590 −0.395795 0.918339i \(-0.629531\pi\)
−0.395795 + 0.918339i \(0.629531\pi\)
\(542\) −10847.7 + 18788.7i −0.859682 + 1.48901i
\(543\) −783.123 + 12659.7i −0.0618914 + 1.00051i
\(544\) −15292.6 26487.6i −1.20527 2.08758i
\(545\) 0 0
\(546\) −9421.65 6245.47i −0.738478 0.489526i
\(547\) 4297.17 7442.93i 0.335894 0.581785i −0.647762 0.761843i \(-0.724295\pi\)
0.983656 + 0.180057i \(0.0576283\pi\)
\(548\) 34869.4 2.71815
\(549\) 9720.98 12863.0i 0.755704 0.999960i
\(550\) 0 0
\(551\) 3141.10 5440.55i 0.242859 0.420645i
\(552\) 31827.4 15841.0i 2.45410 1.22144i
\(553\) 9485.85 + 16430.0i 0.729438 + 1.26342i
\(554\) 2267.97 + 3928.24i 0.173929 + 0.301255i
\(555\) 0 0
\(556\) −17432.5 + 30194.0i −1.32968 + 2.30308i
\(557\) 9469.85 0.720378 0.360189 0.932879i \(-0.382712\pi\)
0.360189 + 0.932879i \(0.382712\pi\)
\(558\) 41098.5 + 5104.21i 3.11799 + 0.387238i
\(559\) 4501.13 0.340568
\(560\) 0 0
\(561\) 975.585 + 646.701i 0.0734211 + 0.0486697i
\(562\) −14312.2 24789.4i −1.07424 1.86064i
\(563\) −4.38733 7.59907i −0.000328426 0.000568850i 0.865861 0.500284i \(-0.166771\pi\)
−0.866190 + 0.499716i \(0.833438\pi\)
\(564\) −607.595 + 9822.14i −0.0453623 + 0.733310i
\(565\) 0 0
\(566\) 39621.9 2.94246
\(567\) −13058.4 + 13447.5i −0.967202 + 0.996015i
\(568\) 93949.2 6.94018
\(569\) 123.467 213.851i 0.00909667 0.0157559i −0.861441 0.507857i \(-0.830438\pi\)
0.870538 + 0.492101i \(0.163771\pi\)
\(570\) 0 0
\(571\) −1723.59 2985.35i −0.126323 0.218797i 0.795927 0.605393i \(-0.206984\pi\)
−0.922249 + 0.386596i \(0.873651\pi\)
\(572\) 1085.33 + 1879.84i 0.0793354 + 0.137413i
\(573\) −5743.37 3807.19i −0.418731 0.277570i
\(574\) −11356.1 + 19669.4i −0.825775 + 1.43028i
\(575\) 0 0
\(576\) −68068.3 8453.72i −4.92392 0.611525i
\(577\) 21137.2 1.52505 0.762525 0.646959i \(-0.223960\pi\)
0.762525 + 0.646959i \(0.223960\pi\)
\(578\) −10025.2 + 17364.1i −0.721441 + 1.24957i
\(579\) 6736.76 3352.98i 0.483541 0.240665i
\(580\) 0 0
\(581\) 4755.59 + 8236.92i 0.339578 + 0.588167i
\(582\) 307.254 152.925i 0.0218833 0.0108916i
\(583\) −466.117 + 807.339i −0.0331125 + 0.0573526i
\(584\) 10645.5 0.754305
\(585\) 0 0
\(586\) 8122.77 0.572608
\(587\) −2655.50 + 4599.47i −0.186720 + 0.323408i −0.944155 0.329503i \(-0.893119\pi\)
0.757435 + 0.652910i \(0.226452\pi\)
\(588\) −31330.0 20768.2i −2.19732 1.45657i
\(589\) 7297.10 + 12638.9i 0.510478 + 0.884174i
\(590\) 0 0
\(591\) 769.593 12440.9i 0.0535648 0.865908i
\(592\) 15935.1 27600.4i 1.10630 1.91616i
\(593\) 11575.8 0.801624 0.400812 0.916160i \(-0.368728\pi\)
0.400812 + 0.916160i \(0.368728\pi\)
\(594\) 4590.23 1614.73i 0.317070 0.111537i
\(595\) 0 0
\(596\) 28457.4 49289.7i 1.95581 3.38756i
\(597\) −997.475 + 16124.8i −0.0683818 + 1.10543i
\(598\) 3542.12 + 6135.13i 0.242221 + 0.419539i
\(599\) 3563.32 + 6171.85i 0.243061 + 0.420993i 0.961585 0.274509i \(-0.0885153\pi\)
−0.718524 + 0.695502i \(0.755182\pi\)
\(600\) 0 0
\(601\) 3860.93 6687.32i 0.262047 0.453879i −0.704739 0.709467i \(-0.748936\pi\)
0.966786 + 0.255588i \(0.0822690\pi\)
\(602\) 42048.7 2.84681
\(603\) −3470.18 8206.90i −0.234356 0.554247i
\(604\) −34576.4 −2.32929
\(605\) 0 0
\(606\) −19769.3 + 9839.49i −1.32521 + 0.659574i
\(607\) −7180.72 12437.4i −0.480159 0.831659i 0.519582 0.854420i \(-0.326088\pi\)
−0.999741 + 0.0227612i \(0.992754\pi\)
\(608\) −22403.8 38804.6i −1.49440 2.58838i
\(609\) 14244.6 7089.76i 0.947817 0.471743i
\(610\) 0 0
\(611\) −1271.03 −0.0841575
\(612\) −8609.17 20360.5i −0.568636 1.34481i
\(613\) −12086.0 −0.796330 −0.398165 0.917314i \(-0.630353\pi\)
−0.398165 + 0.917314i \(0.630353\pi\)
\(614\) −2191.49 + 3795.77i −0.144041 + 0.249487i
\(615\) 0 0
\(616\) 6571.71 + 11382.5i 0.429840 + 0.744505i
\(617\) 12617.9 + 21854.8i 0.823301 + 1.42600i 0.903210 + 0.429198i \(0.141204\pi\)
−0.0799090 + 0.996802i \(0.525463\pi\)
\(618\) −2756.02 + 44552.7i −0.179391 + 2.89996i
\(619\) 2452.72 4248.24i 0.159262 0.275850i −0.775341 0.631543i \(-0.782422\pi\)
0.934603 + 0.355693i \(0.115755\pi\)
\(620\) 0 0
\(621\) 11081.9 3898.34i 0.716104 0.251908i
\(622\) −21762.6 −1.40290
\(623\) 2900.88 5024.47i 0.186551 0.323116i
\(624\) 1327.28 21456.3i 0.0851503 1.37651i
\(625\) 0 0
\(626\) 15918.4 + 27571.5i 1.01634 + 1.76035i
\(627\) 1429.24 + 947.423i 0.0910342 + 0.0603452i
\(628\) 29478.4 51058.1i 1.87312 3.24433i
\(629\) 4232.79 0.268318
\(630\) 0 0
\(631\) −11240.9 −0.709181 −0.354590 0.935022i \(-0.615380\pi\)
−0.354590 + 0.935022i \(0.615380\pi\)
\(632\) −30144.3 + 52211.5i −1.89727 + 3.28617i
\(633\) −15395.6 + 7662.64i −0.966702 + 0.481142i
\(634\) 22555.7 + 39067.6i 1.41293 + 2.44727i
\(635\) 0 0
\(636\) 15762.1 7845.05i 0.982719 0.489114i
\(637\) 2427.41 4204.39i 0.150985 0.261514i
\(638\) −4130.51 −0.256314
\(639\) 30807.5 + 3826.13i 1.90724 + 0.236869i
\(640\) 0 0
\(641\) −5579.48 + 9663.94i −0.343800 + 0.595480i −0.985135 0.171781i \(-0.945048\pi\)
0.641335 + 0.767261i \(0.278381\pi\)
\(642\) −29256.8 19393.9i −1.79856 1.19224i
\(643\) −13622.4 23594.7i −0.835483 1.44710i −0.893636 0.448792i \(-0.851854\pi\)
0.0581529 0.998308i \(-0.481479\pi\)
\(644\) 24477.7 + 42396.7i 1.49776 + 2.59420i
\(645\) 0 0
\(646\) 5265.40 9119.93i 0.320688 0.555447i
\(647\) 31360.6 1.90559 0.952793 0.303620i \(-0.0981955\pi\)
0.952793 + 0.303620i \(0.0981955\pi\)
\(648\) −57757.1 14571.0i −3.50141 0.883337i
\(649\) 3975.34 0.240440
\(650\) 0 0
\(651\) −2282.21 + 36893.3i −0.137399 + 2.22114i
\(652\) −7680.67 13303.3i −0.461347 0.799076i
\(653\) −3537.24 6126.67i −0.211980 0.367160i 0.740354 0.672217i \(-0.234658\pi\)
−0.952334 + 0.305057i \(0.901324\pi\)
\(654\) −31870.3 21126.3i −1.90554 1.26316i
\(655\) 0 0
\(656\) −43194.0 −2.57080
\(657\) 3490.84 + 433.544i 0.207292 + 0.0257446i
\(658\) −11873.7 −0.703473
\(659\) −9249.31 + 16020.3i −0.546740 + 0.946982i 0.451755 + 0.892142i \(0.350798\pi\)
−0.998495 + 0.0548399i \(0.982535\pi\)
\(660\) 0 0
\(661\) −3200.38 5543.23i −0.188321 0.326182i 0.756369 0.654145i \(-0.226971\pi\)
−0.944691 + 0.327963i \(0.893638\pi\)
\(662\) −17538.9 30378.2i −1.02971 1.78351i
\(663\) 2556.04 1272.18i 0.149726 0.0745209i
\(664\) −15112.4 + 26175.4i −0.883245 + 1.52982i
\(665\) 0 0
\(666\) 10609.6 14038.8i 0.617288 0.816806i
\(667\) −9972.01 −0.578887
\(668\) −44292.8 + 76717.4i −2.56548 + 4.44354i
\(669\) −12121.8 8035.34i −0.700531 0.464371i
\(670\) 0 0
\(671\) −1867.84 3235.19i −0.107462 0.186130i
\(672\) 7006.92 113271.i 0.402229 6.50228i
\(673\) 7115.68 12324.7i 0.407562 0.705918i −0.587054 0.809548i \(-0.699712\pi\)
0.994616 + 0.103630i \(0.0330456\pi\)
\(674\) −26468.0 −1.51263
\(675\) 0 0
\(676\) −44660.4 −2.54099
\(677\) 9953.99 17240.8i 0.565085 0.978756i −0.431956 0.901894i \(-0.642177\pi\)
0.997042 0.0768620i \(-0.0244901\pi\)
\(678\) −771.336 + 12469.1i −0.0436917 + 0.706303i
\(679\) 153.163 + 265.286i 0.00865663 + 0.0149937i
\(680\) 0 0
\(681\) −13552.5 8983.72i −0.762601 0.505517i
\(682\) 4797.79 8310.02i 0.269380 0.466579i
\(683\) −26204.1 −1.46804 −0.734021 0.679126i \(-0.762359\pi\)
−0.734021 + 0.679126i \(0.762359\pi\)
\(684\) −12612.5 29828.4i −0.705047 1.66742i
\(685\) 0 0
\(686\) −1771.91 + 3069.03i −0.0986177 + 0.170811i
\(687\) 13841.9 6889.30i 0.768705 0.382596i
\(688\) 39984.1 + 69254.4i 2.21567 + 3.83765i
\(689\) 1137.01 + 1969.35i 0.0628687 + 0.108892i
\(690\) 0 0
\(691\) 13281.2 23003.8i 0.731176 1.26643i −0.225205 0.974311i \(-0.572305\pi\)
0.956381 0.292122i \(-0.0943614\pi\)
\(692\) 1174.66 0.0645289
\(693\) 1691.42 + 4000.16i 0.0927151 + 0.219269i
\(694\) 10087.3 0.551741
\(695\) 0 0
\(696\) 42144.9 + 27937.2i 2.29526 + 1.52149i
\(697\) −2868.38 4968.17i −0.155879 0.269990i
\(698\) −8253.56 14295.6i −0.447567 0.775209i
\(699\) 297.045 4801.91i 0.0160734 0.259836i
\(700\) 0 0
\(701\) 35417.5 1.90827 0.954137 0.299372i \(-0.0967771\pi\)
0.954137 + 0.299372i \(0.0967771\pi\)
\(702\) 2187.38 11666.3i 0.117603 0.627232i
\(703\) 6201.08 0.332686
\(704\) −7946.22 + 13763.3i −0.425404 + 0.736821i
\(705\) 0 0
\(706\) 19259.9 + 33359.1i 1.02671 + 1.77831i
\(707\) −9854.81 17069.0i −0.524227 0.907987i
\(708\) −62579.2 41482.8i −3.32185 2.20200i
\(709\) 8339.20 14443.9i 0.441728 0.765096i −0.556090 0.831122i \(-0.687699\pi\)
0.997818 + 0.0660267i \(0.0210322\pi\)
\(710\) 0 0
\(711\) −12011.2 + 15893.4i −0.633550 + 0.838324i
\(712\) 18436.9 0.970439
\(713\) 11583.0 20062.3i 0.608396 1.05377i
\(714\) 23878.1 11884.5i 1.25156 0.622920i
\(715\) 0 0
\(716\) −51767.2 89663.5i −2.70200 4.68000i
\(717\) 12145.1 6044.78i 0.632588 0.314849i
\(718\) −10161.3 + 17599.8i −0.528154 + 0.914790i
\(719\) 3273.36 0.169786 0.0848928 0.996390i \(-0.472945\pi\)
0.0848928 + 0.996390i \(0.472945\pi\)
\(720\) 0 0
\(721\) −39841.1 −2.05792
\(722\) −11299.9 + 19572.0i −0.582465 + 1.00886i
\(723\) 2899.49 + 1922.03i 0.149147 + 0.0988672i
\(724\) −27751.8 48067.6i −1.42457 2.46743i
\(725\) 0 0
\(726\) −2297.82 + 37145.6i −0.117465 + 1.89890i
\(727\) −16970.3 + 29393.3i −0.865738 + 1.49950i 0.000573784 1.00000i \(0.499817\pi\)
−0.866312 + 0.499503i \(0.833516\pi\)
\(728\) 32060.9 1.63222
\(729\) −18346.1 7130.26i −0.932079 0.362255i
\(730\) 0 0
\(731\) −5310.42 + 9197.92i −0.268691 + 0.465386i
\(732\) −4356.09 + 70418.8i −0.219953 + 3.55567i
\(733\) 952.351 + 1649.52i 0.0479890 + 0.0831193i 0.889022 0.457864i \(-0.151385\pi\)
−0.841033 + 0.540984i \(0.818052\pi\)
\(734\) 26787.0 + 46396.4i 1.34704 + 2.33314i
\(735\) 0 0
\(736\) −35562.5 + 61596.0i −1.78105 + 3.08486i
\(737\) −2064.52 −0.103185
\(738\) −23667.5 2939.38i −1.18051 0.146612i
\(739\) 23159.4 1.15282 0.576408 0.817162i \(-0.304454\pi\)
0.576408 + 0.817162i \(0.304454\pi\)
\(740\) 0 0
\(741\) 3744.63 1863.76i 0.185644 0.0923979i
\(742\) 10621.7 + 18397.3i 0.525519 + 0.910226i
\(743\) 10943.4 + 18954.5i 0.540342 + 0.935900i 0.998884 + 0.0472272i \(0.0150385\pi\)
−0.458542 + 0.888673i \(0.651628\pi\)
\(744\) −105159. + 52339.3i −5.18189 + 2.57910i
\(745\) 0 0
\(746\) 33396.7 1.63906
\(747\) −6021.62 + 7967.91i −0.294939 + 0.390268i
\(748\) −5121.87 −0.250367
\(749\) 15664.5 27131.8i 0.764179 1.32360i
\(750\) 0 0
\(751\) 15830.7 + 27419.5i 0.769200 + 1.33229i 0.937997 + 0.346643i \(0.112678\pi\)
−0.168797 + 0.985651i \(0.553988\pi\)
\(752\) −11290.7 19556.1i −0.547512 0.948319i
\(753\) 2073.45 33518.7i 0.100346 1.62216i
\(754\) −5037.81 + 8725.74i −0.243324 + 0.421449i
\(755\) 0 0
\(756\) 15115.8 80619.9i 0.727191 3.87846i
\(757\) 29482.4 1.41553 0.707764 0.706449i \(-0.249704\pi\)
0.707764 + 0.706449i \(0.249704\pi\)
\(758\) −3407.80 + 5902.48i −0.163294 + 0.282834i
\(759\) 168.054 2716.69i 0.00803684 0.129920i
\(760\) 0 0
\(761\) 13012.0 + 22537.4i 0.619822 + 1.07356i 0.989518 + 0.144410i \(0.0461284\pi\)
−0.369696 + 0.929153i \(0.620538\pi\)
\(762\) 44426.3 + 29449.5i 2.11207 + 1.40006i
\(763\) 17063.8 29555.4i 0.809636 1.40233i
\(764\) 30153.0 1.42788
\(765\) 0 0
\(766\) 11829.0 0.557964
\(767\) 4848.56 8397.94i 0.228254 0.395348i
\(768\) 93452.6 46512.8i 4.39086 2.18540i
\(769\) −839.198 1453.53i −0.0393527 0.0681609i 0.845678 0.533693i \(-0.179196\pi\)
−0.885031 + 0.465532i \(0.845863\pi\)
\(770\) 0 0
\(771\) −13189.5 + 6564.59i −0.616092 + 0.306638i
\(772\) −16464.5 + 28517.4i −0.767580 + 1.32949i
\(773\) 25777.0 1.19940 0.599698 0.800226i \(-0.295287\pi\)
0.599698 + 0.800226i \(0.295287\pi\)
\(774\) 17195.8 + 40667.8i 0.798568 + 1.88860i
\(775\) 0 0
\(776\) −486.724 + 843.030i −0.0225159 + 0.0389987i
\(777\) 13090.9 + 8677.79i 0.604421 + 0.400661i
\(778\) 27281.6 + 47253.1i 1.25719 + 2.17752i
\(779\) −4202.20 7278.43i −0.193273 0.334758i
\(780\)