Properties

Label 225.4.k.c.49.3
Level $225$
Weight $4$
Character 225.49
Analytic conductor $13.275$
Analytic rank $0$
Dimension $12$
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.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 23 x^{10} + 198 x^{8} - 719 x^{6} + 886 x^{4} + 585 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.3
Root \(1.98116 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 225.49
Dual form 225.4.k.c.124.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.151541 + 0.0874923i) q^{2} +(-0.151541 - 5.19394i) q^{3} +(-3.98469 + 6.90169i) q^{4} +(0.477395 + 0.773837i) q^{6} +(7.32979 - 4.23186i) q^{7} -2.79440i q^{8} +(-26.9541 + 1.57419i) q^{9} +O(q^{10})\) \(q+(-0.151541 + 0.0874923i) q^{2} +(-0.151541 - 5.19394i) q^{3} +(-3.98469 + 6.90169i) q^{4} +(0.477395 + 0.773837i) q^{6} +(7.32979 - 4.23186i) q^{7} -2.79440i q^{8} +(-26.9541 + 1.57419i) q^{9} +(15.7541 + 27.2870i) q^{11} +(36.4508 + 19.6504i) q^{12} +(23.2697 + 13.4348i) q^{13} +(-0.740510 + 1.28260i) q^{14} +(-31.6330 - 54.7900i) q^{16} -44.3307i q^{17} +(3.94692 - 2.59683i) q^{18} +90.2082 q^{19} +(-23.0908 - 37.4292i) q^{21} +(-4.77480 - 2.75673i) q^{22} +(168.232 + 97.1287i) q^{23} +(-14.5139 + 0.423466i) q^{24} -4.70176 q^{26} +(12.2609 + 139.759i) q^{27} +67.4506i q^{28} +(1.87186 + 3.24215i) q^{29} +(125.832 - 217.947i) q^{31} +(28.9476 + 16.7129i) q^{32} +(139.339 - 85.9611i) q^{33} +(3.87859 + 6.71792i) q^{34} +(96.5390 - 192.301i) q^{36} -62.2293i q^{37} +(-13.6703 + 7.89252i) q^{38} +(66.2532 - 122.898i) q^{39} +(102.173 - 176.969i) q^{41} +(6.77397 + 3.65180i) q^{42} +(456.968 - 263.831i) q^{43} -251.101 q^{44} -33.9920 q^{46} +(134.864 - 77.8637i) q^{47} +(-279.782 + 172.603i) q^{48} +(-135.683 + 235.009i) q^{49} +(-230.251 + 6.71792i) q^{51} +(-185.445 + 107.067i) q^{52} +141.694i q^{53} +(-14.0859 - 20.1065i) q^{54} +(-11.8255 - 20.4823i) q^{56} +(-13.6703 - 468.536i) q^{57} +(-0.567326 - 0.327546i) q^{58} +(-246.923 + 427.683i) q^{59} +(379.742 + 657.732i) q^{61} +44.0373i q^{62} +(-190.906 + 125.604i) q^{63} +500.280 q^{64} +(-13.5947 + 25.2178i) q^{66} +(470.763 + 271.795i) q^{67} +(305.956 + 176.644i) q^{68} +(478.987 - 888.505i) q^{69} -928.207 q^{71} +(4.39891 + 75.3203i) q^{72} -608.739i q^{73} +(5.44459 + 9.43030i) q^{74} +(-359.452 + 622.589i) q^{76} +(230.949 + 133.338i) q^{77} +(0.712510 + 24.4207i) q^{78} +(307.420 + 532.467i) q^{79} +(724.044 - 84.8617i) q^{81} +35.7573i q^{82} +(-931.246 + 537.655i) q^{83} +(350.334 - 10.2215i) q^{84} +(-46.1663 + 79.9623i) q^{86} +(16.5559 - 10.2136i) q^{87} +(76.2506 - 44.0233i) q^{88} -1505.15 q^{89} +227.416 q^{91} +(-1340.70 + 774.055i) q^{92} +(-1151.07 - 620.536i) q^{93} +(-13.6249 + 23.5991i) q^{94} +(82.4190 - 152.885i) q^{96} +(-288.160 + 166.369i) q^{97} -47.4848i q^{98} +(-467.593 - 710.695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 22 q^{4} + 168 q^{6} - 114 q^{9} + O(q^{10}) \) \( 12 q + 22 q^{4} + 168 q^{6} - 114 q^{9} - 28 q^{11} - 54 q^{14} + 26 q^{16} + 656 q^{19} - 288 q^{21} + 126 q^{24} + 1736 q^{26} - 670 q^{29} + 704 q^{31} - 104 q^{34} + 2172 q^{36} + 780 q^{39} - 374 q^{41} - 3928 q^{44} - 804 q^{46} + 860 q^{49} - 360 q^{51} - 1278 q^{54} - 1410 q^{56} - 596 q^{59} + 2878 q^{61} + 6276 q^{64} - 1932 q^{66} + 1746 q^{69} + 280 q^{71} - 640 q^{74} - 408 q^{76} - 764 q^{79} - 2502 q^{81} + 1818 q^{84} - 3160 q^{86} - 6876 q^{89} - 2840 q^{91} - 4154 q^{94} + 2310 q^{96} + 1524 q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.151541 + 0.0874923i −0.0535779 + 0.0309332i −0.526550 0.850144i \(-0.676515\pi\)
0.472972 + 0.881078i \(0.343181\pi\)
\(3\) −0.151541 5.19394i −0.0291641 0.999575i
\(4\) −3.98469 + 6.90169i −0.498086 + 0.862711i
\(5\) 0 0
\(6\) 0.477395 + 0.773837i 0.0324826 + 0.0526529i
\(7\) 7.32979 4.23186i 0.395772 0.228499i −0.288886 0.957363i \(-0.593285\pi\)
0.684658 + 0.728865i \(0.259952\pi\)
\(8\) 2.79440i 0.123496i
\(9\) −26.9541 + 1.57419i −0.998299 + 0.0583034i
\(10\) 0 0
\(11\) 15.7541 + 27.2870i 0.431823 + 0.747939i 0.997030 0.0770098i \(-0.0245373\pi\)
−0.565208 + 0.824949i \(0.691204\pi\)
\(12\) 36.4508 + 19.6504i 0.876870 + 0.472714i
\(13\) 23.2697 + 13.4348i 0.496451 + 0.286626i 0.727247 0.686376i \(-0.240800\pi\)
−0.230796 + 0.973002i \(0.574133\pi\)
\(14\) −0.740510 + 1.28260i −0.0141364 + 0.0244850i
\(15\) 0 0
\(16\) −31.6330 54.7900i −0.494266 0.856094i
\(17\) 44.3307i 0.632457i −0.948683 0.316229i \(-0.897583\pi\)
0.948683 0.316229i \(-0.102417\pi\)
\(18\) 3.94692 2.59683i 0.0516832 0.0340044i
\(19\) 90.2082 1.08922 0.544610 0.838689i \(-0.316678\pi\)
0.544610 + 0.838689i \(0.316678\pi\)
\(20\) 0 0
\(21\) −23.0908 37.4292i −0.239944 0.388939i
\(22\) −4.77480 2.75673i −0.0462723 0.0267153i
\(23\) 168.232 + 97.1287i 1.52516 + 0.880553i 0.999555 + 0.0298265i \(0.00949548\pi\)
0.525608 + 0.850727i \(0.323838\pi\)
\(24\) −14.5139 + 0.423466i −0.123443 + 0.00360165i
\(25\) 0 0
\(26\) −4.70176 −0.0354650
\(27\) 12.2609 + 139.759i 0.0873931 + 0.996174i
\(28\) 67.4506i 0.455248i
\(29\) 1.87186 + 3.24215i 0.0119860 + 0.0207604i 0.871956 0.489584i \(-0.162851\pi\)
−0.859970 + 0.510344i \(0.829518\pi\)
\(30\) 0 0
\(31\) 125.832 217.947i 0.729035 1.26273i −0.228257 0.973601i \(-0.573303\pi\)
0.957292 0.289124i \(-0.0933641\pi\)
\(32\) 28.9476 + 16.7129i 0.159914 + 0.0923265i
\(33\) 139.339 85.9611i 0.735027 0.453452i
\(34\) 3.87859 + 6.71792i 0.0195639 + 0.0338857i
\(35\) 0 0
\(36\) 96.5390 192.301i 0.446940 0.890283i
\(37\) 62.2293i 0.276498i −0.990397 0.138249i \(-0.955853\pi\)
0.990397 0.138249i \(-0.0441475\pi\)
\(38\) −13.6703 + 7.89252i −0.0583581 + 0.0336931i
\(39\) 66.2532 122.898i 0.272026 0.504599i
\(40\) 0 0
\(41\) 102.173 176.969i 0.389188 0.674094i −0.603152 0.797626i \(-0.706089\pi\)
0.992341 + 0.123532i \(0.0394223\pi\)
\(42\) 6.77397 + 3.65180i 0.0248868 + 0.0134163i
\(43\) 456.968 263.831i 1.62063 0.935669i 0.633874 0.773436i \(-0.281464\pi\)
0.986752 0.162233i \(-0.0518696\pi\)
\(44\) −251.101 −0.860340
\(45\) 0 0
\(46\) −33.9920 −0.108953
\(47\) 134.864 77.8637i 0.418551 0.241651i −0.275906 0.961185i \(-0.588978\pi\)
0.694457 + 0.719534i \(0.255645\pi\)
\(48\) −279.782 + 172.603i −0.841315 + 0.519023i
\(49\) −135.683 + 235.009i −0.395577 + 0.685159i
\(50\) 0 0
\(51\) −230.251 + 6.71792i −0.632188 + 0.0184450i
\(52\) −185.445 + 107.067i −0.494551 + 0.285529i
\(53\) 141.694i 0.367230i 0.982998 + 0.183615i \(0.0587800\pi\)
−0.982998 + 0.183615i \(0.941220\pi\)
\(54\) −14.0859 20.1065i −0.0354972 0.0506695i
\(55\) 0 0
\(56\) −11.8255 20.4823i −0.0282187 0.0488762i
\(57\) −13.6703 468.536i −0.0317661 1.08876i
\(58\) −0.567326 0.327546i −0.00128437 0.000741533i
\(59\) −246.923 + 427.683i −0.544857 + 0.943721i 0.453758 + 0.891125i \(0.350083\pi\)
−0.998616 + 0.0525961i \(0.983250\pi\)
\(60\) 0 0
\(61\) 379.742 + 657.732i 0.797065 + 1.38056i 0.921520 + 0.388331i \(0.126948\pi\)
−0.124455 + 0.992225i \(0.539718\pi\)
\(62\) 44.0373i 0.0902055i
\(63\) −190.906 + 125.604i −0.381776 + 0.251185i
\(64\) 500.280 0.977108
\(65\) 0 0
\(66\) −13.5947 + 25.2178i −0.0253545 + 0.0470317i
\(67\) 470.763 + 271.795i 0.858401 + 0.495598i 0.863476 0.504389i \(-0.168282\pi\)
−0.00507574 + 0.999987i \(0.501616\pi\)
\(68\) 305.956 + 176.644i 0.545627 + 0.315018i
\(69\) 478.987 888.505i 0.835699 1.55019i
\(70\) 0 0
\(71\) −928.207 −1.55152 −0.775760 0.631028i \(-0.782633\pi\)
−0.775760 + 0.631028i \(0.782633\pi\)
\(72\) 4.39891 + 75.3203i 0.00720024 + 0.123286i
\(73\) 608.739i 0.975993i −0.872845 0.487997i \(-0.837728\pi\)
0.872845 0.487997i \(-0.162272\pi\)
\(74\) 5.44459 + 9.43030i 0.00855298 + 0.0148142i
\(75\) 0 0
\(76\) −359.452 + 622.589i −0.542526 + 0.939682i
\(77\) 230.949 + 133.338i 0.341806 + 0.197342i
\(78\) 0.712510 + 24.4207i 0.00103431 + 0.0354500i
\(79\) 307.420 + 532.467i 0.437816 + 0.758319i 0.997521 0.0703726i \(-0.0224188\pi\)
−0.559705 + 0.828692i \(0.689085\pi\)
\(80\) 0 0
\(81\) 724.044 84.8617i 0.993201 0.116408i
\(82\) 35.7573i 0.0481553i
\(83\) −931.246 + 537.655i −1.23154 + 0.711028i −0.967350 0.253444i \(-0.918437\pi\)
−0.264186 + 0.964472i \(0.585103\pi\)
\(84\) 350.334 10.2215i 0.455055 0.0132769i
\(85\) 0 0
\(86\) −46.1663 + 79.9623i −0.0578865 + 0.100262i
\(87\) 16.5559 10.2136i 0.0204020 0.0125864i
\(88\) 76.2506 44.0233i 0.0923675 0.0533284i
\(89\) −1505.15 −1.79265 −0.896324 0.443400i \(-0.853772\pi\)
−0.896324 + 0.443400i \(0.853772\pi\)
\(90\) 0 0
\(91\) 227.416 0.261975
\(92\) −1340.70 + 774.055i −1.51933 + 0.877183i
\(93\) −1151.07 620.536i −1.28345 0.691898i
\(94\) −13.6249 + 23.5991i −0.0149501 + 0.0258943i
\(95\) 0 0
\(96\) 82.4190 152.885i 0.0876234 0.162539i
\(97\) −288.160 + 166.369i −0.301631 + 0.174147i −0.643175 0.765719i \(-0.722383\pi\)
0.341544 + 0.939866i \(0.389050\pi\)
\(98\) 47.4848i 0.0489458i
\(99\) −467.593 710.695i −0.474695 0.721490i
\(100\) 0 0
\(101\) 247.493 + 428.670i 0.243826 + 0.422319i 0.961801 0.273750i \(-0.0882640\pi\)
−0.717975 + 0.696069i \(0.754931\pi\)
\(102\) 34.3047 21.1632i 0.0333007 0.0205438i
\(103\) −545.622 315.015i −0.521959 0.301353i 0.215777 0.976443i \(-0.430772\pi\)
−0.737736 + 0.675090i \(0.764105\pi\)
\(104\) 37.5421 65.0248i 0.0353972 0.0613097i
\(105\) 0 0
\(106\) −12.3971 21.4725i −0.0113596 0.0196754i
\(107\) 1561.00i 1.41035i −0.709034 0.705175i \(-0.750869\pi\)
0.709034 0.705175i \(-0.249131\pi\)
\(108\) −1013.43 472.277i −0.902939 0.420786i
\(109\) 936.140 0.822623 0.411311 0.911495i \(-0.365071\pi\)
0.411311 + 0.911495i \(0.365071\pi\)
\(110\) 0 0
\(111\) −323.215 + 9.43030i −0.276381 + 0.00806382i
\(112\) −463.727 267.733i −0.391233 0.225878i
\(113\) 1173.45 + 677.490i 0.976890 + 0.564008i 0.901330 0.433134i \(-0.142592\pi\)
0.0755602 + 0.997141i \(0.475925\pi\)
\(114\) 43.0649 + 69.8065i 0.0353807 + 0.0573506i
\(115\) 0 0
\(116\) −29.8351 −0.0238803
\(117\) −648.363 325.491i −0.512318 0.257194i
\(118\) 86.4153i 0.0674167i
\(119\) −187.601 324.935i −0.144516 0.250309i
\(120\) 0 0
\(121\) 169.115 292.915i 0.127058 0.220071i
\(122\) −115.093 66.4490i −0.0854101 0.0493115i
\(123\) −934.648 503.862i −0.685157 0.369363i
\(124\) 1002.80 + 1736.90i 0.726244 + 1.25789i
\(125\) 0 0
\(126\) 17.9407 35.7370i 0.0126848 0.0252675i
\(127\) 1182.37i 0.826126i −0.910702 0.413063i \(-0.864459\pi\)
0.910702 0.413063i \(-0.135541\pi\)
\(128\) −307.393 + 177.474i −0.212266 + 0.122552i
\(129\) −1439.57 2333.48i −0.982535 1.59265i
\(130\) 0 0
\(131\) −1126.87 + 1951.80i −0.751569 + 1.30176i 0.195494 + 0.980705i \(0.437369\pi\)
−0.947062 + 0.321050i \(0.895964\pi\)
\(132\) 38.0522 + 1304.21i 0.0250910 + 0.859974i
\(133\) 661.207 381.748i 0.431082 0.248885i
\(134\) −95.1199 −0.0613217
\(135\) 0 0
\(136\) −123.877 −0.0781059
\(137\) 410.246 236.856i 0.255837 0.147708i −0.366597 0.930380i \(-0.619477\pi\)
0.622434 + 0.782672i \(0.286144\pi\)
\(138\) 5.15119 + 176.553i 0.00317753 + 0.108907i
\(139\) −68.5193 + 118.679i −0.0418110 + 0.0724188i −0.886174 0.463353i \(-0.846646\pi\)
0.844363 + 0.535772i \(0.179979\pi\)
\(140\) 0 0
\(141\) −424.857 688.675i −0.253755 0.411326i
\(142\) 140.662 81.2110i 0.0831272 0.0479935i
\(143\) 846.613i 0.495086i
\(144\) 938.889 + 1427.02i 0.543339 + 0.825820i
\(145\) 0 0
\(146\) 53.2600 + 92.2490i 0.0301906 + 0.0522917i
\(147\) 1241.19 + 669.115i 0.696404 + 0.375426i
\(148\) 429.487 + 247.965i 0.238538 + 0.137720i
\(149\) −71.5553 + 123.937i −0.0393426 + 0.0681433i −0.885026 0.465541i \(-0.845860\pi\)
0.845684 + 0.533685i \(0.179193\pi\)
\(150\) 0 0
\(151\) −108.421 187.790i −0.0584314 0.101206i 0.835330 0.549749i \(-0.185277\pi\)
−0.893761 + 0.448543i \(0.851943\pi\)
\(152\) 252.077i 0.134514i
\(153\) 69.7850 + 1194.89i 0.0368744 + 0.631381i
\(154\) −46.6644 −0.0244177
\(155\) 0 0
\(156\) 584.202 + 946.967i 0.299831 + 0.486013i
\(157\) −1167.78 674.215i −0.593622 0.342728i 0.172906 0.984938i \(-0.444684\pi\)
−0.766528 + 0.642211i \(0.778017\pi\)
\(158\) −93.1736 53.7938i −0.0469145 0.0270861i
\(159\) 735.951 21.4725i 0.367074 0.0107099i
\(160\) 0 0
\(161\) 1644.14 0.804822
\(162\) −102.298 + 76.2083i −0.0496127 + 0.0369598i
\(163\) 1039.85i 0.499676i −0.968288 0.249838i \(-0.919623\pi\)
0.968288 0.249838i \(-0.0803774\pi\)
\(164\) 814.254 + 1410.33i 0.387699 + 0.671514i
\(165\) 0 0
\(166\) 94.0813 162.954i 0.0439887 0.0761907i
\(167\) 2881.31 + 1663.52i 1.33510 + 0.770822i 0.986077 0.166291i \(-0.0531792\pi\)
0.349026 + 0.937113i \(0.386513\pi\)
\(168\) −104.592 + 64.5248i −0.0480324 + 0.0296321i
\(169\) −737.513 1277.41i −0.335691 0.581434i
\(170\) 0 0
\(171\) −2431.48 + 142.005i −1.08737 + 0.0635052i
\(172\) 4205.13i 1.86418i
\(173\) 1034.25 597.127i 0.454525 0.262420i −0.255214 0.966885i \(-0.582146\pi\)
0.709740 + 0.704464i \(0.248813\pi\)
\(174\) −1.61528 + 2.99630i −0.000703760 + 0.00130545i
\(175\) 0 0
\(176\) 996.702 1726.34i 0.426871 0.739362i
\(177\) 2258.78 + 1217.69i 0.959210 + 0.517103i
\(178\) 228.092 131.689i 0.0960463 0.0554523i
\(179\) −2323.70 −0.970288 −0.485144 0.874434i \(-0.661233\pi\)
−0.485144 + 0.874434i \(0.661233\pi\)
\(180\) 0 0
\(181\) 2527.12 1.03779 0.518893 0.854839i \(-0.326344\pi\)
0.518893 + 0.854839i \(0.326344\pi\)
\(182\) −34.4629 + 19.8972i −0.0140361 + 0.00810372i
\(183\) 3358.68 2072.03i 1.35672 0.836988i
\(184\) 271.416 470.106i 0.108745 0.188352i
\(185\) 0 0
\(186\) 228.727 6.67346i 0.0901671 0.00263076i
\(187\) 1209.65 698.391i 0.473039 0.273109i
\(188\) 1241.05i 0.481452i
\(189\) 681.311 + 972.520i 0.262212 + 0.374288i
\(190\) 0 0
\(191\) −1194.43 2068.82i −0.452493 0.783741i 0.546047 0.837754i \(-0.316132\pi\)
−0.998540 + 0.0540134i \(0.982799\pi\)
\(192\) −75.8129 2598.42i −0.0284965 0.976693i
\(193\) 3072.64 + 1773.99i 1.14597 + 0.661629i 0.947903 0.318559i \(-0.103199\pi\)
0.198072 + 0.980188i \(0.436532\pi\)
\(194\) 29.1120 50.4235i 0.0107738 0.0186608i
\(195\) 0 0
\(196\) −1081.31 1872.88i −0.394063 0.682536i
\(197\) 1239.26i 0.448192i −0.974567 0.224096i \(-0.928057\pi\)
0.974567 0.224096i \(-0.0719430\pi\)
\(198\) 133.040 + 66.7887i 0.0477512 + 0.0239720i
\(199\) −516.657 −0.184044 −0.0920222 0.995757i \(-0.529333\pi\)
−0.0920222 + 0.995757i \(0.529333\pi\)
\(200\) 0 0
\(201\) 1340.35 2486.30i 0.470353 0.872489i
\(202\) −75.0107 43.3074i −0.0261274 0.0150847i
\(203\) 27.4406 + 15.8429i 0.00948746 + 0.00547759i
\(204\) 871.114 1615.89i 0.298971 0.554583i
\(205\) 0 0
\(206\) 110.246 0.0372873
\(207\) −4687.43 2353.18i −1.57391 0.790133i
\(208\) 1699.93i 0.566678i
\(209\) 1421.15 + 2461.51i 0.470350 + 0.814670i
\(210\) 0 0
\(211\) 8.92159 15.4527i 0.00291084 0.00504173i −0.864566 0.502519i \(-0.832407\pi\)
0.867477 + 0.497477i \(0.165740\pi\)
\(212\) −977.928 564.607i −0.316813 0.182912i
\(213\) 140.662 + 4821.05i 0.0452487 + 1.55086i
\(214\) 136.575 + 236.555i 0.0436266 + 0.0755635i
\(215\) 0 0
\(216\) 390.543 34.2618i 0.123024 0.0107927i
\(217\) 2130.01i 0.666334i
\(218\) −141.864 + 81.9050i −0.0440744 + 0.0254464i
\(219\) −3161.76 + 92.2490i −0.975578 + 0.0284640i
\(220\) 0 0
\(221\) 595.573 1031.56i 0.181279 0.313984i
\(222\) 48.1554 29.7079i 0.0145584 0.00898138i
\(223\) −856.978 + 494.777i −0.257343 + 0.148577i −0.623122 0.782125i \(-0.714136\pi\)
0.365779 + 0.930702i \(0.380803\pi\)
\(224\) 282.906 0.0843860
\(225\) 0 0
\(226\) −237.101 −0.0697863
\(227\) −2967.98 + 1713.57i −0.867806 + 0.501028i −0.866619 0.498971i \(-0.833711\pi\)
−0.00118754 + 0.999999i \(0.500378\pi\)
\(228\) 3288.16 + 1772.62i 0.955104 + 0.514890i
\(229\) 549.805 952.290i 0.158656 0.274800i −0.775728 0.631067i \(-0.782617\pi\)
0.934384 + 0.356267i \(0.115951\pi\)
\(230\) 0 0
\(231\) 657.554 1219.74i 0.187290 0.347416i
\(232\) 9.05985 5.23071i 0.00256383 0.00148023i
\(233\) 4459.91i 1.25399i −0.779025 0.626993i \(-0.784285\pi\)
0.779025 0.626993i \(-0.215715\pi\)
\(234\) 126.732 7.40147i 0.0354047 0.00206773i
\(235\) 0 0
\(236\) −1967.82 3408.37i −0.542772 0.940109i
\(237\) 2719.02 1677.41i 0.745228 0.459745i
\(238\) 56.8586 + 32.8273i 0.0154857 + 0.00894067i
\(239\) 3272.23 5667.66i 0.885618 1.53394i 0.0406148 0.999175i \(-0.487068\pi\)
0.845003 0.534761i \(-0.179598\pi\)
\(240\) 0 0
\(241\) 105.162 + 182.147i 0.0281083 + 0.0486851i 0.879737 0.475460i \(-0.157718\pi\)
−0.851629 + 0.524145i \(0.824385\pi\)
\(242\) 59.1849i 0.0157213i
\(243\) −550.489 3747.78i −0.145325 0.989384i
\(244\) −6052.61 −1.58803
\(245\) 0 0
\(246\) 185.722 5.41871i 0.0481349 0.00140441i
\(247\) 2099.12 + 1211.93i 0.540744 + 0.312199i
\(248\) −609.031 351.624i −0.155942 0.0900329i
\(249\) 2933.67 + 4755.36i 0.746642 + 1.21028i
\(250\) 0 0
\(251\) 816.143 0.205237 0.102618 0.994721i \(-0.467278\pi\)
0.102618 + 0.994721i \(0.467278\pi\)
\(252\) −106.180 1818.07i −0.0265425 0.454474i
\(253\) 6120.71i 1.52097i
\(254\) 103.448 + 179.177i 0.0255547 + 0.0442621i
\(255\) 0 0
\(256\) −1970.06 + 3412.25i −0.480972 + 0.833069i
\(257\) 3613.36 + 2086.17i 0.877023 + 0.506350i 0.869676 0.493623i \(-0.164328\pi\)
0.00734758 + 0.999973i \(0.497661\pi\)
\(258\) 422.316 + 227.667i 0.101908 + 0.0549378i
\(259\) −263.346 456.128i −0.0631795 0.109430i
\(260\) 0 0
\(261\) −55.5579 84.4425i −0.0131760 0.0200263i
\(262\) 394.371i 0.0929937i
\(263\) 2439.64 1408.52i 0.571994 0.330241i −0.185951 0.982559i \(-0.559537\pi\)
0.757945 + 0.652318i \(0.226203\pi\)
\(264\) −240.209 389.370i −0.0559995 0.0907729i
\(265\) 0 0
\(266\) −66.8001 + 115.701i −0.0153976 + 0.0266695i
\(267\) 228.092 + 7817.66i 0.0522810 + 1.79189i
\(268\) −3751.69 + 2166.04i −0.855115 + 0.493701i
\(269\) 102.610 0.0232573 0.0116287 0.999932i \(-0.496298\pi\)
0.0116287 + 0.999932i \(0.496298\pi\)
\(270\) 0 0
\(271\) −3337.27 −0.748061 −0.374031 0.927416i \(-0.622025\pi\)
−0.374031 + 0.927416i \(0.622025\pi\)
\(272\) −2428.88 + 1402.31i −0.541443 + 0.312602i
\(273\) −34.4629 1181.19i −0.00764026 0.261863i
\(274\) −41.4461 + 71.7867i −0.00913814 + 0.0158277i
\(275\) 0 0
\(276\) 4223.57 + 6846.23i 0.921120 + 1.49310i
\(277\) 548.959 316.941i 0.119075 0.0687479i −0.439280 0.898350i \(-0.644766\pi\)
0.558354 + 0.829603i \(0.311433\pi\)
\(278\) 23.9796i 0.00517339i
\(279\) −3048.59 + 6072.65i −0.654173 + 1.30308i
\(280\) 0 0
\(281\) 3101.20 + 5371.44i 0.658370 + 1.14033i 0.981037 + 0.193818i \(0.0620872\pi\)
−0.322667 + 0.946513i \(0.604579\pi\)
\(282\) 124.637 + 67.1909i 0.0263193 + 0.0141885i
\(283\) −6477.98 3740.06i −1.36069 0.785596i −0.370976 0.928642i \(-0.620977\pi\)
−0.989716 + 0.143047i \(0.954310\pi\)
\(284\) 3698.62 6406.19i 0.772791 1.33851i
\(285\) 0 0
\(286\) −74.0722 128.297i −0.0153146 0.0265257i
\(287\) 1729.52i 0.355716i
\(288\) −806.564 404.911i −0.165025 0.0828459i
\(289\) 2947.79 0.599998
\(290\) 0 0
\(291\) 907.780 + 1471.47i 0.182869 + 0.296424i
\(292\) 4201.33 + 2425.64i 0.842000 + 0.486129i
\(293\) −4188.54 2418.26i −0.835144 0.482171i 0.0204666 0.999791i \(-0.493485\pi\)
−0.855611 + 0.517620i \(0.826818\pi\)
\(294\) −246.633 + 7.19590i −0.0489250 + 0.00142746i
\(295\) 0 0
\(296\) −173.893 −0.0341464
\(297\) −3620.45 + 2536.35i −0.707339 + 0.495535i
\(298\) 25.0422i 0.00486796i
\(299\) 2609.81 + 4520.31i 0.504779 + 0.874303i
\(300\) 0 0
\(301\) 2232.99 3867.65i 0.427599 0.740623i
\(302\) 32.8604 + 18.9719i 0.00626126 + 0.00361494i
\(303\) 2188.98 1350.42i 0.415029 0.256039i
\(304\) −2853.56 4942.51i −0.538365 0.932475i
\(305\) 0 0
\(306\) −115.119 174.970i −0.0215063 0.0326874i
\(307\) 5611.86i 1.04328i −0.853167 0.521638i \(-0.825321\pi\)
0.853167 0.521638i \(-0.174679\pi\)
\(308\) −1840.52 + 1062.63i −0.340498 + 0.196587i
\(309\) −1553.49 + 2881.67i −0.286002 + 0.530525i
\(310\) 0 0
\(311\) −5460.70 + 9458.21i −0.995653 + 1.72452i −0.417163 + 0.908831i \(0.636976\pi\)
−0.578489 + 0.815690i \(0.696358\pi\)
\(312\) −343.424 185.138i −0.0623159 0.0335941i
\(313\) −4313.44 + 2490.36i −0.778946 + 0.449724i −0.836056 0.548643i \(-0.815144\pi\)
0.0571109 + 0.998368i \(0.481811\pi\)
\(314\) 235.955 0.0424067
\(315\) 0 0
\(316\) −4899.89 −0.872280
\(317\) −3252.90 + 1878.06i −0.576344 + 0.332752i −0.759679 0.650298i \(-0.774644\pi\)
0.183335 + 0.983050i \(0.441311\pi\)
\(318\) −109.648 + 67.6440i −0.0193357 + 0.0119286i
\(319\) −58.9789 + 102.154i −0.0103517 + 0.0179296i
\(320\) 0 0
\(321\) −8107.73 + 236.555i −1.40975 + 0.0411316i
\(322\) −249.155 + 143.849i −0.0431206 + 0.0248957i
\(323\) 3998.99i 0.688885i
\(324\) −2299.40 + 5335.27i −0.394273 + 0.914827i
\(325\) 0 0
\(326\) 90.9788 + 157.580i 0.0154566 + 0.0267716i
\(327\) −141.864 4862.25i −0.0239911 0.822273i
\(328\) −494.520 285.511i −0.0832479 0.0480632i
\(329\) 659.016 1141.45i 0.110434 0.191277i
\(330\) 0 0
\(331\) 453.477 + 785.445i 0.0753031 + 0.130429i 0.901218 0.433366i \(-0.142674\pi\)
−0.825915 + 0.563795i \(0.809341\pi\)
\(332\) 8569.55i 1.41661i
\(333\) 97.9609 + 1677.33i 0.0161208 + 0.276028i
\(334\) −582.182 −0.0953759
\(335\) 0 0
\(336\) −1320.32 + 2449.14i −0.214372 + 0.397654i
\(337\) −8555.20 4939.35i −1.38288 0.798408i −0.390383 0.920653i \(-0.627657\pi\)
−0.992500 + 0.122245i \(0.960991\pi\)
\(338\) 223.527 + 129.053i 0.0359712 + 0.0207680i
\(339\) 3341.02 6197.48i 0.535278 0.992923i
\(340\) 0 0
\(341\) 7929.49 1.25925
\(342\) 356.045 234.255i 0.0562944 0.0370382i
\(343\) 5199.81i 0.818553i
\(344\) −737.247 1276.95i −0.115551 0.200141i
\(345\) 0 0
\(346\) −104.488 + 180.979i −0.0162350 + 0.0281199i
\(347\) 3039.50 + 1754.86i 0.470228 + 0.271486i 0.716335 0.697757i \(-0.245818\pi\)
−0.246107 + 0.969243i \(0.579152\pi\)
\(348\) 4.52124 + 154.962i 0.000696448 + 0.0238702i
\(349\) −5196.48 9000.57i −0.797024 1.38049i −0.921546 0.388269i \(-0.873073\pi\)
0.124522 0.992217i \(-0.460260\pi\)
\(350\) 0 0
\(351\) −1592.33 + 3416.88i −0.242143 + 0.519600i
\(352\) 1053.19i 0.159475i
\(353\) −7002.16 + 4042.70i −1.05577 + 0.609550i −0.924259 0.381765i \(-0.875316\pi\)
−0.131512 + 0.991315i \(0.541983\pi\)
\(354\) −448.836 + 13.0955i −0.0673881 + 0.00196615i
\(355\) 0 0
\(356\) 5997.56 10388.1i 0.892893 1.54654i
\(357\) −1659.26 + 1023.63i −0.245987 + 0.151754i
\(358\) 352.136 203.306i 0.0519860 0.0300141i
\(359\) 8189.49 1.20397 0.601984 0.798508i \(-0.294377\pi\)
0.601984 + 0.798508i \(0.294377\pi\)
\(360\) 0 0
\(361\) 1278.52 0.186400
\(362\) −382.962 + 221.103i −0.0556024 + 0.0321020i
\(363\) −1547.01 833.983i −0.223683 0.120586i
\(364\) −906.184 + 1569.56i −0.130486 + 0.226008i
\(365\) 0 0
\(366\) −327.691 + 607.856i −0.0467996 + 0.0868119i
\(367\) −7789.60 + 4497.33i −1.10794 + 0.639669i −0.938295 0.345836i \(-0.887595\pi\)
−0.169645 + 0.985505i \(0.554262\pi\)
\(368\) 12289.9i 1.74091i
\(369\) −2475.39 + 4930.86i −0.349224 + 0.695638i
\(370\) 0 0
\(371\) 599.629 + 1038.59i 0.0839116 + 0.145339i
\(372\) 8869.42 5471.71i 1.23618 0.762621i
\(373\) −805.288 464.934i −0.111786 0.0645398i 0.443064 0.896490i \(-0.353891\pi\)
−0.554851 + 0.831950i \(0.687225\pi\)
\(374\) −122.208 + 211.670i −0.0168963 + 0.0292652i
\(375\) 0 0
\(376\) −217.582 376.863i −0.0298429 0.0516894i
\(377\) 100.592i 0.0137420i
\(378\) −188.335 87.7673i −0.0256267 0.0119425i
\(379\) −3449.71 −0.467546 −0.233773 0.972291i \(-0.575107\pi\)
−0.233773 + 0.972291i \(0.575107\pi\)
\(380\) 0 0
\(381\) −6141.14 + 179.177i −0.825775 + 0.0240932i
\(382\) 362.012 + 209.007i 0.0484872 + 0.0279941i
\(383\) −4629.89 2673.07i −0.617692 0.356625i 0.158278 0.987395i \(-0.449406\pi\)
−0.775970 + 0.630770i \(0.782739\pi\)
\(384\) 968.370 + 1569.69i 0.128690 + 0.208601i
\(385\) 0 0
\(386\) −620.841 −0.0818652
\(387\) −11901.8 + 7830.66i −1.56332 + 1.02857i
\(388\) 2651.72i 0.346960i
\(389\) 3861.72 + 6688.70i 0.503334 + 0.871801i 0.999993 + 0.00385448i \(0.00122692\pi\)
−0.496658 + 0.867946i \(0.665440\pi\)
\(390\) 0 0
\(391\) 4305.78 7457.83i 0.556912 0.964600i
\(392\) 656.709 + 379.151i 0.0846144 + 0.0488521i
\(393\) 10308.3 + 5557.14i 1.32312 + 0.713284i
\(394\) 108.426 + 187.799i 0.0138640 + 0.0240132i
\(395\) 0 0
\(396\) 6768.20 395.282i 0.858876 0.0501607i
\(397\) 7125.03i 0.900744i 0.892841 + 0.450372i \(0.148709\pi\)
−0.892841 + 0.450372i \(0.851291\pi\)
\(398\) 78.2948 45.2035i 0.00986071 0.00569308i
\(399\) −2082.98 3376.42i −0.261352 0.423640i
\(400\) 0 0
\(401\) 896.547 1552.86i 0.111649 0.193382i −0.804786 0.593565i \(-0.797720\pi\)
0.916435 + 0.400183i \(0.131053\pi\)
\(402\) 14.4146 + 494.047i 0.00178839 + 0.0612956i
\(403\) 5856.15 3381.05i 0.723860 0.417921i
\(404\) −3944.73 −0.485786
\(405\) 0 0
\(406\) −5.54451 −0.000677757
\(407\) 1698.05 980.369i 0.206804 0.119398i
\(408\) 18.7725 + 643.412i 0.00227789 + 0.0780727i
\(409\) 1569.87 2719.09i 0.189792 0.328729i −0.755389 0.655277i \(-0.772552\pi\)
0.945181 + 0.326548i \(0.105885\pi\)
\(410\) 0 0
\(411\) −1292.38 2094.90i −0.155106 0.251420i
\(412\) 4348.27 2510.48i 0.519961 0.300200i
\(413\) 4179.77i 0.497997i
\(414\) 916.224 53.5100i 0.108768 0.00635235i
\(415\) 0 0
\(416\) 449.068 + 777.808i 0.0529263 + 0.0916711i
\(417\) 626.795 + 337.900i 0.0736074 + 0.0396812i
\(418\) −430.726 248.680i −0.0504007 0.0290989i
\(419\) 1228.70 2128.17i 0.143260 0.248133i −0.785463 0.618909i \(-0.787575\pi\)
0.928722 + 0.370776i \(0.120908\pi\)
\(420\) 0 0
\(421\) 1339.33 + 2319.80i 0.155048 + 0.268551i 0.933076 0.359678i \(-0.117113\pi\)
−0.778029 + 0.628229i \(0.783780\pi\)
\(422\) 3.12228i 0.000360167i
\(423\) −3512.56 + 2311.04i −0.403750 + 0.265643i
\(424\) 395.949 0.0453514
\(425\) 0 0
\(426\) −443.121 718.281i −0.0503974 0.0816921i
\(427\) 5566.86 + 3214.03i 0.630911 + 0.364257i
\(428\) 10773.5 + 6220.09i 1.21672 + 0.702476i
\(429\) 4397.26 128.297i 0.494876 0.0144388i
\(430\) 0 0
\(431\) −9472.42 −1.05863 −0.529316 0.848425i \(-0.677551\pi\)
−0.529316 + 0.848425i \(0.677551\pi\)
\(432\) 7269.57 5092.79i 0.809623 0.567192i
\(433\) 4238.21i 0.470382i 0.971949 + 0.235191i \(0.0755715\pi\)
−0.971949 + 0.235191i \(0.924428\pi\)
\(434\) 186.360 + 322.784i 0.0206119 + 0.0357008i
\(435\) 0 0
\(436\) −3730.23 + 6460.94i −0.409737 + 0.709686i
\(437\) 15175.9 + 8761.80i 1.66124 + 0.959116i
\(438\) 471.065 290.609i 0.0513889 0.0317028i
\(439\) 2429.47 + 4207.96i 0.264128 + 0.457483i 0.967335 0.253503i \(-0.0815826\pi\)
−0.703207 + 0.710985i \(0.748249\pi\)
\(440\) 0 0
\(441\) 3287.25 6548.05i 0.354957 0.707057i
\(442\) 208.432i 0.0224301i
\(443\) −2022.82 + 1167.88i −0.216946 + 0.125254i −0.604535 0.796578i \(-0.706641\pi\)
0.387589 + 0.921832i \(0.373308\pi\)
\(444\) 1222.83 2268.31i 0.130705 0.242453i
\(445\) 0 0
\(446\) 86.5783 149.958i 0.00919193 0.0159209i
\(447\) 654.568 + 352.873i 0.0692617 + 0.0373385i
\(448\) 3666.94 2117.11i 0.386712 0.223268i
\(449\) −13290.5 −1.39692 −0.698460 0.715649i \(-0.746131\pi\)
−0.698460 + 0.715649i \(0.746131\pi\)
\(450\) 0 0
\(451\) 6438.58 0.672241
\(452\) −9351.64 + 5399.17i −0.973151 + 0.561849i
\(453\) −958.941 + 591.588i −0.0994591 + 0.0613582i
\(454\) 299.848 519.351i 0.0309968 0.0536880i
\(455\) 0 0
\(456\) −1309.28 + 38.2001i −0.134457 + 0.00392299i
\(457\) 4481.35 2587.31i 0.458706 0.264834i −0.252794 0.967520i \(-0.581350\pi\)
0.711500 + 0.702686i \(0.248016\pi\)
\(458\) 192.415i 0.0196309i
\(459\) 6195.63 543.534i 0.630037 0.0552724i
\(460\) 0 0
\(461\) −3170.44 5491.37i −0.320309 0.554791i 0.660243 0.751052i \(-0.270453\pi\)
−0.980552 + 0.196261i \(0.937120\pi\)
\(462\) 7.07157 + 242.372i 0.000712119 + 0.0244073i
\(463\) 2756.38 + 1591.40i 0.276673 + 0.159737i 0.631916 0.775036i \(-0.282269\pi\)
−0.355243 + 0.934774i \(0.615602\pi\)
\(464\) 118.425 205.118i 0.0118486 0.0205223i
\(465\) 0 0
\(466\) 390.208 + 675.860i 0.0387898 + 0.0671859i
\(467\) 8576.23i 0.849808i −0.905238 0.424904i \(-0.860308\pi\)
0.905238 0.424904i \(-0.139692\pi\)
\(468\) 4829.96 3177.82i 0.477062 0.313877i
\(469\) 4600.79 0.452974
\(470\) 0 0
\(471\) −3324.87 + 6167.53i −0.325269 + 0.603365i
\(472\) 1195.11 + 690.000i 0.116546 + 0.0672877i
\(473\) 14398.3 + 8312.84i 1.39965 + 0.808086i
\(474\) −265.282 + 492.090i −0.0257064 + 0.0476845i
\(475\) 0 0
\(476\) 2990.13 0.287925
\(477\) −223.054 3819.23i −0.0214107 0.366605i
\(478\) 1145.18i 0.109580i
\(479\) 1458.82 + 2526.76i 0.139155 + 0.241024i 0.927177 0.374623i \(-0.122228\pi\)
−0.788022 + 0.615647i \(0.788895\pi\)
\(480\) 0 0
\(481\) 836.037 1448.06i 0.0792516 0.137268i
\(482\) −31.8729 18.4018i −0.00301197 0.00173896i
\(483\) −249.155 8539.56i −0.0234719 0.804479i
\(484\) 1347.74 + 2334.35i 0.126572 + 0.219229i
\(485\) 0 0
\(486\) 411.324 + 519.779i 0.0383910 + 0.0485137i
\(487\) 14061.0i 1.30834i −0.756346 0.654172i \(-0.773017\pi\)
0.756346 0.654172i \(-0.226983\pi\)
\(488\) 1837.96 1061.15i 0.170493 0.0984343i
\(489\) −5400.92 + 157.580i −0.499464 + 0.0145726i
\(490\) 0 0
\(491\) 466.331 807.709i 0.0428620 0.0742391i −0.843799 0.536660i \(-0.819686\pi\)
0.886661 + 0.462421i \(0.153019\pi\)
\(492\) 7201.78 4442.91i 0.659921 0.407118i
\(493\) 143.727 82.9806i 0.0131301 0.00758065i
\(494\) −424.137 −0.0386292
\(495\) 0 0
\(496\) −15921.8 −1.44135
\(497\) −6803.57 + 3928.04i −0.614048 + 0.354521i
\(498\) −860.629 463.959i −0.0774412 0.0417480i
\(499\) −7215.39 + 12497.4i −0.647305 + 1.12117i 0.336459 + 0.941698i \(0.390771\pi\)
−0.983764 + 0.179467i \(0.942563\pi\)
\(500\) 0 0
\(501\) 8203.60 15217.4i 0.731557 1.35701i
\(502\) −123.679 + 71.4062i −0.0109962 + 0.00634864i
\(503\) 3230.55i 0.286368i 0.989696 + 0.143184i \(0.0457341\pi\)
−0.989696 + 0.143184i \(0.954266\pi\)
\(504\) 350.988 + 533.467i 0.0310203 + 0.0471478i
\(505\) 0 0
\(506\) −535.515 927.539i −0.0470485 0.0814904i
\(507\) −6523.03 + 4024.18i −0.571397 + 0.352505i
\(508\) 8160.32 + 4711.36i 0.712708 + 0.411482i
\(509\) −180.378 + 312.424i −0.0157075 + 0.0272062i −0.873772 0.486335i \(-0.838333\pi\)
0.858065 + 0.513541i \(0.171667\pi\)
\(510\) 0 0
\(511\) −2576.10 4461.93i −0.223013 0.386270i
\(512\) 3529.04i 0.304615i
\(513\) 1106.03 + 12607.4i 0.0951903 + 1.08505i
\(514\) −730.096 −0.0626521
\(515\) 0 0
\(516\) 21841.2 637.250i 1.86338 0.0543670i
\(517\) 4249.33 + 2453.35i 0.361480 + 0.208701i
\(518\) 79.8154 + 46.0814i 0.00677005 + 0.00390869i
\(519\) −3258.18 5281.37i −0.275565 0.446679i
\(520\) 0 0
\(521\) −11698.8 −0.983747 −0.491873 0.870667i \(-0.663688\pi\)
−0.491873 + 0.870667i \(0.663688\pi\)
\(522\) 15.8074 + 7.93562i 0.00132542 + 0.000665388i
\(523\) 18557.3i 1.55154i −0.631015 0.775770i \(-0.717362\pi\)
0.631015 0.775770i \(-0.282638\pi\)
\(524\) −8980.49 15554.7i −0.748692 1.29677i
\(525\) 0 0
\(526\) −246.470 + 426.899i −0.0204308 + 0.0353872i
\(527\) −9661.75 5578.21i −0.798619 0.461083i
\(528\) −9117.54 4915.20i −0.751496 0.405126i
\(529\) 12784.5 + 22143.3i 1.05075 + 1.81995i
\(530\) 0 0
\(531\) 5982.32 11916.5i 0.488909 0.973883i
\(532\) 6084.59i 0.495866i
\(533\) 4755.07 2745.34i 0.386426 0.223103i
\(534\) −718.551 1164.74i −0.0582298 0.0943882i
\(535\) 0 0
\(536\) 759.503 1315.50i 0.0612044 0.106009i
\(537\) 352.136 + 12069.2i 0.0282976 + 0.969875i
\(538\) −15.5496 + 8.97756i −0.00124608 + 0.000719424i
\(539\) −8550.26 −0.683276
\(540\) 0 0
\(541\) 22755.3 1.80837 0.904185 0.427140i \(-0.140479\pi\)
0.904185 + 0.427140i \(0.140479\pi\)
\(542\) 505.733 291.985i 0.0400795 0.0231399i
\(543\) −382.962 13125.7i −0.0302661 1.03734i
\(544\) 740.893 1283.26i 0.0583925 0.101139i
\(545\) 0 0
\(546\) 108.567 + 175.983i 0.00850962 + 0.0137937i
\(547\) 5021.30 2899.05i 0.392496 0.226608i −0.290745 0.956801i \(-0.593903\pi\)
0.683241 + 0.730193i \(0.260570\pi\)
\(548\) 3775.18i 0.294284i
\(549\) −11271.0 17130.8i −0.876200 1.33174i
\(550\) 0 0
\(551\) 168.857 + 292.468i 0.0130554 + 0.0226127i
\(552\) −2482.84 1338.48i −0.191443 0.103205i
\(553\) 4506.65 + 2601.92i 0.346550 + 0.200081i
\(554\) −55.4599 + 96.0593i −0.00425318 + 0.00736673i
\(555\) 0 0
\(556\) −546.056 945.797i −0.0416510 0.0721416i
\(557\) 15740.3i 1.19738i 0.800982 + 0.598688i \(0.204311\pi\)
−0.800982 + 0.598688i \(0.795689\pi\)
\(558\) −69.3231 1186.98i −0.00525929 0.0900521i
\(559\) 14178.0 1.07275
\(560\) 0 0
\(561\) −3810.72 6177.01i −0.286789 0.464873i
\(562\) −939.919 542.662i −0.0705482 0.0407310i
\(563\) 3307.45 + 1909.56i 0.247589 + 0.142946i 0.618660 0.785659i \(-0.287676\pi\)
−0.371071 + 0.928605i \(0.621009\pi\)
\(564\) 6445.94 188.070i 0.481247 0.0140411i
\(565\) 0 0
\(566\) 1308.91 0.0972040
\(567\) 4947.97 3686.07i 0.366482 0.273016i
\(568\) 2593.78i 0.191607i
\(569\) 4445.56 + 7699.93i 0.327535 + 0.567308i 0.982022 0.188766i \(-0.0604487\pi\)
−0.654487 + 0.756073i \(0.727115\pi\)
\(570\) 0 0
\(571\) −4193.31 + 7263.03i −0.307329 + 0.532309i −0.977777 0.209647i \(-0.932768\pi\)
0.670448 + 0.741956i \(0.266102\pi\)
\(572\) −5843.06 3373.49i −0.427116 0.246596i
\(573\) −10564.3 + 6517.33i −0.770211 + 0.475158i
\(574\) 151.320 + 262.094i 0.0110034 + 0.0190585i
\(575\) 0 0
\(576\) −13484.6 + 787.536i −0.975446 + 0.0569687i
\(577\) 16922.3i 1.22095i 0.792037 + 0.610473i \(0.209021\pi\)
−0.792037 + 0.610473i \(0.790979\pi\)
\(578\) −446.711 + 257.909i −0.0321466 + 0.0185599i
\(579\) 8748.35 16227.9i 0.627926 1.16478i
\(580\) 0 0
\(581\) −4550.56 + 7881.80i −0.324938 + 0.562809i
\(582\) −266.309 143.565i −0.0189671 0.0102250i
\(583\) −3866.40 + 2232.27i −0.274666 + 0.158578i
\(584\) −1701.06 −0.120531
\(585\) 0 0
\(586\) 846.315 0.0596603
\(587\) 13197.0 7619.29i 0.927936 0.535744i 0.0417777 0.999127i \(-0.486698\pi\)
0.886158 + 0.463383i \(0.153365\pi\)
\(588\) −9563.77 + 5900.07i −0.670754 + 0.413800i
\(589\) 11351.1 19660.6i 0.794079 1.37539i
\(590\) 0 0
\(591\) −6436.66 + 187.799i −0.448002 + 0.0130711i
\(592\) −3409.55 + 1968.50i −0.236709 + 0.136664i
\(593\) 16960.2i 1.17449i 0.809409 + 0.587245i \(0.199787\pi\)
−0.809409 + 0.587245i \(0.800213\pi\)
\(594\) 326.735 701.123i 0.0225692 0.0484300i
\(595\) 0 0
\(596\) −570.252 987.705i −0.0391920 0.0678825i
\(597\) 78.2948 + 2683.49i 0.00536749 + 0.183966i
\(598\) −790.986 456.676i −0.0540900 0.0312289i
\(599\) −12456.1 + 21574.5i −0.849651 + 1.47164i 0.0318690 + 0.999492i \(0.489854\pi\)
−0.881520 + 0.472147i \(0.843479\pi\)
\(600\) 0 0
\(601\) 2175.63 + 3768.31i 0.147664 + 0.255761i 0.930364 0.366638i \(-0.119491\pi\)
−0.782700 + 0.622399i \(0.786158\pi\)
\(602\) 781.476i 0.0529080i
\(603\) −13116.8 6584.91i −0.885835 0.444707i
\(604\) 1728.09 0.116416
\(605\) 0 0
\(606\) −213.569 + 396.164i −0.0143163 + 0.0265562i
\(607\) −24096.0 13911.8i −1.61125 0.930254i −0.989082 0.147369i \(-0.952919\pi\)
−0.622166 0.782885i \(-0.713747\pi\)
\(608\) 2611.31 + 1507.64i 0.174182 + 0.100564i
\(609\) 78.1285 144.926i 0.00519856 0.00964317i
\(610\) 0 0
\(611\) 4184.33 0.277054
\(612\) −8524.84 4279.64i −0.563066 0.282670i
\(613\) 20034.6i 1.32005i −0.751244 0.660024i \(-0.770546\pi\)
0.751244 0.660024i \(-0.229454\pi\)
\(614\) 490.994 + 850.427i 0.0322719 + 0.0558965i
\(615\) 0 0
\(616\) 372.600 645.363i 0.0243709 0.0422117i
\(617\) −6541.86 3776.95i −0.426848 0.246441i 0.271155 0.962536i \(-0.412595\pi\)
−0.698003 + 0.716095i \(0.745928\pi\)
\(618\) −16.7067 572.609i −0.00108745 0.0372714i
\(619\) 6192.54 + 10725.8i 0.402099 + 0.696456i 0.993979 0.109570i \(-0.0349474\pi\)
−0.591880 + 0.806026i \(0.701614\pi\)
\(620\) 0 0
\(621\) −11512.0 + 24702.8i −0.743896 + 1.59628i
\(622\) 1911.08i 0.123195i
\(623\) −11032.4 + 6369.58i −0.709479 + 0.409618i
\(624\) −8829.35 + 257.610i −0.566437 + 0.0165267i
\(625\) 0 0
\(626\) 435.775 754.785i 0.0278228 0.0481906i
\(627\) 12569.6 7754.40i 0.800606 0.493909i
\(628\) 9306.45 5373.08i 0.591350 0.341416i
\(629\) −2758.67 −0.174873
\(630\) 0 0
\(631\) −1325.17 −0.0836043 −0.0418022 0.999126i \(-0.513310\pi\)
−0.0418022 + 0.999126i \(0.513310\pi\)
\(632\) 1487.92 859.053i 0.0936494 0.0540685i
\(633\) −81.6122 43.9965i −0.00512447 0.00276257i
\(634\) 328.632 569.207i 0.0205862 0.0356563i
\(635\) 0 0
\(636\) −2784.34 + 5164.86i −0.173595 + 0.322013i
\(637\) −6314.60 + 3645.74i −0.392769 + 0.226765i
\(638\) 20.6408i 0.00128084i
\(639\) 25019.0 1461.18i 1.54888 0.0904589i
\(640\) 0 0
\(641\) 11255.8 + 19495.6i 0.693568 + 1.20129i 0.970661 + 0.240451i \(0.0772955\pi\)
−0.277094 + 0.960843i \(0.589371\pi\)
\(642\) 1207.96 745.212i 0.0742590 0.0458118i
\(643\) 4862.40 + 2807.31i 0.298218 + 0.172176i 0.641642 0.767004i \(-0.278253\pi\)
−0.343424 + 0.939180i \(0.611587\pi\)
\(644\) −6551.38 + 11347.3i −0.400871 + 0.694328i
\(645\) 0 0
\(646\) 349.881 + 606.012i 0.0213094 + 0.0369090i
\(647\) 11753.6i 0.714188i −0.934068 0.357094i \(-0.883768\pi\)
0.934068 0.357094i \(-0.116232\pi\)
\(648\) −237.137 2023.27i −0.0143760 0.122656i
\(649\) −15560.2 −0.941127
\(650\) 0 0
\(651\) −11063.2 + 322.784i −0.666051 + 0.0194330i
\(652\) 7176.71 + 4143.48i 0.431076 + 0.248882i
\(653\) −22393.9 12929.1i −1.34202 0.774816i −0.354916 0.934898i \(-0.615491\pi\)
−0.987104 + 0.160082i \(0.948824\pi\)
\(654\) 446.908 + 724.420i 0.0267209 + 0.0433135i
\(655\) 0 0
\(656\) −12928.1 −0.769450
\(657\) 958.272 + 16408.0i 0.0569037 + 0.974333i
\(658\) 230.635i 0.0136643i
\(659\) −8847.75 15324.8i −0.523004 0.905869i −0.999642 0.0267695i \(-0.991478\pi\)
0.476638 0.879100i \(-0.341855\pi\)
\(660\) 0 0
\(661\) −3115.05 + 5395.42i −0.183300 + 0.317485i −0.943002 0.332786i \(-0.892011\pi\)
0.759702 + 0.650271i \(0.225345\pi\)
\(662\) −137.441 79.3515i −0.00806916 0.00465873i
\(663\) −5448.13 2937.05i −0.319137 0.172044i
\(664\) 1502.42 + 2602.27i 0.0878091 + 0.152090i
\(665\) 0 0
\(666\) −161.599 245.614i −0.00940214 0.0142903i
\(667\) 727.243i 0.0422174i
\(668\) −22962.2 + 13257.2i −1.32999 + 0.767872i
\(669\) 2699.71 + 4376.12i 0.156019 + 0.252901i
\(670\) 0 0
\(671\) −11965.0 + 20724.0i −0.688381 + 1.19231i
\(672\) −42.8719 1469.40i −0.00246104 0.0843501i
\(673\) 5240.91 3025.84i 0.300182 0.173310i −0.342343 0.939575i \(-0.611220\pi\)
0.642524 + 0.766265i \(0.277887\pi\)
\(674\) 1728.62 0.0987892
\(675\) 0 0
\(676\) 11755.0 0.668812
\(677\) 24334.1 14049.3i 1.38144 0.797576i 0.389112 0.921190i \(-0.372782\pi\)
0.992330 + 0.123614i \(0.0394485\pi\)
\(678\) 35.9305 + 1231.49i 0.00203525 + 0.0697566i
\(679\) −1408.10 + 2438.90i −0.0795846 + 0.137845i
\(680\) 0 0
\(681\) 9349.93 + 15155.9i 0.526124 + 0.852825i
\(682\) −1201.64 + 693.769i −0.0674682 + 0.0389528i
\(683\) 8335.71i 0.466994i 0.972358 + 0.233497i \(0.0750169\pi\)
−0.972358 + 0.233497i \(0.924983\pi\)
\(684\) 8708.61 17347.1i 0.486816 0.969714i
\(685\) 0 0
\(686\) −454.944 787.986i −0.0253205 0.0438563i
\(687\) −5029.46 2711.34i −0.279310 0.150574i
\(688\) −28910.6 16691.5i −1.60204 0.924939i
\(689\) −1903.63 + 3297.18i −0.105258 + 0.182312i
\(690\) 0 0
\(691\) 8442.55 + 14622.9i 0.464790 + 0.805039i 0.999192 0.0401909i \(-0.0127966\pi\)
−0.534402 + 0.845230i \(0.679463\pi\)
\(692\) 9517.46i 0.522832i
\(693\) −6434.92 3230.46i −0.352731 0.177078i
\(694\) −614.146 −0.0335917
\(695\) 0 0
\(696\) −28.5409 46.2637i −0.00155437 0.00251957i
\(697\) −7845.14 4529.39i −0.426335 0.246145i
\(698\) 1574.96 + 909.305i 0.0854057 + 0.0493090i
\(699\) −23164.5 + 675.860i −1.25345 + 0.0365714i
\(700\) 0 0
\(701\) 16875.2 0.909226 0.454613 0.890689i \(-0.349778\pi\)
0.454613 + 0.890689i \(0.349778\pi\)
\(702\) −57.6479 657.115i −0.00309940 0.0353293i
\(703\) 5613.59i 0.301167i
\(704\) 7881.47 + 13651.1i 0.421938 + 0.730817i
\(705\) 0 0
\(706\) 707.410 1225.27i 0.0377106 0.0653168i
\(707\) 3628.14 + 2094.71i 0.192999 + 0.111428i
\(708\) −17404.6 + 10737.3i −0.923879 + 0.569959i
\(709\) −9503.71 16460.9i −0.503412 0.871936i −0.999992 0.00394482i \(-0.998744\pi\)
0.496580 0.867991i \(-0.334589\pi\)
\(710\) 0 0
\(711\) −9124.43 13868.2i −0.481284 0.731503i
\(712\) 4205.99i 0.221385i
\(713\) 42337.9 24443.8i 2.22379 1.28391i
\(714\) 161.887 300.295i 0.00848524 0.0157398i
\(715\) 0 0
\(716\) 9259.23 16037.4i 0.483287 0.837078i
\(717\) −29933.4 16136.9i −1.55911 0.840506i
\(718\) −1241.04 + 716.517i −0.0645061 + 0.0372426i
\(719\) −17588.1 −0.912275 −0.456138 0.889909i \(-0.650767\pi\)
−0.456138 + 0.889909i \(0.650767\pi\)
\(720\) 0 0
\(721\) −5332.40 −0.275435
\(722\) −193.748 + 111.861i −0.00998693 + 0.00576596i
\(723\) 930.123 573.810i 0.0478446 0.0295162i
\(724\) −10069.8 + 17441.4i −0.516907 + 0.895309i
\(725\) 0 0
\(726\) 307.403 8.96895i 0.0157146 0.000458497i
\(727\) 4854.40 2802.69i 0.247648 0.142979i −0.371039 0.928617i \(-0.620998\pi\)
0.618687 + 0.785638i \(0.287665\pi\)
\(728\) 635.491i 0.0323528i
\(729\) −19382.3 + 3427.15i −0.984725 + 0.174117i
\(730\) 0 0
\(731\) −11695.8 20257.7i −0.591771 1.02498i
\(732\) 917.220 + 31436.9i 0.0463134 + 1.58735i
\(733\) 12921.2 + 7460.04i 0.651097 + 0.375911i 0.788877 0.614552i \(-0.210663\pi\)
−0.137779 + 0.990463i \(0.543996\pi\)
\(734\) 786.963 1363.06i 0.0395740 0.0685443i
\(735\) 0 0
\(736\) 3246.60 + 5623.27i 0.162597 + 0.281626i
\(737\) 17127.6i 0.856042i
\(738\) −56.2889 963.806i −0.00280762 0.0480734i
\(739\) 27418.8 1.36484 0.682421 0.730959i \(-0.260927\pi\)
0.682421 + 0.730959i \(0.260927\pi\)
\(740\) 0 0
\(741\) 5976.58 11086.4i 0.296296 0.549619i
\(742\) −181.737 104.926i −0.00899161 0.00519131i
\(743\) −21255.9 12272.1i −1.04953 0.605948i −0.127014 0.991901i \(-0.540539\pi\)
−0.922518 + 0.385953i \(0.873873\pi\)
\(744\) −1734.02 + 3216.56i −0.0854467 + 0.158501i
\(745\) 0 0
\(746\) 162.712 0.00798569
\(747\) 24254.5 15957.9i 1.18799 0.781621i
\(748\) 11131.5i 0.544128i
\(749\) −6605.92 11441.8i −0.322263 0.558176i
\(750\) 0 0
\(751\) −767.283 + 1328.97i −0.0372817 + 0.0645738i −0.884064 0.467365i \(-0.845203\pi\)
0.846782 + 0.531939i \(0.178537\pi\)
\(752\) −8532.30 4926.13i −0.413752 0.238880i
\(753\) −123.679 4239.00i −0.00598555 0.205150i
\(754\) −8.80102 15.2438i −0.000425085 0.000736269i
\(755\) 0 0
\(756\) −9426.85 + 827.005i −0.453507 + 0.0397856i
\(757\) 18051.1i 0.866681i −0.901230 0.433341i \(-0.857335\pi\)
0.901230 0.433341i \(-0.142665\pi\)
\(758\) 522.773 301.823i 0.0250501 0.0144627i
\(759\) 31790.6 927.539i 1.52032 0.0443578i
\(760\) 0 0
\(761\) −6462.29 + 11193.0i −0.307829 + 0.533176i −0.977887 0.209133i \(-0.932936\pi\)
0.670058 + 0.742309i \(0.266269\pi\)
\(762\) 914.958 564.455i 0.0434980 0.0268347i
\(763\) 6861.71 3961.61i 0.325571 0.187968i
\(764\) 19037.8 0.901522
\(765\) 0 0
\(766\) 935.491 0.0441262
\(767\) −11491.6 + 6634.70i −0.540990 + 0.312341i
\(768\) 18021.6 + 9715.30i 0.846741 + 0.456472i
\(769\) −1686.16 + 2920.51i −0.0790695 + 0.136952i −0.902849 0.429958i \(-0.858528\pi\)
0.823779 + 0.566911i \(0.191862\pi\)
\(770\) 0 0
\(771\) 10287.9 19083.7i 0.480557 0.891418i
\(772\) −24487.0 + 14137.6i −1.14159 + 0.659097i
\(773\) 27152.6i 1.26341i 0.775211 + 0.631703i \(0.217644\pi\)
−0.775211 + 0.631703i \(0.782356\pi\)
\(774\) 1118.49 2227.99i 0.0519424 0.103467i
\(775\) 0 0
\(776\) 464.901 + 805.232i 0.0215064 + 0.0372502i
\(777\) −2329.19 + 1436.92i −0.107541 + 0.0663441