Properties

Label 33.5.c.a.10.8
Level $33$
Weight $5$
Character 33.10
Analytic conductor $3.411$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 33.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.41120878177\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 102 x^{6} + 2913 x^{4} + 23292 x^{2} + 41364\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 10.8
Root \(7.70102i\) of defining polynomial
Character \(\chi\) \(=\) 33.10
Dual form 33.5.c.a.10.1

$q$-expansion

\(f(q)\) \(=\) \(q+7.70102i q^{2} +5.19615 q^{3} -43.3057 q^{4} -12.5296 q^{5} +40.0157i q^{6} +63.6540i q^{7} -210.281i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q+7.70102i q^{2} +5.19615 q^{3} -43.3057 q^{4} -12.5296 q^{5} +40.0157i q^{6} +63.6540i q^{7} -210.281i q^{8} +27.0000 q^{9} -96.4909i q^{10} +(119.745 - 17.3819i) q^{11} -225.023 q^{12} +194.814i q^{13} -490.200 q^{14} -65.1059 q^{15} +926.491 q^{16} +108.192i q^{17} +207.927i q^{18} -69.0344i q^{19} +542.604 q^{20} +330.756i q^{21} +(133.858 + 922.159i) q^{22} +576.600 q^{23} -1092.65i q^{24} -468.008 q^{25} -1500.26 q^{26} +140.296 q^{27} -2756.58i q^{28} -382.039i q^{29} -501.381i q^{30} -36.6327 q^{31} +3770.42i q^{32} +(622.213 - 90.3190i) q^{33} -833.186 q^{34} -797.560i q^{35} -1169.25 q^{36} +1791.57 q^{37} +531.635 q^{38} +1012.28i q^{39} +2634.75i q^{40} -2882.25i q^{41} -2547.16 q^{42} -319.351i q^{43} +(-5185.64 + 752.735i) q^{44} -338.300 q^{45} +4440.41i q^{46} +2299.80 q^{47} +4814.19 q^{48} -1650.83 q^{49} -3604.14i q^{50} +562.181i q^{51} -8436.53i q^{52} +857.015 q^{53} +1080.42i q^{54} +(-1500.36 + 217.789i) q^{55} +13385.2 q^{56} -358.713i q^{57} +2942.09 q^{58} -2149.26 q^{59} +2819.45 q^{60} +4966.14i q^{61} -282.109i q^{62} +1718.66i q^{63} -14212.2 q^{64} -2440.94i q^{65} +(695.548 + 4791.68i) q^{66} -5369.49 q^{67} -4685.32i q^{68} +2996.10 q^{69} +6142.03 q^{70} -4954.38 q^{71} -5677.60i q^{72} +3583.14i q^{73} +13796.9i q^{74} -2431.84 q^{75} +2989.58i q^{76} +(1106.43 + 7622.24i) q^{77} -7795.59 q^{78} -7143.06i q^{79} -11608.6 q^{80} +729.000 q^{81} +22196.2 q^{82} +156.911i q^{83} -14323.6i q^{84} -1355.60i q^{85} +2459.33 q^{86} -1985.14i q^{87} +(-3655.09 - 25180.2i) q^{88} +7181.21 q^{89} -2605.25i q^{90} -12400.7 q^{91} -24970.1 q^{92} -190.349 q^{93} +17710.8i q^{94} +864.975i q^{95} +19591.7i q^{96} +2419.65 q^{97} -12713.0i q^{98} +(3233.12 - 469.311i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 76q^{4} - 36q^{5} + 216q^{9} + O(q^{10}) \) \( 8q - 76q^{4} - 36q^{5} + 216q^{9} + 36q^{11} - 360q^{12} - 1140q^{14} + 108q^{15} + 1412q^{16} + 2532q^{20} - 780q^{22} + 516q^{23} - 2280q^{25} - 1524q^{26} + 2752q^{31} + 1008q^{33} - 4920q^{34} - 2052q^{36} + 5296q^{37} + 696q^{38} - 4356q^{42} - 6540q^{44} - 972q^{45} + 420q^{47} + 9936q^{48} - 6832q^{49} + 3540q^{53} + 3784q^{55} + 17964q^{56} + 21624q^{58} - 16632q^{59} - 612q^{60} - 27508q^{64} + 360q^{66} - 3656q^{67} + 9036q^{69} + 3312q^{70} - 13212q^{71} - 9288q^{75} + 23268q^{77} - 13140q^{78} - 4476q^{80} + 5832q^{81} + 17088q^{82} + 19896q^{86} - 12516q^{88} + 15528q^{89} - 19752q^{91} - 81180q^{92} - 21384q^{93} + 7624q^{97} + 972q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.70102i 1.92525i 0.270830 + 0.962627i \(0.412702\pi\)
−0.270830 + 0.962627i \(0.587298\pi\)
\(3\) 5.19615 0.577350
\(4\) −43.3057 −2.70660
\(5\) −12.5296 −0.501185 −0.250593 0.968093i \(-0.580625\pi\)
−0.250593 + 0.968093i \(0.580625\pi\)
\(6\) 40.0157i 1.11155i
\(7\) 63.6540i 1.29906i 0.760336 + 0.649530i \(0.225034\pi\)
−0.760336 + 0.649530i \(0.774966\pi\)
\(8\) 210.281i 3.28565i
\(9\) 27.0000 0.333333
\(10\) 96.4909i 0.964909i
\(11\) 119.745 17.3819i 0.989628 0.143652i
\(12\) −225.023 −1.56266
\(13\) 194.814i 1.15274i 0.817188 + 0.576371i \(0.195532\pi\)
−0.817188 + 0.576371i \(0.804468\pi\)
\(14\) −490.200 −2.50102
\(15\) −65.1059 −0.289359
\(16\) 926.491 3.61910
\(17\) 108.192i 0.374366i 0.982325 + 0.187183i \(0.0599357\pi\)
−0.982325 + 0.187183i \(0.940064\pi\)
\(18\) 207.927i 0.641751i
\(19\) 69.0344i 0.191231i −0.995418 0.0956155i \(-0.969518\pi\)
0.995418 0.0956155i \(-0.0304819\pi\)
\(20\) 542.604 1.35651
\(21\) 330.756i 0.750013i
\(22\) 133.858 + 922.159i 0.276567 + 1.90529i
\(23\) 576.600 1.08998 0.544991 0.838442i \(-0.316533\pi\)
0.544991 + 0.838442i \(0.316533\pi\)
\(24\) 1092.65i 1.89697i
\(25\) −468.008 −0.748813
\(26\) −1500.26 −2.21932
\(27\) 140.296 0.192450
\(28\) 2756.58i 3.51604i
\(29\) 382.039i 0.454268i −0.973864 0.227134i \(-0.927064\pi\)
0.973864 0.227134i \(-0.0729356\pi\)
\(30\) 501.381i 0.557090i
\(31\) −36.6327 −0.0381193 −0.0190597 0.999818i \(-0.506067\pi\)
−0.0190597 + 0.999818i \(0.506067\pi\)
\(32\) 3770.42i 3.68205i
\(33\) 622.213 90.3190i 0.571362 0.0829376i
\(34\) −833.186 −0.720749
\(35\) 797.560i 0.651070i
\(36\) −1169.25 −0.902202
\(37\) 1791.57 1.30867 0.654334 0.756205i \(-0.272949\pi\)
0.654334 + 0.756205i \(0.272949\pi\)
\(38\) 531.635 0.368168
\(39\) 1012.28i 0.665536i
\(40\) 2634.75i 1.64672i
\(41\) 2882.25i 1.71460i −0.514815 0.857301i \(-0.672139\pi\)
0.514815 0.857301i \(-0.327861\pi\)
\(42\) −2547.16 −1.44397
\(43\) 319.351i 0.172716i −0.996264 0.0863579i \(-0.972477\pi\)
0.996264 0.0863579i \(-0.0275228\pi\)
\(44\) −5185.64 + 752.735i −2.67853 + 0.388809i
\(45\) −338.300 −0.167062
\(46\) 4440.41i 2.09849i
\(47\) 2299.80 1.04110 0.520552 0.853830i \(-0.325726\pi\)
0.520552 + 0.853830i \(0.325726\pi\)
\(48\) 4814.19 2.08949
\(49\) −1650.83 −0.687558
\(50\) 3604.14i 1.44166i
\(51\) 562.181i 0.216140i
\(52\) 8436.53i 3.12002i
\(53\) 857.015 0.305096 0.152548 0.988296i \(-0.451252\pi\)
0.152548 + 0.988296i \(0.451252\pi\)
\(54\) 1080.42i 0.370515i
\(55\) −1500.36 + 217.789i −0.495987 + 0.0719963i
\(56\) 13385.2 4.26826
\(57\) 358.713i 0.110407i
\(58\) 2942.09 0.874582
\(59\) −2149.26 −0.617427 −0.308714 0.951155i \(-0.599898\pi\)
−0.308714 + 0.951155i \(0.599898\pi\)
\(60\) 2819.45 0.783182
\(61\) 4966.14i 1.33462i 0.744778 + 0.667312i \(0.232555\pi\)
−0.744778 + 0.667312i \(0.767445\pi\)
\(62\) 282.109i 0.0733894i
\(63\) 1718.66i 0.433020i
\(64\) −14212.2 −3.46978
\(65\) 2440.94i 0.577738i
\(66\) 695.548 + 4791.68i 0.159676 + 1.10002i
\(67\) −5369.49 −1.19614 −0.598072 0.801443i \(-0.704066\pi\)
−0.598072 + 0.801443i \(0.704066\pi\)
\(68\) 4685.32i 1.01326i
\(69\) 2996.10 0.629301
\(70\) 6142.03 1.25347
\(71\) −4954.38 −0.982817 −0.491408 0.870929i \(-0.663518\pi\)
−0.491408 + 0.870929i \(0.663518\pi\)
\(72\) 5677.60i 1.09522i
\(73\) 3583.14i 0.672386i 0.941793 + 0.336193i \(0.109139\pi\)
−0.941793 + 0.336193i \(0.890861\pi\)
\(74\) 13796.9i 2.51952i
\(75\) −2431.84 −0.432328
\(76\) 2989.58i 0.517587i
\(77\) 1106.43 + 7622.24i 0.186613 + 1.28559i
\(78\) −7795.59 −1.28133
\(79\) 7143.06i 1.14454i −0.820066 0.572269i \(-0.806063\pi\)
0.820066 0.572269i \(-0.193937\pi\)
\(80\) −11608.6 −1.81384
\(81\) 729.000 0.111111
\(82\) 22196.2 3.30105
\(83\) 156.911i 0.0227771i 0.999935 + 0.0113885i \(0.00362516\pi\)
−0.999935 + 0.0113885i \(0.996375\pi\)
\(84\) 14323.6i 2.02999i
\(85\) 1355.60i 0.187627i
\(86\) 2459.33 0.332522
\(87\) 1985.14i 0.262272i
\(88\) −3655.09 25180.2i −0.471990 3.25157i
\(89\) 7181.21 0.906604 0.453302 0.891357i \(-0.350246\pi\)
0.453302 + 0.891357i \(0.350246\pi\)
\(90\) 2605.25i 0.321636i
\(91\) −12400.7 −1.49748
\(92\) −24970.1 −2.95015
\(93\) −190.349 −0.0220082
\(94\) 17710.8i 2.00439i
\(95\) 864.975i 0.0958421i
\(96\) 19591.7i 2.12583i
\(97\) 2419.65 0.257164 0.128582 0.991699i \(-0.458958\pi\)
0.128582 + 0.991699i \(0.458958\pi\)
\(98\) 12713.0i 1.32372i
\(99\) 3233.12 469.311i 0.329876 0.0478840i
\(100\) 20267.4 2.02674
\(101\) 3839.47i 0.376381i 0.982133 + 0.188191i \(0.0602623\pi\)
−0.982133 + 0.188191i \(0.939738\pi\)
\(102\) −4329.36 −0.416125
\(103\) −6804.82 −0.641420 −0.320710 0.947177i \(-0.603921\pi\)
−0.320710 + 0.947177i \(0.603921\pi\)
\(104\) 40965.7 3.78751
\(105\) 4144.25i 0.375895i
\(106\) 6599.89i 0.587388i
\(107\) 5960.40i 0.520604i 0.965527 + 0.260302i \(0.0838222\pi\)
−0.965527 + 0.260302i \(0.916178\pi\)
\(108\) −6075.62 −0.520886
\(109\) 21808.4i 1.83557i −0.397080 0.917784i \(-0.629976\pi\)
0.397080 0.917784i \(-0.370024\pi\)
\(110\) −1677.20 11554.3i −0.138611 0.954901i
\(111\) 9309.26 0.755560
\(112\) 58974.8i 4.70144i
\(113\) 2293.56 0.179619 0.0898097 0.995959i \(-0.471374\pi\)
0.0898097 + 0.995959i \(0.471374\pi\)
\(114\) 2762.46 0.212562
\(115\) −7224.59 −0.546283
\(116\) 16544.5i 1.22952i
\(117\) 5259.96i 0.384248i
\(118\) 16551.5i 1.18870i
\(119\) −6886.83 −0.486324
\(120\) 13690.6i 0.950733i
\(121\) 14036.7 4162.79i 0.958728 0.284324i
\(122\) −38244.3 −2.56949
\(123\) 14976.6i 0.989926i
\(124\) 1586.40 0.103174
\(125\) 13695.0 0.876479
\(126\) −13235.4 −0.833674
\(127\) 8755.61i 0.542849i −0.962460 0.271424i \(-0.912505\pi\)
0.962460 0.271424i \(-0.0874947\pi\)
\(128\) 49121.7i 2.99815i
\(129\) 1659.40i 0.0997175i
\(130\) 18797.7 1.11229
\(131\) 13196.5i 0.768981i −0.923129 0.384490i \(-0.874377\pi\)
0.923129 0.384490i \(-0.125623\pi\)
\(132\) −26945.4 + 3911.33i −1.54645 + 0.224479i
\(133\) 4394.31 0.248421
\(134\) 41350.5i 2.30288i
\(135\) −1757.86 −0.0964531
\(136\) 22750.7 1.23003
\(137\) −2034.69 −0.108407 −0.0542034 0.998530i \(-0.517262\pi\)
−0.0542034 + 0.998530i \(0.517262\pi\)
\(138\) 23073.0i 1.21157i
\(139\) 24766.1i 1.28183i 0.767614 + 0.640913i \(0.221444\pi\)
−0.767614 + 0.640913i \(0.778556\pi\)
\(140\) 34538.9i 1.76219i
\(141\) 11950.1 0.601082
\(142\) 38153.8i 1.89217i
\(143\) 3386.23 + 23327.9i 0.165594 + 1.14079i
\(144\) 25015.3 1.20637
\(145\) 4786.81i 0.227672i
\(146\) −27593.9 −1.29451
\(147\) −8577.94 −0.396962
\(148\) −77585.0 −3.54205
\(149\) 20475.5i 0.922277i 0.887328 + 0.461138i \(0.152559\pi\)
−0.887328 + 0.461138i \(0.847441\pi\)
\(150\) 18727.7i 0.832341i
\(151\) 17123.5i 0.750996i 0.926823 + 0.375498i \(0.122528\pi\)
−0.926823 + 0.375498i \(0.877472\pi\)
\(152\) −14516.7 −0.628318
\(153\) 2921.18i 0.124789i
\(154\) −58699.0 + 8520.61i −2.47508 + 0.359277i
\(155\) 458.994 0.0191048
\(156\) 43837.5i 1.80134i
\(157\) 42755.1 1.73456 0.867279 0.497823i \(-0.165867\pi\)
0.867279 + 0.497823i \(0.165867\pi\)
\(158\) 55008.8 2.20353
\(159\) 4453.18 0.176147
\(160\) 47241.9i 1.84539i
\(161\) 36702.9i 1.41595i
\(162\) 5614.04i 0.213917i
\(163\) −32922.2 −1.23912 −0.619561 0.784949i \(-0.712689\pi\)
−0.619561 + 0.784949i \(0.712689\pi\)
\(164\) 124818.i 4.64075i
\(165\) −7796.10 + 1131.66i −0.286358 + 0.0415671i
\(166\) −1208.38 −0.0438516
\(167\) 22705.4i 0.814136i −0.913398 0.407068i \(-0.866551\pi\)
0.913398 0.407068i \(-0.133449\pi\)
\(168\) 69551.8 2.46428
\(169\) −9391.31 −0.328816
\(170\) 10439.5 0.361229
\(171\) 1863.93i 0.0637437i
\(172\) 13829.7i 0.467473i
\(173\) 32607.5i 1.08949i −0.838600 0.544747i \(-0.816626\pi\)
0.838600 0.544747i \(-0.183374\pi\)
\(174\) 15287.6 0.504940
\(175\) 29790.6i 0.972754i
\(176\) 110943. 16104.2i 3.58157 0.519892i
\(177\) −11167.9 −0.356472
\(178\) 55302.6i 1.74544i
\(179\) 4293.51 0.134001 0.0670003 0.997753i \(-0.478657\pi\)
0.0670003 + 0.997753i \(0.478657\pi\)
\(180\) 14650.3 0.452170
\(181\) 24070.9 0.734743 0.367371 0.930074i \(-0.380258\pi\)
0.367371 + 0.930074i \(0.380258\pi\)
\(182\) 95497.6i 2.88303i
\(183\) 25804.8i 0.770546i
\(184\) 121248.i 3.58130i
\(185\) −22447.7 −0.655885
\(186\) 1465.88i 0.0423714i
\(187\) 1880.58 + 12955.4i 0.0537784 + 0.370483i
\(188\) −99594.4 −2.81786
\(189\) 8930.40i 0.250004i
\(190\) −6661.19 −0.184520
\(191\) −15866.1 −0.434913 −0.217457 0.976070i \(-0.569776\pi\)
−0.217457 + 0.976070i \(0.569776\pi\)
\(192\) −73848.8 −2.00328
\(193\) 29252.3i 0.785319i 0.919684 + 0.392659i \(0.128445\pi\)
−0.919684 + 0.392659i \(0.871555\pi\)
\(194\) 18633.8i 0.495105i
\(195\) 12683.5i 0.333557i
\(196\) 71490.1 1.86095
\(197\) 54943.2i 1.41573i −0.706346 0.707867i \(-0.749658\pi\)
0.706346 0.707867i \(-0.250342\pi\)
\(198\) 3614.17 + 24898.3i 0.0921889 + 0.635095i
\(199\) 31818.1 0.803468 0.401734 0.915756i \(-0.368408\pi\)
0.401734 + 0.915756i \(0.368408\pi\)
\(200\) 98413.5i 2.46034i
\(201\) −27900.7 −0.690594
\(202\) −29567.8 −0.724630
\(203\) 24318.3 0.590122
\(204\) 24345.6i 0.585006i
\(205\) 36113.5i 0.859333i
\(206\) 52404.1i 1.23490i
\(207\) 15568.2 0.363327
\(208\) 180493.i 4.17190i
\(209\) −1199.95 8266.52i −0.0274707 0.189248i
\(210\) 31914.9 0.723694
\(211\) 59860.2i 1.34454i −0.740306 0.672270i \(-0.765320\pi\)
0.740306 0.672270i \(-0.234680\pi\)
\(212\) −37113.6 −0.825774
\(213\) −25743.7 −0.567430
\(214\) −45901.1 −1.00230
\(215\) 4001.35i 0.0865626i
\(216\) 29501.7i 0.632323i
\(217\) 2331.81i 0.0495193i
\(218\) 167947. 3.53394
\(219\) 18618.6i 0.388202i
\(220\) 64974.1 9431.49i 1.34244 0.194866i
\(221\) −21077.2 −0.431547
\(222\) 71690.8i 1.45465i
\(223\) −8345.72 −0.167824 −0.0839120 0.996473i \(-0.526741\pi\)
−0.0839120 + 0.996473i \(0.526741\pi\)
\(224\) −240002. −4.78320
\(225\) −12636.2 −0.249604
\(226\) 17662.8i 0.345813i
\(227\) 59279.0i 1.15040i −0.818013 0.575200i \(-0.804924\pi\)
0.818013 0.575200i \(-0.195076\pi\)
\(228\) 15534.3i 0.298829i
\(229\) −45919.1 −0.875634 −0.437817 0.899064i \(-0.644248\pi\)
−0.437817 + 0.899064i \(0.644248\pi\)
\(230\) 55636.7i 1.05173i
\(231\) 5749.16 + 39606.3i 0.107741 + 0.742234i
\(232\) −80335.8 −1.49257
\(233\) 69926.9i 1.28805i −0.765005 0.644025i \(-0.777263\pi\)
0.765005 0.644025i \(-0.222737\pi\)
\(234\) −40507.1 −0.739774
\(235\) −28815.7 −0.521786
\(236\) 93075.4 1.67113
\(237\) 37116.4i 0.660799i
\(238\) 53035.6i 0.936297i
\(239\) 16074.1i 0.281404i −0.990052 0.140702i \(-0.955064\pi\)
0.990052 0.140702i \(-0.0449359\pi\)
\(240\) −60320.0 −1.04722
\(241\) 6183.67i 0.106466i −0.998582 0.0532332i \(-0.983047\pi\)
0.998582 0.0532332i \(-0.0169527\pi\)
\(242\) 32057.7 + 108097.i 0.547397 + 1.84580i
\(243\) 3788.00 0.0641500
\(244\) 215062.i 3.61230i
\(245\) 20684.2 0.344594
\(246\) 115335. 1.90586
\(247\) 13448.8 0.220440
\(248\) 7703.17i 0.125247i
\(249\) 815.334i 0.0131503i
\(250\) 105465.i 1.68745i
\(251\) −50585.6 −0.802933 −0.401467 0.915874i \(-0.631499\pi\)
−0.401467 + 0.915874i \(0.631499\pi\)
\(252\) 74427.6i 1.17201i
\(253\) 69045.0 10022.4i 1.07868 0.156578i
\(254\) 67427.1 1.04512
\(255\) 7043.92i 0.108326i
\(256\) 150892. 2.30243
\(257\) −26033.8 −0.394159 −0.197080 0.980387i \(-0.563146\pi\)
−0.197080 + 0.980387i \(0.563146\pi\)
\(258\) 12779.1 0.191982
\(259\) 114040.i 1.70004i
\(260\) 105707.i 1.56371i
\(261\) 10315.1i 0.151423i
\(262\) 101626. 1.48048
\(263\) 79564.2i 1.15029i 0.818053 + 0.575143i \(0.195054\pi\)
−0.818053 + 0.575143i \(0.804946\pi\)
\(264\) −18992.4 130840.i −0.272504 1.87730i
\(265\) −10738.1 −0.152910
\(266\) 33840.7i 0.478273i
\(267\) 37314.6 0.523428
\(268\) 232529. 3.23749
\(269\) −101837. −1.40734 −0.703671 0.710526i \(-0.748457\pi\)
−0.703671 + 0.710526i \(0.748457\pi\)
\(270\) 13537.3i 0.185697i
\(271\) 84386.2i 1.14903i −0.818493 0.574517i \(-0.805190\pi\)
0.818493 0.574517i \(-0.194810\pi\)
\(272\) 100239.i 1.35487i
\(273\) −64435.7 −0.864572
\(274\) 15669.2i 0.208711i
\(275\) −56041.7 + 8134.88i −0.741047 + 0.107569i
\(276\) −129748. −1.70327
\(277\) 77513.5i 1.01022i 0.863054 + 0.505112i \(0.168549\pi\)
−0.863054 + 0.505112i \(0.831451\pi\)
\(278\) −190725. −2.46784
\(279\) −989.082 −0.0127064
\(280\) −167712. −2.13919
\(281\) 31892.6i 0.403903i 0.979395 + 0.201952i \(0.0647284\pi\)
−0.979395 + 0.201952i \(0.935272\pi\)
\(282\) 92028.0i 1.15724i
\(283\) 91416.2i 1.14143i 0.821147 + 0.570716i \(0.193334\pi\)
−0.821147 + 0.570716i \(0.806666\pi\)
\(284\) 214553. 2.66010
\(285\) 4494.54i 0.0553345i
\(286\) −179649. + 26077.4i −2.19630 + 0.318810i
\(287\) 183466. 2.22737
\(288\) 101801.i 1.22735i
\(289\) 71815.6 0.859850
\(290\) −36863.3 −0.438327
\(291\) 12572.9 0.148473
\(292\) 155170.i 1.81988i
\(293\) 98100.1i 1.14271i 0.820704 + 0.571353i \(0.193581\pi\)
−0.820704 + 0.571353i \(0.806419\pi\)
\(294\) 66058.9i 0.764252i
\(295\) 26929.5 0.309445
\(296\) 376733.i 4.29982i
\(297\) 16799.8 2438.61i 0.190454 0.0276459i
\(298\) −157682. −1.77562
\(299\) 112330.i 1.25647i
\(300\) 105313. 1.17014
\(301\) 20328.0 0.224368
\(302\) −131868. −1.44586
\(303\) 19950.4i 0.217304i
\(304\) 63959.7i 0.692085i
\(305\) 62223.9i 0.668894i
\(306\) −22496.0 −0.240250
\(307\) 142750.i 1.51461i −0.653063 0.757304i \(-0.726516\pi\)
0.653063 0.757304i \(-0.273484\pi\)
\(308\) −47914.6 330086.i −0.505087 3.47958i
\(309\) −35358.9 −0.370324
\(310\) 3534.72i 0.0367817i
\(311\) 165392. 1.70999 0.854996 0.518635i \(-0.173560\pi\)
0.854996 + 0.518635i \(0.173560\pi\)
\(312\) 212864. 2.18672
\(313\) 73167.5 0.746843 0.373422 0.927662i \(-0.378185\pi\)
0.373422 + 0.927662i \(0.378185\pi\)
\(314\) 329258.i 3.33946i
\(315\) 21534.1i 0.217023i
\(316\) 309335.i 3.09781i
\(317\) −112606. −1.12058 −0.560292 0.828295i \(-0.689311\pi\)
−0.560292 + 0.828295i \(0.689311\pi\)
\(318\) 34294.0i 0.339128i
\(319\) −6640.57 45747.3i −0.0652566 0.449557i
\(320\) 178074. 1.73900
\(321\) 30971.1i 0.300571i
\(322\) −282650. −2.72607
\(323\) 7468.95 0.0715903
\(324\) −31569.8 −0.300734
\(325\) 91174.4i 0.863189i
\(326\) 253535.i 2.38562i
\(327\) 113320.i 1.05977i
\(328\) −606083. −5.63358
\(329\) 146391.i 1.35246i
\(330\) −8714.96 60037.9i −0.0800272 0.551312i
\(331\) −72976.7 −0.666083 −0.333041 0.942912i \(-0.608075\pi\)
−0.333041 + 0.942912i \(0.608075\pi\)
\(332\) 6795.14i 0.0616485i
\(333\) 48372.3 0.436223
\(334\) 174855. 1.56742
\(335\) 67277.7 0.599489
\(336\) 306442.i 2.71437i
\(337\) 196562.i 1.73077i −0.501108 0.865384i \(-0.667074\pi\)
0.501108 0.865384i \(-0.332926\pi\)
\(338\) 72322.6i 0.633054i
\(339\) 11917.7 0.103703
\(340\) 58705.3i 0.507831i
\(341\) −4386.58 + 636.745i −0.0377240 + 0.00547592i
\(342\) 14354.1 0.122723
\(343\) 47751.5i 0.405881i
\(344\) −67153.7 −0.567483
\(345\) −37540.1 −0.315397
\(346\) 251111. 2.09755
\(347\) 206637.i 1.71612i −0.513546 0.858062i \(-0.671668\pi\)
0.513546 0.858062i \(-0.328332\pi\)
\(348\) 85967.6i 0.709866i
\(349\) 210273.i 1.72636i 0.504894 + 0.863181i \(0.331532\pi\)
−0.504894 + 0.863181i \(0.668468\pi\)
\(350\) 229418. 1.87280
\(351\) 27331.6i 0.221845i
\(352\) 65537.0 + 451489.i 0.528934 + 3.64386i
\(353\) −140022. −1.12369 −0.561847 0.827241i \(-0.689909\pi\)
−0.561847 + 0.827241i \(0.689909\pi\)
\(354\) 86004.2i 0.686299i
\(355\) 62076.5 0.492573
\(356\) −310987. −2.45382
\(357\) −35785.0 −0.280779
\(358\) 33064.4i 0.257985i
\(359\) 90549.6i 0.702583i 0.936266 + 0.351292i \(0.114257\pi\)
−0.936266 + 0.351292i \(0.885743\pi\)
\(360\) 71138.2i 0.548906i
\(361\) 125555. 0.963431
\(362\) 185370.i 1.41457i
\(363\) 72937.0 21630.5i 0.553522 0.164155i
\(364\) 537019. 4.05309
\(365\) 44895.5i 0.336990i
\(366\) −198723. −1.48350
\(367\) −60682.5 −0.450538 −0.225269 0.974297i \(-0.572326\pi\)
−0.225269 + 0.974297i \(0.572326\pi\)
\(368\) 534215. 3.94476
\(369\) 77820.7i 0.571534i
\(370\) 172870.i 1.26275i
\(371\) 54552.4i 0.396338i
\(372\) 8243.19 0.0595675
\(373\) 100208.i 0.720252i −0.932904 0.360126i \(-0.882734\pi\)
0.932904 0.360126i \(-0.117266\pi\)
\(374\) −99769.9 + 14482.4i −0.713274 + 0.103537i
\(375\) 71161.3 0.506036
\(376\) 483606.i 3.42070i
\(377\) 74426.5 0.523654
\(378\) −68773.2 −0.481322
\(379\) −228068. −1.58777 −0.793883 0.608070i \(-0.791944\pi\)
−0.793883 + 0.608070i \(0.791944\pi\)
\(380\) 37458.3i 0.259407i
\(381\) 45495.5i 0.313414i
\(382\) 122185.i 0.837319i
\(383\) −13819.4 −0.0942091 −0.0471045 0.998890i \(-0.514999\pi\)
−0.0471045 + 0.998890i \(0.514999\pi\)
\(384\) 255244.i 1.73098i
\(385\) −13863.1 95503.9i −0.0935275 0.644317i
\(386\) −225273. −1.51194
\(387\) 8622.49i 0.0575719i
\(388\) −104785. −0.696040
\(389\) −159107. −1.05145 −0.525726 0.850654i \(-0.676206\pi\)
−0.525726 + 0.850654i \(0.676206\pi\)
\(390\) 97675.9 0.642182
\(391\) 62383.4i 0.408052i
\(392\) 347138.i 2.25907i
\(393\) 68570.9i 0.443971i
\(394\) 423118. 2.72565
\(395\) 89499.9i 0.573625i
\(396\) −140012. + 20323.8i −0.892844 + 0.129603i
\(397\) −76802.1 −0.487295 −0.243648 0.969864i \(-0.578344\pi\)
−0.243648 + 0.969864i \(0.578344\pi\)
\(398\) 245032.i 1.54688i
\(399\) 22833.5 0.143426
\(400\) −433605. −2.71003
\(401\) 121201. 0.753732 0.376866 0.926268i \(-0.377002\pi\)
0.376866 + 0.926268i \(0.377002\pi\)
\(402\) 214864.i 1.32957i
\(403\) 7136.54i 0.0439418i
\(404\) 166271.i 1.01872i
\(405\) −9134.10 −0.0556872
\(406\) 187276.i 1.13613i
\(407\) 214531. 31140.8i 1.29510 0.187993i
\(408\) 118216. 0.710161
\(409\) 81034.4i 0.484421i 0.970224 + 0.242210i \(0.0778724\pi\)
−0.970224 + 0.242210i \(0.922128\pi\)
\(410\) −278111. −1.65444
\(411\) −10572.5 −0.0625887
\(412\) 294687. 1.73607
\(413\) 136809.i 0.802075i
\(414\) 119891.i 0.699498i
\(415\) 1966.04i 0.0114155i
\(416\) −734528. −4.24445
\(417\) 128689.i 0.740062i
\(418\) 63660.6 9240.83i 0.364350 0.0528881i
\(419\) 160750. 0.915635 0.457817 0.889046i \(-0.348631\pi\)
0.457817 + 0.889046i \(0.348631\pi\)
\(420\) 179469.i 1.01740i
\(421\) −92831.1 −0.523756 −0.261878 0.965101i \(-0.584342\pi\)
−0.261878 + 0.965101i \(0.584342\pi\)
\(422\) 460985. 2.58858
\(423\) 62094.6 0.347035
\(424\) 180214.i 1.00244i
\(425\) 50634.6i 0.280330i
\(426\) 198253.i 1.09245i
\(427\) −316114. −1.73376
\(428\) 258119.i 1.40907i
\(429\) 17595.4 + 121216.i 0.0956057 + 0.658634i
\(430\) −30814.5 −0.166655
\(431\) 213351.i 1.14853i 0.818671 + 0.574263i \(0.194711\pi\)
−0.818671 + 0.574263i \(0.805289\pi\)
\(432\) 129983. 0.696497
\(433\) −33161.8 −0.176873 −0.0884366 0.996082i \(-0.528187\pi\)
−0.0884366 + 0.996082i \(0.528187\pi\)
\(434\) 17957.3 0.0953372
\(435\) 24873.0i 0.131447i
\(436\) 944427.i 4.96816i
\(437\) 39805.3i 0.208438i
\(438\) −143382. −0.747388
\(439\) 293728.i 1.52411i 0.647513 + 0.762055i \(0.275809\pi\)
−0.647513 + 0.762055i \(0.724191\pi\)
\(440\) 45797.0 + 315498.i 0.236555 + 1.62964i
\(441\) −44572.3 −0.229186
\(442\) 162316.i 0.830839i
\(443\) −274048. −1.39643 −0.698215 0.715888i \(-0.746022\pi\)
−0.698215 + 0.715888i \(0.746022\pi\)
\(444\) −403144. −2.04500
\(445\) −89977.9 −0.454376
\(446\) 64270.6i 0.323104i
\(447\) 106394.i 0.532477i
\(448\) 904663.i 4.50745i
\(449\) −231379. −1.14771 −0.573854 0.818958i \(-0.694552\pi\)
−0.573854 + 0.818958i \(0.694552\pi\)
\(450\) 97311.8i 0.480552i
\(451\) −50098.9 345135.i −0.246306 1.69682i
\(452\) −99324.2 −0.486159
\(453\) 88976.1i 0.433588i
\(454\) 456509. 2.21481
\(455\) 155376. 0.750516
\(456\) −75430.7 −0.362759
\(457\) 271864.i 1.30172i 0.759196 + 0.650862i \(0.225593\pi\)
−0.759196 + 0.650862i \(0.774407\pi\)
\(458\) 353624.i 1.68582i
\(459\) 15178.9i 0.0720467i
\(460\) 312866. 1.47857
\(461\) 264865.i 1.24630i 0.782102 + 0.623150i \(0.214148\pi\)
−0.782102 + 0.623150i \(0.785852\pi\)
\(462\) −305009. + 44274.4i −1.42899 + 0.207429i
\(463\) 255889. 1.19369 0.596843 0.802358i \(-0.296422\pi\)
0.596843 + 0.802358i \(0.296422\pi\)
\(464\) 353956.i 1.64404i
\(465\) 2385.00 0.0110302
\(466\) 538508. 2.47982
\(467\) −184125. −0.844264 −0.422132 0.906534i \(-0.638718\pi\)
−0.422132 + 0.906534i \(0.638718\pi\)
\(468\) 227786.i 1.04001i
\(469\) 341789.i 1.55386i
\(470\) 221910.i 1.00457i
\(471\) 222162. 1.00145
\(472\) 451951.i 2.02865i
\(473\) −5550.93 38240.7i −0.0248110 0.170924i
\(474\) 285834. 1.27221
\(475\) 32308.7i 0.143196i
\(476\) 298239. 1.31629
\(477\) 23139.4 0.101699
\(478\) 123787. 0.541774
\(479\) 452588.i 1.97257i −0.165062 0.986283i \(-0.552782\pi\)
0.165062 0.986283i \(-0.447218\pi\)
\(480\) 245476.i 1.06544i
\(481\) 349022.i 1.50856i
\(482\) 47620.6 0.204975
\(483\) 190714.i 0.817500i
\(484\) −607870. + 180273.i −2.59490 + 0.769554i
\(485\) −30317.3 −0.128887
\(486\) 29171.4i 0.123505i
\(487\) 10896.3 0.0459432 0.0229716 0.999736i \(-0.492687\pi\)
0.0229716 + 0.999736i \(0.492687\pi\)
\(488\) 1.04429e6 4.38511
\(489\) −171069. −0.715407
\(490\) 159290.i 0.663431i
\(491\) 178944.i 0.742256i −0.928582 0.371128i \(-0.878971\pi\)
0.928582 0.371128i \(-0.121029\pi\)
\(492\) 648572.i 2.67934i
\(493\) 41333.5 0.170062
\(494\) 103570.i 0.424403i
\(495\) −40509.7 + 5880.30i −0.165329 + 0.0239988i
\(496\) −33939.8 −0.137958
\(497\) 315366.i 1.27674i
\(498\) −6278.90 −0.0253177
\(499\) −402187. −1.61520 −0.807601 0.589729i \(-0.799235\pi\)
−0.807601 + 0.589729i \(0.799235\pi\)
\(500\) −593071. −2.37228
\(501\) 117981.i 0.470041i
\(502\) 389561.i 1.54585i
\(503\) 211540.i 0.836096i −0.908425 0.418048i \(-0.862714\pi\)
0.908425 0.418048i \(-0.137286\pi\)
\(504\) 361402. 1.42275
\(505\) 48107.1i 0.188637i
\(506\) 77182.8 + 531717.i 0.301453 + 2.07673i
\(507\) −48798.7 −0.189842
\(508\) 379167.i 1.46928i
\(509\) 185877. 0.717446 0.358723 0.933444i \(-0.383212\pi\)
0.358723 + 0.933444i \(0.383212\pi\)
\(510\) 54245.3 0.208556
\(511\) −228081. −0.873470
\(512\) 376076.i 1.43461i
\(513\) 9685.26i 0.0368024i
\(514\) 200487.i 0.758857i
\(515\) 85261.9 0.321470
\(516\) 71861.4i 0.269896i
\(517\) 275390. 39974.9i 1.03031 0.149557i
\(518\) −878227. −3.27301
\(519\) 169433.i 0.629020i
\(520\) −513285. −1.89824
\(521\) 324045. 1.19380 0.596898 0.802317i \(-0.296400\pi\)
0.596898 + 0.802317i \(0.296400\pi\)
\(522\) 79436.5 0.291527
\(523\) 159328.i 0.582492i 0.956648 + 0.291246i \(0.0940698\pi\)
−0.956648 + 0.291246i \(0.905930\pi\)
\(524\) 571482.i 2.08133i
\(525\) 154796.i 0.561620i
\(526\) −612725. −2.21459
\(527\) 3963.35i 0.0142706i
\(528\) 576475. 83679.7i 2.06782 0.300160i
\(529\) 52627.1 0.188061
\(530\) 82694.1i 0.294390i
\(531\) −58030.1 −0.205809
\(532\) −190299. −0.672376
\(533\) 561501. 1.97650
\(534\) 287361.i 1.00773i
\(535\) 74681.6i 0.260919i
\(536\) 1.12910e6i 3.93011i
\(537\) 22309.7 0.0773653
\(538\) 784246.i 2.70949i
\(539\) −197678. + 28694.5i −0.680426 + 0.0987691i
\(540\) 76125.2 0.261061
\(541\) 94598.0i 0.323212i 0.986855 + 0.161606i \(0.0516674\pi\)
−0.986855 + 0.161606i \(0.948333\pi\)
\(542\) 649860. 2.21218
\(543\) 125076. 0.424204
\(544\) −407928. −1.37843
\(545\) 273251.i 0.919960i
\(546\) 496220.i 1.66452i
\(547\) 65315.6i 0.218294i 0.994026 + 0.109147i \(0.0348119\pi\)
−0.994026 + 0.109147i \(0.965188\pi\)
\(548\) 88113.5 0.293414
\(549\) 134086.i 0.444875i
\(550\) −62646.8 431578.i −0.207097 1.42670i
\(551\) −26373.9 −0.0868701
\(552\) 630025.i 2.06766i
\(553\) 454684. 1.48682
\(554\) −596933. −1.94494
\(555\) −116642. −0.378676
\(556\) 1.07251e6i 3.46939i
\(557\) 334291.i 1.07749i −0.842468 0.538747i \(-0.818898\pi\)
0.842468 0.538747i \(-0.181102\pi\)
\(558\) 7616.94i 0.0244631i
\(559\) 62214.0 0.199097
\(560\) 738932.i 2.35629i
\(561\) 9771.77 + 67318.3i 0.0310490 + 0.213898i
\(562\) −245606. −0.777617
\(563\) 296644.i 0.935876i 0.883761 + 0.467938i \(0.155003\pi\)
−0.883761 + 0.467938i \(0.844997\pi\)
\(564\) −517508. −1.62689
\(565\) −28737.5 −0.0900226
\(566\) −703998. −2.19755
\(567\) 46403.7i 0.144340i
\(568\) 1.04181e6i 3.22919i
\(569\) 87509.9i 0.270292i −0.990826 0.135146i \(-0.956850\pi\)
0.990826 0.135146i \(-0.0431503\pi\)
\(570\) −34612.6 −0.106533
\(571\) 615448.i 1.88764i −0.330462 0.943819i \(-0.607205\pi\)
0.330462 0.943819i \(-0.392795\pi\)
\(572\) −146643. 1.01023e6i −0.448197 3.08766i
\(573\) −82442.6 −0.251097
\(574\) 1.41288e6i 4.28826i
\(575\) −269854. −0.816193
\(576\) −383729. −1.15659
\(577\) 516552. 1.55154 0.775770 0.631016i \(-0.217362\pi\)
0.775770 + 0.631016i \(0.217362\pi\)
\(578\) 553053.i 1.65543i
\(579\) 152000.i 0.453404i
\(580\) 207296.i 0.616219i
\(581\) −9988.01 −0.0295888
\(582\) 96824.0i 0.285849i
\(583\) 102623. 14896.5i 0.301932 0.0438277i
\(584\) 753469. 2.20922
\(585\) 65905.4i 0.192579i
\(586\) −755471. −2.20000
\(587\) −523368. −1.51891 −0.759453 0.650562i \(-0.774533\pi\)
−0.759453 + 0.650562i \(0.774533\pi\)
\(588\) 371474. 1.07442
\(589\) 2528.91i 0.00728960i
\(590\) 207384.i 0.595761i
\(591\) 285493.i 0.817374i
\(592\) 1.65987e6 4.73621
\(593\) 221167.i 0.628942i 0.949267 + 0.314471i \(0.101827\pi\)
−0.949267 + 0.314471i \(0.898173\pi\)
\(594\) 18779.8 + 129375.i 0.0532253 + 0.366673i
\(595\) 86289.4 0.243738
\(596\) 886704.i 2.49624i
\(597\) 165332. 0.463882
\(598\) −865052. −2.41902
\(599\) 293216. 0.817210 0.408605 0.912711i \(-0.366015\pi\)
0.408605 + 0.912711i \(0.366015\pi\)
\(600\) 511372.i 1.42048i
\(601\) 256959.i 0.711401i 0.934600 + 0.355701i \(0.115758\pi\)
−0.934600 + 0.355701i \(0.884242\pi\)
\(602\) 156546.i 0.431966i
\(603\) −144976. −0.398714
\(604\) 741543.i 2.03265i
\(605\) −175875. + 52158.2i −0.480500 + 0.142499i
\(606\) −153639. −0.418365
\(607\) 182631.i 0.495676i 0.968802 + 0.247838i \(0.0797200\pi\)
−0.968802 + 0.247838i \(0.920280\pi\)
\(608\) 260288. 0.704122
\(609\) 126362. 0.340707
\(610\) 479187. 1.28779
\(611\) 448032.i 1.20013i
\(612\) 126504.i 0.337753i
\(613\) 199000.i 0.529580i 0.964306 + 0.264790i \(0.0853026\pi\)
−0.964306 + 0.264790i \(0.914697\pi\)
\(614\) 1.09932e6 2.91601
\(615\) 187651.i 0.496136i
\(616\) 1.60282e6 232661.i 4.22399 0.613144i
\(617\) 385966. 1.01386 0.506931 0.861987i \(-0.330780\pi\)
0.506931 + 0.861987i \(0.330780\pi\)
\(618\) 272300.i 0.712968i
\(619\) −287681. −0.750809 −0.375404 0.926861i \(-0.622496\pi\)
−0.375404 + 0.926861i \(0.622496\pi\)
\(620\) −19877.0 −0.0517092
\(621\) 80894.8 0.209767
\(622\) 1.27369e6i 3.29217i
\(623\) 457112.i 1.17773i
\(624\) 937869.i 2.40865i
\(625\) 120912. 0.309535
\(626\) 563464.i 1.43786i
\(627\) −6235.12 42954.1i −0.0158602 0.109262i
\(628\) −1.85154e6 −4.69476
\(629\) 193833.i 0.489921i
\(630\) 165835. 0.417825
\(631\) 505556. 1.26973 0.634863 0.772625i \(-0.281056\pi\)
0.634863 + 0.772625i \(0.281056\pi\)
\(632\) −1.50205e6 −3.76055
\(633\) 311043.i 0.776270i
\(634\) 867184.i 2.15741i
\(635\) 109704.i 0.272068i
\(636\) −192848. −0.476761
\(637\) 321603.i 0.792577i
\(638\) 352301. 51139.2i 0.865511 0.125635i
\(639\) −133768. −0.327606
\(640\) 615477.i 1.50263i
\(641\) −729128. −1.77455 −0.887274 0.461242i \(-0.847404\pi\)
−0.887274 + 0.461242i \(0.847404\pi\)
\(642\) −238509. −0.578676
\(643\) −548088. −1.32565 −0.662824 0.748775i \(-0.730642\pi\)
−0.662824 + 0.748775i \(0.730642\pi\)
\(644\) 1.58944e6i 3.83242i
\(645\) 20791.6i 0.0499769i
\(646\) 57518.5i 0.137830i
\(647\) −301562. −0.720390 −0.360195 0.932877i \(-0.617290\pi\)
−0.360195 + 0.932877i \(0.617290\pi\)
\(648\) 153295.i 0.365072i
\(649\) −257364. + 37358.3i −0.611024 + 0.0886947i
\(650\) 702135. 1.66186
\(651\) 12116.5i 0.0285900i
\(652\) 1.42572e6 3.35381
\(653\) 184146. 0.431853 0.215926 0.976410i \(-0.430723\pi\)
0.215926 + 0.976410i \(0.430723\pi\)
\(654\) 872677. 2.04032
\(655\) 165347.i 0.385402i
\(656\) 2.67038e6i 6.20533i
\(657\) 96744.9i 0.224129i
\(658\) −1.12736e6 −2.60383
\(659\) 608904.i 1.40210i −0.713114 0.701048i \(-0.752716\pi\)
0.713114 0.701048i \(-0.247284\pi\)
\(660\) 337616. 49007.5i 0.775059 0.112506i
\(661\) −211140. −0.483246 −0.241623 0.970370i \(-0.577680\pi\)
−0.241623 + 0.970370i \(0.577680\pi\)
\(662\) 561995.i 1.28238i
\(663\) −109520. −0.249154
\(664\) 32995.5 0.0748374
\(665\) −55059.1 −0.124505
\(666\) 372516.i 0.839840i
\(667\) 220284.i 0.495144i
\(668\) 983274.i 2.20354i
\(669\) −43365.7 −0.0968933
\(670\) 518107.i 1.15417i
\(671\) 86320.9 + 594670.i 0.191722 + 1.32078i
\(672\) −1.24709e6 −2.76158
\(673\) 207518.i 0.458169i −0.973406 0.229085i \(-0.926427\pi\)
0.973406 0.229085i \(-0.0735733\pi\)
\(674\) 1.51373e6 3.33217
\(675\) −65659.8 −0.144109
\(676\) 406697. 0.889974
\(677\) 419679.i 0.915673i 0.889037 + 0.457836i \(0.151375\pi\)
−0.889037 + 0.457836i \(0.848625\pi\)
\(678\) 91778.4i 0.199655i
\(679\) 154020.i 0.334071i
\(680\) −285058. −0.616475
\(681\) 308023.i 0.664184i
\(682\) −4903.59 33781.1i −0.0105425 0.0726282i
\(683\) 266045. 0.570313 0.285156 0.958481i \(-0.407954\pi\)
0.285156 + 0.958481i \(0.407954\pi\)
\(684\) 80718.7i 0.172529i
\(685\) 25493.9 0.0543319
\(686\) −367736. −0.781425
\(687\) −238603. −0.505547
\(688\) 295876.i 0.625076i
\(689\) 166958.i 0.351697i
\(690\) 289097.i 0.607219i
\(691\) 594449. 1.24497 0.622485 0.782632i \(-0.286123\pi\)
0.622485 + 0.782632i \(0.286123\pi\)
\(692\) 1.41209e6i 2.94883i
\(693\) 29873.5 + 205801.i 0.0622042 + 0.428529i
\(694\) 1.59131e6 3.30398
\(695\) 310311.i 0.642432i
\(696\) −417437. −0.861733
\(697\) 311835. 0.641889
\(698\) −1.61931e6 −3.32369
\(699\) 363351.i 0.743656i
\(700\) 1.29010e6i 2.63286i
\(701\) 329130.i 0.669779i −0.942257 0.334890i \(-0.891301\pi\)
0.942257 0.334890i \(-0.108699\pi\)
\(702\) −210481. −0.427109
\(703\) 123680.i 0.250258i
\(704\) −1.70184e6 + 247035.i −3.43379 + 0.498441i
\(705\) −149731. −0.301253
\(706\) 1.07832e6i 2.16340i
\(707\) −244397. −0.488942
\(708\) 483634. 0.964828
\(709\) −148161. −0.294742 −0.147371 0.989081i \(-0.547081\pi\)
−0.147371 + 0.989081i \(0.547081\pi\)
\(710\) 478053.i 0.948329i
\(711\) 192863.i 0.381513i
\(712\) 1.51008e6i 2.97878i
\(713\) −21122.4 −0.0415494
\(714\) 275581.i 0.540571i
\(715\) −42428.2 292291.i −0.0829932 0.571745i
\(716\) −185933. −0.362687
\(717\) 83523.3i 0.162469i
\(718\) −697324. −1.35265
\(719\) −140295. −0.271384 −0.135692 0.990751i \(-0.543326\pi\)
−0.135692 + 0.990751i \(0.543326\pi\)
\(720\) −313432. −0.604614
\(721\) 433154.i 0.833243i
\(722\) 966903.i 1.85485i
\(723\) 32131.3i 0.0614684i
\(724\) −1.04241e6 −1.98866
\(725\) 178798.i 0.340162i
\(726\) 166577. + 561689.i 0.316040 + 1.06567i
\(727\) −116812. −0.221013 −0.110507 0.993875i \(-0.535247\pi\)
−0.110507 + 0.993875i \(0.535247\pi\)
\(728\) 2.60763e6i 4.92020i
\(729\) 19683.0 0.0370370
\(730\) 345741. 0.648791
\(731\) 34551.2 0.0646589
\(732\) 1.11749e6i 2.08556i
\(733\) 645954.i 1.20225i 0.799156 + 0.601123i \(0.205280\pi\)
−0.799156 + 0.601123i \(0.794720\pi\)
\(734\) 467317.i 0.867400i
\(735\) 107478. 0.198951
\(736\) 2.17402e6i 4.01337i
\(737\) −642969. + 93331.9i −1.18374 + 0.171828i
\(738\) 599298. 1.10035
\(739\) 72867.2i 0.133427i −0.997772 0.0667134i \(-0.978749\pi\)
0.997772 0.0667134i \(-0.0212513\pi\)
\(740\) 972112. 1.77522
\(741\) 69882.2 0.127271
\(742\) −420109. −0.763052
\(743\) 675603.i 1.22381i −0.790932 0.611905i \(-0.790404\pi\)
0.790932 0.611905i \(-0.209596\pi\)
\(744\) 40026.9i 0.0723112i
\(745\) 256550.i 0.462231i
\(746\) 771703. 1.38667
\(747\) 4236.60i 0.00759235i
\(748\) −81439.7 561043.i −0.145557 1.00275i
\(749\) −379403. −0.676296
\(750\) 548014.i 0.974247i
\(751\) −168392. −0.298567 −0.149283 0.988794i \(-0.547697\pi\)
−0.149283 + 0.988794i \(0.547697\pi\)
\(752\) 2.13074e6 3.76787
\(753\) −262850. −0.463574
\(754\) 573159.i 1.00817i
\(755\) 214551.i 0.376388i
\(756\) 386737.i 0.676663i
\(757\) −63422.1 −0.110675 −0.0553374 0.998468i \(-0.517623\pi\)
−0.0553374 + 0.998468i \(0.517623\pi\)
\(758\) 1.75636e6i 3.05685i
\(759\) 358769. 52078.0i 0.622774 0.0904004i
\(760\) 181888. 0.314904
\(761\) 377856.i 0.652464i −0.945290 0.326232i \(-0.894221\pi\)
0.945290 0.326232i \(-0.105779\pi\)
\(762\) 350361. 0.603401
\(763\) 1.38819e6 2.38451
\(764\) 687091. 1.17714
\(765\) 36601.3i 0.0625422i
\(766\) 106424.i 0.181376i
\(767\) 418706.i 0.711735i
\(768\) 784059. 1.32931
\(769\) 795673.i 1.34549i −0.739872 0.672747i \(-0.765114\pi\)
0.739872 0.672747i \(-0.234886\pi\)
\(770\) 735477. 106760.i 1.24047 0.180064i
\(771\) −135276. −0.227568
\(772\) 1.26679e6i 2.12555i
\(773\) 929744. 1.55598 0.777991 0.628276i \(-0.216239\pi\)
0.777991 + 0.628276i \(0.216239\pi\)
\(774\) 66401.9 0.110841
\(775\) 17144.4 0.0285443
\(776\) 508808.i 0.844949i
\(777\) 592571.i 0.981518i
\(778\) 1.22528e6i 2.02431i
\(779\) −198974. −0.327885
\(780\) 549268.i 0.902807i
\(781\) −593262. + 86116.5i −0.972623 + 0.141184i
\(782\) −480416. −0.785604
\(783\) 53598.7i 0.0874239i
\(784\) −1.52947e6 −2.48834
\(785\) −535706. −0.869334
\(786\)