Properties

Label 37.8.f.a.7.20
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 7.20
Character \(\chi\) \(=\) 37.7
Dual form 37.8.f.a.16.20

$q$-expansion

\(f(q)\) \(=\) \(q+(16.4964 - 6.00419i) q^{2} +(64.3192 + 23.4103i) q^{3} +(138.026 - 115.818i) q^{4} +(23.4987 + 133.267i) q^{5} +1201.59 q^{6} +(-96.3778 - 546.586i) q^{7} +(458.016 - 793.306i) q^{8} +(1913.58 + 1605.68i) q^{9} +O(q^{10})\) \(q+(16.4964 - 6.00419i) q^{2} +(64.3192 + 23.4103i) q^{3} +(138.026 - 115.818i) q^{4} +(23.4987 + 133.267i) q^{5} +1201.59 q^{6} +(-96.3778 - 546.586i) q^{7} +(458.016 - 793.306i) q^{8} +(1913.58 + 1605.68i) q^{9} +(1187.81 + 2057.34i) q^{10} +(1368.96 - 2371.10i) q^{11} +(11589.1 - 4218.07i) q^{12} +(-4632.81 + 3887.39i) q^{13} +(-4871.69 - 8438.01i) q^{14} +(-1608.41 + 9121.76i) q^{15} +(-1212.43 + 6876.03i) q^{16} +(-2262.74 - 1898.66i) q^{17} +(41207.9 + 14998.4i) q^{18} +(-18878.4 - 6871.16i) q^{19} +(18678.2 + 15672.8i) q^{20} +(6596.78 - 37412.2i) q^{21} +(8346.27 - 47334.0i) q^{22} +(-31572.3 - 54684.8i) q^{23} +(48030.7 - 40302.5i) q^{24} +(56205.4 - 20457.1i) q^{25} +(-53084.0 + 91944.2i) q^{26} +(10643.4 + 18434.9i) q^{27} +(-76607.0 - 64280.9i) q^{28} +(-21304.9 + 36901.2i) q^{29} +(28235.8 + 160133. i) q^{30} -42681.3 q^{31} +(41644.9 + 236180. i) q^{32} +(143558. - 120460. i) q^{33} +(-48726.9 - 17735.2i) q^{34} +(70577.4 - 25688.1i) q^{35} +450090. q^{36} +(303528. - 52940.5i) q^{37} -352680. q^{38} +(-388984. + 141578. i) q^{39} +(116485. + 42397.0i) q^{40} +(-516084. + 433046. i) q^{41} +(-115807. - 656773. i) q^{42} -966988. q^{43} +(-85663.8 - 485824. i) q^{44} +(-169019. + 292749. i) q^{45} +(-849166. - 712535. i) q^{46} +(226274. + 391918. i) q^{47} +(-238952. + 413877. i) q^{48} +(484410. - 176311. i) q^{49} +(804357. - 674936. i) q^{50} +(-101089. - 175092. i) q^{51} +(-189221. + 1.07312e6i) q^{52} +(-211704. + 1.20063e6i) q^{53} +(286264. + 240204. i) q^{54} +(348159. + 126720. i) q^{55} +(-477752. - 173888. i) q^{56} +(-1.05339e6 - 883895. i) q^{57} +(-129892. + 736654. i) q^{58} +(187829. - 1.06523e6i) q^{59} +(834459. + 1.44533e6i) q^{60} +(1.75373e6 - 1.47156e6i) q^{61} +(-704086. + 256266. i) q^{62} +(693216. - 1.20069e6i) q^{63} +(1.65820e6 + 2.87209e6i) q^{64} +(-626928. - 526055. i) q^{65} +(1.64493e6 - 2.84910e6i) q^{66} +(367637. + 2.08497e6i) q^{67} -532216. q^{68} +(-750518. - 4.25640e6i) q^{69} +(1.01003e6 - 847520. i) q^{70} +(5.14406e6 + 1.87229e6i) q^{71} +(2.15024e6 - 782625. i) q^{72} +5.11369e6 q^{73} +(4.68924e6 - 2.69576e6i) q^{74} +4.09399e6 q^{75} +(-3.40151e6 + 1.23805e6i) q^{76} +(-1.42795e6 - 519731. i) q^{77} +(-5.56675e6 + 4.67106e6i) q^{78} +(282809. + 1.60389e6i) q^{79} -944842. q^{80} +(-695652. - 3.94524e6i) q^{81} +(-5.91342e6 + 1.02424e7i) q^{82} +(-4.01567e6 - 3.36955e6i) q^{83} +(-3.42247e6 - 5.92789e6i) q^{84} +(199859. - 346166. i) q^{85} +(-1.59518e7 + 5.80597e6i) q^{86} +(-2.23418e6 + 1.87470e6i) q^{87} +(-1.25401e6 - 2.17200e6i) q^{88} +(1.56085e6 - 8.85201e6i) q^{89} +(-1.03047e6 + 5.84411e6i) q^{90} +(2.57129e6 + 2.15757e6i) q^{91} +(-1.06913e7 - 3.89131e6i) q^{92} +(-2.74523e6 - 999180. i) q^{93} +(6.08585e6 + 5.10663e6i) q^{94} +(472087. - 2.67734e6i) q^{95} +(-2.85047e6 + 1.61658e7i) q^{96} +(-2.92526e6 - 5.06670e6i) q^{97} +(6.93240e6 - 5.81697e6i) q^{98} +(6.42684e6 - 2.33918e6i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 16.4964 6.00419i 1.45809 0.530700i 0.513249 0.858240i \(-0.328442\pi\)
0.944838 + 0.327539i \(0.106219\pi\)
\(3\) 64.3192 + 23.4103i 1.37536 + 0.500590i 0.920768 0.390111i \(-0.127563\pi\)
0.454591 + 0.890700i \(0.349785\pi\)
\(4\) 138.026 115.818i 1.07833 0.904826i
\(5\) 23.4987 + 133.267i 0.0840713 + 0.476792i 0.997553 + 0.0699126i \(0.0222720\pi\)
−0.913482 + 0.406880i \(0.866617\pi\)
\(6\) 1201.59 2.27106
\(7\) −96.3778 546.586i −0.106202 0.602303i −0.990733 0.135822i \(-0.956633\pi\)
0.884531 0.466481i \(-0.154479\pi\)
\(8\) 458.016 793.306i 0.316275 0.547805i
\(9\) 1913.58 + 1605.68i 0.874978 + 0.734194i
\(10\) 1187.81 + 2057.34i 0.375617 + 0.650588i
\(11\) 1368.96 2371.10i 0.310110 0.537126i −0.668276 0.743913i \(-0.732968\pi\)
0.978386 + 0.206788i \(0.0663009\pi\)
\(12\) 11589.1 4218.07i 1.93604 0.704660i
\(13\) −4632.81 + 3887.39i −0.584848 + 0.490746i −0.886535 0.462661i \(-0.846895\pi\)
0.301687 + 0.953407i \(0.402450\pi\)
\(14\) −4871.69 8438.01i −0.474495 0.821849i
\(15\) −1608.41 + 9121.76i −0.123049 + 0.697846i
\(16\) −1212.43 + 6876.03i −0.0740009 + 0.419680i
\(17\) −2262.74 1898.66i −0.111703 0.0937296i 0.585226 0.810871i \(-0.301006\pi\)
−0.696928 + 0.717141i \(0.745450\pi\)
\(18\) 41207.9 + 14998.4i 1.66543 + 0.606167i
\(19\) −18878.4 6871.16i −0.631432 0.229823i 0.00642224 0.999979i \(-0.497956\pi\)
−0.637855 + 0.770157i \(0.720178\pi\)
\(20\) 18678.2 + 15672.8i 0.522071 + 0.438069i
\(21\) 6596.78 37412.2i 0.155441 0.881547i
\(22\) 8346.27 47334.0i 0.167114 0.947751i
\(23\) −31572.3 54684.8i −0.541076 0.937172i −0.998843 0.0480991i \(-0.984684\pi\)
0.457766 0.889073i \(-0.348650\pi\)
\(24\) 48030.7 40302.5i 0.709218 0.595104i
\(25\) 56205.4 20457.1i 0.719430 0.261851i
\(26\) −53084.0 + 91944.2i −0.592320 + 1.02593i
\(27\) 10643.4 + 18434.9i 0.104066 + 0.180247i
\(28\) −76607.0 64280.9i −0.659501 0.553387i
\(29\) −21304.9 + 36901.2i −0.162213 + 0.280962i −0.935662 0.352897i \(-0.885197\pi\)
0.773449 + 0.633859i \(0.218530\pi\)
\(30\) 28235.8 + 160133.i 0.190931 + 1.08282i
\(31\) −42681.3 −0.257319 −0.128659 0.991689i \(-0.541067\pi\)
−0.128659 + 0.991689i \(0.541067\pi\)
\(32\) 41644.9 + 236180.i 0.224666 + 1.27414i
\(33\) 143558. 120460.i 0.695392 0.583503i
\(34\) −48726.9 17735.2i −0.212614 0.0773853i
\(35\) 70577.4 25688.1i 0.278245 0.101273i
\(36\) 450090. 1.60783
\(37\) 303528. 52940.5i 0.985128 0.171823i
\(38\) −352680. −1.04265
\(39\) −388984. + 141578.i −1.05004 + 0.382183i
\(40\) 116485. + 42397.0i 0.287779 + 0.104743i
\(41\) −516084. + 433046.i −1.16944 + 0.981275i −0.999991 0.00426478i \(-0.998642\pi\)
−0.169447 + 0.985539i \(0.554198\pi\)
\(42\) −115807. 656773.i −0.241191 1.36786i
\(43\) −966988. −1.85473 −0.927366 0.374155i \(-0.877933\pi\)
−0.927366 + 0.374155i \(0.877933\pi\)
\(44\) −85663.8 485824.i −0.151605 0.859794i
\(45\) −169019. + 292749.i −0.276497 + 0.478907i
\(46\) −849166. 712535.i −1.28629 1.07933i
\(47\) 226274. + 391918.i 0.317901 + 0.550621i 0.980050 0.198751i \(-0.0636886\pi\)
−0.662149 + 0.749373i \(0.730355\pi\)
\(48\) −238952. + 413877.i −0.311865 + 0.540166i
\(49\) 484410. 176311.i 0.588202 0.214088i
\(50\) 804357. 674936.i 0.910027 0.763603i
\(51\) −101089. 175092.i −0.106711 0.184829i
\(52\) −189221. + 1.07312e6i −0.186620 + 1.05837i
\(53\) −211704. + 1.20063e6i −0.195327 + 1.10776i 0.716624 + 0.697459i \(0.245686\pi\)
−0.911952 + 0.410298i \(0.865425\pi\)
\(54\) 286264. + 240204.i 0.247394 + 0.207588i
\(55\) 348159. + 126720.i 0.282169 + 0.102701i
\(56\) −477752. 173888.i −0.363534 0.132316i
\(57\) −1.05339e6 883895.i −0.753399 0.632177i
\(58\) −129892. + 736654.i −0.0874147 + 0.495753i
\(59\) 187829. 1.06523e6i 0.119064 0.675245i −0.865594 0.500747i \(-0.833059\pi\)
0.984658 0.174498i \(-0.0558302\pi\)
\(60\) 834459. + 1.44533e6i 0.498742 + 0.863846i
\(61\) 1.75373e6 1.47156e6i 0.989256 0.830085i 0.00379653 0.999993i \(-0.498792\pi\)
0.985460 + 0.169908i \(0.0543471\pi\)
\(62\) −704086. + 256266.i −0.375193 + 0.136559i
\(63\) 693216. 1.20069e6i 0.349283 0.604975i
\(64\) 1.65820e6 + 2.87209e6i 0.790693 + 1.36952i
\(65\) −626928. 526055.i −0.283153 0.237593i
\(66\) 1.64493e6 2.84910e6i 0.704276 1.21984i
\(67\) 367637. + 2.08497e6i 0.149333 + 0.846912i 0.963785 + 0.266680i \(0.0859268\pi\)
−0.814452 + 0.580231i \(0.802962\pi\)
\(68\) −532216. −0.205261
\(69\) −750518. 4.25640e6i −0.275036 1.55980i
\(70\) 1.01003e6 847520.i 0.351960 0.295329i
\(71\) 5.14406e6 + 1.87229e6i 1.70570 + 0.620823i 0.996454 0.0841395i \(-0.0268142\pi\)
0.709244 + 0.704963i \(0.249036\pi\)
\(72\) 2.15024e6 782625.i 0.678929 0.247110i
\(73\) 5.11369e6 1.53852 0.769262 0.638934i \(-0.220624\pi\)
0.769262 + 0.638934i \(0.220624\pi\)
\(74\) 4.68924e6 2.69576e6i 1.34522 0.773341i
\(75\) 4.09399e6 1.12055
\(76\) −3.40151e6 + 1.23805e6i −0.888842 + 0.323512i
\(77\) −1.42795e6 519731.i −0.356447 0.129736i
\(78\) −5.56675e6 + 4.67106e6i −1.32822 + 1.11451i
\(79\) 282809. + 1.60389e6i 0.0645355 + 0.365999i 0.999923 + 0.0123756i \(0.00393936\pi\)
−0.935388 + 0.353623i \(0.884950\pi\)
\(80\) −944842. −0.206321
\(81\) −695652. 3.94524e6i −0.145444 0.824851i
\(82\) −5.91342e6 + 1.02424e7i −1.18438 + 2.05140i
\(83\) −4.01567e6 3.36955e6i −0.770877 0.646842i 0.170057 0.985434i \(-0.445605\pi\)
−0.940933 + 0.338592i \(0.890049\pi\)
\(84\) −3.42247e6 5.92789e6i −0.630031 1.09125i
\(85\) 199859. 346166.i 0.0352986 0.0611389i
\(86\) −1.59518e7 + 5.80597e6i −2.70436 + 0.984307i
\(87\) −2.23418e6 + 1.87470e6i −0.363748 + 0.305221i
\(88\) −1.25401e6 2.17200e6i −0.196160 0.339759i
\(89\) 1.56085e6 8.85201e6i 0.234690 1.33100i −0.608574 0.793497i \(-0.708258\pi\)
0.843264 0.537499i \(-0.180631\pi\)
\(90\) −1.03047e6 + 5.84411e6i −0.149001 + 0.845026i
\(91\) 2.57129e6 + 2.15757e6i 0.357690 + 0.300138i
\(92\) −1.06913e7 3.89131e6i −1.43144 0.521000i
\(93\) −2.74523e6 999180.i −0.353906 0.128811i
\(94\) 6.08585e6 + 5.10663e6i 0.755742 + 0.634143i
\(95\) 472087. 2.67734e6i 0.0564923 0.320384i
\(96\) −2.85047e6 + 1.61658e7i −0.328827 + 1.86487i
\(97\) −2.92526e6 5.06670e6i −0.325435 0.563669i 0.656166 0.754617i \(-0.272177\pi\)
−0.981600 + 0.190948i \(0.938844\pi\)
\(98\) 6.93240e6 5.81697e6i 0.744033 0.624318i
\(99\) 6.42684e6 2.33918e6i 0.665693 0.242293i
\(100\) 5.38853e6 9.33321e6i 0.538853 0.933321i
\(101\) −2.15284e6 3.72883e6i −0.207916 0.360121i 0.743142 0.669134i \(-0.233335\pi\)
−0.951058 + 0.309013i \(0.900001\pi\)
\(102\) −2.71889e6 2.28142e6i −0.253683 0.212865i
\(103\) 266144. 460975.i 0.0239986 0.0415668i −0.853777 0.520639i \(-0.825694\pi\)
0.877775 + 0.479073i \(0.159027\pi\)
\(104\) 961992. + 5.45573e6i 0.0838600 + 0.475594i
\(105\) 5.14084e6 0.433383
\(106\) 3.71648e6 + 2.10772e7i 0.303082 + 1.71887i
\(107\) −1.40223e6 + 1.17661e6i −0.110656 + 0.0928514i −0.696437 0.717618i \(-0.745232\pi\)
0.585781 + 0.810469i \(0.300788\pi\)
\(108\) 3.60416e6 + 1.31181e6i 0.275309 + 0.100204i
\(109\) 2.67230e6 972636.i 0.197648 0.0719379i −0.241300 0.970451i \(-0.577574\pi\)
0.438947 + 0.898513i \(0.355351\pi\)
\(110\) 6.50422e6 0.465930
\(111\) 2.07620e7 + 3.70058e6i 1.44092 + 0.256826i
\(112\) 3.87519e6 0.260634
\(113\) 1.12598e7 4.09823e6i 0.734102 0.267191i 0.0522016 0.998637i \(-0.483376\pi\)
0.681900 + 0.731445i \(0.261154\pi\)
\(114\) −2.26841e7 8.25634e6i −1.43402 0.521940i
\(115\) 6.54580e6 5.49258e6i 0.401347 0.336770i
\(116\) 1.33318e6 + 7.56081e6i 0.0793020 + 0.449744i
\(117\) −1.51072e7 −0.872032
\(118\) −3.29735e6 1.87002e7i −0.184747 1.04775i
\(119\) −819705. + 1.41977e6i −0.0445906 + 0.0772332i
\(120\) 6.49967e6 + 5.45387e6i 0.343366 + 0.288118i
\(121\) 5.99550e6 + 1.03845e7i 0.307664 + 0.532890i
\(122\) 2.00947e7 3.48051e7i 1.00190 1.73533i
\(123\) −4.33318e7 + 1.57715e7i −2.09961 + 0.764196i
\(124\) −5.89114e6 + 4.94325e6i −0.277475 + 0.232829i
\(125\) 9.33309e6 + 1.61654e7i 0.427406 + 0.740288i
\(126\) 4.22641e6 2.39692e7i 0.188224 1.06747i
\(127\) −2.72844e6 + 1.54738e7i −0.118196 + 0.670321i 0.866922 + 0.498443i \(0.166095\pi\)
−0.985118 + 0.171878i \(0.945016\pi\)
\(128\) 2.10833e7 + 1.76910e7i 0.888596 + 0.745621i
\(129\) −6.21958e7 2.26374e7i −2.55092 0.928460i
\(130\) −1.35006e7 4.91380e6i −0.538952 0.196163i
\(131\) 1.94635e7 + 1.63318e7i 0.756435 + 0.634724i 0.937196 0.348803i \(-0.113412\pi\)
−0.180761 + 0.983527i \(0.557856\pi\)
\(132\) 5.86344e6 3.32532e7i 0.221893 1.25842i
\(133\) −1.93622e6 + 1.09809e7i −0.0713633 + 0.404722i
\(134\) 1.85832e7 + 3.21871e7i 0.667197 + 1.15562i
\(135\) −2.20667e6 + 1.85162e6i −0.0771914 + 0.0647713i
\(136\) −2.54259e6 + 925428.i −0.0866743 + 0.0315469i
\(137\) −1.95979e7 + 3.39446e7i −0.651161 + 1.12784i 0.331681 + 0.943392i \(0.392384\pi\)
−0.982842 + 0.184452i \(0.940949\pi\)
\(138\) −3.79370e7 6.57088e7i −1.22881 2.12837i
\(139\) −2.28450e7 1.91693e7i −0.721506 0.605416i 0.206295 0.978490i \(-0.433859\pi\)
−0.927802 + 0.373074i \(0.878304\pi\)
\(140\) 6.76639e6 1.17197e7i 0.208406 0.360969i
\(141\) 5.37885e6 + 3.05050e7i 0.161593 + 0.916440i
\(142\) 9.60999e7 2.81653
\(143\) 2.87528e6 + 1.63065e7i 0.0822251 + 0.466322i
\(144\) −1.33608e7 + 1.12110e7i −0.372875 + 0.312880i
\(145\) −5.41836e6 1.97212e6i −0.147598 0.0537212i
\(146\) 8.43573e7 3.07035e7i 2.24330 0.816495i
\(147\) 3.52843e7 0.916160
\(148\) 3.57634e7 4.24611e7i 0.906823 1.07665i
\(149\) 3.59457e7 0.890215 0.445107 0.895477i \(-0.353165\pi\)
0.445107 + 0.895477i \(0.353165\pi\)
\(150\) 6.75360e7 2.45811e7i 1.63387 0.594678i
\(151\) −1.84106e7 6.70091e6i −0.435159 0.158385i 0.115146 0.993349i \(-0.463266\pi\)
−0.550305 + 0.834964i \(0.685489\pi\)
\(152\) −1.40975e7 + 1.18292e7i −0.325604 + 0.273215i
\(153\) −1.28128e6 7.26648e6i −0.0289216 0.164023i
\(154\) −2.66765e7 −0.588581
\(155\) −1.00295e6 5.68803e6i −0.0216331 0.122688i
\(156\) −3.72926e7 + 6.45928e7i −0.786479 + 1.36222i
\(157\) −4.21536e7 3.53711e7i −0.869333 0.729457i 0.0946244 0.995513i \(-0.469835\pi\)
−0.963958 + 0.266056i \(0.914279\pi\)
\(158\) 1.42954e7 + 2.47603e7i 0.288334 + 0.499409i
\(159\) −4.17237e7 + 7.22676e7i −0.823177 + 1.42578i
\(160\) −3.04965e7 + 1.10998e7i −0.588613 + 0.214238i
\(161\) −2.68471e7 + 2.25274e7i −0.506998 + 0.425422i
\(162\) −3.51637e7 6.09053e7i −0.649818 1.12552i
\(163\) 8.79656e6 4.98878e7i 0.159095 0.902272i −0.795851 0.605492i \(-0.792976\pi\)
0.954946 0.296780i \(-0.0959127\pi\)
\(164\) −2.10787e7 + 1.19543e8i −0.373156 + 2.11628i
\(165\) 1.94268e7 + 1.63010e7i 0.336672 + 0.282501i
\(166\) −8.64754e7 3.14745e7i −1.46728 0.534048i
\(167\) 4.69070e7 + 1.70728e7i 0.779346 + 0.283659i 0.700900 0.713260i \(-0.252782\pi\)
0.0784459 + 0.996918i \(0.475004\pi\)
\(168\) −2.66579e7 2.23686e7i −0.433754 0.363963i
\(169\) −4.54502e6 + 2.57761e7i −0.0724323 + 0.410784i
\(170\) 1.21850e6 6.91047e6i 0.0190219 0.107879i
\(171\) −2.50923e7 4.34611e7i −0.383755 0.664683i
\(172\) −1.33470e8 + 1.11994e8i −2.00001 + 1.67821i
\(173\) 6.37754e7 2.32123e7i 0.936465 0.340845i 0.171696 0.985150i \(-0.445075\pi\)
0.764769 + 0.644305i \(0.222853\pi\)
\(174\) −2.55998e7 + 4.43402e7i −0.368395 + 0.638080i
\(175\) −1.65985e7 2.87495e7i −0.234119 0.405506i
\(176\) 1.46440e7 + 1.22878e7i 0.202472 + 0.169894i
\(177\) 3.70183e7 6.41176e7i 0.501776 0.869102i
\(178\) −2.74008e7 1.55398e8i −0.364161 2.06526i
\(179\) −1.06628e8 −1.38959 −0.694796 0.719207i \(-0.744505\pi\)
−0.694796 + 0.719207i \(0.744505\pi\)
\(180\) 1.05765e7 + 5.99824e7i 0.135173 + 0.766602i
\(181\) 4.98984e6 4.18697e6i 0.0625477 0.0524838i −0.610978 0.791648i \(-0.709224\pi\)
0.673526 + 0.739164i \(0.264779\pi\)
\(182\) 5.53715e7 + 2.01536e7i 0.680826 + 0.247801i
\(183\) 1.47248e8 5.35939e7i 1.77611 0.646453i
\(184\) −5.78424e7 −0.684516
\(185\) 1.41877e7 + 3.92064e7i 0.164745 + 0.455256i
\(186\) −5.12855e7 −0.584385
\(187\) −7.59952e6 + 2.76600e6i −0.0849847 + 0.0309319i
\(188\) 7.66228e7 + 2.78884e7i 0.841019 + 0.306106i
\(189\) 9.05048e6 7.59425e6i 0.0975114 0.0818217i
\(190\) −8.28751e6 4.70008e7i −0.0876570 0.497128i
\(191\) −3.42851e6 −0.0356032 −0.0178016 0.999842i \(-0.505667\pi\)
−0.0178016 + 0.999842i \(0.505667\pi\)
\(192\) 3.94178e7 + 2.23550e8i 0.401919 + 2.27939i
\(193\) −5.48743e7 + 9.50451e7i −0.549438 + 0.951654i 0.448875 + 0.893594i \(0.351825\pi\)
−0.998313 + 0.0580597i \(0.981509\pi\)
\(194\) −7.86776e7 6.60184e7i −0.773651 0.649171i
\(195\) −2.80084e7 4.85120e7i −0.270500 0.468520i
\(196\) 4.64413e7 8.04388e7i 0.440564 0.763078i
\(197\) 6.52672e7 2.37553e7i 0.608223 0.221375i −0.0195023 0.999810i \(-0.506208\pi\)
0.627726 + 0.778435i \(0.283986\pi\)
\(198\) 9.19746e7 7.71759e7i 0.842054 0.706567i
\(199\) −8.45525e7 1.46449e8i −0.760573 1.31735i −0.942556 0.334049i \(-0.891585\pi\)
0.181983 0.983302i \(-0.441749\pi\)
\(200\) 9.51422e6 5.39578e7i 0.0840946 0.476924i
\(201\) −2.51636e7 + 1.42710e8i −0.218568 + 1.23956i
\(202\) −5.79027e7 4.85861e7i −0.494275 0.414746i
\(203\) 2.22230e7 + 8.08850e6i 0.186452 + 0.0678628i
\(204\) −3.42317e7 1.24593e7i −0.282308 0.102752i
\(205\) −6.98382e7 5.86012e7i −0.566180 0.475082i
\(206\) 1.62263e6 9.20238e6i 0.0129325 0.0733441i
\(207\) 2.73904e7 1.55339e8i 0.214636 1.21726i
\(208\) −2.11129e7 3.65686e7i −0.162677 0.281765i
\(209\) −4.21359e7 + 3.53562e7i −0.319257 + 0.267888i
\(210\) 8.48052e7 3.08666e7i 0.631910 0.229996i
\(211\) −9.06588e7 + 1.57026e8i −0.664387 + 1.15075i 0.315064 + 0.949071i \(0.397974\pi\)
−0.979451 + 0.201682i \(0.935359\pi\)
\(212\) 1.09834e8 + 1.90238e8i 0.791700 + 1.37126i
\(213\) 2.87031e8 + 2.40848e8i 2.03517 + 1.70771i
\(214\) −1.60671e7 + 2.78290e7i −0.112070 + 0.194111i
\(215\) −2.27229e7 1.28868e8i −0.155930 0.884322i
\(216\) 1.94994e7 0.131654
\(217\) 4.11353e6 + 2.33290e7i 0.0273279 + 0.154984i
\(218\) 3.82433e7 3.20899e7i 0.250010 0.209783i
\(219\) 3.28908e8 + 1.19713e8i 2.11602 + 0.770169i
\(220\) 6.27315e7 2.28324e7i 0.397197 0.144568i
\(221\) 1.78637e7 0.111327
\(222\) 3.64717e8 6.36129e7i 2.23728 0.390220i
\(223\) −1.34378e8 −0.811451 −0.405726 0.913995i \(-0.632981\pi\)
−0.405726 + 0.913995i \(0.632981\pi\)
\(224\) 1.25079e8 4.55250e7i 0.743560 0.270634i
\(225\) 1.40401e8 + 5.11018e7i 0.821734 + 0.299087i
\(226\) 1.61139e8 1.35212e8i 0.928585 0.779176i
\(227\) −3.41116e7 1.93456e8i −0.193558 1.09772i −0.914457 0.404682i \(-0.867382\pi\)
0.720899 0.693040i \(-0.243729\pi\)
\(228\) −2.47766e8 −1.38442
\(229\) 3.15794e7 + 1.79096e8i 0.173772 + 0.985510i 0.939552 + 0.342407i \(0.111242\pi\)
−0.765780 + 0.643103i \(0.777647\pi\)
\(230\) 7.50035e7 1.29910e8i 0.406475 0.704035i
\(231\) −7.96774e7 6.68573e7i −0.425298 0.356867i
\(232\) 1.95159e7 + 3.38026e7i 0.102608 + 0.177722i
\(233\) −1.62629e8 + 2.81682e8i −0.842272 + 1.45886i 0.0456969 + 0.998955i \(0.485449\pi\)
−0.887969 + 0.459903i \(0.847884\pi\)
\(234\) −2.49213e8 + 9.07062e7i −1.27150 + 0.462787i
\(235\) −4.69128e7 + 3.93645e7i −0.235806 + 0.197864i
\(236\) −9.74472e7 1.68784e8i −0.482589 0.835869i
\(237\) −1.93574e7 + 1.09781e8i −0.0944558 + 0.535685i
\(238\) −4.99759e6 + 2.83427e7i −0.0240293 + 0.136277i
\(239\) −1.86275e8 1.56303e8i −0.882595 0.740585i 0.0841163 0.996456i \(-0.473193\pi\)
−0.966711 + 0.255871i \(0.917638\pi\)
\(240\) −6.07715e7 2.21190e7i −0.283766 0.103282i
\(241\) −3.73691e7 1.36012e7i −0.171970 0.0625920i 0.254600 0.967046i \(-0.418056\pi\)
−0.426570 + 0.904454i \(0.640278\pi\)
\(242\) 1.61255e8 + 1.35309e8i 0.731406 + 0.613722i
\(243\) 5.56994e7 3.15887e8i 0.249017 1.41224i
\(244\) 7.16287e7 4.06227e8i 0.315662 1.79021i
\(245\) 3.48795e7 + 6.04130e7i 0.151527 + 0.262452i
\(246\) −6.20123e8 + 5.20345e8i −2.65586 + 2.22853i
\(247\) 1.14171e8 4.15548e7i 0.482077 0.175462i
\(248\) −1.95487e7 + 3.38593e7i −0.0813836 + 0.140961i
\(249\) −1.79403e8 3.10735e8i −0.736429 1.27553i
\(250\) 2.51022e8 + 2.10633e8i 1.01607 + 0.852580i
\(251\) 2.20684e7 3.82236e7i 0.0880873 0.152572i −0.818615 0.574342i \(-0.805258\pi\)
0.906703 + 0.421771i \(0.138591\pi\)
\(252\) −4.33787e7 2.46013e8i −0.170756 0.968403i
\(253\) −1.72884e8 −0.671172
\(254\) 4.78980e7 + 2.71643e8i 0.183400 + 1.04011i
\(255\) 2.09586e7 1.75863e7i 0.0791537 0.0664179i
\(256\) 5.51192e7 + 2.00618e7i 0.205335 + 0.0747359i
\(257\) 2.77344e8 1.00945e8i 1.01919 0.370953i 0.222232 0.974994i \(-0.428666\pi\)
0.796954 + 0.604040i \(0.206443\pi\)
\(258\) −1.16192e9 −4.21220
\(259\) −5.81899e7 1.60802e8i −0.208113 0.575098i
\(260\) −1.47459e8 −0.520313
\(261\) −1.00020e8 + 3.64043e7i −0.348213 + 0.126739i
\(262\) 4.19137e8 + 1.52553e8i 1.43980 + 0.524043i
\(263\) −1.76857e8 + 1.48400e8i −0.599482 + 0.503025i −0.891279 0.453455i \(-0.850191\pi\)
0.291797 + 0.956480i \(0.405747\pi\)
\(264\) −2.98095e7 1.69058e8i −0.0997105 0.565486i
\(265\) −1.64980e8 −0.544591
\(266\) 3.39906e7 + 1.92770e8i 0.110732 + 0.627992i
\(267\) 3.07620e8 5.32814e8i 0.989067 1.71311i
\(268\) 2.92220e8 + 2.45202e8i 0.927339 + 0.778130i
\(269\) 1.13299e8 + 1.96239e8i 0.354888 + 0.614684i 0.987099 0.160112i \(-0.0511856\pi\)
−0.632211 + 0.774797i \(0.717852\pi\)
\(270\) −2.52846e7 + 4.37942e7i −0.0781777 + 0.135408i
\(271\) −3.85368e8 + 1.40263e8i −1.17621 + 0.428104i −0.854861 0.518858i \(-0.826357\pi\)
−0.321346 + 0.946962i \(0.604135\pi\)
\(272\) 1.57987e7 1.32567e7i 0.0476025 0.0399433i
\(273\) 1.14874e8 + 1.98968e8i 0.341707 + 0.591853i
\(274\) −1.19485e8 + 6.77633e8i −0.350902 + 1.99007i
\(275\) 2.84369e7 1.61274e8i 0.0824552 0.467627i
\(276\) −5.96557e8 5.00571e8i −1.70793 1.43312i
\(277\) 4.45634e8 + 1.62198e8i 1.25979 + 0.458527i 0.883700 0.468055i \(-0.155045\pi\)
0.376093 + 0.926582i \(0.377267\pi\)
\(278\) −4.91956e8 1.79057e8i −1.37331 0.499845i
\(279\) −8.16739e7 6.85326e7i −0.225148 0.188922i
\(280\) 1.19470e7 6.77550e7i 0.0325242 0.184454i
\(281\) −6.60210e7 + 3.74423e8i −0.177505 + 1.00668i 0.757708 + 0.652593i \(0.226319\pi\)
−0.935213 + 0.354086i \(0.884792\pi\)
\(282\) 2.71889e8 + 4.70926e8i 0.721972 + 1.25049i
\(283\) −3.47282e8 + 2.91404e8i −0.910814 + 0.764263i −0.972274 0.233846i \(-0.924869\pi\)
0.0614599 + 0.998110i \(0.480424\pi\)
\(284\) 9.26860e8 3.37349e8i 2.40104 0.873908i
\(285\) 9.30414e7 1.61152e8i 0.238078 0.412363i
\(286\) 1.45339e8 + 2.51735e8i 0.367369 + 0.636301i
\(287\) 2.86436e8 + 2.40348e8i 0.715222 + 0.600142i
\(288\) −2.99539e8 + 5.18817e8i −0.738890 + 1.27979i
\(289\) −6.97395e7 3.95512e8i −0.169956 0.963868i
\(290\) −1.01224e8 −0.243720
\(291\) −6.95376e7 3.94367e8i −0.165422 0.938157i
\(292\) 7.05823e8 5.92256e8i 1.65904 1.39210i
\(293\) −2.13248e8 7.76160e7i −0.495278 0.180266i 0.0822910 0.996608i \(-0.473776\pi\)
−0.577569 + 0.816342i \(0.695999\pi\)
\(294\) 5.82063e8 2.11854e8i 1.33584 0.486206i
\(295\) 1.46374e8 0.331961
\(296\) 9.70225e7 2.65038e8i 0.217446 0.594001i
\(297\) 5.82814e7 0.129087
\(298\) 5.92973e8 2.15825e8i 1.29801 0.472437i
\(299\) 3.58850e8 + 1.30611e8i 0.776361 + 0.282572i
\(300\) 5.65079e8 4.74157e8i 1.20833 1.01391i
\(301\) 9.31962e7 + 5.28542e8i 0.196977 + 1.11711i
\(302\) −3.43941e8 −0.718555
\(303\) −5.11761e7 2.90234e8i −0.105686 0.599376i
\(304\) 7.01351e7 1.21477e8i 0.143178 0.247992i
\(305\) 2.37321e8 + 1.99136e8i 0.478946 + 0.401883i
\(306\) −6.47657e7 1.12177e8i −0.129217 0.223811i
\(307\) 2.27196e8 3.93515e8i 0.448143 0.776206i −0.550122 0.835084i \(-0.685419\pi\)
0.998265 + 0.0588779i \(0.0187523\pi\)
\(308\) −2.57288e8 + 9.36453e7i −0.501756 + 0.182624i
\(309\) 2.79097e7 2.34190e7i 0.0538146 0.0451558i
\(310\) −5.06971e7 8.78099e7i −0.0966533 0.167409i
\(311\) −1.97636e7 + 1.12085e8i −0.0372568 + 0.211294i −0.997753 0.0669992i \(-0.978657\pi\)
0.960496 + 0.278293i \(0.0897686\pi\)
\(312\) −6.58455e7 + 3.73428e8i −0.122740 + 0.696091i
\(313\) −7.29151e8 6.11830e8i −1.34404 1.12778i −0.980568 0.196178i \(-0.937147\pi\)
−0.363472 0.931605i \(-0.618409\pi\)
\(314\) −9.07757e8 3.30396e8i −1.65469 0.602257i
\(315\) 1.76302e8 + 6.41687e7i 0.317812 + 0.115674i
\(316\) 2.24794e8 + 1.88624e8i 0.400756 + 0.336274i
\(317\) 1.86888e8 1.05989e9i 0.329514 1.86877i −0.146327 0.989236i \(-0.546745\pi\)
0.475841 0.879531i \(-0.342144\pi\)
\(318\) −2.54382e8 + 1.44267e9i −0.443600 + 2.51578i
\(319\) 5.83310e7 + 1.01032e8i 0.100608 + 0.174258i
\(320\) −3.43791e8 + 2.88475e8i −0.586502 + 0.492134i
\(321\) −1.17735e8 + 4.28519e7i −0.198672 + 0.0723108i
\(322\) −3.07621e8 + 5.32815e8i −0.513476 + 0.889366i
\(323\) 2.96708e7 + 5.13913e7i 0.0489915 + 0.0848557i
\(324\) −5.52947e8 4.63977e8i −0.903183 0.757861i
\(325\) −1.80865e8 + 3.13267e8i −0.292255 + 0.506200i
\(326\) −1.54424e8 8.75783e8i −0.246862 1.40002i
\(327\) 1.94650e8 0.307848
\(328\) 1.07164e8 + 6.07755e8i 0.167683 + 0.950976i
\(329\) 1.92409e8 1.61450e8i 0.297879 0.249950i
\(330\) 4.18346e8 + 1.52265e8i 0.640821 + 0.233240i
\(331\) 3.42221e8 1.24558e8i 0.518692 0.188788i −0.0693905 0.997590i \(-0.522105\pi\)
0.588082 + 0.808801i \(0.299883\pi\)
\(332\) −9.44521e8 −1.41654
\(333\) 6.65829e8 + 3.86063e8i 0.988117 + 0.572933i
\(334\) 8.76303e8 1.28689
\(335\) −2.69220e8 + 9.79880e7i −0.391246 + 0.142402i
\(336\) 2.49249e8 + 9.07193e7i 0.358465 + 0.130470i
\(337\) −5.00853e8 + 4.20266e8i −0.712863 + 0.598163i −0.925401 0.378990i \(-0.876271\pi\)
0.212538 + 0.977153i \(0.431827\pi\)
\(338\) 7.97881e7 + 4.52501e8i 0.112391 + 0.637399i
\(339\) 8.20162e8 1.14341
\(340\) −1.25064e7 7.09272e7i −0.0172566 0.0978670i
\(341\) −5.84288e7 + 1.01202e8i −0.0797970 + 0.138213i
\(342\) −6.74881e8 5.66292e8i −0.912296 0.765507i
\(343\) −3.71596e8 6.43623e8i −0.497212 0.861196i
\(344\) −4.42895e8 + 7.67117e8i −0.586606 + 1.01603i
\(345\) 5.49603e8 2.00039e8i 0.720580 0.262270i
\(346\) 9.12691e8 7.65838e8i 1.18456 0.993964i
\(347\) −284749. 493200.i −0.000365855 0.000633680i 0.865842 0.500317i \(-0.166783\pi\)
−0.866208 + 0.499683i \(0.833450\pi\)
\(348\) −9.12519e7 + 5.17515e8i −0.116069 + 0.658258i
\(349\) −2.15734e8 + 1.22349e9i −0.271663 + 1.54068i 0.477703 + 0.878521i \(0.341469\pi\)
−0.749366 + 0.662156i \(0.769642\pi\)
\(350\) −4.46433e8 3.74602e8i −0.556568 0.467016i
\(351\) −1.20973e8 4.40305e7i −0.149318 0.0543473i
\(352\) 6.17017e8 + 2.24576e8i 0.754046 + 0.274450i
\(353\) −8.36067e8 7.01544e8i −1.01165 0.848874i −0.0230936 0.999733i \(-0.507352\pi\)
−0.988555 + 0.150859i \(0.951796\pi\)
\(354\) 2.25694e8 1.27997e9i 0.270401 1.53352i
\(355\) −1.28636e8 + 7.29533e8i −0.152603 + 0.865457i
\(356\) −8.09782e8 1.40258e9i −0.951246 1.64761i
\(357\) −8.59600e7 + 7.21290e7i −0.0999902 + 0.0839017i
\(358\) −1.75898e9 + 6.40217e8i −2.02615 + 0.737457i
\(359\) 5.09662e8 8.82760e8i 0.581368 1.00696i −0.413949 0.910300i \(-0.635851\pi\)
0.995318 0.0966595i \(-0.0308158\pi\)
\(360\) 1.54826e8 + 2.68167e8i 0.174899 + 0.302933i
\(361\) −3.75566e8 3.15137e8i −0.420156 0.352553i
\(362\) 5.71748e7 9.90297e7i 0.0633468 0.109720i
\(363\) 1.42522e8 + 8.08280e8i 0.156389 + 0.886928i
\(364\) 6.04791e8 0.657280
\(365\) 1.20165e8 + 6.81488e8i 0.129346 + 0.733556i
\(366\) 2.10727e9 1.76821e9i 2.24666 1.88517i
\(367\) 4.32865e8 + 1.57550e8i 0.457110 + 0.166374i 0.560304 0.828287i \(-0.310684\pi\)
−0.103194 + 0.994661i \(0.532906\pi\)
\(368\) 4.14294e8 1.50791e8i 0.433352 0.157727i
\(369\) −1.68290e9 −1.74368
\(370\) 4.69449e8 + 5.61577e8i 0.481817 + 0.576372i
\(371\) 6.76652e8 0.687950
\(372\) −4.94636e8 + 1.80033e8i −0.498179 + 0.181322i
\(373\) 1.60216e9 + 5.83138e8i 1.59854 + 0.581822i 0.979129 0.203241i \(-0.0651475\pi\)
0.619415 + 0.785064i \(0.287370\pi\)
\(374\) −1.08757e8 + 9.12579e7i −0.107499 + 0.0902027i
\(375\) 2.21861e8 + 1.25823e9i 0.217256 + 1.23212i
\(376\) 4.14548e8 0.402177
\(377\) −4.47477e7 2.53777e8i −0.0430106 0.243925i
\(378\) 1.03703e8 1.79618e8i 0.0987572 0.171052i
\(379\) −1.03878e9 8.71641e8i −0.980137 0.822432i 0.00397317 0.999992i \(-0.498735\pi\)
−0.984110 + 0.177560i \(0.943180\pi\)
\(380\) −2.44923e8 4.24219e8i −0.228974 0.396595i
\(381\) −5.37736e8 + 9.31386e8i −0.498117 + 0.862765i
\(382\) −5.65580e7 + 2.05854e7i −0.0519125 + 0.0188946i
\(383\) −8.52088e8 + 7.14987e8i −0.774977 + 0.650283i −0.941978 0.335674i \(-0.891036\pi\)
0.167002 + 0.985957i \(0.446592\pi\)
\(384\) 9.41911e8 + 1.63144e9i 0.848889 + 1.47032i
\(385\) 3.57083e7 2.02512e8i 0.0318902 0.180858i
\(386\) −3.34558e8 + 1.89737e9i −0.296085 + 1.67918i
\(387\) −1.85040e9 1.55267e9i −1.62285 1.36173i
\(388\) −9.90577e8 3.60541e8i −0.860949 0.313360i
\(389\) 1.37303e9 + 4.99741e8i 1.18265 + 0.430449i 0.857136 0.515089i \(-0.172241\pi\)
0.325512 + 0.945538i \(0.394463\pi\)
\(390\) −7.53312e8 6.32104e8i −0.643056 0.539588i
\(391\) −3.23882e7 + 1.83683e8i −0.0274011 + 0.155399i
\(392\) 8.19988e7 4.65038e8i 0.0687553 0.389931i
\(393\) 8.69545e8 + 1.50610e9i 0.722633 + 1.25164i
\(394\) 9.34040e8 7.83753e8i 0.769359 0.645569i
\(395\) −2.07101e8 + 7.53785e7i −0.169080 + 0.0615400i
\(396\) 6.16154e8 1.06721e9i 0.498604 0.863608i
\(397\) −5.37580e8 9.31116e8i −0.431198 0.746857i 0.565779 0.824557i \(-0.308576\pi\)
−0.996977 + 0.0777004i \(0.975242\pi\)
\(398\) −2.27412e9 1.90821e9i −1.80810 1.51718i
\(399\) −3.81602e8 + 6.60953e8i −0.300750 + 0.520914i
\(400\) 7.25186e7 + 4.11273e8i 0.0566551 + 0.321307i
\(401\) 3.31623e8 0.256826 0.128413 0.991721i \(-0.459012\pi\)
0.128413 + 0.991721i \(0.459012\pi\)
\(402\) 4.41749e8 + 2.50529e9i 0.339145 + 1.92338i
\(403\) 1.97734e8 1.65919e8i 0.150492 0.126278i
\(404\) −7.29014e8 2.65339e8i −0.550048 0.200201i
\(405\) 5.09425e8 1.85416e8i 0.381055 0.138693i
\(406\) 4.15163e8 0.307877
\(407\) 2.89989e8 7.92169e8i 0.213207 0.582421i
\(408\) −1.85202e8 −0.135000
\(409\) −2.11382e9 + 7.69367e8i −1.52769 + 0.556035i −0.963055 0.269305i \(-0.913206\pi\)
−0.564637 + 0.825339i \(0.690984\pi\)
\(410\) −1.50393e9 5.47386e8i −1.07767 0.392238i
\(411\) −2.05518e9 + 1.72450e9i −1.46017 + 1.22523i
\(412\) −1.66542e7 9.44507e7i −0.0117323 0.0665373i
\(413\) −6.00342e8 −0.419347
\(414\) −4.80840e8 2.72698e9i −0.333042 1.88878i
\(415\) 3.54688e8 6.14338e8i 0.243601 0.421929i
\(416\) −1.11106e9 9.32288e8i −0.756676 0.634926i
\(417\) −1.02062e9 1.76776e9i −0.689265 1.19384i
\(418\) −4.82804e8 + 8.36241e8i −0.323336 + 0.560034i
\(419\) 5.50298e8 2.00292e8i 0.365467 0.133019i −0.152757 0.988264i \(-0.548815\pi\)
0.518225 + 0.855245i \(0.326593\pi\)
\(420\) 7.09571e8 5.95401e8i 0.467330 0.392136i
\(421\) −5.08564e8 8.80859e8i −0.332169 0.575333i 0.650768 0.759276i \(-0.274447\pi\)
−0.982937 + 0.183944i \(0.941114\pi\)
\(422\) −5.52730e8 + 3.13469e9i −0.358030 + 2.03049i
\(423\) −1.96303e8 + 1.11329e9i −0.126106 + 0.715182i
\(424\) 8.55505e8 + 7.17854e8i 0.545057 + 0.457357i
\(425\) −1.66020e8 6.04262e7i −0.104905 0.0381824i
\(426\) 6.18107e9 + 2.24973e9i 3.87374 + 1.40992i
\(427\) −9.73353e8 8.16740e8i −0.605024 0.507676i
\(428\) −5.72720e7 + 3.24805e8i −0.0353093 + 0.200249i
\(429\) −1.96805e8 + 1.11613e9i −0.120347 + 0.682521i
\(430\) −1.14859e9 1.98942e9i −0.696669 1.20667i
\(431\) 1.96591e9 1.64960e9i 1.18275 0.992447i 0.182795 0.983151i \(-0.441485\pi\)
0.999957 0.00929581i \(-0.00295899\pi\)
\(432\) −1.39663e8 + 5.08334e7i −0.0833470 + 0.0303358i
\(433\) 1.38437e9 2.39781e9i 0.819494 1.41941i −0.0865617 0.996246i \(-0.527588\pi\)
0.906056 0.423159i \(-0.139079\pi\)
\(434\) 2.07930e8 + 3.60145e8i 0.122096 + 0.211477i
\(435\) −3.02337e8 2.53691e8i −0.176108 0.147772i
\(436\) 2.56198e8 4.43749e8i 0.148038 0.256410i
\(437\) 2.20285e8 + 1.24930e9i 0.126270 + 0.716112i
\(438\) 6.14457e9 3.49407
\(439\) −2.95363e7 1.67509e8i −0.0166621 0.0944957i 0.975343 0.220696i \(-0.0708329\pi\)
−0.992005 + 0.126200i \(0.959722\pi\)
\(440\) 2.59990e8 2.18157e8i 0.145503 0.122092i
\(441\) 1.21005e9 + 4.40424e8i 0.671846 + 0.244532i
\(442\) 2.94686e8 1.07257e8i 0.162324 0.0590810i
\(443\) 2.66594e9 1.45693 0.728464 0.685084i \(-0.240235\pi\)
0.728464 + 0.685084i \(0.240235\pi\)
\(444\) 3.29430e9 1.89383e9i 1.78617 1.02684i
\(445\) 1.21636e9 0.654339
\(446\) −2.21676e9 + 8.06833e8i −1.18317 + 0.430637i
\(447\) 2.31200e9 + 8.41498e8i 1.22436 + 0.445632i
\(448\) 1.41003e9 1.18316e9i 0.740893 0.621683i
\(449\) 2.49246e8 + 1.41355e9i 0.129947 + 0.736966i 0.978246 + 0.207449i \(0.0665160\pi\)
−0.848299 + 0.529518i \(0.822373\pi\)
\(450\) 2.62293e9 1.35689
\(451\) 3.20300e8 + 1.81651e9i 0.164414 + 0.932438i
\(452\) 1.07950e9 1.86975e9i 0.549842 0.952355i
\(453\) −1.02728e9 8.61993e8i −0.519214 0.435673i
\(454\) −1.72426e9 2.98651e9i −0.864785 1.49785i
\(455\) −2.27112e8 + 3.93370e8i −0.113032 + 0.195777i
\(456\) −1.18367e9 + 4.30819e8i −0.584591 + 0.212774i
\(457\) −1.88876e9 + 1.58486e9i −0.925701 + 0.776755i −0.975041 0.222027i \(-0.928733\pi\)
0.0493395 + 0.998782i \(0.484288\pi\)
\(458\) 1.59627e9 + 2.76482e9i 0.776385 + 1.34474i
\(459\) 1.09185e7 6.19217e7i 0.00527008 0.0298881i
\(460\) 2.67354e8 1.51624e9i 0.128066 0.726299i
\(461\) 6.91941e8 + 5.80607e8i 0.328939 + 0.276013i 0.792267 0.610174i \(-0.208900\pi\)
−0.463328 + 0.886187i \(0.653345\pi\)
\(462\) −1.71581e9 6.24504e8i −0.809511 0.294638i
\(463\) −2.97424e9 1.08253e9i −1.39265 0.506883i −0.466662 0.884436i \(-0.654544\pi\)
−0.925988 + 0.377552i \(0.876766\pi\)
\(464\) −2.27903e8 1.91233e8i −0.105910 0.0888690i
\(465\) 6.86491e7 3.89329e8i 0.0316628 0.179569i
\(466\) −9.91519e8 + 5.62318e9i −0.453890 + 2.57414i
\(467\) −6.12382e8 1.06068e9i −0.278236 0.481919i 0.692711 0.721216i \(-0.256416\pi\)
−0.970946 + 0.239297i \(0.923083\pi\)
\(468\) −2.08518e9 + 1.74968e9i −0.940338 + 0.789037i
\(469\) 1.10418e9 4.01890e8i 0.494238 0.179888i
\(470\) −5.37539e8 + 9.31045e8i −0.238818 + 0.413645i
\(471\) −1.88324e9 3.26187e9i −0.830486 1.43844i
\(472\) −7.59025e8 6.36897e8i −0.332245 0.278787i
\(473\) −1.32376e9 + 2.29283e9i −0.575170 + 0.996224i
\(474\) 3.39821e8 + 1.92722e9i 0.146564 + 0.831204i
\(475\) −1.20163e9 −0.514451
\(476\) 5.12939e7 + 2.90902e8i 0.0217992 + 0.123630i
\(477\) −2.33294e9 + 1.95757e9i −0.984215 + 0.825855i
\(478\) −4.01133e9 1.46000e9i −1.67993 0.611444i
\(479\) 2.43759e9 8.87210e8i 1.01341 0.368852i 0.218670 0.975799i \(-0.429828\pi\)
0.794742 + 0.606947i \(0.207606\pi\)
\(480\) −2.22136e9 −0.916800
\(481\) −1.20039e9 + 1.42520e9i −0.491829 + 0.583938i
\(482\) −6.98119e8 −0.283965
\(483\) −2.25415e9 + 8.20445e8i −0.910266 + 0.331310i
\(484\) 2.03025e9 + 7.38950e8i 0.813936 + 0.296248i
\(485\) 6.06487e8 5.08903e8i 0.241393 0.202553i
\(486\) −9.77806e8 5.54542e9i −0.386390 2.19133i
\(487\) 5.91998e8 0.232257 0.116128 0.993234i \(-0.462952\pi\)
0.116128 + 0.993234i \(0.462952\pi\)
\(488\) −3.64158e8 2.06524e9i −0.141847 0.804455i
\(489\) 1.73367e9 3.00281e9i 0.670481 1.16131i
\(490\) 9.38116e8 + 7.87173e8i 0.360222 + 0.302262i
\(491\) −1.02182e9 1.76984e9i −0.389572 0.674758i 0.602820 0.797877i \(-0.294044\pi\)
−0.992392 + 0.123119i \(0.960710\pi\)
\(492\) −4.15431e9 + 7.19547e9i −1.57261 + 2.72384i
\(493\) 1.18270e8 4.30469e7i 0.0444541 0.0161800i
\(494\) 1.63390e9 1.37101e9i 0.609792 0.511676i
\(495\) 4.62758e8 + 8.01521e8i 0.171489 + 0.297028i
\(496\) 5.17481e7 2.93478e8i 0.0190418 0.107992i
\(497\) 5.27591e8 2.99212e9i 0.192775 1.09328i
\(498\) −4.82520e9 4.04882e9i −1.75070 1.46901i
\(499\) −1.69626e9 6.17389e8i −0.611141 0.222437i 0.0178617 0.999840i \(-0.494314\pi\)
−0.629002 + 0.777403i \(0.716536\pi\)
\(500\) 3.16045e9 + 1.15031e9i 1.13072 + 0.411547i
\(501\) 2.61734e9 + 2.19621e9i 0.929884 + 0.780265i
\(502\) 1.34547e8 7.63054e8i 0.0474691 0.269211i
\(503\) −6.52125e8 + 3.69839e9i −0.228477 + 1.29576i 0.627447 + 0.778659i \(0.284100\pi\)
−0.855925 + 0.517100i \(0.827011\pi\)
\(504\) −6.35008e8 1.09987e9i −0.220939 0.382677i
\(505\) 4.46343e8 3.74526e8i 0.154223 0.129408i
\(506\) −2.85196e9 + 1.03803e9i −0.978627 + 0.356191i
\(507\) −8.95757e8 + 1.55150e9i −0.305255 + 0.528717i
\(508\) 1.41554e9 + 2.45179e9i 0.479070 + 0.829774i
\(509\) 3.20798e9 + 2.69182e9i 1.07825 + 0.904760i 0.995774 0.0918333i \(-0.0292727\pi\)
0.0824763 + 0.996593i \(0.473717\pi\)
\(510\) 2.40149e8 4.15950e8i 0.0801650 0.138850i
\(511\) −4.92846e8 2.79507e9i −0.163395 0.926658i
\(512\) −2.49314e9 −0.820921
\(513\) −7.42608e7 4.21154e8i −0.0242856 0.137730i
\(514\) 3.96908e9 3.33046e9i 1.28920 1.08176i
\(515\) 6.76869e7 + 2.46360e7i 0.0218363 + 0.00794777i
\(516\) −1.12065e10 + 4.07882e9i −3.59083 + 1.30696i
\(517\) 1.23904e9 0.394337
\(518\) −1.92541e9 2.30326e9i −0.608651 0.728097i
\(519\) 4.64539e9 1.45860
\(520\) −7.04466e8 + 2.56404e8i −0.219709 + 0.0799676i
\(521\) 4.02777e9 + 1.46599e9i 1.24776 + 0.454149i 0.879645 0.475630i \(-0.157780\pi\)
0.368118 + 0.929779i \(0.380002\pi\)
\(522\) −1.43139e9 + 1.20108e9i −0.440465 + 0.369594i
\(523\) 2.07025e8 + 1.17410e9i 0.0632801 + 0.358879i 0.999962 + 0.00869833i \(0.00276880\pi\)
−0.936682 + 0.350181i \(0.886120\pi\)
\(524\) 4.57799e9 1.39000
\(525\) −3.94570e8 2.23772e9i −0.119005 0.674913i
\(526\) −2.02647e9 + 3.50995e9i −0.607141 + 1.05160i
\(527\) 9.65767e7 + 8.10374e7i 0.0287432 + 0.0241184i
\(528\) 6.54230e8 + 1.13316e9i 0.193425 + 0.335021i
\(529\) −2.91205e8 + 5.04382e8i −0.0855272 + 0.148137i
\(530\) −2.72157e9 + 9.90571e8i −0.794061 + 0.289015i
\(531\) 2.06984e9 1.73681e9i 0.599939 0.503408i
\(532\) 1.00453e9 + 1.73990e9i 0.289249 + 0.500995i
\(533\) 7.07502e8 4.01244e9i 0.202387 1.14779i
\(534\) 1.87550e9 1.06365e10i 0.532995 3.02277i
\(535\) −1.89754e8 1.59223e8i −0.0535738 0.0449538i
\(536\) 1.82240e9 + 6.63301e8i 0.511173 + 0.186052i
\(537\) −6.85825e9 2.49620e9i −1.91119 0.695616i
\(538\) 3.04727e9 + 2.55696e9i 0.843671 + 0.707924i
\(539\) 2.45085e8 1.38995e9i 0.0674150 0.382329i
\(540\) −9.01283e7 + 5.11143e8i −0.0246311 + 0.139690i
\(541\) 3.96648e8 + 6.87014e8i 0.107700 + 0.186542i 0.914838 0.403821i \(-0.132318\pi\)
−0.807138 + 0.590362i \(0.798985\pi\)
\(542\) −5.51502e9 + 4.62765e9i −1.48782 + 1.24843i
\(543\) 4.18960e8 1.52489e8i 0.112298 0.0408733i
\(544\) 3.54195e8 6.13483e8i 0.0943292 0.163383i
\(545\) 1.92416e8 + 3.33275e8i 0.0509159 + 0.0881890i
\(546\) 3.08965e9 + 2.59252e9i 0.812334 + 0.681629i
\(547\) 2.50034e9 4.33072e9i 0.653197 1.13137i −0.329146 0.944279i \(-0.606761\pi\)
0.982343 0.187091i \(-0.0599059\pi\)
\(548\) 1.22636e9 + 6.95504e9i 0.318336 + 1.80537i
\(549\) 5.71875e9 1.47502
\(550\) −4.99212e8 2.83117e9i −0.127943 0.725599i
\(551\) 6.55756e8 5.50244e8i 0.166998 0.140128i
\(552\) −3.72037e9 1.35411e9i −0.941456 0.342662i
\(553\) 8.49407e8 3.09159e8i 0.213588 0.0777398i
\(554\) 8.32521e9 2.08023
\(555\) −5.28751e6 + 2.85386e9i −0.00131288 + 0.708610i
\(556\) −5.37336e9 −1.32582
\(557\) 2.43989e9 8.88047e8i 0.598242 0.217742i −0.0251086 0.999685i \(-0.507993\pi\)
0.623351 + 0.781942i \(0.285771\pi\)
\(558\) −1.75881e9 6.40153e8i −0.428547 0.155978i
\(559\) 4.47987e9 3.75906e9i 1.08474 0.910202i
\(560\) 9.10618e7 + 5.16437e8i 0.0219118 + 0.124268i
\(561\) −5.53548e8 −0.132369
\(562\) 1.15900e9 + 6.57303e9i 0.275427 + 1.56203i
\(563\) 2.67321e9 4.63013e9i 0.631326 1.09349i −0.355955 0.934503i \(-0.615844\pi\)
0.987281 0.158985i \(-0.0508222\pi\)
\(564\) 4.27544e9 + 3.58752e9i 1.00347 + 0.842011i
\(565\) 8.10751e8 + 1.40426e9i 0.189112 + 0.327551i
\(566\) −3.97924e9 + 6.89225e9i −0.922451 + 1.59773i
\(567\) −2.08937e9 + 7.60467e8i −0.481364 + 0.175202i
\(568\) 3.84136e9 3.22328e9i 0.879560 0.738039i
\(569\) −1.81273e9 3.13973e9i −0.412514 0.714496i 0.582649 0.812724i \(-0.302016\pi\)
−0.995164 + 0.0982275i \(0.968683\pi\)
\(570\) 5.67256e8 3.21707e9i 0.128297 0.727609i
\(571\) 4.16205e8 2.36041e9i 0.0935579 0.530593i −0.901622 0.432525i \(-0.857623\pi\)
0.995180 0.0980680i \(-0.0312663\pi\)
\(572\) 2.28545e9 + 1.91772e9i 0.510606 + 0.428449i
\(573\) −2.20519e8 8.02623e7i −0.0489671 0.0178226i
\(574\) 6.16825e9 + 2.24506e9i 1.36135 + 0.495491i
\(575\) −2.89323e9 2.42771e9i −0.634666 0.532548i
\(576\) −1.43857e9 + 8.15851e9i −0.313654 + 1.77882i
\(577\) −5.00448e8 + 2.83818e9i −0.108454 + 0.615071i 0.881331 + 0.472500i \(0.156648\pi\)
−0.989785 + 0.142571i \(0.954463\pi\)
\(578\) −3.52518e9 6.10579e9i −0.759335 1.31521i
\(579\) −5.75450e9 + 4.82860e9i −1.23206 + 1.03382i
\(580\) −9.76283e8 + 3.55338e8i −0.207768 + 0.0756212i
\(581\) −1.45473e9 + 2.51966e9i −0.307726 + 0.532998i
\(582\) −3.51497e9 6.08811e9i −0.739080 1.28012i
\(583\) 2.55701e9 + 2.14558e9i 0.534432 + 0.448441i
\(584\) 2.34215e9 4.05672e9i 0.486597 0.842811i
\(585\) −3.54998e8 2.01329e9i −0.0733129 0.415778i
\(586\) −3.98384e9 −0.817826
\(587\) −8.58698e8 4.86992e9i −0.175229 0.993776i −0.937879 0.346963i \(-0.887213\pi\)
0.762649 0.646812i \(-0.223898\pi\)
\(588\) 4.87016e9 4.08655e9i 0.987922 0.828965i
\(589\) 8.05753e8 + 2.93270e8i 0.162479 + 0.0591377i
\(590\) 2.41464e9 8.78858e8i 0.484028 0.176172i
\(591\) 4.75405e9 0.947344
\(592\) −3.98575e6 + 2.15125e9i −0.000789559 + 0.426153i
\(593\) −4.45258e9 −0.876841 −0.438420 0.898770i \(-0.644462\pi\)
−0.438420 + 0.898770i \(0.644462\pi\)
\(594\) 9.61432e8 3.49933e8i 0.188220 0.0685065i
\(595\) −2.08471e8 7.58773e7i −0.0405730 0.0147674i
\(596\) 4.96145e9 4.16315e9i 0.959945 0.805490i
\(597\) −2.00993e9 1.13989e10i −0.386609 2.19257i
\(598\) 6.70393e9 1.28196
\(599\) 1.22033e9 + 6.92081e9i 0.231997 + 1.31572i 0.848847 + 0.528638i \(0.177297\pi\)
−0.616850 + 0.787080i \(0.711592\pi\)
\(600\) 1.87511e9 3.24779e9i 0.354404 0.613845i
\(601\) −4.66100e9 3.91105e9i −0.875828 0.734907i 0.0894889 0.995988i \(-0.471477\pi\)
−0.965317 + 0.261081i \(0.915921\pi\)
\(602\) 4.71086e9 + 8.15945e9i 0.880061 + 1.52431i
\(603\) −2.64430e9 + 4.58006e9i −0.491134 + 0.850669i
\(604\) −3.31723e9 + 1.20737e9i −0.612556 + 0.222952i
\(605\) −1.24303e9 + 1.04303e9i −0.228212 + 0.191493i
\(606\) −2.58684e9 4.48054e9i −0.472188 0.817854i
\(607\) −1.88222e9 + 1.06746e10i −0.341593 + 1.93727i 0.00694589 + 0.999976i \(0.497789\pi\)
−0.348539 + 0.937294i \(0.613322\pi\)
\(608\) 8.36643e8 4.74484e9i 0.150966 0.856168i
\(609\) 1.24001e9 + 1.04049e9i 0.222466 + 0.186672i
\(610\) 5.11058e9 + 1.86010e9i 0.911625 + 0.331804i
\(611\) −2.57183e9 9.36068e8i −0.456139 0.166021i
\(612\) −1.01844e9 8.54570e8i −0.179599 0.150702i
\(613\) −1.13912e9 + 6.46026e9i −0.199736 + 1.13276i 0.705774 + 0.708437i \(0.250599\pi\)
−0.905510 + 0.424324i \(0.860512\pi\)
\(614\) 1.38517e9 7.85570e9i 0.241498 1.36961i
\(615\) −3.12007e9 5.40412e9i −0.540880 0.936832i
\(616\) −1.06633e9 + 8.94755e8i −0.183805 + 0.154231i
\(617\) 2.10745e9 7.67049e8i 0.361210 0.131470i −0.155039 0.987908i \(-0.549550\pi\)
0.516249 + 0.856439i \(0.327328\pi\)
\(618\) 3.19796e8 5.53903e8i 0.0545022 0.0944005i
\(619\) 2.12680e9 + 3.68372e9i 0.360420 + 0.624266i 0.988030 0.154262i \(-0.0492999\pi\)
−0.627610 + 0.778528i \(0.715967\pi\)
\(620\) −7.97208e8 6.68937e8i −0.134339 0.112724i
\(621\) 6.72073e8 1.16406e9i 0.112615 0.195055i
\(622\) 3.46952e8 + 1.96766e9i 0.0578100 + 0.327857i
\(623\) −4.98881e9 −0.826588
\(624\) −5.01883e8 2.84632e9i −0.0826906 0.468962i
\(625\) 1.64461e9 1.37999e9i 0.269453 0.226098i
\(626\) −1.57019e10 5.71502e9i −2.55824 0.931124i
\(627\) −3.53784e9 + 1.28767e9i −0.573195 + 0.208626i
\(628\) −9.91491e9 −1.59746
\(629\) −7.87321e8 4.56507e8i −0.126146 0.0731426i
\(630\) 3.29362e9 0.524786
\(631\) −5.62438e9 + 2.04711e9i −0.891193 + 0.324368i −0.746718 0.665141i \(-0.768371\pi\)
−0.144475 + 0.989508i \(0.546149\pi\)
\(632\) 1.40191e9 + 5.10252e8i 0.220907 + 0.0804035i
\(633\) −9.50711e9 + 7.97741e9i −1.48983 + 1.25011i
\(634\) −3.28083e9 1.86065e10i −0.511295 2.89970i
\(635\) −2.12626e9 −0.329541
\(636\) 2.61091e9 + 1.48072e10i 0.402431 + 2.28230i
\(637\) −1.55879e9 + 2.69991e9i −0.238946 + 0.413867i
\(638\) 1.56887e9 + 1.31643e9i 0.239174 + 0.200690i
\(639\) 6.83727e9 + 1.18425e10i 1.03664 + 1.79552i
\(640\) −1.86221e9 + 3.22544e9i −0.280801 + 0.486361i
\(641\) 1.82991e9 6.66033e8i 0.274427 0.0998833i −0.201141 0.979562i \(-0.564465\pi\)
0.475568 + 0.879679i \(0.342243\pi\)
\(642\) −1.68490e9 + 1.41380e9i −0.251306 + 0.210871i
\(643\) 2.44433e9 + 4.23371e9i 0.362595 + 0.628033i 0.988387 0.151957i \(-0.0485575\pi\)
−0.625792 + 0.779990i \(0.715224\pi\)
\(644\) −1.09653e9 + 6.21873e9i −0.161778 + 0.917490i
\(645\) 1.55532e9 8.82063e9i 0.228223 1.29432i
\(646\) 7.98024e8 + 6.69621e8i 0.116467 + 0.0977272i
\(647\) 7.30226e9 + 2.65780e9i 1.05997 + 0.385796i 0.812416 0.583079i \(-0.198152\pi\)
0.247551 + 0.968875i \(0.420374\pi\)
\(648\) −3.44840e9 1.25512e9i −0.497858 0.181205i
\(649\) −2.26864e9 1.90361e9i −0.325768 0.273352i
\(650\) −1.10270e9 + 6.25371e9i −0.157492 + 0.893184i
\(651\) −2.81559e8 + 1.59680e9i −0.0399978 + 0.226839i
\(652\) −4.56373e9 7.90462e9i −0.644843 1.11690i
\(653\) −7.08345e8 + 5.94372e8i −0.0995516 + 0.0835337i −0.691205 0.722659i \(-0.742920\pi\)
0.591653 + 0.806192i \(0.298475\pi\)
\(654\) 3.21101e9 1.16871e9i 0.448869 0.163375i
\(655\) −1.71914e9 + 2.97763e9i −0.239037 + 0.414025i
\(656\) −2.35192e9 4.07365e9i −0.325282 0.563404i
\(657\) 9.78543e9 + 8.21095e9i 1.34617 + 1.12957i
\(658\) 2.20467e9 3.81861e9i 0.301685 0.522534i
\(659\) 7.08084e8 + 4.01574e9i 0.0963798 + 0.546597i 0.994316 + 0.106471i \(0.0339551\pi\)
−0.897936 + 0.440126i \(0.854934\pi\)
\(660\) 4.56935e9 0.618658
\(661\) −9.51401e8 5.39566e9i −0.128132 0.726674i −0.979398 0.201939i \(-0.935276\pi\)
0.851266 0.524735i \(-0.175835\pi\)
\(662\) 4.89754e9 4.10952e9i 0.656107 0.550539i
\(663\) 1.14898e9 + 4.18194e8i 0.153114 + 0.0557289i
\(664\) −4.51232e9 + 1.64235e9i −0.598153 + 0.217710i
\(665\) −1.50889e9 −0.198968
\(666\) 1.33018e10 + 2.37088e9i 1.74482 + 0.310992i
\(667\) 2.69058e9 0.351079
\(668\) 8.45173e9 3.07618e9i 1.09705 0.399295i
\(669\) −8.64311e9 3.14583e9i −1.11604 0.406204i
\(670\) −3.85281e9 + 3.23289e9i −0.494898 + 0.415269i
\(671\) −1.08843e9 6.17277e9i −0.139082 0.788772i
\(672\) 9.11073e9 1.15814
\(673\) −1.65640e8 9.39388e8i −0.0209465 0.118793i 0.972542 0.232729i \(-0.0747654\pi\)
−0.993488 + 0.113935i \(0.963654\pi\)
\(674\) −5.73891e9 + 9.94008e9i −0.721971 + 1.25049i
\(675\) 9.75343e8 + 8.18410e8i 0.122066 + 0.102425i
\(676\) 2.35800e9 + 4.08417e9i 0.293582 + 0.508499i
\(677\) 2.27490e9 3.94023e9i 0.281774 0.488047i −0.690048 0.723764i \(-0.742410\pi\)
0.971822 + 0.235717i \(0.0757438\pi\)
\(678\) 1.35297e10 4.92441e9i 1.66719 0.606806i
\(679\) −2.48746e9 + 2.08722e9i −0.304938 + 0.255873i
\(680\) −1.83077e8 3.17099e8i −0.0223281 0.0386735i
\(681\) 2.33483e9 1.32415e10i 0.283297 1.60665i
\(682\) −3.56230e8 + 2.02028e9i −0.0430016 + 0.243874i
\(683\) 9.23164e9 + 7.74627e9i 1.10868 + 0.930294i 0.997978 0.0635599i \(-0.0202454\pi\)
0.110703 + 0.993854i \(0.464690\pi\)
\(684\) −8.49697e9 3.09264e9i −1.01524 0.369516i
\(685\) −4.98424e9 1.81411e9i −0.592491 0.215649i
\(686\) −9.99441e9 8.38631e9i −1.18201 0.991828i
\(687\) −2.16152e9 + 1.22586e10i −0.254337 + 1.44242i
\(688\) 1.17240e9 6.64904e9i 0.137252 0.778394i
\(689\) −3.68654e9 6.38528e9i −0.429390 0.743726i
\(690\) 7.86538e9 6.59984e9i 0.911482 0.764824i
\(691\) 4.88957e9 1.77966e9i 0.563764 0.205193i −0.0443871 0.999014i \(-0.514134\pi\)
0.608152 + 0.793821i \(0.291911\pi\)
\(692\) 6.11427e9 1.05902e10i 0.701412 1.21488i
\(693\) −1.89797e9 3.28737e9i −0.216632 0.375217i
\(694\) −7.65859e6 6.42632e6i −0.000869743 0.000729801i
\(695\) 2.01781e9 3.49495e9i 0.228000 0.394907i
\(696\) 4.63922e8 + 2.63103e9i 0.0521570 + 0.295797i
\(697\) 1.98997e9 0.222604
\(698\) 3.78723e9 + 2.14785e10i 0.421529 + 2.39061i
\(699\) −1.70544e10 + 1.43104e10i −1.88872 + 1.58482i
\(700\) −5.62073e9 2.04578e9i −0.619370 0.225432i
\(701\) 3.59308e9 1.30777e9i 0.393961 0.143390i −0.137441 0.990510i \(-0.543888\pi\)
0.531402 + 0.847120i \(0.321665\pi\)
\(702\) −2.25998e9 −0.246561
\(703\) −6.09387e9 1.08616e9i −0.661530 0.117910i
\(704\) 9.08003e9 0.980806
\(705\) −3.93893e9 + 1.43365e9i −0.423366 + 0.154093i
\(706\) −1.80043e10 6.55302e9i −1.92557 0.700850i
\(707\) −1.83064e9 + 1.53609e9i −0.194821 + 0.163474i
\(708\) −2.31646e9 1.31373e10i −0.245306 1.39120i
\(709\) −1.76868e9 −0.186375 −0.0931873 0.995649i \(-0.529706\pi\)
−0.0931873 + 0.995649i \(0.529706\pi\)
\(710\) 2.25822e9 + 1.28070e10i 0.236789 + 1.34290i
\(711\) −2.03416e9 + 3.52327e9i −0.212247 + 0.367622i
\(712\) −6.30746e9 5.29259e9i −0.654899 0.549526i
\(713\) 1.34755e9 + 2.33402e9i 0.139229 + 0.241152i
\(714\) −9.84951e8 + 1.70599e9i −0.101268 + 0.175401i
\(715\) −2.10557e9 + 7.66364e8i −0.215426 + 0.0784086i
\(716\) −1.47175e10 + 1.23495e10i −1.49844 + 1.25734i
\(717\) −8.32194e9 1.44140e10i −0.843155 1.46039i
\(718\) 3.10731e9 1.76224e10i 0.313292 1.77677i
\(719\) −2.62238e9 + 1.48723e10i −0.263115 + 1.49220i 0.511236 + 0.859441i \(0.329188\pi\)
−0.774350 + 0.632757i \(0.781923\pi\)
\(720\) −1.80803e9 1.51712e9i −0.180527 0.151480i
\(721\) −2.77613e8 1.01043e8i −0.0275845 0.0100399i
\(722\) −8.08761e9 2.94365e9i −0.799724 0.291076i
\(723\) −2.08514e9 1.74964e9i −0.205188 0.172173i
\(724\) 2.03803e8 1.15582e9i 0.0199584 0.113190i
\(725\) −4.42560e8 + 2.50988e9i −0.0431310 + 0.244608i
\(726\) 7.20415e9 + 1.24780e10i 0.698722 + 1.21022i
\(727\) 2.57090e9 2.15724e9i 0.248150 0.208223i −0.510225 0.860041i \(-0.670438\pi\)
0.758375 + 0.651818i \(0.225993\pi\)
\(728\) 2.88931e9 1.05162e9i 0.277545 0.101018i
\(729\) 6.59686e9 1.14261e10i 0.630654 1.09232i
\(730\) 6.07407e9 + 1.05206e10i 0.577896 + 1.00094i
\(731\) 2.18804e9 + 1.83598e9i 0.207179 + 0.173843i
\(732\) 1.41170e10 2.44513e10i 1.33031 2.30416i
\(733\) 1.68294e9 + 9.54441e9i 0.157835 + 0.895128i 0.956148 + 0.292884i \(0.0946151\pi\)
−0.798313 + 0.602243i \(0.794274\pi\)
\(734\) 8.08665e9 0.754801
\(735\) 8.29134e8 + 4.70225e9i 0.0770228 + 0.436818i
\(736\) 1.16006e10 9.73408e9i 1.07253 0.899959i
\(737\) 5.44696e9 + 1.98253e9i 0.501208 + 0.182425i
\(738\) −2.77617e10 + 1.01044e10i −2.54243 + 0.925370i
\(739\) 9.43550e9 0.860022 0.430011 0.902824i \(-0.358510\pi\)
0.430011 + 0.902824i \(0.358510\pi\)
\(740\) 6.49907e9 + 3.76831e9i 0.589577 + 0.341850i
\(741\) 8.31619e9 0.750863
\(742\) 1.11623e10 4.06275e9i 1.00309 0.365095i
\(743\) 8.00606e9 + 2.91397e9i 0.716075 + 0.260630i 0.674258 0.738496i \(-0.264463\pi\)
0.0418161 + 0.999125i \(0.486686\pi\)
\(744\) −2.05001e9 + 1.72016e9i −0.182495 + 0.153132i
\(745\) 8.44675e8 + 4.79039e9i 0.0748416 + 0.424448i
\(746\) 2.99311e10 2.63959
\(747\) −2.27387e9 1.28958e10i −0.199592 1.13195i
\(748\) −7.28581e8 + 1.26194e9i −0.0636535 + 0.110251i
\(749\) 7.78261e8 + 6.53038e8i 0.0676766 + 0.0567874i
\(750\) 1.12146e10 + 1.94242e10i 0.970662 + 1.68124i
\(751\) 8.57374e9 1.48502e10i 0.738636 1.27936i −0.214473 0.976730i \(-0.568804\pi\)
0.953110 0.302626i \(-0.0978632\pi\)
\(752\) −2.96918e9 + 1.08069e9i −0.254610 + 0.0926703i
\(753\) 2.31425e9 1.94189e9i 0.197528 0.165745i
\(754\) −2.26190e9 3.91772e9i −0.192165 0.332839i
\(755\) 4.60389e8 2.61099e9i 0.0389323 0.220796i
\(756\) 3.69654e8 2.09641e9i 0.0311150 0.176462i
\(757\) 4.91922e9 + 4.12772e9i 0.412155 + 0.345839i 0.825169 0.564885i \(-0.191080\pi\)
−0.413014 + 0.910725i \(0.635524\pi\)
\(758\) −2.23696e10 8.14187e9i −1.86559 0.679019i
\(759\) −1.11198e10 4.04727e9i −0.923102 0.335982i
\(760\) −1.90772e9 1.60077e9i −0.157641 0.132276i
\(761\) −1.90125e9 + 1.07825e10i −0.156384 + 0.886899i 0.801125 + 0.598497i \(0.204235\pi\)
−0.957509 + 0.288402i \(0.906876\pi\)
\(762\) −3.27848e9 + 1.85932e10i −0.268429 + 1.52234i
\(763\) −7.89179e8 1.36690e9i −0.0643191 0.111404i
\(764\) −4.73224e8 + 3.97082e8i −0.0383920 + 0.0322147i