Properties

Label 33.7.h.a.5.18
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 5.18
Character \(\chi\) \(=\) 33.5
Dual form 33.7.h.a.20.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(10.0445 - 3.26364i) q^{2} +(-26.0385 + 7.14109i) q^{3} +(38.4627 - 27.9448i) q^{4} +(-135.541 - 44.0400i) q^{5} +(-238.237 + 156.709i) q^{6} +(-206.442 + 149.989i) q^{7} +(-102.165 + 140.618i) q^{8} +(627.010 - 371.887i) q^{9} +O(q^{10})\) \(q+(10.0445 - 3.26364i) q^{2} +(-26.0385 + 7.14109i) q^{3} +(38.4627 - 27.9448i) q^{4} +(-135.541 - 44.0400i) q^{5} +(-238.237 + 156.709i) q^{6} +(-206.442 + 149.989i) q^{7} +(-102.165 + 140.618i) q^{8} +(627.010 - 371.887i) q^{9} -1505.17 q^{10} +(-1234.47 + 497.650i) q^{11} +(-801.956 + 1002.31i) q^{12} +(-971.087 - 2988.70i) q^{13} +(-1584.09 + 2180.31i) q^{14} +(3843.78 + 178.825i) q^{15} +(-1507.52 + 4639.66i) q^{16} +(7847.69 + 2549.87i) q^{17} +(5084.27 - 5781.74i) q^{18} +(-5137.49 - 3732.60i) q^{19} +(-6443.97 + 2093.77i) q^{20} +(4304.36 - 5379.70i) q^{21} +(-10775.4 + 9027.48i) q^{22} +3776.99i q^{23} +(1656.06 - 4391.05i) q^{24} +(3790.97 + 2754.30i) q^{25} +(-19508.1 - 26850.6i) q^{26} +(-13670.7 + 14160.9i) q^{27} +(-3748.91 + 11537.9i) q^{28} +(-1436.79 - 1977.57i) q^{29} +(39192.3 - 10748.5i) q^{30} +(-5446.57 - 16762.8i) q^{31} +40398.8i q^{32} +(28589.9 - 21773.5i) q^{33} +87147.7 q^{34} +(34586.8 - 11237.9i) q^{35} +(13724.2 - 31825.4i) q^{36} +(29569.5 - 21483.5i) q^{37} +(-63785.2 - 20725.1i) q^{38} +(46628.2 + 70886.7i) q^{39} +(20040.3 - 14560.2i) q^{40} +(-52836.6 + 72723.4i) q^{41} +(25677.5 - 68084.1i) q^{42} -109788. q^{43} +(-33574.2 + 53637.9i) q^{44} +(-101363. + 22792.5i) q^{45} +(12326.7 + 37937.8i) q^{46} +(-1653.97 + 2276.50i) q^{47} +(6121.29 - 131575. i) q^{48} +(-16234.0 + 49963.0i) q^{49} +(47067.3 + 15293.1i) q^{50} +(-222551. - 10353.8i) q^{51} +(-120869. - 87816.7i) q^{52} +(-150754. + 48982.8i) q^{53} +(-91098.9 + 186855. i) q^{54} +(189237. - 13086.2i) q^{55} -44353.0i q^{56} +(160428. + 60504.2i) q^{57} +(-20885.9 - 15174.5i) q^{58} +(19479.0 + 26810.6i) q^{59} +(152840. - 100536. i) q^{60} +(26978.7 - 83031.9i) q^{61} +(-109416. - 150598. i) q^{62} +(-73662.1 + 170817. i) q^{63} +(35366.3 + 108846. i) q^{64} +447858. i q^{65} +(216109. - 312010. i) q^{66} -313862. q^{67} +(373099. - 121227. i) q^{68} +(-26971.8 - 98347.2i) q^{69} +(310729. - 225758. i) q^{70} +(-47149.1 - 15319.7i) q^{71} +(-11764.4 + 126163. i) q^{72} +(170002. - 123514. i) q^{73} +(226895. - 312294. i) q^{74} +(-118380. - 44646.3i) q^{75} -301909. q^{76} +(180203. - 287892. i) q^{77} +(699704. + 559841. i) q^{78} +(281643. + 866807. i) q^{79} +(408661. - 562474. i) q^{80} +(254841. - 466353. i) q^{81} +(-293372. + 902907. i) q^{82} +(-47743.4 - 15512.8i) q^{83} +(15222.5 - 327202. i) q^{84} +(-951388. - 691224. i) q^{85} +(-1.10276e6 + 358309. i) q^{86} +(51533.9 + 41232.8i) q^{87} +(56140.5 - 224430. i) q^{88} -884246. i q^{89} +(-943754. + 559752. i) q^{90} +(648744. + 471340. i) q^{91} +(105547. + 145273. i) q^{92} +(261525. + 397585. i) q^{93} +(-9183.58 + 28264.2i) q^{94} +(531957. + 732176. i) q^{95} +(-288492. - 1.05193e6i) q^{96} +(-482465. - 1.48487e6i) q^{97} +554833. i q^{98} +(-588952. + 771113. 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.0445 3.26364i 1.25556 0.407955i 0.395648 0.918402i \(-0.370520\pi\)
0.859909 + 0.510447i \(0.170520\pi\)
\(3\) −26.0385 + 7.14109i −0.964390 + 0.264485i
\(4\) 38.4627 27.9448i 0.600980 0.436638i
\(5\) −135.541 44.0400i −1.08433 0.352320i −0.288276 0.957547i \(-0.593082\pi\)
−0.796052 + 0.605228i \(0.793082\pi\)
\(6\) −238.237 + 156.709i −1.10295 + 0.725504i
\(7\) −206.442 + 149.989i −0.601871 + 0.437285i −0.846542 0.532321i \(-0.821320\pi\)
0.244672 + 0.969606i \(0.421320\pi\)
\(8\) −102.165 + 140.618i −0.199541 + 0.274644i
\(9\) 627.010 371.887i 0.860096 0.510133i
\(10\) −1505.17 −1.50517
\(11\) −1234.47 + 497.650i −0.927472 + 0.373892i
\(12\) −801.956 + 1002.31i −0.464095 + 0.580039i
\(13\) −971.087 2988.70i −0.442006 1.36035i −0.885734 0.464193i \(-0.846344\pi\)
0.443728 0.896161i \(-0.353656\pi\)
\(14\) −1584.09 + 2180.31i −0.577291 + 0.794573i
\(15\) 3843.78 + 178.825i 1.13890 + 0.0529851i
\(16\) −1507.52 + 4639.66i −0.368046 + 1.13273i
\(17\) 7847.69 + 2549.87i 1.59733 + 0.519005i 0.966446 0.256870i \(-0.0826914\pi\)
0.630886 + 0.775875i \(0.282691\pi\)
\(18\) 5084.27 5781.74i 0.871788 0.991382i
\(19\) −5137.49 3732.60i −0.749014 0.544191i 0.146507 0.989210i \(-0.453197\pi\)
−0.895521 + 0.445019i \(0.853197\pi\)
\(20\) −6443.97 + 2093.77i −0.805496 + 0.261721i
\(21\) 4304.36 5379.70i 0.464783 0.580899i
\(22\) −10775.4 + 9027.48i −1.01196 + 0.847810i
\(23\) 3776.99i 0.310429i 0.987881 + 0.155214i \(0.0496069\pi\)
−0.987881 + 0.155214i \(0.950393\pi\)
\(24\) 1656.06 4391.05i 0.119796 0.317640i
\(25\) 3790.97 + 2754.30i 0.242622 + 0.176275i
\(26\) −19508.1 26850.6i −1.10993 1.52768i
\(27\) −13670.7 + 14160.9i −0.694545 + 0.719449i
\(28\) −3748.91 + 11537.9i −0.170777 + 0.525599i
\(29\) −1436.79 1977.57i −0.0589114 0.0810845i 0.778545 0.627589i \(-0.215958\pi\)
−0.837456 + 0.546504i \(0.815958\pi\)
\(30\) 39192.3 10748.5i 1.45157 0.398094i
\(31\) −5446.57 16762.8i −0.182826 0.562681i 0.817078 0.576527i \(-0.195592\pi\)
−0.999904 + 0.0138464i \(0.995592\pi\)
\(32\) 40398.8i 1.23287i
\(33\) 28589.9 21773.5i 0.795556 0.605880i
\(34\) 87147.7 2.21727
\(35\) 34586.8 11237.9i 0.806690 0.262109i
\(36\) 13724.2 31825.4i 0.294157 0.682130i
\(37\) 29569.5 21483.5i 0.583766 0.424131i −0.256314 0.966594i \(-0.582508\pi\)
0.840080 + 0.542463i \(0.182508\pi\)
\(38\) −63785.2 20725.1i −1.16244 0.377698i
\(39\) 46628.2 + 70886.7i 0.786059 + 1.19501i
\(40\) 20040.3 14560.2i 0.313130 0.227503i
\(41\) −52836.6 + 72723.4i −0.766626 + 1.05517i 0.230008 + 0.973189i \(0.426125\pi\)
−0.996634 + 0.0819815i \(0.973875\pi\)
\(42\) 25677.5 68084.1i 0.346581 0.918962i
\(43\) −109788. −1.38086 −0.690429 0.723400i \(-0.742578\pi\)
−0.690429 + 0.723400i \(0.742578\pi\)
\(44\) −33574.2 + 53637.9i −0.394137 + 0.629671i
\(45\) −101363. + 22792.5i −1.11236 + 0.250123i
\(46\) 12326.7 + 37937.8i 0.126641 + 0.389761i
\(47\) −1653.97 + 2276.50i −0.0159307 + 0.0219267i −0.816908 0.576768i \(-0.804314\pi\)
0.800977 + 0.598695i \(0.204314\pi\)
\(48\) 6121.29 131575.i 0.0553502 1.18974i
\(49\) −16234.0 + 49963.0i −0.137986 + 0.424679i
\(50\) 47067.3 + 15293.1i 0.376538 + 0.122345i
\(51\) −222551. 10353.8i −1.67772 0.0780528i
\(52\) −120869. 87816.7i −0.859619 0.624549i
\(53\) −150754. + 48982.8i −1.01261 + 0.329015i −0.767892 0.640580i \(-0.778694\pi\)
−0.244714 + 0.969595i \(0.578694\pi\)
\(54\) −91098.9 + 186855.i −0.578538 + 1.18665i
\(55\) 189237. 13086.2i 1.13741 0.0786550i
\(56\) 44353.0i 0.252557i
\(57\) 160428. + 60504.2i 0.866272 + 0.326709i
\(58\) −20885.9 15174.5i −0.107045 0.0777731i
\(59\) 19479.0 + 26810.6i 0.0948443 + 0.130542i 0.853802 0.520598i \(-0.174291\pi\)
−0.758958 + 0.651140i \(0.774291\pi\)
\(60\) 152840. 100536.i 0.707591 0.465443i
\(61\) 26978.7 83031.9i 0.118859 0.365810i −0.873873 0.486153i \(-0.838400\pi\)
0.992732 + 0.120344i \(0.0383996\pi\)
\(62\) −109416. 150598.i −0.459097 0.631893i
\(63\) −73662.1 + 170817.i −0.294593 + 0.683141i
\(64\) 35366.3 + 108846.i 0.134912 + 0.415215i
\(65\) 447858.i 1.63080i
\(66\) 216109. 312010.i 0.751694 1.08527i
\(67\) −313862. −1.04355 −0.521776 0.853083i \(-0.674730\pi\)
−0.521776 + 0.853083i \(0.674730\pi\)
\(68\) 373099. 121227.i 1.18658 0.385544i
\(69\) −26971.8 98347.2i −0.0821037 0.299375i
\(70\) 310729. 225758.i 0.905916 0.658187i
\(71\) −47149.1 15319.7i −0.131734 0.0428031i 0.242408 0.970174i \(-0.422063\pi\)
−0.374142 + 0.927371i \(0.622063\pi\)
\(72\) −11764.4 + 126163.i −0.0315191 + 0.338013i
\(73\) 170002. 123514.i 0.437004 0.317502i −0.347439 0.937703i \(-0.612949\pi\)
0.784444 + 0.620200i \(0.212949\pi\)
\(74\) 226895. 312294.i 0.559925 0.770671i
\(75\) −118380. 44646.3i −0.280604 0.105828i
\(76\) −301909. −0.687757
\(77\) 180203. 287892.i 0.394721 0.630604i
\(78\) 699704. + 559841.i 1.47445 + 1.17972i
\(79\) 281643. + 866807.i 0.571238 + 1.75809i 0.648645 + 0.761091i \(0.275336\pi\)
−0.0774066 + 0.997000i \(0.524664\pi\)
\(80\) 408661. 562474.i 0.798166 1.09858i
\(81\) 254841. 466353.i 0.479529 0.877526i
\(82\) −293372. + 902907.i −0.532081 + 1.63758i
\(83\) −47743.4 15512.8i −0.0834986 0.0271303i 0.266970 0.963705i \(-0.413978\pi\)
−0.350468 + 0.936575i \(0.613978\pi\)
\(84\) 15222.5 327202.i 0.0256831 0.552050i
\(85\) −951388. 691224.i −1.54918 1.12554i
\(86\) −1.10276e6 + 358309.i −1.73375 + 0.563329i
\(87\) 51533.9 + 41232.8i 0.0782592 + 0.0626160i
\(88\) 56140.5 224430.i 0.0823813 0.329332i
\(89\) 884246.i 1.25431i −0.778896 0.627153i \(-0.784220\pi\)
0.778896 0.627153i \(-0.215780\pi\)
\(90\) −943754. + 559752.i −1.29459 + 0.767835i
\(91\) 648744. + 471340.i 0.860893 + 0.625475i
\(92\) 105547. + 145273.i 0.135545 + 0.186562i
\(93\) 261525. + 397585.i 0.325136 + 0.494289i
\(94\) −9183.58 + 28264.2i −0.0110568 + 0.0340293i
\(95\) 531957. + 732176.i 0.620448 + 0.853974i
\(96\) −288492. 1.05193e6i −0.326077 1.18897i
\(97\) −482465. 1.48487e6i −0.528629 1.62695i −0.757027 0.653384i \(-0.773349\pi\)
0.228398 0.973568i \(-0.426651\pi\)
\(98\) 554833.i 0.589501i
\(99\) −588952. + 771113.i −0.606980 + 0.794717i
\(100\) 222779. 0.222779
\(101\) 1.08562e6 352738.i 1.05369 0.342364i 0.269574 0.962980i \(-0.413117\pi\)
0.784115 + 0.620615i \(0.213117\pi\)
\(102\) −2.26920e6 + 622330.i −2.13832 + 0.586435i
\(103\) 716424. 520513.i 0.655630 0.476343i −0.209554 0.977797i \(-0.567201\pi\)
0.865184 + 0.501454i \(0.167201\pi\)
\(104\) 519476. + 168788.i 0.461812 + 0.150052i
\(105\) −820339. + 539607.i −0.708639 + 0.466133i
\(106\) −1.35438e6 + 984012.i −1.13716 + 0.826196i
\(107\) 277961. 382580.i 0.226899 0.312299i −0.680355 0.732882i \(-0.738175\pi\)
0.907254 + 0.420583i \(0.138175\pi\)
\(108\) −130089. + 926693.i −0.103269 + 0.735639i
\(109\) 1.69565e6 1.30935 0.654676 0.755910i \(-0.272805\pi\)
0.654676 + 0.755910i \(0.272805\pi\)
\(110\) 1.85808e6 749047.i 1.39600 0.562770i
\(111\) −616531. + 770557.i −0.450802 + 0.563425i
\(112\) −384682. 1.18393e6i −0.273809 0.842698i
\(113\) −1.13894e6 + 1.56762e6i −0.789344 + 1.08644i 0.204846 + 0.978794i \(0.434331\pi\)
−0.994190 + 0.107644i \(0.965669\pi\)
\(114\) 1.80887e6 + 84154.4i 1.22094 + 0.0568018i
\(115\) 166338. 511937.i 0.109370 0.336607i
\(116\) −110526. 35912.0i −0.0708091 0.0230073i
\(117\) −1.72034e6 1.51281e6i −1.07413 0.944553i
\(118\) 283156. + 205725.i 0.172338 + 0.125211i
\(119\) −2.00254e6 + 650666.i −1.18834 + 0.386115i
\(120\) −417846. + 522235.i −0.241809 + 0.302219i
\(121\) 1.27625e6 1.22866e6i 0.720410 0.693549i
\(122\) 922059.i 0.507784i
\(123\) 856464. 2.27092e6i 0.460250 1.22036i
\(124\) −677924. 492540.i −0.355562 0.258331i
\(125\) 916358. + 1.26126e6i 0.469175 + 0.645764i
\(126\) −182410. + 1.95617e6i −0.0911876 + 0.977903i
\(127\) −327393. + 1.00761e6i −0.159830 + 0.491906i −0.998618 0.0525517i \(-0.983265\pi\)
0.838788 + 0.544458i \(0.183265\pi\)
\(128\) −809264. 1.11386e6i −0.385887 0.531128i
\(129\) 2.85872e6 784005.i 1.33169 0.365216i
\(130\) 1.46165e6 + 4.49849e6i 0.665293 + 2.04756i
\(131\) 2.58757e6i 1.15101i −0.817799 0.575504i \(-0.804806\pi\)
0.817799 0.575504i \(-0.195194\pi\)
\(132\) 491189. 1.63641e6i 0.213563 0.711491i
\(133\) 1.62044e6 0.688776
\(134\) −3.15257e6 + 1.02433e6i −1.31024 + 0.425722i
\(135\) 2.47659e6 1.31733e6i 1.00659 0.535417i
\(136\) −1.16032e6 + 843019.i −0.461275 + 0.335136i
\(137\) −3.75807e6 1.22107e6i −1.46151 0.474874i −0.532981 0.846127i \(-0.678928\pi\)
−0.928532 + 0.371253i \(0.878928\pi\)
\(138\) −591888. 899819.i −0.225217 0.342387i
\(139\) −1.19535e6 + 868470.i −0.445092 + 0.323378i −0.787655 0.616117i \(-0.788705\pi\)
0.342563 + 0.939495i \(0.388705\pi\)
\(140\) 1.01626e6 1.39876e6i 0.370358 0.509753i
\(141\) 26810.3 71087.8i 0.00956411 0.0253593i
\(142\) −523586. −0.182862
\(143\) 2.68610e6 + 3.20618e6i 0.918574 + 1.09643i
\(144\) 780201. + 3.46974e6i 0.261288 + 1.16201i
\(145\) 107652. + 331318.i 0.0353116 + 0.108678i
\(146\) 1.30447e6 1.79546e6i 0.419157 0.576921i
\(147\) 65918.2 1.41689e6i 0.0207517 0.446051i
\(148\) 536971. 1.65263e6i 0.165640 0.509788i
\(149\) −1.34940e6 438447.i −0.407927 0.132544i 0.0978635 0.995200i \(-0.468799\pi\)
−0.505791 + 0.862656i \(0.668799\pi\)
\(150\) −1.33477e6 62097.8i −0.395488 0.0183993i
\(151\) −2.67678e6 1.94479e6i −0.777467 0.564863i 0.126751 0.991935i \(-0.459545\pi\)
−0.904218 + 0.427072i \(0.859545\pi\)
\(152\) 1.04974e6 341082.i 0.298918 0.0971243i
\(153\) 5.86884e6 1.31966e6i 1.63862 0.368458i
\(154\) 870469. 3.47983e6i 0.238337 0.952788i
\(155\) 2.51192e6i 0.674544i
\(156\) 3.77436e6 + 1.42348e6i 0.994191 + 0.374953i
\(157\) −1.47658e6 1.07280e6i −0.381555 0.277216i 0.380431 0.924809i \(-0.375776\pi\)
−0.761986 + 0.647593i \(0.775776\pi\)
\(158\) 5.65790e6 + 7.78743e6i 1.43445 + 1.97434i
\(159\) 3.57561e6 2.35199e6i 0.889527 0.585118i
\(160\) 1.77916e6 5.47570e6i 0.434366 1.33684i
\(161\) −566506. 779728.i −0.135746 0.186838i
\(162\) 1.03773e6 5.51598e6i 0.244085 1.29741i
\(163\) 2.49910e6 + 7.69143e6i 0.577059 + 1.77601i 0.629058 + 0.777359i \(0.283441\pi\)
−0.0519984 + 0.998647i \(0.516559\pi\)
\(164\) 4.27365e6i 0.968874i
\(165\) −4.83401e6 + 1.69211e6i −1.07611 + 0.376683i
\(166\) −530185. −0.115905
\(167\) −3.74558e6 + 1.21701e6i −0.804210 + 0.261304i −0.682144 0.731218i \(-0.738952\pi\)
−0.122066 + 0.992522i \(0.538952\pi\)
\(168\) 316729. + 1.15489e6i 0.0667974 + 0.243563i
\(169\) −4.08434e6 + 2.96745e6i −0.846178 + 0.614784i
\(170\) −1.18121e7 3.83798e6i −2.40425 0.781189i
\(171\) −4.60936e6 429814.i −0.921834 0.0859592i
\(172\) −4.22274e6 + 3.06800e6i −0.829868 + 0.602935i
\(173\) −2.52783e6 + 3.47926e6i −0.488213 + 0.671968i −0.980057 0.198715i \(-0.936323\pi\)
0.491844 + 0.870683i \(0.336323\pi\)
\(174\) 652199. + 245973.i 0.123803 + 0.0466917i
\(175\) −1.19573e6 −0.223110
\(176\) −447950. 6.47772e6i −0.0821660 1.18819i
\(177\) −698662. 559006.i −0.125993 0.100808i
\(178\) −2.88586e6 8.88178e6i −0.511701 1.57485i
\(179\) 2.97558e6 4.09553e6i 0.518814 0.714086i −0.466560 0.884489i \(-0.654507\pi\)
0.985374 + 0.170403i \(0.0545069\pi\)
\(180\) −3.26178e6 + 3.70924e6i −0.559291 + 0.636015i
\(181\) −1.94390e6 + 5.98272e6i −0.327823 + 1.00893i 0.642327 + 0.766430i \(0.277969\pi\)
−0.970150 + 0.242505i \(0.922031\pi\)
\(182\) 8.05457e6 + 2.61709e6i 1.33607 + 0.434114i
\(183\) −109547. + 2.35469e6i −0.0178751 + 0.384220i
\(184\) −531113. 385876.i −0.0852576 0.0619433i
\(185\) −4.95401e6 + 1.60966e6i −0.782424 + 0.254225i
\(186\) 3.92446e6 + 3.14000e6i 0.609875 + 0.487967i
\(187\) −1.09567e7 + 757680.i −1.67553 + 0.115867i
\(188\) 133780.i 0.0201335i
\(189\) 698231. 4.97386e6i 0.103422 0.736729i
\(190\) 7.73278e6 + 5.61819e6i 1.12739 + 0.819098i
\(191\) 5.31810e6 + 7.31974e6i 0.763232 + 1.05050i 0.996938 + 0.0781916i \(0.0249146\pi\)
−0.233706 + 0.972307i \(0.575085\pi\)
\(192\) −1.69817e6 2.58164e6i −0.239926 0.364747i
\(193\) 980718. 3.01834e6i 0.136418 0.419852i −0.859390 0.511321i \(-0.829156\pi\)
0.995808 + 0.0914691i \(0.0291563\pi\)
\(194\) −9.69220e6 1.33402e7i −1.32745 1.82707i
\(195\) −3.19819e6 1.16616e7i −0.431321 1.57273i
\(196\) 771804. + 2.37537e6i 0.102504 + 0.315473i
\(197\) 6.15139e6i 0.804590i 0.915510 + 0.402295i \(0.131787\pi\)
−0.915510 + 0.402295i \(0.868213\pi\)
\(198\) −3.39907e6 + 9.66754e6i −0.437889 + 1.24543i
\(199\) 4.23624e6 0.537553 0.268776 0.963203i \(-0.413381\pi\)
0.268776 + 0.963203i \(0.413381\pi\)
\(200\) −774608. + 251685.i −0.0968260 + 0.0314607i
\(201\) 8.17249e6 2.24131e6i 1.00639 0.276003i
\(202\) 9.75322e6 7.08613e6i 1.18330 0.859716i
\(203\) 593226. + 192751.i 0.0709141 + 0.0230414i
\(204\) −8.84926e6 + 5.82092e6i −1.04236 + 0.685647i
\(205\) 1.03643e7 7.53008e6i 1.20303 0.874054i
\(206\) 5.49733e6 7.56642e6i 0.628854 0.865544i
\(207\) 1.40461e6 + 2.36821e6i 0.158360 + 0.266999i
\(208\) 1.53305e7 1.70359
\(209\) 8.19959e6 + 2.05110e6i 0.898159 + 0.224671i
\(210\) −6.47877e6 + 8.09735e6i −0.699576 + 0.874350i
\(211\) 1.22862e6 + 3.78130e6i 0.130789 + 0.402526i 0.994911 0.100755i \(-0.0321259\pi\)
−0.864123 + 0.503281i \(0.832126\pi\)
\(212\) −4.42958e6 + 6.09679e6i −0.464895 + 0.639873i
\(213\) 1.33709e6 + 62205.8i 0.138364 + 0.00643712i
\(214\) 1.54336e6 4.74997e6i 0.157480 0.484674i
\(215\) 1.48808e7 + 4.83506e6i 1.49730 + 0.486504i
\(216\) −594610. 3.36910e6i −0.0590026 0.334312i
\(217\) 3.63863e6 + 2.64362e6i 0.356089 + 0.258714i
\(218\) 1.70319e7 5.53399e6i 1.64397 0.534157i
\(219\) −3.54458e6 + 4.43012e6i −0.337468 + 0.421777i
\(220\) 6.91289e6 5.79153e6i 0.649219 0.543908i
\(221\) 2.59305e7i 2.40234i
\(222\) −3.67789e6 + 9.75196e6i −0.336155 + 0.891319i
\(223\) −4.90865e6 3.56634e6i −0.442637 0.321595i 0.344045 0.938953i \(-0.388203\pi\)
−0.786682 + 0.617359i \(0.788203\pi\)
\(224\) −6.05937e6 8.34001e6i −0.539117 0.742031i
\(225\) 3.40126e6 + 317161.i 0.298602 + 0.0278441i
\(226\) −6.32390e6 + 1.94630e7i −0.547848 + 1.68610i
\(227\) 7.00472e6 + 9.64117e6i 0.598843 + 0.824237i 0.995602 0.0936860i \(-0.0298650\pi\)
−0.396759 + 0.917923i \(0.629865\pi\)
\(228\) 7.86126e6 2.15596e6i 0.663266 0.181901i
\(229\) −4.11403e6 1.26617e7i −0.342579 1.05435i −0.962867 0.269976i \(-0.912984\pi\)
0.620288 0.784374i \(-0.287016\pi\)
\(230\) 5.68500e6i 0.467248i
\(231\) −2.63637e6 + 8.78312e6i −0.213880 + 0.712546i
\(232\) 424871. 0.0340246
\(233\) −1.50003e7 + 4.87389e6i −1.18586 + 0.385308i −0.834539 0.550949i \(-0.814266\pi\)
−0.351316 + 0.936257i \(0.614266\pi\)
\(234\) −2.22171e7 9.58077e6i −1.73397 0.747744i
\(235\) 324438. 235718.i 0.0249993 0.0181631i
\(236\) 1.49843e6 + 486870.i 0.113999 + 0.0370405i
\(237\) −1.35235e7 2.05591e7i −1.01588 1.54440i
\(238\) −1.79909e7 + 1.30712e7i −1.33451 + 0.969580i
\(239\) −8.21506e6 + 1.13071e7i −0.601751 + 0.828240i −0.995867 0.0908211i \(-0.971051\pi\)
0.394116 + 0.919061i \(0.371051\pi\)
\(240\) −6.62426e6 + 1.75643e7i −0.479185 + 1.27056i
\(241\) −1.47461e7 −1.05348 −0.526740 0.850027i \(-0.676586\pi\)
−0.526740 + 0.850027i \(0.676586\pi\)
\(242\) 8.80932e6 1.65065e7i 0.621579 1.16469i
\(243\) −3.30542e6 + 1.39630e7i −0.230360 + 0.973105i
\(244\) −1.28264e6 3.94755e6i −0.0882945 0.271743i
\(245\) 4.40074e6 6.05710e6i 0.299245 0.411876i
\(246\) 1.19124e6 2.56054e7i 0.0800193 1.71999i
\(247\) −6.16668e6 + 1.89791e7i −0.409224 + 1.25946i
\(248\) 2.91360e6 + 946687.i 0.191018 + 0.0620656i
\(249\) 1.35395e6 + 62989.8i 0.0877007 + 0.00408011i
\(250\) 1.33206e7 + 9.67799e6i 0.852519 + 0.619392i
\(251\) −2.07778e7 + 6.75111e6i −1.31395 + 0.426927i −0.880412 0.474209i \(-0.842734\pi\)
−0.433535 + 0.901137i \(0.642734\pi\)
\(252\) 1.94021e6 + 8.62857e6i 0.121240 + 0.539184i
\(253\) −1.87962e6 4.66256e6i −0.116067 0.287914i
\(254\) 1.11894e7i 0.682820i
\(255\) 2.97088e7 + 1.12045e7i 1.79170 + 0.675729i
\(256\) −1.76896e7 1.28523e7i −1.05438 0.766054i
\(257\) 2.87805e6 + 3.96130e6i 0.169551 + 0.233367i 0.885334 0.464956i \(-0.153930\pi\)
−0.715783 + 0.698323i \(0.753930\pi\)
\(258\) 2.61555e7 1.72047e7i 1.52302 1.00182i
\(259\) −2.88210e6 + 8.87018e6i −0.165886 + 0.510544i
\(260\) 1.25153e7 + 1.72258e7i 0.712068 + 0.980077i
\(261\) −1.63631e6 705633.i −0.0920333 0.0396878i
\(262\) −8.44491e6 2.59908e7i −0.469560 1.44516i
\(263\) 2.07218e7i 1.13910i −0.821958 0.569549i \(-0.807118\pi\)
0.821958 0.569549i \(-0.192882\pi\)
\(264\) 140861. + 6.24474e6i 0.00765561 + 0.339393i
\(265\) 2.25905e7 1.21392
\(266\) 1.62764e7 5.28854e6i 0.864798 0.280990i
\(267\) 6.31448e6 + 2.30245e7i 0.331745 + 1.20964i
\(268\) −1.20720e7 + 8.77080e6i −0.627153 + 0.455654i
\(269\) 8.80161e6 + 2.85982e6i 0.452174 + 0.146920i 0.526245 0.850333i \(-0.323599\pi\)
−0.0740717 + 0.997253i \(0.523599\pi\)
\(270\) 2.05767e7 2.13146e7i 1.04541 1.08289i
\(271\) 4.17936e6 3.03648e6i 0.209992 0.152568i −0.477818 0.878459i \(-0.658572\pi\)
0.687810 + 0.725891i \(0.258572\pi\)
\(272\) −2.36611e7 + 3.25667e7i −1.17578 + 1.61833i
\(273\) −2.02582e7 7.64026e6i −0.995665 0.375509i
\(274\) −4.17329e7 −2.02874
\(275\) −6.05050e6 1.51351e6i −0.290933 0.0727759i
\(276\) −3.78570e6 3.02898e6i −0.180061 0.144069i
\(277\) −8.43003e6 2.59450e7i −0.396634 1.22071i −0.927682 0.373372i \(-0.878202\pi\)
0.531048 0.847342i \(-0.321798\pi\)
\(278\) −9.17224e6 + 1.26245e7i −0.426914 + 0.587597i
\(279\) −9.64892e6 8.48494e6i −0.444290 0.390694i
\(280\) −1.95330e6 + 6.01165e6i −0.0889807 + 0.273854i
\(281\) 1.90708e6 + 619649.i 0.0859509 + 0.0279271i 0.351677 0.936121i \(-0.385612\pi\)
−0.265726 + 0.964049i \(0.585612\pi\)
\(282\) 37290.0 801538.i 0.00166282 0.0357418i
\(283\) −1.39701e7 1.01499e7i −0.616369 0.447818i 0.235282 0.971927i \(-0.424399\pi\)
−0.851651 + 0.524109i \(0.824399\pi\)
\(284\) −2.24159e6 + 728337.i −0.0978591 + 0.0317963i
\(285\) −1.90799e7 1.52660e7i −0.824217 0.659465i
\(286\) 3.74443e7 + 2.34379e7i 1.60062 + 1.00189i
\(287\) 2.29380e7i 0.970310i
\(288\) 1.50238e7 + 2.53305e7i 0.628930 + 1.06039i
\(289\) 3.55568e7 + 2.58335e7i 1.47309 + 1.07026i
\(290\) 2.16261e6 + 2.97658e6i 0.0886715 + 0.122046i
\(291\) 2.31663e7 + 3.52186e7i 0.940108 + 1.42920i
\(292\) 3.08718e6 9.50135e6i 0.123997 0.381625i
\(293\) −6.06794e6 8.35180e6i −0.241234 0.332030i 0.671183 0.741292i \(-0.265786\pi\)
−0.912417 + 0.409261i \(0.865786\pi\)
\(294\) −3.96211e6 1.44470e7i −0.155914 0.568509i
\(295\) −1.45947e6 4.49179e6i −0.0568498 0.174966i
\(296\) 6.35286e6i 0.244959i
\(297\) 9.82886e6 2.42844e7i 0.375175 0.926954i
\(298\) −1.49849e7 −0.566248
\(299\) 1.12883e7 3.66779e6i 0.422293 0.137211i
\(300\) −5.80085e6 + 1.59089e6i −0.214846 + 0.0589217i
\(301\) 2.26648e7 1.64669e7i 0.831099 0.603828i
\(302\) −3.32339e7 1.07984e7i −1.20659 0.392046i
\(303\) −2.57489e7 + 1.69373e7i −0.925617 + 0.608858i
\(304\) 2.50629e7 1.82092e7i 0.892093 0.648144i
\(305\) −7.31344e6 + 1.00661e7i −0.257764 + 0.354782i
\(306\) 5.46425e7 3.24091e7i 1.90707 1.13110i
\(307\) 5.01564e6 0.173345 0.0866725 0.996237i \(-0.472377\pi\)
0.0866725 + 0.996237i \(0.472377\pi\)
\(308\) −1.11397e6 1.61088e7i −0.0381259 0.551331i
\(309\) −1.49376e7 + 1.86694e7i −0.506297 + 0.632784i
\(310\) 8.19800e6 + 2.52308e7i 0.275184 + 0.846928i
\(311\) −3.71519e6 + 5.11352e6i −0.123509 + 0.169996i −0.866294 0.499534i \(-0.833505\pi\)
0.742785 + 0.669530i \(0.233505\pi\)
\(312\) −1.47317e7 685365.i −0.485053 0.0225662i
\(313\) −6.21419e6 + 1.91253e7i −0.202652 + 0.623699i 0.797149 + 0.603782i \(0.206340\pi\)
−0.999802 + 0.0199173i \(0.993660\pi\)
\(314\) −1.83326e7 5.95664e6i −0.592156 0.192403i
\(315\) 1.75070e7 1.99087e7i 0.560120 0.636958i
\(316\) 3.50555e7 + 2.54693e7i 1.11095 + 0.807153i
\(317\) −3.00316e6 + 975787.i −0.0942760 + 0.0306321i −0.355775 0.934572i \(-0.615783\pi\)
0.261499 + 0.965204i \(0.415783\pi\)
\(318\) 2.82391e7 3.52940e7i 0.878150 1.09754i
\(319\) 2.75781e6 + 1.72622e6i 0.0849555 + 0.0531772i
\(320\) 1.63107e7i 0.497762i
\(321\) −4.50565e6 + 1.19468e7i −0.136220 + 0.361189i
\(322\) −8.23500e6 5.98308e6i −0.246658 0.179208i
\(323\) −3.07998e7 4.23923e7i −0.913987 1.25800i
\(324\) −3.23026e6 2.50587e7i −0.0949736 0.736756i
\(325\) 4.55041e6 1.40047e7i 0.132556 0.407967i
\(326\) 5.02042e7 + 6.91001e7i 1.44906 + 1.99446i
\(327\) −4.41522e7 + 1.21088e7i −1.26273 + 0.346304i
\(328\) −4.82816e6 1.48596e7i −0.136823 0.421099i
\(329\) 718041.i 0.0201633i
\(330\) −4.30326e7 + 3.27728e7i −1.19745 + 0.911951i
\(331\) 3.60128e7 0.993055 0.496527 0.868021i \(-0.334608\pi\)
0.496527 + 0.868021i \(0.334608\pi\)
\(332\) −2.26984e6 + 737516.i −0.0620271 + 0.0201538i
\(333\) 1.05509e7 2.44669e7i 0.285731 0.662591i
\(334\) −3.36504e7 + 2.44485e7i −0.903132 + 0.656163i
\(335\) 4.25411e7 + 1.38224e7i 1.13155 + 0.367664i
\(336\) 1.84711e7 + 2.80807e7i 0.486940 + 0.740271i
\(337\) 3.29503e7 2.39398e7i 0.860935 0.625506i −0.0672043 0.997739i \(-0.521408\pi\)
0.928139 + 0.372233i \(0.121408\pi\)
\(338\) −3.13403e7 + 4.31362e7i −0.811621 + 1.11710i
\(339\) 1.84619e7 4.89518e7i 0.473889 1.25652i
\(340\) −5.59091e7 −1.42248
\(341\) 1.50656e7 + 1.79826e7i 0.379948 + 0.453513i
\(342\) −4.77013e7 + 1.07261e7i −1.19248 + 0.268140i
\(343\) −1.34196e7 4.13012e7i −0.332550 1.02348i
\(344\) 1.12165e7 1.54382e7i 0.275538 0.379245i
\(345\) −675419. + 1.45179e7i −0.0164481 + 0.353547i
\(346\) −1.40356e7 + 4.31972e7i −0.338847 + 1.04286i
\(347\) 5.98365e6 + 1.94420e6i 0.143211 + 0.0465322i 0.379746 0.925091i \(-0.376012\pi\)
−0.236534 + 0.971623i \(0.576012\pi\)
\(348\) 3.13438e6 + 145821.i 0.0743727 + 0.00346005i
\(349\) 2.45319e7 + 1.78234e7i 0.577104 + 0.419291i 0.837679 0.546163i \(-0.183912\pi\)
−0.260575 + 0.965454i \(0.583912\pi\)
\(350\) −1.20104e7 + 3.90243e6i −0.280127 + 0.0910187i
\(351\) 5.55982e7 + 2.71062e7i 1.28570 + 0.626827i
\(352\) −2.01045e7 4.98710e7i −0.460962 1.14346i
\(353\) 1.20349e7i 0.273601i −0.990599 0.136800i \(-0.956318\pi\)
0.990599 0.136800i \(-0.0436819\pi\)
\(354\) −8.84208e6 3.33473e6i −0.199317 0.0751712i
\(355\) 5.71597e6 + 4.15289e6i 0.127763 + 0.0928251i
\(356\) −2.47101e7 3.40105e7i −0.547677 0.753813i
\(357\) 4.74968e7 3.12427e7i 1.04390 0.686664i
\(358\) 1.65217e7 5.08486e7i 0.360086 1.10823i
\(359\) −8.77100e6 1.20722e7i −0.189568 0.260918i 0.703645 0.710552i \(-0.251555\pi\)
−0.893213 + 0.449634i \(0.851555\pi\)
\(360\) 7.15076e6 1.65821e7i 0.153266 0.355412i
\(361\) −2.07652e6 6.39086e6i −0.0441381 0.135843i
\(362\) 6.64374e7i 1.40051i
\(363\) −2.44577e7 + 4.11064e7i −0.511323 + 0.859389i
\(364\) 3.81240e7 0.790485
\(365\) −2.84818e7 + 9.25430e6i −0.585719 + 0.190311i
\(366\) 6.58451e6 + 2.40091e7i 0.134301 + 0.489702i
\(367\) −4.45588e7 + 3.23738e7i −0.901436 + 0.654932i −0.938834 0.344369i \(-0.888093\pi\)
0.0373983 + 0.999300i \(0.488093\pi\)
\(368\) −1.75240e7 5.69388e6i −0.351632 0.114252i
\(369\) −6.08421e6 + 6.52475e7i −0.121095 + 1.29863i
\(370\) −4.45070e7 + 3.23363e7i −0.878665 + 0.638388i
\(371\) 2.37750e7 3.27234e7i 0.465584 0.640822i
\(372\) 2.11694e7 + 7.98391e6i 0.411225 + 0.155091i
\(373\) −6.02904e7 −1.16177 −0.580887 0.813984i \(-0.697294\pi\)
−0.580887 + 0.813984i \(0.697294\pi\)
\(374\) −1.07581e8 + 4.33691e7i −2.05646 + 0.829021i
\(375\) −3.28674e7 2.62975e7i −0.623263 0.498679i
\(376\) −151138. 465156.i −0.00284323 0.00875055i
\(377\) −4.51512e6 + 6.21452e6i −0.0842645 + 0.115980i
\(378\) −9.21954e6 5.22385e7i −0.170700 0.967198i
\(379\) 2.86676e7 8.82299e7i 0.526592 1.62068i −0.234554 0.972103i \(-0.575363\pi\)
0.761146 0.648580i \(-0.224637\pi\)
\(380\) 4.09210e7 + 1.32960e7i 0.745754 + 0.242310i
\(381\) 1.32938e6 2.85747e7i 0.0240367 0.516662i
\(382\) 7.73065e7 + 5.61665e7i 1.38684 + 1.00760i
\(383\) 6.49406e7 2.11005e7i 1.15590 0.375575i 0.332537 0.943090i \(-0.392095\pi\)
0.823363 + 0.567516i \(0.192095\pi\)
\(384\) 2.90262e7 + 2.32241e7i 0.512621 + 0.410153i
\(385\) −3.71037e7 + 3.10850e7i −0.650182 + 0.544714i
\(386\) 3.35183e7i 0.582801i
\(387\) −6.88381e7 + 4.08287e7i −1.18767 + 0.704421i
\(388\) −6.00514e7 4.36299e7i −1.02808 0.746946i
\(389\) 3.86085e7 + 5.31401e7i 0.655895 + 0.902763i 0.999337 0.0364114i \(-0.0115927\pi\)
−0.343441 + 0.939174i \(0.611593\pi\)
\(390\) −7.01833e7 1.06696e8i −1.18315 1.79869i
\(391\) −9.63083e6 + 2.96407e7i −0.161114 + 0.495858i
\(392\) −5.36715e6 7.38725e6i −0.0891017 0.122638i
\(393\) 1.84781e7 + 6.73765e7i 0.304424 + 1.11002i
\(394\) 2.00759e7 + 6.17874e7i 0.328237 + 1.01021i
\(395\) 1.29892e8i 2.10761i
\(396\) −1.10410e6 + 4.61173e7i −0.0177797 + 0.742639i
\(397\) −9.96613e7 −1.59278 −0.796389 0.604785i \(-0.793259\pi\)
−0.796389 + 0.604785i \(0.793259\pi\)
\(398\) 4.25507e7 1.38256e7i 0.674928 0.219298i
\(399\) −4.21939e7 + 1.15717e7i −0.664249 + 0.182171i
\(400\) −1.84940e7 + 1.34367e7i −0.288968 + 0.209948i
\(401\) −4.05665e6 1.31808e6i −0.0629121 0.0204414i 0.277392 0.960757i \(-0.410530\pi\)
−0.340304 + 0.940315i \(0.610530\pi\)
\(402\) 7.47734e7 4.91849e7i 1.15098 0.757100i
\(403\) −4.48099e7 + 3.25563e7i −0.684635 + 0.497416i
\(404\) 3.18986e7 4.39046e7i 0.483757 0.665834i
\(405\) −5.50796e7 + 5.19868e7i −0.829136 + 0.782579i
\(406\) 6.58771e6 0.0984365
\(407\) −2.58113e7 + 4.12359e7i −0.382848 + 0.611635i
\(408\) 2.41929e7 3.02369e7i 0.356210 0.445202i
\(409\) −3.69746e6 1.13796e7i −0.0540423 0.166325i 0.920392 0.390996i \(-0.127869\pi\)
−0.974435 + 0.224671i \(0.927869\pi\)
\(410\) 7.95280e7 1.09461e8i 1.15390 1.58821i
\(411\) 1.06574e8 + 4.95817e6i 1.53507 + 0.0714160i
\(412\) 1.30100e7 4.00407e7i 0.186031 0.572545i
\(413\) −8.04256e6 2.61319e6i −0.114168 0.0370954i
\(414\) 2.18376e7 + 1.92032e7i 0.307754 + 0.270628i
\(415\) 5.78801e6 + 4.20523e6i 0.0809813 + 0.0588364i
\(416\) 1.20740e8 3.92308e7i 1.67715 0.544938i
\(417\) 2.49232e7 3.11498e7i 0.343713 0.429583i
\(418\) 8.90545e7 6.15834e6i 1.21935 0.0843208i
\(419\) 3.74494e7i 0.509099i 0.967060 + 0.254550i \(0.0819272\pi\)
−0.967060 + 0.254550i \(0.918073\pi\)
\(420\) −1.64732e7 + 4.36790e7i −0.222347 + 0.589555i
\(421\) 9.95942e7 + 7.23594e7i 1.33471 + 0.969726i 0.999621 + 0.0275404i \(0.00876748\pi\)
0.335092 + 0.942185i \(0.391233\pi\)
\(422\) 2.46816e7 + 3.39714e7i 0.328425 + 0.452039i
\(423\) −190457. + 2.04248e6i −0.00251638 + 0.0269858i
\(424\) 8.51387e6 2.62030e7i 0.111694 0.343758i
\(425\) 2.27273e7 + 3.12814e7i 0.296060 + 0.407492i
\(426\) 1.36334e7 3.73897e6i 0.176350 0.0483641i
\(427\) 6.88432e6 + 2.11877e7i 0.0884254 + 0.272145i
\(428\) 2.24826e7i 0.286758i
\(429\) −9.28377e7 6.43026e7i −1.17585 0.814436i
\(430\) 1.65249e8 2.07842
\(431\) −5.28232e7 + 1.71633e7i −0.659770 + 0.214372i −0.619717 0.784825i \(-0.712753\pi\)
−0.0400531 + 0.999198i \(0.512753\pi\)
\(432\) −4.50930e7 8.47754e7i −0.559317 1.05152i
\(433\) −9.86475e7 + 7.16716e7i −1.21513 + 0.882843i −0.995686 0.0927821i \(-0.970424\pi\)
−0.219443 + 0.975625i \(0.570424\pi\)
\(434\) 4.51759e7 + 1.46785e7i 0.552634 + 0.179562i
\(435\) −5.16907e6 7.85829e6i −0.0627978 0.0954685i
\(436\) 6.52193e7 4.73846e7i 0.786894 0.571712i
\(437\) 1.40980e7 1.94042e7i 0.168933 0.232516i
\(438\) −2.11451e7 + 5.60664e7i −0.251644 + 0.667237i
\(439\) 8.29399e7 0.980324 0.490162 0.871631i \(-0.336938\pi\)
0.490162 + 0.871631i \(0.336938\pi\)
\(440\) −1.74933e7 + 2.79471e7i −0.205358 + 0.328079i
\(441\) 8.40173e6 + 3.73645e7i 0.0979610 + 0.435656i
\(442\) −8.46280e7 2.60458e8i −0.980048 3.01628i
\(443\) −5.35037e7 + 7.36415e7i −0.615421 + 0.847054i −0.997010 0.0772778i \(-0.975377\pi\)
0.381588 + 0.924332i \(0.375377\pi\)
\(444\) −2.18038e6 + 4.68665e7i −0.0249105 + 0.535444i
\(445\) −3.89422e7 + 1.19852e8i −0.441916 + 1.36008i
\(446\) −6.09440e7 1.98019e7i −0.686952 0.223204i
\(447\) 3.82674e7 + 1.78032e6i 0.428456 + 0.0199331i
\(448\) −2.36268e7 1.71659e7i −0.262767 0.190911i
\(449\) 5.95904e7 1.93621e7i 0.658320 0.213901i 0.0392409 0.999230i \(-0.487506\pi\)
0.619079 + 0.785329i \(0.287506\pi\)
\(450\) 3.51989e7 7.91479e6i 0.386271 0.0868564i
\(451\) 2.90342e7 1.16069e8i 0.316505 1.26528i
\(452\) 9.21224e7i 0.997585i
\(453\) 8.35874e7 + 3.15245e7i 0.899179 + 0.339120i
\(454\) 1.01824e8 + 7.39794e7i 1.08813 + 0.790576i
\(455\) −6.71736e7 9.24566e7i −0.713123 0.981530i
\(456\) −2.48980e7 + 1.63776e7i −0.262586 + 0.172725i
\(457\) −8.47932e6 + 2.60967e7i −0.0888408 + 0.273424i −0.985600 0.169096i \(-0.945915\pi\)
0.896759 + 0.442520i \(0.145915\pi\)
\(458\) −8.26464e7 1.13753e8i −0.860255 1.18404i
\(459\) −1.43392e8 + 7.62720e7i −1.48282 + 0.788727i
\(460\) −7.90815e6 2.43388e7i −0.0812459 0.250049i
\(461\) 4.89091e7i 0.499214i −0.968347 0.249607i \(-0.919699\pi\)
0.968347 0.249607i \(-0.0803015\pi\)
\(462\) 2.18408e6 + 9.68259e7i 0.0221484 + 0.981896i
\(463\) −5.57209e7 −0.561404 −0.280702 0.959795i \(-0.590567\pi\)
−0.280702 + 0.959795i \(0.590567\pi\)
\(464\) 1.13412e7 3.68499e6i 0.113529 0.0368878i
\(465\) −1.79378e7 6.54066e7i −0.178407 0.650523i
\(466\) −1.34763e8 + 9.79111e7i −1.33172 + 0.967552i
\(467\) −1.01374e7 3.29385e6i −0.0995353 0.0323410i 0.258826 0.965924i \(-0.416664\pi\)
−0.358361 + 0.933583i \(0.616664\pi\)
\(468\) −1.08444e8 1.01122e7i −1.05796 0.0986525i
\(469\) 6.47941e7 4.70757e7i 0.628083 0.456329i
\(470\) 2.48950e6 3.42651e6i 0.0239784 0.0330034i
\(471\) 4.61088e7 + 1.73897e7i 0.441287 + 0.166429i
\(472\) −5.76012e6 −0.0547779
\(473\) 1.35529e8 5.46360e7i 1.28071 0.516292i
\(474\) −2.02934e8 1.62370e8i −1.90555 1.52465i
\(475\) −9.19535e6 2.83004e7i −0.0858000 0.264065i
\(476\) −5.88405e7 + 8.09870e7i −0.545577 + 0.750922i
\(477\) −7.63079e7 + 8.67760e7i −0.703096 + 0.799548i
\(478\) −4.56136e7 + 1.40384e8i −0.417649 + 1.28539i
\(479\) −8.29121e7 2.69398e7i −0.754417 0.245125i −0.0935361 0.995616i \(-0.529817\pi\)
−0.660881 + 0.750491i \(0.729817\pi\)
\(480\) −7.22432e6 + 1.55284e8i −0.0653240 + 1.40412i
\(481\) −9.29223e7 6.75120e7i −0.834996 0.606660i
\(482\) −1.48117e8 + 4.81260e7i −1.32270 + 0.429773i
\(483\) 2.03191e7 + 1.62575e7i 0.180328 + 0.144282i
\(484\) 1.47532e7 8.29223e7i 0.130122 0.731367i
\(485\) 2.22509e8i 1.95040i
\(486\) 1.23691e7 + 1.51038e8i 0.107753 + 1.31577i
\(487\) 8.50574e7 + 6.17978e7i 0.736419 + 0.535040i 0.891588 0.452848i \(-0.149592\pi\)
−0.155168 + 0.987888i \(0.549592\pi\)
\(488\) 8.91950e6 + 1.22766e7i 0.0767505 + 0.105638i
\(489\) −1.19998e8 1.82427e8i −1.02624 1.56014i
\(490\) 2.44348e7 7.52027e7i 0.207693 0.639212i
\(491\) −1.64779e7 2.26798e7i −0.139206 0.191600i 0.733722 0.679450i \(-0.237781\pi\)
−0.872928 + 0.487850i \(0.837781\pi\)
\(492\) −3.05185e7 1.11280e8i −0.256252 0.934372i
\(493\) −6.23293e6 1.91830e7i −0.0520178 0.160094i
\(494\) 2.10761e8i 1.74827i
\(495\) 1.13787e8 7.85800e7i 0.938160 0.647883i
\(496\) 8.59846e7 0.704654
\(497\) 1.20313e7 3.90922e6i 0.0980041 0.0318435i
\(498\) 1.38052e7 3.78610e6i 0.111778 0.0306552i
\(499\) 1.57359e8 1.14328e8i 1.26645 0.920131i 0.267396 0.963587i \(-0.413837\pi\)
0.999055 + 0.0434556i \(0.0138367\pi\)
\(500\) 7.04912e7 + 2.29040e7i 0.563930 + 0.183232i
\(501\) 8.88385e7 5.84367e7i 0.706461 0.464700i
\(502\) −1.86668e8 + 1.35622e8i −1.47557 + 1.07206i
\(503\) 1.05943e8 1.45818e8i 0.832467 1.14579i −0.154992 0.987916i \(-0.549535\pi\)
0.987459 0.157877i \(-0.0504649\pi\)
\(504\) −1.64943e7 2.78098e7i −0.128837 0.217223i
\(505\) −1.62680e8 −1.26317
\(506\) −3.40967e7 4.06985e7i −0.263185 0.314143i
\(507\) 8.51594e7 1.06435e8i 0.653444 0.816693i
\(508\) 1.55651e7 + 4.79044e7i 0.118730 + 0.365414i
\(509\) −8.58441e7 + 1.18154e8i −0.650964 + 0.895975i −0.999140 0.0414541i \(-0.986801\pi\)
0.348177 + 0.937429i \(0.386801\pi\)
\(510\) 3.34977e8 + 1.55842e7i 2.52525 + 0.117483i
\(511\) −1.65699e7 + 5.09968e7i −0.124181 + 0.382191i
\(512\) −1.35825e8 4.41323e7i −1.01198 0.328811i
\(513\) 1.23090e8 2.17241e7i 0.911742 0.160913i
\(514\) 4.18368e7 + 3.03962e7i 0.308084 + 0.223836i
\(515\) −1.20028e8 + 3.89996e7i −0.878743 + 0.285521i
\(516\) 8.80451e7 1.10041e8i 0.640850 0.800952i
\(517\) 908872. 3.63336e6i 0.00657705 0.0262928i
\(518\) 9.85023e7i 0.708691i
\(519\) 4.09753e7 1.08646e8i 0.293103 0.777164i
\(520\) −6.29769e7 4.57554e7i −0.447890 0.325411i
\(521\) 1.36628e8 + 1.88053e8i 0.966113 + 1.32974i 0.943986 + 0.329985i \(0.107044\pi\)
0.0221262 + 0.999755i \(0.492956\pi\)
\(522\) −1.87388e7 1.74736e6i −0.131744 0.0122849i
\(523\) 8.20002e6 2.52371e7i 0.0573205 0.176414i −0.918297 0.395892i \(-0.870435\pi\)
0.975617 + 0.219478i \(0.0704354\pi\)
\(524\) −7.23092e7 9.95250e7i −0.502573 0.691733i
\(525\) 3.11350e7 8.53880e6i 0.215165 0.0590091i
\(526\) −6.76287e7 2.08140e8i −0.464701 1.43020i
\(527\) 1.45438e8i 0.993675i
\(528\) 5.79219e7 + 1.65471e8i 0.393497 + 1.12414i
\(529\) 1.33770e8 0.903634
\(530\) 2.26909e8 7.37274e7i 1.52414 0.495223i
\(531\) 2.21840e7 + 9.56649e6i 0.148169 + 0.0638954i
\(532\) 6.23265e7 4.52829e7i 0.413941 0.300746i
\(533\) 2.68657e8 + 8.72921e7i 1.77426 + 0.576492i
\(534\) 1.38569e8 + 2.10660e8i 0.910003 + 1.38343i
\(535\) −5.45239e7 + 3.96139e7i −0.356062 + 0.258694i
\(536\) 3.20656e7 4.41346e7i 0.208231 0.286605i
\(537\) −4.82331e7 + 1.27890e8i −0.311474 + 0.825876i
\(538\) 9.77408e7 0.627667
\(539\) −4.82383e6 6.97565e7i −0.0308053 0.445470i
\(540\) 5.84440e7 1.19876e8i 0.371158 0.761291i
\(541\) 6.03079e7 + 1.85609e8i 0.380875 + 1.17221i 0.939429 + 0.342744i \(0.111356\pi\)
−0.558554 + 0.829468i \(0.688644\pi\)
\(542\) 3.20694e7 4.41398e7i 0.201416 0.277225i
\(543\) 7.89325e6 1.69663e8i 0.0493011 1.05971i
\(544\) −1.03012e8 + 3.17038e8i −0.639868 + 1.96931i
\(545\) −2.29830e8 7.46763e7i −1.41977 0.461310i
\(546\) −2.28418e8 1.06267e7i −1.40331 0.0652862i
\(547\) −1.95931e6 1.42352e6i −0.0119713 0.00869767i 0.581784 0.813344i \(-0.302355\pi\)
−0.593755 + 0.804646i \(0.702355\pi\)
\(548\) −1.78668e8 + 5.80527e7i −1.08569 + 0.352761i
\(549\) −1.39626e7 6.20948e7i −0.0843817 0.375265i
\(550\) −6.57135e7 + 4.54426e6i −0.394972 + 0.0273133i
\(551\) 1.55227e7i 0.0927925i
\(552\) 1.65850e7 + 6.25492e6i 0.0986046 + 0.0371881i
\(553\) −1.88154e8 1.36702e8i −1.11260 0.808350i
\(554\) −1.69350e8 2.33091e8i −0.995993 1.37087i
\(555\) 1.17500e8 7.72901e7i 0.687323 0.452111i
\(556\) −2.17071e7 + 6.68075e7i −0.126292 + 0.388688i
\(557\) −1.00867e8 1.38831e8i −0.583690 0.803380i 0.410404 0.911904i \(-0.365388\pi\)
−0.994094 + 0.108524i \(0.965388\pi\)
\(558\) −1.24610e8 5.37360e7i −0.717217 0.309288i
\(559\) 1.06614e8 + 3.28123e8i 0.610348 + 1.87846i
\(560\) 1.77413e8i 1.01023i
\(561\) 2.79884e8 9.79713e7i 1.58522 0.554894i
\(562\) 2.11779e7 0.119309
\(563\) −2.47702e8 + 8.04832e7i −1.38805 + 0.451003i −0.905306 0.424760i \(-0.860358\pi\)
−0.482740 + 0.875764i \(0.660358\pi\)
\(564\) −955336. 3.48344e6i −0.00532499 0.0194165i
\(565\) 2.23411e8 1.62318e8i 1.23868 0.899955i
\(566\) −1.73448e8 5.63566e7i −0.956577 0.310811i
\(567\) 1.73379e7 + 1.34498e8i 0.0951144 + 0.737848i
\(568\) 6.97121e6 5.06488e6i 0.0380420 0.0276391i
\(569\) 2.85023e7 3.92300e7i 0.154719 0.212952i −0.724620 0.689148i \(-0.757985\pi\)
0.879339 + 0.476196i \(0.157985\pi\)
\(570\) −2.41470e8 9.10690e7i −1.30388 0.491752i
\(571\) −3.61066e8 −1.93945 −0.969724 0.244202i \(-0.921474\pi\)
−0.969724 + 0.244202i \(0.921474\pi\)
\(572\) 1.92911e8 + 4.82560e7i 1.03079 + 0.257848i
\(573\) −1.90746e8 1.52618e8i −1.01389 0.811227i
\(574\) −7.48616e7 2.30400e8i −0.395843 1.21828i
\(575\) −1.04030e7 + 1.43184e7i −0.0547209 + 0.0753169i
\(576\) 6.26535e7 + 5.50954e7i 0.327852 + 0.288302i
\(577\) 5.57239e7 1.71501e8i 0.290078 0.892767i −0.694753 0.719248i \(-0.744486\pi\)
0.984831 0.173519i \(-0.0555137\pi\)
\(578\) 4.41460e8 + 1.43439e8i 2.28616 + 0.742820i
\(579\) −3.98222e6 + 8.55965e7i −0.0205158 + 0.440982i
\(580\) 1.33992e7 + 9.73509e6i 0.0686744 + 0.0498949i
\(581\) 1.21830e7 3.95849e6i 0.0621190 0.0201837i
\(582\) 3.47634e8 + 2.78146e8i 1.76341 + 1.41092i
\(583\) 1.61724e8 1.35490e8i 0.816147 0.683758i
\(584\) 3.65241e7i 0.183375i
\(585\) 1.66553e8 + 2.80811e8i 0.831924 + 1.40264i
\(586\) −8.82065e7 6.40858e7i −0.438336 0.318470i
\(587\) −1.27544e8 1.75549e8i −0.630586 0.867928i 0.367483 0.930030i \(-0.380219\pi\)
−0.998070 + 0.0621025i \(0.980219\pi\)
\(588\) −3.70594e7 5.63396e7i −0.182291 0.277129i
\(589\) −3.45873e7 + 1.06449e8i −0.169266 + 0.520948i
\(590\) −2.93192e7 4.03544e7i −0.142756 0.196487i
\(591\) −4.39276e7 1.60173e8i −0.212802 0.775938i
\(592\) 5.50996e7 + 1.69579e8i 0.265573 + 0.817349i
\(593\) 3.07418e8i 1.47423i 0.675767 + 0.737115i \(0.263813\pi\)
−0.675767 + 0.737115i \(0.736187\pi\)
\(594\) 1.94700e7 2.76002e8i 0.0928979 1.31690i
\(595\) 3.00082e8 1.42459
\(596\) −6.41540e7 + 2.08449e7i −0.303029 + 0.0984602i
\(597\) −1.10305e8 + 3.02514e7i −0.518410 + 0.142175i
\(598\) 1.01414e8 7.36819e7i 0.474238 0.344554i
\(599\) 1.26713e8 + 4.11716e7i 0.589578 + 0.191566i 0.588587 0.808434i \(-0.299684\pi\)
0.000991319 1.00000i \(0.499684\pi\)
\(600\) 1.83723e7 1.20851e7i 0.0850571 0.0559494i
\(601\) −2.36793e7 + 1.72040e7i −0.109080 + 0.0792512i −0.640988 0.767551i \(-0.721475\pi\)
0.531908 + 0.846802i \(0.321475\pi\)
\(602\) 1.73914e8 2.39371e8i 0.797157 1.09719i
\(603\) −1.96794e8 + 1.16721e8i −0.897554 + 0.532350i
\(604\) −1.57303e8 −0.713882
\(605\) −2.27095e8 + 1.10328e8i −1.02551 + 0.498220i
\(606\) −2.03357e8 + 2.54161e8i −0.913779 + 1.14207i
\(607\) −2.00083e7 6.15793e7i −0.0894632 0.275340i 0.896308 0.443432i \(-0.146239\pi\)
−0.985771 + 0.168093i \(0.946239\pi\)
\(608\) 1.50793e8 2.07549e8i 0.670919 0.923441i
\(609\) −1.68232e7 782668.i −0.0744829 0.00346518i
\(610\) −4.06075e7 + 1.24977e8i −0.178902 + 0.550605i
\(611\) 8.40992e6 + 2.73255e6i 0.0368696 + 0.0119796i
\(612\) 1.88854e8 2.14761e8i 0.823895 0.936919i
\(613\) 9.99793e7 + 7.26392e7i 0.434039 + 0.315348i 0.783262 0.621692i \(-0.213554\pi\)
−0.349223 + 0.937040i \(0.613554\pi\)
\(614\) 5.03794e7 1.63693e7i 0.217645 0.0707170i
\(615\) −2.16097e8 + 2.70084e8i −0.929018 + 1.16111i
\(616\) 2.20723e7 + 5.47522e7i 0.0944289 + 0.234239i
\(617\) 8.47744e7i 0.360918i 0.983582 + 0.180459i \(0.0577584\pi\)
−0.983582 + 0.180459i \(0.942242\pi\)
\(618\) −8.91098e7 + 2.36275e8i −0.377538 + 1.00104i
\(619\) −1.92409e8 1.39793e8i −0.811246 0.589405i 0.102946 0.994687i \(-0.467173\pi\)
−0.914192 + 0.405282i \(0.867173\pi\)
\(620\) 7.01950e7 + 9.66152e7i 0.294531 + 0.405387i
\(621\) −5.34856e7 5.16342e7i −0.223338 0.215607i
\(622\) −2.06284e7 + 6.34876e7i −0.0857222 + 0.263826i
\(623\) 1.32627e8 + 1.82545e8i 0.548489 + 0.754930i
\(624\) −3.99183e8 + 1.09476e8i −1.64293 + 0.450574i
\(625\) −9.12837e7 2.80942e8i −0.373898 1.15074i
\(626\) 2.12384e8i 0.865764i
\(627\) −2.28152e8 + 5.14638e6i −0.925597 + 0.0208785i
\(628\) −8.67723e7 −0.350350
\(629\) 2.86832e8 9.31975e7i 1.15259 0.374501i
\(630\) 1.10874e8 2.57109e8i 0.443412 1.02824i
\(631\) 1.84923e8 1.34354e8i 0.736042 0.534766i −0.155427 0.987847i \(-0.549675\pi\)
0.891469 + 0.453082i \(0.149675\pi\)
\(632\) −1.50663e8 4.89533e7i −0.596835 0.193924i
\(633\) −5.89941e7 8.96858e7i −0.232593 0.353600i
\(634\) −2.69805e7 + 1.96025e7i −0.105872 + 0.0769208i
\(635\) 8.87504e7 1.22154e8i 0.346616 0.477077i
\(636\) 7.18020e7 1.90384e8i 0.279103 0.740045i
\(637\) 1.65089e8 0.638704
\(638\) 3.33344e7 + 8.33850e6i 0.128360 + 0.0321089i
\(639\) −3.52602e7 + 7.92856e6i −0.135139 + 0.0303873i
\(640\) 6.06343e7 + 1.86613e8i 0.231301 + 0.711873i
\(641\) 2.25556e6 3.10451e6i 0.00856406 0.0117874i −0.804713 0.593663i \(-0.797681\pi\)
0.813278 + 0.581876i \(0.197681\pi\)
\(642\) −6.26683e6 + 1.34704e8i −0.0236833 + 0.509066i
\(643\) 3.92825e7 1.20899e8i 0.147763 0.454768i −0.849593 0.527439i \(-0.823152\pi\)
0.997356 + 0.0726710i \(0.0231523\pi\)
\(644\) −4.35787e7 1.41596e7i −0.163161 0.0530143i
\(645\) −4.22001e8 1.96328e7i −1.57266 0.0731650i
\(646\) −4.47720e8 3.25288e8i −1.66077 1.20662i
\(647\) −8.58944e7 + 2.79088e7i −0.317141 + 0.103045i −0.463262 0.886221i \(-0.653321\pi\)
0.146121 + 0.989267i \(0.453321\pi\)
\(648\) 3.95418e7 + 8.34802e7i 0.145322 + 0.306802i
\(649\) −3.73885e7 2.34030e7i −0.136774 0.0856125i
\(650\) 1.55521e8i 0.566303i
\(651\) −1.13623e8 4.28522e7i −0.411835 0.155321i
\(652\) 3.11058e8 + 2.25997e8i 1.12227 + 0.815378i
\(653\) 2.64500e8 + 3.64053e8i 0.949918 + 1.30745i 0.951564 + 0.307451i \(0.0994761\pi\)
−0.00164586 + 0.999999i \(0.500524\pi\)
\(654\) −4.03966e8 + 2.65723e8i −1.44415 + 0.949940i
\(655\) −1.13957e8 + 3.50722e8i −0.405523 + 1.24807i
\(656\) −2.57760e8 3.54776e8i −0.913069 1.25673i
\(657\) 6.06598e7 1.40666e8i 0.213897 0.496013i
\(658\) −2.34343e6 7.21233e6i −0.00822572 0.0253162i
\(659\) 3.80187e8i 1.32844i −0.747538 0.664219i \(-0.768764\pi\)
0.747538 0.664219i \(-0.231236\pi\)
\(660\) −1.38644e8 + 2.00168e8i −0.482245 + 0.696248i
\(661\) −4.82773e7 −0.167163 −0.0835813 0.996501i \(-0.526636\pi\)
−0.0835813 + 0.996501i \(0.526636\pi\)
\(662\) 3.61729e8 1.17533e8i 1.24684 0.405122i
\(663\) 1.85172e8 + 6.75193e8i 0.635383 + 2.31679i
\(664\) 7.05907e6 5.12872e6i 0.0241126 0.0175188i
\(665\) −2.19636e8 7.13641e7i −0.746860 0.242669i
\(666\) 2.61273e7 2.80191e8i 0.0884446 0.948487i
\(667\) 7.46926e6 5.42674e6i 0.0251710 0.0182878i
\(668\) −1.10056e8 + 1.51479e8i −0.369219 + 0.508186i
\(669\) 1.53282e8 + 5.78092e7i 0.511932 + 0.193072i
\(670\) 4.72414e8 1.57072
\(671\) 8.01657e6 + 1.15926e8i 0.0265351 + 0.383719i
\(672\) 2.17334e8 + 1.73891e8i 0.716175 + 0.573019i
\(673\) −1.16614e8 3.58900e8i −0.382564 1.17741i −0.938232 0.346008i \(-0.887537\pi\)
0.555667 0.831405i \(-0.312463\pi\)
\(674\) 2.52837e8 3.48001e8i 0.825775 1.13658i
\(675\) −9.08287e7 + 1.60303e7i −0.295333 + 0.0521231i
\(676\) −7.41701e7 + 2.28272e8i −0.240098 + 0.738946i
\(677\) −3.79191e8 1.23207e8i −1.22206 0.397071i −0.374227 0.927337i \(-0.622092\pi\)
−0.847831 + 0.530267i \(0.822092\pi\)
\(678\) 2.56783e7 5.51947e8i 0.0823905 1.77096i
\(679\) 3.22315e8 + 2.34176e8i 1.02961 + 0.748053i
\(680\) 1.94397e8 6.31634e7i 0.618248 0.200881i
\(681\) −2.51241e8 2.01020e8i −0.795516 0.636501i
\(682\) 2.10015e8 + 1.31457e8i 0.662060 + 0.414410i
\(683\) 2.59910e8i 0.815757i −0.913036 0.407878i \(-0.866269\pi\)
0.913036 0.407878i \(-0.133731\pi\)
\(684\) −1.89300e8 + 1.12276e8i −0.591537 + 0.350847i
\(685\) 4.55596e8 + 3.31010e8i 1.41745 + 1.02984i
\(686\) −2.69585e8 3.71052e8i −0.835070 1.14938i
\(687\) 1.97541e8 + 3.00313e8i 0.609239 + 0.926197i
\(688\) 1.65507e8 5.09379e8i 0.508220 1.56414i
\(689\) 2.92790e8 + 4.02991e8i 0.895155 + 1.23208i
\(690\) 4.05971e7 + 1.48029e8i 0.123580 + 0.450609i
\(691\) −5.90013e7 1.81587e8i −0.178825 0.550366i 0.820963 0.570982i \(-0.193437\pi\)
−0.999787 + 0.0206159i \(0.993437\pi\)
\(692\) 2.04462e8i 0.617012i
\(693\) 5.92608e6 2.47526e8i 0.0178060 0.743740i
\(694\) 6.64477e7 0.198793
\(695\) 2.00266e8 6.50704e7i 0.596558 0.193833i
\(696\) −1.10630e7 + 3.03405e6i −0.0328130 + 0.00899900i
\(697\) −6.00081e8 + 4.35984e8i −1.77220 + 1.28758i
\(698\) 3.04579e8 + 9.89636e7i 0.895639 + 0.291011i
\(699\) 3.55780e8 2.34027e8i 1.04172 0.685228i
\(700\) −4.59909e7 + 3.34144e7i −0.134084 + 0.0974180i
\(701\) −6.75855e7 + 9.30235e7i −0.196200 + 0.270047i −0.895770 0.444518i \(-0.853375\pi\)
0.699570 + 0.714564i \(0.253375\pi\)
\(702\) 6.46919e8 + 9.08146e7i 1.86999 + 0.262509i
\(703\) −2.32102e8 −0.668057
\(704\) −9.78258e7 1.16767e8i −0.280372 0.334658i
\(705\) −6.76460e6 + 8.45459e6i −0.0193052 + 0.0241282i
\(706\) −3.92775e7 1.20884e8i −0.111617 0.343521i
\(707\) −1.71210e8 + 2.35650e8i −0.484474 + 0.666821i
\(708\) −4.24937e7 1.97694e6i −0.119736 0.00557050i
\(709\) 8.02102e7 2.46862e8i 0.225056 0.692652i −0.773230 0.634126i \(-0.781360\pi\)
0.998286 0.0585256i \(-0.0186399\pi\)
\(710\) 7.09673e7 + 2.30587e7i 0.198282 + 0.0644258i
\(711\) 4.98947e8 + 4.38757e8i 1.38818 + 1.22072i
\(712\) 1.24341e8 + 9.03390e7i 0.344488 + 0.250285i
\(713\) 6.33130e7 2.05716e7i 0.174672 0.0567545i
\(714\) 3.75115e8 4.68829e8i 1.03055 1.28801i
\(715\) −2.22877e8 5.52865e8i −0.609742 1.51252i
\(716\) 2.40677e8i 0.655685i
\(717\) 1.33163e8 3.53084e8i 0.361266 0.957900i
\(718\) −1.27499e8 9.26337e7i −0.344457 0.250263i
\(719\) 3.21105e8 + 4.41963e8i 0.863894 + 1.18905i 0.980627 + 0.195885i \(0.0627580\pi\)
−0.116733 + 0.993163i \(0.537242\pi\)
\(720\) 4.70578e7 5.04652e8i 0.126077 1.35206i
\(721\) −6.98289e7 + 2.14911e8i −0.186307 + 0.573394i
\(722\) −4.17150e7 5.74157e7i −0.110836 0.152553i
\(723\) 3.83967e8 1.05303e8i 1.01596 0.278629i
\(724\) 9.24181e7 + 2.84434e8i 0.243524 + 0.749489i
\(725\) 1.14543e7i 0.0300575i
\(726\) −1.11507e8 + 4.92713e8i −0.291403 + 1.28761i
\(727\) −2.00344e8 −0.521402 −0.260701 0.965420i \(-0.583954\pi\)
−0.260701 + 0.965420i \(0.583954\pi\)
\(728\) −1.32558e8 + 4.30706e7i −0.343567 + 0.111632i
\(729\) −1.36427e7 3.87180e8i −0.0352143 0.999380i
\(730\) −2.55882e8 + 1.85909e8i −0.657765 + 0.477894i
\(731\) −8.61582e8 2.79945e8i −2.20569 0.716672i
\(732\) 6.15877e7 + 9.36289e7i 0.157022 + 0.238713i
\(733\) −3.44906e8 + 2.50589e8i −0.875768 + 0.636283i −0.932129 0.362127i \(-0.882050\pi\)
0.0563601 + 0.998411i \(0.482050\pi\)
\(734\) −3.41912e8 + 4.70602e8i −0.864622 + 1.19005i
\(735\) −7.13345e7 + 1.89144e8i −0.179654 + 0.476355i
\(736\) −1.52586e8 −0.382720
\(737\) 3.87451e8 1.56193e8i 0.967865 0.390175i
\(738\) 1.51832e8 + 6.75233e8i 0.377741 + 1.67990i
\(739\) 4.36200e7 + 1.34248e8i 0.108082 + 0.332641i 0.990441 0.137934i \(-0.0440463\pi\)
−0.882360 + 0.470576i \(0.844046\pi\)
\(740\) −1.45563e8 + 2.00351e8i −0.359217 + 0.494420i
\(741\) 2.50399e7 5.38224e8i 0.0615429 1.32284i
\(742\) 1.32009e8 4.06282e8i 0.323141 0.994526i
\(743\) 2.87932e8 + 9.35548e7i 0.701978 + 0.228086i 0.638192 0.769877i \(-0.279683\pi\)
0.0637858 + 0.997964i \(0.479683\pi\)
\(744\) −8.26263e7 3.84403e6i −0.200632 0.00933401i
\(745\) 1.63590e8 + 1.18855e8i 0.395629 + 0.287441i
\(746\) −6.05585e8 + 1.96766e8i −1.45868 + 0.473952i
\(747\) −3.57046e7 + 8.02848e6i −0.0856568 + 0.0192607i
\(748\) −4.00249e8 + 3.35324e8i −0.956370 + 0.801235i
\(749\) 1.20671e8i 0.287183i
\(750\) −4.15961e8 1.56877e8i −0.985981 0.371857i
\(751\) −5.87382e8 4.26758e8i −1.38676 1.00754i −0.996212 0.0869564i \(-0.972286\pi\)
−0.390547 0.920583i \(-0.627714\pi\)
\(752\) −8.06879e6 1.11057e7i −0.0189738 0.0261152i
\(753\) 4.92812e8 3.24165e8i 1.15424 0.759243i
\(754\) −2.50699e7 + 7.71573e7i −0.0584842 + 0.179996i
\(755\) 2.77165e8 + 3.81485e8i 0.644017 + 0.886413i
\(756\) −1.12138e8 2.10820e8i −0.259529 0.487918i
\(757\) 1.86541e8 + 5.74113e8i 0.430017 + 1.32346i 0.898107 + 0.439777i \(0.144942\pi\)
−0.468090 + 0.883681i \(0.655058\pi\)
\(758\) 9.79783e8i 2.24969i
\(759\) 8.22383e7 + 1.07984e8i 0.188083 + 0.246964i
\(760\) −1.57304e8 −0.358344
\(761\) −6.87176e8 + 2.23277e8i −1.55924 + 0.506629i −0.956606 0.291385i \(-0.905884\pi\)
−0.602639 + 0.798014i \(0.705884\pi\)
\(762\) −7.99046e7 2.91356e8i −0.180595 0.658505i
\(763\) −3.50053e8 + 2.54328e8i −0.788061 + 0.572560i
\(764\) 4.09097e8 + 1.32924e8i 0.917374 + 0.298073i
\(765\) −8.53587e8 7.95954e7i −1.90662 0.177788i
\(766\) 5.83429e8 4.23886e8i 1.29808 0.943111i
\(767\) 6.12129e7 8.42523e7i 0.135662 0.186722i
\(768\) 5.52391e8 + 2.08331e8i 1.21945 + 0.459907i
\(769\) 4.78916e8 1.05313 0.526563 0.850136i \(-0.323480\pi\)
0.526563 + 0.850136i \(0.323480\pi\)
\(770\) −2.71236e8 + 4.33325e8i −0.594122 + 0.949165i
\(771\) −1.03228e8 8.25940e7i −0.225235 0.180213i
\(772\) −4.66258e7 1.43500e8i −0.101339 0.311888i
\(773\) 3.57900e7 4.92607e7i 0.0774860 0.106650i −0.768515 0.639832i \(-0.779004\pi\)
0.846001 + 0.533182i \(0.179004\pi\)
\(774\) −5.58191e8 + 6.34765e8i −1.20382 + 1.36896i
\(775\) 2.55221e7 7.85488e7i 0.0548290 0.168746i
\(776\) 2.58091e8 + 8.38589e7i 0.552316 + 0.179458i
\(777\) 1.17028e7 2.51548e8i 0.0249475 0.536238i
\(778\) 5.61232e8 + 4.07759e8i 1.19180 + 0.865894i
\(779\) 5.42895e8 1.76397e8i 1.14843 0.373147i
\(780\) −4.48891e8 3.59163e8i −0.945927 0.756845i
\(781\) 6.58278e7 4.55216e6i 0.138184 0.00955574i
\(782\) 3.29156e8i 0.688306i
\(783\) 4.76462e7 + 6.68858e6i 0.0992528 + 0.0139331i
\(784\) −2.07339e8 1.50640e8i −0.430261 0.312603i
\(785\) 1.52891e8 + 2.10436e8i 0.316062 + 0.435022i
\(786\) 4.05495e8 + 6.16455e8i 0.835061 + 1.26950i
\(787\) 7.24159e7 2.22873e8i 0.148563 0.457229i −0.848889 0.528571i \(-0.822728\pi\)
0.997452 + 0.0713419i \(0.0227281\pi\)
\(788\) 1.71899e8 + 2.36599e8i 0.351314 + 0.483542i
\(789\) 1.47976e8 + 5.39566e8i 0.301274 + 1.09853i
\(790\) −4.23919e8 1.30469e9i −0.859809 2.64622i
\(791\) 4.94450e8i 0.999063i
\(792\) −4.82621e7 1.61598e8i −0.0971472 0.325282i
\(793\) −2.74356e8 −0.550167
\(794\) −1.00104e9 + 3.25259e8i −1.99982 + 0.649782i
\(795\) −5.88224e8 + 1.61321e8i −1.17069 + 0.321062i
\(796\) 1.62937e8 1.18381e8i 0.323058 0.234716i
\(797\) −2.39172e8 7.77117e7i −0.472428 0.153501i 0.0631202 0.998006i \(-0.479895\pi\)
−0.535548 + 0.844505i \(0.679895\pi\)
\(798\) −3.86049e8 + 2.53937e8i −0.759685 + 0.499710i
\(799\) −1.87846e7 + 1.36478e7i −0.0368267 + 0.0267561i
\(800\) −1.11271e8 + 1.53151e8i −0.217325 + 0.299123i
\(801\) −3.28840e8 5.54431e8i −0.639862 1.07882i
\(802\) −4.50486e7 −0.0873289
\(803\) −1.48395e8 + 2.37075e8i −0.286598 + 0.457867i
\(804\) 2.51703e8 3.14586e8i 0.484307 0.605300i
\(805\) 4.24456e7 + 1.30634e8i 0.0813663 + 0.250420i
\(806\) −3.43839e8 + 4.73254e8i −0.656675 + 0.903835i
\(807\) −2.49603e8 1.16123e7i −0.474930 0.0220952i
\(808\) −6.13106e7 + 1.88695e8i −0.116226 + 0.357706i
\(809\) −6.57781e8 2.13726e8i −1.24233 0.403656i −0.387161 0.922012i \(-0.626544\pi\)
−0.855165 + 0.518356i \(0.826544\pi\)
\(810\) −3.83579e8 + 7.01940e8i −0.721771 + 1.32082i
\(811\) −2.21164e8 1.60685e8i −0.414622 0.301241i 0.360848 0.932625i \(-0.382487\pi\)
−0.775470 + 0.631384i \(0.782487\pi\)
\(812\) 2.82035e7 9.16387e6i 0.0526787 0.0171163i
\(813\) −8.71406e7 + 1.08911e8i −0.162162 + 0.202675i
\(814\) −1.24681e8 + 4.98431e8i −0.231167 + 0.924128i
\(815\) 1.15256e9i 2.12908i
\(816\) 3.83538e8 1.01695e9i 0.705891 1.87168i
\(817\) 5.64034e8 + 4.09795e8i 1.03428 + 0.751450i
\(818\) −7.42780e7 1.02235e8i −0.135706 0.186784i
\(819\) 5.82054e8 + 5.42754e7i 1.05953 + 0.0987987i
\(820\) 1.88211e8 5.79255e8i 0.341353 1.05058i
\(821\) 3.38557e8 + 4.65984e8i 0.611790 + 0.842056i 0.996723 0.0808879i \(-0.0257756\pi\)
−0.384933 + 0.922944i \(0.625776\pi\)
\(822\) 1.08666e9 2.98018e8i 1.95650 0.536571i
\(823\) 2.53263e8 + 7.79463e8i 0.454331 + 1.39829i 0.871919 + 0.489650i \(0.162875\pi\)
−0.417589 + 0.908636i \(0.637125\pi\)
\(824\) 1.53920e8i 0.275115i
\(825\) 1.68354e8 3.79753e6i 0.299821 0.00676300i
\(826\) −8.93117e7 −0.158478
\(827\) −3.04417e8 + 9.89111e7i −0.538211 + 0.174875i −0.565494 0.824752i \(-0.691314\pi\)
0.0272832 + 0.999628i \(0.491314\pi\)
\(828\) 1.20204e8 + 5.18361e7i 0.211753 + 0.0913149i
\(829\) 7.29239e8 5.29823e8i 1.27999 0.929967i 0.280437 0.959872i \(-0.409521\pi\)
0.999553 + 0.0299052i \(0.00952055\pi\)
\(830\) 7.18618e7 + 2.33493e7i 0.125679 + 0.0408357i
\(831\) 4.04781e8 + 6.15369e8i 0.705370 + 1.07234i
\(832\) 2.90965e8 2.11398e8i 0.505208 0.367055i
\(833\) −2.54798e8 + 3.50700e8i −0.440820 + 0.606737i
\(834\) 1.48679e8 3.94223e8i 0.256301 0.679585i
\(835\) 5.61277e8 0.964090
\(836\) 3.72696e8 1.50245e8i 0.637875 0.257147i
\(837\) 3.11835e8 + 1.52032e8i 0.531801 + 0.259273i
\(838\) 1.22221e8 + 3.76159e8i 0.207690 + 0.639204i
\(839\) 8.42355e7 1.15940e8i 0.142629 0.196313i −0.731726 0.681599i \(-0.761285\pi\)
0.874355 + 0.485287i \(0.161285\pi\)
\(840\) 7.93142e6 1.70483e8i 0.0133817 0.287636i
\(841\) 1.81964e8 5.60028e8i 0.305913 0.941503i
\(842\) 1.23653e9 + 4.01772e8i 2.07141 + 0.673043i
\(843\) −5.40826e7 2.51609e6i −0.0902765 0.00419995i
\(844\) 1.52924e8 + 1.11106e8i 0.254359 + 0.184803i
\(845\) 6.84282e8 2.22337e8i 1.13414 0.368503i
\(846\) 4.75287e6 + 2.11372e7i 0.00784956 + 0.0349088i
\(847\) −7.91854e7 + 4.45070e8i −0.130315 + 0.732451i
\(848\) 7.73289e8i 1.26810i
\(849\) 4.36243e8 + 1.64526e8i 0.712861 + 0.268851i
\(850\) 3.30374e8 + 2.40031e8i 0.537959 + 0.390850i
\(851\) 8.11429e7 + 1.11684e8i 0.131662 + 0.181218i
\(852\) 5.31666e7 3.49722e7i 0.0859646 0.0565463i
\(853\) 2.79720e8 8.60890e8i 0.450689 1.38708i −0.425434 0.904989i \(-0.639879\pi\)
0.876123 0.482088i \(-0.160121\pi\)
\(854\) 1.38298e8 + 1.90352e8i 0.222046 + 0.305621i
\(855\) 6.05829e8 + 2.61254e8i 0.969285 + 0.417988i
\(856\) 2.53998e7 + 7.81725e7i 0.0404957 + 0.124633i
\(857\) 7.54218e8i 1.19827i −0.800648 0.599135i \(-0.795511\pi\)
0.800648 0.599135i \(-0.204489\pi\)
\(858\) −1.14237e9 3.42896e8i −1.80860 0.542876i
\(859\) −3.52866e8 −0.556712 −0.278356 0.960478i \(-0.589790\pi\)
−0.278356 + 0.960478i \(0.589790\pi\)
\(860\) 7.07470e8 2.29871e8i 1.11228 0.361400i
\(861\) 1.63803e8 + 5.97273e8i 0.256632 + 0.935757i
\(862\) −4.74565e8 + 3.44792e8i −0.740925 + 0.538314i
\(863\) 8.15817e7 + 2.65075e7i 0.126929 + 0.0412417i 0.371793 0.928316i \(-0.378743\pi\)
−0.244864 + 0.969557i \(0.578743\pi\)
\(864\) −5.72085e8 5.52282e8i −0.886991 0.856287i
\(865\) 4.95851e8 3.60257e8i 0.766131 0.556627i
\(866\) −7.56951e8 + 1.04185e9i −1.16550 + 1.60418i
\(867\) −1.11032e9 4.18752e8i −1.70370 0.642539i
\(868\) 2.13827e8 0.326967
\(869\) −7.79045e8 9.29884e8i −1.18714 1.41700i
\(870\) −7.75671e7 6.20623e7i −0.117793 0.0942475i
\(871\) 3.04787e8 + 9.38038e8i 0.461256 + 1.41960i
\(872\) −1.73236e8 + 2.38439e8i −0.261269 + 0.359606i
\(873\) −8.54716e8 7.51608e8i −1.28463 1.12966i
\(874\) 7.82784e7 2.40916e8i 0.117249 0.360854i
\(875\) −3.78349e8 1.22933e8i −0.564766 0.183503i
\(876\) −1.25355e7 + 2.69447e8i −0.0186479 + 0.400831i
\(877\) −8.44320e8 6.13434e8i −1.25172 0.909430i −0.253402 0.967361i \(-0.581550\pi\)
−0.998321 + 0.0579313i \(0.981550\pi\)
\(878\) 8.33086e8 2.70686e8i 1.23085 0.399929i
\(879\) 2.17641e8 + 1.74137e8i 0.320460 + 0.256404i
\(880\) −2.24563e8 + 8.97725e8i −0.329526 + 1.31733i
\(881\) 2.16699e7i 0.0316904i −0.999874 0.0158452i \(-0.994956\pi\)
0.999874 0.0158452i \(-0.00504390\pi\)
\(882\) 2.06335e8 + 3.47886e8i 0.300724 + 0.507027i
\(883\) 3.14240e8 + 2.28309e8i 0.456435 + 0.331620i 0.792131 0.610351i \(-0.208971\pi\)
−0.335696 + 0.941970i \(0.608971\pi\)
\(884\) −7.24624e8 9.97359e8i −1.04895 1.44376i
\(885\) 7.00787e7 + 1.06537e8i 0.101101 + 0.153699i
\(886\) −2.97076e8 + 9.14306e8i −0.427136 + 1.31459i
\(887\) −2.92584e8 4.02708e8i −0.419257 0.577058i 0.546189 0.837662i \(-0.316078\pi\)
−0.965446 + 0.260604i \(0.916078\pi\)
\(888\) −4.53664e7 1.65419e8i −0.0647881 0.236236i
\(889\) −8.35428e7 2.57118e8i −0.118906 0.365955i
\(890\) 1.33094e9i 1.88794i
\(891\) −8.25119e7 + 7.02519e8i −0.116650 + 0.993173i
\(892\) −2.88461e8 −0.406436
\(893\) 1.69945e7 5.52186e6i 0.0238646 0.00775409i
\(894\) 3.90186e8 1.07009e8i 0.546084 0.149764i
\(895\) −5.83679e8 + 4.24068e8i −0.814152 + 0.591516i
\(896\) 3.34132e8 + 1.08566e8i 0.464508 + 0.150928i
\(897\) −2.67738e8 + 1.76114e8i −0.370965 + 0.244016i
\(898\) 5.35362e8 3.88963e8i 0.739297 0.537130i
\(899\) −2.53241e7 + 3.48556e7i −0.0348542 + 0.0479726i
\(900\) 1.39685e8 8.28487e7i 0.191612 0.113647i
\(901\) −1.30797e9 −1.78823
\(902\) −8.71739e7 1.26060e9i −0.118787 1.71775i
\(903\) −4.72566e8 + 5.90626e8i −0.641800 + 0.802139i
\(904\) −1.04075e8 3.20311e8i −0.140878 0.433578i
\(905\) 5.26958e8 7.25295e8i 0.710935 0.978518i
\(906\) 9.42474e8 + 4.38469e7i 1.26732 + 0.0589595i
\(907\) −8.16604e7 + 2.51325e8i −0.109443 + 0.336832i −0.990748 0.135717i \(-0.956666\pi\)
0.881304 + 0.472549i \(0.156666\pi\)
\(908\) 5.38841e8 + 1.75080e8i 0.719786 + 0.233873i
\(909\) 5.49514e8 6.24897e8i 0.731622 0.831988i
\(910\) −9.76468e8 7.09446e8i −1.29579 0.941445i
\(911\) −2.65159e8 + 8.61554e7i −0.350712 + 0.113953i −0.479075 0.877774i \(-0.659028\pi\)
0.128363 + 0.991727i \(0.459028\pi\)
\(912\) −5.22567e8 + 6.53118e8i −0.688901 + 0.861008i
\(913\) 6.66575e7 4.60953e6i 0.0875864 0.00605682i
\(914\) 2.89800e8i 0.379542i
\(915\) 1.18548e8 3.14332e8i 0.154751 0.410323i
\(916\) −5.12065e8 3.72037e8i −0.666252 0.484060i
\(917\) 3.88106e8 + 5.34183e8i 0.503318 + 0.692758i
\(918\) −1.19137e9 + 1.23409e9i −1.54000 + 1.59522i
\(919\) −2.82966e8 + 8.70880e8i −0.364576 + 1.12205i 0.585670 + 0.810549i \(0.300831\pi\)
−0.950246 + 0.311500i \(0.899169\pi\)
\(920\) 5.49936e7 + 7.56922e7i 0.0706234 + 0.0972048i
\(921\) −1.30600e8 + 3.58171e7i −0.167172 + 0.0458471i
\(922\) −1.59622e8 4.91266e8i −0.203657 0.626792i
\(923\) 1.55791e8i 0.198124i
\(924\) 1.44041e8 + 4.11496e8i 0.182587 + 0.521614i
\(925\) 1.71269e8 0.216398
\(926\) −5.59687e8 + 1.81853e8i −0.704875 + 0.229028i
\(927\) 2.55633e8 5.92795e8i 0.320906 0.744159i
\(928\) 7.98916e7 5.80446e7i 0.0999671 0.0726304i
\(929\) 3.99636e8 + 1.29850e8i 0.498446 + 0.161955i 0.547441 0.836844i \(-0.315602\pi\)
−0.0489955 + 0.998799i \(0.515602\pi\)
\(930\) −3.93640e8 5.98431e8i −0.489384 0.743987i
\(931\) 2.69894e8 1.96089e8i 0.334460 0.242999i
\(932\) −4.40752e8 + 6.06643e8i −0.544436 + 0.749351i
\(933\) 6.02219e7 1.59679e8i 0.0741498 0.196609i
\(934\) −1.12575e8 −0.138166
\(935\) 1.51844e9 + 3.79834e8i 1.85765 + 0.464685i
\(936\) 3.88486e8 8.73546e7i 0.473749 0.106527i
\(937\) 1.36192e8 + 4.19155e8i 0.165551 + 0.509514i 0.999076 0.0429672i \(-0.0136811\pi\)
−0.833525 + 0.552481i \(0.813681\pi\)
\(938\) 4.97184e8 6.84315e8i 0.602432 0.829177i
\(939\) 2.52328e7 5.42371e8i 0.0304767 0.655088i
\(940\) 5.89167e6 1.81327e7i 0.00709341 0.0218313i
\(941\) 8.19156e8 + 2.66160e8i 0.983100 + 0.319428i 0.756093 0.654465i \(-0.227106\pi\)
0.227007 + 0.973893i \(0.427106\pi\)
\(942\) 5.19892e8 + 2.41870e7i 0.621957 + 0.0289354i
\(943\) −2.74676e8 1.99563e8i −0.327555 0.237983i
\(944\) −1.53757e8 + 4.99587e7i −0.182776 + 0.0593875i
\(945\) −3.13688e8 + 6.43412e8i −0.371708 + 0.762419i
\(946\) 1.18301e9 9.91109e8i 1.39738 1.17071i
\(947\) 7.28493e8i 0.857778i 0.903357 + 0.428889i \(0.141095\pi\)
−0.903357 + 0.428889i \(0.858905\pi\)
\(948\) −1.09467e9 4.12849e8i −1.28487 0.484581i
\(949\) −5.34232e8 3.88143e8i −0.625074 0.454143i
\(950\) −1.84725e8 2.54252e8i −0.215454 0.296547i
\(951\) 7.12298e7 4.68539e7i 0.0828171 0.0544759i
\(952\) 1.13094e8 3.48069e8i 0.131078 0.403417i
\(953\) −2.07574e8 2.85701e8i −0.239825 0.330091i 0.672090 0.740469i \(-0.265397\pi\)
−0.911915 + 0.410378i \(0.865397\pi\)
\(954\) −4.83266e8 + 1.12066e9i −0.556597 + 1.29071i
\(955\) −3.98460e8 1.22633e9i −0.457483 1.40799i
\(956\) 6.64469e8i 0.760503i
\(957\) −8.41363e7 2.52546e7i −0.0959948 0.0288141i
\(958\) −9.20729e8 −1.04721
\(959\) 9.58968e8 3.11588e8i 1.08730 0.353284i
\(960\) 1.16476e8 + 4.24705e8i 0.131650 + 0.480036i
\(961\) 4.66679e8 3.39062e8i 0.525833 0.382040i
\(962\) −1.15369e9 3.74856e8i −1.29588 0.421056i
\(963\) 3.20075e7 3.43251e8i 0.0358404 0.384356i
\(964\) −5.67175e8 + 4.12077e8i −0.633120 + 0.459989i
\(965\) −2.65855e8 + 3.65918e8i −0.295844 + 0.407195i
\(966\) 2.57153e8 + 9.69836e7i 0.285273 + 0.107589i
\(967\) 8.36817e7 0.0925446 0.0462723 0.998929i \(-0.485266\pi\)
0.0462723 + 0.998929i \(0.485266\pi\)
\(968\) 4.23843e7 + 3.04990e8i 0.0467282 + 0.336248i
\(969\) 1.10471e9 + 8.83888e8i 1.21416 + 0.971462i
\(970\) 7.26191e8 + 2.23498e9i 0.795674 + 2.44883i
\(971\) −6.15026e7 + 8.46510e7i −0.0671793 + 0.0924644i −0.841285 0.540593i \(-0.818200\pi\)
0.774105 + 0.633057i \(0.218200\pi\)
\(972\) 2.63058e8 + 6.29424e8i 0.286452 + 0.685401i
\(973\) 1.16509e8 3.58577e8i 0.126479 0.389264i
\(974\) 1.05604e9 + 3.43129e8i 1.14289 + 0.371347i
\(975\) −1.84770e7 + 3.97157e8i −0.0199351 + 0.428498i
\(976\) 3.44569e8 + 2.50344e8i 0.370618 + 0.269270i
\(977\) −2.55098e8 + 8.28864e7i −0.273542 + 0.0888790i −0.442576 0.896731i \(-0.645935\pi\)
0.169034 + 0.985610i \(0.445935\pi\)
\(978\) −1.80069e9 1.44075e9i −1.92497 1.54018i
\(979\) 4.40045e8 + 1.09157e9i 0.468975 + 1.16333i
\(980\) 3.55950e8i 0.378191i
\(981\) 1.06319e9 6.30589e8i 1.12617 0.667943i
\(982\) −2.39530e8 1.74029e8i −0.252945 0.183775i
\(983\) −7.81995e8 1.07632e9i −0.823272 1.13314i −0.989138 0.146989i \(-0.953042\pi\)
0.165866 0.986148i \(-0.446958\pi\)
\(984\) 2.31832e8 + 3.52443e8i 0.243325 + 0.369916i
\(985\) 2.70907e8 8.33766e8i 0.283473 0.872440i
\(986\) −1.25213e8 1.72341e8i −0.130623 0.179787i
\(987\) 5.12759e6 + 1.86967e7i 0.00533289 + 0.0194453i
\(988\) 2.93180e8 + 9.02314e8i 0.303993 + 0.935593i
\(989\) 4.14668e8i 0.428659i
\(990\) 8.86472e8 1.16065e9i 0.913607 1.19618i
\(991\) 9.76094e7 0.100293 0.0501465 0.998742i \(-0.484031\pi\)
0.0501465 + 0.998742i \(0.484031\pi\)
\(992\) 6.77198e8 2.20035e8i 0.693715 0.225402i
\(993\) −9.37721e8 + 2.57171e8i −0.957692 + 0.262648i
\(994\) 1.08090e8 7.85319e7i 0.110059 0.0799626i
\(995\) −5.74184e8 1.86564e8i −0.582884 0.189390i
\(996\) 5.38367e7 3.54130e7i 0.0544879 0.0358414i
\(997\) −9.16315e8 + 6.65742e8i −0.924611 + 0.671770i −0.944668 0.328029i \(-0.893616\pi\)
0.0200561 + 0.999799i \(0.493616\pi\)
\(998\) 1.20746e9 1.66192e9i 1.21473 1.67193i
\(999\) −1.00011e8 + 7.12426e8i −0.100311 + 0.714568i
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.5.18 yes 88
3.2 odd 2 inner 33.7.h.a.5.5 88
11.9 even 5 inner 33.7.h.a.20.5 yes 88
33.20 odd 10 inner 33.7.h.a.20.18 yes 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.7.h.a.5.5 88 3.2 odd 2 inner
33.7.h.a.5.18 yes 88 1.1 even 1 trivial
33.7.h.a.20.5 yes 88 11.9 even 5 inner
33.7.h.a.20.18 yes 88 33.20 odd 10 inner