Properties

Label 32.8.g.a.21.24
Level $32$
Weight $8$
Character 32.21
Analytic conductor $9.996$
Analytic rank $0$
Dimension $108$
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] = [32,8,Mod(5,32)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(32, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("32.5");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 32.g (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.99632081549\)
Analytic rank: \(0\)
Dimension: \(108\)
Relative dimension: \(27\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 21.24
Character \(\chi\) \(=\) 32.21
Dual form 32.8.g.a.29.24

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(10.5954 + 3.96698i) q^{2} +(-64.5670 + 26.7445i) q^{3} +(96.5262 + 84.0636i) q^{4} +(-11.3056 + 27.2941i) q^{5} +(-790.210 + 27.2339i) q^{6} +(-730.571 - 730.571i) q^{7} +(689.258 + 1273.61i) q^{8} +(1907.19 - 1907.19i) q^{9} +O(q^{10})\) \(q+(10.5954 + 3.96698i) q^{2} +(-64.5670 + 26.7445i) q^{3} +(96.5262 + 84.0636i) q^{4} +(-11.3056 + 27.2941i) q^{5} +(-790.210 + 27.2339i) q^{6} +(-730.571 - 730.571i) q^{7} +(689.258 + 1273.61i) q^{8} +(1907.19 - 1907.19i) q^{9} +(-228.063 + 244.344i) q^{10} +(-4613.88 - 1911.13i) q^{11} +(-8480.65 - 2846.19i) q^{12} +(-4631.15 - 11180.6i) q^{13} +(-4842.56 - 10638.9i) q^{14} -2064.66i q^{15} +(2250.61 + 16228.7i) q^{16} +24389.7i q^{17} +(27773.3 - 12641.7i) q^{18} +(-6499.78 - 15691.9i) q^{19} +(-3385.73 + 1684.21i) q^{20} +(66709.6 + 27632.0i) q^{21} +(-41304.6 - 38552.4i) q^{22} +(-55239.7 + 55239.7i) q^{23} +(-78565.4 - 63799.2i) q^{24} +(54625.6 + 54625.6i) q^{25} +(-4715.90 - 136835. i) q^{26} +(-13644.4 + 32940.4i) q^{27} +(-9104.79 - 131934. i) q^{28} +(-78625.3 + 32567.7i) q^{29} +(8190.47 - 21876.0i) q^{30} -106864. q^{31} +(-40532.6 + 180878. i) q^{32} +349017. q^{33} +(-96753.3 + 258419. i) q^{34} +(28199.8 - 11680.8i) q^{35} +(344419. - 23768.5i) q^{36} +(-106114. + 256182. i) q^{37} +(-6618.73 - 192047. i) q^{38} +(598039. + 598039. i) q^{39} +(-42554.4 + 4413.80i) q^{40} +(332894. - 332894. i) q^{41} +(597201. + 557409. i) q^{42} +(-186265. - 77153.3i) q^{43} +(-284704. - 572334. i) q^{44} +(30493.1 + 73617.0i) q^{45} +(-804423. + 366154. i) q^{46} +475186. i q^{47} +(-579344. - 987647. i) q^{48} +243926. i q^{49} +(362083. + 795480. i) q^{50} +(-652291. - 1.57477e6i) q^{51} +(492853. - 1.46853e6i) q^{52} +(-1.47108e6 - 609343. i) q^{53} +(-275242. + 294891. i) q^{54} +(104325. - 104325. i) q^{55} +(426909. - 1.43401e6i) q^{56} +(839344. + 839344. i) q^{57} +(-962264. + 33163.6i) q^{58} +(-786490. + 1.89875e6i) q^{59} +(173563. - 199294. i) q^{60} +(1.04240e6 - 431777. i) q^{61} +(-1.13227e6 - 423928. i) q^{62} -2.78668e6 q^{63} +(-1.14700e6 + 1.75569e6i) q^{64} +357522. q^{65} +(3.69798e6 + 1.38454e6i) q^{66} +(119955. - 49687.1i) q^{67} +(-2.05028e6 + 2.35424e6i) q^{68} +(2.08930e6 - 5.04403e6i) q^{69} +(345127. - 11894.5i) q^{70} +(-2.75098e6 - 2.75098e6i) q^{71} +(3.74356e6 + 1.11447e6i) q^{72} +(3.77513e6 - 3.77513e6i) q^{73} +(-2.14059e6 + 2.29340e6i) q^{74} +(-4.98795e6 - 2.06608e6i) q^{75} +(691716. - 2.06107e6i) q^{76} +(1.97455e6 + 4.76699e6i) q^{77} +(3.96407e6 + 8.70889e6i) q^{78} -2.84528e6i q^{79} +(-468392. - 122046. i) q^{80} +3.40694e6i q^{81} +(4.84774e6 - 2.20657e6i) q^{82} +(-441301. - 1.06539e6i) q^{83} +(4.11638e6 + 8.27507e6i) q^{84} +(-665694. - 275740. i) q^{85} +(-1.66749e6 - 1.55638e6i) q^{86} +(4.20560e6 - 4.20560e6i) q^{87} +(-746122. - 7.19353e6i) q^{88} +(5.80216e6 + 5.80216e6i) q^{89} +(31051.1 + 900969. i) q^{90} +(-4.78483e6 + 1.15516e7i) q^{91} +(-9.97573e6 + 688428. i) q^{92} +(6.89991e6 - 2.85804e6i) q^{93} +(-1.88505e6 + 5.03480e6i) q^{94} +501779. q^{95} +(-2.22043e6 - 1.27628e7i) q^{96} -1.53110e7 q^{97} +(-967649. + 2.58450e6i) q^{98} +(-1.24444e7 + 5.15466e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 13004 q^{10} - 4 q^{11} + 30668 q^{12} - 4 q^{13} - 26196 q^{14} - 52784 q^{16} + 102056 q^{18} - 4 q^{19} + 81996 q^{20} - 4 q^{21} - 374240 q^{22} - 143420 q^{23} + 380880 q^{24} - 4 q^{25} - 363984 q^{26} + 476084 q^{27} - 195464 q^{28} - 4 q^{29} + 870468 q^{30} - 714992 q^{31} + 535656 q^{32} - 8 q^{33} - 201072 q^{34} + 816500 q^{35} - 1669712 q^{36} - 4 q^{37} - 2533100 q^{38} - 283948 q^{39} + 2746344 q^{40} - 4 q^{41} + 4924936 q^{42} + 366180 q^{43} - 1585404 q^{44} + 8744 q^{45} - 2715812 q^{46} - 5044368 q^{48} - 1653804 q^{50} + 3002072 q^{51} + 8882212 q^{52} - 1815636 q^{53} + 6815776 q^{54} - 4191012 q^{55} - 3655000 q^{56} - 4 q^{57} - 12448736 q^{58} - 1835940 q^{59} - 6364808 q^{60} - 4559780 q^{61} + 12948600 q^{62} + 10001872 q^{63} + 16915544 q^{64} - 8 q^{65} - 11246068 q^{66} - 1940684 q^{67} - 8895536 q^{68} + 9580892 q^{69} - 8149480 q^{70} - 12348708 q^{71} + 12884564 q^{72} - 4 q^{73} + 10931436 q^{74} + 11573008 q^{75} + 14443516 q^{76} - 11914452 q^{77} - 38252364 q^{78} - 11333192 q^{80} + 15827196 q^{82} - 9565884 q^{83} + 8101984 q^{84} + 312496 q^{85} - 14812992 q^{86} + 40789108 q^{87} + 5716448 q^{88} - 4 q^{89} + 5335400 q^{90} - 3406996 q^{91} + 27562664 q^{92} - 8752 q^{93} - 14227032 q^{94} - 54872008 q^{95} - 25080448 q^{96} - 8 q^{97} + 57598104 q^{98} - 9738480 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(31\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.5954 + 3.96698i 0.936512 + 0.350635i
\(3\) −64.5670 + 26.7445i −1.38066 + 0.571888i −0.944658 0.328058i \(-0.893606\pi\)
−0.436002 + 0.899946i \(0.643606\pi\)
\(4\) 96.5262 + 84.0636i 0.754111 + 0.656747i
\(5\) −11.3056 + 27.2941i −0.0404481 + 0.0976504i −0.942813 0.333323i \(-0.891830\pi\)
0.902364 + 0.430974i \(0.141830\pi\)
\(6\) −790.210 + 27.2339i −1.49353 + 0.0514732i
\(7\) −730.571 730.571i −0.805044 0.805044i 0.178835 0.983879i \(-0.442767\pi\)
−0.983879 + 0.178835i \(0.942767\pi\)
\(8\) 689.258 + 1273.61i 0.475956 + 0.879469i
\(9\) 1907.19 1907.19i 0.872058 0.872058i
\(10\) −228.063 + 244.344i −0.0721197 + 0.0772683i
\(11\) −4613.88 1911.13i −1.04518 0.432929i −0.207012 0.978338i \(-0.566374\pi\)
−0.838170 + 0.545410i \(0.816374\pi\)
\(12\) −8480.65 2846.19i −1.41676 0.475477i
\(13\) −4631.15 11180.6i −0.584638 1.41144i −0.888567 0.458746i \(-0.848299\pi\)
0.303929 0.952695i \(-0.401701\pi\)
\(14\) −4842.56 10638.9i −0.471657 1.03621i
\(15\) 2064.66i 0.157954i
\(16\) 2250.61 + 16228.7i 0.137366 + 0.990520i
\(17\) 24389.7i 1.20402i 0.798487 + 0.602012i \(0.205634\pi\)
−0.798487 + 0.602012i \(0.794366\pi\)
\(18\) 27773.3 12641.7i 1.12247 0.510919i
\(19\) −6499.78 15691.9i −0.217401 0.524852i 0.777125 0.629347i \(-0.216678\pi\)
−0.994525 + 0.104495i \(0.966678\pi\)
\(20\) −3385.73 + 1684.21i −0.0946339 + 0.0470750i
\(21\) 66709.6 + 27632.0i 1.57189 + 0.651096i
\(22\) −41304.6 38552.4i −0.827026 0.771920i
\(23\) −55239.7 + 55239.7i −0.946682 + 0.946682i −0.998649 0.0519670i \(-0.983451\pi\)
0.0519670 + 0.998649i \(0.483451\pi\)
\(24\) −78565.4 63799.2i −1.16009 0.942054i
\(25\) 54625.6 + 54625.6i 0.699207 + 0.699207i
\(26\) −4715.90 136835.i −0.0526208 1.52683i
\(27\) −13644.4 + 32940.4i −0.133408 + 0.322074i
\(28\) −9104.79 131934.i −0.0783821 1.13580i
\(29\) −78625.3 + 32567.7i −0.598645 + 0.247967i −0.661365 0.750064i \(-0.730023\pi\)
0.0627199 + 0.998031i \(0.480023\pi\)
\(30\) 8190.47 21876.0i 0.0553840 0.147926i
\(31\) −106864. −0.644268 −0.322134 0.946694i \(-0.604400\pi\)
−0.322134 + 0.946694i \(0.604400\pi\)
\(32\) −40532.6 + 180878.i −0.218665 + 0.975800i
\(33\) 349017. 1.69063
\(34\) −96753.3 + 258419.i −0.422172 + 1.12758i
\(35\) 28199.8 11680.8i 0.111175 0.0460503i
\(36\) 344419. 23768.5i 1.23035 0.0849068i
\(37\) −106114. + 256182.i −0.344403 + 0.831462i 0.652857 + 0.757481i \(0.273570\pi\)
−0.997260 + 0.0739805i \(0.976430\pi\)
\(38\) −6618.73 192047.i −0.0195673 0.567759i
\(39\) 598039. + 598039.i 1.61437 + 1.61437i
\(40\) −42554.4 + 4413.80i −0.105132 + 0.0109044i
\(41\) 332894. 332894.i 0.754332 0.754332i −0.220953 0.975285i \(-0.570917\pi\)
0.975285 + 0.220953i \(0.0709166\pi\)
\(42\) 597201. + 557409.i 1.24379 + 1.16092i
\(43\) −186265. 77153.3i −0.357265 0.147984i 0.196829 0.980438i \(-0.436935\pi\)
−0.554095 + 0.832454i \(0.686935\pi\)
\(44\) −284704. 572334.i −0.503859 1.01290i
\(45\) 30493.1 + 73617.0i 0.0498837 + 0.120430i
\(46\) −804423. + 366154.i −1.21852 + 0.554640i
\(47\) 475186.i 0.667607i 0.942643 + 0.333804i \(0.108332\pi\)
−0.942643 + 0.333804i \(0.891668\pi\)
\(48\) −579344. 987647.i −0.756123 1.28901i
\(49\) 243926.i 0.296191i
\(50\) 362083. + 795480.i 0.409650 + 0.899982i
\(51\) −652291. 1.57477e6i −0.688566 1.66235i
\(52\) 492853. 1.46853e6i 0.486078 1.44834i
\(53\) −1.47108e6 609343.i −1.35729 0.562207i −0.418976 0.907997i \(-0.637611\pi\)
−0.938312 + 0.345791i \(0.887611\pi\)
\(54\) −275242. + 294891.i −0.237868 + 0.254849i
\(55\) 104325. 104325.i 0.0845513 0.0845513i
\(56\) 426909. 1.43401e6i 0.324846 1.09118i
\(57\) 839344. + 839344.i 0.600313 + 0.600313i
\(58\) −962264. + 33163.6i −0.647584 + 0.0223185i
\(59\) −786490. + 1.89875e6i −0.498553 + 1.20361i 0.451710 + 0.892165i \(0.350814\pi\)
−0.950263 + 0.311448i \(0.899186\pi\)
\(60\) 173563. 199294.i 0.103736 0.119115i
\(61\) 1.04240e6 431777.i 0.588005 0.243560i −0.0687871 0.997631i \(-0.521913\pi\)
0.656792 + 0.754072i \(0.271913\pi\)
\(62\) −1.13227e6 423928.i −0.603365 0.225903i
\(63\) −2.78668e6 −1.40409
\(64\) −1.14700e6 + 1.75569e6i −0.546932 + 0.837177i
\(65\) 357522. 0.161475
\(66\) 3.69798e6 + 1.38454e6i 1.58329 + 0.592792i
\(67\) 119955. 49687.1i 0.0487257 0.0201828i −0.358188 0.933650i \(-0.616605\pi\)
0.406913 + 0.913467i \(0.366605\pi\)
\(68\) −2.05028e6 + 2.35424e6i −0.790739 + 0.907967i
\(69\) 2.08930e6 5.04403e6i 0.765649 1.84844i
\(70\) 345127. 11894.5i 0.120264 0.00414479i
\(71\) −2.75098e6 2.75098e6i −0.912186 0.912186i 0.0842581 0.996444i \(-0.473148\pi\)
−0.996444 + 0.0842581i \(0.973148\pi\)
\(72\) 3.74356e6 + 1.11447e6i 1.18201 + 0.351887i
\(73\) 3.77513e6 3.77513e6i 1.13580 1.13580i 0.146604 0.989195i \(-0.453166\pi\)
0.989195 0.146604i \(-0.0468342\pi\)
\(74\) −2.14059e6 + 2.29340e6i −0.614077 + 0.657915i
\(75\) −4.98795e6 2.06608e6i −1.36524 0.565499i
\(76\) 691716. 2.06107e6i 0.180751 0.538574i
\(77\) 1.97455e6 + 4.76699e6i 0.492891 + 1.18994i
\(78\) 3.96407e6 + 8.70889e6i 0.945825 + 2.07793i
\(79\) 2.84528e6i 0.649277i −0.945838 0.324639i \(-0.894757\pi\)
0.945838 0.324639i \(-0.105243\pi\)
\(80\) −468392. 122046.i −0.102281 0.0266508i
\(81\) 3.40694e6i 0.712307i
\(82\) 4.84774e6 2.20657e6i 0.970936 0.441946i
\(83\) −441301. 1.06539e6i −0.0847152 0.204521i 0.875845 0.482592i \(-0.160305\pi\)
−0.960560 + 0.278072i \(0.910305\pi\)
\(84\) 4.11638e6 + 8.27507e6i 0.757771 + 1.52333i
\(85\) −665694. 275740.i −0.117573 0.0487004i
\(86\) −1.66749e6 1.55638e6i −0.282695 0.263858i
\(87\) 4.20560e6 4.20560e6i 0.684716 0.684716i
\(88\) −746122. 7.19353e6i −0.116713 1.12526i
\(89\) 5.80216e6 + 5.80216e6i 0.872417 + 0.872417i 0.992735 0.120318i \(-0.0383914\pi\)
−0.120318 + 0.992735i \(0.538391\pi\)
\(90\) 31051.1 + 900969.i 0.00448982 + 0.130275i
\(91\) −4.78483e6 + 1.15516e7i −0.665613 + 1.60693i
\(92\) −9.97573e6 + 688428.i −1.33563 + 0.0921725i
\(93\) 6.89991e6 2.85804e6i 0.889515 0.368449i
\(94\) −1.88505e6 + 5.03480e6i −0.234086 + 0.625222i
\(95\) 501779. 0.0600455
\(96\) −2.22043e6 1.27628e7i −0.256146 1.47230i
\(97\) −1.53110e7 −1.70335 −0.851673 0.524073i \(-0.824412\pi\)
−0.851673 + 0.524073i \(0.824412\pi\)
\(98\) −967649. + 2.58450e6i −0.103855 + 0.277386i
\(99\) −1.24444e7 + 5.15466e6i −1.28900 + 0.533920i
\(100\) 680774. + 9.86482e6i 0.0680774 + 0.986482i
\(101\) 3.16931e6 7.65138e6i 0.306083 0.738950i −0.693741 0.720224i \(-0.744039\pi\)
0.999825 0.0187261i \(-0.00596105\pi\)
\(102\) −664227. 1.92730e7i −0.0619749 1.79824i
\(103\) 1.35196e7 + 1.35196e7i 1.21908 + 1.21908i 0.967953 + 0.251132i \(0.0808028\pi\)
0.251132 + 0.967953i \(0.419197\pi\)
\(104\) 1.10476e7 1.36046e7i 0.963057 1.18595i
\(105\) −1.50838e6 + 1.50838e6i −0.127160 + 0.127160i
\(106\) −1.31695e7 1.22920e7i −1.07399 1.00243i
\(107\) 1.62701e7 + 6.73932e6i 1.28395 + 0.531830i 0.917177 0.398480i \(-0.130462\pi\)
0.366774 + 0.930310i \(0.380462\pi\)
\(108\) −4.08613e6 + 2.03262e6i −0.312126 + 0.155265i
\(109\) −1.12249e6 2.70992e6i −0.0830210 0.200430i 0.876918 0.480641i \(-0.159596\pi\)
−0.959939 + 0.280210i \(0.909596\pi\)
\(110\) 1.51923e6 691515.i 0.108830 0.0495367i
\(111\) 1.93789e7i 1.34492i
\(112\) 1.02120e7 1.35004e7i 0.686826 0.907998i
\(113\) 1.78381e7i 1.16299i 0.813551 + 0.581493i \(0.197531\pi\)
−0.813551 + 0.581493i \(0.802469\pi\)
\(114\) 5.56355e6 + 1.22229e7i 0.351710 + 0.772691i
\(115\) −883201. 2.13224e6i −0.0541523 0.130735i
\(116\) −1.03272e7 3.46590e6i −0.614296 0.206164i
\(117\) −3.01560e7 1.24910e7i −1.74070 0.721020i
\(118\) −1.58655e7 + 1.69981e7i −0.888929 + 0.952389i
\(119\) 1.78184e7 1.78184e7i 0.969291 0.969291i
\(120\) 2.62957e6 1.42308e6i 0.138915 0.0751790i
\(121\) 3.85596e6 + 3.85596e6i 0.197872 + 0.197872i
\(122\) 1.27576e7 439678.i 0.636074 0.0219218i
\(123\) −1.25909e7 + 3.03971e7i −0.610082 + 1.47287i
\(124\) −1.03152e7 8.98340e6i −0.485850 0.423121i
\(125\) −4.24088e6 + 1.75663e6i −0.194210 + 0.0804443i
\(126\) −2.95260e7 1.10547e7i −1.31495 0.492322i
\(127\) 1.17900e7 0.510742 0.255371 0.966843i \(-0.417802\pi\)
0.255371 + 0.966843i \(0.417802\pi\)
\(128\) −1.91177e7 + 1.40521e7i −0.805752 + 0.592254i
\(129\) 1.40900e7 0.577892
\(130\) 3.78810e6 + 1.41828e6i 0.151224 + 0.0566188i
\(131\) 4.50360e7 1.86545e7i 1.75029 0.724994i 0.752498 0.658594i \(-0.228849\pi\)
0.997793 0.0664005i \(-0.0211515\pi\)
\(132\) 3.36893e7 + 2.93396e7i 1.27492 + 1.11031i
\(133\) −6.71547e6 + 1.62126e7i −0.247512 + 0.597546i
\(134\) 1.46809e6 50596.3i 0.0527090 0.00181657i
\(135\) −744822. 744822.i −0.0260546 0.0260546i
\(136\) −3.10629e7 + 1.68108e7i −1.05890 + 0.573062i
\(137\) −1.40587e7 + 1.40587e7i −0.467115 + 0.467115i −0.900979 0.433863i \(-0.857150\pi\)
0.433863 + 0.900979i \(0.357150\pi\)
\(138\) 4.21466e7 4.51554e7i 1.36517 1.46262i
\(139\) −4.16033e7 1.72326e7i −1.31394 0.544252i −0.387909 0.921698i \(-0.626803\pi\)
−0.926032 + 0.377445i \(0.876803\pi\)
\(140\) 3.70395e6 + 1.24308e6i 0.114082 + 0.0382870i
\(141\) −1.27086e7 3.06813e7i −0.381796 0.921738i
\(142\) −1.82347e7 4.00609e7i −0.534430 1.17412i
\(143\) 6.04366e7i 1.72832i
\(144\) 3.52435e7 + 2.66588e7i 0.983582 + 0.743999i
\(145\) 2.51420e6i 0.0684877i
\(146\) 5.49749e7 2.50232e7i 1.46194 0.665439i
\(147\) −6.52369e6 1.57496e7i −0.169388 0.408939i
\(148\) −3.17783e7 + 1.58079e7i −0.805778 + 0.400829i
\(149\) −2.49069e7 1.03168e7i −0.616833 0.255501i 0.0523138 0.998631i \(-0.483340\pi\)
−0.669147 + 0.743130i \(0.733340\pi\)
\(150\) −4.46534e7 4.16780e7i −1.08028 1.00830i
\(151\) 1.35835e7 1.35835e7i 0.321066 0.321066i −0.528110 0.849176i \(-0.677099\pi\)
0.849176 + 0.528110i \(0.177099\pi\)
\(152\) 1.55053e7 1.90939e7i 0.358118 0.441004i
\(153\) 4.65157e7 + 4.65157e7i 1.04998 + 1.04998i
\(154\) 2.01068e6 + 5.83413e7i 0.0443630 + 1.28722i
\(155\) 1.20816e6 2.91677e6i 0.0260594 0.0629130i
\(156\) 7.45310e6 + 1.08000e8i 0.157181 + 2.27765i
\(157\) −1.97689e7 + 8.18855e6i −0.407694 + 0.168872i −0.577099 0.816674i \(-0.695815\pi\)
0.169405 + 0.985546i \(0.445815\pi\)
\(158\) 1.12872e7 3.01470e7i 0.227659 0.608056i
\(159\) 1.11280e8 2.19547
\(160\) −4.47866e6 3.15123e6i −0.0864426 0.0608220i
\(161\) 8.07131e7 1.52424
\(162\) −1.35153e7 + 3.60980e7i −0.249759 + 0.667084i
\(163\) −5.71855e7 + 2.36870e7i −1.03426 + 0.428404i −0.834248 0.551389i \(-0.814098\pi\)
−0.200011 + 0.979794i \(0.564098\pi\)
\(164\) 6.01173e7 4.14871e6i 1.06426 0.0734446i
\(165\) −3.94584e6 + 9.52611e6i −0.0683827 + 0.165090i
\(166\) −449376. 1.30389e7i −0.00762486 0.221240i
\(167\) −3.92256e7 3.92256e7i −0.651722 0.651722i 0.301686 0.953407i \(-0.402451\pi\)
−0.953407 + 0.301686i \(0.902451\pi\)
\(168\) 1.07878e7 + 1.04007e8i 0.175529 + 1.69232i
\(169\) −5.91880e7 + 5.91880e7i −0.943258 + 0.943258i
\(170\) −5.95946e6 5.56237e6i −0.0930328 0.0868338i
\(171\) −4.23237e7 1.75311e7i −0.647288 0.268115i
\(172\) −1.14936e7 2.31054e7i −0.172229 0.346229i
\(173\) −3.30227e7 7.97239e7i −0.484899 1.17065i −0.957256 0.289242i \(-0.906597\pi\)
0.472357 0.881407i \(-0.343403\pi\)
\(174\) 6.12436e7 2.78766e7i 0.881330 0.401160i
\(175\) 7.98157e7i 1.12578i
\(176\) 2.06311e7 7.91784e7i 0.285252 1.09474i
\(177\) 1.43631e8i 1.94690i
\(178\) 3.84593e7 + 8.44933e7i 0.511130 + 1.12293i
\(179\) −4.72784e6 1.14140e7i −0.0616137 0.148749i 0.890074 0.455816i \(-0.150652\pi\)
−0.951688 + 0.307067i \(0.900652\pi\)
\(180\) −3.24512e6 + 9.66933e6i −0.0414741 + 0.123578i
\(181\) −1.05032e8 4.35056e7i −1.31657 0.545343i −0.389779 0.920909i \(-0.627449\pi\)
−0.926796 + 0.375565i \(0.877449\pi\)
\(182\) −9.65222e7 + 1.03413e8i −1.18680 + 1.27152i
\(183\) −5.57572e7 + 5.57572e7i −0.672546 + 0.672546i
\(184\) −1.08428e8 3.22793e7i −1.28316 0.381999i
\(185\) −5.79257e6 5.79257e6i −0.0672621 0.0672621i
\(186\) 8.44453e7 2.91034e6i 0.962233 0.0331626i
\(187\) 4.66119e7 1.12531e8i 0.521256 1.25842i
\(188\) −3.99459e7 + 4.58679e7i −0.438449 + 0.503450i
\(189\) 3.40335e7 1.40972e7i 0.366683 0.151885i
\(190\) 5.31657e6 + 1.99055e6i 0.0562333 + 0.0210540i
\(191\) 1.52149e8 1.57998 0.789992 0.613117i \(-0.210085\pi\)
0.789992 + 0.613117i \(0.210085\pi\)
\(192\) 2.71033e7 1.44036e8i 0.276355 1.46864i
\(193\) −1.30908e8 −1.31074 −0.655369 0.755309i \(-0.727487\pi\)
−0.655369 + 0.755309i \(0.727487\pi\)
\(194\) −1.62227e8 6.07385e7i −1.59521 0.597252i
\(195\) −2.30841e7 + 9.56176e6i −0.222942 + 0.0923457i
\(196\) −2.05053e7 + 2.35452e7i −0.194523 + 0.223361i
\(197\) −1.79424e7 + 4.33168e7i −0.167205 + 0.403669i −0.985166 0.171605i \(-0.945105\pi\)
0.817961 + 0.575274i \(0.195105\pi\)
\(198\) −1.52303e8 + 5.24898e6i −1.39437 + 0.0480559i
\(199\) −1.14175e8 1.14175e8i −1.02703 1.02703i −0.999624 0.0274098i \(-0.991274\pi\)
−0.0274098 0.999624i \(-0.508726\pi\)
\(200\) −3.19204e7 + 1.07223e8i −0.282139 + 0.947723i
\(201\) −6.41630e6 + 6.41630e6i −0.0557312 + 0.0557312i
\(202\) 6.39330e7 6.84971e7i 0.545752 0.584713i
\(203\) 8.12344e7 + 3.36484e7i 0.681560 + 0.282311i
\(204\) 6.94177e7 2.06840e8i 0.572486 1.70581i
\(205\) 5.32248e6 + 1.28496e7i 0.0431495 + 0.104172i
\(206\) 8.96141e7 + 1.96878e8i 0.714235 + 1.56914i
\(207\) 2.10705e8i 1.65112i
\(208\) 1.71023e8 1.00321e8i 1.31775 0.772980i
\(209\) 8.48224e7i 0.642685i
\(210\) −2.19657e7 + 9.99825e6i −0.163673 + 0.0745000i
\(211\) 8.16120e7 + 1.97029e8i 0.598089 + 1.44391i 0.875527 + 0.483170i \(0.160515\pi\)
−0.277438 + 0.960744i \(0.589485\pi\)
\(212\) −9.07745e7 1.82482e8i −0.654317 1.31536i
\(213\) 2.51196e8 + 1.04049e8i 1.78109 + 0.737750i
\(214\) 1.45654e8 + 1.35949e8i 1.01596 + 0.948263i
\(215\) 4.21166e6 4.21166e6i 0.0289014 0.0289014i
\(216\) −5.13577e7 + 5.32688e6i −0.346751 + 0.0359654i
\(217\) 7.80720e7 + 7.80720e7i 0.518664 + 0.518664i
\(218\) −1.14303e6 3.31656e7i −0.00747237 0.216816i
\(219\) −1.42785e8 + 3.44713e8i −0.918602 + 2.21770i
\(220\) 1.88401e7 1.30016e6i 0.119290 0.00823223i
\(221\) 2.72691e8 1.12952e8i 1.69941 0.703918i
\(222\) 7.68755e7 2.05327e8i 0.471577 1.25954i
\(223\) −8.34043e7 −0.503642 −0.251821 0.967774i \(-0.581029\pi\)
−0.251821 + 0.967774i \(0.581029\pi\)
\(224\) 1.61756e8 1.02532e8i 0.961597 0.609527i
\(225\) 2.08363e8 1.21950
\(226\) −7.07634e7 + 1.89003e8i −0.407783 + 1.08915i
\(227\) 9.59743e7 3.97539e7i 0.544584 0.225574i −0.0933934 0.995629i \(-0.529771\pi\)
0.637977 + 0.770055i \(0.279771\pi\)
\(228\) 1.04604e7 + 1.51577e8i 0.0584487 + 0.846957i
\(229\) −2.41874e7 + 5.83935e7i −0.133096 + 0.321322i −0.976351 0.216192i \(-0.930636\pi\)
0.843255 + 0.537514i \(0.180636\pi\)
\(230\) −899363. 2.60956e7i −0.00487402 0.141423i
\(231\) −2.54982e8 2.54982e8i −1.36103 1.36103i
\(232\) −9.56715e7 7.76903e7i −0.503008 0.408469i
\(233\) −1.54702e8 + 1.54702e8i −0.801217 + 0.801217i −0.983286 0.182068i \(-0.941721\pi\)
0.182068 + 0.983286i \(0.441721\pi\)
\(234\) −2.69964e8 2.51976e8i −1.37737 1.28559i
\(235\) −1.29698e7 5.37226e6i −0.0651921 0.0270034i
\(236\) −2.35533e8 + 1.17164e8i −1.16643 + 0.580234i
\(237\) 7.60957e7 + 1.83711e8i 0.371314 + 0.896431i
\(238\) 2.59479e8 1.18108e8i 1.24762 0.567886i
\(239\) 4.01707e7i 0.190334i −0.995461 0.0951672i \(-0.969661\pi\)
0.995461 0.0951672i \(-0.0303386\pi\)
\(240\) 3.35068e7 4.64675e6i 0.156456 0.0216975i
\(241\) 2.69789e8i 1.24155i −0.783989 0.620774i \(-0.786818\pi\)
0.783989 0.620774i \(-0.213182\pi\)
\(242\) 2.55590e7 + 5.61520e7i 0.115929 + 0.254690i
\(243\) −1.20957e8 2.92017e8i −0.540767 1.30553i
\(244\) 1.36916e8 + 4.59503e7i 0.603378 + 0.202500i
\(245\) −6.65774e6 2.75773e6i −0.0289232 0.0119804i
\(246\) −2.53990e8 + 2.72122e8i −1.08779 + 1.16544i
\(247\) −1.45343e8 + 1.45343e8i −0.613697 + 0.613697i
\(248\) −7.36571e7 1.36103e8i −0.306643 0.566614i
\(249\) 5.69870e7 + 5.69870e7i 0.233926 + 0.233926i
\(250\) −5.19025e7 + 1.78878e6i −0.210086 + 0.00724045i
\(251\) −4.35059e7 + 1.05033e8i −0.173656 + 0.419243i −0.986613 0.163081i \(-0.947857\pi\)
0.812956 + 0.582324i \(0.197857\pi\)
\(252\) −2.68987e8 2.34258e8i −1.05884 0.922132i
\(253\) 3.60440e8 1.49299e8i 1.39930 0.579609i
\(254\) 1.24920e8 + 4.67707e7i 0.478316 + 0.179084i
\(255\) 5.03564e7 0.190180
\(256\) −2.58305e8 + 7.30489e7i −0.962261 + 0.272128i
\(257\) −1.02156e8 −0.375402 −0.187701 0.982226i \(-0.560104\pi\)
−0.187701 + 0.982226i \(0.560104\pi\)
\(258\) 1.49289e8 + 5.58947e7i 0.541203 + 0.202629i
\(259\) 2.64683e8 1.09635e8i 0.946622 0.392104i
\(260\) 3.45102e7 + 3.00546e7i 0.121770 + 0.106048i
\(261\) −8.78407e7 + 2.12066e8i −0.305812 + 0.738294i
\(262\) 5.51178e8 1.89959e7i 1.89338 0.0652537i
\(263\) 6.42815e7 + 6.42815e7i 0.217892 + 0.217892i 0.807610 0.589718i \(-0.200761\pi\)
−0.589718 + 0.807610i \(0.700761\pi\)
\(264\) 2.40563e8 + 4.44511e8i 0.804664 + 1.48685i
\(265\) 3.32629e7 3.32629e7i 0.109799 0.109799i
\(266\) −1.35468e8 + 1.45139e8i −0.441318 + 0.472823i
\(267\) −5.29804e8 2.19452e8i −1.70344 0.705586i
\(268\) 1.57557e7 + 5.28777e6i 0.0499996 + 0.0167803i
\(269\) 1.12007e8 + 2.70408e8i 0.350841 + 0.847006i 0.996517 + 0.0833938i \(0.0265759\pi\)
−0.645675 + 0.763612i \(0.723424\pi\)
\(270\) −4.93702e6 1.08464e7i −0.0152648 0.0335361i
\(271\) 1.71659e8i 0.523930i 0.965077 + 0.261965i \(0.0843704\pi\)
−0.965077 + 0.261965i \(0.915630\pi\)
\(272\) −3.95812e8 + 5.48917e7i −1.19261 + 0.165392i
\(273\) 8.73821e8i 2.59928i
\(274\) −2.04729e8 + 9.31876e7i −0.601246 + 0.273673i
\(275\) −1.47639e8 3.56433e8i −0.428092 1.03351i
\(276\) 6.25692e8 3.11246e8i 1.79134 0.891091i
\(277\) −3.71173e8 1.53745e8i −1.04929 0.434631i −0.209654 0.977776i \(-0.567234\pi\)
−0.839639 + 0.543144i \(0.817234\pi\)
\(278\) −3.72443e8 3.47627e8i −1.03969 0.970412i
\(279\) −2.03811e8 + 2.03811e8i −0.561839 + 0.561839i
\(280\) 3.43136e7 + 2.78645e7i 0.0934144 + 0.0758573i
\(281\) 5.52788e7 + 5.52788e7i 0.148623 + 0.148623i 0.777503 0.628880i \(-0.216486\pi\)
−0.628880 + 0.777503i \(0.716486\pi\)
\(282\) −1.29412e7 3.75497e8i −0.0343639 0.997090i
\(283\) −4.94025e7 + 1.19268e8i −0.129568 + 0.312804i −0.975329 0.220758i \(-0.929147\pi\)
0.845761 + 0.533562i \(0.179147\pi\)
\(284\) −3.42843e7 4.96799e8i −0.0888138 1.28696i
\(285\) −3.23984e7 + 1.34199e7i −0.0829023 + 0.0343393i
\(286\) −2.39751e8 + 6.40352e8i −0.606008 + 1.61859i
\(287\) −4.86406e8 −1.21454
\(288\) 2.67665e8 + 4.22272e8i 0.660265 + 1.04164i
\(289\) −1.84518e8 −0.449671
\(290\) 9.97379e6 2.66391e7i 0.0240141 0.0641396i
\(291\) 9.88587e8 4.09486e8i 2.35174 0.974123i
\(292\) 6.81749e8 4.70477e7i 1.60245 0.110586i
\(293\) −1.65403e8 + 3.99319e8i −0.384156 + 0.927435i 0.606996 + 0.794705i \(0.292374\pi\)
−0.991152 + 0.132730i \(0.957626\pi\)
\(294\) −6.64307e6 1.92753e8i −0.0152459 0.442370i
\(295\) −4.29331e7 4.29331e7i −0.0973677 0.0973677i
\(296\) −3.99415e8 + 4.14278e7i −0.895165 + 0.0928476i
\(297\) 1.25907e8 1.25907e8i 0.278870 0.278870i
\(298\) −2.22973e8 2.08116e8i −0.488085 0.455563i
\(299\) 8.73436e8 + 3.61789e8i 1.88965 + 0.782719i
\(300\) −3.07786e8 6.18735e8i −0.658149 1.32306i
\(301\) 7.97136e7 + 1.92446e8i 0.168480 + 0.406748i
\(302\) 1.97809e8 9.00379e7i 0.413259 0.188105i
\(303\) 5.78789e8i 1.19528i
\(304\) 2.40030e8 1.40799e8i 0.490013 0.287437i
\(305\) 3.33329e7i 0.0672704i
\(306\) 3.08327e8 + 6.77381e8i 0.615159 + 1.35148i
\(307\) −1.02232e8 2.46809e8i −0.201652 0.486830i 0.790411 0.612577i \(-0.209867\pi\)
−0.992062 + 0.125747i \(0.959867\pi\)
\(308\) −2.10134e8 + 6.26127e8i −0.409798 + 1.22105i
\(309\) −1.23450e9 5.11346e8i −2.38032 0.985961i
\(310\) 2.43718e7 2.61116e7i 0.0464645 0.0497815i
\(311\) 3.64335e8 3.64335e8i 0.686814 0.686814i −0.274712 0.961526i \(-0.588583\pi\)
0.961526 + 0.274712i \(0.0885826\pi\)
\(312\) −3.49464e8 + 1.17387e9i −0.651420 + 2.18816i
\(313\) −6.99647e7 6.99647e7i −0.128966 0.128966i 0.639678 0.768643i \(-0.279068\pi\)
−0.768643 + 0.639678i \(0.779068\pi\)
\(314\) −2.41944e8 + 8.33839e6i −0.441023 + 0.0151995i
\(315\) 3.15050e7 7.60599e7i 0.0567927 0.137110i
\(316\) 2.39185e8 2.74644e8i 0.426411 0.489627i
\(317\) −2.81674e8 + 1.16673e8i −0.496637 + 0.205714i −0.616920 0.787026i \(-0.711620\pi\)
0.120283 + 0.992740i \(0.461620\pi\)
\(318\) 1.17906e9 + 4.41446e8i 2.05609 + 0.769808i
\(319\) 4.25009e8 0.733045
\(320\) −3.49524e7 5.11554e7i −0.0596283 0.0872703i
\(321\) −1.23076e9 −2.07685
\(322\) 8.55190e8 + 3.20187e8i 1.42747 + 0.534451i
\(323\) 3.82720e8 1.58528e8i 0.631934 0.261756i
\(324\) −2.86400e8 + 3.28859e8i −0.467805 + 0.537158i
\(325\) 3.57767e8 8.63725e8i 0.578107 1.39567i
\(326\) −6.99871e8 + 2.41205e7i −1.11881 + 0.0385589i
\(327\) 1.44951e8 + 1.44951e8i 0.229247 + 0.229247i
\(328\) 6.53426e8 + 1.94526e8i 1.02244 + 0.304383i
\(329\) 3.47157e8 3.47157e8i 0.537453 0.537453i
\(330\) −7.95977e7 + 8.52801e7i −0.121928 + 0.130632i
\(331\) 2.28794e8 + 9.47696e7i 0.346774 + 0.143639i 0.549271 0.835644i \(-0.314906\pi\)
−0.202497 + 0.979283i \(0.564906\pi\)
\(332\) 4.69638e7 1.39936e8i 0.0704337 0.209868i
\(333\) 2.86208e8 + 6.90967e8i 0.424744 + 1.02542i
\(334\) −2.60005e8 5.71219e8i −0.381829 0.838861i
\(335\) 3.83582e6i 0.00557443i
\(336\) −2.98294e8 + 1.14480e9i −0.429000 + 1.64642i
\(337\) 9.11022e8i 1.29665i 0.761362 + 0.648327i \(0.224531\pi\)
−0.761362 + 0.648327i \(0.775469\pi\)
\(338\) −8.61920e8 + 3.92325e8i −1.21411 + 0.552634i
\(339\) −4.77073e8 1.15176e9i −0.665098 1.60569i
\(340\) −4.10773e7 8.25768e7i −0.0566794 0.113941i
\(341\) 4.93059e8 + 2.04232e8i 0.673378 + 0.278922i
\(342\) −3.78892e8 3.53646e8i −0.512182 0.478055i
\(343\) −4.23452e8 + 4.23452e8i −0.566597 + 0.566597i
\(344\) −3.01213e7 2.90407e8i −0.0398951 0.384638i
\(345\) 1.14051e8 + 1.14051e8i 0.149532 + 0.149532i
\(346\) −3.36270e7 9.75709e8i −0.0436437 1.26635i
\(347\) −1.53413e8 + 3.70371e8i −0.197110 + 0.475865i −0.991271 0.131843i \(-0.957911\pi\)
0.794161 + 0.607707i \(0.207911\pi\)
\(348\) 7.59488e8 5.24125e7i 0.966037 0.0666665i
\(349\) 8.82573e8 3.65574e8i 1.11138 0.460348i 0.249966 0.968255i \(-0.419581\pi\)
0.861412 + 0.507907i \(0.169581\pi\)
\(350\) 3.16627e8 8.45682e8i 0.394739 1.05431i
\(351\) 4.31483e8 0.532584
\(352\) 5.32694e8 7.57086e8i 0.650997 0.925222i
\(353\) −4.58997e7 −0.0555390 −0.0277695 0.999614i \(-0.508840\pi\)
−0.0277695 + 0.999614i \(0.508840\pi\)
\(354\) 5.69782e8 1.52184e9i 0.682649 1.82329i
\(355\) 1.06187e8 4.39841e7i 0.125971 0.0521791i
\(356\) 7.23097e7 + 1.04781e9i 0.0849418 + 1.23086i
\(357\) −6.73936e8 + 1.62703e9i −0.783935 + 1.89259i
\(358\) −4.81436e6 1.39692e8i −0.00554559 0.160909i
\(359\) −8.94944e7 8.94944e7i −0.102086 0.102086i 0.654219 0.756305i \(-0.272997\pi\)
−0.756305 + 0.654219i \(0.772997\pi\)
\(360\) −7.27415e7 + 8.95774e7i −0.0821719 + 0.101190i
\(361\) 4.28075e8 4.28075e8i 0.478900 0.478900i
\(362\) −9.40270e8 8.77618e8i −1.04177 0.972357i
\(363\) −3.52094e8 1.45842e8i −0.386354 0.160033i
\(364\) −1.43293e9 + 7.12802e8i −1.55729 + 0.774665i
\(365\) 6.03587e7 + 1.45719e8i 0.0649703 + 0.156852i
\(366\) −8.11958e8 + 3.69584e8i −0.865665 + 0.394030i
\(367\) 3.18809e8i 0.336666i 0.985730 + 0.168333i \(0.0538384\pi\)
−0.985730 + 0.168333i \(0.946162\pi\)
\(368\) −1.02079e9 7.72145e8i −1.06775 0.807665i
\(369\) 1.26978e9i 1.31564i
\(370\) −3.83958e7 8.43538e7i −0.0394074 0.0865762i
\(371\) 6.29563e8 + 1.51990e9i 0.640075 + 1.54528i
\(372\) 9.06279e8 + 3.04156e8i 0.912771 + 0.306335i
\(373\) 2.02626e8 + 8.39305e7i 0.202169 + 0.0837411i 0.481470 0.876462i \(-0.340103\pi\)
−0.279301 + 0.960203i \(0.590103\pi\)
\(374\) 9.40281e8 1.00741e9i 0.929409 0.995759i
\(375\) 2.26841e8 2.26841e8i 0.222132 0.222132i
\(376\) −6.05200e8 + 3.27526e8i −0.587140 + 0.317752i
\(377\) 7.28251e8 + 7.28251e8i 0.699981 + 0.699981i
\(378\) 4.16523e8 1.43551e7i 0.396659 0.0136705i
\(379\) −5.37813e8 + 1.29840e9i −0.507451 + 1.22510i 0.437895 + 0.899026i \(0.355724\pi\)
−0.945346 + 0.326069i \(0.894276\pi\)
\(380\) 4.84349e7 + 4.21814e7i 0.0452809 + 0.0394347i
\(381\) −7.61247e8 + 3.15319e8i −0.705160 + 0.292087i
\(382\) 1.61208e9 + 6.03572e8i 1.47967 + 0.553997i
\(383\) 2.96534e8 0.269699 0.134849 0.990866i \(-0.456945\pi\)
0.134849 + 0.990866i \(0.456945\pi\)
\(384\) 8.58557e8 1.41860e9i 0.773766 1.27850i
\(385\) −1.52434e8 −0.136135
\(386\) −1.38703e9 5.19310e8i −1.22752 0.459590i
\(387\) −5.02388e8 + 2.08096e8i −0.440607 + 0.182505i
\(388\) −1.47791e9 1.28710e9i −1.28451 1.11867i
\(389\) 3.45031e8 8.32980e8i 0.297191 0.717482i −0.702791 0.711397i \(-0.748063\pi\)
0.999981 0.00608511i \(-0.00193696\pi\)
\(390\) −2.82518e8 + 9.73673e6i −0.241168 + 0.00831165i
\(391\) −1.34728e9 1.34728e9i −1.13983 1.13983i
\(392\) −3.10666e8 + 1.68128e8i −0.260491 + 0.140974i
\(393\) −2.40894e9 + 2.40894e9i −2.00194 + 2.00194i
\(394\) −3.61945e8 + 3.87783e8i −0.298130 + 0.319413i
\(395\) 7.76594e7 + 3.21676e7i 0.0634022 + 0.0262620i
\(396\) −1.63453e9 5.48566e8i −1.32270 0.443910i
\(397\) 1.15407e8 + 2.78618e8i 0.0925692 + 0.223482i 0.963382 0.268133i \(-0.0864068\pi\)
−0.870813 + 0.491615i \(0.836407\pi\)
\(398\) −7.56803e8 1.66266e9i −0.601717 1.32194i
\(399\) 1.22640e9i 0.966557i
\(400\) −7.63560e8 + 1.00944e9i −0.596531 + 0.788627i
\(401\) 8.02031e8i 0.621135i −0.950551 0.310567i \(-0.899481\pi\)
0.950551 0.310567i \(-0.100519\pi\)
\(402\) −9.34368e7 + 4.25301e7i −0.0717343 + 0.0326517i
\(403\) 4.94905e8 + 1.19481e9i 0.376664 + 0.909347i
\(404\) 9.49124e8 4.72136e8i 0.716124 0.356231i
\(405\) −9.29894e7 3.85175e7i −0.0695570 0.0288114i
\(406\) 7.27231e8 + 6.78774e8i 0.539301 + 0.503366i
\(407\) 9.79194e8 9.79194e8i 0.719927 0.719927i
\(408\) 1.55604e9 1.91618e9i 1.13425 1.39678i
\(409\) −9.82334e8 9.82334e8i −0.709949 0.709949i 0.256575 0.966524i \(-0.417406\pi\)
−0.966524 + 0.256575i \(0.917406\pi\)
\(410\) 5.41988e6 + 1.57261e8i 0.00388370 + 0.112688i
\(411\) 5.31736e8 1.28372e9i 0.377790 0.912065i
\(412\) 1.68489e8 + 2.44150e9i 0.118695 + 1.71996i
\(413\) 1.96176e9 8.12589e8i 1.37032 0.567604i
\(414\) −8.35863e8 + 2.23251e9i −0.578940 + 1.54630i
\(415\) 3.40681e7 0.0233981
\(416\) 2.21003e9 3.84495e8i 1.50512 0.261857i
\(417\) 3.14708e9 2.12536
\(418\) −3.36488e8 + 8.98729e8i −0.225348 + 0.601883i
\(419\) −1.78398e8 + 7.38949e7i −0.118479 + 0.0490756i −0.441135 0.897441i \(-0.645424\pi\)
0.322656 + 0.946516i \(0.395424\pi\)
\(420\) −2.72399e8 + 1.87983e7i −0.179404 + 0.0123807i
\(421\) 4.80189e8 1.15928e9i 0.313635 0.757183i −0.685929 0.727669i \(-0.740604\pi\)
0.999564 0.0295145i \(-0.00939611\pi\)
\(422\) 8.31054e7 + 2.41136e9i 0.0538314 + 1.56195i
\(423\) 9.06270e8 + 9.06270e8i 0.582192 + 0.582192i
\(424\) −2.37892e8 2.29358e9i −0.151565 1.46128i
\(425\) −1.33230e9 + 1.33230e9i −0.841862 + 0.841862i
\(426\) 2.24877e9 + 2.09893e9i 1.40933 + 1.31542i
\(427\) −1.07699e9 4.46105e8i −0.669446 0.277294i
\(428\) 1.00396e9 + 2.01825e9i 0.618963 + 1.24429i
\(429\) −1.61635e9 3.90221e9i −0.988405 2.38622i
\(430\) 6.13319e7 2.79168e7i 0.0372004 0.0169327i
\(431\) 3.72987e8i 0.224400i −0.993686 0.112200i \(-0.964210\pi\)
0.993686 0.112200i \(-0.0357897\pi\)
\(432\) −5.65288e8 1.47294e8i −0.337347 0.0879007i
\(433\) 1.88188e9i 1.11400i 0.830514 + 0.556998i \(0.188047\pi\)
−0.830514 + 0.556998i \(0.811953\pi\)
\(434\) 5.17496e8 + 1.13692e9i 0.303874 + 0.667597i
\(435\) 6.72413e7 + 1.62335e8i 0.0391673 + 0.0945582i
\(436\) 1.19456e8 3.55938e8i 0.0690251 0.205671i
\(437\) 1.22586e9 + 5.07768e8i 0.702678 + 0.291059i
\(438\) −2.88033e9 + 3.08596e9i −1.63788 + 1.75481i
\(439\) −1.34569e9 + 1.34569e9i −0.759136 + 0.759136i −0.976165 0.217029i \(-0.930363\pi\)
0.217029 + 0.976165i \(0.430363\pi\)
\(440\) 2.04776e8 + 6.09624e7i 0.114603 + 0.0341175i
\(441\) 4.65213e8 + 4.65213e8i 0.258296 + 0.258296i
\(442\) 3.33735e9 1.15019e8i 1.83833 0.0633567i
\(443\) −3.53134e8 + 8.52540e8i −0.192986 + 0.465909i −0.990521 0.137364i \(-0.956137\pi\)
0.797535 + 0.603273i \(0.206137\pi\)
\(444\) 1.62906e9 1.87057e9i 0.883276 1.01422i
\(445\) −2.23961e8 + 9.27679e7i −0.120480 + 0.0499042i
\(446\) −8.83705e8 3.30863e8i −0.471667 0.176594i
\(447\) 1.88408e9 0.997754
\(448\) 2.12062e9 4.44690e8i 1.11427 0.233660i
\(449\) −2.44887e8 −0.127675 −0.0638373 0.997960i \(-0.520334\pi\)
−0.0638373 + 0.997960i \(0.520334\pi\)
\(450\) 2.20769e9 + 8.26570e8i 1.14208 + 0.427598i
\(451\) −2.17214e9 + 8.99729e8i −1.11499 + 0.461842i
\(452\) −1.49954e9 + 1.72185e9i −0.763788 + 0.877021i
\(453\) −5.13764e8 + 1.24034e9i −0.259669 + 0.626896i
\(454\) 1.17459e9 4.04813e7i 0.589103 0.0203030i
\(455\) −2.61195e8 2.61195e8i −0.129995 0.129995i
\(456\) −4.90470e8 + 1.64752e9i −0.242234 + 0.813680i
\(457\) 2.23799e9 2.23799e9i 1.09686 1.09686i 0.102087 0.994775i \(-0.467448\pi\)
0.994775 0.102087i \(-0.0325521\pi\)
\(458\) −4.87921e8 + 5.22753e8i −0.237313 + 0.254254i
\(459\) −8.03407e8 3.32782e8i −0.387785 0.160626i
\(460\) 9.39915e7 2.80062e8i 0.0450232 0.134153i
\(461\) −8.06327e8 1.94665e9i −0.383317 0.925409i −0.991320 0.131474i \(-0.958029\pi\)
0.608003 0.793935i \(-0.291971\pi\)
\(462\) −1.69013e9 3.71315e9i −0.797397 1.75184i
\(463\) 5.07475e8i 0.237619i 0.992917 + 0.118810i \(0.0379078\pi\)
−0.992917 + 0.118810i \(0.962092\pi\)
\(464\) −7.05485e8 1.20269e9i −0.327850 0.558908i
\(465\) 2.20639e8i 0.101765i
\(466\) −2.25283e9 + 1.02544e9i −1.03128 + 0.469416i
\(467\) −5.58457e8 1.34824e9i −0.253735 0.612571i 0.744764 0.667327i \(-0.232562\pi\)
−0.998500 + 0.0547562i \(0.982562\pi\)
\(468\) −1.86080e9 3.74073e9i −0.839150 1.68693i
\(469\) −1.23936e8 5.13359e7i −0.0554743 0.0229782i
\(470\) −1.16109e8 1.08372e8i −0.0515849 0.0481477i
\(471\) 1.05742e9 1.05742e9i 0.466310 0.466310i
\(472\) −2.96036e9 + 3.07052e8i −1.29583 + 0.134405i
\(473\) 7.11953e8 + 7.11953e8i 0.309341 + 0.309341i
\(474\) 7.74882e7 + 2.24837e9i 0.0334204 + 0.969714i
\(475\) 5.02123e8 1.21223e9i 0.214972 0.518989i
\(476\) 3.21782e9 2.22063e8i 1.36753 0.0943738i
\(477\) −3.96777e9 + 1.64350e9i −1.67391 + 0.693356i
\(478\) 1.59356e8 4.25626e8i 0.0667378 0.178250i
\(479\) 2.56546e7 0.0106657 0.00533286 0.999986i \(-0.498302\pi\)
0.00533286 + 0.999986i \(0.498302\pi\)
\(480\) 3.73452e8 + 8.36862e7i 0.154131 + 0.0345390i
\(481\) 3.35569e9 1.37491
\(482\) 1.07024e9 2.85852e9i 0.435330 1.16273i
\(483\) −5.21141e9 + 2.15864e9i −2.10446 + 0.871695i
\(484\) 4.80551e7 + 6.96347e8i 0.0192655 + 0.279169i
\(485\) 1.73100e8 4.17901e8i 0.0688971 0.166332i
\(486\) −1.23171e8 3.57388e9i −0.0486722 1.41225i
\(487\) −1.03856e9 1.03856e9i −0.407456 0.407456i 0.473395 0.880850i \(-0.343028\pi\)
−0.880850 + 0.473395i \(0.843028\pi\)
\(488\) 1.26840e9 + 1.03001e9i 0.494068 + 0.401209i
\(489\) 3.05880e9 3.05880e9i 1.18296 1.18296i
\(490\) −5.96018e7 5.56304e7i −0.0228862 0.0213612i
\(491\) −2.84918e9 1.18017e9i −1.08626 0.449945i −0.233561 0.972342i \(-0.575038\pi\)
−0.852702 + 0.522397i \(0.825038\pi\)
\(492\) −3.77064e9 + 1.87568e9i −1.42737 + 0.710037i
\(493\) −7.94315e8 1.91765e9i −0.298558 0.720782i
\(494\) −2.11654e9 + 9.63398e8i −0.789918 + 0.359552i
\(495\) 3.97936e8i 0.147467i
\(496\) −2.40510e8 1.73427e9i −0.0885008 0.638161i
\(497\) 4.01958e9i 1.46870i
\(498\) 3.77735e8 + 8.29867e8i 0.137052 + 0.301097i
\(499\) −2.96905e8 7.16793e8i −0.106971 0.258251i 0.861326 0.508053i \(-0.169635\pi\)
−0.968297 + 0.249802i \(0.919635\pi\)
\(500\) −5.57025e8 1.86943e8i −0.199287 0.0668828i
\(501\) 3.58175e9 + 1.48361e9i 1.27252 + 0.527094i
\(502\) −8.77625e8 + 9.40278e8i −0.309632 + 0.331736i
\(503\) −6.66288e8 + 6.66288e8i −0.233439 + 0.233439i −0.814127 0.580687i \(-0.802784\pi\)
0.580687 + 0.814127i \(0.302784\pi\)
\(504\) −1.92074e9 3.54913e9i −0.668285 1.23485i
\(505\) 1.73007e8 + 1.73007e8i 0.0597783 + 0.0597783i
\(506\) 4.41128e9 1.52031e8i 1.51369 0.0521682i
\(507\) 2.23864e9 5.40455e9i 0.762880 1.84175i
\(508\) 1.13805e9 + 9.91112e8i 0.385156 + 0.335428i
\(509\) −2.94186e9 + 1.21856e9i −0.988802 + 0.409575i −0.817679 0.575674i \(-0.804740\pi\)
−0.171123 + 0.985250i \(0.554740\pi\)
\(510\) 5.33548e8 + 1.99763e8i 0.178106 + 0.0666836i
\(511\) −5.51600e9 −1.82874
\(512\) −3.02663e9 2.50705e8i −0.996587 0.0825502i
\(513\) 6.05583e8 0.198044
\(514\) −1.08238e9 4.05249e8i −0.351569 0.131629i
\(515\) −5.21853e8 + 2.16159e8i −0.168354 + 0.0697344i
\(516\) 1.36005e9 + 1.18446e9i 0.435795 + 0.379529i
\(517\) 9.08143e8 2.19245e9i 0.289026 0.697771i
\(518\) 3.23935e9 1.11641e8i 1.02401 0.0352916i
\(519\) 4.26436e9 + 4.26436e9i 1.33896 + 1.33896i
\(520\) 2.46425e8 + 4.55343e8i 0.0768551 + 0.142012i
\(521\) −8.33749e8 + 8.33749e8i −0.258287 + 0.258287i −0.824357 0.566070i \(-0.808463\pi\)
0.566070 + 0.824357i \(0.308463\pi\)
\(522\) −1.77197e9 + 1.89847e9i −0.545268 + 0.584194i
\(523\) 3.16637e9 + 1.31156e9i 0.967846 + 0.400895i 0.809910 0.586554i \(-0.199516\pi\)
0.157936 + 0.987449i \(0.449516\pi\)
\(524\) 5.91532e9 + 1.98524e9i 1.79605 + 0.602773i
\(525\) 2.13464e9 + 5.15347e9i 0.643823 + 1.55433i
\(526\) 4.26087e8 + 9.36094e8i 0.127658 + 0.280459i
\(527\) 2.60639e9i 0.775714i
\(528\) 7.85502e8 + 5.66409e9i 0.232235 + 1.67460i
\(529\) 2.69803e9i 0.792413i
\(530\) 4.84388e8 2.20482e8i 0.141328 0.0643290i
\(531\) 2.12130e9 + 5.12127e9i 0.614853 + 1.48439i
\(532\) −2.01111e9 + 1.00041e9i −0.579088 + 0.288064i
\(533\) −5.26363e9 2.18027e9i −1.50571 0.623684i
\(534\) −4.74294e9 4.42691e9i −1.34789 1.25807i
\(535\) −3.67887e8 + 3.67887e8i −0.103867 + 0.103867i
\(536\) 1.45962e8 + 1.18529e8i 0.0409414 + 0.0332466i
\(537\) 6.10525e8 + 6.10525e8i 0.170135 + 0.170135i
\(538\) 1.14056e8 + 3.30942e9i 0.0315777 + 0.916249i
\(539\) 4.66175e8 1.12545e9i 0.128230 0.309573i
\(540\) −9.28239e6 1.34507e8i −0.00253677 0.0367593i
\(541\) 5.09983e9 2.11242e9i 1.38473 0.573574i 0.438988 0.898493i \(-0.355337\pi\)
0.945742 + 0.324920i \(0.105337\pi\)
\(542\) −6.80966e8 + 1.81880e9i −0.183708 + 0.490667i
\(543\) 7.94512e9 2.12962
\(544\) −4.41156e9 9.88578e8i −1.17489 0.263278i
\(545\) 8.66552e7 0.0229301
\(546\) 3.46643e9 9.25850e9i 0.911397 2.43426i
\(547\) −2.28637e9 + 9.47047e8i −0.597299 + 0.247409i −0.660787 0.750573i \(-0.729777\pi\)
0.0634885 + 0.997983i \(0.479777\pi\)
\(548\) −2.53886e9 + 1.75208e8i −0.659033 + 0.0454801i
\(549\) 1.16458e9 2.81154e9i 0.300376 0.725172i
\(550\) −1.50341e8 4.36224e9i −0.0385308 1.11799i
\(551\) 1.02210e9 + 1.02210e9i 0.260292 + 0.260292i
\(552\) 7.86418e9 8.15682e8i 1.99006 0.206412i
\(553\) −2.07868e9 + 2.07868e9i −0.522697 + 0.522697i
\(554\) −3.32283e9 3.10143e9i −0.830279 0.774956i
\(555\) 5.28929e8 + 2.19090e8i 0.131332 + 0.0543997i
\(556\) −2.56717e9 5.16073e9i −0.633421 1.27335i
\(557\) −9.69891e7 2.34152e8i −0.0237810 0.0574124i 0.911543 0.411205i \(-0.134892\pi\)
−0.935324 + 0.353792i \(0.884892\pi\)
\(558\) −2.96797e9 + 1.35095e9i −0.723169 + 0.329169i
\(559\) 2.43986e9i 0.590776i
\(560\) 2.53030e8 + 4.31357e8i 0.0608855 + 0.103796i
\(561\) 8.51241e9i 2.03555i
\(562\) 3.66413e8 + 8.04992e8i 0.0870750 + 0.191300i
\(563\) 5.49072e8 + 1.32558e9i 0.129673 + 0.313059i 0.975359 0.220622i \(-0.0708086\pi\)
−0.845686 + 0.533680i \(0.820809\pi\)
\(564\) 1.35247e9 4.02989e9i 0.317432 0.945836i
\(565\) −4.86876e8 2.01671e8i −0.113566 0.0470406i
\(566\) −9.96575e8 + 1.06772e9i −0.231022 + 0.247514i
\(567\) 2.48901e9 2.48901e9i 0.573438 0.573438i
\(568\) 1.60753e9 5.39980e9i 0.368079 1.23640i
\(569\) −2.01268e9 2.01268e9i −0.458017 0.458017i 0.439987 0.898004i \(-0.354983\pi\)
−0.898004 + 0.439987i \(0.854983\pi\)
\(570\) −3.96511e8 + 1.36654e7i −0.0896796 + 0.00309073i
\(571\) −2.32202e9 + 5.60585e9i −0.521962 + 1.26013i 0.414720 + 0.909949i \(0.363879\pi\)
−0.936683 + 0.350179i \(0.886121\pi\)
\(572\) −5.08052e9 + 5.83372e9i −1.13507 + 1.30334i
\(573\) −9.82382e9 + 4.06916e9i −2.18142 + 0.903573i
\(574\) −5.15368e9 1.92956e9i −1.13743 0.425860i
\(575\) −6.03500e9 −1.32385
\(576\) 1.16088e9 + 5.53598e9i 0.253111 + 1.20702i
\(577\) −8.58343e9 −1.86014 −0.930070 0.367382i \(-0.880254\pi\)
−0.930070 + 0.367382i \(0.880254\pi\)
\(578\) −1.95504e9 7.31977e8i −0.421123 0.157670i
\(579\) 8.45235e9 3.50108e9i 1.80968 0.749595i
\(580\) 2.11353e8 2.42687e8i 0.0449791 0.0516473i
\(581\) −4.55945e8 + 1.10075e9i −0.0964486 + 0.232847i
\(582\) 1.20989e10 4.16979e8i 2.54400 0.0876767i
\(583\) 5.62287e9 + 5.62287e9i 1.17522 + 1.17522i
\(584\) 7.41006e9 + 2.20599e9i 1.53949 + 0.458310i
\(585\) 6.81862e8 6.81862e8i 0.140816 0.140816i
\(586\) −3.33661e9 + 3.57481e9i −0.684958 + 0.733856i
\(587\) 5.98229e9 + 2.47795e9i 1.22077 + 0.505660i 0.897655 0.440699i \(-0.145269\pi\)
0.323117 + 0.946359i \(0.395269\pi\)
\(588\) 6.94260e8 2.06865e9i 0.140832 0.419630i
\(589\) 6.94595e8 + 1.67690e9i 0.140065 + 0.338146i
\(590\) −2.84580e8 6.25209e8i −0.0570456 0.125327i
\(591\) 3.27670e9i 0.652951i
\(592\) −4.39631e9 1.14552e9i −0.870889 0.226923i
\(593\) 1.14477e8i 0.0225438i 0.999936 + 0.0112719i \(0.00358803\pi\)
−0.999936 + 0.0112719i \(0.996412\pi\)
\(594\) 1.83351e9 8.34569e8i 0.358947 0.163384i
\(595\) 2.84890e8 + 6.87785e8i 0.0554456 + 0.133858i
\(596\) −1.53690e9 3.08960e9i −0.297361 0.597779i
\(597\) 1.04255e10 + 4.31838e9i 2.00533 + 0.830636i
\(598\) 7.81922e9 + 7.29821e9i 1.49523 + 1.39560i
\(599\) 4.03680e9 4.03680e9i 0.767439 0.767439i −0.210216 0.977655i \(-0.567417\pi\)
0.977655 + 0.210216i \(0.0674168\pi\)
\(600\) −8.06613e8 7.77675e9i −0.152453 1.46983i
\(601\) −5.28884e9 5.28884e9i −0.993802 0.993802i 0.00617937 0.999981i \(-0.498033\pi\)
−0.999981 + 0.00617937i \(0.998033\pi\)
\(602\) 8.11723e7 + 2.35527e9i 0.0151642 + 0.439999i
\(603\) 1.34015e8 3.23540e8i 0.0248910 0.0600922i
\(604\) 2.45305e9 1.69286e8i 0.452978 0.0312602i
\(605\) −1.48839e8 + 6.16511e7i −0.0273258 + 0.0113187i
\(606\) −2.29604e9 + 6.13252e9i −0.419108 + 1.11940i
\(607\) −8.74563e9 −1.58720 −0.793598 0.608443i \(-0.791795\pi\)
−0.793598 + 0.608443i \(0.791795\pi\)
\(608\) 3.10177e9 5.39635e8i 0.559689 0.0973728i
\(609\) −6.14498e9 −1.10245
\(610\) −1.32231e8 + 3.53177e8i −0.0235873 + 0.0629996i
\(611\) 5.31286e9 2.20066e9i 0.942288 0.390309i
\(612\) 5.79705e8 + 8.40027e9i 0.102230 + 1.48137i
\(613\) 1.30271e9 3.14502e9i 0.228421 0.551456i −0.767565 0.640971i \(-0.778532\pi\)
0.995985 + 0.0895150i \(0.0285317\pi\)
\(614\) −1.04103e8 3.02060e9i −0.0181498 0.526629i
\(615\) −6.87314e8 6.87314e8i −0.119149 0.119149i
\(616\) −4.71030e9 + 5.80049e9i −0.811924 + 0.999843i
\(617\) 4.47770e9 4.47770e9i 0.767463 0.767463i −0.210196 0.977659i \(-0.567410\pi\)
0.977659 + 0.210196i \(0.0674104\pi\)
\(618\) −1.10515e10 1.03151e10i −1.88349 1.75799i
\(619\) 3.80014e9 + 1.57407e9i 0.643995 + 0.266751i 0.680686 0.732575i \(-0.261682\pi\)
−0.0366914 + 0.999327i \(0.511682\pi\)
\(620\) 3.61813e8 1.79982e8i 0.0609696 0.0303289i
\(621\) −1.06591e9 2.57333e9i −0.178607 0.431197i
\(622\) 5.30559e9 2.41498e9i 0.884031 0.402389i
\(623\) 8.47778e9i 1.40467i
\(624\) −8.35944e9 + 1.10513e10i −1.37731 + 1.82083i
\(625\) 5.89972e9i 0.966610i
\(626\) −4.63757e8 1.01885e9i −0.0755581 0.165998i
\(627\) −2.26854e9 5.47673e9i −0.367544 0.887329i
\(628\) −2.59658e9 8.71437e8i −0.418353 0.140403i
\(629\) −6.24819e9 2.58809e9i −1.00110 0.414669i
\(630\) 6.35537e8 6.80907e8i 0.101263 0.108492i
\(631\) 5.30759e9 5.30759e9i 0.840997 0.840997i −0.147992 0.988989i \(-0.547281\pi\)
0.988989 + 0.147992i \(0.0472810\pi\)
\(632\) 3.62377e9 1.96113e9i 0.571019 0.309027i
\(633\) −1.05389e10 1.05389e10i −1.65151 1.65151i
\(634\) −3.44730e9 + 1.18808e8i −0.537238 + 0.0185154i
\(635\) −1.33293e8 + 3.21798e8i −0.0206585 + 0.0498741i
\(636\) 1.07414e10 + 9.35461e9i 1.65563 + 1.44187i
\(637\) 2.72723e9 1.12966e9i 0.418056 0.173164i
\(638\) 4.50315e9 + 1.68600e9i 0.686506 + 0.257031i
\(639\) −1.04933e10 −1.59096
\(640\) −1.67404e8 6.80669e8i −0.0252426 0.102637i
\(641\) −3.60633e9 −0.540832 −0.270416 0.962744i \(-0.587161\pi\)
−0.270416 + 0.962744i \(0.587161\pi\)
\(642\) −1.30404e10 4.88238e9i −1.94499 0.728214i
\(643\) −5.45540e9 + 2.25970e9i −0.809260 + 0.335206i −0.748659 0.662956i \(-0.769302\pi\)
−0.0606011 + 0.998162i \(0.519302\pi\)
\(644\) 7.79093e9 + 6.78504e9i 1.14945 + 1.00104i
\(645\) −1.59296e8 + 3.84574e8i −0.0233746 + 0.0564314i
\(646\) 4.68395e9 1.61429e8i 0.683595 0.0235595i
\(647\) −1.82400e9 1.82400e9i −0.264764 0.264764i 0.562222 0.826986i \(-0.309947\pi\)
−0.826986 + 0.562222i \(0.809947\pi\)
\(648\) −4.33910e9 + 2.34826e9i −0.626452 + 0.339027i
\(649\) 7.25754e9 7.25754e9i 1.04216 1.04216i
\(650\) 7.21707e9 7.73228e9i 1.03078 1.10436i
\(651\) −7.12888e9 2.95288e9i −1.01272 0.419481i
\(652\) −7.51112e9 2.52081e9i −1.06130 0.356183i
\(653\) 4.38425e9 + 1.05845e10i 0.616168 + 1.48756i 0.856121 + 0.516776i \(0.172868\pi\)
−0.239953 + 0.970785i \(0.577132\pi\)
\(654\) 9.60802e8 + 2.11084e9i 0.134311 + 0.295075i
\(655\) 1.44012e9i 0.200241i
\(656\) 6.15165e9 + 4.65322e9i 0.850801 + 0.643561i
\(657\) 1.43998e10i 1.98096i
\(658\) 5.05544e9 2.30111e9i 0.691781 0.314882i
\(659\) −2.80867e9 6.78073e9i −0.382298 0.922949i −0.991521 0.129950i \(-0.958518\pi\)
0.609223 0.792999i \(-0.291482\pi\)
\(660\) −1.18168e9 + 5.87817e8i −0.159991 + 0.0795863i
\(661\) 2.85761e9 + 1.18366e9i 0.384856 + 0.159413i 0.566719 0.823911i \(-0.308213\pi\)
−0.181863 + 0.983324i \(0.558213\pi\)
\(662\) 2.04822e9 + 1.91175e9i 0.274394 + 0.256110i
\(663\) −1.45860e10 + 1.45860e10i −1.94374 + 1.94374i
\(664\) 1.05272e9 1.29638e9i 0.139549 0.171847i
\(665\) −3.66586e8 3.66586e8i −0.0483392 0.0483392i
\(666\) 2.91445e8 + 8.45647e9i 0.0382294 + 1.10925i
\(667\) 2.54421e9 6.14227e9i 0.331981 0.801472i
\(668\) −4.88852e8 7.08375e9i −0.0634541 0.919487i
\(669\) 5.38517e9 2.23061e9i 0.695357 0.288026i
\(670\) −1.52166e7 + 4.06421e7i −0.00195459 + 0.00522053i
\(671\) −5.63470e9 −0.720016
\(672\) −7.70194e9 + 1.09463e10i −0.979057 + 1.39147i
\(673\) 1.12084e10 1.41740 0.708700 0.705510i \(-0.249282\pi\)
0.708700 + 0.705510i \(0.249282\pi\)
\(674\) −3.61400e9 + 9.65267e9i −0.454652 + 1.21433i
\(675\) −2.54472e9 + 1.05406e9i −0.318476 + 0.131917i
\(676\) −1.06888e10 + 7.37634e8i −1.33080 + 0.0918391i
\(677\) 2.76468e7 6.67452e7i 0.00342440 0.00826723i −0.922158 0.386813i \(-0.873576\pi\)
0.925582 + 0.378546i \(0.123576\pi\)
\(678\) −4.85803e8 1.40959e10i −0.0598626 1.73695i
\(679\) 1.11858e10 + 1.11858e10i 1.37127 + 1.37127i
\(680\) −1.07651e8 1.03789e9i −0.0131292 0.126581i
\(681\) −5.13358e9 + 5.13358e9i −0.622882 + 0.622882i
\(682\) 4.41399e9 + 4.11988e9i 0.532827 + 0.497324i
\(683\) 7.47948e9 + 3.09810e9i 0.898253 + 0.372069i 0.783548 0.621331i \(-0.213408\pi\)
0.114705 + 0.993400i \(0.463408\pi\)
\(684\) −2.61162e9 5.25009e9i −0.312043 0.627293i
\(685\) −2.24778e8 5.42663e8i −0.0267200 0.0645079i
\(686\) −6.16647e9 + 2.80683e9i −0.729294 + 0.331957i
\(687\) 4.41718e9i 0.519752i
\(688\) 8.32888e8 3.19647e9i 0.0975050 0.374207i
\(689\) 1.92695e10i 2.24442i
\(690\) 7.55984e8 + 1.66086e9i 0.0876074 + 0.192469i
\(691\) 5.37320e8 + 1.29721e9i 0.0619526 + 0.149567i 0.951824 0.306644i \(-0.0992062\pi\)
−0.889872 + 0.456211i \(0.849206\pi\)
\(692\) 3.51432e9 1.04714e10i 0.403153 1.20126i
\(693\) 1.28574e10 + 5.32571e9i 1.46753 + 0.607870i
\(694\) −3.09472e9 + 3.31565e9i −0.351450 + 0.376540i
\(695\) 9.40699e8 9.40699e8i 0.106293 0.106293i
\(696\) 8.25502e9 + 2.45754e9i 0.928081 + 0.276292i
\(697\) 8.11918e9 + 8.11918e9i 0.908233 + 0.908233i
\(698\) 1.08015e10 3.72263e8i 1.20223 0.0414339i
\(699\) 5.85122e9 1.41261e10i 0.648002 1.56441i
\(700\) 6.70960e9 7.70431e9i 0.739356 0.848967i
\(701\) −1.60182e10 + 6.63495e9i −1.75631 + 0.727485i −0.759250 + 0.650799i \(0.774434\pi\)
−0.997055 + 0.0766862i \(0.975566\pi\)
\(702\) 4.57174e9 + 1.71168e9i 0.498772 + 0.186742i
\(703\) 4.70969e9 0.511268
\(704\) 8.64747e9 5.90847e9i 0.934081 0.638220i
\(705\) 9.81099e8 0.105451
\(706\) −4.86327e8 1.82083e8i −0.0520130 0.0194739i
\(707\) −7.90529e9 + 3.27448e9i −0.841298 + 0.348477i
\(708\) 1.20742e10 1.38642e10i 1.27862 1.46818i
\(709\) −4.09324e9 + 9.88196e9i −0.431326 + 1.04131i 0.547535 + 0.836783i \(0.315566\pi\)
−0.978860 + 0.204530i \(0.934434\pi\)
\(710\) 1.29958e9 4.47890e7i 0.136270 0.00469642i
\(711\) −5.42649e9 5.42649e9i −0.566207 0.566207i
\(712\) −3.39049e9 + 1.13888e10i −0.352032 + 1.18250i
\(713\) 5.90315e9 5.90315e9i 0.609917 0.609917i
\(714\) −1.35950e10 + 1.45656e10i −1.39777 + 1.49756i
\(715\) −1.64956e9 6.83272e8i −0.168771 0.0699072i
\(716\) 5.03143e8 1.49919e9i 0.0512267 0.152638i
\(717\) 1.07435e9 + 2.59371e9i 0.108850 + 0.262787i
\(718\) −5.93209e8 1.30325e9i −0.0598098 0.131399i
\(719\) 1.50764e10i 1.51268i 0.654181 + 0.756338i \(0.273014\pi\)
−0.654181 + 0.756338i \(0.726986\pi\)
\(720\) −1.12608e9 + 6.60547e8i −0.112436 + 0.0659538i
\(721\) 1.97541e10i 1.96283i
\(722\) 6.23380e9 2.83748e9i 0.616415 0.280577i
\(723\) 7.21537e9 + 1.74194e10i 0.710027 + 1.71416i
\(724\) −6.48108e9 1.30288e10i −0.634691 1.27591i
\(725\) −6.07398e9 2.51592e9i −0.591957 0.245197i
\(726\) −3.15203e9 2.94201e9i −0.305712 0.285342i
\(727\) −3.19467e9 + 3.19467e9i −0.308358 + 0.308358i −0.844272 0.535914i \(-0.819967\pi\)
0.535914 + 0.844272i \(0.319967\pi\)
\(728\) −1.80102e10 + 1.86804e9i −1.73005 + 0.179443i
\(729\) 1.03511e10 + 1.03511e10i 0.989553 + 0.989553i
\(730\) 6.14632e7 + 1.78339e9i 0.00584770 + 0.169675i
\(731\) 1.88174e9 4.54293e9i 0.178176 0.430156i
\(732\) −1.00692e10 + 6.94877e8i −0.948867 + 0.0654816i
\(733\) 7.27284e9 3.01251e9i 0.682088 0.282530i −0.0146115 0.999893i \(-0.504651\pi\)
0.696699 + 0.717363i \(0.254651\pi\)
\(734\) −1.26471e9 + 3.37792e9i −0.118047 + 0.315292i
\(735\) 5.03625e8 0.0467844
\(736\) −7.75264e9 1.22307e10i −0.716766 1.13078i
\(737\) −6.48418e8 −0.0596649
\(738\) 5.03721e9 1.34539e10i 0.461309 1.23212i
\(739\) 1.20771e10 5.00251e9i 1.10080 0.455966i 0.243039 0.970017i \(-0.421856\pi\)
0.857760 + 0.514051i \(0.171856\pi\)
\(740\) −7.21903e7 1.04608e9i −0.00654889 0.0948973i
\(741\) 5.49723e9 1.32715e10i 0.496341 1.19827i
\(742\) 6.41084e8 + 1.86015e10i 0.0576104 + 1.67160i
\(743\) −1.00649e10 1.00649e10i −0.900221 0.900221i 0.0952340 0.995455i \(-0.469640\pi\)
−0.995455 + 0.0952340i \(0.969640\pi\)
\(744\) 8.39584e9 + 6.81785e9i 0.747410 + 0.606935i
\(745\) 5.63174e8 5.63174e8i 0.0498995 0.0498995i
\(746\) 1.81396e9 + 1.69309e9i 0.159971 + 0.149312i
\(747\) −2.87355e9 1.19026e9i −0.252230 0.104477i
\(748\) 1.39590e10 6.94383e9i 1.21955 0.606657i
\(749\) −6.96295e9 1.68101e10i −0.605490 1.46178i
\(750\) 3.30335e9 1.50360e9i 0.285917 0.130142i
\(751\) 1.89780e10i 1.63497i 0.575948 + 0.817486i \(0.304633\pi\)
−0.575948 + 0.817486i \(0.695367\pi\)
\(752\) −7.71164e9 + 1.06946e9i −0.661279 + 0.0917068i
\(753\) 7.94519e9i 0.678144i
\(754\) 4.82718e9 + 1.06051e10i 0.410104 + 0.900979i
\(755\) 2.17181e8 + 5.24321e8i 0.0183657 + 0.0443387i
\(756\) 4.47019e9 + 1.50024e9i 0.376270 + 0.126280i
\(757\) 9.59431e9 + 3.97409e9i 0.803856 + 0.332968i 0.746500 0.665386i \(-0.231733\pi\)
0.0573564 + 0.998354i \(0.481733\pi\)
\(758\) −1.08491e10 + 1.16236e10i −0.904795 + 0.969387i
\(759\) −1.92796e10 + 1.92796e10i −1.60049 + 1.60049i
\(760\) 3.45855e8 + 6.39070e8i 0.0285790 + 0.0528081i
\(761\) −8.59159e9 8.59159e9i −0.706687 0.706687i 0.259150 0.965837i \(-0.416558\pi\)
−0.965837 + 0.259150i \(0.916558\pi\)
\(762\) −9.31659e9 + 3.21089e8i −0.762807 + 0.0262895i
\(763\) −1.15973e9 + 2.79985e9i −0.0945197 + 0.228191i
\(764\) 1.46864e10 + 1.27902e10i 1.19148 + 1.03765i
\(765\) −1.79549e9 + 7.43718e8i −0.145000 + 0.0600611i
\(766\) 3.14190e9 + 1.17634e9i 0.252576 + 0.0945657i
\(767\) 2.48715e10 1.99030
\(768\) 1.47243e10 1.16248e10i 1.17293 0.926022i
\(769\) 6.96732e9 0.552489 0.276244 0.961087i \(-0.410910\pi\)
0.276244 + 0.961087i \(0.410910\pi\)
\(770\) −1.61510e9 6.04703e8i −0.127492 0.0477336i
\(771\) 6.59589e9 2.73211e9i 0.518302 0.214688i
\(772\) −1.26361e10 1.10046e10i −0.988442 0.860824i
\(773\) −7.52329e9 + 1.81628e10i −0.585840 + 1.41434i 0.301606 + 0.953433i \(0.402477\pi\)
−0.887446 + 0.460911i \(0.847523\pi\)
\(774\) −6.14853e9 + 2.11904e8i −0.476626 + 0.0164265i
\(775\) −5.83752e9 5.83752e9i −0.450477 0.450477i
\(776\) −1.05532e10 1.95002e10i −0.810718 1.49804i
\(777\) −1.41576e10 + 1.41576e10i −1.08272 + 1.08272i
\(778\) 6.96017e9 7.45704e9i 0.529897 0.567725i
\(779\) −7.38747e9 3.05999e9i −0.559905 0.231920i
\(780\) −3.03202e9 1.01758e9i −0.228771 0.0767778i
\(781\) 7.43521e9 + 1.79502e10i 0.558489 + 1.34831i
\(782\) −8.93037e9 1.96196e10i −0.667799 1.46712i
\(783\) 3.03432e9i 0.225889i
\(784\) −3.95860e9 + 5.48983e8i −0.293383 + 0.0406867i
\(785\) 6.32151e8i 0.0466420i
\(786\) −3.50799e10 + 1.59675e10i −2.57679 + 1.17289i
\(787\) −8.86625e9 2.14050e10i −0.648378 1.56532i −0.815100 0.579320i \(-0.803318\pi\)
0.166722 0.986004i \(-0.446682\pi\)
\(788\) −5.37328e9 + 2.67290e9i −0.391199 + 0.194599i
\(789\) −5.86965e9 2.43129e9i −0.425444 0.176225i
\(790\) 6.95226e8 + 6.48902e8i 0.0501685 + 0.0468257i
\(791\) 1.30320e10 1.30320e10i 0.936255 0.936255i
\(792\) −1.51424e10 1.22964e10i −1.08307 0.879511i
\(793\) −9.65504e9 9.65504e9i −0.687540 0.687540i
\(794\) 1.17519e8 + 3.40989e9i 0.00833176 + 0.241751i
\(795\) −1.25809e9 + 3.03729e9i −0.0888026 + 0.214388i
\(796\) −1.42291e9 2.06188e10i −0.0999959 1.44900i
\(797\) 1.48524e10 6.15206e9i 1.03918 0.430444i 0.203165 0.979145i \(-0.434877\pi\)
0.836019 + 0.548701i \(0.184877\pi\)
\(798\) 4.86510e9 1.29942e10i 0.338908 0.905192i
\(799\) −1.15896e10 −0.803814
\(800\) −1.20947e10 + 7.66644e9i −0.835179 + 0.529394i
\(801\) 2.21316e10 1.52160
\(802\) 3.18164e9 8.49786e9i 0.217791 0.581700i
\(803\) −2.46327e10 + 1.02032e10i −1.67884 + 0.695397i
\(804\) −1.15872e9 + 7.99635e7i −0.0786288 + 0.00542620i
\(805\) −9.12509e8 + 2.20299e9i −0.0616526 + 0.148843i
\(806\) 5.03961e8 + 1.46227e10i 0.0339019 + 0.983686i
\(807\) −1.44639e10 1.44639e10i −0.968785 0.968785i
\(808\) 1.19293e10 1.23732e9i 0.795566 0.0825170i
\(809\) 5.65055e8 5.65055e8i 0.0375207 0.0375207i −0.688098 0.725618i \(-0.741554\pi\)
0.725618 + 0.688098i \(0.241554\pi\)
\(810\) −8.32464e8 7.76996e8i −0.0550387 0.0513714i
\(811\) −5.91335e9 2.44939e9i −0.389279 0.161244i 0.179455 0.983766i \(-0.442567\pi\)
−0.568734 + 0.822522i \(0.692567\pi\)
\(812\) 5.01264e9 + 1.00768e10i 0.328564 + 0.660506i
\(813\) −4.59093e9 1.10835e10i −0.299629 0.723368i
\(814\) 1.42594e10 6.49054e9i 0.926652 0.421789i
\(815\) 1.82862e9i 0.118324i
\(816\) 2.40884e10 1.41300e10i 1.55200 0.910389i
\(817\) 3.42432e9i 0.219683i
\(818\) −6.51135e9 1.43051e10i −0.415944 0.913809i
\(819\) 1.29055e10 + 3.11567e10i 0.820884 + 1.98179i
\(820\) −5.66426e8 + 1.68775e9i −0.0358752 + 0.106896i
\(821\) −1.10478e10 4.57617e9i −0.696749 0.288603i 0.00605955 0.999982i \(-0.498071\pi\)
−0.702809 + 0.711379i \(0.748071\pi\)
\(822\) 1.07265e10 1.14922e10i 0.673606 0.721694i
\(823\) 1.22369e10 1.22369e10i 0.765197 0.765197i −0.212060 0.977257i \(-0.568017\pi\)
0.977257 + 0.212060i \(0.0680172\pi\)
\(824\) −7.90018e9 + 2.65372e10i −0.491917 + 1.65238i
\(825\) 1.90653e10 + 1.90653e10i 1.18210 + 1.18210i
\(826\) 2.40092e10 8.27458e8i 1.48234 0.0510877i
\(827\) −4.74499e9 + 1.14554e10i −0.291720 + 0.704275i −0.999999 0.00165837i \(-0.999472\pi\)
0.708278 + 0.705933i \(0.249472\pi\)
\(828\) −1.77127e10 + 2.03386e10i −1.08437 + 1.24513i
\(829\) −5.95927e9 + 2.46841e9i −0.363289 + 0.150479i −0.556858 0.830607i \(-0.687993\pi\)
0.193570 + 0.981087i \(0.437993\pi\)
\(830\) 3.60967e8 + 1.35148e8i 0.0219126 + 0.00820417i
\(831\) 2.80774e10 1.69728
\(832\) 2.49415e10 + 4.69327e9i 1.50138 + 0.282517i
\(833\) −5.94928e9 −0.356621
\(834\) 3.33447e10 + 1.24844e10i 1.99042 + 0.745223i
\(835\) 1.51410e9 6.27159e8i 0.0900017 0.0372799i
\(836\) −7.13048e9 + 8.18758e9i −0.422082 + 0.484656i
\(837\) 1.45810e9 3.52016e9i 0.0859503 0.207502i
\(838\) −2.18334e9 + 7.52472e7i −0.128165 + 0.00441709i
\(839\) 6.93929e9 + 6.93929e9i 0.405647 + 0.405647i 0.880217 0.474571i \(-0.157397\pi\)
−0.474571 + 0.880217i \(0.657397\pi\)
\(840\) −2.96075e9 8.81423e8i −0.172355 0.0513106i
\(841\) −7.07622e9 + 7.07622e9i −0.410218 + 0.410218i
\(842\) 9.68665e9 1.03782e10i 0.559218 0.599140i
\(843\) −5.04759e9 2.09078e9i −0.290194 0.120202i
\(844\) −8.68526e9 + 2.58790e10i −0.497261 + 1.48166i
\(845\) −9.46329e8 2.28464e9i −0.0539565 0.130262i
\(846\) 6.00717e9 + 1.31975e10i 0.341093 + 0.749367i
\(847\) 5.63411e9i 0.318591i
\(848\) 6.57799e9 2.52451e10i 0.370432 1.42165i
\(849\) 9.02204e9i 0.505974i
\(850\) −1.94015e10 + 8.83108e9i −1.08360 + 0.493228i
\(851\) −8.28970e9 2.00131e10i −0.461090 1.11317i
\(852\) 1.55003e10 + 3.11599e10i 0.858621 + 1.72607i
\(853\) 1.05569e10 + 4.37283e9i 0.582393 + 0.241235i 0.654374 0.756171i \(-0.272932\pi\)
−0.0719809 + 0.997406i \(0.522932\pi\)
\(854\) −9.64152e9 8.99908e9i −0.529716 0.494420i
\(855\) 9.56989e8 9.56989e8i 0.0523631 0.0523631i
\(856\) 2.63109e9 + 2.53669e10i 0.143376 + 1.38232i
\(857\) 5.09015e9 + 5.09015e9i 0.276247 + 0.276247i 0.831609 0.555362i \(-0.187420\pi\)
−0.555362 + 0.831609i \(0.687420\pi\)
\(858\) −1.64593e9 4.77577e10i −0.0889621 2.58129i
\(859\) −1.14106e10 + 2.75475e10i −0.614230 + 1.48288i 0.244083 + 0.969754i \(0.421513\pi\)
−0.858313 + 0.513127i \(0.828487\pi\)
\(860\) 7.60583e8 5.24881e7i 0.0407758 0.00281395i
\(861\) 3.14058e10 1.30087e10i 1.67687 0.694581i
\(862\) 1.47963e9 3.95195e9i 0.0786824 0.210153i
\(863\) −7.81562e9 −0.413929 −0.206964 0.978348i \(-0.566358\pi\)
−0.206964 + 0.978348i \(0.566358\pi\)
\(864\) −5.40516e9 3.80313e9i −0.285109 0.200606i
\(865\) 2.54933e9 0.133928
\(866\) −7.46536e9 + 1.99393e10i −0.390606 + 1.04327i
\(867\) 1.19138e10 4.93484e9i 0.620843 0.257162i
\(868\) 9.72977e8 + 1.40990e10i 0.0504991 + 0.731761i
\(869\) −5.43771e9 + 1.31278e10i −0.281091 + 0.678613i
\(870\) 6.84717e7 + 1.98675e9i 0.00352528 + 0.102288i
\(871\) −1.11106e9 1.11106e9i −0.0569737 0.0569737i
\(872\) 2.67769e9 3.29744e9i 0.136758 0.168410i
\(873\) −2.92010e10 + 2.92010e10i −1.48542 + 1.48542i
\(874\) 1.09742e10 + 1.02430e10i 0.556011 + 0.518963i
\(875\) 4.38161e9 + 1.81492e9i 0.221109 + 0.0915862i
\(876\) −4.27603e10 + 2.12708e10i −2.14920 + 1.06910i
\(877\) −1.44551e10 3.48978e10i −0.723641 1.74702i −0.662703 0.748882i \(-0.730591\pi\)
−0.0609381 0.998142i \(-0.519409\pi\)
\(878\) −1.95965e10 + 8.91985e9i −0.977119 + 0.444761i
\(879\) 3.02065e10i 1.50017i
\(880\) 1.92786e9 + 1.45827e9i 0.0953642 + 0.0721352i
\(881\) 4.95413e9i 0.244091i −0.992525 0.122046i \(-0.961055\pi\)
0.992525 0.122046i \(-0.0389454\pi\)
\(882\) 3.08364e9 + 6.77462e9i 0.151330 + 0.332464i
\(883\) −2.21940e9 5.35811e9i −0.108486 0.261908i 0.860309 0.509774i \(-0.170271\pi\)
−0.968794 + 0.247866i \(0.920271\pi\)
\(884\) 3.58170e10 + 1.20205e10i 1.74384 + 0.585249i
\(885\) 3.92029e9 + 1.62384e9i 0.190115 + 0.0787482i
\(886\) −7.12361e9 + 7.63215e9i −0.344098 + 0.368662i
\(887\) 7.81548e9 7.81548e9i 0.376030 0.376030i −0.493637 0.869668i \(-0.664333\pi\)
0.869668 + 0.493637i \(0.164333\pi\)
\(888\) 2.46811e10 1.33570e10i 1.18282 0.640125i
\(889\) −8.61345e9 8.61345e9i −0.411170 0.411170i
\(890\) −2.74098e9 + 9.44654e7i −0.130329 + 0.00449167i
\(891\) 6.51111e9 1.57192e10i 0.308378 0.744490i
\(892\) −8.05070e9 7.01127e9i −0.379802 0.330765i
\(893\) 7.45655e9 3.08861e9i 0.350395 0.145138i
\(894\) 1.99627e10 + 7.47411e9i 0.934409 + 0.349847i
\(895\) 3.64986e8 0.0170175
\(896\) 2.42330e10 + 3.70077e9i 1.12546 + 0.171875i
\(897\) −6.60710e10 −3.05659
\(898\) −2.59469e9 9.71463e8i −0.119569 0.0447671i
\(899\) 8.40224e9 3.48032e9i 0.385688 0.159757i
\(900\) 2.01125e10 + 1.75157e10i 0.919637 + 0.800902i
\(901\) 1.48617e10 3.58792e10i 0.676910 1.63421i
\(902\) −2.65839e10 + 9.16193e8i −1.20614 + 0.0415685i
\(903\) −1.02937e10 1.02937e10i −0.465228 0.465228i
\(904\) −2.27188e10 + 1.22951e10i −1.02281 + 0.553530i
\(905\) 2.37489e9 2.37489e9i 0.106506 0.106506i
\(906\) −1.03639e10 + 1.11038e10i −0.462994 + 0.496047i
\(907\) 1.91598e10 + 7.93623e9i 0.852638 + 0.353174i 0.765824 0.643050i \(-0.222331\pi\)
0.0868140 + 0.996225i \(0.472331\pi\)
\(908\) 1.26059e10 + 4.23066e9i 0.558821 + 0.187546i
\(909\) −8.54817e9 2.06371e10i −0.377485 0.911329i
\(910\) −1.73132e9 3.80363e9i −0.0761610 0.167322i
\(911\) 2.90852e10i 1.27455i −0.770636 0.637275i \(-0.780061\pi\)
0.770636 0.637275i \(-0.219939\pi\)
\(912\) −1.17324e10 + 1.55105e10i −0.512160 + 0.677085i
\(913\) 5.75899e9i 0.250437i
\(914\) 3.25906e10 1.48344e10i 1.41182 0.642628i
\(915\) −8.91474e8 2.15221e9i −0.0384711 0.0928775i
\(916\) −7.24349e9 + 3.60322e9i −0.311396 + 0.154902i
\(917\) −4.65305e10 1.92736e10i −1.99271 0.825409i
\(918\) −7.19230e9 6.71306e9i −0.306845 0.286399i
\(919\) −9.54829e9 + 9.54829e9i −0.405809 + 0.405809i −0.880274 0.474465i \(-0.842641\pi\)
0.474465 + 0.880274i \(0.342641\pi\)
\(920\) 2.10688e9 2.59451e9i 0.0892035 0.109850i
\(921\) 1.32016e10 + 1.32016e10i 0.556824 + 0.556824i
\(922\) −8.21082e8 2.38242e10i −0.0345007 1.00106i
\(923\) −1.80174e10 + 4.34978e10i −0.754198 + 1.82080i
\(924\) −3.17773e9 4.60471e10i −0.132515 1.92022i
\(925\) −1.97906e10 + 8.19754e9i −0.822173 + 0.340555i
\(926\) −2.01314e9 + 5.37692e9i −0.0833174 + 0.222533i
\(927\) 5.15689e10 2.12622
\(928\) −2.70388e9 1.55416e10i −0.111063 0.638380i
\(929\) 4.01671e10 1.64367 0.821837 0.569723i \(-0.192950\pi\)
0.821837 + 0.569723i \(0.192950\pi\)
\(930\) −8.75269e8 + 2.33776e9i −0.0356822 + 0.0953037i
\(931\) 3.82765e9 1.58547e9i 0.155456 0.0643922i
\(932\) −2.79376e10 + 1.92798e9i −1.13040 + 0.0780095i
\(933\) −1.37801e10 + 3.32680e10i −0.555476 + 1.34104i
\(934\) −5.68677e8 1.65005e10i −0.0228376 0.662649i
\(935\) 2.54446e9 + 2.54446e9i 0.101802 + 0.101802i
\(936\) −4.87660e9 4.70164e10i −0.194380 1.87406i
\(937\) 1.88526e10 1.88526e10i 0.748657 0.748657i −0.225570 0.974227i \(-0.572425\pi\)
0.974227 + 0.225570i \(0.0724245\pi\)
\(938\) −1.10951e9 1.03558e9i −0.0438955 0.0409706i
\(939\) 6.38859e9 + 2.64624e9i 0.251811 + 0.104304i
\(940\) −8.00311e8 1.60885e9i −0.0314276 0.0631783i
\(941\) 1.57043e10 + 3.79135e10i 0.614405 + 1.48330i 0.858116 + 0.513456i \(0.171635\pi\)
−0.243711 + 0.969848i \(0.578365\pi\)
\(942\) 1.53986e10 7.00906e9i 0.600210 0.273201i
\(943\) 3.67779e10i 1.42822i
\(944\) −3.25844e10 8.49034e9i −1.26069 0.328491i
\(945\) 1.08829e9i 0.0419502i
\(946\) 4.71914e9 + 1.03677e10i 0.181236 + 0.398167i
\(947\) 7.63256e9 + 1.84266e10i 0.292042 + 0.705052i 0.999999 0.00120333i \(-0.000383030\pi\)
−0.707957 + 0.706255i \(0.750383\pi\)
\(948\) −8.09821e9 + 2.41298e10i −0.308717 + 0.919868i
\(949\) −5.96913e10 2.47249e10i −2.26714 0.939082i
\(950\) 1.01291e10 1.08522e10i 0.383300 0.410663i
\(951\) 1.50665e10 1.50665e10i 0.568042 0.568042i
\(952\) 3.49751e10 + 1.04122e10i 1.31380 + 0.391122i
\(953\) 2.33783e10 + 2.33783e10i 0.874960 + 0.874960i 0.993008 0.118048i \(-0.0376636\pi\)
−0.118048 + 0.993008i \(0.537664\pi\)
\(954\) −4.85599e10 + 1.67358e9i −1.81075 + 0.0624061i
\(955\) −1.72014e9 + 4.15277e9i −0.0639073 + 0.154286i
\(956\) 3.37690e9 3.87753e9i 0.125002 0.143533i
\(957\) −2.74416e10 + 1.13667e10i −1.01209 + 0.419220i
\(958\) 2.71821e8 + 1.01771e8i 0.00998858 + 0.00373977i
\(959\) 2.05418e10 0.752097
\(960\) 3.62490e9 + 2.36817e9i 0.132235 + 0.0863899i
\(961\) −1.60926e10 −0.584918
\(962\) 3.55550e10 + 1.33120e10i 1.28762 + 0.482091i
\(963\) 4.38834e10 1.81771e10i 1.58347 0.655893i
\(964\) 2.26794e10 2.60417e10i 0.815384 0.936266i
\(965\) 1.47999e9 3.57302e9i 0.0530169 0.127994i
\(966\) −6.37803e10 + 2.19814e9i −2.27650 + 0.0784575i
\(967\) 1.74555e10 + 1.74555e10i 0.620781 + 0.620781i 0.945731 0.324950i \(-0.105347\pi\)
−0.324950 + 0.945731i \(0.605347\pi\)
\(968\) −2.25323e9 + 7.56873e9i −0.0798438 + 0.268200i
\(969\) −2.04713e10 + 2.04713e10i −0.722791 + 0.722791i
\(970\) 3.49187e9 3.74115e9i 0.122845 0.131615i
\(971\) −2.72101e10 1.12708e10i −0.953813 0.395082i −0.149151 0.988814i \(-0.547654\pi\)
−0.804663 + 0.593732i \(0.797654\pi\)
\(972\) 1.28724e10 3.83554e10i 0.449603 1.33966i
\(973\) 1.78045e10 + 4.29839e10i 0.619633 + 1.49593i
\(974\) −6.88405e9 1.51239e10i −0.238719 0.524456i
\(975\) 6.53365e10i 2.25756i
\(976\) 9.35322e9 + 1.59451e10i 0.322023 + 0.548974i
\(977\) 1.81081e10i 0.621216i −0.950538 0.310608i \(-0.899467\pi\)
0.950538 0.310608i \(-0.100533\pi\)
\(978\) 4.45435e10 2.02751e10i 1.52264 0.693071i
\(979\) −1.56818e10 3.78591e10i −0.534141 1.28953i
\(980\) −4.10822e8 8.25867e8i −0.0139432 0.0280297i
\(981\) −7.30913e9 3.02754e9i −0.247186 0.102388i
\(982\) −2.55066e10 2.38071e10i −0.859533 0.802261i
\(983\) 3.29245e10 3.29245e10i 1.10556 1.10556i 0.111830 0.993727i \(-0.464329\pi\)
0.993727 0.111830i \(-0.0356712\pi\)
\(984\) −4.73923e10 + 4.91559e9i −1.58571 + 0.164472i
\(985\) −9.79445e8 9.79445e8i −0.0326553 0.0326553i
\(986\) −8.08850e8 2.34693e10i −0.0268719 0.779706i
\(987\) −1.31304e10 + 3.16995e10i −0.434677 + 1.04940i
\(988\) −2.62474e10 + 1.81134e9i −0.865840 + 0.0597519i
\(989\) 1.45511e10 6.02728e9i 0.478310 0.198123i
\(990\) 1.57860e9 4.21630e9i 0.0517071 0.138105i
\(991\) −8.18134e9 −0.267034 −0.133517 0.991047i \(-0.542627\pi\)
−0.133517 + 0.991047i \(0.542627\pi\)
\(992\) 4.33149e9 1.93294e10i 0.140879 0.628677i
\(993\) −1.73071e10 −0.560922
\(994\) −1.59456e10 + 4.25891e10i −0.514977 + 1.37545i
\(995\) 4.40712e9 1.82549e9i 0.141832 0.0587487i
\(996\) 7.10203e8 + 1.02913e10i 0.0227759 + 0.330036i
\(997\) 2.12062e9 5.11962e9i 0.0677687 0.163608i −0.886366 0.462984i \(-0.846779\pi\)
0.954135 + 0.299376i \(0.0967786\pi\)
\(998\) −3.02339e8 8.77255e9i −0.00962801 0.279363i
\(999\) −6.99088e9 6.99088e9i −0.221847 0.221847i
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 32.8.g.a.21.24 108
32.29 even 8 inner 32.8.g.a.29.24 yes 108
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.8.g.a.21.24 108 1.1 even 1 trivial
32.8.g.a.29.24 yes 108 32.29 even 8 inner