Properties

Label 33.6.f.a.17.2
Level $33$
Weight $6$
Character 33.17
Analytic conductor $5.293$
Analytic rank $0$
Dimension $72$
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] = [33,6,Mod(2,33)]
 
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, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("33.2");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 33.f (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: \(5.29266605383\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 17.2
Character \(\chi\) \(=\) 33.17
Dual form 33.6.f.a.2.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.95379 - 9.09083i) q^{2} +(10.1153 + 11.8609i) q^{3} +(-48.0298 + 34.8957i) q^{4} +(91.6682 + 29.7848i) q^{5} +(77.9468 - 126.991i) q^{6} +(70.5766 + 97.1403i) q^{7} +(211.641 + 153.766i) q^{8} +(-38.3609 + 239.953i) q^{9} +O(q^{10})\) \(q+(-2.95379 - 9.09083i) q^{2} +(10.1153 + 11.8609i) q^{3} +(-48.0298 + 34.8957i) q^{4} +(91.6682 + 29.7848i) q^{5} +(77.9468 - 126.991i) q^{6} +(70.5766 + 97.1403i) q^{7} +(211.641 + 153.766i) q^{8} +(-38.3609 + 239.953i) q^{9} -921.319i q^{10} +(-277.875 - 289.545i) q^{11} +(-899.731 - 216.695i) q^{12} +(390.347 - 126.831i) q^{13} +(674.618 - 928.532i) q^{14} +(573.979 + 1388.55i) q^{15} +(185.656 - 571.392i) q^{16} +(-39.0029 + 120.038i) q^{17} +(2294.68 - 360.039i) q^{18} +(1063.98 - 1464.45i) q^{19} +(-5442.17 + 1768.27i) q^{20} +(-438.265 + 1819.70i) q^{21} +(-1811.43 + 3381.37i) q^{22} +379.653i q^{23} +(317.013 + 4065.65i) q^{24} +(4987.75 + 3623.81i) q^{25} +(-2306.01 - 3173.95i) q^{26} +(-3234.09 + 1972.21i) q^{27} +(-6779.56 - 2202.81i) q^{28} +(-582.330 + 423.088i) q^{29} +(10927.6 - 9319.43i) q^{30} +(-2348.72 - 7228.62i) q^{31} +2628.48 q^{32} +(623.472 - 6224.68i) q^{33} +1206.46 q^{34} +(3576.32 + 11006.8i) q^{35} +(-6530.87 - 12863.5i) q^{36} +(-9263.80 + 6730.55i) q^{37} +(-16455.9 - 5346.83i) q^{38} +(5452.81 + 3346.92i) q^{39} +(14820.9 + 20399.2i) q^{40} +(-6792.51 - 4935.05i) q^{41} +(17837.2 - 1390.83i) q^{42} -7794.19i q^{43} +(23450.2 + 4210.18i) q^{44} +(-10663.4 + 20853.5i) q^{45} +(3451.36 - 1121.42i) q^{46} +(1576.98 - 2170.53i) q^{47} +(8655.18 - 3577.76i) q^{48} +(738.460 - 2272.75i) q^{49} +(18210.7 - 56046.8i) q^{50} +(-1818.29 + 751.618i) q^{51} +(-14322.4 + 19713.1i) q^{52} +(-25601.9 + 8318.56i) q^{53} +(27481.8 + 23575.1i) q^{54} +(-16848.2 - 34818.6i) q^{55} +31411.2i q^{56} +(28132.2 - 2193.57i) q^{57} +(5566.30 + 4044.16i) q^{58} +(7740.08 + 10653.3i) q^{59} +(-76022.5 - 46662.4i) q^{60} +(-5205.04 - 1691.22i) q^{61} +(-58776.6 + 42703.7i) q^{62} +(-26016.5 + 13208.7i) q^{63} +(-13705.0 - 42179.6i) q^{64} +39560.1 q^{65} +(-58429.2 + 12718.5i) q^{66} +47737.6 q^{67} +(-2315.53 - 7126.46i) q^{68} +(-4503.02 + 3840.31i) q^{69} +(89497.2 - 65023.5i) q^{70} +(8273.65 + 2688.27i) q^{71} +(-45015.5 + 44885.4i) q^{72} +(-8641.33 - 11893.8i) q^{73} +(88549.6 + 64335.1i) q^{74} +(7471.05 + 95815.1i) q^{75} +107466. i q^{76} +(8515.08 - 47428.0i) q^{77} +(14319.8 - 59456.7i) q^{78} +(-54109.7 + 17581.3i) q^{79} +(34037.6 - 46848.7i) q^{80} +(-56105.9 - 18409.6i) q^{81} +(-24800.0 + 76326.7i) q^{82} +(15446.3 - 47538.8i) q^{83} +(-42450.1 - 102694. i) q^{84} +(-7150.65 + 9842.02i) q^{85} +(-70855.7 + 23022.4i) q^{86} +(-10908.6 - 2627.28i) q^{87} +(-14287.4 - 104008. i) q^{88} +69906.5i q^{89} +(221073. + 35342.6i) q^{90} +(39869.8 + 28967.1i) q^{91} +(-13248.3 - 18234.7i) q^{92} +(61979.8 - 100978. i) q^{93} +(-24390.0 - 7924.78i) q^{94} +(141152. - 102553. i) q^{95} +(26587.9 + 31176.1i) q^{96} +(-5484.25 - 16878.8i) q^{97} -22842.4 q^{98} +(80136.8 - 55569.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 18 q^{3} - 262 q^{4} + 15 q^{6} - 10 q^{7} + 292 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 18 q^{3} - 262 q^{4} + 15 q^{6} - 10 q^{7} + 292 q^{9} + 1854 q^{12} - 10 q^{13} - 762 q^{15} - 10122 q^{16} + 4815 q^{18} + 4460 q^{19} + 4628 q^{22} - 805 q^{24} + 13708 q^{25} + 6108 q^{27} - 28130 q^{28} - 15470 q^{30} + 4340 q^{31} - 508 q^{33} + 18732 q^{34} - 56461 q^{36} + 978 q^{37} + 23360 q^{39} + 69750 q^{40} + 60788 q^{42} - 31356 q^{45} - 52090 q^{46} + 4238 q^{48} - 58448 q^{49} - 178950 q^{51} - 14190 q^{52} + 86600 q^{55} + 266190 q^{57} + 137102 q^{58} + 284090 q^{60} - 77890 q^{61} - 120330 q^{63} - 379114 q^{64} - 323304 q^{66} + 42668 q^{67} - 271816 q^{69} + 87176 q^{70} + 343960 q^{72} + 116440 q^{73} + 326202 q^{75} + 155512 q^{78} - 350590 q^{79} - 208088 q^{81} - 606424 q^{82} - 220680 q^{84} + 665610 q^{85} + 1152974 q^{88} + 293440 q^{90} + 621014 q^{91} + 478456 q^{93} - 521270 q^{94} - 1246430 q^{96} - 1030446 q^{97} - 590000 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(13\) \(23\)
\(\chi(n)\) \(e\left(\frac{9}{10}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.95379 9.09083i −0.522161 1.60705i −0.769862 0.638211i \(-0.779675\pi\)
0.247700 0.968837i \(-0.420325\pi\)
\(3\) 10.1153 + 11.8609i 0.648898 + 0.760876i
\(4\) −48.0298 + 34.8957i −1.50093 + 1.09049i
\(5\) 91.6682 + 29.7848i 1.63981 + 0.532807i 0.976496 0.215534i \(-0.0691492\pi\)
0.663315 + 0.748341i \(0.269149\pi\)
\(6\) 77.9468 126.991i 0.883934 1.44011i
\(7\) 70.5766 + 97.1403i 0.544397 + 0.749298i 0.989239 0.146311i \(-0.0467401\pi\)
−0.444842 + 0.895609i \(0.646740\pi\)
\(8\) 211.641 + 153.766i 1.16916 + 0.849448i
\(9\) −38.3609 + 239.953i −0.157864 + 0.987461i
\(10\) 921.319i 2.91347i
\(11\) −277.875 289.545i −0.692417 0.721498i
\(12\) −899.731 216.695i −1.80368 0.434406i
\(13\) 390.347 126.831i 0.640608 0.208146i 0.0293397 0.999569i \(-0.490660\pi\)
0.611269 + 0.791423i \(0.290660\pi\)
\(14\) 674.618 928.532i 0.919894 1.26613i
\(15\) 573.979 + 1388.55i 0.658670 + 1.59343i
\(16\) 185.656 571.392i 0.181305 0.558000i
\(17\) −39.0029 + 120.038i −0.0327321 + 0.100739i −0.966088 0.258214i \(-0.916866\pi\)
0.933356 + 0.358953i \(0.116866\pi\)
\(18\) 2294.68 360.039i 1.66933 0.261920i
\(19\) 1063.98 1464.45i 0.676163 0.930658i −0.323717 0.946154i \(-0.604933\pi\)
0.999880 + 0.0154955i \(0.00493256\pi\)
\(20\) −5442.17 + 1768.27i −3.04227 + 0.988492i
\(21\) −438.265 + 1819.70i −0.216865 + 0.900436i
\(22\) −1811.43 + 3381.37i −0.797928 + 1.48948i
\(23\) 379.653i 0.149647i 0.997197 + 0.0748234i \(0.0238393\pi\)
−0.997197 + 0.0748234i \(0.976161\pi\)
\(24\) 317.013 + 4065.65i 0.112344 + 1.44079i
\(25\) 4987.75 + 3623.81i 1.59608 + 1.15962i
\(26\) −2306.01 3173.95i −0.669002 0.920802i
\(27\) −3234.09 + 1972.21i −0.853772 + 0.520646i
\(28\) −6779.56 2202.81i −1.63421 0.530986i
\(29\) −582.330 + 423.088i −0.128580 + 0.0934190i −0.650217 0.759749i \(-0.725322\pi\)
0.521636 + 0.853168i \(0.325322\pi\)
\(30\) 10927.6 9319.43i 2.21679 1.89054i
\(31\) −2348.72 7228.62i −0.438963 1.35099i −0.888971 0.457963i \(-0.848579\pi\)
0.450008 0.893024i \(-0.351421\pi\)
\(32\) 2628.48 0.453764
\(33\) 623.472 6224.68i 0.0996626 0.995021i
\(34\) 1206.46 0.178984
\(35\) 3576.32 + 11006.8i 0.493477 + 1.51876i
\(36\) −6530.87 12863.5i −0.839875 1.65426i
\(37\) −9263.80 + 6730.55i −1.11246 + 0.808251i −0.983049 0.183340i \(-0.941309\pi\)
−0.129412 + 0.991591i \(0.541309\pi\)
\(38\) −16455.9 5346.83i −1.84868 0.600672i
\(39\) 5452.81 + 3346.92i 0.574063 + 0.352358i
\(40\) 14820.9 + 20399.2i 1.46462 + 2.01587i
\(41\) −6792.51 4935.05i −0.631060 0.458492i 0.225707 0.974195i \(-0.427531\pi\)
−0.856767 + 0.515703i \(0.827531\pi\)
\(42\) 17837.2 1390.83i 1.56028 0.121661i
\(43\) 7794.19i 0.642835i −0.946938 0.321418i \(-0.895841\pi\)
0.946938 0.321418i \(-0.104159\pi\)
\(44\) 23450.2 + 4210.18i 1.82606 + 0.327845i
\(45\) −10663.4 + 20853.5i −0.784993 + 1.53514i
\(46\) 3451.36 1121.42i 0.240490 0.0781398i
\(47\) 1576.98 2170.53i 0.104131 0.143325i −0.753771 0.657137i \(-0.771767\pi\)
0.857903 + 0.513812i \(0.171767\pi\)
\(48\) 8655.18 3577.76i 0.542217 0.224134i
\(49\) 738.460 2272.75i 0.0439376 0.135226i
\(50\) 18210.7 56046.8i 1.03015 3.17048i
\(51\) −1818.29 + 751.618i −0.0978897 + 0.0404643i
\(52\) −14322.4 + 19713.1i −0.734528 + 1.01099i
\(53\) −25601.9 + 8318.56i −1.25194 + 0.406779i −0.858615 0.512622i \(-0.828674\pi\)
−0.393322 + 0.919401i \(0.628674\pi\)
\(54\) 27481.8 + 23575.1i 1.28251 + 1.10019i
\(55\) −16848.2 34818.6i −0.751014 1.55204i
\(56\) 31411.2i 1.33849i
\(57\) 28132.2 2193.57i 1.14688 0.0894261i
\(58\) 5566.30 + 4044.16i 0.217269 + 0.157855i
\(59\) 7740.08 + 10653.3i 0.289478 + 0.398432i 0.928844 0.370470i \(-0.120803\pi\)
−0.639367 + 0.768902i \(0.720803\pi\)
\(60\) −76022.5 46662.4i −2.72624 1.67336i
\(61\) −5205.04 1691.22i −0.179102 0.0581937i 0.218093 0.975928i \(-0.430016\pi\)
−0.397195 + 0.917734i \(0.630016\pi\)
\(62\) −58776.6 + 42703.7i −1.94189 + 1.41087i
\(63\) −26016.5 + 13208.7i −0.825843 + 0.419284i
\(64\) −13705.0 42179.6i −0.418243 1.28722i
\(65\) 39560.1 1.16138
\(66\) −58429.2 + 12718.5i −1.65109 + 0.359399i
\(67\) 47737.6 1.29919 0.649597 0.760279i \(-0.274938\pi\)
0.649597 + 0.760279i \(0.274938\pi\)
\(68\) −2315.53 7126.46i −0.0607264 0.186897i
\(69\) −4503.02 + 3840.31i −0.113863 + 0.0971055i
\(70\) 89497.2 65023.5i 2.18305 1.58608i
\(71\) 8273.65 + 2688.27i 0.194783 + 0.0632889i 0.404784 0.914412i \(-0.367347\pi\)
−0.210001 + 0.977701i \(0.567347\pi\)
\(72\) −45015.5 + 44885.4i −1.02336 + 1.02041i
\(73\) −8641.33 11893.8i −0.189790 0.261224i 0.703509 0.710686i \(-0.251615\pi\)
−0.893299 + 0.449463i \(0.851615\pi\)
\(74\) 88549.6 + 64335.1i 1.87978 + 1.36574i
\(75\) 7471.05 + 95815.1i 0.153366 + 1.96689i
\(76\) 107466.i 2.13421i
\(77\) 8515.08 47428.0i 0.163667 0.911607i
\(78\) 14319.8 59456.7i 0.266502 1.10653i
\(79\) −54109.7 + 17581.3i −0.975455 + 0.316945i −0.753016 0.658002i \(-0.771402\pi\)
−0.222439 + 0.974947i \(0.571402\pi\)
\(80\) 34037.6 46848.7i 0.594612 0.818413i
\(81\) −56105.9 18409.6i −0.950158 0.311768i
\(82\) −24800.0 + 76326.7i −0.407303 + 1.25355i
\(83\) 15446.3 47538.8i 0.246110 0.757448i −0.749342 0.662183i \(-0.769630\pi\)
0.995452 0.0952652i \(-0.0303699\pi\)
\(84\) −42450.1 102694.i −0.656418 1.58798i
\(85\) −7150.65 + 9842.02i −0.107349 + 0.147753i
\(86\) −70855.7 + 23022.4i −1.03307 + 0.335664i
\(87\) −10908.6 2627.28i −0.154516 0.0372142i
\(88\) −14287.4 104008.i −0.196674 1.43172i
\(89\) 69906.5i 0.935498i 0.883861 + 0.467749i \(0.154935\pi\)
−0.883861 + 0.467749i \(0.845065\pi\)
\(90\) 221073. + 35342.6i 2.87693 + 0.459930i
\(91\) 39869.8 + 28967.1i 0.504708 + 0.366692i
\(92\) −13248.3 18234.7i −0.163189 0.224610i
\(93\) 61979.8 100978.i 0.743092 1.21065i
\(94\) −24390.0 7924.78i −0.284703 0.0925055i
\(95\) 141152. 102553.i 1.60464 1.16584i
\(96\) 26587.9 + 31176.1i 0.294447 + 0.345258i
\(97\) −5484.25 16878.8i −0.0591818 0.182143i 0.917095 0.398668i \(-0.130528\pi\)
−0.976277 + 0.216526i \(0.930528\pi\)
\(98\) −22842.4 −0.240257
\(99\) 80136.8 55569.7i 0.821758 0.569836i
\(100\) −366016. −3.66016
\(101\) −15886.0 48892.0i −0.154957 0.476908i 0.843200 0.537600i \(-0.180669\pi\)
−0.998157 + 0.0606925i \(0.980669\pi\)
\(102\) 12203.7 + 14309.6i 0.116142 + 0.136185i
\(103\) 121685. 88409.1i 1.13017 0.821115i 0.144448 0.989512i \(-0.453859\pi\)
0.985719 + 0.168397i \(0.0538592\pi\)
\(104\) 102116. + 33179.5i 0.925786 + 0.300806i
\(105\) −94374.6 + 153755.i −0.835376 + 1.36100i
\(106\) 151245. + 208171.i 1.30743 + 1.79952i
\(107\) −114518. 83202.4i −0.966975 0.702549i −0.0122150 0.999925i \(-0.503888\pi\)
−0.954760 + 0.297377i \(0.903888\pi\)
\(108\) 86511.1 207581.i 0.713694 1.71249i
\(109\) 20912.8i 0.168595i 0.996441 + 0.0842976i \(0.0268646\pi\)
−0.996441 + 0.0842976i \(0.973135\pi\)
\(110\) −266764. + 256011.i −2.10206 + 2.01733i
\(111\) −173536. 41795.2i −1.33685 0.321973i
\(112\) 68608.1 22292.1i 0.516810 0.167922i
\(113\) 54553.6 75086.6i 0.401909 0.553180i −0.559313 0.828957i \(-0.688935\pi\)
0.961222 + 0.275777i \(0.0889350\pi\)
\(114\) −103038. 249266.i −0.742566 1.79639i
\(115\) −11307.9 + 34802.1i −0.0797328 + 0.245392i
\(116\) 13205.3 40641.7i 0.0911177 0.280431i
\(117\) 15459.5 + 98530.3i 0.104407 + 0.665434i
\(118\) 73984.8 101831.i 0.489145 0.673251i
\(119\) −14413.3 + 4683.15i −0.0933028 + 0.0303159i
\(120\) −92034.5 + 382133.i −0.583442 + 2.42249i
\(121\) −6622.12 + 160915.i −0.0411182 + 0.999154i
\(122\) 52313.7i 0.318212i
\(123\) −10174.4 130485.i −0.0606380 0.777673i
\(124\) 365057. + 265229.i 2.13209 + 1.54906i
\(125\) 172240. + 237067.i 0.985957 + 1.35705i
\(126\) 196925. + 197496.i 1.10503 + 1.10823i
\(127\) −333795. 108457.i −1.83641 0.596687i −0.998722 0.0505444i \(-0.983904\pi\)
−0.837692 0.546143i \(-0.816096\pi\)
\(128\) −274919. + 199740.i −1.48313 + 1.07756i
\(129\) 92445.9 78840.6i 0.489118 0.417134i
\(130\) −116852. 359634.i −0.606427 1.86639i
\(131\) −11791.4 −0.0600328 −0.0300164 0.999549i \(-0.509556\pi\)
−0.0300164 + 0.999549i \(0.509556\pi\)
\(132\) 187270. + 320727.i 0.935475 + 1.60214i
\(133\) 217349. 1.06544
\(134\) −141007. 433975.i −0.678389 2.08787i
\(135\) −355205. + 84462.0i −1.67743 + 0.398866i
\(136\) −26712.5 + 19407.8i −0.123842 + 0.0899764i
\(137\) 229704. + 74635.5i 1.04561 + 0.339738i 0.780942 0.624603i \(-0.214739\pi\)
0.264663 + 0.964341i \(0.414739\pi\)
\(138\) 48212.6 + 29592.7i 0.215508 + 0.132278i
\(139\) −127049. 174867.i −0.557741 0.767665i 0.433296 0.901252i \(-0.357351\pi\)
−0.991037 + 0.133587i \(0.957351\pi\)
\(140\) −555860. 403856.i −2.39688 1.74143i
\(141\) 41696.0 3251.19i 0.176623 0.0137719i
\(142\) 83155.0i 0.346073i
\(143\) −145191. 77779.9i −0.593745 0.318074i
\(144\) 129985. + 66467.9i 0.522381 + 0.267120i
\(145\) −65982.8 + 21439.1i −0.260622 + 0.0846811i
\(146\) −82599.6 + 113689.i −0.320698 + 0.441402i
\(147\) 34426.5 14230.8i 0.131401 0.0543168i
\(148\) 210072. 646534.i 0.788339 2.42626i
\(149\) −143829. + 442661.i −0.530740 + 1.63345i 0.221939 + 0.975061i \(0.428761\pi\)
−0.752679 + 0.658388i \(0.771239\pi\)
\(150\) 848971. 350936.i 3.08081 1.27350i
\(151\) 35033.2 48219.1i 0.125037 0.172098i −0.741909 0.670500i \(-0.766080\pi\)
0.866946 + 0.498402i \(0.166080\pi\)
\(152\) 450366. 146333.i 1.58109 0.513728i
\(153\) −27307.4 13963.6i −0.0943087 0.0482247i
\(154\) −456312. + 62683.1i −1.55046 + 0.212985i
\(155\) 732591.i 2.44925i
\(156\) −378691. + 29527.9i −1.24587 + 0.0971452i
\(157\) 250320. + 181868.i 0.810488 + 0.588854i 0.913972 0.405777i \(-0.132999\pi\)
−0.103484 + 0.994631i \(0.532999\pi\)
\(158\) 319657. + 439971.i 1.01869 + 1.40211i
\(159\) −357637. 219516.i −1.12189 0.688611i
\(160\) 240948. + 78288.9i 0.744088 + 0.241769i
\(161\) −36879.6 + 26794.6i −0.112130 + 0.0814672i
\(162\) −1633.71 + 564427.i −0.00489089 + 1.68974i
\(163\) 106241. + 326976.i 0.313201 + 0.963932i 0.976489 + 0.215568i \(0.0691603\pi\)
−0.663288 + 0.748364i \(0.730840\pi\)
\(164\) 498455. 1.44716
\(165\) 242554. 552036.i 0.693582 1.57855i
\(166\) −477792. −1.34576
\(167\) −70695.0 217577.i −0.196154 0.603700i −0.999961 0.00881022i \(-0.997196\pi\)
0.803807 0.594890i \(-0.202804\pi\)
\(168\) −372565. + 317734.i −1.01842 + 0.868542i
\(169\) −164098. + 119224.i −0.441963 + 0.321105i
\(170\) 110594. + 35934.1i 0.293500 + 0.0953639i
\(171\) 310584. + 311484.i 0.812247 + 0.814602i
\(172\) 271984. + 374354.i 0.701006 + 0.964852i
\(173\) 606298. + 440501.i 1.54018 + 1.11900i 0.950224 + 0.311567i \(0.100854\pi\)
0.589953 + 0.807438i \(0.299146\pi\)
\(174\) 8337.65 + 106929.i 0.0208771 + 0.267746i
\(175\) 740268.i 1.82723i
\(176\) −217033. + 105019.i −0.528134 + 0.255557i
\(177\) −48064.2 + 199566.i −0.115316 + 0.478798i
\(178\) 635509. 206489.i 1.50339 0.488481i
\(179\) 133755. 184098.i 0.312016 0.429453i −0.623993 0.781430i \(-0.714491\pi\)
0.936009 + 0.351977i \(0.114491\pi\)
\(180\) −215535. 1.37370e6i −0.495834 3.16017i
\(181\) −58633.2 + 180454.i −0.133029 + 0.409422i −0.995278 0.0970625i \(-0.969055\pi\)
0.862249 + 0.506485i \(0.169055\pi\)
\(182\) 145568. 448013.i 0.325752 1.00256i
\(183\) −32591.3 78843.6i −0.0719405 0.174036i
\(184\) −58377.9 + 80350.3i −0.127117 + 0.174962i
\(185\) −1.04966e6 + 341057.i −2.25487 + 0.732651i
\(186\) −1.10105e6 265181.i −2.33358 0.562030i
\(187\) 45594.5 22062.6i 0.0953473 0.0461373i
\(188\) 159280.i 0.328675i
\(189\) −419831. 174969.i −0.854910 0.356292i
\(190\) −1.34922e6 980269.i −2.71144 1.96998i
\(191\) 240841. + 331489.i 0.477690 + 0.657484i 0.978059 0.208328i \(-0.0668023\pi\)
−0.500369 + 0.865812i \(0.666802\pi\)
\(192\) 361657. 589214.i 0.708018 1.15351i
\(193\) 336632. + 109378.i 0.650521 + 0.211367i 0.615644 0.788024i \(-0.288896\pi\)
0.0348773 + 0.999392i \(0.488896\pi\)
\(194\) −137243. + 99712.8i −0.261810 + 0.190216i
\(195\) 400162. + 469217.i 0.753616 + 0.883664i
\(196\) 43841.0 + 134929.i 0.0815155 + 0.250879i
\(197\) 591565. 1.08602 0.543009 0.839727i \(-0.317285\pi\)
0.543009 + 0.839727i \(0.317285\pi\)
\(198\) −741882. 564369.i −1.34484 1.02306i
\(199\) 240641. 0.430762 0.215381 0.976530i \(-0.430901\pi\)
0.215381 + 0.976530i \(0.430901\pi\)
\(200\) 498393. + 1.53390e6i 0.881043 + 2.71157i
\(201\) 482881. + 566210.i 0.843043 + 0.988525i
\(202\) −397545. + 288834.i −0.685501 + 0.498046i
\(203\) −82197.7 26707.7i −0.139997 0.0454879i
\(204\) 61103.8 99550.6i 0.102800 0.167482i
\(205\) −475668. 654701.i −0.790531 1.08807i
\(206\) −1.16314e6 845073.i −1.90970 1.38748i
\(207\) −91098.9 14563.8i −0.147770 0.0236238i
\(208\) 246588.i 0.395197i
\(209\) −719679. + 98861.7i −1.13965 + 0.156553i
\(210\) 1.67653e6 + 403782.i 2.62339 + 0.631828i
\(211\) 142739. 46378.8i 0.220718 0.0717155i −0.196571 0.980490i \(-0.562980\pi\)
0.417288 + 0.908774i \(0.362980\pi\)
\(212\) 939373. 1.29294e6i 1.43548 1.97577i
\(213\) 51805.3 + 125325.i 0.0782393 + 0.189274i
\(214\) −418116. + 1.28683e6i −0.624112 + 1.92082i
\(215\) 232148. 714479.i 0.342507 1.05413i
\(216\) −987725. 79893.5i −1.44046 0.116514i
\(217\) 536426. 738327.i 0.773322 1.06439i
\(218\) 190114. 61771.9i 0.270940 0.0880339i
\(219\) 53660.8 222803.i 0.0756043 0.313914i
\(220\) 2.02424e6 + 1.08440e6i 2.81971 + 1.51054i
\(221\) 51803.4i 0.0713474i
\(222\) 132637. + 1.70105e6i 0.180626 + 2.31651i
\(223\) −285255. 207250.i −0.384124 0.279082i 0.378920 0.925430i \(-0.376296\pi\)
−0.763043 + 0.646347i \(0.776296\pi\)
\(224\) 185509. + 255332.i 0.247028 + 0.340005i
\(225\) −1.06088e6 + 1.05781e6i −1.39704 + 1.39300i
\(226\) −843740. 274148.i −1.09885 0.357037i
\(227\) −480558. + 349146.i −0.618987 + 0.449720i −0.852568 0.522617i \(-0.824956\pi\)
0.233581 + 0.972337i \(0.424956\pi\)
\(228\) −1.27464e6 + 1.08705e6i −1.62387 + 1.38488i
\(229\) −8267.06 25443.4i −0.0104175 0.0320617i 0.945713 0.325004i \(-0.105366\pi\)
−0.956130 + 0.292942i \(0.905366\pi\)
\(230\) 349782. 0.435991
\(231\) 648670. 378752.i 0.799823 0.467009i
\(232\) −188302. −0.229686
\(233\) −41684.4 128291.i −0.0503019 0.154813i 0.922750 0.385398i \(-0.125936\pi\)
−0.973052 + 0.230585i \(0.925936\pi\)
\(234\) 850059. 431578.i 1.01487 0.515252i
\(235\) 209208. 151998.i 0.247120 0.179543i
\(236\) −743509. 241581.i −0.868973 0.282347i
\(237\) −755866. 463948.i −0.874126 0.536536i
\(238\) 85147.5 + 117196.i 0.0974383 + 0.134112i
\(239\) 1.36402e6 + 991016.i 1.54463 + 1.12224i 0.947346 + 0.320213i \(0.103754\pi\)
0.597287 + 0.802028i \(0.296246\pi\)
\(240\) 899968. 70173.8i 1.00855 0.0786406i
\(241\) 1.31312e6i 1.45633i −0.685400 0.728167i \(-0.740373\pi\)
0.685400 0.728167i \(-0.259627\pi\)
\(242\) 1.48241e6 415108.i 1.62716 0.455641i
\(243\) −349174. 851684.i −0.379338 0.925258i
\(244\) 309014. 100405.i 0.332279 0.107964i
\(245\) 135387. 186344.i 0.144099 0.198335i
\(246\) −1.15616e6 + 477918.i −1.21809 + 0.503519i
\(247\) 229585. 706590.i 0.239443 0.736928i
\(248\) 614433. 1.89103e6i 0.634374 1.95240i
\(249\) 720096. 297663.i 0.736024 0.304247i
\(250\) 1.64638e6 2.26605e6i 1.66602 2.29308i
\(251\) −66780.3 + 21698.2i −0.0669058 + 0.0217390i −0.342279 0.939598i \(-0.611199\pi\)
0.275373 + 0.961338i \(0.411199\pi\)
\(252\) 788642. 1.54227e6i 0.782309 1.52989i
\(253\) 109927. 105496.i 0.107970 0.103618i
\(254\) 3.35483e6i 3.26277i
\(255\) −189066. + 14742.2i −0.182080 + 0.0141975i
\(256\) 1.47969e6 + 1.07506e6i 1.41115 + 1.02526i
\(257\) −336991. 463828.i −0.318262 0.438051i 0.619673 0.784860i \(-0.287265\pi\)
−0.937936 + 0.346809i \(0.887265\pi\)
\(258\) −989793. 607532.i −0.925753 0.568224i
\(259\) −1.30761e6 424870.i −1.21124 0.393556i
\(260\) −1.90006e6 + 1.38048e6i −1.74315 + 1.26647i
\(261\) −79182.5 155962.i −0.0719495 0.141715i
\(262\) 34829.5 + 107194.i 0.0313468 + 0.0964756i
\(263\) −1.06257e6 −0.947259 −0.473629 0.880724i \(-0.657056\pi\)
−0.473629 + 0.880724i \(0.657056\pi\)
\(264\) 1.08910e6 1.22153e6i 0.961740 1.07869i
\(265\) −2.59465e6 −2.26967
\(266\) −642005. 1.97589e6i −0.556332 1.71221i
\(267\) −829153. + 707127.i −0.711798 + 0.607042i
\(268\) −2.29283e6 + 1.66584e6i −1.95000 + 1.41676i
\(269\) −254015. 82534.4i −0.214032 0.0695432i 0.200039 0.979788i \(-0.435893\pi\)
−0.414070 + 0.910245i \(0.635893\pi\)
\(270\) 1.81703e6 + 2.97962e6i 1.51689 + 2.48744i
\(271\) 418731. + 576334.i 0.346348 + 0.476707i 0.946282 0.323343i \(-0.104807\pi\)
−0.599934 + 0.800049i \(0.704807\pi\)
\(272\) 61347.8 + 44571.8i 0.0502779 + 0.0365290i
\(273\) 59720.2 + 765902.i 0.0484970 + 0.621966i
\(274\) 2.30866e6i 1.85774i
\(275\) −336712. 2.45115e6i −0.268489 1.95451i
\(276\) 82268.9 341586.i 0.0650075 0.269915i
\(277\) 694976. 225811.i 0.544215 0.176826i −0.0239917 0.999712i \(-0.507638\pi\)
0.568206 + 0.822886i \(0.307638\pi\)
\(278\) −1.21442e6 + 1.67150e6i −0.942443 + 1.29716i
\(279\) 1.82463e6 286287.i 1.40334 0.220186i
\(280\) −935577. + 2.87941e6i −0.713156 + 2.19487i
\(281\) −402333. + 1.23825e6i −0.303962 + 0.935500i 0.676100 + 0.736810i \(0.263669\pi\)
−0.980062 + 0.198690i \(0.936331\pi\)
\(282\) −152717. 369448.i −0.114358 0.276650i
\(283\) −1.17802e6 + 1.62140e6i −0.874350 + 1.20344i 0.103604 + 0.994619i \(0.466963\pi\)
−0.977954 + 0.208821i \(0.933037\pi\)
\(284\) −491191. + 159598.i −0.361372 + 0.117417i
\(285\) 2.64416e6 + 636831.i 1.92831 + 0.464421i
\(286\) −278220. + 1.54965e6i −0.201129 + 1.12026i
\(287\) 1.00813e6i 0.722453i
\(288\) −100831. + 630712.i −0.0716329 + 0.448074i
\(289\) 1.13580e6 + 825207.i 0.799940 + 0.581190i
\(290\) 389799. + 536512.i 0.272173 + 0.374614i
\(291\) 144722. 235782.i 0.100185 0.163222i
\(292\) 830083. + 269710.i 0.569724 + 0.185115i
\(293\) 1.71267e6 1.24433e6i 1.16548 0.846772i 0.175021 0.984565i \(-0.444001\pi\)
0.990461 + 0.137793i \(0.0440007\pi\)
\(294\) −231058. 270931.i −0.155902 0.182806i
\(295\) 392213. + 1.20711e6i 0.262402 + 0.807589i
\(296\) −2.99554e6 −1.98722
\(297\) 1.46971e6 + 388388.i 0.966812 + 0.255491i
\(298\) 4.44900e6 2.90216
\(299\) 48152.0 + 148197.i 0.0311484 + 0.0958650i
\(300\) −3.70237e6 4.34128e6i −2.37507 2.78493i
\(301\) 757130. 550087.i 0.481675 0.349957i
\(302\) −541833. 176052.i −0.341860 0.111077i
\(303\) 419211. 682980.i 0.262317 0.427367i
\(304\) −639238. 879836.i −0.396715 0.546032i
\(305\) −426764. 310063.i −0.262687 0.190853i
\(306\) −46280.7 + 289493.i −0.0282551 + 0.176740i
\(307\) 2.28943e6i 1.38637i −0.720757 0.693187i \(-0.756206\pi\)
0.720757 0.693187i \(-0.243794\pi\)
\(308\) 1.24606e6 + 2.57510e6i 0.748446 + 1.54674i
\(309\) 2.27949e6 + 549002.i 1.35813 + 0.327098i
\(310\) −6.65987e6 + 2.16392e6i −3.93606 + 1.27890i
\(311\) −1.42811e6 + 1.96563e6i −0.837263 + 1.15239i 0.149264 + 0.988797i \(0.452310\pi\)
−0.986527 + 0.163597i \(0.947690\pi\)
\(312\) 639397. + 1.54681e6i 0.371864 + 0.899600i
\(313\) −264631. + 814449.i −0.152679 + 0.469897i −0.997918 0.0644904i \(-0.979458\pi\)
0.845239 + 0.534388i \(0.179458\pi\)
\(314\) 913940. 2.81282e6i 0.523111 1.60997i
\(315\) −2.77830e6 + 435919.i −1.57762 + 0.247531i
\(316\) 1.98537e6 2.73262e6i 1.11847 1.53944i
\(317\) −2.59415e6 + 842889.i −1.44993 + 0.471110i −0.924977 0.380023i \(-0.875916\pi\)
−0.524950 + 0.851133i \(0.675916\pi\)
\(318\) −939201. + 3.89962e6i −0.520824 + 2.16249i
\(319\) 284318. + 51045.6i 0.156433 + 0.0280855i
\(320\) 4.27473e6i 2.33364i
\(321\) −171535. 2.19991e6i −0.0929158 1.19163i
\(322\) 352520. + 256121.i 0.189472 + 0.137659i
\(323\) 134292. + 184837.i 0.0716215 + 0.0985785i
\(324\) 3.33717e6 1.07364e6i 1.76610 0.568196i
\(325\) 2.40657e6 + 781941.i 1.26383 + 0.410644i
\(326\) 2.65867e6 1.93164e6i 1.38554 1.00666i
\(327\) −248044. + 211539.i −0.128280 + 0.109401i
\(328\) −678731. 2.08892e6i −0.348348 1.07210i
\(329\) 322143. 0.164081
\(330\) −5.73492e6 574417.i −2.89896 0.290364i
\(331\) −406510. −0.203939 −0.101970 0.994788i \(-0.532514\pi\)
−0.101970 + 0.994788i \(0.532514\pi\)
\(332\) 917018. + 2.82229e6i 0.456597 + 1.40526i
\(333\) −1.25965e6 2.48107e6i −0.622499 1.22611i
\(334\) −1.76914e6 + 1.28535e6i −0.867751 + 0.630458i
\(335\) 4.37602e6 + 1.42186e6i 2.13043 + 0.692219i
\(336\) 958397. + 588261.i 0.463124 + 0.284264i
\(337\) −782650. 1.07723e6i −0.375399 0.516692i 0.578959 0.815356i \(-0.303459\pi\)
−0.954358 + 0.298664i \(0.903459\pi\)
\(338\) 1.56856e6 + 1.13962e6i 0.746807 + 0.542587i
\(339\) 1.44242e6 112471.i 0.681699 0.0531545i
\(340\) 722238.i 0.338831i
\(341\) −1.44036e6 + 2.68871e6i −0.670790 + 1.25216i
\(342\) 1.91425e6 3.74352e6i 0.884980 1.73067i
\(343\) 2.19217e6 712280.i 1.00610 0.326901i
\(344\) 1.19848e6 1.64957e6i 0.546055 0.751580i
\(345\) −527167. + 217913.i −0.238452 + 0.0985678i
\(346\) 2.21365e6 6.81290e6i 0.994072 3.05944i
\(347\) −869217. + 2.67517e6i −0.387529 + 1.19269i 0.547100 + 0.837067i \(0.315732\pi\)
−0.934629 + 0.355625i \(0.884268\pi\)
\(348\) 615621. 254477.i 0.272499 0.112642i
\(349\) −2.53030e6 + 3.48266e6i −1.11201 + 1.53055i −0.293586 + 0.955933i \(0.594849\pi\)
−0.818423 + 0.574617i \(0.805151\pi\)
\(350\) 6.72965e6 2.18660e6i 2.93645 0.954110i
\(351\) −1.01228e6 + 1.18003e6i −0.438563 + 0.511240i
\(352\) −730389. 761065.i −0.314194 0.327390i
\(353\) 1.52326e6i 0.650633i 0.945605 + 0.325316i \(0.105471\pi\)
−0.945605 + 0.325316i \(0.894529\pi\)
\(354\) 1.95619e6 152531.i 0.829665 0.0646920i
\(355\) 678361. + 492858.i 0.285687 + 0.207564i
\(356\) −2.43944e6 3.35760e6i −1.02015 1.40412i
\(357\) −201341. 123582.i −0.0836107 0.0513199i
\(358\) −2.06868e6 672156.i −0.853074 0.277181i
\(359\) 1.31009e6 951835.i 0.536494 0.389786i −0.286287 0.958144i \(-0.592421\pi\)
0.822781 + 0.568358i \(0.192421\pi\)
\(360\) −5.46339e6 + 2.77378e6i −2.22181 + 1.12802i
\(361\) −247392. 761393.i −0.0999119 0.307497i
\(362\) 1.81367e6 0.727424
\(363\) −1.97558e6 + 1.54916e6i −0.786914 + 0.617063i
\(364\) −2.92577e6 −1.15741
\(365\) −437881. 1.34766e6i −0.172038 0.529479i
\(366\) −620487. + 529170.i −0.242119 + 0.206487i
\(367\) 918272. 667163.i 0.355882 0.258563i −0.395450 0.918487i \(-0.629412\pi\)
0.751332 + 0.659924i \(0.229412\pi\)
\(368\) 216931. + 70485.0i 0.0835029 + 0.0271317i
\(369\) 1.44475e6 1.44057e6i 0.552364 0.550768i
\(370\) 6.20098e6 + 8.53491e6i 2.35481 + 3.24112i
\(371\) −2.61496e6 1.89988e6i −0.986349 0.716624i
\(372\) 546812. + 7.01277e6i 0.204871 + 2.62744i
\(373\) 1.21196e6i 0.451041i 0.974238 + 0.225520i \(0.0724082\pi\)
−0.974238 + 0.225520i \(0.927592\pi\)
\(374\) −335244. 349324.i −0.123932 0.129137i
\(375\) −1.06957e6 + 4.44092e6i −0.392764 + 1.63078i
\(376\) 667508. 216887.i 0.243493 0.0791158i
\(377\) −173650. + 239009.i −0.0629248 + 0.0866085i
\(378\) −350516. + 4.33344e6i −0.126176 + 1.55992i
\(379\) −999226. + 3.07530e6i −0.357327 + 1.09974i 0.597321 + 0.802002i \(0.296232\pi\)
−0.954648 + 0.297737i \(0.903768\pi\)
\(380\) −3.20085e6 + 9.85120e6i −1.13712 + 3.49969i
\(381\) −2.09005e6 5.05617e6i −0.737640 1.78447i
\(382\) 2.30212e6 3.16859e6i 0.807177 1.11098i
\(383\) 309499. 100562.i 0.107811 0.0350299i −0.254615 0.967043i \(-0.581949\pi\)
0.362426 + 0.932013i \(0.381949\pi\)
\(384\) −5.14998e6 1.24034e6i −1.78229 0.429254i
\(385\) 2.19320e6 4.09402e6i 0.754094 1.40766i
\(386\) 3.38334e6i 1.15579i
\(387\) 1.87024e6 + 298992.i 0.634775 + 0.101480i
\(388\) 852405. + 619309.i 0.287453 + 0.208847i
\(389\) −2.67594e6 3.68311e6i −0.896606 1.23407i −0.971538 0.236884i \(-0.923874\pi\)
0.0749317 0.997189i \(-0.476126\pi\)
\(390\) 3.08358e6 5.02378e6i 1.02658 1.67251i
\(391\) −45573.0 14807.6i −0.0150753 0.00489826i
\(392\) 505761. 367457.i 0.166238 0.120779i
\(393\) −119274. 139857.i −0.0389552 0.0456775i
\(394\) −1.74736e6 5.37782e6i −0.567076 1.74528i
\(395\) −5.48380e6 −1.76843
\(396\) −1.90981e6 + 5.46544e6i −0.612003 + 1.75141i
\(397\) −715291. −0.227775 −0.113888 0.993494i \(-0.536330\pi\)
−0.113888 + 0.993494i \(0.536330\pi\)
\(398\) −710804. 2.18763e6i −0.224927 0.692255i
\(399\) 2.19856e6 + 2.57796e6i 0.691362 + 0.810668i
\(400\) 2.99662e6 2.17717e6i 0.936445 0.680367i
\(401\) 2.04260e6 + 663680.i 0.634340 + 0.206109i 0.608496 0.793557i \(-0.291773\pi\)
0.0258431 + 0.999666i \(0.491773\pi\)
\(402\) 3.72099e6 6.06226e6i 1.14840 1.87098i
\(403\) −1.83363e6 2.52378e6i −0.562406 0.774085i
\(404\) 2.46912e6 + 1.79392e6i 0.752644 + 0.546828i
\(405\) −4.59480e6 3.35868e6i −1.39197 1.01749i
\(406\) 826135.i 0.248734i
\(407\) 4.52298e6 + 812042.i 1.35344 + 0.242992i
\(408\) −500399. 120518.i −0.148822 0.0358428i
\(409\) −5.06194e6 + 1.64472e6i −1.49627 + 0.486166i −0.938926 0.344119i \(-0.888178\pi\)
−0.557339 + 0.830285i \(0.688178\pi\)
\(410\) −4.54675e6 + 6.25807e6i −1.33580 + 1.83857i
\(411\) 1.43829e6 + 3.47946e6i 0.419993 + 1.01603i
\(412\) −2.75940e6 + 8.49255e6i −0.800887 + 2.46488i
\(413\) −488597. + 1.50375e6i −0.140953 + 0.433810i
\(414\) 136690. + 871184.i 0.0391954 + 0.249809i
\(415\) 2.83187e6 3.89773e6i 0.807147 1.11094i
\(416\) 1.02602e6 333374.i 0.290685 0.0944493i
\(417\) 788944. 3.27575e6i 0.222181 0.922508i
\(418\) 3.02452e6 + 6.25047e6i 0.846672 + 1.74973i
\(419\) 1.71145e6i 0.476244i −0.971235 0.238122i \(-0.923468\pi\)
0.971235 0.238122i \(-0.0765318\pi\)
\(420\) −832612. 1.06781e7i −0.230314 2.95374i
\(421\) 2.44833e6 + 1.77881e6i 0.673231 + 0.489131i 0.871105 0.491097i \(-0.163404\pi\)
−0.197874 + 0.980227i \(0.563404\pi\)
\(422\) −843244. 1.16063e6i −0.230501 0.317257i
\(423\) 460330. + 461664.i 0.125089 + 0.125451i
\(424\) −6.69754e6 2.17616e6i −1.80926 0.587863i
\(425\) −629533. + 457383.i −0.169062 + 0.122831i
\(426\) 986291. 841139.i 0.263318 0.224566i
\(427\) −203068. 624980.i −0.0538980 0.165881i
\(428\) 8.40370e6 2.21749
\(429\) −546115. 2.50886e6i −0.143265 0.658163i
\(430\) −7.18093e6 −1.87288
\(431\) 511802. + 1.57517e6i 0.132712 + 0.408444i 0.995227 0.0975864i \(-0.0311122\pi\)
−0.862515 + 0.506031i \(0.831112\pi\)
\(432\) 526473. + 2.21408e6i 0.135727 + 0.570800i
\(433\) 1.68879e6 1.22698e6i 0.432868 0.314497i −0.349927 0.936777i \(-0.613794\pi\)
0.782795 + 0.622280i \(0.213794\pi\)
\(434\) −8.29650e6 2.69570e6i −2.11432 0.686984i
\(435\) −921723. 565750.i −0.233549 0.143351i
\(436\) −729766. 1.00444e6i −0.183852 0.253050i
\(437\) 555983. + 403945.i 0.139270 + 0.101186i
\(438\) −2.18397e6 + 170292.i −0.543952 + 0.0424139i
\(439\) 5.32419e6i 1.31854i 0.751908 + 0.659268i \(0.229134\pi\)
−0.751908 + 0.659268i \(0.770866\pi\)
\(440\) 1.78814e6 9.95974e6i 0.440322 2.45254i
\(441\) 517024. + 264380.i 0.126594 + 0.0647340i
\(442\) 470937. 153017.i 0.114659 0.0372548i
\(443\) 2.31158e6 3.18162e6i 0.559629 0.770263i −0.431650 0.902041i \(-0.642069\pi\)
0.991279 + 0.131778i \(0.0420685\pi\)
\(444\) 9.79340e6 4.04826e6i 2.35763 0.974566i
\(445\) −2.08215e6 + 6.40821e6i −0.498440 + 1.53404i
\(446\) −1.04149e6 + 3.20538e6i −0.247924 + 0.763031i
\(447\) −6.70522e6 + 2.77171e6i −1.58725 + 0.656114i
\(448\) 3.13009e6 4.30820e6i 0.736821 1.01415i
\(449\) 5.15921e6 1.67633e6i 1.20772 0.392413i 0.365126 0.930958i \(-0.381026\pi\)
0.842596 + 0.538546i \(0.181026\pi\)
\(450\) 1.27500e7 + 6.51972e6i 2.96811 + 1.51774i
\(451\) 458547. + 3.33807e6i 0.106156 + 0.772776i
\(452\) 5.51009e6i 1.26856i
\(453\) 926293. 72226.5i 0.212082 0.0165368i
\(454\) 4.59350e6 + 3.33737e6i 1.04593 + 0.759915i
\(455\) 2.79201e6 + 3.84288e6i 0.632250 + 0.870218i
\(456\) 6.29123e6 + 3.86154e6i 1.41685 + 0.869657i
\(457\) −2.15486e6 700158.i −0.482647 0.156821i 0.0575800 0.998341i \(-0.481662\pi\)
−0.540227 + 0.841519i \(0.681662\pi\)
\(458\) −206882. + 150309.i −0.0460850 + 0.0334827i
\(459\) −110602. 465136.i −0.0245037 0.103050i
\(460\) −671329. 2.06614e6i −0.147925 0.455266i
\(461\) −94509.9 −0.0207121 −0.0103561 0.999946i \(-0.503296\pi\)
−0.0103561 + 0.999946i \(0.503296\pi\)
\(462\) −5.35921e6 4.77820e6i −1.16814 1.04150i
\(463\) −4.10098e6 −0.889068 −0.444534 0.895762i \(-0.646631\pi\)
−0.444534 + 0.895762i \(0.646631\pi\)
\(464\) 133635. + 411287.i 0.0288155 + 0.0886851i
\(465\) 8.68918e6 7.41039e6i 1.86357 1.58931i
\(466\) −1.04315e6 + 757892.i −0.222526 + 0.161675i
\(467\) −2.01586e6 654993.i −0.427729 0.138977i 0.0872384 0.996187i \(-0.472196\pi\)
−0.514967 + 0.857210i \(0.672196\pi\)
\(468\) −4.18081e6 4.19292e6i −0.882359 0.884917i
\(469\) 3.36916e6 + 4.63725e6i 0.707276 + 0.973483i
\(470\) −1.99975e6 1.45290e6i −0.417571 0.303383i
\(471\) 374949. + 4.80867e6i 0.0778790 + 0.998786i
\(472\) 3.44484e6i 0.711729i
\(473\) −2.25677e6 + 2.16581e6i −0.463804 + 0.445110i
\(474\) −1.98500e6 + 8.24186e6i −0.405803 + 1.68492i
\(475\) 1.06138e7 3.44863e6i 2.15842 0.701313i
\(476\) 528845. 727892.i 0.106982 0.147248i
\(477\) −1.01395e6 6.46236e6i −0.204043 1.30045i
\(478\) 4.98014e6 1.53273e7i 0.996947 3.06829i
\(479\) 1.03361e6 3.18114e6i 0.205835 0.633496i −0.793843 0.608123i \(-0.791923\pi\)
0.999678 0.0253729i \(-0.00807731\pi\)
\(480\) 1.50869e6 + 3.64978e6i 0.298881 + 0.723041i
\(481\) −2.76245e6 + 3.80219e6i −0.544418 + 0.749327i
\(482\) −1.19373e7 + 3.87867e6i −2.34040 + 0.760441i
\(483\) −690857. 166389.i −0.134747 0.0324531i
\(484\) −5.29718e6 7.95980e6i −1.02785 1.54450i
\(485\) 1.71060e6i 0.330212i
\(486\) −6.71113e6 + 5.68998e6i −1.28886 + 1.09275i
\(487\) −5.61963e6 4.08290e6i −1.07371 0.780094i −0.0971319 0.995272i \(-0.530967\pi\)
−0.976575 + 0.215178i \(0.930967\pi\)
\(488\) −841550. 1.15829e6i −0.159967 0.220176i
\(489\) −2.80356e6 + 4.56757e6i −0.530197 + 0.863800i
\(490\) −2.09392e6 680357.i −0.393977 0.128011i
\(491\) 2.47432e6 1.79770e6i 0.463182 0.336522i −0.331596 0.943421i \(-0.607587\pi\)
0.794778 + 0.606900i \(0.207587\pi\)
\(492\) 5.04203e6 + 5.91212e6i 0.939059 + 1.10111i
\(493\) −28074.2 86403.7i −0.00520225 0.0160109i
\(494\) −7.10164e6 −1.30931
\(495\) 9.00113e6 2.70711e6i 1.65114 0.496585i
\(496\) −4.56643e6 −0.833437
\(497\) 322786. + 993434.i 0.0586171 + 0.180405i
\(498\) −4.83302e6 5.66704e6i −0.873263 1.02396i
\(499\) 3.48962e6 2.53536e6i 0.627374 0.455814i −0.228115 0.973634i \(-0.573256\pi\)
0.855490 + 0.517820i \(0.173256\pi\)
\(500\) −1.65453e7 5.37589e6i −2.95971 0.961668i
\(501\) 1.86555e6 3.03936e6i 0.332057 0.540989i
\(502\) 394510. + 542997.i 0.0698713 + 0.0961696i
\(503\) −1.10376e6 801926.i −0.194515 0.141324i 0.486265 0.873811i \(-0.338359\pi\)
−0.680780 + 0.732488i \(0.738359\pi\)
\(504\) −7.53722e6 1.20496e6i −1.32171 0.211299i
\(505\) 4.95500e6i 0.864601i
\(506\) −1.28375e6 687713.i −0.222897 0.119407i
\(507\) −3.07400e6 740355.i −0.531110 0.127915i
\(508\) 1.98168e7 6.43887e6i 3.40702 1.10701i
\(509\) 1.04578e6 1.43939e6i 0.178915 0.246255i −0.710135 0.704066i \(-0.751366\pi\)
0.889050 + 0.457810i \(0.151366\pi\)
\(510\) 692480. + 1.67522e6i 0.117891 + 0.285198i
\(511\) 545489. 1.67884e6i 0.0924131 0.284418i
\(512\) 2.04218e6 6.28518e6i 0.344286 1.05960i
\(513\) −552822. + 6.83455e6i −0.0927453 + 1.14661i
\(514\) −3.22118e6 + 4.43358e6i −0.537784 + 0.740196i
\(515\) 1.37879e7 4.47995e6i 2.29076 0.744312i
\(516\) −1.68896e6 + 7.01267e6i −0.279251 + 1.15947i
\(517\) −1.06667e6 + 146527.i −0.175511 + 0.0241097i
\(518\) 1.31423e7i 2.15202i
\(519\) 908161. + 1.16470e7i 0.147994 + 1.89800i
\(520\) 8.37255e6 + 6.08301e6i 1.35784 + 0.986530i
\(521\) −6.11192e6 8.41233e6i −0.986468 1.35776i −0.933271 0.359173i \(-0.883059\pi\)
−0.0531969 0.998584i \(-0.516941\pi\)
\(522\) −1.18394e6 + 1.18051e6i −0.190174 + 0.189625i
\(523\) −3.16332e6 1.02782e6i −0.505695 0.164310i 0.0450486 0.998985i \(-0.485656\pi\)
−0.550743 + 0.834675i \(0.685656\pi\)
\(524\) 566341. 411471.i 0.0901052 0.0654653i
\(525\) −8.78023e6 + 7.48804e6i −1.39030 + 1.18569i
\(526\) 3.13861e6 + 9.65966e6i 0.494622 + 1.52229i
\(527\) 959320. 0.150465
\(528\) −3.44098e6 1.51190e6i −0.537152 0.236014i
\(529\) 6.29221e6 0.977606
\(530\) 7.66405e6 + 2.35875e7i 1.18514 + 3.64748i
\(531\) −2.85321e6 + 1.44858e6i −0.439134 + 0.222950i
\(532\) −1.04393e7 + 7.58457e6i −1.59916 + 1.16185i
\(533\) −3.27736e6 1.06488e6i −0.499696 0.162361i
\(534\) 8.87752e6 + 5.44899e6i 1.34722 + 0.826919i
\(535\) −8.01952e6 1.10379e7i −1.21133 1.66726i
\(536\) 1.01033e7 + 7.34044e6i 1.51897 + 1.10360i
\(537\) 3.53653e6 275756.i 0.529227 0.0412657i
\(538\) 2.55300e6i 0.380272i
\(539\) −863263. + 417721.i −0.127989 + 0.0619319i
\(540\) 1.41131e7 1.64518e7i 2.08275 2.42789i
\(541\) −2.05521e6 + 667778.i −0.301900 + 0.0980932i −0.456050 0.889954i \(-0.650736\pi\)
0.154150 + 0.988047i \(0.450736\pi\)
\(542\) 4.00252e6 5.50899e6i 0.585241 0.805515i
\(543\) −2.73344e6 + 1.12991e6i −0.397842 + 0.164454i
\(544\) −102518. + 315519.i −0.0148527 + 0.0457118i
\(545\) −622882. + 1.91704e6i −0.0898286 + 0.276464i
\(546\) 6.78629e6 2.80522e6i 0.974206 0.402704i
\(547\) −1.35637e6 + 1.86689e6i −0.193826 + 0.266778i −0.894858 0.446352i \(-0.852723\pi\)
0.701032 + 0.713130i \(0.252723\pi\)
\(548\) −1.36371e7 + 4.43097e6i −1.93986 + 0.630300i
\(549\) 605484. 1.18409e6i 0.0857377 0.167669i
\(550\) −2.12884e7 + 1.03012e7i −3.00079 + 1.45204i
\(551\) 1.30295e6i 0.182831i
\(552\) −1.54354e6 + 120355.i −0.215610 + 0.0168119i
\(553\) −5.52673e6 4.01540e6i −0.768520 0.558363i
\(554\) −4.10563e6 5.65091e6i −0.568336 0.782247i
\(555\) −1.46629e7 9.00005e6i −2.02063 1.24026i
\(556\) 1.22042e7 + 3.96540e6i 1.67426 + 0.544001i
\(557\) −5.72045e6 + 4.15615e6i −0.781254 + 0.567614i −0.905355 0.424655i \(-0.860395\pi\)
0.124101 + 0.992270i \(0.460395\pi\)
\(558\) −7.99216e6 1.57418e7i −1.08662 2.14027i
\(559\) −988548. 3.04244e6i −0.133804 0.411806i
\(560\) 6.95315e6 0.936940
\(561\) 722884. + 317621.i 0.0969754 + 0.0426091i
\(562\) 1.24452e7 1.66211
\(563\) −2.97741e6 9.16354e6i −0.395884 1.21841i −0.928271 0.371905i \(-0.878705\pi\)
0.532387 0.846501i \(-0.321295\pi\)
\(564\) −1.88920e6 + 1.61117e6i −0.250081 + 0.213276i
\(565\) 7.23727e6 5.25819e6i 0.953792 0.692971i
\(566\) 1.82195e7 + 5.91988e6i 2.39054 + 0.776733i
\(567\) −2.17144e6 6.74943e6i −0.283655 0.881677i
\(568\) 1.33768e6 + 1.84116e6i 0.173973 + 0.239453i
\(569\) 9.87475e6 + 7.17443e6i 1.27863 + 0.928980i 0.999511 0.0312754i \(-0.00995691\pi\)
0.279121 + 0.960256i \(0.409957\pi\)
\(570\) −2.02098e6 2.59187e7i −0.260540 3.34138i
\(571\) 1.21484e7i 1.55930i 0.626217 + 0.779649i \(0.284603\pi\)
−0.626217 + 0.779649i \(0.715397\pi\)
\(572\) 9.68769e6 1.33079e6i 1.23803 0.170067i
\(573\) −1.49557e6 + 6.20969e6i −0.190292 + 0.790103i
\(574\) −9.16470e6 + 2.97779e6i −1.16102 + 0.377237i
\(575\) −1.37579e6 + 1.89361e6i −0.173533 + 0.238848i
\(576\) 1.06469e7 1.67051e6i 1.33711 0.209793i
\(577\) 3.43440e6 1.05700e7i 0.429448 1.32171i −0.469222 0.883080i \(-0.655465\pi\)
0.898670 0.438626i \(-0.144535\pi\)
\(578\) 4.14691e6 1.27629e7i 0.516303 1.58902i
\(579\) 2.10781e6 + 5.09914e6i 0.261298 + 0.632121i
\(580\) 2.42101e6 3.33223e6i 0.298832 0.411306i
\(581\) 5.70808e6 1.85467e6i 0.701536 0.227943i
\(582\) −2.57094e6 619195.i −0.314618 0.0757740i
\(583\) 9.52273e6 + 5.10139e6i 1.16035 + 0.621609i
\(584\) 3.84596e6i 0.466630i
\(585\) −1.51756e6 + 9.49256e6i −0.183339 + 1.14682i
\(586\) −1.63709e7 1.18941e7i −1.96937 1.43083i
\(587\) −1.84061e6 2.53338e6i −0.220478 0.303462i 0.684422 0.729086i \(-0.260055\pi\)
−0.904900 + 0.425624i \(0.860055\pi\)
\(588\) −1.15691e6 + 1.88484e6i −0.137992 + 0.224818i
\(589\) −1.30850e7 4.25156e6i −1.55412 0.504964i
\(590\) 9.81509e6 7.13108e6i 1.16082 0.843384i
\(591\) 5.98386e6 + 7.01648e6i 0.704714 + 0.826324i
\(592\) 2.12589e6 + 6.54283e6i 0.249309 + 0.767293i
\(593\) −390659. −0.0456206 −0.0228103 0.999740i \(-0.507261\pi\)
−0.0228103 + 0.999740i \(0.507261\pi\)
\(594\) −810455. 1.45081e7i −0.0942460 1.68712i
\(595\) −1.46072e6 −0.169152
\(596\) −8.53888e6 2.62800e7i −0.984657 3.03046i
\(597\) 2.43416e6 + 2.85421e6i 0.279520 + 0.327756i
\(598\) 1.20500e6 875483.i 0.137795 0.100114i
\(599\) 1.44025e7 + 4.67965e6i 1.64010 + 0.532901i 0.976561 0.215240i \(-0.0690533\pi\)
0.663540 + 0.748141i \(0.269053\pi\)
\(600\) −1.31520e7 + 2.14272e7i −1.49146 + 2.42990i
\(601\) −3.74592e6 5.15581e6i −0.423031 0.582252i 0.543305 0.839535i \(-0.317173\pi\)
−0.966336 + 0.257283i \(0.917173\pi\)
\(602\) −7.23715e6 5.25810e6i −0.813910 0.591340i
\(603\) −1.83126e6 + 1.14548e7i −0.205095 + 1.28290i
\(604\) 3.53847e6i 0.394660i
\(605\) −5.39985e6 + 1.45535e7i −0.599782 + 1.61652i
\(606\) −7.44712e6 1.79359e6i −0.823771 0.198400i
\(607\) 1.40402e6 456194.i 0.154668 0.0502548i −0.230659 0.973035i \(-0.574088\pi\)
0.385328 + 0.922780i \(0.374088\pi\)
\(608\) 2.79667e6 3.84928e6i 0.306819 0.422300i
\(609\) −514680. 1.24509e6i −0.0562333 0.136038i
\(610\) −1.55815e6 + 4.79550e6i −0.169545 + 0.521807i
\(611\) 340278. 1.04727e6i 0.0368749 0.113489i
\(612\) 1.79884e6 282240.i 0.194140 0.0304608i
\(613\) 8.15850e6 1.12292e7i 0.876918 1.20697i −0.100346 0.994953i \(-0.531995\pi\)
0.977265 0.212022i \(-0.0680049\pi\)
\(614\) −2.08128e7 + 6.76249e6i −2.22797 + 0.723911i
\(615\) 2.95380e6 1.22643e7i 0.314914 1.30754i
\(616\) 9.09497e6 8.72839e6i 0.965717 0.926792i
\(617\) 2.43985e6i 0.258018i 0.991643 + 0.129009i \(0.0411796\pi\)
−0.991643 + 0.129009i \(0.958820\pi\)
\(618\) −1.74225e6 2.23441e7i −0.183501 2.35338i
\(619\) 9.38770e6 + 6.82056e6i 0.984765 + 0.715474i 0.958768 0.284188i \(-0.0917241\pi\)
0.0259964 + 0.999662i \(0.491724\pi\)
\(620\) 2.55643e7 + 3.51862e7i 2.67088 + 3.67615i
\(621\) −748754. 1.22783e6i −0.0779131 0.127764i
\(622\) 2.20876e7 + 7.17669e6i 2.28914 + 0.743786i
\(623\) −6.79074e6 + 4.93376e6i −0.700966 + 0.509282i
\(624\) 2.92475e6 2.49432e6i 0.300696 0.256442i
\(625\) 2.77429e6 + 8.53838e6i 0.284087 + 0.874331i
\(626\) 8.18568e6 0.834871
\(627\) −8.45237e6 7.53601e6i −0.858637 0.765548i
\(628\) −1.83693e7 −1.85863
\(629\) −446610. 1.37452e6i −0.0450092 0.138524i
\(630\) 1.21694e7 + 2.39695e7i 1.22157 + 2.40606i
\(631\) −1.03709e7 + 7.53488e6i −1.03691 + 0.753360i −0.969680 0.244377i \(-0.921417\pi\)
−0.0672314 + 0.997737i \(0.521417\pi\)
\(632\) −1.41553e7 4.59932e6i −1.40970 0.458038i
\(633\) 1.99395e6 + 1.22388e6i 0.197790 + 0.121403i
\(634\) 1.53251e7 + 2.10932e7i 1.51419 + 2.08411i
\(635\) −2.73680e7 1.98840e7i −2.69345 1.95691i
\(636\) 2.48374e7 1.93666e6i 2.43480 0.189850i
\(637\) 980820.i 0.0957724i
\(638\) −375769. 2.73547e6i −0.0365484 0.266060i
\(639\) −962443. + 1.88216e6i −0.0932445 + 0.182350i
\(640\) −3.11505e7 + 1.01214e7i −3.00618 + 0.976769i
\(641\) −1.11350e7 + 1.53260e7i −1.07040 + 1.47328i −0.200728 + 0.979647i \(0.564331\pi\)
−0.869671 + 0.493631i \(0.835669\pi\)
\(642\) −1.94923e7 + 8.05746e6i −1.86649 + 0.771543i
\(643\) −4.60668e6 + 1.41779e7i −0.439401 + 1.35234i 0.449108 + 0.893477i \(0.351742\pi\)
−0.888509 + 0.458859i \(0.848258\pi\)
\(644\) 836305. 2.57388e6i 0.0794603 0.244554i
\(645\) 1.08226e7 4.47370e6i 1.02431 0.423416i
\(646\) 1.28365e6 1.76679e6i 0.121022 0.166573i
\(647\) 1.11214e7 3.61357e6i 1.04448 0.339371i 0.263979 0.964528i \(-0.414965\pi\)
0.780499 + 0.625157i \(0.214965\pi\)
\(648\) −9.04354e6 1.25234e7i −0.846060 1.17162i
\(649\) 933842. 5.20139e6i 0.0870286 0.484739i
\(650\) 2.41874e7i 2.24546i
\(651\) 1.41833e7 1.10593e6i 1.31167 0.102276i
\(652\) −1.65128e7 1.19972e7i −1.52125 1.10525i
\(653\) 8.21505e6 + 1.13071e7i 0.753924 + 1.03769i 0.997695 + 0.0678544i \(0.0216153\pi\)
−0.243771 + 0.969833i \(0.578385\pi\)
\(654\) 2.65574e6 + 1.63008e6i 0.242795 + 0.149027i
\(655\) −1.08090e6 351206.i −0.0984425 0.0319859i
\(656\) −4.08092e6 + 2.96496e6i −0.370253 + 0.269004i
\(657\) 3.18543e6 1.61726e6i 0.287909 0.146172i
\(658\) −951545. 2.92855e6i −0.0856770 0.263687i
\(659\) 3.88498e6 0.348478 0.174239 0.984703i \(-0.444253\pi\)
0.174239 + 0.984703i \(0.444253\pi\)
\(660\) 7.61387e6 + 3.49783e7i 0.680371 + 3.12564i
\(661\) −8.87493e6 −0.790062 −0.395031 0.918668i \(-0.629266\pi\)
−0.395031 + 0.918668i \(0.629266\pi\)
\(662\) 1.20074e6 + 3.69551e6i 0.106489 + 0.327740i
\(663\) −614434. + 524008.i −0.0542865 + 0.0462971i
\(664\) 1.05789e7 7.68606e6i 0.931156 0.676524i
\(665\) 1.99240e7 + 6.47371e6i 1.74712 + 0.567674i
\(666\) −1.88342e7 + 1.87798e7i −1.64537 + 1.64061i
\(667\) −160627. 221084.i −0.0139799 0.0192416i
\(668\) 1.09880e7 + 7.98323e6i 0.952744 + 0.692209i
\(669\) −427278. 5.47977e6i −0.0369101 0.473366i
\(670\) 4.39816e7i 3.78515i
\(671\) 956666. + 1.97704e6i 0.0820264 + 0.169516i
\(672\) −1.15197e6 + 4.78306e6i −0.0984055 + 0.408586i
\(673\) 1.09499e7 3.55783e6i 0.931904 0.302794i 0.196563 0.980491i \(-0.437022\pi\)
0.735341 + 0.677697i \(0.237022\pi\)
\(674\) −7.48110e6 + 1.02968e7i −0.634330 + 0.873081i
\(675\) −2.32777e7 1.88285e6i −1.96644 0.159058i
\(676\) 3.72118e6 1.14526e7i 0.313195 0.963914i
\(677\) −1.54294e6 + 4.74869e6i −0.129383 + 0.398200i −0.994674 0.103069i \(-0.967134\pi\)
0.865291 + 0.501270i \(0.167134\pi\)
\(678\) −5.28306e6 1.27806e7i −0.441379 1.06777i
\(679\) 1.25255e6 1.72399e6i 0.104261 0.143503i
\(680\) −3.02674e6 + 983449.i −0.251017 + 0.0815604i
\(681\) −9.00218e6 2.16812e6i −0.743840 0.179150i
\(682\) 2.86972e7 + 5.15221e6i 2.36254 + 0.424163i
\(683\) 5.47780e6i 0.449319i −0.974437 0.224659i \(-0.927873\pi\)
0.974437 0.224659i \(-0.0721269\pi\)
\(684\) −2.57867e7 4.12248e6i −2.10744 0.336914i
\(685\) 1.88336e7 + 1.36834e7i 1.53358 + 1.11421i
\(686\) −1.29504e7 1.78248e7i −1.05069 1.44615i
\(687\) 218157. 355422.i 0.0176351 0.0287311i
\(688\) −4.45353e6 1.44704e6i −0.358702 0.116549i
\(689\) −8.93857e6 + 6.49425e6i −0.717332 + 0.521172i
\(690\) 3.53815e6 + 4.14872e6i 0.282913 + 0.331735i
\(691\) −2.96672e6 9.13063e6i −0.236364 0.727454i −0.996938 0.0782022i \(-0.975082\pi\)
0.760573 0.649252i \(-0.224918\pi\)
\(692\) −4.44920e7 −3.53197
\(693\) 1.10538e7 + 3.86260e6i 0.874339 + 0.305525i
\(694\) 2.68870e7 2.11907
\(695\) −6.43793e6 1.98139e7i −0.505573 1.55599i
\(696\) −1.90473e6 2.23343e6i −0.149043 0.174763i
\(697\) 857323. 622882.i 0.0668440 0.0485650i
\(698\) 3.91342e7 + 1.27155e7i 3.04031 + 0.987858i
\(699\) 1.10000e6 1.79212e6i 0.0851528 0.138731i
\(700\) −2.58322e7 3.55549e7i −1.99258 2.74255i
\(701\) −7.59425e6 5.51755e6i −0.583700 0.424083i 0.256356 0.966582i \(-0.417478\pi\)
−0.840056 + 0.542499i \(0.817478\pi\)
\(702\) 1.37175e7 + 5.71689e6i 1.05059 + 0.437842i
\(703\) 2.07276e7i 1.58183i
\(704\) −8.40465e6 + 1.56889e7i −0.639128 + 1.19305i
\(705\) 3.91903e6 + 943877.i 0.296966 + 0.0715225i
\(706\) 1.38477e7 4.49938e6i 1.04560 0.339735i
\(707\) 3.62821e6 4.99380e6i 0.272988 0.375736i
\(708\) −4.65547e6 1.12623e7i −0.349044 0.844395i
\(709\) −3.32598e6 + 1.02363e7i −0.248487 + 0.764765i 0.746556 + 0.665322i \(0.231706\pi\)
−0.995043 + 0.0994424i \(0.968294\pi\)
\(710\) 2.47675e6 7.62267e6i 0.184390 0.567494i
\(711\) −2.14299e6 1.36582e7i −0.158981 1.01326i
\(712\) −1.07493e7 + 1.47951e7i −0.794656 + 1.09375i
\(713\) 2.74437e6 891700.i 0.202171 0.0656893i
\(714\) −528748. + 2.19539e6i −0.0388153 + 0.161164i
\(715\) −1.09927e7 1.14544e7i −0.804158 0.837932i
\(716\) 1.35097e7i 0.984831i
\(717\) 2.04313e6 + 2.62029e7i 0.148422 + 1.90349i
\(718\) −1.25227e7 9.09828e6i −0.906540 0.658640i
\(719\) −2.98681e6 4.11100e6i −0.215470 0.296568i 0.687577 0.726112i \(-0.258675\pi\)
−0.903046 + 0.429543i \(0.858675\pi\)
\(720\) 9.93578e6 + 9.96458e6i 0.714283 + 0.716354i
\(721\) 1.71762e7 + 5.58088e6i 1.23052 + 0.399820i
\(722\) −6.19096e6 + 4.49799e6i −0.441992 + 0.321126i
\(723\) 1.55747e7 1.32826e7i 1.10809 0.945011i
\(724\) −3.48095e6 1.07133e7i −0.246803 0.759582i
\(725\) −4.43771e6 −0.313555
\(726\) 1.99186e7 + 1.33837e7i 1.40255 + 0.942401i
\(727\) 1.40886e7 0.988629 0.494314 0.869283i \(-0.335419\pi\)
0.494314 + 0.869283i \(0.335419\pi\)
\(728\) 3.98393e6 + 1.22613e7i 0.278601 + 0.857447i
\(729\) 6.56971e6 1.27566e7i 0.457855 0.889027i
\(730\) −1.09579e7 + 7.96142e6i −0.761066 + 0.552947i
\(731\) 935602. + 303996.i 0.0647586 + 0.0210414i
\(732\) 4.31666e6 + 2.64955e6i 0.297763 + 0.182766i
\(733\) 2.00607e6 + 2.76112e6i 0.137907 + 0.189813i 0.872384 0.488820i \(-0.162573\pi\)
−0.734477 + 0.678633i \(0.762573\pi\)
\(734\) −8.77745e6 6.37719e6i −0.601352 0.436907i
\(735\) 3.57968e6 279121.i 0.244414 0.0190578i
\(736\) 997912.i 0.0679044i
\(737\) −1.32651e7 1.38222e7i −0.899583 0.937365i
\(738\) −1.73635e7 8.87880e6i −1.17353 0.600086i
\(739\) −2.24982e7 + 7.31012e6i −1.51544 + 0.492395i −0.944475 0.328583i \(-0.893429\pi\)
−0.570960 + 0.820978i \(0.693429\pi\)
\(740\) 3.85138e7 5.30097e7i 2.58546 3.55857i
\(741\) 1.07031e7 4.42430e6i 0.716084 0.296005i
\(742\) −9.54745e6 + 2.93840e7i −0.636616 + 1.95930i
\(743\) −3.78094e6 + 1.16365e7i −0.251263 + 0.773307i 0.743280 + 0.668980i \(0.233269\pi\)
−0.994543 + 0.104327i \(0.966731\pi\)
\(744\) 2.86445e7 1.18407e7i 1.89718 0.784230i
\(745\) −2.63691e7 + 3.62940e7i −1.74063 + 2.39577i
\(746\) 1.10177e7 3.57987e6i 0.724844 0.235516i
\(747\) 1.08145e7 + 5.53001e6i 0.709099 + 0.362597i
\(748\) −1.42001e6 + 2.65072e6i −0.0927976 + 0.173224i
\(749\) 1.69965e7i 1.10702i
\(750\) 4.35310e7 3.39427e6i 2.82583 0.220340i
\(751\) 5.82098e6 + 4.22919e6i 0.376614 + 0.273626i 0.759948 0.649984i \(-0.225224\pi\)
−0.383334 + 0.923610i \(0.625224\pi\)
\(752\) −947444. 1.30405e6i −0.0610955 0.0840907i
\(753\) −932864. 572589.i −0.0599557 0.0368006i
\(754\) 2.68572e6 + 872642.i 0.172041 + 0.0558995i
\(755\) 4.64763e6 3.37670e6i 0.296732 0.215588i
\(756\) 2.62701e7 6.24661e6i 1.67170 0.397502i
\(757\) −4.24655e6 1.30695e7i −0.269338 0.828936i −0.990662 0.136339i \(-0.956466\pi\)
0.721325 0.692597i \(-0.243534\pi\)
\(758\) 3.09086e7 1.95392
\(759\) 2.36322e6 + 236703.i 0.148902 + 0.0149142i
\(760\) 4.56428e7 2.86641
\(761\) 4.19040e6 + 1.28967e7i 0.262298 + 0.807269i 0.992304 + 0.123828i \(0.0395172\pi\)
−0.730006 + 0.683441i \(0.760483\pi\)
\(762\) −3.97913e7 + 3.39352e7i −2.48256 + 2.11720i
\(763\) −2.03147e6 + 1.47595e6i −0.126328 + 0.0917826i
\(764\) −2.31351e7 7.51704e6i −1.43396 0.465922i
\(765\) −2.08732e6 2.09337e6i −0.128954 0.129328i
\(766\) −1.82839e6 2.51657e6i −0.112589 0.154966i
\(767\) 4.37249e6 + 3.17680e6i 0.268374 + 0.194985i
\(768\) 2.21640e6 + 2.84250e7i 0.135596 + 1.73899i
\(769\) 1.32723e7i 0.809339i −0.914463 0.404669i \(-0.867387\pi\)
0.914463 0.404669i \(-0.132613\pi\)
\(770\) −4.36963e7 7.84510e6i −2.65594 0.476839i
\(771\) 2.09264e6 8.68877e6i 0.126782 0.526408i
\(772\) −1.99852e7 + 6.49358e6i −1.20688 + 0.392140i
\(773\) −8.15315e6 + 1.12219e7i −0.490769 + 0.675485i −0.980530 0.196372i \(-0.937084\pi\)
0.489761 + 0.871857i \(0.337084\pi\)
\(774\) −2.80621e6 1.78852e7i −0.168371 1.07310i
\(775\) 1.44803e7 4.45659e7i 0.866013 2.66531i
\(776\) 1.43470e6 4.41554e6i 0.0855275 0.263227i
\(777\) −8.18760e6 1.98072e7i −0.486524 1.17698i
\(778\) −2.55784e7 + 3.52056e7i −1.51504 + 2.08527i
\(779\) −1.44543e7 + 4.69647e6i −0.853399 + 0.277286i
\(780\) −3.55934e7 8.57247e6i −2.09475 0.504510i
\(781\) −1.52066e6 3.14260e6i −0.0892083 0.184358i
\(782\) 458035.i 0.0267844i
\(783\) 1.04889e6 2.51678e6i 0.0611400 0.146703i
\(784\) −1.16153e6 843899.i −0.0674900 0.0490344i
\(785\) 1.75295e7 + 2.41273e7i 1.01530 + 1.39744i
\(786\) −919105. + 1.49741e6i −0.0530651 + 0.0864539i
\(787\) −1.42304e7 4.62374e6i −0.818994 0.266107i −0.130592 0.991436i \(-0.541688\pi\)
−0.688403 + 0.725329i \(0.741688\pi\)
\(788\) −2.84128e7 + 2.06431e7i −1.63004 + 1.18429i
\(789\) −1.07482e7 1.26030e7i −0.614674 0.720746i
\(790\) 1.61980e7 + 4.98523e7i 0.923407 + 2.84196i
\(791\) 1.11441e7 0.633294
\(792\) 2.55050e7 + 561510.i 1.44482 + 0.0318086i
\(793\) −2.24627e6 −0.126847
\(794\) 2.11282e6 + 6.50259e6i 0.118935 + 0.366045i
\(795\) −2.62457e7 3.07748e7i −1.47279 1.72694i
\(796\) −1.15580e7 + 8.39735e6i −0.646544 + 0.469742i
\(797\) −7.67016e6 2.49219e6i −0.427719 0.138974i 0.0872435 0.996187i \(-0.472194\pi\)
−0.514963 + 0.857213i \(0.672194\pi\)
\(798\) 1.69417e7 2.76015e7i 0.941780 1.53435i
\(799\) 199040. + 273955.i 0.0110299 + 0.0151814i
\(800\) 1.31102e7 + 9.52513e6i 0.724244 + 0.526194i
\(801\) −1.67743e7 2.68168e6i −0.923768 0.147681i
\(802\) 2.05293e7i 1.12704i
\(803\) −1.04258e6 + 5.80704e6i −0.0570584 + 0.317809i
\(804\) −4.29510e7 1.03445e7i −2.34333 0.564377i
\(805\) −4.17876e6 + 1.35776e6i −0.227278 + 0.0738472i
\(806\) −1.75271e7 + 2.41240e7i −0.950326 + 1.30801i
\(807\) −1.59051e6 3.84770e6i −0.0859711 0.207978i
\(808\) 4.15582e6 1.27903e7i 0.223938 0.689211i
\(809\) 2.80769e6 8.64117e6i 0.150826 0.464196i −0.846888 0.531772i \(-0.821526\pi\)
0.997714 + 0.0675758i \(0.0215265\pi\)
\(810\) −1.69611e7 + 5.16914e7i −0.908327 + 2.76825i
\(811\) 5.74282e6 7.90432e6i 0.306601 0.422000i −0.627717 0.778442i \(-0.716010\pi\)
0.934317 + 0.356442i \(0.116010\pi\)
\(812\) 4.87993e6 1.58558e6i 0.259731 0.0843916i
\(813\) −2.60023e6 + 1.07963e7i −0.137970 + 0.572861i
\(814\) −5.97779e6 4.35162e7i −0.316213 2.30192i
\(815\) 3.31376e7i 1.74754i
\(816\) 91891.7 + 1.17850e6i 0.00483116 + 0.0619588i
\(817\) −1.14142e7 8.29290e6i −0.598260 0.434661i
\(818\) 2.99038e7 + 4.11591e7i 1.56258 + 2.15071i
\(819\) −8.48019e6 + 8.45568e6i −0.441769 + 0.440493i
\(820\) 4.56925e7 + 1.48464e7i 2.37307 + 0.771057i
\(821\) 2.45033e7 1.78027e7i 1.26873 0.921783i 0.269574 0.962980i \(-0.413117\pi\)
0.999151 + 0.0411969i \(0.0131171\pi\)
\(822\) 2.73828e7 2.33528e7i 1.41351 1.20548i
\(823\) 1.09180e7 + 3.36022e7i 0.561880 + 1.72929i 0.677044 + 0.735943i \(0.263261\pi\)
−0.115163 + 0.993347i \(0.536739\pi\)
\(824\) 3.93479e7 2.01885
\(825\) 2.56668e7 2.87878e7i 1.31292 1.47256i
\(826\) 1.51135e7 0.770754
\(827\) −1.19820e7 3.68769e7i −0.609210 1.87496i −0.464740 0.885447i \(-0.653852\pi\)
−0.144471 0.989509i \(-0.546148\pi\)
\(828\) 4.88368e6 2.47946e6i 0.247555 0.125685i
\(829\) 1.65302e7 1.20099e7i 0.835396 0.606951i −0.0856847 0.996322i \(-0.527308\pi\)
0.921081 + 0.389372i \(0.127308\pi\)
\(830\) −4.37984e7 1.42310e7i −2.20680 0.717033i
\(831\) 9.70822e6 + 5.95887e6i 0.487682 + 0.299338i
\(832\) −1.06994e7 1.47265e7i −0.535860 0.737548i
\(833\) 244015. + 177287.i 0.0121844 + 0.00885248i
\(834\) −3.21096e7 + 2.50371e6i −1.59853 + 0.124643i
\(835\) 2.20505e7i 1.09447i
\(836\) 3.11162e7 2.98620e7i 1.53982 1.47776i
\(837\) 2.18523e7 + 1.87458e7i 1.07816 + 0.924892i
\(838\) −1.55585e7 + 5.05527e6i −0.765347 + 0.248676i
\(839\) 1.58020e7 2.17496e7i 0.775012 1.06671i −0.220803 0.975318i \(-0.570868\pi\)
0.995815 0.0913938i \(-0.0291322\pi\)
\(840\) −4.36160e7 + 1.80294e7i −2.13279 + 0.881622i
\(841\) −6.17819e6 + 1.90145e7i −0.301211 + 0.927033i
\(842\) 8.93905e6 2.75116e7i 0.434521 1.33732i
\(843\) −1.87565e7 + 7.75330e6i −0.909040 + 0.375766i
\(844\) −5.23732e6 + 7.20856e6i −0.253077 + 0.348331i
\(845\) −1.85936e7 + 6.04143e6i −0.895823 + 0.291070i
\(846\) 2.83720e6 5.54844e6i 0.136290 0.266530i
\(847\) −1.60987e7 + 1.07135e7i −0.771049 + 0.513127i
\(848\) 1.61731e7i 0.772331i
\(849\) −3.11473e7 + 2.42867e6i −1.48303 + 0.115637i
\(850\) 6.01750e6 + 4.37197e6i 0.285673 + 0.207553i
\(851\) −2.55527e6 3.51703e6i −0.120952 0.166476i
\(852\) −6.86152e6 4.21158e6i −0.323833 0.198768i
\(853\) −7.89282e6 2.56453e6i −0.371415 0.120680i 0.117361 0.993089i \(-0.462557\pi\)
−0.488776 + 0.872409i \(0.662557\pi\)
\(854\) −5.08177e6 + 3.69212e6i −0.238435 + 0.173233i
\(855\) 1.91932e7 + 3.78038e7i 0.897907 + 1.76856i
\(856\) −1.14431e7 3.52181e7i −0.533775 1.64279i
\(857\) −3.64231e7 −1.69404 −0.847021 0.531559i \(-0.821606\pi\)
−0.847021 + 0.531559i \(0.821606\pi\)
\(858\) −2.11945e7 + 1.23753e7i −0.982892 + 0.573902i
\(859\) 9.11498e6 0.421476 0.210738 0.977543i \(-0.432413\pi\)
0.210738 + 0.977543i \(0.432413\pi\)
\(860\) 1.37822e7 + 4.24173e7i 0.635438 + 1.95568i
\(861\) 1.19573e7 1.01975e7i 0.549697 0.468798i
\(862\) 1.28078e7 9.30542e6i 0.587093 0.426548i
\(863\) −1.49151e7 4.84622e6i −0.681710 0.221501i −0.0523662 0.998628i \(-0.516676\pi\)
−0.629344 + 0.777127i \(0.716676\pi\)
\(864\) −8.50074e6 + 5.18391e6i −0.387411 + 0.236251i
\(865\) 4.24580e7 + 5.84384e7i 1.92939 + 2.65557i
\(866\) −1.61426e7 1.17283e7i −0.731438 0.531421i
\(867\) 1.70129e6 + 2.18188e7i 0.0768655 + 0.985788i
\(868\) 5.41807e7i 2.44087i
\(869\) 2.01263e7 + 1.07818e7i 0.904096 + 0.484331i
\(870\) −2.42057e6 + 1.00503e7i −0.108422 + 0.450176i
\(871\) 1.86342e7 6.05463e6i 0.832274 0.270422i
\(872\) −3.21568e6 + 4.42600e6i −0.143213 + 0.197115i
\(873\) 4.26050e6 668477.i 0.189202 0.0296860i
\(874\) 2.02994e6 6.24752e6i 0.0898887 0.276649i
\(875\) −1.08727e7 + 3.34628e7i −0.480085 + 1.47755i
\(876\) 5.19755e6 + 1.25737e7i 0.228843 + 0.553610i
\(877\) 1.26723e7 1.74419e7i 0.556361 0.765766i −0.434497 0.900673i \(-0.643074\pi\)
0.990858 + 0.134908i \(0.0430738\pi\)
\(878\) 4.84013e7 1.57265e7i 2.11895 0.688488i
\(879\) 3.20831e7 + 7.72702e6i 1.40057 + 0.337318i
\(880\) −2.30230e7 + 3.16265e6i −1.00220 + 0.137672i
\(881\) 2.85398e7i 1.23883i −0.785065 0.619413i \(-0.787371\pi\)
0.785065 0.619413i \(-0.212629\pi\)
\(882\) 876255. 5.48111e6i 0.0379279 0.237245i
\(883\) −1.84629e7 1.34141e7i −0.796890 0.578975i 0.113110 0.993582i \(-0.463919\pi\)
−0.910000 + 0.414608i \(0.863919\pi\)
\(884\) −1.80772e6 2.48811e6i −0.0778037 0.107088i
\(885\) −1.03500e7 + 1.68622e7i −0.444203 + 0.723698i
\(886\) −3.57515e7 1.16164e7i −1.53007 0.497149i
\(887\) 2.35627e7 1.71193e7i 1.00558 0.730595i 0.0423004 0.999105i \(-0.486531\pi\)
0.963277 + 0.268510i \(0.0865313\pi\)
\(888\) −3.03008e7 3.55297e7i −1.28950 1.51202i
\(889\) −1.30226e7 4.00795e7i −0.552641 1.70086i
\(890\) 6.44062e7 2.72554
\(891\) 1.02600e7 + 2.13608e7i 0.432965 + 0.901411i
\(892\) 2.09329e7 0.880881
\(893\) −1.50074e6 4.61881e6i −0.0629764 0.193821i
\(894\) 4.50030e7 + 5.27690e7i 1.88321 + 2.20818i
\(895\) 1.77444e7 1.28920e7i 0.740463 0.537978i
\(896\) −3.88057e7 1.26087e7i −1.61482 0.524688i
\(897\) −1.27067e6 + 2.07018e6i −0.0527292 + 0.0859066i
\(898\) −3.04784e7 4.19500e7i −1.26125 1.73596i
\(899\) 4.42607e6 + 3.21573e6i 0.182650 + 0.132703i
\(900\) 1.40407e7 8.78267e7i 0.577807 3.61427i
\(901\) 3.39766e6i 0.139434i
\(902\) 2.89914e7 1.40285e7i 1.18646 0.574111i
\(903\) 1.41831e7 + 3.41592e6i 0.578832 + 0.139408i
\(904\) 2.30916e7 7.50292e6i 0.939795 0.305358i
\(905\) −1.07496e7 + 1.47956e7i −0.436286 + 0.600496i
\(906\) −3.39268e6 8.20744e6i −0.137316 0.332190i
\(907\) 1.52393e6 4.69019e6i 0.0615103 0.189309i −0.915579 0.402137i \(-0.868267\pi\)
0.977090 + 0.212828i \(0.0682674\pi\)
\(908\) 1.08974e7 3.35389e7i 0.438642 1.35000i
\(909\) 1.23412e7 1.93635e6i 0.495390 0.0777273i
\(910\) 2.66879e7 3.67328e7i 1.06835 1.47045i
\(911\) −3.33982e7 + 1.08517e7i −1.33330 + 0.433215i −0.887041 0.461690i \(-0.847243\pi\)
−0.446257 + 0.894905i \(0.647243\pi\)
\(912\) 3.96953e6 1.64817e7i 0.158035 0.656170i
\(913\) −1.80568e7 + 8.73743e6i −0.716908 + 0.346902i
\(914\) 2.16576e7i 0.857523i
\(915\) −639242. 8.19818e6i −0.0252414 0.323716i
\(916\) 1.28493e6 + 933557.i 0.0505989 + 0.0367622i
\(917\) −832200. 1.14542e6i −0.0326817 0.0449825i
\(918\) −3.90178e6 + 2.37938e6i −0.152812 + 0.0931874i
\(919\) 1.35936e7 + 4.41684e6i 0.530942 + 0.172514i 0.562205 0.826998i \(-0.309953\pi\)
−0.0312632 + 0.999511i \(0.509953\pi\)
\(920\) −7.74462e6 + 5.62680e6i −0.301669 + 0.219175i
\(921\) 2.71546e7 2.31583e7i 1.05486 0.899615i
\(922\) 279162. + 859173.i 0.0108151 + 0.0332854i
\(923\) 3.57055e6 0.137953
\(924\) −1.79387e7 + 4.08272e7i −0.691211 + 1.57315i
\(925\) −7.05958e7 −2.71284
\(926\) 1.21134e7 + 3.72813e7i 0.464237 + 1.42877i
\(927\) 1.65461e7 + 3.25901e7i 0.632406 + 1.24562i
\(928\) −1.53065e6 + 1.11208e6i −0.0583451 + 0.0423902i
\(929\) 1.84838e7 + 6.00577e6i 0.702673 + 0.228312i 0.638495 0.769626i \(-0.279557\pi\)
0.0641780 + 0.997938i \(0.479557\pi\)
\(930\) −9.30327e7 5.71031e7i −3.52718 2.16497i
\(931\) −2.54261e6 3.49960e6i −0.0961404 0.132326i
\(932\) 6.47892e6 + 4.70721e6i 0.244322 + 0.177510i
\(933\) −3.77599e7 + 2.94428e6i −1.42013 + 0.110732i
\(934\) 2.02606e7i 0.759949i
\(935\) 4.83670e6 664413.i 0.180934 0.0248547i
\(936\) −1.18788e7 + 2.32302e7i −0.443182 + 0.866691i
\(937\) 2.08876e7 6.78679e6i 0.777211 0.252531i 0.106562 0.994306i \(-0.466016\pi\)
0.670649 + 0.741775i \(0.266016\pi\)
\(938\) 3.22047e7 4.43259e7i 1.19512 1.64494i
\(939\) −1.23369e7 + 5.09966e6i −0.456607 + 0.188746i
\(940\) −4.74412e6 + 1.46009e7i −0.175120 + 0.538964i
\(941\) 8.32276e6 2.56148e7i 0.306403 0.943012i −0.672747 0.739873i \(-0.734886\pi\)
0.979150 0.203139i \(-0.0651143\pi\)
\(942\) 4.26073e7 1.76124e7i 1.56443 0.646683i
\(943\) 1.87361e6 2.57880e6i 0.0686119 0.0944361i
\(944\) 7.52420e6 2.44476e6i 0.274809 0.0892908i
\(945\) −3.32738e7 2.85437e7i −1.21206 1.03975i
\(946\) 2.63550e7 + 1.41186e7i 0.957493 + 0.512936i
\(947\) 1.70260e6i 0.0616932i 0.999524 + 0.0308466i \(0.00982033\pi\)
−0.999524 + 0.0308466i \(0.990180\pi\)
\(948\) 5.24939e7 4.09314e6i 1.89709 0.147923i
\(949\) −4.88162e6 3.54670e6i −0.175954 0.127838i
\(950\) −6.27018e7 8.63016e7i −2.25409 3.10249i
\(951\) −3.62380e7 2.22428e7i −1.29931 0.797512i
\(952\) −3.77055e6 1.22513e6i −0.134838 0.0438116i
\(953\) −3.84161e7 + 2.79109e7i −1.37019 + 0.995501i −0.372468 + 0.928045i \(0.621488\pi\)
−0.997722 + 0.0674561i \(0.978512\pi\)
\(954\) −5.57532e7 + 2.83061e7i −1.98335 + 1.00695i
\(955\) 1.22041e7 + 3.75604e7i 0.433009 + 1.33267i
\(956\) −1.00096e8 −3.54218
\(957\) 2.27052e6 + 3.88860e6i 0.0801393 + 0.137250i
\(958\) −3.19723e7 −1.12554
\(959\) 8.96163e6 + 2.75811e7i 0.314659 + 0.968422i
\(960\) 5.07021e7 4.32403e7i 1.77561 1.51429i
\(961\) −2.35750e7 + 1.71283e7i −0.823463 + 0.598281i
\(962\) 4.27248e7 + 1.38821e7i 1.48848 + 0.483636i
\(963\) 2.43577e7 2.42873e7i 0.846390 0.843943i
\(964\) 4.58222e7 + 6.30688e7i 1.58812 + 2.18586i
\(965\) 2.76006e7 + 2.00530e7i 0.954114 + 0.693204i
\(966\) 528033. + 6.77194e6i 0.0182062 + 0.233491i
\(967\) 1.33415e7i 0.458815i 0.973330 + 0.229407i \(0.0736788\pi\)
−0.973330 + 0.229407i \(0.926321\pi\)
\(968\) −2.61448e7 + 3.30380e7i −0.896803 + 1.13325i
\(969\) −833923. + 3.46250e6i −0.0285310 + 0.118462i
\(970\) −1.55507e7 + 5.05274e6i −0.530667 + 0.172424i
\(971\) −2.04468e7 + 2.81426e7i −0.695949 + 0.957892i 0.304037 + 0.952660i \(0.401665\pi\)
−0.999986 + 0.00523162i \(0.998335\pi\)
\(972\) 4.64909e7 + 2.87216e7i 1.57835 + 0.975085i
\(973\) 8.02002e6 2.46831e7i 0.271577 0.835829i
\(974\) −2.05178e7 + 6.31472e7i −0.692999 + 2.13283i
\(975\) 1.50687e7 + 3.64536e7i 0.507649 + 1.22809i
\(976\) −1.93270e6 + 2.66013e6i −0.0649441 + 0.0893879i
\(977\) 1.84100e7 5.98176e6i 0.617045 0.200490i 0.0162169 0.999868i \(-0.494838\pi\)
0.600828 + 0.799379i \(0.294838\pi\)
\(978\) 4.98042e7 + 1.19950e7i 1.66502 + 0.401010i
\(979\) 2.02411e7 1.94253e7i 0.674960 0.647754i
\(980\) 1.36745e7i 0.454826i
\(981\) −5.01808e6 802232.i −0.166481 0.0266151i
\(982\) −2.36512e7 1.71836e7i −0.782662 0.568637i
\(983\) 2.98011e7 + 4.10177e7i 0.983667 + 1.35390i 0.934830 + 0.355095i \(0.115552\pi\)
0.0488374 + 0.998807i \(0.484448\pi\)
\(984\) 1.79109e7 2.91804e7i 0.589696 0.960736i
\(985\) 5.42277e7 + 1.76196e7i 1.78086 + 0.578637i
\(986\) −702556. + 510437.i −0.0230138 + 0.0167205i
\(987\) 3.25858e6 + 3.82090e6i 0.106472 + 0.124846i
\(988\) 1.36300e7 + 4.19490e7i 0.444227 + 1.36719i
\(989\) 2.95909e6 0.0961982
\(990\) −5.11974e7 7.38316e7i −1.66020 2.39416i
\(991\) −1.84861e7 −0.597943 −0.298972 0.954262i \(-0.596644\pi\)
−0.298972 + 0.954262i \(0.596644\pi\)
\(992\) −6.17358e6 1.90003e7i −0.199186 0.613030i
\(993\) −4.11197e6 4.82156e6i −0.132336 0.155172i
\(994\) 8.07770e6 5.86879e6i 0.259311 0.188401i
\(995\) 2.20591e7 + 7.16745e6i 0.706368 + 0.229513i
\(996\) −2.41989e7 + 3.94250e7i −0.772943 + 1.25928i
\(997\) −5.95739e6 8.19964e6i −0.189809 0.261250i 0.703497 0.710698i \(-0.251621\pi\)
−0.893307 + 0.449448i \(0.851621\pi\)
\(998\) −3.33561e7 2.42346e7i −1.06011 0.770212i
\(999\) 1.66859e7 4.00373e7i 0.528976 1.26926i
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 33.6.f.a.17.2 yes 72
3.2 odd 2 inner 33.6.f.a.17.17 yes 72
11.2 odd 10 inner 33.6.f.a.2.17 yes 72
33.2 even 10 inner 33.6.f.a.2.2 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.6.f.a.2.2 72 33.2 even 10 inner
33.6.f.a.2.17 yes 72 11.2 odd 10 inner
33.6.f.a.17.2 yes 72 1.1 even 1 trivial
33.6.f.a.17.17 yes 72 3.2 odd 2 inner