Properties

Label 162.7.d.f.107.2
Level $162$
Weight $7$
Character 162.107
Analytic conductor $37.269$
Analytic rank $0$
Dimension $8$
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] = [162,7,Mod(53,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.53");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 162.d (of order \(6\), degree \(2\), not 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: \(37.2687615464\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.2
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 162.107
Dual form 162.7.d.f.53.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.89898 - 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-21.4919 + 12.4084i) q^{5} +(3.09808 - 5.36603i) q^{7} -181.019i q^{8} +O(q^{10})\) \(q+(-4.89898 - 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-21.4919 + 12.4084i) q^{5} +(3.09808 - 5.36603i) q^{7} -181.019i q^{8} +140.385 q^{10} +(-113.360 - 65.4483i) q^{11} +(461.004 + 798.482i) q^{13} +(-30.3548 + 17.5254i) q^{14} +(-512.000 + 886.810i) q^{16} -3384.11i q^{17} +5403.30 q^{19} +(-687.742 - 397.068i) q^{20} +(370.232 + 641.260i) q^{22} +(2045.32 - 1180.87i) q^{23} +(-7504.56 + 12998.3i) q^{25} -5215.66i q^{26} +198.277 q^{28} +(-30256.9 - 17468.8i) q^{29} +(-2330.16 - 4035.96i) q^{31} +(5016.55 - 2896.31i) q^{32} +(-9571.71 + 16578.7i) q^{34} +153.768i q^{35} +6916.74 q^{37} +(-26470.6 - 15282.8i) q^{38} +(2246.16 + 3890.46i) q^{40} +(46637.1 - 26926.0i) q^{41} +(-61566.4 + 106636. i) q^{43} -4188.69i q^{44} -13360.0 q^{46} +(-83183.9 - 48026.3i) q^{47} +(58805.3 + 101854. i) q^{49} +(73529.4 - 42452.2i) q^{50} +(-14752.1 + 25551.4i) q^{52} +132310. i q^{53} +3248.43 q^{55} +(-971.354 - 560.812i) q^{56} +(98818.5 + 171159. i) q^{58} +(25181.5 - 14538.6i) q^{59} +(-160333. + 277705. i) q^{61} +26362.8i q^{62} -32768.0 q^{64} +(-19815.7 - 11440.6i) q^{65} +(264909. + 458837. i) q^{67} +(93783.3 - 54145.8i) q^{68} +(434.923 - 753.308i) q^{70} +628518. i q^{71} -68777.7 q^{73} +(-33885.0 - 19563.5i) q^{74} +(86452.7 + 149741. i) q^{76} +(-702.395 + 405.528i) q^{77} +(-235877. + 408551. i) q^{79} -25412.4i q^{80} -304633. q^{82} +(-29055.1 - 16775.0i) q^{83} +(41991.3 + 72731.1i) q^{85} +(603225. - 348272. i) q^{86} +(-11847.4 + 20520.3i) q^{88} +1.01543e6i q^{89} +5712.90 q^{91} +(65450.3 + 37787.7i) q^{92} +(271678. + 470559. i) q^{94} +(-116127. + 67046.1i) q^{95} +(-209094. + 362162. i) q^{97} -665306. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 128 q^{4} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 128 q^{4} + 4 q^{7} + 5280 q^{10} - 3836 q^{13} - 4096 q^{16} + 20488 q^{19} + 27072 q^{22} + 25700 q^{25} + 256 q^{28} + 40096 q^{31} - 60528 q^{34} - 40400 q^{37} + 84480 q^{40} - 184940 q^{43} + 325440 q^{46} + 470484 q^{49} + 122752 q^{52} + 1899720 q^{55} - 24624 q^{58} - 609056 q^{61} - 262144 q^{64} + 2008972 q^{67} - 8160 q^{70} + 1051648 q^{73} + 327808 q^{76} + 848716 q^{79} + 1411584 q^{82} + 987840 q^{85} - 866304 q^{88} + 70520 q^{91} + 1965408 q^{94} - 3621728 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.89898 2.82843i −0.612372 0.353553i
\(3\) 0 0
\(4\) 16.0000 + 27.7128i 0.250000 + 0.433013i
\(5\) −21.4919 + 12.4084i −0.171936 + 0.0992670i −0.583498 0.812114i \(-0.698316\pi\)
0.411563 + 0.911381i \(0.364983\pi\)
\(6\) 0 0
\(7\) 3.09808 5.36603i 0.00903229 0.0156444i −0.861474 0.507802i \(-0.830458\pi\)
0.870506 + 0.492157i \(0.163792\pi\)
\(8\) 181.019i 0.353553i
\(9\) 0 0
\(10\) 140.385 0.140385
\(11\) −113.360 65.4483i −0.0851689 0.0491723i 0.456811 0.889564i \(-0.348992\pi\)
−0.541980 + 0.840392i \(0.682325\pi\)
\(12\) 0 0
\(13\) 461.004 + 798.482i 0.209833 + 0.363442i 0.951662 0.307148i \(-0.0993746\pi\)
−0.741829 + 0.670589i \(0.766041\pi\)
\(14\) −30.3548 + 17.5254i −0.0110623 + 0.00638680i
\(15\) 0 0
\(16\) −512.000 + 886.810i −0.125000 + 0.216506i
\(17\) 3384.11i 0.688808i −0.938822 0.344404i \(-0.888081\pi\)
0.938822 0.344404i \(-0.111919\pi\)
\(18\) 0 0
\(19\) 5403.30 0.787767 0.393884 0.919160i \(-0.371131\pi\)
0.393884 + 0.919160i \(0.371131\pi\)
\(20\) −687.742 397.068i −0.0859678 0.0496335i
\(21\) 0 0
\(22\) 370.232 + 641.260i 0.0347701 + 0.0602235i
\(23\) 2045.32 1180.87i 0.168104 0.0970549i −0.413588 0.910464i \(-0.635724\pi\)
0.581692 + 0.813409i \(0.302391\pi\)
\(24\) 0 0
\(25\) −7504.56 + 12998.3i −0.480292 + 0.831890i
\(26\) 5215.66i 0.296749i
\(27\) 0 0
\(28\) 198.277 0.00903229
\(29\) −30256.9 17468.8i −1.24060 0.716258i −0.271380 0.962472i \(-0.587480\pi\)
−0.969215 + 0.246214i \(0.920813\pi\)
\(30\) 0 0
\(31\) −2330.16 4035.96i −0.0782170 0.135476i 0.824264 0.566206i \(-0.191589\pi\)
−0.902481 + 0.430730i \(0.858256\pi\)
\(32\) 5016.55 2896.31i 0.153093 0.0883883i
\(33\) 0 0
\(34\) −9571.71 + 16578.7i −0.243530 + 0.421807i
\(35\) 153.768i 0.00358643i
\(36\) 0 0
\(37\) 6916.74 0.136551 0.0682757 0.997666i \(-0.478250\pi\)
0.0682757 + 0.997666i \(0.478250\pi\)
\(38\) −26470.6 15282.8i −0.482407 0.278518i
\(39\) 0 0
\(40\) 2246.16 + 3890.46i 0.0350962 + 0.0607884i
\(41\) 46637.1 26926.0i 0.676675 0.390679i −0.121926 0.992539i \(-0.538907\pi\)
0.798601 + 0.601860i \(0.205574\pi\)
\(42\) 0 0
\(43\) −61566.4 + 106636.i −0.774352 + 1.34122i 0.160805 + 0.986986i \(0.448591\pi\)
−0.935158 + 0.354231i \(0.884743\pi\)
\(44\) 4188.69i 0.0491723i
\(45\) 0 0
\(46\) −13360.0 −0.137256
\(47\) −83183.9 48026.3i −0.801209 0.462578i 0.0426847 0.999089i \(-0.486409\pi\)
−0.843894 + 0.536510i \(0.819742\pi\)
\(48\) 0 0
\(49\) 58805.3 + 101854.i 0.499837 + 0.865743i
\(50\) 73529.4 42452.2i 0.588235 0.339618i
\(51\) 0 0
\(52\) −14752.1 + 25551.4i −0.104917 + 0.181721i
\(53\) 132310.i 0.888722i 0.895848 + 0.444361i \(0.146569\pi\)
−0.895848 + 0.444361i \(0.853431\pi\)
\(54\) 0 0
\(55\) 3248.43 0.0195247
\(56\) −971.354 560.812i −0.00553113 0.00319340i
\(57\) 0 0
\(58\) 98818.5 + 171159.i 0.506471 + 0.877233i
\(59\) 25181.5 14538.6i 0.122610 0.0707889i −0.437441 0.899247i \(-0.644115\pi\)
0.560051 + 0.828458i \(0.310782\pi\)
\(60\) 0 0
\(61\) −160333. + 277705.i −0.706372 + 1.22347i 0.259822 + 0.965657i \(0.416336\pi\)
−0.966194 + 0.257816i \(0.916997\pi\)
\(62\) 26362.8i 0.110616i
\(63\) 0 0
\(64\) −32768.0 −0.125000
\(65\) −19815.7 11440.6i −0.0721556 0.0416590i
\(66\) 0 0
\(67\) 264909. + 458837.i 0.880791 + 1.52558i 0.850463 + 0.526036i \(0.176322\pi\)
0.0303290 + 0.999540i \(0.490345\pi\)
\(68\) 93783.3 54145.8i 0.298262 0.172202i
\(69\) 0 0
\(70\) 434.923 753.308i 0.00126800 0.00219623i
\(71\) 628518.i 1.75607i 0.478594 + 0.878036i \(0.341146\pi\)
−0.478594 + 0.878036i \(0.658854\pi\)
\(72\) 0 0
\(73\) −68777.7 −0.176799 −0.0883994 0.996085i \(-0.528175\pi\)
−0.0883994 + 0.996085i \(0.528175\pi\)
\(74\) −33885.0 19563.5i −0.0836203 0.0482782i
\(75\) 0 0
\(76\) 86452.7 + 149741.i 0.196942 + 0.341113i
\(77\) −702.395 + 405.528i −0.00153854 + 0.000888277i
\(78\) 0 0
\(79\) −235877. + 408551.i −0.478415 + 0.828638i −0.999694 0.0247478i \(-0.992122\pi\)
0.521279 + 0.853386i \(0.325455\pi\)
\(80\) 25412.4i 0.0496335i
\(81\) 0 0
\(82\) −304633. −0.552503
\(83\) −29055.1 16775.0i −0.0508146 0.0293378i 0.474377 0.880322i \(-0.342673\pi\)
−0.525192 + 0.850984i \(0.676007\pi\)
\(84\) 0 0
\(85\) 41991.3 + 72731.1i 0.0683759 + 0.118431i
\(86\) 603225. 348272.i 0.948384 0.547550i
\(87\) 0 0
\(88\) −11847.4 + 20520.3i −0.0173850 + 0.0301118i
\(89\) 1.01543e6i 1.44039i 0.693772 + 0.720195i \(0.255947\pi\)
−0.693772 + 0.720195i \(0.744053\pi\)
\(90\) 0 0
\(91\) 5712.90 0.00758110
\(92\) 65450.3 + 37787.7i 0.0840520 + 0.0485275i
\(93\) 0 0
\(94\) 271678. + 470559.i 0.327092 + 0.566540i
\(95\) −116127. + 67046.1i −0.135445 + 0.0781993i
\(96\) 0 0
\(97\) −209094. + 362162.i −0.229101 + 0.396815i −0.957542 0.288294i \(-0.906912\pi\)
0.728441 + 0.685109i \(0.240245\pi\)
\(98\) 665306.i 0.706876i
\(99\) 0 0
\(100\) −480292. −0.480292
\(101\) −581679. 335833.i −0.564572 0.325956i 0.190406 0.981705i \(-0.439019\pi\)
−0.754979 + 0.655749i \(0.772353\pi\)
\(102\) 0 0
\(103\) −350999. 607949.i −0.321214 0.556359i 0.659525 0.751683i \(-0.270758\pi\)
−0.980739 + 0.195324i \(0.937424\pi\)
\(104\) 144541. 83450.6i 0.128496 0.0741872i
\(105\) 0 0
\(106\) 374230. 648185.i 0.314211 0.544229i
\(107\) 350565.i 0.286166i −0.989711 0.143083i \(-0.954298\pi\)
0.989711 0.143083i \(-0.0457016\pi\)
\(108\) 0 0
\(109\) 724369. 0.559345 0.279673 0.960095i \(-0.409774\pi\)
0.279673 + 0.960095i \(0.409774\pi\)
\(110\) −15914.0 9187.95i −0.0119564 0.00690304i
\(111\) 0 0
\(112\) 3172.43 + 5494.81i 0.00225807 + 0.00391110i
\(113\) −1.09419e6 + 631732.i −0.758330 + 0.437822i −0.828696 0.559699i \(-0.810917\pi\)
0.0703658 + 0.997521i \(0.477583\pi\)
\(114\) 0 0
\(115\) −29305.3 + 50758.2i −0.0192687 + 0.0333744i
\(116\) 1.11800e6i 0.716258i
\(117\) 0 0
\(118\) −164485. −0.100111
\(119\) −18159.2 10484.2i −0.0107760 0.00622151i
\(120\) 0 0
\(121\) −877214. 1.51938e6i −0.495164 0.857650i
\(122\) 1.57094e6 906981.i 0.865126 0.499481i
\(123\) 0 0
\(124\) 74565.2 129151.i 0.0391085 0.0677379i
\(125\) 760240.i 0.389243i
\(126\) 0 0
\(127\) 2.67398e6 1.30541 0.652706 0.757611i \(-0.273634\pi\)
0.652706 + 0.757611i \(0.273634\pi\)
\(128\) 160530. + 92681.9i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 64717.9 + 112095.i 0.0294574 + 0.0510217i
\(131\) −3.10743e6 + 1.79407e6i −1.38225 + 0.798043i −0.992426 0.122846i \(-0.960798\pi\)
−0.389825 + 0.920889i \(0.627465\pi\)
\(132\) 0 0
\(133\) 16739.8 28994.2i 0.00711534 0.0123241i
\(134\) 2.99711e6i 1.24563i
\(135\) 0 0
\(136\) −612590. −0.243530
\(137\) 1.32548e6 + 765268.i 0.515481 + 0.297613i 0.735084 0.677976i \(-0.237143\pi\)
−0.219603 + 0.975589i \(0.570476\pi\)
\(138\) 0 0
\(139\) −1.76383e6 3.05504e6i −0.656769 1.13756i −0.981447 0.191732i \(-0.938589\pi\)
0.324679 0.945824i \(-0.394744\pi\)
\(140\) −4261.35 + 2460.29i −0.00155297 + 0.000896609i
\(141\) 0 0
\(142\) 1.77772e6 3.07909e6i 0.620865 1.07537i
\(143\) 120688.i 0.0412719i
\(144\) 0 0
\(145\) 867039. 0.284403
\(146\) 336941. + 194533.i 0.108267 + 0.0625078i
\(147\) 0 0
\(148\) 110668. + 191682.i 0.0341379 + 0.0591285i
\(149\) −2.07440e6 + 1.19765e6i −0.627094 + 0.362053i −0.779626 0.626246i \(-0.784591\pi\)
0.152532 + 0.988299i \(0.451257\pi\)
\(150\) 0 0
\(151\) 1.50837e6 2.61258e6i 0.438105 0.758820i −0.559438 0.828872i \(-0.688983\pi\)
0.997543 + 0.0700517i \(0.0223164\pi\)
\(152\) 978101.i 0.278518i
\(153\) 0 0
\(154\) 4588.02 0.00125621
\(155\) 100159. + 57827.1i 0.0268966 + 0.0155287i
\(156\) 0 0
\(157\) −2.79226e6 4.83633e6i −0.721533 1.24973i −0.960385 0.278676i \(-0.910104\pi\)
0.238852 0.971056i \(-0.423229\pi\)
\(158\) 2.31111e6 1.33432e6i 0.585936 0.338290i
\(159\) 0 0
\(160\) −71877.0 + 124495.i −0.0175481 + 0.0303942i
\(161\) 14633.7i 0.00350651i
\(162\) 0 0
\(163\) −2.46039e6 −0.568121 −0.284061 0.958806i \(-0.591682\pi\)
−0.284061 + 0.958806i \(0.591682\pi\)
\(164\) 1.49239e6 + 861631.i 0.338338 + 0.195339i
\(165\) 0 0
\(166\) 94893.6 + 164361.i 0.0207450 + 0.0359313i
\(167\) −3.48381e6 + 2.01138e6i −0.748005 + 0.431861i −0.824973 0.565173i \(-0.808810\pi\)
0.0769675 + 0.997034i \(0.475476\pi\)
\(168\) 0 0
\(169\) 1.98836e6 3.44393e6i 0.411940 0.713501i
\(170\) 475078.i 0.0966981i
\(171\) 0 0
\(172\) −3.94025e6 −0.774352
\(173\) 3.58412e6 + 2.06929e6i 0.692220 + 0.399653i 0.804443 0.594030i \(-0.202464\pi\)
−0.112223 + 0.993683i \(0.535797\pi\)
\(174\) 0 0
\(175\) 46499.4 + 80539.4i 0.00867628 + 0.0150278i
\(176\) 116080. 67019.1i 0.0212922 0.0122931i
\(177\) 0 0
\(178\) 2.87207e6 4.97457e6i 0.509254 0.882055i
\(179\) 4.64610e6i 0.810083i 0.914298 + 0.405042i \(0.132743\pi\)
−0.914298 + 0.405042i \(0.867257\pi\)
\(180\) 0 0
\(181\) 2.01455e6 0.339737 0.169868 0.985467i \(-0.445666\pi\)
0.169868 + 0.985467i \(0.445666\pi\)
\(182\) −27987.4 16158.5i −0.00464246 0.00268032i
\(183\) 0 0
\(184\) −213760. 370243.i −0.0343141 0.0594337i
\(185\) −148654. + 85825.5i −0.0234780 + 0.0135551i
\(186\) 0 0
\(187\) −221484. + 383622.i −0.0338703 + 0.0586650i
\(188\) 3.07368e6i 0.462578i
\(189\) 0 0
\(190\) 758540. 0.110591
\(191\) 3.29614e6 + 1.90303e6i 0.473049 + 0.273115i 0.717515 0.696543i \(-0.245279\pi\)
−0.244466 + 0.969658i \(0.578613\pi\)
\(192\) 0 0
\(193\) 647738. + 1.12191e6i 0.0901005 + 0.156059i 0.907553 0.419937i \(-0.137948\pi\)
−0.817453 + 0.575996i \(0.804614\pi\)
\(194\) 2.04870e6 1.18282e6i 0.280590 0.161999i
\(195\) 0 0
\(196\) −1.88177e6 + 3.25932e6i −0.249918 + 0.432871i
\(197\) 5.99463e6i 0.784086i 0.919947 + 0.392043i \(0.128231\pi\)
−0.919947 + 0.392043i \(0.871769\pi\)
\(198\) 0 0
\(199\) −1.04921e6 −0.133139 −0.0665694 0.997782i \(-0.521205\pi\)
−0.0665694 + 0.997782i \(0.521205\pi\)
\(200\) 2.35294e6 + 1.35847e6i 0.294118 + 0.169809i
\(201\) 0 0
\(202\) 1.89976e6 + 3.29047e6i 0.230486 + 0.399213i
\(203\) −187476. + 108239.i −0.0224108 + 0.0129389i
\(204\) 0 0
\(205\) −668215. + 1.15738e6i −0.0775630 + 0.134343i
\(206\) 3.97110e6i 0.454265i
\(207\) 0 0
\(208\) −944135. −0.104917
\(209\) −612517. 353637.i −0.0670933 0.0387363i
\(210\) 0 0
\(211\) 2.77104e6 + 4.79958e6i 0.294982 + 0.510923i 0.974981 0.222290i \(-0.0713532\pi\)
−0.679999 + 0.733213i \(0.738020\pi\)
\(212\) −3.66669e6 + 2.11696e6i −0.384828 + 0.222180i
\(213\) 0 0
\(214\) −991549. + 1.71741e6i −0.101175 + 0.175240i
\(215\) 3.05576e6i 0.307471i
\(216\) 0 0
\(217\) −28876.1 −0.00282592
\(218\) −3.54867e6 2.04882e6i −0.342528 0.197758i
\(219\) 0 0
\(220\) 51974.9 + 90023.1i 0.00488119 + 0.00845446i
\(221\) 2.70215e6 1.56009e6i 0.250342 0.144535i
\(222\) 0 0
\(223\) −2.06883e6 + 3.58332e6i −0.186557 + 0.323125i −0.944100 0.329659i \(-0.893066\pi\)
0.757543 + 0.652785i \(0.226399\pi\)
\(224\) 35891.9i 0.00319340i
\(225\) 0 0
\(226\) 7.14723e6 0.619174
\(227\) −1.27830e7 7.38025e6i −1.09283 0.630948i −0.158504 0.987358i \(-0.550667\pi\)
−0.934329 + 0.356410i \(0.884000\pi\)
\(228\) 0 0
\(229\) 7.31735e6 + 1.26740e7i 0.609323 + 1.05538i 0.991352 + 0.131228i \(0.0418919\pi\)
−0.382030 + 0.924150i \(0.624775\pi\)
\(230\) 287132. 165776.i 0.0235992 0.0136250i
\(231\) 0 0
\(232\) −3.16219e6 + 5.47708e6i −0.253235 + 0.438617i
\(233\) 1.51778e6i 0.119989i −0.998199 0.0599946i \(-0.980892\pi\)
0.998199 0.0599946i \(-0.0191083\pi\)
\(234\) 0 0
\(235\) 2.38371e6 0.183675
\(236\) 805809. + 465234.i 0.0613050 + 0.0353945i
\(237\) 0 0
\(238\) 59307.8 + 102724.i 0.00439927 + 0.00761977i
\(239\) 1.20904e7 6.98040e6i 0.885619 0.511312i 0.0131121 0.999914i \(-0.495826\pi\)
0.872507 + 0.488602i \(0.162493\pi\)
\(240\) 0 0
\(241\) −1.26582e7 + 2.19246e7i −0.904317 + 1.56632i −0.0824864 + 0.996592i \(0.526286\pi\)
−0.821831 + 0.569731i \(0.807047\pi\)
\(242\) 9.92454e6i 0.700268i
\(243\) 0 0
\(244\) −1.02613e7 −0.706372
\(245\) −2.52768e6 1.45936e6i −0.171879 0.0992346i
\(246\) 0 0
\(247\) 2.49094e6 + 4.31443e6i 0.165300 + 0.286308i
\(248\) −730587. + 421805.i −0.0478979 + 0.0276539i
\(249\) 0 0
\(250\) −2.15028e6 + 3.72440e6i −0.137618 + 0.238361i
\(251\) 3.58400e6i 0.226645i −0.993558 0.113323i \(-0.963851\pi\)
0.993558 0.113323i \(-0.0361494\pi\)
\(252\) 0 0
\(253\) −309143. −0.0190896
\(254\) −1.30998e7 7.56317e6i −0.799398 0.461533i
\(255\) 0 0
\(256\) −524288. 908093.i −0.0312500 0.0541266i
\(257\) 2.00837e7 1.15953e7i 1.18316 0.683098i 0.226417 0.974031i \(-0.427299\pi\)
0.956743 + 0.290933i \(0.0939656\pi\)
\(258\) 0 0
\(259\) 21428.6 37115.4i 0.00123337 0.00213626i
\(260\) 732199.i 0.0416590i
\(261\) 0 0
\(262\) 2.02976e7 1.12860
\(263\) −1.72997e7 9.98800e6i −0.950981 0.549049i −0.0575954 0.998340i \(-0.518343\pi\)
−0.893386 + 0.449291i \(0.851677\pi\)
\(264\) 0 0
\(265\) −1.64176e6 2.84360e6i −0.0882208 0.152803i
\(266\) −164016. + 94694.7i −0.00871448 + 0.00503131i
\(267\) 0 0
\(268\) −8.47710e6 + 1.46828e7i −0.440396 + 0.762788i
\(269\) 1.05394e7i 0.541453i −0.962656 0.270726i \(-0.912736\pi\)
0.962656 0.270726i \(-0.0872639\pi\)
\(270\) 0 0
\(271\) −2.76838e7 −1.39097 −0.695485 0.718540i \(-0.744811\pi\)
−0.695485 + 0.718540i \(0.744811\pi\)
\(272\) 3.00106e6 + 1.73267e6i 0.149131 + 0.0861010i
\(273\) 0 0
\(274\) −4.32901e6 7.49806e6i −0.210444 0.364500i
\(275\) 1.70143e6 982322.i 0.0818119 0.0472341i
\(276\) 0 0
\(277\) −4.08298e6 + 7.07192e6i −0.192104 + 0.332735i −0.945947 0.324320i \(-0.894865\pi\)
0.753843 + 0.657055i \(0.228198\pi\)
\(278\) 1.99555e7i 0.928811i
\(279\) 0 0
\(280\) 27835.1 0.00126800
\(281\) −3.85847e6 2.22769e6i −0.173899 0.100400i 0.410524 0.911850i \(-0.365346\pi\)
−0.584423 + 0.811449i \(0.698679\pi\)
\(282\) 0 0
\(283\) 1.59414e7 + 2.76112e7i 0.703341 + 1.21822i 0.967287 + 0.253685i \(0.0816426\pi\)
−0.263946 + 0.964537i \(0.585024\pi\)
\(284\) −1.74180e7 + 1.00563e7i −0.760402 + 0.439018i
\(285\) 0 0
\(286\) −341356. + 591246.i −0.0145918 + 0.0252738i
\(287\) 333675.i 0.0141149i
\(288\) 0 0
\(289\) 1.26854e7 0.525544
\(290\) −4.24760e6 2.45236e6i −0.174161 0.100552i
\(291\) 0 0
\(292\) −1.10044e6 1.90602e6i −0.0441997 0.0765561i
\(293\) 3.09320e7 1.78586e7i 1.22972 0.709977i 0.262746 0.964865i \(-0.415372\pi\)
0.966971 + 0.254888i \(0.0820385\pi\)
\(294\) 0 0
\(295\) −360800. + 624924.i −0.0140540 + 0.0243423i
\(296\) 1.25206e6i 0.0482782i
\(297\) 0 0
\(298\) 1.35499e7 0.512020
\(299\) 1.88580e6 + 1.08877e6i 0.0705476 + 0.0407307i
\(300\) 0 0
\(301\) 381475. + 660734.i 0.0139884 + 0.0242285i
\(302\) −1.47790e7 + 8.53265e6i −0.536567 + 0.309787i
\(303\) 0 0
\(304\) −2.76649e6 + 4.79170e6i −0.0984709 + 0.170557i
\(305\) 7.95789e6i 0.280478i
\(306\) 0 0
\(307\) −5.01121e6 −0.173192 −0.0865959 0.996244i \(-0.527599\pi\)
−0.0865959 + 0.996244i \(0.527599\pi\)
\(308\) −22476.6 12976.9i −0.000769270 0.000444138i
\(309\) 0 0
\(310\) −327119. 566587.i −0.0109805 0.0190187i
\(311\) −2.52550e7 + 1.45810e7i −0.839587 + 0.484736i −0.857124 0.515111i \(-0.827751\pi\)
0.0175371 + 0.999846i \(0.494417\pi\)
\(312\) 0 0
\(313\) 1.53413e7 2.65719e7i 0.500298 0.866541i −0.499702 0.866197i \(-0.666557\pi\)
1.00000 0.000343995i \(-0.000109497\pi\)
\(314\) 3.15908e7i 1.02040i
\(315\) 0 0
\(316\) −1.50961e7 −0.478415
\(317\) 4.39431e7 + 2.53706e7i 1.37947 + 0.796439i 0.992096 0.125483i \(-0.0400479\pi\)
0.387377 + 0.921922i \(0.373381\pi\)
\(318\) 0 0
\(319\) 2.28661e6 + 3.96052e6i 0.0704401 + 0.122006i
\(320\) 704248. 406598.i 0.0214919 0.0124084i
\(321\) 0 0
\(322\) −41390.3 + 71690.0i −0.00123974 + 0.00214729i
\(323\) 1.82854e7i 0.542620i
\(324\) 0 0
\(325\) −1.38385e7 −0.403125
\(326\) 1.20534e7 + 6.95903e6i 0.347902 + 0.200861i
\(327\) 0 0
\(328\) −4.87412e6 8.44223e6i −0.138126 0.239241i
\(329\) −515420. + 297578.i −0.0144735 + 0.00835628i
\(330\) 0 0
\(331\) 2.10713e7 3.64966e7i 0.581042 1.00639i −0.414314 0.910134i \(-0.635978\pi\)
0.995356 0.0962608i \(-0.0306883\pi\)
\(332\) 1.07360e6i 0.0293378i
\(333\) 0 0
\(334\) 2.27561e7 0.610744
\(335\) −1.13868e7 6.57419e6i −0.302879 0.174867i
\(336\) 0 0
\(337\) −30716.4 53202.3i −0.000802565 0.00139008i 0.865624 0.500695i \(-0.166922\pi\)
−0.866426 + 0.499305i \(0.833589\pi\)
\(338\) −1.94818e7 + 1.12478e7i −0.504521 + 0.291286i
\(339\) 0 0
\(340\) −1.34372e6 + 2.32740e6i −0.0341879 + 0.0592153i
\(341\) 610021.i 0.0153844i
\(342\) 0 0
\(343\) 1.45770e6 0.0361233
\(344\) 1.93032e7 + 1.11447e7i 0.474192 + 0.273775i
\(345\) 0 0
\(346\) −1.17057e7 2.02748e7i −0.282598 0.489473i
\(347\) 2.10694e7 1.21644e7i 0.504271 0.291141i −0.226205 0.974080i \(-0.572632\pi\)
0.730476 + 0.682939i \(0.239298\pi\)
\(348\) 0 0
\(349\) 1.26014e7 2.18263e7i 0.296444 0.513456i −0.678876 0.734253i \(-0.737532\pi\)
0.975320 + 0.220797i \(0.0708658\pi\)
\(350\) 526081.i 0.0122701i
\(351\) 0 0
\(352\) −758234. −0.0173850
\(353\) 5.98516e7 + 3.45553e7i 1.36067 + 0.785581i 0.989713 0.143070i \(-0.0456974\pi\)
0.370954 + 0.928651i \(0.379031\pi\)
\(354\) 0 0
\(355\) −7.79888e6 1.35081e7i −0.174320 0.301931i
\(356\) −2.81404e7 + 1.62469e7i −0.623707 + 0.360097i
\(357\) 0 0
\(358\) 1.31412e7 2.27612e7i 0.286408 0.496073i
\(359\) 1.41061e7i 0.304876i −0.988313 0.152438i \(-0.951288\pi\)
0.988313 0.152438i \(-0.0487124\pi\)
\(360\) 0 0
\(361\) −1.78503e7 −0.379423
\(362\) −9.86925e6 5.69801e6i −0.208046 0.120115i
\(363\) 0 0
\(364\) 91406.4 + 158320.i 0.00189527 + 0.00328271i
\(365\) 1.47817e6 853420.i 0.0303980 0.0175503i
\(366\) 0 0
\(367\) 4.07223e7 7.05331e7i 0.823823 1.42690i −0.0789923 0.996875i \(-0.525170\pi\)
0.902815 0.430028i \(-0.141496\pi\)
\(368\) 2.41842e6i 0.0485275i
\(369\) 0 0
\(370\) 971005. 0.0191697
\(371\) 709980. + 409907.i 0.0139035 + 0.00802719i
\(372\) 0 0
\(373\) −3.79860e7 6.57937e7i −0.731977 1.26782i −0.956037 0.293246i \(-0.905265\pi\)
0.224060 0.974575i \(-0.428069\pi\)
\(374\) 2.17010e6 1.25291e6i 0.0414824 0.0239499i
\(375\) 0 0
\(376\) −8.69368e6 + 1.50579e7i −0.163546 + 0.283270i
\(377\) 3.22127e7i 0.601179i
\(378\) 0 0
\(379\) −4.48086e7 −0.823083 −0.411541 0.911391i \(-0.635009\pi\)
−0.411541 + 0.911391i \(0.635009\pi\)
\(380\) −3.71607e6 2.14548e6i −0.0677226 0.0390996i
\(381\) 0 0
\(382\) −1.07652e7 1.86458e7i −0.193121 0.334496i
\(383\) −7.76185e7 + 4.48131e7i −1.38156 + 0.797643i −0.992344 0.123504i \(-0.960587\pi\)
−0.389214 + 0.921147i \(0.627253\pi\)
\(384\) 0 0
\(385\) 10063.9 17431.2i 0.000176353 0.000305453i
\(386\) 7.32832e6i 0.127421i
\(387\) 0 0
\(388\) −1.33820e7 −0.229101
\(389\) −3.03701e7 1.75342e7i −0.515938 0.297877i 0.219333 0.975650i \(-0.429612\pi\)
−0.735271 + 0.677773i \(0.762945\pi\)
\(390\) 0 0
\(391\) −3.99619e6 6.92160e6i −0.0668522 0.115791i
\(392\) 1.84375e7 1.06449e7i 0.306086 0.176719i
\(393\) 0 0
\(394\) 1.69554e7 2.93676e7i 0.277216 0.480152i
\(395\) 1.17074e7i 0.189963i
\(396\) 0 0
\(397\) 8.17666e7 1.30679 0.653393 0.757019i \(-0.273345\pi\)
0.653393 + 0.757019i \(0.273345\pi\)
\(398\) 5.14008e6 + 2.96762e6i 0.0815305 + 0.0470717i
\(399\) 0 0
\(400\) −7.68467e6 1.33102e7i −0.120073 0.207973i
\(401\) 5.28941e7 3.05384e7i 0.820303 0.473602i −0.0302179 0.999543i \(-0.509620\pi\)
0.850521 + 0.525941i \(0.176287\pi\)
\(402\) 0 0
\(403\) 2.14843e6 3.72119e6i 0.0328251 0.0568547i
\(404\) 2.14933e7i 0.325956i
\(405\) 0 0
\(406\) 1.22459e6 0.0182984
\(407\) −784080. 452689.i −0.0116299 0.00671455i
\(408\) 0 0
\(409\) −3.34641e7 5.79615e7i −0.489113 0.847168i 0.510809 0.859694i \(-0.329346\pi\)
−0.999922 + 0.0125261i \(0.996013\pi\)
\(410\) 6.54714e6 3.78000e6i 0.0949949 0.0548453i
\(411\) 0 0
\(412\) 1.12320e7 1.94544e7i 0.160607 0.278180i
\(413\) 180166.i 0.00255755i
\(414\) 0 0
\(415\) 832601. 0.0116491
\(416\) 4.62530e6 + 2.67042e6i 0.0642480 + 0.0370936i
\(417\) 0 0
\(418\) 2.00047e6 + 3.46492e6i 0.0273907 + 0.0474421i
\(419\) −8.43503e7 + 4.86997e7i −1.14669 + 0.662040i −0.948078 0.318039i \(-0.896976\pi\)
−0.198609 + 0.980079i \(0.563642\pi\)
\(420\) 0 0
\(421\) −3.79673e7 + 6.57613e7i −0.508819 + 0.881300i 0.491129 + 0.871087i \(0.336584\pi\)
−0.999948 + 0.0102133i \(0.996749\pi\)
\(422\) 3.13507e7i 0.417167i
\(423\) 0 0
\(424\) 2.39507e7 0.314211
\(425\) 4.39877e7 + 2.53963e7i 0.573012 + 0.330829i
\(426\) 0 0
\(427\) 993448. + 1.72070e6i 0.0127603 + 0.0221015i
\(428\) 9.71515e6 5.60905e6i 0.123913 0.0715415i
\(429\) 0 0
\(430\) −8.64299e6 + 1.49701e7i −0.108707 + 0.188287i
\(431\) 1.10356e8i 1.37836i −0.724590 0.689180i \(-0.757971\pi\)
0.724590 0.689180i \(-0.242029\pi\)
\(432\) 0 0
\(433\) 7.04803e7 0.868168 0.434084 0.900872i \(-0.357072\pi\)
0.434084 + 0.900872i \(0.357072\pi\)
\(434\) 141463. + 81673.9i 0.00173051 + 0.000999112i
\(435\) 0 0
\(436\) 1.15899e7 + 2.00743e7i 0.139836 + 0.242204i
\(437\) 1.10515e7 6.38057e6i 0.132427 0.0764567i
\(438\) 0 0
\(439\) 5.59868e6 9.69720e6i 0.0661747 0.114618i −0.831040 0.556213i \(-0.812254\pi\)
0.897214 + 0.441595i \(0.145587\pi\)
\(440\) 588029.i 0.00690304i
\(441\) 0 0
\(442\) −1.76504e7 −0.204403
\(443\) −1.34069e8 7.74049e7i −1.54212 0.890343i −0.998705 0.0508793i \(-0.983798\pi\)
−0.543415 0.839464i \(-0.682869\pi\)
\(444\) 0 0
\(445\) −1.25998e7 2.18236e7i −0.142983 0.247654i
\(446\) 2.02703e7 1.17031e7i 0.228484 0.131915i
\(447\) 0 0
\(448\) −101518. + 175834.i −0.00112904 + 0.00195555i
\(449\) 9.20846e7i 1.01730i 0.860974 + 0.508648i \(0.169855\pi\)
−0.860974 + 0.508648i \(0.830145\pi\)
\(450\) 0 0
\(451\) −7.04904e6 −0.0768423
\(452\) −3.50142e7 2.02154e7i −0.379165 0.218911i
\(453\) 0 0
\(454\) 4.17490e7 + 7.23114e7i 0.446147 + 0.772750i
\(455\) −122781. + 70887.8i −0.00130346 + 0.000752553i
\(456\) 0 0
\(457\) −4.18331e7 + 7.24571e7i −0.438300 + 0.759159i −0.997559 0.0698349i \(-0.977753\pi\)
0.559258 + 0.828994i \(0.311086\pi\)
\(458\) 8.27864e7i 0.861712i
\(459\) 0 0
\(460\) −1.87554e6 −0.0192687
\(461\) 1.03069e8 + 5.95070e7i 1.05203 + 0.607387i 0.923216 0.384282i \(-0.125551\pi\)
0.128809 + 0.991669i \(0.458884\pi\)
\(462\) 0 0
\(463\) 5.67866e7 + 9.83573e7i 0.572141 + 0.990977i 0.996346 + 0.0854109i \(0.0272203\pi\)
−0.424205 + 0.905566i \(0.639446\pi\)
\(464\) 3.09830e7 1.78881e7i 0.310149 0.179065i
\(465\) 0 0
\(466\) −4.29294e6 + 7.43559e6i −0.0424226 + 0.0734781i
\(467\) 1.34722e8i 1.32278i 0.750044 + 0.661388i \(0.230032\pi\)
−0.750044 + 0.661388i \(0.769968\pi\)
\(468\) 0 0
\(469\) 3.28284e6 0.0318223
\(470\) −1.16778e7 6.74215e6i −0.112478 0.0649389i
\(471\) 0 0
\(472\) −2.63176e6 4.55834e6i −0.0250277 0.0433492i
\(473\) 1.39583e7 8.05884e6i 0.131901 0.0761534i
\(474\) 0 0
\(475\) −4.05494e7 + 7.02336e7i −0.378358 + 0.655336i
\(476\) 670991.i 0.00622151i
\(477\) 0 0
\(478\) −7.89742e7 −0.723105
\(479\) −1.39409e8 8.04877e7i −1.26848 0.732357i −0.293779 0.955873i \(-0.594913\pi\)
−0.974700 + 0.223516i \(0.928246\pi\)
\(480\) 0 0
\(481\) 3.18864e6 + 5.52289e6i 0.0286530 + 0.0496285i
\(482\) 1.24025e8 7.16056e7i 1.10756 0.639449i
\(483\) 0 0
\(484\) 2.80708e7 4.86201e7i 0.247582 0.428825i
\(485\) 1.03781e7i 0.0909687i
\(486\) 0 0
\(487\) 1.14964e7 0.0995351 0.0497676 0.998761i \(-0.484152\pi\)
0.0497676 + 0.998761i \(0.484152\pi\)
\(488\) 5.02700e7 + 2.90234e7i 0.432563 + 0.249740i
\(489\) 0 0
\(490\) 8.25537e6 + 1.42987e7i 0.0701695 + 0.121537i
\(491\) −1.20638e8 + 6.96503e7i −1.01915 + 0.588408i −0.913858 0.406033i \(-0.866912\pi\)
−0.105294 + 0.994441i \(0.533578\pi\)
\(492\) 0 0
\(493\) −5.91164e7 + 1.02393e8i −0.493364 + 0.854532i
\(494\) 2.81818e7i 0.233769i
\(495\) 0 0
\(496\) 4.77217e6 0.0391085
\(497\) 3.37264e6 + 1.94720e6i 0.0274727 + 0.0158614i
\(498\) 0 0
\(499\) 4.67348e7 + 8.09470e7i 0.376130 + 0.651477i 0.990496 0.137545i \(-0.0439211\pi\)
−0.614365 + 0.789022i \(0.710588\pi\)
\(500\) 2.10684e7 1.21638e7i 0.168547 0.0973107i
\(501\) 0 0
\(502\) −1.01371e7 + 1.75579e7i −0.0801313 + 0.138791i
\(503\) 2.32808e8i 1.82934i 0.404200 + 0.914671i \(0.367550\pi\)
−0.404200 + 0.914671i \(0.632450\pi\)
\(504\) 0 0
\(505\) 1.66686e7 0.129427
\(506\) 1.51449e6 + 874389.i 0.0116900 + 0.00674921i
\(507\) 0 0
\(508\) 4.27837e7 + 7.41036e7i 0.326353 + 0.565260i
\(509\) 1.48895e8 8.59645e7i 1.12908 0.651877i 0.185380 0.982667i \(-0.440648\pi\)
0.943705 + 0.330790i \(0.107315\pi\)
\(510\) 0 0
\(511\) −213079. + 369063.i −0.00159690 + 0.00276591i
\(512\) 5.93164e6i 0.0441942i
\(513\) 0 0
\(514\) −1.31186e8 −0.966046
\(515\) 1.50873e7 + 8.71067e6i 0.110456 + 0.0637719i
\(516\) 0 0
\(517\) 6.28648e6 + 1.08885e7i 0.0454921 + 0.0787946i
\(518\) −209956. + 121218.i −0.00151057 + 0.000872126i
\(519\) 0 0
\(520\) −2.07097e6 + 3.58703e6i −0.0147287 + 0.0255108i
\(521\) 2.02142e8i 1.42937i 0.699447 + 0.714684i \(0.253430\pi\)
−0.699447 + 0.714684i \(0.746570\pi\)
\(522\) 0 0
\(523\) −8.40337e7 −0.587419 −0.293710 0.955895i \(-0.594890\pi\)
−0.293710 + 0.955895i \(0.594890\pi\)
\(524\) −9.94376e7 5.74103e7i −0.691125 0.399021i
\(525\) 0 0
\(526\) 5.65006e7 + 9.78620e7i 0.388236 + 0.672445i
\(527\) −1.36581e7 + 7.88553e6i −0.0933168 + 0.0538765i
\(528\) 0 0
\(529\) −7.12291e7 + 1.23372e8i −0.481161 + 0.833395i
\(530\) 1.85743e7i 0.124763i
\(531\) 0 0
\(532\) 1.07135e6 0.00711534
\(533\) 4.29998e7 + 2.48259e7i 0.283978 + 0.163955i
\(534\) 0 0
\(535\) 4.34995e6 + 7.53433e6i 0.0284068 + 0.0492021i
\(536\) 8.30583e7 4.79537e7i 0.539372 0.311407i
\(537\) 0 0
\(538\) −2.98100e7 + 5.16325e7i −0.191432 + 0.331571i
\(539\) 1.53948e7i 0.0983125i
\(540\) 0 0
\(541\) 5.27746e7 0.333299 0.166649 0.986016i \(-0.446705\pi\)
0.166649 + 0.986016i \(0.446705\pi\)
\(542\) 1.35622e8 + 7.83016e7i 0.851792 + 0.491782i
\(543\) 0 0
\(544\) −9.80144e6 1.69766e7i −0.0608826 0.105452i
\(545\) −1.55681e7 + 8.98824e6i −0.0961713 + 0.0555246i
\(546\) 0 0
\(547\) −3.12323e7 + 5.40959e7i −0.190828 + 0.330523i −0.945525 0.325550i \(-0.894451\pi\)
0.754697 + 0.656073i \(0.227784\pi\)
\(548\) 4.89771e7i 0.297613i
\(549\) 0 0
\(550\) −1.11137e7 −0.0667991
\(551\) −1.63487e8 9.43892e7i −0.977300 0.564245i
\(552\) 0 0
\(553\) 1.46153e6 + 2.53144e6i 0.00864236 + 0.0149690i
\(554\) 4.00048e7 2.30968e7i 0.235279 0.135838i
\(555\) 0 0
\(556\) 5.64426e7 9.77614e7i 0.328384 0.568778i
\(557\) 1.98446e8i 1.14836i 0.818730 + 0.574178i \(0.194678\pi\)
−0.818730 + 0.574178i \(0.805322\pi\)
\(558\) 0 0
\(559\) −1.13529e8 −0.649939
\(560\) −136363. 78729.4i −0.000776486 0.000448304i
\(561\) 0 0
\(562\) 1.26017e7 + 2.18268e7i 0.0709938 + 0.122965i
\(563\) −8.55525e7 + 4.93937e7i −0.479410 + 0.276788i −0.720171 0.693797i \(-0.755937\pi\)
0.240760 + 0.970585i \(0.422603\pi\)
\(564\) 0 0
\(565\) 1.56775e7 2.71543e7i 0.0869226 0.150554i
\(566\) 1.80356e8i 0.994674i
\(567\) 0 0
\(568\) 1.13774e8 0.620865
\(569\) 1.42132e8 + 8.20597e7i 0.771531 + 0.445444i 0.833421 0.552639i \(-0.186379\pi\)
−0.0618893 + 0.998083i \(0.519713\pi\)
\(570\) 0 0
\(571\) 9.76077e7 + 1.69061e8i 0.524295 + 0.908106i 0.999600 + 0.0282845i \(0.00900442\pi\)
−0.475305 + 0.879821i \(0.657662\pi\)
\(572\) 3.34459e6 1.93100e6i 0.0178713 0.0103180i
\(573\) 0 0
\(574\) −943775. + 1.63467e6i −0.00499037 + 0.00864357i
\(575\) 3.54476e7i 0.186459i
\(576\) 0 0
\(577\) 1.93319e8 1.00634 0.503172 0.864186i \(-0.332166\pi\)
0.503172 + 0.864186i \(0.332166\pi\)
\(578\) −6.21453e7 3.58796e7i −0.321829 0.185808i
\(579\) 0 0
\(580\) 1.38726e7 + 2.40281e7i 0.0711008 + 0.123150i
\(581\) −180030. + 103940.i −0.000917944 + 0.000529975i
\(582\) 0 0
\(583\) 8.65948e6 1.49987e7i 0.0437005 0.0756915i
\(584\) 1.24501e7i 0.0625078i
\(585\) 0 0
\(586\) −2.02047e8 −1.00406
\(587\) −2.90014e7 1.67440e7i −0.143385 0.0827835i 0.426591 0.904445i \(-0.359714\pi\)
−0.569976 + 0.821661i \(0.693048\pi\)
\(588\) 0 0
\(589\) −1.25906e7 2.18075e7i −0.0616168 0.106723i
\(590\) 3.53510e6 2.04099e6i 0.0172126 0.00993769i
\(591\) 0 0
\(592\) −3.54137e6 + 6.13383e6i −0.0170689 + 0.0295642i
\(593\) 3.75231e8i 1.79943i −0.436479 0.899715i \(-0.643775\pi\)
0.436479 0.899715i \(-0.356225\pi\)
\(594\) 0 0
\(595\) 520369. 0.00247036
\(596\) −6.63806e7 3.83249e7i −0.313547 0.181026i
\(597\) 0 0
\(598\) −6.15900e6 1.06677e7i −0.0288009 0.0498847i
\(599\) −2.57196e8 + 1.48492e8i −1.19670 + 0.690913i −0.959817 0.280626i \(-0.909458\pi\)
−0.236879 + 0.971539i \(0.576125\pi\)
\(600\) 0 0
\(601\) −7.77944e7 + 1.34744e8i −0.358365 + 0.620706i −0.987688 0.156438i \(-0.949999\pi\)
0.629323 + 0.777144i \(0.283332\pi\)
\(602\) 4.31590e6i 0.0197825i
\(603\) 0 0
\(604\) 9.65360e7 0.438105
\(605\) 3.77060e7 + 2.17696e7i 0.170273 + 0.0983069i
\(606\) 0 0
\(607\) −1.11404e8 1.92958e8i −0.498122 0.862773i 0.501875 0.864940i \(-0.332644\pi\)
−0.999998 + 0.00216674i \(0.999310\pi\)
\(608\) 2.71059e7 1.56496e7i 0.120602 0.0696294i
\(609\) 0 0
\(610\) −2.25083e7 + 3.89855e7i −0.0991639 + 0.171757i
\(611\) 8.85611e7i 0.388257i
\(612\) 0 0
\(613\) 1.22144e8 0.530262 0.265131 0.964212i \(-0.414585\pi\)
0.265131 + 0.964212i \(0.414585\pi\)
\(614\) 2.45498e7 + 1.41738e7i 0.106058 + 0.0612326i
\(615\) 0 0
\(616\) 73408.4 + 127147.i 0.000314053 + 0.000543956i
\(617\) 3.26624e8 1.88577e8i 1.39057 0.802846i 0.397191 0.917736i \(-0.369985\pi\)
0.993378 + 0.114890i \(0.0366516\pi\)
\(618\) 0 0
\(619\) 2.18072e8 3.77712e8i 0.919450 1.59253i 0.119198 0.992871i \(-0.461968\pi\)
0.800252 0.599663i \(-0.204699\pi\)
\(620\) 3.70093e6i 0.0155287i
\(621\) 0 0
\(622\) 1.64965e8 0.685520
\(623\) 5.44882e6 + 3.14588e6i 0.0225340 + 0.0130100i
\(624\) 0 0
\(625\) −1.07825e8 1.86759e8i −0.441653 0.764966i
\(626\) −1.50313e8 + 8.67834e7i −0.612737 + 0.353764i
\(627\) 0 0
\(628\) 8.93522e7 1.54763e8i 0.360767 0.624866i
\(629\) 2.34070e7i 0.0940577i
\(630\) 0 0
\(631\) −8.46175e7 −0.336800 −0.168400 0.985719i \(-0.553860\pi\)
−0.168400 + 0.985719i \(0.553860\pi\)
\(632\) 7.39556e7 + 4.26983e7i 0.292968 + 0.169145i
\(633\) 0 0
\(634\) −1.43518e8 2.48580e8i −0.563167 0.975434i
\(635\) −5.74691e7 + 3.31798e7i −0.224447 + 0.129584i
\(636\) 0 0
\(637\) −5.42189e7 + 9.39099e7i −0.209765 + 0.363323i
\(638\) 2.58700e7i 0.0996173i
\(639\) 0 0
\(640\) −4.60013e6 −0.0175481
\(641\) 9.93835e7 + 5.73791e7i 0.377347 + 0.217861i 0.676663 0.736293i \(-0.263425\pi\)
−0.299317 + 0.954154i \(0.596759\pi\)
\(642\) 0 0
\(643\) −1.03843e7 1.79862e7i −0.0390612 0.0676560i 0.845834 0.533446i \(-0.179103\pi\)
−0.884895 + 0.465790i \(0.845770\pi\)
\(644\) 405540. 234139.i 0.00151836 0.000876628i
\(645\) 0 0
\(646\) −5.17188e7 + 8.95796e7i −0.191845 + 0.332286i
\(647\) 5.18773e8i 1.91542i −0.287734 0.957710i \(-0.592902\pi\)
0.287734 0.957710i \(-0.407098\pi\)
\(648\) 0 0
\(649\) −3.80610e6 −0.0139234
\(650\) 6.77946e7 + 3.91413e7i 0.246863 + 0.142526i
\(651\) 0 0
\(652\) −3.93662e7 6.81843e7i −0.142030 0.246004i
\(653\) −1.08224e8 + 6.24831e7i −0.388673 + 0.224400i −0.681585 0.731739i \(-0.738709\pi\)
0.292912 + 0.956139i \(0.405376\pi\)
\(654\) 0 0
\(655\) 4.45231e7 7.71162e7i 0.158439 0.274424i
\(656\) 5.51444e7i 0.195339i
\(657\) 0 0
\(658\) 3.36671e6 0.0118176
\(659\) −4.37563e8 2.52627e8i −1.52892 0.882721i −0.999408 0.0344179i \(-0.989042\pi\)
−0.529511 0.848303i \(-0.677624\pi\)
\(660\) 0 0
\(661\) −2.09467e8 3.62807e8i −0.725289 1.25624i −0.958855 0.283896i \(-0.908373\pi\)
0.233567 0.972341i \(-0.424960\pi\)
\(662\) −2.06456e8 + 1.19197e8i −0.711629 + 0.410859i
\(663\) 0 0
\(664\) −3.03659e6 + 5.25954e6i −0.0103725 + 0.0179657i
\(665\) 830856.i 0.00282528i
\(666\) 0 0
\(667\) −8.25134e7 −0.278065
\(668\) −1.11482e8 6.43641e7i −0.374003 0.215931i
\(669\) 0 0
\(670\) 3.71893e7 + 6.44137e7i 0.123650 + 0.214168i
\(671\) 3.63506e7 2.09871e7i 0.120322 0.0694679i
\(672\) 0 0
\(673\) 1.99125e8 3.44894e8i 0.653250 1.13146i −0.329079 0.944302i \(-0.606738\pi\)
0.982329 0.187160i \(-0.0599284\pi\)
\(674\) 347516.i 0.00113500i
\(675\) 0 0
\(676\) 1.27255e8 0.411940
\(677\) 4.73100e8 + 2.73145e8i 1.52471 + 0.880292i 0.999571 + 0.0292753i \(0.00931996\pi\)
0.525139 + 0.851017i \(0.324013\pi\)
\(678\) 0 0
\(679\) 1.29558e6 + 2.24401e6i 0.00413862 + 0.00716829i
\(680\) 1.31657e7 7.60124e6i 0.0418715 0.0241745i
\(681\) 0 0
\(682\) 1.72540e6 2.98848e6i 0.00543922 0.00942101i
\(683\) 3.24992e7i 0.102002i −0.998699 0.0510012i \(-0.983759\pi\)
0.998699 0.0510012i \(-0.0162412\pi\)
\(684\) 0 0
\(685\) −3.79829e7 −0.118173
\(686\) −7.14126e6 4.12301e6i −0.0221209 0.0127715i
\(687\) 0 0
\(688\) −6.30440e7 1.09195e8i −0.193588 0.335304i
\(689\) −1.05647e8 + 6.09955e7i −0.322999 + 0.186483i
\(690\) 0 0
\(691\) 1.43850e8 2.49156e8i 0.435989 0.755156i −0.561386 0.827554i \(-0.689732\pi\)
0.997376 + 0.0723981i \(0.0230652\pi\)
\(692\) 1.32435e8i 0.399653i
\(693\) 0 0
\(694\) −1.37625e8 −0.411736
\(695\) 7.58163e7 + 4.37725e7i 0.225844 + 0.130391i
\(696\) 0 0
\(697\) −9.11205e7 1.57825e8i −0.269103 0.466099i
\(698\) −1.23468e8 + 7.12843e7i −0.363068 + 0.209618i
\(699\) 0 0
\(700\) −1.48798e6 + 2.57726e6i −0.00433814 + 0.00751388i
\(701\) 2.82907e8i 0.821278i −0.911798 0.410639i \(-0.865306\pi\)
0.911798 0.410639i \(-0.134694\pi\)
\(702\) 0 0
\(703\) 3.73732e7 0.107571
\(704\) 3.71457e6 + 2.14461e6i 0.0106461 + 0.00614654i
\(705\) 0 0
\(706\) −1.95475e8 3.38572e8i −0.555490 0.962137i
\(707\) −3.60417e6 + 2.08087e6i −0.0101988 + 0.00588826i
\(708\) 0 0
\(709\) 1.19975e8 2.07803e8i 0.336629 0.583059i −0.647167 0.762348i \(-0.724046\pi\)
0.983796 + 0.179289i \(0.0573798\pi\)
\(710\) 8.82343e7i 0.246526i
\(711\) 0 0
\(712\) 1.83812e8 0.509254
\(713\) −9.53187e6 5.50323e6i −0.0262972 0.0151827i
\(714\) 0 0
\(715\) 1.49754e6 + 2.59381e6i 0.00409694 + 0.00709611i
\(716\) −1.28757e8 + 7.43376e7i −0.350776 + 0.202521i
\(717\) 0 0
\(718\) −3.98980e7 + 6.91054e7i −0.107790 + 0.186698i
\(719\) 2.12836e7i 0.0572611i 0.999590 + 0.0286305i \(0.00911463\pi\)
−0.999590 + 0.0286305i \(0.990885\pi\)
\(720\) 0 0
\(721\) −4.34969e6 −0.0116052
\(722\) 8.74482e7 + 5.04882e7i 0.232348 + 0.134146i
\(723\) 0 0
\(724\) 3.22328e7 + 5.58289e7i 0.0849342 + 0.147110i
\(725\) 4.54129e8 2.62192e8i 1.19170 0.688026i
\(726\) 0 0
\(727\) 8.88685e7 1.53925e8i 0.231283 0.400595i −0.726903 0.686741i \(-0.759041\pi\)
0.958186 + 0.286146i \(0.0923742\pi\)
\(728\) 1.03414e6i 0.00268032i
\(729\) 0 0
\(730\) −9.65535e6 −0.0248199
\(731\) 3.60869e8 + 2.08348e8i 0.923841 + 0.533380i
\(732\) 0 0
\(733\) 2.61308e8 + 4.52599e8i 0.663501 + 1.14922i 0.979690 + 0.200520i \(0.0642633\pi\)
−0.316189 + 0.948696i \(0.602403\pi\)
\(734\) −3.98995e8 + 2.30360e8i −1.00897 + 0.582531i
\(735\) 0 0
\(736\) 6.84031e6 1.18478e7i 0.0171570 0.0297169i
\(737\) 6.93515e7i 0.173242i
\(738\) 0 0
\(739\) −5.12661e8 −1.27027 −0.635137 0.772400i \(-0.719056\pi\)
−0.635137 + 0.772400i \(0.719056\pi\)
\(740\) −4.75693e6 2.74642e6i −0.0117390 0.00677753i
\(741\) 0 0
\(742\) −2.31879e6 4.01625e6i −0.00567608 0.00983127i
\(743\) −9.47357e7 + 5.46957e7i −0.230966 + 0.133348i −0.611017 0.791617i \(-0.709239\pi\)
0.380052 + 0.924965i \(0.375906\pi\)
\(744\) 0 0
\(745\) 2.97219e7 5.14798e7i 0.0718798 0.124500i
\(746\) 4.29763e8i 1.03517i
\(747\) 0 0
\(748\) −1.41750e7 −0.0338703
\(749\) −1.88114e6 1.08608e6i −0.00447689 0.00258473i
\(750\) 0 0
\(751\) 1.80758e8 + 3.13082e8i 0.426755 + 0.739161i 0.996583 0.0826034i \(-0.0263235\pi\)
−0.569828 + 0.821764i \(0.692990\pi\)
\(752\) 8.51803e7 4.91789e7i 0.200302 0.115645i
\(753\) 0 0
\(754\) −9.11114e7 + 1.57810e8i −0.212549 + 0.368145i
\(755\) 7.48659e7i 0.173958i
\(756\) 0 0
\(757\) 8.46631e7 0.195167 0.0975835 0.995227i \(-0.468889\pi\)
0.0975835 + 0.995227i \(0.468889\pi\)
\(758\) 2.19516e8 + 1.26738e8i 0.504033 + 0.291004i
\(759\) 0 0
\(760\) 1.21366e7 + 2.10213e7i 0.0276476 + 0.0478871i
\(761\) 8.57072e7 4.94831e7i 0.194475 0.112280i −0.399601 0.916689i \(-0.630851\pi\)
0.594076 + 0.804409i \(0.297518\pi\)
\(762\) 0 0
\(763\) 2.24415e6 3.88698e6i 0.00505217 0.00875062i
\(764\) 1.21794e8i 0.273115i
\(765\) 0 0
\(766\) 5.07002e8 1.12804
\(767\) 2.32175e7 + 1.34047e7i 0.0514553 + 0.0297077i
\(768\) 0 0
\(769\) 2.70757e7 + 4.68965e7i 0.0595390 + 0.103124i 0.894259 0.447551i \(-0.147704\pi\)
−0.834720 + 0.550675i \(0.814370\pi\)
\(770\) −98605.5 + 56929.9i −0.000215988 + 0.000124701i
\(771\) 0 0
\(772\) −2.07276e7 + 3.59013e7i −0.0450503 + 0.0780293i
\(773\) 9.36821e7i 0.202823i −0.994845 0.101412i \(-0.967664\pi\)
0.994845 0.101412i \(-0.0323359\pi\)
\(774\) 0 0
\(775\)