Properties

Label 43.8.g.a.9.6
Level $43$
Weight $8$
Character 43.9
Analytic conductor $13.433$
Analytic rank $0$
Dimension $300$
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] = [43,8,Mod(9,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.9");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 43.g (of order \(21\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(13.4325560958\)
Analytic rank: \(0\)
Dimension: \(300\)
Relative dimension: \(25\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 9.6
Character \(\chi\) \(=\) 43.9
Dual form 43.8.g.a.24.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-7.47390 - 9.37197i) q^{2} +(-35.4123 - 5.33754i) q^{3} +(-3.49202 + 15.2995i) q^{4} +(-37.7951 - 25.7682i) q^{5} +(214.645 + 371.775i) q^{6} +(-223.831 + 387.687i) q^{7} +(-1212.93 + 584.115i) q^{8} +(-864.297 - 266.600i) q^{9} +O(q^{10})\) \(q+(-7.47390 - 9.37197i) q^{2} +(-35.4123 - 5.33754i) q^{3} +(-3.49202 + 15.2995i) q^{4} +(-37.7951 - 25.7682i) q^{5} +(214.645 + 371.775i) q^{6} +(-223.831 + 387.687i) q^{7} +(-1212.93 + 584.115i) q^{8} +(-864.297 - 266.600i) q^{9} +(40.9773 + 546.804i) q^{10} +(1767.34 + 7743.21i) q^{11} +(205.322 - 523.152i) q^{12} +(748.065 - 9982.24i) q^{13} +(5306.29 - 799.794i) q^{14} +(1200.87 + 1114.25i) q^{15} +(16349.4 + 7873.44i) q^{16} +(14168.6 - 9659.96i) q^{17} +(3961.10 + 10092.7i) q^{18} +(-15385.5 + 4745.80i) q^{19} +(526.223 - 488.263i) q^{20} +(9995.68 - 12534.2i) q^{21} +(59360.3 - 74435.4i) q^{22} +(43177.8 - 40063.1i) q^{23} +(46070.2 - 14210.8i) q^{24} +(-27777.8 - 70776.7i) q^{25} +(-99144.2 + 67595.4i) q^{26} +(99748.9 + 48036.6i) q^{27} +(-5149.81 - 4778.32i) q^{28} +(169913. - 25610.3i) q^{29} +(1467.49 - 19582.3i) q^{30} +(-90284.8 + 230042. i) q^{31} +(-10059.1 - 44071.9i) q^{32} +(-21255.7 - 283638. i) q^{33} +(-196427. - 60589.8i) q^{34} +(18449.7 - 8884.93i) q^{35} +(7096.99 - 12292.4i) q^{36} +(264453. + 458047. i) q^{37} +(159467. + 108723. i) q^{38} +(-79771.4 + 349501. i) q^{39} +(60894.2 + 9178.33i) q^{40} +(-437128. - 548141. i) q^{41} -192177. q^{42} +(-123428. + 506541. i) q^{43} -124639. q^{44} +(25796.3 + 32347.6i) q^{45} +(-698176. - 105233. i) q^{46} +(98544.1 - 431750. i) q^{47} +(-536944. - 366082. i) q^{48} +(311570. + 539656. i) q^{49} +(-455709. + 789310. i) q^{50} +(-553301. + 266456. i) q^{51} +(150111. + 46303.2i) q^{52} +(99612.1 + 1.32923e6i) q^{53} +(-295316. - 1.29386e6i) q^{54} +(132732. - 338197. i) q^{55} +(45037.2 - 600980. i) q^{56} +(570166. - 85938.7i) q^{57} +(-1.50993e6 - 1.40101e6i) q^{58} +(-16604.4 - 7996.26i) q^{59} +(-21240.9 + 14481.8i) q^{60} +(-138551. - 353022. i) q^{61} +(2.83072e6 - 873163. i) q^{62} +(296814. - 275403. i) q^{63} +(1.11035e6 - 1.39233e6i) q^{64} +(-285498. + 358003. i) q^{65} +(-2.49939e6 + 2.31909e6i) q^{66} +(3.53244e6 - 1.08961e6i) q^{67} +(98315.9 + 250505. i) q^{68} +(-1.74286e6 + 1.18826e6i) q^{69} +(-221161. - 106505. i) q^{70} +(1.55360e6 + 1.44153e6i) q^{71} +(1.20405e6 - 181482. i) q^{72} +(-417703. + 5.57386e6i) q^{73} +(2.31630e6 - 5.90184e6i) q^{74} +(605902. + 2.65463e6i) q^{75} +(-18882.0 - 251963. i) q^{76} +(-3.39753e6 - 1.04800e6i) q^{77} +(3.87172e6 - 1.86452e6i) q^{78} +(-383200. + 663722. i) q^{79} +(-415041. - 718872. i) q^{80} +(-1.64156e6 - 1.11920e6i) q^{81} +(-1.87011e6 + 8.19350e6i) q^{82} +(5.25249e6 + 791686. i) q^{83} +(156862. + 196699. i) q^{84} -784422. q^{85} +(5.66978e6 - 2.62908e6i) q^{86} -6.15371e6 q^{87} +(-6.66658e6 - 8.35962e6i) q^{88} +(6.58533e6 + 992579. i) q^{89} +(110361. - 483525. i) q^{90} +(3.70255e6 + 2.52435e6i) q^{91} +(462169. + 800500. i) q^{92} +(4.42505e6 - 7.66441e6i) q^{93} +(-4.78286e6 + 2.30330e6i) q^{94} +(703787. + 217089. i) q^{95} +(120981. + 1.61438e6i) q^{96} +(763208. + 3.34383e6i) q^{97} +(2.72899e6 - 6.95336e6i) q^{98} +(536838. - 7.16361e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9} - 1681 q^{10} + 4580 q^{11} + 9330 q^{12} - 20444 q^{13} - 45798 q^{14} + 50477 q^{15} - 74504 q^{16} - 25312 q^{17} + 2046 q^{18} + 4046 q^{19} + 140781 q^{20} + 100555 q^{21} + 95810 q^{22} + 1648 q^{23} - 292592 q^{24} + 419068 q^{25} + 393435 q^{26} + 274140 q^{27} + 233644 q^{28} + 605697 q^{29} - 1216016 q^{30} + 358580 q^{31} - 19194 q^{32} + 1280291 q^{33} + 1137255 q^{34} + 652739 q^{35} - 8980975 q^{36} - 2360047 q^{37} - 308490 q^{38} + 536339 q^{39} + 3057993 q^{40} - 1376320 q^{41} + 8417790 q^{42} + 7173000 q^{43} - 3856780 q^{44} + 2761486 q^{45} - 7073993 q^{46} + 1437090 q^{47} - 9543469 q^{48} - 16053170 q^{49} - 3046893 q^{50} + 2972901 q^{51} + 17415142 q^{52} + 3320604 q^{53} + 6000486 q^{54} + 13427750 q^{55} - 5450793 q^{56} + 3333100 q^{57} - 7876190 q^{58} - 7084765 q^{59} + 7356443 q^{60} + 3354606 q^{61} - 719427 q^{62} + 14716815 q^{63} - 16086234 q^{64} - 19914646 q^{65} - 8293345 q^{66} + 13025470 q^{67} - 22191927 q^{68} - 33964295 q^{69} + 8094727 q^{70} + 30843495 q^{71} + 93841607 q^{72} - 3067637 q^{73} + 18179570 q^{74} - 41508571 q^{75} - 19751872 q^{76} - 15169179 q^{77} - 69509396 q^{78} - 12090149 q^{79} - 69662530 q^{80} + 3387954 q^{81} + 39226888 q^{82} + 16408777 q^{83} + 98603231 q^{84} - 13423424 q^{85} + 111906660 q^{86} + 49022010 q^{87} + 76213954 q^{88} - 12540205 q^{89} - 92608607 q^{90} - 59091937 q^{91} - 50489370 q^{92} - 52218334 q^{93} - 3441600 q^{94} - 79947551 q^{95} - 23449784 q^{96} - 116467587 q^{97} + 73909552 q^{98} - 20061115 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{21}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.47390 9.37197i −0.660605 0.828373i 0.332804 0.942996i \(-0.392005\pi\)
−0.993409 + 0.114623i \(0.963434\pi\)
\(3\) −35.4123 5.33754i −0.757233 0.114135i −0.240932 0.970542i \(-0.577453\pi\)
−0.516301 + 0.856407i \(0.672691\pi\)
\(4\) −3.49202 + 15.2995i −0.0272814 + 0.119528i
\(5\) −37.7951 25.7682i −0.135220 0.0921913i 0.493821 0.869564i \(-0.335600\pi\)
−0.629041 + 0.777372i \(0.716552\pi\)
\(6\) 214.645 + 371.775i 0.405686 + 0.702669i
\(7\) −223.831 + 387.687i −0.246648 + 0.427207i −0.962594 0.270949i \(-0.912663\pi\)
0.715946 + 0.698156i \(0.245996\pi\)
\(8\) −1212.93 + 584.115i −0.837567 + 0.403351i
\(9\) −864.297 266.600i −0.395197 0.121902i
\(10\) 40.9773 + 546.804i 0.0129581 + 0.172914i
\(11\) 1767.34 + 7743.21i 0.400355 + 1.75407i 0.625964 + 0.779852i \(0.284706\pi\)
−0.225609 + 0.974218i \(0.572437\pi\)
\(12\) 205.322 523.152i 0.0343006 0.0873964i
\(13\) 748.065 9982.24i 0.0944361 1.26016i −0.725707 0.688004i \(-0.758487\pi\)
0.820143 0.572158i \(-0.193894\pi\)
\(14\) 5306.29 799.794i 0.516824 0.0778987i
\(15\) 1200.87 + 1114.25i 0.0918707 + 0.0852435i
\(16\) 16349.4 + 7873.44i 0.997886 + 0.480557i
\(17\) 14168.6 9659.96i 0.699446 0.476874i −0.160647 0.987012i \(-0.551358\pi\)
0.860093 + 0.510138i \(0.170406\pi\)
\(18\) 3961.10 + 10092.7i 0.160089 + 0.407900i
\(19\) −15385.5 + 4745.80i −0.514605 + 0.158735i −0.541171 0.840913i \(-0.682019\pi\)
0.0265664 + 0.999647i \(0.491543\pi\)
\(20\) 526.223 488.263i 0.0147084 0.0136474i
\(21\) 9995.68 12534.2i 0.235529 0.295344i
\(22\) 59360.3 74435.4i 1.18855 1.49039i
\(23\) 43177.8 40063.1i 0.739968 0.686590i −0.217199 0.976127i \(-0.569692\pi\)
0.957167 + 0.289538i \(0.0935016\pi\)
\(24\) 46070.2 14210.8i 0.680270 0.209835i
\(25\) −27777.8 70776.7i −0.355556 0.905942i
\(26\) −99144.2 + 67595.4i −1.10627 + 0.754241i
\(27\) 99748.9 + 48036.6i 0.975293 + 0.469676i
\(28\) −5149.81 4778.32i −0.0443341 0.0411360i
\(29\) 169913. 25610.3i 1.29370 0.194994i 0.534121 0.845408i \(-0.320643\pi\)
0.759580 + 0.650414i \(0.225405\pi\)
\(30\) 1467.49 19582.3i 0.00992317 0.132416i
\(31\) −90284.8 + 230042.i −0.544313 + 1.38689i 0.348861 + 0.937175i \(0.386569\pi\)
−0.893174 + 0.449712i \(0.851527\pi\)
\(32\) −10059.1 44071.9i −0.0542670 0.237759i
\(33\) −21255.7 283638.i −0.102962 1.37393i
\(34\) −196427. 60589.8i −0.857088 0.264377i
\(35\) 18449.7 8884.93i 0.0727365 0.0350280i
\(36\) 7096.99 12292.4i 0.0253522 0.0439113i
\(37\) 264453. + 458047.i 0.858308 + 1.48663i 0.873542 + 0.486748i \(0.161817\pi\)
−0.0152345 + 0.999884i \(0.504849\pi\)
\(38\) 159467. + 108723.i 0.471442 + 0.321424i
\(39\) −79771.4 + 349501.i −0.215338 + 0.943458i
\(40\) 60894.2 + 9178.33i 0.150441 + 0.0226753i
\(41\) −437128. 548141.i −0.990524 1.24208i −0.970205 0.242284i \(-0.922104\pi\)
−0.0203180 0.999794i \(-0.506468\pi\)
\(42\) −192177. −0.400247
\(43\) −123428. + 506541.i −0.236741 + 0.971573i
\(44\) −124639. −0.220582
\(45\) 25796.3 + 32347.6i 0.0422002 + 0.0529173i
\(46\) −698176. 105233.i −1.05758 0.159404i
\(47\) 98544.1 431750.i 0.138448 0.606582i −0.857328 0.514771i \(-0.827877\pi\)
0.995776 0.0918117i \(-0.0292658\pi\)
\(48\) −536944. 366082.i −0.700785 0.477787i
\(49\) 311570. + 539656.i 0.378329 + 0.655286i
\(50\) −455709. + 789310.i −0.515575 + 0.893003i
\(51\) −553301. + 266456.i −0.584072 + 0.281274i
\(52\) 150111. + 46303.2i 0.148048 + 0.0456667i
\(53\) 99612.1 + 1.32923e6i 0.0919066 + 1.22641i 0.832335 + 0.554273i \(0.187004\pi\)
−0.740428 + 0.672135i \(0.765377\pi\)
\(54\) −295316. 1.29386e6i −0.255217 1.11818i
\(55\) 132732. 338197.i 0.107574 0.274094i
\(56\) 45037.2 600980.i 0.0342699 0.457300i
\(57\) 570166. 85938.7i 0.407793 0.0614649i
\(58\) −1.50993e6 1.40101e6i −1.01615 0.942853i
\(59\) −16604.4 7996.26i −0.0105255 0.00506880i 0.428614 0.903488i \(-0.359002\pi\)
−0.439139 + 0.898419i \(0.644716\pi\)
\(60\) −21240.9 + 14481.8i −0.0126953 + 0.00865551i
\(61\) −138551. 353022.i −0.0781547 0.199135i 0.886456 0.462813i \(-0.153160\pi\)
−0.964611 + 0.263678i \(0.915064\pi\)
\(62\) 2.83072e6 873163.i 1.50844 0.465291i
\(63\) 296814. 275403.i 0.149552 0.138764i
\(64\) 1.11035e6 1.39233e6i 0.529455 0.663915i
\(65\) −285498. + 358003.i −0.128946 + 0.161693i
\(66\) −2.49939e6 + 2.31909e6i −1.07011 + 0.992919i
\(67\) 3.53244e6 1.08961e6i 1.43487 0.442599i 0.522738 0.852493i \(-0.324910\pi\)
0.912133 + 0.409894i \(0.134434\pi\)
\(68\) 98315.9 + 250505.i 0.0379178 + 0.0966129i
\(69\) −1.74286e6 + 1.18826e6i −0.638692 + 0.435453i
\(70\) −221161. 106505.i −0.0770664 0.0371132i
\(71\) 1.55360e6 + 1.44153e6i 0.515153 + 0.477992i 0.894378 0.447313i \(-0.147619\pi\)
−0.379225 + 0.925304i \(0.623809\pi\)
\(72\) 1.20405e6 181482.i 0.380174 0.0573020i
\(73\) −417703. + 5.57386e6i −0.125672 + 1.67697i 0.476937 + 0.878937i \(0.341747\pi\)
−0.602609 + 0.798036i \(0.705872\pi\)
\(74\) 2.31630e6 5.90184e6i 0.664484 1.69308i
\(75\) 605902. + 2.65463e6i 0.165839 + 0.726590i
\(76\) −18882.0 251963.i −0.00493402 0.0658399i
\(77\) −3.39753e6 1.04800e6i −0.848098 0.261604i
\(78\) 3.87172e6 1.86452e6i 0.923789 0.444873i
\(79\) −383200. + 663722.i −0.0874442 + 0.151458i −0.906430 0.422356i \(-0.861203\pi\)
0.818986 + 0.573814i \(0.194537\pi\)
\(80\) −415041. 718872.i −0.0906308 0.156977i
\(81\) −1.64156e6 1.11920e6i −0.343209 0.233996i
\(82\) −1.87011e6 + 8.19350e6i −0.374558 + 1.64105i
\(83\) 5.25249e6 + 791686.i 1.00831 + 0.151978i 0.632369 0.774668i \(-0.282083\pi\)
0.375937 + 0.926645i \(0.377321\pi\)
\(84\) 156862. + 196699.i 0.0288762 + 0.0362096i
\(85\) −784422. −0.138543
\(86\) 5.66978e6 2.62908e6i 0.961217 0.445717i
\(87\) −6.15371e6 −1.00189
\(88\) −6.66658e6 8.35962e6i −1.04283 1.30767i
\(89\) 6.58533e6 + 992579.i 0.990177 + 0.149245i 0.624104 0.781341i \(-0.285464\pi\)
0.366073 + 0.930586i \(0.380702\pi\)
\(90\) 110361. 483525.i 0.0159576 0.0699150i
\(91\) 3.70255e6 + 2.52435e6i 0.515058 + 0.351160i
\(92\) 462169. + 800500.i 0.0618790 + 0.107178i
\(93\) 4.42505e6 7.66441e6i 0.570463 0.988071i
\(94\) −4.78286e6 + 2.30330e6i −0.593936 + 0.286025i
\(95\) 703787. + 217089.i 0.0842187 + 0.0259780i
\(96\) 120981. + 1.61438e6i 0.0139562 + 0.186233i
\(97\) 763208. + 3.34383e6i 0.0849067 + 0.372001i 0.999474 0.0324334i \(-0.0103257\pi\)
−0.914567 + 0.404434i \(0.867469\pi\)
\(98\) 2.72899e6 6.95336e6i 0.292895 0.746283i
\(99\) 536838. 7.16361e6i 0.0556058 0.742008i
\(100\) 1.17985e6 177834.i 0.117985 0.0177834i
\(101\) −1.12886e7 1.04742e7i −1.09022 1.01157i −0.999877 0.0156638i \(-0.995014\pi\)
−0.0903409 0.995911i \(-0.528796\pi\)
\(102\) 6.63254e6 + 3.19406e6i 0.618841 + 0.298018i
\(103\) −1.41216e7 + 9.62797e6i −1.27337 + 0.868169i −0.995712 0.0925102i \(-0.970511\pi\)
−0.277659 + 0.960680i \(0.589559\pi\)
\(104\) 4.92342e6 + 1.25447e7i 0.429191 + 1.09356i
\(105\) −700772. + 216159.i −0.0590764 + 0.0182227i
\(106\) 1.17130e7 1.08681e7i 0.955210 0.886305i
\(107\) −341172. + 427816.i −0.0269234 + 0.0337609i −0.795111 0.606464i \(-0.792587\pi\)
0.768188 + 0.640225i \(0.221159\pi\)
\(108\) −1.08326e6 + 1.35837e6i −0.0827466 + 0.103761i
\(109\) −7.09127e6 + 6.57974e6i −0.524483 + 0.486649i −0.897401 0.441215i \(-0.854548\pi\)
0.372918 + 0.927864i \(0.378357\pi\)
\(110\) −4.16160e6 + 1.28368e6i −0.298116 + 0.0919567i
\(111\) −6.92005e6 1.76320e7i −0.480263 1.22369i
\(112\) −6.71194e6 + 4.57612e6i −0.451424 + 0.307776i
\(113\) 3.12540e6 + 1.50511e6i 0.203766 + 0.0981285i 0.532984 0.846126i \(-0.321071\pi\)
−0.329218 + 0.944254i \(0.606785\pi\)
\(114\) −5.06678e6 4.70128e6i −0.320306 0.297201i
\(115\) −2.66426e6 + 401573.i −0.163356 + 0.0246219i
\(116\) −201514. + 2.68902e6i −0.0119868 + 0.159953i
\(117\) −3.30782e6 + 8.42818e6i −0.190937 + 0.486501i
\(118\) 49158.9 + 215379.i 0.00275433 + 0.0120675i
\(119\) 573676. + 7.65517e6i 0.0312070 + 0.416429i
\(120\) −2.10742e6 650051.i −0.111331 0.0343410i
\(121\) −3.92765e7 + 1.89146e7i −2.01551 + 0.970617i
\(122\) −2.27300e6 + 3.93695e6i −0.113329 + 0.196291i
\(123\) 1.25540e7 + 2.17441e7i 0.608293 + 1.05359i
\(124\) −3.20425e6 2.18462e6i −0.150921 0.102897i
\(125\) −1.56915e6 + 6.87491e6i −0.0718588 + 0.314834i
\(126\) −4.79943e6 723398.i −0.213744 0.0322167i
\(127\) 7.14175e6 + 8.95547e6i 0.309380 + 0.387950i 0.912076 0.410021i \(-0.134478\pi\)
−0.602697 + 0.797970i \(0.705907\pi\)
\(128\) −2.71338e7 −1.14360
\(129\) 7.07454e6 1.72790e7i 0.290158 0.708687i
\(130\) 5.48898e6 0.219124
\(131\) 1.72964e7 + 2.16890e7i 0.672211 + 0.842926i 0.994611 0.103678i \(-0.0330610\pi\)
−0.322400 + 0.946604i \(0.604490\pi\)
\(132\) 4.41375e6 + 665266.i 0.167032 + 0.0251760i
\(133\) 1.60387e6 7.02702e6i 0.0591138 0.258994i
\(134\) −3.66129e7 2.49623e7i −1.31452 0.896225i
\(135\) −2.53220e6 4.38590e6i −0.0885788 0.153423i
\(136\) −1.15429e7 + 1.99929e7i −0.393485 + 0.681537i
\(137\) 4.66351e7 2.24583e7i 1.54950 0.746200i 0.553274 0.833000i \(-0.313378\pi\)
0.996226 + 0.0868002i \(0.0276642\pi\)
\(138\) 2.41623e7 + 7.45310e6i 0.782640 + 0.241413i
\(139\) 188259. + 2.51214e6i 0.00594571 + 0.0793399i 0.999387 0.0350010i \(-0.0111434\pi\)
−0.993442 + 0.114341i \(0.963524\pi\)
\(140\) 71508.4 + 313299.i 0.00220246 + 0.00964962i
\(141\) −5.79416e6 + 1.47633e7i −0.174070 + 0.443523i
\(142\) 1.89854e6 2.53342e7i 0.0556429 0.742502i
\(143\) 7.86167e7 1.18496e7i 2.24822 0.338865i
\(144\) −1.20316e7 1.11637e7i −0.335781 0.311559i
\(145\) −7.08181e6 3.41042e6i −0.192911 0.0929009i
\(146\) 5.53600e7 3.77438e7i 1.47218 1.00371i
\(147\) −8.15299e6 2.07735e7i −0.211693 0.539384i
\(148\) −7.93137e6 + 2.44650e6i −0.201109 + 0.0620340i
\(149\) −1.44893e7 + 1.34441e7i −0.358836 + 0.332951i −0.838903 0.544281i \(-0.816803\pi\)
0.480067 + 0.877232i \(0.340612\pi\)
\(150\) 2.03507e7 2.55189e7i 0.492333 0.617366i
\(151\) 1.67119e7 2.09560e7i 0.395008 0.495325i −0.544064 0.839043i \(-0.683115\pi\)
0.939073 + 0.343719i \(0.111687\pi\)
\(152\) 1.58894e7 1.47432e7i 0.366990 0.340517i
\(153\) −1.48212e7 + 4.57173e6i −0.334551 + 0.103195i
\(154\) 1.55710e7 + 3.96742e7i 0.343553 + 0.875358i
\(155\) 9.34009e6 6.36797e6i 0.201461 0.137354i
\(156\) −5.06864e6 2.44093e6i −0.106894 0.0514777i
\(157\) 1.63538e7 + 1.51741e7i 0.337265 + 0.312936i 0.830563 0.556924i \(-0.188019\pi\)
−0.493299 + 0.869860i \(0.664209\pi\)
\(158\) 9.08438e6 1.36925e6i 0.183230 0.0276174i
\(159\) 3.56734e6 4.76028e7i 0.0703808 0.939167i
\(160\) −755471. + 1.92491e6i −0.0145813 + 0.0371527i
\(161\) 5.86742e6 + 2.57069e7i 0.110804 + 0.485466i
\(162\) 1.77977e6 + 2.37494e7i 0.0328898 + 0.438884i
\(163\) −2.57897e7 7.95508e6i −0.466434 0.143876i 0.0526249 0.998614i \(-0.483241\pi\)
−0.519059 + 0.854739i \(0.673717\pi\)
\(164\) 9.91275e6 4.77373e6i 0.175485 0.0845092i
\(165\) −6.50550e6 + 1.12678e7i −0.112742 + 0.195275i
\(166\) −3.18369e7 5.51432e7i −0.540198 0.935650i
\(167\) −2.12195e7 1.44672e7i −0.352556 0.240369i 0.374072 0.927400i \(-0.377961\pi\)
−0.726628 + 0.687031i \(0.758914\pi\)
\(168\) −4.80262e6 + 2.10417e7i −0.0781441 + 0.342372i
\(169\) −3.70378e7 5.58256e6i −0.590259 0.0889672i
\(170\) 5.86269e6 + 7.35158e6i 0.0915220 + 0.114765i
\(171\) 1.45629e7 0.222721
\(172\) −7.31883e6 3.65723e6i −0.109671 0.0548029i
\(173\) 6.04291e7 0.887329 0.443664 0.896193i \(-0.353678\pi\)
0.443664 + 0.896193i \(0.353678\pi\)
\(174\) 4.59922e7 + 5.76724e7i 0.661853 + 0.829937i
\(175\) 3.36568e7 + 5.07294e6i 0.474722 + 0.0715528i
\(176\) −3.20709e7 + 1.40512e8i −0.443421 + 1.94276i
\(177\) 545320. + 371793.i 0.00739171 + 0.00503958i
\(178\) −3.99157e7 6.91360e7i −0.530486 0.918828i
\(179\) −1.53254e7 + 2.65443e7i −0.199722 + 0.345929i −0.948438 0.316962i \(-0.897337\pi\)
0.748716 + 0.662891i \(0.230671\pi\)
\(180\) −584984. + 281713.i −0.00747636 + 0.00360042i
\(181\) −1.21527e8 3.74862e7i −1.52335 0.469891i −0.583681 0.811983i \(-0.698388\pi\)
−0.939666 + 0.342092i \(0.888864\pi\)
\(182\) −4.01429e6 5.35669e7i −0.0493581 0.658638i
\(183\) 3.02214e6 + 1.32408e7i 0.0364532 + 0.159712i
\(184\) −2.89700e7 + 7.38144e7i −0.342836 + 0.873531i
\(185\) 1.80802e6 2.41264e7i 0.0209944 0.280151i
\(186\) −1.04903e8 + 1.58116e7i −1.19534 + 0.180169i
\(187\) 9.98398e7 + 9.26378e7i 1.11650 + 1.03596i
\(188\) 6.26145e6 + 3.01536e6i 0.0687262 + 0.0330968i
\(189\) −4.09501e7 + 2.79193e7i −0.441203 + 0.300807i
\(190\) −3.22547e6 8.21837e6i −0.0341158 0.0869257i
\(191\) −2.22771e7 + 6.87158e6i −0.231335 + 0.0713575i −0.408256 0.912868i \(-0.633863\pi\)
0.176920 + 0.984225i \(0.443387\pi\)
\(192\) −4.67515e7 + 4.33791e7i −0.476696 + 0.442309i
\(193\) 1.02800e8 1.28907e8i 1.02930 1.29070i 0.0733060 0.997309i \(-0.476645\pi\)
0.955993 0.293390i \(-0.0947836\pi\)
\(194\) 2.56342e7 3.21442e7i 0.252065 0.316080i
\(195\) 1.20210e7 1.11539e7i 0.116097 0.107722i
\(196\) −9.34449e6 + 2.88239e6i −0.0886460 + 0.0273437i
\(197\) −2.45990e7 6.26772e7i −0.229238 0.584088i 0.769257 0.638940i \(-0.220627\pi\)
−0.998495 + 0.0548518i \(0.982531\pi\)
\(198\) −7.11494e7 + 4.85088e7i −0.651393 + 0.444112i
\(199\) −8.44234e7 4.06562e7i −0.759412 0.365713i 0.0137640 0.999905i \(-0.495619\pi\)
−0.773176 + 0.634192i \(0.781333\pi\)
\(200\) 7.50341e7 + 6.96215e7i 0.663214 + 0.615373i
\(201\) −1.30908e8 + 1.97312e7i −1.13705 + 0.171382i
\(202\) −1.37948e7 + 1.84079e8i −0.117757 + 1.57136i
\(203\) −2.81031e7 + 7.16055e7i −0.235786 + 0.600773i
\(204\) −2.14451e6 9.39572e6i −0.0176857 0.0774862i
\(205\) 2.39665e6 + 3.19810e7i 0.0194297 + 0.259271i
\(206\) 1.95777e8 + 6.03891e7i 1.56036 + 0.481308i
\(207\) −4.79992e7 + 2.31152e7i −0.376130 + 0.181135i
\(208\) 9.08250e7 1.57313e8i 0.699816 1.21212i
\(209\) −6.39391e7 1.10746e8i −0.484456 0.839102i
\(210\) 7.26333e6 + 4.95206e6i 0.0541213 + 0.0368993i
\(211\) 4.00013e7 1.75257e8i 0.293147 1.28436i −0.586971 0.809608i \(-0.699680\pi\)
0.880119 0.474754i \(-0.157463\pi\)
\(212\) −2.06845e7 3.11768e6i −0.149097 0.0224727i
\(213\) −4.73224e7 5.93404e7i −0.335535 0.420748i
\(214\) 6.55936e6 0.0457523
\(215\) 1.77176e7 1.59643e7i 0.121583 0.109550i
\(216\) −1.49047e8 −1.00632
\(217\) −6.89757e7 8.64929e7i −0.458234 0.574607i
\(218\) 1.14665e8 + 1.72829e7i 0.749603 + 0.112985i
\(219\) 4.45426e7 1.95154e8i 0.286563 1.25552i
\(220\) 4.71074e6 + 3.21173e6i 0.0298270 + 0.0203357i
\(221\) −8.58290e7 1.48660e8i −0.534886 0.926450i
\(222\) −1.13527e8 + 1.96634e8i −0.696407 + 1.20621i
\(223\) −2.62947e7 + 1.26628e7i −0.158782 + 0.0764652i −0.511587 0.859232i \(-0.670942\pi\)
0.352805 + 0.935697i \(0.385228\pi\)
\(224\) 1.93377e7 + 5.96488e6i 0.114957 + 0.0354596i
\(225\) 5.13918e6 + 6.85776e7i 0.0300784 + 0.401369i
\(226\) −9.25305e6 4.05403e7i −0.0533219 0.233618i
\(227\) −1.78116e7 + 4.53833e7i −0.101068 + 0.257517i −0.972460 0.233071i \(-0.925123\pi\)
0.871392 + 0.490588i \(0.163218\pi\)
\(228\) −676208. + 9.02337e6i −0.00377840 + 0.0504193i
\(229\) 1.58368e8 2.38702e7i 0.871453 0.131350i 0.301934 0.953329i \(-0.402368\pi\)
0.569519 + 0.821978i \(0.307130\pi\)
\(230\) 2.36760e7 + 2.19681e7i 0.128310 + 0.119054i
\(231\) 1.14721e8 + 5.52466e7i 0.612350 + 0.294892i
\(232\) −1.91133e8 + 1.30312e8i −1.00491 + 0.685136i
\(233\) 8.92749e7 + 2.27469e8i 0.462364 + 1.17808i 0.951984 + 0.306148i \(0.0990402\pi\)
−0.489620 + 0.871936i \(0.662865\pi\)
\(234\) 1.03711e8 3.19906e7i 0.529138 0.163218i
\(235\) −1.48499e7 + 1.37787e7i −0.0746426 + 0.0692582i
\(236\) 180322. 226117.i 0.000893010 0.00111980i
\(237\) 1.71126e7 2.14586e7i 0.0835022 0.104708i
\(238\) 6.74565e7 6.25904e7i 0.324343 0.300946i
\(239\) −5.68889e7 + 1.75479e7i −0.269547 + 0.0831443i −0.426582 0.904449i \(-0.640283\pi\)
0.157035 + 0.987593i \(0.449806\pi\)
\(240\) 1.08605e7 + 2.76722e7i 0.0507121 + 0.129212i
\(241\) 1.54214e8 1.05142e8i 0.709684 0.483854i −0.153883 0.988089i \(-0.549178\pi\)
0.863567 + 0.504235i \(0.168225\pi\)
\(242\) 4.70816e8 + 2.26733e8i 2.13549 + 1.02840i
\(243\) −1.25336e8 1.16295e8i −0.560342 0.519921i
\(244\) 5.88489e6 887005.i 0.0259343 0.00390896i
\(245\) 2.13016e6 2.84250e7i 0.00925401 0.123486i
\(246\) 1.09958e8 2.80169e8i 0.470928 1.19990i
\(247\) 3.58643e7 + 1.57132e8i 0.151434 + 0.663475i
\(248\) −2.48620e7 3.31760e8i −0.103504 1.38116i
\(249\) −1.81777e8 5.60708e7i −0.746177 0.230165i
\(250\) 7.61591e7 3.66763e7i 0.308270 0.148455i
\(251\) −4.65195e7 + 8.05741e7i −0.185685 + 0.321616i −0.943807 0.330497i \(-0.892784\pi\)
0.758122 + 0.652113i \(0.226117\pi\)
\(252\) 3.17706e6 + 5.50283e6i 0.0125062 + 0.0216613i
\(253\) 3.86527e8 + 2.63530e8i 1.50058 + 1.02308i
\(254\) 3.05537e7 1.33865e8i 0.116989 0.512564i
\(255\) 2.77782e7 + 4.18689e6i 0.104909 + 0.0158125i
\(256\) 6.06707e7 + 7.60787e7i 0.226016 + 0.283415i
\(257\) −1.59975e8 −0.587875 −0.293937 0.955825i \(-0.594966\pi\)
−0.293937 + 0.955825i \(0.594966\pi\)
\(258\) −2.14813e8 + 6.28390e7i −0.778737 + 0.227804i
\(259\) −2.36772e8 −0.846800
\(260\) −4.48031e6 5.61814e6i −0.0158089 0.0198237i
\(261\) −1.53683e8 2.31640e7i −0.535037 0.0806439i
\(262\) 7.39971e7 3.24202e8i 0.254191 1.11368i
\(263\) 3.37928e8 + 2.30396e8i 1.14546 + 0.780961i 0.978752 0.205046i \(-0.0657343\pi\)
0.166707 + 0.986007i \(0.446687\pi\)
\(264\) 1.91459e8 + 3.31616e8i 0.640415 + 1.10923i
\(265\) 3.04871e7 5.28052e7i 0.100637 0.174308i
\(266\) −7.78442e7 + 3.74878e7i −0.253595 + 0.122125i
\(267\) −2.27904e8 7.02990e7i −0.732761 0.226027i
\(268\) 4.33523e6 + 5.78496e7i 0.0137575 + 0.183581i
\(269\) 8.54251e7 + 3.74272e8i 0.267579 + 1.17234i 0.912820 + 0.408362i \(0.133900\pi\)
−0.645241 + 0.763979i \(0.723243\pi\)
\(270\) −2.21791e7 + 5.65115e7i −0.0685758 + 0.174728i
\(271\) −1.13546e7 + 1.51516e8i −0.0346560 + 0.462452i 0.952698 + 0.303919i \(0.0982953\pi\)
−0.987354 + 0.158532i \(0.949324\pi\)
\(272\) 3.07704e8 4.63789e7i 0.927133 0.139743i
\(273\) −1.17642e8 1.09156e8i −0.349939 0.324696i
\(274\) −5.59025e8 2.69212e8i −1.64174 0.790620i
\(275\) 4.98946e8 3.40176e8i 1.44674 0.986368i
\(276\) −1.20938e7 3.08144e7i −0.0346242 0.0882210i
\(277\) −9.39170e7 + 2.89695e7i −0.265500 + 0.0818960i −0.424647 0.905359i \(-0.639602\pi\)
0.159147 + 0.987255i \(0.449126\pi\)
\(278\) 2.21367e7 2.05398e7i 0.0617953 0.0573376i
\(279\) 1.39362e8 1.74754e8i 0.384176 0.481741i
\(280\) −1.71884e7 + 2.15535e7i −0.0467931 + 0.0586767i
\(281\) −3.63108e8 + 3.36915e8i −0.976257 + 0.905834i −0.995574 0.0939792i \(-0.970041\pi\)
0.0193170 + 0.999813i \(0.493851\pi\)
\(282\) 1.81666e8 5.60365e7i 0.482394 0.148799i
\(283\) 6.40628e7 + 1.63229e8i 0.168017 + 0.428100i 0.989938 0.141501i \(-0.0451929\pi\)
−0.821921 + 0.569601i \(0.807098\pi\)
\(284\) −2.74800e7 + 1.87355e7i −0.0711872 + 0.0485346i
\(285\) −2.37640e7 1.14441e7i −0.0608082 0.0292837i
\(286\) −6.98627e8 6.48231e8i −1.76589 1.63851i
\(287\) 3.10350e8 4.67778e7i 0.774935 0.116803i
\(288\) −3.05551e6 + 4.07730e7i −0.00753721 + 0.100577i
\(289\) −4.24804e7 + 1.08238e8i −0.103525 + 0.263778i
\(290\) 2.09664e7 + 9.18596e7i 0.0504812 + 0.221173i
\(291\) −9.17909e6 1.22487e8i −0.0218361 0.291382i
\(292\) −8.38188e7 2.58547e7i −0.197016 0.0607714i
\(293\) 3.93378e8 1.89441e8i 0.913636 0.439984i 0.0828412 0.996563i \(-0.473601\pi\)
0.830795 + 0.556579i \(0.187886\pi\)
\(294\) −1.33754e8 + 2.31668e8i −0.306966 + 0.531681i
\(295\) 421515. + 730086.i 0.000955953 + 0.00165576i
\(296\) −5.88314e8 4.01106e8i −1.31852 0.898955i
\(297\) −1.95667e8 + 8.57274e8i −0.433382 + 1.89877i
\(298\) 2.34290e8 + 3.53135e7i 0.512857 + 0.0773007i
\(299\) −3.67620e8 4.60981e8i −0.795334 0.997318i
\(300\) −4.27304e7 −0.0913718
\(301\) −1.68753e8 1.61231e8i −0.356671 0.340774i
\(302\) −3.21302e8 −0.671258
\(303\) 3.43847e8 + 4.31170e8i 0.710094 + 0.890429i
\(304\) −2.88909e8 4.35460e7i −0.589798 0.0888977i
\(305\) −3.86022e6 + 1.69127e7i −0.00779045 + 0.0341322i
\(306\) 1.53618e8 + 1.04735e8i 0.306491 + 0.208962i
\(307\) −1.30543e7 2.26106e7i −0.0257494 0.0445994i 0.852864 0.522134i \(-0.174864\pi\)
−0.878613 + 0.477535i \(0.841531\pi\)
\(308\) 2.78981e7 4.83210e7i 0.0544061 0.0942341i
\(309\) 5.51469e8 2.65574e8i 1.06333 0.512071i
\(310\) −1.29487e8 3.99415e7i −0.246866 0.0761481i
\(311\) 1.36170e7 + 1.81707e8i 0.0256697 + 0.342538i 0.995221 + 0.0976495i \(0.0311324\pi\)
−0.969551 + 0.244889i \(0.921249\pi\)
\(312\) −1.07392e8 4.70515e8i −0.200185 0.877066i
\(313\) 1.34400e8 3.42446e8i 0.247739 0.631229i −0.751866 0.659316i \(-0.770846\pi\)
0.999605 + 0.0280864i \(0.00894135\pi\)
\(314\) 1.99847e7 2.66678e8i 0.0364288 0.486108i
\(315\) −1.83148e7 + 2.76051e6i −0.0330153 + 0.00497625i
\(316\) −8.81649e6 8.18051e6i −0.0157178 0.0145840i
\(317\) −5.35423e8 2.57846e8i −0.944039 0.454625i −0.102447 0.994738i \(-0.532667\pi\)
−0.841592 + 0.540113i \(0.818381\pi\)
\(318\) −4.72794e8 + 3.22346e8i −0.824474 + 0.562117i
\(319\) 4.98600e8 + 1.27041e9i 0.859972 + 2.19117i
\(320\) −7.78436e7 + 2.40116e7i −0.132800 + 0.0409633i
\(321\) 1.43652e7 1.33289e7i 0.0242406 0.0224920i
\(322\) 1.97071e8 2.47120e8i 0.328949 0.412489i
\(323\) −1.72146e8 + 2.15864e8i −0.284242 + 0.356428i
\(324\) 2.28555e7 2.12068e7i 0.0373322 0.0346392i
\(325\) −7.27289e8 + 2.24339e8i −1.17521 + 0.362504i
\(326\) 1.18195e8 + 3.01156e8i 0.188946 + 0.481426i
\(327\) 2.86238e8 1.95154e8i 0.452699 0.308645i
\(328\) 8.50381e8 + 4.09522e8i 1.33062 + 0.640794i
\(329\) 1.45327e8 + 1.34844e8i 0.224988 + 0.208759i
\(330\) 1.54223e8 2.32454e7i 0.236239 0.0356073i
\(331\) −8.81692e7 + 1.17654e9i −0.133635 + 1.78323i 0.379767 + 0.925082i \(0.376004\pi\)
−0.513402 + 0.858148i \(0.671615\pi\)
\(332\) −3.04542e7 + 7.75961e7i −0.0456735 + 0.116374i
\(333\) −1.06451e8 4.66392e8i −0.157977 0.692143i
\(334\) 2.30061e7 + 3.06996e8i 0.0337856 + 0.450837i
\(335\) −1.61586e8 4.98428e7i −0.234827 0.0724345i
\(336\) 2.62110e8 1.26226e8i 0.376961 0.181535i
\(337\) 2.29024e7 3.96681e7i 0.0325969 0.0564595i −0.849267 0.527964i \(-0.822956\pi\)
0.881864 + 0.471505i \(0.156289\pi\)
\(338\) 2.24498e8 + 3.88841e8i 0.316230 + 0.547726i
\(339\) −1.02644e8 6.99815e7i −0.143098 0.0975628i
\(340\) 2.73921e6 1.20013e7i 0.00377963 0.0165597i
\(341\) −1.94083e9 2.92533e8i −2.65061 0.399516i
\(342\) −1.08841e8 1.36483e8i −0.147130 0.184496i
\(343\) −6.47627e8 −0.866553
\(344\) −1.46170e8 6.86493e8i −0.193599 0.909247i
\(345\) 9.64911e7 0.126509
\(346\) −4.51641e8 5.66340e8i −0.586174 0.735039i
\(347\) 9.42238e8 + 1.42020e8i 1.21062 + 0.182472i 0.723164 0.690676i \(-0.242687\pi\)
0.487455 + 0.873148i \(0.337925\pi\)
\(348\) 2.14888e7 9.41488e7i 0.0273329 0.119753i
\(349\) 6.80287e8 + 4.63812e8i 0.856650 + 0.584054i 0.910040 0.414520i \(-0.136050\pi\)
−0.0533906 + 0.998574i \(0.517003\pi\)
\(350\) −2.04004e8 3.53345e8i −0.254331 0.440515i
\(351\) 5.54131e8 9.59783e8i 0.683971 1.18467i
\(352\) 3.23481e8 1.55780e8i 0.395320 0.190376i
\(353\) 8.42388e7 + 2.59842e7i 0.101930 + 0.0314411i 0.345301 0.938492i \(-0.387777\pi\)
−0.243371 + 0.969933i \(0.578253\pi\)
\(354\) −591234. 7.88946e6i −0.000708350 0.00945227i
\(355\) −2.15728e7 9.45165e7i −0.0255921 0.112126i
\(356\) −3.81821e7 + 9.72864e7i −0.0448523 + 0.114282i
\(357\) 2.05446e7 2.74149e8i 0.0238979 0.318895i
\(358\) 3.63313e8 5.47606e7i 0.418495 0.0630780i
\(359\) 9.48125e8 + 8.79731e8i 1.08152 + 1.00350i 0.999977 + 0.00683509i \(0.00217569\pi\)
0.0815443 + 0.996670i \(0.474015\pi\)
\(360\) −5.01838e7 2.41672e7i −0.0566897 0.0273003i
\(361\) −5.24361e8 + 3.57503e8i −0.586617 + 0.399949i
\(362\) 5.56963e8 + 1.41912e9i 0.617087 + 1.57231i
\(363\) 1.49183e9 4.60169e8i 1.63699 0.504945i
\(364\) −5.15508e7 + 4.78321e7i −0.0560248 + 0.0519834i
\(365\) 1.59416e8 1.99901e8i 0.171596 0.215174i
\(366\) 1.01506e8 1.27284e8i 0.108220 0.135703i
\(367\) −6.08182e7 + 5.64311e7i −0.0642248 + 0.0595919i −0.711632 0.702552i \(-0.752044\pi\)
0.647407 + 0.762144i \(0.275853\pi\)
\(368\) 1.02136e9 3.15049e8i 1.06835 0.329542i
\(369\) 2.31674e8 + 5.90295e8i 0.240040 + 0.611613i
\(370\) −2.39625e8 + 1.63373e8i −0.245938 + 0.167678i
\(371\) −5.37623e8 2.58905e8i −0.546599 0.263228i
\(372\) 1.01809e8 + 9.44654e7i 0.102539 + 0.0951420i
\(373\) −1.41350e9 + 2.13051e8i −1.41031 + 0.212570i −0.809640 0.586927i \(-0.800338\pi\)
−0.600670 + 0.799497i \(0.705099\pi\)
\(374\) 1.22006e8 1.62806e9i 0.120596 1.60924i
\(375\) 9.22624e7 2.35081e8i 0.0903473 0.230201i
\(376\) 1.32665e8 + 5.81242e8i 0.128706 + 0.563897i
\(377\) −1.28542e8 1.71527e9i −0.123552 1.64869i
\(378\) 5.67716e8 + 1.75117e8i 0.540642 + 0.166766i
\(379\) 1.45607e9 7.01208e8i 1.37387 0.661622i 0.406188 0.913790i \(-0.366858\pi\)
0.967683 + 0.252168i \(0.0811435\pi\)
\(380\) −5.77900e6 + 1.00095e7i −0.00540269 + 0.00935773i
\(381\) −2.05106e8 3.55253e8i −0.189994 0.329079i
\(382\) 2.30897e8 + 1.57423e8i 0.211932 + 0.144493i
\(383\) 3.00637e8 1.31718e9i 0.273431 1.19798i −0.632503 0.774558i \(-0.717972\pi\)
0.905933 0.423420i \(-0.139171\pi\)
\(384\) 9.60869e8 + 1.44828e8i 0.865974 + 0.130525i
\(385\) 1.01405e8 + 1.27158e8i 0.0905620 + 0.113561i
\(386\) −1.97643e9 −1.74914
\(387\) 2.41722e8 4.04896e8i 0.211996 0.355104i
\(388\) −5.38242e7 −0.0467807
\(389\) 9.69040e8 + 1.21514e9i 0.834676 + 1.04665i 0.998192 + 0.0601100i \(0.0191451\pi\)
−0.163516 + 0.986541i \(0.552283\pi\)
\(390\) −1.94377e8 2.92977e7i −0.165928 0.0250096i
\(391\) 2.24759e8 9.84732e8i 0.190151 0.833104i
\(392\) −6.93133e8 4.72570e8i −0.581186 0.396246i
\(393\) −4.96739e8 8.60376e8i −0.412814 0.715014i
\(394\) −4.03559e8 + 6.98985e8i −0.332407 + 0.575746i
\(395\) 3.15860e7 1.52110e7i 0.0257873 0.0124185i
\(396\) 1.07725e8 + 3.32288e7i 0.0871734 + 0.0268894i
\(397\) −9.61784e7 1.28341e9i −0.0771455 1.02944i −0.892669 0.450712i \(-0.851170\pi\)
0.815524 0.578724i \(-0.196449\pi\)
\(398\) 2.49944e8 + 1.09507e9i 0.198724 + 0.870668i
\(399\) −9.43038e7 + 2.40282e8i −0.0743231 + 0.189372i
\(400\) 1.03107e8 1.37586e9i 0.0805520 1.07489i
\(401\) −1.58279e8 + 2.38568e7i −0.122580 + 0.0184759i −0.210046 0.977692i \(-0.567361\pi\)
0.0874658 + 0.996168i \(0.472123\pi\)
\(402\) 1.16331e9 + 1.07939e9i 0.893109 + 0.828684i
\(403\) 2.22879e9 + 1.07333e9i 1.69630 + 0.816894i
\(404\) 1.99671e8 1.36133e8i 0.150654 0.102714i
\(405\) 3.32031e7 + 8.46002e7i 0.0248363 + 0.0632818i
\(406\) 8.81125e8 2.71791e8i 0.653426 0.201555i
\(407\) −3.07937e9 + 2.85724e9i −2.26403 + 2.10071i
\(408\) 5.15473e8 6.46383e8i 0.375747 0.471172i
\(409\) −1.22300e9 + 1.53359e9i −0.883882 + 1.10835i 0.109555 + 0.993981i \(0.465057\pi\)
−0.993438 + 0.114373i \(0.963514\pi\)
\(410\) 2.81813e8 2.61484e8i 0.201938 0.187371i
\(411\) −1.77133e9 + 5.46383e8i −1.25850 + 0.388196i
\(412\) −9.79904e7 2.49675e8i −0.0690308 0.175888i
\(413\) 6.81664e6 4.64751e6i 0.00476152 0.00324635i
\(414\) 5.75377e8 + 2.77087e8i 0.398521 + 0.191917i
\(415\) −1.78118e8 1.65269e8i −0.122332 0.113507i
\(416\) −4.47461e8 + 6.74440e7i −0.304740 + 0.0459321i
\(417\) 6.74198e6 8.99654e7i 0.00455314 0.0607574i
\(418\) −5.60032e8 + 1.42694e9i −0.375056 + 0.955626i
\(419\) 1.05297e8 + 4.61335e8i 0.0699304 + 0.306385i 0.997782 0.0665641i \(-0.0212037\pi\)
−0.927852 + 0.372949i \(0.878347\pi\)
\(420\) −860030. 1.14763e7i −0.000566423 0.00755839i
\(421\) −7.06439e8 2.17907e8i −0.461410 0.142326i 0.0553306 0.998468i \(-0.482379\pi\)
−0.516741 + 0.856142i \(0.672855\pi\)
\(422\) −1.94147e9 + 9.34963e8i −1.25759 + 0.605621i
\(423\) −2.00276e8 + 3.46888e8i −0.128658 + 0.222843i
\(424\) −8.97246e8 1.55408e9i −0.571651 0.990128i
\(425\) −1.07727e9 7.34471e8i −0.680713 0.464102i
\(426\) −2.02454e8 + 8.87008e8i −0.126880 + 0.555897i
\(427\) 1.67874e8 + 2.53030e7i 0.104349 + 0.0157280i
\(428\) −5.35400e6 6.71370e6i −0.00330084 0.00413913i
\(429\) −2.84725e9 −1.74110
\(430\) −2.82036e8 4.67340e7i −0.171067 0.0283461i
\(431\) 1.34895e9 0.811569 0.405784 0.913969i \(-0.366998\pi\)
0.405784 + 0.913969i \(0.366998\pi\)
\(432\) 1.25262e9 + 1.57073e9i 0.747525 + 0.937367i
\(433\) 3.29223e8 + 4.96223e7i 0.194887 + 0.0293744i 0.245760 0.969331i \(-0.420962\pi\)
−0.0508736 + 0.998705i \(0.516201\pi\)
\(434\) −2.95091e8 + 1.29288e9i −0.173277 + 0.759177i
\(435\) 2.32580e8 + 1.58570e8i 0.135475 + 0.0923654i
\(436\) −7.59040e7 1.31470e8i −0.0438593 0.0759666i
\(437\) −4.74180e8 + 8.21303e8i −0.271805 + 0.470781i
\(438\) −2.16188e9 + 1.04111e9i −1.22934 + 0.592020i
\(439\) −1.43742e9 4.43386e8i −0.810884 0.250125i −0.138534 0.990358i \(-0.544239\pi\)
−0.672350 + 0.740233i \(0.734715\pi\)
\(440\) 3.65509e7 + 4.87738e8i 0.0204557 + 0.272962i
\(441\) −1.25417e8 5.49488e8i −0.0696340 0.305086i
\(442\) −7.51762e8 + 1.91546e9i −0.414097 + 1.05510i
\(443\) 2.07523e8 2.76920e9i 0.113410 1.51336i −0.592797 0.805352i \(-0.701976\pi\)
0.706208 0.708005i \(-0.250405\pi\)
\(444\) 2.93926e8 4.43023e7i 0.159367 0.0240207i
\(445\) −2.23316e8 2.07207e8i −0.120132 0.111467i
\(446\) 3.15199e8 + 1.51792e8i 0.168234 + 0.0810171i
\(447\) 5.84858e8 3.98750e8i 0.309724 0.211166i
\(448\) 2.91259e8 + 7.42115e8i 0.153040 + 0.389940i
\(449\) −1.61683e9 + 4.98726e8i −0.842951 + 0.260016i −0.686010 0.727592i \(-0.740639\pi\)
−0.156941 + 0.987608i \(0.550163\pi\)
\(450\) 6.04298e8 5.60706e8i 0.312613 0.290063i
\(451\) 3.47182e9 4.35352e9i 1.78213 2.23472i
\(452\) −3.39415e7 + 4.25613e7i −0.0172881 + 0.0216785i
\(453\) −7.03660e8 + 6.52901e8i −0.355647 + 0.329992i
\(454\) 5.58453e8 1.72260e8i 0.280086 0.0863951i
\(455\) −7.48899e7 1.90816e8i −0.0372721 0.0949676i
\(456\) −6.41372e8 + 4.37280e8i −0.316762 + 0.215965i
\(457\) 1.69294e9 + 8.15277e8i 0.829727 + 0.399575i 0.800013 0.599983i \(-0.204826\pi\)
0.0297140 + 0.999558i \(0.490540\pi\)
\(458\) −1.40734e9 1.30582e9i −0.684494 0.635118i
\(459\) 1.87733e9 2.82962e8i 0.906142 0.136579i
\(460\) 3.15977e6 4.21642e7i 0.00151357 0.0201972i
\(461\) 7.88414e8 2.00885e9i 0.374801 0.954978i −0.611680 0.791105i \(-0.709506\pi\)
0.986481 0.163873i \(-0.0523987\pi\)
\(462\) −3.39641e8 1.48807e9i −0.160241 0.702062i
\(463\) 8.79401e7 + 1.17348e9i 0.0411769 + 0.549468i 0.979200 + 0.202896i \(0.0650353\pi\)
−0.938023 + 0.346572i \(0.887346\pi\)
\(464\) 2.97961e9 + 9.19089e8i 1.38467 + 0.427115i
\(465\) −3.64743e8 + 1.75651e8i −0.168229 + 0.0810150i
\(466\) 1.46460e9 2.53676e9i 0.670453 1.16126i
\(467\) 2.29586e8 + 3.97654e8i 0.104312 + 0.180674i 0.913457 0.406935i \(-0.133403\pi\)
−0.809145 + 0.587609i \(0.800069\pi\)
\(468\) −1.17396e8 8.00394e7i −0.0529412 0.0360947i
\(469\) −3.68242e8 + 1.61337e9i −0.164827 + 0.722154i
\(470\) 2.40120e8 + 3.61923e7i 0.106681 + 0.0160796i
\(471\) −4.98134e8 6.24641e8i −0.219671 0.275459i
\(472\) 2.48107e7 0.0108603
\(473\) −4.14040e9 6.04961e7i −1.79899 0.0262853i
\(474\) −3.29007e8 −0.141900
\(475\) 7.63267e8 + 9.57106e8i 0.326775 + 0.409763i
\(476\) −1.19124e8 1.79550e7i −0.0506261 0.00763065i
\(477\) 2.68279e8 1.17541e9i 0.113181 0.495877i
\(478\) 5.89640e8 + 4.02010e8i 0.246939 + 0.168360i
\(479\) −4.38276e7 7.59116e7i −0.0182210 0.0315598i 0.856771 0.515697i \(-0.172467\pi\)
−0.874992 + 0.484137i \(0.839134\pi\)
\(480\) 3.70272e7 6.41330e7i 0.0152819 0.0264690i
\(481\) 4.77016e9 2.29719e9i 1.95445 0.941215i
\(482\) −2.13797e9 6.59475e8i −0.869633 0.268246i
\(483\) −7.05674e7 9.41656e8i −0.0284963 0.380257i
\(484\) −1.52230e8 6.66962e8i −0.0610297 0.267388i
\(485\) 5.73192e7 1.46047e8i 0.0228141 0.0581295i
\(486\) −1.53163e8 + 2.04382e9i −0.0605238 + 0.807634i
\(487\) 1.93654e9 2.91886e8i 0.759756 0.114515i 0.242273 0.970208i \(-0.422107\pi\)
0.517483 + 0.855693i \(0.326869\pi\)
\(488\) 3.74258e8 + 3.47260e8i 0.145781 + 0.135265i
\(489\) 8.70813e8 + 4.19361e8i 0.336778 + 0.162184i
\(490\) −2.82318e8 + 1.92481e8i −0.108406 + 0.0739099i
\(491\) 3.88318e8 + 9.89418e8i 0.148048 + 0.377220i 0.985590 0.169153i \(-0.0541033\pi\)
−0.837542 + 0.546373i \(0.816008\pi\)
\(492\) −3.76513e8 + 1.16139e8i −0.142529 + 0.0439643i
\(493\) 2.16003e9 2.00421e9i 0.811886 0.753320i
\(494\) 1.20459e9 1.51051e9i 0.449567 0.563739i
\(495\) −2.04883e8 + 2.56916e8i −0.0759257 + 0.0952078i
\(496\) −3.28732e9 + 3.05019e9i −1.20964 + 1.12238i
\(497\) −9.06609e8 + 2.79652e8i −0.331263 + 0.102181i
\(498\) 8.33090e8 + 2.12268e9i 0.302266 + 0.770161i
\(499\) −7.91772e6 + 5.39821e6i −0.00285265 + 0.00194490i −0.564746 0.825265i \(-0.691026\pi\)
0.561893 + 0.827210i \(0.310073\pi\)
\(500\) −9.97033e7 4.80146e7i −0.0356709 0.0171782i
\(501\) 6.74213e8 + 6.25578e8i 0.239533 + 0.222254i
\(502\) 1.10282e9 1.66223e8i 0.389082 0.0586447i
\(503\) −4.90836e6 + 6.54975e7i −0.00171968 + 0.0229476i −0.997998 0.0632514i \(-0.979853\pi\)
0.996278 + 0.0861989i \(0.0274721\pi\)
\(504\) −1.99147e8 + 5.07418e8i −0.0692893 + 0.176546i
\(505\) 1.56749e8 + 6.86761e8i 0.0541607 + 0.237293i
\(506\) −4.19071e8 5.59211e9i −0.143801 1.91889i
\(507\) 1.28180e9 + 3.95382e8i 0.436809 + 0.134738i
\(508\) −1.61954e8 + 7.79927e7i −0.0548110 + 0.0263956i
\(509\) 1.81747e9 3.14794e9i 0.610877 1.05807i −0.380216 0.924898i \(-0.624150\pi\)
0.991093 0.133172i \(-0.0425164\pi\)
\(510\) −1.68372e8 2.91629e8i −0.0562049 0.0973497i
\(511\) −2.06742e9 1.40954e9i −0.685419 0.467310i
\(512\) −5.13282e8 + 2.24884e9i −0.169010 + 0.740480i
\(513\) −1.76266e9 2.65678e8i −0.576444 0.0868850i
\(514\) 1.19563e9 + 1.49928e9i 0.388353 + 0.486980i
\(515\) 7.81824e8 0.252223
\(516\) 2.39656e8 + 1.68576e8i 0.0767917 + 0.0540158i
\(517\) 3.51729e9 1.11942
\(518\) 1.76961e9 + 2.21902e9i 0.559401 + 0.701466i
\(519\) −2.13993e9 3.22543e8i −0.671915 0.101275i
\(520\) 1.37173e8 6.00995e8i 0.0427817 0.187439i
\(521\) 1.97703e9 + 1.34792e9i 0.612465 + 0.417571i 0.829432 0.558607i \(-0.188664\pi\)
−0.216967 + 0.976179i \(0.569617\pi\)
\(522\) 9.31519e8 + 1.61344e9i 0.286645 + 0.496484i
\(523\) −2.00426e9 + 3.47148e9i −0.612629 + 1.06111i 0.378166 + 0.925738i \(0.376555\pi\)
−0.990795 + 0.135367i \(0.956779\pi\)
\(524\) −3.92230e8 + 1.88888e8i −0.119092 + 0.0573515i
\(525\) −1.16479e9 3.59289e8i −0.351309 0.108364i
\(526\) −3.66381e8 4.88901e9i −0.109770 1.46477i
\(527\) 9.42990e8 + 4.13151e9i 0.280653 + 1.22962i
\(528\) 1.88569e9 4.80466e9i 0.557509 1.42051i
\(529\) 4.82359e6 6.43663e7i 0.00141669 0.0189044i
\(530\) −7.22747e8 + 1.08937e8i −0.210873 + 0.0317840i
\(531\) 1.22193e7 + 1.13379e7i 0.00354174 + 0.00328626i
\(532\) 1.01909e8 + 4.90769e7i 0.0293443 + 0.0141314i
\(533\) −5.79867e9 + 3.95347e9i −1.65876 + 1.13092i
\(534\) 1.04449e9 + 2.66132e9i 0.296831 + 0.756314i
\(535\) 2.39187e7 7.37793e6i 0.00675303 0.00208303i
\(536\) −3.64813e9 + 3.38497e9i −1.02328 + 0.949463i
\(537\) 6.84389e8 8.58196e8i 0.190718 0.239153i
\(538\) 2.86920e9 3.59787e9i 0.794371 0.996110i
\(539\) −3.62802e9 + 3.36631e9i −0.997951 + 0.925963i
\(540\) 7.59447e7 2.34258e7i 0.0207548 0.00640202i
\(541\) −7.06146e7 1.79923e8i −0.0191736 0.0488536i 0.920966 0.389642i \(-0.127401\pi\)
−0.940140 + 0.340788i \(0.889306\pi\)
\(542\) 1.50487e9 1.02600e9i 0.405976 0.276790i
\(543\) 4.10348e9 + 1.97613e9i 1.09990 + 0.529683i
\(544\) −5.68256e8 5.27265e8i −0.151338 0.140421i
\(545\) 4.37563e8 6.59521e7i 0.115785 0.0174518i
\(546\) −1.43761e8 + 1.91835e9i −0.0377978 + 0.504376i
\(547\) 1.42949e9 3.64228e9i 0.373444 0.951520i −0.613389 0.789781i \(-0.710194\pi\)
0.986834 0.161739i \(-0.0517104\pi\)
\(548\) 1.80751e8 + 7.91920e8i 0.0469189 + 0.205565i
\(549\) 2.56334e7 + 3.42054e8i 0.00661154 + 0.0882249i
\(550\) −6.91719e9 2.13367e9i −1.77280 0.546837i
\(551\) −2.49265e9 + 1.20040e9i −0.634792 + 0.305700i
\(552\) 1.41988e9 2.45931e9i 0.359307 0.622338i
\(553\) −1.71544e8 2.97124e8i −0.0431359 0.0747136i
\(554\) 9.73428e8 + 6.63672e8i 0.243231 + 0.165832i
\(555\) −1.92802e8 + 8.44721e8i −0.0478725 + 0.209743i
\(556\) −3.90919e7 5.89216e6i −0.00964551 0.00145383i
\(557\) 2.66130e9 + 3.33716e9i 0.652530 + 0.818247i 0.992507 0.122187i \(-0.0389908\pi\)
−0.339977 + 0.940434i \(0.610419\pi\)
\(558\) −2.67937e9 −0.652850
\(559\) 4.96409e9 + 1.61101e9i 1.20198 + 0.390083i
\(560\) 3.71597e8 0.0894157
\(561\) −3.04110e9 3.81341e9i −0.727210 0.911893i
\(562\) 5.87140e9 + 8.84971e8i 1.39529 + 0.210306i
\(563\) 1.70609e9 7.47486e9i 0.402923 1.76532i −0.212538 0.977153i \(-0.568173\pi\)
0.615461 0.788168i \(-0.288970\pi\)
\(564\) −2.05638e8 1.40201e8i −0.0482643 0.0329060i
\(565\) −7.93407e7 1.37422e8i −0.0185066 0.0320543i
\(566\) 1.05098e9 1.82035e9i 0.243634 0.421986i
\(567\) 8.01331e8 3.85901e8i 0.184617 0.0889068i
\(568\) −2.72643e9 8.40991e8i −0.624273 0.192563i
\(569\) −3.57575e6 4.77151e7i −0.000813719 0.0108583i 0.996782 0.0801581i \(-0.0255425\pi\)
−0.997596 + 0.0692998i \(0.977923\pi\)
\(570\) 7.03555e7 + 3.08247e8i 0.0159124 + 0.0697168i
\(571\) 9.92812e8 2.52964e9i 0.223173 0.568634i −0.774805 0.632200i \(-0.782152\pi\)
0.997978 + 0.0635658i \(0.0202473\pi\)
\(572\) −9.32382e7 + 1.24418e9i −0.0208309 + 0.277969i
\(573\) 8.25561e8 1.24433e8i 0.183319 0.0276309i
\(574\) −2.75793e9 2.55898e9i −0.608683 0.564775i
\(575\) −4.03492e9 1.94311e9i −0.885110 0.426246i
\(576\) −1.33086e9 + 9.07368e8i −0.290172 + 0.197836i
\(577\) 1.48374e9 + 3.78050e9i 0.321545 + 0.819283i 0.996667 + 0.0815769i \(0.0259956\pi\)
−0.675122 + 0.737706i \(0.735909\pi\)
\(578\) 1.33190e9 4.10836e8i 0.286896 0.0884956i
\(579\) −4.32842e9 + 4.01619e9i −0.926733 + 0.859882i
\(580\) 7.69076e7 9.64390e7i 0.0163671 0.0205237i
\(581\) −1.48260e9 + 1.85912e9i −0.313623 + 0.393270i
\(582\) −1.07934e9 + 1.00148e9i −0.226948 + 0.210577i
\(583\) −1.01165e10 + 3.12052e9i −2.11441 + 0.652209i
\(584\) −2.74913e9 7.00467e9i −0.571150 1.45527i
\(585\) 3.42199e8 2.33307e8i 0.0706696 0.0481817i
\(586\) −4.71550e9 2.27086e9i −0.968024 0.466176i
\(587\) −5.81108e8 5.39189e8i −0.118583 0.110029i 0.618653 0.785665i \(-0.287679\pi\)
−0.737236 + 0.675635i \(0.763869\pi\)
\(588\) 3.46295e8 5.21955e7i 0.0702466 0.0105880i
\(589\) 2.97344e8 3.96778e9i 0.0599592 0.800099i
\(590\) 3.69198e6 9.40702e6i 0.000740078 0.00188569i
\(591\) 5.36565e8 + 2.35084e9i 0.106922 + 0.468455i
\(592\) 7.17242e8 + 9.57093e9i 0.142082 + 1.89596i
\(593\) −1.21514e9 3.74822e8i −0.239296 0.0738132i 0.172787 0.984959i \(-0.444723\pi\)
−0.412084 + 0.911146i \(0.635199\pi\)
\(594\) 9.49675e9 4.57339e9i 1.85918 0.895336i
\(595\) 1.75578e8 3.04110e8i 0.0341713 0.0591864i
\(596\) −1.55092e8 2.68627e8i −0.0300073 0.0519741i
\(597\) 2.77262e9 + 1.89034e9i 0.533311 + 0.363605i
\(598\) −1.57274e9 + 6.89064e9i −0.300749 + 1.31767i
\(599\) 9.87169e9 + 1.48792e9i 1.87671 + 0.282869i 0.985366 0.170453i \(-0.0545232\pi\)
0.891347 + 0.453322i \(0.149761\pi\)
\(600\) −2.28552e9 2.86595e9i −0.431973 0.541676i
\(601\) −9.65768e9 −1.81473 −0.907365 0.420343i \(-0.861910\pi\)
−0.907365 + 0.420343i \(0.861910\pi\)
\(602\) −2.49813e8 + 2.78657e9i −0.0466689 + 0.520574i
\(603\) −3.34357e9 −0.621011
\(604\) 2.62259e8 + 3.28863e8i 0.0484285 + 0.0607275i
\(605\) 1.97186e9 + 2.97209e8i 0.362019 + 0.0545656i
\(606\) 1.47104e9 6.44504e9i 0.268516 1.17645i
\(607\) −6.81404e9 4.64574e9i −1.23664 0.843129i −0.244674 0.969605i \(-0.578681\pi\)
−0.991970 + 0.126476i \(0.959633\pi\)
\(608\) 3.63921e8 + 6.30330e8i 0.0656666 + 0.113738i
\(609\) 1.37739e9 2.38571e9i 0.247114 0.428014i
\(610\) 1.87356e8 9.02261e7i 0.0334206 0.0160945i
\(611\) −4.23611e9 1.30667e9i −0.751317 0.231751i
\(612\) −1.81895e7 2.42722e8i −0.00320767 0.0428034i
\(613\) 7.19716e8 + 3.15328e9i 0.126197 + 0.552905i 0.998009 + 0.0630654i \(0.0200877\pi\)
−0.871812 + 0.489840i \(0.837055\pi\)
\(614\) −1.14340e8 + 2.91334e8i −0.0199347 + 0.0507927i
\(615\) 8.58294e7 1.14531e9i 0.0148790 0.198546i
\(616\) 4.73311e9 7.13401e8i 0.815857 0.122971i
\(617\) 3.69205e9 + 3.42572e9i 0.632804 + 0.587156i 0.929955 0.367674i \(-0.119846\pi\)
−0.297151 + 0.954831i \(0.596036\pi\)
\(618\) −6.61057e9 3.18348e9i −1.12663 0.542554i
\(619\) −5.98916e9 + 4.08334e9i −1.01496 + 0.691988i −0.952022 0.306030i \(-0.900999\pi\)
−0.0629374 + 0.998017i \(0.520047\pi\)
\(620\) 6.48111e7 + 1.65136e8i 0.0109214 + 0.0278273i
\(621\) 6.23143e9 1.92214e9i 1.04416 0.322081i
\(622\) 1.60118e9 1.48567e9i 0.266792 0.247547i
\(623\) −1.85882e9 + 2.33088e9i −0.307984 + 0.386200i
\(624\) −4.05599e9 + 5.08605e9i −0.668268 + 0.837981i
\(625\) −4.11790e9 + 3.82085e9i −0.674676 + 0.626008i
\(626\) −4.21389e9 + 1.29981e9i −0.686551 + 0.211773i
\(627\) 1.67312e9 + 4.26304e9i 0.271076 + 0.690689i
\(628\) −2.89265e8 + 1.97218e8i −0.0466055 + 0.0317751i
\(629\) 8.17163e9 + 3.93525e9i 1.30928 + 0.630515i
\(630\) 1.62754e8 + 1.51014e8i 0.0259323 + 0.0240616i
\(631\) 5.35856e9 8.07673e8i 0.849074 0.127977i 0.289930 0.957048i \(-0.406368\pi\)
0.559144 + 0.829071i \(0.311130\pi\)
\(632\) 7.71038e7 1.02888e9i 0.0121497 0.162127i
\(633\) −2.35198e9 + 5.99275e9i −0.368571 + 0.939103i
\(634\) 1.58517e9 + 6.94509e9i 0.247038 + 1.08234i
\(635\) −3.91562e7 5.22503e8i −0.00606866 0.0809806i
\(636\) 7.15843e8 + 2.20808e8i 0.110336 + 0.0340342i
\(637\) 5.62005e9 2.70647e9i 0.861494 0.414874i
\(638\) 8.17977e9 1.41678e10i 1.24701 2.15988i
\(639\) −9.58461e8 1.66010e9i −0.145319 0.251699i
\(640\) 1.02552e9 + 6.99190e8i 0.154638 + 0.105430i
\(641\) 1.33931e9 5.86790e9i 0.200853 0.879993i −0.769566 0.638567i \(-0.779528\pi\)
0.970419 0.241426i \(-0.0776153\pi\)
\(642\) −2.32282e8 3.50109e7i −0.0346452 0.00522192i
\(643\) −2.72511e9 3.41718e9i −0.404246 0.506909i 0.537486 0.843273i \(-0.319374\pi\)
−0.941732 + 0.336364i \(0.890803\pi\)
\(644\) −4.13792e8 −0.0610494
\(645\) −7.12632e8 + 4.70762e8i −0.104570 + 0.0690785i
\(646\) 3.30968e9 0.483027
\(647\) 6.22783e9 + 7.80946e9i 0.904008 + 1.13359i 0.990524 + 0.137339i \(0.0438551\pi\)
−0.0865165 + 0.996250i \(0.527574\pi\)
\(648\) 2.64483e9 + 3.98644e8i 0.381843 + 0.0575536i
\(649\) 3.25712e7 1.42704e8i 0.00467710 0.0204917i
\(650\) 7.53819e9 + 5.13945e9i 1.07664 + 0.734040i
\(651\) 1.98093e9 + 3.43107e9i 0.281407 + 0.487412i
\(652\) 2.11767e8 3.66791e8i 0.0299221 0.0518266i
\(653\) −5.96999e9 + 2.87500e9i −0.839031 + 0.404056i −0.803494 0.595313i \(-0.797028\pi\)
−0.0355364 + 0.999368i \(0.511314\pi\)
\(654\) −3.96829e9 1.22405e9i −0.554729 0.171111i
\(655\) −9.48311e7 1.26543e9i −0.0131858 0.175952i
\(656\) −2.83101e9 1.24035e10i −0.391541 1.71545i
\(657\) 1.84701e9 4.70611e9i 0.254092 0.647416i
\(658\) 1.77592e8 2.36980e9i 0.0243015 0.324281i
\(659\) −8.39273e9 + 1.26500e9i −1.14236 + 0.172184i −0.692844 0.721087i \(-0.743643\pi\)
−0.449519 + 0.893271i \(0.648405\pi\)
\(660\) −1.49675e8 1.38878e8i −0.0202650 0.0188032i
\(661\) −4.22119e8 2.03282e8i −0.0568499 0.0273775i 0.405243 0.914209i \(-0.367187\pi\)
−0.462093 + 0.886832i \(0.652901\pi\)
\(662\) 1.16854e10 7.96699e9i 1.56546 1.06731i
\(663\) 2.24592e9 + 5.72251e9i 0.299293 + 0.762587i
\(664\) −6.83332e9 + 2.10780e9i −0.905824 + 0.279410i
\(665\) −2.41692e8 + 2.24258e8i −0.0318704 + 0.0295714i
\(666\) −3.57541e9 + 4.48342e9i −0.468992 + 0.588097i
\(667\) 6.31044e9 7.91304e9i 0.823416 1.03253i
\(668\) 2.95441e8 2.74129e8i 0.0383489 0.0355826i
\(669\) 9.98742e8 3.08071e8i 0.128962 0.0397795i
\(670\) 7.40554e8 + 1.88690e9i 0.0951251 + 0.242375i
\(671\) 2.48866e9 1.69674e9i 0.318007 0.216814i
\(672\) −6.52954e8 3.14446e8i −0.0830023 0.0399718i
\(673\) 9.52179e9 + 8.83493e9i 1.20411 + 1.11725i 0.990092 + 0.140421i \(0.0448455\pi\)
0.214018 + 0.976830i \(0.431345\pi\)
\(674\) −5.42939e8 + 8.18349e7i −0.0683032 + 0.0102951i
\(675\) 6.29062e8 8.39425e9i 0.0787282 1.05055i
\(676\) 2.14747e8 5.47167e8i 0.0267371 0.0681250i
\(677\) −1.95873e9 8.58176e9i −0.242613 1.06296i −0.938628 0.344930i \(-0.887902\pi\)
0.696015 0.718027i \(-0.254955\pi\)
\(678\) 1.11286e8 + 1.48501e9i 0.0137132 + 0.182989i
\(679\) −1.46719e9 4.52569e8i −0.179863 0.0554805i
\(680\) 9.51446e8 4.58192e8i 0.116039 0.0558813i
\(681\) 8.72986e8 1.51206e9i 0.105924 0.183465i
\(682\) 1.17639e10 + 2.03757e10i 1.42006 + 2.45962i
\(683\) −7.57665e9 5.16567e9i −0.909923 0.620375i 0.0152654 0.999883i \(-0.495141\pi\)
−0.925188 + 0.379509i \(0.876093\pi\)
\(684\) −5.08537e7 + 2.22805e8i −0.00607612 + 0.0266212i
\(685\) −2.34129e9 3.52893e8i −0.278316 0.0419494i
\(686\) 4.84030e9 + 6.06954e9i 0.572450 + 0.717829i
\(687\) −5.73559e9 −0.674885
\(688\) −6.00619e9 + 7.30983e9i −0.703136 + 0.855752i
\(689\) 1.33432e10 1.55415
\(690\) −7.21164e8 9.04311e8i −0.0835723 0.104796i
\(691\) 5.97937e7 + 9.01245e6i 0.00689417 + 0.00103913i 0.152488 0.988305i \(-0.451271\pi\)
−0.145594 + 0.989344i \(0.546509\pi\)
\(692\) −2.11019e8 + 9.24536e8i −0.0242076 + 0.106060i
\(693\) 2.65708e9 + 1.81157e9i 0.303276 + 0.206770i
\(694\) −5.71119e9 9.89207e9i −0.648587 1.12339i
\(695\) 5.76181e7 9.97976e7i 0.00651047 0.0112765i
\(696\) 7.46399e9 3.59447e9i 0.839149 0.404113i
\(697\) −1.14885e10 3.54373e9i −1.28513 0.396411i
\(698\) −7.37564e8 9.84211e9i −0.0820930 1.09545i
\(699\) −1.94731e9 8.53170e9i −0.215657 0.944856i
\(700\) −1.95144e8 + 4.97218e8i −0.0215036 + 0.0547903i
\(701\) −1.58997e8 + 2.12166e9i −0.0174331 + 0.232629i 0.981681 + 0.190534i \(0.0610220\pi\)
−0.999114 + 0.0420943i \(0.986597\pi\)
\(702\) −1.31366e10 + 1.98002e9i −1.43319 + 0.216018i
\(703\) −6.24254e9 5.79223e9i −0.677669 0.628785i
\(704\) 1.27435e10 + 6.13693e9i 1.37652 + 0.662899i
\(705\) 5.99414e8 4.08674e8i 0.0644266 0.0439253i
\(706\) −3.86069e8 9.83687e8i −0.0412903 0.105206i
\(707\) 6.58747e9 2.03196e9i 0.701052 0.216246i
\(708\) −7.59252e6 + 7.04483e6i −0.000804025 + 0.000746026i
\(709\) 6.11813e9 7.67189e9i 0.644699 0.808427i −0.346883 0.937908i \(-0.612760\pi\)
0.991582 + 0.129482i \(0.0413313\pi\)
\(710\) −7.24573e8 + 9.08586e8i −0.0759763 + 0.0952712i
\(711\) 5.08147e8 4.71492e8i 0.0530208 0.0491961i
\(712\) −8.56731e9 + 2.64266e9i −0.889538 + 0.274386i
\(713\) 5.31790e9 + 1.35498e10i 0.549448 + 1.39997i
\(714\) −2.72287e9 + 1.85642e9i −0.279951 + 0.190868i
\(715\) −3.27667e9 1.57796e9i −0.335244 0.161445i
\(716\) −3.52599e8 3.27164e8i −0.0358993 0.0333097i
\(717\) 2.10823e9 3.17765e8i 0.213600 0.0321950i
\(718\) 1.15863e9 1.54608e10i 0.116818 1.55882i
\(719\) 7.83351e8 1.99595e9i 0.0785969 0.200262i −0.886174 0.463352i \(-0.846647\pi\)
0.964771 + 0.263090i \(0.0847418\pi\)
\(720\) 1.67067e8 + 7.31969e8i 0.0166812 + 0.0730851i
\(721\) −5.71776e8 7.62982e9i −0.0568137 0.758126i
\(722\) 7.26953e9 + 2.24235e9i 0.718830 + 0.221730i
\(723\) −6.02228e9 + 2.90018e9i −0.592621 + 0.285391i
\(724\) 9.97897e8 1.72841e9i 0.0977239 0.169263i
\(725\) −6.53242e9 1.13145e10i −0.636636 1.10269i
\(726\) −1.54625e10 1.05421e10i −1.49969 1.02247i
\(727\) −1.76854e9 + 7.74846e9i −0.170704 + 0.747903i 0.815006 + 0.579452i \(0.196733\pi\)
−0.985710 + 0.168450i \(0.946124\pi\)
\(728\) −5.96543e9 8.99144e8i −0.573036 0.0863713i
\(729\) 6.52682e9 + 8.18438e9i 0.623958 + 0.782419i
\(730\) −3.06492e9 −0.291601
\(731\) 3.14438e9 + 8.36927e9i 0.297731 + 0.792459i
\(732\) −2.13132e8 −0.0200844
\(733\) 3.15392e9 + 3.95489e9i 0.295792 + 0.370912i 0.907414 0.420239i \(-0.138054\pi\)
−0.611621 + 0.791151i \(0.709482\pi\)
\(734\) 9.83419e8 + 1.48227e8i 0.0917915 + 0.0138353i
\(735\) −2.27153e8 + 9.95223e8i −0.0211015 + 0.0924517i
\(736\) −2.19999e9 1.49993e9i −0.203399 0.138675i
\(737\) 1.46801e10 + 2.54267e10i 1.35081 + 2.33967i
\(738\) 3.80072e9 6.58304e9i 0.348072 0.602878i
\(739\) −5.33974e9 + 2.57148e9i −0.486704 + 0.234384i −0.661109 0.750290i \(-0.729914\pi\)
0.174406 + 0.984674i \(0.444200\pi\)
\(740\) 3.62809e8 + 1.11912e8i 0.0329129 + 0.0101523i
\(741\) −4.31339e8 5.75583e9i −0.0389453 0.519689i
\(742\) 1.59168e9 + 6.97362e9i 0.143035 + 0.626678i
\(743\) −3.12015e9 + 7.95002e9i −0.279071 + 0.711062i 0.720769 + 0.693176i \(0.243789\pi\)
−0.999840 + 0.0178864i \(0.994306\pi\)
\(744\) −8.90365e8 + 1.18811e10i −0.0792616 + 1.05767i
\(745\) 8.94056e8 1.34757e8i 0.0792169 0.0119400i
\(746\) 1.25610e10 + 1.16550e10i 1.10775 + 1.02784i
\(747\) −4.32865e9 2.08457e9i −0.379953 0.182976i
\(748\) −1.76596e9 + 1.20401e9i −0.154285 + 0.105190i
\(749\) −8.94938e7 2.28027e8i −0.00778228 0.0198289i
\(750\) −2.89273e9 + 8.92289e8i −0.250376 + 0.0772309i
\(751\) −4.68298e9 + 4.34517e9i −0.403443 + 0.374341i −0.855635 0.517580i \(-0.826833\pi\)
0.452191 + 0.891921i \(0.350642\pi\)
\(752\) 5.01049e9 6.28296e9i 0.429653 0.538768i
\(753\) 2.07743e9 2.60501e9i 0.177314 0.222345i
\(754\) −1.51148e10 + 1.40244e10i −1.28411 + 1.19148i
\(755\) −1.17163e9 + 3.61399e8i −0.0990775 + 0.0305614i
\(756\) −2.84154e8 7.24012e8i −0.0239181 0.0609424i
\(757\) −1.21608e10 + 8.29108e9i −1.01889 + 0.694665i −0.952940 0.303158i \(-0.901959\pi\)
−0.0659462 + 0.997823i \(0.521007\pi\)
\(758\) −1.74542e10 8.40552e9i −1.45566 0.701007i
\(759\) −1.22812e10 1.13953e10i −1.01952 0.945974i
\(760\) −9.80446e8 + 1.47779e8i −0.0810170 + 0.0122114i
\(761\) 1.14199e9 1.52388e10i 0.0939324 1.25344i −0.728687 0.684847i \(-0.759869\pi\)
0.822619 0.568593i \(-0.192512\pi\)
\(762\) −1.79649e9 + 4.57737e9i −0.147089 + 0.374778i
\(763\) −9.63632e8 4.22195e9i −0.0785372 0.344094i
\(764\) −2.73398e7 3.64825e8i −0.00221804 0.0295977i
\(765\) 6.77973e8 + 2.09127e8i 0.0547517 + 0.0168887i
\(766\) −1.45915e10 + 7.02689e9i −1.17300 + 0.564888i
\(767\) −9.22418e7 + 1.59768e8i −0.00738149 + 0.0127851i
\(768\) −1.74242e9 3.01795e9i −0.138799 0.240408i
\(769\) −7.30670e9 4.98162e9i −0.579401 0.395029i 0.237858 0.971300i \(-0.423555\pi\)
−0.817259 + 0.576271i \(0.804507\pi\)
\(770\) 4.33828e8 1.90073e9i 0.0342453 0.150038i
\(771\) 5.66507e9 + 8.53871e8i 0.445158 + 0.0670968i
\(772\) 1.61323e9 + 2.02293e9i 0.126193 + 0.158242i
\(773\) 5.97118e9 0.464978 0.232489 0.972599i \(-0.425313\pi\)
0.232489 + 0.972599i \(0.425313\pi\)
\(774\) −5.60128e9 + 7.60741e8i −0.434204 + 0.0589717i
\(775\) 1.87895e10 1.44997
\(776\) −2.87890e9 3.61002e9i −0.221162 0.277328i
\(777\) 8.38463e9 + 1.26378e9i 0.641225 + 0.0966491i
\(778\) 4.14573e9 1.81636e10i 0.315626 1.38285i
\(779\) 9.32679e9 + 6.35890e9i 0.706889 + 0.481948i
\(780\) 1.28671e8 + 2.22865e8i 0.00970845 + 0.0168155i
\(781\) −8.41636e9 + 1.45776e10i −0.632187 + 1.09498i
\(782\) −1.09087e10 + 5.25335e9i −0.815736 + 0.392838i
\(783\) 1.81789e10 + 5.60744e9i 1.35332 + 0.417444i
\(784\) 8.45032e8 + 1.12762e10i 0.0626278 + 0.835709i
\(785\) −2.27083e8 9.94918e8i −0.0167549 0.0734080i
\(786\) −4.35085e9 + 1.10858e10i −0.319591 + 0.814306i
\(787\) −5.51476e8 + 7.35894e9i −0.0403288 + 0.538150i 0.940051 + 0.341033i \(0.110777\pi\)
−0.980380 + 0.197117i \(0.936842\pi\)
\(788\) 1.04483e9 1.57483e8i 0.0760685 0.0114655i
\(789\) −1.07371e10 9.96255e9i −0.778245 0.722106i
\(790\) −3.78628e8 1.82338e8i −0.0273223 0.0131577i
\(791\) −1.28308e9 + 8.74787e8i −0.0921797 + 0.0628470i
\(792\) 3.53322e9 + 9.00250e9i 0.252716 + 0.643910i
\(793\) −3.62760e9 + 1.11897e9i −0.258323 + 0.0796821i
\(794\) −1.13093e10 + 1.04935e10i −0.801794 + 0.743956i
\(795\) −1.36147e9 + 1.70723e9i −0.0960998 + 0.120505i
\(796\) 9.16828e8 1.14967e9i 0.0644306 0.0807934i
\(797\) 1.55399e10 1.44190e10i 1.08729 1.00886i 0.0873702 0.996176i \(-0.472154\pi\)
0.999920 0.0126816i \(-0.00403679\pi\)
\(798\) 2.95673e9 9.12032e8i 0.205969 0.0635331i
\(799\) −2.77446e9 7.06921e9i −0.192426 0.490294i
\(800\) −2.83984e9 + 1.93617e9i −0.196101 + 0.133699i
\(801\) −5.42706e9 2.61354e9i −0.373122 0.179686i
\(802\) 1.40655e9 + 1.30509e9i 0.0962818 + 0.0893364i
\(803\) −4.38978e10 + 6.61653e9i −2.99184 + 0.450948i
\(804\) 1.55254e8 2.07173e9i 0.0105353 0.140584i
\(805\) 4.40661e8 1.12279e9i 0.0297728 0.0758597i
\(806\) −6.59855e9 2.89102e10i −0.443891 1.94481i
\(807\) −1.02741e9 1.37098e10i −0.0688152 0.918275i
\(808\) 1.98103e10 + 6.11068e9i 1.32115 + 0.407521i
\(809\) 8.26153e9 3.97854e9i 0.548581 0.264183i −0.138998 0.990293i \(-0.544388\pi\)
0.687578 + 0.726110i \(0.258674\pi\)
\(810\) 5.44714e8 9.43472e8i 0.0360140 0.0623780i
\(811\) 2.70213e9 + 4.68022e9i 0.177882 + 0.308101i 0.941155 0.337975i \(-0.109742\pi\)
−0.763273 + 0.646076i \(0.776409\pi\)
\(812\) −9.97394e8 6.80012e8i −0.0653763 0.0445728i
\(813\) 1.21082e9 5.30493e9i 0.0790244 0.346228i
\(814\) 4.97929e10 + 7.50507e9i 3.23580 + 0.487719i
\(815\) 7.69736e8 + 9.65219e8i 0.0498070 + 0.0624560i
\(816\) −1.11441e10 −0.718005
\(817\) −5.04948e8 8.37915e9i −0.0323944 0.537555i
\(818\) 2.35133e10 1.50203
\(819\) −2.52711e9 3.16889e9i −0.160742 0.201564i
\(820\) −4.97664e8 7.50107e7i −0.0315201 0.00475089i
\(821\) 7.33479e7 3.21358e8i 0.00462580 0.0202670i −0.972562 0.232642i \(-0.925263\pi\)
0.977188 + 0.212375i \(0.0681200\pi\)
\(822\) 1.83594e10 + 1.25172e10i 1.15294 + 0.786063i
\(823\) −3.73294e9 6.46565e9i −0.233428 0.404308i 0.725387 0.688341i \(-0.241661\pi\)
−0.958815 + 0.284033i \(0.908328\pi\)
\(824\) 1.15047e10 1.99267e10i 0.716356 1.24077i
\(825\) −1.94845e10 + 9.38326e9i −1.20810 + 0.581788i
\(826\) −9.45032e7 2.91504e7i −0.00583467 0.00179976i
\(827\) −9.32162e8 1.24388e10i −0.0573089 0.764734i −0.949638 0.313349i \(-0.898549\pi\)
0.892329 0.451385i \(-0.149070\pi\)
\(828\) −1.86038e8 8.15084e8i −0.0113892 0.0498995i
\(829\) 8.25170e9 2.10250e10i 0.503040 1.28173i −0.423625 0.905838i \(-0.639243\pi\)
0.926665 0.375888i \(-0.122662\pi\)
\(830\) −2.17664e8 + 2.90452e9i −0.0132134 + 0.176320i
\(831\) 3.48044e9 5.24592e8i 0.210393 0.0317116i
\(832\) −1.30680e10 1.21253e10i −0.786641 0.729896i
\(833\) 9.62756e9 + 4.63639e9i 0.577110 + 0.277922i
\(834\) −8.93542e8 + 6.09207e8i −0.0533376 + 0.0363650i
\(835\) 4.29199e8 + 1.09358e9i 0.0255127 + 0.0650052i
\(836\) 1.91763e9 5.91511e8i 0.113512 0.0350140i
\(837\) −2.00562e10 + 1.86095e10i −1.18225 + 1.09697i
\(838\) 3.53664e9 4.43481e9i 0.207605 0.260328i
\(839\) −3.02851e9 + 3.79763e9i −0.177036 + 0.221996i −0.862430 0.506176i \(-0.831059\pi\)
0.685394 + 0.728172i \(0.259630\pi\)
\(840\) 7.23722e8 6.71516e8i 0.0421303 0.0390912i
\(841\) 1.17310e10 3.61855e9i 0.680066 0.209772i
\(842\) 3.23763e9 + 8.24934e9i 0.186911 + 0.476241i
\(843\) 1.46568e10 9.99284e9i 0.842641 0.574503i
\(844\) 2.54167e9 + 1.22400e9i 0.145519 + 0.0700783i
\(845\) 1.25600e9 + 1.16539e9i 0.0716126 + 0.0664468i
\(846\) 4.74787e9 7.15626e8i 0.269589 0.0406340i
\(847\) 1.45838e9 1.94607e10i 0.0824666 1.10044i
\(848\) −8.83703e9 + 2.25164e10i −0.497646 + 1.26798i
\(849\) −1.39737e9 6.12226e9i −0.0783670 0.343348i
\(850\) 1.16797e9 + 1.55855e10i 0.0652329 + 0.870472i
\(851\) 2.97693e10 + 9.18260e9i 1.65583 + 0.510755i
\(852\) 1.07313e9 5.16792e8i 0.0594448 0.0286271i
\(853\) 1.27340e10 2.20559e10i 0.702493 1.21675i −0.265096 0.964222i \(-0.585404\pi\)
0.967589 0.252531i \(-0.0812630\pi\)
\(854\) −1.01754e9 1.76243e9i −0.0559046 0.0968296i
\(855\) −5.50404e8 3.75259e8i −0.0301162 0.0205329i
\(856\) 1.63923e8 7.18192e8i 0.00893266 0.0391366i
\(857\) 4.56684e9 + 6.88340e8i 0.247846 + 0.0373568i 0.271790 0.962356i \(-0.412384\pi\)
−0.0239440 + 0.999713i \(0.507622\pi\)
\(858\) 2.12800e10 + 2.66843e10i 1.15018 + 1.44228i
\(859\) 1.81748e10 0.978347 0.489173 0.872187i \(-0.337299\pi\)
0.489173 + 0.872187i \(0.337299\pi\)
\(860\) 1.82375e8 + 3.26819e8i 0.00977735 + 0.0175211i
\(861\) −1.12399e10 −0.600138
\(862\) −1.00819e10 1.26423e10i −0.536127 0.672282i
\(863\) −3.17968e9 4.79260e8i −0.168402 0.0253825i 0.0643001 0.997931i \(-0.479519\pi\)
−0.232702 + 0.972548i \(0.574757\pi\)
\(864\) 1.11368e9 4.87933e9i 0.0587436 0.257373i
\(865\) −2.28392e9 1.55715e9i −0.119984 0.0818040i
\(866\) −1.99552e9 3.45634e9i −0.104410 0.180844i
\(867\) 2.08205e9 3.60622e9i 0.108499 0.187925i
\(868\) 1.56416e9 7.53262e8i 0.0811826 0.0390955i
\(869\) −5.81659e9 1.79418e9i −0.300676 0.0927463i
\(870\) −2.52162e8 3.36487e9i −0.0129826 0.173241i
\(871\) −8.23429e9 3.60768e10i −0.422243 1.84997i
\(872\) 4.75787e9 1.21229e10i 0.242999 0.619152i
\(873\) 2.31829e8 3.09354e9i 0.0117928 0.157364i
\(874\) 1.12412e10 1.69434e9i 0.569538 0.0858441i
\(875\) −2.31409e9 2.14716e9i −0.116776 0.108352i
\(876\) 2.83022e9 + 1.36296e9i 0.142251 + 0.0685044i
\(877\) 2.06977e10 1.41114e10i 1.03615 0.706436i 0.0792514 0.996855i \(-0.474747\pi\)
0.956900 + 0.290419i \(0.0937946\pi\)
\(878\) 6.58775e9 + 1.67853e10i 0.328478 + 0.836948i
\(879\) −1.49416e10 + 4.60886e9i −0.742053 + 0.228893i
\(880\) 4.83286e9 4.48424e9i 0.239064 0.221819i
\(881\) −1.58288e10 + 1.98486e10i −0.779886 + 0.977946i 0.220111 + 0.975475i \(0.429358\pi\)
−0.999997 + 0.00247122i \(0.999213\pi\)
\(882\) −4.21243e9 + 5.28222e9i −0.206725 + 0.259225i
\(883\) −2.01710e10 + 1.87160e10i −0.985974 + 0.914850i −0.996373 0.0850961i \(-0.972880\pi\)
0.0103991 + 0.999946i \(0.496690\pi\)
\(884\) 2.57415e9 7.94019e8i 0.125329 0.0386588i
\(885\) −1.10300e7 2.81039e7i −0.000534900 0.00136290i
\(886\) −2.75039e10 + 1.87518e10i −1.32854 + 0.905786i
\(887\) −2.39560e10 1.15366e10i −1.15261 0.555068i −0.242793 0.970078i \(-0.578064\pi\)
−0.909817 + 0.415010i \(0.863778\pi\)
\(888\) 1.86926e10 + 1.73442e10i 0.895829 + 0.831208i
\(889\) −5.07047e9 + 7.64251e8i −0.242043 + 0.0364821i
\(890\) −2.72897e8 + 3.64156e9i −0.0129758 + 0.173150i
\(891\) 5.76499e9 1.46889e10i 0.273040 0.695695i
\(892\) −1.01914e8 4.46514e8i −0.00480792 0.0210649i
\(893\) 5.32847e8 + 7.11036e9i 0.0250393 + 0.334127i
\(894\) −8.10824e9 2.50106e9i −0.379529 0.117069i
\(895\) 1.26323e9 6.08337e8i 0.0588979 0.0283638i
\(896\) 6.07339e9 1.05194e10i 0.282068 0.488556i
\(897\) 1.05578e10 + 1.82866e10i 0.488425 + 0.845977i
\(898\) 1.67581e10 + 1.14255e10i 0.772248 + 0.526510i
\(899\) −9.44913e9 + 4.13993e10i −0.433743 + 1.90035i
\(900\) −1.06715e9 1.60847e8i −0.0487952 0.00735469i
\(901\) 1.42517e10 + 1.78710e10i 0.649126 + 0.813979i
\(902\) −6.67491e10 −3.02847
\(903\) 5.11534e9 + 6.61029e9i 0.231189 + 0.298754i
\(904\) −4.67004e9 −0.210248
\(905\) 3.62718e9 + 4.54834e9i 0.162667 + 0.203978i
\(906\) 1.13780e10 + 1.71496e9i 0.508299 + 0.0766137i
\(907\) 7.76428e8 3.40175e9i 0.0345522 0.151383i −0.954709 0.297541i \(-0.903834\pi\)
0.989261 + 0.146158i \(0.0466907\pi\)
\(908\) −6.32144e8 4.30989e8i −0.0280231 0.0191058i
\(909\) 6.96422e9 + 1.20624e10i 0.307538 + 0.532672i
\(910\) −1.22861e9 + 2.12801e9i −0.0540465 + 0.0936113i
\(911\) −2.25043e10 + 1.08375e10i −0.986169 + 0.474914i −0.856223 0.516607i \(-0.827195\pi\)
−0.129946 + 0.991521i \(0.541481\pi\)
\(912\) 9.99849e9 + 3.08413e9i 0.436468 + 0.134633i
\(913\) 3.15274e9 + 4.20704e10i 0.137101 + 1.82948i
\(914\) −5.01211e9 2.19595e10i −0.217125 0.951285i
\(915\) 2.26972e8 5.78314e8i 0.00979484 0.0249569i
\(916\) −1.87822e8 + 2.50631e9i −0.00807445 + 0.107746i
\(917\) −1.22800e10 + 1.85091e9i −0.525904 + 0.0792672i
\(918\) −1.66829e10 1.54794e10i −0.711740 0.660399i
\(919\) −3.13327e10 1.50891e10i −1.33166 0.641295i −0.373529 0.927618i \(-0.621852\pi\)
−0.958133 + 0.286324i \(0.907567\pi\)
\(920\) 2.99699e9 2.04331e9i 0.126890 0.0865122i
\(921\) 3.41596e8 + 8.70372e8i 0.0144080 + 0.0367110i
\(922\) −2.47194e10 + 7.62491e9i −1.03867 + 0.320388i
\(923\) 1.55519e10 1.44301e10i 0.650996 0.604036i
\(924\) −1.24585e9 + 1.56225e9i −0.0519535 + 0.0651476i
\(925\) 2.50731e10 3.14407e10i 1.04163 1.30616i
\(926\) 1.03406e10 9.59464e9i 0.427962 0.397091i
\(927\) 1.47721e10 4.55659e9i 0.609065 0.187872i
\(928\) −2.83787e9 7.23078e9i −0.116567 0.297007i
\(929\) −3.15073e10 + 2.14813e10i −1.28931 + 0.879035i −0.997009 0.0772915i \(-0.975373\pi\)
−0.292299 + 0.956327i \(0.594420\pi\)
\(930\) 4.37225e9 + 2.10557e9i 0.178244 + 0.0858378i
\(931\) −7.35476e9 6.82422e9i −0.298707 0.277159i
\(932\) −3.79191e9 + 5.71539e8i −0.153427 + 0.0231255i
\(933\) 4.87657e8 6.50733e9i 0.0196575 0.262311i
\(934\) 2.01090e9 5.12370e9i 0.0807564 0.205764i
\(935\) −1.38634e9 6.07395e9i −0.0554662 0.243013i
\(936\) −9.10885e8 1.21549e10i −0.0363076 0.484492i
\(937\) −1.74970e10 5.39712e9i −0.694826 0.214325i −0.0728280 0.997345i \(-0.523202\pi\)
−0.621998 + 0.783019i \(0.713679\pi\)
\(938\) 1.78727e10 8.60703e9i 0.707098 0.340521i
\(939\) −6.58724e9 + 1.14094e10i −0.259641 + 0.449712i
\(940\) −1.58952e8 2.75312e8i −0.00624191 0.0108113i
\(941\) −7.01414e9 4.78216e9i −0.274417 0.187094i 0.418290 0.908314i \(-0.362630\pi\)
−0.692707 + 0.721219i \(0.743582\pi\)
\(942\) −2.13111e9 + 9.33700e9i −0.0830668 + 0.363940i
\(943\) −4.08344e10 6.15480e9i −1.58575 0.239014i
\(944\) −2.08514e8 2.61468e8i −0.00806738 0.0101162i
\(945\) 2.26714e9 0.0873912
\(946\) 3.03779e10 + 3.92558e10i 1.16665 + 1.50760i
\(947\) 4.90596e9 0.187715 0.0938575 0.995586i \(-0.470080\pi\)
0.0938575 + 0.995586i \(0.470080\pi\)
\(948\) 2.68548e8 + 3.36749e8i 0.0102375 + 0.0128374i
\(949\) 5.53272e10 + 8.33923e9i 2.10139 + 0.316734i
\(950\) 3.26539e9 1.43066e10i 0.123567 0.541383i
\(951\) 1.75843e10 + 1.19888e10i 0.662969 + 0.452005i
\(952\) −5.16732e9 8.95007e9i −0.194105 0.336200i
\(953\) 3.04400e8 5.27236e8i 0.0113925 0.0197324i −0.860273 0.509834i \(-0.829707\pi\)
0.871665 + 0.490101i \(0.163040\pi\)
\(954\) −1.30210e10 + 6.27057e9i −0.485539 + 0.233823i
\(955\) 1.01903e9 + 3.14330e8i 0.0378597 + 0.0116782i
\(956\) −6.98176e7 9.31651e8i −0.00258441 0.0344866i
\(957\) −1.08757e10 4.76495e10i −0.401111 1.75738i
\(958\) −3.83878e8 + 9.78106e8i −0.0141063 + 0.0359424i
\(959\) −1.73161e9 + 2.31067e10i −0.0633994 + 0.846006i
\(960\) 2.88478e9 4.34811e8i 0.105236 0.0158617i
\(961\) −2.45997e10 2.28252e10i −0.894125 0.829627i
\(962\) −5.71809e10 2.75368e10i −2.07080 0.997244i
\(963\) 4.08929e8 2.78803e8i 0.0147556 0.0100602i
\(964\) 1.07010e9 + 2.72656e9i 0.0384727 + 0.0980270i
\(965\) −7.20703e9 + 2.22307e9i −0.258173 + 0.0796358i
\(966\) −8.29776e9 + 7.69920e9i −0.296170 + 0.274806i
\(967\) 9.95757e9 1.24864e10i 0.354128 0.444063i −0.572577 0.819851i \(-0.694056\pi\)
0.926706 + 0.375788i \(0.122628\pi\)
\(968\) 3.65913e10 4.58840e10i 1.29662 1.62591i
\(969\) 7.24827e9 6.72541e9i 0.255918 0.237457i
\(970\) −1.79715e9 + 5.54346e8i −0.0632241 + 0.0195020i
\(971\) 1.78076e10 + 4.53730e10i 0.624221 + 1.59049i 0.795962 + 0.605347i \(0.206965\pi\)
−0.171741 + 0.985142i \(0.554939\pi\)
\(972\) 2.21692e9 1.51147e9i 0.0774317 0.0527921i
\(973\) −1.01606e9 4.89310e8i −0.0353611 0.0170290i
\(974\) −1.72090e10 1.59676e10i −0.596760 0.553713i
\(975\) 2.69524e10 4.06242e9i 0.931282 0.140368i
\(976\) 5.14278e8 6.86256e9i 0.0177061 0.236272i
\(977\) −1.12026e10 + 2.85438e10i −0.384316 + 0.979221i 0.599554 + 0.800335i \(0.295345\pi\)
−0.983870 + 0.178887i \(0.942750\pi\)
\(978\) −2.57812e9 1.12955e10i −0.0881288 0.386117i
\(979\) 3.95276e9 + 5.27459e10i 0.134636 + 1.79659i
\(980\) 4.27450e8 + 1.31851e8i 0.0145075 + 0.00447498i
\(981\) 7.88312e9 3.79631e9i 0.266598 0.128387i
\(982\) 6.37055e9 1.10341e10i 0.214678 0.371832i
\(983\) 1.41843e9 + 2.45680e9i 0.0476290 + 0.0824959i 0.888857 0.458185i \(-0.151500\pi\)
−0.841228 + 0.540680i \(0.818167\pi\)
\(984\) −2.79281e10 1.90410e10i −0.934455 0.637101i
\(985\) −6.85361e8 + 3.00276e9i −0.0228503 + 0.100114i
\(986\) −3.49273e10 5.26444e9i −1.16037 0.174897i
\(987\) −4.42662e9 5.55081e9i −0.146542 0.183758i
\(988\) −2.52928e9 −0.0834349
\(989\) 1.49643e10 + 2.68162e10i 0.491892 + 0.881476i
\(990\) 3.93908e9 0.129024
\(991\) −1.16953e10 1.46655e10i −0.381728 0.478672i 0.553433 0.832893i \(-0.313317\pi\)
−0.935162 + 0.354222i \(0.884746\pi\)
\(992\) 1.10466e10 + 1.66500e9i 0.359283 + 0.0541532i
\(993\) 9.40209e9 4.11932e10i 0.304721 1.33507i
\(994\) 9.39680e9 + 6.40663e9i 0.303478 + 0.206908i
\(995\) 2.14315e9 + 3.71205e9i 0.0689719 + 0.119463i
\(996\) 1.49263e9 2.58530e9i 0.0478678 0.0829094i
\(997\) 4.48425e10 2.15950e10i 1.43304 0.690114i 0.453476 0.891268i \(-0.350184\pi\)
0.979559 + 0.201155i \(0.0644694\pi\)
\(998\) 1.09768e8 + 3.38590e7i 0.00349558 + 0.00107824i
\(999\) 4.37596e9 + 5.83931e10i 0.138865 + 1.85303i
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 43.8.g.a.9.6 300
43.24 even 21 inner 43.8.g.a.24.6 yes 300
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.8.g.a.9.6 300 1.1 even 1 trivial
43.8.g.a.24.6 yes 300 43.24 even 21 inner