Properties

Label 84.9.m.b.61.4
Level $84$
Weight $9$
Character 84.61
Analytic conductor $34.220$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [84,9,Mod(61,84)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(84, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 5]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("84.61");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 84.m (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(34.2198032451\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + \cdots + 45\!\cdots\!96 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{20}\cdot 3^{10}\cdot 7^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 61.4
Root \(-122.377 - 211.963i\) of defining polynomial
Character \(\chi\) \(=\) 84.61
Dual form 84.9.m.b.73.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(40.5000 - 23.3827i) q^{3} +(-133.903 - 77.3091i) q^{5} +(-2234.88 + 877.558i) q^{7} +(1093.50 - 1894.00i) q^{9} +O(q^{10})\) \(q+(40.5000 - 23.3827i) q^{3} +(-133.903 - 77.3091i) q^{5} +(-2234.88 + 877.558i) q^{7} +(1093.50 - 1894.00i) q^{9} +(3950.92 + 6843.20i) q^{11} +4177.64i q^{13} -7230.78 q^{15} +(110620. - 63866.3i) q^{17} +(139247. + 80394.4i) q^{19} +(-69993.0 + 87798.6i) q^{21} +(-16422.4 + 28444.4i) q^{23} +(-183359. - 317587. i) q^{25} -102276. i q^{27} +659560. q^{29} +(-5163.53 + 2981.17i) q^{31} +(320025. + 184766. i) q^{33} +(367101. + 55268.8i) q^{35} +(329534. - 570770. i) q^{37} +(97684.5 + 169195. i) q^{39} -1.10208e6i q^{41} +4.57153e6 q^{43} +(-292847. + 169075. i) q^{45} +(-1.35905e6 - 784649. i) q^{47} +(4.22459e6 - 3.92247e6i) q^{49} +(2.98673e6 - 5.17317e6i) q^{51} +(4.31027e6 + 7.46560e6i) q^{53} -1.22177e6i q^{55} +7.51934e6 q^{57} +(1.85511e7 - 1.07105e7i) q^{59} +(2.16597e7 + 1.25052e7i) q^{61} +(-781750. + 5.19247e6i) q^{63} +(322970. - 559400. i) q^{65} +(-9.65705e6 - 1.67265e7i) q^{67} +1.53600e6i q^{69} +9.50918e6 q^{71} +(6.91695e6 - 3.99350e6i) q^{73} +(-1.48521e7 - 8.57486e6i) q^{75} +(-1.48351e7 - 1.18266e7i) q^{77} +(-1.32777e6 + 2.29977e6i) q^{79} +(-2.39148e6 - 4.14217e6i) q^{81} +5.37421e7i q^{83} -1.97498e7 q^{85} +(2.67122e7 - 1.54223e7i) q^{87} +(-3.33121e7 - 1.92328e7i) q^{89} +(-3.66612e6 - 9.33654e6i) q^{91} +(-139415. + 241475. i) q^{93} +(-1.24304e7 - 2.15302e7i) q^{95} +2.56754e7i q^{97} +1.72813e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 486 q^{3} + 285 q^{5} + 198 q^{7} + 13122 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 486 q^{3} + 285 q^{5} + 198 q^{7} + 13122 q^{9} - 17919 q^{11} + 15390 q^{15} - 205782 q^{17} + 74313 q^{19} - 39609 q^{21} - 62832 q^{23} + 878679 q^{25} - 575454 q^{29} + 1442952 q^{31} - 1451439 q^{33} - 3989514 q^{35} - 2058621 q^{37} - 930933 q^{39} + 7721322 q^{43} + 623295 q^{45} + 12088194 q^{47} - 16964694 q^{49} - 5556114 q^{51} - 5506743 q^{53} + 4012902 q^{57} + 7511901 q^{59} - 37215576 q^{61} - 3641355 q^{63} + 5047122 q^{65} - 36824553 q^{67} - 30011556 q^{71} + 95080185 q^{73} + 71172999 q^{75} - 38333727 q^{77} + 8514456 q^{79} - 28697814 q^{81} + 20121540 q^{85} - 23305887 q^{87} + 83038554 q^{89} - 198538635 q^{91} + 38959704 q^{93} - 221605224 q^{95} - 78377706 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(43\) \(73\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 40.5000 23.3827i 0.500000 0.288675i
\(4\) 0 0
\(5\) −133.903 77.3091i −0.214245 0.123695i 0.389037 0.921222i \(-0.372808\pi\)
−0.603283 + 0.797527i \(0.706141\pi\)
\(6\) 0 0
\(7\) −2234.88 + 877.558i −0.930813 + 0.365497i
\(8\) 0 0
\(9\) 1093.50 1894.00i 0.166667 0.288675i
\(10\) 0 0
\(11\) 3950.92 + 6843.20i 0.269853 + 0.467400i 0.968824 0.247751i \(-0.0796914\pi\)
−0.698970 + 0.715151i \(0.746358\pi\)
\(12\) 0 0
\(13\) 4177.64i 0.146271i 0.997322 + 0.0731354i \(0.0233005\pi\)
−0.997322 + 0.0731354i \(0.976699\pi\)
\(14\) 0 0
\(15\) −7230.78 −0.142830
\(16\) 0 0
\(17\) 110620. 63866.3i 1.32445 0.764674i 0.340019 0.940419i \(-0.389567\pi\)
0.984436 + 0.175745i \(0.0562333\pi\)
\(18\) 0 0
\(19\) 139247. + 80394.4i 1.06849 + 0.616895i 0.927769 0.373154i \(-0.121724\pi\)
0.140724 + 0.990049i \(0.455057\pi\)
\(20\) 0 0
\(21\) −69993.0 + 87798.6i −0.359896 + 0.451451i
\(22\) 0 0
\(23\) −16422.4 + 28444.4i −0.0586847 + 0.101645i −0.893875 0.448316i \(-0.852024\pi\)
0.835191 + 0.549961i \(0.185357\pi\)
\(24\) 0 0
\(25\) −183359. 317587.i −0.469399 0.813023i
\(26\) 0 0
\(27\) 102276.i 0.192450i
\(28\) 0 0
\(29\) 659560. 0.932528 0.466264 0.884646i \(-0.345600\pi\)
0.466264 + 0.884646i \(0.345600\pi\)
\(30\) 0 0
\(31\) −5163.53 + 2981.17i −0.00559114 + 0.00322804i −0.502793 0.864407i \(-0.667694\pi\)
0.497202 + 0.867635i \(0.334361\pi\)
\(32\) 0 0
\(33\) 320025. + 184766.i 0.269853 + 0.155800i
\(34\) 0 0
\(35\) 367101. + 55268.8i 0.244632 + 0.0368305i
\(36\) 0 0
\(37\) 329534. 570770.i 0.175830 0.304547i −0.764618 0.644484i \(-0.777072\pi\)
0.940448 + 0.339937i \(0.110406\pi\)
\(38\) 0 0
\(39\) 97684.5 + 169195.i 0.0422248 + 0.0731354i
\(40\) 0 0
\(41\) 1.10208e6i 0.390013i −0.980802 0.195007i \(-0.937527\pi\)
0.980802 0.195007i \(-0.0624728\pi\)
\(42\) 0 0
\(43\) 4.57153e6 1.33717 0.668586 0.743635i \(-0.266900\pi\)
0.668586 + 0.743635i \(0.266900\pi\)
\(44\) 0 0
\(45\) −292847. + 169075.i −0.0714151 + 0.0412315i
\(46\) 0 0
\(47\) −1.35905e6 784649.i −0.278512 0.160799i 0.354237 0.935156i \(-0.384740\pi\)
−0.632750 + 0.774356i \(0.718074\pi\)
\(48\) 0 0
\(49\) 4.22459e6 3.92247e6i 0.732824 0.680418i
\(50\) 0 0
\(51\) 2.98673e6 5.17317e6i 0.441485 0.764674i
\(52\) 0 0
\(53\) 4.31027e6 + 7.46560e6i 0.546262 + 0.946153i 0.998526 + 0.0542691i \(0.0172829\pi\)
−0.452265 + 0.891884i \(0.649384\pi\)
\(54\) 0 0
\(55\) 1.22177e6i 0.133518i
\(56\) 0 0
\(57\) 7.51934e6 0.712329
\(58\) 0 0
\(59\) 1.85511e7 1.07105e7i 1.53095 0.883895i 0.531634 0.846974i \(-0.321578\pi\)
0.999318 0.0369211i \(-0.0117550\pi\)
\(60\) 0 0
\(61\) 2.16597e7 + 1.25052e7i 1.56435 + 0.903177i 0.996808 + 0.0798301i \(0.0254378\pi\)
0.567539 + 0.823346i \(0.307896\pi\)
\(62\) 0 0
\(63\) −781750. + 5.19247e6i −0.0496256 + 0.329619i
\(64\) 0 0
\(65\) 322970. 559400.i 0.0180929 0.0313379i
\(66\) 0 0
\(67\) −9.65705e6 1.67265e7i −0.479231 0.830053i 0.520485 0.853871i \(-0.325751\pi\)
−0.999716 + 0.0238177i \(0.992418\pi\)
\(68\) 0 0
\(69\) 1.53600e6i 0.0677632i
\(70\) 0 0
\(71\) 9.50918e6 0.374205 0.187103 0.982340i \(-0.440090\pi\)
0.187103 + 0.982340i \(0.440090\pi\)
\(72\) 0 0
\(73\) 6.91695e6 3.99350e6i 0.243570 0.140625i −0.373247 0.927732i \(-0.621755\pi\)
0.616816 + 0.787107i \(0.288422\pi\)
\(74\) 0 0
\(75\) −1.48521e7 8.57486e6i −0.469399 0.271008i
\(76\) 0 0
\(77\) −1.48351e7 1.18266e7i −0.422016 0.336431i
\(78\) 0 0
\(79\) −1.32777e6 + 2.29977e6i −0.0340891 + 0.0590441i −0.882567 0.470187i \(-0.844186\pi\)
0.848478 + 0.529231i \(0.177520\pi\)
\(80\) 0 0
\(81\) −2.39148e6 4.14217e6i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 5.37421e7i 1.13241i 0.824266 + 0.566203i \(0.191588\pi\)
−0.824266 + 0.566203i \(0.808412\pi\)
\(84\) 0 0
\(85\) −1.97498e7 −0.378344
\(86\) 0 0
\(87\) 2.67122e7 1.54223e7i 0.466264 0.269198i
\(88\) 0 0
\(89\) −3.33121e7 1.92328e7i −0.530936 0.306536i 0.210461 0.977602i \(-0.432503\pi\)
−0.741398 + 0.671066i \(0.765837\pi\)
\(90\) 0 0
\(91\) −3.66612e6 9.33654e6i −0.0534615 0.136151i
\(92\) 0 0
\(93\) −139415. + 241475.i −0.00186371 + 0.00322804i
\(94\) 0 0
\(95\) −1.24304e7 2.15302e7i −0.152613 0.264334i
\(96\) 0 0
\(97\) 2.56754e7i 0.290021i 0.989430 + 0.145011i \(0.0463216\pi\)
−0.989430 + 0.145011i \(0.953678\pi\)
\(98\) 0 0
\(99\) 1.72813e7 0.179902
\(100\) 0 0
\(101\) −1.37265e8 + 7.92500e7i −1.31909 + 0.761577i −0.983582 0.180461i \(-0.942241\pi\)
−0.335507 + 0.942038i \(0.608908\pi\)
\(102\) 0 0
\(103\) −2.36862e7 1.36753e7i −0.210449 0.121503i 0.391071 0.920361i \(-0.372105\pi\)
−0.601520 + 0.798858i \(0.705438\pi\)
\(104\) 0 0
\(105\) 1.61599e7 6.34543e6i 0.132948 0.0522040i
\(106\) 0 0
\(107\) −8.08597e7 + 1.40053e8i −0.616875 + 1.06846i 0.373178 + 0.927760i \(0.378268\pi\)
−0.990053 + 0.140698i \(0.955065\pi\)
\(108\) 0 0
\(109\) −2.95165e7 5.11241e7i −0.209102 0.362176i 0.742330 0.670035i \(-0.233721\pi\)
−0.951432 + 0.307859i \(0.900388\pi\)
\(110\) 0 0
\(111\) 3.08216e7i 0.203031i
\(112\) 0 0
\(113\) −1.64113e8 −1.00654 −0.503268 0.864131i \(-0.667869\pi\)
−0.503268 + 0.864131i \(0.667869\pi\)
\(114\) 0 0
\(115\) 4.39802e6 2.53920e6i 0.0251458 0.0145180i
\(116\) 0 0
\(117\) 7.91245e6 + 4.56825e6i 0.0422248 + 0.0243785i
\(118\) 0 0
\(119\) −1.91176e8 + 2.39809e8i −0.953333 + 1.19585i
\(120\) 0 0
\(121\) 7.59599e7 1.31566e8i 0.354358 0.613767i
\(122\) 0 0
\(123\) −2.57697e7 4.46344e7i −0.112587 0.195007i
\(124\) 0 0
\(125\) 1.17099e8i 0.479638i
\(126\) 0 0
\(127\) 1.21072e8 0.465403 0.232702 0.972548i \(-0.425243\pi\)
0.232702 + 0.972548i \(0.425243\pi\)
\(128\) 0 0
\(129\) 1.85147e8 1.06895e8i 0.668586 0.386008i
\(130\) 0 0
\(131\) 5.54093e7 + 3.19906e7i 0.188147 + 0.108627i 0.591115 0.806587i \(-0.298688\pi\)
−0.402968 + 0.915214i \(0.632021\pi\)
\(132\) 0 0
\(133\) −3.81751e8 5.74744e7i −1.22004 0.183683i
\(134\) 0 0
\(135\) −7.90686e6 + 1.36951e7i −0.0238050 + 0.0412315i
\(136\) 0 0
\(137\) −1.56859e8 2.71688e8i −0.445274 0.771237i 0.552797 0.833316i \(-0.313560\pi\)
−0.998071 + 0.0620787i \(0.980227\pi\)
\(138\) 0 0
\(139\) 2.04519e8i 0.547867i 0.961749 + 0.273934i \(0.0883248\pi\)
−0.961749 + 0.273934i \(0.911675\pi\)
\(140\) 0 0
\(141\) −7.33888e7 −0.185675
\(142\) 0 0
\(143\) −2.85884e7 + 1.65055e7i −0.0683670 + 0.0394717i
\(144\) 0 0
\(145\) −8.83172e7 5.09900e7i −0.199790 0.115349i
\(146\) 0 0
\(147\) 7.93777e7 2.57642e8i 0.169992 0.551757i
\(148\) 0 0
\(149\) −3.34340e8 + 5.79093e8i −0.678333 + 1.17491i 0.297150 + 0.954831i \(0.403964\pi\)
−0.975483 + 0.220076i \(0.929369\pi\)
\(150\) 0 0
\(151\) 1.10149e8 + 1.90784e8i 0.211872 + 0.366973i 0.952300 0.305162i \(-0.0987107\pi\)
−0.740428 + 0.672135i \(0.765377\pi\)
\(152\) 0 0
\(153\) 2.79351e8i 0.509783i
\(154\) 0 0
\(155\) 921886. 0.00159717
\(156\) 0 0
\(157\) 7.29270e8 4.21044e8i 1.20030 0.692994i 0.239678 0.970852i \(-0.422958\pi\)
0.960622 + 0.277859i \(0.0896247\pi\)
\(158\) 0 0
\(159\) 3.49132e8 + 2.01571e8i 0.546262 + 0.315384i
\(160\) 0 0
\(161\) 1.17405e7 7.79814e7i 0.0174736 0.116061i
\(162\) 0 0
\(163\) 5.08666e8 8.81036e8i 0.720581 1.24808i −0.240187 0.970727i \(-0.577209\pi\)
0.960767 0.277355i \(-0.0894580\pi\)
\(164\) 0 0
\(165\) −2.85683e7 4.94817e7i −0.0385432 0.0667588i
\(166\) 0 0
\(167\) 7.85051e8i 1.00933i 0.863316 + 0.504664i \(0.168383\pi\)
−0.863316 + 0.504664i \(0.831617\pi\)
\(168\) 0 0
\(169\) 7.98278e8 0.978605
\(170\) 0 0
\(171\) 3.04533e8 1.75822e8i 0.356164 0.205632i
\(172\) 0 0
\(173\) −4.30544e8 2.48575e8i −0.480655 0.277506i 0.240035 0.970764i \(-0.422841\pi\)
−0.720689 + 0.693258i \(0.756175\pi\)
\(174\) 0 0
\(175\) 6.88487e8 + 5.48862e8i 0.734080 + 0.585208i
\(176\) 0 0
\(177\) 5.00880e8 8.67549e8i 0.510317 0.883895i
\(178\) 0 0
\(179\) 8.80361e8 + 1.52483e9i 0.857529 + 1.48528i 0.874279 + 0.485424i \(0.161335\pi\)
−0.0167496 + 0.999860i \(0.505332\pi\)
\(180\) 0 0
\(181\) 1.40594e9i 1.30994i −0.755653 0.654972i \(-0.772680\pi\)
0.755653 0.654972i \(-0.227320\pi\)
\(182\) 0 0
\(183\) 1.16962e9 1.04290
\(184\) 0 0
\(185\) −8.82515e7 + 5.09520e7i −0.0753417 + 0.0434985i
\(186\) 0 0
\(187\) 8.74100e8 + 5.04662e8i 0.714817 + 0.412700i
\(188\) 0 0
\(189\) 8.97530e7 + 2.28574e8i 0.0703399 + 0.179135i
\(190\) 0 0
\(191\) 3.46452e8 6.00072e8i 0.260321 0.450889i −0.706006 0.708206i \(-0.749505\pi\)
0.966327 + 0.257317i \(0.0828383\pi\)
\(192\) 0 0
\(193\) −5.17803e8 8.96861e8i −0.373195 0.646392i 0.616860 0.787073i \(-0.288404\pi\)
−0.990055 + 0.140680i \(0.955071\pi\)
\(194\) 0 0
\(195\) 3.02076e7i 0.0208919i
\(196\) 0 0
\(197\) −1.58650e9 −1.05335 −0.526676 0.850066i \(-0.676562\pi\)
−0.526676 + 0.850066i \(0.676562\pi\)
\(198\) 0 0
\(199\) 4.38090e8 2.52932e8i 0.279352 0.161284i −0.353778 0.935329i \(-0.615103\pi\)
0.633130 + 0.774046i \(0.281770\pi\)
\(200\) 0 0
\(201\) −7.82221e8 4.51616e8i −0.479231 0.276684i
\(202\) 0 0
\(203\) −1.47404e9 + 5.78802e8i −0.868009 + 0.340836i
\(204\) 0 0
\(205\) −8.52012e7 + 1.47573e8i −0.0482425 + 0.0835585i
\(206\) 0 0
\(207\) 3.59157e7 + 6.22079e7i 0.0195616 + 0.0338816i
\(208\) 0 0
\(209\) 1.27053e9i 0.665885i
\(210\) 0 0
\(211\) 8.53493e8 0.430596 0.215298 0.976548i \(-0.430928\pi\)
0.215298 + 0.976548i \(0.430928\pi\)
\(212\) 0 0
\(213\) 3.85122e8 2.22350e8i 0.187103 0.108024i
\(214\) 0 0
\(215\) −6.12143e8 3.53421e8i −0.286483 0.165401i
\(216\) 0 0
\(217\) 8.92373e6 1.11939e7i 0.00402446 0.00504825i
\(218\) 0 0
\(219\) 1.86758e8 3.23474e8i 0.0811899 0.140625i
\(220\) 0 0
\(221\) 2.66811e8 + 4.62130e8i 0.111850 + 0.193729i
\(222\) 0 0
\(223\) 1.19055e9i 0.481426i 0.970596 + 0.240713i \(0.0773812\pi\)
−0.970596 + 0.240713i \(0.922619\pi\)
\(224\) 0 0
\(225\) −8.02013e8 −0.312933
\(226\) 0 0
\(227\) −1.55248e9 + 8.96322e8i −0.584684 + 0.337567i −0.762993 0.646407i \(-0.776271\pi\)
0.178309 + 0.983975i \(0.442937\pi\)
\(228\) 0 0
\(229\) −3.51985e9 2.03219e9i −1.27992 0.738961i −0.303085 0.952964i \(-0.598016\pi\)
−0.976833 + 0.214003i \(0.931350\pi\)
\(230\) 0 0
\(231\) −8.77360e8 1.32091e8i −0.308127 0.0463900i
\(232\) 0 0
\(233\) 4.96945e8 8.60734e8i 0.168610 0.292042i −0.769321 0.638862i \(-0.779405\pi\)
0.937932 + 0.346820i \(0.112739\pi\)
\(234\) 0 0
\(235\) 1.21321e8 + 2.10134e8i 0.0397800 + 0.0689010i
\(236\) 0 0
\(237\) 1.24188e8i 0.0393627i
\(238\) 0 0
\(239\) 1.71719e9 0.526291 0.263145 0.964756i \(-0.415240\pi\)
0.263145 + 0.964756i \(0.415240\pi\)
\(240\) 0 0
\(241\) −3.95118e9 + 2.28121e9i −1.17127 + 0.676235i −0.953980 0.299872i \(-0.903056\pi\)
−0.217293 + 0.976106i \(0.569723\pi\)
\(242\) 0 0
\(243\) −1.93710e8 1.11839e8i −0.0555556 0.0320750i
\(244\) 0 0
\(245\) −8.68929e8 + 1.98633e8i −0.241168 + 0.0551300i
\(246\) 0 0
\(247\) −3.35859e8 + 5.81725e8i −0.0902338 + 0.156289i
\(248\) 0 0
\(249\) 1.25664e9 + 2.17656e9i 0.326898 + 0.566203i
\(250\) 0 0
\(251\) 1.49784e8i 0.0377373i 0.999822 + 0.0188687i \(0.00600644\pi\)
−0.999822 + 0.0188687i \(0.993994\pi\)
\(252\) 0 0
\(253\) −2.59534e8 −0.0633450
\(254\) 0 0
\(255\) −7.99867e8 + 4.61804e8i −0.189172 + 0.109219i
\(256\) 0 0
\(257\) −6.35751e9 3.67051e9i −1.45732 0.841384i −0.458440 0.888725i \(-0.651592\pi\)
−0.998879 + 0.0473414i \(0.984925\pi\)
\(258\) 0 0
\(259\) −2.35586e8 + 1.56479e9i −0.0523541 + 0.347742i
\(260\) 0 0
\(261\) 7.21228e8 1.24920e9i 0.155421 0.269198i
\(262\) 0 0
\(263\) 2.40019e9 + 4.15725e9i 0.501675 + 0.868926i 0.999998 + 0.00193513i \(0.000615971\pi\)
−0.498323 + 0.866991i \(0.666051\pi\)
\(264\) 0 0
\(265\) 1.33289e9i 0.270278i
\(266\) 0 0
\(267\) −1.79886e9 −0.353958
\(268\) 0 0
\(269\) −2.69474e9 + 1.55581e9i −0.514645 + 0.297131i −0.734741 0.678348i \(-0.762696\pi\)
0.220096 + 0.975478i \(0.429363\pi\)
\(270\) 0 0
\(271\) −3.16838e9 1.82927e9i −0.587436 0.339156i 0.176647 0.984274i \(-0.443475\pi\)
−0.764083 + 0.645118i \(0.776808\pi\)
\(272\) 0 0
\(273\) −3.66791e8 2.92406e8i −0.0660341 0.0526424i
\(274\) 0 0
\(275\) 1.44888e9 2.50953e9i 0.253338 0.438794i
\(276\) 0 0
\(277\) 5.24448e9 + 9.08370e9i 0.890806 + 1.54292i 0.838911 + 0.544269i \(0.183193\pi\)
0.0518958 + 0.998653i \(0.483474\pi\)
\(278\) 0 0
\(279\) 1.30396e7i 0.00215203i
\(280\) 0 0
\(281\) 1.88553e9 0.302419 0.151210 0.988502i \(-0.451683\pi\)
0.151210 + 0.988502i \(0.451683\pi\)
\(282\) 0 0
\(283\) 1.50968e9 8.71616e8i 0.235364 0.135887i −0.377680 0.925936i \(-0.623278\pi\)
0.613044 + 0.790049i \(0.289945\pi\)
\(284\) 0 0
\(285\) −1.00687e9 5.81314e8i −0.152613 0.0881113i
\(286\) 0 0
\(287\) 9.67143e8 + 2.46303e9i 0.142549 + 0.363029i
\(288\) 0 0
\(289\) 4.66994e9 8.08857e9i 0.669453 1.15953i
\(290\) 0 0
\(291\) 6.00359e8 + 1.03985e9i 0.0837219 + 0.145011i
\(292\) 0 0
\(293\) 7.68210e9i 1.04234i −0.853453 0.521170i \(-0.825496\pi\)
0.853453 0.521170i \(-0.174504\pi\)
\(294\) 0 0
\(295\) −3.31207e9 −0.437333
\(296\) 0 0
\(297\) 6.99894e8 4.04084e8i 0.0899511 0.0519333i
\(298\) 0 0
\(299\) −1.18831e8 6.86068e7i −0.0148677 0.00858386i
\(300\) 0 0
\(301\) −1.02168e10 + 4.01178e9i −1.24466 + 0.488732i
\(302\) 0 0
\(303\) −3.70615e9 + 6.41925e9i −0.439696 + 0.761577i
\(304\) 0 0
\(305\) −1.93354e9 3.34899e9i −0.223436 0.387003i
\(306\) 0 0
\(307\) 8.93846e9i 1.00626i 0.864211 + 0.503129i \(0.167818\pi\)
−0.864211 + 0.503129i \(0.832182\pi\)
\(308\) 0 0
\(309\) −1.27906e9 −0.140299
\(310\) 0 0
\(311\) 1.36754e10 7.89550e9i 1.46184 0.843992i 0.462740 0.886494i \(-0.346866\pi\)
0.999096 + 0.0425024i \(0.0135330\pi\)
\(312\) 0 0
\(313\) −8.18174e9 4.72373e9i −0.852449 0.492162i 0.00902752 0.999959i \(-0.497126\pi\)
−0.861476 + 0.507798i \(0.830460\pi\)
\(314\) 0 0
\(315\) 5.06104e8 6.34853e8i 0.0514041 0.0644808i
\(316\) 0 0
\(317\) 8.46257e9 1.46576e10i 0.838041 1.45153i −0.0534897 0.998568i \(-0.517034\pi\)
0.891530 0.452961i \(-0.149632\pi\)
\(318\) 0 0
\(319\) 2.60587e9 + 4.51350e9i 0.251646 + 0.435863i
\(320\) 0 0
\(321\) 7.56287e9i 0.712305i
\(322\) 0 0
\(323\) 2.05380e10 1.88689
\(324\) 0 0
\(325\) 1.32677e9 7.66009e8i 0.118922 0.0686595i
\(326\) 0 0
\(327\) −2.39084e9 1.38035e9i −0.209102 0.120725i
\(328\) 0 0
\(329\) 3.72589e9 + 5.60950e8i 0.318014 + 0.0478785i
\(330\) 0 0
\(331\) 1.02406e10 1.77372e10i 0.853123 1.47765i −0.0252519 0.999681i \(-0.508039\pi\)
0.878375 0.477972i \(-0.158628\pi\)
\(332\) 0 0
\(333\) −7.20691e8 1.24827e9i −0.0586101 0.101516i
\(334\) 0 0
\(335\) 2.98631e9i 0.237113i
\(336\) 0 0
\(337\) 2.14997e10 1.66691 0.833456 0.552586i \(-0.186359\pi\)
0.833456 + 0.552586i \(0.186359\pi\)
\(338\) 0 0
\(339\) −6.64657e9 + 3.83740e9i −0.503268 + 0.290562i
\(340\) 0 0
\(341\) −4.08014e7 2.35567e7i −0.00301757 0.00174220i
\(342\) 0 0
\(343\) −5.99925e9 + 1.24736e10i −0.433431 + 0.901187i
\(344\) 0 0
\(345\) 1.18747e8 2.05675e8i 0.00838195 0.0145180i
\(346\) 0 0
\(347\) 7.58609e9 + 1.31395e10i 0.523239 + 0.906277i 0.999634 + 0.0270456i \(0.00860994\pi\)
−0.476395 + 0.879231i \(0.658057\pi\)
\(348\) 0 0
\(349\) 1.30313e9i 0.0878387i 0.999035 + 0.0439194i \(0.0139845\pi\)
−0.999035 + 0.0439194i \(0.986016\pi\)
\(350\) 0 0
\(351\) 4.27272e8 0.0281498
\(352\) 0 0
\(353\) 1.83413e10 1.05893e10i 1.18122 0.681978i 0.224924 0.974376i \(-0.427787\pi\)
0.956297 + 0.292399i \(0.0944534\pi\)
\(354\) 0 0
\(355\) −1.27331e9 7.35147e8i −0.0801717 0.0462872i
\(356\) 0 0
\(357\) −2.13523e9 + 1.41825e10i −0.131454 + 0.873130i
\(358\) 0 0
\(359\) 1.50520e10 2.60708e10i 0.906184 1.56956i 0.0868642 0.996220i \(-0.472315\pi\)
0.819320 0.573337i \(-0.194351\pi\)
\(360\) 0 0
\(361\) 4.43472e9 + 7.68117e9i 0.261119 + 0.452271i
\(362\) 0 0
\(363\) 7.10458e9i 0.409178i
\(364\) 0 0
\(365\) −1.23494e9 −0.0695783
\(366\) 0 0
\(367\) −5.68403e9 + 3.28168e9i −0.313323 + 0.180897i −0.648412 0.761289i \(-0.724567\pi\)
0.335090 + 0.942186i \(0.391233\pi\)
\(368\) 0 0
\(369\) −2.08734e9 1.20513e9i −0.112587 0.0650022i
\(370\) 0 0
\(371\) −1.61844e10 1.29022e10i −0.854283 0.681034i
\(372\) 0 0
\(373\) −6.45827e9 + 1.11861e10i −0.333642 + 0.577885i −0.983223 0.182407i \(-0.941611\pi\)
0.649581 + 0.760293i \(0.274944\pi\)
\(374\) 0 0
\(375\) 2.73809e9 + 4.74251e9i 0.138460 + 0.239819i
\(376\) 0 0
\(377\) 2.75540e9i 0.136402i
\(378\) 0 0
\(379\) −2.24358e10 −1.08739 −0.543694 0.839283i \(-0.682975\pi\)
−0.543694 + 0.839283i \(0.682975\pi\)
\(380\) 0 0
\(381\) 4.90342e9 2.83099e9i 0.232702 0.134350i
\(382\) 0 0
\(383\) −2.40505e10 1.38855e10i −1.11771 0.645309i −0.176894 0.984230i \(-0.556605\pi\)
−0.940815 + 0.338921i \(0.889938\pi\)
\(384\) 0 0
\(385\) 1.07217e9 + 2.73051e9i 0.0488003 + 0.124280i
\(386\) 0 0
\(387\) 4.99896e9 8.65846e9i 0.222862 0.386008i
\(388\) 0 0
\(389\) 8.31848e9 + 1.44080e10i 0.363284 + 0.629226i 0.988499 0.151226i \(-0.0483223\pi\)
−0.625216 + 0.780452i \(0.714989\pi\)
\(390\) 0 0
\(391\) 4.19535e9i 0.179499i
\(392\) 0 0
\(393\) 2.99210e9 0.125431
\(394\) 0 0
\(395\) 3.55587e8 2.05298e8i 0.0146069 0.00843329i
\(396\) 0 0
\(397\) −1.08327e10 6.25426e9i −0.436088 0.251776i 0.265849 0.964015i \(-0.414348\pi\)
−0.701937 + 0.712239i \(0.747681\pi\)
\(398\) 0 0
\(399\) −1.68048e10 + 6.59866e9i −0.663045 + 0.260354i
\(400\) 0 0
\(401\) −8.27309e8 + 1.43294e9i −0.0319956 + 0.0554180i −0.881580 0.472035i \(-0.843520\pi\)
0.849584 + 0.527453i \(0.176853\pi\)
\(402\) 0 0
\(403\) −1.24543e7 2.15714e7i −0.000472169 0.000817821i
\(404\) 0 0
\(405\) 7.39534e8i 0.0274877i
\(406\) 0 0
\(407\) 5.20786e9 0.189794
\(408\) 0 0
\(409\) 1.00393e10 5.79619e9i 0.358765 0.207133i −0.309774 0.950810i \(-0.600253\pi\)
0.668539 + 0.743677i \(0.266920\pi\)
\(410\) 0 0
\(411\) −1.27056e10 7.33557e9i −0.445274 0.257079i
\(412\) 0 0
\(413\) −3.20604e10 + 4.02163e10i −1.10197 + 1.38230i
\(414\) 0 0
\(415\) 4.15476e9 7.19625e9i 0.140073 0.242613i
\(416\) 0 0
\(417\) 4.78221e9 + 8.28303e9i 0.158156 + 0.273934i
\(418\) 0 0
\(419\) 2.35810e10i 0.765079i 0.923939 + 0.382540i \(0.124950\pi\)
−0.923939 + 0.382540i \(0.875050\pi\)
\(420\) 0 0
\(421\) 8.62676e9 0.274612 0.137306 0.990529i \(-0.456156\pi\)
0.137306 + 0.990529i \(0.456156\pi\)
\(422\) 0 0
\(423\) −2.97225e9 + 1.71603e9i −0.0928375 + 0.0535997i
\(424\) 0 0
\(425\) −4.05663e10 2.34209e10i −1.24340 0.717875i
\(426\) 0 0
\(427\) −5.93809e10 8.94007e9i −1.78622 0.268924i
\(428\) 0 0
\(429\) −7.71888e8 + 1.33695e9i −0.0227890 + 0.0394717i
\(430\) 0 0
\(431\) −1.28994e10 2.23424e10i −0.373818 0.647472i 0.616331 0.787487i \(-0.288618\pi\)
−0.990149 + 0.140015i \(0.955285\pi\)
\(432\) 0 0
\(433\) 4.11174e10i 1.16970i 0.811142 + 0.584849i \(0.198846\pi\)
−0.811142 + 0.584849i \(0.801154\pi\)
\(434\) 0 0
\(435\) −4.76913e9 −0.133193
\(436\) 0 0
\(437\) −4.57354e9 + 2.64053e9i −0.125408 + 0.0724046i
\(438\) 0 0
\(439\) −3.33223e10 1.92386e10i −0.897174 0.517983i −0.0208914 0.999782i \(-0.506650\pi\)
−0.876282 + 0.481798i \(0.839984\pi\)
\(440\) 0 0
\(441\) −2.80957e9 1.22906e10i −0.0742824 0.324951i
\(442\) 0 0
\(443\) 6.20399e9 1.07456e10i 0.161085 0.279008i −0.774173 0.632974i \(-0.781834\pi\)
0.935258 + 0.353966i \(0.115167\pi\)
\(444\) 0 0
\(445\) 2.97374e9 + 5.15067e9i 0.0758338 + 0.131348i
\(446\) 0 0
\(447\) 3.12710e10i 0.783271i
\(448\) 0 0
\(449\) 3.45902e10 0.851076 0.425538 0.904941i \(-0.360085\pi\)
0.425538 + 0.904941i \(0.360085\pi\)
\(450\) 0 0
\(451\) 7.54178e9 4.35425e9i 0.182292 0.105246i
\(452\) 0 0
\(453\) 8.92208e9 + 5.15117e9i 0.211872 + 0.122324i
\(454\) 0 0
\(455\) −2.30893e8 + 1.53362e9i −0.00538723 + 0.0357826i
\(456\) 0 0
\(457\) −2.64356e9 + 4.57878e9i −0.0606072 + 0.104975i −0.894737 0.446593i \(-0.852637\pi\)
0.834130 + 0.551568i \(0.185970\pi\)
\(458\) 0 0
\(459\) −6.53199e9 1.13137e10i −0.147162 0.254891i
\(460\) 0 0
\(461\) 3.55209e10i 0.786466i 0.919439 + 0.393233i \(0.128643\pi\)
−0.919439 + 0.393233i \(0.871357\pi\)
\(462\) 0 0
\(463\) 5.68452e8 0.0123700 0.00618500 0.999981i \(-0.498031\pi\)
0.00618500 + 0.999981i \(0.498031\pi\)
\(464\) 0 0
\(465\) 3.73364e7 2.15562e7i 0.000798584 0.000461062i
\(466\) 0 0
\(467\) 1.20351e9 + 6.94848e8i 0.0253036 + 0.0146091i 0.512598 0.858628i \(-0.328683\pi\)
−0.487295 + 0.873238i \(0.662016\pi\)
\(468\) 0 0
\(469\) 3.62608e10 + 2.89071e10i 0.749456 + 0.597466i
\(470\) 0 0
\(471\) 1.96903e10 3.41046e10i 0.400100 0.692994i
\(472\) 0 0
\(473\) 1.80617e10 + 3.12839e10i 0.360840 + 0.624994i
\(474\) 0 0
\(475\) 5.89641e10i 1.15828i
\(476\) 0 0
\(477\) 1.88531e10 0.364174
\(478\) 0 0
\(479\) −4.91139e10 + 2.83559e10i −0.932958 + 0.538644i −0.887746 0.460334i \(-0.847730\pi\)
−0.0452122 + 0.998977i \(0.514396\pi\)
\(480\) 0 0
\(481\) 2.38447e9 + 1.37668e9i 0.0445464 + 0.0257189i
\(482\) 0 0
\(483\) −1.34793e9 3.43277e9i −0.0247672 0.0630749i
\(484\) 0 0
\(485\) 1.98494e9 3.43802e9i 0.0358741 0.0621357i
\(486\) 0 0
\(487\) 2.00673e10 + 3.47576e10i 0.356758 + 0.617923i 0.987417 0.158137i \(-0.0505487\pi\)
−0.630659 + 0.776060i \(0.717215\pi\)
\(488\) 0 0
\(489\) 4.75759e10i 0.832055i
\(490\) 0 0
\(491\) −6.70262e8 −0.0115324 −0.00576619 0.999983i \(-0.501835\pi\)
−0.00576619 + 0.999983i \(0.501835\pi\)
\(492\) 0 0
\(493\) 7.29603e10 4.21237e10i 1.23509 0.713080i
\(494\) 0 0
\(495\) −2.31403e9 1.33601e9i −0.0385432 0.0222529i
\(496\) 0 0
\(497\) −2.12519e10 + 8.34486e9i −0.348315 + 0.136771i
\(498\) 0 0
\(499\) 4.56562e10 7.90788e10i 0.736372 1.27543i −0.217747 0.976005i \(-0.569871\pi\)
0.954119 0.299428i \(-0.0967959\pi\)
\(500\) 0 0
\(501\) 1.83566e10 + 3.17946e10i 0.291368 + 0.504664i
\(502\) 0 0
\(503\) 4.38153e10i 0.684468i 0.939615 + 0.342234i \(0.111184\pi\)
−0.939615 + 0.342234i \(0.888816\pi\)
\(504\) 0 0
\(505\) 2.45070e10 0.376812
\(506\) 0 0
\(507\) 3.23303e10 1.86659e10i 0.489302 0.282499i
\(508\) 0 0
\(509\) −5.28346e10 3.05041e10i −0.787132 0.454451i 0.0518199 0.998656i \(-0.483498\pi\)
−0.838952 + 0.544206i \(0.816831\pi\)
\(510\) 0 0
\(511\) −1.19540e10 + 1.49950e10i −0.175320 + 0.219920i
\(512\) 0 0
\(513\) 8.22240e9 1.42416e10i 0.118721 0.205632i
\(514\) 0 0
\(515\) 2.11444e9 + 3.66232e9i 0.0300585 + 0.0520628i
\(516\) 0 0
\(517\) 1.24004e10i 0.173569i
\(518\) 0 0
\(519\) −2.32494e10 −0.320436
\(520\) 0 0
\(521\) −9.04455e10 + 5.22187e10i −1.22754 + 0.708721i −0.966515 0.256611i \(-0.917394\pi\)
−0.261026 + 0.965332i \(0.584061\pi\)
\(522\) 0 0
\(523\) −6.17123e10 3.56296e10i −0.824831 0.476216i 0.0272488 0.999629i \(-0.491325\pi\)
−0.852079 + 0.523413i \(0.824659\pi\)
\(524\) 0 0
\(525\) 4.07176e10 + 6.13022e9i 0.535975 + 0.0806935i
\(526\) 0 0
\(527\) −3.80792e8 + 6.59552e8i −0.00493680 + 0.00855079i
\(528\) 0 0
\(529\) 3.86161e10 + 6.68851e10i 0.493112 + 0.854095i
\(530\) 0 0
\(531\) 4.68476e10i 0.589264i
\(532\) 0 0
\(533\) 4.60411e9 0.0570476
\(534\) 0 0
\(535\) 2.16548e10 1.25024e10i 0.264325 0.152608i
\(536\) 0 0
\(537\) 7.13093e10 + 4.11704e10i 0.857529 + 0.495095i
\(538\) 0 0
\(539\) 4.35333e10 + 1.34123e10i 0.515782 + 0.158909i
\(540\) 0 0
\(541\) 5.99851e10 1.03897e11i 0.700251 1.21287i −0.268127 0.963384i \(-0.586405\pi\)
0.968378 0.249487i \(-0.0802621\pi\)
\(542\) 0 0
\(543\) −3.28747e10 5.69406e10i −0.378148 0.654972i
\(544\) 0 0
\(545\) 9.12759e9i 0.103459i
\(546\) 0 0
\(547\) 7.67882e10 0.857720 0.428860 0.903371i \(-0.358915\pi\)
0.428860 + 0.903371i \(0.358915\pi\)
\(548\) 0 0
\(549\) 4.73698e10 2.73490e10i 0.521449 0.301059i
\(550\) 0 0
\(551\) 9.18418e10 + 5.30249e10i 0.996400 + 0.575272i
\(552\) 0 0
\(553\) 9.49234e8 6.30492e9i 0.0101502 0.0674185i
\(554\) 0 0
\(555\) −2.38279e9 + 4.12711e9i −0.0251139 + 0.0434985i
\(556\) 0 0
\(557\) −6.00412e9 1.03994e10i −0.0623775 0.108041i 0.833150 0.553047i \(-0.186535\pi\)
−0.895528 + 0.445006i \(0.853202\pi\)
\(558\) 0 0
\(559\) 1.90982e10i 0.195589i
\(560\) 0 0
\(561\) 4.72014e10 0.476545
\(562\) 0 0
\(563\) 7.79826e10 4.50233e10i 0.776183 0.448129i −0.0588931 0.998264i \(-0.518757\pi\)
0.835076 + 0.550135i \(0.185424\pi\)
\(564\) 0 0
\(565\) 2.19753e10 + 1.26874e10i 0.215645 + 0.124503i
\(566\) 0 0
\(567\) 8.97968e9 + 7.15860e9i 0.0868818 + 0.0692621i
\(568\) 0 0
\(569\) −5.50444e10 + 9.53398e10i −0.525127 + 0.909547i 0.474445 + 0.880285i \(0.342649\pi\)
−0.999572 + 0.0292615i \(0.990684\pi\)
\(570\) 0 0
\(571\) 2.27688e9 + 3.94367e9i 0.0214188 + 0.0370985i 0.876536 0.481336i \(-0.159848\pi\)
−0.855117 + 0.518435i \(0.826515\pi\)
\(572\) 0 0
\(573\) 3.24039e10i 0.300593i
\(574\) 0 0
\(575\) 1.20448e10 0.110186
\(576\) 0 0
\(577\) 2.58023e10 1.48969e10i 0.232785 0.134398i −0.379071 0.925367i \(-0.623757\pi\)
0.611856 + 0.790969i \(0.290423\pi\)
\(578\) 0 0
\(579\) −4.19420e10 2.42153e10i −0.373195 0.215464i
\(580\) 0 0
\(581\) −4.71618e10 1.20107e11i −0.413891 1.05406i
\(582\) 0 0
\(583\) −3.40591e10 + 5.89920e10i −0.294821 + 0.510645i
\(584\) 0 0
\(585\) −7.06335e8 1.22341e9i −0.00603097 0.0104460i
\(586\) 0 0
\(587\) 4.87063e10i 0.410235i 0.978737 + 0.205118i \(0.0657577\pi\)
−0.978737 + 0.205118i \(0.934242\pi\)
\(588\) 0 0
\(589\) −9.58676e8 −0.00796546
\(590\) 0 0
\(591\) −6.42531e10 + 3.70965e10i −0.526676 + 0.304077i
\(592\) 0 0
\(593\) −1.48606e11 8.57978e10i −1.20176 0.693837i −0.240815 0.970571i \(-0.577415\pi\)
−0.960947 + 0.276734i \(0.910748\pi\)
\(594\) 0 0
\(595\) 4.41385e10 1.73316e10i 0.352168 0.138284i
\(596\) 0 0
\(597\) 1.18284e10 2.04875e10i 0.0931173 0.161284i
\(598\) 0 0
\(599\) 1.22733e11 + 2.12580e11i 0.953355 + 1.65126i 0.738087 + 0.674705i \(0.235729\pi\)
0.215268 + 0.976555i \(0.430937\pi\)
\(600\) 0 0
\(601\) 6.97408e10i 0.534551i −0.963620 0.267275i \(-0.913877\pi\)
0.963620 0.267275i \(-0.0861233\pi\)
\(602\) 0 0
\(603\) −4.22399e10 −0.319488
\(604\) 0 0
\(605\) −2.03426e10 + 1.17448e10i −0.151839 + 0.0876644i
\(606\) 0 0
\(607\) 8.32636e10 + 4.80723e10i 0.613339 + 0.354111i 0.774271 0.632854i \(-0.218117\pi\)
−0.160932 + 0.986965i \(0.551450\pi\)
\(608\) 0 0
\(609\) −4.61646e10 + 5.79084e10i −0.335614 + 0.420991i
\(610\) 0 0
\(611\) 3.27798e9 5.67763e9i 0.0235202 0.0407383i
\(612\) 0 0
\(613\) −5.64299e10 9.77394e10i −0.399638 0.692194i 0.594043 0.804433i \(-0.297531\pi\)
−0.993681 + 0.112239i \(0.964198\pi\)
\(614\) 0 0
\(615\) 7.96893e9i 0.0557057i
\(616\) 0 0
\(617\) −1.66934e11 −1.15187 −0.575936 0.817495i \(-0.695362\pi\)
−0.575936 + 0.817495i \(0.695362\pi\)
\(618\) 0 0
\(619\) −2.13512e11 + 1.23271e11i −1.45432 + 0.839650i −0.998722 0.0505371i \(-0.983907\pi\)
−0.455595 + 0.890187i \(0.650573\pi\)
\(620\) 0 0
\(621\) 2.90918e9 + 1.67961e9i 0.0195616 + 0.0112939i
\(622\) 0 0
\(623\) 9.13266e10 + 1.37496e10i 0.606240 + 0.0912723i
\(624\) 0 0
\(625\) −6.25718e10 + 1.08378e11i −0.410071 + 0.710263i
\(626\) 0 0
\(627\) 2.97084e10 + 5.14564e10i 0.192224 + 0.332942i
\(628\) 0 0
\(629\) 8.41846e10i 0.537811i
\(630\) 0 0
\(631\) −2.85012e11 −1.79782 −0.898910 0.438133i \(-0.855640\pi\)
−0.898910 + 0.438133i \(0.855640\pi\)
\(632\) 0 0
\(633\) 3.45665e10 1.99570e10i 0.215298 0.124302i
\(634\) 0 0
\(635\) −1.62120e10 9.35998e9i −0.0997104 0.0575679i
\(636\) 0 0
\(637\) 1.63867e10 + 1.76488e10i 0.0995254 + 0.107191i
\(638\) 0 0
\(639\) 1.03983e10 1.80104e10i 0.0623675 0.108024i
\(640\) 0 0
\(641\) −1.12062e11 1.94098e11i −0.663785 1.14971i −0.979613 0.200893i \(-0.935616\pi\)
0.315828 0.948816i \(-0.397718\pi\)
\(642\) 0 0
\(643\) 2.37170e11i 1.38745i −0.720241 0.693724i \(-0.755969\pi\)
0.720241 0.693724i \(-0.244031\pi\)
\(644\) 0 0
\(645\) −3.30557e10 −0.190989
\(646\) 0 0
\(647\) −1.95163e11 + 1.12678e11i −1.11373 + 0.643014i −0.939794 0.341742i \(-0.888983\pi\)
−0.173940 + 0.984756i \(0.555650\pi\)
\(648\) 0 0
\(649\) 1.46588e11 + 8.46326e10i 0.826265 + 0.477044i
\(650\) 0 0
\(651\) 9.96689e7 6.62012e8i 0.000554927 0.00368589i
\(652\) 0 0
\(653\) −9.06390e10 + 1.56991e11i −0.498497 + 0.863422i −0.999998 0.00173469i \(-0.999448\pi\)
0.501502 + 0.865157i \(0.332781\pi\)
\(654\) 0 0
\(655\) −4.94632e9 8.56729e9i −0.0268731 0.0465455i
\(656\) 0 0
\(657\) 1.74676e10i 0.0937501i
\(658\) 0 0
\(659\) 2.00364e11 1.06238 0.531189 0.847253i \(-0.321745\pi\)
0.531189 + 0.847253i \(0.321745\pi\)
\(660\) 0 0
\(661\) −8.46518e10 + 4.88737e10i −0.443435 + 0.256017i −0.705054 0.709154i \(-0.749077\pi\)
0.261618 + 0.965171i \(0.415744\pi\)
\(662\) 0 0
\(663\) 2.16117e10 + 1.24775e10i 0.111850 + 0.0645764i
\(664\) 0 0
\(665\) 4.66745e10 + 3.72089e10i 0.238667 + 0.190266i
\(666\) 0 0
\(667\) −1.08315e10 + 1.87608e10i −0.0547251 + 0.0947867i
\(668\) 0 0
\(669\) 2.78383e10 + 4.82174e10i 0.138976 + 0.240713i
\(670\) 0 0
\(671\) 1.97629e11i 0.974901i
\(672\) 0 0
\(673\) −2.14833e11 −1.04723 −0.523614 0.851956i \(-0.675416\pi\)
−0.523614 + 0.851956i \(0.675416\pi\)
\(674\) 0 0
\(675\) −3.24815e10 + 1.87532e10i −0.156466 + 0.0903359i
\(676\) 0 0
\(677\) −2.10418e11 1.21485e11i −1.00168 0.578320i −0.0929348 0.995672i \(-0.529625\pi\)
−0.908745 + 0.417352i \(0.862958\pi\)
\(678\) 0 0
\(679\) −2.25316e10 5.73814e10i −0.106002 0.269955i
\(680\) 0 0
\(681\) −4.19168e10 + 7.26021e10i −0.194895 + 0.337567i
\(682\) 0 0
\(683\) −1.78386e11 3.08973e11i −0.819742 1.41984i −0.905872 0.423552i \(-0.860783\pi\)
0.0861296 0.996284i \(-0.472550\pi\)
\(684\) 0 0
\(685\) 4.85065e10i 0.220312i
\(686\) 0 0
\(687\) −1.90072e11 −0.853278
\(688\) 0 0
\(689\) −3.11886e10 + 1.80068e10i −0.138395 + 0.0799022i
\(690\) 0 0
\(691\) 3.06169e11 + 1.76767e11i 1.34291 + 0.775332i 0.987234 0.159275i \(-0.0509158\pi\)
0.355680 + 0.934608i \(0.384249\pi\)
\(692\) 0 0
\(693\) −3.86217e10 + 1.51654e10i −0.167455 + 0.0657537i
\(694\) 0 0
\(695\) 1.58112e10 2.73858e10i 0.0677682 0.117378i
\(696\) 0 0
\(697\) −7.03861e10 1.21912e11i −0.298233 0.516555i
\(698\) 0 0
\(699\) 4.64796e10i 0.194695i
\(700\) 0 0
\(701\) 3.14132e11 1.30089 0.650445 0.759553i \(-0.274582\pi\)
0.650445 + 0.759553i \(0.274582\pi\)
\(702\) 0 0
\(703\) 9.17734e10 5.29854e10i 0.375747 0.216938i
\(704\) 0 0
\(705\) 9.82701e9 + 5.67362e9i 0.0397800 + 0.0229670i
\(706\) 0 0
\(707\) 2.37224e11 2.97572e11i 0.949471 1.19101i
\(708\) 0 0
\(709\) −1.40578e11 + 2.43487e11i −0.556328 + 0.963589i 0.441471 + 0.897276i \(0.354457\pi\)
−0.997799 + 0.0663130i \(0.978876\pi\)
\(710\) 0 0
\(711\) 2.90384e9 + 5.02960e9i 0.0113630 + 0.0196814i
\(712\) 0 0
\(713\) 1.95831e8i 0.000757747i
\(714\) 0 0
\(715\) 5.10412e9 0.0195297
\(716\) 0 0
\(717\) 6.95460e10 4.01524e10i 0.263145 0.151927i
\(718\) 0 0
\(719\) 4.14076e11 + 2.39067e11i 1.54940 + 0.894548i 0.998187 + 0.0601845i \(0.0191689\pi\)
0.551215 + 0.834363i \(0.314164\pi\)
\(720\) 0 0
\(721\) 6.49367e10 + 9.77652e9i 0.240298 + 0.0361779i
\(722\) 0 0
\(723\) −1.06682e11 + 1.84778e11i −0.390424 + 0.676235i
\(724\) 0 0
\(725\) −1.20936e11 2.09468e11i −0.437728 0.758167i
\(726\) 0 0
\(727\) 5.00817e11i 1.79284i 0.443206 + 0.896420i \(0.353841\pi\)
−0.443206 + 0.896420i \(0.646159\pi\)
\(728\) 0 0
\(729\) −1.04604e10 −0.0370370
\(730\) 0 0
\(731\) 5.05701e11 2.91967e11i 1.77102 1.02250i
\(732\) 0 0
\(733\) −8.44252e10 4.87429e10i −0.292453 0.168848i 0.346594 0.938015i \(-0.387338\pi\)
−0.639048 + 0.769167i \(0.720671\pi\)
\(734\) 0 0
\(735\) −3.05471e10 + 2.83626e10i −0.104669 + 0.0971843i
\(736\) 0 0
\(737\) 7.63085e10 1.32170e11i 0.258644 0.447985i
\(738\) 0 0
\(739\) −1.10837e11 1.91976e11i −0.371628 0.643678i 0.618188 0.786030i \(-0.287867\pi\)
−0.989816 + 0.142352i \(0.954534\pi\)
\(740\) 0 0
\(741\) 3.14131e10i 0.104193i
\(742\) 0 0
\(743\) 2.62831e11 0.862426 0.431213 0.902250i \(-0.358086\pi\)
0.431213 + 0.902250i \(0.358086\pi\)
\(744\) 0 0
\(745\) 8.95384e10 5.16950e10i 0.290659 0.167812i
\(746\) 0 0
\(747\) 1.01787e11 + 5.87670e10i 0.326898 + 0.188734i
\(748\) 0 0
\(749\) 5.78071e10 3.83961e11i 0.183677 1.22000i
\(750\) 0 0
\(751\) −1.37391e11 + 2.37969e11i −0.431917 + 0.748102i −0.997038 0.0769059i \(-0.975496\pi\)
0.565122 + 0.825008i \(0.308829\pi\)
\(752\) 0 0
\(753\) 3.50236e9 + 6.06626e9i 0.0108938 + 0.0188687i
\(754\) 0 0
\(755\) 3.40622e10i 0.104830i
\(756\) 0 0
\(757\) 1.73327e11 0.527817 0.263909 0.964548i \(-0.414988\pi\)
0.263909 + 0.964548i \(0.414988\pi\)
\(758\) 0 0
\(759\) −1.05111e10 + 6.06861e9i −0.0316725 + 0.0182861i
\(760\) 0 0
\(761\) 3.50804e11 + 2.02537e11i 1.04599 + 0.603901i 0.921523 0.388323i \(-0.126946\pi\)
0.124464 + 0.992224i \(0.460279\pi\)
\(762\) 0 0
\(763\) 1.10830e11 + 8.83538e10i 0.327009 + 0.260692i
\(764\) 0 0
\(765\) −2.15964e10 + 3.74061e10i −0.0630574 + 0.109219i
\(766\) 0 0
\(767\) 4.47446e10 + 7.74999e10i 0.129288 + 0.223934i
\(768\) 0 0
\(769\) 6.69043e11i 1.91315i −0.291488 0.956574i \(-0.594150\pi\)
0.291488 0.956574i \(-0.405850\pi\)
\(770\) 0 0
\(771\) −3.43306e11 −0.971546
\(772\) 0 0
\(773\) −7.11009e10 + 4.10502e10i −0.199140 + 0.114973i −0.596254 0.802796i \(-0.703345\pi\)
0.397115 + 0.917769i \(0.370012\pi\)
\(774\) 0 0
\(775\) 1.89356e9 + 1.09325e9i 0.00524895 + 0.00303048i
\(776\) 0 0
\(777\) 2.70477e10 + 6.88826e10i 0.0742073 + 0.188984i
\(778\) 0 0
\(779\) 8.86014e10 1.53462e11i 0.240597 0.416727i
\(780\) 0 0
\(781\) 3.75701e10 + 6.50732e10i 0.100981 + 0.174903i
\(782\) 0 0
\(783\) 6.74570e10i 0.179465i
\(784\) 0 0
\(785\) −1.30202e11 −0.342878
\(786\) 0 0
\(787\) 1.30594e11 7.53983e10i 0.340427 0.196545i −0.320034 0.947406i \(-0.603694\pi\)
0.660461 + 0.750861i \(0.270361\pi\)
\(788\) 0 0
\(789\) 1.94415e11 + 1.12246e11i 0.501675 + 0.289642i
\(790\) 0 0
\(791\) 3.66773e11 1.44019e11i 0.936896 0.367885i
\(792\) 0 0
\(793\) −5.22424e10 + 9.04865e10i −0.132108 + 0.228819i
\(794\) 0 0
\(795\) −3.11666e10 5.39821e10i −0.0780227 0.135139i
\(796\) 0 0
\(797\) 2.07975e11i 0.515439i −0.966220 0.257720i \(-0.917029\pi\)
0.966220 0.257720i \(-0.0829711\pi\)
\(798\) 0 0
\(799\) −2.00451e11 −0.491836
\(800\) 0 0
\(801\) −7.28537e10 + 4.20621e10i −0.176979 + 0.102179i
\(802\) 0 0
\(803\) 5.46567e10 + 3.15561e10i 0.131456 + 0.0758963i
\(804\) 0 0
\(805\) −7.60077e9 + 9.53433e9i −0.0180998 + 0.0227042i
\(806\) 0 0
\(807\) −7.27580e10 + 1.26021e11i −0.171548 + 0.297131i
\(808\) 0 0
\(809\) −3.44290e11 5.96328e11i −0.803768 1.39217i −0.917120 0.398612i \(-0.869492\pi\)
0.113352 0.993555i \(-0.463841\pi\)
\(810\) 0 0
\(811\) 1.52097e10i 0.0351591i −0.999845 0.0175795i \(-0.994404\pi\)
0.999845 0.0175795i \(-0.00559603\pi\)
\(812\) 0 0
\(813\) −1.71093e11 −0.391624
\(814\) 0 0
\(815\) −1.36224e11 + 7.86491e10i −0.308762 + 0.178264i
\(816\) 0 0
\(817\) 6.36572e11 + 3.67525e11i 1.42876 + 0.824895i
\(818\) 0 0
\(819\) −2.16923e10 3.26587e9i −0.0482136 0.00725878i
\(820\) 0 0
\(821\) −3.67890e11 + 6.37204e11i −0.809740 + 1.40251i 0.103305 + 0.994650i \(0.467058\pi\)
−0.913044 + 0.407860i \(0.866275\pi\)
\(822\) 0 0
\(823\) −9.71200e10 1.68217e11i −0.211694 0.366665i 0.740551 0.672001i \(-0.234565\pi\)
−0.952245 + 0.305335i \(0.901231\pi\)
\(824\) 0 0
\(825\) 1.35514e11i 0.292529i
\(826\) 0 0
\(827\) 5.50782e11 1.17749 0.588746 0.808318i \(-0.299622\pi\)
0.588746 + 0.808318i \(0.299622\pi\)
\(828\) 0 0
\(829\) −9.83589e10 + 5.67875e10i −0.208255 + 0.120236i −0.600500 0.799625i \(-0.705032\pi\)
0.392245 + 0.919861i \(0.371698\pi\)
\(830\) 0 0
\(831\) 4.24803e11 + 2.45260e11i 0.890806 + 0.514307i
\(832\) 0 0
\(833\) 2.16808e11 7.03712e11i 0.450294 1.46155i
\(834\) 0 0
\(835\) 6.06916e10 1.05121e11i 0.124848 0.216244i
\(836\) 0 0
\(837\) 3.04901e8 + 5.28105e8i 0.000621237 + 0.00107601i
\(838\) 0 0
\(839\) 5.71368e11i 1.15310i 0.817061 + 0.576551i \(0.195602\pi\)
−0.817061 + 0.576551i \(0.804398\pi\)
\(840\) 0 0
\(841\) −6.52276e10 −0.130391
\(842\) 0 0
\(843\) 7.63641e10 4.40888e10i 0.151210 0.0873008i
\(844\) 0 0
\(845\) −1.06892e11 6.17142e10i −0.209662 0.121048i
\(846\) 0 0
\(847\) −5.43042e10 + 3.60694e11i −0.105511 + 0.700819i
\(848\) 0 0
\(849\) 4.07614e10 7.06009e10i 0.0784546 0.135887i
\(850\) 0 0
\(851\) 1.08235e10 + 1.87468e10i 0.0206371 + 0.0357445i
\(852\) 0 0
\(853\) 1.61864e11i 0.305742i −0.988246 0.152871i \(-0.951148\pi\)
0.988246 0.152871i \(-0.0488519\pi\)
\(854\) 0 0
\(855\) −5.43707e10 −0.101742
\(856\) 0 0
\(857\) −1.38704e11 + 8.00810e10i −0.257138 + 0.148459i −0.623028 0.782199i \(-0.714098\pi\)
0.365890 + 0.930658i \(0.380765\pi\)
\(858\) 0 0
\(859\) −2.45231e11 1.41584e11i −0.450405 0.260042i 0.257596 0.966253i \(-0.417070\pi\)
−0.708001 + 0.706211i \(0.750403\pi\)
\(860\) 0 0
\(861\) 9.67615e10 + 7.71382e10i 0.176072 + 0.140364i
\(862\) 0 0
\(863\) −3.89609e11 + 6.74823e11i −0.702402 + 1.21660i 0.265219 + 0.964188i \(0.414556\pi\)
−0.967621 + 0.252408i \(0.918778\pi\)
\(864\) 0 0
\(865\) 3.84342e10 + 6.65700e10i 0.0686520 + 0.118909i
\(866\) 0 0
\(867\) 4.36783e11i 0.773018i
\(868\) 0 0
\(869\) −2.09837e10 −0.0367963
\(870\) 0 0
\(871\) 6.98774e10 4.03437e10i 0.121413 0.0700976i
\(872\) 0 0
\(873\) 4.86291e10 + 2.80760e10i 0.0837219 + 0.0483369i
\(874\) 0 0
\(875\) −1.02761e11 2.61703e11i −0.175306 0.446453i
\(876\) 0 0
\(877\) −3.57632e10 + 6.19436e10i −0.0604557 + 0.104712i −0.894669 0.446729i \(-0.852589\pi\)
0.834213 + 0.551442i \(0.185922\pi\)
\(878\) 0 0
\(879\) −1.79628e11 3.11125e11i −0.300898 0.521170i
\(880\) 0 0
\(881\) 8.68861e11i 1.44227i 0.692795 + 0.721135i \(0.256379\pi\)
−0.692795 + 0.721135i \(0.743621\pi\)
\(882\) 0 0
\(883\) −8.82118e11 −1.45105 −0.725527 0.688194i \(-0.758404\pi\)
−0.725527 + 0.688194i \(0.758404\pi\)
\(884\) 0 0
\(885\) −1.34139e11 + 7.74451e10i −0.218666 + 0.126247i
\(886\) 0 0
\(887\) −7.26589e11 4.19496e11i −1.17380 0.677694i −0.219229 0.975674i \(-0.570354\pi\)
−0.954572 + 0.297979i \(0.903687\pi\)
\(888\) 0 0
\(889\) −2.70582e11 + 1.06248e11i −0.433203 + 0.170103i
\(890\) 0 0
\(891\) 1.88971e10 3.27308e10i 0.0299837 0.0519333i
\(892\) 0 0
\(893\) −1.26163e11 2.18520e11i −0.198392 0.343626i
\(894\) 0 0
\(895\) 2.72240e11i 0.424287i
\(896\) 0 0
\(897\) −6.41685e9 −0.00991179
\(898\) 0 0
\(899\) −3.40566e9 + 1.96626e9i −0.00521389 + 0.00301024i
\(900\) 0 0
\(901\) 9.53601e11 + 5.50562e11i 1.44700 + 0.835424i
\(902\) 0 0
\(903\) −3.19975e11 + 4.01374e11i −0.481244 + 0.603668i
\(904\) 0 0
\(905\) −1.08692e11 + 1.88260e11i −0.162033 + 0.280649i
\(906\) 0 0
\(907\) −4.38453e11 7.59423e11i −0.647879 1.12216i −0.983628 0.180208i \(-0.942323\pi\)
0.335749 0.941951i \(-0.391011\pi\)
\(908\) 0 0
\(909\) 3.46639e11i 0.507718i
\(910\) 0 0
\(911\) 1.09312e10 0.0158706 0.00793529 0.999969i \(-0.497474\pi\)
0.00793529 + 0.999969i \(0.497474\pi\)
\(912\) 0 0
\(913\) −3.67768e11 + 2.12331e11i −0.529287 + 0.305584i
\(914\) 0 0
\(915\) −1.56617e11 9.04227e10i −0.223436 0.129001i
\(916\) 0 0
\(917\) −1.51907e11 2.28702e10i −0.214832 0.0323440i
\(918\) 0 0
\(919\) −3.27143e11 + 5.66628e11i −0.458643 + 0.794394i −0.998890 0.0471134i \(-0.984998\pi\)
0.540246 + 0.841507i \(0.318331\pi\)
\(920\) 0 0
\(921\) 2.09005e11 + 3.62008e11i 0.290482 + 0.503129i
\(922\) 0 0
\(923\) 3.97260e10i 0.0547353i
\(924\) 0 0
\(925\) −2.41692e11 −0.330138
\(926\) 0 0
\(927\) −5.18018e10 + 2.99078e10i −0.0701497 + 0.0405009i
\(928\) 0 0
\(929\) −1.55844e11 8.99765e10i −0.209231 0.120800i 0.391723 0.920083i \(-0.371879\pi\)
−0.600954 + 0.799283i \(0.705213\pi\)
\(930\) 0 0
\(931\) 9.03606e11 2.06560e11i 1.20276 0.274947i
\(932\) 0 0
\(933\) 3.69236e11 6.39536e11i 0.487279 0.843992i
\(934\) 0 0
\(935\) −7.80300e10 1.35152e11i −0.102097 0.176838i
\(936\) 0 0
\(937\) 7.66845e11i 0.994831i −0.867512 0.497415i \(-0.834282\pi\)
0.867512 0.497415i \(-0.165718\pi\)
\(938\) 0 0
\(939\) −4.41814e11 −0.568299
\(940\) 0 0
\(941\) −1.22218e12 + 7.05627e11i −1.55875 + 0.899946i −0.561376 + 0.827561i \(0.689728\pi\)
−0.997377 + 0.0723858i \(0.976939\pi\)
\(942\) 0 0
\(943\) 3.13481e10 + 1.80988e10i 0.0396428 + 0.0228878i
\(944\) 0 0
\(945\) 5.65266e9 3.75456e10i 0.00708804 0.0470795i
\(946\) 0 0
\(947\) 1.03071e10 1.78523e10i 0.0128155 0.0221971i −0.859547 0.511057i \(-0.829254\pi\)
0.872362 + 0.488860i \(0.162587\pi\)
\(948\) 0 0
\(949\) 1.66834e10 + 2.88966e10i 0.0205694 + 0.0356272i
\(950\) 0 0
\(951\) 7.91510e11i 0.967686i
\(952\) 0 0
\(953\) 2.06006e10 0.0249752 0.0124876 0.999922i \(-0.496025\pi\)
0.0124876 + 0.999922i \(0.496025\pi\)
\(954\) 0 0
\(955\) −9.27821e10 + 5.35677e10i −0.111545 + 0.0644006i
\(956\) 0 0
\(957\) 2.11075e11 + 1.21864e11i 0.251646 + 0.145288i
\(958\) 0 0
\(959\) 5.88983e11 + 4.69537e11i 0.696351 + 0.555131i
\(960\) 0 0
\(961\) −4.26428e11 + 7.38595e11i −0.499979 + 0.865989i
\(962\) 0 0
\(963\) 1.76840e11 + 3.06296e11i 0.205625 + 0.356153i
\(964\) 0 0
\(965\) 1.60124e11i 0.184649i
\(966\) 0 0
\(967\) −1.50116e12 −1.71681 −0.858405 0.512973i \(-0.828544\pi\)
−0.858405 + 0.512973i \(0.828544\pi\)
\(968\) 0 0
\(969\) 8.31788e11 4.80233e11i 0.943447 0.544699i
\(970\) 0 0
\(971\) −6.65121e11 3.84008e11i −0.748210 0.431979i 0.0768368 0.997044i \(-0.475518\pi\)
−0.825047 + 0.565064i \(0.808851\pi\)
\(972\) 0 0
\(973\) −1.79478e11 4.57076e11i −0.200244 0.509962i
\(974\) 0 0
\(975\) 3.58227e10 6.20467e10i 0.0396406 0.0686595i
\(976\) 0 0
\(977\) 5.61187e11 + 9.72004e11i 0.615927 + 1.06682i 0.990221 + 0.139507i \(0.0445516\pi\)
−0.374294 + 0.927310i \(0.622115\pi\)
\(978\) 0 0
\(979\) 3.03949e11i 0.330879i
\(980\) 0 0
\(981\) −1.29105e11 −0.139402
\(982\) 0 0
\(983\) −1.27850e12 + 7.38145e11i −1.36927 + 0.790546i −0.990834 0.135083i \(-0.956870\pi\)
−0.378432 + 0.925629i \(0.623537\pi\)
\(984\) 0 0
\(985\) 2.12437e11 + 1.22651e11i 0.225676 + 0.130294i
\(986\) 0 0
\(987\) 1.64015e11 6.44029e10i 0.172829 0.0678636i
\(988\) 0 0
\(989\) −7.50753e10 + 1.30034e11i −0.0784715 + 0.135917i
\(990\) 0 0
\(991\) 7.05075e11 + 1.22123e12i 0.731039 + 1.26620i 0.956439 + 0.291931i \(0.0942978\pi\)
−0.225400 + 0.974266i \(0.572369\pi\)
\(992\) 0 0
\(993\) 9.57807e11i 0.985102i
\(994\) 0 0
\(995\) −7.82157e10 −0.0797998
\(996\) 0 0
\(997\) 9.23084e11 5.32943e11i 0.934244 0.539386i 0.0460928 0.998937i \(-0.485323\pi\)
0.888151 + 0.459551i \(0.151990\pi\)
\(998\) 0 0
\(999\) −5.83760e10 3.37034e10i −0.0586101 0.0338386i
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 84.9.m.b.61.4 12
3.2 odd 2 252.9.z.d.145.3 12
7.3 odd 6 inner 84.9.m.b.73.4 yes 12
21.17 even 6 252.9.z.d.73.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.9.m.b.61.4 12 1.1 even 1 trivial
84.9.m.b.73.4 yes 12 7.3 odd 6 inner
252.9.z.d.73.3 12 21.17 even 6
252.9.z.d.145.3 12 3.2 odd 2