Properties

Label 43.8.g.a.24.14
Level 43
Weight 8
Character 43.24
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 24.14
Character \(\chi\) \(=\) 43.24
Dual form 43.8.g.a.9.14

$q$-expansion

\(f(q)\) \(=\) \(q+(2.22112 - 2.78519i) q^{2} +(-37.3010 + 5.62222i) q^{3} +(25.6587 + 112.418i) q^{4} +(39.7972 - 27.1333i) q^{5} +(-67.1910 + 116.378i) q^{6} +(-76.5793 - 132.639i) q^{7} +(780.928 + 376.075i) q^{8} +(-730.081 + 225.200i) q^{9} +O(q^{10})\) \(q+(2.22112 - 2.78519i) q^{2} +(-37.3010 + 5.62222i) q^{3} +(25.6587 + 112.418i) q^{4} +(39.7972 - 27.1333i) q^{5} +(-67.1910 + 116.378i) q^{6} +(-76.5793 - 132.639i) q^{7} +(780.928 + 376.075i) q^{8} +(-730.081 + 225.200i) q^{9} +(12.8229 - 171.109i) q^{10} +(247.552 - 1084.60i) q^{11} +(-1589.14 - 4049.06i) q^{12} +(-542.368 - 7237.40i) q^{13} +(-539.517 - 81.3192i) q^{14} +(-1331.93 + 1235.85i) q^{15} +(-10516.0 + 5064.22i) q^{16} +(-23860.6 - 16267.9i) q^{17} +(-994.370 + 2533.61i) q^{18} +(-33347.5 - 10286.3i) q^{19} +(4071.42 + 3777.73i) q^{20} +(3602.21 + 4517.03i) q^{21} +(-2470.97 - 3098.50i) q^{22} +(-8253.57 - 7658.19i) q^{23} +(-31243.8 - 9637.43i) q^{24} +(-27694.7 + 70564.9i) q^{25} +(-21362.2 - 14564.5i) q^{26} +(100295. - 48299.8i) q^{27} +(12946.1 - 12012.3i) q^{28} +(-15211.5 - 2292.76i) q^{29} +(483.708 + 6454.63i) q^{30} +(-102376. - 260849. i) q^{31} +(-33940.1 + 148701. i) q^{32} +(-3136.10 + 41848.3i) q^{33} +(-98306.4 + 30323.5i) q^{34} +(-6646.57 - 3200.82i) q^{35} +(-44049.6 - 76296.1i) q^{36} +(100741. - 174489. i) q^{37} +(-102718. + 70032.0i) q^{38} +(60921.2 + 266913. i) q^{39} +(41282.9 - 6222.39i) q^{40} +(140957. - 176755. i) q^{41} +20581.7 q^{42} +(209663. + 477347. i) q^{43} +128280. q^{44} +(-22944.8 + 28771.8i) q^{45} +(-39661.7 + 5978.04i) q^{46} +(55359.6 + 242546. i) q^{47} +(363784. - 248024. i) q^{48} +(400043. - 692894. i) q^{49} +(135024. + 233868. i) q^{50} +(981486. + 472659. i) q^{51} +(799700. - 246675. i) q^{52} +(-115274. + 1.53823e6i) q^{53} +(88243.9 - 386622. i) q^{54} +(-19576.8 - 49880.8i) q^{55} +(-9920.59 - 132381. i) q^{56} +(1.30173e6 + 196204. i) q^{57} +(-40172.3 + 37274.4i) q^{58} +(-1.58742e6 + 764461. i) q^{59} +(-173107. - 118023. i) q^{60} +(-573411. + 1.46103e6i) q^{61} +(-953903. - 294240. i) q^{62} +(85779.5 + 79591.7i) q^{63} +(-592713. - 743239. i) q^{64} +(-217959. - 273312. i) q^{65} +(109590. + 101685. i) q^{66} +(-2.80244e6 - 864439. i) q^{67} +(1.21657e6 - 3.09978e6i) q^{68} +(350922. + 239255. i) q^{69} +(-23677.7 + 11402.6i) q^{70} +(-1.85678e6 + 1.72284e6i) q^{71} +(-654833. - 98700.2i) q^{72} +(-65828.0 - 878413. i) q^{73} +(-262227. - 668144. i) q^{74} +(636308. - 2.78785e6i) q^{75} +(300718. - 4.01280e6i) q^{76} +(-162817. + 50222.5i) q^{77} +(878718. + 423168. i) q^{78} +(330578. + 572578. i) q^{79} +(-281097. + 486874. i) q^{80} +(-2.08899e6 + 1.42425e6i) q^{81} +(-179213. - 785185. i) q^{82} +(-4.32122e6 + 651319. i) q^{83} +(-415369. + 520856. i) q^{84} -1.39099e6 q^{85} +(1.79519e6 + 476293. i) q^{86} +580294. q^{87} +(601210. - 753893. i) q^{88} +(-2.92399e6 + 440720. i) q^{89} +(29172.1 + 127811. i) q^{90} +(-918429. + 626174. i) q^{91} +(649145. - 1.12435e6i) q^{92} +(5.28526e6 + 9.15435e6i) q^{93} +(798498. + 384537. i) q^{94} +(-1.60624e6 + 495458. i) q^{95} +(429969. - 5.73753e6i) q^{96} +(-1.26764e6 + 5.55388e6i) q^{97} +(-1.04130e6 - 2.65320e6i) q^{98} +(63518.3 + 847592. i) 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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{20}{21}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.22112 2.78519i 0.196321 0.246179i −0.673921 0.738804i \(-0.735391\pi\)
0.870242 + 0.492625i \(0.163963\pi\)
\(3\) −37.3010 + 5.62222i −0.797620 + 0.120222i −0.535193 0.844730i \(-0.679761\pi\)
−0.262427 + 0.964952i \(0.584523\pi\)
\(4\) 25.6587 + 112.418i 0.200459 + 0.878268i
\(5\) 39.7972 27.1333i 0.142383 0.0970749i −0.490034 0.871703i \(-0.663016\pi\)
0.632416 + 0.774629i \(0.282063\pi\)
\(6\) −67.1910 + 116.378i −0.126994 + 0.219959i
\(7\) −76.5793 132.639i −0.0843855 0.146160i 0.820744 0.571297i \(-0.193559\pi\)
−0.905129 + 0.425137i \(0.860226\pi\)
\(8\) 780.928 + 376.075i 0.539257 + 0.259693i
\(9\) −730.081 + 225.200i −0.333828 + 0.102972i
\(10\) 12.8229 171.109i 0.00405494 0.0541094i
\(11\) 247.552 1084.60i 0.0560779 0.245694i −0.939118 0.343594i \(-0.888356\pi\)
0.995196 + 0.0979006i \(0.0312127\pi\)
\(12\) −1589.14 4049.06i −0.265477 0.676425i
\(13\) −542.368 7237.40i −0.0684688 0.913653i −0.920646 0.390399i \(-0.872337\pi\)
0.852177 0.523254i \(-0.175282\pi\)
\(14\) −539.517 81.3192i −0.0525481 0.00792036i
\(15\) −1331.93 + 1235.85i −0.101897 + 0.0945465i
\(16\) −10516.0 + 5064.22i −0.641843 + 0.309095i
\(17\) −23860.6 16267.9i −1.17790 0.803082i −0.193864 0.981028i \(-0.562102\pi\)
−0.984040 + 0.177947i \(0.943055\pi\)
\(18\) −994.370 + 2533.61i −0.0401878 + 0.102397i
\(19\) −33347.5 10286.3i −1.11539 0.344051i −0.318344 0.947975i \(-0.603127\pi\)
−0.797042 + 0.603924i \(0.793603\pi\)
\(20\) 4071.42 + 3777.73i 0.113800 + 0.105591i
\(21\) 3602.21 + 4517.03i 0.0848793 + 0.106435i
\(22\) −2470.97 3098.50i −0.0494752 0.0620400i
\(23\) −8253.57 7658.19i −0.141447 0.131244i 0.606276 0.795254i \(-0.292663\pi\)
−0.747723 + 0.664010i \(0.768853\pi\)
\(24\) −31243.8 9637.43i −0.461343 0.142306i
\(25\) −27694.7 + 70564.9i −0.354492 + 0.903230i
\(26\) −21362.2 14564.5i −0.238364 0.162514i
\(27\) 100295. 48299.8i 0.980637 0.472250i
\(28\) 12946.1 12012.3i 0.111452 0.103412i
\(29\) −15211.5 2292.76i −0.115819 0.0174568i 0.0908772 0.995862i \(-0.471033\pi\)
−0.206696 + 0.978405i \(0.566271\pi\)
\(30\) 483.708 + 6454.63i 0.00327084 + 0.0436463i
\(31\) −102376. 260849.i −0.617207 1.57262i −0.806845 0.590763i \(-0.798827\pi\)
0.189639 0.981854i \(-0.439268\pi\)
\(32\) −33940.1 + 148701.i −0.183100 + 0.802214i
\(33\) −3136.10 + 41848.3i −0.0151912 + 0.202712i
\(34\) −98306.4 + 30323.5i −0.428949 + 0.132313i
\(35\) −6646.57 3200.82i −0.0262035 0.0126189i
\(36\) −44049.6 76296.1i −0.157356 0.272548i
\(37\) 100741. 174489.i 0.326965 0.566320i −0.654943 0.755678i \(-0.727307\pi\)
0.981908 + 0.189358i \(0.0606407\pi\)
\(38\) −102718. + 70032.0i −0.303672 + 0.207040i
\(39\) 60921.2 + 266913.i 0.164453 + 0.720516i
\(40\) 41282.9 6222.39i 0.101991 0.0153726i
\(41\) 140957. 176755.i 0.319406 0.400523i −0.596045 0.802951i \(-0.703262\pi\)
0.915452 + 0.402428i \(0.131834\pi\)
\(42\) 20581.7 0.0428657
\(43\) 209663. + 477347.i 0.402144 + 0.915576i
\(44\) 128280. 0.227026
\(45\) −22944.8 + 28771.8i −0.0375353 + 0.0470678i
\(46\) −39661.7 + 5978.04i −0.0600785 + 0.00905537i
\(47\) 55359.6 + 242546.i 0.0777769 + 0.340763i 0.998813 0.0487151i \(-0.0155126\pi\)
−0.921036 + 0.389478i \(0.872656\pi\)
\(48\) 363784. 248024.i 0.474787 0.323704i
\(49\) 400043. 692894.i 0.485758 0.841358i
\(50\) 135024. + 233868.i 0.152762 + 0.264591i
\(51\) 981486. + 472659.i 1.03607 + 0.498944i
\(52\) 799700. 246675.i 0.788706 0.243284i
\(53\) −115274. + 1.53823e6i −0.106357 + 1.41924i 0.647432 + 0.762123i \(0.275843\pi\)
−0.753789 + 0.657116i \(0.771776\pi\)
\(54\) 88243.9 386622.i 0.0762617 0.334124i
\(55\) −19576.8 49880.8i −0.0158661 0.0404263i
\(56\) −9920.59 132381.i −0.00754883 0.100732i
\(57\) 1.30173e6 + 196204.i 0.931017 + 0.140328i
\(58\) −40172.3 + 37274.4i −0.0270351 + 0.0250849i
\(59\) −1.58742e6 + 764461.i −1.00626 + 0.484589i −0.863058 0.505105i \(-0.831454\pi\)
−0.143201 + 0.989694i \(0.545740\pi\)
\(60\) −173107. 118023.i −0.103463 0.0705400i
\(61\) −573411. + 1.46103e6i −0.323453 + 0.824145i 0.672972 + 0.739668i \(0.265017\pi\)
−0.996425 + 0.0844776i \(0.973078\pi\)
\(62\) −953903. 294240.i −0.508315 0.156794i
\(63\) 85779.5 + 79591.7i 0.0432207 + 0.0401029i
\(64\) −592713. 743239.i −0.282628 0.354404i
\(65\) −217959. 273312.i −0.0984415 0.123442i
\(66\) 109590. + 101685.i 0.0469210 + 0.0435363i
\(67\) −2.80244e6 864439.i −1.13835 0.351134i −0.332410 0.943135i \(-0.607862\pi\)
−0.805937 + 0.592001i \(0.798338\pi\)
\(68\) 1.21657e6 3.09978e6i 0.469199 1.19550i
\(69\) 350922. + 239255.i 0.128600 + 0.0876777i
\(70\) −23677.7 + 11402.6i −0.00825082 + 0.00397338i
\(71\) −1.85678e6 + 1.72284e6i −0.615682 + 0.571269i −0.925132 0.379647i \(-0.876046\pi\)
0.309450 + 0.950916i \(0.399855\pi\)
\(72\) −654833. 98700.2i −0.206760 0.0311641i
\(73\) −65828.0 878413.i −0.0198053 0.264283i −0.998312 0.0580703i \(-0.981505\pi\)
0.978507 0.206213i \(-0.0661138\pi\)
\(74\) −262227. 668144.i −0.0752258 0.191672i
\(75\) 636308. 2.78785e6i 0.174162 0.763053i
\(76\) 300718. 4.01280e6i 0.0785799 1.04858i
\(77\) −162817. + 50222.5i −0.0406427 + 0.0125366i
\(78\) 878718. + 423168.i 0.209661 + 0.100968i
\(79\) 330578. + 572578.i 0.0754360 + 0.130659i 0.901276 0.433246i \(-0.142632\pi\)
−0.825840 + 0.563905i \(0.809298\pi\)
\(80\) −281097. + 486874.i −0.0613820 + 0.106317i
\(81\) −2.08899e6 + 1.42425e6i −0.436756 + 0.297775i
\(82\) −179213. 785185.i −0.0358940 0.157262i
\(83\) −4.32122e6 + 651319.i −0.829531 + 0.125032i −0.550063 0.835123i \(-0.685396\pi\)
−0.279468 + 0.960155i \(0.590158\pi\)
\(84\) −415369. + 520856.i −0.0764638 + 0.0958826i
\(85\) −1.39099e6 −0.245672
\(86\) 1.79519e6 + 476293.i 0.304345 + 0.0807475i
\(87\) 580294. 0.0944780
\(88\) 601210. 753893.i 0.0940452 0.117929i
\(89\) −2.92399e6 + 440720.i −0.439653 + 0.0662670i −0.365139 0.930953i \(-0.618979\pi\)
−0.0745139 + 0.997220i \(0.523741\pi\)
\(90\) 29172.1 + 127811.i 0.00421812 + 0.0184808i
\(91\) −918429. + 626174.i −0.127762 + 0.0871065i
\(92\) 649145. 1.12435e6i 0.0869129 0.150537i
\(93\) 5.28526e6 + 9.15435e6i 0.681360 + 1.18015i
\(94\) 798498. + 384537.i 0.0991577 + 0.0477518i
\(95\) −1.60624e6 + 495458.i −0.192210 + 0.0592891i
\(96\) 429969. 5.73753e6i 0.0496007 0.661875i
\(97\) −1.26764e6 + 5.55388e6i −0.141024 + 0.617868i 0.854174 + 0.519987i \(0.174063\pi\)
−0.995198 + 0.0978803i \(0.968794\pi\)
\(98\) −1.04130e6 2.65320e6i −0.111760 0.284759i
\(99\) 63518.3 + 847592.i 0.00657924 + 0.0877938i
\(100\) −8.64339e6 1.30278e6i −0.864339 0.130278i
\(101\) 4.57259e6 4.24274e6i 0.441608 0.409753i −0.427779 0.903883i \(-0.640704\pi\)
0.869388 + 0.494130i \(0.164513\pi\)
\(102\) 3.49644e6 1.68380e6i 0.326231 0.157105i
\(103\) 1.17204e6 + 799082.i 0.105685 + 0.0720545i 0.615009 0.788520i \(-0.289152\pi\)
−0.509325 + 0.860575i \(0.670105\pi\)
\(104\) 2.29826e6 5.85586e6i 0.200346 0.510474i
\(105\) 265920. + 82025.3i 0.0224175 + 0.00691489i
\(106\) 4.02823e6 + 3.73765e6i 0.328506 + 0.304809i
\(107\) −2.66088e6 3.33664e6i −0.209982 0.263309i 0.665676 0.746241i \(-0.268143\pi\)
−0.875658 + 0.482932i \(0.839572\pi\)
\(108\) 8.00323e6 + 1.00357e7i 0.611339 + 0.766595i
\(109\) 5.70526e6 + 5.29371e6i 0.421971 + 0.391532i 0.862377 0.506267i \(-0.168975\pi\)
−0.440406 + 0.897799i \(0.645165\pi\)
\(110\) −182410. 56266.0i −0.0130669 0.00403062i
\(111\) −2.77673e6 + 7.07500e6i −0.192710 + 0.491017i
\(112\) 1.47702e6 + 1.00701e6i 0.0993397 + 0.0677287i
\(113\) 1.78244e7 8.58377e6i 1.16209 0.559633i 0.249447 0.968389i \(-0.419751\pi\)
0.912644 + 0.408755i \(0.134037\pi\)
\(114\) 3.43775e6 3.18977e6i 0.217324 0.201647i
\(115\) −536260. 80828.3i −0.0328801 0.00495588i
\(116\) −132559. 1.76888e6i −0.00788508 0.105219i
\(117\) 2.02584e6 + 5.16175e6i 0.116938 + 0.297952i
\(118\) −1.39667e6 + 6.11923e6i −0.0782543 + 0.342855i
\(119\) −330531. + 4.41063e6i −0.0179803 + 0.239931i
\(120\) −1.50491e6 + 464203.i −0.0795016 + 0.0245230i
\(121\) 1.64423e7 + 7.91818e6i 0.843748 + 0.406328i
\(122\) 2.79563e6 + 4.84217e6i 0.139386 + 0.241424i
\(123\) −4.26409e6 + 7.38562e6i −0.206613 + 0.357865i
\(124\) 2.66973e7 1.82019e7i 1.25745 0.857318i
\(125\) 1.64984e6 + 7.22841e6i 0.0755537 + 0.331022i
\(126\) 412205. 62129.9i 0.0183576 0.00276696i
\(127\) −1.05318e6 + 1.32064e6i −0.0456234 + 0.0572100i −0.804120 0.594467i \(-0.797363\pi\)
0.758496 + 0.651677i \(0.225934\pi\)
\(128\) −2.29098e7 −0.965577
\(129\) −1.05044e7 1.66268e7i −0.430831 0.681936i
\(130\) −1.24534e6 −0.0497149
\(131\) −1.65803e7 + 2.07911e7i −0.644382 + 0.808030i −0.991543 0.129776i \(-0.958574\pi\)
0.347161 + 0.937805i \(0.387146\pi\)
\(132\) −4.78499e6 + 721221.i −0.181081 + 0.0272935i
\(133\) 1.18935e6 + 5.21090e6i 0.0438359 + 0.192058i
\(134\) −8.63218e6 + 5.88532e6i −0.309923 + 0.211302i
\(135\) 2.68095e6 4.64354e6i 0.0937821 0.162435i
\(136\) −1.25155e7 2.16774e7i −0.426639 0.738960i
\(137\) 3.89585e6 + 1.87614e6i 0.129444 + 0.0623367i 0.497485 0.867473i \(-0.334257\pi\)
−0.368041 + 0.929810i \(0.619971\pi\)
\(138\) 1.44581e6 445974.i 0.0468312 0.0144455i
\(139\) 2.83376e6 3.78139e7i 0.0894975 1.19426i −0.753907 0.656982i \(-0.771833\pi\)
0.843404 0.537280i \(-0.180548\pi\)
\(140\) 189288. 829325.i 0.00583009 0.0255433i
\(141\) −3.42862e6 8.73598e6i −0.103004 0.262449i
\(142\) 674316. + 8.99812e6i 0.0197631 + 0.263720i
\(143\) −7.98393e6 1.20338e6i −0.228318 0.0344134i
\(144\) 6.53704e6 6.06549e6i 0.182437 0.169277i
\(145\) −667584. + 321492.i −0.0181852 + 0.00875753i
\(146\) −2.59276e6 1.76772e6i −0.0689490 0.0470086i
\(147\) −1.10264e7 + 2.80948e7i −0.286301 + 0.729483i
\(148\) 2.22006e7 + 6.84799e6i 0.562924 + 0.173639i
\(149\) −4.16993e7 3.86913e7i −1.03271 0.958211i −0.0335556 0.999437i \(-0.510683\pi\)
−0.999150 + 0.0412262i \(0.986874\pi\)
\(150\) −6.35138e6 7.96438e6i −0.153656 0.192678i
\(151\) −4.75736e6 5.96554e6i −0.112447 0.141004i 0.722423 0.691452i \(-0.243028\pi\)
−0.834870 + 0.550448i \(0.814457\pi\)
\(152\) −2.21735e7 2.05740e7i −0.512132 0.475189i
\(153\) 2.10837e7 + 6.50346e6i 0.475912 + 0.146800i
\(154\) −221757. + 565028.i −0.00489277 + 0.0124666i
\(155\) −1.11519e7 7.60326e6i −0.240541 0.163998i
\(156\) −2.84428e7 + 1.36973e7i −0.599840 + 0.288868i
\(157\) −3.97423e7 + 3.68755e7i −0.819605 + 0.760482i −0.973763 0.227564i \(-0.926924\pi\)
0.154158 + 0.988046i \(0.450733\pi\)
\(158\) 2.32899e6 + 351039.i 0.0469752 + 0.00708036i
\(159\) −4.34842e6 5.80256e7i −0.0857910 1.14480i
\(160\) 2.68403e6 + 6.83880e6i 0.0518045 + 0.131996i
\(161\) −383724. + 1.68120e6i −0.00724650 + 0.0317490i
\(162\) −673083. + 8.98167e6i −0.0124384 + 0.165980i
\(163\) 4.63882e7 1.43089e7i 0.838978 0.258790i 0.154654 0.987969i \(-0.450574\pi\)
0.684324 + 0.729178i \(0.260097\pi\)
\(164\) 2.34872e7 + 1.13108e7i 0.415794 + 0.200236i
\(165\) 1.01067e6 + 1.75054e6i 0.0175153 + 0.0303374i
\(166\) −7.78388e6 + 1.34821e7i −0.132074 + 0.228759i
\(167\) −7.38087e7 + 5.03219e7i −1.22631 + 0.836084i −0.990740 0.135774i \(-0.956648\pi\)
−0.235570 + 0.971857i \(0.575696\pi\)
\(168\) 1.11432e6 + 4.88218e6i 0.0181313 + 0.0794385i
\(169\) 9.96182e6 1.50150e6i 0.158758 0.0239289i
\(170\) −3.08954e6 + 3.87416e6i −0.0482306 + 0.0604793i
\(171\) 2.66628e7 0.407775
\(172\) −4.82828e7 + 3.58180e7i −0.723508 + 0.536726i
\(173\) 1.48057e7 0.217404 0.108702 0.994074i \(-0.465331\pi\)
0.108702 + 0.994074i \(0.465331\pi\)
\(174\) 1.28890e6 1.61623e6i 0.0185480 0.0232585i
\(175\) 1.14805e7 1.73041e6i 0.161930 0.0244070i
\(176\) 2.88939e6 + 1.26592e7i 0.0399495 + 0.175030i
\(177\) 5.49144e7 3.74400e7i 0.744355 0.507493i
\(178\) −5.26703e6 + 9.12276e6i −0.0699996 + 0.121243i
\(179\) −2.28281e6 3.95394e6i −0.0297498 0.0515281i 0.850767 0.525543i \(-0.176138\pi\)
−0.880517 + 0.474015i \(0.842804\pi\)
\(180\) −3.82321e6 1.84116e6i −0.0488624 0.0235309i
\(181\) 1.34447e8 4.14713e7i 1.68529 0.519843i 0.703644 0.710552i \(-0.251555\pi\)
0.981647 + 0.190709i \(0.0610787\pi\)
\(182\) −295922. + 3.94881e6i −0.00363855 + 0.0485530i
\(183\) 1.31746e7 5.77216e7i 0.158913 0.696241i
\(184\) −3.56539e6 9.08445e6i −0.0421934 0.107507i
\(185\) −725236. 9.67761e6i −0.00842129 0.112374i
\(186\) 3.72358e7 + 5.61240e6i 0.424293 + 0.0639518i
\(187\) −2.35508e7 + 2.18520e7i −0.263366 + 0.244368i
\(188\) −2.58462e7 + 1.24469e7i −0.283690 + 0.136618i
\(189\) −1.40870e7 9.60435e6i −0.151776 0.103479i
\(190\) −2.18769e6 + 5.57415e6i −0.0231392 + 0.0589578i
\(191\) −1.47185e8 4.54007e7i −1.52844 0.471461i −0.587267 0.809393i \(-0.699796\pi\)
−0.941170 + 0.337932i \(0.890272\pi\)
\(192\) 2.62875e7 + 2.43912e7i 0.268037 + 0.248702i
\(193\) 1.78593e7 + 2.23948e7i 0.178819 + 0.224232i 0.863160 0.504930i \(-0.168482\pi\)
−0.684342 + 0.729162i \(0.739910\pi\)
\(194\) 1.26531e7 + 1.58664e7i 0.124420 + 0.156018i
\(195\) 9.66672e6 + 8.96940e6i 0.0933594 + 0.0866248i
\(196\) 8.81586e7 + 2.71933e7i 0.836312 + 0.257968i
\(197\) 2.00073e7 5.09777e7i 0.186447 0.475060i −0.806835 0.590777i \(-0.798821\pi\)
0.993282 + 0.115717i \(0.0369166\pi\)
\(198\) 2.50179e6 + 1.70569e6i 0.0229046 + 0.0156161i
\(199\) 1.10720e8 5.33200e7i 0.995957 0.479627i 0.136392 0.990655i \(-0.456449\pi\)
0.859564 + 0.511028i \(0.170735\pi\)
\(200\) −4.81652e7 + 4.46908e7i −0.425724 + 0.395014i
\(201\) 1.09394e8 + 1.64885e7i 0.950183 + 0.143217i
\(202\) −1.66060e6 2.21592e7i −0.0141754 0.189158i
\(203\) 860774. + 2.19322e6i 0.00722192 + 0.0184012i
\(204\) −2.79518e7 + 1.22465e8i −0.230518 + 1.00996i
\(205\) 813766. 1.08590e7i 0.00659722 0.0880338i
\(206\) 4.82883e6 1.48950e6i 0.0384864 0.0118715i
\(207\) 7.75040e6 + 3.73240e6i 0.0607335 + 0.0292477i
\(208\) 4.23553e7 + 7.33616e7i 0.326352 + 0.565258i
\(209\) −1.94117e7 + 3.36221e7i −0.147080 + 0.254749i
\(210\) 819095. 558450.i 0.00610333 0.00416118i
\(211\) 1.18427e7 + 5.18861e7i 0.0867882 + 0.380244i 0.999604 0.0281269i \(-0.00895424\pi\)
−0.912816 + 0.408371i \(0.866097\pi\)
\(212\) −1.75883e8 + 2.65101e7i −1.26779 + 0.191089i
\(213\) 5.95736e7 7.47029e7i 0.422401 0.529674i
\(214\) −1.52033e7 −0.106045
\(215\) 2.12960e7 + 1.33082e7i 0.146138 + 0.0913242i
\(216\) 9.64878e7 0.651455
\(217\) −2.67589e7 + 3.35546e7i −0.177770 + 0.222917i
\(218\) 2.74161e7 4.13231e6i 0.179229 0.0270144i
\(219\) 7.39409e6 + 3.23956e7i 0.0475697 + 0.208416i
\(220\) 5.10520e6 3.48066e6i 0.0323246 0.0220385i
\(221\) −1.04796e8 + 1.81512e8i −0.653088 + 1.13118i
\(222\) 1.35378e7 + 2.34482e7i 0.0830449 + 0.143838i
\(223\) 1.01338e8 + 4.88016e7i 0.611933 + 0.294691i 0.714065 0.700080i \(-0.246852\pi\)
−0.102132 + 0.994771i \(0.532566\pi\)
\(224\) 2.23227e7 6.88565e6i 0.132703 0.0409333i
\(225\) 4.32813e6 5.77549e7i 0.0253316 0.338026i
\(226\) 1.56826e7 6.87099e7i 0.0903729 0.395950i
\(227\) −9.36428e7 2.38598e8i −0.531354 1.35387i −0.904650 0.426155i \(-0.859868\pi\)
0.373296 0.927712i \(-0.378228\pi\)
\(228\) 1.13438e7 + 1.51372e8i 0.0633849 + 0.845812i
\(229\) 3.82427e7 + 5.76416e6i 0.210438 + 0.0317185i 0.253415 0.967358i \(-0.418446\pi\)
−0.0429770 + 0.999076i \(0.513684\pi\)
\(230\) −1.41622e6 + 1.31406e6i −0.00767509 + 0.00712144i
\(231\) 5.79089e6 2.78874e6i 0.0309103 0.0148856i
\(232\) −1.10168e7 7.51114e6i −0.0579226 0.0394910i
\(233\) 4.92890e7 1.25586e8i 0.255273 0.650424i −0.744581 0.667532i \(-0.767351\pi\)
0.999854 + 0.0171079i \(0.00544589\pi\)
\(234\) 1.88761e7 + 5.82251e6i 0.0963068 + 0.0297067i
\(235\) 8.78423e6 + 8.15057e6i 0.0441536 + 0.0409685i
\(236\) −1.26671e8 1.58840e8i −0.627313 0.786625i
\(237\) −1.55500e7 1.94991e7i −0.0758774 0.0951473i
\(238\) 1.15503e7 + 1.07171e7i 0.0555360 + 0.0515299i
\(239\) −1.72463e7 5.31977e6i −0.0817152 0.0252058i 0.253628 0.967302i \(-0.418376\pi\)
−0.335343 + 0.942096i \(0.608852\pi\)
\(240\) 7.74788e6 1.97413e7i 0.0361779 0.0921799i
\(241\) −2.42960e8 1.65647e8i −1.11809 0.762298i −0.144247 0.989542i \(-0.546076\pi\)
−0.973838 + 0.227244i \(0.927028\pi\)
\(242\) 5.85739e7 2.82077e7i 0.265675 0.127942i
\(243\) −1.08552e8 + 1.00721e8i −0.485305 + 0.450298i
\(244\) −1.78959e8 2.69738e7i −0.788660 0.118871i
\(245\) −2.87991e6 3.84297e7i −0.0125112 0.166950i
\(246\) 1.10993e7 + 2.82806e7i 0.0475361 + 0.121120i
\(247\) −5.63597e7 + 2.46928e8i −0.237974 + 1.04263i
\(248\) 1.81508e7 2.42205e8i 0.0755638 1.00833i
\(249\) 1.57524e8 4.85897e7i 0.646620 0.199456i
\(250\) 2.37970e7 + 1.14600e7i 0.0963235 + 0.0463869i
\(251\) −2.27800e8 3.94561e8i −0.909275 1.57491i −0.815073 0.579358i \(-0.803303\pi\)
−0.0942021 0.995553i \(-0.530030\pi\)
\(252\) −6.74657e6 + 1.16854e7i −0.0265571 + 0.0459983i
\(253\) −1.03492e7 + 7.05599e6i −0.0401778 + 0.0273928i
\(254\) 1.33901e6 + 5.86660e6i 0.00512704 + 0.0224630i
\(255\) 5.18852e7 7.82043e6i 0.195953 0.0295352i
\(256\) 2.49819e7 3.13263e7i 0.0930648 0.116700i
\(257\) −5.33180e8 −1.95933 −0.979666 0.200635i \(-0.935699\pi\)
−0.979666 + 0.200635i \(0.935699\pi\)
\(258\) −6.96402e7 7.67324e6i −0.252459 0.0278170i
\(259\) −3.08588e7 −0.110364
\(260\) 2.51327e7 3.15154e7i 0.0886814 0.111203i
\(261\) 1.16219e7 1.75173e6i 0.0404610 0.00609852i
\(262\) 2.10803e7 + 9.23588e7i 0.0724140 + 0.317266i
\(263\) −3.78403e8 + 2.57991e8i −1.28265 + 0.874499i −0.996492 0.0836823i \(-0.973332\pi\)
−0.286162 + 0.958181i \(0.592380\pi\)
\(264\) −1.81872e7 + 3.15011e7i −0.0608347 + 0.105369i
\(265\) 3.71496e7 + 6.43450e7i 0.122629 + 0.212400i
\(266\) 1.71551e7 + 8.26144e6i 0.0558864 + 0.0269135i
\(267\) 1.06590e8 3.28786e7i 0.342710 0.105712i
\(268\) 2.52716e7 3.37226e8i 0.0801975 1.07016i
\(269\) −1.55129e7 + 6.79663e7i −0.0485914 + 0.212893i −0.993395 0.114744i \(-0.963395\pi\)
0.944804 + 0.327637i \(0.106252\pi\)
\(270\) −6.97845e6 1.77808e7i −0.0215767 0.0549766i
\(271\) 1.26320e7 + 1.68562e8i 0.0385548 + 0.514478i 0.982731 + 0.185038i \(0.0592408\pi\)
−0.944177 + 0.329440i \(0.893140\pi\)
\(272\) 3.33301e8 + 5.02371e7i 1.00426 + 0.151368i
\(273\) 3.07378e7 2.85206e7i 0.0914332 0.0848377i
\(274\) 1.38786e7 6.68357e6i 0.0407585 0.0196282i
\(275\) 6.96785e7 + 4.75060e7i 0.202039 + 0.137748i
\(276\) −1.78924e7 + 4.55891e7i −0.0512256 + 0.130521i
\(277\) 1.96055e8 + 6.04749e7i 0.554241 + 0.170961i 0.559209 0.829027i \(-0.311105\pi\)
−0.00496779 + 0.999988i \(0.501581\pi\)
\(278\) −9.90249e7 9.18817e7i −0.276431 0.256491i
\(279\) 1.33486e8 + 1.67386e8i 0.367977 + 0.461428i
\(280\) −3.98674e6 4.99922e6i −0.0108534 0.0136097i
\(281\) 4.29249e8 + 3.98285e8i 1.15408 + 1.07083i 0.996523 + 0.0833231i \(0.0265533\pi\)
0.157560 + 0.987509i \(0.449637\pi\)
\(282\) −3.19468e7 9.85427e6i −0.0848310 0.0261669i
\(283\) 9.44548e7 2.40667e8i 0.247726 0.631195i −0.751879 0.659301i \(-0.770852\pi\)
0.999605 + 0.0281058i \(0.00894755\pi\)
\(284\) −2.41321e8 1.64530e8i −0.625146 0.426217i
\(285\) 5.71287e7 2.75117e7i 0.146183 0.0703981i
\(286\) −2.10849e7 + 1.95639e7i −0.0532955 + 0.0494510i
\(287\) −3.42390e7 5.16069e6i −0.0854937 0.0128861i
\(288\) −8.70854e6 1.16207e8i −0.0214819 0.286655i
\(289\) 1.54771e8 + 3.94349e8i 0.377178 + 0.961033i
\(290\) −587367. + 2.57342e6i −0.00141422 + 0.00619609i
\(291\) 1.60590e7 2.14292e8i 0.0382026 0.509778i
\(292\) 9.70607e7 2.99393e7i 0.228141 0.0703722i
\(293\) 7.34364e8 + 3.53651e8i 1.70559 + 0.821370i 0.992771 + 0.120023i \(0.0382968\pi\)
0.712820 + 0.701347i \(0.247418\pi\)
\(294\) 5.37585e7 + 9.31125e7i 0.123376 + 0.213694i
\(295\) −4.24325e7 + 7.34953e7i −0.0962325 + 0.166680i
\(296\) 1.44293e8 9.83770e7i 0.323387 0.220482i
\(297\) −2.75574e7 1.20737e8i −0.0610366 0.267419i
\(298\) −2.00382e8 + 3.02027e7i −0.438633 + 0.0661133i
\(299\) −5.09489e7 + 6.38880e7i −0.110227 + 0.138220i
\(300\) 3.29732e8 0.705077
\(301\) 4.72591e7 6.43644e7i 0.0998855 0.136039i
\(302\) −2.71819e7 −0.0567878
\(303\) −1.46709e8 + 1.83967e8i −0.302975 + 0.379918i
\(304\) 4.02773e8 6.07082e7i 0.822248 0.123934i
\(305\) 1.68223e7 + 7.37033e7i 0.0339497 + 0.148743i
\(306\) 6.49428e7 4.42773e7i 0.129570 0.0883396i
\(307\) −3.39774e8 + 5.88506e8i −0.670202 + 1.16082i 0.307644 + 0.951502i \(0.400459\pi\)
−0.977847 + 0.209323i \(0.932874\pi\)
\(308\) −9.82361e6 1.70150e7i −0.0191577 0.0331821i
\(309\) −4.82108e7 2.32171e7i −0.0929587 0.0447665i
\(310\) −4.59463e7 + 1.41726e7i −0.0875961 + 0.0270198i
\(311\) 1.72402e7 2.30055e8i 0.0324999 0.433680i −0.957093 0.289782i \(-0.906417\pi\)
0.989592 0.143898i \(-0.0459638\pi\)
\(312\) −5.28043e7 + 2.31351e8i −0.0984302 + 0.431251i
\(313\) −2.88752e8 7.35727e8i −0.532254 1.35616i −0.903883 0.427780i \(-0.859296\pi\)
0.371629 0.928382i \(-0.378800\pi\)
\(314\) 1.44330e7 + 1.92595e8i 0.0263089 + 0.351068i
\(315\) 5.57336e6 + 840049.i 0.0100469 + 0.00151432i
\(316\) −5.58860e7 + 5.18546e7i −0.0996318 + 0.0924448i
\(317\) −2.00742e8 + 9.66721e7i −0.353940 + 0.170449i −0.602402 0.798193i \(-0.705789\pi\)
0.248461 + 0.968642i \(0.420075\pi\)
\(318\) −1.71271e8 1.16771e8i −0.298668 0.203628i
\(319\) −6.25235e6 + 1.59307e7i −0.0107839 + 0.0274769i
\(320\) −4.37548e7 1.34966e7i −0.0746451 0.0230250i
\(321\) 1.18013e8 + 1.09500e8i 0.199142 + 0.184777i
\(322\) 3.83018e6 + 4.80290e6i 0.00639329 + 0.00801693i
\(323\) 6.28354e8 + 7.87930e8i 1.03752 + 1.30101i
\(324\) −2.13713e8 1.98296e8i −0.349078 0.323897i
\(325\) 5.25727e8 + 1.62165e8i 0.849510 + 0.262039i
\(326\) 6.31807e7 1.60982e8i 0.101000 0.257345i
\(327\) −2.42575e8 1.65385e8i −0.383644 0.261564i
\(328\) 1.76550e8 8.50221e7i 0.276255 0.133037i
\(329\) 2.79317e7 2.59169e7i 0.0432426 0.0401233i
\(330\) 7.12042e6 + 1.07323e6i 0.0109070 + 0.00164397i
\(331\) −8.50264e7 1.13460e9i −0.128871 1.71967i −0.569512 0.821983i \(-0.692868\pi\)
0.440641 0.897684i \(-0.354751\pi\)
\(332\) −1.84097e8 4.69072e8i −0.276098 0.703487i
\(333\) −3.42543e7 + 1.50078e8i −0.0508348 + 0.222722i
\(334\) −2.37815e7 + 3.17343e8i −0.0349243 + 0.466032i
\(335\) −1.34984e8 + 4.16372e7i −0.196167 + 0.0605096i
\(336\) −6.07559e7 2.92585e7i −0.0873778 0.0420789i
\(337\) 2.66128e8 + 4.60948e8i 0.378780 + 0.656066i 0.990885 0.134711i \(-0.0430105\pi\)
−0.612105 + 0.790776i \(0.709677\pi\)
\(338\) 1.79444e7 3.10806e7i 0.0252767 0.0437805i
\(339\) −6.16608e8 + 4.20396e8i −0.859627 + 0.586084i
\(340\) −3.56909e7 1.56372e8i −0.0492472 0.215766i
\(341\) −3.08259e8 + 4.64626e7i −0.420993 + 0.0634545i
\(342\) 5.92213e7 7.42612e7i 0.0800547 0.100385i
\(343\) −2.48673e8 −0.332735
\(344\) −1.57868e7 + 4.51622e8i −0.0209093 + 0.598165i
\(345\) 2.04575e7 0.0268217
\(346\) 3.28852e7 4.12367e7i 0.0426809 0.0535202i
\(347\) 9.36838e7 1.41206e7i 0.120368 0.0181426i −0.0885819 0.996069i \(-0.528234\pi\)
0.208950 + 0.977926i \(0.432995\pi\)
\(348\) 1.48896e7 + 6.52356e7i 0.0189390 + 0.0829770i
\(349\) 7.92195e8 5.40109e8i 0.997569 0.680131i 0.0496912 0.998765i \(-0.484176\pi\)
0.947878 + 0.318633i \(0.103224\pi\)
\(350\) 2.06800e7 3.58189e7i 0.0257818 0.0446554i
\(351\) −4.03962e8 6.99683e8i −0.498615 0.863627i
\(352\) 1.52879e8 + 7.36227e7i 0.186831 + 0.0899730i
\(353\) 7.57114e8 2.33539e8i 0.916115 0.282584i 0.199374 0.979923i \(-0.436109\pi\)
0.716741 + 0.697339i \(0.245633\pi\)
\(354\) 1.76937e7 2.36106e8i 0.0211986 0.282876i
\(355\) −2.71483e7 + 1.18945e8i −0.0322065 + 0.141106i
\(356\) −1.24571e8 3.17401e8i −0.146333 0.372849i
\(357\) −1.24684e7 1.66379e8i −0.0145035 0.193536i
\(358\) −1.60829e7 2.42410e6i −0.0185256 0.00279229i
\(359\) −8.10093e8 + 7.51656e8i −0.924069 + 0.857410i −0.990094 0.140408i \(-0.955159\pi\)
0.0660251 + 0.997818i \(0.478968\pi\)
\(360\) −2.87386e7 + 1.38398e7i −0.0324643 + 0.0156340i
\(361\) 2.67693e8 + 1.82510e8i 0.299476 + 0.204179i
\(362\) 1.83116e8 4.66573e8i 0.202884 0.516939i
\(363\) −6.57831e8 2.02914e8i −0.721840 0.222658i
\(364\) −9.39592e7 8.71814e7i −0.102114 0.0947477i
\(365\) −2.64540e7 3.31723e7i −0.0284752 0.0357067i
\(366\) −1.31504e8 1.64900e8i −0.140202 0.175808i
\(367\) −2.07797e8 1.92807e8i −0.219436 0.203607i 0.562793 0.826598i \(-0.309727\pi\)
−0.782229 + 0.622991i \(0.785917\pi\)
\(368\) 1.25577e8 + 3.87354e7i 0.131354 + 0.0405173i
\(369\) −6.31049e7 + 1.60789e8i −0.0653839 + 0.166596i
\(370\) −2.85649e7 1.94752e7i −0.0293174 0.0199883i
\(371\) 2.12857e8 1.02507e8i 0.216411 0.104218i
\(372\) −8.93503e8 + 8.29049e8i −0.899903 + 0.834988i
\(373\) −1.20044e9 1.80938e8i −1.19774 0.180530i −0.480269 0.877121i \(-0.659461\pi\)
−0.717468 + 0.696592i \(0.754699\pi\)
\(374\) 8.55282e6 + 1.14129e8i 0.00845393 + 0.112810i
\(375\) −1.02180e8 2.60351e8i −0.100059 0.254947i
\(376\) −4.79837e7 + 2.10230e8i −0.0465518 + 0.203957i
\(377\) −8.34341e6 + 1.11335e8i −0.00801953 + 0.107013i
\(378\) −5.80388e7 + 1.79026e7i −0.0552710 + 0.0170488i
\(379\) −1.23622e9 5.95333e8i −1.16643 0.561723i −0.252501 0.967597i \(-0.581253\pi\)
−0.913929 + 0.405873i \(0.866967\pi\)
\(380\) −9.69126e7 1.67858e8i −0.0906020 0.156927i
\(381\) 3.18596e7 5.51824e7i 0.0295123 0.0511168i
\(382\) −4.53366e8 + 3.09099e8i −0.416128 + 0.283711i
\(383\) 2.84533e8 + 1.24662e9i 0.258784 + 1.13381i 0.922553 + 0.385869i \(0.126099\pi\)
−0.663769 + 0.747937i \(0.731044\pi\)
\(384\) 8.54560e8 1.28804e8i 0.770164 0.116084i
\(385\) −5.11697e6 + 6.41648e6i −0.00456983 + 0.00573039i
\(386\) 1.02041e8 0.0903069
\(387\) −2.60570e8 3.01286e8i −0.228526 0.264235i
\(388\) −6.56884e8 −0.570923
\(389\) −7.04350e8 + 8.83227e8i −0.606688 + 0.760762i −0.986404 0.164341i \(-0.947450\pi\)
0.379716 + 0.925103i \(0.376022\pi\)
\(390\) 4.64525e7 7.00158e6i 0.0396536 0.00597682i
\(391\) 7.23525e7 + 3.16997e8i 0.0612118 + 0.268186i
\(392\) 5.72985e8 3.90654e8i 0.480443 0.327560i
\(393\) 5.01571e8 8.68746e8i 0.416830 0.721970i
\(394\) −9.75443e7 1.68952e8i −0.0803461 0.139164i
\(395\) 2.86920e7 + 1.38173e7i 0.0234245 + 0.0112806i
\(396\) −9.36551e7 + 2.88888e7i −0.0757876 + 0.0233774i
\(397\) 9.36157e7 1.24921e9i 0.0750900 1.00201i −0.824668 0.565617i \(-0.808638\pi\)
0.899758 0.436389i \(-0.143743\pi\)
\(398\) 9.74158e7 4.26807e8i 0.0774531 0.339344i
\(399\) −7.36609e7 1.87685e8i −0.0580540 0.147919i
\(400\) −6.61199e7 8.82309e8i −0.0516562 0.689304i
\(401\) 2.07718e9 + 3.13084e8i 1.60868 + 0.242469i 0.891031 0.453942i \(-0.149983\pi\)
0.717644 + 0.696410i \(0.245221\pi\)
\(402\) 2.88901e8 2.68061e8i 0.221798 0.205798i
\(403\) −1.83234e9 + 8.82410e8i −1.39457 + 0.671588i
\(404\) 5.94289e8 + 4.05179e8i 0.448397 + 0.305712i
\(405\) −4.44914e7 + 1.13362e8i −0.0332800 + 0.0847961i
\(406\) 8.02041e6 + 2.47397e6i 0.00594779 + 0.00183465i
\(407\) −1.64311e8 1.52459e8i −0.120806 0.112091i
\(408\) 5.88715e8 + 7.38225e8i 0.429135 + 0.538119i
\(409\) 3.94593e8 + 4.94804e8i 0.285179 + 0.357604i 0.903701 0.428164i \(-0.140840\pi\)
−0.618522 + 0.785768i \(0.712268\pi\)
\(410\) −2.84368e7 2.63855e7i −0.0203769 0.0189070i
\(411\) −1.55867e8 4.80787e7i −0.110741 0.0341591i
\(412\) −5.97584e7 + 1.52262e8i −0.0420977 + 0.107263i
\(413\) 2.22961e8 + 1.52012e8i 0.155741 + 0.106183i
\(414\) 2.76100e7 1.32963e7i 0.0191234 0.00920935i
\(415\) −1.54300e8 + 1.43169e8i −0.105974 + 0.0983290i
\(416\) 1.09462e9 + 1.64987e8i 0.745481 + 0.112363i
\(417\) 1.06896e8 + 1.42643e9i 0.0721914 + 0.963327i
\(418\) 5.05284e7 + 1.28744e8i 0.0338391 + 0.0862205i
\(419\) 2.94436e8 1.29001e9i 0.195543 0.856730i −0.778007 0.628256i \(-0.783769\pi\)
0.973550 0.228474i \(-0.0733737\pi\)
\(420\) −2.39799e6 + 3.19989e7i −0.00157933 + 0.0210748i
\(421\) 2.27327e9 7.01211e8i 1.48478 0.457995i 0.556810 0.830640i \(-0.312025\pi\)
0.927974 + 0.372644i \(0.121549\pi\)
\(422\) 1.70817e8 + 8.22610e7i 0.110646 + 0.0532844i
\(423\) −9.50385e7 1.64611e8i −0.0610532 0.105747i
\(424\) −6.68511e8 + 1.15789e9i −0.425920 + 0.737715i
\(425\) 1.80875e9 1.23319e9i 1.14292 0.779233i
\(426\) −7.57421e7 3.31848e8i −0.0474683 0.207972i
\(427\) 2.37701e8 3.58276e7i 0.147752 0.0222700i
\(428\) 3.06825e8 3.84746e8i 0.189163 0.237203i
\(429\) 3.04574e8 0.186248
\(430\) 8.43669e7 2.97542e7i 0.0511720 0.0180472i
\(431\) −4.07943e8 −0.245431 −0.122715 0.992442i \(-0.539160\pi\)
−0.122715 + 0.992442i \(0.539160\pi\)
\(432\) −8.10103e8 + 1.01584e9i −0.483445 + 0.606221i
\(433\) 2.09620e9 3.15951e8i 1.24087 0.187030i 0.504379 0.863482i \(-0.331721\pi\)
0.736487 + 0.676452i \(0.236483\pi\)
\(434\) 3.40214e7 + 1.49058e8i 0.0199774 + 0.0875266i
\(435\) 2.30941e7 1.57453e7i 0.0134520 0.00917144i
\(436\) −4.48720e8 + 7.77206e8i −0.259282 + 0.449090i
\(437\) 1.96461e8 + 3.40280e8i 0.112614 + 0.195053i
\(438\) 1.06651e8 + 5.13605e7i 0.0606466 + 0.0292059i
\(439\) −1.20616e9 + 3.72051e8i −0.680423 + 0.209883i −0.615653 0.788017i \(-0.711108\pi\)
−0.0647702 + 0.997900i \(0.520631\pi\)
\(440\) 3.47088e6 4.63156e7i 0.00194247 0.0259205i
\(441\) −1.36024e8 + 5.95959e8i −0.0755231 + 0.330888i
\(442\) 2.72782e8 + 6.95037e8i 0.150258 + 0.382851i
\(443\) −1.25819e7 1.67894e8i −0.00687596 0.0917533i 0.992710 0.120528i \(-0.0384586\pi\)
−0.999586 + 0.0287743i \(0.990840\pi\)
\(444\) −8.66607e8 1.30620e8i −0.469875 0.0708222i
\(445\) −1.04408e8 + 9.68767e7i −0.0561661 + 0.0521146i
\(446\) 3.61005e8 1.73851e8i 0.192682 0.0927907i
\(447\) 1.77296e9 + 1.20878e9i 0.938905 + 0.640135i
\(448\) −5.31931e7 + 1.35534e8i −0.0279500 + 0.0712155i
\(449\) −4.21163e8 1.29911e8i −0.219577 0.0677307i 0.183015 0.983110i \(-0.441414\pi\)
−0.402592 + 0.915380i \(0.631891\pi\)
\(450\) −1.51245e8 1.40335e8i −0.0782417 0.0725977i
\(451\) −1.56813e8 1.96637e8i −0.0804942 0.100937i
\(452\) 1.42232e9 + 1.78354e9i 0.724459 + 0.908443i
\(453\) 2.10994e8 + 1.95774e8i 0.106642 + 0.0989489i
\(454\) −8.72533e8 2.69141e8i −0.437609 0.134985i
\(455\) −1.95607e7 + 4.98400e7i −0.00973521 + 0.0248049i
\(456\) 9.42767e8 + 6.42768e8i 0.465615 + 0.317451i
\(457\) −1.13187e9 + 5.45080e8i −0.554741 + 0.267149i −0.690181 0.723636i \(-0.742469\pi\)
0.135441 + 0.990785i \(0.456755\pi\)
\(458\) 1.00996e8 9.37105e7i 0.0491218 0.0455784i
\(459\) −3.17884e9 4.79134e8i −1.53435 0.231266i
\(460\) −4.67319e6 6.23594e7i −0.00223852 0.0298710i
\(461\) −2.10795e8 5.37097e8i −0.100209 0.255329i 0.871973 0.489553i \(-0.162840\pi\)
−0.972183 + 0.234225i \(0.924745\pi\)
\(462\) 5.09505e6 2.23229e7i 0.00240382 0.0105318i
\(463\) 2.62481e7 3.50257e8i 0.0122904 0.164004i −0.987681 0.156479i \(-0.949986\pi\)
0.999972 0.00752483i \(-0.00239525\pi\)
\(464\) 1.71574e8 5.29237e7i 0.0797332 0.0245944i
\(465\) 4.58726e8 + 2.20911e8i 0.211577 + 0.101890i
\(466\) −2.40306e8 4.16222e8i −0.110005 0.190535i
\(467\) 7.29689e8 1.26386e9i 0.331535 0.574235i −0.651278 0.758839i \(-0.725767\pi\)
0.982813 + 0.184604i \(0.0591003\pi\)
\(468\) −5.28295e8 + 3.60185e8i −0.238241 + 0.162430i
\(469\) 9.99505e7 + 4.37912e8i 0.0447383 + 0.196011i
\(470\) 4.22117e7 6.36239e6i 0.0187539 0.00282669i
\(471\) 1.27511e9 1.59893e9i 0.562307 0.705111i
\(472\) −1.52716e9 −0.668477
\(473\) 5.69631e8 1.09231e8i 0.247503 0.0474606i
\(474\) −8.88474e7 −0.0383196
\(475\) 1.64940e9 2.06828e9i 0.706152 0.885487i
\(476\) −5.04317e8 + 7.60135e7i −0.214328 + 0.0323048i
\(477\) −2.62250e8 1.14899e9i −0.110637 0.484733i
\(478\) −5.31226e7 + 3.62184e7i −0.0222475 + 0.0151681i
\(479\) 4.56155e8 7.90084e8i 0.189644 0.328472i −0.755488 0.655163i \(-0.772600\pi\)
0.945131 + 0.326690i \(0.105933\pi\)
\(480\) −1.38566e8 2.40004e8i −0.0571892 0.0990545i
\(481\) −1.31749e9 6.34468e8i −0.539807 0.259957i
\(482\) −1.00100e9 + 3.08768e8i −0.407165 + 0.125594i
\(483\) 4.86119e6 6.48680e7i 0.00196303 0.0261948i
\(484\) −4.68260e8 + 2.05158e9i −0.187728 + 0.822489i
\(485\) 1.00247e8 + 2.55424e8i 0.0399000 + 0.101664i
\(486\) 3.94221e7 + 5.26052e8i 0.0155781 + 0.207875i
\(487\) −2.44364e9 3.68319e8i −0.958706 0.144502i −0.348994 0.937125i \(-0.613477\pi\)
−0.609712 + 0.792623i \(0.708715\pi\)
\(488\) −9.97248e8 + 9.25311e8i −0.388449 + 0.360428i
\(489\) −1.64988e9 + 7.94539e8i −0.638074 + 0.307280i
\(490\) −1.13431e8 7.73358e7i −0.0435557 0.0296958i
\(491\) 1.55904e9 3.97237e9i 0.594391 1.51448i −0.244201 0.969725i \(-0.578526\pi\)
0.838593 0.544759i \(-0.183379\pi\)
\(492\) −9.39689e8 2.89856e8i −0.355718 0.109725i
\(493\) 3.25657e8 + 3.02165e8i 0.122404 + 0.113574i
\(494\) 5.62561e8 + 7.05429e8i 0.209955 + 0.263275i
\(495\) 2.55258e7 + 3.20083e7i 0.00945934 + 0.0118616i
\(496\) 2.39757e9 + 2.22462e9i 0.882239 + 0.818598i
\(497\) 3.70707e8 + 1.14348e8i 0.135451 + 0.0417812i
\(498\) 2.14548e8 5.46658e8i 0.0778432 0.198341i
\(499\) −1.80635e9 1.23155e9i −0.650803 0.443710i 0.192392 0.981318i \(-0.438376\pi\)
−0.843195 + 0.537608i \(0.819328\pi\)
\(500\) −7.70272e8 + 3.70944e8i −0.275581 + 0.132713i
\(501\) 2.47022e9 2.29203e9i 0.877614 0.814307i
\(502\) −1.60490e9 2.41900e8i −0.566219 0.0853438i
\(503\) 1.76007e8 + 2.34865e9i 0.0616655 + 0.822869i 0.939203 + 0.343361i \(0.111566\pi\)
−0.877538 + 0.479507i \(0.840815\pi\)
\(504\) 3.70551e7 + 9.44149e7i 0.0128926 + 0.0328499i
\(505\) 6.68567e7 2.92918e8i 0.0231007 0.101211i
\(506\) −3.33457e6 + 4.44968e7i −0.00114423 + 0.0152687i
\(507\) −3.63144e8 + 1.12015e8i −0.123752 + 0.0381723i
\(508\) −1.75487e8 8.45103e7i −0.0593913 0.0286013i
\(509\) 4.64237e8 + 8.04082e8i 0.156037 + 0.270264i 0.933436 0.358744i \(-0.116795\pi\)
−0.777399 + 0.629008i \(0.783461\pi\)
\(510\) 9.34617e7 1.61880e8i 0.0311988 0.0540379i
\(511\) −1.11471e8 + 7.59996e7i −0.0369563 + 0.0251964i
\(512\) −6.84295e8 2.99809e9i −0.225319 0.987189i
\(513\) −3.84143e9 + 5.79002e8i −1.25627 + 0.189352i
\(514\) −1.18426e9 + 1.48501e9i −0.384658 + 0.482346i
\(515\) 6.83255e7 0.0220423
\(516\) 1.59962e9 1.60751e9i 0.512559 0.515085i
\(517\) 2.76769e8 0.0880847
\(518\) −6.85409e7 + 8.59476e7i −0.0216669 + 0.0271694i
\(519\) −5.52267e8 + 8.32409e7i −0.173406 + 0.0261367i
\(520\) −6.74245e7 2.95406e8i −0.0210284 0.0921314i
\(521\) 1.95765e9 1.33470e9i 0.606461 0.413478i −0.220781 0.975323i \(-0.570861\pi\)
0.827242 + 0.561845i \(0.189908\pi\)
\(522\) 2.09348e7 3.62602e7i 0.00644202 0.0111579i
\(523\) 1.00270e9 + 1.73673e9i 0.306490 + 0.530856i 0.977592 0.210509i \(-0.0675121\pi\)
−0.671102 + 0.741365i \(0.734179\pi\)
\(524\) −2.76273e9 1.33046e9i −0.838839 0.403963i
\(525\) −4.18506e8 + 1.29092e8i −0.126225 + 0.0389351i
\(526\) −1.21923e8 + 1.62695e9i −0.0365289 + 0.487445i
\(527\) −1.80071e9 + 7.88944e9i −0.535929 + 2.34806i
\(528\) −1.78950e8 4.55957e8i −0.0529070 0.134805i
\(529\) −2.44969e8 3.26889e9i −0.0719477 0.960076i
\(530\) 2.61727e8 + 3.94490e7i 0.0763630 + 0.0115099i
\(531\) 9.86789e8 9.15607e8i 0.286018 0.265386i
\(532\) −5.55283e8 + 2.67410e8i −0.159891 + 0.0769994i
\(533\) −1.35569e9 9.24297e8i −0.387808 0.264403i
\(534\) 1.45175e8 3.69900e8i 0.0412570 0.105121i
\(535\) −1.96430e8 6.05905e7i −0.0554586 0.0171067i
\(536\) −1.86341e9 1.72899e9i −0.522675 0.484972i
\(537\) 1.07381e8 + 1.34652e8i 0.0299239 + 0.0375233i
\(538\) 1.54844e8 + 1.94168e8i 0.0428702 + 0.0537575i
\(539\) −6.52479e8 6.05412e8i −0.179476 0.166529i
\(540\) 5.90808e8 + 1.82240e8i 0.161461 + 0.0498042i
\(541\) 5.59672e8 1.42602e9i 0.151965 0.387200i −0.834537 0.550952i \(-0.814265\pi\)
0.986501 + 0.163752i \(0.0523598\pi\)
\(542\) 4.97534e8 + 3.39213e8i 0.134223 + 0.0915114i
\(543\) −4.78183e9 + 2.30281e9i −1.28173 + 0.617247i
\(544\) 3.22889e9 2.99597e9i 0.859918 0.797887i
\(545\) 3.70689e8 + 5.58724e7i 0.0980894 + 0.0147846i
\(546\) −1.11629e7 1.48958e8i −0.00293496 0.0391643i
\(547\) −1.64422e9 4.18941e9i −0.429541 1.09445i −0.967811 0.251679i \(-0.919017\pi\)
0.538270 0.842773i \(-0.319078\pi\)
\(548\) −1.10950e8 + 4.86104e8i −0.0288002 + 0.126182i
\(549\) 8.96129e7 1.19580e9i 0.0231136 0.308429i
\(550\) 2.87078e8 8.85517e7i 0.0735749 0.0226949i
\(551\) 4.83680e8 + 2.32928e8i 0.123176 + 0.0593186i
\(552\) 1.84067e8 + 3.18814e8i 0.0465790 + 0.0806771i
\(553\) 5.06308e7 8.76951e7i 0.0127314 0.0220515i
\(554\) 6.03895e8 4.11729e8i 0.150896 0.102879i
\(555\) 8.14617e7 + 3.56907e8i 0.0202268 + 0.0886196i
\(556\) 4.32368e9 6.51690e8i 1.06682 0.160798i
\(557\) 6.89273e7 8.64320e7i 0.0169004 0.0211925i −0.773309 0.634029i \(-0.781400\pi\)
0.790210 + 0.612836i \(0.209971\pi\)
\(558\) 7.62689e8 0.185835
\(559\) 3.34104e9 1.77631e9i 0.808984 0.430108i
\(560\) 8.61047e7 0.0207190
\(561\) 7.55613e8 9.47509e8i 0.180688 0.226576i
\(562\) 2.06271e9 3.10904e8i 0.490187 0.0738838i
\(563\) 1.23535e9 + 5.41241e9i 0.291749 + 1.27824i 0.882090 + 0.471082i \(0.156136\pi\)
−0.590341 + 0.807154i \(0.701007\pi\)
\(564\) 8.94109e8 6.09593e8i 0.209852 0.143075i
\(565\) 4.76455e8 8.25244e8i 0.111135 0.192492i
\(566\) −4.60509e8 7.97624e8i −0.106753 0.184902i
\(567\) 3.48885e8 + 1.68014e8i 0.0803787 + 0.0387083i
\(568\) −2.09793e9 + 6.47125e8i −0.480365 + 0.148173i
\(569\) −2.29684e8 + 3.06493e9i −0.0522683 + 0.697473i 0.908103 + 0.418748i \(0.137531\pi\)
−0.960371 + 0.278725i \(0.910088\pi\)
\(570\) 5.02641e7 2.20221e8i 0.0113683 0.0498078i
\(571\) 1.31510e9 + 3.35082e9i 0.295619 + 0.753225i 0.999096 + 0.0425071i \(0.0135345\pi\)
−0.703477 + 0.710718i \(0.748370\pi\)
\(572\) −6.95752e7 9.28417e8i −0.0155442 0.207423i
\(573\) 5.74541e9 + 8.65982e8i 1.27579 + 0.192295i
\(574\) −9.04223e7 + 8.38996e7i −0.0199565 + 0.0185169i
\(575\) 7.68979e8 3.70321e8i 0.168685 0.0812345i
\(576\) 6.00107e8 + 4.09146e8i 0.130843 + 0.0892071i
\(577\) −2.40566e9 + 6.12952e9i −0.521338 + 1.32835i 0.391558 + 0.920154i \(0.371936\pi\)
−0.912896 + 0.408193i \(0.866159\pi\)
\(578\) 1.44210e9 + 4.44830e8i 0.310634 + 0.0958178i
\(579\) −7.92078e8 7.34941e8i −0.169587 0.157354i
\(580\) −5.32709e7 6.67996e7i −0.0113368 0.0142159i
\(581\) 4.17306e8 + 5.23285e8i 0.0882751 + 0.110693i
\(582\) −5.61177e8 5.20696e8i −0.117997 0.109485i
\(583\) 1.63982e9 + 5.05818e8i 0.342734 + 0.105719i
\(584\) 2.78942e8 7.10734e8i 0.0579522 0.147660i
\(585\) 2.20678e8 + 1.50456e8i 0.0455736 + 0.0310715i
\(586\) 2.61610e9 1.25985e9i 0.537047 0.258628i
\(587\) −3.83789e9 + 3.56105e9i −0.783177 + 0.726682i −0.966583 0.256356i \(-0.917478\pi\)
0.183406 + 0.983037i \(0.441288\pi\)
\(588\) −3.44129e9 5.18691e8i −0.698073 0.105218i
\(589\) 7.30790e8 + 9.75171e9i 0.147363 + 1.96643i
\(590\) 1.10451e8 + 2.81425e8i 0.0221405 + 0.0564131i
\(591\) −4.59684e8 + 2.01401e9i −0.0916015 + 0.401333i
\(592\) −1.75741e8 + 2.34509e9i −0.0348134 + 0.464552i
\(593\) −4.01872e8 + 1.23961e8i −0.0791400 + 0.0244115i −0.334072 0.942547i \(-0.608423\pi\)
0.254932 + 0.966959i \(0.417947\pi\)
\(594\) −3.97484e8 1.91418e8i −0.0778156 0.0374740i
\(595\) 1.06521e8 + 1.84499e8i 0.0207312 + 0.0359075i
\(596\) 3.27965e9 5.68053e9i 0.634551 1.09907i
\(597\) −3.83019e9 + 2.61138e9i −0.736734 + 0.502296i
\(598\) 6.47767e7 + 2.83805e8i 0.0123870 + 0.0542708i
\(599\) 9.64563e9 1.45384e9i 1.83374 0.276391i 0.861050 0.508520i \(-0.169807\pi\)
0.972685 + 0.232129i \(0.0745690\pi\)
\(600\) 1.54535e9 1.93781e9i 0.292077 0.366253i
\(601\) −2.70574e9 −0.508424 −0.254212 0.967149i \(-0.581816\pi\)
−0.254212 + 0.967149i \(0.581816\pi\)
\(602\) −7.42992e7 2.74587e8i −0.0138802 0.0512970i
\(603\) 2.24068e9 0.416169
\(604\) 5.48568e8 6.87883e8i 0.101298 0.127024i
\(605\) 8.69202e8 1.31011e8i 0.159579 0.0240527i
\(606\) 1.86526e8 + 8.17224e8i 0.0340475 + 0.149172i
\(607\) 2.92523e9 1.99439e9i 0.530884 0.361951i −0.268016 0.963415i \(-0.586368\pi\)
0.798900 + 0.601464i \(0.205416\pi\)
\(608\) 2.66141e9 4.60970e9i 0.480230 0.831782i
\(609\) −4.44385e7 7.69697e7i −0.00797258 0.0138089i
\(610\) 2.42642e8 + 1.16850e8i 0.0432825 + 0.0208437i
\(611\) 1.72538e9 5.32209e8i 0.306013 0.0943926i
\(612\) −1.90127e8 + 2.53706e9i −0.0335284 + 0.447406i
\(613\) 6.21695e8 2.72383e9i 0.109010 0.477604i −0.890724 0.454544i \(-0.849802\pi\)
0.999734 0.0230594i \(-0.00734069\pi\)
\(614\) 8.84425e8 + 2.25348e9i 0.154196 + 0.392884i
\(615\) 3.06972e7 + 4.09625e8i 0.00532152 + 0.0710107i
\(616\) −1.46036e8 2.20114e7i −0.0251726 0.00379415i
\(617\) −7.80307e9 + 7.24019e9i −1.33742 + 1.24094i −0.390053 + 0.920793i \(0.627543\pi\)
−0.947366 + 0.320151i \(0.896266\pi\)
\(618\) −1.71746e8 + 8.27085e7i −0.0292703 + 0.0140958i
\(619\) 3.93126e9 + 2.68029e9i 0.666216 + 0.454218i 0.848618 0.529006i \(-0.177435\pi\)
−0.182403 + 0.983224i \(0.558387\pi\)
\(620\) 5.68601e8 1.44877e9i 0.0958157 0.244134i
\(621\) −1.19768e9 3.69437e8i −0.200688 0.0619041i
\(622\) −6.02454e8 5.58996e8i −0.100382 0.0931413i
\(623\) 2.82373e8 + 3.54085e8i 0.0467860 + 0.0586677i
\(624\) −1.99235e9 2.49833e9i −0.328262 0.411627i
\(625\) −4.07954e9 3.78526e9i −0.668391 0.620177i
\(626\) −2.69049e9 8.29907e8i −0.438351 0.135213i
\(627\) 5.35047e8 1.36328e9i 0.0866873 0.220876i
\(628\) −5.16522e9 3.52159e9i −0.832204 0.567387i
\(629\) −5.24231e9 + 2.52456e9i −0.839935 + 0.404491i
\(630\) 1.47188e7 1.36571e7i 0.00234520 0.00217603i
\(631\) 7.11639e8 + 1.07262e8i 0.112760 + 0.0169959i 0.205180 0.978724i \(-0.434222\pi\)
−0.0924196 + 0.995720i \(0.529460\pi\)
\(632\) 4.28253e7 + 5.71464e8i 0.00674824 + 0.0900490i
\(633\) −7.33458e8 1.86882e9i −0.114938 0.292856i
\(634\) −1.76620e8 + 7.73824e8i −0.0275251 + 0.120595i
\(635\) −6.08014e6 + 8.11339e7i −0.000942336 + 0.0125746i
\(636\) 6.41157e9 1.97771e9i 0.988244 0.304833i
\(637\) −5.23173e9 2.51947e9i −0.801968 0.386207i
\(638\) 3.04830e7 + 5.27981e7i 0.00464713 + 0.00804907i
\(639\) 9.67616e8 1.67596e9i 0.146707 0.254104i
\(640\) −9.11746e8 + 6.21618e8i −0.137481 + 0.0937333i
\(641\) −2.22716e9 9.75783e9i −0.334002 1.46336i −0.811308 0.584620i \(-0.801244\pi\)
0.477306 0.878737i \(-0.341613\pi\)
\(642\) 5.67100e8 8.54765e7i 0.0845837 0.0127489i
\(643\) 7.23150e9 9.06801e9i 1.07273 1.34516i 0.137745 0.990468i \(-0.456015\pi\)
0.934983 0.354691i \(-0.115414\pi\)
\(644\) −1.98844e8 −0.0293368
\(645\) −8.69183e8 3.76680e8i −0.127542 0.0552730i
\(646\) 3.59019e9 0.523966
\(647\) −4.98692e9 + 6.25340e9i −0.723881 + 0.907718i −0.998551 0.0538207i \(-0.982860\pi\)
0.274670 + 0.961539i \(0.411431\pi\)
\(648\) −2.16697e9 + 3.26619e8i −0.312854 + 0.0471551i
\(649\) 4.36163e8 + 1.91095e9i 0.0626314 + 0.274406i
\(650\) 1.61936e9 1.10406e9i 0.231285 0.157688i
\(651\) 8.09483e8 1.40207e9i 0.114994 0.199175i
\(652\) 2.79884e9 + 4.84773e9i 0.395468 + 0.684971i
\(653\) −1.01773e10 4.90114e9i −1.43033 0.688812i −0.451274 0.892386i \(-0.649030\pi\)
−0.979060 + 0.203573i \(0.934744\pi\)
\(654\) −9.99415e8 + 3.08279e8i −0.139709 + 0.0430945i
\(655\) −9.57207e7 + 1.27730e9i −0.0133095 + 0.177603i
\(656\) −5.87175e8 + 2.57258e9i −0.0812090 + 0.355800i
\(657\) 2.45879e8 + 6.26489e8i 0.0338253 + 0.0861856i
\(658\) −1.01438e7 1.35360e8i −0.00138807 0.0185225i
\(659\) −1.21258e10 1.82767e9i −1.65049 0.248771i −0.743134 0.669143i \(-0.766662\pi\)
−0.907352 + 0.420372i \(0.861900\pi\)
\(660\) −1.70860e8 + 1.58535e8i −0.0231332 + 0.0214645i
\(661\) 5.05330e8 2.43354e8i 0.0680566 0.0327743i −0.399546 0.916713i \(-0.630832\pi\)
0.467602 + 0.883939i \(0.345118\pi\)
\(662\) −3.34893e9 2.28326e9i −0.448645 0.305881i
\(663\) 2.88850e9 7.35977e9i 0.384923 0.980769i
\(664\) −3.61950e9 1.11647e9i −0.479800 0.147999i
\(665\) 1.88722e8 + 1.75108e8i 0.0248855 + 0.0230903i
\(666\) 3.41914e8 + 4.28746e8i 0.0448494 + 0.0562394i
\(667\) 1.07991e8 + 1.35416e8i 0.0140911 + 0.0176697i
\(668\) −7.55095e9 7.00625e9i −0.980130 0.909428i
\(669\) −4.05437e9 1.25061e9i −0.523518 0.161484i
\(670\) −1.83849e8 + 4.68439e8i −0.0236156 + 0.0601715i
\(671\) 1.44268e9 + 9.83600e8i 0.184349 + 0.125687i
\(672\) −7.93948e8 + 3.82345e8i −0.100925 + 0.0486030i
\(673\) 7.23514e8 6.71323e8i 0.0914944 0.0848944i −0.633100 0.774070i \(-0.718218\pi\)
0.724594 + 0.689176i \(0.242027\pi\)
\(674\) 1.87493e9 + 2.82601e8i 0.235872 + 0.0355519i
\(675\) 6.30616e8 + 8.41498e9i 0.0789226 + 1.05315i
\(676\) 4.24404e8 + 1.08136e9i 0.0528404 + 0.134635i
\(677\) −1.27426e9 + 5.58289e9i −0.157833 + 0.691510i 0.832642 + 0.553812i \(0.186827\pi\)
−0.990474 + 0.137698i \(0.956030\pi\)
\(678\) −1.98674e8 + 2.65112e9i −0.0244815 + 0.326682i
\(679\) 8.33737e8 2.57174e8i 0.102208 0.0315270i
\(680\) −1.08626e9 5.23115e8i −0.132481 0.0637993i
\(681\) 4.83442e9 + 8.37346e9i 0.586583 + 1.01599i
\(682\) −5.55272e8 + 9.61760e8i −0.0670287 + 0.116097i
\(683\) −1.52972e9 + 1.04295e9i −0.183713 + 0.125253i −0.651684 0.758490i \(-0.725937\pi\)
0.467972 + 0.883744i \(0.344985\pi\)
\(684\) 6.84135e8 + 2.99739e9i 0.0817420 + 0.358135i
\(685\) 2.05950e8 3.10419e7i 0.0244819 0.00369005i
\(686\) −5.52331e8 + 6.92601e8i −0.0653228 + 0.0819122i
\(687\) −1.45890e9 −0.171663
\(688\) −4.62220e9 3.95798e9i −0.541114 0.463356i
\(689\) 1.11953e10 1.30397
\(690\) 4.54385e7 5.69781e7i 0.00526565 0.00660292i
\(691\) 1.32057e10 1.99044e9i 1.52261 0.229496i 0.666190 0.745782i \(-0.267924\pi\)
0.856416 + 0.516286i \(0.172686\pi\)
\(692\) 3.79895e8 + 1.66443e9i 0.0435805 + 0.190939i
\(693\) 1.07560e8 7.33330e7i 0.0122768 0.00837015i
\(694\) 1.68754e8 2.92291e8i 0.0191645 0.0331938i
\(695\) −9.13238e8 1.58178e9i −0.103190 0.178730i
\(696\) 4.53168e8 + 2.18234e8i 0.0509479 + 0.0245352i
\(697\) −6.23874e9 + 1.92440e9i −0.697882 + 0.215268i
\(698\) 2.55249e8 3.40606e9i 0.0284099 0.379104i
\(699\) −1.13246e9 + 4.96161e9i −0.125415 + 0.549481i
\(700\) 4.89105e8 + 1.24622e9i 0.0538963 + 0.137325i
\(701\) −9.62914e8 1.28492e10i −0.105578 1.40884i −0.758626 0.651527i \(-0.774129\pi\)
0.653047 0.757317i \(-0.273490\pi\)
\(702\) −2.84600e9 4.28965e8i −0.310495 0.0467996i
\(703\) −5.15432e9 + 4.78251e9i −0.559535 + 0.519173i
\(704\) −9.52842e8 + 4.58864e8i −0.102924 + 0.0495656i
\(705\) −3.73485e8 2.54638e8i −0.0401431 0.0273691i
\(706\) 1.03119e9 2.62743e9i 0.110286 0.281005i
\(707\) −9.12919e8 2.81598e8i −0.0971548 0.0299683i
\(708\) 5.61798e9 + 5.21272e9i 0.594927 + 0.552011i
\(709\) −3.09478e9 3.88073e9i −0.326113 0.408933i 0.591565 0.806257i \(-0.298510\pi\)
−0.917678 + 0.397324i \(0.869939\pi\)
\(710\) 2.70984e8 + 3.39804e8i 0.0284145 + 0.0356306i
\(711\) −3.70293e8 3.43582e8i −0.0386369 0.0358498i
\(712\) −2.44916e9 7.55467e8i −0.254295 0.0784397i
\(713\) −1.15267e9 + 2.93694e9i −0.119094 + 0.303447i
\(714\) −4.91093e8 3.34821e8i −0.0504917 0.0344246i
\(715\) −3.50390e8 + 1.68739e8i −0.0358492 + 0.0172641i
\(716\) 3.85921e8 3.58083e8i 0.0392919 0.0364576i
\(717\) 6.73213e8 + 1.01470e8i 0.0682080 + 0.0102807i
\(718\) 2.94197e8 + 3.92578e9i 0.0296621 + 0.395814i
\(719\) 1.65771e9 + 4.22379e9i 0.166325 + 0.423790i 0.989599 0.143855i \(-0.0459498\pi\)
−0.823273 + 0.567645i \(0.807855\pi\)
\(720\) 9.55794e7 4.18761e8i 0.00954334 0.0418121i
\(721\) 1.62358e7 2.16651e8i 0.00161324 0.0215272i
\(722\) 1.10290e9 3.40201e8i 0.109058 0.0336399i
\(723\) 9.99395e9 + 4.81283e9i 0.983452 + 0.473606i
\(724\) 8.11186e9 + 1.40502e10i 0.794393 + 1.37593i
\(725\) 5.83065e8 1.00990e9i 0.0568243 0.0984226i
\(726\) −2.02628e9 + 1.38149e9i −0.196526 + 0.133989i
\(727\) −4.92532e8 2.15792e9i −0.0475406 0.208289i 0.945579 0.325392i \(-0.105496\pi\)
−0.993120 + 0.117103i \(0.962639\pi\)
\(728\) −9.52715e8 + 1.43599e8i −0.0915173 + 0.0137940i
\(729\) 6.93035e9 8.69039e9i 0.662535 0.830793i
\(730\) −1.51149e8 −0.0143805
\(731\) 2.76274e9 1.48006e10i 0.261595 1.40142i
\(732\) 6.82701e9 0.643342
\(733\) 4.91720e9 6.16597e9i 0.461162 0.578279i −0.495820 0.868425i \(-0.665132\pi\)
0.956982 + 0.290146i \(0.0937039\pi\)
\(734\) −9.98547e8 + 1.50507e8i −0.0932035 + 0.0140482i
\(735\) 3.23484e8 + 1.41728e9i 0.0300502 + 0.131658i
\(736\) 1.41891e9 9.67397e8i 0.131185 0.0894401i
\(737\) −1.63132e9 + 2.82552e9i −0.150107 + 0.259994i
\(738\) 3.07664e8 + 5.32890e8i 0.0281760 + 0.0488023i
\(739\) 4.87743e9 + 2.34885e9i 0.444565 + 0.214091i 0.642754 0.766072i \(-0.277792\pi\)
−0.198189 + 0.980164i \(0.563506\pi\)
\(740\) 1.06933e9 3.29845e8i 0.0970066 0.0299226i
\(741\) 7.13990e8 9.52753e9i 0.0644656 0.860234i
\(742\) 1.87280e8 8.20528e8i 0.0168298 0.0737360i
\(743\) 1.58861e9 + 4.04771e9i 0.142088 + 0.362033i 0.984148 0.177350i \(-0.0567526\pi\)
−0.842060 + 0.539384i \(0.818657\pi\)
\(744\) 6.84689e8 + 9.13654e9i 0.0609520 + 0.813348i
\(745\) −2.70933e9 4.08366e8i −0.240058 0.0361829i
\(746\) −3.17028e9 + 2.94159e9i −0.279583 + 0.259415i
\(747\) 3.00816e9 1.44865e9i 0.264046 0.127158i
\(748\) −3.06085e9 2.08685e9i −0.267415 0.182320i
\(749\) −2.38801e8 + 6.08455e8i −0.0207659 + 0.0529105i
\(750\) −9.52083e8 2.93679e8i −0.0824063 0.0254190i
\(751\) −1.58518e10 1.47083e10i −1.36565 1.26714i −0.930264 0.366890i \(-0.880422\pi\)
−0.435383 0.900245i \(-0.643387\pi\)
\(752\) −1.81047e9 2.27025e9i −0.155249