Properties

Label 38.10.c.b.11.7
Level $38$
Weight $10$
Character 38.11
Analytic conductor $19.571$
Analytic rank $0$
Dimension $16$
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] = [38,10,Mod(7,38)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(38, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("38.7");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 38.c (of order \(3\), 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: \(19.5713617742\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 104960 x^{14} - 3899480 x^{13} + 8040649724 x^{12} - 270026959304 x^{11} + 275078771318560 x^{10} + \cdots + 13\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{12}\cdot 3^{5}\cdot 19^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 11.7
Root \(-89.8616 + 155.645i\) of defining polynomial
Character \(\chi\) \(=\) 38.11
Dual form 38.10.c.b.7.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-8.00000 + 13.8564i) q^{2} +(94.3616 - 163.439i) q^{3} +(-128.000 - 221.703i) q^{4} +(1091.71 - 1890.90i) q^{5} +(1509.79 + 2615.03i) q^{6} +6918.71 q^{7} +4096.00 q^{8} +(-7966.73 - 13798.8i) q^{9} +O(q^{10})\) \(q+(-8.00000 + 13.8564i) q^{2} +(94.3616 - 163.439i) q^{3} +(-128.000 - 221.703i) q^{4} +(1091.71 - 1890.90i) q^{5} +(1509.79 + 2615.03i) q^{6} +6918.71 q^{7} +4096.00 q^{8} +(-7966.73 - 13798.8i) q^{9} +(17467.4 + 30254.4i) q^{10} +37826.2 q^{11} -48313.1 q^{12} +(-38053.7 - 65911.0i) q^{13} +(-55349.7 + 95868.5i) q^{14} +(-206031. - 356857. i) q^{15} +(-32768.0 + 56755.8i) q^{16} +(-57442.7 + 99493.8i) q^{17} +254935. q^{18} +(-41670.6 + 566526. i) q^{19} -558957. q^{20} +(652861. - 1.13079e6i) q^{21} +(-302610. + 524135. i) q^{22} +(-150029. - 259857. i) q^{23} +(386505. - 669447. i) q^{24} +(-1.40711e6 - 2.43718e6i) q^{25} +1.21772e6 q^{26} +707625. q^{27} +(-885595. - 1.53390e6i) q^{28} +(-2.39490e6 - 4.14809e6i) q^{29} +6.59301e6 q^{30} +8.93537e6 q^{31} +(-524288. - 908093. i) q^{32} +(3.56934e6 - 6.18228e6i) q^{33} +(-919084. - 1.59190e6i) q^{34} +(7.55325e6 - 1.30826e7i) q^{35} +(-2.03948e6 + 3.53249e6i) q^{36} -4.52289e6 q^{37} +(-7.51664e6 - 5.10961e6i) q^{38} -1.43632e7 q^{39} +(4.47165e6 - 7.74513e6i) q^{40} +(-8.17432e6 + 1.41583e7i) q^{41} +(1.04458e7 + 1.80926e7i) q^{42} +(-2.12430e7 + 3.67939e7i) q^{43} +(-4.84175e6 - 8.38616e6i) q^{44} -3.47895e7 q^{45} +4.80092e6 q^{46} +(-2.50212e7 - 4.33380e7i) q^{47} +(6.18408e6 + 1.07111e7i) q^{48} +7.51500e6 q^{49} +4.50275e7 q^{50} +(1.08408e7 + 1.87768e7i) q^{51} +(-9.74175e6 + 1.68732e7i) q^{52} +(1.92327e7 + 3.33120e7i) q^{53} +(-5.66100e6 + 9.80514e6i) q^{54} +(4.12953e7 - 7.15256e7i) q^{55} +2.83391e7 q^{56} +(8.86603e7 + 6.02689e7i) q^{57} +7.66369e7 q^{58} +(-4.24144e7 + 7.34638e7i) q^{59} +(-5.27441e7 + 9.13554e7i) q^{60} +(-7.12676e7 - 1.23439e8i) q^{61} +(-7.14829e7 + 1.23812e8i) q^{62} +(-5.51195e7 - 9.54698e7i) q^{63} +1.67772e7 q^{64} -1.66175e8 q^{65} +(5.71095e7 + 9.89165e7i) q^{66} +(9.02171e7 + 1.56261e8i) q^{67} +2.94107e7 q^{68} -5.66278e7 q^{69} +(1.20852e8 + 2.09322e8i) q^{70} +(7.16885e7 - 1.24168e8i) q^{71} +(-3.26317e7 - 5.65198e7i) q^{72} +(3.77482e7 - 6.53818e7i) q^{73} +(3.61831e7 - 6.26710e7i) q^{74} -5.31108e8 q^{75} +(1.30934e8 - 6.32768e7i) q^{76} +2.61709e8 q^{77} +(1.14906e8 - 1.99023e8i) q^{78} +(-9.93343e7 + 1.72052e8i) q^{79} +(7.15465e7 + 1.23922e8i) q^{80} +(2.23582e8 - 3.87255e8i) q^{81} +(-1.30789e8 - 2.26533e8i) q^{82} -1.57357e8 q^{83} -3.34265e8 q^{84} +(1.25422e8 + 2.17237e8i) q^{85} +(-3.39888e8 - 5.88702e8i) q^{86} -9.03947e8 q^{87} +1.54936e8 q^{88} +(5.16270e8 + 8.94205e8i) q^{89} +(2.78316e8 - 4.82058e8i) q^{90} +(-2.63283e8 - 4.56019e8i) q^{91} +(-3.84073e7 + 6.65235e7i) q^{92} +(8.43156e8 - 1.46039e9i) q^{93} +8.00678e8 q^{94} +(1.02575e9 + 6.97278e8i) q^{95} -1.97891e8 q^{96} +(2.76869e8 - 4.79551e8i) q^{97} +(-6.01200e7 + 1.04131e8i) q^{98} +(-3.01351e8 - 5.21955e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 128 q^{2} + 70 q^{3} - 2048 q^{4} - 341 q^{5} + 1120 q^{6} + 3704 q^{7} + 65536 q^{8} - 53064 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 128 q^{2} + 70 q^{3} - 2048 q^{4} - 341 q^{5} + 1120 q^{6} + 3704 q^{7} + 65536 q^{8} - 53064 q^{9} - 5456 q^{10} + 106682 q^{11} - 35840 q^{12} - 683 q^{13} - 29632 q^{14} + 2299 q^{15} - 524288 q^{16} - 611267 q^{17} + 1698048 q^{18} - 1609677 q^{19} + 174592 q^{20} - 941048 q^{21} - 853456 q^{22} - 416119 q^{23} + 286720 q^{24} - 3309027 q^{25} + 21856 q^{26} - 16903604 q^{27} - 474112 q^{28} - 5079157 q^{29} - 73568 q^{30} + 8618324 q^{31} - 8388608 q^{32} - 7592195 q^{33} - 9780272 q^{34} - 2035632 q^{35} - 13584384 q^{36} - 33091520 q^{37} + 18612624 q^{38} + 37931126 q^{39} - 1396736 q^{40} - 7394646 q^{41} - 15056768 q^{42} - 98675599 q^{43} - 13655296 q^{44} + 89231852 q^{45} + 13315808 q^{46} + 34129475 q^{47} + 4587520 q^{48} + 65004400 q^{49} + 105888864 q^{50} + 16027749 q^{51} - 174848 q^{52} - 110053995 q^{53} + 135228832 q^{54} + 135992300 q^{55} + 15171584 q^{56} + 14986101 q^{57} + 162533024 q^{58} - 2017760 q^{59} + 588544 q^{60} - 221861413 q^{61} - 68946592 q^{62} + 56812456 q^{63} + 268435456 q^{64} + 262635974 q^{65} - 121475120 q^{66} + 237580440 q^{67} + 312968704 q^{68} - 135348410 q^{69} - 32570112 q^{70} - 431190909 q^{71} - 217350144 q^{72} + 199873544 q^{73} + 264732160 q^{74} - 1822944486 q^{75} + 114275328 q^{76} + 2014342624 q^{77} - 303449008 q^{78} - 296762835 q^{79} - 22347776 q^{80} - 1069077456 q^{81} - 118314336 q^{82} + 1592138306 q^{83} + 481816576 q^{84} - 293558115 q^{85} - 1578809584 q^{86} - 1647860854 q^{87} + 436969472 q^{88} - 444394631 q^{89} - 713854816 q^{90} - 284099544 q^{91} - 106526464 q^{92} + 1322110374 q^{93} - 1092143200 q^{94} + 8705459 q^{95} - 146800640 q^{96} - 611719542 q^{97} - 520035200 q^{98} + 1201848626 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.00000 + 13.8564i −0.353553 + 0.612372i
\(3\) 94.3616 163.439i 0.672589 1.16496i −0.304578 0.952487i \(-0.598516\pi\)
0.977167 0.212471i \(-0.0681511\pi\)
\(4\) −128.000 221.703i −0.250000 0.433013i
\(5\) 1091.71 1890.90i 0.781166 1.35302i −0.150097 0.988671i \(-0.547959\pi\)
0.931263 0.364348i \(-0.118708\pi\)
\(6\) 1509.79 + 2615.03i 0.475592 + 0.823750i
\(7\) 6918.71 1.08914 0.544571 0.838715i \(-0.316693\pi\)
0.544571 + 0.838715i \(0.316693\pi\)
\(8\) 4096.00 0.353553
\(9\) −7966.73 13798.8i −0.404752 0.701051i
\(10\) 17467.4 + 30254.4i 0.552368 + 0.956729i
\(11\) 37826.2 0.778979 0.389489 0.921031i \(-0.372651\pi\)
0.389489 + 0.921031i \(0.372651\pi\)
\(12\) −48313.1 −0.672589
\(13\) −38053.7 65911.0i −0.369532 0.640048i 0.619960 0.784633i \(-0.287149\pi\)
−0.989492 + 0.144585i \(0.953815\pi\)
\(14\) −55349.7 + 95868.5i −0.385070 + 0.666960i
\(15\) −206031. 356857.i −1.05081 1.82005i
\(16\) −32768.0 + 56755.8i −0.125000 + 0.216506i
\(17\) −57442.7 + 99493.8i −0.166807 + 0.288919i −0.937296 0.348535i \(-0.886679\pi\)
0.770488 + 0.637454i \(0.220012\pi\)
\(18\) 254935. 0.572406
\(19\) −41670.6 + 566526.i −0.0733565 + 0.997306i
\(20\) −558957. −0.781166
\(21\) 652861. 1.13079e6i 0.732544 1.26880i
\(22\) −302610. + 524135.i −0.275411 + 0.477025i
\(23\) −150029. 259857.i −0.111789 0.193624i 0.804703 0.593678i \(-0.202325\pi\)
−0.916492 + 0.400054i \(0.868991\pi\)
\(24\) 386505. 669447.i 0.237796 0.411875i
\(25\) −1.40711e6 2.43718e6i −0.720440 1.24784i
\(26\) 1.21772e6 0.522597
\(27\) 707625. 0.256251
\(28\) −885595. 1.53390e6i −0.272285 0.471612i
\(29\) −2.39490e6 4.14809e6i −0.628777 1.08907i −0.987797 0.155744i \(-0.950222\pi\)
0.359020 0.933330i \(-0.383111\pi\)
\(30\) 6.59301e6 1.48607
\(31\) 8.93537e6 1.73774 0.868870 0.495041i \(-0.164847\pi\)
0.868870 + 0.495041i \(0.164847\pi\)
\(32\) −524288. 908093.i −0.0883883 0.153093i
\(33\) 3.56934e6 6.18228e6i 0.523933 0.907478i
\(34\) −919084. 1.59190e6i −0.117951 0.204296i
\(35\) 7.55325e6 1.30826e7i 0.850800 1.47363i
\(36\) −2.03948e6 + 3.53249e6i −0.202376 + 0.350525i
\(37\) −4.52289e6 −0.396742 −0.198371 0.980127i \(-0.563565\pi\)
−0.198371 + 0.980127i \(0.563565\pi\)
\(38\) −7.51664e6 5.10961e6i −0.584787 0.397522i
\(39\) −1.43632e7 −0.994172
\(40\) 4.47165e6 7.74513e6i 0.276184 0.478364i
\(41\) −8.17432e6 + 1.41583e7i −0.451777 + 0.782501i −0.998497 0.0548147i \(-0.982543\pi\)
0.546719 + 0.837316i \(0.315877\pi\)
\(42\) 1.04458e7 + 1.80926e7i 0.517987 + 0.897180i
\(43\) −2.12430e7 + 3.67939e7i −0.947561 + 1.64122i −0.197020 + 0.980399i \(0.563127\pi\)
−0.750541 + 0.660824i \(0.770207\pi\)
\(44\) −4.84175e6 8.38616e6i −0.194745 0.337308i
\(45\) −3.47895e7 −1.26471
\(46\) 4.80092e6 0.158093
\(47\) −2.50212e7 4.33380e7i −0.747942 1.29547i −0.948808 0.315854i \(-0.897709\pi\)
0.200866 0.979619i \(-0.435624\pi\)
\(48\) 6.18408e6 + 1.07111e7i 0.168147 + 0.291240i
\(49\) 7.51500e6 0.186229
\(50\) 4.50275e7 1.01886
\(51\) 1.08408e7 + 1.87768e7i 0.224385 + 0.388647i
\(52\) −9.74175e6 + 1.68732e7i −0.184766 + 0.320024i
\(53\) 1.92327e7 + 3.33120e7i 0.334810 + 0.579908i 0.983448 0.181189i \(-0.0579945\pi\)
−0.648638 + 0.761097i \(0.724661\pi\)
\(54\) −5.66100e6 + 9.80514e6i −0.0905986 + 0.156921i
\(55\) 4.12953e7 7.15256e7i 0.608512 1.05397i
\(56\) 2.83391e7 0.385070
\(57\) 8.86603e7 + 6.02689e7i 1.11248 + 0.756234i
\(58\) 7.66369e7 0.889225
\(59\) −4.24144e7 + 7.34638e7i −0.455700 + 0.789295i −0.998728 0.0504191i \(-0.983944\pi\)
0.543028 + 0.839714i \(0.317278\pi\)
\(60\) −5.27441e7 + 9.13554e7i −0.525403 + 0.910025i
\(61\) −7.12676e7 1.23439e8i −0.659034 1.14148i −0.980866 0.194684i \(-0.937632\pi\)
0.321832 0.946797i \(-0.395701\pi\)
\(62\) −7.14829e7 + 1.23812e8i −0.614384 + 1.06414i
\(63\) −5.51195e7 9.54698e7i −0.440832 0.763543i
\(64\) 1.67772e7 0.125000
\(65\) −1.66175e8 −1.15466
\(66\) 5.71095e7 + 9.89165e7i 0.370476 + 0.641684i
\(67\) 9.02171e7 + 1.56261e8i 0.546956 + 0.947355i 0.998481 + 0.0550966i \(0.0175467\pi\)
−0.451525 + 0.892258i \(0.649120\pi\)
\(68\) 2.94107e7 0.166807
\(69\) −5.66278e7 −0.300752
\(70\) 1.20852e8 + 2.09322e8i 0.601606 + 1.04201i
\(71\) 7.16885e7 1.24168e8i 0.334801 0.579893i −0.648645 0.761091i \(-0.724664\pi\)
0.983447 + 0.181198i \(0.0579975\pi\)
\(72\) −3.26317e7 5.65198e7i −0.143101 0.247859i
\(73\) 3.77482e7 6.53818e7i 0.155576 0.269466i −0.777692 0.628645i \(-0.783610\pi\)
0.933269 + 0.359179i \(0.116943\pi\)
\(74\) 3.61831e7 6.26710e7i 0.140269 0.242954i
\(75\) −5.31108e8 −1.93824
\(76\) 1.30934e8 6.32768e7i 0.450185 0.217562i
\(77\) 2.61709e8 0.848418
\(78\) 1.14906e8 1.99023e8i 0.351493 0.608804i
\(79\) −9.93343e7 + 1.72052e8i −0.286931 + 0.496979i −0.973076 0.230486i \(-0.925968\pi\)
0.686145 + 0.727465i \(0.259302\pi\)
\(80\) 7.15465e7 + 1.23922e8i 0.195291 + 0.338255i
\(81\) 2.23582e8 3.87255e8i 0.577104 0.999573i
\(82\) −1.30789e8 2.26533e8i −0.319455 0.553312i
\(83\) −1.57357e8 −0.363944 −0.181972 0.983304i \(-0.558248\pi\)
−0.181972 + 0.983304i \(0.558248\pi\)
\(84\) −3.34265e8 −0.732544
\(85\) 1.25422e8 + 2.17237e8i 0.260608 + 0.451387i
\(86\) −3.39888e8 5.88702e8i −0.670027 1.16052i
\(87\) −9.03947e8 −1.69163
\(88\) 1.54936e8 0.275411
\(89\) 5.16270e8 + 8.94205e8i 0.872211 + 1.51071i 0.859704 + 0.510792i \(0.170648\pi\)
0.0125068 + 0.999922i \(0.496019\pi\)
\(90\) 2.78316e8 4.82058e8i 0.447144 0.774475i
\(91\) −2.63283e8 4.56019e8i −0.402472 0.697103i
\(92\) −3.84073e7 + 6.65235e7i −0.0558945 + 0.0968121i
\(93\) 8.43156e8 1.46039e9i 1.16878 2.02439i
\(94\) 8.00678e8 1.05775
\(95\) 1.02575e9 + 6.97278e8i 1.29207 + 0.878314i
\(96\) −1.97891e8 −0.237796
\(97\) 2.76869e8 4.79551e8i 0.317542 0.549999i −0.662432 0.749122i \(-0.730476\pi\)
0.979975 + 0.199123i \(0.0638092\pi\)
\(98\) −6.01200e7 + 1.04131e8i −0.0658418 + 0.114041i
\(99\) −3.01351e8 5.21955e8i −0.315293 0.546104i
\(100\) −3.60220e8 + 6.23919e8i −0.360220 + 0.623919i
\(101\) 5.81532e8 + 1.00724e9i 0.556067 + 0.963136i 0.997820 + 0.0659994i \(0.0210236\pi\)
−0.441753 + 0.897137i \(0.645643\pi\)
\(102\) −3.46905e8 −0.317329
\(103\) −1.17081e9 −1.02499 −0.512493 0.858692i \(-0.671278\pi\)
−0.512493 + 0.858692i \(0.671278\pi\)
\(104\) −1.55868e8 2.69971e8i −0.130649 0.226291i
\(105\) −1.42547e9 2.46899e9i −1.14448 1.98229i
\(106\) −6.15446e8 −0.473493
\(107\) 1.65101e9 1.21765 0.608824 0.793305i \(-0.291642\pi\)
0.608824 + 0.793305i \(0.291642\pi\)
\(108\) −9.05760e7 1.56882e8i −0.0640629 0.110960i
\(109\) −3.15218e8 + 5.45973e8i −0.213891 + 0.370469i −0.952929 0.303194i \(-0.901947\pi\)
0.739038 + 0.673663i \(0.235280\pi\)
\(110\) 6.60725e8 + 1.14441e9i 0.430283 + 0.745271i
\(111\) −4.26787e8 + 7.39217e8i −0.266844 + 0.462188i
\(112\) −2.26712e8 + 3.92677e8i −0.136143 + 0.235806i
\(113\) 3.22899e9 1.86301 0.931503 0.363734i \(-0.118498\pi\)
0.931503 + 0.363734i \(0.118498\pi\)
\(114\) −1.54439e9 + 7.46363e8i −0.856418 + 0.413883i
\(115\) −6.55153e8 −0.349303
\(116\) −6.13095e8 + 1.06191e9i −0.314389 + 0.544537i
\(117\) −6.06327e8 + 1.05019e9i −0.299137 + 0.518121i
\(118\) −6.78630e8 1.17542e9i −0.322228 0.558116i
\(119\) −3.97430e8 + 6.88369e8i −0.181677 + 0.314673i
\(120\) −8.43905e8 1.46169e9i −0.371516 0.643485i
\(121\) −9.27126e8 −0.393192
\(122\) 2.28056e9 0.932015
\(123\) 1.54268e9 + 2.67201e9i 0.607721 + 1.05260i
\(124\) −1.14373e9 1.98099e9i −0.434435 0.752463i
\(125\) −1.88013e9 −0.688800
\(126\) 1.76382e9 0.623430
\(127\) 1.66363e9 + 2.88149e9i 0.567465 + 0.982879i 0.996816 + 0.0797408i \(0.0254093\pi\)
−0.429350 + 0.903138i \(0.641257\pi\)
\(128\) −1.34218e8 + 2.32472e8i −0.0441942 + 0.0765466i
\(129\) 4.00904e9 + 6.94386e9i 1.27464 + 2.20774i
\(130\) 1.32940e9 2.30259e9i 0.408235 0.707084i
\(131\) 2.08032e9 3.60322e9i 0.617176 1.06898i −0.372822 0.927903i \(-0.621610\pi\)
0.989998 0.141078i \(-0.0450568\pi\)
\(132\) −1.82750e9 −0.523933
\(133\) −2.88307e8 + 3.91963e9i −0.0798956 + 1.08621i
\(134\) −2.88695e9 −0.773512
\(135\) 7.72523e8 1.33805e9i 0.200175 0.346713i
\(136\) −2.35285e8 + 4.07526e8i −0.0589753 + 0.102148i
\(137\) 2.18691e9 + 3.78784e9i 0.530381 + 0.918647i 0.999372 + 0.0354437i \(0.0112844\pi\)
−0.468991 + 0.883203i \(0.655382\pi\)
\(138\) 4.53022e8 7.84658e8i 0.106332 0.184172i
\(139\) −1.59219e9 2.75775e9i −0.361767 0.626598i 0.626485 0.779433i \(-0.284493\pi\)
−0.988252 + 0.152835i \(0.951160\pi\)
\(140\) −3.86726e9 −0.850800
\(141\) −9.44416e9 −2.01223
\(142\) 1.14702e9 + 1.98669e9i 0.236740 + 0.410046i
\(143\) −1.43943e9 2.49316e9i −0.287858 0.498584i
\(144\) 1.04422e9 0.202376
\(145\) −1.04582e10 −1.96472
\(146\) 6.03971e8 + 1.04611e9i 0.110009 + 0.190541i
\(147\) 7.09127e8 1.22824e9i 0.125255 0.216949i
\(148\) 5.78930e8 + 1.00274e9i 0.0991855 + 0.171794i
\(149\) −1.43095e9 + 2.47847e9i −0.237840 + 0.411951i −0.960094 0.279677i \(-0.909773\pi\)
0.722254 + 0.691628i \(0.243106\pi\)
\(150\) 4.24887e9 7.35925e9i 0.685271 1.18692i
\(151\) 2.88094e9 0.450959 0.225480 0.974248i \(-0.427605\pi\)
0.225480 + 0.974248i \(0.427605\pi\)
\(152\) −1.70683e8 + 2.32049e9i −0.0259354 + 0.352601i
\(153\) 1.83052e9 0.270062
\(154\) −2.09367e9 + 3.62634e9i −0.299961 + 0.519548i
\(155\) 9.75485e9 1.68959e10i 1.35746 2.35119i
\(156\) 1.83849e9 + 3.18437e9i 0.248543 + 0.430489i
\(157\) −2.74991e9 + 4.76298e9i −0.361219 + 0.625649i −0.988162 0.153416i \(-0.950973\pi\)
0.626943 + 0.779065i \(0.284306\pi\)
\(158\) −1.58935e9 2.75283e9i −0.202891 0.351417i
\(159\) 7.25931e9 0.900758
\(160\) −2.28949e9 −0.276184
\(161\) −1.03801e9 1.79788e9i −0.121754 0.210884i
\(162\) 3.57731e9 + 6.19608e9i 0.408074 + 0.706805i
\(163\) 1.57961e10 1.75269 0.876347 0.481680i \(-0.159973\pi\)
0.876347 + 0.481680i \(0.159973\pi\)
\(164\) 4.18525e9 0.451777
\(165\) −7.79339e9 1.34985e10i −0.818556 1.41778i
\(166\) 1.25886e9 2.18040e9i 0.128674 0.222869i
\(167\) 8.30349e7 + 1.43821e8i 0.00826107 + 0.0143086i 0.870126 0.492829i \(-0.164037\pi\)
−0.861865 + 0.507137i \(0.830704\pi\)
\(168\) 2.67412e9 4.63171e9i 0.258994 0.448590i
\(169\) 2.40608e9 4.16745e9i 0.226892 0.392989i
\(170\) −4.01350e9 −0.368556
\(171\) 8.14934e9 3.93835e9i 0.728853 0.352235i
\(172\) 1.08764e10 0.947561
\(173\) 2.57782e9 4.46492e9i 0.218799 0.378971i −0.735642 0.677371i \(-0.763119\pi\)
0.954441 + 0.298399i \(0.0964527\pi\)
\(174\) 7.23158e9 1.25255e10i 0.598083 1.03591i
\(175\) −9.73539e9 1.68622e10i −0.784661 1.35907i
\(176\) −1.23949e9 + 2.14686e9i −0.0973723 + 0.168654i
\(177\) 8.00458e9 + 1.38643e10i 0.612997 + 1.06174i
\(178\) −1.65206e10 −1.23349
\(179\) −2.26645e10 −1.65009 −0.825044 0.565069i \(-0.808850\pi\)
−0.825044 + 0.565069i \(0.808850\pi\)
\(180\) 4.45306e9 + 7.71292e9i 0.316178 + 0.547637i
\(181\) −9.97129e9 1.72708e10i −0.690554 1.19607i −0.971657 0.236397i \(-0.924033\pi\)
0.281103 0.959678i \(-0.409300\pi\)
\(182\) 8.42505e9 0.569182
\(183\) −2.68997e10 −1.77304
\(184\) −6.14517e8 1.06438e9i −0.0395234 0.0684565i
\(185\) −4.93769e9 + 8.55233e9i −0.309921 + 0.536799i
\(186\) 1.34905e10 + 2.33662e10i 0.826456 + 1.43146i
\(187\) −2.17284e9 + 3.76347e9i −0.129939 + 0.225062i
\(188\) −6.40543e9 + 1.10945e10i −0.373971 + 0.647736i
\(189\) 4.89586e9 0.279094
\(190\) −1.78678e10 + 8.63501e9i −0.994671 + 0.480697i
\(191\) 2.11403e10 1.14937 0.574687 0.818373i \(-0.305124\pi\)
0.574687 + 0.818373i \(0.305124\pi\)
\(192\) 1.58313e9 2.74205e9i 0.0840736 0.145620i
\(193\) −1.34287e10 + 2.32593e10i −0.696671 + 1.20667i 0.272944 + 0.962030i \(0.412003\pi\)
−0.969614 + 0.244639i \(0.921331\pi\)
\(194\) 4.42990e9 + 7.67281e9i 0.224536 + 0.388908i
\(195\) −1.56805e10 + 2.71595e10i −0.776613 + 1.34513i
\(196\) −9.61920e8 1.66609e9i −0.0465572 0.0806394i
\(197\) −8.39663e9 −0.397198 −0.198599 0.980081i \(-0.563639\pi\)
−0.198599 + 0.980081i \(0.563639\pi\)
\(198\) 9.64324e9 0.445892
\(199\) −2.10670e10 3.64890e10i −0.952276 1.64939i −0.740482 0.672077i \(-0.765403\pi\)
−0.211795 0.977314i \(-0.567931\pi\)
\(200\) −5.76352e9 9.98271e9i −0.254714 0.441177i
\(201\) 3.40521e10 1.47151
\(202\) −1.86090e10 −0.786398
\(203\) −1.65696e10 2.86995e10i −0.684827 1.18616i
\(204\) 2.77524e9 4.80686e9i 0.112193 0.194324i
\(205\) 1.78480e10 + 3.09137e10i 0.705826 + 1.22253i
\(206\) 9.36645e9 1.62232e10i 0.362387 0.627673i
\(207\) −2.39048e9 + 4.14043e9i −0.0904936 + 0.156739i
\(208\) 4.98778e9 0.184766
\(209\) −1.57624e9 + 2.14295e10i −0.0571431 + 0.776880i
\(210\) 4.56151e10 1.61854
\(211\) −3.18826e9 + 5.52224e9i −0.110735 + 0.191798i −0.916067 0.401026i \(-0.868654\pi\)
0.805332 + 0.592824i \(0.201987\pi\)
\(212\) 4.92357e9 8.52787e9i 0.167405 0.289954i
\(213\) −1.35293e10 2.34334e10i −0.450367 0.780059i
\(214\) −1.32081e10 + 2.28770e10i −0.430504 + 0.745654i
\(215\) 4.63824e10 + 8.03367e10i 1.48040 + 2.56414i
\(216\) 2.89843e9 0.0905986
\(217\) 6.18212e10 1.89264
\(218\) −5.04349e9 8.73557e9i −0.151243 0.261961i
\(219\) −7.12396e9 1.23391e10i −0.209278 0.362480i
\(220\) −2.11432e10 −0.608512
\(221\) 8.74364e9 0.246562
\(222\) −6.82859e9 1.18275e10i −0.188687 0.326816i
\(223\) −2.27988e8 + 3.94888e8i −0.00617363 + 0.0106930i −0.869096 0.494644i \(-0.835298\pi\)
0.862922 + 0.505337i \(0.168632\pi\)
\(224\) −3.62740e9 6.28284e9i −0.0962674 0.166740i
\(225\) −2.24201e10 + 3.88328e10i −0.583199 + 1.01013i
\(226\) −2.58319e10 + 4.47422e10i −0.658672 + 1.14085i
\(227\) 3.05603e10 0.763909 0.381955 0.924181i \(-0.375251\pi\)
0.381955 + 0.924181i \(0.375251\pi\)
\(228\) 2.01324e9 2.73706e10i 0.0493388 0.670777i
\(229\) −4.51630e10 −1.08523 −0.542616 0.839981i \(-0.682566\pi\)
−0.542616 + 0.839981i \(0.682566\pi\)
\(230\) 5.24122e9 9.07806e9i 0.123497 0.213903i
\(231\) 2.46953e10 4.27734e10i 0.570637 0.988371i
\(232\) −9.80952e9 1.69906e10i −0.222306 0.385046i
\(233\) −9.47607e8 + 1.64130e9i −0.0210633 + 0.0364827i −0.876365 0.481648i \(-0.840038\pi\)
0.855302 + 0.518130i \(0.173372\pi\)
\(234\) −9.70124e9 1.68030e10i −0.211522 0.366367i
\(235\) −1.09264e11 −2.33707
\(236\) 2.17162e10 0.455700
\(237\) 1.87467e10 + 3.24702e10i 0.385973 + 0.668525i
\(238\) −6.35888e9 1.10139e10i −0.128465 0.222508i
\(239\) 6.74111e10 1.33641 0.668207 0.743976i \(-0.267062\pi\)
0.668207 + 0.743976i \(0.267062\pi\)
\(240\) 2.70050e10 0.525403
\(241\) 1.60322e10 + 2.77686e10i 0.306137 + 0.530245i 0.977514 0.210871i \(-0.0676300\pi\)
−0.671377 + 0.741116i \(0.734297\pi\)
\(242\) 7.41701e9 1.28466e10i 0.139014 0.240780i
\(243\) −3.52310e10 6.10219e10i −0.648181 1.12268i
\(244\) −1.82445e10 + 3.16004e10i −0.329517 + 0.570740i
\(245\) 8.20421e9 1.42101e10i 0.145475 0.251971i
\(246\) −4.93659e10 −0.859447
\(247\) 3.89260e10 1.88119e10i 0.665431 0.321585i
\(248\) 3.65993e10 0.614384
\(249\) −1.48485e10 + 2.57183e10i −0.244785 + 0.423980i
\(250\) 1.50411e10 2.60519e10i 0.243528 0.421802i
\(251\) −5.49346e10 9.51496e10i −0.873604 1.51313i −0.858243 0.513244i \(-0.828444\pi\)
−0.0153608 0.999882i \(-0.504890\pi\)
\(252\) −1.41106e10 + 2.44403e10i −0.220416 + 0.381772i
\(253\) −5.67501e9 9.82941e9i −0.0870812 0.150829i
\(254\) −5.32361e10 −0.802517
\(255\) 4.73401e10 0.701129
\(256\) −2.14748e9 3.71955e9i −0.0312500 0.0541266i
\(257\) −1.94059e9 3.36120e9i −0.0277481 0.0480612i 0.851818 0.523838i \(-0.175500\pi\)
−0.879566 + 0.475777i \(0.842167\pi\)
\(258\) −1.28289e11 −1.80261
\(259\) −3.12926e10 −0.432108
\(260\) 2.12704e10 + 3.68414e10i 0.288666 + 0.499984i
\(261\) −3.81591e10 + 6.60935e10i −0.508997 + 0.881609i
\(262\) 3.32851e10 + 5.76515e10i 0.436410 + 0.755884i
\(263\) 7.66595e9 1.32778e10i 0.0988018 0.171130i −0.812387 0.583118i \(-0.801832\pi\)
0.911189 + 0.411989i \(0.135166\pi\)
\(264\) 1.46200e10 2.53226e10i 0.185238 0.320842i
\(265\) 8.39862e10 1.04617
\(266\) −5.20055e10 3.53519e10i −0.636916 0.432958i
\(267\) 1.94864e11 2.34656
\(268\) 2.30956e10 4.00027e10i 0.273478 0.473677i
\(269\) 4.88672e10 8.46405e10i 0.569026 0.985582i −0.427636 0.903951i \(-0.640654\pi\)
0.996663 0.0816316i \(-0.0260131\pi\)
\(270\) 1.23604e10 + 2.14088e10i 0.141545 + 0.245163i
\(271\) −1.41690e10 + 2.45415e10i −0.159580 + 0.276401i −0.934717 0.355392i \(-0.884347\pi\)
0.775137 + 0.631793i \(0.217681\pi\)
\(272\) −3.76457e9 6.52042e9i −0.0417018 0.0722297i
\(273\) −9.93751e10 −1.08279
\(274\) −6.99811e10 −0.750072
\(275\) −5.32256e10 9.21894e10i −0.561207 0.972040i
\(276\) 7.24836e9 + 1.25545e10i 0.0751880 + 0.130229i
\(277\) −5.34624e10 −0.545619 −0.272809 0.962068i \(-0.587953\pi\)
−0.272809 + 0.962068i \(0.587953\pi\)
\(278\) 5.09501e10 0.511615
\(279\) −7.11857e10 1.23297e11i −0.703353 1.21824i
\(280\) 3.09381e10 5.35863e10i 0.300803 0.521006i
\(281\) 8.83508e10 + 1.53028e11i 0.845342 + 1.46417i 0.885324 + 0.464974i \(0.153936\pi\)
−0.0399826 + 0.999200i \(0.512730\pi\)
\(282\) 7.55533e10 1.30862e11i 0.711430 1.23223i
\(283\) 2.76970e10 4.79727e10i 0.256681 0.444585i −0.708669 0.705541i \(-0.750704\pi\)
0.965351 + 0.260955i \(0.0840375\pi\)
\(284\) −3.67045e10 −0.334801
\(285\) 2.10754e11 1.01852e11i 1.89223 0.914463i
\(286\) 4.60617e10 0.407092
\(287\) −5.65558e10 + 9.79575e10i −0.492049 + 0.852254i
\(288\) −8.35372e9 + 1.44691e10i −0.0715507 + 0.123929i
\(289\) 5.26946e10 + 9.12697e10i 0.444351 + 0.769638i
\(290\) 8.36654e10 1.44913e11i 0.694632 1.20314i
\(291\) −5.22516e10 9.05024e10i −0.427151 0.739847i
\(292\) −1.93271e10 −0.155576
\(293\) −8.74370e10 −0.693092 −0.346546 0.938033i \(-0.612646\pi\)
−0.346546 + 0.938033i \(0.612646\pi\)
\(294\) 1.13460e10 + 1.96519e10i 0.0885689 + 0.153406i
\(295\) 9.26086e10 + 1.60403e11i 0.711954 + 1.23314i
\(296\) −1.85257e10 −0.140269
\(297\) 2.67668e10 0.199614
\(298\) −2.28951e10 3.96555e10i −0.168178 0.291293i
\(299\) −1.14183e10 + 1.97771e10i −0.0826192 + 0.143101i
\(300\) 6.79819e10 + 1.17748e11i 0.484560 + 0.839282i
\(301\) −1.46974e11 + 2.54566e11i −1.03203 + 1.78752i
\(302\) −2.30475e10 + 3.99194e10i −0.159438 + 0.276155i
\(303\) 2.19497e11 1.49602
\(304\) −3.07882e10 2.09290e10i −0.206753 0.140545i
\(305\) −3.11215e11 −2.05926
\(306\) −1.46442e10 + 2.53645e10i −0.0954814 + 0.165379i
\(307\) −1.53591e11 + 2.66027e11i −0.986830 + 1.70924i −0.353325 + 0.935501i \(0.614949\pi\)
−0.633505 + 0.773739i \(0.718384\pi\)
\(308\) −3.34987e10 5.80215e10i −0.212104 0.367376i
\(309\) −1.10479e11 + 1.91356e11i −0.689394 + 1.19406i
\(310\) 1.56078e11 + 2.70334e11i 0.959871 + 1.66255i
\(311\) 2.76594e11 1.67657 0.838283 0.545235i \(-0.183560\pi\)
0.838283 + 0.545235i \(0.183560\pi\)
\(312\) −5.88318e10 −0.351493
\(313\) −1.07591e11 1.86354e11i −0.633619 1.09746i −0.986806 0.161908i \(-0.948235\pi\)
0.353187 0.935553i \(-0.385098\pi\)
\(314\) −4.39986e10 7.62078e10i −0.255420 0.442401i
\(315\) −2.40699e11 −1.37745
\(316\) 5.08591e10 0.286931
\(317\) 4.12686e10 + 7.14793e10i 0.229537 + 0.397570i 0.957671 0.287865i \(-0.0929454\pi\)
−0.728134 + 0.685435i \(0.759612\pi\)
\(318\) −5.80745e10 + 1.00588e11i −0.318466 + 0.551599i
\(319\) −9.05900e10 1.56907e11i −0.489804 0.848365i
\(320\) 1.83159e10 3.17241e10i 0.0976457 0.169127i
\(321\) 1.55792e11 2.69839e11i 0.818977 1.41851i
\(322\) 3.32162e10 0.172186
\(323\) −5.39721e10 3.66887e10i −0.275904 0.187552i
\(324\) −1.14474e11 −0.577104
\(325\) −1.07091e11 + 1.85488e11i −0.532451 + 0.922232i
\(326\) −1.26369e11 + 2.18877e11i −0.619671 + 1.07330i
\(327\) 5.94889e10 + 1.03038e11i 0.287721 + 0.498347i
\(328\) −3.34820e10 + 5.79926e10i −0.159727 + 0.276656i
\(329\) −1.73114e11 2.99843e11i −0.814614 1.41095i
\(330\) 2.49388e11 1.15761
\(331\) −3.68203e11 −1.68601 −0.843007 0.537903i \(-0.819217\pi\)
−0.843007 + 0.537903i \(0.819217\pi\)
\(332\) 2.01417e10 + 3.48865e10i 0.0909861 + 0.157593i
\(333\) 3.60326e10 + 6.24103e10i 0.160582 + 0.278136i
\(334\) −2.65712e9 −0.0116829
\(335\) 3.93964e11 1.70905
\(336\) 4.27859e10 + 7.41074e10i 0.183136 + 0.317201i
\(337\) 4.02171e9 6.96580e9i 0.0169854 0.0294196i −0.857408 0.514638i \(-0.827926\pi\)
0.874393 + 0.485218i \(0.161260\pi\)
\(338\) 3.84973e10 + 6.66792e10i 0.160437 + 0.277885i
\(339\) 3.04693e11 5.27744e11i 1.25304 2.17032i
\(340\) 3.21080e10 5.56127e10i 0.130304 0.225693i
\(341\) 3.37991e11 1.35366
\(342\) −1.06233e10 + 1.44427e11i −0.0419896 + 0.570863i
\(343\) −2.27201e11 −0.886312
\(344\) −8.70112e10 + 1.50708e11i −0.335013 + 0.580260i
\(345\) −6.18213e10 + 1.07078e11i −0.234937 + 0.406923i
\(346\) 4.12452e10 + 7.14387e10i 0.154714 + 0.267973i
\(347\) 5.75021e10 9.95966e10i 0.212913 0.368775i −0.739712 0.672923i \(-0.765038\pi\)
0.952625 + 0.304148i \(0.0983717\pi\)
\(348\) 1.15705e11 + 2.00407e11i 0.422909 + 0.732499i
\(349\) 2.19182e11 0.790843 0.395421 0.918500i \(-0.370599\pi\)
0.395421 + 0.918500i \(0.370599\pi\)
\(350\) 3.11532e11 1.10968
\(351\) −2.69278e10 4.66403e10i −0.0946931 0.164013i
\(352\) −1.98318e10 3.43497e10i −0.0688526 0.119256i
\(353\) −2.27691e11 −0.780475 −0.390237 0.920714i \(-0.627607\pi\)
−0.390237 + 0.920714i \(0.627607\pi\)
\(354\) −2.56146e11 −0.866909
\(355\) −1.56526e11 2.71112e11i −0.523070 0.905985i
\(356\) 1.32165e11 2.28917e11i 0.436106 0.755357i
\(357\) 7.50043e10 + 1.29911e11i 0.244387 + 0.423292i
\(358\) 1.81316e11 3.14048e11i 0.583394 1.01047i
\(359\) −2.52112e10 + 4.36670e10i −0.0801066 + 0.138749i −0.903296 0.429019i \(-0.858859\pi\)
0.823189 + 0.567767i \(0.192193\pi\)
\(360\) −1.42498e11 −0.447144
\(361\) −3.19215e11 4.72149e10i −0.989238 0.146318i
\(362\) 3.19081e11 0.976591
\(363\) −8.74851e10 + 1.51529e11i −0.264457 + 0.458052i
\(364\) −6.74004e10 + 1.16741e11i −0.201236 + 0.348551i
\(365\) −8.24203e10 1.42756e11i −0.243062 0.420995i
\(366\) 2.15198e11 3.72733e11i 0.626863 1.08576i
\(367\) −2.41691e11 4.18622e11i −0.695447 1.20455i −0.970030 0.242986i \(-0.921873\pi\)
0.274583 0.961563i \(-0.411460\pi\)
\(368\) 1.96646e10 0.0558945
\(369\) 2.60491e11 0.731431
\(370\) −7.90031e10 1.36837e11i −0.219147 0.379574i
\(371\) 1.33065e11 + 2.30476e11i 0.364655 + 0.631602i
\(372\) −4.31696e11 −1.16878
\(373\) −1.96088e11 −0.524520 −0.262260 0.964997i \(-0.584468\pi\)
−0.262260 + 0.964997i \(0.584468\pi\)
\(374\) −3.47655e10 6.02155e10i −0.0918810 0.159143i
\(375\) −1.77412e11 + 3.07287e11i −0.463279 + 0.802423i
\(376\) −1.02487e11 1.77512e11i −0.264437 0.458019i
\(377\) −1.82270e11 + 3.15701e11i −0.464706 + 0.804895i
\(378\) −3.91669e10 + 6.78390e10i −0.0986746 + 0.170909i
\(379\) −2.07237e9 −0.00515931 −0.00257965 0.999997i \(-0.500821\pi\)
−0.00257965 + 0.999997i \(0.500821\pi\)
\(380\) 2.32921e10 3.16663e11i 0.0573036 0.779061i
\(381\) 6.27930e11 1.52668
\(382\) −1.69122e11 + 2.92929e11i −0.406365 + 0.703845i
\(383\) −8.46482e10 + 1.46615e11i −0.201013 + 0.348164i −0.948855 0.315712i \(-0.897757\pi\)
0.747842 + 0.663876i \(0.231090\pi\)
\(384\) 2.53300e10 + 4.38729e10i 0.0594490 + 0.102969i
\(385\) 2.85711e11 4.94865e11i 0.662755 1.14793i
\(386\) −2.14860e11 3.72148e11i −0.492621 0.853244i
\(387\) 6.76948e11 1.53411
\(388\) −1.41757e11 −0.317542
\(389\) 6.96735e10 + 1.20678e11i 0.154275 + 0.267211i 0.932795 0.360408i \(-0.117363\pi\)
−0.778520 + 0.627620i \(0.784029\pi\)
\(390\) −2.50888e11 4.34551e11i −0.549149 0.951153i
\(391\) 3.44722e10 0.0745889
\(392\) 3.07814e10 0.0658418
\(393\) −3.92605e11 6.80011e11i −0.830212 1.43797i
\(394\) 6.71730e10 1.16347e11i 0.140431 0.243233i
\(395\) 2.16889e11 + 3.75663e11i 0.448281 + 0.776446i
\(396\) −7.71459e10 + 1.33621e11i −0.157647 + 0.273052i
\(397\) 7.98038e10 1.38224e11i 0.161238 0.279272i −0.774075 0.633094i \(-0.781785\pi\)
0.935313 + 0.353822i \(0.115118\pi\)
\(398\) 6.74143e11 1.34672
\(399\) 6.13416e11 + 4.16983e11i 1.21165 + 0.823646i
\(400\) 1.84433e11 0.360220
\(401\) −2.37185e11 + 4.10816e11i −0.458076 + 0.793411i −0.998859 0.0477512i \(-0.984795\pi\)
0.540783 + 0.841162i \(0.318128\pi\)
\(402\) −2.72417e11 + 4.71840e11i −0.520256 + 0.901109i
\(403\) −3.40024e11 5.88939e11i −0.642150 1.11224i
\(404\) 1.48872e11 2.57854e11i 0.278034 0.481568i
\(405\) −4.88174e11 8.45542e11i −0.901627 1.56166i
\(406\) 5.30229e11 0.968492
\(407\) −1.71084e11 −0.309053
\(408\) 4.44038e10 + 7.69097e10i 0.0793323 + 0.137407i
\(409\) 4.63708e11 + 8.03165e11i 0.819387 + 1.41922i 0.906134 + 0.422990i \(0.139020\pi\)
−0.0867467 + 0.996230i \(0.527647\pi\)
\(410\) −5.71137e11 −0.998189
\(411\) 8.25441e11 1.42691
\(412\) 1.49863e11 + 2.59571e11i 0.256246 + 0.443832i
\(413\) −2.93453e11 + 5.08275e11i −0.496321 + 0.859654i
\(414\) −3.82476e10 6.62468e10i −0.0639886 0.110832i
\(415\) −1.71789e11 + 2.97547e11i −0.284301 + 0.492424i
\(416\) −3.99022e10 + 6.91127e10i −0.0653246 + 0.113146i
\(417\) −6.00967e11 −0.973281
\(418\) −2.84326e11 1.93277e11i −0.455537 0.309661i
\(419\) −2.28844e11 −0.362724 −0.181362 0.983416i \(-0.558051\pi\)
−0.181362 + 0.983416i \(0.558051\pi\)
\(420\) −3.64921e11 + 6.32062e11i −0.572239 + 0.991146i
\(421\) 5.76474e11 9.98483e11i 0.894356 1.54907i 0.0597573 0.998213i \(-0.480967\pi\)
0.834599 0.550858i \(-0.185699\pi\)
\(422\) −5.10122e10 8.83558e10i −0.0783012 0.135622i
\(423\) −3.98674e11 + 6.90524e11i −0.605461 + 1.04869i
\(424\) 7.87771e10 + 1.36446e11i 0.118373 + 0.205028i
\(425\) 3.23313e11 0.480698
\(426\) 4.32937e11 0.636915
\(427\) −4.93080e11 8.54040e11i −0.717781 1.24323i
\(428\) −2.11329e11 3.66032e11i −0.304412 0.527257i
\(429\) −5.43307e11 −0.774439
\(430\) −1.48424e12 −2.09361
\(431\) 5.46111e11 + 9.45892e11i 0.762313 + 1.32036i 0.941656 + 0.336578i \(0.109270\pi\)
−0.179343 + 0.983787i \(0.557397\pi\)
\(432\) −2.31875e10 + 4.01619e10i −0.0320314 + 0.0554801i
\(433\) 4.68151e11 + 8.10862e11i 0.640016 + 1.10854i 0.985429 + 0.170089i \(0.0544055\pi\)
−0.345413 + 0.938451i \(0.612261\pi\)
\(434\) −4.94570e11 + 8.56620e11i −0.669151 + 1.15900i
\(435\) −9.86850e11 + 1.70927e12i −1.32145 + 2.28881i
\(436\) 1.61392e11 0.213891
\(437\) 1.53468e11 7.41667e10i 0.201303 0.0972842i
\(438\) 2.27967e11 0.295963
\(439\) 6.73033e10 1.16573e11i 0.0864860 0.149798i −0.819537 0.573026i \(-0.805770\pi\)
0.906023 + 0.423227i \(0.139103\pi\)
\(440\) 1.69146e11 2.92969e11i 0.215141 0.372636i
\(441\) −5.98700e10 1.03698e11i −0.0753764 0.130556i
\(442\) −6.99491e10 + 1.21155e11i −0.0871730 + 0.150988i
\(443\) −2.83345e10 4.90768e10i −0.0349541 0.0605424i 0.848019 0.529966i \(-0.177795\pi\)
−0.882973 + 0.469423i \(0.844462\pi\)
\(444\) 2.18515e11 0.266844
\(445\) 2.25447e12 2.72537
\(446\) −3.64781e9 6.31820e9i −0.00436542 0.00756113i
\(447\) 2.70053e11 + 4.67745e11i 0.319937 + 0.554148i
\(448\) 1.16077e11 0.136143
\(449\) 9.25835e11 1.07504 0.537521 0.843251i \(-0.319361\pi\)
0.537521 + 0.843251i \(0.319361\pi\)
\(450\) −3.58722e11 6.21325e11i −0.412384 0.714270i
\(451\) −3.09204e11 + 5.35556e11i −0.351925 + 0.609552i
\(452\) −4.13311e11 7.15876e11i −0.465751 0.806705i
\(453\) 2.71850e11 4.70858e11i 0.303310 0.525349i
\(454\) −2.44483e11 + 4.23456e11i −0.270083 + 0.467797i
\(455\) −1.14972e12 −1.25759
\(456\) 3.63153e11 + 2.46861e11i 0.393321 + 0.267369i
\(457\) −8.34766e11 −0.895245 −0.447622 0.894223i \(-0.647729\pi\)
−0.447622 + 0.894223i \(0.647729\pi\)
\(458\) 3.61304e11 6.25796e11i 0.383688 0.664566i
\(459\) −4.06479e10 + 7.04043e10i −0.0427446 + 0.0740358i
\(460\) 8.38595e10 + 1.45249e11i 0.0873257 + 0.151253i
\(461\) −1.29091e11 + 2.23591e11i −0.133119 + 0.230569i −0.924877 0.380266i \(-0.875833\pi\)
0.791758 + 0.610834i \(0.209166\pi\)
\(462\) 3.95124e11 + 6.84375e11i 0.403501 + 0.698884i
\(463\) 8.08979e11 0.818131 0.409066 0.912505i \(-0.365855\pi\)
0.409066 + 0.912505i \(0.365855\pi\)
\(464\) 3.13905e11 0.314389
\(465\) −1.84097e12 3.18865e12i −1.82603 3.16277i
\(466\) −1.51617e10 2.62609e10i −0.0148940 0.0257972i
\(467\) −3.08478e11 −0.300122 −0.150061 0.988677i \(-0.547947\pi\)
−0.150061 + 0.988677i \(0.547947\pi\)
\(468\) 3.10440e11 0.299137
\(469\) 6.24186e11 + 1.08112e12i 0.595712 + 1.03180i
\(470\) 8.74110e11 1.51400e12i 0.826277 1.43115i
\(471\) 5.18972e11 + 8.98886e11i 0.485903 + 0.841609i
\(472\) −1.73729e11 + 3.00908e11i −0.161114 + 0.279058i
\(473\) −8.03541e11 + 1.39177e12i −0.738130 + 1.27848i
\(474\) −5.99894e11 −0.545848
\(475\) 1.43936e12 6.95604e11i 1.29733 0.626962i
\(476\) 2.03484e11 0.181677
\(477\) 3.06443e11 5.30775e11i 0.271030 0.469438i
\(478\) −5.39289e11 + 9.34076e11i −0.472494 + 0.818383i
\(479\) 1.25271e11 + 2.16976e11i 0.108728 + 0.188322i 0.915255 0.402875i \(-0.131989\pi\)
−0.806527 + 0.591197i \(0.798656\pi\)
\(480\) −2.16040e11 + 3.74192e11i −0.185758 + 0.321743i
\(481\) 1.72113e11 + 2.98108e11i 0.146609 + 0.253934i
\(482\) −5.13030e11 −0.432943
\(483\) −3.91791e11 −0.327562
\(484\) 1.18672e11 + 2.05546e11i 0.0982980 + 0.170257i
\(485\) −6.04522e11 1.04706e12i −0.496106 0.859281i
\(486\) 1.12739e12 0.916667
\(487\) −1.38791e12 −1.11810 −0.559052 0.829133i \(-0.688835\pi\)
−0.559052 + 0.829133i \(0.688835\pi\)
\(488\) −2.91912e11 5.05606e11i −0.233004 0.403574i
\(489\) 1.49055e12 2.58170e12i 1.17884 2.04182i
\(490\) 1.31267e11 + 2.27362e11i 0.102867 + 0.178170i
\(491\) 1.93342e11 3.34879e11i 0.150127 0.260028i −0.781147 0.624348i \(-0.785365\pi\)
0.931274 + 0.364319i \(0.118698\pi\)
\(492\) 3.94927e11 6.84034e11i 0.303860 0.526302i
\(493\) 5.50279e11 0.419538
\(494\) −5.07431e10 + 6.89869e11i −0.0383359 + 0.521189i
\(495\) −1.31595e12 −0.985185
\(496\) −2.92794e11 + 5.07134e11i −0.217217 + 0.376232i
\(497\) 4.95992e11 8.59084e11i 0.364646 0.631585i
\(498\) −2.37576e11 4.11493e11i −0.173089 0.299799i
\(499\) −6.42263e11 + 1.11243e12i −0.463725 + 0.803195i −0.999143 0.0413922i \(-0.986821\pi\)
0.535418 + 0.844587i \(0.320154\pi\)
\(500\) 2.40657e11 + 4.16830e11i 0.172200 + 0.298259i
\(501\) 3.13412e10 0.0222252
\(502\) 1.75791e12 1.23546
\(503\) −2.47510e11 4.28700e11i −0.172400 0.298605i 0.766859 0.641816i \(-0.221819\pi\)
−0.939258 + 0.343211i \(0.888485\pi\)
\(504\) −2.25770e11 3.91044e11i −0.155858 0.269953i
\(505\) 2.53946e12 1.73752
\(506\) 1.81600e11 0.123151
\(507\) −4.54083e11 7.86495e11i −0.305211 0.528640i
\(508\) 4.25889e11 7.37661e11i 0.283733 0.491439i
\(509\) 1.10606e11 + 1.91575e11i 0.0730377 + 0.126505i 0.900231 0.435412i \(-0.143397\pi\)
−0.827194 + 0.561917i \(0.810064\pi\)
\(510\) −3.78720e11 + 6.55963e11i −0.247887 + 0.429352i
\(511\) 2.61169e11 4.52358e11i 0.169444 0.293486i
\(512\) 6.87195e10 0.0441942
\(513\) −2.94872e10 + 4.00888e11i −0.0187977 + 0.255561i
\(514\) 6.20988e10 0.0392418
\(515\) −1.27818e12 + 2.21388e12i −0.800683 + 1.38682i
\(516\) 1.02631e12 1.77763e12i 0.637319 1.10387i
\(517\) −9.46457e11 1.63931e12i −0.582631 1.00915i
\(518\) 2.50341e11 4.33603e11i 0.152773 0.264611i
\(519\) −4.86495e11 8.42634e11i −0.294324 0.509784i
\(520\) −6.80652e11 −0.408235
\(521\) −1.96389e12 −1.16774 −0.583872 0.811846i \(-0.698463\pi\)
−0.583872 + 0.811846i \(0.698463\pi\)
\(522\) −6.10545e11 1.05750e12i −0.359916 0.623392i
\(523\) −4.89915e11 8.48558e11i −0.286328 0.495934i 0.686603 0.727033i \(-0.259101\pi\)
−0.972930 + 0.231099i \(0.925768\pi\)
\(524\) −1.06512e12 −0.617176
\(525\) −3.67459e12 −2.11102
\(526\) 1.22655e11 + 2.12445e11i 0.0698634 + 0.121007i
\(527\) −5.13272e11 + 8.89013e11i −0.289868 + 0.502066i
\(528\) 2.33920e11 + 4.05162e11i 0.130983 + 0.226869i
\(529\) 8.55559e11 1.48187e12i 0.475006 0.822735i
\(530\) −6.71890e11 + 1.16375e12i −0.369876 + 0.640645i
\(531\) 1.35162e12 0.737781
\(532\) 9.05895e11 4.37794e11i 0.490315 0.236956i
\(533\) 1.24425e12 0.667785
\(534\) −1.55891e12 + 2.70012e12i −0.829634 + 1.43697i
\(535\) 1.80242e12 3.12189e12i 0.951185 1.64750i
\(536\) 3.69529e11 + 6.40043e11i 0.193378 + 0.334941i
\(537\) −2.13866e12 + 3.70426e12i −1.10983 + 1.92228i
\(538\) 7.81875e11 + 1.35425e12i 0.402362 + 0.696912i
\(539\) 2.84264e11 0.145068
\(540\) −3.95532e11 −0.200175
\(541\) −2.90238e11 5.02706e11i −0.145669 0.252305i 0.783954 0.620819i \(-0.213200\pi\)
−0.929622 + 0.368514i \(0.879867\pi\)
\(542\) −2.26705e11 3.92664e11i −0.112840 0.195445i
\(543\) −3.76363e12 −1.85784
\(544\) 1.20466e11 0.0589753
\(545\) 6.88254e11 + 1.19209e12i 0.334168 + 0.578796i
\(546\) 7.95001e11 1.37698e12i 0.382826 0.663073i
\(547\) 2.01741e10 + 3.49426e10i 0.00963500 + 0.0166883i 0.870803 0.491633i \(-0.163600\pi\)
−0.861168 + 0.508321i \(0.830266\pi\)
\(548\) 5.59848e11 9.69686e11i 0.265190 0.459323i
\(549\) −1.13554e12 + 1.96681e12i −0.533490 + 0.924032i
\(550\) 1.70322e12 0.793667
\(551\) 2.44980e12 1.18392e12i 1.13226 0.547192i
\(552\) −2.31947e11 −0.106332
\(553\) −6.87265e11 + 1.19038e12i −0.312508 + 0.541280i
\(554\) 4.27699e11 7.40797e11i 0.192905 0.334122i
\(555\) 9.31857e11 + 1.61402e12i 0.416899 + 0.722090i
\(556\) −4.07601e11 + 7.05985e11i −0.180883 + 0.313299i
\(557\) −7.18163e11 1.24389e12i −0.316136 0.547564i 0.663542 0.748139i \(-0.269052\pi\)
−0.979678 + 0.200575i \(0.935719\pi\)
\(558\) 2.27794e12 0.994692
\(559\) 3.23350e12 1.40062
\(560\) 4.95009e11 + 8.57382e11i 0.212700 + 0.368407i
\(561\) 4.10066e11 + 7.10254e11i 0.174792 + 0.302748i
\(562\) −2.82723e12 −1.19549
\(563\) −1.73146e12 −0.726317 −0.363158 0.931727i \(-0.618302\pi\)
−0.363158 + 0.931727i \(0.618302\pi\)
\(564\) 1.20885e12 + 2.09379e12i 0.503057 + 0.871321i
\(565\) 3.52513e12 6.10571e12i 1.45532 2.52068i
\(566\) 4.43153e11 + 7.67563e11i 0.181501 + 0.314369i
\(567\) 1.54690e12 2.67931e12i 0.628547 1.08868i
\(568\) 2.93636e11 5.08593e11i 0.118370 0.205023i
\(569\) 9.72739e11 0.389037 0.194519 0.980899i \(-0.437686\pi\)
0.194519 + 0.980899i \(0.437686\pi\)
\(570\) −2.74735e11 + 3.73511e12i −0.109013 + 1.48206i
\(571\) 2.32743e12 0.916249 0.458124 0.888888i \(-0.348521\pi\)
0.458124 + 0.888888i \(0.348521\pi\)
\(572\) −3.68493e11 + 6.38249e11i −0.143929 + 0.249292i
\(573\) 1.99483e12 3.45515e12i 0.773056 1.33897i
\(574\) −9.04893e11 1.56732e12i −0.347931 0.602635i
\(575\) −4.22213e11 + 7.31295e11i −0.161074 + 0.278989i
\(576\) −1.33660e11 2.31505e11i −0.0505940 0.0876313i
\(577\) −1.16932e12 −0.439181 −0.219590 0.975592i \(-0.570472\pi\)
−0.219590 + 0.975592i \(0.570472\pi\)
\(578\) −1.68623e12 −0.628407
\(579\) 2.53432e12 + 4.38956e12i 0.937146 + 1.62318i
\(580\) 1.33865e12 + 2.31860e12i 0.491179 + 0.850747i
\(581\) −1.08871e12 −0.396387
\(582\) 1.67205e12 0.604082
\(583\) 7.27499e11 + 1.26007e12i 0.260810 + 0.451736i
\(584\) 1.54617e11 2.67804e11i 0.0550045 0.0952706i
\(585\) 1.32387e12 + 2.29301e12i 0.467352 + 0.809477i
\(586\) 6.99496e11 1.21156e12i 0.245045 0.424430i
\(587\) −1.22260e12 + 2.11761e12i −0.425025 + 0.736165i −0.996423 0.0845081i \(-0.973068\pi\)
0.571398 + 0.820673i \(0.306401\pi\)
\(588\) −3.63073e11 −0.125255
\(589\) −3.72342e11 + 5.06211e12i −0.127474 + 1.73306i
\(590\) −2.96347e12 −1.00686
\(591\) −7.92320e11 + 1.37234e12i −0.267151 + 0.462719i
\(592\) 1.48206e11 2.56700e11i 0.0495927 0.0858971i
\(593\) −2.27343e10 3.93769e10i −0.00754979 0.0130766i 0.862226 0.506524i \(-0.169070\pi\)
−0.869776 + 0.493447i \(0.835737\pi\)
\(594\) −2.14134e11 + 3.70891e11i −0.0705744 + 0.122238i
\(595\) 8.67758e11 + 1.50300e12i 0.283839 + 0.491624i
\(596\) 7.32644e11 0.237840
\(597\) −7.95165e12 −2.56196
\(598\) −1.82693e11 3.16433e11i −0.0584206 0.101187i
\(599\) −1.75315e12 3.03654e12i −0.556413 0.963736i −0.997792 0.0664151i \(-0.978844\pi\)
0.441379 0.897321i \(-0.354490\pi\)
\(600\) −2.17542e12 −0.685271
\(601\) −1.51764e12 −0.474499 −0.237249 0.971449i \(-0.576246\pi\)
−0.237249 + 0.971449i \(0.576246\pi\)
\(602\) −2.35158e12 4.07306e12i −0.729754 1.26397i
\(603\) 1.43747e12 2.48977e12i 0.442763 0.766887i
\(604\) −3.68760e11 6.38711e11i −0.112740 0.195271i
\(605\) −1.01216e12 + 1.75310e12i −0.307148 + 0.531996i
\(606\) −1.75598e12 + 3.04144e12i −0.528922 + 0.916120i
\(607\) −3.22964e12 −0.965617 −0.482808 0.875726i \(-0.660383\pi\)
−0.482808 + 0.875726i \(0.660383\pi\)
\(608\) 5.36306e11 2.59182e11i 0.159165 0.0769198i
\(609\) −6.25415e12 −1.84243
\(610\) 2.48972e12 4.31232e12i 0.728058 1.26103i
\(611\) −1.90430e12 + 3.29834e12i −0.552777 + 0.957437i
\(612\) −2.34307e11 4.05832e11i −0.0675156 0.116940i
\(613\) −2.45407e12 + 4.25057e12i −0.701964 + 1.21584i 0.265812 + 0.964025i \(0.414360\pi\)
−0.967776 + 0.251812i \(0.918973\pi\)
\(614\) −2.45745e12 4.25643e12i −0.697794 1.20861i
\(615\) 6.73667e12 1.89892
\(616\) 1.07196e12 0.299961
\(617\) 1.47411e12 + 2.55323e12i 0.409493 + 0.709262i 0.994833 0.101526i \(-0.0323724\pi\)
−0.585340 + 0.810788i \(0.699039\pi\)
\(618\) −1.76767e12 3.06169e12i −0.487475 0.844331i
\(619\) −1.73984e10 −0.00476323 −0.00238161 0.999997i \(-0.500758\pi\)
−0.00238161 + 0.999997i \(0.500758\pi\)
\(620\) −4.99448e12 −1.35746
\(621\) −1.06164e11 1.83882e11i −0.0286461 0.0496165i
\(622\) −2.21275e12 + 3.83260e12i −0.592756 + 1.02668i
\(623\) 3.57192e12 + 6.18675e12i 0.949961 + 1.64538i
\(624\) 4.70655e11 8.15198e11i 0.124272 0.215245i
\(625\) 6.95697e11 1.20498e12i 0.182373 0.315879i
\(626\) 3.44293e12 0.896073
\(627\) 3.35368e12 + 2.27974e12i 0.866599 + 0.589090i
\(628\) 1.40795e12 0.361219
\(629\) 2.59807e11 4.49999e11i 0.0661794 0.114626i
\(630\) 1.92559e12 3.33522e12i 0.487003 0.843513i
\(631\) −2.87298e12 4.97615e12i −0.721440 1.24957i −0.960423 0.278547i \(-0.910147\pi\)
0.238982 0.971024i \(-0.423186\pi\)
\(632\) −4.06873e11 + 7.04725e11i −0.101445 + 0.175709i
\(633\) 6.01700e11 + 1.04217e12i 0.148958 + 0.258002i
\(634\) −1.32060e12 −0.324615
\(635\) 7.26481e12 1.77314
\(636\) −9.29192e11 1.60941e12i −0.225190 0.390040i
\(637\) −2.85974e11 4.95321e11i −0.0688174 0.119195i
\(638\) 2.89888e12 0.692687
\(639\) −2.28449e12 −0.542046
\(640\) 2.93054e11 + 5.07585e11i 0.0690459 + 0.119591i
\(641\) 2.20755e12 3.82359e12i 0.516475 0.894560i −0.483342 0.875431i \(-0.660577\pi\)
0.999817 0.0191289i \(-0.00608929\pi\)
\(642\) 2.49267e12 + 4.31743e12i 0.579104 + 1.00304i
\(643\) 3.06319e11 5.30561e11i 0.0706683 0.122401i −0.828526 0.559951i \(-0.810820\pi\)
0.899194 + 0.437549i \(0.144153\pi\)
\(644\) −2.65729e11 + 4.60257e11i −0.0608770 + 0.105442i
\(645\) 1.75069e13 3.98281
\(646\) 9.40151e11 4.54349e11i 0.212398 0.102646i
\(647\) −7.34361e12 −1.64756 −0.823779 0.566911i \(-0.808138\pi\)
−0.823779 + 0.566911i \(0.808138\pi\)
\(648\) 9.15791e11 1.58620e12i 0.204037 0.353402i
\(649\) −1.60437e12 + 2.77886e12i −0.354980 + 0.614844i
\(650\) −1.71346e12 2.96781e12i −0.376500 0.652117i
\(651\) 5.83355e12 1.01040e13i 1.27297 2.20485i
\(652\) −2.02190e12 3.50204e12i −0.438174 0.758939i
\(653\) −1.20611e12 −0.259583 −0.129791 0.991541i \(-0.541431\pi\)
−0.129791 + 0.991541i \(0.541431\pi\)
\(654\) −1.90365e12 −0.406899
\(655\) −4.54222e12 7.86736e12i −0.964234 1.67010i
\(656\) −5.35712e11 9.27881e11i −0.112944 0.195625i
\(657\) −1.20292e12 −0.251879
\(658\) 5.53966e12 1.15204
\(659\) −4.61056e12 7.98572e12i −0.952290 1.64941i −0.740451 0.672110i \(-0.765388\pi\)
−0.211839 0.977305i \(-0.567945\pi\)
\(660\) −1.99511e12 + 3.45563e12i −0.409278 + 0.708891i
\(661\) 1.30032e12 + 2.25222e12i 0.264938 + 0.458886i 0.967547 0.252690i \(-0.0813152\pi\)
−0.702609 + 0.711576i \(0.747982\pi\)
\(662\) 2.94562e12 5.10197e12i 0.596096 1.03247i
\(663\) 8.25064e11 1.42905e12i 0.165835 0.287235i
\(664\) −6.44535e11 −0.128674
\(665\) 7.09688e12 + 4.82427e12i 1.40725 + 0.956608i
\(666\) −1.15304e12 −0.227097
\(667\) −7.18608e11 + 1.24467e12i −0.140581 + 0.243493i
\(668\) 2.12569e10 3.68181e10i 0.00413054 0.00715430i
\(669\) 4.30267e10 + 7.45245e10i 0.00830464 + 0.0143841i
\(670\) −3.15171e12 + 5.45893e12i −0.604241 + 1.04658i
\(671\) −2.69578e12 4.66923e12i −0.513373 0.889189i
\(672\) −1.36915e12 −0.258994
\(673\) −1.06846e12 −0.200765 −0.100383 0.994949i \(-0.532007\pi\)
−0.100383 + 0.994949i \(0.532007\pi\)
\(674\) 6.43473e10 + 1.11453e11i 0.0120105 + 0.0208028i
\(675\) −9.95706e11 1.72461e12i −0.184614 0.319760i
\(676\) −1.23191e12 −0.226892
\(677\) 1.75754e12 0.321555 0.160778 0.986991i \(-0.448600\pi\)
0.160778 + 0.986991i \(0.448600\pi\)
\(678\) 4.87509e12 + 8.44390e12i 0.886031 + 1.53465i
\(679\) 1.91558e12 3.31788e12i 0.345848 0.599027i
\(680\) 5.13728e11 + 8.89803e11i 0.0921389 + 0.159589i
\(681\) 2.88372e12 4.99475e12i 0.513797 0.889922i
\(682\) −2.70393e12 + 4.68334e12i −0.478592 + 0.828946i
\(683\) −9.81846e12 −1.72644 −0.863218 0.504832i \(-0.831555\pi\)
−0.863218 + 0.504832i \(0.831555\pi\)
\(684\) −1.91626e12 1.30262e12i −0.334735 0.227544i
\(685\) 9.54990e12 1.65726
\(686\) 1.81761e12 3.14819e12i 0.313359 0.542753i
\(687\) −4.26165e12 + 7.38139e12i −0.729915 + 1.26425i
\(688\) −1.39218e12 2.41133e12i −0.236890 0.410306i
\(689\) 1.46375e12 2.53529e12i 0.247446 0.428589i
\(690\) −9.89140e11 1.71324e12i −0.166126 0.287738i
\(691\) 6.91232e12 1.15338 0.576690 0.816963i \(-0.304344\pi\)
0.576690 + 0.816963i \(0.304344\pi\)
\(692\) −1.31985e12 −0.218799
\(693\) −2.08496e12 3.61126e12i −0.343399 0.594784i
\(694\) 9.20034e11 + 1.59355e12i 0.150552 + 0.260764i
\(695\) −6.95286e12 −1.13040
\(696\) −3.70257e12 −0.598083
\(697\) −9.39111e11 1.62659e12i −0.150720 0.261054i
\(698\) −1.75346e12 + 3.03707e12i −0.279605 + 0.484290i
\(699\) 1.78835e11 + 3.09752e11i 0.0283339 + 0.0490758i
\(700\) −2.49226e12 + 4.31672e12i −0.392330 + 0.679536i
\(701\) 6.72941e11 1.16557e12i 0.105256 0.182308i −0.808587 0.588377i \(-0.799767\pi\)
0.913843 + 0.406068i \(0.133101\pi\)
\(702\) 8.61689e11 0.133916
\(703\) 1.88471e11 2.56233e12i 0.0291036 0.395673i
\(704\) 6.34618e11 0.0973723
\(705\) −1.03103e13 + 1.78580e13i −1.57188 + 2.72258i
\(706\) 1.82152e12 3.15497e12i 0.275939 0.477941i
\(707\) 4.02345e12 + 6.96882e12i 0.605636 + 1.04899i
\(708\) 2.04917e12 3.54927e12i 0.306499 0.530871i
\(709\) −1.72859e12 2.99400e12i −0.256911 0.444983i 0.708502 0.705709i \(-0.249371\pi\)
−0.965413 + 0.260726i \(0.916038\pi\)
\(710\) 5.00885e12 0.739733
\(711\) 3.16548e12 0.464543
\(712\) 2.11464e12 + 3.66266e12i 0.308373 + 0.534118i
\(713\) −1.34056e12 2.32192e12i −0.194260 0.336468i
\(714\) −2.40014e12 −0.345616
\(715\) −6.28576e12 −0.899458
\(716\) 2.90105e12 + 5.02477e12i 0.412522 + 0.714509i
\(717\) 6.36102e12 1.10176e13i 0.898857 1.55687i
\(718\) −4.03379e11 6.98673e11i −0.0566439 0.0981101i
\(719\) −5.48261e12 + 9.49616e12i −0.765081 + 1.32516i 0.175122 + 0.984547i \(0.443968\pi\)
−0.940204 + 0.340613i \(0.889365\pi\)
\(720\) 1.13998e12 1.97451e12i 0.158089 0.273818i
\(721\) −8.10047e12 −1.11635
\(722\) 3.20795e12 4.04545e12i 0.439349 0.554051i
\(723\) 6.05129e12 0.823618
\(724\) −2.55265e12 + 4.42132e12i −0.345277 + 0.598037i
\(725\) −6.73978e12 + 1.16736e13i −0.905992 + 1.56922i
\(726\) −1.39976e12 2.42446e12i −0.186999 0.323892i
\(727\) −2.94719e12 + 5.10468e12i −0.391294 + 0.677740i −0.992620 0.121263i \(-0.961306\pi\)
0.601327 + 0.799003i \(0.294639\pi\)
\(728\) −1.07841e12 1.86785e12i −0.142295 0.246463i
\(729\) −4.49629e12 −0.589631
\(730\) 2.63745e12 0.343741
\(731\) −2.44051e12 4.22709e12i −0.316120 0.547536i
\(732\) 3.44316e12 + 5.96373e12i 0.443259 + 0.767747i
\(733\) 4.11595e12 0.526626 0.263313 0.964710i \(-0.415185\pi\)
0.263313 + 0.964710i \(0.415185\pi\)
\(734\) 7.73413e12 0.983510
\(735\) −1.54833e12 2.68178e12i −0.195690 0.338946i
\(736\) −1.57316e11 + 2.72480e11i −0.0197617 + 0.0342282i
\(737\) 3.41257e12 + 5.91074e12i 0.426067 + 0.737969i
\(738\) −2.08392e12 + 3.60946e12i −0.258600 + 0.447908i
\(739\) −5.33634e12 + 9.24282e12i −0.658178 + 1.14000i 0.322908 + 0.946430i \(0.395339\pi\)
−0.981087 + 0.193568i \(0.937994\pi\)
\(740\) 2.52810e12 0.309921
\(741\) 5.98525e11 8.13714e12i 0.0729290 0.991494i
\(742\) −4.25809e12 −0.515701
\(743\) 9.24872e11 1.60193e12i 0.111335 0.192838i −0.804974 0.593310i \(-0.797821\pi\)
0.916309 + 0.400472i \(0.131154\pi\)
\(744\) 3.45357e12 5.98175e12i 0.413228 0.715731i
\(745\) 3.12436e12 + 5.41156e12i 0.371585 + 0.643604i
\(746\) 1.56871e12 2.71708e12i 0.185446 0.321201i
\(747\) 1.25362e12 + 2.17134e12i 0.147307 + 0.255143i
\(748\) 1.11249e12 0.129939
\(749\) 1.14228e13 1.32619
\(750\) −2.83860e12 4.91659e12i −0.327588 0.567399i
\(751\) 4.60822e12 + 7.98167e12i 0.528632 + 0.915617i 0.999443 + 0.0333830i \(0.0106281\pi\)
−0.470811 + 0.882234i \(0.656039\pi\)
\(752\) 3.27958e12 0.373971
\(753\) −2.07349e13 −2.35030
\(754\) −2.91632e12 5.05121e12i −0.328597 0.569147i
\(755\) 3.14515e12 5.44757e12i 0.352274 0.610156i
\(756\) −6.26670e11 1.08542e12i −0.0697735 0.120851i
\(757\) −5.74920e12 + 9.95790e12i −0.636320 + 1.10214i 0.349913 + 0.936782i \(0.386211\pi\)
−0.986234 + 0.165357i \(0.947122\pi\)
\(758\) 1.65790e10 2.87156e10i 0.00182409 0.00315942i
\(759\) −2.14201e12 −0.234280
\(760\) 4.20148e12 + 2.85605e12i 0.456816 + 0.310531i
\(761\) 9.51792e12 1.02875 0.514376 0.857565i \(-0.328023\pi\)
0.514376 + 0.857565i \(0.328023\pi\)
\(762\) −5.02344e12 + 8.70086e12i −0.539764 + 0.934899i
\(763\) −2.18090e12 + 3.77743e12i −0.232957 + 0.403493i
\(764\) −2.70596e12 4.68686e12i −0.287343 0.497693i
\(765\) 1.99840e12 3.46134e12i 0.210963 0.365399i
\(766\) −1.35437e12 2.34584e12i −0.142137 0.246189i
\(767\) 6.45610e12 0.673583
\(768\) −8.10560e11 −0.0840736
\(769\) −5.64051e12 9.76965e12i −0.581634 1.00742i −0.995286 0.0969843i \(-0.969080\pi\)
0.413652 0.910435i \(-0.364253\pi\)
\(770\) 4.57137e12 + 7.91784e12i 0.468639 + 0.811706i
\(771\) −7.32468e11 −0.0746524
\(772\) 6.87552e12 0.696671
\(773\) 5.45498e12 + 9.44830e12i 0.549522 + 0.951800i 0.998307 + 0.0581606i \(0.0185236\pi\)
−0.448785 + 0.893640i \(0.648143\pi\)
\(774\) −5.41558e12 + 9.38007e12i −0.542389 + 0.939446i
\(775\) −1.25730e13 2.17771e13i −1.25194 2.16842i
\(776\) 1.13405e12 1.96424e12i 0.112268 0.194454i
\(777\) −2.95282e12 + 5.11443e12i −0.290631 + 0.503388i
\(778\) −2.22955e12 −0.218177
\(779\) −7.68043e12 5.22095e12i −0.747252 0.507962i
\(780\) 8.02843e12 0.776613
\(781\) 2.71170e12 4.69681e12i 0.260803 0.451724i
\(782\) −2.75778e11 + 4.77661e11i −0.0263711 + 0.0456762i
\(783\) −1.69469e12 2.93529e12i −0.161125 0.279077i
\(784\) −2.46251e11 + 4.26520e11i −0.0232786 + 0.0403197i
\(785\) 6.00422e12 + 1.03996e13i 0.564343 + 0.977471i
\(786\) 1.25634e13 1.17410
\(787\) 5.92047e12 0.550136 0.275068 0.961425i \(-0.411300\pi\)
0.275068 + 0.961425i \(0.411300\pi\)
\(788\) 1.07477e12 + 1.86155e12i 0.0992995 + 0.171992i
\(789\) −1.44674e12 2.50583e12i −0.132906 0.230200i
\(790\) −6.94044e12 −0.633965
\(791\) 2.23405e13 2.02908
\(792\) −1.23433e12 2.13793e12i −0.111473 0.193077i
\(793\) −5.42399e12 + 9.39463e12i −0.487068 + 0.843627i
\(794\) 1.27686e12 + 2.21159e12i 0.114012 + 0.197475i
\(795\) 7.92508e12 1.37266e13i 0.703641 1.21874i
\(796\) −5.39314e12 + 9.34119e12i −0.476138 + 0.824695i
\(797\) −6.57466e11 −0.0577180 −0.0288590 0.999583i \(-0.509187\pi\)
−0.0288590 + 0.999583i \(0.509187\pi\)
\(798\) −1.06852e13 + 5.16387e12i −0.932760 + 0.450778i
\(799\) 5.74914e12 0.499048
\(800\) −1.47546e12 + 2.55557e12i −0.127357 + 0.220589i
\(801\) 8.22596e12 1.42478e13i 0.706058 1.22293i
\(802\) −3.79496e12 6.57306e12i −0.323909 0.561026i
\(803\) 1.42787e12 2.47314e12i 0.121191 0.209908i
\(804\) −4.35867e12 7.54944e12i −0.367876 0.637180i
\(805\) −4.53281e12 −0.380440
\(806\) 1.08808e13 0.908138
\(807\) −9.22238e12 1.59736e13i −0.765442 1.32578i
\(808\) 2.38195e12 + 4.12566e12i 0.196599 + 0.340520i
\(809\) −2.00189e13 −1.64313 −0.821566 0.570114i \(-0.806899\pi\)
−0.821566 + 0.570114i \(0.806899\pi\)
\(810\) 1.56216e13 1.27509
\(811\) −3.24412e12 5.61898e12i −0.263332 0.456104i 0.703793 0.710405i \(-0.251488\pi\)
−0.967125 + 0.254301i \(0.918155\pi\)
\(812\) −4.24183e12 + 7.34706e12i −0.342414 + 0.593078i
\(813\) 2.67403e12 + 4.63155e12i 0.214664 + 0.371808i
\(814\) 1.36867e12 2.37060e12i 0.109267 0.189256i
\(815\) 1.72448e13 2.98689e13i 1.36914 2.37143i
\(816\) −1.42092e12 −0.112193
\(817\) −1.99595e13 1.35679e13i −1.56729 1.06540i
\(818\) −1.48386e13 −1.15879
\(819\) −4.19501e12 + 7.26596e12i −0.325803 + 0.564307i
\(820\) 4.56909e12 7.91390e12i 0.352913 0.611263i
\(821\) 9.49346e12 + 1.64432e13i 0.729257 + 1.26311i 0.957198 + 0.289435i \(0.0934673\pi\)
−0.227941 + 0.973675i \(0.573199\pi\)
\(822\) −6.60353e12 + 1.14376e13i −0.504490 + 0.873803i
\(823\) 5.84641e12 + 1.01263e13i 0.444212 + 0.769398i 0.997997 0.0632620i \(-0.0201504\pi\)
−0.553785 + 0.832660i \(0.686817\pi\)
\(824\) −4.79562e12 −0.362387
\(825\) −2.00898e13 −1.50985
\(826\) −4.69525e12 8.13240e12i −0.350952 0.607867i
\(827\) −8.90715e11 1.54276e12i −0.0662161 0.114690i 0.831017 0.556247i \(-0.187759\pi\)
−0.897233 + 0.441558i \(0.854426\pi\)
\(828\) 1.22392e12 0.0904936
\(829\) 1.27400e13 0.936855 0.468428 0.883502i \(-0.344821\pi\)
0.468428 + 0.883502i \(0.344821\pi\)
\(830\) −2.74862e12 4.76075e12i −0.201031 0.348196i
\(831\) −5.04480e12 + 8.73785e12i −0.366977 + 0.635623i
\(832\) −6.38435e11 1.10580e12i −0.0461915 0.0800060i
\(833\) −4.31682e11 + 7.47695e11i −0.0310643 + 0.0538049i
\(834\) 4.80773e12 8.32724e12i 0.344107 0.596010i
\(835\) 3.62601e11 0.0258131
\(836\) 4.95273e12 2.39352e12i 0.350685 0.169476i
\(837\) 6.32289e12 0.445298
\(838\) 1.83075e12 3.17096e12i 0.128242 0.222122i
\(839\) −5.73513e12 + 9.93353e12i −0.399590 + 0.692109i −0.993675 0.112292i \(-0.964181\pi\)
0.594086 + 0.804402i \(0.297514\pi\)
\(840\) −5.83874e12 1.01130e13i −0.404634 0.700846i
\(841\) −4.21754e12 + 7.30499e12i −0.290721 + 0.503544i
\(842\) 9.22359e12 + 1.59757e13i 0.632405 + 1.09536i
\(843\) 3.33477e13 2.27427
\(844\) 1.63239e12 0.110735
\(845\) −5.25349e12 9.09932e12i −0.354481 0.613979i
\(846\) −6.37879e12 1.10484e13i −0.428126 0.741536i
\(847\) −6.41452e12 −0.428242
\(848\) −2.52087e12 −0.167405
\(849\) −5.22708e12 9.05356e12i −0.345282 0.598046i
\(850\) −2.58650e12 + 4.47995e12i −0.169953 + 0.294366i
\(851\) 6.78563e11 + 1.17531e12i 0.0443514 + 0.0768188i
\(852\) −3.46350e12 + 5.99895e12i −0.225184 + 0.390029i
\(853\) −1.17151e13 + 2.02912e13i −0.757664 + 1.31231i 0.186375 + 0.982479i \(0.440326\pi\)
−0.944039 + 0.329834i \(0.893007\pi\)
\(854\) 1.57786e13 1.01510
\(855\) 1.44970e12 1.97091e13i 0.0927749 1.26131i
\(856\) 6.76252e12 0.430504
\(857\) 1.98481e12 3.43779e12i 0.125691 0.217703i −0.796312 0.604886i \(-0.793219\pi\)
0.922003 + 0.387183i \(0.126552\pi\)
\(858\) 4.34645e12 7.52828e12i 0.273806 0.474245i
\(859\) 1.81838e12 + 3.14953e12i 0.113951 + 0.197368i 0.917360 0.398059i \(-0.130316\pi\)
−0.803409 + 0.595427i \(0.796983\pi\)
\(860\) 1.18739e13 2.05662e13i 0.740202 1.28207i
\(861\) 1.06734e13 + 1.84869e13i 0.661894 + 1.14643i
\(862\) −1.74756e13 −1.07807
\(863\) 2.31927e13 1.42332 0.711661 0.702523i \(-0.247943\pi\)
0.711661 + 0.702523i \(0.247943\pi\)
\(864\) −3.70999e11 6.42590e11i −0.0226496 0.0392303i
\(865\) −5.62848e12 9.74881e12i −0.341837 0.592079i
\(866\) −1.49808e13 −0.905119
\(867\) 1.98894e13 1.19546
\(868\) −7.91312e12 1.37059e13i −0.473161 0.819539i
\(869\) −3.75744e12 + 6.50807e12i −0.223513 + 0.387136i
\(870\) −1.57896e13 2.73484e13i −0.934404 1.61844i
\(871\) 6.86619e12 1.18926e13i 0.404235 0.700156i
\(872\) −1.29113e12 + 2.23631e12i −0.0756217 + 0.130981i
\(873\) −8.82296e12 −0.514103
\(874\) −2.00057e11 + 2.71984e12i −0.0115972 + 0.157668i
\(875\) −1.30081e13 −0.750201
\(876\) −1.82373e12 + 3.15880e12i −0.104639 + 0.181240i
\(877\) 2.92689e12 5.06952e12i 0.167074 0.289380i −0.770316 0.637662i \(-0.779902\pi\)
0.937390 + 0.348282i \(0.113235\pi\)
\(878\) 1.07685e12 + 1.86516e12i 0.0611548 + 0.105923i
\(879\) −8.25070e12 + 1.42906e13i −0.466166 + 0.807423i
\(880\) 2.70633e12 + 4.68750e12i 0.152128 + 0.263493i
\(881\) −8.82872e12 −0.493749 −0.246874 0.969048i \(-0.579403\pi\)
−0.246874 + 0.969048i \(0.579403\pi\)
\(882\) 1.91584e12 0.106598
\(883\) 6.53385e11 + 1.13170e12i 0.0361698 + 0.0626479i 0.883544 0.468349i \(-0.155151\pi\)
−0.847374 + 0.530997i \(0.821818\pi\)
\(884\) −1.11919e12 1.93849e12i −0.0616406 0.106765i
\(885\) 3.49548e13 1.91541
\(886\) 9.06704e11 0.0494326
\(887\) 4.43696e12 + 7.68504e12i 0.240674 + 0.416860i 0.960906 0.276873i \(-0.0892982\pi\)
−0.720232 + 0.693733i \(0.755965\pi\)
\(888\) −1.74812e12 + 3.02783e12i −0.0943437 + 0.163408i
\(889\) 1.15102e13 + 1.99362e13i 0.618050 + 1.07049i
\(890\) −1.80358e13 + 3.12389e13i −0.963562 + 1.66894i
\(891\) 8.45725e12 1.46484e13i 0.449552 0.778646i
\(892\) 1.16730e11 0.00617363
\(893\) 2.55947e13 1.23692e13i 1.34685 0.650895i
\(894\) −8.64169e12 −0.452460
\(895\) −2.47431e13 + 4.28563e13i −1.28899 + 2.23260i
\(896\) −9.28614e11 + 1.60841e12i −0.0481337 + 0.0833700i
\(897\) 2.15490e12 + 3.73239e12i 0.111138 + 0.192496i
\(898\) −7.40668e12 + 1.28287e13i −0.380084 + 0.658326i
\(899\) −2.13993e13 3.70647e13i −1.09265 1.89253i
\(900\) 1.14791e13 0.583199
\(901\) −4.41911e12 −0.223395
\(902\) −4.94726e12 8.56890e12i −0.248849 0.431018i
\(903\) 2.77374e13 + 4.80426e13i 1.38826 + 2.40454i
\(904\) 1.32260e13 0.658672
\(905\) −4.35431e13 −2.15775
\(906\) 4.34960e12 + 7.53372e12i 0.214473 + 0.371478i
\(907\) −1.17419e13 + 2.03376e13i −0.576112 + 0.997856i 0.419807 + 0.907613i \(0.362098\pi\)
−0.995920 + 0.0902427i \(0.971236\pi\)
\(908\) −3.91172e12 6.77530e12i −0.190977 0.330782i
\(909\) 9.26581e12 1.60489e13i 0.450138 0.779662i
\(910\) 9.19773e12 1.59309e13i 0.444625 0.770114i
\(911\) −2.16450e13 −1.04118 −0.520589 0.853808i \(-0.674287\pi\)
−0.520589 + 0.853808i \(0.674287\pi\)
\(912\) −6.32583e12 + 3.05710e12i −0.302790 + 0.146330i
\(913\) −5.95222e12 −0.283505
\(914\) 6.67813e12 1.15669e13i 0.316517 0.548223i
\(915\) −2.93667e13 + 5.08647e13i −1.38503 + 2.39895i
\(916\) 5.78086e12 + 1.00127e13i 0.271308 + 0.469919i
\(917\) 1.43931e13 2.49296e13i 0.672192 1.16427i
\(918\) −6.50367e11 1.12647e12i −0.0302250 0.0523512i
\(919\) −6.26285e12 −0.289636 −0.144818 0.989458i \(-0.546260\pi\)
−0.144818 + 0.989458i \(0.546260\pi\)
\(920\) −2.68350e12 −0.123497
\(921\) 2.89861e13 + 5.02055e13i 1.32746 + 2.29923i
\(922\) −2.06545e12 3.57746e12i −0.0941294 0.163037i
\(923\) −1.09121e13 −0.494879
\(924\) −1.26440e13 −0.570637
\(925\) 6.36420e12 + 1.10231e13i 0.285829 + 0.495070i
\(926\) −6.47183e12 + 1.12095e13i −0.289253 + 0.501001i
\(927\) 9.32750e12 + 1.61557e13i 0.414865 + 0.718566i
\(928\) −2.51124e12 + 4.34959e12i −0.111153 + 0.192523i
\(929\) 2.58410e12 4.47579e12i 0.113825 0.197151i −0.803484 0.595326i \(-0.797023\pi\)
0.917309 + 0.398175i \(0.130356\pi\)
\(930\) 5.89109e13 2.58239
\(931\) −3.13154e11 + 4.25744e12i −0.0136611 + 0.185727i
\(932\) 4.85175e11 0.0210633
\(933\) 2.60998e13 4.52063e13i 1.12764 1.95313i
\(934\) 2.46782e12 4.27439e12i 0.106109 0.183786i
\(935\) 4.74423e12 + 8.21725e12i 0.203008 + 0.351621i
\(936\) −2.48352e12 + 4.30158e12i −0.105761 + 0.183184i
\(937\) −1.11839e13 1.93711e13i −0.473987 0.820969i 0.525570 0.850750i \(-0.323852\pi\)
−0.999556 + 0.0297816i \(0.990519\pi\)
\(938\) −1.99740e13 −0.842464
\(939\) −4.06100e13 −1.70466
\(940\) 1.39858e13 + 2.42241e13i 0.584266 + 1.01198i
\(941\) −1.84414e13 3.19414e13i −0.766725 1.32801i −0.939330 0.343015i \(-0.888552\pi\)
0.172605 0.984991i \(-0.444782\pi\)
\(942\) −1.66071e13 −0.687171
\(943\) 4.90553e12 0.202015
\(944\) −2.77967e12 4.81453e12i −0.113925 0.197324i
\(945\) 5.34487e12 9.25758e12i 0.218019 0.377619i
\(946\) −1.28567e13 2.22684e13i −0.521937 0.904021i
\(947\) 1.11516e12 1.93151e12i 0.0450569 0.0780408i −0.842617 0.538513i \(-0.818986\pi\)
0.887674 + 0.460472i \(0.152320\pi\)
\(948\) 4.79915e12 8.31237e12i 0.192986 0.334262i
\(949\) −5.74583e12 −0.229961
\(950\) −1.87632e12 + 2.55092e13i −0.0747397 + 1.01611i
\(951\) 1.55767e13 0.617537
\(952\) −1.62787e12 + 2.81956e12i −0.0642324 + 0.111254i
\(953\) 2.20481e13 3.81885e13i 0.865873 1.49974i −0.000305570 1.00000i \(-0.500097\pi\)
0.866178 0.499735i \(-0.166569\pi\)
\(954\) 4.90309e12 + 8.49240e12i 0.191647 + 0.331943i
\(955\) 2.30791e13 3.99742e13i 0.897851 1.55512i
\(956\) −8.62862e12 1.49452e13i −0.334103 0.578684i
\(957\) −3.41929e13 −1.31775
\(958\) −4.00868e12 −0.153765
\(959\) 1.51306e13 + 2.62070e13i 0.577660 + 1.00054i
\(960\) −3.45663e12 5.98707e12i −0.131351 0.227506i
\(961\) 5.34011e13 2.01974
\(962\) −5.50761e12 −0.207336
\(963\) −1.31531e13 2.27819e13i −0.492845 0.853633i
\(964\) 4.10424e12 7.10875e12i 0.153069 0.265123i
\(965\) 2.93207e13 + 5.07849e13i 1.08843 + 1.88522i
\(966\) 3.13433e12 5.42882e12i 0.115810 0.200590i
\(967\) 5.82150e12 1.00831e13i 0.214100 0.370832i −0.738894 0.673822i \(-0.764652\pi\)
0.952994 + 0.302990i \(0.0979849\pi\)
\(968\) −3.79751e12 −0.139014
\(969\) −1.10893e13 + 5.35914e12i −0.404060 + 0.195271i
\(970\) 1.93447e13 0.701600
\(971\) 8.09635e12 1.40233e13i 0.292283 0.506248i −0.682067 0.731290i \(-0.738919\pi\)
0.974349 + 0.225042i \(0.0722519\pi\)
\(972\) −9.01913e12 + 1.56216e13i −0.324091 + 0.561342i
\(973\) −1.10159e13 1.90801e13i −0.394015 0.682454i
\(974\) 1.11033e13 1.92315e13i 0.395310 0.684696i
\(975\) 2.02106e13 + 3.50059e13i 0.716241 + 1.24057i
\(976\) 9.34118e12 0.329517
\(977\) −2.13391e13 −0.749291 −0.374645 0.927168i \(-0.622236\pi\)
−0.374645 + 0.927168i \(0.622236\pi\)
\(978\) 2.38488e13 + 4.13073e13i 0.833568 + 1.44378i
\(979\) 1.95285e13 + 3.38244e13i 0.679434 + 1.17681i
\(980\) −4.20056e12 −0.145475
\(981\) 1.00450e13 0.346290
\(982\) 3.09348e12 + 5.35806e12i 0.106156 + 0.183868i
\(983\) 1.84906e13 3.20266e13i 0.631626 1.09401i −0.355593 0.934641i \(-0.615721\pi\)
0.987219 0.159367i \(-0.0509455\pi\)
\(984\) 6.31884e12 + 1.09445e13i 0.214862 + 0.372152i
\(985\) −9.16671e12 + 1.58772e13i −0.310277 + 0.537416i
\(986\) −4.40223e12 + 7.62489e12i −0.148329 + 0.256914i
\(987\) −6.53415e13 −2.19160
\(988\) −9.15316e12 6.22207e12i −0.305608 0.207744i
\(989\) 1.27482e13 0.423707
\(990\) 1.05276e13 1.82344e13i 0.348315 0.603300i
\(991\) −1.56787e13 + 2.71564e13i −0.516393 + 0.894418i 0.483426 + 0.875385i \(0.339392\pi\)
−0.999819 + 0.0190330i \(0.993941\pi\)
\(992\) −4.68471e12 8.11415e12i −0.153596 0.266036i
\(993\) −3.47442e13 + 6.01787e13i −1.13399 + 1.96413i
\(994\) 7.93588e12 + 1.37453e13i 0.257844 + 0.446598i
\(995\) −9.19962e13 −2.97554
\(996\) 7.60242e12 0.244785
\(997\) −2.39556e13 4.14923e13i −0.767853 1.32996i −0.938725 0.344668i \(-0.887992\pi\)
0.170871 0.985293i \(-0.445342\pi\)
\(998\) −1.02762e13 1.77989e13i −0.327903 0.567945i
\(999\) −3.20051e12 −0.101666
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 38.10.c.b.11.7 yes 16
19.7 even 3 inner 38.10.c.b.7.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.10.c.b.7.7 16 19.7 even 3 inner
38.10.c.b.11.7 yes 16 1.1 even 1 trivial