Properties

Label 14.7.b.a.13.3
Level $14$
Weight $7$
Character 14.13
Analytic conductor $3.221$
Analytic rank $0$
Dimension $4$
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] = [14,7,Mod(13,14)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(14, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("14.13");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 14.b (of order \(2\), degree \(1\), 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: \(3.22075717068\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.211968.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 30x^{2} + 207 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 13.3
Root \(-4.38664i\) of defining polynomial
Character \(\chi\) \(=\) 14.13
Dual form 14.7.b.a.13.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.65685 q^{2} -29.9539i q^{3} +32.0000 q^{4} -98.3767i q^{5} -169.445i q^{6} +(195.794 + 281.627i) q^{7} +181.019 q^{8} -168.235 q^{9} +O(q^{10})\) \(q+5.65685 q^{2} -29.9539i q^{3} +32.0000 q^{4} -98.3767i q^{5} -169.445i q^{6} +(195.794 + 281.627i) q^{7} +181.019 q^{8} -168.235 q^{9} -556.502i q^{10} -1042.12 q^{11} -958.524i q^{12} +3661.70i q^{13} +(1107.58 + 1593.12i) q^{14} -2946.76 q^{15} +1024.00 q^{16} +1856.59i q^{17} -951.679 q^{18} -7493.18i q^{19} -3148.05i q^{20} +(8435.82 - 5864.79i) q^{21} -5895.11 q^{22} +11639.4 q^{23} -5422.23i q^{24} +5947.03 q^{25} +20713.7i q^{26} -16797.1i q^{27} +(6265.41 + 9012.06i) q^{28} -41697.6 q^{29} -16669.4 q^{30} +22040.5i q^{31} +5792.62 q^{32} +31215.5i q^{33} +10502.4i q^{34} +(27705.5 - 19261.6i) q^{35} -5383.51 q^{36} -49174.8 q^{37} -42387.8i q^{38} +109682. q^{39} -17808.1i q^{40} +18029.8i q^{41} +(47720.2 - 33176.2i) q^{42} -114355. q^{43} -33347.8 q^{44} +16550.4i q^{45} +65842.4 q^{46} -139635. i q^{47} -30672.8i q^{48} +(-40978.5 + 110282. i) q^{49} +33641.5 q^{50} +55612.0 q^{51} +117175. i q^{52} +124198. q^{53} -95018.7i q^{54} +102520. i q^{55} +(35442.5 + 50979.9i) q^{56} -224450. q^{57} -235877. q^{58} -271907. i q^{59} -94296.4 q^{60} +338552. i q^{61} +124680. i q^{62} +(-32939.3 - 47379.4i) q^{63} +32768.0 q^{64} +360226. q^{65} +176581. i q^{66} -106386. q^{67} +59410.8i q^{68} -348645. i q^{69} +(156726. - 108960. i) q^{70} +216021. q^{71} -30453.7 q^{72} -111927. i q^{73} -278174. q^{74} -178137. i q^{75} -239782. i q^{76} +(-204040. - 293488. i) q^{77} +620456. q^{78} +451441. q^{79} -100738. i q^{80} -625781. q^{81} +101992. i q^{82} +225775. i q^{83} +(269946. - 187673. i) q^{84} +182645. q^{85} -646890. q^{86} +1.24900e6i q^{87} -188643. q^{88} +411409. i q^{89} +93623.0i q^{90} +(-1.03123e6 + 716939. i) q^{91} +372461. q^{92} +660198. q^{93} -789893. i q^{94} -737154. q^{95} -173511. i q^{96} -117248. i q^{97} +(-231809. + 623847. i) q^{98} +175320. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 128 q^{4} + 308 q^{7} + 1092 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 128 q^{4} + 308 q^{7} + 1092 q^{9} - 4440 q^{11} + 2688 q^{14} - 4320 q^{15} + 4096 q^{16} - 9984 q^{18} + 19488 q^{21} + 1536 q^{22} + 40584 q^{23} - 40700 q^{25} + 9856 q^{28} - 18264 q^{29} - 42240 q^{30} - 84000 q^{35} + 34944 q^{36} - 23192 q^{37} + 208608 q^{39} + 80640 q^{42} - 44696 q^{43} - 142080 q^{44} + 33792 q^{46} - 310268 q^{49} + 364800 q^{50} + 157824 q^{51} + 248616 q^{53} + 86016 q^{56} - 472992 q^{57} - 840192 q^{58} - 138240 q^{60} - 125580 q^{63} + 131072 q^{64} + 1293600 q^{65} - 434776 q^{67} + 1102080 q^{70} - 451608 q^{71} - 319488 q^{72} - 981504 q^{74} - 309624 q^{77} + 1301760 q^{78} + 2092904 q^{79} - 252828 q^{81} + 623616 q^{84} - 2117760 q^{85} - 2334720 q^{86} + 49152 q^{88} - 1109472 q^{91} + 1298688 q^{92} + 995328 q^{93} - 190560 q^{95} + 827904 q^{98} - 1331928 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.65685 0.707107
\(3\) 29.9539i 1.10940i −0.832049 0.554701i \(-0.812833\pi\)
0.832049 0.554701i \(-0.187167\pi\)
\(4\) 32.0000 0.500000
\(5\) 98.3767i 0.787013i −0.919322 0.393507i \(-0.871262\pi\)
0.919322 0.393507i \(-0.128738\pi\)
\(6\) 169.445i 0.784466i
\(7\) 195.794 + 281.627i 0.570828 + 0.821070i
\(8\) 181.019 0.353553
\(9\) −168.235 −0.230775
\(10\) 556.502i 0.556502i
\(11\) −1042.12 −0.782958 −0.391479 0.920187i \(-0.628037\pi\)
−0.391479 + 0.920187i \(0.628037\pi\)
\(12\) 958.524i 0.554701i
\(13\) 3661.70i 1.66668i 0.552758 + 0.833342i \(0.313575\pi\)
−0.552758 + 0.833342i \(0.686425\pi\)
\(14\) 1107.58 + 1593.12i 0.403636 + 0.580584i
\(15\) −2946.76 −0.873115
\(16\) 1024.00 0.250000
\(17\) 1856.59i 0.377893i 0.981987 + 0.188946i \(0.0605072\pi\)
−0.981987 + 0.188946i \(0.939493\pi\)
\(18\) −951.679 −0.163182
\(19\) 7493.18i 1.09246i −0.837635 0.546230i \(-0.816063\pi\)
0.837635 0.546230i \(-0.183937\pi\)
\(20\) 3148.05i 0.393507i
\(21\) 8435.82 5864.79i 0.910897 0.633278i
\(22\) −5895.11 −0.553635
\(23\) 11639.4 0.956638 0.478319 0.878186i \(-0.341246\pi\)
0.478319 + 0.878186i \(0.341246\pi\)
\(24\) 5422.23i 0.392233i
\(25\) 5947.03 0.380610
\(26\) 20713.7i 1.17852i
\(27\) 16797.1i 0.853381i
\(28\) 6265.41 + 9012.06i 0.285414 + 0.410535i
\(29\) −41697.6 −1.70969 −0.854844 0.518885i \(-0.826347\pi\)
−0.854844 + 0.518885i \(0.826347\pi\)
\(30\) −16669.4 −0.617385
\(31\) 22040.5i 0.739838i 0.929064 + 0.369919i \(0.120614\pi\)
−0.929064 + 0.369919i \(0.879386\pi\)
\(32\) 5792.62 0.176777
\(33\) 31215.5i 0.868616i
\(34\) 10502.4i 0.267211i
\(35\) 27705.5 19261.6i 0.646193 0.449249i
\(36\) −5383.51 −0.115387
\(37\) −49174.8 −0.970816 −0.485408 0.874288i \(-0.661329\pi\)
−0.485408 + 0.874288i \(0.661329\pi\)
\(38\) 42387.8i 0.772486i
\(39\) 109682. 1.84902
\(40\) 17808.1i 0.278251i
\(41\) 18029.8i 0.261601i 0.991409 + 0.130801i \(0.0417548\pi\)
−0.991409 + 0.130801i \(0.958245\pi\)
\(42\) 47720.2 33176.2i 0.644102 0.447795i
\(43\) −114355. −1.43830 −0.719151 0.694854i \(-0.755469\pi\)
−0.719151 + 0.694854i \(0.755469\pi\)
\(44\) −33347.8 −0.391479
\(45\) 16550.4i 0.181623i
\(46\) 65842.4 0.676445
\(47\) 139635.i 1.34493i −0.740129 0.672465i \(-0.765235\pi\)
0.740129 0.672465i \(-0.234765\pi\)
\(48\) 30672.8i 0.277351i
\(49\) −40978.5 + 110282.i −0.348311 + 0.937379i
\(50\) 33641.5 0.269132
\(51\) 55612.0 0.419235
\(52\) 117175.i 0.833342i
\(53\) 124198. 0.834235 0.417117 0.908853i \(-0.363040\pi\)
0.417117 + 0.908853i \(0.363040\pi\)
\(54\) 95018.7i 0.603431i
\(55\) 102520.i 0.616199i
\(56\) 35442.5 + 50979.9i 0.201818 + 0.290292i
\(57\) −224450. −1.21198
\(58\) −235877. −1.20893
\(59\) 271907.i 1.32393i −0.749537 0.661963i \(-0.769724\pi\)
0.749537 0.661963i \(-0.230276\pi\)
\(60\) −94296.4 −0.436557
\(61\) 338552.i 1.49154i 0.666202 + 0.745771i \(0.267919\pi\)
−0.666202 + 0.745771i \(0.732081\pi\)
\(62\) 124680.i 0.523144i
\(63\) −32939.3 47379.4i −0.131733 0.189482i
\(64\) 32768.0 0.125000
\(65\) 360226. 1.31170
\(66\) 176581.i 0.614204i
\(67\) −106386. −0.353720 −0.176860 0.984236i \(-0.556594\pi\)
−0.176860 + 0.984236i \(0.556594\pi\)
\(68\) 59410.8i 0.188946i
\(69\) 348645.i 1.06130i
\(70\) 156726. 108960.i 0.456927 0.317667i
\(71\) 216021. 0.603562 0.301781 0.953377i \(-0.402419\pi\)
0.301781 + 0.953377i \(0.402419\pi\)
\(72\) −30453.7 −0.0815911
\(73\) 111927.i 0.287718i −0.989598 0.143859i \(-0.954049\pi\)
0.989598 0.143859i \(-0.0459512\pi\)
\(74\) −278174. −0.686471
\(75\) 178137.i 0.422250i
\(76\) 239782.i 0.546230i
\(77\) −204040. 293488.i −0.446934 0.642864i
\(78\) 620456. 1.30746
\(79\) 451441. 0.915628 0.457814 0.889048i \(-0.348632\pi\)
0.457814 + 0.889048i \(0.348632\pi\)
\(80\) 100738.i 0.196753i
\(81\) −625781. −1.17752
\(82\) 101992.i 0.184980i
\(83\) 225775.i 0.394859i 0.980317 + 0.197430i \(0.0632594\pi\)
−0.980317 + 0.197430i \(0.936741\pi\)
\(84\) 269946. 187673.i 0.455449 0.316639i
\(85\) 182645. 0.297407
\(86\) −646890. −1.01703
\(87\) 1.24900e6i 1.89673i
\(88\) −188643. −0.276818
\(89\) 411409.i 0.583585i 0.956482 + 0.291792i \(0.0942516\pi\)
−0.956482 + 0.291792i \(0.905748\pi\)
\(90\) 93623.0i 0.128427i
\(91\) −1.03123e6 + 716939.i −1.36846 + 0.951389i
\(92\) 372461. 0.478319
\(93\) 660198. 0.820778
\(94\) 789893.i 0.951010i
\(95\) −737154. −0.859780
\(96\) 173511.i 0.196117i
\(97\) 117248.i 0.128467i −0.997935 0.0642333i \(-0.979540\pi\)
0.997935 0.0642333i \(-0.0204602\pi\)
\(98\) −231809. + 623847.i −0.246293 + 0.662827i
\(99\) 175320. 0.180687
\(100\) 190305. 0.190305
\(101\) 706191.i 0.685422i −0.939441 0.342711i \(-0.888655\pi\)
0.939441 0.342711i \(-0.111345\pi\)
\(102\) 314589. 0.296444
\(103\) 1.61841e6i 1.48107i −0.672016 0.740536i \(-0.734572\pi\)
0.672016 0.740536i \(-0.265428\pi\)
\(104\) 662839.i 0.589262i
\(105\) −576958. 829888.i −0.498398 0.716888i
\(106\) 702572. 0.589893
\(107\) 439211. 0.358527 0.179264 0.983801i \(-0.442629\pi\)
0.179264 + 0.983801i \(0.442629\pi\)
\(108\) 537507.i 0.426690i
\(109\) 1.80395e6 1.39298 0.696490 0.717567i \(-0.254744\pi\)
0.696490 + 0.717567i \(0.254744\pi\)
\(110\) 579941.i 0.435718i
\(111\) 1.47297e6i 1.07703i
\(112\) 200493. + 288386.i 0.142707 + 0.205267i
\(113\) 1.20195e6 0.833014 0.416507 0.909133i \(-0.363254\pi\)
0.416507 + 0.909133i \(0.363254\pi\)
\(114\) −1.26968e6 −0.856998
\(115\) 1.14505e6i 0.752886i
\(116\) −1.33432e6 −0.854844
\(117\) 616025.i 0.384628i
\(118\) 1.53814e6i 0.936157i
\(119\) −522865. + 363508.i −0.310276 + 0.215712i
\(120\) −533421. −0.308693
\(121\) −685552. −0.386976
\(122\) 1.91514e6i 1.05468i
\(123\) 540063. 0.290221
\(124\) 705296.i 0.369919i
\(125\) 2.12218e6i 1.08656i
\(126\) −186333. 268018.i −0.0931490 0.133984i
\(127\) −1.39321e6 −0.680150 −0.340075 0.940398i \(-0.610452\pi\)
−0.340075 + 0.940398i \(0.610452\pi\)
\(128\) 185364. 0.0883883
\(129\) 3.42538e6i 1.59566i
\(130\) 2.03775e6 0.927513
\(131\) 2.60277e6i 1.15777i 0.815410 + 0.578884i \(0.196511\pi\)
−0.815410 + 0.578884i \(0.803489\pi\)
\(132\) 998895.i 0.434308i
\(133\) 2.11028e6 1.46712e6i 0.896986 0.623606i
\(134\) −601810. −0.250118
\(135\) −1.65244e6 −0.671622
\(136\) 336078.i 0.133605i
\(137\) −692462. −0.269299 −0.134649 0.990893i \(-0.542991\pi\)
−0.134649 + 0.990893i \(0.542991\pi\)
\(138\) 1.97224e6i 0.750450i
\(139\) 481984.i 0.179469i 0.995966 + 0.0897343i \(0.0286018\pi\)
−0.995966 + 0.0897343i \(0.971398\pi\)
\(140\) 886576. 616370.i 0.323096 0.224625i
\(141\) −4.18260e6 −1.49207
\(142\) 1.22200e6 0.426783
\(143\) 3.81593e6i 1.30494i
\(144\) −172272. −0.0576936
\(145\) 4.10207e6i 1.34555i
\(146\) 633156.i 0.203447i
\(147\) 3.30336e6 + 1.22746e6i 1.03993 + 0.386417i
\(148\) −1.57359e6 −0.485408
\(149\) −655599. −0.198189 −0.0990945 0.995078i \(-0.531595\pi\)
−0.0990945 + 0.995078i \(0.531595\pi\)
\(150\) 1.00769e6i 0.298576i
\(151\) 47651.6 0.0138403 0.00692017 0.999976i \(-0.497797\pi\)
0.00692017 + 0.999976i \(0.497797\pi\)
\(152\) 1.35641e6i 0.386243i
\(153\) 312342.i 0.0872080i
\(154\) −1.15423e6 1.66022e6i −0.316030 0.454573i
\(155\) 2.16827e6 0.582262
\(156\) 3.50983e6 0.924512
\(157\) 2.08512e6i 0.538806i −0.963027 0.269403i \(-0.913174\pi\)
0.963027 0.269403i \(-0.0868264\pi\)
\(158\) 2.55373e6 0.647447
\(159\) 3.72022e6i 0.925502i
\(160\) 569858.i 0.139126i
\(161\) 2.27893e6 + 3.27797e6i 0.546075 + 0.785466i
\(162\) −3.53995e6 −0.832631
\(163\) 1.59326e6 0.367894 0.183947 0.982936i \(-0.441112\pi\)
0.183947 + 0.982936i \(0.441112\pi\)
\(164\) 576955.i 0.130801i
\(165\) 3.07087e6 0.683613
\(166\) 1.27718e6i 0.279208i
\(167\) 1.21740e6i 0.261387i −0.991423 0.130693i \(-0.958280\pi\)
0.991423 0.130693i \(-0.0417203\pi\)
\(168\) 1.52705e6 1.06164e6i 0.322051 0.223898i
\(169\) −8.58126e6 −1.77783
\(170\) 1.03320e6 0.210298
\(171\) 1.26061e6i 0.252112i
\(172\) −3.65936e6 −0.719151
\(173\) 4.61804e6i 0.891907i −0.895056 0.445953i \(-0.852865\pi\)
0.895056 0.445953i \(-0.147135\pi\)
\(174\) 7.06544e6i 1.34119i
\(175\) 1.16439e6 + 1.67485e6i 0.217263 + 0.312508i
\(176\) −1.06713e6 −0.195740
\(177\) −8.14465e6 −1.46877
\(178\) 2.32728e6i 0.412657i
\(179\) −2.87045e6 −0.500484 −0.250242 0.968183i \(-0.580510\pi\)
−0.250242 + 0.968183i \(0.580510\pi\)
\(180\) 529612.i 0.0908113i
\(181\) 6.81242e6i 1.14886i 0.818555 + 0.574428i \(0.194776\pi\)
−0.818555 + 0.574428i \(0.805224\pi\)
\(182\) −5.83354e6 + 4.05562e6i −0.967650 + 0.672734i
\(183\) 1.01409e7 1.65472
\(184\) 2.10696e6 0.338222
\(185\) 4.83765e6i 0.764045i
\(186\) 3.73465e6 0.580378
\(187\) 1.93478e6i 0.295874i
\(188\) 4.46831e6i 0.672465i
\(189\) 4.73051e6 3.28877e6i 0.700685 0.487134i
\(190\) −4.16997e6 −0.607956
\(191\) −5.00597e6 −0.718435 −0.359218 0.933254i \(-0.616956\pi\)
−0.359218 + 0.933254i \(0.616956\pi\)
\(192\) 981529.i 0.138675i
\(193\) 1.94995e6 0.271238 0.135619 0.990761i \(-0.456698\pi\)
0.135619 + 0.990761i \(0.456698\pi\)
\(194\) 663255.i 0.0908396i
\(195\) 1.07902e7i 1.45521i
\(196\) −1.31131e6 + 3.52901e6i −0.174156 + 0.468689i
\(197\) 1.16023e7 1.51756 0.758782 0.651345i \(-0.225795\pi\)
0.758782 + 0.651345i \(0.225795\pi\)
\(198\) 991761. 0.127765
\(199\) 727194.i 0.0922765i −0.998935 0.0461382i \(-0.985309\pi\)
0.998935 0.0461382i \(-0.0146915\pi\)
\(200\) 1.07653e6 0.134566
\(201\) 3.18667e6i 0.392418i
\(202\) 3.99482e6i 0.484666i
\(203\) −8.16414e6 1.17432e7i −0.975938 1.40377i
\(204\) 1.77958e6 0.209618
\(205\) 1.77371e6 0.205884
\(206\) 9.15510e6i 1.04728i
\(207\) −1.95815e6 −0.220768
\(208\) 3.74958e6i 0.416671i
\(209\) 7.80878e6i 0.855350i
\(210\) −3.26377e6 4.69455e6i −0.352421 0.506916i
\(211\) 5.82550e6 0.620134 0.310067 0.950715i \(-0.399648\pi\)
0.310067 + 0.950715i \(0.399648\pi\)
\(212\) 3.97435e6 0.417117
\(213\) 6.47068e6i 0.669593i
\(214\) 2.48455e6 0.253517
\(215\) 1.12499e7i 1.13196i
\(216\) 3.04060e6i 0.301716i
\(217\) −6.20720e6 + 4.31540e6i −0.607458 + 0.422320i
\(218\) 1.02047e7 0.984985
\(219\) −3.35265e6 −0.319195
\(220\) 3.28064e6i 0.308099i
\(221\) −6.79827e6 −0.629828
\(222\) 8.33240e6i 0.761573i
\(223\) 6.05484e6i 0.545994i 0.962015 + 0.272997i \(0.0880150\pi\)
−0.962015 + 0.272997i \(0.911985\pi\)
\(224\) 1.13416e6 + 1.63136e6i 0.100909 + 0.145146i
\(225\) −1.00050e6 −0.0878351
\(226\) 6.79927e6 0.589030
\(227\) 1.70220e7i 1.45524i 0.685981 + 0.727619i \(0.259373\pi\)
−0.685981 + 0.727619i \(0.740627\pi\)
\(228\) −7.18239e6 −0.605989
\(229\) 8.49217e6i 0.707151i −0.935406 0.353576i \(-0.884966\pi\)
0.935406 0.353576i \(-0.115034\pi\)
\(230\) 6.47736e6i 0.532371i
\(231\) −8.79112e6 + 6.11180e6i −0.713195 + 0.495830i
\(232\) −7.54807e6 −0.604466
\(233\) −4.76243e6 −0.376496 −0.188248 0.982122i \(-0.560281\pi\)
−0.188248 + 0.982122i \(0.560281\pi\)
\(234\) 3.48477e6i 0.271973i
\(235\) −1.37368e7 −1.05848
\(236\) 8.70101e6i 0.661963i
\(237\) 1.35224e7i 1.01580i
\(238\) −2.95777e6 + 2.05631e6i −0.219398 + 0.152531i
\(239\) 1.58931e7 1.16416 0.582082 0.813130i \(-0.302238\pi\)
0.582082 + 0.813130i \(0.302238\pi\)
\(240\) −3.01748e6 −0.218279
\(241\) 266157.i 0.0190146i −0.999955 0.00950730i \(-0.996974\pi\)
0.999955 0.00950730i \(-0.00302631\pi\)
\(242\) −3.87807e6 −0.273633
\(243\) 6.49949e6i 0.452960i
\(244\) 1.08337e7i 0.745771i
\(245\) 1.08491e7 + 4.03132e6i 0.737730 + 0.274126i
\(246\) 3.05506e6 0.205217
\(247\) 2.74378e7 1.82078
\(248\) 3.98976e6i 0.261572i
\(249\) 6.76285e6 0.438058
\(250\) 1.20049e7i 0.768313i
\(251\) 1.01995e7i 0.644999i 0.946570 + 0.322499i \(0.104523\pi\)
−0.946570 + 0.322499i \(0.895477\pi\)
\(252\) −1.05406e6 1.51614e6i −0.0658663 0.0947410i
\(253\) −1.21296e7 −0.749008
\(254\) −7.88117e6 −0.480939
\(255\) 5.47092e6i 0.329944i
\(256\) 1.04858e6 0.0625000
\(257\) 2.68033e7i 1.57902i −0.613735 0.789512i \(-0.710333\pi\)
0.613735 0.789512i \(-0.289667\pi\)
\(258\) 1.93769e7i 1.12830i
\(259\) −9.62812e6 1.38489e7i −0.554169 0.797108i
\(260\) 1.15272e7 0.655851
\(261\) 7.01498e6 0.394553
\(262\) 1.47235e7i 0.818665i
\(263\) −2.62513e7 −1.44306 −0.721529 0.692385i \(-0.756560\pi\)
−0.721529 + 0.692385i \(0.756560\pi\)
\(264\) 5.65060e6i 0.307102i
\(265\) 1.22182e7i 0.656554i
\(266\) 1.19376e7 8.29928e6i 0.634265 0.440956i
\(267\) 1.23233e7 0.647431
\(268\) −3.40435e6 −0.176860
\(269\) 3.58901e7i 1.84382i −0.387408 0.921909i \(-0.626629\pi\)
0.387408 0.921909i \(-0.373371\pi\)
\(270\) −9.34762e6 −0.474908
\(271\) 1.64221e6i 0.0825127i −0.999149 0.0412563i \(-0.986864\pi\)
0.999149 0.0412563i \(-0.0131360\pi\)
\(272\) 1.90115e6i 0.0944732i
\(273\) 2.14751e7 + 3.08895e7i 1.05547 + 1.51818i
\(274\) −3.91715e6 −0.190423
\(275\) −6.19751e6 −0.298002
\(276\) 1.11567e7i 0.530648i
\(277\) 3.84263e7 1.80796 0.903980 0.427574i \(-0.140632\pi\)
0.903980 + 0.427574i \(0.140632\pi\)
\(278\) 2.72652e6i 0.126904i
\(279\) 3.70798e6i 0.170736i
\(280\) 5.01523e6 3.48671e6i 0.228464 0.158834i
\(281\) −3.78655e7 −1.70657 −0.853286 0.521443i \(-0.825394\pi\)
−0.853286 + 0.521443i \(0.825394\pi\)
\(282\) −2.36604e7 −1.05505
\(283\) 3.58026e6i 0.157963i 0.996876 + 0.0789815i \(0.0251668\pi\)
−0.996876 + 0.0789815i \(0.974833\pi\)
\(284\) 6.91269e6 0.301781
\(285\) 2.20806e7i 0.953842i
\(286\) 2.15861e7i 0.922735i
\(287\) −5.07769e6 + 3.53013e6i −0.214793 + 0.149329i
\(288\) −974519. −0.0407956
\(289\) 2.06907e7 0.857197
\(290\) 2.32048e7i 0.951446i
\(291\) −3.51203e6 −0.142521
\(292\) 3.58167e6i 0.143859i
\(293\) 3.57198e7i 1.42006i 0.704172 + 0.710030i \(0.251318\pi\)
−0.704172 + 0.710030i \(0.748682\pi\)
\(294\) 1.86866e7 + 6.94358e6i 0.735342 + 0.273238i
\(295\) −2.67493e7 −1.04195
\(296\) −8.90158e6 −0.343235
\(297\) 1.75046e7i 0.668162i
\(298\) −3.70863e6 −0.140141
\(299\) 4.26201e7i 1.59441i
\(300\) 5.70038e6i 0.211125i
\(301\) −2.23900e7 3.22055e7i −0.821022 1.18095i
\(302\) 269558. 0.00978660
\(303\) −2.11531e7 −0.760409
\(304\) 7.67302e6i 0.273115i
\(305\) 3.33056e7 1.17386
\(306\) 1.76687e6i 0.0616654i
\(307\) 3.71810e7i 1.28501i −0.766282 0.642504i \(-0.777895\pi\)
0.766282 0.642504i \(-0.222105\pi\)
\(308\) −6.52929e6 9.39163e6i −0.223467 0.321432i
\(309\) −4.84776e7 −1.64311
\(310\) 1.22656e7 0.411721
\(311\) 1.37937e7i 0.458563i 0.973360 + 0.229281i \(0.0736376\pi\)
−0.973360 + 0.229281i \(0.926362\pi\)
\(312\) 1.98546e7 0.653728
\(313\) 9.13790e6i 0.297998i 0.988837 + 0.148999i \(0.0476051\pi\)
−0.988837 + 0.148999i \(0.952395\pi\)
\(314\) 1.17952e7i 0.380994i
\(315\) −4.66103e6 + 3.24046e6i −0.149125 + 0.103675i
\(316\) 1.44461e7 0.457814
\(317\) −1.28223e7 −0.402520 −0.201260 0.979538i \(-0.564504\pi\)
−0.201260 + 0.979538i \(0.564504\pi\)
\(318\) 2.10448e7i 0.654429i
\(319\) 4.34538e7 1.33862
\(320\) 3.22361e6i 0.0983767i
\(321\) 1.31561e7i 0.397751i
\(322\) 1.28916e7 + 1.85430e7i 0.386134 + 0.555408i
\(323\) 1.39117e7 0.412833
\(324\) −2.00250e7 −0.588759
\(325\) 2.17763e7i 0.634357i
\(326\) 9.01282e6 0.260141
\(327\) 5.40353e7i 1.54538i
\(328\) 3.26375e6i 0.0924901i
\(329\) 3.93249e7 2.73396e7i 1.10428 0.767724i
\(330\) 1.73715e7 0.483387
\(331\) 6.24496e7 1.72205 0.861025 0.508563i \(-0.169823\pi\)
0.861025 + 0.508563i \(0.169823\pi\)
\(332\) 7.22481e6i 0.197430i
\(333\) 8.27290e6 0.224040
\(334\) 6.88665e6i 0.184828i
\(335\) 1.04659e7i 0.278383i
\(336\) 8.63828e6 6.00554e6i 0.227724 0.158319i
\(337\) −5.54168e7 −1.44794 −0.723972 0.689829i \(-0.757686\pi\)
−0.723972 + 0.689829i \(0.757686\pi\)
\(338\) −4.85430e7 −1.25712
\(339\) 3.60031e7i 0.924148i
\(340\) 5.84463e6 0.148703
\(341\) 2.29688e7i 0.579262i
\(342\) 7.13110e6i 0.178270i
\(343\) −3.90816e7 + 1.00518e7i −0.968479 + 0.249094i
\(344\) −2.07005e7 −0.508516
\(345\) −3.42986e7 −0.835254
\(346\) 2.61236e7i 0.630673i
\(347\) −1.00493e7 −0.240518 −0.120259 0.992743i \(-0.538372\pi\)
−0.120259 + 0.992743i \(0.538372\pi\)
\(348\) 3.99681e7i 0.948367i
\(349\) 7.23514e7i 1.70204i 0.525130 + 0.851022i \(0.324017\pi\)
−0.525130 + 0.851022i \(0.675983\pi\)
\(350\) 6.58680e6 + 9.47435e6i 0.153628 + 0.220976i
\(351\) 6.15060e7 1.42232
\(352\) −6.03659e6 −0.138409
\(353\) 3.04434e7i 0.692099i 0.938216 + 0.346050i \(0.112477\pi\)
−0.938216 + 0.346050i \(0.887523\pi\)
\(354\) −4.60731e7 −1.03858
\(355\) 2.12515e7i 0.475011i
\(356\) 1.31651e7i 0.291792i
\(357\) 1.08885e7 + 1.56618e7i 0.239311 + 0.344221i
\(358\) −1.62377e7 −0.353896
\(359\) 7.98054e6 0.172484 0.0862420 0.996274i \(-0.472514\pi\)
0.0862420 + 0.996274i \(0.472514\pi\)
\(360\) 2.99594e6i 0.0642133i
\(361\) −9.10187e6 −0.193468
\(362\) 3.85369e7i 0.812364i
\(363\) 2.05349e7i 0.429312i
\(364\) −3.29995e7 + 2.29421e7i −0.684232 + 0.475695i
\(365\) −1.10110e7 −0.226438
\(366\) 5.73658e7 1.17006
\(367\) 2.06363e7i 0.417478i −0.977971 0.208739i \(-0.933064\pi\)
0.977971 0.208739i \(-0.0669360\pi\)
\(368\) 1.19188e7 0.239159
\(369\) 3.03324e6i 0.0603709i
\(370\) 2.73659e7i 0.540262i
\(371\) 2.43173e7 + 3.49776e7i 0.476204 + 0.684965i
\(372\) 2.11264e7 0.410389
\(373\) −9.06283e6 −0.174637 −0.0873187 0.996180i \(-0.527830\pi\)
−0.0873187 + 0.996180i \(0.527830\pi\)
\(374\) 1.09448e7i 0.209215i
\(375\) −6.35676e7 −1.20543
\(376\) 2.52766e7i 0.475505i
\(377\) 1.52684e8i 2.84951i
\(378\) 2.67598e7 1.86041e7i 0.495459 0.344455i
\(379\) 3.92591e7 0.721146 0.360573 0.932731i \(-0.382581\pi\)
0.360573 + 0.932731i \(0.382581\pi\)
\(380\) −2.35889e7 −0.429890
\(381\) 4.17320e7i 0.754560i
\(382\) −2.83180e7 −0.508011
\(383\) 4.25901e7i 0.758075i −0.925381 0.379037i \(-0.876255\pi\)
0.925381 0.379037i \(-0.123745\pi\)
\(384\) 5.55236e6i 0.0980583i
\(385\) −2.88724e7 + 2.00728e7i −0.505942 + 0.351743i
\(386\) 1.10306e7 0.191795
\(387\) 1.92385e7 0.331923
\(388\) 3.75194e6i 0.0642333i
\(389\) −3.23230e7 −0.549114 −0.274557 0.961571i \(-0.588531\pi\)
−0.274557 + 0.961571i \(0.588531\pi\)
\(390\) 6.10384e7i 1.02899i
\(391\) 2.16096e7i 0.361506i
\(392\) −7.41789e6 + 1.99631e7i −0.123147 + 0.331414i
\(393\) 7.79629e7 1.28443
\(394\) 6.56327e7 1.07308
\(395\) 4.44112e7i 0.720612i
\(396\) 5.61025e6 0.0903434
\(397\) 1.21097e8i 1.93536i 0.252186 + 0.967679i \(0.418851\pi\)
−0.252186 + 0.967679i \(0.581149\pi\)
\(398\) 4.11363e6i 0.0652493i
\(399\) −4.39459e7 6.32111e7i −0.691831 0.995118i
\(400\) 6.08976e6 0.0951526
\(401\) 4.98925e7 0.773753 0.386876 0.922132i \(-0.373554\pi\)
0.386876 + 0.922132i \(0.373554\pi\)
\(402\) 1.80265e7i 0.277482i
\(403\) −8.07058e7 −1.23308
\(404\) 2.25981e7i 0.342711i
\(405\) 6.15623e7i 0.926722i
\(406\) −4.61833e7 6.64294e7i −0.690092 0.992618i
\(407\) 5.12459e7 0.760109
\(408\) 1.00668e7 0.148222
\(409\) 1.08411e7i 0.158454i 0.996857 + 0.0792269i \(0.0252452\pi\)
−0.996857 + 0.0792269i \(0.974755\pi\)
\(410\) 1.00336e7 0.145582
\(411\) 2.07419e7i 0.298761i
\(412\) 5.17891e7i 0.740536i
\(413\) 7.65762e7 5.32377e7i 1.08704 0.755734i
\(414\) −1.10770e7 −0.156106
\(415\) 2.22110e7 0.310759
\(416\) 2.12109e7i 0.294631i
\(417\) 1.44373e7 0.199103
\(418\) 4.41731e7i 0.604824i
\(419\) 3.85015e7i 0.523402i 0.965149 + 0.261701i \(0.0842834\pi\)
−0.965149 + 0.261701i \(0.915717\pi\)
\(420\) −1.84627e7 2.65564e7i −0.249199 0.358444i
\(421\) −6.80531e7 −0.912014 −0.456007 0.889976i \(-0.650721\pi\)
−0.456007 + 0.889976i \(0.650721\pi\)
\(422\) 3.29540e7 0.438501
\(423\) 2.34914e7i 0.310376i
\(424\) 2.24823e7 0.294947
\(425\) 1.10412e7i 0.143830i
\(426\) 3.66037e7i 0.473474i
\(427\) −9.53453e7 + 6.62864e7i −1.22466 + 0.851414i
\(428\) 1.40548e7 0.179264
\(429\) −1.14302e8 −1.44771
\(430\) 6.36388e7i 0.800418i
\(431\) −5.94074e7 −0.742008 −0.371004 0.928631i \(-0.620986\pi\)
−0.371004 + 0.928631i \(0.620986\pi\)
\(432\) 1.72002e7i 0.213345i
\(433\) 6.40026e7i 0.788377i −0.919030 0.394189i \(-0.871026\pi\)
0.919030 0.394189i \(-0.128974\pi\)
\(434\) −3.51132e7 + 2.44116e7i −0.429538 + 0.298625i
\(435\) 1.22873e8 1.49275
\(436\) 5.77264e7 0.696490
\(437\) 8.72162e7i 1.04509i
\(438\) −1.89655e7 −0.225705
\(439\) 5.84728e7i 0.691131i 0.938395 + 0.345565i \(0.112313\pi\)
−0.938395 + 0.345565i \(0.887687\pi\)
\(440\) 1.85581e7i 0.217859i
\(441\) 6.89400e6 1.85532e7i 0.0803814 0.216323i
\(442\) −3.84568e7 −0.445355
\(443\) −1.54616e8 −1.77845 −0.889227 0.457467i \(-0.848757\pi\)
−0.889227 + 0.457467i \(0.848757\pi\)
\(444\) 4.71352e7i 0.538513i
\(445\) 4.04731e7 0.459289
\(446\) 3.42513e7i 0.386076i
\(447\) 1.96377e7i 0.219871i
\(448\) 6.41578e6 + 9.22835e6i 0.0713535 + 0.102634i
\(449\) 8.30902e7 0.917933 0.458966 0.888454i \(-0.348220\pi\)
0.458966 + 0.888454i \(0.348220\pi\)
\(450\) −5.65967e6 −0.0621088
\(451\) 1.87892e7i 0.204823i
\(452\) 3.84625e7 0.416507
\(453\) 1.42735e6i 0.0153545i
\(454\) 9.62913e7i 1.02901i
\(455\) 7.05301e7 + 1.01449e8i 0.748756 + 1.07700i
\(456\) −4.06298e7 −0.428499
\(457\) 3.71422e7 0.389152 0.194576 0.980887i \(-0.437667\pi\)
0.194576 + 0.980887i \(0.437667\pi\)
\(458\) 4.80390e7i 0.500031i
\(459\) 3.11853e7 0.322486
\(460\) 3.66415e7i 0.376443i
\(461\) 3.38118e6i 0.0345116i 0.999851 + 0.0172558i \(0.00549296\pi\)
−0.999851 + 0.0172558i \(0.994507\pi\)
\(462\) −4.97301e7 + 3.45736e7i −0.504305 + 0.350605i
\(463\) 6.63410e7 0.668404 0.334202 0.942502i \(-0.391533\pi\)
0.334202 + 0.942502i \(0.391533\pi\)
\(464\) −4.26983e7 −0.427422
\(465\) 6.49481e7i 0.645963i
\(466\) −2.69404e7 −0.266223
\(467\) 9.97322e7i 0.979230i −0.871939 0.489615i \(-0.837137\pi\)
0.871939 0.489615i \(-0.162863\pi\)
\(468\) 1.97128e7i 0.192314i
\(469\) −2.08297e7 2.99612e7i −0.201913 0.290429i
\(470\) −7.77071e7 −0.748457
\(471\) −6.24575e7 −0.597753
\(472\) 4.92203e7i 0.468078i
\(473\) 1.19171e8 1.12613
\(474\) 7.64942e7i 0.718280i
\(475\) 4.45622e7i 0.415801i
\(476\) −1.67317e7 + 1.16323e7i −0.155138 + 0.107856i
\(477\) −2.08945e7 −0.192520
\(478\) 8.99048e7 0.823188
\(479\) 8.50867e7i 0.774203i 0.922037 + 0.387102i \(0.126524\pi\)
−0.922037 + 0.387102i \(0.873476\pi\)
\(480\) −1.70695e7 −0.154346
\(481\) 1.80063e8i 1.61804i
\(482\) 1.50561e6i 0.0134453i
\(483\) 9.81879e7 6.82627e7i 0.871398 0.605818i
\(484\) −2.19377e7 −0.193488
\(485\) −1.15345e7 −0.101105
\(486\) 3.67667e7i 0.320291i
\(487\) 1.19789e8 1.03712 0.518560 0.855041i \(-0.326468\pi\)
0.518560 + 0.855041i \(0.326468\pi\)
\(488\) 6.12844e7i 0.527340i
\(489\) 4.77242e7i 0.408143i
\(490\) 6.13720e7 + 2.28046e7i 0.521654 + 0.193836i
\(491\) −2.24857e8 −1.89960 −0.949800 0.312859i \(-0.898713\pi\)
−0.949800 + 0.312859i \(0.898713\pi\)
\(492\) 1.72820e7 0.145111
\(493\) 7.74152e7i 0.646079i
\(494\) 1.55212e8 1.28749
\(495\) 1.72474e7i 0.142203i
\(496\) 2.25695e7i 0.184959i
\(497\) 4.22957e7 + 6.08375e7i 0.344530 + 0.495566i
\(498\) 3.82564e7 0.309754
\(499\) 5.80019e7 0.466810 0.233405 0.972380i \(-0.425013\pi\)
0.233405 + 0.972380i \(0.425013\pi\)
\(500\) 6.79099e7i 0.543279i
\(501\) −3.64658e7 −0.289983
\(502\) 5.76972e7i 0.456083i
\(503\) 9.94846e7i 0.781721i 0.920450 + 0.390860i \(0.127823\pi\)
−0.920450 + 0.390860i \(0.872177\pi\)
\(504\) −5.96265e6 8.57659e6i −0.0465745 0.0669920i
\(505\) −6.94727e7 −0.539436
\(506\) −6.86156e7 −0.529628
\(507\) 2.57042e8i 1.97233i
\(508\) −4.45826e7 −0.340075
\(509\) 1.51579e8i 1.14944i 0.818350 + 0.574721i \(0.194889\pi\)
−0.818350 + 0.574721i \(0.805111\pi\)
\(510\) 3.09482e7i 0.233305i
\(511\) 3.15217e7 2.19147e7i 0.236237 0.164237i
\(512\) 5.93164e6 0.0441942
\(513\) −1.25864e8 −0.932284
\(514\) 1.51622e8i 1.11654i
\(515\) −1.59214e8 −1.16562
\(516\) 1.09612e8i 0.797828i
\(517\) 1.45516e8i 1.05302i
\(518\) −5.44649e7 7.83414e7i −0.391857 0.563640i
\(519\) −1.38328e8 −0.989484
\(520\) 6.52079e7 0.463757
\(521\) 1.36113e8i 0.962469i 0.876592 + 0.481234i \(0.159811\pi\)
−0.876592 + 0.481234i \(0.840189\pi\)
\(522\) 3.96827e7 0.278991
\(523\) 1.02678e8i 0.717749i −0.933386 0.358874i \(-0.883161\pi\)
0.933386 0.358874i \(-0.116839\pi\)
\(524\) 8.32885e7i 0.578884i
\(525\) 5.01681e7 3.48781e7i 0.346697 0.241032i
\(526\) −1.48500e8 −1.02040
\(527\) −4.09201e7 −0.279579
\(528\) 3.19646e7i 0.217154i
\(529\) −1.25600e7 −0.0848445
\(530\) 6.91167e7i 0.464254i
\(531\) 4.57441e7i 0.305528i
\(532\) 6.75290e7 4.69478e7i 0.448493 0.311803i
\(533\) −6.60199e7 −0.436007
\(534\) 6.97111e7 0.457803
\(535\) 4.32081e7i 0.282166i
\(536\) −1.92579e7 −0.125059
\(537\) 8.59810e7i 0.555239i
\(538\) 2.03025e8i 1.30378i
\(539\) 4.27044e7 1.14927e8i 0.272713 0.733929i
\(540\) −5.28781e7 −0.335811
\(541\) 1.71991e8 1.08621 0.543104 0.839665i \(-0.317249\pi\)
0.543104 + 0.839665i \(0.317249\pi\)
\(542\) 9.28974e6i 0.0583453i
\(543\) 2.04058e8 1.27454
\(544\) 1.07545e7i 0.0668026i
\(545\) 1.77466e8i 1.09629i
\(546\) 1.21482e8 + 1.74737e8i 0.746333 + 1.07351i
\(547\) −3.57048e7 −0.218154 −0.109077 0.994033i \(-0.534790\pi\)
−0.109077 + 0.994033i \(0.534790\pi\)
\(548\) −2.21588e7 −0.134649
\(549\) 5.69561e7i 0.344210i
\(550\) −3.50584e7 −0.210719
\(551\) 3.12448e8i 1.86777i
\(552\) 6.31116e7i 0.375225i
\(553\) 8.83893e7 + 1.27138e8i 0.522666 + 0.751795i
\(554\) 2.17372e8 1.27842
\(555\) 1.44906e8 0.847634
\(556\) 1.54235e7i 0.0897343i
\(557\) −7.51706e7 −0.434993 −0.217497 0.976061i \(-0.569789\pi\)
−0.217497 + 0.976061i \(0.569789\pi\)
\(558\) 2.09755e7i 0.120728i
\(559\) 4.18734e8i 2.39719i
\(560\) 2.83704e7 1.97238e7i 0.161548 0.112312i
\(561\) −5.79542e7 −0.328244
\(562\) −2.14200e8 −1.20673
\(563\) 2.09618e8i 1.17464i −0.809356 0.587318i \(-0.800184\pi\)
0.809356 0.587318i \(-0.199816\pi\)
\(564\) −1.33843e8 −0.746035
\(565\) 1.18244e8i 0.655593i
\(566\) 2.02530e7i 0.111697i
\(567\) −1.22524e8 1.76237e8i −0.672160 0.966824i
\(568\) 3.91041e7 0.213391
\(569\) 3.85572e7 0.209300 0.104650 0.994509i \(-0.466628\pi\)
0.104650 + 0.994509i \(0.466628\pi\)
\(570\) 1.24907e8i 0.674468i
\(571\) 6.50282e7 0.349296 0.174648 0.984631i \(-0.444121\pi\)
0.174648 + 0.984631i \(0.444121\pi\)
\(572\) 1.22110e8i 0.652472i
\(573\) 1.49948e8i 0.797034i
\(574\) −2.87237e7 + 1.99694e7i −0.151882 + 0.105592i
\(575\) 6.92200e7 0.364106
\(576\) −5.51271e6 −0.0288468
\(577\) 1.17548e8i 0.611909i 0.952046 + 0.305954i \(0.0989755\pi\)
−0.952046 + 0.305954i \(0.901025\pi\)
\(578\) 1.17044e8 0.606130
\(579\) 5.84085e7i 0.300913i
\(580\) 1.31266e8i 0.672774i
\(581\) −6.35844e7 + 4.42055e7i −0.324207 + 0.225397i
\(582\) −1.98671e7 −0.100778
\(583\) −1.29429e8 −0.653171
\(584\) 2.02610e7i 0.101724i
\(585\) −6.06025e7 −0.302707
\(586\) 2.02062e8i 1.00413i
\(587\) 2.41814e8i 1.19555i 0.801664 + 0.597775i \(0.203948\pi\)
−0.801664 + 0.597775i \(0.796052\pi\)
\(588\) 1.05708e8 + 3.92788e7i 0.519965 + 0.193209i
\(589\) 1.65153e8 0.808243
\(590\) −1.51317e8 −0.736768
\(591\) 3.47535e8i 1.68359i
\(592\) −5.03550e7 −0.242704
\(593\) 2.31180e8i 1.10863i −0.832307 0.554314i \(-0.812981\pi\)
0.832307 0.554314i \(-0.187019\pi\)
\(594\) 9.90207e7i 0.472462i
\(595\) 3.57607e7 + 5.14377e7i 0.169768 + 0.244192i
\(596\) −2.09792e7 −0.0990945
\(597\) −2.17823e7 −0.102372
\(598\) 2.41096e8i 1.12742i
\(599\) −3.84910e7 −0.179093 −0.0895464 0.995983i \(-0.528542\pi\)
−0.0895464 + 0.995983i \(0.528542\pi\)
\(600\) 3.22462e7i 0.149288i
\(601\) 3.32931e8i 1.53367i 0.641847 + 0.766833i \(0.278168\pi\)
−0.641847 + 0.766833i \(0.721832\pi\)
\(602\) −1.26657e8 1.82182e8i −0.580550 0.835055i
\(603\) 1.78978e7 0.0816297
\(604\) 1.52485e6 0.00692017
\(605\) 6.74423e7i 0.304555i
\(606\) −1.19660e8 −0.537690
\(607\) 5.87633e7i 0.262749i 0.991333 + 0.131374i \(0.0419390\pi\)
−0.991333 + 0.131374i \(0.958061\pi\)
\(608\) 4.34051e7i 0.193121i
\(609\) −3.51753e8 + 2.44547e8i −1.55735 + 1.08271i
\(610\) 1.88405e8 0.830047
\(611\) 5.11301e8 2.24157
\(612\) 9.99495e6i 0.0436040i
\(613\) −1.11411e7 −0.0483665 −0.0241833 0.999708i \(-0.507699\pi\)
−0.0241833 + 0.999708i \(0.507699\pi\)
\(614\) 2.10328e8i 0.908639i
\(615\) 5.31296e7i 0.228408i
\(616\) −3.69352e7 5.31271e7i −0.158015 0.227287i
\(617\) 6.61360e7 0.281567 0.140784 0.990040i \(-0.455038\pi\)
0.140784 + 0.990040i \(0.455038\pi\)
\(618\) −2.74231e8 −1.16185
\(619\) 1.81247e8i 0.764185i 0.924124 + 0.382093i \(0.124796\pi\)
−0.924124 + 0.382093i \(0.875204\pi\)
\(620\) 6.93847e7 0.291131
\(621\) 1.95508e8i 0.816376i
\(622\) 7.80288e7i 0.324253i
\(623\) −1.15864e8 + 8.05514e7i −0.479164 + 0.333126i
\(624\) 1.12315e8 0.462256
\(625\) −1.15851e8 −0.474526
\(626\) 5.16918e7i 0.210716i
\(627\) 2.33903e8 0.948928
\(628\) 6.67239e7i 0.269403i
\(629\) 9.12972e7i 0.366864i
\(630\) −2.63668e7 + 1.83308e7i −0.105447 + 0.0733095i
\(631\) −1.25706e8 −0.500344 −0.250172 0.968201i \(-0.580487\pi\)
−0.250172 + 0.968201i \(0.580487\pi\)
\(632\) 8.17195e7 0.323724
\(633\) 1.74496e8i 0.687979i
\(634\) −7.25338e7 −0.284625
\(635\) 1.37059e8i 0.535287i
\(636\) 1.19047e8i 0.462751i
\(637\) −4.03819e8 1.50051e8i −1.56231 0.580525i
\(638\) 2.45812e8 0.946544
\(639\) −3.63423e7 −0.139287
\(640\) 1.82355e7i 0.0695628i
\(641\) −5.14744e8 −1.95442 −0.977209 0.212281i \(-0.931911\pi\)
−0.977209 + 0.212281i \(0.931911\pi\)
\(642\) 7.44220e7i 0.281252i
\(643\) 2.77852e8i 1.04515i −0.852592 0.522577i \(-0.824971\pi\)
0.852592 0.522577i \(-0.175029\pi\)
\(644\) 7.29256e7 + 1.04895e8i 0.273038 + 0.392733i
\(645\) 3.36977e8 1.25580
\(646\) 7.86967e7 0.291917
\(647\) 1.33880e8i 0.494315i 0.968975 + 0.247157i \(0.0794965\pi\)
−0.968975 + 0.247157i \(0.920504\pi\)
\(648\) −1.13278e8 −0.416315
\(649\) 2.83359e8i 1.03658i
\(650\) 1.23185e8i 0.448558i
\(651\) 1.29263e8 + 1.85930e8i 0.468523 + 0.673916i
\(652\) 5.09842e7 0.183947
\(653\) 3.72064e8 1.33622 0.668110 0.744062i \(-0.267103\pi\)
0.668110 + 0.744062i \(0.267103\pi\)
\(654\) 3.05670e8i 1.09275i
\(655\) 2.56051e8 0.911178
\(656\) 1.84625e7i 0.0654003i
\(657\) 1.88300e7i 0.0663980i
\(658\) 2.22455e8 1.54656e8i 0.780845 0.542863i
\(659\) −4.95336e7 −0.173079 −0.0865394 0.996248i \(-0.527581\pi\)
−0.0865394 + 0.996248i \(0.527581\pi\)
\(660\) 9.82679e7 0.341806
\(661\) 6.94997e7i 0.240646i −0.992735 0.120323i \(-0.961607\pi\)
0.992735 0.120323i \(-0.0383930\pi\)
\(662\) 3.53268e8 1.21767
\(663\) 2.03635e8i 0.698732i
\(664\) 4.08697e7i 0.139604i
\(665\) −1.44330e8 2.07602e8i −0.490786 0.705939i
\(666\) 4.67986e7 0.158420
\(667\) −4.85335e8 −1.63555
\(668\) 3.89568e7i 0.130693i
\(669\) 1.81366e8 0.605728
\(670\) 5.92041e7i 0.196846i
\(671\) 3.52811e8i 1.16782i
\(672\) 4.88655e7 3.39725e7i 0.161025 0.111949i
\(673\) 1.80776e8 0.593056 0.296528 0.955024i \(-0.404171\pi\)
0.296528 + 0.955024i \(0.404171\pi\)
\(674\) −3.13485e8 −1.02385
\(675\) 9.98929e7i 0.324805i
\(676\) −2.74600e8 −0.888917
\(677\) 2.40792e8i 0.776024i −0.921654 0.388012i \(-0.873162\pi\)
0.921654 0.388012i \(-0.126838\pi\)
\(678\) 2.03665e8i 0.653471i
\(679\) 3.30202e7 2.29564e7i 0.105480 0.0733323i
\(680\) 3.30622e7 0.105149
\(681\) 5.09876e8 1.61445
\(682\) 1.29931e8i 0.409600i
\(683\) −5.06433e8 −1.58950 −0.794749 0.606939i \(-0.792397\pi\)
−0.794749 + 0.606939i \(0.792397\pi\)
\(684\) 4.03396e7i 0.126056i
\(685\) 6.81221e7i 0.211942i
\(686\) −2.21079e8 + 5.68618e7i −0.684818 + 0.176136i
\(687\) −2.54373e8 −0.784515
\(688\) −1.17100e8 −0.359575
\(689\) 4.54778e8i 1.39041i
\(690\) −1.94022e8 −0.590614
\(691\) 3.85108e7i 0.116721i 0.998296 + 0.0583604i \(0.0185873\pi\)
−0.998296 + 0.0583604i \(0.981413\pi\)
\(692\) 1.47777e8i 0.445953i
\(693\) 3.43267e7 + 4.93749e7i 0.103141 + 0.148357i
\(694\) −5.68474e7 −0.170072
\(695\) 4.74160e7 0.141244
\(696\) 2.26094e8i 0.670596i
\(697\) −3.34739e7 −0.0988573
\(698\) 4.09281e8i 1.20353i
\(699\) 1.42653e8i 0.417686i
\(700\) 3.72606e7 + 5.35950e7i 0.108631 + 0.156254i
\(701\) 3.57882e8 1.03893 0.519464 0.854492i \(-0.326132\pi\)
0.519464 + 0.854492i \(0.326132\pi\)
\(702\) 3.47930e8 1.00573
\(703\) 3.68475e8i 1.06058i
\(704\) −3.41481e7 −0.0978698
\(705\) 4.11470e8i 1.17428i
\(706\) 1.72214e8i 0.489388i
\(707\) 1.98882e8 1.38268e8i 0.562779 0.391258i
\(708\) −2.60629e8 −0.734383
\(709\) −2.84537e8 −0.798361 −0.399181 0.916872i \(-0.630705\pi\)
−0.399181 + 0.916872i \(0.630705\pi\)
\(710\) 1.20216e8i 0.335884i
\(711\) −7.59479e7 −0.211304
\(712\) 7.44730e7i 0.206328i
\(713\) 2.56538e8i 0.707756i
\(714\) 6.15946e7 + 8.85967e7i 0.169219 + 0.243401i
\(715\) −3.75398e8 −1.02701
\(716\) −9.18543e7 −0.250242
\(717\) 4.76059e8i 1.29153i
\(718\) 4.51447e7 0.121965
\(719\) 3.52700e8i 0.948896i −0.880283 0.474448i \(-0.842648\pi\)
0.880283 0.474448i \(-0.157352\pi\)
\(720\) 1.69476e7i 0.0454057i
\(721\) 4.55787e8 3.16874e8i 1.21606 0.845437i
\(722\) −5.14879e7 −0.136802
\(723\) −7.97244e6 −0.0210948
\(724\) 2.17997e8i 0.574428i
\(725\) −2.47977e8 −0.650725
\(726\) 1.16163e8i 0.303570i
\(727\) 7.48885e8i 1.94900i 0.224387 + 0.974500i \(0.427962\pi\)
−0.224387 + 0.974500i \(0.572038\pi\)
\(728\) −1.86673e8 + 1.29780e8i −0.483825 + 0.336367i
\(729\) −2.61510e8 −0.675002
\(730\) −6.22877e7 −0.160116
\(731\) 2.12310e8i 0.543524i
\(732\) 3.24510e8 0.827361
\(733\) 6.35196e8i 1.61286i −0.591331 0.806429i \(-0.701398\pi\)
0.591331 0.806429i \(-0.298602\pi\)
\(734\) 1.16737e8i 0.295202i
\(735\) 1.20754e8 3.24974e8i 0.304116 0.818439i
\(736\) 6.74227e7 0.169111
\(737\) 1.10867e8 0.276948
\(738\) 1.71586e7i 0.0426887i
\(739\) 3.65308e8 0.905161 0.452580 0.891724i \(-0.350504\pi\)
0.452580 + 0.891724i \(0.350504\pi\)
\(740\) 1.54805e8i 0.382023i
\(741\) 8.21869e8i 2.01998i
\(742\) 1.37559e8 + 1.97863e8i 0.336727 + 0.484343i
\(743\) −2.84817e8 −0.694384 −0.347192 0.937794i \(-0.612865\pi\)
−0.347192 + 0.937794i \(0.612865\pi\)
\(744\) 1.19509e8 0.290189
\(745\) 6.44956e7i 0.155977i
\(746\) −5.12671e7 −0.123487
\(747\) 3.79832e7i 0.0911235i
\(748\) 6.19130e7i 0.147937i
\(749\) 8.59949e7 + 1.23694e8i 0.204657 + 0.294376i
\(750\) −3.59593e8 −0.852368
\(751\) −1.41864e8 −0.334929 −0.167465 0.985878i \(-0.553558\pi\)
−0.167465 + 0.985878i \(0.553558\pi\)
\(752\) 1.42986e8i 0.336233i
\(753\) 3.05515e8 0.715563
\(754\) 8.63712e8i 2.01491i
\(755\) 4.68781e6i 0.0108925i
\(756\) 1.51376e8 1.05241e8i 0.350343 0.243567i
\(757\) 4.81270e8 1.10943 0.554716 0.832040i \(-0.312827\pi\)
0.554716 + 0.832040i \(0.312827\pi\)
\(758\) 2.22083e8 0.509927
\(759\) 3.63330e8i 0.830951i
\(760\) −1.33439e8 −0.303978
\(761\) 4.55601e8i 1.03379i −0.856050 0.516893i \(-0.827088\pi\)
0.856050 0.516893i \(-0.172912\pi\)
\(762\) 2.36072e8i 0.533555i
\(763\) 3.53202e8 + 5.08041e8i 0.795151 + 1.14373i
\(764\) −1.60191e8 −0.359218
\(765\) −3.07272e7 −0.0686339
\(766\) 2.40926e8i 0.536040i
\(767\) 9.95641e8 2.20657
\(768\) 3.14089e7i 0.0693377i
\(769\) 3.23170e8i 0.710643i −0.934744 0.355322i \(-0.884371\pi\)
0.934744 0.355322i \(-0.115629\pi\)
\(770\) −1.63327e8 + 1.13549e8i −0.357755 + 0.248720i
\(771\) −8.02863e8 −1.75177
\(772\) 6.23984e7 0.135619
\(773\) 2.14005e8i 0.463324i 0.972796 + 0.231662i \(0.0744164\pi\)
−0.972796 + 0.231662i \(0.925584\pi\)
\(774\) 1.08829e8 0.234705
\(775\) 1.31076e8i 0.281590i
\(776\) 2.12242e7i 0.0454198i
\(777\) −4.14829e8 + 2.88399e8i −0.884314 + 0.614797i
\(778\) −1.82846e8 −0.388282
\(779\) 1.35101e8 0.285789
\(780\) 3.45285e8i 0.727603i
\(781\) −2.25120e8 −0.472564
\(782\) 1.22242e8i 0.255624i
\(783\) 7.00398e8i 1.45902i
\(784\) −4.19619e7 + 1.12928e8i −0.0870778 + 0.234345i
\(785\) −2.05127e8 −0.424048
\(786\) 4.41025e8 0.908229
\(787\) 6.93076e8i 1.42186i −0.703263 0.710930i \(-0.748274\pi\)
0.703263 0.710930i \(-0.251726\pi\)
\(788\) 3.71275e8 0.758782
\(789\) 7.86328e8i 1.60093i
\(790\) 2.51228e8i 0.509549i
\(791\) 2.35335e8 + 3.38502e8i 0.475507 + 0.683962i
\(792\) 3.17364e7 0.0638825
\(793\) −1.23968e9 −2.48593
\(794\) 6.85027e8i 1.36850i
\(795\) −3.65983e8 −0.728383
\(796\) 2.32702e7i 0.0461382i
\(797\) 1.42327e8i 0.281134i 0.990071 + 0.140567i \(0.0448926\pi\)
−0.990071 + 0.140567i \(0.955107\pi\)
\(798\) −2.48596e8 3.57576e8i −0.489198 0.703655i
\(799\) 2.59244e8 0.508240
\(800\) 3.44489e7 0.0672830
\(801\) 6.92133e7i 0.134676i
\(802\) 2.82235e8 0.547126
\(803\) 1.16641e8i 0.225271i
\(804\) 1.01974e8i 0.196209i
\(805\) 3.22476e8 2.24193e8i 0.618172 0.429769i
\(806\) −4.56541e8 −0.871916
\(807\) −1.07505e9 −2.04554
\(808\) 1.27834e8i 0.242333i
\(809\) −2.01624e8 −0.380800 −0.190400 0.981707i \(-0.560979\pi\)
−0.190400 + 0.981707i \(0.560979\pi\)
\(810\) 3.48249e8i 0.655291i
\(811\) 1.69349e7i 0.0317483i 0.999874 + 0.0158741i \(0.00505311\pi\)
−0.999874 + 0.0158741i \(0.994947\pi\)
\(812\) −2.61252e8 3.75781e8i −0.487969 0.701887i
\(813\) −4.91905e7 −0.0915398
\(814\) 2.89891e8 0.537478
\(815\) 1.56739e8i 0.289538i
\(816\) 5.69467e7 0.104809
\(817\) 8.56883e8i 1.57129i
\(818\) 6.13264e7i 0.112044i
\(819\) 1.73489e8 1.20614e8i 0.315806 0.219556i
\(820\) 5.67589e7 0.102942
\(821\) 3.77973e8 0.683018 0.341509 0.939879i \(-0.389062\pi\)
0.341509 + 0.939879i \(0.389062\pi\)
\(822\) 1.17334e8i 0.211256i
\(823\) 5.19539e8 0.932006 0.466003 0.884783i \(-0.345694\pi\)
0.466003 + 0.884783i \(0.345694\pi\)
\(824\) 2.92963e8i 0.523638i
\(825\) 1.85639e8i 0.330604i
\(826\) 4.33180e8 3.01158e8i 0.768650 0.534384i
\(827\) 5.17270e7 0.0914536 0.0457268 0.998954i \(-0.485440\pi\)
0.0457268 + 0.998954i \(0.485440\pi\)
\(828\) −6.26609e7 −0.110384
\(829\) 7.51588e7i 0.131922i 0.997822 + 0.0659609i \(0.0210113\pi\)
−0.997822 + 0.0659609i \(0.978989\pi\)
\(830\) 1.25645e8 0.219740
\(831\) 1.15102e9i 2.00576i
\(832\) 1.19987e8i 0.208335i
\(833\) −2.04748e8 7.60801e7i −0.354229 0.131624i
\(834\) 8.16697e7 0.140787
\(835\) −1.19764e8 −0.205715
\(836\) 2.49881e8i 0.427675i
\(837\) 3.70216e8 0.631363
\(838\) 2.17797e8i 0.370101i
\(839\) 8.14179e8i 1.37859i −0.724483 0.689293i \(-0.757921\pi\)
0.724483 0.689293i \(-0.242079\pi\)
\(840\) −1.04441e8 1.50226e8i −0.176210 0.253458i
\(841\) 1.14387e9 1.92303
\(842\) −3.84966e8 −0.644891
\(843\) 1.13422e9i 1.89328i
\(844\) 1.86416e8 0.310067
\(845\) 8.44196e8i 1.39918i
\(846\) 1.32887e8i 0.219469i
\(847\) −1.34227e8 1.93070e8i −0.220897 0.317734i
\(848\) 1.27179e8 0.208559
\(849\) 1.07243e8 0.175245
\(850\) 6.24584e7i 0.101703i
\(851\) −5.72365e8 −0.928719
\(852\) 2.07062e8i 0.334797i
\(853\) 9.81909e8i 1.58206i −0.611774 0.791032i \(-0.709544\pi\)
0.611774 0.791032i \(-0.290456\pi\)
\(854\) −5.39354e8 + 3.74972e8i −0.865966 + 0.602040i
\(855\) 1.24015e8 0.198415
\(856\) 7.95057e7 0.126759
\(857\) 1.05751e9i 1.68013i −0.542487 0.840064i \(-0.682517\pi\)
0.542487 0.840064i \(-0.317483\pi\)
\(858\) −6.46588e8 −1.02368
\(859\) 1.43809e8i 0.226886i −0.993545 0.113443i \(-0.963812\pi\)
0.993545 0.113443i \(-0.0361879\pi\)
\(860\) 3.59996e8i 0.565981i
\(861\) 1.05741e8 + 1.52096e8i 0.165666 + 0.238292i
\(862\) −3.36059e8 −0.524679
\(863\) 3.42007e8 0.532111 0.266056 0.963958i \(-0.414280\pi\)
0.266056 + 0.963958i \(0.414280\pi\)
\(864\) 9.72992e7i 0.150858i
\(865\) −4.54307e8 −0.701942
\(866\) 3.62054e8i 0.557467i
\(867\) 6.19765e8i 0.950977i
\(868\) −1.98630e8 + 1.38093e8i −0.303729 + 0.211160i
\(869\) −4.70454e8 −0.716899
\(870\) 6.95074e8 1.05554
\(871\) 3.89554e8i 0.589540i
\(872\) 3.26550e8 0.492493
\(873\) 1.97252e7i 0.0296468i
\(874\) 4.93369e8i 0.738989i
\(875\) 5.97664e8 4.15511e8i 0.892140 0.620238i
\(876\) −1.07285e8 −0.159598
\(877\) −2.00898e8 −0.297836 −0.148918 0.988850i \(-0.547579\pi\)
−0.148918 + 0.988850i \(0.547579\pi\)
\(878\) 3.30772e8i 0.488703i
\(879\) 1.06995e9 1.57542
\(880\) 1.04981e8i 0.154050i
\(881\) 1.00494e9i 1.46964i 0.678262 + 0.734820i \(0.262733\pi\)
−0.678262 + 0.734820i \(0.737267\pi\)
\(882\) 3.89983e7 1.04953e8i 0.0568382 0.152964i
\(883\) 5.37005e8 0.780003 0.390001 0.920814i \(-0.372475\pi\)
0.390001 + 0.920814i \(0.372475\pi\)
\(884\) −2.17545e8 −0.314914
\(885\) 8.01244e8i 1.15594i
\(886\) −8.74639e8 −1.25756
\(887\) 1.31599e8i 0.188574i −0.995545 0.0942871i \(-0.969943\pi\)
0.995545 0.0942871i \(-0.0300572\pi\)
\(888\) 2.66637e8i 0.380786i
\(889\) −2.72782e8 3.92365e8i −0.388249 0.558451i
\(890\) 2.28950e8 0.324766
\(891\) 6.52138e8 0.921947
\(892\) 1.93755e8i 0.272997i
\(893\) −1.04631e9 −1.46928
\(894\) 1.11088e8i 0.155473i
\(895\) 2.82385e8i 0.393888i
\(896\) 3.62931e7 + 5.22034e7i 0.0504545 + 0.0725730i
\(897\) 1.27664e9 1.76885
\(898\) 4.70029e8 0.649076
\(899\) 9.19036e8i 1.26489i
\(900\) −3.20159e7 −0.0439176
\(901\) 2.30585e8i 0.315251i
\(902\) 1.06288e8i 0.144832i
\(903\) −9.64678e8 + 6.70668e8i −1.31014 + 0.910845i
\(904\) 2.17577e8 0.294515
\(905\) 6.70183e8 0.904165
\(906\) 8.07432e6i 0.0108573i
\(907\) −1.20778e9 −1.61870 −0.809349 0.587328i \(-0.800180\pi\)
−0.809349 + 0.587328i \(0.800180\pi\)
\(908\) 5.44706e8i 0.727619i
\(909\) 1.18806e8i 0.158178i
\(910\) 3.98978e8 + 5.73884e8i 0.529450 + 0.761553i
\(911\) −1.08236e8 −0.143158 −0.0715792 0.997435i \(-0.522804\pi\)
−0.0715792 + 0.997435i \(0.522804\pi\)
\(912\) −2.29837e8 −0.302994
\(913\) 2.35285e8i 0.309158i
\(914\) 2.10108e8 0.275172
\(915\) 9.97631e8i 1.30229i
\(916\) 2.71749e8i 0.353576i
\(917\) −7.33009e8 + 5.09606e8i −0.950608 + 0.660886i
\(918\) 1.76411e8 0.228032
\(919\) −8.87506e8 −1.14347 −0.571735 0.820438i \(-0.693729\pi\)
−0.571735 + 0.820438i \(0.693729\pi\)
\(920\) 2.07275e8i 0.266186i
\(921\) −1.11372e9 −1.42559
\(922\) 1.91268e7i 0.0244034i
\(923\) 7.91006e8i 1.00595i
\(924\) −2.81316e8 + 1.95578e8i −0.356597 + 0.247915i
\(925\) −2.92444e8 −0.369503
\(926\) 3.75281e8 0.472633
\(927\) 2.72272e8i 0.341794i
\(928\) −2.41538e8 −0.302233
\(929\) 5.79061e7i 0.0722233i −0.999348 0.0361116i \(-0.988503\pi\)
0.999348 0.0361116i \(-0.0114972\pi\)
\(930\) 3.67402e8i 0.456765i
\(931\) 8.26361e8 + 3.07059e8i 1.02405 + 0.380516i
\(932\) −1.52398e8 −0.188248
\(933\) 4.13174e8 0.508731
\(934\) 5.64171e8i 0.692420i
\(935\) −1.90337e8 −0.232857
\(936\) 1.11512e8i 0.135987i
\(937\) 1.01207e9i 1.23024i 0.788432 + 0.615122i \(0.210893\pi\)
−0.788432 + 0.615122i \(0.789107\pi\)
\(938\) −1.17831e8 1.69486e8i −0.142774 0.205364i
\(939\) 2.73715e8 0.330600
\(940\) −4.39578e8 −0.529239
\(941\) 9.96415e8i 1.19584i 0.801557 + 0.597918i \(0.204005\pi\)
−0.801557 + 0.597918i \(0.795995\pi\)
\(942\) −3.53313e8 −0.422675
\(943\) 2.09857e8i 0.250258i
\(944\) 2.78432e8i 0.330981i
\(945\) −3.23538e8 4.65372e8i −0.383381 0.551449i
\(946\) 6.74135e8 0.796294
\(947\) 8.94254e8 1.05296 0.526479 0.850188i \(-0.323512\pi\)
0.526479 + 0.850188i \(0.323512\pi\)
\(948\) 4.32717e8i 0.507900i
\(949\) 4.09844e8 0.479535
\(950\) 2.52082e8i 0.294016i
\(951\) 3.84077e8i 0.446557i
\(952\) −9.46487e7 + 6.58021e7i −0.109699 + 0.0762656i
\(953\) −7.60395e8 −0.878538 −0.439269 0.898355i \(-0.644763\pi\)
−0.439269 + 0.898355i \(0.644763\pi\)
\(954\) −1.18197e8 −0.136132
\(955\) 4.92470e8i 0.565418i
\(956\) 5.08578e8 0.582082
\(957\) 1.30161e9i 1.48506i
\(958\) 4.81323e8i 0.547444i
\(959\) −1.35580e8 1.95016e8i −0.153723 0.221113i
\(960\) −9.65595e7 −0.109139
\(961\) 4.01720e8 0.452640
\(962\) 1.01859e9i 1.14413i
\(963\) −7.38905e7 −0.0827389
\(964\) 8.51703e6i 0.00950730i
\(965\) 1.91829e8i 0.213468i
\(966\) 5.55435e8 3.86152e8i 0.616172 0.428378i
\(967\) 9.71735e8 1.07465 0.537327 0.843374i \(-0.319434\pi\)
0.537327 + 0.843374i \(0.319434\pi\)
\(968\) −1.24098e8 −0.136817
\(969\) 4.16711e8i 0.457998i
\(970\) −6.52488e7 −0.0714920
\(971\) 1.27689e9i 1.39475i 0.716708 + 0.697374i \(0.245648\pi\)
−0.716708 + 0.697374i \(0.754352\pi\)
\(972\) 2.07984e8i 0.226480i
\(973\) −1.35740e8 + 9.43696e7i −0.147356 + 0.102446i
\(974\) 6.77628e8 0.733355
\(975\) 6.52284e8 0.703757
\(976\) 3.46677e8i 0.372886i
\(977\) 1.53509e9 1.64608 0.823040 0.567984i \(-0.192276\pi\)
0.823040 + 0.567984i \(0.192276\pi\)
\(978\) 2.69969e8i 0.288601i
\(979\) 4.28737e8i 0.456923i
\(980\) 3.47173e8 + 1.29002e8i 0.368865 + 0.137063i
\(981\) −3.03487e8 −0.321464
\(982\) −1.27198e9 −1.34322
\(983\) 9.46892e8i 0.996873i −0.866926 0.498436i \(-0.833908\pi\)
0.866926 0.498436i \(-0.166092\pi\)
\(984\) 9.77619e7 0.102609
\(985\) 1.14140e9i 1.19434i
\(986\) 4.37927e8i 0.456847i
\(987\) −8.18928e8 1.17793e9i −0.851715 1.22509i
\(988\) 8.78010e8 0.910392
\(989\) −1.33102e9 −1.37593
\(990\) 9.75662e7i 0.100553i
\(991\) −1.27731e9 −1.31242 −0.656211 0.754577i \(-0.727842\pi\)
−0.656211 + 0.754577i \(0.727842\pi\)
\(992\) 1.27672e8i 0.130786i
\(993\) 1.87061e9i 1.91045i
\(994\) 2.39261e8 + 3.44149e8i 0.243619 + 0.350418i
\(995\) −7.15389e7 −0.0726228
\(996\) 2.16411e8 0.219029
\(997\) 1.51510e9i 1.52882i 0.644731 + 0.764409i \(0.276969\pi\)
−0.644731 + 0.764409i \(0.723031\pi\)
\(998\) 3.28108e8 0.330085
\(999\) 8.25993e8i 0.828476i
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 14.7.b.a.13.3 4
3.2 odd 2 126.7.c.a.55.2 4
4.3 odd 2 112.7.c.c.97.4 4
5.2 odd 4 350.7.d.a.349.5 8
5.3 odd 4 350.7.d.a.349.4 8
5.4 even 2 350.7.b.a.251.2 4
7.2 even 3 98.7.d.b.31.2 8
7.3 odd 6 98.7.d.b.19.2 8
7.4 even 3 98.7.d.b.19.1 8
7.5 odd 6 98.7.d.b.31.1 8
7.6 odd 2 inner 14.7.b.a.13.4 yes 4
8.3 odd 2 448.7.c.e.321.1 4
8.5 even 2 448.7.c.h.321.4 4
21.20 even 2 126.7.c.a.55.1 4
28.27 even 2 112.7.c.c.97.1 4
35.13 even 4 350.7.d.a.349.1 8
35.27 even 4 350.7.d.a.349.8 8
35.34 odd 2 350.7.b.a.251.1 4
56.13 odd 2 448.7.c.h.321.1 4
56.27 even 2 448.7.c.e.321.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.7.b.a.13.3 4 1.1 even 1 trivial
14.7.b.a.13.4 yes 4 7.6 odd 2 inner
98.7.d.b.19.1 8 7.4 even 3
98.7.d.b.19.2 8 7.3 odd 6
98.7.d.b.31.1 8 7.5 odd 6
98.7.d.b.31.2 8 7.2 even 3
112.7.c.c.97.1 4 28.27 even 2
112.7.c.c.97.4 4 4.3 odd 2
126.7.c.a.55.1 4 21.20 even 2
126.7.c.a.55.2 4 3.2 odd 2
350.7.b.a.251.1 4 35.34 odd 2
350.7.b.a.251.2 4 5.4 even 2
350.7.d.a.349.1 8 35.13 even 4
350.7.d.a.349.4 8 5.3 odd 4
350.7.d.a.349.5 8 5.2 odd 4
350.7.d.a.349.8 8 35.27 even 4
448.7.c.e.321.1 4 8.3 odd 2
448.7.c.e.321.4 4 56.27 even 2
448.7.c.h.321.1 4 56.13 odd 2
448.7.c.h.321.4 4 8.5 even 2