Properties

Label 37.8.e.a.11.13
Level $37$
Weight $8$
Character 37.11
Analytic conductor $11.558$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [37,8,Mod(11,37)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(37, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("37.11");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 37 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 37.e (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.5582459429\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.13
Character \(\chi\) \(=\) 37.11
Dual form 37.8.e.a.27.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.63260 - 2.09728i) q^{2} +(24.6553 - 42.7042i) q^{3} +(-55.2028 + 95.6141i) q^{4} +(292.816 + 169.058i) q^{5} -206.836i q^{6} +(-480.087 + 831.535i) q^{7} +1000.01i q^{8} +(-122.265 - 211.770i) q^{9} +O(q^{10})\) \(q+(3.63260 - 2.09728i) q^{2} +(24.6553 - 42.7042i) q^{3} +(-55.2028 + 95.6141i) q^{4} +(292.816 + 169.058i) q^{5} -206.836i q^{6} +(-480.087 + 831.535i) q^{7} +1000.01i q^{8} +(-122.265 - 211.770i) q^{9} +1418.24 q^{10} +333.058 q^{11} +(2722.08 + 4714.78i) q^{12} +(4185.38 + 2416.43i) q^{13} +4027.51i q^{14} +(14438.9 - 8336.32i) q^{15} +(-4968.66 - 8605.98i) q^{16} +(15806.4 - 9125.82i) q^{17} +(-888.282 - 512.850i) q^{18} +(7849.66 + 4532.00i) q^{19} +(-32328.6 + 18664.9i) q^{20} +(23673.3 + 41003.4i) q^{21} +(1209.86 - 698.516i) q^{22} +57449.5i q^{23} +(42704.5 + 24655.5i) q^{24} +(18098.4 + 31347.4i) q^{25} +20271.7 q^{26} +95784.2 q^{27} +(-53004.3 - 91806.1i) q^{28} +56174.4i q^{29} +(34967.2 - 60565.0i) q^{30} -135018. i q^{31} +(-146950. - 84841.8i) q^{32} +(8211.63 - 14223.0i) q^{33} +(38278.8 - 66300.9i) q^{34} +(-281154. + 162325. i) q^{35} +26997.6 q^{36} +(-227421. - 207874. i) q^{37} +38019.5 q^{38} +(206383. - 119156. i) q^{39} +(-169059. + 292818. i) q^{40} +(-216168. + 374414. i) q^{41} +(171991. + 99299.3i) q^{42} -667300. i q^{43} +(-18385.7 + 31845.0i) q^{44} -82679.5i q^{45} +(120488. + 208691. i) q^{46} -569600. q^{47} -490015. q^{48} +(-49195.0 - 85208.2i) q^{49} +(131488. + 75914.9i) q^{50} -899999. i q^{51} +(-462090. + 266788. i) q^{52} +(-235008. - 407046. i) q^{53} +(347946. - 200886. i) q^{54} +(97524.7 + 56305.9i) q^{55} +(-831541. - 480090. i) q^{56} +(387071. - 223476. i) q^{57} +(117814. + 204059. i) q^{58} +(2.23076e6 - 1.28793e6i) q^{59} +1.84075e6i q^{60} +(1.76510e6 + 1.01908e6i) q^{61} +(-283171. - 490466. i) q^{62} +234792. q^{63} +560229. q^{64} +(817032. + 1.41514e6i) q^{65} -68888.4i q^{66} +(-614213. + 1.06385e6i) q^{67} +2.01508e6i q^{68} +(2.45333e6 + 1.41643e6i) q^{69} +(-680880. + 1.17932e6i) q^{70} +(-1.51939e6 + 2.63167e6i) q^{71} +(211771. - 122266. i) q^{72} +2.37565e6 q^{73} +(-1.26210e6 - 278157. i) q^{74} +1.78488e6 q^{75} +(-866647. + 500359. i) q^{76} +(-159897. + 276949. i) q^{77} +(499805. - 865688. i) q^{78} +(-5.10200e6 - 2.94564e6i) q^{79} -3.35996e6i q^{80} +(2.62898e6 - 4.55353e6i) q^{81} +1.81346e6i q^{82} +(-1.48157e6 - 2.56616e6i) q^{83} -5.22734e6 q^{84} +6.17116e6 q^{85} +(-1.39952e6 - 2.42403e6i) q^{86} +(2.39888e6 + 1.38500e6i) q^{87} +333060. i q^{88} +(7.69370e6 - 4.44196e6i) q^{89} +(-173402. - 300341. i) q^{90} +(-4.01869e6 + 2.32019e6i) q^{91} +(-5.49298e6 - 3.17137e6i) q^{92} +(-5.76584e6 - 3.32891e6i) q^{93} +(-2.06913e6 + 1.19461e6i) q^{94} +(1.53234e6 + 2.65409e6i) q^{95} +(-7.24620e6 + 4.18360e6i) q^{96} +2.55162e6i q^{97} +(-357411. - 206351. i) q^{98} +(-40721.4 - 70531.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 18 q^{2} - 42 q^{3} + 1114 q^{4} - 672 q^{5} + 156 q^{7} - 9128 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 18 q^{2} - 42 q^{3} + 1114 q^{4} - 672 q^{5} + 156 q^{7} - 9128 q^{9} - 5124 q^{10} + 12468 q^{11} + 6926 q^{12} + 10512 q^{13} + 36402 q^{15} - 31094 q^{16} - 22440 q^{17} - 153504 q^{18} + 49086 q^{19} + 28662 q^{20} + 7736 q^{21} + 132018 q^{22} + 2754 q^{24} + 72328 q^{25} - 680244 q^{26} + 42984 q^{27} + 105488 q^{28} + 382084 q^{30} + 523656 q^{32} + 9228 q^{33} + 276914 q^{34} - 904452 q^{35} - 204828 q^{36} + 1333776 q^{37} + 50208 q^{38} + 122040 q^{39} - 1205236 q^{40} - 871440 q^{41} + 1436094 q^{42} - 994326 q^{44} - 987942 q^{46} - 586932 q^{47} + 3984388 q^{48} - 1766072 q^{49} + 1818708 q^{50} - 2745228 q^{52} + 1661988 q^{53} + 1102554 q^{54} - 2733258 q^{55} - 5943924 q^{56} + 3920592 q^{57} + 5021672 q^{58} + 5296632 q^{59} - 4588524 q^{61} - 8143398 q^{62} - 2503648 q^{63} + 10662964 q^{64} - 1652736 q^{65} + 1940622 q^{67} - 10266552 q^{69} - 5038546 q^{70} + 6420528 q^{71} - 6576036 q^{72} - 3313032 q^{73} + 16192386 q^{74} - 5168536 q^{75} + 10328022 q^{76} - 8599404 q^{77} + 18210222 q^{78} - 15094374 q^{79} + 1733956 q^{81} - 191670 q^{83} + 1175224 q^{84} - 18053592 q^{85} + 18575940 q^{86} - 3762762 q^{87} - 14873004 q^{89} + 37293212 q^{90} - 76496700 q^{91} + 27846618 q^{92} + 26687652 q^{93} + 35421402 q^{94} + 14310774 q^{95} - 30894534 q^{96} - 13793868 q^{98} - 37141758 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.63260 2.09728i 0.321079 0.185375i −0.330794 0.943703i \(-0.607317\pi\)
0.651874 + 0.758328i \(0.273983\pi\)
\(3\) 24.6553 42.7042i 0.527212 0.913158i −0.472285 0.881446i \(-0.656571\pi\)
0.999497 0.0317124i \(-0.0100961\pi\)
\(4\) −55.2028 + 95.6141i −0.431272 + 0.746985i
\(5\) 292.816 + 169.058i 1.04761 + 0.604839i 0.921980 0.387238i \(-0.126571\pi\)
0.125632 + 0.992077i \(0.459904\pi\)
\(6\) 206.836i 0.390928i
\(7\) −480.087 + 831.535i −0.529025 + 0.916299i 0.470402 + 0.882452i \(0.344109\pi\)
−0.999427 + 0.0338464i \(0.989224\pi\)
\(8\) 1000.01i 0.690539i
\(9\) −122.265 211.770i −0.0559055 0.0968312i
\(10\) 1418.24 0.448488
\(11\) 333.058 0.0754476 0.0377238 0.999288i \(-0.487989\pi\)
0.0377238 + 0.999288i \(0.487989\pi\)
\(12\) 2722.08 + 4714.78i 0.454744 + 0.787639i
\(13\) 4185.38 + 2416.43i 0.528364 + 0.305051i 0.740350 0.672222i \(-0.234660\pi\)
−0.211986 + 0.977273i \(0.567993\pi\)
\(14\) 4027.51i 0.392273i
\(15\) 14438.9 8336.32i 1.10463 0.637757i
\(16\) −4968.66 8605.98i −0.303263 0.525267i
\(17\) 15806.4 9125.82i 0.780300 0.450506i −0.0562367 0.998417i \(-0.517910\pi\)
0.836537 + 0.547911i \(0.184577\pi\)
\(18\) −888.282 512.850i −0.0359002 0.0207270i
\(19\) 7849.66 + 4532.00i 0.262551 + 0.151584i 0.625498 0.780226i \(-0.284896\pi\)
−0.362947 + 0.931810i \(0.618229\pi\)
\(20\) −32328.6 + 18664.9i −0.903611 + 0.521700i
\(21\) 23673.3 + 41003.4i 0.557817 + 0.966168i
\(22\) 1209.86 698.516i 0.0242246 0.0139861i
\(23\) 57449.5i 0.984552i 0.870439 + 0.492276i \(0.163835\pi\)
−0.870439 + 0.492276i \(0.836165\pi\)
\(24\) 42704.5 + 24655.5i 0.630572 + 0.364061i
\(25\) 18098.4 + 31347.4i 0.231660 + 0.401246i
\(26\) 20271.7 0.226196
\(27\) 95784.2 0.936528
\(28\) −53004.3 91806.1i −0.456308 0.790348i
\(29\) 56174.4i 0.427706i 0.976866 + 0.213853i \(0.0686014\pi\)
−0.976866 + 0.213853i \(0.931399\pi\)
\(30\) 34967.2 60565.0i 0.236449 0.409541i
\(31\) 135018.i 0.814003i −0.913427 0.407002i \(-0.866574\pi\)
0.913427 0.407002i \(-0.133426\pi\)
\(32\) −146950. 84841.8i −0.792767 0.457704i
\(33\) 8211.63 14223.0i 0.0397769 0.0688956i
\(34\) 38278.8 66300.9i 0.167025 0.289296i
\(35\) −281154. + 162325.i −1.10843 + 0.639950i
\(36\) 26997.6 0.0964419
\(37\) −227421. 207874.i −0.738115 0.674674i
\(38\) 38019.5 0.112399
\(39\) 206383. 119156.i 0.557120 0.321653i
\(40\) −169059. + 292818.i −0.417665 + 0.723416i
\(41\) −216168. + 374414.i −0.489833 + 0.848415i −0.999932 0.0117007i \(-0.996275\pi\)
0.510099 + 0.860116i \(0.329609\pi\)
\(42\) 171991. + 99299.3i 0.358207 + 0.206811i
\(43\) 667300.i 1.27992i −0.768410 0.639958i \(-0.778952\pi\)
0.768410 0.639958i \(-0.221048\pi\)
\(44\) −18385.7 + 31845.0i −0.0325384 + 0.0563582i
\(45\) 82679.5i 0.135255i
\(46\) 120488. + 208691.i 0.182512 + 0.316119i
\(47\) −569600. −0.800253 −0.400127 0.916460i \(-0.631034\pi\)
−0.400127 + 0.916460i \(0.631034\pi\)
\(48\) −490015. −0.639536
\(49\) −49195.0 85208.2i −0.0597357 0.103465i
\(50\) 131488. + 75914.9i 0.148762 + 0.0858879i
\(51\) 899999.i 0.950050i
\(52\) −462090. + 266788.i −0.455737 + 0.263120i
\(53\) −235008. 407046.i −0.216829 0.375559i 0.737008 0.675884i \(-0.236238\pi\)
−0.953837 + 0.300325i \(0.902905\pi\)
\(54\) 347946. 200886.i 0.300700 0.173609i
\(55\) 97524.7 + 56305.9i 0.0790397 + 0.0456336i
\(56\) −831541. 480090.i −0.632740 0.365313i
\(57\) 387071. 223476.i 0.276840 0.159834i
\(58\) 117814. + 204059.i 0.0792861 + 0.137328i
\(59\) 2.23076e6 1.28793e6i 1.41407 0.816415i 0.418303 0.908308i \(-0.362625\pi\)
0.995769 + 0.0918928i \(0.0292917\pi\)
\(60\) 1.84075e6i 1.10019i
\(61\) 1.76510e6 + 1.01908e6i 0.995667 + 0.574848i 0.906963 0.421210i \(-0.138394\pi\)
0.0887034 + 0.996058i \(0.471728\pi\)
\(62\) −283171. 490466.i −0.150896 0.261360i
\(63\) 234792. 0.118302
\(64\) 560229. 0.267138
\(65\) 817032. + 1.41514e6i 0.369013 + 0.639150i
\(66\) 68888.4i 0.0294946i
\(67\) −614213. + 1.06385e6i −0.249492 + 0.432133i −0.963385 0.268122i \(-0.913597\pi\)
0.713893 + 0.700255i \(0.246930\pi\)
\(68\) 2.01508e6i 0.777163i
\(69\) 2.45333e6 + 1.41643e6i 0.899052 + 0.519068i
\(70\) −680880. + 1.17932e6i −0.237262 + 0.410949i
\(71\) −1.51939e6 + 2.63167e6i −0.503809 + 0.872624i 0.496181 + 0.868219i \(0.334735\pi\)
−0.999990 + 0.00440434i \(0.998598\pi\)
\(72\) 211771. 122266.i 0.0668657 0.0386049i
\(73\) 2.37565e6 0.714747 0.357374 0.933961i \(-0.383672\pi\)
0.357374 + 0.933961i \(0.383672\pi\)
\(74\) −1.26210e6 278157.i −0.362061 0.0797957i
\(75\) 1.78488e6 0.488535
\(76\) −866647. + 500359.i −0.226462 + 0.130748i
\(77\) −159897. + 276949.i −0.0399137 + 0.0691325i
\(78\) 499805. 865688.i 0.119253 0.206552i
\(79\) −5.10200e6 2.94564e6i −1.16425 0.672179i −0.211930 0.977285i \(-0.567975\pi\)
−0.952318 + 0.305106i \(0.901308\pi\)
\(80\) 3.35996e6i 0.733701i
\(81\) 2.62898e6 4.55353e6i 0.549655 0.952030i
\(82\) 1.81346e6i 0.363211i
\(83\) −1.48157e6 2.56616e6i −0.284413 0.492618i 0.688053 0.725660i \(-0.258465\pi\)
−0.972467 + 0.233042i \(0.925132\pi\)
\(84\) −5.22734e6 −0.962284
\(85\) 6.17116e6 1.08993
\(86\) −1.39952e6 2.42403e6i −0.237265 0.410955i
\(87\) 2.39888e6 + 1.38500e6i 0.390564 + 0.225492i
\(88\) 333060.i 0.0520995i
\(89\) 7.69370e6 4.44196e6i 1.15683 0.667897i 0.206289 0.978491i \(-0.433861\pi\)
0.950543 + 0.310594i \(0.100528\pi\)
\(90\) −173402. 300341.i −0.0250730 0.0434277i
\(91\) −4.01869e6 + 2.32019e6i −0.559036 + 0.322760i
\(92\) −5.49298e6 3.17137e6i −0.735446 0.424610i
\(93\) −5.76584e6 3.32891e6i −0.743314 0.429152i
\(94\) −2.06913e6 + 1.19461e6i −0.256945 + 0.148347i
\(95\) 1.53234e6 + 2.65409e6i 0.183367 + 0.317602i
\(96\) −7.24620e6 + 4.18360e6i −0.835913 + 0.482615i
\(97\) 2.55162e6i 0.283867i 0.989876 + 0.141934i \(0.0453319\pi\)
−0.989876 + 0.141934i \(0.954668\pi\)
\(98\) −357411. 206351.i −0.0383598 0.0221471i
\(99\) −40721.4 70531.6i −0.00421793 0.00730568i
\(100\) −3.99633e6 −0.399633
\(101\) −9.55080e6 −0.922391 −0.461195 0.887299i \(-0.652579\pi\)
−0.461195 + 0.887299i \(0.652579\pi\)
\(102\) −1.88755e6 3.26933e6i −0.176116 0.305041i
\(103\) 9.76895e6i 0.880882i −0.897782 0.440441i \(-0.854822\pi\)
0.897782 0.440441i \(-0.145178\pi\)
\(104\) −2.41645e6 + 4.18541e6i −0.210650 + 0.364856i
\(105\) 1.60086e7i 1.34956i
\(106\) −1.70738e6 985756.i −0.139239 0.0803894i
\(107\) 7.48747e6 1.29687e7i 0.590870 1.02342i −0.403246 0.915092i \(-0.632118\pi\)
0.994116 0.108325i \(-0.0345486\pi\)
\(108\) −5.28756e6 + 9.15832e6i −0.403898 + 0.699573i
\(109\) 1.96196e7 1.13274e7i 1.45110 0.837792i 0.452554 0.891737i \(-0.350513\pi\)
0.998544 + 0.0539457i \(0.0171798\pi\)
\(110\) 472357. 0.0338373
\(111\) −1.44842e7 + 4.58663e6i −1.00523 + 0.318320i
\(112\) 9.54156e6 0.641736
\(113\) 2.23930e7 1.29286e7i 1.45995 0.842903i 0.460943 0.887430i \(-0.347511\pi\)
0.999008 + 0.0445269i \(0.0141781\pi\)
\(114\) 937382. 1.62359e6i 0.0592584 0.102638i
\(115\) −9.71227e6 + 1.68221e7i −0.595495 + 1.03143i
\(116\) −5.37107e6 3.10099e6i −0.319490 0.184458i
\(117\) 1.18178e6i 0.0682162i
\(118\) 5.40231e6 9.35708e6i 0.302686 0.524268i
\(119\) 1.75247e7i 0.953317i
\(120\) 8.33638e6 + 1.44390e7i 0.440396 + 0.762788i
\(121\) −1.93762e7 −0.994308
\(122\) 8.54918e6 0.426251
\(123\) 1.06594e7 + 1.84626e7i 0.516492 + 0.894590i
\(124\) 1.29096e7 + 7.45338e6i 0.608048 + 0.351057i
\(125\) 1.41766e7i 0.649211i
\(126\) 852904. 492425.i 0.0379842 0.0219302i
\(127\) −1.60711e7 2.78360e7i −0.696200 1.20585i −0.969775 0.244003i \(-0.921539\pi\)
0.273575 0.961851i \(-0.411794\pi\)
\(128\) 2.08447e7 1.20347e7i 0.878540 0.507225i
\(129\) −2.84965e7 1.64525e7i −1.16877 0.674788i
\(130\) 5.93590e6 + 3.42709e6i 0.236965 + 0.136812i
\(131\) −8.15356e6 + 4.70746e6i −0.316882 + 0.182952i −0.650002 0.759933i \(-0.725232\pi\)
0.333120 + 0.942884i \(0.391899\pi\)
\(132\) 906610. + 1.57030e6i 0.0343093 + 0.0594255i
\(133\) −7.53703e6 + 4.35151e6i −0.277792 + 0.160383i
\(134\) 5.15271e6i 0.184999i
\(135\) 2.80472e7 + 1.61930e7i 0.981118 + 0.566448i
\(136\) 9.12589e6 + 1.58065e7i 0.311092 + 0.538827i
\(137\) 2.59733e7 0.862989 0.431494 0.902116i \(-0.357986\pi\)
0.431494 + 0.902116i \(0.357986\pi\)
\(138\) 1.18826e7 0.384889
\(139\) 7.63162e6 + 1.32184e7i 0.241027 + 0.417470i 0.961007 0.276524i \(-0.0891826\pi\)
−0.719980 + 0.693994i \(0.755849\pi\)
\(140\) 3.58431e7i 1.10397i
\(141\) −1.40436e7 + 2.43243e7i −0.421903 + 0.730758i
\(142\) 1.27464e7i 0.373575i
\(143\) 1.39397e6 + 804811.i 0.0398638 + 0.0230154i
\(144\) −1.21499e6 + 2.10443e6i −0.0339082 + 0.0587307i
\(145\) −9.49671e6 + 1.64488e7i −0.258693 + 0.448070i
\(146\) 8.62978e6 4.98241e6i 0.229491 0.132496i
\(147\) −4.85166e6 −0.125974
\(148\) 3.24300e7 1.02694e7i 0.822300 0.260393i
\(149\) −2.88591e7 −0.714711 −0.357355 0.933969i \(-0.616321\pi\)
−0.357355 + 0.933969i \(0.616321\pi\)
\(150\) 6.48377e6 3.74340e6i 0.156858 0.0905623i
\(151\) −1.30489e7 + 2.26014e7i −0.308429 + 0.534214i −0.978019 0.208517i \(-0.933136\pi\)
0.669590 + 0.742731i \(0.266470\pi\)
\(152\) −4.53204e6 + 7.84972e6i −0.104674 + 0.181301i
\(153\) −3.86515e6 2.23154e6i −0.0872461 0.0503716i
\(154\) 1.34139e6i 0.0295960i
\(155\) 2.28258e7 3.95355e7i 0.492341 0.852759i
\(156\) 2.63109e7i 0.554881i
\(157\) 3.88606e7 + 6.73085e7i 0.801420 + 1.38810i 0.918681 + 0.394999i \(0.129255\pi\)
−0.117261 + 0.993101i \(0.537411\pi\)
\(158\) −2.47113e7 −0.498421
\(159\) −2.31768e7 −0.457259
\(160\) −2.86863e7 4.96861e7i −0.553675 0.958993i
\(161\) −4.77712e7 2.75807e7i −0.902144 0.520853i
\(162\) 2.20549e7i 0.407569i
\(163\) 2.20358e7 1.27224e7i 0.398540 0.230097i −0.287314 0.957836i \(-0.592762\pi\)
0.685854 + 0.727739i \(0.259429\pi\)
\(164\) −2.38662e7 4.13374e7i −0.422502 0.731795i
\(165\) 4.80900e6 2.77648e6i 0.0833414 0.0481172i
\(166\) −1.07639e7 6.21455e6i −0.182638 0.105446i
\(167\) −9.29195e7 5.36471e7i −1.54383 0.891331i −0.998592 0.0530493i \(-0.983106\pi\)
−0.545238 0.838281i \(-0.683561\pi\)
\(168\) −4.10037e7 + 2.36735e7i −0.667177 + 0.385195i
\(169\) −1.96960e7 3.41144e7i −0.313888 0.543669i
\(170\) 2.24173e7 1.29427e7i 0.349955 0.202047i
\(171\) 2.21643e6i 0.0338975i
\(172\) 6.38033e7 + 3.68368e7i 0.956078 + 0.551992i
\(173\) 4.69150e7 + 8.12592e7i 0.688891 + 1.19319i 0.972197 + 0.234165i \(0.0752357\pi\)
−0.283305 + 0.959030i \(0.591431\pi\)
\(174\) 1.16189e7 0.167203
\(175\) −3.47552e7 −0.490215
\(176\) −1.65485e6 2.86629e6i −0.0228805 0.0396301i
\(177\) 1.27017e8i 1.72170i
\(178\) 1.86321e7 3.22717e7i 0.247623 0.428896i
\(179\) 2.99691e6i 0.0390560i −0.999809 0.0195280i \(-0.993784\pi\)
0.999809 0.0195280i \(-0.00621636\pi\)
\(180\) 7.90533e6 + 4.56414e6i 0.101034 + 0.0583318i
\(181\) −7.54173e7 + 1.30627e8i −0.945358 + 1.63741i −0.190325 + 0.981721i \(0.560954\pi\)
−0.755033 + 0.655687i \(0.772379\pi\)
\(182\) −9.73219e6 + 1.68567e7i −0.119663 + 0.207263i
\(183\) 8.70379e7 5.02513e7i 1.04986 0.606134i
\(184\) −5.74499e7 −0.679872
\(185\) −3.14498e7 9.93161e7i −0.365189 1.15324i
\(186\) −2.79266e7 −0.318217
\(187\) 5.26444e6 3.03943e6i 0.0588717 0.0339896i
\(188\) 3.14435e7 5.44618e7i 0.345127 0.597777i
\(189\) −4.59847e7 + 7.96479e7i −0.495447 + 0.858140i
\(190\) 1.11327e7 + 6.42749e6i 0.117751 + 0.0679835i
\(191\) 1.22934e8i 1.27660i −0.769788 0.638300i \(-0.779638\pi\)
0.769788 0.638300i \(-0.220362\pi\)
\(192\) 1.38126e7 2.39241e7i 0.140839 0.243940i
\(193\) 1.33916e8i 1.34085i 0.741976 + 0.670427i \(0.233889\pi\)
−0.741976 + 0.670427i \(0.766111\pi\)
\(194\) 5.35147e6 + 9.26901e6i 0.0526219 + 0.0911438i
\(195\) 8.05766e7 0.778194
\(196\) 1.08628e7 0.103049
\(197\) 1.94932e7 + 3.37633e7i 0.181657 + 0.314639i 0.942445 0.334361i \(-0.108521\pi\)
−0.760788 + 0.649001i \(0.775187\pi\)
\(198\) −295849. 170809.i −0.00270858 0.00156380i
\(199\) 1.54091e8i 1.38609i 0.720896 + 0.693044i \(0.243731\pi\)
−0.720896 + 0.693044i \(0.756269\pi\)
\(200\) −3.13476e7 + 1.80985e7i −0.277076 + 0.159970i
\(201\) 3.02872e7 + 5.24589e7i 0.263071 + 0.455652i
\(202\) −3.46942e7 + 2.00307e7i −0.296161 + 0.170988i
\(203\) −4.67110e7 2.69686e7i −0.391907 0.226267i
\(204\) 8.60526e7 + 4.96825e7i 0.709673 + 0.409730i
\(205\) −1.26595e8 + 7.30896e7i −1.02631 + 0.592539i
\(206\) −2.04882e7 3.54867e7i −0.163294 0.282833i
\(207\) 1.21661e7 7.02408e6i 0.0953353 0.0550419i
\(208\) 4.80257e7i 0.370043i
\(209\) 2.61439e6 + 1.50942e6i 0.0198088 + 0.0114366i
\(210\) 3.35746e7 + 5.81529e7i 0.250175 + 0.433315i
\(211\) 1.29229e8 0.947048 0.473524 0.880781i \(-0.342982\pi\)
0.473524 + 0.880781i \(0.342982\pi\)
\(212\) 5.18924e7 0.374049
\(213\) 7.49222e7 + 1.29769e8i 0.531229 + 0.920116i
\(214\) 6.28133e7i 0.438130i
\(215\) 1.12812e8 1.95396e8i 0.774143 1.34085i
\(216\) 9.57849e7i 0.646709i
\(217\) 1.12272e8 + 6.48204e7i 0.745870 + 0.430628i
\(218\) 4.75133e7 8.22955e7i 0.310612 0.537995i
\(219\) 5.85723e7 1.01450e8i 0.376824 0.652678i
\(220\) −1.07673e7 + 6.21649e6i −0.0681752 + 0.0393610i
\(221\) 8.82077e7 0.549710
\(222\) −4.29959e7 + 4.70389e7i −0.263749 + 0.288550i
\(223\) −3.13462e8 −1.89286 −0.946428 0.322914i \(-0.895338\pi\)
−0.946428 + 0.322914i \(0.895338\pi\)
\(224\) 1.41098e8 8.14629e7i 0.838788 0.484275i
\(225\) 4.42562e6 7.66539e6i 0.0259021 0.0448637i
\(226\) 5.42299e7 9.39289e7i 0.312507 0.541277i
\(227\) 9.91164e7 + 5.72249e7i 0.562412 + 0.324709i 0.754113 0.656744i \(-0.228067\pi\)
−0.191701 + 0.981453i \(0.561400\pi\)
\(228\) 4.93459e7i 0.275727i
\(229\) 9.29813e7 1.61048e8i 0.511648 0.886201i −0.488260 0.872698i \(-0.662368\pi\)
0.999909 0.0135030i \(-0.00429827\pi\)
\(230\) 8.14774e7i 0.441560i
\(231\) 7.88459e6 + 1.36565e7i 0.0420860 + 0.0728950i
\(232\) −5.61748e7 −0.295348
\(233\) 9.96162e7 0.515922 0.257961 0.966155i \(-0.416949\pi\)
0.257961 + 0.966155i \(0.416949\pi\)
\(234\) −2.47853e6 4.29294e6i −0.0126456 0.0219028i
\(235\) −1.66788e8 9.62952e7i −0.838355 0.484024i
\(236\) 2.84390e8i 1.40839i
\(237\) −2.51582e8 + 1.45251e8i −1.22761 + 0.708762i
\(238\) 3.67543e7 + 6.36603e7i 0.176721 + 0.306090i
\(239\) −7.10420e7 + 4.10161e7i −0.336607 + 0.194340i −0.658770 0.752344i \(-0.728923\pi\)
0.322164 + 0.946684i \(0.395590\pi\)
\(240\) −1.43484e8 8.28408e7i −0.669986 0.386816i
\(241\) 7.52865e7 + 4.34667e7i 0.346464 + 0.200031i 0.663127 0.748507i \(-0.269229\pi\)
−0.316663 + 0.948538i \(0.602562\pi\)
\(242\) −7.03861e7 + 4.06374e7i −0.319252 + 0.184320i
\(243\) −2.48965e7 4.31219e7i −0.111305 0.192786i
\(244\) −1.94877e8 + 1.12512e8i −0.858807 + 0.495832i
\(245\) 3.32671e7i 0.144522i
\(246\) 7.74423e7 + 4.47113e7i 0.331669 + 0.191489i
\(247\) 2.19025e7 + 3.79363e7i 0.0924816 + 0.160183i
\(248\) 1.35019e8 0.562101
\(249\) −1.46114e8 −0.599785
\(250\) −2.97322e7 5.14977e7i −0.120348 0.208448i
\(251\) 3.10556e8i 1.23960i −0.784760 0.619800i \(-0.787214\pi\)
0.784760 0.619800i \(-0.212786\pi\)
\(252\) −1.29612e7 + 2.24494e7i −0.0510202 + 0.0883696i
\(253\) 1.91340e7i 0.0742820i
\(254\) −1.16760e8 6.74114e7i −0.447071 0.258116i
\(255\) 1.52152e8 2.63534e8i 0.574627 0.995283i
\(256\) 1.46257e7 2.53324e7i 0.0544849 0.0943706i
\(257\) −2.22051e8 + 1.28201e8i −0.815995 + 0.471115i −0.849033 0.528339i \(-0.822815\pi\)
0.0330385 + 0.999454i \(0.489482\pi\)
\(258\) −1.38022e8 −0.500356
\(259\) 2.82036e8 8.93107e7i 1.00869 0.319414i
\(260\) −1.80410e8 −0.636581
\(261\) 1.18960e7 6.86819e6i 0.0414153 0.0239111i
\(262\) −1.97457e7 + 3.42006e7i −0.0678295 + 0.117484i
\(263\) −1.62194e7 + 2.80928e7i −0.0549781 + 0.0952248i −0.892205 0.451631i \(-0.850842\pi\)
0.837227 + 0.546856i \(0.184176\pi\)
\(264\) 1.42231e7 + 8.21169e6i 0.0475751 + 0.0274675i
\(265\) 1.58920e8i 0.524586i
\(266\) −1.82527e7 + 3.16146e7i −0.0594622 + 0.102991i
\(267\) 4.38071e8i 1.40849i
\(268\) −6.78125e7 1.17455e8i −0.215198 0.372734i
\(269\) 1.79214e8 0.561356 0.280678 0.959802i \(-0.409441\pi\)
0.280678 + 0.959802i \(0.409441\pi\)
\(270\) 1.35845e8 0.420022
\(271\) −6.60958e7 1.14481e8i −0.201735 0.349416i 0.747352 0.664428i \(-0.231325\pi\)
−0.949088 + 0.315012i \(0.897991\pi\)
\(272\) −1.57073e8 9.06863e7i −0.473272 0.273244i
\(273\) 2.28820e8i 0.680651i
\(274\) 9.43505e7 5.44733e7i 0.277088 0.159977i
\(275\) 6.02781e6 + 1.04405e7i 0.0174781 + 0.0302730i
\(276\) −2.70862e8 + 1.56382e8i −0.775472 + 0.447719i
\(277\) −1.36070e8 7.85598e7i −0.384664 0.222086i 0.295181 0.955441i \(-0.404620\pi\)
−0.679846 + 0.733355i \(0.737953\pi\)
\(278\) 5.54452e7 + 3.20113e7i 0.154777 + 0.0893607i
\(279\) −2.85928e7 + 1.65080e7i −0.0788209 + 0.0455073i
\(280\) −1.62326e8 2.81156e8i −0.441910 0.765411i
\(281\) −7.11162e7 + 4.10590e7i −0.191204 + 0.110392i −0.592546 0.805537i \(-0.701877\pi\)
0.401342 + 0.915928i \(0.368544\pi\)
\(282\) 1.17814e8i 0.312842i
\(283\) 2.92152e8 + 1.68674e8i 0.766226 + 0.442381i 0.831527 0.555485i \(-0.187467\pi\)
−0.0653009 + 0.997866i \(0.520801\pi\)
\(284\) −1.67750e8 2.90551e8i −0.434558 0.752676i
\(285\) 1.51121e8 0.386694
\(286\) 6.75166e6 0.0170659
\(287\) −2.07559e8 3.59502e8i −0.518268 0.897666i
\(288\) 4.14929e7i 0.102353i
\(289\) −3.86080e7 + 6.68710e7i −0.0940882 + 0.162965i
\(290\) 7.96691e7i 0.191821i
\(291\) 1.08965e8 + 6.29109e7i 0.259216 + 0.149658i
\(292\) −1.31143e8 + 2.27146e8i −0.308251 + 0.533906i
\(293\) −3.86372e8 + 6.69215e8i −0.897364 + 1.55428i −0.0665118 + 0.997786i \(0.521187\pi\)
−0.830852 + 0.556494i \(0.812146\pi\)
\(294\) −1.76241e7 + 1.01753e7i −0.0404475 + 0.0233524i
\(295\) 8.70938e8 1.97520
\(296\) 2.07876e8 2.27423e8i 0.465889 0.509697i
\(297\) 3.19017e7 0.0706588
\(298\) −1.04833e8 + 6.05256e7i −0.229479 + 0.132490i
\(299\) −1.38823e8 + 2.40448e8i −0.300339 + 0.520202i
\(300\) −9.85307e7 + 1.70660e8i −0.210692 + 0.364928i
\(301\) 5.54883e8 + 3.20362e8i 1.17279 + 0.677108i
\(302\) 1.09469e8i 0.228700i
\(303\) −2.35478e8 + 4.07859e8i −0.486296 + 0.842289i
\(304\) 9.00720e7i 0.183879i
\(305\) 3.44566e8 + 5.96806e8i 0.695381 + 1.20444i
\(306\) −1.87207e7 −0.0373506
\(307\) 9.30643e8 1.83569 0.917844 0.396942i \(-0.129928\pi\)
0.917844 + 0.396942i \(0.129928\pi\)
\(308\) −1.76535e7 3.05767e7i −0.0344273 0.0596298i
\(309\) −4.17175e8 2.40856e8i −0.804385 0.464412i
\(310\) 1.91489e8i 0.365071i
\(311\) −2.42245e8 + 1.39860e8i −0.456661 + 0.263653i −0.710639 0.703557i \(-0.751594\pi\)
0.253978 + 0.967210i \(0.418261\pi\)
\(312\) 1.19156e8 + 2.06385e8i 0.222114 + 0.384713i
\(313\) −6.83678e7 + 3.94721e7i −0.126022 + 0.0727588i −0.561686 0.827351i \(-0.689847\pi\)
0.435664 + 0.900109i \(0.356514\pi\)
\(314\) 2.82330e8 + 1.63003e8i 0.514639 + 0.297127i
\(315\) 6.87509e7 + 3.96933e7i 0.123934 + 0.0715535i
\(316\) 5.63289e8 3.25215e8i 1.00422 0.579784i
\(317\) 840676. + 1.45609e6i 0.00148225 + 0.00256733i 0.866766 0.498716i \(-0.166195\pi\)
−0.865283 + 0.501283i \(0.832862\pi\)
\(318\) −8.41918e7 + 4.86082e7i −0.146817 + 0.0847646i
\(319\) 1.87093e7i 0.0322694i
\(320\) 1.64044e8 + 9.47110e7i 0.279857 + 0.161576i
\(321\) −3.69211e8 6.39492e8i −0.623027 1.07912i
\(322\) −2.31378e8 −0.386213
\(323\) 1.65433e8 0.273158
\(324\) 2.90254e8 + 5.02735e8i 0.474101 + 0.821168i
\(325\) 1.74934e8i 0.282672i
\(326\) 5.33647e7 9.24304e7i 0.0853086 0.147759i
\(327\) 1.11712e9i 1.76678i
\(328\) −3.74417e8 2.16169e8i −0.585864 0.338249i
\(329\) 2.73457e8 4.73642e8i 0.423354 0.733271i
\(330\) 1.16461e7 2.01716e7i 0.0178395 0.0308989i
\(331\) −4.89597e8 + 2.82669e8i −0.742063 + 0.428430i −0.822819 0.568304i \(-0.807600\pi\)
0.0807562 + 0.996734i \(0.474266\pi\)
\(332\) 3.27148e8 0.490638
\(333\) −1.62158e7 + 7.35767e7i −0.0240648 + 0.109191i
\(334\) −4.50052e8 −0.660922
\(335\) −3.59703e8 + 2.07675e8i −0.522742 + 0.301805i
\(336\) 2.35250e8 4.07465e8i 0.338331 0.586006i
\(337\) 5.28739e8 9.15802e8i 0.752552 1.30346i −0.194031 0.980995i \(-0.562156\pi\)
0.946582 0.322462i \(-0.104511\pi\)
\(338\) −1.43095e8 8.26160e7i −0.201566 0.116374i
\(339\) 1.27503e9i 1.77756i
\(340\) −3.40665e8 + 5.90050e8i −0.470058 + 0.814165i
\(341\) 4.49688e7i 0.0614145i
\(342\) −4.64847e6 8.05139e6i −0.00628375 0.0108838i
\(343\) −6.96273e8 −0.931644
\(344\) 6.67305e8 0.883832
\(345\) 4.78917e8 + 8.29509e8i 0.627905 + 1.08756i
\(346\) 3.40847e8 + 1.96788e8i 0.442378 + 0.255407i
\(347\) 8.55533e8i 1.09922i 0.835422 + 0.549609i \(0.185223\pi\)
−0.835422 + 0.549609i \(0.814777\pi\)
\(348\) −2.64850e8 + 1.52911e8i −0.336878 + 0.194497i
\(349\) −6.31642e7 1.09404e8i −0.0795393 0.137766i 0.823512 0.567299i \(-0.192012\pi\)
−0.903051 + 0.429533i \(0.858678\pi\)
\(350\) −1.26252e8 + 7.28914e7i −0.157398 + 0.0908737i
\(351\) 4.00894e8 + 2.31456e8i 0.494828 + 0.285689i
\(352\) −4.89430e7 2.82572e7i −0.0598124 0.0345327i
\(353\) −3.03642e8 + 1.75308e8i −0.367409 + 0.212124i −0.672326 0.740255i \(-0.734705\pi\)
0.304917 + 0.952379i \(0.401371\pi\)
\(354\) −2.66391e8 4.61403e8i −0.319160 0.552801i
\(355\) −8.89807e8 + 5.13730e8i −1.05559 + 0.609447i
\(356\) 9.80835e8i 1.15218i
\(357\) 7.48380e8 + 4.32077e8i 0.870530 + 0.502600i
\(358\) −6.28537e6 1.08866e7i −0.00724002 0.0125401i
\(359\) −1.08710e9 −1.24005 −0.620025 0.784582i \(-0.712877\pi\)
−0.620025 + 0.784582i \(0.712877\pi\)
\(360\) 8.26801e7 0.0933990
\(361\) −4.05858e8 7.02966e8i −0.454045 0.786429i
\(362\) 6.32685e8i 0.700984i
\(363\) −4.77727e8 + 8.27447e8i −0.524211 + 0.907960i
\(364\) 5.12325e8i 0.556789i
\(365\) 6.95629e8 + 4.01622e8i 0.748777 + 0.432307i
\(366\) 2.10782e8 3.65086e8i 0.224725 0.389234i
\(367\) 5.11009e8 8.85094e8i 0.539632 0.934670i −0.459292 0.888285i \(-0.651897\pi\)
0.998924 0.0463843i \(-0.0147699\pi\)
\(368\) 4.94409e8 2.85447e8i 0.517153 0.298578i
\(369\) 1.05719e8 0.109537
\(370\) −3.22538e8 2.94816e8i −0.331036 0.302584i
\(371\) 4.51297e8 0.458832
\(372\) 6.36581e8 3.67530e8i 0.641141 0.370163i
\(373\) −4.33973e8 + 7.51663e8i −0.432994 + 0.749968i −0.997130 0.0757147i \(-0.975876\pi\)
0.564136 + 0.825682i \(0.309210\pi\)
\(374\) 1.27491e7 2.20820e7i 0.0126017 0.0218267i
\(375\) −6.05398e8 3.49527e8i −0.592832 0.342272i
\(376\) 5.69604e8i 0.552606i
\(377\) −1.35742e8 + 2.35111e8i −0.130472 + 0.225985i
\(378\) 3.85772e8i 0.367375i
\(379\) −7.01870e8 1.21567e9i −0.662246 1.14704i −0.980024 0.198879i \(-0.936270\pi\)
0.317778 0.948165i \(-0.397063\pi\)
\(380\) −3.38358e8 −0.316325
\(381\) −1.58495e9 −1.46818
\(382\) −2.57827e8 4.46569e8i −0.236650 0.409890i
\(383\) −6.58289e8 3.80063e8i −0.598716 0.345669i 0.169820 0.985475i \(-0.445681\pi\)
−0.768536 + 0.639806i \(0.779015\pi\)
\(384\) 1.18688e9i 1.06966i
\(385\) −9.36406e7 + 5.40635e7i −0.0836280 + 0.0482827i
\(386\) 2.80859e8 + 4.86462e8i 0.248561 + 0.430520i
\(387\) −1.41314e8 + 8.15877e7i −0.123936 + 0.0715544i
\(388\) −2.43971e8 1.40857e8i −0.212044 0.122424i
\(389\) −7.53409e8 4.34981e8i −0.648944 0.374668i 0.139108 0.990277i \(-0.455577\pi\)
−0.788051 + 0.615609i \(0.788910\pi\)
\(390\) 2.92702e8 1.68992e8i 0.249862 0.144258i
\(391\) 5.24274e8 + 9.08069e8i 0.443547 + 0.768246i
\(392\) 8.52088e7 4.91953e7i 0.0714469 0.0412499i
\(393\) 4.64255e8i 0.385818i
\(394\) 1.41622e8 + 8.17656e7i 0.116653 + 0.0673494i
\(395\) −9.95965e8 1.72506e9i −0.813120 1.40836i
\(396\) 8.99175e6 0.00727631
\(397\) −4.53054e8 −0.363399 −0.181699 0.983354i \(-0.558160\pi\)
−0.181699 + 0.983354i \(0.558160\pi\)
\(398\) 3.23171e8 + 5.59749e8i 0.256946 + 0.445044i
\(399\) 4.29151e8i 0.338224i
\(400\) 1.79850e8 3.11509e8i 0.140508 0.243366i
\(401\) 1.54661e9i 1.19778i 0.800833 + 0.598888i \(0.204391\pi\)
−0.800833 + 0.598888i \(0.795609\pi\)
\(402\) 2.20042e8 + 1.27041e8i 0.168933 + 0.0975336i
\(403\) 3.26262e8 5.65102e8i 0.248313 0.430090i
\(404\) 5.27231e8 9.13191e8i 0.397801 0.689012i
\(405\) 1.53962e9 8.88898e8i 1.15165 0.664905i
\(406\) −2.26243e8 −0.167778
\(407\) −7.57443e7 6.92341e7i −0.0556890 0.0509025i
\(408\) 9.00005e8 0.656046
\(409\) 7.10850e8 4.10409e8i 0.513743 0.296610i −0.220628 0.975358i \(-0.570811\pi\)
0.734371 + 0.678748i \(0.237477\pi\)
\(410\) −3.06579e8 + 5.31010e8i −0.219684 + 0.380504i
\(411\) 6.40379e8 1.10917e9i 0.454978 0.788045i
\(412\) 9.34050e8 + 5.39274e8i 0.658006 + 0.379900i
\(413\) 2.47328e9i 1.72762i
\(414\) 2.94629e7 5.10313e7i 0.0204068 0.0353456i
\(415\) 1.00188e9i 0.688096i
\(416\) −4.10029e8 7.10191e8i −0.279247 0.483669i
\(417\) 7.52639e8 0.508289
\(418\) 1.26627e7 0.00848026
\(419\) 4.73879e8 + 8.20782e8i 0.314716 + 0.545103i 0.979377 0.202041i \(-0.0647575\pi\)
−0.664661 + 0.747145i \(0.731424\pi\)
\(420\) −1.53065e9 8.83721e8i −1.00810 0.582027i
\(421\) 2.13523e9i 1.39462i 0.716767 + 0.697312i \(0.245621\pi\)
−0.716767 + 0.697312i \(0.754379\pi\)
\(422\) 4.69438e8 2.71030e8i 0.304077 0.175559i
\(423\) 6.96424e7 + 1.20624e8i 0.0447386 + 0.0774895i
\(424\) 4.07049e8 2.35010e8i 0.259338 0.149729i
\(425\) 5.72141e8 + 3.30326e8i 0.361528 + 0.208728i
\(426\) 5.44324e8 + 3.14266e8i 0.341133 + 0.196953i
\(427\) −1.69480e9 + 9.78492e8i −1.05347 + 0.608219i
\(428\) 8.26659e8 + 1.43181e9i 0.509651 + 0.882742i
\(429\) 6.87376e7 3.96857e7i 0.0420333 0.0242680i
\(430\) 9.46395e8i 0.574028i
\(431\) −4.68687e8 2.70596e8i −0.281976 0.162799i 0.352342 0.935871i \(-0.385386\pi\)
−0.634318 + 0.773072i \(0.718719\pi\)
\(432\) −4.75920e8 8.24317e8i −0.284015 0.491928i
\(433\) −1.52965e9 −0.905493 −0.452746 0.891639i \(-0.649556\pi\)
−0.452746 + 0.891639i \(0.649556\pi\)
\(434\) 5.43786e8 0.319311
\(435\) 4.68288e8 + 8.11099e8i 0.272773 + 0.472456i
\(436\) 2.50121e9i 1.44526i
\(437\) −2.60361e8 + 4.50959e8i −0.149242 + 0.258495i
\(438\) 4.91371e8i 0.279415i
\(439\) 1.32660e9 + 7.65915e8i 0.748368 + 0.432070i 0.825104 0.564981i \(-0.191117\pi\)
−0.0767359 + 0.997051i \(0.524450\pi\)
\(440\) −5.63063e7 + 9.75254e7i −0.0315118 + 0.0545800i
\(441\) −1.20297e7 + 2.08360e7i −0.00667912 + 0.0115686i
\(442\) 3.20423e8 1.84996e8i 0.176500 0.101903i
\(443\) 7.58752e8 0.414655 0.207328 0.978272i \(-0.433523\pi\)
0.207328 + 0.978272i \(0.433523\pi\)
\(444\) 3.61023e8 1.63809e9i 0.195747 0.888173i
\(445\) 3.00379e9 1.61588
\(446\) −1.13868e9 + 6.57418e8i −0.607757 + 0.350889i
\(447\) −7.11528e8 + 1.23240e9i −0.376804 + 0.652644i
\(448\) −2.68959e8 + 4.65850e8i −0.141323 + 0.244778i
\(449\) −3.61505e8 2.08715e8i −0.188474 0.108816i 0.402794 0.915291i \(-0.368039\pi\)
−0.591268 + 0.806475i \(0.701372\pi\)
\(450\) 3.71270e7i 0.0192064i
\(451\) −7.19964e7 + 1.24701e8i −0.0369567 + 0.0640108i
\(452\) 2.85479e9i 1.45408i
\(453\) 6.43449e8 + 1.11449e9i 0.325215 + 0.563288i
\(454\) 4.80067e8 0.240772
\(455\) −1.56898e9 −0.780870
\(456\) 2.23477e8 + 3.87074e8i 0.110371 + 0.191169i
\(457\) −1.77753e8 1.02626e8i −0.0871185 0.0502979i 0.455808 0.890078i \(-0.349350\pi\)
−0.542926 + 0.839780i \(0.682684\pi\)
\(458\) 7.80032e8i 0.379388i
\(459\) 1.51400e9 8.74110e8i 0.730773 0.421912i
\(460\) −1.07229e9 1.85726e9i −0.513641 0.889652i
\(461\) 1.04582e9 6.03802e8i 0.497166 0.287039i −0.230376 0.973102i \(-0.573996\pi\)
0.727543 + 0.686062i \(0.240662\pi\)
\(462\) 5.72831e7 + 3.30724e7i 0.0270259 + 0.0156034i
\(463\) −2.83697e8 1.63792e8i −0.132838 0.0766938i 0.432109 0.901822i \(-0.357770\pi\)
−0.564946 + 0.825128i \(0.691103\pi\)
\(464\) 4.83436e8 2.79112e8i 0.224660 0.129708i
\(465\) −1.12555e9 1.94952e9i −0.519136 0.899170i
\(466\) 3.61866e8 2.08923e8i 0.165652 0.0956392i
\(467\) 3.44950e9i 1.56728i −0.621214 0.783641i \(-0.713360\pi\)
0.621214 0.783641i \(-0.286640\pi\)
\(468\) 1.12995e8 + 6.52378e7i 0.0509565 + 0.0294197i
\(469\) −5.89751e8 1.02148e9i −0.263975 0.457219i
\(470\) −8.07832e8 −0.358904
\(471\) 3.83247e9 1.69007
\(472\) 1.28794e9 + 2.23078e9i 0.563766 + 0.976472i
\(473\) 2.22249e8i 0.0965666i
\(474\) −6.09265e8 + 1.05528e9i −0.262774 + 0.455138i
\(475\) 3.28088e8i 0.140463i
\(476\) −1.67561e9 9.67415e8i −0.712114 0.411139i
\(477\) −5.74667e7 + 9.95352e7i −0.0242439 + 0.0419916i
\(478\) −1.72045e8 + 2.97990e8i −0.0720516 + 0.124797i
\(479\) 3.36916e9 1.94518e9i 1.40071 0.808698i 0.406241 0.913766i \(-0.366839\pi\)
0.994465 + 0.105068i \(0.0335061\pi\)
\(480\) −2.82908e9 −1.16762
\(481\) −4.49530e8 1.41958e9i −0.184183 0.581637i
\(482\) 3.64648e8 0.148323
\(483\) −2.35563e9 + 1.36002e9i −0.951243 + 0.549200i
\(484\) 1.06962e9 1.85264e9i 0.428817 0.742733i
\(485\) −4.31371e8 + 7.47156e8i −0.171694 + 0.297382i
\(486\) −1.80878e8 1.04430e8i −0.0714756 0.0412665i
\(487\) 2.59058e9i 1.01636i 0.861252 + 0.508178i \(0.169681\pi\)
−0.861252 + 0.508178i \(0.830319\pi\)
\(488\) −1.01909e9 + 1.76511e9i −0.396955 + 0.687547i
\(489\) 1.25469e9i 0.485240i
\(490\) −6.97705e7 1.20846e8i −0.0267908 0.0464030i
\(491\) −2.28149e9 −0.869827 −0.434913 0.900472i \(-0.643221\pi\)
−0.434913 + 0.900472i \(0.643221\pi\)
\(492\) −2.35371e9 −0.890993
\(493\) 5.12638e8 + 8.87915e8i 0.192684 + 0.333739i
\(494\) 1.59126e8 + 9.18716e7i 0.0593878 + 0.0342876i
\(495\) 2.75371e7i 0.0102047i
\(496\) −1.16196e9 + 6.70860e8i −0.427569 + 0.246857i
\(497\) −1.45888e9 2.52686e9i −0.533056 0.923280i
\(498\) −5.30775e8 + 3.06443e8i −0.192578 + 0.111185i
\(499\) −3.41110e9 1.96940e9i −1.22897 0.709548i −0.262157 0.965025i \(-0.584434\pi\)
−0.966815 + 0.255478i \(0.917767\pi\)
\(500\) 1.35548e9 + 7.82586e8i 0.484951 + 0.279986i
\(501\) −4.58191e9 + 2.64537e9i −1.62785 + 0.939841i
\(502\) −6.51323e8 1.12812e9i −0.229791 0.398010i
\(503\) 4.15971e9 2.40161e9i 1.45739 0.841424i 0.458507 0.888691i \(-0.348384\pi\)
0.998882 + 0.0472669i \(0.0150511\pi\)
\(504\) 2.34794e8i 0.0816920i
\(505\) −2.79663e9 1.61463e9i −0.966307 0.557898i
\(506\) 4.01294e7 + 6.95061e7i 0.0137700 + 0.0238504i
\(507\) −1.94244e9 −0.661942
\(508\) 3.54869e9 1.20101
\(509\) −2.50346e9 4.33612e9i −0.841450 1.45743i −0.888669 0.458549i \(-0.848369\pi\)
0.0472192 0.998885i \(-0.484964\pi\)
\(510\) 1.27642e9i 0.426086i
\(511\) −1.14052e9 + 1.97544e9i −0.378120 + 0.654922i
\(512\) 2.95819e9i 0.974050i
\(513\) 7.51873e8 + 4.34094e8i 0.245886 + 0.141962i
\(514\) −5.37749e8 + 9.31408e8i −0.174666 + 0.302530i
\(515\) 1.65152e9 2.86051e9i 0.532792 0.922822i
\(516\) 3.14618e9 1.81645e9i 1.00811 0.582034i
\(517\) −1.89710e8 −0.0603772
\(518\) 8.37214e8 9.15939e8i 0.264656 0.289543i
\(519\) 4.62681e9 1.45277
\(520\) −1.41515e9 + 8.17038e8i −0.441358 + 0.254818i
\(521\) −2.16536e9 + 3.75051e9i −0.670808 + 1.16187i 0.306868 + 0.951752i \(0.400719\pi\)
−0.977675 + 0.210121i \(0.932614\pi\)
\(522\) 2.88090e7 4.98987e7i 0.00886507 0.0153547i
\(523\) 3.70639e9 + 2.13989e9i 1.13291 + 0.654086i 0.944665 0.328036i \(-0.106387\pi\)
0.188245 + 0.982122i \(0.439720\pi\)
\(524\) 1.03946e9i 0.315608i
\(525\) −8.56899e8 + 1.48419e9i −0.258447 + 0.447644i
\(526\) 1.36066e8i 0.0407663i
\(527\) −1.23215e9 2.13415e9i −0.366714 0.635166i
\(528\) −1.63203e8 −0.0482515
\(529\) 1.04383e8 0.0306573
\(530\) −3.33299e8 5.77291e8i −0.0972452 0.168434i
\(531\) −5.45490e8 3.14939e8i −0.158109 0.0912842i
\(532\) 9.60862e8i 0.276675i
\(533\) −1.80949e9 + 1.04471e9i −0.517620 + 0.298848i
\(534\) −9.18758e8 1.59133e9i −0.261100 0.452238i
\(535\) 4.38490e9 2.53163e9i 1.23800 0.714762i
\(536\) −1.06386e9 6.14217e8i −0.298405 0.172284i
\(537\) −1.27981e8 7.38897e7i −0.0356644 0.0205908i
\(538\) 6.51011e8 3.75861e8i 0.180240 0.104061i
\(539\) −1.63848e7 2.83792e7i −0.00450692 0.00780621i
\(540\) −3.09657e9 + 1.78780e9i −0.846257 + 0.488587i
\(541\) 6.43195e8i 0.174643i −0.996180 0.0873217i \(-0.972169\pi\)
0.996180 0.0873217i \(-0.0278308\pi\)
\(542\) −4.80199e8 2.77243e8i −0.129546 0.0747934i
\(543\) 3.71887e9 + 6.44127e9i 0.996808 + 1.72652i
\(544\) −3.09701e9 −0.824795
\(545\) 7.65990e9 2.02691
\(546\) 4.79900e8 + 8.31211e8i 0.126176 + 0.218543i
\(547\) 5.25471e9i 1.37276i 0.727245 + 0.686378i \(0.240800\pi\)
−0.727245 + 0.686378i \(0.759200\pi\)
\(548\) −1.43380e9 + 2.48341e9i −0.372183 + 0.644640i
\(549\) 4.98392e8i 0.128549i
\(550\) 4.37932e7 + 2.52840e7i 0.0112237 + 0.00648003i
\(551\) −2.54583e8 + 4.40950e8i −0.0648333 + 0.112295i
\(552\) −1.41644e9 + 2.45335e9i −0.358437 + 0.620830i
\(553\) 4.89880e9 2.82833e9i 1.23183 0.711199i
\(554\) −6.59048e8 −0.164677
\(555\) −5.01662e9 1.10563e9i −1.24562 0.274526i
\(556\) −1.68515e9 −0.415792
\(557\) −3.86018e8 + 2.22867e8i −0.0946486 + 0.0546454i −0.546577 0.837409i \(-0.684069\pi\)
0.451929 + 0.892054i \(0.350736\pi\)
\(558\) −6.92440e7 + 1.19934e8i −0.0168718 + 0.0292229i
\(559\) 1.61248e9 2.79291e9i 0.390440 0.676262i
\(560\) 2.79392e9 + 1.61307e9i 0.672290 + 0.388147i
\(561\) 2.99752e8i 0.0716789i
\(562\) −1.72224e8 + 2.98302e8i −0.0409277 + 0.0708889i
\(563\) 4.77628e8i 0.112800i −0.998408 0.0564002i \(-0.982038\pi\)
0.998408 0.0564002i \(-0.0179623\pi\)
\(564\) −1.55050e9 2.68554e9i −0.363910 0.630311i
\(565\) 8.74272e9 2.03928
\(566\) 1.41503e9 0.328026
\(567\) 2.52428e9 + 4.37218e9i 0.581563 + 1.00730i
\(568\) −2.63169e9 1.51941e9i −0.602581 0.347900i
\(569\) 1.68826e9i 0.384191i −0.981376 0.192095i \(-0.938472\pi\)
0.981376 0.192095i \(-0.0615283\pi\)
\(570\) 5.48961e8 3.16943e8i 0.124159 0.0716835i
\(571\) 1.08547e8 + 1.88009e8i 0.0244001 + 0.0422623i 0.877968 0.478720i \(-0.158899\pi\)
−0.853567 + 0.520982i \(0.825566\pi\)
\(572\) −1.53903e8 + 8.88557e7i −0.0343843 + 0.0198518i
\(573\) −5.24979e9 3.03097e9i −1.16574 0.673039i
\(574\) −1.50795e9 8.70618e8i −0.332810 0.192148i
\(575\) −1.80089e9 + 1.03974e9i −0.395048 + 0.228081i
\(576\) −6.84967e7 1.18640e8i −0.0149345 0.0258673i
\(577\) −2.14682e8 + 1.23947e8i −0.0465243 + 0.0268608i −0.523082 0.852283i \(-0.675218\pi\)
0.476557 + 0.879143i \(0.341884\pi\)
\(578\) 3.23887e8i 0.0697665i
\(579\) 5.71877e9 + 3.30173e9i 1.22441 + 0.706914i
\(580\) −1.04849e9 1.81604e9i −0.223134 0.386480i
\(581\) 2.84513e9 0.601847
\(582\) 5.27767e8 0.110972
\(583\) −7.82713e7 1.35570e8i −0.0163592 0.0283350i
\(584\) 2.37567e9i 0.493561i
\(585\) 1.99789e8 3.46045e8i 0.0412598 0.0714640i
\(586\) 3.24132e9i 0.665396i
\(587\) −1.35546e9 7.82574e8i −0.276600 0.159695i 0.355283 0.934759i \(-0.384385\pi\)
−0.631883 + 0.775063i \(0.717718\pi\)
\(588\) 2.67825e8 4.63887e8i 0.0543289 0.0941005i
\(589\) 6.11902e8 1.05985e9i 0.123390 0.213717i
\(590\) 3.16377e9 1.82660e9i 0.634195 0.366153i
\(591\) 1.92245e9 0.383087
\(592\) −6.58982e8 + 2.99004e9i −0.130541 + 0.592312i
\(593\) 2.59503e9 0.511036 0.255518 0.966804i \(-0.417754\pi\)
0.255518 + 0.966804i \(0.417754\pi\)
\(594\) 1.15886e8 6.69068e7i 0.0226871 0.0130984i
\(595\) −2.96269e9 + 5.13153e9i −0.576603 + 0.998706i
\(596\) 1.59310e9 2.75933e9i 0.308235 0.533878i
\(597\) 6.58032e9 + 3.79915e9i 1.26572 + 0.730762i
\(598\) 1.16460e9i 0.222701i
\(599\) 1.29751e9 2.24735e9i 0.246670 0.427246i −0.715930 0.698173i \(-0.753997\pi\)
0.962600 + 0.270927i \(0.0873302\pi\)
\(600\) 1.78490e9i 0.337353i
\(601\) −6.16628e8 1.06803e9i −0.115868 0.200689i 0.802259 0.596977i \(-0.203632\pi\)
−0.918126 + 0.396288i \(0.870298\pi\)
\(602\) 2.68756e9 0.502076
\(603\) 3.00388e8 0.0557920
\(604\) −1.44067e9 2.49532e9i −0.266033 0.460783i
\(605\) −5.67368e9 3.27570e9i −1.04165 0.601396i
\(606\) 1.97545e9i 0.360589i
\(607\) −2.42922e9 + 1.40251e9i −0.440867 + 0.254535i −0.703965 0.710234i \(-0.748589\pi\)
0.263098 + 0.964769i \(0.415256\pi\)
\(608\) −7.69007e8 1.33196e9i −0.138761 0.240341i
\(609\) −2.30334e9 + 1.32984e9i −0.413236 + 0.238582i
\(610\) 2.50334e9 + 1.44530e9i 0.446545 + 0.257813i
\(611\) −2.38399e9 1.37640e9i −0.422825 0.244118i
\(612\) 4.26734e8 2.46375e8i 0.0752536 0.0434477i
\(613\) −1.97694e9 3.42416e9i −0.346642 0.600402i 0.639008 0.769200i \(-0.279345\pi\)
−0.985651 + 0.168798i \(0.946012\pi\)
\(614\) 3.38065e9 1.95182e9i 0.589401 0.340291i
\(615\) 7.20818e9i 1.24958i
\(616\) −2.76951e8 1.59898e8i −0.0477387 0.0275619i
\(617\) −4.07654e9 7.06077e9i −0.698704 1.21019i −0.968916 0.247391i \(-0.920427\pi\)
0.270211 0.962801i \(-0.412906\pi\)
\(618\) −2.02057e9 −0.344362
\(619\) −5.51472e9 −0.934558 −0.467279 0.884110i \(-0.654766\pi\)
−0.467279 + 0.884110i \(0.654766\pi\)
\(620\) 2.52010e9 + 4.36494e9i 0.424665 + 0.735542i
\(621\) 5.50275e9i 0.922061i
\(622\) −5.86653e8 + 1.01611e9i −0.0977496 + 0.169307i
\(623\) 8.53010e9i 1.41334i
\(624\) −2.05090e9 1.18409e9i −0.337908 0.195091i
\(625\) 3.81059e9 6.60014e9i 0.624327 1.08137i
\(626\) −1.65568e8 + 2.86773e8i −0.0269754 + 0.0467227i
\(627\) 1.28917e8 7.44303e7i 0.0208869 0.0120591i
\(628\) −8.58085e9 −1.38252
\(629\) −5.49173e9 1.21034e9i −0.879896 0.193923i
\(630\) 3.32992e8 0.0530570
\(631\) −8.57232e9 + 4.94923e9i −1.35830 + 0.784214i −0.989395 0.145253i \(-0.953600\pi\)
−0.368905 + 0.929467i \(0.620267\pi\)
\(632\) 2.94566e9 5.10204e9i 0.464166 0.803959i
\(633\) 3.18618e9 5.51863e9i 0.499295 0.864805i
\(634\) 6.10767e6 + 3.52627e6i 0.000951839 + 0.000549544i
\(635\) 1.08678e10i 1.68435i
\(636\) 1.27942e9 2.21602e9i 0.197203 0.341566i
\(637\) 4.75505e8i 0.0728898i
\(638\) 3.92387e7 + 6.79635e7i 0.00598195 + 0.0103610i
\(639\) 7.43077e8 0.112663
\(640\) 8.13824e9 1.22716
\(641\) −3.29397e9 5.70533e9i −0.493989 0.855614i 0.505987 0.862541i \(-0.331128\pi\)
−0.999976 + 0.00692740i \(0.997795\pi\)
\(642\) −2.68239e9 1.54868e9i −0.400082 0.230988i
\(643\) 9.58757e9i 1.42223i 0.703075 + 0.711116i \(0.251810\pi\)
−0.703075 + 0.711116i \(0.748190\pi\)
\(644\) 5.27421e9 3.04507e9i 0.778139 0.449259i
\(645\) −5.56283e9 9.63510e9i −0.816275 1.41383i
\(646\) 6.00952e8 3.46960e8i 0.0877053 0.0506367i
\(647\) −1.14672e10 6.62061e9i −1.66454 0.961021i −0.970506 0.241076i \(-0.922500\pi\)
−0.694031 0.719945i \(-0.744167\pi\)
\(648\) 4.55356e9 + 2.62900e9i 0.657414 + 0.379558i
\(649\) 7.42973e8 4.28956e8i 0.106688 0.0615965i
\(650\) 3.66886e8 + 6.35465e8i 0.0524004 + 0.0907601i
\(651\) 5.53621e9 3.19633e9i 0.786464 0.454065i
\(652\) 2.80924e9i 0.396938i
\(653\) −1.44787e9 8.35928e8i −0.203485 0.117482i 0.394795 0.918769i \(-0.370816\pi\)
−0.598280 + 0.801287i \(0.704149\pi\)
\(654\) −2.34291e9 4.05804e9i −0.327516 0.567275i
\(655\) −3.18333e9 −0.442626
\(656\) 4.29626e9 0.594193
\(657\) −2.90460e8 5.03091e8i −0.0399583 0.0692098i
\(658\) 2.29407e9i 0.313918i
\(659\) −5.72213e9 + 9.91102e9i −0.778859 + 1.34902i 0.153741 + 0.988111i \(0.450868\pi\)
−0.932600 + 0.360912i \(0.882466\pi\)
\(660\) 6.13077e8i 0.0830064i
\(661\) 6.91922e9 + 3.99481e9i 0.931863 + 0.538011i 0.887400 0.461000i \(-0.152509\pi\)
0.0444626 + 0.999011i \(0.485842\pi\)
\(662\) −1.18567e9 + 2.05364e9i −0.158841 + 0.275120i
\(663\) 2.17479e9 3.76684e9i 0.289814 0.501972i
\(664\) 2.56618e9 1.48158e9i 0.340172 0.196398i
\(665\) −2.94262e9 −0.388024
\(666\) 9.54056e7 + 3.01283e8i 0.0125145 + 0.0395199i
\(667\) −3.22719e9 −0.421099
\(668\) 1.02588e10 5.92295e9i 1.33162 0.768812i
\(669\) −7.72849e9 + 1.33861e10i −0.997937 + 1.72848i
\(670\) −8.71104e8 + 1.50880e9i −0.111894 + 0.193807i
\(671\) 5.87879e8 + 3.39412e8i 0.0751206 + 0.0433709i
\(672\) 8.03396e9i 1.02126i
\(673\) −6.60708e9 + 1.14438e10i −0.835520 + 1.44716i 0.0580855 + 0.998312i \(0.481500\pi\)
−0.893606 + 0.448852i \(0.851833\pi\)
\(674\) 4.43565e9i 0.558018i
\(675\) 1.73354e9 + 3.00258e9i 0.216956 + 0.375778i
\(676\) 4.34910e9 0.541484
\(677\) 1.00405e10 1.24364 0.621821 0.783159i \(-0.286393\pi\)
0.621821 + 0.783159i \(0.286393\pi\)
\(678\) −2.67411e9 4.63169e9i −0.329515 0.570736i
\(679\) −2.12176e9 1.22500e9i −0.260107 0.150173i
\(680\) 6.17120e9i 0.752642i
\(681\) 4.88748e9 2.82179e9i 0.593022 0.342381i
\(682\) −9.43123e7 1.63354e8i −0.0113847 0.0197189i
\(683\) −9.27278e9 + 5.35364e9i −1.11362 + 0.642950i −0.939765 0.341821i \(-0.888956\pi\)
−0.173857 + 0.984771i \(0.555623\pi\)
\(684\) 2.11922e8 + 1.22353e8i 0.0253209 + 0.0146190i
\(685\) 7.60540e9 + 4.39098e9i 0.904077 + 0.521969i
\(686\) −2.52928e9 + 1.46028e9i −0.299132 + 0.172704i
\(687\) −4.58496e9 7.94139e9i −0.539495 0.934432i
\(688\) −5.74277e9 + 3.31559e9i −0.672298 + 0.388152i
\(689\) 2.27152e9i 0.264576i
\(690\) 3.47943e9 + 2.00885e9i 0.403214 + 0.232796i
\(691\) −2.74340e9 4.75171e9i −0.316313 0.547869i 0.663403 0.748262i \(-0.269111\pi\)
−0.979716 + 0.200393i \(0.935778\pi\)
\(692\) −1.03594e10 −1.18840
\(693\) 7.81993e7 0.00892558
\(694\) 1.79429e9 + 3.10781e9i 0.203768 + 0.352936i
\(695\) 5.16073e9i 0.583129i
\(696\) −1.38501e9 + 2.39890e9i −0.155711 + 0.269699i
\(697\) 7.89084e9i 0.882691i
\(698\) −4.58900e8 2.64946e8i −0.0510769 0.0294892i
\(699\) 2.45607e9 4.25403e9i 0.272001 0.471119i
\(700\) 1.91859e9 3.32309e9i 0.211416 0.366183i
\(701\) −3.19425e9 + 1.84420e9i −0.350232 + 0.202207i −0.664788 0.747032i \(-0.731478\pi\)
0.314555 + 0.949239i \(0.398145\pi\)
\(702\) 1.94171e9 0.211839
\(703\) −8.43090e8 2.66241e9i −0.0915230 0.289022i
\(704\) 1.86589e8 0.0201549
\(705\) −8.22442e9 + 4.74837e9i −0.883982 + 0.510367i
\(706\) −7.35339e8 + 1.27364e9i −0.0786450 + 0.136217i
\(707\) 4.58521e9 7.94182e9i 0.487968 0.845186i
\(708\) 1.21446e10 + 7.01171e9i 1.28608 + 0.742519i
\(709\) 1.62488e10i 1.71222i −0.516796 0.856108i \(-0.672875\pi\)
0.516796 0.856108i \(-0.327125\pi\)
\(710\) −2.15487e9 + 3.73235e9i −0.225953 + 0.391361i
\(711\) 1.44060e9i 0.150314i
\(712\) 4.44199e9 + 7.69375e9i 0.461209 + 0.798837i
\(713\) 7.75672e9 0.801428
\(714\) 3.62475e9 0.372679
\(715\) 2.72119e8 + 4.71324e8i 0.0278412 + 0.0482223i
\(716\) 2.86547e8 + 1.65438e8i 0.0291743 + 0.0168438i
\(717\) 4.04506e9i 0.409833i
\(718\) −3.94900e9 + 2.27995e9i −0.398154 + 0.229874i
\(719\) 2.68176e9 + 4.64495e9i 0.269072 + 0.466047i 0.968623 0.248537i \(-0.0799496\pi\)
−0.699550 + 0.714583i \(0.746616\pi\)
\(720\) −7.11538e8 + 4.10807e8i −0.0710452 + 0.0410179i
\(721\) 8.12322e9 + 4.68994e9i 0.807151 + 0.466009i
\(722\) −2.94864e9 1.70240e9i −0.291569 0.168337i
\(723\) 3.71242e9 2.14337e9i 0.365320 0.210917i
\(724\) −8.32650e9 1.44219e10i −0.815413 1.41234i
\(725\) −1.76092e9 + 1.01667e9i −0.171615 + 0.0990823i
\(726\) 4.00771e9i 0.388703i
\(727\) 1.44856e10 + 8.36329e9i 1.39819 + 0.807247i 0.994203 0.107516i \(-0.0342898\pi\)
0.403990 + 0.914763i \(0.367623\pi\)
\(728\) −2.32021e9 4.01872e9i −0.222878 0.386036i
\(729\) 9.04385e9 0.864583
\(730\) 3.36925e9 0.320556
\(731\) −6.08966e9 1.05476e10i −0.576610 0.998718i
\(732\) 1.10961e10i 1.04564i
\(733\) 9.09847e9 1.57590e10i 0.853305 1.47797i −0.0249035 0.999690i \(-0.507928\pi\)
0.878209 0.478278i \(-0.158739\pi\)
\(734\) 4.28692e9i 0.400137i
\(735\) −1.42065e9 8.20210e8i −0.131971 0.0761937i
\(736\) 4.87412e9 8.44222e9i 0.450634 0.780521i
\(737\) −2.04568e8 + 3.54323e8i −0.0188236 + 0.0326034i
\(738\) 3.84036e8 2.21723e8i 0.0351702 0.0203055i
\(739\) 4.14450e9 0.377760 0.188880 0.982000i \(-0.439514\pi\)
0.188880 + 0.982000i \(0.439514\pi\)
\(740\) 1.12321e10 + 2.47548e9i 1.01895 + 0.224568i
\(741\) 2.16005e9 0.195030
\(742\) 1.63938e9 9.46497e8i 0.147321 0.0850561i
\(743\) −9.20362e9 + 1.59411e10i −0.823185 + 1.42580i 0.0801128 + 0.996786i \(0.474472\pi\)
−0.903298 + 0.429013i \(0.858861\pi\)
\(744\) 3.32893e9 5.76588e9i 0.296347 0.513287i
\(745\) −8.45040e9 4.87884e9i −0.748739 0.432285i
\(746\) 3.64065e9i 0.321065i
\(747\) −3.62290e8 + 6.27505e8i −0.0318005 + 0.0550801i
\(748\) 6.71140e8i 0.0586351i
\(749\) 7.18927e9 + 1.24522e10i 0.625170 + 1.08283i
\(750\) −2.93222e9 −0.253795
\(751\) 1.19263e10 1.02746 0.513730 0.857952i \(-0.328263\pi\)
0.513730 + 0.857952i \(0.328263\pi\)
\(752\) 2.83015e9 + 4.90197e9i 0.242687 + 0.420347i
\(753\) −1.32620e10 7.65684e9i −1.13195 0.653532i
\(754\) 1.13875e9i 0.0967453i
\(755\) −7.64186e9 + 4.41203e9i −0.646227 + 0.373099i
\(756\) −5.07697e9 8.79358e9i −0.427345 0.740183i
\(757\) 2.09957e9 1.21219e9i 0.175912 0.101563i −0.409459 0.912329i \(-0.634282\pi\)
0.585371 + 0.810766i \(0.300949\pi\)
\(758\) −5.09922e9 2.94404e9i −0.425267 0.245528i
\(759\) 8.17102e8 + 4.71754e8i 0.0678313 + 0.0391624i
\(760\) −2.65411e9 + 1.53235e9i −0.219316 + 0.126622i
\(761\) −9.79673e9 1.69684e10i −0.805814 1.39571i −0.915740 0.401771i \(-0.868395\pi\)
0.109926 0.993940i \(-0.464939\pi\)
\(762\) −5.75750e9 + 3.32410e9i −0.471402 + 0.272164i
\(763\) 2.17525e10i 1.77285i
\(764\) 1.17542e10 + 6.78630e9i 0.953601 + 0.550562i
\(765\) −7.54519e8 1.30686e9i −0.0609333 0.105540i
\(766\) −3.18840e9 −0.256314
\(767\) 1.24488e10 0.996193
\(768\) −7.21200e8 1.24916e9i −0.0574502 0.0995067i
\(769\) 5.04629e9i 0.400156i 0.979780 + 0.200078i \(0.0641196\pi\)
−0.979780 + 0.200078i \(0.935880\pi\)
\(770\) −2.26773e8 + 3.92782e8i −0.0179008 + 0.0310051i
\(771\) 1.26434e10i 0.993510i
\(772\) −1.28042e10 7.39253e9i −1.00160 0.578273i
\(773\) 9.65837e9 1.67288e10i 0.752100 1.30268i −0.194703 0.980862i \(-0.562374\pi\)
0.946803 0.321813i \(-0.104292\pi\)
\(774\) −3.42225e8 + 5.92750e8i −0.0265288 + 0.0459493i
\(775\) 4.23246e9 2.44361e9i 0.326616 0.188572i
\(776\) −2.55164e9 −0.196021
\(777\) 3.13974e9 1.42461e10i 0.240115 1.08949i
\(778\) −3.64911e9 −0.277816
\(779\) −3.39369e9 + 1.95935e9i −0.257212 + 0.148501i
\(780\) −4.44805e9 + 7.70426e9i −0.335613 + 0.581299i
\(781\) −5.06046e8 + 8.76498e8i −0.0380112 + 0.0658373i
\(782\) 3.80895e9 + 2.19910e9i 0.284827 + 0.164445i
\(783\) 5.38062e9i 0.400559i
\(784\) −4.88867e8 + 8.46742e8i −0.0362313 + 0.0627545i
\(785\) 2.62787e10i 1.93892i
\(786\) 9.73673e8 + 1.68645e9i 0.0715211 + 0.123878i
\(787\) −3.88090e8 −0.0283805 −0.0141903 0.999899i \(-0.504517\pi\)
−0.0141903 + 0.999899i \(0.504517\pi\)
\(788\) −4.30433e9 −0.313375
\(789\) 7.99787e8 + 1.38527e9i 0.0579702 + 0.100407i
\(790\) −7.23588e9 4.17764e9i −0.522152 0.301464i
\(791\) 2.48274e10i 1.78367i
\(792\) 7.05321e7 4.07217e7i 0.00504485 0.00291265i
\(793\) 4.92507e9 + 8.53047e9i 0.350716 + 0.607459i
\(794\) −1.64576e9 + 9.50182e8i −0.116680 + 0.0673651i
\(795\) −6.78653e9 3.91821e9i −0.479030 0.276568i
\(796\) −1.47332e10 8.50624e9i −1.03539 0.597781i
\(797\) 5.53982e9 3.19842e9i 0.387607 0.223785i −0.293516 0.955954i \(-0.594825\pi\)
0.681123 + 0.732169i \(0.261492\pi\)
\(798\) 9.00049e8 + 1.55893e9i 0.0626984 + 0.108597i
\(799\) −9.00332e9 + 5.19807e9i −0.624438 + 0.360519i
\(800\) 6.14201e9i 0.424126i
\(801\) −1.88135e9 1.08620e9i −0.129347 0.0746782i
\(802\) 3.24368e9 + 5.61822e9i 0.222038 + 0.384581i
\(803\) 7.91229e8 0.0539259
\(804\) −6.68775e9 −0.453820
\(805\) −9.32546e9 1.61522e10i −0.630064 1.09130i
\(806\) 2.73705e9i 0.184124i
\(807\) 4.41856e9 7.65317e9i 0.295954 0.512607i
\(808\) 9.55087e9i 0.636947i
\(809\) −5.52856e9 3.19192e9i −0.367107 0.211949i 0.305087 0.952325i \(-0.401314\pi\)
−0.672194 + 0.740375i \(0.734648\pi\)
\(810\) 3.72854e9 6.45802e9i 0.246514 0.426974i
\(811\) 5.44469e9 9.43047e9i 0.358426 0.620813i −0.629272 0.777185i \(-0.716647\pi\)
0.987698 + 0.156373i \(0.0499801\pi\)
\(812\) 5.15716e9 2.97749e9i 0.338037 0.195166i
\(813\) −6.51844e9 −0.425429
\(814\) −4.20352e8 9.26425e7i −0.0273167 0.00602039i
\(815\) 8.60324e9 0.556686
\(816\) −7.74537e9 + 4.47179e9i −0.499030 + 0.288115i
\(817\) 3.02421e9 5.23808e9i 0.194014 0.336043i
\(818\) 1.72149e9 2.98170e9i 0.109968 0.190471i
\(819\) 9.82694e8 + 5.67358e8i 0.0625064 + 0.0360881i
\(820\) 1.61390e10i 1.02218i
\(821\) 1.06843e10 1.85057e10i 0.673821 1.16709i −0.302990 0.952994i \(-0.597985\pi\)
0.976812 0.214099i \(-0.0686816\pi\)
\(822\) 5.37222e9i 0.337367i
\(823\) −7.55701e9 1.30891e10i −0.472553 0.818485i 0.526954 0.849894i \(-0.323334\pi\)
−0.999507 + 0.0314085i \(0.990001\pi\)
\(824\) 9.76903e9 0.608283
\(825\) 5.94470e8 0.0368588
\(826\) 5.18715e9 + 8.98442e9i 0.320257 + 0.554702i
\(827\) −1.08638e10 6.27224e9i −0.667904 0.385615i 0.127378 0.991854i \(-0.459344\pi\)
−0.795282 + 0.606240i \(0.792677\pi\)
\(828\) 1.55100e9i 0.0949521i
\(829\) −1.92413e10 + 1.11090e10i −1.17299 + 0.677226i −0.954382 0.298587i \(-0.903485\pi\)
−0.218607 + 0.975813i \(0.570151\pi\)
\(830\) −2.10123e9 3.63944e9i −0.127556 0.220934i
\(831\) −6.70967e9 + 3.87383e9i −0.405599 + 0.234173i
\(832\) 2.34477e9 + 1.35376e9i 0.141146 + 0.0814908i
\(833\) −1.55519e9 8.97889e8i −0.0932236 0.0538227i
\(834\) 2.73403e9 1.57849e9i 0.163201 0.0942241i
\(835\) −1.81389e10 3.14175e10i −1.07822 1.86754i
\(836\) −2.88643e8 + 1.66648e8i −0.0170860 + 0.00986459i
\(837\) 1.29326e10i 0.762337i
\(838\) 3.44282e9 + 1.98771e9i 0.202097 + 0.116681i
\(839\) −9.06886e7 1.57077e8i −0.00530134 0.00918219i 0.863363 0.504584i \(-0.168354\pi\)
−0.868664 + 0.495402i \(0.835021\pi\)
\(840\) −1.60087e10 −0.931922
\(841\) 1.40943e10 0.817067
\(842\) 4.47818e9 + 7.75643e9i 0.258529 + 0.447785i
\(843\) 4.04928e9i 0.232799i
\(844\) −7.13381e9 + 1.23561e10i −0.408435 + 0.707431i
\(845\) 1.33190e10i 0.759405i
\(846\) 5.05965e8 + 2.92119e8i 0.0287293 + 0.0165868i
\(847\) 9.30228e9 1.61120e10i 0.526014 0.911083i
\(848\) −2.33535e9 + 4.04495e9i −0.131512 + 0.227786i
\(849\) 1.44062e10 8.31742e9i 0.807927 0.466457i
\(850\) 2.77114e9 0.154772
\(851\) 1.19423e10 1.30652e10i 0.664252 0.726713i
\(852\) −1.65437e10 −0.916417
\(853\) −1.66232e10 + 9.59742e9i −0.917051 + 0.529460i −0.882693 0.469950i \(-0.844272\pi\)
−0.0343580 + 0.999410i \(0.510939\pi\)
\(854\) −4.10435e9 + 7.10894e9i −0.225497 + 0.390573i
\(855\) 3.74704e8 6.49006e8i 0.0205025 0.0355114i
\(856\) 1.29688e10 + 7.48752e9i 0.706709 + 0.408019i
\(857\) 7.84995e9i 0.426024i 0.977050 + 0.213012i \(0.0683273\pi\)
−0.977050 + 0.213012i \(0.931673\pi\)
\(858\) 1.66464e8 2.88324e8i 0.00899736 0.0155839i
\(859\) 1.13403e8i 0.00610450i −0.999995 0.00305225i \(-0.999028\pi\)
0.999995 0.00305225i \(-0.000971563\pi\)
\(860\) 1.24551e10 + 2.15729e10i 0.667732 + 1.15655i
\(861\) −2.04697e10 −1.09295
\(862\) −2.27007e9 −0.120716
\(863\) −1.67169e9 2.89546e9i −0.0885358 0.153349i 0.818357 0.574711i \(-0.194885\pi\)
−0.906892 + 0.421362i \(0.861552\pi\)
\(864\) −1.40755e10 8.12651e9i −0.742449 0.428653i
\(865\) 3.17254e10i 1.66667i
\(866\) −5.55661e9 + 3.20811e9i −0.290735 + 0.167856i
\(867\) 1.90378e9 + 3.29745e9i 0.0992089 + 0.171835i
\(868\) −1.23955e10 + 7.15654e9i −0.643346 + 0.371436i
\(869\) −1.69926e9 9.81068e8i −0.0878397 0.0507143i
\(870\) 3.40220e9 + 1.96426e9i 0.175163 + 0.101131i
\(871\) −5.14143e9 + 2.96840e9i −0.263645 + 0.152216i
\(872\) 1.13274e10 + 1.96197e10i 0.578528 + 1.00204i
\(873\) 5.40356e8 3.11975e8i 0.0274872 0.0158697i
\(874\) 2.18420e9i 0.110663i
\(875\) 1.17883e10 + 6.80597e9i 0.594871 + 0.343449i
\(876\) 6.46672e9 + 1.12007e10i 0.325027 + 0.562963i
\(877\) 1.18023e10 0.590839 0.295420 0.955368i \(-0.404541\pi\)
0.295420 + 0.955368i \(0.404541\pi\)
\(878\) 6.42535e9 0.320381
\(879\) 1.90522e10 + 3.29994e10i 0.946202 + 1.63887i
\(880\) 1.11906e9i 0.0553560i
\(881\) −1.70658e10 + 2.95589e10i −0.840836 + 1.45637i 0.0483529 + 0.998830i \(0.484603\pi\)
−0.889189 + 0.457540i \(0.848731\pi\)
\(882\) 1.00918e8i 0.00495257i
\(883\) 1.29465e10 + 7.47465e9i 0.632833 + 0.365366i 0.781848 0.623469i \(-0.214277\pi\)
−0.149016 + 0.988835i \(0.547610\pi\)
\(884\) −4.86931e9 + 8.43390e9i −0.237075 + 0.410625i
\(885\) 2.14732e10 3.71927e10i 1.04135 1.80367i
\(886\) 2.75624e9 1.59132e9i 0.133137 0.0768668i
\(887\) 7.70123e9 0.370533 0.185267 0.982688i \(-0.440685\pi\)
0.185267 + 0.982688i \(0.440685\pi\)
\(888\) −4.58667e9 1.44843e10i −0.219812 0.694149i
\(889\) 3.08622e10 1.47323
\(890\) 1.09115e10 6.29978e9i 0.518825 0.299544i
\(891\) 8.75603e8 1.51659e9i 0.0414701 0.0718283i
\(892\) 1.73040e10 2.99714e10i 0.816336 1.41394i
\(893\) −4.47117e9 2.58143e9i −0.210107 0.121305i
\(894\) 5.96910e9i 0.279401i
\(895\) 5.06650e8 8.77544e8i 0.0236226 0.0409156i
\(896\) 2.31108e10i 1.07334i
\(897\) 6.84542e9 + 1.18566e10i 0.316685 + 0.548514i
\(898\) −1.75094e9 −0.0806869
\(899\) 7.58456e9 0.348154
\(900\) 4.88613e8 + 8.46302e8i 0.0223417 + 0.0386970i
\(901\) −7.42926e9 4.28928e9i −0.338383 0.195366i
\(902\) 6.03987e8i 0.0274034i
\(903\) 2.73616e10 1.57972e10i 1.23661 0.713960i
\(904\) 1.29287e10 + 2.23932e10i 0.582057 + 1.00815i
\(905\) −4.41668e10 + 2.54997e10i −1.98073 + 1.14358i
\(906\) 4.67478e9 + 2.69899e9i 0.208839 + 0.120573i
\(907\) −1.68183e10 9.71006e9i −0.748440 0.432112i 0.0766900 0.997055i \(-0.475565\pi\)
−0.825130 + 0.564943i \(0.808898\pi\)
\(908\) −1.09430e10 + 6.31795e9i −0.485106 + 0.280076i
\(909\) 1.16773e9 + 2.02257e9i 0.0515667 + 0.0893162i
\(910\) −5.69949e9 + 3.29060e9i −0.250721 + 0.144754i
\(911\) 3.61760e10i 1.58528i −0.609690 0.792640i \(-0.708706\pi\)
0.609690 0.792640i \(-0.291294\pi\)
\(912\) −3.84645e9 2.22075e9i −0.167911 0.0969433i
\(913\) −4.93449e8 8.54680e8i −0.0214583 0.0371668i
\(914\) −8.60940e8 −0.0372959
\(915\) 3.39815e10 1.46645
\(916\) 1.02657e10 + 1.77807e10i 0.441319 + 0.764387i
\(917\) 9.03996e9i 0.387145i
\(918\) 3.66651e9 6.35058e9i 0.156424 0.270934i
\(919\) 2.89899e10i 1.23209i 0.787711 + 0.616045i \(0.211266\pi\)
−0.787711 + 0.616045i \(0.788734\pi\)
\(920\) −1.68223e10 9.71234e9i −0.712241 0.411213i
\(921\) 2.29453e10 3.97424e10i 0.967797 1.67627i
\(922\) 2.53268e9 4.38674e9i 0.106420 0.184325i
\(923\) −1.27185e10 + 7.34302e9i −0.532390 + 0.307375i
\(924\) −1.74101e9 −0.0726020
\(925\) 2.40035e9 1.08912e10i 0.0997190 0.452461i
\(926\) −1.37407e9 −0.0568685
\(927\) −2.06877e9 + 1.19440e9i −0.0852969 + 0.0492462i
\(928\) 4.76594e9 8.25485e9i 0.195763 0.339072i
\(929\) −1.32831e10 + 2.30070e10i −0.543557 + 0.941468i 0.455139 + 0.890420i \(0.349589\pi\)
−0.998696 + 0.0510480i \(0.983744\pi\)
\(930\) −8.17737e9 4.72121e9i −0.333368 0.192470i
\(931\) 8.91807e8i 0.0362199i
\(932\) −5.49910e9 + 9.52472e9i −0.222503 + 0.385386i
\(933\) 1.37932e10i 0.556005i
\(934\) −7.23457e9 1.25306e10i −0.290535 0.503222i
\(935\) 2.05535e9 0.0822329
\(936\) 1.18179e9 0.0471059
\(937\) 8.49551e9 + 1.47147e10i 0.337366 + 0.584335i 0.983936 0.178520i \(-0.0571308\pi\)
−0.646571 + 0.762854i \(0.723797\pi\)
\(938\) −4.28465e9 2.47375e9i −0.169514 0.0978690i
\(939\) 3.89279e9i 0.153437i
\(940\) 1.84144e10 1.06315e10i 0.723118 0.417492i
\(941\) −7.91381e9 1.37071e10i −0.309615 0.536269i 0.668663 0.743565i \(-0.266867\pi\)
−0.978278 + 0.207297i \(0.933534\pi\)
\(942\) 1.39218e10 8.03777e9i 0.542648 0.313298i
\(943\) −2.15099e10 1.24187e10i −0.835309 0.482266i
\(944\) −2.21678e10 1.27986e10i −0.857672 0.495177i
\(945\) −2.69302e10 + 1.55481e10i −1.03807 + 0.599331i
\(946\) −4.66120e8 8.07343e8i −0.0179010 0.0310055i
\(947\) 1.45277e10 8.38754e9i 0.555867 0.320930i −0.195618 0.980680i \(-0.562671\pi\)
0.751485 + 0.659750i \(0.229338\pi\)
\(948\) 3.20731e10i 1.22268i
\(949\) 9.94300e9 + 5.74060e9i 0.377647 + 0.218035i
\(950\) 6.88093e8 + 1.19181e9i 0.0260384 + 0.0450998i
\(951\) 8.29084e7 0.00312584
\(952\) −1.75249e10 −0.658303
\(953\) 2.17036e10 + 3.75918e10i 0.812283 + 1.40692i 0.911263 + 0.411826i \(0.135109\pi\)
−0.0989795 + 0.995089i \(0.531558\pi\)
\(954\) 4.82095e8i 0.0179768i
\(955\) 2.07829e10 3.59970e10i 0.772137 1.33738i
\(956\) 9.05682e9i 0.335253i
\(957\) 7.98967e8 + 4.61284e8i 0.0294671 + 0.0170128i
\(958\) 8.15919e9 1.41321e10i 0.299825 0.519312i
\(959\) −1.24694e10 + 2.15977e10i −0.456543 + 0.790756i
\(960\) 8.08911e9 4.67025e9i 0.295088 0.170369i
\(961\) 9.28272e9 0.337399
\(962\) −4.61022e9 4.21397e9i −0.166959 0.152608i
\(963\) −3.66183e9 −0.132131
\(964\) −8.31206e9 + 4.79897e9i −0.298840 + 0.172535i
\(965\) −2.26395e10 + 3.92127e10i −0.811000 + 1.40469i
\(966\) −5.70469e9 + 9.88082e9i −0.203616 + 0.352674i
\(967\) 4.83679e9 + 2.79252e9i 0.172014 + 0.0993126i 0.583535 0.812088i \(-0.301669\pi\)
−0.411521 + 0.911400i \(0.635002\pi\)
\(968\) 1.93764e10i 0.686608i
\(969\) 4.07880e9 7.06468e9i 0.144012 0.249436i
\(970\) 3.61882e9i 0.127311i
\(971\) −1.07828e10 1.86764e10i −0.377977 0.654676i 0.612790 0.790245i \(-0.290047\pi\)
−0.990768 + 0.135569i \(0.956714\pi\)
\(972\) 5.49742e9 0.192011
\(973\) −1.46554e10 −0.510037
\(974\) 5.43318e9 + 9.41054e9i 0.188407 + 0.326331i
\(975\) 7.47042e9 + 4.31305e9i 0.258124 + 0.149028i
\(976\) 2.02538e10i 0.697322i
\(977\) −5.74079e9 + 3.31444e9i −0.196943 + 0.113705i −0.595229 0.803556i \(-0.702939\pi\)
0.398286 + 0.917261i \(0.369605\pi\)
\(978\) −2.63144e9 4.55780e9i −0.0899515 0.155800i
\(979\) 2.56245e9 1.47943e9i 0.0872801 0.0503912i
\(980\) 3.18080e9 + 1.83644e9i 0.107956 + 0.0623283i
\(981\) −4.79759e9 2.76989e9i −0.162249 0.0936743i
\(982\) −8.28772e9 + 4.78492e9i −0.279283 + 0.161244i
\(983\) −2.68447e9 4.64964e9i −0.0901409 0.156129i 0.817429 0.576029i \(-0.195398\pi\)
−0.907570 + 0.419900i \(0.862065\pi\)
\(984\) −1.84627e10 + 1.06594e10i −0.617749 + 0.356658i
\(985\) 1.31819e10i 0.439493i
\(986\) 3.72441e9 + 2.15029e9i 0.123734 + 0.0714378i
\(987\) −1.34843e10 2.33556e10i −0.446395 0.773179i
\(988\) −4.83633e9 −0.159539
\(989\) 3.83360e10 1.26014
\(990\) −5.77529e7 1.00031e8i −0.00189169 0.00327651i
\(991\) 1.77185e10i 0.578322i 0.957280 + 0.289161i \(0.0933763\pi\)
−0.957280 + 0.289161i \(0.906624\pi\)
\(992\) −1.14552e10 + 1.98410e10i −0.372573 + 0.645315i
\(993\) 2.78771e10i 0.903494i
\(994\) −1.05991e10 6.11937e9i −0.342306 0.197631i
\(995\) −2.60502e10 + 4.51203e10i −0.838359 + 1.45208i
\(996\) 8.06593e9 1.39706e10i 0.258670 0.448030i
\(997\) 8.71584e9 5.03209e9i 0.278533 0.160811i −0.354226 0.935160i \(-0.615256\pi\)
0.632759 + 0.774349i \(0.281922\pi\)
\(998\) −1.65215e10 −0.526130
\(999\) −2.17833e10 1.99111e10i −0.691266 0.631852i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 37.8.e.a.11.13 40
37.27 even 6 inner 37.8.e.a.27.13 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
37.8.e.a.11.13 40 1.1 even 1 trivial
37.8.e.a.27.13 yes 40 37.27 even 6 inner