Properties

Label 124.6.f.a.33.2
Level $124$
Weight $6$
Character 124.33
Analytic conductor $19.888$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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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 33.2
Character \(\chi\) \(=\) 124.33
Dual form 124.6.f.a.109.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-21.3000 + 15.4753i) q^{3} +92.0001 q^{5} +(26.8893 + 82.7567i) q^{7} +(139.112 - 428.142i) q^{9} +O(q^{10})\) \(q+(-21.3000 + 15.4753i) q^{3} +92.0001 q^{5} +(26.8893 + 82.7567i) q^{7} +(139.112 - 428.142i) q^{9} +(-196.836 - 605.799i) q^{11} +(225.634 - 163.933i) q^{13} +(-1959.60 + 1423.73i) q^{15} +(382.219 - 1176.35i) q^{17} +(1587.34 + 1153.27i) q^{19} +(-1853.43 - 1346.60i) q^{21} +(726.521 - 2236.00i) q^{23} +5339.02 q^{25} +(1685.54 + 5187.57i) q^{27} +(3261.85 + 2369.87i) q^{29} +(851.215 + 5282.48i) q^{31} +(13567.5 + 9857.39i) q^{33} +(2473.82 + 7613.63i) q^{35} +3614.50 q^{37} +(-2269.08 + 6983.52i) q^{39} +(-6762.45 - 4913.21i) q^{41} +(6386.36 + 4639.96i) q^{43} +(12798.3 - 39389.1i) q^{45} +(-12861.0 + 9344.07i) q^{47} +(7471.51 - 5428.37i) q^{49} +(10063.1 + 30971.1i) q^{51} +(5266.64 - 16209.1i) q^{53} +(-18108.9 - 55733.5i) q^{55} -51657.5 q^{57} +(-19214.1 + 13959.9i) q^{59} -746.505 q^{61} +39172.2 q^{63} +(20758.3 - 15081.8i) q^{65} +52388.5 q^{67} +(19128.0 + 58869.9i) q^{69} +(-2993.42 + 9212.79i) q^{71} +(22224.9 + 68401.1i) q^{73} +(-113721. + 82623.1i) q^{75} +(44841.1 - 32579.0i) q^{77} +(23898.1 - 73550.7i) q^{79} +(-27681.1 - 20111.5i) q^{81} +(-87903.8 - 63865.8i) q^{83} +(35164.2 - 108224. i) q^{85} -106152. q^{87} +(42405.2 + 130510. i) q^{89} +(19633.7 + 14264.7i) q^{91} +(-99879.0 - 99343.8i) q^{93} +(146035. + 106101. i) q^{95} +(-25537.7 - 78596.9i) q^{97} -286750. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).

\(n\) \(63\) \(65\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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
\(3\) −21.3000 + 15.4753i −1.36639 + 0.992743i −0.368385 + 0.929674i \(0.620089\pi\)
−0.998009 + 0.0630696i \(0.979911\pi\)
\(4\) 0 0
\(5\) 92.0001 1.64575 0.822874 0.568224i \(-0.192369\pi\)
0.822874 + 0.568224i \(0.192369\pi\)
\(6\) 0 0
\(7\) 26.8893 + 82.7567i 0.207412 + 0.638349i 0.999606 + 0.0280791i \(0.00893904\pi\)
−0.792194 + 0.610270i \(0.791061\pi\)
\(8\) 0 0
\(9\) 139.112 428.142i 0.572476 1.76190i
\(10\) 0 0
\(11\) −196.836 605.799i −0.490482 1.50955i −0.823882 0.566762i \(-0.808196\pi\)
0.333400 0.942785i \(-0.391804\pi\)
\(12\) 0 0
\(13\) 225.634 163.933i 0.370293 0.269034i −0.387039 0.922063i \(-0.626502\pi\)
0.757333 + 0.653029i \(0.226502\pi\)
\(14\) 0 0
\(15\) −1959.60 + 1423.73i −2.24874 + 1.63380i
\(16\) 0 0
\(17\) 382.219 1176.35i 0.320767 0.987219i −0.652548 0.757747i \(-0.726300\pi\)
0.973315 0.229472i \(-0.0737000\pi\)
\(18\) 0 0
\(19\) 1587.34 + 1153.27i 1.00876 + 0.732904i 0.963948 0.266092i \(-0.0857325\pi\)
0.0448077 + 0.998996i \(0.485732\pi\)
\(20\) 0 0
\(21\) −1853.43 1346.60i −0.917123 0.666329i
\(22\) 0 0
\(23\) 726.521 2236.00i 0.286371 0.881358i −0.699614 0.714521i \(-0.746645\pi\)
0.985984 0.166837i \(-0.0533554\pi\)
\(24\) 0 0
\(25\) 5339.02 1.70849
\(26\) 0 0
\(27\) 1685.54 + 5187.57i 0.444970 + 1.36948i
\(28\) 0 0
\(29\) 3261.85 + 2369.87i 0.720227 + 0.523275i 0.886457 0.462812i \(-0.153159\pi\)
−0.166230 + 0.986087i \(0.553159\pi\)
\(30\) 0 0
\(31\) 851.215 + 5282.48i 0.159087 + 0.987265i
\(32\) 0 0
\(33\) 13567.5 + 9857.39i 2.16878 + 1.57571i
\(34\) 0 0
\(35\) 2473.82 + 7613.63i 0.341348 + 1.05056i
\(36\) 0 0
\(37\) 3614.50 0.434054 0.217027 0.976166i \(-0.430364\pi\)
0.217027 + 0.976166i \(0.430364\pi\)
\(38\) 0 0
\(39\) −2269.08 + 6983.52i −0.238885 + 0.735213i
\(40\) 0 0
\(41\) −6762.45 4913.21i −0.628267 0.456463i 0.227532 0.973771i \(-0.426934\pi\)
−0.855800 + 0.517308i \(0.826934\pi\)
\(42\) 0 0
\(43\) 6386.36 + 4639.96i 0.526723 + 0.382686i 0.819130 0.573607i \(-0.194456\pi\)
−0.292408 + 0.956294i \(0.594456\pi\)
\(44\) 0 0
\(45\) 12798.3 39389.1i 0.942151 2.89964i
\(46\) 0 0
\(47\) −12861.0 + 9344.07i −0.849240 + 0.617009i −0.924936 0.380122i \(-0.875882\pi\)
0.0756961 + 0.997131i \(0.475882\pi\)
\(48\) 0 0
\(49\) 7471.51 5428.37i 0.444547 0.322982i
\(50\) 0 0
\(51\) 10063.1 + 30971.1i 0.541761 + 1.66737i
\(52\) 0 0
\(53\) 5266.64 16209.1i 0.257540 0.792625i −0.735779 0.677222i \(-0.763184\pi\)
0.993319 0.115404i \(-0.0368162\pi\)
\(54\) 0 0
\(55\) −18108.9 55733.5i −0.807209 2.48433i
\(56\) 0 0
\(57\) −51657.5 −2.10594
\(58\) 0 0
\(59\) −19214.1 + 13959.9i −0.718606 + 0.522098i −0.885938 0.463803i \(-0.846485\pi\)
0.167333 + 0.985900i \(0.446485\pi\)
\(60\) 0 0
\(61\) −746.505 −0.0256867 −0.0128433 0.999918i \(-0.504088\pi\)
−0.0128433 + 0.999918i \(0.504088\pi\)
\(62\) 0 0
\(63\) 39172.2 1.24345
\(64\) 0 0
\(65\) 20758.3 15081.8i 0.609410 0.442762i
\(66\) 0 0
\(67\) 52388.5 1.42577 0.712884 0.701282i \(-0.247389\pi\)
0.712884 + 0.701282i \(0.247389\pi\)
\(68\) 0 0
\(69\) 19128.0 + 58869.9i 0.483667 + 1.48858i
\(70\) 0 0
\(71\) −2993.42 + 9212.79i −0.0704727 + 0.216893i −0.980090 0.198555i \(-0.936375\pi\)
0.909617 + 0.415448i \(0.136375\pi\)
\(72\) 0 0
\(73\) 22224.9 + 68401.1i 0.488126 + 1.50230i 0.827402 + 0.561610i \(0.189818\pi\)
−0.339276 + 0.940687i \(0.610182\pi\)
\(74\) 0 0
\(75\) −113721. + 82623.1i −2.33446 + 1.69609i
\(76\) 0 0
\(77\) 44841.1 32579.0i 0.861886 0.626197i
\(78\) 0 0
\(79\) 23898.1 73550.7i 0.430819 1.32592i −0.466492 0.884526i \(-0.654482\pi\)
0.897311 0.441399i \(-0.145518\pi\)
\(80\) 0 0
\(81\) −27681.1 20111.5i −0.468783 0.340591i
\(82\) 0 0
\(83\) −87903.8 63865.8i −1.40059 1.01759i −0.994607 0.103713i \(-0.966928\pi\)
−0.405987 0.913879i \(-0.633072\pi\)
\(84\) 0 0
\(85\) 35164.2 108224.i 0.527902 1.62471i
\(86\) 0 0
\(87\) −106152. −1.50359
\(88\) 0 0
\(89\) 42405.2 + 130510.i 0.567471 + 1.74650i 0.660493 + 0.750832i \(0.270347\pi\)
−0.0930219 + 0.995664i \(0.529653\pi\)
\(90\) 0 0
\(91\) 19633.7 + 14264.7i 0.248541 + 0.180576i
\(92\) 0 0
\(93\) −99879.0 99343.8i −1.19748 1.19106i
\(94\) 0 0
\(95\) 146035. + 106101.i 1.66016 + 1.20617i
\(96\) 0 0
\(97\) −25537.7 78596.9i −0.275583 0.848157i −0.989065 0.147483i \(-0.952883\pi\)
0.713482 0.700674i \(-0.247117\pi\)
\(98\) 0 0
\(99\) −286750. −2.94046
\(100\) 0 0
\(101\) −39449.7 + 121414.i −0.384805 + 1.18431i 0.551817 + 0.833965i \(0.313935\pi\)
−0.936622 + 0.350342i \(0.886065\pi\)
\(102\) 0 0
\(103\) 151684. + 110205.i 1.40879 + 1.02354i 0.993497 + 0.113855i \(0.0363199\pi\)
0.415290 + 0.909689i \(0.363680\pi\)
\(104\) 0 0
\(105\) −170516. 123887.i −1.50935 1.09661i
\(106\) 0 0
\(107\) 59717.1 183790.i 0.504242 1.55190i −0.297799 0.954628i \(-0.596253\pi\)
0.802041 0.597269i \(-0.203747\pi\)
\(108\) 0 0
\(109\) −35378.8 + 25704.2i −0.285218 + 0.207223i −0.721190 0.692737i \(-0.756405\pi\)
0.435972 + 0.899960i \(0.356405\pi\)
\(110\) 0 0
\(111\) −76988.7 + 55935.5i −0.593088 + 0.430904i
\(112\) 0 0
\(113\) −60304.0 185597.i −0.444273 1.36733i −0.883279 0.468847i \(-0.844669\pi\)
0.439006 0.898484i \(-0.355331\pi\)
\(114\) 0 0
\(115\) 66840.0 205712.i 0.471294 1.45049i
\(116\) 0 0
\(117\) −38798.1 119408.i −0.262027 0.806435i
\(118\) 0 0
\(119\) 107628. 0.696722
\(120\) 0 0
\(121\) −197955. + 143823.i −1.22914 + 0.893025i
\(122\) 0 0
\(123\) 220074. 1.31161
\(124\) 0 0
\(125\) 203690. 1.16599
\(126\) 0 0
\(127\) 133806. 97215.9i 0.736151 0.534845i −0.155352 0.987859i \(-0.549651\pi\)
0.891503 + 0.453014i \(0.149651\pi\)
\(128\) 0 0
\(129\) −207834. −1.09962
\(130\) 0 0
\(131\) −928.745 2858.38i −0.00472845 0.0145527i 0.948664 0.316284i \(-0.102435\pi\)
−0.953393 + 0.301732i \(0.902435\pi\)
\(132\) 0 0
\(133\) −52758.4 + 162374.i −0.258620 + 0.795951i
\(134\) 0 0
\(135\) 155070. + 477257.i 0.732309 + 2.25381i
\(136\) 0 0
\(137\) 247431. 179769.i 1.12630 0.818301i 0.141144 0.989989i \(-0.454922\pi\)
0.985151 + 0.171688i \(0.0549220\pi\)
\(138\) 0 0
\(139\) −260998. + 189626.i −1.14578 + 0.832455i −0.987913 0.155006i \(-0.950460\pi\)
−0.157862 + 0.987461i \(0.550460\pi\)
\(140\) 0 0
\(141\) 129337. 398057.i 0.547865 1.68616i
\(142\) 0 0
\(143\) −143723. 104421.i −0.587741 0.427019i
\(144\) 0 0
\(145\) 300091. + 218029.i 1.18531 + 0.861179i
\(146\) 0 0
\(147\) −75137.1 + 231248.i −0.286788 + 0.882642i
\(148\) 0 0
\(149\) 81148.0 0.299442 0.149721 0.988728i \(-0.452163\pi\)
0.149721 + 0.988728i \(0.452163\pi\)
\(150\) 0 0
\(151\) 84746.8 + 260824.i 0.302469 + 0.930904i 0.980610 + 0.195972i \(0.0627861\pi\)
−0.678140 + 0.734932i \(0.737214\pi\)
\(152\) 0 0
\(153\) −450472. 327287.i −1.55575 1.13032i
\(154\) 0 0
\(155\) 78311.8 + 485989.i 0.261817 + 1.62479i
\(156\) 0 0
\(157\) −285793. 207641.i −0.925342 0.672300i 0.0195060 0.999810i \(-0.493791\pi\)
−0.944848 + 0.327510i \(0.893791\pi\)
\(158\) 0 0
\(159\) 138661. + 426755.i 0.434973 + 1.33871i
\(160\) 0 0
\(161\) 204580. 0.622011
\(162\) 0 0
\(163\) −5140.88 + 15822.0i −0.0151554 + 0.0466436i −0.958348 0.285602i \(-0.907806\pi\)
0.943193 + 0.332246i \(0.107806\pi\)
\(164\) 0 0
\(165\) 1.24821e6 + 906881.i 3.56927 + 2.59323i
\(166\) 0 0
\(167\) −335277. 243593.i −0.930279 0.675887i 0.0157823 0.999875i \(-0.494976\pi\)
−0.946061 + 0.323988i \(0.894976\pi\)
\(168\) 0 0
\(169\) −90699.1 + 279143.i −0.244279 + 0.751814i
\(170\) 0 0
\(171\) 714580. 519173.i 1.86879 1.35776i
\(172\) 0 0
\(173\) 316373. 229858.i 0.803681 0.583908i −0.108311 0.994117i \(-0.534544\pi\)
0.911992 + 0.410209i \(0.134544\pi\)
\(174\) 0 0
\(175\) 143562. + 441840.i 0.354361 + 1.09061i
\(176\) 0 0
\(177\) 193226. 594690.i 0.463589 1.42678i
\(178\) 0 0
\(179\) −211623. 651310.i −0.493664 1.51934i −0.819029 0.573752i \(-0.805487\pi\)
0.325366 0.945588i \(-0.394513\pi\)
\(180\) 0 0
\(181\) 160308. 0.363712 0.181856 0.983325i \(-0.441789\pi\)
0.181856 + 0.983325i \(0.441789\pi\)
\(182\) 0 0
\(183\) 15900.5 11552.4i 0.0350981 0.0255003i
\(184\) 0 0
\(185\) 332534. 0.714343
\(186\) 0 0
\(187\) −787865. −1.64758
\(188\) 0 0
\(189\) −383984. + 278980.i −0.781912 + 0.568093i
\(190\) 0 0
\(191\) 425784. 0.844512 0.422256 0.906477i \(-0.361238\pi\)
0.422256 + 0.906477i \(0.361238\pi\)
\(192\) 0 0
\(193\) −23069.6 71001.0i −0.0445807 0.137205i 0.926289 0.376815i \(-0.122981\pi\)
−0.970869 + 0.239609i \(0.922981\pi\)
\(194\) 0 0
\(195\) −208756. + 642485.i −0.393144 + 1.20997i
\(196\) 0 0
\(197\) −58729.3 180750.i −0.107818 0.331828i 0.882564 0.470193i \(-0.155816\pi\)
−0.990381 + 0.138364i \(0.955816\pi\)
\(198\) 0 0
\(199\) 493567. 358597.i 0.883513 0.641910i −0.0506653 0.998716i \(-0.516134\pi\)
0.934179 + 0.356806i \(0.116134\pi\)
\(200\) 0 0
\(201\) −1.11587e6 + 810729.i −1.94816 + 1.41542i
\(202\) 0 0
\(203\) −108414. + 333664.i −0.184649 + 0.568290i
\(204\) 0 0
\(205\) −622146. 452016.i −1.03397 0.751223i
\(206\) 0 0
\(207\) −856258. 622108.i −1.38892 1.00911i
\(208\) 0 0
\(209\) 386204. 1.18861e6i 0.611577 1.88224i
\(210\) 0 0
\(211\) 433626. 0.670515 0.335258 0.942126i \(-0.391177\pi\)
0.335258 + 0.942126i \(0.391177\pi\)
\(212\) 0 0
\(213\) −78811.3 242556.i −0.119025 0.366322i
\(214\) 0 0
\(215\) 587545. + 426877.i 0.866852 + 0.629805i
\(216\) 0 0
\(217\) −414272. + 212486.i −0.597223 + 0.306324i
\(218\) 0 0
\(219\) −1.53192e6 1.11300e6i −2.15837 1.56815i
\(220\) 0 0
\(221\) −106600. 328082.i −0.146818 0.451858i
\(222\) 0 0
\(223\) 403593. 0.543478 0.271739 0.962371i \(-0.412401\pi\)
0.271739 + 0.962371i \(0.412401\pi\)
\(224\) 0 0
\(225\) 742719. 2.28585e6i 0.978067 3.01018i
\(226\) 0 0
\(227\) 475055. + 345147.i 0.611898 + 0.444570i 0.850082 0.526650i \(-0.176552\pi\)
−0.238184 + 0.971220i \(0.576552\pi\)
\(228\) 0 0
\(229\) −930234. 675854.i −1.17220 0.851657i −0.180933 0.983495i \(-0.557912\pi\)
−0.991271 + 0.131839i \(0.957912\pi\)
\(230\) 0 0
\(231\) −450944. + 1.38786e6i −0.556023 + 1.71126i
\(232\) 0 0
\(233\) −703630. + 511217.i −0.849092 + 0.616901i −0.924896 0.380221i \(-0.875848\pi\)
0.0758036 + 0.997123i \(0.475848\pi\)
\(234\) 0 0
\(235\) −1.18321e6 + 859656.i −1.39764 + 1.01544i
\(236\) 0 0
\(237\) 629193. + 1.93646e6i 0.727634 + 2.23943i
\(238\) 0 0
\(239\) 235545. 724932.i 0.266734 0.820923i −0.724555 0.689217i \(-0.757955\pi\)
0.991289 0.131706i \(-0.0420454\pi\)
\(240\) 0 0
\(241\) 502696. + 1.54714e6i 0.557523 + 1.71588i 0.689185 + 0.724585i \(0.257969\pi\)
−0.131662 + 0.991295i \(0.542031\pi\)
\(242\) 0 0
\(243\) −424612. −0.461293
\(244\) 0 0
\(245\) 687379. 499410.i 0.731613 0.531548i
\(246\) 0 0
\(247\) 547216. 0.570711
\(248\) 0 0
\(249\) 2.86069e6 2.92397
\(250\) 0 0
\(251\) −1.11268e6 + 808410.i −1.11477 + 0.809930i −0.983409 0.181404i \(-0.941936\pi\)
−0.131364 + 0.991334i \(0.541936\pi\)
\(252\) 0 0
\(253\) −1.49757e6 −1.47091
\(254\) 0 0
\(255\) 925809. + 2.84935e6i 0.891602 + 2.74407i
\(256\) 0 0
\(257\) −172755. + 531684.i −0.163154 + 0.502135i −0.998895 0.0469874i \(-0.985038\pi\)
0.835742 + 0.549122i \(0.185038\pi\)
\(258\) 0 0
\(259\) 97191.3 + 299124.i 0.0900280 + 0.277078i
\(260\) 0 0
\(261\) 1.46840e6 1.06686e6i 1.33427 0.969405i
\(262\) 0 0
\(263\) −485571. + 352788.i −0.432876 + 0.314503i −0.782798 0.622276i \(-0.786208\pi\)
0.349922 + 0.936779i \(0.386208\pi\)
\(264\) 0 0
\(265\) 484531. 1.49123e6i 0.423845 1.30446i
\(266\) 0 0
\(267\) −2.92291e6 2.12362e6i −2.50921 1.82305i
\(268\) 0 0
\(269\) −1.29546e6 941209.i −1.09155 0.793059i −0.111892 0.993720i \(-0.535691\pi\)
−0.979661 + 0.200661i \(0.935691\pi\)
\(270\) 0 0
\(271\) 340093. 1.04670e6i 0.281303 0.865762i −0.706179 0.708033i \(-0.749583\pi\)
0.987482 0.157729i \(-0.0504172\pi\)
\(272\) 0 0
\(273\) −638947. −0.518870
\(274\) 0 0
\(275\) −1.05091e6 3.23437e6i −0.837981 2.57904i
\(276\) 0 0
\(277\) −370053. 268859.i −0.289778 0.210536i 0.433393 0.901205i \(-0.357316\pi\)
−0.723171 + 0.690669i \(0.757316\pi\)
\(278\) 0 0
\(279\) 2.38006e6 + 370414.i 1.83053 + 0.284890i
\(280\) 0 0
\(281\) 1.21900e6 + 885652.i 0.920951 + 0.669110i 0.943760 0.330630i \(-0.107261\pi\)
−0.0228099 + 0.999740i \(0.507261\pi\)
\(282\) 0 0
\(283\) 379910. + 1.16924e6i 0.281977 + 0.867837i 0.987288 + 0.158939i \(0.0508073\pi\)
−0.705311 + 0.708898i \(0.749193\pi\)
\(284\) 0 0
\(285\) −4.75250e6 −3.46585
\(286\) 0 0
\(287\) 224764. 691751.i 0.161072 0.495730i
\(288\) 0 0
\(289\) −89015.7 64673.7i −0.0626934 0.0455494i
\(290\) 0 0
\(291\) 1.76027e6 + 1.27891e6i 1.21856 + 0.885333i
\(292\) 0 0
\(293\) −256614. + 789777.i −0.174627 + 0.537447i −0.999616 0.0277019i \(-0.991181\pi\)
0.824989 + 0.565148i \(0.191181\pi\)
\(294\) 0 0
\(295\) −1.76770e6 + 1.28431e6i −1.18264 + 0.859241i
\(296\) 0 0
\(297\) 2.81085e6 2.04220e6i 1.84904 1.34341i
\(298\) 0 0
\(299\) −202626. 623618.i −0.131074 0.403405i
\(300\) 0 0
\(301\) −212263. + 653279.i −0.135039 + 0.415607i
\(302\) 0 0
\(303\) −1.03864e6 3.19661e6i −0.649918 2.00024i
\(304\) 0 0
\(305\) −68678.5 −0.0422738
\(306\) 0 0
\(307\) 402908. 292730.i 0.243983 0.177264i −0.459073 0.888399i \(-0.651818\pi\)
0.703056 + 0.711135i \(0.251818\pi\)
\(308\) 0 0
\(309\) −4.93631e6 −2.94107
\(310\) 0 0
\(311\) −1.84521e6 −1.08180 −0.540899 0.841088i \(-0.681916\pi\)
−0.540899 + 0.841088i \(0.681916\pi\)
\(312\) 0 0
\(313\) −1.19380e6 + 867344.i −0.688763 + 0.500415i −0.876253 0.481851i \(-0.839965\pi\)
0.187491 + 0.982266i \(0.439965\pi\)
\(314\) 0 0
\(315\) 3.60385e6 2.04640
\(316\) 0 0
\(317\) 749684. + 2.30729e6i 0.419016 + 1.28960i 0.908609 + 0.417647i \(0.137145\pi\)
−0.489594 + 0.871951i \(0.662855\pi\)
\(318\) 0 0
\(319\) 793617. 2.44250e6i 0.436651 1.34387i
\(320\) 0 0
\(321\) 1.57224e6 + 4.83887e6i 0.851642 + 2.62108i
\(322\) 0 0
\(323\) 1.96336e6 1.42646e6i 1.04711 0.760771i
\(324\) 0 0
\(325\) 1.20466e6 875239.i 0.632641 0.459641i
\(326\) 0 0
\(327\) 355786. 1.09500e6i 0.184001 0.566297i
\(328\) 0 0
\(329\) −1.11911e6 813080.i −0.570010 0.414137i
\(330\) 0 0
\(331\) −298376. 216783.i −0.149691 0.108757i 0.510419 0.859926i \(-0.329490\pi\)
−0.660110 + 0.751169i \(0.729490\pi\)
\(332\) 0 0
\(333\) 502818. 1.54752e6i 0.248485 0.764759i
\(334\) 0 0
\(335\) 4.81975e6 2.34645
\(336\) 0 0
\(337\) 124044. + 381769.i 0.0594979 + 0.183116i 0.976388 0.216024i \(-0.0693089\pi\)
−0.916890 + 0.399140i \(0.869309\pi\)
\(338\) 0 0
\(339\) 4.15664e6 + 3.01998e6i 1.96446 + 1.42726i
\(340\) 0 0
\(341\) 3.03257e6 1.55545e6i 1.41229 0.724384i
\(342\) 0 0
\(343\) 1.83330e6 + 1.33197e6i 0.841392 + 0.611307i
\(344\) 0 0
\(345\) 1.75978e6 + 5.41604e6i 0.795994 + 2.44982i
\(346\) 0 0
\(347\) −4.31110e6 −1.92205 −0.961025 0.276463i \(-0.910838\pi\)
−0.961025 + 0.276463i \(0.910838\pi\)
\(348\) 0 0
\(349\) −181554. + 558765.i −0.0797888 + 0.245565i −0.982992 0.183649i \(-0.941209\pi\)
0.903203 + 0.429213i \(0.141209\pi\)
\(350\) 0 0
\(351\) 1.23073e6 + 894177.i 0.533205 + 0.387396i
\(352\) 0 0
\(353\) 1.47323e6 + 1.07036e6i 0.629263 + 0.457187i 0.856145 0.516736i \(-0.172853\pi\)
−0.226882 + 0.973922i \(0.572853\pi\)
\(354\) 0 0
\(355\) −275394. + 847577.i −0.115980 + 0.356951i
\(356\) 0 0
\(357\) −2.29248e6 + 1.66558e6i −0.951996 + 0.691665i
\(358\) 0 0
\(359\) 227973. 165632.i 0.0933570 0.0678278i −0.540128 0.841583i \(-0.681624\pi\)
0.633485 + 0.773755i \(0.281624\pi\)
\(360\) 0 0
\(361\) 424459. + 1.30635e6i 0.171423 + 0.527584i
\(362\) 0 0
\(363\) 1.99073e6 6.12683e6i 0.792949 2.44045i
\(364\) 0 0
\(365\) 2.04469e6 + 6.29291e6i 0.803332 + 2.47240i
\(366\) 0 0
\(367\) −1.30343e6 −0.505152 −0.252576 0.967577i \(-0.581278\pi\)
−0.252576 + 0.967577i \(0.581278\pi\)
\(368\) 0 0
\(369\) −3.04428e6 + 2.21180e6i −1.16391 + 0.845630i
\(370\) 0 0
\(371\) 1.48302e6 0.559388
\(372\) 0 0
\(373\) −1.89977e6 −0.707015 −0.353507 0.935432i \(-0.615011\pi\)
−0.353507 + 0.935432i \(0.615011\pi\)
\(374\) 0 0
\(375\) −4.33859e6 + 3.15217e6i −1.59320 + 1.15753i
\(376\) 0 0
\(377\) 1.12448e6 0.407474
\(378\) 0 0
\(379\) 534798. + 1.64594e6i 0.191246 + 0.588594i 1.00000 0.000447235i \(0.000142359\pi\)
−0.808754 + 0.588147i \(0.799858\pi\)
\(380\) 0 0
\(381\) −1.34562e6 + 4.14139e6i −0.474908 + 1.46162i
\(382\) 0 0
\(383\) −1.10330e6 3.39562e6i −0.384324 1.18283i −0.936969 0.349412i \(-0.886381\pi\)
0.552645 0.833417i \(-0.313619\pi\)
\(384\) 0 0
\(385\) 4.12539e6 2.99727e6i 1.41845 1.03056i
\(386\) 0 0
\(387\) 2.87498e6 2.08879e6i 0.975791 0.708954i
\(388\) 0 0
\(389\) 190079. 585003.i 0.0636883 0.196013i −0.914149 0.405378i \(-0.867140\pi\)
0.977837 + 0.209366i \(0.0671399\pi\)
\(390\) 0 0
\(391\) −2.35263e6 1.70928e6i −0.778236 0.565421i
\(392\) 0 0
\(393\) 64016.7 + 46510.9i 0.0209080 + 0.0151905i
\(394\) 0 0
\(395\) 2.19862e6 6.76667e6i 0.709020 2.18214i
\(396\) 0 0
\(397\) −1.74680e6 −0.556245 −0.278123 0.960546i \(-0.589712\pi\)
−0.278123 + 0.960546i \(0.589712\pi\)
\(398\) 0 0
\(399\) −1.38903e6 4.27501e6i −0.436798 1.34433i
\(400\) 0 0
\(401\) 1.90297e6 + 1.38259e6i 0.590978 + 0.429371i 0.842665 0.538438i \(-0.180985\pi\)
−0.251687 + 0.967809i \(0.580985\pi\)
\(402\) 0 0
\(403\) 1.05803e6 + 1.05236e6i 0.324517 + 0.322778i
\(404\) 0 0
\(405\) −2.54667e6 1.85026e6i −0.771498 0.560526i
\(406\) 0 0
\(407\) −711463. 2.18966e6i −0.212895 0.655224i
\(408\) 0 0
\(409\) 243721. 0.0720419 0.0360210 0.999351i \(-0.488532\pi\)
0.0360210 + 0.999351i \(0.488532\pi\)
\(410\) 0 0
\(411\) −2.48828e6 + 7.65815e6i −0.726600 + 2.23624i
\(412\) 0 0
\(413\) −1.67193e6 1.21473e6i −0.482328 0.350432i
\(414\) 0 0
\(415\) −8.08716e6 5.87566e6i −2.30502 1.67470i
\(416\) 0 0
\(417\) 2.62472e6 8.07805e6i 0.739167 2.27492i
\(418\) 0 0
\(419\) 1.04588e6 759873.i 0.291035 0.211449i −0.432681 0.901547i \(-0.642432\pi\)
0.723716 + 0.690098i \(0.242432\pi\)
\(420\) 0 0
\(421\) −3.67580e6 + 2.67063e6i −1.01076 + 0.734358i −0.964368 0.264565i \(-0.914772\pi\)
−0.0463897 + 0.998923i \(0.514772\pi\)
\(422\) 0 0
\(423\) 2.21147e6 + 6.80620e6i 0.600939 + 1.84950i
\(424\) 0 0
\(425\) 2.04067e6 6.28054e6i 0.548026 1.68665i
\(426\) 0 0
\(427\) −20073.0 61778.3i −0.00532773 0.0163971i
\(428\) 0 0
\(429\) 4.67724e6 1.22701
\(430\) 0 0
\(431\) 5.08870e6 3.69715e6i 1.31951 0.958682i 0.319574 0.947561i \(-0.396460\pi\)
0.999938 0.0111204i \(-0.00353981\pi\)
\(432\) 0 0
\(433\) −4.24187e6 −1.08727 −0.543636 0.839321i \(-0.682953\pi\)
−0.543636 + 0.839321i \(0.682953\pi\)
\(434\) 0 0
\(435\) −9.76599e6 −2.47453
\(436\) 0 0
\(437\) 3.73195e6 2.71142e6i 0.934829 0.679193i
\(438\) 0 0
\(439\) −5.51917e6 −1.36682 −0.683412 0.730033i \(-0.739505\pi\)
−0.683412 + 0.730033i \(0.739505\pi\)
\(440\) 0 0
\(441\) −1.28474e6 3.95401e6i −0.314570 0.968147i
\(442\) 0 0
\(443\) −1.54539e6 + 4.75621e6i −0.374134 + 1.15147i 0.569926 + 0.821696i \(0.306972\pi\)
−0.944061 + 0.329772i \(0.893028\pi\)
\(444\) 0 0
\(445\) 3.90128e6 + 1.20069e7i 0.933914 + 2.87429i
\(446\) 0 0
\(447\) −1.72845e6 + 1.25579e6i −0.409155 + 0.297269i
\(448\) 0 0
\(449\) −1.90141e6 + 1.38146e6i −0.445103 + 0.323387i −0.787659 0.616111i \(-0.788707\pi\)
0.342556 + 0.939497i \(0.388707\pi\)
\(450\) 0 0
\(451\) −1.64532e6 + 5.06378e6i −0.380899 + 1.17229i
\(452\) 0 0
\(453\) −5.84144e6 4.24406e6i −1.33744 0.971707i
\(454\) 0 0
\(455\) 1.80630e6 + 1.31235e6i 0.409036 + 0.297182i
\(456\) 0 0
\(457\) 435833. 1.34135e6i 0.0976179 0.300437i −0.890309 0.455356i \(-0.849512\pi\)
0.987927 + 0.154920i \(0.0495118\pi\)
\(458\) 0 0
\(459\) 6.74664e6 1.49471
\(460\) 0 0
\(461\) 681148. + 2.09636e6i 0.149276 + 0.459423i 0.997536 0.0701562i \(-0.0223498\pi\)
−0.848260 + 0.529579i \(0.822350\pi\)
\(462\) 0 0
\(463\) 3.30779e6 + 2.40325e6i 0.717109 + 0.521010i 0.885459 0.464717i \(-0.153844\pi\)
−0.168350 + 0.985727i \(0.553844\pi\)
\(464\) 0 0
\(465\) −9.18887e6 9.13964e6i −1.97074 1.96018i
\(466\) 0 0
\(467\) −4.62498e6 3.36025e6i −0.981336 0.712983i −0.0233296 0.999728i \(-0.507427\pi\)
−0.958007 + 0.286745i \(0.907427\pi\)
\(468\) 0 0
\(469\) 1.40869e6 + 4.33550e6i 0.295722 + 0.910138i
\(470\) 0 0
\(471\) 9.30069e6 1.93180
\(472\) 0 0
\(473\) 1.55382e6 4.78216e6i 0.319335 0.982813i
\(474\) 0 0
\(475\) 8.47483e6 + 6.15733e6i 1.72344 + 1.25216i
\(476\) 0 0
\(477\) −6.20712e6 4.50973e6i −1.24909 0.907518i
\(478\) 0 0
\(479\) 845373. 2.60179e6i 0.168349 0.518124i −0.830919 0.556394i \(-0.812185\pi\)
0.999267 + 0.0382699i \(0.0121847\pi\)
\(480\) 0 0
\(481\) 815553. 592534.i 0.160727 0.116775i
\(482\) 0 0
\(483\) −4.35754e6 + 3.16594e6i −0.849912 + 0.617497i
\(484\) 0 0
\(485\) −2.34947e6 7.23092e6i −0.453540 1.39585i
\(486\) 0 0
\(487\) 474428. 1.46014e6i 0.0906458 0.278979i −0.895449 0.445165i \(-0.853145\pi\)
0.986094 + 0.166186i \(0.0531451\pi\)
\(488\) 0 0
\(489\) −135350. 416565.i −0.0255968 0.0787790i
\(490\) 0 0
\(491\) −2.38069e6 −0.445655 −0.222827 0.974858i \(-0.571529\pi\)
−0.222827 + 0.974858i \(0.571529\pi\)
\(492\) 0 0
\(493\) 4.03454e6 2.93126e6i 0.747612 0.543172i
\(494\) 0 0
\(495\) −2.63810e7 −4.83925
\(496\) 0 0
\(497\) −842911. −0.153070
\(498\) 0 0
\(499\) 3.08363e6 2.24039e6i 0.554384 0.402784i −0.275015 0.961440i \(-0.588683\pi\)
0.829399 + 0.558656i \(0.188683\pi\)
\(500\) 0 0
\(501\) 1.09111e7 1.94211
\(502\) 0 0
\(503\) −216949. 667701.i −0.0382329 0.117669i 0.930118 0.367260i \(-0.119704\pi\)
−0.968351 + 0.249591i \(0.919704\pi\)
\(504\) 0 0
\(505\) −3.62938e6 + 1.11701e7i −0.633292 + 1.94907i
\(506\) 0 0
\(507\) −2.38794e6 7.34934e6i −0.412576 1.26978i
\(508\) 0 0
\(509\) 596994. 433742.i 0.102135 0.0742056i −0.535545 0.844506i \(-0.679894\pi\)
0.637681 + 0.770301i \(0.279894\pi\)
\(510\) 0 0
\(511\) −5.06304e6 + 3.67851e6i −0.857747 + 0.623190i
\(512\) 0 0
\(513\) −3.30714e6 + 1.01783e7i −0.554829 + 1.70759i
\(514\) 0 0
\(515\) 1.39549e7 + 1.01388e7i 2.31851 + 1.68450i
\(516\) 0 0
\(517\) 8.19214e6 + 5.95194e6i 1.34794 + 0.979337i
\(518\) 0 0
\(519\) −3.18160e6 + 9.79195e6i −0.518474 + 1.59570i
\(520\) 0 0
\(521\) 758303. 0.122391 0.0611954 0.998126i \(-0.480509\pi\)
0.0611954 + 0.998126i \(0.480509\pi\)
\(522\) 0 0
\(523\) −2.40674e6 7.40719e6i −0.384747 1.18413i −0.936664 0.350230i \(-0.886103\pi\)
0.551917 0.833899i \(-0.313897\pi\)
\(524\) 0 0
\(525\) −9.89549e6 7.18949e6i −1.56689 1.13841i
\(526\) 0 0
\(527\) 6.53939e6 + 1.01774e6i 1.02568 + 0.159628i
\(528\) 0 0
\(529\) 735240. + 534183.i 0.114233 + 0.0829948i
\(530\) 0 0
\(531\) 3.30390e6 + 1.01683e7i 0.508499 + 1.56500i
\(532\) 0 0
\(533\) −2.33127e6 −0.355447
\(534\) 0 0
\(535\) 5.49397e6 1.69087e7i 0.829855 2.55403i
\(536\) 0 0
\(537\) 1.45868e7 + 1.05979e7i 2.18285 + 1.58594i
\(538\) 0 0
\(539\) −4.75916e6 3.45773e6i −0.705599 0.512648i
\(540\) 0 0
\(541\) 2.41122e6 7.42096e6i 0.354196 1.09010i −0.602279 0.798286i \(-0.705740\pi\)
0.956474 0.291816i \(-0.0942596\pi\)
\(542\) 0 0
\(543\) −3.41455e6 + 2.48082e6i −0.496974 + 0.361073i
\(544\) 0 0
\(545\) −3.25485e6 + 2.36479e6i −0.469397 + 0.341037i
\(546\) 0 0
\(547\) −2.82431e6 8.69234e6i −0.403594 1.24213i −0.922064 0.387038i \(-0.873498\pi\)
0.518470 0.855096i \(-0.326502\pi\)
\(548\) 0 0
\(549\) −103847. + 319610.i −0.0147050 + 0.0452573i
\(550\) 0 0
\(551\) 2.44456e6 + 7.52359e6i 0.343022 + 1.05571i
\(552\) 0 0
\(553\) 6.72942e6 0.935760
\(554\) 0 0
\(555\) −7.08296e6 + 5.14607e6i −0.976074 + 0.709159i
\(556\) 0 0
\(557\) 812063. 0.110905 0.0554526 0.998461i \(-0.482340\pi\)
0.0554526 + 0.998461i \(0.482340\pi\)
\(558\) 0 0
\(559\) 2.20162e6 0.297998
\(560\) 0 0
\(561\) 1.67815e7 1.21925e7i 2.25125 1.63563i
\(562\) 0 0
\(563\) 3.50634e6 0.466211 0.233105 0.972451i \(-0.425111\pi\)
0.233105 + 0.972451i \(0.425111\pi\)
\(564\) 0 0
\(565\) −5.54797e6 1.70749e7i −0.731161 2.25028i
\(566\) 0 0
\(567\) 920038. 2.83159e6i 0.120184 0.369890i
\(568\) 0 0
\(569\) 2.32677e6 + 7.16107e6i 0.301282 + 0.927251i 0.981038 + 0.193813i \(0.0620855\pi\)
−0.679756 + 0.733438i \(0.737914\pi\)
\(570\) 0 0
\(571\) 2.60569e6 1.89314e6i 0.334450 0.242992i −0.407866 0.913042i \(-0.633727\pi\)
0.742317 + 0.670049i \(0.233727\pi\)
\(572\) 0 0
\(573\) −9.06919e6 + 6.58915e6i −1.15394 + 0.838384i
\(574\) 0 0
\(575\) 3.87891e6 1.19381e7i 0.489260 1.50579i
\(576\) 0 0
\(577\) 2.84653e6 + 2.06813e6i 0.355940 + 0.258605i 0.751357 0.659896i \(-0.229400\pi\)
−0.395417 + 0.918502i \(0.629400\pi\)
\(578\) 0 0
\(579\) 1.59015e6 + 1.15531e6i 0.197125 + 0.143219i
\(580\) 0 0
\(581\) 2.92166e6 8.99194e6i 0.359078 1.10513i
\(582\) 0 0
\(583\) −1.08561e7 −1.32282
\(584\) 0 0
\(585\) −3.56943e6 1.09856e7i −0.431230 1.32719i
\(586\) 0 0
\(587\) 9.66206e6 + 7.01990e6i 1.15738 + 0.840883i 0.989444 0.144915i \(-0.0462909\pi\)
0.167933 + 0.985798i \(0.446291\pi\)
\(588\) 0 0
\(589\) −4.74096e6 + 9.36677e6i −0.563090 + 1.11250i
\(590\) 0 0
\(591\) 4.04810e6 + 2.94112e6i 0.476741 + 0.346373i
\(592\) 0 0
\(593\) 1.27919e6 + 3.93693e6i 0.149382 + 0.459749i 0.997548 0.0699799i \(-0.0222935\pi\)
−0.848167 + 0.529729i \(0.822294\pi\)
\(594\) 0 0
\(595\) 9.90182e6 1.14663
\(596\) 0 0
\(597\) −4.96354e6 + 1.52762e7i −0.569975 + 1.75420i
\(598\) 0 0
\(599\) −2.51390e6 1.82645e6i −0.286273 0.207990i 0.435376 0.900249i \(-0.356616\pi\)
−0.721649 + 0.692259i \(0.756616\pi\)
\(600\) 0 0
\(601\) 1.92636e6 + 1.39959e6i 0.217547 + 0.158057i 0.691222 0.722643i \(-0.257073\pi\)
−0.473675 + 0.880700i \(0.657073\pi\)
\(602\) 0 0
\(603\) 7.28785e6 2.24297e7i 0.816218 2.51206i
\(604\) 0 0
\(605\) −1.82118e7 + 1.32317e7i −2.02286 + 1.46969i
\(606\) 0 0
\(607\) −1.05726e7 + 7.68141e6i −1.16468 + 0.846193i −0.990363 0.138496i \(-0.955773\pi\)
−0.174322 + 0.984689i \(0.555773\pi\)
\(608\) 0 0
\(609\) −2.85435e6 8.78479e6i −0.311863 0.959816i
\(610\) 0 0
\(611\) −1.37008e6 + 4.21668e6i −0.148472 + 0.456949i
\(612\) 0 0
\(613\) −50272.2 154722.i −0.00540352 0.0166303i 0.948318 0.317320i \(-0.102783\pi\)
−0.953722 + 0.300690i \(0.902783\pi\)
\(614\) 0 0
\(615\) 2.02468e7 2.15858
\(616\) 0 0
\(617\) −4.33384e6 + 3.14872e6i −0.458310 + 0.332982i −0.792868 0.609393i \(-0.791413\pi\)
0.334558 + 0.942375i \(0.391413\pi\)
\(618\) 0 0
\(619\) −1.41681e6 −0.148623 −0.0743115 0.997235i \(-0.523676\pi\)
−0.0743115 + 0.997235i \(0.523676\pi\)
\(620\) 0 0
\(621\) 1.28240e7 1.33443
\(622\) 0 0
\(623\) −9.66031e6 + 7.01863e6i −0.997174 + 0.724489i
\(624\) 0 0
\(625\) 2.05505e6 0.210437
\(626\) 0 0
\(627\) 1.01681e7 + 3.12941e7i 1.03293 + 3.17902i
\(628\) 0 0
\(629\) 1.38153e6 4.25191e6i 0.139230 0.428506i
\(630\) 0 0
\(631\) −1.85188e6 5.69950e6i −0.185157 0.569853i 0.814794 0.579750i \(-0.196850\pi\)
−0.999951 + 0.00989658i \(0.996850\pi\)
\(632\) 0 0
\(633\) −9.23621e6 + 6.71050e6i −0.916188 + 0.665650i
\(634\) 0 0
\(635\) 1.23102e7 8.94387e6i 1.21152 0.880220i
\(636\) 0 0
\(637\) 795939. 2.44965e6i 0.0777197 0.239197i
\(638\) 0 0
\(639\) 3.52796e6 + 2.56321e6i 0.341799 + 0.248332i
\(640\) 0 0
\(641\) −2.20751e6 1.60385e6i −0.212206 0.154176i 0.476606 0.879117i \(-0.341867\pi\)
−0.688811 + 0.724941i \(0.741867\pi\)
\(642\) 0 0
\(643\) 299728. 922467.i 0.0285890 0.0879880i −0.935744 0.352680i \(-0.885270\pi\)
0.964333 + 0.264692i \(0.0852704\pi\)
\(644\) 0 0
\(645\) −1.91208e7 −1.80970
\(646\) 0 0
\(647\) −139635. 429753.i −0.0131140 0.0403606i 0.944285 0.329128i \(-0.106755\pi\)
−0.957399 + 0.288767i \(0.906755\pi\)
\(648\) 0 0
\(649\) 1.22389e7 + 8.89209e6i 1.14059 + 0.828690i
\(650\) 0 0
\(651\) 5.53569e6 1.09369e7i 0.511941 1.01145i
\(652\) 0 0
\(653\) 4.77836e6 + 3.47168e6i 0.438527 + 0.318608i 0.785049 0.619433i \(-0.212638\pi\)
−0.346523 + 0.938042i \(0.612638\pi\)
\(654\) 0 0
\(655\) −85444.6 262972.i −0.00778183 0.0239500i
\(656\) 0 0
\(657\) 3.23771e7 2.92634
\(658\) 0 0
\(659\) −5.15107e6 + 1.58534e7i −0.462045 + 1.42203i 0.400617 + 0.916246i \(0.368796\pi\)
−0.862661 + 0.505782i \(0.831204\pi\)
\(660\) 0 0
\(661\) −1.21323e7 8.81464e6i −1.08004 0.784695i −0.102350 0.994748i \(-0.532636\pi\)
−0.977690 + 0.210054i \(0.932636\pi\)
\(662\) 0 0
\(663\) 7.34777e6 + 5.33846e6i 0.649190 + 0.471664i
\(664\) 0 0
\(665\) −4.85378e6 + 1.49384e7i −0.425624 + 1.30993i
\(666\) 0 0
\(667\) 7.66885e6 5.57174e6i 0.667445 0.484927i
\(668\) 0 0
\(669\) −8.59653e6 + 6.24574e6i −0.742605 + 0.539534i
\(670\) 0 0
\(671\) 146939. + 452232.i 0.0125988 + 0.0387752i
\(672\) 0 0
\(673\) 3.13440e6 9.64669e6i 0.266758 0.820995i −0.724526 0.689248i \(-0.757941\pi\)
0.991283 0.131748i \(-0.0420588\pi\)
\(674\) 0 0
\(675\) 8.99915e6 + 2.76965e7i 0.760225 + 2.33973i
\(676\) 0 0
\(677\) −1.00296e7 −0.841031 −0.420515 0.907285i \(-0.638151\pi\)
−0.420515 + 0.907285i \(0.638151\pi\)
\(678\) 0 0
\(679\) 5.81773e6 4.22683e6i 0.484261 0.351836i
\(680\) 0 0
\(681\) −1.54599e7 −1.27744
\(682\) 0 0
\(683\) −1.72101e7 −1.41167 −0.705833 0.708378i \(-0.749427\pi\)
−0.705833 + 0.708378i \(0.749427\pi\)
\(684\) 0 0
\(685\) 2.27637e7 1.65388e7i 1.85360 1.34672i
\(686\) 0 0
\(687\) 3.02730e7 2.44717
\(688\) 0 0
\(689\) −1.46886e6 4.52069e6i −0.117878 0.362791i
\(690\) 0 0
\(691\) −659314. + 2.02916e6i −0.0525288 + 0.161667i −0.973880 0.227065i \(-0.927087\pi\)
0.921351 + 0.388732i \(0.127087\pi\)
\(692\) 0 0
\(693\) −7.71050e6 2.37305e7i −0.609887 1.87704i
\(694\) 0 0
\(695\) −2.40118e7 + 1.74456e7i −1.88566 + 1.37001i
\(696\) 0 0
\(697\) −8.36438e6 + 6.07708e6i −0.652156 + 0.473819i
\(698\) 0 0
\(699\) 7.07604e6 2.17778e7i 0.547769 1.68586i
\(700\) 0 0
\(701\) −1.93968e7 1.40926e7i −1.49086 1.08317i −0.973851 0.227188i \(-0.927047\pi\)
−0.517005 0.855982i \(-0.672953\pi\)
\(702\) 0 0
\(703\) 5.73743e6 + 4.16849e6i 0.437854 + 0.318120i
\(704\) 0 0
\(705\) 1.18990e7 3.66213e7i 0.901648 2.77499i
\(706\) 0 0
\(707\) −1.11086e7 −0.835815
\(708\) 0 0
\(709\) 3.13045e6 + 9.63453e6i 0.233879 + 0.719805i 0.997268 + 0.0738663i \(0.0235338\pi\)
−0.763389 + 0.645939i \(0.776466\pi\)
\(710\) 0 0
\(711\) −2.81656e7 2.04635e7i −2.08951 1.51812i
\(712\) 0 0
\(713\) 1.24301e7 + 1.93451e6i 0.915692 + 0.142511i
\(714\) 0 0
\(715\) −1.32225e7 9.60673e6i −0.967274 0.702766i
\(716\) 0 0
\(717\) 6.20147e6 + 1.90862e7i 0.450502 + 1.38650i
\(718\) 0 0
\(719\) −2.18439e7 −1.57583 −0.787913 0.615787i \(-0.788838\pi\)
−0.787913 + 0.615787i \(0.788838\pi\)
\(720\) 0 0
\(721\) −5.04151e6 + 1.55162e7i −0.361179 + 1.11159i
\(722\) 0 0
\(723\) −3.46499e7 2.51746e7i −2.46522 1.79109i
\(724\) 0 0
\(725\) 1.74151e7 + 1.26528e7i 1.23050 + 0.894008i
\(726\) 0 0
\(727\) −5.69539e6 + 1.75286e7i −0.399657 + 1.23002i 0.525618 + 0.850721i \(0.323834\pi\)
−0.925275 + 0.379297i \(0.876166\pi\)
\(728\) 0 0
\(729\) 1.57708e7 1.14581e7i 1.09909 0.798536i
\(730\) 0 0
\(731\) 7.89919e6 5.73910e6i 0.546751 0.397238i
\(732\) 0 0
\(733\) −6.70308e6 2.06300e7i −0.460802 1.41820i −0.864186 0.503173i \(-0.832166\pi\)
0.403384 0.915031i \(-0.367834\pi\)
\(734\) 0 0
\(735\) −6.91262e6 + 2.12748e7i −0.471981 + 1.45261i
\(736\) 0 0
\(737\) −1.03119e7 3.17369e7i −0.699313 2.15226i
\(738\) 0 0
\(739\) −2.08603e7 −1.40511 −0.702555 0.711630i \(-0.747957\pi\)
−0.702555 + 0.711630i \(0.747957\pi\)
\(740\) 0 0
\(741\) −1.16557e7 + 8.46835e6i −0.779817 + 0.566570i
\(742\) 0 0
\(743\) −1.24362e7 −0.826447 −0.413223 0.910630i \(-0.635597\pi\)
−0.413223 + 0.910630i \(0.635597\pi\)
\(744\) 0 0
\(745\) 7.46562e6 0.492805
\(746\) 0 0
\(747\) −3.95721e7 + 2.87508e7i −2.59470 + 1.88516i
\(748\) 0 0
\(749\) 1.68156e7 1.09524
\(750\) 0 0
\(751\) −1.98666e6 6.11430e6i −0.128536 0.395592i 0.865993 0.500056i \(-0.166687\pi\)
−0.994529 + 0.104464i \(0.966687\pi\)
\(752\) 0 0
\(753\) 1.11897e7 3.44382e7i 0.719166 2.21337i
\(754\) 0 0
\(755\) 7.79671e6 + 2.39958e7i 0.497788 + 1.53203i
\(756\) 0 0
\(757\) −1.18273e6 + 859304.i −0.0750147 + 0.0545014i −0.624661 0.780896i \(-0.714763\pi\)
0.549646 + 0.835398i \(0.314763\pi\)
\(758\) 0 0
\(759\) 3.18982e7 2.31754e7i 2.00984 1.46024i
\(760\) 0 0
\(761\) 690805. 2.12608e6i 0.0432408 0.133081i −0.927105 0.374800i \(-0.877711\pi\)
0.970346 + 0.241719i \(0.0777112\pi\)
\(762\) 0 0
\(763\) −3.07851e6 2.23667e6i −0.191438 0.139088i
\(764\) 0 0
\(765\) −4.14435e7 3.01105e7i −2.56037 1.86022i
\(766\) 0 0
\(767\) −2.04688e6 + 6.29964e6i −0.125633 + 0.386659i
\(768\) 0 0
\(769\) 2.30960e6 0.140838 0.0704191 0.997517i \(-0.477566\pi\)
0.0704191 + 0.997517i \(0.477566\pi\)
\(770\) 0 0
\(771\) −4.54832e6 1.39983e7i −0.275559 0.848084i
\(772\) 0 0
\(773\) −5.24266e6 3.80901e6i −0.315575 0.229279i 0.418710 0.908120i \(-0.362482\pi\)
−0.734285 + 0.678841i \(0.762482\pi\)
\(774\) 0 0
\(775\) 4.54465e6 + 2.82032e7i 0.271798 + 1.68673i
\(776\) 0 0
\(777\) −6.69921e6 4.86726e6i −0.398081 0.289223i
\(778\) 0 0
\(779\) −5.06805e6 1.55979e7i −0.299225 0.920919i
\(780\) 0 0
\(781\) 6.17031e6 0.361975
\(782\) 0 0
\(783\) −6.79590e6 + 2.09156e7i −0.396134 + 1.21918i
\(784\) 0 0
\(785\) −2.62930e7 1.91030e7i −1.52288 1.10644i
\(786\) 0 0
\(787\) −1.31585e7 9.56018e6i −0.757301 0.550211i 0.140781 0.990041i \(-0.455039\pi\)
−0.898081 + 0.439830i \(0.855039\pi\)
\(788\) 0 0
\(789\) 4.88314e6 1.50288e7i