Properties

Label 21.11.f.a.10.4
Level $21$
Weight $11$
Character 21.10
Analytic conductor $13.343$
Analytic rank $0$
Dimension $12$
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] = [21,11,Mod(10,21)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(21, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 11, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("21.10");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 21.f (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(13.3425023061\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + 3773 x^{10} + 44516 x^{9} + 11068388 x^{8} + 100480832 x^{7} + 11177140432 x^{6} + 67553728512 x^{5} + 8140577253696 x^{4} + \cdots + 30\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10}\cdot 3^{7}\cdot 7^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 10.4
Root \(-10.2102 - 17.6846i\) of defining polynomial
Character \(\chi\) \(=\) 21.10
Dual form 21.11.f.a.19.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(11.2102 + 19.4166i) q^{2} +(-121.500 - 70.1481i) q^{3} +(260.663 - 451.481i) q^{4} +(-354.602 + 204.730i) q^{5} -3145.50i q^{6} +(-12291.7 + 11462.5i) q^{7} +34646.8 q^{8} +(9841.50 + 17046.0i) q^{9} +O(q^{10})\) \(q+(11.2102 + 19.4166i) q^{2} +(-121.500 - 70.1481i) q^{3} +(260.663 - 451.481i) q^{4} +(-354.602 + 204.730i) q^{5} -3145.50i q^{6} +(-12291.7 + 11462.5i) q^{7} +34646.8 q^{8} +(9841.50 + 17046.0i) q^{9} +(-7950.32 - 4590.12i) q^{10} +(-96426.7 + 167016. i) q^{11} +(-63341.0 + 36570.0i) q^{12} +402089. i q^{13} +(-360356. - 110168. i) q^{14} +57445.5 q^{15} +(121479. + 210408. i) q^{16} +(-1.52683e6 - 881513. i) q^{17} +(-220650. + 382178. i) q^{18} +(-1.84304e6 + 1.06408e6i) q^{19} +213461. i q^{20} +(2.29752e6 - 530449. i) q^{21} -4.32385e6 q^{22} +(2.62281e6 + 4.54283e6i) q^{23} +(-4.20959e6 - 2.43041e6i) q^{24} +(-4.79898e6 + 8.31208e6i) q^{25} +(-7.80723e6 + 4.50750e6i) q^{26} -2.76145e6i q^{27} +(1.97109e6 + 8.53733e6i) q^{28} -1.81738e6 q^{29} +(643976. + 1.11540e6i) q^{30} +(3.01113e7 + 1.73848e7i) q^{31} +(1.50156e7 - 2.60077e7i) q^{32} +(2.34317e7 - 1.35283e7i) q^{33} -3.95278e7i q^{34} +(2.01197e6 - 6.58110e6i) q^{35} +1.02612e7 q^{36} +(-1.14229e7 - 1.97850e7i) q^{37} +(-4.13217e7 - 2.38571e7i) q^{38} +(2.82058e7 - 4.88539e7i) q^{39} +(-1.22858e7 + 7.09323e6i) q^{40} -1.15604e8i q^{41} +(3.60552e7 + 3.86636e7i) q^{42} +2.21239e8 q^{43} +(5.02697e7 + 8.70697e7i) q^{44} +(-6.97963e6 - 4.02969e6i) q^{45} +(-5.88044e7 + 1.01852e8i) q^{46} +(-2.74103e8 + 1.58253e8i) q^{47} -3.40862e7i q^{48} +(1.96986e7 - 2.81788e8i) q^{49} -2.15190e8 q^{50} +(1.23673e8 + 2.14208e8i) q^{51} +(1.81536e8 + 1.04810e8i) q^{52} +(-1.80041e8 + 3.11840e8i) q^{53} +(5.36181e7 - 3.09564e7i) q^{54} -7.89656e7i q^{55} +(-4.25870e8 + 3.97138e8i) q^{56} +2.98573e8 q^{57} +(-2.03732e7 - 3.52874e7i) q^{58} +(-9.22381e8 - 5.32537e8i) q^{59} +(1.49739e7 - 2.59356e7i) q^{60} +(-7.16800e8 + 4.13844e8i) q^{61} +7.79548e8i q^{62} +(-3.16358e8 - 9.67168e7i) q^{63} +9.22100e8 q^{64} +(-8.23196e7 - 1.42582e8i) q^{65} +(5.25348e8 + 3.03310e8i) q^{66} +(1.16507e9 - 2.01795e9i) q^{67} +(-7.95973e8 + 4.59555e8i) q^{68} -7.35939e8i q^{69} +(1.50337e8 - 3.47098e7i) q^{70} -1.12725e8 q^{71} +(3.40977e8 + 5.90589e8i) q^{72} +(1.82727e8 + 1.05497e8i) q^{73} +(2.56105e8 - 4.43588e8i) q^{74} +(1.16615e9 - 6.73279e8i) q^{75} +1.10946e9i q^{76} +(-7.29164e8 - 3.15821e9i) q^{77} +1.26477e9 q^{78} +(1.37537e9 + 2.38221e9i) q^{79} +(-8.61536e7 - 4.97408e7i) q^{80} +(-1.93710e8 + 3.35516e8i) q^{81} +(2.24464e9 - 1.29594e9i) q^{82} -2.39968e9i q^{83} +(3.59389e8 - 1.17555e9i) q^{84} +7.21887e8 q^{85} +(2.48013e9 + 4.29571e9i) q^{86} +(2.20811e8 + 1.27485e8i) q^{87} +(-3.34088e9 + 5.78657e9i) q^{88} +(-8.15490e8 + 4.70823e8i) q^{89} -1.80695e8i q^{90} +(-4.60894e9 - 4.94238e9i) q^{91} +2.73467e9 q^{92} +(-2.43902e9 - 4.22450e9i) q^{93} +(-6.14550e9 - 3.54810e9i) q^{94} +(4.35697e8 - 7.54650e8i) q^{95} +(-3.64878e9 + 2.10662e9i) q^{96} +2.45152e9i q^{97} +(5.69219e9 - 2.77642e9i) q^{98} -3.79593e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 11 q^{2} - 1458 q^{3} - 1421 q^{4} - 1287 q^{5} + 20090 q^{7} + 99310 q^{8} + 118098 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 11 q^{2} - 1458 q^{3} - 1421 q^{4} - 1287 q^{5} + 20090 q^{7} + 99310 q^{8} + 118098 q^{9} + 359661 q^{10} + 236165 q^{11} + 345303 q^{12} + 223832 q^{14} + 208494 q^{15} + 1350895 q^{16} - 2038782 q^{17} - 216513 q^{18} + 1012389 q^{19} - 5131917 q^{21} + 29162074 q^{22} - 4341928 q^{23} - 12066165 q^{24} + 12365439 q^{25} + 4398486 q^{26} + 37097165 q^{28} + 95444234 q^{29} - 29132541 q^{30} + 9658932 q^{31} - 49606359 q^{32} - 57388095 q^{33} - 77592186 q^{35} - 55939086 q^{36} - 87545045 q^{37} - 319584648 q^{38} + 1789695 q^{39} - 607773201 q^{40} - 180831609 q^{42} + 700816306 q^{43} + 133692537 q^{44} - 25332021 q^{45} - 74981552 q^{46} - 181842702 q^{47} + 333171090 q^{49} + 3398506976 q^{50} + 165141342 q^{51} - 1573473588 q^{52} - 695152867 q^{53} + 52612659 q^{54} + 1977142699 q^{56} - 164007018 q^{57} - 1023653321 q^{58} + 1373785545 q^{59} + 35593425 q^{60} - 2524633584 q^{61} + 851624361 q^{63} - 482439838 q^{64} + 2692260666 q^{65} - 3543191991 q^{66} - 2255105709 q^{67} + 4313617758 q^{68} - 650925555 q^{70} - 3878911780 q^{71} + 977359365 q^{72} - 1888675383 q^{73} - 445804820 q^{74} - 3004801677 q^{75} - 7759715803 q^{77} - 712554732 q^{78} + 8260659900 q^{79} - 5477579577 q^{80} - 2324522934 q^{81} + 14912212206 q^{82} + 665315532 q^{84} + 15563062356 q^{85} - 257575928 q^{86} - 11596474431 q^{87} - 10015831801 q^{88} + 9451951530 q^{89} - 3182715375 q^{91} + 20533179072 q^{92} - 782373492 q^{93} - 54481927140 q^{94} - 33375267288 q^{95} + 12054345237 q^{96} - 3841749499 q^{98} + 9296871390 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 11.2102 + 19.4166i 0.350319 + 0.606770i 0.986305 0.164930i \(-0.0527399\pi\)
−0.635986 + 0.771700i \(0.719407\pi\)
\(3\) −121.500 70.1481i −0.500000 0.288675i
\(4\) 260.663 451.481i 0.254553 0.440899i
\(5\) −354.602 + 204.730i −0.113473 + 0.0655134i −0.555662 0.831408i \(-0.687535\pi\)
0.442190 + 0.896922i \(0.354202\pi\)
\(6\) 3145.50i 0.404513i
\(7\) −12291.7 + 11462.5i −0.731347 + 0.682006i
\(8\) 34646.8 1.05734
\(9\) 9841.50 + 17046.0i 0.166667 + 0.288675i
\(10\) −7950.32 4590.12i −0.0795032 0.0459012i
\(11\) −96426.7 + 167016.i −0.598734 + 1.03704i 0.394274 + 0.918993i \(0.370996\pi\)
−0.993008 + 0.118045i \(0.962337\pi\)
\(12\) −63341.0 + 36570.0i −0.254553 + 0.146966i
\(13\) 402089.i 1.08294i 0.840719 + 0.541472i \(0.182133\pi\)
−0.840719 + 0.541472i \(0.817867\pi\)
\(14\) −360356. 110168.i −0.670025 0.204840i
\(15\) 57445.5 0.0756484
\(16\) 121479. + 210408.i 0.115852 + 0.200661i
\(17\) −1.52683e6 881513.i −1.07534 0.620846i −0.145702 0.989328i \(-0.546544\pi\)
−0.929635 + 0.368482i \(0.879878\pi\)
\(18\) −220650. + 382178.i −0.116773 + 0.202257i
\(19\) −1.84304e6 + 1.06408e6i −0.744333 + 0.429741i −0.823643 0.567109i \(-0.808062\pi\)
0.0793097 + 0.996850i \(0.474728\pi\)
\(20\) 213461.i 0.0667067i
\(21\) 2.29752e6 530449.i 0.562551 0.129881i
\(22\) −4.32385e6 −0.838991
\(23\) 2.62281e6 + 4.54283e6i 0.407499 + 0.705810i 0.994609 0.103698i \(-0.0330675\pi\)
−0.587109 + 0.809508i \(0.699734\pi\)
\(24\) −4.20959e6 2.43041e6i −0.528669 0.305227i
\(25\) −4.79898e6 + 8.31208e6i −0.491416 + 0.851157i
\(26\) −7.80723e6 + 4.50750e6i −0.657098 + 0.379376i
\(27\) 2.76145e6i 0.192450i
\(28\) 1.97109e6 + 8.53733e6i 0.114529 + 0.496057i
\(29\) −1.81738e6 −0.0886044 −0.0443022 0.999018i \(-0.514106\pi\)
−0.0443022 + 0.999018i \(0.514106\pi\)
\(30\) 643976. + 1.11540e6i 0.0265011 + 0.0459012i
\(31\) 3.01113e7 + 1.73848e7i 1.05177 + 0.607241i 0.923145 0.384452i \(-0.125610\pi\)
0.128627 + 0.991693i \(0.458943\pi\)
\(32\) 1.50156e7 2.60077e7i 0.447498 0.775090i
\(33\) 2.34317e7 1.35283e7i 0.598734 0.345679i
\(34\) 3.95278e7i 0.869977i
\(35\) 2.01197e6 6.58110e6i 0.0383072 0.125302i
\(36\) 1.02612e7 0.169702
\(37\) −1.14229e7 1.97850e7i −0.164728 0.285317i 0.771831 0.635828i \(-0.219341\pi\)
−0.936559 + 0.350511i \(0.886008\pi\)
\(38\) −4.13217e7 2.38571e7i −0.521508 0.301093i
\(39\) 2.82058e7 4.88539e7i 0.312619 0.541472i
\(40\) −1.22858e7 + 7.09323e6i −0.119979 + 0.0692698i
\(41\) 1.15604e8i 0.997822i −0.866653 0.498911i \(-0.833733\pi\)
0.866653 0.498911i \(-0.166267\pi\)
\(42\) 3.60552e7 + 3.86636e7i 0.275881 + 0.295839i
\(43\) 2.21239e8 1.50494 0.752469 0.658628i \(-0.228863\pi\)
0.752469 + 0.658628i \(0.228863\pi\)
\(44\) 5.02697e7 + 8.70697e7i 0.304820 + 0.527963i
\(45\) −6.97963e6 4.02969e6i −0.0378242 0.0218378i
\(46\) −5.88044e7 + 1.01852e8i −0.285509 + 0.494517i
\(47\) −2.74103e8 + 1.58253e8i −1.19515 + 0.690023i −0.959471 0.281807i \(-0.909066\pi\)
−0.235684 + 0.971830i \(0.575733\pi\)
\(48\) 3.40862e7i 0.133774i
\(49\) 1.96986e7 2.81788e8i 0.0697356 0.997566i
\(50\) −2.15190e8 −0.688609
\(51\) 1.23673e8 + 2.14208e8i 0.358446 + 0.620846i
\(52\) 1.81536e8 + 1.04810e8i 0.477469 + 0.275667i
\(53\) −1.80041e8 + 3.11840e8i −0.430518 + 0.745680i −0.996918 0.0784511i \(-0.975003\pi\)
0.566400 + 0.824131i \(0.308336\pi\)
\(54\) 5.36181e7 3.09564e7i 0.116773 0.0674189i
\(55\) 7.89656e7i 0.156901i
\(56\) −4.25870e8 + 3.97138e8i −0.773280 + 0.721110i
\(57\) 2.98573e8 0.496222
\(58\) −2.03732e7 3.52874e7i −0.0310398 0.0537625i
\(59\) −9.22381e8 5.32537e8i −1.29018 0.744886i −0.311494 0.950248i \(-0.600830\pi\)
−0.978686 + 0.205362i \(0.934163\pi\)
\(60\) 1.49739e7 2.59356e7i 0.0192566 0.0333533i
\(61\) −7.16800e8 + 4.13844e8i −0.848689 + 0.489991i −0.860208 0.509943i \(-0.829667\pi\)
0.0115194 + 0.999934i \(0.496333\pi\)
\(62\) 7.79548e8i 0.850911i
\(63\) −3.16358e8 9.67168e7i −0.318769 0.0974539i
\(64\) 9.22100e8 0.858772
\(65\) −8.23196e7 1.42582e8i −0.0709474 0.122884i
\(66\) 5.25348e8 + 3.03310e8i 0.419496 + 0.242196i
\(67\) 1.16507e9 2.01795e9i 0.862932 1.49464i −0.00615382 0.999981i \(-0.501959\pi\)
0.869086 0.494661i \(-0.164708\pi\)
\(68\) −7.95973e8 + 4.59555e8i −0.547461 + 0.316077i
\(69\) 7.35939e8i 0.470540i
\(70\) 1.50337e8 3.47098e7i 0.0894493 0.0206520i
\(71\) −1.12725e8 −0.0624784 −0.0312392 0.999512i \(-0.509945\pi\)
−0.0312392 + 0.999512i \(0.509945\pi\)
\(72\) 3.40977e8 + 5.90589e8i 0.176223 + 0.305227i
\(73\) 1.82727e8 + 1.05497e8i 0.0881431 + 0.0508894i 0.543424 0.839459i \(-0.317128\pi\)
−0.455281 + 0.890348i \(0.650461\pi\)
\(74\) 2.56105e8 4.43588e8i 0.115414 0.199904i
\(75\) 1.16615e9 6.73279e8i 0.491416 0.283719i
\(76\) 1.10946e9i 0.437568i
\(77\) −7.29164e8 3.15821e9i −0.269384 1.16677i
\(78\) 1.26477e9 0.438065
\(79\) 1.37537e9 + 2.38221e9i 0.446976 + 0.774185i 0.998188 0.0601806i \(-0.0191677\pi\)
−0.551212 + 0.834365i \(0.685834\pi\)
\(80\) −8.61536e7 4.97408e7i −0.0262920 0.0151797i
\(81\) −1.93710e8 + 3.35516e8i −0.0555556 + 0.0962250i
\(82\) 2.24464e9 1.29594e9i 0.605448 0.349556i
\(83\) 2.39968e9i 0.609203i −0.952480 0.304602i \(-0.901477\pi\)
0.952480 0.304602i \(-0.0985233\pi\)
\(84\) 3.59389e8 1.17555e9i 0.0859347 0.281090i
\(85\) 7.21887e8 0.162695
\(86\) 2.48013e9 + 4.29571e9i 0.527208 + 0.913151i
\(87\) 2.20811e8 + 1.27485e8i 0.0443022 + 0.0255779i
\(88\) −3.34088e9 + 5.78657e9i −0.633064 + 1.09650i
\(89\) −8.15490e8 + 4.70823e8i −0.146039 + 0.0843156i −0.571239 0.820784i \(-0.693537\pi\)
0.425200 + 0.905099i \(0.360204\pi\)
\(90\) 1.80695e8i 0.0306008i
\(91\) −4.60894e9 4.94238e9i −0.738574 0.792007i
\(92\) 2.73467e9 0.414921
\(93\) −2.43902e9 4.22450e9i −0.350591 0.607241i
\(94\) −6.14550e9 3.54810e9i −0.837371 0.483456i
\(95\) 4.35697e8 7.54650e8i 0.0563076 0.0975276i
\(96\) −3.64878e9 + 2.10662e9i −0.447498 + 0.258363i
\(97\) 2.45152e9i 0.285481i 0.989760 + 0.142740i \(0.0455914\pi\)
−0.989760 + 0.142740i \(0.954409\pi\)
\(98\) 5.69219e9 2.77642e9i 0.629723 0.307153i
\(99\) −3.79593e9 −0.399156
\(100\) 2.50183e9 + 4.33330e9i 0.250183 + 0.433330i
\(101\) −5.37358e9 3.10244e9i −0.511278 0.295186i 0.222081 0.975028i \(-0.428715\pi\)
−0.733359 + 0.679842i \(0.762048\pi\)
\(102\) −2.77280e9 + 4.80262e9i −0.251141 + 0.434988i
\(103\) 4.99638e9 2.88466e9i 0.430992 0.248833i −0.268777 0.963202i \(-0.586619\pi\)
0.699769 + 0.714369i \(0.253286\pi\)
\(104\) 1.39311e10i 1.14504i
\(105\) −7.06105e8 + 6.58468e8i −0.0553252 + 0.0515927i
\(106\) −8.07318e9 −0.603275
\(107\) 1.06583e9 + 1.84607e9i 0.0759921 + 0.131622i 0.901517 0.432743i \(-0.142454\pi\)
−0.825525 + 0.564365i \(0.809121\pi\)
\(108\) −1.24674e9 7.19807e8i −0.0848511 0.0489888i
\(109\) −1.00407e10 + 1.73910e10i −0.652575 + 1.13029i 0.329921 + 0.944009i \(0.392978\pi\)
−0.982496 + 0.186284i \(0.940355\pi\)
\(110\) 1.53325e9 8.85220e8i 0.0952025 0.0549652i
\(111\) 3.20517e9i 0.190211i
\(112\) −3.90499e9 1.19383e9i −0.221580 0.0677412i
\(113\) 1.93070e10 1.04791 0.523954 0.851747i \(-0.324456\pi\)
0.523954 + 0.851747i \(0.324456\pi\)
\(114\) 3.34706e9 + 5.79728e9i 0.173836 + 0.301093i
\(115\) −1.86010e9 1.07393e9i −0.0924801 0.0533934i
\(116\) −4.73722e8 + 8.20511e8i −0.0225545 + 0.0390656i
\(117\) −6.85401e9 + 3.95716e9i −0.312619 + 0.180491i
\(118\) 2.38794e10i 1.04379i
\(119\) 2.88717e10 6.66587e9i 1.20987 0.279333i
\(120\) 1.99030e9 0.0799859
\(121\) −5.62751e9 9.74713e9i −0.216965 0.375794i
\(122\) −1.60709e10 9.27856e9i −0.594623 0.343306i
\(123\) −8.10939e9 + 1.40459e10i −0.288046 + 0.498911i
\(124\) 1.56978e10 9.06313e9i 0.535464 0.309150i
\(125\) 7.92860e9i 0.259804i
\(126\) −1.66853e9 7.22683e9i −0.0525388 0.227560i
\(127\) 3.71909e10 1.12569 0.562844 0.826563i \(-0.309707\pi\)
0.562844 + 0.826563i \(0.309707\pi\)
\(128\) −5.03901e9 8.72782e9i −0.146654 0.254013i
\(129\) −2.68805e10 1.55195e10i −0.752469 0.434438i
\(130\) 1.84564e9 3.19674e9i 0.0497084 0.0860975i
\(131\) 5.46632e10 3.15598e10i 1.41690 0.818047i 0.420874 0.907119i \(-0.361724\pi\)
0.996025 + 0.0890724i \(0.0283903\pi\)
\(132\) 1.41053e10i 0.351975i
\(133\) 1.04572e10 3.42052e10i 0.251279 0.821929i
\(134\) 5.22425e10 1.20921
\(135\) 5.65350e8 + 9.79215e8i 0.0126081 + 0.0218378i
\(136\) −5.28996e10 3.05416e10i −1.13699 0.656444i
\(137\) −3.83016e10 + 6.63403e10i −0.793623 + 1.37459i 0.130088 + 0.991502i \(0.458474\pi\)
−0.923710 + 0.383092i \(0.874859\pi\)
\(138\) 1.42895e10 8.25003e9i 0.285509 0.164839i
\(139\) 1.02312e11i 1.97176i 0.167464 + 0.985878i \(0.446442\pi\)
−0.167464 + 0.985878i \(0.553558\pi\)
\(140\) −2.44680e9 2.62381e9i −0.0454944 0.0487857i
\(141\) 4.44047e10 0.796770
\(142\) −1.26367e9 2.18875e9i −0.0218874 0.0379100i
\(143\) −6.71553e10 3.87722e10i −1.12305 0.648395i
\(144\) −2.39108e9 + 4.14147e9i −0.0386172 + 0.0668870i
\(145\) 6.44445e8 3.72071e8i 0.0100542 0.00580478i
\(146\) 4.73059e9i 0.0713101i
\(147\) −2.21602e10 + 3.28554e10i −0.322840 + 0.478652i
\(148\) −1.19101e10 −0.167728
\(149\) 1.09124e10 + 1.89008e10i 0.148590 + 0.257365i 0.930706 0.365767i \(-0.119193\pi\)
−0.782117 + 0.623132i \(0.785860\pi\)
\(150\) 2.61456e10 + 1.50952e10i 0.344305 + 0.198784i
\(151\) −7.11114e10 + 1.23169e11i −0.905846 + 1.56897i −0.0860683 + 0.996289i \(0.527430\pi\)
−0.819778 + 0.572682i \(0.805903\pi\)
\(152\) −6.38555e10 + 3.68670e10i −0.787011 + 0.454381i
\(153\) 3.47016e10i 0.413897i
\(154\) 5.31477e10 4.95620e10i 0.613593 0.572197i
\(155\) −1.42367e10 −0.159130
\(156\) −1.47044e10 2.54688e10i −0.159156 0.275667i
\(157\) 1.71019e10 + 9.87377e9i 0.179286 + 0.103511i 0.586957 0.809618i \(-0.300326\pi\)
−0.407671 + 0.913129i \(0.633659\pi\)
\(158\) −3.08364e10 + 5.34101e10i −0.313168 + 0.542423i
\(159\) 4.37499e10 2.52590e10i 0.430518 0.248560i
\(160\) 1.22965e10i 0.117269i
\(161\) −8.43110e10 2.57755e10i −0.779390 0.238274i
\(162\) −8.68613e9 −0.0778486
\(163\) 3.38032e10 + 5.85488e10i 0.293778 + 0.508839i 0.974700 0.223517i \(-0.0717539\pi\)
−0.680922 + 0.732356i \(0.738421\pi\)
\(164\) −5.21929e10 3.01336e10i −0.439939 0.253999i
\(165\) −5.53928e9 + 9.59432e9i −0.0452933 + 0.0784503i
\(166\) 4.65937e10 2.69009e10i 0.369646 0.213415i
\(167\) 6.46662e10i 0.497846i −0.968523 0.248923i \(-0.919923\pi\)
0.968523 0.248923i \(-0.0800766\pi\)
\(168\) 7.96017e10 1.83784e10i 0.594807 0.137328i
\(169\) −2.38174e10 −0.172767
\(170\) 8.09250e9 + 1.40166e10i 0.0569952 + 0.0987185i
\(171\) −3.62766e10 2.09443e10i −0.248111 0.143247i
\(172\) 5.76686e10 9.98850e10i 0.383087 0.663526i
\(173\) −1.09261e11 + 6.30821e10i −0.705077 + 0.407076i −0.809236 0.587484i \(-0.800118\pi\)
0.104159 + 0.994561i \(0.466785\pi\)
\(174\) 5.71655e9i 0.0358417i
\(175\) −3.62892e10 1.57178e11i −0.221099 0.957640i
\(176\) −4.68554e10 −0.277458
\(177\) 7.47129e10 + 1.29407e11i 0.430060 + 0.744886i
\(178\) −1.82836e10 1.05560e10i −0.102320 0.0590747i
\(179\) −1.10844e10 + 1.91987e10i −0.0603179 + 0.104474i −0.894608 0.446853i \(-0.852545\pi\)
0.834290 + 0.551326i \(0.185878\pi\)
\(180\) −3.63866e9 + 2.10078e9i −0.0192566 + 0.0111178i
\(181\) 6.27344e10i 0.322933i 0.986878 + 0.161467i \(0.0516224\pi\)
−0.986878 + 0.161467i \(0.948378\pi\)
\(182\) 4.42972e10 1.44895e11i 0.221830 0.725600i
\(183\) 1.16122e11 0.565793
\(184\) 9.08719e10 + 1.57395e11i 0.430864 + 0.746279i
\(185\) 8.10114e9 + 4.67720e9i 0.0373842 + 0.0215838i
\(186\) 5.46838e10 9.47151e10i 0.245637 0.425456i
\(187\) 2.94453e11 1.70003e11i 1.28768 0.743444i
\(188\) 1.65003e11i 0.702591i
\(189\) 3.16530e10 + 3.39430e10i 0.131252 + 0.140748i
\(190\) 1.95370e10 0.0789024
\(191\) −5.07369e10 8.78789e10i −0.199599 0.345715i 0.748800 0.662796i \(-0.230630\pi\)
−0.948398 + 0.317081i \(0.897297\pi\)
\(192\) −1.12035e11 6.46835e10i −0.429386 0.247906i
\(193\) 1.28884e11 2.23233e11i 0.481296 0.833629i −0.518474 0.855094i \(-0.673500\pi\)
0.999770 + 0.0214647i \(0.00683295\pi\)
\(194\) −4.76003e10 + 2.74821e10i −0.173221 + 0.100009i
\(195\) 2.30982e10i 0.0819230i
\(196\) −1.22087e11 8.23450e10i −0.422075 0.284680i
\(197\) 4.29568e11 1.44777 0.723887 0.689919i \(-0.242354\pi\)
0.723887 + 0.689919i \(0.242354\pi\)
\(198\) −4.25532e10 7.37043e10i −0.139832 0.242196i
\(199\) 1.02742e11 + 5.93183e10i 0.329219 + 0.190074i 0.655494 0.755200i \(-0.272460\pi\)
−0.326276 + 0.945275i \(0.605794\pi\)
\(200\) −1.66270e11 + 2.87987e11i −0.519592 + 0.899960i
\(201\) −2.83111e11 + 1.63454e11i −0.862932 + 0.498214i
\(202\) 1.39116e11i 0.413638i
\(203\) 2.23387e10 2.08316e10i 0.0648005 0.0604287i
\(204\) 1.28948e11 0.364974
\(205\) 2.36675e10 + 4.09933e10i 0.0653707 + 0.113225i
\(206\) 1.12021e11 + 6.46753e10i 0.301969 + 0.174342i
\(207\) −5.16247e10 + 8.94166e10i −0.135833 + 0.235270i
\(208\) −8.46030e10 + 4.88456e10i −0.217305 + 0.125461i
\(209\) 4.10423e11i 1.02920i
\(210\) −2.07008e10 6.32864e9i −0.0506863 0.0154958i
\(211\) −5.61277e11 −1.34204 −0.671019 0.741440i \(-0.734143\pi\)
−0.671019 + 0.741440i \(0.734143\pi\)
\(212\) 9.38599e10 + 1.62570e11i 0.219180 + 0.379631i
\(213\) 1.36961e10 + 7.90746e9i 0.0312392 + 0.0180360i
\(214\) −2.38963e10 + 4.13896e10i −0.0532429 + 0.0922195i
\(215\) −7.84516e10 + 4.52941e10i −0.170769 + 0.0985936i
\(216\) 9.56754e10i 0.203485i
\(217\) −5.69393e11 + 1.31461e11i −1.18335 + 0.273211i
\(218\) −4.50232e11 −0.914437
\(219\) −1.48009e10 2.56359e10i −0.0293810 0.0508894i
\(220\) −3.56515e10 2.05834e10i −0.0691773 0.0399396i
\(221\) 3.54447e11 6.13920e11i 0.672341 1.16453i
\(222\) −6.22336e10 + 3.59306e10i −0.115414 + 0.0666346i
\(223\) 5.82567e11i 1.05638i 0.849125 + 0.528192i \(0.177130\pi\)
−0.849125 + 0.528192i \(0.822870\pi\)
\(224\) 1.13545e11 + 4.91795e11i 0.201340 + 0.872056i
\(225\) −1.88917e11 −0.327611
\(226\) 2.16436e11 + 3.74878e11i 0.367102 + 0.635839i
\(227\) 6.63245e11 + 3.82925e11i 1.10039 + 0.635308i 0.936322 0.351142i \(-0.114207\pi\)
0.164063 + 0.986450i \(0.447540\pi\)
\(228\) 7.78268e10 1.34800e11i 0.126315 0.218784i
\(229\) −2.72694e11 + 1.57440e11i −0.433010 + 0.249999i −0.700628 0.713526i \(-0.747097\pi\)
0.267618 + 0.963525i \(0.413764\pi\)
\(230\) 4.81560e10i 0.0748188i
\(231\) −1.32949e11 + 4.34871e11i −0.202127 + 0.661152i
\(232\) −6.29664e10 −0.0936847
\(233\) −6.51989e11 1.12928e12i −0.949426 1.64445i −0.746638 0.665231i \(-0.768333\pi\)
−0.202788 0.979223i \(-0.565000\pi\)
\(234\) −1.53670e11 8.87212e10i −0.219033 0.126459i
\(235\) 6.47983e10 1.12234e11i 0.0904116 0.156597i
\(236\) −4.80861e11 + 2.77625e11i −0.656840 + 0.379227i
\(237\) 3.85918e11i 0.516123i
\(238\) 4.53086e11 + 4.85865e11i 0.593329 + 0.636254i
\(239\) 1.32639e12 1.70091 0.850454 0.526049i \(-0.176327\pi\)
0.850454 + 0.526049i \(0.176327\pi\)
\(240\) 6.97844e9 + 1.20870e10i 0.00876400 + 0.0151797i
\(241\) −4.15030e11 2.39618e11i −0.510498 0.294736i 0.222540 0.974924i \(-0.428565\pi\)
−0.733039 + 0.680187i \(0.761899\pi\)
\(242\) 1.26171e11 2.18535e11i 0.152014 0.263296i
\(243\) 4.70716e10 2.71768e10i 0.0555556 0.0320750i
\(244\) 4.31495e11i 0.498915i
\(245\) 5.07051e10 + 1.03955e11i 0.0574409 + 0.117765i
\(246\) −3.63631e11 −0.403632
\(247\) −4.27856e11 7.41068e11i −0.465385 0.806070i
\(248\) 1.04326e12 + 6.02327e11i 1.11208 + 0.642058i
\(249\) −1.68333e11 + 2.91561e11i −0.175862 + 0.304602i
\(250\) 1.53947e11 8.88812e10i 0.157641 0.0910143i
\(251\) 4.24521e11i 0.426118i −0.977039 0.213059i \(-0.931657\pi\)
0.977039 0.213059i \(-0.0683427\pi\)
\(252\) −1.26129e11 + 1.17619e11i −0.124111 + 0.115738i
\(253\) −1.01163e12 −0.975935
\(254\) 4.16917e11 + 7.22122e11i 0.394350 + 0.683034i
\(255\) −8.77092e10 5.06390e10i −0.0813475 0.0469660i
\(256\) 5.85092e11 1.01341e12i 0.532138 0.921689i
\(257\) 7.01528e11 4.05027e11i 0.625719 0.361259i −0.153373 0.988168i \(-0.549014\pi\)
0.779092 + 0.626909i \(0.215680\pi\)
\(258\) 6.95905e11i 0.608767i
\(259\) 3.67192e11 + 1.12258e11i 0.315061 + 0.0963201i
\(260\) −8.58305e10 −0.0722396
\(261\) −1.78857e10 3.09790e10i −0.0147674 0.0255779i
\(262\) 1.22557e12 + 7.07584e11i 0.992733 + 0.573154i
\(263\) 1.22800e11 2.12696e11i 0.0975935 0.169037i −0.813095 0.582132i \(-0.802219\pi\)
0.910688 + 0.413095i \(0.135552\pi\)
\(264\) 8.11834e11 4.68712e11i 0.633064 0.365499i
\(265\) 1.47439e11i 0.112819i
\(266\) 7.81378e11 1.80404e11i 0.586750 0.135468i
\(267\) 1.32109e11 0.0973592
\(268\) −6.07379e11 1.05201e12i −0.439325 0.760933i
\(269\) −6.03594e11 3.48485e11i −0.428533 0.247413i 0.270189 0.962807i \(-0.412914\pi\)
−0.698721 + 0.715394i \(0.746247\pi\)
\(270\) −1.26754e10 + 2.19544e10i −0.00883369 + 0.0153004i
\(271\) 1.24353e12 7.17950e11i 0.850762 0.491188i −0.0101458 0.999949i \(-0.503230\pi\)
0.860908 + 0.508761i \(0.169896\pi\)
\(272\) 4.28342e11i 0.287704i
\(273\) 2.13288e11 + 9.23807e11i 0.140654 + 0.609211i
\(274\) −1.71747e12 −1.11208
\(275\) −9.25501e11 1.60301e12i −0.588455 1.01923i
\(276\) −3.32262e11 1.91832e11i −0.207461 0.119778i
\(277\) 1.30719e11 2.26412e11i 0.0801567 0.138836i −0.823160 0.567809i \(-0.807791\pi\)
0.903317 + 0.428973i \(0.141125\pi\)
\(278\) −1.98656e12 + 1.14694e12i −1.19640 + 0.690743i
\(279\) 6.84369e11i 0.404827i
\(280\) 6.97083e10 2.28014e11i 0.0405037 0.132486i
\(281\) −3.09022e12 −1.76383 −0.881916 0.471407i \(-0.843746\pi\)
−0.881916 + 0.471407i \(0.843746\pi\)
\(282\) 4.97785e11 + 8.62189e11i 0.279124 + 0.483456i
\(283\) 2.40387e12 + 1.38787e12i 1.32428 + 0.764571i 0.984408 0.175901i \(-0.0562840\pi\)
0.339869 + 0.940473i \(0.389617\pi\)
\(284\) −2.93833e10 + 5.08933e10i −0.0159041 + 0.0275467i
\(285\) −1.05874e11 + 6.11267e10i −0.0563076 + 0.0325092i
\(286\) 1.73858e12i 0.908580i
\(287\) 1.32511e12 + 1.42097e12i 0.680521 + 0.729754i
\(288\) 5.91102e11 0.298332
\(289\) 5.46133e11 + 9.45930e11i 0.270900 + 0.469213i
\(290\) 1.44487e10 + 8.34198e9i 0.00704433 + 0.00406705i
\(291\) 1.71969e11 2.97860e11i 0.0824112 0.142740i
\(292\) 9.52602e10 5.49985e10i 0.0448742 0.0259082i
\(293\) 3.93981e12i 1.82447i 0.409667 + 0.912235i \(0.365645\pi\)
−0.409667 + 0.912235i \(0.634355\pi\)
\(294\) −8.86362e11 6.19618e10i −0.403529 0.0282090i
\(295\) 4.36104e11 0.195200
\(296\) −3.95766e11 6.85487e11i −0.174173 0.301676i
\(297\) 4.61206e11 + 2.66277e11i 0.199578 + 0.115226i
\(298\) −2.44660e11 + 4.23764e11i −0.104108 + 0.180319i
\(299\) −1.82663e12 + 1.05460e12i −0.764352 + 0.441299i
\(300\) 7.01995e11i 0.288887i
\(301\) −2.71941e12 + 2.53594e12i −1.10063 + 1.02638i
\(302\) −3.18869e12 −1.26934
\(303\) 4.35260e11 + 7.53893e11i 0.170426 + 0.295186i
\(304\) −4.47783e11 2.58528e11i −0.172465 0.0995724i
\(305\) 1.69452e11 2.93500e11i 0.0642020 0.111201i
\(306\) 6.73789e11 3.89012e11i 0.251141 0.144996i
\(307\) 1.50730e12i 0.552722i 0.961054 + 0.276361i \(0.0891285\pi\)
−0.961054 + 0.276361i \(0.910872\pi\)
\(308\) −1.61594e12 4.94023e11i −0.583003 0.178235i
\(309\) −8.09414e11 −0.287328
\(310\) −1.59596e11 2.76429e11i −0.0557461 0.0965551i
\(311\) 2.52223e12 + 1.45621e12i 0.866926 + 0.500520i 0.866326 0.499480i \(-0.166475\pi\)
0.000600798 1.00000i \(0.499809\pi\)
\(312\) 9.77241e11 1.69263e12i 0.330544 0.572518i
\(313\) 1.66977e12 9.64042e11i 0.555821 0.320903i −0.195645 0.980675i \(-0.562680\pi\)
0.751466 + 0.659771i \(0.229347\pi\)
\(314\) 4.42748e11i 0.145047i
\(315\) 1.31982e11 3.04719e10i 0.0425561 0.00982532i
\(316\) 1.43403e12 0.455117
\(317\) −2.64614e12 4.58325e12i −0.826640 1.43178i −0.900659 0.434526i \(-0.856916\pi\)
0.0740189 0.997257i \(-0.476417\pi\)
\(318\) 9.80891e11 + 5.66318e11i 0.301637 + 0.174150i
\(319\) 1.75244e11 3.03531e11i 0.0530504 0.0918861i
\(320\) −3.26978e11 + 1.88781e11i −0.0974471 + 0.0562611i
\(321\) 2.99063e11i 0.0877481i
\(322\) −4.44670e11 1.92598e12i −0.128457 0.556382i
\(323\) 3.75200e12 1.06721
\(324\) 1.00986e11 + 1.74913e11i 0.0282837 + 0.0489888i
\(325\) −3.34220e12 1.92962e12i −0.921755 0.532176i
\(326\) −7.57881e11 + 1.31269e12i −0.205832 + 0.356512i
\(327\) 2.43988e12 1.40867e12i 0.652575 0.376764i
\(328\) 4.00531e12i 1.05503i
\(329\) 1.55523e12 5.08711e12i 0.403473 1.31975i
\(330\) −2.48386e11 −0.0634684
\(331\) 3.29361e12 + 5.70470e12i 0.828957 + 1.43580i 0.898857 + 0.438242i \(0.144399\pi\)
−0.0698998 + 0.997554i \(0.522268\pi\)
\(332\) −1.08341e12 6.25506e11i −0.268597 0.155075i
\(333\) 2.24836e11 3.89428e11i 0.0549092 0.0951056i
\(334\) 1.25560e12 7.24921e11i 0.302078 0.174405i
\(335\) 9.54094e11i 0.226135i
\(336\) 3.90712e11 + 4.18978e11i 0.0912347 + 0.0978352i
\(337\) 1.35678e12 0.312147 0.156074 0.987745i \(-0.450116\pi\)
0.156074 + 0.987745i \(0.450116\pi\)
\(338\) −2.66998e11 4.62453e11i −0.0605235 0.104830i
\(339\) −2.34580e12 1.35435e12i −0.523954 0.302505i
\(340\) 1.88169e11 3.25918e11i 0.0414146 0.0717322i
\(341\) −5.80707e12 + 3.35271e12i −1.25946 + 0.727151i
\(342\) 9.39159e11i 0.200728i
\(343\) 2.98785e12 + 3.68945e12i 0.629345 + 0.777126i
\(344\) 7.66521e12 1.59123
\(345\) 1.50668e11 + 2.60965e11i 0.0308267 + 0.0533934i
\(346\) −2.44969e12 1.41433e12i −0.494004 0.285213i
\(347\) 1.83513e12 3.17853e12i 0.364769 0.631799i −0.623970 0.781449i \(-0.714481\pi\)
0.988739 + 0.149649i \(0.0478145\pi\)
\(348\) 1.15115e11 6.64614e10i 0.0225545 0.0130219i
\(349\) 5.41166e11i 0.104521i −0.998633 0.0522605i \(-0.983357\pi\)
0.998633 0.0522605i \(-0.0166426\pi\)
\(350\) 2.64506e12 2.46661e12i 0.503612 0.469636i
\(351\) 1.11035e12 0.208413
\(352\) 2.89580e12 + 5.01568e12i 0.535865 + 0.928146i
\(353\) 2.94116e12 + 1.69808e12i 0.536592 + 0.309802i 0.743697 0.668517i \(-0.233071\pi\)
−0.207104 + 0.978319i \(0.566404\pi\)
\(354\) −1.67509e12 + 2.90135e12i −0.301316 + 0.521895i
\(355\) 3.99726e10 2.30782e10i 0.00708958 0.00409317i
\(356\) 4.90904e11i 0.0858513i
\(357\) −3.97550e12 1.21539e12i −0.685569 0.209592i
\(358\) −4.97033e11 −0.0845220
\(359\) 1.05539e12 + 1.82799e12i 0.176987 + 0.306550i 0.940847 0.338832i \(-0.110032\pi\)
−0.763860 + 0.645382i \(0.776698\pi\)
\(360\) −2.41822e11 1.39616e11i −0.0399929 0.0230899i
\(361\) −8.00998e11 + 1.38737e12i −0.130646 + 0.226285i
\(362\) −1.21809e12 + 7.03266e11i −0.195946 + 0.113130i
\(363\) 1.57904e12i 0.250529i
\(364\) −3.43277e12 + 7.92555e11i −0.537202 + 0.124029i
\(365\) −8.63937e10 −0.0133358
\(366\) 1.30175e12 + 2.25469e12i 0.198208 + 0.343306i
\(367\) −9.12008e12 5.26548e12i −1.36984 0.790875i −0.378929 0.925426i \(-0.623708\pi\)
−0.990907 + 0.134551i \(0.957041\pi\)
\(368\) −6.37234e11 + 1.10372e12i −0.0944190 + 0.163539i
\(369\) 1.97058e12 1.13772e12i 0.288046 0.166304i
\(370\) 2.09729e11i 0.0302448i
\(371\) −1.36144e12 5.89677e12i −0.193700 0.838966i
\(372\) −2.54304e12 −0.356976
\(373\) −4.38051e12 7.58726e12i −0.606709 1.05085i −0.991779 0.127963i \(-0.959156\pi\)
0.385070 0.922887i \(-0.374177\pi\)
\(374\) 6.60177e12 + 3.81153e12i 0.902199 + 0.520885i
\(375\) −5.56176e11 + 9.63325e11i −0.0749990 + 0.129902i
\(376\) −9.49679e12 + 5.48298e12i −1.26368 + 0.729587i
\(377\) 7.30748e11i 0.0959535i
\(378\) −3.04222e11 + 9.95104e11i −0.0394214 + 0.128946i
\(379\) 8.72597e12 1.11588 0.557940 0.829881i \(-0.311592\pi\)
0.557940 + 0.829881i \(0.311592\pi\)
\(380\) −2.27140e11 3.93418e11i −0.0286666 0.0496520i
\(381\) −4.51869e12 2.60887e12i −0.562844 0.324958i
\(382\) 1.13754e12 1.97028e12i 0.139846 0.242221i
\(383\) 7.87098e11 4.54431e11i 0.0955069 0.0551409i −0.451486 0.892278i \(-0.649106\pi\)
0.546993 + 0.837137i \(0.315773\pi\)
\(384\) 1.41391e12i 0.169342i
\(385\) 9.05141e11 + 9.70624e11i 0.107007 + 0.114749i
\(386\) 5.77926e12 0.674428
\(387\) 2.17732e12 + 3.77123e12i 0.250823 + 0.434438i
\(388\) 1.10682e12 + 6.39020e11i 0.125868 + 0.0726701i
\(389\) −8.88243e12 + 1.53848e13i −0.997204 + 1.72721i −0.433882 + 0.900970i \(0.642856\pi\)
−0.563322 + 0.826237i \(0.690477\pi\)
\(390\) −4.48490e11 + 2.58936e11i −0.0497084 + 0.0286992i
\(391\) 9.24815e12i 1.01198i
\(392\) 6.82493e11 9.76304e12i 0.0737340 1.05476i
\(393\) −8.85544e12 −0.944599
\(394\) 4.81554e12 + 8.34076e12i 0.507182 + 0.878465i
\(395\) −9.75418e11 5.63158e11i −0.101439 0.0585658i
\(396\) −9.89458e11 + 1.71379e12i −0.101607 + 0.175988i
\(397\) 2.79267e12 1.61235e12i 0.283183 0.163496i −0.351680 0.936120i \(-0.614390\pi\)
0.634864 + 0.772624i \(0.281056\pi\)
\(398\) 2.65988e12i 0.266347i
\(399\) −3.66998e12 + 3.42238e12i −0.362910 + 0.338426i
\(400\) −2.33191e12 −0.227726
\(401\) −1.40188e12 2.42813e12i −0.135204 0.234180i 0.790471 0.612499i \(-0.209836\pi\)
−0.925675 + 0.378319i \(0.876502\pi\)
\(402\) −6.34747e12 3.66471e12i −0.604603 0.349068i
\(403\) −6.99024e12 + 1.21074e13i −0.657607 + 1.13901i
\(404\) −2.80138e12 + 1.61738e12i −0.260295 + 0.150281i
\(405\) 1.58633e11i 0.0145585i
\(406\) 6.54902e11 + 2.00216e11i 0.0593672 + 0.0181497i
\(407\) 4.40588e12 0.394512
\(408\) 4.28487e12 + 7.42161e12i 0.378998 + 0.656444i
\(409\) −1.65617e13 9.56192e12i −1.44707 0.835465i −0.448763 0.893651i \(-0.648135\pi\)
−0.998306 + 0.0581856i \(0.981468\pi\)
\(410\) −5.30635e11 + 9.19088e11i −0.0458012 + 0.0793300i
\(411\) 9.30729e12 5.37356e12i 0.793623 0.458198i
\(412\) 3.00769e12i 0.253366i
\(413\) 1.74419e13 4.02696e12i 1.45159 0.335141i
\(414\) −2.31489e12 −0.190340
\(415\) 4.91285e11 + 8.50930e11i 0.0399110 + 0.0691279i
\(416\) 1.04574e13 + 6.03760e12i 0.839379 + 0.484616i
\(417\) 7.17700e12 1.24309e13i 0.569197 0.985878i
\(418\) 7.96904e12 4.60093e12i 0.624489 0.360549i
\(419\) 1.76120e13i 1.36376i 0.731463 + 0.681882i \(0.238838\pi\)
−0.731463 + 0.681882i \(0.761162\pi\)
\(420\) 1.13230e11 + 4.90431e11i 0.00866396 + 0.0375259i
\(421\) 1.07462e13 0.812536 0.406268 0.913754i \(-0.366830\pi\)
0.406268 + 0.913754i \(0.366830\pi\)
\(422\) −6.29203e12 1.08981e13i −0.470141 0.814309i
\(423\) −5.39517e12 3.11490e12i −0.398385 0.230008i
\(424\) −6.23784e12 + 1.08043e13i −0.455203 + 0.788435i
\(425\) 1.46544e13 8.46073e12i 1.05688 0.610188i
\(426\) 3.54577e11i 0.0252733i
\(427\) 4.06703e12 1.33032e13i 0.286509 0.937164i
\(428\) 1.11129e12 0.0773762
\(429\) 5.43958e12 + 9.42163e12i 0.374351 + 0.648395i
\(430\) −1.75892e12 1.01551e12i −0.119647 0.0690784i
\(431\) −9.56880e11 + 1.65737e12i −0.0643385 + 0.111438i −0.896400 0.443245i \(-0.853827\pi\)
0.832062 + 0.554683i \(0.187160\pi\)
\(432\) 5.81032e11 3.35459e11i 0.0386172 0.0222957i
\(433\) 2.03704e12i 0.133832i 0.997759 + 0.0669162i \(0.0213160\pi\)
−0.997759 + 0.0669162i \(0.978684\pi\)
\(434\) −8.93555e12 9.58200e12i −0.580327 0.622311i
\(435\) −1.04400e11 −0.00670278
\(436\) 5.23446e12 + 9.06635e12i 0.332230 + 0.575440i
\(437\) −9.66788e12 5.58175e12i −0.606630 0.350238i
\(438\) 3.31842e11 5.74767e11i 0.0205855 0.0356551i
\(439\) 1.46635e13 8.46597e12i 0.899321 0.519223i 0.0223412 0.999750i \(-0.492888\pi\)
0.876980 + 0.480527i \(0.159555\pi\)
\(440\) 2.73591e12i 0.165897i
\(441\) 4.99721e12 2.43743e12i 0.299595 0.146130i
\(442\) 1.58937e13 0.942136
\(443\) −1.55037e13 2.68531e13i −0.908690 1.57390i −0.815886 0.578213i \(-0.803750\pi\)
−0.0928046 0.995684i \(-0.529583\pi\)
\(444\) 1.44707e12 + 8.35468e11i 0.0838640 + 0.0484189i
\(445\) 1.92783e11 3.33910e11i 0.0110476 0.0191350i
\(446\) −1.13115e13 + 6.53070e12i −0.640982 + 0.370071i
\(447\) 3.06193e12i 0.171577i
\(448\) −1.13342e13 + 1.05695e13i −0.628060 + 0.585688i
\(449\) −1.16247e13 −0.637016 −0.318508 0.947920i \(-0.603182\pi\)
−0.318508 + 0.947920i \(0.603182\pi\)
\(450\) −2.11780e12 3.66813e12i −0.114768 0.198784i
\(451\) 1.93077e13 + 1.11473e13i 1.03478 + 0.597430i
\(452\) 5.03262e12 8.71676e12i 0.266749 0.462022i
\(453\) 1.72801e13 9.97665e12i 0.905846 0.522990i
\(454\) 1.71707e13i 0.890241i
\(455\) 2.64619e12 + 8.08991e11i 0.135695 + 0.0414846i
\(456\) 1.03446e13 0.524674
\(457\) −1.08090e13 1.87217e13i −0.542254 0.939212i −0.998774 0.0494986i \(-0.984238\pi\)
0.456520 0.889713i \(-0.349096\pi\)
\(458\) −6.11391e12 3.52987e12i −0.303383 0.175159i
\(459\) −2.43425e12 + 4.21625e12i −0.119482 + 0.206949i
\(460\) −9.69719e11 + 5.59868e11i −0.0470822 + 0.0271829i
\(461\) 1.92854e13i 0.926243i 0.886295 + 0.463122i \(0.153271\pi\)
−0.886295 + 0.463122i \(0.846729\pi\)
\(462\) −9.93412e12 + 2.29358e12i −0.471976 + 0.108969i
\(463\) −2.94452e13 −1.38392 −0.691958 0.721938i \(-0.743252\pi\)
−0.691958 + 0.721938i \(0.743252\pi\)
\(464\) −2.20774e11 3.82391e11i −0.0102650 0.0177794i
\(465\) 1.72976e12 + 9.98678e11i 0.0795648 + 0.0459368i
\(466\) 1.46179e13 2.53189e13i 0.665203 1.15217i
\(467\) −3.46042e13 + 1.99788e13i −1.55792 + 0.899464i −0.560462 + 0.828180i \(0.689376\pi\)
−0.997456 + 0.0712841i \(0.977290\pi\)
\(468\) 4.12594e12i 0.183778i
\(469\) 8.81005e12 + 3.81587e13i 0.388253 + 1.68163i
\(470\) 2.90561e12 0.126692
\(471\) −1.38525e12 2.39933e12i −0.0597618 0.103511i
\(472\) −3.19576e13 1.84507e13i −1.36416 0.787596i
\(473\) −2.13333e13 + 3.69504e13i −0.901057 + 1.56068i
\(474\) 7.49323e12 4.32622e12i 0.313168 0.180808i
\(475\) 2.04260e13i 0.844726i
\(476\) 4.51625e12 1.47725e13i 0.184818 0.604534i
\(477\) −7.08749e12 −0.287012
\(478\) 1.48691e13 + 2.57540e13i 0.595860 + 1.03206i
\(479\) 4.15854e13 + 2.40093e13i 1.64916 + 0.952143i 0.977406 + 0.211368i \(0.0677920\pi\)
0.671754 + 0.740775i \(0.265541\pi\)
\(480\) 8.62576e11 1.49403e12i 0.0338525 0.0586343i
\(481\) 7.95533e12 4.59301e12i 0.308982 0.178391i
\(482\) 1.07447e13i 0.413007i
\(483\) 8.43568e12 + 9.04597e12i 0.320911 + 0.344128i
\(484\) −5.86753e12 −0.220917
\(485\) −5.01899e11 8.69314e11i −0.0187028 0.0323943i
\(486\) 1.05536e12 + 6.09315e11i 0.0389243 + 0.0224730i
\(487\) −2.60250e12 + 4.50766e12i −0.0950048 + 0.164553i −0.909611 0.415462i \(-0.863620\pi\)
0.814606 + 0.580015i \(0.196953\pi\)
\(488\) −2.48348e13 + 1.43384e13i −0.897350 + 0.518085i
\(489\) 9.48491e12i 0.339226i
\(490\) −1.45005e12 + 2.14988e12i −0.0513336 + 0.0761087i
\(491\) −2.71231e13 −0.950455 −0.475227 0.879863i \(-0.657634\pi\)
−0.475227 + 0.879863i \(0.657634\pi\)
\(492\) 4.22763e12 + 7.32247e12i 0.146646 + 0.253999i
\(493\) 2.77482e12 + 1.60204e12i 0.0952796 + 0.0550097i
\(494\) 9.59270e12 1.66150e13i 0.326066 0.564763i
\(495\) 1.34605e12 7.77140e11i 0.0452933 0.0261501i
\(496\) 8.44757e12i 0.281400i
\(497\) 1.38559e12 1.29211e12i 0.0456933 0.0426106i
\(498\) −7.54817e12 −0.246431
\(499\) 3.08518e12 + 5.34369e12i 0.0997190 + 0.172718i 0.911568 0.411149i \(-0.134872\pi\)
−0.811849 + 0.583867i \(0.801539\pi\)
\(500\) −3.57961e12 2.06669e12i −0.114548 0.0661341i
\(501\) −4.53621e12 + 7.85694e12i −0.143716 + 0.248923i
\(502\) 8.24276e12 4.75896e12i 0.258556 0.149277i
\(503\) 2.17759e13i 0.676296i 0.941093 + 0.338148i \(0.109800\pi\)
−0.941093 + 0.338148i \(0.890200\pi\)
\(504\) −1.09608e13 3.35093e12i −0.337047 0.103042i
\(505\) 2.54064e12 0.0773547
\(506\) −1.13406e13 1.96425e13i −0.341888 0.592168i
\(507\) 2.89381e12 + 1.67074e12i 0.0863834 + 0.0498735i
\(508\) 9.69428e12 1.67910e13i 0.286548 0.496315i
\(509\) −2.41685e13 + 1.39537e13i −0.707392 + 0.408413i −0.810095 0.586299i \(-0.800584\pi\)
0.102702 + 0.994712i \(0.467251\pi\)
\(510\) 2.27069e12i 0.0658123i
\(511\) −3.45529e12 + 7.97756e11i −0.0991700 + 0.0228963i
\(512\) 1.59161e13 0.452363
\(513\) 2.93840e12 + 5.08946e12i 0.0827037 + 0.143247i
\(514\) 1.57285e13 + 9.08088e12i 0.438402 + 0.253112i
\(515\) −1.18115e12 + 2.04581e12i −0.0326039 + 0.0564716i
\(516\) −1.40135e13 + 8.09068e12i −0.383087 + 0.221175i
\(517\) 6.10394e13i 1.65256i
\(518\) 1.93663e12 + 8.38806e12i 0.0519276 + 0.224912i
\(519\) 1.77004e13 0.470051
\(520\) −2.85211e12 4.94000e12i −0.0750153 0.129930i
\(521\) 2.41504e13 + 1.39433e13i 0.629124 + 0.363225i 0.780413 0.625265i \(-0.215009\pi\)
−0.151289 + 0.988490i \(0.548342\pi\)
\(522\) 4.01005e11 6.94561e11i 0.0103466 0.0179208i
\(523\) 2.70588e13 1.56224e13i 0.691512 0.399245i −0.112666 0.993633i \(-0.535939\pi\)
0.804178 + 0.594388i \(0.202606\pi\)
\(524\) 3.29059e13i 0.832946i
\(525\) −6.61661e12 + 2.16428e13i −0.165897 + 0.542646i
\(526\) 5.50647e12 0.136755
\(527\) −3.06498e13 5.30870e13i −0.754006 1.30598i
\(528\) 5.69293e12 + 3.28682e12i 0.138729 + 0.0800951i
\(529\) 6.95503e12 1.20465e13i 0.167888 0.290791i
\(530\) 2.86276e12 1.65282e12i 0.0684552 0.0395226i
\(531\) 2.09639e13i 0.496591i
\(532\) −1.27172e13 1.36373e13i −0.298424 0.320014i
\(533\) 4.64831e13 1.08058
\(534\) 1.48097e12 + 2.56512e12i 0.0341068 + 0.0590747i
\(535\) −7.55890e11 4.36413e11i −0.0172460 0.00995701i
\(536\) 4.03658e13 6.99157e13i 0.912410 1.58034i
\(537\) 2.69350e12 1.55510e12i 0.0603179 0.0348246i
\(538\) 1.56264e13i 0.346694i
\(539\) 4.51636e13 + 3.04618e13i 0.992760 + 0.669595i
\(540\) 5.89463e11 0.0128377
\(541\) 3.62347e13 + 6.27603e13i 0.781876 + 1.35425i 0.930848 + 0.365408i \(0.119070\pi\)
−0.148971 + 0.988842i \(0.547596\pi\)
\(542\) 2.78803e13 + 1.60967e13i 0.596076 + 0.344145i
\(543\) 4.40070e12 7.62223e12i 0.0932228 0.161467i
\(544\) −4.58523e13 + 2.64728e13i −0.962424 + 0.555655i
\(545\) 8.22249e12i 0.171010i
\(546\) −1.55462e13 + 1.44974e13i −0.320377 + 0.298763i
\(547\) −8.00788e13 −1.63524 −0.817619 0.575760i \(-0.804706\pi\)
−0.817619 + 0.575760i \(0.804706\pi\)
\(548\) 1.99676e13 + 3.45849e13i 0.404039 + 0.699815i
\(549\) −1.41088e13 8.14570e12i −0.282896 0.163330i
\(550\) 2.07501e13 3.59402e13i 0.412294 0.714114i
\(551\) 3.34950e12 1.93384e12i 0.0659511 0.0380769i
\(552\) 2.54980e13i 0.497519i
\(553\) −4.42117e13 1.35164e13i −0.854893 0.261357i
\(554\) 5.86155e12 0.112322
\(555\) −6.56193e11 1.13656e12i −0.0124614 0.0215838i
\(556\) 4.61920e13 + 2.66690e13i 0.869346 + 0.501917i
\(557\) 3.68766e13 6.38721e13i 0.687820 1.19134i −0.284721 0.958610i \(-0.591901\pi\)
0.972542 0.232729i \(-0.0747656\pi\)
\(558\) −1.32882e13 + 7.67192e12i −0.245637 + 0.141819i
\(559\) 8.89577e13i 1.62976i
\(560\) 1.62913e12 3.76133e11i 0.0295812 0.00682969i
\(561\) −4.77015e13 −0.858455
\(562\) −3.46419e13 6.00016e13i −0.617904 1.07024i
\(563\) −1.25607e12 7.25193e11i −0.0222061 0.0128207i 0.488856 0.872365i \(-0.337414\pi\)
−0.511062 + 0.859544i \(0.670748\pi\)
\(564\) 1.15746e13 2.00479e13i 0.202820 0.351295i
\(565\) −6.84631e12 + 3.95272e12i −0.118909 + 0.0686521i
\(566\) 6.22334e13i 1.07138i
\(567\) −1.46481e12 6.34447e12i −0.0249957 0.108263i
\(568\) −3.90557e12 −0.0660607
\(569\) 2.41974e13 + 4.19111e13i 0.405702 + 0.702697i 0.994403 0.105654i \(-0.0336936\pi\)
−0.588701 + 0.808351i \(0.700360\pi\)
\(570\) −2.37375e12 1.37048e12i −0.0394512 0.0227772i
\(571\) −1.47155e13 + 2.54880e13i −0.242435 + 0.419910i −0.961407 0.275129i \(-0.911279\pi\)
0.718972 + 0.695039i \(0.244613\pi\)
\(572\) −3.50098e13 + 2.02129e13i −0.571754 + 0.330102i
\(573\) 1.42364e13i 0.230477i
\(574\) −1.27358e13 + 4.16585e13i −0.204393 + 0.668566i
\(575\) −5.03472e13 −0.801007
\(576\) 9.07484e12 + 1.57181e13i 0.143129 + 0.247906i
\(577\) 9.08727e13 + 5.24654e13i 1.42087 + 0.820340i 0.996373 0.0850900i \(-0.0271178\pi\)
0.424497 + 0.905430i \(0.360451\pi\)
\(578\) −1.22445e13 + 2.12081e13i −0.189803 + 0.328748i
\(579\) −3.13188e13 + 1.80819e13i −0.481296 + 0.277876i
\(580\) 3.87940e11i 0.00591050i
\(581\) 2.75062e13 + 2.94962e13i 0.415480 + 0.445539i
\(582\) 7.71125e12 0.115481
\(583\) −3.47215e13 6.01394e13i −0.515532 0.892928i
\(584\) 6.33091e12 + 3.65515e12i 0.0931970 + 0.0538073i
\(585\) 1.62030e12 2.80643e12i 0.0236491 0.0409615i
\(586\) −7.64978e13 + 4.41660e13i −1.10703 + 0.639146i
\(587\) 1.16227e14i 1.66770i −0.551994 0.833848i \(-0.686133\pi\)
0.551994 0.833848i \(-0.313867\pi\)
\(588\) 9.05723e12 + 1.85691e13i 0.128857 + 0.264182i
\(589\) −7.39952e13 −1.04382
\(590\) 4.88882e12 + 8.46768e12i 0.0683823 + 0.118442i
\(591\) −5.21925e13 3.01333e13i −0.723887 0.417936i
\(592\) 2.77529e12 4.80694e12i 0.0381680 0.0661089i
\(593\) 6.40260e13 3.69654e13i 0.873137 0.504106i 0.00474784 0.999989i \(-0.498489\pi\)
0.868390 + 0.495883i \(0.165155\pi\)
\(594\) 1.19401e13i 0.161464i
\(595\) −8.87325e12 + 8.27461e12i −0.118987 + 0.110959i
\(596\) 1.13778e13 0.151296
\(597\) −8.32213e12 1.44144e13i −0.109740 0.190074i
\(598\) −4.09537e13 2.36446e13i −0.535534 0.309191i
\(599\) −1.50156e13 + 2.60078e13i −0.194720 + 0.337264i −0.946809 0.321797i \(-0.895713\pi\)
0.752089 + 0.659062i \(0.229046\pi\)
\(600\) 4.04035e13 2.33270e13i 0.519592 0.299987i
\(601\) 3.22689e13i 0.411540i 0.978600 + 0.205770i \(0.0659699\pi\)
−0.978600 + 0.205770i \(0.934030\pi\)
\(602\) −7.97246e13 2.43733e13i −1.00835 0.308271i
\(603\) 4.58640e13 0.575288
\(604\) 3.70722e13 + 6.42109e13i 0.461172 + 0.798774i
\(605\) 3.99105e12 + 2.30423e12i 0.0492391 + 0.0284282i
\(606\) −9.75871e12 + 1.69026e13i −0.119407 + 0.206819i
\(607\) 1.12293e14 6.48326e13i 1.36273 0.786775i 0.372746 0.927933i \(-0.378416\pi\)
0.989987 + 0.141159i \(0.0450828\pi\)
\(608\) 6.39111e13i 0.769233i
\(609\) −4.17546e12 + 9.64026e11i −0.0498445 + 0.0115081i
\(610\) 7.59838e12 0.0899646
\(611\) −6.36320e13 1.10214e14i −0.747256 1.29429i
\(612\) −1.56671e13 9.04542e12i −0.182487 0.105359i
\(613\) −1.87753e13 + 3.25197e13i −0.216912 + 0.375703i −0.953862 0.300244i \(-0.902932\pi\)
0.736950 + 0.675947i \(0.236265\pi\)
\(614\) −2.92666e13 + 1.68971e13i −0.335375 + 0.193629i
\(615\) 6.64092e12i 0.0754836i
\(616\) −2.52632e13 1.09422e14i −0.284830 1.23367i
\(617\) 5.76872e13 0.645139 0.322569 0.946546i \(-0.395453\pi\)
0.322569 + 0.946546i \(0.395453\pi\)
\(618\) −9.07369e12 1.57161e13i −0.100656 0.174342i
\(619\) −2.12295e13 1.22568e13i −0.233607 0.134873i 0.378628 0.925549i \(-0.376396\pi\)
−0.612235 + 0.790676i \(0.709729\pi\)
\(620\) −3.71098e12 + 6.42760e12i −0.0405070 + 0.0701602i
\(621\) 1.25448e13 7.24274e12i 0.135833 0.0784233i
\(622\) 6.52976e13i 0.701367i
\(623\) 4.62699e12 1.51348e13i 0.0493013 0.161263i
\(624\) 1.37057e13 0.144870
\(625\) −4.52419e13 7.83612e13i −0.474395 0.821677i
\(626\) 3.74369e13 + 2.16142e13i 0.389429 + 0.224837i
\(627\) −2.87904e13 + 4.98664e13i −0.297105 + 0.514601i
\(628\) 8.91564e12 5.14744e12i 0.0912755 0.0526979i
\(629\) 4.02776e13i 0.409082i
\(630\) 2.07121e12 + 2.22105e12i 0.0208699 + 0.0223798i
\(631\) 1.15221e13 0.115182 0.0575911 0.998340i \(-0.481658\pi\)
0.0575911 + 0.998340i \(0.481658\pi\)
\(632\) 4.76522e13 + 8.25360e13i 0.472604 + 0.818574i
\(633\) 6.81951e13 + 3.93725e13i 0.671019 + 0.387413i
\(634\) 5.93275e13 1.02758e14i 0.579175 1.00316i
\(635\) −1.31880e13 + 7.61407e12i −0.127735 + 0.0737477i
\(636\) 2.63363e13i 0.253087i
\(637\) 1.13304e14 + 7.92059e12i 1.08031 + 0.0755197i
\(638\) 7.85807e12 0.0743383
\(639\) −1.10939e12 1.92151e12i −0.0104131 0.0180360i
\(640\) 3.57368e12 + 2.06327e12i 0.0332825 + 0.0192157i
\(641\) −1.74415e13 + 3.02096e13i −0.161174 + 0.279161i −0.935290 0.353882i \(-0.884861\pi\)
0.774116 + 0.633044i \(0.218195\pi\)
\(642\) 5.80680e12 3.35256e12i 0.0532429 0.0307398i
\(643\) 4.91365e13i 0.447043i 0.974699 + 0.223521i \(0.0717552\pi\)
−0.974699 + 0.223521i \(0.928245\pi\)
\(644\) −3.36139e13 + 3.13461e13i −0.303451 + 0.282979i
\(645\) 1.27092e13 0.113846
\(646\) 4.20607e13 + 7.28513e13i 0.373864 + 0.647552i
\(647\) −1.35858e14 7.84374e13i −1.19829 0.691834i −0.238118 0.971236i \(-0.576530\pi\)
−0.960174 + 0.279402i \(0.909864\pi\)
\(648\) −6.71144e12 + 1.16246e13i −0.0587410 + 0.101742i
\(649\) 1.77884e14 1.02702e14i 1.54495 0.891977i
\(650\) 8.65258e13i 0.745725i
\(651\) 7.84030e13 + 2.39693e13i 0.670545 + 0.204998i
\(652\) 3.52449e13 0.299129
\(653\) 5.34059e12 + 9.25017e12i 0.0449804 + 0.0779083i 0.887639 0.460540i \(-0.152344\pi\)
−0.842659 + 0.538448i \(0.819011\pi\)
\(654\) 5.47032e13 + 3.15829e13i 0.457219 + 0.263975i
\(655\) −1.29225e13 + 2.23824e13i −0.107186 + 0.185652i
\(656\) 2.43240e13 1.40435e13i 0.200224 0.115599i
\(657\) 4.15301e12i 0.0339263i
\(658\) 1.16209e14 2.68302e13i 0.942128 0.217518i
\(659\) −1.38421e14 −1.11372 −0.556858 0.830608i \(-0.687993\pi\)
−0.556858 + 0.830608i \(0.687993\pi\)
\(660\) 2.88777e12 + 5.00176e12i 0.0230591 + 0.0399396i
\(661\) −7.13843e13 4.12137e13i −0.565712 0.326614i 0.189723 0.981838i \(-0.439241\pi\)
−0.755435 + 0.655224i \(0.772574\pi\)
\(662\) −7.38441e13 + 1.27902e14i −0.580799 + 1.00597i
\(663\) −8.61306e13 + 4.97275e13i −0.672341 + 0.388177i
\(664\) 8.31412e13i 0.644133i
\(665\) 3.29468e12 + 1.42701e13i 0.0253341 + 0.109729i
\(666\) 1.00818e13 0.0769430
\(667\) −4.76663e12 8.25604e12i −0.0361062 0.0625378i
\(668\) −2.91955e13 1.68561e13i −0.219500 0.126728i
\(669\) 4.08660e13 7.07819e13i 0.304952 0.528192i
\(670\) −1.85253e13 + 1.06956e13i −0.137212 + 0.0792192i
\(671\) 1.59623e14i 1.17350i
\(672\) 2.07027e13 6.77181e13i 0.151071 0.494150i
\(673\) 4.49603e13 0.325652 0.162826 0.986655i \(-0.447939\pi\)
0.162826 + 0.986655i \(0.447939\pi\)
\(674\) 1.52098e13 + 2.63441e13i 0.109351 + 0.189402i
\(675\) 2.29534e13 + 1.32521e13i 0.163805 + 0.0945730i
\(676\) −6.20830e12 + 1.07531e13i −0.0439784 + 0.0761728i
\(677\) 9.88063e13 5.70459e13i 0.694771 0.401126i −0.110626 0.993862i \(-0.535286\pi\)
0.805397 + 0.592736i \(0.201952\pi\)
\(678\) 6.07302e13i 0.423893i
\(679\) −2.81005e13 3.01335e13i −0.194700 0.208785i
\(680\) 2.50111e13 0.172024
\(681\) −5.37228e13 9.30507e13i −0.366795 0.635308i
\(682\) −1.30197e14 7.51692e13i −0.882427 0.509470i
\(683\) −6.11574e13 + 1.05928e14i −0.411477 + 0.712699i −0.995051 0.0993607i \(-0.968320\pi\)
0.583575 + 0.812060i \(0.301654\pi\)
\(684\) −1.89119e13 + 1.09188e13i −0.126315 + 0.0729280i
\(685\) 3.13659e13i 0.207972i
\(686\) −3.81424e13 + 9.93736e13i −0.251066 + 0.654110i
\(687\) 4.41764e13 0.288674
\(688\) 2.68759e13 + 4.65505e13i 0.174350 + 0.301982i
\(689\) −1.25387e14 7.23925e13i −0.807529 0.466227i
\(690\) −3.37805e12 + 5.85095e12i −0.0215983 + 0.0374094i
\(691\) −1.32714e14 + 7.66222e13i −0.842413 + 0.486367i −0.858084 0.513510i \(-0.828345\pi\)
0.0156706 + 0.999877i \(0.495012\pi\)
\(692\) 6.57726e13i 0.414491i
\(693\) 4.66586e13 4.35108e13i 0.291921 0.272227i
\(694\) 8.22885e13 0.511142
\(695\) −2.09463e13 3.62801e13i −0.129177 0.223740i
\(696\) 7.65041e12 + 4.41697e12i 0.0468423 + 0.0270444i
\(697\) −1.01906e14 + 1.76507e14i −0.619494 + 1.07300i
\(698\) 1.05076e13 6.06658e12i 0.0634202 0.0366157i
\(699\) 1.82943e14i 1.09630i
\(700\) −8.04222e13 2.45866e13i −0.478504 0.146288i
\(701\) 3.26430e12 0.0192841 0.00964207 0.999954i \(-0.496931\pi\)
0.00964207 + 0.999954i \(0.496931\pi\)
\(702\) 1.24472e13 + 2.15593e13i 0.0730109 + 0.126459i
\(703\) 4.21057e13 + 2.43097e13i 0.245224 + 0.141580i
\(704\) −8.89150e13 + 1.54005e14i −0.514176 + 0.890579i
\(705\) −1.57460e13 + 9.09094e12i −0.0904116 + 0.0521991i
\(706\) 7.61431e13i 0.434117i
\(707\) 1.01612e14 2.34602e13i 0.575240 0.132811i
\(708\) 7.78994e13 0.437893
\(709\) −4.12823e12 7.15031e12i −0.0230427 0.0399111i 0.854274 0.519823i \(-0.174002\pi\)
−0.877317 + 0.479912i \(0.840669\pi\)
\(710\) 8.96202e11 + 5.17423e11i 0.00496723 + 0.00286783i
\(711\) −2.70714e13 + 4.68890e13i −0.148992 + 0.258062i
\(712\) −2.82541e13 + 1.63125e13i −0.154412 + 0.0891500i
\(713\) 1.82388e14i 0.989801i
\(714\) −2.09675e13 9.08157e13i −0.112994 0.489407i
\(715\) 3.17512e13 0.169914
\(716\) 5.77857e12 + 1.00088e13i 0.0307083 + 0.0531883i
\(717\) −1.61156e14 9.30435e13i −0.850454 0.491010i
\(718\) −2.36623e13 + 4.09843e13i −0.124004 + 0.214781i
\(719\) 1.04264e14 6.01969e13i 0.542613 0.313278i −0.203524 0.979070i \(-0.565240\pi\)
0.746137 + 0.665792i \(0.231906\pi\)
\(720\) 1.95810e12i 0.0101198i
\(721\) −2.83489e13 + 9.27284e13i −0.145499 + 0.475923i
\(722\) −3.59174e13 −0.183071
\(723\) 3.36174e13 + 5.82271e13i 0.170166 + 0.294736i
\(724\) 2.83234e13 + 1.63525e13i 0.142381 + 0.0822038i
\(725\) 8.72157e12 1.51062e13i 0.0435416 0.0754163i
\(726\) −3.06596e13 + 1.77013e13i −0.152014 + 0.0877652i
\(727\) 1.67274e14i 0.823676i 0.911257 + 0.411838i \(0.135113\pi\)
−0.911257 + 0.411838i \(0.864887\pi\)
\(728\) −1.59685e14 1.71238e14i −0.780922 0.837418i
\(729\) −7.62560e12 −0.0370370
\(730\) −9.68492e11 1.67748e12i −0.00467177 0.00809174i
\(731\) −3.37793e14 1.95025e14i −1.61832 0.934335i
\(732\) 3.02685e13 5.24267e13i 0.144024 0.249458i
\(733\) −1.39896e14 + 8.07690e13i −0.661128 + 0.381702i −0.792707 0.609603i \(-0.791329\pi\)
0.131579 + 0.991306i \(0.457995\pi\)
\(734\) 2.36109e14i 1.10823i
\(735\) 1.13159e12 1.61874e13i 0.00527538 0.0754642i
\(736\) 1.57532e14 0.729422
\(737\) 2.24687e14 + 3.89169e14i 1.03333 + 1.78979i
\(738\) 4.41812e13 + 2.55080e13i 0.201816 + 0.116519i
\(739\) −1.06338e14 + 1.84183e14i −0.482467 + 0.835658i −0.999797 0.0201281i \(-0.993593\pi\)
0.517330 + 0.855786i \(0.326926\pi\)
\(740\) 4.22333e12 2.43834e12i 0.0190325 0.0109884i
\(741\) 1.20053e14i 0.537380i
\(742\) 9.92334e13 9.25386e13i 0.441203 0.411437i
\(743\) 4.10878e14 1.81455 0.907275 0.420539i \(-0.138159\pi\)
0.907275 + 0.420539i \(0.138159\pi\)
\(744\) −8.45042e13 1.46366e14i −0.370692 0.642058i
\(745\) −7.73911e12 4.46818e12i −0.0337217 0.0194692i
\(746\) 9.82127e13 1.70109e14i 0.425083 0.736265i
\(747\) 4.09048e13 2.36164e13i 0.175862 0.101534i
\(748\) 1.77254e14i 0.756984i
\(749\) −3.42614e13 1.04744e13i −0.145344 0.0444344i
\(750\) −2.49394e13 −0.105094
\(751\) −6.39216e13 1.10716e14i −0.267577 0.463456i 0.700659 0.713496i \(-0.252890\pi\)
−0.968235 + 0.250040i \(0.919556\pi\)
\(752\) −6.65957e13 3.84490e13i −0.276922 0.159881i
\(753\) −2.97793e13 + 5.15793e13i −0.123010 + 0.213059i
\(754\) 1.41887e13 8.19184e12i 0.0582217 0.0336143i
\(755\) 5.82344e13i 0.237380i
\(756\) 2.35754e13 5.44307e12i 0.0954663 0.0220412i
\(757\) 2.20498e14 0.887002 0.443501 0.896274i \(-0.353736\pi\)
0.443501 + 0.896274i \(0.353736\pi\)
\(758\) 9.78199e13 + 1.69429e14i 0.390914 + 0.677083i
\(759\) 1.22914e14 + 7.09642e13i 0.487968 + 0.281728i
\(760\) 1.50955e13 2.61462e13i 0.0595361 0.103120i
\(761\) 4.11760e14 2.37730e14i 1.61332 0.931451i 0.624727 0.780843i \(-0.285210\pi\)
0.988594 0.150608i \(-0.0481232\pi\)
\(762\) 1.16984e14i 0.455356i
\(763\) −7.59261e13 3.28856e14i −0.293608 1.27170i
\(764\) −5.29009e13 −0.203234
\(765\) 7.10445e12 + 1.23053e13i 0.0271158 + 0.0469660i
\(766\) 1.76470e13 + 1.01885e13i 0.0669157 + 0.0386338i
\(767\) 2.14128e14 3.70880e14i 0.806670 1.39719i
\(768\) −1.42177e14 + 8.20861e13i −0.532138 + 0.307230i
\(769\) 1.79281e14i 0.666656i −0.942811 0.333328i \(-0.891828\pi\)
0.942811 0.333328i \(-0.108172\pi\)
\(770\) −8.69945e12 + 2.84557e13i −0.0321394 + 0.105127i
\(771\) −1.13648e14 −0.417146
\(772\) −6.71904e13 1.16377e14i −0.245031 0.424406i
\(773\) 1.92713e14 + 1.11263e14i 0.698252 + 0.403136i 0.806696 0.590966i \(-0.201253\pi\)
−0.108444 + 0.994103i \(0.534587\pi\)
\(774\) −4.88164e13 + 8.45525e13i −0.175736 + 0.304384i
\(775\) −2.89008e14 + 1.66859e14i −1.03371 + 0.596815i
\(776\) 8.49374e13i 0.301850i
\(777\) −3.67392e13 3.93971e13i −0.129725 0.139110i
\(778\) −3.98295e14 −1.39736
\(779\) 1.23012e14 + 2.13063e14i 0.428805 + 0.742712i
\(780\) 1.04284e13 + 6.02085e12i 0.0361198 + 0.0208538i
\(781\) 1.08697e13 1.88269e13i 0.0374079 0.0647924i
\(782\) 1.79568e14 1.03674e14i 0.614038 0.354515i
\(783\) 5.01859e12i 0.0170519i
\(784\) 6.16834e13 3.00866e13i 0.208252 0.101576i
\(785\) −8.08580e12 −0.0271253
\(786\) −9.92713e13 1.71943e14i −0.330911 0.573154i
\(787\) 3.65332e14 + 2.10925e14i 1.21008 + 0.698641i 0.962777 0.270297i \(-0.0871219\pi\)
0.247305 + 0.968938i \(0.420455\pi\)
\(788\) 1.11972e14 1.93942e14i 0.368536 0.638322i
\(789\) −2.98405e13 + 1.72284e13i −0.0975935 + 0.0563456i
\(790\) 2.52524e13i 0.0820669i
\(791\) −2.37317e14 + 2.21306e14i −0.766384 + 0.714680i
\(792\) −1.31517e14 −0.422042
\(793\) −1.66402e14 2.88217e14i −0.530632 0.919082i
\(794\) 6.26129e13 + 3.61496e13i 0.198409 + 0.114551i
\(795\) −1.03425e13 + 1.79138e13i −0.0325680 + 0.0564095i
\(796\) 5.35622e13 3.09242e13i 0.167607 0.0967682i
\(797\) 2.79320e14i 0.868582i 0.900773 + 0.434291i \(0.143001\pi\)
−0.900773 + 0.434291i \(0.856999\pi\)
\(798\) −1.07592e14 3.28931e13i −0.332481 0.101646i
\(799\) 5.58009e14 1.71359
\(800\) 1.44119e14 + 2.49621e14i 0.439816 + 0.761783i
\(801\) −1.60513e13 9.26721e12i −0.0486796 0.0281052i
\(802\) 3.14307e13 5.44396e13i 0.0947289 0.164075i
\(803\) −3.52395e13 + 2.03455e13i −0.105549 + 0.0609385i
\(804\) 1.70426e14i 0.507288i
\(805\) 3.51738e13 8.12091e12i 0.104050 0.0240229i
\(806\) −3.13448e14 −0.921489
\(807\) 4.88911e13 + 8.46819e13i 0.142844 + 0.247413i
\(808\) −1.86178e14 1.07490e14i −0.540593 0.312112i
\(809\) −4.36961e12 + 7.56838e12i −0.0126096 + 0.0218404i −0.872261 0.489040i \(-0.837347\pi\)
0.859652 + 0.510880i \(0.170681\pi\)
\(810\) 3.08012e12 1.77831e12i 0.00883369 0.00510013i
\(811\) 1.63354e14i 0.465614i 0.972523 + 0.232807i \(0.0747910\pi\)
−0.972523 + 0.232807i \(0.925209\pi\)
\(812\) −3.58222e12 1.55155e13i −0.0101478 0.0439528i
\(813\) −2.01451e14 −0.567175
\(814\) 4.93908e13 + 8.55474e13i 0.138205 + 0.239378i
\(815\) −2.39734e13 1.38410e13i −0.0666716 0.0384929i
\(816\) −3.00474e13 + 5.20436e13i −0.0830531 + 0.143852i
\(817\) −4.07752e14 + 2.35416e14i −1.12017 + 0.646733i
\(818\) 4.28764e14i 1.17072i
\(819\) 3.88888e13 1.27204e14i 0.105537 0.345209i
\(820\) 2.46770e13 0.0665614
\(821\) 7.89153e12 + 1.36685e13i 0.0211566 + 0.0366442i 0.876410 0.481566i \(-0.159932\pi\)
−0.855253 + 0.518210i \(0.826598\pi\)
\(822\) 2.08673e14 + 1.20478e14i 0.556042 + 0.321031i
\(823\) 1.25919e14 2.18099e14i 0.333498 0.577636i −0.649697 0.760193i \(-0.725104\pi\)
0.983195 + 0.182557i \(0.0584375\pi\)
\(824\) 1.73109e14 9.99443e13i 0.455704 0.263101i
\(825\) 2.59688e14i 0.679489i
\(826\) 2.73717e14 + 2.93519e14i 0.711871 + 0.763373i
\(827\) −4.57149e14 −1.18176 −0.590882 0.806758i \(-0.701220\pi\)
−0.590882 + 0.806758i \(0.701220\pi\)
\(828\) 2.69133e13 + 4.66151e13i 0.0691536 + 0.119778i
\(829\) −4.85859e14 2.80511e14i −1.24090 0.716435i −0.271624 0.962403i \(-0.587561\pi\)
−0.969278 + 0.245968i \(0.920894\pi\)
\(830\) −1.10148e13 + 1.90782e13i −0.0279632 + 0.0484336i
\(831\) −3.17647e13 + 1.83394e13i −0.0801567 + 0.0462785i
\(832\) 3.70766e14i 0.930002i
\(833\) −2.78476e14 + 4.12876e14i −0.694324 + 1.02942i
\(834\) 3.21823e14 0.797602
\(835\) 1.32391e13 + 2.29307e13i 0.0326156 + 0.0564919i
\(836\) −1.85298e14 1.06982e14i −0.453774 0.261987i
\(837\) 4.80072e13 8.31509e13i 0.116864 0.202414i
\(838\) −3.41966e14 + 1.97434e14i −0.827491 + 0.477752i
\(839\) 1.70360e14i 0.409787i 0.978784 + 0.204894i \(0.0656848\pi\)
−0.978784 + 0.204894i \(0.934315\pi\)
\(840\) −2.44643e13 + 2.28138e13i −0.0584974 + 0.0545508i
\(841\) −4.17404e14 −0.992149
\(842\) 1.20467e14 + 2.08654e14i 0.284647 + 0.493022i
\(843\) 3.75461e14 + 2.16773e14i 0.881916 + 0.509174i
\(844\) −1.46304e14 + 2.53406e14i −0.341620 + 0.591704i
\(845\) 8.44569e12 4.87612e12i 0.0196043 0.0113185i
\(846\) 1.39675e14i 0.322304i
\(847\) 1.80898e14 + 5.53040e13i 0.414970 + 0.126864i
\(848\) −8.74850e13 −0.199505
\(849\) −1.94713e14 3.37254e14i −0.441426 0.764571i
\(850\) 3.28558e14 + 1.89693e14i 0.740487 + 0.427520i
\(851\) 5.99199e13 1.03784e14i 0.134253 0.232533i
\(852\) 7.14014e12 4.12236e12i 0.0159041 0.00918223i
\(853\) 7.66036e14i 1.69631i −0.529752 0.848153i \(-0.677715\pi\)
0.529752 0.848153i \(-0.322285\pi\)
\(854\) 3.03895e14 7.01631e13i 0.669013 0.154461i
\(855\) 1.71517e13 0.0375384
\(856\) 3.69276e13 + 6.39604e13i 0.0803493 + 0.139169i
\(857\) −4.21214e14 2.43188e14i −0.911169 0.526064i −0.0303618 0.999539i \(-0.509666\pi\)
−0.880807 + 0.473475i \(0.842999\pi\)
\(858\) −1.21958e14 + 2.11237e14i −0.262285 + 0.454290i
\(859\) 2.21234e14 1.27730e14i 0.473028 0.273103i −0.244478 0.969655i \(-0.578617\pi\)
0.717506 + 0.696552i \(0.245283\pi\)
\(860\) 4.72259e13i 0.100389i
\(861\) −6.13219e13 2.65602e14i −0.129599 0.561326i
\(862\) −4.29073e13 −0.0901560
\(863\) −1.74136e14 3.01613e14i −0.363777 0.630080i 0.624802 0.780783i \(-0.285180\pi\)
−0.988579 + 0.150703i \(0.951846\pi\)
\(864\) −7.18189e13 4.14647e13i −0.149166 0.0861211i
\(865\) 2.58296e13 4.47381e13i 0.0533379 0.0923840i
\(866\) −3.95526e13 + 2.28357e13i −0.0812054 + 0.0468840i
\(867\) 1.53241e14i 0.312809i
\(868\) −8.90674e13 + 2.91337e14i −0.180767 + 0.591286i
\(869\) −5.30490e14 −1.07048
\(870\) −1.17035e12 2.02710e12i −0.00234811 0.00406705i
\(871\) 8.11398e14 + 4.68461e14i 1.61861 + 0.934507i
\(872\) −3.47878e14 + 6.02542e14i −0.689992 + 1.19510i
\(873\) −4.17886e13 + 2.41267e13i −0.0824112 + 0.0475802i
\(874\) 2.50290e14i 0.490780i
\(875\) 9.08814e13 + 9.74563e13i 0.177188 + 0.190007i
\(876\) −1.54321e13 −0.0299162
\(877\) −5.71038e13 9.89067e13i −0.110069 0.190646i 0.805729 0.592285i \(-0.201774\pi\)
−0.915798 + 0.401639i \(0.868441\pi\)
\(878\) 3.28761e14 + 1.89810e14i 0.630098 + 0.363787i
\(879\) 2.76370e14 4.78687e14i 0.526679 0.912235i
\(880\) 1.66150e13 9.59269e12i 0.0314838 0.0181772i
\(881\) 5.86760e14i 1.10556i −0.833328 0.552779i \(-0.813567\pi\)
0.833328 0.552779i \(-0.186433\pi\)
\(882\) 1.03346e14 + 6.97049e13i 0.193621 + 0.130593i
\(883\) −1.43320e14 −0.266994 −0.133497 0.991049i \(-0.542621\pi\)
−0.133497 + 0.991049i \(0.542621\pi\)
\(884\) −1.84782e14 3.20052e14i −0.342294 0.592870i
\(885\) −5.29867e13 3.05919e13i −0.0976001 0.0563494i
\(886\) 3.47599e14 6.02058e14i 0.636663 1.10273i
\(887\) −5.26442e13 + 3.03942e13i −0.0958810 + 0.0553569i −0.547174 0.837019i \(-0.684296\pi\)
0.451293 + 0.892376i \(0.350963\pi\)
\(888\) 1.11049e14i 0.201117i
\(889\) −4.57141e14 + 4.26300e14i −0.823268 + 0.767726i
\(890\) 8.64454e12 0.0154807
\(891\) −3.73577e13 6.47054e13i −0.0665260 0.115226i
\(892\) 2.63018e14 + 1.51854e14i 0.465759 + 0.268906i
\(893\) 3.36789e14 5.83335e14i 0.593062 1.02721i
\(894\) 5.94524e13 3.43249e13i 0.104108 0.0601065i
\(895\) 9.07720e12i 0.0158065i
\(896\) 1.61981e14 + 4.95206e13i 0.280494 + 0.0857523i
\(897\) 2.95913e14 0.509568
\(898\) −1.30315e14 2.25713e14i −0.223159 0.386522i
\(899\) −5.47236e13 3.15947e13i −0.0931915 0.0538042i
\(900\) −4.92436e13 + 8.52924e13i −0.0833944 + 0.144443i
\(901\) 5.49782e14 3.17417e14i 0.925905 0.534571i
\(902\) 4.99854e14i 0.837164i
\(903\) 5.08299e14 1.17356e14i 0.846605 0.195463i
\(904\) 6.68927e14 1.10799
\(905\) −1.28436e13 2.22457e13i −0.0211565 0.0366441i
\(906\) 3.87426e14 + 2.23681e14i 0.634670 + 0.366427i
\(907\) −1.28682e14 + 2.22883e14i −0.209643 + 0.363113i −0.951602 0.307333i \(-0.900564\pi\)
0.741959 + 0.670445i \(0.233897\pi\)
\(908\) 3.45766e14 1.99628e14i 0.560213 0.323439i
\(909\) 1.22131e14i 0.196791i
\(910\) 1.39564e13 + 6.04491e13i 0.0223649 + 0.0968685i
\(911\) 4.61711e13 0.0735832 0.0367916 0.999323i \(-0.488286\pi\)
0.0367916 + 0.999323i \(0.488286\pi\)
\(912\) 3.62704e13 + 6.28222e13i 0.0574882 + 0.0995724i
\(913\) 4.00784e14 + 2.31393e14i 0.631767 + 0.364751i
\(914\) 2.42341e14 4.19747e14i 0.379924 0.658047i
\(915\) −4.11769e13 + 2.37735e13i −0.0642020 + 0.0370670i
\(916\) 1.64155e14i 0.254552i
\(917\) −3.10153e14 + 1.01450e15i −0.478331 + 1.56461i
\(918\) −1.09154e14 −0.167427
\(919\) −3.97775e14 6.88967e14i −0.606821 1.05104i −0.991761 0.128103i \(-0.959111\pi\)
0.384940 0.922941i \(-0.374222\pi\)
\(920\) −6.44467e13 3.72083e13i −0.0977826 0.0564548i
\(921\) 1.05734e14 1.83136e14i 0.159557 0.276361i
\(922\) −3.74459e14 + 2.16194e14i −0.562017 + 0.324480i
\(923\) 4.53257e13i 0.0676606i
\(924\) 1.61681e14 + 1.73379e14i 0.240049 + 0.257416i
\(925\) 2.19273e14 0.323799
\(926\) −3.30087e14 5.71727e14i −0.484812 0.839719i
\(927\) 9.83437e13 + 5.67788e13i 0.143664 + 0.0829445i
\(928\) −2.72889e13 + 4.72658e13i −0.0396503 + 0.0686764i
\(929\) −5.14642e14 + 2.97128e14i −0.743749 + 0.429404i −0.823431 0.567417i \(-0.807943\pi\)
0.0796819 + 0.996820i \(0.474610\pi\)
\(930\) 4.47815e13i 0.0643701i
\(931\) 2.63539e14 + 5.40307e14i 0.376788 + 0.772489i
\(932\) −6.79797e14 −0.966718
\(933\) −2.04300e14 3.53859e14i −0.288975 0.500520i
\(934\) −7.75841e14 4.47932e14i −1.09154 0.630199i
\(935\) −6.96092e13 + 1.20567e14i −0.0974111 + 0.168721i
\(936\) −2.37470e14 + 1.37103e14i −0.330544 + 0.190839i
\(937\) 3.17963e14i 0.440229i −0.975474 0.220114i \(-0.929357\pi\)
0.975474 0.220114i \(-0.0706431\pi\)
\(938\) −6.42152e14 + 5.98829e14i −0.884348 + 0.824685i
\(939\) −2.70503e14 −0.370547
\(940\) −3.37810e13 5.85104e13i −0.0460291 0.0797248i
\(941\) 3.92034e14 + 2.26341e14i 0.531343 + 0.306771i 0.741563 0.670883i \(-0.234085\pi\)
−0.210220 + 0.977654i \(0.567418\pi\)
\(942\) 3.10579e13 5.37938e13i 0.0418714 0.0725234i
\(943\) 5.25169e14 3.03207e14i 0.704272 0.406612i
\(944\) 2.58769e14i 0.345185i
\(945\) −1.81734e13 5.55595e12i −0.0241144 0.00737223i
\(946\) −9.56603e14 −1.26263
\(947\) 4.42256e14 + 7.66010e14i 0.580663 + 1.00574i 0.995401 + 0.0957963i \(0.0305398\pi\)
−0.414738 + 0.909941i \(0.636127\pi\)
\(948\) −1.74235e14 1.00594e14i −0.227558 0.131381i
\(949\) −4.24194e13 + 7.34726e13i −0.0551104 + 0.0954540i
\(950\) 3.96605e14 2.28980e14i 0.512554 0.295923i
\(951\) 7.42486e14i 0.954522i
\(952\) 1.00031e15 2.30951e14i 1.27924 0.295349i
\(953\) 5.18429e14 0.659515 0.329758 0.944066i \(-0.393033\pi\)
0.329758 + 0.944066i \(0.393033\pi\)
\(954\) −7.94522e13 1.37615e14i −0.100546 0.174150i
\(955\) 3.59828e13 + 2.07747e13i 0.0452979 + 0.0261528i
\(956\) 3.45740e14 5.98839e14i 0.432972 0.749930i
\(957\) −4.25842e13 + 2.45860e13i −0.0530504 + 0.0306287i
\(958\) 1.07660e15i 1.33421i
\(959\) −2.89631e14 1.25447e15i −0.357069 1.54656i
\(960\) 5.29705e13 0.0649647
\(961\) 1.94647e14 + 3.37139e14i 0.237482 + 0.411331i
\(962\) 1.78362e14 + 1.02977e14i 0.216484 + 0.124987i
\(963\) −2.09787e13 + 3.63362e13i −0.0253307 + 0.0438741i
\(964\) −2.16366e14 + 1.24919e14i −0.259898 + 0.150052i
\(965\) 1.05545e14i 0.126125i
\(966\) −8.10767e13 + 2.65200e14i −0.0963852 + 0.315274i
\(967\) 1.76168e14 0.208350 0.104175 0.994559i \(-0.466780\pi\)
0.104175 + 0.994559i \(0.466780\pi\)
\(968\) −1.94975e14 3.37707e14i −0.229405 0.397341i
\(969\) −4.55868e14 2.63196e14i −0.533606 0.308078i
\(970\) 1.12528e13 1.94904e13i 0.0131039 0.0226966i
\(971\) −7.28251e14 + 4.20456e14i −0.843694 + 0.487107i −0.858518 0.512783i \(-0.828615\pi\)
0.0148238 + 0.999890i \(0.495281\pi\)
\(972\) 2.83359e13i 0.0326592i
\(973\) −1.17275e15 1.25759e15i −1.34475 1.44204i
\(974\) −1.16698e14 −0.133128
\(975\) 2.70718e14 + 4.68898e14i 0.307252 + 0.532176i
\(976\) −1.74153e14 1.00547e14i −0.196644 0.113533i
\(977\) −7.52039e14 + 1.30257e15i −0.844827 + 1.46328i 0.0409445 + 0.999161i \(0.486963\pi\)
−0.885771 + 0.464122i \(0.846370\pi\)
\(978\) 1.84165e14 1.06328e14i 0.205832 0.118837i
\(979\) 1.81600e14i 0.201930i
\(980\) 6.01508e13 + 4.20488e12i 0.0665443 + 0.00465183i
\(981\) −3.95261e14 −0.435050
\(982\) −3.04055e14 5.26639e14i −0.332962 0.576708i
\(983\) 1.10681e13 + 6.39017e12i 0.0120588 + 0.00696217i 0.506017 0.862523i \(-0.331117\pi\)
−0.493958 + 0.869485i \(0.664451\pi\)
\(984\) −2.80964e14 + 4.86645e14i −0.304562 + 0.527517i
\(985\) −1.52326e14 + 8.79452e13i −0.164283 + 0.0948486i
\(986\) 7.18368e13i 0.0770837i
\(987\) −5.45811e14 + 5.08987e14i −0.582715 + 0.543402i
\(988\) −4.46104e14 −0.473861
\(989\) 5.80266e14 + 1.00505e15i 0.613261 + 1.06220i
\(990\) 3.01789e13 + 1.74238e13i 0.0317342 + 0.0183217i
\(991\) 3.16984e14 5.49032e14i 0.331641 0.574419i −0.651193 0.758913i \(-0.725731\pi\)
0.982834 + 0.184493i \(0.0590643\pi\)
\(992\) 9.04277e14 5.22084e14i 0.941332 0.543478i
\(993\) 9.24161e14i 0.957197i
\(994\) 4.06212e13 + 1.24187e13i 0.0418621 + 0.0127980i
\(995\) −4.85769e13 −0.0498097
\(996\) 8.77561e13 + 1.51998e14i 0.0895325 + 0.155075i
\(997\) 2.65124e14 + 1.53069e14i 0.269137 + 0.155386i 0.628495 0.777813i \(-0.283671\pi\)
−0.359359 + 0.933200i \(0.617005\pi\)
\(998\) −6.91710e13 + 1.19808e14i −0.0698669 + 0.121013i
\(999\) −5.46352e13 + 3.15437e13i −0.0549092 + 0.0317019i
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 21.11.f.a.10.4 12
3.2 odd 2 63.11.m.b.10.3 12
7.3 odd 6 147.11.d.a.97.5 12
7.4 even 3 147.11.d.a.97.6 12
7.5 odd 6 inner 21.11.f.a.19.4 yes 12
21.5 even 6 63.11.m.b.19.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.11.f.a.10.4 12 1.1 even 1 trivial
21.11.f.a.19.4 yes 12 7.5 odd 6 inner
63.11.m.b.10.3 12 3.2 odd 2
63.11.m.b.19.3 12 21.5 even 6
147.11.d.a.97.5 12 7.3 odd 6
147.11.d.a.97.6 12 7.4 even 3