Properties

Label 37.8.f.a.7.17
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 7.17
Character \(\chi\) \(=\) 37.7
Dual form 37.8.f.a.16.17

$q$-expansion

\(f(q)\) \(=\) \(q+(10.2566 - 3.73308i) q^{2} +(-19.4495 - 7.07902i) q^{3} +(-6.79263 + 5.69969i) q^{4} +(7.78053 + 44.1256i) q^{5} -225.911 q^{6} +(-27.0245 - 153.264i) q^{7} +(-746.939 + 1293.74i) q^{8} +(-1347.17 - 1130.41i) q^{9} +O(q^{10})\) \(q+(10.2566 - 3.73308i) q^{2} +(-19.4495 - 7.07902i) q^{3} +(-6.79263 + 5.69969i) q^{4} +(7.78053 + 44.1256i) q^{5} -225.911 q^{6} +(-27.0245 - 153.264i) q^{7} +(-746.939 + 1293.74i) q^{8} +(-1347.17 - 1130.41i) q^{9} +(244.526 + 423.531i) q^{10} +(-2705.34 + 4685.79i) q^{11} +(172.461 - 62.7707i) q^{12} +(-8543.72 + 7169.03i) q^{13} +(-849.324 - 1471.07i) q^{14} +(161.039 - 913.297i) q^{15} +(-2634.31 + 14939.9i) q^{16} +(6729.32 + 5646.57i) q^{17} +(-18037.2 - 6565.02i) q^{18} +(18120.0 + 6595.15i) q^{19} +(-304.352 - 255.382i) q^{20} +(-559.345 + 3172.20i) q^{21} +(-10255.1 + 58159.4i) q^{22} +(-51284.0 - 88826.4i) q^{23} +(23685.9 - 19874.9i) q^{24} +(71527.0 - 26033.7i) q^{25} +(-60866.6 + 105424. i) q^{26} +(40832.4 + 70723.9i) q^{27} +(1057.12 + 887.031i) q^{28} +(-25745.7 + 44592.9i) q^{29} +(-1757.71 - 9968.45i) q^{30} -269079. q^{31} +(-4451.41 - 25245.2i) q^{32} +(85788.3 - 71985.0i) q^{33} +(90098.8 + 32793.3i) q^{34} +(6552.58 - 2384.94i) q^{35} +15593.8 q^{36} +(-275058. - 138833. i) q^{37} +210469. q^{38} +(216921. - 78952.6i) q^{39} +(-62898.4 - 22893.1i) q^{40} +(340316. - 285559. i) q^{41} +(6105.13 + 34623.9i) q^{42} +668153. q^{43} +(-8331.18 - 47248.5i) q^{44} +(39398.3 - 68239.8i) q^{45} +(-857593. - 719606. i) q^{46} +(70323.5 + 121804. i) q^{47} +(156996. - 271925. i) q^{48} +(751118. - 273385. i) q^{49} +(636434. - 534032. i) q^{50} +(-90909.4 - 157460. i) q^{51} +(17173.0 - 97393.2i) q^{52} +(-204788. + 1.16141e6i) q^{53} +(682818. + 572953. i) q^{54} +(-227812. - 82916.9i) q^{55} +(218468. + 79516.0i) q^{56} +(-305737. - 256544. i) q^{57} +(-97593.4 + 553480. i) q^{58} +(-25807.0 + 146359. i) q^{59} +(4111.63 + 7121.56i) q^{60} +(-2.49088e6 + 2.09009e6i) q^{61} +(-2.75983e6 + 1.00449e6i) q^{62} +(-136844. + 237021. i) q^{63} +(-1.11080e6 - 1.92397e6i) q^{64} +(-382812. - 321218. i) q^{65} +(611167. - 1.05857e6i) q^{66} +(730861. + 4.14492e6i) q^{67} -77893.5 q^{68} +(368641. + 2.09067e6i) q^{69} +(58303.7 - 48922.6i) q^{70} +(626834. + 228149. i) q^{71} +(2.46871e6 - 898536. i) q^{72} -2.82910e6 q^{73} +(-3.33943e6 - 397137. i) q^{74} -1.57545e6 q^{75} +(-160673. + 58480.2i) q^{76} +(791272. + 288000. i) q^{77} +(1.93012e6 - 1.61956e6i) q^{78} +(-158368. - 898151. i) q^{79} -679728. q^{80} +(374350. + 2.12305e6i) q^{81} +(2.42446e6 - 4.19928e6i) q^{82} +(3.49804e6 + 2.93521e6i) q^{83} +(-14281.1 - 24735.7i) q^{84} +(-196800. + 340868. i) q^{85} +(6.85295e6 - 2.49427e6i) q^{86} +(816414. - 685052. i) q^{87} +(-4.04145e6 - 7.00000e6i) q^{88} +(-555099. + 3.14812e6i) q^{89} +(149346. - 846983. i) q^{90} +(1.32964e6 + 1.11570e6i) q^{91} +(854636. + 311062. i) q^{92} +(5.23344e6 + 1.90482e6i) q^{93} +(1.17598e6 + 986765. i) q^{94} +(-150031. + 850870. i) q^{95} +(-92133.9 + 522518. i) q^{96} +(-5.58716e6 - 9.67725e6i) q^{97} +(6.68332e6 - 5.60797e6i) q^{98} +(8.94143e6 - 3.25441e6i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.2566 3.73308i 0.906560 0.329961i 0.153682 0.988120i \(-0.450887\pi\)
0.752879 + 0.658160i \(0.228665\pi\)
\(3\) −19.4495 7.07902i −0.415894 0.151373i 0.125593 0.992082i \(-0.459917\pi\)
−0.541488 + 0.840709i \(0.682139\pi\)
\(4\) −6.79263 + 5.69969i −0.0530674 + 0.0445288i
\(5\) 7.78053 + 44.1256i 0.0278365 + 0.157868i 0.995558 0.0941553i \(-0.0300150\pi\)
−0.967721 + 0.252024i \(0.918904\pi\)
\(6\) −225.911 −0.426980
\(7\) −27.0245 153.264i −0.0297793 0.168887i 0.966291 0.257452i \(-0.0828829\pi\)
−0.996070 + 0.0885652i \(0.971772\pi\)
\(8\) −746.939 + 1293.74i −0.515787 + 0.893369i
\(9\) −1347.17 1130.41i −0.615990 0.516877i
\(10\) 244.526 + 423.531i 0.0773258 + 0.133932i
\(11\) −2705.34 + 4685.79i −0.612842 + 1.06147i 0.377918 + 0.925839i \(0.376640\pi\)
−0.990759 + 0.135633i \(0.956693\pi\)
\(12\) 172.461 62.7707i 0.0288109 0.0104863i
\(13\) −8543.72 + 7169.03i −1.07856 + 0.905022i −0.995801 0.0915477i \(-0.970819\pi\)
−0.0827621 + 0.996569i \(0.526374\pi\)
\(14\) −849.324 1471.07i −0.0827228 0.143280i
\(15\) 161.039 913.297i 0.0123200 0.0698703i
\(16\) −2634.31 + 14939.9i −0.160785 + 0.911860i
\(17\) 6729.32 + 5646.57i 0.332200 + 0.278749i 0.793596 0.608445i \(-0.208207\pi\)
−0.461395 + 0.887195i \(0.652651\pi\)
\(18\) −18037.2 6565.02i −0.728981 0.265328i
\(19\) 18120.0 + 6595.15i 0.606068 + 0.220591i 0.626782 0.779195i \(-0.284372\pi\)
−0.0207140 + 0.999785i \(0.506594\pi\)
\(20\) −304.352 255.382i −0.00850691 0.00713814i
\(21\) −559.345 + 3172.20i −0.0131799 + 0.0747469i
\(22\) −10255.1 + 58159.4i −0.205333 + 1.16450i
\(23\) −51284.0 88826.4i −0.878889 1.52228i −0.852561 0.522627i \(-0.824952\pi\)
−0.0263280 0.999653i \(-0.508381\pi\)
\(24\) 23685.9 19874.9i 0.349745 0.293471i
\(25\) 71527.0 26033.7i 0.915545 0.333231i
\(26\) −60866.6 + 105424.i −0.679160 + 1.17634i
\(27\) 40832.4 + 70723.9i 0.399238 + 0.691501i
\(28\) 1057.12 + 887.031i 0.00910065 + 0.00763635i
\(29\) −25745.7 + 44592.9i −0.196025 + 0.339525i −0.947236 0.320537i \(-0.896137\pi\)
0.751211 + 0.660062i \(0.229470\pi\)
\(30\) −1757.71 9968.45i −0.0118856 0.0674067i
\(31\) −269079. −1.62224 −0.811118 0.584882i \(-0.801141\pi\)
−0.811118 + 0.584882i \(0.801141\pi\)
\(32\) −4451.41 25245.2i −0.0240145 0.136193i
\(33\) 85788.3 71985.0i 0.415556 0.348693i
\(34\) 90098.8 + 32793.3i 0.393136 + 0.143090i
\(35\) 6552.58 2384.94i 0.0258330 0.00940243i
\(36\) 15593.8 0.0557049
\(37\) −275058. 138833.i −0.892728 0.450597i
\(38\) 210469. 0.622223
\(39\) 216921. 78952.6i 0.585564 0.213128i
\(40\) −62898.4 22893.1i −0.155392 0.0565582i
\(41\) 340316. 285559.i 0.771151 0.647072i −0.169853 0.985469i \(-0.554329\pi\)
0.941003 + 0.338397i \(0.109885\pi\)
\(42\) 6105.13 + 34623.9i 0.0127152 + 0.0721114i
\(43\) 668153. 1.28155 0.640776 0.767728i \(-0.278613\pi\)
0.640776 + 0.767728i \(0.278613\pi\)
\(44\) −8331.18 47248.5i −0.0147442 0.0836187i
\(45\) 39398.3 68239.8i 0.0644516 0.111633i
\(46\) −857593. 719606.i −1.29906 1.09004i
\(47\) 70323.5 + 121804.i 0.0988002 + 0.171127i 0.911188 0.411990i \(-0.135166\pi\)
−0.812388 + 0.583117i \(0.801833\pi\)
\(48\) 156996. 271925.i 0.204901 0.354899i
\(49\) 751118. 273385.i 0.912057 0.331961i
\(50\) 636434. 534032.i 0.720043 0.604188i
\(51\) −90909.4 157460.i −0.0959651 0.166216i
\(52\) 17173.0 97393.2i 0.0169370 0.0960543i
\(53\) −204788. + 1.16141e6i −0.188947 + 1.07157i 0.731832 + 0.681485i \(0.238665\pi\)
−0.920779 + 0.390085i \(0.872446\pi\)
\(54\) 682818. + 572953.i 0.590102 + 0.495154i
\(55\) −227812. 82916.9i −0.184632 0.0672007i
\(56\) 218468. + 79516.0i 0.166238 + 0.0605057i
\(57\) −305737. 256544.i −0.218669 0.183485i
\(58\) −97593.4 + 553480.i −0.0656784 + 0.372481i
\(59\) −25807.0 + 146359.i −0.0163590 + 0.0927764i −0.991894 0.127067i \(-0.959444\pi\)
0.975535 + 0.219844i \(0.0705547\pi\)
\(60\) 4111.63 + 7121.56i 0.00245745 + 0.00425643i
\(61\) −2.49088e6 + 2.09009e6i −1.40507 + 1.17899i −0.446274 + 0.894897i \(0.647249\pi\)
−0.958796 + 0.284097i \(0.908306\pi\)
\(62\) −2.75983e6 + 1.00449e6i −1.47065 + 0.535275i
\(63\) −136844. + 237021.i −0.0689500 + 0.119425i
\(64\) −1.11080e6 1.92397e6i −0.529672 0.917419i
\(65\) −382812. 321218.i −0.172898 0.145078i
\(66\) 611167. 1.05857e6i 0.261671 0.453228i
\(67\) 730861. + 4.14492e6i 0.296875 + 1.68366i 0.659484 + 0.751719i \(0.270775\pi\)
−0.362609 + 0.931941i \(0.618114\pi\)
\(68\) −77893.5 −0.0300414
\(69\) 368641. + 2.09067e6i 0.135093 + 0.766148i
\(70\) 58303.7 48922.6i 0.0203167 0.0170477i
\(71\) 626834. + 228149.i 0.207849 + 0.0756509i 0.443847 0.896103i \(-0.353613\pi\)
−0.235998 + 0.971754i \(0.575836\pi\)
\(72\) 2.46871e6 898536.i 0.779481 0.283708i
\(73\) −2.82910e6 −0.851173 −0.425587 0.904918i \(-0.639932\pi\)
−0.425587 + 0.904918i \(0.639932\pi\)
\(74\) −3.33943e6 397137.i −0.957991 0.113928i
\(75\) −1.57545e6 −0.431212
\(76\) −160673. + 58480.2i −0.0419851 + 0.0152813i
\(77\) 791272. + 288000.i 0.197519 + 0.0718910i
\(78\) 1.93012e6 1.61956e6i 0.460525 0.386427i
\(79\) −158368. 898151.i −0.0361388 0.204953i 0.961392 0.275182i \(-0.0887381\pi\)
−0.997531 + 0.0702289i \(0.977627\pi\)
\(80\) −679728. −0.148430
\(81\) 374350. + 2.12305e6i 0.0782674 + 0.443876i
\(82\) 2.42446e6 4.19928e6i 0.485586 0.841060i
\(83\) 3.49804e6 + 2.93521e6i 0.671509 + 0.563463i 0.913512 0.406812i \(-0.133360\pi\)
−0.242002 + 0.970276i \(0.577804\pi\)
\(84\) −14281.1 24735.7i −0.00262897 0.00455351i
\(85\) −196800. + 340868.i −0.0347584 + 0.0602033i
\(86\) 6.85295e6 2.49427e6i 1.16180 0.422862i
\(87\) 816414. 685052.i 0.132921 0.111534i
\(88\) −4.04145e6 7.00000e6i −0.632191 1.09499i
\(89\) −555099. + 3.14812e6i −0.0834652 + 0.473355i 0.914212 + 0.405236i \(0.132811\pi\)
−0.997677 + 0.0681185i \(0.978300\pi\)
\(90\) 149346. 846983.i 0.0215946 0.122469i
\(91\) 1.32964e6 + 1.11570e6i 0.184965 + 0.155204i
\(92\) 854636. + 311062.i 0.114426 + 0.0416476i
\(93\) 5.23344e6 + 1.90482e6i 0.674679 + 0.245563i
\(94\) 1.17598e6 + 986765.i 0.146034 + 0.122537i
\(95\) −150031. + 850870.i −0.0179535 + 0.101819i
\(96\) −92133.9 + 522518.i −0.0106285 + 0.0602770i
\(97\) −5.58716e6 9.67725e6i −0.621570 1.07659i −0.989193 0.146616i \(-0.953162\pi\)
0.367623 0.929975i \(-0.380172\pi\)
\(98\) 6.68332e6 5.60797e6i 0.717300 0.601886i
\(99\) 8.94143e6 3.25441e6i 0.926155 0.337093i
\(100\) −337472. + 584519.i −0.0337472 + 0.0584519i
\(101\) −3.35299e6 5.80755e6i −0.323823 0.560877i 0.657451 0.753498i \(-0.271635\pi\)
−0.981273 + 0.192620i \(0.938301\pi\)
\(102\) −1.52023e6 1.27562e6i −0.141843 0.119020i
\(103\) −2.27991e6 + 3.94892e6i −0.205583 + 0.356081i −0.950318 0.311279i \(-0.899242\pi\)
0.744735 + 0.667360i \(0.232576\pi\)
\(104\) −2.89320e6 1.64082e7i −0.252210 1.43035i
\(105\) −144327. −0.0121671
\(106\) 2.23522e6 + 1.26766e7i 0.182285 + 1.03379i
\(107\) −1.74051e7 + 1.46046e7i −1.37352 + 1.15252i −0.401976 + 0.915650i \(0.631676\pi\)
−0.971542 + 0.236868i \(0.923879\pi\)
\(108\) −680464. 247669.i −0.0519783 0.0189185i
\(109\) 436151. 158746.i 0.0322585 0.0117411i −0.325841 0.945425i \(-0.605647\pi\)
0.358099 + 0.933684i \(0.383425\pi\)
\(110\) −2.64611e6 −0.189554
\(111\) 4.36693e6 + 4.64738e6i 0.303072 + 0.322536i
\(112\) 2.36094e6 0.158789
\(113\) −1.18330e6 + 430685.i −0.0771471 + 0.0280793i −0.380305 0.924861i \(-0.624181\pi\)
0.303158 + 0.952940i \(0.401959\pi\)
\(114\) −4.09351e6 1.48992e6i −0.258779 0.0941879i
\(115\) 3.52050e6 2.95405e6i 0.215855 0.181124i
\(116\) −79284.6 449645.i −0.00471613 0.0267465i
\(117\) 1.96138e7 1.13217
\(118\) 281679. + 1.59748e6i 0.0157822 + 0.0895052i
\(119\) 683557. 1.18396e6i 0.0371844 0.0644052i
\(120\) 1.06128e6 + 890518.i 0.0560654 + 0.0470445i
\(121\) −4.89419e6 8.47699e6i −0.251150 0.435004i
\(122\) −1.77453e7 + 3.07358e7i −0.884758 + 1.53245i
\(123\) −8.64045e6 + 3.14487e6i −0.418667 + 0.152382i
\(124\) 1.82775e6 1.53367e6i 0.0860879 0.0722363i
\(125\) 3.45551e6 + 5.98512e6i 0.158244 + 0.274087i
\(126\) −518731. + 2.94187e6i −0.0231018 + 0.131017i
\(127\) 1.66110e6 9.42058e6i 0.0719587 0.408098i −0.927457 0.373929i \(-0.878010\pi\)
0.999416 0.0341692i \(-0.0108785\pi\)
\(128\) −1.60618e7 1.34774e7i −0.676953 0.568031i
\(129\) −1.29952e7 4.72987e6i −0.532991 0.193993i
\(130\) −5.12547e6 1.86552e6i −0.204612 0.0744728i
\(131\) 7.47402e6 + 6.27145e6i 0.290472 + 0.243735i 0.776365 0.630283i \(-0.217061\pi\)
−0.485893 + 0.874018i \(0.661506\pi\)
\(132\) −172436. + 977934.i −0.00652559 + 0.0370084i
\(133\) 521112. 2.95537e6i 0.0192066 0.108926i
\(134\) 2.29694e7 + 3.97842e7i 0.824677 + 1.42838i
\(135\) −2.80303e6 + 2.35202e6i −0.0980528 + 0.0822761i
\(136\) −1.23316e7 + 4.48832e6i −0.420370 + 0.153002i
\(137\) 5.05851e6 8.76159e6i 0.168074 0.291113i −0.769669 0.638443i \(-0.779579\pi\)
0.937743 + 0.347331i \(0.112912\pi\)
\(138\) 1.15856e7 + 2.00669e7i 0.375269 + 0.649984i
\(139\) 2.21757e7 + 1.86076e7i 0.700366 + 0.587677i 0.921878 0.387481i \(-0.126655\pi\)
−0.221512 + 0.975158i \(0.571099\pi\)
\(140\) −30915.8 + 53547.7i −0.000952209 + 0.00164927i
\(141\) −505501. 2.86684e6i −0.0151864 0.0861265i
\(142\) 7.28086e6 0.213390
\(143\) −1.04789e7 5.94288e7i −0.299668 1.69950i
\(144\) 2.04371e7 1.71488e7i 0.570362 0.478590i
\(145\) −2.16800e6 789087.i −0.0590570 0.0214950i
\(146\) −2.90168e7 + 1.05613e7i −0.771640 + 0.280854i
\(147\) −1.65441e7 −0.429569
\(148\) 2.65968e6 624705.i 0.0674393 0.0158401i
\(149\) −6.92230e7 −1.71435 −0.857173 0.515028i \(-0.827782\pi\)
−0.857173 + 0.515028i \(0.827782\pi\)
\(150\) −1.61587e7 + 5.88130e6i −0.390920 + 0.142283i
\(151\) 6.12994e7 + 2.23112e7i 1.44890 + 0.527355i 0.942283 0.334819i \(-0.108675\pi\)
0.506613 + 0.862174i \(0.330897\pi\)
\(152\) −2.20669e7 + 1.85164e7i −0.509670 + 0.427664i
\(153\) −2.68260e6 1.52138e7i −0.0605531 0.343413i
\(154\) 9.19086e6 0.202784
\(155\) −2.09358e6 1.18733e7i −0.0451573 0.256100i
\(156\) −1.02346e6 + 1.77268e6i −0.0215840 + 0.0373846i
\(157\) 8.37400e6 + 7.02662e6i 0.172697 + 0.144910i 0.725039 0.688707i \(-0.241822\pi\)
−0.552343 + 0.833617i \(0.686266\pi\)
\(158\) −4.97718e6 8.62074e6i −0.100388 0.173878i
\(159\) 1.22047e7 2.11391e7i 0.240789 0.417058i
\(160\) 1.07933e6 392842.i 0.0208321 0.00758225i
\(161\) −1.22279e7 + 1.02605e7i −0.230921 + 0.193765i
\(162\) 1.17651e7 + 2.03777e7i 0.217416 + 0.376575i
\(163\) 2.79159e6 1.58319e7i 0.0504889 0.286337i −0.949101 0.314972i \(-0.898005\pi\)
0.999590 + 0.0286351i \(0.00911608\pi\)
\(164\) −684042. + 3.87940e6i −0.0121096 + 0.0686769i
\(165\) 3.84385e6 + 3.22538e6i 0.0666152 + 0.0558968i
\(166\) 4.68353e7 + 1.70466e7i 0.794684 + 0.289241i
\(167\) 1.93769e7 + 7.05260e6i 0.321941 + 0.117177i 0.497935 0.867214i \(-0.334092\pi\)
−0.175994 + 0.984391i \(0.556314\pi\)
\(168\) −3.68619e6 3.09308e6i −0.0599785 0.0503279i
\(169\) 1.07040e7 6.07053e7i 0.170585 0.967437i
\(170\) −746006. + 4.23081e6i −0.0116458 + 0.0660468i
\(171\) −1.69555e7 2.93679e7i −0.259314 0.449144i
\(172\) −4.53852e6 + 3.80827e6i −0.0680087 + 0.0570661i
\(173\) −7.61702e6 + 2.77237e6i −0.111847 + 0.0407089i −0.397337 0.917673i \(-0.630066\pi\)
0.285490 + 0.958382i \(0.407844\pi\)
\(174\) 5.81624e6 1.00740e7i 0.0836989 0.144971i
\(175\) −5.92300e6 1.02589e7i −0.0835427 0.144700i
\(176\) −6.28786e7 5.27614e7i −0.869378 0.729495i
\(177\) 1.53801e6 2.66391e6i 0.0208475 0.0361089i
\(178\) 6.05880e6 + 3.43611e7i 0.0805223 + 0.456665i
\(179\) −3.28925e6 −0.0428658 −0.0214329 0.999770i \(-0.506823\pi\)
−0.0214329 + 0.999770i \(0.506823\pi\)
\(180\) 121328. + 688086.i 0.00155063 + 0.00879405i
\(181\) 9.24904e7 7.76087e7i 1.15937 0.972826i 0.159473 0.987202i \(-0.449021\pi\)
0.999897 + 0.0143758i \(0.00457613\pi\)
\(182\) 1.78026e7 + 6.47960e6i 0.218893 + 0.0796707i
\(183\) 6.32420e7 2.30182e7i 0.762828 0.277647i
\(184\) 1.53224e8 1.81328
\(185\) 3.98600e6 1.32173e7i 0.0462846 0.153477i
\(186\) 6.07879e7 0.692663
\(187\) −4.46638e7 + 1.62563e7i −0.499471 + 0.181792i
\(188\) −1.17193e6 426546.i −0.0128632 0.00468181i
\(189\) 9.73592e6 8.16941e6i 0.104896 0.0880185i
\(190\) 1.63756e6 + 9.28708e6i 0.0173205 + 0.0982294i
\(191\) −9.08216e7 −0.943132 −0.471566 0.881831i \(-0.656311\pi\)
−0.471566 + 0.881831i \(0.656311\pi\)
\(192\) 7.98470e6 + 4.52835e7i 0.0814150 + 0.461728i
\(193\) 3.46987e7 6.00999e7i 0.347426 0.601760i −0.638365 0.769734i \(-0.720389\pi\)
0.985791 + 0.167974i \(0.0537224\pi\)
\(194\) −9.34310e7 7.83979e7i −0.918724 0.770901i
\(195\) 5.17158e6 + 8.95745e6i 0.0499462 + 0.0865094i
\(196\) −3.54386e6 + 6.13814e6i −0.0336186 + 0.0582292i
\(197\) −1.55141e8 + 5.64668e7i −1.44576 + 0.526213i −0.941403 0.337284i \(-0.890492\pi\)
−0.504355 + 0.863497i \(0.668270\pi\)
\(198\) 7.95593e7 6.67582e7i 0.728388 0.611190i
\(199\) 6.82555e7 + 1.18222e8i 0.613977 + 1.06344i 0.990563 + 0.137058i \(0.0437646\pi\)
−0.376586 + 0.926382i \(0.622902\pi\)
\(200\) −1.97455e7 + 1.11983e8i −0.174528 + 0.989795i
\(201\) 1.51271e7 8.57902e7i 0.131392 0.745164i
\(202\) −5.60702e7 4.70485e7i −0.478632 0.401620i
\(203\) 7.53023e6 + 2.74078e6i 0.0631789 + 0.0229952i
\(204\) 1.51499e6 + 551410.i 0.0124940 + 0.00454746i
\(205\) 1.52483e7 + 1.27948e7i 0.123618 + 0.103728i
\(206\) −8.64240e6 + 4.90135e7i −0.0688809 + 0.390643i
\(207\) −3.13221e7 + 1.77636e8i −0.245445 + 1.39199i
\(208\) −8.45979e7 1.46528e8i −0.651835 1.12901i
\(209\) −7.99244e7 + 6.70646e7i −0.605574 + 0.508137i
\(210\) −1.48030e6 + 538785.i −0.0110302 + 0.00401465i
\(211\) −6.89554e7 + 1.19434e8i −0.505336 + 0.875267i 0.494645 + 0.869095i \(0.335298\pi\)
−0.999981 + 0.00617202i \(0.998035\pi\)
\(212\) −5.22863e6 9.05626e6i −0.0376888 0.0652790i
\(213\) −1.05765e7 8.87474e6i −0.0749918 0.0629256i
\(214\) −1.23996e8 + 2.14768e8i −0.864890 + 1.49803i
\(215\) 5.19858e6 + 2.94826e7i 0.0356739 + 0.202317i
\(216\) −1.21997e8 −0.823687
\(217\) 7.27173e6 + 4.12400e7i 0.0483091 + 0.273974i
\(218\) 3.88080e6 3.25637e6i 0.0253702 0.0212881i
\(219\) 5.50244e7 + 2.00272e7i 0.353998 + 0.128845i
\(220\) 2.02005e6 735236.i 0.0127903 0.00465530i
\(221\) −9.79739e7 −0.610573
\(222\) 6.21387e7 + 3.13640e7i 0.381177 + 0.192396i
\(223\) 1.47446e8 0.890363 0.445181 0.895440i \(-0.353139\pi\)
0.445181 + 0.895440i \(0.353139\pi\)
\(224\) −3.74888e6 + 1.36448e6i −0.0222861 + 0.00811146i
\(225\) −1.25788e8 4.57830e7i −0.736206 0.267957i
\(226\) −1.05288e7 + 8.83470e6i −0.0606734 + 0.0509111i
\(227\) 1.83448e7 + 1.04038e8i 0.104093 + 0.590341i 0.991579 + 0.129505i \(0.0413390\pi\)
−0.887486 + 0.460835i \(0.847550\pi\)
\(228\) 3.53898e6 0.0197745
\(229\) −3.72972e7 2.11523e8i −0.205235 1.16395i −0.897069 0.441890i \(-0.854308\pi\)
0.691834 0.722057i \(-0.256803\pi\)
\(230\) 2.50805e7 4.34407e7i 0.135922 0.235423i
\(231\) −1.33511e7 1.12029e7i −0.0712646 0.0597981i
\(232\) −3.84609e7 6.66163e7i −0.202214 0.350245i
\(233\) −1.54015e8 + 2.66761e8i −0.797657 + 1.38158i 0.123482 + 0.992347i \(0.460594\pi\)
−0.921138 + 0.389235i \(0.872739\pi\)
\(234\) 2.01170e8 7.32199e7i 1.02638 0.373571i
\(235\) −4.82751e6 + 4.05076e6i −0.0242653 + 0.0203610i
\(236\) −658904. 1.14125e6i −0.00326310 0.00565185i
\(237\) −3.27786e6 + 1.85896e7i −0.0159945 + 0.0907093i
\(238\) 2.59114e6 1.46951e7i 0.0124587 0.0706566i
\(239\) −3.51860e7 2.95246e7i −0.166716 0.139891i 0.555613 0.831441i \(-0.312484\pi\)
−0.722329 + 0.691550i \(0.756928\pi\)
\(240\) 1.32203e7 + 4.81181e6i 0.0617310 + 0.0224682i
\(241\) 2.96633e8 + 1.07966e8i 1.36509 + 0.496851i 0.917623 0.397451i \(-0.130105\pi\)
0.447463 + 0.894302i \(0.352328\pi\)
\(242\) −8.18429e7 6.86743e7i −0.371216 0.311488i
\(243\) 3.87619e7 2.19830e8i 0.173294 0.982799i
\(244\) 5.00671e6 2.83945e7i 0.0220642 0.125132i
\(245\) 1.79073e7 + 3.10164e7i 0.0777947 + 0.134744i
\(246\) −7.68812e7 + 6.45110e7i −0.329266 + 0.276287i
\(247\) −2.02093e8 + 7.35560e7i −0.853321 + 0.310584i
\(248\) 2.00986e8 3.48117e8i 0.836728 1.44925i
\(249\) −4.72567e7 8.18509e7i −0.193984 0.335990i
\(250\) 5.77846e7 + 4.84871e7i 0.233896 + 0.196262i
\(251\) 1.86720e8 3.23409e8i 0.745303 1.29090i −0.204750 0.978814i \(-0.565638\pi\)
0.950053 0.312089i \(-0.101029\pi\)
\(252\) −421415. 2.38997e6i −0.00165886 0.00940783i
\(253\) 5.54963e8 2.15448
\(254\) −1.81306e7 1.02824e8i −0.0694215 0.393709i
\(255\) 6.24068e6 5.23655e6i 0.0235690 0.0197767i
\(256\) 5.21655e7 + 1.89867e7i 0.194332 + 0.0707309i
\(257\) 1.04085e8 3.78837e7i 0.382490 0.139215i −0.143617 0.989633i \(-0.545873\pi\)
0.526107 + 0.850418i \(0.323651\pi\)
\(258\) −1.50943e8 −0.547198
\(259\) −1.38448e7 + 4.59084e7i −0.0495150 + 0.164188i
\(260\) 4.43114e6 0.0156354
\(261\) 8.50921e7 3.09710e7i 0.296242 0.107823i
\(262\) 1.00070e8 + 3.64223e7i 0.343754 + 0.125116i
\(263\) 1.60755e8 1.34889e8i 0.544902 0.457227i −0.328308 0.944571i \(-0.606479\pi\)
0.873210 + 0.487344i \(0.162034\pi\)
\(264\) 2.90509e7 + 1.64756e8i 0.0971730 + 0.551096i
\(265\) −5.28413e7 −0.174427
\(266\) −5.68783e6 3.22573e7i −0.0185294 0.105085i
\(267\) 3.30820e7 5.72997e7i 0.106366 0.184231i
\(268\) −2.85892e7 2.39892e7i −0.0907258 0.0761280i
\(269\) −2.26005e8 3.91453e8i −0.707922 1.22616i −0.965627 0.259933i \(-0.916299\pi\)
0.257704 0.966224i \(-0.417034\pi\)
\(270\) −1.99692e7 + 3.45876e7i −0.0617429 + 0.106942i
\(271\) −4.60396e7 + 1.67570e7i −0.140520 + 0.0511452i −0.411323 0.911490i \(-0.634933\pi\)
0.270803 + 0.962635i \(0.412711\pi\)
\(272\) −1.02086e8 + 8.56606e7i −0.307593 + 0.258101i
\(273\) −1.79627e7 3.11124e7i −0.0534322 0.0925473i
\(274\) 1.91751e7 1.08748e8i 0.0563134 0.319369i
\(275\) −7.15166e7 + 4.05591e8i −0.207368 + 1.17604i
\(276\) −1.44202e7 1.21000e7i −0.0412847 0.0346420i
\(277\) −4.15983e8 1.51405e8i −1.17597 0.428018i −0.321194 0.947014i \(-0.604084\pi\)
−0.854777 + 0.518995i \(0.826306\pi\)
\(278\) 2.96910e8 + 1.08066e8i 0.828835 + 0.301671i
\(279\) 3.62495e8 + 3.04170e8i 0.999282 + 0.838497i
\(280\) −1.80889e6 + 1.02587e7i −0.00492446 + 0.0279280i
\(281\) −1.04943e8 + 5.95164e8i −0.282152 + 1.60016i 0.433132 + 0.901330i \(0.357408\pi\)
−0.715284 + 0.698834i \(0.753703\pi\)
\(282\) −1.58869e7 2.75168e7i −0.0421858 0.0730679i
\(283\) −8.30252e7 + 6.96664e7i −0.217750 + 0.182714i −0.745137 0.666911i \(-0.767616\pi\)
0.527388 + 0.849625i \(0.323172\pi\)
\(284\) −5.55823e6 + 2.02303e6i −0.0143987 + 0.00524068i
\(285\) 8.94136e6 1.54869e7i 0.0228795 0.0396284i
\(286\) −3.29330e8 5.70417e8i −0.832435 1.44182i
\(287\) −5.29627e7 4.44410e7i −0.132246 0.110968i
\(288\) −2.25406e7 + 3.90415e7i −0.0556023 + 0.0963060i
\(289\) −5.78546e7 3.28110e8i −0.140992 0.799607i
\(290\) −2.51819e7 −0.0606312
\(291\) 4.01618e7 + 2.27769e8i 0.0955405 + 0.541837i
\(292\) 1.92170e7 1.61250e7i 0.0451696 0.0379018i
\(293\) −4.00684e8 1.45837e8i −0.930606 0.338713i −0.168156 0.985760i \(-0.553781\pi\)
−0.762450 + 0.647048i \(0.776003\pi\)
\(294\) −1.69686e8 + 6.17606e7i −0.389430 + 0.141741i
\(295\) −6.65896e6 −0.0151018
\(296\) 3.85066e8 2.52153e8i 0.863006 0.565123i
\(297\) −4.41863e8 −0.978679
\(298\) −7.09990e8 + 2.58415e8i −1.55416 + 0.565667i
\(299\) 1.07496e9 + 3.91252e8i 2.32563 + 0.846462i
\(300\) 1.07015e7 8.97960e6i 0.0228833 0.0192014i
\(301\) −1.80565e7 1.02404e8i −0.0381638 0.216437i
\(302\) 7.12010e8 1.48752
\(303\) 2.41020e7 + 1.36689e8i 0.0497742 + 0.282284i
\(304\) −1.46265e8 + 2.53338e8i −0.298595 + 0.517181i
\(305\) −1.11607e8 9.36493e7i −0.225238 0.188997i
\(306\) −8.43086e7 1.46027e8i −0.168208 0.291345i
\(307\) −2.71297e8 + 4.69899e8i −0.535131 + 0.926874i 0.464026 + 0.885821i \(0.346404\pi\)
−0.999157 + 0.0410523i \(0.986929\pi\)
\(308\) −7.01633e6 + 2.55374e6i −0.0136830 + 0.00498022i
\(309\) 7.22976e7 6.06649e7i 0.139402 0.116972i
\(310\) −6.57968e7 1.13963e8i −0.125441 0.217270i
\(311\) −1.21762e8 + 6.90548e8i −0.229536 + 1.30176i 0.624284 + 0.781197i \(0.285391\pi\)
−0.853821 + 0.520567i \(0.825721\pi\)
\(312\) −5.98825e7 + 3.39611e8i −0.111624 + 0.633053i
\(313\) −7.08517e8 5.94516e8i −1.30601 1.09587i −0.989074 0.147420i \(-0.952903\pi\)
−0.316931 0.948448i \(-0.602652\pi\)
\(314\) 1.12119e8 + 4.08081e7i 0.204374 + 0.0743862i
\(315\) −1.15234e7 4.19418e6i −0.0207727 0.00756066i
\(316\) 6.19492e6 + 5.19816e6i 0.0110441 + 0.00926712i
\(317\) 2.21082e7 1.25382e8i 0.0389804 0.221069i −0.959095 0.283085i \(-0.908642\pi\)
0.998075 + 0.0620164i \(0.0197531\pi\)
\(318\) 4.62639e7 2.62375e8i 0.0806765 0.457539i
\(319\) −1.39302e8 2.41278e8i −0.240265 0.416151i
\(320\) 7.62535e7 6.39843e7i 0.130087 0.109156i
\(321\) 4.41907e8 1.60841e8i 0.745699 0.271412i
\(322\) −8.71134e7 + 1.50885e8i −0.145408 + 0.251855i
\(323\) 8.46955e7 + 1.46697e8i 0.139846 + 0.242221i
\(324\) −1.46435e7 1.22874e7i −0.0239187 0.0200702i
\(325\) −4.24470e8 + 7.35204e8i −0.685891 + 1.18800i
\(326\) −3.04697e7 1.72802e8i −0.0487087 0.276241i
\(327\) −9.60667e6 −0.0151934
\(328\) 1.15243e8 + 6.53575e8i 0.180325 + 1.02267i
\(329\) 1.67676e7 1.40697e7i 0.0259589 0.0217821i
\(330\) 5.14653e7 + 1.87318e7i 0.0788344 + 0.0286934i
\(331\) 5.92719e8 2.15732e8i 0.898360 0.326976i 0.148765 0.988873i \(-0.452470\pi\)
0.749595 + 0.661896i \(0.230248\pi\)
\(332\) −4.04907e7 −0.0607256
\(333\) 2.13612e8 + 4.97961e8i 0.317008 + 0.738994i
\(334\) 2.25068e8 0.330522
\(335\) −1.77210e8 + 6.44993e7i −0.257533 + 0.0937343i
\(336\) −4.59189e7 1.67131e7i −0.0660395 0.0240364i
\(337\) 2.70752e8 2.27188e8i 0.385360 0.323355i −0.429442 0.903094i \(-0.641290\pi\)
0.814802 + 0.579739i \(0.196845\pi\)
\(338\) −1.16832e8 6.62586e8i −0.164571 0.933327i
\(339\) 2.60633e7 0.0363355
\(340\) −606052. 3.43709e6i −0.000836246 0.00474259i
\(341\) 7.27952e8 1.26085e9i 0.994174 1.72196i
\(342\) −2.83538e8 2.37917e8i −0.383283 0.321613i
\(343\) −1.26282e8 2.18726e8i −0.168970 0.292665i
\(344\) −4.99069e8 + 8.64414e8i −0.661008 + 1.14490i
\(345\) −8.93836e7 + 3.25330e7i −0.117190 + 0.0426537i
\(346\) −6.77750e7 + 5.68699e7i −0.0879636 + 0.0738102i
\(347\) 5.84900e8 + 1.01308e9i 0.751499 + 1.30163i 0.947096 + 0.320950i \(0.104002\pi\)
−0.195598 + 0.980684i \(0.562665\pi\)
\(348\) −1.64101e6 + 9.30661e6i −0.00208729 + 0.0118376i
\(349\) −4.56071e7 + 2.58651e8i −0.0574307 + 0.325705i −0.999965 0.00840472i \(-0.997325\pi\)
0.942534 + 0.334110i \(0.108436\pi\)
\(350\) −9.90470e7 8.31103e7i −0.123482 0.103614i
\(351\) −8.55883e8 3.11516e8i −1.05643 0.384508i
\(352\) 1.30337e8 + 4.74386e7i 0.159282 + 0.0579739i
\(353\) −6.89160e8 5.78274e8i −0.833889 0.699716i 0.122291 0.992494i \(-0.460976\pi\)
−0.956180 + 0.292778i \(0.905420\pi\)
\(354\) 5.83009e6 3.30641e7i 0.00698496 0.0396137i
\(355\) −5.19010e6 + 2.94345e7i −0.00615710 + 0.0349187i
\(356\) −1.41728e7 2.45479e7i −0.0166487 0.0288363i
\(357\) −2.16761e7 + 1.81884e7i −0.0252140 + 0.0211571i
\(358\) −3.37363e7 + 1.22790e7i −0.0388604 + 0.0141440i
\(359\) −4.04858e8 + 7.01235e8i −0.461820 + 0.799896i −0.999052 0.0435390i \(-0.986137\pi\)
0.537232 + 0.843435i \(0.319470\pi\)
\(360\) 5.88562e7 + 1.01942e8i 0.0664865 + 0.115158i
\(361\) −3.99906e8 3.35561e8i −0.447386 0.375402i
\(362\) 6.58914e8 1.14127e9i 0.730043 1.26447i
\(363\) 3.51806e7 + 1.99519e8i 0.0386038 + 0.218933i
\(364\) −1.53909e7 −0.0167267
\(365\) −2.20119e7 1.24836e8i −0.0236936 0.134373i
\(366\) 5.62716e8 4.72175e8i 0.599937 0.503407i
\(367\) 9.81852e8 + 3.57365e8i 1.03685 + 0.377381i 0.803684 0.595056i \(-0.202870\pi\)
0.233163 + 0.972438i \(0.425092\pi\)
\(368\) 1.46216e9 5.32181e8i 1.52942 0.556663i
\(369\) −7.81263e8 −0.809478
\(370\) −8.45863e6 1.50444e8i −0.00868149 0.154408i
\(371\) 1.83536e8 0.186601
\(372\) −4.64057e7 + 1.68903e7i −0.0467381 + 0.0170113i
\(373\) 4.68581e8 + 1.70549e8i 0.467524 + 0.170165i 0.565030 0.825070i \(-0.308865\pi\)
−0.0975067 + 0.995235i \(0.531087\pi\)
\(374\) −3.97411e8 + 3.33467e8i −0.392816 + 0.329612i
\(375\) −2.48390e7 1.40869e8i −0.0243234 0.137945i
\(376\) −2.10109e8 −0.203839
\(377\) −9.97236e7 5.65561e8i −0.0958525 0.543606i
\(378\) 6.93599e7 1.20135e8i 0.0660522 0.114406i
\(379\) −1.82732e8 1.53330e8i −0.172416 0.144674i 0.552496 0.833515i \(-0.313675\pi\)
−0.724912 + 0.688841i \(0.758120\pi\)
\(380\) −3.83059e6 6.63478e6i −0.00358116 0.00620274i
\(381\) −9.89960e7 + 1.71466e8i −0.0917023 + 0.158833i
\(382\) −9.31517e8 + 3.39044e8i −0.855005 + 0.311197i
\(383\) 1.31092e9 1.09999e9i 1.19228 1.00044i 0.192467 0.981303i \(-0.438351\pi\)
0.999817 0.0191412i \(-0.00609321\pi\)
\(384\) 2.16986e8 + 3.75830e8i 0.195556 + 0.338713i
\(385\) −6.55163e6 + 3.71561e7i −0.00585109 + 0.0331832i
\(386\) 1.31531e8 7.45951e8i 0.116405 0.660168i
\(387\) −9.00116e8 7.55287e8i −0.789424 0.662405i
\(388\) 9.31089e7 + 3.38889e7i 0.0809245 + 0.0294541i
\(389\) 5.22200e8 + 1.90065e8i 0.449793 + 0.163711i 0.556977 0.830528i \(-0.311961\pi\)
−0.107184 + 0.994239i \(0.534183\pi\)
\(390\) 8.64815e7 + 7.25666e7i 0.0738239 + 0.0619456i
\(391\) 1.56458e8 8.87320e8i 0.132367 0.750692i
\(392\) −2.07352e8 + 1.17595e9i −0.173863 + 0.986024i
\(393\) −1.00970e8 1.74885e8i −0.0839108 0.145338i
\(394\) −1.38042e9 + 1.15831e9i −1.13704 + 0.954087i
\(395\) 3.83992e7 1.39762e7i 0.0313496 0.0114103i
\(396\) −4.21867e7 + 7.30694e7i −0.0341383 + 0.0591293i
\(397\) −1.71047e8 2.96261e8i −0.137198 0.237634i 0.789237 0.614089i \(-0.210476\pi\)
−0.926435 + 0.376455i \(0.877143\pi\)
\(398\) 1.14140e9 + 9.57748e8i 0.907500 + 0.761483i
\(399\) −3.10565e7 + 5.37914e7i −0.0244764 + 0.0423943i
\(400\) 2.00517e8 + 1.13719e9i 0.156654 + 0.888427i
\(401\) −2.54444e8 −0.197055 −0.0985275 0.995134i \(-0.531413\pi\)
−0.0985275 + 0.995134i \(0.531413\pi\)
\(402\) −1.65110e8 9.36383e8i −0.126760 0.718890i
\(403\) 2.29894e9 1.92904e9i 1.74968 1.46816i
\(404\) 5.58768e7 + 2.03375e7i 0.0421597 + 0.0153449i
\(405\) −9.07680e7 + 3.30368e7i −0.0678954 + 0.0247119i
\(406\) 8.74658e7 0.0648630
\(407\) 1.39467e9 9.13275e8i 1.02540 0.671462i
\(408\) 2.71615e8 0.197990
\(409\) −5.20781e8 + 1.89549e8i −0.376377 + 0.136990i −0.523280 0.852161i \(-0.675292\pi\)
0.146903 + 0.989151i \(0.453070\pi\)
\(410\) 2.04159e8 + 7.43079e7i 0.146294 + 0.0532466i
\(411\) −1.60409e8 + 1.34599e8i −0.113968 + 0.0956302i
\(412\) −7.02106e6 3.98184e7i −0.00494609 0.0280507i
\(413\) 2.31289e7 0.0161559
\(414\) 3.41874e8 + 1.93886e9i 0.236791 + 1.34291i
\(415\) −1.02301e8 + 1.77191e8i −0.0702606 + 0.121695i
\(416\) 2.19016e8 + 1.83776e8i 0.149159 + 0.125159i
\(417\) −2.99581e8 5.18890e8i −0.202320 0.350428i
\(418\) −5.69392e8 + 9.86216e8i −0.381324 + 0.660473i
\(419\) −1.60333e9 + 5.83564e8i −1.06481 + 0.387560i −0.814235 0.580536i \(-0.802843\pi\)
−0.250579 + 0.968096i \(0.580621\pi\)
\(420\) 980361. 822620.i 0.000645674 0.000541785i
\(421\) −5.59060e8 9.68321e8i −0.365150 0.632459i 0.623650 0.781704i \(-0.285649\pi\)
−0.988800 + 0.149245i \(0.952316\pi\)
\(422\) −2.61387e8 + 1.48240e9i −0.169313 + 0.960223i
\(423\) 4.29506e7 2.43585e8i 0.0275917 0.156480i
\(424\) −1.34959e9 1.13244e9i −0.859850 0.721500i
\(425\) 6.28329e8 + 2.28693e8i 0.397032 + 0.144508i
\(426\) −1.41609e8 5.15413e7i −0.0887475 0.0323015i
\(427\) 3.87650e8 + 3.25277e8i 0.240958 + 0.202188i
\(428\) 3.49847e7 1.98408e8i 0.0215687 0.122322i
\(429\) −2.16889e8 + 1.23004e9i −0.132629 + 0.752174i
\(430\) 1.63381e8 + 2.82984e8i 0.0990971 + 0.171641i
\(431\) −2.41785e9 + 2.02881e9i −1.45465 + 1.22060i −0.525552 + 0.850762i \(0.676141\pi\)
−0.929098 + 0.369834i \(0.879414\pi\)
\(432\) −1.16417e9 + 4.23724e8i −0.694743 + 0.252866i
\(433\) 1.41743e9 2.45507e9i 0.839065 1.45330i −0.0516131 0.998667i \(-0.516436\pi\)
0.890678 0.454635i \(-0.150230\pi\)
\(434\) 2.28535e8 + 3.95835e8i 0.134196 + 0.232434i
\(435\) 3.65804e7 + 3.06946e7i 0.0213077 + 0.0178793i
\(436\) −2.05781e6 + 3.56423e6i −0.00118906 + 0.00205951i
\(437\) −3.43443e8 1.94776e9i −0.196866 1.11648i
\(438\) 6.39124e8 0.363434
\(439\) 3.07903e8 + 1.74621e9i 0.173695 + 0.985075i 0.939639 + 0.342168i \(0.111161\pi\)
−0.765944 + 0.642908i \(0.777728\pi\)
\(440\) 2.77434e8 2.32795e8i 0.155266 0.130284i
\(441\) −1.32092e9 4.80776e8i −0.733401 0.266936i
\(442\) −1.00487e9 + 3.65745e8i −0.553521 + 0.201465i
\(443\) −1.66772e9 −0.911400 −0.455700 0.890133i \(-0.650611\pi\)
−0.455700 + 0.890133i \(0.650611\pi\)
\(444\) −5.61516e7 6.67775e6i −0.0304454 0.00362068i
\(445\) −1.43232e8 −0.0770511
\(446\) 1.51229e9 5.50429e8i 0.807168 0.293785i
\(447\) 1.34635e9 + 4.90031e8i 0.712987 + 0.259506i
\(448\) −2.64855e8 + 2.22240e8i −0.139167 + 0.116775i
\(449\) 2.45601e8 + 1.39287e9i 0.128047 + 0.726189i 0.979452 + 0.201680i \(0.0646400\pi\)
−0.851405 + 0.524509i \(0.824249\pi\)
\(450\) −1.46106e9 −0.755831
\(451\) 4.17399e8 + 2.36719e9i 0.214256 + 1.21511i
\(452\) 5.58293e6 9.66992e6i 0.00284366 0.00492536i
\(453\) −1.03430e9 8.67880e8i −0.522760 0.438648i
\(454\) 5.76537e8 + 9.98592e8i 0.289156 + 0.500833i
\(455\) −3.88857e7 + 6.73520e7i −0.0193531 + 0.0335205i
\(456\) 5.60268e8 2.03921e8i 0.276706 0.100713i
\(457\) −3.47588e8 + 2.91661e8i −0.170356 + 0.142946i −0.723980 0.689821i \(-0.757689\pi\)
0.553624 + 0.832767i \(0.313245\pi\)
\(458\) −1.17217e9 2.03026e9i −0.570115 0.987468i
\(459\) −1.24573e8 + 7.06487e8i −0.0601282 + 0.341004i
\(460\) −7.07627e6 + 4.01315e7i −0.00338963 + 0.0192235i
\(461\) 2.57633e7 + 2.16180e7i 0.0122475 + 0.0102769i 0.648891 0.760882i \(-0.275233\pi\)
−0.636643 + 0.771158i \(0.719678\pi\)
\(462\) −1.78757e8 6.50623e7i −0.0843367 0.0306960i
\(463\) 1.59880e8 + 5.81917e7i 0.0748620 + 0.0272475i 0.379180 0.925323i \(-0.376206\pi\)
−0.304318 + 0.952571i \(0.598428\pi\)
\(464\) −5.98391e8 5.02110e8i −0.278082 0.233338i
\(465\) −4.33322e7 + 2.45749e8i −0.0199860 + 0.113346i
\(466\) −5.83818e8 + 3.31100e9i −0.267256 + 1.51568i
\(467\) −1.61231e9 2.79260e9i −0.732553 1.26882i −0.955789 0.294054i \(-0.904995\pi\)
0.223236 0.974764i \(-0.428338\pi\)
\(468\) −1.33229e8 + 1.11793e8i −0.0600813 + 0.0504142i
\(469\) 6.15514e8 2.24029e8i 0.275507 0.100276i
\(470\) −3.43918e7 + 5.95684e7i −0.0152796 + 0.0264651i
\(471\) −1.13128e8 1.95944e8i −0.0498881 0.0864088i
\(472\) −1.70074e8 1.42709e8i −0.0744457 0.0624674i
\(473\) −1.80758e9 + 3.13083e9i −0.785389 + 1.36033i
\(474\) 3.57771e7 + 2.02902e8i 0.0154305 + 0.0875110i
\(475\) 1.46777e9 0.628390
\(476\) 2.10503e6 + 1.19382e7i 0.000894612 + 0.00507360i
\(477\) 1.58875e9 1.33312e9i 0.670259 0.562414i
\(478\) −4.71105e8 1.71468e8i −0.197297 0.0718102i
\(479\) −4.17500e8 + 1.51957e8i −0.173573 + 0.0631753i −0.427345 0.904089i \(-0.640551\pi\)
0.253772 + 0.967264i \(0.418329\pi\)
\(480\) −2.37732e7 −0.00981169
\(481\) 3.34532e9 7.85750e8i 1.37066 0.321941i
\(482\) 3.44548e9 1.40147
\(483\) 3.10461e8 1.12998e8i 0.125369 0.0456307i
\(484\) 8.15607e7 + 2.96857e7i 0.0326981 + 0.0119011i
\(485\) 3.83543e8 3.21831e8i 0.152657 0.128095i
\(486\) −4.23079e8 2.39940e9i −0.167184 0.948147i
\(487\) 3.21591e9 1.26169 0.630844 0.775909i \(-0.282709\pi\)
0.630844 + 0.775909i \(0.282709\pi\)
\(488\) −8.43497e8 4.78371e9i −0.328560 1.86335i
\(489\) −1.66369e8 + 2.88160e8i −0.0643417 + 0.111443i
\(490\) 2.99454e8 + 2.51272e8i 0.114986 + 0.0964846i
\(491\) 6.51613e8 + 1.12863e9i 0.248430 + 0.430294i 0.963090 0.269178i \(-0.0867520\pi\)
−0.714660 + 0.699472i \(0.753419\pi\)
\(492\) 4.07666e7 7.06098e7i 0.0154322 0.0267293i
\(493\) −4.25048e8 + 1.54705e8i −0.159762 + 0.0581486i
\(494\) −1.79819e9 + 1.50886e9i −0.671107 + 0.563125i
\(495\) 2.13172e8 + 3.69225e8i 0.0789972 + 0.136827i
\(496\) 7.08837e8 4.02002e9i 0.260832 1.47925i
\(497\) 1.80270e7 1.02236e8i 0.00658684 0.0373558i
\(498\) −7.90247e8 6.63096e8i −0.286721 0.240588i
\(499\) −1.44747e9 5.26834e8i −0.521502 0.189811i 0.0678378 0.997696i \(-0.478390\pi\)
−0.589340 + 0.807885i \(0.700612\pi\)
\(500\) −5.75854e7 2.09594e7i −0.0206024 0.00749865i
\(501\) −3.26944e8 2.74339e8i −0.116156 0.0974664i
\(502\) 7.07794e8 4.01410e9i 0.249715 1.41620i
\(503\) 2.08315e8 1.18141e9i 0.0729847 0.413917i −0.926324 0.376729i \(-0.877049\pi\)
0.999308 0.0371878i \(-0.0118400\pi\)
\(504\) −2.04428e8 3.54080e8i −0.0711270 0.123196i
\(505\) 2.30173e8 1.93138e8i 0.0795307 0.0667342i
\(506\) 5.69201e9 2.07172e9i 1.95316 0.710894i
\(507\) −6.37920e8 + 1.10491e9i −0.217390 + 0.376530i
\(508\) 4.24112e7 + 7.34583e7i 0.0143535 + 0.0248609i
\(509\) 3.37285e9 + 2.83016e9i 1.13367 + 0.951259i 0.999213 0.0396606i \(-0.0126277\pi\)
0.134453 + 0.990920i \(0.457072\pi\)
\(510\) 4.44594e7 7.70059e7i 0.0148412 0.0257056i
\(511\) 7.64550e7 + 4.33598e8i 0.0253474 + 0.143752i
\(512\) 3.28971e9 1.08321
\(513\) 2.73450e8 + 1.55081e9i 0.0894268 + 0.507165i
\(514\) 9.26127e8 7.77113e8i 0.300815 0.252414i
\(515\) −1.91987e8 6.98777e7i −0.0619366 0.0225431i
\(516\) 1.15230e8 4.19405e7i 0.0369227 0.0134388i
\(517\) −7.60997e8 −0.242196
\(518\) 2.93798e7 + 5.22545e8i 0.00928742 + 0.165185i
\(519\) 1.67773e8 0.0526787
\(520\) 7.01508e8 2.55328e8i 0.218787 0.0796319i
\(521\) −1.47520e9 5.36929e8i −0.457003 0.166336i 0.103253 0.994655i \(-0.467075\pi\)
−0.560256 + 0.828320i \(0.689297\pi\)
\(522\) 7.57134e8 6.35311e8i 0.232984 0.195497i
\(523\) −7.27673e8 4.12684e9i −0.222423 1.26143i −0.867550 0.497350i \(-0.834306\pi\)
0.645126 0.764076i \(-0.276805\pi\)
\(524\) −8.65136e7 −0.0262679
\(525\) 4.25759e7 + 2.41460e8i 0.0128412 + 0.0728261i
\(526\) 1.14524e9 1.98361e9i 0.343119 0.594300i
\(527\) −1.81072e9 1.51937e9i −0.538907 0.452197i
\(528\) 8.49456e8 + 1.47130e9i 0.251143 + 0.434993i
\(529\) −3.55768e9 + 6.16208e9i −1.04489 + 1.80981i
\(530\) −5.41969e8 + 1.97261e8i −0.158128 + 0.0575539i
\(531\) 2.00212e8 1.67998e8i 0.0580309 0.0486937i
\(532\) 1.33050e7 + 2.30449e7i 0.00383110 + 0.00663567i
\(533\) −8.60384e8 + 4.87948e9i −0.246120 + 1.39582i
\(534\) 1.25403e8 7.11196e8i 0.0356380 0.202113i
\(535\) −7.79859e8 6.54380e8i −0.220180 0.184753i
\(536\) −5.90834e9 2.15046e9i −1.65725 0.603191i
\(537\) 6.39741e7 + 2.32847e7i 0.0178276 + 0.00648873i
\(538\) −3.77936e9 3.17126e9i −1.04636 0.877998i
\(539\) −7.51009e8 + 4.25918e9i −0.206578 + 1.17156i
\(540\) 5.63415e6 3.19528e7i 0.00153975 0.00873235i
\(541\) 1.63412e9 + 2.83038e9i 0.443705 + 0.768519i 0.997961 0.0638268i \(-0.0203305\pi\)
−0.554256 + 0.832346i \(0.686997\pi\)
\(542\) −4.09652e8 + 3.43739e8i −0.110514 + 0.0927324i
\(543\) −2.34828e9 + 8.54705e8i −0.629435 + 0.229096i
\(544\) 1.12594e8 1.95018e8i 0.0299860 0.0519373i
\(545\) 1.03982e7 + 1.80103e7i 0.00275152 + 0.00476577i
\(546\) −3.00381e8 2.52049e8i −0.0789765 0.0662692i
\(547\) 2.96346e9 5.13286e9i 0.774182 1.34092i −0.161072 0.986943i \(-0.551495\pi\)
0.935253 0.353979i \(-0.115172\pi\)
\(548\) 1.55778e7 + 8.83462e7i 0.00404366 + 0.0229327i
\(549\) 5.71830e9 1.47490
\(550\) 7.80589e8 + 4.42694e9i 0.200057 + 1.13458i
\(551\) −7.60609e8 + 6.38227e8i −0.193701 + 0.162534i
\(552\) −2.98012e9 1.08468e9i −0.754132 0.274481i
\(553\) −1.33374e8 + 4.85442e7i −0.0335377 + 0.0122067i
\(554\) −4.83176e9 −1.20732
\(555\) −1.71091e8 + 2.28852e8i −0.0424817 + 0.0568238i
\(556\) −2.56689e8 −0.0633352
\(557\) −1.69533e9 + 6.17049e8i −0.415682 + 0.151296i −0.541390 0.840772i \(-0.682102\pi\)
0.125709 + 0.992067i \(0.459880\pi\)
\(558\) 4.85345e9 + 1.76651e9i 1.18258 + 0.430424i
\(559\) −5.70852e9 + 4.79001e9i −1.38223 + 1.15983i
\(560\) 1.83693e7 + 1.04178e8i 0.00442013 + 0.0250678i
\(561\) 9.83765e8 0.235246
\(562\) 1.14544e9 + 6.49610e9i 0.272204 + 1.54374i
\(563\) 5.33799e8 9.24566e8i 0.126066 0.218353i −0.796083 0.605187i \(-0.793098\pi\)
0.922149 + 0.386835i \(0.126432\pi\)
\(564\) 1.97738e7 + 1.65922e7i 0.00464102 + 0.00389427i
\(565\) −2.82109e7 4.88627e7i −0.00658033 0.0113975i
\(566\) −5.91482e8 + 1.02448e9i −0.137115 + 0.237490i
\(567\) 3.15269e8 1.14749e8i 0.0726341 0.0264367i
\(568\) −7.63371e8 + 6.40544e8i −0.174790 + 0.146666i
\(569\) 2.14305e8 + 3.71187e8i 0.0487684 + 0.0844694i 0.889379 0.457170i \(-0.151137\pi\)
−0.840611 + 0.541640i \(0.817804\pi\)
\(570\) 3.38937e7 1.92221e8i 0.00766580 0.0434749i
\(571\) −4.80175e8 + 2.72321e9i −0.107938 + 0.612145i 0.882068 + 0.471121i \(0.156151\pi\)
−0.990006 + 0.141024i \(0.954961\pi\)
\(572\) 4.09905e8 + 3.43952e8i 0.0915794 + 0.0768442i
\(573\) 1.76643e9 + 6.42928e8i 0.392243 + 0.142765i
\(574\) −7.09117e8 2.58098e8i −0.156504 0.0569629i
\(575\) −5.98066e9 5.01837e9i −1.31193 1.10084i
\(576\) −6.78431e8 + 3.84757e9i −0.147920 + 0.838896i
\(577\) 1.69665e8 9.62216e8i 0.0367685 0.208525i −0.960889 0.276935i \(-0.910681\pi\)
0.997657 + 0.0684100i \(0.0217926\pi\)
\(578\) −1.81825e9 3.14930e9i −0.391657 0.678370i
\(579\) −1.10032e9 + 9.23277e8i −0.235583 + 0.197677i
\(580\) 1.92240e7 6.99695e6i 0.00409115 0.00148906i
\(581\) 3.55328e8 6.15446e8i 0.0751645 0.130189i
\(582\) 1.26220e9 + 2.18620e9i 0.265398 + 0.459683i
\(583\) −4.88811e9 4.10161e9i −1.02165 0.857264i
\(584\) 2.11316e9 3.66010e9i 0.439024 0.760411i
\(585\) 1.52606e8 + 8.65470e8i 0.0315156 + 0.178734i
\(586\) −4.65406e9 −0.955412
\(587\) 1.03751e9 + 5.88400e9i 0.211718 + 1.20071i 0.886511 + 0.462707i \(0.153122\pi\)
−0.674793 + 0.738007i \(0.735767\pi\)
\(588\) 1.12378e8 9.42964e7i 0.0227961 0.0191282i
\(589\) −4.87572e9 1.77462e9i −0.983185 0.357850i
\(590\) −6.82980e7 + 2.48585e7i −0.0136907 + 0.00498301i
\(591\) 3.41714e9 0.680937
\(592\) 2.79875e9 3.74362e9i 0.554418 0.741593i
\(593\) 5.77480e9 1.13722 0.568612 0.822606i \(-0.307481\pi\)
0.568612 + 0.822606i \(0.307481\pi\)
\(594\) −4.53200e9 + 1.64951e9i −0.887232 + 0.322926i
\(595\) 5.75612e7 + 2.09505e7i 0.0112026 + 0.00407742i
\(596\) 4.70206e8 3.94550e8i 0.0909759 0.0763379i
\(597\) −4.90636e8 2.78254e9i −0.0943734 0.535218i
\(598\) 1.24859e10 2.38763
\(599\) 1.34973e9 + 7.65471e9i 0.256598 + 1.45524i 0.791937 + 0.610603i \(0.209073\pi\)
−0.535339 + 0.844637i \(0.679816\pi\)
\(600\) 1.17677e9 2.03822e9i 0.222414 0.385232i
\(601\) 3.64429e9 + 3.05792e9i 0.684781 + 0.574600i 0.917399 0.397969i \(-0.130285\pi\)
−0.232618 + 0.972568i \(0.574729\pi\)
\(602\) −5.67478e8 9.82902e8i −0.106014 0.183621i
\(603\) 3.70087e9 6.41009e9i 0.687373 1.19057i
\(604\) −5.43551e8 + 1.97836e8i −0.100372 + 0.0365323i
\(605\) 3.35973e8 2.81915e8i 0.0616822 0.0517575i
\(606\) 7.57477e8 + 1.31199e9i 0.138266 + 0.239484i
\(607\) 1.54813e9 8.77989e9i 0.280962 1.59341i −0.438401 0.898780i \(-0.644455\pi\)
0.719363 0.694635i \(-0.244434\pi\)
\(608\) 8.58363e7 4.86802e8i 0.0154885 0.0878395i
\(609\) −1.27057e8 1.06613e8i −0.0227949 0.0191272i
\(610\) −1.49430e9 5.43882e8i −0.266553 0.0970175i
\(611\) −1.47404e9 5.36507e8i −0.261436 0.0951549i
\(612\) 1.04936e8 + 8.80516e7i 0.0185052 + 0.0155277i
\(613\) −2.72013e8 + 1.54266e9i −0.0476956 + 0.270495i −0.999324 0.0367551i \(-0.988298\pi\)
0.951629 + 0.307251i \(0.0994089\pi\)
\(614\) −1.02840e9 + 5.83232e9i −0.179296 + 1.01684i
\(615\) −2.05996e8 3.56796e8i −0.0357105 0.0618525i
\(616\) −9.63627e8 + 8.08579e8i −0.166103 + 0.139377i
\(617\) −2.67586e9 + 9.73934e8i −0.458633 + 0.166929i −0.560996 0.827818i \(-0.689582\pi\)
0.102363 + 0.994747i \(0.467360\pi\)
\(618\) 5.15057e8 8.92106e8i 0.0877801 0.152040i
\(619\) −4.48342e8 7.76550e8i −0.0759787 0.131599i 0.825533 0.564354i \(-0.190875\pi\)
−0.901511 + 0.432755i \(0.857541\pi\)
\(620\) 8.18949e7 + 6.87180e7i 0.0138002 + 0.0115798i
\(621\) 4.18810e9 7.25400e9i 0.701772 1.21551i
\(622\) 1.32901e9 + 7.53719e9i 0.221443 + 1.25587i
\(623\) 4.97494e8 0.0824289
\(624\) 6.08109e8 + 3.44876e9i 0.100193 + 0.568220i
\(625\) 4.31820e9 3.62340e9i 0.707494 0.593658i
\(626\) −9.48632e9 3.45274e9i −1.54557 0.562540i
\(627\) 2.02924e9 7.38582e8i 0.328773 0.119664i
\(628\) −9.69310e7 −0.0156172
\(629\) −1.06702e9 2.48739e9i −0.170961 0.398535i
\(630\) −1.33848e8 −0.0213265
\(631\) 1.27034e9 4.62366e8i 0.201288 0.0732627i −0.239409 0.970919i \(-0.576954\pi\)
0.440697 + 0.897656i \(0.354731\pi\)
\(632\) 1.28026e9 + 4.65977e8i 0.201739 + 0.0734268i
\(633\) 2.18662e9 1.83480e9i 0.342658 0.287524i
\(634\) −2.41307e8 1.36852e9i −0.0376060 0.213274i
\(635\) 4.28613e8 0.0664289
\(636\) 3.75846e7 + 2.13153e8i 0.00579309 + 0.0328542i
\(637\) −4.45744e9 + 7.72051e9i −0.683278 + 1.18347i
\(638\) −2.32947e9 1.95466e9i −0.355128 0.297988i
\(639\) −5.86550e8 1.01593e9i −0.0889308 0.154033i
\(640\) 4.69730e8 8.13596e8i 0.0708302 0.122681i
\(641\) −1.32471e9 + 4.82153e8i −0.198663 + 0.0723073i −0.439435 0.898274i \(-0.644821\pi\)
0.240773 + 0.970582i \(0.422599\pi\)
\(642\) 3.93201e9 3.29935e9i 0.586465 0.492103i
\(643\) −4.76033e9 8.24514e9i −0.706153 1.22309i −0.966274 0.257517i \(-0.917096\pi\)
0.260121 0.965576i \(-0.416238\pi\)
\(644\) 2.45784e7 1.39391e8i 0.00362621 0.0205653i
\(645\) 1.07599e8 6.10222e8i 0.0157887 0.0895424i
\(646\) 1.41632e9 + 1.18843e9i 0.206703 + 0.173444i
\(647\) −6.01401e9 2.18892e9i −0.872969 0.317735i −0.133600 0.991035i \(-0.542654\pi\)
−0.739369 + 0.673301i \(0.764876\pi\)
\(648\) −3.02628e9 1.10148e9i −0.436914 0.159024i
\(649\) −6.15991e8 5.16878e8i −0.0884541 0.0742218i
\(650\) −1.60903e9 + 9.12524e9i −0.229809 + 1.30331i
\(651\) 1.50508e8 8.53573e8i 0.0213809 0.121257i
\(652\) 7.12748e7 + 1.23452e8i 0.0100709 + 0.0174434i
\(653\) 8.14312e9 6.83289e9i 1.14444 0.960303i 0.144870 0.989451i \(-0.453724\pi\)
0.999575 + 0.0291477i \(0.00927930\pi\)
\(654\) −9.85313e7 + 3.58625e7i −0.0137737 + 0.00501323i
\(655\) −2.18579e8 + 3.78591e8i −0.0303924 + 0.0526411i
\(656\) 3.36973e9 + 5.83655e9i 0.466049 + 0.807221i
\(657\) 3.81128e9 + 3.19804e9i 0.524314 + 0.439952i
\(658\) 1.19455e8 2.06902e8i 0.0163461 0.0283122i
\(659\) 1.83426e9 + 1.04026e10i 0.249667 + 1.41593i 0.809400 + 0.587258i \(0.199793\pi\)
−0.559733 + 0.828673i \(0.689096\pi\)
\(660\) −4.44935e7 −0.00602411
\(661\) −2.30467e8 1.30704e9i −0.0310387 0.176029i 0.965347 0.260968i \(-0.0840417\pi\)
−0.996386 + 0.0849386i \(0.972931\pi\)
\(662\) 5.27391e9 4.42533e9i 0.706528 0.592847i
\(663\) 1.90554e9 + 6.93560e8i 0.253934 + 0.0924244i
\(664\) −6.41021e9 + 2.33313e9i −0.849736 + 0.309279i
\(665\) 1.34462e8 0.0177306
\(666\) 4.04985e9 + 4.30994e9i 0.531226 + 0.565342i
\(667\) 5.28137e9 0.689137
\(668\) −1.71817e8 + 6.25365e7i −0.0223023 + 0.00811738i
\(669\) −2.86775e9 1.04378e9i −0.370297 0.134777i
\(670\) −1.57679e9 + 1.32308e9i −0.202540 + 0.169951i
\(671\) −3.05507e9 1.73262e10i −0.390384 2.21398i
\(672\) 8.25728e7 0.0104965
\(673\) −4.87828e8 2.76661e9i −0.0616899 0.349861i −0.999992 0.00404371i \(-0.998713\pi\)
0.938302 0.345817i \(-0.112398\pi\)
\(674\) 1.92887e9 3.34090e9i 0.242657 0.420295i
\(675\) 4.76182e9 + 3.99564e9i 0.595950 + 0.500062i
\(676\) 2.73293e8 + 4.73358e8i 0.0340264 + 0.0589354i
\(677\) −6.01013e9 + 1.04099e10i −0.744430 + 1.28939i 0.206031 + 0.978546i \(0.433945\pi\)
−0.950461 + 0.310845i \(0.899388\pi\)
\(678\) 2.67320e8 9.72966e7i 0.0329403 0.0119893i
\(679\) −1.33218e9 + 1.11783e9i −0.163312 + 0.137035i
\(680\) −2.93996e8 5.09216e8i −0.0358558 0.0621041i
\(681\) 3.79694e8 2.15335e9i 0.0460701 0.261276i
\(682\) 2.75943e9 1.56495e10i 0.333099 1.88910i
\(683\) −6.98316e9 5.85956e9i −0.838647 0.703709i 0.118612 0.992941i \(-0.462156\pi\)
−0.957259 + 0.289232i \(0.906600\pi\)
\(684\) 2.82560e8 + 1.02844e8i 0.0337610 + 0.0122880i
\(685\) 4.25968e8 + 1.55040e8i 0.0506361 + 0.0184300i
\(686\) −2.11174e9 1.77196e9i −0.249750 0.209565i
\(687\) −7.71965e8 + 4.37803e9i −0.0908342 + 0.515146i
\(688\) −1.76012e9 + 9.98215e9i −0.206055 + 1.16860i
\(689\) −6.57654e9 1.13909e10i −0.766003 1.32676i
\(690\) −7.95320e8 + 6.67352e8i −0.0921658 + 0.0773363i
\(691\) 8.64724e9 3.14734e9i 0.997021 0.362886i 0.208586 0.978004i \(-0.433114\pi\)
0.788435 + 0.615118i \(0.210892\pi\)
\(692\) 3.59380e7 6.22464e7i 0.00412270 0.00714073i
\(693\) −7.40421e8 1.28245e9i −0.0845109 0.146377i
\(694\) 9.78095e9 + 8.20719e9i 1.11077 + 0.932044i
\(695\) −6.48533e8 + 1.12329e9i −0.0732799 + 0.126925i
\(696\) 2.76466e8 + 1.56792e9i 0.0310820 + 0.176275i
\(697\) 3.90253e9 0.436547
\(698\) 4.97793e8 + 2.82312e9i 0.0554057 + 0.314221i
\(699\) 4.88391e9 4.09808e9i 0.540875 0.453848i
\(700\) 9.87055e7 + 3.59259e7i 0.0108767 + 0.00395880i
\(701\) −1.47394e10 + 5.36472e9i −1.61610 + 0.588212i −0.982633 0.185559i \(-0.940590\pi\)
−0.633466 + 0.773771i \(0.718368\pi\)
\(702\) −9.94133e9 −1.08459
\(703\) −4.06844e9 4.32972e9i −0.441656 0.470019i
\(704\) 1.20204e10 1.29842
\(705\) 1.22568e8 4.46111e7i 0.0131739 0.00479491i
\(706\) −9.22715e9 3.35841e9i −0.986850 0.359184i
\(707\) −7.99473e8 + 6.70837e8i −0.0850816 + 0.0713919i
\(708\) 4.73635e6 + 2.68612e7i 0.000501565 + 0.00284452i
\(709\) 1.16674e10 1.22945 0.614727 0.788740i \(-0.289266\pi\)
0.614727 + 0.788740i \(0.289266\pi\)
\(710\) 5.66489e7 + 3.21272e8i 0.00594001 + 0.0336875i
\(711\) −8.01930e8 + 1.38898e9i −0.0836745 + 0.144928i
\(712\) −3.65822e9 3.06961e9i −0.379830 0.318715i
\(713\) 1.37994e10 + 2.39013e10i 1.42577 + 2.46950i
\(714\) −1.54423e8 + 2.67469e8i −0.0158770 + 0.0274998i
\(715\) 2.54080e9 9.24775e8i 0.259956 0.0946161i
\(716\) 2.23426e7 1.87477e7i 0.00227478 0.00190876i
\(717\) 4.75344e8 + 8.23320e8i 0.0481605 + 0.0834164i
\(718\) −1.53469e9 + 8.70363e9i −0.154733 + 0.877536i
\(719\) 1.31343e9 7.44883e9i 0.131782 0.747372i −0.845265 0.534347i \(-0.820557\pi\)
0.977047 0.213025i \(-0.0683315\pi\)
\(720\) 9.15710e8 + 7.68372e8i 0.0914311 + 0.0767198i
\(721\) 6.66840e8 + 2.42710e8i 0.0662595 + 0.0241165i
\(722\) −5.35434e9 1.94882e9i −0.529451 0.192704i
\(723\) −5.00506e9 4.19975e9i −0.492522 0.413275i
\(724\) −1.85908e8 + 1.05433e9i −0.0182059 + 0.103251i
\(725\) −6.80595e8 + 3.85985e9i −0.0663294 + 0.376172i
\(726\) 1.10565e9 + 1.91505e9i 0.107236 + 0.185738i
\(727\) −3.86337e9 + 3.24176e9i −0.372903 + 0.312903i −0.809909 0.586556i \(-0.800483\pi\)
0.437005 + 0.899459i \(0.356039\pi\)
\(728\) −2.43659e9 + 8.86844e8i −0.234057 + 0.0851898i
\(729\) 4.72857e7 8.19013e7i 0.00452047 0.00782969i
\(730\) −6.91787e8 1.19821e9i −0.0658177 0.114000i
\(731\) 4.49622e9 + 3.77277e9i 0.425732 + 0.357232i
\(732\) −2.98383e8 + 5.16814e8i −0.0281180 + 0.0487019i
\(733\) 1.76514e9 + 1.00106e10i 0.165545 + 0.938851i 0.948501 + 0.316774i \(0.102600\pi\)
−0.782956 + 0.622077i \(0.786289\pi\)
\(734\) 1.14045e10 1.06449
\(735\) −1.28722e8 7.30019e8i −0.0119577 0.0678154i
\(736\) −2.01416e9 + 1.69008e9i −0.186218 + 0.156255i
\(737\) −2.13995e10 7.78877e9i −1.96910 0.716692i
\(738\) −8.01307e9 + 2.91652e9i −0.733841 + 0.267096i
\(739\) 2.76665e9 0.252173 0.126087 0.992019i \(-0.459758\pi\)
0.126087 + 0.992019i \(0.459758\pi\)
\(740\) 4.82592e7 + 1.12499e8i 0.00437793 + 0.0102056i
\(741\) 4.45131e9 0.401906
\(742\) 1.88245e9 6.85156e8i 0.169165 0.0615709i
\(743\) −6.87558e9 2.50251e9i −0.614962 0.223828i 0.0157109 0.999877i \(-0.494999\pi\)
−0.630673 + 0.776049i \(0.717221\pi\)
\(744\) −6.37339e9 + 5.34791e9i −0.567369 + 0.476079i
\(745\) −5.38592e8 3.05450e9i −0.0477213 0.270641i
\(746\) 5.44270e9 0.479986
\(747\) −1.39447e9 7.90845e9i −0.122402 0.694176i
\(748\) 2.10729e8 3.64993e8i 0.0184106 0.0318881i
\(749\) 2.70873e9 + 2.27289e9i 0.235548 + 0.197648i
\(750\) −7.80638e8 1.35211e9i −0.0675671 0.117030i
\(751\) −3.43240e9 + 5.94509e9i −0.295705 + 0.512176i −0.975149 0.221552i \(-0.928888\pi\)
0.679444 + 0.733727i \(0.262221\pi\)
\(752\) −2.00499e9 + 7.29757e8i −0.171929 + 0.0625772i
\(753\) −5.92102e9 + 4.96833e9i −0.505376 + 0.424061i
\(754\) −3.13411e9 5.42843e9i −0.266265 0.461184i
\(755\) −5.07551e8 + 2.87846e9i −0.0429205 + 0.243415i
\(756\) −1.95694e7 + 1.10983e8i −0.00164722 + 0.00934183i
\(757\) 9.61974e9 + 8.07192e9i 0.805986 + 0.676303i 0.949646 0.313324i \(-0.101443\pi\)
−0.143660 + 0.989627i \(0.545887\pi\)
\(758\) −2.44659e9 8.90488e8i −0.204042 0.0742653i
\(759\) −1.07937e10 3.92860e9i −0.896036 0.326130i
\(760\) −9.88737e8 8.29649e8i −0.0817021 0.0685562i
\(761\) −3.20042e9 + 1.81505e10i −0.263245 + 1.49294i 0.510742 + 0.859734i \(0.329371\pi\)
−0.773987 + 0.633202i \(0.781740\pi\)
\(762\) −3.75261e8 + 2.12821e9i −0.0307250 + 0.174250i
\(763\) −3.61168e7 6.25560e7i −0.00294356 0.00509839i
\(764\) 6.16917e8