Properties

Label 37.9.g.a.8.18
Level $37$
Weight $9$
Character 37.8
Analytic conductor $15.073$
Analytic rank $0$
Dimension $100$
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] = [37,9,Mod(8,37)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(37, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("37.8");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 37 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 37.g (of order \(12\), degree \(4\), 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: \(15.0730085723\)
Analytic rank: \(0\)
Dimension: \(100\)
Relative dimension: \(25\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 8.18
Character \(\chi\) \(=\) 37.8
Dual form 37.9.g.a.14.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(13.2543 + 3.55149i) q^{2} +(86.8010 + 50.1146i) q^{3} +(-58.6381 - 33.8547i) q^{4} +(964.131 - 258.338i) q^{5} +(972.509 + 972.509i) q^{6} +(1465.21 - 2537.82i) q^{7} +(-3140.90 - 3140.90i) q^{8} +(1742.45 + 3018.00i) q^{9} +O(q^{10})\) \(q+(13.2543 + 3.55149i) q^{2} +(86.8010 + 50.1146i) q^{3} +(-58.6381 - 33.8547i) q^{4} +(964.131 - 258.338i) q^{5} +(972.509 + 972.509i) q^{6} +(1465.21 - 2537.82i) q^{7} +(-3140.90 - 3140.90i) q^{8} +(1742.45 + 3018.00i) q^{9} +13696.4 q^{10} +3965.91i q^{11} +(-3393.23 - 5877.25i) q^{12} +(15470.9 - 4145.42i) q^{13} +(28433.5 - 28433.5i) q^{14} +(96634.1 + 25893.0i) q^{15} +(-21808.9 - 37774.1i) q^{16} +(-25897.5 + 96650.9i) q^{17} +(12376.5 + 46189.9i) q^{18} +(-199942. + 53574.2i) q^{19} +(-65280.8 - 17491.9i) q^{20} +(254364. - 146857. i) q^{21} +(-14084.9 + 52565.5i) q^{22} +(346204. + 346204. i) q^{23} +(-115229. - 430039. i) q^{24} +(524520. - 302832. i) q^{25} +219779. q^{26} -308316. i q^{27} +(-171835. + 99208.8i) q^{28} +(-473679. + 473679. i) q^{29} +(1.18886e6 + 686390. i) q^{30} +(382450. - 382450. i) q^{31} +(139402. + 520257. i) q^{32} +(-198750. + 344245. i) q^{33} +(-686509. + 1.18907e6i) q^{34} +(757041. - 2.82532e6i) q^{35} -235960. i q^{36} +(680804. + 1.74613e6i) q^{37} -2.84036e6 q^{38} +(1.55064e6 + 415492. i) q^{39} +(-3.83966e6 - 2.21683e6i) q^{40} +(-3.98057e6 - 2.29818e6i) q^{41} +(3.89299e6 - 1.04312e6i) q^{42} +(1.78609e6 + 1.78609e6i) q^{43} +(134265. - 232554. i) q^{44} +(2.45961e6 + 2.45961e6i) q^{45} +(3.35917e6 + 5.81825e6i) q^{46} -6.68425e6 q^{47} -4.37178e6i q^{48} +(-1.41130e6 - 2.44444e6i) q^{49} +(8.02766e6 - 2.15101e6i) q^{50} +(-7.09155e6 + 7.09155e6i) q^{51} +(-1.04753e6 - 280684. i) q^{52} +(-5.37863e6 - 9.31606e6i) q^{53} +(1.09498e6 - 4.08652e6i) q^{54} +(1.02455e6 + 3.82366e6i) q^{55} +(-1.25732e7 + 3.36897e6i) q^{56} +(-2.00400e7 - 5.36970e6i) q^{57} +(-7.96057e6 + 4.59604e6i) q^{58} +(-214451. + 800341. i) q^{59} +(-4.78984e6 - 4.78984e6i) q^{60} +(2.74098e6 + 1.02295e7i) q^{61} +(6.42740e6 - 3.71086e6i) q^{62} +1.02122e7 q^{63} +1.85569e7i q^{64} +(1.38451e7 - 7.99346e6i) q^{65} +(-3.85688e6 + 3.85688e6i) q^{66} +(2.08437e6 + 1.20341e6i) q^{67} +(4.79067e6 - 4.79067e6i) q^{68} +(1.27010e7 + 4.74008e7i) q^{69} +(2.00682e7 - 3.47591e7i) q^{70} +(2.13059e6 - 3.69029e6i) q^{71} +(4.00641e6 - 1.49521e7i) q^{72} -4.09453e7i q^{73} +(2.82223e6 + 2.55617e7i) q^{74} +6.07051e7 q^{75} +(1.35379e7 + 3.62748e6i) q^{76} +(1.00648e7 + 5.81090e6i) q^{77} +(1.90770e7 + 1.10141e7i) q^{78} +(2.28751e7 - 6.12935e6i) q^{79} +(-3.07852e7 - 3.07852e7i) q^{80} +(2.68833e7 - 4.65633e7i) q^{81} +(-4.45978e7 - 4.45978e7i) q^{82} +(8.84049e6 + 1.53122e7i) q^{83} -1.98872e7 q^{84} +9.98745e7i q^{85} +(1.73302e7 + 3.00167e7i) q^{86} +(-6.48541e7 + 1.73776e7i) q^{87} +(1.24565e7 - 1.24565e7i) q^{88} +(5.47148e7 + 1.46608e7i) q^{89} +(2.38652e7 + 4.13358e7i) q^{90} +(1.21478e7 - 4.53364e7i) q^{91} +(-8.58012e6 - 3.20214e7i) q^{92} +(5.23634e7 - 1.40307e7i) q^{93} +(-8.85953e7 - 2.37390e7i) q^{94} +(-1.78930e8 + 1.03305e8i) q^{95} +(-1.39722e7 + 5.21449e7i) q^{96} +(1.28065e7 + 1.28065e7i) q^{97} +(-1.00244e7 - 3.74117e7i) q^{98} +(-1.19691e7 + 6.91038e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100 q - 10 q^{2} - 6 q^{3} + 552 q^{4} - 1642 q^{5} - 516 q^{6} - 2 q^{7} - 7440 q^{8} + 117258 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 100 q - 10 q^{2} - 6 q^{3} + 552 q^{4} - 1642 q^{5} - 516 q^{6} - 2 q^{7} - 7440 q^{8} + 117258 q^{9} + 10744 q^{10} - 62086 q^{12} - 63598 q^{13} - 62648 q^{14} + 53318 q^{15} + 1056692 q^{16} - 53050 q^{17} - 150954 q^{18} - 161388 q^{19} - 922330 q^{20} + 589656 q^{21} - 713044 q^{22} + 32888 q^{23} - 1193742 q^{24} + 1859250 q^{25} + 900088 q^{26} - 7001094 q^{28} + 2288858 q^{29} + 9620658 q^{30} + 5782072 q^{31} - 4920832 q^{32} - 719444 q^{33} - 5308306 q^{34} - 10575422 q^{35} + 14052530 q^{37} - 10994096 q^{38} + 3417088 q^{39} + 9928698 q^{40} + 16320936 q^{41} + 39067848 q^{42} - 9546800 q^{43} - 19056984 q^{44} - 12333970 q^{45} - 15608210 q^{46} - 844736 q^{47} - 54639310 q^{49} - 52548004 q^{50} + 25866216 q^{51} + 31025896 q^{52} - 17856728 q^{53} + 8699372 q^{54} - 14191504 q^{55} - 23168766 q^{56} + 74736160 q^{57} + 109856484 q^{58} + 499856 q^{59} - 286204560 q^{60} - 34778024 q^{61} + 6537756 q^{62} + 154042660 q^{63} - 107386782 q^{65} - 14426072 q^{66} + 84112848 q^{67} + 247473908 q^{68} - 74383808 q^{69} - 55414618 q^{70} - 57046730 q^{71} - 172153588 q^{72} + 315393932 q^{74} + 164078200 q^{75} - 141128756 q^{76} + 272235456 q^{77} + 655339260 q^{78} + 18584140 q^{79} + 43263824 q^{80} - 337954862 q^{81} - 363936872 q^{82} - 86956118 q^{83} - 505940536 q^{84} + 41750098 q^{86} + 195776154 q^{87} + 425134052 q^{88} + 253234298 q^{89} - 139130828 q^{90} - 327702612 q^{91} - 572151958 q^{92} - 608615132 q^{93} - 502568260 q^{94} - 115562040 q^{95} + 1165361934 q^{96} - 123302218 q^{97} + 537492294 q^{98} + 533594376 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 13.2543 + 3.55149i 0.828396 + 0.221968i 0.648014 0.761629i \(-0.275600\pi\)
0.180382 + 0.983597i \(0.442267\pi\)
\(3\) 86.8010 + 50.1146i 1.07162 + 0.618699i 0.928623 0.371025i \(-0.120994\pi\)
0.142995 + 0.989723i \(0.454327\pi\)
\(4\) −58.6381 33.8547i −0.229055 0.132245i
\(5\) 964.131 258.338i 1.54261 0.413341i 0.615502 0.788135i \(-0.288953\pi\)
0.927108 + 0.374794i \(0.122287\pi\)
\(6\) 972.509 + 972.509i 0.750392 + 0.750392i
\(7\) 1465.21 2537.82i 0.610251 1.05699i −0.380947 0.924597i \(-0.624402\pi\)
0.991198 0.132389i \(-0.0422648\pi\)
\(8\) −3140.90 3140.90i −0.766822 0.766822i
\(9\) 1742.45 + 3018.00i 0.265576 + 0.459991i
\(10\) 13696.4 1.36964
\(11\) 3965.91i 0.270877i 0.990786 + 0.135439i \(0.0432443\pi\)
−0.990786 + 0.135439i \(0.956756\pi\)
\(12\) −3393.23 5877.25i −0.163640 0.283432i
\(13\) 15470.9 4145.42i 0.541680 0.145143i 0.0224033 0.999749i \(-0.492868\pi\)
0.519276 + 0.854606i \(0.326202\pi\)
\(14\) 28433.5 28433.5i 0.740147 0.740147i
\(15\) 96634.1 + 25893.0i 1.90882 + 0.511467i
\(16\) −21808.9 37774.1i −0.332777 0.576387i
\(17\) −25897.5 + 96650.9i −0.310072 + 1.15720i 0.618418 + 0.785849i \(0.287774\pi\)
−0.928491 + 0.371356i \(0.878893\pi\)
\(18\) 12376.5 + 46189.9i 0.117899 + 0.440004i
\(19\) −199942. + 53574.2i −1.53422 + 0.411094i −0.924394 0.381439i \(-0.875429\pi\)
−0.609829 + 0.792533i \(0.708762\pi\)
\(20\) −65280.8 17491.9i −0.408005 0.109325i
\(21\) 254364. 146857.i 1.30791 0.755123i
\(22\) −14084.9 + 52565.5i −0.0601261 + 0.224393i
\(23\) 346204. + 346204.i 1.23715 + 1.23715i 0.961162 + 0.275985i \(0.0890040\pi\)
0.275985 + 0.961162i \(0.410996\pi\)
\(24\) −115229. 430039.i −0.347308 1.29617i
\(25\) 524520. 302832.i 1.34277 0.775249i
\(26\) 219779. 0.480942
\(27\) 308316.i 0.580151i
\(28\) −171835. + 99208.8i −0.279562 + 0.161405i
\(29\) −473679. + 473679.i −0.669719 + 0.669719i −0.957651 0.287932i \(-0.907032\pi\)
0.287932 + 0.957651i \(0.407032\pi\)
\(30\) 1.18886e6 + 686390.i 1.46773 + 0.847395i
\(31\) 382450. 382450.i 0.414122 0.414122i −0.469050 0.883172i \(-0.655403\pi\)
0.883172 + 0.469050i \(0.155403\pi\)
\(32\) 139402. + 520257.i 0.132944 + 0.496156i
\(33\) −198750. + 344245.i −0.167591 + 0.290277i
\(34\) −686509. + 1.18907e6i −0.513725 + 0.889798i
\(35\) 757041. 2.82532e6i 0.504484 1.88276i
\(36\) 235960.i 0.140485i
\(37\) 680804. + 1.74613e6i 0.363258 + 0.931689i
\(38\) −2.84036e6 −1.36219
\(39\) 1.55064e6 + 415492.i 0.670273 + 0.179599i
\(40\) −3.83966e6 2.21683e6i −1.49987 0.865949i
\(41\) −3.98057e6 2.29818e6i −1.40867 0.813297i −0.413411 0.910545i \(-0.635663\pi\)
−0.995260 + 0.0972478i \(0.968996\pi\)
\(42\) 3.89299e6 1.04312e6i 1.25108 0.335227i
\(43\) 1.78609e6 + 1.78609e6i 0.522432 + 0.522432i 0.918305 0.395873i \(-0.129558\pi\)
−0.395873 + 0.918305i \(0.629558\pi\)
\(44\) 134265. 232554.i 0.0358221 0.0620458i
\(45\) 2.45961e6 + 2.45961e6i 0.599814 + 0.599814i
\(46\) 3.35917e6 + 5.81825e6i 0.750241 + 1.29945i
\(47\) −6.68425e6 −1.36981 −0.684906 0.728631i \(-0.740157\pi\)
−0.684906 + 0.728631i \(0.740157\pi\)
\(48\) 4.37178e6i 0.823556i
\(49\) −1.41130e6 2.44444e6i −0.244813 0.424029i
\(50\) 8.02766e6 2.15101e6i 1.28443 0.344161i
\(51\) −7.09155e6 + 7.09155e6i −1.04824 + 1.04824i
\(52\) −1.04753e6 280684.i −0.143269 0.0383888i
\(53\) −5.37863e6 9.31606e6i −0.681660 1.18067i −0.974474 0.224501i \(-0.927925\pi\)
0.292814 0.956170i \(-0.405408\pi\)
\(54\) 1.09498e6 4.08652e6i 0.128775 0.480595i
\(55\) 1.02455e6 + 3.82366e6i 0.111965 + 0.417858i
\(56\) −1.25732e7 + 3.36897e6i −1.27847 + 0.342566i
\(57\) −2.00400e7 5.36970e6i −1.89844 0.508687i
\(58\) −7.96057e6 + 4.59604e6i −0.703448 + 0.406136i
\(59\) −214451. + 800341.i −0.0176978 + 0.0660491i −0.974210 0.225643i \(-0.927552\pi\)
0.956512 + 0.291692i \(0.0942183\pi\)
\(60\) −4.78984e6 4.78984e6i −0.369586 0.369586i
\(61\) 2.74098e6 + 1.02295e7i 0.197964 + 0.738813i 0.991480 + 0.130263i \(0.0415820\pi\)
−0.793515 + 0.608550i \(0.791751\pi\)
\(62\) 6.42740e6 3.71086e6i 0.434979 0.251135i
\(63\) 1.02122e7 0.648273
\(64\) 1.85569e7i 1.10608i
\(65\) 1.38451e7 7.99346e6i 0.775607 0.447797i
\(66\) −3.85688e6 + 3.85688e6i −0.203264 + 0.203264i
\(67\) 2.08437e6 + 1.20341e6i 0.103437 + 0.0597194i 0.550826 0.834620i \(-0.314313\pi\)
−0.447389 + 0.894339i \(0.647646\pi\)
\(68\) 4.79067e6 4.79067e6i 0.224058 0.224058i
\(69\) 1.27010e7 + 4.74008e7i 0.560327 + 2.09117i
\(70\) 2.00682e7 3.47591e7i 0.835825 1.44769i
\(71\) 2.13059e6 3.69029e6i 0.0838430 0.145220i −0.821055 0.570850i \(-0.806614\pi\)
0.904898 + 0.425629i \(0.139947\pi\)
\(72\) 4.00641e6 1.49521e7i 0.149082 0.556381i
\(73\) 4.09453e7i 1.44182i −0.693027 0.720912i \(-0.743723\pi\)
0.693027 0.720912i \(-0.256277\pi\)
\(74\) 2.82223e6 + 2.55617e7i 0.0941166 + 0.852439i
\(75\) 6.07051e7 1.91858
\(76\) 1.35379e7 + 3.62748e6i 0.405787 + 0.108730i
\(77\) 1.00648e7 + 5.81090e6i 0.286313 + 0.165303i
\(78\) 1.90770e7 + 1.10141e7i 0.515386 + 0.297558i
\(79\) 2.28751e7 6.12935e6i 0.587292 0.157364i 0.0470766 0.998891i \(-0.485010\pi\)
0.540215 + 0.841527i \(0.318343\pi\)
\(80\) −3.07852e7 3.07852e7i −0.751591 0.751591i
\(81\) 2.68833e7 4.65633e7i 0.624515 1.08169i
\(82\) −4.45978e7 4.45978e7i −0.986412 0.986412i
\(83\) 8.84049e6 + 1.53122e7i 0.186279 + 0.322645i 0.944007 0.329926i \(-0.107024\pi\)
−0.757728 + 0.652571i \(0.773690\pi\)
\(84\) −1.98872e7 −0.399445
\(85\) 9.98745e7i 1.91328i
\(86\) 1.73302e7 + 3.00167e7i 0.316817 + 0.548744i
\(87\) −6.48541e7 + 1.73776e7i −1.13204 + 0.303328i
\(88\) 1.24565e7 1.24565e7i 0.207715 0.207715i
\(89\) 5.47148e7 + 1.46608e7i 0.872056 + 0.233667i 0.666977 0.745079i \(-0.267588\pi\)
0.205080 + 0.978745i \(0.434255\pi\)
\(90\) 2.38652e7 + 4.13358e7i 0.363744 + 0.630023i
\(91\) 1.21478e7 4.53364e7i 0.177147 0.661121i
\(92\) −8.58012e6 3.20214e7i −0.119768 0.446981i
\(93\) 5.23634e7 1.40307e7i 0.699997 0.187564i
\(94\) −8.85953e7 2.37390e7i −1.13475 0.304055i
\(95\) −1.78930e8 + 1.03305e8i −2.19679 + 1.26832i
\(96\) −1.39722e7 + 5.21449e7i −0.164505 + 0.613942i
\(97\) 1.28065e7 + 1.28065e7i 0.144658 + 0.144658i 0.775727 0.631069i \(-0.217383\pi\)
−0.631069 + 0.775727i \(0.717383\pi\)
\(98\) −1.00244e7 3.74117e7i −0.108681 0.405605i
\(99\) −1.19691e7 + 6.91038e6i −0.124601 + 0.0719385i
\(100\) −4.10091e7 −0.410091
\(101\) 5.30884e7i 0.510169i −0.966919 0.255084i \(-0.917897\pi\)
0.966919 0.255084i \(-0.0821032\pi\)
\(102\) −1.19179e8 + 6.88083e7i −1.10103 + 0.635682i
\(103\) −7.02788e6 + 7.02788e6i −0.0624418 + 0.0624418i −0.737638 0.675196i \(-0.764059\pi\)
0.675196 + 0.737638i \(0.264059\pi\)
\(104\) −6.16130e7 3.55723e7i −0.526671 0.304073i
\(105\) 2.07302e8 2.07302e8i 1.70547 1.70547i
\(106\) −3.82043e7 1.42580e8i −0.302614 1.12937i
\(107\) 1.80031e7 3.11823e7i 0.137345 0.237888i −0.789146 0.614206i \(-0.789476\pi\)
0.926491 + 0.376317i \(0.122810\pi\)
\(108\) −1.04380e7 + 1.80791e7i −0.0767221 + 0.132887i
\(109\) −1.42548e7 + 5.31995e7i −0.100984 + 0.376878i −0.997859 0.0654069i \(-0.979165\pi\)
0.896874 + 0.442285i \(0.145832\pi\)
\(110\) 5.43187e7i 0.371004i
\(111\) −2.84123e7 + 1.85684e8i −0.187161 + 1.22316i
\(112\) −1.27819e8 −0.812311
\(113\) −4.64593e7 1.24487e7i −0.284944 0.0763505i 0.113516 0.993536i \(-0.463789\pi\)
−0.398460 + 0.917186i \(0.630455\pi\)
\(114\) −2.46546e8 1.42344e8i −1.45975 0.842788i
\(115\) 4.23224e8 + 2.44349e8i 2.41980 + 1.39707i
\(116\) 4.38119e7 1.17394e7i 0.241969 0.0648355i
\(117\) 3.94681e7 + 3.94681e7i 0.210622 + 0.210622i
\(118\) −5.68481e6 + 9.84637e6i −0.0293216 + 0.0507865i
\(119\) 2.07338e8 + 2.07338e8i 1.03393 + 1.03393i
\(120\) −2.22191e8 3.84846e8i −1.07152 1.85593i
\(121\) 1.98630e8 0.926626
\(122\) 1.45320e8i 0.655971i
\(123\) −2.30345e8 3.98969e8i −1.00637 1.74309i
\(124\) −3.53739e7 + 9.47842e6i −0.149622 + 0.0400912i
\(125\) 1.51773e8 1.51773e8i 0.621660 0.621660i
\(126\) 1.35356e8 + 3.62686e7i 0.537027 + 0.143896i
\(127\) −2.97708e7 5.15645e7i −0.114439 0.198215i 0.803116 0.595823i \(-0.203174\pi\)
−0.917555 + 0.397608i \(0.869840\pi\)
\(128\) −3.02176e7 + 1.12774e8i −0.112569 + 0.420115i
\(129\) 6.55253e7 + 2.44544e8i 0.236619 + 0.883075i
\(130\) 2.11896e8 5.67773e7i 0.741907 0.198793i
\(131\) −4.97337e8 1.33261e8i −1.68875 0.452500i −0.718685 0.695336i \(-0.755256\pi\)
−0.970067 + 0.242836i \(0.921922\pi\)
\(132\) 2.33087e7 1.34573e7i 0.0767753 0.0443262i
\(133\) −1.56995e8 + 5.85914e8i −0.501741 + 1.87252i
\(134\) 2.33531e7 + 2.33531e7i 0.0724310 + 0.0724310i
\(135\) −7.96498e7 2.97257e8i −0.239800 0.894947i
\(136\) 3.84913e8 2.22230e8i 1.12514 0.649600i
\(137\) 5.20584e7 0.147778 0.0738888 0.997266i \(-0.476459\pi\)
0.0738888 + 0.997266i \(0.476459\pi\)
\(138\) 6.73374e8i 1.85669i
\(139\) −8.32637e7 + 4.80723e7i −0.223047 + 0.128776i −0.607360 0.794426i \(-0.707772\pi\)
0.384313 + 0.923203i \(0.374438\pi\)
\(140\) −1.40042e8 + 1.40042e8i −0.364540 + 0.364540i
\(141\) −5.80199e8 3.34978e8i −1.46791 0.847501i
\(142\) 4.13456e7 4.13456e7i 0.101689 0.101689i
\(143\) 1.64404e7 + 6.13563e7i 0.0393158 + 0.146729i
\(144\) 7.60016e7 1.31639e8i 0.176756 0.306150i
\(145\) −3.34320e8 + 5.79059e8i −0.756293 + 1.30994i
\(146\) 1.45417e8 5.42702e8i 0.320039 1.19440i
\(147\) 2.82907e8i 0.605862i
\(148\) 1.91938e7 1.25438e8i 0.0400050 0.261447i
\(149\) 6.58326e8 1.33566 0.667830 0.744314i \(-0.267223\pi\)
0.667830 + 0.744314i \(0.267223\pi\)
\(150\) 8.04606e8 + 2.15594e8i 1.58935 + 0.425864i
\(151\) −3.94810e8 2.27944e8i −0.759417 0.438450i 0.0696694 0.997570i \(-0.477806\pi\)
−0.829086 + 0.559121i \(0.811139\pi\)
\(152\) 7.96268e8 + 4.59726e8i 1.49171 + 0.861241i
\(153\) −3.36818e8 + 9.02501e7i −0.614652 + 0.164696i
\(154\) 1.12765e8 + 1.12765e8i 0.200489 + 0.200489i
\(155\) 2.69931e8 4.67534e8i 0.467655 0.810003i
\(156\) −7.68601e7 7.68601e7i −0.129778 0.129778i
\(157\) 1.79923e8 + 3.11636e8i 0.296134 + 0.512918i 0.975248 0.221114i \(-0.0709693\pi\)
−0.679114 + 0.734032i \(0.737636\pi\)
\(158\) 3.24962e8 0.521440
\(159\) 1.07819e9i 1.68697i
\(160\) 2.68804e8 + 4.65583e8i 0.410163 + 0.710423i
\(161\) 1.38587e9 3.71343e8i 2.06262 0.552677i
\(162\) 5.21689e8 5.21689e8i 0.757447 0.757447i
\(163\) 3.44998e8 + 9.24419e7i 0.488726 + 0.130954i 0.494763 0.869028i \(-0.335255\pi\)
−0.00603661 + 0.999982i \(0.501922\pi\)
\(164\) 1.55609e8 + 2.69522e8i 0.215109 + 0.372580i
\(165\) −1.02689e8 + 3.83242e8i −0.138545 + 0.517056i
\(166\) 6.27938e7 + 2.34350e8i 0.0826960 + 0.308626i
\(167\) −1.02508e9 + 2.74669e8i −1.31792 + 0.353137i −0.848200 0.529676i \(-0.822314\pi\)
−0.469725 + 0.882813i \(0.655647\pi\)
\(168\) −1.26020e9 3.37669e8i −1.58198 0.423891i
\(169\) −4.84279e8 + 2.79599e8i −0.593675 + 0.342758i
\(170\) −3.54703e8 + 1.32377e9i −0.424687 + 1.58496i
\(171\) −5.10074e8 5.10074e8i −0.596553 0.596553i
\(172\) −4.42654e7 1.65201e8i −0.0505767 0.188755i
\(173\) −1.26631e9 + 7.31104e8i −1.41369 + 0.816197i −0.995734 0.0922681i \(-0.970588\pi\)
−0.417961 + 0.908465i \(0.637255\pi\)
\(174\) −9.21314e8 −1.00510
\(175\) 1.77485e9i 1.89239i
\(176\) 1.49809e8 8.64922e7i 0.156130 0.0901418i
\(177\) −5.87233e7 + 5.87233e7i −0.0598298 + 0.0598298i
\(178\) 6.73140e8 + 3.88638e8i 0.670541 + 0.387137i
\(179\) −1.27936e9 + 1.27936e9i −1.24618 + 1.24618i −0.288789 + 0.957393i \(0.593253\pi\)
−0.957393 + 0.288789i \(0.906747\pi\)
\(180\) −6.09575e7 2.27497e8i −0.0580680 0.216713i
\(181\) 9.72827e8 1.68499e9i 0.906403 1.56994i 0.0873794 0.996175i \(-0.472151\pi\)
0.819023 0.573760i \(-0.194516\pi\)
\(182\) 3.22023e8 5.57761e8i 0.293496 0.508349i
\(183\) −2.74726e8 + 1.02529e9i −0.244961 + 0.914205i
\(184\) 2.17479e9i 1.89734i
\(185\) 1.10748e9 + 1.50763e9i 0.945471 + 1.28708i
\(186\) 7.43873e8 0.621508
\(187\) −3.83309e8 1.02707e8i −0.313460 0.0839914i
\(188\) 3.91952e8 + 2.26293e8i 0.313762 + 0.181151i
\(189\) −7.82452e8 4.51749e8i −0.613211 0.354038i
\(190\) −2.73848e9 + 7.33774e8i −2.10134 + 0.563051i
\(191\) 1.22511e9 + 1.22511e9i 0.920541 + 0.920541i 0.997068 0.0765264i \(-0.0243829\pi\)
−0.0765264 + 0.997068i \(0.524383\pi\)
\(192\) −9.29972e8 + 1.61076e9i −0.684329 + 1.18529i
\(193\) −5.21021e8 5.21021e8i −0.375514 0.375514i 0.493967 0.869481i \(-0.335546\pi\)
−0.869481 + 0.493967i \(0.835546\pi\)
\(194\) 1.24259e8 + 2.15223e8i 0.0877246 + 0.151943i
\(195\) 1.60236e9 1.10821
\(196\) 1.91117e8i 0.129501i
\(197\) −6.32526e8 1.09557e9i −0.419966 0.727402i 0.575970 0.817471i \(-0.304625\pi\)
−0.995936 + 0.0900691i \(0.971291\pi\)
\(198\) −1.83185e8 + 4.90843e7i −0.119187 + 0.0319361i
\(199\) 1.13782e9 1.13782e9i 0.725542 0.725542i −0.244186 0.969728i \(-0.578521\pi\)
0.969728 + 0.244186i \(0.0785207\pi\)
\(200\) −2.59863e9 6.96301e8i −1.62414 0.435188i
\(201\) 1.20617e8 + 2.08915e8i 0.0738966 + 0.127993i
\(202\) 1.88543e8 7.03651e8i 0.113241 0.422622i
\(203\) 5.08073e8 + 1.89616e9i 0.299187 + 1.11658i
\(204\) 6.55918e8 1.75753e8i 0.378729 0.101480i
\(205\) −4.43150e9 1.18742e9i −2.50920 0.672338i
\(206\) −1.18109e8 + 6.81904e7i −0.0655866 + 0.0378664i
\(207\) −4.41604e8 + 1.64809e9i −0.240520 + 0.897634i
\(208\) −4.93993e8 4.93993e8i −0.263917 0.263917i
\(209\) −2.12470e8 7.92950e8i −0.111356 0.415586i
\(210\) 3.48387e9 2.01142e9i 1.79137 1.03425i
\(211\) −2.51796e8 −0.127034 −0.0635169 0.997981i \(-0.520232\pi\)
−0.0635169 + 0.997981i \(0.520232\pi\)
\(212\) 7.28368e8i 0.360585i
\(213\) 3.69875e8 2.13547e8i 0.179695 0.103747i
\(214\) 3.49363e8 3.49363e8i 0.166580 0.166580i
\(215\) 2.18344e9 + 1.26061e9i 1.02185 + 0.589966i
\(216\) −9.68391e8 + 9.68391e8i −0.444873 + 0.444873i
\(217\) −4.10220e8 1.53096e9i −0.185003 0.690440i
\(218\) −3.77875e8 + 6.54498e8i −0.167310 + 0.289789i
\(219\) 2.05196e9 3.55409e9i 0.892055 1.54508i
\(220\) 6.93715e7 2.58898e8i 0.0296135 0.110519i
\(221\) 1.60263e9i 0.671839i
\(222\) −1.03604e9 + 2.36022e9i −0.426546 + 0.971718i
\(223\) −8.84740e8 −0.357764 −0.178882 0.983871i \(-0.557248\pi\)
−0.178882 + 0.983871i \(0.557248\pi\)
\(224\) 1.52457e9 + 4.08508e8i 0.605559 + 0.162259i
\(225\) 1.82789e9 + 1.05533e9i 0.713216 + 0.411775i
\(226\) −5.71576e8 3.30000e8i −0.219099 0.126497i
\(227\) 2.58649e8 6.93048e7i 0.0974108 0.0261011i −0.209784 0.977748i \(-0.567276\pi\)
0.307195 + 0.951647i \(0.400610\pi\)
\(228\) 9.93317e8 + 9.93317e8i 0.367577 + 0.367577i
\(229\) 1.75694e9 3.04311e9i 0.638875 1.10656i −0.346805 0.937937i \(-0.612734\pi\)
0.985680 0.168626i \(-0.0539331\pi\)
\(230\) 4.74176e9 + 4.74176e9i 1.69445 + 1.69445i
\(231\) 5.82422e8 + 1.00878e9i 0.204546 + 0.354283i
\(232\) 2.97556e9 1.02711
\(233\) 4.45113e9i 1.51024i −0.655586 0.755121i \(-0.727578\pi\)
0.655586 0.755121i \(-0.272422\pi\)
\(234\) 3.82953e8 + 6.63294e8i 0.127727 + 0.221229i
\(235\) −6.44449e9 + 1.72680e9i −2.11309 + 0.566200i
\(236\) 3.96703e7 3.96703e7i 0.0127884 0.0127884i
\(237\) 2.29275e9 + 6.14340e8i 0.726713 + 0.194722i
\(238\) 2.01176e9 + 3.48448e9i 0.627003 + 1.08600i
\(239\) −7.38431e8 + 2.75586e9i −0.226317 + 0.844628i 0.755555 + 0.655085i \(0.227367\pi\)
−0.981872 + 0.189543i \(0.939299\pi\)
\(240\) −1.12940e9 4.21497e9i −0.340410 1.27043i
\(241\) 4.02091e8 1.07740e8i 0.119194 0.0319381i −0.198729 0.980055i \(-0.563681\pi\)
0.317923 + 0.948116i \(0.397015\pi\)
\(242\) 2.63271e9 + 7.05434e8i 0.767613 + 0.205681i
\(243\) 2.91515e9 1.68306e9i 0.836057 0.482697i
\(244\) 1.85590e8 6.92633e8i 0.0523596 0.195409i
\(245\) −1.99217e9 1.99217e9i −0.552920 0.552920i
\(246\) −1.63613e9 6.10614e9i −0.446765 1.66735i
\(247\) −2.87119e9 + 1.65768e9i −0.771390 + 0.445362i
\(248\) −2.40248e9 −0.635116
\(249\) 1.77215e9i 0.461003i
\(250\) 2.55066e9 1.47263e9i 0.652970 0.376992i
\(251\) 4.70031e9 4.70031e9i 1.18422 1.18422i 0.205577 0.978641i \(-0.434093\pi\)
0.978641 0.205577i \(-0.0659071\pi\)
\(252\) −5.98825e8 3.45732e8i −0.148490 0.0857309i
\(253\) −1.37302e9 + 1.37302e9i −0.335115 + 0.335115i
\(254\) −2.11461e8 7.89184e8i −0.0508038 0.189602i
\(255\) −5.00517e9 + 8.66921e9i −1.18374 + 2.05031i
\(256\) 1.57425e9 2.72669e9i 0.366535 0.634857i
\(257\) 4.30864e8 1.60801e9i 0.0987660 0.368600i −0.898797 0.438364i \(-0.855558\pi\)
0.997564 + 0.0697643i \(0.0222247\pi\)
\(258\) 3.47398e9i 0.784058i
\(259\) 5.42890e9 + 8.30697e8i 1.20646 + 0.184605i
\(260\) −1.08247e9 −0.236876
\(261\) −2.25493e9 6.04206e8i −0.485926 0.130203i
\(262\) −6.11860e9 3.53258e9i −1.29852 0.749698i
\(263\) 3.62488e9 + 2.09283e9i 0.757654 + 0.437432i 0.828453 0.560059i \(-0.189222\pi\)
−0.0707989 + 0.997491i \(0.522555\pi\)
\(264\) 1.70550e9 4.56986e8i 0.351103 0.0940778i
\(265\) −7.59240e9 7.59240e9i −1.53956 1.53956i
\(266\) −4.16173e9 + 7.20833e9i −0.831281 + 1.43982i
\(267\) 4.01458e9 + 4.01458e9i 0.789941 + 0.789941i
\(268\) −8.14824e7 1.41132e8i −0.0157952 0.0273581i
\(269\) −2.36986e9 −0.452600 −0.226300 0.974058i \(-0.572663\pi\)
−0.226300 + 0.974058i \(0.572663\pi\)
\(270\) 4.22282e9i 0.794598i
\(271\) 4.56336e9 + 7.90397e9i 0.846073 + 1.46544i 0.884687 + 0.466186i \(0.154372\pi\)
−0.0386140 + 0.999254i \(0.512294\pi\)
\(272\) 4.21570e9 1.12959e9i 0.770183 0.206370i
\(273\) 3.32646e9 3.32646e9i 0.598869 0.598869i
\(274\) 6.90000e8 + 1.84885e8i 0.122418 + 0.0328019i
\(275\) 1.20100e9 + 2.08020e9i 0.209997 + 0.363726i
\(276\) 8.59978e8 3.20948e9i 0.148201 0.553094i
\(277\) −5.60085e8 2.09027e9i −0.0951338 0.355044i 0.901906 0.431933i \(-0.142168\pi\)
−0.997040 + 0.0768884i \(0.975501\pi\)
\(278\) −1.27433e9 + 3.41457e8i −0.213356 + 0.0571684i
\(279\) 1.82064e9 + 4.87838e8i 0.300474 + 0.0805116i
\(280\) −1.12518e10 + 6.49625e9i −1.83059 + 1.05689i
\(281\) 8.72872e8 3.25760e9i 0.139999 0.522484i −0.859928 0.510415i \(-0.829492\pi\)
0.999927 0.0120684i \(-0.00384158\pi\)
\(282\) −6.50049e9 6.50049e9i −1.02790 1.02790i
\(283\) 2.88332e8 + 1.07607e9i 0.0449518 + 0.167762i 0.984753 0.173960i \(-0.0556564\pi\)
−0.939801 + 0.341722i \(0.888990\pi\)
\(284\) −2.49868e8 + 1.44261e8i −0.0384093 + 0.0221756i
\(285\) −2.07084e10 −3.13882
\(286\) 8.71624e8i 0.130276i
\(287\) −1.16648e10 + 6.73465e9i −1.71929 + 0.992631i
\(288\) −1.32724e9 + 1.32724e9i −0.192920 + 0.192920i
\(289\) −2.62953e9 1.51816e9i −0.376953 0.217634i
\(290\) −6.48770e9 + 6.48770e9i −0.917274 + 0.917274i
\(291\) 4.69823e8 + 1.75340e9i 0.0655183 + 0.244518i
\(292\) −1.38619e9 + 2.40095e9i −0.190674 + 0.330257i
\(293\) 4.41594e9 7.64864e9i 0.599174 1.03780i −0.393769 0.919209i \(-0.628829\pi\)
0.992943 0.118591i \(-0.0378377\pi\)
\(294\) 1.00474e9 3.74974e9i 0.134482 0.501894i
\(295\) 8.27035e8i 0.109203i
\(296\) 3.34610e9 7.62278e9i 0.435885 0.992994i
\(297\) 1.22275e9 0.157150
\(298\) 8.72568e9 + 2.33804e9i 1.10646 + 0.296474i
\(299\) 6.79126e9 + 3.92094e9i 0.849700 + 0.490575i
\(300\) −3.55963e9 2.05516e9i −0.439461 0.253723i
\(301\) 7.14979e9 1.91578e9i 0.871018 0.233389i
\(302\) −4.42340e9 4.42340e9i −0.531776 0.531776i
\(303\) 2.66050e9 4.60812e9i 0.315641 0.546706i
\(304\) 6.38422e9 + 6.38422e9i 0.747504 + 0.747504i
\(305\) 5.28534e9 + 9.15447e9i 0.610764 + 1.05787i
\(306\) −4.78482e9 −0.545732
\(307\) 2.41168e9i 0.271498i 0.990743 + 0.135749i \(0.0433441\pi\)
−0.990743 + 0.135749i \(0.956656\pi\)
\(308\) −3.93453e8 6.81481e8i −0.0437210 0.0757270i
\(309\) −9.62226e8 + 2.57828e8i −0.105546 + 0.0282811i
\(310\) 5.23820e9 5.23820e9i 0.567199 0.567199i
\(311\) 1.23011e10 + 3.29607e9i 1.31493 + 0.352334i 0.847076 0.531472i \(-0.178361\pi\)
0.467853 + 0.883806i \(0.345028\pi\)
\(312\) −3.56538e9 6.17542e9i −0.376260 0.651701i
\(313\) 2.94398e9 1.09871e10i 0.306731 1.14473i −0.624715 0.780853i \(-0.714785\pi\)
0.931445 0.363881i \(-0.118549\pi\)
\(314\) 1.27799e9 + 4.76952e9i 0.131464 + 0.490632i
\(315\) 9.84592e9 2.63821e9i 1.00003 0.267958i
\(316\) −1.54886e9 4.15015e8i −0.155333 0.0416213i
\(317\) −6.18029e9 + 3.56819e9i −0.612028 + 0.353355i −0.773759 0.633480i \(-0.781626\pi\)
0.161731 + 0.986835i \(0.448292\pi\)
\(318\) 3.82918e9 1.42907e10i 0.374453 1.39748i
\(319\) −1.87857e9 1.87857e9i −0.181411 0.181411i
\(320\) 4.79396e9 + 1.78913e10i 0.457187 + 1.70625i
\(321\) 3.12538e9 1.80444e9i 0.294363 0.169950i
\(322\) 1.96876e10 1.83134
\(323\) 2.07120e10i 1.90288i
\(324\) −3.15277e9 + 1.82025e9i −0.286097 + 0.165178i
\(325\) 6.85943e9 6.85943e9i 0.614830 0.614830i
\(326\) 4.24441e9 + 2.45051e9i 0.375791 + 0.216963i
\(327\) −3.90340e9 + 3.90340e9i −0.341391 + 0.341391i
\(328\) 5.28421e9 + 1.97210e10i 0.456546 + 1.70385i
\(329\) −9.79385e9 + 1.69634e10i −0.835930 + 1.44787i
\(330\) −2.72216e9 + 4.71492e9i −0.229540 + 0.397575i
\(331\) 3.03886e9 1.13412e10i 0.253162 0.944812i −0.715942 0.698160i \(-0.754003\pi\)
0.969104 0.246653i \(-0.0793307\pi\)
\(332\) 1.19717e9i 0.0985380i
\(333\) −4.08358e9 + 5.09721e9i −0.332096 + 0.414530i
\(334\) −1.45622e10 −1.17015
\(335\) 2.32050e9 + 6.21775e8i 0.184248 + 0.0493690i
\(336\) −1.10948e10 6.40559e9i −0.870487 0.502576i
\(337\) −3.01661e9 1.74164e9i −0.233883 0.135033i 0.378479 0.925610i \(-0.376447\pi\)
−0.612362 + 0.790577i \(0.709781\pi\)
\(338\) −7.41179e9 + 1.98598e9i −0.567879 + 0.152163i
\(339\) −3.40885e9 3.40885e9i −0.258113 0.258113i
\(340\) 3.38122e9 5.85645e9i 0.253022 0.438247i
\(341\) 1.51676e9 + 1.51676e9i 0.112176 + 0.112176i
\(342\) −4.94917e9 8.57222e9i −0.361766 0.626598i
\(343\) 8.62191e9 0.622912
\(344\) 1.12199e10i 0.801225i
\(345\) 2.44909e10 + 4.24194e10i 1.72873 + 2.99425i
\(346\) −1.93806e10 + 5.19302e9i −1.35227 + 0.362339i
\(347\) −1.79535e10 + 1.79535e10i −1.23832 + 1.23832i −0.277626 + 0.960689i \(0.589548\pi\)
−0.960689 + 0.277626i \(0.910452\pi\)
\(348\) 4.39124e9 + 1.17663e9i 0.299412 + 0.0802273i
\(349\) −2.78062e8 4.81618e8i −0.0187431 0.0324639i 0.856502 0.516144i \(-0.172633\pi\)
−0.875245 + 0.483680i \(0.839300\pi\)
\(350\) 6.30337e9 2.35245e10i 0.420049 1.56765i
\(351\) −1.27810e9 4.76993e9i −0.0842046 0.314256i
\(352\) −2.06329e9 + 5.52857e8i −0.134397 + 0.0360116i
\(353\) −1.64906e10 4.41865e9i −1.06203 0.284571i −0.314817 0.949152i \(-0.601943\pi\)
−0.747216 + 0.664581i \(0.768610\pi\)
\(354\) −9.86894e8 + 5.69783e8i −0.0628431 + 0.0362825i
\(355\) 1.10083e9 4.10834e9i 0.0693115 0.258674i
\(356\) −2.71203e9 2.71203e9i −0.168848 0.168848i
\(357\) 7.60647e9 + 2.83878e10i 0.468285 + 1.74766i
\(358\) −2.15007e10 + 1.24135e10i −1.30894 + 0.755720i
\(359\) 2.65373e10 1.59764 0.798821 0.601569i \(-0.205457\pi\)
0.798821 + 0.601569i \(0.205457\pi\)
\(360\) 1.54508e10i 0.919901i
\(361\) 2.23982e10 1.29316e10i 1.31882 0.761420i
\(362\) 1.88784e10 1.88784e10i 1.09934 1.09934i
\(363\) 1.72413e10 + 9.95428e9i 0.992988 + 0.573302i
\(364\) −2.24718e9 + 2.24718e9i −0.128006 + 0.128006i
\(365\) −1.05777e10 3.94766e10i −0.595965 2.22417i
\(366\) −7.28263e9 + 1.26139e10i −0.405849 + 0.702951i
\(367\) −9.48648e9 + 1.64311e10i −0.522926 + 0.905735i 0.476718 + 0.879056i \(0.341826\pi\)
−0.999644 + 0.0266787i \(0.991507\pi\)
\(368\) 5.52723e9 2.06279e10i 0.301381 1.12477i
\(369\) 1.60178e10i 0.863969i
\(370\) 9.32458e9 + 2.39158e10i 0.497533 + 1.27608i
\(371\) −3.15233e10 −1.66394
\(372\) −3.54550e9 9.50014e8i −0.185142 0.0496087i
\(373\) 2.75339e10 + 1.58967e10i 1.42244 + 0.821244i 0.996507 0.0835116i \(-0.0266136\pi\)
0.425930 + 0.904756i \(0.359947\pi\)
\(374\) −4.71574e9 2.72263e9i −0.241026 0.139156i
\(375\) 2.07800e10 5.56799e9i 1.05080 0.281562i
\(376\) 2.09946e10 + 2.09946e10i 1.05040 + 1.05040i
\(377\) −5.36465e9 + 9.29185e9i −0.265568 + 0.459978i
\(378\) −8.76650e9 8.76650e9i −0.429397 0.429397i
\(379\) −1.70667e10 2.95604e10i −0.827166 1.43269i −0.900253 0.435367i \(-0.856618\pi\)
0.0730872 0.997326i \(-0.476715\pi\)
\(380\) 1.39895e10 0.670914
\(381\) 5.96780e9i 0.283214i
\(382\) 1.18871e10 + 2.05891e10i 0.558242 + 0.966903i
\(383\) 1.41066e10 3.77985e9i 0.655582 0.175663i 0.0843305 0.996438i \(-0.473125\pi\)
0.571251 + 0.820775i \(0.306458\pi\)
\(384\) −8.27453e9 + 8.27453e9i −0.380556 + 0.380556i
\(385\) 1.12050e10 + 3.00236e9i 0.509996 + 0.136653i
\(386\) −5.05539e9 8.75619e9i −0.227722 0.394426i
\(387\) −2.27826e9 + 8.50259e9i −0.101569 + 0.379060i
\(388\) −3.17387e8 1.18451e9i −0.0140043 0.0522649i
\(389\) −6.71302e9 + 1.79875e9i −0.293170 + 0.0785547i −0.402406 0.915461i \(-0.631826\pi\)
0.109236 + 0.994016i \(0.465159\pi\)
\(390\) 2.12382e10 + 5.69075e9i 0.918033 + 0.245986i
\(391\) −4.24268e10 + 2.44951e10i −1.81524 + 1.04803i
\(392\) −3.24500e9 + 1.21105e10i −0.137427 + 0.512883i
\(393\) −3.64911e10 3.64911e10i −1.52974 1.52974i
\(394\) −4.49282e9 1.67674e10i −0.186438 0.695796i
\(395\) 2.04711e10 1.18190e10i 0.840917 0.485504i
\(396\) 9.35796e8 0.0380540
\(397\) 2.88531e10i 1.16153i −0.814071 0.580765i \(-0.802753\pi\)
0.814071 0.580765i \(-0.197247\pi\)
\(398\) 1.91221e10 1.10401e10i 0.762084 0.439989i
\(399\) −4.29902e10 + 4.29902e10i −1.69620 + 1.69620i
\(400\) −2.28784e10 1.32089e10i −0.893687 0.515971i
\(401\) −2.67906e10 + 2.67906e10i −1.03611 + 1.03611i −0.0367861 + 0.999323i \(0.511712\pi\)
−0.999323 + 0.0367861i \(0.988288\pi\)
\(402\) 8.56741e8 + 3.19740e9i 0.0328054 + 0.122431i
\(403\) 4.33144e9 7.50227e9i 0.164215 0.284428i
\(404\) −1.79729e9 + 3.11300e9i −0.0674673 + 0.116857i
\(405\) 1.38900e10 5.18381e10i 0.516275 1.92677i
\(406\) 2.69367e10i 0.991380i
\(407\) −6.92501e9 + 2.70001e9i −0.252373 + 0.0983983i
\(408\) 4.45478e10 1.60763
\(409\) −3.62524e10 9.71379e9i −1.29552 0.347133i −0.455763 0.890101i \(-0.650634\pi\)
−0.839753 + 0.542968i \(0.817300\pi\)
\(410\) −5.45195e10 3.14768e10i −1.92937 1.11392i
\(411\) 4.51873e9 + 2.60889e9i 0.158361 + 0.0914299i
\(412\) 6.50028e8 1.74175e8i 0.0225602 0.00604499i
\(413\) 1.71691e9 + 1.71691e9i 0.0590129 + 0.0590129i
\(414\) −1.17063e10 + 2.02760e10i −0.398492 + 0.690208i
\(415\) 1.24791e10 + 1.24791e10i 0.420719 + 0.420719i
\(416\) 4.31336e9 + 7.47097e9i 0.144027 + 0.249461i
\(417\) −9.63650e9 −0.318695
\(418\) 1.12646e10i 0.368987i
\(419\) −7.32416e8 1.26858e9i −0.0237630 0.0411588i 0.853899 0.520438i \(-0.174231\pi\)
−0.877662 + 0.479279i \(0.840898\pi\)
\(420\) −1.91739e10 + 5.13763e9i −0.616188 + 0.165107i
\(421\) 5.67663e9 5.67663e9i 0.180702 0.180702i −0.610960 0.791662i \(-0.709216\pi\)
0.791662 + 0.610960i \(0.209216\pi\)
\(422\) −3.33739e9 8.94251e8i −0.105234 0.0281974i
\(423\) −1.16469e10 2.01731e10i −0.363789 0.630102i
\(424\) −1.23671e10 + 4.61546e10i −0.382652 + 1.42808i
\(425\) 1.56852e10 + 5.85379e10i 0.480766 + 1.79424i
\(426\) 5.66086e9 1.51682e9i 0.171887 0.0460571i
\(427\) 2.99768e10 + 8.03225e9i 0.901723 + 0.241616i
\(428\) −2.11134e9 + 1.21898e9i −0.0629191 + 0.0363264i
\(429\) −1.64780e9 + 6.14969e9i −0.0486493 + 0.181562i
\(430\) 2.44630e10 + 2.44630e10i 0.715544 + 0.715544i
\(431\) 8.87935e9 + 3.31382e10i 0.257319 + 0.960328i 0.966786 + 0.255589i \(0.0822694\pi\)
−0.709466 + 0.704739i \(0.751064\pi\)
\(432\) −1.16464e10 + 6.72403e9i −0.334392 + 0.193061i
\(433\) −2.31372e9 −0.0658203 −0.0329101 0.999458i \(-0.510478\pi\)
−0.0329101 + 0.999458i \(0.510478\pi\)
\(434\) 2.17488e10i 0.613022i
\(435\) −5.80386e10 + 3.35086e10i −1.62091 + 0.935834i
\(436\) 2.63693e9 2.63693e9i 0.0729713 0.0729713i
\(437\) −8.77683e10 5.06730e10i −2.40664 1.38948i
\(438\) 3.98196e10 3.98196e10i 1.08193 1.08193i
\(439\) −1.29872e10 4.84689e10i −0.349669 1.30498i −0.887062 0.461651i \(-0.847257\pi\)
0.537393 0.843332i \(-0.319409\pi\)
\(440\) 8.79174e9 1.52277e10i 0.234566 0.406280i
\(441\) 4.91822e9 8.51861e9i 0.130033 0.225224i
\(442\) −5.69174e9 + 2.12418e10i −0.149127 + 0.556549i
\(443\) 1.06993e10i 0.277806i −0.990306 0.138903i \(-0.955642\pi\)
0.990306 0.138903i \(-0.0443576\pi\)
\(444\) 7.95234e9 9.92630e9i 0.204627 0.255420i
\(445\) 5.65397e10 1.44183
\(446\) −1.17266e10 3.14215e9i −0.296370 0.0794121i
\(447\) 5.71434e10 + 3.29918e10i 1.43132 + 0.826371i
\(448\) 4.70942e10 + 2.71898e10i 1.16911 + 0.674985i
\(449\) 3.18743e10 8.54070e9i 0.784252 0.210140i 0.155593 0.987821i \(-0.450271\pi\)
0.628658 + 0.777681i \(0.283604\pi\)
\(450\) 2.04795e10 + 2.04795e10i 0.499424 + 0.499424i
\(451\) 9.11439e9 1.57866e10i 0.220303 0.381577i
\(452\) 2.30284e9 + 2.30284e9i 0.0551709 + 0.0551709i
\(453\) −2.28466e10 3.95715e10i −0.542536 0.939701i
\(454\) 3.67435e9 0.0864884
\(455\) 4.68485e10i 1.09307i
\(456\) 4.60779e10 + 7.98093e10i 1.06570 + 1.84584i
\(457\) −7.72683e9 + 2.07040e9i −0.177148 + 0.0474667i −0.346303 0.938123i \(-0.612563\pi\)
0.169155 + 0.985590i \(0.445896\pi\)
\(458\) 3.40947e10 3.40947e10i 0.774863 0.774863i
\(459\) 2.97990e10 + 7.98462e9i 0.671353 + 0.179889i
\(460\) −1.65447e10 2.86563e10i −0.369512 0.640013i
\(461\) 1.73256e10 6.46602e10i 0.383606 1.43164i −0.456746 0.889597i \(-0.650985\pi\)
0.840352 0.542041i \(-0.182348\pi\)
\(462\) 4.13693e9 + 1.54392e10i 0.0908052 + 0.338889i
\(463\) −1.91944e10 + 5.14313e9i −0.417687 + 0.111919i −0.461541 0.887119i \(-0.652703\pi\)
0.0438537 + 0.999038i \(0.486036\pi\)
\(464\) 2.82232e10 + 7.56240e9i 0.608885 + 0.163150i
\(465\) 4.68606e10 2.70550e10i 1.00230 0.578675i
\(466\) 1.58081e10 5.89968e10i 0.335225 1.25108i
\(467\) −8.66503e9 8.66503e9i −0.182181 0.182181i 0.610125 0.792305i \(-0.291119\pi\)
−0.792305 + 0.610125i \(0.791119\pi\)
\(468\) −9.78153e8 3.65052e9i −0.0203903 0.0760976i
\(469\) 6.10810e9 3.52651e9i 0.126245 0.0728877i
\(470\) −9.15502e10 −1.87615
\(471\) 3.60670e10i 0.732870i
\(472\) 3.18736e9 1.84023e9i 0.0642190 0.0370769i
\(473\) −7.08348e9 + 7.08348e9i −0.141515 + 0.141515i
\(474\) 2.82070e10 + 1.62853e10i 0.558784 + 0.322614i
\(475\) −8.86493e10 + 8.86493e10i −1.74141 + 1.74141i
\(476\) −5.13853e9 1.91772e10i −0.100095 0.373558i
\(477\) 1.87439e10 3.24654e10i 0.362065 0.627116i
\(478\) −1.95748e10 + 3.39046e10i −0.374961 + 0.649452i
\(479\) −1.36448e10 + 5.09232e10i −0.259195 + 0.967328i 0.706514 + 0.707699i \(0.250267\pi\)
−0.965709 + 0.259629i \(0.916400\pi\)
\(480\) 5.38841e10i 1.01507i
\(481\) 1.77711e10 + 2.41921e10i 0.331997 + 0.451952i
\(482\) 5.71208e9 0.105829
\(483\) 1.38905e11 + 3.72194e10i 2.55228 + 0.683881i
\(484\) −1.16473e10 6.72458e9i −0.212248 0.122542i
\(485\) 1.56555e10 + 9.03871e9i 0.282944 + 0.163358i
\(486\) 4.46157e10 1.19548e10i 0.799729 0.214287i
\(487\) 4.52429e10 + 4.52429e10i 0.804331 + 0.804331i 0.983769 0.179438i \(-0.0574280\pi\)
−0.179438 + 0.983769i \(0.557428\pi\)
\(488\) 2.35207e10 4.07390e10i 0.414735 0.718342i
\(489\) 2.53135e10 + 2.53135e10i 0.442707 + 0.442707i
\(490\) −1.93297e10 3.34801e10i −0.335306 0.580767i
\(491\) 7.98144e10 1.37327 0.686634 0.727003i \(-0.259087\pi\)
0.686634 + 0.727003i \(0.259087\pi\)
\(492\) 3.11931e10i 0.532350i
\(493\) −3.35144e10 5.80487e10i −0.567341 0.982663i
\(494\) −4.39430e10 + 1.17745e10i −0.737873 + 0.197712i
\(495\) −9.75460e9 + 9.75460e9i −0.162476 + 0.162476i
\(496\) −2.27876e10 6.10591e9i −0.376505 0.100884i
\(497\) −6.24354e9 1.08141e10i −0.102331 0.177242i
\(498\) −6.29377e9 + 2.34887e10i −0.102328 + 0.381893i
\(499\) −2.23794e10 8.35211e10i −0.360950 1.34708i −0.872830 0.488025i \(-0.837717\pi\)
0.511880 0.859057i \(-0.328949\pi\)
\(500\) −1.40379e10 + 3.76144e9i −0.224606 + 0.0601830i
\(501\) −1.02743e11 2.75298e10i −1.63080 0.436971i
\(502\) 7.89926e10 4.56064e10i 1.24386 0.718143i
\(503\) 2.00227e9 7.47257e9i 0.0312788 0.116734i −0.948521 0.316713i \(-0.897421\pi\)
0.979800 + 0.199979i \(0.0640874\pi\)
\(504\) −3.20756e10 3.20756e10i −0.497110 0.497110i
\(505\) −1.37148e10 5.11842e10i −0.210874 0.786991i
\(506\) −2.30747e10 + 1.33222e10i −0.351992 + 0.203223i
\(507\) −5.60479e10 −0.848257
\(508\) 4.03153e9i 0.0605361i
\(509\) −1.02171e11 + 5.89885e10i −1.52215 + 0.878812i −0.522490 + 0.852646i \(0.674997\pi\)
−0.999658 + 0.0261666i \(0.991670\pi\)
\(510\) −9.71288e10 + 9.71288e10i −1.43571 + 1.43571i
\(511\) −1.03912e11 5.99935e10i −1.52399 0.879875i
\(512\) 5.16839e10 5.16839e10i 0.752099 0.752099i
\(513\) 1.65178e10 + 6.16452e10i 0.238497 + 0.890081i
\(514\) 1.14216e10 1.97828e10i 0.163635 0.283424i
\(515\) −4.96023e9 + 8.59137e9i −0.0705136 + 0.122133i
\(516\) 4.43668e9 1.65579e10i 0.0625834 0.233565i
\(517\) 2.65091e10i 0.371051i
\(518\) 6.90063e10 + 3.02910e10i 0.958451 + 0.420722i
\(519\) −1.46556e11 −2.01992
\(520\) −6.85927e10 1.83794e10i −0.938133 0.251372i
\(521\) 6.83525e10 + 3.94633e10i 0.927691 + 0.535603i 0.886081 0.463531i \(-0.153418\pi\)
0.0416106 + 0.999134i \(0.486751\pi\)
\(522\) −2.77417e10 1.60167e10i −0.373638 0.215720i
\(523\) −7.56472e10 + 2.02696e10i −1.01108 + 0.270919i −0.726081 0.687609i \(-0.758660\pi\)
−0.285000 + 0.958527i \(0.591994\pi\)
\(524\) 2.46514e10 + 2.46514e10i 0.326976 + 0.326976i
\(525\) 8.89460e10 1.54059e11i 1.17082 2.02791i
\(526\) 4.06128e10 + 4.06128e10i 0.530542 + 0.530542i
\(527\) 2.70597e10 + 4.68687e10i 0.350816 + 0.607632i
\(528\) 1.73381e10 0.223082
\(529\) 1.61404e11i 2.06107i
\(530\) −7.36679e10 1.27597e11i −0.933630 1.61709i
\(531\) −2.78910e9 + 7.47337e8i −0.0350821 + 0.00940023i
\(532\) 2.90419e10 2.90419e10i 0.362558 0.362558i
\(533\) −7.11099e10 1.90539e10i −0.881092 0.236088i
\(534\) 3.89528e10 + 6.74683e10i 0.479043 + 0.829726i
\(535\) 9.30179e9 3.47148e10i 0.113541 0.423740i
\(536\) −2.76701e9 1.03266e10i −0.0335237 0.125112i
\(537\) −1.75165e11 + 4.69352e10i −2.10644 + 0.564419i
\(538\) −3.14110e10 8.41654e9i −0.374932 0.100463i
\(539\) 9.69444e9 5.59709e9i 0.114860 0.0663143i
\(540\) −5.39305e9 + 2.01271e10i −0.0634248 + 0.236705i
\(541\) 6.29364e10 + 6.29364e10i 0.734704 + 0.734704i 0.971548 0.236844i \(-0.0761129\pi\)
−0.236844 + 0.971548i \(0.576113\pi\)
\(542\) 3.24134e10 + 1.20969e11i 0.375602 + 1.40177i
\(543\) 1.68885e11 9.75056e10i 1.94263 1.12158i
\(544\) −5.38935e10 −0.615376
\(545\) 5.49738e10i 0.623117i
\(546\) 5.59039e10 3.22761e10i 0.629030 0.363171i
\(547\) 1.84351e9 1.84351e9i 0.0205919 0.0205919i −0.696736 0.717328i \(-0.745365\pi\)
0.717328 + 0.696736i \(0.245365\pi\)
\(548\) −3.05261e9 1.76242e9i −0.0338492 0.0195429i
\(549\) −2.60966e10 + 2.60966e10i −0.287273 + 0.287273i
\(550\) 8.53070e9 + 3.18370e10i 0.0932253 + 0.347922i
\(551\) 6.93312e10 1.20085e11i 0.752181 1.30282i
\(552\) 1.08989e11 1.88774e11i 1.17388 2.03323i
\(553\) 1.79616e10 6.70337e10i 0.192064 0.716791i
\(554\) 2.96942e10i 0.315234i
\(555\) 2.05762e10 + 1.86364e11i 0.216867 + 1.96422i
\(556\) 6.50990e9 0.0681201
\(557\) −1.64131e11 4.39789e10i −1.70518 0.456902i −0.730947 0.682435i \(-0.760921\pi\)
−0.974236 + 0.225532i \(0.927588\pi\)
\(558\) 2.23988e10 + 1.29319e10i 0.231040 + 0.133391i
\(559\) 3.50365e10 + 2.02284e10i 0.358818 + 0.207164i
\(560\) −1.23234e11 + 3.30205e10i −1.25308 + 0.335762i
\(561\) −2.81245e10 2.81245e10i −0.283944 0.283944i
\(562\) 2.31387e10 4.00773e10i 0.231949 0.401748i
\(563\) 8.50290e10 + 8.50290e10i 0.846318 + 0.846318i 0.989672 0.143353i \(-0.0457885\pi\)
−0.143353 + 0.989672i \(0.545789\pi\)
\(564\) 2.26812e10 + 3.92850e10i 0.224156 + 0.388249i
\(565\) −4.80089e10 −0.471116
\(566\) 1.52866e10i 0.148952i
\(567\) −7.87796e10 1.36450e11i −0.762222 1.32021i
\(568\) −1.82828e10 + 4.89887e9i −0.175651 + 0.0470655i
\(569\) 7.54606e10 7.54606e10i 0.719898 0.719898i −0.248686 0.968584i \(-0.579999\pi\)
0.968584 + 0.248686i \(0.0799988\pi\)
\(570\) −2.74476e11 7.35455e10i −2.60019 0.696718i
\(571\) 1.83891e10 + 3.18508e10i 0.172988 + 0.299624i 0.939463 0.342650i \(-0.111325\pi\)
−0.766475 + 0.642274i \(0.777991\pi\)
\(572\) 1.11317e9 4.15440e9i 0.0103986 0.0388083i
\(573\) 4.49451e10 + 1.67737e11i 0.416930 + 1.55601i
\(574\) −1.78527e11 + 4.78361e10i −1.64458 + 0.440665i
\(575\) 2.86433e11 + 7.67494e10i 2.62030 + 0.702108i
\(576\) −5.60048e10 + 3.23344e10i −0.508786 + 0.293748i
\(577\) 4.59526e10 1.71498e11i 0.414579 1.54723i −0.371099 0.928593i \(-0.621019\pi\)
0.785678 0.618636i \(-0.212314\pi\)
\(578\) −2.94610e10 2.94610e10i −0.263959 0.263959i
\(579\) −1.91144e10 7.13359e10i −0.170077 0.634737i
\(580\) 3.92077e10 2.26366e10i 0.346465 0.200032i
\(581\) 5.18128e10 0.454708
\(582\) 2.49088e10i 0.217100i
\(583\) 3.69466e10 2.13312e10i 0.319816 0.184646i
\(584\) −1.28605e11 + 1.28605e11i −1.10562 + 1.10562i
\(585\) 4.82486e10 + 2.78563e10i 0.411966 + 0.237848i
\(586\) 8.56945e10 8.56945e10i 0.726712 0.726712i
\(587\) 4.13572e10 + 1.54347e11i 0.348336 + 1.30001i 0.888666 + 0.458555i \(0.151633\pi\)
−0.540330 + 0.841453i \(0.681701\pi\)
\(588\) −9.57773e9 + 1.65891e10i −0.0801223 + 0.138776i
\(589\) −5.59783e10 + 9.69572e10i −0.465113 + 0.805599i
\(590\) −2.93721e9 + 1.09618e10i −0.0242396 + 0.0904636i
\(591\) 1.26795e11i 1.03933i
\(592\) 5.11111e10 6.37981e10i 0.416129 0.519422i
\(593\) −4.57916e10 −0.370312 −0.185156 0.982709i \(-0.559279\pi\)
−0.185156 + 0.982709i \(0.559279\pi\)
\(594\) 1.62068e10 + 4.34260e9i 0.130182 + 0.0348822i
\(595\) 2.53464e11 + 1.46337e11i 2.02231 + 1.16758i
\(596\) −3.86030e10 2.22875e10i −0.305940 0.176634i
\(597\) 1.55786e11 4.17427e10i 1.22640 0.328612i
\(598\) 7.60885e10 + 7.60885e10i 0.594996 + 0.594996i
\(599\) 1.93212e9 3.34653e9i 0.0150081 0.0259949i −0.858424 0.512941i \(-0.828556\pi\)
0.873432 + 0.486946i \(0.161889\pi\)
\(600\) −1.90669e11 1.90669e11i −1.47121 1.47121i
\(601\) 3.09640e10 + 5.36312e10i 0.237334 + 0.411074i 0.959948 0.280177i \(-0.0903932\pi\)
−0.722615 + 0.691251i \(0.757060\pi\)
\(602\) 1.01570e11 0.773353
\(603\) 8.38752e9i 0.0634402i
\(604\) 1.54339e10 + 2.67324e10i 0.115966 + 0.200858i
\(605\) 1.91506e11 5.13138e10i 1.42942 0.383013i
\(606\) 5.16289e10 5.16289e10i 0.382827 0.382827i
\(607\) 2.09330e11 + 5.60899e10i 1.54198 + 0.413171i 0.926903 0.375300i \(-0.122460\pi\)
0.615072 + 0.788471i \(0.289127\pi\)
\(608\) −5.57447e10 9.65526e10i −0.407933 0.706561i
\(609\) −5.09238e10 + 1.90050e11i −0.370213 + 1.38165i
\(610\) 3.75416e10 + 1.40107e11i 0.271140 + 1.01191i
\(611\) −1.03411e11 + 2.77090e10i −0.741999 + 0.198818i
\(612\) 2.28058e10 + 6.11078e9i 0.162569 + 0.0435603i
\(613\) 2.94222e10 1.69869e10i 0.208369 0.120302i −0.392184 0.919887i \(-0.628280\pi\)
0.600553 + 0.799585i \(0.294947\pi\)
\(614\) −8.56507e9 + 3.19653e10i −0.0602639 + 0.224908i
\(615\) −3.25152e11 3.25152e11i −2.27293 2.27293i
\(616\) −1.33610e10 4.98640e10i −0.0927933 0.346309i
\(617\) −2.02098e10 + 1.16681e10i −0.139451 + 0.0805120i −0.568102 0.822958i \(-0.692322\pi\)
0.428651 + 0.903470i \(0.358989\pi\)
\(618\) −1.36693e10 −0.0937117
\(619\) 2.71720e11i 1.85080i 0.378994 + 0.925399i \(0.376270\pi\)
−0.378994 + 0.925399i \(0.623730\pi\)
\(620\) −3.16565e10 + 1.82769e10i −0.214238 + 0.123690i
\(621\) 1.06740e11 1.06740e11i 0.717732 0.717732i
\(622\) 1.51337e11 + 8.73744e10i 1.01107 + 0.583744i
\(623\) 1.17375e11 1.17375e11i 0.779156 0.779156i
\(624\) −1.81228e10 6.76354e10i −0.119533 0.446103i
\(625\) −1.11736e10 + 1.93532e10i −0.0732272 + 0.126833i
\(626\) 7.80410e10 1.35171e11i 0.508189 0.880209i
\(627\) 2.12957e10 7.94768e10i 0.137792 0.514245i
\(628\) 2.43650e10i 0.156649i
\(629\) −1.86397e11 + 2.05798e10i −1.19079 + 0.131474i
\(630\) 1.39871e11 0.887901
\(631\) 8.99677e10 + 2.41068e10i 0.567504 + 0.152062i 0.531152 0.847277i \(-0.321759\pi\)
0.0363525 + 0.999339i \(0.488426\pi\)
\(632\) −9.11001e10 5.25967e10i −0.571019 0.329678i
\(633\) −2.18562e10 1.26187e10i −0.136132 0.0785956i
\(634\) −9.45880e10 + 2.53448e10i −0.585435 + 0.156867i
\(635\) −4.20240e10 4.20240e10i −0.258466 0.258466i
\(636\) −3.65019e10 + 6.32231e10i −0.223093 + 0.386409i
\(637\) −3.19673e10 3.19673e10i −0.194155 0.194155i
\(638\) −1.82275e10 3.15709e10i −0.110013 0.190548i
\(639\) 1.48498e10 0.0890668
\(640\) 1.16535e11i 0.694603i
\(641\) 3.68801e10 + 6.38783e10i 0.218454 + 0.378374i 0.954336 0.298737i \(-0.0965652\pi\)
−0.735881 + 0.677110i \(0.763232\pi\)
\(642\) 4.78333e10 1.28169e10i 0.281572 0.0754471i
\(643\) −2.93988e10 + 2.93988e10i −0.171983 + 0.171983i −0.787850 0.615867i \(-0.788806\pi\)
0.615867 + 0.787850i \(0.288806\pi\)
\(644\) −9.38365e10 2.51434e10i −0.545542 0.146178i
\(645\) 1.26350e11 + 2.18845e11i 0.730023 + 1.26444i
\(646\) 7.35583e10 2.74523e11i 0.422378 1.57634i
\(647\) 3.11300e10 + 1.16179e11i 0.177649 + 0.662993i 0.996085 + 0.0883968i \(0.0281743\pi\)
−0.818437 + 0.574597i \(0.805159\pi\)
\(648\) −2.30689e11 + 6.18128e10i −1.30836 + 0.350573i
\(649\) −3.17408e9 8.50493e8i −0.0178912 0.00479393i
\(650\) 1.15278e11 6.65560e10i 0.645795 0.372850i
\(651\) 4.11161e10 1.53447e11i 0.228922 0.854348i
\(652\) −1.71004e10 1.71004e10i −0.0946273 0.0946273i
\(653\) 4.43154e10 + 1.65387e11i 0.243726 + 0.909597i 0.974020 + 0.226464i \(0.0727166\pi\)
−0.730294 + 0.683133i \(0.760617\pi\)
\(654\) −6.55998e10 + 3.78741e10i −0.358585 + 0.207029i
\(655\) −5.13925e11 −2.79212
\(656\) 2.00483e11i 1.08259i
\(657\) 1.23573e11 7.13449e10i 0.663227 0.382914i
\(658\) −1.90056e11 + 1.90056e11i −1.01386 + 1.01386i
\(659\) −1.99904e11 1.15415e11i −1.05994 0.611956i −0.134523 0.990910i \(-0.542950\pi\)
−0.925415 + 0.378955i \(0.876284\pi\)
\(660\) 1.89961e10 1.89961e10i 0.100112 0.100112i
\(661\) −8.21349e10 3.06531e11i −0.430251 1.60572i −0.752183 0.658955i \(-0.770999\pi\)
0.321932 0.946763i \(-0.395668\pi\)
\(662\) 8.05560e10 1.39527e11i 0.419436 0.726485i
\(663\) −8.03153e10 + 1.39110e11i −0.415666 + 0.719954i
\(664\) 2.03270e10 7.58612e10i 0.104568 0.390254i
\(665\) 6.05456e11i 3.09596i
\(666\) −7.22278e10 + 5.30574e10i −0.367119 + 0.269680i
\(667\) −3.27980e11 −1.65708
\(668\) 6.94074e10 + 1.85977e10i 0.348578 + 0.0934012i
\(669\) −7.67964e10 4.43384e10i −0.383386 0.221348i
\(670\) 2.85484e10 + 1.64824e10i 0.141672 + 0.0817941i
\(671\) −4.05692e10 + 1.08705e10i −0.200127 + 0.0536240i
\(672\) 1.11862e11 + 1.11862e11i 0.548538 + 0.548538i
\(673\) 1.31767e11 2.28227e11i 0.642313 1.11252i −0.342603 0.939480i \(-0.611308\pi\)
0.984915 0.173038i \(-0.0553582\pi\)
\(674\) −3.37977e10 3.37977e10i −0.163775 0.163775i
\(675\) −9.33678e10 1.61718e11i −0.449761 0.779010i
\(676\) 3.78629e10 0.181312
\(677\) 8.92656e10i 0.424942i −0.977167 0.212471i \(-0.931849\pi\)
0.977167 0.212471i \(-0.0681511\pi\)
\(678\) −3.30756e10 5.72886e10i −0.156527 0.271112i
\(679\) 5.12647e10 1.37363e10i 0.241179 0.0646237i
\(680\) 3.13696e11 3.13696e11i 1.46715 1.46715i
\(681\) 2.59242e10 + 6.94636e9i 0.120536 + 0.0322975i
\(682\) 1.47169e10 + 2.54905e10i 0.0680268 + 0.117826i
\(683\) −4.78190e10 + 1.78463e11i −0.219744 + 0.820096i 0.764698 + 0.644389i \(0.222888\pi\)
−0.984442 + 0.175708i \(0.943779\pi\)
\(684\) 1.26414e10 + 4.71782e10i 0.0577523 + 0.215535i
\(685\) 5.01912e10 1.34487e10i 0.227963 0.0610826i
\(686\) 1.14278e11 + 3.06206e10i 0.516018 + 0.138267i
\(687\) 3.05009e11 1.76097e11i 1.36926 0.790542i
\(688\) 2.85153e10 1.06421e11i 0.127270 0.474977i
\(689\) −1.21831e11 1.21831e11i −0.540607 0.540607i
\(690\) 1.73958e11 + 6.49221e11i 0.767447 + 2.86415i
\(691\) −4.71683e10 + 2.72326e10i −0.206889 + 0.119448i −0.599865 0.800101i \(-0.704779\pi\)
0.392976 + 0.919549i \(0.371446\pi\)
\(692\) 9.90054e10 0.431752
\(693\) 4.05007e10i 0.175602i
\(694\) −3.01723e11 + 1.74200e11i −1.30068 + 0.750949i
\(695\) −6.78582e10 + 6.78582e10i −0.290846 + 0.290846i
\(696\) 2.58282e11 + 1.49119e11i 1.10067 + 0.635472i
\(697\) 3.25208e11 3.25208e11i 1.37794 1.37794i
\(698\) −1.97507e9 7.37106e9i −0.00832072 0.0310533i
\(699\) 2.23066e11 3.86363e11i 0.934385 1.61840i
\(700\) −6.00871e10 + 1.04074e11i −0.250259 + 0.433461i
\(701\) −4.36991e10 + 1.63087e11i −0.180968 + 0.675380i 0.814490 + 0.580177i \(0.197017\pi\)
−0.995458 + 0.0952029i \(0.969650\pi\)
\(702\) 6.77614e10i 0.279019i
\(703\) −2.29669e11 3.12651e11i −0.940331 1.28009i
\(704\) −7.35950e10 −0.299611
\(705\) −6.45926e11 1.73075e11i −2.61473 0.700614i
\(706\) −2.02879e11 1.17132e11i −0.816618 0.471475i
\(707\) −1.34729e11 7.77858e10i −0.539241 0.311331i
\(708\) 5.43149e9 1.45536e9i 0.0216165 0.00579213i
\(709\) −2.41632e11 2.41632e11i −0.956247 0.956247i 0.0428355 0.999082i \(-0.486361\pi\)
−0.999082 + 0.0428355i \(0.986361\pi\)
\(710\) 2.91815e10 5.05438e10i 0.114835 0.198900i
\(711\) 5.83570e10 + 5.83570e10i 0.228357 + 0.228357i
\(712\) −1.25806e11 2.17902e11i −0.489531 0.847893i
\(713\) 2.64812e11 1.02466
\(714\) 4.03275e11i 1.55170i
\(715\) 3.17013e10 + 5.49083e10i 0.121298 + 0.210094i
\(716\) 1.18332e11 3.17069e10i 0.450246 0.120643i
\(717\) −2.02205e11 + 2.02205e11i −0.765096 + 0.765096i
\(718\) 3.51735e11 + 9.42471e10i 1.32348 + 0.354626i
\(719\) −6.33756e10 1.09770e11i −0.237141 0.410740i 0.722752 0.691108i \(-0.242877\pi\)
−0.959893 + 0.280368i \(0.909544\pi\)
\(720\) 3.92683e10 1.46551e11i 0.146121 0.545330i
\(721\) 7.53817e9 + 2.81328e10i 0.0278949 + 0.104105i
\(722\) 3.42800e11 9.18530e10i 1.26151 0.338022i
\(723\) 4.03012e10 + 1.07987e10i 0.147491 + 0.0395201i
\(724\) −1.14089e11 + 6.58696e10i −0.415232 + 0.239735i
\(725\) −1.05009e11 + 3.91899e11i −0.380080 + 1.41848i
\(726\) 1.93170e11 + 1.93170e11i 0.695333 + 0.695333i
\(727\) 1.13343e11 + 4.23000e11i 0.405747 + 1.51427i 0.802674 + 0.596418i \(0.203410\pi\)
−0.396927 + 0.917850i \(0.629923\pi\)
\(728\) −1.80552e11 + 1.04242e11i −0.642803 + 0.371122i
\(729\) −1.53789e10 −0.0544523
\(730\) 5.60803e11i 1.97478i
\(731\) −2.18883e11 + 1.26372e11i −0.766552 + 0.442569i
\(732\) 5.08205e10 5.08205e10i 0.177009 0.177009i
\(733\) −1.11316e11 6.42686e10i −0.385606 0.222630i 0.294649 0.955606i \(-0.404797\pi\)
−0.680254 + 0.732976i \(0.738131\pi\)
\(734\) −1.84092e11 + 1.84092e11i −0.634235 + 0.634235i
\(735\) −7.30856e10 2.72759e11i −0.250428 0.934610i
\(736\) −1.31853e11 + 2.28377e11i −0.449346 + 0.778289i
\(737\) −4.77263e9 + 8.26644e9i −0.0161766 + 0.0280187i
\(738\) 5.68871e10 2.12306e11i 0.191773 0.715708i
\(739\) 3.23845e11i 1.08582i 0.839790 + 0.542912i \(0.182678\pi\)
−0.839790 + 0.542912i \(0.817322\pi\)
\(740\) −1.39002e10 1.25898e11i −0.0463547 0.419847i
\(741\) −3.32296e11 −1.10218
\(742\) −4.17821e11 1.11955e11i −1.37840 0.369341i
\(743\) 5.17840e10 + 2.98975e10i 0.169918 + 0.0981023i 0.582547 0.812797i \(-0.302056\pi\)
−0.412629 + 0.910899i \(0.635389\pi\)
\(744\) −2.08538e11 1.20399e11i −0.680602 0.392945i
\(745\) 6.34713e11 1.70071e11i 2.06040 0.552084i
\(746\) 3.08487e11 + 3.08487e11i 0.996051 + 0.996051i
\(747\) −3.08081e10 + 5.33613e10i −0.0989426 + 0.171374i
\(748\) 1.89994e10 + 1.89994e10i 0.0606922 + 0.0606922i
\(749\) −5.27568e10 9.13775e10i −0.167630 0.290343i
\(750\) 2.95200e11 0.932978
\(751\) 1.70767e11i 0.536839i −0.963302 0.268420i \(-0.913499\pi\)
0.963302 0.268420i \(-0.0865014\pi\)
\(752\) 1.45776e11 + 2.52492e11i 0.455843 + 0.789543i
\(753\) 6.43546e11 1.72438e11i 2.00170 0.536355i
\(754\) −1.04105e11 + 1.04105e11i −0.322096 + 0.322096i
\(755\) −4.39535e11 1.17773e11i −1.35271 0.362459i
\(756\) 3.05877e10 + 5.29794e10i 0.0936395 + 0.162188i
\(757\) −2.03120e10 + 7.58053e10i −0.0618541 + 0.230843i −0.989932 0.141543i \(-0.954794\pi\)
0.928078 + 0.372386i \(0.121460\pi\)
\(758\) −1.21224e11 4.52415e11i −0.367209 1.37044i
\(759\) −1.87987e11 + 5.03711e10i −0.566450 + 0.151780i
\(760\) 8.86472e11 + 2.37530e11i 2.65712 + 0.711972i
\(761\) −3.61710e11 + 2.08834e11i −1.07851 + 0.622676i −0.930493 0.366310i \(-0.880621\pi\)
−0.148013 + 0.988985i \(0.547288\pi\)
\(762\) 2.11946e10 7.90993e10i 0.0628644 0.234613i
\(763\) 1.14125e11 + 1.14125e11i 0.336729 + 0.336729i
\(764\) −3.03625e10 1.13314e11i −0.0891177 0.332592i
\(765\) −3.01422e11 + 1.74026e11i −0.880093 + 0.508122i
\(766\) 2.00398e11 0.582073
\(767\) 1.32710e10i 0.0383462i
\(768\) 2.73294e11 1.57786e11i 0.785570 0.453549i
\(769\) −1.25635e11 + 1.25635e11i −0.359256 + 0.359256i −0.863539 0.504283i \(-0.831757\pi\)
0.504283 + 0.863539i \(0.331757\pi\)
\(770\) 1.37851e11 + 7.95885e10i 0.392146 + 0.226406i
\(771\) 1.17984e11 1.17984e11i 0.333892 0.333892i
\(772\) 1.29127e10 + 4.81907e10i 0.0363535 + 0.135673i
\(773\) 6.54220e10 1.13314e11i 0.183234 0.317370i −0.759746 0.650220i \(-0.774677\pi\)
0.942980 + 0.332850i \(0.108010\pi\)
\(774\) −6.03937e10 + 1.04605e11i −0.168278 + 0.291466i
\(775\) 8.47847e10 3.16421e11i 0.235023 0.877119i
\(776\) 8.04477e10i 0.221854i
\(777\) 4.29604e11 + 3.44173e11i 1.17865 + 0.944262i
\(778\) −9.53649e10 −0.260298
\(779\) 9.19004e11 + 2.46246e11i 2.49556 + 0.668683i
\(780\) −9.39591e10 5.42473e10i −0.253840 0.146555i
\(781\) 1.46354e10 + 8.44973e9i 0.0393368 + 0.0227111i
\(782\) −6.49334e11 + 1.73988e11i −1.73636 + 0.465257i
\(783\) 1.46043e11 + 1.46043e11i 0.388538 + 0.388538i
\(784\) −6.15578e10 + 1.06621e11i −0.162937 + 0.282214i
\(785\) 2.53977e11 + 2.53977e11i 0.668829 + 0.668829i
\(786\) −3.54067e11 6.13262e11i −0.927674 1.60678i
\(787\) −6.55704e11 −1.70926 −0.854632 0.519234i \(-0.826217\pi\)
−0.854632 + 0.519234i \(0.826217\pi\)
\(788\) 8.56560e10i 0.222153i
\(789\) 2.09762e11 + 3.63319e11i 0.541277 + 0.937519i
\(790\) 3.13306e11 8.39501e10i 0.804379 0.215533i
\(791\) −9.96655e10 + 9.96655e10i −0.254589 + 0.254589i
\(792\) 5.92987e10 + 1.58890e10i 0.150711 + 0.0403829i
\(793\) 8.48110e10 + 1.46897e11i 0.214466 + 0.371467i
\(794\) 1.02472e11 3.82429e11i 0.257823 0.962207i
\(795\) −2.78538e11 1.03952e12i −0.697294 2.60234i
\(796\) −1.05241e11 + 2.81991e10i −0.262139 + 0.0702398i
\(797\) 1.04486e11 + 2.79968e10i 0.258954 + 0.0693866i 0.385960 0.922515i \(-0.373870\pi\)
−0.127006 + 0.991902i \(0.540537\pi\)
\(798\) −7.22485e11 + 4.17127e11i −1.78163 + 1.02862i
\(799\) 1.73105e11 6.46038e11i 0.424741 1.58515i
\(800\) 2.30670e11 + 2.30670e11i 0.563158 + 0.563158i
\(801\) 5.10912e10 + 1.90675e11i 0.124113 + 0.463195i
\(802\) −4.50239e11 + 2.59945e11i −1.08829 + 0.628326i
\(803\) 1.62385e11 0.390557
\(804\) 1.63338e10i 0.0390899i
\(805\) 1.24023e12 7.16046e11i 2.95337 1.70513i
\(806\) 8.40546e10 8.40546e10i 0.199169 0.199169i
\(807\) −2.05707e11 1.18765e11i −0.485014 0.280023i
\(808\) −1.66745e11 + 1.66745e11i −0.391209 + 0.391209i
\(809\) 9.50026e10 + 3.54554e11i 0.221790 + 0.827730i 0.983665 + 0.180007i \(0.0576120\pi\)
−0.761876 + 0.647723i \(0.775721\pi\)
\(810\) 3.68205e11 6.37750e11i 0.855361 1.48153i
\(811\) 9.17788e10 1.58965e11i 0.212158 0.367468i −0.740232 0.672352i \(-0.765284\pi\)
0.952390 + 0.304884i \(0.0986176\pi\)
\(812\) 3.44014e10 1.28388e11i 0.0791319 0.295324i
\(813\) 9.14764e11i 2.09386i
\(814\) −1.01376e11 + 1.11927e10i −0.230906 + 0.0254940i
\(815\) 3.56504e11 0.808043
\(816\) 4.22536e11 + 1.13218e11i 0.953023 + 0.255362i
\(817\) −4.52802e11 2.61425e11i −1.01630 0.586759i
\(818\) −4.46003e11 2.57500e11i −0.996149 0.575127i
\(819\) 1.57992e11 4.23339e10i 0.351156 0.0940920i
\(820\) 2.19655e11 + 2.19655e11i 0.485832 + 0.485832i
\(821\) 4.12969e11 7.15283e11i 0.908959 1.57436i 0.0934463 0.995624i \(-0.470212\pi\)
0.815513 0.578739i \(-0.196455\pi\)
\(822\) 5.06273e10 + 5.06273e10i 0.110891 + 0.110891i
\(823\) −6.69883e10 1.16027e11i −0.146016 0.252907i 0.783736 0.621094i \(-0.213312\pi\)
−0.929751 + 0.368188i \(0.879978\pi\)
\(824\) 4.41478e10 0.0957635
\(825\) 2.40751e11i 0.519700i
\(826\) 1.66589e10 + 2.88541e10i 0.0357871 + 0.0619850i
\(827\) −1.14695e11 + 3.07323e10i −0.245200 + 0.0657012i −0.379326 0.925263i \(-0.623844\pi\)
0.134126 + 0.990964i \(0.457177\pi\)
\(828\) 8.16904e10 8.16904e10i 0.173800 0.173800i
\(829\) 2.43751e11 + 6.53128e10i 0.516093 + 0.138287i 0.507459 0.861676i \(-0.330585\pi\)
0.00863412 + 0.999963i \(0.497252\pi\)
\(830\) 1.21083e11 + 2.09722e11i 0.255135 + 0.441908i
\(831\) 5.61369e10 2.09506e11i 0.117718 0.439331i
\(832\) 7.69261e10 + 2.87092e11i 0.160539 + 0.599140i
\(833\) 2.72807e11 7.30983e10i 0.566598 0.151819i
\(834\) −1.27725e11 3.42239e10i −0.264006 0.0707401i
\(835\) −9.17352e11 + 5.29633e11i −1.88708 + 1.08951i
\(836\) −1.43863e10 + 5.36902e10i −0.0294525 + 0.109918i
\(837\) −1.17916e11 1.17916e11i −0.240253 0.240253i
\(838\) −5.20234e9 1.94154e10i −0.0105493 0.0393704i
\(839\) −4.13364e11 + 2.38656e11i −0.834229 + 0.481642i −0.855298 0.518136i \(-0.826626\pi\)
0.0210694 + 0.999778i \(0.493293\pi\)
\(840\) −1.30223e12 −2.61559
\(841\) 5.15024e10i 0.102954i
\(842\) 9.54005e10 5.50795e10i 0.189803 0.109583i
\(843\) 2.39019e11 2.39019e11i 0.473285 0.473285i
\(844\) 1.47648e10 + 8.52449e9i 0.0290977 + 0.0167996i
\(845\) −3.94678e11 + 3.94678e11i −0.774133 + 0.774133i
\(846\) −8.27279e10 3.08745e11i −0.161499 0.602723i
\(847\) 2.91036e11 5.04089e11i 0.565474 0.979430i
\(848\) −2.34604e11 + 4.06346e11i −0.453682 + 0.785801i
\(849\) −2.88993e10 + 1.07854e11i −0.0556232 + 0.207589i
\(850\) 8.31587e11i 1.59306i
\(851\) −3.68822e11 + 8.40217e11i −0.703232 + 1.60204i
\(852\) −2.89184e10 −0.0548802
\(853\) 2.09820e11 + 5.62211e10i 0.396325 + 0.106195i 0.451476 0.892283i \(-0.350898\pi\)
−0.0551516 + 0.998478i \(0.517564\pi\)
\(854\) 3.68796e11 + 2.12924e11i 0.693353 + 0.400307i
\(855\) −6.23550e11 3.60007e11i −1.16683 0.673669i
\(856\) −1.54487e11 + 4.13946e10i −0.287737 + 0.0770990i
\(857\) −2.87728e11 2.87728e11i −0.533407 0.533407i 0.388177 0.921585i \(-0.373105\pi\)
−0.921585 + 0.388177i \(0.873105\pi\)
\(858\) −4.36811e10 + 7.56579e10i −0.0806017 + 0.139606i
\(859\) −2.29525e11 2.29525e11i −0.421558 0.421558i 0.464182 0.885740i \(-0.346348\pi\)
−0.885740 + 0.464182i \(0.846348\pi\)
\(860\) −8.53553e10 1.47840e11i −0.156040 0.270270i
\(861\) −1.35002e12 −2.45656
\(862\) 4.70760e11i 0.852649i
\(863\) −3.96991e11 6.87609e11i −0.715711 1.23965i −0.962685 0.270626i \(-0.912769\pi\)
0.246974 0.969022i \(-0.420564\pi\)
\(864\) 1.60403e11 4.29800e10i 0.287845 0.0771279i
\(865\) −1.03202e12 + 1.03202e12i −1.84341 + 1.84341i
\(866\) −3.06669e10 8.21716e9i −0.0545253 0.0146100i
\(867\) −1.52164e11 2.63556e11i −0.269300 0.466441i
\(868\) −2.77758e10 + 1.03661e11i −0.0489314 + 0.182615i
\(869\) 2.43085e10 + 9.07205e10i 0.0426264 + 0.159084i
\(870\) −8.88268e11 + 2.38011e11i −1.55048 + 0.415451i
\(871\) 3.72358e10 + 9.97730e9i 0.0646976 + 0.0173357i
\(872\) 2.11867e11 1.22322e11i 0.366436 0.211562i
\(873\) −1.63354e10 + 6.09645e10i −0.0281237 + 0.104959i
\(874\) −9.83345e11 9.83345e11i −1.68523 1.68523i
\(875\) −1.62793e11 6.07551e11i −0.277717 1.03646i
\(876\) −2.40646e11 + 1.38937e11i −0.408659 + 0.235940i
\(877\) −4.22325e11 −0.713918 −0.356959 0.934120i \(-0.616186\pi\)
−0.356959 + 0.934120i \(0.616186\pi\)
\(878\) 6.88546e11i 1.15866i
\(879\) 7.66617e11 4.42607e11i 1.28417 0.741417i
\(880\) 1.22091e11 1.22091e11i 0.203589 0.203589i
\(881\) 3.17612e11 + 1.83373e11i 0.527222 + 0.304392i 0.739884 0.672734i \(-0.234880\pi\)
−0.212663 + 0.977126i \(0.568214\pi\)
\(882\) 9.54415e10 9.54415e10i 0.157711 0.157711i
\(883\) −1.27619e11 4.76279e11i −0.209928 0.783463i −0.987891 0.155152i \(-0.950413\pi\)
0.777962 0.628311i \(-0.216253\pi\)
\(884\) 5.42567e10 9.39754e10i 0.0888474 0.153888i
\(885\) −4.14465e10 + 7.17875e10i −0.0675639 + 0.117024i
\(886\) 3.79985e10 1.41812e11i 0.0616640 0.230133i
\(887\) 3.71105e11i 0.599518i 0.954015 + 0.299759i \(0.0969063\pi\)
−0.954015 + 0.299759i \(0.903094\pi\)
\(888\) 6.72457e11 4.93977e11i 1.08147 0.794428i
\(889\) −1.74482e11 −0.279347
\(890\) 7.49396e11 + 2.00800e11i 1.19440 + 0.320040i
\(891\) 1.84666e11 + 1.06617e11i 0.293005 + 0.169167i
\(892\) 5.18795e10 + 2.99526e10i 0.0819476 + 0.0473125i
\(893\) 1.33646e12 3.58103e11i 2.10160 0.563121i
\(894\) 6.40228e11 + 6.40228e11i 1.00227 + 1.00227i
\(895\) −9.02965e11 + 1.56398e12i −1.40727 + 2.43747i
\(896\) 2.41925e11 + 2.41925e11i 0.375360 + 0.375360i
\(897\) 3.92992e11 + 6.80683e11i 0.607036 + 1.05142i
\(898\) 4.52805e11 0.696316
\(899\) 3.62318e11i 0.554691i
\(900\) −7.14562e10 1.23766e11i −0.108910 0.188638i
\(901\) 1.03970e12 2.78586e11i 1.57764 0.422728i
\(902\) 1.76871e11 1.76871e11i 0.267196 0.267196i
\(903\) 7.16617e11 + 1.92017e11i 1.07780 + 0.288794i
\(904\) 1.06824e11 + 1.85025e11i 0.159954 + 0.277048i
\(905\) 5.02637e11 1.87587e12i 0.749307 2.79645i
\(906\) −1.62279e11 6.05633e11i −0.240851 0.898870i
\(907\) 1.15953e12 3.10694e11i 1.71337 0.459096i 0.737124 0.675757i \(-0.236183\pi\)
0.976247 + 0.216661i \(0.0695166\pi\)
\(908\) −1.75130e10 4.69259e9i −0.0257642 0.00690349i
\(909\) 1.60221e11 9.25035e10i 0.234673 0.135489i
\(910\) 1.66382e11 6.20945e11i 0.242628 0.905499i
\(911\) 1.80243e11 + 1.80243e11i 0.261688 + 0.261688i 0.825740 0.564052i \(-0.190758\pi\)
−0.564052 + 0.825740i \(0.690758\pi\)
\(912\) 2.34214e11 + 8.74100e11i 0.338559 + 1.26352i
\(913\) −6.07268e10 + 3.50606e10i −0.0873971 + 0.0504587i
\(914\) −1.09767e11 −0.157285
\(915\) 1.05949e12i 1.51151i
\(916\) −2.06048e11 + 1.18962e11i −0.292675 + 0.168976i
\(917\) −1.06690e12 + 1.06690e12i −1.50885 + 1.50885i
\(918\) 3.66609e11 + 2.11662e11i 0.516217 + 0.298038i
\(919\) −3.56203e11 + 3.56203e11i −0.499385 + 0.499385i −0.911247 0.411861i \(-0.864879\pi\)
0.411861 + 0.911247i \(0.364879\pi\)
\(920\) −5.61831e11 2.09678e12i −0.784250 2.92686i
\(921\) −1.20861e11 + 2.09337e11i −0.167976 + 0.290942i
\(922\) 4.59280e11 7.95496e11i 0.635556 1.10081i
\(923\) 1.76644e10 6.59244e10i 0.0243384 0.0908321i
\(924\) 7.88710e10i 0.108201i
\(925\) 8.85880e11 + 7.09713e11i 1.21006 + 0.969428i
\(926\) −2.72675e11 −0.370853
\(927\) −3.34558e10 8.96447e9i −0.0453057 0.0121396i
\(928\) −3.12467e11 1.80403e11i −0.421320 0.243249i
\(929\) −5.34963e11 3.08861e11i −0.718226 0.414668i 0.0958736 0.995394i \(-0.469436\pi\)
−0.814099 + 0.580726i \(0.802769\pi\)
\(930\) 7.17191e11 1.92171e11i 0.958745 0.256895i
\(931\) 4.13136e11 + 4.13136e11i 0.549914 + 0.549914i
\(932\) −1.50692e11 + 2.61006e11i −0.199722 + 0.345929i
\(933\) 9.02566e11 + 9.02566e11i 1.19111 + 1.19111i
\(934\) −8.40755e10 1.45623e11i −0.110480 0.191356i
\(935\) −3.96093e11 −0.518264
\(936\) 2.47931e11i 0.323019i
\(937\) 2.40686e10 + 4.16880e10i 0.0312242 + 0.0540820i 0.881215 0.472715i \(-0.156726\pi\)
−0.849991 + 0.526797i \(0.823393\pi\)
\(938\) 9.34832e10 2.50487e10i 0.120760 0.0323575i
\(939\) 8.06153e11 8.06153e11i 1.03694 1.03694i
\(940\) 4.36353e11 + 1.16920e11i 0.558890 + 0.149754i
\(941\) 6.00653e11 + 1.04036e12i 0.766065 + 1.32686i 0.939682 + 0.342050i \(0.111121\pi\)
−0.173617 + 0.984813i \(0.555546\pi\)
\(942\) −1.28092e11 + 4.78045e11i −0.162674 + 0.607107i
\(943\) −5.82450e11 2.17373e12i −0.736566 2.74890i
\(944\) 3.49091e10 9.35387e9i 0.0439593 0.0117789i
\(945\) −8.71090e11 2.33408e11i −1.09228 0.292677i
\(946\) −1.19044e11 + 6.87299e10i −0.148642 + 0.0858185i
\(947\) −5.30422e10 + 1.97956e11i −0.0659510 + 0.246132i −0.991029 0.133644i \(-0.957332\pi\)
0.925078 + 0.379776i \(0.123999\pi\)
\(948\) −1.13644e11 1.13644e11i −0.140706 0.140706i
\(949\) −1.69735e11 6.33461e11i −0.209270 0.781007i
\(950\) −1.48983e12 + 8.60151e11i −1.82911 + 1.05604i
\(951\) −7.15273e11 −0.874480
\(952\) 1.30245e12i 1.58568i
\(953\) −1.31948e11 + 7.61802e10i −0.159967 + 0.0923572i −0.577847 0.816145i \(-0.696107\pi\)
0.417879 + 0.908503i \(0.362773\pi\)
\(954\) 3.63739e11 3.63739e11i 0.439133 0.439133i
\(955\) 1.49767e12 + 8.64678e11i 1.80053 + 1.03954i
\(956\) 1.36599e11 1.36599e11i 0.163537 0.163537i
\(957\) −6.89180e10 2.57206e11i −0.0821646 0.306643i
\(958\) −3.61707e11 + 6.26494e11i −0.429432 + 0.743798i
\(959\) 7.62767e10 1.32115e11i 0.0901815 0.156199i
\(960\) −4.80495e11 + 1.79323e12i −0.565723 + 2.11131i
\(961\) 5.60354e11i 0.657006i
\(962\) 1.49627e11 + 3.83764e11i 0.174706 + 0.448088i
\(963\) 1.25478e11 0.145902
\(964\) −2.72254e10 7.29501e9i −0.0315257 0.00844730i
\(965\) −6.36932e11 3.67733e11i −0.734487 0.424056i
\(966\) 1.70890e12 + 9.86636e11i 1.96250 + 1.13305i
\(967\) −8.88815e11 + 2.38157e11i −1.01650 + 0.272369i −0.728341 0.685215i \(-0.759708\pi\)
−0.288154 + 0.957584i \(0.593042\pi\)
\(968\) −6.23879e11 6.23879e11i −0.710557 0.710557i
\(969\) 1.03797e12 1.79782e12i 1.17731 2.03916i
\(970\) 1.75403e11 + 1.75403e11i 0.198129 + 0.198129i
\(971\) −3.20008e11 5.54271e11i −0.359985 0.623512i 0.627973 0.778235i \(-0.283885\pi\)
−0.987958 + 0.154723i \(0.950552\pi\)
\(972\) −2.27918e11 −0.255337
\(973\) 2.81745e11i 0.314344i
\(974\) 4.38985e11 + 7.60345e11i 0.487769 + 0.844840i
\(975\) 9.39164e11 2.51648e11i 1.03926 0.278468i
\(976\) 3.26632e11 3.26632e11i 0.359964 0.359964i
\(977\) −5.82269e11 1.56019e11i −0.639066 0.171237i −0.0752856 0.997162i \(-0.523987\pi\)
−0.563780 + 0.825925i \(0.690654\pi\)
\(978\) 2.45613e11 + 4.25414e11i 0.268470 + 0.465003i
\(979\) −5.81433e10 + 2.16994e11i −0.0632950 + 0.236220i
\(980\) 4.93727e10 + 1.84262e11i 0.0535282 + 0.199770i
\(981\) −1.85394e11 + 4.96762e10i −0.200180 + 0.0536380i
\(982\) 1.05789e12 + 2.83460e11i 1.13761 + 0.304822i
\(983\) −5.45359e11 + 3.14863e11i −0.584075 + 0.337216i −0.762751 0.646692i \(-0.776152\pi\)
0.178676 + 0.983908i \(0.442818\pi\)
\(984\) −5.29632e11 + 1.97661e12i −0.564929 + 2.10834i
\(985\) −8.92866e11 8.92866e11i −0.948508 0.948508i
\(986\) −2.38052e11 8.88422e11i −0.251863 0.939965i
\(987\) −1.70023e12 + 9.81629e11i −1.79159 + 1.03438i
\(988\) 2.24482e11 0.235588
\(989\) 1.23670e12i 1.29265i
\(990\) −1.63934e11 + 9.46474e10i −0.170659 + 0.0985299i
\(991\) 3.42397e11 3.42397e11i 0.355006 0.355006i −0.506962 0.861968i \(-0.669232\pi\)
0.861968 + 0.506962i \(0.169232\pi\)
\(992\) 2.52287e11 + 1.45658e11i 0.260524 + 0.150414i
\(993\) 8.32133e11 8.32133e11i 0.855847 0.855847i
\(994\) −4.43477e10 1.65508e11i −0.0454282 0.169541i
\(995\) 8.03069e11 1.39096e12i 0.819333 1.41913i
\(996\) 5.99957e10 1.03916e11i 0.0609653 0.105595i
\(997\) −1.21117e11 + 4.52014e11i −0.122581 + 0.457479i −0.999742 0.0227179i \(-0.992768\pi\)
0.877161 + 0.480197i \(0.159435\pi\)
\(998\) 1.18650e12i 1.19604i
\(999\) 5.38361e11 2.09903e11i 0.540520 0.210745i
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 37.9.g.a.8.18 100
37.14 odd 12 inner 37.9.g.a.14.18 yes 100
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
37.9.g.a.8.18 100 1.1 even 1 trivial
37.9.g.a.14.18 yes 100 37.14 odd 12 inner