Properties

Label 126.9.s.b.53.10
Level $126$
Weight $9$
Character 126.53
Analytic conductor $51.330$
Analytic rank $0$
Dimension $20$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [126,9,Mod(53,126)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(126, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("126.53");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 126.s (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(51.3297048677\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 10 x^{19} + 3140415 x^{18} - 28263450 x^{17} + 4166681580501 x^{16} - 33332812007100 x^{15} + \cdots + 75\!\cdots\!79 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{16}\cdot 3^{18}\cdot 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 53.10
Root \(0.500000 - 778.834i\) of defining polynomial
Character \(\chi\) \(=\) 126.53
Dual form 126.9.s.b.107.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(9.79796 - 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(675.240 - 389.850i) q^{5} +(-2257.29 + 818.185i) q^{7} -1448.15i q^{8} +O(q^{10})\) \(q+(9.79796 - 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(675.240 - 389.850i) q^{5} +(-2257.29 + 818.185i) q^{7} -1448.15i q^{8} +(4410.65 - 7639.47i) q^{10} +(22350.7 + 12904.2i) q^{11} +2645.78 q^{13} +(-17488.5 + 20785.7i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(64112.8 + 37015.5i) q^{17} +(-19975.2 - 34598.0i) q^{19} -99801.6i q^{20} +291989. q^{22} +(391111. - 225808. i) q^{23} +(108654. - 188193. i) q^{25} +(25923.2 - 14966.8i) q^{26} +(-53769.9 + 302588. i) q^{28} -16119.2i q^{29} +(-130548. + 226117. i) q^{31} +(-160530. - 92681.9i) q^{32} +837566. q^{34} +(-1.20525e6 + 1.43248e6i) q^{35} +(-704165. - 1.21965e6i) q^{37} +(-391432. - 225993. i) q^{38} +(-564563. - 977852. i) q^{40} +1.52892e6i q^{41} -1.63384e6 q^{43} +(2.86090e6 - 1.65174e6i) q^{44} +(2.55473e6 - 4.42492e6i) q^{46} +(8.03301e6 - 4.63786e6i) q^{47} +(4.42595e6 - 3.69377e6i) q^{49} -2.45855e6i q^{50} +(169330. - 293288. i) q^{52} +(2.72214e6 + 1.57163e6i) q^{53} +2.01228e7 q^{55} +(1.18486e6 + 3.26891e6i) q^{56} +(-91184.2 - 157936. i) q^{58} +(-1.44666e7 - 8.35227e6i) q^{59} +(4.37015e6 + 7.56932e6i) q^{61} +2.95397e6i q^{62} -2.09715e6 q^{64} +(1.78653e6 - 1.03146e6i) q^{65} +(1.40514e7 - 2.43378e7i) q^{67} +(8.20644e6 - 4.73799e6i) q^{68} +(-3.70563e6 + 2.08533e7i) q^{70} -4.04624e7i q^{71} +(5.58975e6 - 9.68173e6i) q^{73} +(-1.37988e7 - 7.96672e6i) q^{74} -5.11364e6 q^{76} +(-6.10102e7 - 1.08415e7i) q^{77} +(3.35502e7 + 5.81107e7i) q^{79} +(-1.10631e7 - 6.38730e6i) q^{80} +(8.64888e6 + 1.49803e7i) q^{82} -4.64460e7i q^{83} +5.77220e7 q^{85} +(-1.60083e7 + 9.24239e6i) q^{86} +(1.86873e7 - 3.23673e7i) q^{88} +(-3.34937e7 + 1.93376e7i) q^{89} +(-5.97229e6 + 2.16474e6i) q^{91} -5.78069e7i q^{92} +(5.24714e7 - 9.08831e7i) q^{94} +(-2.69761e7 - 1.55746e7i) q^{95} +9.56235e7 q^{97} +(2.24701e7 - 6.12283e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 1280 q^{4} + 3778 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 1280 q^{4} + 3778 q^{7} + 14816 q^{10} + 17700 q^{13} - 163840 q^{16} - 267794 q^{19} + 453568 q^{22} - 765890 q^{25} - 232448 q^{28} - 2604342 q^{31} + 4087936 q^{34} + 1127530 q^{37} - 1896448 q^{40} - 4460924 q^{43} - 180416 q^{46} - 25278034 q^{49} + 1132800 q^{52} - 18833120 q^{55} + 5146496 q^{58} - 25730232 q^{61} - 41943040 q^{64} + 58134374 q^{67} - 76724864 q^{70} + 5811002 q^{73} - 68555264 q^{76} + 74799798 q^{79} - 9883296 q^{82} + 119739328 q^{85} + 29028352 q^{88} - 479039766 q^{91} + 169364448 q^{94} - 658133608 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(29\) \(73\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 9.79796 5.65685i 0.612372 0.353553i
\(3\) 0 0
\(4\) 64.0000 110.851i 0.250000 0.433013i
\(5\) 675.240 389.850i 1.08038 0.623760i 0.149384 0.988779i \(-0.452271\pi\)
0.931000 + 0.365019i \(0.118938\pi\)
\(6\) 0 0
\(7\) −2257.29 + 818.185i −0.940147 + 0.340769i
\(8\) 1448.15i 0.353553i
\(9\) 0 0
\(10\) 4410.65 7639.47i 0.441065 0.763947i
\(11\) 22350.7 + 12904.2i 1.52659 + 0.881375i 0.999502 + 0.0315619i \(0.0100481\pi\)
0.527084 + 0.849813i \(0.323285\pi\)
\(12\) 0 0
\(13\) 2645.78 0.0926360 0.0463180 0.998927i \(-0.485251\pi\)
0.0463180 + 0.998927i \(0.485251\pi\)
\(14\) −17488.5 + 20785.7i −0.455240 + 0.541069i
\(15\) 0 0
\(16\) −8192.00 14189.0i −0.125000 0.216506i
\(17\) 64112.8 + 37015.5i 0.767625 + 0.443188i 0.832027 0.554736i \(-0.187181\pi\)
−0.0644020 + 0.997924i \(0.520514\pi\)
\(18\) 0 0
\(19\) −19975.2 34598.0i −0.153277 0.265483i 0.779154 0.626833i \(-0.215649\pi\)
−0.932430 + 0.361350i \(0.882316\pi\)
\(20\) 99801.6i 0.623760i
\(21\) 0 0
\(22\) 291989. 1.24645
\(23\) 391111. 225808.i 1.39762 0.806916i 0.403477 0.914990i \(-0.367801\pi\)
0.994143 + 0.108073i \(0.0344681\pi\)
\(24\) 0 0
\(25\) 108654. 188193.i 0.278153 0.481775i
\(26\) 25923.2 14966.8i 0.0567277 0.0327518i
\(27\) 0 0
\(28\) −53769.9 + 302588.i −0.0874797 + 0.492288i
\(29\) 16119.2i 0.0227904i −0.999935 0.0113952i \(-0.996373\pi\)
0.999935 0.0113952i \(-0.00362729\pi\)
\(30\) 0 0
\(31\) −130548. + 226117.i −0.141359 + 0.244842i −0.928009 0.372558i \(-0.878481\pi\)
0.786649 + 0.617400i \(0.211814\pi\)
\(32\) −160530. 92681.9i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 837566. 0.626763
\(35\) −1.20525e6 + 1.43248e6i −0.803162 + 0.954587i
\(36\) 0 0
\(37\) −704165. 1.21965e6i −0.375723 0.650771i 0.614712 0.788751i \(-0.289272\pi\)
−0.990435 + 0.137981i \(0.955939\pi\)
\(38\) −391432. 225993.i −0.187725 0.108383i
\(39\) 0 0
\(40\) −564563. 977852.i −0.220532 0.381973i
\(41\) 1.52892e6i 0.541065i 0.962711 + 0.270533i \(0.0871998\pi\)
−0.962711 + 0.270533i \(0.912800\pi\)
\(42\) 0 0
\(43\) −1.63384e6 −0.477898 −0.238949 0.971032i \(-0.576803\pi\)
−0.238949 + 0.971032i \(0.576803\pi\)
\(44\) 2.86090e6 1.65174e6i 0.763293 0.440687i
\(45\) 0 0
\(46\) 2.55473e6 4.42492e6i 0.570576 0.988267i
\(47\) 8.03301e6 4.63786e6i 1.64622 0.950443i 0.667658 0.744468i \(-0.267297\pi\)
0.978557 0.205975i \(-0.0660365\pi\)
\(48\) 0 0
\(49\) 4.42595e6 3.69377e6i 0.767754 0.640745i
\(50\) 2.45855e6i 0.393368i
\(51\) 0 0
\(52\) 169330. 293288.i 0.0231590 0.0401126i
\(53\) 2.72214e6 + 1.57163e6i 0.344991 + 0.199181i 0.662477 0.749082i \(-0.269505\pi\)
−0.317486 + 0.948263i \(0.602839\pi\)
\(54\) 0 0
\(55\) 2.01228e7 2.19907
\(56\) 1.18486e6 + 3.26891e6i 0.120480 + 0.332392i
\(57\) 0 0
\(58\) −91184.2 157936.i −0.00805764 0.0139562i
\(59\) −1.44666e7 8.35227e6i −1.19387 0.689282i −0.234689 0.972071i \(-0.575407\pi\)
−0.959182 + 0.282789i \(0.908740\pi\)
\(60\) 0 0
\(61\) 4.37015e6 + 7.56932e6i 0.315629 + 0.546686i 0.979571 0.201099i \(-0.0644511\pi\)
−0.663942 + 0.747784i \(0.731118\pi\)
\(62\) 2.95397e6i 0.199913i
\(63\) 0 0
\(64\) −2.09715e6 −0.125000
\(65\) 1.78653e6 1.03146e6i 0.100082 0.0577826i
\(66\) 0 0
\(67\) 1.40514e7 2.43378e7i 0.697302 1.20776i −0.272096 0.962270i \(-0.587717\pi\)
0.969398 0.245493i \(-0.0789497\pi\)
\(68\) 8.20644e6 4.73799e6i 0.383812 0.221594i
\(69\) 0 0
\(70\) −3.70563e6 + 2.08533e7i −0.154337 + 0.868524i
\(71\) 4.04624e7i 1.59228i −0.605115 0.796138i \(-0.706873\pi\)
0.605115 0.796138i \(-0.293127\pi\)
\(72\) 0 0
\(73\) 5.58975e6 9.68173e6i 0.196834 0.340927i −0.750666 0.660682i \(-0.770267\pi\)
0.947500 + 0.319755i \(0.103601\pi\)
\(74\) −1.37988e7 7.96672e6i −0.460164 0.265676i
\(75\) 0 0
\(76\) −5.11364e6 −0.153277
\(77\) −6.10102e7 1.08415e7i −1.73556 0.308410i
\(78\) 0 0
\(79\) 3.35502e7 + 5.81107e7i 0.861364 + 1.49193i 0.870612 + 0.491969i \(0.163723\pi\)
−0.00924818 + 0.999957i \(0.502944\pi\)
\(80\) −1.10631e7 6.38730e6i −0.270096 0.155940i
\(81\) 0 0
\(82\) 8.64888e6 + 1.49803e7i 0.191295 + 0.331333i
\(83\) 4.64460e7i 0.978670i −0.872096 0.489335i \(-0.837240\pi\)
0.872096 0.489335i \(-0.162760\pi\)
\(84\) 0 0
\(85\) 5.77220e7 1.10577
\(86\) −1.60083e7 + 9.24239e6i −0.292652 + 0.168963i
\(87\) 0 0
\(88\) 1.86873e7 3.23673e7i 0.311613 0.539730i
\(89\) −3.34937e7 + 1.93376e7i −0.533831 + 0.308207i −0.742575 0.669763i \(-0.766396\pi\)
0.208744 + 0.977970i \(0.433062\pi\)
\(90\) 0 0
\(91\) −5.97229e6 + 2.16474e6i −0.0870915 + 0.0315674i
\(92\) 5.78069e7i 0.806916i
\(93\) 0 0
\(94\) 5.24714e7 9.08831e7i 0.672065 1.16405i
\(95\) −2.69761e7 1.55746e7i −0.331195 0.191216i
\(96\) 0 0
\(97\) 9.56235e7 1.08013 0.540067 0.841622i \(-0.318399\pi\)
0.540067 + 0.841622i \(0.318399\pi\)
\(98\) 2.24701e7 6.12283e7i 0.243614 0.663817i
\(99\) 0 0
\(100\) −1.39077e7 2.40888e7i −0.139077 0.240888i
\(101\) 1.35263e8 + 7.80940e7i 1.29985 + 0.750468i 0.980378 0.197129i \(-0.0631616\pi\)
0.319470 + 0.947596i \(0.396495\pi\)
\(102\) 0 0
\(103\) −5.25743e7 9.10614e7i −0.467116 0.809069i 0.532178 0.846633i \(-0.321374\pi\)
−0.999294 + 0.0375634i \(0.988040\pi\)
\(104\) 3.83149e6i 0.0327518i
\(105\) 0 0
\(106\) 3.55619e7 0.281684
\(107\) −1.38955e8 + 8.02260e7i −1.06008 + 0.612040i −0.925456 0.378856i \(-0.876318\pi\)
−0.134629 + 0.990896i \(0.542984\pi\)
\(108\) 0 0
\(109\) −8.80822e7 + 1.52563e8i −0.623996 + 1.08079i 0.364738 + 0.931110i \(0.381159\pi\)
−0.988734 + 0.149683i \(0.952175\pi\)
\(110\) 1.97163e8 1.13832e8i 1.34665 0.777487i
\(111\) 0 0
\(112\) 3.01009e7 + 2.53261e7i 0.191297 + 0.160952i
\(113\) 1.00369e8i 0.615579i −0.951454 0.307789i \(-0.900411\pi\)
0.951454 0.307789i \(-0.0995892\pi\)
\(114\) 0 0
\(115\) 1.76063e8 3.04950e8i 1.00664 1.74356i
\(116\) −1.78684e6 1.03163e6i −0.00986855 0.00569761i
\(117\) 0 0
\(118\) −1.88990e8 −0.974791
\(119\) −1.75007e8 3.10988e7i −0.872705 0.155080i
\(120\) 0 0
\(121\) 2.25858e8 + 3.91197e8i 1.05364 + 1.82496i
\(122\) 8.56371e7 + 4.94426e7i 0.386565 + 0.223183i
\(123\) 0 0
\(124\) 1.67102e7 + 2.89429e7i 0.0706797 + 0.122421i
\(125\) 1.35136e8i 0.553517i
\(126\) 0 0
\(127\) −1.64854e8 −0.633701 −0.316850 0.948476i \(-0.602625\pi\)
−0.316850 + 0.948476i \(0.602625\pi\)
\(128\) −2.05478e7 + 1.18633e7i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 1.16696e7 2.02123e7i 0.0408585 0.0707690i
\(131\) −1.72726e8 + 9.97232e7i −0.586505 + 0.338619i −0.763714 0.645554i \(-0.776626\pi\)
0.177209 + 0.984173i \(0.443293\pi\)
\(132\) 0 0
\(133\) 7.33974e7 + 6.17545e7i 0.234571 + 0.197361i
\(134\) 3.17947e8i 0.986134i
\(135\) 0 0
\(136\) 5.36042e7 9.28452e7i 0.156691 0.271396i
\(137\) 4.44341e8 + 2.56540e8i 1.26135 + 0.728238i 0.973335 0.229389i \(-0.0736729\pi\)
0.288010 + 0.957627i \(0.407006\pi\)
\(138\) 0 0
\(139\) −1.58313e8 −0.424089 −0.212045 0.977260i \(-0.568012\pi\)
−0.212045 + 0.977260i \(0.568012\pi\)
\(140\) 8.16562e7 + 2.25282e8i 0.212558 + 0.586426i
\(141\) 0 0
\(142\) −2.28890e8 3.96449e8i −0.562955 0.975066i
\(143\) 5.91351e7 + 3.41417e7i 0.141417 + 0.0816470i
\(144\) 0 0
\(145\) −6.28409e6 1.08844e7i −0.0142158 0.0246224i
\(146\) 1.26482e8i 0.278366i
\(147\) 0 0
\(148\) −1.80266e8 −0.375723
\(149\) 3.10376e8 1.79196e8i 0.629714 0.363565i −0.150928 0.988545i \(-0.548226\pi\)
0.780641 + 0.624980i \(0.214893\pi\)
\(150\) 0 0
\(151\) 1.69312e8 2.93257e8i 0.325671 0.564079i −0.655977 0.754781i \(-0.727743\pi\)
0.981648 + 0.190702i \(0.0610763\pi\)
\(152\) −5.01033e7 + 2.89271e7i −0.0938624 + 0.0541915i
\(153\) 0 0
\(154\) −6.59105e8 + 2.38901e8i −1.17185 + 0.424752i
\(155\) 2.03577e8i 0.352698i
\(156\) 0 0
\(157\) −2.32041e8 + 4.01907e8i −0.381915 + 0.661495i −0.991336 0.131351i \(-0.958068\pi\)
0.609421 + 0.792847i \(0.291402\pi\)
\(158\) 6.57447e8 + 3.79577e8i 1.05495 + 0.609077i
\(159\) 0 0
\(160\) −1.44528e8 −0.220532
\(161\) −6.98100e8 + 8.29717e8i −1.03900 + 1.23489i
\(162\) 0 0
\(163\) 1.56909e7 + 2.71775e7i 0.0222279 + 0.0384998i 0.876925 0.480627i \(-0.159591\pi\)
−0.854698 + 0.519126i \(0.826257\pi\)
\(164\) 1.69483e8 + 9.78509e7i 0.234288 + 0.135266i
\(165\) 0 0
\(166\) −2.62738e8 4.55076e8i −0.346012 0.599310i
\(167\) 1.40833e9i 1.81067i 0.424700 + 0.905334i \(0.360380\pi\)
−0.424700 + 0.905334i \(0.639620\pi\)
\(168\) 0 0
\(169\) −8.08731e8 −0.991419
\(170\) 5.65558e8 3.26525e8i 0.677145 0.390950i
\(171\) 0 0
\(172\) −1.04566e8 + 1.81113e8i −0.119475 + 0.206936i
\(173\) −7.55605e8 + 4.36249e8i −0.843549 + 0.487023i −0.858469 0.512865i \(-0.828584\pi\)
0.0149198 + 0.999889i \(0.495251\pi\)
\(174\) 0 0
\(175\) −9.12858e7 + 5.13707e8i −0.0973310 + 0.547725i
\(176\) 4.22845e8i 0.440687i
\(177\) 0 0
\(178\) −2.18780e8 + 3.78938e8i −0.217935 + 0.377475i
\(179\) −8.41666e8 4.85936e8i −0.819838 0.473333i 0.0305229 0.999534i \(-0.490283\pi\)
−0.850360 + 0.526201i \(0.823616\pi\)
\(180\) 0 0
\(181\) −1.54973e9 −1.44392 −0.721958 0.691937i \(-0.756758\pi\)
−0.721958 + 0.691937i \(0.756758\pi\)
\(182\) −4.62707e7 + 5.49944e7i −0.0421716 + 0.0501225i
\(183\) 0 0
\(184\) −3.27005e8 5.66390e8i −0.285288 0.494133i
\(185\) −9.50961e8 5.49037e8i −0.811850 0.468722i
\(186\) 0 0
\(187\) 9.55312e8 + 1.65465e9i 0.781230 + 1.35313i
\(188\) 1.18729e9i 0.950443i
\(189\) 0 0
\(190\) −3.52414e8 −0.270420
\(191\) −2.28740e8 + 1.32063e8i −0.171873 + 0.0992312i −0.583469 0.812135i \(-0.698305\pi\)
0.411595 + 0.911367i \(0.364972\pi\)
\(192\) 0 0
\(193\) −7.73659e7 + 1.34002e8i −0.0557597 + 0.0965787i −0.892558 0.450933i \(-0.851091\pi\)
0.836798 + 0.547511i \(0.184425\pi\)
\(194\) 9.36915e8 5.40928e8i 0.661444 0.381885i
\(195\) 0 0
\(196\) −1.26198e8 7.27023e8i −0.0855124 0.492633i
\(197\) 2.10067e9i 1.39474i 0.716712 + 0.697369i \(0.245646\pi\)
−0.716712 + 0.697369i \(0.754354\pi\)
\(198\) 0 0
\(199\) −1.13927e9 + 1.97327e9i −0.726464 + 1.25827i 0.231904 + 0.972739i \(0.425504\pi\)
−0.958368 + 0.285534i \(0.907829\pi\)
\(200\) −2.72533e8 1.57347e8i −0.170333 0.0983420i
\(201\) 0 0
\(202\) 1.76706e9 1.06132
\(203\) 1.31885e7 + 3.63859e7i 0.00776627 + 0.0214264i
\(204\) 0 0
\(205\) 5.96050e8 + 1.03239e9i 0.337495 + 0.584558i
\(206\) −1.03024e9 5.94811e8i −0.572098 0.330301i
\(207\) 0 0
\(208\) −2.16742e7 3.75408e7i −0.0115795 0.0200563i
\(209\) 1.03106e9i 0.540377i
\(210\) 0 0
\(211\) 3.13704e9 1.58267 0.791335 0.611383i \(-0.209387\pi\)
0.791335 + 0.611383i \(0.209387\pi\)
\(212\) 3.48434e8 2.01169e8i 0.172495 0.0995903i
\(213\) 0 0
\(214\) −9.07653e8 + 1.57210e9i −0.432778 + 0.749593i
\(215\) −1.10323e9 + 6.36952e8i −0.516314 + 0.298094i
\(216\) 0 0
\(217\) 1.09681e8 6.17224e8i 0.0494643 0.278358i
\(218\) 1.99307e9i 0.882464i
\(219\) 0 0
\(220\) 1.28786e9 2.23064e9i 0.549766 0.952223i
\(221\) 1.69628e8 + 9.79348e7i 0.0711097 + 0.0410552i
\(222\) 0 0
\(223\) −4.46779e9 −1.80665 −0.903323 0.428961i \(-0.858880\pi\)
−0.903323 + 0.428961i \(0.858880\pi\)
\(224\) 4.38194e8 + 7.78672e7i 0.174050 + 0.0309287i
\(225\) 0 0
\(226\) −5.67770e8 9.83407e8i −0.217640 0.376964i
\(227\) 2.67606e9 + 1.54503e9i 1.00784 + 0.581879i 0.910559 0.413378i \(-0.135651\pi\)
0.0972837 + 0.995257i \(0.468985\pi\)
\(228\) 0 0
\(229\) −1.00286e9 1.73700e9i −0.364668 0.631623i 0.624055 0.781380i \(-0.285484\pi\)
−0.988723 + 0.149757i \(0.952151\pi\)
\(230\) 3.98384e9i 1.42361i
\(231\) 0 0
\(232\) −2.33432e7 −0.00805764
\(233\) 2.53529e9 1.46375e9i 0.860210 0.496642i −0.00387268 0.999993i \(-0.501233\pi\)
0.864083 + 0.503350i \(0.167899\pi\)
\(234\) 0 0
\(235\) 3.61614e9 6.26333e9i 1.18570 2.05369i
\(236\) −1.85172e9 + 1.06909e9i −0.596935 + 0.344641i
\(237\) 0 0
\(238\) −1.89063e9 + 6.85284e8i −0.589249 + 0.213581i
\(239\) 1.79081e9i 0.548855i 0.961608 + 0.274427i \(0.0884883\pi\)
−0.961608 + 0.274427i \(0.911512\pi\)
\(240\) 0 0
\(241\) 1.40746e9 2.43779e9i 0.417222 0.722650i −0.578437 0.815727i \(-0.696337\pi\)
0.995659 + 0.0930775i \(0.0296704\pi\)
\(242\) 4.42589e9 + 2.55529e9i 1.29044 + 0.745038i
\(243\) 0 0
\(244\) 1.11876e9 0.315629
\(245\) 1.54856e9 4.21964e9i 0.429798 1.17114i
\(246\) 0 0
\(247\) −5.28498e7 9.15386e7i −0.0141989 0.0245933i
\(248\) 3.27452e8 + 1.89054e8i 0.0865647 + 0.0499781i
\(249\) 0 0
\(250\) 7.64445e8 + 1.32406e9i 0.195698 + 0.338959i
\(251\) 7.21522e9i 1.81784i −0.416976 0.908918i \(-0.636910\pi\)
0.416976 0.908918i \(-0.363090\pi\)
\(252\) 0 0
\(253\) 1.16555e10 2.84478
\(254\) −1.61523e9 + 9.32554e8i −0.388061 + 0.224047i
\(255\) 0 0
\(256\) −1.34218e8 + 2.32472e8i −0.0312500 + 0.0541266i
\(257\) −5.64972e9 + 3.26187e9i −1.29507 + 0.747711i −0.979549 0.201206i \(-0.935514\pi\)
−0.315525 + 0.948917i \(0.602181\pi\)
\(258\) 0 0
\(259\) 2.58741e9 + 2.17697e9i 0.574997 + 0.483786i
\(260\) 2.64053e8i 0.0577826i
\(261\) 0 0
\(262\) −1.12824e9 + 1.95417e9i −0.239440 + 0.414722i
\(263\) −1.34840e9 7.78501e8i −0.281836 0.162718i 0.352418 0.935843i \(-0.385359\pi\)
−0.634254 + 0.773124i \(0.718693\pi\)
\(264\) 0 0
\(265\) 2.45080e9 0.496964
\(266\) 1.06848e9 + 1.89869e8i 0.213423 + 0.0379252i
\(267\) 0 0
\(268\) −1.79858e9 3.11523e9i −0.348651 0.603881i
\(269\) −2.73106e9 1.57678e9i −0.521581 0.301135i 0.216000 0.976393i \(-0.430699\pi\)
−0.737581 + 0.675258i \(0.764032\pi\)
\(270\) 0 0
\(271\) 5.86553e8 + 1.01594e9i 0.108750 + 0.188361i 0.915264 0.402854i \(-0.131982\pi\)
−0.806514 + 0.591215i \(0.798648\pi\)
\(272\) 1.21292e9i 0.221594i
\(273\) 0 0
\(274\) 5.80484e9 1.02988
\(275\) 4.85698e9 2.80418e9i 0.849249 0.490314i
\(276\) 0 0
\(277\) 1.24447e9 2.15548e9i 0.211380 0.366121i −0.740767 0.671762i \(-0.765538\pi\)
0.952147 + 0.305641i \(0.0988709\pi\)
\(278\) −1.55114e9 + 8.95553e8i −0.259701 + 0.149938i
\(279\) 0 0
\(280\) 2.07445e9 + 1.74538e9i 0.337498 + 0.283961i
\(281\) 3.91158e9i 0.627375i −0.949526 0.313688i \(-0.898436\pi\)
0.949526 0.313688i \(-0.101564\pi\)
\(282\) 0 0
\(283\) −3.37066e9 + 5.83815e9i −0.525495 + 0.910184i 0.474064 + 0.880490i \(0.342787\pi\)
−0.999559 + 0.0296938i \(0.990547\pi\)
\(284\) −4.48531e9 2.58960e9i −0.689476 0.398069i
\(285\) 0 0
\(286\) 7.72538e8 0.115466
\(287\) −1.25094e9 3.45122e9i −0.184378 0.508681i
\(288\) 0 0
\(289\) −7.47580e8 1.29485e9i −0.107168 0.185621i
\(290\) −1.23143e8 7.10964e7i −0.0174107 0.0100521i
\(291\) 0 0
\(292\) −7.15488e8 1.23926e9i −0.0984172 0.170464i
\(293\) 2.94512e7i 0.00399607i −0.999998 0.00199803i \(-0.999364\pi\)
0.999998 0.00199803i \(-0.000635994\pi\)
\(294\) 0 0
\(295\) −1.30245e10 −1.71979
\(296\) −1.76624e9 + 1.01974e9i −0.230082 + 0.132838i
\(297\) 0 0
\(298\) 2.02737e9 3.51150e9i 0.257079 0.445275i
\(299\) 1.03479e9 5.97438e8i 0.129470 0.0747495i
\(300\) 0 0
\(301\) 3.68806e9 1.33678e9i 0.449295 0.162853i
\(302\) 3.83109e9i 0.460569i
\(303\) 0 0
\(304\) −3.27273e8 + 5.66854e8i −0.0383192 + 0.0663708i
\(305\) 5.90180e9 + 3.40741e9i 0.682001 + 0.393754i
\(306\) 0 0
\(307\) 3.89847e9 0.438875 0.219438 0.975627i \(-0.429578\pi\)
0.219438 + 0.975627i \(0.429578\pi\)
\(308\) −5.10645e9 + 6.06920e9i −0.567435 + 0.674417i
\(309\) 0 0
\(310\) 1.15161e9 + 1.99464e9i 0.124697 + 0.215982i
\(311\) 3.80983e9 + 2.19960e9i 0.407252 + 0.235127i 0.689608 0.724182i \(-0.257783\pi\)
−0.282356 + 0.959310i \(0.591116\pi\)
\(312\) 0 0
\(313\) −2.94059e9 5.09325e9i −0.306377 0.530661i 0.671190 0.741286i \(-0.265784\pi\)
−0.977567 + 0.210625i \(0.932450\pi\)
\(314\) 5.25049e9i 0.540109i
\(315\) 0 0
\(316\) 8.58885e9 0.861364
\(317\) 9.34717e9 5.39659e9i 0.925643 0.534420i 0.0402117 0.999191i \(-0.487197\pi\)
0.885431 + 0.464771i \(0.153863\pi\)
\(318\) 0 0
\(319\) 2.08006e8 3.60277e8i 0.0200869 0.0347916i
\(320\) −1.41608e9 + 8.17575e8i −0.135048 + 0.0779700i
\(321\) 0 0
\(322\) −2.14637e9 + 1.20786e10i −0.199655 + 1.12355i
\(323\) 2.95757e9i 0.271722i
\(324\) 0 0
\(325\) 2.87473e8 4.97918e8i 0.0257670 0.0446297i
\(326\) 3.07478e8 + 1.77522e8i 0.0272235 + 0.0157175i
\(327\) 0 0
\(328\) 2.21411e9 0.191295
\(329\) −1.43382e10 + 1.70415e10i −1.22380 + 1.45453i
\(330\) 0 0
\(331\) −3.47821e9 6.02443e9i −0.289763 0.501885i 0.683990 0.729492i \(-0.260243\pi\)
−0.973753 + 0.227607i \(0.926910\pi\)
\(332\) −5.14860e9 2.97254e9i −0.423776 0.244667i
\(333\) 0 0
\(334\) 7.96672e9 + 1.37988e10i 0.640168 + 1.10880i
\(335\) 2.19118e10i 1.73980i
\(336\) 0 0
\(337\) −1.06229e10 −0.823612 −0.411806 0.911272i \(-0.635102\pi\)
−0.411806 + 0.911272i \(0.635102\pi\)
\(338\) −7.92391e9 + 4.57487e9i −0.607117 + 0.350519i
\(339\) 0 0
\(340\) 3.69421e9 6.39856e9i 0.276443 0.478814i
\(341\) −5.83571e9 + 3.36925e9i −0.431595 + 0.249181i
\(342\) 0 0
\(343\) −6.96847e9 + 1.19592e10i −0.503456 + 0.864021i
\(344\) 2.36605e9i 0.168963i
\(345\) 0 0
\(346\) −4.93559e9 + 8.54870e9i −0.344378 + 0.596479i
\(347\) 3.30767e9 + 1.90969e9i 0.228142 + 0.131718i 0.609714 0.792621i \(-0.291284\pi\)
−0.381573 + 0.924339i \(0.624617\pi\)
\(348\) 0 0
\(349\) −2.32842e10 −1.56950 −0.784748 0.619815i \(-0.787208\pi\)
−0.784748 + 0.619815i \(0.787208\pi\)
\(350\) 2.01155e9 + 5.54967e9i 0.134047 + 0.369824i
\(351\) 0 0
\(352\) −2.39197e9 4.14302e9i −0.155807 0.269865i
\(353\) 2.16865e10 + 1.25207e10i 1.39666 + 0.806362i 0.994041 0.109005i \(-0.0347666\pi\)
0.402619 + 0.915368i \(0.368100\pi\)
\(354\) 0 0
\(355\) −1.57743e10 2.73218e10i −0.993198 1.72027i
\(356\) 4.95043e9i 0.308207i
\(357\) 0 0
\(358\) −1.09955e10 −0.669395
\(359\) 1.61578e9 9.32869e8i 0.0972755 0.0561620i −0.450573 0.892740i \(-0.648780\pi\)
0.547849 + 0.836578i \(0.315447\pi\)
\(360\) 0 0
\(361\) 7.69377e9 1.33260e10i 0.453013 0.784641i
\(362\) −1.51842e10 + 8.76660e9i −0.884215 + 0.510502i
\(363\) 0 0
\(364\) −1.42263e8 + 8.00579e8i −0.00810377 + 0.0456036i
\(365\) 8.71666e9i 0.491110i
\(366\) 0 0
\(367\) −1.42157e10 + 2.46223e10i −0.783616 + 1.35726i 0.146206 + 0.989254i \(0.453294\pi\)
−0.929822 + 0.368009i \(0.880040\pi\)
\(368\) −6.40797e9 3.69964e9i −0.349405 0.201729i
\(369\) 0 0
\(370\) −1.24233e10 −0.662872
\(371\) −7.43056e9 1.32041e9i −0.392217 0.0696970i
\(372\) 0 0
\(373\) 1.45252e10 + 2.51585e10i 0.750392 + 1.29972i 0.947633 + 0.319362i \(0.103469\pi\)
−0.197241 + 0.980355i \(0.563198\pi\)
\(374\) 1.87202e10 + 1.08081e10i 0.956807 + 0.552413i
\(375\) 0 0
\(376\) −6.71634e9 1.16330e10i −0.336032 0.582025i
\(377\) 4.26479e7i 0.00211122i
\(378\) 0 0
\(379\) 1.73844e9 0.0842562 0.0421281 0.999112i \(-0.486586\pi\)
0.0421281 + 0.999112i \(0.486586\pi\)
\(380\) −3.45294e9 + 1.99355e9i −0.165598 + 0.0956079i
\(381\) 0 0
\(382\) −1.49412e9 + 2.58790e9i −0.0701671 + 0.121533i
\(383\) −1.46545e10 + 8.46078e9i −0.681046 + 0.393202i −0.800249 0.599668i \(-0.795299\pi\)
0.119203 + 0.992870i \(0.461966\pi\)
\(384\) 0 0
\(385\) −4.54231e10 + 1.64642e10i −2.06745 + 0.749372i
\(386\) 1.75059e9i 0.0788561i
\(387\) 0 0
\(388\) 6.11990e9 1.06000e10i 0.270033 0.467712i
\(389\) 2.16794e10 + 1.25166e10i 0.946778 + 0.546623i 0.892079 0.451880i \(-0.149247\pi\)
0.0546996 + 0.998503i \(0.482580\pi\)
\(390\) 0 0
\(391\) 3.34337e10 1.43046
\(392\) −5.34915e9 6.40946e9i −0.226538 0.271442i
\(393\) 0 0
\(394\) 1.18832e10 + 2.05823e10i 0.493114 + 0.854099i
\(395\) 4.53089e10 + 2.61591e10i 1.86121 + 1.07457i
\(396\) 0 0
\(397\) −2.48881e9 4.31075e9i −0.100191 0.173536i 0.811572 0.584252i \(-0.198612\pi\)
−0.911763 + 0.410716i \(0.865279\pi\)
\(398\) 2.57787e10i 1.02738i
\(399\) 0 0
\(400\) −3.56036e9 −0.139077
\(401\) −1.60657e10 + 9.27552e9i −0.621329 + 0.358724i −0.777386 0.629024i \(-0.783455\pi\)
0.156057 + 0.987748i \(0.450122\pi\)
\(402\) 0 0
\(403\) −3.45402e8 + 5.98254e8i −0.0130950 + 0.0226812i
\(404\) 1.73136e10 9.99603e9i 0.649924 0.375234i
\(405\) 0 0
\(406\) 3.35050e8 + 2.81902e8i 0.0123312 + 0.0103751i
\(407\) 3.63468e10i 1.32461i
\(408\) 0 0
\(409\) 2.58593e10 4.47897e10i 0.924111 1.60061i 0.131126 0.991366i \(-0.458141\pi\)
0.792985 0.609241i \(-0.208526\pi\)
\(410\) 1.16801e10 + 6.74353e9i 0.413345 + 0.238645i
\(411\) 0 0
\(412\) −1.34590e10 −0.467116
\(413\) 3.94890e10 + 7.01721e9i 1.35730 + 0.241193i
\(414\) 0 0
\(415\) −1.81070e10 3.13622e10i −0.610455 1.05734i
\(416\) −4.24726e8 2.45216e8i −0.0141819 0.00818794i
\(417\) 0 0
\(418\) −5.83253e9 1.01022e10i −0.191052 0.330912i
\(419\) 1.89186e9i 0.0613808i −0.999529 0.0306904i \(-0.990229\pi\)
0.999529 0.0306904i \(-0.00977059\pi\)
\(420\) 0 0
\(421\) 5.72596e10 1.82272 0.911361 0.411609i \(-0.135033\pi\)
0.911361 + 0.411609i \(0.135033\pi\)
\(422\) 3.07366e10 1.77458e10i 0.969183 0.559558i
\(423\) 0 0
\(424\) 2.27596e9 3.94209e9i 0.0704210 0.121973i
\(425\) 1.39322e10 8.04374e9i 0.427034 0.246548i
\(426\) 0 0
\(427\) −1.60578e10 1.35106e10i −0.483031 0.406408i
\(428\) 2.05378e10i 0.612040i
\(429\) 0 0
\(430\) −7.20629e9 + 1.24817e10i −0.210784 + 0.365089i
\(431\) −2.34325e10 1.35288e10i −0.679062 0.392057i 0.120439 0.992721i \(-0.461570\pi\)
−0.799502 + 0.600664i \(0.794903\pi\)
\(432\) 0 0
\(433\) −3.99631e10 −1.13686 −0.568431 0.822731i \(-0.692449\pi\)
−0.568431 + 0.822731i \(0.692449\pi\)
\(434\) −2.41690e9 6.66799e9i −0.0681239 0.187947i
\(435\) 0 0
\(436\) 1.12745e10 + 1.95280e10i 0.311998 + 0.540397i
\(437\) −1.56250e10 9.02112e9i −0.428445 0.247363i
\(438\) 0 0
\(439\) −1.50184e10 2.60126e10i −0.404358 0.700368i 0.589889 0.807485i \(-0.299172\pi\)
−0.994246 + 0.107116i \(0.965838\pi\)
\(440\) 2.91410e10i 0.777487i
\(441\) 0 0
\(442\) 2.21601e9 0.0580608
\(443\) −3.55301e10 + 2.05133e10i −0.922531 + 0.532624i −0.884442 0.466651i \(-0.845460\pi\)
−0.0380893 + 0.999274i \(0.512127\pi\)
\(444\) 0 0
\(445\) −1.50775e10 + 2.61151e10i −0.384495 + 0.665965i
\(446\) −4.37752e10 + 2.52736e10i −1.10634 + 0.638746i
\(447\) 0 0
\(448\) 4.73389e9 1.71586e9i 0.117518 0.0425961i
\(449\) 6.29285e9i 0.154832i 0.996999 + 0.0774162i \(0.0246670\pi\)
−0.996999 + 0.0774162i \(0.975333\pi\)
\(450\) 0 0
\(451\) −1.97295e10 + 3.41725e10i −0.476881 + 0.825982i
\(452\) −1.11260e10 6.42359e9i −0.266554 0.153895i
\(453\) 0 0
\(454\) 3.49599e10 0.822901
\(455\) −3.18881e9 + 3.79002e9i −0.0744017 + 0.0884291i
\(456\) 0 0
\(457\) 2.44547e10 + 4.23568e10i 0.560658 + 0.971088i 0.997439 + 0.0715201i \(0.0227850\pi\)
−0.436781 + 0.899568i \(0.643882\pi\)
\(458\) −1.96519e10 1.13460e10i −0.446625 0.257859i
\(459\) 0 0
\(460\) −2.25360e10 3.90335e10i −0.503322 0.871780i
\(461\) 3.67947e10i 0.814670i 0.913279 + 0.407335i \(0.133542\pi\)
−0.913279 + 0.407335i \(0.866458\pi\)
\(462\) 0 0
\(463\) 6.59669e10 1.43550 0.717748 0.696303i \(-0.245173\pi\)
0.717748 + 0.696303i \(0.245173\pi\)
\(464\) −2.28715e8 + 1.32049e8i −0.00493428 + 0.00284881i
\(465\) 0 0
\(466\) 1.65605e10 2.86836e10i 0.351179 0.608260i
\(467\) −3.96405e10 + 2.28865e10i −0.833435 + 0.481184i −0.855027 0.518583i \(-0.826460\pi\)
0.0215925 + 0.999767i \(0.493126\pi\)
\(468\) 0 0
\(469\) −1.18054e10 + 6.64342e10i −0.243999 + 1.37309i
\(470\) 8.18239e10i 1.67683i
\(471\) 0 0
\(472\) −1.20954e10 + 2.09498e10i −0.243698 + 0.422097i
\(473\) −3.65175e10 2.10834e10i −0.729553 0.421208i
\(474\) 0 0
\(475\) −8.68149e9 −0.170538
\(476\) −1.46478e10 + 1.74094e10i −0.285328 + 0.339122i
\(477\) 0 0
\(478\) 1.01303e10 + 1.75463e10i 0.194049 + 0.336103i
\(479\) −7.57248e10 4.37197e10i −1.43845 0.830491i −0.440711 0.897649i \(-0.645274\pi\)
−0.997742 + 0.0671575i \(0.978607\pi\)
\(480\) 0 0
\(481\) −1.86306e9 3.22692e9i −0.0348054 0.0602848i
\(482\) 3.18471e10i 0.590041i
\(483\) 0 0
\(484\) 5.78196e10 1.05364
\(485\) 6.45688e10 3.72788e10i 1.16696 0.673744i
\(486\) 0 0
\(487\) 1.25118e10 2.16712e10i 0.222436 0.385271i −0.733111 0.680109i \(-0.761932\pi\)
0.955547 + 0.294838i \(0.0952657\pi\)
\(488\) 1.09615e10 6.32865e9i 0.193283 0.111592i
\(489\) 0 0
\(490\) −8.69713e9 5.01038e10i −0.150866 0.869133i
\(491\) 4.17596e10i 0.718507i −0.933240 0.359253i \(-0.883031\pi\)
0.933240 0.359253i \(-0.116969\pi\)
\(492\) 0 0
\(493\) 5.96663e8 1.03345e9i 0.0101005 0.0174945i
\(494\) −1.03564e9 5.97928e8i −0.0173901 0.0100402i
\(495\) 0 0
\(496\) 4.27781e9 0.0706797
\(497\) 3.31058e10 + 9.13356e10i 0.542598 + 1.49697i
\(498\) 0 0
\(499\) −6.67262e9 1.15573e10i −0.107620 0.186404i 0.807185 0.590298i \(-0.200990\pi\)
−0.914806 + 0.403894i \(0.867656\pi\)
\(500\) 1.49800e10 + 8.64870e9i 0.239680 + 0.138379i
\(501\) 0 0
\(502\) −4.08154e10 7.06944e10i −0.642702 1.11319i
\(503\) 8.73433e10i 1.36445i −0.731143 0.682225i \(-0.761013\pi\)
0.731143 0.682225i \(-0.238987\pi\)
\(504\) 0 0
\(505\) 1.21780e11 1.87245
\(506\) 1.14200e11 6.59335e10i 1.74207 1.00578i
\(507\) 0 0
\(508\) −1.05506e10 + 1.82743e10i −0.158425 + 0.274400i
\(509\) −7.12548e10 + 4.11390e10i −1.06156 + 0.612889i −0.925862 0.377861i \(-0.876660\pi\)
−0.135694 + 0.990751i \(0.543326\pi\)
\(510\) 0 0
\(511\) −4.69626e9 + 2.64280e10i −0.0688761 + 0.387597i
\(512\) 3.03700e9i 0.0441942i
\(513\) 0 0
\(514\) −3.69038e10 + 6.39193e10i −0.528712 + 0.915756i
\(515\) −7.10006e10 4.09922e10i −1.00933 0.582737i
\(516\) 0 0
\(517\) 2.39392e11 3.35079
\(518\) 3.76661e10 + 6.69328e9i 0.523156 + 0.0929651i
\(519\) 0 0
\(520\) −1.49371e9 2.58718e9i −0.0204292 0.0353845i
\(521\) −6.46157e10 3.73059e10i −0.876975 0.506322i −0.00731548 0.999973i \(-0.502329\pi\)
−0.869660 + 0.493651i \(0.835662\pi\)
\(522\) 0 0
\(523\) −2.98505e9 5.17026e9i −0.0398975 0.0691044i 0.845387 0.534154i \(-0.179370\pi\)
−0.885285 + 0.465050i \(0.846036\pi\)
\(524\) 2.55291e10i 0.338619i
\(525\) 0 0
\(526\) −1.76155e10 −0.230118
\(527\) −1.67396e10 + 9.66464e9i −0.217022 + 0.125298i
\(528\) 0 0
\(529\) 6.28233e10 1.08813e11i 0.802228 1.38950i
\(530\) 2.40128e10 1.38638e10i 0.304327 0.175703i
\(531\) 0 0
\(532\) 1.15430e10 4.18391e9i 0.144103 0.0522319i
\(533\) 4.04518e9i 0.0501221i
\(534\) 0 0
\(535\) −6.25522e10 + 1.08344e11i −0.763532 + 1.32248i
\(536\) −3.52449e10 2.03486e10i −0.427009 0.246534i
\(537\) 0 0
\(538\) −3.56784e10 −0.425869
\(539\) 1.46588e11 2.54451e10i 1.73678 0.301474i
\(540\) 0 0
\(541\) 2.29828e10 + 3.98074e10i 0.268296 + 0.464702i 0.968422 0.249317i \(-0.0802062\pi\)
−0.700126 + 0.714019i \(0.746873\pi\)
\(542\) 1.14940e10 + 6.63609e9i 0.133191 + 0.0768980i
\(543\) 0 0
\(544\) −6.86134e9 1.18842e10i −0.0783454 0.135698i
\(545\) 1.37355e11i 1.55690i
\(546\) 0 0
\(547\) 7.80036e10 0.871295 0.435648 0.900117i \(-0.356519\pi\)
0.435648 + 0.900117i \(0.356519\pi\)
\(548\) 5.68756e10 3.28372e10i 0.630673 0.364119i
\(549\) 0 0
\(550\) 3.17256e10 5.49504e10i 0.346705 0.600510i
\(551\) −5.57694e8 + 3.21985e8i −0.00605048 + 0.00349324i
\(552\) 0 0
\(553\) −1.23278e11 1.03723e11i −1.31821 1.10910i
\(554\) 2.81591e10i 0.298937i
\(555\) 0 0
\(556\) −1.01320e10 + 1.75492e10i −0.106022 + 0.183636i
\(557\) −6.47127e10 3.73619e10i −0.672308 0.388157i 0.124642 0.992202i \(-0.460222\pi\)
−0.796951 + 0.604044i \(0.793555\pi\)
\(558\) 0 0
\(559\) −4.32278e9 −0.0442706
\(560\) 3.01987e10 + 5.36632e9i 0.307069 + 0.0545663i
\(561\) 0 0
\(562\) −2.21273e10 3.83255e10i −0.221811 0.384187i
\(563\) 8.31674e10 + 4.80167e10i 0.827789 + 0.477924i 0.853095 0.521755i \(-0.174723\pi\)
−0.0253059 + 0.999680i \(0.508056\pi\)
\(564\) 0 0
\(565\) −3.91287e10 6.77728e10i −0.383974 0.665062i
\(566\) 7.62692e10i 0.743162i
\(567\) 0 0
\(568\) −5.85959e10 −0.562955
\(569\) −5.54903e10 + 3.20374e10i −0.529381 + 0.305638i −0.740764 0.671765i \(-0.765536\pi\)
0.211383 + 0.977403i \(0.432203\pi\)
\(570\) 0 0
\(571\) −6.16135e10 + 1.06718e11i −0.579604 + 1.00390i 0.415920 + 0.909401i \(0.363460\pi\)
−0.995525 + 0.0945029i \(0.969874\pi\)
\(572\) 7.56929e9 4.37013e9i 0.0707084 0.0408235i
\(573\) 0 0
\(574\) −3.17797e10 2.67386e10i −0.292754 0.246315i
\(575\) 9.81395e10i 0.897785i
\(576\) 0 0
\(577\) 2.48192e10 4.29881e10i 0.223916 0.387834i −0.732078 0.681221i \(-0.761449\pi\)
0.955994 + 0.293387i \(0.0947826\pi\)
\(578\) −1.46495e10 8.45790e9i −0.131254 0.0757794i
\(579\) 0 0
\(580\) −1.60873e9 −0.0142158
\(581\) 3.80014e10 + 1.04842e11i 0.333500 + 0.920093i
\(582\) 0 0
\(583\) 4.05613e10 + 7.02542e10i 0.351106 + 0.608133i
\(584\) −1.40206e10 8.09482e9i −0.120536 0.0695915i
\(585\) 0 0
\(586\) −1.66601e8 2.88562e8i −0.00141282 0.00244708i
\(587\) 7.25661e10i 0.611198i −0.952160 0.305599i \(-0.901143\pi\)
0.952160 0.305599i \(-0.0988566\pi\)
\(588\) 0 0
\(589\) 1.04309e10 0.0866685
\(590\) −1.27614e11 + 7.36779e10i −1.05315 + 0.608036i
\(591\) 0 0
\(592\) −1.15370e10 + 1.99827e10i −0.0939307 + 0.162693i
\(593\) −1.49261e11 + 8.61757e10i −1.20705 + 0.696893i −0.962115 0.272645i \(-0.912102\pi\)
−0.244940 + 0.969538i \(0.578768\pi\)
\(594\) 0 0
\(595\) −1.30296e11 + 4.72273e10i −1.03959 + 0.376812i
\(596\) 4.58741e10i 0.363565i
\(597\) 0 0
\(598\) 6.75924e9 1.17074e10i 0.0528559 0.0915491i
\(599\) −8.64440e10 4.99085e10i −0.671472 0.387674i 0.125162 0.992136i \(-0.460055\pi\)
−0.796634 + 0.604462i \(0.793388\pi\)
\(600\) 0 0
\(601\) −1.58869e10 −0.121770 −0.0608850 0.998145i \(-0.519392\pi\)
−0.0608850 + 0.998145i \(0.519392\pi\)
\(602\) 2.85734e10 3.39605e10i 0.217559 0.258576i
\(603\) 0 0
\(604\) −2.16719e10 3.75369e10i −0.162836 0.282040i
\(605\) 3.05016e11 + 1.76101e11i 2.27668 + 1.31444i
\(606\) 0 0
\(607\) −1.17901e11 2.04211e11i −0.868486 1.50426i −0.863543 0.504275i \(-0.831760\pi\)
−0.00494305 0.999988i \(-0.501573\pi\)
\(608\) 7.40535e9i 0.0541915i
\(609\) 0 0
\(610\) 7.71008e10 0.556852
\(611\) 2.12535e10 1.22707e10i 0.152499 0.0880452i
\(612\) 0 0
\(613\) 1.74582e10 3.02385e10i 0.123640 0.214150i −0.797561 0.603239i \(-0.793877\pi\)
0.921200 + 0.389089i \(0.127210\pi\)
\(614\) 3.81971e10 2.20531e10i 0.268755 0.155166i
\(615\) 0 0
\(616\) −1.57002e10 + 8.83522e10i −0.109039 + 0.613613i
\(617\) 2.41723e11i 1.66793i 0.551819 + 0.833964i \(0.313934\pi\)
−0.551819 + 0.833964i \(0.686066\pi\)
\(618\) 0 0
\(619\) −1.23409e11 + 2.13750e11i −0.840589 + 1.45594i 0.0488090 + 0.998808i \(0.484457\pi\)
−0.889398 + 0.457134i \(0.848876\pi\)
\(620\) 2.25668e10 + 1.30289e10i 0.152723 + 0.0881744i
\(621\) 0 0
\(622\) 4.97714e10 0.332520
\(623\) 5.97834e10 7.10548e10i 0.396852 0.471673i
\(624\) 0 0
\(625\) 9.51256e10 + 1.64762e11i 0.623415 + 1.07979i
\(626\) −5.76235e10 3.32689e10i −0.375234 0.216641i
\(627\) 0 0
\(628\) 2.97013e10 + 5.14441e10i 0.190957 + 0.330748i
\(629\) 1.04260e11i 0.666064i
\(630\) 0 0
\(631\) 3.28164e10 0.207002 0.103501 0.994629i \(-0.466996\pi\)
0.103501 + 0.994629i \(0.466996\pi\)
\(632\) 8.41532e10 4.85859e10i 0.527476 0.304538i
\(633\) 0 0
\(634\) 6.10555e10 1.05751e11i 0.377892 0.654528i
\(635\) −1.11316e11 + 6.42683e10i −0.684640 + 0.395277i
\(636\) 0 0
\(637\) 1.17101e10 9.77289e9i 0.0711216 0.0593561i
\(638\) 4.70664e9i 0.0284072i
\(639\) 0 0
\(640\) −9.24980e9 + 1.60211e10i −0.0551331 + 0.0954934i
\(641\) 7.20582e10 + 4.16028e10i 0.426826 + 0.246428i 0.697994 0.716104i \(-0.254076\pi\)
−0.271167 + 0.962532i \(0.587410\pi\)
\(642\) 0 0
\(643\) −2.05289e11 −1.20094 −0.600472 0.799646i \(-0.705020\pi\)
−0.600472 + 0.799646i \(0.705020\pi\)
\(644\) 4.72968e10 + 1.30487e11i 0.274972 + 0.758620i
\(645\) 0 0
\(646\) −1.67305e10 2.89781e10i −0.0960681 0.166395i
\(647\) 2.52702e11 + 1.45897e11i 1.44208 + 0.832588i 0.997989 0.0633912i \(-0.0201916\pi\)
0.444096 + 0.895979i \(0.353525\pi\)
\(648\) 0 0
\(649\) −2.15559e11 3.73359e11i −1.21503 2.10450i
\(650\) 6.50477e9i 0.0364400i
\(651\) 0 0
\(652\) 4.01687e9 0.0222279
\(653\) −2.34842e11 + 1.35586e11i −1.29158 + 0.745697i −0.978935 0.204172i \(-0.934550\pi\)
−0.312650 + 0.949868i \(0.601217\pi\)
\(654\) 0 0
\(655\) −7.77542e10 + 1.34674e11i −0.422434 + 0.731677i
\(656\) 2.16938e10 1.25249e10i 0.117144 0.0676331i
\(657\) 0 0
\(658\) −4.40841e10 + 2.48081e11i −0.235168 + 1.32340i
\(659\) 3.60700e11i 1.91251i −0.292529 0.956257i \(-0.594497\pi\)
0.292529 0.956257i \(-0.405503\pi\)
\(660\) 0 0
\(661\) −8.46973e10 + 1.46700e11i −0.443674 + 0.768465i −0.997959 0.0638616i \(-0.979658\pi\)
0.554285 + 0.832327i \(0.312992\pi\)
\(662\) −6.81587e10 3.93514e10i −0.354886 0.204894i
\(663\) 0 0
\(664\) −6.72610e10 −0.346012
\(665\) 7.36359e10 + 1.30851e10i 0.376533 + 0.0669100i
\(666\) 0 0
\(667\) −3.63986e9 6.30442e9i −0.0183900 0.0318524i
\(668\) 1.56115e11 + 9.01332e10i 0.784042 + 0.452667i
\(669\) 0 0
\(670\) −1.23952e11 2.14691e11i −0.615111 1.06540i
\(671\) 2.25573e11i 1.11275i
\(672\) 0 0
\(673\) −1.16293e11 −0.566885 −0.283442 0.958989i \(-0.591476\pi\)
−0.283442 + 0.958989i \(0.591476\pi\)
\(674\) −1.04083e11 + 6.00921e10i −0.504357 + 0.291191i
\(675\) 0 0
\(676\) −5.17588e10 + 8.96488e10i −0.247855 + 0.429297i
\(677\) 1.79007e10 1.03350e10i 0.0852150 0.0491989i −0.456787 0.889576i \(-0.651000\pi\)
0.542002 + 0.840377i \(0.317667\pi\)
\(678\) 0 0
\(679\) −2.15850e11 + 7.82377e10i −1.01548 + 0.368076i
\(680\) 8.35904e10i 0.390950i
\(681\) 0 0
\(682\) −3.81187e10 + 6.60235e10i −0.176198 + 0.305184i
\(683\) −1.75494e11 1.01321e11i −0.806452 0.465605i 0.0392701 0.999229i \(-0.487497\pi\)
−0.845722 + 0.533623i \(0.820830\pi\)
\(684\) 0 0
\(685\) 4.00049e11 1.81698
\(686\) −6.25575e8 + 1.56595e11i −0.00282477 + 0.707101i
\(687\) 0 0
\(688\) 1.33844e10 + 2.31825e10i 0.0597373 + 0.103468i
\(689\) 7.20219e9 + 4.15818e9i 0.0319586 + 0.0184513i
\(690\) 0 0
\(691\) −8.23091e10 1.42564e11i −0.361024 0.625311i 0.627106 0.778934i \(-0.284239\pi\)
−0.988130 + 0.153623i \(0.950906\pi\)
\(692\) 1.11680e11i 0.487023i
\(693\) 0 0
\(694\) 4.32113e10 0.186277
\(695\) −1.06899e11 + 6.17183e10i −0.458179 + 0.264530i
\(696\) 0 0
\(697\) −5.65938e10 + 9.80234e10i −0.239794 + 0.415335i
\(698\) −2.28138e11 + 1.31716e11i −0.961116 + 0.554901i
\(699\) 0 0
\(700\) 5.11027e10 + 4.29964e10i 0.212839 + 0.179077i
\(701\) 2.11004e11i 0.873814i −0.899507 0.436907i \(-0.856074\pi\)
0.899507 0.436907i \(-0.143926\pi\)
\(702\) 0 0
\(703\) −2.81316e10 + 4.87254e10i −0.115179 + 0.199496i
\(704\) −4.68729e10 2.70621e10i −0.190823 0.110172i
\(705\) 0 0
\(706\) 2.83311e11 1.14037
\(707\) −3.69223e11 6.56110e10i −1.47778 0.262603i
\(708\) 0 0
\(709\) 1.64436e11 + 2.84812e11i 0.650748 + 1.12713i 0.982942 + 0.183917i \(0.0588778\pi\)
−0.332194 + 0.943211i \(0.607789\pi\)
\(710\) −3.09111e11 1.78466e11i −1.21641 0.702297i
\(711\) 0 0
\(712\) 2.80039e10 + 4.85041e10i 0.108968 + 0.188738i
\(713\) 1.17916e11i 0.456261i
\(714\) 0 0
\(715\) 5.32405e10 0.203713
\(716\) −1.07733e11 + 6.21998e10i −0.409919 + 0.236667i
\(717\) 0 0
\(718\) 1.05542e10 1.82804e10i 0.0397125 0.0687841i
\(719\) 2.84195e11 1.64080e11i 1.06341 0.613960i 0.137036 0.990566i \(-0.456242\pi\)
0.926374 + 0.376606i \(0.122909\pi\)
\(720\) 0 0
\(721\) 1.93181e11 + 1.62537e11i 0.714863 + 0.601466i
\(722\) 1.74090e11i 0.640656i
\(723\) 0 0
\(724\) −9.91828e10 + 1.71790e11i −0.360979 + 0.625234i
\(725\) −3.03354e9 1.75141e9i −0.0109799 0.00633923i
\(726\) 0 0
\(727\) −2.26272e11 −0.810015 −0.405007 0.914313i \(-0.632731\pi\)
−0.405007 + 0.914313i \(0.632731\pi\)
\(728\) 3.13487e9 + 8.64881e9i 0.0111608 + 0.0307915i
\(729\) 0 0
\(730\) −4.93089e10 8.54055e10i −0.173634 0.300742i
\(731\) −1.04750e11 6.04774e10i −0.366847 0.211799i
\(732\) 0 0
\(733\) −7.42855e10 1.28666e11i −0.257329 0.445706i 0.708197 0.706015i \(-0.249509\pi\)
−0.965525 + 0.260309i \(0.916176\pi\)
\(734\) 3.21664e11i 1.10820i
\(735\) 0 0
\(736\) −8.37134e10 −0.285288
\(737\) 6.28119e11 3.62645e11i 2.12898 1.22917i
\(738\) 0 0
\(739\) 2.25140e11 3.89955e11i 0.754876 1.30748i −0.190559 0.981676i \(-0.561030\pi\)
0.945436 0.325809i \(-0.105637\pi\)
\(740\) −1.21723e11 + 7.02768e10i −0.405925 + 0.234361i
\(741\) 0 0
\(742\) −8.02737e10 + 2.90963e10i −0.264824 + 0.0959890i
\(743\) 3.77594e11i 1.23900i −0.784998 0.619498i \(-0.787336\pi\)
0.784998 0.619498i \(-0.212664\pi\)
\(744\) 0 0
\(745\) 1.39719e11 2.42000e11i 0.453555 0.785580i
\(746\) 2.84636e11 + 1.64334e11i 0.919039 + 0.530607i
\(747\) 0 0
\(748\) 2.44560e11 0.781230
\(749\) 2.48024e11 2.94785e11i 0.788071 0.936651i
\(750\) 0 0
\(751\) −1.02313e11 1.77211e11i −0.321641 0.557099i 0.659186 0.751980i \(-0.270901\pi\)
−0.980827 + 0.194882i \(0.937568\pi\)
\(752\) −1.31613e11 7.59867e10i −0.411554 0.237611i
\(753\) 0 0
\(754\) −2.41253e8 4.17863e8i −0.000746427 0.00129285i
\(755\) 2.64025e11i 0.812563i
\(756\) 0 0
\(757\) −8.70658e10 −0.265133 −0.132567 0.991174i \(-0.542322\pi\)
−0.132567 + 0.991174i \(0.542322\pi\)
\(758\) 1.70331e10 9.83408e9i 0.0515962 0.0297891i
\(759\) 0 0
\(760\) −2.25545e10 + 3.90655e10i −0.0676050 + 0.117095i
\(761\) −2.84741e11 + 1.64395e11i −0.849006 + 0.490174i −0.860315 0.509762i \(-0.829733\pi\)
0.0113090 + 0.999936i \(0.496400\pi\)
\(762\) 0 0
\(763\) 7.40027e10 4.16447e11i 0.218348 1.22874i
\(764\) 3.38082e10i 0.0992312i
\(765\) 0 0
\(766\) −9.57229e10 + 1.65797e11i −0.278036 + 0.481572i
\(767\) −3.82753e10 2.20983e10i −0.110595 0.0638523i
\(768\) 0 0
\(769\) −9.18048e10 −0.262519 −0.131259 0.991348i \(-0.541902\pi\)
−0.131259 + 0.991348i \(0.541902\pi\)
\(770\) −3.51918e11 + 4.18268e11i −1.00110 + 1.18985i
\(771\) 0 0
\(772\) 9.90284e9 + 1.71522e10i 0.0278799 + 0.0482893i
\(773\) 5.47968e11 + 3.16370e11i 1.53475 + 0.886088i 0.999133 + 0.0416263i \(0.0132539\pi\)
0.535616 + 0.844462i \(0.320079\pi\)
\(774\) 0 0
\(775\) 2.83691e10 + 4.91367e10i 0.0786392 + 0.136207i
\(776\) 1.38478e11i 0.381885i
\(777\) 0 0
\(778\) 2.83218e11 0.773041
\(779\) 5.28976e10 3.05405e10i 0.143644 0.0829327i
\(780\) 0 0
\(781\) 5.22136e11 9.04365e11i 1.40339 2.43075i
\(782\) 3.27582e11 1.89129e11i 0.875976 0.505745i
\(783\) 0 0
\(784\) −8.86681e10 3.25402e10i −0.234695 0.0861304i
\(785\) 3.61845e11i 0.952892i
\(786\) 0 0
\(787\) 1.28463e11 2.22504e11i 0.334872 0.580015i −0.648589 0.761139i \(-0.724640\pi\)
0.983460 + 0.181125i \(0.0579737\pi\)
\(788\) 2.32862e11 + 1.34443e11i 0.603939 + 0.348685i
\(789\) 0 0
\(790\) 5.91913e11 1.51967
\(791\) 8.21200e10 + 2.26561e11i 0.209770 + 0.578735i
\(792\) 0 0
\(793\) 1.15624e10 + 2.00267e10i 0.0292386 + 0.0506428i
\(794\) −4.87705e10 2.81577e10i −0.122709 0.0708459i
\(795\) 0 0
\(796\) 1.45827e11 + 2.52579e11i 0.363232 + 0.629136i
\(797\) 3.19145e11i 0.790961i −0.918474 0.395480i \(-0.870578\pi\)
0.918474 0.395480i \(-0.129422\pi\)
\(798\) 0 0
\(799\) 6.86691e11 1.68490
\(800\) −3.48843e10 + 2.01404e10i −0.0851666 + 0.0491710i
\(801\) 0 0
\(802\) −1.04941e11 + 1.81762e11i −0.253656 + 0.439346i
\(803\) 2.49870e11 1.44263e11i 0.600969 0.346970i
\(804\) 0 0
\(805\) −1.47920e11 + 8.32413e11i −0.352244 + 1.98223i
\(806\) 7.81556e9i 0.0185191i
\(807\) 0 0
\(808\) 1.13092e11 1.95881e11i 0.265330 0.459566i
\(809\) −4.48871e10 2.59156e10i −0.104792 0.0605016i 0.446688 0.894690i \(-0.352603\pi\)
−0.551480 + 0.834188i \(0.685937\pi\)
\(810\) 0 0
\(811\) −4.00088e11 −0.924851 −0.462426 0.886658i \(-0.653021\pi\)
−0.462426 + 0.886658i \(0.653021\pi\)
\(812\) 4.87749e9 + 8.66731e8i 0.0112195 + 0.00199370i
\(813\) 0 0
\(814\) −2.05608e11 3.56124e11i −0.468320 0.811155i
\(815\) 2.11903e10 + 1.22342e10i 0.0480293 + 0.0277297i
\(816\) 0 0
\(817\) 3.26362e10 + 5.65276e10i 0.0732507 + 0.126874i
\(818\) 5.85130e11i 1.30689i
\(819\) 0 0
\(820\) 1.52589e11 0.337495
\(821\) −1.01508e11 + 5.86055e10i −0.223422 + 0.128993i −0.607534 0.794294i \(-0.707841\pi\)
0.384112 + 0.923287i \(0.374508\pi\)
\(822\) 0 0
\(823\) 5.46164e10 9.45984e10i 0.119048 0.206198i −0.800342 0.599543i \(-0.795349\pi\)
0.919391 + 0.393345i \(0.128682\pi\)
\(824\) −1.31871e11 + 7.61358e10i −0.286049 + 0.165151i
\(825\) 0 0
\(826\) 4.26607e11 1.54629e11i 0.916448 0.332178i
\(827\) 7.08230e11i 1.51409i −0.653362 0.757046i \(-0.726642\pi\)
0.653362 0.757046i \(-0.273358\pi\)
\(828\) 0 0
\(829\) 3.10465e10 5.37741e10i 0.0657347 0.113856i −0.831285 0.555847i \(-0.812394\pi\)
0.897020 + 0.441991i \(0.145728\pi\)
\(830\) −3.54823e11 2.04857e11i −0.747652 0.431657i
\(831\) 0 0
\(832\) −5.54860e9 −0.0115795
\(833\) 4.20487e11 7.29890e10i 0.873317 0.151592i
\(834\) 0 0
\(835\) 5.49038e11 + 9.50962e11i 1.12942 + 1.95622i
\(836\) −1.14294e11 6.59875e10i −0.233990 0.135094i
\(837\) 0 0
\(838\) −1.07020e10 1.85363e10i −0.0217014 0.0375879i
\(839\) 7.16019e11i 1.44503i −0.691356 0.722515i \(-0.742986\pi\)
0.691356 0.722515i \(-0.257014\pi\)
\(840\) 0 0
\(841\) 4.99987e11 0.999481
\(842\) 5.61028e11 3.23909e11i 1.11618 0.644429i
\(843\) 0 0
\(844\) 2.00770e11 3.47745e11i 0.395667 0.685316i
\(845\) −5.46087e11 + 3.15284e11i −1.07111 + 0.618407i
\(846\) 0 0
\(847\) −8.29899e11 6.98253e11i −1.61247 1.35669i
\(848\) 5.14992e10i 0.0995903i
\(849\) 0 0
\(850\) 9.10045e10 1.57624e11i 0.174336 0.301959i
\(851\) −5.50814e11 3.18013e11i −1.05024 0.606354i
\(852\) 0 0
\(853\) −4.62404e11 −0.873424 −0.436712 0.899601i \(-0.643857\pi\)
−0.436712 + 0.899601i \(0.643857\pi\)
\(854\) −2.33761e11 4.15395e10i −0.439482 0.0780961i
\(855\) 0 0
\(856\) 1.16180e11 + 2.01229e11i 0.216389 + 0.374796i
\(857\) 3.27193e10 + 1.88905e10i 0.0606570 + 0.0350203i 0.530022 0.847984i \(-0.322184\pi\)
−0.469365 + 0.883004i \(0.655517\pi\)
\(858\) 0 0
\(859\) 2.93184e11 + 5.07809e11i 0.538477 + 0.932670i 0.998986 + 0.0450151i \(0.0143336\pi\)
−0.460509 + 0.887655i \(0.652333\pi\)
\(860\) 1.63060e11i 0.298094i
\(861\) 0 0
\(862\) −3.06121e11 −0.554452
\(863\) 1.31160e11 7.57251e10i 0.236460 0.136520i −0.377089 0.926177i \(-0.623075\pi\)
0.613549 + 0.789657i \(0.289742\pi\)
\(864\) 0 0
\(865\) −3.40143e11 + 5.89145e11i −0.607571 + 1.05234i
\(866\) −3.91557e11 + 2.26066e11i −0.696183 + 0.401941i
\(867\) 0 0
\(868\) −6.14005e10 5.16606e10i −0.108167 0.0910082i
\(869\) 1.73176e12i 3.03674i
\(870\) 0 0
\(871\) 3.71769e10 6.43923e10i 0.0645953 0.111882i
\(872\) 2.20935e11 + 1.27557e11i 0.382118 + 0.220616i
\(873\) 0 0
\(874\) −2.04125e11 −0.349824
\(875\) −1.10566e11 3.05042e11i −0.188621 0.520387i
\(876\) 0 0
\(877\) −2.79915e11 4.84827e11i −0.473182 0.819575i 0.526347 0.850270i \(-0.323561\pi\)
−0.999529 + 0.0306947i \(0.990228\pi\)
\(878\) −2.94300e11 1.69914e11i −0.495235 0.285924i
\(879\) 0 0
\(880\) −1.64846e11 2.85522e11i −0.274883 0.476112i
\(881\) 2.92022e11i 0.484743i −0.970184 0.242371i \(-0.922075\pi\)
0.970184 0.242371i \(-0.0779253\pi\)
\(882\) 0 0
\(883\) 2.88065e11 0.473857 0.236929 0.971527i \(-0.423859\pi\)
0.236929 + 0.971527i \(0.423859\pi\)
\(884\) 2.17124e10 1.25357e10i 0.0355548 0.0205276i
\(885\) 0 0
\(886\) −2.32081e11 + 4.01977e11i −0.376622 + 0.652328i
\(887\) −5.79275e11 + 3.34444e11i −0.935815 + 0.540293i −0.888646 0.458594i \(-0.848353\pi\)
−0.0471692 + 0.998887i \(0.515020\pi\)
\(888\) 0 0
\(889\) 3.72123e11 1.34881e11i 0.595772 0.215945i
\(890\) 3.41166e11i 0.543758i
\(891\) 0 0
\(892\) −2.85938e11 + 4.95260e11i −0.451661 + 0.782301i
\(893\) −3.20921e11 1.85284e11i −0.504653 0.291361i
\(894\) 0 0
\(895\) −7.57769e11 −1.18099
\(896\) 3.66761e10 4.35908e10i 0.0569050 0.0676337i
\(897\) 0 0
\(898\) 3.55977e10 + 6.16571e10i 0.0547415 + 0.0948151i
\(899\) 3.64483e9 + 2.10434e9i 0.00558005 + 0.00322165i
\(900\) 0 0
\(901\) 1.16349e11 + 2.01523e11i 0.176549 + 0.305792i
\(902\) 4.46428e11i 0.674412i
\(903\) 0 0
\(904\) −1.45349e11 −0.217640
\(905\) −1.04644e12 + 6.04163e11i −1.55998 + 0.900657i
\(906\) 0 0
\(907\) −4.59412e11 + 7.95724e11i −0.678848 + 1.17580i 0.296480 + 0.955039i \(0.404187\pi\)
−0.975328 + 0.220761i \(0.929146\pi\)
\(908\) 3.42536e11 1.97763e11i 0.503922 0.290939i
\(909\) 0 0
\(910\) −9.80427e9 + 5.51730e10i −0.0142972 + 0.0804565i
\(911\) 5.97229e11i 0.867097i 0.901130 + 0.433548i \(0.142739\pi\)
−0.901130 + 0.433548i \(0.857261\pi\)
\(912\) 0 0
\(913\) 5.99349e11 1.03810e12i 0.862575 1.49402i
\(914\) 4.79213e11 + 2.76674e11i 0.686663 + 0.396445i
\(915\) 0 0
\(916\) −2.56732e11 −0.364668
\(917\) 3.08300e11 3.66426e11i 0.436010 0.518214i
\(918\) 0 0
\(919\) −3.20081e11 5.54397e11i −0.448743 0.777246i 0.549561 0.835453i \(-0.314795\pi\)
−0.998305 + 0.0582073i \(0.981462\pi\)
\(920\) −4.41614e11 2.54966e11i −0.616441 0.355903i
\(921\) 0 0
\(922\) 2.08142e11 + 3.60513e11i 0.288029 + 0.498882i
\(923\) 1.07055e11i 0.147502i
\(924\) 0 0
\(925\) −3.06040e11 −0.418034
\(926\) 6.46341e11 3.73165e11i 0.879058 0.507524i
\(927\) 0 0
\(928\) −1.49396e9 + 2.58762e9i −0.00201441 + 0.00348906i
\(929\) 5.18326e11 2.99255e11i 0.695889 0.401772i −0.109926 0.993940i \(-0.535061\pi\)
0.805814 + 0.592168i \(0.201728\pi\)
\(930\) 0 0
\(931\) −2.16206e11 7.93453e10i −0.287786 0.105614i
\(932\) 3.74720e11i 0.496642i
\(933\) 0 0
\(934\) −2.58931e11 + 4.48481e11i −0.340248 + 0.589327i
\(935\) 1.29013e12 + 7.44857e11i 1.68806 + 0.974600i
\(936\) 0 0
\(937\) 7.39512e10 0.0959372 0.0479686 0.998849i \(-0.484725\pi\)
0.0479686 + 0.998849i \(0.484725\pi\)
\(938\) 2.60140e11 + 7.17700e11i 0.336043 + 0.927111i
\(939\) 0 0
\(940\) −4.62866e11 8.01707e11i −0.592848 1.02684i
\(941\) −1.52415e11 8.79969e10i −0.194388 0.112230i 0.399647 0.916669i \(-0.369133\pi\)
−0.594035 + 0.804439i \(0.702466\pi\)
\(942\) 0 0
\(943\) 3.45243e11 + 5.97978e11i 0.436594 + 0.756204i
\(944\) 2.73687e11i 0.344641i
\(945\) 0 0
\(946\) −4.77063e11 −0.595678
\(947\) 6.03824e11 3.48618e11i 0.750776 0.433461i −0.0751982 0.997169i \(-0.523959\pi\)
0.825974 + 0.563708i \(0.190626\pi\)
\(948\) 0 0
\(949\) 1.47892e10 2.56157e10i 0.0182340 0.0315821i
\(950\) −8.50609e10 + 4.91099e10i −0.104432 + 0.0602941i
\(951\) 0 0
\(952\) −4.50358e10 + 2.53437e11i −0.0548290 + 0.308548i
\(953\) 1.12350e11i 0.136208i −0.997678 0.0681040i \(-0.978305\pi\)
0.997678 0.0681040i \(-0.0216950\pi\)
\(954\) 0 0
\(955\) −1.02970e11 + 1.78349e11i −0.123793 + 0.214416i
\(956\) 1.98513e11 + 1.14612e11i 0.237661 + 0.137214i
\(957\) 0 0
\(958\) −9.89264e11 −1.17449
\(959\) −1.21291e12 2.15534e11i −1.43401 0.254824i
\(960\) 0 0
\(961\) 3.92360e11 + 6.79587e11i 0.460035 + 0.796804i
\(962\) −3.65084e10 2.10782e10i −0.0426278 0.0246112i
\(963\) 0 0
\(964\) −1.80155e11 3.12037e11i −0.208611 0.361325i
\(965\) 1.20644e11i 0.139123i
\(966\) 0 0
\(967\) 8.88077e10 0.101565 0.0507826 0.998710i \(-0.483828\pi\)
0.0507826 + 0.998710i \(0.483828\pi\)
\(968\) 5.66514e11 3.27077e11i 0.645222 0.372519i
\(969\) 0 0
\(970\) 4.21762e11 7.30513e11i 0.476409 0.825165i
\(971\) −7.75014e11 + 4.47455e11i −0.871832 + 0.503352i −0.867957 0.496640i \(-0.834567\pi\)
−0.00387540 + 0.999992i \(0.501234\pi\)
\(972\) 0 0
\(973\) 3.57359e11 1.29529e11i 0.398706 0.144516i
\(974\) 2.83111e11i 0.314572i
\(975\) 0 0
\(976\) 7.16005e10 1.24016e11i 0.0789073 0.136671i
\(977\) 1.10216e12 + 6.36332e11i 1.20967 + 0.698402i 0.962687 0.270618i \(-0.0872280\pi\)
0.246981 + 0.969020i \(0.420561\pi\)
\(978\) 0 0
\(979\) −9.98147e11 −1.08658
\(980\) −3.68644e11 4.41717e11i −0.399671 0.478894i
\(981\) 0 0
\(982\) −2.36228e11 4.09159e11i −0.254030 0.439994i
\(983\) −2.88779e11 1.66726e11i −0.309279 0.178563i 0.337325 0.941388i \(-0.390478\pi\)
−0.646604 + 0.762826i \(0.723811\pi\)
\(984\) 0 0
\(985\) 8.18946e11 + 1.41846e12i 0.869982 + 1.50685i
\(986\) 1.35009e10i 0.0142842i
\(987\) 0 0
\(988\) −1.35296e10 −0.0141989
\(989\) −6.39013e11 + 3.68935e11i −0.667921 + 0.385624i
\(990\) 0 0
\(991\) −6.75362e11 + 1.16976e12i −0.700232 + 1.21284i 0.268153 + 0.963376i \(0.413587\pi\)
−0.968385 + 0.249461i \(0.919746\pi\)
\(992\) 4.19138e10 2.41990e10i 0.0432823 0.0249891i
\(993\) 0 0
\(994\) 8.41041e11 + 7.07628e11i 0.861532 + 0.724869i
\(995\) 1.77658e12i 1.81256i
\(996\) 0 0
\(997\) −6.12674e11 + 1.06118e12i −0.620082 + 1.07401i 0.369388 + 0.929275i \(0.379567\pi\)
−0.989470 + 0.144738i \(0.953766\pi\)
\(998\) −1.30756e11 7.54921e10i −0.131808 0.0760991i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 126.9.s.b.53.10 yes 20
3.2 odd 2 inner 126.9.s.b.53.1 20
7.2 even 3 inner 126.9.s.b.107.1 yes 20
21.2 odd 6 inner 126.9.s.b.107.10 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.9.s.b.53.1 20 3.2 odd 2 inner
126.9.s.b.53.10 yes 20 1.1 even 1 trivial
126.9.s.b.107.1 yes 20 7.2 even 3 inner
126.9.s.b.107.10 yes 20 21.2 odd 6 inner