Properties

Label 37.8.c.a.10.17
Level $37$
Weight $8$
Character 37.10
Analytic conductor $11.558$
Analytic rank $0$
Dimension $42$
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] = [37,8,Mod(10,37)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(37, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("37.10");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 37 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 37.c (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.5582459429\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(21\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 10.17
Character \(\chi\) \(=\) 37.10
Dual form 37.8.c.a.26.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(6.29543 - 10.9040i) q^{2} +(-9.44168 - 16.3535i) q^{3} +(-15.2650 - 26.4397i) q^{4} +(125.405 + 217.208i) q^{5} -237.758 q^{6} +(817.371 + 1415.73i) q^{7} +1227.23 q^{8} +(915.209 - 1585.19i) q^{9} +O(q^{10})\) \(q+(6.29543 - 10.9040i) q^{2} +(-9.44168 - 16.3535i) q^{3} +(-15.2650 - 26.4397i) q^{4} +(125.405 + 217.208i) q^{5} -237.758 q^{6} +(817.371 + 1415.73i) q^{7} +1227.23 q^{8} +(915.209 - 1585.19i) q^{9} +3157.91 q^{10} -3267.72 q^{11} +(-288.254 + 499.270i) q^{12} +(285.328 + 494.203i) q^{13} +20582.8 q^{14} +(2368.07 - 4101.61i) q^{15} +(9679.88 - 16766.0i) q^{16} +(-7432.84 + 12874.1i) q^{17} +(-11523.3 - 19958.9i) q^{18} +(-2699.93 - 4676.41i) q^{19} +(3828.60 - 6631.33i) q^{20} +(15434.7 - 26733.7i) q^{21} +(-20571.7 + 35631.2i) q^{22} +59967.8 q^{23} +(-11587.1 - 20069.5i) q^{24} +(7609.68 - 13180.4i) q^{25} +7185.06 q^{26} -75862.4 q^{27} +(24954.3 - 43222.1i) q^{28} +180212. q^{29} +(-29816.0 - 51642.9i) q^{30} +34853.9 q^{31} +(-43335.1 - 75058.6i) q^{32} +(30852.8 + 53438.5i) q^{33} +(93585.9 + 162096. i) q^{34} +(-205005. + 355079. i) q^{35} -55882.5 q^{36} +(-27020.0 + 306923. i) q^{37} -67988.8 q^{38} +(5387.96 - 9332.22i) q^{39} +(153901. + 266565. i) q^{40} +(-324720. - 562432. i) q^{41} +(-194336. - 336601. i) q^{42} -549580. q^{43} +(49881.6 + 86397.4i) q^{44} +459087. q^{45} +(377523. - 653889. i) q^{46} -1.06832e6 q^{47} -365577. q^{48} +(-924420. + 1.60114e6i) q^{49} +(-95812.5 - 165952. i) q^{50} +280714. q^{51} +(8711.05 - 15088.0i) q^{52} +(482032. - 834903. i) q^{53} +(-477586. + 827204. i) q^{54} +(-409788. - 709774. i) q^{55} +(1.00310e6 + 1.73743e6i) q^{56} +(-50983.7 + 88306.3i) q^{57} +(1.13451e6 - 1.96503e6i) q^{58} +(582905. - 1.00962e6i) q^{59} -144594. q^{60} +(-374247. - 648215. i) q^{61} +(219420. - 380047. i) q^{62} +2.99226e6 q^{63} +1.38679e6 q^{64} +(-71563.2 + 123951. i) q^{65} +776926. q^{66} +(-712036. - 1.23328e6i) q^{67} +453848. q^{68} +(-566196. - 980681. i) q^{69} +(2.58119e6 + 4.47075e6i) q^{70} +(2.01428e6 + 3.48884e6i) q^{71} +(1.12318e6 - 1.94540e6i) q^{72} -4.04944e6 q^{73} +(3.17659e6 + 2.22684e6i) q^{74} -287393. q^{75} +(-82428.5 + 142770. i) q^{76} +(-2.67094e6 - 4.62620e6i) q^{77} +(-67839.1 - 117501. i) q^{78} +(15409.3 + 26689.7i) q^{79} +4.85562e6 q^{80} +(-1.28529e6 - 2.22620e6i) q^{81} -8.17702e6 q^{82} +(2.14696e6 - 3.71865e6i) q^{83} -942441. q^{84} -3.72846e6 q^{85} +(-3.45985e6 + 5.99263e6i) q^{86} +(-1.70150e6 - 2.94708e6i) q^{87} -4.01025e6 q^{88} +(3.82252e6 - 6.62080e6i) q^{89} +(2.89015e6 - 5.00589e6i) q^{90} +(-466438. + 807895. i) q^{91} +(-915405. - 1.58553e6i) q^{92} +(-329079. - 569982. i) q^{93} +(-6.72554e6 + 1.16490e7i) q^{94} +(677168. - 1.17289e6i) q^{95} +(-818313. + 1.41736e6i) q^{96} -9.54599e6 q^{97} +(1.16392e7 + 2.01598e7i) q^{98} +(-2.99065e6 + 5.17995e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42 q - 16 q^{2} - 68 q^{3} - 1126 q^{4} - 337 q^{5} + 252 q^{6} - 158 q^{7} + 6264 q^{8} - 12773 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 42 q - 16 q^{2} - 68 q^{3} - 1126 q^{4} - 337 q^{5} + 252 q^{6} - 158 q^{7} + 6264 q^{8} - 12773 q^{9} + 10028 q^{10} + 14876 q^{11} - 4836 q^{12} - 5922 q^{13} + 20176 q^{14} - 8460 q^{15} - 36726 q^{16} - 19095 q^{17} - 7338 q^{18} - 34334 q^{19} - 75668 q^{20} - 32764 q^{21} + 18526 q^{22} - 99896 q^{23} - 203760 q^{24} - 322660 q^{25} + 101516 q^{26} + 846616 q^{27} - 73490 q^{28} + 168186 q^{29} - 88790 q^{30} - 38052 q^{31} - 172292 q^{32} - 54536 q^{33} + 90724 q^{34} - 247046 q^{35} + 352004 q^{36} + 740185 q^{37} + 1994976 q^{38} - 591380 q^{39} - 38962 q^{40} - 292827 q^{41} - 1499386 q^{42} + 630980 q^{43} - 1727390 q^{44} - 994286 q^{45} + 576988 q^{46} + 3394668 q^{47} - 79840 q^{48} + 728851 q^{49} - 69656 q^{50} - 3970200 q^{51} - 2043140 q^{52} + 584438 q^{53} - 2160774 q^{54} + 2019874 q^{55} - 658986 q^{56} + 4295748 q^{57} - 5684872 q^{58} - 1773152 q^{59} + 20208544 q^{60} - 3596569 q^{61} - 1538738 q^{62} + 11795092 q^{63} - 9622852 q^{64} - 5027290 q^{65} - 17464952 q^{66} - 3249754 q^{67} + 5608668 q^{68} + 9599384 q^{69} - 5102080 q^{70} - 1162530 q^{71} - 4730172 q^{72} - 5266532 q^{73} + 4052290 q^{74} + 35543072 q^{75} - 13781226 q^{76} + 121180 q^{77} - 7012890 q^{78} - 13545718 q^{79} - 17840888 q^{80} - 16689077 q^{81} - 43173544 q^{82} + 7359048 q^{83} + 41186680 q^{84} + 21047382 q^{85} + 6732838 q^{86} + 7672800 q^{87} + 42023140 q^{88} + 2955725 q^{89} - 14596808 q^{90} - 19887752 q^{91} + 13352900 q^{92} + 9156784 q^{93} + 690474 q^{94} - 5667270 q^{95} + 29986904 q^{96} + 52065982 q^{97} - 53664462 q^{98} - 35534038 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.29543 10.9040i 0.556443 0.963787i −0.441347 0.897337i \(-0.645499\pi\)
0.997790 0.0664508i \(-0.0211675\pi\)
\(3\) −9.44168 16.3535i −0.201895 0.349692i 0.747244 0.664550i \(-0.231377\pi\)
−0.949139 + 0.314858i \(0.898043\pi\)
\(4\) −15.2650 26.4397i −0.119257 0.206560i
\(5\) 125.405 + 217.208i 0.448662 + 0.777106i 0.998299 0.0582975i \(-0.0185672\pi\)
−0.549637 + 0.835404i \(0.685234\pi\)
\(6\) −237.758 −0.449371
\(7\) 817.371 + 1415.73i 0.900692 + 1.56004i 0.826598 + 0.562793i \(0.190273\pi\)
0.0740936 + 0.997251i \(0.476394\pi\)
\(8\) 1227.23 0.847446
\(9\) 915.209 1585.19i 0.418477 0.724824i
\(10\) 3157.91 0.998620
\(11\) −3267.72 −0.740236 −0.370118 0.928985i \(-0.620683\pi\)
−0.370118 + 0.928985i \(0.620683\pi\)
\(12\) −288.254 + 499.270i −0.0481549 + 0.0834067i
\(13\) 285.328 + 494.203i 0.0360200 + 0.0623884i 0.883473 0.468481i \(-0.155199\pi\)
−0.847453 + 0.530870i \(0.821865\pi\)
\(14\) 20582.8 2.00473
\(15\) 2368.07 4101.61i 0.181165 0.313787i
\(16\) 9679.88 16766.0i 0.590813 1.02332i
\(17\) −7432.84 + 12874.1i −0.366930 + 0.635542i −0.989084 0.147353i \(-0.952925\pi\)
0.622153 + 0.782895i \(0.286258\pi\)
\(18\) −11523.3 19958.9i −0.465717 0.806646i
\(19\) −2699.93 4676.41i −0.0903055 0.156414i 0.817334 0.576164i \(-0.195451\pi\)
−0.907640 + 0.419750i \(0.862118\pi\)
\(20\) 3828.60 6631.33i 0.107013 0.185351i
\(21\) 15434.7 26733.7i 0.363690 0.629929i
\(22\) −20571.7 + 35631.2i −0.411899 + 0.713430i
\(23\) 59967.8 1.02771 0.513855 0.857877i \(-0.328217\pi\)
0.513855 + 0.857877i \(0.328217\pi\)
\(24\) −11587.1 20069.5i −0.171095 0.296345i
\(25\) 7609.68 13180.4i 0.0974039 0.168709i
\(26\) 7185.06 0.0801722
\(27\) −75862.4 −0.741743
\(28\) 24954.3 43222.1i 0.214828 0.372094i
\(29\) 180212. 1.37211 0.686056 0.727549i \(-0.259340\pi\)
0.686056 + 0.727549i \(0.259340\pi\)
\(30\) −29816.0 51642.9i −0.201616 0.349209i
\(31\) 34853.9 0.210129 0.105064 0.994465i \(-0.466495\pi\)
0.105064 + 0.994465i \(0.466495\pi\)
\(32\) −43335.1 75058.6i −0.233784 0.404926i
\(33\) 30852.8 + 53438.5i 0.149450 + 0.258855i
\(34\) 93585.9 + 162096.i 0.408352 + 0.707286i
\(35\) −205005. + 355079.i −0.808213 + 1.39987i
\(36\) −55882.5 −0.199626
\(37\) −27020.0 + 306923.i −0.0876960 + 0.996147i
\(38\) −67988.8 −0.200999
\(39\) 5387.96 9332.22i 0.0145445 0.0251918i
\(40\) 153901. + 266565.i 0.380217 + 0.658556i
\(41\) −324720. 562432.i −0.735811 1.27446i −0.954367 0.298637i \(-0.903468\pi\)
0.218556 0.975824i \(-0.429865\pi\)
\(42\) −194336. 336601.i −0.404745 0.701039i
\(43\) −549580. −1.05412 −0.527062 0.849827i \(-0.676706\pi\)
−0.527062 + 0.849827i \(0.676706\pi\)
\(44\) 49881.6 + 86397.4i 0.0882787 + 0.152903i
\(45\) 459087. 0.751020
\(46\) 377523. 653889.i 0.571862 0.990494i
\(47\) −1.06832e6 −1.50092 −0.750462 0.660913i \(-0.770169\pi\)
−0.750462 + 0.660913i \(0.770169\pi\)
\(48\) −365577. −0.477128
\(49\) −924420. + 1.60114e6i −1.12249 + 1.94421i
\(50\) −95812.5 165952.i −0.108399 0.187753i
\(51\) 280714. 0.296325
\(52\) 8711.05 15088.0i 0.00859130 0.0148806i
\(53\) 482032. 834903.i 0.444744 0.770319i −0.553290 0.832988i \(-0.686628\pi\)
0.998034 + 0.0626694i \(0.0199614\pi\)
\(54\) −477586. + 827204.i −0.412737 + 0.714882i
\(55\) −409788. 709774.i −0.332116 0.575242i
\(56\) 1.00310e6 + 1.73743e6i 0.763288 + 1.32205i
\(57\) −50983.7 + 88306.3i −0.0364644 + 0.0631582i
\(58\) 1.13451e6 1.96503e6i 0.763502 1.32242i
\(59\) 582905. 1.00962e6i 0.369501 0.639995i −0.619986 0.784613i \(-0.712862\pi\)
0.989488 + 0.144618i \(0.0461952\pi\)
\(60\) −144594. −0.0864212
\(61\) −374247. 648215.i −0.211108 0.365649i 0.740954 0.671556i \(-0.234374\pi\)
−0.952061 + 0.305907i \(0.901040\pi\)
\(62\) 219420. 380047.i 0.116925 0.202519i
\(63\) 2.99226e6 1.50768
\(64\) 1.38679e6 0.661275
\(65\) −71563.2 + 123951.i −0.0323216 + 0.0559827i
\(66\) 776926. 0.332641
\(67\) −712036. 1.23328e6i −0.289228 0.500957i 0.684398 0.729109i \(-0.260065\pi\)
−0.973626 + 0.228151i \(0.926732\pi\)
\(68\) 453848. 0.175037
\(69\) −566196. 980681.i −0.207489 0.359382i
\(70\) 2.58119e6 + 4.47075e6i 0.899449 + 1.55789i
\(71\) 2.01428e6 + 3.48884e6i 0.667907 + 1.15685i 0.978488 + 0.206302i \(0.0661428\pi\)
−0.310582 + 0.950547i \(0.600524\pi\)
\(72\) 1.12318e6 1.94540e6i 0.354637 0.614249i
\(73\) −4.04944e6 −1.21833 −0.609165 0.793043i \(-0.708495\pi\)
−0.609165 + 0.793043i \(0.708495\pi\)
\(74\) 3.17659e6 + 2.22684e6i 0.911276 + 0.638819i
\(75\) −287393. −0.0786613
\(76\) −82428.5 + 142770.i −0.0215392 + 0.0373070i
\(77\) −2.67094e6 4.62620e6i −0.666725 1.15480i
\(78\) −67839.1 117501.i −0.0161863 0.0280356i
\(79\) 15409.3 + 26689.7i 0.00351632 + 0.00609044i 0.867778 0.496952i \(-0.165547\pi\)
−0.864262 + 0.503042i \(0.832214\pi\)
\(80\) 4.85562e6 1.06030
\(81\) −1.28529e6 2.22620e6i −0.268723 0.465442i
\(82\) −8.17702e6 −1.63775
\(83\) 2.14696e6 3.71865e6i 0.412146 0.713858i −0.582978 0.812488i \(-0.698113\pi\)
0.995124 + 0.0986302i \(0.0314461\pi\)
\(84\) −942441. −0.173491
\(85\) −3.72846e6 −0.658512
\(86\) −3.45985e6 + 5.99263e6i −0.586560 + 1.01595i
\(87\) −1.70150e6 2.94708e6i −0.277022 0.479816i
\(88\) −4.01025e6 −0.627310
\(89\) 3.82252e6 6.62080e6i 0.574758 0.995510i −0.421310 0.906917i \(-0.638430\pi\)
0.996068 0.0885933i \(-0.0282371\pi\)
\(90\) 2.89015e6 5.00589e6i 0.417900 0.723824i
\(91\) −466438. + 807895.i −0.0648858 + 0.112385i
\(92\) −915405. 1.58553e6i −0.122562 0.212284i
\(93\) −329079. 569982.i −0.0424239 0.0734803i
\(94\) −6.72554e6 + 1.16490e7i −0.835179 + 1.44657i
\(95\) 677168. 1.17289e6i 0.0810334 0.140354i
\(96\) −818313. + 1.41736e6i −0.0943996 + 0.163505i
\(97\) −9.54599e6 −1.06199 −0.530995 0.847375i \(-0.678182\pi\)
−0.530995 + 0.847375i \(0.678182\pi\)
\(98\) 1.16392e7 + 2.01598e7i 1.24920 + 2.16369i
\(99\) −2.99065e6 + 5.17995e6i −0.309772 + 0.536541i
\(100\) −464646. −0.0464646
\(101\) −1.07638e7 −1.03954 −0.519770 0.854306i \(-0.673982\pi\)
−0.519770 + 0.854306i \(0.673982\pi\)
\(102\) 1.76722e6 3.06091e6i 0.164888 0.285595i
\(103\) −5.27263e6 −0.475442 −0.237721 0.971333i \(-0.576400\pi\)
−0.237721 + 0.971333i \(0.576400\pi\)
\(104\) 350164. + 606502.i 0.0305250 + 0.0528708i
\(105\) 7.74236e6 0.652696
\(106\) −6.06920e6 1.05122e7i −0.494949 0.857277i
\(107\) 9.41135e6 + 1.63009e7i 0.742692 + 1.28638i 0.951265 + 0.308373i \(0.0997846\pi\)
−0.208574 + 0.978007i \(0.566882\pi\)
\(108\) 1.15804e6 + 2.00578e6i 0.0884583 + 0.153214i
\(109\) 1.16982e7 2.02620e7i 0.865223 1.49861i −0.00160237 0.999999i \(-0.500510\pi\)
0.866825 0.498612i \(-0.166157\pi\)
\(110\) −1.03192e7 −0.739215
\(111\) 5.27437e6 2.45600e6i 0.366050 0.170450i
\(112\) 3.16482e7 2.12856
\(113\) −9.24994e6 + 1.60214e7i −0.603065 + 1.04454i 0.389289 + 0.921116i \(0.372721\pi\)
−0.992354 + 0.123424i \(0.960613\pi\)
\(114\) 641929. + 1.11185e6i 0.0405807 + 0.0702879i
\(115\) 7.52026e6 + 1.30255e7i 0.461095 + 0.798640i
\(116\) −2.75092e6 4.76473e6i −0.163635 0.283423i
\(117\) 1.04454e6 0.0602941
\(118\) −7.33928e6 1.27120e7i −0.411213 0.712241i
\(119\) −2.43016e7 −1.32197
\(120\) 2.90617e6 5.03363e6i 0.153528 0.265918i
\(121\) −8.80918e6 −0.452050
\(122\) −9.42419e6 −0.469877
\(123\) −6.13181e6 + 1.06206e7i −0.297113 + 0.514614i
\(124\) −532043. 921526.i −0.0250594 0.0434042i
\(125\) 2.34117e7 1.07213
\(126\) 1.88376e7 3.26277e7i 0.838935 1.45308i
\(127\) 1.59078e6 2.75532e6i 0.0689125 0.119360i −0.829510 0.558491i \(-0.811380\pi\)
0.898423 + 0.439131i \(0.144714\pi\)
\(128\) 1.42774e7 2.47291e7i 0.601746 1.04225i
\(129\) 5.18896e6 + 8.98754e6i 0.212822 + 0.368618i
\(130\) 901043. + 1.56065e6i 0.0359703 + 0.0623023i
\(131\) 1.39265e7 2.41215e7i 0.541245 0.937463i −0.457588 0.889164i \(-0.651287\pi\)
0.998833 0.0482991i \(-0.0153800\pi\)
\(132\) 941932. 1.63147e6i 0.0356460 0.0617407i
\(133\) 4.41368e6 7.64472e6i 0.162675 0.281761i
\(134\) −1.79303e7 −0.643755
\(135\) −9.51352e6 1.64779e7i −0.332792 0.576413i
\(136\) −9.12183e6 + 1.57995e7i −0.310954 + 0.538588i
\(137\) −1.47887e7 −0.491368 −0.245684 0.969350i \(-0.579013\pi\)
−0.245684 + 0.969350i \(0.579013\pi\)
\(138\) −1.42578e7 −0.461823
\(139\) −7.47473e6 + 1.29466e7i −0.236072 + 0.408888i −0.959584 0.281424i \(-0.909193\pi\)
0.723512 + 0.690312i \(0.242527\pi\)
\(140\) 1.25176e7 0.385542
\(141\) 1.00867e7 + 1.74707e7i 0.303029 + 0.524861i
\(142\) 5.07231e7 1.48661
\(143\) −932373. 1.61492e6i −0.0266633 0.0461822i
\(144\) −1.77182e7 3.06889e7i −0.494483 0.856470i
\(145\) 2.25994e7 + 3.91434e7i 0.615615 + 1.06628i
\(146\) −2.54930e7 + 4.41551e7i −0.677931 + 1.17421i
\(147\) 3.49123e7 0.906500
\(148\) 8.52741e6 3.97077e6i 0.216223 0.100684i
\(149\) 9.99917e6 0.247635 0.123818 0.992305i \(-0.460486\pi\)
0.123818 + 0.992305i \(0.460486\pi\)
\(150\) −1.80926e6 + 3.13373e6i −0.0437706 + 0.0758128i
\(151\) −1.97815e7 3.42626e7i −0.467564 0.809844i 0.531749 0.846902i \(-0.321535\pi\)
−0.999313 + 0.0370575i \(0.988202\pi\)
\(152\) −3.31344e6 5.73904e6i −0.0765290 0.132552i
\(153\) 1.36052e7 + 2.35649e7i 0.307104 + 0.531920i
\(154\) −6.72589e7 −1.48398
\(155\) 4.37085e6 + 7.57054e6i 0.0942769 + 0.163292i
\(156\) −328988. −0.00693815
\(157\) 4.23608e7 7.33711e7i 0.873607 1.51313i 0.0153668 0.999882i \(-0.495108\pi\)
0.858240 0.513249i \(-0.171558\pi\)
\(158\) 388033. 0.00782652
\(159\) −1.82048e7 −0.359166
\(160\) 1.08689e7 1.88255e7i 0.209780 0.363350i
\(161\) 4.90159e7 + 8.48981e7i 0.925650 + 1.60327i
\(162\) −3.23659e7 −0.598117
\(163\) −3.66314e7 + 6.34475e7i −0.662518 + 1.14751i 0.317434 + 0.948280i \(0.397179\pi\)
−0.979952 + 0.199234i \(0.936155\pi\)
\(164\) −9.91368e6 + 1.71710e7i −0.175502 + 0.303978i
\(165\) −7.73818e6 + 1.34029e7i −0.134105 + 0.232277i
\(166\) −2.70321e7 4.68210e7i −0.458671 0.794442i
\(167\) 3.28576e7 + 5.69110e7i 0.545919 + 0.945559i 0.998548 + 0.0538607i \(0.0171527\pi\)
−0.452629 + 0.891699i \(0.649514\pi\)
\(168\) 1.89420e7 3.28085e7i 0.308207 0.533831i
\(169\) 3.12114e7 5.40598e7i 0.497405 0.861531i
\(170\) −2.34723e7 + 4.06552e7i −0.366424 + 0.634665i
\(171\) −9.88399e6 −0.151163
\(172\) 8.38932e6 + 1.45307e7i 0.125712 + 0.217740i
\(173\) −3.06876e7 + 5.31524e7i −0.450610 + 0.780480i −0.998424 0.0561204i \(-0.982127\pi\)
0.547814 + 0.836600i \(0.315460\pi\)
\(174\) −4.28467e7 −0.616588
\(175\) 2.48797e7 0.350924
\(176\) −3.16311e7 + 5.47867e7i −0.437341 + 0.757497i
\(177\) −2.20144e7 −0.298401
\(178\) −4.81289e7 8.33616e7i −0.639640 1.10789i
\(179\) −7.39476e7 −0.963692 −0.481846 0.876256i \(-0.660034\pi\)
−0.481846 + 0.876256i \(0.660034\pi\)
\(180\) −7.00795e6 1.21381e7i −0.0895647 0.155131i
\(181\) −5.61014e7 9.71704e7i −0.703232 1.21803i −0.967326 0.253536i \(-0.918406\pi\)
0.264094 0.964497i \(-0.414927\pi\)
\(182\) 5.87286e6 + 1.01721e7i 0.0722104 + 0.125072i
\(183\) −7.06704e6 + 1.22405e7i −0.0852430 + 0.147645i
\(184\) 7.35944e7 0.870928
\(185\) −7.00545e7 + 3.26207e7i −0.813458 + 0.378785i
\(186\) −8.28679e6 −0.0944259
\(187\) 2.42884e7 4.20688e7i 0.271615 0.470451i
\(188\) 1.63079e7 + 2.82460e7i 0.178996 + 0.310031i
\(189\) −6.20077e7 1.07400e8i −0.668081 1.15715i
\(190\) −8.52614e6 1.47677e7i −0.0901809 0.156198i
\(191\) 6.06221e7 0.629526 0.314763 0.949170i \(-0.398075\pi\)
0.314763 + 0.949170i \(0.398075\pi\)
\(192\) −1.30937e7 2.26789e7i −0.133508 0.231243i
\(193\) 7.20386e6 0.0721298 0.0360649 0.999349i \(-0.488518\pi\)
0.0360649 + 0.999349i \(0.488518\pi\)
\(194\) −6.00962e7 + 1.04090e8i −0.590936 + 1.02353i
\(195\) 2.70271e6 0.0261022
\(196\) 5.64449e7 0.535462
\(197\) 7.40157e7 1.28199e8i 0.689751 1.19468i −0.282168 0.959365i \(-0.591053\pi\)
0.971918 0.235318i \(-0.0756132\pi\)
\(198\) 3.76548e7 + 6.52201e7i 0.344741 + 0.597109i
\(199\) −2.73003e7 −0.245573 −0.122787 0.992433i \(-0.539183\pi\)
−0.122787 + 0.992433i \(0.539183\pi\)
\(200\) 9.33885e6 1.61754e7i 0.0825446 0.142971i
\(201\) −1.34456e7 + 2.32885e7i −0.116787 + 0.202281i
\(202\) −6.77628e7 + 1.17369e8i −0.578444 + 1.00190i
\(203\) 1.47300e8 + 2.55131e8i 1.23585 + 2.14056i
\(204\) −4.28509e6 7.42199e6i −0.0353390 0.0612089i
\(205\) 8.14431e7 1.41064e8i 0.660261 1.14361i
\(206\) −3.31935e7 + 5.74929e7i −0.264556 + 0.458225i
\(207\) 5.48831e7 9.50603e7i 0.430073 0.744908i
\(208\) 1.10478e7 0.0851242
\(209\) 8.82260e6 + 1.52812e7i 0.0668474 + 0.115783i
\(210\) 4.87415e7 8.44228e7i 0.363188 0.629060i
\(211\) 1.38799e8 1.01718 0.508590 0.861009i \(-0.330167\pi\)
0.508590 + 0.861009i \(0.330167\pi\)
\(212\) −2.94328e7 −0.212156
\(213\) 3.80364e7 6.58810e7i 0.269694 0.467123i
\(214\) 2.36994e8 1.65306
\(215\) −6.89201e7 1.19373e8i −0.472946 0.819166i
\(216\) −9.31008e7 −0.628587
\(217\) 2.84886e7 + 4.93437e7i 0.189261 + 0.327810i
\(218\) −1.47291e8 2.55116e8i −0.962895 1.66778i
\(219\) 3.82335e7 + 6.62224e7i 0.245974 + 0.426040i
\(220\) −1.25108e7 + 2.16693e7i −0.0792147 + 0.137204i
\(221\) −8.48320e6 −0.0528673
\(222\) 6.42422e6 7.29734e7i 0.0394081 0.447640i
\(223\) 6.20526e7 0.374708 0.187354 0.982292i \(-0.440009\pi\)
0.187354 + 0.982292i \(0.440009\pi\)
\(224\) 7.08418e7 1.22702e8i 0.421135 0.729427i
\(225\) −1.39289e7 2.41256e7i −0.0815226 0.141201i
\(226\) 1.16465e8 + 2.01723e8i 0.671143 + 1.16245i
\(227\) 7.62857e7 + 1.32131e8i 0.432865 + 0.749744i 0.997119 0.0758572i \(-0.0241693\pi\)
−0.564254 + 0.825601i \(0.690836\pi\)
\(228\) 3.11305e6 0.0173946
\(229\) 2.81538e7 + 4.87637e7i 0.154922 + 0.268332i 0.933031 0.359797i \(-0.117154\pi\)
−0.778109 + 0.628129i \(0.783821\pi\)
\(230\) 1.89373e8 1.02629
\(231\) −5.04363e7 + 8.73583e7i −0.269216 + 0.466296i
\(232\) 2.21162e8 1.16279
\(233\) −7.32717e6 −0.0379481 −0.0189741 0.999820i \(-0.506040\pi\)
−0.0189741 + 0.999820i \(0.506040\pi\)
\(234\) 6.57584e6 1.13897e7i 0.0335502 0.0581107i
\(235\) −1.33973e8 2.32047e8i −0.673409 1.16638i
\(236\) −3.55921e7 −0.176263
\(237\) 290979. 503991.i 0.00141985 0.00245925i
\(238\) −1.52989e8 + 2.64985e8i −0.735598 + 1.27409i
\(239\) −1.36855e8 + 2.37039e8i −0.648436 + 1.12312i 0.335060 + 0.942197i \(0.391243\pi\)
−0.983496 + 0.180928i \(0.942090\pi\)
\(240\) −4.58452e7 7.94062e7i −0.214069 0.370779i
\(241\) −1.39506e8 2.41632e8i −0.641998 1.11197i −0.984986 0.172634i \(-0.944772\pi\)
0.342988 0.939340i \(-0.388561\pi\)
\(242\) −5.54576e7 + 9.60554e7i −0.251540 + 0.435680i
\(243\) −1.07226e8 + 1.85721e8i −0.479379 + 0.830308i
\(244\) −1.14257e7 + 1.97899e7i −0.0503523 + 0.0872128i
\(245\) −4.63707e8 −2.01448
\(246\) 7.72048e7 + 1.33723e8i 0.330652 + 0.572707i
\(247\) 1.54073e6 2.66862e6i 0.00650560 0.0112680i
\(248\) 4.27738e7 0.178073
\(249\) −8.10837e7 −0.332840
\(250\) 1.47387e8 2.55281e8i 0.596580 1.03331i
\(251\) −4.95378e7 −0.197733 −0.0988663 0.995101i \(-0.531522\pi\)
−0.0988663 + 0.995101i \(0.531522\pi\)
\(252\) −4.56768e7 7.91145e7i −0.179802 0.311425i
\(253\) −1.95958e8 −0.760748
\(254\) −2.00293e7 3.46918e7i −0.0766918 0.132834i
\(255\) 3.52030e7 + 6.09733e7i 0.132950 + 0.230276i
\(256\) −9.10096e7 1.57633e8i −0.339037 0.587230i
\(257\) 1.48021e8 2.56380e8i 0.543949 0.942147i −0.454724 0.890633i \(-0.650262\pi\)
0.998672 0.0515142i \(-0.0164047\pi\)
\(258\) 1.30667e8 0.473693
\(259\) −4.56605e8 + 2.12617e8i −1.63302 + 0.760412i
\(260\) 4.36964e6 0.0154184
\(261\) 1.64931e8 2.85669e8i 0.574197 0.994539i
\(262\) −1.75347e8 3.03710e8i −0.602344 1.04329i
\(263\) 1.05473e8 + 1.82685e8i 0.357517 + 0.619238i 0.987545 0.157334i \(-0.0502900\pi\)
−0.630028 + 0.776572i \(0.716957\pi\)
\(264\) 3.78635e7 + 6.55815e7i 0.126651 + 0.219365i
\(265\) 2.41797e8 0.798160
\(266\) −5.55721e7 9.62537e7i −0.181039 0.313568i
\(267\) −1.44364e8 −0.464162
\(268\) −2.17384e7 + 3.76520e7i −0.0689852 + 0.119486i
\(269\) 1.83358e7 0.0574336 0.0287168 0.999588i \(-0.490858\pi\)
0.0287168 + 0.999588i \(0.490858\pi\)
\(270\) −2.39567e8 −0.740719
\(271\) −2.69284e8 + 4.66414e8i −0.821899 + 1.42357i 0.0823667 + 0.996602i \(0.473752\pi\)
−0.904266 + 0.426969i \(0.859581\pi\)
\(272\) 1.43898e8 + 2.49239e8i 0.433574 + 0.750973i
\(273\) 1.76158e7 0.0524004
\(274\) −9.31011e7 + 1.61256e8i −0.273419 + 0.473575i
\(275\) −2.48663e7 + 4.30697e7i −0.0721019 + 0.124884i
\(276\) −1.72859e7 + 2.99401e7i −0.0494892 + 0.0857179i
\(277\) 1.72627e8 + 2.98999e8i 0.488011 + 0.845260i 0.999905 0.0137885i \(-0.00438916\pi\)
−0.511894 + 0.859049i \(0.671056\pi\)
\(278\) 9.41133e7 + 1.63009e8i 0.262721 + 0.455046i
\(279\) 3.18986e7 5.52500e7i 0.0879341 0.152306i
\(280\) −2.51589e8 + 4.35764e8i −0.684917 + 1.18631i
\(281\) −8.93412e7 + 1.54744e8i −0.240204 + 0.416045i −0.960772 0.277339i \(-0.910548\pi\)
0.720568 + 0.693384i \(0.243881\pi\)
\(282\) 2.54001e8 0.674473
\(283\) −2.50278e8 4.33494e8i −0.656403 1.13692i −0.981540 0.191256i \(-0.938744\pi\)
0.325138 0.945667i \(-0.394589\pi\)
\(284\) 6.14958e7 1.06514e8i 0.159306 0.275926i
\(285\) −2.55744e7 −0.0654408
\(286\) −2.34788e7 −0.0593464
\(287\) 5.30834e8 9.19432e8i 1.32548 2.29579i
\(288\) −1.58643e8 −0.391333
\(289\) 9.46750e7 + 1.63982e8i 0.230724 + 0.399626i
\(290\) 5.69093e8 1.37022
\(291\) 9.01302e7 + 1.56110e8i 0.214410 + 0.371369i
\(292\) 6.18145e7 + 1.07066e8i 0.145295 + 0.251658i
\(293\) 2.52432e8 + 4.37225e8i 0.586284 + 1.01547i 0.994714 + 0.102684i \(0.0327430\pi\)
−0.408430 + 0.912790i \(0.633924\pi\)
\(294\) 2.19788e8 3.80684e8i 0.504416 0.873673i
\(295\) 2.92397e8 0.663126
\(296\) −3.31599e7 + 3.76666e8i −0.0743176 + 0.844181i
\(297\) 2.47897e8 0.549065
\(298\) 6.29491e7 1.09031e8i 0.137795 0.238668i
\(299\) 1.71105e7 + 2.96363e7i 0.0370181 + 0.0641172i
\(300\) 4.38704e6 + 7.59857e6i 0.00938095 + 0.0162483i
\(301\) −4.49211e8 7.78056e8i −0.949440 1.64448i
\(302\) −4.98134e8 −1.04069
\(303\) 1.01628e8 + 1.76026e8i 0.209877 + 0.363518i
\(304\) −1.04540e8 −0.213415
\(305\) 9.38649e7 1.62579e8i 0.189432 0.328106i
\(306\) 3.42603e8 0.683543
\(307\) −4.27954e8 −0.844136 −0.422068 0.906564i \(-0.638696\pi\)
−0.422068 + 0.906564i \(0.638696\pi\)
\(308\) −8.15435e7 + 1.41238e8i −0.159024 + 0.275437i
\(309\) 4.97825e7 + 8.62259e7i 0.0959892 + 0.166258i
\(310\) 1.10066e8 0.209839
\(311\) 4.31780e7 7.47865e7i 0.0813957 0.140981i −0.822454 0.568832i \(-0.807396\pi\)
0.903850 + 0.427850i \(0.140729\pi\)
\(312\) 6.61228e6 1.14528e7i 0.0123257 0.0213487i
\(313\) −8.66189e7 + 1.50028e8i −0.159664 + 0.276546i −0.934748 0.355313i \(-0.884374\pi\)
0.775083 + 0.631859i \(0.217708\pi\)
\(314\) −5.33360e8 9.23806e8i −0.972224 1.68394i
\(315\) 3.75245e8 + 6.49943e8i 0.676437 + 1.17162i
\(316\) 470444. 814834.i 0.000838694 0.00145266i
\(317\) 4.74274e8 8.21467e8i 0.836223 1.44838i −0.0568077 0.998385i \(-0.518092\pi\)
0.893031 0.449996i \(-0.148574\pi\)
\(318\) −1.14607e8 + 1.98505e8i −0.199855 + 0.346159i
\(319\) −5.88881e8 −1.01569
\(320\) 1.73911e8 + 3.01223e8i 0.296689 + 0.513881i
\(321\) 1.77718e8 3.07816e8i 0.299891 0.519427i
\(322\) 1.23431e9 2.06028
\(323\) 8.02725e7 0.132543
\(324\) −3.92399e7 + 6.79656e7i −0.0640945 + 0.111015i
\(325\) 8.68503e6 0.0140339
\(326\) 4.61222e8 + 7.98859e8i 0.737306 + 1.27705i
\(327\) −4.41804e8 −0.698736
\(328\) −3.98508e8 6.90235e8i −0.623560 1.08004i
\(329\) −8.73214e8 1.51245e9i −1.35187 2.34151i
\(330\) 9.74304e7 + 1.68754e8i 0.149244 + 0.258497i
\(331\) −3.11571e8 + 5.39657e8i −0.472237 + 0.817938i −0.999495 0.0317671i \(-0.989887\pi\)
0.527259 + 0.849705i \(0.323220\pi\)
\(332\) −1.31093e8 −0.196606
\(333\) 4.61802e8 + 3.23731e8i 0.685332 + 0.480429i
\(334\) 8.27411e8 1.21509
\(335\) 1.78586e8 3.09320e8i 0.259531 0.449522i
\(336\) −2.98812e8 5.17558e8i −0.429745 0.744340i
\(337\) 3.42146e8 + 5.92614e8i 0.486975 + 0.843466i 0.999888 0.0149749i \(-0.00476683\pi\)
−0.512913 + 0.858441i \(0.671433\pi\)
\(338\) −3.92979e8 6.80660e8i −0.553555 0.958786i
\(339\) 3.49340e8 0.487023
\(340\) 5.69148e7 + 9.85794e7i 0.0785324 + 0.136022i
\(341\) −1.13893e8 −0.155545
\(342\) −6.22240e7 + 1.07775e8i −0.0841137 + 0.145689i
\(343\) −1.67610e9 −2.24269
\(344\) −6.74463e8 −0.893313
\(345\) 1.42008e8 2.45965e8i 0.186185 0.322482i
\(346\) 3.86383e8 + 6.69235e8i 0.501478 + 0.868585i
\(347\) 6.59456e8 0.847292 0.423646 0.905828i \(-0.360750\pi\)
0.423646 + 0.905828i \(0.360750\pi\)
\(348\) −5.19466e7 + 8.99742e7i −0.0660739 + 0.114443i
\(349\) 1.27398e8 2.20660e8i 0.160425 0.277865i −0.774596 0.632456i \(-0.782047\pi\)
0.935021 + 0.354591i \(0.115380\pi\)
\(350\) 1.56629e8 2.71289e8i 0.195269 0.338216i
\(351\) −2.16457e7 3.74914e7i −0.0267175 0.0462761i
\(352\) 1.41607e8 + 2.45271e8i 0.173056 + 0.299741i
\(353\) −2.88949e8 + 5.00474e8i −0.349631 + 0.605578i −0.986184 0.165655i \(-0.947026\pi\)
0.636553 + 0.771233i \(0.280360\pi\)
\(354\) −1.38590e8 + 2.40045e8i −0.166043 + 0.287596i
\(355\) −5.05202e8 + 8.75035e8i −0.599329 + 1.03807i
\(356\) −2.33403e8 −0.274177
\(357\) 2.29448e8 + 3.97415e8i 0.266898 + 0.462280i
\(358\) −4.65532e8 + 8.06325e8i −0.536240 + 0.928794i
\(359\) 1.14540e9 1.30656 0.653278 0.757118i \(-0.273393\pi\)
0.653278 + 0.757118i \(0.273393\pi\)
\(360\) 5.63407e8 0.636449
\(361\) 4.32357e8 7.48864e8i 0.483690 0.837775i
\(362\) −1.41273e9 −1.56523
\(363\) 8.31735e7 + 1.44061e8i 0.0912665 + 0.158078i
\(364\) 2.84806e7 0.0309524
\(365\) −5.07820e8 8.79570e8i −0.546619 0.946772i
\(366\) 8.89802e7 + 1.54118e8i 0.0948658 + 0.164312i
\(367\) 9.40165e8 + 1.62841e9i 0.992825 + 1.71962i 0.599967 + 0.800025i \(0.295180\pi\)
0.392858 + 0.919599i \(0.371486\pi\)
\(368\) 5.80481e8 1.00542e9i 0.607184 1.05167i
\(369\) −1.18875e9 −1.23168
\(370\) −8.53269e7 + 9.69237e8i −0.0875750 + 0.994773i
\(371\) 1.57600e9 1.60231
\(372\) −1.00468e7 + 1.74015e7i −0.0101187 + 0.0175261i
\(373\) 5.98933e8 + 1.03738e9i 0.597582 + 1.03504i 0.993177 + 0.116618i \(0.0372052\pi\)
−0.395595 + 0.918425i \(0.629461\pi\)
\(374\) −3.05813e8 5.29683e8i −0.302277 0.523559i
\(375\) −2.21046e8 3.82862e8i −0.216458 0.374915i
\(376\) −1.31108e9 −1.27195
\(377\) 5.14195e7 + 8.90611e7i 0.0494234 + 0.0856039i
\(378\) −1.56146e9 −1.48700
\(379\) 4.13194e8 7.15673e8i 0.389868 0.675270i −0.602564 0.798071i \(-0.705854\pi\)
0.992431 + 0.122800i \(0.0391875\pi\)
\(380\) −4.13478e7 −0.0386553
\(381\) −6.00787e7 −0.0556523
\(382\) 3.81642e8 6.61024e8i 0.350295 0.606730i
\(383\) 5.91130e8 + 1.02387e9i 0.537635 + 0.931211i 0.999031 + 0.0440169i \(0.0140155\pi\)
−0.461396 + 0.887194i \(0.652651\pi\)
\(384\) −5.39209e8 −0.485957
\(385\) 6.69898e8 1.16030e9i 0.598269 1.03623i
\(386\) 4.53514e7 7.85509e7i 0.0401361 0.0695178i
\(387\) −5.02981e8 + 8.71188e8i −0.441126 + 0.764053i
\(388\) 1.45719e8 + 2.52393e8i 0.126650 + 0.219364i
\(389\) 7.12007e7 + 1.23323e8i 0.0613283 + 0.106224i 0.895059 0.445947i \(-0.147133\pi\)
−0.833731 + 0.552171i \(0.813800\pi\)
\(390\) 1.70147e7 2.94703e7i 0.0145244 0.0251570i
\(391\) −4.45731e8 + 7.72029e8i −0.377098 + 0.653153i
\(392\) −1.13448e9 + 1.96497e9i −0.951251 + 1.64761i
\(393\) −5.25960e8 −0.437098
\(394\) −9.31922e8 1.61414e9i −0.767614 1.32955i
\(395\) −3.86480e6 + 6.69404e6i −0.00315528 + 0.00546510i
\(396\) 1.82608e8 0.147770
\(397\) −1.69466e9 −1.35930 −0.679650 0.733536i \(-0.737868\pi\)
−0.679650 + 0.733536i \(0.737868\pi\)
\(398\) −1.71867e8 + 2.97683e8i −0.136648 + 0.236681i
\(399\) −1.66690e8 −0.131373
\(400\) −1.47322e8 2.55168e8i −0.115095 0.199350i
\(401\) −1.78839e9 −1.38502 −0.692511 0.721407i \(-0.743496\pi\)
−0.692511 + 0.721407i \(0.743496\pi\)
\(402\) 1.69292e8 + 2.93223e8i 0.129971 + 0.225116i
\(403\) 9.94481e6 + 1.72249e7i 0.00756883 + 0.0131096i
\(404\) 1.64309e8 + 2.84591e8i 0.123973 + 0.214727i
\(405\) 3.22365e8 5.58352e8i 0.241132 0.417653i
\(406\) 3.70926e9 2.75072
\(407\) 8.82939e7 1.00294e9i 0.0649157 0.737384i
\(408\) 3.44502e8 0.251120
\(409\) 1.15646e9 2.00305e9i 0.835797 1.44764i −0.0575834 0.998341i \(-0.518340\pi\)
0.893380 0.449302i \(-0.148327\pi\)
\(410\) −1.02544e9 1.77611e9i −0.734795 1.27270i
\(411\) 1.39630e8 + 2.41846e8i 0.0992047 + 0.171828i
\(412\) 8.04865e7 + 1.39407e8i 0.0567000 + 0.0982073i
\(413\) 1.90580e9 1.33123
\(414\) −6.91025e8 1.19689e9i −0.478622 0.828998i
\(415\) 1.07696e9 0.739658
\(416\) 2.47295e7 4.28327e7i 0.0168418 0.0291708i
\(417\) 2.82296e8 0.190646
\(418\) 2.22168e8 0.148787
\(419\) −2.83769e8 + 4.91502e8i −0.188459 + 0.326420i −0.944736 0.327831i \(-0.893682\pi\)
0.756278 + 0.654250i \(0.227016\pi\)
\(420\) −1.18187e8 2.04705e8i −0.0778388 0.134821i
\(421\) −1.84012e9 −1.20187 −0.600937 0.799297i \(-0.705206\pi\)
−0.600937 + 0.799297i \(0.705206\pi\)
\(422\) 8.73800e8 1.51347e9i 0.566003 0.980346i
\(423\) −9.77736e8 + 1.69349e9i −0.628103 + 1.08791i
\(424\) 5.91565e8 1.02462e9i 0.376896 0.652804i
\(425\) 1.13123e8 + 1.95935e8i 0.0714810 + 0.123809i
\(426\) −4.78911e8 8.29498e8i −0.300138 0.519855i
\(427\) 6.11798e8 1.05966e9i 0.380286 0.658674i
\(428\) 2.87328e8 4.97666e8i 0.177143 0.306821i
\(429\) −1.76063e7 + 3.04951e7i −0.0107663 + 0.0186479i
\(430\) −1.73553e9 −1.05267
\(431\) 9.26283e8 + 1.60437e9i 0.557279 + 0.965236i 0.997722 + 0.0674557i \(0.0214881\pi\)
−0.440443 + 0.897781i \(0.645179\pi\)
\(432\) −7.34338e8 + 1.27191e9i −0.438231 + 0.759038i
\(433\) −8.83922e7 −0.0523246 −0.0261623 0.999658i \(-0.508329\pi\)
−0.0261623 + 0.999658i \(0.508329\pi\)
\(434\) 7.17392e8 0.421252
\(435\) 4.26753e8 7.39158e8i 0.248579 0.430551i
\(436\) −7.14293e8 −0.412737
\(437\) −1.61909e8 2.80434e8i −0.0928079 0.160748i
\(438\) 9.62786e8 0.547483
\(439\) 1.36887e9 + 2.37096e9i 0.772213 + 1.33751i 0.936347 + 0.351075i \(0.114184\pi\)
−0.164134 + 0.986438i \(0.552483\pi\)
\(440\) −5.02906e8 8.71058e8i −0.281451 0.487487i
\(441\) 1.69208e9 + 2.93076e9i 0.939474 + 1.62722i
\(442\) −5.34054e7 + 9.25009e7i −0.0294176 + 0.0509528i
\(443\) 8.96644e8 0.490012 0.245006 0.969522i \(-0.421210\pi\)
0.245006 + 0.969522i \(0.421210\pi\)
\(444\) −1.45449e8 1.01962e8i −0.0788624 0.0552838i
\(445\) 1.91745e9 1.03149
\(446\) 3.90648e8 6.76622e8i 0.208504 0.361139i
\(447\) −9.44090e7 1.63521e8i −0.0499962 0.0865960i
\(448\) 1.13353e9 + 1.96332e9i 0.595605 + 1.03162i
\(449\) 4.19703e8 + 7.26947e8i 0.218817 + 0.379001i 0.954446 0.298382i \(-0.0964470\pi\)
−0.735630 + 0.677384i \(0.763114\pi\)
\(450\) −3.50754e8 −0.181451
\(451\) 1.06110e9 + 1.83787e9i 0.544674 + 0.943403i
\(452\) 5.64799e8 0.287680
\(453\) −3.73542e8 + 6.46994e8i −0.188797 + 0.327006i
\(454\) 1.92101e9 0.963459
\(455\) −2.33975e8 −0.116447
\(456\) −6.25688e7 + 1.08372e8i −0.0309016 + 0.0535232i
\(457\) −1.40426e9 2.43226e9i −0.688244 1.19207i −0.972406 0.233297i \(-0.925049\pi\)
0.284162 0.958776i \(-0.408285\pi\)
\(458\) 7.08960e8 0.344820
\(459\) 5.63873e8 9.76657e8i 0.272168 0.471409i
\(460\) 2.29593e8 3.97666e8i 0.109978 0.190487i
\(461\) −1.17831e9 + 2.04090e9i −0.560154 + 0.970216i 0.437328 + 0.899302i \(0.355925\pi\)
−0.997482 + 0.0709139i \(0.977408\pi\)
\(462\) 6.35037e8 + 1.09992e9i 0.299607 + 0.518935i
\(463\) −9.64064e8 1.66981e9i −0.451411 0.781868i 0.547063 0.837092i \(-0.315746\pi\)
−0.998474 + 0.0552242i \(0.982413\pi\)
\(464\) 1.74443e9 3.02143e9i 0.810661 1.40411i
\(465\) 8.25364e7 1.42957e8i 0.0380680 0.0659357i
\(466\) −4.61277e7 + 7.98955e7i −0.0211160 + 0.0365739i
\(467\) −3.36821e9 −1.53035 −0.765174 0.643824i \(-0.777347\pi\)
−0.765174 + 0.643824i \(0.777347\pi\)
\(468\) −1.59449e7 2.76173e7i −0.00719052 0.0124543i
\(469\) 1.16400e9 2.01610e9i 0.521010 0.902416i
\(470\) −3.37366e9 −1.49885
\(471\) −1.59983e9 −0.705506
\(472\) 7.15361e8 1.23904e9i 0.313132 0.542361i
\(473\) 1.79587e9 0.780300
\(474\) −3.66368e6 6.34568e6i −0.00158013 0.00273687i
\(475\) −8.21823e7 −0.0351845
\(476\) 3.70962e8 + 6.42526e8i 0.157654 + 0.273065i
\(477\) −8.82320e8 1.52822e9i −0.372230 0.644722i
\(478\) 1.72312e9 + 2.98453e9i 0.721636 + 1.24991i
\(479\) 2.23171e9 3.86543e9i 0.927819 1.60703i 0.140855 0.990030i \(-0.455015\pi\)
0.786964 0.616999i \(-0.211652\pi\)
\(480\) −4.10482e8 −0.169414
\(481\) −1.59392e8 + 7.42205e7i −0.0653068 + 0.0304100i
\(482\) −3.51301e9 −1.42894
\(483\) 9.25585e8 1.60316e9i 0.373767 0.647384i
\(484\) 1.34472e8 + 2.32912e8i 0.0539104 + 0.0933755i
\(485\) −1.19712e9 2.07346e9i −0.476475 0.825278i
\(486\) 1.35007e9 + 2.33839e9i 0.533494 + 0.924039i
\(487\) −3.64168e9 −1.42873 −0.714366 0.699773i \(-0.753285\pi\)
−0.714366 + 0.699773i \(0.753285\pi\)
\(488\) −4.59288e8 7.95511e8i −0.178902 0.309868i
\(489\) 1.38345e9 0.535035
\(490\) −2.91924e9 + 5.05627e9i −1.12094 + 1.94153i
\(491\) −2.11729e9 −0.807227 −0.403614 0.914929i \(-0.632246\pi\)
−0.403614 + 0.914929i \(0.632246\pi\)
\(492\) 3.74407e8 0.141732
\(493\) −1.33948e9 + 2.32005e9i −0.503470 + 0.872035i
\(494\) −1.93991e7 3.36003e7i −0.00723999 0.0125400i
\(495\) −1.50017e9 −0.555932
\(496\) 3.37381e8 5.84362e8i 0.124147 0.215028i
\(497\) −3.29283e9 + 5.70335e9i −1.20316 + 2.08393i
\(498\) −5.10457e8 + 8.84137e8i −0.185207 + 0.320787i
\(499\) 5.02366e8 + 8.70123e8i 0.180996 + 0.313494i 0.942220 0.334995i \(-0.108735\pi\)
−0.761224 + 0.648489i \(0.775401\pi\)
\(500\) −3.57378e8 6.18998e8i −0.127860 0.221459i
\(501\) 6.20462e8 1.07467e9i 0.220436 0.381807i
\(502\) −3.11862e8 + 5.40160e8i −0.110027 + 0.190572i
\(503\) −6.11389e8 + 1.05896e9i −0.214205 + 0.371014i −0.953026 0.302887i \(-0.902049\pi\)
0.738821 + 0.673901i \(0.235383\pi\)
\(504\) 3.67220e9 1.27767
\(505\) −1.34983e9 2.33798e9i −0.466402 0.807833i
\(506\) −1.23364e9 + 2.13673e9i −0.423313 + 0.733199i
\(507\) −1.17875e9 −0.401694
\(508\) −9.71330e7 −0.0328733
\(509\) −1.18753e9 + 2.05687e9i −0.399147 + 0.691343i −0.993621 0.112772i \(-0.964027\pi\)
0.594474 + 0.804115i \(0.297360\pi\)
\(510\) 8.86471e8 0.295916
\(511\) −3.30990e9 5.73291e9i −1.09734 1.90065i
\(512\) 1.36323e9 0.448873
\(513\) 2.04823e8 + 3.54763e8i 0.0669834 + 0.116019i
\(514\) −1.86371e9 3.22805e9i −0.605353 1.04850i
\(515\) −6.61215e8 1.14526e9i −0.213313 0.369469i
\(516\) 1.58418e8 2.74389e8i 0.0507612 0.0879210i
\(517\) 3.49097e9 1.11104
\(518\) −5.56148e8 + 6.31734e9i −0.175807 + 1.99701i
\(519\) 1.15897e9 0.363903
\(520\) −8.78247e7 + 1.52117e8i −0.0273908 + 0.0474423i
\(521\) 6.74939e8 + 1.16903e9i 0.209090 + 0.362154i 0.951428 0.307871i \(-0.0996166\pi\)
−0.742338 + 0.670025i \(0.766283\pi\)
\(522\) −2.07663e9 3.59682e9i −0.639016 1.10681i
\(523\) −1.16735e9 2.02190e9i −0.356816 0.618023i 0.630611 0.776099i \(-0.282804\pi\)
−0.987427 + 0.158076i \(0.949471\pi\)
\(524\) −8.50352e8 −0.258190
\(525\) −2.34907e8 4.06870e8i −0.0708496 0.122715i
\(526\) 2.65600e9 0.795752
\(527\) −2.59064e8 + 4.48711e8i −0.0771026 + 0.133546i
\(528\) 1.19460e9 0.353187
\(529\) 1.91308e8 0.0561872
\(530\) 1.52221e9 2.63655e9i 0.444130 0.769256i
\(531\) −1.06696e9 1.84803e9i −0.309256 0.535647i
\(532\) −2.69499e8 −0.0776008
\(533\) 1.85304e8 3.20956e8i 0.0530077 0.0918121i
\(534\) −9.08835e8 + 1.57415e9i −0.258280 + 0.447354i
\(535\) −2.36046e9 + 4.08844e9i −0.666436 + 1.15430i
\(536\) −8.73834e8 1.51352e9i −0.245105 0.424534i
\(537\) 6.98189e8 + 1.20930e9i 0.194564 + 0.336995i
\(538\) 1.15432e8 1.99933e8i 0.0319585 0.0553538i
\(539\) 3.02074e9 5.23208e9i 0.830909 1.43918i
\(540\) −2.90447e8 + 5.03069e8i −0.0793759 + 0.137483i
\(541\) 2.84831e9 0.773388 0.386694 0.922208i \(-0.373617\pi\)
0.386694 + 0.922208i \(0.373617\pi\)
\(542\) 3.39052e9 + 5.87256e9i 0.914680 + 1.58427i
\(543\) −1.05938e9 + 1.83490e9i −0.283957 + 0.491829i
\(544\) 1.28841e9 0.343130
\(545\) 5.86807e9 1.55277
\(546\) 1.10899e8 1.92083e8i 0.0291578 0.0505028i
\(547\) −9.19476e8 −0.240206 −0.120103 0.992761i \(-0.538323\pi\)
−0.120103 + 0.992761i \(0.538323\pi\)
\(548\) 2.25748e8 + 3.91008e8i 0.0585994 + 0.101497i
\(549\) −1.37006e9 −0.353375
\(550\) 3.13088e8 + 5.42285e8i 0.0802412 + 0.138982i
\(551\) −4.86558e8 8.42743e8i −0.123909 0.214617i
\(552\) −6.94855e8 1.20352e9i −0.175836 0.304557i
\(553\) −2.51902e7 + 4.36308e7i −0.00633423 + 0.0109712i
\(554\) 4.34705e9 1.08620
\(555\) 1.19489e9 + 8.37640e8i 0.296691 + 0.207985i
\(556\) 4.56406e8 0.112613
\(557\) 7.78853e8 1.34901e9i 0.190969 0.330768i −0.754603 0.656182i \(-0.772170\pi\)
0.945572 + 0.325414i \(0.105504\pi\)
\(558\) −4.01631e8 6.95646e8i −0.0978606 0.169499i
\(559\) −1.56811e8 2.71604e8i −0.0379695 0.0657651i
\(560\) 3.96884e9 + 6.87424e9i 0.955005 + 1.65412i
\(561\) −9.17295e8 −0.219351
\(562\) 1.12488e9 + 1.94836e9i 0.267319 + 0.463011i
\(563\) 6.11210e9 1.44348 0.721740 0.692164i \(-0.243343\pi\)
0.721740 + 0.692164i \(0.243343\pi\)
\(564\) 3.07947e8 5.33380e8i 0.0722769 0.125187i
\(565\) −4.63995e9 −1.08229
\(566\) −6.30244e9 −1.46100
\(567\) 2.10113e9 3.63926e9i 0.484074 0.838440i
\(568\) 2.47199e9 + 4.28162e9i 0.566015 + 0.980367i
\(569\) −2.80768e9 −0.638931 −0.319466 0.947598i \(-0.603503\pi\)
−0.319466 + 0.947598i \(0.603503\pi\)
\(570\) −1.61002e8 + 2.78864e8i −0.0364141 + 0.0630711i
\(571\) 3.07855e9 5.33221e9i 0.692022 1.19862i −0.279152 0.960247i \(-0.590053\pi\)
0.971174 0.238371i \(-0.0766133\pi\)
\(572\) −2.84653e7 + 4.93033e7i −0.00635959 + 0.0110151i
\(573\) −5.72374e8 9.91381e8i −0.127098 0.220140i
\(574\) −6.68366e9 1.15764e10i −1.47510 2.55496i
\(575\) 4.56336e8 7.90397e8i 0.100103 0.173383i
\(576\) 1.26921e9 2.19833e9i 0.276729 0.479308i
\(577\) −9.43212e8 + 1.63369e9i −0.204406 + 0.354042i −0.949943 0.312422i \(-0.898860\pi\)
0.745537 + 0.666464i \(0.232193\pi\)
\(578\) 2.38408e9 0.513539
\(579\) −6.80165e7 1.17808e8i −0.0145626 0.0252232i
\(580\) 6.89958e8 1.19504e9i 0.146833 0.254323i
\(581\) 7.01946e9 1.48487
\(582\) 2.26963e9 0.477228
\(583\) −1.57514e9 + 2.72823e9i −0.329216 + 0.570218i
\(584\) −4.96961e9 −1.03247
\(585\) 1.30991e8 + 2.26882e8i 0.0270517 + 0.0468549i
\(586\) 6.35668e9 1.30493
\(587\) 1.09972e9 + 1.90478e9i 0.224414 + 0.388696i 0.956143 0.292899i \(-0.0946199\pi\)
−0.731730 + 0.681595i \(0.761287\pi\)
\(588\) −5.32935e8 9.23070e8i −0.108107 0.187247i
\(589\) −9.41030e7 1.62991e8i −0.0189758 0.0328670i
\(590\) 1.84077e9 3.18830e9i 0.368992 0.639112i
\(591\) −2.79533e9 −0.557028
\(592\) 4.88433e9 + 3.42400e9i 0.967563 + 0.678277i
\(593\) −9.45812e8 −0.186257 −0.0931286 0.995654i \(-0.529687\pi\)
−0.0931286 + 0.995654i \(0.529687\pi\)
\(594\) 1.56062e9 2.70307e9i 0.305523 0.529182i
\(595\) −3.04754e9 5.27849e9i −0.593116 1.02731i
\(596\) −1.52637e8 2.64375e8i −0.0295323 0.0511515i
\(597\) 2.57761e8 + 4.46454e8i 0.0495800 + 0.0858750i
\(598\) 4.30872e8 0.0823937
\(599\) 8.17028e8 + 1.41513e9i 0.155326 + 0.269032i 0.933178 0.359416i \(-0.117024\pi\)
−0.777852 + 0.628448i \(0.783691\pi\)
\(600\) −3.52698e8 −0.0666612
\(601\) −2.97606e9 + 5.15469e9i −0.559218 + 0.968594i 0.438344 + 0.898807i \(0.355565\pi\)
−0.997562 + 0.0697870i \(0.977768\pi\)
\(602\) −1.13119e10 −2.11324
\(603\) −2.60665e9 −0.484141
\(604\) −6.03929e8 + 1.04604e9i −0.111521 + 0.193160i
\(605\) −1.10472e9 1.91342e9i −0.202818 0.351291i
\(606\) 2.55918e9 0.467139
\(607\) −4.11366e9 + 7.12507e9i −0.746566 + 1.29309i 0.202894 + 0.979201i \(0.434965\pi\)
−0.949460 + 0.313889i \(0.898368\pi\)
\(608\) −2.34003e8 + 4.05306e8i −0.0422240 + 0.0731341i
\(609\) 2.78151e9 4.81772e9i 0.499023 0.864333i
\(610\) −1.18184e9 2.04701e9i −0.210816 0.365145i
\(611\) −3.04822e8 5.27967e8i −0.0540632 0.0936403i
\(612\) 4.15366e8 7.19435e8i 0.0732489 0.126871i
\(613\) −2.60353e8 + 4.50944e8i −0.0456510 + 0.0790698i −0.887948 0.459944i \(-0.847870\pi\)
0.842297 + 0.539014i \(0.181203\pi\)
\(614\) −2.69415e9 + 4.66641e9i −0.469713 + 0.813567i
\(615\) −3.07584e9 −0.533213
\(616\) −3.27786e9 5.67743e9i −0.565013 0.978631i
\(617\) −2.59579e9 + 4.49604e9i −0.444909 + 0.770606i −0.998046 0.0624849i \(-0.980097\pi\)
0.553136 + 0.833091i \(0.313431\pi\)
\(618\) 1.25361e9 0.213650
\(619\) −5.52933e7 −0.00937034 −0.00468517 0.999989i \(-0.501491\pi\)
−0.00468517 + 0.999989i \(0.501491\pi\)
\(620\) 1.33442e8 2.31128e8i 0.0224864 0.0389477i
\(621\) −4.54930e9 −0.762296
\(622\) −5.43649e8 9.41627e8i −0.0905841 0.156896i
\(623\) 1.24977e10 2.07072
\(624\) −1.04310e8 1.80669e8i −0.0171861 0.0297672i
\(625\) 2.34144e9 + 4.05549e9i 0.383621 + 0.664451i
\(626\) 1.09061e9 + 1.88899e9i 0.177688 + 0.307764i
\(627\) 1.66600e8 2.88560e8i 0.0269923 0.0467520i
\(628\) −2.58655e9 −0.416736
\(629\) −3.75051e9 2.62917e9i −0.600915 0.421251i
\(630\) 9.44931e9 1.50560
\(631\) −3.21427e9 + 5.56727e9i −0.509306 + 0.882144i 0.490636 + 0.871365i \(0.336765\pi\)
−0.999942 + 0.0107796i \(0.996569\pi\)
\(632\) 1.89108e7 + 3.27545e7i 0.00297989 + 0.00516132i
\(633\) −1.31050e9 2.26985e9i −0.205363 0.355700i
\(634\) −5.97152e9 1.03430e10i −0.930621 1.61188i
\(635\) 7.97969e8 0.123674
\(636\) 2.77895e8 + 4.81328e8i 0.0428332 + 0.0741893i
\(637\) −1.05505e9 −0.161728
\(638\) −3.70726e9 + 6.42116e9i −0.565172 + 0.978907i
\(639\) 7.37396e9 1.11801
\(640\) 7.16181e9 1.07992
\(641\) −4.43730e9 + 7.68562e9i −0.665450 + 1.15259i 0.313714 + 0.949518i \(0.398427\pi\)
−0.979163 + 0.203075i \(0.934906\pi\)
\(642\) −2.23762e9 3.87568e9i −0.333745 0.578062i
\(643\) 2.06661e9 0.306563 0.153281 0.988183i \(-0.451016\pi\)
0.153281 + 0.988183i \(0.451016\pi\)
\(644\) 1.49645e9 2.59193e9i 0.220781 0.382404i
\(645\) −1.30144e9 + 2.25416e9i −0.190970 + 0.330770i
\(646\) 5.05350e8 8.75292e8i 0.0737528 0.127744i
\(647\) −2.03913e9 3.53187e9i −0.295991 0.512672i 0.679224 0.733931i \(-0.262317\pi\)
−0.975215 + 0.221259i \(0.928983\pi\)
\(648\) −1.57736e9 2.73206e9i −0.227728 0.394437i
\(649\) −1.90477e9 + 3.29916e9i −0.273518 + 0.473748i
\(650\) 5.46760e7 9.47017e7i 0.00780909 0.0135257i
\(651\) 5.37960e8 9.31774e8i 0.0764217 0.132366i
\(652\) 2.23671e9 0.316041
\(653\) −3.70648e8 6.41981e8i −0.0520913 0.0902249i 0.838804 0.544434i \(-0.183255\pi\)
−0.890895 + 0.454209i \(0.849922\pi\)
\(654\) −2.78135e9 + 4.81744e9i −0.388807 + 0.673433i
\(655\) 6.98583e9 0.971345
\(656\) −1.25730e10 −1.73891
\(657\) −3.70609e9 + 6.41913e9i −0.509843 + 0.883075i
\(658\) −2.19890e10 −3.00895
\(659\) 4.02794e9 + 6.97659e9i 0.548256 + 0.949608i 0.998394 + 0.0566489i \(0.0180416\pi\)
−0.450138 + 0.892959i \(0.648625\pi\)
\(660\) 4.72492e8 0.0639721
\(661\) 5.12852e9 + 8.88286e9i 0.690696 + 1.19632i 0.971610 + 0.236588i \(0.0760291\pi\)
−0.280914 + 0.959733i \(0.590638\pi\)
\(662\) 3.92295e9 + 6.79475e9i 0.525545 + 0.910271i
\(663\) 8.00957e7 + 1.38730e8i 0.0106736 + 0.0184873i
\(664\) 2.63482e9 4.56365e9i 0.349271 0.604956i
\(665\) 2.21399e9 0.291944
\(666\) 6.43721e9 2.99747e9i 0.844380 0.393183i
\(667\) 1.08069e10 1.41013
\(668\) 1.00314e9 1.73749e9i 0.130210 0.225530i
\(669\) −5.85881e8 1.01478e9i −0.0756516 0.131032i
\(670\) −2.24855e9 3.89460e9i −0.288829 0.500266i
\(671\) 1.22293e9 + 2.11818e9i 0.156270 + 0.270667i
\(672\) −2.67546e9 −0.340100
\(673\) 4.85771e9 + 8.41381e9i 0.614298 + 1.06400i 0.990507 + 0.137461i \(0.0438941\pi\)
−0.376209 + 0.926535i \(0.622773\pi\)
\(674\) 8.61583e9 1.08390
\(675\) −5.77289e8 + 9.99893e8i −0.0722486 + 0.125138i
\(676\) −1.90576e9 −0.237277
\(677\) 9.91844e8 0.122852 0.0614261 0.998112i \(-0.480435\pi\)
0.0614261 + 0.998112i \(0.480435\pi\)
\(678\) 2.19925e9 3.80920e9i 0.271000 0.469386i
\(679\) −7.80262e9 1.35145e10i −0.956525 1.65675i
\(680\) −4.57569e9 −0.558053
\(681\) 1.44053e9 2.49507e9i 0.174786 0.302739i
\(682\) −7.17004e8 + 1.24189e9i −0.0865519 + 0.149912i
\(683\) 5.66022e9 9.80379e9i 0.679768 1.17739i −0.295283 0.955410i \(-0.595414\pi\)
0.975051 0.221983i \(-0.0712529\pi\)
\(684\) 1.50879e8 + 2.61330e8i 0.0180273 + 0.0312243i
\(685\) −1.85457e9 3.21222e9i −0.220459 0.381845i
\(686\) −1.05517e10 + 1.82762e10i −1.24793 + 2.16148i
\(687\) 5.31637e8 9.20823e8i 0.0625557 0.108350i
\(688\) −5.31987e9 + 9.21428e9i −0.622790 + 1.07870i
\(689\) 5.50149e8 0.0640786
\(690\) −1.78800e9 3.09691e9i −0.207203 0.358886i
\(691\) −5.36697e9 + 9.29586e9i −0.618808 + 1.07181i 0.370896 + 0.928675i \(0.379051\pi\)
−0.989704 + 0.143132i \(0.954283\pi\)
\(692\) 1.87378e9 0.214955
\(693\) −9.77788e9 −1.11604
\(694\) 4.15156e9 7.19072e9i 0.471469 0.816609i
\(695\) −3.74947e9 −0.423666
\(696\) −2.08814e9 3.61676e9i −0.234761 0.406618i
\(697\) 9.65438e9 1.07997
\(698\) −1.60405e9 2.77830e9i −0.178535 0.309232i
\(699\) 6.91808e7 + 1.19825e8i 0.00766153 + 0.0132702i
\(700\) −3.79788e8 6.57812e8i −0.0418503 0.0724868i
\(701\) 5.78617e9 1.00219e10i 0.634422 1.09885i −0.352216 0.935919i \(-0.614572\pi\)
0.986637 0.162932i \(-0.0520950\pi\)
\(702\) −5.45076e8 −0.0594671
\(703\) 1.50825e9 7.02313e8i 0.163731 0.0762407i
\(704\) −4.53166e9 −0.489500
\(705\) −2.52985e9 + 4.38183e9i −0.271915 + 0.470971i
\(706\) 3.63812e9 + 6.30140e9i 0.389099 + 0.673939i
\(707\) −8.79802e9 1.52386e10i −0.936305 1.62173i
\(708\) 3.36049e8 + 5.82054e8i 0.0355866 + 0.0616378i
\(709\) 5.64416e9 0.594754 0.297377 0.954760i \(-0.403888\pi\)
0.297377 + 0.954760i \(0.403888\pi\)
\(710\) 6.36093e9 + 1.10174e10i 0.666985 + 1.15525i
\(711\) 5.64109e7 0.00588599
\(712\) 4.69113e9 8.12527e9i 0.487076 0.843641i
\(713\) 2.09011e9 0.215951
\(714\) 5.77789e9 0.594053
\(715\) 2.33848e8 4.05037e8i 0.0239256 0.0414404i
\(716\) 1.12881e9 + 1.95515e9i 0.114927 + 0.199060i
\(717\) 5.16856e9 0.523663
\(718\) 7.21081e9 1.24895e10i 0.727024 1.25924i
\(719\) −2.29705e8 + 3.97860e8i −0.0230472 + 0.0399190i −0.877319 0.479908i \(-0.840670\pi\)
0.854272 + 0.519827i \(0.174003\pi\)
\(720\) 4.44391e9 7.69707e9i 0.443712 0.768532i
\(721\) −4.30970e9 7.46462e9i −0.428227 0.741710i
\(722\) −5.44374e9 9.42884e9i −0.538292 0.932348i
\(723\) −2.63435e9 + 4.56282e9i −0.259232 + 0.449003i
\(724\) −1.71277e9 + 2.96660e9i −0.167731 + 0.290519i
\(725\) 1.37135e9 2.37525e9i 0.133649 0.231487i
\(726\) 2.09445e9 0.203138
\(727\) −5.18082e8 8.97344e8i −0.0500067 0.0866141i 0.839939 0.542681i \(-0.182591\pi\)
−0.889945 + 0.456067i \(0.849258\pi\)
\(728\) −5.72428e8 + 9.91475e8i −0.0549872 + 0.0952406i
\(729\) −1.57230e9 −0.150310
\(730\) −1.27878e10 −1.21665
\(731\) 4.08494e9 7.07533e9i 0.386790 0.669940i
\(732\) 4.31512e8 0.0406635
\(733\) 4.79930e9 + 8.31263e9i 0.450105 + 0.779605i 0.998392 0.0566851i \(-0.0180531\pi\)
−0.548287 + 0.836290i \(0.684720\pi\)
\(734\) 2.36750e10 2.20980
\(735\) 4.37818e9 + 7.58322e9i 0.406713 + 0.704447i
\(736\) −2.59871e9 4.50110e9i −0.240262 0.416146i
\(737\) 2.32673e9 + 4.03002e9i 0.214097 + 0.370827i
\(738\) −7.48369e9 + 1.29621e10i −0.685359 + 1.18708i
\(739\) −1.79680e10 −1.63774 −0.818868 0.573982i \(-0.805398\pi\)
−0.818868 + 0.573982i \(0.805398\pi\)
\(740\) 1.93186e9 + 1.35427e9i 0.175253 + 0.122855i
\(741\) −5.81883e7 −0.00525379
\(742\) 9.92157e9 1.71847e10i 0.891593 1.54428i
\(743\) −7.34255e9 1.27177e10i −0.656729 1.13749i −0.981457 0.191681i \(-0.938606\pi\)
0.324728 0.945807i \(-0.394727\pi\)
\(744\) −4.03857e8 6.99501e8i −0.0359519 0.0622706i
\(745\) 1.25395e9 + 2.17190e9i 0.111105 + 0.192439i
\(746\) 1.50822e10 1.33008
\(747\) −3.92984e9 6.80668e9i −0.344947 0.597466i
\(748\) −1.48305e9 −0.129569
\(749\) −1.53851e10 + 2.66478e10i −1.33787 + 2.31726i
\(750\) −5.56631e9 −0.481785
\(751\) 1.86756e10 1.60892 0.804462 0.594004i \(-0.202454\pi\)
0.804462 + 0.594004i \(0.202454\pi\)
\(752\) −1.03412e10 + 1.79115e10i −0.886765 + 1.53592i
\(753\) 4.67720e8 + 8.10114e8i 0.0399212 + 0.0691455i
\(754\) 1.29483e9 0.110005
\(755\) 4.96141e9 8.59341e9i 0.419557 0.726694i
\(756\) −1.89309e9 + 3.27893e9i −0.159347 + 0.275998i
\(757\) 8.39144e9 1.45344e10i 0.703074 1.21776i −0.264308 0.964438i \(-0.585144\pi\)
0.967382 0.253322i \(-0.0815231\pi\)
\(758\) −5.20247e9 9.01095e9i −0.433878 0.751499i
\(759\) 1.85017e9 + 3.20459e9i 0.153591 + 0.266027i
\(760\) 8.31043e8 1.43941e9i 0.0686714 0.118942i
\(761\) 4.52400e9 7.83581e9i 0.372115 0.644521i −0.617776 0.786354i \(-0.711966\pi\)
0.989891 + 0.141833i \(0.0452995\pi\)
\(762\) −3.78221e8 + 6.55099e8i −0.0309673 + 0.0536370i
\(763\) 3.82472e10 3.11720
\(764\) −9.25393e8 1.60283e9i −0.0750757 0.130035i
\(765\) −3.41232e9 + 5.91032e9i −0.275572 + 0.477305i
\(766\) 1.48857e10 1.19665
\(767\) 6.65278e8 0.0532377
\(768\) −1.71857e9 + 2.97664e9i −0.136900 + 0.237117i
\(769\) −2.21033e10 −1.75273 −0.876366 0.481645i \(-0.840039\pi\)
−0.876366 + 0.481645i \(0.840039\pi\)
\(770\) −8.43460e9 1.46092e10i −0.665805 1.15321i
\(771\) −5.59027e9 −0.439281
\(772\) −1.09967e8 1.90468e8i −0.00860201 0.0148991i
\(773\) 9.83576e9 + 1.70360e10i 0.765914 + 1.32660i 0.939762 + 0.341829i \(0.111046\pi\)
−0.173848 + 0.984772i \(0.555620\pi\)
\(774\) 6.33297e9 + 1.09690e10i 0.490923 + 0.850304i
\(775\) 2.65227e8 4.59387e8i 0.0204674 0.0354505i
\(776\) −1.17152e10 −0.899978
\(777\) 7.78815e9 + 5.45962e9i 0.595608 + 0.417531i
\(778\) 1.79296e9 0.136503
\(779\) −1.75344e9 + 3.03705e9i −0.132896 + 0.230182i
\(780\) −4.12567e7 7.14587e7i −0.00311289 0.00539168i
\(781\) −6.58211e9 1.14005e10i −0.494409 0.856341i
\(782\) 5.61214e9 + 9.72051e9i 0.419667 + 0.726885i
\(783\) −1.36713e10 −1.01775
\(784\) 1.78965e10 + 3.09977e10i 1.32636 + 2.29733i
\(785\) 2.12490e10 1.56782
\(786\) −3.31114e9 + 5.73507e9i −0.243220 + 0.421269i
\(787\) −6.64574e9 −0.485995 −0.242997 0.970027i \(-0.578131\pi\)
−0.242997 + 0.970027i \(0.578131\pi\)
\(788\) −4.51939e9 −0.329032
\(789\) 1.99169e9 3.44971e9i 0.144362 0.250042i
\(790\) 4.86612e7 + 8.42837e7i 0.00351146 + 0.00608204i
\(791\) −3.02425e10 −2.17270
\(792\) −3.67022e9 + 6.35701e9i −0.262515 + 0.454689i
\(793\) 2.13567e8 3.69908e8i 0.0152082 0.0263413i
\(794\) −1.06686e10 + 1.84786e10i −0.756373 + 1.31008i
\(795\) −2.28297e9 3.95421e9i −0.161144 0.279110i
\(796\) 4.16738e8 + 7.21811e8i 0.0292865 + 0.0507256i
\(797\) 1.02356e10 1.77286e10i 0.716157 1.24042i −0.246354 0.969180i \(-0.579233\pi\)
0.962511 0.271241i \(-0.0874341\pi\)
\(798\) −1.04939e9 + 1.81759e9i −0.0731014 + 0.126615i
\(799\) 7.94066e9 1.37536e10i 0.550735 0.953901i
\(800\) −1.31907e9 −0.0910860
\(801\) −6.99682e9 1.21188e10i −0.481046 0.833196i
\(802\) −1.12587e10 + 1.95006e10i −0.770686 + 1.33487i
\(803\) 1.32324e10 0.901852
\(804\) 8.20988e8 0.0557109
\(805\) −1.22937e10 + 2.12933e10i −0.830609 + 1.43866i
\(806\) 2.50427e8 0.0168465
\(807\) −1.73120e8 2.99853e8i −0.0115955 0.0200841i
\(808\) −1.32097e10 −0.880953
\(809\) −1.03828e10 1.79836e10i −0.689440 1.19414i −0.972019 0.234901i \(-0.924524\pi\)
0.282580 0.959244i \(-0.408810\pi\)
\(810\) −4.05885e9 7.03014e9i −0.268352 0.464800i
\(811\) 3.42330e9 + 5.92933e9i 0.225358 + 0.390331i 0.956427 0.291973i \(-0.0943117\pi\)
−0.731069 + 0.682303i \(0.760978\pi\)
\(812\) 4.49705e9 7.78911e9i 0.294769 0.510554i
\(813\) 1.01700e10 0.663748
\(814\) −1.03802e10 7.27669e9i −0.674560 0.472877i
\(815\) −1.83751e10 −1.18899
\(816\) 2.71728e9 4.70646e9i 0.175073 0.303235i
\(817\) 1.48383e9 + 2.57006e9i 0.0951932 + 0.164879i
\(818\) −1.45609e10 2.52202e10i −0.930146 1.61106i
\(819\) 8.53777e8 + 1.47879e9i 0.0543064 + 0.0940614i
\(820\) −4.97290e9 −0.314964
\(821\) 9.35613e8 + 1.62053e9i 0.0590059 + 0.102201i 0.894019 0.448028i \(-0.147874\pi\)
−0.835014 + 0.550229i \(0.814540\pi\)
\(822\) 3.51612e9 0.220807
\(823\) −1.26231e10 + 2.18638e10i −0.789344 + 1.36718i 0.137026 + 0.990567i \(0.456246\pi\)
−0.926369 + 0.376616i \(0.877088\pi\)
\(824\) −6.47075e9 −0.402911
\(825\) 9.39119e8 0.0582280
\(826\) 1.19978e10 2.07809e10i 0.740752 1.28302i
\(827\) −8.35941e9 1.44789e10i −0.513933 0.890157i −0.999869 0.0161633i \(-0.994855\pi\)
0.485937 0.873994i \(-0.338479\pi\)
\(828\) −3.35115e9 −0.205158
\(829\) −1.04671e10 + 1.81295e10i −0.638094 + 1.10521i 0.347756 + 0.937585i \(0.386944\pi\)
−0.985851 + 0.167627i \(0.946390\pi\)
\(830\) 6.77992e9 1.17432e10i 0.411577 0.712873i
\(831\) 3.25978e9 5.64610e9i 0.197054 0.341307i
\(832\) 3.95692e8 + 6.85358e8i 0.0238191 + 0.0412559i
\(833\) −1.37421e10 2.38021e10i −0.823753 1.42678i
\(834\) 1.77718e9 3.07816e9i 0.106084 0.183743i
\(835\) −8.24101e9 + 1.42739e10i −0.489867 + 0.848474i
\(836\) 2.69353e8 4.66533e8i 0.0159441 0.0276160i
\(837\) −2.64410e9 −0.155861
\(838\) 3.57290e9 + 6.18844e9i 0.209733 + 0.363268i
\(839\) −5.29041e8 + 9.16326e8i −0.0309259 + 0.0535653i −0.881074 0.472978i \(-0.843179\pi\)
0.850148 + 0.526543i \(0.176512\pi\)
\(840\) 9.50168e9 0.553124
\(841\) 1.52263e10 0.882692
\(842\) −1.15843e10 + 2.00647e10i −0.668774 + 1.15835i
\(843\) 3.37413e9 0.193983
\(844\) −2.11876e9 3.66980e9i −0.121306 0.210109i
\(845\) 1.56563e10 0.892668
\(846\) 1.23105e10 + 2.13225e10i 0.699006 + 1.21071i
\(847\) −7.20037e9 1.24714e10i −0.407158 0.705218i
\(848\) −9.33201e9 1.61635e10i −0.525521 0.910229i
\(849\) −4.72609e9 + 8.18583e9i −0.265048 + 0.459077i
\(850\) 2.84864e9 0.159100
\(851\) −1.62033e9 + 1.84055e10i −0.0901260 + 1.02375i
\(852\) −2.32250e9 −0.128652
\(853\) −2.32232e9 + 4.02237e9i −0.128115 + 0.221902i −0.922946 0.384929i \(-0.874226\pi\)
0.794831 + 0.606831i \(0.207559\pi\)
\(854\) −7.70306e9 1.33421e10i −0.423215 0.733030i
\(855\) −1.23950e9 2.14688e9i −0.0678212 0.117470i
\(856\) 1.15499e10 + 2.00050e10i 0.629391 + 1.09014i
\(857\) −1.30047e10 −0.705777 −0.352889 0.935665i \(-0.614801\pi\)
−0.352889 + 0.935665i \(0.614801\pi\)
\(858\) 2.21679e8 + 3.83959e8i 0.0119817 + 0.0207529i
\(859\) 3.01314e10 1.62197 0.810987 0.585064i \(-0.198931\pi\)
0.810987 + 0.585064i \(0.198931\pi\)
\(860\) −2.10412e9 + 3.64445e9i −0.112805 + 0.195383i
\(861\) −2.00479e10 −1.07043
\(862\) 2.33254e10 1.24038
\(863\) −1.28729e10 + 2.22966e10i −0.681773 + 1.18086i 0.292667 + 0.956214i \(0.405457\pi\)
−0.974439 + 0.224650i \(0.927876\pi\)
\(864\) 3.28750e9 + 5.69413e9i 0.173408 + 0.300351i
\(865\) −1.53935e10 −0.808688
\(866\) −5.56467e8 + 9.63829e8i −0.0291157 + 0.0504298i
\(867\) 1.78778e9 3.09653e9i 0.0931639 0.161365i
\(868\) 8.69754e8 1.50646e9i 0.0451416 0.0781876i
\(869\) −5.03532e7 8.72144e7i −0.00260290 0.00450836i
\(870\) −5.37319e9 9.30664e9i −0.276640 0.479154i
\(871\) 4.06328e8 7.03781e8i 0.0208360 0.0360889i
\(872\) 1.43565e10 2.48661e10i 0.733230 1.26999i
\(873\) −8.73658e9 + 1.51322e10i −0.444418 + 0.769755i
\(874\) −4.07714e9 −0.206569
\(875\) 1.91360e10 + 3.31446e10i 0.965659 + 1.67257i
\(876\) 1.16727e9 2.02176e9i 0.0586686 0.101617i
\(877\) −1.30051e10 −0.651052 −0.325526 0.945533i \(-0.605541\pi\)
−0.325526 + 0.945533i \(0.605541\pi\)
\(878\) 3.44706e10 1.71877
\(879\) 4.76677e9 8.25628e9i 0.236735 0.410037i
\(880\) −1.58668e10 −0.784874
\(881\) −1.58924e10 2.75264e10i −0.783019 1.35623i −0.930175 0.367116i \(-0.880345\pi\)
0.147156 0.989113i \(-0.452988\pi\)
\(882\) 4.26094e10 2.09105
\(883\) −1.45423e10 2.51879e10i −0.710837 1.23120i −0.964544 0.263924i \(-0.914983\pi\)
0.253707 0.967281i \(-0.418350\pi\)
\(884\) 1.29496e8 + 2.24293e8i 0.00630482 + 0.0109203i
\(885\) −2.76072e9 4.78170e9i −0.133882 0.231890i
\(886\) 5.64476e9 9.77701e9i 0.272664 0.472268i
\(887\) 1.56009e10 0.750616 0.375308 0.926900i \(-0.377537\pi\)
0.375308 + 0.926900i \(0.377537\pi\)
\(888\) 6.47288e9 3.01408e9i 0.310208 0.144447i
\(889\) 5.20104e9 0.248276
\(890\) 1.20712e10 2.09079e10i 0.573965 0.994137i
\(891\) 4.19998e9 + 7.27458e9i 0.198919 + 0.344537i
\(892\) −9.47230e8 1.64065e9i −0.0446867 0.0773997i
\(893\) 2.88439e9 + 4.99590e9i 0.135542 + 0.234765i
\(894\) −2.37738e9 −0.111280
\(895\) −9.27339e9 1.60620e10i −0.432372 0.748891i
\(896\) 4.66796e10 2.16795
\(897\) 3.23104e8 5.59632e8i 0.0149475 0.0258898i
\(898\) 1.05689e10 0.487036
\(899\) 6.28107e9 0.288320
\(900\) −4.25248e8 + 7.36552e8i −0.0194444 + 0.0336786i
\(901\) 7.16573e9 + 1.24114e10i 0.326380 + 0.565307i
\(902\) 2.67202e10 1.21232
\(903\) −8.48261e9 + 1.46923e10i −0.383374 + 0.664023i
\(904\) −1.13518e10 + 1.96619e10i −0.511065 + 0.885191i
\(905\) 1.40708e10 2.43713e10i 0.631027 1.09297i
\(906\) 4.70322e9 + 8.14621e9i 0.210110 + 0.363921i
\(907\) −1.50756e10 2.61117e10i −0.670886 1.16201i −0.977653 0.210224i \(-0.932581\pi\)
0.306767 0.951785i \(-0.400753\pi\)
\(908\) 2.32899e9 4.03394e9i 0.103245 0.178825i
\(909\) −9.85113e9 + 1.70627e10i −0.435023 + 0.753483i
\(910\) −1.47297e9 + 2.55126e9i −0.0647962 + 0.112230i
\(911\) −6.16049e9 −0.269961 −0.134980 0.990848i \(-0.543097\pi\)
−0.134980 + 0.990848i \(0.543097\pi\)
\(912\) 9.87031e8 + 1.70959e9i 0.0430873 + 0.0746293i
\(913\) −7.01567e9 + 1.21515e10i −0.305085 + 0.528423i
\(914\) −3.53618e10 −1.53187
\(915\) −3.54497e9 −0.152981
\(916\) 8.59532e8 1.48875e9i 0.0369511 0.0640012i
\(917\) 4.55326e10 1.94998
\(918\) −7.09965e9 1.22970e10i −0.302892 0.524624i
\(919\) 1.04249e10 0.443066 0.221533 0.975153i \(-0.428894\pi\)
0.221533 + 0.975153i \(0.428894\pi\)
\(920\) 9.22911e9 + 1.59853e10i 0.390753 + 0.676804i
\(921\) 4.04060e9 + 6.99852e9i 0.170427 + 0.295187i
\(922\) 1.48360e10 + 2.56967e10i 0.623388 + 1.07974i
\(923\) −1.14946e9 + 1.99093e9i −0.0481159 + 0.0833393i
\(924\) 3.07963e9 0.128424
\(925\) 3.83974e9 + 2.69172e9i 0.159517 + 0.111824i
\(926\) −2.42768e10 −1.00474
\(927\) −4.82556e9 + 8.35812e9i −0.198962 + 0.344611i
\(928\) −7.80949e9 1.35264e10i −0.320778 0.555604i
\(929\) 1.54547e10 + 2.67683e10i 0.632420 + 1.09538i 0.987055 + 0.160379i \(0.0512718\pi\)
−0.354635 + 0.935005i \(0.615395\pi\)
\(930\) −1.03920e9 1.79995e9i −0.0423653 0.0733789i
\(931\) 9.98346e9 0.405469
\(932\) 1.11849e8 + 1.93728e8i 0.00452560 + 0.00783857i
\(933\) −1.63069e9 −0.0657334
\(934\) −2.12043e10 + 3.67270e10i −0.851551 + 1.47493i
\(935\) 1.21836e10 0.487454
\(936\) 1.28189e9 0.0510960
\(937\) 1.85849e10 3.21900e10i 0.738026 1.27830i −0.215357 0.976535i \(-0.569092\pi\)
0.953383 0.301763i \(-0.0975751\pi\)
\(938\) −1.46557e10 2.53844e10i −0.579825 1.00429i
\(939\) 3.27131e9 0.128941
\(940\) −4.09017e9 + 7.08439e9i −0.160618 + 0.278199i
\(941\) −9.47622e9 + 1.64133e10i −0.370742 + 0.642143i −0.989680 0.143296i \(-0.954230\pi\)
0.618938 + 0.785440i \(0.287563\pi\)
\(942\) −1.00716e10 + 1.74446e10i −0.392574 + 0.679958i
\(943\) −1.94728e10 3.37278e10i −0.756200 1.30978i
\(944\) −1.12849e10 1.95460e10i −0.436612 0.756235i
\(945\) 1.55522e10 2.69371e10i 0.599486 1.03834i
\(946\) 1.13058e10 1.95822e10i 0.434193 0.752044i
\(947\) 3.28817e9 5.69527e9i 0.125814 0.217916i −0.796237 0.604985i \(-0.793179\pi\)
0.922051 + 0.387069i \(0.126512\pi\)
\(948\) −1.77671e7 −0.000677311
\(949\) −1.15542e9 2.00125e9i −0.0438842 0.0760097i
\(950\) −5.17373e8 + 8.96117e8i −0.0195781 + 0.0339103i
\(951\) −1.79118e10 −0.675316
\(952\) −2.98237e10 −1.12029
\(953\) 1.42117e10 2.46154e10i 0.531889 0.921259i −0.467418 0.884037i \(-0.654816\pi\)
0.999307 0.0372228i \(-0.0118511\pi\)
\(954\) −2.22183e10 −0.828500
\(955\) 7.60231e9 + 1.31676e10i 0.282445 + 0.489209i
\(956\) 8.35633e9 0.309324
\(957\) 5.56002e9 + 9.63024e9i 0.205062 + 0.355178i
\(958\) −2.80991e10 4.86691e10i −1.03256 1.78844i
\(959\) −1.20878e10 2.09367e10i −0.442572 0.766556i
\(960\) 3.28402e9 5.68810e9i 0.119800 0.207500i
\(961\) −2.62978e10 −0.955846
\(962\) −1.94141e8 + 2.20526e9i −0.00703078 + 0.0798633i
\(963\) 3.44534e10 1.24320
\(964\) −4.25911e9 + 7.37700e9i −0.153126 + 0.265222i
\(965\) 9.03400e8 + 1.56473e9i 0.0323619 + 0.0560525i
\(966\) −1.16539e10 2.01852e10i −0.415961 0.720465i
\(967\) 2.19962e10 + 3.80986e10i 0.782267 + 1.35493i 0.930618 + 0.365992i \(0.119270\pi\)
−0.148350 + 0.988935i \(0.547396\pi\)
\(968\) −1.08109e10 −0.383088
\(969\) −7.57907e8 1.31273e9i −0.0267598 0.0463493i
\(970\) −3.01454e10 −1.06052
\(971\) 7.81449e9 1.35351e10i 0.273926 0.474454i −0.695938 0.718102i \(-0.745011\pi\)
0.969864 + 0.243648i \(0.0783443\pi\)
\(972\) 6.54721e9 0.228678
\(973\) −2.44385e10 −0.850511
\(974\) −2.29260e10 + 3.97089e10i −0.795007 + 1.37699i
\(975\) −8.20013e7 1.42030e8i −0.00283338 0.00490756i
\(976\) −1.44907e10 −0.498900
\(977\) 1.84648e10 3.19820e10i 0.633453 1.09717i −0.353388 0.935477i \(-0.614970\pi\)
0.986841 0.161696i \(-0.0516964\pi\)
\(978\) 8.70941e9 1.50851e10i 0.297716 0.515660i
\(979\) −1.24909e10 + 2.16349e10i −0.425457 + 0.736913i
\(980\) 7.07847e9 + 1.22603e10i 0.240242 + 0.416111i
\(981\) −2.14127e10 3.70879e10i −0.724152 1.25427i
\(982\) −1.33293e10 + 2.30870e10i −0.449176 + 0.777996i
\(983\) −5.26055e9 + 9.11155e9i −0.176642 + 0.305953i −0.940728 0.339161i \(-0.889857\pi\)
0.764086 + 0.645114i \(0.223190\pi\)
\(984\) −7.52516e9 + 1.30340e10i −0.251787 + 0.436108i
\(985\) 3.71278e10 1.23786
\(986\) 1.68653e10 + 2.92115e10i 0.560304 + 0.970476i
\(987\) −1.64892e10 + 2.85602e10i −0.545871 + 0.945476i
\(988\) −9.40767e7 −0.00310337
\(989\) −3.29571e10 −1.08333
\(990\) −9.44421e9 + 1.63578e10i −0.309345 + 0.535800i
\(991\) −4.39798e10 −1.43547 −0.717736 0.696315i \(-0.754822\pi\)
−0.717736 + 0.696315i \(0.754822\pi\)
\(992\) −1.51040e9 2.61609e9i −0.0491248 0.0850866i
\(993\) 1.17670e10 0.381368
\(994\) 4.14596e10 + 7.18101e10i 1.33898 + 2.31917i
\(995\) −3.42359e9 5.92983e9i −0.110180 0.190837i
\(996\) 1.23774e9 + 2.14383e9i 0.0396937 + 0.0687515i
\(997\) −5.62699e8 + 9.74623e8i −0.0179822 + 0.0311461i −0.874876 0.484346i \(-0.839058\pi\)
0.856894 + 0.515492i \(0.172391\pi\)
\(998\) 1.26504e10 0.402855
\(999\) 2.04980e9 2.32839e10i 0.0650478 0.738885i
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 37.8.c.a.10.17 42
37.26 even 3 inner 37.8.c.a.26.17 yes 42
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
37.8.c.a.10.17 42 1.1 even 1 trivial
37.8.c.a.26.17 yes 42 37.26 even 3 inner