Properties

Label 91.8.q.a.36.19
Level $91$
Weight $8$
Character 91.36
Analytic conductor $28.427$
Analytic rank $0$
Dimension $100$
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] = [91,8,Mod(36,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.36");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 91.q (of order \(6\), 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: \(28.4270373191\)
Analytic rank: \(0\)
Dimension: \(100\)
Relative dimension: \(50\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 36.19
Character \(\chi\) \(=\) 91.36
Dual form 91.8.q.a.43.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.87848 + 3.39394i) q^{2} +(-26.5593 - 46.0020i) q^{3} +(-40.9623 + 70.9488i) q^{4} -36.3394i q^{5} +(312.256 + 180.281i) q^{6} +(-297.047 - 171.500i) q^{7} -1424.94i q^{8} +(-317.289 + 549.560i) q^{9} +O(q^{10})\) \(q+(-5.87848 + 3.39394i) q^{2} +(-26.5593 - 46.0020i) q^{3} +(-40.9623 + 70.9488i) q^{4} -36.3394i q^{5} +(312.256 + 180.281i) q^{6} +(-297.047 - 171.500i) q^{7} -1424.94i q^{8} +(-317.289 + 549.560i) q^{9} +(123.334 + 213.620i) q^{10} +(-1696.35 + 979.391i) q^{11} +4351.72 q^{12} +(-2032.36 - 7656.24i) q^{13} +2328.24 q^{14} +(-1671.68 + 965.147i) q^{15} +(-407.002 - 704.948i) q^{16} +(10290.4 - 17823.5i) q^{17} -4307.44i q^{18} +(-36386.5 - 21007.8i) q^{19} +(2578.23 + 1488.54i) q^{20} +18219.7i q^{21} +(6647.99 - 11514.7i) q^{22} +(-9803.14 - 16979.5i) q^{23} +(-65550.3 + 37845.5i) q^{24} +76804.5 q^{25} +(37932.0 + 38109.4i) q^{26} -82462.4 q^{27} +(24335.4 - 14050.1i) q^{28} +(38900.8 + 67378.1i) q^{29} +(6551.30 - 11347.2i) q^{30} +166365. i q^{31} +(162742. + 93959.1i) q^{32} +(90107.8 + 52023.8i) q^{33} +139700. i q^{34} +(-6232.20 + 10794.5i) q^{35} +(-25993.8 - 45022.6i) q^{36} +(61036.2 - 35239.3i) q^{37} +285197. q^{38} +(-298225. + 296837. i) q^{39} -51781.5 q^{40} +(-463573. + 267644. i) q^{41} +(-61836.4 - 107104. i) q^{42} +(-56260.7 + 97446.4i) q^{43} -160472. i q^{44} +(19970.7 + 11530.1i) q^{45} +(115255. + 66542.6i) q^{46} +1.21361e6i q^{47} +(-21619.3 + 37445.8i) q^{48} +(58824.5 + 101887. i) q^{49} +(-451493. + 260670. i) q^{50} -1.09322e6 q^{51} +(626451. + 169424. i) q^{52} +206009. q^{53} +(484753. - 279872. i) q^{54} +(35590.4 + 61644.4i) q^{55} +(-244378. + 423275. i) q^{56} +2.23180e6i q^{57} +(-457354. - 264054. i) q^{58} +(-2.42692e6 - 1.40118e6i) q^{59} -158139. i q^{60} +(-1.42633e6 + 2.47047e6i) q^{61} +(-564633. - 977972. i) q^{62} +(188499. - 108830. i) q^{63} -1.17137e6 q^{64} +(-278223. + 73854.5i) q^{65} -706263. q^{66} +(2.11821e6 - 1.22295e6i) q^{67} +(843039. + 1.46019e6i) q^{68} +(-520729. + 901928. i) q^{69} -84606.9i q^{70} +(3.43957e6 + 1.98584e6i) q^{71} +(783093. + 452119. i) q^{72} -3.59629e6i q^{73} +(-239200. + 414306. i) q^{74} +(-2.03987e6 - 3.53316e6i) q^{75} +(2.98095e6 - 1.72105e6i) q^{76} +671862. q^{77} +(745660. - 2.75710e6i) q^{78} +3.66583e6 q^{79} +(-25617.4 + 14790.2i) q^{80} +(2.88405e6 + 4.99532e6i) q^{81} +(1.81674e6 - 3.14668e6i) q^{82} +8.26855e6i q^{83} +(-1.29266e6 - 746319. i) q^{84} +(-647695. - 373947. i) q^{85} -763782. i q^{86} +(2.06635e6 - 3.57902e6i) q^{87} +(1.39558e6 + 2.41721e6i) q^{88} +(4.68350e6 - 2.70402e6i) q^{89} -156530. q^{90} +(-709341. + 2.62281e6i) q^{91} +1.60624e6 q^{92} +(7.65312e6 - 4.41853e6i) q^{93} +(-4.11891e6 - 7.13417e6i) q^{94} +(-763409. + 1.32226e6i) q^{95} -9.98194e6i q^{96} +(-8.60557e6 - 4.96843e6i) q^{97} +(-691597. - 399294. i) q^{98} -1.24300e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100 q + 3328 q^{4} + 522 q^{6} - 38792 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 100 q + 3328 q^{4} + 522 q^{6} - 38792 q^{9} - 2728 q^{10} - 3954 q^{11} - 54708 q^{12} - 32008 q^{13} + 21952 q^{14} + 46398 q^{15} - 228808 q^{16} + 16832 q^{17} - 203520 q^{20} + 148982 q^{22} + 154164 q^{23} - 436560 q^{24} - 1918852 q^{25} - 624246 q^{26} + 661404 q^{27} - 451396 q^{29} + 313736 q^{30} + 1854432 q^{32} + 315450 q^{33} - 372498 q^{35} + 2704174 q^{36} + 1777146 q^{37} - 338468 q^{38} + 189708 q^{39} - 2875580 q^{40} - 2158998 q^{41} - 296352 q^{42} + 1876346 q^{43} + 7252980 q^{45} + 234336 q^{46} + 1316674 q^{48} + 5882450 q^{49} + 6432894 q^{50} - 3602684 q^{51} - 14093326 q^{52} + 1719628 q^{53} - 14915976 q^{54} - 1225470 q^{55} + 2107392 q^{56} + 18792564 q^{58} + 5131962 q^{59} + 886858 q^{61} + 3663272 q^{62} - 1848084 q^{63} - 38282980 q^{64} - 17072760 q^{65} + 54390948 q^{66} - 15529368 q^{67} + 2633716 q^{68} + 12342620 q^{69} + 20194104 q^{71} + 12742440 q^{72} - 23243862 q^{74} - 12055866 q^{75} - 7828698 q^{76} - 11143384 q^{77} - 32361130 q^{78} + 38408264 q^{79} - 38368944 q^{80} - 55140914 q^{81} + 27439818 q^{82} + 46422306 q^{84} + 16353300 q^{85} - 15866954 q^{87} - 39468942 q^{88} + 11465844 q^{89} - 22072424 q^{90} - 3481450 q^{91} + 67780968 q^{92} - 71319114 q^{93} - 6119236 q^{94} + 60860930 q^{95} + 45060702 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.87848 + 3.39394i −0.519589 + 0.299985i −0.736766 0.676147i \(-0.763648\pi\)
0.217177 + 0.976132i \(0.430315\pi\)
\(3\) −26.5593 46.0020i −0.567926 0.983676i −0.996771 0.0802983i \(-0.974413\pi\)
0.428845 0.903378i \(-0.358921\pi\)
\(4\) −40.9623 + 70.9488i −0.320018 + 0.554288i
\(5\) 36.3394i 0.130012i −0.997885 0.0650058i \(-0.979293\pi\)
0.997885 0.0650058i \(-0.0207066\pi\)
\(6\) 312.256 + 180.281i 0.590176 + 0.340738i
\(7\) −297.047 171.500i −0.327327 0.188982i
\(8\) 1424.94i 0.983972i
\(9\) −317.289 + 549.560i −0.145080 + 0.251285i
\(10\) 123.334 + 213.620i 0.0390015 + 0.0675526i
\(11\) −1696.35 + 979.391i −0.384275 + 0.221861i −0.679677 0.733512i \(-0.737880\pi\)
0.295402 + 0.955373i \(0.404547\pi\)
\(12\) 4351.72 0.726986
\(13\) −2032.36 7656.24i −0.256565 0.966527i
\(14\) 2328.24 0.226767
\(15\) −1671.68 + 965.147i −0.127889 + 0.0738370i
\(16\) −407.002 704.948i −0.0248414 0.0430266i
\(17\) 10290.4 17823.5i 0.507998 0.879878i −0.491960 0.870618i \(-0.663719\pi\)
0.999957 0.00925952i \(-0.00294744\pi\)
\(18\) 4307.44i 0.174087i
\(19\) −36386.5 21007.8i −1.21703 0.702655i −0.252752 0.967531i \(-0.581336\pi\)
−0.964283 + 0.264876i \(0.914669\pi\)
\(20\) 2578.23 + 1488.54i 0.0720639 + 0.0416061i
\(21\) 18219.7i 0.429312i
\(22\) 6647.99 11514.7i 0.133110 0.230553i
\(23\) −9803.14 16979.5i −0.168003 0.290990i 0.769714 0.638388i \(-0.220399\pi\)
−0.937718 + 0.347398i \(0.887065\pi\)
\(24\) −65550.3 + 37845.5i −0.967910 + 0.558823i
\(25\) 76804.5 0.983097
\(26\) 37932.0 + 38109.4i 0.423252 + 0.425231i
\(27\) −82462.4 −0.806274
\(28\) 24335.4 14050.1i 0.209501 0.120955i
\(29\) 38900.8 + 67378.1i 0.296186 + 0.513010i 0.975260 0.221060i \(-0.0709517\pi\)
−0.679074 + 0.734070i \(0.737618\pi\)
\(30\) 6551.30 11347.2i 0.0442999 0.0767298i
\(31\) 166365.i 1.00299i 0.865161 + 0.501494i \(0.167216\pi\)
−0.865161 + 0.501494i \(0.832784\pi\)
\(32\) 162742. + 93959.1i 0.877960 + 0.506890i
\(33\) 90107.8 + 52023.8i 0.436479 + 0.252002i
\(34\) 139700.i 0.609566i
\(35\) −6232.20 + 10794.5i −0.0245699 + 0.0425563i
\(36\) −25993.8 45022.6i −0.0928562 0.160832i
\(37\) 61036.2 35239.3i 0.198099 0.114372i −0.397670 0.917529i \(-0.630181\pi\)
0.595768 + 0.803156i \(0.296848\pi\)
\(38\) 285197. 0.843144
\(39\) −298225. + 296837.i −0.805040 + 0.801293i
\(40\) −51781.5 −0.127928
\(41\) −463573. + 267644.i −1.05045 + 0.606477i −0.922775 0.385339i \(-0.874085\pi\)
−0.127674 + 0.991816i \(0.540751\pi\)
\(42\) −61836.4 107104.i −0.128787 0.223066i
\(43\) −56260.7 + 97446.4i −0.107911 + 0.186907i −0.914924 0.403627i \(-0.867749\pi\)
0.807013 + 0.590534i \(0.201083\pi\)
\(44\) 160472.i 0.283999i
\(45\) 19970.7 + 11530.1i 0.0326700 + 0.0188620i
\(46\) 115255. + 66542.6i 0.174585 + 0.100797i
\(47\) 1.21361e6i 1.70504i 0.522691 + 0.852522i \(0.324928\pi\)
−0.522691 + 0.852522i \(0.675072\pi\)
\(48\) −21619.3 + 37445.8i −0.0282162 + 0.0488719i
\(49\) 58824.5 + 101887.i 0.0714286 + 0.123718i
\(50\) −451493. + 260670.i −0.510806 + 0.294914i
\(51\) −1.09322e6 −1.15402
\(52\) 626451. + 169424.i 0.617840 + 0.167095i
\(53\) 206009. 0.190073 0.0950365 0.995474i \(-0.469703\pi\)
0.0950365 + 0.995474i \(0.469703\pi\)
\(54\) 484753. 279872.i 0.418931 0.241870i
\(55\) 35590.4 + 61644.4i 0.0288446 + 0.0499602i
\(56\) −244378. + 423275.i −0.185953 + 0.322080i
\(57\) 2.23180e6i 1.59622i
\(58\) −457354. 264054.i −0.307790 0.177703i
\(59\) −2.42692e6 1.40118e6i −1.53842 0.888205i −0.998932 0.0462084i \(-0.985286\pi\)
−0.539484 0.841996i \(-0.681381\pi\)
\(60\) 158139.i 0.0945167i
\(61\) −1.42633e6 + 2.47047e6i −0.804572 + 1.39356i 0.112008 + 0.993707i \(0.464272\pi\)
−0.916580 + 0.399852i \(0.869062\pi\)
\(62\) −564633. 977972.i −0.300881 0.521142i
\(63\) 188499. 108830.i 0.0949768 0.0548349i
\(64\) −1.17137e6 −0.558555
\(65\) −278223. + 73854.5i −0.125660 + 0.0333565i
\(66\) −706263. −0.302387
\(67\) 2.11821e6 1.22295e6i 0.860413 0.496760i −0.00373771 0.999993i \(-0.501190\pi\)
0.864151 + 0.503233i \(0.167856\pi\)
\(68\) 843039. + 1.46019e6i 0.325137 + 0.563154i
\(69\) −520729. + 901928.i −0.190827 + 0.330522i
\(70\) 84606.9i 0.0294824i
\(71\) 3.43957e6 + 1.98584e6i 1.14051 + 0.658475i 0.946558 0.322535i \(-0.104535\pi\)
0.193955 + 0.981010i \(0.437868\pi\)
\(72\) 783093. + 452119.i 0.247258 + 0.142754i
\(73\) 3.59629e6i 1.08199i −0.841024 0.540997i \(-0.818047\pi\)
0.841024 0.540997i \(-0.181953\pi\)
\(74\) −239200. + 414306.i −0.0686199 + 0.118853i
\(75\) −2.03987e6 3.53316e6i −0.558326 0.967049i
\(76\) 2.98095e6 1.72105e6i 0.778947 0.449725i
\(77\) 671862. 0.167711
\(78\) 745660. 2.75710e6i 0.177914 0.657843i
\(79\) 3.66583e6 0.836522 0.418261 0.908327i \(-0.362640\pi\)
0.418261 + 0.908327i \(0.362640\pi\)
\(80\) −25617.4 + 14790.2i −0.00559396 + 0.00322967i
\(81\) 2.88405e6 + 4.99532e6i 0.602983 + 1.04440i
\(82\) 1.81674e6 3.14668e6i 0.363868 0.630238i
\(83\) 8.26855e6i 1.58729i 0.608382 + 0.793644i \(0.291819\pi\)
−0.608382 + 0.793644i \(0.708181\pi\)
\(84\) −1.29266e6 746319.i −0.237962 0.137388i
\(85\) −647695. 373947.i −0.114394 0.0660456i
\(86\) 763782.i 0.129487i
\(87\) 2.06635e6 3.57902e6i 0.336424 0.582703i
\(88\) 1.39558e6 + 2.41721e6i 0.218305 + 0.378116i
\(89\) 4.68350e6 2.70402e6i 0.704216 0.406579i −0.104700 0.994504i \(-0.533388\pi\)
0.808916 + 0.587925i \(0.200055\pi\)
\(90\) −156530. −0.0226333
\(91\) −709341. + 2.62281e6i −0.0986757 + 0.364856i
\(92\) 1.60624e6 0.215057
\(93\) 7.65312e6 4.41853e6i 0.986616 0.569623i
\(94\) −4.11891e6 7.13417e6i −0.511488 0.885923i
\(95\) −763409. + 1.32226e6i −0.0913534 + 0.158229i
\(96\) 9.98194e6i 1.15150i
\(97\) −8.60557e6 4.96843e6i −0.957367 0.552736i −0.0620052 0.998076i \(-0.519750\pi\)
−0.895362 + 0.445340i \(0.853083\pi\)
\(98\) −691597. 399294.i −0.0742270 0.0428550i
\(99\) 1.24300e6i 0.128750i
\(100\) −3.14609e6 + 5.44919e6i −0.314609 + 0.544919i
\(101\) −4.77498e6 8.27050e6i −0.461154 0.798743i 0.537864 0.843031i \(-0.319231\pi\)
−0.999019 + 0.0442886i \(0.985898\pi\)
\(102\) 6.42649e6 3.71034e6i 0.599616 0.346188i
\(103\) −8.46337e6 −0.763156 −0.381578 0.924337i \(-0.624619\pi\)
−0.381578 + 0.924337i \(0.624619\pi\)
\(104\) −1.09097e7 + 2.89599e6i −0.951036 + 0.252453i
\(105\) 662090. 0.0558155
\(106\) −1.21102e6 + 699182.i −0.0987598 + 0.0570190i
\(107\) −4.58442e6 7.94044e6i −0.361777 0.626616i 0.626476 0.779440i \(-0.284496\pi\)
−0.988253 + 0.152824i \(0.951163\pi\)
\(108\) 3.37785e6 5.85061e6i 0.258022 0.446908i
\(109\) 2.58830e6i 0.191435i −0.995409 0.0957176i \(-0.969485\pi\)
0.995409 0.0957176i \(-0.0305146\pi\)
\(110\) −418435. 241584.i −0.0299746 0.0173059i
\(111\) −3.24215e6 1.87186e6i −0.225011 0.129910i
\(112\) 279203.i 0.0187784i
\(113\) 4.00452e6 6.93602e6i 0.261081 0.452206i −0.705448 0.708761i \(-0.749254\pi\)
0.966529 + 0.256556i \(0.0825877\pi\)
\(114\) −7.57461e6 1.31196e7i −0.478843 0.829381i
\(115\) −617026. + 356240.i −0.0378321 + 0.0218424i
\(116\) −6.37386e6 −0.379140
\(117\) 4.85241e6 + 1.31234e6i 0.280096 + 0.0757522i
\(118\) 1.90221e7 1.06579
\(119\) −6.11347e6 + 3.52961e6i −0.332562 + 0.192005i
\(120\) 1.37528e6 + 2.38205e6i 0.0726535 + 0.125840i
\(121\) −7.82517e6 + 1.35536e7i −0.401555 + 0.695514i
\(122\) 1.93635e7i 0.965437i
\(123\) 2.46243e7 + 1.42169e7i 1.19315 + 0.688868i
\(124\) −1.18034e7 6.81469e6i −0.555944 0.320974i
\(125\) 5.63004e6i 0.257826i
\(126\) −738726. + 1.27951e6i −0.0328993 + 0.0569832i
\(127\) 2.09802e7 + 3.63387e7i 0.908858 + 1.57419i 0.815653 + 0.578542i \(0.196378\pi\)
0.0932056 + 0.995647i \(0.470289\pi\)
\(128\) −1.39451e7 + 8.05119e6i −0.587741 + 0.339332i
\(129\) 5.97697e6 0.245142
\(130\) 1.38487e6 1.37842e6i 0.0552850 0.0550277i
\(131\) 1.57343e7 0.611502 0.305751 0.952111i \(-0.401092\pi\)
0.305751 + 0.952111i \(0.401092\pi\)
\(132\) −7.38205e6 + 4.26203e6i −0.279363 + 0.161290i
\(133\) 7.20567e6 + 1.24806e7i 0.265579 + 0.459996i
\(134\) −8.30123e6 + 1.43781e7i −0.298041 + 0.516222i
\(135\) 2.99663e6i 0.104825i
\(136\) −2.53975e7 1.46633e7i −0.865775 0.499855i
\(137\) −377923. 218194.i −0.0125569 0.00724972i 0.493708 0.869628i \(-0.335641\pi\)
−0.506265 + 0.862378i \(0.668974\pi\)
\(138\) 7.06929e6i 0.228981i
\(139\) −7.81524e6 + 1.35364e7i −0.246826 + 0.427515i −0.962643 0.270773i \(-0.912721\pi\)
0.715818 + 0.698287i \(0.246054\pi\)
\(140\) −510571. 884335.i −0.0157256 0.0272376i
\(141\) 5.58284e7 3.22325e7i 1.67721 0.968339i
\(142\) −2.69593e7 −0.790131
\(143\) 1.09460e7 + 1.09972e7i 0.313027 + 0.314490i
\(144\) 516549. 0.0144159
\(145\) 2.44848e6 1.41363e6i 0.0666972 0.0385077i
\(146\) 1.22056e7 + 2.11407e7i 0.324582 + 0.562193i
\(147\) 3.12467e6 5.41209e6i 0.0811323 0.140525i
\(148\) 5.77393e6i 0.146405i
\(149\) −2.27571e7 1.31388e7i −0.563592 0.325390i 0.190994 0.981591i \(-0.438829\pi\)
−0.754586 + 0.656201i \(0.772162\pi\)
\(150\) 2.39827e7 + 1.38464e7i 0.580200 + 0.334979i
\(151\) 5.24821e7i 1.24049i 0.784410 + 0.620243i \(0.212966\pi\)
−0.784410 + 0.620243i \(0.787034\pi\)
\(152\) −2.99349e7 + 5.18488e7i −0.691393 + 1.19753i
\(153\) 6.53007e6 + 1.13104e7i 0.147400 + 0.255304i
\(154\) −3.94953e6 + 2.28026e6i −0.0871410 + 0.0503109i
\(155\) 6.04559e6 0.130400
\(156\) −8.84424e6 3.33178e7i −0.186520 0.702652i
\(157\) 8.22389e7 1.69601 0.848006 0.529987i \(-0.177803\pi\)
0.848006 + 0.529987i \(0.177803\pi\)
\(158\) −2.15495e7 + 1.24416e7i −0.434647 + 0.250944i
\(159\) −5.47144e6 9.47682e6i −0.107947 0.186970i
\(160\) 3.41441e6 5.91394e6i 0.0659016 0.114145i
\(161\) 6.72496e6i 0.126999i
\(162\) −3.39077e7 1.95766e7i −0.626607 0.361772i
\(163\) −8.81882e6 5.09155e6i −0.159497 0.0920859i 0.418127 0.908389i \(-0.362687\pi\)
−0.577624 + 0.816303i \(0.696020\pi\)
\(164\) 4.38533e7i 0.776335i
\(165\) 1.89051e6 3.27446e6i 0.0327631 0.0567474i
\(166\) −2.80630e7 4.86065e7i −0.476163 0.824738i
\(167\) −6.53137e7 + 3.77089e7i −1.08517 + 0.626522i −0.932286 0.361723i \(-0.882189\pi\)
−0.152882 + 0.988244i \(0.548855\pi\)
\(168\) 2.59620e7 0.422431
\(169\) −5.44876e7 + 3.11204e7i −0.868348 + 0.495955i
\(170\) 5.07662e6 0.0792507
\(171\) 2.30901e7 1.33311e7i 0.353134 0.203882i
\(172\) −4.60914e6 7.98326e6i −0.0690669 0.119627i
\(173\) −1.27613e7 + 2.21033e7i −0.187385 + 0.324560i −0.944378 0.328863i \(-0.893335\pi\)
0.756993 + 0.653423i \(0.226668\pi\)
\(174\) 2.80523e7i 0.403688i
\(175\) −2.28145e7 1.31720e7i −0.321794 0.185788i
\(176\) 1.38084e6 + 797228.i 0.0190919 + 0.0110227i
\(177\) 1.48858e8i 2.01774i
\(178\) −1.83546e7 + 3.17911e7i −0.243935 + 0.422508i
\(179\) −5.75898e7 9.97485e7i −0.750516 1.29993i −0.947573 0.319540i \(-0.896472\pi\)
0.197057 0.980392i \(-0.436862\pi\)
\(180\) −1.63609e6 + 944597.i −0.0209100 + 0.0120724i
\(181\) −2.59779e6 −0.0325633 −0.0162816 0.999867i \(-0.505183\pi\)
−0.0162816 + 0.999867i \(0.505183\pi\)
\(182\) −4.73182e6 1.78256e7i −0.0581806 0.219177i
\(183\) 1.51529e8 1.82775
\(184\) −2.41949e7 + 1.39689e7i −0.286326 + 0.165311i
\(185\) −1.28057e6 2.21802e6i −0.0148697 0.0257551i
\(186\) −2.99925e7 + 5.19485e7i −0.341756 + 0.591940i
\(187\) 4.03133e7i 0.450820i
\(188\) −8.61040e7 4.97122e7i −0.945085 0.545645i
\(189\) 2.44952e7 + 1.41423e7i 0.263915 + 0.152371i
\(190\) 1.03639e7i 0.109619i
\(191\) −2.05927e7 + 3.56675e7i −0.213843 + 0.370388i −0.952914 0.303240i \(-0.901932\pi\)
0.739071 + 0.673628i \(0.235265\pi\)
\(192\) 3.11108e7 + 5.38855e7i 0.317218 + 0.549437i
\(193\) 1.38341e8 7.98710e7i 1.38516 0.799721i 0.392393 0.919798i \(-0.371647\pi\)
0.992765 + 0.120076i \(0.0383139\pi\)
\(194\) 6.74502e7 0.663250
\(195\) 1.07869e7 + 1.08373e7i 0.104177 + 0.104665i
\(196\) −9.63835e6 −0.0914338
\(197\) −6.96313e7 + 4.02016e7i −0.648892 + 0.374638i −0.788032 0.615635i \(-0.788900\pi\)
0.139139 + 0.990273i \(0.455566\pi\)
\(198\) 4.21867e6 + 7.30694e6i 0.0386231 + 0.0668971i
\(199\) −3.75301e7 + 6.50041e7i −0.337594 + 0.584730i −0.983980 0.178281i \(-0.942946\pi\)
0.646386 + 0.763011i \(0.276280\pi\)
\(200\) 1.09442e8i 0.967340i
\(201\) −1.12516e8 6.49612e7i −0.977301 0.564245i
\(202\) 5.61392e7 + 3.24120e7i 0.479221 + 0.276679i
\(203\) 2.66859e7i 0.223896i
\(204\) 4.47810e7 7.75629e7i 0.369307 0.639659i
\(205\) 9.72602e6 + 1.68460e7i 0.0788491 + 0.136571i
\(206\) 4.97518e7 2.87242e7i 0.396527 0.228935i
\(207\) 1.24417e7 0.0974954
\(208\) −4.57008e6 + 4.54881e6i −0.0352129 + 0.0350490i
\(209\) 8.22993e7 0.623568
\(210\) −3.89208e6 + 2.24710e6i −0.0290011 + 0.0167438i
\(211\) 4.00181e7 + 6.93134e7i 0.293270 + 0.507959i 0.974581 0.224036i \(-0.0719232\pi\)
−0.681311 + 0.731994i \(0.738590\pi\)
\(212\) −8.43860e6 + 1.46161e7i −0.0608268 + 0.105355i
\(213\) 2.10970e8i 1.49586i
\(214\) 5.38988e7 + 3.11185e7i 0.375951 + 0.217055i
\(215\) 3.54114e6 + 2.04448e6i 0.0243001 + 0.0140297i
\(216\) 1.17504e8i 0.793351i
\(217\) 2.85316e7 4.94181e7i 0.189547 0.328305i
\(218\) 8.78453e6 + 1.52153e7i 0.0574276 + 0.0994676i
\(219\) −1.65437e8 + 9.55149e7i −1.06433 + 0.614493i
\(220\) −5.83147e6 −0.0369231
\(221\) −1.57375e8 4.25622e7i −0.980760 0.265247i
\(222\) 2.54119e7 0.155884
\(223\) −1.49915e8 + 8.65532e7i −0.905267 + 0.522656i −0.878905 0.476996i \(-0.841726\pi\)
−0.0263620 + 0.999652i \(0.508392\pi\)
\(224\) −3.22280e7 5.58205e7i −0.191586 0.331838i
\(225\) −2.43692e7 + 4.22087e7i −0.142627 + 0.247038i
\(226\) 5.43644e7i 0.313282i
\(227\) 1.96513e8 + 1.13457e8i 1.11507 + 0.643785i 0.940137 0.340796i \(-0.110697\pi\)
0.174930 + 0.984581i \(0.444030\pi\)
\(228\) −1.58344e8 9.14199e7i −0.884768 0.510821i
\(229\) 2.34001e8i 1.28764i 0.765178 + 0.643819i \(0.222651\pi\)
−0.765178 + 0.643819i \(0.777349\pi\)
\(230\) 2.41811e6 4.18830e6i 0.0131048 0.0226981i
\(231\) −1.78442e7 3.09070e7i −0.0952476 0.164974i
\(232\) 9.60100e7 5.54314e7i 0.504787 0.291439i
\(233\) 1.18688e8 0.614698 0.307349 0.951597i \(-0.400558\pi\)
0.307349 + 0.951597i \(0.400558\pi\)
\(234\) −3.29788e7 + 8.75425e6i −0.168259 + 0.0446646i
\(235\) 4.41017e7 0.221676
\(236\) 1.98825e8 1.14791e8i 0.984642 0.568483i
\(237\) −9.73617e7 1.68635e8i −0.475082 0.822867i
\(238\) 2.39586e7 4.14975e7i 0.115197 0.199527i
\(239\) 3.73655e8i 1.77043i −0.465185 0.885213i \(-0.654012\pi\)
0.465185 0.885213i \(-0.345988\pi\)
\(240\) 1.36076e6 + 785633.i 0.00635391 + 0.00366843i
\(241\) 3.84014e7 + 2.21711e7i 0.176721 + 0.102030i 0.585751 0.810491i \(-0.300800\pi\)
−0.409030 + 0.912521i \(0.634133\pi\)
\(242\) 1.06233e8i 0.481842i
\(243\) 6.30239e7 1.09161e8i 0.281763 0.488027i
\(244\) −1.16851e8 2.02392e8i −0.514955 0.891928i
\(245\) 3.70251e6 2.13764e6i 0.0160848 0.00928655i
\(246\) −1.93005e8 −0.826600
\(247\) −8.68902e7 + 3.21279e8i −0.366886 + 1.35657i
\(248\) 2.37061e8 0.986912
\(249\) 3.80370e8 2.19607e8i 1.56138 0.901462i
\(250\) 1.91080e7 + 3.30960e7i 0.0773438 + 0.133963i
\(251\) 4.73101e7 8.19435e7i 0.188841 0.327082i −0.756023 0.654545i \(-0.772860\pi\)
0.944864 + 0.327463i \(0.106194\pi\)
\(252\) 1.78317e7i 0.0701927i
\(253\) 3.32592e7 + 1.92022e7i 0.129119 + 0.0745469i
\(254\) −2.46663e8 1.42411e8i −0.944466 0.545287i
\(255\) 3.97270e7i 0.150036i
\(256\) 1.29618e8 2.24506e8i 0.482866 0.836349i
\(257\) −1.80670e8 3.12930e8i −0.663927 1.14996i −0.979575 0.201079i \(-0.935555\pi\)
0.315648 0.948876i \(-0.397778\pi\)
\(258\) −3.51355e7 + 2.02855e7i −0.127373 + 0.0735388i
\(259\) −2.41741e7 −0.0864573
\(260\) 6.15677e6 2.27648e7i 0.0217243 0.0803263i
\(261\) −4.93711e7 −0.171882
\(262\) −9.24938e7 + 5.34013e7i −0.317730 + 0.183441i
\(263\) 7.50204e7 + 1.29939e8i 0.254293 + 0.440448i 0.964703 0.263339i \(-0.0848239\pi\)
−0.710410 + 0.703788i \(0.751491\pi\)
\(264\) 7.41310e7 1.28399e8i 0.247962 0.429484i
\(265\) 7.48623e6i 0.0247117i
\(266\) −8.47167e7 4.89112e7i −0.275984 0.159339i
\(267\) −2.48781e8 1.43634e8i −0.799884 0.461813i
\(268\) 2.00379e8i 0.635888i
\(269\) 1.37641e8 2.38401e8i 0.431135 0.746748i −0.565836 0.824518i \(-0.691446\pi\)
0.996971 + 0.0777695i \(0.0247798\pi\)
\(270\) −1.01704e7 1.76156e7i −0.0314459 0.0544659i
\(271\) 3.86080e8 2.22903e8i 1.17838 0.680337i 0.222739 0.974878i \(-0.428500\pi\)
0.955639 + 0.294541i \(0.0951669\pi\)
\(272\) −1.67529e7 −0.0504775
\(273\) 1.39494e8 3.70288e7i 0.414941 0.110147i
\(274\) 2.96215e6 0.00869922
\(275\) −1.30288e8 + 7.52216e7i −0.377780 + 0.218111i
\(276\) −4.26605e7 7.38902e7i −0.122136 0.211546i
\(277\) 9.90860e7 1.71622e8i 0.280113 0.485170i −0.691299 0.722568i \(-0.742961\pi\)
0.971412 + 0.237399i \(0.0762948\pi\)
\(278\) 1.06098e8i 0.296176i
\(279\) −9.14276e7 5.27857e7i −0.252036 0.145513i
\(280\) 1.53815e7 + 8.88053e6i 0.0418742 + 0.0241761i
\(281\) 8.09263e7i 0.217579i 0.994065 + 0.108790i \(0.0346975\pi\)
−0.994065 + 0.108790i \(0.965302\pi\)
\(282\) −2.18791e8 + 3.78956e8i −0.580974 + 1.00628i
\(283\) 2.73371e8 + 4.73492e8i 0.716968 + 1.24183i 0.962196 + 0.272360i \(0.0878040\pi\)
−0.245227 + 0.969466i \(0.578863\pi\)
\(284\) −2.81786e8 + 1.62689e8i −0.729970 + 0.421448i
\(285\) 8.11023e7 0.207528
\(286\) −1.01670e8 2.74967e7i −0.256987 0.0695024i
\(287\) 1.83604e8 0.458454
\(288\) −1.03272e8 + 5.96244e7i −0.254748 + 0.147079i
\(289\) −6.61589e6 1.14591e7i −0.0161230 0.0279259i
\(290\) −9.59554e6 + 1.66200e7i −0.0231034 + 0.0400163i
\(291\) 5.27831e8i 1.25565i
\(292\) 2.55153e8 + 1.47313e8i 0.599737 + 0.346258i
\(293\) −3.87214e8 2.23558e8i −0.899321 0.519223i −0.0223412 0.999750i \(-0.507112\pi\)
−0.876980 + 0.480527i \(0.840445\pi\)
\(294\) 4.24198e7i 0.0973538i
\(295\) −5.09181e7 + 8.81927e7i −0.115477 + 0.200012i
\(296\) −5.02140e7 8.69731e7i −0.112539 0.194923i
\(297\) 1.39885e8 8.07629e7i 0.309831 0.178881i
\(298\) 1.78369e8 0.390448
\(299\) −1.10076e8 + 1.09564e8i −0.238146 + 0.237038i
\(300\) 3.34231e8 0.714698
\(301\) 3.34241e7 1.92974e7i 0.0706443 0.0407865i
\(302\) −1.78121e8 3.08515e8i −0.372127 0.644543i
\(303\) −2.53640e8 + 4.39317e8i −0.523803 + 0.907253i
\(304\) 3.42008e7i 0.0698199i
\(305\) 8.97753e7 + 5.18318e7i 0.181179 + 0.104604i
\(306\) −7.67737e7 4.43253e7i −0.153175 0.0884356i
\(307\) 6.03021e8i 1.18946i 0.803927 + 0.594728i \(0.202740\pi\)
−0.803927 + 0.594728i \(0.797260\pi\)
\(308\) −2.75210e7 + 4.76678e7i −0.0536707 + 0.0929604i
\(309\) 2.24781e8 + 3.89332e8i 0.433416 + 0.750698i
\(310\) −3.55389e7 + 2.05184e7i −0.0677545 + 0.0391181i
\(311\) 2.48794e6 0.00469005 0.00234503 0.999997i \(-0.499254\pi\)
0.00234503 + 0.999997i \(0.499254\pi\)
\(312\) 4.22975e8 + 4.24953e8i 0.788450 + 0.792136i
\(313\) 8.77163e8 1.61687 0.808435 0.588586i \(-0.200315\pi\)
0.808435 + 0.588586i \(0.200315\pi\)
\(314\) −4.83440e8 + 2.79114e8i −0.881229 + 0.508778i
\(315\) −3.95482e6 6.84994e6i −0.00712917 0.0123481i
\(316\) −1.50161e8 + 2.60086e8i −0.267702 + 0.463674i
\(317\) 7.97891e8i 1.40681i 0.710788 + 0.703406i \(0.248338\pi\)
−0.710788 + 0.703406i \(0.751662\pi\)
\(318\) 6.43275e7 + 3.71395e7i 0.112177 + 0.0647651i
\(319\) −1.31979e8 7.61981e7i −0.227634 0.131425i
\(320\) 4.25670e7i 0.0726186i
\(321\) −2.43517e8 + 4.21785e8i −0.410925 + 0.711743i
\(322\) −2.28241e7 3.95325e7i −0.0380977 0.0659871i
\(323\) −7.48865e8 + 4.32357e8i −1.23650 + 0.713895i
\(324\) −4.72550e8 −0.771863
\(325\) −1.56094e8 5.88033e8i −0.252229 0.950190i
\(326\) 6.91216e7 0.110497
\(327\) −1.19067e8 + 6.87433e7i −0.188310 + 0.108721i
\(328\) 3.81378e8 + 6.60566e8i 0.596757 + 1.03361i
\(329\) 2.08134e8 3.60498e8i 0.322223 0.558107i
\(330\) 2.56651e7i 0.0393138i
\(331\) −1.00749e8 5.81673e7i −0.152701 0.0881619i 0.421703 0.906734i \(-0.361433\pi\)
−0.574404 + 0.818572i \(0.694766\pi\)
\(332\) −5.86644e8 3.38699e8i −0.879815 0.507961i
\(333\) 4.47241e7i 0.0663723i
\(334\) 2.55964e8 4.43342e8i 0.375894 0.651068i
\(335\) −4.44411e7 7.69743e7i −0.0645845 0.111864i
\(336\) 1.28439e7 7.41543e6i 0.0184718 0.0106647i
\(337\) −1.04675e9 −1.48984 −0.744920 0.667153i \(-0.767513\pi\)
−0.744920 + 0.667153i \(0.767513\pi\)
\(338\) 2.14683e8 3.67868e8i 0.302405 0.518184i
\(339\) −4.25428e8 −0.593099
\(340\) 5.30622e7 3.06355e7i 0.0732165 0.0422716i
\(341\) −1.62936e8 2.82214e8i −0.222524 0.385423i
\(342\) −9.04897e7 + 1.56733e8i −0.122323 + 0.211870i
\(343\) 4.03536e7i 0.0539949i
\(344\) 1.38856e8 + 8.01684e7i 0.183912 + 0.106181i
\(345\) 3.27755e7 + 1.89229e7i 0.0429717 + 0.0248097i
\(346\) 1.73245e8i 0.224851i
\(347\) 5.11154e8 8.85345e8i 0.656748 1.13752i −0.324704 0.945816i \(-0.605265\pi\)
0.981452 0.191706i \(-0.0614019\pi\)
\(348\) 1.69285e8 + 2.93210e8i 0.215323 + 0.372951i
\(349\) −3.79303e8 + 2.18991e8i −0.477636 + 0.275763i −0.719431 0.694564i \(-0.755597\pi\)
0.241795 + 0.970327i \(0.422264\pi\)
\(350\) 1.78819e8 0.222934
\(351\) 1.67593e8 + 6.31352e8i 0.206862 + 0.779286i
\(352\) −3.68091e8 −0.449837
\(353\) 3.52335e8 2.03421e8i 0.426329 0.246141i −0.271453 0.962452i \(-0.587504\pi\)
0.697781 + 0.716311i \(0.254171\pi\)
\(354\) −5.05214e8 8.75056e8i −0.605291 1.04839i
\(355\) 7.21641e7 1.24992e8i 0.0856095 0.148280i
\(356\) 4.43052e8i 0.520451i
\(357\) 3.24738e8 + 1.87488e8i 0.377742 + 0.218089i
\(358\) 6.77081e8 + 3.90913e8i 0.779920 + 0.450287i
\(359\) 5.73879e8i 0.654621i 0.944917 + 0.327310i \(0.106142\pi\)
−0.944917 + 0.327310i \(0.893858\pi\)
\(360\) 1.64297e7 2.84571e7i 0.0185597 0.0321464i
\(361\) 4.35717e8 + 7.54684e8i 0.487449 + 0.844287i
\(362\) 1.52710e7 8.81673e6i 0.0169195 0.00976850i
\(363\) 8.31323e8 0.912214
\(364\) −1.57029e8 1.57763e8i −0.170657 0.171455i
\(365\) −1.30687e8 −0.140672
\(366\) −8.90759e8 + 5.14280e8i −0.949678 + 0.548297i
\(367\) −6.47182e8 1.12095e9i −0.683432 1.18374i −0.973927 0.226863i \(-0.927153\pi\)
0.290494 0.956877i \(-0.406180\pi\)
\(368\) −7.97980e6 + 1.38214e7i −0.00834689 + 0.0144572i
\(369\) 3.39682e8i 0.351950i
\(370\) 1.50556e7 + 8.69237e6i 0.0154523 + 0.00892138i
\(371\) −6.11943e7 3.53305e7i −0.0622160 0.0359204i
\(372\) 7.23973e8i 0.729159i
\(373\) 1.00692e8 1.74403e8i 0.100465 0.174010i −0.811412 0.584475i \(-0.801300\pi\)
0.911876 + 0.410465i \(0.134634\pi\)
\(374\) −1.36821e8 2.36981e8i −0.135239 0.234241i
\(375\) −2.58993e8 + 1.49530e8i −0.253617 + 0.146426i
\(376\) 1.72932e9 1.67772
\(377\) 4.36803e8 4.34770e8i 0.419847 0.417893i
\(378\) −1.91993e8 −0.182837
\(379\) −8.39136e7 + 4.84475e7i −0.0791763 + 0.0457125i −0.539065 0.842264i \(-0.681222\pi\)
0.459889 + 0.887976i \(0.347889\pi\)
\(380\) −6.25420e7 1.08326e8i −0.0584695 0.101272i
\(381\) 1.11444e9 1.93026e9i 1.03233 1.78804i
\(382\) 2.79561e8i 0.256599i
\(383\) −7.16879e8 4.13890e8i −0.652004 0.376435i 0.137220 0.990541i \(-0.456183\pi\)
−0.789224 + 0.614106i \(0.789517\pi\)
\(384\) 7.40741e8 + 4.27667e8i 0.667586 + 0.385431i
\(385\) 2.44150e7i 0.0218044i
\(386\) −5.42155e8 + 9.39040e8i −0.479809 + 0.831053i
\(387\) −3.57018e7 6.18373e7i −0.0313113 0.0542328i
\(388\) 7.05008e8 4.07037e8i 0.612750 0.353771i
\(389\) −1.66954e9 −1.43804 −0.719022 0.694988i \(-0.755410\pi\)
−0.719022 + 0.694988i \(0.755410\pi\)
\(390\) −1.00191e8 2.70968e7i −0.0855272 0.0231309i
\(391\) −4.03514e8 −0.341381
\(392\) 1.45183e8 8.38216e7i 0.121735 0.0702837i
\(393\) −4.17891e8 7.23809e8i −0.347288 0.601520i
\(394\) 2.72884e8 4.72649e8i 0.224772 0.389316i
\(395\) 1.33214e8i 0.108758i
\(396\) 8.81893e7 + 5.09161e7i 0.0713646 + 0.0412024i
\(397\) −1.64345e9 9.48845e8i −1.31822 0.761077i −0.334781 0.942296i \(-0.608662\pi\)
−0.983443 + 0.181219i \(0.941996\pi\)
\(398\) 5.09500e8i 0.405092i
\(399\) 3.82754e8 6.62950e8i 0.301658 0.522487i
\(400\) −3.12596e7 5.41431e7i −0.0244215 0.0422993i
\(401\) −4.25968e8 + 2.45933e8i −0.329892 + 0.190463i −0.655793 0.754941i \(-0.727666\pi\)
0.325901 + 0.945404i \(0.394332\pi\)
\(402\) 8.81898e8 0.677060
\(403\) 1.27373e9 3.38113e8i 0.969415 0.257332i
\(404\) 7.82376e8 0.590311
\(405\) 1.81527e8 1.04805e8i 0.135784 0.0783949i
\(406\) 9.05704e7 + 1.56873e8i 0.0671654 + 0.116334i
\(407\) −6.90260e7 + 1.19557e8i −0.0507496 + 0.0879008i
\(408\) 1.55778e9i 1.13552i
\(409\) 8.03221e8 + 4.63740e8i 0.580502 + 0.335153i 0.761333 0.648361i \(-0.224545\pi\)
−0.180831 + 0.983514i \(0.557879\pi\)
\(410\) −1.14348e8 6.60191e7i −0.0819382 0.0473071i
\(411\) 2.31803e7i 0.0164692i
\(412\) 3.46679e8 6.00466e8i 0.244224 0.423008i
\(413\) 4.80606e8 + 8.32434e8i 0.335710 + 0.581466i
\(414\) −7.31384e7 + 4.22265e7i −0.0506575 + 0.0292471i
\(415\) 3.00474e8 0.206366
\(416\) 3.88624e8 1.43695e9i 0.264669 0.978622i
\(417\) 8.30268e8 0.560715
\(418\) −4.83795e8 + 2.79319e8i −0.323999 + 0.187061i
\(419\) −6.13211e8 1.06211e9i −0.407250 0.705377i 0.587331 0.809347i \(-0.300179\pi\)
−0.994580 + 0.103970i \(0.966845\pi\)
\(420\) −2.71208e7 + 4.69745e7i −0.0178620 + 0.0309378i
\(421\) 1.05746e9i 0.690682i 0.938477 + 0.345341i \(0.112237\pi\)
−0.938477 + 0.345341i \(0.887763\pi\)
\(422\) −4.70491e8 2.71638e8i −0.304760 0.175953i
\(423\) −6.66951e8 3.85064e8i −0.428452 0.247367i
\(424\) 2.93551e8i 0.187026i
\(425\) 7.90350e8 1.36893e9i 0.499411 0.865005i
\(426\) 7.16018e8 + 1.24018e9i 0.448736 + 0.777233i
\(427\) 8.47372e8 4.89230e8i 0.526716 0.304099i
\(428\) 7.51154e8 0.463101
\(429\) 2.15175e8 7.95618e8i 0.131581 0.486524i
\(430\) −2.77554e7 −0.0168348
\(431\) −8.23697e8 + 4.75562e8i −0.495561 + 0.286112i −0.726879 0.686766i \(-0.759030\pi\)
0.231318 + 0.972878i \(0.425696\pi\)
\(432\) 3.35623e7 + 5.81317e7i 0.0200290 + 0.0346912i
\(433\) −7.41846e8 + 1.28492e9i −0.439143 + 0.760618i −0.997624 0.0688993i \(-0.978051\pi\)
0.558480 + 0.829518i \(0.311385\pi\)
\(434\) 3.87338e8i 0.227445i
\(435\) −1.30059e8 7.50899e7i −0.0757582 0.0437390i
\(436\) 1.83637e8 + 1.06023e8i 0.106110 + 0.0612627i
\(437\) 8.23769e8i 0.472194i
\(438\) 6.48344e8 1.12296e9i 0.368677 0.638568i
\(439\) −1.80616e8 3.12836e8i −0.101890 0.176478i 0.810574 0.585637i \(-0.199156\pi\)
−0.912463 + 0.409159i \(0.865822\pi\)
\(440\) 8.78398e7 5.07144e7i 0.0491595 0.0283822i
\(441\) −7.46574e7 −0.0414513
\(442\) 1.06958e9 2.83921e8i 0.589162 0.156394i
\(443\) −3.40048e9 −1.85835 −0.929173 0.369645i \(-0.879479\pi\)
−0.929173 + 0.369645i \(0.879479\pi\)
\(444\) 2.65612e8 1.53351e8i 0.144015 0.0831471i
\(445\) −9.82624e7 1.70195e8i −0.0528600 0.0915562i
\(446\) 5.87513e8 1.01760e9i 0.313578 0.543133i
\(447\) 1.39583e9i 0.739190i
\(448\) 3.47953e8 + 2.00891e8i 0.182830 + 0.105557i
\(449\) −1.98571e9 1.14645e9i −1.03527 0.597713i −0.116779 0.993158i \(-0.537257\pi\)
−0.918490 + 0.395445i \(0.870590\pi\)
\(450\) 3.30831e8i 0.171144i
\(451\) 5.24257e8 9.08039e8i 0.269108 0.466108i
\(452\) 3.28069e8 + 5.68231e8i 0.167101 + 0.289428i
\(453\) 2.41428e9 1.39389e9i 1.22024 0.704504i
\(454\) −1.54026e9 −0.772503
\(455\) 9.53113e7 + 2.57770e7i 0.0474356 + 0.0128290i
\(456\) 3.18020e9 1.57064
\(457\) 1.58014e8 9.12297e7i 0.0774444 0.0447125i −0.460778 0.887516i \(-0.652429\pi\)
0.538222 + 0.842803i \(0.319096\pi\)
\(458\) −7.94186e8 1.37557e9i −0.386272 0.669043i
\(459\) −8.48572e8 + 1.46977e9i −0.409585 + 0.709422i
\(460\) 5.83697e7i 0.0279598i
\(461\) 1.14587e9 + 6.61569e8i 0.544732 + 0.314501i 0.746994 0.664830i \(-0.231496\pi\)
−0.202263 + 0.979331i \(0.564830\pi\)
\(462\) 2.09793e8 + 1.21124e8i 0.0989792 + 0.0571457i
\(463\) 1.05511e8i 0.0494042i −0.999695 0.0247021i \(-0.992136\pi\)
0.999695 0.0247021i \(-0.00786373\pi\)
\(464\) 3.16654e7 5.48460e7i 0.0147154 0.0254878i
\(465\) −1.60566e8 2.78109e8i −0.0740576 0.128272i
\(466\) −6.97706e8 + 4.02821e8i −0.319390 + 0.184400i
\(467\) −2.92016e9 −1.32678 −0.663389 0.748275i \(-0.730882\pi\)
−0.663389 + 0.748275i \(0.730882\pi\)
\(468\) −2.91875e8 + 2.90517e8i −0.131624 + 0.131012i
\(469\) −8.38942e8 −0.375515
\(470\) −2.59251e8 + 1.49679e8i −0.115180 + 0.0664993i
\(471\) −2.18421e9 3.78315e9i −0.963208 1.66833i
\(472\) −1.99661e9 + 3.45823e9i −0.873969 + 1.51376i
\(473\) 2.20405e8i 0.0957651i
\(474\) 1.14468e9 + 6.60880e8i 0.493695 + 0.285035i
\(475\) −2.79465e9 1.61349e9i −1.19646 0.690778i
\(476\) 5.78324e8i 0.245780i
\(477\) −6.53643e7 + 1.13214e8i −0.0275757 + 0.0477625i
\(478\) 1.26816e9 + 2.19652e9i 0.531101 + 0.919894i
\(479\) −1.02522e9 + 5.91912e8i −0.426229 + 0.246084i −0.697739 0.716352i \(-0.745810\pi\)
0.271510 + 0.962436i \(0.412477\pi\)
\(480\) −3.62737e8 −0.149709
\(481\) −3.93848e8 3.95689e8i −0.161369 0.162124i
\(482\) −3.00989e8 −0.122430
\(483\) 3.09361e8 1.78610e8i 0.124926 0.0721258i
\(484\) −6.41075e8 1.11037e9i −0.257010 0.445154i
\(485\) −1.80549e8 + 3.12721e8i −0.0718621 + 0.124469i
\(486\) 8.55598e8i 0.338098i
\(487\) 8.76757e8 + 5.06196e8i 0.343976 + 0.198594i 0.662029 0.749478i \(-0.269696\pi\)
−0.318053 + 0.948073i \(0.603029\pi\)
\(488\) 3.52028e9 + 2.03244e9i 1.37122 + 0.791676i
\(489\) 5.40911e8i 0.209192i
\(490\) −1.45101e7 + 2.51322e7i −0.00557165 + 0.00965037i
\(491\) −1.81996e9 3.15226e9i −0.693868 1.20181i −0.970561 0.240856i \(-0.922572\pi\)
0.276693 0.960958i \(-0.410761\pi\)
\(492\) −2.01734e9 + 1.16471e9i −0.763662 + 0.440901i
\(493\) 1.60122e9 0.601848
\(494\) −5.79621e8 2.18353e9i −0.216322 0.814921i
\(495\) −4.51698e7 −0.0167390
\(496\) 1.17279e8 6.77108e7i 0.0431552 0.0249157i
\(497\) −6.81142e8 1.17977e9i −0.248880 0.431073i
\(498\) −1.49066e9 + 2.58191e9i −0.540850 + 0.936780i
\(499\) 2.45454e9i 0.884337i 0.896932 + 0.442168i \(0.145791\pi\)
−0.896932 + 0.442168i \(0.854209\pi\)
\(500\) 3.99444e8 + 2.30619e8i 0.142910 + 0.0825089i
\(501\) 3.46937e9 + 2.00304e9i 1.23259 + 0.711636i
\(502\) 6.42270e8i 0.226597i
\(503\) 1.34776e9 2.33438e9i 0.472197 0.817869i −0.527297 0.849681i \(-0.676794\pi\)
0.999494 + 0.0318120i \(0.0101278\pi\)
\(504\) −1.55077e8 2.68601e8i −0.0539560 0.0934546i
\(505\) −3.00545e8 + 1.73520e8i −0.103846 + 0.0599554i
\(506\) −2.60685e8 −0.0894518
\(507\) 2.87875e9 + 1.68000e9i 0.981016 + 0.572508i
\(508\) −3.43759e9 −1.16340
\(509\) −3.19621e9 + 1.84533e9i −1.07429 + 0.620244i −0.929352 0.369195i \(-0.879633\pi\)
−0.144943 + 0.989440i \(0.546300\pi\)
\(510\) −1.34831e8 2.33534e8i −0.0450085 0.0779571i
\(511\) −6.16765e8 + 1.06827e9i −0.204478 + 0.354166i
\(512\) 3.01435e8i 0.0992540i
\(513\) 3.00052e9 + 1.73235e9i 0.981264 + 0.566533i
\(514\) 2.12413e9 + 1.22637e9i 0.689939 + 0.398336i
\(515\) 3.07554e8i 0.0992191i
\(516\) −2.44831e8 + 4.24059e8i −0.0784498 + 0.135879i
\(517\) −1.18860e9 2.05871e9i −0.378283 0.655206i
\(518\) 1.42107e8 8.20456e7i 0.0449223 0.0259359i
\(519\) 1.35573e9 0.425683
\(520\) 1.05239e8 + 3.96452e8i 0.0328219 + 0.123646i
\(521\) 1.15922e9 0.359114 0.179557 0.983748i \(-0.442534\pi\)
0.179557 + 0.983748i \(0.442534\pi\)
\(522\) 2.90227e8 1.67563e8i 0.0893081 0.0515621i
\(523\) 5.66698e8 + 9.81550e8i 0.173219 + 0.300024i 0.939544 0.342430i \(-0.111250\pi\)
−0.766324 + 0.642454i \(0.777916\pi\)
\(524\) −6.44514e8 + 1.11633e9i −0.195692 + 0.338948i
\(525\) 1.39935e9i 0.422055i
\(526\) −8.82012e8 5.09230e8i −0.264256 0.152568i
\(527\) 2.96521e9 + 1.71196e9i 0.882507 + 0.509515i
\(528\) 8.46951e7i 0.0250403i
\(529\) 1.51021e9 2.61576e9i 0.443550 0.768251i
\(530\) 2.54078e7 + 4.40076e7i 0.00741313 + 0.0128399i
\(531\) 1.54007e9 8.89160e8i 0.446385 0.257721i
\(532\) −1.18064e9 −0.339960
\(533\) 2.99130e9 + 3.00528e9i 0.855685 + 0.859686i
\(534\) 1.94994e9 0.554148
\(535\) −2.88551e8 + 1.66595e8i −0.0814674 + 0.0470352i
\(536\) −1.74263e9 3.01833e9i −0.488798 0.846622i
\(537\) −3.05909e9 + 5.29849e9i −0.852475 + 1.47653i
\(538\) 1.86858e9i 0.517336i
\(539\) −1.99574e8 1.15224e8i −0.0548964 0.0316945i
\(540\) −2.12607e8 1.22749e8i −0.0581032 0.0335459i
\(541\) 5.42076e9i 1.47187i 0.677052 + 0.735935i \(0.263257\pi\)
−0.677052 + 0.735935i \(0.736743\pi\)
\(542\) −1.51304e9 + 2.62066e9i −0.408181 + 0.706991i
\(543\) 6.89953e7 + 1.19503e8i 0.0184935 + 0.0320317i
\(544\) 3.34936e9 1.93376e9i 0.892003 0.514998i
\(545\) −9.40571e7 −0.0248888
\(546\) −6.94339e8 + 6.91108e8i −0.182557 + 0.181707i
\(547\) −5.06201e8 −0.132242 −0.0661208 0.997812i \(-0.521062\pi\)
−0.0661208 + 0.997812i \(0.521062\pi\)
\(548\) 3.09612e7 1.78755e7i 0.00803686 0.00464008i
\(549\) −9.05115e8 1.56771e9i −0.233454 0.404354i
\(550\) 5.10595e8 8.84377e8i 0.130860 0.226656i
\(551\) 3.26887e9i 0.832468i
\(552\) 1.28520e9 + 7.42009e8i 0.325224 + 0.187768i
\(553\) −1.08892e9 6.28689e8i −0.273816 0.158088i
\(554\) 1.34517e9i 0.336118i
\(555\) −6.80221e7 + 1.17818e8i −0.0168898 + 0.0292540i
\(556\) −6.40261e8 1.10896e9i −0.157977 0.273625i
\(557\) 2.44574e8 1.41205e8i 0.0599677 0.0346224i −0.469716 0.882817i \(-0.655644\pi\)
0.529684 + 0.848195i \(0.322310\pi\)
\(558\) 7.16607e8 0.174607
\(559\) 8.60415e8 + 2.32700e8i 0.208337 + 0.0563449i
\(560\) 1.01461e7 0.00244140
\(561\) 1.85449e9 1.07069e9i 0.443461 0.256032i
\(562\) −2.74659e8 4.75724e8i −0.0652705 0.113052i
\(563\) −1.89761e9 + 3.28676e9i −0.448155 + 0.776227i −0.998266 0.0588645i \(-0.981252\pi\)
0.550111 + 0.835091i \(0.314585\pi\)
\(564\) 5.28128e9i 1.23954i
\(565\) −2.52051e8 1.45522e8i −0.0587920 0.0339436i
\(566\) −3.21401e9 1.85561e9i −0.745057 0.430159i
\(567\) 1.97846e9i 0.455813i
\(568\) 2.82971e9 4.90120e9i 0.647922 1.12223i
\(569\) −2.37267e9 4.10959e9i −0.539939 0.935203i −0.998907 0.0467494i \(-0.985114\pi\)
0.458967 0.888453i \(-0.348220\pi\)
\(570\) −4.76758e8 + 2.75257e8i −0.107829 + 0.0622552i
\(571\) 7.66712e9 1.72348 0.861739 0.507352i \(-0.169376\pi\)
0.861739 + 0.507352i \(0.169376\pi\)
\(572\) −1.22862e9 + 3.26137e8i −0.274492 + 0.0728642i
\(573\) 2.18770e9 0.485789
\(574\) −1.07931e9 + 6.23141e8i −0.238207 + 0.137529i
\(575\) −7.52925e8 1.30410e9i −0.165164 0.286072i
\(576\) 3.71664e8 6.43741e8i 0.0810348 0.140356i
\(577\) 6.00431e9i 1.30121i 0.759416 + 0.650605i \(0.225485\pi\)
−0.759416 + 0.650605i \(0.774515\pi\)
\(578\) 7.77828e7 + 4.49079e7i 0.0167547 + 0.00967331i
\(579\) −7.34845e9 4.24263e9i −1.57333 0.908365i
\(580\) 2.31622e8i 0.0492926i
\(581\) 1.41806e9 2.45615e9i 0.299969 0.519562i
\(582\) −1.79143e9 3.10284e9i −0.376677 0.652423i
\(583\) −3.49464e8 + 2.01763e8i −0.0730403 + 0.0421698i
\(584\) −5.12452e9 −1.06465
\(585\) 4.76895e7 1.76334e8i 0.00984866 0.0364158i
\(586\) 3.03497e9 0.623036
\(587\) −3.54048e9 + 2.04410e9i −0.722485 + 0.417127i −0.815667 0.578522i \(-0.803630\pi\)
0.0931817 + 0.995649i \(0.470296\pi\)
\(588\) 2.55988e8 + 4.43383e8i 0.0519276 + 0.0899412i
\(589\) 3.49496e9 6.05344e9i 0.704755 1.22067i
\(590\) 6.91252e8i 0.138565i
\(591\) 3.69871e9 + 2.13545e9i 0.737045 + 0.425533i
\(592\) −4.96837e7 2.86849e7i −0.00984210 0.00568234i
\(593\) 2.22639e9i 0.438439i 0.975676 + 0.219219i \(0.0703511\pi\)
−0.975676 + 0.219219i \(0.929649\pi\)
\(594\) −5.48209e8 + 9.49526e8i −0.107323 + 0.185889i
\(595\) 1.28264e8 + 2.22159e8i 0.0249629 + 0.0432370i
\(596\) 1.86437e9 1.07639e9i 0.360719 0.208261i
\(597\) 3.98709e9 0.766913
\(598\) 2.75227e8 1.01766e9i 0.0526304 0.194602i
\(599\) −6.27832e8 −0.119357 −0.0596787 0.998218i \(-0.519008\pi\)
−0.0596787 + 0.998218i \(0.519008\pi\)
\(600\) −5.03455e9 + 2.90670e9i −0.951550 + 0.549377i
\(601\) 8.69085e8 + 1.50530e9i 0.163306 + 0.282854i 0.936052 0.351861i \(-0.114451\pi\)
−0.772746 + 0.634715i \(0.781118\pi\)
\(602\) −1.30989e8 + 2.26879e8i −0.0244707 + 0.0423845i
\(603\) 1.55211e9i 0.288279i
\(604\) −3.72354e9 2.14979e9i −0.687586 0.396978i
\(605\) 4.92529e8 + 2.84362e8i 0.0904249 + 0.0522068i
\(606\) 3.44335e9i 0.628532i
\(607\) −3.81614e9 + 6.60974e9i −0.692570 + 1.19957i 0.278424 + 0.960458i \(0.410188\pi\)
−0.970993 + 0.239107i \(0.923145\pi\)
\(608\) −3.94774e9 6.83769e9i −0.712338 1.23381i
\(609\) −1.22761e9 + 7.08758e8i −0.220241 + 0.127156i
\(610\) −7.03656e8 −0.125518
\(611\) 9.29167e9 2.46648e9i 1.64797 0.437456i
\(612\) −1.06995e9 −0.188683
\(613\) −8.26409e9 + 4.77128e9i −1.44905 + 0.836610i −0.998425 0.0561036i \(-0.982132\pi\)
−0.450625 + 0.892713i \(0.648799\pi\)
\(614\) −2.04662e9 3.54485e9i −0.356818 0.618028i
\(615\) 5.16632e8 8.94833e8i 0.0895609 0.155124i
\(616\) 9.57366e8i 0.165023i
\(617\) 1.41602e9 + 8.17540e8i 0.242701 + 0.140123i 0.616417 0.787420i \(-0.288583\pi\)
−0.373717 + 0.927543i \(0.621917\pi\)
\(618\) −2.64274e9 1.52579e9i −0.450396 0.260036i
\(619\) 6.56838e9i 1.11312i −0.830808 0.556559i \(-0.812121\pi\)
0.830808 0.556559i \(-0.187879\pi\)
\(620\) −2.47642e8 + 4.28928e8i −0.0417304 + 0.0722792i
\(621\) 8.08391e8 + 1.40017e9i 0.135457 + 0.234618i
\(622\) −1.46253e7 + 8.44391e6i −0.00243690 + 0.00140694i
\(623\) −1.85496e9 −0.307345
\(624\) 3.30632e8 + 8.94197e7i 0.0544753 + 0.0147329i
\(625\) 5.79576e9 0.949577
\(626\) −5.15638e9 + 2.97704e9i −0.840107 + 0.485036i
\(627\) −2.18581e9 3.78593e9i −0.354141 0.613389i
\(628\) −3.36870e9 + 5.83476e9i −0.542754 + 0.940078i
\(629\) 1.45051e9i 0.232403i
\(630\) 4.64966e7 + 2.68448e7i 0.00740848 + 0.00427729i
\(631\) −3.66874e7 2.11815e7i −0.00581318 0.00335624i 0.497091 0.867699i \(-0.334402\pi\)
−0.502904 + 0.864342i \(0.667735\pi\)
\(632\) 5.22360e9i 0.823114i
\(633\) 2.12570e9 3.68182e9i 0.333111 0.576966i
\(634\) −2.70799e9 4.69038e9i −0.422022 0.730964i
\(635\) 1.32053e9 7.62406e8i 0.204663 0.118162i
\(636\) 8.96492e8 0.138180
\(637\) 6.60519e8 6.57445e8i 0.101251 0.100779i
\(638\) 1.03445e9 0.157702
\(639\) −2.18268e9 + 1.26017e9i −0.330930 + 0.191063i
\(640\) 2.92575e8 + 5.06755e8i 0.0441171 + 0.0764131i
\(641\) −2.84933e9 + 4.93519e9i −0.427307 + 0.740118i −0.996633 0.0819945i \(-0.973871\pi\)
0.569326 + 0.822112i \(0.307204\pi\)
\(642\) 3.30594e9i 0.493085i
\(643\) −6.56045e9 3.78768e9i −0.973184 0.561868i −0.0729788 0.997333i \(-0.523251\pi\)
−0.900206 + 0.435465i \(0.856584\pi\)
\(644\) −4.77128e8 2.75470e8i −0.0703938 0.0406419i
\(645\) 2.17199e8i 0.0318713i
\(646\) 2.93479e9 5.08321e9i 0.428315 0.741863i
\(647\) 6.71265e9 + 1.16267e10i 0.974382 + 1.68768i 0.681959 + 0.731390i \(0.261128\pi\)
0.292423 + 0.956289i \(0.405538\pi\)
\(648\) 7.11805e9 4.10961e9i 1.02766 0.593319i
\(649\) 5.48922e9 0.788233
\(650\) 2.91335e9 + 2.92697e9i 0.416098 + 0.418043i
\(651\) −3.03111e9 −0.430594
\(652\) 7.22478e8 4.17123e8i 0.102084 0.0589383i
\(653\) −2.54242e9 4.40359e9i −0.357314 0.618887i 0.630197 0.776435i \(-0.282974\pi\)
−0.987511 + 0.157549i \(0.949641\pi\)
\(654\) 4.66621e8 8.08212e8i 0.0652293 0.112980i
\(655\) 5.71774e8i 0.0795024i
\(656\) 3.77351e8 + 2.17863e8i 0.0521893 + 0.0301315i
\(657\) 1.97638e9 + 1.14106e9i 0.271889 + 0.156975i
\(658\) 2.82557e9i 0.386648i
\(659\) −2.99843e9 + 5.19343e9i −0.408126 + 0.706895i −0.994680 0.103015i \(-0.967151\pi\)
0.586554 + 0.809910i \(0.300484\pi\)
\(660\) 1.54879e8 + 2.68259e8i 0.0209696 + 0.0363204i
\(661\) 5.82679e9 3.36410e9i 0.784737 0.453068i −0.0533697 0.998575i \(-0.516996\pi\)
0.838106 + 0.545507i \(0.183663\pi\)
\(662\) 7.89666e8 0.105789
\(663\) 2.22182e9 + 8.36998e9i 0.296082 + 1.11539i
\(664\) 1.17822e10 1.56185
\(665\) 4.53536e8 2.61849e8i 0.0598048 0.0345283i
\(666\) −1.51791e8 2.62910e8i −0.0199107 0.0344863i
\(667\) 7.62699e8 1.32103e9i 0.0995206 0.172375i
\(668\) 6.17858e9i 0.801993i
\(669\) 7.96324e9 + 4.59758e9i 1.02825 + 0.593660i
\(670\) 5.22493e8 + 3.01661e8i 0.0671148 + 0.0387488i
\(671\) 5.58773e9i 0.714013i
\(672\) −1.71190e9 + 2.96510e9i −0.217614 + 0.376918i
\(673\) −9.85550e7 1.70702e8i −0.0124631 0.0215867i 0.859727 0.510755i \(-0.170634\pi\)
−0.872190 + 0.489168i \(0.837301\pi\)
\(674\) 6.15332e9 3.55262e9i 0.774105 0.446930i
\(675\) −6.33348e9 −0.792646
\(676\) 2.39799e7 5.14059e9i 0.00298561 0.640029i
\(677\) 8.53881e9 1.05764 0.528819 0.848735i \(-0.322635\pi\)
0.528819 + 0.848735i \(0.322635\pi\)
\(678\) 2.50087e9 1.44388e9i 0.308168 0.177921i
\(679\) 1.70417e9 + 2.95171e9i 0.208915 + 0.361851i
\(680\) −5.32853e8 + 9.22929e8i −0.0649870 + 0.112561i
\(681\) 1.20533e10i 1.46249i
\(682\) 1.91563e9 + 1.10599e9i 0.231242 + 0.133508i
\(683\) −6.50645e9 3.75650e9i −0.781397 0.451140i 0.0555282 0.998457i \(-0.482316\pi\)
−0.836925 + 0.547317i \(0.815649\pi\)
\(684\) 2.18429e9i 0.260984i
\(685\) −7.92903e6 + 1.37335e7i −0.000942547 + 0.00163254i
\(686\) 1.36958e8 + 2.37218e8i 0.0161977 + 0.0280552i
\(687\) 1.07645e10 6.21490e9i 1.26662 0.731283i
\(688\) 9.15929e7 0.0107227
\(689\) −4.18683e8 1.57725e9i −0.0487662 0.183711i
\(690\) −2.56893e8 −0.0297702
\(691\) −1.13960e10 + 6.57948e9i −1.31395 + 0.758610i −0.982748 0.184950i \(-0.940788\pi\)
−0.331203 + 0.943560i \(0.607454\pi\)
\(692\) −1.04547e9 1.81080e9i −0.119933 0.207730i
\(693\) −2.13174e8 + 3.69229e8i −0.0243315 + 0.0421434i
\(694\) 6.93931e9i 0.788058i
\(695\) 4.91904e8 + 2.84001e8i 0.0555819 + 0.0320902i
\(696\) −5.09991e9 2.94443e9i −0.573364 0.331032i
\(697\) 1.10167e10i 1.23236i
\(698\) 1.48648e9 2.57466e9i 0.165450 0.286567i
\(699\) −3.15227e9 5.45989e9i −0.349103 0.604664i
\(700\) 1.86907e9 1.07911e9i 0.205960 0.118911i
\(701\) 1.17809e10 1.29171 0.645855 0.763460i \(-0.276501\pi\)
0.645855 + 0.763460i \(0.276501\pi\)
\(702\) −3.12796e9 3.14259e9i −0.341257 0.342853i
\(703\) −2.96119e9 −0.321457
\(704\) 1.98707e9 1.14723e9i 0.214639 0.123922i
\(705\) −1.17131e9 2.02877e9i −0.125895 0.218057i
\(706\) −1.38080e9 + 2.39161e9i −0.147677 + 0.255784i
\(707\) 3.27563e9i 0.348600i
\(708\) −1.05613e10 6.09755e9i −1.11841 0.645713i
\(709\) 2.01739e9 + 1.16474e9i 0.212582 + 0.122734i 0.602511 0.798111i \(-0.294167\pi\)
−0.389929 + 0.920845i \(0.627500\pi\)
\(710\) 9.79683e8i 0.102726i
\(711\) −1.16313e9 + 2.01459e9i −0.121362 + 0.210205i
\(712\) −3.85308e9 6.67373e9i −0.400062 0.692928i
\(713\) 2.82480e9 1.63090e9i 0.291860 0.168505i
\(714\) −2.54529e9 −0.261694
\(715\) 3.99632e8 3.97772e8i 0.0408874 0.0406971i
\(716\) 9.43605e9 0.960715
\(717\) −1.71889e10 + 9.92400e9i −1.74153 + 1.00547i
\(718\) −1.94771e9 3.37354e9i −0.196376 0.340134i
\(719\) 5.98791e8 1.03714e9i 0.0600792 0.104060i −0.834421 0.551127i \(-0.814198\pi\)
0.894501 + 0.447067i \(0.147531\pi\)
\(720\) 1.87711e7i 0.00187424i
\(721\) 2.51402e9 + 1.45147e9i 0.249801 + 0.144223i
\(722\) −5.12271e9 2.95760e9i −0.506547 0.292455i
\(723\) 2.35539e9i 0.231781i
\(724\) 1.06411e8 1.84310e8i 0.0104208 0.0180494i
\(725\) 2.98775e9 + 5.17494e9i 0.291180 + 0.504338i
\(726\) −4.88692e9 + 2.82146e9i −0.473976 + 0.273650i
\(727\) 3.65324e9 0.352621 0.176310 0.984335i \(-0.443584\pi\)
0.176310 + 0.984335i \(0.443584\pi\)
\(728\) 3.73736e9 + 1.01077e9i 0.359009 + 0.0970941i
\(729\) 5.91936e9 0.565886
\(730\) 7.68241e8 4.43544e8i 0.0730916 0.0421994i
\(731\) 1.15789e9 + 2.00553e9i 0.109637 + 0.189897i
\(732\) −6.20697e9 + 1.07508e10i −0.584913 + 1.01310i
\(733\) 1.33241e10i 1.24961i −0.780782 0.624803i \(-0.785179\pi\)
0.780782 0.624803i \(-0.214821\pi\)
\(734\) 7.60890e9 + 4.39300e9i 0.710208 + 0.410039i
\(735\) −1.96672e8 1.13549e8i −0.0182699 0.0105481i
\(736\) 3.68438e9i 0.340637i
\(737\) −2.39549e9 + 4.14911e9i −0.220423 + 0.381785i
\(738\) 1.15286e9 + 1.99681e9i 0.105580 + 0.182869i
\(739\) −1.30589e10 + 7.53959e9i −1.19029 + 0.687214i −0.958372 0.285522i \(-0.907833\pi\)
−0.231917 + 0.972736i \(0.574500\pi\)
\(740\) 2.09821e8 0.0190343
\(741\) 1.70872e10 4.53582e9i 1.54279 0.409536i
\(742\) 4.79639e8 0.0431023
\(743\) −1.27581e10 + 7.36591e9i −1.14111 + 0.658818i −0.946704 0.322104i \(-0.895610\pi\)
−0.194402 + 0.980922i \(0.562277\pi\)
\(744\) −6.29616e9 1.09053e10i −0.560493 0.970802i
\(745\) −4.77456e8 + 8.26978e8i −0.0423045 + 0.0732735i
\(746\) 1.36697e9i 0.120551i
\(747\) −4.54407e9 2.62352e9i −0.398862 0.230283i
\(748\) −2.86018e9 1.65133e9i −0.249884 0.144271i
\(749\) 3.14491e9i 0.273478i
\(750\) 1.01499e9 1.75801e9i 0.0878511 0.152163i
\(751\) −8.50451e9 1.47302e10i −0.732672 1.26903i −0.955737 0.294222i \(-0.904940\pi\)
0.223065 0.974804i \(-0.428394\pi\)
\(752\) 8.55530e8 4.93941e8i 0.0733623 0.0423558i
\(753\) −5.02608e9 −0.428990
\(754\) −1.09215e9 + 4.03827e9i −0.0927862 + 0.343080i
\(755\) 1.90717e9 0.161278
\(756\) −2.00676e9 + 1.15860e9i −0.168915 + 0.0975233i
\(757\) 7.30793e9 + 1.26577e10i 0.612292 + 1.06052i 0.990853 + 0.134945i \(0.0430856\pi\)
−0.378561 + 0.925576i \(0.623581\pi\)
\(758\) 3.28856e8 5.69596e8i 0.0274261 0.0475034i
\(759\) 2.03999e9i 0.169348i
\(760\) 1.88415e9 + 1.08781e9i 0.155693 + 0.0898892i
\(761\) −3.30821e9 1.91000e9i −0.272112 0.157104i 0.357735 0.933823i \(-0.383549\pi\)
−0.629847 + 0.776719i \(0.716882\pi\)
\(762\) 1.51293e10i 1.23873i
\(763\) −4.43893e8 + 7.68846e8i −0.0361778 + 0.0626619i
\(764\) −1.68705e9 2.92205e9i −0.136868 0.237062i
\(765\) 4.11013e8 2.37298e8i 0.0331925 0.0191637i
\(766\) 5.61888e9 0.451699
\(767\) −5.79543e9 + 2.14288e10i −0.463769 + 1.71480i
\(768\) −1.37703e10 −1.09693
\(769\) −9.05868e7 + 5.23003e7i −0.00718328 + 0.00414727i −0.503587 0.863944i \(-0.667987\pi\)
0.496404 + 0.868092i \(0.334653\pi\)
\(770\) 8.28632e7 + 1.43523e8i 0.00654100 + 0.0113293i
\(771\) −9.59693e9 + 1.66224e10i −0.754123 + 1.30618i
\(772\) 1.30868e10i 1.02370i
\(773\) −1.46025e10 8.43079e9i −1.13710 0.656508i −0.191393 0.981514i \(-0.561300\pi\)
−0.945712 + 0.325006i \(0.894634\pi\)
\(774\) 4.19745e8 + 2.42340e8i 0.0325381 + 0.0187859i
\(775\) 1.27776e10i 0.986034i
\(776\) −7.07973e9 + 1.22624e10i −0.543877 + 0.942022i
\(777\) 6.42047e8 + 1.11206e9i 0.0491013 + 0.0850460i
\(778\) 9.81433e9 5.66631e9i 0.747192 0.431391i
\(779\) 2.24904e10 1.70458
\(780\) −1.21075e9 + 3.21394e8i −0.0913529 + 0.0242497i
\(781\) −7.77964e9 −0.584361
\(782\) 2.37205e9 1.36950e9i 0.177378 0.102409i
\(783\) −3.20785e9 5.55616e9i −0.238807 0.413626i
\(784\) 4.78834e7 8.29364e7i 0.00354878 0.00614666i
\(785\) 2.98851e9i 0.220501i
\(786\) 4.91313e9 + 2.83660e9i 0.360894 + 0.208362i
\(787\) −1.93546e10 1.11744e10i −1.41538 0.817169i −0.419489 0.907760i \(-0.637791\pi\)
−0.995888 + 0.0905916i \(0.971124\pi\)
\(788\) 6.58701e9i 0.479564i
\(789\) 3.98497e9 6.90218e9i 0.288839 0.500284i
\(790\) 4.52120e8 + 7.83094e8i 0.0326256 + 0.0565092i
\(791\) −2.37906e9 + 1.37355e9i −0.170918 + 0.0986794i
\(792\) −1.77120e9 −0.126687
\(793\) 2.18133e10 + 5.89943e9i 1.55334 + 0.420101i
\(794\) 1.28813e10 0.913246
\(795\) −3.44381e8 + 1.98829e8i −0.0243083 + 0.0140344i
\(796\) −3.07464e9 5.32544e9i −0.216072 0.374248i
\(797\) 5.74115e9 9.94397e9i 0.401694 0.695754i −0.592237 0.805764i \(-0.701755\pi\)
0.993930 + 0.110010i \(0.0350884\pi\)
\(798\) 5.19618e9i 0.361971i
\(799\) 2.16308e10 + 1.24885e10i 1.50023 + 0.866159i
\(800\) 1.24993e10 + 7.21648e9i 0.863119 + 0.498322i
\(801\) 3.43182e9i 0.235945i
\(802\) 1.66936e9 2.89142e9i 0.114272 0.197925i
\(803\) 3.52218e9 + 6.10059e9i 0.240053 + 0.415784i
\(804\) 9.21784e9 5.32192e9i 0.625508 0.361137i
\(805\) 2.44381e8 0.0165113
\(806\) −6.34006e9 + 6.31055e9i −0.426502 + 0.424517i
\(807\) −1.46225e10 −0.979412
\(808\) −1.17850e10 + 6.80407e9i −0.785941 + 0.453763i
\(809\) 3.08448e9 + 5.34248e9i 0.204815 + 0.354751i 0.950074 0.312025i \(-0.101007\pi\)
−0.745258 + 0.666776i \(0.767674\pi\)
\(810\) −7.11401e8 + 1.23218e9i −0.0470345 + 0.0814662i
\(811\) 1.40103e8i 0.00922305i 0.999989 + 0.00461152i \(0.00146790\pi\)
−0.999989 + 0.00461152i \(0.998532\pi\)
\(812\) 1.89333e9 + 1.09312e9i 0.124103 + 0.0716507i
\(813\) −2.05080e10 1.18403e10i −1.33846 0.772762i
\(814\) 9.37081e8i 0.0608964i
\(815\) −1.85023e8 + 3.20470e8i −0.0119722 + 0.0207365i
\(816\) 4.44944e8 + 7.70666e8i 0.0286675 + 0.0496536i
\(817\) 4.09426e9 2.36382e9i 0.262663 0.151648i
\(818\) −6.29562e9 −0.402163
\(819\) −1.21633e9 1.22201e9i −0.0773672 0.0777289i
\(820\) −1.59360e9 −0.100933
\(821\) 8.37648e9 4.83616e9i 0.528275 0.305000i −0.212038 0.977261i \(-0.568010\pi\)
0.740314 + 0.672261i \(0.234677\pi\)
\(822\) −7.86726e7 1.36265e8i −0.00494051 0.00855722i
\(823\) −5.45059e9 + 9.44070e9i −0.340835 + 0.590344i −0.984588 0.174890i \(-0.944043\pi\)
0.643753 + 0.765233i \(0.277376\pi\)
\(824\) 1.20598e10i 0.750924i
\(825\) 6.92068e9 + 3.99566e9i 0.429102 + 0.247742i
\(826\) −5.65046e9 3.26230e9i −0.348862 0.201416i
\(827\) 1.84169e10i 1.13227i 0.824314 + 0.566133i \(0.191561\pi\)
−0.824314 + 0.566133i \(0.808439\pi\)
\(828\) −5.09642e8 + 8.82725e8i −0.0312003 + 0.0540405i
\(829\) 6.55515e9 + 1.13539e10i 0.399615 + 0.692154i 0.993678 0.112265i \(-0.0358104\pi\)
−0.594063 + 0.804418i \(0.702477\pi\)
\(830\) −1.76633e9 + 1.01979e9i −0.107226 + 0.0619067i
\(831\) −1.05266e10 −0.636333
\(832\) 2.38065e9 + 8.96832e9i 0.143306 + 0.539858i
\(833\) 2.42131e9 0.145142
\(834\) −4.88071e9 + 2.81788e9i −0.291341 + 0.168206i
\(835\) 1.37032e9 + 2.37346e9i 0.0814551 + 0.141084i
\(836\) −3.37117e9 + 5.83904e9i −0.199553 + 0.345636i
\(837\) 1.37188e10i 0.808683i
\(838\) 7.20950e9 + 4.16240e9i 0.423205 + 0.244338i
\(839\) 3.75138e9 + 2.16586e9i 0.219293 + 0.126609i 0.605623 0.795752i \(-0.292924\pi\)
−0.386330 + 0.922361i \(0.626257\pi\)
\(840\) 9.43442e8i 0.0549209i
\(841\) 5.59840e9 9.69671e9i 0.324547 0.562132i
\(842\) −3.58897e9 6.21628e9i −0.207194 0.358871i
\(843\) 3.72277e9 2.14934e9i 0.214028 0.123569i
\(844\) −6.55694e9 −0.375407
\(845\) 1.13090e9 + 1.98004e9i 0.0644799 + 0.112895i
\(846\) 5.22754e9 0.296826
\(847\) 4.64888e9 2.68403e9i 0.262880 0.151774i
\(848\) −8.38460e7 1.45226e8i −0.00472168 0.00817820i
\(849\) 1.45211e10 2.51512e10i 0.814369 1.41053i
\(850\) 1.07296e10i 0.599263i
\(851\) −1.19669e9 6.90911e8i −0.0665625 0.0384298i
\(852\) 1.49680e10 + 8.64180e9i 0.829137 + 0.478703i
\(853\) 1.29074e10i 0.712059i −0.934475 0.356029i \(-0.884130\pi\)
0.934475 0.356029i \(-0.115870\pi\)
\(854\) −3.32084e9 + 5.75186e9i −0.182450 + 0.316013i
\(855\) −4.84442e8 8.39079e8i −0.0265070 0.0459115i
\(856\) −1.13147e10 + 6.53254e9i −0.616573 + 0.355978i
\(857\) 8.88419e9 0.482153 0.241077 0.970506i \(-0.422499\pi\)
0.241077 + 0.970506i \(0.422499\pi\)
\(858\) 1.43538e9 + 5.40732e9i 0.0775819 + 0.292265i
\(859\) 6.08044e9 0.327310 0.163655 0.986518i \(-0.447672\pi\)
0.163655 + 0.986518i \(0.447672\pi\)
\(860\) −2.90107e8 + 1.67493e8i −0.0155530 + 0.00897951i
\(861\) −4.87639e9 8.44615e9i −0.260368 0.450970i
\(862\) 3.22806e9 5.59116e9i 0.171659 0.297322i
\(863\) 5.35711e9i 0.283722i −0.989887 0.141861i \(-0.954691\pi\)
0.989887 0.141861i \(-0.0453086\pi\)
\(864\) −1.34201e10 7.74809e9i −0.707876 0.408692i
\(865\) 8.03219e8 + 4.63739e8i 0.0421966 + 0.0243622i
\(866\) 1.00711e10i 0.526945i
\(867\) −3.51426e8 + 6.08688e8i −0.0183133 + 0.0317196i
\(868\) 2.33744e9 + 4.04856e9i 0.121317 + 0.210127i
\(869\) −6.21854e9 + 3.59028e9i −0.321454 + 0.185592i
\(870\) 1.01940e9 0.0524842
\(871\) −1.36681e10 1.37320e10i −0.700884 0.704161i
\(872\) −3.68818e9 −0.188367
\(873\) 5.46090e9 3.15285e9i 0.277789 0.160381i
\(874\) −2.79582e9 4.84251e9i −0.141651 0.245347i
\(875\) −9.65551e8 + 1.67238e9i −0.0487245 + 0.0843933i
\(876\) 1.56501e10i 0.786596i
\(877\) −2.01323e10 1.16234e10i −1.00785 0.581881i −0.0972867 0.995256i \(-0.531016\pi\)
−0.910561 + 0.413375i \(0.864350\pi\)
\(878\) 2.12349e9 + 1.22600e9i 0.105881 + 0.0611307i
\(879\) 2.37502e10i 1.17952i
\(880\) 2.89707e7 5.01788e7i 0.00143308 0.00248217i
\(881\) −4.25419e9 7.36847e9i −0.209605 0.363046i 0.741985 0.670416i \(-0.233884\pi\)
−0.951590 + 0.307370i \(0.900551\pi\)
\(882\) 4.38872e8 2.53383e8i 0.0215376 0.0124348i
\(883\) −6.83929e9 −0.334310 −0.167155 0.985931i \(-0.553458\pi\)
−0.167155 + 0.985931i \(0.553458\pi\)
\(884\) 9.46618e9 9.42212e9i 0.460884 0.458739i
\(885\) 5.40939e9 0.262329
\(886\) 1.99896e10 1.15410e10i 0.965576 0.557476i
\(887\) 5.68119e9 + 9.84012e9i 0.273342 + 0.473443i 0.969716 0.244237i \(-0.0785375\pi\)
−0.696373 + 0.717680i \(0.745204\pi\)
\(888\) −2.66729e9 + 4.61988e9i −0.127828 + 0.221404i
\(889\) 1.43924e10i 0.687032i
\(890\) 1.15527e9 + 6.66993e8i 0.0549310 + 0.0317144i
\(891\) −9.78474e9 5.64922e9i −0.463423 0.267557i
\(892\) 1.41817e10i 0.669038i
\(893\) 2.54952e10 4.41590e10i 1.19806 2.07510i
\(894\) −4.73736e9 8.20535e9i −0.221746 0.384075i
\(895\) −3.62480e9 + 2.09278e9i −0.169006 + 0.0975758i
\(896\) 5.52312e9 0.256511
\(897\) 7.96369e9 + 2.15378e9i 0.368418 + 0.0996388i
\(898\) 1.55639e10 0.717219
\(899\) −1.12093e10 + 6.47172e9i −0.514543 + 0.297071i
\(900\) −1.99644e9 3.45793e9i −0.0912866 0.158113i
\(901\) 2.11992e9 3.67180e9i 0.0965566 0.167241i
\(902\) 7.11718e9i 0.322913i
\(903\) −1.77544e9 1.02505e9i −0.0802415 0.0463274i
\(904\) −9.88345e9 5.70621e9i −0.444958 0.256897i
\(905\) 9.44019e7i 0.00423361i
\(906\) −9.46153e9 + 1.63879e10i −0.422681 + 0.732105i
\(907\) −1.73018e10 2.99677e10i −0.769957 1.33361i −0.937585 0.347755i \(-0.886944\pi\)
0.167628 0.985850i \(-0.446389\pi\)
\(908\) −1.60993e10 + 9.29492e9i −0.713684 + 0.412046i
\(909\) 6.06019e9 0.267616
\(910\) −6.47771e8 + 1.71951e8i −0.0284955 + 0.00756416i
\(911\) −1.78214e10 −0.780959 −0.390480 0.920612i \(-0.627691\pi\)
−0.390480 + 0.920612i \(0.627691\pi\)
\(912\) 1.57331e9 9.08349e8i 0.0686801 0.0396525i
\(913\) −8.09814e9 1.40264e10i −0.352158 0.609956i
\(914\) −6.19256e8 + 1.07258e9i −0.0268262 + 0.0464643i
\(915\) 5.50646e9i 0.237628i
\(916\) −1.66021e10 9.58523e9i −0.713722 0.412068i
\(917\) −4.67382e9 2.69843e9i −0.200161 0.115563i
\(918\) 1.15200e10i 0.491477i
\(919\) 1.09355e10 1.89408e10i 0.464765 0.804997i −0.534426 0.845215i \(-0.679472\pi\)
0.999191 + 0.0402188i \(0.0128055\pi\)
\(920\) 5.07622e8 + 8.79227e8i 0.0214923 + 0.0372258i
\(921\) 2.77402e10 1.60158e10i 1.17004 0.675522i
\(922\) −8.98131e9 −0.377382
\(923\) 8.21362e9 3.03701e10i 0.343818 1.27128i
\(924\) 2.92375e9 0.121924
\(925\) 4.68785e9 2.70653e9i 0.194750 0.112439i
\(926\) 3.58098e8 + 6.20244e8i 0.0148205 + 0.0256699i
\(927\) 2.68533e9 4.65114e9i 0.110718 0.191770i
\(928\) 1.46203e10i 0.600536i
\(929\) 1.64829e10 + 9.51639e9i 0.674494 + 0.389419i 0.797777 0.602952i \(-0.206009\pi\)
−0.123284 + 0.992371i \(0.539342\pi\)
\(930\) 1.88777e9 + 1.08991e9i 0.0769590 + 0.0444323i
\(931\) 4.94309e9i 0.200759i
\(932\) −4.86175e9 + 8.42079e9i −0.196715 + 0.340720i
\(933\) −6.60777e7 1.14450e8i −0.00266360 0.00461349i
\(934\) 1.71661e10 9.91087e9i 0.689379 0.398013i
\(935\) 1.46496e9 0.0586118
\(936\) 1.87001e9 6.91442e9i 0.0745380 0.275607i
\(937\) −3.09069e10 −1.22735 −0.613673 0.789560i \(-0.710309\pi\)
−0.613673 + 0.789560i \(0.710309\pi\)
\(938\) 4.93171e9 2.84732e9i 0.195113 0.112649i
\(939\) −2.32968e10 4.03512e10i −0.918262 1.59048i
\(940\) −1.80651e9 + 3.12897e9i −0.0709402 + 0.122872i
\(941\) 2.48692e10i 0.972967i 0.873690 + 0.486484i \(0.161721\pi\)
−0.873690 + 0.486484i \(0.838279\pi\)
\(942\) 2.56796e10 + 1.48261e10i 1.00095 + 0.577896i
\(943\) 9.08896e9 + 5.24751e9i 0.352958 + 0.203780i
\(944\) 2.28114e9i 0.0882571i
\(945\) 5.13922e8 8.90139e8i 0.0198101 0.0343120i
\(946\) 7.48041e8 + 1.29565e9i 0.0287281 + 0.0497585i
\(947\) −2.83328e10 + 1.63579e10i −1.08409 + 0.625898i −0.931996 0.362468i \(-0.881934\pi\)
−0.152091 + 0.988366i \(0.548601\pi\)
\(948\) 1.59526e10 0.608140
\(949\) −2.75341e10 + 7.30895e9i −1.04578 + 0.277603i
\(950\) 2.19044e10 0.828892
\(951\) 3.67046e10 2.11914e10i 1.38385 0.798965i
\(952\) 5.02950e9 + 8.71135e9i 0.188928 + 0.327232i
\(953\) 6.09887e9 1.05636e10i 0.228257 0.395353i −0.729034 0.684477i \(-0.760031\pi\)
0.957292 + 0.289124i \(0.0933639\pi\)
\(954\) 8.87371e8i 0.0330892i
\(955\) 1.29614e9 + 7.48324e8i 0.0481547 + 0.0278021i
\(956\) 2.65104e10 + 1.53058e10i 0.981326 + 0.566569i
\(957\) 8.09506e9i 0.298558i
\(958\) 4.01783e9 6.95908e9i 0.147643 0.255725i
\(959\) 7.48406e7 + 1.29628e8i 0.00274014 + 0.00474605i
\(960\) 1.95817e9 1.13055e9i 0.0714332 0.0412420i
\(961\) −1.64662e8 −0.00598495
\(962\) 3.65817e9 + 9.89354e8i 0.132480 + 0.0358294i
\(963\) 5.81834e9 0.209946
\(964\) −3.14602e9 + 1.81636e9i −0.113108 + 0.0653028i
\(965\) −2.90246e9 5.02721e9i −0.103973 0.180087i
\(966\) −1.21238e9 + 2.09991e9i −0.0432733 + 0.0749515i
\(967\) 4.47455e10i 1.59132i 0.605746 + 0.795658i \(0.292875\pi\)
−0.605746 + 0.795658i \(0.707125\pi\)
\(968\) 1.93131e10 + 1.11504e10i 0.684366 + 0.395119i
\(969\) 3.97786e10 + 2.29662e10i 1.40448 + 0.810878i
\(970\) 2.45110e9i 0.0862302i
\(971\) 1.94597e10 3.37051e10i 0.682131 1.18149i −0.292198 0.956358i \(-0.594387\pi\)
0.974329 0.225128i \(-0.0722799\pi\)
\(972\) 5.16321e9 + 8.94295e9i 0.180338 + 0.312355i
\(973\) 4.64298e9 2.68063e9i 0.161585 0.0932914i
\(974\) −6.87200e9 −0.238301
\(975\) −2.29050e10 + 2.27984e10i −0.791432 + 0.787749i
\(976\) 2.32207e9 0.0799468
\(977\) −2.92966e10 + 1.69144e10i −1.00505 + 0.580264i −0.909738 0.415183i \(-0.863717\pi\)
−0.0953097 + 0.995448i \(0.530384\pi\)
\(978\) −1.83582e9 3.17973e9i −0.0627544 0.108694i
\(979\) −5.29659e9 + 9.17395e9i −0.180408 + 0.312476i
\(980\) 3.50252e8i 0.0118875i
\(981\) 1.42243e9 + 8.21238e8i 0.0481048 + 0.0277733i
\(982\) 2.13972e10 + 1.23537e10i 0.721052 + 0.416300i
\(983\) 1.30404e10i 0.437879i 0.975738 + 0.218940i \(0.0702598\pi\)
−0.975738 + 0.218940i \(0.929740\pi\)
\(984\) 2.02582e10 3.50883e10i 0.677827 1.17403i
\(985\) 1.46090e9 + 2.53036e9i 0.0487073 + 0.0843636i
\(986\) −9.41273e9 + 5.43444e9i −0.312713 + 0.180545i
\(987\) −2.21115e10 −0.731996
\(988\) −1.92352e10 1.93251e10i −0.634522 0.637489i
\(989\) 2.20613e9 0.0725176
\(990\) 2.65530e8 1.53304e8i 0.00869741 0.00502145i
\(991\) −2.79541e9 4.84180e9i −0.0912407 0.158033i 0.816793 0.576931i \(-0.195750\pi\)
−0.908033 + 0.418898i \(0.862417\pi\)
\(992\) −1.56315e10 + 2.70745e10i −0.508405 + 0.880583i
\(993\) 6.17953e9i 0.200278i
\(994\) 8.00816e9 + 4.62351e9i 0.258631 + 0.149321i
\(995\) 2.36221e9 + 1.36382e9i 0.0760217 + 0.0438911i
\(996\) 3.59824e10i 1.15394i
\(997\) −5.76638e9 + 9.98766e9i −0.184276 + 0.319176i −0.943332 0.331849i \(-0.892328\pi\)
0.759056 + 0.651025i \(0.225661\pi\)
\(998\) −8.33055e9 1.44289e10i −0.265288 0.459492i
\(999\) −5.03319e9 + 2.90591e9i −0.159722 + 0.0922154i
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 91.8.q.a.36.19 100
13.4 even 6 inner 91.8.q.a.43.19 yes 100
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.8.q.a.36.19 100 1.1 even 1 trivial
91.8.q.a.43.19 yes 100 13.4 even 6 inner