Properties

Label 33.7.h.a.5.1
Level $33$
Weight $7$
Character 33.5
Analytic conductor $7.592$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [33,7,Mod(5,33)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(33, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 4]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("33.5");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 33.h (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.59178475946\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(22\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 5.1
Character \(\chi\) \(=\) 33.5
Dual form 33.7.h.a.20.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-14.6057 + 4.74569i) q^{2} +(25.8173 - 7.90347i) q^{3} +(139.029 - 101.011i) q^{4} +(-39.7419 - 12.9129i) q^{5} +(-339.574 + 237.957i) q^{6} +(-103.376 + 75.1073i) q^{7} +(-973.541 + 1339.96i) q^{8} +(604.070 - 408.093i) q^{9} +O(q^{10})\) \(q+(-14.6057 + 4.74569i) q^{2} +(25.8173 - 7.90347i) q^{3} +(139.029 - 101.011i) q^{4} +(-39.7419 - 12.9129i) q^{5} +(-339.574 + 237.957i) q^{6} +(-103.376 + 75.1073i) q^{7} +(-973.541 + 1339.96i) q^{8} +(604.070 - 408.093i) q^{9} +641.741 q^{10} +(-961.175 - 920.708i) q^{11} +(2791.03 - 3706.64i) q^{12} +(-481.959 - 1483.32i) q^{13} +(1153.45 - 1587.59i) q^{14} +(-1128.09 - 19.2784i) q^{15} +(4461.55 - 13731.2i) q^{16} +(5866.57 + 1906.16i) q^{17} +(-6886.21 + 8827.24i) q^{18} +(-6525.83 - 4741.29i) q^{19} +(-6829.62 + 2219.08i) q^{20} +(-2075.29 + 2756.10i) q^{21} +(18408.1 + 8886.18i) q^{22} -18919.1i q^{23} +(-14543.9 + 42288.7i) q^{24} +(-11228.2 - 8157.78i) q^{25} +(14078.7 + 19377.7i) q^{26} +(12370.1 - 15310.1i) q^{27} +(-6785.69 + 20884.2i) q^{28} +(-14056.7 - 19347.4i) q^{29} +(16568.0 - 5071.98i) q^{30} +(4426.50 + 13623.4i) q^{31} +115726. i q^{32} +(-32091.8 - 16173.6i) q^{33} -94731.6 q^{34} +(5078.23 - 1650.02i) q^{35} +(42761.6 - 117754. i) q^{36} +(49079.2 - 35658.1i) q^{37} +(117815. + 38280.5i) q^{38} +(-24166.2 - 34486.1i) q^{39} +(55993.2 - 40681.5i) q^{40} +(18284.4 - 25166.3i) q^{41} +(17231.6 - 50103.7i) q^{42} -4482.89 q^{43} +(-226633. - 30916.3i) q^{44} +(-29276.6 + 8418.09i) q^{45} +(89784.5 + 276328. i) q^{46} +(-69320.2 + 95411.1i) q^{47} +(6660.88 - 389766. i) q^{48} +(-31310.0 + 96362.2i) q^{49} +(202711. + 65864.7i) q^{50} +(166524. + 2845.81i) q^{51} +(-216837. - 157541. i) q^{52} +(-100122. + 32531.8i) q^{53} +(-108018. + 282321. i) q^{54} +(26309.9 + 49002.3i) q^{55} -211641. i q^{56} +(-205952. - 70830.8i) q^{57} +(297126. + 215874. i) q^{58} +(16205.0 + 22304.3i) q^{59} +(-158784. + 111268. i) q^{60} +(29326.2 - 90256.7i) q^{61} +(-129305. - 177973. i) q^{62} +(-31795.8 + 87557.3i) q^{63} +(-263660. - 811461. i) q^{64} +65173.3i q^{65} +(545479. + 83929.8i) q^{66} +481745. q^{67} +(1.00817e6 - 327573. i) q^{68} +(-149527. - 488442. i) q^{69} +(-66340.8 + 48199.4i) q^{70} +(-254376. - 82651.7i) q^{71} +(-41256.7 + 1.20673e6i) q^{72} +(507.126 - 368.449i) q^{73} +(-547616. + 753728. i) q^{74} +(-354357. - 121870. i) q^{75} -1.38620e6 q^{76} +(168515. + 22988.1i) q^{77} +(516627. + 389010. i) q^{78} +(100133. + 308177. i) q^{79} +(-354621. + 488094. i) q^{80} +(198361. - 493034. i) q^{81} +(-147626. + 454345. i) q^{82} +(185088. + 60138.8i) q^{83} +(-10130.7 + 592805. i) q^{84} +(-208534. - 151509. i) q^{85} +(65476.0 - 21274.4i) q^{86} +(-515819. - 388402. i) q^{87} +(2.16946e6 - 391593. i) q^{88} +513296. i q^{89} +(387657. - 261890. i) q^{90} +(161231. + 117141. i) q^{91} +(-1.91103e6 - 2.63031e6i) q^{92} +(221953. + 316735. i) q^{93} +(559682. - 1.72252e6i) q^{94} +(198125. + 272695. i) q^{95} +(914635. + 2.98773e6i) q^{96} +(359768. + 1.10725e6i) q^{97} -1.55603e6i q^{98} +(-956352. - 163923. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q + 33 q^{3} + 634 q^{4} + 109 q^{6} + 402 q^{7} - 2471 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 88 q + 33 q^{3} + 634 q^{4} + 109 q^{6} + 402 q^{7} - 2471 q^{9} - 1016 q^{10} + 7594 q^{12} - 1830 q^{13} - 6973 q^{15} - 15506 q^{16} - 291 q^{18} - 32466 q^{19} + 5434 q^{21} + 40940 q^{22} + 10011 q^{24} + 68152 q^{25} + 65385 q^{27} - 37986 q^{28} + 20928 q^{30} + 96222 q^{31} - 67159 q^{33} - 186548 q^{34} - 107169 q^{36} - 112854 q^{37} - 257545 q^{39} + 246958 q^{40} - 130324 q^{42} + 40328 q^{43} + 505478 q^{45} - 30630 q^{46} + 647882 q^{48} - 327700 q^{49} + 88197 q^{51} - 132630 q^{52} - 1639642 q^{54} - 216226 q^{55} + 174477 q^{57} + 1571894 q^{58} + 772854 q^{60} + 559626 q^{61} + 1129495 q^{63} + 1406654 q^{64} + 34620 q^{66} - 3229336 q^{67} - 2492844 q^{69} - 2066360 q^{70} - 2672882 q^{72} + 1068798 q^{73} - 1207057 q^{75} + 913268 q^{76} + 6763180 q^{78} - 255558 q^{79} + 3363409 q^{81} - 3580072 q^{82} - 2958906 q^{84} - 2098978 q^{85} + 365046 q^{87} + 2251838 q^{88} - 813500 q^{90} + 7887166 q^{91} + 4000307 q^{93} + 11260802 q^{94} + 4588186 q^{96} + 3850038 q^{97} - 1274785 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −14.6057 + 4.74569i −1.82572 + 0.593212i −0.826162 + 0.563433i \(0.809480\pi\)
−0.999557 + 0.0297789i \(0.990520\pi\)
\(3\) 25.8173 7.90347i 0.956198 0.292721i
\(4\) 139.029 101.011i 2.17233 1.57829i
\(5\) −39.7419 12.9129i −0.317935 0.103303i 0.145702 0.989329i \(-0.453456\pi\)
−0.463637 + 0.886025i \(0.653456\pi\)
\(6\) −339.574 + 237.957i −1.57210 + 1.10165i
\(7\) −103.376 + 75.1073i −0.301389 + 0.218972i −0.728193 0.685372i \(-0.759639\pi\)
0.426804 + 0.904344i \(0.359639\pi\)
\(8\) −973.541 + 1339.96i −1.90145 + 2.61712i
\(9\) 604.070 408.093i 0.828629 0.559799i
\(10\) 641.741 0.641741
\(11\) −961.175 920.708i −0.722145 0.691741i
\(12\) 2791.03 3706.64i 1.61518 2.14504i
\(13\) −481.959 1483.32i −0.219371 0.675155i −0.998814 0.0486823i \(-0.984498\pi\)
0.779443 0.626473i \(-0.215502\pi\)
\(14\) 1153.45 1587.59i 0.420354 0.578568i
\(15\) −1128.09 19.2784i −0.334248 0.00571212i
\(16\) 4461.55 13731.2i 1.08924 3.35235i
\(17\) 5866.57 + 1906.16i 1.19409 + 0.387983i 0.837584 0.546309i \(-0.183968\pi\)
0.356507 + 0.934293i \(0.383968\pi\)
\(18\) −6886.21 + 8827.24i −1.18076 + 1.51359i
\(19\) −6525.83 4741.29i −0.951425 0.691251i −0.000281797 1.00000i \(-0.500090\pi\)
−0.951144 + 0.308749i \(0.900090\pi\)
\(20\) −6829.62 + 2219.08i −0.853703 + 0.277385i
\(21\) −2075.29 + 2756.10i −0.224090 + 0.297603i
\(22\) 18408.1 + 8886.18i 1.72878 + 0.834540i
\(23\) 18919.1i 1.55495i −0.628911 0.777477i \(-0.716499\pi\)
0.628911 0.777477i \(-0.283501\pi\)
\(24\) −14543.9 + 42288.7i −1.05207 + 3.05907i
\(25\) −11228.2 8157.78i −0.718606 0.522098i
\(26\) 14078.7 + 19377.7i 0.801020 + 1.10251i
\(27\) 12370.1 15310.1i 0.628468 0.777836i
\(28\) −6785.69 + 20884.2i −0.309115 + 0.951358i
\(29\) −14056.7 19347.4i −0.576355 0.793284i 0.416935 0.908936i \(-0.363104\pi\)
−0.993290 + 0.115652i \(0.963104\pi\)
\(30\) 16568.0 5071.98i 0.613631 0.187851i
\(31\) 4426.50 + 13623.4i 0.148585 + 0.457298i 0.997455 0.0713043i \(-0.0227161\pi\)
−0.848869 + 0.528603i \(0.822716\pi\)
\(32\) 115726.i 3.53167i
\(33\) −32091.8 16173.6i −0.893001 0.450054i
\(34\) −94731.6 −2.41023
\(35\) 5078.23 1650.02i 0.118443 0.0384843i
\(36\) 42761.6 117754.i 0.916530 2.52388i
\(37\) 49079.2 35658.1i 0.968930 0.703969i 0.0137223 0.999906i \(-0.495632\pi\)
0.955207 + 0.295937i \(0.0956319\pi\)
\(38\) 117815. + 38280.5i 2.14709 + 0.697633i
\(39\) −24166.2 34486.1i −0.407395 0.581367i
\(40\) 55993.2 40681.5i 0.874894 0.635648i
\(41\) 18284.4 25166.3i 0.265295 0.365147i −0.655499 0.755196i \(-0.727542\pi\)
0.920794 + 0.390049i \(0.127542\pi\)
\(42\) 17231.6 50103.7i 0.232583 0.676272i
\(43\) −4482.89 −0.0563836 −0.0281918 0.999603i \(-0.508975\pi\)
−0.0281918 + 0.999603i \(0.508975\pi\)
\(44\) −226633. 30916.3i −2.66051 0.362936i
\(45\) −29276.6 + 8418.09i −0.321279 + 0.0923796i
\(46\) 89784.5 + 276328.i 0.922418 + 2.83891i
\(47\) −69320.2 + 95411.1i −0.667677 + 0.918978i −0.999705 0.0242912i \(-0.992267\pi\)
0.332028 + 0.943269i \(0.392267\pi\)
\(48\) 6660.88 389766.i 0.0602293 3.52436i
\(49\) −31310.0 + 96362.2i −0.266130 + 0.819065i
\(50\) 202711. + 65864.7i 1.62169 + 0.526918i
\(51\) 166524. + 2845.81i 1.25536 + 0.0214534i
\(52\) −216837. 157541.i −1.54214 1.12043i
\(53\) −100122. + 32531.8i −0.672518 + 0.218514i −0.625317 0.780371i \(-0.715030\pi\)
−0.0472013 + 0.998885i \(0.515030\pi\)
\(54\) −108018. + 282321.i −0.685984 + 1.79292i
\(55\) 26309.9 + 49002.3i 0.158136 + 0.294529i
\(56\) 211641.i 1.20513i
\(57\) −205952. 70830.8i −1.11209 0.382470i
\(58\) 297126. + 215874.i 1.52285 + 1.10641i
\(59\) 16205.0 + 22304.3i 0.0789031 + 0.108601i 0.846644 0.532159i \(-0.178619\pi\)
−0.767741 + 0.640760i \(0.778619\pi\)
\(60\) −158784. + 111268.i −0.735113 + 0.515132i
\(61\) 29326.2 90256.7i 0.129201 0.397640i −0.865442 0.501009i \(-0.832962\pi\)
0.994643 + 0.103369i \(0.0329623\pi\)
\(62\) −129305. 177973.i −0.542550 0.746756i
\(63\) −31795.8 + 87557.3i −0.127159 + 0.350163i
\(64\) −263660. 811461.i −1.00578 3.09548i
\(65\) 65173.3i 0.237317i
\(66\) 545479. + 83929.8i 1.89735 + 0.291934i
\(67\) 481745. 1.60174 0.800871 0.598836i \(-0.204370\pi\)
0.800871 + 0.598836i \(0.204370\pi\)
\(68\) 1.00817e6 327573.i 3.20631 1.04179i
\(69\) −149527. 488442.i −0.455168 1.48684i
\(70\) −66340.8 + 48199.4i −0.193414 + 0.140523i
\(71\) −254376. 82651.7i −0.710724 0.230928i −0.0687271 0.997635i \(-0.521894\pi\)
−0.641997 + 0.766707i \(0.721894\pi\)
\(72\) −41256.7 + 1.20673e6i −0.110534 + 3.23304i
\(73\) 507.126 368.449i 0.00130361 0.000947128i −0.587133 0.809490i \(-0.699744\pi\)
0.588437 + 0.808543i \(0.299744\pi\)
\(74\) −547616. + 753728.i −1.35139 + 1.86003i
\(75\) −354357. 121870.i −0.839958 0.288877i
\(76\) −1.38620e6 −3.15780
\(77\) 168515. + 22988.1i 0.369118 + 0.0503537i
\(78\) 516627. + 389010.i 1.08866 + 0.819742i
\(79\) 100133. + 308177.i 0.203093 + 0.625056i 0.999786 + 0.0206723i \(0.00658066\pi\)
−0.796693 + 0.604384i \(0.793419\pi\)
\(80\) −354621. + 488094.i −0.692619 + 0.953308i
\(81\) 198361. 493034.i 0.373251 0.927731i
\(82\) −147626. + 454345.i −0.267744 + 0.824032i
\(83\) 185088. + 60138.8i 0.323701 + 0.105177i 0.466360 0.884595i \(-0.345565\pi\)
−0.142659 + 0.989772i \(0.545565\pi\)
\(84\) −10130.7 + 592805.i −0.0170924 + 1.00017i
\(85\) −208534. 151509.i −0.339563 0.246707i
\(86\) 65476.0 21274.4i 0.102941 0.0334474i
\(87\) −515819. 388402.i −0.783320 0.589825i
\(88\) 2.16946e6 391593.i 3.18349 0.574629i
\(89\) 513296.i 0.728112i 0.931377 + 0.364056i \(0.118608\pi\)
−0.931377 + 0.364056i \(0.881392\pi\)
\(90\) 387657. 261890.i 0.531765 0.359246i
\(91\) 161231. + 117141.i 0.213956 + 0.155448i
\(92\) −1.91103e6 2.63031e6i −2.45417 3.37788i
\(93\) 221953. + 316735.i 0.275938 + 0.393774i
\(94\) 559682. 1.72252e6i 0.673841 2.07387i
\(95\) 198125. + 272695.i 0.231083 + 0.318059i
\(96\) 914635. + 2.98773e6i 1.03379 + 3.37697i
\(97\) 359768. + 1.10725e6i 0.394192 + 1.21320i 0.929589 + 0.368597i \(0.120162\pi\)
−0.535398 + 0.844600i \(0.679838\pi\)
\(98\) 1.55603e6i 1.65325i
\(99\) −956352. 163923.i −0.985626 0.168941i
\(100\) −2.38507e6 −2.38507
\(101\) 712178. 231401.i 0.691233 0.224595i 0.0577261 0.998332i \(-0.481615\pi\)
0.633506 + 0.773737i \(0.281615\pi\)
\(102\) −2.44572e6 + 748709.i −2.30466 + 0.705525i
\(103\) −418895. + 304345.i −0.383349 + 0.278519i −0.762724 0.646724i \(-0.776139\pi\)
0.379376 + 0.925243i \(0.376139\pi\)
\(104\) 2.45680e6 + 798261.i 2.18408 + 0.709652i
\(105\) 118066. 82734.7i 0.101989 0.0714693i
\(106\) 1.30798e6 950301.i 1.09820 0.797891i
\(107\) 471960. 649597.i 0.385260 0.530264i −0.571709 0.820457i \(-0.693719\pi\)
0.956968 + 0.290192i \(0.0937193\pi\)
\(108\) 173323. 3.37807e6i 0.137589 2.68162i
\(109\) −1.10215e6 −0.851061 −0.425531 0.904944i \(-0.639913\pi\)
−0.425531 + 0.904944i \(0.639913\pi\)
\(110\) −616826. 590856.i −0.463430 0.443919i
\(111\) 985271. 1.30849e6i 0.720422 0.956760i
\(112\) 570097. + 1.75458e6i 0.405784 + 1.24887i
\(113\) 1.11478e6 1.53436e6i 0.772596 1.06339i −0.223465 0.974712i \(-0.571737\pi\)
0.996061 0.0886748i \(-0.0282632\pi\)
\(114\) 3.34423e6 + 57151.0i 2.25726 + 0.0385753i
\(115\) −244301. + 751883.i −0.160632 + 0.494375i
\(116\) −3.90859e6 1.26998e6i −2.50407 0.813620i
\(117\) −896468. 699343.i −0.559728 0.436649i
\(118\) −342536. 248867.i −0.208478 0.151468i
\(119\) −749631. + 243570.i −0.444843 + 0.144538i
\(120\) 1.12407e6 1.49283e6i 0.650504 0.863905i
\(121\) 76154.9 + 1.76992e6i 0.0429875 + 0.999076i
\(122\) 1.45744e6i 0.802622i
\(123\) 273153. 794237.i 0.146788 0.426810i
\(124\) 1.99152e6 + 1.44692e6i 1.04453 + 0.758892i
\(125\) 724669. + 997421.i 0.371030 + 0.510680i
\(126\) 48881.0 1.42973e6i 0.0244359 0.714732i
\(127\) 516908. 1.59088e6i 0.252349 0.776652i −0.741991 0.670410i \(-0.766118\pi\)
0.994340 0.106242i \(-0.0338818\pi\)
\(128\) 3.34850e6 + 4.60881e6i 1.59669 + 2.19765i
\(129\) −115736. + 35430.4i −0.0539139 + 0.0165047i
\(130\) −309293. 951905.i −0.140780 0.433275i
\(131\) 2.60139e6i 1.15716i 0.815627 + 0.578578i \(0.196392\pi\)
−0.815627 + 0.578578i \(0.803608\pi\)
\(132\) −6.09540e6 + 993007.i −2.65021 + 0.431748i
\(133\) 1.03072e6 0.438113
\(134\) −7.03625e6 + 2.28621e6i −2.92433 + 0.950173i
\(135\) −689311. + 448719.i −0.280165 + 0.182378i
\(136\) −8.26553e6 + 6.00526e6i −3.28590 + 2.38734i
\(137\) 1.92209e6 + 624526.i 0.747503 + 0.242879i 0.657907 0.753100i \(-0.271442\pi\)
0.0895967 + 0.995978i \(0.471442\pi\)
\(138\) 4.50195e6 + 6.42445e6i 1.71302 + 2.44455i
\(139\) 792082. 575481.i 0.294935 0.214283i −0.430471 0.902605i \(-0.641652\pi\)
0.725405 + 0.688322i \(0.241652\pi\)
\(140\) 539353. 742355.i 0.196557 0.270538i
\(141\) −1.03558e6 + 3.01113e6i −0.369427 + 1.07417i
\(142\) 4.10759e6 1.43457
\(143\) −902454. + 1.86947e6i −0.308615 + 0.639308i
\(144\) −2.90854e6 1.01154e7i −0.974063 3.38761i
\(145\) 308809. + 950416.i 0.101295 + 0.311752i
\(146\) −5658.41 + 7788.14i −0.00181818 + 0.00250250i
\(147\) −46744.3 + 2.73527e6i −0.0147156 + 0.861090i
\(148\) 3.22159e6 9.91504e6i 0.993768 3.05850i
\(149\) 116753. + 37935.4i 0.0352947 + 0.0114679i 0.326611 0.945159i \(-0.394093\pi\)
−0.291316 + 0.956627i \(0.594093\pi\)
\(150\) 5.75401e6 + 98332.9i 1.70489 + 0.0291357i
\(151\) −4.47352e6 3.25020e6i −1.29933 0.944016i −0.299378 0.954135i \(-0.596779\pi\)
−0.999949 + 0.0101185i \(0.996779\pi\)
\(152\) 1.27063e7 4.12853e6i 3.61817 1.17561i
\(153\) 4.32171e6 1.24265e6i 1.20665 0.346956i
\(154\) −2.57038e6 + 463961.i −0.703776 + 0.127034i
\(155\) 598578.i 0.160741i
\(156\) −6.84328e6 2.35353e6i −1.80256 0.619935i
\(157\) 3.22678e6 + 2.34439e6i 0.833816 + 0.605803i 0.920636 0.390421i \(-0.127671\pi\)
−0.0868203 + 0.996224i \(0.527671\pi\)
\(158\) −2.92503e6 4.02596e6i −0.741581 1.02070i
\(159\) −2.32778e6 + 1.63120e6i −0.579097 + 0.405803i
\(160\) 1.49436e6 4.59916e6i 0.364833 1.12284i
\(161\) 1.42097e6 + 1.95579e6i 0.340491 + 0.468646i
\(162\) −557417. + 8.14249e6i −0.131110 + 1.91519i
\(163\) −945419. 2.90970e6i −0.218304 0.671870i −0.998903 0.0468377i \(-0.985086\pi\)
0.780599 0.625033i \(-0.214914\pi\)
\(164\) 5.34577e6i 1.21193i
\(165\) 1.06654e6 + 1.05717e6i 0.237424 + 0.235338i
\(166\) −2.98875e6 −0.653380
\(167\) −729534. + 237040.i −0.156638 + 0.0508946i −0.386286 0.922379i \(-0.626242\pi\)
0.229649 + 0.973274i \(0.426242\pi\)
\(168\) −1.67270e6 5.46400e6i −0.352768 1.15235i
\(169\) 1.93703e6 1.40733e6i 0.401306 0.291566i
\(170\) 3.76482e6 + 1.22326e6i 0.766297 + 0.248985i
\(171\) −5.87695e6 200926.i −1.17534 0.0401836i
\(172\) −623252. + 452819.i −0.122484 + 0.0889897i
\(173\) 336444. 463075.i 0.0649792 0.0894362i −0.775291 0.631605i \(-0.782397\pi\)
0.840270 + 0.542169i \(0.182397\pi\)
\(174\) 9.37715e6 + 3.22498e6i 1.78001 + 0.612180i
\(175\) 1.77344e6 0.330904
\(176\) −1.69308e7 + 9.09034e6i −3.10555 + 1.66741i
\(177\) 594652. + 447762.i 0.107237 + 0.0807472i
\(178\) −2.43595e6 7.49708e6i −0.431925 1.32933i
\(179\) 776704. 1.06904e6i 0.135424 0.186395i −0.735919 0.677070i \(-0.763250\pi\)
0.871343 + 0.490674i \(0.163250\pi\)
\(180\) −3.21998e6 + 4.12760e6i −0.552123 + 0.707751i
\(181\) −957882. + 2.94806e6i −0.161539 + 0.497165i −0.998765 0.0496924i \(-0.984176\pi\)
0.837226 + 0.546857i \(0.184176\pi\)
\(182\) −2.91082e6 945781.i −0.482837 0.156883i
\(183\) 43782.6 2.56197e6i 0.00714412 0.418043i
\(184\) 2.53510e7 + 1.84185e7i 4.06950 + 2.95666i
\(185\) −2.41095e6 + 783366.i −0.380779 + 0.123723i
\(186\) −4.74491e6 3.57283e6i −0.737376 0.555230i
\(187\) −3.88378e6 7.23355e6i −0.593922 1.10618i
\(188\) 2.02670e7i 3.05011i
\(189\) −128876. + 2.51179e6i −0.0190891 + 0.372048i
\(190\) −4.18789e6 3.04268e6i −0.610569 0.443604i
\(191\) 320815. + 441564.i 0.0460421 + 0.0633715i 0.831417 0.555649i \(-0.187530\pi\)
−0.785375 + 0.619020i \(0.787530\pi\)
\(192\) −1.32204e7 1.88659e7i −1.86784 2.66548i
\(193\) 203998. 627840.i 0.0283761 0.0873327i −0.935865 0.352357i \(-0.885380\pi\)
0.964242 + 0.265025i \(0.0853801\pi\)
\(194\) −1.05094e7 1.44649e7i −1.43937 1.98112i
\(195\) 515096. + 1.68260e6i 0.0694679 + 0.226922i
\(196\) 5.38060e6 + 1.65598e7i 0.714600 + 2.19931i
\(197\) 4.65950e6i 0.609454i −0.952440 0.304727i \(-0.901435\pi\)
0.952440 0.304727i \(-0.0985652\pi\)
\(198\) 1.47462e7 2.14434e6i 1.89969 0.276247i
\(199\) −5.84397e6 −0.741564 −0.370782 0.928720i \(-0.620910\pi\)
−0.370782 + 0.928720i \(0.620910\pi\)
\(200\) 2.18622e7 7.10347e6i 2.73278 0.887934i
\(201\) 1.24374e7 3.80746e6i 1.53158 0.468864i
\(202\) −9.30373e6 + 6.75956e6i −1.12876 + 0.820095i
\(203\) 2.90626e6 + 944302.i 0.347414 + 0.112882i
\(204\) 2.34392e7 1.64251e7i 2.76091 1.93471i
\(205\) −1.05163e6 + 764052.i −0.122068 + 0.0886873i
\(206\) 4.67395e6 6.43314e6i 0.534666 0.735904i
\(207\) −7.72077e6 1.14285e7i −0.870462 1.28848i
\(208\) −2.25180e7 −2.50231
\(209\) 1.90712e6 + 1.05656e7i 0.208900 + 1.15732i
\(210\) −1.33180e6 + 1.76870e6i −0.143807 + 0.190984i
\(211\) −5.10709e6 1.57180e7i −0.543658 1.67321i −0.724160 0.689632i \(-0.757772\pi\)
0.180502 0.983575i \(-0.442228\pi\)
\(212\) −1.06339e7 + 1.46363e7i −1.11605 + 1.53611i
\(213\) −7.22054e6 123395.i −0.747190 0.0127691i
\(214\) −3.81053e6 + 1.17276e7i −0.388816 + 1.19665i
\(215\) 178159. + 57887.2i 0.0179263 + 0.00582462i
\(216\) 8.47220e6 + 3.14806e7i 0.840688 + 3.12379i
\(217\) −1.48081e6 1.07587e6i −0.144917 0.105289i
\(218\) 1.60977e7 5.23046e6i 1.55380 0.504860i
\(219\) 10180.6 13520.4i 0.000969264 0.00128724i
\(220\) 8.60759e6 + 4.15517e6i 0.808376 + 0.390230i
\(221\) 9.62066e6i 0.891309i
\(222\) −8.18091e6 + 2.37873e7i −0.747726 + 2.17414i
\(223\) 1.67059e6 + 1.21376e6i 0.150645 + 0.109450i 0.660555 0.750778i \(-0.270321\pi\)
−0.509909 + 0.860228i \(0.670321\pi\)
\(224\) −8.69184e6 1.19633e7i −0.773335 1.06440i
\(225\) −1.01118e7 345710.i −0.887727 0.0303504i
\(226\) −9.00054e6 + 2.77008e7i −0.779729 + 2.39976i
\(227\) −6.17568e6 8.50010e6i −0.527968 0.726686i 0.458851 0.888513i \(-0.348261\pi\)
−0.986819 + 0.161828i \(0.948261\pi\)
\(228\) −3.57880e7 + 1.09558e7i −3.01949 + 0.924356i
\(229\) −5.79303e6 1.78291e7i −0.482391 1.48465i −0.835724 0.549149i \(-0.814952\pi\)
0.353333 0.935497i \(-0.385048\pi\)
\(230\) 1.21412e7i 0.997878i
\(231\) 4.53229e6 738359.i 0.367690 0.0599007i
\(232\) 3.96096e7 3.17202
\(233\) 1.75604e7 5.70572e6i 1.38825 0.451069i 0.482875 0.875689i \(-0.339592\pi\)
0.905372 + 0.424620i \(0.139592\pi\)
\(234\) 1.64125e7 + 5.96006e6i 1.28093 + 0.465161i
\(235\) 3.98695e6 2.89669e6i 0.307212 0.223202i
\(236\) 4.50594e6 + 1.46407e6i 0.342807 + 0.111385i
\(237\) 5.02083e6 + 7.16492e6i 0.377164 + 0.538228i
\(238\) 9.79301e6 7.11504e6i 0.726416 0.527772i
\(239\) −1.02794e7 + 1.41483e7i −0.752961 + 1.03636i 0.244806 + 0.969572i \(0.421276\pi\)
−0.997767 + 0.0667901i \(0.978724\pi\)
\(240\) −5.29773e6 + 1.54040e7i −0.383227 + 1.11430i
\(241\) 2.29976e7 1.64298 0.821488 0.570226i \(-0.193144\pi\)
0.821488 + 0.570226i \(0.193144\pi\)
\(242\) −9.51182e6 2.54896e7i −0.671146 1.79853i
\(243\) 1.22446e6 1.42966e7i 0.0853350 0.996352i
\(244\) −5.03969e6 1.55106e7i −0.346924 1.06772i
\(245\) 2.48864e6 3.42531e6i 0.169224 0.232918i
\(246\) −220398. + 1.28967e7i −0.0148048 + 0.866312i
\(247\) −3.88765e6 + 1.19650e7i −0.257986 + 0.794001i
\(248\) −2.25642e7 7.33156e6i −1.47933 0.480664i
\(249\) 5.25379e6 + 89784.4i 0.340310 + 0.00581571i
\(250\) −1.53178e7 1.11290e7i −0.980338 0.712257i
\(251\) −1.88585e7 + 6.12751e6i −1.19258 + 0.387492i −0.837026 0.547164i \(-0.815707\pi\)
−0.355553 + 0.934656i \(0.615707\pi\)
\(252\) 4.42367e6 + 1.53847e7i 0.276428 + 0.961364i
\(253\) −1.74190e7 + 1.81846e7i −1.07563 + 1.12290i
\(254\) 2.56891e7i 1.56764i
\(255\) −6.58125e6 2.26342e6i −0.396906 0.136504i
\(256\) −2.66020e7 1.93275e7i −1.58560 1.15201i
\(257\) 839502. + 1.15548e6i 0.0494564 + 0.0680709i 0.833029 0.553229i \(-0.186605\pi\)
−0.783573 + 0.621300i \(0.786605\pi\)
\(258\) 1.52227e6 1.06674e6i 0.0886408 0.0621152i
\(259\) −2.39544e6 + 7.37241e6i −0.137875 + 0.424336i
\(260\) 6.58319e6 + 9.06099e6i 0.374556 + 0.515532i
\(261\) −1.63868e7 5.95074e6i −0.921664 0.334695i
\(262\) −1.23454e7 3.79953e7i −0.686438 2.11264i
\(263\) 1.03039e7i 0.566414i 0.959059 + 0.283207i \(0.0913984\pi\)
−0.959059 + 0.283207i \(0.908602\pi\)
\(264\) 5.29147e7 2.72562e7i 2.87584 1.48133i
\(265\) 4.39914e6 0.236391
\(266\) −1.50545e7 + 4.89149e6i −0.799872 + 0.259894i
\(267\) 4.05682e6 + 1.32519e7i 0.213134 + 0.696219i
\(268\) 6.69766e7 4.86613e7i 3.47951 2.52802i
\(269\) 2.53170e7 + 8.22599e6i 1.30063 + 0.422602i 0.875802 0.482671i \(-0.160333\pi\)
0.424832 + 0.905272i \(0.360333\pi\)
\(270\) 7.93842e6 9.82514e6i 0.403314 0.499169i
\(271\) 9.57678e6 6.95794e6i 0.481185 0.349601i −0.320599 0.947215i \(-0.603884\pi\)
0.801784 + 0.597614i \(0.203884\pi\)
\(272\) 5.23479e7 7.20507e7i 2.60131 3.58040i
\(273\) 5.08838e6 + 1.74999e6i 0.250087 + 0.0860097i
\(274\) −3.10374e7 −1.50881
\(275\) 3.28135e6 + 1.81790e7i 0.157781 + 0.874120i
\(276\) −7.01264e7 5.28038e7i −3.33545 2.51153i
\(277\) 1.08080e7 + 3.32637e7i 0.508520 + 1.56506i 0.794772 + 0.606909i \(0.207591\pi\)
−0.286252 + 0.958154i \(0.592409\pi\)
\(278\) −8.83789e6 + 1.21643e7i −0.411353 + 0.566178i
\(279\) 8.23353e6 + 6.42305e6i 0.379117 + 0.295753i
\(280\) −2.73290e6 + 8.41100e6i −0.124494 + 0.383154i
\(281\) −7.12384e6 2.31468e6i −0.321067 0.104321i 0.144050 0.989570i \(-0.453988\pi\)
−0.465116 + 0.885250i \(0.653988\pi\)
\(282\) 835578. 4.88944e7i 0.0372597 2.18028i
\(283\) 7.71161e6 + 5.60281e6i 0.340240 + 0.247199i 0.744763 0.667329i \(-0.232562\pi\)
−0.404523 + 0.914528i \(0.632562\pi\)
\(284\) −4.37144e7 + 1.42037e7i −1.90840 + 0.620076i
\(285\) 7.27030e6 + 5.47440e6i 0.314064 + 0.236484i
\(286\) 4.30908e6 3.15878e7i 0.184199 1.35027i
\(287\) 3.97489e6i 0.168143i
\(288\) 4.72269e7 + 6.99064e7i 1.97702 + 2.92644i
\(289\) 1.12554e7 + 8.17755e6i 0.466304 + 0.338789i
\(290\) −9.02077e6 1.24160e7i −0.369870 0.509083i
\(291\) 1.80394e7 + 2.57429e7i 0.732054 + 1.04467i
\(292\) 33288.1 102450.i 0.00133703 0.00411495i
\(293\) −9.51969e6 1.31027e7i −0.378460 0.520906i 0.576716 0.816945i \(-0.304334\pi\)
−0.955176 + 0.296039i \(0.904334\pi\)
\(294\) −1.22980e7 4.01725e7i −0.483943 1.58084i
\(295\) −356005. 1.09567e6i −0.0138672 0.0426790i
\(296\) 1.00479e8i 3.87436i
\(297\) −2.59860e7 + 3.32645e6i −0.991906 + 0.126973i
\(298\) −1.88530e6 −0.0712411
\(299\) −2.80631e7 + 9.11824e6i −1.04984 + 0.341112i
\(300\) −6.15762e7 + 1.88503e7i −2.28060 + 0.698161i
\(301\) 463425. 336698.i 0.0169934 0.0123464i
\(302\) 8.07635e7 + 2.62417e7i 2.93221 + 0.952731i
\(303\) 1.65577e7 1.16028e7i 0.595211 0.417096i
\(304\) −9.42190e7 + 6.84541e7i −3.35365 + 2.43657i
\(305\) −2.33096e6 + 3.20829e6i −0.0821552 + 0.113077i
\(306\) −5.72246e7 + 3.86594e7i −1.99718 + 1.34924i
\(307\) 4.31477e6 0.149122 0.0745611 0.997216i \(-0.476244\pi\)
0.0745611 + 0.997216i \(0.476244\pi\)
\(308\) 2.57505e7 1.38257e7i 0.881320 0.473191i
\(309\) −8.40938e6 + 1.11681e7i −0.285029 + 0.378534i
\(310\) 2.84067e6 + 8.74268e6i 0.0953533 + 0.293467i
\(311\) 3.49458e7 4.80988e7i 1.16175 1.59902i 0.457209 0.889359i \(-0.348849\pi\)
0.704545 0.709659i \(-0.251151\pi\)
\(312\) 6.97370e7 + 1.19177e6i 2.29615 + 0.0392399i
\(313\) −1.09361e7 + 3.36579e7i −0.356640 + 1.09763i 0.598412 + 0.801189i \(0.295799\pi\)
−0.955052 + 0.296437i \(0.904201\pi\)
\(314\) −5.82553e7 1.89283e7i −1.88168 0.611396i
\(315\) 2.39425e6 3.06912e6i 0.0766015 0.0981933i
\(316\) 4.50505e7 + 3.27311e7i 1.42771 + 1.03729i
\(317\) 1.35984e7 4.41840e6i 0.426885 0.138703i −0.0876917 0.996148i \(-0.527949\pi\)
0.514577 + 0.857444i \(0.327949\pi\)
\(318\) 2.62578e7 3.48718e7i 0.816540 1.08441i
\(319\) −4.30234e6 + 3.15384e7i −0.132536 + 0.971555i
\(320\) 3.56536e7i 1.08806i
\(321\) 7.05067e6 2.05010e7i 0.213165 0.619811i
\(322\) −3.00359e7 2.18223e7i −0.899647 0.653632i
\(323\) −2.92465e7 4.02544e7i −0.867894 1.19455i
\(324\) −2.22237e7 8.85826e7i −0.653404 2.60443i
\(325\) −6.68903e6 + 2.05867e7i −0.194856 + 0.599704i
\(326\) 2.76171e7 + 3.80117e7i 0.797123 + 1.09715i
\(327\) −2.84546e7 + 8.71081e6i −0.813783 + 0.249124i
\(328\) 1.59213e7 + 4.90008e7i 0.451189 + 1.38862i
\(329\) 1.50697e7i 0.423172i
\(330\) −2.05946e7 1.03793e7i −0.573075 0.288818i
\(331\) 1.92679e7 0.531313 0.265656 0.964068i \(-0.414411\pi\)
0.265656 + 0.964068i \(0.414411\pi\)
\(332\) 3.18073e7 1.03348e7i 0.869186 0.282416i
\(333\) 1.50954e7 4.15689e7i 0.408802 1.12573i
\(334\) 9.53047e6 6.92429e6i 0.255785 0.185839i
\(335\) −1.91455e7 6.22074e6i −0.509251 0.165466i
\(336\) 2.85857e7 + 4.07928e7i 0.753582 + 1.07539i
\(337\) 4.07626e7 2.96158e7i 1.06506 0.773808i 0.0900382 0.995938i \(-0.471301\pi\)
0.975017 + 0.222130i \(0.0713011\pi\)
\(338\) −2.16130e7 + 2.97477e7i −0.559711 + 0.770377i
\(339\) 1.66538e7 4.84236e7i 0.427478 1.24296i
\(340\) −4.42964e7 −1.12702
\(341\) 8.28851e6 1.71700e7i 0.209032 0.433018i
\(342\) 8.67907e7 2.49555e7i 2.16968 0.623862i
\(343\) −8.64631e6 2.66106e7i −0.214264 0.659436i
\(344\) 4.36428e6 6.00691e6i 0.107210 0.147562i
\(345\) −364731. + 2.13424e7i −0.00888209 + 0.519741i
\(346\) −2.71640e6 + 8.36022e6i −0.0655791 + 0.201832i
\(347\) 4.67066e7 + 1.51759e7i 1.11787 + 0.363217i 0.808953 0.587874i \(-0.200035\pi\)
0.308913 + 0.951090i \(0.400035\pi\)
\(348\) −1.10947e8 1.89602e6i −2.63255 0.0449888i
\(349\) −6.83244e7 4.96406e7i −1.60731 1.16778i −0.871217 0.490899i \(-0.836668\pi\)
−0.736093 0.676880i \(-0.763332\pi\)
\(350\) −2.59024e7 + 8.41621e6i −0.604138 + 0.196296i
\(351\) −2.86717e7 1.09700e7i −0.663028 0.253679i
\(352\) 1.06550e8 1.11233e8i 2.44300 2.55038i
\(353\) 1.81354e7i 0.412290i 0.978522 + 0.206145i \(0.0660918\pi\)
−0.978522 + 0.206145i \(0.933908\pi\)
\(354\) −1.08103e7 3.71786e6i −0.243684 0.0838076i
\(355\) 9.04211e6 + 6.56948e6i 0.202109 + 0.146840i
\(356\) 5.18484e7 + 7.13631e7i 1.14917 + 1.58170i
\(357\) −1.74284e7 + 1.22130e7i −0.383048 + 0.268422i
\(358\) −6.27100e6 + 1.93001e7i −0.136675 + 0.420641i
\(359\) −5.46609e6 7.52343e6i −0.118139 0.162605i 0.745852 0.666112i \(-0.232043\pi\)
−0.863991 + 0.503507i \(0.832043\pi\)
\(360\) 1.72220e7 4.74249e7i 0.369127 1.01648i
\(361\) 5.56860e6 + 1.71384e7i 0.118365 + 0.364291i
\(362\) 4.76044e7i 1.00351i
\(363\) 1.59547e7 + 4.50928e7i 0.333555 + 0.942731i
\(364\) 3.42483e7 0.710125
\(365\) −24911.9 + 8094.37i −0.000512305 + 0.000166458i
\(366\) 1.15188e7 + 3.76272e7i 0.234945 + 0.767466i
\(367\) −6.65965e7 + 4.83852e7i −1.34727 + 0.978846i −0.348123 + 0.937449i \(0.613181\pi\)
−0.999143 + 0.0413967i \(0.986819\pi\)
\(368\) −2.59783e8 8.44086e7i −5.21275 1.69373i
\(369\) 774856. 2.26640e7i 0.0154220 0.451083i
\(370\) 3.14961e7 2.28833e7i 0.621802 0.451766i
\(371\) 7.90692e6 1.08829e7i 0.154841 0.213120i
\(372\) 6.28514e7 + 2.16158e7i 1.22092 + 0.419896i
\(373\) 2.35364e7 0.453538 0.226769 0.973949i \(-0.427184\pi\)
0.226769 + 0.973949i \(0.427184\pi\)
\(374\) 9.10537e7 + 8.72202e7i 1.74054 + 1.66726i
\(375\) 2.65921e7 + 2.00234e7i 0.504265 + 0.379702i
\(376\) −6.03613e7 1.85773e8i −1.13552 3.49478i
\(377\) −2.19236e7 + 3.01752e7i −0.409154 + 0.563153i
\(378\) −1.00379e7 3.72982e7i −0.185852 0.690578i
\(379\) −6.35134e6 + 1.95474e7i −0.116667 + 0.359064i −0.992291 0.123929i \(-0.960450\pi\)
0.875624 + 0.482993i \(0.160450\pi\)
\(380\) 5.50902e7 + 1.78999e7i 1.00398 + 0.326212i
\(381\) 771720. 4.51577e7i 0.0139536 0.816501i
\(382\) −6.78128e6 4.92689e6i −0.121653 0.0883858i
\(383\) −5.38491e7 + 1.74966e7i −0.958477 + 0.311428i −0.746156 0.665772i \(-0.768102\pi\)
−0.212322 + 0.977200i \(0.568102\pi\)
\(384\) 1.22875e8 + 9.25225e7i 2.17005 + 1.63401i
\(385\) −6.40025e6 3.08961e6i −0.112154 0.0541404i
\(386\) 1.01382e7i 0.176278i
\(387\) −2.70798e6 + 1.82944e6i −0.0467211 + 0.0315635i
\(388\) 1.61862e8 + 1.17600e8i 2.77109 + 2.01332i
\(389\) −1.19231e7 1.64107e7i −0.202553 0.278790i 0.695641 0.718390i \(-0.255120\pi\)
−0.898194 + 0.439599i \(0.855120\pi\)
\(390\) −1.55085e7 2.21312e7i −0.261442 0.373087i
\(391\) 3.60630e7 1.10990e8i 0.603297 1.85676i
\(392\) −9.86403e7 1.35767e8i −1.63756 2.25390i
\(393\) 2.05600e7 + 6.71610e7i 0.338724 + 1.10647i
\(394\) 2.21126e7 + 6.80555e7i 0.361535 + 1.11269i
\(395\) 1.35406e7i 0.219708i
\(396\) −1.49519e8 + 7.38116e7i −2.40774 + 1.18861i
\(397\) 2.43147e7 0.388595 0.194298 0.980943i \(-0.437757\pi\)
0.194298 + 0.980943i \(0.437757\pi\)
\(398\) 8.53555e7 2.77337e7i 1.35389 0.439905i
\(399\) 2.66105e7 8.14628e6i 0.418923 0.128245i
\(400\) −1.62111e8 + 1.17781e8i −2.53299 + 1.84033i
\(401\) 3.95975e7 + 1.28660e7i 0.614094 + 0.199531i 0.599516 0.800363i \(-0.295360\pi\)
0.0145774 + 0.999894i \(0.495360\pi\)
\(402\) −1.63588e8 + 1.14635e8i −2.51810 + 1.76457i
\(403\) 1.80744e7 1.31318e7i 0.276152 0.200636i
\(404\) 7.56395e7 1.04109e8i 1.14711 1.57886i
\(405\) −1.42497e7 + 1.70327e7i −0.214507 + 0.256400i
\(406\) −4.69295e7 −0.701242
\(407\) −8.00044e7 1.09139e7i −1.18667 0.161881i
\(408\) −1.65932e8 + 2.20366e8i −2.44314 + 3.24462i
\(409\) −1.06532e7 3.27871e7i −0.155707 0.479218i 0.842525 0.538658i \(-0.181068\pi\)
−0.998232 + 0.0594402i \(0.981068\pi\)
\(410\) 1.17338e7 1.61503e7i 0.170251 0.234330i
\(411\) 5.45593e7 + 932389.i 0.785857 + 0.0134299i
\(412\) −2.74966e7 + 8.46257e7i −0.393176 + 1.21007i
\(413\) −3.35043e6 1.08862e6i −0.0475610 0.0154535i
\(414\) 1.67004e8 + 1.30281e8i 2.35356 + 1.83603i
\(415\) −6.57919e6 4.78006e6i −0.0920510 0.0668789i
\(416\) 1.71658e8 5.57750e7i 2.38442 0.774746i
\(417\) 1.59012e7 2.11176e7i 0.219291 0.291230i
\(418\) −7.79960e7 1.45268e8i −1.06793 1.98903i
\(419\) 4.04586e7i 0.550007i −0.961443 0.275004i \(-0.911321\pi\)
0.961443 0.275004i \(-0.0886791\pi\)
\(420\) 8.05747e6 2.34284e7i 0.108755 0.316224i
\(421\) −1.77264e7 1.28790e7i −0.237560 0.172598i 0.462635 0.886549i \(-0.346904\pi\)
−0.700196 + 0.713951i \(0.746904\pi\)
\(422\) 1.49186e8 + 2.05336e8i 1.98513 + 2.73230i
\(423\) −2.93765e6 + 8.59241e7i −0.0388132 + 1.13526i
\(424\) 5.38819e7 1.65831e8i 0.706880 2.17555i
\(425\) −5.03210e7 6.92609e7i −0.655515 0.902239i
\(426\) 1.06047e8 3.24642e7i 1.37173 0.419929i
\(427\) 3.74731e6 + 1.15330e7i 0.0481322 + 0.148136i
\(428\) 1.37986e8i 1.75996i
\(429\) −8.52366e6 + 5.53973e7i −0.107958 + 0.701643i
\(430\) −2.87685e6 −0.0361837
\(431\) −1.72124e7 + 5.59265e6i −0.214986 + 0.0698531i −0.414530 0.910036i \(-0.636054\pi\)
0.199544 + 0.979889i \(0.436054\pi\)
\(432\) −1.55037e8 2.38164e8i −1.92302 2.95410i
\(433\) 4.51832e7 3.28276e7i 0.556562 0.404366i −0.273637 0.961833i \(-0.588227\pi\)
0.830199 + 0.557467i \(0.188227\pi\)
\(434\) 2.67341e7 + 8.68644e6i 0.327037 + 0.106261i
\(435\) 1.54842e7 + 2.20966e7i 0.188114 + 0.268446i
\(436\) −1.53231e8 + 1.11329e8i −1.84879 + 1.34322i
\(437\) −8.97011e7 + 1.23463e8i −1.07486 + 1.47942i
\(438\) −84531.8 + 245790.i −0.00100600 + 0.00292511i
\(439\) 4.98698e7 0.589446 0.294723 0.955583i \(-0.404773\pi\)
0.294723 + 0.955583i \(0.404773\pi\)
\(440\) −9.12750e7 1.24514e7i −1.07150 0.146171i
\(441\) 2.04113e7 + 7.09869e7i 0.237988 + 0.827680i
\(442\) 4.56567e7 + 1.40517e8i 0.528735 + 1.62728i
\(443\) −1.85097e7 + 2.54764e7i −0.212906 + 0.293040i −0.902091 0.431545i \(-0.857969\pi\)
0.689185 + 0.724585i \(0.257969\pi\)
\(444\) 4.80968e6 2.81442e8i 0.0549500 3.21543i
\(445\) 6.62816e6 2.03994e7i 0.0752164 0.231492i
\(446\) −3.01604e7 9.79969e6i −0.339963 0.110461i
\(447\) 3.31408e6 + 56635.7i 0.0371056 + 0.000634115i
\(448\) 8.82029e7 + 6.40831e7i 0.980954 + 0.712705i
\(449\) 8.72806e7 2.83592e7i 0.964226 0.313296i 0.215743 0.976450i \(-0.430783\pi\)
0.748483 + 0.663154i \(0.230783\pi\)
\(450\) 1.49331e8 4.29380e7i 1.63874 0.471199i
\(451\) −4.07453e7 + 7.35465e6i −0.444169 + 0.0801738i
\(452\) 3.25925e8i 3.52941i
\(453\) −1.41182e8 4.85552e7i −1.51875 0.522326i
\(454\) 1.30539e8 + 9.48424e7i 1.39500 + 1.01353i
\(455\) −4.89499e6 6.73738e6i −0.0519658 0.0715248i
\(456\) 2.95414e8 2.07012e8i 3.11556 2.18323i
\(457\) 2.36716e7 7.28536e7i 0.248015 0.763312i −0.747111 0.664700i \(-0.768560\pi\)
0.995126 0.0986126i \(-0.0314405\pi\)
\(458\) 1.69223e8 + 2.32915e8i 1.76142 + 2.42439i
\(459\) 1.01754e8 6.62384e7i 1.05223 0.684971i
\(460\) 4.19831e7 + 1.29211e8i 0.431321 + 1.32747i
\(461\) 1.72567e8i 1.76138i 0.473689 + 0.880692i \(0.342922\pi\)
−0.473689 + 0.880692i \(0.657078\pi\)
\(462\) −6.26934e7 + 3.22931e7i −0.635764 + 0.327480i
\(463\) −4.97029e7 −0.500770 −0.250385 0.968146i \(-0.580557\pi\)
−0.250385 + 0.968146i \(0.580557\pi\)
\(464\) −3.28378e8 + 1.06697e8i −3.28716 + 1.06806i
\(465\) −4.73085e6 1.54537e7i −0.0470522 0.153700i
\(466\) −2.29405e8 + 1.66673e8i −2.26697 + 1.64705i
\(467\) −7.88363e7 2.56155e7i −0.774062 0.251508i −0.104759 0.994498i \(-0.533407\pi\)
−0.669303 + 0.742990i \(0.733407\pi\)
\(468\) −1.95276e8 6.67628e6i −1.90507 0.0651324i
\(469\) −4.98010e7 + 3.61826e7i −0.482747 + 0.350736i
\(470\) −4.44856e7 + 6.12292e7i −0.428476 + 0.589746i
\(471\) 1.01836e8 + 3.50232e7i 0.974624 + 0.335192i
\(472\) −4.56632e7 −0.434251
\(473\) 4.30884e6 + 4.12743e6i 0.0407171 + 0.0390029i
\(474\) −1.07335e8 8.08216e7i −1.00788 0.758914i
\(475\) 3.45950e7 + 1.06472e8i 0.322799 + 0.993474i
\(476\) −7.96174e7 + 1.09584e8i −0.738222 + 1.01608i
\(477\) −4.72050e7 + 6.05108e7i −0.434944 + 0.557542i
\(478\) 8.29941e7 2.55430e8i 0.759913 2.33877i
\(479\) 1.78539e8 + 5.80109e7i 1.62453 + 0.527841i 0.973004 0.230788i \(-0.0741303\pi\)
0.651523 + 0.758629i \(0.274130\pi\)
\(480\) 2.23101e6 1.30549e8i 0.0201733 1.18045i
\(481\) −7.65464e7 5.56142e7i −0.687844 0.499748i
\(482\) −3.35897e8 + 1.09140e8i −2.99961 + 0.974633i
\(483\) 5.21431e7 + 3.92628e7i 0.462760 + 0.348449i
\(484\) 1.89369e8 + 2.38378e8i 1.67021 + 2.10248i
\(485\) 4.86500e7i 0.426440i
\(486\) 4.99629e7 + 2.14623e8i 0.435250 + 1.86968i
\(487\) −9.95950e7 7.23600e7i −0.862285 0.626486i 0.0662209 0.997805i \(-0.478906\pi\)
−0.928506 + 0.371319i \(0.878906\pi\)
\(488\) 9.23905e7 + 1.27165e8i 0.795001 + 1.09423i
\(489\) −4.74049e7 6.76486e7i −0.405412 0.578539i
\(490\) −2.00929e7 + 6.18396e7i −0.170787 + 0.525628i
\(491\) −8.88320e7 1.22267e8i −0.750456 1.03291i −0.997948 0.0640238i \(-0.979607\pi\)
0.247493 0.968890i \(-0.420393\pi\)
\(492\) −4.22501e7 1.38013e8i −0.354758 1.15885i
\(493\) −4.55853e7 1.40297e8i −0.380438 1.17087i
\(494\) 1.93207e8i 1.60266i
\(495\) 3.58905e7 + 1.88639e7i 0.295913 + 0.155531i
\(496\) 2.06815e8 1.69487
\(497\) 3.25042e7 1.05613e7i 0.264771 0.0860293i
\(498\) −7.71617e7 + 2.36215e7i −0.624760 + 0.191258i
\(499\) 7.28026e7 5.28942e7i 0.585930 0.425703i −0.254927 0.966960i \(-0.582052\pi\)
0.840857 + 0.541257i \(0.182052\pi\)
\(500\) 2.01500e8 + 6.54714e7i 1.61200 + 0.523771i
\(501\) −1.69612e7 + 1.18856e7i −0.134879 + 0.0945165i
\(502\) 2.46364e8 1.78994e8i 1.94745 1.41490i
\(503\) 5.68196e7 7.82054e7i 0.446472 0.614516i −0.525163 0.851002i \(-0.675996\pi\)
0.971635 + 0.236486i \(0.0759957\pi\)
\(504\) −8.63691e7 1.27846e8i −0.674632 0.998607i
\(505\) −3.12914e7 −0.242969
\(506\) 1.68119e8 3.48265e8i 1.29767 2.68818i
\(507\) 3.88861e7 5.16428e7i 0.298380 0.396265i
\(508\) −8.88304e7 2.73392e8i −0.677596 2.08542i
\(509\) 1.46456e8 2.01580e8i 1.11059 1.52860i 0.290053 0.957010i \(-0.406327\pi\)
0.820540 0.571590i \(-0.193673\pi\)
\(510\) 1.06866e8 + 1.82627e6i 0.805615 + 0.0137675i
\(511\) −24751.7 + 76177.8i −0.000185499 + 0.000570907i
\(512\) 1.33514e8 + 4.33812e7i 0.994755 + 0.323215i
\(513\) −1.53315e8 + 4.12609e7i −1.13562 + 0.305623i
\(514\) −1.77451e7 1.28926e7i −0.130674 0.0949401i
\(515\) 2.05777e7 6.68610e6i 0.150652 0.0489498i
\(516\) −1.25119e7 + 1.66164e7i −0.0910696 + 0.120945i
\(517\) 1.54475e8 2.78831e7i 1.11786 0.201776i
\(518\) 1.19048e8i 0.856508i
\(519\) 5.02618e6 1.46145e7i 0.0359531 0.104540i
\(520\) −8.73299e7 6.34489e7i −0.621088 0.451246i
\(521\) −4.53354e7 6.23988e7i −0.320571 0.441228i 0.618071 0.786123i \(-0.287915\pi\)
−0.938641 + 0.344895i \(0.887915\pi\)
\(522\) 2.67582e8 + 9.14832e6i 1.88124 + 0.0643176i
\(523\) −8.71355e7 + 2.68176e8i −0.609102 + 1.87462i −0.143445 + 0.989658i \(0.545818\pi\)
−0.465657 + 0.884965i \(0.654182\pi\)
\(524\) 2.62768e8 + 3.61669e8i 1.82633 + 2.51372i
\(525\) 4.57855e7 1.40163e7i 0.316410 0.0968627i
\(526\) −4.88991e7 1.50496e8i −0.336004 1.03411i
\(527\) 8.83601e7i 0.603704i
\(528\) −3.65262e8 + 3.68500e8i −2.48144 + 2.50343i
\(529\) −2.09898e8 −1.41788
\(530\) −6.42527e7 + 2.08770e7i −0.431582 + 0.140230i
\(531\) 1.88912e7 + 6.86021e6i 0.126176 + 0.0458198i
\(532\) 1.43300e8 1.04114e8i 0.951727 0.691470i
\(533\) −4.61419e7 1.49924e7i −0.304729 0.0990125i
\(534\) −1.22143e8 1.74302e8i −0.802128 1.14467i
\(535\) −2.71448e7 + 1.97218e7i −0.177266 + 0.128791i
\(536\) −4.68998e8 + 6.45521e8i −3.04563 + 4.19195i
\(537\) 1.16033e7 3.37385e7i 0.0749304 0.217872i
\(538\) −4.08811e8 −2.62528
\(539\) 1.18816e8 6.37936e7i 0.758766 0.407391i
\(540\) −5.05090e7 + 1.32013e8i −0.320765 + 0.838368i
\(541\) −3.06284e7 9.42644e7i −0.193434 0.595328i −0.999991 0.00417215i \(-0.998672\pi\)
0.806558 0.591155i \(-0.201328\pi\)
\(542\) −1.06856e8 + 1.47074e8i −0.671120 + 0.923718i
\(543\) −1.43007e6 + 8.36816e7i −0.00893221 + 0.522674i
\(544\) −2.20592e8 + 6.78912e8i −1.37023 + 4.21713i
\(545\) 4.38015e7 + 1.42320e7i 0.270582 + 0.0879176i
\(546\) −8.26245e7 1.41201e6i −0.507611 0.00867479i
\(547\) 2.14773e8 + 1.56042e8i 1.31225 + 0.953408i 0.999994 + 0.00341092i \(0.00108573\pi\)
0.312259 + 0.949997i \(0.398914\pi\)
\(548\) 3.30311e8 1.07325e8i 2.00716 0.652165i
\(549\) −1.91181e7 6.64892e7i −0.115539 0.401823i
\(550\) −1.34198e8 2.49945e8i −0.806602 1.50230i
\(551\) 1.92905e8i 1.15316i
\(552\) 8.00065e8 + 2.75157e8i 4.75672 + 1.63593i
\(553\) −3.34977e7 2.43375e7i −0.198080 0.143913i
\(554\) −3.15719e8 4.34550e8i −1.85683 2.55570i
\(555\) −5.60531e7 + 3.92793e7i −0.327884 + 0.229766i
\(556\) 5.19928e7 1.60017e8i 0.302495 0.930985i
\(557\) 1.06971e8 + 1.47232e8i 0.619012 + 0.851996i 0.997281 0.0736994i \(-0.0234805\pi\)
−0.378269 + 0.925696i \(0.623481\pi\)
\(558\) −1.50739e8 5.47396e7i −0.867605 0.315064i
\(559\) 2.16057e6 + 6.64954e6i 0.0123689 + 0.0380677i
\(560\) 7.70919e7i 0.438980i
\(561\) −1.57439e8 1.56056e8i −0.891710 0.883875i
\(562\) 1.15034e8 0.648062
\(563\) 1.08296e8 3.51877e7i 0.606861 0.197181i 0.0105629 0.999944i \(-0.496638\pi\)
0.596298 + 0.802763i \(0.296638\pi\)
\(564\) 1.60180e8 + 5.23240e8i 0.892832 + 2.91651i
\(565\) −6.41164e7 + 4.65833e7i −0.355487 + 0.258276i
\(566\) −1.39223e8 4.52363e7i −0.767825 0.249481i
\(567\) 1.65247e7 + 6.58664e7i 0.0906532 + 0.361339i
\(568\) 3.58396e8 2.60390e8i 1.95577 1.42095i
\(569\) 3.21808e7 4.42931e7i 0.174687 0.240436i −0.712692 0.701477i \(-0.752524\pi\)
0.887379 + 0.461042i \(0.152524\pi\)
\(570\) −1.32168e8 4.54550e7i −0.713677 0.245447i
\(571\) 3.31867e8 1.78261 0.891305 0.453404i \(-0.149791\pi\)
0.891305 + 0.453404i \(0.149791\pi\)
\(572\) 6.33688e7 + 3.51068e8i 0.338600 + 1.87587i
\(573\) 1.17725e7 + 8.86447e6i 0.0625755 + 0.0471182i
\(574\) −1.88636e7 5.80563e7i −0.0997446 0.306982i
\(575\) −1.54338e8 + 2.12428e8i −0.811838 + 1.11740i
\(576\) −4.90421e8 3.82582e8i −2.56627 2.00197i
\(577\) −7.02503e7 + 2.16208e8i −0.365696 + 1.12550i 0.583847 + 0.811863i \(0.301547\pi\)
−0.949544 + 0.313634i \(0.898453\pi\)
\(578\) −2.03202e8 6.60244e7i −1.05231 0.341917i
\(579\) 304559. 1.78214e7i 0.00156905 0.0918137i
\(580\) 1.38936e8 + 1.00943e8i 0.712081 + 0.517357i
\(581\) −2.36506e7 + 7.68455e6i −0.120591 + 0.0391823i
\(582\) −3.85647e8 2.90385e8i −1.95623 1.47301i
\(583\) 1.26188e8 + 6.09148e7i 0.636811 + 0.307410i
\(584\) 1.03823e6i 0.00521261i
\(585\) 2.65968e7 + 3.93693e7i 0.132850 + 0.196648i
\(586\) 2.01224e8 + 1.46198e8i 0.999969 + 0.726520i
\(587\) −1.58749e8 2.18499e8i −0.784866 1.08028i −0.994728 0.102545i \(-0.967302\pi\)
0.209862 0.977731i \(-0.432698\pi\)
\(588\) 2.69793e8 + 3.85004e8i 1.32708 + 1.89380i
\(589\) 3.57058e7 1.09891e8i 0.174740 0.537795i
\(590\) 1.03994e7 + 1.43136e7i 0.0506353 + 0.0696936i
\(591\) −3.68263e7 1.20296e8i −0.178400 0.582759i
\(592\) −2.70661e8 8.33008e8i −1.30455 4.01499i
\(593\) 3.90218e8i 1.87130i 0.352929 + 0.935650i \(0.385186\pi\)
−0.352929 + 0.935650i \(0.614814\pi\)
\(594\) 3.63759e8 1.71907e8i 1.73562 0.820227i
\(595\) 3.29370e7 0.156363
\(596\) 2.00640e7 6.51917e6i 0.0947715 0.0307931i
\(597\) −1.50876e8 + 4.61876e7i −0.709082 + 0.217072i
\(598\) 3.66610e8 2.66357e8i 1.71435 1.24555i
\(599\) −7.26873e7 2.36175e7i −0.338203 0.109889i 0.134991 0.990847i \(-0.456899\pi\)
−0.473195 + 0.880958i \(0.656899\pi\)
\(600\) 5.08283e8 3.56180e8i 2.35316 1.64898i
\(601\) −2.99145e8 + 2.17342e8i −1.37803 + 1.00120i −0.380968 + 0.924588i \(0.624409\pi\)
−0.997061 + 0.0766091i \(0.975591\pi\)
\(602\) −5.17080e6 + 7.11700e6i −0.0237011 + 0.0326218i
\(603\) 2.91008e8 1.96597e8i 1.32725 0.896654i
\(604\) −9.50254e8 −4.31250
\(605\) 1.98284e7 7.13235e7i 0.0895407 0.322082i
\(606\) −1.86774e8 + 2.48046e8i −0.839262 + 1.11459i
\(607\) 5.04088e7 + 1.55142e8i 0.225393 + 0.693688i 0.998251 + 0.0591099i \(0.0188263\pi\)
−0.772858 + 0.634578i \(0.781174\pi\)
\(608\) 5.48689e8 7.55206e8i 2.44127 3.36012i
\(609\) 8.24953e7 + 1.40980e6i 0.365239 + 0.00624174i
\(610\) 1.88198e7 5.79215e7i 0.0829136 0.255182i
\(611\) 1.74934e8 + 5.68396e7i 0.766922 + 0.249188i
\(612\) 4.75323e8 6.09303e8i 2.07364 2.65815i
\(613\) 1.47486e8 + 1.07155e8i 0.640278 + 0.465189i 0.859946 0.510386i \(-0.170497\pi\)
−0.219668 + 0.975575i \(0.570497\pi\)
\(614\) −6.30204e7 + 2.04766e7i −0.272255 + 0.0884611i
\(615\) −2.11116e7 + 2.80373e7i −0.0907601 + 0.120534i
\(616\) −1.94859e8 + 2.03424e8i −0.833640 + 0.870281i
\(617\) 1.19240e8i 0.507652i 0.967250 + 0.253826i \(0.0816891\pi\)
−0.967250 + 0.253826i \(0.918311\pi\)
\(618\) 6.98248e7 2.03027e8i 0.295831 0.860178i
\(619\) −8.77961e7 6.37876e7i −0.370172 0.268946i 0.387110 0.922033i \(-0.373473\pi\)
−0.757282 + 0.653088i \(0.773473\pi\)
\(620\) −6.04627e7 8.32198e7i −0.253695 0.349182i
\(621\) −2.89655e8 2.34032e8i −1.20950 0.977239i
\(622\) −2.82148e8 + 8.68362e8i −1.17248 + 3.60852i
\(623\) −3.85523e7 5.30627e7i −0.159436 0.219445i
\(624\) −5.81356e8 + 1.77971e8i −2.39270 + 0.732478i
\(625\) 5.10924e7 + 1.57246e8i 0.209274 + 0.644080i
\(626\) 5.43499e8i 2.21552i
\(627\) 1.32742e8 + 2.57703e8i 0.538523 + 1.04548i
\(628\) 6.85425e8 2.76746
\(629\) 3.55897e8 1.15638e8i 1.43012 0.464673i
\(630\) −2.04047e7 + 5.61891e7i −0.0816033 + 0.224714i
\(631\) 4.89152e7 3.55389e7i 0.194695 0.141454i −0.486167 0.873866i \(-0.661605\pi\)
0.680862 + 0.732412i \(0.261605\pi\)
\(632\) −5.10429e8 1.65849e8i −2.02202 0.656993i
\(633\) −2.56078e8 3.65433e8i −1.00963 1.44078i
\(634\) −1.77647e8 + 1.29068e8i −0.697092 + 0.506467i
\(635\) −4.10858e7 + 5.65498e7i −0.160462 + 0.220856i
\(636\) −1.58861e8 + 4.61915e8i −0.617514 + 1.79552i
\(637\) 1.58026e8 0.611378
\(638\) −8.68326e7 4.81059e8i −0.334365 1.85241i
\(639\) −1.87391e8 + 5.38816e7i −0.718199 + 0.206509i
\(640\) −7.35624e7 2.26402e8i −0.280618 0.863654i
\(641\) 4.61084e7 6.34627e7i 0.175068 0.240960i −0.712462 0.701711i \(-0.752420\pi\)
0.887529 + 0.460751i \(0.152420\pi\)
\(642\) −5.68895e6 + 3.32892e8i −0.0214994 + 1.25805i
\(643\) 1.23692e8 3.80685e8i 0.465274 1.43197i −0.393363 0.919383i \(-0.628688\pi\)
0.858637 0.512584i \(-0.171312\pi\)
\(644\) 3.95111e8 + 1.28379e8i 1.47932 + 0.480660i
\(645\) 5.05709e6 + 86422.9i 0.0188461 + 0.000322070i
\(646\) 6.18202e8 + 4.49150e8i 2.29315 + 1.66607i
\(647\) −3.25652e8 + 1.05811e8i −1.20238 + 0.390676i −0.840635 0.541602i \(-0.817818\pi\)
−0.361743 + 0.932278i \(0.617818\pi\)
\(648\) 4.67536e8 + 7.45785e8i 1.71826 + 2.74087i
\(649\) 4.95988e6 3.63585e7i 0.0181442 0.133006i
\(650\) 3.32428e8i 1.21048i
\(651\) −4.67337e7 1.60726e7i −0.169390 0.0582564i
\(652\) −4.25351e8 3.09036e8i −1.53463 1.11498i
\(653\) 1.81682e8 + 2.50064e8i 0.652489 + 0.898074i 0.999204 0.0398967i \(-0.0127029\pi\)
−0.346715 + 0.937971i \(0.612703\pi\)
\(654\) 3.74261e8 2.62264e8i 1.33796 0.937575i
\(655\) 3.35916e7 1.03384e8i 0.119538 0.367901i
\(656\) −2.63988e8 3.63348e8i −0.935130 1.28710i
\(657\) 155978. 429524.i 0.000550007 0.00151458i
\(658\) 7.15162e7 + 2.20104e8i 0.251031 + 0.772593i
\(659\) 2.08492e8i 0.728507i 0.931300 + 0.364254i \(0.118676\pi\)
−0.931300 + 0.364254i \(0.881324\pi\)
\(660\) 2.55065e8 + 3.92455e7i 0.887196 + 0.136508i
\(661\) 3.14300e8 1.08828 0.544140 0.838994i \(-0.316856\pi\)
0.544140 + 0.838994i \(0.316856\pi\)
\(662\) −2.81422e8 + 9.14395e7i −0.970027 + 0.315181i
\(663\) −7.60367e7 2.48380e8i −0.260905 0.852268i
\(664\) −2.60775e8 + 1.89464e8i −0.890761 + 0.647176i
\(665\) −4.09628e7 1.33096e7i −0.139292 0.0452586i
\(666\) −2.32068e7 + 6.78783e8i −0.0785585 + 2.29778i
\(667\) −3.66036e8 + 2.65941e8i −1.23352 + 0.896206i
\(668\) −7.74829e7 + 1.06646e8i −0.259942 + 0.357780i
\(669\) 5.27231e7 + 1.81325e7i 0.176085 + 0.0605590i
\(670\) 3.09156e8 1.02790
\(671\) −1.11288e8 + 5.97517e7i −0.368366 + 0.197780i
\(672\) −3.18952e8 2.40165e8i −1.05104 0.791410i
\(673\) −4.40764e6 1.35653e7i −0.0144597 0.0445025i 0.943566 0.331184i \(-0.107448\pi\)
−0.958026 + 0.286681i \(0.907448\pi\)
\(674\) −4.54821e8 + 6.26007e8i −1.48546 + 2.04456i
\(675\) −2.63791e8 + 7.09927e7i −0.857727 + 0.230836i
\(676\) 1.27148e8 3.91321e8i 0.411594 1.26675i
\(677\) 1.32981e7 + 4.32083e6i 0.0428573 + 0.0139252i 0.330367 0.943852i \(-0.392827\pi\)
−0.287510 + 0.957778i \(0.592827\pi\)
\(678\) −1.34374e7 + 7.86297e8i −0.0431147 + 2.52289i
\(679\) −1.20354e8 8.74425e7i −0.384461 0.279327i
\(680\) 4.06033e8 1.31928e8i 1.29132 0.419576i
\(681\) −2.26620e8 1.70641e8i −0.717558 0.540308i
\(682\) −3.95764e7 + 2.90115e8i −0.124762 + 0.914570i
\(683\) 4.10558e8i 1.28858i −0.764780 0.644291i \(-0.777152\pi\)
0.764780 0.644291i \(-0.222848\pi\)
\(684\) −8.37362e8 + 5.65699e8i −2.61665 + 1.76774i
\(685\) −6.83232e7 4.96397e7i −0.212567 0.154439i
\(686\) 2.52572e8 + 3.47635e8i 0.782370 + 1.07684i
\(687\) −2.90472e8 4.14515e8i −0.895849 1.27841i
\(688\) −2.00006e7 + 6.15556e7i −0.0614155 + 0.189018i
\(689\) 9.65098e7 + 1.32834e8i 0.295062 + 0.406118i
\(690\) −9.59575e7 3.13453e8i −0.292100 0.954169i
\(691\) 2.92327e7 + 8.99690e7i 0.0886003 + 0.272684i 0.985533 0.169483i \(-0.0542099\pi\)
−0.896933 + 0.442167i \(0.854210\pi\)
\(692\) 9.83654e7i 0.296841i
\(693\) 1.11176e8 5.48833e7i 0.334050 0.164907i
\(694\) −7.54205e8 −2.25637
\(695\) −3.89100e7 + 1.26426e7i −0.115906 + 0.0376602i
\(696\) 1.02261e9 3.13053e8i 3.03308 0.928519i
\(697\) 1.55238e8 1.12787e8i 0.458457 0.333089i
\(698\) 1.23351e9 + 4.00791e8i 3.62724 + 1.17856i
\(699\) 4.08268e8 2.86095e8i 1.19540 0.837680i
\(700\) 2.46560e8 1.79136e8i 0.718833 0.522263i
\(701\) 4.53216e7 6.23799e7i 0.131568 0.181088i −0.738150 0.674637i \(-0.764300\pi\)
0.869718 + 0.493548i \(0.164300\pi\)
\(702\) 4.70831e8 + 2.41576e7i 1.36099 + 0.0698300i
\(703\) −4.89348e8 −1.40848
\(704\) −4.93696e8 + 1.02271e9i −1.41495 + 2.93113i
\(705\) 8.00386e7 1.06296e8i 0.228419 0.303353i
\(706\) −8.60649e7 2.64881e8i −0.244575 0.752725i
\(707\) −5.62424e7 + 7.74111e7i −0.159150 + 0.219051i
\(708\) 1.27903e8 + 2.18579e6i 0.360396 + 0.00615897i
\(709\) 5.49816e7 1.69216e8i 0.154269 0.474791i −0.843817 0.536631i \(-0.819697\pi\)
0.998086 + 0.0618397i \(0.0196968\pi\)
\(710\) −1.63243e8 5.30410e7i −0.456101 0.148196i
\(711\) 1.86252e8 + 1.45297e8i 0.518194 + 0.404248i
\(712\) −6.87798e8 4.99715e8i −1.90555 1.38447i
\(713\) 2.57743e8 8.37456e7i 0.711078 0.231043i
\(714\) 1.96596e8 2.61090e8i 0.540107 0.717292i
\(715\) 6.00056e7 6.26430e7i 0.164162 0.171378i
\(716\) 2.27083e8i 0.618651i
\(717\) −1.53565e8 + 4.46515e8i −0.416615 + 1.21138i
\(718\) 1.15540e8 + 8.39449e7i 0.312148 + 0.226789i
\(719\) −3.08862e8 4.25112e8i −0.830956 1.14371i −0.987744 0.156080i \(-0.950114\pi\)
0.156789 0.987632i \(-0.449886\pi\)
\(720\) −1.50281e7 + 4.39561e8i −0.0402631 + 1.17767i
\(721\) 2.04453e7 6.29242e7i 0.0545492 0.167885i
\(722\) −1.62667e8 2.23892e8i −0.432203 0.594877i
\(723\) 5.93737e8 1.81761e8i 1.57101 0.480934i
\(724\) 1.64612e8 + 5.06622e8i 0.433755 + 1.33496i
\(725\) 3.31908e8i 0.870972i
\(726\) −4.47026e8 5.82898e8i −1.16822 1.52329i
\(727\) −1.47212e8 −0.383124 −0.191562 0.981480i \(-0.561355\pi\)
−0.191562 + 0.981480i \(0.561355\pi\)
\(728\) −3.13930e8 + 1.02002e8i −0.813652 + 0.264371i
\(729\) −8.13801e7 3.78777e8i −0.210056 0.977689i
\(730\) 325444. 236449.i 0.000836580 0.000607811i
\(731\) −2.62992e7 8.54512e6i −0.0673271 0.0218759i
\(732\) −2.52699e8 3.60611e8i −0.644273 0.919402i
\(733\) 3.70513e8 2.69193e8i 0.940787 0.683521i −0.00782327 0.999969i \(-0.502490\pi\)
0.948610 + 0.316448i \(0.102490\pi\)
\(734\) 7.43070e8 1.02275e9i 1.87906 2.58631i
\(735\) 3.71781e7 1.08101e8i 0.0936322 0.272251i
\(736\) 2.18943e9 5.49158
\(737\) −4.63041e8 4.43546e8i −1.15669 1.10799i
\(738\) 9.62389e7 + 3.34701e8i 0.239432 + 0.832699i
\(739\) 3.54314e7 + 1.09047e8i 0.0877921 + 0.270196i 0.985308 0.170785i \(-0.0546304\pi\)
−0.897516 + 0.440981i \(0.854630\pi\)
\(740\) −2.56064e8 + 3.52442e8i −0.631908 + 0.869747i
\(741\) −5.80409e6 + 3.39630e8i −0.0142652 + 0.834740i
\(742\) −6.38394e7 + 1.96477e8i −0.156270 + 0.480951i
\(743\) −3.06747e8 9.96682e7i −0.747850 0.242991i −0.0897940 0.995960i \(-0.528621\pi\)
−0.658056 + 0.752969i \(0.728621\pi\)
\(744\) −6.40493e8 1.09457e7i −1.55523 0.0265781i
\(745\) −4.15013e6 3.01525e6i −0.0100368 0.00729213i
\(746\) −3.43767e8 + 1.11697e8i −0.828033 + 0.269044i
\(747\) 1.36349e8 3.92052e7i 0.327106 0.0940550i
\(748\) −1.27062e9 6.13371e8i −3.03607 1.46561i
\(749\) 1.02601e8i 0.244177i
\(750\) −4.83422e8 1.66258e8i −1.14589 0.394093i
\(751\) −6.40825e8 4.65587e8i −1.51293 1.09921i −0.964855 0.262783i \(-0.915360\pi\)
−0.548078 0.836427i \(-0.684640\pi\)
\(752\) 1.00084e9 + 1.37753e9i 2.35347 + 3.23928i
\(753\) −4.38449e8 + 3.07244e8i −1.02691 + 0.719612i
\(754\) 1.77008e8 5.44774e8i 0.412932 1.27087i
\(755\) 1.35817e8 + 1.86935e8i 0.315582 + 0.434361i
\(756\) 2.35800e8 + 3.62230e8i 0.545731 + 0.838338i
\(757\) 1.76971e8 + 5.44661e8i 0.407957 + 1.25556i 0.918401 + 0.395652i \(0.129481\pi\)
−0.510443 + 0.859911i \(0.670519\pi\)
\(758\) 3.15646e8i 0.724758i
\(759\) −3.05991e8 + 6.07149e8i −0.699814 + 1.38858i
\(760\) −5.58285e8 −1.27179
\(761\) 7.57600e8 2.46159e8i 1.71904 0.558550i 0.727244 0.686379i \(-0.240801\pi\)
0.991796 + 0.127829i \(0.0408008\pi\)
\(762\) 2.03033e8 + 6.63224e8i 0.458883 + 1.49898i
\(763\) 1.13936e8 8.27795e7i 0.256500 0.186358i
\(764\) 8.92054e7 + 2.89846e7i 0.200037 + 0.0649960i
\(765\) −1.87799e8 6.42065e6i −0.419478 0.0143415i
\(766\) 7.03472e8 5.11102e8i 1.56517 1.13716i
\(767\) 2.52742e7 3.47869e7i 0.0560133 0.0770957i
\(768\) −8.39547e8 2.88736e8i −1.85337 0.637408i
\(769\) 1.65866e8 0.364736 0.182368 0.983230i \(-0.441624\pi\)
0.182368 + 0.983230i \(0.441624\pi\)
\(770\) 1.08143e8 + 1.47524e7i 0.236878 + 0.0323140i
\(771\) 3.08060e7 + 2.31963e7i 0.0672159 + 0.0506123i
\(772\) −3.50569e7 1.07894e8i −0.0761941 0.234501i
\(773\) 3.75023e8 5.16175e8i 0.811932 1.11753i −0.179091 0.983833i \(-0.557316\pi\)
0.991022 0.133696i \(-0.0426845\pi\)
\(774\) 3.08701e7 3.95716e7i 0.0665757 0.0853415i
\(775\) 6.14347e7 1.89077e8i 0.131980 0.406193i
\(776\) −1.83393e9 5.95879e8i −3.92461 1.27518i
\(777\) −3.57628e6 + 2.09268e8i −0.00762375 + 0.446109i
\(778\) 2.52025e8 + 1.83107e8i 0.535186 + 0.388836i
\(779\) −2.38642e8 + 7.75393e7i −0.504817 + 0.164025i
\(780\) 2.41574e8 + 1.81901e8i 0.509057 + 0.383310i
\(781\) 1.68402e8 + 3.13649e8i 0.353503 + 0.658401i
\(782\) 1.79224e9i 3.74780i
\(783\) −4.70095e8 2.41198e7i −0.979265 0.0502445i
\(784\) 1.18348e9 + 8.59849e8i 2.45591 + 1.78433i
\(785\) −9.79654e7 1.34838e8i −0.202518 0.278742i
\(786\) −6.19020e8 8.83365e8i −1.27479 1.81917i
\(787\) 2.05445e8 6.32294e8i 0.421474 1.29716i −0.484857 0.874594i \(-0.661128\pi\)
0.906330 0.422570i \(-0.138872\pi\)
\(788\) −4.70659e8 6.47807e8i −0.961896 1.32394i
\(789\) 8.14365e7 + 2.66019e8i 0.165801 + 0.541604i
\(790\) 6.42593e7 + 1.97770e8i 0.130333 + 0.401124i
\(791\) 2.42344e8i 0.489669i
\(792\) 1.15070e9 1.12189e9i 2.31625 2.25827i
\(793\) −1.48013e8 −0.296812
\(794\) −3.55134e8 + 1.15390e8i −0.709465 + 0.230519i
\(795\) 1.13574e8 3.47685e7i 0.226036 0.0691965i
\(796\) −8.12482e8 + 5.90303e8i −1.61092 + 1.17040i
\(797\) −3.79248e8 1.23225e8i −0.749114 0.243402i −0.0905140 0.995895i \(-0.528851\pi\)
−0.658600 + 0.752493i \(0.728851\pi\)
\(798\) −3.50006e8 + 2.45268e8i −0.688759 + 0.482649i
\(799\) −5.88541e8 + 4.27600e8i −1.15381 + 0.838296i
\(800\) 9.44064e8 1.29939e9i 1.84388 2.53788i
\(801\) 2.09473e8 + 3.10067e8i 0.407596 + 0.603334i
\(802\) −6.39409e8 −1.23953
\(803\) −826671. 112771.i −0.00159656 0.000217797i
\(804\) 1.34456e9 1.78565e9i 2.58710 3.43581i
\(805\) −3.12169e7 9.60757e7i −0.0598414 0.184173i
\(806\) −2.01670e8 + 2.77575e8i −0.385156 + 0.530122i
\(807\) 7.18631e8 + 1.22810e7i 1.36737 + 0.0233676i
\(808\) −3.83265e8 + 1.17957e9i −0.726550 + 2.23609i
\(809\) 6.94085e8 + 2.25522e8i 1.31089 + 0.425935i 0.879358 0.476161i \(-0.157972\pi\)
0.431535 + 0.902096i \(0.357972\pi\)
\(810\) 1.27296e8 3.16400e8i 0.239530 0.595363i
\(811\) 2.90888e7 + 2.11342e7i 0.0545334 + 0.0396208i 0.614718 0.788747i \(-0.289270\pi\)
−0.560185 + 0.828368i \(0.689270\pi\)
\(812\) 4.99440e8 1.62278e8i 0.932857 0.303104i
\(813\) 1.92255e8 2.55325e8i 0.357772 0.475141i
\(814\) 1.22032e9 2.20271e8i 2.26256 0.408398i
\(815\) 1.27845e8i 0.236163i
\(816\) 7.82033e8 2.27389e9i 1.43931 4.18503i
\(817\) 2.92546e7 + 2.12547e7i 0.0536448 + 0.0389752i
\(818\) 3.11195e8 + 4.28323e8i 0.568555 + 0.782549i
\(819\) 1.45199e8 + 4.96421e6i 0.264310 + 0.00903646i
\(820\) −6.90295e7 + 2.12451e8i −0.125197 + 0.385316i
\(821\) 1.88016e8 + 2.58782e8i 0.339755 + 0.467633i 0.944370 0.328885i \(-0.106673\pi\)
−0.604615 + 0.796518i \(0.706673\pi\)
\(822\) −8.01304e8 + 2.45304e8i −1.44272 + 0.441660i
\(823\) −1.66612e8 5.12780e8i −0.298888 0.919882i −0.981888 0.189463i \(-0.939325\pi\)
0.683000 0.730418i \(-0.260675\pi\)
\(824\) 8.57597e8i 1.53286i
\(825\) 2.28393e8 + 4.43398e8i 0.406743 + 0.789646i
\(826\) 5.41019e7 0.0960002
\(827\) −2.80623e7 + 9.11801e6i −0.0496143 + 0.0161207i −0.333719 0.942673i \(-0.608304\pi\)
0.284105 + 0.958793i \(0.408304\pi\)
\(828\) −2.22781e9 8.09013e8i −3.92453 1.42516i
\(829\) −6.83370e8 + 4.96497e8i −1.19948 + 0.871472i −0.994233 0.107239i \(-0.965799\pi\)
−0.205244 + 0.978711i \(0.565799\pi\)
\(830\) 1.18779e8 + 3.85936e7i 0.207732 + 0.0674964i
\(831\) 5.41934e8 + 7.73360e8i 0.944373 + 1.34766i
\(832\) −1.07658e9 + 7.82182e8i −1.86929 + 1.35812i
\(833\) −3.67364e8 + 5.05633e8i −0.635568 + 0.874784i
\(834\) −1.32031e8 + 3.83900e8i −0.227602 + 0.661790i
\(835\) 3.20539e7 0.0550582
\(836\) 1.33238e9 + 1.27629e9i 2.28039 + 2.18438i
\(837\) 2.63332e8 + 1.00753e8i 0.449084 + 0.171822i
\(838\) 1.92004e8 + 5.90928e8i 0.326271 + 1.00416i
\(839\) −6.39594e8 + 8.80326e8i −1.08298 + 1.49059i −0.226774 + 0.973947i \(0.572818\pi\)
−0.856202 + 0.516641i \(0.827182\pi\)
\(840\) −4.08009e6 + 2.38749e8i −0.00688386 + 0.402813i
\(841\) 7.07953e6 2.17886e7i 0.0119019 0.0366303i
\(842\) 3.20027e8 + 1.03983e8i 0.536105 + 0.174191i
\(843\) −2.02213e8 3.45570e6i −0.337540 0.00576838i
\(844\) −2.29772e9 1.66939e9i −3.82181 2.77671i
\(845\) −9.51540e7 + 3.09174e7i −0.157709 + 0.0512428i
\(846\) −3.64863e8 1.26893e9i −0.602586 2.09568i
\(847\) −1.40807e8 1.77248e8i −0.231725 0.291697i
\(848\) 1.51995e9i 2.49253i
\(849\) 2.43375e8 + 8.37013e7i 0.397698 + 0.136776i
\(850\) 1.06367e9 + 7.72800e8i 1.73200 + 1.25837i
\(851\) −6.74621e8 9.28536e8i −1.09464 1.50664i
\(852\) −1.01633e9 + 7.12196e8i −1.64330 + 1.15154i
\(853\) 5.66742e7 1.74425e8i 0.0913142 0.281036i −0.894961 0.446144i \(-0.852797\pi\)
0.986276 + 0.165107i \(0.0527971\pi\)
\(854\) −1.09464e8 1.50665e8i −0.175752 0.241901i
\(855\) 2.30967e8 + 8.38738e7i 0.369531 + 0.134192i
\(856\) 4.10964e8 + 1.26482e9i 0.655213 + 2.01654i
\(857\) 1.88044e8i 0.298756i 0.988780 + 0.149378i \(0.0477272\pi\)
−0.988780 + 0.149378i \(0.952273\pi\)
\(858\) −1.38404e8 8.49569e8i −0.219123 1.34505i
\(859\) 8.98124e8 1.41696 0.708479 0.705732i \(-0.249382\pi\)
0.708479 + 0.705732i \(0.249382\pi\)
\(860\) 3.06165e7 9.94789e6i 0.0481349 0.0156400i
\(861\) 3.14155e7 + 1.02621e8i 0.0492191 + 0.160778i
\(862\) 2.24859e8 1.63370e8i 0.351066 0.255064i
\(863\) −8.72115e7 2.83367e7i −0.135688 0.0440877i 0.240386 0.970677i \(-0.422726\pi\)
−0.376074 + 0.926590i \(0.622726\pi\)
\(864\) 1.77178e9 + 1.43154e9i 2.74706 + 2.21954i
\(865\) −1.93506e7 + 1.40590e7i −0.0298982 + 0.0217223i
\(866\) −5.04146e8 + 6.93897e8i −0.776251 + 1.06842i
\(867\) 3.55217e8 + 1.22166e8i 0.545049 + 0.187453i
\(868\) −3.14550e8 −0.480984
\(869\) 1.87496e8 3.88405e8i 0.285715 0.591869i
\(870\) −3.31022e8 2.49253e8i −0.502689 0.378515i
\(871\) −2.32181e8 7.14580e8i −0.351376 1.08143i
\(872\) 1.07299e9 1.47684e9i 1.61825 2.22733i
\(873\) 6.69188e8 + 5.22039e8i 1.00578 + 0.784622i
\(874\) 7.24234e8 2.22896e9i 1.08479 3.33863i
\(875\) −1.49827e8 4.86818e7i −0.223649 0.0726679i
\(876\) 49697.6 2.90808e6i 7.39304e−5 0.00432608i
\(877\) 4.82169e8 + 3.50316e8i 0.714826 + 0.519352i 0.884727 0.466110i \(-0.154345\pi\)
−0.169901 + 0.985461i \(0.554345\pi\)
\(878\) −7.28386e8 + 2.36667e8i −1.07616 + 0.349666i
\(879\) −3.49330e8 2.63039e8i −0.514363 0.387305i
\(880\) 7.90244e8 1.42641e8i 1.15961 0.209314i
\(881\) 3.47755e8i 0.508564i −0.967130 0.254282i \(-0.918161\pi\)
0.967130 0.254282i \(-0.0818391\pi\)
\(882\) −6.35005e8 9.39951e8i −0.925490 1.36993i
\(883\) 5.45621e8 + 3.96417e8i 0.792517 + 0.575797i 0.908709 0.417429i \(-0.137069\pi\)
−0.116192 + 0.993227i \(0.537069\pi\)
\(884\) −9.71789e8 1.33755e9i −1.40674 1.93622i
\(885\) −1.78507e7 2.54736e7i −0.0257529 0.0367503i
\(886\) 1.49445e8 4.59943e8i 0.214871 0.661306i
\(887\) 6.63964e7 + 9.13868e7i 0.0951423 + 0.130952i 0.853934 0.520381i \(-0.174210\pi\)
−0.758792 + 0.651333i \(0.774210\pi\)
\(888\) 7.94133e8 + 2.59410e9i 1.13411 + 3.70466i
\(889\) 6.60507e7 + 2.03283e8i 0.0940095 + 0.289332i
\(890\) 3.29403e8i 0.467259i
\(891\) −6.44600e8 + 2.91260e8i −0.911291 + 0.411763i
\(892\) 3.54863e8 0.499996
\(893\) 9.04743e8 2.93969e8i 1.27049 0.412807i
\(894\) −4.86733e7 + 1.49004e7i −0.0681206 + 0.0208538i
\(895\) −4.46721e7 + 3.24562e7i −0.0623114 + 0.0452719i
\(896\) −6.92311e8 2.24945e8i −0.962447 0.312718i
\(897\) −6.52448e8 + 4.57204e8i −0.904000 + 0.633480i
\(898\) −1.14021e9 + 8.28414e8i −1.57455 + 1.14398i
\(899\) 2.01355e8 2.77141e8i 0.277130 0.381436i
\(900\) −1.44075e9 + 9.73331e8i −1.97634 + 1.33516i
\(901\) −6.49386e8 −0.887827
\(902\) 5.60213e8 3.00785e8i 0.763367 0.409861i
\(903\) 9.30332e6 1.23553e7i 0.0126350 0.0167799i
\(904\) 9.70704e8 + 2.98752e9i 1.31396 + 4.04395i
\(905\) 7.61361e7 1.04792e8i 0.102718 0.141379i
\(906\) 2.29250e9 + 3.91776e7i 3.08265 + 0.0526809i
\(907\) −3.39605e8 + 1.04520e9i −0.455147 + 1.40080i 0.415816 + 0.909449i \(0.363496\pi\)
−0.870963 + 0.491349i \(0.836504\pi\)
\(908\) −1.71720e9 5.57952e8i −2.29384 0.745314i
\(909\) 3.35772e8 4.30417e8i 0.447047 0.573057i
\(910\) 1.03469e8 + 7.51743e7i 0.137304 + 0.0997574i
\(911\) −3.39666e8 + 1.10364e8i −0.449260 + 0.145973i −0.524904 0.851162i \(-0.675899\pi\)
0.0756442 + 0.997135i \(0.475899\pi\)
\(912\) −1.89146e9 + 2.51196e9i −2.49352 + 3.31153i
\(913\) −1.22532e8 2.28216e8i −0.161004 0.299871i
\(914\) 1.17642e9i 1.54072i
\(915\) −3.48225e7 + 1.01252e8i −0.0454566 + 0.132172i
\(916\) −2.60633e9 1.89361e9i −3.39112 2.46379i
\(917\) −1.95383e8 2.68922e8i −0.253384 0.348754i
\(918\) −1.17184e9 + 1.45035e9i −1.51475 + 1.87476i
\(919\) −9.06802e7 + 2.79085e8i −0.116833 + 0.359575i −0.992325 0.123658i \(-0.960538\pi\)
0.875492 + 0.483233i \(0.160538\pi\)
\(920\) −7.69658e8 1.05934e9i −0.988404 1.36042i
\(921\) 1.11396e8 3.41017e7i 0.142590 0.0436513i
\(922\) −8.18949e8 2.52047e9i −1.04487 3.21579i
\(923\) 4.17155e8i 0.530508i
\(924\) 5.55538e8 5.60462e8i 0.704203 0.710445i
\(925\) −8.41963e8 −1.06382
\(926\) 7.25947e8 2.35875e8i 0.914265 0.297063i
\(927\) −1.28841e8 + 3.54794e8i −0.161739 + 0.445387i
\(928\) 2.23899e9 1.62672e9i 2.80162 2.03549i
\(929\) 1.21084e9 + 3.93427e8i 1.51022 + 0.490701i 0.942980 0.332850i \(-0.108010\pi\)
0.567242 + 0.823551i \(0.308010\pi\)
\(930\) 1.42436e8 + 2.03262e8i 0.177081 + 0.252701i
\(931\) 6.61205e8 4.80393e8i 0.819383 0.595317i
\(932\) 1.86507e9 2.56705e9i 2.30381 3.17093i
\(933\) 5.22061e8 1.51798e9i 0.642801 1.86905i
\(934\) 1.27303e9 1.56242
\(935\) 6.09425e7 + 3.37626e8i 0.0745565 + 0.413049i
\(936\) 1.80984e9 5.20396e8i 2.20706 0.634609i
\(937\) 1.43231e8 + 4.40820e8i 0.174108 + 0.535850i 0.999592 0.0285766i \(-0.00909744\pi\)
−0.825483 + 0.564426i \(0.809097\pi\)
\(938\) 5.55670e8 7.64814e8i 0.673300 0.926717i
\(939\) −1.63271e7 + 9.55392e8i −0.0197203 + 1.15394i
\(940\) 2.61706e8 8.05449e8i 0.315087 0.969738i
\(941\) −6.07150e8 1.97275e8i −0.728663 0.236757i −0.0788880 0.996883i \(-0.525137\pi\)
−0.649775 + 0.760126i \(0.725137\pi\)
\(942\) −1.65360e9 2.82590e7i −1.97823 0.0338069i
\(943\) −4.76125e8 3.45925e8i −0.567787 0.412522i
\(944\) 3.78565e8 1.23003e8i 0.450013 0.146218i
\(945\) 3.75564e7 9.81593e7i 0.0445029 0.116315i
\(946\) −8.25214e7 3.98358e7i −0.0974750 0.0470544i
\(947\) 6.49572e7i 0.0764851i 0.999268 + 0.0382426i \(0.0121760\pi\)
−0.999268 + 0.0382426i \(0.987824\pi\)
\(948\) 1.42177e9 + 4.88975e8i 1.66880 + 0.573933i
\(949\) −790940. 574652.i −0.000925433 0.000672366i
\(950\) −1.01057e9 1.39093e9i −1.17868 1.62232i
\(951\) 3.16155e8 2.21546e8i 0.367585 0.257586i
\(952\) 4.03421e8 1.24160e9i 0.467572 1.43904i
\(953\) −6.64068e8 9.14012e8i −0.767245 1.05602i −0.996577 0.0826739i \(-0.973654\pi\)
0.229332 0.973348i \(-0.426346\pi\)
\(954\) 4.02299e8 1.10783e9i 0.463344 1.27593i
\(955\) −7.04792e6 2.16913e7i −0.00809191 0.0249043i
\(956\) 3.00536e9i 3.43971i
\(957\) 1.38188e8 + 8.48241e8i 0.157664 + 0.967795i
\(958\) −2.88300e9 −3.27905
\(959\) −2.45606e8 + 7.98021e7i −0.278473 + 0.0904812i
\(960\) 2.81788e8 + 9.20482e8i 0.318499 + 1.04040i
\(961\) 5.52003e8 4.01054e8i 0.621973 0.451890i
\(962\) 1.38195e9 + 4.49021e8i 1.55226 + 0.504361i
\(963\) 2.00007e7 5.85006e8i 0.0223958 0.655060i
\(964\) 3.19734e9 2.32300e9i 3.56909 2.59309i
\(965\) −1.62145e7 + 2.23173e7i −0.0180435 + 0.0248348i
\(966\) −9.47918e8 3.26007e8i −1.05157 0.361656i
\(967\) 4.01098e8 0.443579 0.221790 0.975095i \(-0.428810\pi\)
0.221790 + 0.975095i \(0.428810\pi\)
\(968\) −2.44577e9 1.62105e9i −2.69644 1.78719i
\(969\) −1.07322e9 8.08112e8i −1.17955 0.888179i
\(970\) 2.30878e8 + 7.10569e8i 0.252969 + 0.778559i
\(971\) 6.30039e8 8.67174e8i 0.688192 0.947215i −0.311804 0.950146i \(-0.600933\pi\)
0.999996 + 0.00293184i \(0.000933236\pi\)
\(972\) −1.27387e9 2.11132e9i −1.38716 2.29909i
\(973\) −3.86597e7 + 1.18982e8i −0.0419682 + 0.129165i
\(974\) 1.79806e9 + 5.84224e8i 1.94593 + 0.632270i
\(975\) −9.98640e6 + 5.84361e8i −0.0107745 + 0.630474i
\(976\) −1.10850e9 8.05369e8i −1.19230 0.866255i
\(977\) −1.02138e9 + 3.31867e8i −1.09523 + 0.355861i −0.800265 0.599647i \(-0.795308\pi\)
−0.294964 + 0.955508i \(0.595308\pi\)
\(978\) 1.01342e9 + 7.63089e8i 1.08336 + 0.815753i
\(979\) 4.72596e8 4.93368e8i 0.503665 0.525802i
\(980\) 7.27597e8i 0.773059i
\(981\) −6.65775e8 + 4.49780e8i −0.705214 + 0.476423i
\(982\) 1.87770e9 + 1.36423e9i 1.98286 + 1.44063i
\(983\) −4.09681e8 5.63878e8i −0.431306 0.593642i 0.536947 0.843616i \(-0.319578\pi\)
−0.968252 + 0.249975i \(0.919578\pi\)
\(984\) 7.98324e8 + 1.13924e9i 0.837903 + 1.19572i
\(985\) −6.01678e7 + 1.85178e8i −0.0629587 + 0.193767i
\(986\) 1.33162e9 + 1.83281e9i 1.38915 + 1.91200i
\(987\) −1.19103e8 3.89060e8i −0.123871 0.404636i
\(988\) 6.68091e8 + 2.05617e9i 0.692732 + 2.13201i
\(989\) 8.48124e7i 0.0876740i
\(990\) −6.13730e8 1.05196e8i −0.632517 0.108416i
\(991\) 1.18644e8 0.121906 0.0609531 0.998141i \(-0.480586\pi\)
0.0609531 + 0.998141i \(0.480586\pi\)
\(992\) −1.57657e9 + 5.12260e8i −1.61503 + 0.524754i
\(993\) 4.97446e8 1.52283e8i 0.508040 0.155526i
\(994\) −4.24628e8 + 3.08510e8i −0.432364 + 0.314131i
\(995\) 2.32250e8 + 7.54627e7i 0.235769 + 0.0766061i
\(996\) 7.39499e8 5.18206e8i 0.748445 0.524475i
\(997\) −7.16637e8 + 5.20668e8i −0.723126 + 0.525382i −0.887381 0.461036i \(-0.847478\pi\)
0.164255 + 0.986418i \(0.447478\pi\)
\(998\) −8.12317e8 + 1.11806e9i −0.817210 + 1.12479i
\(999\) 6.11854e7 1.19250e9i 0.0613694 1.19609i
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 33.7.h.a.5.1 88
3.2 odd 2 inner 33.7.h.a.5.22 yes 88
11.9 even 5 inner 33.7.h.a.20.22 yes 88
33.20 odd 10 inner 33.7.h.a.20.1 yes 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.7.h.a.5.1 88 1.1 even 1 trivial
33.7.h.a.5.22 yes 88 3.2 odd 2 inner
33.7.h.a.20.1 yes 88 33.20 odd 10 inner
33.7.h.a.20.22 yes 88 11.9 even 5 inner