Properties

Label 37.8.f.a.7.16
Level $37$
Weight $8$
Character 37.7
Analytic conductor $11.558$
Analytic rank $0$
Dimension $132$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 37 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 37.f (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.5582459429\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 7.16
Character \(\chi\) \(=\) 37.7
Dual form 37.8.f.a.16.16

$q$-expansion

\(f(q)\) \(=\) \(q+(10.1961 - 3.71107i) q^{2} +(11.1844 + 4.07079i) q^{3} +(-7.86580 + 6.60019i) q^{4} +(-64.6668 - 366.744i) q^{5} +129.144 q^{6} +(-94.8119 - 537.705i) q^{7} +(-750.134 + 1299.27i) q^{8} +(-1566.82 - 1314.72i) q^{9} +O(q^{10})\) \(q+(10.1961 - 3.71107i) q^{2} +(11.1844 + 4.07079i) q^{3} +(-7.86580 + 6.60019i) q^{4} +(-64.6668 - 366.744i) q^{5} +129.144 q^{6} +(-94.8119 - 537.705i) q^{7} +(-750.134 + 1299.27i) q^{8} +(-1566.82 - 1314.72i) q^{9} +(-2020.36 - 3499.36i) q^{10} +(2403.45 - 4162.90i) q^{11} +(-114.842 + 41.7991i) q^{12} +(4334.59 - 3637.16i) q^{13} +(-2962.17 - 5130.62i) q^{14} +(769.676 - 4365.05i) q^{15} +(-2598.52 + 14736.9i) q^{16} +(-4518.62 - 3791.57i) q^{17} +(-20854.4 - 7590.39i) q^{18} +(-21103.8 - 7681.14i) q^{19} +(2929.23 + 2457.92i) q^{20} +(1128.47 - 6399.86i) q^{21} +(9056.97 - 51364.6i) q^{22} +(21018.4 + 36405.0i) q^{23} +(-13678.8 + 11477.9i) q^{24} +(-56905.5 + 20711.9i) q^{25} +(30698.1 - 53170.7i) q^{26} +(-25187.0 - 43625.2i) q^{27} +(4294.73 + 3603.70i) q^{28} +(-6832.07 + 11833.5i) q^{29} +(-8351.32 - 47362.7i) q^{30} +167088. q^{31} +(-5151.40 - 29215.0i) q^{32} +(43827.5 - 36775.6i) q^{33} +(-60143.0 - 21890.3i) q^{34} +(-191069. + 69543.3i) q^{35} +21001.7 q^{36} +(-41961.6 + 305239. i) q^{37} -243681. q^{38} +(63285.9 - 23034.2i) q^{39} +(525008. + 191087. i) q^{40} +(74980.2 - 62915.8i) q^{41} +(-12244.4 - 69441.3i) q^{42} +708332. q^{43} +(8570.87 + 48607.8i) q^{44} +(-380843. + 659640. i) q^{45} +(349407. + 293187. i) q^{46} +(51231.9 + 88736.3i) q^{47} +(-89053.6 + 154245. i) q^{48} +(493740. - 179707. i) q^{49} +(-503350. + 422360. i) q^{50} +(-35103.3 - 60800.8i) q^{51} +(-10089.1 + 57218.3i) q^{52} +(-229067. + 1.29910e6i) q^{53} +(-418705. - 351335. i) q^{54} +(-1.68214e6 - 612249. i) q^{55} +(769746. + 280165. i) q^{56} +(-204764. - 171818. i) q^{57} +(-25745.4 + 146009. i) q^{58} +(230652. - 1.30809e6i) q^{59} +(22756.0 + 39414.6i) q^{60} +(2.03355e6 - 1.70635e6i) q^{61} +(1.70364e6 - 620074. i) q^{62} +(-558377. + 967138. i) q^{63} +(-1.11866e6 - 1.93757e6i) q^{64} +(-1.61421e6 - 1.35448e6i) q^{65} +(310391. - 537613. i) q^{66} +(-647732. - 3.67347e6i) q^{67} +60567.7 q^{68} +(86881.5 + 492729. i) q^{69} +(-1.69007e6 + 1.41814e6i) q^{70} +(-4.19510e6 - 1.52689e6i) q^{71} +(2.88350e6 - 1.04951e6i) q^{72} -3.69934e6 q^{73} +(704920. + 3.26797e6i) q^{74} -720767. q^{75} +(216695. - 78870.5i) q^{76} +(-2.46629e6 - 897656. i) q^{77} +(559786. - 469716. i) q^{78} +(-19850.9 - 112580. i) q^{79} +5.57270e6 q^{80} +(672642. + 3.81474e6i) q^{81} +(531018. - 919751. i) q^{82} +(1.36504e6 + 1.14541e6i) q^{83} +(33364.0 + 57788.1i) q^{84} +(-1.09833e6 + 1.90236e6i) q^{85} +(7.22221e6 - 2.62867e6i) q^{86} +(-124584. + 104538. i) q^{87} +(3.60583e6 + 6.24547e6i) q^{88} +(-386462. + 2.19174e6i) q^{89} +(-1.43514e6 + 8.13907e6i) q^{90} +(-2.36669e6 - 1.98589e6i) q^{91} +(-405607. - 147629. i) q^{92} +(1.86877e6 + 680178. i) q^{93} +(851671. + 714637. i) q^{94} +(-1.45230e6 + 8.23638e6i) q^{95} +(61312.9 - 347723. i) q^{96} +(1.65396e6 + 2.86475e6i) q^{97} +(4.36731e6 - 3.66461e6i) q^{98} +(-9.23882e6 + 3.36266e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132q + 15q^{2} + 33q^{3} - 279q^{4} + 576q^{5} - 12q^{6} - 597q^{7} - 3750q^{8} - 3243q^{9} + O(q^{10}) \) \( 132q + 15q^{2} + 33q^{3} - 279q^{4} + 576q^{5} - 12q^{6} - 597q^{7} - 3750q^{8} - 3243q^{9} - 6003q^{10} - 15975q^{11} - 4635q^{12} - 15981q^{13} - 13491q^{14} + 38493q^{15} - 74151q^{16} + 37698q^{17} - 20100q^{18} - 66102q^{19} - 176184q^{20} - 142530q^{21} + 132783q^{22} + 140631q^{23} - 38793q^{24} - 544092q^{25} - 423147q^{26} + 130557q^{27} + 603813q^{28} + 22890q^{29} - 319860q^{30} - 1288044q^{31} - 217866q^{32} + 112344q^{33} + 812019q^{34} + 1479252q^{35} + 8118132q^{36} - 1664550q^{37} + 305010q^{38} - 1580340q^{39} - 4681425q^{40} - 2956593q^{41} - 3553029q^{42} - 1023528q^{43} + 6409524q^{44} + 1803336q^{45} + 10219434q^{46} - 2607204q^{47} - 2984043q^{48} - 6819531q^{49} + 5724015q^{50} - 1675833q^{51} + 11768451q^{52} + 2280177q^{53} - 7803897q^{54} - 3542196q^{55} + 12168843q^{56} - 85203q^{57} - 12425487q^{58} - 7014600q^{59} + 2356788q^{60} + 10840332q^{61} + 6334368q^{62} - 3331359q^{63} - 26175624q^{64} - 573195q^{65} - 36720249q^{66} + 6642918q^{67} - 25277742q^{68} - 1236438q^{69} - 27401982q^{70} + 20311041q^{71} + 40093005q^{72} + 38643780q^{73} - 9531q^{74} + 16639446q^{75} + 5787405q^{76} - 316971q^{77} + 9363381q^{78} + 17712534q^{79} - 74410128q^{80} - 10355109q^{81} - 16702371q^{82} - 31021176q^{83} - 61626192q^{84} + 23576445q^{85} + 18579072q^{86} + 104996631q^{87} + 57279702q^{88} - 13471320q^{89} + 56306910q^{90} - 2335911q^{91} - 178133436q^{92} + 24366258q^{93} + 77086020q^{94} - 26254407q^{95} + 152523921q^{96} + 14408415q^{97} - 521205q^{98} + 58375668q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.1961 3.71107i 0.901214 0.328015i 0.150475 0.988614i \(-0.451920\pi\)
0.750739 + 0.660599i \(0.229698\pi\)
\(3\) 11.1844 + 4.07079i 0.239160 + 0.0870470i 0.458819 0.888530i \(-0.348272\pi\)
−0.219660 + 0.975577i \(0.570495\pi\)
\(4\) −7.86580 + 6.60019i −0.0614516 + 0.0515640i
\(5\) −64.6668 366.744i −0.231359 1.31210i −0.850148 0.526544i \(-0.823487\pi\)
0.618789 0.785557i \(-0.287624\pi\)
\(6\) 129.144 0.244087
\(7\) −94.8119 537.705i −0.104477 0.592517i −0.991428 0.130654i \(-0.958292\pi\)
0.886951 0.461863i \(-0.152819\pi\)
\(8\) −750.134 + 1299.27i −0.517993 + 0.897191i
\(9\) −1566.82 1314.72i −0.716424 0.601151i
\(10\) −2020.36 3499.36i −0.638893 1.10660i
\(11\) 2403.45 4162.90i 0.544454 0.943022i −0.454187 0.890906i \(-0.650070\pi\)
0.998641 0.0521159i \(-0.0165965\pi\)
\(12\) −114.842 + 41.7991i −0.0191852 + 0.00698285i
\(13\) 4334.59 3637.16i 0.547201 0.459156i −0.326791 0.945097i \(-0.605967\pi\)
0.873992 + 0.485941i \(0.161523\pi\)
\(14\) −2962.17 5130.62i −0.288510 0.499715i
\(15\) 769.676 4365.05i 0.0588828 0.333941i
\(16\) −2598.52 + 14736.9i −0.158601 + 0.899470i
\(17\) −4518.62 3791.57i −0.223067 0.187175i 0.524405 0.851469i \(-0.324288\pi\)
−0.747471 + 0.664294i \(0.768732\pi\)
\(18\) −20854.4 7590.39i −0.842838 0.306768i
\(19\) −21103.8 7681.14i −0.705866 0.256914i −0.0359526 0.999353i \(-0.511447\pi\)
−0.669913 + 0.742439i \(0.733669\pi\)
\(20\) 2929.23 + 2457.92i 0.0818745 + 0.0687009i
\(21\) 1128.47 6399.86i 0.0265902 0.150801i
\(22\) 9056.97 51364.6i 0.181344 1.02845i
\(23\) 21018.4 + 36405.0i 0.360208 + 0.623898i 0.987995 0.154487i \(-0.0493725\pi\)
−0.627787 + 0.778385i \(0.716039\pi\)
\(24\) −13678.8 + 11477.9i −0.201981 + 0.169482i
\(25\) −56905.5 + 20711.9i −0.728391 + 0.265113i
\(26\) 30698.1 53170.7i 0.342535 0.593288i
\(27\) −25187.0 43625.2i −0.246266 0.426545i
\(28\) 4294.73 + 3603.70i 0.0369728 + 0.0310239i
\(29\) −6832.07 + 11833.5i −0.0520187 + 0.0900990i −0.890862 0.454274i \(-0.849899\pi\)
0.838844 + 0.544373i \(0.183232\pi\)
\(30\) −8351.32 47362.7i −0.0564717 0.320267i
\(31\) 167088. 1.00735 0.503673 0.863894i \(-0.331982\pi\)
0.503673 + 0.863894i \(0.331982\pi\)
\(32\) −5151.40 29215.0i −0.0277908 0.157609i
\(33\) 43827.5 36775.6i 0.212299 0.178140i
\(34\) −60143.0 21890.3i −0.262427 0.0955156i
\(35\) −191069. + 69543.3i −0.753271 + 0.274168i
\(36\) 21001.7 0.0750231
\(37\) −41961.6 + 305239.i −0.136190 + 0.990683i
\(38\) −243681. −0.720408
\(39\) 63285.9 23034.2i 0.170836 0.0621794i
\(40\) 525008. + 191087.i 1.29705 + 0.472087i
\(41\) 74980.2 62915.8i 0.169904 0.142566i −0.553871 0.832602i \(-0.686850\pi\)
0.723775 + 0.690036i \(0.242405\pi\)
\(42\) −12244.4 69441.3i −0.0255014 0.144626i
\(43\) 708332. 1.35862 0.679309 0.733852i \(-0.262280\pi\)
0.679309 + 0.733852i \(0.262280\pi\)
\(44\) 8570.87 + 48607.8i 0.0151684 + 0.0860244i
\(45\) −380843. + 659640.i −0.623020 + 1.07910i
\(46\) 349407. + 293187.i 0.529272 + 0.444112i
\(47\) 51231.9 + 88736.3i 0.0719777 + 0.124669i 0.899768 0.436369i \(-0.143736\pi\)
−0.827790 + 0.561038i \(0.810402\pi\)
\(48\) −89053.6 + 154245.i −0.116227 + 0.201311i
\(49\) 493740. 179707.i 0.599532 0.218212i
\(50\) −503350. + 422360.i −0.569475 + 0.477846i
\(51\) −35103.3 60800.8i −0.0370555 0.0641820i
\(52\) −10089.1 + 57218.3i −0.00995043 + 0.0564317i
\(53\) −229067. + 1.29910e6i −0.211347 + 1.19861i 0.675786 + 0.737098i \(0.263804\pi\)
−0.887134 + 0.461513i \(0.847307\pi\)
\(54\) −418705. 351335.i −0.361851 0.303629i
\(55\) −1.68214e6 612249.i −1.36331 0.496203i
\(56\) 769746. + 280165.i 0.585719 + 0.213184i
\(57\) −204764. 171818.i −0.146451 0.122887i
\(58\) −25745.4 + 146009.i −0.0173261 + 0.0982614i
\(59\) 230652. 1.30809e6i 0.146209 0.829195i −0.820179 0.572107i \(-0.806126\pi\)
0.966388 0.257088i \(-0.0827629\pi\)
\(60\) 22756.0 + 39414.6i 0.0136009 + 0.0235574i
\(61\) 2.03355e6 1.70635e6i 1.14710 0.962527i 0.147448 0.989070i \(-0.452894\pi\)
0.999648 + 0.0265427i \(0.00844979\pi\)
\(62\) 1.70364e6 620074.i 0.907834 0.330425i
\(63\) −558377. + 967138.i −0.281343 + 0.487300i
\(64\) −1.11866e6 1.93757e6i −0.533416 0.923904i
\(65\) −1.61421e6 1.35448e6i −0.729059 0.611753i
\(66\) 310391. 537613.i 0.132894 0.230179i
\(67\) −647732. 3.67347e6i −0.263108 1.49216i −0.774370 0.632733i \(-0.781933\pi\)
0.511262 0.859425i \(-0.329178\pi\)
\(68\) 60567.7 0.0233593
\(69\) 86881.5 + 492729.i 0.0318387 + 0.180566i
\(70\) −1.69007e6 + 1.41814e6i −0.588927 + 0.494168i
\(71\) −4.19510e6 1.52689e6i −1.39103 0.506295i −0.465530 0.885032i \(-0.654136\pi\)
−0.925504 + 0.378737i \(0.876358\pi\)
\(72\) 2.88350e6 1.04951e6i 0.910450 0.331377i
\(73\) −3.69934e6 −1.11300 −0.556498 0.830849i \(-0.687855\pi\)
−0.556498 + 0.830849i \(0.687855\pi\)
\(74\) 704920. + 3.26797e6i 0.202222 + 0.937490i
\(75\) −720767. −0.197279
\(76\) 216695. 78870.5i 0.0566241 0.0206095i
\(77\) −2.46629e6 897656.i −0.615640 0.224074i
\(78\) 559786. 469716.i 0.133564 0.112074i
\(79\) −19850.9 112580.i −0.00452987 0.0256902i 0.982459 0.186479i \(-0.0597075\pi\)
−0.986989 + 0.160788i \(0.948596\pi\)
\(80\) 5.57270e6 1.21689
\(81\) 672642. + 3.81474e6i 0.140633 + 0.797568i
\(82\) 531018. 919751.i 0.106356 0.184214i
\(83\) 1.36504e6 + 1.14541e6i 0.262043 + 0.219880i 0.764337 0.644816i \(-0.223066\pi\)
−0.502294 + 0.864697i \(0.667511\pi\)
\(84\) 33364.0 + 57788.1i 0.00614187 + 0.0106380i
\(85\) −1.09833e6 + 1.90236e6i −0.193984 + 0.335991i
\(86\) 7.22221e6 2.62867e6i 1.22441 0.445647i
\(87\) −124584. + 104538.i −0.0202836 + 0.0170200i
\(88\) 3.60583e6 + 6.24547e6i 0.564047 + 0.976958i
\(89\) −386462. + 2.19174e6i −0.0581088 + 0.329551i −0.999979 0.00642457i \(-0.997955\pi\)
0.941871 + 0.335976i \(0.109066\pi\)
\(90\) −1.43514e6 + 8.13907e6i −0.207513 + 1.17686i
\(91\) −2.36669e6 1.98589e6i −0.329227 0.276255i
\(92\) −405607. 147629.i −0.0543060 0.0197658i
\(93\) 1.86877e6 + 680178.i 0.240917 + 0.0876865i
\(94\) 851671. + 714637.i 0.105761 + 0.0887438i
\(95\) −1.45230e6 + 8.23638e6i −0.173789 + 0.985607i
\(96\) 61312.9 347723.i 0.00707298 0.0401129i
\(97\) 1.65396e6 + 2.86475e6i 0.184003 + 0.318703i 0.943240 0.332112i \(-0.107761\pi\)
−0.759237 + 0.650814i \(0.774428\pi\)
\(98\) 4.36731e6 3.66461e6i 0.468730 0.393311i
\(99\) −9.23882e6 + 3.36266e6i −0.956959 + 0.348305i
\(100\) 310905. 538503.i 0.0310905 0.0538503i
\(101\) −6.07836e6 1.05280e7i −0.587032 1.01677i −0.994619 0.103602i \(-0.966963\pi\)
0.407587 0.913166i \(-0.366370\pi\)
\(102\) −583552. 489658.i −0.0544476 0.0456870i
\(103\) 1.03361e7 1.79027e7i 0.932024 1.61431i 0.152167 0.988355i \(-0.451375\pi\)
0.779857 0.625958i \(-0.215292\pi\)
\(104\) 1.47412e6 + 8.36016e6i 0.128504 + 0.728783i
\(105\) −2.42008e6 −0.204018
\(106\) 2.48548e6 + 1.40958e7i 0.202693 + 1.14953i
\(107\) 2.94223e6 2.46882e6i 0.232184 0.194826i −0.519271 0.854609i \(-0.673797\pi\)
0.751456 + 0.659784i \(0.229352\pi\)
\(108\) 486051. + 176908.i 0.0371277 + 0.0135134i
\(109\) 1.36473e7 4.96720e6i 1.00938 0.367383i 0.216182 0.976353i \(-0.430639\pi\)
0.793193 + 0.608970i \(0.208417\pi\)
\(110\) −1.94233e7 −1.39139
\(111\) −1.71188e6 + 3.24310e6i −0.118807 + 0.225076i
\(112\) 8.17048e6 0.549521
\(113\) −7.86625e6 + 2.86308e6i −0.512853 + 0.186663i −0.585466 0.810697i \(-0.699088\pi\)
0.0726128 + 0.997360i \(0.476866\pi\)
\(114\) −2.72542e6 991972.i −0.172293 0.0627094i
\(115\) 1.19921e7 1.00626e7i 0.735280 0.616973i
\(116\) −24363.6 138173.i −0.00144923 0.00821901i
\(117\) −1.15734e7 −0.668050
\(118\) −2.50268e6 1.41934e7i −0.140222 0.795241i
\(119\) −1.61033e6 + 2.78917e6i −0.0875992 + 0.151726i
\(120\) 5.09402e6 + 4.27439e6i 0.269108 + 0.225808i
\(121\) −1.80959e6 3.13431e6i −0.0928607 0.160840i
\(122\) 1.44018e7 2.49447e7i 0.718055 1.24371i
\(123\) 1.09472e6 398447.i 0.0530441 0.0193065i
\(124\) −1.31428e6 + 1.10281e6i −0.0619030 + 0.0519428i
\(125\) −3.27106e6 5.66565e6i −0.149797 0.259456i
\(126\) −2.10414e6 + 1.19332e7i −0.0937083 + 0.531446i
\(127\) −7.06278e6 + 4.00550e7i −0.305958 + 1.73518i 0.313000 + 0.949753i \(0.398666\pi\)
−0.618959 + 0.785423i \(0.712445\pi\)
\(128\) −1.56875e7 1.31634e7i −0.661179 0.554795i
\(129\) 7.92227e6 + 2.88347e6i 0.324927 + 0.118264i
\(130\) −2.14851e7 7.81995e6i −0.857702 0.312178i
\(131\) 1.17310e7 + 9.84347e6i 0.455916 + 0.382559i 0.841626 0.540061i \(-0.181599\pi\)
−0.385709 + 0.922620i \(0.626043\pi\)
\(132\) −102012. + 578539.i −0.00386049 + 0.0218939i
\(133\) −2.12930e6 + 1.20759e7i −0.0784795 + 0.445079i
\(134\) −2.02368e7 3.50512e7i −0.726567 1.25845i
\(135\) −1.43705e7 + 1.20583e7i −0.502694 + 0.421810i
\(136\) 8.31585e6 3.02672e6i 0.283479 0.103178i
\(137\) 1.11494e7 1.93114e7i 0.370451 0.641641i −0.619184 0.785246i \(-0.712536\pi\)
0.989635 + 0.143606i \(0.0458697\pi\)
\(138\) 2.71440e6 + 4.70148e6i 0.0879219 + 0.152285i
\(139\) 1.63021e7 + 1.36791e7i 0.514864 + 0.432022i 0.862837 0.505482i \(-0.168685\pi\)
−0.347973 + 0.937505i \(0.613130\pi\)
\(140\) 1.04391e6 1.80810e6i 0.0321525 0.0556897i
\(141\) 211771. + 1.20102e6i 0.00636210 + 0.0360813i
\(142\) −4.84399e7 −1.41969
\(143\) −4.72313e6 2.67862e7i −0.135069 0.766012i
\(144\) 2.34463e7 1.96738e7i 0.654343 0.549059i
\(145\) 4.78166e6 + 1.74038e6i 0.130254 + 0.0474086i
\(146\) −3.77187e7 + 1.37285e7i −1.00305 + 0.365080i
\(147\) 6.25373e6 0.162378
\(148\) −1.68458e6 2.67791e6i −0.0427144 0.0679015i
\(149\) 7.56307e7 1.87304 0.936518 0.350620i \(-0.114029\pi\)
0.936518 + 0.350620i \(0.114029\pi\)
\(150\) −7.34900e6 + 2.67482e6i −0.177791 + 0.0647105i
\(151\) 2.35982e7 + 8.58905e6i 0.557776 + 0.203014i 0.605498 0.795847i \(-0.292974\pi\)
−0.0477221 + 0.998861i \(0.515196\pi\)
\(152\) 2.58105e7 2.16576e7i 0.596135 0.500216i
\(153\) 2.09502e6 + 1.18814e7i 0.0472898 + 0.268194i
\(154\) −2.84777e7 −0.628323
\(155\) −1.08050e7 6.12783e7i −0.233058 1.32174i
\(156\) −345764. + 598881.i −0.00729195 + 0.0126300i
\(157\) −2.92521e7 2.45455e7i −0.603266 0.506200i 0.289228 0.957260i \(-0.406602\pi\)
−0.892494 + 0.451060i \(0.851046\pi\)
\(158\) −620195. 1.07421e6i −0.0125092 0.0216665i
\(159\) −7.85034e6 + 1.35972e7i −0.154881 + 0.268262i
\(160\) −1.03813e7 + 3.77849e6i −0.200370 + 0.0729286i
\(161\) 1.75823e7 1.47533e7i 0.332037 0.278612i
\(162\) 2.10151e7 + 3.63992e7i 0.388355 + 0.672650i
\(163\) −1.87778e7 + 1.06494e8i −0.339616 + 1.92606i 0.0361500 + 0.999346i \(0.488491\pi\)
−0.375766 + 0.926714i \(0.622621\pi\)
\(164\) −174523. + 989766.i −0.00308957 + 0.0175218i
\(165\) −1.63214e7 1.36953e7i −0.282855 0.237343i
\(166\) 1.81687e7 + 6.61288e6i 0.308281 + 0.112205i
\(167\) −4.13418e7 1.50472e7i −0.686882 0.250005i −0.0250823 0.999685i \(-0.507985\pi\)
−0.661800 + 0.749681i \(0.730207\pi\)
\(168\) 7.46865e6 + 6.26694e6i 0.121523 + 0.101970i
\(169\) −5.33637e6 + 3.02641e7i −0.0850437 + 0.482307i
\(170\) −4.13886e6 + 2.34726e7i −0.0646114 + 0.366429i
\(171\) 2.29673e7 + 3.97805e7i 0.351255 + 0.608392i
\(172\) −5.57160e6 + 4.67513e6i −0.0834892 + 0.0700558i
\(173\) 8.02917e7 2.92238e7i 1.17899 0.429116i 0.323143 0.946350i \(-0.395260\pi\)
0.855844 + 0.517234i \(0.173038\pi\)
\(174\) −882319. + 1.52822e6i −0.0126971 + 0.0219920i
\(175\) 1.65322e7 + 2.86346e7i 0.233184 + 0.403886i
\(176\) 5.51029e7 + 4.62369e7i 0.761869 + 0.639284i
\(177\) 7.90467e6 1.36913e7i 0.107146 0.185583i
\(178\) 4.19328e6 + 2.37813e7i 0.0557294 + 0.316057i
\(179\) 2.41363e7 0.314547 0.157273 0.987555i \(-0.449730\pi\)
0.157273 + 0.987555i \(0.449730\pi\)
\(180\) −1.35811e6 7.70223e6i −0.0173573 0.0984380i
\(181\) 2.64608e7 2.22033e7i 0.331687 0.278318i −0.461700 0.887036i \(-0.652760\pi\)
0.793387 + 0.608718i \(0.208316\pi\)
\(182\) −3.15007e7 1.14653e7i −0.387320 0.140973i
\(183\) 2.96901e7 1.08063e7i 0.358124 0.130347i
\(184\) −6.30666e7 −0.746340
\(185\) 1.14658e8 4.34970e6i 1.33139 0.0505077i
\(186\) 2.15784e7 0.245880
\(187\) −2.66442e7 + 9.69771e6i −0.297960 + 0.108449i
\(188\) −988656. 359842.i −0.0108516 0.00394965i
\(189\) −2.10695e7 + 1.76794e7i −0.227006 + 0.190481i
\(190\) 1.57580e7 + 8.93683e7i 0.166673 + 0.945248i
\(191\) −1.53795e8 −1.59707 −0.798537 0.601946i \(-0.794392\pi\)
−0.798537 + 0.601946i \(0.794392\pi\)
\(192\) −4.62406e6 2.62243e7i −0.0471486 0.267393i
\(193\) −2.51612e7 + 4.35804e7i −0.251930 + 0.436356i −0.964057 0.265695i \(-0.914399\pi\)
0.712127 + 0.702051i \(0.247732\pi\)
\(194\) 2.74952e7 + 2.30712e7i 0.270365 + 0.226863i
\(195\) −1.25401e7 2.17201e7i −0.121110 0.209769i
\(196\) −2.69756e6 + 4.67231e6i −0.0255903 + 0.0443237i
\(197\) −6.36558e6 + 2.31688e6i −0.0593207 + 0.0215910i −0.371510 0.928429i \(-0.621160\pi\)
0.312189 + 0.950020i \(0.398938\pi\)
\(198\) −8.17207e7 + 6.85718e7i −0.748176 + 0.627794i
\(199\) 3.87034e7 + 6.70362e7i 0.348147 + 0.603009i 0.985920 0.167215i \(-0.0534776\pi\)
−0.637773 + 0.770224i \(0.720144\pi\)
\(200\) 1.57764e7 8.94724e7i 0.139445 0.790832i
\(201\) 7.70942e6 4.37223e7i 0.0669631 0.379767i
\(202\) −1.01046e8 8.47873e7i −0.862556 0.723771i
\(203\) 7.01068e6 + 2.55168e6i 0.0588199 + 0.0214087i
\(204\) 677413. + 246558.i 0.00558660 + 0.00203336i
\(205\) −2.79227e7 2.34299e7i −0.226370 0.189947i
\(206\) 3.89497e7 2.20895e8i 0.310434 1.76056i
\(207\) 1.49302e7 8.46734e7i 0.116996 0.663515i
\(208\) 4.23369e7 + 7.33297e7i 0.326210 + 0.565013i
\(209\) −8.26978e7 + 6.93917e7i −0.626587 + 0.525769i
\(210\) −2.46753e7 + 8.98109e6i −0.183863 + 0.0669208i
\(211\) 1.43656e7 2.48820e7i 0.105277 0.182346i −0.808574 0.588394i \(-0.799760\pi\)
0.913852 + 0.406048i \(0.133094\pi\)
\(212\) −6.77253e6 1.17304e7i −0.0488175 0.0845544i
\(213\) −4.07040e7 3.41547e7i −0.288608 0.242171i
\(214\) 2.08372e7 3.60911e7i 0.145342 0.251740i
\(215\) −4.58056e7 2.59776e8i −0.314328 1.78265i
\(216\) 7.55746e7 0.510256
\(217\) −1.58419e7 8.98439e7i −0.105244 0.596870i
\(218\) 1.20715e8 1.01292e8i 0.789156 0.662181i
\(219\) −4.13748e7 1.50592e7i −0.266184 0.0968830i
\(220\) 1.72724e7 6.28662e6i 0.109363 0.0398050i
\(221\) −3.33769e7 −0.208005
\(222\) −5.41909e6 + 3.94198e7i −0.0332423 + 0.241813i
\(223\) −1.51860e8 −0.917018 −0.458509 0.888690i \(-0.651616\pi\)
−0.458509 + 0.888690i \(0.651616\pi\)
\(224\) −1.52207e7 + 5.53987e6i −0.0904827 + 0.0329330i
\(225\) 1.16391e8 + 4.23629e7i 0.681209 + 0.247940i
\(226\) −6.95798e7 + 5.83844e7i −0.400962 + 0.336447i
\(227\) −1.96132e7 1.11232e8i −0.111290 0.631160i −0.988520 0.151089i \(-0.951722\pi\)
0.877230 0.480071i \(-0.159389\pi\)
\(228\) 2.74467e6 0.0153362
\(229\) 5.17542e7 + 2.93513e8i 0.284788 + 1.61511i 0.706042 + 0.708170i \(0.250479\pi\)
−0.421254 + 0.906943i \(0.638410\pi\)
\(230\) 8.49295e7 1.47102e8i 0.460268 0.797208i
\(231\) −2.39298e7 2.00795e7i −0.127731 0.107179i
\(232\) −1.02499e7 1.77534e7i −0.0538906 0.0933413i
\(233\) −2.14349e7 + 3.71264e7i −0.111014 + 0.192281i −0.916179 0.400769i \(-0.868743\pi\)
0.805166 + 0.593050i \(0.202076\pi\)
\(234\) −1.18003e8 + 4.29495e7i −0.602056 + 0.219130i
\(235\) 2.92305e7 2.45273e7i 0.146926 0.123285i
\(236\) 6.81940e6 + 1.18115e7i 0.0337718 + 0.0584945i
\(237\) 236269. 1.33995e6i 0.00115289 0.00653837i
\(238\) −6.06823e6 + 3.44146e7i −0.0291771 + 0.165472i
\(239\) −1.30056e8 1.09130e8i −0.616224 0.517074i 0.280390 0.959886i \(-0.409536\pi\)
−0.896614 + 0.442813i \(0.853981\pi\)
\(240\) 6.23273e7 + 2.26853e7i 0.291031 + 0.105927i
\(241\) 2.95093e8 + 1.07405e8i 1.35800 + 0.494271i 0.915435 0.402466i \(-0.131847\pi\)
0.442564 + 0.896737i \(0.354069\pi\)
\(242\) −3.00824e7 2.52421e7i −0.136445 0.114491i
\(243\) −2.71364e7 + 1.53898e8i −0.121319 + 0.688036i
\(244\) −4.73325e6 + 2.68436e7i −0.0208591 + 0.118298i
\(245\) −9.78348e7 1.69455e8i −0.425023 0.736161i
\(246\) 9.68323e6 8.12519e6i 0.0414713 0.0347985i
\(247\) −1.19414e8 + 4.34630e7i −0.504214 + 0.183519i
\(248\) −1.25338e8 + 2.17092e8i −0.521798 + 0.903781i
\(249\) 1.06045e7 + 1.83675e7i 0.0435302 + 0.0753966i
\(250\) −5.43776e7 4.56282e7i −0.220105 0.184690i
\(251\) −2.16343e8 + 3.74717e8i −0.863544 + 1.49570i 0.00494128 + 0.999988i \(0.498427\pi\)
−0.868485 + 0.495715i \(0.834906\pi\)
\(252\) −1.99121e6 1.12927e7i −0.00783817 0.0444525i
\(253\) 2.02067e8 0.784466
\(254\) 7.66342e7 + 4.34614e8i 0.293430 + 1.66412i
\(255\) −2.00283e7 + 1.68057e7i −0.0756402 + 0.0634697i
\(256\) 6.03041e7 + 2.19489e7i 0.224650 + 0.0817660i
\(257\) 3.65227e8 1.32932e8i 1.34214 0.488498i 0.431652 0.902040i \(-0.357931\pi\)
0.910485 + 0.413542i \(0.135708\pi\)
\(258\) 9.14768e7 0.331621
\(259\) 1.68107e8 6.37735e6i 0.601225 0.0228082i
\(260\) 2.16369e7 0.0763462
\(261\) 2.62623e7 9.55870e6i 0.0914305 0.0332780i
\(262\) 1.56140e8 + 5.68303e7i 0.536364 + 0.195220i
\(263\) 3.51364e7 2.94829e7i 0.119100 0.0999368i −0.581292 0.813695i \(-0.697453\pi\)
0.700392 + 0.713758i \(0.253008\pi\)
\(264\) 1.49050e7 + 8.45304e7i 0.0498560 + 0.282748i
\(265\) 4.91251e8 1.62160
\(266\) 2.31038e7 + 1.31028e8i 0.0752659 + 0.426854i
\(267\) −1.32444e7 + 2.29400e7i −0.0425837 + 0.0737572i
\(268\) 2.93405e7 + 2.46196e7i 0.0931100 + 0.0781285i
\(269\) −1.05001e8 1.81867e8i −0.328897 0.569666i 0.653396 0.757016i \(-0.273344\pi\)
−0.982293 + 0.187350i \(0.940010\pi\)
\(270\) −1.01774e8 + 1.76277e8i −0.314675 + 0.545033i
\(271\) −1.03111e8 + 3.75293e7i −0.314711 + 0.114545i −0.494546 0.869151i \(-0.664666\pi\)
0.179835 + 0.983697i \(0.442444\pi\)
\(272\) 6.76178e7 5.67381e7i 0.203737 0.170956i
\(273\) −1.83858e7 3.18452e7i −0.0546908 0.0947272i
\(274\) 4.20146e7 2.38277e8i 0.123388 0.699769i
\(275\) −5.05481e7 + 2.86672e8i −0.146568 + 0.831230i
\(276\) −3.93550e6 3.30228e6i −0.0112673 0.00945435i
\(277\) −5.83176e8 2.12259e8i −1.64862 0.600048i −0.660104 0.751174i \(-0.729488\pi\)
−0.988515 + 0.151126i \(0.951710\pi\)
\(278\) 2.16982e8 + 7.89749e7i 0.605712 + 0.220461i
\(279\) −2.61796e8 2.19673e8i −0.721687 0.605567i
\(280\) 5.29716e7 3.00417e8i 0.144208 0.817845i
\(281\) −4.77637e7 + 2.70881e8i −0.128418 + 0.728294i 0.850801 + 0.525488i \(0.176117\pi\)
−0.979219 + 0.202806i \(0.934994\pi\)
\(282\) 6.61629e6 + 1.14597e7i 0.0175688 + 0.0304301i
\(283\) −3.04915e8 + 2.55854e8i −0.799699 + 0.671027i −0.948126 0.317896i \(-0.897024\pi\)
0.148426 + 0.988923i \(0.452579\pi\)
\(284\) 4.30756e7 1.56782e7i 0.111588 0.0406146i
\(285\) −4.97716e7 + 8.62069e7i −0.127358 + 0.220590i
\(286\) −1.47563e8 2.55586e8i −0.372989 0.646036i
\(287\) −4.09392e7 3.43520e7i −0.102224 0.0857760i
\(288\) −3.03382e7 + 5.25474e7i −0.0748370 + 0.129622i
\(289\) −6.52127e7 3.69839e8i −0.158924 0.901303i
\(290\) 5.52129e7 0.132937
\(291\) 6.83680e6 + 3.87734e7i 0.0162640 + 0.0922377i
\(292\) 2.90982e7 2.44163e7i 0.0683954 0.0573905i
\(293\) 7.68774e8 + 2.79811e8i 1.78551 + 0.649872i 0.999499 + 0.0316572i \(0.0100785\pi\)
0.786009 + 0.618215i \(0.212144\pi\)
\(294\) 6.37635e7 2.32080e7i 0.146338 0.0532626i
\(295\) −4.94650e8 −1.12181
\(296\) −3.65112e8 2.83490e8i −0.818286 0.635356i
\(297\) −2.42143e8 −0.536321
\(298\) 7.71136e8 2.80670e8i 1.68801 0.614384i
\(299\) 2.23517e8 + 8.13535e7i 0.483572 + 0.176006i
\(300\) 5.66941e6 4.75720e6i 0.0121231 0.0101725i
\(301\) −6.71583e7 3.80874e8i −0.141944 0.805005i
\(302\) 2.72484e8 0.569267
\(303\) −2.51254e7 1.42493e8i −0.0518876 0.294269i
\(304\) 1.68035e8 2.91045e8i 0.343037 0.594158i
\(305\) −7.57295e8 6.35446e8i −1.52832 1.28242i
\(306\) 6.54537e7 + 1.13369e8i 0.130590 + 0.226188i
\(307\) −2.71038e8 + 4.69451e8i −0.534620 + 0.925990i 0.464561 + 0.885541i \(0.346212\pi\)
−0.999182 + 0.0404488i \(0.987121\pi\)
\(308\) 2.53240e7 9.21720e6i 0.0493862 0.0179751i
\(309\) 1.88481e8 1.58154e8i 0.363424 0.304949i
\(310\) −3.37577e8 5.84700e8i −0.643586 1.11472i
\(311\) −9.78971e7 + 5.55202e8i −0.184548 + 1.04662i 0.741987 + 0.670414i \(0.233883\pi\)
−0.926535 + 0.376208i \(0.877228\pi\)
\(312\) −1.75453e7 + 9.95042e7i −0.0327054 + 0.185481i
\(313\) −3.99623e7 3.35323e7i −0.0736622 0.0618100i 0.605213 0.796063i \(-0.293088\pi\)
−0.678875 + 0.734254i \(0.737532\pi\)
\(314\) −3.89347e8 1.41711e8i −0.709713 0.258314i
\(315\) 3.90800e8 + 1.42240e8i 0.704478 + 0.256409i
\(316\) 899195. + 754514.i 0.00160306 + 0.00134512i
\(317\) 1.35824e8 7.70294e8i 0.239479 1.35816i −0.593492 0.804840i \(-0.702251\pi\)
0.832972 0.553316i \(-0.186638\pi\)
\(318\) −2.95826e7 + 1.67771e8i −0.0515871 + 0.292565i
\(319\) 3.28411e7 + 5.68825e7i 0.0566436 + 0.0981095i
\(320\) −6.38251e8 + 5.35556e8i −1.08885 + 0.913650i
\(321\) 4.29571e7 1.56351e7i 0.0724881 0.0263835i
\(322\) 1.24520e8 2.15675e8i 0.207847 0.360002i
\(323\) 6.62363e7 + 1.14725e8i 0.109367 + 0.189430i
\(324\) −3.04689e7 2.55664e7i −0.0497679 0.0417602i
\(325\) −1.71330e8 + 2.96752e8i −0.276848 + 0.479515i
\(326\) 2.03748e8 + 1.15551e9i 0.325710 + 1.84719i
\(327\) 1.72857e8 0.273381
\(328\) 2.54995e7 + 1.44615e8i 0.0399000 + 0.226284i
\(329\) 4.28565e7 3.59609e7i 0.0663486 0.0556731i
\(330\) −2.17238e8 7.90682e7i −0.332765 0.121116i
\(331\) 8.59406e8 3.12798e8i 1.30257 0.474096i 0.404736 0.914434i \(-0.367363\pi\)
0.897832 + 0.440337i \(0.145141\pi\)
\(332\) −1.82970e7 −0.0274409
\(333\) 4.67050e8 4.23087e8i 0.693120 0.627878i
\(334\) −4.77365e8 −0.701033
\(335\) −1.30533e9 + 4.75103e8i −1.89699 + 0.690448i
\(336\) 9.13819e7 + 3.32603e7i 0.131423 + 0.0478342i
\(337\) −3.51741e7 + 2.95146e7i −0.0500632 + 0.0420080i −0.667476 0.744631i \(-0.732625\pi\)
0.617413 + 0.786639i \(0.288181\pi\)
\(338\) 5.79019e7 + 3.28378e8i 0.0815614 + 0.462558i
\(339\) −9.96342e7 −0.138902
\(340\) −3.91672e6 2.22128e7i −0.00540438 0.0306498i
\(341\) 4.01588e8 6.95570e8i 0.548454 0.949950i
\(342\) 3.81804e8 + 3.20371e8i 0.516118 + 0.433074i
\(343\) −3.68269e8 6.37860e8i −0.492760 0.853485i
\(344\) −5.31344e8 + 9.20316e8i −0.703755 + 1.21894i
\(345\) 1.75087e8 6.37264e7i 0.229555 0.0835512i
\(346\) 7.10208e8 5.95936e8i 0.921763 0.773451i
\(347\) −3.87643e8 6.71418e8i −0.498057 0.862660i 0.501941 0.864902i \(-0.332620\pi\)
−0.999997 + 0.00224224i \(0.999286\pi\)
\(348\) 289980. 1.64456e6i 0.000368842 0.00209181i
\(349\) 8.98192e7 5.09390e8i 0.113105 0.641448i −0.874567 0.484905i \(-0.838854\pi\)
0.987671 0.156542i \(-0.0500348\pi\)
\(350\) 2.74829e8 + 2.30609e8i 0.342629 + 0.287500i
\(351\) −2.67847e8 9.74884e7i −0.330607 0.120331i
\(352\) −1.34001e8 4.87722e7i −0.163760 0.0596037i
\(353\) 8.03023e8 + 6.73817e8i 0.971665 + 0.815324i 0.982811 0.184614i \(-0.0591034\pi\)
−0.0111458 + 0.999938i \(0.503548\pi\)
\(354\) 2.97873e7 1.68932e8i 0.0356878 0.202396i
\(355\) −2.88694e8 + 1.63726e9i −0.342482 + 1.94231i
\(356\) −1.14260e7 1.97905e7i −0.0134221 0.0232478i
\(357\) −2.93647e7 + 2.46399e7i −0.0341575 + 0.0286616i
\(358\) 2.46096e8 8.95715e7i 0.283474 0.103176i
\(359\) 3.75375e8 6.50169e8i 0.428189 0.741645i −0.568524 0.822667i \(-0.692485\pi\)
0.996712 + 0.0810223i \(0.0258185\pi\)
\(360\) −5.71367e8 9.89637e8i −0.645441 1.11794i
\(361\) −2.98377e8 2.50368e8i −0.333803 0.280094i
\(362\) 1.87399e8 3.24584e8i 0.207628 0.359623i
\(363\) −7.48011e6 4.24218e7i −0.00820795 0.0465496i
\(364\) 3.17231e7 0.0344763
\(365\) 2.39224e8 + 1.35671e9i 0.257502 + 1.46036i
\(366\) 2.62620e8 2.20364e8i 0.279991 0.234940i
\(367\) 4.74310e8 + 1.72635e8i 0.500877 + 0.182304i 0.580089 0.814553i \(-0.303018\pi\)
−0.0792112 + 0.996858i \(0.525240\pi\)
\(368\) −5.91114e8 + 2.15148e8i −0.618307 + 0.225045i
\(369\) −2.00197e8 −0.207427
\(370\) 1.15292e9 4.69854e8i 1.18330 0.482233i
\(371\) 7.20252e8 0.732278
\(372\) −1.91887e7 + 6.98412e6i −0.0193262 + 0.00703415i
\(373\) 1.52340e9 + 5.54472e8i 1.51996 + 0.553221i 0.961139 0.276065i \(-0.0890305\pi\)
0.558824 + 0.829286i \(0.311253\pi\)
\(374\) −2.35678e8 + 1.97757e8i −0.232953 + 0.195471i
\(375\) −1.35212e7 7.66826e7i −0.0132406 0.0750909i
\(376\) −1.53723e8 −0.149136
\(377\) 1.34260e7 + 7.61426e7i 0.0129048 + 0.0731869i
\(378\) −1.49216e8 + 2.58450e8i −0.142100 + 0.246125i
\(379\) −3.13773e8 2.63287e8i −0.296059 0.248423i 0.482643 0.875817i \(-0.339677\pi\)
−0.778702 + 0.627394i \(0.784121\pi\)
\(380\) −4.29382e7 7.43712e7i −0.0401422 0.0695283i
\(381\) −2.42048e8 + 4.19240e8i −0.224215 + 0.388352i
\(382\) −1.56810e9 + 5.70743e8i −1.43931 + 0.523864i
\(383\) −7.32802e7 + 6.14894e7i −0.0666486 + 0.0559248i −0.675503 0.737357i \(-0.736074\pi\)
0.608855 + 0.793282i \(0.291629\pi\)
\(384\) −1.21870e8 2.11085e8i −0.109834 0.190238i
\(385\) −1.69723e8 + 9.62544e8i −0.151575 + 0.859623i
\(386\) −9.48153e7 + 5.37724e8i −0.0839118 + 0.475887i
\(387\) −1.10983e9 9.31257e8i −0.973347 0.816735i
\(388\) −3.19176e7 1.16171e7i −0.0277408 0.0100968i
\(389\) −1.32647e8 4.82795e7i −0.114255 0.0415853i 0.284260 0.958747i \(-0.408252\pi\)
−0.398515 + 0.917162i \(0.630474\pi\)
\(390\) −2.08465e8 1.74923e8i −0.177954 0.149321i
\(391\) 4.30579e7 2.44193e8i 0.0364279 0.206593i
\(392\) −1.36884e8 + 7.76306e8i −0.114776 + 0.650926i
\(393\) 9.11334e7 + 1.57848e8i 0.0757362 + 0.131179i
\(394\) −5.63058e7 + 4.72462e7i −0.0463785 + 0.0389161i
\(395\) −4.00044e7 + 1.45604e7i −0.0326601 + 0.0118873i
\(396\) 5.04766e7 8.74280e7i 0.0408467 0.0707485i
\(397\) 9.54288e8 + 1.65288e9i 0.765443 + 1.32579i 0.940012 + 0.341141i \(0.110813\pi\)
−0.174569 + 0.984645i \(0.555853\pi\)
\(398\) 6.43398e8 + 5.39875e8i 0.511551 + 0.429242i
\(399\) −7.29731e7 + 1.26393e8i −0.0575119 + 0.0996136i
\(400\) −1.57360e8 8.92432e8i −0.122937 0.697212i
\(401\) 1.07424e9 0.831951 0.415976 0.909376i \(-0.363440\pi\)
0.415976 + 0.909376i \(0.363440\pi\)
\(402\) −8.36506e7 4.74406e8i −0.0642211 0.364216i
\(403\) 7.24257e8 6.07724e8i 0.551220 0.462529i
\(404\) 1.17298e8 + 4.26930e7i 0.0885026 + 0.0322123i
\(405\) 1.35554e9 4.93374e8i 1.01395 0.369049i
\(406\) 8.09509e7 0.0600317
\(407\) 1.16983e9 + 9.08311e8i 0.860087 + 0.667812i
\(408\) 1.05329e8 0.0767780
\(409\) −3.63872e8 + 1.32439e8i −0.262977 + 0.0957157i −0.470144 0.882590i \(-0.655798\pi\)
0.207167 + 0.978306i \(0.433576\pi\)
\(410\) −3.71652e8 1.35270e8i −0.266313 0.0969301i
\(411\) 2.03312e8 1.70599e8i 0.144450 0.121208i
\(412\) 3.68592e7 + 2.09039e8i 0.0259661 + 0.147261i
\(413\) −7.25237e8 −0.506588
\(414\) −1.61999e8 9.18743e8i −0.112205 0.636345i
\(415\) 3.31797e8 5.74690e8i 0.227879 0.394698i
\(416\) −1.28589e8 1.07899e8i −0.0875743 0.0734836i
\(417\) 1.26645e8 + 2.19355e8i 0.0855285 + 0.148140i
\(418\) −5.85675e8 + 1.01442e9i −0.392229 + 0.679361i
\(419\) −1.84133e9 + 6.70190e8i −1.22288 + 0.445091i −0.871152 0.491013i \(-0.836627\pi\)
−0.351725 + 0.936103i \(0.614405\pi\)
\(420\) 1.90359e7 1.59730e7i 0.0125372 0.0105200i
\(421\) 1.06961e9 + 1.85261e9i 0.698614 + 1.21003i 0.968947 + 0.247268i \(0.0795327\pi\)
−0.270333 + 0.962767i \(0.587134\pi\)
\(422\) 5.41342e7 3.07010e8i 0.0350653 0.198865i
\(423\) 3.63920e7 2.06389e8i 0.0233784 0.132585i
\(424\) −1.51606e9 1.27212e9i −0.965905 0.810491i
\(425\) 3.35665e8 + 1.22172e8i 0.212102 + 0.0771989i
\(426\) −5.41771e8 1.97189e8i −0.339533 0.123580i
\(427\) −1.11032e9 9.31665e8i −0.690158 0.579112i
\(428\) −6.84828e6 + 3.88385e7i −0.00422210 + 0.0239447i
\(429\) 5.62156e7 3.18815e8i 0.0343761 0.194956i
\(430\) −1.43108e9 2.47871e9i −0.868012 1.50344i
\(431\) −3.07767e8 + 2.58247e8i −0.185162 + 0.155369i −0.730657 0.682745i \(-0.760786\pi\)
0.545495 + 0.838114i \(0.316342\pi\)
\(432\) 7.08350e8 2.57818e8i 0.422722 0.153858i
\(433\) −1.06547e8 + 1.84544e8i −0.0630713 + 0.109243i −0.895837 0.444383i \(-0.853423\pi\)
0.832765 + 0.553626i \(0.186756\pi\)
\(434\) −4.94942e8 8.57264e8i −0.290630 0.503386i
\(435\) 4.63953e7 + 3.89302e7i 0.0270247 + 0.0226764i
\(436\) −7.45622e7 + 1.29145e8i −0.0430840 + 0.0746236i
\(437\) −1.63936e8 9.29728e8i −0.0939701 0.532931i
\(438\) −4.77747e8 −0.271668
\(439\) −2.56347e8 1.45381e9i −0.144611 0.820131i −0.967679 0.252187i \(-0.918850\pi\)
0.823067 0.567944i \(-0.192261\pi\)
\(440\) 2.05731e9 1.72629e9i 1.15137 0.966115i
\(441\) −1.00987e9 3.67561e8i −0.560697 0.204077i
\(442\) −3.40314e8 + 1.23864e8i −0.187457 + 0.0682287i
\(443\) −7.80055e8 −0.426297 −0.213148 0.977020i \(-0.568372\pi\)
−0.213148 + 0.977020i \(0.568372\pi\)
\(444\) −7.93978e6 3.68083e7i −0.00430495 0.0199575i
\(445\) 8.28796e8 0.445849
\(446\) −1.54838e9 + 5.63564e8i −0.826429 + 0.300796i
\(447\) 8.45883e8 + 3.07876e8i 0.447955 + 0.163042i
\(448\) −9.35778e8 + 7.85211e8i −0.491699 + 0.412585i
\(449\) −5.47854e8 3.10704e9i −0.285629 1.61988i −0.703029 0.711161i \(-0.748170\pi\)
0.417400 0.908723i \(-0.362942\pi\)
\(450\) 1.34394e9 0.695244
\(451\) −8.17012e7 4.63350e8i −0.0419383 0.237844i
\(452\) 4.29775e7 7.44392e7i 0.0218905 0.0379155i
\(453\) 2.28967e8 + 1.92127e8i 0.115726 + 0.0971054i
\(454\) −6.12767e8 1.06134e9i −0.307326 0.532305i
\(455\) −5.75265e8 + 9.96388e8i −0.286304 + 0.495894i
\(456\) 3.76839e8 1.37158e8i 0.186114 0.0677399i
\(457\) −9.22661e8 + 7.74204e8i −0.452205 + 0.379445i −0.840253 0.542194i \(-0.817594\pi\)
0.388048 + 0.921639i \(0.373149\pi\)
\(458\) 1.61694e9 + 2.80061e9i 0.786436 + 1.36215i
\(459\) −5.15976e7 + 2.92624e8i −0.0249049 + 0.141243i
\(460\) −2.79126e7 + 1.58300e8i −0.0133705 + 0.0758279i
\(461\) −2.73123e9 2.29177e9i −1.29839 1.08948i −0.990421 0.138082i \(-0.955906\pi\)
−0.307969 0.951397i \(-0.599649\pi\)
\(462\) −3.18506e8 1.15927e8i −0.150270 0.0546936i
\(463\) 2.58210e9 + 9.39809e8i 1.20904 + 0.440054i 0.866370 0.499402i \(-0.166447\pi\)
0.342668 + 0.939456i \(0.388669\pi\)
\(464\) −1.56636e8 1.31433e8i −0.0727911 0.0610790i
\(465\) 1.28603e8 7.29346e8i 0.0593153 0.336394i
\(466\) −8.07735e7 + 4.58089e8i −0.0369759 + 0.209701i
\(467\) 8.47309e8 + 1.46758e9i 0.384975 + 0.666796i 0.991766 0.128065i \(-0.0408767\pi\)
−0.606791 + 0.794862i \(0.707543\pi\)
\(468\) 9.10337e7 7.63864e7i 0.0410527 0.0344473i
\(469\) −1.91383e9 + 6.96577e8i −0.856640 + 0.311792i
\(470\) 2.07014e8 3.58558e8i 0.0919721 0.159300i
\(471\) −2.27248e8 3.93605e8i −0.100214 0.173575i
\(472\) 1.52655e9 + 1.28093e9i 0.668210 + 0.560695i
\(473\) 1.70244e9 2.94872e9i 0.739706 1.28121i
\(474\) −2.56363e6 1.45390e7i −0.00110568 0.00627064i
\(475\) 1.36001e9 0.582257
\(476\) −5.74253e6 3.25675e7i −0.00244050 0.0138408i
\(477\) 2.06686e9 1.73430e9i 0.871961 0.731662i
\(478\) −1.73105e9 6.30052e8i −0.724958 0.263863i
\(479\) −1.55884e9 + 5.67370e8i −0.648076 + 0.235880i −0.645080 0.764115i \(-0.723176\pi\)
−0.00299611 + 0.999996i \(0.500954\pi\)
\(480\) −1.31490e8 −0.0542686
\(481\) 9.28317e8 + 1.47571e9i 0.380354 + 0.604635i
\(482\) 3.40738e9 1.38598
\(483\) 2.56706e8 9.34332e7i 0.103662 0.0377299i
\(484\) 3.49209e7 + 1.27102e7i 0.0140000 + 0.00509557i
\(485\) 9.43672e8 7.91835e8i 0.375599 0.315165i
\(486\) 2.94442e8 + 1.66986e9i 0.116352 + 0.659863i
\(487\) 1.83263e9 0.718990 0.359495 0.933147i \(-0.382949\pi\)
0.359495 + 0.933147i \(0.382949\pi\)
\(488\) 6.91575e8 + 3.92212e9i 0.269383 + 1.52775i
\(489\) −6.43534e8 + 1.11463e9i −0.248880 + 0.431074i
\(490\) −1.62639e9 1.36470e9i −0.624508 0.524025i
\(491\) 2.34807e8 + 4.06697e8i 0.0895211 + 0.155055i 0.907309 0.420465i \(-0.138133\pi\)
−0.817788 + 0.575520i \(0.804800\pi\)
\(492\) −5.98106e6 + 1.03595e7i −0.00226412 + 0.00392158i
\(493\) 7.57391e7 2.75668e7i 0.0284679 0.0103615i
\(494\) −1.05626e9 + 8.86304e8i −0.394208 + 0.330780i
\(495\) 1.83068e9 + 3.17083e9i 0.678412 + 1.17504i
\(496\) −4.34180e8 + 2.46236e9i −0.159766 + 0.906077i
\(497\) −4.23271e8 + 2.40049e9i −0.154658 + 0.877107i
\(498\) 1.76287e8 + 1.47922e8i 0.0639613 + 0.0536699i
\(499\) −3.36602e9 1.22513e9i −1.21273 0.441399i −0.345082 0.938573i \(-0.612149\pi\)
−0.867651 + 0.497174i \(0.834371\pi\)
\(500\) 6.31239e7 + 2.29752e7i 0.0225839 + 0.00821986i
\(501\) −4.01129e8 3.36587e8i −0.142512 0.119582i
\(502\) −8.15248e8 + 4.62350e9i −0.287625 + 1.63120i
\(503\) −3.60025e8 + 2.04180e9i −0.126138 + 0.715362i 0.854488 + 0.519471i \(0.173871\pi\)
−0.980626 + 0.195891i \(0.937240\pi\)
\(504\) −8.37716e8 1.45097e9i −0.291467 0.504836i
\(505\) −3.46802e9 + 2.91001e9i −1.19829 + 1.00548i
\(506\) 2.06029e9 7.49885e8i 0.706972 0.257317i
\(507\) −1.82883e8 + 3.16762e8i −0.0623224 + 0.107946i
\(508\) −2.08816e8 3.61680e8i −0.0706710 0.122406i
\(509\) −1.10234e9 9.24971e8i −0.370512 0.310897i 0.438452 0.898755i \(-0.355527\pi\)
−0.808964 + 0.587858i \(0.799971\pi\)
\(510\) −1.41843e8 + 2.45679e8i −0.0473490 + 0.0820109i
\(511\) 3.50741e8 + 1.98915e9i 0.116282 + 0.659469i
\(512\) 3.31758e9 1.09239
\(513\) 1.96450e8 + 1.11412e9i 0.0642452 + 0.364352i
\(514\) 3.23056e9 2.71076e9i 1.04932 0.880483i
\(515\) −7.23409e9 2.63299e9i −2.33377 0.849424i
\(516\) −8.13464e7 + 2.96077e7i −0.0260654 + 0.00948703i
\(517\) 4.92534e8 0.156754
\(518\) 1.69037e9 6.88881e8i 0.534351 0.217766i
\(519\) 1.01698e9 0.319320
\(520\) 2.97071e9 1.08125e9i 0.926506 0.337221i
\(521\) 3.88274e9 + 1.41320e9i 1.20284 + 0.437796i 0.864213 0.503126i \(-0.167817\pi\)
0.338622 + 0.940922i \(0.390039\pi\)
\(522\) 2.32300e8 1.94922e8i 0.0714828 0.0599812i
\(523\) −1.87806e8 1.06510e9i −0.0574054 0.325562i 0.942559 0.334041i \(-0.108412\pi\)
−0.999964 + 0.00847836i \(0.997301\pi\)
\(524\) −1.57242e8 −0.0477431
\(525\) 6.83373e7 + 3.87560e8i 0.0206111 + 0.116891i
\(526\) 2.48840e8 4.31004e8i 0.0745539 0.129131i
\(527\) −7.55006e8 6.33525e8i −0.224705 0.188550i
\(528\) 4.28073e8 + 7.41443e8i 0.126561 + 0.219209i
\(529\) 8.18864e8 1.41831e9i 0.240501 0.416560i
\(530\) 5.00883e9 1.82306e9i 1.46140 0.531908i
\(531\) −2.08116e9 + 1.74630e9i −0.603220 + 0.506161i
\(532\) −6.29543e7 1.09040e8i −0.0181274 0.0313975i
\(533\) 9.61738e7 5.45429e8i 0.0275113 0.156025i
\(534\) −4.99092e7 + 2.83049e8i −0.0141836 + 0.0804391i
\(535\) −1.09569e9 9.19392e8i −0.309349 0.259575i
\(536\) 5.25872e9 + 1.91402e9i 1.47504 + 0.536870i
\(537\) 2.69950e8 + 9.82538e7i 0.0752269 + 0.0273804i
\(538\) −1.74552e9 1.46466e9i −0.483266 0.405508i
\(539\) 4.38580e8 2.48731e9i 0.120639 0.684178i
\(540\) 3.34485e7 1.89696e8i 0.00914111 0.0518418i
\(541\) −2.20364e9 3.81681e9i −0.598343 1.03636i −0.993066 0.117560i \(-0.962493\pi\)
0.394723 0.918800i \(-0.370840\pi\)
\(542\) −9.12052e8 + 7.65302e8i −0.246049 + 0.206460i
\(543\) 3.86333e8 1.40614e8i 0.103553 0.0376902i
\(544\) −8.74938e7 + 1.51544e8i −0.0233013 + 0.0403591i
\(545\) −2.70421e9 4.68383e9i −0.715571 1.23941i
\(546\) −3.05643e8 2.56465e8i −0.0803601 0.0674301i
\(547\) −3.77765e6 + 6.54308e6i −0.000986884 + 0.00170933i −0.866518 0.499145i \(-0.833647\pi\)
0.865532 + 0.500854i \(0.166981\pi\)
\(548\) 3.97596e7 + 2.25488e8i 0.0103207 + 0.0585318i
\(549\) −5.42956e9 −1.40043
\(550\) 5.48468e8 + 3.11052e9i 0.140567 + 0.797193i
\(551\) 2.35077e8 1.97253e8i 0.0598659 0.0502335i
\(552\) −7.05362e8 2.56731e8i −0.178495 0.0649667i
\(553\) −5.86528e7 + 2.13479e7i −0.0147486 + 0.00536806i
\(554\) −6.73381e9 −1.68258
\(555\) 1.30009e9 + 4.18100e8i 0.322810 + 0.103814i
\(556\) −2.18514e8 −0.0539160
\(557\) −5.25393e9 + 1.91227e9i −1.28822 + 0.468875i −0.893143 0.449772i \(-0.851505\pi\)
−0.395080 + 0.918647i \(0.629283\pi\)
\(558\) −3.48452e9 1.26826e9i −0.849030 0.309022i
\(559\) 3.07033e9 2.57631e9i 0.743437 0.623818i
\(560\) −5.28359e8 2.99647e9i −0.127137 0.721028i
\(561\) −3.37477e8 −0.0807001
\(562\) 5.18257e8 + 2.93918e9i 0.123159 + 0.698472i
\(563\) 1.44691e9 2.50613e9i 0.341715 0.591867i −0.643037 0.765835i \(-0.722326\pi\)
0.984751 + 0.173968i \(0.0556591\pi\)
\(564\) −9.59268e6 8.04922e6i −0.00225146 0.00188920i
\(565\) 1.55870e9 + 2.69975e9i 0.363574 + 0.629729i
\(566\) −2.15945e9 + 3.74027e9i −0.500593 + 0.867053i
\(567\) 1.98743e9 7.23366e8i 0.457880 0.166655i
\(568\) 5.13073e9 4.30519e9i 1.17479 0.985765i
\(569\) −4.04116e9 6.99950e9i −0.919630 1.59285i −0.799977 0.600030i \(-0.795155\pi\)
−0.119653 0.992816i \(-0.538178\pi\)
\(570\) −1.87555e8 + 1.06368e9i −0.0424196 + 0.240574i
\(571\) 1.36881e9 7.76291e9i 0.307693 1.74501i −0.302860 0.953035i \(-0.597941\pi\)
0.610552 0.791976i \(-0.290947\pi\)
\(572\) 2.13945e8 + 1.79522e8i 0.0477988 + 0.0401079i
\(573\) −1.72010e9 6.26066e8i −0.381956 0.139021i
\(574\) −5.44901e8 1.98328e8i −0.120261 0.0437716i
\(575\) −1.95008e9 1.63631e9i −0.427775 0.358946i
\(576\) −7.94624e8 + 4.50654e9i −0.173254 + 0.982571i
\(577\) −4.14201e8 + 2.34905e9i −0.0897626 + 0.509069i 0.906464 + 0.422282i \(0.138771\pi\)
−0.996227 + 0.0867866i \(0.972340\pi\)
\(578\) −2.03741e9 3.52890e9i −0.438865 0.760137i
\(579\) −4.58819e8 + 3.84995e8i −0.0982351 + 0.0824290i
\(580\) −4.90985e7 + 1.78704e7i −0.0104489 + 0.00380308i
\(581\) 4.86468e8 8.42588e8i 0.102905 0.178237i
\(582\) 2.13599e8 + 3.69965e8i 0.0449127 + 0.0777911i
\(583\) 4.85749e9 + 4.07592e9i 1.01525 + 0.851894i
\(584\) 2.77500e9 4.80644e9i 0.576525 0.998570i
\(585\) 7.48412e8 + 4.24445e9i 0.154559 + 0.876549i
\(586\) 8.87687e9 1.82229
\(587\) 8.24100e8 + 4.67371e9i 0.168169 + 0.953736i 0.945736 + 0.324935i \(0.105343\pi\)
−0.777567 + 0.628800i \(0.783546\pi\)
\(588\) −4.91906e7 + 4.12758e7i −0.00997841 + 0.00837288i
\(589\) −3.52618e9 1.28342e9i −0.711051 0.258801i
\(590\) −5.04349e9 + 1.83568e9i −1.01100 + 0.367972i
\(591\) −8.06266e7 −0.0160665
\(592\) −4.38925e9 1.41155e9i −0.869489 0.279622i
\(593\) 8.09275e9 1.59369 0.796846 0.604182i \(-0.206500\pi\)
0.796846 + 0.604182i \(0.206500\pi\)
\(594\) −2.46891e9 + 8.98610e8i −0.483340 + 0.175922i
\(595\) 1.12704e9 + 4.10211e8i 0.219347 + 0.0798358i
\(596\) −5.94896e8 + 4.99177e8i −0.115101 + 0.0965812i
\(597\) 1.59984e8 + 9.07312e8i 0.0307727 + 0.174521i
\(598\) 2.58090e9 0.493535
\(599\) −9.84103e8 5.58113e9i −0.187088 1.06103i −0.923243 0.384217i \(-0.874471\pi\)
0.736154 0.676814i \(-0.236640\pi\)
\(600\) 5.40672e8 9.36472e8i 0.102189 0.176997i
\(601\) 3.46276e9 + 2.90560e9i 0.650672 + 0.545978i 0.907275 0.420539i \(-0.138159\pi\)
−0.256603 + 0.966517i \(0.582603\pi\)
\(602\) −2.09820e9 3.63419e9i −0.391976 0.678922i
\(603\) −3.81470e9 + 6.60725e9i −0.708516 + 1.22719i
\(604\) −2.42308e8 + 8.81929e7i −0.0447444 + 0.0162856i
\(605\) −1.03247e9 + 8.66342e8i −0.189554 + 0.159054i
\(606\) −7.84982e8 1.35963e9i −0.143287 0.248180i
\(607\) 2.67927e8 1.51949e9i 0.0486246 0.275764i −0.950795 0.309820i \(-0.899731\pi\)
0.999420 + 0.0340560i \(0.0108425\pi\)
\(608\) −1.15691e8 + 6.56116e8i −0.0208755 + 0.118391i
\(609\) 6.80229e7 + 5.70780e7i 0.0122038 + 0.0102402i
\(610\) −1.00796e10 3.66868e9i −1.79800 0.654418i
\(611\) 5.44817e8 + 1.98297e8i 0.0966288 + 0.0351700i
\(612\) −9.48986e7 7.96294e7i −0.0167352 0.0140425i
\(613\) −8.42050e8 + 4.77550e9i −0.147647 + 0.837350i 0.817556 + 0.575849i \(0.195329\pi\)
−0.965203 + 0.261501i \(0.915783\pi\)
\(614\) −1.02136e9 + 5.79240e9i −0.178069 + 1.00988i
\(615\) −2.16920e8 3.75717e8i −0.0376043 0.0651325i
\(616\) 3.01635e9 2.53102e9i 0.519935 0.436277i
\(617\) −6.32181e8 + 2.30095e8i −0.108354 + 0.0394375i −0.395628 0.918411i \(-0.629473\pi\)
0.287274 + 0.957848i \(0.407251\pi\)
\(618\) 1.33485e9 2.31202e9i 0.227495 0.394032i
\(619\) 4.02885e9 + 6.97818e9i 0.682754 + 1.18256i 0.974137 + 0.225958i \(0.0725511\pi\)
−0.291384 + 0.956606i \(0.594116\pi\)
\(620\) 4.89439e8 + 4.10688e8i 0.0824760 + 0.0692056i
\(621\) 1.05878e9 1.83387e9i 0.177414 0.307289i
\(622\) 1.06223e9 + 6.02419e9i 0.176991 + 1.00376i
\(623\) 1.21515e9 0.201336
\(624\) 1.75003e8 + 9.92493e8i 0.0288337 + 0.163524i
\(625\) −5.49051e9 + 4.60709e9i −0.899566 + 0.754825i
\(626\) −5.31899e8 1.93595e8i −0.0866601 0.0315417i
\(627\) −1.20740e9 + 4.39459e8i −0.195621 + 0.0712003i
\(628\) 3.92096e8 0.0631733
\(629\) 1.34695e9 1.22016e9i 0.215811 0.195497i
\(630\) 4.51248e9 0.718992
\(631\) 1.13281e9 4.12308e8i 0.179496 0.0653310i −0.250709 0.968063i \(-0.580664\pi\)
0.430204 + 0.902731i \(0.358441\pi\)
\(632\) 1.61163e8 + 5.86586e7i 0.0253954 + 0.00924319i
\(633\) 2.61960e8 2.19810e8i 0.0410508 0.0344457i
\(634\) −1.47375e9 8.35803e9i −0.229673 1.30254i
\(635\) 1.51466e10 2.34751
\(636\) −2.79948e7 1.58767e8i −0.00431497 0.0244714i
\(637\) 1.48654e9 2.57476e9i 0.227871 0.394684i
\(638\) 5.45945e8 + 4.58102e8i 0.0832294 + 0.0698377i
\(639\) 4.56553e9 + 7.90773e9i 0.692211 + 1.19894i
\(640\) −3.81312e9 + 6.60452e9i −0.574977 + 0.995890i
\(641\) −7.55496e9 + 2.74978e9i −1.13300 + 0.412377i −0.839380 0.543545i \(-0.817082\pi\)
−0.293618 + 0.955923i \(0.594859\pi\)
\(642\) 3.79970e8 3.18833e8i 0.0566731 0.0475544i
\(643\) −4.31249e9 7.46946e9i −0.639720 1.10803i −0.985494 0.169710i \(-0.945717\pi\)
0.345774 0.938318i \(-0.387616\pi\)
\(644\) −4.09244e7 + 2.32094e8i −0.00603784 + 0.0342423i
\(645\) 5.45186e8 3.09190e9i 0.0799992 0.453698i
\(646\) 1.10110e9 + 9.23933e8i 0.160699 + 0.134842i
\(647\) 5.41286e9 + 1.97012e9i 0.785710 + 0.285975i 0.703551 0.710644i \(-0.251597\pi\)
0.0821582 + 0.996619i \(0.473819\pi\)
\(648\) −5.46096e9 1.98763e9i −0.788418 0.286961i
\(649\) −4.89110e9 4.10412e9i −0.702345 0.589337i
\(650\) −6.45625e8 + 3.66152e9i −0.0922112 + 0.522955i
\(651\) 1.88553e8 1.06934e9i 0.0267855 0.151908i
\(652\) −5.55180e8 9.61601e8i −0.0784454 0.135871i
\(653\) −2.02950e9 + 1.70295e9i −0.285228 + 0.239335i −0.774164 0.632985i \(-0.781830\pi\)
0.488936 + 0.872320i \(0.337385\pi\)
\(654\) 1.76246e9 6.41483e8i 0.246375 0.0896733i
\(655\) 2.85142e9 4.93881e9i 0.396476 0.686717i
\(656\) 7.32348e8 + 1.26846e9i 0.101287 + 0.175434i
\(657\) 5.79619e9 + 4.86358e9i 0.797378 + 0.669079i
\(658\) 3.03515e8 5.25704e8i 0.0415327 0.0719367i
\(659\) 2.92764e8 + 1.66035e9i 0.0398491 + 0.225995i 0.998228 0.0595037i \(-0.0189518\pi\)
−0.958379 + 0.285499i \(0.907841\pi\)
\(660\) 2.18772e8 0.0296202
\(661\) 2.06536e9 + 1.17132e10i 0.278157 + 1.57751i 0.728750 + 0.684780i \(0.240102\pi\)
−0.450593 + 0.892730i \(0.648787\pi\)
\(662\) 7.60175e9 6.37863e9i 1.01838 0.854524i
\(663\) −3.73301e8 1.35870e8i −0.0497464 0.0181062i
\(664\) −2.51216e9 + 9.14351e8i −0.333011 + 0.121206i
\(665\) 4.56644e9 0.602146
\(666\) 3.19197e9 6.04708e9i 0.418696 0.793207i
\(667\) −5.74397e8 −0.0749501
\(668\) 4.24501e8 1.54506e8i 0.0551012 0.0200552i
\(669\) −1.69847e9 6.18191e8i −0.219314 0.0798236i
\(670\) −1.15461e10 + 9.68837e9i −1.48312 + 1.24448i
\(671\) −2.21583e9 1.25666e10i −0.283144 1.60579i
\(672\) −1.92785e8 −0.0245065
\(673\) 1.42679e9 + 8.09175e9i 0.180430 + 1.02327i 0.931688 + 0.363260i \(0.118336\pi\)
−0.751258 + 0.660009i \(0.770553\pi\)
\(674\) −2.49107e8 + 4.31466e8i −0.0313384 + 0.0542797i
\(675\) 2.33684e9 + 1.96084e9i 0.292460 + 0.245403i
\(676\) −1.57774e8 2.73272e8i −0.0196436 0.0340237i
\(677\) 3.31425e9 5.74045e9i 0.410511 0.711026i −0.584434 0.811441i \(-0.698684\pi\)
0.994946 + 0.100415i \(0.0320169\pi\)
\(678\) −1.01588e9 + 3.69749e8i −0.125181 + 0.0455621i
\(679\) 1.38357e9 1.16096e9i 0.169613 0.142322i
\(680\) −1.64779e9 2.85406e9i −0.200965 0.348082i
\(681\) 2.33440e8 1.32390e9i 0.0283244 0.160635i
\(682\) 1.51331e9 8.58240e9i 0.182676 1.03601i
\(683\) 7.37346e9 + 6.18707e9i 0.885521 + 0.743041i 0.967307 0.253609i \(-0.0816178\pi\)
−0.0817854 + 0.996650i \(0.526062\pi\)
\(684\) −4.43214e8 1.61317e8i −0.0529563 0.0192745i
\(685\) −7.80333e9 2.84018e9i −0.927605 0.337621i
\(686\) −6.12204e9 5.13700e9i −0.724038 0.607540i
\(687\) −6.15988e8 + 3.49344e9i −0.0724809 + 0.411060i
\(688\) −1.84061e9 + 1.04386e10i −0.215478 + 1.22204i
\(689\) 3.73213e9 + 6.46423e9i 0.434700 + 0.752922i
\(690\) 1.54871e9 1.29952e9i 0.179472 0.150595i
\(691\) −1.37658e9 + 5.01034e8i −0.158719 + 0.0577689i −0.420158 0.907451i \(-0.638025\pi\)
0.261439 + 0.965220i \(0.415803\pi\)
\(692\) −4.38676e8 + 7.59809e8i −0.0503237 + 0.0871631i
\(693\) 2.68407e9 + 4.64894e9i 0.306356 + 0.530625i
\(694\) −6.44411e9 5.40725e9i −0.731821 0.614071i
\(695\) 3.96252e9 6.86328e9i 0.447739 0.775506i
\(696\) −4.23690e7 2.40286e8i −0.00476338 0.0270145i
\(697\) −5.77357e8 −0.0645847
\(698\) −9.74577e8 5.52710e9i −0.108473 0.615182i
\(699\) −3.90870e8 + 3.27979e8i −0.0432875 + 0.0363225i
\(700\) −3.19033e8 1.16119e8i −0.0351554 0.0127955i
\(701\) −1.03210e10 + 3.75653e9i −1.13164 + 0.411883i −0.838887 0.544305i \(-0.816793\pi\)
−0.292752 + 0.956188i \(0.594571\pi\)
\(702\) −3.09278e9 −0.337418
\(703\) 3.23013e9 6.11939e9i 0.350653 0.664300i
\(704\) −1.07545e10 −1.16168
\(705\) 4.26770e8 1.55332e8i 0.0458704 0.0166954i
\(706\) 1.06883e10 + 3.89021e9i 1.14312 + 0.416061i
\(707\) −5.08467e9 + 4.26654e9i −0.541121 + 0.454055i
\(708\) 2.81886e7 + 1.59865e8i 0.00298508 + 0.0169293i
\(709\) 1.09166e10 1.15034 0.575168 0.818035i \(-0.304937\pi\)
0.575168 + 0.818035i \(0.304937\pi\)
\(710\) 3.13245e9 + 1.77650e10i 0.328458 + 1.86278i
\(711\) −1.16908e8 + 2.02491e8i −0.0121984 + 0.0211282i
\(712\) −2.55776e9 2.14622e9i −0.265570 0.222840i
\(713\) 3.51192e9 + 6.08283e9i 0.362854 + 0.628481i
\(714\) −2.07964e8 + 3.60204e8i −0.0213818 + 0.0370344i
\(715\) −9.51824e9 + 3.46436e9i −0.973836 + 0.354447i
\(716\) −1.89851e8 + 1.59304e8i −0.0193294 + 0.0162193i
\(717\) −1.01036e9 1.74999e9i −0.102366 0.177304i
\(718\) 1.41453e9 8.02222e9i 0.142619 0.808833i
\(719\) 2.25326e9 1.27788e10i 0.226079 1.28216i −0.634534 0.772895i \(-0.718808\pi\)
0.860613 0.509260i \(-0.170081\pi\)
\(720\) −8.73142e9 7.32653e9i −0.871809 0.731535i
\(721\) −1.06063e10 3.86039e9i −1.05388 0.383582i
\(722\) −3.97140e9 1.44547e9i −0.392703 0.142932i
\(723\) 2.86321e9 + 2.40252e9i 0.281754 + 0.236420i
\(724\) −6.15897e7 + 3.49293e8i −0.00603147 + 0.0342062i
\(725\) 1.43688e8 8.14896e8i 0.0140035 0.0794180i
\(726\) −2.33698e8 4.04776e8i −0.0226661 0.0392588i
\(727\) 7.14731e9 5.99731e9i 0.689878 0.578877i −0.228996 0.973427i \(-0.573544\pi\)
0.918874 + 0.394551i \(0.129100\pi\)
\(728\) 4.35554e9 1.58529e9i 0.418391 0.152282i
\(729\) 3.30578e9 5.72579e9i 0.316030 0.547380i
\(730\) 7.47398e9 + 1.29453e10i 0.711086 + 1.23164i
\(731\) −3.20069e9 2.68569e9i −0.303062 0.254300i
\(732\) −1.62213e8 + 2.80961e8i −0.0152861 + 0.0264763i
\(733\) 3.51906e9 + 1.99576e10i 0.330037 + 1.87173i 0.471615 + 0.881804i \(0.343671\pi\)
−0.141578 + 0.989927i \(0.545218\pi\)
\(734\) 5.47676e9 0.511196
\(735\) −4.04409e8 2.29351e9i −0.0375677 0.213057i
\(736\) 9.55299e8 8.01591e8i 0.0883216 0.0741106i
\(737\) −1.68491e10 6.13257e9i −1.55039 0.564295i
\(738\) −2.04122e9 + 7.42944e8i −0.186936 + 0.0680392i
\(739\) 1.41038e10 1.28552 0.642761 0.766067i \(-0.277789\pi\)
0.642761 + 0.766067i \(0.277789\pi\)
\(740\) −8.73169e8 + 7.90979e8i −0.0792113 + 0.0717553i
\(741\) −1.51250e9 −0.136562
\(742\) 7.34374e9 2.67290e9i 0.659939 0.240198i
\(743\) −1.42168e10 5.17451e9i −1.27158 0.462816i −0.383938 0.923359i \(-0.625433\pi\)
−0.887637 + 0.460543i \(0.847655\pi\)
\(744\) −2.28557e9 + 1.91782e9i −0.203465 + 0.170727i
\(745\) −4.89079e9 2.77371e10i −0.433343 2.45761i
\(746\) 1.75904e10 1.55128
\(747\) −6.32889e8 3.58929e9i −0.0555527 0.315055i
\(748\) 1.45572e8 2.52137e8i 0.0127181 0.0220283i
\(749\) −1.60646e9 1.34798e9i −0.139695 0.117218i
\(750\) −4.22438e8 7.31683e8i −0.0365635 0.0633299i
\(751\) −9.57941e8 + 1.65920e9i −0.0825276 + 0.142942i −0.904335 0.426823i \(-0.859633\pi\)
0.821807 + 0.569765i \(0.192966\pi\)
\(752\) −1.44083e9 + 5.24418e8i −0.123552 + 0.0449692i
\(753\) −3.94506e9 + 3.31029e9i −0.336721 + 0.282543i
\(754\) 4.19463e8 + 7.26531e8i 0.0356364 + 0.0617241i
\(755\) 1.62396e9 9.20992e9i 0.137328 0.778828i
\(756\) 4.90409e7 2.78125e8i 0.00412793 0.0234107i
\(757\) 3.82508e9 + 3.20962e9i 0.320483 + 0.268917i 0.788809 0.614639i \(-0.210698\pi\)
−0.468326 + 0.883556i \(0.655143\pi\)
\(758\) −4.17633e9 1.52006e9i −0.348299 0.126770i
\(759\) 2.26000e9 + 8.22573e8i 0.187613 + 0.0682854i
\(760\) −9.61187e9 8.06532e9i −0.794256 0.666460i
\(761\) 1.13391e8 6.43070e8i 0.00932676 0.0528947i −0.979789 0.200033i \(-0.935895\pi\)
0.989116 + 0.147138i \(0.0470062\pi\)
\(762\) −9.12114e8 + 5.17286e9i −0.0746804 + 0.423534i
\(763\) −3.96481e9 6.86725e9i −0.323137 0.559689i
\(764\)