Properties

Label 225.4.k.c.49.4
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 49.4
Root \(-1.98116 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 225.49
Dual form 225.4.k.c.124.4

$q$-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 −0.472972 0.881078i \(-0.656819\pi\)
0.526550 + 0.850144i \(0.323485\pi\)
\(3\) 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 −0.684658 0.728865i \(-0.740048\pi\)
0.288886 + 0.957363i \(0.406715\pi\)
\(8\) 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 0.230796 0.973002i \(-0.425867\pi\)
−0.727247 + 0.686376i \(0.759200\pi\)
\(14\) −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 \(0.102417\pi\)
−0.948683 + 0.316229i \(0.897583\pi\)
\(18\) −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 \(-0.990505\pi\)
−0.525608 0.850727i \(-0.676162\pi\)
\(24\) −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 \(0.0441475\pi\)
−0.990397 + 0.138249i \(0.955853\pi\)
\(38\) 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 \(0.718536\pi\)
−0.986752 + 0.162233i \(0.948130\pi\)
\(44\) −251.101 −0.860340
\(45\) 0 0
\(46\) −33.9920 −0.108953
\(47\) −134.864 + 77.8637i −0.418551 + 0.241651i −0.694457 0.719534i \(-0.744355\pi\)
0.275906 + 0.961185i \(0.411022\pi\)
\(48\) 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 \(-0.941220\pi\)
0.982998 0.183615i \(-0.0587800\pi\)
\(54\) −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 0.00507574 0.999987i \(-0.498384\pi\)
−0.863476 + 0.504389i \(0.831718\pi\)
\(68\) −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 \(0.162272\pi\)
−0.872845 + 0.487997i \(0.837728\pi\)
\(74\) 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 0.264186 0.964472i \(-0.414897\pi\)
0.967350 + 0.253444i \(0.0815634\pi\)
\(84\) 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 −0.341544 0.939866i \(-0.610950\pi\)
0.643175 + 0.765719i \(0.277617\pi\)
\(98\) 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 0.737736 0.675090i \(-0.235895\pi\)
−0.215777 + 0.976443i \(0.569228\pi\)
\(104\) 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 \(0.249131\pi\)
−0.709034 + 0.705175i \(0.750869\pi\)
\(108\) 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 −0.0755602 0.997141i \(-0.524075\pi\)
−0.901330 + 0.433134i \(0.857408\pi\)
\(114\) 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 \(0.135541\pi\)
−0.910702 + 0.413063i \(0.864459\pi\)
\(128\) 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 −0.622434 0.782672i \(-0.713856\pi\)
0.366597 + 0.930380i \(0.380523\pi\)
\(138\) −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 0.766528 0.642211i \(-0.221983\pi\)
−0.172906 + 0.984938i \(0.555316\pi\)
\(158\) 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 \(0.0803774\pi\)
−0.968288 + 0.249838i \(0.919623\pi\)
\(164\) 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 −0.349026 0.937113i \(-0.613487\pi\)
−0.986077 + 0.166291i \(0.946821\pi\)
\(168\) 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 −0.709740 0.704464i \(-0.751187\pi\)
0.255214 + 0.966885i \(0.417854\pi\)
\(174\) −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 −0.198072 0.980188i \(-0.563468\pi\)
−0.947903 + 0.318559i \(0.896801\pi\)
\(194\) 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 \(0.0719430\pi\)
−0.974567 + 0.224096i \(0.928057\pi\)
\(198\) −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 −0.365779 0.930702i \(-0.619197\pi\)
0.623122 + 0.782125i \(0.285864\pi\)
\(224\) 282.906 0.0843860
\(225\) 0 0
\(226\) −237.101 −0.0697863
\(227\) 2967.98 1713.57i 0.867806 0.501028i 0.00118754 0.999999i \(-0.499622\pi\)
0.866619 + 0.498971i \(0.166289\pi\)
\(228\) −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 \(0.215715\pi\)
−0.779025 + 0.626993i \(0.784285\pi\)
\(234\) 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 −0.00734758 0.999973i \(-0.502339\pi\)
−0.869676 + 0.493623i \(0.835672\pi\)
\(258\) −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 −0.757945 0.652318i \(-0.773797\pi\)
0.185951 + 0.982559i \(0.440463\pi\)
\(264\) −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 −0.558354 0.829603i \(-0.688567\pi\)
0.439280 + 0.898350i \(0.355234\pi\)
\(278\) 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 0.989716 0.143047i \(-0.0456899\pi\)
0.370976 + 0.928642i \(0.379023\pi\)
\(284\) 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 0.855611 0.517620i \(-0.173182\pi\)
−0.0204666 + 0.999791i \(0.506515\pi\)
\(294\) −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 \(0.174679\pi\)
−0.853167 + 0.521638i \(0.825321\pi\)
\(308\) 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 −0.0571109 0.998368i \(-0.518189\pi\)
0.836056 + 0.548643i \(0.184856\pi\)
\(314\) 235.955 0.0424067
\(315\) 0 0
\(316\) −4899.89 −0.872280
\(317\) 3252.90 1878.06i 0.576344 0.332752i −0.183335 0.983050i \(-0.558689\pi\)
0.759679 + 0.650298i \(0.225356\pi\)
\(318\) 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 0.992500 0.122245i \(-0.0390093\pi\)
0.390383 + 0.920653i \(0.372343\pi\)
\(338\) −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 0.246107 0.969243i \(-0.420848\pi\)
−0.716335 + 0.697757i \(0.754182\pi\)
\(348\) −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 0.131512 0.991315i \(-0.458017\pi\)
0.924259 + 0.381765i \(0.124684\pi\)
\(354\) −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 0.169645 0.985505i \(-0.445738\pi\)
0.938295 + 0.345836i \(0.112405\pi\)
\(368\) 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 0.554851 0.831950i \(-0.312775\pi\)
−0.443064 + 0.896490i \(0.646109\pi\)
\(374\) −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 0.775970 0.630770i \(-0.217261\pi\)
−0.158278 + 0.987395i \(0.550594\pi\)
\(384\) 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 \(-0.851291\pi\)
0.892841 0.450372i \(-0.148709\pi\)
\(398\) −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 \(-0.924428\pi\)
0.971949 0.235191i \(-0.0755715\pi\)
\(434\) 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 −0.387589 0.921832i \(-0.626692\pi\)
0.604535 + 0.796578i \(0.293359\pi\)
\(444\) 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 −0.711500 0.702686i \(-0.751984\pi\)
0.252794 + 0.967520i \(0.418650\pi\)
\(458\) 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 0.355243 0.934774i \(-0.384398\pi\)
−0.631916 + 0.775036i \(0.717731\pi\)
\(464\) 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 \(0.139692\pi\)
−0.905238 + 0.424904i \(0.860308\pi\)
\(468\) −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 \(0.226983\pi\)
−0.756346 + 0.654172i \(0.773017\pi\)
\(488\) −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 \(-0.954266\pi\)
0.989696 0.143184i \(-0.0457341\pi\)
\(504\) 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 \(0.282638\pi\)
−0.631015 + 0.775770i \(0.717362\pi\)
\(524\) −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 −0.683241 0.730193i \(-0.739430\pi\)
0.290745 + 0.956801i \(0.406097\pi\)
\(548\) 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 \(-0.795689\pi\)
0.800982 0.598688i \(-0.204311\pi\)
\(558\) 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 0.371071 0.928605i \(-0.378991\pi\)
−0.618660 + 0.785659i \(0.712324\pi\)
\(564\) 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 \(-0.790979\pi\)
0.792037 0.610473i \(-0.209021\pi\)
\(578\) 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 −0.886158 0.463383i \(-0.846635\pi\)
−0.0417777 + 0.999127i \(0.513302\pi\)
\(588\) 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 \(-0.800213\pi\)
0.809409 0.587245i \(-0.199787\pi\)
\(594\) 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 \(0.0470805\pi\)
0.622166 + 0.782885i \(0.286253\pi\)
\(608\) −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 \(0.229454\pi\)
−0.751244 + 0.660024i \(0.770546\pi\)
\(614\) 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 0.698003 0.716095i \(-0.254072\pi\)
−0.271155 + 0.962536i \(0.587405\pi\)
\(618\) 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 0.343424 0.939180i \(-0.388413\pi\)
−0.641642 + 0.767004i \(0.721747\pi\)
\(644\) −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 \(0.116232\pi\)
−0.934068 + 0.357094i \(0.883768\pi\)
\(648\) 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 0.987104 0.160082i \(-0.0511760\pi\)
0.354916 + 0.934898i \(0.384509\pi\)
\(654\) 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 −0.642524 0.766265i \(-0.722113\pi\)
0.342343 + 0.939575i \(0.388780\pi\)
\(674\) 1728.62 0.0987892
\(675\) 0 0
\(676\) 11755.0 0.668812
\(677\) −24334.1 + 14049.3i −1.38144 + 0.797576i −0.992330 0.123614i \(-0.960551\pi\)
−0.389112 + 0.921190i \(0.627218\pi\)
\(678\) −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 \(-0.924983\pi\)
0.972358 0.233497i \(-0.0750169\pi\)
\(684\) 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 −0.618687 0.785638i \(-0.712335\pi\)
0.371039 + 0.928617i \(0.379002\pi\)
\(728\) 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 0.137779 0.990463i \(-0.456004\pi\)
−0.788877 + 0.614552i \(0.789337\pi\)
\(734\) 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 0.922518 0.385953i \(-0.126127\pi\)
0.127014 + 0.991901i \(0.459461\pi\)
\(744\) −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 \(0.142665\pi\)
−0.901230 + 0.433341i \(0.857335\pi\)
\(758\) −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 \(-0.782356\pi\)
0.775211 0.631703i \(-0.217644\pi\)
\(774\) 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 0.0663441i