Properties

Label 160.6.n.b.127.7
Level 160
Weight 6
Character 160.127
Analytic conductor 25.661
Analytic rank 0
Dimension 14
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 160.n (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.6614111701\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 4 x^{13} + 8 x^{12} - 4626 x^{11} + 149441 x^{10} - 2113414 x^{9} + 17958066 x^{8} - 97717112 x^{7} + 355171384 x^{6} - 910571904 x^{5} + 2428303248 x^{4} - 9166992192 x^{3} + 32237484304 x^{2} - 66916821408 x + 69451154208\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{31}\cdot 5^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 127.7
Root \(2.75256 - 2.75256i\) of defining polynomial
Character \(\chi\) \(=\) 160.127
Dual form 160.6.n.b.63.7

$q$-expansion

\(f(q)\) \(=\) \(q+(18.9245 + 18.9245i) q^{3} +(-36.4318 - 42.3996i) q^{5} +(112.521 - 112.521i) q^{7} +473.272i q^{9} +O(q^{10})\) \(q+(18.9245 + 18.9245i) q^{3} +(-36.4318 - 42.3996i) q^{5} +(112.521 - 112.521i) q^{7} +473.272i q^{9} +269.371i q^{11} +(-403.647 + 403.647i) q^{13} +(112.936 - 1491.84i) q^{15} +(1098.68 + 1098.68i) q^{17} +1802.73 q^{19} +4258.82 q^{21} +(2833.05 + 2833.05i) q^{23} +(-470.444 + 3089.39i) q^{25} +(-4357.78 + 4357.78i) q^{27} -7856.77i q^{29} +4682.69i q^{31} +(-5097.71 + 5097.71i) q^{33} +(-8870.22 - 671.497i) q^{35} +(5157.30 + 5157.30i) q^{37} -15277.6 q^{39} +1658.51 q^{41} +(-3231.92 - 3231.92i) q^{43} +(20066.5 - 17242.2i) q^{45} +(-6001.67 + 6001.67i) q^{47} -8515.15i q^{49} +41583.7i q^{51} +(-6075.77 + 6075.77i) q^{53} +(11421.2 - 9813.69i) q^{55} +(34115.8 + 34115.8i) q^{57} -39361.1 q^{59} -11975.4 q^{61} +(53253.2 + 53253.2i) q^{63} +(31820.1 + 2408.86i) q^{65} +(43638.2 - 43638.2i) q^{67} +107228. i q^{69} -7043.28i q^{71} +(24461.9 - 24461.9i) q^{73} +(-67367.9 + 49562.1i) q^{75} +(30310.1 + 30310.1i) q^{77} +30620.5 q^{79} -49932.2 q^{81} +(-25676.6 - 25676.6i) q^{83} +(6556.60 - 86610.2i) q^{85} +(148685. - 148685. i) q^{87} -137436. i q^{89} +90838.0i q^{91} +(-88617.5 + 88617.5i) q^{93} +(-65676.9 - 76435.1i) q^{95} +(47906.2 + 47906.2i) q^{97} -127486. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 10q^{3} + 42q^{5} + 66q^{7} + O(q^{10}) \) \( 14q + 10q^{3} + 42q^{5} + 66q^{7} - 414q^{13} + 278q^{15} + 1222q^{17} + 5672q^{19} + 5924q^{21} + 2902q^{23} - 4466q^{25} - 2168q^{27} - 2444q^{33} - 2618q^{35} - 1790q^{37} - 11076q^{39} + 11644q^{41} - 3982q^{43} + 14704q^{45} - 1278q^{47} + 5882q^{53} + 65608q^{55} - 14552q^{57} - 8504q^{59} + 20564q^{61} + 19422q^{63} + 40798q^{65} + 107926q^{67} - 16418q^{73} + 66586q^{75} - 13348q^{77} - 146544q^{79} + 173806q^{81} - 36398q^{83} - 66262q^{85} + 124384q^{87} - 306620q^{93} + 173768q^{95} - 60314q^{97} - 388628q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(101\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

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 0
\(3\) 18.9245 + 18.9245i 1.21401 + 1.21401i 0.969698 + 0.244308i \(0.0785609\pi\)
0.244308 + 0.969698i \(0.421439\pi\)
\(4\) 0 0
\(5\) −36.4318 42.3996i −0.651712 0.758466i
\(6\) 0 0
\(7\) 112.521 112.521i 0.867941 0.867941i −0.124303 0.992244i \(-0.539670\pi\)
0.992244 + 0.124303i \(0.0396696\pi\)
\(8\) 0 0
\(9\) 473.272i 1.94762i
\(10\) 0 0
\(11\) 269.371i 0.671228i 0.942000 + 0.335614i \(0.108944\pi\)
−0.942000 + 0.335614i \(0.891056\pi\)
\(12\) 0 0
\(13\) −403.647 + 403.647i −0.662436 + 0.662436i −0.955954 0.293518i \(-0.905174\pi\)
0.293518 + 0.955954i \(0.405174\pi\)
\(14\) 0 0
\(15\) 112.936 1491.84i 0.129600 1.71197i
\(16\) 0 0
\(17\) 1098.68 + 1098.68i 0.922035 + 0.922035i 0.997173 0.0751382i \(-0.0239398\pi\)
−0.0751382 + 0.997173i \(0.523940\pi\)
\(18\) 0 0
\(19\) 1802.73 1.14564 0.572819 0.819682i \(-0.305850\pi\)
0.572819 + 0.819682i \(0.305850\pi\)
\(20\) 0 0
\(21\) 4258.82 2.10737
\(22\) 0 0
\(23\) 2833.05 + 2833.05i 1.11670 + 1.11670i 0.992223 + 0.124474i \(0.0397243\pi\)
0.124474 + 0.992223i \(0.460276\pi\)
\(24\) 0 0
\(25\) −470.444 + 3089.39i −0.150542 + 0.988604i
\(26\) 0 0
\(27\) −4357.78 + 4357.78i −1.15042 + 1.15042i
\(28\) 0 0
\(29\) 7856.77i 1.73480i −0.497612 0.867400i \(-0.665790\pi\)
0.497612 0.867400i \(-0.334210\pi\)
\(30\) 0 0
\(31\) 4682.69i 0.875167i 0.899178 + 0.437584i \(0.144166\pi\)
−0.899178 + 0.437584i \(0.855834\pi\)
\(32\) 0 0
\(33\) −5097.71 + 5097.71i −0.814874 + 0.814874i
\(34\) 0 0
\(35\) −8870.22 671.497i −1.22395 0.0926561i
\(36\) 0 0
\(37\) 5157.30 + 5157.30i 0.619324 + 0.619324i 0.945358 0.326034i \(-0.105712\pi\)
−0.326034 + 0.945358i \(0.605712\pi\)
\(38\) 0 0
\(39\) −15277.6 −1.60840
\(40\) 0 0
\(41\) 1658.51 0.154084 0.0770421 0.997028i \(-0.475452\pi\)
0.0770421 + 0.997028i \(0.475452\pi\)
\(42\) 0 0
\(43\) −3231.92 3231.92i −0.266557 0.266557i 0.561154 0.827711i \(-0.310357\pi\)
−0.827711 + 0.561154i \(0.810357\pi\)
\(44\) 0 0
\(45\) 20066.5 17242.2i 1.47720 1.26929i
\(46\) 0 0
\(47\) −6001.67 + 6001.67i −0.396303 + 0.396303i −0.876927 0.480624i \(-0.840410\pi\)
0.480624 + 0.876927i \(0.340410\pi\)
\(48\) 0 0
\(49\) 8515.15i 0.506643i
\(50\) 0 0
\(51\) 41583.7i 2.23871i
\(52\) 0 0
\(53\) −6075.77 + 6075.77i −0.297106 + 0.297106i −0.839879 0.542773i \(-0.817374\pi\)
0.542773 + 0.839879i \(0.317374\pi\)
\(54\) 0 0
\(55\) 11421.2 9813.69i 0.509103 0.437447i
\(56\) 0 0
\(57\) 34115.8 + 34115.8i 1.39081 + 1.39081i
\(58\) 0 0
\(59\) −39361.1 −1.47210 −0.736050 0.676927i \(-0.763311\pi\)
−0.736050 + 0.676927i \(0.763311\pi\)
\(60\) 0 0
\(61\) −11975.4 −0.412063 −0.206032 0.978545i \(-0.566055\pi\)
−0.206032 + 0.978545i \(0.566055\pi\)
\(62\) 0 0
\(63\) 53253.2 + 53253.2i 1.69042 + 1.69042i
\(64\) 0 0
\(65\) 31820.1 + 2408.86i 0.934153 + 0.0707176i
\(66\) 0 0
\(67\) 43638.2 43638.2i 1.18763 1.18763i 0.209904 0.977722i \(-0.432685\pi\)
0.977722 0.209904i \(-0.0673153\pi\)
\(68\) 0 0
\(69\) 107228.i 2.71135i
\(70\) 0 0
\(71\) 7043.28i 0.165817i −0.996557 0.0829086i \(-0.973579\pi\)
0.996557 0.0829086i \(-0.0264209\pi\)
\(72\) 0 0
\(73\) 24461.9 24461.9i 0.537257 0.537257i −0.385465 0.922722i \(-0.625959\pi\)
0.922722 + 0.385465i \(0.125959\pi\)
\(74\) 0 0
\(75\) −67367.9 + 49562.1i −1.38293 + 1.01741i
\(76\) 0 0
\(77\) 30310.1 + 30310.1i 0.582586 + 0.582586i
\(78\) 0 0
\(79\) 30620.5 0.552007 0.276003 0.961157i \(-0.410990\pi\)
0.276003 + 0.961157i \(0.410990\pi\)
\(80\) 0 0
\(81\) −49932.2 −0.845606
\(82\) 0 0
\(83\) −25676.6 25676.6i −0.409112 0.409112i 0.472317 0.881429i \(-0.343418\pi\)
−0.881429 + 0.472317i \(0.843418\pi\)
\(84\) 0 0
\(85\) 6556.60 86610.2i 0.0984309 1.30023i
\(86\) 0 0
\(87\) 148685. 148685.i 2.10606 2.10606i
\(88\) 0 0
\(89\) 137436.i 1.83919i −0.392868 0.919595i \(-0.628517\pi\)
0.392868 0.919595i \(-0.371483\pi\)
\(90\) 0 0
\(91\) 90838.0i 1.14991i
\(92\) 0 0
\(93\) −88617.5 + 88617.5i −1.06246 + 1.06246i
\(94\) 0 0
\(95\) −65676.9 76435.1i −0.746627 0.868928i
\(96\) 0 0
\(97\) 47906.2 + 47906.2i 0.516967 + 0.516967i 0.916652 0.399685i \(-0.130881\pi\)
−0.399685 + 0.916652i \(0.630881\pi\)
\(98\) 0 0
\(99\) −127486. −1.30730
\(100\) 0 0
\(101\) −49807.9 −0.485842 −0.242921 0.970046i \(-0.578106\pi\)
−0.242921 + 0.970046i \(0.578106\pi\)
\(102\) 0 0
\(103\) −76305.7 76305.7i −0.708703 0.708703i 0.257560 0.966262i \(-0.417082\pi\)
−0.966262 + 0.257560i \(0.917082\pi\)
\(104\) 0 0
\(105\) −155157. 180572.i −1.37340 1.59837i
\(106\) 0 0
\(107\) −86325.0 + 86325.0i −0.728916 + 0.728916i −0.970404 0.241488i \(-0.922365\pi\)
0.241488 + 0.970404i \(0.422365\pi\)
\(108\) 0 0
\(109\) 85263.0i 0.687376i −0.939084 0.343688i \(-0.888324\pi\)
0.939084 0.343688i \(-0.111676\pi\)
\(110\) 0 0
\(111\) 195198.i 1.50373i
\(112\) 0 0
\(113\) −150561. + 150561.i −1.10922 + 1.10922i −0.115962 + 0.993254i \(0.536995\pi\)
−0.993254 + 0.115962i \(0.963005\pi\)
\(114\) 0 0
\(115\) 16906.9 223334.i 0.119212 1.57474i
\(116\) 0 0
\(117\) −191035. 191035.i −1.29017 1.29017i
\(118\) 0 0
\(119\) 247249. 1.60054
\(120\) 0 0
\(121\) 88490.1 0.549454
\(122\) 0 0
\(123\) 31386.4 + 31386.4i 0.187059 + 0.187059i
\(124\) 0 0
\(125\) 148128. 92605.4i 0.847933 0.530104i
\(126\) 0 0
\(127\) 61749.1 61749.1i 0.339720 0.339720i −0.516542 0.856262i \(-0.672781\pi\)
0.856262 + 0.516542i \(0.172781\pi\)
\(128\) 0 0
\(129\) 122325.i 0.647203i
\(130\) 0 0
\(131\) 228440.i 1.16304i −0.813532 0.581520i \(-0.802458\pi\)
0.813532 0.581520i \(-0.197542\pi\)
\(132\) 0 0
\(133\) 202846. 202846.i 0.994346 0.994346i
\(134\) 0 0
\(135\) 343529. + 26006.0i 1.62229 + 0.122812i
\(136\) 0 0
\(137\) 201798. + 201798.i 0.918579 + 0.918579i 0.996926 0.0783472i \(-0.0249643\pi\)
−0.0783472 + 0.996926i \(0.524964\pi\)
\(138\) 0 0
\(139\) −122666. −0.538503 −0.269252 0.963070i \(-0.586776\pi\)
−0.269252 + 0.963070i \(0.586776\pi\)
\(140\) 0 0
\(141\) −227157. −0.962229
\(142\) 0 0
\(143\) −108731. 108731.i −0.444645 0.444645i
\(144\) 0 0
\(145\) −333124. + 286237.i −1.31579 + 1.13059i
\(146\) 0 0
\(147\) 161145. 161145.i 0.615067 0.615067i
\(148\) 0 0
\(149\) 385846.i 1.42380i 0.702281 + 0.711900i \(0.252165\pi\)
−0.702281 + 0.711900i \(0.747835\pi\)
\(150\) 0 0
\(151\) 325566.i 1.16198i −0.813912 0.580988i \(-0.802666\pi\)
0.813912 0.580988i \(-0.197334\pi\)
\(152\) 0 0
\(153\) −519973. + 519973.i −1.79577 + 1.79577i
\(154\) 0 0
\(155\) 198544. 170599.i 0.663785 0.570357i
\(156\) 0 0
\(157\) −217734. 217734.i −0.704981 0.704981i 0.260495 0.965475i \(-0.416114\pi\)
−0.965475 + 0.260495i \(0.916114\pi\)
\(158\) 0 0
\(159\) −229962. −0.721377
\(160\) 0 0
\(161\) 637559. 1.93845
\(162\) 0 0
\(163\) 128681. + 128681.i 0.379353 + 0.379353i 0.870869 0.491515i \(-0.163557\pi\)
−0.491515 + 0.870869i \(0.663557\pi\)
\(164\) 0 0
\(165\) 401860. + 30421.8i 1.14912 + 0.0869910i
\(166\) 0 0
\(167\) 84402.8 84402.8i 0.234189 0.234189i −0.580250 0.814438i \(-0.697045\pi\)
0.814438 + 0.580250i \(0.197045\pi\)
\(168\) 0 0
\(169\) 45430.5i 0.122358i
\(170\) 0 0
\(171\) 853183.i 2.23127i
\(172\) 0 0
\(173\) 66342.8 66342.8i 0.168530 0.168530i −0.617803 0.786333i \(-0.711977\pi\)
0.786333 + 0.617803i \(0.211977\pi\)
\(174\) 0 0
\(175\) 294687. + 400557.i 0.727388 + 0.988711i
\(176\) 0 0
\(177\) −744888. 744888.i −1.78714 1.78714i
\(178\) 0 0
\(179\) −393894. −0.918855 −0.459427 0.888215i \(-0.651945\pi\)
−0.459427 + 0.888215i \(0.651945\pi\)
\(180\) 0 0
\(181\) 589531. 1.33755 0.668775 0.743465i \(-0.266819\pi\)
0.668775 + 0.743465i \(0.266819\pi\)
\(182\) 0 0
\(183\) −226627. 226627.i −0.500247 0.500247i
\(184\) 0 0
\(185\) 30777.3 406557.i 0.0661153 0.873357i
\(186\) 0 0
\(187\) −295952. + 295952.i −0.618895 + 0.618895i
\(188\) 0 0
\(189\) 980686.i 1.99699i
\(190\) 0 0
\(191\) 146556.i 0.290683i 0.989382 + 0.145342i \(0.0464281\pi\)
−0.989382 + 0.145342i \(0.953572\pi\)
\(192\) 0 0
\(193\) 649988. 649988.i 1.25606 1.25606i 0.303109 0.952956i \(-0.401975\pi\)
0.952956 0.303109i \(-0.0980246\pi\)
\(194\) 0 0
\(195\) 556592. + 647765.i 1.04822 + 1.21992i
\(196\) 0 0
\(197\) −484881. 484881.i −0.890163 0.890163i 0.104375 0.994538i \(-0.466716\pi\)
−0.994538 + 0.104375i \(0.966716\pi\)
\(198\) 0 0
\(199\) −728394. −1.30387 −0.651934 0.758275i \(-0.726042\pi\)
−0.651934 + 0.758275i \(0.726042\pi\)
\(200\) 0 0
\(201\) 1.65166e6 2.88357
\(202\) 0 0
\(203\) −884055. 884055.i −1.50570 1.50570i
\(204\) 0 0
\(205\) −60422.5 70320.0i −0.100419 0.116868i
\(206\) 0 0
\(207\) −1.34080e6 + 1.34080e6i −2.17490 + 2.17490i
\(208\) 0 0
\(209\) 485605.i 0.768984i
\(210\) 0 0
\(211\) 396241.i 0.612708i −0.951918 0.306354i \(-0.900891\pi\)
0.951918 0.306354i \(-0.0991091\pi\)
\(212\) 0 0
\(213\) 133290. 133290.i 0.201303 0.201303i
\(214\) 0 0
\(215\) −19287.2 + 254777.i −0.0284560 + 0.375893i
\(216\) 0 0
\(217\) 526903. + 526903.i 0.759593 + 0.759593i
\(218\) 0 0
\(219\) 925856. 1.30447
\(220\) 0 0
\(221\) −886956. −1.22158
\(222\) 0 0
\(223\) −382870. 382870.i −0.515572 0.515572i 0.400657 0.916228i \(-0.368782\pi\)
−0.916228 + 0.400657i \(0.868782\pi\)
\(224\) 0 0
\(225\) −1.46212e6 222648.i −1.92543 0.293199i
\(226\) 0 0
\(227\) 420420. 420420.i 0.541525 0.541525i −0.382451 0.923976i \(-0.624920\pi\)
0.923976 + 0.382451i \(0.124920\pi\)
\(228\) 0 0
\(229\) 842886.i 1.06214i 0.847329 + 0.531068i \(0.178209\pi\)
−0.847329 + 0.531068i \(0.821791\pi\)
\(230\) 0 0
\(231\) 1.14720e6i 1.41453i
\(232\) 0 0
\(233\) −36169.3 + 36169.3i −0.0436466 + 0.0436466i −0.728593 0.684947i \(-0.759825\pi\)
0.684947 + 0.728593i \(0.259825\pi\)
\(234\) 0 0
\(235\) 473120. + 35816.3i 0.558858 + 0.0423069i
\(236\) 0 0
\(237\) 579477. + 579477.i 0.670139 + 0.670139i
\(238\) 0 0
\(239\) 273532. 0.309751 0.154876 0.987934i \(-0.450502\pi\)
0.154876 + 0.987934i \(0.450502\pi\)
\(240\) 0 0
\(241\) 901321. 0.999624 0.499812 0.866134i \(-0.333402\pi\)
0.499812 + 0.866134i \(0.333402\pi\)
\(242\) 0 0
\(243\) 113998. + 113998.i 0.123846 + 0.123846i
\(244\) 0 0
\(245\) −361038. + 310222.i −0.384272 + 0.330185i
\(246\) 0 0
\(247\) −727669. + 727669.i −0.758912 + 0.758912i
\(248\) 0 0
\(249\) 971832.i 0.993329i
\(250\) 0 0
\(251\) 1.31819e6i 1.32067i 0.750973 + 0.660333i \(0.229585\pi\)
−0.750973 + 0.660333i \(0.770415\pi\)
\(252\) 0 0
\(253\) −763144. + 763144.i −0.749558 + 0.749558i
\(254\) 0 0
\(255\) 1.76313e6 1.51497e6i 1.69799 1.45900i
\(256\) 0 0
\(257\) 684108. + 684108.i 0.646088 + 0.646088i 0.952045 0.305957i \(-0.0989764\pi\)
−0.305957 + 0.952045i \(0.598976\pi\)
\(258\) 0 0
\(259\) 1.16061e6 1.07507
\(260\) 0 0
\(261\) 3.71839e6 3.37873
\(262\) 0 0
\(263\) −974703. 974703.i −0.868926 0.868926i 0.123427 0.992354i \(-0.460611\pi\)
−0.992354 + 0.123427i \(0.960611\pi\)
\(264\) 0 0
\(265\) 478961. + 36258.5i 0.418973 + 0.0317173i
\(266\) 0 0
\(267\) 2.60091e6 2.60091e6i 2.23279 2.23279i
\(268\) 0 0
\(269\) 775071.i 0.653072i 0.945185 + 0.326536i \(0.105881\pi\)
−0.945185 + 0.326536i \(0.894119\pi\)
\(270\) 0 0
\(271\) 102988.i 0.0851848i −0.999093 0.0425924i \(-0.986438\pi\)
0.999093 0.0425924i \(-0.0135617\pi\)
\(272\) 0 0
\(273\) −1.71906e6 + 1.71906e6i −1.39600 + 1.39600i
\(274\) 0 0
\(275\) −832192. 126724.i −0.663578 0.101048i
\(276\) 0 0
\(277\) −1.46313e6 1.46313e6i −1.14573 1.14573i −0.987384 0.158347i \(-0.949384\pi\)
−0.158347 0.987384i \(-0.550616\pi\)
\(278\) 0 0
\(279\) −2.21619e6 −1.70449
\(280\) 0 0
\(281\) −1.69321e6 −1.27922 −0.639611 0.768699i \(-0.720905\pi\)
−0.639611 + 0.768699i \(0.720905\pi\)
\(282\) 0 0
\(283\) 67338.9 + 67338.9i 0.0499804 + 0.0499804i 0.731655 0.681675i \(-0.238748\pi\)
−0.681675 + 0.731655i \(0.738748\pi\)
\(284\) 0 0
\(285\) 203594. 2.68940e6i 0.148475 1.96129i
\(286\) 0 0
\(287\) 186618. 186618.i 0.133736 0.133736i
\(288\) 0 0
\(289\) 994321.i 0.700297i
\(290\) 0 0
\(291\) 1.81320e6i 1.25520i
\(292\) 0 0
\(293\) 342591. 342591.i 0.233135 0.233135i −0.580865 0.814000i \(-0.697286\pi\)
0.814000 + 0.580865i \(0.197286\pi\)
\(294\) 0 0
\(295\) 1.43400e6 + 1.66889e6i 0.959385 + 1.11654i
\(296\) 0 0
\(297\) −1.17386e6 1.17386e6i −0.772192 0.772192i
\(298\) 0 0
\(299\) −2.28711e6 −1.47948
\(300\) 0 0
\(301\) −727321. −0.462711
\(302\) 0 0
\(303\) −942588. 942588.i −0.589815 0.589815i
\(304\) 0 0
\(305\) 436284. + 507750.i 0.268547 + 0.312536i
\(306\) 0 0
\(307\) 8371.33 8371.33i 0.00506931 0.00506931i −0.704568 0.709637i \(-0.748859\pi\)
0.709637 + 0.704568i \(0.248859\pi\)
\(308\) 0 0
\(309\) 2.88809e6i 1.72074i
\(310\) 0 0
\(311\) 112470.i 0.0659383i −0.999456 0.0329691i \(-0.989504\pi\)
0.999456 0.0329691i \(-0.0104963\pi\)
\(312\) 0 0
\(313\) 932889. 932889.i 0.538232 0.538232i −0.384778 0.923009i \(-0.625722\pi\)
0.923009 + 0.384778i \(0.125722\pi\)
\(314\) 0 0
\(315\) 317801. 4.19803e6i 0.180459 2.38379i
\(316\) 0 0
\(317\) −1.24528e6 1.24528e6i −0.696018 0.696018i 0.267531 0.963549i \(-0.413792\pi\)
−0.963549 + 0.267531i \(0.913792\pi\)
\(318\) 0 0
\(319\) 2.11639e6 1.16445
\(320\) 0 0
\(321\) −3.26731e6 −1.76982
\(322\) 0 0
\(323\) 1.98062e6 + 1.98062e6i 1.05632 + 1.05632i
\(324\) 0 0
\(325\) −1.05713e6 1.43692e6i −0.555162 0.754611i
\(326\) 0 0
\(327\) 1.61356e6 1.61356e6i 0.834478 0.834478i
\(328\) 0 0
\(329\) 1.35063e6i 0.687936i
\(330\) 0 0
\(331\) 558197.i 0.280038i −0.990149 0.140019i \(-0.955284\pi\)
0.990149 0.140019i \(-0.0447164\pi\)
\(332\) 0 0
\(333\) −2.44080e6 + 2.44080e6i −1.20621 + 1.20621i
\(334\) 0 0
\(335\) −3.44006e6 260421.i −1.67477 0.126784i
\(336\) 0 0
\(337\) −2.10837e6 2.10837e6i −1.01128 1.01128i −0.999936 0.0113470i \(-0.996388\pi\)
−0.0113470 0.999936i \(-0.503612\pi\)
\(338\) 0 0
\(339\) −5.69857e6 −2.69319
\(340\) 0 0
\(341\) −1.26138e6 −0.587436
\(342\) 0 0
\(343\) 933011. + 933011.i 0.428205 + 0.428205i
\(344\) 0 0
\(345\) 4.54643e6 3.90652e6i 2.05647 1.76702i
\(346\) 0 0
\(347\) 1.22415e6 1.22415e6i 0.545773 0.545773i −0.379442 0.925215i \(-0.623884\pi\)
0.925215 + 0.379442i \(0.123884\pi\)
\(348\) 0 0
\(349\) 1.81586e6i 0.798027i −0.916945 0.399014i \(-0.869353\pi\)
0.916945 0.399014i \(-0.130647\pi\)
\(350\) 0 0
\(351\) 3.51801e6i 1.52416i
\(352\) 0 0
\(353\) −2.92561e6 + 2.92561e6i −1.24963 + 1.24963i −0.293740 + 0.955885i \(0.594900\pi\)
−0.955885 + 0.293740i \(0.905100\pi\)
\(354\) 0 0
\(355\) −298632. + 256600.i −0.125767 + 0.108065i
\(356\) 0 0
\(357\) 4.67906e6 + 4.67906e6i 1.94307 + 1.94307i
\(358\) 0 0
\(359\) −2.12540e6 −0.870372 −0.435186 0.900341i \(-0.643317\pi\)
−0.435186 + 0.900341i \(0.643317\pi\)
\(360\) 0 0
\(361\) 773749. 0.312487
\(362\) 0 0
\(363\) 1.67463e6 + 1.67463e6i 0.667040 + 0.667040i
\(364\) 0 0
\(365\) −1.92836e6 145982.i −0.757629 0.0573544i
\(366\) 0 0
\(367\) 2.48776e6 2.48776e6i 0.964149 0.964149i −0.0352305 0.999379i \(-0.511217\pi\)
0.999379 + 0.0352305i \(0.0112165\pi\)
\(368\) 0 0
\(369\) 784925.i 0.300097i
\(370\) 0 0
\(371\) 1.36731e6i 0.515741i
\(372\) 0 0
\(373\) −1.03845e6 + 1.03845e6i −0.386469 + 0.386469i −0.873426 0.486957i \(-0.838107\pi\)
0.486957 + 0.873426i \(0.338107\pi\)
\(374\) 0 0
\(375\) 4.55575e6 + 1.05073e6i 1.67294 + 0.385846i
\(376\) 0 0
\(377\) 3.17137e6 + 3.17137e6i 1.14919 + 1.14919i
\(378\) 0 0
\(379\) 2.06631e6 0.738921 0.369461 0.929246i \(-0.379542\pi\)
0.369461 + 0.929246i \(0.379542\pi\)
\(380\) 0 0
\(381\) 2.33714e6 0.824845
\(382\) 0 0
\(383\) −413143. 413143.i −0.143914 0.143914i 0.631479 0.775393i \(-0.282448\pi\)
−0.775393 + 0.631479i \(0.782448\pi\)
\(384\) 0 0
\(385\) 180882. 2.38938e6i 0.0621933 0.821550i
\(386\) 0 0
\(387\) 1.52958e6 1.52958e6i 0.519152 0.519152i
\(388\) 0 0
\(389\) 2.20146e6i 0.737628i 0.929503 + 0.368814i \(0.120236\pi\)
−0.929503 + 0.368814i \(0.879764\pi\)
\(390\) 0 0
\(391\) 6.22522e6i 2.05927i
\(392\) 0 0
\(393\) 4.32312e6 4.32312e6i 1.41194 1.41194i
\(394\) 0 0
\(395\) −1.11556e6 1.29829e6i −0.359749 0.418678i
\(396\) 0 0
\(397\) 1.35037e6 + 1.35037e6i 0.430007 + 0.430007i 0.888630 0.458624i \(-0.151657\pi\)
−0.458624 + 0.888630i \(0.651657\pi\)
\(398\) 0 0
\(399\) 7.67752e6 2.41428
\(400\) 0 0
\(401\) −478159. −0.148495 −0.0742474 0.997240i \(-0.523655\pi\)
−0.0742474 + 0.997240i \(0.523655\pi\)
\(402\) 0 0
\(403\) −1.89016e6 1.89016e6i −0.579742 0.579742i
\(404\) 0 0
\(405\) 1.81912e6 + 2.11710e6i 0.551092 + 0.641364i
\(406\) 0 0
\(407\) −1.38923e6 + 1.38923e6i −0.415707 + 0.415707i
\(408\) 0 0
\(409\) 1.52948e6i 0.452101i 0.974116 + 0.226051i \(0.0725815\pi\)
−0.974116 + 0.226051i \(0.927419\pi\)
\(410\) 0 0
\(411\) 7.63786e6i 2.23032i
\(412\) 0 0
\(413\) −4.42897e6 + 4.42897e6i −1.27770 + 1.27770i
\(414\) 0 0
\(415\) −153231. + 2.02412e6i −0.0436743 + 0.576921i
\(416\) 0 0
\(417\) −2.32140e6 2.32140e6i −0.653746 0.653746i
\(418\) 0 0
\(419\) −430992. −0.119932 −0.0599658 0.998200i \(-0.519099\pi\)
−0.0599658 + 0.998200i \(0.519099\pi\)
\(420\) 0 0
\(421\) 532919. 0.146540 0.0732700 0.997312i \(-0.476657\pi\)
0.0732700 + 0.997312i \(0.476657\pi\)
\(422\) 0 0
\(423\) −2.84042e6 2.84042e6i −0.771849 0.771849i
\(424\) 0 0
\(425\) −3.91110e6 + 2.87737e6i −1.05033 + 0.772722i
\(426\) 0 0
\(427\) −1.34748e6 + 1.34748e6i −0.357647 + 0.357647i
\(428\) 0 0
\(429\) 4.11536e6i 1.07960i
\(430\) 0 0
\(431\) 2.91761e6i 0.756544i −0.925695 0.378272i \(-0.876518\pi\)
0.925695 0.378272i \(-0.123482\pi\)
\(432\) 0 0
\(433\) 2.83132e6 2.83132e6i 0.725719 0.725719i −0.244045 0.969764i \(-0.578474\pi\)
0.969764 + 0.244045i \(0.0784744\pi\)
\(434\) 0 0
\(435\) −1.17211e7 887314.i −2.96992 0.224830i
\(436\) 0 0
\(437\) 5.10724e6 + 5.10724e6i 1.27933 + 1.27933i
\(438\) 0 0
\(439\) 3.88608e6 0.962389 0.481195 0.876614i \(-0.340203\pi\)
0.481195 + 0.876614i \(0.340203\pi\)
\(440\) 0 0
\(441\) 4.02998e6 0.986748
\(442\) 0 0
\(443\) −2.65811e6 2.65811e6i −0.643523 0.643523i 0.307897 0.951420i \(-0.400375\pi\)
−0.951420 + 0.307897i \(0.900375\pi\)
\(444\) 0 0
\(445\) −5.82724e6 + 5.00706e6i −1.39496 + 1.19862i
\(446\) 0 0
\(447\) −7.30194e6 + 7.30194e6i −1.72850 + 1.72850i
\(448\) 0 0
\(449\) 2.36957e6i 0.554695i 0.960770 + 0.277347i \(0.0894553\pi\)
−0.960770 + 0.277347i \(0.910545\pi\)
\(450\) 0 0
\(451\) 446755.i 0.103425i
\(452\) 0 0
\(453\) 6.16117e6 6.16117e6i 1.41065 1.41065i
\(454\) 0 0
\(455\) 3.85149e6 3.30939e6i 0.872168 0.749411i
\(456\) 0 0
\(457\) −522790. 522790.i −0.117095 0.117095i 0.646132 0.763226i \(-0.276386\pi\)
−0.763226 + 0.646132i \(0.776386\pi\)
\(458\) 0 0
\(459\) −9.57557e6 −2.12145
\(460\) 0 0
\(461\) −2.50003e6 −0.547890 −0.273945 0.961745i \(-0.588329\pi\)
−0.273945 + 0.961745i \(0.588329\pi\)
\(462\) 0 0
\(463\) 1.66673e6 + 1.66673e6i 0.361338 + 0.361338i 0.864306 0.502967i \(-0.167758\pi\)
−0.502967 + 0.864306i \(0.667758\pi\)
\(464\) 0 0
\(465\) 6.98584e6 + 528845.i 1.49826 + 0.113422i
\(466\) 0 0
\(467\) −694126. + 694126.i −0.147281 + 0.147281i −0.776902 0.629621i \(-0.783210\pi\)
0.629621 + 0.776902i \(0.283210\pi\)
\(468\) 0 0
\(469\) 9.82047e6i 2.06158i
\(470\) 0 0
\(471\) 8.24101e6i 1.71170i
\(472\) 0 0
\(473\) 870588. 870588.i 0.178920 0.178920i
\(474\) 0 0
\(475\) −848085. + 5.56934e6i −0.172467 + 1.13258i
\(476\) 0 0
\(477\) −2.87549e6 2.87549e6i −0.578650 0.578650i
\(478\) 0 0
\(479\) −2.67104e6 −0.531914 −0.265957 0.963985i \(-0.585688\pi\)
−0.265957 + 0.963985i \(0.585688\pi\)
\(480\) 0 0
\(481\) −4.16346e6 −0.820525
\(482\) 0 0
\(483\) 1.20655e7 + 1.20655e7i 2.35329 + 2.35329i
\(484\) 0 0
\(485\) 285891. 3.77652e6i 0.0551883 0.729016i
\(486\) 0 0
\(487\) −3.46493e6 + 3.46493e6i −0.662021 + 0.662021i −0.955856 0.293835i \(-0.905068\pi\)
0.293835 + 0.955856i \(0.405068\pi\)
\(488\) 0 0
\(489\) 4.87043e6i 0.921075i
\(490\) 0 0
\(491\) 4.65929e6i 0.872199i 0.899898 + 0.436100i \(0.143640\pi\)
−0.899898 + 0.436100i \(0.856360\pi\)
\(492\) 0 0
\(493\) 8.63205e6 8.63205e6i 1.59955 1.59955i
\(494\) 0 0
\(495\) 4.64454e6 + 5.40535e6i 0.851981 + 0.991541i
\(496\) 0 0
\(497\) −792520. 792520.i −0.143919 0.143919i
\(498\) 0 0
\(499\) 5.22603e6 0.939551 0.469776 0.882786i \(-0.344335\pi\)
0.469776 + 0.882786i \(0.344335\pi\)
\(500\) 0 0
\(501\) 3.19456e6 0.568613
\(502\) 0 0
\(503\) −3.92987e6 3.92987e6i −0.692561 0.692561i 0.270234 0.962795i \(-0.412899\pi\)
−0.962795 + 0.270234i \(0.912899\pi\)
\(504\) 0 0
\(505\) 1.81459e6 + 2.11183e6i 0.316629 + 0.368494i
\(506\) 0 0
\(507\) −859749. + 859749.i −0.148543 + 0.148543i
\(508\) 0 0
\(509\) 7.30782e6i 1.25024i 0.780529 + 0.625120i \(0.214950\pi\)
−0.780529 + 0.625120i \(0.785050\pi\)
\(510\) 0 0
\(511\) 5.50497e6i 0.932615i
\(512\) 0 0
\(513\) −7.85591e6 + 7.85591e6i −1.31796 + 1.31796i
\(514\) 0 0
\(515\) −455372. + 6.01529e6i −0.0756568 + 0.999398i
\(516\) 0 0
\(517\) −1.61668e6 1.61668e6i −0.266010 0.266010i
\(518\) 0 0
\(519\) 2.51100e6 0.409194
\(520\) 0 0
\(521\) 3.41968e6 0.551940 0.275970 0.961166i \(-0.411001\pi\)
0.275970 + 0.961166i \(0.411001\pi\)
\(522\) 0 0
\(523\) −7.89585e6 7.89585e6i −1.26225 1.26225i −0.950001 0.312248i \(-0.898918\pi\)
−0.312248 0.950001i \(1.39892\pi\)
\(524\) 0 0
\(525\) −2.00354e6 + 1.31571e7i −0.317248 + 2.08335i
\(526\) 0 0
\(527\) −5.14476e6 + 5.14476e6i −0.806935 + 0.806935i
\(528\) 0 0
\(529\) 9.61605e6i 1.49402i
\(530\) 0 0
\(531\) 1.86285e7i 2.86709i
\(532\) 0 0
\(533\) −669452. + 669452.i −0.102071 + 0.102071i
\(534\) 0 0
\(535\) 6.80512e6 + 515164.i 1.02790 + 0.0778146i
\(536\) 0 0
\(537\) −7.45424e6 7.45424e6i −1.11550 1.11550i
\(538\) 0 0
\(539\) 2.29374e6 0.340073
\(540\) 0 0
\(541\) 3.77154e6 0.554020 0.277010 0.960867i \(-0.410656\pi\)
0.277010 + 0.960867i \(0.410656\pi\)
\(542\) 0 0
\(543\) 1.11566e7 + 1.11566e7i 1.62379 + 1.62379i
\(544\) 0 0
\(545\) −3.61511e6 + 3.10629e6i −0.521351 + 0.447971i
\(546\) 0 0
\(547\) 8.30474e6 8.30474e6i 1.18675 1.18675i 0.208783 0.977962i \(-0.433050\pi\)
0.977962 0.208783i \(-0.0669503\pi\)
\(548\) 0 0
\(549\) 5.66760e6i 0.802543i
\(550\) 0 0
\(551\) 1.41637e7i 1.98745i
\(552\) 0 0
\(553\) 3.44546e6 3.44546e6i 0.479109 0.479109i
\(554\) 0 0
\(555\) 8.27632e6 7.11143e6i 1.14053 0.979996i
\(556\) 0 0
\(557\) −3.82357e6 3.82357e6i −0.522193 0.522193i 0.396040 0.918233i \(-0.370384\pi\)
−0.918233 + 0.396040i \(0.870384\pi\)
\(558\) 0 0
\(559\) 2.60912e6 0.353154
\(560\) 0 0
\(561\) −1.12015e7 −1.50269
\(562\) 0 0
\(563\) −7.83668e6 7.83668e6i −1.04198 1.04198i −0.999079 0.0429050i \(-0.986339\pi\)
−0.0429050 0.999079i \(1.48634\pi\)
\(564\) 0 0
\(565\) 1.18689e7 + 898506.i 1.56419 + 0.118413i
\(566\) 0 0
\(567\) −5.61844e6 + 5.61844e6i −0.733936 + 0.733936i
\(568\) 0 0
\(569\) 1.06662e7i 1.38111i −0.723280 0.690555i \(-0.757366\pi\)
0.723280 0.690555i \(-0.242634\pi\)
\(570\) 0 0
\(571\) 103844.i 0.0133288i 0.999978 + 0.00666439i \(0.00212136\pi\)
−0.999978 + 0.00666439i \(0.997879\pi\)
\(572\) 0 0
\(573\) −2.77349e6 + 2.77349e6i −0.352891 + 0.352891i
\(574\) 0 0
\(575\) −1.00852e7 + 7.41960e6i −1.27208 + 0.935861i
\(576\) 0 0
\(577\) 5.35378e6 + 5.35378e6i 0.669455 + 0.669455i 0.957590 0.288135i \(-0.0930352\pi\)
−0.288135 + 0.957590i \(0.593035\pi\)
\(578\) 0 0
\(579\) 2.46014e7 3.04974
\(580\) 0 0
\(581\) −5.77833e6 −0.710170
\(582\) 0 0
\(583\) −1.63664e6 1.63664e6i −0.199426 0.199426i
\(584\) 0 0
\(585\) −1.14004e6 + 1.50596e7i −0.137731 + 1.81938i
\(586\) 0 0
\(587\) 3.02584e6 3.02584e6i 0.362453 0.362453i −0.502263 0.864715i \(-0.667499\pi\)
0.864715 + 0.502263i \(0.167499\pi\)
\(588\) 0 0
\(589\) 8.44164e6i 1.00263i
\(590\) 0 0
\(591\) 1.83522e7i 2.16133i
\(592\) 0 0
\(593\) 7.77341e6 7.77341e6i 0.907768 0.907768i −0.0883240 0.996092i \(-0.528151\pi\)
0.996092 + 0.0883240i \(0.0281511\pi\)
\(594\) 0 0
\(595\) −9.00774e6 1.04833e7i −1.04309 1.21396i
\(596\) 0 0
\(597\) −1.37845e7 1.37845e7i −1.58290 1.58290i
\(598\) 0 0
\(599\) −396440. −0.0451451 −0.0225726 0.999745i \(-0.507186\pi\)
−0.0225726 + 0.999745i \(0.507186\pi\)
\(600\) 0 0
\(601\) −3.27167e6 −0.369474 −0.184737 0.982788i \(-0.559143\pi\)
−0.184737 + 0.982788i \(0.559143\pi\)
\(602\) 0 0
\(603\) 2.06527e7 + 2.06527e7i 2.31305 + 2.31305i
\(604\) 0 0
\(605\) −3.22385e6 3.75194e6i −0.358086 0.416742i
\(606\) 0 0
\(607\) −7.39370e6 + 7.39370e6i −0.814498 + 0.814498i −0.985305 0.170807i \(-0.945363\pi\)
0.170807 + 0.985305i \(0.445363\pi\)
\(608\) 0 0
\(609\) 3.34606e7i 3.65587i
\(610\) 0 0
\(611\) 4.84512e6i 0.525051i
\(612\) 0 0
\(613\) −3.55531e6 + 3.55531e6i −0.382143 + 0.382143i −0.871874 0.489730i \(-0.837095\pi\)
0.489730 + 0.871874i \(0.337095\pi\)
\(614\) 0 0
\(615\) 187305. 2.47423e6i 0.0199693 0.263787i
\(616\) 0 0
\(617\) 3.25539e6 + 3.25539e6i 0.344263 + 0.344263i 0.857967 0.513704i \(-0.171727\pi\)
−0.513704 + 0.857967i \(0.671727\pi\)
\(618\) 0 0
\(619\) −1.78255e7 −1.86989 −0.934943 0.354798i \(-0.884550\pi\)
−0.934943 + 0.354798i \(0.884550\pi\)
\(620\) 0 0
\(621\) −2.46916e7 −2.56933
\(622\) 0 0
\(623\) −1.54645e7 1.54645e7i −1.59631 1.59631i
\(624\) 0 0
\(625\) −9.32299e6 2.90677e6i −0.954674 0.297653i
\(626\) 0 0
\(627\) −9.18982e6 + 9.18982e6i −0.933551 + 0.933551i
\(628\) 0 0
\(629\) 1.13324e7i 1.14208i
\(630\) 0 0
\(631\) 1.77949e7i 1.77919i 0.456754 + 0.889593i \(0.349012\pi\)
−0.456754 + 0.889593i \(0.650988\pi\)
\(632\) 0 0
\(633\) 7.49866e6 7.49866e6i 0.743831 0.743831i
\(634\) 0 0
\(635\) −4.86777e6 368502.i −0.479066 0.0362665i
\(636\) 0 0
\(637\) 3.43712e6 + 3.43712e6i 0.335618 + 0.335618i
\(638\) 0 0
\(639\) 3.33339e6 0.322949
\(640\) 0 0
\(641\) −3.48962e6 −0.335454 −0.167727 0.985833i \(-0.553643\pi\)
−0.167727 + 0.985833i \(0.553643\pi\)
\(642\) 0 0
\(643\) 9.79073e6 + 9.79073e6i 0.933873 + 0.933873i 0.997945 0.0640725i \(-0.0204089\pi\)
−0.0640725 + 0.997945i \(0.520409\pi\)
\(644\) 0 0
\(645\) −5.18652e6 + 4.45652e6i −0.490882 + 0.421790i
\(646\) 0 0
\(647\) 9.53507e6 9.53507e6i 0.895495 0.895495i −0.0995389 0.995034i \(-0.531737\pi\)
0.995034 + 0.0995389i \(0.0317368\pi\)
\(648\) 0 0
\(649\) 1.06028e7i 0.988114i
\(650\) 0 0
\(651\) 1.99427e7i 1.84430i
\(652\) 0 0
\(653\) 1.15953e7 1.15953e7i 1.06414 1.06414i 0.0663484 0.997797i \(-0.478865\pi\)
0.997797 0.0663484i \(-0.0211349\pi\)
\(654\) 0 0
\(655\) −9.68577e6 + 8.32250e6i −0.882127 + 0.757968i
\(656\) 0 0
\(657\) 1.15771e7 + 1.15771e7i 1.04637 + 1.04637i
\(658\) 0 0
\(659\) 6.06117e6 0.543679 0.271840 0.962343i \(-0.412368\pi\)
0.271840 + 0.962343i \(0.412368\pi\)
\(660\) 0 0
\(661\) 4.27293e6 0.380384 0.190192 0.981747i \(-0.439089\pi\)
0.190192 + 0.981747i \(0.439089\pi\)
\(662\) 0 0
\(663\) −1.67852e7 1.67852e7i −1.48300 1.48300i
\(664\) 0 0
\(665\) −1.59906e7 1.21053e6i −1.40221 0.106150i
\(666\) 0 0
\(667\) 2.22587e7 2.22587e7i 1.93724 1.93724i
\(668\) 0 0
\(669\) 1.44912e7i 1.25181i
\(670\) 0 0
\(671\) 3.22582e6i 0.276588i
\(672\) 0 0
\(673\) 5.55486e6 5.55486e6i 0.472755 0.472755i −0.430050 0.902805i \(-0.641504\pi\)
0.902805 + 0.430050i \(0.141504\pi\)
\(674\) 0 0
\(675\) −1.14128e7 1.55129e7i −0.964121 1.31049i
\(676\) 0 0
\(677\) 1.30293e7 + 1.30293e7i 1.09257 + 1.09257i 0.995254 + 0.0973148i \(0.0310253\pi\)
0.0973148 + 0.995254i \(0.468975\pi\)
\(678\) 0 0
\(679\) 1.07810e7 0.897393
\(680\) 0 0
\(681\) 1.59124e7 1.31483
\(682\) 0 0
\(683\) 378888. + 378888.i 0.0310784 + 0.0310784i 0.722475 0.691397i \(-0.243004\pi\)
−0.691397 + 0.722475i \(0.743004\pi\)
\(684\) 0 0
\(685\) 1.20428e6 1.59081e7i 0.0980619 1.29536i
\(686\) 0 0
\(687\) −1.59512e7 + 1.59512e7i −1.28944 + 1.28944i
\(688\) 0 0
\(689\) 4.90494e6i 0.393628i
\(690\) 0 0
\(691\) 2.01178e7i 1.60282i −0.598113 0.801412i \(-0.704083\pi\)
0.598113 0.801412i \(-0.295917\pi\)
\(692\) 0 0
\(693\) −1.43449e7 + 1.43449e7i −1.13466 + 1.13466i
\(694\) 0 0
\(695\) 4.46896e6 + 5.20100e6i 0.350949 + 0.408437i
\(696\) 0 0
\(697\) 1.82216e6 + 1.82216e6i 0.142071 + 0.142071i
\(698\) 0 0
\(699\) −1.36897e6 −0.105974
\(700\) 0 0
\(701\) 891657. 0.0685335 0.0342667 0.999413i \(-0.489090\pi\)
0.0342667 + 0.999413i \(0.489090\pi\)
\(702\) 0 0
\(703\) 9.29723e6 + 9.29723e6i 0.709521 + 0.709521i
\(704\) 0 0
\(705\) 8.27575e6 + 9.63136e6i 0.627097 + 0.729818i
\(706\) 0 0
\(707\) −5.60445e6 + 5.60445e6i −0.421682 + 0.421682i
\(708\) 0 0
\(709\) 1.98980e7i 1.48660i 0.668959 + 0.743299i \(0.266740\pi\)
−0.668959 + 0.743299i \(0.733260\pi\)
\(710\) 0 0
\(711\) 1.44918e7i 1.07510i
\(712\) 0 0
\(713\) −1.32663e7 + 1.32663e7i −0.977296 + 0.977296i
\(714\) 0 0
\(715\) −648877. + 8.57142e6i −0.0474676 + 0.627029i
\(716\) 0 0
\(717\) 5.17644e6 + 5.17644e6i 0.376040 + 0.376040i
\(718\) 0 0
\(719\) 1.06358e7 0.767272 0.383636 0.923484i \(-0.374672\pi\)
0.383636 + 0.923484i \(0.374672\pi\)
\(720\) 0 0
\(721\) −1.71721e7 −1.23022
\(722\) 0 0
\(723\) 1.70570e7 + 1.70570e7i 1.21355 + 1.21355i
\(724\) 0 0
\(725\) 2.42726e7 + 3.69617e6i 1.71503 + 0.261160i
\(726\) 0 0
\(727\) 3.76230e6 3.76230e6i 0.264008 0.264008i −0.562672 0.826680i \(-0.690227\pi\)
0.826680 + 0.562672i \(0.190227\pi\)
\(728\) 0 0
\(729\) 1.64482e7i 1.14631i
\(730\) 0 0
\(731\) 7.10167e6i 0.491550i
\(732\) 0 0
\(733\) 1.16678e7 1.16678e7i 0.802104 0.802104i −0.181320 0.983424i \(-0.558037\pi\)
0.983424 + 0.181320i \(0.0580369\pi\)
\(734\) 0 0
\(735\) −1.27033e7 961668.i −0.867355 0.0656609i
\(736\) 0 0
\(737\) 1.17549e7 + 1.17549e7i 0.797167 + 0.797167i
\(738\) 0 0
\(739\) 1.52408e6 0.102659 0.0513296 0.998682i \(-0.483654\pi\)
0.0513296 + 0.998682i \(0.483654\pi\)
\(740\) 0 0
\(741\) −2.75415e7 −1.84265
\(742\) 0 0
\(743\) 5.92734e6 + 5.92734e6i 0.393901 + 0.393901i 0.876075 0.482174i \(-0.160153\pi\)
−0.482174 + 0.876075i \(0.660153\pi\)
\(744\) 0 0
\(745\) 1.63597e7 1.40571e7i 1.07990 0.927907i
\(746\) 0 0
\(747\) 1.21520e7 1.21520e7i 0.796795 0.796795i
\(748\) 0 0
\(749\) 1.94268e7i 1.26531i
\(750\) 0 0
\(751\) 1.28380e7i 0.830614i −0.909681 0.415307i \(-0.863674\pi\)
0.909681 0.415307i \(-0.136326\pi\)
\(752\) 0 0
\(753\) −2.49460e7 + 2.49460e7i −1.60330 + 1.60330i
\(754\) 0 0
\(755\) −1.38039e7 + 1.18610e7i −0.881319 + 0.757274i
\(756\) 0 0
\(757\) 9.71886e6 + 9.71886e6i 0.616418 + 0.616418i 0.944611 0.328192i \(-0.106439\pi\)
−0.328192 + 0.944611i \(0.606439\pi\)
\(758\) 0 0
\(759\) −2.88842e7 −1.81993
\(760\) 0 0
\(761\) −2.02827e7 −1.26959 −0.634795 0.772680i \(-0.718916\pi\)
−0.634795 + 0.772680i \(0.718916\pi\)
\(762\) 0 0
\(763\) −9.59391e6 9.59391e6i −0.596602 0.596602i
\(764\) 0 0
\(765\) 4.09902e7 + 3.10305e6i 2.53236 + 0.191706i
\(766\) 0 0
\(767\) 1.58880e7 1.58880e7i 0.975171 0.975171i
\(768\) 0 0
\(769\) 4.07161e6i 0.248285i −0.992264 0.124142i \(-0.960382\pi\)
0.992264 0.124142i \(-0.0396180\pi\)
\(770\) 0 0
\(771\) 2.58928e7i 1.56871i
\(772\) 0 0
\(773\) 1.88515e7 1.88515e7i 1.13474 1.13474i 0.145362 0.989378i \(-0.453565\pi\)
0.989378 0.145362i \(-0.0464348\pi\)
\(774\) 0 0
\(775\) −1.44666e7 2.20294e6i −0.865194 0.131750i
\(776\) 0 0
\(777\) 2.19640e7 + 2.19640e7i 1.30514 + 1.30514i
\(778\) 0 0
\(779\) 2.98985e6 0.176525
\(780\) 0 0
\(781\) 1.89726e6 0.111301
\(782\) 0 0
\(783\) 3.42381e7 + 3.42381e7i 1.99574 + 1.99574i
\(784\) 0 0
\(785\) −1.29938e6 + 1.71643e7i −0.0752595 + 0.994148i
\(786\) 0 0
\(787\) −1.81274e6 + 1.81274e6i −0.104327 + 0.104327i −0.757344 0.653016i \(-0.773503\pi\)
0.653016 + 0.757344i \(0.273503\pi\)
\(788\) 0 0
\(789\) 3.68915e7i 2.10976i
\(790\) 0 0
\(791\) 3.38826e7i 1.92547i
\(792\) 0 0
\(793\) 4.83382e6 4.83382e6i 0.272966 0.272966i