Properties

Label 108.6.b.b.107.15
Level 108
Weight 6
Character 108.107
Analytic conductor 17.321
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 108.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.3214525398\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{30}\cdot 3^{32}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 107.15
Root \(1.73205 - 3.53958i\) of \(x^{16} + 30 x^{14} + 619 x^{12} + 5604 x^{10} + 40971 x^{8} - 4866 x^{6} + 568069 x^{4} - 7909632 x^{2} + 20340100\)
Character \(\chi\) \(=\) 108.107
Dual form 108.6.b.b.107.16

$q$-expansion

\(f(q)\) \(=\) \(q+(5.65395 - 0.181119i) q^{2} +(31.9344 - 2.04808i) q^{4} +69.1814i q^{5} -238.886i q^{7} +(180.185 - 17.3637i) q^{8} +O(q^{10})\) \(q+(5.65395 - 0.181119i) q^{2} +(31.9344 - 2.04808i) q^{4} +69.1814i q^{5} -238.886i q^{7} +(180.185 - 17.3637i) q^{8} +(12.5301 + 391.148i) q^{10} +350.956 q^{11} +669.928 q^{13} +(-43.2668 - 1350.65i) q^{14} +(1015.61 - 130.808i) q^{16} +1396.15i q^{17} +1789.28i q^{19} +(141.689 + 2209.26i) q^{20} +(1984.29 - 63.5648i) q^{22} +1322.78 q^{23} -1661.06 q^{25} +(3787.74 - 121.337i) q^{26} +(-489.257 - 7628.68i) q^{28} -6894.21i q^{29} -2334.13i q^{31} +(5718.52 - 923.531i) q^{32} +(252.870 + 7893.79i) q^{34} +16526.5 q^{35} -12929.6 q^{37} +(324.073 + 10116.5i) q^{38} +(1201.24 + 12465.4i) q^{40} +8719.02i q^{41} -10647.8i q^{43} +(11207.6 - 718.785i) q^{44} +(7478.94 - 239.581i) q^{46} -3988.75 q^{47} -40259.6 q^{49} +(-9391.56 + 300.850i) q^{50} +(21393.8 - 1372.07i) q^{52} -4057.38i q^{53} +24279.6i q^{55} +(-4147.94 - 43043.6i) q^{56} +(-1248.67 - 38979.5i) q^{58} -25135.6 q^{59} +8968.91 q^{61} +(-422.756 - 13197.1i) q^{62} +(32165.0 - 6257.33i) q^{64} +46346.6i q^{65} -12405.9i q^{67} +(2859.43 + 44585.3i) q^{68} +(93439.9 - 2993.26i) q^{70} +6503.43 q^{71} -45851.0 q^{73} +(-73103.6 + 2341.81i) q^{74} +(3664.59 + 57139.6i) q^{76} -83838.4i q^{77} +37453.2i q^{79} +(9049.50 + 70261.3i) q^{80} +(1579.18 + 49296.9i) q^{82} -48693.7 q^{83} -96587.8 q^{85} +(-1928.52 - 60202.1i) q^{86} +(63236.8 - 6093.88i) q^{88} -7935.52i q^{89} -160037. i q^{91} +(42242.2 - 2709.16i) q^{92} +(-22552.2 + 722.439i) q^{94} -123785. q^{95} +56596.2 q^{97} +(-227626. + 7291.78i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 94q^{4} + O(q^{10}) \) \( 16q + 94q^{4} + 1454q^{10} + 896q^{13} + 178q^{16} + 30q^{22} + 9888q^{25} + 11454q^{28} - 6172q^{34} - 71008q^{37} - 16618q^{40} + 35304q^{46} - 49376q^{49} + 14876q^{52} - 10492q^{58} + 77888q^{61} + 89206q^{64} + 229398q^{70} - 38032q^{73} + 48960q^{76} - 224488q^{82} - 371264q^{85} + 249102q^{88} + 68772q^{94} - 976q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.65395 0.181119i 0.999487 0.0320176i
\(3\) 0 0
\(4\) 31.9344 2.04808i 0.997950 0.0640025i
\(5\) 69.1814i 1.23755i 0.785567 + 0.618777i \(0.212372\pi\)
−0.785567 + 0.618777i \(0.787628\pi\)
\(6\) 0 0
\(7\) 238.886i 1.84266i −0.388779 0.921331i \(-0.627103\pi\)
0.388779 0.921331i \(-0.372897\pi\)
\(8\) 180.185 17.3637i 0.995389 0.0959216i
\(9\) 0 0
\(10\) 12.5301 + 391.148i 0.0396236 + 1.23692i
\(11\) 350.956 0.874521 0.437261 0.899335i \(-0.355949\pi\)
0.437261 + 0.899335i \(0.355949\pi\)
\(12\) 0 0
\(13\) 669.928 1.09944 0.549718 0.835350i \(-0.314735\pi\)
0.549718 + 0.835350i \(0.314735\pi\)
\(14\) −43.2668 1350.65i −0.0589977 1.84172i
\(15\) 0 0
\(16\) 1015.61 130.808i 0.991807 0.127742i
\(17\) 1396.15i 1.17168i 0.810425 + 0.585842i \(0.199236\pi\)
−0.810425 + 0.585842i \(0.800764\pi\)
\(18\) 0 0
\(19\) 1789.28i 1.13709i 0.822652 + 0.568545i \(0.192493\pi\)
−0.822652 + 0.568545i \(0.807507\pi\)
\(20\) 141.689 + 2209.26i 0.0792065 + 1.23502i
\(21\) 0 0
\(22\) 1984.29 63.5648i 0.874073 0.0280001i
\(23\) 1322.78 0.521397 0.260698 0.965420i \(-0.416047\pi\)
0.260698 + 0.965420i \(0.416047\pi\)
\(24\) 0 0
\(25\) −1661.06 −0.531540
\(26\) 3787.74 121.337i 1.09887 0.0352014i
\(27\) 0 0
\(28\) −489.257 7628.68i −0.117935 1.83888i
\(29\) 6894.21i 1.52226i −0.648598 0.761131i \(-0.724644\pi\)
0.648598 0.761131i \(-0.275356\pi\)
\(30\) 0 0
\(31\) 2334.13i 0.436236i −0.975922 0.218118i \(-0.930008\pi\)
0.975922 0.218118i \(-0.0699918\pi\)
\(32\) 5718.52 923.531i 0.987209 0.159432i
\(33\) 0 0
\(34\) 252.870 + 7893.79i 0.0375146 + 1.17108i
\(35\) 16526.5 2.28039
\(36\) 0 0
\(37\) −12929.6 −1.55268 −0.776341 0.630314i \(-0.782926\pi\)
−0.776341 + 0.630314i \(0.782926\pi\)
\(38\) 324.073 + 10116.5i 0.0364069 + 1.13651i
\(39\) 0 0
\(40\) 1201.24 + 12465.4i 0.118708 + 1.23185i
\(41\) 8719.02i 0.810043i 0.914307 + 0.405021i \(0.132736\pi\)
−0.914307 + 0.405021i \(0.867264\pi\)
\(42\) 0 0
\(43\) 10647.8i 0.878189i −0.898441 0.439095i \(-0.855299\pi\)
0.898441 0.439095i \(-0.144701\pi\)
\(44\) 11207.6 718.785i 0.872728 0.0559715i
\(45\) 0 0
\(46\) 7478.94 239.581i 0.521130 0.0166939i
\(47\) −3988.75 −0.263386 −0.131693 0.991291i \(-0.542041\pi\)
−0.131693 + 0.991291i \(0.542041\pi\)
\(48\) 0 0
\(49\) −40259.6 −2.39540
\(50\) −9391.56 + 300.850i −0.531267 + 0.0170186i
\(51\) 0 0
\(52\) 21393.8 1372.07i 1.09718 0.0703666i
\(53\) 4057.38i 0.198406i −0.995067 0.0992032i \(-0.968371\pi\)
0.995067 0.0992032i \(-0.0316294\pi\)
\(54\) 0 0
\(55\) 24279.6i 1.08227i
\(56\) −4147.94 43043.6i −0.176751 1.83417i
\(57\) 0 0
\(58\) −1248.67 38979.5i −0.0487393 1.52148i
\(59\) −25135.6 −0.940068 −0.470034 0.882648i \(-0.655758\pi\)
−0.470034 + 0.882648i \(0.655758\pi\)
\(60\) 0 0
\(61\) 8968.91 0.308614 0.154307 0.988023i \(-0.450686\pi\)
0.154307 + 0.988023i \(0.450686\pi\)
\(62\) −422.756 13197.1i −0.0139673 0.436012i
\(63\) 0 0
\(64\) 32165.0 6257.33i 0.981598 0.190959i
\(65\) 46346.6i 1.36061i
\(66\) 0 0
\(67\) 12405.9i 0.337631i −0.985648 0.168815i \(-0.946006\pi\)
0.985648 0.168815i \(-0.0539942\pi\)
\(68\) 2859.43 + 44585.3i 0.0749907 + 1.16928i
\(69\) 0 0
\(70\) 93439.9 2993.26i 2.27922 0.0730128i
\(71\) 6503.43 0.153108 0.0765538 0.997065i \(-0.475608\pi\)
0.0765538 + 0.997065i \(0.475608\pi\)
\(72\) 0 0
\(73\) −45851.0 −1.00703 −0.503515 0.863987i \(-0.667960\pi\)
−0.503515 + 0.863987i \(0.667960\pi\)
\(74\) −73103.6 + 2341.81i −1.55189 + 0.0497132i
\(75\) 0 0
\(76\) 3664.59 + 57139.6i 0.0727766 + 1.13476i
\(77\) 83838.4i 1.61145i
\(78\) 0 0
\(79\) 37453.2i 0.675182i 0.941293 + 0.337591i \(0.109612\pi\)
−0.941293 + 0.337591i \(0.890388\pi\)
\(80\) 9049.50 + 70261.3i 0.158088 + 1.22742i
\(81\) 0 0
\(82\) 1579.18 + 49296.9i 0.0259357 + 0.809628i
\(83\) −48693.7 −0.775849 −0.387925 0.921691i \(-0.626808\pi\)
−0.387925 + 0.921691i \(0.626808\pi\)
\(84\) 0 0
\(85\) −96587.8 −1.45002
\(86\) −1928.52 60202.1i −0.0281175 0.877739i
\(87\) 0 0
\(88\) 63236.8 6093.88i 0.870489 0.0838855i
\(89\) 7935.52i 0.106194i −0.998589 0.0530971i \(-0.983091\pi\)
0.998589 0.0530971i \(-0.0169093\pi\)
\(90\) 0 0
\(91\) 160037.i 2.02589i
\(92\) 42242.2 2709.16i 0.520328 0.0333707i
\(93\) 0 0
\(94\) −22552.2 + 722.439i −0.263251 + 0.00843299i
\(95\) −123785. −1.40721
\(96\) 0 0
\(97\) 56596.2 0.610742 0.305371 0.952233i \(-0.401219\pi\)
0.305371 + 0.952233i \(0.401219\pi\)
\(98\) −227626. + 7291.78i −2.39418 + 0.0766952i
\(99\) 0 0
\(100\) −53045.0 + 3401.98i −0.530450 + 0.0340198i
\(101\) 72884.7i 0.710940i −0.934688 0.355470i \(-0.884321\pi\)
0.934688 0.355470i \(-0.115679\pi\)
\(102\) 0 0
\(103\) 97537.9i 0.905900i 0.891536 + 0.452950i \(0.149628\pi\)
−0.891536 + 0.452950i \(0.850372\pi\)
\(104\) 120711. 11632.4i 1.09437 0.105460i
\(105\) 0 0
\(106\) −734.869 22940.2i −0.00635251 0.198305i
\(107\) −16437.8 −0.138798 −0.0693990 0.997589i \(-0.522108\pi\)
−0.0693990 + 0.997589i \(0.522108\pi\)
\(108\) 0 0
\(109\) −173939. −1.40226 −0.701132 0.713032i \(-0.747322\pi\)
−0.701132 + 0.713032i \(0.747322\pi\)
\(110\) 4397.50 + 137276.i 0.0346517 + 1.08171i
\(111\) 0 0
\(112\) −31248.3 242615.i −0.235386 1.82757i
\(113\) 228039.i 1.68002i 0.542573 + 0.840009i \(0.317450\pi\)
−0.542573 + 0.840009i \(0.682550\pi\)
\(114\) 0 0
\(115\) 91511.8i 0.645257i
\(116\) −14119.9 220162.i −0.0974285 1.51914i
\(117\) 0 0
\(118\) −142116. + 4552.54i −0.939586 + 0.0300988i
\(119\) 333522. 2.15902
\(120\) 0 0
\(121\) −37881.2 −0.235212
\(122\) 50709.8 1624.44i 0.308455 0.00988108i
\(123\) 0 0
\(124\) −4780.49 74539.2i −0.0279202 0.435342i
\(125\) 101277.i 0.579745i
\(126\) 0 0
\(127\) 170464.i 0.937827i 0.883244 + 0.468913i \(0.155354\pi\)
−0.883244 + 0.468913i \(0.844646\pi\)
\(128\) 180726. 41204.4i 0.974981 0.222289i
\(129\) 0 0
\(130\) 8394.25 + 262041.i 0.0435636 + 1.35991i
\(131\) −29943.1 −0.152447 −0.0762234 0.997091i \(-0.524286\pi\)
−0.0762234 + 0.997091i \(0.524286\pi\)
\(132\) 0 0
\(133\) 427435. 2.09527
\(134\) −2246.95 70142.5i −0.0108101 0.337458i
\(135\) 0 0
\(136\) 24242.4 + 251565.i 0.112390 + 1.16628i
\(137\) 171047.i 0.778600i −0.921111 0.389300i \(-0.872717\pi\)
0.921111 0.389300i \(-0.127283\pi\)
\(138\) 0 0
\(139\) 263941.i 1.15870i −0.815080 0.579348i \(-0.803307\pi\)
0.815080 0.579348i \(-0.196693\pi\)
\(140\) 527763. 33847.5i 2.27572 0.145951i
\(141\) 0 0
\(142\) 36770.1 1177.90i 0.153029 0.00490215i
\(143\) 235115. 0.961480
\(144\) 0 0
\(145\) 476951. 1.88388
\(146\) −259240. + 8304.50i −1.00651 + 0.0322427i
\(147\) 0 0
\(148\) −412900. + 26480.9i −1.54950 + 0.0993754i
\(149\) 47653.0i 0.175843i −0.996127 0.0879215i \(-0.971978\pi\)
0.996127 0.0879215i \(-0.0280225\pi\)
\(150\) 0 0
\(151\) 351084.i 1.25305i −0.779402 0.626525i \(-0.784477\pi\)
0.779402 0.626525i \(-0.215523\pi\)
\(152\) 31068.5 + 322401.i 0.109072 + 1.13185i
\(153\) 0 0
\(154\) −15184.7 474018.i −0.0515948 1.61062i
\(155\) 161479. 0.539866
\(156\) 0 0
\(157\) 285818. 0.925424 0.462712 0.886509i \(-0.346876\pi\)
0.462712 + 0.886509i \(0.346876\pi\)
\(158\) 6783.49 + 211759.i 0.0216177 + 0.674836i
\(159\) 0 0
\(160\) 63891.1 + 395615.i 0.197306 + 1.22172i
\(161\) 315994.i 0.960758i
\(162\) 0 0
\(163\) 128969.i 0.380203i 0.981764 + 0.190101i \(0.0608816\pi\)
−0.981764 + 0.190101i \(0.939118\pi\)
\(164\) 17857.2 + 278437.i 0.0518447 + 0.808382i
\(165\) 0 0
\(166\) −275312. + 8819.36i −0.775452 + 0.0248409i
\(167\) −559823. −1.55331 −0.776657 0.629924i \(-0.783086\pi\)
−0.776657 + 0.629924i \(0.783086\pi\)
\(168\) 0 0
\(169\) 77511.0 0.208760
\(170\) −546103. + 17493.9i −1.44928 + 0.0464263i
\(171\) 0 0
\(172\) −21807.5 340030.i −0.0562063 0.876389i
\(173\) 523424.i 1.32965i 0.746997 + 0.664827i \(0.231495\pi\)
−0.746997 + 0.664827i \(0.768505\pi\)
\(174\) 0 0
\(175\) 396804.i 0.979448i
\(176\) 356434. 45907.9i 0.867357 0.111714i
\(177\) 0 0
\(178\) −1437.28 44867.1i −0.00340009 0.106140i
\(179\) 715299. 1.66861 0.834305 0.551303i \(-0.185869\pi\)
0.834305 + 0.551303i \(0.185869\pi\)
\(180\) 0 0
\(181\) 286861. 0.650841 0.325420 0.945569i \(-0.394494\pi\)
0.325420 + 0.945569i \(0.394494\pi\)
\(182\) −28985.7 904839.i −0.0648642 2.02485i
\(183\) 0 0
\(184\) 238345. 22968.3i 0.518993 0.0500132i
\(185\) 894490.i 1.92153i
\(186\) 0 0
\(187\) 489988.i 1.02466i
\(188\) −127378. + 8169.28i −0.262846 + 0.0168573i
\(189\) 0 0
\(190\) −699875. + 22419.8i −1.40649 + 0.0450556i
\(191\) −121929. −0.241838 −0.120919 0.992662i \(-0.538584\pi\)
−0.120919 + 0.992662i \(0.538584\pi\)
\(192\) 0 0
\(193\) 237611. 0.459170 0.229585 0.973289i \(-0.426263\pi\)
0.229585 + 0.973289i \(0.426263\pi\)
\(194\) 319992. 10250.7i 0.610429 0.0195545i
\(195\) 0 0
\(196\) −1.28566e6 + 82454.7i −2.39049 + 0.153312i
\(197\) 667755.i 1.22589i 0.790126 + 0.612945i \(0.210015\pi\)
−0.790126 + 0.612945i \(0.789985\pi\)
\(198\) 0 0
\(199\) 230496.i 0.412602i 0.978489 + 0.206301i \(0.0661425\pi\)
−0.978489 + 0.206301i \(0.933857\pi\)
\(200\) −299298. + 28842.1i −0.529089 + 0.0509862i
\(201\) 0 0
\(202\) −13200.8 412087.i −0.0227626 0.710576i
\(203\) −1.64693e6 −2.80502
\(204\) 0 0
\(205\) −603194. −1.00247
\(206\) 17666.0 + 551475.i 0.0290048 + 0.905436i
\(207\) 0 0
\(208\) 680386. 87632.2i 1.09043 0.140445i
\(209\) 627959.i 0.994410i
\(210\) 0 0
\(211\) 788636.i 1.21947i −0.792606 0.609734i \(-0.791276\pi\)
0.792606 0.609734i \(-0.208724\pi\)
\(212\) −8309.83 129570.i −0.0126985 0.198000i
\(213\) 0 0
\(214\) −92938.3 + 2977.19i −0.138727 + 0.00444398i
\(215\) 736628. 1.08681
\(216\) 0 0
\(217\) −557592. −0.803836
\(218\) −983441. + 31503.6i −1.40154 + 0.0448972i
\(219\) 0 0
\(220\) 49726.5 + 775354.i 0.0692678 + 1.08005i
\(221\) 935323.i 1.28819i
\(222\) 0 0
\(223\) 1.42387e6i 1.91738i −0.284450 0.958691i \(-0.591811\pi\)
0.284450 0.958691i \(-0.408189\pi\)
\(224\) −220619. 1.36608e6i −0.293780 1.81909i
\(225\) 0 0
\(226\) 41302.3 + 1.28932e6i 0.0537902 + 1.67916i
\(227\) −714849. −0.920767 −0.460383 0.887720i \(-0.652288\pi\)
−0.460383 + 0.887720i \(0.652288\pi\)
\(228\) 0 0
\(229\) 640469. 0.807066 0.403533 0.914965i \(-0.367782\pi\)
0.403533 + 0.914965i \(0.367782\pi\)
\(230\) 16574.5 + 517404.i 0.0206596 + 0.644926i
\(231\) 0 0
\(232\) −119709. 1.24223e6i −0.146018 1.51524i
\(233\) 965359.i 1.16493i −0.812857 0.582464i \(-0.802089\pi\)
0.812857 0.582464i \(-0.197911\pi\)
\(234\) 0 0
\(235\) 275947.i 0.325954i
\(236\) −802690. + 51479.7i −0.938141 + 0.0601667i
\(237\) 0 0
\(238\) 1.88572e6 60407.2i 2.15791 0.0691267i
\(239\) −657323. −0.744361 −0.372181 0.928160i \(-0.621390\pi\)
−0.372181 + 0.928160i \(0.621390\pi\)
\(240\) 0 0
\(241\) −1.08719e6 −1.20577 −0.602885 0.797828i \(-0.705982\pi\)
−0.602885 + 0.797828i \(0.705982\pi\)
\(242\) −214178. + 6861.00i −0.235092 + 0.00753094i
\(243\) 0 0
\(244\) 286417. 18369.0i 0.307981 0.0197520i
\(245\) 2.78521e6i 2.96444i
\(246\) 0 0
\(247\) 1.19869e6i 1.25016i
\(248\) −40529.1 420575.i −0.0418445 0.434225i
\(249\) 0 0
\(250\) 18343.3 + 572617.i 0.0185621 + 0.579448i
\(251\) −51518.6 −0.0516155 −0.0258077 0.999667i \(-0.508216\pi\)
−0.0258077 + 0.999667i \(0.508216\pi\)
\(252\) 0 0
\(253\) 464237. 0.455973
\(254\) 30874.2 + 963794.i 0.0300270 + 0.937346i
\(255\) 0 0
\(256\) 1.01435e6 265701.i 0.967364 0.253392i
\(257\) 1.05873e6i 0.999888i 0.866058 + 0.499944i \(0.166646\pi\)
−0.866058 + 0.499944i \(0.833354\pi\)
\(258\) 0 0
\(259\) 3.08871e6i 2.86107i
\(260\) 94921.4 + 1.48005e6i 0.0870825 + 1.35782i
\(261\) 0 0
\(262\) −169297. + 5423.26i −0.152369 + 0.00488098i
\(263\) 1.68934e6 1.50601 0.753004 0.658016i \(-0.228604\pi\)
0.753004 + 0.658016i \(0.228604\pi\)
\(264\) 0 0
\(265\) 280695. 0.245539
\(266\) 2.41670e6 77416.6i 2.09420 0.0670857i
\(267\) 0 0
\(268\) −25408.3 396176.i −0.0216092 0.336939i
\(269\) 930054.i 0.783660i 0.920038 + 0.391830i \(0.128158\pi\)
−0.920038 + 0.391830i \(0.871842\pi\)
\(270\) 0 0
\(271\) 2.01579e6i 1.66733i −0.552272 0.833664i \(-0.686239\pi\)
0.552272 0.833664i \(-0.313761\pi\)
\(272\) 182628. + 1.41795e6i 0.149674 + 1.16209i
\(273\) 0 0
\(274\) −30979.9 967093.i −0.0249289 0.778201i
\(275\) −582959. −0.464843
\(276\) 0 0
\(277\) −2.46037e6 −1.92664 −0.963320 0.268354i \(-0.913520\pi\)
−0.963320 + 0.268354i \(0.913520\pi\)
\(278\) −47804.8 1.49231e6i −0.0370987 1.15810i
\(279\) 0 0
\(280\) 2.97782e6 286960.i 2.26988 0.218739i
\(281\) 1.20772e6i 0.912433i 0.889869 + 0.456217i \(0.150796\pi\)
−0.889869 + 0.456217i \(0.849204\pi\)
\(282\) 0 0
\(283\) 516965.i 0.383703i 0.981424 + 0.191852i \(0.0614492\pi\)
−0.981424 + 0.191852i \(0.938551\pi\)
\(284\) 207683. 13319.5i 0.152794 0.00979927i
\(285\) 0 0
\(286\) 1.32933e6 42583.9i 0.960988 0.0307843i
\(287\) 2.08285e6 1.49264
\(288\) 0 0
\(289\) −529388. −0.372846
\(290\) 2.69666e6 86384.9i 1.88292 0.0603175i
\(291\) 0 0
\(292\) −1.46423e6 + 93906.5i −1.00496 + 0.0644523i
\(293\) 2.06534e6i 1.40547i −0.711451 0.702736i \(-0.751962\pi\)
0.711451 0.702736i \(-0.248038\pi\)
\(294\) 0 0
\(295\) 1.73892e6i 1.16338i
\(296\) −2.32972e6 + 224506.i −1.54552 + 0.148936i
\(297\) 0 0
\(298\) −8630.88 269428.i −0.00563008 0.175753i
\(299\) 886169. 0.573243
\(300\) 0 0
\(301\) −2.54361e6 −1.61821
\(302\) −63588.0 1.98501e6i −0.0401197 1.25241i
\(303\) 0 0
\(304\) 234053. + 1.81721e6i 0.145255 + 1.12777i
\(305\) 620481.i 0.381926i
\(306\) 0 0
\(307\) 443153.i 0.268354i 0.990957 + 0.134177i \(0.0428390\pi\)
−0.990957 + 0.134177i \(0.957161\pi\)
\(308\) −171708. 2.67733e6i −0.103137 1.60814i
\(309\) 0 0
\(310\) 912993. 29246.9i 0.539589 0.0172852i
\(311\) 1.59260e6 0.933696 0.466848 0.884338i \(-0.345390\pi\)
0.466848 + 0.884338i \(0.345390\pi\)
\(312\) 0 0
\(313\) −230766. −0.133141 −0.0665703 0.997782i \(-0.521206\pi\)
−0.0665703 + 0.997782i \(0.521206\pi\)
\(314\) 1.61600e6 51767.2i 0.924950 0.0296299i
\(315\) 0 0
\(316\) 76707.0 + 1.19604e6i 0.0432133 + 0.673798i
\(317\) 1.84281e6i 1.02999i 0.857193 + 0.514995i \(0.172206\pi\)
−0.857193 + 0.514995i \(0.827794\pi\)
\(318\) 0 0
\(319\) 2.41956e6i 1.33125i
\(320\) 432891. + 2.22522e6i 0.236322 + 1.21478i
\(321\) 0 0
\(322\) −57232.6 1.78662e6i −0.0307612 0.960266i
\(323\) −2.49811e6 −1.33231
\(324\) 0 0
\(325\) −1.11279e6 −0.584394
\(326\) 23358.7 + 729183.i 0.0121732 + 0.380008i
\(327\) 0 0
\(328\) 151394. + 1.57103e6i 0.0777007 + 0.806308i
\(329\) 952857.i 0.485331i
\(330\) 0 0
\(331\) 2.00465e6i 1.00570i −0.864374 0.502850i \(-0.832285\pi\)
0.864374 0.502850i \(-0.167715\pi\)
\(332\) −1.55500e6 + 99728.5i −0.774259 + 0.0496563i
\(333\) 0 0
\(334\) −3.16521e6 + 101395.i −1.55252 + 0.0497335i
\(335\) 858259. 0.417836
\(336\) 0 0
\(337\) −1.11878e6 −0.536623 −0.268311 0.963332i \(-0.586466\pi\)
−0.268311 + 0.963332i \(0.586466\pi\)
\(338\) 438244. 14038.7i 0.208653 0.00668400i
\(339\) 0 0
\(340\) −3.08447e6 + 197819.i −1.44705 + 0.0928051i
\(341\) 819178.i 0.381498i
\(342\) 0 0
\(343\) 5.60249e6i 2.57126i
\(344\) −184885. 1.91857e6i −0.0842373 0.874140i
\(345\) 0 0
\(346\) 94802.2 + 2.95942e6i 0.0425724 + 1.32897i
\(347\) 351285. 0.156616 0.0783080 0.996929i \(-0.475048\pi\)
0.0783080 + 0.996929i \(0.475048\pi\)
\(348\) 0 0
\(349\) 1.58849e6 0.698105 0.349053 0.937103i \(-0.386503\pi\)
0.349053 + 0.937103i \(0.386503\pi\)
\(350\) 71868.9 + 2.24351e6i 0.0313596 + 0.978946i
\(351\) 0 0
\(352\) 2.00695e6 324118.i 0.863335 0.139427i
\(353\) 1.88702e6i 0.806010i 0.915198 + 0.403005i \(0.132034\pi\)
−0.915198 + 0.403005i \(0.867966\pi\)
\(354\) 0 0
\(355\) 449916.i 0.189479i
\(356\) −16252.6 253416.i −0.00679669 0.105976i
\(357\) 0 0
\(358\) 4.04427e6 129554.i 1.66775 0.0534250i
\(359\) −2.13280e6 −0.873400 −0.436700 0.899607i \(-0.643853\pi\)
−0.436700 + 0.899607i \(0.643853\pi\)
\(360\) 0 0
\(361\) −725432. −0.292974
\(362\) 1.62190e6 51956.0i 0.650507 0.0208384i
\(363\) 0 0
\(364\) −327767. 5.11067e6i −0.129662 2.02174i
\(365\) 3.17204e6i 1.24625i
\(366\) 0 0
\(367\) 1.63065e6i 0.631970i 0.948764 + 0.315985i \(0.102335\pi\)
−0.948764 + 0.315985i \(0.897665\pi\)
\(368\) 1.34343e6 173031.i 0.517125 0.0666045i
\(369\) 0 0
\(370\) −162009. 5.05741e6i −0.0615228 1.92054i
\(371\) −969251. −0.365596
\(372\) 0 0
\(373\) 3.06922e6 1.14224 0.571118 0.820868i \(-0.306510\pi\)
0.571118 + 0.820868i \(0.306510\pi\)
\(374\) 88746.2 + 2.77037e6i 0.0328073 + 1.02414i
\(375\) 0 0
\(376\) −718712. + 69259.4i −0.262171 + 0.0252644i
\(377\) 4.61863e6i 1.67363i
\(378\) 0 0
\(379\) 2.56651e6i 0.917792i −0.888490 0.458896i \(-0.848245\pi\)
0.888490 0.458896i \(-0.151755\pi\)
\(380\) −3.95300e6 + 253521.i −1.40433 + 0.0900649i
\(381\) 0 0
\(382\) −689382. + 22083.7i −0.241714 + 0.00774307i
\(383\) 3.73053e6 1.29949 0.649745 0.760152i \(-0.274876\pi\)
0.649745 + 0.760152i \(0.274876\pi\)
\(384\) 0 0
\(385\) 5.80006e6 1.99425
\(386\) 1.34344e6 43035.9i 0.458934 0.0147015i
\(387\) 0 0
\(388\) 1.80737e6 115913.i 0.609490 0.0390890i
\(389\) 3.32039e6i 1.11254i −0.831002 0.556270i \(-0.812232\pi\)
0.831002 0.556270i \(-0.187768\pi\)
\(390\) 0 0
\(391\) 1.84681e6i 0.610913i
\(392\) −7.25415e6 + 699054.i −2.38436 + 0.229771i
\(393\) 0 0
\(394\) 120943. + 3.77545e6i 0.0392501 + 1.22526i
\(395\) −2.59106e6 −0.835574
\(396\) 0 0
\(397\) 2.24589e6 0.715173 0.357587 0.933880i \(-0.383600\pi\)
0.357587 + 0.933880i \(0.383600\pi\)
\(398\) 41747.3 + 1.30321e6i 0.0132105 + 0.412390i
\(399\) 0 0
\(400\) −1.68699e6 + 217281.i −0.527185 + 0.0679002i
\(401\) 4.54280e6i 1.41079i 0.708814 + 0.705395i \(0.249230\pi\)
−0.708814 + 0.705395i \(0.750770\pi\)
\(402\) 0 0
\(403\) 1.56370e6i 0.479614i
\(404\) −149274. 2.32753e6i −0.0455019 0.709483i
\(405\) 0 0
\(406\) −9.31167e6 + 298291.i −2.80358 + 0.0898100i
\(407\) −4.53773e6 −1.35785
\(408\) 0 0
\(409\) 1.14681e6 0.338986 0.169493 0.985531i \(-0.445787\pi\)
0.169493 + 0.985531i \(0.445787\pi\)
\(410\) −3.41043e6 + 109250.i −1.00196 + 0.0320968i
\(411\) 0 0
\(412\) 199765. + 3.11481e6i 0.0579798 + 0.904043i
\(413\) 6.00455e6i 1.73223i
\(414\) 0 0
\(415\) 3.36870e6i 0.960155i
\(416\) 3.83100e6 618699.i 1.08537 0.175286i
\(417\) 0 0
\(418\) 113735. + 3.55045e6i 0.0318387 + 0.993900i
\(419\) −6.30867e6 −1.75551 −0.877754 0.479112i \(-0.840959\pi\)
−0.877754 + 0.479112i \(0.840959\pi\)
\(420\) 0 0
\(421\) 3.98399e6 1.09550 0.547750 0.836642i \(-0.315484\pi\)
0.547750 + 0.836642i \(0.315484\pi\)
\(422\) −142837. 4.45891e6i −0.0390445 1.21884i
\(423\) 0 0
\(424\) −70451.0 731077.i −0.0190315 0.197492i
\(425\) 2.31910e6i 0.622797i
\(426\) 0 0
\(427\) 2.14255e6i 0.568671i
\(428\) −524930. + 33665.8i −0.138513 + 0.00888341i
\(429\) 0 0
\(430\) 4.16486e6 133417.i 1.08625 0.0347970i
\(431\) 2.55041e6 0.661327 0.330663 0.943749i \(-0.392728\pi\)
0.330663 + 0.943749i \(0.392728\pi\)
\(432\) 0 0
\(433\) 2.49831e6 0.640365 0.320182 0.947356i \(-0.396256\pi\)
0.320182 + 0.947356i \(0.396256\pi\)
\(434\) −3.15260e6 + 100991.i −0.803424 + 0.0257369i
\(435\) 0 0
\(436\) −5.55462e6 + 356240.i −1.39939 + 0.0897483i
\(437\) 2.36683e6i 0.592875i
\(438\) 0 0
\(439\) 3.48279e6i 0.862514i 0.902229 + 0.431257i \(0.141930\pi\)
−0.902229 + 0.431257i \(0.858070\pi\)
\(440\) 421583. + 4.37481e6i 0.103813 + 1.07728i
\(441\) 0 0
\(442\) 169405. + 5.28827e6i 0.0412449 + 1.28753i
\(443\) −5.85754e6 −1.41810 −0.709049 0.705160i \(-0.750875\pi\)
−0.709049 + 0.705160i \(0.750875\pi\)
\(444\) 0 0
\(445\) 548990. 0.131421
\(446\) −257890. 8.05050e6i −0.0613901 1.91640i
\(447\) 0 0
\(448\) −1.49479e6 7.68377e6i −0.351872 1.80875i
\(449\) 208069.i 0.0487071i 0.999703 + 0.0243535i \(0.00775274\pi\)
−0.999703 + 0.0243535i \(0.992247\pi\)
\(450\) 0 0
\(451\) 3.05999e6i 0.708400i
\(452\) 467043. + 7.28230e6i 0.107525 + 1.67657i
\(453\) 0 0
\(454\) −4.04172e6 + 129473.i −0.920295 + 0.0294808i
\(455\) 1.10715e7 2.50715
\(456\) 0 0
\(457\) −15198.4 −0.00340415 −0.00170207 0.999999i \(-0.500542\pi\)
−0.00170207 + 0.999999i \(0.500542\pi\)
\(458\) 3.62118e6 116001.i 0.806652 0.0258404i
\(459\) 0 0
\(460\) 187423. + 2.92237e6i 0.0412980 + 0.643934i
\(461\) 344817.i 0.0755678i −0.999286 0.0377839i \(-0.987970\pi\)
0.999286 0.0377839i \(-0.0120299\pi\)
\(462\) 0 0
\(463\) 60401.9i 0.0130948i −0.999979 0.00654739i \(-0.997916\pi\)
0.999979 0.00654739i \(-0.00208411\pi\)
\(464\) −901820. 7.00183e6i −0.194458 1.50979i
\(465\) 0 0
\(466\) −174845. 5.45810e6i −0.0372982 1.16433i
\(467\) −3.80574e6 −0.807509 −0.403754 0.914867i \(-0.632295\pi\)
−0.403754 + 0.914867i \(0.632295\pi\)
\(468\) 0 0
\(469\) −2.96360e6 −0.622140
\(470\) −49979.3 1.56019e6i −0.0104363 0.325787i
\(471\) 0 0
\(472\) −4.52905e6 + 436446.i −0.935733 + 0.0901729i
\(473\) 3.73690e6i 0.767995i
\(474\) 0 0
\(475\) 2.97211e6i 0.604408i
\(476\) 1.06508e7 683079.i 2.15459 0.138183i
\(477\) 0 0
\(478\) −3.71647e6 + 119054.i −0.743980 + 0.0238327i
\(479\) 4.93357e6 0.982476 0.491238 0.871025i \(-0.336544\pi\)
0.491238 + 0.871025i \(0.336544\pi\)
\(480\) 0 0
\(481\) −8.66194e6 −1.70707
\(482\) −6.14694e6 + 196912.i −1.20515 + 0.0386059i
\(483\) 0 0
\(484\) −1.20971e6 + 77583.6i −0.234730 + 0.0150542i
\(485\) 3.91540e6i 0.755827i
\(486\) 0 0
\(487\) 1.40275e6i 0.268013i −0.990980 0.134007i \(-0.957216\pi\)
0.990980 0.134007i \(-0.0427844\pi\)
\(488\) 1.61606e6 155733.i 0.307191 0.0296027i
\(489\) 0 0
\(490\) −504455. 1.57475e7i −0.0949144 2.96292i
\(491\) 9.21228e6 1.72450 0.862250 0.506483i \(-0.169055\pi\)
0.862250 + 0.506483i \(0.169055\pi\)
\(492\) 0 0
\(493\) 9.62537e6 1.78361
\(494\) 217106. + 6.77734e6i 0.0400271 + 1.24952i
\(495\) 0 0
\(496\) −305324. 2.37057e6i −0.0557259 0.432662i
\(497\) 1.55358e6i 0.282126i
\(498\) 0 0
\(499\) 3.76154e6i 0.676260i 0.941099 + 0.338130i \(0.109794\pi\)
−0.941099 + 0.338130i \(0.890206\pi\)
\(500\) 207424. + 3.23423e6i 0.0371051 + 0.578556i
\(501\) 0 0
\(502\) −291284. + 9331.01i −0.0515890 + 0.00165261i
\(503\) 5.84609e6 1.03026 0.515128 0.857113i \(-0.327744\pi\)
0.515128 + 0.857113i \(0.327744\pi\)
\(504\) 0 0
\(505\) 5.04227e6 0.879827
\(506\) 2.62478e6 84082.3i 0.455739 0.0145992i
\(507\) 0 0
\(508\) 349123. + 5.44366e6i 0.0600232 + 0.935904i
\(509\) 2.06029e6i 0.352480i 0.984347 + 0.176240i \(0.0563934\pi\)
−0.984347 + 0.176240i \(0.943607\pi\)
\(510\) 0 0
\(511\) 1.09532e7i 1.85561i
\(512\) 5.68699e6 1.68598e6i 0.958755 0.284235i
\(513\) 0 0
\(514\) 191756. + 5.98599e6i 0.0320140 + 0.999375i
\(515\) −6.74780e6 −1.12110
\(516\) 0 0
\(517\) −1.39987e6 −0.230337
\(518\) 559425. + 1.74634e7i 0.0916046 + 2.85960i
\(519\) 0 0
\(520\) 804746. + 8.35094e6i 0.130512 + 1.35434i
\(521\) 9.31147e6i 1.50288i −0.659802 0.751439i \(-0.729360\pi\)
0.659802 0.751439i \(-0.270640\pi\)
\(522\) 0 0
\(523\) 6.91429e6i 1.10533i −0.833402 0.552667i \(-0.813610\pi\)
0.833402 0.552667i \(-0.186390\pi\)
\(524\) −956214. + 61325.8i −0.152134 + 0.00975696i
\(525\) 0 0
\(526\) 9.55144e6 305971.i 1.50524 0.0482188i
\(527\) 3.25881e6 0.511131
\(528\) 0 0
\(529\) −4.68659e6 −0.728145
\(530\) 1.58704e6 50839.2i 0.245413 0.00786157i
\(531\) 0 0
\(532\) 1.36499e7 875420.i 2.09098 0.134103i
\(533\) 5.84112e6i 0.890591i
\(534\) 0 0
\(535\) 1.13719e6i 0.171770i
\(536\) −215412. 2.23536e6i −0.0323861 0.336074i
\(537\) 0 0
\(538\) 168451. + 5.25848e6i 0.0250909 + 0.783258i
\(539\) −1.41293e7 −2.09483
\(540\) 0 0
\(541\) −6.91946e6 −1.01643 −0.508217 0.861229i \(-0.669695\pi\)
−0.508217 + 0.861229i \(0.669695\pi\)
\(542\) −365097. 1.13972e7i −0.0533839 1.66647i
\(543\) 0 0
\(544\) 1.28939e6 + 7.98394e6i 0.186804 + 1.15670i
\(545\) 1.20333e7i 1.73538i
\(546\) 0 0
\(547\) 8.94295e6i 1.27795i −0.769229 0.638973i \(-0.779360\pi\)
0.769229 0.638973i \(-0.220640\pi\)
\(548\) −350318. 5.46229e6i −0.0498323 0.777004i
\(549\) 0 0
\(550\) −3.29602e6 + 105585.i −0.464604 + 0.0148832i
\(551\) 1.23357e7 1.73095
\(552\) 0 0
\(553\) 8.94704e6 1.24413
\(554\) −1.39108e7 + 445620.i −1.92565 + 0.0616865i
\(555\) 0 0
\(556\) −540572. 8.42879e6i −0.0741594 1.15632i
\(557\) 3.85092e6i 0.525928i −0.964806 0.262964i \(-0.915300\pi\)
0.964806 0.262964i \(-0.0847000\pi\)
\(558\) 0 0
\(559\) 7.13325e6i 0.965513i
\(560\) 1.67845e7 2.16180e6i 2.26171 0.291303i
\(561\) 0 0
\(562\) 218742. + 6.82841e6i 0.0292140 + 0.911966i
\(563\) 6.40391e6 0.851480 0.425740 0.904846i \(-0.360014\pi\)
0.425740 + 0.904846i \(0.360014\pi\)
\(564\) 0 0
\(565\) −1.57761e7 −2.07911
\(566\) 93632.3 + 2.92290e6i 0.0122853 + 0.383506i
\(567\) 0 0
\(568\) 1.17182e6 112924.i 0.152402 0.0146863i
\(569\) 1.05210e7i 1.36231i 0.732137 + 0.681157i \(0.238523\pi\)
−0.732137 + 0.681157i \(0.761477\pi\)
\(570\) 0 0
\(571\) 1.25121e6i 0.160598i 0.996771 + 0.0802990i \(0.0255875\pi\)
−0.996771 + 0.0802990i \(0.974412\pi\)
\(572\) 7.50826e6 481534.i 0.959509 0.0615371i
\(573\) 0 0
\(574\) 1.17764e7 377244.i 1.49187 0.0477907i
\(575\) −2.19722e6 −0.277143
\(576\) 0 0
\(577\) 578609. 0.0723511 0.0361756 0.999345i \(-0.488482\pi\)
0.0361756 + 0.999345i \(0.488482\pi\)
\(578\) −2.99313e6 + 95882.2i −0.372655 + 0.0119376i
\(579\) 0 0
\(580\) 1.52311e7 976833.i 1.88002 0.120573i
\(581\) 1.16322e7i 1.42963i
\(582\) 0 0
\(583\) 1.42396e6i 0.173511i
\(584\) −8.26165e6 + 796142.i −1.00239 + 0.0965959i
\(585\) 0 0
\(586\) −374072. 1.16773e7i −0.0449999 1.40475i
\(587\) −6.35138e6 −0.760804 −0.380402 0.924821i \(-0.624214\pi\)
−0.380402 + 0.924821i \(0.624214\pi\)
\(588\) 0 0
\(589\) 4.17643e6 0.496040
\(590\) −314951. 9.83175e6i −0.0372488 1.16279i
\(591\) 0 0
\(592\) −1.31315e7 + 1.69130e6i −1.53996 + 0.198343i
\(593\) 1.12494e7i 1.31369i 0.754026 + 0.656845i \(0.228109\pi\)
−0.754026 + 0.656845i \(0.771891\pi\)
\(594\) 0 0
\(595\) 2.30735e7i 2.67190i
\(596\) −97597.2 1.52177e6i −0.0112544 0.175482i
\(597\) 0 0
\(598\) 5.01036e6 160502.i 0.572949 0.0183539i
\(599\) 3.98685e6 0.454007 0.227004 0.973894i \(-0.427107\pi\)
0.227004 + 0.973894i \(0.427107\pi\)
\(600\) 0 0
\(601\) −5.93772e6 −0.670553 −0.335277 0.942120i \(-0.608830\pi\)
−0.335277 + 0.942120i \(0.608830\pi\)
\(602\) −1.43814e7 + 460696.i −1.61738 + 0.0518111i
\(603\) 0 0
\(604\) −719047. 1.12116e7i −0.0801982 1.25048i
\(605\) 2.62067e6i 0.291088i
\(606\) 0 0
\(607\) 7.86463e6i 0.866376i −0.901304 0.433188i \(-0.857389\pi\)
0.901304 0.433188i \(-0.142611\pi\)
\(608\) 1.65246e6 + 1.02321e7i 0.181289 + 1.12255i
\(609\) 0 0
\(610\) 112381. + 3.50817e6i 0.0122284 + 0.381730i
\(611\) −2.67218e6 −0.289576
\(612\) 0 0
\(613\) −6.66739e6 −0.716646 −0.358323 0.933598i \(-0.616651\pi\)
−0.358323 + 0.933598i \(0.616651\pi\)
\(614\) 80263.4 + 2.50556e6i 0.00859205 + 0.268216i
\(615\) 0 0
\(616\) −1.45574e6 1.51064e7i −0.154573 1.60402i
\(617\) 1.13568e7i 1.20100i 0.799627 + 0.600498i \(0.205031\pi\)
−0.799627 + 0.600498i \(0.794969\pi\)
\(618\) 0 0
\(619\) 5.72429e6i 0.600475i −0.953864 0.300237i \(-0.902934\pi\)
0.953864 0.300237i \(-0.0970659\pi\)
\(620\) 5.15672e6 330721.i 0.538759 0.0345527i
\(621\) 0 0
\(622\) 9.00448e6 288450.i 0.933217 0.0298947i
\(623\) −1.89569e6 −0.195680
\(624\) 0 0
\(625\) −1.21973e7 −1.24901
\(626\) −1.30474e6 + 41796.1i −0.133072 + 0.00426285i
\(627\) 0 0
\(628\) 9.12743e6 585378.i 0.923527 0.0592294i
\(629\) 1.80518e7i 1.81925i
\(630\) 0 0
\(631\) 1.24837e7i 1.24816i 0.781360 + 0.624080i \(0.214526\pi\)
−0.781360 + 0.624080i \(0.785474\pi\)
\(632\) 650325. + 6.74849e6i 0.0647646 + 0.672069i
\(633\) 0 0
\(634\) 333769. + 1.04192e7i 0.0329779 + 1.02946i
\(635\) −1.17929e7 −1.16061
\(636\) 0 0
\(637\) −2.69710e7 −2.63359
\(638\) −438229. 1.36801e7i −0.0426235 1.33057i
\(639\) 0 0
\(640\) 2.85058e6 + 1.25029e7i 0.275095 + 1.20659i
\(641\) 1.81736e7i 1.74702i −0.486810 0.873508i \(-0.661840\pi\)
0.486810 0.873508i \(-0.338160\pi\)
\(642\) 0 0
\(643\) 5.93003e6i 0.565626i 0.959175 + 0.282813i \(0.0912676\pi\)
−0.959175 + 0.282813i \(0.908732\pi\)
\(644\) −647181. 1.00911e7i −0.0614909 0.958789i
\(645\) 0 0
\(646\) −1.41242e7 + 452456.i −1.33163 + 0.0426575i
\(647\) −1.54374e7 −1.44982 −0.724909 0.688844i \(-0.758118\pi\)
−0.724909 + 0.688844i \(0.758118\pi\)
\(648\) 0 0
\(649\) −8.82148e6 −0.822110
\(650\) −6.29168e6 + 201548.i −0.584094 + 0.0187109i
\(651\) 0 0
\(652\) 264138. + 4.11854e6i 0.0243339 + 0.379423i
\(653\) 1.88052e7i 1.72582i −0.505357 0.862910i \(-0.668639\pi\)
0.505357 0.862910i \(-0.331361\pi\)
\(654\) 0 0
\(655\) 2.07150e6i 0.188661i
\(656\) 1.14052e6 + 8.85513e6i 0.103477 + 0.803407i
\(657\) 0 0
\(658\) 172581. + 5.38741e6i 0.0155392 + 0.485082i
\(659\) −1.30752e7 −1.17283 −0.586416 0.810010i \(-0.699461\pi\)
−0.586416 + 0.810010i \(0.699461\pi\)
\(660\) 0 0
\(661\) 1.29277e7 1.15085 0.575424 0.817855i \(-0.304837\pi\)
0.575424 + 0.817855i \(0.304837\pi\)
\(662\) −363080. 1.13342e7i −0.0322001 1.00518i
\(663\) 0 0
\(664\) −8.77385e6 + 845501.i −0.772272 + 0.0744208i
\(665\) 2.95705e7i 2.59301i
\(666\) 0 0
\(667\) 9.11953e6i 0.793703i
\(668\) −1.78776e7 + 1.14656e6i −1.55013 + 0.0994159i
\(669\) 0 0
\(670\) 4.85256e6 155447.i 0.417622 0.0133781i
\(671\) 3.14769e6 0.269889
\(672\) 0 0
\(673\) −2.11203e6 −0.179748 −0.0898738 0.995953i \(-0.528646\pi\)
−0.0898738 + 0.995953i \(0.528646\pi\)
\(674\) −6.32552e6 + 202632.i −0.536348 + 0.0171814i
\(675\) 0 0
\(676\) 2.47527e6 158749.i 0.208332 0.0133611i
\(677\) 1.57270e6i 0.131878i −0.997824 0.0659391i \(-0.978996\pi\)
0.997824 0.0659391i \(-0.0210043\pi\)
\(678\) 0 0
\(679\) 1.35200e7i 1.12539i
\(680\) −1.74036e7 + 1.67712e6i −1.44334 + 0.139089i
\(681\) 0 0
\(682\) −148369. 4.63159e6i −0.0122147 0.381302i
\(683\) 990320. 0.0812314 0.0406157 0.999175i \(-0.487068\pi\)
0.0406157 + 0.999175i \(0.487068\pi\)
\(684\) 0 0
\(685\) 1.18333e7 0.963559
\(686\) 1.01472e6 + 3.16762e7i 0.0823256 + 2.56994i
\(687\) 0 0
\(688\) −1.39282e6 1.08140e7i −0.112182 0.870994i
\(689\) 2.71815e6i 0.218135i
\(690\) 0 0
\(691\) 3.19912e6i 0.254880i −0.991846 0.127440i \(-0.959324\pi\)
0.991846 0.127440i \(-0.0406760\pi\)
\(692\) 1.07201e6 + 1.67152e7i 0.0851011 + 1.32693i
\(693\) 0 0
\(694\) 1.98615e6 63624.4i 0.156536 0.00501447i
\(695\) 1.82598e7 1.43395
\(696\) 0 0
\(697\) −1.21731e7 −0.949115
\(698\) 8.98125e6 287706.i 0.697747 0.0223517i
\(699\) 0 0
\(700\) 812687. + 1.26717e7i 0.0626871 + 0.977440i
\(701\) 1.09808e7i 0.843993i −0.906597 0.421996i \(-0.861329\pi\)
0.906597 0.421996i \(-0.138671\pi\)
\(702\) 0 0
\(703\) 2.31348e7i 1.76554i
\(704\) 1.12885e7 2.19605e6i 0.858429 0.166997i
\(705\) 0 0
\(706\) 341776. + 1.06691e7i 0.0258066 + 0.805597i
\(707\) −1.74111e7 −1.31002
\(708\) 0 0
\(709\) 2.37875e7 1.77719 0.888594 0.458694i \(-0.151683\pi\)
0.888594 + 0.458694i \(0.151683\pi\)
\(710\) 81488.5 + 2.54381e6i 0.00606667 + 0.189382i
\(711\) 0 0
\(712\) −137790. 1.42986e6i −0.0101863 0.105704i
\(713\) 3.08755e6i 0.227452i
\(714\) 0 0
\(715\) 1.62656e7i 1.18988i
\(716\) 2.28426e7 1.46499e6i 1.66519 0.106795i
\(717\) 0 0
\(718\) −1.20587e7 + 386290.i −0.872952 + 0.0279642i
\(719\) 1.91638e7 1.38248 0.691239 0.722626i \(-0.257065\pi\)
0.691239 + 0.722626i \(0.257065\pi\)
\(720\) 0 0
\(721\) 2.33004e7 1.66927
\(722\) −4.10156e6 + 131390.i −0.292824 + 0.00938033i
\(723\) 0 0
\(724\) 9.16073e6 587513.i 0.649506 0.0416554i
\(725\) 1.14517e7i 0.809143i
\(726\) 0 0
\(727\) 977419.i 0.0685874i 0.999412 + 0.0342937i \(0.0109182\pi\)
−0.999412 + 0.0342937i \(0.989082\pi\)
\(728\) −2.77882e6 2.88361e7i −0.194327 2.01655i
\(729\) 0 0
\(730\) −574517. 1.79346e7i −0.0399021 1.24561i
\(731\) 1.48659e7 1.02896
\(732\) 0 0
\(733\) 1.68872e6 0.116091 0.0580455 0.998314i \(-0.481513\pi\)
0.0580455 + 0.998314i \(0.481513\pi\)
\(734\) 295343. + 9.21964e6i 0.0202342 + 0.631646i
\(735\) 0 0
\(736\) 7.56436e6 1.22163e6i 0.514728 0.0831275i
\(737\) 4.35393e6i 0.295265i
\(738\) 0 0
\(739\) 5.82227e6i 0.392176i 0.980586 + 0.196088i \(0.0628238\pi\)
−0.980586 + 0.196088i \(0.937176\pi\)
\(740\) −1.83199e6 2.85650e7i −0.122982 1.91759i
\(741\) 0 0
\(742\) −5.48010e6 + 175550.i −0.365409 + 0.0117055i
\(743\) −4.95294e6 −0.329148 −0.164574 0.986365i \(-0.552625\pi\)
−0.164574 + 0.986365i \(0.552625\pi\)
\(744\) 0 0
\(745\) 3.29670e6 0.217615
\(746\) 1.73532e7 555895.i 1.14165 0.0365717i
\(747\) 0 0
\(748\) 1.00353e6 + 1.56475e7i 0.0655810 + 1.02256i
\(749\) 3.92675e6i 0.255758i
\(750\) 0 0
\(751\) 1.06174e7i 0.686940i 0.939164 + 0.343470i \(0.111602\pi\)
−0.939164 + 0.343470i \(0.888398\pi\)
\(752\) −4.05102e6 + 521762.i −0.261228 + 0.0336456i
\(753\) 0 0
\(754\) −836522. 2.61135e7i −0.0535857 1.67277i
\(755\) 2.42884e7 1.55072
\(756\) 0 0
\(757\) −4.59623e6 −0.291516 −0.145758 0.989320i \(-0.546562\pi\)
−0.145758 + 0.989320i \(0.546562\pi\)
\(758\) −464843. 1.45109e7i −0.0293855 0.917322i
\(759\) 0 0
\(760\) −2.23042e7 + 2.14936e6i −1.40072 + 0.134982i
\(761\) 2.15027e7i 1.34596i 0.739661 + 0.672979i \(0.234986\pi\)
−0.739661 + 0.672979i \(0.765014\pi\)
\(762\) 0 0
\(763\) 4.15515e7i 2.58390i
\(764\) −3.89373e6 + 249720.i −0.241342 + 0.0154782i
\(765\) 0 0
\(766\) 2.10922e7 675670.i 1.29882 0.0416066i
\(767\) −1.68391e7 −1.03354
\(768\) 0 0
\(769\) 2.82987e7 1.72564 0.862821 0.505510i \(-0.168696\pi\)
0.862821 + 0.505510i \(0.168696\pi\)
\(770\) 3.27932e7 1.05050e6i 1.99323 0.0638513i
\(771\) 0 0
\(772\) 7.58796e6 486646.i 0.458228 0.0293880i
\(773\) 1.93324e6i 0.116369i −0.998306 0.0581845i \(-0.981469\pi\)
0.998306 0.0581845i \(-0.0185312\pi\)
\(774\) 0 0
\(775\) 3.87714e6i 0.231877i
\(776\) 1.01978e7 982718.i 0.607926 0.0585834i
\(777\) 0 0
\(778\) −601387. 1.87733e7i −0.0356209 1.11197i
\(779\) −1.56008e7 −0.921092
\(780\) 0 0
\(781\) 2.28242e6 0.133896
\(782\) 334492. + 1.04418e7i 0.0195600 + 0.610600i
\(783\) 0 0
\(784\) −4.08880e7 + 5.26628e6i −2.37578 + 0.305995i
\(785\) 1.97733e7i 1.14526i
\(786\) 0 0
\(787\) 7.01512e6i