Properties

Label 126.8.g.j.37.2
Level $126$
Weight $8$
Character 126.37
Analytic conductor $39.361$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [126,8,Mod(37,126)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(126, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("126.37");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 126.g (of order \(3\), 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: \(39.3605132110\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 1111x^{4} + 2838x^{3} + 1231236x^{2} + 959040x + 746496 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.2
Root \(-16.2090 - 28.0749i\) of defining polynomial
Character \(\chi\) \(=\) 126.37
Dual form 126.8.g.j.109.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.00000 - 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-95.0129 + 164.567i) q^{5} +(-515.817 - 746.643i) q^{7} -512.000 q^{8} +(760.103 + 1316.54i) q^{10} +(3127.15 + 5416.38i) q^{11} -4182.79 q^{13} +(-7236.16 + 587.110i) q^{14} +(-2048.00 + 3547.24i) q^{16} +(288.449 + 499.608i) q^{17} +(7721.88 - 13374.7i) q^{19} +12161.7 q^{20} +50034.3 q^{22} +(29335.5 - 50810.6i) q^{23} +(21007.6 + 36386.2i) q^{25} +(-16731.2 + 28979.2i) q^{26} +(-24877.0 + 52482.0i) q^{28} +23161.9 q^{29} +(151094. + 261703. i) q^{31} +(16384.0 + 28377.9i) q^{32} +4615.18 q^{34} +(171882. - 13945.8i) q^{35} +(111538. - 193190. i) q^{37} +(-61775.1 - 106998. i) q^{38} +(48646.6 - 84258.4i) q^{40} +330003. q^{41} +284765. q^{43} +(200137. - 346648. i) q^{44} +(-234684. - 406485. i) q^{46} +(653080. - 1.13117e6i) q^{47} +(-291409. + 770262. i) q^{49} +336122. q^{50} +(133849. + 231834. i) q^{52} +(551149. + 954618. i) q^{53} -1.18848e6 q^{55} +(264098. + 382281. i) q^{56} +(92647.6 - 160470. i) q^{58} +(17976.0 + 31135.3i) q^{59} +(602384. - 1.04336e6i) q^{61} +2.41751e6 q^{62} +262144. q^{64} +(397419. - 688350. i) q^{65} +(111437. + 193014. i) q^{67} +(18460.7 - 31974.9i) q^{68} +(590910. - 1.24662e6i) q^{70} +4.83371e6 q^{71} +(-1.74021e6 - 3.01414e6i) q^{73} +(-892306. - 1.54552e6i) q^{74} -988401. q^{76} +(2.43107e6 - 5.12872e6i) q^{77} +(-3.72576e6 + 6.45321e6i) q^{79} +(-389173. - 674067. i) q^{80} +(1.32001e6 - 2.28633e6i) q^{82} +4.70492e6 q^{83} -109625. q^{85} +(1.13906e6 - 1.97291e6i) q^{86} +(-1.60110e6 - 2.77318e6i) q^{88} +(1.71735e6 - 2.97453e6i) q^{89} +(2.15755e6 + 3.12305e6i) q^{91} -3.75495e6 q^{92} +(-5.22464e6 - 9.04935e6i) q^{94} +(1.46736e6 + 2.54154e6i) q^{95} +3.79727e6 q^{97} +(4.17090e6 + 5.09999e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 24 q^{2} - 192 q^{4} - 718 q^{5} - 1471 q^{7} - 3072 q^{8} + 5744 q^{10} + 208 q^{11} + 19394 q^{13} - 4504 q^{14} - 12288 q^{16} - 19244 q^{17} - 25419 q^{19} + 91904 q^{20} + 3328 q^{22} - 67400 q^{23}+ \cdots + 20461248 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000 6.92820i 0.353553 0.612372i
\(3\) 0 0
\(4\) −32.0000 55.4256i −0.250000 0.433013i
\(5\) −95.0129 + 164.567i −0.339928 + 0.588773i −0.984419 0.175839i \(-0.943736\pi\)
0.644490 + 0.764612i \(0.277070\pi\)
\(6\) 0 0
\(7\) −515.817 746.643i −0.568398 0.822754i
\(8\) −512.000 −0.353553
\(9\) 0 0
\(10\) 760.103 + 1316.54i 0.240366 + 0.416326i
\(11\) 3127.15 + 5416.38i 0.708392 + 1.22697i 0.965453 + 0.260576i \(0.0839125\pi\)
−0.257061 + 0.966395i \(0.582754\pi\)
\(12\) 0 0
\(13\) −4182.79 −0.528037 −0.264018 0.964518i \(-0.585048\pi\)
−0.264018 + 0.964518i \(0.585048\pi\)
\(14\) −7236.16 + 587.110i −0.704791 + 0.0571836i
\(15\) 0 0
\(16\) −2048.00 + 3547.24i −0.125000 + 0.216506i
\(17\) 288.449 + 499.608i 0.0142396 + 0.0246637i 0.873057 0.487617i \(-0.162134\pi\)
−0.858818 + 0.512281i \(0.828801\pi\)
\(18\) 0 0
\(19\) 7721.88 13374.7i 0.258277 0.447349i −0.707503 0.706710i \(-0.750179\pi\)
0.965780 + 0.259361i \(0.0835120\pi\)
\(20\) 12161.7 0.339928
\(21\) 0 0
\(22\) 50034.3 1.00182
\(23\) 29335.5 50810.6i 0.502744 0.870777i −0.497251 0.867606i \(-0.665657\pi\)
0.999995 0.00317085i \(-0.00100932\pi\)
\(24\) 0 0
\(25\) 21007.6 + 36386.2i 0.268897 + 0.465744i
\(26\) −16731.2 + 28979.2i −0.186689 + 0.323355i
\(27\) 0 0
\(28\) −24877.0 + 52482.0i −0.214163 + 0.451812i
\(29\) 23161.9 0.176352 0.0881762 0.996105i \(-0.471896\pi\)
0.0881762 + 0.996105i \(0.471896\pi\)
\(30\) 0 0
\(31\) 151094. + 261703.i 0.910923 + 1.57776i 0.812764 + 0.582593i \(0.197962\pi\)
0.0981589 + 0.995171i \(0.468705\pi\)
\(32\) 16384.0 + 28377.9i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 4615.18 0.0201378
\(35\) 171882. 13945.8i 0.677630 0.0549799i
\(36\) 0 0
\(37\) 111538. 193190.i 0.362008 0.627015i −0.626284 0.779595i \(-0.715425\pi\)
0.988291 + 0.152580i \(0.0487581\pi\)
\(38\) −61775.1 106998.i −0.182629 0.316323i
\(39\) 0 0
\(40\) 48646.6 84258.4i 0.120183 0.208163i
\(41\) 330003. 0.747782 0.373891 0.927473i \(-0.378023\pi\)
0.373891 + 0.927473i \(0.378023\pi\)
\(42\) 0 0
\(43\) 284765. 0.546194 0.273097 0.961986i \(-0.411952\pi\)
0.273097 + 0.961986i \(0.411952\pi\)
\(44\) 200137. 346648.i 0.354196 0.613486i
\(45\) 0 0
\(46\) −234684. 406485.i −0.355493 0.615733i
\(47\) 653080. 1.13117e6i 0.917538 1.58922i 0.114396 0.993435i \(-0.463507\pi\)
0.803142 0.595788i \(-0.203160\pi\)
\(48\) 0 0
\(49\) −291409. + 770262.i −0.353848 + 0.935303i
\(50\) 336122. 0.380278
\(51\) 0 0
\(52\) 133849. + 231834.i 0.132009 + 0.228647i
\(53\) 551149. + 954618.i 0.508514 + 0.880773i 0.999951 + 0.00985975i \(0.00313851\pi\)
−0.491437 + 0.870913i \(0.663528\pi\)
\(54\) 0 0
\(55\) −1.18848e6 −0.963211
\(56\) 264098. + 382281.i 0.200959 + 0.290887i
\(57\) 0 0
\(58\) 92647.6 160470.i 0.0623500 0.107993i
\(59\) 17976.0 + 31135.3i 0.0113949 + 0.0197366i 0.871667 0.490099i \(-0.163039\pi\)
−0.860272 + 0.509836i \(0.829706\pi\)
\(60\) 0 0
\(61\) 602384. 1.04336e6i 0.339797 0.588545i −0.644598 0.764522i \(-0.722975\pi\)
0.984394 + 0.175977i \(0.0563085\pi\)
\(62\) 2.41751e6 1.28824
\(63\) 0 0
\(64\) 262144. 0.125000
\(65\) 397419. 688350.i 0.179495 0.310894i
\(66\) 0 0
\(67\) 111437. + 193014.i 0.0452654 + 0.0784020i 0.887770 0.460287i \(-0.152253\pi\)
−0.842505 + 0.538688i \(0.818920\pi\)
\(68\) 18460.7 31974.9i 0.00711980 0.0123319i
\(69\) 0 0
\(70\) 590910. 1.24662e6i 0.205910 0.434400i
\(71\) 4.83371e6 1.60279 0.801395 0.598135i \(-0.204091\pi\)
0.801395 + 0.598135i \(0.204091\pi\)
\(72\) 0 0
\(73\) −1.74021e6 3.01414e6i −0.523567 0.906844i −0.999624 0.0274299i \(-0.991268\pi\)
0.476057 0.879414i \(-0.342066\pi\)
\(74\) −892306. 1.54552e6i −0.255978 0.443367i
\(75\) 0 0
\(76\) −988401. −0.258277
\(77\) 2.43107e6 5.12872e6i 0.606847 1.28024i
\(78\) 0 0
\(79\) −3.72576e6 + 6.45321e6i −0.850198 + 1.47259i 0.0308315 + 0.999525i \(0.490184\pi\)
−0.881029 + 0.473061i \(0.843149\pi\)
\(80\) −389173. 674067.i −0.0849821 0.147193i
\(81\) 0 0
\(82\) 1.32001e6 2.28633e6i 0.264381 0.457921i
\(83\) 4.70492e6 0.903189 0.451594 0.892223i \(-0.350855\pi\)
0.451594 + 0.892223i \(0.350855\pi\)
\(84\) 0 0
\(85\) −109625. −0.0193618
\(86\) 1.13906e6 1.97291e6i 0.193109 0.334474i
\(87\) 0 0
\(88\) −1.60110e6 2.77318e6i −0.250454 0.433800i
\(89\) 1.71735e6 2.97453e6i 0.258222 0.447253i −0.707544 0.706669i \(-0.750197\pi\)
0.965766 + 0.259416i \(0.0835301\pi\)
\(90\) 0 0
\(91\) 2.15755e6 + 3.12305e6i 0.300135 + 0.434444i
\(92\) −3.75495e6 −0.502744
\(93\) 0 0
\(94\) −5.22464e6 9.04935e6i −0.648797 1.12375i
\(95\) 1.46736e6 + 2.54154e6i 0.175591 + 0.304133i
\(96\) 0 0
\(97\) 3.79727e6 0.422445 0.211223 0.977438i \(-0.432256\pi\)
0.211223 + 0.977438i \(0.432256\pi\)
\(98\) 4.17090e6 + 5.09999e6i 0.447649 + 0.547366i
\(99\) 0 0
\(100\) 1.34449e6 2.32872e6i 0.134449 0.232872i
\(101\) −1.98781e6 3.44299e6i −0.191977 0.332514i 0.753928 0.656957i \(-0.228157\pi\)
−0.945905 + 0.324442i \(0.894823\pi\)
\(102\) 0 0
\(103\) −3.47204e6 + 6.01376e6i −0.313080 + 0.542270i −0.979027 0.203728i \(-0.934694\pi\)
0.665948 + 0.745998i \(0.268027\pi\)
\(104\) 2.14159e6 0.186689
\(105\) 0 0
\(106\) 8.81838e6 0.719148
\(107\) −7.61733e6 + 1.31936e7i −0.601118 + 1.04117i 0.391534 + 0.920164i \(0.371945\pi\)
−0.992652 + 0.121003i \(0.961389\pi\)
\(108\) 0 0
\(109\) 9.79401e6 + 1.69637e7i 0.724382 + 1.25467i 0.959228 + 0.282634i \(0.0912082\pi\)
−0.234846 + 0.972033i \(0.575458\pi\)
\(110\) −4.75391e6 + 8.23401e6i −0.340546 + 0.589844i
\(111\) 0 0
\(112\) 3.70492e6 300600.i 0.249181 0.0202175i
\(113\) −8.75407e6 −0.570736 −0.285368 0.958418i \(-0.592116\pi\)
−0.285368 + 0.958418i \(0.592116\pi\)
\(114\) 0 0
\(115\) 5.57451e6 + 9.65533e6i 0.341794 + 0.592004i
\(116\) −741181. 1.28376e6i −0.0440881 0.0763628i
\(117\) 0 0
\(118\) 287616. 0.0161148
\(119\) 224242. 473075.i 0.0121984 0.0257345i
\(120\) 0 0
\(121\) −9.81450e6 + 1.69992e7i −0.503639 + 0.872329i
\(122\) −4.81907e6 8.34688e6i −0.240272 0.416164i
\(123\) 0 0
\(124\) 9.67002e6 1.67490e7i 0.455461 0.788882i
\(125\) −2.28297e7 −1.04548
\(126\) 0 0
\(127\) 3.12686e7 1.35455 0.677275 0.735730i \(-0.263161\pi\)
0.677275 + 0.735730i \(0.263161\pi\)
\(128\) 1.04858e6 1.81619e6i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −3.17935e6 5.50680e6i −0.126922 0.219835i
\(131\) −1.44504e7 + 2.50288e7i −0.561605 + 0.972728i 0.435752 + 0.900067i \(0.356482\pi\)
−0.997357 + 0.0726610i \(0.976851\pi\)
\(132\) 0 0
\(133\) −1.39692e7 + 1.13340e6i −0.514862 + 0.0417736i
\(134\) 1.78299e6 0.0640149
\(135\) 0 0
\(136\) −147686. 255799.i −0.00503446 0.00871994i
\(137\) −1.90023e6 3.29130e6i −0.0631371 0.109357i 0.832729 0.553681i \(-0.186777\pi\)
−0.895866 + 0.444324i \(0.853444\pi\)
\(138\) 0 0
\(139\) −5.87608e7 −1.85582 −0.927911 0.372803i \(-0.878397\pi\)
−0.927911 + 0.372803i \(0.878397\pi\)
\(140\) −6.27318e6 9.08041e6i −0.193215 0.279678i
\(141\) 0 0
\(142\) 1.93349e7 3.34890e7i 0.566672 0.981505i
\(143\) −1.30802e7 2.26556e7i −0.374057 0.647886i
\(144\) 0 0
\(145\) −2.20068e6 + 3.81169e6i −0.0599472 + 0.103832i
\(146\) −2.78434e7 −0.740435
\(147\) 0 0
\(148\) −1.42769e7 −0.362008
\(149\) −2.18958e7 + 3.79246e7i −0.542261 + 0.939224i 0.456512 + 0.889717i \(0.349098\pi\)
−0.998774 + 0.0495073i \(0.984235\pi\)
\(150\) 0 0
\(151\) 5.34472e6 + 9.25733e6i 0.126330 + 0.218810i 0.922252 0.386589i \(-0.126347\pi\)
−0.795922 + 0.605399i \(0.793014\pi\)
\(152\) −3.95360e6 + 6.84784e6i −0.0913147 + 0.158162i
\(153\) 0 0
\(154\) −2.58086e7 3.73578e7i −0.569431 0.824250i
\(155\) −5.74235e7 −1.23859
\(156\) 0 0
\(157\) 2.54849e7 + 4.41411e7i 0.525574 + 0.910320i 0.999556 + 0.0297861i \(0.00948262\pi\)
−0.473983 + 0.880534i \(0.657184\pi\)
\(158\) 2.98061e7 + 5.16256e7i 0.601181 + 1.04128i
\(159\) 0 0
\(160\) −6.22677e6 −0.120183
\(161\) −5.30692e7 + 4.30580e6i −1.00219 + 0.0813136i
\(162\) 0 0
\(163\) −2.77491e6 + 4.80629e6i −0.0501872 + 0.0869268i −0.890028 0.455907i \(-0.849315\pi\)
0.839840 + 0.542833i \(0.182648\pi\)
\(164\) −1.05601e7 1.82906e7i −0.186945 0.323799i
\(165\) 0 0
\(166\) 1.88197e7 3.25966e7i 0.319325 0.553088i
\(167\) 8.69574e7 1.44477 0.722385 0.691491i \(-0.243046\pi\)
0.722385 + 0.691491i \(0.243046\pi\)
\(168\) 0 0
\(169\) −4.52528e7 −0.721177
\(170\) −438502. + 759507.i −0.00684542 + 0.0118566i
\(171\) 0 0
\(172\) −9.11248e6 1.57833e7i −0.136549 0.236509i
\(173\) −5.88732e6 + 1.01971e7i −0.0864483 + 0.149733i −0.906007 0.423262i \(-0.860885\pi\)
0.819559 + 0.572995i \(0.194218\pi\)
\(174\) 0 0
\(175\) 1.63315e7 3.44538e7i 0.230352 0.485964i
\(176\) −2.56176e7 −0.354196
\(177\) 0 0
\(178\) −1.37388e7 2.37962e7i −0.182590 0.316256i
\(179\) −2.28592e7 3.95932e7i −0.297903 0.515983i 0.677753 0.735290i \(-0.262954\pi\)
−0.975656 + 0.219307i \(0.929620\pi\)
\(180\) 0 0
\(181\) −1.74679e7 −0.218960 −0.109480 0.993989i \(-0.534919\pi\)
−0.109480 + 0.993989i \(0.534919\pi\)
\(182\) 3.02673e7 2.45576e6i 0.372155 0.0301950i
\(183\) 0 0
\(184\) −1.50198e7 + 2.60150e7i −0.177747 + 0.307866i
\(185\) 2.11951e7 + 3.67110e7i 0.246113 + 0.426281i
\(186\) 0 0
\(187\) −1.80404e6 + 3.12470e6i −0.0201744 + 0.0349431i
\(188\) −8.35943e7 −0.917538
\(189\) 0 0
\(190\) 2.34777e7 0.248324
\(191\) 1.92433e7 3.33304e7i 0.199831 0.346117i −0.748643 0.662974i \(-0.769294\pi\)
0.948473 + 0.316857i \(0.102627\pi\)
\(192\) 0 0
\(193\) 5.12431e7 + 8.87557e7i 0.513080 + 0.888681i 0.999885 + 0.0151698i \(0.00482890\pi\)
−0.486805 + 0.873511i \(0.661838\pi\)
\(194\) 1.51891e7 2.63083e7i 0.149357 0.258694i
\(195\) 0 0
\(196\) 5.20174e7 8.49685e6i 0.493460 0.0806050i
\(197\) 1.77214e8 1.65145 0.825725 0.564072i \(-0.190766\pi\)
0.825725 + 0.564072i \(0.190766\pi\)
\(198\) 0 0
\(199\) 2.01052e6 + 3.48233e6i 0.0180852 + 0.0313245i 0.874926 0.484256i \(-0.160910\pi\)
−0.856841 + 0.515580i \(0.827576\pi\)
\(200\) −1.07559e7 1.86297e7i −0.0950695 0.164665i
\(201\) 0 0
\(202\) −3.18049e7 −0.271497
\(203\) −1.19473e7 1.72937e7i −0.100238 0.145095i
\(204\) 0 0
\(205\) −3.13546e7 + 5.43077e7i −0.254192 + 0.440274i
\(206\) 2.77764e7 + 4.81101e7i 0.221381 + 0.383443i
\(207\) 0 0
\(208\) 8.56635e6 1.48374e7i 0.0660046 0.114323i
\(209\) 9.65898e7 0.731846
\(210\) 0 0
\(211\) −1.04790e8 −0.767944 −0.383972 0.923345i \(-0.625444\pi\)
−0.383972 + 0.923345i \(0.625444\pi\)
\(212\) 3.52735e7 6.10955e7i 0.254257 0.440386i
\(213\) 0 0
\(214\) 6.09387e7 + 1.05549e8i 0.425055 + 0.736216i
\(215\) −2.70564e7 + 4.68630e7i −0.185667 + 0.321585i
\(216\) 0 0
\(217\) 1.17462e8 2.47804e8i 0.780345 1.64626i
\(218\) 1.56704e8 1.02443
\(219\) 0 0
\(220\) 3.80313e7 + 6.58721e7i 0.240803 + 0.417083i
\(221\) −1.20652e6 2.08975e6i −0.00751903 0.0130233i
\(222\) 0 0
\(223\) −3.55298e7 −0.214548 −0.107274 0.994229i \(-0.534212\pi\)
−0.107274 + 0.994229i \(0.534212\pi\)
\(224\) 1.27370e7 2.68708e7i 0.0757182 0.159740i
\(225\) 0 0
\(226\) −3.50163e7 + 6.06500e7i −0.201786 + 0.349503i
\(227\) −5.81207e7 1.00668e8i −0.329792 0.571217i 0.652678 0.757635i \(-0.273645\pi\)
−0.982470 + 0.186418i \(0.940312\pi\)
\(228\) 0 0
\(229\) 9.46205e7 1.63888e8i 0.520668 0.901824i −0.479043 0.877792i \(-0.659016\pi\)
0.999711 0.0240325i \(-0.00765052\pi\)
\(230\) 8.91921e7 0.483369
\(231\) 0 0
\(232\) −1.18589e7 −0.0623500
\(233\) 1.51010e8 2.61556e8i 0.782094 1.35463i −0.148626 0.988894i \(-0.547485\pi\)
0.930720 0.365733i \(-0.119182\pi\)
\(234\) 0 0
\(235\) 1.24102e8 + 2.14951e8i 0.623795 + 1.08044i
\(236\) 1.15046e6 1.99266e6i 0.00569746 0.00986828i
\(237\) 0 0
\(238\) −2.38059e6 3.44589e6i −0.0114463 0.0165685i
\(239\) 3.00671e8 1.42462 0.712309 0.701866i \(-0.247649\pi\)
0.712309 + 0.701866i \(0.247649\pi\)
\(240\) 0 0
\(241\) 1.91754e7 + 3.32127e7i 0.0882437 + 0.152843i 0.906769 0.421628i \(-0.138541\pi\)
−0.818525 + 0.574471i \(0.805208\pi\)
\(242\) 7.85160e7 + 1.35994e8i 0.356127 + 0.616829i
\(243\) 0 0
\(244\) −7.71051e7 −0.339797
\(245\) −9.90722e7 1.21141e8i −0.430398 0.526272i
\(246\) 0 0
\(247\) −3.22990e7 + 5.59435e7i −0.136380 + 0.236217i
\(248\) −7.73602e7 1.33992e8i −0.322060 0.557824i
\(249\) 0 0
\(250\) −9.13189e7 + 1.58169e8i −0.369633 + 0.640223i
\(251\) 1.78185e7 0.0711234 0.0355617 0.999367i \(-0.488678\pi\)
0.0355617 + 0.999367i \(0.488678\pi\)
\(252\) 0 0
\(253\) 3.66946e8 1.42456
\(254\) 1.25074e8 2.16635e8i 0.478906 0.829490i
\(255\) 0 0
\(256\) −8.38861e6 1.45295e7i −0.0312500 0.0541266i
\(257\) 169674. 293884.i 0.000623518 0.00107996i −0.865713 0.500540i \(-0.833135\pi\)
0.866337 + 0.499460i \(0.166468\pi\)
\(258\) 0 0
\(259\) −2.01777e8 + 1.63713e7i −0.721644 + 0.0585510i
\(260\) −5.08696e7 −0.179495
\(261\) 0 0
\(262\) 1.15603e8 + 2.00231e8i 0.397114 + 0.687822i
\(263\) 9.01614e7 + 1.56164e8i 0.305616 + 0.529342i 0.977398 0.211407i \(-0.0678044\pi\)
−0.671783 + 0.740748i \(0.734471\pi\)
\(264\) 0 0
\(265\) −2.09465e8 −0.691434
\(266\) −4.80244e7 + 1.01315e8i −0.156450 + 0.330057i
\(267\) 0 0
\(268\) 7.13195e6 1.23529e7i 0.0226327 0.0392010i
\(269\) 1.96057e8 + 3.39581e8i 0.614115 + 1.06368i 0.990539 + 0.137230i \(0.0438201\pi\)
−0.376424 + 0.926447i \(0.622847\pi\)
\(270\) 0 0
\(271\) 1.92498e8 3.33417e8i 0.587536 1.01764i −0.407018 0.913420i \(-0.633431\pi\)
0.994554 0.104222i \(-0.0332353\pi\)
\(272\) −2.36297e6 −0.00711980
\(273\) 0 0
\(274\) −3.04037e7 −0.0892894
\(275\) −1.31388e8 + 2.27570e8i −0.380969 + 0.659858i
\(276\) 0 0
\(277\) −2.10950e8 3.65375e8i −0.596348 1.03290i −0.993355 0.115089i \(-0.963285\pi\)
0.397008 0.917815i \(-0.370049\pi\)
\(278\) −2.35043e8 + 4.07107e8i −0.656132 + 1.13645i
\(279\) 0 0
\(280\) −8.80037e7 + 7.14023e6i −0.239578 + 0.0194383i
\(281\) 1.48141e8 0.398294 0.199147 0.979970i \(-0.436183\pi\)
0.199147 + 0.979970i \(0.436183\pi\)
\(282\) 0 0
\(283\) −1.95211e8 3.38115e8i −0.511977 0.886771i −0.999904 0.0138859i \(-0.995580\pi\)
0.487926 0.872885i \(-0.337753\pi\)
\(284\) −1.54679e8 2.67912e8i −0.400698 0.694029i
\(285\) 0 0
\(286\) −2.09283e8 −0.528997
\(287\) −1.70221e8 2.46395e8i −0.425037 0.615240i
\(288\) 0 0
\(289\) 2.05003e8 3.55075e8i 0.499594 0.865323i
\(290\) 1.76054e7 + 3.04935e7i 0.0423891 + 0.0734200i
\(291\) 0 0
\(292\) −1.11374e8 + 1.92905e8i −0.261783 + 0.453422i
\(293\) −4.41291e8 −1.02492 −0.512458 0.858712i \(-0.671265\pi\)
−0.512458 + 0.858712i \(0.671265\pi\)
\(294\) 0 0
\(295\) −6.83181e6 −0.0154938
\(296\) −5.71076e7 + 9.89132e7i −0.127989 + 0.221683i
\(297\) 0 0
\(298\) 1.75166e8 + 3.03397e8i 0.383437 + 0.664132i
\(299\) −1.22704e8 + 2.12530e8i −0.265467 + 0.459802i
\(300\) 0 0
\(301\) −1.46887e8 2.12618e8i −0.310456 0.449383i
\(302\) 8.55156e7 0.178657
\(303\) 0 0
\(304\) 3.16288e7 + 5.47827e7i 0.0645692 + 0.111837i
\(305\) 1.14468e8 + 1.98265e8i 0.231013 + 0.400126i
\(306\) 0 0
\(307\) −8.55663e8 −1.68779 −0.843895 0.536509i \(-0.819743\pi\)
−0.843895 + 0.536509i \(0.819743\pi\)
\(308\) −3.62057e8 + 2.93757e7i −0.706072 + 0.0572876i
\(309\) 0 0
\(310\) −2.29694e8 + 3.97842e8i −0.437909 + 0.758481i
\(311\) −5.01999e8 8.69488e8i −0.946328 1.63909i −0.753070 0.657941i \(-0.771428\pi\)
−0.193258 0.981148i \(-0.561906\pi\)
\(312\) 0 0
\(313\) 1.73099e8 2.99817e8i 0.319073 0.552650i −0.661222 0.750190i \(-0.729962\pi\)
0.980295 + 0.197540i \(0.0632952\pi\)
\(314\) 4.07758e8 0.743273
\(315\) 0 0
\(316\) 4.76897e8 0.850198
\(317\) 2.01572e8 3.49132e8i 0.355404 0.615578i −0.631783 0.775145i \(-0.717677\pi\)
0.987187 + 0.159568i \(0.0510100\pi\)
\(318\) 0 0
\(319\) 7.24307e7 + 1.25454e8i 0.124927 + 0.216379i
\(320\) −2.49071e7 + 4.31403e7i −0.0424911 + 0.0735967i
\(321\) 0 0
\(322\) −1.82445e8 + 3.84897e8i −0.304535 + 0.642465i
\(323\) 8.90947e6 0.0147110
\(324\) 0 0
\(325\) −8.78703e7 1.52196e8i −0.141988 0.245930i
\(326\) 2.21993e7 + 3.84503e7i 0.0354877 + 0.0614665i
\(327\) 0 0
\(328\) −1.68962e8 −0.264381
\(329\) −1.18145e9 + 9.58576e7i −1.82907 + 0.148402i
\(330\) 0 0
\(331\) −1.43426e8 + 2.48421e8i −0.217385 + 0.376521i −0.954008 0.299782i \(-0.903086\pi\)
0.736623 + 0.676304i \(0.236419\pi\)
\(332\) −1.50557e8 2.60773e8i −0.225797 0.391092i
\(333\) 0 0
\(334\) 3.47830e8 6.02459e8i 0.510804 0.884738i
\(335\) −4.23517e7 −0.0615480
\(336\) 0 0
\(337\) 5.69157e8 0.810078 0.405039 0.914299i \(-0.367258\pi\)
0.405039 + 0.914299i \(0.367258\pi\)
\(338\) −1.81011e8 + 3.13521e8i −0.254975 + 0.441629i
\(339\) 0 0
\(340\) 3.50801e6 + 6.07606e6i 0.00484044 + 0.00838389i
\(341\) −9.44986e8 + 1.63676e9i −1.29058 + 2.23535i
\(342\) 0 0
\(343\) 7.25425e8 1.79735e8i 0.970651 0.240494i
\(344\) −1.45800e8 −0.193109
\(345\) 0 0
\(346\) 4.70986e7 + 8.15771e7i 0.0611282 + 0.105877i
\(347\) 5.53764e8 + 9.59148e8i 0.711495 + 1.23234i 0.964296 + 0.264827i \(0.0853148\pi\)
−0.252801 + 0.967518i \(0.581352\pi\)
\(348\) 0 0
\(349\) 1.46957e9 1.85055 0.925274 0.379300i \(-0.123835\pi\)
0.925274 + 0.379300i \(0.123835\pi\)
\(350\) −1.73377e8 2.50963e8i −0.216149 0.312875i
\(351\) 0 0
\(352\) −1.02470e8 + 1.77484e8i −0.125227 + 0.216900i
\(353\) −4.35007e8 7.53453e8i −0.526362 0.911685i −0.999528 0.0307123i \(-0.990222\pi\)
0.473166 0.880973i \(-0.343111\pi\)
\(354\) 0 0
\(355\) −4.59265e8 + 7.95471e8i −0.544834 + 0.943680i
\(356\) −2.19820e8 −0.258222
\(357\) 0 0
\(358\) −3.65747e8 −0.421298
\(359\) −4.00315e8 + 6.93366e8i −0.456638 + 0.790919i −0.998781 0.0493667i \(-0.984280\pi\)
0.542143 + 0.840286i \(0.317613\pi\)
\(360\) 0 0
\(361\) 3.27681e8 + 5.67560e8i 0.366586 + 0.634946i
\(362\) −6.98715e7 + 1.21021e8i −0.0774140 + 0.134085i
\(363\) 0 0
\(364\) 1.04055e8 2.19521e8i 0.113086 0.238573i
\(365\) 6.61370e8 0.711901
\(366\) 0 0
\(367\) −2.49769e8 4.32612e8i −0.263759 0.456844i 0.703479 0.710716i \(-0.251629\pi\)
−0.967238 + 0.253873i \(0.918296\pi\)
\(368\) 1.20158e8 + 2.08120e8i 0.125686 + 0.217694i
\(369\) 0 0
\(370\) 3.39122e8 0.348057
\(371\) 4.28467e8 9.03919e8i 0.435621 0.919012i
\(372\) 0 0
\(373\) −5.15842e8 + 8.93464e8i −0.514678 + 0.891448i 0.485177 + 0.874416i \(0.338755\pi\)
−0.999855 + 0.0170324i \(0.994578\pi\)
\(374\) 1.44323e7 + 2.49976e7i 0.0142655 + 0.0247085i
\(375\) 0 0
\(376\) −3.34377e8 + 5.79158e8i −0.324399 + 0.561875i
\(377\) −9.68814e7 −0.0931205
\(378\) 0 0
\(379\) −8.35481e8 −0.788314 −0.394157 0.919043i \(-0.628963\pi\)
−0.394157 + 0.919043i \(0.628963\pi\)
\(380\) 9.39109e7 1.62658e8i 0.0877957 0.152067i
\(381\) 0 0
\(382\) −1.53946e8 2.66643e8i −0.141302 0.244742i
\(383\) −9.98853e8 + 1.73006e9i −0.908460 + 1.57350i −0.0922557 + 0.995735i \(0.529408\pi\)
−0.816204 + 0.577763i \(0.803926\pi\)
\(384\) 0 0
\(385\) 6.13036e8 + 8.87368e8i 0.547487 + 0.792485i
\(386\) 8.19890e8 0.725605
\(387\) 0 0
\(388\) −1.21513e8 2.10466e8i −0.105611 0.182924i
\(389\) −2.25421e8 3.90441e8i −0.194165 0.336304i 0.752462 0.658636i \(-0.228866\pi\)
−0.946626 + 0.322333i \(0.895533\pi\)
\(390\) 0 0
\(391\) 3.38472e7 0.0286355
\(392\) 1.49202e8 3.94374e8i 0.125104 0.330680i
\(393\) 0 0
\(394\) 7.08855e8 1.22777e9i 0.583876 1.01130i
\(395\) −7.07991e8 1.22628e9i −0.578013 1.00115i
\(396\) 0 0
\(397\) 4.83785e8 8.37940e8i 0.388048 0.672119i −0.604139 0.796879i \(-0.706483\pi\)
0.992187 + 0.124760i \(0.0398160\pi\)
\(398\) 3.21684e7 0.0255763
\(399\) 0 0
\(400\) −1.72094e8 −0.134449
\(401\) 1.24216e9 2.15149e9i 0.961996 1.66623i 0.244517 0.969645i \(-0.421371\pi\)
0.717479 0.696580i \(-0.245296\pi\)
\(402\) 0 0
\(403\) −6.31994e8 1.09465e9i −0.481001 0.833117i
\(404\) −1.27220e8 + 2.20351e8i −0.0959887 + 0.166257i
\(405\) 0 0
\(406\) −1.67603e8 + 1.35986e7i −0.124292 + 0.0100845i
\(407\) 1.39518e9 1.02577
\(408\) 0 0
\(409\) 3.68300e6 + 6.37914e6i 0.00266176 + 0.00461031i 0.867353 0.497693i \(-0.165819\pi\)
−0.864691 + 0.502303i \(0.832486\pi\)
\(410\) 2.50837e8 + 4.34462e8i 0.179741 + 0.311321i
\(411\) 0 0
\(412\) 4.44422e8 0.313080
\(413\) 1.39747e7 2.94818e7i 0.00976150 0.0205934i
\(414\) 0 0
\(415\) −4.47028e8 + 7.74275e8i −0.307020 + 0.531773i
\(416\) −6.85308e7 1.18699e8i −0.0466723 0.0808388i
\(417\) 0 0
\(418\) 3.86359e8 6.69194e8i 0.258746 0.448162i
\(419\) 2.18245e9 1.44942 0.724712 0.689051i \(-0.241973\pi\)
0.724712 + 0.689051i \(0.241973\pi\)
\(420\) 0 0
\(421\) −2.74780e8 −0.179472 −0.0897362 0.995966i \(-0.528602\pi\)
−0.0897362 + 0.995966i \(0.528602\pi\)
\(422\) −4.19158e8 + 7.26003e8i −0.271509 + 0.470268i
\(423\) 0 0
\(424\) −2.82188e8 4.88764e8i −0.179787 0.311400i
\(425\) −1.21192e7 + 2.09911e7i −0.00765798 + 0.0132640i
\(426\) 0 0
\(427\) −1.08974e9 + 8.84165e7i −0.677367 + 0.0549586i
\(428\) 9.75019e8 0.601118
\(429\) 0 0
\(430\) 2.16451e8 + 3.74904e8i 0.131286 + 0.227395i
\(431\) 7.95998e8 + 1.37871e9i 0.478897 + 0.829473i 0.999707 0.0241991i \(-0.00770357\pi\)
−0.520811 + 0.853672i \(0.674370\pi\)
\(432\) 0 0
\(433\) 4.93795e8 0.292307 0.146154 0.989262i \(-0.453311\pi\)
0.146154 + 0.989262i \(0.453311\pi\)
\(434\) −1.24699e9 1.80501e9i −0.732232 1.05990i
\(435\) 0 0
\(436\) 6.26817e8 1.08568e9i 0.362191 0.627333i
\(437\) −4.53051e8 7.84707e8i −0.259694 0.449803i
\(438\) 0 0
\(439\) −1.62501e9 + 2.81460e9i −0.916708 + 1.58778i −0.112326 + 0.993671i \(0.535830\pi\)
−0.804382 + 0.594113i \(0.797503\pi\)
\(440\) 6.08500e8 0.340546
\(441\) 0 0
\(442\) −1.93043e7 −0.0106335
\(443\) 1.24877e9 2.16294e9i 0.682450 1.18204i −0.291782 0.956485i \(-0.594248\pi\)
0.974231 0.225552i \(-0.0724187\pi\)
\(444\) 0 0
\(445\) 3.26340e8 + 5.65238e8i 0.175554 + 0.304068i
\(446\) −1.42119e8 + 2.46157e8i −0.0758543 + 0.131383i
\(447\) 0 0
\(448\) −1.35218e8 1.95728e8i −0.0710497 0.102844i
\(449\) 2.71722e9 1.41665 0.708325 0.705887i \(-0.249451\pi\)
0.708325 + 0.705887i \(0.249451\pi\)
\(450\) 0 0
\(451\) 1.03197e9 + 1.78742e9i 0.529723 + 0.917507i
\(452\) 2.80130e8 + 4.85200e8i 0.142684 + 0.247136i
\(453\) 0 0
\(454\) −9.29931e8 −0.466397
\(455\) −7.18947e8 + 5.83322e7i −0.357814 + 0.0290314i
\(456\) 0 0
\(457\) 1.56358e9 2.70820e9i 0.766326 1.32731i −0.173217 0.984884i \(-0.555416\pi\)
0.939543 0.342431i \(-0.111250\pi\)
\(458\) −7.56964e8 1.31110e9i −0.368168 0.637686i
\(459\) 0 0
\(460\) 3.56768e8 6.17941e8i 0.170897 0.296002i
\(461\) 2.90548e9 1.38123 0.690614 0.723224i \(-0.257341\pi\)
0.690614 + 0.723224i \(0.257341\pi\)
\(462\) 0 0
\(463\) −3.47147e9 −1.62547 −0.812736 0.582632i \(-0.802023\pi\)
−0.812736 + 0.582632i \(0.802023\pi\)
\(464\) −4.74356e7 + 8.21609e7i −0.0220441 + 0.0381814i
\(465\) 0 0
\(466\) −1.20808e9 2.09245e9i −0.553024 0.957866i
\(467\) −1.31417e9 + 2.27621e9i −0.597094 + 1.03420i 0.396154 + 0.918184i \(0.370345\pi\)
−0.993248 + 0.116013i \(0.962989\pi\)
\(468\) 0 0
\(469\) 8.66317e7 1.82763e8i 0.0387768 0.0818058i
\(470\) 1.98563e9 0.882179
\(471\) 0 0
\(472\) −9.20371e6 1.59413e7i −0.00402871 0.00697793i
\(473\) 8.90502e8 + 1.54239e9i 0.386920 + 0.670165i
\(474\) 0 0
\(475\) 6.48873e8 0.277800
\(476\) −3.33962e7 + 2.70962e6i −0.0141930 + 0.00115155i
\(477\) 0 0
\(478\) 1.20268e9 2.08311e9i 0.503679 0.872397i
\(479\) −2.03983e9 3.53309e9i −0.848046 1.46886i −0.882950 0.469468i \(-0.844446\pi\)
0.0349039 0.999391i \(-0.488887\pi\)
\(480\) 0 0
\(481\) −4.66541e8 + 8.08072e8i −0.191153 + 0.331087i
\(482\) 3.06806e8 0.124795
\(483\) 0 0
\(484\) 1.25626e9 0.503639
\(485\) −3.60790e8 + 6.24906e8i −0.143601 + 0.248725i
\(486\) 0 0
\(487\) 7.56219e7 + 1.30981e8i 0.0296685 + 0.0513874i 0.880478 0.474086i \(-0.157221\pi\)
−0.850810 + 0.525474i \(0.823888\pi\)
\(488\) −3.08421e8 + 5.34200e8i −0.120136 + 0.208082i
\(489\) 0 0
\(490\) −1.23558e9 + 2.01828e8i −0.474444 + 0.0774987i
\(491\) 4.20636e9 1.60369 0.801846 0.597531i \(-0.203851\pi\)
0.801846 + 0.597531i \(0.203851\pi\)
\(492\) 0 0
\(493\) 6.68103e6 + 1.15719e7i 0.00251119 + 0.00434950i
\(494\) 2.58392e8 + 4.47548e8i 0.0964350 + 0.167030i
\(495\) 0 0
\(496\) −1.23776e9 −0.455461
\(497\) −2.49331e9 3.60906e9i −0.911022 1.31870i
\(498\) 0 0
\(499\) −9.65358e8 + 1.67205e9i −0.347806 + 0.602417i −0.985859 0.167575i \(-0.946406\pi\)
0.638054 + 0.769992i \(0.279740\pi\)
\(500\) 7.30552e8 + 1.26535e9i 0.261370 + 0.452706i
\(501\) 0 0
\(502\) 7.12739e7 1.23450e8i 0.0251459 0.0435540i
\(503\) −1.22595e9 −0.429522 −0.214761 0.976667i \(-0.568897\pi\)
−0.214761 + 0.976667i \(0.568897\pi\)
\(504\) 0 0
\(505\) 7.55470e8 0.261034
\(506\) 1.46778e9 2.54228e9i 0.503657 0.872360i
\(507\) 0 0
\(508\) −1.00059e9 1.73308e9i −0.338638 0.586538i
\(509\) −2.11547e9 + 3.66410e9i −0.711041 + 1.23156i 0.253426 + 0.967355i \(0.418443\pi\)
−0.964467 + 0.264204i \(0.914891\pi\)
\(510\) 0 0
\(511\) −1.35285e9 + 2.85406e9i −0.448516 + 0.946215i
\(512\) −1.34218e8 −0.0441942
\(513\) 0 0
\(514\) −1.35739e6 2.35107e6i −0.000440894 0.000763650i
\(515\) −6.59778e8 1.14277e9i −0.212849 0.368666i
\(516\) 0 0
\(517\) 8.16911e9 2.59991
\(518\) −6.93685e8 + 1.46344e9i −0.219285 + 0.462616i
\(519\) 0 0
\(520\) −2.03478e8 + 3.52435e8i −0.0634610 + 0.109918i
\(521\) 1.32387e9 + 2.29302e9i 0.410123 + 0.710355i 0.994903 0.100838i \(-0.0321523\pi\)
−0.584779 + 0.811192i \(0.698819\pi\)
\(522\) 0 0
\(523\) −2.30857e9 + 3.99856e9i −0.705647 + 1.22222i 0.260810 + 0.965390i \(0.416010\pi\)
−0.966458 + 0.256827i \(0.917323\pi\)
\(524\) 1.84965e9 0.561605
\(525\) 0 0
\(526\) 1.44258e9 0.432206
\(527\) −8.71658e7 + 1.50976e8i −0.0259423 + 0.0449334i
\(528\) 0 0
\(529\) −1.87337e7 3.24477e7i −0.00550211 0.00952993i
\(530\) −8.37860e8 + 1.45122e9i −0.244459 + 0.423415i
\(531\) 0 0
\(532\) 5.09834e8 + 7.37983e8i 0.146804 + 0.212498i
\(533\) −1.38033e9 −0.394856
\(534\) 0 0
\(535\) −1.44749e9 2.50713e9i −0.408674 0.707845i
\(536\) −5.70556e7 9.88231e7i −0.0160037 0.0277193i
\(537\) 0 0
\(538\) 3.13691e9 0.868489
\(539\) −5.08331e9 + 8.30341e8i −1.39825 + 0.228400i
\(540\) 0 0
\(541\) 1.09381e8 1.89453e8i 0.0296996 0.0514412i −0.850794 0.525500i \(-0.823878\pi\)
0.880493 + 0.474059i \(0.157212\pi\)
\(542\) −1.53999e9 2.66734e9i −0.415451 0.719582i
\(543\) 0 0
\(544\) −9.45189e6 + 1.63712e7i −0.00251723 + 0.00435997i
\(545\) −3.72223e9 −0.984953
\(546\) 0 0
\(547\) −2.39779e9 −0.626405 −0.313203 0.949686i \(-0.601402\pi\)
−0.313203 + 0.949686i \(0.601402\pi\)
\(548\) −1.21615e8 + 2.10643e8i −0.0315686 + 0.0546784i
\(549\) 0 0
\(550\) 1.05110e9 + 1.82056e9i 0.269386 + 0.466590i
\(551\) 1.78854e8 3.09783e8i 0.0455478 0.0788910i
\(552\) 0 0
\(553\) 6.74005e9 5.46858e8i 1.69483 0.137511i
\(554\) −3.37519e9 −0.843363
\(555\) 0 0
\(556\) 1.88035e9 + 3.25686e9i 0.463955 + 0.803594i
\(557\) 3.92372e9 + 6.79609e9i 0.962067 + 1.66635i 0.717297 + 0.696768i \(0.245379\pi\)
0.244770 + 0.969581i \(0.421288\pi\)
\(558\) 0 0
\(559\) −1.19111e9 −0.288411
\(560\) −3.02546e8 + 6.38268e8i −0.0728003 + 0.153584i
\(561\) 0 0
\(562\) 5.92565e8 1.02635e9i 0.140818 0.243904i
\(563\) −1.39537e9 2.41685e9i −0.329541 0.570782i 0.652880 0.757462i \(-0.273561\pi\)
−0.982421 + 0.186679i \(0.940227\pi\)
\(564\) 0 0
\(565\) 8.31749e8 1.44063e9i 0.194009 0.336034i
\(566\) −3.12337e9 −0.724045
\(567\) 0 0
\(568\) −2.47486e9 −0.566672
\(569\) 1.85983e9 3.22131e9i 0.423233 0.733061i −0.573021 0.819541i \(-0.694229\pi\)
0.996254 + 0.0864801i \(0.0275619\pi\)
\(570\) 0 0
\(571\) 2.04386e8 + 3.54007e8i 0.0459435 + 0.0795765i 0.888083 0.459684i \(-0.152037\pi\)
−0.842139 + 0.539260i \(0.818704\pi\)
\(572\) −8.37132e8 + 1.44996e9i −0.187029 + 0.323943i
\(573\) 0 0
\(574\) −2.38796e9 + 1.93748e8i −0.527030 + 0.0427609i
\(575\) 2.46508e9 0.540745
\(576\) 0 0
\(577\) −3.64920e9 6.32059e9i −0.790828 1.36975i −0.925455 0.378857i \(-0.876317\pi\)
0.134628 0.990896i \(-0.457016\pi\)
\(578\) −1.64002e9 2.84060e9i −0.353267 0.611876i
\(579\) 0 0
\(580\) 2.81687e8 0.0599472
\(581\) −2.42687e9 3.51289e9i −0.513370 0.743102i
\(582\) 0 0
\(583\) −3.44705e9 + 5.97046e9i −0.720455 + 1.24787i
\(584\) 8.90989e8 + 1.54324e9i 0.185109 + 0.320618i
\(585\) 0 0
\(586\) −1.76516e9 + 3.05735e9i −0.362362 + 0.627630i
\(587\) −4.58500e9 −0.935633 −0.467817 0.883826i \(-0.654959\pi\)
−0.467817 + 0.883826i \(0.654959\pi\)
\(588\) 0 0
\(589\) 4.66692e9 0.941081
\(590\) −2.73272e7 + 4.73321e7i −0.00547789 + 0.00948799i
\(591\) 0 0
\(592\) 4.56860e8 + 7.91306e8i 0.0905019 + 0.156754i
\(593\) −4.14382e9 + 7.17731e9i −0.816037 + 1.41342i 0.0925446 + 0.995709i \(0.470500\pi\)
−0.908581 + 0.417708i \(0.862833\pi\)
\(594\) 0 0
\(595\) 5.65466e7 + 8.18511e7i 0.0110052 + 0.0159300i
\(596\) 2.80266e9 0.542261
\(597\) 0 0
\(598\) 9.81634e8 + 1.70024e9i 0.187714 + 0.325129i
\(599\) −1.17488e9 2.03496e9i −0.223358 0.386867i 0.732468 0.680802i \(-0.238369\pi\)
−0.955826 + 0.293935i \(0.905035\pi\)
\(600\) 0 0
\(601\) −9.61955e8 −0.180757 −0.0903783 0.995908i \(-0.528808\pi\)
−0.0903783 + 0.995908i \(0.528808\pi\)
\(602\) −2.06061e9 + 1.67189e8i −0.384953 + 0.0312334i
\(603\) 0 0
\(604\) 3.42062e8 5.92469e8i 0.0631649 0.109405i
\(605\) −1.86501e9 3.23029e9i −0.342403 0.593059i
\(606\) 0 0
\(607\) 2.84283e9 4.92392e9i 0.515929 0.893615i −0.483900 0.875123i \(-0.660780\pi\)
0.999829 0.0184920i \(-0.00588652\pi\)
\(608\) 5.06061e8 0.0913147
\(609\) 0 0
\(610\) 1.83150e9 0.326702
\(611\) −2.73170e9 + 4.73144e9i −0.484494 + 0.839168i
\(612\) 0 0
\(613\) −1.64257e9 2.84502e9i −0.288013 0.498853i 0.685322 0.728240i \(-0.259661\pi\)
−0.973335 + 0.229387i \(0.926328\pi\)
\(614\) −3.42265e9 + 5.92820e9i −0.596724 + 1.03356i
\(615\) 0 0
\(616\) −1.24471e9 + 2.62590e9i −0.214553 + 0.452633i
\(617\) 3.69864e9 0.633933 0.316967 0.948437i \(-0.397336\pi\)
0.316967 + 0.948437i \(0.397336\pi\)
\(618\) 0 0
\(619\) −4.78155e9 8.28188e9i −0.810310 1.40350i −0.912647 0.408748i \(-0.865965\pi\)
0.102337 0.994750i \(-0.467368\pi\)
\(620\) 1.83755e9 + 3.18274e9i 0.309649 + 0.536327i
\(621\) 0 0
\(622\) −8.03199e9 −1.33831
\(623\) −3.10675e9 + 2.52068e8i −0.514752 + 0.0417647i
\(624\) 0 0
\(625\) 5.27901e8 9.14351e8i 0.0864913 0.149807i
\(626\) −1.38479e9 2.39853e9i −0.225619 0.390783i
\(627\) 0 0
\(628\) 1.63103e9 2.82503e9i 0.262787 0.455160i
\(629\) 1.28692e8 0.0206194
\(630\) 0 0
\(631\) −5.85026e9 −0.926985 −0.463492 0.886101i \(-0.653404\pi\)
−0.463492 + 0.886101i \(0.653404\pi\)
\(632\) 1.90759e9 3.30404e9i 0.300590 0.520638i
\(633\) 0 0
\(634\) −1.61257e9 2.79306e9i −0.251308 0.435279i
\(635\) −2.97092e9 + 5.14578e9i −0.460450 + 0.797524i
\(636\) 0 0
\(637\) 1.21890e9 3.22184e9i 0.186845 0.493874i
\(638\) 1.15889e9 0.176673
\(639\) 0 0
\(640\) 1.99256e8 + 3.45122e8i 0.0300457 + 0.0520407i
\(641\) −3.63568e9 6.29718e9i −0.545233 0.944371i −0.998592 0.0530435i \(-0.983108\pi\)
0.453359 0.891328i \(-0.350226\pi\)
\(642\) 0 0
\(643\) 2.50221e9 0.371181 0.185591 0.982627i \(-0.440580\pi\)
0.185591 + 0.982627i \(0.440580\pi\)
\(644\) 1.93686e9 + 2.80361e9i 0.285758 + 0.413634i
\(645\) 0 0
\(646\) 3.56379e7 6.17266e7i 0.00520114 0.00900863i
\(647\) 4.44048e9 + 7.69115e9i 0.644563 + 1.11642i 0.984402 + 0.175932i \(0.0562940\pi\)
−0.339839 + 0.940484i \(0.610373\pi\)
\(648\) 0 0
\(649\) −1.12427e8 + 1.94730e8i −0.0161441 + 0.0279625i
\(650\) −1.40593e9 −0.200801
\(651\) 0 0
\(652\) 3.55189e8 0.0501872
\(653\) −2.43457e9 + 4.21681e9i −0.342158 + 0.592635i −0.984833 0.173504i \(-0.944491\pi\)
0.642675 + 0.766139i \(0.277824\pi\)
\(654\) 0 0
\(655\) −2.74595e9 4.75613e9i −0.381811 0.661316i
\(656\) −6.75847e8 + 1.17060e9i −0.0934727 + 0.161899i
\(657\) 0 0
\(658\) −4.06168e9 + 8.56875e9i −0.555795 + 1.17254i
\(659\) 5.44124e9 0.740627 0.370313 0.928907i \(-0.379250\pi\)
0.370313 + 0.928907i \(0.379250\pi\)
\(660\) 0 0
\(661\) 2.58734e9 + 4.48140e9i 0.348456 + 0.603544i 0.985975 0.166891i \(-0.0533726\pi\)
−0.637519 + 0.770435i \(0.720039\pi\)
\(662\) 1.14741e9 + 1.98737e9i 0.153714 + 0.266241i
\(663\) 0 0
\(664\) −2.40892e9 −0.319325
\(665\) 1.14073e9 2.40656e9i 0.150421 0.317337i
\(666\) 0 0
\(667\) 6.79467e8 1.17687e9i 0.0886600 0.153564i
\(668\) −2.78264e9 4.81967e9i −0.361193 0.625604i
\(669\) 0 0
\(670\) −1.69407e8 + 2.93421e8i −0.0217605 + 0.0376903i
\(671\) 7.53497e9 0.962837
\(672\) 0 0
\(673\) 3.74132e9 0.473121 0.236561 0.971617i \(-0.423980\pi\)
0.236561 + 0.971617i \(0.423980\pi\)
\(674\) 2.27663e9 3.94323e9i 0.286406 0.496070i
\(675\) 0 0
\(676\) 1.44809e9 + 2.50816e9i 0.180294 + 0.312279i
\(677\) 6.36566e9 1.10257e10i 0.788467 1.36566i −0.138440 0.990371i \(-0.544209\pi\)
0.926906 0.375293i \(-0.122458\pi\)
\(678\) 0 0
\(679\) −1.95870e9 2.83521e9i −0.240117 0.347568i
\(680\) 5.61282e7 0.00684542
\(681\) 0 0
\(682\) 7.55989e9 + 1.30941e10i 0.912579 + 1.58063i
\(683\) 8.00307e8 + 1.38617e9i 0.0961135 + 0.166473i 0.910073 0.414448i \(-0.136026\pi\)
−0.813959 + 0.580922i \(0.802692\pi\)
\(684\) 0 0
\(685\) 7.22187e8 0.0858484
\(686\) 1.65646e9 5.74483e9i 0.195905 0.679427i
\(687\) 0 0
\(688\) −5.83199e8 + 1.01013e9i −0.0682743 + 0.118255i
\(689\) −2.30534e9 3.99296e9i −0.268514 0.465080i
\(690\) 0 0
\(691\) 1.93237e9 3.34697e9i 0.222801 0.385903i −0.732856 0.680384i \(-0.761813\pi\)
0.955658 + 0.294480i \(0.0951465\pi\)
\(692\) 7.53577e8 0.0864483
\(693\) 0 0
\(694\) 8.86023e9 1.00621
\(695\) 5.58304e9 9.67010e9i 0.630847 1.09266i
\(696\) 0 0
\(697\) 9.51891e7 + 1.64872e8i 0.0106481 + 0.0184431i
\(698\) 5.87826e9 1.01815e10i 0.654267 1.13322i
\(699\) 0 0
\(700\) −2.43223e9 + 1.97340e8i −0.268017 + 0.0217457i
\(701\) −9.59194e9 −1.05170 −0.525852 0.850576i \(-0.676253\pi\)
−0.525852 + 0.850576i \(0.676253\pi\)
\(702\) 0 0
\(703\) −1.72257e9 2.98358e9i −0.186996 0.323887i
\(704\) 8.19763e8 + 1.41987e9i 0.0885490 + 0.153371i
\(705\) 0 0
\(706\) −6.96011e9 −0.744388
\(707\) −1.54534e9 + 3.26013e9i −0.164458 + 0.346951i
\(708\) 0 0
\(709\) 1.80143e9 3.12016e9i 0.189826 0.328787i −0.755366 0.655303i \(-0.772541\pi\)
0.945192 + 0.326515i \(0.105874\pi\)
\(710\) 3.67412e9 + 6.36376e9i 0.385256 + 0.667283i
\(711\) 0 0
\(712\) −8.79281e8 + 1.52296e9i −0.0912952 + 0.158128i
\(713\) 1.77297e10 1.83184
\(714\) 0 0
\(715\) 4.97115e9 0.508611
\(716\) −1.46299e9 + 2.53397e9i −0.148951 + 0.257991i
\(717\) 0 0
\(718\) 3.20252e9 + 5.54693e9i 0.322892 + 0.559265i
\(719\) 4.41578e9 7.64835e9i 0.443053 0.767391i −0.554861 0.831943i \(-0.687229\pi\)
0.997914 + 0.0645520i \(0.0205618\pi\)
\(720\) 0 0
\(721\) 6.28107e9 5.09618e8i 0.624109 0.0506374i
\(722\) 5.24289e9 0.518431
\(723\) 0 0
\(724\) 5.58972e8 + 9.68167e8i 0.0547400 + 0.0948125i
\(725\) 4.86576e8 + 8.42775e8i 0.0474207 + 0.0821350i
\(726\) 0 0
\(727\) −8.30116e9 −0.801250 −0.400625 0.916242i \(-0.631207\pi\)
−0.400625 + 0.916242i \(0.631207\pi\)
\(728\) −1.10467e9 1.59900e9i −0.106114 0.153599i
\(729\) 0 0
\(730\) 2.64548e9 4.58211e9i 0.251695 0.435949i
\(731\) 8.21402e7 + 1.42271e8i 0.00777758 + 0.0134712i
\(732\) 0 0
\(733\) 4.74120e9 8.21199e9i 0.444656 0.770166i −0.553372 0.832934i \(-0.686659\pi\)
0.998028 + 0.0627676i \(0.0199927\pi\)
\(734\) −3.99630e9 −0.373011
\(735\) 0 0
\(736\) 1.92253e9 0.177747
\(737\) −6.96957e8 + 1.20717e9i −0.0641313 + 0.111079i
\(738\) 0 0
\(739\) 6.12549e9 + 1.06097e10i 0.558323 + 0.967043i 0.997637 + 0.0687097i \(0.0218882\pi\)
−0.439314 + 0.898334i \(0.644778\pi\)
\(740\) 1.35649e9 2.34951e9i 0.123057 0.213140i
\(741\) 0 0
\(742\) −4.54867e9 6.58418e9i −0.408762 0.591682i
\(743\) 1.06325e10 0.950989 0.475495 0.879719i \(-0.342269\pi\)
0.475495 + 0.879719i \(0.342269\pi\)
\(744\) 0 0
\(745\) −4.16077e9 7.20666e9i −0.368660 0.638538i
\(746\) 4.12673e9 + 7.14771e9i 0.363932 + 0.630349i
\(747\) 0 0
\(748\) 2.30918e8 0.0201744
\(749\) 1.37801e10 1.11805e9i 1.19830 0.0972246i
\(750\) 0 0
\(751\) −9.99189e9 + 1.73065e10i −0.860811 + 1.49097i 0.0103358 + 0.999947i \(0.496710\pi\)
−0.871147 + 0.491022i \(0.836623\pi\)
\(752\) 2.67502e9 + 4.63327e9i 0.229385 + 0.397306i
\(753\) 0 0
\(754\) −3.87525e8 + 6.71214e8i −0.0329231 + 0.0570245i
\(755\) −2.03127e9 −0.171772
\(756\) 0 0
\(757\) −1.08884e10 −0.912281 −0.456140 0.889908i \(-0.650769\pi\)
−0.456140 + 0.889908i \(0.650769\pi\)
\(758\) −3.34192e9 + 5.78838e9i −0.278711 + 0.482742i
\(759\) 0 0
\(760\) −7.51287e8 1.30127e9i −0.0620809 0.107527i
\(761\) −8.29514e9 + 1.43676e10i −0.682303 + 1.18178i 0.291973 + 0.956427i \(0.405688\pi\)
−0.974276 + 0.225357i \(0.927645\pi\)
\(762\) 0 0
\(763\) 7.61393e9 1.60628e10i 0.620545 1.30914i
\(764\) −2.46314e9 −0.199831
\(765\) 0 0
\(766\) 7.99082e9 + 1.38405e10i 0.642378 + 1.11263i
\(767\) −7.51898e7 1.30233e8i −0.00601693 0.0104216i
\(768\) 0 0
\(769\) 1.24893e10 0.990363 0.495182 0.868790i \(-0.335102\pi\)
0.495182 + 0.868790i \(0.335102\pi\)
\(770\) 8.60001e9 6.97767e8i 0.678862 0.0550799i
\(771\) 0 0
\(772\) 3.27956e9 5.68036e9i 0.256540 0.444340i
\(773\) −3.53844e9 6.12877e9i −0.275540 0.477249i 0.694731 0.719269i \(-0.255523\pi\)
−0.970271 + 0.242020i \(0.922190\pi\)
\(774\) 0 0
\(775\) −6.34825e9 + 1.09955e10i −0.489889 + 0.848513i
\(776\) −1.94420e9 −0.149357
\(777\) 0 0
\(778\) −3.60674e9 −0.274591
\(779\) 2.54825e9 4.41369e9i 0.193135 0.334519i
\(780\) 0 0
\(781\) 1.51157e10 + 2.61812e10i 1.13540 + 1.96658i
\(782\) 1.35389e8 2.34500e8i 0.0101242 0.0175356i
\(783\) 0 0
\(784\) −2.13550e9 2.61120e9i −0.158268 0.193523i
\(785\) −9.68556e9 −0.714630
\(786\) 0 0
\(787\) −2.89271e9 5.01033e9i −0.211541 0.366399i 0.740656 0.671884i \(-0.234515\pi\)
−0.952197 + 0.305485i \(0.901181\pi\)
\(788\) −5.67084e9 9.82218e9i −0.412863 0.715099i
\(789\) 0 0
\(790\) −1.13278e10 −0.817434
\(791\) 4.51550e9 + 6.53617e9i 0.324405 + 0.469575i
\(792\) 0 0
\(793\) −2.51964e9 + 4.36415e9i −0.179425 + 0.310773i
\(794\) −3.87028e9 6.70352e9i −0.274392 0.475260i
\(795\) 0 0
\(796\) 1.28674e8 2.22869e8i 0.00904260 0.0156622i
\(797\) 1.60066e10 1.11994 0.559969 0.828514i \(-0.310813\pi\)
0.559969 + 0.828514i \(0.310813\pi\)
\(798\) 0 0
\(799\) 7.53521e8 0.0522615
\(800\) −6.88377e8 + 1.19230e9i −0.0475348 + 0.0823326i
\(801\) 0 0
\(802\) −9.93730e9 1.72119e10i −0.680234 1.17820i
\(803\) 1.08838e10 1.88513e10i 0.741781 1.28480i
\(804\) 0 0
\(805\) 4.33366e9 9.14255e9i 0.292799 0.617706i
\(806\) −1.01119e10 −0.680238
\(807\) 0 0
\(808\) 1.01776e9 + 1.76281e9i 0.0678742 + 0.117562i
\(809\) 2.59877e9 + 4.50120e9i 0.172563 + 0.298888i 0.939315 0.343055i \(-0.111462\pi\)
−0.766752 + 0.641943i \(0.778128\pi\)
\(810\) 0 0
\(811\) 2.58012e9 0.169850 0.0849252 0.996387i \(-0.472935\pi\)
0.0849252 + 0.996387i \(0.472935\pi\)
\(812\) −5.76200e8 + 1.21558e9i −0.0377683 + 0.0796781i
\(813\) 0 0
\(814\) 5.58074e9 9.66613e9i 0.362666 0.628155i
\(815\) −5.27305e8 9.13320e8i −0.0341201 0.0590978i
\(816\) 0 0
\(817\) 2.19892e9 3.80865e9i 0.141069 0.244339i
\(818\) 5.89279e7 0.00376430
\(819\) 0 0
\(820\) 4.01339e9 0.254192
\(821\) −3.25385e9 + 5.63583e9i −0.205209 + 0.355432i −0.950199 0.311643i \(-0.899121\pi\)
0.744990 + 0.667075i \(0.232454\pi\)
\(822\) 0 0
\(823\) 3.83450e9 + 6.64155e9i 0.239778 + 0.415308i 0.960651 0.277760i \(-0.0895920\pi\)
−0.720872 + 0.693068i \(0.756259\pi\)
\(824\) 1.77769e9 3.07904e9i 0.110690 0.191721i
\(825\) 0 0
\(826\) −1.48357e8 2.14746e8i −0.00915964 0.0132585i
\(827\) −2.19638e9 −0.135032 −0.0675162 0.997718i \(-0.521507\pi\)
−0.0675162 + 0.997718i \(0.521507\pi\)
\(828\) 0 0
\(829\) −9.64024e9 1.66974e10i −0.587688 1.01791i −0.994534 0.104409i \(-0.966705\pi\)
0.406846 0.913497i \(-0.366628\pi\)
\(830\) 3.57622e9 + 6.19420e9i 0.217096 + 0.376021i
\(831\) 0 0
\(832\) −1.09649e9 −0.0660046
\(833\) −4.68886e8 + 7.65909e7i −0.0281067 + 0.00459113i
\(834\) 0 0
\(835\) −8.26207e9 + 1.43103e10i −0.491119 + 0.850642i
\(836\) −3.09087e9 5.35355e9i −0.182961 0.316898i
\(837\) 0 0
\(838\) 8.72981e9 1.51205e10i 0.512449 0.887588i
\(839\) −3.19760e10 −1.86921 −0.934604 0.355689i \(-0.884246\pi\)
−0.934604 + 0.355689i \(0.884246\pi\)
\(840\) 0 0
\(841\) −1.67134e10 −0.968900
\(842\) −1.09912e9 + 1.90373e9i −0.0634531 + 0.109904i
\(843\) 0 0
\(844\) 3.35327e9 + 5.80803e9i 0.191986 + 0.332529i
\(845\) 4.29960e9 7.44713e9i 0.245149 0.424610i
\(846\) 0 0
\(847\) 1.77548e10 1.44055e9i 1.00398 0.0814584i
\(848\) −4.51501e9 −0.254257
\(849\) 0 0
\(850\) 9.69539e7 + 1.67929e8i 0.00541501 + 0.00937907i
\(851\) −6.54406e9 1.13347e10i −0.363994 0.630456i
\(852\) 0 0
\(853\) −1.06299e10 −0.586416 −0.293208 0.956049i \(-0.594723\pi\)
−0.293208 + 0.956049i \(0.594723\pi\)
\(854\) −3.74638e9 + 7.90359e9i −0.205830 + 0.434232i
\(855\) 0 0
\(856\) 3.90008e9 6.75513e9i 0.212527 0.368108i
\(857\) 9.42668e9 + 1.63275e10i 0.511594 + 0.886108i 0.999910 + 0.0134403i \(0.00427830\pi\)
−0.488315 + 0.872667i \(0.662388\pi\)
\(858\) 0 0
\(859\) −9.45689e9 + 1.63798e10i −0.509064 + 0.881725i 0.490881 + 0.871227i \(0.336675\pi\)
−0.999945 + 0.0104981i \(0.996658\pi\)
\(860\) 3.46321e9 0.185667
\(861\) 0 0
\(862\) 1.27360e10 0.677262
\(863\) −1.60330e10 + 2.77700e10i −0.849137 + 1.47075i 0.0328428 + 0.999461i \(0.489544\pi\)
−0.881980 + 0.471288i \(0.843789\pi\)
\(864\) 0 0
\(865\) −1.11874e9 1.93772e9i −0.0587725 0.101797i
\(866\) 1.97518e9 3.42111e9i 0.103346 0.179001i
\(867\) 0 0
\(868\) −1.74935e10 + 1.41934e9i −0.907939 + 0.0736662i
\(869\) −4.66040e10 −2.40909
\(870\) 0 0
\(871\) −4.66116e8 8.07336e8i −0.0239018 0.0413991i
\(872\) −5.01453e9 8.68542e9i −0.256108 0.443592i
\(873\) 0 0
\(874\) −7.24882e9 −0.367263
\(875\) 1.17760e10 + 1.70457e10i 0.594249 + 0.860173i
\(876\) 0 0
\(877\) −1.35871e10 + 2.35335e10i −0.680186 + 1.17812i 0.294738 + 0.955578i \(0.404767\pi\)
−0.974924 + 0.222538i \(0.928566\pi\)
\(878\) 1.30001e10 + 2.25168e10i 0.648210 + 1.12273i
\(879\) 0 0
\(880\) 2.43400e9 4.21581e9i 0.120401 0.208541i
\(881\) −2.80664e10 −1.38284 −0.691418 0.722455i \(-0.743014\pi\)
−0.691418 + 0.722455i \(0.743014\pi\)
\(882\) 0 0
\(883\) −2.55368e10 −1.24826 −0.624129 0.781321i \(-0.714546\pi\)
−0.624129 + 0.781321i \(0.714546\pi\)
\(884\) −7.72173e7 + 1.33744e8i −0.00375951 + 0.00651167i
\(885\) 0 0
\(886\) −9.99019e9 1.73035e10i −0.482565 0.835827i
\(887\) −1.08146e8 + 1.87315e8i −0.00520330 + 0.00901238i −0.868615 0.495487i \(-0.834990\pi\)
0.863412 + 0.504499i \(0.168323\pi\)
\(888\) 0 0
\(889\) −1.61289e10 2.33465e10i −0.769924 1.11446i
\(890\) 5.22144e9 0.248271
\(891\) 0 0
\(892\) 1.13695e9 + 1.96926e9i 0.0536371 + 0.0929022i
\(893\) −1.00860e10 1.74695e10i −0.473958 0.820919i
\(894\) 0 0
\(895\) 8.68766e9 0.405063
\(896\) −1.89692e9 + 1.53907e8i −0.0880988 + 0.00714795i
\(897\) 0 0
\(898\) 1.08689e10 1.88254e10i 0.500861 0.867517i
\(899\) 3.49963e9 + 6.06153e9i 0.160643 + 0.278243i
\(900\) 0 0
\(901\) −3.17957e8 + 5.50717e8i −0.0144821 + 0.0250837i
\(902\) 1.65115e10 0.749141
\(903\) 0 0
\(904\) 4.48208e9 0.201786
\(905\) 1.65967e9 2.87464e9i 0.0744307 0.128918i
\(906\) 0 0
\(907\) 2.60424e9 + 4.51068e9i 0.115893 + 0.200732i 0.918136 0.396265i \(-0.129694\pi\)
−0.802244 + 0.596997i \(0.796360\pi\)
\(908\) −3.71972e9 + 6.44275e9i −0.164896 + 0.285608i
\(909\) 0 0
\(910\) −2.47165e9 + 5.21434e9i −0.108728 + 0.229379i
\(911\) −3.10115e10 −1.35896 −0.679482 0.733692i \(-0.737795\pi\)
−0.679482 + 0.733692i \(0.737795\pi\)
\(912\) 0 0
\(913\) 1.47130e10 + 2.54836e10i 0.639812 + 1.10819i
\(914\) −1.25086e10 2.16656e10i −0.541874 0.938553i
\(915\) 0 0
\(916\) −1.21114e10 −0.520668
\(917\) 2.61414e10 2.12100e9i 1.11953 0.0908338i
\(918\) 0 0
\(919\) 1.24346e10 2.15373e10i 0.528477 0.915349i −0.470972 0.882148i \(-0.656097\pi\)
0.999449 0.0332005i \(-0.0105700\pi\)
\(920\) −2.85415e9 4.94353e9i −0.120842 0.209305i
\(921\) 0 0
\(922\) 1.16219e10 2.01298e10i 0.488338 0.845826i
\(923\) −2.02184e10 −0.846332
\(924\) 0 0
\(925\) 9.37260e9 0.389371
\(926\) −1.38859e10 + 2.40510e10i −0.574691 + 0.995394i
\(927\) 0 0
\(928\) 3.79485e8 + 6.57287e8i 0.0155875 + 0.0269983i
\(929\) 7.19722e9 1.24660e10i 0.294517 0.510118i −0.680356 0.732882i \(-0.738175\pi\)
0.974872 + 0.222764i \(0.0715080\pi\)
\(930\) 0 0
\(931\) 8.05179e9 + 9.84538e9i 0.327016 + 0.399861i
\(932\) −1.93292e10 −0.782094
\(933\) 0 0
\(934\) 1.05134e10 + 1.82097e10i 0.422209 + 0.731288i
\(935\) −3.42815e8 5.93773e8i −0.0137157 0.0237563i
\(936\) 0 0
\(937\) −1.25268e10 −0.497451 −0.248726 0.968574i \(-0.580012\pi\)
−0.248726 + 0.968574i \(0.580012\pi\)
\(938\) −9.19694e8 1.33125e9i −0.0363859 0.0526685i
\(939\) 0 0
\(940\) 7.94254e9 1.37569e10i 0.311897 0.540222i
\(941\) 2.06675e10 + 3.57971e10i 0.808581 + 1.40050i 0.913847 + 0.406059i \(0.133097\pi\)
−0.105266 + 0.994444i \(0.533569\pi\)
\(942\) 0 0
\(943\) 9.68082e9 1.67677e10i 0.375942 0.651151i
\(944\) −1.47259e8 −0.00569746
\(945\) 0 0
\(946\) 1.42480e10 0.547187
\(947\) −1.24770e10 + 2.16108e10i −0.477402 + 0.826885i −0.999665 0.0258999i \(-0.991755\pi\)
0.522262 + 0.852785i \(0.325088\pi\)
\(948\) 0 0
\(949\) 7.27894e9 + 1.26075e10i 0.276463 + 0.478847i
\(950\) 2.59549e9 4.49552e9i 0.0982171 0.170117i
\(951\) 0 0
\(952\) −1.14812e8 + 2.42214e8i −0.00431279 + 0.00909851i
\(953\) 7.15422e9 0.267755 0.133877 0.990998i \(-0.457257\pi\)
0.133877 + 0.990998i \(0.457257\pi\)
\(954\) 0 0
\(955\) 3.65672e9 + 6.33363e9i 0.135856 + 0.235310i
\(956\) −9.62146e9 1.66649e10i −0.356155 0.616878i
\(957\) 0 0
\(958\) −3.26373e10 −1.19932
\(959\) −1.47726e9 + 3.11650e9i −0.0540867 + 0.114104i
\(960\) 0 0
\(961\) −3.19025e10 + 5.52568e10i −1.15956 + 2.00842i
\(962\) 3.73232e9 + 6.46458e9i 0.135166 + 0.234114i
\(963\) 0 0
\(964\) 1.22722e9 2.12561e9i 0.0441219 0.0764213i
\(965\) −1.94750e10 −0.697642
\(966\) 0 0
\(967\) 4.41476e10 1.57006 0.785028 0.619461i \(-0.212649\pi\)
0.785028 + 0.619461i \(0.212649\pi\)
\(968\) 5.02502e9 8.70360e9i 0.178063 0.308415i
\(969\) 0 0
\(970\) 2.88632e9 + 4.99925e9i 0.101541 + 0.175875i
\(971\) 1.93951e10 3.35933e10i 0.679869 1.17757i −0.295152 0.955450i \(-0.595370\pi\)
0.975020 0.222116i \(-0.0712965\pi\)
\(972\) 0 0
\(973\) 3.03098e10 + 4.38734e10i 1.05484 + 1.52688i
\(974\) 1.20995e9 0.0419576
\(975\) 0 0
\(976\) 2.46736e9 + 4.27360e9i 0.0849491 + 0.147136i
\(977\) 1.28118e10 + 2.21907e10i 0.439521 + 0.761272i 0.997652 0.0684801i \(-0.0218150\pi\)
−0.558132 + 0.829752i \(0.688482\pi\)
\(978\) 0 0
\(979\) 2.14816e10 0.731689
\(980\) −3.54402e9 + 9.36766e9i −0.120283 + 0.317936i
\(981\) 0 0
\(982\) 1.68254e10 2.91425e10i 0.566991 0.982057i
\(983\) −1.75271e9 3.03578e9i −0.0588534 0.101937i 0.835098 0.550102i \(-0.185411\pi\)
−0.893951 + 0.448165i \(0.852078\pi\)
\(984\) 0 0
\(985\) −1.68376e10 + 2.91636e10i −0.561375 + 0.972330i
\(986\) 1.06896e8 0.00355135
\(987\) 0 0
\(988\) 4.13427e9 0.136380
\(989\) 8.35373e9 1.44691e10i 0.274596 0.475614i
\(990\) 0 0
\(991\) 1.11508e10 + 1.93137e10i 0.363954 + 0.630387i 0.988608 0.150515i \(-0.0480931\pi\)
−0.624654 + 0.780902i \(0.714760\pi\)
\(992\) −4.95105e9 + 8.57547e9i −0.161030 + 0.278912i
\(993\) 0 0
\(994\) −3.49775e10 + 2.83792e9i −1.12963 + 0.0916533i
\(995\) −7.64103e8 −0.0245907
\(996\) 0 0
\(997\) −2.39697e10 4.15168e10i −0.766002 1.32676i −0.939715 0.341959i \(-0.888910\pi\)
0.173712 0.984796i \(-0.444424\pi\)
\(998\) 7.72286e9 + 1.33764e10i 0.245936 + 0.425973i
\(999\) 0 0
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 126.8.g.j.37.2 yes 6
3.2 odd 2 126.8.g.i.37.2 6
7.4 even 3 inner 126.8.g.j.109.2 yes 6
21.11 odd 6 126.8.g.i.109.2 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.8.g.i.37.2 6 3.2 odd 2
126.8.g.i.109.2 yes 6 21.11 odd 6
126.8.g.j.37.2 yes 6 1.1 even 1 trivial
126.8.g.j.109.2 yes 6 7.4 even 3 inner