Properties

Label 160.6.n.b.127.1
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 127.1
Root \(-15.8126 + 15.8126i\) of defining polynomial
Character \(\chi\) \(=\) 160.127
Dual form 160.6.n.b.63.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-16.5519 - 16.5519i) q^{3} +(13.9288 + 54.1386i) q^{5} +(-2.15894 + 2.15894i) q^{7} +304.928i q^{9} +O(q^{10})\) \(q+(-16.5519 - 16.5519i) q^{3} +(13.9288 + 54.1386i) q^{5} +(-2.15894 + 2.15894i) q^{7} +304.928i q^{9} -255.685i q^{11} +(111.516 - 111.516i) q^{13} +(665.546 - 1126.64i) q^{15} +(998.711 + 998.711i) q^{17} +1946.41 q^{19} +71.4691 q^{21} +(-1615.69 - 1615.69i) q^{23} +(-2736.97 + 1508.18i) q^{25} +(1025.02 - 1025.02i) q^{27} -5843.34i q^{29} -1607.74i q^{31} +(-4232.06 + 4232.06i) q^{33} +(-146.954 - 86.8106i) q^{35} +(-11348.6 - 11348.6i) q^{37} -3691.59 q^{39} -8433.98 q^{41} +(-13638.6 - 13638.6i) q^{43} +(-16508.4 + 4247.29i) q^{45} +(-12797.4 + 12797.4i) q^{47} +16797.7i q^{49} -33061.0i q^{51} +(2038.79 - 2038.79i) q^{53} +(13842.4 - 3561.40i) q^{55} +(-32216.6 - 32216.6i) q^{57} +27506.9 q^{59} +9598.42 q^{61} +(-658.322 - 658.322i) q^{63} +(7590.61 + 4484.03i) q^{65} +(37401.5 - 37401.5i) q^{67} +53485.4i q^{69} -60089.5i q^{71} +(25054.5 - 25054.5i) q^{73} +(70265.1 + 20338.9i) q^{75} +(552.010 + 552.010i) q^{77} -49267.4 q^{79} +40165.4 q^{81} +(-44679.8 - 44679.8i) q^{83} +(-40157.9 + 67979.7i) q^{85} +(-96718.2 + 96718.2i) q^{87} +20469.3i q^{89} +481.514i q^{91} +(-26611.1 + 26611.1i) q^{93} +(27111.2 + 105376. i) q^{95} +(-100982. - 100982. i) q^{97} +77965.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 10q^{3} + 42q^{5} + 66q^{7} + O(q^{10}) \) \( 14q + 10q^{3} + 42q^{5} + 66q^{7} - 414q^{13} + 278q^{15} + 1222q^{17} + 5672q^{19} + 5924q^{21} + 2902q^{23} - 4466q^{25} - 2168q^{27} - 2444q^{33} - 2618q^{35} - 1790q^{37} - 11076q^{39} + 11644q^{41} - 3982q^{43} + 14704q^{45} - 1278q^{47} + 5882q^{53} + 65608q^{55} - 14552q^{57} - 8504q^{59} + 20564q^{61} + 19422q^{63} + 40798q^{65} + 107926q^{67} - 16418q^{73} + 66586q^{75} - 13348q^{77} - 146544q^{79} + 173806q^{81} - 36398q^{83} - 66262q^{85} + 124384q^{87} - 306620q^{93} + 173768q^{95} - 60314q^{97} - 388628q^{99} + O(q^{100}) \)

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
\(3\) −16.5519 16.5519i −1.06180 1.06180i −0.997960 0.0638422i \(-0.979665\pi\)
−0.0638422 0.997960i \(1.47966\pi\)
\(4\) 0 0
\(5\) 13.9288 + 54.1386i 0.249167 + 0.968461i
\(6\) 0 0
\(7\) −2.15894 + 2.15894i −0.0166531 + 0.0166531i −0.715384 0.698731i \(-0.753748\pi\)
0.698731 + 0.715384i \(0.253748\pi\)
\(8\) 0 0
\(9\) 304.928i 1.25485i
\(10\) 0 0
\(11\) 255.685i 0.637124i −0.947902 0.318562i \(-0.896800\pi\)
0.947902 0.318562i \(-0.103200\pi\)
\(12\) 0 0
\(13\) 111.516 111.516i 0.183012 0.183012i −0.609655 0.792667i \(-0.708692\pi\)
0.792667 + 0.609655i \(0.208692\pi\)
\(14\) 0 0
\(15\) 665.546 1126.64i 0.763748 1.29288i
\(16\) 0 0
\(17\) 998.711 + 998.711i 0.838142 + 0.838142i 0.988614 0.150473i \(-0.0480795\pi\)
−0.150473 + 0.988614i \(0.548080\pi\)
\(18\) 0 0
\(19\) 1946.41 1.23694 0.618471 0.785807i \(-0.287752\pi\)
0.618471 + 0.785807i \(0.287752\pi\)
\(20\) 0 0
\(21\) 71.4691 0.0353647
\(22\) 0 0
\(23\) −1615.69 1615.69i −0.636853 0.636853i 0.312925 0.949778i \(-0.398691\pi\)
−0.949778 + 0.312925i \(0.898691\pi\)
\(24\) 0 0
\(25\) −2736.97 + 1508.18i −0.875832 + 0.482616i
\(26\) 0 0
\(27\) 1025.02 1025.02i 0.270598 0.270598i
\(28\) 0 0
\(29\) 5843.34i 1.29023i −0.764087 0.645114i \(-0.776810\pi\)
0.764087 0.645114i \(-0.223190\pi\)
\(30\) 0 0
\(31\) 1607.74i 0.300477i −0.988650 0.150238i \(-0.951996\pi\)
0.988650 0.150238i \(-0.0480041\pi\)
\(32\) 0 0
\(33\) −4232.06 + 4232.06i −0.676499 + 0.676499i
\(34\) 0 0
\(35\) −146.954 86.8106i −0.0202773 0.0119785i
\(36\) 0 0
\(37\) −11348.6 11348.6i −1.36282 1.36282i −0.870306 0.492511i \(-0.836079\pi\)
−0.492511 0.870306i \(-0.663921\pi\)
\(38\) 0 0
\(39\) −3691.59 −0.388644
\(40\) 0 0
\(41\) −8433.98 −0.783561 −0.391781 0.920059i \(-0.628141\pi\)
−0.391781 + 0.920059i \(0.628141\pi\)
\(42\) 0 0
\(43\) −13638.6 13638.6i −1.12486 1.12486i −0.991000 0.133861i \(-0.957262\pi\)
−0.133861 0.991000i \(1.45726\pi\)
\(44\) 0 0
\(45\) −16508.4 + 4247.29i −1.21527 + 0.312666i
\(46\) 0 0
\(47\) −12797.4 + 12797.4i −0.845043 + 0.845043i −0.989510 0.144467i \(-0.953853\pi\)
0.144467 + 0.989510i \(0.453853\pi\)
\(48\) 0 0
\(49\) 16797.7i 0.999445i
\(50\) 0 0
\(51\) 33061.0i 1.77988i
\(52\) 0 0
\(53\) 2038.79 2038.79i 0.0996973 0.0996973i −0.655499 0.755196i \(-0.727542\pi\)
0.755196 + 0.655499i \(0.227542\pi\)
\(54\) 0 0
\(55\) 13842.4 3561.40i 0.617029 0.158750i
\(56\) 0 0
\(57\) −32216.6 32216.6i −1.31339 1.31339i
\(58\) 0 0
\(59\) 27506.9 1.02875 0.514376 0.857565i \(-0.328023\pi\)
0.514376 + 0.857565i \(0.328023\pi\)
\(60\) 0 0
\(61\) 9598.42 0.330275 0.165137 0.986271i \(-0.447193\pi\)
0.165137 + 0.986271i \(0.447193\pi\)
\(62\) 0 0
\(63\) −658.322 658.322i −0.0208972 0.0208972i
\(64\) 0 0
\(65\) 7590.61 + 4484.03i 0.222840 + 0.131639i
\(66\) 0 0
\(67\) 37401.5 37401.5i 1.01789 1.01789i 0.0180552 0.999837i \(-0.494253\pi\)
0.999837 0.0180552i \(-0.00574746\pi\)
\(68\) 0 0
\(69\) 53485.4i 1.35242i
\(70\) 0 0
\(71\) 60089.5i 1.41466i −0.706883 0.707331i \(-0.749899\pi\)
0.706883 0.707331i \(-0.250101\pi\)
\(72\) 0 0
\(73\) 25054.5 25054.5i 0.550274 0.550274i −0.376246 0.926520i \(-0.622785\pi\)
0.926520 + 0.376246i \(0.122785\pi\)
\(74\) 0 0
\(75\) 70265.1 + 20338.9i 1.44240 + 0.417517i
\(76\) 0 0
\(77\) 552.010 + 552.010i 0.0106101 + 0.0106101i
\(78\) 0 0
\(79\) −49267.4 −0.888161 −0.444080 0.895987i \(-0.646470\pi\)
−0.444080 + 0.895987i \(0.646470\pi\)
\(80\) 0 0
\(81\) 40165.4 0.680205
\(82\) 0 0
\(83\) −44679.8 44679.8i −0.711895 0.711895i 0.255036 0.966931i \(-0.417913\pi\)
−0.966931 + 0.255036i \(0.917913\pi\)
\(84\) 0 0
\(85\) −40157.9 + 67979.7i −0.602870 + 1.02054i
\(86\) 0 0
\(87\) −96718.2 + 96718.2i −1.36997 + 1.36997i
\(88\) 0 0
\(89\) 20469.3i 0.273922i 0.990576 + 0.136961i \(0.0437335\pi\)
−0.990576 + 0.136961i \(0.956266\pi\)
\(90\) 0 0
\(91\) 481.514i 0.00609544i
\(92\) 0 0
\(93\) −26611.1 + 26611.1i −0.319047 + 0.319047i
\(94\) 0 0
\(95\) 27111.2 + 105376.i 0.308205 + 1.19793i
\(96\) 0 0
\(97\) −100982. 100982.i −1.08972 1.08972i −0.995557 0.0941648i \(-0.969982\pi\)
−0.0941648 0.995557i \(-0.530018\pi\)
\(98\) 0 0
\(99\) 77965.5 0.799493
\(100\) 0 0
\(101\) 167690. 1.63570 0.817852 0.575429i \(-0.195165\pi\)
0.817852 + 0.575429i \(0.195165\pi\)
\(102\) 0 0
\(103\) −82074.1 82074.1i −0.762277 0.762277i 0.214456 0.976734i \(-0.431202\pi\)
−0.976734 + 0.214456i \(0.931202\pi\)
\(104\) 0 0
\(105\) 995.481 + 3869.23i 0.00881170 + 0.0342493i
\(106\) 0 0
\(107\) −91100.8 + 91100.8i −0.769241 + 0.769241i −0.977973 0.208732i \(-0.933066\pi\)
0.208732 + 0.977973i \(0.433066\pi\)
\(108\) 0 0
\(109\) 188806.i 1.52212i −0.648680 0.761062i \(-0.724678\pi\)
0.648680 0.761062i \(-0.275322\pi\)
\(110\) 0 0
\(111\) 375680.i 2.89408i
\(112\) 0 0
\(113\) 130082. 130082.i 0.958343 0.958343i −0.0408237 0.999166i \(-0.512998\pi\)
0.999166 + 0.0408237i \(0.0129982\pi\)
\(114\) 0 0
\(115\) 64966.6 109976.i 0.458084 0.775449i
\(116\) 0 0
\(117\) 34004.4 + 34004.4i 0.229652 + 0.229652i
\(118\) 0 0
\(119\) −4312.32 −0.0279154
\(120\) 0 0
\(121\) 95676.1 0.594074
\(122\) 0 0
\(123\) 139598. + 139598.i 0.831987 + 0.831987i
\(124\) 0 0
\(125\) −119773. 127169.i −0.685623 0.727957i
\(126\) 0 0
\(127\) −118771. + 118771.i −0.653431 + 0.653431i −0.953818 0.300387i \(-0.902884\pi\)
0.300387 + 0.953818i \(0.402884\pi\)
\(128\) 0 0
\(129\) 451489.i 2.38876i
\(130\) 0 0
\(131\) 53985.4i 0.274852i −0.990512 0.137426i \(-0.956117\pi\)
0.990512 0.137426i \(-0.0438829\pi\)
\(132\) 0 0
\(133\) −4202.18 + 4202.18i −0.0205990 + 0.0205990i
\(134\) 0 0
\(135\) 69770.7 + 41215.9i 0.329487 + 0.194639i
\(136\) 0 0
\(137\) 101234. + 101234.i 0.460813 + 0.460813i 0.898922 0.438109i \(-0.144351\pi\)
−0.438109 + 0.898922i \(0.644351\pi\)
\(138\) 0 0
\(139\) −92974.7 −0.408157 −0.204079 0.978954i \(-0.565420\pi\)
−0.204079 + 0.978954i \(0.565420\pi\)
\(140\) 0 0
\(141\) 423643. 1.79454
\(142\) 0 0
\(143\) −28513.0 28513.0i −0.116601 0.116601i
\(144\) 0 0
\(145\) 316350. 81391.0i 1.24953 0.321482i
\(146\) 0 0
\(147\) 278033. 278033.i 1.06121 1.06121i
\(148\) 0 0
\(149\) 209067.i 0.771470i −0.922610 0.385735i \(-0.873948\pi\)
0.922610 0.385735i \(-0.126052\pi\)
\(150\) 0 0
\(151\) 37816.8i 0.134972i −0.997720 0.0674858i \(-0.978502\pi\)
0.997720 0.0674858i \(-0.0214977\pi\)
\(152\) 0 0
\(153\) −304535. + 304535.i −1.05174 + 1.05174i
\(154\) 0 0
\(155\) 87040.7 22393.9i 0.291000 0.0748688i
\(156\) 0 0
\(157\) 250564. + 250564.i 0.811277 + 0.811277i 0.984825 0.173548i \(-0.0555232\pi\)
−0.173548 + 0.984825i \(0.555523\pi\)
\(158\) 0 0
\(159\) −67491.6 −0.211718
\(160\) 0 0
\(161\) 6976.37 0.0212112
\(162\) 0 0
\(163\) −114285. 114285.i −0.336915 0.336915i 0.518290 0.855205i \(-0.326569\pi\)
−0.855205 + 0.518290i \(0.826569\pi\)
\(164\) 0 0
\(165\) −288066. 170170.i −0.823724 0.486602i
\(166\) 0 0
\(167\) 351508. 351508.i 0.975313 0.975313i −0.0243893 0.999703i \(-0.507764\pi\)
0.999703 + 0.0243893i \(0.00776413\pi\)
\(168\) 0 0
\(169\) 346421.i 0.933013i
\(170\) 0 0
\(171\) 593514.i 1.55217i
\(172\) 0 0
\(173\) −264889. + 264889.i −0.672898 + 0.672898i −0.958383 0.285485i \(-0.907845\pi\)
0.285485 + 0.958383i \(0.407845\pi\)
\(174\) 0 0
\(175\) 2652.91 9165.04i 0.00654828 0.0226224i
\(176\) 0 0
\(177\) −455290. 455290.i −1.09233 1.09233i
\(178\) 0 0
\(179\) −584607. −1.36374 −0.681870 0.731473i \(-0.738833\pi\)
−0.681870 + 0.731473i \(0.738833\pi\)
\(180\) 0 0
\(181\) −224651. −0.509698 −0.254849 0.966981i \(-0.582026\pi\)
−0.254849 + 0.966981i \(0.582026\pi\)
\(182\) 0 0
\(183\) −158872. 158872.i −0.350686 0.350686i
\(184\) 0 0
\(185\) 456324. 772469.i 0.980266 1.65940i
\(186\) 0 0
\(187\) 255355. 255355.i 0.534000 0.534000i
\(188\) 0 0
\(189\) 4425.94i 0.00901261i
\(190\) 0 0
\(191\) 17886.3i 0.0354761i 0.999843 + 0.0177381i \(0.00564650\pi\)
−0.999843 + 0.0177381i \(0.994354\pi\)
\(192\) 0 0
\(193\) 42336.3 42336.3i 0.0818125 0.0818125i −0.665016 0.746829i \(-0.731575\pi\)
0.746829 + 0.665016i \(0.231575\pi\)
\(194\) 0 0
\(195\) −51419.6 199858.i −0.0968372 0.376387i
\(196\) 0 0
\(197\) −209419. 209419.i −0.384459 0.384459i 0.488247 0.872706i \(-0.337637\pi\)
−0.872706 + 0.488247i \(0.837637\pi\)
\(198\) 0 0
\(199\) −447716. −0.801438 −0.400719 0.916201i \(-0.631240\pi\)
−0.400719 + 0.916201i \(0.631240\pi\)
\(200\) 0 0
\(201\) −1.23813e6 −2.16160
\(202\) 0 0
\(203\) 12615.4 + 12615.4i 0.0214863 + 0.0214863i
\(204\) 0 0
\(205\) −117476. 456604.i −0.195237 0.758848i
\(206\) 0 0
\(207\) 492670. 492670.i 0.799153 0.799153i
\(208\) 0 0
\(209\) 497667.i 0.788085i
\(210\) 0 0
\(211\) 1.13095e6i 1.74879i 0.485216 + 0.874394i \(0.338741\pi\)
−0.485216 + 0.874394i \(0.661259\pi\)
\(212\) 0 0
\(213\) −994592. + 994592.i −1.50209 + 1.50209i
\(214\) 0 0
\(215\) 548405. 928345.i 0.809106 1.36966i
\(216\) 0 0
\(217\) 3471.02 + 3471.02i 0.00500388 + 0.00500388i
\(218\) 0 0
\(219\) −829398. −1.16857
\(220\) 0 0
\(221\) 222744. 0.306779
\(222\) 0 0
\(223\) −274750. 274750.i −0.369978 0.369978i 0.497491 0.867469i \(-0.334255\pi\)
−0.867469 + 0.497491i \(0.834255\pi\)
\(224\) 0 0
\(225\) −459885. 834580.i −0.605610 1.09904i
\(226\) 0 0
\(227\) 488532. 488532.i 0.629258 0.629258i −0.318624 0.947881i \(-0.603221\pi\)
0.947881 + 0.318624i \(0.103221\pi\)
\(228\) 0 0
\(229\) 342575.i 0.431685i 0.976428 + 0.215843i \(0.0692498\pi\)
−0.976428 + 0.215843i \(0.930750\pi\)
\(230\) 0 0
\(231\) 18273.6i 0.0225317i
\(232\) 0 0
\(233\) −452353. + 452353.i −0.545868 + 0.545868i −0.925243 0.379375i \(-0.876139\pi\)
0.379375 + 0.925243i \(0.376139\pi\)
\(234\) 0 0
\(235\) −871089. 514582.i −1.02895 0.607834i
\(236\) 0 0
\(237\) 815466. + 815466.i 0.943051 + 0.943051i
\(238\) 0 0
\(239\) 467505. 0.529409 0.264704 0.964330i \(-0.414726\pi\)
0.264704 + 0.964330i \(0.414726\pi\)
\(240\) 0 0
\(241\) 1.38008e6 1.53060 0.765298 0.643676i \(-0.222592\pi\)
0.765298 + 0.643676i \(0.222592\pi\)
\(242\) 0 0
\(243\) −913893. 913893.i −0.992841 0.992841i
\(244\) 0 0
\(245\) −909403. + 233972.i −0.967923 + 0.249028i
\(246\) 0 0
\(247\) 217055. 217055.i 0.226375 0.226375i
\(248\) 0 0
\(249\) 1.47907e6i 1.51178i
\(250\) 0 0
\(251\) 368447.i 0.369140i 0.982819 + 0.184570i \(0.0590893\pi\)
−0.982819 + 0.184570i \(0.940911\pi\)
\(252\) 0 0
\(253\) −413108. + 413108.i −0.405754 + 0.405754i
\(254\) 0 0
\(255\) 1.78988e6 460502.i 1.72374 0.443487i
\(256\) 0 0
\(257\) −75698.4 75698.4i −0.0714915 0.0714915i 0.670457 0.741948i \(-0.266098\pi\)
−0.741948 + 0.670457i \(0.766098\pi\)
\(258\) 0 0
\(259\) 49001.9 0.0453904
\(260\) 0 0
\(261\) 1.78180e6 1.61904
\(262\) 0 0
\(263\) 487680. + 487680.i 0.434756 + 0.434756i 0.890243 0.455487i \(-0.150535\pi\)
−0.455487 + 0.890243i \(0.650535\pi\)
\(264\) 0 0
\(265\) 138775. + 81979.4i 0.121394 + 0.0717117i
\(266\) 0 0
\(267\) 338804. 338804.i 0.290851 0.290851i
\(268\) 0 0
\(269\) 1.45194e6i 1.22340i −0.791091 0.611698i \(-0.790487\pi\)
0.791091 0.611698i \(-0.209513\pi\)
\(270\) 0 0
\(271\) 444992.i 0.368069i −0.982920 0.184034i \(-0.941084\pi\)
0.982920 0.184034i \(-0.0589157\pi\)
\(272\) 0 0
\(273\) 7969.94 7969.94i 0.00647215 0.00647215i
\(274\) 0 0
\(275\) 385618. + 699804.i 0.307486 + 0.558013i
\(276\) 0 0
\(277\) −519577. 519577.i −0.406865 0.406865i 0.473779 0.880644i \(-0.342890\pi\)
−0.880644 + 0.473779i \(0.842890\pi\)
\(278\) 0 0
\(279\) 490244. 0.377053
\(280\) 0 0
\(281\) 1.04138e6 0.786763 0.393381 0.919375i \(-0.371305\pi\)
0.393381 + 0.919375i \(0.371305\pi\)
\(282\) 0 0
\(283\) 448357. + 448357.i 0.332780 + 0.332780i 0.853641 0.520861i \(-0.174389\pi\)
−0.520861 + 0.853641i \(0.674389\pi\)
\(284\) 0 0
\(285\) 1.29542e6 2.19290e6i 0.944712 1.59922i
\(286\) 0 0
\(287\) 18208.5 18208.5i 0.0130488 0.0130488i
\(288\) 0 0
\(289\) 574989.i 0.404963i
\(290\) 0 0
\(291\) 3.34289e6i 2.31414i
\(292\) 0 0
\(293\) 518007. 518007.i 0.352506 0.352506i −0.508535 0.861041i \(-0.669813\pi\)
0.861041 + 0.508535i \(0.169813\pi\)
\(294\) 0 0
\(295\) 383139. + 1.48918e6i 0.256331 + 0.996307i
\(296\) 0 0
\(297\) −262083. 262083.i −0.172404 0.172404i
\(298\) 0 0
\(299\) −360351. −0.233103
\(300\) 0 0
\(301\) 58890.0 0.0374649
\(302\) 0 0
\(303\) −2.77559e6 2.77559e6i −1.73679 1.73679i
\(304\) 0 0
\(305\) 133695. + 519645.i 0.0822934 + 0.319858i
\(306\) 0 0
\(307\) −1.73933e6 + 1.73933e6i −1.05326 + 1.05326i −0.0547590 + 0.998500i \(0.517439\pi\)
−0.998500 + 0.0547590i \(0.982561\pi\)
\(308\) 0 0
\(309\) 2.71696e6i 1.61878i
\(310\) 0 0
\(311\) 1.01730e6i 0.596413i 0.954501 + 0.298207i \(0.0963884\pi\)
−0.954501 + 0.298207i \(0.903612\pi\)
\(312\) 0 0
\(313\) −1.40539e6 + 1.40539e6i −0.810839 + 0.810839i −0.984760 0.173921i \(-0.944356\pi\)
0.173921 + 0.984760i \(0.444356\pi\)
\(314\) 0 0
\(315\) 26471.0 44810.3i 0.0150312 0.0254450i
\(316\) 0 0
\(317\) −2.34064e6 2.34064e6i −1.30824 1.30824i −0.922685 0.385555i \(-0.874010\pi\)
−0.385555 0.922685i \(-0.625990\pi\)
\(318\) 0 0
\(319\) −1.49406e6 −0.822034
\(320\) 0 0
\(321\) 3.01577e6 1.63356
\(322\) 0 0
\(323\) 1.94390e6 + 1.94390e6i 1.03673 + 1.03673i
\(324\) 0 0
\(325\) −137031. + 473402.i −0.0719631 + 0.248612i
\(326\) 0 0
\(327\) −3.12509e6 + 3.12509e6i −1.61619 + 1.61619i
\(328\) 0 0
\(329\) 55257.9i 0.0281452i
\(330\) 0 0
\(331\) 592772.i 0.297384i −0.988884 0.148692i \(-0.952494\pi\)
0.988884 0.148692i \(-0.0475063\pi\)
\(332\) 0 0
\(333\) 3.46050e6 3.46050e6i 1.71013 1.71013i
\(334\) 0 0
\(335\) 2.54582e6 + 1.50390e6i 1.23941 + 0.732164i
\(336\) 0 0
\(337\) 226356. + 226356.i 0.108572 + 0.108572i 0.759306 0.650734i \(-0.225539\pi\)
−0.650734 + 0.759306i \(0.725539\pi\)
\(338\) 0 0
\(339\) −4.30620e6 −2.03514
\(340\) 0 0
\(341\) −411075. −0.191441
\(342\) 0 0
\(343\) −72550.6 72550.6i −0.0332971 0.0332971i
\(344\) 0 0
\(345\) −2.89562e6 + 744989.i −1.30977 + 0.336979i
\(346\) 0 0
\(347\) 1.68068e6 1.68068e6i 0.749312 0.749312i −0.225038 0.974350i \(-0.572251\pi\)
0.974350 + 0.225038i \(0.0722507\pi\)
\(348\) 0 0
\(349\) 2.90392e6i 1.27621i 0.769951 + 0.638103i \(0.220281\pi\)
−0.769951 + 0.638103i \(0.779719\pi\)
\(350\) 0 0
\(351\) 228613.i 0.0990451i
\(352\) 0 0
\(353\) 2.50898e6 2.50898e6i 1.07167 1.07167i 0.0744409 0.997225i \(-0.476283\pi\)
0.997225 0.0744409i \(-0.0237172\pi\)
\(354\) 0 0
\(355\) 3.25316e6 836977.i 1.37004 0.352486i
\(356\) 0 0
\(357\) 71376.9 + 71376.9i 0.0296406 + 0.0296406i
\(358\) 0 0
\(359\) 3.85795e6 1.57987 0.789933 0.613193i \(-0.210115\pi\)
0.789933 + 0.613193i \(0.210115\pi\)
\(360\) 0 0
\(361\) 1.31240e6 0.530027
\(362\) 0 0
\(363\) −1.58362e6 1.58362e6i −0.630789 0.630789i
\(364\) 0 0
\(365\) 1.70540e6 + 1.00744e6i 0.670029 + 0.395809i
\(366\) 0 0
\(367\) −974922. + 974922.i −0.377837 + 0.377837i −0.870321 0.492484i \(-0.836089\pi\)
0.492484 + 0.870321i \(0.336089\pi\)
\(368\) 0 0
\(369\) 2.57176e6i 0.983250i
\(370\) 0 0
\(371\) 8803.28i 0.00332055i
\(372\) 0 0
\(373\) −2.95423e6 + 2.95423e6i −1.09944 + 1.09944i −0.104968 + 0.994476i \(0.533474\pi\)
−0.994476 + 0.104968i \(0.966526\pi\)
\(374\) 0 0
\(375\) −122409. + 4.08735e6i −0.0449505 + 1.50094i
\(376\) 0 0
\(377\) −651626. 651626.i −0.236127 0.236127i
\(378\) 0 0
\(379\) 1.93723e6 0.692760 0.346380 0.938094i \(-0.387411\pi\)
0.346380 + 0.938094i \(0.387411\pi\)
\(380\) 0 0
\(381\) 3.93175e6 1.38763
\(382\) 0 0
\(383\) −456982. 456982.i −0.159185 0.159185i 0.623020 0.782206i \(-0.285905\pi\)
−0.782206 + 0.623020i \(0.785905\pi\)
\(384\) 0 0
\(385\) −22196.2 + 37573.9i −0.00763179 + 0.0129192i
\(386\) 0 0
\(387\) 4.15879e6 4.15879e6i 1.41153 1.41153i
\(388\) 0 0
\(389\) 2.78550e6i 0.933317i 0.884438 + 0.466658i \(0.154542\pi\)
−0.884438 + 0.466658i \(0.845458\pi\)
\(390\) 0 0
\(391\) 3.22722e6i 1.06755i
\(392\) 0 0
\(393\) −893559. + 893559.i −0.291838 + 0.291838i
\(394\) 0 0
\(395\) −686237. 2.66727e6i −0.221300 0.860149i
\(396\) 0 0
\(397\) −965661. 965661.i −0.307502 0.307502i 0.536438 0.843940i \(-0.319770\pi\)
−0.843940 + 0.536438i \(0.819770\pi\)
\(398\) 0 0
\(399\) 139108. 0.0437441
\(400\) 0 0
\(401\) 2.13461e6 0.662916 0.331458 0.943470i \(-0.392460\pi\)
0.331458 + 0.943470i \(0.392460\pi\)
\(402\) 0 0
\(403\) −179289. 179289.i −0.0549908 0.0549908i
\(404\) 0 0
\(405\) 559458. + 2.17450e6i 0.169484 + 0.658752i
\(406\) 0 0
\(407\) −2.90166e6 + 2.90166e6i −0.868283 + 0.868283i
\(408\) 0 0
\(409\) 1.60900e6i 0.475608i −0.971313 0.237804i \(-0.923572\pi\)
0.971313 0.237804i \(-0.0764275\pi\)
\(410\) 0 0
\(411\) 3.35122e6i 0.978585i
\(412\) 0 0
\(413\) −59385.8 + 59385.8i −0.0171320 + 0.0171320i
\(414\) 0 0
\(415\) 1.79656e6 3.04124e6i 0.512062 0.866823i
\(416\) 0 0
\(417\) 1.53890e6 + 1.53890e6i 0.433382 + 0.433382i
\(418\) 0 0
\(419\) 5.37383e6 1.49537 0.747685 0.664053i \(-0.231165\pi\)
0.747685 + 0.664053i \(0.231165\pi\)
\(420\) 0 0
\(421\) −5.58822e6 −1.53663 −0.768313 0.640074i \(-0.778904\pi\)
−0.768313 + 0.640074i \(0.778904\pi\)
\(422\) 0 0
\(423\) −3.90230e6 3.90230e6i −1.06040 1.06040i
\(424\) 0 0
\(425\) −4.23968e6 1.22722e6i −1.13857 0.329571i
\(426\) 0 0
\(427\) −20722.5 + 20722.5i −0.00550011 + 0.00550011i
\(428\) 0 0
\(429\) 943885.i 0.247614i
\(430\) 0 0
\(431\) 2.59273e6i 0.672302i 0.941808 + 0.336151i \(0.109125\pi\)
−0.941808 + 0.336151i \(0.890875\pi\)
\(432\) 0 0
\(433\) −1.81191e6 + 1.81191e6i −0.464428 + 0.464428i −0.900104 0.435676i \(-0.856509\pi\)
0.435676 + 0.900104i \(0.356509\pi\)
\(434\) 0 0
\(435\) −6.58336e6 3.88901e6i −1.66811 0.985409i
\(436\) 0 0
\(437\) −3.14479e6 3.14479e6i −0.787750 0.787750i
\(438\) 0 0
\(439\) −3.09173e6 −0.765669 −0.382834 0.923817i \(-0.625052\pi\)
−0.382834 + 0.923817i \(0.625052\pi\)
\(440\) 0 0
\(441\) −5.12208e6 −1.25415
\(442\) 0 0
\(443\) 3.50150e6 + 3.50150e6i 0.847705 + 0.847705i 0.989846 0.142141i \(-0.0453986\pi\)
−0.142141 + 0.989846i \(0.545399\pi\)
\(444\) 0 0
\(445\) −1.10818e6 + 285113.i −0.265283 + 0.0682522i
\(446\) 0 0
\(447\) −3.46044e6 + 3.46044e6i −0.819149 + 0.819149i
\(448\) 0 0
\(449\) 7.60289e6i 1.77977i −0.456190 0.889883i \(-0.650786\pi\)
0.456190 0.889883i \(-0.349214\pi\)
\(450\) 0 0
\(451\) 2.15644e6i 0.499225i
\(452\) 0 0
\(453\) −625938. + 625938.i −0.143313 + 0.143313i
\(454\) 0 0
\(455\) −26068.5 + 6706.92i −0.00590319 + 0.00151878i
\(456\) 0 0
\(457\) 1.09632e6 + 1.09632e6i 0.245553 + 0.245553i 0.819143 0.573590i \(-0.194450\pi\)
−0.573590 + 0.819143i \(0.694450\pi\)
\(458\) 0 0
\(459\) 2.04740e6 0.453599
\(460\) 0 0
\(461\) −3.67309e6 −0.804969 −0.402484 0.915427i \(-0.631853\pi\)
−0.402484 + 0.915427i \(0.631853\pi\)
\(462\) 0 0
\(463\) −1.59149e6 1.59149e6i −0.345026 0.345026i 0.513227 0.858253i \(-0.328450\pi\)
−0.858253 + 0.513227i \(0.828450\pi\)
\(464\) 0 0
\(465\) −1.81135e6 1.07002e6i −0.388480 0.229489i
\(466\) 0 0
\(467\) 4.91174e6 4.91174e6i 1.04218 1.04218i 0.0431100 0.999070i \(-0.486273\pi\)
0.999070 0.0431100i \(-0.0137266\pi\)
\(468\) 0 0
\(469\) 161495.i 0.0339022i
\(470\) 0 0
\(471\) 8.29460e6i 1.72283i
\(472\) 0 0
\(473\) −3.48719e6 + 3.48719e6i −0.716675 + 0.716675i
\(474\) 0 0
\(475\) −5.32727e6 + 2.93552e6i −1.08335 + 0.596968i
\(476\) 0 0
\(477\) 621685. + 621685.i 0.125105 + 0.125105i
\(478\) 0 0
\(479\) −3.25161e6 −0.647530 −0.323765 0.946138i \(-0.604949\pi\)
−0.323765 + 0.946138i \(0.604949\pi\)
\(480\) 0 0
\(481\) −2.53110e6 −0.498823
\(482\) 0 0
\(483\) −115472. 115472.i −0.0225221 0.0225221i
\(484\) 0 0
\(485\) 4.06047e6 6.87360e6i 0.783830 1.32687i
\(486\) 0 0
\(487\) −1.81453e6 + 1.81453e6i −0.346690 + 0.346690i −0.858875 0.512185i \(-0.828836\pi\)
0.512185 + 0.858875i \(0.328836\pi\)
\(488\) 0 0
\(489\) 3.78326e6i 0.715474i
\(490\) 0 0
\(491\) 2.04842e6i 0.383456i −0.981448 0.191728i \(-0.938591\pi\)
0.981448 0.191728i \(-0.0614092\pi\)
\(492\) 0 0
\(493\) 5.83581e6 5.83581e6i 1.08139 1.08139i
\(494\) 0 0
\(495\) 1.08597e6 + 4.22094e6i 0.199207 + 0.774278i
\(496\) 0 0
\(497\) 129730. + 129730.i 0.0235586 + 0.0235586i
\(498\) 0 0
\(499\) −1.07626e7 −1.93493 −0.967467 0.252995i \(-0.918584\pi\)
−0.967467 + 0.252995i \(0.918584\pi\)
\(500\) 0 0
\(501\) −1.16362e7 −2.07118
\(502\) 0 0
\(503\) 6.61394e6 + 6.61394e6i 1.16558 + 1.16558i 0.983236 + 0.182340i \(0.0583671\pi\)
0.182340 + 0.983236i \(0.441633\pi\)
\(504\) 0 0
\(505\) 2.33573e6 + 9.07852e6i 0.407563 + 1.58411i
\(506\) 0 0
\(507\) 5.73392e6 5.73392e6i 0.990676 0.990676i
\(508\) 0 0
\(509\) 9.31007e6i 1.59279i −0.604777 0.796395i \(-0.706738\pi\)
0.604777 0.796395i \(-0.293262\pi\)
\(510\) 0 0
\(511\) 108183.i 0.0183276i
\(512\) 0 0
\(513\) 1.99511e6 1.99511e6i 0.334714 0.334714i
\(514\) 0 0
\(515\) 3.30018e6 5.58657e6i 0.548302 0.928170i
\(516\) 0 0
\(517\) 3.27212e6 + 3.27212e6i 0.538397 + 0.538397i
\(518\) 0 0
\(519\) 8.76882e6 1.42897
\(520\) 0 0
\(521\) −126938. −0.0204879 −0.0102440 0.999948i \(-0.503261\pi\)
−0.0102440 + 0.999948i \(0.503261\pi\)
\(522\) 0 0
\(523\) 7.33758e6 + 7.33758e6i 1.17300 + 1.17300i 0.981490 + 0.191511i \(0.0613388\pi\)
0.191511 + 0.981490i \(0.438661\pi\)
\(524\) 0 0
\(525\) −195609. + 107788.i −0.0309735 + 0.0170676i
\(526\) 0 0
\(527\) 1.60567e6 1.60567e6i 0.251842 0.251842i
\(528\) 0 0
\(529\) 1.21542e6i 0.188838i
\(530\) 0 0
\(531\) 8.38761e6i 1.29093i
\(532\) 0 0
\(533\) −940524. + 940524.i −0.143401 + 0.143401i
\(534\) 0 0
\(535\) −6.20100e6 3.66314e6i −0.936649 0.553311i
\(536\) 0 0
\(537\) 9.67634e6 + 9.67634e6i 1.44802 + 1.44802i
\(538\) 0 0
\(539\) 4.29492e6 0.636770
\(540\) 0 0
\(541\) 4.43492e6 0.651468 0.325734 0.945462i \(-0.394389\pi\)
0.325734 + 0.945462i \(0.394389\pi\)
\(542\) 0 0
\(543\) 3.71840e6 + 3.71840e6i 0.541198 + 0.541198i
\(544\) 0 0
\(545\) 1.02217e7 2.62985e6i 1.47412 0.379262i
\(546\) 0 0
\(547\) 8.43075e6 8.43075e6i 1.20475 1.20475i 0.232049 0.972704i \(-0.425457\pi\)
0.972704 0.232049i \(-0.0745428\pi\)
\(548\) 0 0
\(549\) 2.92683e6i 0.414444i
\(550\) 0 0
\(551\) 1.13735e7i 1.59594i
\(552\) 0 0
\(553\) 106365. 106365.i 0.0147907 0.0147907i
\(554\) 0 0
\(555\) −2.03388e7 + 5.23279e6i −2.80281 + 0.721109i
\(556\) 0 0
\(557\) 5.80705e6 + 5.80705e6i 0.793081 + 0.793081i 0.981994 0.188913i \(-0.0604963\pi\)
−0.188913 + 0.981994i \(0.560496\pi\)
\(558\) 0 0
\(559\) −3.04185e6 −0.411725
\(560\) 0 0
\(561\) −8.45321e6 −1.13400
\(562\) 0 0
\(563\) −4.54116e6 4.54116e6i −0.603804 0.603804i 0.337516 0.941320i \(-0.390413\pi\)
−0.941320 + 0.337516i \(0.890413\pi\)
\(564\) 0 0
\(565\) 8.85434e6 + 5.23056e6i 1.16690 + 0.689330i
\(566\) 0 0
\(567\) −86714.9 + 86714.9i −0.0113276 + 0.0113276i
\(568\) 0 0
\(569\) 1.81256e6i 0.234700i 0.993091 + 0.117350i \(0.0374399\pi\)
−0.993091 + 0.117350i \(0.962560\pi\)
\(570\) 0 0
\(571\) 6.42241e6i 0.824342i 0.911107 + 0.412171i \(0.135229\pi\)
−0.911107 + 0.412171i \(0.864771\pi\)
\(572\) 0 0
\(573\) 296051. 296051.i 0.0376686 0.0376686i
\(574\) 0 0
\(575\) 6.85885e6 + 1.98536e6i 0.865131 + 0.250421i
\(576\) 0 0
\(577\) 1.17171e6 + 1.17171e6i 0.146515 + 0.146515i 0.776559 0.630044i \(-0.216963\pi\)
−0.630044 + 0.776559i \(0.716963\pi\)
\(578\) 0 0
\(579\) −1.40149e6 −0.173737
\(580\) 0 0
\(581\) 192922. 0.0237106
\(582\) 0 0
\(583\) −521289. 521289.i −0.0635195 0.0635195i
\(584\) 0 0
\(585\) −1.36731e6 + 2.31459e6i −0.165187 + 0.279630i
\(586\) 0 0
\(587\) −1.03287e7 + 1.03287e7i −1.23723 + 1.23723i −0.276099 + 0.961129i \(0.589042\pi\)
−0.961129 + 0.276099i \(0.910958\pi\)
\(588\) 0 0
\(589\) 3.12931e6i 0.371673i
\(590\) 0 0
\(591\) 6.93254e6i 0.816438i
\(592\) 0 0
\(593\) 5.28605e6 5.28605e6i 0.617297 0.617297i −0.327540 0.944837i \(-0.606220\pi\)
0.944837 + 0.327540i \(0.106220\pi\)
\(594\) 0 0
\(595\) −60065.6 233463.i −0.00695558 0.0270350i
\(596\) 0 0
\(597\) 7.41053e6 + 7.41053e6i 0.850968 + 0.850968i
\(598\) 0 0
\(599\) 1.31419e7 1.49655 0.748274 0.663389i \(-0.230883\pi\)
0.748274 + 0.663389i \(0.230883\pi\)
\(600\) 0 0
\(601\) 563134. 0.0635954 0.0317977 0.999494i \(-0.489877\pi\)
0.0317977 + 0.999494i \(0.489877\pi\)
\(602\) 0 0
\(603\) 1.14048e7 + 1.14048e7i 1.27730 + 1.27730i
\(604\) 0 0
\(605\) 1.33266e6 + 5.17977e6i 0.148023 + 0.575337i
\(606\) 0 0
\(607\) −8.33422e6 + 8.33422e6i −0.918107 + 0.918107i −0.996892 0.0787849i \(-0.974896\pi\)
0.0787849 + 0.996892i \(0.474896\pi\)
\(608\) 0 0
\(609\) 417618.i 0.0456285i
\(610\) 0 0
\(611\) 2.85424e6i 0.309305i
\(612\) 0 0
\(613\) −3.43809e6 + 3.43809e6i −0.369544 + 0.369544i −0.867311 0.497767i \(-0.834154\pi\)
0.497767 + 0.867311i \(0.334154\pi\)
\(614\) 0 0
\(615\) −5.61320e6 + 9.50208e6i −0.598443 + 1.01305i
\(616\) 0 0
\(617\) −1.28154e7 1.28154e7i −1.35525 1.35525i −0.879679 0.475568i \(-0.842243\pi\)
−0.475568 0.879679i \(-0.657757\pi\)
\(618\) 0 0
\(619\) −6.06861e6 −0.636594 −0.318297 0.947991i \(-0.603111\pi\)
−0.318297 + 0.947991i \(0.603111\pi\)
\(620\) 0 0
\(621\) −3.31224e6 −0.344662
\(622\) 0 0
\(623\) −44192.0 44192.0i −0.00456166 0.00456166i
\(624\) 0 0
\(625\) 5.21644e6 8.25568e6i 0.534163 0.845381i
\(626\) 0 0
\(627\) −8.23732e6 + 8.23732e6i −0.836791 + 0.836791i
\(628\) 0 0
\(629\) 2.26679e7i 2.28447i
\(630\) 0 0
\(631\) 1.63004e7i 1.62976i −0.579627 0.814882i \(-0.696802\pi\)
0.579627 0.814882i \(-0.303198\pi\)
\(632\) 0 0
\(633\) 1.87193e7 1.87193e7i 1.85687 1.85687i
\(634\) 0 0
\(635\) −8.08441e6 4.77574e6i −0.795635 0.470009i
\(636\) 0 0
\(637\) 1.87321e6 + 1.87321e6i 0.182910 + 0.182910i
\(638\) 0 0
\(639\) 1.83230e7 1.77518
\(640\) 0 0
\(641\) −1.89780e6 −0.182434 −0.0912170 0.995831i \(-0.529076\pi\)
−0.0912170 + 0.995831i \(0.529076\pi\)
\(642\) 0 0
\(643\) 1.27382e7 + 1.27382e7i 1.21501 + 1.21501i 0.969357 + 0.245655i \(0.0790029\pi\)
0.245655 + 0.969357i \(0.420997\pi\)
\(644\) 0 0
\(645\) −2.44430e7 + 6.28871e6i −2.31342 + 0.595199i
\(646\) 0 0
\(647\) −1.46429e6 + 1.46429e6i −0.137520 + 0.137520i −0.772516 0.634996i \(-0.781002\pi\)
0.634996 + 0.772516i \(0.281002\pi\)
\(648\) 0 0
\(649\) 7.03309e6i 0.655443i
\(650\) 0 0
\(651\) 114904.i 0.0106263i
\(652\) 0 0
\(653\) 1.34304e6 1.34304e6i 0.123256 0.123256i −0.642788 0.766044i \(-0.722223\pi\)
0.766044 + 0.642788i \(0.222223\pi\)
\(654\) 0 0
\(655\) 2.92269e6 751954.i 0.266183 0.0684838i
\(656\) 0 0
\(657\) 7.63983e6 + 7.63983e6i 0.690511 + 0.690511i
\(658\) 0 0
\(659\) −1.40391e7 −1.25929 −0.629643 0.776885i \(-0.716799\pi\)
−0.629643 + 0.776885i \(0.716799\pi\)
\(660\) 0 0
\(661\) 1.44204e7 1.28373 0.641866 0.766817i \(-0.278161\pi\)
0.641866 + 0.766817i \(0.278161\pi\)
\(662\) 0 0
\(663\) −3.68683e6 3.68683e6i −0.325739 0.325739i
\(664\) 0 0
\(665\) −286032. 168969.i −0.0250819 0.0148167i
\(666\) 0 0
\(667\) −9.44104e6 + 9.44104e6i −0.821685 + 0.821685i
\(668\) 0 0
\(669\) 9.09525e6i 0.785686i
\(670\) 0 0
\(671\) 2.45417e6i 0.210426i
\(672\) 0 0
\(673\) −8.05670e6 + 8.05670e6i −0.685677 + 0.685677i −0.961273 0.275597i \(-0.911125\pi\)
0.275597 + 0.961273i \(0.411125\pi\)
\(674\) 0 0
\(675\) −1.25955e6 + 4.35138e6i −0.106403 + 0.367593i
\(676\) 0 0
\(677\) 5.78497e6 + 5.78497e6i 0.485098 + 0.485098i 0.906755 0.421657i \(-0.138552\pi\)
−0.421657 + 0.906755i \(0.638552\pi\)
\(678\) 0 0
\(679\) 436030. 0.0362946
\(680\) 0 0
\(681\) −1.61722e7 −1.33629
\(682\) 0 0
\(683\) 6.59840e6 + 6.59840e6i 0.541236 + 0.541236i 0.923891 0.382655i \(-0.124990\pi\)
−0.382655 + 0.923891i \(0.624990\pi\)
\(684\) 0 0
\(685\) −4.07060e6 + 6.89074e6i −0.331460 + 0.561099i
\(686\) 0 0
\(687\) 5.67025e6 5.67025e6i 0.458364 0.458364i
\(688\) 0 0
\(689\) 454716.i 0.0364916i
\(690\) 0 0
\(691\) 1.60816e6i 0.128125i −0.997946 0.0640626i \(-0.979594\pi\)
0.997946 0.0640626i \(-0.0204057\pi\)
\(692\) 0 0
\(693\) −168323. + 168323.i −0.0133141 + 0.0133141i
\(694\) 0 0
\(695\) −1.29503e6 5.03352e6i −0.101699 0.395284i
\(696\) 0 0
\(697\) −8.42311e6 8.42311e6i −0.656735 0.656735i
\(698\) 0 0
\(699\) 1.49746e7 1.15921
\(700\) 0 0
\(701\) 1.89009e6 0.145274 0.0726368 0.997358i \(-0.476859\pi\)
0.0726368 + 0.997358i \(0.476859\pi\)
\(702\) 0 0
\(703\) −2.20890e7 2.20890e7i −1.68573 1.68573i
\(704\) 0 0
\(705\) 5.90085e6 + 2.29354e7i 0.447139 + 1.73794i
\(706\) 0 0
\(707\) −362034. + 362034.i −0.0272396 + 0.0272396i
\(708\) 0 0
\(709\) 2.56522e6i 0.191650i −0.995398 0.0958249i \(-0.969451\pi\)
0.995398 0.0958249i \(-0.0305489\pi\)
\(710\) 0 0
\(711\) 1.50230e7i 1.11451i
\(712\) 0 0
\(713\) −2.59761e6 + 2.59761e6i −0.191359 + 0.191359i
\(714\) 0 0
\(715\) 1.14650e6 1.94081e6i 0.0838704 0.141977i
\(716\) 0 0
\(717\) −7.73807e6 7.73807e6i −0.562127 0.562127i
\(718\) 0 0
\(719\) 1.28532e6 0.0927231 0.0463616 0.998925i \(-0.485237\pi\)
0.0463616 + 0.998925i \(0.485237\pi\)
\(720\) 0 0
\(721\) 354387. 0.0253886
\(722\) 0 0
\(723\) −2.28428e7 2.28428e7i −1.62519 1.62519i
\(724\) 0 0
\(725\) 8.81278e6 + 1.59931e7i 0.622685 + 1.13002i
\(726\) 0 0
\(727\) −2.51635e6 + 2.51635e6i −0.176577 + 0.176577i −0.789862 0.613285i \(-0.789848\pi\)
0.613285 + 0.789862i \(0.289848\pi\)
\(728\) 0 0
\(729\) 2.04931e7i 1.42820i
\(730\) 0 0
\(731\) 2.72420e7i 1.88559i
\(732\) 0 0
\(733\) 6.19797e6 6.19797e6i 0.426078 0.426078i −0.461212 0.887290i \(-0.652585\pi\)
0.887290 + 0.461212i \(0.152585\pi\)
\(734\) 0 0
\(735\) 1.89250e7 + 1.11796e7i 1.29216 + 0.763324i
\(736\) 0 0
\(737\) −9.56300e6 9.56300e6i −0.648523 0.648523i
\(738\) 0 0
\(739\) 1.66087e7 1.11873 0.559363 0.828923i \(-0.311046\pi\)
0.559363 + 0.828923i \(0.311046\pi\)
\(740\) 0 0
\(741\) −7.18534e6 −0.480731
\(742\) 0 0
\(743\) 1.70625e7 + 1.70625e7i 1.13389 + 1.13389i 0.989525 + 0.144361i \(0.0461128\pi\)
0.144361 + 0.989525i \(0.453887\pi\)
\(744\) 0 0
\(745\) 1.13186e7 2.91206e6i 0.747138 0.192225i
\(746\) 0 0
\(747\) 1.36241e7 1.36241e7i 0.893320 0.893320i
\(748\) 0 0
\(749\) 393363.i 0.0256206i
\(750\) 0 0
\(751\) 2.01562e7i 1.30409i −0.758179 0.652047i \(-0.773911\pi\)
0.758179 0.652047i \(-0.226089\pi\)
\(752\) 0 0
\(753\) 6.09849e6 6.09849e6i 0.391954 0.391954i
\(754\) 0 0
\(755\) 2.04735e6 526744.i 0.130715 0.0336304i
\(756\) 0 0
\(757\) −1.27967e7 1.27967e7i −0.811633 0.811633i 0.173246 0.984879i \(-0.444574\pi\)
−0.984879 + 0.173246i \(0.944574\pi\)
\(758\) 0 0
\(759\) 1.36754e7 0.861660
\(760\) 0 0
\(761\) −1.56925e6 −0.0982272 −0.0491136 0.998793i \(-0.515640\pi\)
−0.0491136 + 0.998793i \(0.515640\pi\)
\(762\) 0 0
\(763\) 407622. + 407622.i 0.0253481 + 0.0253481i
\(764\) 0 0
\(765\) −2.07289e7 1.22453e7i −1.28063 0.756510i
\(766\) 0 0
\(767\) 3.06746e6 3.06746e6i 0.188274 0.188274i
\(768\) 0 0
\(769\) 2.88122e7i 1.75696i 0.477783 + 0.878478i \(0.341440\pi\)
−0.477783 + 0.878478i \(0.658560\pi\)
\(770\) 0 0
\(771\) 2.50590e6i 0.151820i
\(772\) 0 0
\(773\) 1.17155e7 1.17155e7i 0.705201 0.705201i −0.260321 0.965522i \(-0.583828\pi\)
0.965522 + 0.260321i \(0.0838284\pi\)
\(774\) 0 0
\(775\) 2.42475e6 + 4.40034e6i 0.145015 + 0.263167i
\(776\) 0 0
\(777\) −811073. 811073.i −0.0481956 0.0481956i
\(778\) 0 0
\(779\) −1.64160e7 −0.969220
\(780\) 0 0
\(781\) −1.53640e7 −0.901314
\(782\) 0 0
\(783\) −5.98956e6 5.98956e6i −0.349133 0.349133i
\(784\) 0 0
\(785\) −1.00751e7 + 1.70552e7i −0.583547 + 0.987833i
\(786\) 0 0
\(787\) 2.61369e6 2.61369e6i 0.150424 0.150424i −0.627883 0.778308i \(-0.716078\pi\)
0.778308 + 0.627883i \(0.216078\pi\)
\(788\) 0 0
\(789\) 1.61440e7i 0.923250i
\(790\) 0 0
\(791\) 561679.i 0.0319188i
\(792\) 0 0