Properties

Label 69.8.e.b.58.14
Level $69$
Weight $8$
Character 69.58
Analytic conductor $21.555$
Analytic rank $0$
Dimension $140$
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] = [69,8,Mod(4,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.4");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 69.e (of order \(11\), degree \(10\), 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: \(21.5545667584\)
Analytic rank: \(0\)
Dimension: \(140\)
Relative dimension: \(14\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 58.14
Character \(\chi\) \(=\) 69.58
Dual form 69.8.e.b.25.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(18.4199 - 11.8377i) q^{2} +(3.84250 - 26.7252i) q^{3} +(145.987 - 319.667i) q^{4} +(-458.339 + 134.580i) q^{5} +(-245.588 - 537.762i) q^{6} +(-332.108 - 383.273i) q^{7} +(-696.213 - 4842.27i) q^{8} +(-699.470 - 205.383i) q^{9} +O(q^{10})\) \(q+(18.4199 - 11.8377i) q^{2} +(3.84250 - 26.7252i) q^{3} +(145.987 - 319.667i) q^{4} +(-458.339 + 134.580i) q^{5} +(-245.588 - 537.762i) q^{6} +(-332.108 - 383.273i) q^{7} +(-696.213 - 4842.27i) q^{8} +(-699.470 - 205.383i) q^{9} +(-6849.43 + 7904.66i) q^{10} +(5716.33 + 3673.66i) q^{11} +(-7982.21 - 5129.86i) q^{12} +(-3752.87 + 4331.04i) q^{13} +(-10654.5 - 3128.44i) q^{14} +(1835.52 + 12766.3i) q^{15} +(-40688.5 - 46957.1i) q^{16} +(-7809.70 - 17100.9i) q^{17} +(-15315.4 + 4497.02i) q^{18} +(3579.81 - 7838.69i) q^{19} +(-23890.6 + 166163. i) q^{20} +(-11519.2 + 7402.92i) q^{21} +148782. q^{22} +(-41553.8 - 40964.7i) q^{23} -132086. q^{24} +(126240. - 81129.4i) q^{25} +(-17857.7 + 124203. i) q^{26} +(-8176.61 + 17904.3i) q^{27} +(-171004. + 50211.2i) q^{28} +(-11959.4 - 26187.4i) q^{29} +(184935. + 213426. i) q^{30} +(-40189.5 - 279524. i) q^{31} +(-704525. - 206867. i) q^{32} +(120144. - 138654. i) q^{33} +(-346289. - 222547. i) q^{34} +(203799. + 130974. i) q^{35} +(-167768. + 193615. i) q^{36} +(30544.4 + 8968.65i) q^{37} +(-26852.7 - 186765. i) q^{38} +(101327. + 116938. i) q^{39} +(970776. + 2.12570e6i) q^{40} +(284918. - 83659.5i) q^{41} +(-124548. + 272722. i) q^{42} +(7110.80 - 49456.7i) q^{43} +(2.00886e6 - 1.29102e6i) q^{44} +348235. q^{45} +(-1.25035e6 - 262661. i) q^{46} -871575. q^{47} +(-1.41128e6 + 906976. i) q^{48} +(80599.8 - 560584. i) q^{49} +(1.36493e6 - 2.98879e6i) q^{50} +(-487032. + 143006. i) q^{51} +(836622. + 1.83195e6i) q^{52} +(1.14584e6 + 1.32237e6i) q^{53} +(61334.1 + 426588. i) q^{54} +(-3.11442e6 - 914476. i) q^{55} +(-1.62469e6 + 1.87500e6i) q^{56} +(-195735. - 125791. i) q^{57} +(-530290. - 340797. i) q^{58} +(-107881. + 124502. i) q^{59} +(4.34894e6 + 1.27696e6i) q^{60} +(192030. + 1.33560e6i) q^{61} +(-4.04922e6 - 4.67305e6i) q^{62} +(153582. + 336298. i) q^{63} +(-7.79525e6 + 2.28889e6i) q^{64} +(1.13721e6 - 2.49015e6i) q^{65} +(571695. - 3.97623e6i) q^{66} +(2.99575e6 - 1.92525e6i) q^{67} -6.60670e6 q^{68} +(-1.25446e6 + 953127. i) q^{69} +5.30440e6 q^{70} +(2.25290e6 - 1.44785e6i) q^{71} +(-507539. + 3.53001e6i) q^{72} +(-300642. + 658313. i) q^{73} +(668794. - 196376. i) q^{74} +(-1.68312e6 - 3.68552e6i) q^{75} +(-1.98317e6 - 2.28870e6i) q^{76} +(-490424. - 3.41097e6i) q^{77} +(3.25073e6 + 954499. i) q^{78} +(691794. - 798373. i) q^{79} +(2.49686e7 + 1.60464e7i) q^{80} +(447077. + 287319. i) q^{81} +(4.25782e6 - 4.91379e6i) q^{82} +(7.04454e6 + 2.06846e6i) q^{83} +(684821. + 4.76304e6i) q^{84} +(5.88093e6 + 6.78695e6i) q^{85} +(-454476. - 995163. i) q^{86} +(-745817. + 218992. i) q^{87} +(1.38091e7 - 3.02377e7i) q^{88} +(-339333. + 2.36011e6i) q^{89} +(6.41445e6 - 4.12232e6i) q^{90} +2.90633e6 q^{91} +(-1.91614e7 + 7.30309e6i) q^{92} -7.62475e6 q^{93} +(-1.60543e7 + 1.03175e7i) q^{94} +(-585831. + 4.07455e6i) q^{95} +(-8.23570e6 + 1.80337e7i) q^{96} +(-2.90476e6 + 852914. i) q^{97} +(-5.15141e6 - 1.12800e7i) q^{98} +(-3.24390e6 - 3.74366e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 140 q - 12 q^{2} + 378 q^{3} - 740 q^{4} + 2 q^{5} - 1755 q^{6} - 394 q^{7} - 1612 q^{8} - 10206 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 140 q - 12 q^{2} + 378 q^{3} - 740 q^{4} + 2 q^{5} - 1755 q^{6} - 394 q^{7} - 1612 q^{8} - 10206 q^{9} + 9178 q^{10} - 5996 q^{11} + 19980 q^{12} - 44394 q^{13} - 9524 q^{14} - 351 q^{15} - 165236 q^{16} + 152531 q^{17} - 8748 q^{18} + 4037 q^{19} - 6167 q^{20} + 10638 q^{21} + 98494 q^{22} - 160732 q^{23} + 5508 q^{24} - 14760 q^{25} + 403412 q^{26} + 275562 q^{27} + 84152 q^{28} + 205532 q^{29} - 247806 q^{30} - 1262119 q^{31} - 1781780 q^{32} + 735399 q^{33} + 2963321 q^{34} - 955354 q^{35} - 1269189 q^{36} - 1369770 q^{37} + 3950922 q^{38} + 1198638 q^{39} - 839075 q^{40} + 4017556 q^{41} - 798390 q^{42} - 2474862 q^{43} - 5279389 q^{44} + 2006208 q^{45} - 3642508 q^{46} - 5306766 q^{47} + 1755999 q^{48} + 4554906 q^{49} + 3476227 q^{50} + 3473280 q^{51} + 15615773 q^{52} + 3269752 q^{53} + 452709 q^{54} - 7825001 q^{55} - 23842824 q^{56} - 6117309 q^{57} - 1584991 q^{58} + 1692452 q^{59} + 4240161 q^{60} + 6133200 q^{61} - 11065051 q^{62} - 287226 q^{63} + 5056548 q^{64} + 13947245 q^{65} - 7185321 q^{66} - 6003959 q^{67} + 37775092 q^{68} - 1069794 q^{69} - 27634536 q^{70} + 5868445 q^{71} - 1175148 q^{72} - 23836857 q^{73} + 8638944 q^{74} + 5583546 q^{75} - 13476319 q^{76} - 19300986 q^{77} + 16707492 q^{78} - 16058510 q^{79} - 1951148 q^{80} - 7440174 q^{81} + 47661526 q^{82} + 21531792 q^{83} + 33361956 q^{84} + 51859503 q^{85} - 20977372 q^{86} + 1565568 q^{87} - 35256744 q^{88} - 26730592 q^{89} + 6690762 q^{90} - 42532184 q^{91} - 71328833 q^{92} - 19877886 q^{93} - 70960921 q^{94} - 43191119 q^{95} + 17543196 q^{96} + 52039436 q^{97} + 98000731 q^{98} - 19855773 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{10}{11}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 18.4199 11.8377i 1.62810 1.04632i 0.677683 0.735354i \(-0.262984\pi\)
0.950421 0.310965i \(-0.100652\pi\)
\(3\) 3.84250 26.7252i 0.0821655 0.571474i
\(4\) 145.987 319.667i 1.14052 2.49740i
\(5\) −458.339 + 134.580i −1.63980 + 0.481490i −0.966241 0.257641i \(-0.917055\pi\)
−0.673562 + 0.739130i \(0.735237\pi\)
\(6\) −245.588 537.762i −0.464170 1.01639i
\(7\) −332.108 383.273i −0.365962 0.422343i 0.542666 0.839949i \(-0.317415\pi\)
−0.908629 + 0.417605i \(0.862869\pi\)
\(8\) −696.213 4842.27i −0.480759 3.34375i
\(9\) −699.470 205.383i −0.319831 0.0939109i
\(10\) −6849.43 + 7904.66i −2.16598 + 2.49967i
\(11\) 5716.33 + 3673.66i 1.29492 + 0.832194i 0.992649 0.121028i \(-0.0386190\pi\)
0.302271 + 0.953222i \(0.402255\pi\)
\(12\) −7982.21 5129.86i −1.33349 0.856980i
\(13\) −3752.87 + 4331.04i −0.473764 + 0.546752i −0.941455 0.337140i \(-0.890541\pi\)
0.467691 + 0.883892i \(0.345086\pi\)
\(14\) −10654.5 3128.44i −1.03773 0.304705i
\(15\) 1835.52 + 12766.3i 0.140423 + 0.976666i
\(16\) −40688.5 46957.1i −2.48343 2.86603i
\(17\) −7809.70 17100.9i −0.385534 0.844202i −0.998534 0.0541196i \(-0.982765\pi\)
0.613000 0.790083i \(-0.289962\pi\)
\(18\) −15315.4 + 4497.02i −0.618979 + 0.181749i
\(19\) 3579.81 7838.69i 0.119735 0.262184i −0.840269 0.542170i \(-0.817603\pi\)
0.960004 + 0.279987i \(0.0903300\pi\)
\(20\) −23890.6 + 166163.i −0.667764 + 4.64440i
\(21\) −11519.2 + 7402.92i −0.271427 + 0.174436i
\(22\) 148782. 2.97901
\(23\) −41553.8 40964.7i −0.712137 0.702040i
\(24\) −132086. −1.95037
\(25\) 126240. 81129.4i 1.61587 1.03846i
\(26\) −17857.7 + 124203.i −0.199259 + 1.38588i
\(27\) −8176.61 + 17904.3i −0.0799467 + 0.175059i
\(28\) −171004. + 50211.2i −1.47215 + 0.432262i
\(29\) −11959.4 26187.4i −0.0910575 0.199388i 0.858624 0.512607i \(-0.171320\pi\)
−0.949681 + 0.313218i \(0.898593\pi\)
\(30\) 184935. + 213426.i 1.25053 + 1.44319i
\(31\) −40189.5 279524.i −0.242296 1.68521i −0.640539 0.767926i \(-0.721289\pi\)
0.398243 0.917280i \(-0.369620\pi\)
\(32\) −704525. 206867.i −3.80077 1.11601i
\(33\) 120144. 138654.i 0.581975 0.671635i
\(34\) −346289. 222547.i −1.51100 0.971058i
\(35\) 203799. + 130974.i 0.803460 + 0.516353i
\(36\) −167768. + 193615.i −0.599308 + 0.691639i
\(37\) 30544.4 + 8968.65i 0.0991347 + 0.0291086i 0.330924 0.943658i \(-0.392640\pi\)
−0.231789 + 0.972766i \(0.574458\pi\)
\(38\) −26852.7 186765.i −0.0793863 0.552144i
\(39\) 101327. + 116938.i 0.273528 + 0.315668i
\(40\) 970776. + 2.12570e6i 2.39833 + 5.25161i
\(41\) 284918. 83659.5i 0.645619 0.189571i 0.0575003 0.998345i \(-0.481687\pi\)
0.588119 + 0.808775i \(0.299869\pi\)
\(42\) −124548. + 272722.i −0.259397 + 0.568000i
\(43\) 7110.80 49456.7i 0.0136389 0.0948605i −0.981865 0.189582i \(-0.939287\pi\)
0.995504 + 0.0947211i \(0.0301959\pi\)
\(44\) 2.00886e6 1.29102e6i 3.55521 2.28480i
\(45\) 348235. 0.569677
\(46\) −1.25035e6 262661.i −1.89399 0.397872i
\(47\) −871575. −1.22451 −0.612255 0.790661i \(-0.709737\pi\)
−0.612255 + 0.790661i \(0.709737\pi\)
\(48\) −1.41128e6 + 906976.i −1.84191 + 1.18373i
\(49\) 80599.8 560584.i 0.0978696 0.680698i
\(50\) 1.36493e6 2.98879e6i 1.54425 3.38143i
\(51\) −487032. + 143006.i −0.514117 + 0.150958i
\(52\) 836622. + 1.83195e6i 0.825121 + 1.80676i
\(53\) 1.14584e6 + 1.32237e6i 1.05721 + 1.22008i 0.974706 + 0.223490i \(0.0717451\pi\)
0.0825002 + 0.996591i \(0.473709\pi\)
\(54\) 61334.1 + 426588.i 0.0530058 + 0.368664i
\(55\) −3.11442e6 914476.i −2.52411 0.741145i
\(56\) −1.62469e6 + 1.87500e6i −1.23627 + 1.42673i
\(57\) −195735. 125791.i −0.139993 0.0899680i
\(58\) −530290. 340797.i −0.356875 0.229349i
\(59\) −107881. + 124502.i −0.0683855 + 0.0789210i −0.788911 0.614507i \(-0.789355\pi\)
0.720526 + 0.693428i \(0.243900\pi\)
\(60\) 4.34894e6 + 1.27696e6i 2.59928 + 0.763219i
\(61\) 192030. + 1.33560e6i 0.108322 + 0.753393i 0.969500 + 0.245090i \(0.0788177\pi\)
−0.861179 + 0.508302i \(0.830273\pi\)
\(62\) −4.04922e6 4.67305e6i −2.15775 2.49017i
\(63\) 153582. + 336298.i 0.0773835 + 0.169446i
\(64\) −7.79525e6 + 2.28889e6i −3.71706 + 1.09143i
\(65\) 1.13721e6 2.49015e6i 0.513623 1.12468i
\(66\) 571695. 3.97623e6i 0.244772 1.70242i
\(67\) 2.99575e6 1.92525e6i 1.21687 0.782034i 0.235073 0.971978i \(-0.424467\pi\)
0.981795 + 0.189944i \(0.0608306\pi\)
\(68\) −6.60670e6 −2.54802
\(69\) −1.25446e6 + 953127.i −0.459711 + 0.349284i
\(70\) 5.30440e6 1.84839
\(71\) 2.25290e6 1.44785e6i 0.747028 0.480086i −0.110915 0.993830i \(-0.535378\pi\)
0.857944 + 0.513744i \(0.171742\pi\)
\(72\) −507539. + 3.53001e6i −0.160253 + 1.11458i
\(73\) −300642. + 658313.i −0.0904522 + 0.198063i −0.949451 0.313914i \(-0.898359\pi\)
0.858999 + 0.511977i \(0.171087\pi\)
\(74\) 668794. 196376.i 0.191859 0.0563348i
\(75\) −1.68312e6 3.68552e6i −0.460681 1.00875i
\(76\) −1.98317e6 2.28870e6i −0.518217 0.598054i
\(77\) −490424. 3.41097e6i −0.122420 0.851452i
\(78\) 3.25073e6 + 954499.i 0.775620 + 0.227743i
\(79\) 691794. 798373.i 0.157864 0.182184i −0.671308 0.741179i \(-0.734267\pi\)
0.829172 + 0.558994i \(0.188813\pi\)
\(80\) 2.49686e7 + 1.60464e7i 5.45230 + 3.50398i
\(81\) 447077. + 287319.i 0.0934726 + 0.0600712i
\(82\) 4.25782e6 4.91379e6i 0.852783 0.984165i
\(83\) 7.04454e6 + 2.06846e6i 1.35232 + 0.397077i 0.876049 0.482222i \(-0.160170\pi\)
0.476270 + 0.879299i \(0.341988\pi\)
\(84\) 684821. + 4.76304e6i 0.126067 + 0.876812i
\(85\) 5.88093e6 + 6.78695e6i 1.03868 + 1.19869i
\(86\) −454476. 995163.i −0.0770488 0.168713i
\(87\) −745817. + 218992.i −0.121427 + 0.0356541i
\(88\) 1.38091e7 3.02377e7i 2.16011 4.72997i
\(89\) −339333. + 2.36011e6i −0.0510224 + 0.354868i 0.948277 + 0.317444i \(0.102825\pi\)
−0.999299 + 0.0374246i \(0.988085\pi\)
\(90\) 6.41445e6 4.12232e6i 0.927494 0.596064i
\(91\) 2.90633e6 0.404297
\(92\) −1.91614e7 + 7.30309e6i −2.56549 + 0.977799i
\(93\) −7.62475e6 −0.982959
\(94\) −1.60543e7 + 1.03175e7i −1.99363 + 1.28123i
\(95\) −585831. + 4.07455e6i −0.0701036 + 0.487581i
\(96\) −8.23570e6 + 1.80337e7i −0.950061 + 2.08034i
\(97\) −2.90476e6 + 852914.i −0.323153 + 0.0948864i −0.439286 0.898347i \(-0.644768\pi\)
0.116132 + 0.993234i \(0.462950\pi\)
\(98\) −5.15141e6 1.12800e7i −0.552885 1.21065i
\(99\) −3.24390e6 3.74366e6i −0.336003 0.387769i
\(100\) −7.50502e6 5.21986e7i −0.750502 5.21986i
\(101\) 1.70764e7 + 5.01408e6i 1.64919 + 0.484246i 0.968643 0.248457i \(-0.0799233\pi\)
0.680549 + 0.732703i \(0.261742\pi\)
\(102\) −7.27822e6 + 8.39951e6i −0.679086 + 0.783706i
\(103\) −1.62273e7 1.04287e7i −1.46325 0.940371i −0.998490 0.0549320i \(-0.982506\pi\)
−0.464756 0.885439i \(-0.653858\pi\)
\(104\) 2.35849e7 + 1.51571e7i 2.05597 + 1.32129i
\(105\) 4.28340e6 4.94330e6i 0.361099 0.416730i
\(106\) 3.67603e7 + 1.07938e7i 2.99784 + 0.880244i
\(107\) −2.81127e6 1.95528e7i −0.221850 1.54300i −0.731034 0.682341i \(-0.760962\pi\)
0.509185 0.860657i \(-0.329947\pi\)
\(108\) 4.52974e6 + 5.22759e6i 0.346011 + 0.399318i
\(109\) −417628. 914477.i −0.0308885 0.0676363i 0.893559 0.448946i \(-0.148200\pi\)
−0.924447 + 0.381310i \(0.875473\pi\)
\(110\) −6.81926e7 + 2.00232e7i −4.88498 + 1.43436i
\(111\) 357056. 781843.i 0.0247802 0.0542612i
\(112\) −4.48440e6 + 3.11897e7i −0.301607 + 2.09772i
\(113\) −692529. + 445061.i −0.0451506 + 0.0290165i −0.563021 0.826442i \(-0.690361\pi\)
0.517871 + 0.855459i \(0.326725\pi\)
\(114\) −5.09450e6 −0.322058
\(115\) 2.45588e7 + 1.31834e7i 1.50579 + 0.808321i
\(116\) −1.01172e7 −0.601805
\(117\) 3.51454e6 2.25866e6i 0.202870 0.130377i
\(118\) −513343. + 3.57038e6i −0.0287621 + 0.200045i
\(119\) −3.96064e6 + 8.67258e6i −0.215452 + 0.471774i
\(120\) 6.05400e7 1.77762e7i 3.19822 0.939082i
\(121\) 1.10854e7 + 2.42736e7i 0.568855 + 1.24562i
\(122\) 1.93477e7 + 2.23284e7i 0.964648 + 1.11326i
\(123\) −1.14102e6 7.93594e6i −0.0552871 0.384530i
\(124\) −9.52218e7 2.79596e7i −4.48498 1.31691i
\(125\) −2.25031e7 + 2.59700e7i −1.03052 + 1.18929i
\(126\) 6.80997e6 + 4.37650e6i 0.303283 + 0.194908i
\(127\) −1.24639e7 8.01006e6i −0.539934 0.346995i 0.242079 0.970257i \(-0.422171\pi\)
−0.782013 + 0.623262i \(0.785807\pi\)
\(128\) −5.49443e7 + 6.34091e7i −2.31573 + 2.67250i
\(129\) −1.29442e6 380075.i −0.0530896 0.0155885i
\(130\) −8.53041e6 5.93303e7i −0.340540 2.36851i
\(131\) 2.27716e7 + 2.62798e7i 0.885001 + 1.02135i 0.999610 + 0.0279347i \(0.00889306\pi\)
−0.114609 + 0.993411i \(0.536561\pi\)
\(132\) −2.67836e7 5.86479e7i −1.01358 2.21944i
\(133\) −4.19324e6 + 1.23125e6i −0.154550 + 0.0453800i
\(134\) 3.23907e7 7.09258e7i 1.16293 2.54646i
\(135\) 1.33809e6 9.30664e6i 0.0468078 0.325555i
\(136\) −7.73697e7 + 4.97225e7i −2.63745 + 1.69499i
\(137\) 3.52485e7 1.17117 0.585583 0.810612i \(-0.300865\pi\)
0.585583 + 0.810612i \(0.300865\pi\)
\(138\) −1.18241e7 + 3.24065e7i −0.382994 + 1.04968i
\(139\) −5.04086e7 −1.59204 −0.796018 0.605273i \(-0.793064\pi\)
−0.796018 + 0.605273i \(0.793064\pi\)
\(140\) 7.16201e7 4.60275e7i 2.20591 1.41765i
\(141\) −3.34903e6 + 2.32930e7i −0.100612 + 0.699775i
\(142\) 2.43589e7 5.33384e7i 0.713917 1.56326i
\(143\) −3.73634e7 + 1.09709e7i −1.06849 + 0.313737i
\(144\) 1.88162e7 + 4.12018e7i 0.525127 + 1.14987i
\(145\) 9.00576e6 + 1.03932e7i 0.245320 + 0.283114i
\(146\) 2.25516e6 + 1.56850e7i 0.0599711 + 0.417108i
\(147\) −1.46720e7 4.30809e6i −0.380959 0.111860i
\(148\) 7.32608e6 8.45475e6i 0.185761 0.214380i
\(149\) −4.60474e6 2.95929e6i −0.114039 0.0732884i 0.482378 0.875963i \(-0.339773\pi\)
−0.596417 + 0.802675i \(0.703410\pi\)
\(150\) −7.46312e7 4.79625e7i −1.80551 1.16033i
\(151\) −9.00241e6 + 1.03893e7i −0.212784 + 0.245566i −0.852101 0.523377i \(-0.824672\pi\)
0.639317 + 0.768943i \(0.279217\pi\)
\(152\) −4.04493e7 1.18770e7i −0.934241 0.274318i
\(153\) 1.95043e6 + 1.35655e7i 0.0440261 + 0.306208i
\(154\) −4.94118e7 5.70242e7i −1.09020 1.25816i
\(155\) 5.60388e7 + 1.22708e8i 1.20873 + 2.64674i
\(156\) 5.21738e7 1.53196e7i 1.10031 0.323081i
\(157\) −2.23947e7 + 4.90376e7i −0.461845 + 1.01130i 0.525218 + 0.850968i \(0.323984\pi\)
−0.987063 + 0.160332i \(0.948743\pi\)
\(158\) 3.29184e6 2.28952e7i 0.0663955 0.461791i
\(159\) 3.97436e7 2.55417e7i 0.784110 0.503917i
\(160\) 3.50752e8 6.76986
\(161\) −1.90029e6 + 2.95312e7i −0.0358863 + 0.557687i
\(162\) 1.16363e7 0.215037
\(163\) −5.04146e7 + 3.23995e7i −0.911801 + 0.585979i −0.910268 0.414020i \(-0.864124\pi\)
−0.00153311 + 0.999999i \(0.500488\pi\)
\(164\) 1.48512e7 1.03292e8i 0.262910 1.82858i
\(165\) −3.64067e7 + 7.97195e7i −0.630939 + 1.38156i
\(166\) 1.54246e8 4.52906e7i 2.61719 0.768475i
\(167\) 4.29141e6 + 9.39687e6i 0.0713004 + 0.156126i 0.941926 0.335819i \(-0.109013\pi\)
−0.870626 + 0.491945i \(0.836286\pi\)
\(168\) 4.38667e7 + 5.06249e7i 0.713761 + 0.823724i
\(169\) 4.25615e6 + 2.96022e7i 0.0678287 + 0.471759i
\(170\) 1.88668e8 + 5.53980e7i 2.94529 + 0.864815i
\(171\) −4.11390e6 + 4.74770e6i −0.0629169 + 0.0726100i
\(172\) −1.47716e7 9.49313e6i −0.221349 0.142253i
\(173\) −5.49944e6 3.53428e6i −0.0807528 0.0518966i 0.499641 0.866232i \(-0.333465\pi\)
−0.580394 + 0.814336i \(0.697101\pi\)
\(174\) −1.11455e7 + 1.28626e7i −0.160390 + 0.185100i
\(175\) −7.30200e7 2.14406e7i −1.02993 0.302415i
\(176\) −6.00847e7 4.17898e8i −0.830748 5.77798i
\(177\) 2.91279e6 + 3.36154e6i 0.0394824 + 0.0455651i
\(178\) 2.16879e7 + 4.74899e7i 0.288236 + 0.631149i
\(179\) −2.07827e7 + 6.10236e6i −0.270843 + 0.0795266i −0.414334 0.910125i \(-0.635985\pi\)
0.143491 + 0.989652i \(0.454167\pi\)
\(180\) 5.08379e7 1.11319e8i 0.649731 1.42271i
\(181\) 2.70583e6 1.88194e7i 0.0339176 0.235902i −0.965810 0.259252i \(-0.916524\pi\)
0.999727 + 0.0233498i \(0.00743316\pi\)
\(182\) 5.35343e7 3.44044e7i 0.658237 0.423023i
\(183\) 3.64320e7 0.439444
\(184\) −1.69432e8 + 2.29735e8i −2.00508 + 2.71872i
\(185\) −1.52067e7 −0.176577
\(186\) −1.40447e8 + 9.02599e7i −1.60036 + 1.02849i
\(187\) 1.81799e7 1.26444e8i 0.203305 1.41401i
\(188\) −1.27239e8 + 2.78614e8i −1.39658 + 3.05809i
\(189\) 9.57776e6 2.81228e6i 0.103192 0.0303000i
\(190\) 3.74425e7 + 8.19877e7i 0.396029 + 0.867183i
\(191\) 8.30349e6 + 9.58274e6i 0.0862272 + 0.0995115i 0.797224 0.603684i \(-0.206301\pi\)
−0.710996 + 0.703196i \(0.751756\pi\)
\(192\) 3.12178e7 + 2.17124e8i 0.318308 + 2.21388i
\(193\) 1.19852e8 + 3.51916e7i 1.20003 + 0.352361i 0.819865 0.572556i \(-0.194048\pi\)
0.380167 + 0.924918i \(0.375866\pi\)
\(194\) −4.34087e7 + 5.00964e7i −0.426846 + 0.492607i
\(195\) −6.21799e7 3.99606e7i −0.600522 0.385932i
\(196\) −1.67434e8 1.07603e8i −1.58835 1.02077i
\(197\) 6.59952e7 7.61625e7i 0.615007 0.709756i −0.359744 0.933051i \(-0.617136\pi\)
0.974751 + 0.223295i \(0.0716813\pi\)
\(198\) −1.04069e8 3.05573e7i −0.952778 0.279761i
\(199\) −9.24947e6 6.43315e7i −0.0832015 0.578679i −0.988189 0.153241i \(-0.951029\pi\)
0.904987 0.425438i \(-0.139880\pi\)
\(200\) −4.80740e8 5.54803e8i −4.24918 4.90381i
\(201\) −3.99415e7 8.74597e7i −0.346927 0.759664i
\(202\) 3.73901e8 1.09787e8i 3.19173 0.937177i
\(203\) −6.06512e6 + 1.32808e7i −0.0508866 + 0.111426i
\(204\) −2.53863e7 + 1.76565e8i −0.209360 + 1.45613i
\(205\) −1.19330e8 + 7.66888e7i −0.967412 + 0.621718i
\(206\) −4.22358e8 −3.36624
\(207\) 2.06522e7 + 3.71880e7i 0.161834 + 0.291412i
\(208\) 3.56072e8 2.74357
\(209\) 4.92600e7 3.16575e7i 0.373235 0.239864i
\(210\) 2.03821e7 1.41761e8i 0.151874 1.05630i
\(211\) 4.55636e7 9.97704e7i 0.333910 0.731161i −0.665980 0.745969i \(-0.731986\pi\)
0.999890 + 0.0148082i \(0.00471376\pi\)
\(212\) 5.89998e8 1.73239e8i 4.25280 1.24874i
\(213\) −3.00373e7 6.57724e7i −0.212976 0.466353i
\(214\) −2.83244e8 3.26881e8i −1.97566 2.28004i
\(215\) 3.39675e6 + 2.36249e7i 0.0233093 + 0.162120i
\(216\) 9.23900e7 + 2.71282e7i 0.623788 + 0.183161i
\(217\) −9.37868e7 + 1.08236e8i −0.623064 + 0.719054i
\(218\) −1.85180e7 1.19008e7i −0.121059 0.0777998i
\(219\) 1.64383e7 + 1.05643e7i 0.105756 + 0.0679650i
\(220\) −7.46994e8 + 8.62077e8i −4.72974 + 5.45841i
\(221\) 1.03373e8 + 3.03531e7i 0.644222 + 0.189161i
\(222\) −2.67833e6 1.86282e7i −0.0164297 0.114271i
\(223\) 9.84554e7 + 1.13624e8i 0.594528 + 0.686122i 0.970663 0.240443i \(-0.0772926\pi\)
−0.376135 + 0.926565i \(0.622747\pi\)
\(224\) 1.54692e8 + 3.38728e8i 0.919601 + 2.01365i
\(225\) −1.04964e8 + 3.08201e7i −0.614327 + 0.180383i
\(226\) −7.48778e6 + 1.63960e7i −0.0431493 + 0.0944838i
\(227\) −2.44184e7 + 1.69834e8i −0.138556 + 0.963682i 0.795346 + 0.606155i \(0.207289\pi\)
−0.933903 + 0.357527i \(0.883620\pi\)
\(228\) −6.87861e7 + 4.42062e7i −0.384352 + 0.247008i
\(229\) −7.13858e7 −0.392815 −0.196407 0.980522i \(-0.562928\pi\)
−0.196407 + 0.980522i \(0.562928\pi\)
\(230\) 6.08432e8 4.78846e7i 3.29735 0.259507i
\(231\) −9.30432e7 −0.496641
\(232\) −1.18480e8 + 7.61425e7i −0.622927 + 0.400331i
\(233\) 4.71842e7 3.28173e8i 0.244372 1.69964i −0.385308 0.922788i \(-0.625905\pi\)
0.629680 0.776855i \(-0.283186\pi\)
\(234\) 3.80001e7 8.32086e7i 0.193878 0.424534i
\(235\) 3.99477e8 1.17297e8i 2.00795 0.589589i
\(236\) 2.40498e7 + 5.26617e7i 0.119102 + 0.260797i
\(237\) −1.86784e7 2.15561e7i −0.0911426 0.105184i
\(238\) 2.97094e7 + 2.06633e8i 0.142848 + 0.993529i
\(239\) 7.37003e7 + 2.16404e7i 0.349202 + 0.102535i 0.451630 0.892206i \(-0.350843\pi\)
−0.102428 + 0.994740i \(0.532661\pi\)
\(240\) 5.24784e8 6.05633e8i 2.45042 2.82794i
\(241\) −9.72664e7 6.25093e7i −0.447614 0.287664i 0.297350 0.954768i \(-0.403897\pi\)
−0.744964 + 0.667105i \(0.767533\pi\)
\(242\) 4.91536e8 + 3.15891e8i 2.22947 + 1.43279i
\(243\) 9.39654e6 1.08442e7i 0.0420093 0.0484814i
\(244\) 4.54981e8 + 1.33595e8i 2.00507 + 0.588741i
\(245\) 3.85016e7 + 2.67785e8i 0.167262 + 1.16333i
\(246\) −1.14961e8 1.32672e8i −0.492355 0.568208i
\(247\) 2.05151e7 + 4.49219e7i 0.0866233 + 0.189679i
\(248\) −1.32555e9 + 3.89216e8i −5.51842 + 1.62035i
\(249\) 8.23487e7 1.80318e8i 0.338033 0.740189i
\(250\) −1.07079e8 + 7.44751e8i −0.433426 + 3.01454i
\(251\) 1.29360e7 8.31348e6i 0.0516348 0.0331837i −0.514569 0.857449i \(-0.672048\pi\)
0.566204 + 0.824265i \(0.308412\pi\)
\(252\) 1.29924e8 0.511433
\(253\) −8.70452e7 3.86822e8i −0.337927 1.50172i
\(254\) −3.24405e8 −1.24214
\(255\) 2.03980e8 1.31090e8i 0.770366 0.495084i
\(256\) −1.13452e8 + 7.89077e8i −0.422642 + 2.93954i
\(257\) 6.95235e7 1.52235e8i 0.255485 0.559434i −0.737814 0.675004i \(-0.764142\pi\)
0.993299 + 0.115569i \(0.0368693\pi\)
\(258\) −2.83422e7 + 8.32203e6i −0.102746 + 0.0301690i
\(259\) −6.70661e6 1.46854e7i −0.0239858 0.0525215i
\(260\) −6.30001e8 7.27059e8i −2.22297 2.56545i
\(261\) 2.98679e6 + 2.07736e7i 0.0103983 + 0.0723218i
\(262\) 7.30544e8 + 2.14507e8i 2.50953 + 0.736864i
\(263\) −6.47073e6 + 7.46763e6i −0.0219335 + 0.0253126i −0.766610 0.642113i \(-0.778058\pi\)
0.744677 + 0.667425i \(0.232604\pi\)
\(264\) −7.55045e8 4.85238e8i −2.52557 1.62308i
\(265\) −7.03150e8 4.51887e8i −2.32107 1.49166i
\(266\) −6.26639e7 + 7.23180e7i −0.204142 + 0.235592i
\(267\) 6.17705e7 + 1.81375e7i 0.198606 + 0.0583159i
\(268\) −1.78099e8 1.23871e9i −0.565183 3.93094i
\(269\) 7.27259e7 + 8.39301e7i 0.227801 + 0.262897i 0.858131 0.513431i \(-0.171626\pi\)
−0.630330 + 0.776328i \(0.717080\pi\)
\(270\) −8.55222e7 1.87267e8i −0.264427 0.579014i
\(271\) 1.35740e8 3.98570e7i 0.414302 0.121650i −0.0679374 0.997690i \(-0.521642\pi\)
0.482239 + 0.876040i \(0.339824\pi\)
\(272\) −4.85241e8 + 1.06253e9i −1.46206 + 3.20147i
\(273\) 1.11676e7 7.76722e7i 0.0332193 0.231045i
\(274\) 6.49274e8 4.17263e8i 1.90678 1.22541i
\(275\) 1.01967e9 2.95662
\(276\) 1.21549e8 + 5.40154e8i 0.347992 + 1.54645i
\(277\) −3.63452e8 −1.02747 −0.513734 0.857950i \(-0.671738\pi\)
−0.513734 + 0.857950i \(0.671738\pi\)
\(278\) −9.28521e8 + 5.96724e8i −2.59200 + 1.66578i
\(279\) −2.92981e7 + 2.03773e8i −0.0807653 + 0.561735i
\(280\) 4.92323e8 1.07804e9i 1.34028 2.93481i
\(281\) 3.49276e8 1.02557e8i 0.939067 0.275735i 0.223839 0.974626i \(-0.428141\pi\)
0.715228 + 0.698891i \(0.246323\pi\)
\(282\) 2.14048e8 + 4.68699e8i 0.568380 + 1.24458i
\(283\) −1.25514e8 1.44851e8i −0.329185 0.379900i 0.566897 0.823789i \(-0.308144\pi\)
−0.896082 + 0.443889i \(0.853598\pi\)
\(284\) −1.33936e8 9.31545e8i −0.346963 2.41318i
\(285\) 1.06642e8 + 3.13129e7i 0.272880 + 0.0801247i
\(286\) −5.58360e8 + 6.44382e8i −1.41134 + 1.62878i
\(287\) −1.26688e8 8.14175e7i −0.316336 0.203297i
\(288\) 4.50308e8 + 2.89395e8i 1.11080 + 0.713867i
\(289\) 3.72669e7 4.30083e7i 0.0908198 0.104812i
\(290\) 2.88917e8 + 8.48338e7i 0.695634 + 0.204256i
\(291\) 1.16327e7 + 8.09075e7i 0.0276730 + 0.192470i
\(292\) 1.66551e8 + 1.92211e8i 0.391479 + 0.451791i
\(293\) 3.41797e8 + 7.48432e8i 0.793838 + 1.73826i 0.665323 + 0.746556i \(0.268294\pi\)
0.128515 + 0.991708i \(0.458979\pi\)
\(294\) −3.21255e8 + 9.43289e7i −0.737283 + 0.216486i
\(295\) 3.26907e7 7.15826e7i 0.0741390 0.162342i
\(296\) 2.21632e7 1.54148e8i 0.0496720 0.345476i
\(297\) −1.12515e8 + 7.23087e7i −0.249207 + 0.160156i
\(298\) −1.19850e8 −0.262350
\(299\) 3.33366e8 2.62364e7i 0.721227 0.0567617i
\(300\) −1.42385e9 −3.04468
\(301\) −2.13170e7 + 1.36996e7i −0.0450550 + 0.0289551i
\(302\) −4.28371e7 + 2.97939e8i −0.0894944 + 0.622447i
\(303\) 1.99618e8 4.37103e8i 0.412241 0.902681i
\(304\) −5.13739e8 + 1.50847e8i −1.04878 + 0.307950i
\(305\) −2.67760e8 5.86313e8i −0.540377 1.18326i
\(306\) 1.96512e8 + 2.26787e8i 0.392070 + 0.452473i
\(307\) −1.40340e8 9.76085e8i −0.276819 1.92532i −0.368694 0.929551i \(-0.620195\pi\)
0.0918746 0.995771i \(-0.470714\pi\)
\(308\) −1.16197e9 3.41186e8i −2.26604 0.665370i
\(309\) −3.41062e8 + 3.93607e8i −0.657626 + 0.758940i
\(310\) 2.48482e9 + 1.59689e9i 4.73727 + 3.04446i
\(311\) −4.07399e7 2.61820e7i −0.0767996 0.0493561i 0.501678 0.865055i \(-0.332716\pi\)
−0.578477 + 0.815699i \(0.696353\pi\)
\(312\) 4.95700e8 5.72069e8i 0.924013 1.06637i
\(313\) −6.96348e8 2.04466e8i −1.28357 0.376891i −0.432356 0.901703i \(-0.642318\pi\)
−0.851218 + 0.524811i \(0.824136\pi\)
\(314\) 1.67986e8 + 1.16837e9i 0.306210 + 2.12974i
\(315\) −1.15652e8 1.33469e8i −0.208480 0.240599i
\(316\) −1.54221e8 3.37696e8i −0.274940 0.602035i
\(317\) −7.91421e8 + 2.32382e8i −1.39541 + 0.409728i −0.891104 0.453800i \(-0.850068\pi\)
−0.504301 + 0.863528i \(0.668250\pi\)
\(318\) 4.29717e8 9.40949e8i 0.749355 1.64086i
\(319\) 2.78399e7 1.93631e8i 0.0480175 0.333969i
\(320\) 3.26482e9 2.09818e9i 5.56974 3.57945i
\(321\) −5.33354e8 −0.900011
\(322\) 3.14580e8 + 5.66456e8i 0.525092 + 0.945521i
\(323\) −1.62005e8 −0.267498
\(324\) 1.57114e8 1.00971e8i 0.256630 0.164926i
\(325\) −1.22387e8 + 8.51217e8i −0.197762 + 1.37546i
\(326\) −5.45095e8 + 1.19359e9i −0.871386 + 1.90807i
\(327\) −2.60443e7 + 7.64729e6i −0.0411903 + 0.0120946i
\(328\) −6.03465e8 1.32140e9i −0.944265 2.06765i
\(329\) 2.89457e8 + 3.34051e8i 0.448124 + 0.517163i
\(330\) 2.73092e8 + 1.89940e9i 0.418322 + 2.90949i
\(331\) −5.58393e8 1.63959e8i −0.846334 0.248506i −0.170315 0.985390i \(-0.554478\pi\)
−0.676020 + 0.736884i \(0.736297\pi\)
\(332\) 1.68963e9 1.94994e9i 2.53401 2.92441i
\(333\) −1.95229e7 1.25466e7i −0.0289727 0.0186197i
\(334\) 1.90285e8 + 1.22289e8i 0.279442 + 0.179587i
\(335\) −1.11397e9 + 1.28559e9i −1.61888 + 1.86829i
\(336\) 8.16318e8 + 2.39693e8i 1.17401 + 0.344720i
\(337\) 9.80125e7 + 6.81692e8i 0.139501 + 0.970250i 0.932537 + 0.361075i \(0.117590\pi\)
−0.793036 + 0.609175i \(0.791501\pi\)
\(338\) 4.28821e8 + 4.94886e8i 0.604042 + 0.697102i
\(339\) 9.23330e6 + 2.02181e7i 0.0128723 + 0.0281865i
\(340\) 3.02811e9 8.89133e8i 4.17826 1.22685i
\(341\) 7.97140e8 1.74549e9i 1.08867 2.38384i
\(342\) −1.95756e7 + 1.36151e8i −0.0264621 + 0.184048i
\(343\) −5.92978e8 + 3.81084e8i −0.793431 + 0.509907i
\(344\) −2.44433e8 −0.323747
\(345\) 4.46695e8 6.05681e8i 0.585658 0.794103i
\(346\) −1.43137e8 −0.185774
\(347\) 2.73309e8 1.75645e8i 0.351156 0.225674i −0.353157 0.935564i \(-0.614892\pi\)
0.704313 + 0.709890i \(0.251255\pi\)
\(348\) −3.88752e7 + 2.70383e8i −0.0494477 + 0.343916i
\(349\) 3.89469e8 8.52819e8i 0.490438 1.07391i −0.489022 0.872271i \(-0.662646\pi\)
0.979460 0.201638i \(-0.0646265\pi\)
\(350\) −1.59883e9 + 4.69459e8i −1.99326 + 0.585274i
\(351\) −4.68585e7 1.02606e8i −0.0578380 0.126647i
\(352\) −3.26734e9 3.77071e9i −3.99296 4.60812i
\(353\) −7.42831e7 5.16650e8i −0.0898832 0.625151i −0.984113 0.177543i \(-0.943185\pi\)
0.894230 0.447608i \(-0.147724\pi\)
\(354\) 9.34464e7 + 2.74383e7i 0.111957 + 0.0328735i
\(355\) −8.37738e8 + 9.66801e8i −0.993823 + 1.14693i
\(356\) 7.04912e8 + 4.53020e8i 0.828057 + 0.532160i
\(357\) 2.16558e8 + 1.39173e8i 0.251904 + 0.161889i
\(358\) −3.10578e8 + 3.58426e8i −0.357750 + 0.412865i
\(359\) −8.48807e8 2.49232e8i −0.968230 0.284298i −0.240872 0.970557i \(-0.577434\pi\)
−0.727357 + 0.686259i \(0.759252\pi\)
\(360\) −2.42446e8 1.68625e9i −0.273877 1.90486i
\(361\) 5.36732e8 + 6.19421e8i 0.600457 + 0.692964i
\(362\) −1.72939e8 3.78683e8i −0.191607 0.419562i
\(363\) 6.91311e8 2.02987e8i 0.758578 0.222739i
\(364\) 4.24287e8 9.29059e8i 0.461111 1.00969i
\(365\) 4.91996e7 3.42191e8i 0.0529587 0.368336i
\(366\) 6.71073e8 4.31273e8i 0.715461 0.459799i
\(367\) 4.49573e8 0.474755 0.237377 0.971418i \(-0.423712\pi\)
0.237377 + 0.971418i \(0.423712\pi\)
\(368\) −2.32815e8 + 3.61804e9i −0.243525 + 3.78448i
\(369\) −2.16474e8 −0.224292
\(370\) −2.80106e8 + 1.80013e8i −0.287486 + 0.184756i
\(371\) 1.26287e8 8.78343e8i 0.128395 0.893008i
\(372\) −1.11312e9 + 2.43738e9i −1.12109 + 2.45484i
\(373\) −1.13898e9 + 3.34435e8i −1.13641 + 0.333680i −0.795224 0.606315i \(-0.792647\pi\)
−0.341186 + 0.939996i \(0.610829\pi\)
\(374\) −1.16194e9 2.54430e9i −1.14851 2.51488i
\(375\) 6.07585e8 + 7.01190e8i 0.594973 + 0.686636i
\(376\) 6.06802e8 + 4.22040e9i 0.588694 + 4.09445i
\(377\) 1.58301e8 + 4.64813e7i 0.152156 + 0.0446769i
\(378\) 1.43130e8 1.65181e8i 0.136304 0.157304i
\(379\) 1.24893e9 + 8.02637e8i 1.17842 + 0.757324i 0.975095 0.221787i \(-0.0711890\pi\)
0.203324 + 0.979111i \(0.434825\pi\)
\(380\) 1.21698e9 + 7.82103e8i 1.13773 + 0.731175i
\(381\) −2.61963e8 + 3.02321e8i −0.242662 + 0.280047i
\(382\) 2.66388e8 + 7.82185e7i 0.244508 + 0.0717939i
\(383\) 1.98927e8 + 1.38357e9i 0.180925 + 1.25836i 0.854582 + 0.519317i \(0.173814\pi\)
−0.673657 + 0.739044i \(0.735277\pi\)
\(384\) 1.48350e9 + 1.71205e9i 1.33699 + 1.54297i
\(385\) 6.83830e8 + 1.49738e9i 0.610711 + 1.33727i
\(386\) 2.62424e9 7.70547e8i 2.32246 0.681936i
\(387\) −1.51314e7 + 3.31331e7i −0.0132706 + 0.0290585i
\(388\) −1.51409e8 + 1.05307e9i −0.131595 + 0.915264i
\(389\) 9.82764e8 6.31584e8i 0.846498 0.544011i −0.0439829 0.999032i \(-0.514005\pi\)
0.890481 + 0.455021i \(0.150368\pi\)
\(390\) −1.61839e9 −1.38152
\(391\) −3.76008e8 + 1.03053e9i −0.318111 + 0.871849i
\(392\) −2.77061e9 −2.32314
\(393\) 7.89832e8 5.07594e8i 0.656389 0.421835i
\(394\) 3.14032e8 2.18414e9i 0.258665 1.79905i
\(395\) −2.09631e8 + 4.59027e8i −0.171145 + 0.374756i
\(396\) −1.67029e9 + 4.90442e8i −1.35163 + 0.396876i
\(397\) −3.41323e8 7.47393e8i −0.273778 0.599491i 0.721938 0.691958i \(-0.243252\pi\)
−0.995716 + 0.0924677i \(0.970525\pi\)
\(398\) −9.31915e8 1.07549e9i −0.740944 0.855095i
\(399\) 1.67928e7 + 1.16796e8i 0.0132348 + 0.0920500i
\(400\) −8.94611e9 2.62681e9i −6.98914 2.05220i
\(401\) −6.75929e8 + 7.80064e8i −0.523475 + 0.604122i −0.954498 0.298219i \(-0.903607\pi\)
0.431023 + 0.902341i \(0.358153\pi\)
\(402\) −1.77104e9 1.13818e9i −1.35968 0.873816i
\(403\) 1.36146e9 + 8.74954e8i 1.03618 + 0.665913i
\(404\) 4.09577e9 4.72677e9i 3.09030 3.56640i
\(405\) −2.43580e8 7.15216e7i −0.182200 0.0534989i
\(406\) 4.54954e7 + 3.16428e8i 0.0337386 + 0.234657i
\(407\) 1.41654e8 + 1.63478e8i 0.104148 + 0.120193i
\(408\) 1.03155e9 + 2.25878e9i 0.751933 + 1.64650i
\(409\) 7.29977e8 2.14341e8i 0.527567 0.154908i −0.00709304 0.999975i \(-0.502258\pi\)
0.534660 + 0.845067i \(0.320440\pi\)
\(410\) −1.29022e9 + 2.82520e9i −0.924532 + 2.02444i
\(411\) 1.35442e8 9.42023e8i 0.0962295 0.669291i
\(412\) −5.70269e9 + 3.66490e9i −4.01735 + 2.58180i
\(413\) 8.35464e7 0.0583583
\(414\) 8.20635e8 + 4.40524e8i 0.568393 + 0.305118i
\(415\) −3.50716e9 −2.40873
\(416\) 3.53994e9 2.27498e9i 2.41085 1.54936i
\(417\) −1.93695e8 + 1.34718e9i −0.130810 + 0.909807i
\(418\) 5.32611e8 1.16626e9i 0.356692 0.781047i
\(419\) −5.95012e8 + 1.74711e8i −0.395163 + 0.116030i −0.473276 0.880914i \(-0.656929\pi\)
0.0781128 + 0.996945i \(0.475111\pi\)
\(420\) −9.54892e8 2.09092e9i −0.628900 1.37710i
\(421\) 1.94510e8 + 2.24477e8i 0.127044 + 0.146617i 0.815708 0.578464i \(-0.196348\pi\)
−0.688664 + 0.725081i \(0.741802\pi\)
\(422\) −3.41780e8 2.37713e9i −0.221387 1.53978i
\(423\) 6.09641e8 + 1.79007e8i 0.391636 + 0.114995i
\(424\) 5.60554e9 6.46914e9i 3.57139 4.12160i
\(425\) −2.37328e9 1.52521e9i −1.49964 0.963760i
\(426\) −1.33188e9 8.55948e8i −0.834702 0.536431i
\(427\) 4.48125e8 5.17163e8i 0.278549 0.321462i
\(428\) −6.66079e9 1.95579e9i −4.10651 1.20578i
\(429\) 1.49630e8 + 1.04070e9i 0.0914994 + 0.636392i
\(430\) 3.42233e8 + 3.94958e8i 0.207579 + 0.239559i
\(431\) −4.31896e8 9.45720e8i −0.259841 0.568973i 0.734080 0.679063i \(-0.237614\pi\)
−0.993922 + 0.110089i \(0.964886\pi\)
\(432\) 1.17343e9 3.44549e8i 0.700266 0.205617i
\(433\) 4.35791e8 9.54248e8i 0.257971 0.564877i −0.735687 0.677321i \(-0.763141\pi\)
0.993658 + 0.112444i \(0.0358680\pi\)
\(434\) −4.46276e8 + 3.10392e9i −0.262053 + 1.82262i
\(435\) 3.12365e8 2.00745e8i 0.181949 0.116932i
\(436\) −3.53297e8 −0.204144
\(437\) −4.69864e8 + 1.79082e8i −0.269331 + 0.102652i
\(438\) 4.27849e8 0.243294
\(439\) 2.47515e9 1.59069e9i 1.39629 0.897343i 0.396507 0.918032i \(-0.370222\pi\)
0.999786 + 0.0206890i \(0.00658598\pi\)
\(440\) −2.25984e9 + 1.57175e10i −1.26472 + 8.79630i
\(441\) −1.71512e8 + 3.75558e8i −0.0952267 + 0.208517i
\(442\) 2.26344e9 6.64605e8i 1.24678 0.366088i
\(443\) −8.23889e7 1.80406e8i −0.0450252 0.0985914i 0.885783 0.464100i \(-0.153622\pi\)
−0.930808 + 0.365509i \(0.880895\pi\)
\(444\) −1.97804e8 2.28278e8i −0.107249 0.123772i
\(445\) −1.62095e8 1.12740e9i −0.0871988 0.606481i
\(446\) 3.15859e9 + 9.27445e8i 1.68586 + 0.495012i
\(447\) −9.67812e7 + 1.11692e8i −0.0512525 + 0.0591485i
\(448\) 3.46614e9 + 2.22755e9i 1.82126 + 1.17045i
\(449\) 3.56168e8 + 2.28895e8i 0.185692 + 0.119337i 0.630184 0.776446i \(-0.282980\pi\)
−0.444492 + 0.895783i \(0.646616\pi\)
\(450\) −1.56858e9 + 1.81023e9i −0.811451 + 0.936464i
\(451\) 1.93602e9 + 5.68467e8i 0.993785 + 0.291802i
\(452\) 4.11712e7 + 2.86352e8i 0.0209705 + 0.145853i
\(453\) 2.43065e8 + 2.80512e8i 0.122851 + 0.141778i
\(454\) 1.56067e9 + 3.41738e9i 0.782734 + 1.71395i
\(455\) −1.33208e9 + 3.91135e8i −0.662967 + 0.194665i
\(456\) −4.72841e8 + 1.03538e9i −0.233528 + 0.511354i
\(457\) −8.14005e7 + 5.66153e8i −0.0398952 + 0.277477i −0.999998 0.00217140i \(-0.999309\pi\)
0.960102 + 0.279648i \(0.0902179\pi\)
\(458\) −1.31492e9 + 8.45048e8i −0.639544 + 0.411010i
\(459\) 3.70035e8 0.178607
\(460\) 7.79956e9 5.92604e9i 3.73609 2.83865i
\(461\) −4.22521e8 −0.200861 −0.100430 0.994944i \(-0.532022\pi\)
−0.100430 + 0.994944i \(0.532022\pi\)
\(462\) −1.71385e9 + 1.10142e9i −0.808584 + 0.519645i
\(463\) −6.82628e7 + 4.74778e8i −0.0319632 + 0.222309i −0.999542 0.0302601i \(-0.990366\pi\)
0.967579 + 0.252569i \(0.0812755\pi\)
\(464\) −7.43073e8 + 1.62710e9i −0.345318 + 0.756140i
\(465\) 3.49472e9 1.02614e9i 1.61186 0.473285i
\(466\) −3.01571e9 6.60347e9i −1.38051 3.02289i
\(467\) −1.43760e9 1.65908e9i −0.653176 0.753805i 0.328471 0.944514i \(-0.393467\pi\)
−0.981647 + 0.190709i \(0.938921\pi\)
\(468\) −2.08942e8 1.45322e9i −0.0942246 0.655346i
\(469\) −1.73281e9 5.08799e8i −0.775615 0.227741i
\(470\) 5.96979e9 6.88950e9i 2.65226 3.06087i
\(471\) 1.22449e9 + 7.86929e8i 0.539984 + 0.347026i
\(472\) 6.77978e8 + 4.35710e8i 0.296769 + 0.190722i
\(473\) 2.22335e8 2.56588e8i 0.0966037 0.111487i
\(474\) −5.99230e8 1.75950e8i −0.258446 0.0758865i
\(475\) −1.84034e8 1.27998e9i −0.0787897 0.547994i
\(476\) 2.19414e9 + 2.53217e9i 0.932481 + 1.07614i
\(477\) −5.29890e8 1.16030e9i −0.223549 0.489503i
\(478\) 1.61372e9 4.73832e8i 0.675821 0.198439i
\(479\) −2.05483e8 + 4.49946e8i −0.0854284 + 0.187062i −0.947525 0.319682i \(-0.896424\pi\)
0.862096 + 0.506744i \(0.169151\pi\)
\(480\) 1.34776e9 9.37390e9i 0.556249 3.86880i
\(481\) −1.53473e8 + 9.86310e7i −0.0628816 + 0.0404116i
\(482\) −2.53161e9 −1.02975
\(483\) 7.81924e8 + 1.64259e8i 0.315755 + 0.0663307i
\(484\) 9.37779e9 3.75960
\(485\) 1.21658e9 7.81847e8i 0.484221 0.311190i
\(486\) 4.47125e7 3.10983e8i 0.0176686 0.122888i
\(487\) 1.42817e9 3.12727e9i 0.560312 1.22691i −0.391485 0.920184i \(-0.628039\pi\)
0.951797 0.306728i \(-0.0992341\pi\)
\(488\) 6.33363e9 1.85972e9i 2.46708 0.724400i
\(489\) 6.72165e8 + 1.47184e9i 0.259953 + 0.569217i
\(490\) 3.87916e9 + 4.47679e9i 1.48954 + 1.71902i
\(491\) 3.03471e8 + 2.11069e9i 0.115700 + 0.804708i 0.962205 + 0.272327i \(0.0877934\pi\)
−0.846505 + 0.532381i \(0.821298\pi\)
\(492\) −2.70344e9 7.93801e8i −1.02338 0.300492i
\(493\) −3.54428e8 + 4.09031e8i −0.133218 + 0.153742i
\(494\) 9.09660e8 + 5.84603e8i 0.339496 + 0.218181i
\(495\) 1.99063e9 + 1.27930e9i 0.737686 + 0.474082i
\(496\) −1.14904e10 + 1.32606e10i −4.22813 + 4.87952i
\(497\) −1.30313e9 3.82633e8i −0.476145 0.139809i
\(498\) −6.17710e8 4.29627e9i −0.224121 1.55879i
\(499\) 4.92143e8 + 5.67963e8i 0.177312 + 0.204629i 0.837448 0.546517i \(-0.184047\pi\)
−0.660136 + 0.751146i \(0.729501\pi\)
\(500\) 5.01659e9 + 1.09848e10i 1.79479 + 3.93004i
\(501\) 2.67623e8 7.85811e7i 0.0950804 0.0279181i
\(502\) 1.39867e8 3.06267e8i 0.0493462 0.108053i
\(503\) 2.73112e8 1.89954e9i 0.0956870 0.665517i −0.884368 0.466790i \(-0.845410\pi\)
0.980055 0.198727i \(-0.0636807\pi\)
\(504\) 1.52152e9 9.77820e8i 0.529383 0.340214i
\(505\) −8.50157e9 −2.93751
\(506\) −6.18247e9 6.09481e9i −2.12146 2.09138i
\(507\) 8.07477e8 0.275171
\(508\) −4.38012e9 + 2.81493e9i −1.48239 + 0.952676i
\(509\) 7.79800e8 5.42363e9i 0.262102 1.82296i −0.254888 0.966971i \(-0.582038\pi\)
0.516990 0.855991i \(-0.327052\pi\)
\(510\) 2.20548e9 4.82933e9i 0.736220 1.61210i
\(511\) 3.52159e8 1.03403e8i 0.116752 0.0342816i
\(512\) 2.78977e9 + 6.10874e9i 0.918593 + 2.01144i
\(513\) 1.11075e8 + 1.28188e8i 0.0363251 + 0.0419214i
\(514\) −5.21507e8 3.62716e9i −0.169390 1.17814i
\(515\) 8.84112e9 + 2.59599e9i 2.85221 + 0.837486i
\(516\) −3.10466e8 + 3.58296e8i −0.0994809 + 0.114807i
\(517\) −4.98221e9 3.20187e9i −1.58564 1.01903i
\(518\) −2.97377e8 1.91113e8i −0.0940056 0.0604137i
\(519\) −1.15586e8 + 1.33393e8i −0.0362927 + 0.0418840i
\(520\) −1.28497e10 3.77301e9i −4.00757 1.17673i
\(521\) 7.54279e7 + 5.24612e8i 0.0233668 + 0.162520i 0.998164 0.0605745i \(-0.0192933\pi\)
−0.974797 + 0.223094i \(0.928384\pi\)
\(522\) 3.00928e8 + 3.47290e8i 0.0926012 + 0.106867i
\(523\) −5.66426e8 1.24030e9i −0.173136 0.379115i 0.803094 0.595852i \(-0.203186\pi\)
−0.976230 + 0.216738i \(0.930458\pi\)
\(524\) 1.17252e10 3.44282e9i 3.56008 1.04533i
\(525\) −8.53583e8 + 1.86909e9i −0.257447 + 0.563731i
\(526\) −3.07904e7 + 2.14152e8i −0.00922497 + 0.0641611i
\(527\) −4.46623e9 + 2.87027e9i −1.32924 + 0.854251i
\(528\) −1.13993e10 −3.37022
\(529\) 4.86188e7 + 3.40448e9i 0.0142794 + 0.999898i
\(530\) −1.83013e10 −5.33969
\(531\) 1.01030e8 6.49282e7i 0.0292833 0.0188193i
\(532\) −2.18570e8 + 1.52019e9i −0.0629362 + 0.437731i
\(533\) −7.06927e8 + 1.54795e9i −0.202222 + 0.442805i
\(534\) 1.35251e9 3.97134e8i 0.384368 0.112861i
\(535\) 3.91993e9 + 8.58346e9i 1.10673 + 2.42339i
\(536\) −1.14083e10 1.31658e10i −3.19995 3.69293i
\(537\) 8.32290e7 + 5.78870e8i 0.0231934 + 0.161314i
\(538\) 2.33315e9 + 6.85074e8i 0.645958 + 0.189670i
\(539\) 2.52013e9 2.90839e9i 0.693206 0.800003i
\(540\) −2.77969e9 1.78640e9i −0.759657 0.488202i
\(541\) 1.61881e9 + 1.04034e9i 0.439547 + 0.282479i 0.741639 0.670799i \(-0.234049\pi\)
−0.302092 + 0.953279i \(0.597685\pi\)
\(542\) 2.02851e9 2.34102e9i 0.547242 0.631551i
\(543\) −4.92555e8 1.44627e8i −0.132025 0.0387660i
\(544\) 1.96452e9 + 1.36636e10i 0.523192 + 3.63888i
\(545\) 3.14486e8 + 3.62936e8i 0.0832172 + 0.0960378i
\(546\) −7.13759e8 1.56291e9i −0.187662 0.410923i
\(547\) 9.59664e8 2.81783e8i 0.250705 0.0736137i −0.153965 0.988076i \(-0.549204\pi\)
0.404671 + 0.914463i \(0.367386\pi\)
\(548\) 5.14583e9 1.12678e10i 1.33575 2.92487i
\(549\) 1.39990e8 9.73651e8i 0.0361072 0.251131i
\(550\) 1.87822e10 1.20706e10i 4.81368 3.09357i
\(551\) −2.48087e8 −0.0631791
\(552\) 5.48867e9 + 5.41084e9i 1.38893 + 1.36924i
\(553\) −5.35746e8 −0.134716
\(554\) −6.69475e9 + 4.30246e9i −1.67282 + 1.07506i
\(555\) −5.84318e7 + 4.06402e8i −0.0145085 + 0.100909i
\(556\) −7.35901e9 + 1.61140e10i −1.81576 + 3.97595i
\(557\) −5.27043e9 + 1.54754e9i −1.29227 + 0.379444i −0.854410 0.519600i \(-0.826081\pi\)
−0.437858 + 0.899044i \(0.644263\pi\)
\(558\) 1.87254e9 + 4.10030e9i 0.456260 + 0.999070i
\(559\) 1.87513e8 + 2.16402e8i 0.0454036 + 0.0523986i
\(560\) −2.14214e9 1.48989e10i −0.515455 3.58507i
\(561\) −3.30939e9 9.71725e8i −0.791367 0.232366i
\(562\) 5.21959e9 6.02373e9i 1.24039 1.43149i
\(563\) 5.35561e9 + 3.44184e9i 1.26482 + 0.812852i 0.988937 0.148338i \(-0.0473924\pi\)
0.275886 + 0.961190i \(0.411029\pi\)
\(564\) 6.95709e9 + 4.47105e9i 1.63287 + 1.04938i
\(565\) 2.57516e8 2.97190e8i 0.0600669 0.0693209i
\(566\) −4.02667e9 1.18234e9i −0.933444 0.274084i
\(567\) −3.83562e7 2.66773e8i −0.00883680 0.0614613i
\(568\) −8.57937e9 9.90112e9i −1.96443 2.26707i
\(569\) 2.81452e9 + 6.16293e9i 0.640488 + 1.40247i 0.899639 + 0.436636i \(0.143830\pi\)
−0.259151 + 0.965837i \(0.583443\pi\)
\(570\) 2.33501e9 6.85620e8i 0.528112 0.155068i
\(571\) −4.52043e8 + 9.89836e8i −0.101614 + 0.222504i −0.953610 0.301045i \(-0.902665\pi\)
0.851996 + 0.523548i \(0.175392\pi\)
\(572\) −1.94755e9 + 1.35455e10i −0.435112 + 3.02627i
\(573\) 2.88007e8 1.85091e8i 0.0639531 0.0411001i
\(574\) −3.29738e9 −0.727742
\(575\) −8.56918e9 1.80013e9i −1.87976 0.394881i
\(576\) 5.92264e9 1.29133
\(577\) 1.16173e9 7.46599e8i 0.251762 0.161798i −0.408673 0.912681i \(-0.634008\pi\)
0.660435 + 0.750883i \(0.270372\pi\)
\(578\) 1.77331e8 1.23336e9i 0.0381977 0.265671i
\(579\) 1.40103e9 3.06783e9i 0.299967 0.656835i
\(580\) 4.63709e9 1.36157e9i 0.986843 0.289763i
\(581\) −1.54676e9 3.38694e9i −0.327195 0.716458i
\(582\) 1.17204e9 + 1.35260e9i 0.246440 + 0.284407i
\(583\) 1.69206e9 + 1.17686e10i 0.353653 + 2.45971i
\(584\) 3.39704e9 + 9.97461e8i 0.705758 + 0.207229i
\(585\) −1.30688e9 + 1.50822e9i −0.269892 + 0.311472i
\(586\) 1.51556e10 + 9.73992e9i 3.11123 + 1.99947i
\(587\) 5.51856e9 + 3.54656e9i 1.12614 + 0.723726i 0.964751 0.263165i \(-0.0847663\pi\)
0.161389 + 0.986891i \(0.448403\pi\)
\(588\) −3.51908e9 + 4.06124e9i −0.713853 + 0.823830i
\(589\) −2.33497e9 6.85609e8i −0.470845 0.138253i
\(590\) −2.45218e8 1.70553e9i −0.0491553 0.341883i
\(591\) −1.78187e9 2.05639e9i −0.355075 0.409778i
\(592\) −8.21666e8 1.79920e9i −0.162768 0.356412i
\(593\) −1.12706e9 + 3.30934e8i −0.221950 + 0.0651703i −0.390817 0.920469i \(-0.627807\pi\)
0.168867 + 0.985639i \(0.445989\pi\)
\(594\) −1.21653e9 + 2.66384e9i −0.238162 + 0.521501i
\(595\) 6.48153e8 4.50801e9i 0.126145 0.877355i
\(596\) −1.61822e9 + 1.03997e9i −0.313095 + 0.201214i
\(597\) −1.75481e9 −0.337536
\(598\) 5.82998e9 4.42957e9i 1.11484 0.847048i
\(599\) 9.57251e9 1.81983 0.909917 0.414789i \(-0.136145\pi\)
0.909917 + 0.414789i \(0.136145\pi\)
\(600\) −1.66745e10 + 1.07160e10i −3.15154 + 2.02537i
\(601\) 2.82436e8 1.96439e9i 0.0530713 0.369119i −0.945927 0.324379i \(-0.894845\pi\)
0.998999 0.0447404i \(-0.0142461\pi\)
\(602\) −2.30484e8 + 5.04690e8i −0.0430580 + 0.0942838i
\(603\) −2.49085e9 + 7.31380e8i −0.462634 + 0.135841i
\(604\) 2.00689e9 + 4.39449e9i 0.370591 + 0.811482i
\(605\) −8.34761e9 9.63365e9i −1.53256 1.76867i
\(606\) −1.49737e9 1.04144e10i −0.273322 1.90099i
\(607\) −4.45198e9 1.30722e9i −0.807965 0.237240i −0.148439 0.988922i \(-0.547425\pi\)
−0.659526 + 0.751682i \(0.729243\pi\)
\(608\) −4.14363e9 + 4.78201e9i −0.747685 + 0.862875i
\(609\) 3.31625e8 + 2.13123e8i 0.0594959 + 0.0382357i
\(610\) −1.18727e10 7.63015e9i −2.11786 1.36106i
\(611\) 3.27091e9 3.77483e9i 0.580128 0.669503i
\(612\) 4.62119e9 + 1.35690e9i 0.814937 + 0.239287i
\(613\) 3.72334e8 + 2.58964e9i 0.0652861 + 0.454075i 0.996075 + 0.0885167i \(0.0282127\pi\)
−0.930789 + 0.365558i \(0.880878\pi\)
\(614\) −1.41397e10 1.63181e10i −2.46519 2.84498i
\(615\) 1.59100e9 + 3.48379e9i 0.275807 + 0.603934i
\(616\) −1.61754e10 + 4.74952e9i −2.78819 + 0.818686i
\(617\) 1.64932e9 3.61151e9i 0.282688 0.619000i −0.714016 0.700130i \(-0.753126\pi\)
0.996704 + 0.0811297i \(0.0258528\pi\)
\(618\) −1.62291e9 + 1.12876e10i −0.276589 + 1.92372i
\(619\) 4.02115e8 2.58424e8i 0.0681449 0.0437941i −0.506125 0.862460i \(-0.668922\pi\)
0.574270 + 0.818666i \(0.305286\pi\)
\(620\) 4.74067e10 7.98856
\(621\) 1.07321e9 4.09040e8i 0.179831 0.0685401i
\(622\) −1.06036e9 −0.176680
\(623\) 1.01726e9 6.53755e8i 0.168549 0.108320i
\(624\) 1.36821e9 9.51608e9i 0.225427 1.56788i
\(625\) 1.94887e9 4.26743e9i 0.319302 0.699175i
\(626\) −1.52471e10 + 4.47695e9i −2.48414 + 0.729410i
\(627\) −6.56771e8 1.43813e9i −0.106409 0.233003i
\(628\) 1.24064e10 + 1.43177e10i 1.99888 + 2.30683i
\(629\) −8.51711e7 5.92378e8i −0.0136463 0.0949121i
\(630\) −3.71027e9 1.08943e9i −0.591171 0.173584i
\(631\) 1.75589e9 2.02640e9i 0.278224 0.321088i −0.599389 0.800458i \(-0.704590\pi\)
0.877613 + 0.479371i \(0.159135\pi\)
\(632\) −4.34757e9 2.79401e9i −0.685073 0.440270i
\(633\) −2.49130e9 1.60106e9i −0.390404 0.250897i
\(634\) −1.18270e10 + 1.36491e10i −1.84316 + 2.12712i
\(635\) 6.79068e9 + 1.99392e9i 1.05246 + 0.309030i
\(636\) −2.36278e9 1.64335e10i −0.364186 2.53297i
\(637\) 2.12543e9 + 2.45288e9i 0.325806 + 0.376000i
\(638\) −1.77934e9 3.89622e9i −0.271261 0.593978i
\(639\) −1.87320e9 + 5.50021e8i −0.284008 + 0.0833923i
\(640\) 1.66495e10 3.64573e10i 2.51056 5.49737i
\(641\) −1.32547e9 + 9.21883e9i −0.198777 + 1.38252i 0.609063 + 0.793122i \(0.291546\pi\)
−0.807840 + 0.589402i \(0.799363\pi\)
\(642\) −9.82432e9 + 6.31371e9i −1.46531 + 0.941699i
\(643\) 2.40438e9 0.356668 0.178334 0.983970i \(-0.442929\pi\)
0.178334 + 0.983970i \(0.442929\pi\)
\(644\) 9.16274e9 + 4.91863e9i 1.35184 + 0.725678i
\(645\) 6.44432e8 0.0945623
\(646\) −2.98412e9 + 1.91778e9i −0.435515 + 0.279888i
\(647\) −1.84306e9 + 1.28188e10i −0.267531 + 1.86072i 0.204136 + 0.978943i \(0.434562\pi\)
−0.471667 + 0.881777i \(0.656348\pi\)
\(648\) 1.08001e9 2.36490e9i 0.155925 0.341429i
\(649\) −1.07406e9 + 3.15373e8i −0.154231 + 0.0452864i
\(650\) 7.82215e9 + 1.71281e10i 1.11720 + 2.44632i
\(651\) 2.53224e9 + 2.92236e9i 0.359726 + 0.415146i
\(652\) 2.99718e9 + 2.08458e10i 0.423493 + 2.94546i
\(653\) −4.29889e9 1.26227e9i −0.604172 0.177401i −0.0346808 0.999398i \(-0.511041\pi\)
−0.569491 + 0.821998i \(0.692860\pi\)
\(654\) −3.89206e8 + 4.49168e8i −0.0544074 + 0.0627895i
\(655\) −1.39739e10 8.98045e9i −1.94299 1.24869i
\(656\) −1.55213e10 9.97493e9i −2.14667 1.37958i
\(657\) 3.45496e8 3.98724e8i 0.0475296 0.0548521i
\(658\) 9.28619e9 + 2.72667e9i 1.27071 + 0.373114i
\(659\) −1.07504e9 7.47704e9i −0.146327 1.01773i −0.922166 0.386795i \(-0.873582\pi\)
0.775839 0.630931i \(-0.217327\pi\)
\(660\) 2.01688e10 + 2.32761e10i 2.73072 + 3.15142i
\(661\) −9.83534e8 2.15364e9i −0.132460 0.290047i 0.831767 0.555125i \(-0.187330\pi\)
−0.964227 + 0.265078i \(0.914602\pi\)
\(662\) −1.22264e10 + 3.59001e9i −1.63794 + 0.480942i
\(663\) 1.20840e9 2.64604e9i 0.161033 0.352613i
\(664\) 5.11155e9 3.55516e10i 0.677586 4.71272i
\(665\) 1.75622e9 1.12866e9i 0.231582 0.148829i
\(666\) −5.08134e8 −0.0666528
\(667\) −5.75799e8 + 1.57810e9i −0.0751330 + 0.205918i
\(668\) 3.63036e9 0.471229
\(669\) 3.41493e9 2.19464e9i 0.440951 0.283382i
\(670\) −5.30071e9 + 3.68672e10i −0.680882 + 4.73564i
\(671\) −3.80883e9 + 8.34018e9i −0.486702 + 1.06573i
\(672\) 9.64697e9 2.83261e9i 1.22631 0.360076i
\(673\) −3.77737e9 8.27129e9i −0.477680 1.04597i −0.983095 0.183096i \(-0.941388\pi\)
0.505415 0.862876i \(-0.331339\pi\)
\(674\) 9.87508e9 + 1.13965e10i 1.24231 + 1.43371i
\(675\) 4.20350e8 + 2.92360e9i 0.0526075 + 0.365893i
\(676\) 1.00842e10 + 2.96098e9i 1.25553 + 0.368657i
\(677\) −6.94431e9 + 8.01417e9i −0.860140 + 0.992654i 0.139857 + 0.990172i \(0.455336\pi\)
−0.999997 + 0.00248257i \(0.999210\pi\)
\(678\) 4.09413e8 + 2.63114e8i 0.0504496 + 0.0324220i
\(679\) 1.29159e9 + 8.30056e8i 0.158337 + 0.101757i
\(680\) 2.87699e10 3.32022e10i 3.50878 4.04935i
\(681\) 4.44501e9 + 1.30517e9i 0.539334 + 0.158363i
\(682\) −5.97947e9 4.15881e10i −0.721801 5.02024i
\(683\) 4.73927e9 + 5.46941e9i 0.569166 + 0.656852i 0.965240 0.261366i \(-0.0841730\pi\)
−0.396074 + 0.918219i \(0.629628\pi\)
\(684\) 9.17107e8 + 2.00818e9i 0.109578 + 0.239942i
\(685\) −1.61558e10 + 4.74376e9i −1.92048 + 0.563905i
\(686\) −6.41142e9 + 1.40390e10i −0.758263 + 1.66036i
\(687\) −2.74300e8 + 1.90780e9i −0.0322758 + 0.224483i
\(688\) −2.61167e9 + 1.67842e9i −0.305744 + 0.196490i
\(689\) −1.00275e10 −1.16795
\(690\) 1.05818e9 1.64444e10i 0.122627 1.90567i
\(691\) 4.50298e8 0.0519191 0.0259595 0.999663i \(-0.491736\pi\)
0.0259595 + 0.999663i \(0.491736\pi\)
\(692\) −1.93264e9 + 1.24203e9i −0.221707 + 0.142483i
\(693\) −3.57519e8 + 2.48660e9i −0.0408068 + 0.283817i
\(694\) 2.95508e9 6.47072e9i 0.335591 0.734843i
\(695\) 2.31042e10 6.78401e9i 2.61063 0.766549i
\(696\) 1.57966e9 + 3.45898e9i 0.177596 + 0.388880i
\(697\) −3.65577e9 4.21898e9i −0.408944 0.471947i
\(698\) −2.92147e9 2.03193e10i −0.325168 2.26159i
\(699\) −8.58919e9 2.52201e9i −0.951222 0.279304i
\(700\) −1.75138e10 + 2.02121e10i −1.92992 + 2.22724i
\(701\) 7.46608e9 + 4.79816e9i 0.818615 + 0.526092i 0.881641 0.471920i \(-0.156439\pi\)
−0.0630265 + 0.998012i \(0.520075\pi\)
\(702\) −2.07775e9 1.33529e9i −0.226680 0.145678i
\(703\) 1.79646e8 2.07322e8i 0.0195017 0.0225062i
\(704\) −5.29688e10 1.55530e10i −5.72158 1.68001i
\(705\) −1.59979e9 1.11268e10i −0.171950 1.19594i
\(706\) −7.48426e9 8.63730e9i −0.800447 0.923765i
\(707\) −3.74945e9 8.21014e9i −0.399024 0.873741i
\(708\) 1.49981e9 4.40383e8i 0.158825 0.0466352i
\(709\) −4.64521e8 + 1.01716e9i −0.0489490 + 0.107183i −0.932526 0.361102i \(-0.882401\pi\)
0.883577 + 0.468285i \(0.155128\pi\)
\(710\) −3.98630e9 + 2.77253e10i −0.417990 + 2.90718i
\(711\) −6.47862e8 + 4.16355e8i −0.0675988 + 0.0434431i
\(712\) 1.16645e10 1.21112
\(713\) −9.78057e9 + 1.32616e10i −1.01053 + 1.37020i
\(714\) 5.63647e9 0.579513
\(715\) 1.56486e10 1.00568e10i 1.60105 1.02893i
\(716\) −1.08329e9 + 7.53443e9i −0.110293 + 0.767105i
\(717\) 8.61536e8 1.88650e9i 0.0872883 0.191135i
\(718\) −1.85853e10 + 5.45713e9i −1.87385 + 0.550211i
\(719\) −4.35722e9 9.54097e9i −0.437178 0.957285i −0.992108 0.125388i \(-0.959982\pi\)
0.554930 0.831897i \(-0.312745\pi\)
\(720\) −1.41692e10 1.63521e10i −1.41475 1.63271i
\(721\) 1.39220e9 + 9.68296e9i 0.138334 + 0.962132i
\(722\) 1.72191e10 + 5.05598e9i 1.70267 + 0.499949i
\(723\) −2.04432e9 + 2.35927e9i −0.201171 + 0.232163i
\(724\) −5.62094e9 3.61236e9i −0.550458 0.353758i
\(725\) −3.63432e9 2.33563e9i −0.354193 0.227626i
\(726\) 1.03310e10 1.19226e10i 1.00199 1.15636i
\(727\) 1.75581e10 + 5.15551e9i 1.69475 + 0.497624i 0.979534 0.201278i \(-0.0645095\pi\)
0.715217 + 0.698902i \(0.246328\pi\)
\(728\) −2.02343e9 1.40732e10i −0.194369 1.35187i
\(729\) −2.53706e8 2.92793e8i −0.0242541 0.0279907i
\(730\) −3.14452e9 6.88554e9i −0.299174 0.655100i
\(731\) −9.01285e8 + 2.64641e8i −0.0853397 + 0.0250580i
\(732\) 5.31860e9 1.16461e10i 0.501197 1.09747i
\(733\) −6.94740e8 + 4.83202e9i −0.0651566 + 0.453174i 0.930959 + 0.365123i \(0.118973\pi\)
−0.996116 + 0.0880511i \(0.971936\pi\)
\(734\) 8.28110e9 5.32194e9i 0.772950 0.496745i
\(735\) 7.30454e9 0.678558
\(736\) 2.08015e10 + 3.74568e10i 1.92319 + 3.46304i
\(737\) 2.41974e10 2.22655
\(738\) −3.98743e9 + 2.56256e9i −0.365170 + 0.234681i
\(739\) 1.52927e9 1.06363e10i 0.139389 0.969470i −0.793311 0.608817i \(-0.791645\pi\)
0.932700 0.360654i \(-0.117446\pi\)
\(740\) −2.21998e9 + 4.86109e9i −0.201390 + 0.440983i
\(741\) 1.27937e9 3.75658e8i 0.115514 0.0339179i
\(742\) −8.07141e9 1.76739e10i −0.725330 1.58825i
\(743\) −1.06149e10 1.22503e10i −0.949415 1.09568i −0.995310 0.0967369i \(-0.969159\pi\)
0.0458952 0.998946i \(-0.485386\pi\)
\(744\) 5.30845e9 + 3.69211e10i 0.472566 + 3.28677i
\(745\) 2.50880e9 + 7.36649e8i 0.222289 + 0.0652700i
\(746\) −1.70209e10 + 1.96432e10i −1.50106 + 1.73231i
\(747\) −4.50262e9 2.89366e9i −0.395224 0.253995i
\(748\) −3.77661e10 2.42708e10i −3.29949 2.12045i
\(749\) −6.56041e9 + 7.57112e9i −0.570486 + 0.658376i
\(750\) 1.94922e10 + 5.72341e9i 1.68712 + 0.495383i
\(751\) 1.29401e9 + 9.00004e9i 0.111480 + 0.775363i 0.966481 + 0.256736i \(0.0826472\pi\)
−0.855001 + 0.518626i \(0.826444\pi\)
\(752\) 3.54631e10 + 4.09266e10i 3.04098 + 3.50948i
\(753\) −1.72473e8 3.77662e8i −0.0147210 0.0322345i
\(754\) 3.46612e9 1.01774e9i 0.294472 0.0864647i
\(755\) 2.72795e9 5.97339e9i 0.230687 0.505134i
\(756\) 4.99235e8 3.47225e9i 0.0420222 0.292271i
\(757\) 5.68568e8 3.65397e8i 0.0476373 0.0306146i −0.516605 0.856224i \(-0.672805\pi\)
0.564243 + 0.825609i \(0.309168\pi\)
\(758\) 3.25065e10 2.71099
\(759\) −1.06724e10 + 8.39933e8i −0.885961 + 0.0697266i
\(760\) 2.01379e10 1.66405
\(761\) 1.23134e10 7.91332e9i 1.01282 0.650897i 0.0746951 0.997206i \(-0.476202\pi\)
0.938120 + 0.346309i \(0.112565\pi\)
\(762\) −1.24653e9 + 8.66977e9i −0.102061 + 0.709848i
\(763\) −2.11797e8 + 4.63771e8i −0.0172617 + 0.0377979i
\(764\) 4.27549e9 1.25540e9i 0.346864 0.101849i
\(765\) −2.71961e9 5.95512e9i −0.219630 0.480923i
\(766\) 2.00426e10 + 2.31304e10i 1.61121 + 1.85944i
\(767\) −1.34357e8 9.34476e8i −0.0107517 0.0747798i
\(768\) 2.06523e10 + 6.06406e9i 1.64514 + 0.483058i
\(769\) 5.13327e9 5.92411e9i 0.407054 0.469765i −0.514796 0.857313i \(-0.672132\pi\)
0.921850 + 0.387548i \(0.126678\pi\)
\(770\) 3.03217e10 + 1.94866e10i 2.39351 + 1.53822i
\(771\) −3.80137e9 2.44299e9i −0.298710 0.191969i
\(772\) 2.87464e10 3.31751e10i 2.24866 2.59509i
\(773\) 8.45264e9 + 2.48192e9i 0.658210 + 0.193268i 0.593746 0.804652i \(-0.297648\pi\)
0.0644633 + 0.997920i \(0.479466\pi\)
\(774\) 1.13503e8 + 7.89429e8i 0.00879859 + 0.0611955i
\(775\) −2.77511e10 3.20265e10i −2.14153 2.47146i
\(776\) 6.15237e9 + 1.34718e10i 0.472635 + 1.03493i
\(777\) −4.18241e8 + 1.22807e8i −0.0319855 + 0.00939178i
\(778\) 1.06259e10 2.32674e10i 0.808977 1.77141i
\(779\) 3.64171e8 2.53287e9i 0.0276010 0.191969i
\(780\) −2.18516e10 + 1.40432e10i −1.64874 + 1.05958i
\(781\) 1.81972e10 1.36687
\(782\) 5.27311e9 + 2.34333e10i 0.394315 + 1.75231i
\(783\) 5.66654e8 0.0421844
\(784\) −2.96029e10 + 1.90246e10i −2.19395 + 1.40997i
\(785\) 3.66487e9 2.54897e10i 0.270405 1.88071i
\(786\) 8.53986e9 1.86997e10i 0.627295 1.37358i
\(787\) −4.24318e9 + 1.24591e9i −0.310298 + 0.0911119i −0.433174 0.901310i \(-0.642607\pi\)
0.122876 + 0.992422i \(0.460788\pi\)
\(788\) −1.47122e10 3.22152e10i −1.07112 2.34542i
\(789\) 1.74710e8 + 2.01626e8i 0.0126633 + 0.0146143i
\(790\) 1.57247e9 + 1.09368e10i 0.113472 + 0.789215i
\(791\) 4.00574e8 + 1.17619e8i 0.0287783 + 0.00845008i
\(792\) −1.58693e10 + 1.83142e10i −1.13506 + 1.30993i
\(793\) −6.50520e9 4.18064e9i −0.463238 0.297705i
\(794\) −1.51346e10 9.72641e9i −1.07300 0.689574i
\(795\) −1.47786e10 + 1.70554e10i −1.04316 + 1.20387i
\(796\) −2.19150e10 6.43482e9i −1.54009 0.452211i
\(797\) 2.61768e9 + 1.82064e10i 0.183152 + 1.27385i 0.849251 + 0.527989i \(0.177054\pi\)
−0.666099 + 0.745863i \(0.732037\pi\)
\(798\) 1.69193e9 + 1.95259e9i 0.117861 + 0.136019i
\(799\) 6.80673e9 + 1.49047e10i 0.472090 + 1.03373i
\(800\) −1.05722e11 + 3.10428e10i −7.30047 + 2.14361i
\(801\) 7.22080e8 1.58113e9i 0.0496445 0.108706i
\(802\) −3.21635e9 + 2.23702e10i −0.220167 + 1.53130i
\(803\) −4.13699e9 + 2.65868e9i −0.281955 + 0.181201i
\(804\) −3.37890e10 −2.29287
\(805\) −3.10334e9 1.37910e10i −0.209674 0.931775i
\(806\) 3.54354e10 2.38377
\(807\) 2.52250e9 1.62111e9i 0.168956 0.108581i
\(808\) 1.23907e10 8.61793e10i 0.826336 5.74729i
\(809\) −1.06616e10 + 2.33457e10i −0.707951 + 1.55020i 0.122106 + 0.992517i \(0.461035\pi\)
−0.830057 + 0.557679i \(0.811692\pi\)
\(810\) −5.33337e9 + 1.56602e9i −0.352618 + 0.103538i
\(811\) 8.64946e9 + 1.89397e10i 0.569398 + 1.24681i 0.947117 + 0.320887i \(0.103981\pi\)
−0.377719 + 0.925920i \(0.623292\pi\)
\(812\) 3.36000e9 + 3.87764e9i 0.220238 + 0.254168i
\(813\) −5.43603e8 3.78084e9i −0.0354784 0.246758i
\(814\) 4.54446e9 + 1.33437e9i 0.295323 + 0.0867146i
\(815\) 1.87466e10 2.16348e10i 1.21303 1.39991i
\(816\) 2.65317e10 + 1.70509e10i 1.70943 + 1.09858i
\(817\) −3.62220e8 2.32785e8i −0.0232378 0.0149340i
\(818\) 1.09088e10 1.25894e10i 0.696851 0.804209i
\(819\) −2.03289e9 5.96911e8i −0.129307 0.0379679i
\(820\) 7.09424e9 + 4.93415e10i 0.449322 + 3.12510i
\(821\) −1.43533e10 1.65645e10i −0.905210 1.04467i −0.998796 0.0490568i \(-0.984378\pi\)
0.0935860 0.995611i \(-0.470167\pi\)
\(822\) −8.65659e9 1.89553e10i −0.543620 1.19036i
\(823\) 6.48168e9 1.90319e9i 0.405311 0.119010i −0.0727215 0.997352i \(-0.523168\pi\)
0.478032 + 0.878342i \(0.341350\pi\)
\(824\) −3.92008e10 + 8.58378e10i −2.44090 + 5.34482i
\(825\) 3.91808e9 2.72509e10i 0.242932 1.68963i
\(826\) 1.53892e9 9.89001e8i 0.0950133 0.0610614i
\(827\) −2.63373e10 −1.61921 −0.809603 0.586978i \(-0.800317\pi\)
−0.809603 + 0.586978i \(0.800317\pi\)
\(828\) 1.49028e10 1.17287e9i 0.912348 0.0718033i
\(829\) 7.56962e9 0.461459 0.230730 0.973018i \(-0.425889\pi\)
0.230730 + 0.973018i \(0.425889\pi\)
\(830\) −6.46015e10 + 4.15169e10i −3.92166 + 2.52030i
\(831\) −1.39657e9 + 9.71333e9i −0.0844224 + 0.587171i
\(832\) 1.93413e10 4.23514e10i 1.16427 2.54939i
\(833\) −1.02159e10 + 2.99967e9i −0.612379 + 0.179811i
\(834\) 1.23797e10 + 2.71078e10i 0.738975 + 1.61813i
\(835\) −3.23155e9 3.72941e9i −0.192092 0.221686i
\(836\) −2.92854e9 2.03684e10i −0.173352 1.20569i
\(837\) 5.33329e9 + 1.56599e9i 0.314381 + 0.0923105i
\(838\) −8.89187e9 + 1.02618e10i −0.521962 + 0.602377i
\(839\) −1.06346e10 6.83442e9i −0.621660 0.399517i 0.191553 0.981482i \(-0.438647\pi\)
−0.813213 + 0.581966i \(0.802284\pi\)
\(840\) −2.69190e10 1.72998e10i −1.56704 1.00708i
\(841\) 1.07535e10 1.24102e10i 0.623397 0.719438i
\(842\) 6.24015e9 + 1.83227e9i 0.360249 + 0.105779i
\(843\) −1.39875e9 9.72854e9i −0.0804164 0.559308i
\(844\) −2.52416e10 2.91304e10i −1.44517 1.66782i
\(845\) −5.93463e9 1.29950e10i −0.338373 0.740933i
\(846\) 1.33486e10 3.91949e9i 0.757945 0.222553i
\(847\) 5.62187e9 1.23102e10i 0.317899 0.696101i
\(848\) 1.54721e10 1.07611e11i 0.871293 6.05997i
\(849\) −4.35346e9 + 2.79780e9i −0.244150 + 0.156906i
\(850\) −6.17706e10 −3.44997
\(851\) −9.01840e8 1.62392e9i −0.0501622 0.0903259i
\(852\) −2.54104e10 −1.40758
\(853\) −1.24190e9 + 7.98119e8i −0.0685116 + 0.0440297i −0.574448 0.818541i \(-0.694783\pi\)
0.505937 + 0.862571i \(0.331147\pi\)
\(854\) 2.13236e9 1.48309e10i 0.117154 0.814825i
\(855\) 1.24661e9 2.72971e9i 0.0682104 0.149360i
\(856\) −9.27226e10 + 2.72258e10i −5.05274 + 1.48362i
\(857\) 5.42475e9 + 1.18786e10i 0.294406 + 0.644660i 0.997811 0.0661296i \(-0.0210651\pi\)
−0.703405 + 0.710790i \(0.748338\pi\)
\(858\) 1.50757e10 + 1.73983e10i 0.814840 + 0.940376i
\(859\) 2.02356e9 + 1.40742e10i 0.108928 + 0.757612i 0.968933 + 0.247325i \(0.0795516\pi\)
−0.860004 + 0.510287i \(0.829539\pi\)
\(860\) 8.04799e9 + 2.36310e9i 0.431462 + 0.126689i
\(861\) −2.66269e9 + 3.07291e9i −0.142171 + 0.164074i
\(862\) −1.91507e10 1.23074e10i −1.01838 0.654471i
\(863\) 2.86087e10 + 1.83857e10i 1.51517 + 0.973738i 0.992638 + 0.121115i \(0.0386470\pi\)
0.522527 + 0.852623i \(0.324989\pi\)
\(864\) 9.46444e9 1.09225e10i 0.499226 0.576137i
\(865\) 2.99625e9 + 8.79779e8i 0.157406 + 0.0462187i
\(866\) −3.26893e9 2.27359e10i −0.171038 1.18960i
\(867\) −1.00621e9 1.16122e9i −0.0524349 0.0605131i
\(868\) 2.09078e10 + 4.57816e10i 1.08515 + 2.37614i
\(869\) 6.88748e9 2.02235e9i 0.356033 0.104541i
\(870\) 3.37736e9 7.39539e9i 0.173884 0.380753i
\(871\) −2.90431e9 + 2.01999e10i −0.148929 + 1.03582i
\(872\) −4.13738e9 + 2.65894e9i −0.211309 + 0.135800i
\(873\) 2.20697e9 0.112265
\(874\) −6.53492e9 + 8.86080e9i −0.331093 + 0.448935i
\(875\) 1.74271e10 0.879420
\(876\) 5.77684e9 3.71255e9i 0.290353 0.186598i
\(877\) −2.23912e9 + 1.55734e10i −0.112093 + 0.779626i 0.853784 + 0.520627i \(0.174302\pi\)
−0.965878 + 0.258999i \(0.916607\pi\)
\(878\) 2.67620e10 5.86005e10i 1.33440 2.92194i
\(879\) 2.13153e10 6.25874e9i 1.05860 0.310832i
\(880\) 8.37800e10 + 1.83453e11i 4.14430 + 9.07475i
\(881\) 4.11861e9 + 4.75313e9i 0.202925 + 0.234187i 0.848086 0.529859i \(-0.177755\pi\)
−0.645161 + 0.764047i \(0.723210\pi\)
\(882\) 1.28654e9 + 8.94805e9i 0.0631367 + 0.439125i
\(883\) −2.55064e10 7.48935e9i −1.24677 0.366085i −0.409216 0.912438i \(-0.634198\pi\)
−0.837555 + 0.546353i \(0.816016\pi\)
\(884\) 2.47941e10 2.86139e10i 1.20716 1.39314i
\(885\) −1.78744e9 1.14872e9i −0.0866824 0.0557074i
\(886\) −3.65320e9 2.34777e9i −0.176464 0.113406i
\(887\) 2.16631e10 2.50006e10i 1.04229 1.20287i 0.0635036 0.997982i \(-0.479773\pi\)
0.978786 0.204885i \(-0.0656820\pi\)
\(888\) −4.03448e9 1.18463e9i −0.193349 0.0567724i
\(889\) 1.06932e9 + 7.43728e9i 0.0510448 + 0.355024i
\(890\) −1.63316e10 1.88477e10i −0.776542 0.896177i
\(891\) 1.50013e9 + 3.28482e9i 0.0710486 + 0.155575i
\(892\) 5.06950e10 1.48854e10i 2.39160 0.702236i
\(893\) −3.12007e9 + 6.83200e9i −0.146617 + 0.321046i
\(894\) −4.60524e8 + 3.20302e9i −0.0215562 + 0.149926i
\(895\) 8.70428e9 5.59390e9i 0.405837 0.260816i
\(896\) 4.25505e10 1.97618
\(897\) 5.79785e8 9.01007e9i 0.0268221 0.416826i
\(898\) 9.27017e9 0.427190
\(899\) −6.83936e9 + 4.39539e9i −0.313947 + 0.201762i
\(900\) −5.47116e9 + 3.80528e10i −0.250167 + 1.73995i
\(901\) 1.36650e10 2.99222e10i 0.622406 1.36288i
\(902\) 4.23907e10 1.24470e10i 1.92330 0.564733i
\(903\) 2.84214e8 + 6.22341e8i 0.0128451 + 0.0281269i
\(904\) 2.63725e9 + 3.04355e9i 0.118730 + 0.137022i
\(905\) 1.29254e9 + 8.98983e9i 0.0579662 + 0.403164i
\(906\) 7.79787e9 + 2.28966e9i 0.348359 + 0.102287i
\(907\) 1.09549e10 1.26427e10i 0.487511 0.562618i −0.457688 0.889113i \(-0.651322\pi\)
0.945199 + 0.326495i \(0.105868\pi\)
\(908\) 5.07255e10 + 3.25993e10i 2.24867 + 1.44513i
\(909\) −1.09146e10 7.01440e9i −0.481987 0.309754i
\(910\) −1.99067e10 + 2.29736e10i −0.875698 + 1.01061i
\(911\) −3.03400e10 8.90862e9i −1.32954 0.390388i −0.461612 0.887082i \(-0.652729\pi\)
−0.867926 + 0.496694i \(0.834547\pi\)
\(912\) 2.05738e9 + 1.43094e10i 0.0898116 + 0.624654i
\(913\) 3.26701e10 + 3.77033e10i 1.42070 + 1.63957i
\(914\) 5.20259e9 + 1.13921e10i 0.225376 + 0.493505i
\(915\) −1.66982e10 + 4.90303e9i −0.720602 + 0.211588i
\(916\) −1.04214e10 + 2.28197e10i −0.448015 + 0.981016i
\(917\) 2.50972e9 1.74555e10i 0.107481 0.747548i
\(918\) 6.81602e9 4.38039e9i 0.290791 0.186880i
\(919\) 2.86136e10 1.21610 0.608048 0.793901i \(-0.291953\pi\)
0.608048 + 0.793901i \(0.291953\pi\)
\(920\) 4.67392e10 1.28099e11i 1.97890 5.42359i
\(921\) −2.66253e10 −1.12302
\(922\) −7.78279e9 + 5.00169e9i −0.327022 + 0.210164i
\(923\) −2.18413e9 + 1.51910e10i −0.0914267 + 0.635887i
\(924\) −1.35831e10 + 2.97429e10i −0.566432 + 1.24031i
\(925\) 4.58354e9 1.34585e9i 0.190417 0.0559114i
\(926\) 4.36291e9 + 9.55344e9i 0.180567 + 0.395386i
\(927\) 9.20867e9 + 1.06274e10i 0.379680 + 0.438174i
\(928\) 3.00837e9 + 2.09237e10i 0.123570 + 0.859449i
\(929\) 3.08689e10 + 9.06391e9i 1.26318 + 0.370903i 0.843677 0.536850i \(-0.180386\pi\)
0.419503 + 0.907754i \(0.362204\pi\)
\(930\) 5.22252e10 6.02711e10i 2.12907 2.45708i
\(931\) −4.10571e9 2.63858e9i −0.166749 0.107163i
\(932\) −9.80180e10 6.29924e10i −3.96598 2.54878i
\(933\) −8.56260e8 + 9.88177e8i −0.0345160 + 0.0398336i
\(934\) −4.61203e10 1.35421e10i −1.85216 0.543843i
\(935\) 8.68435e9 + 6.04010e10i 0.347454 + 2.41659i
\(936\) −1.33839e10 1.54459e10i −0.533479 0.615668i
\(937\) 1.87178e9 + 4.09863e9i 0.0743303 + 0.162761i 0.943149 0.332369i \(-0.107848\pi\)
−0.868819 + 0.495130i \(0.835121\pi\)
\(938\) −3.79412e10 + 1.11405e10i −1.50107 + 0.440754i
\(939\) −8.14011e9 + 1.78244e10i −0.320849 + 0.702562i
\(940\) 2.08225e10 1.44823e11i 0.817683 5.68711i
\(941\) 5.54683e9 3.56473e9i 0.217011 0.139464i −0.427620 0.903959i \(-0.640648\pi\)
0.644630 + 0.764495i \(0.277011\pi\)
\(942\) 3.18704e10 1.24225
\(943\) −1.52665e10 8.19519e9i −0.592856 0.318250i
\(944\) 1.02358e10 0.396021
\(945\) −4.01138e9 + 2.57796e9i −0.154626 + 0.0993721i
\(946\) 1.05796e9 7.35827e9i 0.0406303 0.282590i
\(947\) −1.74493e10 + 3.82086e10i −0.667656 + 1.46196i 0.207556 + 0.978223i \(0.433449\pi\)
−0.875212 + 0.483739i \(0.839278\pi\)
\(948\) −9.61758e9 + 2.82398e9i −0.366637 + 0.107654i
\(949\) −1.72291e9 3.77265e9i −0.0654383 0.143290i
\(950\) −1.85420e10 2.13986e10i −0.701655 0.809753i
\(951\) 3.16942e9 + 2.20438e10i 0.119495 + 0.831103i
\(952\) 4.47524e10 + 1.31405e10i 1.68108 + 0.493608i
\(953\) −2.44939e10 + 2.82675e10i −0.916712 + 1.05794i 0.0814097 + 0.996681i \(0.474058\pi\)
−0.998122 + 0.0612614i \(0.980488\pi\)
\(954\) −2.34958e10 1.50999e10i −0.876137 0.563059i
\(955\) −5.09546e9 3.27466e9i −0.189309 0.121662i
\(956\) 1.76770e10 2.04004e10i 0.654344 0.755154i
\(957\) −5.06784e9 1.48805e9i −0.186909 0.0548815i
\(958\) 1.54136e9 + 1.07204e10i 0.0566403 + 0.393942i
\(959\) −1.17063e10 1.35098e10i −0.428603 0.494634i
\(960\) −4.35290e10 9.53153e10i −1.58792 3.47707i
\(961\) −5.01202e10 + 1.47166e10i −1.82172 + 0.534905i
\(962\) −1.65938e9 + 3.63355e9i −0.0600944 + 0.131588i
\(963\) −2.04941e9 + 1.42540e10i −0.0739499 + 0.514333i
\(964\) −3.41818e10 + 2.19673e10i −1.22893 + 0.789783i
\(965\) −5.96687e10 −2.13748
\(966\) 1.63474e10 6.23059e9i 0.583485 0.222387i
\(967\) 3.73595e9 0.132864 0.0664322 0.997791i \(-0.478838\pi\)
0.0664322 + 0.997791i \(0.478838\pi\)
\(968\) 1.09821e11 7.05779e10i 3.89156 2.50095i
\(969\) −6.22506e8 + 4.32962e9i −0.0219791 + 0.152868i
\(970\) 1.31539e10 2.88031e10i 0.462758 1.01330i
\(971\) 1.06729e9 3.13385e8i 0.0374124 0.0109853i −0.262973 0.964803i \(-0.584703\pi\)
0.300385 + 0.953818i \(0.402885\pi\)
\(972\) −2.09476e9 4.58688e9i −0.0731647 0.160208i
\(973\) 1.67411e10 + 1.93203e10i 0.582625 + 0.672385i
\(974\) −1.07130e10 7.45103e10i −0.371495 2.58381i
\(975\) 2.22787e10 + 6.54161e9i 0.769791 + 0.226031i
\(976\) 5.49024e10 6.33607e10i 1.89024 2.18145i
\(977\) −5.45044e9 3.50278e9i −0.186982 0.120166i 0.443801 0.896125i \(-0.353630\pi\)
−0.630783 + 0.775959i \(0.717266\pi\)
\(978\) 2.98044e10 + 1.91541e10i 1.01881 + 0.654752i
\(979\) −1.06100e10 + 1.22446e10i −0.361389 + 0.417066i
\(980\) 9.12228e10 + 2.67854e10i 3.09608 + 0.909091i
\(981\) 1.04300e8 + 7.25423e8i 0.00352731 + 0.0245330i
\(982\) 3.05757e10 + 3.52862e10i 1.03035 + 1.18909i
\(983\) −1.91521e9 4.19373e9i −0.0643102 0.140820i 0.874748 0.484579i \(-0.161027\pi\)
−0.939058 + 0.343759i \(0.888300\pi\)
\(984\) −3.76336e10 + 1.10502e10i −1.25919 + 0.369733i
\(985\) −1.99982e10 + 4.37899e10i −0.666751 + 1.45998i
\(986\) −1.68651e9 + 1.17299e10i −0.0560299 + 0.389697i
\(987\) 1.00398e10 6.45220e9i 0.332365 0.213598i
\(988\) 1.73550e10 0.572500
\(989\) −2.32146e9 + 1.76382e9i −0.0763086 + 0.0579787i
\(990\) 5.18111e10 1.69707
\(991\) −3.81732e10 + 2.45325e10i −1.24595 + 0.800725i −0.986297 0.164977i \(-0.947245\pi\)
−0.259654 + 0.965702i \(0.583609\pi\)
\(992\) −2.95099e10 + 2.05246e11i −0.959790 + 6.67549i
\(993\) −6.52746e9 + 1.42931e10i −0.211554 + 0.463239i
\(994\) −2.85330e10 + 8.37804e9i −0.921499 + 0.270576i
\(995\) 1.28972e10 + 2.82408e10i 0.415062 + 0.908859i
\(996\) −4.56201e10 5.26484e10i −1.46301 1.68841i
\(997\) −2.74568e9 1.90966e10i −0.0877439 0.610272i −0.985487 0.169752i \(-0.945703\pi\)
0.897743 0.440520i \(-0.145206\pi\)
\(998\) 1.57886e10 + 4.63596e9i 0.502791 + 0.147633i
\(999\) −4.10327e8 + 4.73543e8i −0.0130212 + 0.0150273i
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 69.8.e.b.58.14 yes 140
23.2 even 11 inner 69.8.e.b.25.14 140
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.8.e.b.25.14 140 23.2 even 11 inner
69.8.e.b.58.14 yes 140 1.1 even 1 trivial