Properties

Label 124.6.f.a.97.2
Level $124$
Weight $6$
Character 124.97
Analytic conductor $19.888$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 124.f (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8875936568\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 97.2
Character \(\chi\) \(=\) 124.97
Dual form 124.6.f.a.101.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-8.90517 + 27.4073i) q^{3} +53.9543 q^{5} +(-68.0214 + 49.4205i) q^{7} +(-475.267 - 345.302i) q^{9} +O(q^{10})\) \(q+(-8.90517 + 27.4073i) q^{3} +53.9543 q^{5} +(-68.0214 + 49.4205i) q^{7} +(-475.267 - 345.302i) q^{9} +(-570.436 + 414.446i) q^{11} +(202.866 - 624.358i) q^{13} +(-480.472 + 1478.74i) q^{15} +(806.268 + 585.788i) q^{17} +(402.834 + 1239.80i) q^{19} +(-748.739 - 2304.38i) q^{21} +(-3265.95 - 2372.85i) q^{23} -213.934 q^{25} +(8030.80 - 5834.72i) q^{27} +(-102.805 - 316.400i) q^{29} +(-3100.80 - 4360.53i) q^{31} +(-6279.02 - 19324.8i) q^{33} +(-3670.05 + 2666.45i) q^{35} +11970.3 q^{37} +(15305.4 + 11120.0i) q^{39} +(-3537.21 - 10886.4i) q^{41} +(-260.609 - 802.072i) q^{43} +(-25642.7 - 18630.5i) q^{45} +(1714.66 - 5277.19i) q^{47} +(-3009.12 + 9261.11i) q^{49} +(-23234.8 + 16881.1i) q^{51} +(10514.0 + 7638.88i) q^{53} +(-30777.5 + 22361.2i) q^{55} -37566.7 q^{57} +(-2773.07 + 8534.64i) q^{59} +14715.9 q^{61} +49393.3 q^{63} +(10945.5 - 33686.8i) q^{65} -61044.5 q^{67} +(94117.2 - 68380.1i) q^{69} +(43492.9 + 31599.4i) q^{71} +(-42090.7 + 30580.7i) q^{73} +(1905.12 - 5863.35i) q^{75} +(18319.8 - 56382.5i) q^{77} +(-33933.8 - 24654.4i) q^{79} +(44285.0 + 136295. i) q^{81} +(-11345.9 - 34919.2i) q^{83} +(43501.6 + 31605.8i) q^{85} +9587.17 q^{87} +(-116170. + 84402.6i) q^{89} +(17056.8 + 52495.4i) q^{91} +(147123. - 46153.2i) q^{93} +(21734.6 + 66892.3i) q^{95} +(-50225.9 + 36491.3i) q^{97} +414218. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9} - 509 q^{11} - 117 q^{13} + 89 q^{15} - 3504 q^{17} + 262 q^{19} + 352 q^{21} - 2448 q^{23} + 49618 q^{25} + 14324 q^{27} - 9888 q^{29} - 12771 q^{31} + 27699 q^{33} + 13840 q^{35} + 76096 q^{37} + 33520 q^{39} - 4843 q^{41} - 40778 q^{43} + 56692 q^{45} + 38922 q^{47} - 17126 q^{49} - 69292 q^{51} - 41728 q^{53} - 172096 q^{55} + 57066 q^{57} - 58198 q^{59} + 176328 q^{61} - 37444 q^{63} + 143863 q^{65} + 9812 q^{67} - 9250 q^{69} - 67356 q^{71} - 63512 q^{73} - 198012 q^{75} - 74257 q^{77} + 137651 q^{79} + 196077 q^{81} + 156427 q^{83} + 238828 q^{85} - 558144 q^{87} - 99292 q^{89} - 243609 q^{91} - 325925 q^{93} - 75077 q^{95} - 476340 q^{97} + 745812 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).

\(n\) \(63\) \(65\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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
\(3\) −8.90517 + 27.4073i −0.571267 + 1.75818i 0.0772855 + 0.997009i \(0.475375\pi\)
−0.648552 + 0.761170i \(0.724625\pi\)
\(4\) 0 0
\(5\) 53.9543 0.965164 0.482582 0.875851i \(-0.339699\pi\)
0.482582 + 0.875851i \(0.339699\pi\)
\(6\) 0 0
\(7\) −68.0214 + 49.4205i −0.524687 + 0.381208i −0.818367 0.574696i \(-0.805120\pi\)
0.293679 + 0.955904i \(0.405120\pi\)
\(8\) 0 0
\(9\) −475.267 345.302i −1.95583 1.42099i
\(10\) 0 0
\(11\) −570.436 + 414.446i −1.42143 + 1.03273i −0.429897 + 0.902878i \(0.641450\pi\)
−0.991533 + 0.129851i \(0.958550\pi\)
\(12\) 0 0
\(13\) 202.866 624.358i 0.332929 1.02465i −0.634805 0.772673i \(-0.718919\pi\)
0.967733 0.251976i \(-0.0810806\pi\)
\(14\) 0 0
\(15\) −480.472 + 1478.74i −0.551366 + 1.69693i
\(16\) 0 0
\(17\) 806.268 + 585.788i 0.676639 + 0.491607i 0.872241 0.489076i \(-0.162666\pi\)
−0.195602 + 0.980683i \(0.562666\pi\)
\(18\) 0 0
\(19\) 402.834 + 1239.80i 0.256001 + 0.787891i 0.993631 + 0.112685i \(0.0359451\pi\)
−0.737630 + 0.675206i \(0.764055\pi\)
\(20\) 0 0
\(21\) −748.739 2304.38i −0.370495 1.14027i
\(22\) 0 0
\(23\) −3265.95 2372.85i −1.28733 0.935299i −0.287581 0.957756i \(-0.592851\pi\)
−0.999748 + 0.0224574i \(0.992851\pi\)
\(24\) 0 0
\(25\) −213.934 −0.0684589
\(26\) 0 0
\(27\) 8030.80 5834.72i 2.12007 1.54032i
\(28\) 0 0
\(29\) −102.805 316.400i −0.0226996 0.0698622i 0.939065 0.343740i \(-0.111694\pi\)
−0.961765 + 0.273877i \(0.911694\pi\)
\(30\) 0 0
\(31\) −3100.80 4360.53i −0.579521 0.814957i
\(32\) 0 0
\(33\) −6279.02 19324.8i −1.00371 3.08909i
\(34\) 0 0
\(35\) −3670.05 + 2666.45i −0.506409 + 0.367928i
\(36\) 0 0
\(37\) 11970.3 1.43748 0.718741 0.695278i \(-0.244719\pi\)
0.718741 + 0.695278i \(0.244719\pi\)
\(38\) 0 0
\(39\) 15305.4 + 11120.0i 1.61133 + 1.17070i
\(40\) 0 0
\(41\) −3537.21 10886.4i −0.328625 1.01141i −0.969777 0.243991i \(-0.921543\pi\)
0.641152 0.767414i \(-0.278457\pi\)
\(42\) 0 0
\(43\) −260.609 802.072i −0.0214940 0.0661519i 0.939734 0.341906i \(-0.111072\pi\)
−0.961228 + 0.275754i \(0.911072\pi\)
\(44\) 0 0
\(45\) −25642.7 18630.5i −1.88770 1.37149i
\(46\) 0 0
\(47\) 1714.66 5277.19i 0.113223 0.348464i −0.878349 0.478019i \(-0.841355\pi\)
0.991572 + 0.129555i \(0.0413549\pi\)
\(48\) 0 0
\(49\) −3009.12 + 9261.11i −0.179039 + 0.551027i
\(50\) 0 0
\(51\) −23234.8 + 16881.1i −1.25087 + 0.908814i
\(52\) 0 0
\(53\) 10514.0 + 7638.88i 0.514137 + 0.373543i 0.814391 0.580317i \(-0.197071\pi\)
−0.300253 + 0.953859i \(0.597071\pi\)
\(54\) 0 0
\(55\) −30777.5 + 22361.2i −1.37191 + 0.996753i
\(56\) 0 0
\(57\) −37566.7 −1.53150
\(58\) 0 0
\(59\) −2773.07 + 8534.64i −0.103713 + 0.319194i −0.989426 0.145038i \(-0.953670\pi\)
0.885714 + 0.464232i \(0.153670\pi\)
\(60\) 0 0
\(61\) 14715.9 0.506365 0.253182 0.967419i \(-0.418523\pi\)
0.253182 + 0.967419i \(0.418523\pi\)
\(62\) 0 0
\(63\) 49393.3 1.56789
\(64\) 0 0
\(65\) 10945.5 33686.8i 0.321331 0.988954i
\(66\) 0 0
\(67\) −61044.5 −1.66134 −0.830672 0.556762i \(-0.812043\pi\)
−0.830672 + 0.556762i \(0.812043\pi\)
\(68\) 0 0
\(69\) 94117.2 68380.1i 2.37983 1.72905i
\(70\) 0 0
\(71\) 43492.9 + 31599.4i 1.02393 + 0.743932i 0.967086 0.254451i \(-0.0818946\pi\)
0.0568491 + 0.998383i \(0.481895\pi\)
\(72\) 0 0
\(73\) −42090.7 + 30580.7i −0.924441 + 0.671646i −0.944626 0.328150i \(-0.893575\pi\)
0.0201841 + 0.999796i \(0.493575\pi\)
\(74\) 0 0
\(75\) 1905.12 5863.35i 0.0391083 0.120363i
\(76\) 0 0
\(77\) 18319.8 56382.5i 0.352122 1.08372i
\(78\) 0 0
\(79\) −33933.8 24654.4i −0.611738 0.444454i 0.238288 0.971195i \(-0.423414\pi\)
−0.850026 + 0.526741i \(0.823414\pi\)
\(80\) 0 0
\(81\) 44285.0 + 136295.i 0.749971 + 2.30817i
\(82\) 0 0
\(83\) −11345.9 34919.2i −0.180778 0.556377i 0.819072 0.573690i \(-0.194489\pi\)
−0.999850 + 0.0173132i \(0.994489\pi\)
\(84\) 0 0
\(85\) 43501.6 + 31605.8i 0.653067 + 0.474481i
\(86\) 0 0
\(87\) 9587.17 0.135798
\(88\) 0 0
\(89\) −116170. + 84402.6i −1.55460 + 1.12949i −0.614338 + 0.789043i \(0.710577\pi\)
−0.940265 + 0.340442i \(0.889423\pi\)
\(90\) 0 0
\(91\) 17056.8 + 52495.4i 0.215921 + 0.664535i
\(92\) 0 0
\(93\) 147123. 46153.2i 1.76390 0.553343i
\(94\) 0 0
\(95\) 21734.6 + 66892.3i 0.247083 + 0.760443i
\(96\) 0 0
\(97\) −50225.9 + 36491.3i −0.541999 + 0.393786i −0.824827 0.565385i \(-0.808728\pi\)
0.282828 + 0.959171i \(0.408728\pi\)
\(98\) 0 0
\(99\) 414218. 4.24758
\(100\) 0 0
\(101\) −108431. 78779.7i −1.05767 0.768441i −0.0840132 0.996465i \(-0.526774\pi\)
−0.973656 + 0.228023i \(0.926774\pi\)
\(102\) 0 0
\(103\) 21834.2 + 67198.7i 0.202789 + 0.624120i 0.999797 + 0.0201511i \(0.00641472\pi\)
−0.797008 + 0.603968i \(0.793585\pi\)
\(104\) 0 0
\(105\) −40397.7 124331.i −0.357588 1.10054i
\(106\) 0 0
\(107\) −74260.5 53953.4i −0.627045 0.455575i 0.228330 0.973584i \(-0.426673\pi\)
−0.855375 + 0.518009i \(0.826673\pi\)
\(108\) 0 0
\(109\) −64436.0 + 198314.i −0.519472 + 1.59877i 0.255522 + 0.966803i \(0.417753\pi\)
−0.774994 + 0.631969i \(0.782247\pi\)
\(110\) 0 0
\(111\) −106598. + 328075.i −0.821186 + 2.52735i
\(112\) 0 0
\(113\) −142981. + 103882.i −1.05338 + 0.765323i −0.972852 0.231430i \(-0.925660\pi\)
−0.0805250 + 0.996753i \(0.525660\pi\)
\(114\) 0 0
\(115\) −176212. 128025.i −1.24248 0.902717i
\(116\) 0 0
\(117\) −312007. + 226687.i −2.10717 + 1.53095i
\(118\) 0 0
\(119\) −83793.4 −0.542428
\(120\) 0 0
\(121\) 103864. 319662.i 0.644916 1.98485i
\(122\) 0 0
\(123\) 329867. 1.96596
\(124\) 0 0
\(125\) −180150. −1.03124
\(126\) 0 0
\(127\) 71553.8 220220.i 0.393662 1.21157i −0.536337 0.844004i \(-0.680192\pi\)
0.929999 0.367563i \(-0.119808\pi\)
\(128\) 0 0
\(129\) 24303.4 0.128586
\(130\) 0 0
\(131\) −92114.4 + 66925.0i −0.468974 + 0.340730i −0.797041 0.603925i \(-0.793603\pi\)
0.328067 + 0.944654i \(0.393603\pi\)
\(132\) 0 0
\(133\) −88672.6 64424.4i −0.434671 0.315807i
\(134\) 0 0
\(135\) 433296. 314808.i 2.04621 1.48666i
\(136\) 0 0
\(137\) −91253.4 + 280849.i −0.415382 + 1.27841i 0.496527 + 0.868021i \(0.334608\pi\)
−0.911909 + 0.410393i \(0.865392\pi\)
\(138\) 0 0
\(139\) 68483.8 210771.i 0.300643 0.925283i −0.680625 0.732632i \(-0.738292\pi\)
0.981267 0.192651i \(-0.0617085\pi\)
\(140\) 0 0
\(141\) 129364. + 93988.6i 0.547982 + 0.398132i
\(142\) 0 0
\(143\) 143041. + 440234.i 0.584950 + 1.80029i
\(144\) 0 0
\(145\) −5546.76 17071.2i −0.0219088 0.0674284i
\(146\) 0 0
\(147\) −227025. 164943.i −0.866524 0.629567i
\(148\) 0 0
\(149\) 294859. 1.08805 0.544025 0.839069i \(-0.316900\pi\)
0.544025 + 0.839069i \(0.316900\pi\)
\(150\) 0 0
\(151\) 227053. 164963.i 0.810371 0.588769i −0.103567 0.994622i \(-0.533026\pi\)
0.913938 + 0.405853i \(0.133026\pi\)
\(152\) 0 0
\(153\) −180919. 556811.i −0.624821 1.92300i
\(154\) 0 0
\(155\) −167301. 235269.i −0.559333 0.786567i
\(156\) 0 0
\(157\) −501.124 1542.30i −0.00162254 0.00499367i 0.950242 0.311513i \(-0.100836\pi\)
−0.951865 + 0.306519i \(0.900836\pi\)
\(158\) 0 0
\(159\) −302990. + 220135.i −0.950464 + 0.690553i
\(160\) 0 0
\(161\) 339422. 1.03199
\(162\) 0 0
\(163\) 240608. + 174812.i 0.709320 + 0.515351i 0.882954 0.469459i \(-0.155551\pi\)
−0.173635 + 0.984810i \(0.555551\pi\)
\(164\) 0 0
\(165\) −338780. 1.04266e6i −0.968742 2.98148i
\(166\) 0 0
\(167\) −82293.1 253272.i −0.228335 0.702742i −0.997936 0.0642173i \(-0.979545\pi\)
0.769601 0.638525i \(-0.220455\pi\)
\(168\) 0 0
\(169\) −48285.6 35081.6i −0.130047 0.0944849i
\(170\) 0 0
\(171\) 236650. 728333.i 0.618893 1.90476i
\(172\) 0 0
\(173\) −22381.9 + 68884.4i −0.0568567 + 0.174987i −0.975452 0.220213i \(-0.929325\pi\)
0.918595 + 0.395200i \(0.129325\pi\)
\(174\) 0 0
\(175\) 14552.1 10572.7i 0.0359195 0.0260970i
\(176\) 0 0
\(177\) −209217. 152005.i −0.501953 0.364690i
\(178\) 0 0
\(179\) −438676. + 318717.i −1.02332 + 0.743485i −0.966961 0.254926i \(-0.917949\pi\)
−0.0563586 + 0.998411i \(0.517949\pi\)
\(180\) 0 0
\(181\) −9769.79 −0.0221661 −0.0110830 0.999939i \(-0.503528\pi\)
−0.0110830 + 0.999939i \(0.503528\pi\)
\(182\) 0 0
\(183\) −131048. + 403324.i −0.289270 + 0.890280i
\(184\) 0 0
\(185\) 645851. 1.38741
\(186\) 0 0
\(187\) −702702. −1.46949
\(188\) 0 0
\(189\) −257912. + 793772.i −0.525191 + 1.61637i
\(190\) 0 0
\(191\) −32844.9 −0.0651455 −0.0325727 0.999469i \(-0.510370\pi\)
−0.0325727 + 0.999469i \(0.510370\pi\)
\(192\) 0 0
\(193\) −705496. + 512573.i −1.36333 + 0.990518i −0.365105 + 0.930966i \(0.618967\pi\)
−0.998225 + 0.0595513i \(0.981033\pi\)
\(194\) 0 0
\(195\) 825792. + 599973.i 1.55519 + 1.12991i
\(196\) 0 0
\(197\) −511749. + 371807.i −0.939488 + 0.682578i −0.948297 0.317383i \(-0.897196\pi\)
0.00880928 + 0.999961i \(0.497196\pi\)
\(198\) 0 0
\(199\) 22057.7 67886.6i 0.0394846 0.121521i −0.929371 0.369146i \(-0.879650\pi\)
0.968856 + 0.247625i \(0.0796502\pi\)
\(200\) 0 0
\(201\) 543612. 1.67306e6i 0.949071 2.92094i
\(202\) 0 0
\(203\) 22629.6 + 16441.3i 0.0385422 + 0.0280025i
\(204\) 0 0
\(205\) −190848. 587369.i −0.317177 0.976172i
\(206\) 0 0
\(207\) 732847. + 2.25547e6i 1.18874 + 3.65857i
\(208\) 0 0
\(209\) −743620. 540271.i −1.17757 0.855551i
\(210\) 0 0
\(211\) −48639.8 −0.0752117 −0.0376058 0.999293i \(-0.511973\pi\)
−0.0376058 + 0.999293i \(0.511973\pi\)
\(212\) 0 0
\(213\) −1.25337e6 + 910624.i −1.89291 + 1.37528i
\(214\) 0 0
\(215\) −14061.0 43275.2i −0.0207453 0.0638474i
\(216\) 0 0
\(217\) 426420. + 143366.i 0.614735 + 0.206680i
\(218\) 0 0
\(219\) −463309. 1.42592e6i −0.652771 2.00902i
\(220\) 0 0
\(221\) 529306. 384563.i 0.728997 0.529647i
\(222\) 0 0
\(223\) 173540. 0.233688 0.116844 0.993150i \(-0.462722\pi\)
0.116844 + 0.993150i \(0.462722\pi\)
\(224\) 0 0
\(225\) 101676. + 73871.7i 0.133894 + 0.0972796i
\(226\) 0 0
\(227\) 404916. + 1.24620e6i 0.521556 + 1.60518i 0.771028 + 0.636802i \(0.219743\pi\)
−0.249472 + 0.968382i \(0.580257\pi\)
\(228\) 0 0
\(229\) −188917. 581427.i −0.238058 0.732666i −0.996701 0.0811602i \(-0.974137\pi\)
0.758643 0.651506i \(-0.225863\pi\)
\(230\) 0 0
\(231\) 1.38215e6 + 1.00419e6i 1.70422 + 1.23819i
\(232\) 0 0
\(233\) −265291. + 816481.i −0.320134 + 0.985273i 0.653455 + 0.756966i \(0.273319\pi\)
−0.973589 + 0.228307i \(0.926681\pi\)
\(234\) 0 0
\(235\) 92513.5 284727.i 0.109279 0.336325i
\(236\) 0 0
\(237\) 977897. 710484.i 1.13089 0.821643i
\(238\) 0 0
\(239\) 876983. + 637166.i 0.993108 + 0.721535i 0.960600 0.277936i \(-0.0896503\pi\)
0.0325088 + 0.999471i \(0.489650\pi\)
\(240\) 0 0
\(241\) 485664. 352855.i 0.538633 0.391340i −0.284944 0.958544i \(-0.591975\pi\)
0.823577 + 0.567204i \(0.191975\pi\)
\(242\) 0 0
\(243\) −1.71768e6 −1.86607
\(244\) 0 0
\(245\) −162355. + 499677.i −0.172802 + 0.531831i
\(246\) 0 0
\(247\) 855797. 0.892541
\(248\) 0 0
\(249\) 1.05808e6 1.08148
\(250\) 0 0
\(251\) 179763. 553254.i 0.180101 0.554294i −0.819729 0.572752i \(-0.805876\pi\)
0.999830 + 0.0184582i \(0.00587575\pi\)
\(252\) 0 0
\(253\) 2.84643e6 2.79576
\(254\) 0 0
\(255\) −1.25362e6 + 910807.i −1.20730 + 0.877154i
\(256\) 0 0
\(257\) 819807. + 595625.i 0.774246 + 0.562523i 0.903247 0.429122i \(-0.141177\pi\)
−0.129001 + 0.991645i \(0.541177\pi\)
\(258\) 0 0
\(259\) −814240. + 591580.i −0.754228 + 0.547979i
\(260\) 0 0
\(261\) −60393.9 + 185873.i −0.0548772 + 0.168895i
\(262\) 0 0
\(263\) −196728. + 605465.i −0.175378 + 0.539759i −0.999651 0.0264346i \(-0.991585\pi\)
0.824272 + 0.566194i \(0.191585\pi\)
\(264\) 0 0
\(265\) 567277. + 412151.i 0.496227 + 0.360530i
\(266\) 0 0
\(267\) −1.27873e6 3.93553e6i −1.09774 3.37851i
\(268\) 0 0
\(269\) −362199. 1.11473e6i −0.305187 0.939269i −0.979607 0.200921i \(-0.935606\pi\)
0.674420 0.738348i \(-0.264394\pi\)
\(270\) 0 0
\(271\) −789260. 573431.i −0.652825 0.474305i 0.211407 0.977398i \(-0.432195\pi\)
−0.864232 + 0.503093i \(0.832195\pi\)
\(272\) 0 0
\(273\) −1.59065e6 −1.29172
\(274\) 0 0
\(275\) 122036. 88664.1i 0.0973095 0.0706995i
\(276\) 0 0
\(277\) 140391. + 432078.i 0.109936 + 0.338347i 0.990857 0.134915i \(-0.0430762\pi\)
−0.880921 + 0.473263i \(0.843076\pi\)
\(278\) 0 0
\(279\) −31990.9 + 3.14312e6i −0.0246046 + 2.41741i
\(280\) 0 0
\(281\) 158577. + 488051.i 0.119805 + 0.368722i 0.992919 0.118794i \(-0.0379029\pi\)
−0.873114 + 0.487517i \(0.837903\pi\)
\(282\) 0 0
\(283\) 1.71186e6 1.24374e6i 1.27058 0.923129i 0.271352 0.962480i \(-0.412529\pi\)
0.999225 + 0.0393513i \(0.0125291\pi\)
\(284\) 0 0
\(285\) −2.02689e6 −1.47815
\(286\) 0 0
\(287\) 778617. + 565699.i 0.557981 + 0.405397i
\(288\) 0 0
\(289\) −131840. 405760.i −0.0928541 0.285776i
\(290\) 0 0
\(291\) −552857. 1.70152e6i −0.382719 1.17789i
\(292\) 0 0
\(293\) 350063. + 254335.i 0.238219 + 0.173076i 0.700490 0.713663i \(-0.252965\pi\)
−0.462270 + 0.886739i \(0.652965\pi\)
\(294\) 0 0
\(295\) −149619. + 460480.i −0.100100 + 0.308075i
\(296\) 0 0
\(297\) −2.16288e6 + 6.65667e6i −1.42279 + 4.37891i
\(298\) 0 0
\(299\) −2.14406e6 + 1.55775e6i −1.38694 + 1.00767i
\(300\) 0 0
\(301\) 57365.8 + 41678.7i 0.0364953 + 0.0265154i
\(302\) 0 0
\(303\) 3.12473e6 2.27025e6i 1.95527 1.42059i
\(304\) 0 0
\(305\) 793989. 0.488725
\(306\) 0 0
\(307\) −311652. + 959167.i −0.188723 + 0.580829i −0.999993 0.00384306i \(-0.998777\pi\)
0.811270 + 0.584672i \(0.198777\pi\)
\(308\) 0 0
\(309\) −2.03617e6 −1.21316
\(310\) 0 0
\(311\) 1.22144e6 0.716094 0.358047 0.933704i \(-0.383443\pi\)
0.358047 + 0.933704i \(0.383443\pi\)
\(312\) 0 0
\(313\) 310025. 954159.i 0.178869 0.550503i −0.820920 0.571044i \(-0.806539\pi\)
0.999789 + 0.0205403i \(0.00653865\pi\)
\(314\) 0 0
\(315\) 2.66498e6 1.51327
\(316\) 0 0
\(317\) −1.90578e6 + 1.38463e6i −1.06518 + 0.773901i −0.975040 0.222027i \(-0.928733\pi\)
−0.0901434 + 0.995929i \(0.528733\pi\)
\(318\) 0 0
\(319\) 189775. + 137879.i 0.104415 + 0.0758616i
\(320\) 0 0
\(321\) 2.14002e6 1.55482e6i 1.15919 0.842202i
\(322\) 0 0
\(323\) −401465. + 1.23558e6i −0.214112 + 0.658969i
\(324\) 0 0
\(325\) −43400.0 + 133571.i −0.0227919 + 0.0701463i
\(326\) 0 0
\(327\) −4.86143e6 3.53203e6i −2.51417 1.82665i
\(328\) 0 0
\(329\) 144167. + 443702.i 0.0734307 + 0.225996i
\(330\) 0 0
\(331\) −219788. 676437.i −0.110264 0.339357i 0.880666 0.473738i \(-0.157096\pi\)
−0.990930 + 0.134380i \(0.957096\pi\)
\(332\) 0 0
\(333\) −5.68911e6 4.13338e6i −2.81147 2.04265i
\(334\) 0 0
\(335\) −3.29361e6 −1.60347
\(336\) 0 0
\(337\) 1.12711e6 818893.i 0.540619 0.392783i −0.283696 0.958914i \(-0.591561\pi\)
0.824315 + 0.566132i \(0.191561\pi\)
\(338\) 0 0
\(339\) −1.57385e6 4.84382e6i −0.743815 2.28923i
\(340\) 0 0
\(341\) 3.57601e6 + 1.20229e6i 1.66538 + 0.559916i
\(342\) 0 0
\(343\) −689681. 2.12262e6i −0.316529 0.974175i
\(344\) 0 0
\(345\) 5.07803e6 3.68940e6i 2.29693 1.66882i
\(346\) 0 0
\(347\) 2.65173e6 1.18224 0.591119 0.806584i \(-0.298686\pi\)
0.591119 + 0.806584i \(0.298686\pi\)
\(348\) 0 0
\(349\) 462270. + 335859.i 0.203157 + 0.147602i 0.684712 0.728813i \(-0.259928\pi\)
−0.481555 + 0.876416i \(0.659928\pi\)
\(350\) 0 0
\(351\) −2.01377e6 6.19776e6i −0.872455 2.68514i
\(352\) 0 0
\(353\) −38003.9 116964.i −0.0162327 0.0499592i 0.942612 0.333890i \(-0.108361\pi\)
−0.958845 + 0.283931i \(0.908361\pi\)
\(354\) 0 0
\(355\) 2.34663e6 + 1.70492e6i 0.988265 + 0.718016i
\(356\) 0 0
\(357\) 746194. 2.29655e6i 0.309871 0.953686i
\(358\) 0 0
\(359\) 856226. 2.63519e6i 0.350633 1.07914i −0.607866 0.794040i \(-0.707974\pi\)
0.958499 0.285097i \(-0.0920258\pi\)
\(360\) 0 0
\(361\) 628390. 456552.i 0.253782 0.184383i
\(362\) 0 0
\(363\) 7.83614e6 + 5.69329e6i 3.12130 + 2.26776i
\(364\) 0 0
\(365\) −2.27098e6 + 1.64996e6i −0.892237 + 0.648248i
\(366\) 0 0
\(367\) −3.92298e6 −1.52038 −0.760188 0.649704i \(-0.774893\pi\)
−0.760188 + 0.649704i \(0.774893\pi\)
\(368\) 0 0
\(369\) −2.07798e6 + 6.39535e6i −0.794465 + 2.44511i
\(370\) 0 0
\(371\) −1.09270e6 −0.412159
\(372\) 0 0
\(373\) 1.00314e6 0.373327 0.186664 0.982424i \(-0.440233\pi\)
0.186664 + 0.982424i \(0.440233\pi\)
\(374\) 0 0
\(375\) 1.60427e6 4.93742e6i 0.589112 1.81310i
\(376\) 0 0
\(377\) −218403. −0.0791415
\(378\) 0 0
\(379\) −3.54942e6 + 2.57881e6i −1.26929 + 0.922191i −0.999174 0.0406372i \(-0.987061\pi\)
−0.270113 + 0.962829i \(0.587061\pi\)
\(380\) 0 0
\(381\) 5.39844e6 + 3.92219e6i 1.90527 + 1.38426i
\(382\) 0 0
\(383\) −370603. + 269259.i −0.129096 + 0.0937937i −0.650459 0.759541i \(-0.725424\pi\)
0.521363 + 0.853335i \(0.325424\pi\)
\(384\) 0 0
\(385\) 988430. 3.04208e6i 0.339855 1.04597i
\(386\) 0 0
\(387\) −153098. + 471187.i −0.0519627 + 0.159925i
\(388\) 0 0
\(389\) 2.02536e6 + 1.47151e6i 0.678623 + 0.493048i 0.872901 0.487898i \(-0.162236\pi\)
−0.194278 + 0.980947i \(0.562236\pi\)
\(390\) 0 0
\(391\) −1.24324e6 3.82630e6i −0.411257 1.26572i
\(392\) 0 0
\(393\) −1.01394e6 3.12059e6i −0.331155 1.01919i
\(394\) 0 0
\(395\) −1.83088e6 1.33021e6i −0.590427 0.428971i
\(396\) 0 0
\(397\) −2.98442e6 −0.950350 −0.475175 0.879891i \(-0.657615\pi\)
−0.475175 + 0.879891i \(0.657615\pi\)
\(398\) 0 0
\(399\) 2.55534e6 1.85657e6i 0.803557 0.583819i
\(400\) 0 0
\(401\) 875623. + 2.69489e6i 0.271929 + 0.836913i 0.990016 + 0.140958i \(0.0450184\pi\)
−0.718086 + 0.695954i \(0.754982\pi\)
\(402\) 0 0
\(403\) −3.35158e6 + 1.05140e6i −1.02798 + 0.322483i
\(404\) 0 0
\(405\) 2.38937e6 + 7.35372e6i 0.723845 + 2.22776i
\(406\) 0 0
\(407\) −6.82832e6 + 4.96106e6i −2.04328 + 1.48453i
\(408\) 0 0
\(409\) 5.69151e6 1.68236 0.841181 0.540754i \(-0.181861\pi\)
0.841181 + 0.540754i \(0.181861\pi\)
\(410\) 0 0
\(411\) −6.88469e6 5.00202e6i −2.01039 1.46063i
\(412\) 0 0
\(413\) −233157. 717585.i −0.0672627 0.207013i
\(414\) 0 0
\(415\) −612162. 1.88404e6i −0.174480 0.536995i
\(416\) 0 0
\(417\) 5.16682e6 + 3.75391e6i 1.45507 + 1.05717i
\(418\) 0 0
\(419\) −1.40547e6 + 4.32558e6i −0.391098 + 1.20368i 0.540861 + 0.841112i \(0.318099\pi\)
−0.931959 + 0.362564i \(0.881901\pi\)
\(420\) 0 0
\(421\) 1.27734e6 3.93126e6i 0.351238 1.08100i −0.606920 0.794763i \(-0.707595\pi\)
0.958159 0.286238i \(-0.0924048\pi\)
\(422\) 0 0
\(423\) −2.63715e6 + 1.91600e6i −0.716611 + 0.520648i
\(424\) 0 0
\(425\) −172488. 125320.i −0.0463219 0.0336549i
\(426\) 0 0
\(427\) −1.00100e6 + 727269.i −0.265683 + 0.193030i
\(428\) 0 0
\(429\) −1.33394e7 −3.49940
\(430\) 0 0
\(431\) −1.73237e6 + 5.33170e6i −0.449209 + 1.38252i 0.428592 + 0.903498i \(0.359010\pi\)
−0.877801 + 0.479025i \(0.840990\pi\)
\(432\) 0 0
\(433\) −280591. −0.0719207 −0.0359604 0.999353i \(-0.511449\pi\)
−0.0359604 + 0.999353i \(0.511449\pi\)
\(434\) 0 0
\(435\) 517269. 0.131067
\(436\) 0 0
\(437\) 1.62621e6 5.00497e6i 0.407356 1.25371i
\(438\) 0 0
\(439\) 6.54210e6 1.62015 0.810077 0.586324i \(-0.199425\pi\)
0.810077 + 0.586324i \(0.199425\pi\)
\(440\) 0 0
\(441\) 4.62801e6 3.36244e6i 1.13318 0.823301i
\(442\) 0 0
\(443\) 3.65597e6 + 2.65622e6i 0.885103 + 0.643065i 0.934596 0.355710i \(-0.115761\pi\)
−0.0494938 + 0.998774i \(0.515761\pi\)
\(444\) 0 0
\(445\) −6.26788e6 + 4.55388e6i −1.50045 + 1.09014i
\(446\) 0 0
\(447\) −2.62577e6 + 8.08130e6i −0.621567 + 1.91299i
\(448\) 0 0
\(449\) 1.43245e6 4.40863e6i 0.335324 1.03202i −0.631239 0.775589i \(-0.717453\pi\)
0.966562 0.256432i \(-0.0825468\pi\)
\(450\) 0 0
\(451\) 6.52959e6 + 4.74402e6i 1.51163 + 1.09826i
\(452\) 0 0
\(453\) 2.49926e6 + 7.69193e6i 0.572223 + 1.76112i
\(454\) 0 0
\(455\) 920288. + 2.83235e6i 0.208399 + 0.641386i
\(456\) 0 0
\(457\) −3.98364e6 2.89428e6i −0.892255 0.648262i 0.0442097 0.999022i \(-0.485923\pi\)
−0.936465 + 0.350761i \(0.885923\pi\)
\(458\) 0 0
\(459\) 9.89288e6 2.19175
\(460\) 0 0
\(461\) −3.14038e6 + 2.28162e6i −0.688224 + 0.500024i −0.876076 0.482173i \(-0.839848\pi\)
0.187852 + 0.982197i \(0.439848\pi\)
\(462\) 0 0
\(463\) −524374. 1.61386e6i −0.113681 0.349875i 0.877988 0.478682i \(-0.158885\pi\)
−0.991670 + 0.128807i \(0.958885\pi\)
\(464\) 0 0
\(465\) 7.93794e6 2.49017e6i 1.70245 0.534067i
\(466\) 0 0
\(467\) −1.04586e6 3.21884e6i −0.221913 0.682978i −0.998590 0.0530793i \(-0.983096\pi\)
0.776677 0.629899i \(-0.216904\pi\)
\(468\) 0 0
\(469\) 4.15233e6 3.01685e6i 0.871686 0.633317i
\(470\) 0 0
\(471\) 46732.9 0.00970667
\(472\) 0 0
\(473\) 481077. + 349523.i 0.0988693 + 0.0718327i
\(474\) 0 0
\(475\) −86179.8 265234.i −0.0175255 0.0539381i
\(476\) 0 0
\(477\) −2.35925e6 7.26101e6i −0.474764 1.46117i
\(478\) 0 0
\(479\) 4.45416e6 + 3.23614e6i 0.887008 + 0.644449i 0.935096 0.354394i \(-0.115313\pi\)
−0.0480883 + 0.998843i \(0.515313\pi\)
\(480\) 0 0
\(481\) 2.42838e6 7.47378e6i 0.478579 1.47291i
\(482\) 0 0
\(483\) −3.02261e6 + 9.30263e6i −0.589541 + 1.81442i
\(484\) 0 0
\(485\) −2.70990e6 + 1.96886e6i −0.523118 + 0.380068i
\(486\) 0 0
\(487\) −6.34348e6 4.60881e6i −1.21201 0.880575i −0.216596 0.976261i \(-0.569495\pi\)
−0.995412 + 0.0956865i \(0.969495\pi\)
\(488\) 0 0
\(489\) −6.93379e6 + 5.03770e6i −1.31129 + 0.952708i
\(490\) 0 0
\(491\) −7.81989e6 −1.46385 −0.731925 0.681385i \(-0.761378\pi\)
−0.731925 + 0.681385i \(0.761378\pi\)
\(492\) 0 0
\(493\) 102455. 315325.i 0.0189853 0.0584307i
\(494\) 0 0
\(495\) 2.23489e7 4.09961
\(496\) 0 0
\(497\) −4.52011e6 −0.820838
\(498\) 0 0
\(499\) −1.60718e6 + 4.94640e6i −0.288944 + 0.889278i 0.696245 + 0.717804i \(0.254853\pi\)
−0.985189 + 0.171474i \(0.945147\pi\)
\(500\) 0 0
\(501\) 7.67434e6 1.36599
\(502\) 0 0
\(503\) −2.23990e6 + 1.62738e6i −0.394737 + 0.286793i −0.767394 0.641176i \(-0.778447\pi\)
0.372657 + 0.927969i \(0.378447\pi\)
\(504\) 0 0
\(505\) −5.85031e6 4.25050e6i −1.02082 0.741672i
\(506\) 0 0
\(507\) 1.39148e6 1.01097e6i 0.240413 0.174670i
\(508\) 0 0
\(509\) 379324. 1.16744e6i 0.0648957 0.199729i −0.913351 0.407173i \(-0.866515\pi\)
0.978247 + 0.207444i \(0.0665146\pi\)
\(510\) 0 0
\(511\) 1.35176e6 4.16029e6i 0.229006 0.704808i
\(512\) 0 0
\(513\) 1.04689e7 + 7.60613e6i 1.75634 + 1.27606i
\(514\) 0 0
\(515\) 1.17805e6 + 3.62566e6i 0.195724 + 0.602378i
\(516\) 0 0
\(517\) 1.20901e6 + 3.72094e6i 0.198931 + 0.612247i
\(518\) 0 0
\(519\) −1.68862e6 1.22685e6i −0.275178 0.199929i
\(520\) 0 0
\(521\) 5.51363e6 0.889904 0.444952 0.895554i \(-0.353221\pi\)
0.444952 + 0.895554i \(0.353221\pi\)
\(522\) 0 0
\(523\) 6.28959e6 4.56965e6i 1.00547 0.730515i 0.0422137 0.999109i \(-0.486559\pi\)
0.963254 + 0.268594i \(0.0865590\pi\)
\(524\) 0 0
\(525\) 160181. + 492985.i 0.0253637 + 0.0780613i
\(526\) 0 0
\(527\) 54271.1 5.33216e6i 0.00851220 0.836328i
\(528\) 0 0
\(529\) 3.04705e6 + 9.37787e6i 0.473414 + 1.45702i
\(530\) 0 0
\(531\) 4.26497e6 3.09868e6i 0.656417 0.476915i
\(532\) 0 0
\(533\) −7.51460e6 −1.14574
\(534\) 0 0
\(535\) −4.00668e6 2.91102e6i −0.605201 0.439704i
\(536\) 0 0
\(537\) −4.82868e6 1.48611e7i −0.722591 2.22391i
\(538\) 0 0
\(539\) −2.12172e6 6.52999e6i −0.314570 0.968145i
\(540\) 0 0
\(541\) −9.09907e6 6.61086e6i −1.33661 0.971102i −0.999561 0.0296131i \(-0.990572\pi\)
−0.337045 0.941488i \(-0.609428\pi\)
\(542\) 0 0
\(543\) 87001.6 267763.i 0.0126627 0.0389719i
\(544\) 0 0
\(545\) −3.47660e6 + 1.06999e7i −0.501376 + 1.54308i
\(546\) 0 0
\(547\) −5.83453e6 + 4.23903e6i −0.833753 + 0.605757i −0.920619 0.390463i \(-0.872315\pi\)
0.0868657 + 0.996220i \(0.472315\pi\)
\(548\) 0 0
\(549\) −6.99400e6 5.08144e6i −0.990364 0.719541i
\(550\) 0 0
\(551\) 350858. 254914.i 0.0492326 0.0357696i
\(552\) 0 0
\(553\) 3.52666e6 0.490400
\(554\) 0 0
\(555\) −5.75142e6 + 1.77010e7i −0.792579 + 2.43931i
\(556\) 0 0
\(557\) 1.16795e7 1.59509 0.797544 0.603260i \(-0.206132\pi\)
0.797544 + 0.603260i \(0.206132\pi\)
\(558\) 0 0
\(559\) −553649. −0.0749384
\(560\) 0 0
\(561\) 6.25768e6 1.92592e7i 0.839472 2.58363i
\(562\) 0 0
\(563\) −1.20801e7 −1.60621 −0.803103 0.595840i \(-0.796819\pi\)
−0.803103 + 0.595840i \(0.796819\pi\)
\(564\) 0 0
\(565\) −7.71446e6 + 5.60489e6i −1.01668 + 0.738662i
\(566\) 0 0
\(567\) −9.74811e6 7.08241e6i −1.27339 0.925175i
\(568\) 0 0
\(569\) −233842. + 169896.i −0.0302790 + 0.0219990i −0.602822 0.797876i \(-0.705957\pi\)
0.572543 + 0.819875i \(0.305957\pi\)
\(570\) 0 0
\(571\) −934724. + 2.87678e6i −0.119976 + 0.369247i −0.992952 0.118515i \(-0.962187\pi\)
0.872977 + 0.487762i \(0.162187\pi\)
\(572\) 0 0
\(573\) 292489. 900189.i 0.0372155 0.114537i
\(574\) 0 0
\(575\) 698697. + 507633.i 0.0881291 + 0.0640295i
\(576\) 0 0
\(577\) 4.54243e6 + 1.39801e7i 0.568000 + 1.74812i 0.658866 + 0.752261i \(0.271037\pi\)
−0.0908657 + 0.995863i \(0.528963\pi\)
\(578\) 0 0
\(579\) −7.76567e6 2.39003e7i −0.962681 2.96283i
\(580\) 0 0
\(581\) 2.49749e6 + 1.81453e6i 0.306947 + 0.223010i
\(582\) 0 0
\(583\) −9.16349e6 −1.11658
\(584\) 0 0
\(585\) −1.68341e7 + 1.22307e7i −2.03377 + 1.47762i
\(586\) 0 0
\(587\) −1.11278e6 3.42478e6i −0.133295 0.410239i 0.862026 0.506864i \(-0.169195\pi\)
−0.995321 + 0.0966248i \(0.969195\pi\)
\(588\) 0 0
\(589\) 4.15705e6 5.60092e6i 0.493739 0.665229i
\(590\) 0 0
\(591\) −5.63302e6 1.73367e7i −0.663396 2.04172i
\(592\) 0 0
\(593\) −7.10341e6 + 5.16093e6i −0.829526 + 0.602686i −0.919425 0.393265i \(-0.871346\pi\)
0.0898991 + 0.995951i \(0.471346\pi\)
\(594\) 0 0
\(595\) −4.52101e6 −0.523532
\(596\) 0 0
\(597\) 1.66416e6 + 1.20908e6i 0.191099 + 0.138842i
\(598\) 0 0
\(599\) 3.60536e6 + 1.10962e7i 0.410565 + 1.26359i 0.916159 + 0.400816i \(0.131273\pi\)
−0.505594 + 0.862772i \(0.668727\pi\)
\(600\) 0 0
\(601\) 3.01311e6 + 9.27339e6i 0.340274 + 1.04725i 0.964066 + 0.265664i \(0.0855913\pi\)
−0.623792 + 0.781590i \(0.714409\pi\)
\(602\) 0 0
\(603\) 2.90124e7 + 2.10788e7i 3.24931 + 2.36076i
\(604\) 0 0
\(605\) 5.60393e6 1.72471e7i 0.622450 1.91570i
\(606\) 0 0
\(607\) −1.01612e6 + 3.12730e6i −0.111937 + 0.344507i −0.991296 0.131653i \(-0.957972\pi\)
0.879359 + 0.476160i \(0.157972\pi\)
\(608\) 0 0
\(609\) −652133. + 473802.i −0.0712513 + 0.0517671i
\(610\) 0 0
\(611\) −2.94701e6 2.14113e6i −0.319359 0.232028i
\(612\) 0 0
\(613\) 3.77345e6 2.74157e6i 0.405590 0.294678i −0.366224 0.930527i \(-0.619350\pi\)
0.771814 + 0.635848i \(0.219350\pi\)
\(614\) 0 0
\(615\) 1.77977e7 1.89748
\(616\) 0 0
\(617\) 1.98660e6 6.11413e6i 0.210086 0.646579i −0.789380 0.613905i \(-0.789598\pi\)
0.999466 0.0326741i \(-0.0104023\pi\)
\(618\) 0 0
\(619\) 1.17953e7 1.23732 0.618658 0.785660i \(-0.287677\pi\)
0.618658 + 0.785660i \(0.287677\pi\)
\(620\) 0 0
\(621\) −4.00731e7 −4.16988
\(622\) 0 0
\(623\) 3.73085e6 1.14824e7i 0.385112 1.18525i
\(624\) 0 0
\(625\) −9.05131e6 −0.926855
\(626\) 0 0
\(627\) 2.14294e7 1.55694e7i 2.17692 1.58162i
\(628\) 0 0
\(629\) 9.65130e6 + 7.01208e6i 0.972656 + 0.706676i
\(630\) 0 0
\(631\) −107690. + 78241.4i −0.0107672 + 0.00782282i −0.593156 0.805088i \(-0.702118\pi\)
0.582389 + 0.812910i \(0.302118\pi\)
\(632\) 0 0
\(633\) 433145. 1.33308e6i 0.0429660 0.132236i
\(634\) 0 0
\(635\) 3.86064e6 1.18818e7i 0.379948 1.16936i
\(636\) 0 0
\(637\) 5.17180e6 + 3.75753e6i 0.505002 + 0.366905i
\(638\) 0 0
\(639\) −9.75939e6 3.00363e7i −0.945520 2.91001i
\(640\) 0 0
\(641\) 2.76689e6 + 8.51562e6i 0.265979 + 0.818599i 0.991466 + 0.130363i \(0.0416144\pi\)
−0.725487 + 0.688235i \(0.758386\pi\)
\(642\) 0 0
\(643\) 1.11989e7 + 8.13648e6i 1.06819 + 0.776085i 0.975586 0.219618i \(-0.0704811\pi\)
0.0926033 + 0.995703i \(0.470481\pi\)
\(644\) 0 0
\(645\) 1.31127e6 0.124106
\(646\) 0 0
\(647\) 5.70709e6 4.14644e6i 0.535987 0.389417i −0.286606 0.958049i \(-0.592527\pi\)
0.822592 + 0.568632i \(0.192527\pi\)
\(648\) 0 0
\(649\) −1.95529e6 6.01776e6i −0.182221 0.560819i
\(650\) 0 0
\(651\) −7.72663e6 + 1.04103e7i −0.714558 + 0.962745i
\(652\) 0 0
\(653\) −6.48315e6 1.99531e7i −0.594981 1.83116i −0.554821 0.831970i \(-0.687213\pi\)
−0.0401604 0.999193i \(-0.512787\pi\)
\(654\) 0 0
\(655\) −4.96997e6 + 3.61089e6i −0.452637 + 0.328860i
\(656\) 0 0
\(657\) 3.05639e7 2.76246
\(658\) 0 0
\(659\) 1.16781e6 + 848467.i 0.104751 + 0.0761064i 0.638928 0.769267i \(-0.279378\pi\)
−0.534176 + 0.845373i \(0.679378\pi\)
\(660\) 0 0
\(661\) −5.73184e6 1.76408e7i −0.510259 1.57042i −0.791746 0.610850i \(-0.790828\pi\)
0.281487 0.959565i \(-0.409172\pi\)
\(662\) 0 0
\(663\) 5.82628e6 + 1.79314e7i 0.514763 + 1.58428i
\(664\) 0 0
\(665\) −4.78427e6 3.47597e6i −0.419528 0.304805i
\(666\) 0 0
\(667\) −415016. + 1.27729e6i −0.0361202 + 0.111166i
\(668\) 0 0
\(669\) −1.54540e6 + 4.75626e6i −0.133498 + 0.410866i
\(670\) 0 0
\(671\) −8.39451e6 + 6.09897e6i −0.719762 + 0.522938i
\(672\) 0 0
\(673\) −1.85850e6 1.35028e6i −0.158171 0.114918i 0.505885 0.862601i \(-0.331166\pi\)
−0.664055 + 0.747683i \(0.731166\pi\)
\(674\) 0 0
\(675\) −1.71806e6 + 1.24824e6i −0.145137 + 0.105448i
\(676\) 0 0
\(677\) 3.18695e6 0.267242 0.133621 0.991033i \(-0.457340\pi\)
0.133621 + 0.991033i \(0.457340\pi\)
\(678\) 0 0
\(679\) 1.61302e6 4.96438e6i 0.134266 0.413229i
\(680\) 0 0
\(681\) −3.77610e7 −3.12015
\(682\) 0 0
\(683\) −3.83940e6 −0.314928 −0.157464 0.987525i \(-0.550332\pi\)
−0.157464 + 0.987525i \(0.550332\pi\)
\(684\) 0 0
\(685\) −4.92351e6 + 1.51530e7i −0.400912 + 1.23388i
\(686\) 0 0
\(687\) 1.76177e7 1.42415
\(688\) 0 0
\(689\) 6.90233e6 5.01484e6i 0.553921 0.402447i
\(690\) 0 0
\(691\) 1.10853e7 + 8.05391e6i 0.883183 + 0.641670i 0.934092 0.357033i \(-0.116212\pi\)
−0.0509084 + 0.998703i \(0.516212\pi\)
\(692\) 0 0
\(693\) −2.81757e7 + 2.04709e7i −2.22865 + 1.61921i
\(694\) 0 0
\(695\) 3.69499e6 1.13720e7i 0.290170 0.893050i
\(696\) 0 0
\(697\) 3.52519e6 1.08494e7i 0.274853 0.845911i
\(698\) 0 0
\(699\) −2.00151e7 1.45418e7i −1.54940 1.12571i
\(700\) 0 0
\(701\) 3.65855e6 + 1.12598e7i 0.281199 + 0.865441i 0.987512 + 0.157542i \(0.0503569\pi\)
−0.706314 + 0.707899i \(0.749643\pi\)
\(702\) 0 0
\(703\) 4.82206e6 + 1.48408e7i 0.367997 + 1.13258i
\(704\) 0 0
\(705\) 6.97976e6 + 5.07109e6i 0.528893 + 0.384263i
\(706\) 0 0
\(707\) 1.12690e7 0.847881
\(708\) 0 0
\(709\) 1.77050e7 1.28634e7i 1.32276 0.961039i 0.322864 0.946446i \(-0.395355\pi\)
0.999894 0.0145937i \(-0.00464550\pi\)
\(710\) 0 0
\(711\) 7.61443e6 + 2.34348e7i 0.564890 + 1.73855i
\(712\) 0 0
\(713\) −219836. + 2.15990e7i −0.0161947 + 1.59114i
\(714\) 0 0
\(715\) 7.71765e6 + 2.37525e7i 0.564573 + 1.73758i
\(716\) 0 0
\(717\) −2.52727e7 + 1.83617e7i −1.83592 + 1.33387i
\(718\) 0 0
\(719\) −940278. −0.0678319 −0.0339159 0.999425i \(-0.510798\pi\)
−0.0339159 + 0.999425i \(0.510798\pi\)
\(720\) 0 0
\(721\) −4.80618e6 3.49190e6i −0.344320 0.250163i
\(722\) 0 0
\(723\) 5.34589e6 + 1.64530e7i 0.380342 + 1.17057i
\(724\) 0 0
\(725\) 21993.4 + 67688.8i 0.00155399 + 0.00478268i
\(726\) 0 0
\(727\) 9.18975e6 + 6.67674e6i 0.644863 + 0.468520i 0.861517 0.507728i \(-0.169514\pi\)
−0.216654 + 0.976248i \(0.569514\pi\)
\(728\) 0 0
\(729\) 4.53501e6 1.39573e7i 0.316052 0.972709i
\(730\) 0 0
\(731\) 259723. 799346.i 0.0179770 0.0553276i
\(732\) 0 0
\(733\) 9.90721e6 7.19801e6i 0.681070 0.494826i −0.192643 0.981269i \(-0.561706\pi\)
0.873712 + 0.486443i \(0.161706\pi\)
\(734\) 0 0
\(735\) −1.22490e7 8.89941e6i −0.836338 0.607635i
\(736\) 0 0
\(737\) 3.48220e7 2.52997e7i 2.36148 1.71572i
\(738\) 0 0
\(739\) −1.82301e7 −1.22794 −0.613970 0.789329i \(-0.710428\pi\)
−0.613970 + 0.789329i \(0.710428\pi\)
\(740\) 0 0
\(741\) −7.62102e6 + 2.34551e7i −0.509879 + 1.56925i
\(742\) 0 0
\(743\) −1.99488e7 −1.32570 −0.662849 0.748753i \(-0.730653\pi\)
−0.662849 + 0.748753i \(0.730653\pi\)
\(744\) 0 0
\(745\) 1.59089e7 1.05015
\(746\) 0 0
\(747\) −6.66531e6 + 2.05137e7i −0.437038 + 1.34506i
\(748\) 0 0
\(749\) 7.71771e6 0.502671
\(750\) 0 0
\(751\) −1.31550e6 + 955764.i −0.0851118 + 0.0618373i −0.629527 0.776978i \(-0.716751\pi\)
0.544416 + 0.838816i \(0.316751\pi\)
\(752\) 0 0
\(753\) 1.35624e7 + 9.85364e6i 0.871662 + 0.633300i
\(754\) 0 0
\(755\) 1.22505e7 8.90048e6i 0.782141 0.568259i
\(756\) 0 0
\(757\) −3.99567e6 + 1.22974e7i −0.253426 + 0.779964i 0.740710 + 0.671825i \(0.234489\pi\)
−0.994136 + 0.108139i \(0.965511\pi\)
\(758\) 0 0
\(759\) −2.53480e7 + 7.80130e7i −1.59712 + 4.91544i
\(760\) 0 0
\(761\) −1.34643e7 9.78241e6i −0.842797 0.612328i 0.0803535 0.996766i \(-0.474395\pi\)
−0.923151 + 0.384438i \(0.874395\pi\)
\(762\) 0 0
\(763\) −5.41772e6 1.66740e7i −0.336903 1.03688i
\(764\) 0 0
\(765\) −9.76135e6 3.00423e7i −0.603054 1.85601i
\(766\) 0 0
\(767\) 4.76611e6 + 3.46278e6i 0.292533 + 0.212538i
\(768\) 0 0
\(769\) −6.20254e6 −0.378228 −0.189114 0.981955i \(-0.560562\pi\)
−0.189114 + 0.981955i \(0.560562\pi\)
\(770\) 0 0
\(771\) −2.36250e7 + 1.71646e7i −1.43132 + 1.03991i
\(772\) 0 0
\(773\) 5.43939e6 + 1.67407e7i 0.327417 + 1.00769i 0.970338 + 0.241754i \(0.0777227\pi\)
−0.642920 + 0.765933i \(0.722277\pi\)
\(774\) 0 0
\(775\) 663366. + 932865.i 0.0396733 + 0.0557911i
\(776\) 0 0
\(777\) −8.96266e6 2.75842e7i −0.532579 1.63911i
\(778\) 0 0
\(779\) 1.20720e7 8.77083e6i 0.712748 0.517842i
\(780\) 0 0
\(781\) −3.79062e7 −2.22373
\(782\) 0 0
\(783\) −2.67171e6 1.94111e6i −0.155735 0.113148i
\(784\) 0 0
\(785\) −27037.8 83213.8i −0.00156602 0.00481971i
\(786\) 0 0
\(787\) 4.41165e6 + 1.35777e7i 0.253901 + 0.781427i 0.994044 + 0.108978i \(0.0347577\pi\)
−0.740143 + 0.672449i \(0.765242\pi\)
\(788\) 0 0
\(789\) −1.48423e7 1.0