Properties

Label 11.13.b.b.10.4
Level $11$
Weight $13$
Character 11.10
Analytic conductor $10.054$
Analytic rank $0$
Dimension $10$
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] = [11,13,Mod(10,11)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(11, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 13, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("11.10");
 
S:= CuspForms(chi, 13);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 13 \)
Character orbit: \([\chi]\) \(=\) 11.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: \(10.0539319900\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} + 30654x^{8} + 318945120x^{6} + 1305642637440x^{4} + 2049564619929600x^{2} + 957721368231936000 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{16}\cdot 3^{3}\cdot 11^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 10.4
Root \(-45.2549i\) of defining polynomial
Character \(\chi\) \(=\) 11.10
Dual form 11.13.b.b.10.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-45.2549i q^{2} -583.849 q^{3} +2048.00 q^{4} +15889.4 q^{5} +26422.0i q^{6} -93839.3i q^{7} -278046. i q^{8} -190561. q^{9} +O(q^{10})\) \(q-45.2549i q^{2} -583.849 q^{3} +2048.00 q^{4} +15889.4 q^{5} +26422.0i q^{6} -93839.3i q^{7} -278046. i q^{8} -190561. q^{9} -719072. i q^{10} +(-1.18566e6 + 1.31629e6i) q^{11} -1.19572e6 q^{12} -5.35422e6i q^{13} -4.24668e6 q^{14} -9.27701e6 q^{15} -4.19432e6 q^{16} -4.63980e7i q^{17} +8.62381e6i q^{18} -4.52775e6i q^{19} +3.25414e7 q^{20} +5.47880e7i q^{21} +(5.95687e7 + 5.36570e7i) q^{22} +86765.3 q^{23} +1.62337e8i q^{24} +8.33211e6 q^{25} -2.42305e8 q^{26} +4.21540e8 q^{27} -1.92183e8i q^{28} +5.83163e8i q^{29} +4.19830e8i q^{30} +7.40408e8 q^{31} -9.49062e8i q^{32} +(6.92249e8 - 7.68518e8i) q^{33} -2.09974e9 q^{34} -1.49105e9i q^{35} -3.90268e8 q^{36} -3.08141e9 q^{37} -2.04903e8 q^{38} +3.12606e9i q^{39} -4.41798e9i q^{40} -1.18839e9i q^{41} +2.47942e9 q^{42} +3.38609e9i q^{43} +(-2.42824e9 + 2.69577e9i) q^{44} -3.02790e9 q^{45} -3.92655e6i q^{46} +1.92096e10 q^{47} +2.44885e9 q^{48} +5.03547e9 q^{49} -3.77068e8i q^{50} +2.70895e10i q^{51} -1.09654e10i q^{52} +9.28686e8 q^{53} -1.90767e10i q^{54} +(-1.88395e10 + 2.09151e10i) q^{55} -2.60916e10 q^{56} +2.64352e9i q^{57} +2.63910e10 q^{58} +1.61409e10 q^{59} -1.89993e10 q^{60} -8.95382e9i q^{61} -3.35070e10i q^{62} +1.78821e10i q^{63} -6.01296e10 q^{64} -8.50754e10i q^{65} +(-3.47792e10 - 3.13276e10i) q^{66} +1.68840e10 q^{67} -9.50231e10i q^{68} -5.06579e7 q^{69} -6.74772e10 q^{70} +1.56336e11 q^{71} +5.29847e10i q^{72} +2.47953e11i q^{73} +1.39449e11i q^{74} -4.86470e9 q^{75} -9.27282e9i q^{76} +(1.23520e11 + 1.11262e11i) q^{77} +1.41469e11 q^{78} -1.69948e11i q^{79} -6.66452e10 q^{80} -1.44844e11 q^{81} -5.37802e10 q^{82} +4.27097e11i q^{83} +1.12206e11i q^{84} -7.37237e11i q^{85} +1.53237e11 q^{86} -3.40479e11i q^{87} +(3.65990e11 + 3.29669e11i) q^{88} +2.30558e11 q^{89} +1.37027e11i q^{90} -5.02437e11 q^{91} +1.77695e8 q^{92} -4.32287e11 q^{93} -8.69328e11i q^{94} -7.19432e10i q^{95} +5.54109e11i q^{96} -1.43458e12 q^{97} -2.27880e11i q^{98} +(2.25941e11 - 2.50834e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 2436 q^{3} - 20348 q^{4} + 26492 q^{5} + 756294 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 2436 q^{3} - 20348 q^{4} + 26492 q^{5} + 756294 q^{9} - 1716374 q^{11} - 8491644 q^{12} - 15139368 q^{14} + 9632184 q^{15} + 17974408 q^{16} - 125399668 q^{20} + 83533560 q^{22} + 330297476 q^{23} - 438477018 q^{25} - 372191832 q^{26} + 1665774072 q^{27} - 1921955548 q^{31} - 2301728484 q^{33} + 7677299352 q^{34} - 14333366928 q^{36} + 1788323996 q^{37} + 11254769640 q^{38} - 32091748680 q^{42} + 6124969708 q^{44} + 43304121996 q^{45} - 24975510124 q^{47} + 32578826856 q^{48} - 6325710998 q^{49} - 16325502124 q^{53} + 14298843812 q^{55} + 82892128176 q^{56} - 84518430720 q^{58} + 62339390564 q^{59} - 286034518116 q^{60} + 95192926864 q^{64} + 322939363560 q^{66} - 90035301244 q^{67} + 346118875824 q^{69} - 382808641560 q^{70} - 359910119740 q^{71} + 14209300764 q^{75} + 425991883680 q^{77} - 483427126680 q^{78} + 1147768798712 q^{80} - 515542099806 q^{81} + 625030365960 q^{82} - 1219447545552 q^{86} + 134692485840 q^{88} + 670996780412 q^{89} + 1356772643808 q^{91} - 3181666532764 q^{92} + 1928296959312 q^{93} - 6250704684964 q^{97} - 1402418596722 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 45.2549i 0.707107i −0.935414 0.353554i \(-0.884973\pi\)
0.935414 0.353554i \(-0.115027\pi\)
\(3\) −583.849 −0.800891 −0.400445 0.916321i \(-0.631145\pi\)
−0.400445 + 0.916321i \(0.631145\pi\)
\(4\) 2048.00 0.500000
\(5\) 15889.4 1.01692 0.508461 0.861085i \(-0.330215\pi\)
0.508461 + 0.861085i \(0.330215\pi\)
\(6\) 26422.0i 0.566316i
\(7\) 93839.3i 0.797621i −0.917033 0.398810i \(-0.869423\pi\)
0.917033 0.398810i \(-0.130577\pi\)
\(8\) 278046.i 1.06066i
\(9\) −190561. −0.358574
\(10\) 719072.i 0.719072i
\(11\) −1.18566e6 + 1.31629e6i −0.669276 + 0.743014i
\(12\) −1.19572e6 −0.400445
\(13\) 5.35422e6i 1.10927i −0.832094 0.554634i \(-0.812858\pi\)
0.832094 0.554634i \(-0.187142\pi\)
\(14\) −4.24668e6 −0.564003
\(15\) −9.27701e6 −0.814443
\(16\) −4.19432e6 −0.250001
\(17\) 4.63980e7i 1.92223i −0.276143 0.961117i \(-0.589056\pi\)
0.276143 0.961117i \(-0.410944\pi\)
\(18\) 8.62381e6i 0.253550i
\(19\) 4.52775e6i 0.0962412i −0.998842 0.0481206i \(-0.984677\pi\)
0.998842 0.0481206i \(-0.0153232\pi\)
\(20\) 3.25414e7 0.508460
\(21\) 5.47880e7i 0.638807i
\(22\) 5.95687e7 + 5.36570e7i 0.525390 + 0.473250i
\(23\) 86765.3 0.000586110 0.000293055 1.00000i \(-0.499907\pi\)
0.000293055 1.00000i \(0.499907\pi\)
\(24\) 1.62337e8i 0.849473i
\(25\) 8.33211e6 0.0341283
\(26\) −2.42305e8 −0.784371
\(27\) 4.21540e8 1.08807
\(28\) 1.92183e8i 0.398810i
\(29\) 5.83163e8i 0.980397i 0.871611 + 0.490199i \(0.163076\pi\)
−0.871611 + 0.490199i \(0.836924\pi\)
\(30\) 4.19830e8i 0.575898i
\(31\) 7.40408e8 0.834259 0.417129 0.908847i \(-0.363036\pi\)
0.417129 + 0.908847i \(0.363036\pi\)
\(32\) 9.49062e8i 0.883883i
\(33\) 6.92249e8 7.68518e8i 0.536017 0.595073i
\(34\) −2.09974e9 −1.35922
\(35\) 1.49105e9i 0.811117i
\(36\) −3.90268e8 −0.179287
\(37\) −3.08141e9 −1.20099 −0.600495 0.799628i \(-0.705030\pi\)
−0.600495 + 0.799628i \(0.705030\pi\)
\(38\) −2.04903e8 −0.0680528
\(39\) 3.12606e9i 0.888402i
\(40\) 4.41798e9i 1.07861i
\(41\) 1.18839e9i 0.250181i −0.992145 0.125090i \(-0.960078\pi\)
0.992145 0.125090i \(-0.0399221\pi\)
\(42\) 2.47942e9 0.451705
\(43\) 3.38609e9i 0.535658i 0.963467 + 0.267829i \(0.0863062\pi\)
−0.963467 + 0.267829i \(0.913694\pi\)
\(44\) −2.42824e9 + 2.69577e9i −0.334638 + 0.371507i
\(45\) −3.02790e9 −0.364641
\(46\) 3.92655e6i 0.000414442i
\(47\) 1.92096e10 1.78210 0.891049 0.453907i \(-0.149970\pi\)
0.891049 + 0.453907i \(0.149970\pi\)
\(48\) 2.44885e9 0.200223
\(49\) 5.03547e9 0.363801
\(50\) 3.77068e8i 0.0241324i
\(51\) 2.70895e10i 1.53950i
\(52\) 1.09654e10i 0.554633i
\(53\) 9.28686e8 0.0419000 0.0209500 0.999781i \(-0.493331\pi\)
0.0209500 + 0.999781i \(0.493331\pi\)
\(54\) 1.90767e10i 0.769382i
\(55\) −1.88395e10 + 2.09151e10i −0.680601 + 0.755587i
\(56\) −2.60916e10 −0.846005
\(57\) 2.64352e9i 0.0770787i
\(58\) 2.63910e10 0.693246
\(59\) 1.61409e10 0.382663 0.191331 0.981525i \(-0.438719\pi\)
0.191331 + 0.981525i \(0.438719\pi\)
\(60\) −1.89993e10 −0.407221
\(61\) 8.95382e9i 0.173792i −0.996217 0.0868959i \(-0.972305\pi\)
0.996217 0.0868959i \(-0.0276948\pi\)
\(62\) 3.35070e10i 0.589910i
\(63\) 1.78821e10i 0.286006i
\(64\) −6.01296e10 −0.875001
\(65\) 8.50754e10i 1.12804i
\(66\) −3.47792e10 3.13276e10i −0.420780 0.379021i
\(67\) 1.68840e10 0.186649 0.0933247 0.995636i \(-0.470251\pi\)
0.0933247 + 0.995636i \(0.470251\pi\)
\(68\) 9.50231e10i 0.961116i
\(69\) −5.06579e7 −0.000469410
\(70\) −6.74772e10 −0.573547
\(71\) 1.56336e11 1.22042 0.610209 0.792240i \(-0.291085\pi\)
0.610209 + 0.792240i \(0.291085\pi\)
\(72\) 5.29847e10i 0.380325i
\(73\) 2.47953e11i 1.63844i 0.573477 + 0.819222i \(0.305594\pi\)
−0.573477 + 0.819222i \(0.694406\pi\)
\(74\) 1.39449e11i 0.849229i
\(75\) −4.86470e9 −0.0273331
\(76\) 9.27282e9i 0.0481205i
\(77\) 1.23520e11 + 1.11262e11i 0.592643 + 0.533828i
\(78\) 1.41469e11 0.628196
\(79\) 1.69948e11i 0.699123i −0.936913 0.349562i \(-0.886330\pi\)
0.936913 0.349562i \(-0.113670\pi\)
\(80\) −6.66452e10 −0.254231
\(81\) −1.44844e11 −0.512851
\(82\) −5.37802e10 −0.176905
\(83\) 4.27097e11i 1.30635i 0.757208 + 0.653173i \(0.226563\pi\)
−0.757208 + 0.653173i \(0.773437\pi\)
\(84\) 1.12206e11i 0.319403i
\(85\) 7.37237e11i 1.95476i
\(86\) 1.53237e11 0.378767
\(87\) 3.40479e11i 0.785191i
\(88\) 3.65990e11 + 3.29669e11i 0.788085 + 0.709874i
\(89\) 2.30558e11 0.463918 0.231959 0.972726i \(-0.425487\pi\)
0.231959 + 0.972726i \(0.425487\pi\)
\(90\) 1.37027e11i 0.257841i
\(91\) −5.02437e11 −0.884775
\(92\) 1.77695e8 0.000293055
\(93\) −4.32287e11 −0.668150
\(94\) 8.69328e11i 1.26013i
\(95\) 7.19432e10i 0.0978697i
\(96\) 5.54109e11i 0.707894i
\(97\) −1.43458e12 −1.72224 −0.861119 0.508403i \(-0.830236\pi\)
−0.861119 + 0.508403i \(0.830236\pi\)
\(98\) 2.27880e11i 0.257246i
\(99\) 2.25941e11 2.50834e11i 0.239985 0.266425i
\(100\) 1.70641e10 0.0170641
\(101\) 4.36023e11i 0.410754i −0.978683 0.205377i \(-0.934158\pi\)
0.978683 0.205377i \(-0.0658420\pi\)
\(102\) 1.22593e12 1.08859
\(103\) 4.90318e9 0.00410634 0.00205317 0.999998i \(-0.499346\pi\)
0.00205317 + 0.999998i \(0.499346\pi\)
\(104\) −1.48872e12 −1.17656
\(105\) 8.70548e11i 0.649616i
\(106\) 4.20276e10i 0.0296278i
\(107\) 1.09730e12i 0.731176i 0.930777 + 0.365588i \(0.119132\pi\)
−0.930777 + 0.365588i \(0.880868\pi\)
\(108\) 8.63314e11 0.544034
\(109\) 9.64140e11i 0.574885i −0.957798 0.287443i \(-0.907195\pi\)
0.957798 0.287443i \(-0.0928050\pi\)
\(110\) 9.46511e11 + 8.52577e11i 0.534281 + 0.481258i
\(111\) 1.79908e12 0.961862
\(112\) 3.93592e11i 0.199406i
\(113\) 2.76940e12 1.33019 0.665097 0.746757i \(-0.268390\pi\)
0.665097 + 0.746757i \(0.268390\pi\)
\(114\) 1.19632e11 0.0545029
\(115\) 1.37865e9 0.000596027
\(116\) 1.19432e12i 0.490198i
\(117\) 1.02031e12i 0.397755i
\(118\) 7.30455e11i 0.270584i
\(119\) −4.35396e12 −1.53321
\(120\) 2.57943e12i 0.863847i
\(121\) −3.26834e11 3.12136e12i −0.104140 0.994563i
\(122\) −4.05204e11 −0.122889
\(123\) 6.93838e11i 0.200368i
\(124\) 1.51635e12 0.417129
\(125\) −3.74685e12 −0.982215
\(126\) 8.09252e11 0.202237
\(127\) 5.35860e12i 1.27711i −0.769575 0.638556i \(-0.779532\pi\)
0.769575 0.638556i \(-0.220468\pi\)
\(128\) 1.16620e12i 0.265164i
\(129\) 1.97696e12i 0.429003i
\(130\) −3.85007e12 −0.797644
\(131\) 7.33586e12i 1.45152i 0.687948 + 0.725760i \(0.258512\pi\)
−0.687948 + 0.725760i \(0.741488\pi\)
\(132\) 1.41772e12 1.57392e12i 0.268008 0.297536i
\(133\) −4.24881e11 −0.0767639
\(134\) 7.64083e11i 0.131981i
\(135\) 6.69802e12 1.10648
\(136\) −1.29008e13 −2.03884
\(137\) 1.09495e13 1.65604 0.828020 0.560699i \(-0.189467\pi\)
0.828020 + 0.560699i \(0.189467\pi\)
\(138\) 2.29251e9i 0.000331923i
\(139\) 1.04640e13i 1.45080i −0.688326 0.725401i \(-0.741654\pi\)
0.688326 0.725401i \(-0.258346\pi\)
\(140\) 3.05367e12i 0.405558i
\(141\) −1.12155e13 −1.42727
\(142\) 7.07496e12i 0.862966i
\(143\) 7.04774e12 + 6.34831e12i 0.824202 + 0.742406i
\(144\) 7.99273e11 0.0896438
\(145\) 9.26610e12i 0.996986i
\(146\) 1.12211e13 1.15855
\(147\) −2.93996e12 −0.291365
\(148\) −6.31073e12 −0.600495
\(149\) 7.98543e12i 0.729761i 0.931054 + 0.364880i \(0.118890\pi\)
−0.931054 + 0.364880i \(0.881110\pi\)
\(150\) 2.20151e11i 0.0193274i
\(151\) 1.51955e13i 1.28190i 0.767585 + 0.640948i \(0.221458\pi\)
−0.767585 + 0.640948i \(0.778542\pi\)
\(152\) −1.25892e12 −0.102079
\(153\) 8.84165e12i 0.689263i
\(154\) 5.03514e12 5.58989e12i 0.377474 0.419062i
\(155\) 1.17646e13 0.848375
\(156\) 6.40217e12i 0.444201i
\(157\) 1.21874e13 0.813793 0.406897 0.913474i \(-0.366611\pi\)
0.406897 + 0.913474i \(0.366611\pi\)
\(158\) −7.69098e12 −0.494355
\(159\) −5.42213e11 −0.0335573
\(160\) 1.50800e13i 0.898839i
\(161\) 8.14199e9i 0.000467493i
\(162\) 6.55490e12i 0.362640i
\(163\) −3.06577e13 −1.63461 −0.817304 0.576207i \(-0.804532\pi\)
−0.817304 + 0.576207i \(0.804532\pi\)
\(164\) 2.43381e12i 0.125090i
\(165\) 1.09994e13 1.22113e13i 0.545087 0.605142i
\(166\) 1.93282e13 0.923727
\(167\) 9.57636e12i 0.441471i −0.975334 0.220735i \(-0.929154\pi\)
0.975334 0.220735i \(-0.0708457\pi\)
\(168\) 1.52336e13 0.677557
\(169\) −5.36963e12 −0.230475
\(170\) −3.33635e13 −1.38222
\(171\) 8.62812e11i 0.0345096i
\(172\) 6.93470e12i 0.267829i
\(173\) 4.01016e13i 1.49584i −0.663789 0.747920i \(-0.731053\pi\)
0.663789 0.747920i \(-0.268947\pi\)
\(174\) −1.54083e13 −0.555214
\(175\) 7.81879e11i 0.0272215i
\(176\) 4.97305e12 5.52096e12i 0.167320 0.185754i
\(177\) −9.42387e12 −0.306471
\(178\) 1.04339e13i 0.328040i
\(179\) 2.59046e13 0.787515 0.393757 0.919214i \(-0.371175\pi\)
0.393757 + 0.919214i \(0.371175\pi\)
\(180\) −6.20113e12 −0.182321
\(181\) −4.82686e13 −1.37276 −0.686378 0.727245i \(-0.740800\pi\)
−0.686378 + 0.727245i \(0.740800\pi\)
\(182\) 2.27377e13i 0.625631i
\(183\) 5.22768e12i 0.139188i
\(184\) 2.41247e10i 0.000621663i
\(185\) −4.89618e13 −1.22131
\(186\) 1.95631e13i 0.472454i
\(187\) 6.10735e13 + 5.50124e13i 1.42825 + 1.28650i
\(188\) 3.93413e13 0.891048
\(189\) 3.95570e13i 0.867867i
\(190\) −3.25578e12 −0.0692043
\(191\) −5.63833e12 −0.116132 −0.0580658 0.998313i \(-0.518493\pi\)
−0.0580658 + 0.998313i \(0.518493\pi\)
\(192\) 3.51066e13 0.700780
\(193\) 2.63508e13i 0.509859i −0.966960 0.254929i \(-0.917948\pi\)
0.966960 0.254929i \(-0.0820522\pi\)
\(194\) 6.49216e13i 1.21781i
\(195\) 4.96712e13i 0.903435i
\(196\) 1.03126e13 0.181900
\(197\) 9.38115e13i 1.60494i −0.596693 0.802470i \(-0.703519\pi\)
0.596693 0.802470i \(-0.296481\pi\)
\(198\) −1.13515e13 1.02249e13i −0.188391 0.169695i
\(199\) 3.46444e13 0.557847 0.278923 0.960313i \(-0.410022\pi\)
0.278923 + 0.960313i \(0.410022\pi\)
\(200\) 2.31671e12i 0.0361986i
\(201\) −9.85772e12 −0.149486
\(202\) −1.97322e13 −0.290447
\(203\) 5.47236e13 0.781985
\(204\) 5.54792e13i 0.769749i
\(205\) 1.88827e13i 0.254414i
\(206\) 2.21893e11i 0.00290362i
\(207\) −1.65341e10 −0.000210164
\(208\) 2.24573e13i 0.277318i
\(209\) 5.95985e12 + 5.36839e12i 0.0715085 + 0.0644119i
\(210\) 3.93965e13 0.459348
\(211\) 1.13559e14i 1.28685i 0.765510 + 0.643423i \(0.222487\pi\)
−0.765510 + 0.643423i \(0.777513\pi\)
\(212\) 1.90195e12 0.0209500
\(213\) −9.12766e13 −0.977422
\(214\) 4.96581e13 0.517020
\(215\) 5.38028e13i 0.544721i
\(216\) 1.17208e14i 1.15407i
\(217\) 6.94793e13i 0.665422i
\(218\) −4.36320e13 −0.406505
\(219\) 1.44767e14i 1.31221i
\(220\) −3.85832e13 + 4.28341e13i −0.340300 + 0.377793i
\(221\) −2.48426e14 −2.13227
\(222\) 8.14172e13i 0.680140i
\(223\) 7.27694e12 0.0591724 0.0295862 0.999562i \(-0.490581\pi\)
0.0295862 + 0.999562i \(0.490581\pi\)
\(224\) −8.90593e13 −0.705003
\(225\) −1.58777e12 −0.0122375
\(226\) 1.25329e14i 0.940589i
\(227\) 1.58791e14i 1.16057i 0.814413 + 0.580285i \(0.197059\pi\)
−0.814413 + 0.580285i \(0.802941\pi\)
\(228\) 5.41393e12i 0.0385393i
\(229\) 6.63257e13 0.459906 0.229953 0.973202i \(-0.426143\pi\)
0.229953 + 0.973202i \(0.426143\pi\)
\(230\) 6.23905e10i 0.000421455i
\(231\) −7.21172e13 6.49601e13i −0.474643 0.427538i
\(232\) 1.62146e14 1.03987
\(233\) 1.89857e14i 1.18656i −0.804995 0.593281i \(-0.797832\pi\)
0.804995 0.593281i \(-0.202168\pi\)
\(234\) 4.61738e13 0.281255
\(235\) 3.05229e14 1.81225
\(236\) 3.30566e13 0.191331
\(237\) 9.92241e13i 0.559922i
\(238\) 1.97038e14i 1.08415i
\(239\) 3.28675e13i 0.176351i −0.996105 0.0881757i \(-0.971896\pi\)
0.996105 0.0881757i \(-0.0281037\pi\)
\(240\) 3.89107e13 0.203611
\(241\) 3.63345e14i 1.85446i 0.374496 + 0.927228i \(0.377816\pi\)
−0.374496 + 0.927228i \(0.622184\pi\)
\(242\) −1.41257e14 + 1.47908e13i −0.703262 + 0.0736378i
\(243\) −1.39457e14 −0.677332
\(244\) 1.83374e13i 0.0868959i
\(245\) 8.00106e13 0.369957
\(246\) 3.13995e13 0.141681
\(247\) −2.42426e13 −0.106757
\(248\) 2.05867e14i 0.884865i
\(249\) 2.49361e14i 1.04624i
\(250\) 1.69563e14i 0.694531i
\(251\) 2.63589e14 1.05411 0.527055 0.849831i \(-0.323296\pi\)
0.527055 + 0.849831i \(0.323296\pi\)
\(252\) 3.66225e13i 0.143003i
\(253\) −1.02874e11 + 1.14209e11i −0.000392269 + 0.000435488i
\(254\) −2.42503e14 −0.903055
\(255\) 4.30435e14i 1.56555i
\(256\) −2.99067e14 −1.06250
\(257\) 3.54050e14 1.22876 0.614379 0.789011i \(-0.289407\pi\)
0.614379 + 0.789011i \(0.289407\pi\)
\(258\) −8.94672e13 −0.303351
\(259\) 2.89158e14i 0.957935i
\(260\) 1.74234e14i 0.564018i
\(261\) 1.11128e14i 0.351545i
\(262\) 3.31983e14 1.02638
\(263\) 1.07330e14i 0.324331i 0.986764 + 0.162166i \(0.0518478\pi\)
−0.986764 + 0.162166i \(0.948152\pi\)
\(264\) −2.13683e14 1.92477e14i −0.631170 0.568532i
\(265\) 1.47563e13 0.0426090
\(266\) 1.92279e13i 0.0542803i
\(267\) −1.34611e14 −0.371547
\(268\) 3.45784e13 0.0933246
\(269\) −8.70810e13 −0.229832 −0.114916 0.993375i \(-0.536660\pi\)
−0.114916 + 0.993375i \(0.536660\pi\)
\(270\) 3.03118e14i 0.782400i
\(271\) 5.05202e14i 1.27541i −0.770282 0.637704i \(-0.779884\pi\)
0.770282 0.637704i \(-0.220116\pi\)
\(272\) 1.94608e14i 0.480560i
\(273\) 2.93347e14 0.708608
\(274\) 4.95518e14i 1.17100i
\(275\) −9.87907e12 + 1.09675e13i −0.0228413 + 0.0253578i
\(276\) −1.03747e11 −0.000234705
\(277\) 9.28827e13i 0.205616i 0.994701 + 0.102808i \(0.0327827\pi\)
−0.994701 + 0.102808i \(0.967217\pi\)
\(278\) −4.73546e14 −1.02587
\(279\) −1.41093e14 −0.299144
\(280\) −4.14580e14 −0.860320
\(281\) 3.62924e14i 0.737186i −0.929591 0.368593i \(-0.879840\pi\)
0.929591 0.368593i \(-0.120160\pi\)
\(282\) 5.07557e14i 1.00923i
\(283\) 2.03412e14i 0.395966i −0.980205 0.197983i \(-0.936561\pi\)
0.980205 0.197983i \(-0.0634390\pi\)
\(284\) 3.20176e14 0.610208
\(285\) 4.20040e13i 0.0783829i
\(286\) 2.87292e14 3.18944e14i 0.524961 0.582799i
\(287\) −1.11517e14 −0.199549
\(288\) 1.80854e14i 0.316937i
\(289\) −1.57016e15 −2.69498
\(290\) 4.19336e14 0.704976
\(291\) 8.37577e14 1.37933
\(292\) 5.07806e14i 0.819221i
\(293\) 5.03086e14i 0.795127i −0.917575 0.397563i \(-0.869856\pi\)
0.917575 0.397563i \(-0.130144\pi\)
\(294\) 1.33047e14i 0.206026i
\(295\) 2.56469e14 0.389138
\(296\) 8.56774e14i 1.27384i
\(297\) −4.99805e14 + 5.54871e14i −0.728219 + 0.808451i
\(298\) 3.61379e14 0.516019
\(299\) 4.64561e11i 0.000650153i
\(300\) −9.96289e12 −0.0136665
\(301\) 3.17748e14 0.427252
\(302\) 6.87669e14 0.906437
\(303\) 2.54572e14i 0.328969i
\(304\) 1.89908e13i 0.0240604i
\(305\) 1.42271e14i 0.176733i
\(306\) 4.00128e14 0.487383
\(307\) 5.84980e14i 0.698733i 0.936986 + 0.349366i \(0.113603\pi\)
−0.936986 + 0.349366i \(0.886397\pi\)
\(308\) 2.52969e14 + 2.27864e14i 0.296321 + 0.266914i
\(309\) −2.86272e12 −0.00328873
\(310\) 5.32407e14i 0.599892i
\(311\) 1.16661e14 0.128933 0.0644665 0.997920i \(-0.479465\pi\)
0.0644665 + 0.997920i \(0.479465\pi\)
\(312\) 8.69188e14 0.942293
\(313\) −5.54943e14 −0.590177 −0.295088 0.955470i \(-0.595349\pi\)
−0.295088 + 0.955470i \(0.595349\pi\)
\(314\) 5.51540e14i 0.575439i
\(315\) 2.84136e14i 0.290846i
\(316\) 3.48053e14i 0.349561i
\(317\) 4.97730e14 0.490499 0.245250 0.969460i \(-0.421130\pi\)
0.245250 + 0.969460i \(0.421130\pi\)
\(318\) 2.45378e13i 0.0237286i
\(319\) −7.67614e14 6.91435e14i −0.728449 0.656156i
\(320\) −9.55423e14 −0.889807
\(321\) 6.40657e14i 0.585592i
\(322\) −3.68465e11 −0.000330568
\(323\) −2.10079e14 −0.184998
\(324\) −2.96641e14 −0.256425
\(325\) 4.46120e13i 0.0378575i
\(326\) 1.38741e15i 1.15584i
\(327\) 5.62913e14i 0.460420i
\(328\) −3.30425e14 −0.265357
\(329\) 1.80262e15i 1.42144i
\(330\) −5.52620e14 4.97777e14i −0.427900 0.385435i
\(331\) 3.12132e14 0.237340 0.118670 0.992934i \(-0.462137\pi\)
0.118670 + 0.992934i \(0.462137\pi\)
\(332\) 8.74695e14i 0.653173i
\(333\) 5.87197e14 0.430644
\(334\) −4.33377e14 −0.312167
\(335\) 2.68277e14 0.189808
\(336\) 2.29798e14i 0.159702i
\(337\) 5.21950e14i 0.356328i 0.984001 + 0.178164i \(0.0570157\pi\)
−0.984001 + 0.178164i \(0.942984\pi\)
\(338\) 2.43002e14i 0.162971i
\(339\) −1.61691e15 −1.06534
\(340\) 1.50986e15i 0.977379i
\(341\) −8.77874e14 + 9.74595e14i −0.558349 + 0.619866i
\(342\) 3.90464e13 0.0244020
\(343\) 1.77138e15i 1.08780i
\(344\) 9.41487e14 0.568151
\(345\) −8.04923e11 −0.000477353
\(346\) −1.81479e15 −1.05772
\(347\) 2.41432e15i 1.38299i 0.722383 + 0.691493i \(0.243047\pi\)
−0.722383 + 0.691493i \(0.756953\pi\)
\(348\) 6.97301e14i 0.392595i
\(349\) 9.52967e14i 0.527382i −0.964607 0.263691i \(-0.915060\pi\)
0.964607 0.263691i \(-0.0849399\pi\)
\(350\) −3.53838e13 −0.0192485
\(351\) 2.25702e15i 1.20696i
\(352\) 1.24925e15 + 1.12527e15i 0.656737 + 0.591562i
\(353\) −9.47694e14 −0.489801 −0.244901 0.969548i \(-0.578755\pi\)
−0.244901 + 0.969548i \(0.578755\pi\)
\(354\) 4.26476e14i 0.216708i
\(355\) 2.48408e15 1.24107
\(356\) 4.72183e14 0.231959
\(357\) 2.54206e15 1.22794
\(358\) 1.17231e15i 0.556857i
\(359\) 1.97930e15i 0.924580i −0.886729 0.462290i \(-0.847028\pi\)
0.886729 0.462290i \(-0.152972\pi\)
\(360\) 8.41894e14i 0.386761i
\(361\) 2.19281e15 0.990738
\(362\) 2.18439e15i 0.970685i
\(363\) 1.90822e14 + 1.82241e15i 0.0834044 + 0.796536i
\(364\) −1.02899e15 −0.442387
\(365\) 3.93982e15i 1.66617i
\(366\) 2.36578e14 0.0984210
\(367\) −2.92957e15 −1.19897 −0.599483 0.800387i \(-0.704627\pi\)
−0.599483 + 0.800387i \(0.704627\pi\)
\(368\) −3.63921e11 −0.000146528
\(369\) 2.26460e14i 0.0897083i
\(370\) 2.21576e15i 0.863599i
\(371\) 8.71473e13i 0.0334203i
\(372\) −8.85322e14 −0.334075
\(373\) 2.49431e15i 0.926185i 0.886310 + 0.463093i \(0.153260\pi\)
−0.886310 + 0.463093i \(0.846740\pi\)
\(374\) 2.48958e15 2.76387e15i 0.909696 1.00992i
\(375\) 2.18760e15 0.786647
\(376\) 5.34115e15i 1.89020i
\(377\) 3.12239e15 1.08752
\(378\) −1.79015e15 −0.613675
\(379\) −1.69160e15 −0.570773 −0.285386 0.958413i \(-0.592122\pi\)
−0.285386 + 0.958413i \(0.592122\pi\)
\(380\) 1.47340e14i 0.0489348i
\(381\) 3.12862e15i 1.02283i
\(382\) 2.55162e14i 0.0821175i
\(383\) −3.61809e15 −1.14627 −0.573135 0.819461i \(-0.694273\pi\)
−0.573135 + 0.819461i \(0.694273\pi\)
\(384\) 6.80886e14i 0.212367i
\(385\) 1.96266e15 + 1.76788e15i 0.602672 + 0.542861i
\(386\) −1.19250e15 −0.360525
\(387\) 6.45256e14i 0.192073i
\(388\) −2.93801e15 −0.861119
\(389\) −2.41426e15 −0.696765 −0.348382 0.937352i \(-0.613269\pi\)
−0.348382 + 0.937352i \(0.613269\pi\)
\(390\) 2.24786e15 0.638825
\(391\) 4.02574e12i 0.00112664i
\(392\) 1.40009e15i 0.385869i
\(393\) 4.28303e15i 1.16251i
\(394\) −4.24543e15 −1.13486
\(395\) 2.70037e15i 0.710953i
\(396\) 4.62727e14 5.13708e14i 0.119992 0.133213i
\(397\) 3.56388e15 0.910290 0.455145 0.890417i \(-0.349587\pi\)
0.455145 + 0.890417i \(0.349587\pi\)
\(398\) 1.56783e15i 0.394457i
\(399\) 2.48066e14 0.0614795
\(400\) −3.49475e13 −0.00853211
\(401\) −2.74552e15 −0.660326 −0.330163 0.943924i \(-0.607104\pi\)
−0.330163 + 0.943924i \(0.607104\pi\)
\(402\) 4.46110e14i 0.105702i
\(403\) 3.96431e15i 0.925417i
\(404\) 8.92975e14i 0.205377i
\(405\) −2.30149e15 −0.521529
\(406\) 2.47651e15i 0.552947i
\(407\) 3.65352e15 4.05605e15i 0.803794 0.892353i
\(408\) 7.53211e15 1.63289
\(409\) 6.34707e15i 1.35592i 0.735099 + 0.677959i \(0.237135\pi\)
−0.735099 + 0.677959i \(0.762865\pi\)
\(410\) −8.54535e14 −0.179898
\(411\) −6.39286e15 −1.32631
\(412\) 1.00417e13 0.00205317
\(413\) 1.51465e15i 0.305220i
\(414\) 7.48247e11i 0.000148608i
\(415\) 6.78632e15i 1.32845i
\(416\) −5.08149e15 −0.980463
\(417\) 6.10939e15i 1.16193i
\(418\) 2.42946e14 2.69712e14i 0.0455461 0.0505642i
\(419\) 1.52674e13 0.00282150 0.00141075 0.999999i \(-0.499551\pi\)
0.00141075 + 0.999999i \(0.499551\pi\)
\(420\) 1.78288e15i 0.324808i
\(421\) 8.78015e15 1.57692 0.788459 0.615087i \(-0.210879\pi\)
0.788459 + 0.615087i \(0.210879\pi\)
\(422\) 5.13910e15 0.909939
\(423\) −3.66060e15 −0.639014
\(424\) 2.58217e14i 0.0444417i
\(425\) 3.86594e14i 0.0656026i
\(426\) 4.13071e15i 0.691142i
\(427\) −8.40220e14 −0.138620
\(428\) 2.24726e15i 0.365588i
\(429\) −4.11482e15 3.70645e15i −0.660095 0.594586i
\(430\) 2.43484e15 0.385176
\(431\) 1.60776e15i 0.250817i −0.992105 0.125409i \(-0.959976\pi\)
0.992105 0.125409i \(-0.0400242\pi\)
\(432\) −1.76808e15 −0.272018
\(433\) 4.45744e15 0.676329 0.338165 0.941087i \(-0.390194\pi\)
0.338165 + 0.941087i \(0.390194\pi\)
\(434\) −3.14428e15 −0.470525
\(435\) 5.41001e15i 0.798477i
\(436\) 1.97456e15i 0.287442i
\(437\) 3.92852e11i 5.64079e-5i
\(438\) −6.55141e15 −0.927876
\(439\) 2.62206e15i 0.366315i 0.983084 + 0.183158i \(0.0586319\pi\)
−0.983084 + 0.183158i \(0.941368\pi\)
\(440\) 5.81536e15 + 5.23823e15i 0.801421 + 0.721886i
\(441\) −9.59565e14 −0.130450
\(442\) 1.12425e16i 1.50774i
\(443\) 4.90406e15 0.648833 0.324417 0.945914i \(-0.394832\pi\)
0.324417 + 0.945914i \(0.394832\pi\)
\(444\) 3.68452e15 0.480931
\(445\) 3.66343e15 0.471768
\(446\) 3.29317e14i 0.0418412i
\(447\) 4.66229e15i 0.584459i
\(448\) 5.64252e15i 0.697919i
\(449\) 2.07520e15 0.253268 0.126634 0.991949i \(-0.459583\pi\)
0.126634 + 0.991949i \(0.459583\pi\)
\(450\) 7.18545e13i 0.00865324i
\(451\) 1.56426e15 + 1.40902e15i 0.185888 + 0.167440i
\(452\) 5.67172e15 0.665096
\(453\) 8.87187e15i 1.02666i
\(454\) 7.18608e15 0.820648
\(455\) −7.98341e15 −0.899746
\(456\) 7.35021e14 0.0817543
\(457\) 4.28819e15i 0.470736i 0.971906 + 0.235368i \(0.0756295\pi\)
−0.971906 + 0.235368i \(0.924370\pi\)
\(458\) 3.00156e15i 0.325203i
\(459\) 1.95586e16i 2.09152i
\(460\) 2.82347e12 0.000298013
\(461\) 2.53696e15i 0.264306i 0.991229 + 0.132153i \(0.0421891\pi\)
−0.991229 + 0.132153i \(0.957811\pi\)
\(462\) −2.93976e15 + 3.26365e15i −0.302315 + 0.335623i
\(463\) −1.34919e16 −1.36958 −0.684791 0.728740i \(-0.740106\pi\)
−0.684791 + 0.728740i \(0.740106\pi\)
\(464\) 2.44597e15i 0.245100i
\(465\) −6.86877e15 −0.679456
\(466\) −8.59194e15 −0.839027
\(467\) −2.42591e15 −0.233869 −0.116934 0.993140i \(-0.537307\pi\)
−0.116934 + 0.993140i \(0.537307\pi\)
\(468\) 2.08958e15i 0.198877i
\(469\) 1.58438e15i 0.148875i
\(470\) 1.38131e16i 1.28146i
\(471\) −7.11562e15 −0.651759
\(472\) 4.48792e15i 0.405875i
\(473\) −4.45709e15 4.01476e15i −0.398001 0.358503i
\(474\) 4.49037e15 0.395924
\(475\) 3.77257e13i 0.00328455i
\(476\) −8.91690e15 −0.766606
\(477\) −1.76971e14 −0.0150242
\(478\) −1.48741e15 −0.124699
\(479\) 4.83691e14i 0.0400456i 0.999800 + 0.0200228i \(0.00637388\pi\)
−0.999800 + 0.0200228i \(0.993626\pi\)
\(480\) 8.80446e15i 0.719872i
\(481\) 1.64986e16i 1.33222i
\(482\) 1.64431e16 1.31130
\(483\) 4.75370e12i 0.000374411i
\(484\) −6.69356e14 6.39255e15i −0.0520697 0.497281i
\(485\) −2.27946e16 −1.75138
\(486\) 6.31109e15i 0.478946i
\(487\) 2.09252e16 1.56854 0.784270 0.620419i \(-0.213038\pi\)
0.784270 + 0.620419i \(0.213038\pi\)
\(488\) −2.48957e15 −0.184334
\(489\) 1.78995e16 1.30914
\(490\) 3.62087e15i 0.261599i
\(491\) 1.72260e16i 1.22940i 0.788759 + 0.614702i \(0.210724\pi\)
−0.788759 + 0.614702i \(0.789276\pi\)
\(492\) 1.42098e15i 0.100184i
\(493\) 2.70576e16 1.88455
\(494\) 1.09709e15i 0.0754888i
\(495\) 3.59007e15 3.98560e15i 0.244046 0.270934i
\(496\) −3.10551e15 −0.208566
\(497\) 1.46705e16i 0.973431i
\(498\) −1.12848e16 −0.739804
\(499\) −7.15013e15 −0.463138 −0.231569 0.972818i \(-0.574386\pi\)
−0.231569 + 0.972818i \(0.574386\pi\)
\(500\) −7.67355e15 −0.491107
\(501\) 5.59115e15i 0.353570i
\(502\) 1.19287e16i 0.745368i
\(503\) 2.87430e16i 1.77470i 0.461100 + 0.887348i \(0.347455\pi\)
−0.461100 + 0.887348i \(0.652545\pi\)
\(504\) 4.97204e15 0.303355
\(505\) 6.92815e15i 0.417704i
\(506\) 5.16850e12 + 4.65557e12i 0.000307937 + 0.000277376i
\(507\) 3.13506e15 0.184586
\(508\) 1.09744e16i 0.638556i
\(509\) −9.99694e15 −0.574858 −0.287429 0.957802i \(-0.592800\pi\)
−0.287429 + 0.957802i \(0.592800\pi\)
\(510\) 1.94793e16 1.10701
\(511\) 2.32677e16 1.30686
\(512\) 8.75748e15i 0.486138i
\(513\) 1.90863e15i 0.104717i
\(514\) 1.60225e16i 0.868864i
\(515\) 7.79086e13 0.00417582
\(516\) 4.04882e15i 0.214501i
\(517\) −2.27761e16 + 2.52855e16i −1.19272 + 1.32412i
\(518\) 1.30858e16 0.677363
\(519\) 2.34133e16i 1.19800i
\(520\) −2.36548e16 −1.19647
\(521\) 2.47231e16 1.23617 0.618084 0.786112i \(-0.287909\pi\)
0.618084 + 0.786112i \(0.287909\pi\)
\(522\) −5.02908e15 −0.248580
\(523\) 6.03331e15i 0.294812i −0.989076 0.147406i \(-0.952908\pi\)
0.989076 0.147406i \(-0.0470924\pi\)
\(524\) 1.50238e16i 0.725759i
\(525\) 4.56500e14i 0.0218014i
\(526\) 4.85722e15 0.229337
\(527\) 3.43535e16i 1.60364i
\(528\) −2.90351e15 + 3.22341e15i −0.134005 + 0.148769i
\(529\) −2.19146e16 −1.00000
\(530\) 6.67793e14i 0.0301291i
\(531\) −3.07583e15 −0.137213
\(532\) −8.70155e14 −0.0383819
\(533\) −6.36288e15 −0.277518
\(534\) 6.09182e15i 0.262724i
\(535\) 1.74354e16i 0.743548i
\(536\) 4.69453e15i 0.197972i
\(537\) −1.51244e16 −0.630713
\(538\) 3.94084e15i 0.162516i
\(539\) −5.97038e15 + 6.62817e15i −0.243483 + 0.270309i
\(540\) 1.37175e16 0.553240
\(541\) 3.89009e16i 1.55159i −0.630986 0.775794i \(-0.717350\pi\)
0.630986 0.775794i \(-0.282650\pi\)
\(542\) −2.28628e16 −0.901850
\(543\) 2.81816e16 1.09943
\(544\) −4.40346e16 −1.69903
\(545\) 1.53196e16i 0.584613i
\(546\) 1.32754e16i 0.501062i
\(547\) 2.77072e16i 1.03435i −0.855878 0.517177i \(-0.826983\pi\)
0.855878 0.517177i \(-0.173017\pi\)
\(548\) 2.24245e16 0.828019
\(549\) 1.70625e15i 0.0623172i
\(550\) 4.96333e14 + 4.47076e14i 0.0179307 + 0.0161512i
\(551\) 2.64042e15 0.0943545
\(552\) 1.40852e13i 0.000497885i
\(553\) −1.59478e16 −0.557635
\(554\) 4.20339e15 0.145392
\(555\) 2.85863e16 0.978138
\(556\) 2.14302e16i 0.725401i
\(557\) 1.72578e16i 0.577904i 0.957344 + 0.288952i \(0.0933067\pi\)
−0.957344 + 0.288952i \(0.906693\pi\)
\(558\) 6.38513e15i 0.211527i
\(559\) 1.81299e16 0.594188
\(560\) 6.25394e15i 0.202780i
\(561\) −3.56577e16 3.21190e16i −1.14387 1.03035i
\(562\) −1.64241e16 −0.521270
\(563\) 2.74432e16i 0.861755i 0.902410 + 0.430878i \(0.141796\pi\)
−0.902410 + 0.430878i \(0.858204\pi\)
\(564\) −2.29694e16 −0.713632
\(565\) 4.40041e16 1.35270
\(566\) −9.20537e15 −0.279990
\(567\) 1.35921e16i 0.409060i
\(568\) 4.34685e16i 1.29445i
\(569\) 2.81521e16i 0.829539i −0.909927 0.414769i \(-0.863862\pi\)
0.909927 0.414769i \(-0.136138\pi\)
\(570\) 1.90088e15 0.0554251
\(571\) 6.44451e16i 1.85940i 0.368315 + 0.929701i \(0.379935\pi\)
−0.368315 + 0.929701i \(0.620065\pi\)
\(572\) 1.44338e16 + 1.30013e16i 0.412100 + 0.371203i
\(573\) 3.29194e15 0.0930087
\(574\) 5.04670e15i 0.141103i
\(575\) 7.22938e11 2.00029e−5
\(576\) 1.14584e16 0.313753
\(577\) 7.11084e14 0.0192693 0.00963465 0.999954i \(-0.496933\pi\)
0.00963465 + 0.999954i \(0.496933\pi\)
\(578\) 7.10572e16i 1.90564i
\(579\) 1.53849e16i 0.408341i
\(580\) 1.89770e16i 0.498493i
\(581\) 4.00785e16 1.04197
\(582\) 3.79044e16i 0.975331i
\(583\) −1.10111e15 + 1.22242e15i −0.0280427 + 0.0311323i
\(584\) 6.89422e16 1.73783
\(585\) 1.62120e16i 0.404485i
\(586\) −2.27671e16 −0.562240
\(587\) −4.34217e16 −1.06140 −0.530698 0.847561i \(-0.678070\pi\)
−0.530698 + 0.847561i \(0.678070\pi\)
\(588\) −6.02103e15 −0.145682
\(589\) 3.35238e15i 0.0802900i
\(590\) 1.16065e16i 0.275162i
\(591\) 5.47718e16i 1.28538i
\(592\) 1.29244e16 0.300249
\(593\) 2.06442e16i 0.474755i −0.971417 0.237378i \(-0.923712\pi\)
0.971417 0.237378i \(-0.0762879\pi\)
\(594\) 2.51106e16 + 2.26186e16i 0.571661 + 0.514929i
\(595\) −6.91818e16 −1.55916
\(596\) 1.63541e16i 0.364880i
\(597\) −2.02271e16 −0.446774
\(598\) −2.10236e13 −0.000459728
\(599\) 5.11034e16 1.10634 0.553170 0.833068i \(-0.313418\pi\)
0.553170 + 0.833068i \(0.313418\pi\)
\(600\) 1.35261e15i 0.0289911i
\(601\) 1.59698e16i 0.338885i −0.985540 0.169443i \(-0.945803\pi\)
0.985540 0.169443i \(-0.0541967\pi\)
\(602\) 1.43796e16i 0.302113i
\(603\) −3.21743e15 −0.0669276
\(604\) 3.11203e16i 0.640947i
\(605\) −5.19320e15 4.95966e16i −0.105902 1.01139i
\(606\) 1.15206e16 0.232616
\(607\) 8.43021e16i 1.68541i −0.538374 0.842706i \(-0.680961\pi\)
0.538374 0.842706i \(-0.319039\pi\)
\(608\) −4.29712e15 −0.0850659
\(609\) −3.19503e16 −0.626285
\(610\) −6.43844e15 −0.124969
\(611\) 1.02853e17i 1.97682i
\(612\) 1.81077e16i 0.344631i
\(613\) 5.83080e16i 1.09892i 0.835521 + 0.549459i \(0.185166\pi\)
−0.835521 + 0.549459i \(0.814834\pi\)
\(614\) 2.64732e16 0.494079
\(615\) 1.10247e16i 0.203758i
\(616\) 3.09359e16 3.43443e16i 0.566211 0.628593i
\(617\) −9.24355e16 −1.67544 −0.837718 0.546103i \(-0.816111\pi\)
−0.837718 + 0.546103i \(0.816111\pi\)
\(618\) 1.29552e14i 0.00232548i
\(619\) 7.32170e16 1.30157 0.650786 0.759262i \(-0.274440\pi\)
0.650786 + 0.759262i \(0.274440\pi\)
\(620\) 2.40939e16 0.424187
\(621\) 3.65751e13 0.000637728
\(622\) 5.27948e15i 0.0911694i
\(623\) 2.16354e16i 0.370030i
\(624\) 1.31117e16i 0.222101i
\(625\) −6.15694e16 −1.03296
\(626\) 2.51139e16i 0.417318i
\(627\) −3.47966e15 3.13433e15i −0.0572705 0.0515869i
\(628\) 2.49598e16 0.406896
\(629\) 1.42972e17i 2.30858i
\(630\) 1.28585e16 0.205659
\(631\) −8.52905e16 −1.35121 −0.675607 0.737262i \(-0.736119\pi\)
−0.675607 + 0.737262i \(0.736119\pi\)
\(632\) −4.72534e16 −0.741533
\(633\) 6.63014e16i 1.03062i
\(634\) 2.25247e16i 0.346836i
\(635\) 8.51449e16i 1.29872i
\(636\) −1.11045e15 −0.0167786
\(637\) 2.69611e16i 0.403553i
\(638\) −3.12908e16 + 3.47383e16i −0.463973 + 0.515091i
\(639\) −2.97915e16 −0.437610
\(640\) 1.85302e16i 0.269650i
\(641\) 9.80934e16 1.41414 0.707069 0.707145i \(-0.250017\pi\)
0.707069 + 0.707145i \(0.250017\pi\)
\(642\) −2.89928e16 −0.414076
\(643\) 3.74612e16 0.530048 0.265024 0.964242i \(-0.414620\pi\)
0.265024 + 0.964242i \(0.414620\pi\)
\(644\) 1.66748e13i 0.000233746i
\(645\) 3.14128e16i 0.436262i
\(646\) 9.50708e15i 0.130813i
\(647\) −5.38286e15 −0.0733816 −0.0366908 0.999327i \(-0.511682\pi\)
−0.0366908 + 0.999327i \(0.511682\pi\)
\(648\) 4.02733e16i 0.543960i
\(649\) −1.91377e16 + 2.12462e16i −0.256107 + 0.284324i
\(650\) −2.01891e15 −0.0267693
\(651\) 4.05655e16i 0.532931i
\(652\) −6.27869e16 −0.817303
\(653\) −3.12894e16 −0.403570 −0.201785 0.979430i \(-0.564674\pi\)
−0.201785 + 0.979430i \(0.564674\pi\)
\(654\) 2.54745e16 0.325566
\(655\) 1.16562e17i 1.47608i
\(656\) 4.98447e15i 0.0625454i
\(657\) 4.72501e16i 0.587503i
\(658\) −8.15772e16 −1.00511
\(659\) 8.92827e16i 1.09007i 0.838413 + 0.545035i \(0.183484\pi\)
−0.838413 + 0.545035i \(0.816516\pi\)
\(660\) 2.25268e16 2.50087e16i 0.272543 0.302571i
\(661\) 1.06958e17 1.28234 0.641170 0.767399i \(-0.278449\pi\)
0.641170 + 0.767399i \(0.278449\pi\)
\(662\) 1.41255e16i 0.167825i
\(663\) 1.45043e17 1.70772
\(664\) 1.18753e17 1.38559
\(665\) −6.75110e15 −0.0780629
\(666\) 2.65735e16i 0.304511i
\(667\) 5.05983e13i 0.000574620i
\(668\) 1.96124e16i 0.220735i
\(669\) −4.24863e15 −0.0473906
\(670\) 1.21408e16i 0.134214i
\(671\) 1.17859e16 + 1.06162e16i 0.129130 + 0.116315i
\(672\) 5.19972e16 0.564631
\(673\) 7.50491e16i 0.807709i −0.914823 0.403855i \(-0.867670\pi\)
0.914823 0.403855i \(-0.132330\pi\)
\(674\) 2.36208e16 0.251962
\(675\) 3.51232e15 0.0371340
\(676\) −1.09970e16 −0.115238
\(677\) 8.14864e16i 0.846357i 0.906046 + 0.423178i \(0.139086\pi\)
−0.906046 + 0.423178i \(0.860914\pi\)
\(678\) 7.31731e16i 0.753309i
\(679\) 1.34620e17i 1.37369i
\(680\) −2.04985e17 −2.07334
\(681\) 9.27102e16i 0.929491i
\(682\) 4.41051e16 + 3.97281e16i 0.438312 + 0.394813i
\(683\) 5.33960e16 0.525998 0.262999 0.964796i \(-0.415288\pi\)
0.262999 + 0.964796i \(0.415288\pi\)
\(684\) 1.76704e15i 0.0172548i
\(685\) 1.73981e17 1.68406
\(686\) −8.01636e16 −0.769188
\(687\) −3.87242e16 −0.368335
\(688\) 1.42023e16i 0.133915i
\(689\) 4.97240e15i 0.0464783i
\(690\) 3.64267e13i 0.000337540i
\(691\) 1.48870e13 0.000136753 6.83767e−5 1.00000i \(-0.499978\pi\)
6.83767e−5 1.00000i \(0.499978\pi\)
\(692\) 8.21280e16i 0.747919i
\(693\) −2.35381e16 2.12021e16i −0.212507 0.191417i
\(694\) 1.09260e17 0.977919
\(695\) 1.66266e17i 1.47535i
\(696\) −9.46688e16 −0.832821
\(697\) −5.51387e16 −0.480906
\(698\) −4.31264e16 −0.372915
\(699\) 1.10848e17i 0.950307i
\(700\) 1.60129e15i 0.0136107i
\(701\) 4.73316e16i 0.398881i 0.979910 + 0.199440i \(0.0639124\pi\)
−0.979910 + 0.199440i \(0.936088\pi\)
\(702\) −1.02141e17 −0.853450
\(703\) 1.39519e16i 0.115585i
\(704\) 7.12934e16 7.91483e16i 0.585617 0.650138i
\(705\) −1.78208e17 −1.45142
\(706\) 4.28877e16i 0.346342i
\(707\) −4.09161e16 −0.327626
\(708\) −1.93001e16 −0.153235
\(709\) −7.91916e16 −0.623450 −0.311725 0.950172i \(-0.600907\pi\)
−0.311725 + 0.950172i \(0.600907\pi\)
\(710\) 1.12417e17i 0.877569i
\(711\) 3.23855e16i 0.250687i
\(712\) 6.41058e16i 0.492059i
\(713\) 6.42417e13 0.000488967
\(714\) 1.15040e17i 0.868283i
\(715\) 1.11984e17 + 1.00871e17i 0.838148 + 0.754969i
\(716\) 5.30526e16 0.393757
\(717\) 1.91897e16i 0.141238i
\(718\) −8.95728e16 −0.653777
\(719\) −2.67561e17 −1.93664 −0.968320 0.249713i \(-0.919664\pi\)
−0.968320 + 0.249713i \(0.919664\pi\)
\(720\) 1.27000e16 0.0911607
\(721\) 4.60111e14i 0.00327530i
\(722\) 9.92355e16i 0.700558i
\(723\) 2.12139e17i 1.48522i
\(724\) −9.88540e16 −0.686377
\(725\) 4.85898e15i 0.0334593i
\(726\) 8.24727e16 8.63563e15i 0.563236 0.0589758i
\(727\) 1.63508e17 1.10747 0.553735 0.832693i \(-0.313202\pi\)
0.553735 + 0.832693i \(0.313202\pi\)
\(728\) 1.39700e17i 0.938446i
\(729\) 1.58398e17 1.05532
\(730\) 1.78296e17 1.17816
\(731\) 1.57108e17 1.02966
\(732\) 1.07063e16i 0.0695941i
\(733\) 1.00783e17i 0.649775i 0.945753 + 0.324888i \(0.105326\pi\)
−0.945753 + 0.324888i \(0.894674\pi\)
\(734\) 1.32577e17i 0.847798i
\(735\) −4.67142e16 −0.296295
\(736\) 8.23456e13i 0.000518052i
\(737\) −2.00187e16 + 2.22243e16i −0.124920 + 0.138683i
\(738\) 1.02484e16 0.0634334
\(739\) 5.78425e16i 0.355124i −0.984110 0.177562i \(-0.943179\pi\)
0.984110 0.177562i \(-0.0568211\pi\)
\(740\) −1.00274e17 −0.610656
\(741\) 1.41540e16 0.0855009
\(742\) −3.94384e15 −0.0236317
\(743\) 1.39628e17i 0.829927i −0.909838 0.414964i \(-0.863794\pi\)
0.909838 0.414964i \(-0.136206\pi\)
\(744\) 1.20195e17i 0.708680i
\(745\) 1.26884e17i 0.742109i
\(746\) 1.12880e17 0.654912
\(747\) 8.13881e16i 0.468422i
\(748\) 1.25078e17 + 1.12665e17i 0.714122 + 0.643252i
\(749\) 1.02970e17 0.583201
\(750\) 9.89994e16i 0.556244i
\(751\) −2.06894e17 −1.15321 −0.576604 0.817024i \(-0.695623\pi\)
−0.576604 + 0.817024i \(0.695623\pi\)
\(752\) −8.05713e16 −0.445526
\(753\) −1.53896e17 −0.844226
\(754\) 1.41303e17i 0.768995i
\(755\) 2.41447e17i 1.30359i
\(756\) 8.10128e16i 0.433933i
\(757\) 5.99623e16 0.318642 0.159321 0.987227i \(-0.449070\pi\)
0.159321 + 0.987227i \(0.449070\pi\)
\(758\) 7.65533e16i 0.403598i
\(759\) 6.00632e13 6.66807e13i 0.000314165 0.000348778i
\(760\) −2.00035e16 −0.103806
\(761\) 6.17443e16i 0.317899i −0.987287 0.158949i \(-0.949189\pi\)
0.987287 0.158949i \(-0.0508107\pi\)
\(762\) 1.41585e17 0.723249
\(763\) −9.04742e16 −0.458540
\(764\) −1.15473e16 −0.0580657
\(765\) 1.40488e17i 0.700926i
\(766\) 1.63736e17i 0.810535i
\(767\) 8.64221e16i 0.424476i
\(768\) 1.74610e17 0.850946
\(769\) 4.02843e16i 0.194795i 0.995246 + 0.0973974i \(0.0310518\pi\)
−0.995246 + 0.0973974i \(0.968948\pi\)
\(770\) 8.00052e16 8.88199e16i 0.383861 0.426153i
\(771\) −2.06712e17 −0.984101
\(772\) 5.39664e16i 0.254929i
\(773\) 3.19844e17 1.49921 0.749603 0.661887i \(-0.230244\pi\)
0.749603 + 0.661887i \(0.230244\pi\)
\(774\) −2.92010e16 −0.135816
\(775\) 6.16916e15 0.0284719
\(776\) 3.98878e17i 1.82671i
\(777\) 1.68825e17i 0.767201i
\(778\) 1.09257e17i 0.492687i
\(779\) −5.38071e15 −0.0240777
\(780\) 1.01727e17i 0.451717i
\(781\) −1.85362e17 + 2.05784e17i −0.816796 + 0.906788i
\(782\) −1.82184e14 −0.000796655
\(783\) 2.45827e17i 1.06674i
\(784\) −2.11204e16 −0.0909506
\(785\) 1.93651e17 0.827563
\(786\) −1.93828e17 −0.822018
\(787\) 1.58026e17i 0.665088i −0.943088 0.332544i \(-0.892093\pi\)
0.943088 0.332544i \(-0.107907\pi\)
\(788\) 1.92126e17i 0.802469i
\(789\) 6.26648e16i 0.259754i
\(790\) −1.22205e17 −0.502720
\(791\) 2.59878e17i 1.06099i
\(792\) −6.97434e16 6.28219e16i −0.282587 0.254542i
\(793\) −4.79408e16 −0.192782
\(794\) 1.61283e17i 0.643673i
\(795\) −8.61543e15 −0.0341251
\(796\) 7.09517e16 0.278923
\(797\) 2.90707e17 1.13424 0.567121 0.823634i \(-0.308057\pi\)
0.567121 + 0.823634i \(0.308057\pi\)
\(798\) 1.12262e16i 0.0434726i
\(799\) 8.91289e17i 3.42561i
\(800\) 7.90769e15i 0.0301654i
\(801\) −4.39354e16 −0.166349
\(802\) 1.24248e17i 0.466921i
\(803\) −3.26379e17 2.93988e17i −1.21739 1.09657i
\(804\) −2.01886e16 −0.0747428
\(805\) 1.29371e14i 0.000475404i
\(806\) −1.79404e17 −0.654369
\(807\) 5.08422e16 0.184070
\(808\) −1.21234e17 −0.435670
\(809\) 6.90335e16i 0.246246i 0.992391 + 0.123123i \(0.0392909\pi\)
−0.992391 + 0.123123i \(0.960709\pi\)
\(810\) 1.04153e17i 0.368777i
\(811\) 9.40439e16i 0.330526i −0.986250 0.165263i \(-0.947153\pi\)
0.986250 0.165263i \(-0.0528473\pi\)
\(812\) 1.12074e17 0.390992
\(813\) 2.94962e17i 1.02146i
\(814\) −1.83556e17 1.65339e17i −0.630989 0.568369i
\(815\) −4.87132e17 −1.66227
\(816\) 1.13622e17i 0.384876i
\(817\) 1.53314e16 0.0515523
\(818\) 2.87236e17 0.958780
\(819\) 9.57448e16 0.317257
\(820\) 3.86718e16i 0.127207i
\(821\) 2.96469e17i 0.968100i 0.875040 + 0.484050i \(0.160835\pi\)
−0.875040 + 0.484050i \(0.839165\pi\)
\(822\) 2.89308e17i 0.937841i
\(823\) 1.43405e17 0.461494 0.230747 0.973014i \(-0.425883\pi\)
0.230747 + 0.973014i \(0.425883\pi\)
\(824\) 1.36331e15i 0.00435543i
\(825\) 5.76789e15 6.40337e15i 0.0182934 0.0203088i
\(826\) −6.85454e16 −0.215823
\(827\) 4.94576e17i 1.54597i 0.634426 + 0.772984i \(0.281237\pi\)
−0.634426 + 0.772984i \(0.718763\pi\)
\(828\) −3.38618e13 −0.000105082
\(829\) 2.13899e16 0.0658996 0.0329498 0.999457i \(-0.489510\pi\)
0.0329498 + 0.999457i \(0.489510\pi\)
\(830\) 3.07114e17 0.939357
\(831\) 5.42295e16i 0.164676i
\(832\) 3.21947e17i 0.970610i
\(833\) 2.33636e17i 0.699310i
\(834\) 2.76480e17 0.821612
\(835\) 1.52163e17i 0.448941i
\(836\) 1.22058e16 + 1.09944e16i 0.0357542 + 0.0322059i
\(837\) 3.12112e17 0.907732
\(838\) 6.90923e14i 0.00199510i
\(839\) −4.67383e17 −1.33999 −0.669994 0.742367i \(-0.733703\pi\)
−0.669994 + 0.742367i \(0.733703\pi\)
\(840\) 2.42052e17 0.689022
\(841\) 1.37357e16 0.0388217
\(842\) 3.97344e17i 1.11505i
\(843\) 2.11893e17i 0.590406i
\(844\) 2.32569e17i 0.643423i
\(845\) −8.53202e16 −0.234375
\(846\) 1.65660e17i 0.451851i
\(847\) −2.92907e17 + 3.06699e16i −0.793284 + 0.0830639i
\(848\) −3.89521e15 −0.0104750
\(849\) 1.18762e17i 0.317125i
\(850\) −1.74952e16 −0.0463881
\(851\) −2.67360e14 −0.000703913
\(852\) −1.86934e17 −0.488710
\(853\) 4.39225e16i 0.114023i 0.998374 + 0.0570116i \(0.0181572\pi\)
−0.998374 + 0.0570116i \(0.981843\pi\)
\(854\) 3.80240e16i 0.0980192i
\(855\) 1.37096e16i 0.0350935i
\(856\) 3.05099e17 0.775529
\(857\) 3.73692e17i 0.943255i 0.881798 + 0.471627i \(0.156333\pi\)
−0.881798 + 0.471627i \(0.843667\pi\)
\(858\) −1.67735e17 + 1.86215e17i −0.420436 + 0.466758i
\(859\) −8.11917e16 −0.202094 −0.101047 0.994882i \(-0.532219\pi\)
−0.101047 + 0.994882i \(0.532219\pi\)
\(860\) 1.10188e17i 0.272360i
\(861\) 6.51093e16 0.159817
\(862\) −7.27589e16 −0.177355
\(863\) 6.05756e17 1.46634 0.733168 0.680048i \(-0.238041\pi\)
0.733168 + 0.680048i \(0.238041\pi\)
\(864\) 4.00068e17i 0.961726i
\(865\) 6.37190e17i 1.52115i
\(866\) 2.01721e17i 0.478237i
\(867\) 9.16734e17 2.15839
\(868\) 1.42294e17i 0.332711i
\(869\) 2.23702e17 + 2.01501e17i 0.519458 + 0.467906i
\(870\) −2.44829e17 −0.564609
\(871\) 9.04008e16i 0.207044i
\(872\) −2.68075e17 −0.609758
\(873\) 2.73374e17 0.617550
\(874\) −1.77784e13 −3.98864e−5
\(875\) 3.51602e17i 0.783435i
\(876\) 2.96482e17i 0.656106i
\(877\) 2.56337e17i 0.563397i 0.959503 + 0.281698i \(0.0908978\pi\)
−0.959503 + 0.281698i \(0.909102\pi\)
\(878\) 1.18661e17 0.259024
\(879\) 2.93726e17i 0.636809i
\(880\) 7.90187e16 8.77247e16i 0.170151 0.188897i
\(881\) 4.66763e16 0.0998255 0.0499127 0.998754i \(-0.484106\pi\)
0.0499127 + 0.998754i \(0.484106\pi\)
\(882\) 4.34250e16i 0.0922418i
\(883\) −7.55573e17 −1.59409 −0.797044 0.603922i \(-0.793604\pi\)
−0.797044 + 0.603922i \(0.793604\pi\)
\(884\) −5.08775e17 −1.06613
\(885\) −1.49740e17 −0.311657
\(886\) 2.21932e17i 0.458795i
\(887\) 3.74340e17i 0.768643i 0.923199 + 0.384321i \(0.125565\pi\)
−0.923199 + 0.384321i \(0.874435\pi\)
\(888\) 5.00227e17i 1.02021i
\(889\) −5.02847e17 −1.01865
\(890\) 1.65788e17i 0.333590i
\(891\) 1.71736e17 1.90658e17i 0.343239 0.381055i
\(892\) 1.49032e16 0.0295862
\(893\) 8.69763e16i 0.171511i
\(894\) −2.10991e17 −0.413275
\(895\) 4.11608e17 0.800840
\(896\) −1.09436e17 −0.211500
\(897\) 2.71234e14i 0.000520701i
\(898\) 9.39127e16i 0.179088i
\(899\) 4.31778e17i 0.817905i
\(900\) −3.25176e15 −0.00611876
\(901\) 4.30892e16i 0.0805416i
\(902\) 6.37652e16 7.07906e16i 0.118398 0.131443i
\(903\) −1.85517e17 −0.342182
\(904\) 7.70020e17i 1.41088i
\(905\) −7.66959e17 −1.39598
\(906\) −4.01495e17 −0.725957
\(907\) 1.34785e17 0.242102 0.121051 0.992646i \(-0.461373\pi\)
0.121051 + 0.992646i \(0.461373\pi\)
\(908\) 3.25204e17i 0.580285i
\(909\) 8.30890e16i 0.147286i
\(910\) 3.61288e17i 0.636217i
\(911\) 5.77555e17 1.01038 0.505188 0.863009i \(-0.331423\pi\)
0.505188 + 0.863009i \(0.331423\pi\)
\(912\) 1.10878e16i 0.0192697i
\(913\) −5.62186e17 5.06394e17i −0.970634 0.874306i
\(914\) 1.94062e17 0.332861
\(915\) 8.30647e16i 0.141544i
\(916\) 1.35835e17 0.229953
\(917\) 6.88391e17 1.15776
\(918\) −8.85124e17 −1.47893
\(919\) 2.03581e17i 0.337943i 0.985621 + 0.168972i \(0.0540446\pi\)
−0.985621 + 0.168972i \(0.945955\pi\)
\(920\) 3.83327e14i 0.000632183i
\(921\) 3.41540e17i 0.559609i
\(922\) 1.14810e17 0.186893
\(923\) 8.37058e17i 1.35377i
\(924\) −1.47696e17 1.33038e17i −0.237321 0.213769i
\(925\) −2.56747e16 −0.0409878
\(926\) 6.10575e17i 0.968441i
\(927\) −9.34355e14 −0.00147243
\(928\) 5.53458e17 0.866556
\(929\) −7.33904e17 −1.14168 −0.570841 0.821061i \(-0.693383\pi\)
−0.570841 + 0.821061i \(0.693383\pi\)
\(930\) 3.10845e17i 0.480448i
\(931\) 2.27994e16i 0.0350126i
\(932\) 3.88826e17i 0.593281i
\(933\) −6.81125e16 −0.103261
\(934\) 1.09784e17i 0.165370i
\(935\) 9.70420e17 + 8.74114e17i 1.45241 + 1.30827i
\(936\) 2.83692e17 0.421883
\(937\) 3.99860e17i 0.590841i −0.955367 0.295420i \(-0.904540\pi\)
0.955367 0.295420i \(-0.0954597\pi\)
\(938\) −7.17010e16 −0.105271
\(939\) 3.24003e17 0.472667
\(940\) 6.25109e17 0.906126
\(941\) 2.03014e17i 0.292408i 0.989254 + 0.146204i \(0.0467055\pi\)
−0.989254 + 0.146204i \(0.953294\pi\)
\(942\) 3.22016e17i 0.460864i
\(943\) 1.03111e14i 0.000146633i
\(944\) −6.77002e16 −0.0956661
\(945\) 6.28537e17i 0.882552i
\(946\) −1.81687e17 + 2.01705e17i −0.253500 + 0.281429i
\(947\) −1.59725e17 −0.221449 −0.110725 0.993851i \(-0.535317\pi\)
−0.110725 + 0.993851i \(0.535317\pi\)
\(948\) 2.03211e17i 0.279960i
\(949\) 1.32759e18 1.81747
\(950\) −1.70727e15 −0.00232253
\(951\) −2.90599e17 −0.392836
\(952\) 1.21060e18i 1.62622i
\(953\) 3.94451e17i 0.526545i 0.964722 + 0.263272i \(0.0848018\pi\)
−0.964722 + 0.263272i \(0.915198\pi\)
\(954\) 8.00881e15i 0.0106238i
\(955\) −8.95897e16 −0.118097
\(956\) 6.73125e16i 0.0881756i
\(957\) 4.48171e17 + 4.03694e17i 0.583408 + 0.525509i
\(958\) 2.18893e16 0.0283165
\(959\) 1.02749e18i 1.32089i
\(960\) 5.57823e17 0.712638
\(961\) −2.39459e17 −0.304012
\(962\) 7.46641e17 0.942023
\(963\) 2.09102e17i 0.262181i
\(964\) 7.44129e17i 0.927227i
\(965\) 4.18698e17i 0.518486i
\(966\) 2.15128e14 0.000264749
\(967\) 8.27880e17i 1.01253i 0.862378 + 0.506266i \(0.168974\pi\)
−0.862378 + 0.506266i \(0.831026\pi\)
\(968\) −8.67882e17 + 9.08749e16i −1.05489 + 0.110457i
\(969\) 1.22654e17 0.148163
\(970\) 1.03156e18i 1.23841i
\(971\) −2.82655e17 −0.337242 −0.168621 0.985681i \(-0.553931\pi\)
−0.168621 + 0.985681i \(0.553931\pi\)
\(972\) −2.85607e17 −0.338666
\(973\) −9.81933e17 −1.15719
\(974\) 9.46967e17i 1.10913i
\(975\) 2.60467e16i 0.0303197i
\(976\) 3.75552e16i 0.0434481i
\(977\) −1.27034e18 −1.46068 −0.730338 0.683086i \(-0.760637\pi\)
−0.730338 + 0.683086i \(0.760637\pi\)
\(978\) 8.10038e17i 0.925704i
\(979\) −2.73365e17 + 3.03483e17i −0.310489 + 0.344697i
\(980\) 1.63862e17 0.184978
\(981\) 1.83727e17i 0.206139i
\(982\) 7.79559e17 0.869320
\(983\) −5.26692e17 −0.583762 −0.291881 0.956455i \(-0.594281\pi\)
−0.291881 + 0.956455i \(0.594281\pi\)
\(984\) 1.92919e17 0.212522
\(985\) 1.49061e18i 1.63210i
\(986\) 1.22449e18i 1.33258i
\(987\) 1.05246e18i 1.13842i
\(988\) −4.96488e16 −0.0533786
\(989\) 2.93795e14i 0.000313954i
\(990\) −1.80368e17 1.62468e17i −0.191579 0.172566i
\(991\) 2.71502e17 0.286636 0.143318 0.989677i \(-0.454223\pi\)
0.143318 + 0.989677i \(0.454223\pi\)
\(992\) 7.02693e17i 0.737387i
\(993\) −1.82238e17 −0.190083
\(994\) −6.63909e17 −0.688320
\(995\) 5.50479e17 0.567286
\(996\) 5.10690e17i 0.523120i
\(997\) 1.50550e18i 1.53289i 0.642312 + 0.766443i \(0.277975\pi\)
−0.642312 + 0.766443i \(0.722025\pi\)
\(998\) 3.23578e17i 0.327488i
\(999\) −1.29894e18 −1.30676
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 11.13.b.b.10.4 10
3.2 odd 2 99.13.c.b.10.7 10
4.3 odd 2 176.13.h.c.65.8 10
11.10 odd 2 inner 11.13.b.b.10.7 yes 10
33.32 even 2 99.13.c.b.10.4 10
44.43 even 2 176.13.h.c.65.7 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
11.13.b.b.10.4 10 1.1 even 1 trivial
11.13.b.b.10.7 yes 10 11.10 odd 2 inner
99.13.c.b.10.4 10 33.32 even 2
99.13.c.b.10.7 10 3.2 odd 2
176.13.h.c.65.7 10 44.43 even 2
176.13.h.c.65.8 10 4.3 odd 2