Properties

Label 29.9.f.a.2.9
Level $29$
Weight $9$
Character 29.2
Analytic conductor $11.814$
Analytic rank $0$
Dimension $228$
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] = [29,9,Mod(2,29)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(29, base_ring=CyclotomicField(28))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("29.2");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 29.f (of order \(28\), 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: \(11.8139796918\)
Analytic rank: \(0\)
Dimension: \(228\)
Relative dimension: \(19\) over \(\Q(\zeta_{28})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label 2.9
Character \(\chi\) \(=\) 29.2
Dual form 29.9.f.a.15.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.14353 - 0.466864i) q^{2} +(-78.5126 - 49.3327i) q^{3} +(-232.631 - 53.0964i) q^{4} +(799.859 - 637.866i) q^{5} +(302.287 + 241.066i) q^{6} +(-699.825 - 3066.14i) q^{7} +(1946.68 + 681.171i) q^{8} +(883.797 + 1835.22i) q^{9} +O(q^{10})\) \(q+(-4.14353 - 0.466864i) q^{2} +(-78.5126 - 49.3327i) q^{3} +(-232.631 - 53.0964i) q^{4} +(799.859 - 637.866i) q^{5} +(302.287 + 241.066i) q^{6} +(-699.825 - 3066.14i) q^{7} +(1946.68 + 681.171i) q^{8} +(883.797 + 1835.22i) q^{9} +(-3612.03 + 2269.59i) q^{10} +(-19572.3 + 6848.64i) q^{11} +(15645.0 + 15645.0i) q^{12} +(-8119.18 + 16859.6i) q^{13} +(1468.28 + 13031.3i) q^{14} +(-94266.7 + 10621.3i) q^{15} +(47287.6 + 22772.5i) q^{16} +(70809.4 - 70809.4i) q^{17} +(-2805.24 - 8016.91i) q^{18} +(6619.42 + 10534.7i) q^{19} +(-219940. + 105918. i) q^{20} +(-96315.7 + 275255. i) q^{21} +(84295.7 - 19239.9i) q^{22} +(-287254. + 360206. i) q^{23} +(-119235. - 149515. i) q^{24} +(145979. - 639574. i) q^{25} +(41513.2 - 66067.9i) q^{26} +(-46968.4 + 416856. i) q^{27} +750435. i q^{28} +(90635.6 - 701450. i) q^{29} +395555. q^{30} +(1.11599e6 + 125742. i) q^{31} +(-632357. - 397336. i) q^{32} +(1.87453e6 + 427850. i) q^{33} +(-326459. + 260342. i) q^{34} +(-2.51555e6 - 2.00608e6i) q^{35} +(-108154. - 473856. i) q^{36} +(-344069. - 120395. i) q^{37} +(-22509.5 - 46741.4i) q^{38} +(1.46919e6 - 923153. i) q^{39} +(1.99156e6 - 696878. i) q^{40} +(-2.01020e6 - 2.01020e6i) q^{41} +(527593. - 1.09556e6i) q^{42} +(170357. + 1.51196e6i) q^{43} +(4.91675e6 - 553985. i) q^{44} +(1.87754e6 + 904175. i) q^{45} +(1.35841e6 - 1.35841e6i) q^{46} +(2.04131e6 + 5.83373e6i) q^{47} +(-2.58924e6 - 4.12075e6i) q^{48} +(-3.71753e6 + 1.79027e6i) q^{49} +(-903461. + 2.58194e6i) q^{50} +(-9.05264e6 + 2.06621e6i) q^{51} +(2.78396e6 - 3.49097e6i) q^{52} +(-16351.4 - 20504.0i) q^{53} +(389230. - 1.70533e6i) q^{54} +(-1.12865e7 + 1.79624e7i) q^{55} +(726231. - 6.44547e6i) q^{56} -1.15366e6i q^{57} +(-703032. + 2.86416e6i) q^{58} -8.35555e6 q^{59} +(2.24933e7 + 2.53438e6i) q^{60} +(2.97860e6 + 1.87158e6i) q^{61} +(-4.56542e6 - 1.04203e6i) q^{62} +(5.00854e6 - 3.99418e6i) q^{63} +(-8.07018e6 - 6.43575e6i) q^{64} +(4.26000e6 + 1.86643e7i) q^{65} +(-7.56743e6 - 2.64796e6i) q^{66} +(-1.59797e7 - 3.31822e7i) q^{67} +(-2.02322e7 + 1.27127e7i) q^{68} +(4.03230e7 - 1.41096e7i) q^{69} +(9.48667e6 + 9.48667e6i) q^{70} +(-5.10483e6 + 1.06003e7i) q^{71} +(470365. + 4.17460e6i) q^{72} +(-4.15322e7 + 4.67956e6i) q^{73} +(1.36945e6 + 659493. i) q^{74} +(-4.30131e7 + 4.30131e7i) q^{75} +(-980523. - 2.80217e6i) q^{76} +(3.46960e7 + 5.52184e7i) q^{77} +(-6.51861e6 + 3.13920e6i) q^{78} +(2.28372e6 - 6.52651e6i) q^{79} +(5.23492e7 - 1.19484e7i) q^{80} +(3.25848e7 - 4.08601e7i) q^{81} +(7.39084e6 + 9.26782e6i) q^{82} +(1.26046e7 - 5.52242e7i) q^{83} +(3.70210e7 - 5.89186e7i) q^{84} +(1.14706e7 - 1.01804e8i) q^{85} -6.34439e6i q^{86} +(-4.17205e7 + 5.06013e7i) q^{87} -4.27660e7 q^{88} +(1.65890e7 + 1.86913e6i) q^{89} +(-7.35751e6 - 4.62303e6i) q^{90} +(5.73760e7 + 1.30957e7i) q^{91} +(8.59498e7 - 6.85427e7i) q^{92} +(-8.14159e7 - 6.49270e7i) q^{93} +(-5.73467e6 - 2.51252e7i) q^{94} +(1.20144e7 + 4.20401e6i) q^{95} +(3.00463e7 + 6.23918e7i) q^{96} +(-2.72399e7 + 1.71159e7i) q^{97} +(1.62395e7 - 5.68244e6i) q^{98} +(-2.98667e7 - 2.98667e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9} - 15884 q^{10} + 8376 q^{11} - 5036 q^{12} - 14 q^{13} - 12742 q^{14} + 35516 q^{15} + 245898 q^{16} - 76248 q^{17} + 465008 q^{18} + 164474 q^{19} - 907274 q^{20} - 628270 q^{21} + 1214962 q^{22} + 173408 q^{23} + 1858618 q^{24} + 43976 q^{25} - 4604204 q^{26} - 1727586 q^{27} + 1079922 q^{29} + 8909208 q^{30} + 3657848 q^{31} + 1160364 q^{32} - 4279184 q^{33} - 8655374 q^{34} - 8269058 q^{35} - 3366854 q^{36} - 5622890 q^{37} + 15536626 q^{38} + 16110008 q^{39} - 23544696 q^{40} - 9561672 q^{41} - 14 q^{42} + 5181008 q^{43} + 51041750 q^{44} - 35245194 q^{45} - 43159224 q^{46} - 12806808 q^{47} + 83954488 q^{48} + 10429400 q^{49} + 80809398 q^{50} + 18760882 q^{51} - 93050550 q^{52} - 30960322 q^{53} - 106220916 q^{54} - 126174004 q^{55} - 40136268 q^{56} + 159368354 q^{58} + 11188020 q^{59} + 255893612 q^{60} + 139657128 q^{61} + 102501616 q^{62} + 9797746 q^{63} - 135941792 q^{64} - 14207858 q^{65} - 447597656 q^{66} - 148930894 q^{67} - 167094904 q^{68} + 66986722 q^{69} + 586255934 q^{70} - 15272096 q^{71} + 41230600 q^{72} - 219415072 q^{73} - 347464696 q^{74} + 391507416 q^{75} + 271512490 q^{76} + 240416780 q^{77} + 141747906 q^{78} + 112667220 q^{79} - 375642638 q^{80} - 358099268 q^{81} - 262154910 q^{82} - 109463350 q^{83} - 694921012 q^{84} - 356627386 q^{85} + 199703522 q^{87} + 251202768 q^{88} + 839849154 q^{89} + 675826020 q^{90} + 533256766 q^{91} + 742339570 q^{92} + 78998570 q^{93} - 209116610 q^{94} - 633414122 q^{95} - 431412576 q^{96} - 402046736 q^{97} - 2192087384 q^{98} - 1966368188 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{28}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.14353 0.466864i −0.258971 0.0291790i −0.0184754 0.999829i \(-0.505881\pi\)
−0.240495 + 0.970650i \(0.577310\pi\)
\(3\) −78.5126 49.3327i −0.969291 0.609046i −0.0483843 0.998829i \(-0.515407\pi\)
−0.920907 + 0.389783i \(0.872550\pi\)
\(4\) −232.631 53.0964i −0.908714 0.207408i
\(5\) 799.859 637.866i 1.27977 1.02059i 0.281640 0.959520i \(-0.409122\pi\)
0.998134 0.0610657i \(-0.0194499\pi\)
\(6\) 302.287 + 241.066i 0.233246 + 0.186008i
\(7\) −699.825 3066.14i −0.291472 1.27702i −0.882477 0.470356i \(-0.844126\pi\)
0.591004 0.806668i \(-0.298732\pi\)
\(8\) 1946.68 + 681.171i 0.475263 + 0.166302i
\(9\) 883.797 + 1835.22i 0.134705 + 0.279717i
\(10\) −3612.03 + 2269.59i −0.361203 + 0.226959i
\(11\) −19572.3 + 6848.64i −1.33681 + 0.467771i −0.901606 0.432559i \(-0.857611\pi\)
−0.435208 + 0.900330i \(0.643325\pi\)
\(12\) 15645.0 + 15645.0i 0.754487 + 0.754487i
\(13\) −8119.18 + 16859.6i −0.284275 + 0.590303i −0.993390 0.114790i \(-0.963380\pi\)
0.709115 + 0.705093i \(0.249095\pi\)
\(14\) 1468.28 + 13031.3i 0.0382205 + 0.339217i
\(15\) −94266.7 + 10621.3i −1.86206 + 0.209803i
\(16\) 47287.6 + 22772.5i 0.721551 + 0.347481i
\(17\) 70809.4 70809.4i 0.847803 0.847803i −0.142056 0.989859i \(-0.545371\pi\)
0.989859 + 0.142056i \(0.0453712\pi\)
\(18\) −2805.24 8016.91i −0.0267227 0.0763690i
\(19\) 6619.42 + 10534.7i 0.0507932 + 0.0808369i 0.871156 0.491007i \(-0.163371\pi\)
−0.820362 + 0.571844i \(0.806228\pi\)
\(20\) −219940. + 105918.i −1.37463 + 0.661985i
\(21\) −96315.7 + 275255.i −0.495245 + 1.41533i
\(22\) 84295.7 19239.9i 0.359844 0.0821321i
\(23\) −287254. + 360206.i −1.02649 + 1.28718i −0.0693395 + 0.997593i \(0.522089\pi\)
−0.957152 + 0.289586i \(0.906482\pi\)
\(24\) −119235. 149515.i −0.359383 0.450652i
\(25\) 145979. 639574.i 0.373705 1.63731i
\(26\) 41513.2 66067.9i 0.0908433 0.144576i
\(27\) −46968.4 + 416856.i −0.0883793 + 0.784388i
\(28\) 750435.i 1.22090i
\(29\) 90635.6 701450.i 0.128147 0.991755i
\(30\) 395555. 0.488340
\(31\) 1.11599e6 + 125742.i 1.20841 + 0.136155i 0.693093 0.720848i \(-0.256247\pi\)
0.515312 + 0.857002i \(0.327676\pi\)
\(32\) −632357. 397336.i −0.603063 0.378929i
\(33\) 1.87453e6 + 427850.i 1.58066 + 0.360774i
\(34\) −326459. + 260342.i −0.244294 + 0.194818i
\(35\) −2.51555e6 2.00608e6i −1.67633 1.33683i
\(36\) −108154. 473856.i −0.0643924 0.282121i
\(37\) −344069. 120395.i −0.183586 0.0642394i 0.236921 0.971529i \(-0.423862\pi\)
−0.420506 + 0.907290i \(0.638148\pi\)
\(38\) −22509.5 46741.4i −0.0107952 0.0224165i
\(39\) 1.46919e6 923153.i 0.635067 0.399039i
\(40\) 1.99156e6 696878.i 0.777954 0.272218i
\(41\) −2.01020e6 2.01020e6i −0.711384 0.711384i 0.255440 0.966825i \(-0.417780\pi\)
−0.966825 + 0.255440i \(0.917780\pi\)
\(42\) 527593. 1.09556e6i 0.169552 0.352078i
\(43\) 170357. + 1.51196e6i 0.0498295 + 0.442249i 0.993712 + 0.111967i \(0.0357152\pi\)
−0.943882 + 0.330282i \(0.892856\pi\)
\(44\) 4.91675e6 553985.i 1.31180 0.147804i
\(45\) 1.87754e6 + 904175.i 0.457867 + 0.220497i
\(46\) 1.35841e6 1.35841e6i 0.303390 0.303390i
\(47\) 2.04131e6 + 5.83373e6i 0.418328 + 1.19551i 0.939645 + 0.342151i \(0.111155\pi\)
−0.521317 + 0.853363i \(0.674559\pi\)
\(48\) −2.58924e6 4.12075e6i −0.487761 0.776268i
\(49\) −3.71753e6 + 1.79027e6i −0.644866 + 0.310551i
\(50\) −903461. + 2.58194e6i −0.144554 + 0.413111i
\(51\) −9.05264e6 + 2.06621e6i −1.33812 + 0.305417i
\(52\) 2.78396e6 3.49097e6i 0.380758 0.477455i
\(53\) −16351.4 20504.0i −0.00207229 0.00259857i 0.780794 0.624788i \(-0.214815\pi\)
−0.782867 + 0.622190i \(0.786243\pi\)
\(54\) 389230. 1.70533e6i 0.0457753 0.200555i
\(55\) −1.12865e7 + 1.79624e7i −1.23342 + 1.96297i
\(56\) 726231. 6.44547e6i 0.0738452 0.655394i
\(57\) 1.15366e6i 0.109290i
\(58\) −703032. + 2.86416e6i −0.0621246 + 0.253096i
\(59\) −8.35555e6 −0.689552 −0.344776 0.938685i \(-0.612045\pi\)
−0.344776 + 0.938685i \(0.612045\pi\)
\(60\) 2.24933e7 + 2.53438e6i 1.73559 + 0.195554i
\(61\) 2.97860e6 + 1.87158e6i 0.215126 + 0.135173i 0.635285 0.772278i \(-0.280883\pi\)
−0.420159 + 0.907451i \(0.638026\pi\)
\(62\) −4.56542e6 1.04203e6i −0.308969 0.0705201i
\(63\) 5.00854e6 3.99418e6i 0.317943 0.253551i
\(64\) −8.07018e6 6.43575e6i −0.481020 0.383601i
\(65\) 4.26000e6 + 1.86643e7i 0.238647 + 1.04558i
\(66\) −7.56743e6 2.64796e6i −0.398816 0.139552i
\(67\) −1.59797e7 3.31822e7i −0.792994 1.64667i −0.762372 0.647139i \(-0.775965\pi\)
−0.0306222 0.999531i \(-0.509749\pi\)
\(68\) −2.02322e7 + 1.27127e7i −0.946251 + 0.594569i
\(69\) 4.03230e7 1.41096e7i 1.77892 0.622471i
\(70\) 9.48667e6 + 9.48667e6i 0.395113 + 0.395113i
\(71\) −5.10483e6 + 1.06003e7i −0.200885 + 0.417142i −0.976937 0.213526i \(-0.931505\pi\)
0.776052 + 0.630669i \(0.217219\pi\)
\(72\) 470365. + 4.17460e6i 0.0175027 + 0.155341i
\(73\) −4.15322e7 + 4.67956e6i −1.46249 + 0.164783i −0.807060 0.590470i \(-0.798942\pi\)
−0.655433 + 0.755253i \(0.727514\pi\)
\(74\) 1.36945e6 + 659493.i 0.0456688 + 0.0219930i
\(75\) −4.30131e7 + 4.30131e7i −1.35943 + 1.35943i
\(76\) −980523. 2.80217e6i −0.0293903 0.0839925i
\(77\) 3.46960e7 + 5.52184e7i 0.986999 + 1.57080i
\(78\) −6.51861e6 + 3.13920e6i −0.176107 + 0.0848087i
\(79\) 2.28372e6 6.52651e6i 0.0586320 0.167561i −0.910842 0.412756i \(-0.864566\pi\)
0.969474 + 0.245195i \(0.0788520\pi\)
\(80\) 5.23492e7 1.19484e7i 1.27806 0.291708i
\(81\) 3.25848e7 4.08601e7i 0.756964 0.949202i
\(82\) 7.39084e6 + 9.26782e6i 0.163470 + 0.204985i
\(83\) 1.26046e7 5.52242e7i 0.265592 1.16364i −0.649491 0.760369i \(-0.725018\pi\)
0.915083 0.403266i \(-0.132125\pi\)
\(84\) 3.70210e7 5.89186e7i 0.743586 1.18341i
\(85\) 1.14706e7 1.01804e8i 0.219741 1.95025i
\(86\) 6.34439e6i 0.115983i
\(87\) −4.17205e7 + 5.06013e7i −0.728236 + 0.883252i
\(88\) −4.27660e7 −0.713129
\(89\) 1.65890e7 + 1.86913e6i 0.264399 + 0.0297906i 0.243169 0.969984i \(-0.421813\pi\)
0.0212301 + 0.999775i \(0.493242\pi\)
\(90\) −7.35751e6 4.62303e6i −0.112140 0.0704623i
\(91\) 5.73760e7 + 1.30957e7i 0.836690 + 0.190969i
\(92\) 8.59498e7 6.85427e7i 1.19976 0.956775i
\(93\) −8.14159e7 6.49270e7i −1.08837 0.867948i
\(94\) −5.73467e6 2.51252e7i −0.0734509 0.321809i
\(95\) 1.20144e7 + 4.20401e6i 0.147505 + 0.0516142i
\(96\) 3.00463e7 + 6.23918e7i 0.353758 + 0.734586i
\(97\) −2.72399e7 + 1.71159e7i −0.307693 + 0.193336i −0.677023 0.735962i \(-0.736730\pi\)
0.369330 + 0.929298i \(0.379587\pi\)
\(98\) 1.62395e7 5.68244e6i 0.176063 0.0616071i
\(99\) −2.98667e7 2.98667e7i −0.310918 0.310918i
\(100\) −6.79182e7 + 1.41034e8i −0.679182 + 1.41034i
\(101\) 3.55009e6 + 3.15080e7i 0.0341157 + 0.302785i 0.999170 + 0.0407352i \(0.0129700\pi\)
−0.965054 + 0.262050i \(0.915601\pi\)
\(102\) 3.84745e7 4.33504e6i 0.355445 0.0400490i
\(103\) −6.11306e7 2.94389e7i −0.543137 0.261561i 0.142136 0.989847i \(-0.454603\pi\)
−0.685273 + 0.728286i \(0.740317\pi\)
\(104\) −2.72897e7 + 2.72897e7i −0.233274 + 0.233274i
\(105\) 9.85366e7 + 2.81601e8i 0.810663 + 2.31674i
\(106\) 58179.9 + 92592.7i 0.000460839 + 0.000733421i
\(107\) −9.26056e7 + 4.45965e7i −0.706484 + 0.340225i −0.752387 0.658721i \(-0.771098\pi\)
0.0459032 + 0.998946i \(0.485383\pi\)
\(108\) 3.30598e7 9.44796e7i 0.243000 0.694453i
\(109\) −1.98020e8 + 4.51967e7i −1.40282 + 0.320185i −0.855961 0.517040i \(-0.827034\pi\)
−0.546859 + 0.837225i \(0.684177\pi\)
\(110\) 5.51521e7 6.91586e7i 0.376696 0.472362i
\(111\) 2.10743e7 + 2.64264e7i 0.138823 + 0.174079i
\(112\) 3.67305e7 1.60927e8i 0.233429 1.02272i
\(113\) 1.15556e8 1.83907e8i 0.708728 1.12793i −0.277208 0.960810i \(-0.589409\pi\)
0.985936 0.167124i \(-0.0534481\pi\)
\(114\) −538604. + 4.78024e6i −0.00318897 + 0.0283029i
\(115\) 4.71343e8i 2.69492i
\(116\) −5.83291e7 + 1.58366e8i −0.322146 + 0.874643i
\(117\) −3.81169e7 −0.203411
\(118\) 3.46215e7 + 3.90090e6i 0.178574 + 0.0201204i
\(119\) −2.66665e8 1.67557e8i −1.32978 0.835554i
\(120\) −1.90742e8 4.35355e7i −0.919857 0.209951i
\(121\) 1.68578e8 1.34436e8i 0.786428 0.627155i
\(122\) −1.14681e7 9.14554e6i −0.0517671 0.0412829i
\(123\) 5.86574e7 + 2.56995e8i 0.256273 + 1.12280i
\(124\) −2.52937e8 8.85064e7i −1.06986 0.374358i
\(125\) −1.17807e8 2.44628e8i −0.482536 1.00200i
\(126\) −2.26178e7 + 1.42117e7i −0.0897361 + 0.0563849i
\(127\) 2.71439e8 9.49806e7i 1.04342 0.365107i 0.246465 0.969152i \(-0.420731\pi\)
0.796950 + 0.604045i \(0.206445\pi\)
\(128\) 1.65625e8 + 1.65625e8i 0.617000 + 0.617000i
\(129\) 6.12140e7 1.27112e8i 0.221051 0.459016i
\(130\) −8.93776e6 7.93248e7i −0.0312936 0.277738i
\(131\) 3.03402e8 3.41852e7i 1.03023 0.116079i 0.419367 0.907817i \(-0.362252\pi\)
0.610861 + 0.791738i \(0.290823\pi\)
\(132\) −4.13356e8 1.99062e8i −1.36154 0.655681i
\(133\) 2.76685e7 2.76685e7i 0.0884259 0.0884259i
\(134\) 5.07209e7 + 1.44952e8i 0.157314 + 0.449578i
\(135\) 2.28330e8 + 3.63385e8i 0.687430 + 1.09404i
\(136\) 1.86076e8 8.96096e7i 0.543920 0.261938i
\(137\) −1.17561e8 + 3.35970e8i −0.333719 + 0.953714i 0.647710 + 0.761887i \(0.275727\pi\)
−0.981429 + 0.191827i \(0.938559\pi\)
\(138\) −1.73667e8 + 3.96383e7i −0.478851 + 0.109295i
\(139\) −9.18930e7 + 1.15230e8i −0.246163 + 0.308679i −0.889528 0.456881i \(-0.848966\pi\)
0.643365 + 0.765560i \(0.277538\pi\)
\(140\) 4.78677e8 + 6.00242e8i 1.24604 + 1.56248i
\(141\) 1.27525e8 5.58724e8i 0.322641 1.41358i
\(142\) 2.61009e7 4.15393e7i 0.0641951 0.102166i
\(143\) 4.34452e7 3.85587e8i 0.103896 0.922100i
\(144\) 1.06909e8i 0.248637i
\(145\) −3.74935e8 6.18874e8i −0.848173 1.40001i
\(146\) 1.74275e8 0.383551
\(147\) 3.80191e8 + 4.28373e7i 0.814203 + 0.0917387i
\(148\) 7.36485e7 + 4.62764e7i 0.153503 + 0.0964523i
\(149\) −8.01612e8 1.82963e8i −1.62637 0.371208i −0.690438 0.723391i \(-0.742582\pi\)
−0.935931 + 0.352183i \(0.885439\pi\)
\(150\) 1.98307e8 1.58145e8i 0.391718 0.312385i
\(151\) −1.91488e8 1.52707e8i −0.368327 0.293731i 0.421782 0.906697i \(-0.361405\pi\)
−0.790109 + 0.612966i \(0.789976\pi\)
\(152\) 5.70990e6 + 2.50167e7i 0.0106968 + 0.0468658i
\(153\) 1.92532e8 + 6.73699e7i 0.351348 + 0.122942i
\(154\) −1.17985e8 2.44997e8i −0.209769 0.435591i
\(155\) 9.72839e8 6.11275e8i 1.68544 1.05903i
\(156\) −3.90795e8 + 1.36745e8i −0.659858 + 0.230894i
\(157\) −3.77882e8 3.77882e8i −0.621954 0.621954i 0.324077 0.946031i \(-0.394946\pi\)
−0.946031 + 0.324077i \(0.894946\pi\)
\(158\) −1.25097e7 + 2.59766e7i −0.0200732 + 0.0416825i
\(159\) 272272. + 2.41648e6i 0.000426005 + 0.00378090i
\(160\) −7.59244e8 + 8.55462e7i −1.15851 + 0.130533i
\(161\) 1.30547e9 + 6.28680e8i 1.94295 + 0.935677i
\(162\) −1.54092e8 + 1.54092e8i −0.223728 + 0.223728i
\(163\) −2.11938e8 6.05685e8i −0.300234 0.858019i −0.990871 0.134817i \(-0.956955\pi\)
0.690637 0.723202i \(-0.257330\pi\)
\(164\) 3.60900e8 + 5.74369e8i 0.498898 + 0.793991i
\(165\) 1.77227e9 8.53481e8i 2.39108 1.15148i
\(166\) −7.80095e7 + 2.22938e8i −0.102734 + 0.293597i
\(167\) −1.18649e9 + 2.70808e8i −1.52545 + 0.348174i −0.901322 0.433150i \(-0.857402\pi\)
−0.624126 + 0.781324i \(0.714545\pi\)
\(168\) −3.74991e8 + 4.70224e8i −0.470743 + 0.590293i
\(169\) 2.90273e8 + 3.63991e8i 0.355844 + 0.446215i
\(170\) −9.50575e7 + 4.16474e8i −0.113813 + 0.498646i
\(171\) −1.34834e7 + 2.14587e7i −0.0157694 + 0.0250968i
\(172\) 4.06495e7 3.60774e8i 0.0464452 0.412213i
\(173\) 8.46276e8i 0.944773i 0.881391 + 0.472387i \(0.156607\pi\)
−0.881391 + 0.472387i \(0.843393\pi\)
\(174\) 1.96494e8 1.90190e8i 0.214364 0.207487i
\(175\) −2.06318e9 −2.19981
\(176\) −1.08149e9 1.21854e8i −1.12712 0.126996i
\(177\) 6.56016e8 + 4.12202e8i 0.668377 + 0.419969i
\(178\) −6.78642e7 1.54896e7i −0.0676022 0.0154298i
\(179\) 4.24338e7 3.38399e7i 0.0413333 0.0329622i −0.602605 0.798039i \(-0.705871\pi\)
0.643939 + 0.765077i \(0.277299\pi\)
\(180\) −3.88765e8 3.10029e8i −0.370337 0.295334i
\(181\) 4.05489e8 + 1.77656e9i 0.377803 + 1.65526i 0.704180 + 0.710022i \(0.251315\pi\)
−0.326377 + 0.945240i \(0.605828\pi\)
\(182\) −2.31625e8 8.10491e7i −0.211106 0.0738691i
\(183\) −1.41528e8 2.93885e8i −0.126193 0.262043i
\(184\) −8.04553e8 + 5.05534e8i −0.701913 + 0.441041i
\(185\) −3.52003e8 + 1.23171e8i −0.300510 + 0.105153i
\(186\) 3.07037e8 + 3.07037e8i 0.256531 + 0.256531i
\(187\) −9.00953e8 + 1.87085e9i −0.736776 + 1.52993i
\(188\) −1.65121e8 1.46549e9i −0.132182 1.17314i
\(189\) 1.31101e9 1.47715e8i 1.02744 0.115765i
\(190\) −4.78192e7 2.30285e7i −0.0366934 0.0176706i
\(191\) 1.30908e9 1.30908e9i 0.983629 0.983629i −0.0162391 0.999868i \(-0.505169\pi\)
0.999868 + 0.0162391i \(0.00516928\pi\)
\(192\) 3.16117e8 + 9.03411e8i 0.232618 + 0.664784i
\(193\) −4.78446e8 7.61443e8i −0.344829 0.548792i 0.628615 0.777716i \(-0.283622\pi\)
−0.973444 + 0.228924i \(0.926479\pi\)
\(194\) 1.20860e8 5.82031e7i 0.0853248 0.0410903i
\(195\) 5.86296e8 1.67554e9i 0.405489 1.15882i
\(196\) 9.59867e8 2.19083e8i 0.650410 0.148452i
\(197\) 4.00617e8 5.02358e8i 0.265990 0.333541i −0.630843 0.775911i \(-0.717291\pi\)
0.896833 + 0.442370i \(0.145862\pi\)
\(198\) 1.09810e8 + 1.37697e8i 0.0714464 + 0.0895910i
\(199\) −4.50489e7 + 1.97372e8i −0.0287258 + 0.125856i −0.987258 0.159129i \(-0.949131\pi\)
0.958532 + 0.284985i \(0.0919886\pi\)
\(200\) 7.19833e8 1.14561e9i 0.449896 0.716005i
\(201\) −3.82361e8 + 3.39355e9i −0.234255 + 2.07907i
\(202\) 1.32212e8i 0.0794079i
\(203\) −2.21417e9 + 2.12991e8i −1.30385 + 0.125423i
\(204\) 2.21563e9 1.27931
\(205\) −2.89012e9 3.25638e8i −1.63644 0.184382i
\(206\) 2.39552e8 + 1.50521e8i 0.133024 + 0.0835848i
\(207\) −9.14932e8 2.08827e8i −0.498319 0.113738i
\(208\) −7.67872e8 + 6.12358e8i −0.410238 + 0.327154i
\(209\) −2.01706e8 1.60855e8i −0.105714 0.0843043i
\(210\) −2.76820e8 1.21283e9i −0.142338 0.623622i
\(211\) −1.36011e9 4.75924e8i −0.686190 0.240108i −0.0354083 0.999373i \(-0.511273\pi\)
−0.650782 + 0.759265i \(0.725559\pi\)
\(212\) 2.71515e6 + 5.63806e6i 0.00134416 + 0.00279117i
\(213\) 9.23734e8 5.80421e8i 0.448775 0.281984i
\(214\) 4.04535e8 1.41553e8i 0.192886 0.0674937i
\(215\) 1.10069e9 + 1.10069e9i 0.515123 + 0.515123i
\(216\) −3.75383e8 + 7.79490e8i −0.172448 + 0.358093i
\(217\) −3.95456e8 3.50977e9i −0.178344 1.58285i
\(218\) 8.41600e8 9.48256e7i 0.372632 0.0419855i
\(219\) 3.49166e9 + 1.68149e9i 1.51794 + 0.731002i
\(220\) 3.57934e9 3.57934e9i 1.52796 1.52796i
\(221\) 6.18907e8 + 1.76873e9i 0.259451 + 0.741470i
\(222\) −7.49846e7 1.19337e8i −0.0308717 0.0491320i
\(223\) −3.34349e9 + 1.61014e9i −1.35201 + 0.651094i −0.962840 0.270072i \(-0.912952\pi\)
−0.389170 + 0.921166i \(0.627238\pi\)
\(224\) −7.75747e8 + 2.21696e9i −0.308126 + 0.880573i
\(225\) 1.30278e9 2.97350e8i 0.508323 0.116021i
\(226\) −5.64670e8 + 7.08074e8i −0.216452 + 0.271422i
\(227\) −3.91175e8 4.90518e8i −0.147322 0.184736i 0.702695 0.711491i \(-0.251980\pi\)
−0.850017 + 0.526755i \(0.823408\pi\)
\(228\) −6.12555e7 + 2.68378e8i −0.0226676 + 0.0993132i
\(229\) −1.85023e7 + 2.94463e7i −0.00672798 + 0.0107075i −0.850071 0.526668i \(-0.823441\pi\)
0.843343 + 0.537375i \(0.180584\pi\)
\(230\) 2.20053e8 1.95302e9i 0.0786350 0.697905i
\(231\) 6.04699e9i 2.12369i
\(232\) 6.54246e8 1.30376e9i 0.225834 0.450033i
\(233\) 1.78980e9 0.607268 0.303634 0.952789i \(-0.401800\pi\)
0.303634 + 0.952789i \(0.401800\pi\)
\(234\) 1.57938e8 + 1.77954e7i 0.0526774 + 0.00593532i
\(235\) 5.35390e9 + 3.36408e9i 1.75549 + 1.10305i
\(236\) 1.94376e9 + 4.43650e8i 0.626606 + 0.143019i
\(237\) −5.01271e8 + 3.99751e8i −0.158884 + 0.126706i
\(238\) 1.02671e9 + 8.18773e8i 0.319992 + 0.255185i
\(239\) −1.13771e9 4.98464e9i −0.348691 1.52771i −0.780156 0.625585i \(-0.784861\pi\)
0.431466 0.902129i \(-0.357997\pi\)
\(240\) −4.69951e9 1.64443e9i −1.41647 0.495645i
\(241\) 1.52921e7 + 3.17543e7i 0.00453313 + 0.00941314i 0.903223 0.429171i \(-0.141194\pi\)
−0.898690 + 0.438584i \(0.855480\pi\)
\(242\) −7.61270e8 + 4.78338e8i −0.221961 + 0.139468i
\(243\) −1.97621e9 + 6.91505e8i −0.566771 + 0.198322i
\(244\) −5.93540e8 5.93540e8i −0.167452 0.167452i
\(245\) −1.83155e9 + 3.80324e9i −0.508339 + 1.05558i
\(246\) −1.23067e8 1.09225e9i −0.0336048 0.298251i
\(247\) −2.31356e8 + 2.60676e7i −0.0621575 + 0.00700347i
\(248\) 2.08682e9 + 1.00496e9i 0.551667 + 0.265669i
\(249\) −3.71397e9 + 3.71397e9i −0.966143 + 0.966143i
\(250\) 3.73927e8 + 1.06862e9i 0.0957254 + 0.273567i
\(251\) 5.87649e8 + 9.35239e8i 0.148055 + 0.235628i 0.912515 0.409043i \(-0.134137\pi\)
−0.764460 + 0.644671i \(0.776994\pi\)
\(252\) −1.37722e9 + 6.63232e8i −0.341507 + 0.164461i
\(253\) 3.15531e9 9.01735e9i 0.770122 2.20088i
\(254\) −1.16906e9 + 2.66830e8i −0.280867 + 0.0641061i
\(255\) −5.92287e9 + 7.42705e9i −1.40079 + 1.75653i
\(256\) 1.03861e9 + 1.30237e9i 0.241819 + 0.303232i
\(257\) 2.85080e6 1.24902e7i 0.000653484 0.00286310i −0.974600 0.223952i \(-0.928104\pi\)
0.975254 + 0.221089i \(0.0709612\pi\)
\(258\) −3.12986e8 + 4.98114e8i −0.0706392 + 0.112422i
\(259\) −1.28359e8 + 1.13922e9i −0.0285251 + 0.253167i
\(260\) 4.56807e9i 0.999631i
\(261\) 1.36742e9 4.53602e8i 0.294673 0.0977492i
\(262\) −1.27312e9 −0.270186
\(263\) −3.14147e9 3.53958e8i −0.656613 0.0739825i −0.222629 0.974903i \(-0.571464\pi\)
−0.433984 + 0.900921i \(0.642892\pi\)
\(264\) 3.35767e9 + 2.10976e9i 0.691229 + 0.434328i
\(265\) −2.61576e7 5.97030e6i −0.00530413 0.00121063i
\(266\) −1.27563e8 + 1.01728e8i −0.0254799 + 0.0203195i
\(267\) −1.21023e9 9.65129e8i −0.238135 0.189907i
\(268\) 1.95552e9 + 8.56767e9i 0.379072 + 1.66082i
\(269\) 5.57479e9 + 1.95070e9i 1.06468 + 0.372548i 0.805079 0.593167i \(-0.202123\pi\)
0.259602 + 0.965716i \(0.416408\pi\)
\(270\) −7.76441e8 1.61230e9i −0.146101 0.303382i
\(271\) −2.43190e9 + 1.52806e9i −0.450887 + 0.283311i −0.738271 0.674504i \(-0.764357\pi\)
0.287384 + 0.957816i \(0.407215\pi\)
\(272\) 4.96091e9 1.73590e9i 0.906328 0.317138i
\(273\) −3.85869e9 3.85869e9i −0.694687 0.694687i
\(274\) 6.43969e8 1.33722e9i 0.114252 0.237246i
\(275\) 1.52308e9 + 1.35177e10i 0.266312 + 2.36359i
\(276\) −1.01295e10 + 1.14133e9i −1.74563 + 0.196686i
\(277\) 4.96229e8 + 2.38971e8i 0.0842875 + 0.0405907i 0.475553 0.879687i \(-0.342248\pi\)
−0.391265 + 0.920278i \(0.627962\pi\)
\(278\) 4.34558e8 4.34558e8i 0.0727559 0.0727559i
\(279\) 7.55543e8 + 2.15922e9i 0.124693 + 0.356352i
\(280\) −3.53047e9 5.61871e9i −0.574381 0.914122i
\(281\) 4.37614e9 2.10744e9i 0.701885 0.338010i −0.0486727 0.998815i \(-0.515499\pi\)
0.750558 + 0.660805i \(0.229785\pi\)
\(282\) −7.89252e8 + 2.25555e9i −0.124801 + 0.356662i
\(283\) −3.86877e9 + 8.83021e8i −0.603152 + 0.137666i −0.513183 0.858279i \(-0.671534\pi\)
−0.0899690 + 0.995945i \(0.528677\pi\)
\(284\) 1.75038e9 2.19490e9i 0.269066 0.337398i
\(285\) −7.35883e8 9.22769e8i −0.111540 0.139866i
\(286\) −3.60033e8 + 1.57741e9i −0.0538119 + 0.235765i
\(287\) −4.75676e9 + 7.57034e9i −0.701106 + 1.11580i
\(288\) 1.70325e8 1.51168e9i 0.0247577 0.219730i
\(289\) 3.05217e9i 0.437540i
\(290\) 1.26463e9 + 2.73937e9i 0.178801 + 0.387309i
\(291\) 2.98305e9 0.415995
\(292\) 9.91014e9 + 1.11660e9i 1.36316 + 0.153592i
\(293\) −7.17481e9 4.50823e9i −0.973509 0.611696i −0.0514214 0.998677i \(-0.516375\pi\)
−0.922088 + 0.386981i \(0.873518\pi\)
\(294\) −1.55533e9 3.54995e8i −0.208178 0.0475152i
\(295\) −6.68326e9 + 5.32973e9i −0.882471 + 0.703747i
\(296\) −5.87781e8 4.68740e8i −0.0765683 0.0610612i
\(297\) −1.93562e9 8.48049e9i −0.248767 1.08992i
\(298\) 3.23608e9 + 1.13235e9i 0.410350 + 0.143588i
\(299\) −3.74067e9 7.76758e9i −0.468020 0.971854i
\(300\) 1.22900e10 7.72233e9i 1.51729 0.953374i
\(301\) 4.51666e9 1.58045e9i 0.550239 0.192537i
\(302\) 7.22143e8 + 7.22143e8i 0.0868152 + 0.0868152i
\(303\) 1.27565e9 2.64891e9i 0.151342 0.314265i
\(304\) 7.31139e7 + 6.48904e8i 0.00856062 + 0.0759776i
\(305\) 3.57628e9 4.02950e8i 0.413268 0.0465641i
\(306\) −7.66309e8 3.69035e8i −0.0874014 0.0420903i
\(307\) 9.93677e9 9.93677e9i 1.11864 1.11864i 0.126703 0.991941i \(-0.459560\pi\)
0.991941 0.126703i \(-0.0404395\pi\)
\(308\) −5.13946e9 1.46877e10i −0.571103 1.63212i
\(309\) 3.34722e9 + 5.32707e9i 0.367155 + 0.584325i
\(310\) −4.31637e9 + 2.07865e9i −0.467382 + 0.225079i
\(311\) 2.66262e9 7.60933e9i 0.284621 0.813401i −0.709458 0.704747i \(-0.751060\pi\)
0.994080 0.108654i \(-0.0346540\pi\)
\(312\) 3.48886e9 7.96310e8i 0.368184 0.0840357i
\(313\) 5.19973e9 6.52025e9i 0.541756 0.679340i −0.433313 0.901243i \(-0.642656\pi\)
0.975069 + 0.221903i \(0.0712270\pi\)
\(314\) 1.38935e9 + 1.74219e9i 0.142920 + 0.179216i
\(315\) 1.45837e9 6.38955e9i 0.148124 0.648975i
\(316\) −8.77798e8 + 1.39701e9i −0.0880332 + 0.140104i
\(317\) −6.99798e8 + 6.21088e9i −0.0693004 + 0.615058i 0.910278 + 0.413997i \(0.135868\pi\)
−0.979579 + 0.201061i \(0.935561\pi\)
\(318\) 1.01399e7i 0.000991571i
\(319\) 3.03003e9 + 1.43497e10i 0.292607 + 1.38573i
\(320\) −1.05601e10 −1.00709
\(321\) 9.47078e9 + 1.06710e9i 0.892001 + 0.100504i
\(322\) −5.11573e9 3.21443e9i −0.475866 0.299006i
\(323\) 1.21468e9 + 2.77242e8i 0.111596 + 0.0254712i
\(324\) −9.74975e9 + 7.77516e9i −0.884735 + 0.705553i
\(325\) 9.59777e9 + 7.65396e9i 0.860274 + 0.686046i
\(326\) 5.95401e8 + 2.60862e9i 0.0527156 + 0.230962i
\(327\) 1.77767e10 + 6.22034e9i 1.55475 + 0.544030i
\(328\) −2.54392e9 5.28250e9i −0.219790 0.456399i
\(329\) 1.64584e10 1.03415e10i 1.40477 0.882675i
\(330\) −7.74192e9 + 2.70901e9i −0.652819 + 0.228431i
\(331\) 2.52074e9 + 2.52074e9i 0.209998 + 0.209998i 0.804267 0.594268i \(-0.202558\pi\)
−0.594268 + 0.804267i \(0.702558\pi\)
\(332\) −5.86441e9 + 1.21776e10i −0.482694 + 1.00233i
\(333\) −8.31355e7 7.37848e8i −0.00676098 0.0600054i
\(334\) 5.04268e9 5.68173e8i 0.405205 0.0456557i
\(335\) −3.39474e10 1.63482e10i −2.69542 1.29805i
\(336\) −1.08228e10 + 1.08228e10i −0.849144 + 0.849144i
\(337\) 3.86976e8 + 1.10591e9i 0.0300030 + 0.0857435i 0.957911 0.287066i \(-0.0926800\pi\)
−0.927908 + 0.372810i \(0.878394\pi\)
\(338\) −1.03282e9 1.64373e9i −0.0791331 0.125940i
\(339\) −1.81452e10 + 8.73829e9i −1.37393 + 0.661649i
\(340\) −8.07386e9 + 2.30738e10i −0.604179 + 1.72664i
\(341\) −2.27036e10 + 5.18195e9i −1.67910 + 0.383244i
\(342\) 6.58871e7 8.26198e7i 0.00481610 0.00603920i
\(343\) −3.21319e9 4.02921e9i −0.232145 0.291101i
\(344\) −6.98275e8 + 3.05934e9i −0.0498646 + 0.218471i
\(345\) 2.32527e10 3.70064e10i 1.64133 2.61216i
\(346\) 3.95095e8 3.50657e9i 0.0275675 0.244668i
\(347\) 1.00713e10i 0.694651i 0.937745 + 0.347325i \(0.112910\pi\)
−0.937745 + 0.347325i \(0.887090\pi\)
\(348\) 1.23922e10 9.55621e9i 0.844951 0.651582i
\(349\) 4.72271e9 0.318339 0.159169 0.987251i \(-0.449118\pi\)
0.159169 + 0.987251i \(0.449118\pi\)
\(350\) 8.54885e9 + 9.63224e8i 0.569686 + 0.0641882i
\(351\) −6.64670e9 4.17640e9i −0.437902 0.275152i
\(352\) 1.50979e10 + 3.44599e9i 0.983434 + 0.224462i
\(353\) 1.48053e10 1.18068e10i 0.953493 0.760385i −0.0174126 0.999848i \(-0.505543\pi\)
0.970905 + 0.239463i \(0.0769715\pi\)
\(354\) −2.52578e9 2.01424e9i −0.160836 0.128262i
\(355\) 2.67842e9 + 1.17349e10i 0.168642 + 0.738868i
\(356\) −3.75986e9 1.31563e9i −0.234084 0.0819095i
\(357\) 1.26705e10 + 2.63107e10i 0.780050 + 1.61979i
\(358\) −1.91624e8 + 1.20406e8i −0.0116659 + 0.00733018i
\(359\) 2.02816e10 7.09682e9i 1.22102 0.427254i 0.358622 0.933483i \(-0.383247\pi\)
0.862399 + 0.506229i \(0.168961\pi\)
\(360\) 3.03906e9 + 3.03906e9i 0.180938 + 0.180938i
\(361\) 7.30173e9 1.51622e10i 0.429929 0.892757i
\(362\) −8.50743e8 7.55055e9i −0.0495409 0.439688i
\(363\) −1.98676e10 + 2.23854e9i −1.14424 + 0.128925i
\(364\) −1.26521e10 6.09292e9i −0.720703 0.347072i
\(365\) −3.02350e10 + 3.02350e10i −1.70348 + 1.70348i
\(366\) 4.49219e8 + 1.28379e9i 0.0250342 + 0.0715437i
\(367\) −1.35084e10 2.14986e10i −0.744630 1.18507i −0.977164 0.212484i \(-0.931845\pi\)
0.232534 0.972588i \(-0.425298\pi\)
\(368\) −2.17863e10 + 1.04917e10i −1.18794 + 0.572080i
\(369\) 1.91256e9 5.46578e9i 0.103160 0.294813i
\(370\) 1.51604e9 3.46025e8i 0.0808915 0.0184630i
\(371\) −5.14249e7 + 6.44848e7i −0.00271443 + 0.00340378i
\(372\) 1.54924e10 + 1.94269e10i 0.809000 + 1.01445i
\(373\) 4.00154e9 1.75319e10i 0.206724 0.905719i −0.760005 0.649917i \(-0.774803\pi\)
0.966729 0.255802i \(-0.0823394\pi\)
\(374\) 4.60656e9 7.33129e9i 0.235445 0.374709i
\(375\) −2.81886e9 + 2.50181e10i −0.142544 + 1.26511i
\(376\) 1.27469e10i 0.637752i
\(377\) 1.10903e10 + 7.22328e9i 0.549007 + 0.357576i
\(378\) −5.50115e9 −0.269455
\(379\) −3.52661e10 3.97353e9i −1.70923 0.192584i −0.797484 0.603340i \(-0.793836\pi\)
−0.911745 + 0.410756i \(0.865265\pi\)
\(380\) −2.57169e9 1.61590e9i −0.123334 0.0774962i
\(381\) −2.59970e10 5.93365e9i −1.23374 0.281593i
\(382\) −6.03535e9 + 4.81303e9i −0.283432 + 0.226030i
\(383\) −1.10907e10 8.84452e9i −0.515422 0.411035i 0.330933 0.943654i \(-0.392637\pi\)
−0.846355 + 0.532619i \(0.821208\pi\)
\(384\) −4.83290e9 2.11743e10i −0.222271 0.973834i
\(385\) 6.29739e10 + 2.20355e10i 2.86627 + 1.00295i
\(386\) 1.62697e9 + 3.37843e9i 0.0732874 + 0.152183i
\(387\) −2.62422e9 + 1.64891e9i −0.116992 + 0.0735111i
\(388\) 7.24562e9 2.53535e9i 0.319705 0.111869i
\(389\) 4.38009e9 + 4.38009e9i 0.191286 + 0.191286i 0.796252 0.604965i \(-0.206813\pi\)
−0.604965 + 0.796252i \(0.706813\pi\)
\(390\) −3.21158e9 + 6.66892e9i −0.138823 + 0.288268i
\(391\) 5.16563e9 + 4.58462e10i 0.221012 + 1.96154i
\(392\) −8.45630e9 + 9.52796e8i −0.358126 + 0.0403511i
\(393\) −2.55073e10 1.22837e10i −1.06929 0.514942i
\(394\) −1.89450e9 + 1.89450e9i −0.0786159 + 0.0786159i
\(395\) −2.33638e9 6.67699e9i −0.0959744 0.274279i
\(396\) 5.36209e9 + 8.53372e9i 0.218049 + 0.347023i
\(397\) 2.21405e10 1.06623e10i 0.891302 0.429228i 0.0685624 0.997647i \(-0.478159\pi\)
0.822740 + 0.568418i \(0.192444\pi\)
\(398\) 2.78807e8 7.96786e8i 0.0111115 0.0317548i
\(399\) −3.53729e9 + 8.07364e8i −0.139566 + 0.0318550i
\(400\) 2.14677e10 2.69196e10i 0.838581 1.05155i
\(401\) 2.69811e10 + 3.38332e10i 1.04347 + 1.30847i 0.949795 + 0.312872i \(0.101291\pi\)
0.0936787 + 0.995602i \(0.470137\pi\)
\(402\) 3.16865e9 1.38827e10i 0.121330 0.531583i
\(403\) −1.11809e10 + 1.77942e10i −0.423892 + 0.674620i
\(404\) 8.47099e8 7.51822e9i 0.0317987 0.282221i
\(405\) 5.34670e10i 1.98731i
\(406\) 9.27391e9 + 1.51179e8i 0.341318 + 0.00556402i
\(407\) 7.55876e9 0.275469
\(408\) −1.90300e10 2.14417e9i −0.686749 0.0773781i
\(409\) 4.18361e9 + 2.62873e9i 0.149506 + 0.0939406i 0.604707 0.796448i \(-0.293290\pi\)
−0.455202 + 0.890388i \(0.650433\pi\)
\(410\) 1.18233e10 + 2.69858e9i 0.418410 + 0.0954993i
\(411\) 2.58043e10 2.05783e10i 0.904326 0.721176i
\(412\) 1.26577e10 + 1.00942e10i 0.439306 + 0.350335i
\(413\) 5.84743e9 + 2.56193e10i 0.200986 + 0.880575i
\(414\) 3.69355e9 + 1.29243e9i 0.125731 + 0.0439952i
\(415\) −2.51438e10 5.22116e10i −0.847691 1.76025i
\(416\) 1.18332e10 7.43527e9i 0.395119 0.248270i
\(417\) 1.28994e10 4.51368e9i 0.426603 0.149275i
\(418\) 7.60677e8 + 7.60677e8i 0.0249170 + 0.0249170i
\(419\) 1.54557e10 3.20940e10i 0.501455 1.04128i −0.484581 0.874746i \(-0.661028\pi\)
0.986036 0.166535i \(-0.0532578\pi\)
\(420\) −7.97060e9 7.07410e10i −0.256150 2.27339i
\(421\) −2.94875e10 + 3.32244e9i −0.938662 + 0.105762i −0.568021 0.823014i \(-0.692291\pi\)
−0.370641 + 0.928776i \(0.620862\pi\)
\(422\) 5.41347e9 + 2.60699e9i 0.170697 + 0.0822033i
\(423\) −8.90209e9 + 8.90209e9i −0.278055 + 0.278055i
\(424\) −1.78641e7 5.10527e7i −0.000552737 0.00157963i
\(425\) −3.49512e10 5.56245e10i −1.07129 1.70495i
\(426\) −4.09850e9 + 1.97373e9i −0.124447 + 0.0599308i
\(427\) 3.65401e9 1.04426e10i 0.109915 0.314120i
\(428\) 2.39108e10 5.45749e9i 0.712557 0.162636i
\(429\) −2.24331e10 + 2.81302e10i −0.662307 + 0.830506i
\(430\) −4.04687e9 5.07461e9i −0.118371 0.148433i
\(431\) 4.79536e8 2.10098e9i 0.0138967 0.0608854i −0.967504 0.252855i \(-0.918630\pi\)
0.981401 + 0.191970i \(0.0614875\pi\)
\(432\) −1.17139e10 + 1.86425e10i −0.336330 + 0.535266i
\(433\) −2.31516e9 + 2.05476e10i −0.0658611 + 0.584533i 0.916829 + 0.399279i \(0.130740\pi\)
−0.982691 + 0.185254i \(0.940689\pi\)
\(434\) 1.47274e10i 0.415115i
\(435\) −1.09361e9 + 6.70860e10i −0.0305425 + 1.87359i
\(436\) 4.84652e10 1.34117
\(437\) −5.69613e9 6.41800e8i −0.156190 0.0175984i
\(438\) −1.36828e10 8.59744e9i −0.371772 0.233600i
\(439\) 5.93883e10 + 1.35550e10i 1.59898 + 0.364957i 0.926837 0.375464i \(-0.122517\pi\)
0.672143 + 0.740421i \(0.265374\pi\)
\(440\) −3.42068e10 + 2.72790e10i −0.912643 + 0.727809i
\(441\) −6.57107e9 5.24026e9i −0.173733 0.138547i
\(442\) −1.73870e9 7.61774e9i −0.0455550 0.199589i
\(443\) −5.34865e10 1.87157e10i −1.38877 0.485950i −0.470671 0.882309i \(-0.655988\pi\)
−0.918096 + 0.396359i \(0.870274\pi\)
\(444\) −3.49939e9 7.26656e9i −0.0900452 0.186981i
\(445\) 1.44611e10 9.08650e9i 0.368774 0.231716i
\(446\) 1.46055e10 5.11070e9i 0.369129 0.129164i
\(447\) 5.39106e10 + 5.39106e10i 1.35034 + 1.35034i
\(448\) −1.40852e10 + 2.92482e10i −0.349663 + 0.726083i
\(449\) −5.34598e8 4.74469e9i −0.0131535 0.116741i 0.985420 0.170141i \(-0.0544225\pi\)
−0.998573 + 0.0534008i \(0.982994\pi\)
\(450\) −5.53691e9 + 6.23860e8i −0.135026 + 0.0152138i
\(451\) 5.31114e10 + 2.55771e10i 1.28375 + 0.618223i
\(452\) −3.66467e10 + 3.66467e10i −0.877973 + 0.877973i
\(453\) 7.50079e9 + 2.14360e10i 0.178121 + 0.509040i
\(454\) 1.39184e9 + 2.21510e9i 0.0327617 + 0.0521399i
\(455\) 5.42460e10 2.61235e10i 1.26567 0.609516i
\(456\) 7.85843e8 2.24581e9i 0.0181751 0.0519414i
\(457\) −6.52381e10 + 1.48902e10i −1.49567 + 0.341377i −0.890598 0.454792i \(-0.849714\pi\)
−0.605074 + 0.796169i \(0.706857\pi\)
\(458\) 9.04123e7 1.13373e8i 0.00205478 0.00257662i
\(459\) 2.61915e10 + 3.28431e10i 0.590078 + 0.739935i
\(460\) 2.50267e10 1.09649e11i 0.558948 2.44891i
\(461\) −1.02631e10 + 1.63336e10i −0.227234 + 0.361641i −0.940809 0.338938i \(-0.889932\pi\)
0.713575 + 0.700579i \(0.247075\pi\)
\(462\) −2.82312e9 + 2.50559e10i −0.0619671 + 0.549973i
\(463\) 8.18514e10i 1.78116i −0.454829 0.890579i \(-0.650300\pi\)
0.454829 0.890579i \(-0.349700\pi\)
\(464\) 2.02597e10 3.11059e10i 0.437080 0.671074i
\(465\) −1.06536e11 −2.27869
\(466\) −7.41607e9 8.35591e8i −0.157264 0.0177194i
\(467\) −2.23452e10 1.40404e10i −0.469805 0.295198i 0.276246 0.961087i \(-0.410910\pi\)
−0.746051 + 0.665889i \(0.768052\pi\)
\(468\) 8.86716e9 + 2.02387e9i 0.184842 + 0.0421890i
\(469\) −9.05582e10 + 7.22178e10i −1.87170 + 1.49263i
\(470\) −2.06135e10 1.64387e10i −0.422435 0.336880i
\(471\) 1.10266e10 + 4.83105e10i 0.224056 + 0.981653i
\(472\) −1.62656e10 5.69157e9i −0.327719 0.114674i
\(473\) −1.36892e10 2.84258e10i −0.273484 0.567895i
\(474\) 2.26366e9 1.42235e9i 0.0448433 0.0281769i
\(475\) 7.70405e9 2.69576e9i 0.151337 0.0529551i
\(476\) 5.31379e10 + 5.31379e10i 1.03509 + 1.03509i
\(477\) 2.31781e7 4.81298e7i 0.000447718 0.000929695i
\(478\) 2.38699e9 + 2.11851e10i 0.0457235 + 0.405807i
\(479\) 5.55986e10 6.26445e9i 1.05614 0.118998i 0.433223 0.901287i \(-0.357376\pi\)
0.622917 + 0.782288i \(0.285948\pi\)
\(480\) 6.38304e10 + 3.07391e10i 1.20244 + 0.579064i
\(481\) 4.82337e9 4.82337e9i 0.0901095 0.0901095i
\(482\) −4.85382e7 1.38714e8i −0.000899281 0.00257000i
\(483\) −7.14811e10 1.13762e11i −1.31342 2.09029i
\(484\) −4.63545e10 + 2.23231e10i −0.844715 + 0.406793i
\(485\) −1.08704e10 + 3.10657e10i −0.196461 + 0.561454i
\(486\) 8.51131e9 1.94265e9i 0.152564 0.0348217i
\(487\) −5.85962e10 + 7.34774e10i −1.04173 + 1.30628i −0.0911357 + 0.995838i \(0.529050\pi\)
−0.950591 + 0.310446i \(0.899522\pi\)
\(488\) 4.52351e9 + 5.67230e9i 0.0797620 + 0.100018i
\(489\) −1.32403e10 + 5.80094e10i −0.231559 + 1.01453i
\(490\) 9.36466e9 1.49038e10i 0.162445 0.258530i
\(491\) −3.05871e9 + 2.71468e10i −0.0526274 + 0.467081i 0.939566 + 0.342369i \(0.111229\pi\)
−0.992193 + 0.124712i \(0.960199\pi\)
\(492\) 6.28994e10i 1.07346i
\(493\) −4.32513e10 5.60870e10i −0.732170 0.949456i
\(494\) 9.70802e8 0.0163013
\(495\) −4.29401e10 4.83819e9i −0.715224 0.0805864i
\(496\) 4.99089e10 + 3.13598e10i 0.824615 + 0.518140i
\(497\) 3.60744e10 + 8.23375e9i 0.591253 + 0.134950i
\(498\) 1.71229e10 1.36550e10i 0.278394 0.222012i
\(499\) −7.49531e10 5.97731e10i −1.20889 0.964059i −0.208987 0.977918i \(-0.567017\pi\)
−0.999904 + 0.0138598i \(0.995588\pi\)
\(500\) 1.44166e10 + 6.31631e10i 0.230665 + 1.01061i
\(501\) 1.06514e11 + 3.72708e10i 1.69066 + 0.591586i
\(502\) −1.99831e9 4.14954e9i −0.0314665 0.0653409i
\(503\) 7.41600e10 4.65978e10i 1.15850 0.727937i 0.191200 0.981551i \(-0.438762\pi\)
0.967305 + 0.253614i \(0.0816194\pi\)
\(504\) 1.24707e10 4.36369e9i 0.193272 0.0676289i
\(505\) 2.29374e10 + 2.29374e10i 0.352679 + 0.352679i
\(506\) −1.72840e10 + 3.58905e10i −0.263658 + 0.547492i
\(507\) −4.83343e9 4.28979e10i −0.0731515 0.649238i
\(508\) −6.81882e10 + 7.68296e9i −1.02389 + 0.115365i
\(509\) 4.56433e10 + 2.19806e10i 0.679995 + 0.327468i 0.741801 0.670620i \(-0.233972\pi\)
−0.0618064 + 0.998088i \(0.519686\pi\)
\(510\) 2.80090e10 2.80090e10i 0.414016 0.414016i
\(511\) 4.34135e10 + 1.24069e11i 0.636709 + 1.81961i
\(512\) −3.55974e10 5.66530e10i −0.518011 0.824410i
\(513\) −4.70238e9 + 2.26454e9i −0.0678966 + 0.0326973i
\(514\) −1.76436e7 + 5.04225e7i −0.000252775 + 0.000722390i
\(515\) −6.76739e10 + 1.54461e10i −0.962039 + 0.219579i
\(516\) −2.09895e10 + 2.63199e10i −0.296075 + 0.371267i
\(517\) −7.99062e10 1.00199e11i −1.11845 1.40250i
\(518\) 1.06372e9 4.66046e9i 0.0147743 0.0647306i
\(519\) 4.17491e10 6.64433e10i 0.575410 0.915760i
\(520\) −4.42073e9 + 3.92351e10i −0.0604618 + 0.536613i
\(521\) 1.64271e10i 0.222952i −0.993767 0.111476i \(-0.964442\pi\)
0.993767 0.111476i \(-0.0355578\pi\)
\(522\) −5.87771e9 + 1.24112e9i −0.0791637 + 0.0167159i
\(523\) −2.50753e10 −0.335150 −0.167575 0.985859i \(-0.553594\pi\)
−0.167575 + 0.985859i \(0.553594\pi\)
\(524\) −7.23958e10 8.15704e9i −0.960258 0.108195i
\(525\) 1.61986e11 + 1.01782e11i 2.13226 + 1.33979i
\(526\) 1.28515e10 + 2.93327e9i 0.167885 + 0.0383186i
\(527\) 8.79261e10 7.01187e10i 1.13992 0.909058i
\(528\) 7.88989e10 + 6.29198e10i 1.01516 + 0.809564i
\(529\) −2.98072e10 1.30594e11i −0.380626 1.66763i
\(530\) 1.05597e8 + 3.69502e7i 0.00133829 + 0.000468288i
\(531\) −7.38461e9 1.53343e10i −0.0928858 0.192879i
\(532\) −7.90565e9 + 4.96745e9i −0.0986941 + 0.0620136i
\(533\) 5.02125e10 1.75701e10i 0.622161 0.217704i
\(534\) 4.56405e9 + 4.56405e9i 0.0561288 + 0.0561288i
\(535\) −4.56248e10 + 9.47409e10i −0.556911 + 1.15644i
\(536\) −8.50455e9 7.54800e10i −0.103037 0.914477i
\(537\) −5.00100e9 + 5.63478e8i −0.0601395 + 0.00677610i
\(538\) −2.21886e10 1.06855e10i −0.264851 0.127545i
\(539\) 6.04996e10 6.04996e10i 0.716799 0.716799i
\(540\) −3.38221e10 9.66581e10i −0.397764 1.13675i
\(541\) 2.29042e10 + 3.64519e10i 0.267378 + 0.425530i 0.953246 0.302196i \(-0.0977198\pi\)
−0.685867 + 0.727727i \(0.740577\pi\)
\(542\) 1.07900e10 5.19620e9i 0.125033 0.0602128i
\(543\) 5.58067e10 1.59487e11i 0.641930 1.83453i
\(544\) −7.29119e10 + 1.66417e10i −0.832536 + 0.190021i
\(545\) −1.29558e11 + 1.62461e11i −1.46852 + 1.84146i
\(546\) 1.41871e10 + 1.77901e10i 0.159633 + 0.200174i
\(547\) 9.22487e8 4.04168e9i 0.0103041 0.0451453i −0.969515 0.245034i \(-0.921201\pi\)
0.979819 + 0.199889i \(0.0640580\pi\)
\(548\) 4.51871e10 7.19148e10i 0.501063 0.797437i
\(549\) −8.02287e8 + 7.12049e9i −0.00883162 + 0.0783828i
\(550\) 5.67220e10i 0.619870i
\(551\) 7.98955e9 3.68837e9i 0.0866794 0.0400155i
\(552\) 8.81069e10 0.948973
\(553\) −2.16094e10 2.43479e9i −0.231069 0.0260352i
\(554\) −1.94457e9 1.22186e9i −0.0206436 0.0129712i
\(555\) 3.37130e10 + 7.69477e9i 0.355325 + 0.0811005i
\(556\) 2.74954e10 2.19269e10i 0.287714 0.229444i
\(557\) 9.08472e10 + 7.24483e10i 0.943824 + 0.752674i 0.969013 0.247008i \(-0.0794475\pi\)
−0.0251894 + 0.999683i \(0.508019\pi\)
\(558\) −2.12255e9 9.29951e9i −0.0218938 0.0959231i
\(559\) −2.68743e10 9.40372e9i −0.275226 0.0963058i
\(560\) −7.32706e10 1.52148e11i −0.745036 1.54708i
\(561\) 1.63030e11 1.02439e11i 1.64595 1.03422i
\(562\) −1.91166e10 + 6.68917e9i −0.191630 + 0.0670544i
\(563\) 6.49284e10 + 6.49284e10i 0.646251 + 0.646251i 0.952085 0.305834i \(-0.0989353\pi\)
−0.305834 + 0.952085i \(0.598935\pi\)
\(564\) −5.93325e10 + 1.23205e11i −0.586377 + 1.21762i
\(565\) −2.48792e10 2.20809e11i −0.244142 2.16682i
\(566\) 1.64426e10 1.85264e9i 0.160216 0.0180520i
\(567\) −1.48086e11 7.13145e10i −1.43279 0.689995i
\(568\) −1.71581e10 + 1.71581e10i −0.164845 + 0.164845i
\(569\) 2.47572e10 + 7.07519e10i 0.236185 + 0.674977i 0.999578 + 0.0290432i \(0.00924605\pi\)
−0.763394 + 0.645934i \(0.776468\pi\)
\(570\) 2.61835e9 + 4.16708e9i 0.0248043 + 0.0394759i
\(571\) 7.43188e10 3.57900e10i 0.699124 0.336680i −0.0503338 0.998732i \(-0.516029\pi\)
0.749458 + 0.662052i \(0.230314\pi\)
\(572\) −3.05800e10 + 8.73926e10i −0.285662 + 0.816376i
\(573\) −1.67359e11 + 3.81986e10i −1.55250 + 0.354348i
\(574\) 2.32441e10 2.91472e10i 0.214124 0.268503i
\(575\) 1.88445e11 + 2.36303e11i 1.72391 + 2.16171i
\(576\) 4.67864e9 2.04985e10i 0.0425040 0.186222i
\(577\) −6.00507e10 + 9.55701e10i −0.541770 + 0.862222i −0.999641 0.0267970i \(-0.991469\pi\)
0.457871 + 0.889019i \(0.348612\pi\)
\(578\) −1.42495e9 + 1.26468e10i −0.0127670 + 0.113310i
\(579\) 8.33859e10i 0.741956i
\(580\) 5.43614e10 + 1.63877e11i 0.480373 + 1.44812i
\(581\) −1.78146e11 −1.56340
\(582\) −1.23603e10 1.39268e9i −0.107730 0.0121383i
\(583\) 4.60458e8 + 2.89325e8i 0.00398581 + 0.00250445i
\(584\) −8.40374e10 1.91810e10i −0.722472 0.164900i
\(585\) −3.04881e10 + 2.43135e10i −0.260320 + 0.207598i
\(586\) 2.76243e10 + 2.20297e10i 0.234262 + 0.186817i
\(587\) 1.24301e10 + 5.44598e10i 0.104694 + 0.458695i 0.999915 + 0.0130712i \(0.00416082\pi\)
−0.895221 + 0.445623i \(0.852982\pi\)
\(588\) −8.61697e10 3.01521e10i −0.720850 0.252236i
\(589\) 6.06254e9 + 1.25890e10i 0.0503725 + 0.104600i
\(590\) 3.01805e10 1.89637e10i 0.249069 0.156500i
\(591\) −5.62362e10 + 1.96779e10i −0.460963 + 0.161298i
\(592\) −1.35285e10 1.35285e10i −0.110144 0.110144i
\(593\) −2.63307e10 + 5.46762e10i −0.212933 + 0.442160i −0.979890 0.199539i \(-0.936056\pi\)
0.766957 + 0.641699i \(0.221770\pi\)
\(594\) 4.06105e9 + 3.60428e10i 0.0326206 + 0.289516i
\(595\) −3.20173e11 + 3.60749e10i −2.55457 + 0.287831i
\(596\) 1.76765e11 + 8.51255e10i 1.40091 + 0.674644i
\(597\) 1.32738e10 1.32738e10i 0.104496 0.104496i
\(598\) 1.18732e10 + 3.39316e10i 0.0928457 + 0.265338i
\(599\) 2.97887e9 + 4.74085e9i 0.0231390 + 0.0368255i 0.858093 0.513493i \(-0.171649\pi\)
−0.834954 + 0.550319i \(0.814506\pi\)
\(600\) −1.13032e11 + 5.44333e10i −0.872160 + 0.420010i
\(601\) 5.90647e10 1.68797e11i 0.452720 1.29380i −0.460980 0.887411i \(-0.652502\pi\)
0.913700 0.406389i \(-0.133212\pi\)
\(602\) −1.94528e10 + 4.43996e9i −0.148114 + 0.0338060i
\(603\) 4.67740e10 5.86527e10i 0.353781 0.443628i
\(604\) 3.64378e10 + 4.56916e10i 0.273782 + 0.343312i
\(605\) 4.90861e10 2.15060e11i 0.366384 1.60523i
\(606\) −6.52235e9 + 1.03803e10i −0.0483631 + 0.0769694i
\(607\) 1.52926e10 1.35725e11i 0.112649 0.999784i −0.802496 0.596658i \(-0.796495\pi\)
0.915144 0.403126i \(-0.132076\pi\)
\(608\) 9.29186e9i 0.0679968i
\(609\) 1.84348e11 + 9.25085e10i 1.34020 + 0.672531i
\(610\) −1.50065e10 −0.108383
\(611\) −1.14928e11 1.29493e10i −0.824636 0.0929141i
\(612\) −4.12118e10 2.58951e10i −0.293775 0.184591i
\(613\) −1.81516e11 4.14299e10i −1.28551 0.293408i −0.475440 0.879748i \(-0.657711\pi\)
−0.810065 + 0.586340i \(0.800568\pi\)
\(614\) −4.58124e10 + 3.65342e10i −0.322337 + 0.257055i
\(615\) 2.10846e11 + 1.68144e11i 1.47389 + 1.17539i
\(616\) 2.99287e10 + 1.31126e11i 0.207857 + 0.910683i
\(617\) 1.87841e11 + 6.57285e10i 1.29613 + 0.453537i 0.888193 0.459471i \(-0.151961\pi\)
0.407942 + 0.913008i \(0.366247\pi\)
\(618\) −1.13823e10 2.36355e10i −0.0780324 0.162036i
\(619\) 1.88837e11 1.18654e11i 1.28625 0.808205i 0.297062 0.954858i \(-0.403993\pi\)
0.989188 + 0.146654i \(0.0468503\pi\)
\(620\) −2.58769e11 + 9.05471e10i −1.75124 + 0.612785i
\(621\) −1.36662e11 1.36662e11i −0.918927 0.918927i
\(622\) −1.45852e10 + 3.02864e10i −0.0974427 + 0.202342i
\(623\) −5.87838e9 5.21721e10i −0.0390217 0.346327i
\(624\) 9.04969e10 1.01966e10i 0.596891 0.0672535i
\(625\) −1.93876e10 9.33656e9i −0.127058 0.0611881i
\(626\) −2.45893e10 + 2.45893e10i −0.160121 + 0.160121i
\(627\) 7.90103e9 + 2.25798e10i 0.0511227 + 0.146100i
\(628\) 6.78428e10 + 1.07971e11i 0.436180 + 0.694176i
\(629\) −3.28884e10 + 1.58382e10i −0.210107 + 0.101182i
\(630\) −9.02586e9 + 2.57944e10i −0.0572963 + 0.163743i
\(631\) −1.46696e11 + 3.34825e10i −0.925341 + 0.211203i −0.658538 0.752548i \(-0.728825\pi\)
−0.266804 + 0.963751i \(0.585968\pi\)
\(632\) 8.89134e9 1.11494e10i 0.0557313 0.0698848i
\(633\) 8.33073e10 + 1.04464e11i 0.518881 + 0.650657i
\(634\) 5.79927e9 2.54082e10i 0.0358935 0.157260i
\(635\) 1.56528e11 2.49113e11i 0.962713 1.53215i
\(636\) 6.49677e7 5.76604e8i 0.000397072 0.00352411i
\(637\) 7.72117e10i 0.468948i
\(638\) −5.85566e9 6.08730e10i −0.0353421 0.367402i
\(639\) −2.39655e10 −0.143742
\(640\) 2.38123e11 + 2.68300e10i 1.41932 + 0.159919i
\(641\) 7.60940e10 + 4.78130e10i 0.450732 + 0.283214i 0.738207 0.674575i \(-0.235673\pi\)
−0.287475 + 0.957788i \(0.592816\pi\)
\(642\) −3.87442e10 8.84312e9i −0.228069 0.0520554i
\(643\) 1.53540e10 1.22444e10i 0.0898210 0.0716299i −0.577550 0.816355i \(-0.695991\pi\)
0.667371 + 0.744726i \(0.267420\pi\)
\(644\) −2.70311e11 2.15566e11i −1.57152 1.25325i
\(645\) −3.21180e10 1.40718e11i −0.185571 0.813039i
\(646\) −4.90361e9 1.71585e9i −0.0281570 0.00985255i
\(647\) 3.88482e10 + 8.06692e10i 0.221694 + 0.460353i 0.981918 0.189309i \(-0.0606248\pi\)
−0.760223 + 0.649662i \(0.774911\pi\)
\(648\) 9.12648e10 5.73455e10i 0.517611 0.325236i
\(649\) 1.63537e11 5.72242e10i 0.921803 0.322553i
\(650\) −3.61953e10 3.61953e10i −0.202768 0.202768i
\(651\) −1.42098e11 + 2.95070e11i −0.791160 + 1.64286i
\(652\) 1.71437e10 + 1.52154e11i 0.0948666 + 0.841964i
\(653\) −2.14577e11 + 2.41771e10i −1.18013 + 0.132969i −0.680155 0.733068i \(-0.738087\pi\)
−0.499979 + 0.866038i \(0.666659\pi\)
\(654\) −7.07542e10 3.40734e10i −0.386760 0.186254i
\(655\) 2.20873e11 2.20873e11i 1.19999 1.19999i
\(656\) −4.92803e10 1.40835e11i −0.266108 0.760492i
\(657\) −4.52941e10 7.20851e10i −0.243097 0.386887i
\(658\) −7.30241e10 + 3.51665e10i −0.389549 + 0.187597i
\(659\) −1.47168e10 + 4.20581e10i −0.0780316 + 0.223001i −0.976290 0.216466i \(-0.930547\pi\)
0.898259 + 0.439467i \(0.144833\pi\)
\(660\) −4.57602e11 + 1.04445e11i −2.41164 + 0.550440i
\(661\) −9.43442e10 + 1.18304e11i −0.494207 + 0.619717i −0.964912 0.262575i \(-0.915428\pi\)
0.470704 + 0.882291i \(0.344000\pi\)
\(662\) −9.26791e9 1.16216e10i −0.0482559 0.0605109i
\(663\) 3.86645e10 1.69400e11i 0.200105 0.876718i
\(664\) 6.21541e10 9.89177e10i 0.319740 0.508864i
\(665\) 4.48210e9 3.97797e10i 0.0229190 0.203411i
\(666\) 3.09611e9i 0.0157369i
\(667\) 2.26631e11 + 2.34142e11i 1.14503 + 1.18298i
\(668\) 2.90392e11 1.45841
\(669\) 3.41938e11 + 3.85272e10i 1.70704 + 0.192337i
\(670\) 1.33029e11 + 8.35879e10i 0.660159 + 0.414805i
\(671\) −7.11158e10 1.62317e10i −0.350813 0.0800708i
\(672\) 1.70275e11 1.35789e11i 0.834973 0.665869i
\(673\) −1.99575e11 1.59156e11i −0.972849 0.775821i 0.00169948 0.999999i \(-0.499459\pi\)
−0.974548 + 0.224177i \(0.928030\pi\)
\(674\) −1.08713e9 4.76305e9i −0.00526797 0.0230805i
\(675\) 2.59754e11 + 9.08918e10i 1.25126 + 0.437834i
\(676\) −4.81998e10 1.00088e11i −0.230812 0.479286i
\(677\) 7.44387e10 4.67730e10i 0.354360 0.222659i −0.343074 0.939308i \(-0.611468\pi\)
0.697434 + 0.716649i \(0.254325\pi\)
\(678\) 7.92649e10 2.77360e10i 0.375113 0.131258i
\(679\) 7.15429e10 + 7.15429e10i 0.336580 + 0.336580i
\(680\) 9.16758e10 1.90367e11i 0.428765 0.890339i
\(681\) 6.51358e9 + 5.78096e10i 0.0302853 + 0.268789i
\(682\) 9.64922e10 1.08721e10i 0.446021 0.0502544i
\(683\) −1.95879e11 9.43305e10i −0.900131 0.433480i −0.0741949 0.997244i \(-0.523639\pi\)
−0.825936 + 0.563763i \(0.809353\pi\)
\(684\) 4.27603e9 4.27603e9i 0.0195351 0.0195351i
\(685\) 1.20272e11 + 3.43716e11i 0.546262 + 1.56113i
\(686\) 1.14329e10 + 1.81953e10i 0.0516248 + 0.0821604i
\(687\) 2.90533e9 1.39913e9i 0.0130427 0.00628105i
\(688\) −2.63754e10 + 7.53764e10i −0.117718 + 0.336420i
\(689\) 4.78450e8 1.09203e8i 0.00212305 0.000484572i
\(690\) −1.13625e11 + 1.42481e11i −0.501277 + 0.628581i
\(691\) −1.55911e11 1.95506e11i −0.683856 0.857528i 0.311847 0.950132i \(-0.399052\pi\)
−0.995703 + 0.0926039i \(0.970481\pi\)
\(692\) 4.49342e10 1.96870e11i 0.195953 0.858528i
\(693\) −7.06739e10 + 1.12477e11i −0.306426 + 0.487674i
\(694\) 4.70191e9 4.17306e10i 0.0202692 0.179894i
\(695\) 1.50783e11i 0.646270i
\(696\) −1.15684e11 + 7.00856e10i −0.492990 + 0.298670i
\(697\) −2.84682e11 −1.20623
\(698\) −1.95687e10 2.20486e9i −0.0824404 0.00928880i
\(699\) −1.40522e11 8.82956e10i −0.588619 0.369854i
\(700\) 4.79959e11 + 1.09548e11i 1.99900 + 0.456258i
\(701\) 1.29378e11 1.03175e11i 0.535782 0.427272i −0.317856 0.948139i \(-0.602963\pi\)
0.853638 + 0.520867i \(0.174391\pi\)
\(702\) 2.55910e10 + 2.04081e10i 0.105375 + 0.0840339i
\(703\) −1.00921e9 4.42163e9i −0.00413199 0.0181034i
\(704\) 2.02028e11 + 7.06926e10i 0.822471 + 0.287795i
\(705\) −2.54389e11 5.28245e11i −1.02977 2.13835i
\(706\) −6.68582e10 + 4.20098e10i −0.269114 + 0.169095i
\(707\) 9.41232e10 3.29351e10i 0.376720 0.131820i
\(708\) −1.30723e11 1.30723e11i −0.520258 0.520258i
\(709\) −8.47744e10 + 1.76036e11i −0.335490 + 0.696653i −0.998656 0.0518194i \(-0.983498\pi\)
0.663166 + 0.748472i \(0.269212\pi\)
\(710\) −5.61950e9 4.98745e10i −0.0221139 0.196266i
\(711\) 1.39959e10 1.57696e9i 0.0547676 0.00617082i
\(712\) 3.10201e10 + 1.49385e10i 0.120705 + 0.0581283i
\(713\) −3.65865e11 + 3.65865e11i −1.41567 + 1.41567i
\(714\) −4.02173e10 1.14934e11i −0.154746 0.442239i
\(715\) −2.11203e11 3.36127e11i −0.808119 1.28611i
\(716\) −1.16682e10 + 5.61910e9i −0.0443968 + 0.0213804i
\(717\) −1.56581e11 + 4.47483e11i −0.592465 + 1.69317i
\(718\) −8.73504e10 + 1.99372e10i −0.328675 + 0.0750180i
\(719\) 9.49908e10 1.19115e11i 0.355440 0.445707i −0.571678 0.820478i \(-0.693707\pi\)
0.927117 + 0.374771i \(0.122279\pi\)
\(720\) 6.81939e10 + 8.55125e10i 0.253756 + 0.318200i
\(721\) −4.74830e10 + 2.08037e11i −0.175710 + 0.769838i
\(722\) −3.73336e10 + 5.94161e10i −0.137389 + 0.218653i
\(723\) 3.65907e8 3.24751e9i 0.00133911 0.0118850i
\(724\) 4.34813e11i 1.58252i
\(725\) −4.35398e11 1.60365e11i −1.57592 0.580440i
\(726\) 8.33670e10 0.300087
\(727\) 6.26670e10 + 7.06088e9i 0.224337 + 0.0252767i 0.223418 0.974723i \(-0.428279\pi\)
0.000919785 1.00000i \(0.499707\pi\)
\(728\) 1.02772e11 + 6.45759e10i 0.365889 + 0.229903i
\(729\) −1.45023e11 3.31005e10i −0.513483 0.117199i
\(730\) 1.39395e11 1.11164e11i 0.490858 0.391446i
\(731\) 1.19124e11 + 9.49981e10i 0.417186 + 0.332694i
\(732\) 1.73194e10 + 7.58813e10i 0.0603238 + 0.264296i
\(733\) −9.69585e10 3.39272e10i −0.335869 0.117526i 0.157075 0.987587i \(-0.449794\pi\)
−0.492944 + 0.870061i \(0.664079\pi\)
\(734\) 4.59357e10 + 9.53864e10i 0.158258 + 0.328626i
\(735\) 3.31424e11 2.08247e11i 1.13562 0.713559i
\(736\) 3.24770e11 1.13642e11i 1.10679 0.387282i
\(737\) 5.40013e11 + 5.40013e11i 1.83035 + 1.83035i
\(738\) −1.04765e10 + 2.17547e10i −0.0353176 + 0.0733378i
\(739\) 5.86804e10 + 5.20803e11i 0.196750 + 1.74621i 0.572880 + 0.819639i \(0.305826\pi\)
−0.376130 + 0.926567i \(0.622746\pi\)
\(740\) 8.84265e10 9.96328e9i 0.294887 0.0332258i
\(741\) 1.94504e10 + 9.36681e9i 0.0645142 + 0.0310684i
\(742\) 2.43186e8 2.43186e8i 0.000802275 0.000802275i
\(743\) −6.80049e10 1.94347e11i −0.223144 0.637709i −0.999968 0.00799123i \(-0.997456\pi\)
0.776824 0.629718i \(-0.216829\pi\)
\(744\) −1.14264e11 1.81850e11i −0.372922 0.593501i
\(745\) −7.57882e11 + 3.64977e11i −2.46024 + 1.18479i
\(746\) −2.47655e10 + 7.07757e10i −0.0799635 + 0.228523i
\(747\) 1.12489e11 2.56748e10i 0.361265 0.0824563i
\(748\) 3.08925e11 3.87379e11i 0.986839 1.23746i
\(749\) 2.01547e11 + 2.52732e11i 0.640396 + 0.803031i
\(750\) 2.33601e10 1.02347e11i 0.0738294 0.323468i
\(751\) 2.50538e10 3.98730e10i 0.0787616 0.125348i −0.805021 0.593247i \(-0.797846\pi\)
0.883782 + 0.467898i \(0.154989\pi\)
\(752\) −3.63200e10 + 3.22349e11i −0.113573 + 1.00799i
\(753\) 1.02418e11i 0.318565i
\(754\) −4.25807e10 3.51075e10i −0.131743 0.108621i
\(755\) −2.50570e11 −0.771154
\(756\) −3.12823e11 3.52467e10i −0.957662 0.107903i
\(757\) −2.58993e11 1.62736e11i −0.788686 0.495565i 0.0764668 0.997072i \(-0.475636\pi\)
−0.865153 + 0.501508i \(0.832779\pi\)
\(758\) 1.44271e11 + 3.29289e10i 0.437021 + 0.0997471i
\(759\) −6.92581e11 + 5.52315e11i −2.08691 + 1.66426i
\(760\) 2.05244e10 + 1.63677e10i 0.0615200 + 0.0490606i
\(761\) 7.96785e9 + 3.49094e10i 0.0237576 + 0.104089i 0.985417 0.170159i \(-0.0544282\pi\)
−0.961659 + 0.274248i \(0.911571\pi\)
\(762\) 1.04949e11 + 3.67233e10i 0.311286 + 0.108924i
\(763\) 2.77158e11 + 5.75525e11i 0.817767 + 1.69811i
\(764\) −3.74038e11 + 2.35024e11i −1.09785 + 0.689825i
\(765\) 1.96971e11 6.89233e10i 0.575119 0.201243i
\(766\) 4.18254e10 + 4.18254e10i 0.121486 + 0.121486i
\(767\) 6.78402e10 1.40872e11i 0.196022 0.407045i
\(768\) −1.72941e10 1.53490e11i −0.0497112 0.441199i
\(769\) −2.18009e11 + 2.45637e10i −0.623402 + 0.0702406i −0.418015 0.908440i \(-0.637274\pi\)
−0.205387 + 0.978681i \(0.565845\pi\)
\(770\) −2.50646e11 1.20705e11i −0.713015 0.343370i
\(771\) −8.39999e8 + 8.39999e8i −0.00237717 + 0.00237717i
\(772\) 7.08714e10 + 2.02539e11i 0.199527 + 0.570215i
\(773\) 1.45536e11 + 2.31619e11i 0.407616 + 0.648718i 0.985942 0.167088i \(-0.0534365\pi\)
−0.578326 + 0.815806i \(0.696294\pi\)
\(774\) 1.16434e10 5.60715e9i 0.0324425 0.0156235i
\(775\) 2.43332e11 6.95402e11i 0.674515 1.92765i
\(776\) −6.46861e10 + 1.47642e10i −0.178387 + 0.0407157i
\(777\) 6.62785e10 8.31106e10i 0.181840 0.228020i
\(778\) −1.61041e10 2.01939e10i −0.0439560 0.0551191i
\(779\) 7.87060e9 3.44834e10i 0.0213726 0.0936396i
\(780\) −2.25356e11 + 3.58651e11i −0.608821 + 0.968934i
\(781\) 2.73156e10 2.42433e11i 0.0734188 0.651610i
\(782\) 1.92377e11i 0.514429i
\(783\) 2.88146e11 + 7.07279e10i 0.766595 + 0.188167i
\(784\) −2.16562e11 −0.573215
\(785\) −5.43291e11 6.12142e10i −1.43072 0.161203i
\(786\) 9.99556e10 + 6.28062e10i 0.261889 + 0.164556i
\(787\) 4.95579e11 + 1.13113e11i 1.29185 + 0.294857i 0.812602 0.582820i \(-0.198051\pi\)
0.479253 + 0.877677i \(0.340908\pi\)
\(788\) −1.19869e11 + 9.55926e10i −0.310887 + 0.247924i
\(789\) 2.29183e11 + 1.82767e11i 0.591390 + 0.471618i
\(790\) 6.56361e9 + 2.87571e10i 0.0168514 + 0.0738306i
\(791\) −6.44752e11 2.25609e11i −1.64697 0.576301i
\(792\) −3.77964e10 7.84851e10i −0.0960617 0.199474i
\(793\) −5.57379e10 + 3.50225e10i −0.140948 + 0.0885633i
\(794\) −9.67175e10 + 3.38429e10i −0.243345 + 0.0851502i
\(795\) 1.75917e9 + 1.75917e9i 0.00440392 + 0.00440392i
\(796\) 2.09595e10 4.35229e10i 0.0522071 0.108409i
\(797\) −4.88466e10 4.33525e11i −0.121060 1.07444i −0.896508 0.443027i \(-0.853905\pi\)
0.775448 0.631411i \(-0.217524\pi\)
\(798\) 1.50338e10 1.69390e9i 0.0370730 0.00417712i
\(799\) 5.57626e11 + 2.68539e11i 1.36822 + 0.658900i
\(800\) −3.46437e11 + 3.46437e11i −0.845793 + 0.845793i
\(801\) 1.12310e10 + 3.20964e10i 0.0272828 + 0.0779697i
\(802\) −9.60013e10 1.52785e11i −0.232049 0.369304i
\(803\) 7.80832e11 3.76029e11i 1.87800 0.904397i
\(804\) 2.69134e11 7.69141e11i 0.644087 1.84070i
\(805\) 1.44520e12 3.29858e11i 3.44148 0.785495i
\(806\) 5.46357e10 6.85110e10i 0.129460 0.162338i
\(807\) −3.41458e11 4.28175e11i −0.805087 1.00955i
\(808\) −1.45514e10 + 6.37540e10i −0.0341398 + 0.149576i
\(809\) 1.65352e11 2.63156e11i 0.386024 0.614354i −0.596028 0.802964i \(-0.703255\pi\)
0.982052 + 0.188610i \(0.0603981\pi\)
\(810\) −2.49618e10 + 2.21542e11i −0.0579877 + 0.514655i
\(811\) 4.35295e11i 1.00624i −0.864217 0.503119i \(-0.832186\pi\)
0.864217 0.503119i \(-0.167814\pi\)
\(812\) 5.26393e11 + 6.80162e10i 1.21084 + 0.156455i
\(813\) 2.66318e11 0.609590
\(814\) −3.13199e10 3.52891e9i −0.0713384 0.00803790i
\(815\) −5.55867e11 3.49274e11i −1.25991 0.791656i
\(816\) −4.75130e11 1.08445e11i −1.07165 0.244597i
\(817\) −1.48005e10 + 1.18030e10i −0.0332190 + 0.0264913i
\(818\) −1.61076e10 1.28454e10i −0.0359765 0.0286903i
\(819\) 2.66752e10 + 1.16872e11i 0.0592887 + 0.259761i
\(820\) 6.55040e11 + 2.29208e11i 1.44881 + 0.506962i
\(821\) −1.72156e11 3.57486e11i −0.378922 0.786841i −0.999995 0.00308772i \(-0.999017\pi\)
0.621073 0.783753i \(-0.286697\pi\)
\(822\) −1.16528e11 + 7.32195e10i −0.255237 + 0.160376i
\(823\) 1.25398e11 4.38787e10i 0.273333 0.0956433i −0.190132 0.981758i \(-0.560892\pi\)
0.463465 + 0.886115i \(0.346606\pi\)
\(824\) −9.89485e10 9.89485e10i −0.214635 0.214635i
\(825\) 5.47283e11 1.13645e12i 1.18140 2.45320i
\(826\) −1.22683e10 1.08884e11i −0.0263551 0.233908i
\(827\) −1.16166e11 + 1.30888e10i −0.248347 + 0.0279820i −0.235260 0.971932i \(-0.575594\pi\)
−0.0130865 + 0.999914i \(0.504166\pi\)
\(828\) 2.01753e11 + 9.71592e10i 0.429239 + 0.206711i
\(829\) −3.46945e11 + 3.46945e11i −0.734585 + 0.734585i −0.971524 0.236939i \(-0.923856\pi\)
0.236939 + 0.971524i \(0.423856\pi\)
\(830\) 7.98082e10 + 2.28079e11i 0.168165 + 0.480587i
\(831\) −2.71711e10 4.32426e10i −0.0569775 0.0906791i
\(832\) 1.74028e11 8.38073e10i 0.363182 0.174899i
\(833\) −1.36468e11 + 3.90003e11i −0.283433 + 0.810006i
\(834\) −5.55562e10 + 1.26803e10i −0.114833 + 0.0262100i
\(835\) −7.76283e11 + 9.73429e11i −1.59689 + 2.00243i
\(836\) 3.83821e10 + 4.81297e10i 0.0785786 + 0.0985344i
\(837\) −1.04832e11 + 4.59300e11i −0.213596 + 0.935826i
\(838\) −7.90245e10 + 1.25767e11i −0.160245 + 0.255029i
\(839\) −3.16938e10 + 2.81290e11i −0.0639626 + 0.567684i 0.920331 + 0.391142i \(0.127920\pi\)
−0.984293 + 0.176542i \(0.943509\pi\)
\(840\) 6.15307e11i 1.23588i
\(841\) −4.83817e11 1.27153e11i −0.967157 0.254180i
\(842\) 1.23733e11 0.246172
\(843\) −4.47548e11 5.04265e10i −0.886195 0.0998502i
\(844\) 2.91134e11 + 1.82931e11i 0.573750 + 0.360511i
\(845\) 4.64355e11 + 1.05986e11i 0.910801 + 0.207884i
\(846\) 4.10421e10 3.27300e10i 0.0801213 0.0638946i
\(847\) −5.30175e11 4.22801e11i −1.03011 0.821489i
\(848\) −3.06290e8 1.34195e9i −0.000592311 0.00259509i
\(849\) 3.47309e11 + 1.21529e11i 0.668475 + 0.233909i
\(850\) 1.18852e11 + 2.46799e11i 0.227683 + 0.472790i
\(851\) 1.42202e11 8.93516e10i 0.271137 0.170367i
\(852\) −2.45707e11 + 8.59767e10i −0.466294 + 0.163163i
\(853\) 3.45286e11 + 3.45286e11i 0.652202 + 0.652202i 0.953523 0.301321i \(-0.0974274\pi\)
−0.301321 + 0.953523i \(0.597427\pi\)
\(854\) −2.00158e10 + 4.15632e10i −0.0376306 + 0.0781407i
\(855\) 2.90296e9 + 2.57645e10i 0.00543222 + 0.0482123i
\(856\) −2.10651e11 + 2.37347e10i −0.392345 + 0.0442067i
\(857\) −8.78437e11 4.23033e11i −1.62850 0.784243i −0.999979 0.00644830i \(-0.997947\pi\)
−0.628518 0.777795i \(-0.716338\pi\)
\(858\) 1.06085e11 1.06085e11i 0.195751 0.195751i
\(859\) −2.50223e11 7.15097e11i −0.459574 1.31339i −0.907776 0.419454i \(-0.862221\pi\)
0.448203 0.893932i \(-0.352064\pi\)
\(860\) −1.97612e11 3.14497e11i −0.361259 0.574940i
\(861\) 7.46931e11 3.59703e11i 1.35915 0.654533i
\(862\) −2.96784e9 + 8.48160e9i −0.00537541 + 0.0153620i
\(863\) 4.22097e11 9.63410e10i 0.760973 0.173687i 0.175612 0.984460i \(-0.443810\pi\)
0.585362 + 0.810772i \(0.300953\pi\)
\(864\) 1.95333e11 2.44940e11i 0.350526 0.439546i
\(865\) 5.39811e11 + 6.76901e11i 0.964222 + 1.20910i
\(866\) 1.91858e10 8.40587e10i 0.0341122 0.149455i
\(867\) −1.50572e11 + 2.39634e11i −0.266482 + 0.424104i
\(868\) −9.43610e10 + 8.37477e11i −0.166232 + 1.47535i
\(869\) 1.43379e11i 0.251424i
\(870\) 3.58514e10 2.77462e11i 0.0625791 0.484314i
\(871\) 6.89183e11 1.19746
\(872\) −4.16267e11 4.69020e10i −0.719955 0.0811195i
\(873\) −5.54861e10 3.48642e10i −0.0955272 0.0600237i
\(874\) 2.33025e10 + 5.31863e9i 0.0399352 + 0.00911495i
\(875\) −6.67619e11 + 5.32408e11i −1.13893 + 0.908265i
\(876\) −7.22985e11 5.76562e11i −1.22776 0.979105i
\(877\) −1.87451e11 8.21274e11i −0.316875 1.38832i −0.843000 0.537914i \(-0.819213\pi\)
0.526125 0.850407i \(-0.323644\pi\)
\(878\) −2.39749e11 8.38918e10i −0.403440 0.141170i
\(879\) 3.40910e11 + 7.07906e11i 0.571063 + 1.18582i
\(880\) −9.42763e11 + 5.92377e11i −1.57207 + 0.987797i
\(881\) 4.19028e11 1.46624e11i 0.695568 0.243390i 0.0407422 0.999170i \(-0.487028\pi\)
0.654826 + 0.755780i \(0.272742\pi\)
\(882\) 2.47809e10 + 2.47809e10i 0.0409490 + 0.0409490i
\(883\) −7.14752e10 + 1.48420e11i −0.117574 + 0.244146i −0.951448 0.307810i \(-0.900404\pi\)
0.833874 + 0.551956i \(0.186118\pi\)
\(884\) −5.00632e10 4.44324e11i −0.0819804 0.727596i
\(885\) 7.87650e11 8.87469e10i 1.28399 0.144670i
\(886\) 2.12885e11 + 1.02520e11i 0.345470 + 0.166370i
\(887\) −1.00480e11 + 1.00480e11i −0.162325 + 0.162325i −0.783596 0.621271i \(-0.786617\pi\)
0.621271 + 0.783596i \(0.286617\pi\)
\(888\) 2.30240e10 + 6.57989e10i 0.0370279 + 0.105820i
\(889\) −4.81183e11 7.65799e11i −0.770377 1.22605i
\(890\) −6.41621e10 + 3.08988e10i −0.102263 + 0.0492472i
\(891\) −3.57923e11 + 1.02289e12i −0.567909 + 1.62299i
\(892\) 8.63290e11 1.97040e11i 1.36363 0.311240i
\(893\) −4.79446e10 + 6.01206e10i −0.0753934 + 0.0945404i
\(894\) −1.98211e11 2.48549e11i −0.310297 0.389101i
\(895\) 1.23558e10 5.41342e10i 0.0192565 0.0843684i
\(896\) 3.91919e11 6.23736e11i 0.608085 0.967762i
\(897\) −8.95063e10 + 7.94390e11i −0.138256 + 1.22705i
\(898\) 1.99093e10i 0.0306162i
\(899\) 1.89350e11 7.71413e11i 0.289885 1.18099i
\(900\) −3.18854e11 −0.485984
\(901\) −2.60971e9 2.94043e8i −0.00395997 0.000446182i
\(902\) −2.08128e11 1.30775e11i −0.314415 0.197560i
\(903\) −4.32582e11 9.87341e10i −0.650605 0.148496i
\(904\) 3.50223e11 2.79293e11i 0.524409 0.418203i
\(905\) 1.45754e12 + 1.16235e12i 2.17284 + 1.73278i
\(906\) −2.10720e10 9.23226e10i −0.0312747 0.137024i
\(907\) −8.17678e11 2.86118e11i −1.20824 0.422782i −0.350352 0.936618i \(-0.613938\pi\)
−0.857888 + 0.513836i \(0.828224\pi\)
\(908\) 6.49546e10 + 1.34880e11i 0.0955579 + 0.198428i
\(909\) −5.46866e10 + 3.43618e10i −0.0800986 + 0.0503293i
\(910\) −2.36966e11 + 8.29179e10i −0.345557 + 0.120916i
\(911\) −2.04728e11 2.04728e11i −0.297237 0.297237i 0.542693 0.839931i \(-0.317405\pi\)
−0.839931 + 0.542693i \(0.817405\pi\)
\(912\) 2.62718e10 5.45540e10i 0.0379761 0.0788583i
\(913\) 1.31510e11 + 1.16719e12i 0.189268 + 1.67980i
\(914\) 2.77268e11 3.12406e10i 0.397296 0.0447645i
\(915\) −3.00661e11 1.44791e11i −0.428937 0.206565i
\(916\) 5.86770e9 5.86770e9i 0.00833463 0.00833463i
\(917\) −3.17145e11 9.06348e11i −0.448519 1.28179i
\(918\) −9.31920e10 1.48314e11i −0.131222 0.208839i
\(919\) −5.52485e11 + 2.66063e11i −0.774566 + 0.373011i −0.779036 0.626979i \(-0.784291\pi\)
0.00447064 + 0.999990i \(0.498577\pi\)
\(920\) −3.21066e11 + 9.17553e11i −0.448170 + 1.28080i
\(921\) −1.27037e12 + 2.89954e11i −1.76560 + 0.402986i
\(922\) 5.01509e10 6.28872e10i 0.0693992 0.0870239i
\(923\) −1.37270e11 1.72131e11i −0.189134 0.237166i
\(924\) −3.21074e11 + 1.40672e12i −0.440470 + 1.92983i
\(925\) −1.27228e11 + 2.02483e11i −0.173787 + 0.276580i
\(926\) −3.82134e10 + 3.39154e11i −0.0519723 + 0.461267i
\(927\) 1.38206e11i 0.187158i
\(928\) −3.36025e11 + 4.07554e11i −0.453086 + 0.549532i
\(929\) 1.41154e12 1.89509 0.947544 0.319625i \(-0.103557\pi\)
0.947544 + 0.319625i \(0.103557\pi\)
\(930\) 4.41435e11 + 4.97378e10i 0.590113 + 0.0664897i
\(931\) −4.34679e10 2.73127e10i −0.0578588 0.0363551i
\(932\) −4.16362e11 9.50318e10i −0.551832 0.125952i
\(933\) −5.84438e11 + 4.66074e11i −0.771280 + 0.615075i
\(934\) 8.60332e10 + 6.86092e10i 0.113052 + 0.0901560i
\(935\) 4.72715e11 + 2.07110e12i 0.618519 + 2.70991i
\(936\) −7.42013e10 2.59641e10i −0.0966736 0.0338276i
\(937\) −3.33017e11 6.91516e11i −0.432024 0.897107i −0.997386 0.0722637i \(-0.976978\pi\)
0.565362 0.824843i \(-0.308737\pi\)
\(938\) 4.08946e11 2.56958e11i 0.528269 0.331933i
\(939\) −7.29906e11 + 2.55405e11i −0.938868 + 0.328524i
\(940\) −1.06686e12 1.06686e12i −1.36646 1.36646i
\(941\) 2.26470e11 4.70269e11i 0.288836 0.599774i −0.705177 0.709031i \(-0.749133\pi\)
0.994014 + 0.109256i \(0.0348470\pi\)
\(942\) −2.31344e10 2.05324e11i −0.0293802 0.260757i
\(943\) 1.30153e12 1.46647e11i 1.64591 0.185449i
\(944\) −3.95114e11 1.90277e11i −0.497547 0.239606i
\(945\) 9.54398e11 9.54398e11i 1.19675 1.19675i
\(946\) 4.34504e10 + 1.24174e11i 0.0542537 + 0.155048i
\(947\) 6.46949e11 + 1.02961e12i 0.804396 + 1.28019i 0.956473 + 0.291820i \(0.0942609\pi\)
−0.152077 + 0.988369i \(0.548596\pi\)
\(948\) 1.37836e11 6.63785e10i 0.170660 0.0821853i
\(949\) 2.58312e11 7.38213e11i 0.318478 0.910158i
\(950\) −3.31805e10 + 7.57323e9i −0.0407370 + 0.00929794i
\(951\) 3.61343e11 4.53109e11i 0.441771 0.553963i
\(952\) −4.04976e11 5.07824e11i −0.493039 0.618252i
\(953\) 8.26232e10 3.61996e11i 0.100168 0.438866i −0.899828 0.436244i \(-0.856308\pi\)
0.999997 0.00262168i \(-0.000834508\pi\)
\(954\) −1.18509e8 + 1.88606e8i −0.000143073 + 0.000227700i
\(955\) 2.12061e11 1.88209e12i 0.254945 2.26270i
\(956\) 1.21999e12i 1.46058i
\(957\) 4.70014e11 1.27611e12i 0.560355 1.52139i
\(958\) −2.33299e11 −0.276981
\(959\) 1.11240e12 + 1.25337e11i 1.31519 + 0.148186i
\(960\) 8.29104e11 + 5.20961e11i 0.976167 + 0.613367i
\(961\) 3.98111e11 + 9.08662e10i 0.466778 + 0.106539i
\(962\) −2.22376e10 + 1.77339e10i −0.0259650 + 0.0207064i
\(963\) −1.63689e11 1.30538e11i −0.190333 0.151786i
\(964\) −1.87136e9 8.19898e9i −0.00216696 0.00949405i
\(965\) −8.68388e11 3.03862e11i −1.00139 0.350402i
\(966\) 2.43073e11 + 5.04746e11i 0.279144 + 0.579648i
\(967\) −3.14261e11 + 1.97463e11i −0.359405 + 0.225829i −0.699615 0.714520i \(-0.746645\pi\)
0.340209 + 0.940350i \(0.389502\pi\)
\(968\) 4.19741e11 1.46874e11i 0.478057 0.167279i
\(969\) −8.16902e10 8.16902e10i −0.0926563 0.0926563i
\(970\) 5.95451e10 1.23647e11i 0.0672604 0.139668i
\(971\) 6.17363e10 + 5.47925e11i 0.0694486 + 0.616373i 0.979439 + 0.201743i \(0.0646606\pi\)
−0.909990 + 0.414630i \(0.863911\pi\)
\(972\) 4.96443e11 5.59357e10i 0.556166 0.0626648i
\(973\) 4.17620e11 + 2.01115e11i 0.465940 + 0.224385i
\(974\) 2.77099e11 2.77099e11i 0.307893 0.307893i
\(975\) −3.75955e11 1.07442e12i −0.416023 1.18892i
\(976\) 9.82303e10 + 1.56333e11i 0.108255 + 0.172286i
\(977\) 4.21013e11 2.02749e11i 0.462080 0.222526i −0.188335 0.982105i \(-0.560309\pi\)
0.650415 + 0.759579i \(0.274595\pi\)
\(978\) 8.19439e10 2.34182e11i 0.0895698 0.255976i
\(979\) −3.37485e11 + 7.70287e10i −0.367387 + 0.0838536i
\(980\) 6.28012e11 7.87503e11i 0.680870 0.853784i
\(981\) −2.57955e11 3.23465e11i −0.278527 0.349262i
\(982\) 2.53477e10 1.11055e11i 0.0272579 0.119425i
\(983\) 3.05887e11 4.86817e11i 0.327602 0.521376i −0.641794 0.766877i \(-0.721810\pi\)
0.969396 + 0.245501i \(0.0789524\pi\)
\(984\) −6.08706e10 + 5.40242e11i −0.0649273 + 0.576246i
\(985\) 6.57356e11i 0.698322i
\(986\) 1.53028e11 + 2.52591e11i 0.161906 + 0.267245i
\(987\) −1.80237e12 −1.89922
\(988\) 5.52047e10 + 6.22007e9i 0.0579360 + 0.00652781i
\(989\) −5.93553e11 3.72954e11i −0.620403 0.389825i
\(990\) 1.75665e11 + 4.00943e10i 0.182871 + 0.0417390i
\(991\) 5.74879e11 4.58450e11i 0.596048 0.475333i −0.278391 0.960468i \(-0.589801\pi\)
0.874439 + 0.485135i \(0.161230\pi\)
\(992\) −6.55741e11 5.22936e11i −0.677151 0.540010i
\(993\) −7.35548e10 3.22265e11i −0.0756509 0.331448i
\(994\) −1.45631e11 5.09586e10i −0.149179 0.0522002i
\(995\) 8.98643e10 + 1.86605e11i 0.0916843 + 0.190384i
\(996\) 1.06118e12 6.66786e11i 1.07833 0.677562i
\(997\) −7.51650e11 + 2.63014e11i −0.760738 + 0.266194i −0.682643 0.730752i \(-0.739170\pi\)
−0.0780951 + 0.996946i \(0.524884\pi\)
\(998\) 2.82664e11 + 2.82664e11i 0.284937 + 0.284937i
\(999\) 6.63477e10 1.37772e11i 0.0666138 0.138325i
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 29.9.f.a.2.9 228
29.15 odd 28 inner 29.9.f.a.15.9 yes 228
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.9.f.a.2.9 228 1.1 even 1 trivial
29.9.f.a.15.9 yes 228 29.15 odd 28 inner