Properties

Label 43.8.g.a.9.20
Level 43
Weight 8
Character 43.9
Analytic conductor 13.433
Analytic rank 0
Dimension 300
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 43.g (of order \(21\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.4325560958\)
Analytic rank: \(0\)
Dimension: \(300\)
Relative dimension: \(25\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 9.20
Character \(\chi\) \(=\) 43.9
Dual form 43.8.g.a.24.20

$q$-expansion

\(f(q)\) \(=\) \(q+(8.65759 + 10.8563i) q^{2} +(35.8811 + 5.40821i) q^{3} +(-14.4222 + 63.1876i) q^{4} +(369.067 + 251.626i) q^{5} +(251.931 + 436.357i) q^{6} +(471.340 - 816.384i) q^{7} +(790.511 - 380.690i) q^{8} +(-831.633 - 256.525i) q^{9} +O(q^{10})\) \(q+(8.65759 + 10.8563i) q^{2} +(35.8811 + 5.40821i) q^{3} +(-14.4222 + 63.1876i) q^{4} +(369.067 + 251.626i) q^{5} +(251.931 + 436.357i) q^{6} +(471.340 - 816.384i) q^{7} +(790.511 - 380.690i) q^{8} +(-831.633 - 256.525i) q^{9} +(463.514 + 6185.17i) q^{10} +(355.960 + 1559.56i) q^{11} +(-859.215 + 2189.24i) q^{12} +(300.304 - 4007.28i) q^{13} +(12943.6 - 1950.93i) q^{14} +(11881.7 + 11024.6i) q^{15} +(18451.2 + 8885.65i) q^{16} +(-4287.33 + 2923.05i) q^{17} +(-4415.03 - 11249.3i) q^{18} +(-50959.8 + 15719.0i) q^{19} +(-21222.4 + 19691.5i) q^{20} +(21327.4 - 26743.7i) q^{21} +(-13849.3 + 17366.4i) q^{22} +(-31263.1 + 29007.9i) q^{23} +(30423.3 - 9384.33i) q^{24} +(44352.8 + 113009. i) q^{25} +(46104.1 - 31433.2i) q^{26} +(-99952.0 - 48134.3i) q^{27} +(44787.6 + 41556.9i) q^{28} +(-67427.5 + 10163.1i) q^{29} +(-16819.3 + 224437. i) q^{30} +(49677.7 - 126577. i) q^{31} +(38287.5 + 167749. i) q^{32} +(4337.80 + 57883.9i) q^{33} +(-68851.4 - 21237.8i) q^{34} +(379379. - 182699. i) q^{35} +(28203.1 - 48849.2i) q^{36} +(83601.8 + 144803. i) q^{37} +(-611839. - 417145. i) q^{38} +(32447.5 - 142162. i) q^{39} +(387543. + 58412.7i) q^{40} +(-341934. - 428772. i) q^{41} +474980. q^{42} +(508207. + 116379. i) q^{43} -103679. q^{44} +(-242380. - 303935. i) q^{45} +(-585581. - 88262.1i) q^{46} +(80755.5 - 353813. i) q^{47} +(613996. + 418615. i) q^{48} +(-32550.8 - 56379.6i) q^{49} +(-842869. + 1.45989e6i) q^{50} +(-169643. + 81695.5i) q^{51} +(248880. + 76769.2i) q^{52} +(-131889. - 1.75993e6i) q^{53} +(-342784. - 1.50183e6i) q^{54} +(-261053. + 665151. i) q^{55} +(61809.9 - 824795. i) q^{56} +(-1.91351e6 + 288415. i) q^{57} +(-694093. - 644024. i) q^{58} +(683048. + 328939. i) q^{59} +(-867978. + 591777. i) q^{60} +(-461679. - 1.17634e6i) q^{61} +(1.80424e6 - 556534. i) q^{62} +(-601404. + 558022. i) q^{63} +(144741. - 181500. i) q^{64} +(1.11917e6 - 1.40339e6i) q^{65} +(-590848. + 548227. i) q^{66} +(1.13208e6 - 349201. i) q^{67} +(-122868. - 313063. i) q^{68} +(-1.27863e6 + 871758. i) q^{69} +(5.26795e6 + 2.53691e6i) q^{70} +(-898849. - 834010. i) q^{71} +(-755072. + 113809. i) q^{72} +(-440838. + 5.88258e6i) q^{73} +(-848226. + 2.16125e6i) q^{74} +(980250. + 4.29476e6i) q^{75} +(-258297. - 3.44673e6i) q^{76} +(1.44098e6 + 444483. i) q^{77} +(1.82426e6 - 878518. i) q^{78} +(-1.93302e6 + 3.34809e6i) q^{79} +(4.57389e6 + 7.92221e6i) q^{80} +(-1.75345e6 - 1.19548e6i) q^{81} +(1.69454e6 - 7.42426e6i) q^{82} +(9.27437e6 + 1.39789e6i) q^{83} +(1.38228e6 + 1.73333e6i) q^{84} -2.31783e6 q^{85} +(3.13641e6 + 6.52480e6i) q^{86} -2.47434e6 q^{87} +(875100. + 1.09734e6i) q^{88} +(-8.68361e6 - 1.30884e6i) q^{89} +(1.20117e6 - 5.26269e6i) q^{90} +(-3.12994e6 - 2.13396e6i) q^{91} +(-1.38206e6 - 2.39380e6i) q^{92} +(2.46704e6 - 4.27304e6i) q^{93} +(4.54024e6 - 2.18646e6i) q^{94} +(-2.27629e7 - 7.02143e6i) q^{95} +(466580. + 6.22607e6i) q^{96} +(2.94208e6 + 1.28901e7i) q^{97} +(330261. - 841491. i) q^{98} +(104038. - 1.38829e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 300q - 40q^{2} - 12q^{3} - 3028q^{4} + 235q^{5} + 1274q^{6} - 4122q^{7} + 762q^{8} + 8097q^{9} + O(q^{10}) \) \( 300q - 40q^{2} - 12q^{3} - 3028q^{4} + 235q^{5} + 1274q^{6} - 4122q^{7} + 762q^{8} + 8097q^{9} - 1681q^{10} + 4580q^{11} + 9330q^{12} - 20444q^{13} - 45798q^{14} + 50477q^{15} - 74504q^{16} - 25312q^{17} + 2046q^{18} + 4046q^{19} + 140781q^{20} + 100555q^{21} + 95810q^{22} + 1648q^{23} - 292592q^{24} + 419068q^{25} + 393435q^{26} + 274140q^{27} + 233644q^{28} + 605697q^{29} - 1216016q^{30} + 358580q^{31} - 19194q^{32} + 1280291q^{33} + 1137255q^{34} + 652739q^{35} - 8980975q^{36} - 2360047q^{37} - 308490q^{38} + 536339q^{39} + 3057993q^{40} - 1376320q^{41} + 8417790q^{42} + 7173000q^{43} - 3856780q^{44} + 2761486q^{45} - 7073993q^{46} + 1437090q^{47} - 9543469q^{48} - 16053170q^{49} - 3046893q^{50} + 2972901q^{51} + 17415142q^{52} + 3320604q^{53} + 6000486q^{54} + 13427750q^{55} - 5450793q^{56} + 3333100q^{57} - 7876190q^{58} - 7084765q^{59} + 7356443q^{60} + 3354606q^{61} - 719427q^{62} + 14716815q^{63} - 16086234q^{64} - 19914646q^{65} - 8293345q^{66} + 13025470q^{67} - 22191927q^{68} - 33964295q^{69} + 8094727q^{70} + 30843495q^{71} + 93841607q^{72} - 3067637q^{73} + 18179570q^{74} - 41508571q^{75} - 19751872q^{76} - 15169179q^{77} - 69509396q^{78} - 12090149q^{79} - 69662530q^{80} + 3387954q^{81} + 39226888q^{82} + 16408777q^{83} + 98603231q^{84} - 13423424q^{85} + 111906660q^{86} + 49022010q^{87} + 76213954q^{88} - 12540205q^{89} - 92608607q^{90} - 59091937q^{91} - 50489370q^{92} - 52218334q^{93} - 3441600q^{94} - 79947551q^{95} - 23449784q^{96} - 116467587q^{97} + 73909552q^{98} - 20061115q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{21}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.65759 + 10.8563i 0.765230 + 0.959568i 0.999922 0.0125016i \(-0.00397949\pi\)
−0.234692 + 0.972070i \(0.575408\pi\)
\(3\) 35.8811 + 5.40821i 0.767258 + 0.115646i 0.520998 0.853558i \(-0.325560\pi\)
0.246260 + 0.969204i \(0.420798\pi\)
\(4\) −14.4222 + 63.1876i −0.112673 + 0.493653i
\(5\) 369.067 + 251.626i 1.32041 + 0.900243i 0.998911 0.0466648i \(-0.0148593\pi\)
0.321504 + 0.946908i \(0.395812\pi\)
\(6\) 251.931 + 436.357i 0.476159 + 0.824732i
\(7\) 471.340 816.384i 0.519387 0.899604i −0.480359 0.877072i \(-0.659494\pi\)
0.999746 0.0225325i \(-0.00717293\pi\)
\(8\) 790.511 380.690i 0.545875 0.262879i
\(9\) −831.633 256.525i −0.380262 0.117295i
\(10\) 463.514 + 6185.17i 0.146576 + 1.95592i
\(11\) 355.960 + 1559.56i 0.0806355 + 0.353287i 0.999109 0.0421943i \(-0.0134348\pi\)
−0.918474 + 0.395482i \(0.870578\pi\)
\(12\) −859.215 + 2189.24i −0.143538 + 0.365729i
\(13\) 300.304 4007.28i 0.0379105 0.505881i −0.945636 0.325227i \(-0.894559\pi\)
0.983547 0.180654i \(-0.0578215\pi\)
\(14\) 12943.6 1950.93i 1.26068 0.190017i
\(15\) 11881.7 + 11024.6i 0.908989 + 0.843419i
\(16\) 18451.2 + 8885.65i 1.12617 + 0.542337i
\(17\) −4287.33 + 2923.05i −0.211649 + 0.144300i −0.664505 0.747284i \(-0.731357\pi\)
0.452856 + 0.891584i \(0.350405\pi\)
\(18\) −4415.03 11249.3i −0.178435 0.454645i
\(19\) −50959.8 + 15719.0i −1.70447 + 0.525761i −0.985558 0.169337i \(-0.945838\pi\)
−0.718916 + 0.695097i \(0.755361\pi\)
\(20\) −21222.4 + 19691.5i −0.593183 + 0.550394i
\(21\) 21327.4 26743.7i 0.502539 0.630164i
\(22\) −13849.3 + 17366.4i −0.277299 + 0.347721i
\(23\) −31263.1 + 29007.9i −0.535777 + 0.497129i −0.901016 0.433785i \(-0.857178\pi\)
0.365239 + 0.930914i \(0.380987\pi\)
\(24\) 30423.3 9384.33i 0.449228 0.138568i
\(25\) 44352.8 + 113009.i 0.567715 + 1.44652i
\(26\) 46104.1 31433.2i 0.514437 0.350738i
\(27\) −99952.0 48134.3i −0.977278 0.470632i
\(28\) 44787.6 + 41556.9i 0.385572 + 0.357758i
\(29\) −67427.5 + 10163.1i −0.513386 + 0.0773805i −0.400626 0.916242i \(-0.631207\pi\)
−0.112760 + 0.993622i \(0.535969\pi\)
\(30\) −16819.3 + 224437.i −0.113732 + 1.51765i
\(31\) 49677.7 126577.i 0.299499 0.763111i −0.699333 0.714796i \(-0.746520\pi\)
0.998832 0.0483149i \(-0.0153851\pi\)
\(32\) 38287.5 + 167749.i 0.206553 + 0.904969i
\(33\) 4337.80 + 57883.9i 0.0210121 + 0.280388i
\(34\) −68851.4 21237.8i −0.300425 0.0926689i
\(35\) 379379. 182699.i 1.49567 0.720276i
\(36\) 28203.1 48849.2i 0.100748 0.174501i
\(37\) 83601.8 + 144803.i 0.271337 + 0.469970i 0.969205 0.246257i \(-0.0792008\pi\)
−0.697867 + 0.716227i \(0.745867\pi\)
\(38\) −611839. 417145.i −1.80882 1.23323i
\(39\) 32447.5 142162.i 0.0875900 0.383757i
\(40\) 387543. + 58412.7i 0.957437 + 0.144310i
\(41\) −341934. 428772.i −0.774816 0.971589i 0.225180 0.974317i \(-0.427703\pi\)
−0.999996 + 0.00272829i \(0.999132\pi\)
\(42\) 474980. 0.989243
\(43\) 508207. + 116379.i 0.974768 + 0.223221i
\(44\) −103679. −0.183487
\(45\) −242380. 303935.i −0.396509 0.497207i
\(46\) −585581. 88262.1i −0.887022 0.133697i
\(47\) 80755.5 353813.i 0.113457 0.497085i −0.885986 0.463711i \(-0.846518\pi\)
0.999443 0.0333742i \(-0.0106253\pi\)
\(48\) 613996. + 418615.i 0.801348 + 0.546350i
\(49\) −32550.8 56379.6i −0.0395253 0.0684598i
\(50\) −842869. + 1.45989e6i −0.953597 + 1.65168i
\(51\) −169643. + 81695.5i −0.179077 + 0.0862388i
\(52\) 248880. + 76769.2i 0.245458 + 0.0757138i
\(53\) −131889. 1.75993e6i −0.121686 1.62379i −0.639844 0.768505i \(-0.721001\pi\)
0.518157 0.855285i \(-0.326618\pi\)
\(54\) −342784. 1.50183e6i −0.296239 1.29791i
\(55\) −261053. + 665151.i −0.211572 + 0.539077i
\(56\) 61809.9 824795.i 0.0470327 0.627607i
\(57\) −1.91351e6 + 288415.i −1.36857 + 0.206279i
\(58\) −694093. 644024.i −0.467111 0.433415i
\(59\) 683048. + 328939.i 0.432981 + 0.208513i 0.637662 0.770316i \(-0.279901\pi\)
−0.204681 + 0.978829i \(0.565616\pi\)
\(60\) −867978. + 591777.i −0.518775 + 0.353695i
\(61\) −461679. 1.17634e6i −0.260427 0.663557i 0.739527 0.673126i \(-0.235049\pi\)
−0.999954 + 0.00956974i \(0.996954\pi\)
\(62\) 1.80424e6 556534.i 0.961442 0.296566i
\(63\) −601404. + 558022.i −0.303022 + 0.281164i
\(64\) 144741. 181500.i 0.0690180 0.0865459i
\(65\) 1.11917e6 1.40339e6i 0.505473 0.633844i
\(66\) −590848. + 548227.i −0.252972 + 0.234724i
\(67\) 1.13208e6 349201.i 0.459850 0.141845i −0.0561703 0.998421i \(-0.517889\pi\)
0.516021 + 0.856576i \(0.327413\pi\)
\(68\) −122868. 313063.i −0.0473868 0.120740i
\(69\) −1.27863e6 + 871758.i −0.468570 + 0.319466i
\(70\) 5.26795e6 + 2.53691e6i 1.83568 + 0.884019i
\(71\) −898849. 834010.i −0.298045 0.276546i 0.516947 0.856017i \(-0.327068\pi\)
−0.814992 + 0.579472i \(0.803259\pi\)
\(72\) −755072. + 113809.i −0.238410 + 0.0359345i
\(73\) −440838. + 5.88258e6i −0.132632 + 1.76985i 0.393378 + 0.919377i \(0.371306\pi\)
−0.526010 + 0.850478i \(0.676313\pi\)
\(74\) −848226. + 2.16125e6i −0.243333 + 0.620002i
\(75\) 980250. + 4.29476e6i 0.268301 + 1.17550i
\(76\) −258297. 3.44673e6i −0.0674950 0.900658i
\(77\) 1.44098e6 + 444483.i 0.359700 + 0.110953i
\(78\) 1.82426e6 878518.i 0.435267 0.209614i
\(79\) −1.93302e6 + 3.34809e6i −0.441105 + 0.764016i −0.997772 0.0667200i \(-0.978747\pi\)
0.556667 + 0.830736i \(0.312080\pi\)
\(80\) 4.57389e6 + 7.92221e6i 0.998782 + 1.72994i
\(81\) −1.75345e6 1.19548e6i −0.366603 0.249946i
\(82\) 1.69454e6 7.42426e6i 0.339393 1.48698i
\(83\) 9.27437e6 + 1.39789e6i 1.78037 + 0.268348i 0.955078 0.296354i \(-0.0957709\pi\)
0.825295 + 0.564702i \(0.191009\pi\)
\(84\) 1.38228e6 + 1.73333e6i 0.254460 + 0.319082i
\(85\) −2.31783e6 −0.409369
\(86\) 3.13641e6 + 6.52480e6i 0.531726 + 1.10617i
\(87\) −2.47434e6 −0.402848
\(88\) 875100. + 1.09734e6i 0.136889 + 0.171653i
\(89\) −8.68361e6 1.30884e6i −1.30567 0.196799i −0.540895 0.841090i \(-0.681914\pi\)
−0.764780 + 0.644291i \(0.777152\pi\)
\(90\) 1.20117e6 5.26269e6i 0.173683 0.760955i
\(91\) −3.12994e6 2.13396e6i −0.435402 0.296852i
\(92\) −1.38206e6 2.39380e6i −0.185041 0.320501i
\(93\) 2.46704e6 4.27304e6i 0.318043 0.550867i
\(94\) 4.54024e6 2.18646e6i 0.563808 0.271515i
\(95\) −2.27629e7 7.02143e6i −2.72393 0.840220i
\(96\) 466580. + 6.22607e6i 0.0538240 + 0.718232i
\(97\) 2.94208e6 + 1.28901e7i 0.327306 + 1.43402i 0.824244 + 0.566235i \(0.191600\pi\)
−0.496938 + 0.867786i \(0.665543\pi\)
\(98\) 330261. 841491.i 0.0354459 0.0903147i
\(99\) 104038. 1.38829e6i 0.0107763 0.143800i
\(100\) −7.78043e6 + 1.17271e6i −0.778043 + 0.117271i
\(101\) −1.26123e7 1.17025e7i −1.21807 1.13020i −0.987579 0.157125i \(-0.949778\pi\)
−0.230487 0.973075i \(-0.574032\pi\)
\(102\) −2.35560e6 1.13440e6i −0.219787 0.105844i
\(103\) 1.01433e7 6.91561e6i 0.914641 0.623592i −0.0118415 0.999930i \(-0.503769\pi\)
0.926482 + 0.376338i \(0.122817\pi\)
\(104\) −1.28814e6 3.28212e6i −0.112291 0.286114i
\(105\) 1.46006e7 4.50370e6i 1.23086 0.379670i
\(106\) 1.79645e7 1.66686e7i 1.46502 1.35934i
\(107\) −1.04481e7 + 1.31015e7i −0.824505 + 1.03390i 0.174284 + 0.984695i \(0.444239\pi\)
−0.998789 + 0.0492006i \(0.984333\pi\)
\(108\) 4.48302e6 5.62152e6i 0.342442 0.429409i
\(109\) −7.33377e6 + 6.80474e6i −0.542418 + 0.503291i −0.903119 0.429391i \(-0.858728\pi\)
0.360700 + 0.932682i \(0.382538\pi\)
\(110\) −9.48115e6 + 2.92455e6i −0.679183 + 0.209500i
\(111\) 2.21660e6 + 5.64781e6i 0.153836 + 0.391967i
\(112\) 1.59509e7 1.08751e7i 1.07281 0.731429i
\(113\) −8.46223e6 4.07519e6i −0.551709 0.265689i 0.137192 0.990544i \(-0.456192\pi\)
−0.688901 + 0.724855i \(0.741907\pi\)
\(114\) −1.96975e7 1.82766e7i −1.24521 1.15539i
\(115\) −1.88373e7 + 2.83927e6i −1.15499 + 0.174086i
\(116\) 330271. 4.40716e6i 0.0196457 0.262153i
\(117\) −1.27771e6 + 3.25555e6i −0.0737534 + 0.187920i
\(118\) 2.34250e6 + 1.02632e7i 0.131248 + 0.575035i
\(119\) 365545. + 4.87786e6i 0.0198850 + 0.265347i
\(120\) 1.35896e7 + 4.19183e6i 0.717912 + 0.221447i
\(121\) 1.52518e7 7.34488e6i 0.782659 0.376909i
\(122\) 8.77363e6 1.51964e7i 0.437442 0.757671i
\(123\) −9.95008e6 1.72340e7i −0.482124 0.835063i
\(124\) 7.28161e6 + 4.96452e6i 0.342966 + 0.233831i
\(125\) −4.30148e6 + 1.88460e7i −0.196985 + 0.863047i
\(126\) −1.12648e7 1.69789e6i −0.501678 0.0756157i
\(127\) 8.87109e6 + 1.11240e7i 0.384294 + 0.481890i 0.935925 0.352198i \(-0.114566\pi\)
−0.551631 + 0.834088i \(0.685994\pi\)
\(128\) 2.52475e7 1.06410
\(129\) 1.76056e7 + 6.92429e6i 0.722084 + 0.283996i
\(130\) 2.49249e7 0.995020
\(131\) 1.12463e7 + 1.41024e7i 0.437078 + 0.548079i 0.950771 0.309896i \(-0.100294\pi\)
−0.513692 + 0.857974i \(0.671723\pi\)
\(132\) −3.72010e6 560715.i −0.140782 0.0212194i
\(133\) −1.11866e7 + 4.90118e7i −0.412305 + 1.80643i
\(134\) 1.35921e7 + 9.26696e6i 0.488001 + 0.332714i
\(135\) −2.47771e7 4.29153e7i −0.866729 1.50122i
\(136\) −2.27640e6 + 3.94285e6i −0.0776003 + 0.134408i
\(137\) 2.50748e7 1.20754e7i 0.833135 0.401217i 0.0318451 0.999493i \(-0.489862\pi\)
0.801290 + 0.598276i \(0.204147\pi\)
\(138\) −2.05339e7 6.33388e6i −0.665113 0.205160i
\(139\) −429995. 5.73789e6i −0.0135804 0.181218i −0.999869 0.0161878i \(-0.994847\pi\)
0.986289 0.165030i \(-0.0527720\pi\)
\(140\) 6.07287e6 + 2.66070e7i 0.187045 + 0.819497i
\(141\) 4.81109e6 1.22585e7i 0.144536 0.368272i
\(142\) 1.27238e6 1.69787e7i 0.0372912 0.497616i
\(143\) 6.35650e6 958088.i 0.181778 0.0273987i
\(144\) −1.30653e7 1.21228e7i −0.364628 0.338325i
\(145\) −2.74426e7 1.32156e7i −0.747544 0.359998i
\(146\) −6.76795e7 + 4.61431e7i −1.79979 + 1.22708i
\(147\) −863045. 2.19900e6i −0.0224090 0.0570972i
\(148\) −1.03554e7 + 3.19423e6i −0.262575 + 0.0809935i
\(149\) 1.11857e7 1.03788e7i 0.277020 0.257037i −0.529411 0.848366i \(-0.677587\pi\)
0.806431 + 0.591329i \(0.201396\pi\)
\(150\) −3.81385e7 + 4.78241e7i −0.922664 + 1.15698i
\(151\) 2.99058e7 3.75007e7i 0.706865 0.886380i −0.290651 0.956829i \(-0.593872\pi\)
0.997515 + 0.0704491i \(0.0224432\pi\)
\(152\) −3.43002e7 + 3.18260e7i −0.792218 + 0.735071i
\(153\) 4.31532e6 1.33110e6i 0.0974076 0.0300463i
\(154\) 7.64998e6 + 1.94918e7i 0.168786 + 0.430061i
\(155\) 5.01843e7 3.42151e7i 1.08245 0.738001i
\(156\) 8.51489e6 + 4.10055e6i 0.179574 + 0.0864782i
\(157\) −6.68515e6 6.20291e6i −0.137868 0.127922i 0.608225 0.793765i \(-0.291882\pi\)
−0.746092 + 0.665842i \(0.768072\pi\)
\(158\) −5.30831e7 + 8.00099e6i −1.07067 + 0.161378i
\(159\) 4.78576e6 6.38615e7i 0.0944194 1.25994i
\(160\) −2.80792e7 + 7.15446e7i −0.541957 + 1.38088i
\(161\) 8.94606e6 + 3.91953e7i 0.168943 + 0.740190i
\(162\) −2.20217e6 2.93860e7i −0.0406957 0.543047i
\(163\) −7.31161e7 2.25533e7i −1.32238 0.407901i −0.448388 0.893839i \(-0.648002\pi\)
−0.873993 + 0.485938i \(0.838478\pi\)
\(164\) 3.20245e7 1.54222e7i 0.566929 0.273019i
\(165\) −1.29641e7 + 2.24545e7i −0.224672 + 0.389144i
\(166\) 6.51178e7 + 1.12787e8i 1.10490 + 1.91374i
\(167\) 6.57657e7 + 4.48383e7i 1.09268 + 0.744974i 0.968929 0.247339i \(-0.0795562\pi\)
0.123748 + 0.992314i \(0.460509\pi\)
\(168\) 6.67847e6 2.92603e7i 0.108666 0.476098i
\(169\) 4.60795e7 + 6.94537e6i 0.734353 + 0.110686i
\(170\) −2.00668e7 2.51630e7i −0.313261 0.392817i
\(171\) 4.64122e7 0.709816
\(172\) −1.46832e7 + 3.04340e7i −0.220024 + 0.456046i
\(173\) 9.45968e7 1.38904 0.694521 0.719473i \(-0.255616\pi\)
0.694521 + 0.719473i \(0.255616\pi\)
\(174\) −2.14218e7 2.68621e7i −0.308272 0.386561i
\(175\) 1.13164e8 + 1.70567e7i 1.59616 + 0.240582i
\(176\) −7.28982e6 + 3.19388e7i −0.100791 + 0.441595i
\(177\) 2.27295e7 + 1.54967e7i 0.308095 + 0.210055i
\(178\) −6.09699e7 1.05603e8i −0.810300 1.40348i
\(179\) −2.77042e7 + 4.79851e7i −0.361044 + 0.625346i −0.988133 0.153601i \(-0.950913\pi\)
0.627089 + 0.778948i \(0.284246\pi\)
\(180\) 2.27006e7 1.09320e7i 0.290124 0.139716i
\(181\) −1.93052e7 5.95487e6i −0.241991 0.0746444i 0.171387 0.985204i \(-0.445175\pi\)
−0.413378 + 0.910559i \(0.635651\pi\)
\(182\) −3.93091e6 5.24544e7i −0.0483330 0.644959i
\(183\) −1.02037e7 4.47052e7i −0.123077 0.539236i
\(184\) −1.36708e7 + 3.48326e7i −0.161782 + 0.412215i
\(185\) −5.58137e6 + 7.44782e7i −0.0648097 + 0.864825i
\(186\) 6.77479e7 1.02114e7i 0.771971 0.116356i
\(187\) −6.08479e6 5.64586e6i −0.0680456 0.0631371i
\(188\) 2.11919e7 + 1.02055e7i 0.232604 + 0.112016i
\(189\) −8.64074e7 + 5.89116e7i −0.930968 + 0.634723i
\(190\) −1.20845e8 3.07909e8i −1.27818 3.25675i
\(191\) −1.36321e8 + 4.20496e7i −1.41562 + 0.436661i −0.905832 0.423638i \(-0.860753\pi\)
−0.509790 + 0.860299i \(0.670277\pi\)
\(192\) 6.17507e6 5.72962e6i 0.0629633 0.0584214i
\(193\) 7.32821e7 9.18928e7i 0.733748 0.920091i −0.265280 0.964171i \(-0.585464\pi\)
0.999028 + 0.0440803i \(0.0140358\pi\)
\(194\) −1.14467e8 + 1.43537e8i −1.12558 + 1.41143i
\(195\) 4.77468e7 4.43026e7i 0.461130 0.427866i
\(196\) 4.03194e6 1.24369e6i 0.0382488 0.0117982i
\(197\) −1.61933e7 4.12599e7i −0.150905 0.384500i 0.835352 0.549715i \(-0.185264\pi\)
−0.986258 + 0.165215i \(0.947168\pi\)
\(198\) 1.59724e7 1.08898e7i 0.146232 0.0996994i
\(199\) −1.44307e8 6.94946e7i −1.29808 0.625123i −0.348108 0.937454i \(-0.613176\pi\)
−0.949973 + 0.312332i \(0.898890\pi\)
\(200\) 7.80828e7 + 7.24502e7i 0.690161 + 0.640376i
\(201\) 4.25089e7 6.40719e6i 0.369227 0.0556521i
\(202\) 1.78535e7 2.38239e8i 0.152403 2.03368i
\(203\) −2.34843e7 + 5.98370e7i −0.197034 + 0.502035i
\(204\) −2.71553e6 1.18975e7i −0.0223949 0.0981186i
\(205\) −1.83066e7 2.44285e8i −0.148412 1.98042i
\(206\) 1.62895e8 + 5.02463e7i 1.29829 + 0.400469i
\(207\) 3.34407e7 1.61042e7i 0.262047 0.126195i
\(208\) 4.11483e7 7.12710e7i 0.317052 0.549150i
\(209\) −4.26544e7 7.38796e7i −0.323186 0.559774i
\(210\) 1.75300e8 + 1.19517e8i 1.30621 + 0.890560i
\(211\) −5.45398e7 + 2.38954e8i −0.399691 + 1.75116i 0.228923 + 0.973444i \(0.426479\pi\)
−0.628615 + 0.777717i \(0.716378\pi\)
\(212\) 1.13108e8 + 1.70483e7i 0.815300 + 0.122887i
\(213\) −2.77412e7 3.47864e7i −0.196696 0.246650i
\(214\) −2.32688e8 −1.62303
\(215\) 1.58279e8 + 1.70830e8i 1.08614 + 1.17227i
\(216\) −9.73374e7 −0.657191
\(217\) −7.99201e7 1.00217e8i −0.530942 0.665780i
\(218\) −1.37367e8 2.07047e7i −0.898017 0.135354i
\(219\) −4.76320e7 + 2.08689e8i −0.306439 + 1.34260i
\(220\) −3.82644e7 2.60882e7i −0.242279 0.165183i
\(221\) 1.04260e7 + 1.80583e7i 0.0649747 + 0.112539i
\(222\) −4.21238e7 + 7.29605e7i −0.258400 + 0.447561i
\(223\) 1.71028e7 8.23628e6i 0.103276 0.0497352i −0.381532 0.924355i \(-0.624604\pi\)
0.484809 + 0.874620i \(0.338889\pi\)
\(224\) 1.54994e8 + 4.78092e7i 0.921396 + 0.284213i
\(225\) −7.89561e6 1.05360e8i −0.0462112 0.616645i
\(226\) −2.90211e7 1.27150e8i −0.167238 0.732716i
\(227\) −6.42276e7 + 1.63649e8i −0.364444 + 0.928589i 0.624597 + 0.780947i \(0.285263\pi\)
−0.989041 + 0.147641i \(0.952832\pi\)
\(228\) 9.37266e6 1.25069e8i 0.0523710 0.698843i
\(229\) −1.52181e8 + 2.29376e7i −0.837405 + 0.126219i −0.553724 0.832700i \(-0.686794\pi\)
−0.283681 + 0.958919i \(0.591556\pi\)
\(230\) −1.93910e8 1.79922e8i −1.05088 0.975071i
\(231\) 4.93001e7 + 2.37417e7i 0.263151 + 0.126727i
\(232\) −4.94332e7 + 3.37030e7i −0.259903 + 0.177199i
\(233\) −1.46462e7 3.73179e7i −0.0758541 0.193273i 0.887917 0.460004i \(-0.152152\pi\)
−0.963771 + 0.266730i \(0.914057\pi\)
\(234\) −4.64051e7 + 1.43141e7i −0.236761 + 0.0730310i
\(235\) 1.18833e8 1.10261e8i 0.597308 0.554220i
\(236\) −3.06359e7 + 3.84162e7i −0.151718 + 0.190249i
\(237\) −8.74661e7 + 1.09679e8i −0.426796 + 0.535185i
\(238\) −4.97906e7 + 4.61989e7i −0.239402 + 0.222133i
\(239\) 1.70447e8 5.25760e7i 0.807601 0.249112i 0.136656 0.990619i \(-0.456365\pi\)
0.670946 + 0.741507i \(0.265888\pi\)
\(240\) 1.21271e8 + 3.08994e8i 0.566264 + 1.44282i
\(241\) 6.90449e7 4.70740e7i 0.317740 0.216632i −0.393938 0.919137i \(-0.628888\pi\)
0.711678 + 0.702505i \(0.247935\pi\)
\(242\) 2.11782e8 + 1.01989e8i 0.960584 + 0.462593i
\(243\) 1.21404e8 + 1.12647e8i 0.542765 + 0.503612i
\(244\) 8.09884e7 1.22070e7i 0.356910 0.0537955i
\(245\) 2.17313e6 2.89985e7i 0.00944072 0.125978i
\(246\) 1.00954e8 2.57226e8i 0.432364 1.10165i
\(247\) 4.76871e7 + 2.08931e8i 0.201355 + 0.882193i
\(248\) −8.91572e6 1.18972e8i −0.0371172 0.495295i
\(249\) 3.25214e8 + 1.00315e8i 1.33497 + 0.411784i
\(250\) −2.41838e8 + 1.16463e8i −0.978891 + 0.471409i
\(251\) −1.09885e8 + 1.90327e8i −0.438613 + 0.759700i −0.997583 0.0694879i \(-0.977863\pi\)
0.558970 + 0.829188i \(0.311197\pi\)
\(252\) −2.65865e7 4.60492e7i −0.104655 0.181268i
\(253\) −5.63680e7 3.84311e7i −0.218832 0.149197i
\(254\) −4.39629e7 + 1.92614e8i −0.168333 + 0.737513i
\(255\) −8.31662e7 1.25353e7i −0.314091 0.0473417i
\(256\) 2.00056e8 + 2.50862e8i 0.745266 + 0.934534i
\(257\) 4.23479e8 1.55620 0.778102 0.628138i \(-0.216183\pi\)
0.778102 + 0.628138i \(0.216183\pi\)
\(258\) 7.72503e7 + 2.51079e8i 0.280047 + 0.910211i
\(259\) 1.57619e8 0.563716
\(260\) 7.25361e7 + 9.09575e7i 0.255946 + 0.320946i
\(261\) 5.86820e7 + 8.84489e6i 0.204298 + 0.0307929i
\(262\) −5.57337e7 + 2.44185e8i −0.191453 + 0.838813i
\(263\) 1.75398e7 + 1.19584e7i 0.0594538 + 0.0405349i 0.592682 0.805436i \(-0.298069\pi\)
−0.533228 + 0.845971i \(0.679021\pi\)
\(264\) 2.54649e7 + 4.41065e7i 0.0851782 + 0.147533i
\(265\) 3.94168e8 6.82719e8i 1.30113 2.25362i
\(266\) −6.28935e8 + 3.02879e8i −2.04890 + 0.986697i
\(267\) −3.04499e8 9.39255e7i −0.979031 0.301991i
\(268\) 5.73812e6 + 7.65698e7i 0.0182095 + 0.242989i
\(269\) −4.64277e7 2.03413e8i −0.145427 0.637157i −0.994121 0.108273i \(-0.965468\pi\)
0.848694 0.528884i \(-0.177389\pi\)
\(270\) 2.51390e8 6.40530e8i 0.777274 1.98046i
\(271\) −2.31554e7 + 3.08988e8i −0.0706741 + 0.943080i 0.843335 + 0.537387i \(0.180589\pi\)
−0.914010 + 0.405693i \(0.867030\pi\)
\(272\) −1.05080e8 + 1.58382e7i −0.316612 + 0.0477216i
\(273\) −1.00765e8 9.34960e7i −0.299736 0.278115i
\(274\) 3.48181e8 + 1.67675e8i 1.02253 + 0.492427i
\(275\) −1.60457e8 + 1.09398e8i −0.465257 + 0.317207i
\(276\) −3.66437e7 9.33665e7i −0.104910 0.267306i
\(277\) −2.77015e8 + 8.54477e7i −0.783111 + 0.241558i −0.660429 0.750888i \(-0.729626\pi\)
−0.122682 + 0.992446i \(0.539150\pi\)
\(278\) 5.85694e7 5.43444e7i 0.163498 0.151704i
\(279\) −7.37836e7 + 9.25217e7i −0.203397 + 0.255052i
\(280\) 2.30352e8 2.88852e8i 0.627102 0.786361i
\(281\) 3.24220e7 3.00832e7i 0.0871701 0.0808821i −0.635384 0.772196i \(-0.719158\pi\)
0.722554 + 0.691314i \(0.242968\pi\)
\(282\) 1.74734e8 5.38982e7i 0.463986 0.143121i
\(283\) −1.44663e8 3.68595e8i −0.379407 0.966713i −0.985249 0.171128i \(-0.945259\pi\)
0.605842 0.795585i \(-0.292836\pi\)
\(284\) 6.56624e7 4.47679e7i 0.170099 0.115972i
\(285\) −7.78785e8 3.75043e8i −1.99279 0.959675i
\(286\) 6.54332e7 + 6.07132e7i 0.165393 + 0.153462i
\(287\) −5.11209e8 + 7.70524e7i −1.27647 + 0.192398i
\(288\) 1.11905e7 1.49327e8i 0.0276043 0.368353i
\(289\) −1.40077e8 + 3.56909e8i −0.341368 + 0.869792i
\(290\) −9.41139e7 4.12340e8i −0.226600 0.992801i
\(291\) 3.58528e7 + 4.78423e8i 0.0852899 + 1.13811i
\(292\) −3.65348e8 1.12695e8i −0.858750 0.264889i
\(293\) −4.37690e8 + 2.10780e8i −1.01655 + 0.489546i −0.866524 0.499135i \(-0.833651\pi\)
−0.150029 + 0.988682i \(0.547937\pi\)
\(294\) 1.64011e7 2.84075e7i 0.0376406 0.0651955i
\(295\) 1.69321e8 + 2.93273e8i 0.384003 + 0.665112i
\(296\) 1.21213e8 + 8.26417e7i 0.271662 + 0.185216i
\(297\) 3.94896e7 1.73015e8i 0.0874651 0.383210i
\(298\) 2.09516e8 + 3.15795e7i 0.458628 + 0.0691271i
\(299\) 1.06854e8 + 1.33991e8i 0.231176 + 0.289886i
\(300\) −2.85513e8 −0.610522
\(301\) 3.34548e8 3.60038e8i 0.707092 0.760967i
\(302\) 6.66030e8 1.39146
\(303\) −3.89255e8 4.88110e8i −0.803868 1.00802i
\(304\) −1.07995e9 1.62776e8i −2.20468 0.332301i
\(305\) 1.25607e8 5.50318e8i 0.253491 1.11062i
\(306\) 5.18110e7 + 3.53242e7i 0.103371 + 0.0704769i
\(307\) 4.04424e8 + 7.00482e8i 0.797723 + 1.38170i 0.921095 + 0.389337i \(0.127296\pi\)
−0.123372 + 0.992360i \(0.539371\pi\)
\(308\) −4.88679e7 + 8.46416e7i −0.0953006 + 0.165066i
\(309\) 4.01355e8 1.93282e8i 0.773881 0.372681i
\(310\) 8.05924e8 + 2.48595e8i 1.53648 + 0.473942i
\(311\) −9.69033e6 1.29308e8i −0.0182674 0.243762i −0.998861 0.0477111i \(-0.984807\pi\)
0.980594 0.196051i \(-0.0628117\pi\)
\(312\) −2.84694e7 1.24733e8i −0.0530686 0.232509i
\(313\) 3.19414e8 8.13854e8i 0.588774 1.50017i −0.256881 0.966443i \(-0.582695\pi\)
0.845655 0.533729i \(-0.179210\pi\)
\(314\) 9.46323e6 1.26278e8i 0.0172499 0.230183i
\(315\) −3.62371e8 + 5.46187e7i −0.653231 + 0.0984587i
\(316\) −1.83679e8 1.70430e8i −0.327458 0.303837i
\(317\) −2.54247e8 1.22439e8i −0.448280 0.215880i 0.196103 0.980583i \(-0.437171\pi\)
−0.644383 + 0.764703i \(0.722886\pi\)
\(318\) 7.34732e8 5.00931e8i 1.28125 0.873541i
\(319\) −3.98514e7 1.01540e8i −0.0687347 0.175133i
\(320\) 9.90893e7 3.05650e7i 0.169045 0.0521434i
\(321\) −4.45744e8 + 4.13590e8i −0.752173 + 0.697915i
\(322\) −3.48063e8 + 4.36458e8i −0.580982 + 0.728528i
\(323\) 1.72534e8 2.16351e8i 0.284883 0.357231i
\(324\) 1.00828e8 9.35550e7i 0.164693 0.152813i
\(325\) 4.66178e8 1.43797e8i 0.753287 0.232358i
\(326\) −3.88164e8 9.89026e8i −0.620517 1.58105i
\(327\) −2.99945e8 + 2.04499e8i −0.474378 + 0.323426i
\(328\) −4.33532e8 2.08778e8i −0.678363 0.326683i
\(329\) −2.50784e8 2.32694e8i −0.388252 0.360246i
\(330\) −3.56011e8 + 5.36600e7i −0.545336 + 0.0821962i
\(331\) 9.57728e6 1.27800e8i 0.0145159 0.193701i −0.985232 0.171227i \(-0.945227\pi\)
0.999747 0.0224738i \(-0.00715425\pi\)
\(332\) −2.22085e8 + 5.65864e8i −0.333071 + 0.848651i
\(333\) −3.23806e7 1.41868e8i −0.0480540 0.210538i
\(334\) 8.25956e7 + 1.10216e9i 0.121295 + 1.61857i
\(335\) 5.05683e8 + 1.55982e8i 0.734888 + 0.226683i
\(336\) 6.31151e8 3.03947e8i 0.907708 0.437129i
\(337\) −3.86305e8 + 6.69100e8i −0.549827 + 0.952328i 0.448459 + 0.893803i \(0.351973\pi\)
−0.998286 + 0.0585244i \(0.981360\pi\)
\(338\) 3.23537e8 + 5.60382e8i 0.455738 + 0.789362i
\(339\) −2.81595e8 1.91988e8i −0.392577 0.267655i
\(340\) 3.34281e7 1.46458e8i 0.0461248 0.202086i
\(341\) 2.15087e8 + 3.24192e7i 0.293748 + 0.0442753i
\(342\) 4.01818e8 + 5.03864e8i 0.543172 + 0.681117i
\(343\) 7.14967e8 0.956658
\(344\) 4.46048e8 1.01471e8i 0.590781 0.134396i
\(345\) −6.91259e8 −0.906304
\(346\) 8.18981e8 + 1.02697e9i 1.06294 + 1.33288i
\(347\) 4.07833e8 + 6.14709e7i 0.523997 + 0.0789799i 0.405714 0.914000i \(-0.367023\pi\)
0.118283 + 0.992980i \(0.462261\pi\)
\(348\) 3.56853e7 1.56348e8i 0.0453902 0.198867i
\(349\) 4.01561e7 + 2.73780e7i 0.0505665 + 0.0344757i 0.588340 0.808614i \(-0.299782\pi\)
−0.537773 + 0.843090i \(0.680734\pi\)
\(350\) 7.94555e8 + 1.37621e9i 0.990572 + 1.71572i
\(351\) −2.22904e8 + 3.86081e8i −0.275133 + 0.476544i
\(352\) −2.47985e8 + 1.19423e8i −0.303059 + 0.145945i
\(353\) 7.88630e7 + 2.43260e7i 0.0954250 + 0.0294347i 0.342100 0.939664i \(-0.388862\pi\)
−0.246675 + 0.969098i \(0.579338\pi\)
\(354\) 2.85462e7 + 3.80923e8i 0.0342009 + 0.456379i
\(355\) −1.21877e8 5.33979e8i −0.144585 0.633468i
\(356\) 2.07939e8 5.29820e8i 0.244265 0.622377i
\(357\) −1.32643e7 + 1.77000e8i −0.0154293 + 0.205889i
\(358\) −7.60791e8 + 1.14671e8i −0.876344 + 0.132088i
\(359\) 2.06220e8 + 1.91344e8i 0.235234 + 0.218266i 0.788978 0.614422i \(-0.210611\pi\)
−0.553743 + 0.832687i \(0.686801\pi\)
\(360\) −3.07309e8 1.47992e8i −0.347150 0.167179i
\(361\) 1.61127e9 1.09854e9i 1.80257 1.22897i
\(362\) −1.02489e8 2.61137e8i −0.113553 0.289327i
\(363\) 5.86974e8 1.81058e8i 0.644089 0.198675i
\(364\) 1.79980e8 1.66997e8i 0.195600 0.181490i
\(365\) −1.64291e9 + 2.06014e9i −1.76843 + 2.21754i
\(366\) 3.96993e8 4.97813e8i 0.423252 0.530741i
\(367\) −7.63916e8 + 7.08810e8i −0.806704 + 0.748512i −0.971302 0.237849i \(-0.923558\pi\)
0.164598 + 0.986361i \(0.447367\pi\)
\(368\) −8.34597e8 + 2.57439e8i −0.872990 + 0.269282i
\(369\) 1.74373e8 + 4.44295e8i 0.180670 + 0.460341i
\(370\) −8.56877e8 + 5.84209e8i −0.879453 + 0.599601i
\(371\) −1.49894e9 7.21853e8i −1.52397 0.733906i
\(372\) 2.34423e8 + 2.17513e8i 0.236102 + 0.219071i
\(373\) 8.35926e8 1.25996e8i 0.834040 0.125711i 0.281880 0.959450i \(-0.409042\pi\)
0.552160 + 0.833738i \(0.313804\pi\)
\(374\) 8.61339e6 1.14938e8i 0.00851380 0.113609i
\(375\) −2.56265e8 + 6.52952e8i −0.250946 + 0.639399i
\(376\) −7.08549e7 3.10436e8i −0.0687405 0.301172i
\(377\) 2.04775e7 + 2.73253e8i 0.0196826 + 0.262646i
\(378\) −1.38764e9 4.28030e8i −1.32147 0.407618i
\(379\) 8.67500e7 4.17766e7i 0.0818525 0.0394181i −0.392510 0.919748i \(-0.628393\pi\)
0.474362 + 0.880330i \(0.342679\pi\)
\(380\) 7.71957e8 1.33707e9i 0.721690 1.25000i
\(381\) 2.58144e8 + 4.47118e8i 0.239125 + 0.414176i
\(382\) −1.63672e9 1.11589e9i −1.50228 1.02424i
\(383\) 3.52735e8 1.54543e9i 0.320813 1.40558i −0.515296 0.857012i \(-0.672318\pi\)
0.836109 0.548563i \(-0.184825\pi\)
\(384\) 9.05909e8 + 1.36544e8i 0.816442 + 0.123059i
\(385\) 4.19975e8 + 5.26632e8i 0.375068 + 0.470321i
\(386\) 1.63206e9 1.44438
\(387\) −3.92788e8 2.27152e8i −0.344484 0.199218i
\(388\) −8.56926e8 −0.744787
\(389\) −8.45801e8 1.06060e9i −0.728525 0.913542i 0.270262 0.962787i \(-0.412890\pi\)
−0.998787 + 0.0492454i \(0.984318\pi\)
\(390\) 8.94333e8 + 1.34799e8i 0.763437 + 0.115070i
\(391\) 4.92435e7 2.15750e8i 0.0416611 0.182529i
\(392\) −4.71949e7 3.21769e7i −0.0395725 0.0269801i
\(393\) 3.27260e8 + 5.66831e8i 0.271969 + 0.471064i
\(394\) 3.07734e8 5.33011e8i 0.253477 0.439035i
\(395\) −1.55588e9 + 7.49272e8i −1.27024 + 0.611716i
\(396\) 8.62226e7 + 2.65961e7i 0.0697731 + 0.0215221i
\(397\) 5.85421e7 + 7.81190e8i 0.0469571 + 0.626600i 0.970188 + 0.242354i \(0.0779194\pi\)
−0.923231 + 0.384246i \(0.874462\pi\)
\(398\) −4.94899e8 2.16829e9i −0.393483 1.72396i
\(399\) −6.66454e8 + 1.69810e9i −0.525249 + 1.33831i
\(400\) −1.85795e8 + 2.47926e9i −0.145152 + 1.93692i
\(401\) −1.43246e9 + 2.15908e8i −1.10937 + 0.167211i −0.678069 0.734998i \(-0.737183\pi\)
−0.431300 + 0.902209i \(0.641945\pi\)
\(402\) 4.37583e8 + 4.06018e8i 0.335946 + 0.311712i
\(403\) −4.92310e8 2.37084e8i −0.374689 0.180441i
\(404\) 9.21353e8 6.28168e8i 0.695170 0.473959i
\(405\) −3.46327e8 8.82427e8i −0.259056 0.660064i
\(406\) −8.52925e8 + 2.63092e8i −0.632513 + 0.195105i
\(407\) −1.96070e8 + 1.81926e8i −0.144155 + 0.133756i
\(408\) −1.03004e8 + 1.29162e8i −0.0750831 + 0.0941512i
\(409\) 6.27229e8 7.86521e8i 0.453310 0.568432i −0.501687 0.865049i \(-0.667287\pi\)
0.954997 + 0.296617i \(0.0958585\pi\)
\(410\) 2.49353e9 2.31366e9i 1.78678 1.65789i
\(411\) 9.65018e8 2.97668e8i 0.685628 0.211488i
\(412\) 2.90692e8 + 7.40671e8i 0.204782 + 0.521777i
\(413\) 5.90488e8 4.02588e8i 0.412464 0.281213i
\(414\) 4.64347e8 + 2.23618e8i 0.321619 + 0.154883i
\(415\) 3.07112e9 + 2.84958e9i 2.10925 + 1.95710i
\(416\) 6.83714e8 1.03053e8i 0.465637 0.0701835i
\(417\) 1.56030e7 2.08207e8i 0.0105373 0.140611i
\(418\) 4.32773e8 1.10269e9i 0.289830 0.738475i
\(419\) −2.60291e8 1.14041e9i −0.172867 0.757378i −0.984809 0.173640i \(-0.944447\pi\)
0.811943 0.583737i \(-0.198410\pi\)
\(420\) 7.40052e7 + 9.87531e8i 0.0487405 + 0.650397i
\(421\) 2.03406e9 + 6.27423e8i 1.32854 + 0.409801i 0.876159 0.482022i \(-0.160098\pi\)
0.452384 + 0.891824i \(0.350574\pi\)
\(422\) −3.06634e9 + 1.47667e9i −1.98621 + 0.956511i
\(423\) −1.57921e8 + 2.73527e8i −0.101449 + 0.175715i
\(424\) −7.74248e8 1.34104e9i −0.493287 0.854398i
\(425\) −5.20486e8 3.54861e8i −0.328888 0.224232i
\(426\) 1.37478e8 6.02332e8i 0.0861590 0.377487i
\(427\) −1.17795e9 1.77548e8i −0.732201 0.110362i
\(428\) −6.77167e8 8.49140e8i −0.417487 0.523512i
\(429\) 2.33260e8 0.142639
\(430\) −4.84262e8 + 3.19729e9i −0.293725 + 1.93929i
\(431\) 2.39606e9 1.44154 0.720771 0.693173i \(-0.243788\pi\)
0.720771 + 0.693173i \(0.243788\pi\)
\(432\) −1.41653e9 1.77628e9i −0.845344 1.06003i
\(433\) 2.35890e9 + 3.55547e8i 1.39637 + 0.210469i 0.803729 0.594995i \(-0.202846\pi\)
0.592644 + 0.805464i \(0.298084\pi\)
\(434\) 3.96064e8 1.73527e9i 0.232569 1.01895i
\(435\) −9.13197e8 6.22607e8i −0.531927 0.362662i
\(436\) −3.24207e8 5.61542e8i −0.187335 0.324474i
\(437\) 1.13719e9 1.96966e9i 0.651848 1.12903i
\(438\) −2.67797e9 + 1.28964e9i −1.52281 + 0.733347i
\(439\) 1.13835e9 + 3.51133e8i 0.642168 + 0.198082i 0.598701 0.800972i \(-0.295684\pi\)
0.0434664 + 0.999055i \(0.486160\pi\)
\(440\) 4.68515e7 + 6.25190e8i 0.0262204 + 0.349887i
\(441\) 1.26075e7 + 5.52372e7i 0.00699995 + 0.0306688i
\(442\) −1.05782e8 + 2.69529e8i −0.0582687 + 0.148466i
\(443\) −1.81626e8 + 2.42363e9i −0.0992578 + 1.32450i 0.695917 + 0.718122i \(0.254998\pi\)
−0.795175 + 0.606381i \(0.792621\pi\)
\(444\) −3.88840e8 + 5.86082e7i −0.210829 + 0.0317774i
\(445\) −2.87549e9 2.66807e9i −1.54687 1.43528i
\(446\) 2.37484e8 + 1.14366e8i 0.126754 + 0.0610417i
\(447\) 4.57486e8 3.11908e8i 0.242271 0.165177i
\(448\) −7.99513e7 2.03713e8i −0.0420100 0.107040i
\(449\) −9.19350e8 + 2.83582e8i −0.479312 + 0.147848i −0.524991 0.851108i \(-0.675931\pi\)
0.0456785 + 0.998956i \(0.485455\pi\)
\(450\) 1.07546e9 9.97877e8i 0.556351 0.516218i
\(451\) 5.46981e8 6.85892e8i 0.280772 0.352077i
\(452\) 3.79545e8 4.75935e8i 0.193321 0.242417i
\(453\) 1.27586e9 1.18383e9i 0.644853 0.598336i
\(454\) −2.33268e9 + 7.19536e8i −1.16993 + 0.360875i
\(455\) −6.18199e8 1.57515e9i −0.307672 0.783936i
\(456\) −1.40285e9 + 9.56448e8i −0.692843 + 0.472372i
\(457\) −4.58230e8 2.20672e8i −0.224583 0.108153i 0.318209 0.948021i \(-0.396919\pi\)
−0.542792 + 0.839867i \(0.682633\pi\)
\(458\) −1.56654e9 1.45353e9i −0.761923 0.706961i
\(459\) 5.69226e8 8.57970e7i 0.274752 0.0414121i
\(460\) 9.22681e7 1.23123e9i 0.0441977 0.589777i
\(461\) 1.04816e9 2.67067e9i 0.498281 1.26960i −0.431709 0.902013i \(-0.642089\pi\)
0.929990 0.367586i \(-0.119816\pi\)
\(462\) 1.69074e8 + 7.40761e8i 0.0797681 + 0.349487i
\(463\) 2.20363e8 + 2.94054e9i 0.103182 + 1.37687i 0.773027 + 0.634373i \(0.218742\pi\)
−0.669845 + 0.742501i \(0.733639\pi\)
\(464\) −1.33443e9 4.11616e8i −0.620129 0.191284i
\(465\) 1.98571e9 9.56268e8i 0.915863 0.441056i
\(466\) 2.78333e8 4.82086e8i 0.127413 0.220686i
\(467\) 6.75548e8 + 1.17008e9i 0.306935 + 0.531628i 0.977690 0.210051i \(-0.0673631\pi\)
−0.670755 + 0.741679i \(0.734030\pi\)
\(468\) −1.87283e8 1.27688e8i −0.0844575 0.0575822i
\(469\) 2.48513e8 1.08881e9i 0.111236 0.487356i
\(470\) 2.22582e9 + 3.35489e8i 0.988890 + 0.149051i
\(471\) −2.06324e8 2.58722e8i −0.0909863 0.114093i
\(472\) 6.65181e8 0.291167
\(473\) −598806. + 8.34006e8i −0.000260179 + 0.362373i
\(474\) −1.94795e9 −0.840144
\(475\) −4.03660e9 5.06174e9i −1.72818 2.16707i
\(476\) −3.13492e8 4.72513e7i −0.133230 0.0200812i
\(477\) −3.41783e8 + 1.49745e9i −0.144190 + 0.631739i
\(478\) 2.04644e9 + 1.39524e9i 0.857041 + 0.584321i
\(479\) 7.69008e7 + 1.33196e8i 0.0319710 + 0.0553755i 0.881568 0.472057i \(-0.156488\pi\)
−0.849597 + 0.527432i \(0.823155\pi\)
\(480\) −1.39444e9 + 2.41524e9i −0.575514 + 0.996819i
\(481\) 6.05371e8 2.91531e8i 0.248035 0.119448i
\(482\) 1.10881e9 + 3.42023e8i 0.451017 + 0.139120i
\(483\) 1.09019e8 + 1.45475e9i 0.0440236 + 0.587454i
\(484\) 2.44142e8 + 1.06965e9i 0.0978776 + 0.428830i
\(485\) −2.15766e9 + 5.49762e9i −0.858788 + 2.18816i
\(486\) −1.71855e8 + 2.29325e9i −0.0679102 + 0.906199i
\(487\) 2.54683e8 3.83872e7i 0.0999189 0.0150604i −0.0988925 0.995098i \(-0.531530\pi\)
0.198811 + 0.980038i \(0.436292\pi\)
\(488\) −8.12783e8 7.54152e8i −0.316596 0.293758i
\(489\) −2.50151e9 1.20467e9i −0.967435 0.465892i
\(490\) 3.33629e8 2.27465e8i 0.128108 0.0873429i
\(491\) 8.27674e8 + 2.10888e9i 0.315554 + 0.804019i 0.997369 + 0.0724940i \(0.0230958\pi\)
−0.681815 + 0.731525i \(0.738809\pi\)
\(492\) 1.23248e9 3.80170e8i 0.466554 0.143913i
\(493\) 2.59377e8 2.40666e8i 0.0974915 0.0904589i
\(494\) −1.85536e9 + 2.32654e9i −0.692441 + 0.868294i
\(495\) 3.87728e8 4.86195e8i 0.143684 0.180174i
\(496\) 2.04133e9 1.89408e9i 0.751151 0.696967i
\(497\) −1.10454e9 + 3.40704e8i −0.403583 + 0.124489i
\(498\) 1.72652e9 + 4.39911e9i 0.626426 + 1.59611i
\(499\) −3.49146e9 + 2.38043e9i −1.25792 + 0.857638i −0.994262 0.106977i \(-0.965883\pi\)
−0.263663 + 0.964615i \(0.584931\pi\)
\(500\) −1.12880e9 5.43600e8i −0.403851 0.194484i
\(501\) 2.11725e9 + 1.96452e9i 0.752212 + 0.697951i
\(502\) −3.01758e9 + 4.54828e8i −1.06462 + 0.160466i
\(503\) 2.90410e8 3.87525e9i 0.101747 1.35773i −0.679579 0.733602i \(-0.737838\pi\)
0.781326 0.624123i \(-0.214543\pi\)
\(504\) −2.62984e8 + 6.70071e8i −0.0915001 + 0.233139i
\(505\) −1.71014e9 7.49261e9i −0.590897 2.58889i
\(506\) −7.07930e7 9.44667e8i −0.0242920 0.324154i
\(507\) 1.61582e9 + 4.98415e8i 0.550638 + 0.169849i
\(508\) −8.30839e8 + 4.00111e8i −0.281186 + 0.135412i
\(509\) 1.58807e9 2.75062e9i 0.533774 0.924524i −0.465448 0.885075i \(-0.654107\pi\)
0.999222 0.0394484i \(-0.0125601\pi\)
\(510\) −5.83932e8 1.01140e9i −0.194925 0.337619i
\(511\) 4.59466e9 + 3.13259e9i 1.52328 + 1.03856i
\(512\) −2.72309e8 + 1.19306e9i −0.0896639 + 0.392843i
\(513\) 5.85016e9 + 8.81770e8i 1.91319 + 0.288366i
\(514\) 3.66631e9 + 4.59741e9i 1.19085 + 1.49328i
\(515\) 5.48372e9 1.76909
\(516\) −6.91441e8 + 1.01259e9i −0.221555 + 0.324460i
\(517\) 5.80538e8 0.184763
\(518\) 1.36460e9 + 1.71116e9i 0.431373 + 0.540924i
\(519\) 3.39424e9 + 5.11599e8i 1.06575 + 0.160636i
\(520\) 3.50457e8 1.53545e9i 0.109301 0.478878i
\(521\) −4.76932e9 3.25167e9i −1.47749 1.00734i −0.991031 0.133633i \(-0.957336\pi\)
−0.486459 0.873703i \(-0.661712\pi\)
\(522\) 4.12022e8 + 7.13644e8i 0.126787 + 0.219601i
\(523\) −2.67407e9 + 4.63163e9i −0.817367 + 1.41572i 0.0902484 + 0.995919i \(0.471234\pi\)
−0.907616 + 0.419802i \(0.862099\pi\)
\(524\) −1.05329e9 + 5.07238e8i −0.319808 + 0.154011i
\(525\) 3.96820e9 + 1.22403e9i 1.19684 + 0.369176i
\(526\) 2.20284e7 + 2.93948e8i 0.00659982 + 0.0880685i
\(527\) 1.57005e8 + 6.87886e8i 0.0467280 + 0.204729i
\(528\) −4.34298e8 + 1.10657e9i −0.128401 + 0.327161i
\(529\) −1.18521e8 + 1.58155e9i −0.0348097 + 0.464503i
\(530\) 1.08243e10 1.63151e9i 3.15817 0.476018i
\(531\) −4.83664e8 4.48775e8i −0.140189 0.130076i
\(532\) −2.93560e9 1.41371e9i −0.845292 0.407071i
\(533\) −1.82089e9 + 1.24146e9i −0.520882 + 0.355131i
\(534\) −1.61655e9 4.11889e9i −0.459403 1.17054i
\(535\) −7.15271e9 + 2.20632e9i −2.01945 + 0.622917i
\(536\) 7.61987e8 7.07020e8i 0.213733 0.198315i
\(537\) −1.25357e9 + 1.57193e9i −0.349332 + 0.438049i
\(538\) 1.80636e9 2.26510e9i 0.500110 0.627119i
\(539\) 7.63406e7 7.08338e7i 0.0209988 0.0194841i
\(540\) 3.06905e9 9.46678e8i 0.838738 0.258716i
\(541\) −1.48775e9 3.79073e9i −0.403962 1.02928i −0.977656 0.210209i \(-0.932586\pi\)
0.573694 0.819069i \(-0.305510\pi\)
\(542\) −3.55492e9 + 2.42371e9i −0.959032 + 0.653857i
\(543\) −6.60487e8 3.18074e8i −0.177037 0.0852567i
\(544\) −6.54489e8 6.07277e8i −0.174303 0.161730i
\(545\) −4.41890e9 + 6.66042e8i −1.16930 + 0.176244i
\(546\) 1.42639e8 1.90338e9i 0.0375027 0.500439i
\(547\) −1.68563e8 + 4.29492e8i −0.0440359 + 0.112202i −0.951200 0.308576i \(-0.900148\pi\)
0.907164 + 0.420778i \(0.138243\pi\)
\(548\) 4.01382e8 + 1.75857e9i 0.104190 + 0.456486i
\(549\) 8.21874e7 + 1.09671e9i 0.0211983 + 0.282872i
\(550\) −2.57682e9 7.94843e8i −0.660411 0.203710i
\(551\) 3.27634e9 1.57780e9i 0.834370 0.401811i
\(552\) −6.78905e8 + 1.17590e9i −0.171800 + 0.297566i
\(553\) 1.82222e9 + 3.15618e9i 0.458208 + 0.793639i
\(554\) −3.32592e9 2.26758e9i −0.831052 0.566601i
\(555\) −6.03059e8 + 2.64218e9i −0.149739 + 0.656049i
\(556\) 3.68765e8 + 5.55823e7i 0.0909887 + 0.0137143i
\(557\) 5.27857e8 + 6.61912e8i 0.129427 + 0.162296i 0.842322 0.538974i \(-0.181188\pi\)
−0.712896 + 0.701270i \(0.752617\pi\)
\(558\) −1.64323e9 −0.400386
\(559\) 6.18980e8 2.00158e9i 0.149877 0.484654i
\(560\) 8.62342e9 2.07502
\(561\) −1.87795e8 2.35488e8i −0.0449070 0.0563116i
\(562\) 6.07288e8 + 9.15339e7i 0.144317 + 0.0217523i
\(563\) −8.42092e8 + 3.68945e9i −0.198875 + 0.871329i 0.772733 + 0.634731i \(0.218889\pi\)
−0.971608 + 0.236597i \(0.923968\pi\)
\(564\) 7.05196e8 + 4.80794e8i 0.165513 + 0.112845i
\(565\) −2.09771e9 3.63333e9i −0.489300 0.847492i
\(566\) 2.74914e9 4.76165e9i 0.637293 1.10382i
\(567\) −1.80245e9 + 8.68012e8i −0.415261 + 0.199979i
\(568\) −1.02805e9 3.17111e8i −0.235394 0.0726093i
\(569\) 3.34697e8 + 4.46622e9i 0.0761656 + 1.01636i 0.896086 + 0.443881i \(0.146399\pi\)
−0.819920 + 0.572478i \(0.805982\pi\)
\(570\) −2.67083e9 1.17017e10i −0.604066 2.64659i
\(571\) 2.68725e9 6.84701e9i 0.604063 1.53913i −0.221703 0.975114i \(-0.571162\pi\)
0.825766 0.564013i \(-0.190743\pi\)
\(572\) −3.11351e7 + 4.15470e8i −0.00695608 + 0.0928225i
\(573\) −5.11877e9 + 7.71531e8i −1.13664 + 0.171322i
\(574\) −5.26234e9 4.88274e9i −1.16142 1.07764i
\(575\) −4.66476e9 2.24643e9i −1.02327 0.492783i
\(576\) −1.66931e8 + 1.13812e8i −0.0363963 + 0.0248146i
\(577\) −2.79618e9 7.12454e9i −0.605967 1.54398i −0.823135 0.567845i \(-0.807777\pi\)
0.217168 0.976134i \(-0.430318\pi\)
\(578\) −5.08743e9 + 1.56926e9i −1.09585 + 0.338025i
\(579\) 3.12642e9 2.90089e9i 0.669379 0.621093i
\(580\) 1.23085e9 1.54343e9i 0.261942 0.328465i
\(581\) 5.51259e9 6.91257e9i 1.16611 1.46225i
\(582\) −4.88349e9 + 4.53121e9i −1.02683 + 0.952761i
\(583\) 2.69777e9 8.32153e8i 0.563852 0.173925i
\(584\) 1.89095e9 + 4.81807e9i 0.392858 + 1.00099i
\(585\) −1.29074e9 + 8.80012e8i −0.266559 + 0.181737i
\(586\) −6.07763e9 2.92683e9i −1.24765 0.600837i
\(587\) −4.33724e9 4.02437e9i −0.885075 0.821230i 0.0997082 0.995017i \(-0.468209\pi\)
−0.984783 + 0.173787i \(0.944400\pi\)
\(588\) 1.51397e8 2.28194e7i 0.0307111 0.00462896i
\(589\) −5.41904e8 + 7.23121e9i −0.109275 + 1.45817i
\(590\) −1.71794e9 + 4.37723e9i −0.344370 + 0.877440i
\(591\) −3.57892e8 1.56803e9i −0.0713175 0.312462i
\(592\) 2.55892e8 + 3.41464e9i 0.0506910 + 0.676425i
\(593\) 8.72428e9 + 2.69108e9i 1.71806 + 0.529951i 0.988137 0.153578i \(-0.0490795\pi\)
0.729923 + 0.683529i \(0.239556\pi\)
\(594\) 2.22018e9 1.06918e9i 0.434647 0.209315i
\(595\) −1.09248e9 + 1.89224e9i −0.212621 + 0.368270i
\(596\) 4.94490e8 + 8.56482e8i 0.0956744 + 0.165713i
\(597\) −4.80206e9 3.27399e9i −0.923670 0.629748i
\(598\) −5.29544e8 + 2.32008e9i −0.101262 + 0.443659i
\(599\) −6.46835e9 9.74947e8i −1.22970 0.185348i −0.498124 0.867106i \(-0.665978\pi\)
−0.731578 + 0.681758i \(0.761216\pi\)
\(600\) 2.40987e9 + 3.02188e9i 0.455475 + 0.571147i
\(601\) −8.78947e9 −1.65159 −0.825794 0.563971i \(-0.809273\pi\)
−0.825794 + 0.563971i \(0.809273\pi\)
\(602\) 6.80506e9 + 5.14882e8i 1.27129 + 0.0961878i
\(603\) −1.03106e9 −0.191501
\(604\) 1.93827e9 + 2.43052e9i 0.357920 + 0.448817i
\(605\) 7.47710e9 + 1.12699e9i 1.37274 + 0.206908i
\(606\) 1.92905e9 8.45172e9i 0.352119 1.54273i
\(607\) 7.58080e9 + 5.16850e9i 1.37580 + 0.938003i 0.999936 + 0.0113278i \(0.00360582\pi\)
0.375862 + 0.926676i \(0.377347\pi\)
\(608\) −4.58797e9 7.94660e9i −0.827862 1.43390i
\(609\) −1.16625e9 + 2.02001e9i −0.209234 + 0.362404i
\(610\) 7.06186e9 3.40081e9i 1.25969 0.606636i
\(611\) −1.39358e9 4.29861e8i −0.247165 0.0762402i
\(612\) 2.18728e7 + 2.91872e8i 0.00385722 + 0.0514710i
\(613\) 1.96435e9 + 8.60639e9i 0.344435 + 1.50907i 0.789601 + 0.613621i \(0.210288\pi\)
−0.445166 + 0.895448i \(0.646855\pi\)
\(614\) −4.10329e9 + 1.04550e10i −0.715391 + 1.82279i
\(615\) 6.64281e8 8.86422e9i 0.115157 1.53666i
\(616\) 1.30832e9 1.97198e8i 0.225518 0.0339914i
\(617\) −7.14493e9 6.62952e9i −1.22462 1.13628i −0.986278 0.165095i \(-0.947207\pi\)
−0.238338 0.971182i \(-0.576603\pi\)
\(618\) 5.57310e9 + 2.68386e9i 0.949810 + 0.457405i
\(619\) 2.13207e9 1.45362e9i 0.361314 0.246339i −0.369033 0.929416i \(-0.620311\pi\)
0.730346 + 0.683077i \(0.239359\pi\)
\(620\) 1.43820e9 + 3.66448e9i 0.242353 + 0.617507i
\(621\) 4.52108e9 1.39457e9i 0.757568 0.233679i
\(622\) 1.31991e9 1.22470e9i 0.219927 0.204063i
\(623\) −5.16145e9 + 6.47225e9i −0.855191 + 1.07238i
\(624\) 1.86189e9 2.33474e9i 0.306767 0.384674i
\(625\) 6.22921e8 5.77986e8i 0.102059 0.0946973i
\(626\) 1.16008e10 3.57837e9i 1.89007 0.583008i
\(627\) −1.13093e9 2.88157e9i −0.183231 0.466866i
\(628\) 4.88361e8 3.32959e8i 0.0786833 0.0536453i
\(629\) −7.81694e8 3.76444e8i −0.125245 0.0603147i
\(630\) −3.73022e9 3.46114e9i −0.594350 0.551476i
\(631\) −6.13912e9 + 9.25324e8i −0.972755 + 0.146619i −0.616144 0.787634i \(-0.711306\pi\)
−0.356611 + 0.934253i \(0.616068\pi\)
\(632\) −2.53490e8 + 3.38258e9i −0.0399439 + 0.533014i
\(633\) −3.24926e9 + 8.27898e9i −0.509180 + 1.29737i
\(634\) −8.71937e8 3.82021e9i −0.135885 0.595353i
\(635\) 4.74945e8 + 6.33770e9i 0.0736097 + 0.982253i
\(636\) 3.96624e9 + 1.22342e9i 0.611334 + 0.188572i
\(637\) −2.35704e8 + 1.13509e8i −0.0361309 + 0.0173997i
\(638\) 7.57326e8 1.31173e9i 0.115454 0.199973i
\(639\) 5.33568e8 + 9.24167e8i 0.0808978 + 0.140119i
\(640\) 9.31803e9 + 6.35293e9i 1.40506 + 0.957952i
\(641\) −1.37595e8 + 6.02845e8i −0.0206348 + 0.0904070i −0.984197 0.177078i \(-0.943335\pi\)
0.963562 + 0.267485i \(0.0861926\pi\)
\(642\) −8.34911e9 1.25843e9i −1.24528 0.187696i
\(643\) 1.74452e9 + 2.18756e9i 0.258785 + 0.324505i 0.894202 0.447663i \(-0.147744\pi\)
−0.635418 + 0.772168i \(0.719172\pi\)
\(644\) −2.60568e9 −0.384432
\(645\) 4.75533e9 + 6.98556e9i 0.697785 + 1.02504i
\(646\) 3.84249e9 0.560789
\(647\) 1.49142e7 + 1.87018e7i 0.00216489 + 0.00271468i 0.782913 0.622132i \(-0.213733\pi\)
−0.780748 + 0.624846i \(0.785162\pi\)
\(648\) −1.84123e9 2.77521e8i −0.265825 0.0400667i
\(649\) −2.69862e8 + 1.18234e9i −0.0387513 + 0.169780i
\(650\) 5.59708e9 + 3.81603e9i 0.799401 + 0.545023i
\(651\) −2.32563e9 4.02811e9i −0.330375 0.572226i
\(652\) 2.47958e9 4.29477e9i 0.350358 0.606838i
\(653\) −4.12173e8 + 1.98492e8i −0.0579272 + 0.0278963i −0.462623 0.886555i \(-0.653092\pi\)
0.404696 + 0.914451i \(0.367377\pi\)
\(654\) −4.81690e9 1.48582e9i −0.673357 0.207703i
\(655\) 6.02108e8 + 8.03458e9i 0.0837201 + 1.11717i
\(656\) −2.49919e9 1.09497e10i −0.345650 1.51439i
\(657\) 1.87564e9 4.77906e9i 0.258031 0.657451i
\(658\) 3.55000e8 4.73714e9i 0.0485778 0.648225i
\(659\) −1.06771e9 + 1.60932e8i −0.145330 + 0.0219050i −0.221304 0.975205i \(-0.571031\pi\)
0.0759742 + 0.997110i \(0.475793\pi\)
\(660\) −1.23188e9 1.14302e9i −0.166788 0.154756i
\(661\) 1.71633e9 + 8.26541e8i 0.231151 + 0.111316i 0.545875 0.837867i \(-0.316198\pi\)
−0.314724 + 0.949183i \(0.601912\pi\)
\(662\) 1.47035e9 1.00247e9i 0.196978 0.134297i
\(663\) 2.76433e8 + 7.04339e8i 0.0368377 + 0.0938608i
\(664\) 7.86365e9 2.42562e9i 1.04240 0.321539i
\(665\) −1.64612e10 + 1.52738e10i −2.17064 + 2.01406i
\(666\) 1.25983e9 1.57977e9i 0.165254 0.207221i
\(667\) 1.81318e9 2.27366e9i 0.236593 0.296678i
\(668\) −3.78171e9 + 3.50891e9i −0.490874 + 0.455465i
\(669\) 6.58211e8 2.03031e8i 0.0849912 0.0262163i
\(670\) 2.68460e9 + 6.84026e9i 0.344841 + 0.878640i
\(671\) 1.67023e9 1.13875e9i 0.213427 0.145512i
\(672\) 5.30278e9 + 2.55369e9i 0.674080 + 0.324620i
\(673\) −9.23774e8 8.57137e8i −0.116819 0.108392i 0.619601 0.784917i \(-0.287295\pi\)
−0.736420 + 0.676525i \(0.763485\pi\)
\(674\) −1.06084e10 + 1.59896e9i −1.33457 + 0.201154i
\(675\) 1.00647e9 1.34304e10i 0.125961 1.68083i
\(676\) −1.10343e9 + 2.81149e9i −0.137382 + 0.350044i
\(677\) 2.91636e9 + 1.27774e10i 0.361227 + 1.58264i 0.750084 + 0.661342i \(0.230013\pi\)
−0.388857 + 0.921298i \(0.627130\pi\)
\(678\) −3.53657e8 4.71922e9i −0.0435791 0.581522i
\(679\) 1.19100e10 + 3.67375e9i 1.46005 + 0.450366i
\(680\) −1.83227e9 + 8.82374e8i −0.223464 + 0.107615i
\(681\) −3.18960e9 + 5.52456e9i −0.387010 + 0.670321i
\(682\) 1.51019e9 + 2.61572e9i 0.182299 + 0.315752i
\(683\) −1.29846e10 8.85275e9i −1.55940 1.06318i −0.966092 0.258199i \(-0.916871\pi\)
−0.593303 0.804979i \(-0.702177\pi\)
\(684\) −6.69364e8 + 2.93268e9i −0.0799772 + 0.350403i
\(685\) 1.22928e10 + 1.85284e9i 1.46128 + 0.220252i
\(686\) 6.18989e9 + 7.76188e9i 0.732063 + 0.917979i
\(687\) −5.58447e9 −0.657102
\(688\) 8.34295e9 + 6.66309e9i 0.976698 + 0.780039i
\(689\) −7.09215e9 −0.826058
\(690\) −5.98464e9 7.50450e9i −0.693531 0.869660i
\(691\) 3.08598e9 + 4.65137e8i 0.355812 + 0.0536300i 0.324516 0.945880i \(-0.394799\pi\)
0.0312958 + 0.999510i \(0.490037\pi\)
\(692\) −1.36429e9 + 5.97735e9i −0.156508 + 0.685705i
\(693\) −1.08434e9 7.39294e8i −0.123766 0.0843822i
\(694\) 2.86350e9 + 4.95974e9i 0.325192 + 0.563249i
\(695\) 1.28510e9 2.22586e9i 0.145208 0.251508i
\(696\) −1.95599e9 + 9.41956e8i −0.219905 + 0.105901i
\(697\) 2.71930e9 + 8.38794e8i 0.304189 + 0.0938298i
\(698\) 5.04324e7 + 6.72974e8i 0.00561327 + 0.0749038i
\(699\) −3.23699e8 1.41822e9i −0.0358485 0.157063i
\(700\) −2.70984e9 + 6.90457e9i −0.298608 + 0.760840i
\(701\) 1.02340e9 1.36563e10i 0.112210 1.49734i −0.602610 0.798036i \(-0.705873\pi\)
0.714821 0.699308i \(-0.246508\pi\)
\(702\) −6.12121e9 + 9.22624e8i −0.667817 + 0.100657i
\(703\) −6.53649e9 6.06498e9i −0.709579 0.658393i
\(704\) 3.34582e8 + 1.61126e8i 0.0361409 + 0.0174045i
\(705\) 4.86016e9 3.31360e9i 0.522382 0.356154i
\(706\) 4.18674e8 + 1.06676e9i 0.0447774 + 0.114091i
\(707\) −1.54985e10 + 4.78064e9i −1.64938 + 0.508766i
\(708\) −1.30701e9 + 1.21273e9i −0.138409 + 0.128424i
\(709\) 3.79759e9 4.76203e9i 0.400172 0.501800i −0.540393 0.841412i \(-0.681725\pi\)
0.940565 + 0.339613i \(0.110296\pi\)
\(710\) 4.74186e9 5.94610e9i 0.497215 0.623488i
\(711\) 2.46643e9 2.28851e9i 0.257351 0.238787i
\(712\) −7.36275e9 + 2.27111e9i −0.764470 + 0.235808i
\(713\) 2.11865e9 + 5.39822e9i 0.218900 + 0.557747i
\(714\) −2.03640e9 + 1.38839e9i −0.209372 + 0.142747i
\(715\) 2.58705e9 + 1.24586e9i 0.264688 + 0.127467i
\(716\) −2.63251e9 2.44261e9i −0.268024 0.248690i
\(717\) 6.40017e9 9.64671e8i 0.648447 0.0977377i
\(718\) −2.91917e8 + 3.89537e9i −0.0294323 + 0.392747i
\(719\) 1.96074e9 4.99588e9i 0.196729 0.501257i −0.798135 0.602479i \(-0.794180\pi\)
0.994864 + 0.101222i \(0.0322751\pi\)
\(720\) −1.77155e9 7.76169e9i −0.176885 0.774983i
\(721\) −8.64838e8 1.15405e10i −0.0859333 1.14670i
\(722\) 2.58758e10 + 7.98161e9i 2.55866 + 0.789242i
\(723\) 2.73199e9 1.31566e9i 0.268841 0.129467i
\(724\) 6.54697e8 1.13397e9i 0.0641143 0.111049i
\(725\) −4.13912e9 7.16916e9i −0.403389 0.698691i
\(726\) 7.04740e9 + 4.80483e9i 0.683519 + 0.466015i
\(727\) 2.16438e9 9.48276e9i 0.208912 0.915302i −0.756381 0.654131i \(-0.773034\pi\)
0.965293 0.261171i \(-0.0841085\pi\)
\(728\) −3.28663e9 4.95379e8i −0.315712 0.0475859i
\(729\) 6.64069e9 + 8.32716e9i 0.634843 + 0.796068i
\(730\) −3.65891e10 −3.48114
\(731\) −2.51903e9 + 9.86561e8i −0.238519 + 0.0934142i
\(732\) 2.97197e9 0.280063
\(733\) −9.34055e9 1.17127e10i −0.876009 1.09848i −0.994418 0.105515i \(-0.966351\pi\)
0.118409 0.992965i \(-0.462221\pi\)
\(734\) −1.43087e10 2.15669e9i −1.33556 0.201304i
\(735\) 2.34804e8 1.02874e9i 0.0218122 0.0955656i
\(736\) −6.06302e9 4.13370e9i −0.560553 0.382179i
\(737\) 9.47577e8 + 1.64125e9i 0.0871923 + 0.151021i
\(738\) −3.31374e9 + 5.73957e9i −0.303474 + 0.525632i
\(739\) −6.47958e9 + 3.12040e9i −0.590597 + 0.284416i −0.705215 0.708993i \(-0.749150\pi\)
0.114619 + 0.993410i \(0.463435\pi\)
\(740\) −4.62560e9 1.42681e9i −0.419621 0.129436i
\(741\) 5.81125e8 + 7.75457e9i 0.0524694 + 0.700155i
\(742\) −5.14061e9 2.25225e10i −0.461956 2.02396i
\(743\) 5.92467e9 1.50958e10i 0.529911 1.35019i −0.375959 0.926636i \(-0.622686\pi\)
0.905870 0.423556i \(-0.139218\pi\)
\(744\) 3.23519e8 4.31707e9i 0.0288002 0.384311i
\(745\) 6.73984e9 1.01587e9i 0.597177 0.0900099i
\(746\) 8.60495e9 + 7.98423e9i 0.758861 + 0.704121i
\(747\) −7.35428e9 3.54163e9i −0.645532 0.310872i
\(748\) 4.44504e8 3.03058e8i 0.0388347 0.0264771i
\(749\) 5.77124e9 + 1.47049e10i 0.501861 + 1.27872i
\(750\) −9.30727e9 + 2.87091e9i −0.805578 + 0.248488i
\(751\) 2.72164e9 2.52531e9i 0.234472 0.217558i −0.554182 0.832396i \(-0.686969\pi\)
0.788654 + 0.614837i \(0.210778\pi\)